LMFDB - Embedded newform 105.3.l.a.22.5

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			22.5
Character	$\chi$	$=$	105.22
Dual form			105.3.l.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.867675 - 0.867675i) q^{2} +(1.22474 - 1.22474i) q^{3} -2.49428i q^{4} +(-4.93004 - 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.63493 + 5.63493i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-0.867675 - 0.867675i) q^{2} +(1.22474 - 1.22474i) q^{3} -2.49428i q^{4} +(-4.93004 - 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.63493 + 5.63493i) q^{8} -3.00000i q^{9} +(3.55449 + 5.00086i) q^{10} -1.49884 q^{11} +(-3.05486 - 3.05486i) q^{12} +(2.15706 - 2.15706i) q^{13} +3.24654i q^{14} +(-7.05884 + 5.01725i) q^{15} -0.198550 q^{16} +(-2.96697 - 2.96697i) q^{17} +(-2.60303 + 2.60303i) q^{18} -34.8524i q^{19} +(-2.07893 + 12.2969i) q^{20} -4.58258 q^{21} +(1.30051 + 1.30051i) q^{22} +(-7.50682 + 7.50682i) q^{23} +13.8027i q^{24} +(23.6106 + 8.21817i) q^{25} -3.74326 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-4.66637 + 4.66637i) q^{28} -37.1782i q^{29} +(10.4781 + 1.77144i) q^{30} +47.0705 q^{31} +(22.7120 + 22.7120i) q^{32} +(-1.83570 + 1.83570i) q^{33} +5.14873i q^{34} +(7.66397 + 10.7826i) q^{35} -7.48284 q^{36} +(16.3936 + 16.3936i) q^{37} +(-30.2406 + 30.2406i) q^{38} -5.28371i q^{39} +(32.4770 - 23.0838i) q^{40} +73.4639 q^{41} +(3.97619 + 3.97619i) q^{42} +(-0.244769 + 0.244769i) q^{43} +3.73853i q^{44} +(-2.50043 + 14.7901i) q^{45} +13.0270 q^{46} +(-38.9392 - 38.9392i) q^{47} +(-0.243173 + 0.243173i) q^{48} +7.00000i q^{49} +(-13.3557 - 27.6171i) q^{50} -7.26756 q^{51} +(-5.38032 - 5.38032i) q^{52} +(-33.0957 + 33.0957i) q^{53} +6.37608i q^{54} +(7.38936 + 1.24925i) q^{55} +21.0840 q^{56} +(-42.6853 - 42.6853i) q^{57} +(-32.2586 + 32.2586i) q^{58} -31.6176i q^{59} +(12.5144 + 17.6067i) q^{60} -106.415 q^{61} +(-40.8419 - 40.8419i) q^{62} +(-5.61249 + 5.61249i) q^{63} -38.6190i q^{64} +(-12.4323 + 8.83655i) q^{65} +3.18558 q^{66} +(28.6607 + 28.6607i) q^{67} +(-7.40045 + 7.40045i) q^{68} +18.3879i q^{69} +(2.70592 - 16.0056i) q^{70} +15.8493 q^{71} +(16.9048 + 16.9048i) q^{72} +(-26.2684 + 26.2684i) q^{73} -28.4486i q^{74} +(38.9822 - 18.8518i) q^{75} -86.9316 q^{76} +(2.80408 + 2.80408i) q^{77} +(-4.58454 + 4.58454i) q^{78} +73.8402i q^{79} +(0.978860 + 0.165487i) q^{80} -9.00000 q^{81} +(-63.7428 - 63.7428i) q^{82} +(58.6690 - 58.6690i) q^{83} +11.4302i q^{84} +(12.1544 + 17.1002i) q^{85} +0.424760 q^{86} +(-45.5338 - 45.5338i) q^{87} +(8.44587 - 8.44587i) q^{88} -83.2528i q^{89} +(15.0026 - 10.6635i) q^{90} -8.07100 q^{91} +(18.7241 + 18.7241i) q^{92} +(57.6493 - 57.6493i) q^{93} +67.5732i q^{94} +(-29.0487 + 171.824i) q^{95} +55.6328 q^{96} +(-103.272 - 103.272i) q^{97} +(6.07373 - 6.07373i) q^{98} +4.49653i 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 $

$2$	−0.867675	−	0.867675i	−0.433838	−	0.433838i	0.456094	−	0.889932i	$-0.349248\pi$
$2$	−0.867675	−	0.867675i	−0.433838	−	0.433838i	−0.889932	+	0.456094i	$0.849248\pi$
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$		−	2.49428i		−	0.623570i
$5$	−4.93004	−	0.833478i	−0.986008	−	0.166696i
$5$	−4.93004	−	0.833478i	−0.986008	−	0.166696i
$6$	−2.12536			−0.354227
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−5.63493	+	5.63493i	−0.704366	+	0.704366i
$9$		−	3.00000i		−	0.333333i
$10$	3.55449	+	5.00086i	0.355449	+	0.500086i
$11$	−1.49884			−0.136258			−0.0681292	−	0.997677i	$-0.521703\pi$
$11$	−1.49884			−0.136258			−0.0681292	+	0.997677i	$0.521703\pi$
$12$	−3.05486	−	3.05486i	−0.254571	−	0.254571i
$13$	2.15706	−	2.15706i	0.165928	−	0.165928i	−0.619259	−	0.785187i	$-0.712567\pi$
$13$	2.15706	−	2.15706i	0.165928	−	0.165928i	0.785187	+	0.619259i	$0.212567\pi$
$14$			3.24654i			0.231896i
$15$	−7.05884	+	5.01725i	−0.470589	+	0.334483i
$16$	−0.198550			−0.0124094
$17$	−2.96697	−	2.96697i	−0.174528	−	0.174528i	0.614438	−	0.788965i	$-0.289383\pi$
$17$	−2.96697	−	2.96697i	−0.174528	−	0.174528i	−0.788965	+	0.614438i	$0.789383\pi$
$18$	−2.60303	+	2.60303i	−0.144613	+	0.144613i
$19$		−	34.8524i		−	1.83434i	−0.398501	−	0.917168i	$-0.630469\pi$
$19$		−	34.8524i		−	1.83434i	0.398501	−	0.917168i	$-0.369531\pi$
$20$	−2.07893	+	12.2969i	−0.103946	+	0.614845i
$21$	−4.58258			−0.218218
$22$	1.30051	+	1.30051i	0.0591140	+	0.0591140i
$23$	−7.50682	+	7.50682i	−0.326383	+	0.326383i	−0.851209	−	0.524826i	$-0.824130\pi$
$23$	−7.50682	+	7.50682i	−0.326383	+	0.326383i	0.524826	+	0.851209i	$0.324130\pi$
$24$			13.8027i			0.575112i
$25$	23.6106	+	8.21817i	0.944425	+	0.328727i
$26$	−3.74326			−0.143972
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−4.66637	+	4.66637i	−0.166656	+	0.166656i
$29$		−	37.1782i		−	1.28201i	−0.767538	−	0.641004i	$-0.778518\pi$
$29$		−	37.1782i		−	1.28201i	0.767538	−	0.641004i	$-0.221482\pi$
$30$	10.4781	+	1.77144i	0.349271	+	0.0590481i
$31$	47.0705			1.51840			0.759201	−	0.650856i	$-0.225590\pi$
$31$	47.0705			1.51840			0.759201	+	0.650856i	$0.225590\pi$
$32$	22.7120	+	22.7120i	0.709749	+	0.709749i
$33$	−1.83570	+	1.83570i	−0.0556273	+	0.0556273i
$34$			5.14873i			0.151433i
$35$	7.66397	+	10.7826i	0.218971	+	0.308073i
$36$	−7.48284			−0.207857
$37$	16.3936	+	16.3936i	0.443070	+	0.443070i	0.893043	−	0.449972i	$-0.148566\pi$
$37$	16.3936	+	16.3936i	0.443070	+	0.443070i	−0.449972	+	0.893043i	$0.648566\pi$
$38$	−30.2406	+	30.2406i	−0.795804	+	0.795804i
$39$		−	5.28371i		−	0.135480i
$40$	32.4770	−	23.0838i	0.811925	−	0.577096i
$41$	73.4639			1.79180			0.895902	−	0.444252i	$-0.146531\pi$
$41$	73.4639			1.79180			0.895902	+	0.444252i	$0.146531\pi$
$42$	3.97619	+	3.97619i	0.0946711	+	0.0946711i
$43$	−0.244769	+	0.244769i	−0.00569230	+	0.00569230i	−0.709947	−	0.704255i	$-0.751281\pi$
$43$	−0.244769	+	0.244769i	−0.00569230	+	0.00569230i	0.704255	+	0.709947i	$0.251281\pi$
$44$			3.73853i			0.0849667i
$45$	−2.50043	+	14.7901i	−0.0555652	+	0.328669i
$46$	13.0270			0.283195
$47$	−38.9392	−	38.9392i	−0.828494	−	0.828494i	0.158814	−	0.987308i	$-0.449233\pi$
$47$	−38.9392	−	38.9392i	−0.828494	−	0.828494i	−0.987308	+	0.158814i	$0.949233\pi$
$48$	−0.243173	+	0.243173i	−0.00506611	+	0.00506611i
$49$			7.00000i			0.142857i
$50$	−13.3557	−	27.6171i	−0.267113	−	0.552341i
$51$	−7.26756			−0.142501
$52$	−5.38032	−	5.38032i	−0.103468	−	0.103468i
$53$	−33.0957	+	33.0957i	−0.624447	+	0.624447i	−0.946665	−	0.322218i	$-0.895571\pi$
$53$	−33.0957	+	33.0957i	−0.624447	+	0.624447i	0.322218	+	0.946665i	$0.395571\pi$
$54$			6.37608i			0.118076i
$55$	7.38936	+	1.24925i	0.134352	+	0.0227137i
$56$	21.0840			0.376499
$57$	−42.6853	−	42.6853i	−0.748865	−	0.748865i
$58$	−32.2586	+	32.2586i	−0.556183	+	0.556183i
$59$		−	31.6176i		−	0.535891i	−0.963434	−	0.267946i	$-0.913655\pi$
$59$		−	31.6176i		−	0.535891i	0.963434	−	0.267946i	$-0.0863447\pi$
$60$	12.5144	+	17.6067i	0.208574	+	0.293445i
$61$	−106.415			−1.74451			−0.872256	−	0.489049i	$-0.837344\pi$
$61$	−106.415			−1.74451			−0.872256	+	0.489049i	$0.837344\pi$
$62$	−40.8419	−	40.8419i	−0.658740	−	0.658740i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	38.6190i		−	0.603422i
$65$	−12.4323	+	8.83655i	−0.191266	+	0.135947i
$66$	3.18558			0.0482664
$67$	28.6607	+	28.6607i	0.427771	+	0.427771i	0.887868	−	0.460097i	$-0.152186\pi$
$67$	28.6607	+	28.6607i	0.427771	+	0.427771i	−0.460097	+	0.887868i	$0.652186\pi$
$68$	−7.40045	+	7.40045i	−0.108830	+	0.108830i
$69$			18.3879i			0.266491i
$70$	2.70592	−	16.0056i	0.0386560	−	0.228651i
$71$	15.8493			0.223229			0.111615	−	0.993752i	$-0.464398\pi$
$71$	15.8493			0.223229			0.111615	+	0.993752i	$0.464398\pi$
$72$	16.9048	+	16.9048i	0.234789	+	0.234789i
$73$	−26.2684	+	26.2684i	−0.359841	+	0.359841i	−0.863754	−	0.503913i	$-0.831893\pi$
$73$	−26.2684	+	26.2684i	−0.359841	+	0.359841i	0.503913	+	0.863754i	$0.331893\pi$
$74$		−	28.4486i		−	0.384441i
$75$	38.9822	−	18.8518i	0.519762	−	0.251358i
$76$	−86.9316			−1.14384
$77$	2.80408	+	2.80408i	0.0364166	+	0.0364166i
$78$	−4.58454	+	4.58454i	−0.0587762	+	0.0587762i
$79$			73.8402i			0.934686i	0.884076	+	0.467343i	$0.154789\pi$
$79$			73.8402i			0.934686i	−0.884076	+	0.467343i	$0.845211\pi$
$80$	0.978860	+	0.165487i	0.0122358	+	0.00206859i
$81$	−9.00000			−0.111111
$82$	−63.7428	−	63.7428i	−0.777352	−	0.777352i
$83$	58.6690	−	58.6690i	0.706856	−	0.706856i	−0.259017	−	0.965873i	$-0.583399\pi$
$83$	58.6690	−	58.6690i	0.706856	−	0.706856i	0.965873	+	0.259017i	$0.0833986\pi$
$84$			11.4302i			0.136074i
$85$	12.1544	+	17.1002i	0.142993	+	0.201179i
$86$	0.424760			0.00493907
$87$	−45.5338	−	45.5338i	−0.523377	−	0.523377i
$88$	8.44587	−	8.44587i	0.0959758	−	0.0959758i
$89$		−	83.2528i		−	0.935424i	−0.883881	−	0.467712i	$-0.845078\pi$
$89$		−	83.2528i		−	0.935424i	0.883881	−	0.467712i	$-0.154922\pi$
$90$	15.0026	−	10.6635i	0.166695	−	0.118483i
$91$	−8.07100			−0.0886923
$92$	18.7241	+	18.7241i	0.203523	+	0.203523i
$93$	57.6493	−	57.6493i	0.619885	−	0.619885i
$94$			67.5732i			0.718864i
$95$	−29.0487	+	171.824i	−0.305776	+	1.80867i
$96$	55.6328			0.579508
$97$	−103.272	−	103.272i	−1.06466	−	1.06466i	−0.997759	−	0.0669049i	$-0.978688\pi$
$97$	−103.272	−	103.272i	−1.06466	−	1.06466i	−0.0669049	−	0.997759i	$-0.521312\pi$
$98$	6.07373	−	6.07373i	0.0619768	−	0.0619768i
$99$			4.49653i			0.0454195i
$100$	20.4984	−	58.8915i	0.204984	−	0.588915i
$101$	88.5891			0.877120			0.438560	−	0.898702i	$-0.355489\pi$
$101$	88.5891			0.877120			0.438560	+	0.898702i	$0.355489\pi$
$102$	6.30588	+	6.30588i	0.0618224	+	0.0618224i
$103$	22.0312	−	22.0312i	0.213895	−	0.213895i	−0.592025	−	0.805920i	$-0.701671\pi$
$103$	22.0312	−	22.0312i	0.213895	−	0.213895i	0.805920	+	0.592025i	$0.201671\pi$
$104$			24.3098i			0.233748i
$105$	22.5923	+	3.81948i	0.215165	+	0.0363760i
$106$	57.4326			0.541817
$107$	108.746	+	108.746i	1.01632	+	1.01632i	0.999865	+	0.0164543i	$0.00523781\pi$
$107$	108.746	+	108.746i	1.01632	+	1.01632i	0.0164543	+	0.999865i	$0.494762\pi$
$108$	−9.16457	+	9.16457i	−0.0848571	+	0.0848571i
$109$			75.8376i			0.695758i	0.937539	+	0.347879i	$0.113098\pi$
$109$			75.8376i			0.695758i	−0.937539	+	0.347879i	$0.886902\pi$
$110$	−5.32762	−	7.49551i	−0.0484329	−	0.0681410i
$111$	40.1560			0.361765
$112$	0.371453	+	0.371453i	0.00331655	+	0.00331655i
$113$	−22.0544	+	22.0544i	−0.195171	+	0.195171i	−0.797926	−	0.602755i	$-0.794070\pi$
$113$	−22.0544	+	22.0544i	−0.195171	+	0.195171i	0.602755	+	0.797926i	$0.294070\pi$
$114$			74.0739i			0.649771i
$115$	43.2657	−	30.7522i	0.376223	−	0.267410i
$116$	−92.7329			−0.799421
$117$	−6.47119	−	6.47119i	−0.0553093	−	0.0553093i
$118$	−27.4338	+	27.4338i	−0.232490	+	0.232490i
$119$			11.1014i			0.0932890i
$120$	11.5042	−	68.0478i	0.0958687	−	0.567065i
$121$	−118.753			−0.981434
$122$	92.3339	+	92.3339i	0.756835	+	0.756835i
$123$	89.9746	−	89.9746i	0.731501	−	0.731501i
$124$		−	117.407i		−	0.946830i
$125$	−109.552	−	60.1948i	−0.876414	−	0.481559i
$126$	9.73963			0.0772986
$127$	168.587	+	168.587i	1.32746	+	1.32746i	0.907579	+	0.419880i	$0.137928\pi$
$127$	168.587	+	168.587i	1.32746	+	1.32746i	0.419880	+	0.907579i	$0.362072\pi$
$128$	57.3391	−	57.3391i	0.447962	−	0.447962i
$129$			0.599559i			0.00464774i
$130$	18.4544	+	3.11993i	0.141957	+	0.0239994i
$131$	21.2016			0.161845			0.0809223	−	0.996720i	$-0.474213\pi$
$131$	21.2016			0.161845			0.0809223	+	0.996720i	$0.474213\pi$
$132$	4.57875	+	4.57875i	0.0346875	+	0.0346875i
$133$	−65.2028	+	65.2028i	−0.490247	+	0.490247i
$134$		−	49.7363i		−	0.371166i
$135$	15.0517	+	21.1765i	0.111494	+	0.156863i
$136$	33.4373			0.245863
$137$	−104.237	−	104.237i	−0.760851	−	0.760851i	0.215625	−	0.976476i	$-0.430821\pi$
$137$	−104.237	−	104.237i	−0.760851	−	0.760851i	−0.976476	+	0.215625i	$0.930821\pi$
$138$	15.9547	−	15.9547i	0.115614	−	0.115614i
$139$			120.516i			0.867019i	0.901149	+	0.433509i	$0.142725\pi$
$139$			120.516i			0.867019i	−0.901149	+	0.433509i	$0.857275\pi$
$140$	26.8947	−	19.1161i	0.192105	−	0.136543i
$141$	−95.3812			−0.676463
$142$	−13.7520	−	13.7520i	−0.0968452	−	0.0968452i
$143$	−3.23310	+	3.23310i	−0.0226091	+	0.0226091i
$144$			0.595650i			0.00413646i
$145$	−30.9872	+	183.290i	−0.213705	+	1.26407i
$146$	45.5849			0.312225
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	40.8902	−	40.8902i	0.276285	−	0.276285i
$149$			11.2725i			0.0756543i	0.999284	+	0.0378272i	$0.0120436\pi$
$149$			11.2725i			0.0756543i	−0.999284	+	0.0378272i	$0.987956\pi$
$150$	−50.1811	−	17.4666i	−0.334541	−	0.116444i
$151$	−19.8815			−0.131666			−0.0658328	−	0.997831i	$-0.520970\pi$
$151$	−19.8815			−0.131666			−0.0658328	+	0.997831i	$0.520970\pi$
$152$	196.391	+	196.391i	1.29204	+	1.29204i
$153$	−8.90091	+	8.90091i	−0.0581759	+	0.0581759i
$154$		−	4.86606i		−	0.0315978i
$155$	−232.059	−	39.2322i	−1.49716	−	0.253111i
$156$	−13.1790			−0.0844810
$157$	−35.1027	−	35.1027i	−0.223584	−	0.223584i	0.586422	−	0.810006i	$-0.300536\pi$
$157$	−35.1027	−	35.1027i	−0.223584	−	0.223584i	−0.810006	+	0.586422i	$0.800536\pi$
$158$	64.0693	−	64.0693i	0.405502	−	0.405502i
$159$			81.0676i			0.509859i
$160$	−93.0411	−	130.901i	−0.581507	−	0.818131i
$161$	28.0879			0.174459
$162$	7.80908	+	7.80908i	0.0482042	+	0.0482042i
$163$	172.736	−	172.736i	1.05973	−	1.05973i	0.0616300	−	0.998099i	$-0.480370\pi$
$163$	172.736	−	172.736i	1.05973	−	1.05973i	0.998099	−	0.0616300i	$-0.0196299\pi$
$164$		−	183.240i		−	1.11731i
$165$	10.5801	−	7.52006i	0.0641218	−	0.0455761i
$166$	−101.811			−0.613321
$167$	173.446	+	173.446i	1.03860	+	1.03860i	0.999225	+	0.0393730i	$0.0125361\pi$
$167$	173.446	+	173.446i	1.03860	+	1.03860i	0.0393730	+	0.999225i	$0.487464\pi$
$168$	25.8225	−	25.8225i	0.153705	−	0.153705i
$169$			159.694i			0.944936i
$170$	4.29136	−	25.3835i	0.0252433	−	0.149315i
$171$	−104.557			−0.611445
$172$	0.610522	+	0.610522i	0.00354955	+	0.00354955i
$173$	13.5601	−	13.5601i	0.0783823	−	0.0783823i	−0.666829	−	0.745211i	$-0.732349\pi$
$173$	13.5601	−	13.5601i	0.0783823	−	0.0783823i	0.745211	+	0.666829i	$0.232349\pi$
$174$			79.0172i			0.454122i
$175$	−28.7967	−	59.5462i	−0.164552	−	0.340264i
$176$	0.297595			0.00169088
$177$	−38.7235	−	38.7235i	−0.218777	−	0.218777i
$178$	−72.2364	+	72.2364i	−0.405822	+	0.405822i
$179$		−	288.985i		−	1.61444i	−0.590249	−	0.807222i	$-0.700970\pi$
$179$		−	288.985i		−	1.61444i	0.590249	−	0.807222i	$-0.299030\pi$
$180$	36.8907	+	6.23678i	0.204948	+	0.0346488i
$181$	20.6446			0.114059			0.0570293	−	0.998373i	$-0.481837\pi$
$181$	20.6446			0.114059			0.0570293	+	0.998373i	$0.481837\pi$
$182$	7.00300	+	7.00300i	0.0384780	+	0.0384780i
$183$	−130.332	+	130.332i	−0.712194	+	0.712194i
$184$		−	84.6007i		−	0.459786i
$185$	−67.1575	−	94.4849i	−0.363013	−	0.510729i
$186$	−100.042			−0.537859
$187$	4.44702	+	4.44702i	0.0237809	+	0.0237809i
$188$	−97.1253	+	97.1253i	−0.516624	+	0.516624i
$189$			13.7477i			0.0727393i
$190$	174.292	−	123.882i	0.917326	−	0.652012i
$191$	−140.214			−0.734104			−0.367052	−	0.930200i	$-0.619633\pi$
$191$	−140.214			−0.734104			−0.367052	+	0.930200i	$0.619633\pi$
$192$	−47.2985	−	47.2985i	−0.246346	−	0.246346i
$193$	196.589	−	196.589i	1.01860	−	1.01860i	0.0187736	−	0.999824i	$-0.494024\pi$
$193$	196.589	−	196.589i	1.01860	−	1.01860i	0.999824	−	0.0187736i	$-0.00597619\pi$
$194$			179.214i			0.923783i
$195$	−4.40385	+	26.0489i	−0.0225839	+	0.133584i
$196$	17.4600			0.0890814
$197$	−206.963	−	206.963i	−1.05057	−	1.05057i	−0.998651	−	0.0519216i	$-0.983465\pi$
$197$	−206.963	−	206.963i	−1.05057	−	1.05057i	−0.0519216	−	0.998651i	$-0.516535\pi$
$198$	3.90153	−	3.90153i	0.0197047	−	0.0197047i
$199$			160.567i			0.806869i	0.915009	+	0.403435i	$0.132184\pi$
$199$			160.567i			0.806869i	−0.915009	+	0.403435i	$0.867816\pi$
$200$	−179.353	+	86.7354i	−0.896764	+	0.433677i
$201$	70.2040			0.349274
$202$	−76.8666	−	76.8666i	−0.380528	−	0.380528i
$203$	−69.5541	+	69.5541i	−0.342631	+	0.342631i
$204$			18.1273i			0.0888595i
$205$	−362.180	−	61.2306i	−1.76673	−	0.298686i
$206$	−38.2318			−0.185591
$207$	22.5204	+	22.5204i	0.108794	+	0.108794i
$208$	−0.428285	+	0.428285i	−0.00205906	+	0.00205906i
$209$			52.2383i			0.249944i
$210$	−16.2887	−	22.9168i	−0.0775653	−	0.109128i
$211$	265.902			1.26020			0.630099	−	0.776515i	$-0.283014\pi$
$211$	265.902			1.26020			0.630099	+	0.776515i	$0.283014\pi$
$212$	82.5499	+	82.5499i	0.389386	+	0.389386i
$213$	19.4113	−	19.4113i	0.0911329	−	0.0911329i
$214$		−	188.713i		−	0.881835i
$215$	1.41073	−	1.00271i	0.00656154	−	0.00466377i
$216$	41.4081			0.191704
$217$	−88.0608	−	88.0608i	−0.405810	−	0.405810i
$218$	65.8024	−	65.8024i	0.301846	−	0.301846i
$219$			64.3442i			0.293809i
$220$	3.11599	−	18.4311i	0.0141636	−	0.0837779i
$221$	−12.7999			−0.0579181
$222$	−34.8423	−	34.8423i	−0.156947	−	0.156947i
$223$	143.987	−	143.987i	0.645683	−	0.645683i	−0.306264	−	0.951947i	$-0.599079\pi$
$223$	143.987	−	143.987i	0.645683	−	0.645683i	0.951947	+	0.306264i	$0.0990789\pi$
$224$		−	84.9804i		−	0.379377i
$225$	24.6545	−	70.8319i	0.109576	−	0.314808i
$226$	38.2720			0.169345
$227$	−174.471	−	174.471i	−0.768596	−	0.768596i	0.209264	−	0.977859i	$-0.432893\pi$
$227$	−174.471	−	174.471i	−0.768596	−	0.768596i	−0.977859	+	0.209264i	$0.932893\pi$
$228$	−106.469	+	106.469i	−0.466969	+	0.466969i
$229$			41.2978i			0.180340i	0.995926	+	0.0901700i	$0.0287410\pi$
$229$			41.2978i			0.180340i	−0.995926	+	0.0901700i	$0.971259\pi$
$230$	−64.2234	−	10.8577i	−0.279232	−	0.0472073i
$231$	6.86856			0.0297340
$232$	209.497	+	209.497i	0.903002	+	0.903002i
$233$	−72.8228	+	72.8228i	−0.312544	+	0.312544i	−0.845894	−	0.533350i	$-0.820933\pi$
$233$	−72.8228	+	72.8228i	−0.312544	+	0.312544i	0.533350	+	0.845894i	$0.320933\pi$
$234$			11.2298i			0.0479905i
$235$	159.517	+	224.427i	0.678796	+	0.955008i
$236$	−78.8631			−0.334166
$237$	90.4354	+	90.4354i	0.381584	+	0.381584i
$238$	9.63240	−	9.63240i	0.0404723	−	0.0404723i
$239$			418.650i			1.75168i	0.482606	+	0.875838i	$0.339690\pi$
$239$			418.650i			1.75168i	−0.482606	+	0.875838i	$0.660310\pi$
$240$	1.40153	−	0.996174i	0.00583972	−	0.00415073i
$241$	371.820			1.54282			0.771410	−	0.636338i	$-0.219552\pi$
$241$	371.820			1.54282			0.771410	+	0.636338i	$0.219552\pi$
$242$	103.039	+	103.039i	0.425783	+	0.425783i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			265.429i			1.08783i
$245$	5.83435	−	34.5103i	0.0238137	−	0.140858i
$246$	−156.137			−0.634705
$247$	−75.1788	−	75.1788i	−0.304368	−	0.304368i
$248$	−265.238	+	265.238i	−1.06951	+	1.06951i
$249$		−	143.709i		−	0.577145i
$250$	42.8257	+	147.285i	0.171303	+	0.589140i
$251$	469.550			1.87072			0.935358	−	0.353702i	$-0.115077\pi$
$251$	469.550			1.87072			0.935358	+	0.353702i	$0.115077\pi$
$252$	13.9991	+	13.9991i	0.0555520	+	0.0555520i
$253$	11.2515	−	11.2515i	0.0444725	−	0.0444725i
$254$		−	292.558i		−	1.15180i
$255$	35.8294	+	6.05736i	0.140507	+	0.0237543i
$256$	−253.980			−0.992108
$257$	215.003	+	215.003i	0.836589	+	0.836589i	0.988408	−	0.151819i	$-0.0485131\pi$
$257$	215.003	+	215.003i	0.836589	+	0.836589i	−0.151819	+	0.988408i	$0.548513\pi$
$258$	0.520222	−	0.520222i	0.00201637	−	0.00201637i
$259$		−	61.3393i		−	0.236831i
$260$	22.0408	+	31.0096i	0.0847724	+	0.119268i
$261$	−111.535			−0.427336
$262$	−18.3961	−	18.3961i	−0.0702142	−	0.0702142i
$263$	95.9799	−	95.9799i	0.364943	−	0.364943i	−0.500686	−	0.865629i	$-0.666919\pi$
$263$	95.9799	−	95.9799i	0.364943	−	0.364943i	0.865629	+	0.500686i	$0.166919\pi$
$264$		−	20.6881i		−	0.0783639i
$265$	190.748	−	135.579i	0.719803	−	0.511617i
$266$	113.150			0.425375
$267$	−101.963	−	101.963i	−0.381885	−	0.381885i
$268$	71.4877	−	71.4877i	0.266745	−	0.266745i
$269$			53.9055i			0.200392i	0.994968	+	0.100196i	$0.0319470\pi$
$269$			53.9055i			0.200392i	−0.994968	+	0.100196i	$0.968053\pi$
$270$	5.31433	−	31.4344i	0.0196827	−	0.116424i
$271$	−163.641			−0.603843			−0.301921	−	0.953333i	$-0.597628\pi$
$271$	−163.641			−0.603843			−0.301921	+	0.953333i	$0.597628\pi$
$272$	0.589092	+	0.589092i	0.00216578	+	0.00216578i
$273$	−9.88491	+	9.88491i	−0.0362085	+	0.0362085i
$274$			180.887i			0.660171i
$275$	−35.3886	−	12.3177i	−0.128686	−	0.0447918i
$276$	45.8645			0.166176
$277$	25.4139	+	25.4139i	0.0917470	+	0.0917470i	0.751491	−	0.659744i	$-0.229335\pi$
$277$	25.4139	+	25.4139i	0.0917470	+	0.0917470i	−0.659744	+	0.751491i	$0.729335\pi$
$278$	104.568	−	104.568i	0.376145	−	0.376145i
$279$		−	141.211i		−	0.506134i
$280$	−103.945	−	17.5730i	−0.371231	−	0.0627608i
$281$	113.158			0.402698			0.201349	−	0.979520i	$-0.435468\pi$
$281$	113.158			0.402698			0.201349	+	0.979520i	$0.435468\pi$
$282$	82.7599	+	82.7599i	0.293475	+	0.293475i
$283$	351.039	−	351.039i	1.24042	−	1.24042i	0.280593	−	0.959827i	$-0.409469\pi$
$283$	351.039	−	351.039i	1.24042	−	1.24042i	0.959827	−	0.280593i	$-0.0905312\pi$
$284$		−	39.5325i		−	0.139199i
$285$	174.863	+	246.017i	0.613554	+	0.863219i
$286$	5.61056			0.0196174
$287$	−137.438	−	137.438i	−0.478880	−	0.478880i
$288$	68.1359	−	68.1359i	0.236583	−	0.236583i
$289$		−	271.394i		−	0.939080i
$290$	185.923	−	132.149i	0.641115	−	0.455688i
$291$	−252.965			−0.869295
$292$	65.5207	+	65.5207i	0.224386	+	0.224386i
$293$	−86.4775	+	86.4775i	−0.295145	+	0.295145i	−0.839109	−	0.543964i	$-0.816923\pi$
$293$	−86.4775	+	86.4775i	−0.295145	+	0.295145i	0.543964	+	0.839109i	$0.316923\pi$
$294$		−	14.8775i		−	0.0506038i
$295$	−26.3526	+	155.876i	−0.0893307	+	0.528393i
$296$	−184.753			−0.624167
$297$	5.50710	+	5.50710i	0.0185424	+	0.0185424i
$298$	9.78086	−	9.78086i	0.0328217	−	0.0328217i
$299$			32.3854i			0.108312i
$300$	−47.0218	−	97.2324i	−0.156739	−	0.324108i
$301$	0.915841			0.00304266
$302$	17.2507	+	17.2507i	0.0571215	+	0.0571215i
$303$	108.499	−	108.499i	0.358083	−	0.358083i
$304$			6.91994i			0.0227630i
$305$	524.632	+	88.6948i	1.72010	+	0.290803i
$306$	15.4462			0.0504778
$307$	−113.083	−	113.083i	−0.368348	−	0.368348i	0.498526	−	0.866874i	$-0.333875\pi$
$307$	−113.083	−	113.083i	−0.368348	−	0.368348i	−0.866874	+	0.498526i	$0.833875\pi$
$308$	6.99416	−	6.99416i	0.0227083	−	0.0227083i
$309$		−	53.9651i		−	0.174644i
$310$	167.311	+	235.393i	0.539714	+	0.759332i
$311$	−73.9659			−0.237832			−0.118916	−	0.992904i	$-0.537942\pi$
$311$	−73.9659			−0.237832			−0.118916	+	0.992904i	$0.537942\pi$
$312$	29.7733	+	29.7733i	0.0954272	+	0.0954272i
$313$	−324.281	+	324.281i	−1.03604	+	1.03604i	−0.0367164	+	0.999326i	$0.511690\pi$
$313$	−324.281	+	324.281i	−1.03604	+	1.03604i	−0.999326	+	0.0367164i	$0.988310\pi$
$314$			60.9154i			0.193998i
$315$	32.3477	−	22.9919i	0.102691	−	0.0729902i
$316$	184.178			0.582842
$317$	−151.033	−	151.033i	−0.476445	−	0.476445i	0.427547	−	0.903993i	$-0.359378\pi$
$317$	−151.033	−	151.033i	−0.476445	−	0.476445i	−0.903993	+	0.427547i	$0.859378\pi$
$318$	70.3403	−	70.3403i	0.221196	−	0.221196i
$319$			55.7243i			0.174684i
$320$	−32.1881	+	190.393i	−0.100588	+	0.594980i
$321$	266.373			0.829821
$322$	−24.3712	−	24.3712i	−0.0756870	−	0.0756870i
$323$	−103.406	+	103.406i	−0.320142	+	0.320142i
$324$			22.4485i			0.0692855i
$325$	68.6568	−	33.2025i	0.211252	−	0.102162i
$326$	−299.757			−0.919501
$327$	92.8818	+	92.8818i	0.284042	+	0.284042i
$328$	−413.964	+	413.964i	−1.26208	+	1.26208i
$329$			145.697i			0.442849i
$330$	−15.7051	−	2.65511i	−0.0475911	−	0.00804580i
$331$	−181.099			−0.547128			−0.273564	−	0.961854i	$-0.588202\pi$
$331$	−181.099			−0.547128			−0.273564	+	0.961854i	$0.588202\pi$
$332$	−146.337	−	146.337i	−0.440774	−	0.440774i
$333$	49.1808	−	49.1808i	0.147690	−	0.147690i
$334$		−	300.989i		−	0.901165i
$335$	−117.410	−	165.186i	−0.350478	−	0.493093i
$336$	0.909871			0.00270795
$337$	−388.741	−	388.741i	−1.15353	−	1.15353i	−0.985839	−	0.167693i	$-0.946368\pi$
$337$	−388.741	−	388.741i	−1.15353	−	1.15353i	−0.167693	−	0.985839i	$-0.553632\pi$
$338$	138.563	−	138.563i	0.409949	−	0.409949i
$339$			54.0219i			0.159357i
$340$	42.6527	−	30.3164i	0.125449	−	0.0891660i
$341$	−70.5512			−0.206895
$342$	90.7217	+	90.7217i	0.265268	+	0.265268i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	2.75851i		−	0.00801892i
$345$	15.3259	−	90.6530i	0.0444229	−	0.262762i
$346$	−23.5316			−0.0680104
$347$	16.1754	+	16.1754i	0.0466151	+	0.0466151i	0.730030	−	0.683415i	$-0.239506\pi$
$347$	16.1754	+	16.1754i	0.0466151	+	0.0466151i	−0.683415	+	0.730030i	$0.739506\pi$
$348$	−113.574	+	113.574i	−0.326362	+	0.326362i
$349$		−	249.140i		−	0.713868i	−0.934130	−	0.356934i	$-0.883822\pi$
$349$		−	249.140i		−	0.713868i	0.934130	−	0.356934i	$-0.116178\pi$
$350$	−26.6806	+	76.6529i	−0.0762304	+	0.219008i
$351$	−15.8511			−0.0451599
$352$	−34.0417	−	34.0417i	−0.0967094	−	0.0967094i
$353$	−315.334	+	315.334i	−0.893298	+	0.893298i	−0.994832	−	0.101534i	$-0.967625\pi$
$353$	−315.334	+	315.334i	−0.893298	+	0.893298i	0.101534	+	0.994832i	$0.467625\pi$
$354$			67.1988i			0.189827i
$355$	−78.1376	−	13.2100i	−0.220106	−	0.0372113i
$356$	−207.656			−0.583302
$357$	13.5964	+	13.5964i	0.0380851	+	0.0380851i
$358$	−250.745	+	250.745i	−0.700406	+	0.700406i
$359$			84.4547i			0.235250i	0.993058	+	0.117625i	$0.0375281\pi$
$359$			84.4547i			0.235250i	−0.993058	+	0.117625i	$0.962472\pi$
$360$	−69.2515	−	97.4310i	−0.192365	−	0.270642i
$361$	−853.689			−2.36479
$362$	−17.9128	−	17.9128i	−0.0494829	−	0.0494829i
$363$	−145.443	+	145.443i	−0.400669	+	0.400669i
$364$			20.1313i			0.0553058i
$365$	151.398	−	107.610i	0.414790	−	0.294822i
$366$	226.171			0.617953
$367$	−199.907	−	199.907i	−0.544707	−	0.544707i	0.380198	−	0.924905i	$-0.375856\pi$
$367$	−199.907	−	199.907i	−0.544707	−	0.544707i	−0.924905	+	0.380198i	$0.875856\pi$
$368$	1.49048	−	1.49048i	0.00405021	−	0.00405021i
$369$		−	220.392i		−	0.597268i
$370$	−23.7113	+	140.253i	−0.0640847	+	0.379062i
$371$	123.833			0.333781
$372$	−143.793	−	143.793i	−0.386542	−	0.386542i
$373$	−392.541	+	392.541i	−1.05239	+	1.05239i	−0.0538401	+	0.998550i	$0.517146\pi$
$373$	−392.541	+	392.541i	−1.05239	+	1.05239i	−0.998550	+	0.0538401i	$0.982854\pi$
$374$		−	7.71714i		−	0.0206341i
$375$	−207.896	+	60.4496i	−0.554390	+	0.161199i
$376$	438.839			1.16713
$377$	−80.1958	−	80.1958i	−0.212721	−	0.212721i
$378$	11.9286	−	11.9286i	0.0315570	−	0.0315570i
$379$		−	360.732i		−	0.951798i	−0.879500	−	0.475899i	$-0.842123\pi$
$379$		−	360.732i		−	0.951798i	0.879500	−	0.475899i	$-0.157877\pi$
$380$	428.576	+	72.4556i	1.12783	+	0.190673i
$381$	412.953			1.08387
$382$	121.660	+	121.660i	0.318482	+	0.318482i
$383$	337.526	−	337.526i	0.881268	−	0.881268i	−0.112395	−	0.993664i	$-0.535852\pi$
$383$	337.526	−	337.526i	0.881268	−	0.881268i	0.993664	+	0.112395i	$0.0358523\pi$
$384$		−	140.452i		−	0.365759i
$385$	−11.4871	−	16.1614i	−0.0298366	−	0.0419776i
$386$	−341.151			−0.883812
$387$	0.734307	+	0.734307i	0.00189743	+	0.00189743i
$388$	−257.590	+	257.590i	−0.663893	+	0.663893i
$389$		−	585.722i		−	1.50571i	−0.658185	−	0.752856i	$-0.728676\pi$
$389$		−	585.722i		−	1.50571i	0.658185	−	0.752856i	$-0.271324\pi$
$390$	26.4231	−	18.7809i	0.0677515	−	0.0481561i
$391$	44.5450			0.113926
$392$	−39.4445	−	39.4445i	−0.100624	−	0.100624i
$393$	25.9666	−	25.9666i	0.0660728	−	0.0660728i
$394$			359.153i			0.911556i
$395$	61.5442	−	364.035i	0.155808	−	0.921608i
$396$	11.2156			0.0283222
$397$	−165.106	−	165.106i	−0.415883	−	0.415883i	0.467899	−	0.883782i	$-0.345011\pi$
$397$	−165.106	−	165.106i	−0.415883	−	0.415883i	−0.883782	+	0.467899i	$0.845011\pi$
$398$	139.320	−	139.320i	0.350050	−	0.350050i
$399$			159.714i			0.400285i
$400$	−4.68789	−	1.63172i	−0.0117197	−	0.00407929i
$401$	593.726			1.48061			0.740307	−	0.672269i	$-0.234680\pi$
$401$	593.726			1.48061			0.740307	+	0.672269i	$0.234680\pi$
$402$	−60.9143	−	60.9143i	−0.151528	−	0.151528i
$403$	101.534	−	101.534i	0.251945	−	0.251945i
$404$		−	220.966i		−	0.546946i
$405$	44.3704	+	7.50130i	0.109556	+	0.0185217i
$406$	120.701			0.297292
$407$	−24.5714	−	24.5714i	−0.0603721	−	0.0603721i
$408$	40.9522	−	40.9522i	0.100373	−	0.100373i
$409$			354.736i			0.867324i	0.901076	+	0.433662i	$0.142779\pi$
$409$			354.736i			0.867324i	−0.901076	+	0.433662i	$0.857221\pi$
$410$	261.127	+	367.383i	0.636894	+	0.896056i
$411$	−255.326			−0.621232
$412$	−54.9519	−	54.9519i	−0.133378	−	0.133378i
$413$	−59.1511	+	59.1511i	−0.143223	+	0.143223i
$414$		−	39.0809i		−	0.0943982i
$415$	−338.140	+	240.341i	−0.814795	+	0.579136i
$416$	97.9824			0.235535
$417$	147.601	+	147.601i	0.353959	+	0.353959i
$418$	45.3258	−	45.3258i	0.108435	−	0.108435i
$419$			107.473i			0.256498i	0.991742	+	0.128249i	$0.0409356\pi$
$419$			107.473i			0.256498i	−0.991742	+	0.128249i	$0.959064\pi$
$420$	9.52684	−	56.3515i	0.0226830	−	0.134170i
$421$	572.426			1.35968			0.679841	−	0.733359i	$-0.262049\pi$
$421$	572.426			1.35968			0.679841	+	0.733359i	$0.262049\pi$
$422$	−230.716	−	230.716i	−0.546721	−	0.546721i
$423$	−116.818	+	116.818i	−0.276165	+	0.276165i
$424$		−	372.984i		−	0.879678i
$425$	−45.6690	−	94.4351i	−0.107456	−	0.222200i
$426$	−33.6854			−0.0790738
$427$	199.085	+	199.085i	0.466241	+	0.466241i
$428$	271.243	−	271.243i	0.633746	−	0.633746i
$429$			7.91945i			0.0184603i
$430$	−2.09408	−	0.354028i	−0.00486996	−	0.000823321i
$431$	346.647			0.804285			0.402142	−	0.915577i	$-0.368266\pi$
$431$	346.647			0.804285			0.402142	+	0.915577i	$0.368266\pi$
$432$	0.729519	+	0.729519i	0.00168870	+	0.00168870i
$433$	−103.330	+	103.330i	−0.238637	+	0.238637i	−0.816285	−	0.577649i	$-0.803970\pi$
$433$	−103.330	+	103.330i	−0.238637	+	0.238637i	0.577649	+	0.816285i	$0.303970\pi$
$434$			152.816i			0.352111i
$435$	186.532	+	262.435i	0.428810	+	0.603299i
$436$	189.160			0.433854
$437$	261.630	+	261.630i	0.598697	+	0.598697i
$438$	55.8298	−	55.8298i	0.127465	−	0.127465i
$439$		−	324.757i		−	0.739766i	−0.929078	−	0.369883i	$-0.879398\pi$
$439$		−	324.757i		−	0.739766i	0.929078	−	0.369883i	$-0.120602\pi$
$440$	−48.6779	+	34.5990i	−0.110632	+	0.0786342i
$441$	21.0000			0.0476190
$442$	11.1061	+	11.1061i	0.0251270	+	0.0251270i
$443$	−226.450	+	226.450i	−0.511173	+	0.511173i	−0.914886	−	0.403713i	$-0.867720\pi$
$443$	−226.450	+	226.450i	−0.511173	+	0.511173i	0.403713	+	0.914886i	$0.367720\pi$
$444$		−	100.160i		−	0.225586i
$445$	−69.3894	+	410.440i	−0.155931	+	0.922336i
$446$	−249.868			−0.560243
$447$	13.8059	+	13.8059i	0.0308857	+	0.0308857i
$448$	−72.2496	+	72.2496i	−0.161271	+	0.161271i
$449$			221.579i			0.493494i	0.969080	+	0.246747i	$0.0793617\pi$
$449$			221.579i			0.493494i	−0.969080	+	0.246747i	$0.920638\pi$
$450$	−82.8512	+	40.0670i	−0.184114	+	0.0890377i
$451$	−110.111			−0.244148
$452$	55.0097	+	55.0097i	0.121703	+	0.121703i
$453$	−24.3498	+	24.3498i	−0.0537523	+	0.0537523i
$454$			302.769i			0.666891i
$455$	39.7903	+	6.72700i	0.0874513	+	0.0147846i
$456$	481.057			1.05495
$457$	631.757	+	631.757i	1.38240	+	1.38240i	0.840337	+	0.542064i	$0.182357\pi$
$457$	631.757	+	631.757i	1.38240	+	1.38240i	0.542064	+	0.840337i	$0.317643\pi$
$458$	35.8331	−	35.8331i	0.0782382	−	0.0782382i
$459$			21.8027i			0.0475004i
$460$	−76.7045	−	107.917i	−0.166749	−	0.234602i
$461$	10.7536			0.0233266			0.0116633	−	0.999932i	$-0.496287\pi$
$461$	10.7536			0.0233266			0.0116633	+	0.999932i	$0.496287\pi$
$462$	−5.95968	−	5.95968i	−0.0128997	−	0.0128997i
$463$	−87.0943	+	87.0943i	−0.188109	+	0.188109i	−0.794878	−	0.606769i	$-0.792465\pi$
$463$	−87.0943	+	87.0943i	−0.188109	+	0.188109i	0.606769	+	0.794878i	$0.292465\pi$
$464$			7.38174i			0.0159089i
$465$	−332.263	+	236.164i	−0.714544	+	0.507880i
$466$	126.373			0.271187
$467$	−168.883	−	168.883i	−0.361633	−	0.361633i	0.502781	−	0.864414i	$-0.332310\pi$
$467$	−168.883	−	168.883i	−0.361633	−	0.361633i	−0.864414	+	0.502781i	$0.832310\pi$
$468$	−16.1410	+	16.1410i	−0.0344892	+	0.0344892i
$469$		−	107.238i		−	0.228653i
$470$	56.3208	−	333.139i	0.119831	−	0.708806i
$471$	−85.9836			−0.182555
$472$	178.163	+	178.163i	0.377463	+	0.377463i
$473$	0.366870	−	0.366870i	0.000775624	−	0.000775624i
$474$		−	156.937i		−	0.331091i
$475$	286.423	−	822.887i	0.602995	−	1.73239i
$476$	27.6900			0.0581722
$477$	99.2871	+	99.2871i	0.208149	+	0.208149i
$478$	363.253	−	363.253i	0.759943	−	0.759943i
$479$			591.385i			1.23462i	0.786718	+	0.617312i	$0.211779\pi$
$479$			591.385i			1.23462i	−0.786718	+	0.617312i	$0.788221\pi$
$480$	−274.272	−	46.3687i	−0.571400	−	0.0966014i
$481$	70.7241			0.147036
$482$	−322.619	−	322.619i	−0.669334	−	0.669334i
$483$	34.4006	−	34.4006i	0.0712227	−	0.0712227i
$484$			296.204i			0.611992i
$485$	423.062	+	595.213i	0.872293	+	1.22724i
$486$	19.1283			0.0393585
$487$	454.628	+	454.628i	0.933527	+	0.933527i	0.997924	−	0.0643972i	$-0.0205125\pi$
$487$	454.628	+	454.628i	0.933527	+	0.933527i	−0.0643972	+	0.997924i	$0.520512\pi$
$488$	599.642	−	599.642i	1.22877	−	1.22877i
$489$		−	423.115i		−	0.865265i
$490$	−35.0060	+	24.8814i	−0.0714409	+	0.0507784i
$491$	−267.659			−0.545130			−0.272565	−	0.962137i	$-0.587872\pi$
$491$	−267.659			−0.545130			−0.272565	+	0.962137i	$0.587872\pi$
$492$	−224.422	−	224.422i	−0.456142	−	0.456142i
$493$	−110.307	+	110.307i	−0.223746	+	0.223746i
$494$			130.462i			0.264092i
$495$	3.74776	−	22.1681i	0.00757123	−	0.0447840i
$496$	−9.34584			−0.0188424
$497$	−29.6513	−	29.6513i	−0.0596605	−	0.0596605i
$498$	−124.693	+	124.693i	−0.250387	+	0.250387i
$499$		−	598.541i		−	1.19948i	−0.800194	−	0.599741i	$-0.795270\pi$
$499$		−	598.541i		−	1.19948i	0.800194	−	0.599741i	$-0.204730\pi$
$500$	−150.143	+	273.253i	−0.300286	+	0.546505i
$501$	424.854			0.848011
$502$	−407.417	−	407.417i	−0.811587	−	0.811587i
$503$	−597.424	+	597.424i	−1.18772	+	1.18772i	−0.210027	+	0.977696i	$0.567355\pi$
$503$	−597.424	+	597.424i	−1.18772	+	1.18772i	−0.977696	+	0.210027i	$0.932645\pi$
$504$		−	63.2519i		−	0.125500i
$505$	−436.748	−	73.8371i	−0.864848	−	0.146212i
$506$	−19.5254			−0.0385877
$507$	195.585	+	195.585i	0.385768	+	0.385768i
$508$	420.504	−	420.504i	0.827764	−	0.827764i
$509$			734.407i			1.44284i	0.692496	+	0.721422i	$0.256511\pi$
$509$			734.407i			1.44284i	−0.692496	+	0.721422i	$0.743489\pi$
$510$	−25.8325	−	36.3441i	−0.0506519	−	0.0712629i
$511$	98.2873			0.192343
$512$	−8.98472	−	8.98472i	−0.0175483	−	0.0175483i
$513$	−128.056	+	128.056i	−0.249622	+	0.249622i
$514$		−	373.106i		−	0.725888i
$515$	−126.977	+	90.2521i	−0.246557	+	0.175247i
$516$	1.49547			0.00289819
$517$	58.3638	+	58.3638i	0.112889	+	0.112889i
$518$	−53.2225	+	53.2225i	−0.102746	+	0.102746i
$519$		−	33.2154i		−	0.0639989i
$520$	20.2617	−	119.848i	0.0389648	−	0.230477i
$521$	207.188			0.397674			0.198837	−	0.980033i	$-0.436284\pi$
$521$	207.188			0.397674			0.198837	+	0.980033i	$0.436284\pi$
$522$	96.7759	+	96.7759i	0.185394	+	0.185394i
$523$	143.359	−	143.359i	0.274110	−	0.274110i	−0.556642	−	0.830752i	$-0.687911\pi$
$523$	143.359	−	143.359i	0.274110	−	0.274110i	0.830752	+	0.556642i	$0.187911\pi$
$524$		−	52.8828i		−	0.100921i
$525$	−108.197	−	37.6604i	−0.206090	−	0.0717340i
$526$	−166.559			−0.316652
$527$	−139.657	−	139.657i	−0.265003	−	0.265003i
$528$	0.364478	−	0.364478i	0.000690300	−	0.000690300i
$529$			416.295i			0.786948i
$530$	−283.145	−	47.8688i	−0.534236	−	0.0903186i
$531$	−94.8527			−0.178630
$532$	162.634	+	162.634i	0.305703	+	0.305703i
$533$	158.466	−	158.466i	0.297310	−	0.297310i
$534$			176.942i			0.331352i
$535$	−445.485	−	626.760i	−0.832683	−	1.17151i
$536$	−323.001			−0.602614
$537$	−353.933	−	353.933i	−0.659094	−	0.659094i
$538$	46.7724	−	46.7724i	0.0869376	−	0.0869376i
$539$		−	10.4919i		−	0.0194655i
$540$	52.8202	−	37.5432i	0.0978151	−	0.0695245i
$541$	−22.1387			−0.0409219			−0.0204609	−	0.999791i	$-0.506513\pi$
$541$	−22.1387			−0.0409219			−0.0204609	+	0.999791i	$0.506513\pi$
$542$	141.988	+	141.988i	0.261970	+	0.261970i
$543$	25.2844	−	25.2844i	0.0465642	−	0.0465642i
$544$		−	134.772i		−	0.247742i
$545$	63.2090	−	373.883i	0.115980	−	0.686023i
$546$	17.1538			0.0314172
$547$	113.508	+	113.508i	0.207509	+	0.207509i	0.803208	−	0.595699i	$-0.203125\pi$
$547$	113.508	+	113.508i	0.207509	+	0.207509i	−0.595699	+	0.803208i	$0.703125\pi$
$548$	−259.995	+	259.995i	−0.474444	+	0.474444i
$549$			319.246i			0.581504i
$550$	20.0180	+	41.3936i	0.0363964	+	0.0752612i
$551$	−1295.75			−2.35163
$552$	−103.614	−	103.614i	−0.187707	−	0.187707i
$553$	138.142	−	138.142i	0.249805	−	0.249805i
$554$		−	44.1020i		−	0.0796066i
$555$	−197.971	−	33.4691i	−0.356704	−	0.0603047i
$556$	300.600			0.540647
$557$	−229.622	−	229.622i	−0.412248	−	0.412248i	0.470273	−	0.882521i	$-0.344155\pi$
$557$	−229.622	−	229.622i	−0.412248	−	0.412248i	−0.882521	+	0.470273i	$0.844155\pi$
$558$	−122.526	+	122.526i	−0.219580	+	0.219580i
$559$			1.05596i			0.00188902i
$560$	−1.52168	−	2.14088i	−0.00271729	−	0.00382300i
$561$	10.8929			0.0194170
$562$	−98.1844	−	98.1844i	−0.174705	−	0.174705i
$563$	92.9885	−	92.9885i	0.165166	−	0.165166i	−0.619685	−	0.784851i	$-0.712740\pi$
$563$	92.9885	−	92.9885i	0.165166	−	0.165166i	0.784851	+	0.619685i	$0.212740\pi$
$564$			237.907i			0.421822i
$565$	127.111	−	90.3471i	0.224975	−	0.159906i
$566$	−609.175			−1.07628
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−89.3094	+	89.3094i	−0.157235	+	0.157235i
$569$			388.149i			0.682160i	0.940034	+	0.341080i	$0.110793\pi$
$569$			388.149i			0.682160i	−0.940034	+	0.341080i	$0.889207\pi$
$570$	61.7390	−	365.188i	0.108314	−	0.640680i
$571$	−488.529			−0.855568			−0.427784	−	0.903881i	$-0.640706\pi$
$571$	−488.529			−0.855568			−0.427784	+	0.903881i	$0.640706\pi$
$572$	8.06426	+	8.06426i	0.0140984	+	0.0140984i
$573$	−171.726	+	171.726i	−0.299697	+	0.299697i
$574$			238.504i			0.415512i
$575$	−238.933	+	115.548i	−0.415536	+	0.200954i
$576$	−115.857			−0.201141
$577$	365.601	+	365.601i	0.633624	+	0.633624i	0.948975	−	0.315351i	$-0.102122\pi$
$577$	365.601	+	365.601i	0.633624	+	0.633624i	−0.315351	+	0.948975i	$0.602122\pi$
$578$	−235.482	+	235.482i	−0.407408	+	0.407408i
$579$		−	481.543i		−	0.831681i
$580$	457.177	+	77.2909i	0.788236	+	0.133260i
$581$	−219.519			−0.377830
$582$	219.491	+	219.491i	0.377133	+	0.377133i
$583$	49.6053	−	49.6053i	0.0850862	−	0.0850862i
$584$		−	296.041i		−	0.506919i
$585$	26.5097	+	37.2969i	0.0453156	+	0.0637553i
$586$	150.069			0.256090
$587$	410.771	+	410.771i	0.699780	+	0.699780i	0.964363	−	0.264583i	$-0.0852343\pi$
$587$	410.771	+	410.771i	0.699780	+	0.699780i	−0.264583	+	0.964363i	$0.585234\pi$
$588$	21.3840	−	21.3840i	0.0363673	−	0.0363673i
$589$		−	1640.52i		−	2.78526i
$590$	158.115	−	112.384i	0.267992	−	0.190482i
$591$	−506.953			−0.857789
$592$	−3.25495	−	3.25495i	−0.00549823	−	0.00549823i
$593$	776.361	−	776.361i	1.30921	−	1.30921i	0.387224	−	0.921986i	$-0.373434\pi$
$593$	776.361	−	776.361i	1.30921	−	1.30921i	0.921986	−	0.387224i	$-0.126566\pi$
$594$		−	9.55675i		−	0.0160888i
$595$	9.25277	−	54.7303i	0.0155509	−	0.0919837i
$596$	28.1167			0.0471757
$597$	196.654	+	196.654i	0.329403	+	0.329403i
$598$	28.1000	−	28.1000i	0.0469899	−	0.0469899i
$599$			573.555i			0.957521i	0.877946	+	0.478760i	$0.158914\pi$
$599$			573.555i			0.957521i	−0.877946	+	0.478760i	$0.841086\pi$
$600$	−113.433	+	325.890i	−0.189055	+	0.543150i
$601$	345.953			0.575628			0.287814	−	0.957686i	$-0.407071\pi$
$601$	345.953			0.575628			0.287814	+	0.957686i	$0.407071\pi$
$602$	−0.794653	−	0.794653i	−0.00132002	−	0.00132002i
$603$	85.9820	−	85.9820i	0.142590	−	0.142590i
$604$			49.5901i			0.0821028i
$605$	585.460	+	98.9784i	0.967702	+	0.163601i
$606$	−188.284			−0.310700
$607$	627.891	+	627.891i	1.03442	+	1.03442i	0.999386	+	0.0350309i	$0.0111530\pi$
$607$	627.891	+	627.891i	1.03442	+	1.03442i	0.0350309	+	0.999386i	$0.488847\pi$
$608$	791.567	−	791.567i	1.30192	−	1.30192i
$609$			170.372i			0.279757i
$610$	−378.252	−	532.168i	−0.620085	−	0.872407i
$611$	−167.989			−0.274941
$612$	22.2014	+	22.2014i	0.0362767	+	0.0362767i
$613$	114.845	−	114.845i	0.187349	−	0.187349i	−0.607200	−	0.794549i	$-0.707707\pi$
$613$	114.845	−	114.845i	0.187349	−	0.187349i	0.794549	+	0.607200i	$0.207707\pi$
$614$			196.238i			0.319606i
$615$	−518.570	+	368.587i	−0.843204	+	0.599328i
$616$	−31.6016			−0.0513012
$617$	−271.304	−	271.304i	−0.439715	−	0.439715i	0.452201	−	0.891916i	$-0.350639\pi$
$617$	−271.304	−	271.304i	−0.439715	−	0.439715i	−0.891916	+	0.452201i	$0.850639\pi$
$618$	−46.8242	+	46.8242i	−0.0757673	+	0.0757673i
$619$			346.221i			0.559323i	0.960099	+	0.279662i	$0.0902223\pi$
$619$			346.221i			0.559323i	−0.960099	+	0.279662i	$0.909778\pi$
$620$	−97.8561	+	578.821i	−0.157832	+	0.933582i
$621$	55.1636			0.0888303
$622$	64.1784	+	64.1784i	0.103181	+	0.103181i
$623$	−155.752	+	155.752i	−0.250003	+	0.250003i
$624$			1.04908i			0.00168122i
$625$	489.923	+	388.072i	0.783878	+	0.620915i
$626$	562.741			0.898948
$627$	63.9786	+	63.9786i	0.102039	+	0.102039i
$628$	−87.5558	+	87.5558i	−0.139420	+	0.139420i
$629$		−	97.2787i		−	0.154656i
$630$	−48.0168	−	8.11777i	−0.0762171	−	0.0128853i
$631$	−828.209			−1.31253			−0.656267	−	0.754528i	$-0.727866\pi$
$631$	−828.209			−1.31253			−0.656267	+	0.754528i	$0.727866\pi$
$632$	−416.084	−	416.084i	−0.658361	−	0.658361i
$633$	325.662	−	325.662i	0.514474	−	0.514474i
$634$			262.096i			0.413400i
$635$	−690.629	−	971.657i	−1.08760	−	1.53017i
$636$	202.205			0.317933
$637$	15.0994	+	15.0994i	0.0237040	+	0.0237040i
$638$	48.3506	−	48.3506i	0.0757847	−	0.0757847i
$639$		−	47.5478i		−	0.0744097i
$640$	−330.475	+	234.893i	−0.516368	+	0.367021i
$641$	−167.603			−0.261471			−0.130736	−	0.991417i	$-0.541734\pi$
$641$	−167.603			−0.261471			−0.130736	+	0.991417i	$0.541734\pi$
$642$	−231.125	−	231.125i	−0.360007	−	0.360007i
$643$	442.638	−	442.638i	0.688395	−	0.688395i	−0.273482	−	0.961877i	$-0.588176\pi$
$643$	442.638	−	442.638i	0.688395	−	0.688395i	0.961877	+	0.273482i	$0.0881755\pi$
$644$		−	70.0592i		−	0.108788i
$645$	0.499719	−	2.95585i	0.000774759	−	0.00458271i
$646$	179.446			0.277780
$647$	−494.631	−	494.631i	−0.764500	−	0.764500i	0.212632	−	0.977132i	$-0.431796\pi$
$647$	−494.631	−	494.631i	−0.764500	−	0.764500i	−0.977132	+	0.212632i	$0.931796\pi$
$648$	50.7143	−	50.7143i	0.0782628	−	0.0782628i
$649$			47.3898i			0.0730197i
$650$	−88.3808	−	30.7627i	−0.135970	−	0.0473273i
$651$	−215.704			−0.331342
$652$	−430.851	−	430.851i	−0.660815	−	0.660815i
$653$	−106.722	+	106.722i	−0.163434	+	0.163434i	−0.784086	−	0.620652i	$-0.786868\pi$
$653$	−106.722	+	106.722i	−0.163434	+	0.163434i	0.620652	+	0.784086i	$0.286868\pi$
$654$		−	161.182i		−	0.246456i
$655$	−104.525	−	17.6711i	−0.159580	−	0.0269788i
$656$	−14.5863			−0.0222352
$657$	78.8052	+	78.8052i	0.119947	+	0.119947i
$658$	126.418	−	126.418i	0.192124	−	0.192124i
$659$			712.593i			1.08132i	0.841240	+	0.540662i	$0.181826\pi$
$659$			712.593i			1.08132i	−0.841240	+	0.540662i	$0.818174\pi$
$660$	−18.7571	−	26.3897i	−0.0284199	−	0.0399844i
$661$	−1217.06			−1.84123			−0.920617	−	0.390466i	$-0.872314\pi$
$661$	−1217.06			−1.84123			−0.920617	+	0.390466i	$0.872314\pi$
$662$	157.135	+	157.135i	0.237365	+	0.237365i
$663$	−15.6766	+	15.6766i	−0.0236450	+	0.0236450i
$664$			661.191i			0.995770i
$665$	375.798	−	267.108i	0.565110	−	0.401666i
$666$	−85.3459			−0.128147
$667$	279.090	+	279.090i	0.418426	+	0.418426i
$668$	432.622	−	432.622i	0.647638	−	0.647638i
$669$		−	352.696i		−	0.527198i
$670$	−41.4541	+	245.202i	−0.0618718	+	0.365973i
$671$	159.500			0.237705
$672$	−104.079	−	104.079i	−0.154880	−	0.154880i
$673$	−545.679	+	545.679i	−0.810816	+	0.810816i	−0.984756	−	0.173940i	$-0.944350\pi$
$673$	−545.679	+	545.679i	−0.810816	+	0.810816i	0.173940	+	0.984756i	$0.444350\pi$
$674$			674.601i			1.00089i
$675$	−56.5555	−	116.946i	−0.0837859	−	0.173254i
$676$	398.322			0.589234
$677$	297.552	+	297.552i	0.439515	+	0.439515i	0.891849	−	0.452333i	$-0.149408\pi$
$677$	297.552	+	297.552i	0.439515	+	0.439515i	−0.452333	+	0.891849i	$0.649408\pi$
$678$	46.8735	−	46.8735i	0.0691349	−	0.0691349i
$679$			386.410i			0.569087i
$680$	−164.847	−	27.8693i	−0.242423	−	0.0409842i
$681$	−427.365			−0.627556
$682$	61.2155	+	61.2155i	0.0897589	+	0.0897589i
$683$	156.734	−	156.734i	0.229479	−	0.229479i	−0.582996	−	0.812475i	$-0.698120\pi$
$683$	156.734	−	156.734i	0.229479	−	0.229479i	0.812475	+	0.582996i	$0.198120\pi$
$684$			260.795i			0.381279i
$685$	427.012	+	600.770i	0.623375	+	0.877036i
$686$	−22.7258			−0.0331280
$687$	50.5793	+	50.5793i	0.0736235	+	0.0736235i
$688$	0.0485989	−	0.0485989i	7.06379e−5	−	7.06379e-5i
$689$			142.779i			0.207227i
$690$	−91.9552	+	65.3594i	−0.133268	+	0.0947238i
$691$	330.267			0.477955			0.238977	−	0.971025i	$-0.423188\pi$
$691$	330.267			0.477955			0.238977	+	0.971025i	$0.423188\pi$
$692$	−33.8228	−	33.8228i	−0.0488769	−	0.0488769i
$693$	8.41224	−	8.41224i	0.0121389	−	0.0121389i
$694$		−	28.0700i		−	0.0404468i
$695$	100.447	−	594.147i	0.144528	−	0.854888i
$696$	513.160			0.737298
$697$	−217.965	−	217.965i	−0.312719	−	0.312719i
$698$	−216.172	+	216.172i	−0.309703	+	0.309703i
$699$			178.379i			0.255191i
$700$	−148.525	+	71.8269i	−0.212178	+	0.102610i
$701$	1362.28			1.94334			0.971671	−	0.236336i	$-0.0759465\pi$
$701$	1362.28			1.94334			0.971671	+	0.236336i	$0.0759465\pi$
$702$	13.7536	+	13.7536i	0.0195921	+	0.0195921i
$703$	571.356	−	571.356i	0.812740	−	0.812740i
$704$			57.8839i			0.0822214i
$705$	470.233	+	79.4982i	0.666998	+	0.112763i
$706$	547.215			0.775093
$707$	−165.735	−	165.735i	−0.234420	−	0.234420i
$708$	−96.5871	+	96.5871i	−0.136423	+	0.136423i
$709$		−	370.256i		−	0.522222i	−0.965309	−	0.261111i	$-0.915911\pi$
$709$		−	370.256i		−	0.522222i	0.965309	−	0.261111i	$-0.0840889\pi$
$710$	56.3360	+	79.2600i	0.0793465	+	0.111634i
$711$	221.521			0.311562
$712$	469.123	+	469.123i	0.658881	+	0.658881i
$713$	−353.349	+	353.349i	−0.495581	+	0.495581i
$714$		−	23.5945i		−	0.0330455i
$715$	18.6340	−	13.2446i	0.0260616	−	0.0185239i
$716$	−720.810			−1.00672
$717$	512.740	+	512.740i	0.715119	+	0.715119i
$718$	73.2793	−	73.2793i	0.102060	−	0.102060i
$719$			883.893i			1.22934i	0.788786	+	0.614668i	$0.210710\pi$
$719$			883.893i			1.22934i	−0.788786	+	0.614668i	$0.789290\pi$
$720$	0.496461	−	2.93658i	0.000689530	−	0.00407858i
$721$	−82.4331			−0.114332
$722$	740.725	+	740.725i	1.02593	+	1.02593i
$723$	455.384	−	455.384i	0.629854	−	0.629854i
$724$		−	51.4934i		−	0.0711235i
$725$	305.537	−	877.801i	0.421430	−	1.21076i
$726$	252.394			0.347650
$727$	−264.156	−	264.156i	−0.363351	−	0.363351i	0.501694	−	0.865045i	$-0.332710\pi$
$727$	−264.156	−	264.156i	−0.363351	−	0.363351i	−0.865045	+	0.501694i	$0.832710\pi$
$728$	45.4795	−	45.4795i	0.0624718	−	0.0624718i
$729$			27.0000i			0.0370370i
$730$	−224.735	−	37.9940i	−0.307857	−	0.0520466i
$731$	1.45244			0.00198693
$732$	325.083	+	325.083i	0.444103	+	0.444103i
$733$	−335.629	+	335.629i	−0.457884	+	0.457884i	−0.897960	−	0.440076i	$-0.854951\pi$
$733$	−335.629	+	335.629i	−0.457884	+	0.457884i	0.440076	+	0.897960i	$0.354951\pi$
$734$			346.909i			0.472628i
$735$	−35.1207	−	49.4119i	−0.0477833	−	0.0672271i
$736$	−340.989			−0.463301
$737$	−42.9578	−	42.9578i	−0.0582874	−	0.0582874i
$738$	−191.229	+	191.229i	−0.259117	+	0.259117i
$739$			622.823i			0.842791i	0.906877	+	0.421396i	$0.138460\pi$
$739$			622.823i			0.842791i	−0.906877	+	0.421396i	$0.861540\pi$
$740$	−235.672	+	167.509i	−0.318475	+	0.226364i
$741$	−184.150			−0.248515
$742$	−107.447	−	107.447i	−0.144807	−	0.144807i
$743$	626.571	−	626.571i	0.843299	−	0.843299i	−0.145988	−	0.989286i	$-0.546636\pi$
$743$	626.571	−	626.571i	0.843299	−	0.843299i	0.989286	+	0.145988i	$0.0466360\pi$
$744$			649.699i			0.873251i
$745$	9.39538	−	55.5739i	0.0126112	−	0.0745958i
$746$	681.197			0.913132
$747$	−176.007	−	176.007i	−0.235619	−	0.235619i
$748$	11.0921	−	11.0921i	0.0148290	−	0.0148290i
$749$		−	406.891i		−	0.543245i
$750$	232.837	+	127.936i	0.310449	+	0.170581i
$751$	953.276			1.26934			0.634671	−	0.772783i	$-0.281136\pi$
$751$	953.276			1.26934			0.634671	+	0.772783i	$0.281136\pi$
$752$	7.73138	+	7.73138i	0.0102811	+	0.0102811i
$753$	575.079	−	575.079i	0.763717	−	0.763717i
$754$			139.168i			0.184573i
$755$	98.0167	+	16.5708i	0.129823	+	0.0219481i
$756$	34.2907			0.0453580
$757$	−202.867	−	202.867i	−0.267988	−	0.267988i	0.560301	−	0.828289i	$-0.310685\pi$
$757$	−202.867	−	202.867i	−0.267988	−	0.267988i	−0.828289	+	0.560301i	$0.810685\pi$
$758$	−312.998	+	312.998i	−0.412926	+	0.412926i
$759$		−	27.5605i		−	0.0363116i
$760$	−804.527	−	1131.90i	−1.05859	−	1.48934i
$761$	−721.550			−0.948160			−0.474080	−	0.880482i	$-0.657219\pi$
$761$	−721.550			−0.948160			−0.474080	+	0.880482i	$0.657219\pi$
$762$	−358.309	−	358.309i	−0.470222	−	0.470222i
$763$	141.879	−	141.879i	0.185949	−	0.185949i
$764$			349.733i			0.457765i
$765$	51.3006	−	36.4632i	0.0670596	−	0.0476643i
$766$	−585.725			−0.764655
$767$	−68.2011	−	68.2011i	−0.0889193	−	0.0889193i
$768$	−311.060	+	311.060i	−0.405026	+	0.405026i
$769$			266.011i			0.345918i	0.984929	+	0.172959i	$0.0553329\pi$
$769$			266.011i			0.345918i	−0.984929	+	0.172959i	$0.944667\pi$
$770$	−4.05575	+	23.9899i	−0.00526721	+	0.0311557i
$771$	526.649			0.683072
$772$	−490.349	−	490.349i	−0.635167	−	0.635167i
$773$	97.5944	−	97.5944i	0.126254	−	0.126254i	−0.641156	−	0.767410i	$-0.721545\pi$
$773$	97.5944	−	97.5944i	0.126254	−	0.126254i	0.767410	+	0.641156i	$0.221545\pi$
$774$		−	1.27428i		−	0.00164636i
$775$	1111.36	+	386.833i	1.43402	+	0.499139i
$776$	1163.86			1.49983
$777$	−75.1249	−	75.1249i	−0.0966859	−	0.0966859i
$778$	−508.216	+	508.216i	−0.653234	+	0.653234i
$779$		−	2560.39i		−	3.28677i
$780$	64.9732	+	10.9844i	0.0832990	+	0.0140826i
$781$	−23.7556			−0.0304169
$782$	−38.6506	−	38.6506i	−0.0494253	−	0.0494253i
$783$	−136.602	+	136.602i	−0.174459	+	0.174459i
$784$		−	1.38985i		−	0.00177277i
$785$	143.800	+	202.315i	0.183185	+	0.257726i
$786$	−45.0611			−0.0573297
$787$	−475.724	−	475.724i	−0.604477	−	0.604477i	0.337020	−	0.941497i	$-0.390581\pi$
$787$	−475.724	−	475.724i	−0.604477	−	0.604477i	−0.941497	+	0.337020i	$0.890581\pi$
$788$	−516.223	+	516.223i	−0.655106	+	0.655106i
$789$		−	235.102i		−	0.297974i
$790$	−369.265	+	262.464i	−0.467424	+	0.332233i
$791$	82.5199			0.104323
$792$	−25.3376	−	25.3376i	−0.0319919	−	0.0319919i
$793$	−229.545	+	229.545i	−0.289464	+	0.289464i
$794$			286.516i			0.360851i
$795$	67.5681	−	399.667i	0.0849913	−	0.502725i
$796$	400.499			0.503139
$797$	−195.835	−	195.835i	−0.245715	−	0.245715i	0.573495	−	0.819209i	$-0.305587\pi$
$797$	−195.835	−	195.835i	−0.245715	−	0.245715i	−0.819209	+	0.573495i	$0.805587\pi$
$798$	138.580	−	138.580i	0.173659	−	0.173659i
$799$			231.063i			0.289190i
$800$	349.593	+	722.895i	0.436992	+	0.903619i
$801$	−249.758			−0.311808
$802$	−515.161	−	515.161i	−0.642346	−	0.642346i
$803$	39.3722	−	39.3722i	0.0490314	−	0.0490314i
$804$		−	175.108i		−	0.217796i
$805$	−138.475	−	23.4107i	−0.172018	−	0.0290816i
$806$	−176.197			−0.218607
$807$	66.0204	+	66.0204i	0.0818097	+	0.0818097i
$808$	−499.193	+	499.193i	−0.617813	+	0.617813i
$809$		−	1068.26i		−	1.32046i	−0.751062	−	0.660232i	$-0.770458\pi$
$809$		−	1068.26i		−	1.32046i	0.751062	−	0.660232i	$-0.229542\pi$
$810$	−31.9904	−	45.0078i	−0.0394943	−	0.0555651i
$811$	−705.937			−0.870453			−0.435226	−	0.900321i	$-0.643332\pi$
$811$	−705.937			−0.870453			−0.435226	+	0.900321i	$0.643332\pi$
$812$	173.487	+	173.487i	0.213654	+	0.213654i
$813$	−200.419	+	200.419i	−0.246518	+	0.246518i
$814$			42.6401i			0.0523834i
$815$	−995.567	+	707.623i	−1.22155	+	0.868250i
$816$	1.44298			0.00176835
$817$	8.53078	+	8.53078i	0.0104416	+	0.0104416i
$818$	307.795	−	307.795i	0.376278	−	0.376278i
$819$			24.2130i			0.0295641i
$820$	−152.726	+	903.379i	−0.186252	+	1.10168i
$821$	471.239			0.573982			0.286991	−	0.957933i	$-0.407345\pi$
$821$	471.239			0.573982			0.286991	+	0.957933i	$0.407345\pi$
$822$	221.540	+	221.540i	0.269514	+	0.269514i
$823$	−394.220	+	394.220i	−0.479004	+	0.479004i	−0.904813	−	0.425809i	$-0.859990\pi$
$823$	−394.220	+	394.220i	−0.479004	+	0.479004i	0.425809	+	0.904813i	$0.359990\pi$
$824$			248.288i			0.301320i
$825$	−58.4281	+	28.2560i	−0.0708220	+	0.0342496i
$826$	102.648			0.124271
$827$	1059.35	+	1059.35i	1.28095	+	1.28095i	0.940127	+	0.340825i	$0.110706\pi$
$827$	1059.35	+	1059.35i	1.28095	+	1.28095i	0.340825	+	0.940127i	$0.389294\pi$
$828$	56.1723	−	56.1723i	0.0678409	−	0.0678409i
$829$		−	82.5862i		−	0.0996215i	−0.998759	−	0.0498107i	$-0.984138\pi$
$829$		−	82.5862i		−	0.0996215i	0.998759	−	0.0498107i	$-0.0158618\pi$
$830$	501.934	+	84.8575i	0.604740	+	0.102238i
$831$	62.2511			0.0749111
$832$	−83.3037	−	83.3037i	−0.100125	−	0.100125i
$833$	20.7688	−	20.7688i	0.0249325	−	0.0249325i
$834$		−	256.139i		−	0.307121i
$835$	−710.532	−	999.658i	−0.850936	−	1.19720i
$836$	130.297			0.155857
$837$	−172.948	−	172.948i	−0.206628	−	0.206628i
$838$	93.2512	−	93.2512i	0.111278	−	0.111278i
$839$		−	340.123i		−	0.405391i	−0.979242	−	0.202696i	$-0.935030\pi$
$839$		−	340.123i		−	0.405391i	0.979242	−	0.202696i	$-0.0649702\pi$
$840$	−148.828	+	105.783i	−0.177177	+	0.125933i
$841$	−541.220			−0.643544
$842$	−496.680	−	496.680i	−0.589881	−	0.589881i
$843$	138.590	−	138.590i	0.164401	−	0.164401i
$844$		−	663.234i		−	0.785822i
$845$	133.102	−	787.299i	0.157517	−	0.931715i
$846$	202.720			0.239621
$847$	222.167	+	222.167i	0.262299	+	0.262299i
$848$	6.57115	−	6.57115i	0.00774900	−	0.00774900i
$849$		−	859.866i		−	1.01280i
$850$	−42.3131	+	121.565i	−0.0497802	+	0.143017i
$851$	−246.128			−0.289222
$852$	−48.4172	−	48.4172i	−0.0568277	−	0.0568277i
$853$	−111.572	+	111.572i	−0.130800	+	0.130800i	−0.769476	−	0.638676i	$-0.779482\pi$
$853$	−111.572	+	111.572i	−0.130800	+	0.130800i	0.638676	+	0.769476i	$0.279482\pi$
$854$		−	345.482i		−	0.404545i
$855$	515.471	+	87.1461i	0.602890	+	0.101925i
$856$	−1225.55			−1.43172
$857$	−396.513	−	396.513i	−0.462675	−	0.462675i	0.436856	−	0.899531i	$-0.356092\pi$
$857$	−396.513	−	396.513i	−0.462675	−	0.462675i	−0.899531	+	0.436856i	$0.856092\pi$
$858$	6.87151	−	6.87151i	0.00800875	−	0.00800875i
$859$			581.785i			0.677281i	0.940916	+	0.338641i	$0.109967\pi$
$859$			581.785i			0.677281i	−0.940916	+	0.338641i	$0.890033\pi$
$860$	−2.50104	−	3.51876i	−0.00290819	−	0.00409158i
$861$	−336.654			−0.391004
$862$	−300.777	−	300.777i	−0.348929	−	0.348929i
$863$	−1069.82	+	1069.82i	−1.23965	+	1.23965i	−0.279504	+	0.960145i	$0.590170\pi$
$863$	−1069.82	+	1069.82i	−1.23965	+	1.23965i	−0.960145	+	0.279504i	$0.909830\pi$
$864$		−	166.898i		−	0.193169i
$865$	−78.1542	+	55.5500i	−0.0903517	+	0.0642197i
$866$	179.313			0.207059
$867$	−332.389	−	332.389i	−0.383378	−	0.383378i
$868$	−219.648	+	219.648i	−0.253051	+	0.253051i
$869$		−	110.675i		−	0.127359i
$870$	65.8591	−	389.558i	0.0757001	−	0.447768i
$871$	123.646			0.141958
$872$	−427.339	−	427.339i	−0.490068	−	0.490068i
$873$	−309.817	+	309.817i	−0.354888	+	0.354888i
$874$		−	454.021i		−	0.519474i
$875$	92.3383	+	317.567i	0.105529	+	0.362933i
$876$	160.492			0.183210
$877$	826.081	+	826.081i	0.941939	+	0.941939i	0.998405	−	0.0564653i	$-0.0179830\pi$
$877$	826.081	+	826.081i	0.941939	+	0.941939i	−0.0564653	+	0.998405i	$0.517983\pi$
$878$	−281.784	+	281.784i	−0.320938	+	0.320938i
$879$			211.826i			0.240985i
$880$	−1.46716	−	0.248039i	−0.00166722	−	0.000281863i
$881$	−1184.11			−1.34406			−0.672029	−	0.740525i	$-0.734577\pi$
$881$	−1184.11			−1.34406			−0.672029	+	0.740525i	$0.734577\pi$
$882$	−18.2212	−	18.2212i	−0.0206589	−	0.0206589i
$883$	376.671	−	376.671i	0.426581	−	0.426581i	−0.460881	−	0.887462i	$-0.652467\pi$
$883$	376.671	−	376.671i	0.426581	−	0.426581i	0.887462	+	0.460881i	$0.152467\pi$
$884$			31.9265i			0.0361160i
$885$	158.633	+	223.183i	0.179246	+	0.252185i
$886$	392.970			0.443532
$887$	727.292	+	727.292i	0.819946	+	0.819946i	0.986100	−	0.166154i	$-0.0531349\pi$
$887$	727.292	+	727.292i	0.819946	+	0.819946i	−0.166154	+	0.986100i	$0.553135\pi$
$888$	−226.276	+	226.276i	−0.254815	+	0.254815i
$889$		−	630.796i		−	0.709557i
$890$	416.336	−	295.921i	0.467793	−	0.332495i
$891$	13.4896			0.0151398
$892$	−359.145	−	359.145i	−0.402629	−	0.402629i
$893$	−1357.12	+	1357.12i	−1.51974	+	1.51974i
$894$		−	23.9581i		−	0.0267988i
$895$	−240.863	+	1424.71i	−0.269121	+	1.59185i
$896$	−214.543			−0.239446
$897$	39.6638	+	39.6638i	0.0442183	+	0.0442183i
$898$	192.258	−	192.258i	0.214096	−	0.214096i
$899$		−	1750.00i		−	1.94660i
$900$	−176.675	−	61.4952i	−0.196305	−	0.0683280i
$901$	196.388			0.217967
$902$	95.5405	+	95.5405i	0.105921	+	0.105921i
$903$	1.12167	−	1.12167i	0.00124216	−	0.00124216i
$904$		−	248.549i		−	0.274944i
$905$	−101.779	−	17.2068i	−0.112463	−	0.0190131i
$906$	42.2554			0.0466395
$907$	−302.758	−	302.758i	−0.333801	−	0.333801i	0.520227	−	0.854028i	$-0.325847\pi$
$907$	−302.758	−	302.758i	−0.333801	−	0.333801i	−0.854028	+	0.520227i	$0.825847\pi$
$908$	−435.180	+	435.180i	−0.479273	+	0.479273i
$909$		−	265.767i		−	0.292373i
$910$	−28.6882	−	40.3619i	−0.0315255	−	0.0443538i
$911$	−111.452			−0.122340			−0.0611701	−	0.998127i	$-0.519483\pi$
$911$	−111.452			−0.122340			−0.0611701	+	0.998127i	$0.519483\pi$
$912$	8.47517	+	8.47517i	0.00929294	+	0.00929294i
$913$	−87.9357	+	87.9357i	−0.0963151	+	0.0963151i
$914$		−	1096.32i		−	1.19948i
$915$	751.169	−	533.912i	0.820949	−	0.583510i
$916$	103.008			0.112455
$917$	−39.6646	−	39.6646i	−0.0432548	−	0.0432548i
$918$	18.9177	−	18.9177i	0.0206075	−	0.0206075i
$919$			568.949i			0.619095i	0.950884	+	0.309548i	$0.100178\pi$
$919$			568.949i			0.619095i	−0.950884	+	0.309548i	$0.899822\pi$
$920$	−70.5128	+	417.085i	−0.0766444	+	0.453353i
$921$	−276.995			−0.300755
$922$	−9.33059	−	9.33059i	−0.0101199	−	0.0101199i
$923$	34.1879	−	34.1879i	0.0370400	−	0.0370400i
$924$		−	17.1321i		−	0.0185413i
$925$	252.338	+	521.789i	0.272798	+	0.564096i
$926$	151.139			0.163217
$927$	−66.0935	−	66.0935i	−0.0712983	−	0.0712983i
$928$	844.391	−	844.391i	0.909904	−	0.909904i
$929$			1231.06i			1.32515i	0.748997	+	0.662574i	$0.230536\pi$
$929$			1231.06i			1.32515i	−0.748997	+	0.662574i	$0.769464\pi$
$930$	493.210	+	83.3826i	0.530333	+	0.0896587i
$931$	243.967			0.262048
$932$	181.640	+	181.640i	0.194893	+	0.194893i
$933$	−90.5893	+	90.5893i	−0.0970947	+	0.0970947i
$934$			293.071i			0.313780i
$935$	−18.2175	−	25.6305i	−0.0194840	−	0.0274123i
$936$	72.9294			0.0779160
$937$	−160.482	−	160.482i	−0.171272	−	0.171272i	0.616266	−	0.787538i	$-0.288645\pi$
$937$	−160.482	−	160.482i	−0.171272	−	0.171272i	−0.787538	+	0.616266i	$0.788645\pi$
$938$	−93.0481	+	93.0481i	−0.0991984	+	0.0991984i
$939$			794.323i			0.845925i
$940$	559.784	−	397.880i	0.595515	−	0.423277i
$941$	149.861			0.159258			0.0796288	−	0.996825i	$-0.474627\pi$
$941$	149.861			0.159258			0.0796288	+	0.996825i	$0.474627\pi$
$942$	74.6058	+	74.6058i	0.0791994	+	0.0791994i
$943$	−551.480	+	551.480i	−0.584815	+	0.584815i
$944$			6.27767i			0.00665008i
$945$	11.4584	−	67.7769i	0.0121253	−	0.0717216i
$946$	−0.636648			−0.000672990
$947$	128.238	+	128.238i	0.135415	+	0.135415i	0.771565	−	0.636150i	$-0.219474\pi$
$947$	128.238	+	128.238i	0.135415	+	0.135415i	−0.636150	+	0.771565i	$0.719474\pi$
$948$	225.571	−	225.571i	0.237944	−	0.237944i
$949$			113.325i			0.119415i
$950$	−962.520	+	465.477i	−1.01318	+	0.489975i
$951$	−369.954			−0.389016
$952$	−62.5555	−	62.5555i	−0.0657095	−	0.0657095i
$953$	−361.782	+	361.782i	−0.379625	+	0.379625i	−0.870967	−	0.491342i	$-0.836506\pi$
$953$	−361.782	+	361.782i	−0.379625	+	0.379625i	0.491342	+	0.870967i	$0.336506\pi$
$954$		−	172.298i		−	0.180606i
$955$	691.260	+	116.865i	0.723833	+	0.122372i
$956$	1044.23			1.09229
$957$	68.2481	+	68.2481i	0.0713146	+	0.0713146i
$958$	513.130	−	513.130i	0.535627	−	0.535627i
$959$			390.017i			0.406692i
$960$	193.761	+	272.606i	0.201835	+	0.283964i
$961$	1254.63			1.30554
$962$	−61.3656	−	61.3656i	−0.0637896	−	0.0637896i
$963$	326.238	−	326.238i	0.338773	−	0.338773i
$964$		−	927.423i		−	0.962057i
$965$	−1133.05	+	805.341i	−1.17414	+	0.834550i
$966$	−59.6970			−0.0617981
$967$	−187.671	−	187.671i	−0.194075	−	0.194075i	0.603379	−	0.797454i	$-0.293821\pi$
$967$	−187.671	−	187.671i	−0.194075	−	0.194075i	−0.797454	+	0.603379i	$0.793821\pi$
$968$	669.167	−	669.167i	0.691288	−	0.691288i
$969$			253.292i			0.261395i
$970$	149.371	−	883.532i	0.153991	−	0.910858i
$971$	1651.98			1.70132			0.850659	−	0.525718i	$-0.176203\pi$
$971$	1651.98			1.70132			0.850659	+	0.525718i	$0.176203\pi$
$972$	27.4937	+	27.4937i	0.0282857	+	0.0282857i
$973$	225.464	−	225.464i	0.231721	−	0.231721i
$974$		−	788.938i		−	0.809998i
$975$	43.4224	−	124.752i	0.0445358	−	0.127950i
$976$	21.1288			0.0216483
$977$	−772.134	−	772.134i	−0.790311	−	0.790311i	0.191234	−	0.981545i	$-0.438751\pi$
$977$	−772.134	−	772.134i	−0.790311	−	0.790311i	−0.981545	+	0.191234i	$0.938751\pi$
$978$	−367.126	+	367.126i	−0.375385	+	0.375385i
$979$			124.783i			0.127459i
$980$	−86.0783	−	14.5525i	−0.0878350	−	0.0148495i
$981$	227.513			0.231919
$982$	232.241	+	232.241i	0.236498	+	0.236498i
$983$	235.236	−	235.236i	0.239304	−	0.239304i	−0.577258	−	0.816562i	$-0.695877\pi$
$983$	235.236	−	235.236i	0.239304	−	0.239304i	0.816562	+	0.577258i	$0.195877\pi$
$984$			1014.00i			1.03049i
$985$	847.836	+	1192.83i	0.860748	+	1.21100i
$986$	191.421			0.194139
$987$	178.442	+	178.442i	0.180792	+	0.180792i
$988$	−187.517	+	187.517i	−0.189795	+	0.189795i
$989$		−	3.67487i		−	0.00371574i
$990$	−22.4865	+	15.9829i	−0.0227137	+	0.0161443i
$991$	308.024			0.310822			0.155411	−	0.987850i	$-0.450330\pi$
$991$	308.024			0.310822			0.155411	+	0.987850i	$0.450330\pi$
$992$	1069.06	+	1069.06i	1.07768	+	1.07768i
$993$	−221.800	+	221.800i	−0.223364	+	0.223364i
$994$			51.4553i			0.0517659i
$995$	133.829	−	791.602i	0.134502	−	0.795580i
$996$	−358.451			−0.359890
$997$	−663.237	−	663.237i	−0.665232	−	0.665232i	0.291376	−	0.956609i	$-0.405887\pi$
$997$	−663.237	−	663.237i	−0.665232	−	0.665232i	−0.956609	+	0.291376i	$0.905887\pi$
$998$	−519.339	+	519.339i	−0.520380	+	0.520380i
$999$		−	120.468i		−	0.120588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.22.5	✓	24
3.2	odd	2		315.3.o.b.127.8		24
5.2	odd	4		525.3.l.e.43.8		24
5.3	odd	4	inner	105.3.l.a.43.5	yes	24
5.4	even	2		525.3.l.e.232.8		24
15.8	even	4		315.3.o.b.253.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.5	✓	24	1.1	even	1	trivial
105.3.l.a.43.5	yes	24	5.3	odd	4	inner
315.3.o.b.127.8		24	3.2	odd	2
315.3.o.b.253.8		24	15.8	even	4
525.3.l.e.43.8		24	5.2	odd	4
525.3.l.e.232.8		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)

\(f(q)\)	\(=\)	\(q+(-0.867675 - 0.867675i) q^{2} +(1.22474 - 1.22474i) q^{3} -2.49428i q^{4} +(-4.93004 - 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.63493 + 5.63493i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-0.867675 - 0.867675i) q^{2} +(1.22474 - 1.22474i) q^{3} -2.49428i q^{4} +(-4.93004 - 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.63493 + 5.63493i) q^{8} -3.00000i q^{9} +(3.55449 + 5.00086i) q^{10} -1.49884 q^{11} +(-3.05486 - 3.05486i) q^{12} +(2.15706 - 2.15706i) q^{13} +3.24654i q^{14} +(-7.05884 + 5.01725i) q^{15} -0.198550 q^{16} +(-2.96697 - 2.96697i) q^{17} +(-2.60303 + 2.60303i) q^{18} -34.8524i q^{19} +(-2.07893 + 12.2969i) q^{20} -4.58258 q^{21} +(1.30051 + 1.30051i) q^{22} +(-7.50682 + 7.50682i) q^{23} +13.8027i q^{24} +(23.6106 + 8.21817i) q^{25} -3.74326 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-4.66637 + 4.66637i) q^{28} -37.1782i q^{29} +(10.4781 + 1.77144i) q^{30} +47.0705 q^{31} +(22.7120 + 22.7120i) q^{32} +(-1.83570 + 1.83570i) q^{33} +5.14873i q^{34} +(7.66397 + 10.7826i) q^{35} -7.48284 q^{36} +(16.3936 + 16.3936i) q^{37} +(-30.2406 + 30.2406i) q^{38} -5.28371i q^{39} +(32.4770 - 23.0838i) q^{40} +73.4639 q^{41} +(3.97619 + 3.97619i) q^{42} +(-0.244769 + 0.244769i) q^{43} +3.73853i q^{44} +(-2.50043 + 14.7901i) q^{45} +13.0270 q^{46} +(-38.9392 - 38.9392i) q^{47} +(-0.243173 + 0.243173i) q^{48} +7.00000i q^{49} +(-13.3557 - 27.6171i) q^{50} -7.26756 q^{51} +(-5.38032 - 5.38032i) q^{52} +(-33.0957 + 33.0957i) q^{53} +6.37608i q^{54} +(7.38936 + 1.24925i) q^{55} +21.0840 q^{56} +(-42.6853 - 42.6853i) q^{57} +(-32.2586 + 32.2586i) q^{58} -31.6176i q^{59} +(12.5144 + 17.6067i) q^{60} -106.415 q^{61} +(-40.8419 - 40.8419i) q^{62} +(-5.61249 + 5.61249i) q^{63} -38.6190i q^{64} +(-12.4323 + 8.83655i) q^{65} +3.18558 q^{66} +(28.6607 + 28.6607i) q^{67} +(-7.40045 + 7.40045i) q^{68} +18.3879i q^{69} +(2.70592 - 16.0056i) q^{70} +15.8493 q^{71} +(16.9048 + 16.9048i) q^{72} +(-26.2684 + 26.2684i) q^{73} -28.4486i q^{74} +(38.9822 - 18.8518i) q^{75} -86.9316 q^{76} +(2.80408 + 2.80408i) q^{77} +(-4.58454 + 4.58454i) q^{78} +73.8402i q^{79} +(0.978860 + 0.165487i) q^{80} -9.00000 q^{81} +(-63.7428 - 63.7428i) q^{82} +(58.6690 - 58.6690i) q^{83} +11.4302i q^{84} +(12.1544 + 17.1002i) q^{85} +0.424760 q^{86} +(-45.5338 - 45.5338i) q^{87} +(8.44587 - 8.44587i) q^{88} -83.2528i q^{89} +(15.0026 - 10.6635i) q^{90} -8.07100 q^{91} +(18.7241 + 18.7241i) q^{92} +(57.6493 - 57.6493i) q^{93} +67.5732i q^{94} +(-29.0487 + 171.824i) q^{95} +55.6328 q^{96} +(-103.272 - 103.272i) q^{97} +(6.07373 - 6.07373i) q^{98} +4.49653i 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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