LMFDB - Embedded newform 105.3.l.a.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(22,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.6
Character	$\chi$	$=$	105.22
Dual form			105.3.l.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +(2.25992 - 1.79965i) q^{10} -6.25808 q^{11} +(4.49011 + 4.49011i) q^{12} +(16.4621 - 16.4621i) q^{13} -1.52868i q^{14} +(5.39486 + 6.77462i) q^{15} -12.1054 q^{16} +(20.4811 + 20.4811i) q^{17} +(1.22567 - 1.22567i) q^{18} -7.15227i q^{19} +(-18.2141 - 2.06511i) q^{20} +4.58258 q^{21} +(-2.55679 - 2.55679i) q^{22} +(-12.0129 + 12.0129i) q^{23} +7.67197i q^{24} +(-24.3654 - 5.59702i) q^{25} +13.4514 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.85876 + 6.85876i) q^{28} +18.1286i q^{29} +(-0.563715 + 4.97193i) q^{30} -33.3500 q^{31} +(-17.4740 - 17.4740i) q^{32} +(7.66455 - 7.66455i) q^{33} +16.7354i q^{34} +(-10.3484 + 8.24078i) q^{35} -10.9985 q^{36} +(18.8529 + 18.8529i) q^{37} +(2.92211 - 2.92211i) q^{38} +40.3237i q^{39} +(-13.7964 - 17.3249i) q^{40} +50.8319 q^{41} +(1.87225 + 1.87225i) q^{42} +(53.3589 - 53.3589i) q^{43} +22.9431i q^{44} +(-14.9045 - 1.68986i) q^{45} -9.81596 q^{46} +(46.9338 + 46.9338i) q^{47} +(14.8260 - 14.8260i) q^{48} +7.00000i q^{49} +(-7.66797 - 12.2414i) q^{50} -50.1682 q^{51} +(-60.3527 - 60.3527i) q^{52} +(-28.9805 + 28.9805i) q^{53} +3.00227i q^{54} +(-3.52510 + 31.0912i) q^{55} -11.7191 q^{56} +(8.75971 + 8.75971i) q^{57} +(-7.40656 + 7.40656i) q^{58} -10.0079i q^{59} +(24.8369 - 19.7784i) q^{60} +85.6806 q^{61} +(-13.6254 - 13.6254i) q^{62} +(-5.61249 + 5.61249i) q^{63} +34.1432i q^{64} +(-72.5135 - 91.0593i) q^{65} +6.26283 q^{66} +(11.9931 + 11.9931i) q^{67} +(75.0869 - 75.0869i) q^{68} -29.4256i q^{69} +(-7.59476 - 0.861089i) q^{70} -20.8660 q^{71} +(-9.39621 - 9.39621i) q^{72} +(35.2913 - 35.2913i) q^{73} +15.4050i q^{74} +(36.6963 - 22.9865i) q^{75} -26.2214 q^{76} +(11.7078 + 11.7078i) q^{77} +(-16.4746 + 16.4746i) q^{78} +31.9858i q^{79} +(-6.81882 + 60.1416i) q^{80} -9.00000 q^{81} +(20.7677 + 20.7677i) q^{82} +(6.49178 - 6.49178i) q^{83} -16.8005i q^{84} +(113.290 - 90.2167i) q^{85} +43.6003 q^{86} +(-22.2029 - 22.2029i) q^{87} +(-19.6007 + 19.6007i) q^{88} -145.472i q^{89} +(-5.39894 - 6.77976i) q^{90} -61.5955 q^{91} +(44.0414 + 44.0414i) q^{92} +(40.8453 - 40.8453i) q^{93} +38.3503i q^{94} +(-35.5337 - 4.02879i) q^{95} +42.8024 q^{96} +(31.5344 + 31.5344i) q^{97} +(-2.85990 + 2.85990i) q^{98} +18.7742i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.408558	+	0.408558i	0.204279	+	0.204279i	0.801830	−	0.597552i	$-0.203860\pi$
$2$	0.408558	+	0.408558i	0.204279	+	0.204279i	−0.597552	+	0.801830i	$0.703860\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		−	3.66616i		−	0.916540i
$5$	0.563288	−	4.96817i	0.112658	−	0.993634i
$5$	0.563288	−	4.96817i	0.112658	−	0.993634i
$6$	−1.00076			−0.166793
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	3.13207	−	3.13207i	0.391509	−	0.391509i
$9$		−	3.00000i		−	0.333333i
$10$	2.25992	−	1.79965i	0.225992	−	0.179965i
$11$	−6.25808			−0.568917			−0.284458	−	0.958688i	$-0.591814\pi$
$11$	−6.25808			−0.568917			−0.284458	+	0.958688i	$0.591814\pi$
$12$	4.49011	+	4.49011i	0.374176	+	0.374176i
$13$	16.4621	−	16.4621i	1.26631	−	1.26631i	0.318337	−	0.947978i	$-0.396876\pi$
$13$	16.4621	−	16.4621i	1.26631	−	1.26631i	0.947978	−	0.318337i	$-0.103124\pi$
$14$		−	1.52868i		−	0.109192i
$15$	5.39486	+	6.77462i	0.359657	+	0.451642i
$16$	−12.1054			−0.756586
$17$	20.4811	+	20.4811i	1.20477	+	1.20477i	0.972699	+	0.232071i	$0.0745500\pi$
$17$	20.4811	+	20.4811i	1.20477	+	1.20477i	0.232071	+	0.972699i	$0.425450\pi$
$18$	1.22567	−	1.22567i	0.0680929	−	0.0680929i
$19$		−	7.15227i		−	0.376435i	−0.982127	−	0.188218i	$-0.939729\pi$
$19$		−	7.15227i		−	0.376435i	0.982127	−	0.188218i	$-0.0602710\pi$
$20$	−18.2141	−	2.06511i	−0.910705	−	0.103255i
$21$	4.58258			0.218218
$22$	−2.55679	−	2.55679i	−0.116218	−	0.116218i
$23$	−12.0129	+	12.0129i	−0.522302	+	0.522302i	−0.918266	−	0.395964i	$-0.870410\pi$
$23$	−12.0129	+	12.0129i	−0.522302	+	0.522302i	0.395964	+	0.918266i	$0.370410\pi$
$24$			7.67197i			0.319665i
$25$	−24.3654	−	5.59702i	−0.974617	−	0.223881i
$26$	13.4514			0.517362
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−6.85876	+	6.85876i	−0.244956	+	0.244956i
$29$			18.1286i			0.625123i	0.949898	+	0.312561i	$0.101187\pi$
$29$			18.1286i			0.625123i	−0.949898	+	0.312561i	$0.898813\pi$
$30$	−0.563715	+	4.97193i	−0.0187905	+	0.165731i
$31$	−33.3500			−1.07581			−0.537904	−	0.843006i	$-0.680784\pi$
$31$	−33.3500			−1.07581			−0.537904	+	0.843006i	$0.680784\pi$
$32$	−17.4740	−	17.4740i	−0.546063	−	0.546063i
$33$	7.66455	−	7.66455i	0.232259	−	0.232259i
$34$			16.7354i			0.492218i
$35$	−10.3484	+	8.24078i	−0.295669	+	0.235451i
$36$	−10.9985			−0.305513
$37$	18.8529	+	18.8529i	0.509538	+	0.509538i	0.914384	−	0.404847i	$-0.132675\pi$
$37$	18.8529	+	18.8529i	0.509538	+	0.509538i	−0.404847	+	0.914384i	$0.632675\pi$
$38$	2.92211	−	2.92211i	0.0768978	−	0.0768978i
$39$			40.3237i			1.03394i
$40$	−13.7964	−	17.3249i	−0.344910	−	0.433123i
$41$	50.8319			1.23980			0.619901	−	0.784680i	$-0.287173\pi$
$41$	50.8319			1.23980			0.619901	+	0.784680i	$0.287173\pi$
$42$	1.87225	+	1.87225i	0.0445773	+	0.0445773i
$43$	53.3589	−	53.3589i	1.24090	−	1.24090i	0.281277	−	0.959627i	$-0.409242\pi$
$43$	53.3589	−	53.3589i	1.24090	−	1.24090i	0.959627	−	0.281277i	$-0.0907581\pi$
$44$			22.9431i			0.521435i
$45$	−14.9045	−	1.68986i	−0.331211	−	0.0375525i
$46$	−9.81596			−0.213390
$47$	46.9338	+	46.9338i	0.998592	+	0.998592i	0.999999	−	0.00140698i	$-0.000447856\pi$
$47$	46.9338	+	46.9338i	0.998592	+	0.998592i	−0.00140698	+	0.999999i	$0.500448\pi$
$48$	14.8260	−	14.8260i	0.308875	−	0.308875i
$49$			7.00000i			0.142857i
$50$	−7.66797	−	12.2414i	−0.153359	−	0.244828i
$51$	−50.1682			−0.983690
$52$	−60.3527	−	60.3527i	−1.16063	−	1.16063i
$53$	−28.9805	+	28.9805i	−0.546801	+	0.546801i	−0.925514	−	0.378713i	$-0.876367\pi$
$53$	−28.9805	+	28.9805i	−0.546801	+	0.546801i	0.378713	+	0.925514i	$0.376367\pi$
$54$			3.00227i			0.0555977i
$55$	−3.52510	+	31.0912i	−0.0640928	+	0.565295i
$56$	−11.7191			−0.209270
$57$	8.75971	+	8.75971i	0.153679	+	0.153679i
$58$	−7.40656	+	7.40656i	−0.127699	+	0.127699i
$59$		−	10.0079i		−	0.169626i	−0.996397	−	0.0848128i	$-0.972971\pi$
$59$		−	10.0079i		−	0.169626i	0.996397	−	0.0848128i	$-0.0270292\pi$
$60$	24.8369	−	19.7784i	0.413948	−	0.329640i
$61$	85.6806			1.40460			0.702300	−	0.711881i	$-0.252157\pi$
$61$	85.6806			1.40460			0.702300	+	0.711881i	$0.252157\pi$
$62$	−13.6254	−	13.6254i	−0.219765	−	0.219765i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$			34.1432i			0.533488i
$65$	−72.5135	−	91.0593i	−1.11559	−	1.40091i
$66$	6.26283			0.0948913
$67$	11.9931	+	11.9931i	0.179001	+	0.179001i	0.790920	−	0.611919i	$-0.209602\pi$
$67$	11.9931	+	11.9931i	0.179001	+	0.179001i	−0.611919	+	0.790920i	$0.709602\pi$
$68$	75.0869	−	75.0869i	1.10422	−	1.10422i
$69$		−	29.4256i		−	0.426458i
$70$	−7.59476	−	0.861089i	−0.108497	−	0.0123013i
$71$	−20.8660			−0.293887			−0.146943	−	0.989145i	$-0.546944\pi$
$71$	−20.8660			−0.293887			−0.146943	+	0.989145i	$0.546944\pi$
$72$	−9.39621	−	9.39621i	−0.130503	−	0.130503i
$73$	35.2913	−	35.2913i	0.483443	−	0.483443i	−0.422787	−	0.906229i	$-0.638948\pi$
$73$	35.2913	−	35.2913i	0.483443	−	0.483443i	0.906229	+	0.422787i	$0.138948\pi$
$74$			15.4050i			0.208176i
$75$	36.6963	−	22.9865i	0.489285	−	0.306487i
$76$	−26.2214			−0.345018
$77$	11.7078	+	11.7078i	0.152049	+	0.152049i
$78$	−16.4746	+	16.4746i	−0.211212	+	0.211212i
$79$			31.9858i			0.404884i	0.979294	+	0.202442i	$0.0648877\pi$
$79$			31.9858i			0.404884i	−0.979294	+	0.202442i	$0.935112\pi$
$80$	−6.81882	+	60.1416i	−0.0852352	+	0.751770i
$81$	−9.00000			−0.111111
$82$	20.7677	+	20.7677i	0.253265	+	0.253265i
$83$	6.49178	−	6.49178i	0.0782142	−	0.0782142i	−0.666917	−	0.745132i	$-0.732387\pi$
$83$	6.49178	−	6.49178i	0.0782142	−	0.0782142i	0.745132	+	0.666917i	$0.232387\pi$
$84$		−	16.8005i		−	0.200005i
$85$	113.290	−	90.2167i	1.33283	−	1.06137i
$86$	43.6003			0.506981
$87$	−22.2029	−	22.2029i	−0.255205	−	0.255205i
$88$	−19.6007	+	19.6007i	−0.222736	+	0.222736i
$89$		−	145.472i		−	1.63452i	−0.576273	−	0.817258i	$-0.695493\pi$
$89$		−	145.472i		−	1.63452i	0.576273	−	0.817258i	$-0.304507\pi$
$90$	−5.39894	−	6.77976i	−0.0599883	−	0.0753306i
$91$	−61.5955			−0.676873
$92$	44.0414	+	44.0414i	0.478711	+	0.478711i
$93$	40.8453	−	40.8453i	0.439197	−	0.439197i
$94$			38.3503i			0.407982i
$95$	−35.5337	−	4.02879i	−0.374039	−	0.0424083i
$96$	42.8024			0.445859
$97$	31.5344	+	31.5344i	0.325097	+	0.325097i	0.850719	−	0.525621i	$-0.176167\pi$
$97$	31.5344	+	31.5344i	0.325097	+	0.325097i	−0.525621	+	0.850719i	$0.676167\pi$
$98$	−2.85990	+	2.85990i	−0.0291827	+	0.0291827i
$99$			18.7742i			0.189639i
$100$	−20.5196	+	89.3275i	−0.205196	+	0.893275i
$101$	−128.207			−1.26938			−0.634688	−	0.772768i	$-0.718871\pi$
$101$	−128.207			−1.26938			−0.634688	+	0.772768i	$0.718871\pi$
$102$	−20.4966	−	20.4966i	−0.200947	−	0.200947i
$103$	−89.6356	+	89.6356i	−0.870248	+	0.870248i	−0.992499	−	0.122251i	$-0.960989\pi$
$103$	−89.6356	+	89.6356i	−0.870248	+	0.870248i	0.122251	+	0.992499i	$0.460989\pi$
$104$		−	103.121i		−	0.991546i
$105$	2.58131	−	22.7670i	0.0245839	−	0.216829i
$106$	−23.6804			−0.223400
$107$	32.4213	+	32.4213i	0.303003	+	0.303003i	0.842188	−	0.539185i	$-0.181268\pi$
$107$	32.4213	+	32.4213i	0.303003	+	0.303003i	−0.539185	+	0.842188i	$0.681268\pi$
$108$	13.4703	−	13.4703i	0.124725	−	0.124725i
$109$			87.2642i			0.800589i	0.916387	+	0.400294i	$0.131092\pi$
$109$			87.2642i			0.800589i	−0.916387	+	0.400294i	$0.868908\pi$
$110$	−14.1428	+	11.2623i	−0.128571	+	0.102385i
$111$	−46.1800			−0.416036
$112$	22.6471	+	22.6471i	0.202206	+	0.202206i
$113$	−14.4360	+	14.4360i	−0.127752	+	0.127752i	−0.768092	−	0.640340i	$-0.778794\pi$
$113$	−14.4360	+	14.4360i	−0.127752	+	0.127752i	0.640340	+	0.768092i	$0.278794\pi$
$114$			7.15769i			0.0627868i
$115$	52.9156	+	66.4491i	0.460136	+	0.577818i
$116$	66.4622			0.572950
$117$	−49.3863	−	49.3863i	−0.422105	−	0.422105i
$118$	4.08881	−	4.08881i	0.0346509	−	0.0346509i
$119$		−	76.6332i		−	0.643976i
$120$	38.1157	+	4.32153i	0.317630	+	0.0360128i
$121$	−81.8364			−0.676334
$122$	35.0055	+	35.0055i	0.286930	+	0.286930i
$123$	−62.2561	+	62.2561i	−0.506147	+	0.506147i
$124$			122.267i			0.986021i
$125$	−41.5317	+	117.899i	−0.332254	+	0.943190i
$126$	−4.58605			−0.0363972
$127$	−54.2946	−	54.2946i	−0.427517	−	0.427517i	0.460265	−	0.887782i	$-0.347754\pi$
$127$	−54.2946	−	54.2946i	−0.427517	−	0.427517i	−0.887782	+	0.460265i	$0.847754\pi$
$128$	−83.8456	+	83.8456i	−0.655044	+	0.655044i
$129$			130.702i			1.01319i
$130$	7.57703	−	66.8289i	0.0582848	−	0.514069i
$131$	36.7377			0.280440			0.140220	−	0.990120i	$-0.455219\pi$
$131$	36.7377			0.280440			0.140220	+	0.990120i	$0.455219\pi$
$132$	−28.0995	−	28.0995i	−0.212875	−	0.212875i
$133$	−13.3807	+	13.3807i	−0.100607	+	0.100607i
$134$			9.79973i			0.0731323i
$135$	20.3239	−	16.1846i	0.150547	−	0.119886i
$136$	128.296			0.943355
$137$	−90.1192	−	90.1192i	−0.657804	−	0.657804i	0.297056	−	0.954860i	$-0.403995\pi$
$137$	−90.1192	−	90.1192i	−0.657804	−	0.657804i	−0.954860	+	0.297056i	$0.903995\pi$
$138$	12.0220	−	12.0220i	0.0871163	−	0.0871163i
$139$			88.5028i			0.636711i	0.947971	+	0.318355i	$0.103131\pi$
$139$			88.5028i			0.636711i	−0.947971	+	0.318355i	$0.896869\pi$
$140$	30.2120	+	37.9389i	0.215800	+	0.270992i
$141$	−114.964			−0.815347
$142$	−8.52495	−	8.52495i	−0.0600349	−	0.0600349i
$143$	−103.021	+	103.021i	−0.720427	+	0.720427i
$144$			36.3161i			0.252195i
$145$	90.0657	+	10.2116i	0.621143	+	0.0704248i
$146$	28.8371			0.197514
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	69.1177	−	69.1177i	0.467012	−	0.467012i
$149$		−	205.375i		−	1.37835i	−0.724594	−	0.689176i	$-0.757973\pi$
$149$		−	205.375i		−	1.37835i	0.724594	−	0.689176i	$-0.242027\pi$
$150$	24.3839	+	5.60126i	0.162559	+	0.0373418i
$151$	175.527			1.16243			0.581214	−	0.813751i	$-0.302578\pi$
$151$	175.527			1.16243			0.581214	+	0.813751i	$0.302578\pi$
$152$	−22.4014	−	22.4014i	−0.147378	−	0.147378i
$153$	61.4432	−	61.4432i	0.401590	−	0.401590i
$154$			9.56662i			0.0621209i
$155$	−18.7857	+	165.689i	−0.121198	+	1.06896i
$156$	147.833			0.947649
$157$	22.5653	+	22.5653i	0.143728	+	0.143728i	0.775310	−	0.631581i	$-0.217594\pi$
$157$	22.5653	+	22.5653i	0.143728	+	0.143728i	−0.631581	+	0.775310i	$0.717594\pi$
$158$	−13.0681	+	13.0681i	−0.0827092	+	0.0827092i
$159$		−	70.9874i		−	0.446461i
$160$	−96.6568	+	76.9710i	−0.604105	+	0.481069i
$161$	44.9483			0.279182
$162$	−3.67702	−	3.67702i	−0.0226976	−	0.0226976i
$163$	−6.70761	+	6.70761i	−0.0411510	+	0.0411510i	−0.727383	−	0.686232i	$-0.759264\pi$
$163$	−6.70761	+	6.70761i	−0.0411510	+	0.0411510i	0.686232	+	0.727383i	$0.259264\pi$
$164$		−	186.358i		−	1.13633i
$165$	−33.7615	−	42.3962i	−0.204615	−	0.256946i
$166$	5.30453			0.0319550
$167$	105.816	+	105.816i	0.633630	+	0.633630i	0.948977	−	0.315347i	$-0.102121\pi$
$167$	105.816	+	105.816i	0.633630	+	0.633630i	−0.315347	+	0.948977i	$0.602121\pi$
$168$	14.3529	−	14.3529i	0.0854342	−	0.0854342i
$169$		−	373.001i		−	2.20710i
$170$	83.1443	+	9.42686i	0.489084	+	0.0554521i
$171$	−21.4568			−0.125478
$172$	−195.622	−	195.622i	−1.13734	−	1.13734i
$173$	−174.772	+	174.772i	−1.01024	+	1.01024i	−0.0102943	+	0.999947i	$0.503277\pi$
$173$	−174.772	+	174.772i	−1.01024	+	1.01024i	−0.999947	+	0.0102943i	$0.996723\pi$
$174$		−	18.1423i		−	0.104266i
$175$	35.1124	+	56.0546i	0.200643	+	0.320312i
$176$	75.7565			0.430435
$177$	12.2571	+	12.2571i	0.0692494	+	0.0692494i
$178$	59.4336	−	59.4336i	0.333897	−	0.333897i
$179$		−	18.1770i		−	0.101547i	−0.998710	−	0.0507736i	$-0.983831\pi$
$179$		−	18.1770i		−	0.101547i	0.998710	−	0.0507736i	$-0.0161687\pi$
$180$	−6.19532	+	54.6423i	−0.0344184	+	0.303568i
$181$	−120.550			−0.666021			−0.333010	−	0.942923i	$-0.608064\pi$
$181$	−120.550			−0.666021			−0.333010	+	0.942923i	$0.608064\pi$
$182$	−25.1653	−	25.1653i	−0.138271	−	0.138271i
$183$	−104.937	+	104.937i	−0.573425	+	0.573425i
$184$			75.2507i			0.408971i
$185$	104.284	−	83.0447i	0.563697	−	0.448891i
$186$	33.3753			0.179437
$187$	−128.172	−	128.172i	−0.685413	−	0.685413i
$188$	172.067	−	172.067i	0.915250	−	0.915250i
$189$		−	13.7477i		−	0.0727393i
$190$	−12.8716	−	16.1636i	−0.0677451	−	0.0850713i
$191$	58.8671			0.308205			0.154102	−	0.988055i	$-0.450751\pi$
$191$	58.8671			0.308205			0.154102	+	0.988055i	$0.450751\pi$
$192$	−41.8168	−	41.8168i	−0.217796	−	0.217796i
$193$	3.25902	−	3.25902i	0.0168861	−	0.0168861i	−0.698613	−	0.715499i	$-0.746199\pi$
$193$	3.25902	−	3.25902i	0.0168861	−	0.0168861i	0.715499	+	0.698613i	$0.246199\pi$
$194$			25.7673i			0.132821i
$195$	200.335	+	22.7139i	1.02736	+	0.116481i
$196$	25.6631			0.130934
$197$	−12.5485	−	12.5485i	−0.0636980	−	0.0636980i	0.674540	−	0.738238i	$-0.264342\pi$
$197$	−12.5485	−	12.5485i	−0.0636980	−	0.0636980i	−0.738238	+	0.674540i	$0.764342\pi$
$198$	−7.67036	+	7.67036i	−0.0387392	+	0.0387392i
$199$		−	391.240i		−	1.96603i	−0.183526	−	0.983015i	$-0.558751\pi$
$199$		−	391.240i		−	1.96603i	0.183526	−	0.983015i	$-0.441249\pi$
$200$	−93.8444	+	58.7839i	−0.469222	+	0.293919i
$201$	−29.3769			−0.146154
$202$	−52.3800	−	52.3800i	−0.259307	−	0.259307i
$203$	33.9154	−	33.9154i	0.167071	−	0.167071i
$204$			183.925i			0.901592i
$205$	28.6330	−	252.541i	0.139673	−	1.23191i
$206$	−73.2426			−0.355547
$207$	36.0388	+	36.0388i	0.174101	+	0.174101i
$208$	−199.280	+	199.280i	−0.958076	+	0.958076i
$209$			44.7595i			0.214160i
$210$	10.3563	−	8.24702i	0.0493155	−	0.0392715i
$211$	−80.9281			−0.383546			−0.191773	−	0.981439i	$-0.561424\pi$
$211$	−80.9281			−0.383546			−0.191773	+	0.981439i	$0.561424\pi$
$212$	106.247	+	106.247i	0.501166	+	0.501166i
$213$	25.5555	−	25.5555i	0.119979	−	0.119979i
$214$			26.4919i			0.123794i
$215$	−235.039	−	295.152i	−1.09321	−	1.37280i
$216$	23.0159			0.106555
$217$	62.3922	+	62.3922i	0.287522	+	0.287522i
$218$	−35.6525	+	35.6525i	−0.163543	+	0.163543i
$219$			86.4457i			0.394729i
$220$	113.985	+	12.9236i	0.518115	+	0.0587436i
$221$	674.323			3.05123
$222$	−18.8672	−	18.8672i	−0.0849873	−	0.0849873i
$223$	−227.428	+	227.428i	−1.01986	+	1.01986i	−0.0200565	+	0.999799i	$0.506385\pi$
$223$	−227.428	+	227.428i	−1.01986	+	1.01986i	−0.999799	+	0.0200565i	$0.993615\pi$
$224$			65.3818i			0.291883i
$225$	−16.7911	+	73.0962i	−0.0746270	+	0.324872i
$226$	−11.7959			−0.0521941
$227$	186.163	+	186.163i	0.820101	+	0.820101i	0.986122	−	0.166022i	$-0.0530921\pi$
$227$	186.163	+	186.163i	0.820101	+	0.820101i	−0.166022	+	0.986122i	$0.553092\pi$
$228$	32.1145	−	32.1145i	0.140853	−	0.140853i
$229$			299.882i			1.30953i	0.755832	+	0.654765i	$0.227232\pi$
$229$			299.882i			1.30953i	−0.755832	+	0.654765i	$0.772768\pi$
$230$	−5.52921	+	48.7674i	−0.0240401	+	0.212032i
$231$	−28.6781			−0.124148
$232$	56.7799	+	56.7799i	0.244741	+	0.244741i
$233$	46.9263	−	46.9263i	0.201400	−	0.201400i	−0.599199	−	0.800600i	$-0.704514\pi$
$233$	46.9263	−	46.9263i	0.201400	−	0.201400i	0.800600	+	0.599199i	$0.204514\pi$
$234$		−	40.3543i		−	0.172454i
$235$	259.612	−	206.738i	1.10473	−	0.879736i
$236$	−36.6906			−0.155469
$237$	−39.1745	−	39.1745i	−0.165293	−	0.165293i
$238$	31.3091	−	31.3091i	0.131551	−	0.131551i
$239$			155.118i			0.649030i	0.945881	+	0.324515i	$0.105201\pi$
$239$			155.118i			0.649030i	−0.945881	+	0.324515i	$0.894799\pi$
$240$	−65.3068	−	82.0094i	−0.272112	−	0.341706i
$241$	−113.600			−0.471370			−0.235685	−	0.971829i	$-0.575733\pi$
$241$	−113.600			−0.471370			−0.235685	+	0.971829i	$0.575733\pi$
$242$	−33.4349	−	33.4349i	−0.138161	−	0.138161i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	314.119i		−	1.28737i
$245$	34.7772	+	3.94302i	0.141948	+	0.0160939i
$246$	−50.8704			−0.206790
$247$	−117.741	−	117.741i	−0.476685	−	0.476685i
$248$	−104.455	+	104.455i	−0.421188	+	0.421188i
$249$			15.9015i			0.0638616i
$250$	−65.1365	+	31.2004i	−0.260546	+	0.124801i
$251$	−295.062			−1.17554			−0.587772	−	0.809027i	$-0.699995\pi$
$251$	−295.062			−1.17554			−0.587772	+	0.809027i	$0.699995\pi$
$252$	20.5763	+	20.5763i	0.0816519	+	0.0816519i
$253$	75.1780	−	75.1780i	0.297146	−	0.297146i
$254$		−	44.3650i		−	0.174665i
$255$	−28.2591	+	249.244i	−0.110820	+	0.977428i
$256$	68.0615			0.265865
$257$	18.1666	+	18.1666i	0.0706872	+	0.0706872i	0.741567	−	0.670879i	$-0.234083\pi$
$257$	18.1666	+	18.1666i	0.0706872	+	0.0706872i	−0.670879	+	0.741567i	$0.734083\pi$
$258$	−53.3993	+	53.3993i	−0.206974	+	0.206974i
$259$		−	70.5411i		−	0.272359i
$260$	−333.838	+	265.846i	−1.28399	+	1.02249i
$261$	54.3857			0.208374
$262$	15.0095	+	15.0095i	0.0572880	+	0.0572880i
$263$	−364.409	+	364.409i	−1.38559	+	1.38559i	−0.551237	+	0.834349i	$0.685844\pi$
$263$	−364.409	+	364.409i	−1.38559	+	1.38559i	−0.834349	+	0.551237i	$0.814156\pi$
$264$		−	48.0118i		−	0.181863i
$265$	127.656	+	160.304i	0.481719	+	0.604922i
$266$	−10.9336			−0.0411036
$267$	178.166	+	178.166i	0.667288	+	0.667288i
$268$	43.9686	−	43.9686i	0.164062	−	0.164062i
$269$		−	0.809793i		−	0.00301038i	−0.999999	−	0.00150519i	$-0.999521\pi$
$269$		−	0.809793i		−	0.00301038i	0.999999	−	0.00150519i	$-0.000479118\pi$
$270$	14.9158	+	1.69114i	0.0552437	+	0.00626350i
$271$	−341.910			−1.26166			−0.630831	−	0.775921i	$-0.717286\pi$
$271$	−341.910			−1.26166			−0.630831	+	0.775921i	$0.717286\pi$
$272$	−247.931	−	247.931i	−0.911512	−	0.911512i
$273$	75.4388	−	75.4388i	0.276332	−	0.276332i
$274$		−	73.6378i		−	0.268751i
$275$	152.481	+	35.0266i	0.554476	+	0.127370i
$276$	−107.879			−0.390866
$277$	279.570	+	279.570i	1.00928	+	1.00928i	0.999957	+	0.00932280i	$0.00296758\pi$
$277$	279.570	+	279.570i	1.00928	+	1.00928i	0.00932280	+	0.999957i	$0.497032\pi$
$278$	−36.1585	+	36.1585i	−0.130067	+	0.130067i
$279$			100.050i			0.358602i
$280$	−6.60125	+	58.2226i	−0.0235759	+	0.207938i
$281$	−383.827			−1.36593			−0.682967	−	0.730449i	$-0.739311\pi$
$281$	−383.827			−1.36593			−0.682967	+	0.730449i	$0.739311\pi$
$282$	−46.9694	−	46.9694i	−0.166558	−	0.166558i
$283$	335.505	−	335.505i	1.18553	−	1.18553i	0.207238	−	0.978291i	$-0.433553\pi$
$283$	335.505	−	335.505i	1.18553	−	1.18553i	0.978291	−	0.207238i	$-0.0664474\pi$
$284$			76.4980i			0.269359i
$285$	48.4539	−	38.5855i	0.170014	−	0.135388i
$286$	−84.1801			−0.294336
$287$	−95.0977	−	95.0977i	−0.331351	−	0.331351i
$288$	−52.4221	+	52.4221i	−0.182021	+	0.182021i
$289$			549.949i			1.90294i
$290$	32.6250	+	40.9691i	0.112500	+	0.141273i
$291$	−77.2432			−0.265441
$292$	−129.384	−	129.384i	−0.443095	−	0.443095i
$293$	222.379	−	222.379i	0.758972	−	0.758972i	−0.217163	−	0.976135i	$-0.569680\pi$
$293$	222.379	−	222.379i	0.758972	−	0.758972i	0.976135	+	0.217163i	$0.0696804\pi$
$294$		−	7.00530i		−	0.0238276i
$295$	−49.7210	−	5.63734i	−0.168546	−	0.0191096i
$296$	118.097			0.398977
$297$	−22.9937	−	22.9937i	−0.0774197	−	0.0774197i
$298$	83.9073	−	83.9073i	0.281568	−	0.281568i
$299$			395.516i			1.32280i
$300$	−84.2722	−	134.535i	−0.280907	−	0.448449i
$301$	−199.651			−0.663291
$302$	71.7128	+	71.7128i	0.237460	+	0.237460i
$303$	157.021	−	157.021i	0.518221	−	0.518221i
$304$			86.5810i			0.284806i
$305$	48.2629	−	425.676i	0.158239	−	1.39566i
$306$	50.2062			0.164073
$307$	264.406	+	264.406i	0.861257	+	0.861257i	0.991484	−	0.130227i	$-0.0415706\pi$
$307$	264.406	+	264.406i	0.861257	+	0.861257i	−0.130227	+	0.991484i	$0.541571\pi$
$308$	42.9227	−	42.9227i	0.139359	−	0.139359i
$309$		−	219.561i		−	0.710555i
$310$	−75.3684	+	60.0183i	−0.243124	+	0.193607i
$311$	307.452			0.988592			0.494296	−	0.869294i	$-0.335426\pi$
$311$	307.452			0.988592			0.494296	+	0.869294i	$0.335426\pi$
$312$	126.297	+	126.297i	0.404797	+	0.404797i
$313$	−67.0805	+	67.0805i	−0.214315	+	0.214315i	−0.806098	−	0.591783i	$-0.798424\pi$
$313$	−67.0805	+	67.0805i	−0.214315	+	0.214315i	0.591783	+	0.806098i	$0.298424\pi$
$314$			18.4385i			0.0587213i
$315$	24.7223	+	31.0452i	0.0784836	+	0.0985563i
$316$	117.265			0.371092
$317$	−96.9267	−	96.9267i	−0.305762	−	0.305762i	0.537501	−	0.843263i	$-0.319369\pi$
$317$	−96.9267	−	96.9267i	−0.305762	−	0.305762i	−0.843263	+	0.537501i	$0.819369\pi$
$318$	29.0024	−	29.0024i	0.0912026	−	0.0912026i
$319$		−	113.450i		−	0.355643i
$320$	169.629	+	19.2325i	0.530092	+	0.0601015i
$321$	−79.4157			−0.247401
$322$	18.3640	+	18.3640i	0.0570310	+	0.0570310i
$323$	146.486	−	146.486i	0.453518	−	0.453518i
$324$			32.9955i			0.101838i
$325$	−493.244	+	308.967i	−1.51767	+	0.950667i
$326$	−5.48089			−0.0168126
$327$	−106.876	−	106.876i	−0.326839	−	0.326839i
$328$	159.209	−	159.209i	0.485393	−	0.485393i
$329$		−	175.610i		−	0.533770i
$330$	3.52777	−	31.1148i	0.0106902	−	0.0942872i
$331$	300.702			0.908464			0.454232	−	0.890883i	$-0.349914\pi$
$331$	300.702			0.908464			0.454232	+	0.890883i	$0.349914\pi$
$332$	−23.7999	−	23.7999i	−0.0716864	−	0.0716864i
$333$	56.5587	−	56.5587i	0.169846	−	0.169846i
$334$			86.4640i			0.258874i
$335$	66.3392	−	52.8281i	0.198028	−	0.157696i
$336$	−55.4738			−0.165101
$337$	−43.5765	−	43.5765i	−0.129307	−	0.129307i	0.639491	−	0.768798i	$-0.279145\pi$
$337$	−43.5765	−	43.5765i	−0.129307	−	0.129307i	−0.768798	+	0.639491i	$0.779145\pi$
$338$	152.392	−	152.392i	0.450865	−	0.450865i
$339$		−	35.3608i		−	0.104309i
$340$	−330.749	−	415.340i	−0.972791	−	1.22159i
$341$	208.707			0.612045
$342$	−8.76634	−	8.76634i	−0.0256326	−	0.0256326i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	334.247i		−	0.971649i
$345$	−146.191	−	16.5751i	−0.423743	−	0.0480437i
$346$	−142.809			−0.412742
$347$	−190.647	−	190.647i	−0.549416	−	0.549416i	0.376856	−	0.926272i	$-0.377005\pi$
$347$	−190.647	−	190.647i	−0.549416	−	0.549416i	−0.926272	+	0.376856i	$0.877005\pi$
$348$	−81.3992	+	81.3992i	−0.233906	+	0.233906i
$349$			186.770i			0.535158i	0.963536	+	0.267579i	$0.0862237\pi$
$349$			186.770i			0.535158i	−0.963536	+	0.267579i	$0.913776\pi$
$350$	−8.55607	+	37.2470i	−0.0244459	+	0.106420i
$351$	120.971			0.344647
$352$	109.354	+	109.354i	0.310664	+	0.310664i
$353$	105.217	−	105.217i	0.298066	−	0.298066i	−0.542190	−	0.840256i	$-0.682405\pi$
$353$	105.217	−	105.217i	0.298066	−	0.298066i	0.840256	+	0.542190i	$0.182405\pi$
$354$			10.0155i			0.0282924i
$355$	−11.7536	+	103.666i	−0.0331086	+	0.292016i
$356$	−533.323			−1.49810
$357$	93.8561	+	93.8561i	0.262902	+	0.262902i
$358$	7.42633	−	7.42633i	0.0207440	−	0.0207440i
$359$			44.2544i			0.123271i	0.998099	+	0.0616356i	$0.0196317\pi$
$359$			44.2544i			0.123271i	−0.998099	+	0.0616356i	$0.980368\pi$
$360$	−51.9747	+	41.3892i	−0.144374	+	0.114970i
$361$	309.845			0.858297
$362$	−49.2515	−	49.2515i	−0.136054	−	0.136054i
$363$	100.229	−	100.229i	0.276112	−	0.276112i
$364$			225.819i			0.620382i
$365$	−155.454	−	195.212i	−0.425901	−	0.534828i
$366$	−85.7455			−0.234277
$367$	133.204	+	133.204i	0.362953	+	0.362953i	0.864899	−	0.501946i	$-0.167382\pi$
$367$	133.204	+	133.204i	0.362953	+	0.362953i	−0.501946	+	0.864899i	$0.667382\pi$
$368$	145.421	−	145.421i	0.395167	−	0.395167i
$369$		−	152.496i		−	0.413267i
$370$	76.5346	+	8.67745i	0.206850	+	0.0234526i
$371$	108.435			0.292278
$372$	−149.745	−	149.745i	−0.402541	−	0.402541i
$373$	54.6349	−	54.6349i	0.146474	−	0.146474i	−0.630067	−	0.776541i	$-0.716972\pi$
$373$	54.6349	−	54.6349i	0.146474	−	0.146474i	0.776541	+	0.630067i	$0.216972\pi$
$374$		−	104.732i		−	0.280031i
$375$	−93.5302	−	195.262i	−0.249414	−	0.520698i
$376$	294.000			0.781915
$377$	298.434	+	298.434i	0.791602	+	0.791602i
$378$	5.61674	−	5.61674i	0.0148591	−	0.0148591i
$379$		−	189.045i		−	0.498799i	−0.968401	−	0.249400i	$-0.919767\pi$
$379$		−	189.045i		−	0.498799i	0.968401	−	0.249400i	$-0.0802333\pi$
$380$	−14.7702	+	130.272i	−0.0388689	+	0.342822i
$381$	132.994			0.349066
$382$	24.0506	+	24.0506i	0.0629597	+	0.0629597i
$383$	477.999	−	477.999i	1.24804	−	1.24804i	0.291455	−	0.956585i	$-0.405861\pi$
$383$	477.999	−	477.999i	1.24804	−	1.24804i	0.956585	−	0.291455i	$-0.0941394\pi$
$384$		−	205.379i		−	0.534841i
$385$	64.7612	−	51.5715i	0.168211	−	0.133952i
$386$	2.66300			0.00689896
$387$	−160.077	−	160.077i	−0.413635	−	0.413635i
$388$	115.610	−	115.610i	0.297965	−	0.297965i
$389$			667.365i			1.71559i	0.513990	+	0.857796i	$0.328167\pi$
$389$			667.365i			1.71559i	−0.513990	+	0.857796i	$0.671833\pi$
$390$	72.5685	+	91.1283i	0.186073	+	0.233662i
$391$	−492.076			−1.25851
$392$	21.9245	+	21.9245i	0.0559298	+	0.0559298i
$393$	−44.9943	+	44.9943i	−0.114489	+	0.114489i
$394$		−	10.2536i		−	0.0260243i
$395$	158.911	+	18.0172i	0.402306	+	0.0456132i
$396$	68.8294			0.173812
$397$	98.8649	+	98.8649i	0.249030	+	0.249030i	0.820572	−	0.571543i	$-0.193655\pi$
$397$	98.8649	+	98.8649i	0.249030	+	0.249030i	−0.571543	+	0.820572i	$0.693655\pi$
$398$	159.844	−	159.844i	0.401618	−	0.401618i
$399$		−	32.7758i		−	0.0821449i
$400$	294.953	+	67.7541i	0.737382	+	0.169385i
$401$	−505.616			−1.26089			−0.630444	−	0.776235i	$-0.717127\pi$
$401$	−505.616			−1.26089			−0.630444	+	0.776235i	$0.717127\pi$
$402$	−12.0022	−	12.0022i	−0.0298561	−	0.0298561i
$403$	−549.011	+	549.011i	−1.36231	+	1.36231i
$404$			470.028i			1.16343i
$405$	−5.06959	+	44.7135i	−0.0125175	+	0.110404i
$406$	27.7128			0.0682581
$407$	−117.983	−	117.983i	−0.289884	−	0.289884i
$408$	−157.130	+	157.130i	−0.385123	+	0.385123i
$409$			173.212i			0.423502i	0.977324	+	0.211751i	$0.0679166\pi$
$409$			173.212i			0.423502i	−0.977324	+	0.211751i	$0.932083\pi$
$410$	114.876	−	91.4795i	0.280185	−	0.223121i
$411$	220.746			0.537095
$412$	328.619	+	328.619i	0.797618	+	0.797618i
$413$	−18.7231	+	18.7231i	−0.0453344	+	0.0453344i
$414$			29.4479i			0.0711301i
$415$	−28.5955	−	35.9090i	−0.0689048	−	0.0865277i
$416$	−575.318			−1.38298
$417$	−108.393	−	108.393i	−0.259936	−	0.259936i
$418$	−18.2868	+	18.2868i	−0.0437484	+	0.0437484i
$419$		−	69.3107i		−	0.165419i	−0.996574	−	0.0827096i	$-0.973643\pi$
$419$		−	69.3107i		−	0.165419i	0.996574	−	0.0827096i	$-0.0263574\pi$
$420$	−83.4675	−	9.46350i	−0.198732	−	0.0225321i
$421$	153.026			0.363483			0.181742	−	0.983346i	$-0.441827\pi$
$421$	153.026			0.363483			0.181742	+	0.983346i	$0.441827\pi$
$422$	−33.0638	−	33.0638i	−0.0783502	−	0.0783502i
$423$	140.801	−	140.801i	0.332864	−	0.332864i
$424$			181.538i			0.428155i
$425$	−384.397	−	613.663i	−0.904463	−	1.44391i
$426$	20.8818			0.0490183
$427$	−160.294	−	160.294i	−0.375395	−	0.375395i
$428$	118.862	−	118.862i	0.277714	−	0.277714i
$429$		−	252.349i		−	0.588226i
$430$	24.5596	−	216.614i	0.0571153	−	0.503753i
$431$	−138.173			−0.320588			−0.160294	−	0.987069i	$-0.551244\pi$
$431$	−138.173			−0.320588			−0.160294	+	0.987069i	$0.551244\pi$
$432$	−44.4780	−	44.4780i	−0.102958	−	0.102958i
$433$	79.3560	−	79.3560i	0.183270	−	0.183270i	−0.609509	−	0.792779i	$-0.708633\pi$
$433$	79.3560	−	79.3560i	0.183270	−	0.183270i	0.792779	+	0.609509i	$0.208633\pi$
$434$			50.9816i			0.117469i
$435$	−122.814	+	97.8009i	−0.282331	+	0.224830i
$436$	319.925			0.733772
$437$	85.9198	+	85.9198i	0.196613	+	0.196613i
$438$	−35.3180	+	35.3180i	−0.0806348	+	0.0806348i
$439$		−	541.986i		−	1.23459i	−0.786731	−	0.617296i	$-0.788228\pi$
$439$		−	541.986i		−	1.23459i	0.786731	−	0.617296i	$-0.211772\pi$
$440$	86.3390	+	108.421i	0.196225	+	0.246411i
$441$	21.0000			0.0476190
$442$	275.500	+	275.500i	0.623302	+	0.623302i
$443$	−395.555	+	395.555i	−0.892901	+	0.892901i	−0.994795	−	0.101894i	$-0.967510\pi$
$443$	−395.555	+	395.555i	−0.892901	+	0.892901i	0.101894	+	0.994795i	$0.467510\pi$
$444$			169.303i			0.381314i
$445$	−722.729	−	81.9426i	−1.62411	−	0.184141i
$446$	−185.835			−0.416670
$447$	251.531	+	251.531i	0.562710	+	0.562710i
$448$	63.8762	−	63.8762i	0.142581	−	0.142581i
$449$			478.107i			1.06483i	0.846485	+	0.532413i	$0.178715\pi$
$449$			478.107i			1.06483i	−0.846485	+	0.532413i	$0.821285\pi$
$450$	−36.7241	+	23.0039i	−0.0816092	+	0.0511198i
$451$	−318.110			−0.705344
$452$	52.9246	+	52.9246i	0.117090	+	0.117090i
$453$	−214.975	+	214.975i	−0.474560	+	0.474560i
$454$			152.117i			0.335058i
$455$	−34.6960	+	306.017i	−0.0762550	+	0.672564i
$456$	54.8720			0.120333
$457$	−6.40164	−	6.40164i	−0.0140080	−	0.0140080i	0.700068	−	0.714076i	$-0.253153\pi$
$457$	−6.40164	−	6.40164i	−0.0140080	−	0.0140080i	−0.714076	+	0.700068i	$0.753153\pi$
$458$	−122.519	+	122.519i	−0.267509	+	0.267509i
$459$			150.505i			0.327897i
$460$	243.613	−	193.997i	0.529594	−	0.421733i
$461$	227.575			0.493655			0.246828	−	0.969059i	$-0.420612\pi$
$461$	227.575			0.493655			0.246828	+	0.969059i	$0.420612\pi$
$462$	−11.7167	−	11.7167i	−0.0253608	−	0.0253608i
$463$	−5.28403	+	5.28403i	−0.0114126	+	0.0114126i	−0.712790	−	0.701377i	$-0.752569\pi$
$463$	−5.28403	+	5.28403i	−0.0114126	+	0.0114126i	0.701377	+	0.712790i	$0.252569\pi$
$464$		−	219.453i		−	0.472959i
$465$	−179.919	−	225.934i	−0.386922	−	0.485879i
$466$	38.3442			0.0822836
$467$	176.806	+	176.806i	0.378599	+	0.378599i	0.870597	−	0.491997i	$-0.163733\pi$
$467$	176.806	+	176.806i	0.378599	+	0.378599i	−0.491997	+	0.870597i	$0.663733\pi$
$468$	−181.058	+	181.058i	−0.386876	+	0.386876i
$469$		−	44.8740i		−	0.0956802i
$470$	190.531	+	21.6023i	0.405385	+	0.0459623i
$471$	−55.2735			−0.117354
$472$	−31.3455	−	31.3455i	−0.0664099	−	0.0664099i
$473$	−333.924	+	333.924i	−0.705971	+	0.705971i
$474$		−	32.0101i		−	0.0675318i
$475$	−40.0314	+	174.268i	−0.0842766	+	0.366880i
$476$	−280.950			−0.590230
$477$	86.9414	+	86.9414i	0.182267	+	0.182267i
$478$	−63.3747	+	63.3747i	−0.132583	+	0.132583i
$479$		−	355.453i		−	0.742074i	−0.928618	−	0.371037i	$-0.879002\pi$
$479$		−	355.453i		−	0.742074i	0.928618	−	0.371037i	$-0.120998\pi$
$480$	24.1101	−	212.650i	0.0502294	−	0.443020i
$481$	620.716			1.29047
$482$	−46.4123	−	46.4123i	−0.0962910	−	0.0962910i
$483$	−55.0502	+	55.0502i	−0.113976	+	0.113976i
$484$			300.025i			0.619887i
$485$	174.431	−	138.905i	0.359652	−	0.286403i
$486$	9.00682			0.0185326
$487$	−261.155	−	261.155i	−0.536253	−	0.536253i	0.386173	−	0.922426i	$-0.373797\pi$
$487$	−261.155	−	261.155i	−0.536253	−	0.536253i	−0.922426	+	0.386173i	$0.873797\pi$
$488$	268.358	−	268.358i	0.549913	−	0.549913i
$489$		−	16.4302i		−	0.0335997i
$490$	12.5975	+	15.8194i	0.0257093	+	0.0322846i
$491$	648.152			1.32006			0.660032	−	0.751237i	$-0.270543\pi$
$491$	648.152			1.32006			0.660032	+	0.751237i	$0.270543\pi$
$492$	228.241	+	228.241i	0.463904	+	0.463904i
$493$	−371.292	+	371.292i	−0.753129	+	0.753129i
$494$		−	96.2082i		−	0.194753i
$495$	93.2736	+	10.5753i	0.188432	+	0.0213643i
$496$	403.715			0.813941
$497$	39.0367	+	39.0367i	0.0785446	+	0.0785446i
$498$	−6.49670	+	6.49670i	−0.0130456	+	0.0130456i
$499$		−	177.417i		−	0.355545i	−0.984072	−	0.177772i	$-0.943111\pi$
$499$		−	177.417i		−	0.355545i	0.984072	−	0.177772i	$-0.0568891\pi$
$500$	432.236	+	152.262i	0.864472	+	0.304524i
$501$	−259.196			−0.517357
$502$	−120.550	−	120.550i	−0.240139	−	0.240139i
$503$	−336.836	+	336.836i	−0.669654	+	0.669654i	−0.957636	−	0.287982i	$-0.907016\pi$
$503$	−336.836	+	336.836i	−0.669654	+	0.669654i	0.287982	+	0.957636i	$0.407016\pi$
$504$			35.1574i			0.0697567i
$505$	−72.2175	+	636.954i	−0.143005	+	1.26130i
$506$	61.4291			0.121401
$507$	456.831	+	456.831i	0.901046	+	0.901046i
$508$	−199.053	+	199.053i	−0.391836	+	0.391836i
$509$			315.435i			0.619715i	0.950783	+	0.309857i	$0.100281\pi$
$509$			315.435i			0.619715i	−0.950783	+	0.309857i	$0.899719\pi$
$510$	−113.376	+	90.2851i	−0.222306	+	0.177030i
$511$	−132.048			−0.258411
$512$	363.189	+	363.189i	0.709354	+	0.709354i
$513$	26.2791	−	26.2791i	0.0512263	−	0.0512263i
$514$			14.8442i			0.0288798i
$515$	394.834	+	495.815i	0.766668	+	0.962748i
$516$	479.175			0.928633
$517$	−293.716	−	293.716i	−0.568116	−	0.568116i
$518$	28.8201	−	28.8201i	0.0556372	−	0.0556372i
$519$		−	428.102i		−	0.824859i
$520$	−512.321	−	58.0867i	−0.985234	−	0.111705i
$521$	−999.113			−1.91768			−0.958842	−	0.283940i	$-0.908358\pi$
$521$	−999.113			−1.91768			−0.958842	+	0.283940i	$0.908358\pi$
$522$	22.2197	+	22.2197i	0.0425664	+	0.0425664i
$523$	284.638	−	284.638i	0.544241	−	0.544241i	−0.380529	−	0.924769i	$-0.624258\pi$
$523$	284.638	−	284.638i	0.544241	−	0.544241i	0.924769	+	0.380529i	$0.124258\pi$
$524$		−	134.686i		−	0.257035i
$525$	−111.656	−	25.6488i	−0.212679	−	0.0488548i
$526$	−297.764			−0.566092
$527$	−683.045	−	683.045i	−1.29610	−	1.29610i
$528$	−92.7824	+	92.7824i	−0.175724	+	0.175724i
$529$			240.378i			0.454402i
$530$	−13.3389	+	117.648i	−0.0251677	+	0.221978i
$531$	−30.0237			−0.0565419
$532$	49.0557	+	49.0557i	0.0922100	+	0.0922100i
$533$	836.799	−	836.799i	1.56998	−	1.56998i
$534$			145.582i			0.272626i
$535$	179.337	−	142.812i	0.335210	−	0.266938i
$536$	75.1263			0.140161
$537$	22.2621	+	22.2621i	0.0414565	+	0.0414565i
$538$	0.330847	−	0.330847i	0.000614958	−	0.000614958i
$539$		−	43.8066i		−	0.0812738i
$540$	−59.3352	−	74.5106i	−0.109880	−	0.137983i
$541$	−662.246			−1.22411			−0.612057	−	0.790814i	$-0.709658\pi$
$541$	−662.246			−1.22411			−0.612057	+	0.790814i	$0.709658\pi$
$542$	−139.690	−	139.690i	−0.257731	−	0.257731i
$543$	147.643	−	147.643i	0.271902	−	0.271902i
$544$		−	715.774i		−	1.31576i
$545$	433.543	+	49.1549i	0.795492	+	0.0901925i
$546$	61.6422			0.112898
$547$	−596.362	−	596.362i	−1.09024	−	1.09024i	−0.995502	−	0.0947395i	$-0.969798\pi$
$547$	−596.362	−	596.362i	−1.09024	−	1.09024i	−0.0947395	−	0.995502i	$-0.530202\pi$
$548$	−330.391	+	330.391i	−0.602904	+	0.602904i
$549$		−	257.042i		−	0.468200i
$550$	47.9868	+	76.6076i	0.0872487	+	0.139287i
$551$	129.660			0.235318
$552$	−92.1629	−	92.1629i	−0.166962	−	0.166962i
$553$	59.8400	−	59.8400i	0.108210	−	0.108210i
$554$			228.441i			0.412349i
$555$	−26.0126	+	229.430i	−0.0468696	+	0.413387i
$556$	324.465			0.583571
$557$	−703.702	−	703.702i	−1.26338	−	1.26338i	−0.949444	−	0.313935i	$-0.898353\pi$
$557$	−703.702	−	703.702i	−1.26338	−	1.26338i	−0.313935	−	0.949444i	$-0.601647\pi$
$558$	−40.8762	+	40.8762i	−0.0732549	+	0.0732549i
$559$		−	1756.80i		−	3.14275i
$560$	125.271	−	99.7578i	0.223699	−	0.178139i
$561$	313.957			0.559638
$562$	−156.816	−	156.816i	−0.279031	−	0.279031i
$563$	30.9148	−	30.9148i	0.0549109	−	0.0549109i	−0.679118	−	0.734029i	$-0.737638\pi$
$563$	30.9148	−	30.9148i	0.0549109	−	0.0549109i	0.734029	+	0.679118i	$0.237638\pi$
$564$			421.476i			0.747298i
$565$	63.5888	+	79.8520i	0.112546	+	0.141331i
$566$	274.146			0.484357
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−65.3537	+	65.3537i	−0.115059	+	0.115059i
$569$			661.719i			1.16295i	0.813564	+	0.581475i	$0.197524\pi$
$569$			661.719i			1.16295i	−0.813564	+	0.581475i	$0.802476\pi$
$570$	35.5606	+	4.03184i	0.0623870	+	0.00707341i
$571$	862.831			1.51109			0.755544	−	0.655098i	$-0.227373\pi$
$571$	862.831			1.51109			0.755544	+	0.655098i	$0.227373\pi$
$572$	377.692	+	377.692i	0.660301	+	0.660301i
$573$	−72.0972	+	72.0972i	−0.125824	+	0.125824i
$574$		−	77.7058i		−	0.135376i
$575$	359.937	−	225.464i	0.625977	−	0.392111i
$576$	102.430			0.177829
$577$	110.827	+	110.827i	0.192074	+	0.192074i	0.796592	−	0.604518i	$-0.206634\pi$
$577$	110.827	+	110.827i	0.192074	+	0.192074i	−0.604518	+	0.796592i	$0.706634\pi$
$578$	−224.686	+	224.686i	−0.388730	+	0.388730i
$579$			7.98294i			0.0137875i
$580$	37.4374	−	330.195i	0.0645472	−	0.569303i
$581$	−24.2900			−0.0418072
$582$	−31.5583	−	31.5583i	−0.0542239	−	0.0542239i
$583$	181.362	−	181.362i	0.311084	−	0.311084i
$584$		−	221.070i		−	0.378544i
$585$	−273.178	+	217.541i	−0.466971	+	0.371864i
$586$	181.709			0.310084
$587$	−224.917	−	224.917i	−0.383164	−	0.383164i	0.489077	−	0.872241i	$-0.337334\pi$
$587$	−224.917	−	224.917i	−0.383164	−	0.383164i	−0.872241	+	0.489077i	$0.837334\pi$
$588$	−31.4308	+	31.4308i	−0.0534537	+	0.0534537i
$589$			238.528i			0.404972i
$590$	−18.0107	−	22.6171i	−0.0305267	−	0.0383340i
$591$	30.7374			0.0520092
$592$	−228.221	−	228.221i	−0.385509	−	0.385509i
$593$	456.305	−	456.305i	0.769485	−	0.769485i	−0.208531	−	0.978016i	$-0.566868\pi$
$593$	456.305	−	456.305i	0.769485	−	0.769485i	0.978016	+	0.208531i	$0.0668681\pi$
$594$		−	18.7885i		−	0.0316304i
$595$	−380.727	−	43.1666i	−0.639877	−	0.0725488i
$596$	−752.936			−1.26332
$597$	479.169	+	479.169i	0.802628	+	0.802628i
$598$	−161.591	+	161.591i	−0.270219	+	0.270219i
$599$		−	507.846i		−	0.847823i	−0.905704	−	0.423911i	$-0.860657\pi$
$599$		−	507.846i		−	0.847823i	0.905704	−	0.423911i	$-0.139343\pi$
$600$	42.9402	−	186.931i	0.0715670	−	0.311551i
$601$	382.086			0.635751			0.317875	−	0.948132i	$-0.397031\pi$
$601$	382.086			0.635751			0.317875	+	0.948132i	$0.397031\pi$
$602$	−81.5688	−	81.5688i	−0.135496	−	0.135496i
$603$	35.9792	−	35.9792i	0.0596671	−	0.0596671i
$604$		−	643.509i		−	1.06541i
$605$	−46.0975	+	406.577i	−0.0761942	+	0.672028i
$606$	128.304			0.211723
$607$	138.297	+	138.297i	0.227837	+	0.227837i	0.811788	−	0.583952i	$-0.198494\pi$
$607$	138.297	+	138.297i	0.227837	+	0.227837i	−0.583952	+	0.811788i	$0.698494\pi$
$608$	−124.979	+	124.979i	−0.205557	+	0.205557i
$609$			83.0755i			0.136413i
$610$	193.631	−	154.195i	0.317428	−	0.252779i
$611$	1545.26			2.52906
$612$	−225.261	−	225.261i	−0.368073	−	0.368073i
$613$	438.734	−	438.734i	0.715715	−	0.715715i	−0.252009	−	0.967725i	$-0.581091\pi$
$613$	438.734	−	438.734i	0.715715	−	0.715715i	0.967725	+	0.252009i	$0.0810914\pi$
$614$			216.050i			0.351873i
$615$	274.231	+	344.367i	0.445903	+	0.559946i
$616$	73.3393			0.119057
$617$	−442.672	−	442.672i	−0.717458	−	0.717458i	0.250626	−	0.968084i	$-0.419364\pi$
$617$	−442.672	−	442.672i	−0.717458	−	0.717458i	−0.968084	+	0.250626i	$0.919364\pi$
$618$	89.7035	−	89.7035i	0.145151	−	0.145151i
$619$			186.618i			0.301483i	0.988573	+	0.150741i	$0.0481661\pi$
$619$			186.618i			0.301483i	−0.988573	+	0.150741i	$0.951834\pi$
$620$	607.441	+	68.8713i	0.979744	+	0.111083i
$621$	−88.2767			−0.142153
$622$	125.612	+	125.612i	0.201948	+	0.201948i
$623$	−272.153	+	272.153i	−0.436843	+	0.436843i
$624$		−	488.134i		−	0.782266i
$625$	562.347	+	272.747i	0.899755	+	0.436396i
$626$	−54.8125			−0.0875600
$627$	−54.8190	−	54.8190i	−0.0874306	−	0.0874306i
$628$	82.7281	−	82.7281i	0.131733	−	0.131733i
$629$			772.255i			1.22775i
$630$	−2.58327	+	22.7843i	−0.00410042	+	0.0361655i
$631$	−973.263			−1.54241			−0.771207	−	0.636585i	$-0.780346\pi$
$631$	−973.263			−1.54241			−0.771207	+	0.636585i	$0.780346\pi$
$632$	100.182	+	100.182i	0.158516	+	0.158516i
$633$	99.1163	−	99.1163i	0.156582	−	0.156582i
$634$		−	79.2003i		−	0.124922i
$635$	−300.328	+	239.161i	−0.472958	+	0.376632i
$636$	−260.251			−0.409200
$637$	115.235	+	115.235i	0.180902	+	0.180902i
$638$	46.3509	−	46.3509i	0.0726502	−	0.0726502i
$639$			62.5979i			0.0979623i
$640$	369.330	+	463.788i	0.577078	+	0.724669i
$641$	11.4492			0.0178614			0.00893072	−	0.999960i	$-0.497157\pi$
$641$	11.4492			0.0178614			0.00893072	+	0.999960i	$0.497157\pi$
$642$	−32.4459	−	32.4459i	−0.0505388	−	0.0505388i
$643$	132.472	−	132.472i	0.206021	−	0.206021i	−0.596553	−	0.802574i	$-0.703463\pi$
$643$	132.472	−	132.472i	0.206021	−	0.206021i	0.802574	+	0.596553i	$0.203463\pi$
$644$		−	164.788i		−	0.255882i
$645$	649.350	+	73.6229i	1.00674	+	0.114144i
$646$	119.696			0.185288
$647$	−488.968	−	488.968i	−0.755746	−	0.755746i	0.219799	−	0.975545i	$-0.429460\pi$
$647$	−488.968	−	488.968i	−0.755746	−	0.755746i	−0.975545	+	0.219799i	$0.929460\pi$
$648$	−28.1886	+	28.1886i	−0.0435010	+	0.0435010i
$649$			62.6304i			0.0965029i
$650$	−327.749	−	75.2879i	−0.504230	−	0.115828i
$651$	−152.829			−0.234760
$652$	24.5912	+	24.5912i	0.0377166	+	0.0377166i
$653$	−866.784	+	866.784i	−1.32739	+	1.32739i	−0.419745	+	0.907642i	$0.637880\pi$
$653$	−866.784	+	866.784i	−1.32739	+	1.32739i	−0.907642	+	0.419745i	$0.862120\pi$
$654$		−	87.3303i		−	0.133533i
$655$	20.6939	−	182.519i	0.0315937	−	0.278655i
$656$	−615.339			−0.938017
$657$	−105.874	−	105.874i	−0.161148	−	0.161148i
$658$	71.7469	−	71.7469i	0.109038	−	0.109038i
$659$		−	32.6504i		−	0.0495454i	−0.999693	−	0.0247727i	$-0.992114\pi$
$659$		−	32.6504i		−	0.0495454i	0.999693	−	0.0247727i	$-0.00788620\pi$
$660$	−155.431	+	123.775i	−0.235502	+	0.187538i
$661$	−417.442			−0.631532			−0.315766	−	0.948837i	$-0.602261\pi$
$661$	−417.442			−0.631532			−0.315766	+	0.948837i	$0.602261\pi$
$662$	122.854	+	122.854i	0.185580	+	0.185580i
$663$	−825.873	+	825.873i	−1.24566	+	1.24566i
$664$		−	40.6654i		−	0.0612430i
$665$	58.9403	+	74.0146i	0.0886320	+	0.111300i
$666$	46.2150			0.0693918
$667$	−217.777	−	217.777i	−0.326503	−	0.326503i
$668$	387.939	−	387.939i	0.580747	−	0.580747i
$669$		−	557.082i		−	0.832708i
$670$	48.6867	+	5.52007i	0.0726668	+	0.00823891i
$671$	−536.196			−0.799100
$672$	−80.0760	−	80.0760i	−0.119161	−	0.119161i
$673$	−668.058	+	668.058i	−0.992657	+	0.992657i	−0.999973	−	0.00731589i	$-0.997671\pi$
$673$	−668.058	+	668.058i	−0.992657	+	0.992657i	0.00731589	+	0.999973i	$0.497671\pi$
$674$		−	35.6070i		−	0.0528294i
$675$	−68.9595	−	110.089i	−0.102162	−	0.163095i
$676$	−1367.48			−2.02290
$677$	287.193	+	287.193i	0.424214	+	0.424214i	0.886652	−	0.462438i	$-0.153025\pi$
$677$	287.193	+	287.193i	0.424214	+	0.424214i	−0.462438	+	0.886652i	$0.653025\pi$
$678$	14.4469	−	14.4469i	0.0213081	−	0.0213081i
$679$		−	117.991i		−	0.173772i
$680$	72.2678	−	637.398i	0.106276	−	0.937350i
$681$	−456.004			−0.669609
$682$	85.2689	+	85.2689i	0.125028	+	0.125028i
$683$	−142.312	+	142.312i	−0.208364	+	0.208364i	−0.803572	−	0.595208i	$-0.797070\pi$
$683$	−142.312	+	142.312i	−0.208364	+	0.208364i	0.595208	+	0.803572i	$0.297070\pi$
$684$			78.6641i			0.115006i
$685$	−498.490	+	396.964i	−0.727723	+	0.579510i
$686$	10.7008			0.0155988
$687$	−367.279	−	367.279i	−0.534613	−	0.534613i
$688$	−645.930	+	645.930i	−0.938851	+	0.938851i
$689$			954.158i			1.38484i
$690$	−52.9557	−	66.4994i	−0.0767474	−	0.0963760i
$691$	1281.91			1.85515			0.927577	−	0.373632i	$-0.121888\pi$
$691$	1281.91			1.85515			0.927577	+	0.373632i	$0.121888\pi$
$692$	640.741	+	640.741i	0.925927	+	0.925927i
$693$	35.1234	−	35.1234i	0.0506831	−	0.0506831i
$694$		−	155.781i		−	0.224468i
$695$	439.697	+	49.8526i	0.632657	+	0.0717303i
$696$	−139.082			−0.199830
$697$	1041.09	+	1041.09i	1.49368	+	1.49368i
$698$	−76.3064	+	76.3064i	−0.109322	+	0.109322i
$699$			114.945i			0.164443i
$700$	205.505	−	128.728i	0.293579	−	0.183897i
$701$	−122.572			−0.174854			−0.0874268	−	0.996171i	$-0.527864\pi$
$701$	−122.572			−0.174854			−0.0874268	+	0.996171i	$0.527864\pi$
$702$	49.4237	+	49.4237i	0.0704041	+	0.0704041i
$703$	134.841	−	134.841i	0.191808	−	0.191808i
$704$		−	213.671i		−	0.303510i
$705$	−64.7578	+	571.160i	−0.0918551	+	0.810156i
$706$	85.9748			0.121777
$707$	239.853	+	239.853i	0.339255	+	0.339255i
$708$	44.9367	−	44.9367i	0.0634699	−	0.0634699i
$709$		−	140.031i		−	0.197504i	−0.995112	−	0.0987522i	$-0.968515\pi$
$709$		−	140.031i		−	0.197504i	0.995112	−	0.0987522i	$-0.0314851\pi$
$710$	−47.1554	+	37.5514i	−0.0664161	+	0.0528893i
$711$	95.9575			0.134961
$712$	−455.628	−	455.628i	−0.639927	−	0.639927i
$713$	400.632	−	400.632i	0.561896	−	0.561896i
$714$			76.6913i			0.107411i
$715$	453.796	+	569.857i	0.634679	+	0.797003i
$716$	−66.6396			−0.0930721
$717$	−189.980	−	189.980i	−0.264965	−	0.264965i
$718$	−18.0805	+	18.0805i	−0.0251817	+	0.0251817i
$719$		−	247.009i		−	0.343545i	−0.985137	−	0.171773i	$-0.945051\pi$
$719$		−	247.009i		−	0.343545i	0.985137	−	0.171773i	$-0.0549494\pi$
$720$	180.425	+	20.4565i	0.250590	+	0.0284117i
$721$	335.386			0.465167
$722$	126.590	+	126.590i	0.175332	+	0.175332i
$723$	139.131	−	139.131i	0.192436	−	0.192436i
$724$			441.955i			0.610435i
$725$	101.466	−	441.710i	0.139953	−	0.609255i
$726$	81.8984			0.112808
$727$	−663.212	−	663.212i	−0.912259	−	0.912259i	0.0841908	−	0.996450i	$-0.473169\pi$
$727$	−663.212	−	663.212i	−0.912259	−	0.912259i	−0.996450	+	0.0841908i	$0.973169\pi$
$728$	−192.921	+	192.921i	−0.265002	+	0.265002i
$729$			27.0000i			0.0370370i
$730$	16.2436	−	143.267i	0.0222515	−	0.196257i
$731$	2185.69			2.99001
$732$	384.715	+	384.715i	0.525568	+	0.525568i
$733$	−648.037	+	648.037i	−0.884089	+	0.884089i	−0.993947	−	0.109858i	$-0.964960\pi$
$733$	−648.037	+	648.037i	−0.884089	+	0.884089i	0.109858	+	0.993947i	$0.464960\pi$
$734$			108.843i			0.148287i
$735$	−47.4224	+	37.7640i	−0.0645202	+	0.0513796i
$736$	419.829			0.570420
$737$	−75.0537	−	75.0537i	−0.101837	−	0.101837i
$738$	62.3032	−	62.3032i	0.0844217	−	0.0844217i
$739$			1233.42i			1.66904i	0.550980	+	0.834519i	$0.314254\pi$
$739$			1233.42i			1.66904i	−0.550980	+	0.834519i	$0.685746\pi$
$740$	−304.455	−	382.322i	−0.411426	−	0.516651i
$741$	288.406			0.389212
$742$	44.3020	+	44.3020i	0.0597061	+	0.0597061i
$743$	−877.884	+	877.884i	−1.18154	+	1.18154i	−0.202195	+	0.979345i	$0.564807\pi$
$743$	−877.884	+	877.884i	−1.18154	+	1.18154i	−0.979345	+	0.202195i	$0.935193\pi$
$744$		−	255.860i		−	0.343898i
$745$	−1020.34	−	115.685i	−1.36958	−	0.155282i
$746$	44.6430			0.0598431
$747$	−19.4753	−	19.4753i	−0.0260714	−	0.0260714i
$748$	−469.900	+	469.900i	−0.628209	+	0.628209i
$749$		−	121.309i		−	0.161962i
$750$	41.5632	−	117.988i	0.0554176	−	0.157317i
$751$	−495.029			−0.659160			−0.329580	−	0.944128i	$-0.606907\pi$
$751$	−495.029			−0.659160			−0.329580	+	0.944128i	$0.606907\pi$
$752$	−568.152	−	568.152i	−0.755521	−	0.755521i
$753$	361.375	−	361.375i	0.479914	−	0.479914i
$754$			243.855i			0.323415i
$755$	98.8721	−	872.047i	0.130956	−	1.15503i
$756$	−50.4014			−0.0666685
$757$	700.188	+	700.188i	0.924951	+	0.924951i	0.997374	−	0.0724227i	$-0.0230731\pi$
$757$	700.188	+	700.188i	0.924951	+	0.924951i	−0.0724227	+	0.997374i	$0.523073\pi$
$758$	77.2358	−	77.2358i	0.101894	−	0.101894i
$759$			184.148i			0.242619i
$760$	−123.912	+	98.6755i	−0.163043	+	0.129836i
$761$	−658.430			−0.865216			−0.432608	−	0.901582i	$-0.642407\pi$
$761$	−658.430			−0.865216			−0.432608	+	0.901582i	$0.642407\pi$
$762$	54.3358	+	54.3358i	0.0713068	+	0.0713068i
$763$	163.256	−	163.256i	0.213966	−	0.213966i
$764$		−	215.816i		−	0.282482i
$765$	−270.650	−	339.871i	−0.353791	−	0.444275i
$766$	390.580			0.509896
$767$	−164.751	−	164.751i	−0.214799	−	0.214799i
$768$	−83.3579	+	83.3579i	−0.108539	+	0.108539i
$769$		−	121.021i		−	0.157375i	−0.996899	−	0.0786873i	$-0.974927\pi$
$769$		−	121.021i		−	0.157375i	0.996899	−	0.0786873i	$-0.0250729\pi$
$770$	47.5286	+	5.38877i	0.0617255	+	0.00699840i
$771$	−44.4990			−0.0577159
$772$	−11.9481	−	11.9481i	−0.0154768	−	0.0154768i
$773$	191.617	−	191.617i	0.247888	−	0.247888i	−0.572215	−	0.820103i	$-0.693916\pi$
$773$	191.617	−	191.617i	0.247888	−	0.247888i	0.820103	+	0.572215i	$0.193916\pi$
$774$		−	130.801i		−	0.168994i
$775$	812.587	+	186.661i	1.04850	+	0.240853i
$776$	197.536			0.254557
$777$	86.3948	+	86.3948i	0.111190	+	0.111190i
$778$	−272.657	+	272.657i	−0.350459	+	0.350459i
$779$		−	363.563i		−	0.466705i
$780$	83.2727	−	734.461i	0.106760	−	0.941616i
$781$	130.581			0.167197
$782$	−201.041	−	201.041i	−0.257086	−	0.257086i
$783$	−66.6086	+	66.6086i	−0.0850684	+	0.0850684i
$784$		−	84.7377i		−	0.108084i
$785$	124.819	−	99.3976i	0.159005	−	0.126621i
$786$	−36.7655			−0.0467755
$787$	52.6931	+	52.6931i	0.0669544	+	0.0669544i	0.739791	−	0.672837i	$-0.234924\pi$
$787$	52.6931	+	52.6931i	0.0669544	+	0.0669544i	−0.672837	+	0.739791i	$0.734924\pi$
$788$	−46.0048	+	46.0048i	−0.0583818	+	0.0583818i
$789$		−	892.616i		−	1.13133i
$790$	57.5632	+	72.2854i	0.0728648	+	0.0915005i
$791$	54.0145			0.0682863
$792$	58.8022	+	58.8022i	0.0742453	+	0.0742453i
$793$	1410.48	−	1410.48i	1.77866	−	1.77866i
$794$			80.7840i			0.101743i
$795$	−352.677	−	39.9863i	−0.443619	−	0.0502973i
$796$	−1434.35			−1.80195
$797$	−369.849	−	369.849i	−0.464051	−	0.464051i	0.435930	−	0.899981i	$-0.356420\pi$
$797$	−369.849	−	369.849i	−0.464051	−	0.464051i	−0.899981	+	0.435930i	$0.856420\pi$
$798$	13.3908	−	13.3908i	0.0167805	−	0.0167805i
$799$			1922.51i			2.40615i
$800$	327.959	+	523.564i	0.409949	+	0.654455i
$801$	−436.416			−0.544838
$802$	−206.573	−	206.573i	−0.257573	−	0.257573i
$803$	−220.856	+	220.856i	−0.275038	+	0.275038i
$804$			107.701i			0.133956i
$805$	25.3189	−	223.311i	0.0314520	−	0.277405i
$806$	−448.605			−0.556582
$807$	0.991790	+	0.991790i	0.00122898	+	0.00122898i
$808$	−401.553	+	401.553i	−0.496972	+	0.496972i
$809$		−	1351.17i		−	1.67017i	−0.550121	−	0.835085i	$-0.685418\pi$
$809$		−	1351.17i		−	1.67017i	0.550121	−	0.835085i	$-0.314582\pi$
$810$	−20.3393	+	16.1968i	−0.0251102	+	0.0199961i
$811$	509.726			0.628516			0.314258	−	0.949338i	$-0.398244\pi$
$811$	509.726			0.628516			0.314258	+	0.949338i	$0.398244\pi$
$812$	−124.339	−	124.339i	−0.153127	−	0.153127i
$813$	418.753	−	418.753i	0.515071	−	0.515071i
$814$		−	96.4057i		−	0.118434i
$815$	29.5462	+	37.1029i	0.0362531	+	0.0455250i
$816$	607.305			0.744247
$817$	−381.637	−	381.637i	−0.467120	−	0.467120i
$818$	−70.7672	+	70.7672i	−0.0865125	+	0.0865125i
$819$			184.786i			0.225624i
$820$	−925.857	−	104.973i	−1.12909	−	0.128016i
$821$	−220.673			−0.268785			−0.134393	−	0.990928i	$-0.542908\pi$
$821$	−220.673			−0.268785			−0.134393	+	0.990928i	$0.542908\pi$
$822$	90.1875	+	90.1875i	0.109717	+	0.109717i
$823$	864.049	−	864.049i	1.04988	−	1.04988i	0.0511881	−	0.998689i	$-0.483699\pi$
$823$	864.049	−	864.049i	1.04988	−	1.04988i	0.998689	−	0.0511881i	$-0.0163008\pi$
$824$			561.490i			0.681420i
$825$	−229.649	+	143.851i	−0.278362	+	0.174365i
$826$	−15.2989			−0.0185217
$827$	289.315	+	289.315i	0.349837	+	0.349837i	0.860049	−	0.510212i	$-0.170433\pi$
$827$	289.315	+	289.315i	0.349837	+	0.349837i	−0.510212	+	0.860049i	$0.670433\pi$
$828$	132.124	−	132.124i	0.159570	−	0.159570i
$829$		−	460.234i		−	0.555167i	−0.960701	−	0.277584i	$-0.910466\pi$
$829$		−	460.234i		−	0.555167i	0.960701	−	0.277584i	$-0.0895336\pi$
$830$	2.98798	−	26.3538i	0.00359997	−	0.0317516i
$831$	−684.805			−0.824073
$832$	562.069	+	562.069i	0.675564	+	0.675564i
$833$	−143.368	+	143.368i	−0.172110	+	0.172110i
$834$		−	88.5699i		−	0.106199i
$835$	585.318	−	466.108i	0.700979	−	0.558213i
$836$	164.096			0.196287
$837$	−122.536	−	122.536i	−0.146399	−	0.146399i
$838$	28.3174	−	28.3174i	0.0337917	−	0.0337917i
$839$			859.488i			1.02442i	0.858860	+	0.512210i	$0.171173\pi$
$839$			859.488i			1.02442i	−0.858860	+	0.512210i	$0.828827\pi$
$840$	−63.2230	−	79.3927i	−0.0752655	−	0.0945151i
$841$	512.356			0.609222
$842$	62.5201	+	62.5201i	0.0742519	+	0.0742519i
$843$	470.091	−	470.091i	0.557640	−	0.557640i
$844$			296.696i			0.351535i
$845$	−1853.13	−	210.107i	−2.19305	−	0.248647i
$846$	115.051			0.135994
$847$	153.102	+	153.102i	0.180758	+	0.180758i
$848$	350.820	−	350.820i	0.413703	−	0.413703i
$849$			821.815i			0.967980i
$850$	93.6684	−	407.765i	0.110198	−	0.479724i
$851$	−452.957			−0.532265
$852$	−93.6906	−	93.6906i	−0.109965	−	0.109965i
$853$	717.258	−	717.258i	0.840865	−	0.840865i	−0.148107	−	0.988971i	$-0.547318\pi$
$853$	717.258	−	717.258i	0.840865	−	0.840865i	0.988971	+	0.148107i	$0.0473179\pi$
$854$		−	130.978i		−	0.153371i
$855$	−12.0864	+	106.601i	−0.0141361	+	0.124680i
$856$	203.092			0.237256
$857$	−36.5861	−	36.5861i	−0.0426909	−	0.0426909i	0.685439	−	0.728130i	$-0.259610\pi$
$857$	−36.5861	−	36.5861i	−0.0426909	−	0.0426909i	−0.728130	+	0.685439i	$0.759610\pi$
$858$	103.099	−	103.099i	0.120162	−	0.120162i
$859$		−	1379.61i		−	1.60607i	−0.595935	−	0.803033i	$-0.703218\pi$
$859$		−	1379.61i		−	1.60607i	0.595935	−	0.803033i	$-0.296782\pi$
$860$	−1082.08	+	861.693i	−1.25823	+	1.00197i
$861$	232.941			0.270547
$862$	−56.4518	−	56.4518i	−0.0654893	−	0.0654893i
$863$	914.825	−	914.825i	1.06005	−	1.06005i	0.0619741	−	0.998078i	$-0.480260\pi$
$863$	914.825	−	914.825i	1.06005	−	1.06005i	0.998078	−	0.0619741i	$-0.0197396\pi$
$864$		−	128.407i		−	0.148620i
$865$	769.849	+	966.743i	0.889999	+	1.11762i
$866$	64.8430			0.0748765
$867$	−673.548	−	673.548i	−0.776872	−	0.776872i
$868$	228.740	−	228.740i	0.263525	−	0.263525i
$869$		−	200.170i		−	0.230345i
$870$	−90.1340	−	10.2193i	−0.103602	−	0.0117464i
$871$	394.862			0.453344
$872$	273.317	+	273.317i	0.313437	+	0.313437i
$873$	94.6033	−	94.6033i	0.108366	−	0.108366i
$874$			70.2064i			0.0803277i
$875$	298.267	−	142.870i	0.340877	−	0.163280i
$876$	316.924			0.361785
$877$	1008.35	+	1008.35i	1.14977	+	1.14977i	0.986597	+	0.163175i	$0.0521736\pi$
$877$	1008.35	+	1008.35i	1.14977	+	1.14977i	0.163175	+	0.986597i	$0.447826\pi$
$878$	221.432	−	221.432i	0.252201	−	0.252201i
$879$			544.715i			0.619698i
$880$	42.6727	−	376.371i	0.0484917	−	0.427694i
$881$	−199.243			−0.226155			−0.113077	−	0.993586i	$-0.536071\pi$
$881$	−199.243			−0.226155			−0.113077	+	0.993586i	$0.536071\pi$
$882$	8.57971	+	8.57971i	0.00972756	+	0.00972756i
$883$	−555.536	+	555.536i	−0.629146	+	0.629146i	−0.947853	−	0.318707i	$-0.896751\pi$
$883$	−555.536	+	555.536i	−0.629146	+	0.629146i	0.318707	+	0.947853i	$0.396751\pi$
$884$		−	2472.18i		−	2.79658i
$885$	67.7999	−	53.9913i	0.0766100	−	0.0610071i
$886$	−323.214			−0.364802
$887$	633.737	+	633.737i	0.714473	+	0.714473i	0.967468	−	0.252995i	$-0.0814156\pi$
$887$	633.737	+	633.737i	0.714473	+	0.714473i	−0.252995	+	0.967468i	$0.581416\pi$
$888$	−144.639	+	144.639i	−0.162882	+	0.162882i
$889$			203.152i			0.228517i
$890$	−261.798	−	328.755i	−0.294155	−	0.369387i
$891$	56.3227			0.0632130
$892$	833.787	+	833.787i	0.934739	+	0.934739i
$893$	335.683	−	335.683i	0.375905	−	0.375905i
$894$			205.530i			0.229899i
$895$	−90.3062	−	10.2389i	−0.100901	−	0.0114401i
$896$	313.721			0.350136
$897$	−484.406	−	484.406i	−0.540029	−	0.540029i
$898$	−195.334	+	195.334i	−0.217522	+	0.217522i
$899$		−	604.588i		−	0.672511i
$900$	267.983	+	61.5587i	0.297758	+	0.0683986i
$901$	−1187.10			−1.31754
$902$	−129.966	−	129.966i	−0.144087	−	0.144087i
$903$	244.521	−	244.521i	0.270787	−	0.270787i
$904$			90.4289i			0.100032i
$905$	−67.9042	+	598.911i	−0.0750323	+	0.661781i
$906$	−175.660			−0.193885
$907$	−54.4248	−	54.4248i	−0.0600053	−	0.0600053i	0.676467	−	0.736473i	$-0.263510\pi$
$907$	−54.4248	−	54.4248i	−0.0600053	−	0.0600053i	−0.736473	+	0.676467i	$0.763510\pi$
$908$	682.503	−	682.503i	0.751655	−	0.751655i
$909$			384.621i			0.423125i
$910$	−139.201	+	110.850i	−0.152968	+	0.121813i
$911$	413.285			0.453660			0.226830	−	0.973934i	$-0.427164\pi$
$911$	413.285			0.453660			0.226830	+	0.973934i	$0.427164\pi$
$912$	−106.040	−	106.040i	−0.116271	−	0.116271i
$913$	−40.6261	+	40.6261i	−0.0444973	+	0.0444973i
$914$		−	5.23088i		−	0.00572307i
$915$	462.234	+	580.454i	0.505174	+	0.634376i
$916$	1099.42			1.20024
$917$	−68.7299	−	68.7299i	−0.0749508	−	0.0749508i
$918$	−61.4898	+	61.4898i	−0.0669824	+	0.0669824i
$919$			1275.48i			1.38790i	0.720023	+	0.693951i	$0.244131\pi$
$919$			1275.48i			1.38790i	−0.720023	+	0.693951i	$0.755869\pi$
$920$	373.858	+	42.3878i	0.406368	+	0.0460737i
$921$	−647.660			−0.703214
$922$	92.9775	+	92.9775i	0.100843	+	0.100843i
$923$	−343.497	+	343.497i	−0.372153	+	0.372153i
$924$			105.139i			0.113786i
$925$	−353.838	−	564.879i	−0.382528	−	0.610679i
$926$	−4.31766			−0.00466270
$927$	268.907	+	268.907i	0.290083	+	0.290083i
$928$	316.779	−	316.779i	0.341356	−	0.341356i
$929$			1580.92i			1.70174i	0.525375	+	0.850871i	$0.323925\pi$
$929$			1580.92i			1.70174i	−0.525375	+	0.850871i	$0.676075\pi$
$930$	18.7999	−	165.814i	0.0202150	−	0.178295i
$931$	50.0659			0.0537765
$932$	−172.039	−	172.039i	−0.184592	−	0.184592i
$933$	−376.550	+	376.550i	−0.403591	+	0.403591i
$934$			144.471i			0.154680i
$935$	−708.980	+	564.584i	−0.758267	+	0.603833i
$936$	−309.362			−0.330515
$937$	−716.815	−	716.815i	−0.765010	−	0.765010i	0.212213	−	0.977223i	$-0.431933\pi$
$937$	−716.815	−	716.815i	−0.765010	−	0.765010i	−0.977223	+	0.212213i	$0.931933\pi$
$938$	18.3336	−	18.3336i	0.0195454	−	0.0195454i
$939$		−	164.313i		−	0.174987i
$940$	−757.935	−	951.781i	−0.806313	−	1.01253i
$941$	1118.51			1.18864			0.594321	−	0.804228i	$-0.297421\pi$
$941$	1118.51			1.18864			0.594321	+	0.804228i	$0.297421\pi$
$942$	−22.5824	−	22.5824i	−0.0239729	−	0.0239729i
$943$	−610.640	+	610.640i	−0.647551	+	0.647551i
$944$			121.150i			0.128336i
$945$	−68.3010	−	7.74393i	−0.0722762	−	0.00819464i
$946$	−272.855			−0.288430
$947$	−61.6150	−	61.6150i	−0.0650633	−	0.0650633i	0.673826	−	0.738890i	$-0.264650\pi$
$947$	−61.6150	−	61.6150i	−0.0650633	−	0.0650633i	−0.738890	+	0.673826i	$0.764650\pi$
$948$	−143.620	+	143.620i	−0.151498	+	0.151498i
$949$		−	1161.94i		−	1.22438i
$950$	−87.5537	+	54.8434i	−0.0921618	+	0.0577299i
$951$	237.421			0.249654
$952$	−240.020	−	240.020i	−0.252122	−	0.252122i
$953$	984.214	−	984.214i	1.03275	−	1.03275i	0.0333085	−	0.999445i	$-0.489396\pi$
$953$	984.214	−	984.214i	1.03275	−	1.03275i	0.999445	−	0.0333085i	$-0.0106044\pi$
$954$			71.0412i			0.0744666i
$955$	33.1591	−	292.462i	0.0347216	−	0.306243i
$956$	568.688			0.594862
$957$	138.947	+	138.947i	0.145190	+	0.145190i
$958$	145.223	−	145.223i	0.151590	−	0.151590i
$959$			337.195i			0.351611i
$960$	−231.308	+	184.198i	−0.240945	+	0.191873i
$961$	151.224			0.157361
$962$	253.598	+	253.598i	0.263616	+	0.263616i
$963$	97.2639	−	97.2639i	0.101001	−	0.101001i
$964$			416.477i			0.432030i
$965$	−14.3556	−	18.0271i	−0.0148763	−	0.0186810i
$966$	−44.9824			−0.0465656
$967$	−822.841	−	822.841i	−0.850921	−	0.850921i	0.139325	−	0.990247i	$-0.455507\pi$
$967$	−822.841	−	822.841i	−0.850921	−	0.850921i	−0.990247	+	0.139325i	$0.955507\pi$
$968$	−256.317	+	256.317i	−0.264791	+	0.264791i
$969$			358.816i			0.370296i
$970$	128.016	+	14.5144i	0.131975	+	0.0149633i
$971$	−1691.65			−1.74217			−0.871086	−	0.491131i	$-0.836584\pi$
$971$	−1691.65			−1.74217			−0.871086	+	0.491131i	$0.836584\pi$
$972$	−40.4110	−	40.4110i	−0.0415751	−	0.0415751i
$973$	165.574	−	165.574i	0.170168	−	0.170168i
$974$		−	213.394i		−	0.219090i
$975$	225.693	−	982.504i	0.231480	−	1.00770i
$976$	−1037.20			−1.06270
$977$	926.154	+	926.154i	0.947957	+	0.947957i	0.998711	−	0.0507539i	$-0.0161624\pi$
$977$	926.154	+	926.154i	0.947957	+	0.947957i	−0.0507539	+	0.998711i	$0.516162\pi$
$978$	6.71270	−	6.71270i	0.00686370	−	0.00686370i
$979$			910.375i			0.929903i
$980$	14.4557	−	127.499i	0.0147508	−	0.130101i
$981$	261.793			0.266863
$982$	264.807	+	264.807i	0.269661	+	0.269661i
$983$	−821.842	+	821.842i	−0.836055	+	0.836055i	−0.988337	−	0.152282i	$-0.951338\pi$
$983$	−821.842	+	821.842i	−0.836055	+	0.836055i	0.152282	+	0.988337i	$0.451338\pi$
$984$			389.981i			0.396322i
$985$	−69.4115	+	55.2747i	−0.0704686	+	0.0561164i
$986$	−303.389			−0.307696
$987$	215.078	+	215.078i	0.217911	+	0.217911i
$988$	−431.659	+	431.659i	−0.436901	+	0.436901i
$989$			1281.99i			1.29625i
$990$	33.7870	+	42.4283i	0.0341283	+	0.0428569i
$991$	−765.742			−0.772696			−0.386348	−	0.922353i	$-0.626264\pi$
$991$	−765.742			−0.772696			−0.386348	+	0.922353i	$0.626264\pi$
$992$	582.759	+	582.759i	0.587459	+	0.587459i
$993$	−368.283	+	368.283i	−0.370879	+	0.370879i
$994$			31.8975i			0.0320900i
$995$	−1943.75	−	220.381i	−1.95351	−	0.221488i
$996$	58.2976			0.0585317
$997$	−406.099	−	406.099i	−0.407321	−	0.407321i	0.473483	−	0.880803i	$-0.342997\pi$
$997$	−406.099	−	406.099i	−0.407321	−	0.407321i	−0.880803	+	0.473483i	$0.842997\pi$
$998$	72.4850	−	72.4850i	0.0726303	−	0.0726303i
$999$			138.540i			0.138679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.22.6	✓	24
3.2	odd	2		315.3.o.b.127.7		24
5.2	odd	4		525.3.l.e.43.7		24
5.3	odd	4	inner	105.3.l.a.43.6	yes	24
5.4	even	2		525.3.l.e.232.7		24
15.8	even	4		315.3.o.b.253.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.6	✓	24	1.1	even	1	trivial
105.3.l.a.43.6	yes	24	5.3	odd	4	inner
315.3.o.b.127.7		24	3.2	odd	2
315.3.o.b.253.7		24	15.8	even	4
525.3.l.e.43.7		24	5.2	odd	4
525.3.l.e.232.7		24	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +(2.25992 - 1.79965i) q^{10} -6.25808 q^{11} +(4.49011 + 4.49011i) q^{12} +(16.4621 - 16.4621i) q^{13} -1.52868i q^{14} +(5.39486 + 6.77462i) q^{15} -12.1054 q^{16} +(20.4811 + 20.4811i) q^{17} +(1.22567 - 1.22567i) q^{18} -7.15227i q^{19} +(-18.2141 - 2.06511i) q^{20} +4.58258 q^{21} +(-2.55679 - 2.55679i) q^{22} +(-12.0129 + 12.0129i) q^{23} +7.67197i q^{24} +(-24.3654 - 5.59702i) q^{25} +13.4514 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.85876 + 6.85876i) q^{28} +18.1286i q^{29} +(-0.563715 + 4.97193i) q^{30} -33.3500 q^{31} +(-17.4740 - 17.4740i) q^{32} +(7.66455 - 7.66455i) q^{33} +16.7354i q^{34} +(-10.3484 + 8.24078i) q^{35} -10.9985 q^{36} +(18.8529 + 18.8529i) q^{37} +(2.92211 - 2.92211i) q^{38} +40.3237i q^{39} +(-13.7964 - 17.3249i) q^{40} +50.8319 q^{41} +(1.87225 + 1.87225i) q^{42} +(53.3589 - 53.3589i) q^{43} +22.9431i q^{44} +(-14.9045 - 1.68986i) q^{45} -9.81596 q^{46} +(46.9338 + 46.9338i) q^{47} +(14.8260 - 14.8260i) q^{48} +7.00000i q^{49} +(-7.66797 - 12.2414i) q^{50} -50.1682 q^{51} +(-60.3527 - 60.3527i) q^{52} +(-28.9805 + 28.9805i) q^{53} +3.00227i q^{54} +(-3.52510 + 31.0912i) q^{55} -11.7191 q^{56} +(8.75971 + 8.75971i) q^{57} +(-7.40656 + 7.40656i) q^{58} -10.0079i q^{59} +(24.8369 - 19.7784i) q^{60} +85.6806 q^{61} +(-13.6254 - 13.6254i) q^{62} +(-5.61249 + 5.61249i) q^{63} +34.1432i q^{64} +(-72.5135 - 91.0593i) q^{65} +6.26283 q^{66} +(11.9931 + 11.9931i) q^{67} +(75.0869 - 75.0869i) q^{68} -29.4256i q^{69} +(-7.59476 - 0.861089i) q^{70} -20.8660 q^{71} +(-9.39621 - 9.39621i) q^{72} +(35.2913 - 35.2913i) q^{73} +15.4050i q^{74} +(36.6963 - 22.9865i) q^{75} -26.2214 q^{76} +(11.7078 + 11.7078i) q^{77} +(-16.4746 + 16.4746i) q^{78} +31.9858i q^{79} +(-6.81882 + 60.1416i) q^{80} -9.00000 q^{81} +(20.7677 + 20.7677i) q^{82} +(6.49178 - 6.49178i) q^{83} -16.8005i q^{84} +(113.290 - 90.2167i) q^{85} +43.6003 q^{86} +(-22.2029 - 22.2029i) q^{87} +(-19.6007 + 19.6007i) q^{88} -145.472i q^{89} +(-5.39894 - 6.77976i) q^{90} -61.5955 q^{91} +(44.0414 + 44.0414i) q^{92} +(40.8453 - 40.8453i) q^{93} +38.3503i q^{94} +(-35.5337 - 4.02879i) q^{95} +42.8024 q^{96} +(31.5344 + 31.5344i) q^{97} +(-2.85990 + 2.85990i) q^{98} +18.7742i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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