LMFDB - Embedded newform 560.2.bc.a.251.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.9
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30320 + 0.549239i) q^{2} +(-0.985188 + 0.985188i) q^{3} +(1.39667 - 1.43154i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.742796 - 1.82500i) q^{6} +(1.76064 - 1.97488i) q^{7} +(-1.03389 + 2.63269i) q^{8} +1.05881i q^{9} +O(q^{10})$	\(q+(-1.30320 + 0.549239i) q^{2} +(-0.985188 + 0.985188i) q^{3} +(1.39667 - 1.43154i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.742796 - 1.82500i) q^{6} +(1.76064 - 1.97488i) q^{7} +(-1.03389 + 2.63269i) q^{8} +1.05881i q^{9} +(-0.533133 + 1.30987i) q^{10} +(0.405187 - 0.405187i) q^{11} +(0.0343498 + 2.78632i) q^{12} +(-1.82151 - 1.82151i) q^{13} +(-1.20978 + 3.54068i) q^{14} +1.39327i q^{15} +(-0.0986091 - 3.99878i) q^{16} -1.46824i q^{17} +(-0.581539 - 1.37984i) q^{18} +(5.32883 - 5.32883i) q^{19} +(-0.0246542 - 1.99985i) q^{20} +(0.211071 + 3.68019i) q^{21} +(-0.305496 + 0.750586i) q^{22} -7.25429 q^{23} +(-1.57512 - 3.61227i) q^{24} -1.00000i q^{25} +(3.37424 + 1.37335i) q^{26} +(-3.99869 - 3.99869i) q^{27} +(-0.368086 - 5.27868i) q^{28} +(4.61815 - 4.61815i) q^{29} +(-0.765236 - 1.81571i) q^{30} -4.43809 q^{31} +(2.32480 + 5.15707i) q^{32} +0.798372i q^{33} +(0.806416 + 1.91342i) q^{34} +(-0.151493 - 2.64141i) q^{35} +(1.51573 + 1.47881i) q^{36} +(7.71720 + 7.71720i) q^{37} +(-4.01775 + 9.87135i) q^{38} +3.58907 q^{39} +(1.13052 + 2.59267i) q^{40} +10.8464 q^{41} +(-2.29637 - 4.68010i) q^{42} +(8.76250 - 8.76250i) q^{43} +(-0.0141274 - 1.14596i) q^{44} +(0.748690 + 0.748690i) q^{45} +(9.45381 - 3.98434i) q^{46} -7.41216 q^{47} +(4.03670 + 3.84241i) q^{48} +(-0.800313 - 6.95410i) q^{49} +(0.549239 + 1.30320i) q^{50} +(1.44650 + 1.44650i) q^{51} +(-5.15162 + 0.0635093i) q^{52} +(6.34365 + 6.34365i) q^{53} +(7.40734 + 3.01487i) q^{54} -0.573022i q^{55} +(3.37895 + 6.67703i) q^{56} +10.4998i q^{57} +(-3.48192 + 8.55486i) q^{58} +(3.05463 + 3.05463i) q^{59} +(1.99452 + 1.94594i) q^{60} +(0.507538 + 0.507538i) q^{61} +(5.78373 - 2.43757i) q^{62} +(2.09102 + 1.86418i) q^{63} +(-5.86214 - 5.44383i) q^{64} -2.57601 q^{65} +(-0.438497 - 1.04044i) q^{66} +(-1.35509 - 1.35509i) q^{67} +(-2.10185 - 2.05066i) q^{68} +(7.14685 - 7.14685i) q^{69} +(1.64819 + 3.35909i) q^{70} +1.63188 q^{71} +(-2.78752 - 1.09469i) q^{72} -3.84744 q^{73} +(-14.2957 - 5.81849i) q^{74} +(0.985188 + 0.985188i) q^{75} +(-0.185796 - 15.0711i) q^{76} +(-0.0868090 - 1.51359i) q^{77} +(-4.67728 + 1.97125i) q^{78} -12.0208i q^{79} +(-2.89729 - 2.75784i) q^{80} +4.70250 q^{81} +(-14.1350 + 5.95726i) q^{82} +(7.84919 - 7.84919i) q^{83} +(5.56313 + 4.83786i) q^{84} +(-1.03820 - 1.03820i) q^{85} +(-6.60661 + 16.2320i) q^{86} +9.09950i q^{87} +(0.647815 + 1.48565i) q^{88} +7.29312 q^{89} +(-1.38690 - 0.564485i) q^{90} +(-6.80429 + 0.390248i) q^{91} +(-10.1319 + 10.3848i) q^{92} +(4.37236 - 4.37236i) q^{93} +(9.65954 - 4.07105i) q^{94} -7.53611i q^{95} +(-7.37104 - 2.79032i) q^{96} -5.11183i q^{97} +(4.86243 + 8.62304i) q^{98} +(0.429016 + 0.429016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.30320	+	0.549239i	−0.921503	+	0.388371i
$2$	−1.30320	+	0.549239i	−0.921503	+	0.388371i
$3$	−0.985188	+	0.985188i	−0.568799	+	0.568799i	−0.931792	−	0.362993i	$-0.881755\pi$
$3$	−0.985188	+	0.985188i	−0.568799	+	0.568799i	0.362993	+	0.931792i	$0.381755\pi$
$4$	1.39667	−	1.43154i	0.698336	−	0.715770i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.742796	−	1.82500i	0.303245	−	0.745055i
$7$	1.76064	−	1.97488i	0.665458	−	0.746435i
$7$	1.76064	−	1.97488i	0.665458	−	0.746435i
$8$	−1.03389	+	2.63269i	−0.365535	+	0.930797i
$9$			1.05881i			0.352936i
$10$	−0.533133	+	1.30987i	−0.168591	+	0.414218i
$11$	0.405187	−	0.405187i	0.122169	−	0.122169i	−0.643379	−	0.765548i	$-0.722468\pi$
$11$	0.405187	−	0.405187i	0.122169	−	0.122169i	0.765548	+	0.643379i	$0.222468\pi$
$12$	0.0343498	+	2.78632i	0.00991594	+	0.804342i
$13$	−1.82151	−	1.82151i	−0.505197	−	0.505197i	0.407852	−	0.913048i	$-0.366278\pi$
$13$	−1.82151	−	1.82151i	−0.505197	−	0.505197i	−0.913048	+	0.407852i	$0.866278\pi$
$14$	−1.20978	+	3.54068i	−0.323329	+	0.946287i
$15$			1.39327i			0.359740i
$16$	−0.0986091	−	3.99878i	−0.0246523	−	0.999696i
$17$		−	1.46824i		−	0.356101i	−0.984021	−	0.178051i	$-0.943021\pi$
$17$		−	1.46824i		−	0.356101i	0.984021	−	0.178051i	$-0.0569791\pi$
$18$	−0.581539	−	1.37984i	−0.137070	−	0.325232i
$19$	5.32883	−	5.32883i	1.22252	−	1.22252i	0.255785	−	0.966734i	$-0.417666\pi$
$19$	5.32883	−	5.32883i	1.22252	−	1.22252i	0.966734	−	0.255785i	$-0.0823339\pi$
$20$	−0.0246542	−	1.99985i	−0.00551284	−	0.447180i
$21$	0.211071	+	3.68019i	0.0460594	+	0.803083i
$22$	−0.305496	+	0.750586i	−0.0651321	+	0.160025i
$23$	−7.25429			−1.51262			−0.756312	−	0.654211i	$-0.773001\pi$
$23$	−7.25429			−1.51262			−0.756312	+	0.654211i	$0.773001\pi$
$24$	−1.57512	−	3.61227i	−0.321520	−	0.737353i
$25$		−	1.00000i		−	0.200000i
$26$	3.37424	+	1.37335i	0.661744	+	0.269337i
$27$	−3.99869	−	3.99869i	−0.769548	−	0.769548i
$28$	−0.368086	−	5.27868i	−0.0695616	−	0.997578i
$29$	4.61815	−	4.61815i	0.857570	−	0.857570i	−0.133482	−	0.991051i	$-0.542616\pi$
$29$	4.61815	−	4.61815i	0.857570	−	0.857570i	0.991051	+	0.133482i	$0.0426157\pi$
$30$	−0.765236	−	1.81571i	−0.139712	−	0.331502i
$31$	−4.43809			−0.797105			−0.398552	−	0.917146i	$-0.630487\pi$
$31$	−4.43809			−0.797105			−0.398552	+	0.917146i	$0.630487\pi$
$32$	2.32480	+	5.15707i	0.410970	+	0.911649i
$33$			0.798372i			0.138979i
$34$	0.806416	+	1.91342i	0.138299	+	0.328148i
$35$	−0.151493	−	2.64141i	−0.0256071	−	0.446480i
$36$	1.51573	+	1.47881i	0.252621	+	0.246468i
$37$	7.71720	+	7.71720i	1.26870	+	1.26870i	0.946760	+	0.321940i	$0.104335\pi$
$37$	7.71720	+	7.71720i	1.26870	+	1.26870i	0.321940	+	0.946760i	$0.395665\pi$
$38$	−4.01775	+	9.87135i	−0.651765	+	1.60135i
$39$	3.58907			0.574710
$40$	1.13052	+	2.59267i	0.178752	+	0.409936i
$41$	10.8464			1.69392			0.846960	−	0.531656i	$-0.178430\pi$
$41$	10.8464			1.69392			0.846960	+	0.531656i	$0.178430\pi$
$42$	−2.29637	−	4.68010i	−0.354338	−	0.722156i
$43$	8.76250	−	8.76250i	1.33627	−	1.33627i	0.436626	−	0.899643i	$-0.356173\pi$
$43$	8.76250	−	8.76250i	1.33627	−	1.33627i	0.899643	−	0.436626i	$-0.143827\pi$
$44$	−0.0141274	−	1.14596i	−0.00212978	−	0.172759i
$45$	0.748690	+	0.748690i	0.111608	+	0.111608i
$46$	9.45381	−	3.98434i	1.39389	−	0.587459i
$47$	−7.41216			−1.08117			−0.540587	−	0.841288i	$-0.681798\pi$
$47$	−7.41216			−1.08117			−0.540587	+	0.841288i	$0.681798\pi$
$48$	4.03670	+	3.84241i	0.582648	+	0.554604i
$49$	−0.800313	−	6.95410i	−0.114330	−	0.993443i
$50$	0.549239	+	1.30320i	0.0776741	+	0.184301i
$51$	1.44650	+	1.44650i	0.202550	+	0.202550i
$52$	−5.15162	+	0.0635093i	−0.714402	+	0.00880715i
$53$	6.34365	+	6.34365i	0.871367	+	0.871367i	0.992621	−	0.121254i	$-0.0386916\pi$
$53$	6.34365	+	6.34365i	0.871367	+	0.871367i	−0.121254	+	0.992621i	$0.538692\pi$
$54$	7.40734	+	3.01487i	1.00801	+	0.410271i
$55$		−	0.573022i		−	0.0772662i
$56$	3.37895	+	6.67703i	0.451531	+	0.892255i
$57$			10.4998i			1.39073i
$58$	−3.48192	+	8.55486i	−0.457198	+	1.12331i
$59$	3.05463	+	3.05463i	0.397679	+	0.397679i	0.877414	−	0.479735i	$-0.159267\pi$
$59$	3.05463	+	3.05463i	0.397679	+	0.397679i	−0.479735	+	0.877414i	$0.659267\pi$
$60$	1.99452	+	1.94594i	0.257491	+	0.251220i
$61$	0.507538	+	0.507538i	0.0649836	+	0.0649836i	0.738852	−	0.673868i	$-0.235368\pi$
$61$	0.507538	+	0.507538i	0.0649836	+	0.0649836i	−0.673868	+	0.738852i	$0.735368\pi$
$62$	5.78373	−	2.43757i	0.734535	−	0.309572i
$63$	2.09102	+	1.86418i	0.263444	+	0.234864i
$64$	−5.86214	−	5.44383i	−0.732768	−	0.680479i
$65$	−2.57601			−0.319514
$66$	−0.438497	−	1.04044i	−0.0539752	−	0.128069i
$67$	−1.35509	−	1.35509i	−0.165551	−	0.165551i	0.619470	−	0.785020i	$-0.287348\pi$
$67$	−1.35509	−	1.35509i	−0.165551	−	0.165551i	−0.785020	+	0.619470i	$0.787348\pi$
$68$	−2.10185	−	2.05066i	−0.254886	−	0.248678i
$69$	7.14685	−	7.14685i	0.860379	−	0.860379i
$70$	1.64819	+	3.35909i	0.196997	+	0.401488i
$71$	1.63188			0.193669			0.0968343	−	0.995301i	$-0.469128\pi$
$71$	1.63188			0.193669			0.0968343	+	0.995301i	$0.469128\pi$
$72$	−2.78752	−	1.09469i	−0.328512	−	0.129011i
$73$	−3.84744			−0.450308			−0.225154	−	0.974323i	$-0.572289\pi$
$73$	−3.84744			−0.450308			−0.225154	+	0.974323i	$0.572289\pi$
$74$	−14.2957	−	5.81849i	−1.66184	−	0.676385i
$75$	0.985188	+	0.985188i	0.113760	+	0.113760i
$76$	−0.185796	−	15.0711i	−0.0213123	−	1.72877i
$77$	−0.0868090	−	1.51359i	−0.00989280	−	0.172489i
$78$	−4.67728	+	1.97125i	−0.529597	+	0.223201i
$79$		−	12.0208i		−	1.35244i	−0.736698	−	0.676222i	$-0.763616\pi$
$79$		−	12.0208i		−	1.35244i	0.736698	−	0.676222i	$-0.236384\pi$
$80$	−2.89729	−	2.75784i	−0.323927	−	0.308336i
$81$	4.70250			0.522500
$82$	−14.1350	+	5.95726i	−1.56095	+	0.657869i
$83$	7.84919	−	7.84919i	0.861561	−	0.861561i	−0.129959	−	0.991519i	$-0.541484\pi$
$83$	7.84919	−	7.84919i	0.861561	−	0.861561i	0.991519	+	0.129959i	$0.0414844\pi$
$84$	5.56313	+	4.83786i	0.606987	+	0.527854i
$85$	−1.03820	−	1.03820i	−0.112609	−	0.112609i
$86$	−6.60661	+	16.2320i	−0.712409	+	1.75034i
$87$			9.09950i			0.975569i
$88$	0.647815	+	1.48565i	0.0690573	+	0.158371i
$89$	7.29312			0.773070			0.386535	−	0.922275i	$-0.373672\pi$
$89$	7.29312			0.773070			0.386535	+	0.922275i	$0.373672\pi$
$90$	−1.38690	−	0.564485i	−0.146193	−	0.0595019i
$91$	−6.80429	+	0.390248i	−0.713284	+	0.0409091i
$92$	−10.1319	+	10.3848i	−1.05632	+	1.08269i
$93$	4.37236	−	4.37236i	0.453392	−	0.453392i
$94$	9.65954	−	4.07105i	0.996306	−	0.419896i
$95$		−	7.53611i		−	0.773189i
$96$	−7.37104	−	2.79032i	−0.752304	−	0.284786i
$97$		−	5.11183i		−	0.519028i	−0.965739	−	0.259514i	$-0.916438\pi$
$97$		−	5.11183i		−	0.519028i	0.965739	−	0.259514i	$-0.0835623\pi$
$98$	4.86243	+	8.62304i	0.491180	+	0.871058i
$99$	0.429016	+	0.429016i	0.0431177	+	0.0431177i
$100$	−1.43154	−	1.39667i	−0.143154	−	0.139667i
$101$	−9.07779	+	9.07779i	−0.903274	+	0.903274i	−0.995718	−	0.0924443i	$-0.970532\pi$
$101$	−9.07779	+	9.07779i	−0.903274	+	0.903274i	0.0924443	+	0.995718i	$0.470532\pi$
$102$	−2.67955	−	1.09060i	−0.265315	−	0.107986i
$103$			6.38731i			0.629360i	0.949198	+	0.314680i	$0.101897\pi$
$103$			6.38731i			0.629360i	−0.949198	+	0.314680i	$0.898103\pi$
$104$	6.67873	−	2.91224i	0.654903	−	0.285568i
$105$	2.75154	+	2.45304i	0.268522	+	0.239392i
$106$	−11.7512	−	4.78288i	−1.14138	−	0.464554i
$107$	5.81264	−	5.81264i	0.561929	−	0.561929i	−0.367926	−	0.929855i	$-0.619932\pi$
$107$	5.81264	−	5.81264i	0.561929	−	0.561929i	0.929855	+	0.367926i	$0.119932\pi$
$108$	−11.3091	+	0.139419i	−1.08822	+	0.0134156i
$109$	−1.25642	+	1.25642i	−0.120343	+	0.120343i	−0.764713	−	0.644371i	$-0.777119\pi$
$109$	−1.25642	+	1.25642i	−0.120343	+	0.120343i	0.644371	+	0.764713i	$0.277119\pi$
$110$	0.314726	+	0.746763i	0.0300079	+	0.0712011i
$111$	−15.2058			−1.44327
$112$	−8.07074	−	6.84567i	−0.762613	−	0.646855i
$113$	−8.72070			−0.820374			−0.410187	−	0.912001i	$-0.634537\pi$
$113$	−8.72070			−0.820374			−0.410187	+	0.912001i	$0.634537\pi$
$114$	−5.76691	−	13.6834i	−0.540120	−	1.28157i
$115$	−5.12956	+	5.12956i	−0.478334	+	0.478334i
$116$	−0.161018	−	13.0611i	−0.0149501	−	1.21269i
$117$	1.92863	−	1.92863i	0.178302	−	0.178302i
$118$	−5.65852	−	2.30308i	−0.520909	−	0.212016i
$119$	−2.89961	−	2.58504i	−0.265806	−	0.236971i
$120$	−3.66804	−	1.44049i	−0.334845	−	0.131498i
$121$			10.6716i			0.970150i
$122$	−0.940184	−	0.382665i	−0.0851203	−	0.0346449i
$123$	−10.6857	+	10.6857i	−0.963500	+	0.963500i
$124$	−6.19856	+	6.35330i	−0.556647	+	0.570543i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−3.74890	−	1.28093i	−0.333979	−	0.114114i
$127$		−	15.6722i		−	1.39068i	−0.718680	−	0.695341i	$-0.755253\pi$
$127$		−	15.6722i		−	1.39068i	0.718680	−	0.695341i	$-0.244747\pi$
$128$	10.6295	+	3.87470i	0.939526	+	0.342478i
$129$			17.2654i			1.52014i
$130$	3.35706	−	1.41484i	0.294434	−	0.124090i
$131$	−14.2071	+	14.2071i	−1.24128	+	1.24128i	−0.281809	+	0.959471i	$0.590934\pi$
$131$	−14.2071	+	14.2071i	−1.24128	+	1.24128i	−0.959471	+	0.281809i	$0.909066\pi$
$132$	1.14290	+	1.11506i	0.0994767	+	0.0970539i
$133$	−1.14167	−	19.9060i	−0.0989955	−	1.72607i
$134$	2.51023	+	1.02169i	0.216851	+	0.0882605i
$135$	−5.65500			−0.486705
$136$	3.86543	+	1.51800i	0.331458	+	0.130168i
$137$			3.75529i			0.320836i	0.987049	+	0.160418i	$0.0512842\pi$
$137$			3.75529i			0.320836i	−0.987049	+	0.160418i	$0.948716\pi$
$138$	−5.38846	+	13.2391i	−0.458696	+	1.12699i
$139$	6.43789	+	6.43789i	0.546055	+	0.546055i	0.925297	−	0.379242i	$-0.123815\pi$
$139$	6.43789	+	6.43789i	0.546055	+	0.546055i	−0.379242	+	0.925297i	$0.623815\pi$
$140$	−3.99287	−	3.47232i	−0.337459	−	0.293464i
$141$	7.30237	−	7.30237i	0.614971	−	0.614971i
$142$	−2.12667	+	0.896293i	−0.178466	+	0.0752152i
$143$	−1.47611			−0.123438
$144$	4.23394	−	0.104408i	0.352829	−	0.00870068i
$145$		−	6.53106i		−	0.542375i
$146$	5.01399	−	2.11316i	0.414961	−	0.174887i
$147$	7.63956	+	6.06264i	0.630100	+	0.500038i
$148$	21.8259	−	0.269070i	1.79408	−	0.0221174i
$149$	−9.61501	−	9.61501i	−0.787692	−	0.787692i	0.193423	−	0.981115i	$-0.438041\pi$
$149$	−9.61501	−	9.61501i	−0.787692	−	0.787692i	−0.981115	+	0.193423i	$0.938041\pi$
$150$	−1.82500	−	0.742796i	−0.149011	−	0.0606490i
$151$	−12.0478			−0.980440			−0.490220	−	0.871599i	$-0.663084\pi$
$151$	−12.0478			−0.980440			−0.490220	+	0.871599i	$0.663084\pi$
$152$	8.51975	+	19.5386i	0.691043	+	1.58479i
$153$	1.55459			0.125681
$154$	0.944450	+	1.92483i	0.0761059	+	0.155107i
$155$	−3.13821	+	3.13821i	−0.252067	+	0.252067i
$156$	5.01275	−	5.13789i	0.401341	−	0.411360i
$157$	−2.38515	−	2.38515i	−0.190356	−	0.190356i	0.605494	−	0.795850i	$-0.292976\pi$
$157$	−2.38515	−	2.38515i	−0.190356	−	0.190356i	−0.795850	+	0.605494i	$0.792976\pi$
$158$	6.60228	+	15.6655i	0.525249	+	1.24628i
$159$	−12.4994			−0.991265
$160$	5.29047	+	2.00272i	0.418249	+	0.158329i
$161$	−12.7722	+	14.3264i	−1.00659	+	1.12908i
$162$	−6.12831	+	2.58280i	−0.481486	+	0.202924i
$163$	1.99450	+	1.99450i	0.156221	+	0.156221i	0.780890	−	0.624669i	$-0.214766\pi$
$163$	1.99450	+	1.99450i	0.156221	+	0.156221i	−0.624669	+	0.780890i	$0.714766\pi$
$164$	15.1489	−	15.5270i	1.18293	−	1.21246i
$165$	0.564534	+	0.564534i	0.0439489	+	0.0439489i
$166$	−5.91800	+	14.5402i	−0.459326	+	1.12854i
$167$			21.3503i			1.65213i	0.563571	+	0.826067i	$0.309427\pi$
$167$			21.3503i			1.65213i	−0.563571	+	0.826067i	$0.690573\pi$
$168$	−9.90703	−	3.24923i	−0.764344	−	0.250683i
$169$		−	6.36419i		−	0.489553i
$170$	1.92321	+	0.782768i	0.147504	+	0.0600356i
$171$	5.64221	+	5.64221i	0.431471	+	0.431471i
$172$	−0.305516	−	24.7822i	−0.0232953	−	1.88963i
$173$	−6.46712	−	6.46712i	−0.491686	−	0.491686i	0.417151	−	0.908837i	$-0.363029\pi$
$173$	−6.46712	−	6.46712i	−0.491686	−	0.491686i	−0.908837	+	0.417151i	$0.863029\pi$
$174$	−4.99780	−	11.8585i	−0.378882	−	0.898990i
$175$	−1.97488	−	1.76064i	−0.149287	−	0.133092i
$176$	−1.66021	−	1.58030i	−0.125143	−	0.119120i
$177$	−6.01877			−0.452398
$178$	−9.50442	+	4.00567i	−0.712386	+	0.300238i
$179$	−7.35666	−	7.35666i	−0.549863	−	0.549863i	0.376538	−	0.926401i	$-0.377114\pi$
$179$	−7.35666	−	7.35666i	−0.549863	−	0.549863i	−0.926401	+	0.376538i	$0.877114\pi$
$180$	2.11745	−	0.0261040i	0.157826	−	0.00194568i
$181$	10.6681	−	10.6681i	0.792952	−	0.792952i	−0.189021	−	0.981973i	$-0.560532\pi$
$181$	10.6681	−	10.6681i	0.792952	−	0.792952i	0.981973	+	0.189021i	$0.0605315\pi$
$182$	8.65303	−	4.24576i	0.641405	−	0.314716i
$183$	−1.00004			−0.0739251
$184$	7.50014	−	19.0983i	0.552918	−	1.40795i
$185$	10.9138			0.802396
$186$	−3.29660	+	8.09953i	−0.241718	+	0.593887i
$187$	−0.594914	−	0.594914i	−0.0435044	−	0.0435044i
$188$	−10.3524	+	10.6108i	−0.755023	+	0.773872i
$189$	−14.9372	+	0.856696i	−1.08652	+	0.0623154i
$190$	4.13913	+	9.82108i	0.300284	+	0.712496i
$191$			17.3330i			1.25417i	0.778952	+	0.627084i	$0.215752\pi$
$191$			17.3330i			1.25417i	−0.778952	+	0.627084i	$0.784248\pi$
$192$	11.1385	−	0.412114i	0.803853	−	0.0297418i
$193$	−5.73872			−0.413082			−0.206541	−	0.978438i	$-0.566221\pi$
$193$	−5.73872			−0.413082			−0.206541	+	0.978438i	$0.566221\pi$
$194$	2.80762	+	6.66175i	0.201575	+	0.478286i
$195$	2.53785	−	2.53785i	0.181739	−	0.181739i
$196$	−11.0728	−	8.56692i	−0.790917	−	0.611923i
$197$	3.19125	+	3.19125i	0.227367	+	0.227367i	0.811592	−	0.584225i	$-0.198601\pi$
$197$	3.19125	+	3.19125i	0.227367	+	0.227367i	−0.584225	+	0.811592i	$0.698601\pi$
$198$	−0.794726	−	0.323462i	−0.0564787	−	0.0229875i
$199$			7.94881i			0.563476i	0.959491	+	0.281738i	$0.0909110\pi$
$199$			7.94881i			0.563476i	−0.959491	+	0.281738i	$0.909089\pi$
$200$	2.63269	+	1.03389i	0.186159	+	0.0731071i
$201$	2.67004			0.188330
$202$	6.84432	−	16.8161i	0.481565	−	1.18317i
$203$	−0.989412	−	17.2512i	−0.0694431	−	1.21080i
$204$	4.09100	−	0.0504339i	0.286427	−	0.00353108i
$205$	7.66955	−	7.66955i	0.535665	−	0.535665i
$206$	−3.50816	−	8.32396i	−0.244425	−	0.579958i
$207$		−	7.68090i		−	0.533860i
$208$	−7.10422	+	7.46345i	−0.492589	+	0.517497i
$209$		−	4.31835i		−	0.298707i
$210$	−4.93311	−	1.68555i	−0.340417	−	0.116314i
$211$	8.39332	+	8.39332i	0.577820	+	0.577820i	0.934302	−	0.356482i	$-0.116024\pi$
$211$	8.39332	+	8.39332i	0.577820	+	0.577820i	−0.356482	+	0.934302i	$0.616024\pi$
$212$	17.9412	−	0.221179i	1.23221	−	0.0151907i
$213$	−1.60771	+	1.60771i	−0.110158	+	0.110158i
$214$	−4.38252	+	10.7676i	−0.299583	+	0.736056i
$215$		−	12.3921i		−	0.845131i
$216$	14.6615	−	6.39312i	0.997591	−	0.434996i
$217$	−7.81387	+	8.76471i	−0.530440	+	0.594987i
$218$	0.947291	−	2.32744i	0.0641586	−	0.157634i
$219$	3.79045	−	3.79045i	0.256135	−	0.256135i
$220$	−0.820303	−	0.800324i	−0.0553048	−	0.0539578i
$221$	−2.67442	+	2.67442i	−0.179901	+	0.179901i
$222$	19.8162	−	8.35162i	1.32998	−	0.560524i
$223$	3.31042			0.221682			0.110841	−	0.993838i	$-0.464646\pi$
$223$	3.31042			0.221682			0.110841	+	0.993838i	$0.464646\pi$
$224$	14.2777	+	4.48853i	0.953970	+	0.299902i
$225$	1.05881			0.0705872
$226$	11.3648	−	4.78975i	0.755977	−	0.318609i
$227$	6.77176	−	6.77176i	0.449457	−	0.449457i	−0.445717	−	0.895174i	$-0.647051\pi$
$227$	6.77176	−	6.77176i	0.449457	−	0.449457i	0.895174	+	0.445717i	$0.147051\pi$
$228$	15.0309	+	14.6648i	0.995445	+	0.971200i
$229$	−17.6300	+	17.6300i	−1.16502	+	1.16502i	−0.181658	+	0.983362i	$0.558146\pi$
$229$	−17.6300	+	17.6300i	−1.16502	+	1.16502i	−0.983362	+	0.181658i	$0.941854\pi$
$230$	3.86750	−	9.50221i	0.255015	−	0.626557i
$231$	1.57669	+	1.40564i	0.103739	+	0.0924845i
$232$	7.38352	+	16.9328i	0.484752	+	1.11170i
$233$			10.7313i			0.703033i	0.936182	+	0.351516i	$0.114334\pi$
$233$			10.7313i			0.703033i	−0.936182	+	0.351516i	$0.885666\pi$
$234$	−1.45412	+	3.57268i	−0.0950586	+	0.233553i
$235$	−5.24119	+	5.24119i	−0.341897	+	0.341897i
$236$	8.63914	−	0.106503i	0.562360	−	0.00693278i
$237$	11.8427	+	11.8427i	0.769268	+	0.769268i
$238$	5.19858	+	1.77626i	0.336974	+	0.115138i
$239$			7.04585i			0.455758i	0.973689	+	0.227879i	$0.0731791\pi$
$239$			7.04585i			0.455758i	−0.973689	+	0.227879i	$0.926821\pi$
$240$	5.57137	−	0.137389i	0.359631	−	0.00886841i
$241$			17.8133i			1.14746i	0.819045	+	0.573729i	$0.194504\pi$
$241$			17.8133i			1.14746i	−0.819045	+	0.573729i	$0.805496\pi$
$242$	−5.86128	−	13.9073i	−0.376778	−	0.893996i
$243$	7.36322	−	7.36322i	0.472351	−	0.472351i
$244$	1.43542	−	0.0176959i	0.0918937	−	0.00113287i
$245$	−5.48320	−	4.35138i	−0.350309	−	0.278000i
$246$	8.05665	−	19.7947i	0.513673	−	1.26206i
$247$	−19.4131			−1.23522
$248$	4.58850	−	11.6841i	0.291370	−	0.741943i
$249$			15.4659i			0.980109i
$250$	1.30987	+	0.533133i	0.0828437	+	0.0337183i
$251$	−15.5338	−	15.5338i	−0.980487	−	0.980487i	0.0193266	−	0.999813i	$-0.493848\pi$
$251$	−15.5338	−	15.5338i	−0.980487	−	0.980487i	−0.999813	+	0.0193266i	$0.993848\pi$
$252$	5.58911	−	0.389732i	0.352081	−	0.0245508i
$253$	−2.93935	+	2.93935i	−0.184795	+	0.184795i
$254$	8.60778	+	20.4240i	0.540100	+	1.28152i
$255$	2.04565			0.128104
$256$	−15.9806	+	0.788633i	−0.998785	+	0.0492896i
$257$		−	3.44926i		−	0.215159i	−0.994196	−	0.107580i	$-0.965690\pi$
$257$		−	3.44926i		−	0.215159i	0.994196	−	0.107580i	$-0.0343100\pi$
$258$	−9.48285	−	22.5004i	−0.590376	−	1.40081i
$259$	28.8278	−	1.65336i	1.79127	−	0.102735i
$260$	−3.59784	+	3.68766i	−0.223129	+	0.228699i
$261$	4.88974	+	4.88974i	0.302667	+	0.302667i
$262$	10.7116	−	26.3178i	0.661767	−	1.62592i
$263$	−2.29834			−0.141722			−0.0708610	−	0.997486i	$-0.522575\pi$
$263$	−2.29834			−0.141722			−0.0708610	+	0.997486i	$0.522575\pi$
$264$	−2.10187	−	0.825429i	−0.129361	−	0.0508016i
$265$	8.97127			0.551101
$266$	12.4210	+	25.3144i	0.761578	+	1.55213i
$267$	−7.18510	+	7.18510i	−0.439721	+	0.439721i
$268$	−3.83248	+	0.0472469i	−0.234106	+	0.00288607i
$269$	−9.49941	−	9.49941i	−0.579189	−	0.579189i	0.355491	−	0.934680i	$-0.384314\pi$
$269$	−9.49941	−	9.49941i	−0.579189	−	0.579189i	−0.934680	+	0.355491i	$0.884314\pi$
$270$	7.36961	−	3.10595i	0.448500	−	0.189022i
$271$	−4.66066			−0.283115			−0.141557	−	0.989930i	$-0.545211\pi$
$271$	−4.66066			−0.283115			−0.141557	+	0.989930i	$0.545211\pi$
$272$	−5.87119	+	0.144782i	−0.355993	+	0.00877871i
$273$	6.31904	−	7.08798i	0.382446	−	0.428984i
$274$	−2.06255	−	4.89390i	−0.124603	−	0.295652i
$275$	−0.405187	−	0.405187i	−0.0244337	−	0.0244337i
$276$	−0.249184	−	20.2128i	−0.0149991	−	1.21667i
$277$	9.78911	+	9.78911i	0.588171	+	0.588171i	0.937136	−	0.348965i	$-0.113467\pi$
$277$	9.78911	+	9.78911i	0.588171	+	0.588171i	−0.348965	+	0.937136i	$0.613467\pi$
$278$	−11.9258	−	4.85394i	−0.715263	−	0.291120i
$279$		−	4.69909i		−	0.281327i
$280$	7.11065	+	2.33209i	0.424943	+	0.139369i
$281$		−	2.88586i		−	0.172156i	−0.996288	−	0.0860781i	$-0.972567\pi$
$281$		−	2.88586i		−	0.172156i	0.996288	−	0.0860781i	$-0.0274335\pi$
$282$	−5.50572	+	13.5272i	−0.327861	+	0.805534i
$283$	13.9174	+	13.9174i	0.827302	+	0.827302i	0.987143	−	0.159841i	$-0.0510982\pi$
$283$	13.9174	+	13.9174i	0.827302	+	0.827302i	−0.159841	+	0.987143i	$0.551098\pi$
$284$	2.27920	−	2.33610i	0.135246	−	0.138622i
$285$	7.42449	+	7.42449i	0.439789	+	0.439789i
$286$	1.92367	−	0.810736i	0.113749	−	0.0479398i
$287$	19.0966	−	21.4203i	1.12723	−	1.26440i
$288$	−5.46034	+	2.46151i	−0.321754	+	0.145046i
$289$	14.8443			0.873192
$290$	3.58711	+	8.51129i	0.210642	+	0.499800i
$291$	5.03612	+	5.03612i	0.295222	+	0.295222i
$292$	−5.37361	+	5.50775i	−0.314467	+	0.322317i
$293$	9.59651	−	9.59651i	0.560634	−	0.560634i	−0.368853	−	0.929488i	$-0.620250\pi$
$293$	9.59651	−	9.59651i	0.560634	−	0.560634i	0.929488	+	0.368853i	$0.120250\pi$
$294$	−13.2857	−	3.70490i	−0.774839	−	0.216074i
$295$	4.31990			0.251514
$296$	−28.2958	+	12.3383i	−1.64466	+	0.717148i
$297$	−3.24044			−0.188029
$298$	17.8112	+	7.24937i	1.03178	+	0.419945i
$299$	13.2138	+	13.2138i	0.764173	+	0.764173i
$300$	2.78632	−	0.0343498i	0.160868	−	0.00198319i
$301$	−1.87731	−	32.7325i	−0.108207	−	1.88667i
$302$	15.7008	−	6.61715i	0.903479	−	0.380774i
$303$		−	17.8867i		−	1.02756i
$304$	−21.8343	−	20.7834i	−1.25228	−	1.19201i
$305$	0.717767			0.0410992
$306$	−2.02594	+	0.853840i	−0.115815	+	0.0488108i
$307$	−24.1008	+	24.1008i	−1.37551	+	1.37551i	−0.523449	+	0.852057i	$0.675355\pi$
$307$	−24.1008	+	24.1008i	−1.37551	+	1.37551i	−0.852057	+	0.523449i	$0.824645\pi$
$308$	−2.28800	−	1.98971i	−0.130371	−	0.113374i
$309$	−6.29270	−	6.29270i	−0.357979	−	0.357979i
$310$	2.36609	−	5.81334i	0.134385	−	0.330176i
$311$			9.89342i			0.561005i	0.959853	+	0.280502i	$0.0905010\pi$
$311$			9.89342i			0.561005i	−0.959853	+	0.280502i	$0.909499\pi$
$312$	−3.71070	+	9.44891i	−0.210077	+	0.534939i
$313$	15.5639			0.879724			0.439862	−	0.898065i	$-0.355027\pi$
$313$	15.5639			0.879724			0.439862	+	0.898065i	$0.355027\pi$
$314$	4.41836	+	1.79832i	0.249342	+	0.101485i
$315$	2.79675	−	0.160402i	0.157579	−	0.00903765i
$316$	−17.2082	−	16.7891i	−0.968038	−	0.944461i
$317$	5.14616	−	5.14616i	0.289037	−	0.289037i	−0.547662	−	0.836700i	$-0.684482\pi$
$317$	5.14616	−	5.14616i	0.289037	−	0.289037i	0.836700	+	0.547662i	$0.184482\pi$
$318$	16.2892	−	6.86515i	0.913454	−	0.384978i
$319$		−	3.74244i		−	0.209536i
$320$	−7.99453	+	0.295790i	−0.446908	+	0.0165352i
$321$			11.4531i			0.639249i
$322$	8.77614	−	25.6851i	0.489075	−	1.43138i
$323$	−7.82402	−	7.82402i	−0.435340	−	0.435340i
$324$	6.56786	−	6.73182i	0.364881	−	0.373990i
$325$	−1.82151	+	1.82151i	−0.101039	+	0.101039i
$326$	−3.69470	−	1.50378i	−0.204630	−	0.0832867i
$327$		−	2.47561i		−	0.136902i
$328$	−11.2140	+	28.5552i	−0.619188	+	1.57670i
$329$	−13.0501	+	14.6381i	−0.719476	+	0.807026i
$330$	−1.04577	−	0.425638i	−0.0575675	−	0.0234306i
$331$	−6.05602	+	6.05602i	−0.332869	+	0.332869i	−0.853675	−	0.520806i	$-0.825631\pi$
$331$	−6.05602	+	6.05602i	−0.332869	+	0.332869i	0.520806	+	0.853675i	$0.325631\pi$
$332$	−0.273672	−	22.1992i	−0.0150197	−	1.21834i
$333$	−8.17103	+	8.17103i	−0.447770	+	0.447770i
$334$	−11.7264	−	27.8237i	−0.641641	−	1.52245i
$335$	−1.91639			−0.104703
$336$	14.6955	−	1.20693i	0.801704	−	0.0658433i
$337$	−30.2450			−1.64755			−0.823775	−	0.566917i	$-0.808136\pi$
$337$	−30.2450			−1.64755			−0.823775	+	0.566917i	$0.808136\pi$
$338$	3.49546	+	8.29382i	0.190128	+	0.451124i
$339$	8.59153	−	8.59153i	0.466628	−	0.466628i
$340$	−2.93626	+	0.0361983i	−0.159241	+	0.00196313i
$341$	−1.79826	+	1.79826i	−0.0973812	+	0.0973812i
$342$	−10.4519	−	4.25402i	−0.565172	−	0.230031i
$343$	−15.1426	−	10.6631i	−0.817623	−	0.575755i
$344$	14.0095	+	32.1284i	0.755342	+	1.73225i
$345$		−	10.1072i		−	0.544152i
$346$	11.9800	+	4.87597i	0.644047	+	0.262134i
$347$	6.76043	−	6.76043i	0.362919	−	0.362919i	−0.501968	−	0.864886i	$-0.667390\pi$
$347$	6.76043	−	6.76043i	0.362919	−	0.362919i	0.864886	+	0.501968i	$0.167390\pi$
$348$	13.0263	+	12.7090i	0.698283	+	0.681276i
$349$	−3.15932	−	3.15932i	−0.169114	−	0.169114i	0.617476	−	0.786590i	$-0.288155\pi$
$349$	−3.15932	−	3.15932i	−0.169114	−	0.169114i	−0.786590	+	0.617476i	$0.788155\pi$
$350$	3.54068	+	1.20978i	0.189257	+	0.0646657i
$351$			14.5673i			0.777546i
$352$	3.03156	+	1.14760i	0.161582	+	0.0611673i
$353$			22.8261i			1.21491i	0.794353	+	0.607456i	$0.207810\pi$
$353$			22.8261i			1.21491i	−0.794353	+	0.607456i	$0.792190\pi$
$354$	7.84368	−	3.30574i	0.416887	−	0.175698i
$355$	1.15391	−	1.15391i	0.0612434	−	0.0612434i
$356$	10.1861	−	10.4404i	0.539863	−	0.553340i
$357$	5.40341	−	0.309903i	0.285979	−	0.0164018i
$358$	13.6278	+	5.54665i	0.720251	+	0.293150i
$359$	−3.19677			−0.168719			−0.0843595	−	0.996435i	$-0.526884\pi$
$359$	−3.19677			−0.168719			−0.0843595	+	0.996435i	$0.526884\pi$
$360$	−2.74514	+	1.19701i	−0.144681	+	0.0630878i
$361$		−	37.7930i		−	1.98910i
$362$	−8.04334	+	19.7620i	−0.422748	+	1.03867i
$363$	−10.5136	−	10.5136i	−0.551820	−	0.551820i
$364$	−8.94472	+	10.2857i	−0.468831	+	0.539115i
$365$	−2.72055	+	2.72055i	−0.142400	+	0.142400i
$366$	1.30326	−	0.549261i	0.0681223	−	0.0287104i
$367$	30.8026			1.60788			0.803942	−	0.594708i	$-0.202732\pi$
$367$	30.8026			1.60788			0.803942	+	0.594708i	$0.202732\pi$
$368$	0.715340	+	29.0084i	0.0372897	+	1.51217i
$369$			11.4842i			0.597846i
$370$	−14.2229	+	5.99427i	−0.739411	+	0.311627i
$371$	23.6968	−	1.35909i	1.23028	−	0.0705604i
$372$	−0.152448	−	12.3660i	−0.00790404	−	0.641145i
$373$	−2.14944	−	2.14944i	−0.111294	−	0.111294i	0.649267	−	0.760561i	$-0.275076\pi$
$373$	−2.14944	−	2.14944i	−0.111294	−	0.111294i	−0.760561	+	0.649267i	$0.775076\pi$
$374$	1.10204	+	0.448543i	0.0569853	+	0.0231936i
$375$	1.39327			0.0719480
$376$	7.66336	−	19.5139i	0.395207	−	1.00635i
$377$	−16.8240			−0.866483
$378$	18.9956	−	9.32053i	0.977030	−	0.479396i
$379$	−5.08557	+	5.08557i	−0.261228	+	0.261228i	−0.825553	−	0.564325i	$-0.809137\pi$
$379$	−5.08557	+	5.08557i	−0.261228	+	0.261228i	0.564325	+	0.825553i	$0.309137\pi$
$380$	−10.7882	−	10.5255i	−0.553425	−	0.539946i
$381$	15.4401	+	15.4401i	0.791019	+	0.791019i
$382$	−9.51993	−	22.5883i	−0.487082	−	1.15572i
$383$	−11.6303			−0.594283			−0.297142	−	0.954833i	$-0.596033\pi$
$383$	−11.6303			−0.594283			−0.297142	+	0.954833i	$0.596033\pi$
$384$	−14.2894	+	6.65477i	−0.729202	+	0.339600i
$385$	−1.13165	−	1.00888i	−0.0576742	−	0.0514174i
$386$	7.47871	−	3.15193i	0.380656	−	0.160429i
$387$	9.27781	+	9.27781i	0.471617	+	0.471617i
$388$	−7.31779	−	7.13956i	−0.371504	−	0.362456i
$389$	−12.5151	−	12.5151i	−0.634539	−	0.634539i	0.314664	−	0.949203i	$-0.398108\pi$
$389$	−12.5151	−	12.5151i	−0.634539	−	0.634539i	−0.949203	+	0.314664i	$0.898108\pi$
$390$	−1.91345	+	4.70122i	−0.0968912	+	0.238056i
$391$			10.6511i			0.538648i
$392$	19.1354	+	5.08280i	0.966486	+	0.256720i
$393$		−	27.9933i		−	1.41208i
$394$	−5.91160	−	2.40608i	−0.297822	−	0.121217i
$395$	−8.49998	−	8.49998i	−0.427680	−	0.427680i
$396$	1.21335	−	0.0149582i	0.0609730	−	0.000751676i
$397$	−22.2370	−	22.2370i	−1.11604	−	1.11604i	−0.992316	−	0.123729i	$-0.960515\pi$
$397$	−22.2370	−	22.2370i	−1.11604	−	1.11604i	−0.123729	−	0.992316i	$-0.539485\pi$
$398$	−4.36580	−	10.3589i	−0.218838	−	0.519245i
$399$	20.7359	+	18.4864i	1.03809	+	0.925476i
$400$	−3.99878	+	0.0986091i	−0.199939	+	0.00493046i
$401$	32.5221			1.62408			0.812038	−	0.583604i	$-0.198358\pi$
$401$	32.5221			1.62408			0.812038	+	0.583604i	$0.198358\pi$
$402$	−3.47960	+	1.46649i	−0.173547	+	0.0731419i
$403$	8.08404	+	8.08404i	0.402695	+	0.402695i
$404$	0.316508	+	25.6739i	0.0157469	+	1.27732i
$405$	3.32517	−	3.32517i	0.165229	−	0.165229i
$406$	10.7644	+	21.9384i	0.534230	+	1.08878i
$407$	6.25383			0.309991
$408$	−5.30370	+	2.31266i	−0.262572	+	0.114494i
$409$	2.27070			0.112279			0.0561394	−	0.998423i	$-0.482121\pi$
$409$	2.27070			0.112279			0.0561394	+	0.998423i	$0.482121\pi$
$410$	−5.78256	+	14.2074i	−0.285580	+	0.701653i
$411$	−3.69967	−	3.69967i	−0.182491	−	0.182491i
$412$	9.14369	+	8.92098i	0.450477	+	0.439505i
$413$	11.4106	−	0.654436i	0.561480	−	0.0322027i
$414$	4.21865	+	10.0098i	0.207335	+	0.491953i
$415$		−	11.1004i		−	0.544899i
$416$	5.15901	−	13.6283i	0.252941	−	0.668182i
$417$	−12.6851			−0.621191
$418$	2.37181	+	5.62769i	0.116009	+	0.275259i
$419$	−13.4549	+	13.4549i	−0.657314	+	0.657314i	−0.954744	−	0.297430i	$-0.903871\pi$
$419$	−13.4549	+	13.4549i	−0.657314	+	0.657314i	0.297430	+	0.954744i	$0.403871\pi$
$420$	7.35462	−	0.512841i	0.358868	−	0.0250241i
$421$	19.6199	+	19.6199i	0.956215	+	0.956215i	0.999081	−	0.0428662i	$-0.0136489\pi$
$421$	19.6199	+	19.6199i	0.956215	+	0.956215i	−0.0428662	+	0.999081i	$0.513649\pi$
$422$	−15.5481	−	6.32825i	−0.756871	−	0.308055i
$423$		−	7.84805i		−	0.381585i
$424$	−23.2595	+	10.1422i	−1.12958	+	0.492551i
$425$	−1.46824			−0.0712202
$426$	1.21215	−	2.97819i	0.0587291	−	0.144294i
$427$	1.89592	−	0.108737i	0.0917499	−	0.00526215i
$428$	−0.202665	−	16.4394i	−0.00979618	−	0.794627i
$429$	1.45424	−	1.45424i	0.0702116	−	0.0702116i
$430$	6.80620	+	16.1494i	0.328224	+	0.778791i
$431$		−	5.98978i		−	0.288518i	−0.989540	−	0.144259i	$-0.953920\pi$
$431$		−	5.98978i		−	0.288518i	0.989540	−	0.144259i	$-0.0460798\pi$
$432$	−15.5956	+	16.3842i	−0.750343	+	0.788286i
$433$			28.5132i			1.37026i	0.728422	+	0.685129i	$0.240254\pi$
$433$			28.5132i			1.37026i	−0.728422	+	0.685129i	$0.759746\pi$
$434$	5.36914	−	15.7139i	0.257727	−	0.754290i
$435$	6.43432	+	6.43432i	0.308502	+	0.308502i
$436$	0.0438065	+	3.55341i	0.00209795	+	0.170177i
$437$	−38.6569	+	38.6569i	−1.84921	+	1.84921i
$438$	−2.85786	+	7.02158i	−0.136554	+	0.335504i
$439$			2.50087i			0.119360i	0.998218	+	0.0596801i	$0.0190081\pi$
$439$			2.50087i			0.119360i	−0.998218	+	0.0596801i	$0.980992\pi$
$440$	1.50859	+	0.592441i	0.0719192	+	0.0282435i
$441$	7.36306	−	0.847377i	0.350622	−	0.0403513i
$442$	2.01642	−	4.95421i	0.0959111	−	0.235648i
$443$	3.87388	−	3.87388i	0.184053	−	0.184053i	−0.609066	−	0.793120i	$-0.708456\pi$
$443$	3.87388	−	3.87388i	0.184053	−	0.184053i	0.793120	+	0.609066i	$0.208456\pi$
$444$	−21.2375	+	21.7677i	−1.00789	+	1.03305i
$445$	5.15702	−	5.15702i	0.244466	−	0.244466i
$446$	−4.31415	+	1.81821i	−0.204281	+	0.0860949i
$447$	18.9452			0.896077
$448$	−21.0720	+	1.99242i	−0.995560	+	0.0941331i
$449$	−3.11578			−0.147043			−0.0735213	−	0.997294i	$-0.523424\pi$
$449$	−3.11578			−0.147043			−0.0735213	+	0.997294i	$0.523424\pi$
$450$	−1.37984	+	0.581539i	−0.0650463	+	0.0274140i
$451$	4.39482	−	4.39482i	0.206944	−	0.206944i
$452$	−12.1800	+	12.4840i	−0.572897	+	0.587199i
$453$	11.8694	−	11.8694i	0.557673	−	0.557673i
$454$	−5.10566	+	12.5443i	−0.239620	+	0.588732i
$455$	−4.53541	+	5.08731i	−0.212624	+	0.238497i
$456$	−27.6428	−	10.8557i	−1.29449	−	0.508363i
$457$			8.39035i			0.392484i	0.980555	+	0.196242i	$0.0628738\pi$
$457$			8.39035i			0.392484i	−0.980555	+	0.196242i	$0.937126\pi$
$458$	13.2923	−	32.6585i	0.621110	−	1.52603i
$459$	−5.87105	+	5.87105i	−0.274037	+	0.274037i
$460$	0.178849	+	14.5075i	0.00833886	+	0.676415i
$461$	4.92812	+	4.92812i	0.229525	+	0.229525i	0.812494	−	0.582969i	$-0.198109\pi$
$461$	4.92812	+	4.92812i	0.229525	+	0.229525i	−0.582969	+	0.812494i	$0.698109\pi$
$462$	−2.82678	−	0.965858i	−0.131514	−	0.0449358i
$463$			22.0095i			1.02287i	0.859322	+	0.511434i	$0.170886\pi$
$463$			22.0095i			1.02287i	−0.859322	+	0.511434i	$0.829114\pi$
$464$	−18.9224	−	18.0116i	−0.878450	−	0.836168i
$465$		−	6.18345i		−	0.286750i
$466$	−5.89407	−	13.9851i	−0.273037	−	0.647847i
$467$	13.6995	−	13.6995i	0.633935	−	0.633935i	−0.315117	−	0.949053i	$-0.602044\pi$
$467$	13.6995	−	13.6995i	0.633935	−	0.633935i	0.949053	+	0.315117i	$0.102044\pi$
$468$	−0.0672441	−	5.45458i	−0.00310836	−	0.252138i
$469$	−5.06197	+	0.290320i	−0.233740	+	0.0134057i
$470$	3.95166	−	9.70899i	0.182277	−	0.447842i
$471$	4.69965			0.216549
$472$	−11.2001	+	4.88375i	−0.515524	+	0.224793i
$473$		−	7.10091i		−	0.326500i
$474$	−21.9380	−	8.92899i	−1.00764	−	0.410122i
$475$	−5.32883	−	5.32883i	−0.244504	−	0.244504i
$476$	−7.75039	+	0.540439i	−0.355239	+	0.0247710i
$477$	−6.71671	+	6.71671i	−0.307537	+	0.307537i
$478$	−3.86986	−	9.18217i	−0.177003	−	0.419983i
$479$	−26.9921			−1.23330			−0.616651	−	0.787236i	$-0.711511\pi$
$479$	−26.9921			−1.23330			−0.616651	+	0.787236i	$0.711511\pi$
$480$	−7.18517	+	3.23906i	−0.327957	+	0.147842i
$481$		−	28.1140i		−	1.28189i
$482$	−9.78379	−	23.2144i	−0.445639	−	1.05739i
$483$	−1.53117	−	26.6972i	−0.0696706	−	1.21476i
$484$	15.2769	+	14.9048i	0.694404	+	0.677491i
$485$	−3.61461	−	3.61461i	−0.164131	−	0.164131i
$486$	−5.55160	+	13.6399i	−0.251826	+	0.618720i
$487$	25.7669			1.16761			0.583804	−	0.811894i	$-0.301564\pi$
$487$	25.7669			1.16761			0.583804	+	0.811894i	$0.301564\pi$
$488$	−1.86093	+	0.811453i	−0.0842403	+	0.0367327i
$489$	−3.92992			−0.177717
$490$	9.53567	+	2.65915i	0.430777	+	0.120128i
$491$	−0.453997	+	0.453997i	−0.0204886	+	0.0204886i	−0.717277	−	0.696788i	$-0.754612\pi$
$491$	−0.453997	+	0.453997i	−0.0204886	+	0.0204886i	0.696788	+	0.717277i	$0.254612\pi$
$492$	0.372571	+	30.2215i	0.0167968	+	1.36249i
$493$	−6.78057	−	6.78057i	−0.305382	−	0.305382i
$494$	25.2992	−	10.6624i	1.13826	−	0.479725i
$495$	0.606720			0.0272700
$496$	0.437636	+	17.7470i	0.0196505	+	0.796863i
$497$	2.87315	−	3.22277i	0.128878	−	0.144561i
$498$	−8.49446	−	20.1552i	−0.380646	−	0.903174i
$499$	−11.3869	−	11.3869i	−0.509747	−	0.509747i	0.404702	−	0.914449i	$-0.367375\pi$
$499$	−11.3869	−	11.3869i	−0.509747	−	0.509747i	−0.914449	+	0.404702i	$0.867375\pi$
$500$	−1.99985	+	0.0246542i	−0.0894359	+	0.00110257i
$501$	−21.0341	−	21.0341i	−0.939732	−	0.939732i
$502$	28.7755	+	11.7119i	1.28431	+	0.522729i
$503$			18.1668i			0.810019i	0.914312	+	0.405010i	$0.132732\pi$
$503$			18.1668i			0.810019i	−0.914312	+	0.405010i	$0.867268\pi$
$504$	−7.06969	+	3.57766i	−0.314909	+	0.159362i
$505$			12.8379i			0.571280i
$506$	2.21616	−	5.44497i	0.0985204	−	0.242059i
$507$	6.26992	+	6.26992i	0.278457	+	0.278457i
$508$	−22.4354	−	21.8889i	−0.995408	−	0.971164i
$509$	−16.3711	−	16.3711i	−0.725635	−	0.725635i	0.244112	−	0.969747i	$-0.421503\pi$
$509$	−16.3711	−	16.3711i	−0.725635	−	0.725635i	−0.969747	+	0.244112i	$0.921503\pi$
$510$	−2.66590	+	1.12355i	−0.118048	+	0.0497518i
$511$	−6.77394	+	7.59823i	−0.299661	+	0.336126i
$512$	20.3927	−	9.80489i	0.901241	−	0.433319i
$513$	−42.6167			−1.88157
$514$	1.89447	+	4.49509i	0.0835615	+	0.198270i
$515$	4.51651	+	4.51651i	0.199021	+	0.199021i
$516$	24.7161	+	24.1142i	1.08807	+	1.06157i
$517$	−3.00331	+	3.00331i	−0.132086	+	0.132086i
$518$	−36.6603	+	17.9880i	−1.61076	+	0.790347i
$519$	12.7427			0.559341
$520$	2.66331	−	6.78184i	0.116794	−	0.297403i
$521$	−28.5671			−1.25155			−0.625773	−	0.780005i	$-0.715217\pi$
$521$	−28.5671			−1.25155			−0.625773	+	0.780005i	$0.715217\pi$
$522$	−9.05795	−	3.68668i	−0.396456	−	0.161362i
$523$	7.72864	+	7.72864i	0.337950	+	0.337950i	0.855595	−	0.517645i	$-0.173191\pi$
$523$	7.72864	+	7.72864i	0.337950	+	0.337950i	−0.517645	+	0.855595i	$0.673191\pi$
$524$	0.495348	+	40.1807i	0.0216394	+	1.75530i
$525$	3.68019	−	0.211071i	0.160617	−	0.00921188i
$526$	2.99521	−	1.26234i	0.130597	−	0.0550406i
$527$			6.51620i			0.283850i
$528$	3.19252	−	0.0787268i	0.138936	−	0.00342614i
$529$	29.6248			1.28803
$530$	−11.6914	+	4.92737i	−0.507841	+	0.214031i
$531$	−3.23427	+	3.23427i	−0.140355	+	0.140355i
$532$	−30.0907	−	26.1678i	−1.30460	−	1.13452i
$533$	−19.7568	−	19.7568i	−0.855763	−	0.855763i
$534$	5.41730	−	13.3100i	0.234430	−	0.575979i
$535$		−	8.22031i		−	0.355395i
$536$	4.96855	−	2.16652i	0.214609	−	0.0935795i
$537$	14.4954			0.625522
$538$	17.5971	+	7.16221i	0.758665	+	0.308785i
$539$	−3.14199	−	2.49344i	−0.135335	−	0.107400i
$540$	−7.89819	+	8.09536i	−0.339884	+	0.348369i
$541$	8.26993	−	8.26993i	0.355552	−	0.355552i	−0.506618	−	0.862170i	$-0.669105\pi$
$541$	8.26993	−	8.26993i	0.355552	−	0.355552i	0.862170	+	0.506618i	$0.169105\pi$
$542$	6.07378	−	2.55982i	0.260891	−	0.109953i
$543$			21.0201i			0.902060i
$544$	7.57182	−	3.41337i	0.324639	−	0.146347i
$545$			1.77684i			0.0761114i
$546$	−4.34200	+	12.7077i	−0.185820	+	0.543841i
$547$	−2.09706	−	2.09706i	−0.0896637	−	0.0896637i	0.660852	−	0.750516i	$-0.270195\pi$
$547$	−2.09706	−	2.09706i	−0.0896637	−	0.0896637i	−0.750516	+	0.660852i	$0.770195\pi$
$548$	5.37585	+	5.24491i	0.229645	+	0.224052i
$549$	−0.537385	+	0.537385i	−0.0229350	+	0.0229350i
$550$	0.750586	+	0.305496i	0.0320051	+	0.0130264i
$551$		−	49.2188i		−	2.09679i
$552$	11.4264	+	26.2045i	0.486340	+	1.11534i
$553$	−23.7396	−	21.1642i	−1.00951	−	0.899995i
$554$	−18.1338	−	7.38063i	−0.770429	−	0.313573i
$555$	−10.7521	+	10.7521i	−0.456402	+	0.456402i
$556$	18.2077	−	0.224465i	0.772180	−	0.00951945i
$557$	10.4537	−	10.4537i	0.442938	−	0.442938i	−0.450060	−	0.892998i	$-0.648597\pi$
$557$	10.4537	−	10.4537i	0.442938	−	0.442938i	0.892998	+	0.450060i	$0.148597\pi$
$558$	2.58092	+	6.12386i	0.109259	+	0.259244i
$559$	−31.9220			−1.35016
$560$	−10.5475	+	0.866257i	−0.445713	+	0.0366060i
$561$	1.17220			0.0494905
$562$	1.58503	+	3.76087i	0.0668604	+	0.158643i
$563$	9.24959	−	9.24959i	0.389824	−	0.389824i	−0.484801	−	0.874625i	$-0.661108\pi$
$563$	9.24959	−	9.24959i	0.389824	−	0.389824i	0.874625	+	0.484801i	$0.161108\pi$
$564$	−0.254606	−	20.6527i	−0.0107209	−	0.869634i
$565$	−6.16646	+	6.16646i	−0.259425	+	0.259425i
$566$	−25.7811	−	10.4932i	−1.08366	−	0.441061i
$567$	8.27940	−	9.28688i	0.347702	−	0.390012i
$568$	−1.68719	+	4.29624i	−0.0707927	+	0.180266i
$569$			14.9972i			0.628714i	0.949305	+	0.314357i	$0.101789\pi$
$569$			14.9972i			0.628714i	−0.949305	+	0.314357i	$0.898211\pi$
$570$	−13.7534	−	5.59779i	−0.576068	−	0.234466i
$571$	−11.5924	+	11.5924i	−0.485129	+	0.485129i	−0.906765	−	0.421636i	$-0.861456\pi$
$571$	−11.5924	+	11.5924i	−0.485129	+	0.485129i	0.421636	+	0.906765i	$0.361456\pi$
$572$	−2.06164	+	2.11311i	−0.0862015	+	0.0883534i
$573$	−17.0762	−	17.0762i	−0.713369	−	0.713369i
$574$	−13.1218	+	38.4036i	−0.547693	+	1.60293i
$575$			7.25429i			0.302525i
$576$	5.76397	−	6.20688i	0.240165	−	0.258620i
$577$		−	19.4690i		−	0.810507i	−0.914204	−	0.405253i	$-0.867183\pi$
$577$		−	19.4690i		−	0.810507i	0.914204	−	0.405253i	$-0.132817\pi$
$578$	−19.3451	+	8.15305i	−0.804649	+	0.339122i
$579$	5.65372	−	5.65372i	0.234960	−	0.234960i
$580$	−9.34946	−	9.12175i	−0.388215	−	0.378760i
$581$	−1.68164	−	29.3208i	−0.0697663	−	1.21643i
$582$	−9.32911	−	3.79705i	−0.386704	−	0.157393i
$583$	5.14073			0.212907
$584$	3.97783	−	10.1291i	0.164604	−	0.419146i
$585$		−	2.72750i		−	0.112768i
$586$	−7.23542	+	17.7770i	−0.298892	+	0.734360i
$587$	1.60893	+	1.60893i	0.0664078	+	0.0664078i	0.739531	−	0.673123i	$-0.235047\pi$
$587$	1.60893	+	1.60893i	0.0664078	+	0.0664078i	−0.673123	+	0.739531i	$0.735047\pi$
$588$	19.3489	−	2.46880i	0.797934	−	0.101812i
$589$	−23.6499	+	23.6499i	−0.974475	+	0.974475i
$590$	−5.62970	+	2.37266i	−0.231771	+	0.0976807i
$591$	−6.28796			−0.258652
$592$	30.0984	−	31.6204i	1.23704	−	1.29959i
$593$		−	32.9347i		−	1.35247i	−0.736687	−	0.676234i	$-0.763611\pi$
$593$		−	32.9347i		−	1.35247i	0.736687	−	0.676234i	$-0.236389\pi$
$594$	4.22295	−	1.77978i	0.173270	−	0.0730251i
$595$	−3.87823	+	0.222429i	−0.158992	+	0.00911871i
$596$	−27.1933	+	0.335239i	−1.11388	+	0.0137319i
$597$	−7.83108	−	7.83108i	−0.320505	−	0.320505i
$598$	−24.4778	−	9.96271i	−1.00097	−	0.407406i
$599$	39.2666			1.60439			0.802195	−	0.597062i	$-0.203666\pi$
$599$	39.2666			1.60439			0.802195	+	0.597062i	$0.203666\pi$
$600$	−3.61227	+	1.57512i	−0.147471	+	0.0643041i
$601$	6.67770			0.272389			0.136194	−	0.990682i	$-0.456513\pi$
$601$	6.67770			0.272389			0.136194	+	0.990682i	$0.456513\pi$
$602$	20.4245	+	41.6260i	0.832440	+	1.69655i
$603$	1.43478	−	1.43478i	0.0584288	−	0.0584288i
$604$	−16.8269	+	17.2470i	−0.684677	+	0.701769i
$605$	7.54599	+	7.54599i	0.306788	+	0.306788i
$606$	9.82405	+	23.3099i	0.399075	+	0.946901i
$607$	15.3071			0.621296			0.310648	−	0.950525i	$-0.399454\pi$
$607$	15.3071			0.621296			0.310648	+	0.950525i	$0.399454\pi$
$608$	39.8696	+	15.0927i	1.61693	+	0.612090i
$609$	17.9704	+	16.0209i	0.728199	+	0.649201i
$610$	−0.935396	+	0.394226i	−0.0378731	+	0.0159617i
$611$	13.5013	+	13.5013i	0.546206	+	0.546206i
$612$	2.17125	−	2.22545i	0.0877676	−	0.0899586i
$613$	29.2917	+	29.2917i	1.18308	+	1.18308i	0.978942	+	0.204141i	$0.0654401\pi$
$613$	29.2917	+	29.2917i	1.18308	+	1.18308i	0.204141	+	0.978942i	$0.434560\pi$
$614$	18.1711	−	44.6453i	0.733327	−	1.80174i
$615$			15.1119i			0.609371i
$616$	4.07456	+	1.33634i	0.164169	+	0.0538427i
$617$		−	20.7855i		−	0.836792i	−0.908265	−	0.418396i	$-0.862592\pi$
$617$		−	20.7855i		−	0.836792i	0.908265	−	0.418396i	$-0.137408\pi$
$618$	11.6569	+	4.74447i	0.468908	+	0.190850i
$619$	29.7022	+	29.7022i	1.19383	+	1.19383i	0.975982	+	0.217851i	$0.0699047\pi$
$619$	29.7022	+	29.7022i	1.19383	+	1.19383i	0.217851	+	0.975982i	$0.430095\pi$
$620$	0.109417	+	8.87551i	0.00439431	+	0.356449i
$621$	29.0077	+	29.0077i	1.16404	+	1.16404i
$622$	−5.43385	−	12.8931i	−0.217878	−	0.516968i
$623$	12.8405	−	14.4031i	0.514446	−	0.577046i
$624$	−0.353915	−	14.3519i	−0.0141679	−	0.574536i
$625$	−1.00000			−0.0400000
$626$	−20.2829	+	8.54831i	−0.810669	+	0.341659i
$627$	4.25439	+	4.25439i	0.169904	+	0.169904i
$628$	−6.74572	+	0.0831614i	−0.269184	+	0.00331850i
$629$	11.3307	−	11.3307i	0.451786	−	0.451786i
$630$	−3.55663	+	1.74512i	−0.141699	+	0.0695272i
$631$	−6.47212			−0.257651			−0.128825	−	0.991667i	$-0.541121\pi$
$631$	−6.47212			−0.257651			−0.128825	+	0.991667i	$0.541121\pi$
$632$	31.6470	+	12.4282i	1.25885	+	0.494366i
$633$	−16.5380			−0.657326
$634$	−3.88002	+	9.53297i	−0.154095	+	0.378603i
$635$	−11.0819	−	11.0819i	−0.439772	−	0.439772i
$636$	−17.4575	+	17.8933i	−0.692237	+	0.709517i
$637$	−11.2092	+	14.1248i	−0.444125	+	0.559643i
$638$	2.05549	+	4.87715i	0.0813777	+	0.193088i
$639$			1.72785i			0.0683526i
$640$	10.2560	−	4.77638i	0.405405	−	0.188803i
$641$	−14.1491			−0.558857			−0.279429	−	0.960166i	$-0.590145\pi$
$641$	−14.1491			−0.558857			−0.279429	+	0.960166i	$0.590145\pi$
$642$	−6.29048	−	14.9257i	−0.248266	−	0.589070i
$643$	−3.23713	+	3.23713i	−0.127660	+	0.127660i	−0.768050	−	0.640390i	$-0.778773\pi$
$643$	−3.23713	+	3.23713i	−0.127660	+	0.127660i	0.640390	+	0.768050i	$0.278773\pi$
$644$	2.67020	+	38.2931i	0.105221	+	1.50896i
$645$	12.2085	+	12.2085i	0.480709	+	0.480709i
$646$	14.4935	+	5.89903i	0.570241	+	0.232094i
$647$		−	11.7160i		−	0.460605i	−0.973119	−	0.230302i	$-0.926028\pi$
$647$		−	11.7160i		−	0.460605i	0.973119	−	0.230302i	$-0.0739715\pi$
$648$	−4.86187	+	12.3802i	−0.190992	+	0.486342i
$649$	2.47539			0.0971677
$650$	1.37335	−	3.37424i	0.0538674	−	0.132349i
$651$	−0.936751	−	16.3330i	−0.0367142	−	0.640142i
$652$	5.64087	−	0.0695408i	0.220914	−	0.00272343i
$653$	−1.61439	+	1.61439i	−0.0631761	+	0.0631761i	−0.737989	−	0.674813i	$-0.764224\pi$
$653$	−1.61439	+	1.61439i	−0.0631761	+	0.0631761i	0.674813	+	0.737989i	$0.264224\pi$
$654$	1.35970	+	3.22622i	0.0531686	+	0.126155i
$655$			20.0919i			0.785054i
$656$	−1.06955	−	43.3724i	−0.0417590	−	1.69341i
$657$		−	4.07370i		−	0.158930i
$658$	8.96712	−	26.2441i	0.349575	−	1.02310i
$659$	−6.77830	−	6.77830i	−0.264045	−	0.264045i	0.562650	−	0.826695i	$-0.309782\pi$
$659$	−6.77830	−	6.77830i	−0.264045	−	0.264045i	−0.826695	+	0.562650i	$0.809782\pi$
$660$	1.59662	−	0.0196832i	0.0621484	−	0.000766167i
$661$	−0.215290	+	0.215290i	−0.00837381	+	0.00837381i	−0.711281	−	0.702907i	$-0.751885\pi$
$661$	−0.215290	+	0.215290i	−0.00837381	+	0.00837381i	0.702907	+	0.711281i	$0.251885\pi$
$662$	4.56601	−	11.2184i	0.177463	−	0.436016i
$663$		−	5.26962i		−	0.204655i
$664$	12.5493	+	28.7797i	0.487008	+	1.11687i
$665$	−14.8829	−	13.2684i	−0.577135	−	0.514525i
$666$	6.16066	−	15.1364i	0.238721	−	0.586522i
$667$	−33.5014	+	33.5014i	−1.29718	+	1.29718i
$668$	30.5638	+	29.8194i	1.18255	+	1.15375i
$669$	−3.26139	+	3.26139i	−0.126093	+	0.126093i
$670$	2.49744	−	1.05256i	0.0964846	−	0.0406637i
$671$	0.411296			0.0158779
$672$	−18.4883	+	9.64420i	−0.713201	+	0.372033i
$673$	38.0030			1.46491			0.732453	−	0.680817i	$-0.238375\pi$
$673$	38.0030			1.46491			0.732453	+	0.680817i	$0.238375\pi$
$674$	39.4153	−	16.6117i	1.51822	−	0.639860i
$675$	−3.99869	+	3.99869i	−0.153910	+	0.153910i
$676$	−9.11058	−	8.88869i	−0.350407	−	0.341873i
$677$	−18.3992	+	18.3992i	−0.707138	+	0.707138i	−0.965933	−	0.258794i	$-0.916675\pi$
$677$	−18.3992	+	18.3992i	−0.707138	+	0.707138i	0.258794	+	0.965933i	$0.416675\pi$
$678$	−6.47770	+	15.9153i	−0.248774	+	0.611224i
$679$	−10.0953	−	9.00008i	−0.387420	−	0.345391i
$680$	3.80666	−	1.65988i	0.145979	−	0.0636536i
$681$			13.3429i			0.511301i
$682$	1.35582	−	3.33117i	0.0519171	−	0.127557i
$683$	30.0142	−	30.0142i	1.14846	−	1.14846i	0.161607	−	0.986855i	$-0.448332\pi$
$683$	30.0142	−	30.0142i	1.14846	−	1.14846i	0.986855	−	0.161607i	$-0.0516678\pi$
$684$	15.9574	−	0.196723i	0.610145	−	0.00752188i
$685$	2.65539	+	2.65539i	0.101457	+	0.101457i
$686$	25.5905	+	5.57931i	0.977048	+	0.213019i
$687$		−	34.7376i		−	1.32532i
$688$	−35.9034	−	34.1753i	−1.36881	−	1.30292i
$689$		−	23.1101i		−	0.880423i
$690$	5.55125	+	13.1717i	0.211332	+	0.501437i
$691$	−4.28169	+	4.28169i	−0.162883	+	0.162883i	−0.783843	−	0.620960i	$-0.786743\pi$
$691$	−4.28169	+	4.28169i	−0.162883	+	0.162883i	0.620960	+	0.783843i	$0.286743\pi$
$692$	−18.2904	+	0.225484i	−0.695296	+	0.00857162i
$693$	1.60260	−	0.0919141i	0.0608776	−	0.00349153i
$694$	−5.09711	+	12.5233i	−0.193484	+	0.475378i
$695$	9.10456			0.345356
$696$	−23.9562	−	9.40789i	−0.908057	−	0.356605i
$697$		−	15.9251i		−	0.603207i
$698$	5.85245	+	2.38201i	0.221518	+	0.0901604i
$699$	−10.5724	−	10.5724i	−0.399884	−	0.399884i
$700$	−5.27868	+	0.368086i	−0.199516	+	0.0139123i
$701$	8.20856	−	8.20856i	0.310033	−	0.310033i	−0.534889	−	0.844922i	$-0.679647\pi$
$701$	8.20856	−	8.20856i	0.310033	−	0.310033i	0.844922	+	0.534889i	$0.179647\pi$
$702$	−8.00094	−	18.9842i	−0.301976	−	0.716511i
$703$	82.2474			3.10202
$704$	−4.58104	+	0.169494i	−0.172654	+	0.00638805i
$705$		−	10.3271i		−	0.388942i
$706$	−12.5370	−	29.7471i	−0.471836	−	1.11955i
$707$	1.94486	+	33.9102i	0.0731441	+	1.27533i
$708$	−8.40625	+	8.61611i	−0.315926	+	0.323813i
$709$	8.29863	+	8.29863i	0.311661	+	0.311661i	0.845553	−	0.533892i	$-0.179271\pi$
$709$	8.29863	+	8.29863i	0.311661	+	0.311661i	−0.533892	+	0.845553i	$0.679271\pi$
$710$	−0.870009	+	2.13756i	−0.0326509	+	0.0802211i
$711$	12.7277			0.477326
$712$	−7.54029	+	19.2006i	−0.282584	+	0.719571i
$713$	32.1952			1.20572
$714$	−6.87153	+	3.37163i	−0.257160	+	0.126180i
$715$	−1.04377	+	1.04377i	−0.0390346	+	0.0390346i
$716$	−20.8062	+	0.256499i	−0.777564	+	0.00958582i
$717$	−6.94149	−	6.94149i	−0.259235	−	0.259235i
$718$	4.16604	−	1.75579i	0.155475	−	0.0655255i
$719$	−12.0027			−0.447624			−0.223812	−	0.974632i	$-0.571850\pi$
$719$	−12.0027			−0.447624			−0.223812	+	0.974632i	$0.571850\pi$
$720$	2.92002	−	3.06768i	0.108823	−	0.114326i
$721$	12.6142	+	11.2457i	0.469777	+	0.418813i
$722$	20.7574	+	49.2519i	0.772509	+	1.83297i
$723$	−17.5495	−	17.5495i	−0.652673	−	0.652673i
$724$	−0.371956	−	30.1716i	−0.0138236	−	1.12132i
$725$	−4.61815	−	4.61815i	−0.171514	−	0.171514i
$726$	19.4758	+	7.92686i	0.722814	+	0.294193i
$727$		−	8.21815i		−	0.304794i	−0.988319	−	0.152397i	$-0.951301\pi$
$727$		−	8.21815i		−	0.304794i	0.988319	−	0.152397i	$-0.0486993\pi$
$728$	6.00749	−	18.3171i	0.222652	−	0.678876i
$729$			28.6158i			1.05985i
$730$	2.05119	−	5.03966i	0.0759181	−	0.186526i
$731$	−12.8655	−	12.8655i	−0.475847	−	0.475847i
$732$	−1.39673	+	1.43160i	−0.0516246	+	0.0529134i
$733$	14.8153	+	14.8153i	0.547215	+	0.547215i	0.925634	−	0.378420i	$-0.123532\pi$
$733$	14.8153	+	14.8153i	0.547215	+	0.547215i	−0.378420	+	0.925634i	$0.623532\pi$
$734$	−40.1421	+	16.9180i	−1.48167	+	0.624455i
$735$	9.68892	−	1.11505i	0.357381	−	0.0411292i
$736$	−16.8648	−	37.4109i	−0.621643	−	1.37898i
$737$	−1.09813			−0.0404502
$738$	−6.30759	−	14.9663i	−0.232186	−	0.550917i
$739$	−11.5169	−	11.5169i	−0.423657	−	0.423657i	0.462803	−	0.886461i	$-0.346844\pi$
$739$	−11.5169	−	11.5169i	−0.423657	−	0.423657i	−0.886461	+	0.462803i	$0.846844\pi$
$740$	15.2430	−	15.6235i	0.560343	−	0.574331i
$741$	19.1255	−	19.1255i	0.702594	−	0.702594i
$742$	−30.1353	+	14.7864i	−1.10630	+	0.542825i
$743$	−10.1141			−0.371050			−0.185525	−	0.982639i	$-0.559399\pi$
$743$	−10.1141			−0.371050			−0.185525	+	0.982639i	$0.559399\pi$
$744$	6.99053	+	16.0316i	0.256285	+	0.587747i
$745$	−13.5977			−0.498180
$746$	3.98171	+	1.62060i	0.145781	+	0.0593343i
$747$	8.31079	+	8.31079i	0.304076	+	0.304076i
$748$	−1.68254	+	0.0207424i	−0.0615198	+	0.000758417i
$749$	−1.24532	−	21.7132i	−0.0455031	−	0.793384i
$750$	−1.81571	+	0.765236i	−0.0663003	+	0.0279425i
$751$			38.3609i			1.39981i	0.714236	+	0.699905i	$0.246774\pi$
$751$			38.3609i			1.39981i	−0.714236	+	0.699905i	$0.753226\pi$
$752$	0.730906	+	29.6396i	0.0266534	+	1.08085i
$753$	30.6075			1.11540
$754$	21.9251	−	9.24042i	0.798467	−	0.336516i
$755$	−8.51912	+	8.51912i	−0.310042	+	0.310042i
$756$	−19.6360	+	22.5797i	−0.714153	+	0.821215i
$757$	−4.22002	−	4.22002i	−0.153379	−	0.153379i	0.626246	−	0.779625i	$-0.284590\pi$
$757$	−4.22002	−	4.22002i	−0.153379	−	0.153379i	−0.779625	+	0.626246i	$0.784590\pi$
$758$	3.83433	−	9.42072i	0.139269	−	0.342176i
$759$		−	5.79162i		−	0.210223i
$760$	19.8403	+	7.79151i	0.719682	+	0.282628i
$761$	29.9173			1.08450			0.542251	−	0.840217i	$-0.317572\pi$
$761$	29.9173			1.08450			0.542251	+	0.840217i	$0.317572\pi$
$762$	−28.6018	−	11.6412i	−1.03613	−	0.421718i
$763$	0.269179	+	4.69336i	0.00974495	+	0.169911i
$764$	24.8128	+	24.2085i	0.897696	+	0.875831i
$765$	1.09926	−	1.09926i	0.0397438	−	0.0397438i
$766$	15.1567	−	6.38784i	0.547634	−	0.230802i
$767$		−	11.1281i		−	0.401812i
$768$	14.9669	−	16.5208i	0.540072	−	0.596143i
$769$			14.1092i			0.508791i	0.967100	+	0.254395i	$0.0818764\pi$
$769$			14.1092i			0.508791i	−0.967100	+	0.254395i	$0.918124\pi$
$770$	2.02889	+	0.693233i	0.0731160	+	0.0249824i
$771$	3.39817	+	3.39817i	0.122382	+	0.122382i
$772$	−8.01511	+	8.21520i	−0.288470	+	0.295671i
$773$	−16.9477	+	16.9477i	−0.609566	+	0.609566i	−0.942833	−	0.333267i	$-0.891849\pi$
$773$	−16.9477	+	16.9477i	−0.609566	+	0.609566i	0.333267	+	0.942833i	$0.391849\pi$
$774$	−17.1866	−	6.99513i	−0.617759	−	0.251435i
$775$			4.43809i			0.159421i
$776$	13.4579	+	5.28507i	0.483110	+	0.189723i
$777$	−26.7719	+	30.0296i	−0.960436	+	1.07731i
$778$	23.1834	+	9.43590i	0.831166	+	0.338294i
$779$	57.7986	−	57.7986i	2.07085	−	2.07085i
$780$	−0.0884854	−	7.17759i	−0.00316829	−	0.256999i
$781$	0.661218	−	0.661218i	0.0236602	−	0.0236602i
$782$	−5.84998	−	13.8805i	−0.209195	−	0.496365i
$783$	−36.9331			−1.31988
$784$	−27.7290	+	3.88602i	−0.990322	+	0.138786i
$785$	−3.37312			−0.120392
$786$	15.3750	+	36.4810i	0.548409	+	1.30123i
$787$	−1.31243	+	1.31243i	−0.0467831	+	0.0467831i	−0.730111	−	0.683328i	$-0.760532\pi$
$787$	−1.31243	+	1.31243i	−0.0467831	+	0.0467831i	0.683328	+	0.730111i	$0.260532\pi$
$788$	9.02553	−	0.111267i	0.321521	−	0.00396372i
$789$	2.26430	−	2.26430i	0.0806112	−	0.0806112i
$790$	15.7457	+	6.40867i	0.560207	+	0.228010i
$791$	−15.3540	+	17.2223i	−0.545925	+	0.612356i
$792$	−1.57302	+	0.685911i	−0.0558949	+	0.0243728i
$793$		−	1.84897i		−	0.0656590i
$794$	41.1928	+	16.7659i	1.46188	+	0.595000i
$795$	−8.83839	+	8.83839i	−0.313466	+	0.313466i
$796$	11.3790	+	11.1019i	0.403319	+	0.393496i
$797$	33.1213	+	33.1213i	1.17322	+	1.17322i	0.981438	+	0.191777i	$0.0614251\pi$
$797$	33.1213	+	33.1213i	1.17322	+	1.17322i	0.191777	+	0.981438i	$0.438575\pi$
$798$	−37.1765	−	12.7025i	−1.31603	−	0.449664i
$799$			10.8828i			0.385007i
$800$	5.15707	−	2.32480i	0.182330	−	0.0821940i
$801$			7.72202i			0.272844i
$802$	−42.3829	+	17.8624i	−1.49659	+	0.630744i
$803$	−1.55893	+	1.55893i	−0.0550135	+	0.0550135i
$804$	3.72917	−	3.82227i	0.131518	−	0.134801i
$805$	1.09898	+	19.1616i	0.0387339	+	0.675357i
$806$	−14.9752	−	6.09507i	−0.527479	−	0.214690i
$807$	18.7174			0.658884
$808$	−14.5136	−	33.2845i	−0.510586	−	1.17094i
$809$		−	19.6801i		−	0.691914i	−0.938250	−	0.345957i	$-0.887554\pi$
$809$		−	19.6801i		−	0.691914i	0.938250	−	0.345957i	$-0.112446\pi$
$810$	−2.50706	+	6.15968i	−0.0880890	+	0.216429i
$811$	−6.89904	−	6.89904i	−0.242258	−	0.242258i	0.575526	−	0.817784i	$-0.304797\pi$
$811$	−6.89904	−	6.89904i	−0.242258	−	0.242258i	−0.817784	+	0.575526i	$0.804797\pi$
$812$	−26.0777	−	22.6779i	−0.915146	−	0.795838i
$813$	4.59163	−	4.59163i	0.161035	−	0.161035i
$814$	−8.15000	+	3.43485i	−0.285657	+	0.120391i
$815$	2.82065			0.0988031
$816$	5.64159	−	5.92686i	0.197495	−	0.207482i
$817$		−	93.3879i		−	3.26723i
$818$	−2.95918	+	1.24716i	−0.103465	+	0.0436058i
$819$	−0.413198	−	7.20444i	−0.0144383	−	0.251743i
$820$	−0.267409	−	21.6911i	−0.00933831	−	0.757487i
$821$	−14.5170	−	14.5170i	−0.506648	−	0.506648i	0.406848	−	0.913496i	$-0.366628\pi$
$821$	−14.5170	−	14.5170i	−0.506648	−	0.506648i	−0.913496	+	0.406848i	$0.866628\pi$
$822$	6.85342	+	2.78941i	0.239040	+	0.0972920i
$823$	9.81087			0.341985			0.170993	−	0.985272i	$-0.445303\pi$
$823$	9.81087			0.341985			0.170993	+	0.985272i	$0.445303\pi$
$824$	−16.8158	−	6.60378i	−0.585807	−	0.230054i
$825$	0.798372			0.0277957
$826$	−14.5109	+	7.12002i	−0.504899	+	0.247737i
$827$	37.1265	−	37.1265i	1.29101	−	1.29101i	0.356855	−	0.934160i	$-0.383849\pi$
$827$	37.1265	−	37.1265i	1.29101	−	1.29101i	0.934160	−	0.356855i	$-0.116151\pi$
$828$	−10.9955	−	10.7277i	−0.382121	−	0.372814i
$829$	24.3268	+	24.3268i	0.844904	+	0.844904i	0.989492	−	0.144588i	$-0.0461857\pi$
$829$	24.3268	+	24.3268i	0.844904	+	0.844904i	−0.144588	+	0.989492i	$0.546186\pi$
$830$	6.09679	+	14.4661i	0.211623	+	0.502126i
$831$	−19.2882			−0.669101
$832$	0.761957	+	20.5940i	0.0264161	+	0.713967i
$833$	−10.2103	+	1.17505i	−0.353766	+	0.0407132i
$834$	16.5312	−	6.96714i	0.572429	−	0.241252i
$835$	15.0969	+	15.0969i	0.522451	+	0.522451i
$836$	−6.18189	−	6.03133i	−0.213805	−	0.208598i
$837$	17.7466	+	17.7466i	0.613411	+	0.613411i
$838$	10.1445	−	24.9244i	0.350435	−	0.860998i
$839$			21.6408i			0.747122i	0.927606	+	0.373561i	$0.121863\pi$
$839$			21.6408i			0.747122i	−0.927606	+	0.373561i	$0.878137\pi$
$840$	−9.30288	+	4.70778i	−0.320980	+	0.162434i
$841$		−	13.6547i		−	0.470852i
$842$	−36.3447	−	14.7927i	−1.25252	−	0.509789i
$843$	2.84312	+	2.84312i	0.0979222	+	0.0979222i
$844$	23.7381	−	0.292644i	0.817099	−	0.0100732i
$845$	−4.50016	−	4.50016i	−0.154810	−	0.154810i
$846$	4.31046	+	10.2276i	0.148197	+	0.351632i
$847$	21.0752	+	18.7889i	0.724154	+	0.645594i
$848$	24.7413	−	25.9924i	0.849621	−	0.892584i
$849$	−27.4225			−0.941136
$850$	1.91342	−	0.806416i	0.0656297	−	0.0276598i
$851$	−55.9829	−	55.9829i	−1.91907	−	1.91907i
$852$	0.0560548	+	4.54694i	0.00192041	+	0.155776i
$853$	33.9317	−	33.9317i	1.16180	−	1.16180i	0.177717	−	0.984082i	$-0.443129\pi$
$853$	33.9317	−	33.9317i	1.16180	−	1.16180i	0.984082	−	0.177717i	$-0.0568713\pi$
$854$	−2.41104	+	1.18302i	−0.0825041	+	0.0404820i
$855$	7.97929			0.272886
$856$	9.29326	+	21.3125i	0.317637	+	0.728447i
$857$	−18.5703			−0.634351			−0.317175	−	0.948367i	$-0.602734\pi$
$857$	−18.5703			−0.634351			−0.317175	+	0.948367i	$0.602734\pi$
$858$	−1.09645	+	2.69390i	−0.0374321	+	0.0919683i
$859$	36.8464	+	36.8464i	1.25718	+	1.25718i	0.952432	+	0.304751i	$0.0985733\pi$
$859$	36.8464	+	36.8464i	1.25718	+	1.25718i	0.304751	+	0.952432i	$0.401427\pi$
$860$	−17.7397	−	17.3076i	−0.604919	−	0.590186i
$861$	2.28935	+	39.9168i	0.0780210	+	1.36036i
$862$	3.28982	+	7.80589i	0.112052	+	0.265870i
$863$			20.2640i			0.689795i	0.938640	+	0.344897i	$0.112086\pi$
$863$			20.2640i			0.689795i	−0.938640	+	0.344897i	$0.887914\pi$
$864$	11.3254	−	29.9176i	0.385297	−	1.01782i
$865$	−9.14589			−0.310970
$866$	−15.6606	−	37.1585i	−0.532168	−	1.26270i
$867$	−14.6244	+	14.6244i	−0.496670	+	0.496670i
$868$	1.63360	+	23.4273i	0.0554479	+	0.795174i
$869$	−4.87067	−	4.87067i	−0.165226	−	0.165226i
$870$	−11.9192	−	4.85124i	−0.404099	−	0.164473i
$871$			4.93663i			0.167271i
$872$	−2.00876	−	4.60675i	−0.0680252	−	0.156004i
$873$	5.41245			0.183184
$874$	29.1459	−	71.6097i	0.985875	−	2.42223i
$875$	−2.64141	+	0.151493i	−0.0892960	+	0.00512141i
$876$	−0.132159	−	10.7202i	−0.00446523	−	0.362202i
$877$	27.1127	−	27.1127i	0.915532	−	0.915532i	−0.0811687	−	0.996700i	$-0.525865\pi$
$877$	27.1127	−	27.1127i	0.915532	−	0.915532i	0.996700	+	0.0811687i	$0.0258653\pi$
$878$	−1.37358	−	3.25915i	−0.0463560	−	0.109991i
$879$			18.9087i			0.637776i
$880$	−2.29139	+	0.0565052i	−0.0772427	+	0.00190479i
$881$		−	16.8211i		−	0.566718i	−0.959014	−	0.283359i	$-0.908551\pi$
$881$		−	16.8211i		−	0.566718i	0.959014	−	0.283359i	$-0.0914488\pi$
$882$	−9.13014	+	5.14838i	−0.307428	+	0.173355i
$883$	2.72937	+	2.72937i	0.0918506	+	0.0918506i	0.751539	−	0.659689i	$-0.229312\pi$
$883$	2.72937	+	2.72937i	0.0918506	+	0.0918506i	−0.659689	+	0.751539i	$0.729312\pi$
$884$	0.0932471	+	7.56383i	0.00313624	+	0.254399i
$885$	−4.25591	+	4.25591i	−0.143061	+	0.143061i
$886$	−2.92076	+	7.17613i	−0.0981249	+	0.241087i
$887$		−	42.0877i		−	1.41317i	−0.707630	−	0.706583i	$-0.750236\pi$
$887$		−	42.0877i		−	1.41317i	0.707630	−	0.706583i	$-0.249764\pi$
$888$	15.7211	−	40.0322i	0.527566	−	1.34339i
$889$	−30.9507	−	27.5931i	−1.03805	−	0.925441i
$890$	−3.88820	+	9.55307i	−0.130333	+	0.320220i
$891$	1.90539	−	1.90539i	0.0638331	−	0.0638331i
$892$	4.62358	−	4.73900i	0.154809	−	0.158673i
$893$	−39.4982	+	39.4982i	−1.32176	+	1.32176i
$894$	−24.6894	+	10.4054i	−0.825738	+	0.348010i
$895$	−10.4039			−0.347764
$896$	26.3668	−	14.1701i	0.880853	−	0.473390i
$897$	−26.0361			−0.869321
$898$	4.06049	−	1.71131i	0.135500	−	0.0571070i
$899$	−20.4958	+	20.4958i	−0.683573	+	0.683573i
$900$	1.47881	−	1.51573i	0.0492936	−	0.0505242i
$901$	9.31402	−	9.31402i	0.310295	−	0.310295i
$902$	−3.31353	+	8.14115i	−0.110329	+	0.271070i
$903$	34.0972	+	30.3982i	1.13468	+	1.01159i
$904$	9.01624	−	22.9589i	0.299876	−	0.763602i
$905$		−	15.0869i		−	0.501507i
$906$	−8.94909	+	21.9874i	−0.297314	+	0.730481i
$907$	−35.8077	+	35.8077i	−1.18898	+	1.18898i	−0.211626	+	0.977351i	$0.567876\pi$
$907$	−35.8077	+	35.8077i	−1.18898	+	1.18898i	−0.977351	+	0.211626i	$0.932124\pi$
$908$	−0.236106	−	19.1520i	−0.00783544	−	0.635580i
$909$	−9.61163	−	9.61163i	−0.318798	−	0.318798i
$910$	3.11641	−	9.12082i	0.103308	−	0.302352i
$911$			28.3640i			0.939742i	0.882735	+	0.469871i	$0.155700\pi$
$911$			28.3640i			0.939742i	−0.882735	+	0.469871i	$0.844300\pi$
$912$	41.9865	−	1.03538i	1.39031	−	0.0342848i
$913$		−	6.36079i		−	0.210511i
$914$	−4.60831	−	10.9343i	−0.152429	−	0.361675i
$915$	−0.707136	+	0.707136i	−0.0233772	+	0.0233772i
$916$	0.614690	+	49.8612i	0.0203099	+	1.64746i
$917$	3.04379	+	53.0709i	0.100515	+	1.75255i
$918$	4.42656	−	10.8758i	0.146098	−	0.358954i
$919$	−10.6163			−0.350200			−0.175100	−	0.984551i	$-0.556025\pi$
$919$	−10.6163			−0.350200			−0.175100	+	0.984551i	$0.556025\pi$
$920$	−8.20115	−	18.8080i	−0.270384	−	0.620080i
$921$		−	47.4877i		−	1.56477i
$922$	−9.12905	−	3.71562i	−0.300649	−	0.122367i
$923$	−2.97249	−	2.97249i	−0.0978407	−	0.0978407i
$924$	4.21435	−	0.293869i	0.138642	−	0.00966759i
$925$	7.71720	−	7.71720i	0.253740	−	0.253740i
$926$	−12.0885	−	28.6828i	−0.397252	−	0.942577i
$927$	−6.76293			−0.222124
$928$	34.5524	+	13.0799i	1.13424	+	0.429367i
$929$			11.0804i			0.363536i	0.983341	+	0.181768i	$0.0581820\pi$
$929$			11.0804i			0.363536i	−0.983341	+	0.181768i	$0.941818\pi$
$930$	3.39619	+	8.05828i	0.111365	+	0.264241i
$931$	−41.3220	−	32.7925i	−1.35427	−	1.07473i
$932$	15.3623	+	14.9882i	0.503210	+	0.490954i
$933$	−9.74688	−	9.74688i	−0.319099	−	0.319099i
$934$	−10.3289	+	25.3774i	−0.337972	+	0.830375i
$935$	−0.841335			−0.0275146
$936$	3.08350	+	7.07149i	0.100787	+	0.231139i
$937$	−17.2086			−0.562180			−0.281090	−	0.959681i	$-0.590696\pi$
$937$	−17.2086			−0.562180			−0.281090	+	0.959681i	$0.590696\pi$
$938$	6.43731	−	3.15858i	0.210186	−	0.103131i
$939$	−15.3334	+	15.3334i	−0.500386	+	0.500386i
$940$	0.182741	+	14.8232i	0.00596034	+	0.483479i
$941$	−7.62437	−	7.62437i	−0.248547	−	0.248547i	0.571827	−	0.820374i	$-0.306235\pi$
$941$	−7.62437	−	7.62437i	−0.248547	−	0.248547i	−0.820374	+	0.571827i	$0.806235\pi$
$942$	−6.12460	+	2.58123i	−0.199550	+	0.0841011i
$943$	−78.6829			−2.56227
$944$	11.9136	−	12.5160i	0.387754	−	0.407362i
$945$	−9.95641	+	11.1680i	−0.323882	+	0.363294i
$946$	3.90010	+	9.25393i	0.126803	+	0.300871i
$947$	4.77230	+	4.77230i	0.155079	+	0.155079i	0.780382	−	0.625303i	$-0.215025\pi$
$947$	4.77230	+	4.77230i	0.155079	+	0.155079i	−0.625303	+	0.780382i	$0.715025\pi$
$948$	33.4938	−	0.412912i	1.08783	−	0.0134107i
$949$	7.00815	+	7.00815i	0.227494	+	0.227494i
$950$	9.87135	+	4.01775i	0.320269	+	0.130353i
$951$			10.1399i			0.328808i
$952$	9.80350	−	4.96112i	0.317733	−	0.160791i
$953$			35.0088i			1.13405i	0.823702	+	0.567024i	$0.191905\pi$
$953$			35.0088i			1.13405i	−0.823702	+	0.567024i	$0.808095\pi$
$954$	5.06415	−	12.4423i	0.163958	−	0.402834i
$955$	12.2562	+	12.2562i	0.396603	+	0.396603i
$956$	10.0864	+	9.84075i	0.326218	+	0.318273i
$957$	3.68700	+	3.68700i	0.119184	+	0.119184i
$958$	35.1762	−	14.8251i	1.13649	−	0.478978i
$959$	7.41625	+	6.61171i	0.239483	+	0.213503i
$960$	7.58471	−	8.16753i	0.244795	−	0.263606i
$961$	−11.3033			−0.364624
$962$	15.4413	+	36.6382i	0.497847	+	1.18126i
$963$	6.15447	+	6.15447i	0.198325	+	0.198325i
$964$	25.5005	+	24.8794i	0.821316	+	0.801312i
$965$	−4.05789	+	4.05789i	−0.130628	+	0.130628i
$966$	16.6586	+	33.9508i	0.535980	+	1.09235i
$967$	−38.1790			−1.22776			−0.613878	−	0.789401i	$-0.710391\pi$
$967$	−38.1790			−1.22776			−0.613878	+	0.789401i	$0.710391\pi$
$968$	−28.0952	−	11.0333i	−0.903013	−	0.354624i
$969$	15.4163			0.495242
$970$	6.69585	+	2.72528i	0.214991	+	0.0875036i
$971$	5.68620	+	5.68620i	0.182479	+	0.182479i	0.792435	−	0.609956i	$-0.208813\pi$
$971$	5.68620	+	5.68620i	0.182479	+	0.182479i	−0.609956	+	0.792435i	$0.708813\pi$
$972$	−0.256728	−	20.8247i	−0.00823455	−	0.667954i
$973$	24.0489	−	1.37928i	0.770972	−	0.0442177i
$974$	−33.5795	+	14.1522i	−1.07596	+	0.453465i
$975$		−	3.58907i		−	0.114942i
$976$	1.97949	−	2.07958i	0.0633618	−	0.0665658i
$977$	−24.1218			−0.771723			−0.385862	−	0.922557i	$-0.626096\pi$
$977$	−24.1218			−0.771723			−0.385862	+	0.922557i	$0.626096\pi$
$978$	5.12148	−	2.15847i	0.163767	−	0.0690201i
$979$	2.95508	−	2.95508i	0.0944448	−	0.0944448i
$980$	−13.8874	+	1.77195i	−0.443617	+	0.0566029i
$981$	−1.33030	−	1.33030i	−0.0424733	−	0.0424733i
$982$	0.342297	−	0.841003i	0.0109231	−	0.0268375i
$983$		−	43.6080i		−	1.39088i	−0.718585	−	0.695439i	$-0.755210\pi$
$983$		−	43.6080i		−	1.39088i	0.718585	−	0.695439i	$-0.244790\pi$
$984$	−17.0844	−	39.1801i	−0.544630	−	1.24902i
$985$	4.51311			0.143800
$986$	12.5606	+	5.11230i	0.400011	+	0.162809i
$987$	−1.56449	−	27.2781i	−0.0497983	−	0.868273i
$988$	−27.1137	+	27.7906i	−0.862602	+	0.884136i
$989$	−63.5658	+	63.5658i	−2.02127	+	2.02127i
$990$	−0.790679	+	0.333234i	−0.0251294	+	0.0105909i
$991$		−	39.2218i		−	1.24592i	−0.782253	−	0.622961i	$-0.785929\pi$
$991$		−	39.2218i		−	1.24592i	0.782253	−	0.622961i	$-0.214071\pi$
$992$	−10.3177	−	22.8875i	−0.327586	−	0.726680i
$993$		−	11.9326i		−	0.378671i
$994$	−1.97422	+	5.77797i	−0.0626186	+	0.183266i
$995$	5.62066	+	5.62066i	0.178187	+	0.178187i
$996$	22.1400	+	21.6008i	0.701533	+	0.684446i
$997$	20.4292	−	20.4292i	0.646998	−	0.646998i	−0.305268	−	0.952266i	$-0.598746\pi$
$997$	20.4292	−	20.4292i	0.646998	−	0.646998i	0.952266	+	0.305268i	$0.0987462\pi$
$998$	21.0935	+	8.58529i	0.667704	+	0.271763i
$999$		−	61.7174i		−	1.95265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.9	✓	128
7.6	odd	2	inner	560.2.bc.a.251.10	yes	128
16.3	odd	4	inner	560.2.bc.a.531.10	yes	128
112.83	even	4	inner	560.2.bc.a.531.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.9	✓	128	1.1	even	1	trivial
560.2.bc.a.251.10	yes	128	7.6	odd	2	inner
560.2.bc.a.531.9	yes	128	112.83	even	4	inner
560.2.bc.a.531.10	yes	128	16.3	odd	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30320 + 0.549239i) q^{2} +(-0.985188 + 0.985188i) q^{3} +(1.39667 - 1.43154i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.742796 - 1.82500i) q^{6} +(1.76064 - 1.97488i) q^{7} +(-1.03389 + 2.63269i) q^{8} +1.05881i q^{9} +O(q^{10})\)	\(q+(-1.30320 + 0.549239i) q^{2} +(-0.985188 + 0.985188i) q^{3} +(1.39667 - 1.43154i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.742796 - 1.82500i) q^{6} +(1.76064 - 1.97488i) q^{7} +(-1.03389 + 2.63269i) q^{8} +1.05881i q^{9} +(-0.533133 + 1.30987i) q^{10} +(0.405187 - 0.405187i) q^{11} +(0.0343498 + 2.78632i) q^{12} +(-1.82151 - 1.82151i) q^{13} +(-1.20978 + 3.54068i) q^{14} +1.39327i q^{15} +(-0.0986091 - 3.99878i) q^{16} -1.46824i q^{17} +(-0.581539 - 1.37984i) q^{18} +(5.32883 - 5.32883i) q^{19} +(-0.0246542 - 1.99985i) q^{20} +(0.211071 + 3.68019i) q^{21} +(-0.305496 + 0.750586i) q^{22} -7.25429 q^{23} +(-1.57512 - 3.61227i) q^{24} -1.00000i q^{25} +(3.37424 + 1.37335i) q^{26} +(-3.99869 - 3.99869i) q^{27} +(-0.368086 - 5.27868i) q^{28} +(4.61815 - 4.61815i) q^{29} +(-0.765236 - 1.81571i) q^{30} -4.43809 q^{31} +(2.32480 + 5.15707i) q^{32} +0.798372i q^{33} +(0.806416 + 1.91342i) q^{34} +(-0.151493 - 2.64141i) q^{35} +(1.51573 + 1.47881i) q^{36} +(7.71720 + 7.71720i) q^{37} +(-4.01775 + 9.87135i) q^{38} +3.58907 q^{39} +(1.13052 + 2.59267i) q^{40} +10.8464 q^{41} +(-2.29637 - 4.68010i) q^{42} +(8.76250 - 8.76250i) q^{43} +(-0.0141274 - 1.14596i) q^{44} +(0.748690 + 0.748690i) q^{45} +(9.45381 - 3.98434i) q^{46} -7.41216 q^{47} +(4.03670 + 3.84241i) q^{48} +(-0.800313 - 6.95410i) q^{49} +(0.549239 + 1.30320i) q^{50} +(1.44650 + 1.44650i) q^{51} +(-5.15162 + 0.0635093i) q^{52} +(6.34365 + 6.34365i) q^{53} +(7.40734 + 3.01487i) q^{54} -0.573022i q^{55} +(3.37895 + 6.67703i) q^{56} +10.4998i q^{57} +(-3.48192 + 8.55486i) q^{58} +(3.05463 + 3.05463i) q^{59} +(1.99452 + 1.94594i) q^{60} +(0.507538 + 0.507538i) q^{61} +(5.78373 - 2.43757i) q^{62} +(2.09102 + 1.86418i) q^{63} +(-5.86214 - 5.44383i) q^{64} -2.57601 q^{65} +(-0.438497 - 1.04044i) q^{66} +(-1.35509 - 1.35509i) q^{67} +(-2.10185 - 2.05066i) q^{68} +(7.14685 - 7.14685i) q^{69} +(1.64819 + 3.35909i) q^{70} +1.63188 q^{71} +(-2.78752 - 1.09469i) q^{72} -3.84744 q^{73} +(-14.2957 - 5.81849i) q^{74} +(0.985188 + 0.985188i) q^{75} +(-0.185796 - 15.0711i) q^{76} +(-0.0868090 - 1.51359i) q^{77} +(-4.67728 + 1.97125i) q^{78} -12.0208i q^{79} +(-2.89729 - 2.75784i) q^{80} +4.70250 q^{81} +(-14.1350 + 5.95726i) q^{82} +(7.84919 - 7.84919i) q^{83} +(5.56313 + 4.83786i) q^{84} +(-1.03820 - 1.03820i) q^{85} +(-6.60661 + 16.2320i) q^{86} +9.09950i q^{87} +(0.647815 + 1.48565i) q^{88} +7.29312 q^{89} +(-1.38690 - 0.564485i) q^{90} +(-6.80429 + 0.390248i) q^{91} +(-10.1319 + 10.3848i) q^{92} +(4.37236 - 4.37236i) q^{93} +(9.65954 - 4.07105i) q^{94} -7.53611i q^{95} +(-7.37104 - 2.79032i) q^{96} -5.11183i q^{97} +(4.86243 + 8.62304i) q^{98} +(0.429016 + 0.429016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

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