LMFDB - Embedded newform 570.2.s.b.221.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.8
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.800591 + 1.53592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.929852 + 1.46129i) q^{6} -4.66317 q^{7} -1.00000 q^{8} +(-1.71811 + 2.45929i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.800591 + 1.53592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.929852 + 1.46129i) q^{6} -4.66317 q^{7} -1.00000 q^{8} +(-1.71811 + 2.45929i) q^{9} +(-0.866025 - 0.500000i) q^{10} -3.04774i q^{11} +(-1.73044 - 0.0746290i) q^{12} +(3.56832 + 2.06017i) q^{13} +(-2.33159 - 4.03843i) q^{14} +(-1.46129 - 0.929852i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.22857 + 1.28666i) q^{17} +(-2.98886 - 0.258282i) q^{18} +(-3.71368 + 2.28223i) q^{19} -1.00000i q^{20} +(-3.73329 - 7.16227i) q^{21} +(2.63942 - 1.52387i) q^{22} +(-0.586222 - 0.338456i) q^{23} +(-0.800591 - 1.53592i) q^{24} +(0.500000 - 0.866025i) q^{25} +4.12034i q^{26} +(-5.15278 - 0.669999i) q^{27} +(2.33159 - 4.03843i) q^{28} +(0.992204 - 1.71855i) q^{29} +(0.0746290 - 1.73044i) q^{30} +4.29688i q^{31} +(0.500000 - 0.866025i) q^{32} +(4.68109 - 2.43999i) q^{33} +(-2.22857 - 1.28666i) q^{34} +(4.03843 - 2.33159i) q^{35} +(-1.27075 - 2.71757i) q^{36} +4.49734i q^{37} +(-3.83331 - 2.07503i) q^{38} +(-0.307497 + 7.13001i) q^{39} +(0.866025 - 0.500000i) q^{40} +(1.65691 + 2.86985i) q^{41} +(4.33606 - 6.81426i) q^{42} +(2.86613 + 4.96428i) q^{43} +(2.63942 + 1.52387i) q^{44} +(0.258282 - 2.98886i) q^{45} -0.676911i q^{46} +(7.58882 + 4.38141i) q^{47} +(0.929852 - 1.46129i) q^{48} +14.7452 q^{49} +1.00000 q^{50} +(-3.76038 - 2.39281i) q^{51} +(-3.56832 + 2.06017i) q^{52} +(-4.57343 + 7.92141i) q^{53} +(-1.99615 - 4.79743i) q^{54} +(1.52387 + 2.63942i) q^{55} +4.66317 q^{56} +(-6.47846 - 3.87680i) q^{57} +1.98441 q^{58} +(-6.02522 - 10.4360i) q^{59} +(1.53592 - 0.800591i) q^{60} +(-6.95089 + 12.0393i) q^{61} +(-3.72120 + 2.14844i) q^{62} +(8.01184 - 11.4681i) q^{63} +1.00000 q^{64} -4.12034 q^{65} +(4.45364 + 2.83395i) q^{66} +(-2.56373 - 1.48017i) q^{67} -2.57333i q^{68} +(0.0505172 - 1.17136i) q^{69} +(4.03843 + 2.33159i) q^{70} +(-6.25422 - 10.8326i) q^{71} +(1.71811 - 2.45929i) q^{72} +(2.18577 + 3.78586i) q^{73} +(-3.89481 + 2.24867i) q^{74} +(1.73044 + 0.0746290i) q^{75} +(-0.119625 - 4.35726i) q^{76} +14.2121i q^{77} +(-6.32852 + 3.29871i) q^{78} +(6.74543 - 3.89448i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-3.09620 - 8.45065i) q^{81} +(-1.65691 + 2.86985i) q^{82} +2.61607i q^{83} +(8.06935 + 0.348008i) q^{84} +(1.28666 - 2.22857i) q^{85} +(-2.86613 + 4.96428i) q^{86} +(3.43390 + 0.148094i) q^{87} +3.04774i q^{88} +(4.81262 - 8.33571i) q^{89} +(2.71757 - 1.27075i) q^{90} +(-16.6397 - 9.60693i) q^{91} +(0.586222 - 0.338456i) q^{92} +(-6.59966 + 3.44004i) q^{93} +8.76281i q^{94} +(2.07503 - 3.83331i) q^{95} +(1.73044 + 0.0746290i) q^{96} +(-8.00346 + 4.62080i) q^{97} +(7.37259 + 12.7697i) q^{98} +(7.49527 + 5.23635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.800591	+	1.53592i	0.462221	+	0.886765i
$3$	0.800591	+	1.53592i	0.462221	+	0.886765i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.929852	+	1.46129i	−0.379610	+	0.596570i
$7$	−4.66317			−1.76251			−0.881257	−	0.472638i	$-0.843302\pi$
$7$	−4.66317			−1.76251			−0.881257	+	0.472638i	$0.843302\pi$
$8$	−1.00000			−0.353553
$9$	−1.71811	+	2.45929i	−0.572703	+	0.819763i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	3.04774i		−	0.918928i	−0.888196	−	0.459464i	$-0.848041\pi$
$11$		−	3.04774i		−	0.918928i	0.888196	−	0.459464i	$-0.151959\pi$
$12$	−1.73044	−	0.0746290i	−0.499536	−	0.0215435i
$13$	3.56832	+	2.06017i	0.989674	+	0.571389i	0.905177	−	0.425035i	$-0.139738\pi$
$13$	3.56832	+	2.06017i	0.989674	+	0.571389i	0.0844972	+	0.996424i	$0.473072\pi$
$14$	−2.33159	−	4.03843i	−0.623143	−	1.07931i
$15$	−1.46129	−	0.929852i	−0.377304	−	0.240087i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.22857	+	1.28666i	−0.540506	+	0.312062i	−0.745284	−	0.666747i	$-0.767686\pi$
$17$	−2.22857	+	1.28666i	−0.540506	+	0.312062i	0.204778	+	0.978808i	$0.434353\pi$
$18$	−2.98886	−	0.258282i	−0.704481	−	0.0608777i
$19$	−3.71368	+	2.28223i	−0.851977	+	0.523579i
$19$	−3.71368	+	2.28223i	−0.851977	+	0.523579i
$20$		−	1.00000i		−	0.223607i
$21$	−3.73329	−	7.16227i	−0.814671	−	1.56293i
$22$	2.63942	−	1.52387i	0.562726	−	0.324890i
$23$	−0.586222	−	0.338456i	−0.122236	−	0.0705729i	0.437635	−	0.899153i	$-0.355816\pi$
$23$	−0.586222	−	0.338456i	−0.122236	−	0.0705729i	−0.559871	+	0.828580i	$0.689149\pi$
$24$	−0.800591	−	1.53592i	−0.163420	−	0.313519i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			4.12034i			0.808066i
$27$	−5.15278	−	0.669999i	−0.991652	−	0.128941i
$28$	2.33159	−	4.03843i	0.440628	−	0.763191i
$29$	0.992204	−	1.71855i	0.184248	−	0.319126i	−0.759075	−	0.651003i	$-0.774348\pi$
$29$	0.992204	−	1.71855i	0.184248	−	0.319126i	0.943323	+	0.331877i	$0.107682\pi$
$30$	0.0746290	−	1.73044i	0.0136253	−	0.315934i
$31$			4.29688i			0.771742i	0.922553	+	0.385871i	$0.126099\pi$
$31$			4.29688i			0.771742i	−0.922553	+	0.385871i	$0.873901\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.68109	−	2.43999i	0.814873	−	0.424748i
$34$	−2.22857	−	1.28666i	−0.382196	−	0.220661i
$35$	4.03843	−	2.33159i	0.682619	−	0.394110i
$36$	−1.27075	−	2.71757i	−0.211792	−	0.452928i
$37$			4.49734i			0.739358i	0.929160	+	0.369679i	$0.120532\pi$
$37$			4.49734i			0.739358i	−0.929160	+	0.369679i	$0.879468\pi$
$38$	−3.83331	−	2.07503i	−0.621845	−	0.336614i
$39$	−0.307497	+	7.13001i	−0.0492389	+	1.14172i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	1.65691	+	2.86985i	0.258766	+	0.448195i	0.965912	−	0.258872i	$-0.0833509\pi$
$41$	1.65691	+	2.86985i	0.258766	+	0.448195i	−0.707146	+	0.707068i	$0.750018\pi$
$42$	4.33606	−	6.81426i	0.669069	−	1.05146i
$43$	2.86613	+	4.96428i	0.437080	+	0.757045i	0.997463	−	0.0711889i	$-0.0226793\pi$
$43$	2.86613	+	4.96428i	0.437080	+	0.757045i	−0.560383	+	0.828234i	$0.689346\pi$
$44$	2.63942	+	1.52387i	0.397908	+	0.229732i
$45$	0.258282	−	2.98886i	0.0385025	−	0.445553i
$46$		−	0.676911i		−	0.0998051i
$47$	7.58882	+	4.38141i	1.10694	+	0.639094i	0.938036	−	0.346538i	$-0.112643\pi$
$47$	7.58882	+	4.38141i	1.10694	+	0.639094i	0.168907	+	0.985632i	$0.445976\pi$
$48$	0.929852	−	1.46129i	0.134213	−	0.210919i
$49$	14.7452			2.10645
$50$	1.00000			0.141421
$51$	−3.76038	−	2.39281i	−0.526559	−	0.335061i
$52$	−3.56832	+	2.06017i	−0.494837	+	0.285694i
$53$	−4.57343	+	7.92141i	−0.628209	+	1.08809i	0.359702	+	0.933067i	$0.382878\pi$
$53$	−4.57343	+	7.92141i	−0.628209	+	1.08809i	−0.987911	+	0.155023i	$0.950455\pi$
$54$	−1.99615	−	4.79743i	−0.271642	−	0.652848i
$55$	1.52387	+	2.63942i	0.205479	+	0.355899i
$56$	4.66317			0.623143
$57$	−6.47846	−	3.87680i	−0.858093	−	0.513494i
$58$	1.98441			0.260566
$59$	−6.02522	−	10.4360i	−0.784417	−	1.35865i	−0.929347	−	0.369208i	$-0.879629\pi$
$59$	−6.02522	−	10.4360i	−0.784417	−	1.35865i	0.144930	−	0.989442i	$-0.453704\pi$
$60$	1.53592	−	0.800591i	0.198287	−	0.103356i
$61$	−6.95089	+	12.0393i	−0.889971	+	1.54147i	−0.0500626	+	0.998746i	$0.515942\pi$
$61$	−6.95089	+	12.0393i	−0.889971	+	1.54147i	−0.839908	+	0.542729i	$0.817391\pi$
$62$	−3.72120	+	2.14844i	−0.472593	+	0.272852i
$63$	8.01184	−	11.4681i	1.00940	−	1.44484i
$64$	1.00000			0.125000
$65$	−4.12034			−0.511066
$66$	4.45364	+	2.83395i	0.548205	+	0.348835i
$67$	−2.56373	−	1.48017i	−0.313210	−	0.180832i	0.335152	−	0.942164i	$-0.391212\pi$
$67$	−2.56373	−	1.48017i	−0.313210	−	0.180832i	−0.648362	+	0.761332i	$0.724546\pi$
$68$		−	2.57333i		−	0.312062i
$69$	0.0505172	−	1.17136i	0.00608156	−	0.141015i
$70$	4.03843	+	2.33159i	0.482684	+	0.278678i
$71$	−6.25422	−	10.8326i	−0.742239	−	1.28560i	−0.951473	−	0.307731i	$-0.900430\pi$
$71$	−6.25422	−	10.8326i	−0.742239	−	1.28560i	0.209234	−	0.977866i	$-0.432903\pi$
$72$	1.71811	−	2.45929i	0.202481	−	0.289830i
$73$	2.18577	+	3.78586i	0.255825	+	0.443101i	0.965119	−	0.261811i	$-0.0843197\pi$
$73$	2.18577	+	3.78586i	0.255825	+	0.443101i	−0.709295	+	0.704912i	$0.750986\pi$
$74$	−3.89481	+	2.24867i	−0.452763	+	0.261403i
$75$	1.73044	+	0.0746290i	0.199814	+	0.00861742i
$76$	−0.119625	−	4.35726i	−0.0137219	−	0.499812i
$77$			14.2121i			1.61962i
$78$	−6.32852	+	3.29871i	−0.716564	+	0.373505i
$79$	6.74543	−	3.89448i	0.758921	−	0.438163i	−0.0699875	−	0.997548i	$-0.522296\pi$
$79$	6.74543	−	3.89448i	0.758921	−	0.438163i	0.828908	+	0.559385i	$0.188963\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	−3.09620	−	8.45065i	−0.344022	−	0.938962i
$82$	−1.65691	+	2.86985i	−0.182975	+	0.316922i
$83$			2.61607i			0.287151i	0.989639	+	0.143576i	$0.0458601\pi$
$83$			2.61607i			0.287151i	−0.989639	+	0.143576i	$0.954140\pi$
$84$	8.06935	+	0.348008i	0.880438	+	0.0379708i
$85$	1.28666	−	2.22857i	0.139558	−	0.241722i
$86$	−2.86613	+	4.96428i	−0.309062	+	0.535312i
$87$	3.43390	+	0.148094i	0.368153	+	0.0158774i
$88$			3.04774i			0.324890i
$89$	4.81262	−	8.33571i	0.510137	−	0.883583i	−0.489794	−	0.871838i	$-0.662928\pi$
$89$	4.81262	−	8.33571i	0.510137	−	0.883583i	0.999931	−	0.0117449i	$-0.00373860\pi$
$90$	2.71757	−	1.27075i	0.286457	−	0.133949i
$91$	−16.6397	−	9.60693i	−1.74431	−	1.00708i
$92$	0.586222	−	0.338456i	0.0611179	−	0.0352864i
$93$	−6.59966	+	3.44004i	−0.684353	+	0.356715i
$94$			8.76281i			0.903815i
$95$	2.07503	−	3.83331i	0.212894	−	0.393289i
$96$	1.73044	+	0.0746290i	0.176613	+	0.00761679i
$97$	−8.00346	+	4.62080i	−0.812628	+	0.469171i	−0.847868	−	0.530208i	$-0.822114\pi$
$97$	−8.00346	+	4.62080i	−0.812628	+	0.469171i	0.0352396	+	0.999379i	$0.488781\pi$
$98$	7.37259	+	12.7697i	0.744744	+	1.28993i
$99$	7.49527	+	5.23635i	0.753303	+	0.526273i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	9.90594	+	5.71920i	0.985678	+	0.569081i	0.903980	−	0.427576i	$-0.140632\pi$
$101$	9.90594	+	5.71920i	0.985678	+	0.569081i	0.0816985	+	0.996657i	$0.473966\pi$
$102$	0.192045	−	4.45299i	0.0190153	−	0.440912i
$103$			17.4744i			1.72181i	0.508767	+	0.860904i	$0.330101\pi$
$103$			17.4744i			1.72181i	−0.508767	+	0.860904i	$0.669899\pi$
$104$	−3.56832	−	2.06017i	−0.349903	−	0.202016i
$105$	6.81426	+	4.33606i	0.665004	+	0.423156i
$106$	−9.14686			−0.888422
$107$	18.8110			1.81853			0.909265	−	0.416217i	$-0.136644\pi$
$107$	18.8110			1.81853			0.909265	+	0.416217i	$0.136644\pi$
$108$	3.15662	−	4.12744i	0.303746	−	0.397163i
$109$	−6.30002	+	3.63732i	−0.603432	+	0.348392i	−0.770391	−	0.637572i	$-0.779939\pi$
$109$	−6.30002	+	3.63732i	−0.603432	+	0.348392i	0.166958	+	0.985964i	$0.446605\pi$
$110$	−1.52387	+	2.63942i	−0.145295	+	0.251659i
$111$	−6.90756	+	3.60053i	−0.655637	+	0.341747i
$112$	2.33159	+	4.03843i	0.220314	+	0.381595i
$113$	12.7918			1.20335			0.601675	−	0.798741i	$-0.294500\pi$
$113$	12.7918			1.20335			0.601675	+	0.798741i	$0.294500\pi$
$114$	0.118175	−	7.54891i	0.0110681	−	0.707020i
$115$	0.676911			0.0631223
$116$	0.992204	+	1.71855i	0.0921238	+	0.159563i
$117$	−11.1973	+	5.23593i	−1.03519	+	0.484062i
$118$	6.02522	−	10.4360i	0.554667	−	0.960711i
$119$	10.3922	−	5.99993i	0.952650	−	0.550013i
$120$	1.46129	+	0.929852i	0.133397	+	0.0848835i
$121$	1.71128			0.155571
$122$	−13.9018			−1.25861
$123$	−3.08136	+	4.84246i	−0.277837	+	0.436630i
$124$	−3.72120	−	2.14844i	−0.334174	−	0.192935i
$125$			1.00000i			0.0894427i
$126$	13.9376	+	1.20442i	1.24166	+	0.107298i
$127$	−17.7898	−	10.2710i	−1.57859	−	0.911401i	−0.995056	−	0.0993135i	$-0.968335\pi$
$127$	−17.7898	−	10.2710i	−1.57859	−	0.911401i	−0.583536	−	0.812087i	$-0.698331\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−5.33014	+	8.37650i	−0.469293	+	0.737509i
$130$	−2.06017	−	3.56832i	−0.180689	−	0.312962i
$131$	−3.28692	+	1.89770i	−0.287180	+	0.165803i	−0.636669	−	0.771137i	$-0.719688\pi$
$131$	−3.28692	+	1.89770i	−0.287180	+	0.165803i	0.349490	+	0.936940i	$0.386355\pi$
$132$	−0.227450	+	5.27394i	−0.0197970	+	0.459037i
$133$	17.3175	−	10.6424i	1.50162	−	0.922815i
$134$		−	2.96034i		−	0.255735i
$135$	4.79743	−	1.99615i	0.412897	−	0.171801i
$136$	2.22857	−	1.28666i	0.191098	−	0.110330i
$137$	−5.64269	−	3.25781i	−0.482087	−	0.278333i	0.239199	−	0.970971i	$-0.423115\pi$
$137$	−5.64269	−	3.25781i	−0.482087	−	0.278333i	−0.721286	+	0.692637i	$0.756449\pi$
$138$	1.03968	−	0.541929i	0.0885037	−	0.0461320i
$139$	4.11100	−	7.12045i	0.348690	−	0.603949i	−0.637327	−	0.770594i	$-0.719960\pi$
$139$	4.11100	−	7.12045i	0.348690	−	0.603949i	0.986017	+	0.166645i	$0.0532932\pi$
$140$			4.66317i			0.394110i
$141$	−0.653960	+	15.1635i	−0.0550734	+	1.27700i
$142$	6.25422	−	10.8326i	0.524843	−	0.909054i
$143$	6.27887	−	10.8753i	0.525065	−	0.909439i
$144$	2.98886	+	0.258282i	0.249072	+	0.0215235i
$145$			1.98441i			0.164796i
$146$	−2.18577	+	3.78586i	−0.180895	+	0.313320i
$147$	11.8049	+	22.6474i	0.973648	+	1.86793i
$148$	−3.89481	−	2.24867i	−0.320151	−	0.184840i
$149$	−2.16323	+	1.24894i	−0.177219	+	0.102317i	−0.585985	−	0.810322i	$-0.699292\pi$
$149$	−2.16323	+	1.24894i	−0.177219	+	0.102317i	0.408767	+	0.912639i	$0.365959\pi$
$150$	0.800591	+	1.53592i	0.0653679	+	0.125407i
$151$			9.36390i			0.762023i	0.924570	+	0.381012i	$0.124424\pi$
$151$			9.36390i			0.762023i	−0.924570	+	0.381012i	$0.875576\pi$
$152$	3.71368	−	2.28223i	0.301219	−	0.185113i
$153$	0.664645	−	7.69131i	0.0537333	−	0.621806i
$154$	−12.3081	+	7.10607i	−0.991813	+	0.572623i
$155$	−2.14844	−	3.72120i	−0.172567	−	0.298894i
$156$	−6.02102	−	3.83131i	−0.482068	−	0.306750i
$157$	7.71370	+	13.3605i	0.615620	+	1.06629i	0.990275	+	0.139121i	$0.0444277\pi$
$157$	7.71370	+	13.3605i	0.615620	+	1.06629i	−0.374655	+	0.927164i	$0.622239\pi$
$158$	6.74543	+	3.89448i	0.536638	+	0.309828i
$159$	−15.8281	−	0.682621i	−1.25525	−	0.0541354i
$160$			1.00000i			0.0790569i
$161$	2.73366	+	1.57828i	0.215442	+	0.124386i
$162$	5.77038	−	6.90671i	0.453364	−	0.542643i
$163$	7.94366			0.622196			0.311098	−	0.950378i	$-0.399303\pi$
$163$	7.94366			0.622196			0.311098	+	0.950378i	$0.399303\pi$
$164$	−3.31382			−0.258766
$165$	−2.83395	+	4.45364i	−0.220622	+	0.346715i
$166$	−2.26559	+	1.30804i	−0.175844	+	0.101523i
$167$	2.97913	−	5.16001i	0.230532	−	0.399293i	−0.727433	−	0.686179i	$-0.759287\pi$
$167$	2.97913	−	5.16001i	0.230532	−	0.399293i	0.957965	+	0.286886i	$0.0926200\pi$
$168$	3.73329	+	7.16227i	0.288030	+	0.552581i
$169$	1.98861	+	3.44437i	0.152970	+	0.264952i
$170$	2.57333			0.197365
$171$	0.767862	−	13.0541i	0.0587199	−	0.998275i
$172$	−5.73225			−0.437080
$173$	4.02441	+	6.97047i	0.305970	+	0.529955i	0.977477	−	0.211043i	$-0.0676860\pi$
$173$	4.02441	+	6.97047i	0.305970	+	0.529955i	−0.671507	+	0.740998i	$0.734353\pi$
$174$	1.58870	+	3.04790i	0.120439	+	0.231060i
$175$	−2.33159	+	4.03843i	−0.176251	+	0.305276i
$176$	−2.63942	+	1.52387i	−0.198954	+	0.114866i
$177$	11.2051	−	17.6092i	0.842229	−	1.32359i
$178$	9.62524			0.721443
$179$	−9.52738			−0.712109			−0.356055	−	0.934465i	$-0.615878\pi$
$179$	−9.52738			−0.712109			−0.356055	+	0.934465i	$0.615878\pi$
$180$	2.45929	+	1.71811i	0.183305	+	0.128060i
$181$	−14.9311	−	8.62045i	−1.10982	−	0.640753i	−0.171035	−	0.985265i	$-0.554711\pi$
$181$	−14.9311	−	8.62045i	−1.10982	−	0.640753i	−0.938782	+	0.344512i	$0.888045\pi$
$182$		−	19.2139i		−	1.42423i
$183$	−24.0562	−	1.03748i	−1.77829	−	0.0766925i
$184$	0.586222	+	0.338456i	0.0432169	+	0.0249513i
$185$	−2.24867	−	3.89481i	−0.165325	−	0.286352i
$186$	−6.27899	−	3.99546i	−0.460398	−	0.292961i
$187$	3.92141	+	6.79209i	0.286762	+	0.496687i
$188$	−7.58882	+	4.38141i	−0.553472	+	0.319547i
$189$	24.0283	+	3.12432i	1.74780	+	0.227261i
$190$	4.35726	−	0.119625i	0.316109	−	0.00867847i
$191$			14.9575i			1.08228i	0.840931	+	0.541142i	$0.182008\pi$
$191$			14.9575i			1.08228i	−0.840931	+	0.541142i	$0.817992\pi$
$192$	0.800591	+	1.53592i	0.0577776	+	0.110846i
$193$	18.0958	−	10.4476i	1.30257	−	0.752037i	0.321723	−	0.946834i	$-0.395738\pi$
$193$	18.0958	−	10.4476i	1.30257	−	0.752037i	0.980844	+	0.194797i	$0.0624047\pi$
$194$	−8.00346	−	4.62080i	−0.574615	−	0.331754i
$195$	−3.29871	−	6.32852i	−0.236225	−	0.453195i
$196$	−7.37259	+	12.7697i	−0.526614	+	0.912122i
$197$		−	22.6541i		−	1.61404i	−0.590526	−	0.807019i	$-0.701080\pi$
$197$		−	22.6541i		−	1.61404i	0.590526	−	0.807019i	$-0.298920\pi$
$198$	−0.787178	+	9.10927i	−0.0559423	+	0.647368i
$199$	3.33437	−	5.77531i	0.236367	−	0.409401i	−0.723302	−	0.690532i	$-0.757376\pi$
$199$	3.33437	−	5.77531i	0.236367	−	0.409401i	0.959669	+	0.281132i	$0.0907097\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	0.220927	−	5.12270i	0.0155830	−	0.361327i
$202$			11.4384i			0.804803i
$203$	−4.62682	+	8.01389i	−0.324739	+	0.562465i
$204$	3.95243	−	2.06018i	0.276725	−	0.144241i
$205$	−2.86985	−	1.65691i	−0.200439	−	0.115724i
$206$	−15.1333	+	8.73722i	−1.05439	+	0.608751i
$207$	1.83955	−	0.860186i	0.127858	−	0.0597871i
$208$		−	4.12034i		−	0.285694i
$209$	6.95563	+	11.3183i	0.481131	+	0.782906i
$210$	−0.348008	+	8.06935i	−0.0240148	+	0.556838i
$211$	21.3930	−	12.3513i	1.47276	−	0.850297i	0.473227	−	0.880941i	$-0.343089\pi$
$211$	21.3930	−	12.3513i	1.47276	−	0.850297i	0.999530	+	0.0306440i	$0.00975581\pi$
$212$	−4.57343	−	7.92141i	−0.314104	−	0.544045i
$213$	11.6310	−	18.2785i	0.796943	−	1.25242i
$214$	9.40551	+	16.2908i	0.642948	+	1.11362i
$215$	−4.96428	−	2.86613i	−0.338561	−	0.195468i
$216$	5.15278	+	0.669999i	0.350602	+	0.0455876i
$217$		−	20.0371i		−	1.36021i
$218$	−6.30002	−	3.63732i	−0.426691	−	0.246350i
$219$	−4.06488	+	6.38809i	−0.274679	+	0.431667i
$220$	−3.04774			−0.205479
$221$	−10.6030			−0.713234
$222$	−6.57193	−	4.18186i	−0.441079	−	0.280668i
$223$	−4.59604	+	2.65352i	−0.307774	+	0.177693i	−0.645930	−	0.763397i	$-0.723530\pi$
$223$	−4.59604	+	2.65352i	−0.307774	+	0.177693i	0.338156	+	0.941090i	$0.390197\pi$
$224$	−2.33159	+	4.03843i	−0.155786	+	0.269829i
$225$	1.27075	+	2.71757i	0.0847168	+	0.181171i
$226$	6.39589	+	11.0780i	0.425448	+	0.736898i
$227$	5.17010			0.343152			0.171576	−	0.985171i	$-0.445114\pi$
$227$	5.17010			0.343152			0.171576	+	0.985171i	$0.445114\pi$
$228$	6.59663	−	3.67211i	0.436873	−	0.243192i
$229$	−12.5671			−0.830459			−0.415230	−	0.909717i	$-0.636299\pi$
$229$	−12.5671			−0.830459			−0.415230	+	0.909717i	$0.636299\pi$
$230$	0.338456	+	0.586222i	0.0223171	+	0.0386544i
$231$	−21.8287	+	11.3781i	−1.43623	+	0.748624i
$232$	−0.992204	+	1.71855i	−0.0651414	+	0.112828i
$233$	20.8093	−	12.0142i	1.36326	−	0.787079i	0.373205	−	0.927749i	$-0.378259\pi$
$233$	20.8093	−	12.0142i	1.36326	−	0.787079i	0.990057	+	0.140669i	$0.0449255\pi$
$234$	−10.1331	−	7.07920i	−0.662422	−	0.462782i
$235$	−8.76281			−0.571623
$236$	12.0504			0.784417
$237$	11.3819	+	7.24257i	0.739337	+	0.470456i
$238$	10.3922	+	5.99993i	0.673625	+	0.388918i
$239$			12.9191i			0.835668i	0.908523	+	0.417834i	$0.137211\pi$
$239$			12.9191i			0.835668i	−0.908523	+	0.417834i	$0.862789\pi$
$240$	−0.0746290	+	1.73044i	−0.00481728	+	0.111700i
$241$	18.3610	+	10.6007i	1.18273	+	0.682851i	0.956645	−	0.291256i	$-0.0940731\pi$
$241$	18.3610	+	10.6007i	1.18273	+	0.682851i	0.226088	+	0.974107i	$0.427406\pi$
$242$	0.855640	+	1.48201i	0.0550026	+	0.0952674i
$243$	10.5008	−	11.5210i	0.673624	−	0.739075i
$244$	−6.95089	−	12.0393i	−0.444985	−	0.770737i
$245$	−12.7697	+	7.37259i	−0.815826	+	0.471018i
$246$	−5.73437	−	0.247307i	−0.365610	−	0.0157677i
$247$	−17.9534	+	0.492894i	−1.14235	+	0.0313621i
$248$		−	4.29688i		−	0.272852i
$249$	−4.01809	+	2.09440i	−0.254636	+	0.132727i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−16.2979	−	9.40959i	−1.02871	−	0.593928i	−0.112098	−	0.993697i	$-0.535757\pi$
$251$	−16.2979	−	9.40959i	−1.02871	−	0.593928i	−0.916616	+	0.399769i	$0.869090\pi$
$252$	5.92573	+	12.6725i	0.373286	+	0.798293i
$253$	−1.03152	+	1.78665i	−0.0648514	+	0.112326i
$254$		−	20.5419i		−	1.28892i
$255$	4.45299	+	0.192045i	0.278857	+	0.0120263i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.00449	+	6.93597i	−0.249793	+	0.432654i	−0.963468	−	0.267823i	$-0.913696\pi$
$257$	−4.00449	+	6.93597i	−0.249793	+	0.432654i	0.713675	+	0.700477i	$0.247029\pi$
$258$	−9.91933	−	0.427792i	−0.617550	−	0.0266332i
$259$		−	20.9719i		−	1.30313i
$260$	2.06017	−	3.56832i	0.127766	−	0.221298i
$261$	2.52169	+	5.39277i	0.156089	+	0.333804i
$262$	−3.28692	−	1.89770i	−0.203067	−	0.117241i
$263$	−24.6525	+	14.2331i	−1.52014	+	0.877653i	−0.520421	+	0.853910i	$0.674225\pi$
$263$	−24.6525	+	14.2331i	−1.52014	+	0.877653i	−0.999718	+	0.0237431i	$0.992442\pi$
$264$	−4.68109	+	2.43999i	−0.288101	+	0.150171i
$265$		−	9.14686i		−	0.561887i
$266$	17.8754	+	9.67623i	1.09601	+	0.593288i
$267$	16.6559	+	0.718322i	1.01933	+	0.0439606i
$268$	2.56373	−	1.48017i	0.156605	−	0.0904158i
$269$	−2.93694	−	5.08693i	−0.179068	−	0.310155i	0.762493	−	0.646996i	$-0.223975\pi$
$269$	−2.93694	−	5.08693i	−0.179068	−	0.310155i	−0.941562	+	0.336841i	$0.890642\pi$
$270$	4.12744	+	3.15662i	0.251188	+	0.192106i
$271$	−6.85354	−	11.8707i	−0.416323	−	0.721092i	0.579243	−	0.815155i	$-0.303348\pi$
$271$	−6.85354	−	11.8707i	−0.416323	−	0.721092i	−0.995566	+	0.0940622i	$0.970015\pi$
$272$	2.22857	+	1.28666i	0.135127	+	0.0780154i
$273$	1.43391	−	33.2485i	0.0867843	−	2.01229i
$274$		−	6.51561i		−	0.393622i
$275$	−2.63942	−	1.52387i	−0.159163	−	0.0918928i
$276$	0.989165	+	0.629427i	0.0595408	+	0.0378871i
$277$	15.1954			0.913004			0.456502	−	0.889722i	$-0.349102\pi$
$277$	15.1954			0.913004			0.456502	+	0.889722i	$0.349102\pi$
$278$	8.22199			0.493122
$279$	−10.5673	−	7.38250i	−0.632645	−	0.441979i
$280$	−4.03843	+	2.33159i	−0.241342	+	0.139339i
$281$	−4.27607	+	7.40636i	−0.255089	+	0.441827i	−0.964920	−	0.262545i	$-0.915438\pi$
$281$	−4.27607	+	7.40636i	−0.255089	+	0.441827i	0.709831	+	0.704372i	$0.248771\pi$
$282$	−13.4590	+	7.01543i	−0.801472	+	0.417763i
$283$	−14.1879	−	24.5741i	−0.843382	−	1.46078i	−0.887019	−	0.461734i	$-0.847228\pi$
$283$	−14.1879	−	24.5741i	−0.843382	−	1.46078i	0.0436361	−	0.999047i	$-0.486106\pi$
$284$	12.5084			0.742239
$285$	7.54891	+	0.118175i	0.447159	+	0.00700005i
$286$	12.5577			0.742554
$287$	−7.72645	−	13.3826i	−0.456078	−	0.789950i
$288$	1.27075	+	2.71757i	0.0748797	+	0.160134i
$289$	−5.18900	+	8.98761i	−0.305235	+	0.528683i
$290$	−1.71855	+	0.992204i	−0.100917	+	0.0582642i
$291$	−13.5047	−	8.59332i	−0.791658	−	0.503749i
$292$	−4.37153			−0.255825
$293$	7.22309			0.421977			0.210989	−	0.977489i	$-0.432332\pi$
$293$	7.22309			0.421977			0.210989	+	0.977489i	$0.432332\pi$
$294$	−13.7108	+	21.5470i	−0.799632	+	1.25665i
$295$	10.4360	+	6.02522i	0.607607	+	0.350802i
$296$		−	4.49734i		−	0.261403i
$297$	−2.04198	+	15.7043i	−0.118488	+	0.911257i
$298$	−2.16323	−	1.24894i	−0.125313	−	0.0723493i
$299$	−1.39455	−	2.41544i	−0.0806491	−	0.139688i
$300$	−0.929852	+	1.46129i	−0.0536850	+	0.0843678i
$301$	−13.3652	−	23.1493i	−0.770360	−	1.33430i
$302$	−8.10937	+	4.68195i	−0.466642	+	0.269416i
$303$	−0.853636	+	19.7935i	−0.0490401	+	1.13711i
$304$	3.83331	+	2.07503i	0.219855	+	0.119011i
$305$		−	13.9018i		−	0.796014i
$306$	6.99319	−	3.27006i	0.399774	−	0.186937i
$307$	0.356034	−	0.205556i	0.0203199	−	0.0117317i	−0.489806	−	0.871832i	$-0.662932\pi$
$307$	0.356034	−	0.205556i	0.0203199	−	0.0117317i	0.510126	+	0.860100i	$0.329599\pi$
$308$	−12.3081	−	7.10607i	−0.701318	−	0.404906i
$309$	−26.8394	+	13.9899i	−1.52684	+	0.795856i
$310$	2.14844	−	3.72120i	0.122023	−	0.211350i
$311$		−	10.4640i		−	0.593361i	−0.954977	−	0.296680i	$-0.904120\pi$
$311$		−	10.4640i		−	0.593361i	0.954977	−	0.296680i	$-0.0958796\pi$
$312$	0.307497	−	7.13001i	0.0174086	−	0.403658i
$313$	−0.872105	+	1.51053i	−0.0492943	+	0.0853802i	−0.889620	−	0.456702i	$-0.849031\pi$
$313$	−0.872105	+	1.51053i	−0.0492943	+	0.0853802i	0.840325	+	0.542082i	$0.182364\pi$
$314$	−7.71370	+	13.3605i	−0.435309	+	0.753978i
$315$	−1.20442	+	13.9376i	−0.0678611	+	0.785293i
$316$			7.78896i			0.438163i
$317$	−10.2023	+	17.6710i	−0.573021	+	0.992501i	0.423233	+	0.906021i	$0.360895\pi$
$317$	−10.2023	+	17.6710i	−0.573021	+	0.992501i	−0.996254	+	0.0864798i	$0.972438\pi$
$318$	−7.32289	−	14.0489i	−0.410647	−	0.787821i
$319$	−5.23769	−	3.02398i	−0.293254	−	0.169310i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	15.0599	+	28.8923i	0.840563	+	1.61261i
$322$			3.15655i			0.175908i
$323$	5.33973	−	9.86435i	0.297110	−	0.548867i
$324$	8.86658	+	1.54394i	0.492588	+	0.0857745i
$325$	3.56832	−	2.06017i	0.197935	−	0.114278i
$326$	3.97183	+	6.87941i	0.219979	+	0.381015i
$327$	−10.6304	−	6.76433i	−0.587861	−	0.374068i
$328$	−1.65691	−	2.86985i	−0.0914875	−	0.158461i
$329$	−35.3880	−	20.4313i	−1.95100	−	1.12641i
$330$	−5.27394	−	0.227450i	−0.290321	−	0.0125207i
$331$			3.45155i			0.189714i	0.995491	+	0.0948572i	$0.0302395\pi$
$331$			3.45155i			0.189714i	−0.995491	+	0.0948572i	$0.969761\pi$
$332$	−2.26559	−	1.30804i	−0.124340	−	0.0717879i
$333$	−11.0603	−	7.72692i	−0.606098	−	0.423433i
$334$	5.95826			0.326022
$335$	2.96034			0.161741
$336$	−4.33606	+	6.81426i	−0.236551	+	0.371748i
$337$	−23.1281	+	13.3530i	−1.25987	+	0.727384i	−0.973049	−	0.230601i	$-0.925931\pi$
$337$	−23.1281	+	13.3530i	−1.25987	+	0.727384i	−0.286818	+	0.957985i	$0.592598\pi$
$338$	−1.98861	+	3.44437i	−0.108166	+	0.187349i
$339$	10.2410	+	19.6472i	0.556214	+	1.06709i
$340$	1.28666	+	2.22857i	0.0697791	+	0.120861i
$341$	13.0958			0.709175
$342$	11.6891	−	5.86208i	0.632076	−	0.316985i
$343$	−36.1171			−1.95014
$344$	−2.86613	−	4.96428i	−0.154531	−	0.267656i
$345$	0.541929	+	1.03968i	0.0291765	+	0.0559746i
$346$	−4.02441	+	6.97047i	−0.216353	+	0.374735i
$347$	−14.4663	+	8.35210i	−0.776590	+	0.448364i	−0.835220	−	0.549915i	$-0.814660\pi$
$347$	−14.4663	+	8.35210i	−0.776590	+	0.448364i	0.0586306	+	0.998280i	$0.481327\pi$
$348$	−1.84521	+	2.89980i	−0.0989134	+	0.155446i
$349$	32.2768			1.72773			0.863867	−	0.503719i	$-0.168035\pi$
$349$	32.2768			1.72773			0.863867	+	0.503719i	$0.168035\pi$
$350$	−4.66317			−0.249257
$351$	−17.0064	−	13.0064i	−0.907737	−	0.694229i
$352$	−2.63942	−	1.52387i	−0.140682	−	0.0812225i
$353$		−	15.2843i		−	0.813501i	−0.913539	−	0.406751i	$-0.866662\pi$
$353$		−	15.2843i		−	0.813501i	0.913539	−	0.406751i	$-0.133338\pi$
$354$	20.8526	+	0.899313i	1.10830	+	0.0477979i
$355$	10.8326	+	6.25422i	0.574936	+	0.331940i
$356$	4.81262	+	8.33571i	0.255068	+	0.441792i
$357$	17.5353	+	11.1581i	0.928067	+	0.590549i
$358$	−4.76369	−	8.25095i	−0.251769	−	0.436076i
$359$	−0.917556	+	0.529751i	−0.0484267	+	0.0279592i	−0.524018	−	0.851707i	$-0.675568\pi$
$359$	−0.917556	+	0.529751i	−0.0484267	+	0.0279592i	0.475591	+	0.879666i	$0.342234\pi$
$360$	−0.258282	+	2.98886i	−0.0136127	+	0.157527i
$361$	8.58288	−	16.9509i	0.451731	−	0.892154i
$362$		−	17.2409i		−	0.906162i
$363$	1.37003	+	2.62839i	0.0719082	+	0.137955i
$364$	16.6397	−	9.60693i	0.872157	−	0.503540i
$365$	−3.78586	−	2.18577i	−0.198161	−	0.114408i
$366$	−11.1296	−	21.3521i	−0.581756	−	1.11609i
$367$	10.2507	−	17.7547i	0.535080	−	0.926786i	−0.464079	−	0.885794i	$-0.653615\pi$
$367$	10.2507	−	17.7547i	0.535080	−	0.926786i	0.999159	−	0.0409927i	$-0.0130520\pi$
$368$			0.676911i			0.0352864i
$369$	−9.90454	−	0.855901i	−0.515610	−	0.0445564i
$370$	2.24867	−	3.89481i	0.116903	−	0.202482i
$371$	21.3267	−	36.9389i	1.10723	−	1.91777i
$372$	0.320672	−	7.43549i	0.0166260	−	0.385512i
$373$			14.8122i			0.766944i	0.923552	+	0.383472i	$0.125272\pi$
$373$			14.8122i			0.766944i	−0.923552	+	0.383472i	$0.874728\pi$
$374$	−3.92141	+	6.79209i	−0.202771	+	0.351210i
$375$	−1.53592	+	0.800591i	−0.0793146	+	0.0413423i
$376$	−7.58882	−	4.38141i	−0.391364	−	0.225954i
$377$	7.08101	−	4.08822i	0.364690	−	0.210554i
$378$	9.30840	+	22.3713i	0.478773	+	1.15065i
$379$		−	4.23226i		−	0.217397i	−0.994075	−	0.108698i	$-0.965332\pi$
$379$		−	4.23226i		−	0.217397i	0.994075	−	0.108698i	$-0.0346682\pi$
$380$	2.28223	+	3.71368i	0.117076	+	0.190508i
$381$	1.53302	−	35.5466i	0.0785392	−	1.82111i
$382$	−12.9535	+	7.47873i	−0.662761	+	0.382645i
$383$	11.7377	+	20.3303i	0.599768	+	1.03883i	0.992855	+	0.119328i	$0.0380740\pi$
$383$	11.7377	+	20.3303i	0.599768	+	1.03883i	−0.393087	+	0.919501i	$0.628593\pi$
$384$	−0.929852	+	1.46129i	−0.0474513	+	0.0745713i
$385$	−7.10607	−	12.3081i	−0.362159	−	0.627278i
$386$	18.0958	+	10.4476i	0.921054	+	0.531771i
$387$	−17.1329	−	1.48054i	−0.870914	−	0.0752601i
$388$		−	9.24160i		−	0.469171i
$389$	14.8140	+	8.55289i	0.751102	+	0.433649i	0.826092	−	0.563536i	$-0.190559\pi$
$389$	14.8140	+	8.55289i	0.751102	+	0.433649i	−0.0749902	+	0.997184i	$0.523893\pi$
$390$	3.83131	−	6.02102i	0.194006	−	0.304886i
$391$	1.74191			0.0880923
$392$	−14.7452			−0.744744
$393$	−5.54620	−	3.52917i	−0.279769	−	0.178023i
$394$	19.6190	−	11.3270i	0.988392	−	0.570648i
$395$	−3.89448	+	6.74543i	−0.195952	+	0.339400i
$396$	−8.28245	+	3.87292i	−0.416209	+	0.194622i
$397$	3.27587	+	5.67397i	0.164411	+	0.284768i	0.936446	−	0.350812i	$-0.114094\pi$
$397$	3.27587	+	5.67397i	0.164411	+	0.284768i	−0.772035	+	0.635580i	$0.780761\pi$
$398$	6.66875			0.334274
$399$	30.2102	+	18.0782i	1.51240	+	0.905041i
$400$	−1.00000			−0.0500000
$401$	−12.4043	−	21.4849i	−0.619442	−	1.07290i	−0.989588	−	0.143931i	$-0.954026\pi$
$401$	−12.4043	−	21.4849i	−0.619442	−	1.07290i	0.370146	−	0.928974i	$-0.379308\pi$
$402$	4.54685	−	2.37002i	0.226776	−	0.118206i
$403$	−8.85230	+	15.3326i	−0.440964	+	0.763773i
$404$	−9.90594	+	5.71920i	−0.492839	+	0.284541i
$405$	6.90671	+	5.77038i	0.343197	+	0.286733i
$406$	−9.25364			−0.459250
$407$	13.7067			0.679417
$408$	3.76038	+	2.39281i	0.186167	+	0.118462i
$409$	2.94189	+	1.69850i	0.145467	+	0.0839854i	0.570967	−	0.820973i	$-0.306568\pi$
$409$	2.94189	+	1.69850i	0.145467	+	0.0839854i	−0.425500	+	0.904958i	$0.639902\pi$
$410$		−	3.31382i		−	0.163658i
$411$	0.486254	−	11.2749i	0.0239851	−	0.556149i
$412$	−15.1333	−	8.73722i	−0.745565	−	0.430452i
$413$	28.0966	+	48.6648i	1.38255	+	2.39464i
$414$	1.66472	+	1.16301i	0.0818165	+	0.0571587i
$415$	−1.30804	−	2.26559i	−0.0642090	−	0.111213i
$416$	3.56832	−	2.06017i	0.174951	−	0.101008i
$417$	14.2277	+	0.613599i	0.696733	+	0.0300481i
$418$	−6.32415	+	11.6829i	−0.309324	+	0.571431i
$419$			25.4266i			1.24217i	0.783742	+	0.621086i	$0.213308\pi$
$419$			25.4266i			1.24217i	−0.783742	+	0.621086i	$0.786692\pi$
$420$	−7.16227	+	3.73329i	−0.349483	+	0.182166i
$421$	9.79175	−	5.65327i	0.477221	−	0.275523i	−0.242037	−	0.970267i	$-0.577815\pi$
$421$	9.79175	−	5.65327i	0.477221	−	0.275523i	0.719257	+	0.694744i	$0.244482\pi$
$422$	21.3930	+	12.3513i	1.04140	+	0.601251i
$423$	−23.8136	+	11.1354i	−1.15786	+	0.541420i
$424$	4.57343	−	7.92141i	0.222105	−	0.384698i
$425$			2.57333i			0.124825i
$426$	21.6451	+	0.933493i	1.04871	+	0.0452279i
$427$	32.4132	−	56.1413i	1.56859	−	2.71687i
$428$	−9.40551	+	16.2908i	−0.454633	+	0.787447i
$429$	21.7304	+	0.937171i	1.04915	+	0.0452470i
$430$		−	5.73225i		−	0.276434i
$431$	−0.210664	+	0.364881i	−0.0101473	+	0.0175757i	−0.871054	−	0.491186i	$-0.836563\pi$
$431$	−0.210664	+	0.364881i	−0.0101473	+	0.0175757i	0.860907	+	0.508762i	$0.169897\pi$
$432$	1.99615	+	4.79743i	0.0960399	+	0.230817i
$433$	4.84430	+	2.79686i	0.232802	+	0.134409i	0.611864	−	0.790963i	$-0.290420\pi$
$433$	4.84430	+	2.79686i	0.232802	+	0.134409i	−0.379062	+	0.925371i	$0.623753\pi$
$434$	17.3526	−	10.0185i	0.832952	−	0.480905i
$435$	−3.04790	+	1.58870i	−0.146135	+	0.0761723i
$436$		−	7.27464i		−	0.348392i
$437$	2.94948	−	0.0809752i	0.141093	−	0.00387357i
$438$	−7.56469	−	0.326243i	−0.361455	−	0.0155885i
$439$	−33.0674	+	19.0915i	−1.57822	+	0.911186i	−0.583113	+	0.812391i	$0.698165\pi$
$439$	−33.0674	+	19.0915i	−1.57822	+	0.911186i	−0.995108	+	0.0987947i	$0.968501\pi$
$440$	−1.52387	−	2.63942i	−0.0726477	−	0.125829i
$441$	−25.3338	+	36.2627i	−1.20637	+	1.72679i
$442$	−5.30149	−	9.18245i	−0.252166	−	0.436765i
$443$	−22.2103	−	12.8231i	−1.05524	−	0.609246i	−0.131132	−	0.991365i	$-0.541861\pi$
$443$	−22.2103	−	12.8231i	−1.05524	−	0.609246i	−0.924113	+	0.382119i	$0.875194\pi$
$444$	0.335632	−	7.78239i	0.0159284	−	0.369336i
$445$			9.62524i			0.456280i
$446$	−4.59604	−	2.65352i	−0.217629	−	0.125648i
$447$	−3.65014	−	2.32266i	−0.172646	−	0.109858i
$448$	−4.66317			−0.220314
$449$	−23.6894			−1.11797			−0.558986	−	0.829177i	$-0.688809\pi$
$449$	−23.6894			−1.11797			−0.558986	+	0.829177i	$0.688809\pi$
$450$	−1.71811	+	2.45929i	−0.0809925	+	0.115932i
$451$	8.74656	−	5.04983i	0.411859	−	0.237787i
$452$	−6.39589	+	11.0780i	−0.300837	+	0.521066i
$453$	−14.3822	+	7.49665i	−0.675735	+	0.352223i
$454$	2.58505	+	4.47744i	0.121322	+	0.210137i
$455$	19.2139			0.900760
$456$	6.47846	+	3.87680i	0.303382	+	0.181548i
$457$	−17.2801			−0.808330			−0.404165	−	0.914686i	$-0.632438\pi$
$457$	−17.2801			−0.808330			−0.404165	+	0.914686i	$0.632438\pi$
$458$	−6.28356	−	10.8835i	−0.293612	−	0.508550i
$459$	12.3454	−	5.13675i	0.576232	−	0.239763i
$460$	−0.338456	+	0.586222i	−0.0157806	+	0.0273328i
$461$	27.4943	−	15.8738i	1.28053	−	0.739317i	0.303589	−	0.952803i	$-0.401815\pi$
$461$	27.4943	−	15.8738i	1.28053	−	0.739317i	0.976946	+	0.213486i	$0.0684818\pi$
$462$	−20.7681	−	13.2152i	−0.966219	−	0.614826i
$463$	−24.4190			−1.13485			−0.567423	−	0.823426i	$-0.692060\pi$
$463$	−24.4190			−1.13485			−0.567423	+	0.823426i	$0.692060\pi$
$464$	−1.98441			−0.0921238
$465$	3.99546	−	6.27899i	0.185285	−	0.291181i
$466$	20.8093	+	12.0142i	0.963972	+	0.556549i
$467$			13.4425i			0.622047i	0.950402	+	0.311023i	$0.100672\pi$
$467$			13.4425i			0.622047i	−0.950402	+	0.311023i	$0.899328\pi$
$468$	1.06421	−	12.3151i	0.0491932	−	0.569267i
$469$	11.9551	+	6.90229i	0.552036	+	0.318718i
$470$	−4.38141	−	7.58882i	−0.202099	−	0.350046i
$471$	−14.3452	+	22.5439i	−0.660991	+	1.03877i
$472$	6.02522	+	10.4360i	0.277333	+	0.480355i
$473$	15.1298	−	8.73521i	0.695670	−	0.401645i
$474$	−0.581282	+	13.4783i	−0.0266992	+	0.619081i
$475$	0.119625	+	4.35726i	0.00548875	+	0.199925i
$476$			11.9999i			0.550013i
$477$	−11.6234	−	24.8572i	−0.532198	−	1.13813i
$478$	−11.1883	+	6.45956i	−0.511740	+	0.295453i
$479$	8.44584	+	4.87621i	0.385900	+	0.222800i	0.680382	−	0.732857i	$-0.261814\pi$
$479$	8.44584	+	4.87621i	0.385900	+	0.222800i	−0.294482	+	0.955657i	$0.595147\pi$
$480$	−1.53592	+	0.800591i	−0.0701049	+	0.0365418i
$481$	−9.26529	+	16.0480i	−0.422461	+	0.731724i
$482$			21.2014i			0.965697i
$483$	−0.235571	+	5.46224i	−0.0107188	+	0.248540i
$484$	−0.855640	+	1.48201i	−0.0388927	+	0.0673642i
$485$	4.62080	−	8.00346i	0.209820	−	0.363418i
$486$	15.2279	+	3.33340i	0.690751	+	0.151206i
$487$			16.0127i			0.725606i	0.931866	+	0.362803i	$0.118180\pi$
$487$			16.0127i			0.725606i	−0.931866	+	0.362803i	$0.881820\pi$
$488$	6.95089	−	12.0393i	0.314652	−	0.544994i
$489$	6.35962	+	12.2008i	0.287592	+	0.551741i
$490$	−12.7697	−	7.37259i	−0.576876	−	0.333060i
$491$	−18.5831	+	10.7290i	−0.838645	+	0.484192i	−0.856803	−	0.515643i	$-0.827553\pi$
$491$	−18.5831	+	10.7290i	−0.838645	+	0.484192i	0.0181585	+	0.999835i	$0.494220\pi$
$492$	−2.65301	−	5.08976i	−0.119607	−	0.229464i
$493$			5.10653i			0.229986i
$494$	−9.40355	−	15.3016i	−0.423086	−	0.688454i
$495$	−9.10927	−	0.787178i	−0.409431	−	0.0353810i
$496$	3.72120	−	2.14844i	0.167087	−	0.0964677i
$497$	29.1645	+	50.5144i	1.30821	+	2.26588i
$498$	−3.82285	−	2.43256i	−0.171306	−	0.109006i
$499$	9.93532	+	17.2085i	0.444766	+	0.770358i	0.998036	−	0.0626445i	$-0.0199534\pi$
$499$	9.93532	+	17.2085i	0.444766	+	0.770358i	−0.553270	+	0.833002i	$0.686620\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	10.3104	+	0.444659i	0.460636	+	0.0198659i
$502$		−	18.8192i		−	0.839941i
$503$	25.5440	+	14.7478i	1.13895	+	0.657574i	0.946171	−	0.323668i	$-0.104916\pi$
$503$	25.5440	+	14.7478i	1.13895	+	0.657574i	0.192780	+	0.981242i	$0.438250\pi$
$504$	−8.01184	+	11.4681i	−0.356876	+	0.510829i
$505$	−11.4384			−0.509002
$506$	−2.06305			−0.0917137
$507$	−3.69822	+	5.81188i	−0.164244	+	0.258115i
$508$	17.7898	−	10.2710i	0.789296	−	0.455700i
$509$	−7.10434	+	12.3051i	−0.314894	+	0.545413i	−0.979415	−	0.201857i	$-0.935302\pi$
$509$	−7.10434	+	12.3051i	−0.314894	+	0.545413i	0.664521	+	0.747270i	$0.268636\pi$
$510$	2.06018	+	3.95243i	0.0912263	+	0.175016i
$511$	−10.1926	−	17.6541i	−0.450894	−	0.780972i
$512$	−1.00000			−0.0441942
$513$	20.6649	−	9.27164i	0.912376	−	0.409353i
$514$	−8.00897			−0.353261
$515$	−8.73722	−	15.1333i	−0.385008	−	0.666854i
$516$	−4.58919	−	8.80429i	−0.202028	−	0.387587i
$517$	13.3534	−	23.1288i	0.587281	−	1.01720i
$518$	18.1622	−	10.4859i	0.798000	−	0.460726i
$519$	−7.48420	+	11.7617i	−0.328520	+	0.516280i
$520$	4.12034			0.180689
$521$	−6.13334			−0.268707			−0.134353	−	0.990934i	$-0.542896\pi$
$521$	−6.13334			−0.268707			−0.134353	+	0.990934i	$0.542896\pi$
$522$	−3.40943	+	4.88023i	−0.149227	+	0.213602i
$523$	3.86418	+	2.23098i	0.168969	+	0.0975541i	0.582099	−	0.813118i	$-0.302231\pi$
$523$	3.86418	+	2.23098i	0.168969	+	0.0975541i	−0.413131	+	0.910672i	$0.635565\pi$
$524$		−	3.79541i		−	0.165803i
$525$	−8.06935	−	0.348008i	−0.352175	−	0.0151883i
$526$	−24.6525	−	14.2331i	−1.07490	−	0.620594i
$527$	−5.52863	−	9.57587i	−0.240831	−	0.417131i
$528$	−4.45364	−	2.83395i	−0.193820	−	0.123332i
$529$	−11.2709	−	19.5218i	−0.490039	−	0.848772i
$530$	7.92141	−	4.57343i	0.344084	−	0.198657i
$531$	36.0171	+	3.11242i	1.56301	+	0.135067i
$532$	0.557830	+	20.3186i	0.0241850	+	0.880925i
$533$			13.6541i			0.591423i
$534$	7.70588	+	14.7836i	0.333466	+	0.639750i
$535$	−16.2908	+	9.40551i	−0.704314	+	0.406636i
$536$	2.56373	+	1.48017i	0.110736	+	0.0639336i
$537$	−7.62753	−	14.6333i	−0.329152	−	0.631474i
$538$	2.93694	−	5.08693i	0.126620	−	0.219313i
$539$		−	44.9395i		−	1.93568i
$540$	−0.669999	+	5.15278i	−0.0288321	+	0.221740i
$541$	0.177929	−	0.308182i	0.00764975	−	0.0132498i	−0.862175	−	0.506610i	$-0.830898\pi$
$541$	0.177929	−	0.308182i	0.00764975	−	0.0132498i	0.869825	+	0.493360i	$0.164232\pi$
$542$	6.85354	−	11.8707i	0.294385	−	0.509889i
$543$	1.28667	−	29.8344i	0.0552164	−	1.28032i
$544$			2.57333i			0.110330i
$545$	3.63732	−	6.30002i	0.155806	−	0.269863i
$546$	29.5110	−	15.3824i	1.26295	−	0.658308i
$547$	29.5616	+	17.0674i	1.26396	+	0.729750i	0.973839	−	0.227239i	$-0.0729700\pi$
$547$	29.5616	+	17.0674i	1.26396	+	0.729750i	0.290124	+	0.956989i	$0.406303\pi$
$548$	5.64269	−	3.25781i	0.241044	−	0.139167i
$549$	−17.6657	−	37.7791i	−0.753954	−	1.61237i
$550$		−	3.04774i		−	0.129956i
$551$	0.237384	+	8.64658i	0.0101129	+	0.368357i
$552$	−0.0505172	+	1.17136i	−0.00215016	+	0.0498562i
$553$	−31.4551	+	18.1606i	−1.33761	+	0.772268i
$554$	7.59771	+	13.1596i	0.322796	+	0.559098i
$555$	4.18186	−	6.57193i	0.177510	−	0.278963i
$556$	4.11100	+	7.12045i	0.174345	+	0.301974i
$557$	22.5889	+	13.0417i	0.957124	+	0.552596i	0.895287	−	0.445490i	$-0.146971\pi$
$557$	22.5889	+	13.0417i	0.957124	+	0.552596i	0.0618376	+	0.998086i	$0.480304\pi$
$558$	1.10981	−	12.8428i	0.0469819	−	0.543677i
$559$			23.6188i			0.998970i
$560$	−4.03843	−	2.33159i	−0.170655	−	0.0985275i
$561$	−7.29267	+	11.4607i	−0.307897	+	0.483870i
$562$	−8.55213			−0.360750
$563$	17.0740			0.719585			0.359792	−	0.933032i	$-0.382847\pi$
$563$	17.0740			0.719585			0.359792	+	0.933032i	$0.382847\pi$
$564$	−12.8050	−	8.14812i	−0.539189	−	0.343098i
$565$	−11.0780	+	6.39589i	−0.466055	+	0.269077i
$566$	14.1879	−	24.5741i	0.596361	−	1.03293i
$567$	14.4381	+	39.4069i	0.606344	+	1.65493i
$568$	6.25422	+	10.8326i	0.262421	+	0.454527i
$569$	15.0406			0.630534			0.315267	−	0.949003i	$-0.397906\pi$
$569$	15.0406			0.630534			0.315267	+	0.949003i	$0.397906\pi$
$570$	3.67211	+	6.59663i	0.153808	+	0.276303i
$571$	39.0424			1.63388			0.816938	−	0.576726i	$-0.195670\pi$
$571$	39.0424			1.63388			0.816938	+	0.576726i	$0.195670\pi$
$572$	6.27887	+	10.8753i	0.262533	+	0.454720i
$573$	−22.9735	+	11.9748i	−0.959731	+	0.500255i
$574$	7.72645	−	13.3826i	0.322496	−	0.558579i
$575$	−0.586222	+	0.338456i	−0.0244472	+	0.0141146i
$576$	−1.71811	+	2.45929i	−0.0715879	+	0.102470i
$577$	23.9982			0.999059			0.499529	−	0.866297i	$-0.333506\pi$
$577$	23.9982			0.999059			0.499529	+	0.866297i	$0.333506\pi$
$578$	−10.3780			−0.431668
$579$	30.5341	+	19.4295i	1.26895	+	0.807463i
$580$	−1.71855	−	0.992204i	−0.0713588	−	0.0411990i
$581$		−	12.1992i		−	0.506108i
$582$	0.689691	−	15.9921i	0.0285886	−	0.662892i
$583$	24.1424	+	13.9386i	0.999876	+	0.577279i
$584$	−2.18577	−	3.78586i	−0.0904477	−	0.156660i
$585$	7.07920	−	10.1331i	0.292689	−	0.418952i
$586$	3.61154	+	6.25538i	0.149191	+	0.258407i
$587$	−28.1004	+	16.2238i	−1.15983	+	0.669626i	−0.951262	−	0.308382i	$-0.900212\pi$
$587$	−28.1004	+	16.2238i	−1.15983	+	0.669626i	−0.208564	+	0.978009i	$0.566879\pi$
$588$	−25.5157	−	1.10042i	−1.05225	−	0.0453805i
$589$	−9.80644	−	15.9572i	−0.404067	−	0.657506i
$590$			12.0504i			0.496109i
$591$	34.7949	−	18.1367i	1.43127	−	0.746042i
$592$	3.89481	−	2.24867i	0.160076	−	0.0924198i
$593$	−15.6411	−	9.03038i	−0.642302	−	0.370833i	0.143199	−	0.989694i	$-0.454261\pi$
$593$	−15.6411	−	9.03038i	−0.642302	−	0.370833i	−0.785501	+	0.618861i	$0.787594\pi$
$594$	−14.6213	+	6.08375i	−0.599921	+	0.249619i
$595$	−5.99993	+	10.3922i	−0.245973	+	0.426038i
$596$		−	2.49788i		−	0.102317i
$597$	11.5399	+	0.497682i	0.472296	+	0.0203688i
$598$	1.39455	−	2.41544i	0.0570275	−	0.0987745i
$599$	20.2381	−	35.0535i	0.826907	−	1.43225i	−0.0735458	−	0.997292i	$-0.523432\pi$
$599$	20.2381	−	35.0535i	0.826907	−	1.43225i	0.900453	−	0.434953i	$-0.143235\pi$
$600$	−1.73044	−	0.0746290i	−0.0706450	−	0.00304672i
$601$			20.2964i			0.827907i	0.910298	+	0.413953i	$0.135852\pi$
$601$			20.2964i			0.827907i	−0.910298	+	0.413953i	$0.864148\pi$
$602$	13.3652	−	23.1493i	0.544727	−	0.943494i
$603$	8.04494	−	3.76186i	0.327615	−	0.153195i
$604$	−8.10937	−	4.68195i	−0.329966	−	0.190506i
$605$	−1.48201	+	0.855640i	−0.0602524	+	0.0347867i
$606$	−17.5685	+	9.15747i	−0.713671	+	0.371997i
$607$			9.59148i			0.389306i	0.980872	+	0.194653i	$0.0623581\pi$
$607$			9.59148i			0.389306i	−0.980872	+	0.194653i	$0.937642\pi$
$608$	0.119625	+	4.35726i	0.00485141	+	0.176710i
$609$	−16.0129	−	0.690590i	−0.648875	−	0.0279841i
$610$	12.0393	−	6.95089i	0.487457	−	0.281433i
$611$	18.0529	+	31.2685i	0.730342	+	1.26499i
$612$	6.32855	+	4.42125i	0.255816	+	0.178719i
$613$	−9.78722	−	16.9520i	−0.395302	−	0.684683i	0.597838	−	0.801617i	$-0.296027\pi$
$613$	−9.78722	−	16.9520i	−0.395302	−	0.684683i	−0.993140	+	0.116934i	$0.962693\pi$
$614$	0.356034	+	0.205556i	0.0143684	+	0.00829558i
$615$	0.247307	−	5.73437i	0.00997238	−	0.231232i
$616$		−	14.2121i		−	0.572623i
$617$	−15.9625	−	9.21594i	−0.642625	−	0.371020i	0.143000	−	0.989723i	$-0.454325\pi$
$617$	−15.9625	−	9.21594i	−0.642625	−	0.371020i	−0.785625	+	0.618703i	$0.787659\pi$
$618$	−25.5353	−	16.2486i	−1.02718	−	0.653616i
$619$	−24.8517			−0.998874			−0.499437	−	0.866350i	$-0.666460\pi$
$619$	−24.8517			−0.998874			−0.499437	+	0.866350i	$0.666460\pi$
$620$	4.29688			0.172567
$621$	2.79391	+	2.13675i	0.112116	+	0.0857450i
$622$	9.06212	−	5.23202i	0.363358	−	0.209785i
$623$	−22.4421	+	38.8708i	−0.899123	+	1.55733i
$624$	6.32852	−	3.29871i	0.253344	−	0.132054i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.74421			−0.0697126
$627$	−11.8155	+	19.7447i	−0.471864	+	0.788526i
$628$	−15.4274			−0.615620
$629$	−5.78656	−	10.0226i	−0.230725	−	0.399628i
$630$	−12.6725	+	5.92573i	−0.504885	+	0.236087i
$631$	−1.80191	+	3.12099i	−0.0717327	+	0.124245i	−0.899661	−	0.436590i	$-0.856186\pi$
$631$	−1.80191	+	3.12099i	−0.0717327	+	0.124245i	0.827928	+	0.560834i	$0.189520\pi$
$632$	−6.74543	+	3.89448i	−0.268319	+	0.154914i
$633$	36.0976	+	22.9697i	1.43475	+	0.912964i
$634$	−20.4047			−0.810373
$635$	20.5419			0.815182
$636$	8.50522	−	13.3662i	0.337254	−	0.530006i
$637$	52.6155	+	30.3776i	2.08470	+	1.20360i
$638$		−	6.04796i		−	0.239441i
$639$	37.3860	+	3.23071i	1.47897	+	0.127805i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−3.94155	−	6.82697i	−0.155682	−	0.269649i	0.777625	−	0.628728i	$-0.216424\pi$
$641$	−3.94155	−	6.82697i	−0.155682	−	0.269649i	−0.933307	+	0.359079i	$0.883091\pi$
$642$	−17.4915	+	27.4884i	−0.690333	+	1.08488i
$643$	−2.98629	−	5.17241i	−0.117768	−	0.203980i	0.801115	−	0.598510i	$-0.204241\pi$
$643$	−2.98629	−	5.17241i	−0.117768	−	0.203980i	−0.918883	+	0.394531i	$0.870907\pi$
$644$	−2.73366	+	1.57828i	−0.107721	+	0.0621928i
$645$	0.427792	−	9.91933i	0.0168443	−	0.390573i
$646$	11.2126	−	0.307833i	0.441155	−	0.0121115i
$647$			27.9832i			1.10013i	0.835120	+	0.550067i	$0.185398\pi$
$647$			27.9832i			1.10013i	−0.835120	+	0.550067i	$0.814602\pi$
$648$	3.09620	+	8.45065i	0.121630	+	0.331973i
$649$	−31.8062	+	18.3633i	−1.24850	+	0.720823i
$650$	3.56832	+	2.06017i	0.139961	+	0.0808066i
$651$	30.7754	−	16.0415i	1.20618	−	0.628716i
$652$	−3.97183	+	6.87941i	−0.155549	+	0.269419i
$653$			20.3397i			0.795953i	0.917396	+	0.397976i	$0.130287\pi$
$653$			20.3397i			0.795953i	−0.917396	+	0.397976i	$0.869713\pi$
$654$	0.542899	−	12.5883i	0.0212290	−	0.492243i
$655$	1.89770	−	3.28692i	0.0741494	−	0.128431i
$656$	1.65691	−	2.86985i	0.0646914	−	0.112049i
$657$	−13.0659	−	1.12909i	−0.509750	−	0.0440500i
$658$		−	40.8625i		−	1.59299i
$659$	12.9141	−	22.3678i	0.503061	−	0.871327i	−0.496933	−	0.867789i	$-0.665540\pi$
$659$	12.9141	−	22.3678i	0.503061	−	0.871327i	0.999994	−	0.00353811i	$-0.00112622\pi$
$660$	−2.43999	−	4.68109i	−0.0949766	−	0.182211i
$661$	24.4404	+	14.1107i	0.950623	+	0.548842i	0.893274	−	0.449512i	$-0.148402\pi$
$661$	24.4404	+	14.1107i	0.950623	+	0.548842i	0.0573484	+	0.998354i	$0.481735\pi$
$662$	−2.98913	+	1.72578i	−0.116176	+	0.0670742i
$663$	−8.48864	−	16.2853i	−0.329672	−	0.632470i
$664$		−	2.61607i		−	0.101523i
$665$	−9.67623	+	17.8754i	−0.375228	+	0.693177i
$666$	1.16158	−	13.4419i	0.0450105	−	0.520864i
$667$	−1.16330	+	0.671634i	−0.0450433	+	0.0260058i
$668$	2.97913	+	5.16001i	0.115266	+	0.199647i
$669$	−7.75515	−	4.93477i	−0.299831	−	0.190789i
$670$	1.48017	+	2.56373i	0.0571840	+	0.0990456i
$671$	36.6927	+	21.1845i	1.41650	+	0.817819i
$672$	−8.06935	−	0.348008i	−0.311282	−	0.0134247i
$673$		−	3.94270i		−	0.151980i	−0.997109	−	0.0759900i	$-0.975788\pi$
$673$		−	3.94270i		−	0.151980i	0.997109	−	0.0759900i	$-0.0242117\pi$
$674$	−23.1281	−	13.3530i	−0.890860	−	0.514338i
$675$	−3.15662	+	4.12744i	−0.121499	+	0.158865i
$676$	−3.97722			−0.152970
$677$	45.0353			1.73085			0.865424	−	0.501040i	$-0.167049\pi$
$677$	45.0353			1.73085			0.865424	+	0.501040i	$0.167049\pi$
$678$	−11.8945	+	18.6925i	−0.456804	+	0.717883i
$679$	37.3215	−	21.5476i	1.43227	−	0.826920i
$680$	−1.28666	+	2.22857i	−0.0493413	+	0.0854616i
$681$	4.13913	+	7.94087i	0.158612	+	0.304295i
$682$	6.54788	+	11.3413i	0.250731	+	0.434279i
$683$	−36.9898			−1.41538			−0.707688	−	0.706525i	$-0.750262\pi$
$683$	−36.9898			−1.41538			−0.707688	+	0.706525i	$0.750262\pi$
$684$	10.9213	+	7.19205i	0.417586	+	0.274995i
$685$	6.51561			0.248949
$686$	−18.0586	−	31.2784i	−0.689479	−	1.19421i
$687$	−10.0611	−	19.3021i	−0.383856	−	0.736422i
$688$	2.86613	−	4.96428i	0.109270	−	0.189261i
$689$	−32.6389	+	18.8441i	−1.24344	+	0.717903i
$690$	−0.629427	+	0.989165i	−0.0239619	+	0.0376569i
$691$	40.1246			1.52641			0.763206	−	0.646155i	$-0.223624\pi$
$691$	40.1246			1.52641			0.763206	+	0.646155i	$0.223624\pi$
$692$	−8.04881			−0.305970
$693$	−34.9517	−	24.4180i	−1.32771	−	0.927564i
$694$	−14.4663	−	8.35210i	−0.549132	−	0.317041i
$695$			8.22199i			0.311878i
$696$	−3.43390	−	0.148094i	−0.130162	−	0.00561351i
$697$	−7.38506	−	4.26376i	−0.279729	−	0.161502i
$698$	16.1384	+	27.9525i	0.610847	+	1.05802i
$699$	35.1127	+	22.3429i	1.32808	+	0.845087i
$700$	−2.33159	−	4.03843i	−0.0881257	−	0.152638i
$701$	−35.9481	+	20.7546i	−1.35774	+	0.783892i	−0.989319	−	0.145766i	$-0.953435\pi$
$701$	−35.9481	+	20.7546i	−1.35774	+	0.783892i	−0.368422	+	0.929659i	$0.620102\pi$
$702$	2.76062	−	21.2312i	0.104193	−	0.801320i
$703$	−10.2639	−	16.7017i	−0.387112	−	0.629916i
$704$		−	3.04774i		−	0.114866i
$705$	−7.01543	−	13.4590i	−0.264216	−	0.506895i
$706$	13.2366	−	7.64215i	0.498166	−	0.287616i
$707$	−46.1931	−	26.6696i	−1.73727	−	1.00301i
$708$	9.64747	+	18.5085i	0.362574	+	0.695593i
$709$	−6.05340	+	10.4848i	−0.227340	+	0.393765i	−0.957019	−	0.290025i	$-0.906336\pi$
$709$	−6.05340	+	10.4848i	−0.227340	+	0.393765i	0.729679	+	0.683790i	$0.239670\pi$
$710$			12.5084i			0.469433i
$711$	−2.01175	+	23.2801i	−0.0754465	+	0.873072i
$712$	−4.81262	+	8.33571i	−0.180361	+	0.312394i
$713$	1.45430	−	2.51892i	0.0544640	−	0.0943345i
$714$	−0.895538	+	20.7651i	−0.0335147	+	0.777113i
$715$			12.5577i			0.469633i
$716$	4.76369	−	8.25095i	0.178027	−	0.308352i
$717$	−19.8428	+	10.3429i	−0.741041	+	0.386264i
$718$	−0.917556	−	0.529751i	−0.0342429	−	0.0197701i
$719$	43.2306	−	24.9592i	1.61223	−	0.930821i	0.623376	−	0.781922i	$-0.285760\pi$
$719$	43.2306	−	24.9592i	1.61223	−	0.930821i	0.988852	−	0.148899i	$-0.0475729\pi$
$720$	−2.71757	+	1.27075i	−0.101278	+	0.0473581i
$721$		−	81.4864i		−	3.03471i
$722$	18.9714	−	1.04247i	0.706042	−	0.0387967i
$723$	−1.58224	+	36.6878i	−0.0588441	+	1.36443i
$724$	14.9311	−	8.62045i	0.554909	−	0.320377i
$725$	−0.992204	−	1.71855i	−0.0368495	−	0.0638253i
$726$	−1.59124	+	2.50068i	−0.0590564	+	0.0928090i
$727$	3.21384	+	5.56653i	0.119195	+	0.206451i	0.919449	−	0.393210i	$-0.128635\pi$
$727$	3.21384	+	5.56653i	0.119195	+	0.206451i	−0.800254	+	0.599661i	$0.795302\pi$
$728$	16.6397	+	9.60693i	0.616708	+	0.356057i
$729$	26.1022	+	6.90471i	0.966748	+	0.255730i
$730$		−	4.37153i		−	0.161798i
$731$	−12.7747	−	7.37547i	−0.472489	−	0.272792i
$732$	12.9266	−	20.3146i	0.477781	−	0.750848i
$733$	−16.0152			−0.591537			−0.295768	−	0.955260i	$-0.595576\pi$
$733$	−16.0152			−0.591537			−0.295768	+	0.955260i	$0.595576\pi$
$734$	20.5013			0.756718
$735$	−21.5470	−	13.7108i	−0.794774	−	0.505732i
$736$	−0.586222	+	0.338456i	−0.0216084	+	0.0124756i
$737$	−4.51118	+	7.81359i	−0.166171	+	0.287817i
$738$	−4.21104	−	9.00553i	−0.155010	−	0.331498i
$739$	−9.73673	−	16.8645i	−0.358172	−	0.620371i	0.629484	−	0.777014i	$-0.283266\pi$
$739$	−9.73673	−	16.8645i	−0.358172	−	0.620371i	−0.987655	+	0.156642i	$0.949933\pi$
$740$	4.49734			0.165325
$741$	−15.1304	−	27.1804i	−0.555828	−	0.998497i
$742$	42.6534			1.56586
$743$	−25.7244	−	44.5560i	−0.943738	−	1.63460i	−0.758258	−	0.651955i	$-0.773949\pi$
$743$	−25.7244	−	44.5560i	−0.943738	−	1.63460i	−0.185480	−	0.982648i	$-0.559384\pi$
$744$	6.59966	−	3.44004i	0.241955	−	0.126118i
$745$	1.24894	−	2.16323i	0.0457577	−	0.0792546i
$746$	−12.8277	+	7.40608i	−0.469656	+	0.271156i
$747$	−6.43368	−	4.49470i	−0.235396	−	0.164453i
$748$	−7.84283			−0.286762
$749$	−87.7191			−3.20518
$750$	−1.46129	−	0.929852i	−0.0533589	−	0.0339534i
$751$	29.8285	+	17.2215i	1.08846	+	0.628421i	0.933165	−	0.359448i	$-0.117035\pi$
$751$	29.8285	+	17.2215i	1.08846	+	0.628421i	0.155292	+	0.987869i	$0.450368\pi$
$752$		−	8.76281i		−	0.319547i
$753$	1.40446	−	32.5655i	0.0511812	−	1.18675i
$754$	7.08101	+	4.08822i	0.257875	+	0.148884i
$755$	−4.68195	−	8.10937i	−0.170394	−	0.295130i
$756$	−14.7199	+	19.2469i	−0.535357	+	0.700005i
$757$	−5.05555	−	8.75646i	−0.183747	−	0.318259i	0.759407	−	0.650616i	$-0.225489\pi$
$757$	−5.05555	−	8.75646i	−0.183747	−	0.318259i	−0.943154	+	0.332357i	$0.892156\pi$
$758$	3.66524	−	2.11613i	0.133128	−	0.0768613i
$759$	−3.56999	−	0.153963i	−0.129582	−	0.00558852i
$760$	−2.07503	+	3.83331i	−0.0752693	+	0.139049i
$761$			27.1963i			0.985865i	0.870067	+	0.492933i	$0.164075\pi$
$761$			27.1963i			0.985865i	−0.870067	+	0.492933i	$0.835925\pi$
$762$	31.5508	−	16.4457i	1.14296	−	0.595764i
$763$	29.3781	−	16.9614i	1.06356	−	0.614045i
$764$	−12.9535	−	7.47873i	−0.468643	−	0.270571i
$765$	3.27006	+	6.99319i	0.118229	+	0.252839i
$766$	−11.7377	+	20.3303i	−0.424100	+	0.734563i
$767$		−	49.6519i		−	1.79283i
$768$	−1.73044	−	0.0746290i	−0.0624420	−	0.00269294i
$769$	−8.24048	+	14.2729i	−0.297159	+	0.514695i	−0.975485	−	0.220067i	$-0.929373\pi$
$769$	−8.24048	+	14.2729i	−0.297159	+	0.514695i	0.678326	+	0.734761i	$0.262706\pi$
$770$	7.10607	−	12.3081i	0.256085	−	0.443552i
$771$	−13.8591	−	0.597702i	−0.499122	−	0.0215257i
$772$			20.8953i			0.752037i
$773$	−1.86208	+	3.22522i	−0.0669743	+	0.116003i	−0.897568	−	0.440876i	$-0.854668\pi$
$773$	−1.86208	+	3.22522i	−0.0669743	+	0.116003i	0.830594	+	0.556879i	$0.188001\pi$
$774$	−7.28427	−	15.5778i	−0.261828	−	0.559932i
$775$	3.72120	+	2.14844i	0.133670	+	0.0771742i
$776$	8.00346	−	4.62080i	0.287307	−	0.165877i
$777$	32.2112	−	16.7899i	1.15557	−	0.602334i
$778$			17.1058i			0.613272i
$779$	−12.7029	−	6.87627i	−0.455128	−	0.246368i
$780$	7.13001	+	0.307497i	0.255295	+	0.0110102i
$781$	−33.0150	+	19.0612i	−1.18137	+	0.682065i
$782$	0.870956	+	1.50854i	0.0311453	+	0.0539453i
$783$	−6.26403	+	8.19052i	−0.223858	+	0.292705i
$784$	−7.37259	−	12.7697i	−0.263307	−	0.456061i
$785$	−13.3605	−	7.71370i	−0.476857	−	0.275314i
$786$	0.283248	−	6.56773i	0.0101031	−	0.234263i
$787$		−	1.38060i		−	0.0492131i	−0.999697	−	0.0246066i	$-0.992167\pi$
$787$		−	1.38060i		−	0.0492131i	0.999697	−	0.0246066i	$-0.00783330\pi$
$788$	19.6190	+	11.3270i	0.698899	+	0.403509i
$789$	−41.5976	−	26.4694i	−1.48091	−	0.942336i
$790$	−7.78896			−0.277119
$791$	−59.6503			−2.12092
$792$	−7.49527	−	5.23635i	−0.266333	−	0.186066i
$793$	−49.6060	+	28.6401i	−1.76156	+	1.01704i
$794$	−3.27587	+	5.67397i	−0.116256	+	0.201362i
$795$	14.0489	−	7.32289i	0.498262	−	0.259716i
$796$	3.33437	+	5.77531i	0.118184	+	0.204700i
$797$	−16.3638			−0.579634			−0.289817	−	0.957082i	$-0.593594\pi$
$797$	−16.3638			−0.579634			−0.289817	+	0.957082i	$0.593594\pi$
$798$	−0.551068	+	35.2019i	−0.0195076	+	1.24613i
$799$	−22.5496			−0.797747
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	12.2313	+	26.1573i	0.432171	+	0.924222i
$802$	12.4043	−	21.4849i	0.438012	−	0.758658i
$803$	11.5383	−	6.66165i	0.407178	−	0.235085i
$804$	4.32592	+	2.75268i	0.152564	+	0.0970795i
$805$	−3.15655			−0.111254
$806$	−17.7046			−0.623618
$807$	5.46184	−	8.58345i	0.192266	−	0.302152i
$808$	−9.90594	−	5.71920i	−0.348490	−	0.201201i
$809$		−	3.23485i		−	0.113731i	−0.998382	−	0.0568657i	$-0.981889\pi$
$809$		−	3.23485i		−	0.113731i	0.998382	−	0.0568657i	$-0.0181107\pi$
$810$	−1.54394	+	8.86658i	−0.0542485	+	0.311540i
$811$	34.3026	+	19.8046i	1.20453	+	0.695434i	0.961558	−	0.274601i	$-0.0885457\pi$
$811$	34.3026	+	19.8046i	1.20453	+	0.695434i	0.242968	+	0.970034i	$0.421879\pi$
$812$	−4.62682	−	8.01389i	−0.162370	−	0.281232i
$813$	12.7456	−	20.0301i	0.447006	−	0.702485i
$814$	6.85336	+	11.8704i	0.240210	+	0.416056i
$815$	−6.87941	+	3.97183i	−0.240975	+	0.139127i
$816$	−0.192045	+	4.45299i	−0.00672291	+	0.155886i
$817$	−21.9735	−	11.8946i	−0.768755	−	0.416139i
$818$			3.39700i			0.118773i
$819$	52.2150	−	24.4160i	1.82454	−	0.853166i
$820$	2.86985	−	1.65691i	0.100219	−	0.0578618i
$821$	47.1571	+	27.2262i	1.64580	+	0.950200i	0.978717	+	0.205213i	$0.0657886\pi$
$821$	47.1571	+	27.2262i	1.64580	+	0.950200i	0.667078	+	0.744988i	$0.267545\pi$
$822$	10.0075	−	5.21634i	0.349051	−	0.181941i
$823$	−26.5810	+	46.0397i	−0.926556	+	1.60484i	−0.137517	+	0.990499i	$0.543912\pi$
$823$	−26.5810	+	46.0397i	−0.926556	+	1.60484i	−0.789039	+	0.614343i	$0.789421\pi$
$824$		−	17.4744i		−	0.608751i
$825$	0.227450	−	5.27394i	0.00791879	−	0.183615i
$826$	−28.0966	+	48.6648i	−0.977607	+	1.69327i
$827$	−12.2301	+	21.1832i	−0.425282	+	0.736610i	−0.996447	−	0.0842252i	$-0.973158\pi$
$827$	−12.2301	+	21.1832i	−0.425282	+	0.736610i	0.571165	+	0.820836i	$0.306492\pi$
$828$	−0.174834	+	2.02319i	−0.00607591	+	0.0703108i
$829$		−	16.6270i		−	0.577480i	−0.957408	−	0.288740i	$-0.906764\pi$
$829$		−	16.6270i		−	0.577480i	0.957408	−	0.288740i	$-0.0932364\pi$
$830$	1.30804	−	2.26559i	0.0454026	−	0.0786397i
$831$	12.1653	+	23.3390i	0.422010	+	0.809620i
$832$	3.56832	+	2.06017i	0.123709	+	0.0714236i
$833$	−32.8606	+	18.9721i	−1.13855	+	0.657343i
$834$	6.58245	+	12.6283i	0.227932	+	0.437283i
$835$			5.95826i			0.206194i
$836$	−13.2798	+	0.364584i	−0.459291	+	0.0126094i
$837$	2.87890	−	22.1408i	0.0995093	−	0.765299i
$838$	−22.0201	+	12.7133i	−0.760672	+	0.439174i
$839$	−6.13190	−	10.6208i	−0.211697	−	0.366669i	0.740549	−	0.672002i	$-0.234566\pi$
$839$	−6.13190	−	10.6208i	−0.211697	−	0.366669i	−0.952246	+	0.305333i	$0.901232\pi$
$840$	−6.81426	−	4.33606i	−0.235114	−	0.149608i
$841$	12.5311	+	21.7044i	0.432106	+	0.748429i
$842$	9.79175	+	5.65327i	0.337446	+	0.194825i
$843$	−14.7990	−	0.638237i	−0.509704	−	0.0219821i
$844$			24.7025i			0.850297i
$845$	−3.44437	−	1.98861i	−0.118490	−	0.0684102i
$846$	−21.5503	−	15.0555i	−0.740914	−	0.517618i
$847$	−7.98000			−0.274196
$848$	9.14686			0.314104
$849$	26.3853	−	41.4653i	0.905540	−	1.42309i
$850$	−2.22857	+	1.28666i	−0.0764391	+	0.0441322i
$851$	1.52215	−	2.63644i	0.0521786	−	0.0903760i
$852$	10.0141	+	19.2120i	0.343079	+	0.658192i
$853$	−17.0728	−	29.5710i	−0.584562	−	1.01249i	−0.994930	−	0.100571i	$-0.967933\pi$
$853$	−17.0728	−	29.5710i	−0.584562	−	1.01249i	0.410368	−	0.911920i	$-0.365400\pi$
$854$	64.8264			2.21832
$855$	5.86208	+	11.6891i	0.200479	+	0.399760i
$856$	−18.8110			−0.642948
$857$	1.80576	+	3.12767i	0.0616837	+	0.106839i	0.895218	−	0.445628i	$-0.147020\pi$
$857$	1.80576	+	3.12767i	0.0616837	+	0.106839i	−0.833534	+	0.552468i	$0.813686\pi$
$858$	10.0536	+	19.2877i	0.343224	+	0.658471i
$859$	−0.655628	+	1.13558i	−0.0223697	+	0.0387455i	−0.876994	−	0.480502i	$-0.840454\pi$
$859$	−0.655628	+	1.13558i	−0.0223697	+	0.0387455i	0.854624	+	0.519248i	$0.173788\pi$
$860$	4.96428	−	2.86613i	0.169280	−	0.0977341i
$861$	14.3689	−	22.5812i	0.489691	−	0.769566i
$862$	−0.421328			−0.0143505
$863$	5.56476			0.189427			0.0947134	−	0.995505i	$-0.469807\pi$
$863$	5.56476			0.189427			0.0947134	+	0.995505i	$0.469807\pi$
$864$	−3.15662	+	4.12744i	−0.107391	+	0.140418i
$865$	−6.97047	−	4.02441i	−0.237003	−	0.136834i
$866$			5.59372i			0.190082i
$867$	−17.9585	−	0.774500i	−0.609903	−	0.0263034i
$868$	17.3526	+	10.0185i	0.588986	+	0.340051i
$869$	−11.8694	−	20.5583i	−0.402640	−	0.697394i
$870$	−2.89980	−	1.84521i	−0.0983125	−	0.0625583i
$871$	−6.09881	−	10.5634i	−0.206650	−	0.357929i
$872$	6.30002	−	3.63732i	0.213346	−	0.123175i
$873$	2.38694	−	27.6218i	0.0807857	−	0.934858i
$874$	1.54486	+	2.51383i	0.0522558	+	0.0850317i
$875$		−	4.66317i		−	0.157644i
$876$	−3.49981	−	6.71433i	−0.118248	−	0.226856i
$877$	−23.6061	+	13.6290i	−0.797120	+	0.460218i	−0.842463	−	0.538754i	$-0.818895\pi$
$877$	−23.6061	+	13.6290i	−0.797120	+	0.460218i	0.0453429	+	0.998971i	$0.485562\pi$
$878$	−33.0674	−	19.0915i	−1.11597	−	0.644306i
$879$	5.78273	+	11.0941i	0.195047	+	0.374194i
$880$	1.52387	−	2.63942i	0.0513696	−	0.0889748i
$881$			32.5415i			1.09635i	0.836363	+	0.548176i	$0.184678\pi$
$881$			32.5415i			1.09635i	−0.836363	+	0.548176i	$0.815322\pi$
$882$	−44.0713	−	3.80842i	−1.48396	−	0.128236i
$883$	−19.8287	+	34.3444i	−0.667291	+	1.15578i	0.311368	+	0.950289i	$0.399213\pi$
$883$	−19.8287	+	34.3444i	−0.667291	+	1.15578i	−0.978659	+	0.205492i	$0.934121\pi$
$884$	5.30149	−	9.18245i	0.178308	−	0.308839i
$885$	−0.899313	+	20.8526i	−0.0302301	+	0.700952i
$886$		−	25.6463i		−	0.861604i
$887$	14.5283	−	25.1638i	0.487814	−	0.844918i	−0.512088	−	0.858933i	$-0.671128\pi$
$887$	14.5283	−	25.1638i	0.487814	−	0.844918i	0.999902	+	0.0140147i	$0.00446115\pi$
$888$	6.90756	−	3.60053i	0.231803	−	0.120826i
$889$	82.9571	+	47.8953i	2.78229	+	1.60636i
$890$	−8.33571	+	4.81262i	−0.279413	+	0.161319i
$891$	−25.7554	+	9.43641i	−0.862838	+	0.316132i
$892$		−	5.30705i		−	0.177693i
$893$	−38.1818	+	1.04825i	−1.27771	+	0.0350783i
$894$	0.186415	−	4.32244i	0.00623464	−	0.144564i
$895$	8.25095	−	4.76369i	0.275799	−	0.159233i
$896$	−2.33159	−	4.03843i	−0.0778928	−	0.134914i
$897$	2.59345	−	4.07570i	0.0865929	−	0.136084i
$898$	−11.8447	−	20.5156i	−0.395263	−	0.684615i
$899$	7.38439	+	4.26338i	0.246283	+	0.142192i
$900$	−2.98886	−	0.258282i	−0.0996287	−	0.00860941i
$901$		−	23.5378i		−	0.784159i
$902$	8.74656	+	5.04983i	0.291228	+	0.168141i
$903$	24.8554	−	39.0610i	0.827135	−	1.29987i
$904$	−12.7918			−0.425448
$905$	17.2409			0.573107
$906$	−13.6834	−	8.70704i	−0.454600	−	0.289272i
$907$	−22.5403	+	13.0136i	−0.748438	+	0.432111i	−0.825129	−	0.564944i	$-0.808898\pi$
$907$	−22.5403	+	13.0136i	−0.748438	+	0.432111i	0.0766912	+	0.997055i	$0.475564\pi$
$908$	−2.58505	+	4.47744i	−0.0857879	+	0.148589i
$909$	−31.0847	+	14.5354i	−1.03101	+	0.482107i
$910$	9.60693	+	16.6397i	0.318467	+	0.551601i
$911$	−47.2123			−1.56421			−0.782107	−	0.623144i	$-0.785855\pi$
$911$	−47.2123			−1.56421			−0.782107	+	0.623144i	$0.785855\pi$
$912$	−0.118175	+	7.54891i	−0.00391315	+	0.249969i
$913$	7.97312			0.263872
$914$	−8.64006	−	14.9650i	−0.285788	−	0.494999i
$915$	21.3521	−	11.1296i	0.705877	−	0.367935i
$916$	6.28356	−	10.8835i	0.207615	−	0.359599i
$917$	15.3275	−	8.84932i	0.506158	−	0.292230i
$918$	10.6212	+	8.12302i	0.350553	+	0.268100i
$919$	40.9787			1.35176			0.675881	−	0.737010i	$-0.263763\pi$
$919$	40.9787			1.35176			0.675881	+	0.737010i	$0.263763\pi$
$920$	−0.676911			−0.0223171
$921$	0.600756	+	0.382274i	0.0197956	+	0.0125963i
$922$	27.4943	+	15.8738i	0.905475	+	0.522776i
$923$		−	51.5391i		−	1.69643i
$924$	1.06064	−	24.5933i	0.0348924	−	0.809060i
$925$	3.89481	+	2.24867i	0.128061	+	0.0739358i
$926$	−12.2095	−	21.1475i	−0.401229	−	0.694949i
$927$	−42.9747	−	30.0230i	−1.41147	−	0.986085i
$928$	−0.992204	−	1.71855i	−0.0325707	−	0.0564141i
$929$	−21.9076	+	12.6484i	−0.718767	+	0.414980i	−0.814299	−	0.580446i	$-0.802878\pi$
$929$	−21.9076	+	12.6484i	−0.718767	+	0.414980i	0.0955319	+	0.995426i	$0.469545\pi$
$930$	7.43549	+	0.320672i	0.243819	+	0.0105152i
$931$	−54.7589	+	33.6518i	−1.79465	+	1.10289i
$932$			24.0285i			0.787079i
$933$	16.0719	−	8.37741i	0.526172	−	0.274264i
$934$	−11.6416	+	6.72127i	−0.380924	+	0.219927i
$935$	−6.79209	−	3.92141i	−0.222125	−	0.128244i
$936$	11.1973	−	5.23593i	0.365996	−	0.171142i
$937$	−2.97906	+	5.15989i	−0.0973218	+	0.168566i	−0.910575	−	0.413343i	$-0.864361\pi$
$937$	−2.97906	+	5.15989i	−0.0973218	+	0.168566i	0.813253	+	0.581910i	$0.197694\pi$
$938$			13.8046i			0.450736i
$939$	−3.01825	−	0.130169i	−0.0984970	−	0.00424789i
$940$	4.38141	−	7.58882i	0.142906	−	0.247520i
$941$	18.2842	−	31.6692i	0.596048	−	1.03239i	−0.397350	−	0.917667i	$-0.630070\pi$
$941$	18.2842	−	31.6692i	0.596048	−	1.03239i	0.993398	−	0.114719i	$-0.0365967\pi$
$942$	−26.6962	−	1.15133i	−0.869810	−	0.0375124i
$943$		−	2.24316i		−	0.0730473i
$944$	−6.02522	+	10.4360i	−0.196104	+	0.339663i
$945$	−22.3713	+	9.30840i	−0.727737	+	0.302802i
$946$	15.1298	+	8.73521i	0.491913	+	0.284006i
$947$	8.39698	−	4.84800i	0.272865	−	0.157539i	−0.357324	−	0.933981i	$-0.616311\pi$
$947$	8.39698	−	4.84800i	0.272865	−	0.157539i	0.630189	+	0.776442i	$0.282977\pi$
$948$	−11.9632	+	6.23576i	−0.388547	+	0.202528i
$949$			18.0122i			0.584701i
$950$	−3.71368	+	2.28223i	−0.120488	+	0.0740452i
$951$	−35.3091	−	1.52278i	−1.14498	−	0.0493796i
$952$	−10.3922	+	5.99993i	−0.336813	+	0.194459i
$953$	−5.66534	−	9.81266i	−0.183518	−	0.317863i	0.759558	−	0.650440i	$-0.225415\pi$
$953$	−5.66534	−	9.81266i	−0.183518	−	0.317863i	−0.943076	+	0.332577i	$0.892082\pi$
$954$	15.7153	−	22.4948i	0.508802	−	0.728295i
$955$	−7.47873	−	12.9535i	−0.242006	−	0.419167i
$956$	−11.1883	−	6.45956i	−0.361855	−	0.208917i
$957$	0.451353	−	10.4656i	0.0145902	−	0.338306i
$958$			9.75241i			0.315086i
$959$	26.3128	+	15.1917i	0.849685	+	0.490566i
$960$	−1.46129	−	0.929852i	−0.0471630	−	0.0300108i
$961$	12.5369			0.404415
$962$	−18.5306			−0.597450
$963$	−32.3194	+	46.2617i	−1.04148	+	1.49076i
$964$	−18.3610	+	10.6007i	−0.591366	+	0.341426i
$965$	−10.4476	+	18.0958i	−0.336321	+	0.582526i
$966$	−4.84822	+	2.52711i	−0.155989	+	0.0813084i
$967$	7.32741	+	12.6915i	0.235634	+	0.408130i	0.959457	−	0.281856i	$-0.0909501\pi$
$967$	7.32741	+	12.6915i	0.235634	+	0.408130i	−0.723823	+	0.689986i	$0.757617\pi$
$968$	−1.71128			−0.0550026
$969$	19.4258	+	0.304101i	0.624047	+	0.00976915i
$970$	9.24160			0.296730
$971$	13.8936	+	24.0645i	0.445868	+	0.772266i	0.998112	−	0.0614163i	$-0.0195617\pi$
$971$	13.8936	+	24.0645i	0.445868	+	0.772266i	−0.552244	+	0.833682i	$0.686228\pi$
$972$	4.72713	+	14.8544i	0.151623	+	0.476456i
$973$	−19.1703	+	33.2039i	−0.614571	+	1.06447i
$974$	−13.8674	+	8.00637i	−0.444341	+	0.256541i
$975$	6.02102	+	3.83131i	0.192827	+	0.122700i
$976$	13.9018			0.444985
$977$	−57.1541			−1.82852			−0.914261	−	0.405125i	$-0.867228\pi$
$977$	−57.1541			−1.82852			−0.914261	+	0.405125i	$0.867228\pi$
$978$	−7.38643	+	11.6080i	−0.236192	+	0.371183i
$979$	−25.4051	−	14.6676i	−0.811949	−	0.468779i
$980$		−	14.7452i		−	0.471018i
$981$	1.87891	−	21.7429i	0.0599890	−	0.694197i
$982$	−18.5831	−	10.7290i	−0.593012	−	0.342375i
$983$	−15.6251	−	27.0635i	−0.498363	−	0.863190i	0.501635	−	0.865079i	$-0.332732\pi$
$983$	−15.6251	−	27.0635i	−0.498363	−	0.863190i	−0.999998	+	0.00188891i	$0.999399\pi$
$984$	3.08136	−	4.84246i	0.0982301	−	0.154372i
$985$	11.3270	+	19.6190i	0.360910	+	0.625114i
$986$	−4.42238	+	2.55326i	−0.140837	+	0.0813125i
$987$	3.04953	−	70.7102i	0.0970676	−	2.25073i
$988$	8.54984	−	15.7945i	0.272007	−	0.502491i
$989$		−	3.88023i		−	0.123384i
$990$	−3.87292	−	8.28245i	−0.123089	−	0.263234i
$991$	−37.0778	+	21.4069i	−1.17782	+	0.680012i	−0.955508	−	0.294965i	$-0.904692\pi$
$991$	−37.0778	+	21.4069i	−1.17782	+	0.680012i	−0.222307	+	0.974977i	$0.571359\pi$
$992$	3.72120	+	2.14844i	0.118148	+	0.0682130i
$993$	−5.30131	+	2.76328i	−0.168232	+	0.0876900i
$994$	−29.1645	+	50.5144i	−0.925042	+	1.60222i
$995$			6.66875i			0.211414i
$996$	0.195235	−	4.52697i	0.00618626	−	0.143442i
$997$	0.595831	−	1.03201i	0.0188702	−	0.0326841i	−0.856436	−	0.516253i	$-0.827326\pi$
$997$	0.595831	−	1.03201i	0.0188702	−	0.0326841i	0.875306	+	0.483569i	$0.160660\pi$
$998$	−9.93532	+	17.2085i	−0.314497	+	0.544725i
$999$	3.01321	−	23.1738i	0.0953338	−	0.733186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.221.8	yes	24
3.2	odd	2		570.2.s.a.221.4	✓	24
19.8	odd	6		570.2.s.a.521.4	yes	24
57.8	even	6	inner	570.2.s.b.521.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.4	✓	24	3.2	odd	2
570.2.s.a.521.4	yes	24	19.8	odd	6
570.2.s.b.221.8	yes	24	1.1	even	1	trivial
570.2.s.b.521.8	yes	24	57.8	even	6	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.800591 + 1.53592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.929852 + 1.46129i) q^{6} -4.66317 q^{7} -1.00000 q^{8} +(-1.71811 + 2.45929i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.800591 + 1.53592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.929852 + 1.46129i) q^{6} -4.66317 q^{7} -1.00000 q^{8} +(-1.71811 + 2.45929i) q^{9} +(-0.866025 - 0.500000i) q^{10} -3.04774i q^{11} +(-1.73044 - 0.0746290i) q^{12} +(3.56832 + 2.06017i) q^{13} +(-2.33159 - 4.03843i) q^{14} +(-1.46129 - 0.929852i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.22857 + 1.28666i) q^{17} +(-2.98886 - 0.258282i) q^{18} +(-3.71368 + 2.28223i) q^{19} -1.00000i q^{20} +(-3.73329 - 7.16227i) q^{21} +(2.63942 - 1.52387i) q^{22} +(-0.586222 - 0.338456i) q^{23} +(-0.800591 - 1.53592i) q^{24} +(0.500000 - 0.866025i) q^{25} +4.12034i q^{26} +(-5.15278 - 0.669999i) q^{27} +(2.33159 - 4.03843i) q^{28} +(0.992204 - 1.71855i) q^{29} +(0.0746290 - 1.73044i) q^{30} +4.29688i q^{31} +(0.500000 - 0.866025i) q^{32} +(4.68109 - 2.43999i) q^{33} +(-2.22857 - 1.28666i) q^{34} +(4.03843 - 2.33159i) q^{35} +(-1.27075 - 2.71757i) q^{36} +4.49734i q^{37} +(-3.83331 - 2.07503i) q^{38} +(-0.307497 + 7.13001i) q^{39} +(0.866025 - 0.500000i) q^{40} +(1.65691 + 2.86985i) q^{41} +(4.33606 - 6.81426i) q^{42} +(2.86613 + 4.96428i) q^{43} +(2.63942 + 1.52387i) q^{44} +(0.258282 - 2.98886i) q^{45} -0.676911i q^{46} +(7.58882 + 4.38141i) q^{47} +(0.929852 - 1.46129i) q^{48} +14.7452 q^{49} +1.00000 q^{50} +(-3.76038 - 2.39281i) q^{51} +(-3.56832 + 2.06017i) q^{52} +(-4.57343 + 7.92141i) q^{53} +(-1.99615 - 4.79743i) q^{54} +(1.52387 + 2.63942i) q^{55} +4.66317 q^{56} +(-6.47846 - 3.87680i) q^{57} +1.98441 q^{58} +(-6.02522 - 10.4360i) q^{59} +(1.53592 - 0.800591i) q^{60} +(-6.95089 + 12.0393i) q^{61} +(-3.72120 + 2.14844i) q^{62} +(8.01184 - 11.4681i) q^{63} +1.00000 q^{64} -4.12034 q^{65} +(4.45364 + 2.83395i) q^{66} +(-2.56373 - 1.48017i) q^{67} -2.57333i q^{68} +(0.0505172 - 1.17136i) q^{69} +(4.03843 + 2.33159i) q^{70} +(-6.25422 - 10.8326i) q^{71} +(1.71811 - 2.45929i) q^{72} +(2.18577 + 3.78586i) q^{73} +(-3.89481 + 2.24867i) q^{74} +(1.73044 + 0.0746290i) q^{75} +(-0.119625 - 4.35726i) q^{76} +14.2121i q^{77} +(-6.32852 + 3.29871i) q^{78} +(6.74543 - 3.89448i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-3.09620 - 8.45065i) q^{81} +(-1.65691 + 2.86985i) q^{82} +2.61607i q^{83} +(8.06935 + 0.348008i) q^{84} +(1.28666 - 2.22857i) q^{85} +(-2.86613 + 4.96428i) q^{86} +(3.43390 + 0.148094i) q^{87} +3.04774i q^{88} +(4.81262 - 8.33571i) q^{89} +(2.71757 - 1.27075i) q^{90} +(-16.6397 - 9.60693i) q^{91} +(0.586222 - 0.338456i) q^{92} +(-6.59966 + 3.44004i) q^{93} +8.76281i q^{94} +(2.07503 - 3.83331i) q^{95} +(1.73044 + 0.0746290i) q^{96} +(-8.00346 + 4.62080i) q^{97} +(7.37259 + 12.7697i) q^{98} +(7.49527 + 5.23635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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