LMFDB - Embedded newform 105.3.l.a.43.7

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			43.7
Character	$\chi$	$=$	105.43
Dual form			105.3.l.a.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +(-0.186396 - 4.77318i) q^{10} +7.59829 q^{11} +(-3.78113 + 3.78113i) q^{12} +(1.12200 + 1.12200i) q^{13} +2.52765i q^{14} +(8.65366 - 0.337932i) q^{15} -5.88043 q^{16} +(-3.43635 + 3.43635i) q^{17} +(2.02663 + 2.02663i) q^{18} -26.3120i q^{19} +(11.3328 + 10.4810i) q^{20} -4.58258 q^{21} +(5.13298 - 5.13298i) q^{22} +(-24.2663 - 24.2663i) q^{23} +11.7276i q^{24} +(-1.94957 - 24.9239i) q^{25} +1.51592 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-5.77577 - 5.77577i) q^{28} +22.3579i q^{29} +(5.61764 - 6.07421i) q^{30} -18.3927 q^{31} +(-23.1236 + 23.1236i) q^{32} +(9.30597 + 9.30597i) q^{33} +4.64281i q^{34} +(0.516200 + 13.2187i) q^{35} -9.26184 q^{36} +(-34.4244 + 34.4244i) q^{37} +(-17.7749 - 17.7749i) q^{38} +2.74832i q^{39} +(33.8289 - 1.32104i) q^{40} +37.4590 q^{41} +(-3.09573 + 3.09573i) q^{42} +(-55.1278 - 55.1278i) q^{43} +23.4581i q^{44} +(11.0124 + 10.1846i) q^{45} -32.7859 q^{46} +(40.8541 - 40.8541i) q^{47} +(-7.20203 - 7.20203i) q^{48} -7.00000i q^{49} +(-18.1542 - 15.5201i) q^{50} -8.41731 q^{51} +(-3.46392 + 3.46392i) q^{52} +(-9.39948 - 9.39948i) q^{53} +4.96421i q^{54} +(25.7953 - 27.8918i) q^{55} -17.9142 q^{56} +(32.2255 - 32.2255i) q^{57} +(15.1037 + 15.1037i) q^{58} +49.7795i q^{59} +(1.04329 + 26.7163i) q^{60} +88.3465 q^{61} +(-12.4251 + 12.4251i) q^{62} +(-5.61249 - 5.61249i) q^{63} +7.72024i q^{64} +(7.92767 - 0.309582i) q^{65} +12.5732 q^{66} +(-40.5887 + 40.5887i) q^{67} +(-10.6090 - 10.6090i) q^{68} -59.4401i q^{69} +(9.27851 + 8.58108i) q^{70} +136.425 q^{71} +(-14.3633 + 14.3633i) q^{72} +(5.85157 + 5.85157i) q^{73} +46.5103i q^{74} +(28.1377 - 32.9131i) q^{75} +81.2325 q^{76} +(-14.2151 + 14.2151i) q^{77} +(1.85661 + 1.85661i) q^{78} +66.4377i q^{79} +(-19.9634 + 21.5859i) q^{80} -9.00000 q^{81} +(25.3052 - 25.3052i) q^{82} +(-34.8615 - 34.8615i) q^{83} -14.1477i q^{84} +(0.948160 + 24.2802i) q^{85} -74.4824 q^{86} +(-27.3827 + 27.3827i) q^{87} +(36.3789 + 36.3789i) q^{88} -2.03390i q^{89} +(14.3195 - 0.559189i) q^{90} -4.19813 q^{91} +(74.9170 - 74.9170i) q^{92} +(-22.5264 - 22.5264i) q^{93} -55.1975i q^{94} +(-96.5860 - 89.3260i) q^{95} -56.6409 q^{96} +(-58.4649 + 58.4649i) q^{97} +(-4.72881 - 4.72881i) q^{98} +22.7949i 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.675544	−	0.675544i	0.337772	−	0.337772i	−0.517756	−	0.855528i	$-0.673233\pi$
$2$	0.675544	−	0.675544i	0.337772	−	0.337772i	0.855528	+	0.517756i	$0.173233\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$			3.08728i			0.771820i
$5$	3.39488	−	3.67080i	0.678976	−	0.734160i
$5$	3.39488	−	3.67080i	0.678976	−	0.734160i
$6$	1.65474			0.275790
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	4.78777	+	4.78777i	0.598471	+	0.598471i
$9$			3.00000i			0.333333i
$10$	−0.186396	−	4.77318i	−0.0186396	−	0.477318i
$11$	7.59829			0.690754			0.345377	−	0.938464i	$-0.387751\pi$
$11$	7.59829			0.690754			0.345377	+	0.938464i	$0.387751\pi$
$12$	−3.78113	+	3.78113i	−0.315094	+	0.315094i
$13$	1.12200	+	1.12200i	0.0863074	+	0.0863074i	0.748942	−	0.662635i	$-0.230562\pi$
$13$	1.12200	+	1.12200i	0.0863074	+	0.0863074i	−0.662635	+	0.748942i	$0.730562\pi$
$14$			2.52765i			0.180547i
$15$	8.65366	−	0.337932i	0.576911	−	0.0225288i
$16$	−5.88043			−0.367527
$17$	−3.43635	+	3.43635i	−0.202138	+	0.202138i	−0.800916	−	0.598777i	$-0.795653\pi$
$17$	−3.43635	+	3.43635i	−0.202138	+	0.202138i	0.598777	+	0.800916i	$0.295653\pi$
$18$	2.02663	+	2.02663i	0.112591	+	0.112591i
$19$		−	26.3120i		−	1.38484i	−0.721494	−	0.692420i	$-0.756544\pi$
$19$		−	26.3120i		−	1.38484i	0.721494	−	0.692420i	$-0.243456\pi$
$20$	11.3328	+	10.4810i	0.566640	+	0.524048i
$21$	−4.58258			−0.218218
$22$	5.13298	−	5.13298i	0.233317	−	0.233317i
$23$	−24.2663	−	24.2663i	−1.05506	−	1.05506i	−0.998393	−	0.0566642i	$-0.981954\pi$
$23$	−24.2663	−	24.2663i	−1.05506	−	1.05506i	−0.0566642	−	0.998393i	$-0.518046\pi$
$24$			11.7276i			0.488650i
$25$	−1.94957	−	24.9239i	−0.0779827	−	0.996955i
$26$	1.51592			0.0583044
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−5.77577	−	5.77577i	−0.206278	−	0.206278i
$29$			22.3579i			0.770962i	0.922716	+	0.385481i	$0.125965\pi$
$29$			22.3579i			0.770962i	−0.922716	+	0.385481i	$0.874035\pi$
$30$	5.61764	−	6.07421i	0.187255	−	0.202474i
$31$	−18.3927			−0.593314			−0.296657	−	0.954984i	$-0.595872\pi$
$31$	−18.3927			−0.593314			−0.296657	+	0.954984i	$0.595872\pi$
$32$	−23.1236	+	23.1236i	−0.722611	+	0.722611i
$33$	9.30597	+	9.30597i	0.281999	+	0.281999i
$34$			4.64281i			0.136553i
$35$	0.516200	+	13.2187i	0.0147486	+	0.377677i
$36$	−9.26184			−0.257273
$37$	−34.4244	+	34.4244i	−0.930388	+	0.930388i	−0.997730	−	0.0673418i	$-0.978548\pi$
$37$	−34.4244	+	34.4244i	−0.930388	+	0.930388i	0.0673418	+	0.997730i	$0.478548\pi$
$38$	−17.7749	−	17.7749i	−0.467760	−	0.467760i
$39$			2.74832i			0.0704697i
$40$	33.8289	−	1.32104i	0.845721	−	0.0330261i
$41$	37.4590			0.913633			0.456817	−	0.889561i	$-0.348990\pi$
$41$	37.4590			0.913633			0.456817	+	0.889561i	$0.348990\pi$
$42$	−3.09573	+	3.09573i	−0.0737079	+	0.0737079i
$43$	−55.1278	−	55.1278i	−1.28204	−	1.28204i	−0.939504	−	0.342537i	$-0.888714\pi$
$43$	−55.1278	−	55.1278i	−1.28204	−	1.28204i	−0.342537	−	0.939504i	$-0.611286\pi$
$44$			23.4581i			0.533138i
$45$	11.0124	+	10.1846i	0.244720	+	0.226325i
$46$	−32.7859			−0.712738
$47$	40.8541	−	40.8541i	0.869236	−	0.869236i	−0.123151	−	0.992388i	$-0.539300\pi$
$47$	40.8541	−	40.8541i	0.869236	−	0.869236i	0.992388	+	0.123151i	$0.0393001\pi$
$48$	−7.20203	−	7.20203i	−0.150042	−	0.150042i
$49$		−	7.00000i		−	0.142857i
$50$	−18.1542	−	15.5201i	−0.363084	−	0.310403i
$51$	−8.41731			−0.165045
$52$	−3.46392	+	3.46392i	−0.0666138	+	0.0666138i
$53$	−9.39948	−	9.39948i	−0.177349	−	0.177349i	0.612850	−	0.790199i	$-0.290023\pi$
$53$	−9.39948	−	9.39948i	−0.177349	−	0.177349i	−0.790199	+	0.612850i	$0.790023\pi$
$54$			4.96421i			0.0919299i
$55$	25.7953	−	27.8918i	0.469005	−	0.507124i
$56$	−17.9142			−0.319896
$57$	32.2255	−	32.2255i	0.565359	−	0.565359i
$58$	15.1037	+	15.1037i	0.260409	+	0.260409i
$59$			49.7795i			0.843720i	0.906661	+	0.421860i	$0.138623\pi$
$59$			49.7795i			0.843720i	−0.906661	+	0.421860i	$0.861377\pi$
$60$	1.04329	+	26.7163i	0.0173882	+	0.445271i
$61$	88.3465			1.44830			0.724152	−	0.689641i	$-0.242232\pi$
$61$	88.3465			1.44830			0.724152	+	0.689641i	$0.242232\pi$
$62$	−12.4251	+	12.4251i	−0.200405	+	0.200405i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			7.72024i			0.120629i
$65$	7.92767	−	0.309582i	0.121964	−	0.00476280i
$66$	12.5732			0.190503
$67$	−40.5887	+	40.5887i	−0.605802	+	0.605802i	−0.941846	−	0.336044i	$-0.890911\pi$
$67$	−40.5887	+	40.5887i	−0.605802	+	0.605802i	0.336044	+	0.941846i	$0.390911\pi$
$68$	−10.6090	−	10.6090i	−0.156014	−	0.156014i
$69$		−	59.4401i		−	0.861451i
$70$	9.27851	+	8.58108i	0.132550	+	0.122587i
$71$	136.425			1.92148			0.960740	−	0.277451i	$-0.0894897\pi$
$71$	136.425			1.92148			0.960740	+	0.277451i	$0.0894897\pi$
$72$	−14.3633	+	14.3633i	−0.199490	+	0.199490i
$73$	5.85157	+	5.85157i	0.0801585	+	0.0801585i	0.746049	−	0.665891i	$-0.231948\pi$
$73$	5.85157	+	5.85157i	0.0801585	+	0.0801585i	−0.665891	+	0.746049i	$0.731948\pi$
$74$			46.5103i			0.628518i
$75$	28.1377	−	32.9131i	0.375169	−	0.438841i
$76$	81.2325			1.06885
$77$	−14.2151	+	14.2151i	−0.184612	+	0.184612i
$78$	1.85661	+	1.85661i	0.0238027	+	0.0238027i
$79$			66.4377i			0.840984i	0.907296	+	0.420492i	$0.138143\pi$
$79$			66.4377i			0.840984i	−0.907296	+	0.420492i	$0.861857\pi$
$80$	−19.9634	+	21.5859i	−0.249542	+	0.269824i
$81$	−9.00000			−0.111111
$82$	25.3052	−	25.3052i	0.308600	−	0.308600i
$83$	−34.8615	−	34.8615i	−0.420018	−	0.420018i	0.465192	−	0.885210i	$-0.345985\pi$
$83$	−34.8615	−	34.8615i	−0.420018	−	0.420018i	−0.885210	+	0.465192i	$0.845985\pi$
$84$		−	14.1477i		−	0.168425i
$85$	0.948160	+	24.2802i	0.0111548	+	0.285649i
$86$	−74.4824			−0.866075
$87$	−27.3827	+	27.3827i	−0.314744	+	0.314744i
$88$	36.3789	+	36.3789i	0.413396	+	0.413396i
$89$		−	2.03390i		−	0.0228528i	−0.999935	−	0.0114264i	$-0.996363\pi$
$89$		−	2.03390i		−	0.0228528i	0.999935	−	0.0114264i	$-0.00363721\pi$
$90$	14.3195	−	0.559189i	0.159106	−	0.00621321i
$91$	−4.19813			−0.0461332
$92$	74.9170	−	74.9170i	0.814315	−	0.814315i
$93$	−22.5264	−	22.5264i	−0.242220	−	0.242220i
$94$		−	55.1975i		−	0.587207i
$95$	−96.5860	−	89.3260i	−1.01670	−	0.940274i
$96$	−56.6409			−0.590010
$97$	−58.4649	+	58.4649i	−0.602731	+	0.602731i	−0.941036	−	0.338305i	$-0.890146\pi$
$97$	−58.4649	+	58.4649i	−0.602731	+	0.602731i	0.338305	+	0.941036i	$0.390146\pi$
$98$	−4.72881	−	4.72881i	−0.0482531	−	0.0482531i
$99$			22.7949i			0.230251i
$100$	76.9470	−	6.01886i	0.769470	−	0.0601886i
$101$	72.4773			0.717597			0.358798	−	0.933415i	$-0.383187\pi$
$101$	72.4773			0.717597			0.358798	+	0.933415i	$0.383187\pi$
$102$	−5.68626	+	5.68626i	−0.0557476	+	0.0557476i
$103$	96.7717	+	96.7717i	0.939531	+	0.939531i	0.998273	−	0.0587421i	$-0.0187090\pi$
$103$	96.7717	+	96.7717i	0.939531	+	0.939531i	−0.0587421	+	0.998273i	$0.518709\pi$
$104$			10.7437i			0.103305i
$105$	−15.5573	+	16.8217i	−0.148165	+	0.160207i
$106$	−12.6995			−0.119807
$107$	12.4803	−	12.4803i	0.116638	−	0.116638i	−0.646379	−	0.763017i	$-0.723717\pi$
$107$	12.4803	−	12.4803i	0.116638	−	0.116638i	0.763017	+	0.646379i	$0.223717\pi$
$108$	−11.3434	−	11.3434i	−0.105031	−	0.105031i
$109$			87.3675i			0.801537i	0.916179	+	0.400769i	$0.131257\pi$
$109$			87.3675i			0.801537i	−0.916179	+	0.400769i	$0.868743\pi$
$110$	−1.41629	−	36.2680i	−0.0128754	−	0.329709i
$111$	−84.3221			−0.759659
$112$	11.0013	−	11.0013i	0.0982257	−	0.0982257i
$113$	21.7147	+	21.7147i	0.192165	+	0.192165i	0.796631	−	0.604466i	$-0.206613\pi$
$113$	21.7147	+	21.7147i	0.192165	+	0.192165i	−0.604466	+	0.796631i	$0.706613\pi$
$114$		−	43.5394i		−	0.381925i
$115$	−171.458	+	6.69558i	−1.49094	+	0.0582224i
$116$	−69.0251			−0.595044
$117$	−3.36599	+	3.36599i	−0.0287691	+	0.0287691i
$118$	33.6282	+	33.6282i	0.284985	+	0.284985i
$119$		−	12.8576i		−	0.108047i
$120$	43.0497	+	39.8138i	0.358747	+	0.331781i
$121$	−63.2659			−0.522859
$122$	59.6819	−	59.6819i	0.489196	−	0.489196i
$123$	45.8777	+	45.8777i	0.372989	+	0.372989i
$124$		−	56.7836i		−	0.457932i
$125$	−98.1091	−	77.4571i	−0.784873	−	0.619657i
$126$	−7.58296			−0.0601822
$127$	−82.7648	+	82.7648i	−0.651692	+	0.651692i	−0.953400	−	0.301709i	$-0.902443\pi$
$127$	−82.7648	+	82.7648i	−0.651692	+	0.651692i	0.301709	+	0.953400i	$0.402443\pi$
$128$	−87.2789	−	87.2789i	−0.681866	−	0.681866i
$129$		−	135.035i		−	1.04678i
$130$	5.14635	−	5.56462i	0.0395873	−	0.0428048i
$131$	−190.287			−1.45257			−0.726285	−	0.687394i	$-0.758755\pi$
$131$	−190.287			−1.45257			−0.726285	+	0.687394i	$0.758755\pi$
$132$	−28.7301	+	28.7301i	−0.217653	+	0.217653i
$133$	49.2252	+	49.2252i	0.370114	+	0.370114i
$134$			54.8390i			0.409246i
$135$	1.01380	+	25.9610i	0.00750961	+	0.192304i
$136$	−32.9049			−0.241948
$137$	122.593	−	122.593i	0.894841	−	0.894841i	−0.100133	−	0.994974i	$-0.531927\pi$
$137$	122.593	−	122.593i	0.894841	−	0.894841i	0.994974	+	0.100133i	$0.0319268\pi$
$138$	−40.1544	−	40.1544i	−0.290974	−	0.290974i
$139$		−	149.073i		−	1.07247i	−0.844070	−	0.536233i	$-0.819847\pi$
$139$		−	149.073i		−	1.07247i	0.844070	−	0.536233i	$-0.180153\pi$
$140$	−40.8098	+	1.59366i	−0.291498	+	0.0113833i
$141$	100.072			0.709729
$142$	92.1611	−	92.1611i	0.649022	−	0.649022i
$143$	8.52526	+	8.52526i	0.0596172	+	0.0596172i
$144$		−	17.6413i		−	0.122509i
$145$	82.0714	+	75.9024i	0.566010	+	0.523465i
$146$	7.90599			0.0541506
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	−106.278	−	106.278i	−0.718093	−	0.718093i
$149$			157.639i			1.05798i	0.848628	+	0.528990i	$0.177429\pi$
$149$			157.639i			1.05798i	−0.848628	+	0.528990i	$0.822571\pi$
$150$	−3.22602	−	41.2425i	−0.0215068	−	0.274950i
$151$	−234.309			−1.55172			−0.775858	−	0.630908i	$-0.782682\pi$
$151$	−234.309			−1.55172			−0.775858	+	0.630908i	$0.782682\pi$
$152$	125.976	−	125.976i	0.828787	−	0.828787i
$153$	−10.3091	−	10.3091i	−0.0673794	−	0.0673794i
$154$			19.2059i			0.124713i
$155$	−62.4412	+	67.5161i	−0.402846	+	0.435588i
$156$	−8.48483			−0.0543899
$157$	−75.2106	+	75.2106i	−0.479048	+	0.479048i	−0.904827	−	0.425779i	$-0.860000\pi$
$157$	−75.2106	+	75.2106i	−0.479048	+	0.479048i	0.425779	+	0.904827i	$0.360000\pi$
$158$	44.8816	+	44.8816i	0.284061	+	0.284061i
$159$		−	23.0239i		−	0.144805i
$160$	6.38027	+	163.384i	0.0398767	+	1.02115i
$161$	90.7963			0.563952
$162$	−6.07989	+	6.07989i	−0.0375302	+	0.0375302i
$163$	124.557	+	124.557i	0.764153	+	0.764153i	0.977070	−	0.212918i	$-0.0682966\pi$
$163$	124.557	+	124.557i	0.764153	+	0.764153i	−0.212918	+	0.977070i	$0.568297\pi$
$164$			115.646i			0.705161i
$165$	65.7530	−	2.56771i	0.398503	−	0.0155619i
$166$	−47.1010			−0.283741
$167$	−136.411	+	136.411i	−0.816834	+	0.816834i	−0.985648	−	0.168814i	$-0.946006\pi$
$167$	−136.411	+	136.411i	−0.816834	+	0.816834i	0.168814	+	0.985648i	$0.446006\pi$
$168$	−21.9403	−	21.9403i	−0.130597	−	0.130597i
$169$		−	166.482i		−	0.985102i
$170$	17.0428	+	15.7618i	0.100252	+	0.0927164i
$171$	78.9359			0.461614
$172$	170.195	−	170.195i	0.989505	−	0.989505i
$173$	121.020	+	121.020i	0.699538	+	0.699538i	0.964311	−	0.264773i	$-0.0852969\pi$
$173$	121.020	+	121.020i	0.699538	+	0.699538i	−0.264773	+	0.964311i	$0.585297\pi$
$174$			36.9965i			0.212623i
$175$	50.2756	+	42.9810i	0.287289	+	0.245606i
$176$	−44.6812			−0.253871
$177$	−60.9672	+	60.9672i	−0.344447	+	0.344447i
$178$	−1.37399	−	1.37399i	−0.00771902	−	0.00771902i
$179$		−	57.2144i		−	0.319634i	−0.987147	−	0.159817i	$-0.948910\pi$
$179$		−	57.2144i		−	0.319634i	0.987147	−	0.159817i	$-0.0510904\pi$
$180$	−31.4429	+	33.9984i	−0.174683	+	0.188880i
$181$	294.230			1.62558			0.812791	−	0.582555i	$-0.197947\pi$
$181$	294.230			1.62558			0.812791	+	0.582555i	$0.197947\pi$
$182$	−2.83602	+	2.83602i	−0.0155825	+	0.0155825i
$183$	108.202	+	108.202i	0.591267	+	0.591267i
$184$		−	232.363i		−	1.26284i
$185$	9.49839	+	243.232i	0.0513427	+	1.31477i
$186$	−30.4352			−0.163630
$187$	−26.1104	+	26.1104i	−0.139628	+	0.139628i
$188$	126.128	+	126.128i	0.670894	+	0.670894i
$189$		−	13.7477i		−	0.0727393i
$190$	−125.592	+	4.90446i	−0.661009	+	0.0258129i
$191$	246.643			1.29133			0.645663	−	0.763622i	$-0.276581\pi$
$191$	246.643			1.29133			0.645663	+	0.763622i	$0.276581\pi$
$192$	−9.45532	+	9.45532i	−0.0492465	+	0.0492465i
$193$	100.720	+	100.720i	0.521867	+	0.521867i	0.918135	−	0.396268i	$-0.129695\pi$
$193$	100.720	+	100.720i	0.521867	+	0.521867i	−0.396268	+	0.918135i	$0.629695\pi$
$194$			78.9913i			0.407171i
$195$	10.0885	+	9.33021i	0.0517361	+	0.0478472i
$196$	21.6110			0.110260
$197$	−14.9915	+	14.9915i	−0.0760991	+	0.0760991i	−0.744132	−	0.668033i	$-0.767137\pi$
$197$	−14.9915	+	14.9915i	−0.0760991	+	0.0760991i	0.668033	+	0.744132i	$0.267137\pi$
$198$	15.3989	+	15.3989i	0.0777724	+	0.0777724i
$199$		−	287.332i		−	1.44388i	−0.691957	−	0.721939i	$-0.743251\pi$
$199$		−	287.332i		−	1.44388i	0.691957	−	0.721939i	$-0.256749\pi$
$200$	109.996	−	128.664i	0.549978	−	0.643319i
$201$	−99.4217			−0.494635
$202$	48.9616	−	48.9616i	0.242384	−	0.242384i
$203$	−41.8278	−	41.8278i	−0.206048	−	0.206048i
$204$		−	25.9866i		−	0.127385i
$205$	127.169	−	137.504i	0.620335	−	0.670753i
$206$	130.747			0.634694
$207$	72.7990	−	72.7990i	0.351686	−	0.351686i
$208$	−6.59782	−	6.59782i	−0.0317203	−	0.0317203i
$209$		−	199.926i		−	0.956584i
$210$	0.854176	+	21.8734i	0.00406750	+	0.104159i
$211$	−399.559			−1.89365			−0.946823	−	0.321755i	$-0.895727\pi$
$211$	−399.559			−1.89365			−0.946823	+	0.321755i	$0.895727\pi$
$212$	29.0188	−	29.0188i	0.136881	−	0.136881i
$213$	167.086	+	167.086i	0.784441	+	0.784441i
$214$		−	16.8619i		−	0.0787940i
$215$	−389.515	+	15.2109i	−1.81170	+	0.0707483i
$216$	−35.1828			−0.162883
$217$	34.4097	−	34.4097i	0.158570	−	0.158570i
$218$	59.0206	+	59.0206i	0.270737	+	0.270737i
$219$			14.3334i			0.0654492i
$220$	86.1099	+	79.6373i	0.391409	+	0.361988i
$221$	−7.71115			−0.0348921
$222$	−56.9633	+	56.9633i	−0.256591	+	0.256591i
$223$	−210.325	−	210.325i	−0.943162	−	0.943162i	0.0553078	−	0.998469i	$-0.482386\pi$
$223$	−210.325	−	210.325i	−0.943162	−	0.943162i	−0.998469	+	0.0553078i	$0.982386\pi$
$224$		−	86.5204i		−	0.386252i
$225$	74.7716	−	5.84870i	0.332318	−	0.0259942i
$226$	29.3384			0.129816
$227$	130.724	−	130.724i	0.575877	−	0.575877i	−0.357888	−	0.933765i	$-0.616503\pi$
$227$	130.724	−	130.724i	0.575877	−	0.575877i	0.933765	+	0.357888i	$0.116503\pi$
$228$	99.4891	+	99.4891i	0.436356	+	0.436356i
$229$			256.942i			1.12202i	0.827809	+	0.561010i	$0.189587\pi$
$229$			256.942i			1.12202i	−0.827809	+	0.561010i	$0.810413\pi$
$230$	−111.304	+	120.351i	−0.483932	+	0.523264i
$231$	−34.8198			−0.150735
$232$	−107.044	+	107.044i	−0.461399	+	0.461399i
$233$	−60.6918	−	60.6918i	−0.260480	−	0.260480i	0.564769	−	0.825249i	$-0.308965\pi$
$233$	−60.6918	−	60.6918i	−0.260480	−	0.260480i	−0.825249	+	0.564769i	$0.808965\pi$
$234$			4.54775i			0.0194348i
$235$	−11.2725	−	288.662i	−0.0479680	−	1.22835i
$236$	−153.683			−0.651200
$237$	−81.3693	+	81.3693i	−0.343330	+	0.343330i
$238$	−8.68591	−	8.68591i	−0.0364954	−	0.0364954i
$239$			66.9426i			0.280095i	0.990145	+	0.140047i	$0.0447255\pi$
$239$			66.9426i			0.280095i	−0.990145	+	0.140047i	$0.955275\pi$
$240$	−50.8872	+	1.98719i	−0.212030	+	0.00827995i
$241$	82.5830			0.342668			0.171334	−	0.985213i	$-0.445192\pi$
$241$	82.5830			0.342668			0.171334	+	0.985213i	$0.445192\pi$
$242$	−42.7389	+	42.7389i	−0.176607	+	0.176607i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			272.750i			1.11783i
$245$	−25.6956	−	23.7642i	−0.104880	−	0.0969966i
$246$	61.9848			0.251971
$247$	29.5219	−	29.5219i	0.119522	−	0.119522i
$248$	−88.0602	−	88.0602i	−0.355081	−	0.355081i
$249$		−	85.3929i		−	0.342943i
$250$	−118.603	+	13.9514i	−0.474411	+	0.0558054i
$251$	197.943			0.788619			0.394309	−	0.918978i	$-0.370984\pi$
$251$	197.943			0.788619			0.394309	+	0.918978i	$0.370984\pi$
$252$	17.3273	−	17.3273i	0.0687592	−	0.0687592i
$253$	−184.383	−	184.383i	−0.728785	−	0.728785i
$254$			111.823i			0.440246i
$255$	−28.5758	+	30.8983i	−0.112062	+	0.121170i
$256$	−148.802			−0.581259
$257$	−206.394	+	206.394i	−0.803091	+	0.803091i	−0.983577	−	0.180487i	$-0.942233\pi$
$257$	−206.394	+	206.394i	−0.803091	+	0.803091i	0.180487	+	0.983577i	$0.442233\pi$
$258$	−91.2220	−	91.2220i	−0.353574	−	0.353574i
$259$		−	128.804i		−	0.497313i
$260$	0.955766	+	24.4749i	0.00367602	+	0.0941344i
$261$	−67.0737			−0.256987
$262$	−128.547	+	128.547i	−0.490637	+	0.490637i
$263$	235.719	+	235.719i	0.896270	+	0.896270i	0.995104	−	0.0988340i	$-0.0315113\pi$
$263$	235.719	+	235.719i	0.896270	+	0.896270i	−0.0988340	+	0.995104i	$0.531511\pi$
$264$			89.1097i			0.337537i
$265$	−66.4137	+	2.59351i	−0.250618	+	0.00978683i
$266$	66.5076			0.250028
$267$	2.49100	−	2.49100i	0.00932960	−	0.00932960i
$268$	−125.309	−	125.309i	−0.467570	−	0.467570i
$269$		−	379.956i		−	1.41248i	−0.707974	−	0.706238i	$-0.750391\pi$
$269$		−	379.956i		−	1.41248i	0.707974	−	0.706238i	$-0.249609\pi$
$270$	18.2226	+	16.8529i	0.0674913	+	0.0624182i
$271$	−239.134			−0.882414			−0.441207	−	0.897405i	$-0.645450\pi$
$271$	−239.134			−0.882414			−0.441207	+	0.897405i	$0.645450\pi$
$272$	20.2072	−	20.2072i	0.0742913	−	0.0742913i
$273$	−5.14163	−	5.14163i	−0.0188338	−	0.0188338i
$274$		−	165.634i		−	0.604504i
$275$	−14.8134	−	189.379i	−0.0538668	−	0.688650i
$276$	183.508			0.664885
$277$	118.114	−	118.114i	0.426403	−	0.426403i	−0.460998	−	0.887401i	$-0.652509\pi$
$277$	118.114	−	118.114i	0.426403	−	0.426403i	0.887401	+	0.460998i	$0.152509\pi$
$278$	−100.705	−	100.705i	−0.362249	−	0.362249i
$279$		−	55.1782i		−	0.197771i
$280$	−60.8165	+	65.7594i	−0.217202	+	0.234855i
$281$	337.248			1.20017			0.600086	−	0.799936i	$-0.295133\pi$
$281$	337.248			1.20017			0.600086	+	0.799936i	$0.295133\pi$
$282$	67.6028	−	67.6028i	0.239726	−	0.239726i
$283$	−91.9392	−	91.9392i	−0.324873	−	0.324873i	0.525760	−	0.850633i	$-0.323781\pi$
$283$	−91.9392	−	91.9392i	−0.324873	−	0.324873i	−0.850633	+	0.525760i	$0.823781\pi$
$284$			421.182i			1.48304i
$285$	−8.89167	−	227.695i	−0.0311988	−	0.798929i
$286$	11.5184			0.0402740
$287$	−70.0793	+	70.0793i	−0.244179	+	0.244179i
$288$	−69.3707	−	69.3707i	−0.240870	−	0.240870i
$289$			265.383i			0.918280i
$290$	106.718	−	4.16743i	0.367994	−	0.0143705i
$291$	−143.209			−0.492128
$292$	−18.0654	+	18.0654i	−0.0618680	+	0.0618680i
$293$	−348.854	−	348.854i	−1.19063	−	1.19063i	−0.976891	−	0.213736i	$-0.931437\pi$
$293$	−348.854	−	348.854i	−1.19063	−	1.19063i	−0.213736	−	0.976891i	$-0.568563\pi$
$294$		−	11.5832i		−	0.0393985i
$295$	182.731	+	168.995i	0.619426	+	0.572866i
$296$	−329.632			−1.11362
$297$	−27.9179	+	27.9179i	−0.0939997	+	0.0939997i
$298$	106.492	+	106.492i	0.357356	+	0.357356i
$299$		−	54.4534i		−	0.182119i
$300$	101.612	+	86.8689i	0.338707	+	0.289563i
$301$	206.269			0.685280
$302$	−158.286	+	158.286i	−0.524126	+	0.524126i
$303$	88.7662	+	88.7662i	0.292958	+	0.292958i
$304$			154.726i			0.508966i
$305$	299.926	−	324.302i	0.983363	−	1.06329i
$306$	−13.9284			−0.0455178
$307$	306.607	−	306.607i	0.998720	−	0.998720i	−0.00127914	−	0.999999i	$-0.500407\pi$
$307$	306.607	−	306.607i	0.998720	−	0.998720i	0.999999	+	0.00127914i	$0.000407163\pi$
$308$	−43.8860	−	43.8860i	−0.142487	−	0.142487i
$309$			237.041i			0.767124i
$310$	3.42834	+	87.7918i	0.0110592	+	0.283199i
$311$	−74.8228			−0.240588			−0.120294	−	0.992738i	$-0.538384\pi$
$311$	−74.8228			−0.240588			−0.120294	+	0.992738i	$0.538384\pi$
$312$	−13.1583	+	13.1583i	−0.0421741	+	0.0421741i
$313$	101.601	+	101.601i	0.324605	+	0.324605i	0.850531	−	0.525925i	$-0.176281\pi$
$313$	101.601	+	101.601i	0.324605	+	0.324605i	−0.525925	+	0.850531i	$0.676281\pi$
$314$			101.616i			0.323618i
$315$	−39.6560	+	1.54860i	−0.125892	+	0.00491619i
$316$	−205.112			−0.649089
$317$	124.097	−	124.097i	0.391475	−	0.391475i	−0.483738	−	0.875213i	$-0.660721\pi$
$317$	124.097	−	124.097i	0.391475	−	0.391475i	0.875213	+	0.483738i	$0.160721\pi$
$318$	−15.5537	−	15.5537i	−0.0489109	−	0.0489109i
$319$			169.882i			0.532545i
$320$	28.3395	+	26.2093i	0.0885608	+	0.0819040i
$321$	30.5703			0.0952345
$322$	61.3369	−	61.3369i	0.190487	−	0.190487i
$323$	90.4172	+	90.4172i	0.279929	+	0.279929i
$324$		−	27.7855i		−	0.0857578i
$325$	25.7771	−	30.1519i	0.0793141	−	0.0927751i
$326$	168.287			0.516219
$327$	−107.003	+	107.003i	−0.327226	+	0.327226i
$328$	179.345	+	179.345i	0.546783	+	0.546783i
$329$			152.862i			0.464626i
$330$	42.6844	−	46.1536i	0.129347	−	0.139860i
$331$	397.089			1.19966			0.599832	−	0.800126i	$-0.295234\pi$
$331$	397.089			1.19966			0.599832	+	0.800126i	$0.295234\pi$
$332$	107.627	−	107.627i	0.324179	−	0.324179i
$333$	−103.273	−	103.273i	−0.310129	−	0.310129i
$334$			184.304i			0.551807i
$335$	11.1993	+	286.787i	0.0334307	+	0.856081i
$336$	26.9475			0.0802009
$337$	−185.463	+	185.463i	−0.550334	+	0.550334i	−0.926537	−	0.376203i	$-0.877230\pi$
$337$	−185.463	+	185.463i	−0.550334	+	0.550334i	0.376203	+	0.926537i	$0.377230\pi$
$338$	−112.466	−	112.466i	−0.332740	−	0.332740i
$339$			53.1898i			0.156902i
$340$	−74.9597	+	2.92724i	−0.220470	+	0.00860952i
$341$	−139.753			−0.409834
$342$	53.3247	−	53.3247i	0.155920	−	0.155920i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	527.878i		−	1.53453i
$345$	−218.193	−	201.792i	−0.632443	−	0.584905i
$346$	163.509			0.472569
$347$	−182.221	+	182.221i	−0.525133	+	0.525133i	−0.919117	−	0.393984i	$-0.871097\pi$
$347$	−182.221	+	182.221i	−0.525133	+	0.525133i	0.393984	+	0.919117i	$0.371097\pi$
$348$	−84.5382	−	84.5382i	−0.242926	−	0.242926i
$349$			416.140i			1.19238i	0.802844	+	0.596189i	$0.203319\pi$
$349$			416.140i			1.19238i	−0.802844	+	0.596189i	$0.796681\pi$
$350$	62.9989	−	4.92783i	0.179997	−	0.0140795i
$351$	−8.24495			−0.0234899
$352$	−175.700	+	175.700i	−0.499147	+	0.499147i
$353$	−402.531	−	402.531i	−1.14031	−	1.14031i	−0.988393	−	0.151921i	$-0.951454\pi$
$353$	−402.531	−	402.531i	−1.14031	−	1.14031i	−0.151921	−	0.988393i	$-0.548546\pi$
$354$			82.3720i			0.232689i
$355$	463.147	−	500.789i	1.30464	−	1.41067i
$356$	6.27921			0.0176382
$357$	15.7473	−	15.7473i	0.0441102	−	0.0441102i
$358$	−38.6508	−	38.6508i	−0.107963	−	0.107963i
$359$			120.174i			0.334747i	0.985894	+	0.167373i	$0.0535285\pi$
$359$			120.174i			0.334747i	−0.985894	+	0.167373i	$0.946471\pi$
$360$	3.96313	+	101.487i	0.0110087	+	0.281907i
$361$	−331.320			−0.917785
$362$	198.766	−	198.766i	0.549076	−	0.549076i
$363$	−77.4846	−	77.4846i	−0.213456	−	0.213456i
$364$		−	12.9608i		−	0.0356066i
$365$	41.3453	−	1.61457i	0.113275	−	0.00442348i
$366$	146.190			0.399427
$367$	162.325	−	162.325i	0.442301	−	0.442301i	−0.450483	−	0.892785i	$-0.648748\pi$
$367$	162.325	−	162.325i	0.442301	−	0.442301i	0.892785	+	0.450483i	$0.148748\pi$
$368$	142.696	+	142.696i	0.387762	+	0.387762i
$369$			112.377i			0.304544i
$370$	170.730	+	157.897i	0.461433	+	0.426749i
$371$	35.1696			0.0947968
$372$	69.5454	−	69.5454i	0.186950	−	0.186950i
$373$	306.523	+	306.523i	0.821776	+	0.821776i	0.986363	−	0.164586i	$-0.0526289\pi$
$373$	306.523	+	306.523i	0.821776	+	0.821776i	−0.164586	+	0.986363i	$0.552629\pi$
$374$			35.2774i			0.0943247i
$375$	−25.2935	−	215.024i	−0.0674493	−	0.573397i
$376$	391.200			1.04043
$377$	−25.0855	+	25.0855i	−0.0665398	+	0.0665398i
$378$	−9.28719	−	9.28719i	−0.0245693	−	0.0245693i
$379$			126.143i			0.332830i	0.986056	+	0.166415i	$0.0532192\pi$
$379$			126.143i			0.332830i	−0.986056	+	0.166415i	$0.946781\pi$
$380$	275.775	−	298.188i	0.725723	−	0.784706i
$381$	−202.732			−0.532104
$382$	166.618	−	166.618i	0.436174	−	0.436174i
$383$	349.571	+	349.571i	0.912717	+	0.912717i	0.996485	−	0.0837685i	$-0.0266956\pi$
$383$	349.571	+	349.571i	0.912717	+	0.912717i	−0.0837685	+	0.996485i	$0.526696\pi$
$384$		−	213.789i		−	0.556742i
$385$	3.92224	+	100.439i	0.0101876	+	0.260882i
$386$	136.082			0.352544
$387$	165.383	−	165.383i	0.427347	−	0.427347i
$388$	−180.498	−	180.498i	−0.465200	−	0.465200i
$389$			165.348i			0.425060i	0.977155	+	0.212530i	$0.0681704\pi$
$389$			165.348i			0.425060i	−0.977155	+	0.212530i	$0.931830\pi$
$390$	13.1182	−	0.512277i	0.0336364	−	0.00131353i
$391$	166.775			0.426535
$392$	33.5144	−	33.5144i	0.0854959	−	0.0854959i
$393$	−233.053	−	233.053i	−0.593009	−	0.593009i
$394$			20.2549i			0.0514083i
$395$	243.880	+	225.548i	0.617417	+	0.571008i
$396$	−70.3742			−0.177713
$397$	−42.7811	+	42.7811i	−0.107761	+	0.107761i	−0.758931	−	0.651171i	$-0.774278\pi$
$397$	−42.7811	+	42.7811i	−0.107761	+	0.107761i	0.651171	+	0.758931i	$0.274278\pi$
$398$	−194.105	−	194.105i	−0.487701	−	0.487701i
$399$			120.577i			0.302197i
$400$	11.4643	+	146.563i	0.0286607	+	0.366408i
$401$	92.5492			0.230796			0.115398	−	0.993319i	$-0.463186\pi$
$401$	92.5492			0.230796			0.115398	+	0.993319i	$0.463186\pi$
$402$	−67.1637	+	67.1637i	−0.167074	+	0.167074i
$403$	−20.6366	−	20.6366i	−0.0512074	−	0.0512074i
$404$			223.758i			0.553856i
$405$	−30.5539	+	33.0372i	−0.0754418	+	0.0815734i
$406$	−56.5130			−0.139195
$407$	−261.566	+	261.566i	−0.642669	+	0.642669i
$408$	−40.3001	−	40.3001i	−0.0987748	−	0.0987748i
$409$			71.7158i			0.175344i	0.996149	+	0.0876721i	$0.0279428\pi$
$409$			71.7158i			0.175344i	−0.996149	+	0.0876721i	$0.972057\pi$
$410$	−6.98222	−	178.798i	−0.0170298	−	0.436094i
$411$	300.291			0.730635
$412$	−298.761	+	298.761i	−0.725149	+	0.725149i
$413$	−93.1289	−	93.1289i	−0.225494	−	0.225494i
$414$		−	98.3578i		−	0.237579i
$415$	−246.320	+	9.61901i	−0.593543	+	0.0231783i
$416$	−51.8891			−0.124733
$417$	182.576	−	182.576i	0.437832	−	0.437832i
$418$	−135.059	−	135.059i	−0.323107	−	0.323107i
$419$		−	472.026i		−	1.12655i	−0.826268	−	0.563277i	$-0.809540\pi$
$419$		−	472.026i		−	1.12655i	0.826268	−	0.563277i	$-0.190460\pi$
$420$	−51.9334	−	48.0298i	−0.123651	−	0.114357i
$421$	746.988			1.77432			0.887159	−	0.461464i	$-0.152676\pi$
$421$	746.988			1.77432			0.887159	+	0.461464i	$0.152676\pi$
$422$	−269.920	+	269.920i	−0.639620	+	0.639620i
$423$	122.562	+	122.562i	0.289745	+	0.289745i
$424$		−	90.0051i		−	0.212276i
$425$	92.3466	+	78.9478i	0.217286	+	0.185759i
$426$	225.748			0.529924
$427$	−165.281	+	165.281i	−0.387075	+	0.387075i
$428$	38.5301	+	38.5301i	0.0900235	+	0.0900235i
$429$			20.8825i			0.0486772i
$430$	−252.859	+	273.410i	−0.588044	+	0.635838i
$431$	−754.426			−1.75041			−0.875204	−	0.483754i	$-0.839273\pi$
$431$	−754.426			−1.75041			−0.875204	+	0.483754i	$0.839273\pi$
$432$	21.6061	−	21.6061i	0.0500141	−	0.0500141i
$433$	−344.305	−	344.305i	−0.795162	−	0.795162i	0.187166	−	0.982328i	$-0.440070\pi$
$433$	−344.305	−	344.305i	−0.795162	−	0.795162i	−0.982328	+	0.187166i	$0.940070\pi$
$434$		−	46.4905i		−	0.107121i
$435$	7.55546	+	193.478i	0.0173689	+	0.444776i
$436$	−269.728			−0.618643
$437$	−638.495	+	638.495i	−1.46109	+	1.46109i
$438$	9.68282	+	9.68282i	0.0221069	+	0.0221069i
$439$			49.1546i			0.111970i	0.998432	+	0.0559848i	$0.0178298\pi$
$439$			49.1546i			0.111970i	−0.998432	+	0.0559848i	$0.982170\pi$
$440$	257.042	−	10.0377i	0.584185	−	0.0228129i
$441$	21.0000			0.0476190
$442$	−5.20922	+	5.20922i	−0.0117856	+	0.0117856i
$443$	117.289	+	117.289i	0.264762	+	0.264762i	0.826985	−	0.562224i	$-0.190054\pi$
$443$	117.289	+	117.289i	0.264762	+	0.264762i	−0.562224	+	0.826985i	$0.690054\pi$
$444$		−	260.326i		−	0.586320i
$445$	−7.46603	−	6.90484i	−0.0167776	−	0.0155165i
$446$	−284.168			−0.637147
$447$	−193.068	+	193.068i	−0.431918	+	0.431918i
$448$	−14.4432	−	14.4432i	−0.0322394	−	0.0322394i
$449$		−	296.976i		−	0.661416i	−0.943733	−	0.330708i	$-0.892712\pi$
$449$		−	296.976i		−	0.661416i	0.943733	−	0.330708i	$-0.107288\pi$
$450$	46.5604	−	54.4625i	0.103468	−	0.121028i
$451$	284.624			0.631096
$452$	−67.0393	+	67.0393i	−0.148317	+	0.148317i
$453$	−286.969	−	286.969i	−0.633485	−	0.633485i
$454$		−	176.620i		−	0.389030i
$455$	−14.2521	+	15.4105i	−0.0313234	+	0.0338692i
$456$	308.576			0.676702
$457$	−257.425	+	257.425i	−0.563293	+	0.563293i	−0.930241	−	0.366948i	$-0.880403\pi$
$457$	−257.425	+	257.425i	−0.563293	+	0.563293i	0.366948	+	0.930241i	$0.380403\pi$
$458$	173.576	+	173.576i	0.378987	+	0.378987i
$459$		−	25.2519i		−	0.0550151i
$460$	−20.6711	−	529.339i	−0.0449372	−	1.15074i
$461$	−357.600			−0.775704			−0.387852	−	0.921722i	$-0.626783\pi$
$461$	−357.600			−0.775704			−0.387852	+	0.921722i	$0.626783\pi$
$462$	−23.5223	+	23.5223i	−0.0509140	+	0.0509140i
$463$	78.7851	+	78.7851i	0.170162	+	0.170162i	0.787051	−	0.616888i	$-0.211607\pi$
$463$	78.7851	+	78.7851i	0.170162	+	0.170162i	−0.616888	+	0.787051i	$0.711607\pi$
$464$		−	131.474i		−	0.283349i
$465$	−159.165	+	6.21550i	−0.342289	+	0.0133667i
$466$	−81.9999			−0.175965
$467$	654.767	−	654.767i	1.40207	−	1.40207i	0.608570	−	0.793500i	$-0.291743\pi$
$467$	654.767	−	654.767i	1.40207	−	1.40207i	0.793500	−	0.608570i	$-0.208257\pi$
$468$	−10.3918	−	10.3918i	−0.0222046	−	0.0222046i
$469$		−	151.869i		−	0.323815i
$470$	−202.619	−	187.389i	−0.431104	−	0.398700i
$471$	−184.228			−0.391141
$472$	−238.333	+	238.333i	−0.504942	+	0.504942i
$473$	−418.877	−	418.877i	−0.885575	−	0.885575i
$474$			109.937i			0.231935i
$475$	−655.796	+	51.2970i	−1.38062	+	0.107994i
$476$	39.6952			0.0833932
$477$	28.1984	−	28.1984i	0.0591162	−	0.0591162i
$478$	45.2227	+	45.2227i	0.0946081	+	0.0946081i
$479$			262.707i			0.548449i	0.961666	+	0.274225i	$0.0884212\pi$
$479$			262.707i			0.548449i	−0.961666	+	0.274225i	$0.911579\pi$
$480$	−192.289	+	207.918i	−0.400603	+	0.433162i
$481$	−77.2480			−0.160599
$482$	55.7884	−	55.7884i	0.115744	−	0.115744i
$483$	111.202	+	111.202i	0.230232	+	0.230232i
$484$		−	195.320i		−	0.403553i
$485$	16.1317	+	413.095i	0.0332612	+	0.851742i
$486$	−14.8926			−0.0306433
$487$	−42.8848	+	42.8848i	−0.0880591	+	0.0880591i	−0.749764	−	0.661705i	$-0.769833\pi$
$487$	−42.8848	+	42.8848i	−0.0880591	+	0.0880591i	0.661705	+	0.749764i	$0.269833\pi$
$488$	422.983	+	422.983i	0.866768	+	0.866768i
$489$			305.101i			0.623928i
$490$	−33.4122	+	1.30478i	−0.0681883	+	0.00266281i
$491$	−58.5988			−0.119346			−0.0596730	−	0.998218i	$-0.519006\pi$
$491$	−58.5988			−0.119346			−0.0596730	+	0.998218i	$0.519006\pi$
$492$	−141.637	+	141.637i	−0.287881	+	0.287881i
$493$	−76.8296	−	76.8296i	−0.155841	−	0.155841i
$494$		−	39.8867i		−	0.0807424i
$495$	83.6755	+	77.3859i	0.169041	+	0.156335i
$496$	108.157			0.218059
$497$	−255.228	+	255.228i	−0.513537	+	0.513537i
$498$	−57.6867	−	57.6867i	−0.115837	−	0.115837i
$499$		−	421.048i		−	0.843784i	−0.906646	−	0.421892i	$-0.861366\pi$
$499$		−	421.048i		−	0.843784i	0.906646	−	0.421892i	$-0.138634\pi$
$500$	239.132	−	302.890i	0.478264	−	0.605781i
$501$	−334.138			−0.666942
$502$	133.719	−	133.719i	0.266373	−	0.266373i
$503$	357.650	+	357.650i	0.711034	+	0.711034i	0.966751	−	0.255718i	$-0.0823118\pi$
$503$	357.650	+	357.650i	0.711034	+	0.711034i	−0.255718	+	0.966751i	$0.582312\pi$
$504$		−	53.7426i		−	0.106632i
$505$	246.052	−	266.050i	0.487231	−	0.526831i
$506$	−249.117			−0.492326
$507$	203.898	−	203.898i	0.402166	−	0.402166i
$508$	−255.518	−	255.518i	−0.502989	−	0.502989i
$509$		−	934.911i		−	1.83676i	−0.395700	−	0.918380i	$-0.629498\pi$
$509$		−	934.911i		−	1.83676i	0.395700	−	0.918380i	$-0.370502\pi$
$510$	1.56896	+	40.1773i	0.00307638	+	0.0787790i
$511$	−21.8946			−0.0428465
$512$	248.593	−	248.593i	0.485533	−	0.485533i
$513$	96.6764	+	96.6764i	0.188453	+	0.188453i
$514$			278.857i			0.542523i
$515$	683.758	−	26.7013i	1.32769	−	0.0518472i
$516$	416.891			0.807928
$517$	310.421	−	310.421i	0.600428	−	0.600428i
$518$	−87.0129	−	87.0129i	−0.167978	−	0.167978i
$519$			296.438i			0.571171i
$520$	39.4381	+	36.4736i	0.0758424	+	0.0701416i
$521$	−73.1865			−0.140473			−0.0702366	−	0.997530i	$-0.522375\pi$
$521$	−73.1865			−0.140473			−0.0702366	+	0.997530i	$0.522375\pi$
$522$	−45.3112	+	45.3112i	−0.0868031	+	0.0868031i
$523$	53.6581	+	53.6581i	0.102597	+	0.102597i	0.756542	−	0.653945i	$-0.226887\pi$
$523$	53.6581	+	53.6581i	0.102597	+	0.102597i	−0.653945	+	0.756542i	$0.726887\pi$
$524$		−	587.469i		−	1.12112i
$525$	8.93404	+	114.216i	0.0170172	+	0.217553i
$526$	318.477			0.605470
$527$	63.2039	−	63.2039i	0.119932	−	0.119932i
$528$	−54.7231	−	54.7231i	−0.103642	−	0.103642i
$529$			648.709i			1.22629i
$530$	−43.1134	+	46.6174i	−0.0813460	+	0.0879574i
$531$	−149.338			−0.281240
$532$	−151.972	+	151.972i	−0.285662	+	0.285662i
$533$	42.0288	+	42.0288i	0.0788533	+	0.0788533i
$534$		−	3.36556i		−	0.00630256i
$535$	−3.44356	−	88.1816i	−0.00643656	−	0.164825i
$536$	−388.659			−0.725110
$537$	70.0731	−	70.0731i	0.130490	−	0.130490i
$538$	−256.677	−	256.677i	−0.477095	−	0.477095i
$539$		−	53.1880i		−	0.0986791i
$540$	−80.1488	+	3.12988i	−0.148424	+	0.00579607i
$541$	−1071.71			−1.98098			−0.990490	−	0.137581i	$-0.956067\pi$
$541$	−1071.71			−1.98098			−0.990490	+	0.137581i	$0.956067\pi$
$542$	−161.546	+	161.546i	−0.298055	+	0.298055i
$543$	360.357	+	360.357i	0.663641	+	0.663641i
$544$		−	158.921i		−	0.292135i
$545$	320.709	+	296.602i	0.588457	+	0.544225i
$546$	−6.94680			−0.0127231
$547$	601.898	−	601.898i	1.10036	−	1.10036i	0.105994	−	0.994367i	$-0.466197\pi$
$547$	601.898	−	601.898i	1.10036	−	1.10036i	0.994367	−	0.105994i	$-0.0338026\pi$
$548$	378.480	+	378.480i	0.690656	+	0.690656i
$549$			265.039i			0.482768i
$550$	−137.941	−	117.927i	−0.250801	−	0.214412i
$551$	588.281			1.06766
$552$	284.586	−	284.586i	0.515553	−	0.515553i
$553$	−124.294	−	124.294i	−0.224762	−	0.224762i
$554$		−	159.582i		−	0.288054i
$555$	−286.264	+	309.530i	−0.515790	+	0.557711i
$556$	460.229			0.827751
$557$	−242.099	+	242.099i	−0.434648	+	0.434648i	−0.890206	−	0.455558i	$-0.849440\pi$
$557$	−242.099	+	242.099i	−0.434648	+	0.434648i	0.455558	+	0.890206i	$0.349440\pi$
$558$	−37.2753	−	37.2753i	−0.0668016	−	0.0668016i
$559$		−	123.706i		−	0.221299i
$560$	−3.03548	−	77.7315i	−0.00542050	−	0.138806i
$561$	−63.9572			−0.114006
$562$	227.826	−	227.826i	0.405384	−	0.405384i
$563$	76.1930	+	76.1930i	0.135334	+	0.135334i	0.771529	−	0.636195i	$-0.219492\pi$
$563$	76.1930	+	76.1930i	0.135334	+	0.135334i	−0.636195	+	0.771529i	$0.719492\pi$
$564$			308.950i			0.547783i
$565$	153.429	−	5.99152i	0.271556	−	0.0106045i
$566$	−124.218			−0.219466
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	653.172	+	653.172i	1.14995	+	1.14995i
$569$			319.028i			0.560683i	0.959900	+	0.280341i	$0.0904476\pi$
$569$			319.028i			0.560683i	−0.959900	+	0.280341i	$0.909552\pi$
$570$	−159.825	−	147.811i	−0.280394	−	0.259318i
$571$	−26.8933			−0.0470987			−0.0235493	−	0.999723i	$-0.507497\pi$
$571$	−26.8933			−0.0470987			−0.0235493	+	0.999723i	$0.507497\pi$
$572$	−26.3199	+	26.3199i	−0.0460137	+	0.0460137i
$573$	302.075	+	302.075i	0.527182	+	0.527182i
$574$			94.6833i			0.164953i
$575$	−557.502	+	652.119i	−0.969568	+	1.13412i
$576$	−23.1607			−0.0402096
$577$	302.359	−	302.359i	0.524019	−	0.524019i	−0.394764	−	0.918783i	$-0.629174\pi$
$577$	302.359	−	302.359i	0.524019	−	0.524019i	0.918783	+	0.394764i	$0.129174\pi$
$578$	179.278	+	179.278i	0.310169	+	0.310169i
$579$			246.713i			0.426102i
$580$	−234.332	+	253.378i	−0.404021	+	0.436858i
$581$	130.440			0.224509
$582$	−96.7441	+	96.7441i	−0.166227	+	0.166227i
$583$	−71.4200	−	71.4200i	−0.122504	−	0.122504i
$584$			56.0319i			0.0959451i
$585$	0.928746	+	23.7830i	0.00158760	+	0.0406547i
$586$	−471.332			−0.804321
$587$	16.9036	−	16.9036i	0.0287966	−	0.0287966i	−0.692562	−	0.721358i	$-0.743518\pi$
$587$	16.9036	−	16.9036i	0.0287966	−	0.0287966i	0.721358	+	0.692562i	$0.243518\pi$
$588$	26.4679	+	26.4679i	0.0450135	+	0.0450135i
$589$			483.949i			0.821646i
$590$	237.606	−	9.27872i	0.402723	−	0.0157266i
$591$	−36.7216			−0.0621347
$592$	202.430	−	202.430i	0.341943	−	0.341943i
$593$	411.219	+	411.219i	0.693456	+	0.693456i	0.962991	−	0.269535i	$-0.0868699\pi$
$593$	411.219	+	411.219i	0.693456	+	0.693456i	−0.269535	+	0.962991i	$0.586870\pi$
$594$			37.7195i			0.0635009i
$595$	−47.1979	−	43.6502i	−0.0793242	−	0.0733617i
$596$	−486.676			−0.816570
$597$	351.908	−	351.908i	0.589461	−	0.589461i
$598$	−36.7857	−	36.7857i	−0.0615145	−	0.0615145i
$599$			637.724i			1.06465i	0.846541	+	0.532324i	$0.178681\pi$
$599$			637.724i			1.06465i	−0.846541	+	0.532324i	$0.821319\pi$
$600$	292.297	−	22.8637i	0.487162	−	0.0381062i
$601$	576.764			0.959674			0.479837	−	0.877358i	$-0.340696\pi$
$601$	576.764			0.959674			0.479837	+	0.877358i	$0.340696\pi$
$602$	139.344	−	139.344i	0.231468	−	0.231468i
$603$	−121.766	−	121.766i	−0.201934	−	0.201934i
$604$		−	723.378i		−	1.19765i
$605$	−214.780	+	232.237i	−0.355009	+	0.383862i
$606$	119.931			0.197906
$607$	−144.949	+	144.949i	−0.238796	+	0.238796i	−0.816352	−	0.577555i	$-0.804007\pi$
$607$	−144.949	+	144.949i	−0.238796	+	0.238796i	0.577555	+	0.816352i	$0.304007\pi$
$608$	608.427	+	608.427i	1.00070	+	1.00070i
$609$		−	102.457i		−	0.168238i
$610$	−16.4675	−	421.694i	−0.0269959	−	0.691301i
$611$	91.6763			0.150043
$612$	31.8269	−	31.8269i	0.0520048	−	0.0520048i
$613$	588.190	+	588.190i	0.959527	+	0.959527i	0.999212	−	0.0396852i	$-0.0126355\pi$
$613$	588.190	+	588.190i	0.959527	+	0.959527i	−0.0396852	+	0.999212i	$0.512636\pi$
$614$		−	414.253i		−	0.674679i
$615$	324.157	−	12.6586i	0.527085	−	0.0205831i
$616$	−136.117			−0.220970
$617$	688.254	−	688.254i	1.11548	−	1.11548i	0.123088	−	0.992396i	$-0.460720\pi$
$617$	688.254	−	688.254i	1.11548	−	1.11548i	0.992396	−	0.123088i	$-0.0392798\pi$
$618$	160.132	+	160.132i	0.259113	+	0.259113i
$619$		−	1033.56i		−	1.66972i	−0.550459	−	0.834862i	$-0.685547\pi$
$619$		−	1033.56i		−	1.66972i	0.550459	−	0.834862i	$-0.314453\pi$
$620$	−208.441	−	192.773i	−0.336195	−	0.310925i
$621$	178.320			0.287150
$622$	−50.5461	+	50.5461i	−0.0812638	+	0.0812638i
$623$	3.80507	+	3.80507i	0.00610766	+	0.00610766i
$624$		−	16.1613i		−	0.0258995i
$625$	−617.398	+	97.1815i	−0.987837	+	0.155490i
$626$	137.272			0.219285
$627$	244.858	−	244.858i	0.390524	−	0.390524i
$628$	−232.196	−	232.196i	−0.369739	−	0.369739i
$629$		−	236.588i		−	0.376134i
$630$	−25.7432	+	27.8355i	−0.0408623	+	0.0441834i
$631$	−53.6569			−0.0850346			−0.0425173	−	0.999096i	$-0.513538\pi$
$631$	−53.6569			−0.0850346			−0.0425173	+	0.999096i	$0.513538\pi$
$632$	−318.089	+	318.089i	−0.503305	+	0.503305i
$633$	−489.358	−	489.358i	−0.773078	−	0.773078i
$634$		−	167.666i		−	0.264458i
$635$	22.8365	+	584.790i	0.0359630	+	0.920929i
$636$	71.0813			0.111763
$637$	7.85397	−	7.85397i	0.0123296	−	0.0123296i
$638$	114.763	+	114.763i	0.179879	+	0.179879i
$639$			409.275i			0.640493i
$640$	−616.685	+	24.0820i	−0.963570	+	0.0376282i
$641$	−120.207			−0.187531			−0.0937653	−	0.995594i	$-0.529890\pi$
$641$	−120.207			−0.187531			−0.0937653	+	0.995594i	$0.529890\pi$
$642$	20.6516	−	20.6516i	0.0321675	−	0.0321675i
$643$	18.2639	+	18.2639i	0.0284042	+	0.0284042i	0.721166	−	0.692762i	$-0.243606\pi$
$643$	18.2639	+	18.2639i	0.0284042	+	0.0284042i	−0.692762	+	0.721166i	$0.743606\pi$
$644$			280.314i			0.435270i
$645$	−495.686	−	458.427i	−0.768506	−	0.710740i
$646$	122.162			0.189105
$647$	281.286	−	281.286i	0.434754	−	0.434754i	−0.455488	−	0.890242i	$-0.650535\pi$
$647$	281.286	−	281.286i	0.434754	−	0.434754i	0.890242	+	0.455488i	$0.150535\pi$
$648$	−43.0899	−	43.0899i	−0.0664968	−	0.0664968i
$649$			378.239i			0.582803i
$650$	−2.95538	−	37.7825i	−0.00454674	−	0.0581269i
$651$	84.2861			0.129472
$652$	−384.542	+	384.542i	−0.589789	+	0.589789i
$653$	−554.289	−	554.289i	−0.848835	−	0.848835i	0.141152	−	0.989988i	$-0.454919\pi$
$653$	−554.289	−	554.289i	−0.848835	−	0.848835i	−0.989988	+	0.141152i	$0.954919\pi$
$654$			144.570i			0.221056i
$655$	−646.001	+	698.505i	−0.986261	+	1.06642i
$656$	−220.275			−0.335785
$657$	−17.5547	+	17.5547i	−0.0267195	+	0.0267195i
$658$	103.265	+	103.265i	0.156938	+	0.156938i
$659$		−	317.311i		−	0.481504i	−0.970587	−	0.240752i	$-0.922606\pi$
$659$		−	317.311i		−	0.481504i	0.970587	−	0.240752i	$-0.0773941\pi$
$660$	7.92724	+	202.998i	0.0120110	+	0.307573i
$661$	−533.264			−0.806753			−0.403377	−	0.915034i	$-0.632164\pi$
$661$	−533.264			−0.806753			−0.403377	+	0.915034i	$0.632164\pi$
$662$	268.251	−	268.251i	0.405213	−	0.405213i
$663$	−9.44419	−	9.44419i	−0.0142446	−	0.0142446i
$664$		−	333.818i		−	0.502738i
$665$	347.810	−	13.5822i	0.523022	−	0.0204244i
$666$	−139.531			−0.209506
$667$	542.544	−	542.544i	0.813410	−	0.813410i
$668$	−421.140	−	421.140i	−0.630449	−	0.630449i
$669$		−	515.189i		−	0.770088i
$670$	201.303	+	186.172i	0.300452	+	0.277868i
$671$	671.282			1.00042
$672$	105.965	−	105.965i	0.157687	−	0.157687i
$673$	−244.707	−	244.707i	−0.363606	−	0.363606i	0.501533	−	0.865139i	$-0.332770\pi$
$673$	−244.707	−	244.707i	−0.363606	−	0.363606i	−0.865139	+	0.501533i	$0.832770\pi$
$674$			250.576i			0.371775i
$675$	98.7393	+	84.4130i	0.146280	+	0.125056i
$676$	513.978			0.760322
$677$	−380.155	+	380.155i	−0.561529	+	0.561529i	−0.929742	−	0.368213i	$-0.879970\pi$
$677$	−380.155	+	380.155i	−0.561529	+	0.561529i	0.368213	+	0.929742i	$0.379970\pi$
$678$	35.9321	+	35.9321i	0.0529971	+	0.0529971i
$679$		−	218.756i		−	0.322173i
$680$	−111.708	+	120.787i	−0.164277	+	0.177629i
$681$	320.207			0.470202
$682$	−94.4096	+	94.4096i	−0.138430	+	0.138430i
$683$	−739.822	−	739.822i	−1.08319	−	1.08319i	−0.996210	−	0.0869848i	$-0.972277\pi$
$683$	−739.822	−	739.822i	−1.08319	−	1.08319i	−0.0869848	−	0.996210i	$-0.527723\pi$
$684$			243.697i			0.356283i
$685$	−33.8260	−	866.205i	−0.0493810	−	1.26453i
$686$	17.6936			0.0257924
$687$	−314.689	+	314.689i	−0.458062	+	0.458062i
$688$	324.175	+	324.175i	0.471185	+	0.471185i
$689$		−	21.0924i		−	0.0306130i
$690$	−283.718	+	11.0794i	−0.411186	+	0.0160571i
$691$	−909.333			−1.31597			−0.657984	−	0.753032i	$-0.728590\pi$
$691$	−909.333			−1.31597			−0.657984	+	0.753032i	$0.728590\pi$
$692$	−373.623	+	373.623i	−0.539918	+	0.539918i
$693$	−42.6453	−	42.6453i	−0.0615372	−	0.0615372i
$694$			246.197i			0.354750i
$695$	−547.216	−	506.084i	−0.787362	−	0.728179i
$696$	−262.204			−0.376730
$697$	−128.722	+	128.722i	−0.184680	+	0.184680i
$698$	281.121	+	281.121i	0.402752	+	0.402752i
$699$		−	148.664i		−	0.212681i
$700$	−132.694	+	155.215i	−0.189563	+	0.221736i
$701$	−794.647			−1.13359			−0.566795	−	0.823859i	$-0.691817\pi$
$701$	−794.647			−1.13359			−0.566795	+	0.823859i	$0.691817\pi$
$702$	−5.56983	+	5.56983i	−0.00793423	+	0.00793423i
$703$	905.773	+	905.773i	1.28844	+	1.28844i
$704$			58.6606i			0.0833248i
$705$	339.732	−	367.343i	0.481889	−	0.521055i
$706$	−543.854			−0.770332
$707$	−135.593	+	135.593i	−0.191786	+	0.191786i
$708$	−188.223	−	188.223i	−0.265851	−	0.265851i
$709$		−	281.184i		−	0.396592i	−0.980142	−	0.198296i	$-0.936459\pi$
$709$		−	281.184i		−	0.396592i	0.980142	−	0.198296i	$-0.0635407\pi$
$710$	−25.4291	−	651.181i	−0.0358157	−	0.917156i
$711$	−199.313			−0.280328
$712$	9.73783	−	9.73783i	0.0136767	−	0.0136767i
$713$	446.324	+	446.324i	0.625981	+	0.625981i
$714$		−	21.2760i		−	0.0297984i
$715$	60.2368	−	2.35229i	0.0842472	−	0.00328992i
$716$	176.637			0.246700
$717$	−81.9877	+	81.9877i	−0.114348	+	0.114348i
$718$	81.1829	+	81.1829i	0.113068	+	0.113068i
$719$		−	1122.66i		−	1.56143i	−0.624890	−	0.780713i	$-0.714856\pi$
$719$		−	1122.66i		−	1.56143i	0.624890	−	0.780713i	$-0.285144\pi$
$720$	−64.7577	−	59.8901i	−0.0899412	−	0.0831807i
$721$	−362.087			−0.502201
$722$	−223.821	+	223.821i	−0.310002	+	0.310002i
$723$	101.143	+	101.143i	0.139894	+	0.139894i
$724$			908.372i			1.25466i
$725$	557.245	−	43.5882i	0.768614	−	0.0601217i
$726$	−104.689			−0.144199
$727$	−208.125	+	208.125i	−0.286279	+	0.286279i	−0.835607	−	0.549328i	$-0.814884\pi$
$727$	−208.125	+	208.125i	−0.286279	+	0.286279i	0.549328	+	0.835607i	$0.314884\pi$
$728$	−20.0997	−	20.0997i	−0.0276094	−	0.0276094i
$729$		−	27.0000i		−	0.0370370i
$730$	26.8399	−	29.0213i	0.0367670	−	0.0397552i
$731$	378.877			0.518299
$732$	−334.050	+	334.050i	−0.456352	+	0.456352i
$733$	−760.380	−	760.380i	−1.03735	−	1.03735i	−0.999275	−	0.0380787i	$-0.987876\pi$
$733$	−760.380	−	760.380i	−1.03735	−	1.03735i	−0.0380787	−	0.999275i	$-0.512124\pi$
$734$		−	219.315i		−	0.298794i
$735$	−2.36553	−	60.5756i	−0.00321840	−	0.0824158i
$736$	1122.25			1.52479
$737$	−308.405	+	308.405i	−0.418460	+	0.418460i
$738$	75.9155	+	75.9155i	0.102867	+	0.102867i
$739$			425.934i			0.576365i	0.957575	+	0.288183i	$0.0930510\pi$
$739$			425.934i			0.576365i	−0.957575	+	0.288183i	$0.906949\pi$
$740$	−750.924	+	29.3242i	−1.01476	+	0.0396273i
$741$	72.3137			0.0975893
$742$	23.7586	−	23.7586i	0.0320197	−	0.0320197i
$743$	−325.298	−	325.298i	−0.437818	−	0.437818i	0.453459	−	0.891277i	$-0.350190\pi$
$743$	−325.298	−	325.298i	−0.437818	−	0.437818i	−0.891277	+	0.453459i	$0.850190\pi$
$744$		−	215.703i		−	0.289923i
$745$	578.661	+	535.166i	0.776727	+	0.718343i
$746$	414.139			0.555146
$747$	104.585	−	104.585i	0.140006	−	0.140006i
$748$	−80.6102	−	80.6102i	−0.107768	−	0.107768i
$749$			46.6969i			0.0623456i
$750$	−162.345	−	128.171i	−0.216460	−	0.170895i
$751$	−107.270			−0.142836			−0.0714182	−	0.997446i	$-0.522752\pi$
$751$	−107.270			−0.142836			−0.0714182	+	0.997446i	$0.522752\pi$
$752$	−240.240	+	240.240i	−0.319468	+	0.319468i
$753$	242.430	+	242.430i	0.321952	+	0.321952i
$754$			33.8927i			0.0449505i
$755$	−795.451	+	860.102i	−1.05358	+	1.13921i
$756$	42.4431			0.0561417
$757$	537.483	−	537.483i	0.710017	−	0.710017i	−0.256521	−	0.966539i	$-0.582576\pi$
$757$	537.483	−	537.483i	0.710017	−	0.710017i	0.966539	+	0.256521i	$0.0825764\pi$
$758$	85.2149	+	85.2149i	0.112421	+	0.112421i
$759$		−	451.643i		−	0.595051i
$760$	−34.7593	−	890.104i	−0.0457359	−	1.17119i
$761$	−547.917			−0.719996			−0.359998	−	0.932953i	$-0.617223\pi$
$761$	−547.917			−0.719996			−0.359998	+	0.932953i	$0.617223\pi$
$762$	−136.954	+	136.954i	−0.179730	+	0.179730i
$763$	−163.450	−	163.450i	−0.214220	−	0.214220i
$764$			761.458i			0.996672i
$765$	−72.8405	+	2.84448i	−0.0952163	+	0.00371828i
$766$	472.300			0.616580
$767$	−55.8524	+	55.8524i	−0.0728193	+	0.0728193i
$768$	−182.245	−	182.245i	−0.237298	−	0.237298i
$769$			354.375i			0.460826i	0.973093	+	0.230413i	$0.0740077\pi$
$769$			354.375i			0.460826i	−0.973093	+	0.230413i	$0.925992\pi$
$770$	70.5009	+	65.2016i	0.0915596	+	0.0846774i
$771$	−505.561			−0.655721
$772$	−310.952	+	310.952i	−0.402787	+	0.402787i
$773$	−507.940	−	507.940i	−0.657103	−	0.657103i	0.297591	−	0.954694i	$-0.403817\pi$
$773$	−507.940	−	507.940i	−0.657103	−	0.657103i	−0.954694	+	0.297591i	$0.903817\pi$
$774$		−	223.447i		−	0.288692i
$775$	35.8579	+	458.418i	0.0462682	+	0.591507i
$776$	−559.833			−0.721435
$777$	157.752	−	157.752i	0.203027	−	0.203027i
$778$	111.700	+	111.700i	0.143573	+	0.143573i
$779$		−	985.620i		−	1.26524i
$780$	−28.8050	+	31.1461i	−0.0369295	+	0.0399309i
$781$	1036.60			1.32727
$782$	112.664	−	112.664i	0.144072	−	0.144072i
$783$	−82.1482	−	82.1482i	−0.104915	−	0.104915i
$784$			41.1630i			0.0525038i
$785$	20.7521	+	531.414i	0.0264359	+	0.676960i
$786$	−314.875			−0.400604
$787$	630.653	−	630.653i	0.801338	−	0.801338i	−0.181967	−	0.983305i	$-0.558246\pi$
$787$	630.653	−	630.653i	0.801338	−	0.801338i	0.983305	+	0.181967i	$0.0582463\pi$
$788$	−46.2831	−	46.2831i	−0.0587349	−	0.0587349i
$789$			577.391i			0.731801i
$790$	317.119	−	12.3838i	0.401417	−	0.0156756i
$791$	−81.2488			−0.102717
$792$	−109.137	+	109.137i	−0.137799	+	0.137799i
$793$	99.1244	+	99.1244i	0.124999	+	0.124999i
$794$			57.8010i			0.0727972i
$795$	−84.5163	−	78.1635i	−0.106310	−	0.0983189i
$796$	887.074			1.11441
$797$	549.518	−	549.518i	0.689483	−	0.689483i	−0.272634	−	0.962118i	$-0.587895\pi$
$797$	549.518	−	549.518i	0.689483	−	0.689483i	0.962118	+	0.272634i	$0.0878949\pi$
$798$	81.4548	+	81.4548i	0.102074	+	0.102074i
$799$			280.778i			0.351412i
$800$	621.410	+	531.248i	0.776762	+	0.664060i
$801$	6.10169			0.00761759
$802$	62.5210	−	62.5210i	0.0779564	−	0.0779564i
$803$	44.4620	+	44.4620i	0.0553698	+	0.0553698i
$804$		−	306.943i		−	0.381770i
$805$	308.243	−	333.295i	0.382910	−	0.414031i
$806$	−27.8818			−0.0345928
$807$	465.350	−	465.350i	0.576641	−	0.576641i
$808$	347.004	+	347.004i	0.429461	+	0.429461i
$809$		−	1512.58i		−	1.86970i	−0.355048	−	0.934848i	$-0.615536\pi$
$809$		−	1512.58i		−	1.86970i	0.355048	−	0.934848i	$-0.384464\pi$
$810$	1.67757	+	42.9586i	0.00207107	+	0.0530353i
$811$	−1045.50			−1.28915			−0.644573	−	0.764543i	$-0.722965\pi$
$811$	−1045.50			−1.28915			−0.644573	+	0.764543i	$0.722965\pi$
$812$	129.134	−	129.134i	0.159032	−	0.159032i
$813$	−292.879	−	292.879i	−0.360244	−	0.360244i
$814$			353.399i			0.434151i
$815$	880.079	−	34.3678i	1.07985	−	0.0421691i
$816$	49.4974			0.0606586
$817$	−1450.52	+	1450.52i	−1.77542	+	1.77542i
$818$	48.4471	+	48.4471i	0.0592263	+	0.0592263i
$819$		−	12.5944i		−	0.0153777i
$820$	424.515	+	392.606i	0.517701	+	0.478787i
$821$	1039.41			1.26603			0.633013	−	0.774141i	$-0.281818\pi$
$821$	1039.41			1.26603			0.633013	+	0.774141i	$0.281818\pi$
$822$	202.860	−	202.860i	0.246788	−	0.246788i
$823$	631.240	+	631.240i	0.766999	+	0.766999i	0.977577	−	0.210578i	$-0.0675346\pi$
$823$	631.240	+	631.240i	0.766999	+	0.766999i	−0.210578	+	0.977577i	$0.567535\pi$
$824$			926.641i			1.12456i
$825$	213.798	−	250.083i	0.259149	−	0.303131i
$826$	−125.825			−0.152331
$827$	363.393	−	363.393i	0.439411	−	0.439411i	−0.452403	−	0.891814i	$-0.649433\pi$
$827$	363.393	−	363.393i	0.439411	−	0.439411i	0.891814	+	0.452403i	$0.149433\pi$
$828$	224.751	+	224.751i	0.271438	+	0.271438i
$829$			1037.80i			1.25187i	0.779876	+	0.625935i	$0.215282\pi$
$829$			1037.80i			1.25187i	−0.779876	+	0.625935i	$0.784718\pi$
$830$	−159.902	+	172.898i	−0.192653	+	0.208311i
$831$	289.318			0.348156
$832$	−8.66208	+	8.66208i	−0.0104112	+	0.0104112i
$833$	24.0545	+	24.0545i	0.0288769	+	0.0288769i
$834$		−	246.676i		−	0.295775i
$835$	37.6387	+	963.839i	0.0450763	+	1.15430i
$836$	617.228			0.738311
$837$	67.5792	−	67.5792i	0.0807398	−	0.0807398i
$838$	−318.874	−	318.874i	−0.380518	−	0.380518i
$839$			1350.36i			1.60949i	0.593622	+	0.804744i	$0.297698\pi$
$839$			1350.36i			1.60949i	−0.593622	+	0.804744i	$0.702302\pi$
$840$	−155.023	+	6.05378i	−0.184552	+	0.00720689i
$841$	341.124			0.405617
$842$	504.623	−	504.623i	0.599315	−	0.599315i
$843$	413.043	+	413.043i	0.489968	+	0.489968i
$844$		−	1233.55i		−	1.46155i
$845$	−611.123	−	565.187i	−0.723223	−	0.668861i
$846$	165.592			0.195736
$847$	118.360	−	118.360i	0.139740	−	0.139740i
$848$	55.2730	+	55.2730i	0.0651804	+	0.0651804i
$849$		−	225.204i		−	0.265258i
$850$	115.717	−	9.05147i	0.136137	−	0.0106488i
$851$	1670.71			1.96323
$852$	−515.841	+	515.841i	−0.605447	+	0.605447i
$853$	−294.827	−	294.827i	−0.345636	−	0.345636i	0.512845	−	0.858481i	$-0.328591\pi$
$853$	−294.827	−	294.827i	−0.345636	−	0.345636i	−0.858481	+	0.512845i	$0.828591\pi$
$854$			223.309i			0.261486i
$855$	267.978	−	289.758i	0.313425	−	0.338898i
$856$	119.505			0.139609
$857$	−839.471	+	839.471i	−0.979546	+	0.979546i	−0.999795	−	0.0202485i	$-0.993554\pi$
$857$	−839.471	+	839.471i	−0.979546	+	0.979546i	0.0202485	+	0.999795i	$0.493554\pi$
$858$	14.1071	+	14.1071i	0.0164418	+	0.0164418i
$859$			215.750i			0.251164i	0.992083	+	0.125582i	$0.0400798\pi$
$859$			215.750i			0.251164i	−0.992083	+	0.125582i	$0.959920\pi$
$860$	−46.9603	−	1202.54i	−0.0546050	−	1.39831i
$861$	−171.659			−0.199371
$862$	−509.648	+	509.648i	−0.591239	+	0.591239i
$863$	−503.739	−	503.739i	−0.583707	−	0.583707i	0.352213	−	0.935920i	$-0.385429\pi$
$863$	−503.739	−	503.739i	−0.583707	−	0.583707i	−0.935920	+	0.352213i	$0.885429\pi$
$864$		−	169.923i		−	0.196670i
$865$	855.090	−	33.3919i	0.988543	−	0.0386034i
$866$	−465.187			−0.537167
$867$	−325.026	+	325.026i	−0.374886	+	0.374886i
$868$	106.232	+	106.232i	0.122387	+	0.122387i
$869$			504.813i			0.580913i
$870$	135.807	+	125.599i	0.156100	+	0.144366i
$871$	−91.0808			−0.104570
$872$	−418.296	+	418.296i	−0.479697	+	0.479697i
$873$	−175.395	−	175.395i	−0.200910	−	0.200910i
$874$			862.663i			0.987028i
$875$	328.454	−	38.6364i	0.375376	−	0.0441559i
$876$	−44.2511			−0.0505150
$877$	512.283	−	512.283i	0.584131	−	0.584131i	−0.351905	−	0.936036i	$-0.614466\pi$
$877$	512.283	−	512.283i	0.584131	−	0.584131i	0.936036	+	0.351905i	$0.114466\pi$
$878$	33.2061	+	33.2061i	0.0378202	+	0.0378202i
$879$		−	854.514i		−	0.972143i
$880$	−151.687	+	164.016i	−0.172372	+	0.186382i
$881$	−8.98563			−0.0101993			−0.00509967	−	0.999987i	$-0.501623\pi$
$881$	−8.98563			−0.0101993			−0.00509967	+	0.999987i	$0.501623\pi$
$882$	14.1864	−	14.1864i	0.0160844	−	0.0160844i
$883$	−51.0268	−	51.0268i	−0.0577880	−	0.0577880i	0.677622	−	0.735410i	$-0.263011\pi$
$883$	−51.0268	−	51.0268i	−0.0577880	−	0.0577880i	−0.735410	+	0.677622i	$0.763011\pi$
$884$		−	23.8065i		−	0.0269304i
$885$	16.8221	+	430.775i	0.0190080	+	0.486751i
$886$	158.468			0.178858
$887$	502.029	−	502.029i	0.565985	−	0.565985i	−0.365016	−	0.931001i	$-0.618937\pi$
$887$	502.029	−	502.029i	0.565985	−	0.565985i	0.931001	+	0.365016i	$0.118937\pi$
$888$	−403.715	−	403.715i	−0.454634	−	0.454634i
$889$		−	309.678i		−	0.348344i
$890$	−9.70815	+	0.379111i	−0.0109080	+	0.000425967i
$891$	−68.3846			−0.0767504
$892$	649.332	−	649.332i	0.727951	−	0.727951i
$893$	−1074.95	−	1074.95i	−1.20375	−	1.20375i
$894$			260.851i			0.291780i
$895$	−210.023	−	194.236i	−0.234662	−	0.217024i
$896$	326.568			0.364473
$897$	66.6916	−	66.6916i	0.0743496	−	0.0743496i
$898$	−200.620	−	200.620i	−0.223408	−	0.223408i
$899$		−	411.223i		−	0.457423i
$900$	18.0566	+	230.841i	0.0200629	+	0.256490i
$901$	64.5998			0.0716979
$902$	192.276	−	192.276i	0.213166	−	0.213166i
$903$	252.627	+	252.627i	0.279764	+	0.279764i
$904$			207.930i			0.230011i
$905$	998.877	−	1080.06i	1.10373	−	1.19344i
$906$	−387.720			−0.427947
$907$	−185.954	+	185.954i	−0.205021	+	0.205021i	−0.802147	−	0.597126i	$-0.796309\pi$
$907$	−185.954	+	185.954i	−0.205021	+	0.205021i	0.597126	+	0.802147i	$0.296309\pi$
$908$	403.582	+	403.582i	0.444474	+	0.444474i
$909$			217.432i			0.239199i
$910$	0.782516	+	20.0384i	0.000859907	+	0.0220202i
$911$	−1184.97			−1.30073			−0.650365	−	0.759622i	$-0.725384\pi$
$911$	−1184.97			−1.30073			−0.650365	+	0.759622i	$0.725384\pi$
$912$	−189.500	+	189.500i	−0.207785	+	0.207785i
$913$	−264.888	−	264.888i	−0.290129	−	0.290129i
$914$			347.804i			0.380529i
$915$	764.520	−	29.8551i	0.835541	−	0.0326286i
$916$	−793.254			−0.865997
$917$	355.994	−	355.994i	0.388216	−	0.388216i
$918$	−17.0588	−	17.0588i	−0.0185825	−	0.0185825i
$919$			244.007i			0.265514i	0.991149	+	0.132757i	$0.0423830\pi$
$919$			244.007i			0.265514i	−0.991149	+	0.132757i	$0.957617\pi$
$920$	−852.959	−	788.845i	−0.927129	−	0.857440i
$921$	751.031			0.815451
$922$	−241.574	+	241.574i	−0.262011	+	0.262011i
$923$	153.068	+	153.068i	0.165838	+	0.165838i
$924$		−	107.498i		−	0.116340i
$925$	925.101	+	790.876i	1.00011	+	0.855001i
$926$	106.446			0.114952
$927$	−290.315	+	290.315i	−0.313177	+	0.313177i
$928$	−516.994	−	516.994i	−0.557106	−	0.557106i
$929$			319.725i			0.344160i	0.985083	+	0.172080i	$0.0550488\pi$
$929$			319.725i			0.344160i	−0.985083	+	0.172080i	$0.944951\pi$
$930$	−103.324	+	111.721i	−0.111101	+	0.120131i
$931$	−184.184			−0.197834
$932$	187.373	−	187.373i	0.201044	−	0.201044i
$933$	−91.6389	−	91.6389i	−0.0982196	−	0.0982196i
$934$		−	884.647i		−	0.947160i
$935$	7.20440	+	184.488i	0.00770524	+	0.197313i
$936$	−32.2312			−0.0344350
$937$	−815.691	+	815.691i	−0.870535	+	0.870535i	−0.992531	−	0.121996i	$-0.961071\pi$
$937$	−815.691	+	815.691i	−0.870535	+	0.870535i	0.121996	+	0.992531i	$0.461071\pi$
$938$	−102.594	−	102.594i	−0.109376	−	0.109376i
$939$			248.872i			0.265039i
$940$	891.181	−	34.8013i	0.948065	−	0.0370227i
$941$	−506.239			−0.537980			−0.268990	−	0.963143i	$-0.586690\pi$
$941$	−506.239			−0.537980			−0.268990	+	0.963143i	$0.586690\pi$
$942$	−124.454	+	124.454i	−0.132116	+	0.132116i
$943$	−908.992	−	908.992i	−0.963936	−	0.963936i
$944$		−	292.725i		−	0.310090i
$945$	−50.4652	−	46.6719i	−0.0534023	−	0.0493882i
$946$	−565.939			−0.598245
$947$	164.875	−	164.875i	0.174103	−	0.174103i	−0.614677	−	0.788779i	$-0.710713\pi$
$947$	164.875	−	164.875i	0.174103	−	0.174103i	0.788779	+	0.614677i	$0.210713\pi$
$948$	−251.210	−	251.210i	−0.264989	−	0.264989i
$949$			13.1309i			0.0138365i
$950$	−408.366	+	477.672i	−0.429859	+	0.502813i
$951$	303.975			0.319638
$952$	61.5595	−	61.5595i	0.0646633	−	0.0646633i
$953$	232.231	+	232.231i	0.243684	+	0.243684i	0.818372	−	0.574689i	$-0.194877\pi$
$953$	232.231	+	232.231i	0.243684	+	0.243684i	−0.574689	+	0.818372i	$0.694877\pi$
$954$		−	38.0986i		−	0.0399356i
$955$	837.325	−	905.379i	0.876780	−	0.948041i
$956$	−206.671			−0.216183
$957$	−208.062	+	208.062i	−0.217411	+	0.217411i
$958$	177.470	+	177.470i	0.185251	+	0.185251i
$959$			458.702i			0.478313i
$960$	2.60892	+	66.8083i	0.00271762	+	0.0695920i
$961$	−622.707			−0.647978
$962$	−52.1844	+	52.1844i	−0.0542458	+	0.0542458i
$963$	37.4408	+	37.4408i	0.0388793	+	0.0388793i
$964$			254.957i			0.264478i
$965$	711.658	−	27.7908i	0.737469	−	0.0287988i
$966$	150.244			0.155532
$967$	−625.445	+	625.445i	−0.646789	+	0.646789i	−0.952216	−	0.305427i	$-0.901201\pi$
$967$	−625.445	+	625.445i	−0.646789	+	0.646789i	0.305427	+	0.952216i	$0.401201\pi$
$968$	−302.903	−	302.903i	−0.312916	−	0.312916i
$969$			221.476i			0.228561i
$970$	289.961	+	268.166i	0.298929	+	0.276460i
$971$	−513.341			−0.528673			−0.264336	−	0.964431i	$-0.585153\pi$
$971$	−513.341			−0.528673			−0.264336	+	0.964431i	$0.585153\pi$
$972$	34.0302	−	34.0302i	0.0350105	−	0.0350105i
$973$	278.890	+	278.890i	0.286628	+	0.286628i
$974$			57.9411i			0.0594878i
$975$	68.4987	−	5.35803i	0.0702551	−	0.00549542i
$976$	−519.515			−0.532290
$977$	−307.372	+	307.372i	−0.314608	+	0.314608i	−0.846692	−	0.532084i	$-0.821409\pi$
$977$	−307.372	+	307.372i	−0.314608	+	0.314608i	0.532084	+	0.846692i	$0.321409\pi$
$978$	206.109	+	206.109i	0.210745	+	0.210745i
$979$		−	15.4541i		−	0.0157856i
$980$	73.3667	−	79.3296i	0.0748639	−	0.0809485i
$981$	−262.103			−0.267179
$982$	−39.5861	+	39.5861i	−0.0403117	+	0.0403117i
$983$	810.191	+	810.191i	0.824202	+	0.824202i	0.986708	−	0.162506i	$-0.0519576\pi$
$983$	810.191	+	810.191i	0.824202	+	0.824202i	−0.162506	+	0.986708i	$0.551958\pi$
$984$			439.303i			0.446447i
$985$	4.13647	+	105.925i	0.00419946	+	0.107538i
$986$	−103.804			−0.105277
$987$	−187.217	+	187.217i	−0.189683	+	0.189683i
$988$	91.1425	+	91.1425i	0.0922495	+	0.0922495i
$989$			2675.50i			2.70525i
$990$	108.804	−	4.24888i	0.109903	−	0.00429180i
$991$	−833.240			−0.840807			−0.420404	−	0.907337i	$-0.638111\pi$
$991$	−833.240			−0.840807			−0.420404	+	0.907337i	$0.638111\pi$
$992$	425.306	−	425.306i	0.428736	−	0.428736i
$993$	486.332	+	486.332i	0.489761	+	0.489761i
$994$			344.835i			0.346917i
$995$	−1054.74	−	975.457i	−1.06004	−	0.980358i
$996$	263.632			0.264691
$997$	−119.981	+	119.981i	−0.120342	+	0.120342i	−0.764713	−	0.644371i	$-0.777119\pi$
$997$	−119.981	+	119.981i	−0.120342	+	0.120342i	0.644371	+	0.764713i	$0.277119\pi$
$998$	−284.437	−	284.437i	−0.285007	−	0.285007i
$999$		−	252.966i		−	0.253220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.43.7	yes	24
3.2	odd	2		315.3.o.b.253.6		24
5.2	odd	4	inner	105.3.l.a.22.7	✓	24
5.3	odd	4		525.3.l.e.232.6		24
5.4	even	2		525.3.l.e.43.6		24
15.2	even	4		315.3.o.b.127.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.7	✓	24	5.2	odd	4	inner
105.3.l.a.43.7	yes	24	1.1	even	1	trivial
315.3.o.b.127.6		24	15.2	even	4
315.3.o.b.253.6		24	3.2	odd	2
525.3.l.e.43.6		24	5.4	even	2
525.3.l.e.232.6		24	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +(-0.186396 - 4.77318i) q^{10} +7.59829 q^{11} +(-3.78113 + 3.78113i) q^{12} +(1.12200 + 1.12200i) q^{13} +2.52765i q^{14} +(8.65366 - 0.337932i) q^{15} -5.88043 q^{16} +(-3.43635 + 3.43635i) q^{17} +(2.02663 + 2.02663i) q^{18} -26.3120i q^{19} +(11.3328 + 10.4810i) q^{20} -4.58258 q^{21} +(5.13298 - 5.13298i) q^{22} +(-24.2663 - 24.2663i) q^{23} +11.7276i q^{24} +(-1.94957 - 24.9239i) q^{25} +1.51592 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-5.77577 - 5.77577i) q^{28} +22.3579i q^{29} +(5.61764 - 6.07421i) q^{30} -18.3927 q^{31} +(-23.1236 + 23.1236i) q^{32} +(9.30597 + 9.30597i) q^{33} +4.64281i q^{34} +(0.516200 + 13.2187i) q^{35} -9.26184 q^{36} +(-34.4244 + 34.4244i) q^{37} +(-17.7749 - 17.7749i) q^{38} +2.74832i q^{39} +(33.8289 - 1.32104i) q^{40} +37.4590 q^{41} +(-3.09573 + 3.09573i) q^{42} +(-55.1278 - 55.1278i) q^{43} +23.4581i q^{44} +(11.0124 + 10.1846i) q^{45} -32.7859 q^{46} +(40.8541 - 40.8541i) q^{47} +(-7.20203 - 7.20203i) q^{48} -7.00000i q^{49} +(-18.1542 - 15.5201i) q^{50} -8.41731 q^{51} +(-3.46392 + 3.46392i) q^{52} +(-9.39948 - 9.39948i) q^{53} +4.96421i q^{54} +(25.7953 - 27.8918i) q^{55} -17.9142 q^{56} +(32.2255 - 32.2255i) q^{57} +(15.1037 + 15.1037i) q^{58} +49.7795i q^{59} +(1.04329 + 26.7163i) q^{60} +88.3465 q^{61} +(-12.4251 + 12.4251i) q^{62} +(-5.61249 - 5.61249i) q^{63} +7.72024i q^{64} +(7.92767 - 0.309582i) q^{65} +12.5732 q^{66} +(-40.5887 + 40.5887i) q^{67} +(-10.6090 - 10.6090i) q^{68} -59.4401i q^{69} +(9.27851 + 8.58108i) q^{70} +136.425 q^{71} +(-14.3633 + 14.3633i) q^{72} +(5.85157 + 5.85157i) q^{73} +46.5103i q^{74} +(28.1377 - 32.9131i) q^{75} +81.2325 q^{76} +(-14.2151 + 14.2151i) q^{77} +(1.85661 + 1.85661i) q^{78} +66.4377i q^{79} +(-19.9634 + 21.5859i) q^{80} -9.00000 q^{81} +(25.3052 - 25.3052i) q^{82} +(-34.8615 - 34.8615i) q^{83} -14.1477i q^{84} +(0.948160 + 24.2802i) q^{85} -74.4824 q^{86} +(-27.3827 + 27.3827i) q^{87} +(36.3789 + 36.3789i) q^{88} -2.03390i q^{89} +(14.3195 - 0.559189i) q^{90} -4.19813 q^{91} +(74.9170 - 74.9170i) q^{92} +(-22.5264 - 22.5264i) q^{93} -55.1975i q^{94} +(-96.5860 - 89.3260i) q^{95} -56.6409 q^{96} +(-58.4649 + 58.4649i) q^{97} +(-4.72881 - 4.72881i) q^{98} +22.7949i 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

Related objects

Downloads

Learn more