LMFDB - Embedded newform 624.2.bn.a.187.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(187,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("624.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bn (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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.42
Character	$\chi$	$=$	624.187
Dual form			624.2.bn.a.307.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994572 + 1.00540i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.0216533 + 1.99988i) q^{4} -1.78327 q^{5} +(-0.00765570 + 1.41419i) q^{6} +(0.701387 + 0.701387i) q^{7} +(-2.03222 + 1.96726i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.994572 + 1.00540i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.0216533 + 1.99988i) q^{4} -1.78327 q^{5} +(-0.00765570 + 1.41419i) q^{6} +(0.701387 + 0.701387i) q^{7} +(-2.03222 + 1.96726i) q^{8} +1.00000i q^{9} +(-1.77359 - 1.79290i) q^{10} +2.56410 q^{11} +(-1.42944 + 1.39882i) q^{12} +(-3.41200 + 1.16544i) q^{13} +(-0.00759377 + 1.40275i) q^{14} +(-1.26096 - 1.26096i) q^{15} +(-3.99906 - 0.0866080i) q^{16} +6.11030i q^{17} +(-1.00540 + 0.994572i) q^{18} +1.27785 q^{19} +(0.0386136 - 3.56633i) q^{20} +0.991911i q^{21} +(2.55018 + 2.57794i) q^{22} +3.63164i q^{23} +(-2.82805 - 0.0459324i) q^{24} -1.81995 q^{25} +(-4.56521 - 2.27131i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41788 + 1.38750i) q^{28} +(7.20816 - 7.20816i) q^{29} +(0.0136522 - 2.52189i) q^{30} +(-5.68854 - 5.68854i) q^{31} +(-3.89028 - 4.10679i) q^{32} +(1.81309 + 1.81309i) q^{33} +(-6.14329 + 6.07713i) q^{34} +(-1.25076 - 1.25076i) q^{35} +(-1.99988 - 0.0216533i) q^{36} -0.196459i q^{37} +(1.27091 + 1.28475i) q^{38} +(-3.23674 - 1.58856i) q^{39} +(3.62399 - 3.50815i) q^{40} +(4.46214 + 4.46214i) q^{41} +(-0.997266 + 0.986526i) q^{42} +(4.43248 + 4.43248i) q^{43} +(-0.0555210 + 5.12789i) q^{44} -1.78327i q^{45} +(-3.65125 + 3.61193i) q^{46} +(2.81808 - 2.81808i) q^{47} +(-2.76652 - 2.88901i) q^{48} -6.01611i q^{49} +(-1.81007 - 1.82977i) q^{50} +(-4.32063 + 4.32063i) q^{51} +(-2.25686 - 6.84884i) q^{52} +(8.01005 + 8.01005i) q^{53} +(-1.41419 - 0.00765570i) q^{54} -4.57248 q^{55} +(-2.80518 - 0.0455608i) q^{56} +(0.903577 + 0.903577i) q^{57} +(14.4161 + 0.0780412i) q^{58} +1.14334 q^{59} +(2.54908 - 2.49447i) q^{60} +(7.97410 - 7.97410i) q^{61} +(0.0615887 - 11.3769i) q^{62} +(-0.701387 + 0.701387i) q^{63} +(0.259799 - 7.99578i) q^{64} +(6.08452 - 2.07829i) q^{65} +(-0.0196299 + 3.62613i) q^{66} +13.6289 q^{67} +(-12.2199 - 0.132308i) q^{68} +(-2.56796 + 2.56796i) q^{69} +(0.0135417 - 2.50149i) q^{70} +(-7.40757 + 7.40757i) q^{71} +(-1.96726 - 2.03222i) q^{72} +(-0.795059 + 0.795059i) q^{73} +(0.197520 - 0.195393i) q^{74} +(-1.28690 - 1.28690i) q^{75} +(-0.0276696 + 2.55555i) q^{76} +(1.79842 + 1.79842i) q^{77} +(-1.62204 - 4.83415i) q^{78} +0.369263i q^{79} +(7.13141 + 0.154445i) q^{80} -1.00000 q^{81} +(-0.0483106 + 8.92414i) q^{82} +6.64530 q^{83} +(-1.98370 - 0.0214781i) q^{84} -10.8963i q^{85} +(-0.0479896 + 8.86484i) q^{86} +10.1939 q^{87} +(-5.21080 + 5.04424i) q^{88} +(3.71107 - 3.71107i) q^{89} +(1.79290 - 1.77359i) q^{90} +(-3.21056 - 1.57571i) q^{91} +(-7.26285 - 0.0786368i) q^{92} -8.04482i q^{93} +(5.63609 + 0.0305108i) q^{94} -2.27875 q^{95} +(0.153096 - 5.65478i) q^{96} +(1.33699 - 1.33699i) q^{97} +(6.04859 - 5.98346i) q^{98} +2.56410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) $ 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.994572	+	1.00540i	0.703269	+	0.710924i
$2$	0.994572	+	1.00540i	0.703269	+	0.710924i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−0.0216533	+	1.99988i	−0.0108266	+	0.999941i
$5$	−1.78327			−0.797503			−0.398751	−	0.917059i	$-0.630556\pi$
$5$	−1.78327			−0.797503			−0.398751	+	0.917059i	$0.630556\pi$
$6$	−0.00765570	+	1.41419i	−0.00312542	+	0.577342i
$7$	0.701387	+	0.701387i	0.265099	+	0.265099i	0.827122	−	0.562023i	$-0.189977\pi$
$7$	0.701387	+	0.701387i	0.265099	+	0.265099i	−0.562023	+	0.827122i	$0.689977\pi$
$8$	−2.03222	+	1.96726i	−0.718497	+	0.695530i
$9$			1.00000i			0.333333i
$10$	−1.77359	−	1.79290i	−0.560859	−	0.566964i
$11$	2.56410			0.773104			0.386552	−	0.922268i	$-0.373666\pi$
$11$	2.56410			0.773104			0.386552	+	0.922268i	$0.373666\pi$
$12$	−1.42944	+	1.39882i	−0.412644	+	0.403804i
$13$	−3.41200	+	1.16544i	−0.946319	+	0.323235i
$13$	−3.41200	+	1.16544i	−0.946319	+	0.323235i
$14$	−0.00759377	+	1.40275i	−0.00202952	+	0.374901i
$15$	−1.26096	−	1.26096i	−0.325579	−	0.325579i
$16$	−3.99906	−	0.0866080i	−0.999766	−	0.0216520i
$17$			6.11030i			1.48197i	0.671524	+	0.740983i	$0.265640\pi$
$17$			6.11030i			1.48197i	−0.671524	+	0.740983i	$0.734360\pi$
$18$	−1.00540	+	0.994572i	−0.236975	+	0.234423i
$19$	1.27785			0.293159			0.146580	−	0.989199i	$-0.453174\pi$
$19$	1.27785			0.293159			0.146580	+	0.989199i	$0.453174\pi$
$20$	0.0386136	−	3.56633i	0.00863427	−	0.797456i
$21$			0.991911i			0.216453i
$22$	2.55018	+	2.57794i	0.543700	+	0.549618i
$23$			3.63164i			0.757249i	0.925550	+	0.378625i	$0.123603\pi$
$23$			3.63164i			0.757249i	−0.925550	+	0.378625i	$0.876397\pi$
$24$	−2.82805	−	0.0459324i	−0.577274	−	0.00937591i
$25$	−1.81995			−0.363990
$26$	−4.56521	−	2.27131i	−0.895312	−	0.445440i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.41788	+	1.38750i	−0.267954	+	0.262214i
$29$	7.20816	−	7.20816i	1.33852	−	1.33852i	0.441027	−	0.897494i	$-0.354614\pi$
$29$	7.20816	−	7.20816i	1.33852	−	1.33852i	0.897494	−	0.441027i	$-0.145386\pi$
$30$	0.0136522	−	2.52189i	0.00249253	−	0.460432i
$31$	−5.68854	−	5.68854i	−1.02169	−	1.02169i	−0.999759	−	0.0219333i	$-0.993018\pi$
$31$	−5.68854	−	5.68854i	−1.02169	−	1.02169i	−0.0219333	−	0.999759i	$-0.506982\pi$
$32$	−3.89028	−	4.10679i	−0.687711	−	0.725985i
$33$	1.81309	+	1.81309i	0.315618	+	0.315618i
$34$	−6.14329	+	6.07713i	−1.05357	+	1.04222i
$35$	−1.25076	−	1.25076i	−0.211417	−	0.211417i
$36$	−1.99988	−	0.0216533i	−0.333314	−	0.00360888i
$37$		−	0.196459i		−	0.0322977i	−0.999870	−	0.0161488i	$-0.994859\pi$
$37$		−	0.196459i		−	0.0322977i	0.999870	−	0.0161488i	$-0.00514056\pi$
$38$	1.27091	+	1.28475i	0.206170	+	0.208414i
$39$	−3.23674	−	1.58856i	−0.518293	−	0.254373i
$40$	3.62399	−	3.50815i	0.573003	−	0.554687i
$41$	4.46214	+	4.46214i	0.696869	+	0.696869i	0.963734	−	0.266865i	$-0.0859878\pi$
$41$	4.46214	+	4.46214i	0.696869	+	0.696869i	−0.266865	+	0.963734i	$0.585988\pi$
$42$	−0.997266	+	0.986526i	−0.153881	+	0.152224i
$43$	4.43248	+	4.43248i	0.675948	+	0.675948i	0.959081	−	0.283133i	$-0.0913738\pi$
$43$	4.43248	+	4.43248i	0.675948	+	0.675948i	−0.283133	+	0.959081i	$0.591374\pi$
$44$	−0.0555210	+	5.12789i	−0.00837011	+	0.773059i
$45$		−	1.78327i		−	0.265834i
$46$	−3.65125	+	3.61193i	−0.538347	+	0.532550i
$47$	2.81808	−	2.81808i	0.411060	−	0.411060i	−0.471048	−	0.882108i	$-0.656124\pi$
$47$	2.81808	−	2.81808i	0.411060	−	0.411060i	0.882108	+	0.471048i	$0.156124\pi$
$48$	−2.76652	−	2.88901i	−0.399313	−	0.416992i
$49$		−	6.01611i		−	0.859445i
$50$	−1.81007	−	1.82977i	−0.255982	−	0.258769i
$51$	−4.32063	+	4.32063i	−0.605010	+	0.605010i
$52$	−2.25686	−	6.84884i	−0.312970	−	0.949763i
$53$	8.01005	+	8.01005i	1.10026	+	1.10026i	0.994378	+	0.105887i	$0.0337680\pi$
$53$	8.01005	+	8.01005i	1.10026	+	1.10026i	0.105887	+	0.994378i	$0.466232\pi$
$54$	−1.41419	−	0.00765570i	−0.192447	−	0.00104181i
$55$	−4.57248			−0.616552
$56$	−2.80518	−	0.0455608i	−0.374858	−	0.00608832i
$57$	0.903577	+	0.903577i	0.119682	+	0.119682i
$58$	14.4161	+	0.0780412i	1.89293	+	0.0102473i
$59$	1.14334			0.148850			0.0744251	−	0.997227i	$-0.476288\pi$
$59$	1.14334			0.148850			0.0744251	+	0.997227i	$0.476288\pi$
$60$	2.54908	−	2.49447i	0.329085	−	0.322035i
$61$	7.97410	−	7.97410i	1.02098	−	1.02098i	0.0212042	−	0.999775i	$-0.493250\pi$
$61$	7.97410	−	7.97410i	1.02098	−	1.02098i	0.999775	−	0.0212042i	$-0.00675000\pi$
$62$	0.0615887	−	11.3769i	0.00782177	−	1.44487i
$63$	−0.701387	+	0.701387i	−0.0883664	+	0.0883664i
$64$	0.259799	−	7.99578i	0.0324748	−	0.999473i
$65$	6.08452	−	2.07829i	0.754692	−	0.257781i
$66$	−0.0196299	+	3.62613i	−0.00241628	+	0.446345i
$67$	13.6289			1.66503			0.832516	−	0.554002i	$-0.186900\pi$
$67$	13.6289			1.66503			0.832516	+	0.554002i	$0.186900\pi$
$68$	−12.2199	−	0.132308i	−1.48188	−	0.0160447i
$69$	−2.56796	+	2.56796i	−0.309146	+	0.309146i
$70$	0.0135417	−	2.50149i	0.00161855	−	0.298985i
$71$	−7.40757	+	7.40757i	−0.879117	+	0.879117i	−0.993443	−	0.114326i	$-0.963529\pi$
$71$	−7.40757	+	7.40757i	−0.879117	+	0.879117i	0.114326	+	0.993443i	$0.463529\pi$
$72$	−1.96726	−	2.03222i	−0.231843	−	0.239499i
$73$	−0.795059	+	0.795059i	−0.0930547	+	0.0930547i	−0.752102	−	0.659047i	$-0.770960\pi$
$73$	−0.795059	+	0.795059i	−0.0930547	+	0.0930547i	0.659047	+	0.752102i	$0.270960\pi$
$74$	0.197520	−	0.195393i	0.0229612	−	0.0227139i
$75$	−1.28690	−	1.28690i	−0.148598	−	0.148598i
$76$	−0.0276696	+	2.55555i	−0.00317392	+	0.293142i
$77$	1.79842	+	1.79842i	0.204949	+	0.204949i
$78$	−1.62204	−	4.83415i	−0.183659	−	0.547360i
$79$			0.369263i			0.0415453i	0.999784	+	0.0207727i	$0.00661262\pi$
$79$			0.369263i			0.0415453i	−0.999784	+	0.0207727i	$0.993387\pi$
$80$	7.13141	+	0.154445i	0.797316	+	0.0172675i
$81$	−1.00000			−0.111111
$82$	−0.0483106	+	8.92414i	−0.00533501	+	0.985507i
$83$	6.64530			0.729417			0.364708	−	0.931122i	$-0.381169\pi$
$83$	6.64530			0.729417			0.364708	+	0.931122i	$0.381169\pi$
$84$	−1.98370	−	0.0214781i	−0.216440	−	0.00234345i
$85$		−	10.8963i		−	1.18187i
$86$	−0.0479896	+	8.86484i	−0.00517485	+	0.955920i
$87$	10.1939			1.09290
$88$	−5.21080	+	5.04424i	−0.555473	+	0.537717i
$89$	3.71107	−	3.71107i	0.393373	−	0.393373i	−0.482515	−	0.875888i	$-0.660277\pi$
$89$	3.71107	−	3.71107i	0.393373	−	0.393373i	0.875888	+	0.482515i	$0.160277\pi$
$90$	1.79290	−	1.77359i	0.188988	−	0.186953i
$91$	−3.21056	−	1.57571i	−0.336558	−	0.165179i
$92$	−7.26285	−	0.0786368i	−0.757205	−	0.00819846i
$93$		−	8.04482i		−	0.834209i
$94$	5.63609	+	0.0305108i	0.581318	+	0.00314695i
$95$	−2.27875			−0.233795
$96$	0.153096	−	5.65478i	0.0156253	−	0.577139i
$97$	1.33699	−	1.33699i	0.135751	−	0.135751i	−0.635966	−	0.771717i	$-0.719398\pi$
$97$	1.33699	−	1.33699i	0.135751	−	0.135751i	0.771717	+	0.635966i	$0.219398\pi$
$98$	6.04859	−	5.98346i	0.611000	−	0.604421i
$99$			2.56410i			0.257701i
$100$	0.0394078	−	3.63968i	0.00394078	−	0.363968i
$101$	−5.67473	+	5.67473i	−0.564656	+	0.564656i	−0.930627	−	0.365970i	$-0.880737\pi$
$101$	−5.67473	+	5.67473i	−0.564656	+	0.564656i	0.365970	+	0.930627i	$0.380737\pi$
$102$	−8.64114	−	0.0467786i	−0.855601	−	0.00463177i
$103$			2.88923i			0.284685i	0.989817	+	0.142342i	$0.0454634\pi$
$103$			2.88923i			0.284685i	−0.989817	+	0.142342i	$0.954537\pi$
$104$	4.64120	−	9.08071i	0.455107	−	0.890437i
$105$		−	1.76884i		−	0.172622i
$106$	−0.0867231	+	16.0199i	−0.00842329	+	1.55599i
$107$	−13.1003	+	13.1003i	−1.26646	+	1.26646i	−0.318549	+	0.947906i	$0.603196\pi$
$107$	−13.1003	+	13.1003i	−1.26646	+	1.26646i	−0.947906	+	0.318549i	$0.896804\pi$
$108$	−1.39882	−	1.42944i	−0.134601	−	0.137548i
$109$		−	3.66511i		−	0.351054i	−0.984475	−	0.175527i	$-0.943837\pi$
$109$		−	3.66511i		−	0.351054i	0.984475	−	0.175527i	$-0.0561629\pi$
$110$	−4.54766	−	4.59716i	−0.433602	−	0.438322i
$111$	0.138918	−	0.138918i	0.0131855	−	0.0131855i
$112$	−2.74414	−	2.86563i	−0.259297	−	0.270777i
$113$	11.4964			1.08149			0.540747	−	0.841186i	$-0.318142\pi$
$113$	11.4964			1.08149			0.540747	+	0.841186i	$0.318142\pi$
$114$	−0.00978284	+	1.80713i	−0.000916247	+	0.169253i
$115$		−	6.47619i		−	0.603908i
$116$	14.2594	+	14.5715i	1.32395	+	1.35293i
$117$	−1.16544	−	3.41200i	−0.107745	−	0.315440i
$118$	1.13713	+	1.14951i	0.104682	+	0.105821i
$119$	−4.28568	+	4.28568i	−0.392868	+	0.392868i
$120$	5.04318	+	0.0819098i	0.460378	+	0.00747731i
$121$	−4.42541			−0.402310
$122$	15.9480	+	0.0863339i	1.44386	+	0.00781631i
$123$			6.31041i			0.568991i
$124$	11.4996	−	11.2532i	1.03269	−	1.01057i
$125$	12.1618			1.08779
$126$	−1.40275	−	0.00759377i	−0.124967	−	0.000676506i
$127$	−9.53476			−0.846073			−0.423037	−	0.906113i	$-0.639036\pi$
$127$	−9.53476			−0.846073			−0.423037	+	0.906113i	$0.639036\pi$
$128$	8.29734	−	7.69118i	0.733388	−	0.679811i
$129$			6.26848i			0.551909i
$130$	8.14101	+	4.05036i	0.714013	+	0.355240i
$131$	−1.97732	−	1.97732i	−0.172759	−	0.172759i	0.615431	−	0.788191i	$-0.288982\pi$
$131$	−1.97732	−	1.97732i	−0.172759	−	0.172759i	−0.788191	+	0.615431i	$0.788982\pi$
$132$	−3.66523	+	3.58671i	−0.319017	+	0.312183i
$133$	0.896267	+	0.896267i	0.0777162	+	0.0777162i
$134$	13.5549	+	13.7024i	1.17096	+	1.18371i
$135$	1.26096	−	1.26096i	0.108526	−	0.108526i
$136$	−12.0205	−	12.4174i	−1.03075	−	1.06479i
$137$	9.41529	−	9.41529i	0.804403	−	0.804403i	−0.179378	−	0.983780i	$-0.557408\pi$
$137$	9.41529	−	9.41529i	0.804403	−	0.804403i	0.983780	+	0.179378i	$0.0574084\pi$
$138$	−5.13584	−	0.0278027i	−0.437192	−	0.00236673i
$139$	−5.42243	+	5.42243i	−0.459924	+	0.459924i	−0.898630	−	0.438706i	$-0.855437\pi$
$139$	−5.42243	+	5.42243i	−0.459924	+	0.459924i	0.438706	+	0.898630i	$0.355437\pi$
$140$	2.52846	−	2.47429i	0.213694	−	0.209116i
$141$	3.98537			0.335629
$142$	−14.8149	−	0.0802002i	−1.24324	−	0.00673025i
$143$	−8.74870	+	2.98830i	−0.731603	+	0.249894i
$144$	0.0866080	−	3.99906i	0.00721733	−	0.333255i
$145$	−12.8541	+	12.8541i	−1.06747	+	1.06747i
$146$	−1.59010	−	0.00860794i	−0.131597	−	0.000712398i
$147$	4.25403	−	4.25403i	0.350867	−	0.350867i
$148$	0.392895	+	0.00425398i	0.0322958	+	0.000349675i
$149$	13.5669			1.11145			0.555723	−	0.831367i	$-0.312441\pi$
$149$	13.5669			1.11145			0.555723	+	0.831367i	$0.312441\pi$
$150$	0.0139330	−	2.57376i	0.00113762	−	0.210146i
$151$	−12.8419	−	12.8419i	−1.04506	−	1.04506i	−0.998936	−	0.0461198i	$-0.985314\pi$
$151$	−12.8419	−	12.8419i	−1.04506	−	1.04506i	−0.0461198	−	0.998936i	$-0.514686\pi$
$152$	−2.59687	+	2.51386i	−0.210634	+	0.203901i
$153$	−6.11030			−0.493988
$154$	−0.0194711	+	3.59679i	−0.00156903	+	0.289838i
$155$	10.1442	+	10.1442i	0.814803	+	0.814803i
$156$	3.24702	−	6.43870i	0.259969	−	0.515509i
$157$	−5.49919	+	5.49919i	−0.438883	+	0.438883i	−0.891636	−	0.452753i	$-0.850442\pi$
$157$	−5.49919	+	5.49919i	−0.438883	+	0.438883i	0.452753	+	0.891636i	$0.350442\pi$
$158$	−0.371257	+	0.367259i	−0.0295356	+	0.0292175i
$159$			11.3279i			0.898362i
$160$	6.93742	+	7.32352i	0.548451	+	0.578975i
$161$	−2.54718	+	2.54718i	−0.200746	+	0.200746i
$162$	−0.994572	−	1.00540i	−0.0781410	−	0.0789916i
$163$		−	17.0410i		−	1.33476i	−0.744720	−	0.667378i	$-0.767417\pi$
$163$		−	17.0410i		−	1.33476i	0.744720	−	0.667378i	$-0.232583\pi$
$164$	−9.02037	+	8.82713i	−0.704373	+	0.689283i
$165$	−3.23323	−	3.23323i	−0.251707	−	0.251707i
$166$	6.60923	+	6.68118i	0.512976	+	0.518560i
$167$	−12.9395	−	12.9395i	−1.00129	−	1.00129i	−0.999999	−	0.00129035i	$-0.999589\pi$
$167$	−12.9395	−	12.9395i	−1.00129	−	1.00129i	−0.00129035	−	0.999999i	$-0.500411\pi$
$168$	−1.95134	−	2.01578i	−0.150549	−	0.155520i
$169$	10.2835	−	7.95296i	0.791039	−	0.611766i
$170$	10.9551	−	10.8372i	0.840221	−	0.831173i
$171$			1.27785i			0.0977197i
$172$	−8.96043	+	8.76847i	−0.683226	+	0.668590i
$173$	−16.0513	−	16.0513i	−1.22036	−	1.22036i	−0.967505	−	0.252853i	$-0.918631\pi$
$173$	−16.0513	−	16.0513i	−1.22036	−	1.22036i	−0.252853	−	0.967505i	$-0.581369\pi$
$174$	10.1385	+	10.2489i	0.768601	+	0.776968i
$175$	−1.27649	−	1.27649i	−0.0964934	−	0.0964934i
$176$	−10.2540	−	0.222071i	−0.772923	−	0.0167392i
$177$	0.808464	+	0.808464i	0.0607679	+	0.0607679i
$178$	7.42204	+	0.0401790i	0.556305	+	0.00301154i
$179$	4.63083	−	4.63083i	0.346125	−	0.346125i	−0.512539	−	0.858664i	$-0.671295\pi$
$179$	4.63083	−	4.63083i	0.346125	−	0.346125i	0.858664	+	0.512539i	$0.171295\pi$
$180$	3.56633	+	0.0386136i	0.265819	+	0.00287809i
$181$	2.99951	−	2.99951i	0.222952	−	0.222952i	−0.586789	−	0.809740i	$-0.699608\pi$
$181$	2.99951	−	2.99951i	0.222952	−	0.222952i	0.809740	+	0.586789i	$0.199608\pi$
$182$	−1.60891	−	4.79504i	−0.119261	−	0.355432i
$183$	11.2771			0.833626
$184$	−7.14437	−	7.38027i	−0.526690	−	0.544081i
$185$			0.350340i			0.0257575i
$186$	8.08825	−	8.00115i	0.593059	−	0.586673i
$187$			15.6674i			1.14571i
$188$	5.57482	+	5.69686i	0.406585	+	0.415486i
$189$	−0.991911			−0.0721509
$190$	−2.26638	−	2.29106i	−0.164421	−	0.166211i
$191$		−	14.2608i		−	1.03188i	−0.856626	−	0.515938i	$-0.827443\pi$
$191$		−	14.2608i		−	1.03188i	0.856626	−	0.515938i	$-0.172557\pi$
$192$	5.83758	−	5.47017i	0.421291	−	0.394775i
$193$	4.48882	+	4.48882i	0.323113	+	0.323113i	0.849960	−	0.526847i	$-0.176626\pi$
$193$	4.48882	+	4.48882i	0.323113	+	0.323113i	−0.526847	+	0.849960i	$0.676626\pi$
$194$	2.67394	+	0.0144753i	0.191977	+	0.00103926i
$195$	5.77198	+	2.83283i	0.413340	+	0.202863i
$196$	12.0315	+	0.130268i	0.859394	+	0.00930489i
$197$	24.2710			1.72924			0.864619	−	0.502428i	$-0.167560\pi$
$197$	24.2710			1.72924			0.864619	+	0.502428i	$0.167560\pi$
$198$	−2.57794	+	2.55018i	−0.183206	+	0.181233i
$199$			25.8301i			1.83105i	0.402262	+	0.915525i	$0.368224\pi$
$199$			25.8301i			1.83105i	−0.402262	+	0.915525i	$0.631776\pi$
$200$	3.69853	−	3.58031i	0.261525	−	0.253166i
$201$	9.63706	+	9.63706i	0.679746	+	0.679746i
$202$	−11.3493	−	0.0614391i	−0.798533	−	0.00432284i
$203$	10.1114			0.709682
$204$	−8.54721	−	8.73432i	−0.598424	−	0.611525i
$205$	−7.95720	−	7.95720i	−0.555755	−	0.555755i
$206$	−2.90483	+	2.87355i	−0.202389	+	0.200210i
$207$	−3.63164			−0.252416
$208$	13.7457	−	4.36516i	0.953096	−	0.302669i
$209$	3.27653			0.226642
$210$	1.77839	−	1.75924i	0.122721	−	0.121399i
$211$	11.8761	+	11.8761i	0.817582	+	0.817582i	0.985757	−	0.168175i	$-0.0537873\pi$
$211$	11.8761	+	11.8761i	0.817582	+	0.817582i	−0.168175	+	0.985757i	$0.553787\pi$
$212$	−16.1926	+	15.8457i	−1.11211	+	1.08829i
$213$	−10.4759			−0.717796
$214$	−26.2003	−	0.141834i	−1.79101	−	0.00969560i
$215$	−7.90432	−	7.90432i	−0.539070	−	0.539070i
$216$	0.0459324	−	2.82805i	0.00312530	−	0.192425i
$217$		−	7.97974i		−	0.541700i
$218$	3.68490	−	3.64522i	0.249573	−	0.246885i
$219$	−1.12438			−0.0759788
$220$	0.0990090	−	9.14442i	0.00667519	−	0.616516i
$221$	−7.12119	−	20.8483i	−0.479023	−	1.40241i
$222$	0.277831	+	0.00150403i	0.0186468	+	0.000100944i
$223$	−5.97195	−	5.97195i	−0.399911	−	0.399911i	0.478291	−	0.878202i	$-0.341257\pi$
$223$	−5.97195	−	5.97195i	−0.399911	−	0.399911i	−0.878202	+	0.478291i	$0.841257\pi$
$224$	0.151858	−	5.60904i	0.0101464	−	0.374770i
$225$		−	1.81995i		−	0.121330i
$226$	11.4340	+	11.5585i	0.760580	+	0.768860i
$227$	−12.6896			−0.842240			−0.421120	−	0.907005i	$-0.638363\pi$
$227$	−12.6896			−0.842240			−0.421120	+	0.907005i	$0.638363\pi$
$228$	−1.82661	+	1.78748i	−0.120970	+	0.118379i
$229$		−	18.3613i		−	1.21335i	−0.794952	−	0.606673i	$-0.792504\pi$
$229$		−	18.3613i		−	1.21335i	0.794952	−	0.606673i	$-0.207496\pi$
$230$	6.51116	−	6.44104i	0.429333	−	0.424710i
$231$			2.54335i			0.167340i
$232$	−0.468229	+	28.8288i	−0.0307407	+	1.89270i
$233$	5.52774			0.362134			0.181067	−	0.983471i	$-0.442045\pi$
$233$	5.52774			0.362134			0.181067	+	0.983471i	$0.442045\pi$
$234$	2.27131	−	4.56521i	0.148480	−	0.298437i
$235$	−5.02541	+	5.02541i	−0.327821	+	0.327821i
$236$	−0.0247571	+	2.28655i	−0.00161155	+	0.148842i
$237$	−0.261108	+	0.261108i	−0.0169608	+	0.0169608i
$238$	−8.57124	−	0.0464002i	−0.555591	−	0.00300768i
$239$	6.47562	+	6.47562i	0.418873	+	0.418873i	0.884815	−	0.465942i	$-0.154284\pi$
$239$	6.47562	+	6.47562i	0.418873	+	0.418873i	−0.465942	+	0.884815i	$0.654284\pi$
$240$	4.93346	+	5.15188i	0.318453	+	0.332552i
$241$	−9.32262	−	9.32262i	−0.600522	−	0.600522i	0.339929	−	0.940451i	$-0.389597\pi$
$241$	−9.32262	−	9.32262i	−0.600522	−	0.600522i	−0.940451	+	0.339929i	$0.889597\pi$
$242$	−4.40139	−	4.44930i	−0.282932	−	0.286012i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	15.7746	+	16.1199i	1.00987	+	1.03197i
$245$			10.7284i			0.685409i
$246$	−6.34448	+	6.27616i	−0.404509	+	0.400153i
$247$	−4.36003	+	1.48926i	−0.277422	+	0.0947592i
$248$	22.7512	+	0.369518i	1.44470	+	0.0234644i
$249$	4.69894	+	4.69894i	0.297783	+	0.297783i
$250$	12.0958	+	12.2275i	0.765005	+	0.773333i
$251$	−4.83179	−	4.83179i	−0.304980	−	0.304980i	0.537979	−	0.842958i	$-0.319188\pi$
$251$	−4.83179	−	4.83179i	−0.304980	−	0.304980i	−0.842958	+	0.537979i	$0.819188\pi$
$252$	−1.38750	−	1.41788i	−0.0874045	−	0.0893179i
$253$			9.31187i			0.585432i
$254$	−9.48301	−	9.58624i	−0.595017	−	0.601494i
$255$	7.70486	−	7.70486i	0.482497	−	0.482497i
$256$	15.9850	+	0.692701i	0.999062	+	0.0432938i
$257$			7.48385i			0.466830i	0.972377	+	0.233415i	$0.0749901\pi$
$257$			7.48385i			0.466830i	−0.972377	+	0.233415i	$0.925010\pi$
$258$	−6.30232	+	6.23445i	−0.392365	+	0.388140i
$259$	0.137794	−	0.137794i	0.00856209	−	0.00856209i
$260$	4.02459	+	12.2133i	0.249595	+	0.757438i
$261$	7.20816	+	7.20816i	0.446174	+	0.446174i
$262$	0.0214080	−	3.95458i	0.00132259	−	0.244315i
$263$	−2.85922			−0.176307			−0.0881534	−	0.996107i	$-0.528097\pi$
$263$	−2.85922			−0.176307			−0.0881534	+	0.996107i	$0.528097\pi$
$264$	−7.25140	−	0.117775i	−0.446293	−	0.00724855i
$265$	−14.2841	−	14.2841i	−0.877464	−	0.877464i
$266$	−0.00970370	+	1.79251i	−0.000594972	+	0.109906i
$267$	5.24825			0.321188
$268$	−0.295109	+	27.2561i	−0.0180267	+	1.66493i
$269$	−8.03382	+	8.03382i	−0.489831	+	0.489831i	−0.908253	−	0.418422i	$-0.862583\pi$
$269$	−8.03382	+	8.03382i	−0.489831	+	0.489831i	0.418422	+	0.908253i	$0.362583\pi$
$270$	2.52189	+	0.0136522i	0.153477	+	0.000830845i
$271$	−4.93246	+	4.93246i	−0.299625	+	0.299625i	−0.840867	−	0.541242i	$-0.817954\pi$
$271$	−4.93246	+	4.93246i	−0.299625	+	0.299625i	0.541242	+	0.840867i	$0.317954\pi$
$272$	0.529201	−	24.4355i	0.0320875	−	1.48162i
$273$	−1.15601	−	3.38440i	−0.0699650	−	0.204833i
$274$	18.8303	+	0.101937i	1.13758	+	0.00615826i
$275$	−4.66652			−0.281402
$276$	−5.08001	−	5.19122i	−0.305781	−	0.312475i
$277$	−6.07540	+	6.07540i	−0.365035	+	0.365035i	−0.865663	−	0.500627i	$-0.833103\pi$
$277$	−6.07540	+	6.07540i	−0.365035	+	0.365035i	0.500627	+	0.865663i	$0.333103\pi$
$278$	−10.8447	−	0.0587075i	−0.650421	−	0.00352104i
$279$	5.68854	−	5.68854i	0.340564	−	0.340564i
$280$	5.00239	+	0.0812472i	0.298950	+	0.00485545i
$281$	−19.2152	+	19.2152i	−1.14628	+	1.14628i	−0.159003	+	0.987278i	$0.550828\pi$
$281$	−19.2152	+	19.2152i	−1.14628	+	1.14628i	−0.987278	+	0.159003i	$0.949172\pi$
$282$	3.96374	+	4.00689i	0.236037	+	0.238607i
$283$	−20.7007	−	20.7007i	−1.23053	−	1.23053i	−0.963761	−	0.266768i	$-0.914044\pi$
$283$	−20.7007	−	20.7007i	−1.23053	−	1.23053i	−0.266768	−	0.963761i	$-0.585956\pi$
$284$	−14.6539	−	14.9747i	−0.869548	−	0.888584i
$285$	−1.61132	−	1.61132i	−0.0954465	−	0.0954465i
$286$	−11.7056	−	5.82385i	−0.692169	−	0.344372i
$287$			6.25937i			0.369479i
$288$	4.10679	−	3.89028i	0.241995	−	0.229237i
$289$	−20.3358			−1.19622
$290$	−25.7078	−	0.139169i	−1.50961	−	0.00817226i
$291$	1.89079			0.110840
$292$	−1.57281	−	1.60724i	−0.0920417	−	0.0940567i
$293$			15.8498i			0.925955i	0.886370	+	0.462977i	$0.153219\pi$
$293$			15.8498i			0.925955i	−0.886370	+	0.462977i	$0.846781\pi$
$294$	8.50794	+	0.0460575i	0.496193	+	0.00268613i
$295$	−2.03889			−0.118708
$296$	0.386486	+	0.399247i	0.0224640	+	0.0232058i
$297$	−1.81309	+	1.81309i	−0.105206	+	0.105206i
$298$	13.4933	+	13.6402i	0.781646	+	0.790155i
$299$	−4.23246	−	12.3912i	−0.244769	−	0.716599i
$300$	2.60151	−	2.54578i	0.150198	−	0.146981i
$301$			6.21777i			0.358386i
$302$	0.139036	−	25.6833i	0.00800063	−	1.47791i
$303$	−8.02528			−0.461040
$304$	−5.11020	−	0.110672i	−0.293090	−	0.00634748i
$305$	−14.2200	+	14.2200i	−0.814234	+	0.814234i
$306$	−6.07713	−	6.14329i	−0.347407	−	0.351188i
$307$		−	10.3184i		−	0.588904i	−0.955666	−	0.294452i	$-0.904863\pi$
$307$		−	10.3184i		−	0.588904i	0.955666	−	0.294452i	$-0.0951371\pi$
$308$	−3.63558	+	3.55769i	−0.207156	+	0.202718i
$309$	−2.04300	+	2.04300i	−0.116222	+	0.116222i
$310$	−0.109829	+	20.2881i	−0.00623788	+	1.15229i
$311$			5.77614i			0.327535i	0.986499	+	0.163767i	$0.0523647\pi$
$311$			5.77614i			0.327535i	−0.986499	+	0.163767i	$0.947635\pi$
$312$	9.70285	−	3.13920i	0.549316	−	0.177722i
$313$			7.64762i			0.432269i	0.976364	+	0.216135i	$0.0693450\pi$
$313$			7.64762i			0.432269i	−0.976364	+	0.216135i	$0.930655\pi$
$314$	−10.9982	−	0.0595385i	−0.620665	−	0.00335995i
$315$	1.25076	−	1.25076i	0.0704724	−	0.0704724i
$316$	−0.738483	−	0.00799575i	−0.0415429	−	0.000449796i
$317$		−	23.7608i		−	1.33454i	−0.744815	−	0.667271i	$-0.767462\pi$
$317$		−	23.7608i		−	1.33454i	0.744815	−	0.667271i	$-0.232538\pi$
$318$	−11.3891	+	11.2664i	−0.638668	+	0.631790i
$319$	18.4824	−	18.4824i	1.03482	−	1.03482i
$320$	−0.463291	+	14.2586i	−0.0258987	+	0.797082i
$321$	−18.5266			−1.03406
$322$	−5.09429	−	0.0275778i	−0.283894	−	0.00153685i
$323$			7.80805i			0.434452i
$324$	0.0216533	−	1.99988i	0.00120296	−	0.111105i
$325$	6.20966	−	2.12104i	0.344450	−	0.117654i
$326$	17.1330	−	16.9485i	0.948910	−	0.938691i
$327$	2.59163	−	2.59163i	0.143317	−	0.143317i
$328$	−17.8462	−	0.289852i	−0.985391	−	0.0160044i
$329$	3.95313			0.217943
$330$	0.0350055	−	6.46636i	0.00192699	−	0.355962i
$331$		−	2.93087i		−	0.161095i	−0.996751	−	0.0805477i	$-0.974333\pi$
$331$		−	2.93087i		−	0.161095i	0.996751	−	0.0805477i	$-0.0256669\pi$
$332$	−0.143892	+	13.2898i	−0.00789712	+	0.729374i
$333$	0.196459			0.0107659
$334$	0.140093	−	25.8786i	0.00766557	−	1.41602i
$335$	−24.3040			−1.32787
$336$	0.0859074	−	3.96671i	0.00468663	−	0.216402i
$337$			10.5136i			0.572712i	0.958123	+	0.286356i	$0.0924441\pi$
$337$			10.5136i			0.572712i	−0.958123	+	0.286356i	$0.907556\pi$
$338$	18.2236	+	2.42923i	0.991232	+	0.132132i
$339$	8.12920	+	8.12920i	0.441518	+	0.441518i
$340$	21.7914	+	0.235941i	1.18180	+	0.0127957i
$341$	−14.5860	−	14.5860i	−0.789875	−	0.789875i
$342$	−1.28475	+	1.27091i	−0.0694713	+	0.0687232i
$343$	9.12933	−	9.12933i	0.492937	−	0.492937i
$344$	−17.7276	−	0.287926i	−0.955808	−	0.0155239i
$345$	4.57936	−	4.57936i	0.246545	−	0.246545i
$346$	0.173784	−	32.1021i	0.00934269	−	1.72582i
$347$	−9.80433	+	9.80433i	−0.526324	+	0.526324i	−0.919474	−	0.393150i	$-0.871385\pi$
$347$	−9.80433	+	9.80433i	−0.526324	+	0.526324i	0.393150	+	0.919474i	$0.371385\pi$
$348$	−0.220731	+	20.3866i	−0.0118324	+	1.09283i
$349$	6.88446			0.368517			0.184258	−	0.982878i	$-0.441012\pi$
$349$	6.88446			0.368517			0.184258	+	0.982878i	$0.441012\pi$
$350$	0.0138203	−	2.55294i	0.000738724	−	0.136460i
$351$	1.58856	−	3.23674i	0.0847910	−	0.172764i
$352$	−9.97505	−	10.5302i	−0.531672	−	0.561262i
$353$	4.39050	−	4.39050i	0.233683	−	0.233683i	−0.580545	−	0.814228i	$-0.697161\pi$
$353$	4.39050	−	4.39050i	0.233683	−	0.233683i	0.814228	+	0.580545i	$0.197161\pi$
$354$	−0.00875307	+	1.61690i	−0.000465220	+	0.0859375i
$355$	13.2097	−	13.2097i	0.701098	−	0.701098i
$356$	7.34136	+	7.50207i	0.389091	+	0.397609i
$357$	−6.06087			−0.320775
$358$	9.26153	+	0.0501370i	0.489487	+	0.00264983i
$359$	6.51957	+	6.51957i	0.344090	+	0.344090i	0.857902	−	0.513813i	$-0.171767\pi$
$359$	6.51957	+	6.51957i	0.344090	+	0.344090i	−0.513813	+	0.857902i	$0.671767\pi$
$360$	3.50815	+	3.62399i	0.184896	+	0.191001i
$361$	−17.3671			−0.914058
$362$	5.99893	+	0.0324750i	0.315297	+	0.00170685i
$363$	−3.12924	−	3.12924i	−0.164242	−	0.164242i
$364$	3.22075	−	6.38662i	0.168813	−	0.334750i
$365$	1.41781	−	1.41781i	0.0742113	−	0.0742113i
$366$	11.2159	+	11.3380i	0.586263	+	0.592645i
$367$			19.4128i			1.01334i	0.862140	+	0.506670i	$0.169124\pi$
$367$			19.4128i			1.01334i	−0.862140	+	0.506670i	$0.830876\pi$
$368$	0.314529	−	14.5232i	0.0163960	−	0.757072i
$369$	−4.46214	+	4.46214i	−0.232290	+	0.232290i
$370$	−0.352231	+	0.348438i	−0.0183116	+	0.0181144i
$371$			11.2363i			0.583359i
$372$	16.0887	+	0.174197i	0.834160	+	0.00903167i
$373$	5.47223	+	5.47223i	0.283341	+	0.283341i	0.834440	−	0.551099i	$-0.185791\pi$
$373$	5.47223	+	5.47223i	0.283341	+	0.283341i	−0.551099	+	0.834440i	$0.685791\pi$
$374$	−15.7520	+	15.5824i	−0.814515	+	0.805744i
$375$	8.59970	+	8.59970i	0.444086	+	0.444086i
$376$	−0.183058	+	11.2709i	−0.00944048	+	0.581250i
$377$	−16.1936	+	32.9949i	−0.834011	+	1.69932i
$378$	−0.986526	−	0.997266i	−0.0507414	−	0.0512938i
$379$		−	32.5074i		−	1.66979i	−0.550406	−	0.834897i	$-0.685527\pi$
$379$		−	32.5074i		−	1.66979i	0.550406	−	0.834897i	$-0.314473\pi$
$380$	0.0493424	−	4.55724i	0.00253121	−	0.233781i
$381$	−6.74209	−	6.74209i	−0.345408	−	0.345408i
$382$	14.3378	−	14.1834i	0.733586	−	0.725686i
$383$	−8.87144	−	8.87144i	−0.453309	−	0.453309i	0.443142	−	0.896451i	$-0.353864\pi$
$383$	−8.87144	−	8.87144i	−0.453309	−	0.453309i	−0.896451	+	0.443142i	$0.853864\pi$
$384$	11.3056	+	0.428618i	0.576936	+	0.0218728i
$385$	−3.20707	−	3.20707i	−0.163448	−	0.163448i
$386$	−0.0485995	+	8.97751i	−0.00247365	+	0.456943i
$387$	−4.43248	+	4.43248i	−0.225316	+	0.225316i
$388$	2.64487	+	2.70277i	0.134273	+	0.137212i
$389$	16.5675	−	16.5675i	0.840007	−	0.840007i	−0.148852	−	0.988859i	$-0.547558\pi$
$389$	16.5675	−	16.5675i	0.840007	−	0.840007i	0.988859	+	0.148852i	$0.0475578\pi$
$390$	2.89253	+	8.62059i	0.146469	+	0.436521i
$391$	−22.1904			−1.12222
$392$	11.8352	+	12.2260i	0.597770	+	0.617508i
$393$		−	2.79635i		−	0.141057i
$394$	24.1393	+	24.4021i	1.21612	+	1.22936i
$395$		−	0.658496i		−	0.0331325i
$396$	−5.12789	−	0.0555210i	−0.257686	−	0.00279004i
$397$	−30.7857			−1.54509			−0.772545	−	0.634961i	$-0.781016\pi$
$397$	−30.7857			−1.54509			−0.772545	+	0.634961i	$0.781016\pi$
$398$	−25.9696	+	25.6899i	−1.30174	+	1.28772i
$399$			1.26751i			0.0634550i
$400$	7.27808	+	0.157622i	0.363904	+	0.00788110i
$401$	8.51115	+	8.51115i	0.425027	+	0.425027i	0.886930	−	0.461903i	$-0.152833\pi$
$401$	8.51115	+	8.51115i	0.425027	+	0.425027i	−0.461903	+	0.886930i	$0.652833\pi$
$402$	−0.104338	+	19.2738i	−0.00520393	+	0.961292i
$403$	26.0390	+	12.7797i	1.29709	+	0.636600i
$404$	−11.2259	−	11.4717i	−0.558510	−	0.570737i
$405$	1.78327			0.0886114
$406$	10.0565	+	10.1660i	0.499097	+	0.504530i
$407$		−	0.503740i		−	0.0249695i
$408$	0.280661	−	17.2803i	0.0138948	−	0.855500i
$409$	20.7061	+	20.7061i	1.02385	+	1.02385i	0.999708	+	0.0241439i	$0.00768599\pi$
$409$	20.7061	+	20.7061i	1.02385	+	1.02385i	0.0241439	+	0.999708i	$0.492314\pi$
$410$	0.0861509	−	15.9142i	0.00425469	−	0.785944i
$411$	13.3152			0.656792
$412$	−5.77813	−	0.0625613i	−0.284668	−	0.00308217i
$413$	0.801924	+	0.801924i	0.0394601	+	0.0394601i
$414$	−3.61193	−	3.65125i	−0.177517	−	0.179449i
$415$	−11.8504			−0.581712
$416$	18.0599	+	9.47849i	0.885457	+	0.464721i
$417$	−7.66847			−0.375527
$418$	3.25875	+	3.29422i	0.159391	+	0.161126i
$419$	−28.8503	−	28.8503i	−1.40943	−	1.40943i	−0.762824	−	0.646606i	$-0.776188\pi$
$419$	−28.8503	−	28.8503i	−1.40943	−	1.40943i	−0.646606	−	0.762824i	$-0.723812\pi$
$420$	3.53748	+	0.0383012i	0.172611	+	0.00186891i
$421$	1.05635			0.0514835			0.0257418	−	0.999669i	$-0.491805\pi$
$421$	1.05635			0.0514835			0.0257418	+	0.999669i	$0.491805\pi$
$422$	−0.128580	+	23.7518i	−0.00625916	+	1.15622i
$423$	2.81808	+	2.81808i	0.137020	+	0.137020i
$424$	−32.0360	−	0.520318i	−1.55580	−	0.0252689i
$425$		−	11.1204i		−	0.539420i
$426$	−10.4190	−	10.5324i	−0.504804	−	0.510299i
$427$	11.1859			0.541322
$428$	−25.9154	−	26.4828i	−1.25267	−	1.28009i
$429$	−8.29931	−	4.07322i	−0.400694	−	0.196657i
$430$	0.0855784	−	15.8084i	0.00412696	−	0.762349i
$431$	−6.13704	−	6.13704i	−0.295611	−	0.295611i	0.543681	−	0.839292i	$-0.317030\pi$
$431$	−6.13704	−	6.13704i	−0.295611	−	0.295611i	−0.839292	+	0.543681i	$0.817030\pi$
$432$	2.88901	−	2.76652i	0.138997	−	0.133104i
$433$			7.29552i			0.350600i	0.984515	+	0.175300i	$0.0560896\pi$
$433$			7.29552i			0.350600i	−0.984515	+	0.175300i	$0.943910\pi$
$434$	8.02282	−	7.93642i	0.385108	−	0.380961i
$435$	−18.1784			−0.871589
$436$	7.32979	+	0.0793616i	0.351033	+	0.00380073i
$437$			4.64069i			0.221994i
$438$	−1.11828	−	1.13045i	−0.0534335	−	0.0540152i
$439$			28.4802i			1.35929i	0.733542	+	0.679644i	$0.237866\pi$
$439$			28.4802i			1.35929i	−0.733542	+	0.679644i	$0.762134\pi$
$440$	9.29226	−	8.99524i	0.442991	−	0.428831i
$441$	6.01611			0.286482
$442$	13.8784	−	27.8948i	0.660127	−	1.32682i
$443$	−11.1545	+	11.1545i	−0.529964	+	0.529964i	−0.920562	−	0.390598i	$-0.872268\pi$
$443$	−11.1545	+	11.1545i	−0.529964	+	0.529964i	0.390598	+	0.920562i	$0.372268\pi$
$444$	0.274811	+	0.280827i	0.0130419	+	0.0133275i
$445$	−6.61785	+	6.61785i	−0.313716	+	0.313716i
$446$	0.0646570	−	11.9437i	0.00306160	−	0.565551i
$447$	9.59327	+	9.59327i	0.453746	+	0.453746i
$448$	5.79035	−	5.42591i	0.273568	−	0.256350i
$449$	−13.9222	−	13.9222i	−0.657030	−	0.657030i	0.297647	−	0.954676i	$-0.403798\pi$
$449$	−13.9222	−	13.9222i	−0.657030	−	0.657030i	−0.954676	+	0.297647i	$0.903798\pi$
$450$	1.82977	−	1.81007i	0.0862563	−	0.0853275i
$451$	11.4413	+	11.4413i	0.538752	+	0.538752i
$452$	−0.248935	+	22.9915i	−0.0117089	+	1.08143i
$453$		−	18.1611i		−	0.853284i
$454$	−12.6207	−	12.7581i	−0.592321	−	0.598769i
$455$	5.72529	+	2.80991i	0.268406	+	0.131731i
$456$	−3.61383	−	0.0586947i	−0.169233	−	0.00274863i
$457$	−20.7904	−	20.7904i	−0.972533	−	0.972533i	0.0270994	−	0.999633i	$-0.491373\pi$
$457$	−20.7904	−	20.7904i	−0.972533	−	0.972533i	−0.999633	+	0.0270994i	$0.991373\pi$
$458$	18.4604	−	18.2616i	0.862597	−	0.853308i
$459$	−4.32063	−	4.32063i	−0.201670	−	0.201670i
$460$	12.9516	+	0.140231i	0.603873	+	0.00653829i
$461$			19.1568i			0.892219i	0.894978	+	0.446110i	$0.147191\pi$
$461$			19.1568i			0.892219i	−0.894978	+	0.446110i	$0.852809\pi$
$462$	−2.55708	+	2.52955i	−0.118966	+	0.117685i
$463$	10.5071	−	10.5071i	0.488308	−	0.488308i	−0.419464	−	0.907772i	$-0.637782\pi$
$463$	10.5071	−	10.5071i	0.488308	−	0.488308i	0.907772	+	0.419464i	$0.137782\pi$
$464$	−29.4502	+	28.2016i	−1.36719	+	1.30923i
$465$			14.3461i			0.665284i
$466$	5.49773	+	5.55758i	0.254677	+	0.257450i
$467$	4.11133	−	4.11133i	0.190250	−	0.190250i	−0.605554	−	0.795804i	$-0.707049\pi$
$467$	4.11133	−	4.11133i	0.190250	−	0.190250i	0.795804	+	0.605554i	$0.207049\pi$
$468$	6.84884	−	2.25686i	0.316588	−	0.104323i
$469$	9.55911	+	9.55911i	0.441399	+	0.441399i
$470$	−10.0507	−	0.0544090i	−0.463603	−	0.00250970i
$471$	−7.77702			−0.358346
$472$	−2.32351	+	2.24925i	−0.106948	+	0.103530i
$473$	11.3653	+	11.3653i	0.522578	+	0.522578i
$474$	−0.522209	−	0.00282697i	−0.0239859	−	0.000129847i
$475$	−2.32562			−0.106707
$476$	−8.47806	−	8.66366i	−0.388591	−	0.397098i
$477$	−8.01005	+	8.01005i	−0.366755	+	0.366755i
$478$	−0.0701102	+	12.9511i	−0.00320677	+	0.592368i
$479$	−18.1261	+	18.1261i	−0.828202	+	0.828202i	−0.987268	−	0.159066i	$-0.949152\pi$
$479$	−18.1261	+	18.1261i	−0.828202	+	0.828202i	0.159066	+	0.987268i	$0.449152\pi$
$480$	−0.273011	+	10.0840i	−0.0124612	+	0.460270i
$481$	0.228961	+	0.670319i	0.0104397	+	0.0305639i
$482$	0.100934	−	18.6450i	0.00459742	−	0.849255i
$483$	−3.60226			−0.163909
$484$	0.0958246	−	8.85030i	0.00435566	−	0.402287i
$485$	−2.38421	+	2.38421i	−0.108261	+	0.108261i
$486$	0.00765570	−	1.41419i	0.000347269	−	0.0641491i
$487$	−12.0784	+	12.0784i	−0.547326	+	0.547326i	−0.925667	−	0.378340i	$-0.876495\pi$
$487$	−12.0784	+	12.0784i	−0.547326	+	0.547326i	0.378340	+	0.925667i	$0.376495\pi$
$488$	−0.517983	+	31.8922i	−0.0234480	+	1.44369i
$489$	12.0498	−	12.0498i	0.544911	−	0.544911i
$490$	−10.7863	+	10.6701i	−0.487274	+	0.482027i
$491$	18.6029	+	18.6029i	0.839537	+	0.839537i	0.988798	−	0.149261i	$-0.0476894\pi$
$491$	18.6029	+	18.6029i	0.839537	+	0.839537i	−0.149261	+	0.988798i	$0.547689\pi$
$492$	−12.6201	−	0.136641i	−0.568958	−	0.00616025i
$493$	44.0440	+	44.0440i	1.98364	+	1.98364i
$494$	−5.83366	−	2.90239i	−0.262469	−	0.130585i
$495$		−	4.57248i		−	0.205517i
$496$	22.2562	+	23.2415i	0.999332	+	1.04357i
$497$	−10.3911			−0.466107
$498$	−0.0508744	+	9.39774i	−0.00227974	+	0.421123i
$499$	32.9096			1.47324			0.736618	−	0.676309i	$-0.236421\pi$
$499$	32.9096			1.47324			0.736618	+	0.676309i	$0.236421\pi$
$500$	−0.263343	+	24.3222i	−0.0117770	+	1.08772i
$501$		−	18.2992i		−	0.817549i
$502$	0.0523127	−	9.66343i	0.00233483	−	0.431300i
$503$	12.9568			0.577716			0.288858	−	0.957372i	$-0.406724\pi$
$503$	12.9568			0.577716			0.288858	+	0.957372i	$0.406724\pi$
$504$	0.0455608	−	2.80518i	0.00202944	−	0.124953i
$505$	10.1196	−	10.1196i	0.450315	−	0.450315i
$506$	−9.36215	+	9.26133i	−0.416198	+	0.411716i
$507$	12.8951	+	1.64794i	0.572693	+	0.0731876i
$508$	0.206459	−	19.0684i	0.00916012	−	0.846024i
$509$		−	4.54312i		−	0.201370i	−0.994918	−	0.100685i	$-0.967897\pi$
$509$		−	4.54312i		−	0.201370i	0.994918	−	0.100685i	$-0.0321035\pi$
$510$	15.4095	+	0.0834189i	0.682344	+	0.00369385i
$511$	−1.11529			−0.0493374
$512$	15.2018	+	16.7602i	0.671831	+	0.740705i
$513$	−0.903577	+	0.903577i	−0.0398939	+	0.0398939i
$514$	−7.52426	+	7.44323i	−0.331881	+	0.328307i
$515$		−	5.15228i		−	0.227037i
$516$	−12.5362	−	0.135733i	−0.551876	−	0.00597531i
$517$	7.22584	−	7.22584i	0.317792	−	0.317792i
$518$	0.275584	+	0.00149186i	0.0121084	+	6.55488e-5i
$519$		−	22.7000i		−	0.996418i
$520$	−8.27652	+	16.1934i	−0.362949	+	0.710126i
$521$			32.3446i			1.41704i	0.705690	+	0.708520i	$0.250637\pi$
$521$			32.3446i			1.41704i	−0.705690	+	0.708520i	$0.749363\pi$
$522$	−0.0780412	+	14.4161i	−0.00341577	+	0.630976i
$523$	27.1341	−	27.1341i	1.18649	−	1.18649i	0.208459	−	0.978031i	$-0.433155\pi$
$523$	27.1341	−	27.1341i	1.18649	−	1.18649i	0.978031	−	0.208459i	$-0.0668447\pi$
$524$	3.99723	−	3.91159i	0.174620	−	0.170879i
$525$		−	1.80523i		−	0.0787865i
$526$	−2.84370	−	2.87465i	−0.123991	−	0.125341i
$527$	34.7587	−	34.7587i	1.51411	−	1.51411i
$528$	−7.09363	−	7.40769i	−0.308711	−	0.322378i
$529$	9.81119			0.426574
$530$	0.154651	−	28.5677i	0.00671760	−	1.24090i
$531$			1.14334i			0.0496168i
$532$	−1.81184	+	1.77302i	−0.0785531	+	0.0768703i
$533$	−20.4252	−	10.0245i	−0.884712	−	0.434208i
$534$	5.21976	+	5.27659i	0.225881	+	0.228340i
$535$	23.3614	−	23.3614i	1.01000	−	1.01000i
$536$	−27.6968	+	26.8115i	−1.19632	+	1.15808i
$537$	6.54899			0.282610
$538$	−16.0674	−	0.0869805i	−0.692715	−	0.00374999i
$539$		−	15.4259i		−	0.664440i
$540$	2.49447	+	2.54908i	0.107345	+	0.109695i
$541$	22.5789			0.970741			0.485371	−	0.874308i	$-0.338685\pi$
$541$	22.5789			0.970741			0.485371	+	0.874308i	$0.338685\pi$
$542$	−9.86477	−	0.0534027i	−0.423728	−	0.00229384i
$543$	4.24194			0.182039
$544$	25.0937	−	23.7708i	1.07588	−	1.01916i
$545$			6.53588i			0.279966i
$546$	2.25293	−	4.52828i	0.0964167	−	0.193793i
$547$	27.9169	+	27.9169i	1.19364	+	1.19364i	0.976037	+	0.217603i	$0.0698239\pi$
$547$	27.9169	+	27.9169i	1.19364	+	1.19364i	0.217603	+	0.976037i	$0.430176\pi$
$548$	18.6256	+	19.0333i	0.795646	+	0.813064i
$549$	7.97410	+	7.97410i	0.340326	+	0.340326i
$550$	−4.64119	−	4.69171i	−0.197901	−	0.200055i
$551$	9.21095	−	9.21095i	0.392400	−	0.392400i
$552$	0.166810	−	10.2705i	0.00709990	−	0.437140i
$553$	−0.258996	+	0.258996i	−0.0110136	+	0.0110136i
$554$	−12.1506	−	0.0657771i	−0.516230	−	0.00279460i
$555$	−0.247728	+	0.247728i	−0.0105154	+	0.0105154i
$556$	−10.7268	−	10.9616i	−0.454918	−	0.464877i
$557$	−5.58770			−0.236758			−0.118379	−	0.992968i	$-0.537770\pi$
$557$	−5.58770			−0.236758			−0.118379	+	0.992968i	$0.537770\pi$
$558$	11.3769	+	0.0615887i	0.481624	+	0.00260726i
$559$	−20.2894	−	9.95785i	−0.858152	−	0.421172i
$560$	4.89355	+	5.11020i	0.206790	+	0.215945i
$561$	−11.0785	+	11.0785i	−0.467736	+	0.467736i
$562$	−38.4298	−	0.208039i	−1.62106	−	0.00877558i
$563$	0.0171559	−	0.0171559i	0.000723034	−	0.000723034i	−0.706745	−	0.707468i	$-0.749837\pi$
$563$	0.0171559	−	0.0171559i	0.000723034	−	0.000723034i	0.707468	+	0.706745i	$0.249837\pi$
$564$	−0.0862963	+	7.97028i	−0.00363373	+	0.335609i
$565$	−20.5012			−0.862494
$566$	0.224122	−	41.4008i	0.00942056	−	1.74021i
$567$	−0.701387	−	0.701387i	−0.0294555	−	0.0294555i
$568$	0.481183	−	29.6264i	0.0201900	−	1.24310i
$569$	26.1050			1.09438			0.547189	−	0.837009i	$-0.315698\pi$
$569$	26.1050			1.09438			0.547189	+	0.837009i	$0.315698\pi$
$570$	0.0174454	−	3.22260i	0.000730709	−	0.134980i
$571$	−5.29421	−	5.29421i	−0.221556	−	0.221556i	0.587598	−	0.809153i	$-0.300074\pi$
$571$	−5.29421	−	5.29421i	−0.221556	−	0.221556i	−0.809153	+	0.587598i	$0.800074\pi$
$572$	−5.78681	−	17.5611i	−0.241959	−	0.734266i
$573$	10.0839	−	10.0839i	0.421262	−	0.421262i
$574$	−6.29316	+	6.22539i	−0.262671	+	0.259843i
$575$		−	6.60940i		−	0.275631i
$576$	7.99578	+	0.259799i	0.333158	+	0.0108249i
$577$	3.43180	−	3.43180i	0.142868	−	0.142868i	−0.632056	−	0.774923i	$-0.717789\pi$
$577$	3.43180	−	3.43180i	0.142868	−	0.142868i	0.774923	+	0.632056i	$0.217789\pi$
$578$	−20.2254	−	20.4456i	−0.841265	−	0.850423i
$579$			6.34815i			0.263820i
$580$	−25.4283	−	25.9850i	−1.05585	−	1.07897i
$581$	4.66093	+	4.66093i	0.193368	+	0.193368i
$582$	1.88052	+	1.90099i	0.0779502	+	0.0787988i
$583$	20.5385	+	20.5385i	0.850619	+	0.850619i
$584$	0.0516456	−	3.17982i	0.00213711	−	0.131582i
$585$	2.07829	+	6.08452i	0.0859269	+	0.251564i
$586$	−15.9354	+	15.7638i	−0.658284	+	0.651195i
$587$		−	32.4677i		−	1.34009i	−0.742323	−	0.670043i	$-0.766276\pi$
$587$		−	32.4677i		−	1.34009i	0.742323	−	0.670043i	$-0.233724\pi$
$588$	8.41546	+	8.59968i	0.347048	+	0.354645i
$589$	−7.26911	−	7.26911i	−0.299518	−	0.299518i
$590$	−2.02782	−	2.04989i	−0.0834839	−	0.0843927i
$591$	17.1622	+	17.1622i	0.705959	+	0.705959i
$592$	−0.0170149	+	0.785652i	−0.000699309	+	0.0322901i
$593$	11.1467	+	11.1467i	0.457740	+	0.457740i	0.897913	−	0.440173i	$-0.145083\pi$
$593$	11.1467	+	11.1467i	0.457740	+	0.457740i	−0.440173	+	0.897913i	$0.645083\pi$
$594$	−3.62613	−	0.0196299i	−0.148782	−	0.000805426i
$595$	7.64253	−	7.64253i	0.313313	−	0.313313i
$596$	−0.293768	+	27.1323i	−0.0120332	+	1.11138i
$597$	−18.2647	+	18.2647i	−0.747523	+	0.747523i
$598$	8.24857	−	16.5792i	0.337309	−	0.677974i
$599$	−6.64078			−0.271335			−0.135667	−	0.990754i	$-0.543318\pi$
$599$	−6.64078			−0.271335			−0.135667	+	0.990754i	$0.543318\pi$
$600$	5.14691	+	0.0835945i	0.210122	+	0.00341273i
$601$		−	30.6261i		−	1.24926i	−0.780919	−	0.624632i	$-0.785249\pi$
$601$		−	30.6261i		−	1.24926i	0.780919	−	0.624632i	$-0.214751\pi$
$602$	−6.25134	+	6.18402i	−0.254786	+	0.252042i
$603$			13.6289i			0.555010i
$604$	25.9603	−	25.4041i	1.05631	−	1.03368i
$605$	7.89170			0.320843
$606$	−7.98171	−	8.06860i	−0.324235	−	0.327765i
$607$		−	12.2273i		−	0.496290i	−0.968723	−	0.248145i	$-0.920179\pi$
$607$		−	12.2273i		−	0.496290i	0.968723	−	0.248145i	$-0.0798209\pi$
$608$	−4.97120	−	5.24786i	−0.201609	−	0.212829i
$609$	7.14985	+	7.14985i	0.289726	+	0.289726i
$610$	−28.4395	−	0.153957i	−1.15148	−	0.00623353i
$611$	−6.33100	+	12.8996i	−0.256125	+	0.521862i
$612$	0.132308	−	12.2199i	0.00534823	−	0.493960i
$613$	24.0264			0.970415			0.485208	−	0.874399i	$-0.338744\pi$
$613$	24.0264			0.970415			0.485208	+	0.874399i	$0.338744\pi$
$614$	10.3741	−	10.2624i	0.418666	−	0.414158i
$615$		−	11.2532i		−	0.453772i
$616$	−7.19274	−	0.116822i	−0.289804	−	0.00470690i
$617$	0.0972772	+	0.0972772i	0.00391623	+	0.00391623i	0.709062	−	0.705146i	$-0.249119\pi$
$617$	0.0972772	+	0.0972772i	0.00391623	+	0.00391623i	−0.705146	+	0.709062i	$0.749119\pi$
$618$	−4.08593	−	0.0221191i	−0.164360	−	0.000889760i
$619$	30.2325			1.21515			0.607574	−	0.794263i	$-0.292143\pi$
$619$	30.2325			1.21515			0.607574	+	0.794263i	$0.292143\pi$
$620$	−20.5069	+	20.0676i	−0.823576	+	0.805933i
$621$	−2.56796	−	2.56796i	−0.103049	−	0.103049i
$622$	−5.80732	+	5.74479i	−0.232852	+	0.230345i
$623$	5.20580			0.208566
$624$	12.8063	+	6.63307i	0.512664	+	0.265535i
$625$	−12.5881			−0.503522
$626$	−7.68891	+	7.60611i	−0.307311	+	0.304001i
$627$	2.31686	+	2.31686i	0.0925264	+	0.0925264i
$628$	−10.8787	−	11.1168i	−0.434105	−	0.443609i
$629$	1.20042			0.0478640
$630$	2.50149	+	0.0135417i	0.0996616	+	0.000539516i
$631$	11.6179	+	11.6179i	0.462500	+	0.462500i	0.899474	−	0.436974i	$-0.143950\pi$
$631$	11.6179	+	11.6179i	0.462500	+	0.462500i	−0.436974	+	0.899474i	$0.643950\pi$
$632$	−0.726436	−	0.750422i	−0.0288961	−	0.0298502i
$633$			16.7953i			0.667553i
$634$	23.8891	−	23.6319i	0.948758	−	0.938541i
$635$	17.0031			0.674746
$636$	−22.6545	−	0.245286i	−0.898310	−	0.00972624i
$637$	7.01142	+	20.5270i	0.277802	+	0.813309i
$638$	36.9643	+	0.200105i	1.46343	+	0.00792224i
$639$	−7.40757	−	7.40757i	−0.293039	−	0.293039i
$640$	−14.7964	+	13.7154i	−0.584879	+	0.542151i
$641$			10.9034i			0.430658i	0.976542	+	0.215329i	$0.0690823\pi$
$641$			10.9034i			0.430658i	−0.976542	+	0.215329i	$0.930918\pi$
$642$	−18.4261	−	18.6267i	−0.727219	−	0.735136i
$643$	−5.10163			−0.201188			−0.100594	−	0.994928i	$-0.532074\pi$
$643$	−5.10163			−0.201188			−0.100594	+	0.994928i	$0.532074\pi$
$644$	−5.03891	−	5.14922i	−0.198561	−	0.202908i
$645$		−	11.1784i		−	0.440149i
$646$	−7.85020	+	7.76567i	−0.308862	+	0.305536i
$647$		−	21.9533i		−	0.863073i	−0.902095	−	0.431537i	$-0.857972\pi$
$647$		−	21.9533i		−	0.863073i	0.902095	−	0.431537i	$-0.142028\pi$
$648$	2.03222	−	1.96726i	0.0798330	−	0.0772812i
$649$	2.93164			0.115077
$650$	8.30845	+	4.13366i	0.325884	+	0.162136i
$651$	5.64253	−	5.64253i	0.221148	−	0.221148i
$652$	34.0800	+	0.368993i	1.33468	+	0.0144509i
$653$	31.4642	−	31.4642i	1.23129	−	1.23129i	0.267823	−	0.963468i	$-0.413696\pi$
$653$	31.4642	−	31.4642i	1.23129	−	1.23129i	0.963468	−	0.267823i	$-0.0863043\pi$
$654$	5.18317	+	0.0280590i	0.202678	+	0.00109719i
$655$	3.52610	+	3.52610i	0.137776	+	0.137776i
$656$	−17.4579	−	18.2308i	−0.681617	−	0.711794i
$657$	−0.795059	−	0.795059i	−0.0310182	−	0.0310182i
$658$	3.93168	+	3.97448i	0.153273	+	0.154941i
$659$	−14.0152	−	14.0152i	−0.545956	−	0.545956i	0.379313	−	0.925269i	$-0.376160\pi$
$659$	−14.0152	−	14.0152i	−0.545956	−	0.545956i	−0.925269	+	0.379313i	$0.876160\pi$
$660$	6.53609	−	6.39607i	0.254417	−	0.248967i
$661$		−	15.6467i		−	0.608588i	−0.952578	−	0.304294i	$-0.901580\pi$
$661$		−	15.6467i		−	0.608588i	0.952578	−	0.304294i	$-0.0984205\pi$
$662$	2.94670	−	2.91496i	0.114527	−	0.113293i
$663$	9.70657	−	19.7774i	0.376972	−	0.768092i
$664$	−13.5047	+	13.0730i	−0.524083	+	0.507331i
$665$	−1.59829	−	1.59829i	−0.0619789	−	0.0619789i
$666$	0.195393	+	0.197520i	0.00757131	+	0.00765374i
$667$	26.1774	+	26.1774i	1.01359	+	1.01359i
$668$	26.1577	−	25.5973i	1.01207	−	0.990390i
$669$		−	8.44561i		−	0.326526i
$670$	−24.1720	−	24.4352i	−0.933847	−	0.944013i
$671$	20.4464	−	20.4464i	0.789323	−	0.789323i
$672$	4.07357	−	3.85881i	0.157141	−	0.148857i
$673$		−	37.9759i		−	1.46386i	−0.681378	−	0.731932i	$-0.738619\pi$
$673$		−	37.9759i		−	1.46386i	0.681378	−	0.731932i	$-0.261381\pi$
$674$	−10.5704	+	10.4565i	−0.407155	+	0.402771i
$675$	1.28690	−	1.28690i	0.0495327	−	0.0495327i
$676$	15.6823	+	20.7380i	0.603166	+	0.797616i
$677$	0.400265	+	0.400265i	0.0153834	+	0.0153834i	0.714757	−	0.699373i	$-0.246537\pi$
$677$	0.400265	+	0.400265i	0.0153834	+	0.0153834i	−0.699373	+	0.714757i	$0.746537\pi$
$678$	−0.0880132	+	16.2582i	−0.00338013	+	0.624391i
$679$	1.87549			0.0719747
$680$	21.4359	+	22.1437i	0.822027	+	0.849171i
$681$	−8.97292	−	8.97292i	−0.343843	−	0.343843i
$682$	0.157919	−	29.1715i	0.00604704	−	1.11704i
$683$	−16.9890			−0.650066			−0.325033	−	0.945703i	$-0.605375\pi$
$683$	−16.9890			−0.650066			−0.325033	+	0.945703i	$0.605375\pi$
$684$	−2.55555	−	0.0276696i	−0.0977140	−	0.00105797i
$685$	−16.7900	+	16.7900i	−0.641513	+	0.641513i
$686$	18.2584	+	0.0988413i	0.697109	+	0.00377378i
$687$	12.9834	−	12.9834i	0.495346	−	0.495346i
$688$	−17.3419	−	18.1097i	−0.661153	−	0.690425i
$689$	−36.6655	−	17.9951i	−1.39685	−	0.685557i
$690$	9.15859	+	0.0495798i	0.348661	+	0.00188747i
$691$	−45.8777			−1.74527			−0.872635	−	0.488373i	$-0.837591\pi$
$691$	−45.8777			−1.74527			−0.872635	+	0.488373i	$0.837591\pi$
$692$	32.4483	−	31.7532i	1.23350	−	1.20707i
$693$	−1.79842	+	1.79842i	−0.0683164	+	0.0683164i
$694$	−19.6084	−	0.106149i	−0.744323	−	0.00402938i
$695$	9.66965	−	9.66965i	0.366791	−	0.366791i
$696$	−20.7161	+	20.0540i	−0.785243	+	0.760144i
$697$	−27.2650	+	27.2650i	−1.03274	+	1.03274i
$698$	6.84709	+	6.92163i	0.259166	+	0.261988i
$699$	3.90870	+	3.90870i	0.147841	+	0.147841i
$700$	2.58046	−	2.52518i	0.0975324	−	0.0954430i
$701$	−10.7527	−	10.7527i	−0.406125	−	0.406125i	0.474260	−	0.880385i	$-0.342716\pi$
$701$	−10.7527	−	10.7527i	−0.406125	−	0.406125i	−0.880385	+	0.474260i	$0.842716\pi$
$702$	4.83415	−	1.62204i	0.182453	−	0.0612198i
$703$		−	0.251045i		−	0.00946836i
$704$	0.666148	−	20.5019i	0.0251064	−	0.772696i
$705$	−7.10700			−0.267665
$706$	8.78087	+	0.0475350i	0.330473	+	0.00178900i
$707$	−7.96036			−0.299380
$708$	−1.63434	+	1.59933i	−0.0614222	+	0.0601064i
$709$			27.4428i			1.03063i	0.856999	+	0.515317i	$0.172326\pi$
$709$			27.4428i			1.03063i	−0.856999	+	0.515317i	$0.827674\pi$
$710$	26.4190	+	0.143019i	0.991488	+	0.00536740i
$711$	−0.369263			−0.0138484
$712$	−0.241065	+	14.8423i	−0.00903428	+	0.556240i
$713$	20.6587	−	20.6587i	0.773676	−	0.773676i
$714$	−6.02797	−	6.09359i	−0.225591	−	0.228047i
$715$	15.6013	−	5.32894i	0.583455	−	0.199291i
$716$	9.16085	+	9.36140i	0.342357	+	0.349852i
$717$			9.15792i			0.342009i
$718$	−0.0705860	+	13.0389i	−0.00263424	+	0.486609i
$719$	17.5771			0.655516			0.327758	−	0.944762i	$-0.393707\pi$
$719$	17.5771			0.655516			0.327758	+	0.944762i	$0.393707\pi$
$720$	−0.154445	+	7.13141i	−0.00575584	+	0.265772i
$721$	−2.02647	+	2.02647i	−0.0754697	+	0.0754697i
$722$	−17.2728	−	17.4609i	−0.642828	−	0.649826i
$723$		−	13.1842i		−	0.490325i
$724$	5.93371	+	6.06361i	0.220525	+	0.225352i
$725$	−13.1185	+	13.1185i	−0.487208	+	0.487208i
$726$	0.0338796	−	6.25839i	0.00125739	−	0.232270i
$727$			13.9650i			0.517934i	0.965886	+	0.258967i	$0.0833820\pi$
$727$			13.9650i			0.517934i	−0.965886	+	0.258967i	$0.916618\pi$
$728$	9.62436	−	3.11381i	0.356703	−	0.115405i
$729$		−	1.00000i		−	0.0370370i
$730$	2.83557	+	0.0153503i	0.104949	+	0.000568139i
$731$	−27.0838	+	27.0838i	−1.00173	+	1.00173i
$732$	−0.244186	+	22.5528i	−0.00902536	+	0.833577i
$733$			7.54331i			0.278619i	0.990249	+	0.139309i	$0.0444882\pi$
$733$			7.54331i			0.278619i	−0.990249	+	0.139309i	$0.955512\pi$
$734$	−19.5176	+	19.3074i	−0.720409	+	0.712651i
$735$	−7.58609	+	7.58609i	−0.279817	+	0.279817i
$736$	14.9144	−	14.1281i	0.549751	−	0.520768i
$737$	34.9457			1.28724
$738$	−8.92414	−	0.0483106i	−0.328502	−	0.00177834i
$739$			11.3391i			0.417116i	0.978010	+	0.208558i	$0.0668769\pi$
$739$			11.3391i			0.417116i	−0.978010	+	0.208558i	$0.933123\pi$
$740$	−0.700638	−	0.00758600i	−0.0257560	−	0.000278867i
$741$	−4.13607	−	2.02994i	−0.151942	−	0.0745717i
$742$	−11.2969	+	11.1753i	−0.414724	+	0.410258i
$743$	29.0187	−	29.0187i	1.06459	−	1.06459i	0.0668269	−	0.997765i	$-0.478712\pi$
$743$	29.0187	−	29.0187i	1.06459	−	1.06459i	0.997765	−	0.0668269i	$-0.0212875\pi$
$744$	15.8262	+	16.3488i	0.580218	+	0.599376i
$745$	−24.1935			−0.886382
$746$	−0.0592467	+	10.9443i	−0.00216917	+	0.400699i
$747$			6.64530i			0.243139i
$748$	−31.3330	−	0.339250i	−1.14565	−	0.0124042i
$749$	−18.3768			−0.671473
$750$	−0.0931071	+	17.1991i	−0.00339979	+	0.628024i
$751$	−17.3394			−0.632724			−0.316362	−	0.948639i	$-0.602461\pi$
$751$	−17.3394			−0.632724			−0.316362	+	0.948639i	$0.602461\pi$
$752$	−11.5138	+	11.0256i	−0.419864	+	0.402063i
$753$		−	6.83318i		−	0.249015i
$754$	−49.2787	+	16.5348i	−1.79462	+	0.602163i
$755$	22.9005	+	22.9005i	0.833435	+	0.833435i
$756$	0.0214781	−	1.98370i	0.000781151	−	0.0721466i
$757$	2.56432	+	2.56432i	0.0932017	+	0.0932017i	0.752170	−	0.658969i	$-0.229007\pi$
$757$	2.56432	+	2.56432i	0.0932017	+	0.0932017i	−0.658969	+	0.752170i	$0.729007\pi$
$758$	32.6829	−	32.3310i	1.18710	−	1.17431i
$759$	−6.58449	+	6.58449i	−0.239002	+	0.239002i
$760$	4.63092	−	4.48289i	0.167981	−	0.162612i
$761$	10.8439	−	10.8439i	0.393090	−	0.393090i	−0.482697	−	0.875787i	$-0.660343\pi$
$761$	10.8439	−	10.8439i	0.393090	−	0.393090i	0.875787	+	0.482697i	$0.160343\pi$
$762$	0.0729952	−	13.4840i	0.00264434	−	0.488473i
$763$	2.57066	−	2.57066i	0.0930642	−	0.0930642i
$764$	28.5199	+	0.308793i	1.03182	+	0.0111717i
$765$	10.8963			0.393957
$766$	0.0960492	−	17.7426i	0.00347040	−	0.641067i
$767$	−3.90108	+	1.33249i	−0.140860	+	0.0481136i
$768$	10.8133	+	11.7929i	0.390191	+	0.425540i
$769$	37.8398	−	37.8398i	1.36454	−	1.36454i	0.496505	−	0.868034i	$-0.334616\pi$
$769$	37.8398	−	37.8398i	1.36454	−	1.36454i	0.868034	−	0.496505i	$-0.165384\pi$
$770$	0.0347223	−	6.41405i	0.00125131	−	0.231146i
$771$	−5.29188	+	5.29188i	−0.190583	+	0.190583i
$772$	−9.07432	+	8.87992i	−0.326592	+	0.319595i
$773$	−17.3873			−0.625376			−0.312688	−	0.949856i	$-0.601229\pi$
$773$	−17.3873			−0.625376			−0.312688	+	0.949856i	$0.601229\pi$
$774$	−8.86484	−	0.0479896i	−0.318640	−	0.00172495i
$775$	10.3529	+	10.3529i	0.371886	+	0.371886i
$776$	−0.0868483	+	5.34725i	−0.00311767	+	0.191955i
$777$	0.194870			0.00699092
$778$	33.1346	+	0.179373i	1.18793	+	0.00643084i
$779$	5.70194	+	5.70194i	0.204293	+	0.204293i
$780$	−5.79031	+	11.4819i	−0.207326	+	0.411120i
$781$	−18.9937	+	18.9937i	−0.679649	+	0.679649i
$782$	−22.0700	−	22.3102i	−0.789220	−	0.797811i
$783$			10.1939i			0.364299i
$784$	−0.521043	+	24.0588i	−0.0186087	+	0.859243i
$785$	9.80653	−	9.80653i	0.350010	−	0.350010i
$786$	2.81145	−	2.78118i	0.100281	−	0.0992012i
$787$		−	2.21920i		−	0.0791060i	−0.999217	−	0.0395530i	$-0.987407\pi$
$787$		−	2.21920i		−	0.0791060i	0.999217	−	0.0395530i	$-0.0125934\pi$
$788$	−0.525547	+	48.5392i	−0.0187218	+	1.72914i
$789$	−2.02177	−	2.02177i	−0.0719770	−	0.0719770i
$790$	0.662051	−	0.654922i	0.0235547	−	0.0233011i
$791$	8.06344	+	8.06344i	0.286703	+	0.286703i
$792$	−5.04424	−	5.21080i	−0.179239	−	0.185158i
$793$	−17.9143	+	36.5010i	−0.636156	+	1.29619i
$794$	−30.6186	−	30.9519i	−1.08661	−	1.09844i
$795$		−	20.2007i		−	0.716446i
$796$	−51.6572	−	0.559306i	−1.83094	−	0.0198241i
$797$	−6.08175	−	6.08175i	−0.215427	−	0.215427i	0.591141	−	0.806568i	$-0.298678\pi$
$797$	−6.08175	−	6.08175i	−0.215427	−	0.215427i	−0.806568	+	0.591141i	$0.798678\pi$
$798$	−1.27436	+	1.26063i	−0.0451117	+	0.0446259i
$799$	17.2193	+	17.2193i	0.609176	+	0.609176i
$800$	7.08011	+	7.47414i	0.250320	+	0.264251i
$801$	3.71107	+	3.71107i	0.131124	+	0.131124i
$802$	−0.0921485	+	17.0221i	−0.00325388	+	0.601070i
$803$	−2.03861	+	2.03861i	−0.0719409	+	0.0719409i
$804$	−19.4817	+	19.0643i	−0.687066	+	0.672347i
$805$	4.54232	−	4.54232i	0.160096	−	0.160096i
$806$	13.0490	+	38.8898i	0.459631	+	1.36984i
$807$	−11.3615			−0.399945
$808$	0.368620	−	22.6959i	0.0129680	−	0.798439i
$809$		−	0.680568i		−	0.0239275i	−0.999928	−	0.0119638i	$-0.996192\pi$
$809$		−	0.680568i		−	0.0239275i	0.999928	−	0.0119638i	$-0.00380827\pi$
$810$	1.77359	+	1.79290i	0.0623176	+	0.0629960i
$811$		−	42.3502i		−	1.48712i	−0.668671	−	0.743559i	$-0.733136\pi$
$811$		−	42.3502i		−	1.48712i	0.668671	−	0.743559i	$-0.266864\pi$
$812$	−0.218945	+	20.2216i	−0.00768346	+	0.709640i
$813$	−6.97555			−0.244643
$814$	0.506460	−	0.501006i	0.0177514	−	0.0175602i
$815$			30.3887i			1.06447i
$816$	17.6527	−	16.9043i	0.617968	−	0.591768i
$817$	5.66405	+	5.66405i	0.198160	+	0.198160i
$818$	−0.224181	+	41.4117i	−0.00783830	+	1.44792i
$819$	1.57571	−	3.21056i	0.0550597	−	0.112186i
$820$	16.0858	−	15.7412i	0.561739	−	0.549705i
$821$	−52.7041			−1.83939			−0.919693	−	0.392639i	$-0.871562\pi$
$821$	−52.7041			−1.83939			−0.919693	+	0.392639i	$0.871562\pi$
$822$	13.2430	+	13.3871i	0.461901	+	0.466929i
$823$			28.8969i			1.00728i	0.863912	+	0.503642i	$0.168007\pi$
$823$			28.8969i			1.00728i	−0.863912	+	0.503642i	$0.831993\pi$
$824$	−5.68386	−	5.87154i	−0.198007	−	0.204545i
$825$	−3.29973	−	3.29973i	−0.114882	−	0.114882i
$826$	−0.00868226	+	1.60382i	−0.000302094	+	0.0558042i
$827$	5.90926			0.205485			0.102743	−	0.994708i	$-0.467238\pi$
$827$	5.90926			0.205485			0.102743	+	0.994708i	$0.467238\pi$
$828$	0.0786368	−	7.26285i	0.00273282	−	0.252402i
$829$	28.2005	+	28.2005i	0.979444	+	0.979444i	0.999793	−	0.0203494i	$-0.00647785\pi$
$829$	28.2005	+	28.2005i	0.979444	+	0.979444i	−0.0203494	+	0.999793i	$0.506478\pi$
$830$	−11.7860	−	11.9143i	−0.409100	−	0.413553i
$831$	−8.59191			−0.298050
$832$	8.43217	+	27.5844i	0.292333	+	0.956317i
$833$	36.7603			1.27367
$834$	−7.62684	−	7.70987i	−0.264096	−	0.266971i
$835$	23.0746	+	23.0746i	0.798531	+	0.798531i
$836$	−0.0709476	+	6.55268i	−0.00245377	+	0.226629i
$837$	8.04482			0.278070
$838$	0.312356	−	57.6998i	0.0107902	−	1.99321i
$839$	0.936005	+	0.936005i	0.0323145	+	0.0323145i	0.723079	−	0.690765i	$-0.242726\pi$
$839$	0.936005	+	0.936005i	0.0323145	+	0.0323145i	−0.690765	+	0.723079i	$0.742726\pi$
$840$	3.47977	+	3.59467i	0.120064	+	0.124028i
$841$		−	74.9150i		−	2.58328i
$842$	1.05062	+	1.06206i	0.0362068	+	0.0366009i
$843$	−27.1744			−0.935935
$844$	−24.0079	+	23.4936i	−0.826386	+	0.808683i
$845$	−18.3383	+	14.1823i	−0.630855	+	0.487885i
$846$	−0.0305108	+	5.63609i	−0.00104898	+	0.193773i
$847$	−3.10392	−	3.10392i	−0.106652	−	0.106652i
$848$	−31.3389	−	32.7264i	−1.07618	−	1.12383i
$849$		−	29.2752i		−	1.00472i
$850$	11.1805	−	11.0601i	0.383487	−	0.379357i
$851$	0.713469			0.0244574
$852$	0.226837	−	20.9506i	0.00777131	−	0.717754i
$853$			6.74933i			0.231092i	0.993302	+	0.115546i	$0.0368618\pi$
$853$			6.74933i			0.231092i	−0.993302	+	0.115546i	$0.963138\pi$
$854$	11.1251	+	11.2462i	0.380695	+	0.384839i
$855$		−	2.27875i		−	0.0779317i
$856$	0.850973	−	52.3944i	0.0290857	−	1.79080i
$857$	53.4496			1.82580			0.912902	−	0.408179i	$-0.133836\pi$
$857$	53.4496			1.82580			0.912902	+	0.408179i	$0.133836\pi$
$858$	−4.15905	−	12.3952i	−0.141988	−	0.423166i
$859$	−20.8529	+	20.8529i	−0.711490	+	0.711490i	−0.966847	−	0.255357i	$-0.917807\pi$
$859$	−20.8529	+	20.8529i	−0.711490	+	0.711490i	0.255357	+	0.966847i	$0.417807\pi$
$860$	15.9789	−	15.6366i	0.544875	−	0.533202i
$861$	−4.42604	+	4.42604i	−0.150839	+	0.150839i
$862$	0.0664445	−	12.2739i	0.00226311	−	0.418051i
$863$	35.7376	+	35.7376i	1.21652	+	1.21652i	0.968842	+	0.247681i	$0.0796686\pi$
$863$	35.7376	+	35.7376i	1.21652	+	1.21652i	0.247681	+	0.968842i	$0.420331\pi$
$864$	5.65478	+	0.153096i	0.192380	+	0.00520843i
$865$	28.6238	+	28.6238i	0.973239	+	0.973239i
$866$	−7.33490	+	7.25592i	−0.249250	+	0.246566i
$867$	−14.3796	−	14.3796i	−0.488355	−	0.488355i
$868$	15.9585	+	0.172787i	0.541668	+	0.00586479i
$869$			0.946826i			0.0321189i
$870$	−18.0798	−	18.2766i	−0.612961	−	0.619634i
$871$	−46.5017	+	15.8836i	−1.57565	+	0.538196i
$872$	7.21022	+	7.44830i	0.244169	+	0.252231i
$873$	1.33699	+	1.33699i	0.0452502	+	0.0452502i
$874$	−4.66575	+	4.61550i	−0.157821	+	0.156122i
$875$	8.53013	+	8.53013i	0.288371	+	0.288371i
$876$	0.0243466	−	2.24864i	0.000822594	−	0.0759744i
$877$			31.3894i			1.05995i	0.848014	+	0.529973i	$0.177798\pi$
$877$			31.3894i			1.05995i	−0.848014	+	0.529973i	$0.822202\pi$
$878$	−28.6340	+	28.3256i	−0.966350	+	0.955944i
$879$	−11.2075	+	11.2075i	−0.378020	+	0.378020i
$880$	18.2856	+	0.396013i	0.616408	+	0.0133496i
$881$		−	42.2761i		−	1.42432i	−0.702017	−	0.712160i	$-0.747717\pi$
$881$		−	42.2761i		−	1.42432i	0.702017	−	0.712160i	$-0.252283\pi$
$882$	5.98346	+	6.04859i	0.201474	+	0.203667i
$883$	−11.0989	+	11.0989i	−0.373507	+	0.373507i	−0.868753	−	0.495246i	$-0.835078\pi$
$883$	−11.0989	+	11.0989i	−0.373507	+	0.373507i	0.495246	+	0.868753i	$0.335078\pi$
$884$	41.8485	−	13.7901i	1.40752	−	0.463811i
$885$	−1.44171	−	1.44171i	−0.0484625	−	0.0484625i
$886$	−22.3086	−	0.120767i	−0.749471	−	0.00405724i
$887$	−13.1074			−0.440103			−0.220051	−	0.975488i	$-0.570623\pi$
$887$	−13.1074			−0.440103			−0.220051	+	0.975488i	$0.570623\pi$
$888$	−0.00902384	+	0.555597i	−0.000302820	+	0.0186446i
$889$	−6.68755	−	6.68755i	−0.224293	−	0.224293i
$890$	−13.2355	−	0.0716500i	−0.443655	−	0.00240171i
$891$	−2.56410			−0.0859004
$892$	12.0725	−	11.8139i	0.404217	−	0.395558i
$893$	3.60109	−	3.60109i	0.120506	−	0.120506i
$894$	−0.103864	+	19.1863i	−0.00347374	+	0.641685i
$895$	−8.25803	+	8.25803i	−0.276035	+	0.276035i
$896$	11.2141	+	0.425151i	0.374638	+	0.0142033i
$897$	5.76907	−	11.7547i	0.192624	−	0.392477i
$898$	0.150733	−	27.8440i	0.00503002	−	0.929167i
$899$	−82.0078			−2.73511
$900$	3.63968	+	0.0394078i	0.121323	+	0.00131359i
$901$	−48.9438	+	48.9438i	−1.63055	+	1.63055i
$902$	−0.123873	+	22.8824i	−0.00412452	+	0.761899i
$903$	−4.39663	+	4.39663i	−0.146311	+	0.146311i
$904$	−23.3632	+	22.6164i	−0.777049	+	0.752211i
$905$	−5.34893	+	5.34893i	−0.177805	+	0.177805i
$906$	18.2592	−	18.0626i	0.606621	−	0.600088i
$907$	−22.4345	−	22.4345i	−0.744927	−	0.744927i	0.228595	−	0.973522i	$-0.426587\pi$
$907$	−22.4345	−	22.4345i	−0.744927	−	0.744927i	−0.973522	+	0.228595i	$0.926587\pi$
$908$	0.274772	−	25.3778i	0.00911862	−	0.842191i
$909$	−5.67473	−	5.67473i	−0.188219	−	0.188219i
$910$	2.86913	+	8.55086i	0.0951107	+	0.283458i
$911$			1.35077i			0.0447530i	0.999750	+	0.0223765i	$0.00712325\pi$
$911$			1.35077i			0.0447530i	−0.999750	+	0.0223765i	$0.992877\pi$
$912$	−3.53520	−	3.69172i	−0.117062	−	0.122245i
$913$	17.0392			0.563915
$914$	0.225093	−	41.5802i	0.00744542	−	1.37535i
$915$	−20.1101			−0.664819
$916$	36.7204	+	0.397581i	1.21327	+	0.0131364i
$917$		−	2.77373i		−	0.0915967i
$918$	0.0467786	−	8.64114i	0.00154392	−	0.285200i
$919$	41.3804			1.36501			0.682507	−	0.730879i	$-0.260890\pi$
$919$	41.3804			1.36501			0.682507	+	0.730879i	$0.260890\pi$
$920$	12.7403	+	13.1610i	0.420037	+	0.433906i
$921$	7.29623	−	7.29623i	0.240419	−	0.240419i
$922$	−19.2602	+	19.0528i	−0.634300	+	0.627470i
$923$	16.6416	−	33.9077i	0.547764	−	1.11609i
$924$	−5.08641	−	0.0550719i	−0.167331	−	0.00181173i
$925$			0.357545i			0.0117560i
$926$	21.0140	+	0.113759i	0.690562	+	0.00373834i
$927$	−2.88923			−0.0948948
$928$	−57.6441	−	1.56064i	−1.89226	−	0.0512305i
$929$	19.5596	−	19.5596i	0.641728	−	0.641728i	−0.309252	−	0.950980i	$-0.600079\pi$
$929$	19.5596	−	19.5596i	0.641728	−	0.641728i	0.950980	+	0.309252i	$0.100079\pi$
$930$	−14.4235	+	14.2682i	−0.472966	+	0.467873i
$931$		−	7.68769i		−	0.251954i
$932$	−0.119694	+	11.0548i	−0.00392069	+	0.362113i
$933$	−4.08435	+	4.08435i	−0.133716	+	0.133716i
$934$	8.22254	+	0.0445125i	0.269050	+	0.00145649i
$935$		−	27.9392i		−	0.913709i
$936$	9.08071	+	4.64120i	0.296812	+	0.151702i
$937$			29.4629i			0.962511i	0.876580	+	0.481256i	$0.159819\pi$
$937$			29.4629i			0.962511i	−0.876580	+	0.481256i	$0.840181\pi$
$938$	−0.103494	+	19.1179i	−0.00337921	+	0.624223i
$939$	−5.40769	+	5.40769i	−0.176473	+	0.176473i
$940$	−9.94140	−	10.1590i	−0.324253	−	0.331351i
$941$			39.8273i			1.29833i	0.760646	+	0.649167i	$0.224882\pi$
$941$			39.8273i			1.29833i	−0.760646	+	0.649167i	$0.775118\pi$
$942$	−7.73481	−	7.81901i	−0.252014	−	0.254757i
$943$	−16.2049	+	16.2049i	−0.527703	+	0.527703i
$944$	−4.57229	−	0.0990224i	−0.148815	−	0.00322290i
$945$	1.76884			0.0575405
$946$	−0.123050	+	22.7303i	−0.00400070	+	0.739026i
$947$		−	11.1045i		−	0.360849i	−0.983589	−	0.180425i	$-0.942253\pi$
$947$		−	11.1045i		−	0.360849i	0.983589	−	0.180425i	$-0.0577472\pi$
$948$	−0.516532	−	0.527840i	−0.0167762	−	0.0171435i
$949$	1.78615	−	3.63934i	0.0579809	−	0.118138i
$950$	−2.31300	−	2.33818i	−0.0750436	−	0.0758605i
$951$	16.8015	−	16.8015i	0.544824	−	0.544824i
$952$	0.278390	−	17.1405i	0.00902268	−	0.555526i
$953$	−38.3006			−1.24068			−0.620339	−	0.784334i	$-0.713005\pi$
$953$	−38.3006			−1.24068			−0.620339	+	0.784334i	$0.713005\pi$
$954$	−16.0199	−	0.0867231i	−0.518662	−	0.00280776i
$955$			25.4309i			0.822924i
$956$	−13.0907	+	12.8103i	−0.423384	+	0.414314i
$957$	26.1381			0.844924
$958$	−36.2517	−	0.196247i	−1.17124	−	0.00634047i
$959$	13.2075			0.426493
$960$	−10.4100	+	9.75478i	−0.335980	+	0.314834i
$961$			33.7191i			1.08771i
$962$	−0.446219	+	0.896878i	−0.0143867	+	0.0289165i
$963$	−13.1003	−	13.1003i	−0.422152	−	0.422152i
$964$	18.8460	−	18.4423i	0.606989	−	0.593986i
$965$	−8.00478	−	8.00478i	−0.257683	−	0.257683i
$966$	−3.58271	−	3.62171i	−0.115272	−	0.116527i
$967$	4.98797	−	4.98797i	0.160402	−	0.160402i	−0.622343	−	0.782745i	$-0.713819\pi$
$967$	4.98797	−	4.98797i	0.160402	−	0.160402i	0.782745	+	0.622343i	$0.213819\pi$
$968$	8.99339	−	8.70592i	0.289058	−	0.279819i
$969$	−5.52113	+	5.52113i	−0.177364	+	0.177364i
$970$	−4.76835	−	0.0258133i	−0.153103	−	0.000828817i
$971$	−26.3468	+	26.3468i	−0.845511	+	0.845511i	−0.989569	−	0.144059i	$-0.953985\pi$
$971$	−26.3468	+	26.3468i	−0.845511	+	0.845511i	0.144059	+	0.989569i	$0.453985\pi$
$972$	1.42944	−	1.39882i	0.0458494	−	0.0448672i
$973$	−7.60643			−0.243851
$974$	−24.1565	−	0.130771i	−0.774025	−	0.00419016i
$975$	5.89070	+	2.89109i	0.188653	+	0.0925891i
$976$	−32.5796	+	31.1983i	−1.04285	+	0.998634i
$977$	−29.1801	+	29.1801i	−0.933555	+	0.933555i	−0.997926	−	0.0643709i	$-0.979496\pi$
$977$	−29.1801	+	29.1801i	−0.933555	+	0.933555i	0.0643709	+	0.997926i	$0.479496\pi$
$978$	24.0993	+	0.130461i	0.770610	+	0.00417168i
$979$	9.51555	−	9.51555i	0.304118	−	0.304118i
$980$	−21.4555	−	0.232304i	−0.685369	−	0.00742067i
$981$	3.66511			0.117018
$982$	−0.201410	+	37.2053i	−0.00642724	+	1.18727i
$983$	4.97891	+	4.97891i	0.158803	+	0.158803i	0.782036	−	0.623233i	$-0.214181\pi$
$983$	4.97891	+	4.97891i	0.158803	+	0.158803i	−0.623233	+	0.782036i	$0.714181\pi$
$984$	−12.4142	−	12.8241i	−0.395751	−	0.408818i
$985$	−43.2818			−1.37907
$986$	−0.476855	+	88.0867i	−0.0151862	+	2.80525i
$987$	2.79529	+	2.79529i	0.0889750	+	0.0889750i
$988$	−2.88393	−	8.75179i	−0.0917501	−	0.278432i
$989$	−16.0972	+	16.0972i	−0.511861	+	0.511861i
$990$	4.59716	−	4.54766i	0.146107	−	0.144534i
$991$			16.6800i			0.529859i	0.964268	+	0.264929i	$0.0853486\pi$
$991$			16.6800i			0.529859i	−0.964268	+	0.264929i	$0.914651\pi$
$992$	−1.23163	+	45.4917i	−0.0391043	+	1.44436i
$993$	2.07244	−	2.07244i	0.0657669	−	0.0657669i
$994$	−10.3347	−	10.4472i	−0.327798	−	0.331367i
$995$		−	46.0621i		−	1.46027i
$996$	−9.49907	+	9.29558i	−0.300990	+	0.294542i
$997$	1.85841	+	1.85841i	0.0588563	+	0.0588563i	0.735922	−	0.677066i	$-0.236749\pi$
$997$	1.85841	+	1.85841i	0.0588563	+	0.0588563i	−0.677066	+	0.735922i	$0.736749\pi$
$998$	32.7310	+	33.0873i	1.03608	+	1.04736i
$999$	0.138918	+	0.138918i	0.00439516	+	0.00439516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bn.a.187.42	yes	112
13.8	odd	4		624.2.r.a.619.14	yes	112
16.3	odd	4		624.2.r.a.499.14	✓	112
208.99	even	4	inner	624.2.bn.a.307.42	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.r.a.499.14	✓	112	16.3	odd	4
624.2.r.a.619.14	yes	112	13.8	odd	4
624.2.bn.a.187.42	yes	112	1.1	even	1	trivial
624.2.bn.a.307.42	yes	112	208.99	even	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.994572 + 1.00540i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.0216533 + 1.99988i) q^{4} -1.78327 q^{5} +(-0.00765570 + 1.41419i) q^{6} +(0.701387 + 0.701387i) q^{7} +(-2.03222 + 1.96726i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.994572 + 1.00540i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.0216533 + 1.99988i) q^{4} -1.78327 q^{5} +(-0.00765570 + 1.41419i) q^{6} +(0.701387 + 0.701387i) q^{7} +(-2.03222 + 1.96726i) q^{8} +1.00000i q^{9} +(-1.77359 - 1.79290i) q^{10} +2.56410 q^{11} +(-1.42944 + 1.39882i) q^{12} +(-3.41200 + 1.16544i) q^{13} +(-0.00759377 + 1.40275i) q^{14} +(-1.26096 - 1.26096i) q^{15} +(-3.99906 - 0.0866080i) q^{16} +6.11030i q^{17} +(-1.00540 + 0.994572i) q^{18} +1.27785 q^{19} +(0.0386136 - 3.56633i) q^{20} +0.991911i q^{21} +(2.55018 + 2.57794i) q^{22} +3.63164i q^{23} +(-2.82805 - 0.0459324i) q^{24} -1.81995 q^{25} +(-4.56521 - 2.27131i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.41788 + 1.38750i) q^{28} +(7.20816 - 7.20816i) q^{29} +(0.0136522 - 2.52189i) q^{30} +(-5.68854 - 5.68854i) q^{31} +(-3.89028 - 4.10679i) q^{32} +(1.81309 + 1.81309i) q^{33} +(-6.14329 + 6.07713i) q^{34} +(-1.25076 - 1.25076i) q^{35} +(-1.99988 - 0.0216533i) q^{36} -0.196459i q^{37} +(1.27091 + 1.28475i) q^{38} +(-3.23674 - 1.58856i) q^{39} +(3.62399 - 3.50815i) q^{40} +(4.46214 + 4.46214i) q^{41} +(-0.997266 + 0.986526i) q^{42} +(4.43248 + 4.43248i) q^{43} +(-0.0555210 + 5.12789i) q^{44} -1.78327i q^{45} +(-3.65125 + 3.61193i) q^{46} +(2.81808 - 2.81808i) q^{47} +(-2.76652 - 2.88901i) q^{48} -6.01611i q^{49} +(-1.81007 - 1.82977i) q^{50} +(-4.32063 + 4.32063i) q^{51} +(-2.25686 - 6.84884i) q^{52} +(8.01005 + 8.01005i) q^{53} +(-1.41419 - 0.00765570i) q^{54} -4.57248 q^{55} +(-2.80518 - 0.0455608i) q^{56} +(0.903577 + 0.903577i) q^{57} +(14.4161 + 0.0780412i) q^{58} +1.14334 q^{59} +(2.54908 - 2.49447i) q^{60} +(7.97410 - 7.97410i) q^{61} +(0.0615887 - 11.3769i) q^{62} +(-0.701387 + 0.701387i) q^{63} +(0.259799 - 7.99578i) q^{64} +(6.08452 - 2.07829i) q^{65} +(-0.0196299 + 3.62613i) q^{66} +13.6289 q^{67} +(-12.2199 - 0.132308i) q^{68} +(-2.56796 + 2.56796i) q^{69} +(0.0135417 - 2.50149i) q^{70} +(-7.40757 + 7.40757i) q^{71} +(-1.96726 - 2.03222i) q^{72} +(-0.795059 + 0.795059i) q^{73} +(0.197520 - 0.195393i) q^{74} +(-1.28690 - 1.28690i) q^{75} +(-0.0276696 + 2.55555i) q^{76} +(1.79842 + 1.79842i) q^{77} +(-1.62204 - 4.83415i) q^{78} +0.369263i q^{79} +(7.13141 + 0.154445i) q^{80} -1.00000 q^{81} +(-0.0483106 + 8.92414i) q^{82} +6.64530 q^{83} +(-1.98370 - 0.0214781i) q^{84} -10.8963i q^{85} +(-0.0479896 + 8.86484i) q^{86} +10.1939 q^{87} +(-5.21080 + 5.04424i) q^{88} +(3.71107 - 3.71107i) q^{89} +(1.79290 - 1.77359i) q^{90} +(-3.21056 - 1.57571i) q^{91} +(-7.26285 - 0.0786368i) q^{92} -8.04482i q^{93} +(5.63609 + 0.0305108i) q^{94} -2.27875 q^{95} +(0.153096 - 5.65478i) q^{96} +(1.33699 - 1.33699i) q^{97} +(6.04859 - 5.98346i) q^{98} +2.56410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) \) 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

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