LMFDB - Embedded newform 1050.3.l.h.757.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			757.5
Root			$-0.394902 + 0.394902i$ of defining polynomial
Character	$\chi$	$=$	1050.757
Dual form			1050.3.l.h.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -11.5078 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.70521 - 7.70521i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-21.0749 - 21.0749i) q^{17} +(3.00000 - 3.00000i) q^{18} +24.1173i q^{19} -4.58258 q^{21} +(-11.5078 - 11.5078i) q^{22} +(-30.1762 + 30.1762i) q^{23} +4.89898i q^{24} +15.4104 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +51.1392i q^{29} -46.9852 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-14.0941 + 14.0941i) q^{33} -42.1499i q^{34} +6.00000 q^{36} +(8.50020 + 8.50020i) q^{37} +(-24.1173 + 24.1173i) q^{38} -18.8738i q^{39} +18.6089 q^{41} +(-4.58258 - 4.58258i) q^{42} +(26.1383 - 26.1383i) q^{43} -23.0156i q^{44} -60.3523 q^{46} +(-50.1311 - 50.1311i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} -51.6228 q^{51} +(15.4104 + 15.4104i) q^{52} +(-7.08527 + 7.08527i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(29.5376 + 29.5376i) q^{57} +(-51.1392 + 51.1392i) q^{58} -94.3487i q^{59} +8.09003 q^{61} +(-46.9852 - 46.9852i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} -28.1883 q^{66} +(20.6469 + 20.6469i) q^{67} +(42.1499 - 42.1499i) q^{68} +73.9162i q^{69} -63.7595 q^{71} +(6.00000 + 6.00000i) q^{72} +(-50.1883 + 50.1883i) q^{73} +17.0004i q^{74} -48.2346 q^{76} +(21.5292 + 21.5292i) q^{77} +(18.8738 - 18.8738i) q^{78} +1.06121i q^{79} -9.00000 q^{81} +(18.6089 + 18.6089i) q^{82} +(-53.6243 + 53.6243i) q^{83} -9.16515i q^{84} +52.2765 q^{86} +(62.6325 + 62.6325i) q^{87} +(23.0156 - 23.0156i) q^{88} -145.154i q^{89} -28.8303 q^{91} +(-60.3523 - 60.3523i) q^{92} +(-57.5449 + 57.5449i) q^{93} -100.262i q^{94} -9.79796 q^{96} +(-23.7872 - 23.7872i) q^{97} +(-7.00000 + 7.00000i) q^{98} +34.5235i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 - 32 * q^8	$ 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−11.5078			−1.04617			−0.523083	−	0.852282i	$-0.675218\pi$
$11$	−11.5078			−1.04617			−0.523083	+	0.852282i	$0.675218\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	7.70521	−	7.70521i	0.592708	−	0.592708i	−0.345654	−	0.938362i	$-0.612343\pi$
$13$	7.70521	−	7.70521i	0.592708	−	0.592708i	0.938362	+	0.345654i	$0.112343\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−21.0749	−	21.0749i	−1.23970	−	1.23970i	−0.960123	−	0.279579i	$-0.909805\pi$
$17$	−21.0749	−	21.0749i	−1.23970	−	1.23970i	−0.279579	−	0.960123i	$-0.590195\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			24.1173i			1.26933i	0.772786	+	0.634666i	$0.218862\pi$
$19$			24.1173i			1.26933i	−0.772786	+	0.634666i	$0.781138\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	−11.5078	−	11.5078i	−0.523083	−	0.523083i
$23$	−30.1762	+	30.1762i	−1.31201	+	1.31201i	−0.392073	+	0.919934i	$0.628242\pi$
$23$	−30.1762	+	30.1762i	−1.31201	+	1.31201i	−0.919934	+	0.392073i	$0.871758\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	15.4104			0.592708
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$			51.1392i			1.76342i	0.471790	+	0.881711i	$0.343608\pi$
$29$			51.1392i			1.76342i	−0.471790	+	0.881711i	$0.656392\pi$
$30$		0			0
$31$	−46.9852			−1.51565			−0.757826	−	0.652457i	$-0.773738\pi$
$31$	−46.9852			−1.51565			−0.757826	+	0.652457i	$0.773738\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−14.0941	+	14.0941i	−0.427095	+	0.427095i
$34$		−	42.1499i		−	1.23970i
$35$		0			0
$36$	6.00000			0.166667
$37$	8.50020	+	8.50020i	0.229735	+	0.229735i	0.812582	−	0.582847i	$-0.198061\pi$
$37$	8.50020	+	8.50020i	0.229735	+	0.229735i	−0.582847	+	0.812582i	$0.698061\pi$
$38$	−24.1173	+	24.1173i	−0.634666	+	0.634666i
$39$		−	18.8738i		−	0.483944i
$40$		0			0
$41$	18.6089			0.453875			0.226937	−	0.973909i	$-0.427129\pi$
$41$	18.6089			0.453875			0.226937	+	0.973909i	$0.427129\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	26.1383	−	26.1383i	0.607867	−	0.607867i	−0.334522	−	0.942388i	$-0.608575\pi$
$43$	26.1383	−	26.1383i	0.607867	−	0.607867i	0.942388	+	0.334522i	$0.108575\pi$
$44$		−	23.0156i		−	0.523083i
$45$		0			0
$46$	−60.3523			−1.31201
$47$	−50.1311	−	50.1311i	−1.06662	−	1.06662i	−0.997617	−	0.0690016i	$-0.978019\pi$
$47$	−50.1311	−	50.1311i	−1.06662	−	1.06662i	−0.0690016	−	0.997617i	$-0.521981\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	−51.6228			−1.01221
$52$	15.4104	+	15.4104i	0.296354	+	0.296354i
$53$	−7.08527	+	7.08527i	−0.133684	+	0.133684i	−0.770783	−	0.637098i	$-0.780135\pi$
$53$	−7.08527	+	7.08527i	−0.133684	+	0.133684i	0.637098	+	0.770783i	$0.280135\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	29.5376	+	29.5376i	0.518203	+	0.518203i
$58$	−51.1392	+	51.1392i	−0.881711	+	0.881711i
$59$		−	94.3487i		−	1.59913i	−0.600579	−	0.799565i	$-0.705063\pi$
$59$		−	94.3487i		−	1.59913i	0.600579	−	0.799565i	$-0.294937\pi$
$60$		0			0
$61$	8.09003			0.132623			0.0663117	−	0.997799i	$-0.478877\pi$
$61$	8.09003			0.132623			0.0663117	+	0.997799i	$0.478877\pi$
$62$	−46.9852	−	46.9852i	−0.757826	−	0.757826i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−28.1883			−0.427095
$67$	20.6469	+	20.6469i	0.308163	+	0.308163i	0.844197	−	0.536034i	$-0.180078\pi$
$67$	20.6469	+	20.6469i	0.308163	+	0.308163i	−0.536034	+	0.844197i	$0.680078\pi$
$68$	42.1499	−	42.1499i	0.619851	−	0.619851i
$69$			73.9162i			1.07125i
$70$		0			0
$71$	−63.7595			−0.898021			−0.449011	−	0.893526i	$-0.648223\pi$
$71$	−63.7595			−0.898021			−0.449011	+	0.893526i	$0.648223\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−50.1883	+	50.1883i	−0.687511	+	0.687511i	−0.961681	−	0.274170i	$-0.911597\pi$
$73$	−50.1883	+	50.1883i	−0.687511	+	0.687511i	0.274170	+	0.961681i	$0.411597\pi$
$74$			17.0004i			0.229735i
$75$		0			0
$76$	−48.2346			−0.634666
$77$	21.5292	+	21.5292i	0.279599	+	0.279599i
$78$	18.8738	−	18.8738i	0.241972	−	0.241972i
$79$			1.06121i			0.0134331i	0.999977	+	0.00671653i	$0.00213796\pi$
$79$			1.06121i			0.0134331i	−0.999977	+	0.00671653i	$0.997862\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	18.6089	+	18.6089i	0.226937	+	0.226937i
$83$	−53.6243	+	53.6243i	−0.646075	+	0.646075i	−0.952042	−	0.305967i	$-0.901020\pi$
$83$	−53.6243	+	53.6243i	−0.646075	+	0.646075i	0.305967	+	0.952042i	$0.401020\pi$
$84$		−	9.16515i		−	0.109109i
$85$		0			0
$86$	52.2765			0.607867
$87$	62.6325	+	62.6325i	0.719914	+	0.719914i
$88$	23.0156	−	23.0156i	0.261541	−	0.261541i
$89$		−	145.154i		−	1.63095i	−0.578794	−	0.815473i	$-0.696477\pi$
$89$		−	145.154i		−	1.63095i	0.578794	−	0.815473i	$-0.303523\pi$
$90$		0			0
$91$	−28.8303			−0.316816
$92$	−60.3523	−	60.3523i	−0.656003	−	0.656003i
$93$	−57.5449	+	57.5449i	−0.618762	+	0.618762i
$94$		−	100.262i		−	1.06662i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−23.7872	−	23.7872i	−0.245229	−	0.245229i	0.573780	−	0.819009i	$-0.305476\pi$
$97$	−23.7872	−	23.7872i	−0.245229	−	0.245229i	−0.819009	+	0.573780i	$0.805476\pi$
$98$	−7.00000	+	7.00000i	−0.0714286	+	0.0714286i
$99$			34.5235i			0.348722i
$100$		0			0
$101$	50.1467			0.496502			0.248251	−	0.968696i	$-0.420144\pi$
$101$	50.1467			0.496502			0.248251	+	0.968696i	$0.420144\pi$
$102$	−51.6228	−	51.6228i	−0.506106	−	0.506106i
$103$	−56.3876	+	56.3876i	−0.547453	+	0.547453i	−0.925703	−	0.378251i	$-0.876526\pi$
$103$	−56.3876	+	56.3876i	−0.547453	+	0.547453i	0.378251	+	0.925703i	$0.376526\pi$
$104$			30.8208i			0.296354i
$105$		0			0
$106$	−14.1705			−0.133684
$107$	135.365	+	135.365i	1.26510	+	1.26510i	0.948590	+	0.316506i	$0.102510\pi$
$107$	135.365	+	135.365i	1.26510	+	1.26510i	0.316506	+	0.948590i	$0.397490\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	100.934i		−	0.926001i	−0.886358	−	0.463001i	$-0.846773\pi$
$109$		−	100.934i		−	0.926001i	0.886358	−	0.463001i	$-0.153227\pi$
$110$		0			0
$111$	20.8211			0.187578
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	−25.3174	+	25.3174i	−0.224048	+	0.224048i	−0.810201	−	0.586153i	$-0.800642\pi$
$113$	−25.3174	+	25.3174i	−0.224048	+	0.224048i	0.586153	+	0.810201i	$0.300642\pi$
$114$			59.0751i			0.518203i
$115$		0			0
$116$	−102.278			−0.881711
$117$	−23.1156	−	23.1156i	−0.197569	−	0.197569i
$118$	94.3487	−	94.3487i	0.799565	−	0.799565i
$119$			78.8552i			0.662649i
$120$		0			0
$121$	11.4299			0.0944623
$122$	8.09003	+	8.09003i	0.0663117	+	0.0663117i
$123$	22.7911	−	22.7911i	0.185294	−	0.185294i
$124$		−	93.9704i		−	0.757826i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	−116.746	−	116.746i	−0.919262	−	0.919262i	0.0777140	−	0.996976i	$-0.475238\pi$
$127$	−116.746	−	116.746i	−0.919262	−	0.919262i	−0.996976	+	0.0777140i	$0.975238\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	64.0254i		−	0.496321i
$130$		0			0
$131$	34.8004			0.265652			0.132826	−	0.991139i	$-0.457595\pi$
$131$	34.8004			0.265652			0.132826	+	0.991139i	$0.457595\pi$
$132$	−28.1883	−	28.1883i	−0.213548	−	0.213548i
$133$	45.1194	−	45.1194i	0.339243	−	0.339243i
$134$			41.2938i			0.308163i
$135$		0			0
$136$	84.2997			0.619851
$137$	−131.552	−	131.552i	−0.960235	−	0.960235i	0.0390044	−	0.999239i	$-0.487581\pi$
$137$	−131.552	−	131.552i	−0.960235	−	0.960235i	−0.999239	+	0.0390044i	$0.987581\pi$
$138$	−73.9162	+	73.9162i	−0.535625	+	0.535625i
$139$			89.4407i			0.643458i	0.946832	+	0.321729i	$0.104264\pi$
$139$			89.4407i			0.643458i	−0.946832	+	0.321729i	$0.895736\pi$
$140$		0			0
$141$	−122.795			−0.870890
$142$	−63.7595	−	63.7595i	−0.449011	−	0.449011i
$143$	−88.6702	+	88.6702i	−0.620071	+	0.620071i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	−100.377			−0.687511
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	−17.0004	+	17.0004i	−0.114868	+	0.114868i
$149$		−	55.7399i		−	0.374093i	−0.982351	−	0.187047i	$-0.940108\pi$
$149$		−	55.7399i		−	0.374093i	0.982351	−	0.187047i	$-0.0598915\pi$
$150$		0			0
$151$	82.9665			0.549447			0.274724	−	0.961523i	$-0.411414\pi$
$151$	82.9665			0.549447			0.274724	+	0.961523i	$0.411414\pi$
$152$	−48.2346	−	48.2346i	−0.317333	−	0.317333i
$153$	−63.2248	+	63.2248i	−0.413234	+	0.413234i
$154$			43.0583i			0.279599i
$155$		0			0
$156$	37.7477			0.241972
$157$	99.7950	+	99.7950i	0.635637	+	0.635637i	0.949476	−	0.313839i	$-0.101615\pi$
$157$	99.7950	+	99.7950i	0.635637	+	0.635637i	−0.313839	+	0.949476i	$0.601615\pi$
$158$	−1.06121	+	1.06121i	−0.00671653	+	0.00671653i
$159$			17.3553i			0.109153i
$160$		0			0
$161$	112.909			0.701297
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	45.3884	−	45.3884i	0.278457	−	0.278457i	−0.554036	−	0.832493i	$-0.686913\pi$
$163$	45.3884	−	45.3884i	0.278457	−	0.278457i	0.832493	+	0.554036i	$0.186913\pi$
$164$			37.2177i			0.226937i
$165$		0			0
$166$	−107.249			−0.646075
$167$	99.2501	+	99.2501i	0.594312	+	0.594312i	0.938793	−	0.344481i	$-0.111945\pi$
$167$	99.2501	+	99.2501i	0.594312	+	0.594312i	−0.344481	+	0.938793i	$0.611945\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$			50.2595i			0.297393i
$170$		0			0
$171$	72.3520			0.423111
$172$	52.2765	+	52.2765i	0.303933	+	0.303933i
$173$	80.5404	−	80.5404i	0.465551	−	0.465551i	−0.434919	−	0.900470i	$-0.643223\pi$
$173$	80.5404	−	80.5404i	0.465551	−	0.465551i	0.900470	+	0.434919i	$0.143223\pi$
$174$			125.265i			0.719914i
$175$		0			0
$176$	46.0313			0.261541
$177$	−115.553	−	115.553i	−0.652842	−	0.652842i
$178$	145.154	−	145.154i	0.815473	−	0.815473i
$179$			154.267i			0.861824i	0.902394	+	0.430912i	$0.141808\pi$
$179$			154.267i			0.861824i	−0.902394	+	0.430912i	$0.858192\pi$
$180$		0			0
$181$	166.548			0.920155			0.460078	−	0.887879i	$-0.347822\pi$
$181$	166.548			0.920155			0.460078	+	0.887879i	$0.347822\pi$
$182$	−28.8303	−	28.8303i	−0.158408	−	0.158408i
$183$	9.90822	−	9.90822i	0.0541433	−	0.0541433i
$184$		−	120.705i		−	0.656003i
$185$		0			0
$186$	−115.090			−0.618762
$187$	242.527	+	242.527i	1.29693	+	1.29693i
$188$	100.262	−	100.262i	0.533309	−	0.533309i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	−235.646			−1.23375			−0.616873	−	0.787063i	$-0.711601\pi$
$191$	−235.646			−1.23375			−0.616873	+	0.787063i	$0.711601\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	16.2211	−	16.2211i	0.0840471	−	0.0840471i	−0.663833	−	0.747880i	$-0.731072\pi$
$193$	16.2211	−	16.2211i	0.0840471	−	0.0840471i	0.747880	+	0.663833i	$0.231072\pi$
$194$		−	47.5744i		−	0.245229i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	6.68134	+	6.68134i	0.0339154	+	0.0339154i	0.723861	−	0.689946i	$-0.242366\pi$
$197$	6.68134	+	6.68134i	0.0339154	+	0.0339154i	−0.689946	+	0.723861i	$0.742366\pi$
$198$	−34.5235	+	34.5235i	−0.174361	+	0.174361i
$199$		−	32.0712i		−	0.161162i	−0.996748	−	0.0805808i	$-0.974322\pi$
$199$		−	32.0712i		−	0.161162i	0.996748	−	0.0805808i	$-0.0256775\pi$
$200$		0			0
$201$	50.5744			0.251614
$202$	50.1467	+	50.1467i	0.248251	+	0.248251i
$203$	95.6728	−	95.6728i	0.471294	−	0.471294i
$204$		−	103.246i		−	0.506106i
$205$		0			0
$206$	−112.775			−0.547453
$207$	90.5285	+	90.5285i	0.437336	+	0.437336i
$208$	−30.8208	+	30.8208i	−0.148177	+	0.148177i
$209$		−	277.538i		−	1.32793i
$210$		0			0
$211$	123.531			0.585457			0.292728	−	0.956196i	$-0.405437\pi$
$211$	123.531			0.585457			0.292728	+	0.956196i	$0.405437\pi$
$212$	−14.1705	−	14.1705i	−0.0668422	−	0.0668422i
$213$	−78.0891	+	78.0891i	−0.366616	+	0.366616i
$214$			270.731i			1.26510i
$215$		0			0
$216$	14.6969			0.0680414
$217$	87.9013	+	87.9013i	0.405075	+	0.405075i
$218$	100.934	−	100.934i	0.463001	−	0.463001i
$219$			122.936i			0.561350i
$220$		0			0
$221$	−324.774			−1.46956
$222$	20.8211	+	20.8211i	0.0937890	+	0.0937890i
$223$	81.9590	−	81.9590i	0.367529	−	0.367529i	−0.499046	−	0.866575i	$-0.666316\pi$
$223$	81.9590	−	81.9590i	0.367529	−	0.367529i	0.866575	+	0.499046i	$0.166316\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−50.6348			−0.224048
$227$	−93.6089	−	93.6089i	−0.412374	−	0.412374i	0.470191	−	0.882565i	$-0.344185\pi$
$227$	−93.6089	−	93.6089i	−0.412374	−	0.412374i	−0.882565	+	0.470191i	$0.844185\pi$
$228$	−59.0751	+	59.0751i	−0.259101	+	0.259101i
$229$		−	348.973i		−	1.52390i	−0.647635	−	0.761950i	$-0.724242\pi$
$229$		−	348.973i		−	1.52390i	0.647635	−	0.761950i	$-0.275758\pi$
$230$		0			0
$231$	52.7355			0.228292
$232$	−102.278	−	102.278i	−0.440856	−	0.440856i
$233$	−208.319	+	208.319i	−0.894074	+	0.894074i	−0.994904	−	0.100829i	$-0.967850\pi$
$233$	−208.319	+	208.319i	−0.894074	+	0.894074i	0.100829	+	0.994904i	$0.467850\pi$
$234$		−	46.2313i		−	0.197569i
$235$		0			0
$236$	188.697			0.799565
$237$	1.29971	+	1.29971i	0.00548403	+	0.00548403i
$238$	−78.8552	+	78.8552i	−0.331324	+	0.331324i
$239$		−	330.793i		−	1.38407i	−0.721864	−	0.692035i	$-0.756715\pi$
$239$		−	330.793i		−	1.38407i	0.721864	−	0.692035i	$-0.243285\pi$
$240$		0			0
$241$	375.584			1.55844			0.779221	−	0.626749i	$-0.215615\pi$
$241$	375.584			1.55844			0.779221	+	0.626749i	$0.215615\pi$
$242$	11.4299	+	11.4299i	0.0472312	+	0.0472312i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			16.1801i			0.0663117i
$245$		0			0
$246$	45.5822			0.185294
$247$	185.829	+	185.829i	0.752344	+	0.752344i
$248$	93.9704	−	93.9704i	0.378913	−	0.378913i
$249$			131.352i			0.527518i
$250$		0			0
$251$	41.2876			0.164493			0.0822463	−	0.996612i	$-0.473791\pi$
$251$	41.2876			0.164493			0.0822463	+	0.996612i	$0.473791\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	347.262	−	347.262i	1.37258	−	1.37258i
$254$		−	233.492i		−	0.919262i
$255$		0			0
$256$	16.0000			0.0625000
$257$	101.370	+	101.370i	0.394437	+	0.394437i	0.876266	−	0.481828i	$-0.160027\pi$
$257$	101.370	+	101.370i	0.394437	+	0.394437i	−0.481828	+	0.876266i	$0.660027\pi$
$258$	64.0254	−	64.0254i	0.248161	−	0.248161i
$259$		−	31.8048i		−	0.122799i
$260$		0			0
$261$	153.418			0.587807
$262$	34.8004	+	34.8004i	0.132826	+	0.132826i
$263$	−164.594	+	164.594i	−0.625833	+	0.625833i	−0.947017	−	0.321184i	$-0.895919\pi$
$263$	−164.594	+	164.594i	−0.625833	+	0.625833i	0.321184	+	0.947017i	$0.395919\pi$
$264$		−	56.3766i		−	0.213548i
$265$		0			0
$266$	90.2387			0.339243
$267$	−177.777	−	177.777i	−0.665831	−	0.665831i
$268$	−41.2938	+	41.2938i	−0.154081	+	0.154081i
$269$			254.148i			0.944788i	0.881387	+	0.472394i	$0.156610\pi$
$269$			254.148i			0.944788i	−0.881387	+	0.472394i	$0.843390\pi$
$270$		0			0
$271$	22.4723			0.0829237			0.0414619	−	0.999140i	$-0.486798\pi$
$271$	22.4723			0.0829237			0.0414619	+	0.999140i	$0.486798\pi$
$272$	84.2997	+	84.2997i	0.309925	+	0.309925i
$273$	−35.3097	+	35.3097i	−0.129340	+	0.129340i
$274$		−	263.104i		−	0.960235i
$275$		0			0
$276$	−147.832			−0.535625
$277$	−47.3949	−	47.3949i	−0.171101	−	0.171101i	0.616362	−	0.787463i	$-0.288606\pi$
$277$	−47.3949	−	47.3949i	−0.171101	−	0.171101i	−0.787463	+	0.616362i	$0.788606\pi$
$278$	−89.4407	+	89.4407i	−0.321729	+	0.321729i
$279$			140.956i			0.505217i
$280$		0			0
$281$	−18.8810			−0.0671920			−0.0335960	−	0.999435i	$-0.510696\pi$
$281$	−18.8810			−0.0671920			−0.0335960	+	0.999435i	$0.510696\pi$
$282$	−122.795	−	122.795i	−0.435445	−	0.435445i
$283$	115.825	−	115.825i	0.409277	−	0.409277i	−0.472209	−	0.881486i	$-0.656543\pi$
$283$	115.825	−	115.825i	0.409277	−	0.409277i	0.881486	+	0.472209i	$0.156543\pi$
$284$		−	127.519i		−	0.449011i
$285$		0			0
$286$	−177.340			−0.620071
$287$	−34.8140	−	34.8140i	−0.121303	−	0.121303i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			599.306i			2.07372i
$290$		0			0
$291$	−58.2665			−0.200228
$292$	−100.377	−	100.377i	−0.343756	−	0.343756i
$293$	−224.451	+	224.451i	−0.766043	+	0.766043i	−0.977407	−	0.211364i	$-0.932209\pi$
$293$	−224.451	+	224.451i	−0.766043	+	0.766043i	0.211364	+	0.977407i	$0.432209\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−34.0008			−0.114868
$297$	42.2824	+	42.2824i	0.142365	+	0.142365i
$298$	55.7399	−	55.7399i	0.187047	−	0.187047i
$299$			465.027i			1.55528i
$300$		0			0
$301$	−97.8004			−0.324918
$302$	82.9665	+	82.9665i	0.274724	+	0.274724i
$303$	61.4169	−	61.4169i	0.202696	−	0.202696i
$304$		−	96.4693i		−	0.317333i
$305$		0			0
$306$	−126.450			−0.413234
$307$	42.5120	+	42.5120i	0.138476	+	0.138476i	0.772947	−	0.634471i	$-0.218782\pi$
$307$	42.5120	+	42.5120i	0.138476	+	0.138476i	−0.634471	+	0.772947i	$0.718782\pi$
$308$	−43.0583	+	43.0583i	−0.139800	+	0.139800i
$309$			138.121i			0.446993i
$310$		0			0
$311$	−97.1353			−0.312332			−0.156166	−	0.987731i	$-0.549914\pi$
$311$	−97.1353			−0.312332			−0.156166	+	0.987731i	$0.549914\pi$
$312$	37.7477	+	37.7477i	0.120986	+	0.120986i
$313$	94.4913	−	94.4913i	0.301889	−	0.301889i	−0.539863	−	0.841753i	$-0.681524\pi$
$313$	94.4913	−	94.4913i	0.301889	−	0.301889i	0.841753	+	0.539863i	$0.181524\pi$
$314$			199.590i			0.635637i
$315$		0			0
$316$	−2.12242			−0.00671653
$317$	−146.150	−	146.150i	−0.461040	−	0.461040i	0.437956	−	0.898996i	$-0.355703\pi$
$317$	−146.150	−	146.150i	−0.461040	−	0.461040i	−0.898996	+	0.437956i	$0.855703\pi$
$318$	−17.3553	+	17.3553i	−0.0545764	+	0.0545764i
$319$		−	588.501i		−	1.84483i
$320$		0			0
$321$	331.576			1.03295
$322$	112.909	+	112.909i	0.350649	+	0.350649i
$323$	508.271	−	508.271i	1.57359	−	1.57359i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	90.7768			0.278457
$327$	−123.619	−	123.619i	−0.378039	−	0.378039i
$328$	−37.2177	+	37.2177i	−0.113469	+	0.113469i
$329$			187.573i			0.570131i
$330$		0			0
$331$	223.981			0.676679			0.338339	−	0.941024i	$-0.390135\pi$
$331$	223.981			0.676679			0.338339	+	0.941024i	$0.390135\pi$
$332$	−107.249	−	107.249i	−0.323038	−	0.323038i
$333$	25.5006	−	25.5006i	0.0765784	−	0.0765784i
$334$			198.500i			0.594312i
$335$		0			0
$336$	18.3303			0.0545545
$337$	41.7444	+	41.7444i	0.123871	+	0.123871i	0.766324	−	0.642454i	$-0.222084\pi$
$337$	41.7444	+	41.7444i	0.123871	+	0.123871i	−0.642454	+	0.766324i	$0.722084\pi$
$338$	−50.2595	+	50.2595i	−0.148697	+	0.148697i
$339$			62.0147i			0.182934i
$340$		0			0
$341$	540.697			1.58562
$342$	72.3520	+	72.3520i	0.211555	+	0.211555i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			104.553i			0.303933i
$345$		0			0
$346$	161.081			0.465551
$347$	−283.163	−	283.163i	−0.816031	−	0.816031i	0.169500	−	0.985530i	$-0.445785\pi$
$347$	−283.163	−	283.163i	−0.816031	−	0.816031i	−0.985530	+	0.169500i	$0.945785\pi$
$348$	−125.265	+	125.265i	−0.359957	+	0.359957i
$349$			73.8529i			0.211613i	0.994387	+	0.105807i	$0.0337424\pi$
$349$			73.8529i			0.211613i	−0.994387	+	0.105807i	$0.966258\pi$
$350$		0			0
$351$	−56.6215			−0.161315
$352$	46.0313	+	46.0313i	0.130771	+	0.130771i
$353$	221.700	−	221.700i	0.628047	−	0.628047i	−0.319530	−	0.947576i	$-0.603525\pi$
$353$	221.700	−	221.700i	0.628047	−	0.628047i	0.947576	+	0.319530i	$0.103525\pi$
$354$		−	231.106i		−	0.652842i
$355$		0			0
$356$	290.309			0.815473
$357$	96.5775	+	96.5775i	0.270525	+	0.270525i
$358$	−154.267	+	154.267i	−0.430912	+	0.430912i
$359$			351.735i			0.979764i	0.871789	+	0.489882i	$0.162960\pi$
$359$			351.735i			0.979764i	−0.871789	+	0.489882i	$0.837040\pi$
$360$		0			0
$361$	−220.645			−0.611205
$362$	166.548	+	166.548i	0.460078	+	0.460078i
$363$	13.9988	−	13.9988i	0.0385641	−	0.0385641i
$364$		−	57.6605i		−	0.158408i
$365$		0			0
$366$	19.8164			0.0541433
$367$	−9.03767	−	9.03767i	−0.0246258	−	0.0246258i	0.694687	−	0.719312i	$-0.255543\pi$
$367$	−9.03767	−	9.03767i	−0.0246258	−	0.0246258i	−0.719312	+	0.694687i	$0.755543\pi$
$368$	120.705	−	120.705i	0.328002	−	0.328002i
$369$		−	55.8266i		−	0.151292i
$370$		0			0
$371$	26.5107			0.0714573
$372$	−115.090	−	115.090i	−0.309381	−	0.309381i
$373$	151.095	−	151.095i	0.405079	−	0.405079i	−0.474939	−	0.880019i	$-0.657530\pi$
$373$	151.095	−	151.095i	0.405079	−	0.405079i	0.880019	+	0.474939i	$0.157530\pi$
$374$			485.053i			1.29693i
$375$		0			0
$376$	200.524			0.533309
$377$	394.039	+	394.039i	1.04520	+	1.04520i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$			268.787i			0.709201i	0.935018	+	0.354601i	$0.115383\pi$
$379$			268.787i			0.709201i	−0.935018	+	0.354601i	$0.884617\pi$
$380$		0			0
$381$	−285.969			−0.750574
$382$	−235.646	−	235.646i	−0.616873	−	0.616873i
$383$	−304.341	+	304.341i	−0.794625	+	0.794625i	−0.982242	−	0.187618i	$-0.939923\pi$
$383$	−304.341	+	304.341i	−0.794625	+	0.794625i	0.187618	+	0.982242i	$0.439923\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	32.4422			0.0840471
$387$	−78.4148	−	78.4148i	−0.202622	−	0.202622i
$388$	47.5744	−	47.5744i	0.122614	−	0.122614i
$389$		−	50.0127i		−	0.128567i	−0.997932	−	0.0642837i	$-0.979524\pi$
$389$		−	50.0127i		−	0.128567i	0.997932	−	0.0642837i	$-0.0204763\pi$
$390$		0			0
$391$	1271.92			3.25299
$392$	−14.0000	−	14.0000i	−0.0357143	−	0.0357143i
$393$	42.6216	−	42.6216i	0.108452	−	0.108452i
$394$			13.3627i			0.0339154i
$395$		0			0
$396$	−69.0469			−0.174361
$397$	325.002	+	325.002i	0.818644	+	0.818644i	0.985912	−	0.167268i	$-0.0534944\pi$
$397$	325.002	+	325.002i	0.818644	+	0.818644i	−0.167268	+	0.985912i	$0.553494\pi$
$398$	32.0712	−	32.0712i	0.0805808	−	0.0805808i
$399$		−	110.519i		−	0.276991i
$400$		0			0
$401$	−462.981			−1.15457			−0.577283	−	0.816544i	$-0.695887\pi$
$401$	−462.981			−1.15457			−0.577283	+	0.816544i	$0.695887\pi$
$402$	50.5744	+	50.5744i	0.125807	+	0.125807i
$403$	−362.031	+	362.031i	−0.898340	+	0.898340i
$404$			100.293i			0.248251i
$405$		0			0
$406$	191.346			0.471294
$407$	−97.8188	−	97.8188i	−0.240341	−	0.240341i
$408$	103.246	−	103.246i	0.253053	−	0.253053i
$409$			131.630i			0.321834i	0.986968	+	0.160917i	$0.0514451\pi$
$409$			131.630i			0.321834i	−0.986968	+	0.160917i	$0.948555\pi$
$410$		0			0
$411$	−322.236			−0.784028
$412$	−112.775	−	112.775i	−0.273726	−	0.273726i
$413$	−176.510	+	176.510i	−0.427386	+	0.427386i
$414$			181.057i			0.437336i
$415$		0			0
$416$	−61.6417			−0.148177
$417$	109.542	+	109.542i	0.262691	+	0.262691i
$418$	277.538	−	277.538i	0.663966	−	0.663966i
$419$			536.418i			1.28023i	0.768277	+	0.640117i	$0.221114\pi$
$419$			536.418i			1.28023i	−0.768277	+	0.640117i	$0.778886\pi$
$420$		0			0
$421$	−508.770			−1.20848			−0.604240	−	0.796803i	$-0.706523\pi$
$421$	−508.770			−1.20848			−0.604240	+	0.796803i	$0.706523\pi$
$422$	123.531	+	123.531i	0.292728	+	0.292728i
$423$	−150.393	+	150.393i	−0.355539	+	0.355539i
$424$		−	28.3411i		−	0.0668422i
$425$		0			0
$426$	−156.178			−0.366616
$427$	−15.1351	−	15.1351i	−0.0354451	−	0.0354451i
$428$	−270.731	+	270.731i	−0.632548	+	0.632548i
$429$			217.197i			0.506286i
$430$		0			0
$431$	467.561			1.08483			0.542414	−	0.840111i	$-0.317510\pi$
$431$	467.561			1.08483			0.542414	+	0.840111i	$0.317510\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	129.391	−	129.391i	0.298825	−	0.298825i	−0.541729	−	0.840554i	$-0.682230\pi$
$433$	129.391	−	129.391i	0.298825	−	0.298825i	0.840554	+	0.541729i	$0.182230\pi$
$434$			175.803i			0.405075i
$435$		0			0
$436$	201.868			0.463001
$437$	−727.768	−	727.768i	−1.66537	−	1.66537i
$438$	−122.936	+	122.936i	−0.280675	+	0.280675i
$439$		−	51.7818i		−	0.117954i	−0.998259	−	0.0589770i	$-0.981216\pi$
$439$		−	51.7818i		−	0.117954i	0.998259	−	0.0589770i	$-0.0187839\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−324.774	−	324.774i	−0.734782	−	0.734782i
$443$	−357.514	+	357.514i	−0.807029	+	0.807029i	−0.984183	−	0.177154i	$-0.943311\pi$
$443$	−357.514	+	357.514i	−0.807029	+	0.807029i	0.177154	+	0.984183i	$0.443311\pi$
$444$			41.6423i			0.0937890i
$445$		0			0
$446$	163.918			0.367529
$447$	−68.2671	−	68.2671i	−0.152723	−	0.152723i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	615.742i		−	1.37136i	−0.727902	−	0.685681i	$-0.759504\pi$
$449$		−	615.742i		−	1.37136i	0.727902	−	0.685681i	$-0.240496\pi$
$450$		0			0
$451$	−214.148			−0.474828
$452$	−50.6348	−	50.6348i	−0.112024	−	0.112024i
$453$	101.613	−	101.613i	0.224311	−	0.224311i
$454$		−	187.218i		−	0.412374i
$455$		0			0
$456$	−118.150			−0.259101
$457$	502.144	+	502.144i	1.09878	+	1.09878i	0.994553	+	0.104230i	$0.0332379\pi$
$457$	502.144	+	502.144i	1.09878	+	1.09878i	0.104230	+	0.994553i	$0.466762\pi$
$458$	348.973	−	348.973i	0.761950	−	0.761950i
$459$			154.868i			0.337404i
$460$		0			0
$461$	100.965			0.219012			0.109506	−	0.993986i	$-0.465073\pi$
$461$	100.965			0.219012			0.109506	+	0.993986i	$0.465073\pi$
$462$	52.7355	+	52.7355i	0.114146	+	0.114146i
$463$	−312.235	+	312.235i	−0.674374	+	0.674374i	−0.958721	−	0.284347i	$-0.908223\pi$
$463$	−312.235	+	312.235i	−0.674374	+	0.674374i	0.284347	+	0.958721i	$0.408223\pi$
$464$		−	204.557i		−	0.440856i
$465$		0			0
$466$	−416.639			−0.894074
$467$	−502.571	−	502.571i	−1.07617	−	1.07617i	−0.996849	−	0.0793198i	$-0.974725\pi$
$467$	−502.571	−	502.571i	−1.07617	−	1.07617i	−0.0793198	−	0.996849i	$-0.525275\pi$
$468$	46.2313	−	46.2313i	0.0987847	−	0.0987847i
$469$		−	77.2537i		−	0.164720i
$470$		0			0
$471$	244.447			0.518995
$472$	188.697	+	188.697i	0.399783	+	0.399783i
$473$	−300.794	+	300.794i	−0.635929	+	0.635929i
$474$			2.59943i			0.00548403i
$475$		0			0
$476$	−157.710			−0.331324
$477$	21.2558	+	21.2558i	0.0445614	+	0.0445614i
$478$	330.793	−	330.793i	0.692035	−	0.692035i
$479$			270.133i			0.563952i	0.959421	+	0.281976i	$0.0909899\pi$
$479$			270.133i			0.563952i	−0.959421	+	0.281976i	$0.909010\pi$
$480$		0			0
$481$	130.992			0.272332
$482$	375.584	+	375.584i	0.779221	+	0.779221i
$483$	138.285	−	138.285i	0.286303	−	0.286303i
$484$			22.8599i			0.0472312i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	227.632	+	227.632i	0.467417	+	0.467417i	0.901077	−	0.433660i	$-0.142778\pi$
$487$	227.632	+	227.632i	0.467417	+	0.467417i	−0.433660	+	0.901077i	$0.642778\pi$
$488$	−16.1801	+	16.1801i	−0.0331559	+	0.0331559i
$489$		−	111.178i		−	0.227359i
$490$		0			0
$491$	−23.2563			−0.0473652			−0.0236826	−	0.999720i	$-0.507539\pi$
$491$	−23.2563			−0.0473652			−0.0236826	+	0.999720i	$0.507539\pi$
$492$	45.5822	+	45.5822i	0.0926468	+	0.0926468i
$493$	1077.76	−	1077.76i	2.18612	−	2.18612i
$494$			371.658i			0.752344i
$495$		0			0
$496$	187.941			0.378913
$497$	119.283	+	119.283i	0.240006	+	0.240006i
$498$	−131.352	+	131.352i	−0.263759	+	0.263759i
$499$			319.077i			0.639433i	0.947513	+	0.319717i	$0.103588\pi$
$499$			319.077i			0.639433i	−0.947513	+	0.319717i	$0.896412\pi$
$500$		0			0
$501$	243.112			0.485254
$502$	41.2876	+	41.2876i	0.0822463	+	0.0822463i
$503$	−585.731	+	585.731i	−1.16448	+	1.16448i	−0.180990	+	0.983485i	$0.557930\pi$
$503$	−585.731	+	585.731i	−1.16448	+	1.16448i	−0.983485	+	0.180990i	$0.942070\pi$
$504$		−	22.4499i		−	0.0445435i
$505$		0			0
$506$	694.524			1.37258
$507$	61.5551	+	61.5551i	0.121410	+	0.121410i
$508$	233.492	−	233.492i	0.459631	−	0.459631i
$509$			266.157i			0.522902i	0.965217	+	0.261451i	$0.0842009\pi$
$509$			266.157i			0.522902i	−0.965217	+	0.261451i	$0.915799\pi$
$510$		0			0
$511$	187.787			0.367490
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	88.6127	−	88.6127i	0.172734	−	0.172734i
$514$			202.741i			0.394437i
$515$		0			0
$516$	128.051			0.248161
$517$	576.899	+	576.899i	1.11586	+	1.11586i
$518$	31.8048	−	31.8048i	0.0613993	−	0.0613993i
$519$		−	197.283i		−	0.380121i
$520$		0			0
$521$	−1.52542			−0.00292786			−0.00146393	−	0.999999i	$-0.500466\pi$
$521$	−1.52542			−0.00292786			−0.00146393	+	0.999999i	$0.500466\pi$
$522$	153.418	+	153.418i	0.293904	+	0.293904i
$523$	−260.120	+	260.120i	−0.497362	+	0.497362i	−0.910616	−	0.413254i	$-0.864392\pi$
$523$	−260.120	+	260.120i	−0.497362	+	0.497362i	0.413254	+	0.910616i	$0.364392\pi$
$524$			69.6007i			0.132826i
$525$		0			0
$526$	−329.188			−0.625833
$527$	990.210	+	990.210i	1.87896	+	1.87896i
$528$	56.3766	−	56.3766i	0.106774	−	0.106774i
$529$		−	1292.20i		−	2.44272i
$530$		0			0
$531$	−283.046			−0.533044
$532$	90.2387	+	90.2387i	0.169622	+	0.169622i
$533$	143.385	−	143.385i	0.269015	−	0.269015i
$534$		−	355.554i		−	0.665831i
$535$		0			0
$536$	−82.5877			−0.154081
$537$	188.937	+	188.937i	0.351838	+	0.351838i
$538$	−254.148	+	254.148i	−0.472394	+	0.472394i
$539$		−	80.5547i		−	0.149452i
$540$		0			0
$541$	−273.648			−0.505820			−0.252910	−	0.967490i	$-0.581388\pi$
$541$	−273.648			−0.505820			−0.252910	+	0.967490i	$0.581388\pi$
$542$	22.4723	+	22.4723i	0.0414619	+	0.0414619i
$543$	203.979	−	203.979i	0.375652	−	0.375652i
$544$			168.599i			0.309925i
$545$		0			0
$546$	−70.6194			−0.129340
$547$	−355.490	−	355.490i	−0.649890	−	0.649890i	0.303077	−	0.952966i	$-0.401986\pi$
$547$	−355.490	−	355.490i	−0.649890	−	0.649890i	−0.952966	+	0.303077i	$0.901986\pi$
$548$	263.104	−	263.104i	0.480117	−	0.480117i
$549$		−	24.2701i		−	0.0442078i
$550$		0			0
$551$	−1233.34			−2.23837
$552$	−147.832	−	147.832i	−0.267812	−	0.267812i
$553$	1.98535	−	1.98535i	0.00359014	−	0.00359014i
$554$		−	94.7898i		−	0.171101i
$555$		0			0
$556$	−178.881			−0.321729
$557$	270.897	+	270.897i	0.486350	+	0.486350i	0.907152	−	0.420802i	$-0.138251\pi$
$557$	270.897	+	270.897i	0.486350	+	0.486350i	−0.420802	+	0.907152i	$0.638251\pi$
$558$	−140.956	+	140.956i	−0.252609	+	0.252609i
$559$		−	402.802i		−	0.720575i
$560$		0			0
$561$	594.066			1.05894
$562$	−18.8810	−	18.8810i	−0.0335960	−	0.0335960i
$563$	−73.1143	+	73.1143i	−0.129866	+	0.129866i	−0.769052	−	0.639186i	$-0.779271\pi$
$563$	−73.1143	+	73.1143i	−0.129866	+	0.129866i	0.639186	+	0.769052i	$0.279271\pi$
$564$		−	245.591i		−	0.435445i
$565$		0			0
$566$	231.651			0.409277
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	127.519	−	127.519i	0.224505	−	0.224505i
$569$		−	1018.55i		−	1.79007i	−0.445992	−	0.895037i	$-0.647149\pi$
$569$		−	1018.55i		−	1.79007i	0.445992	−	0.895037i	$-0.352851\pi$
$570$		0			0
$571$	−621.517			−1.08847			−0.544236	−	0.838932i	$-0.683180\pi$
$571$	−621.517			−1.08847			−0.544236	+	0.838932i	$0.683180\pi$
$572$	−177.340	−	177.340i	−0.310036	−	0.310036i
$573$	−288.606	+	288.606i	−0.503675	+	0.503675i
$574$		−	69.6280i		−	0.121303i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−760.301	−	760.301i	−1.31768	−	1.31768i	−0.915608	−	0.402071i	$-0.868290\pi$
$577$	−760.301	−	760.301i	−1.31768	−	1.31768i	−0.402071	−	0.915608i	$-0.631710\pi$
$578$	−599.306	+	599.306i	−1.03686	+	1.03686i
$579$		−	39.7334i		−	0.0686242i
$580$		0			0
$581$	200.644			0.345342
$582$	−58.2665	−	58.2665i	−0.100114	−	0.100114i
$583$	81.5360	−	81.5360i	0.139856	−	0.139856i
$584$		−	200.753i		−	0.343756i
$585$		0			0
$586$	−448.901			−0.766043
$587$	−5.94607	−	5.94607i	−0.0101296	−	0.0101296i	0.702024	−	0.712153i	$-0.252280\pi$
$587$	−5.94607	−	5.94607i	−0.0101296	−	0.0101296i	−0.712153	+	0.702024i	$0.752280\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$		−	1133.16i		−	1.92387i
$590$		0			0
$591$	16.3659			0.0276918
$592$	−34.0008	−	34.0008i	−0.0574338	−	0.0574338i
$593$	463.916	−	463.916i	0.782320	−	0.782320i	−0.197902	−	0.980222i	$-0.563413\pi$
$593$	463.916	−	463.916i	0.782320	−	0.782320i	0.980222	+	0.197902i	$0.0634127\pi$
$594$			84.5649i			0.142365i
$595$		0			0
$596$	111.480			0.187047
$597$	−39.2790	−	39.2790i	−0.0657940	−	0.0657940i
$598$	−465.027	+	465.027i	−0.777638	+	0.777638i
$599$			660.745i			1.10308i	0.834148	+	0.551540i	$0.185960\pi$
$599$			660.745i			1.10308i	−0.834148	+	0.551540i	$0.814040\pi$
$600$		0			0
$601$	−905.439			−1.50655			−0.753277	−	0.657704i	$-0.771528\pi$
$601$	−905.439			−1.50655			−0.753277	+	0.657704i	$0.771528\pi$
$602$	−97.8004	−	97.8004i	−0.162459	−	0.162459i
$603$	61.9407	−	61.9407i	0.102721	−	0.102721i
$604$			165.933i			0.274724i
$605$		0			0
$606$	122.834			0.202696
$607$	−518.514	−	518.514i	−0.854224	−	0.854224i	0.136426	−	0.990650i	$-0.456438\pi$
$607$	−518.514	−	518.514i	−0.854224	−	0.854224i	−0.990650	+	0.136426i	$0.956438\pi$
$608$	96.4693	−	96.4693i	0.158667	−	0.158667i
$609$		−	234.349i		−	0.384810i
$610$		0			0
$611$	−772.541			−1.26439
$612$	−126.450	−	126.450i	−0.206617	−	0.206617i
$613$	500.739	−	500.739i	0.816867	−	0.816867i	−0.168786	−	0.985653i	$-0.553985\pi$
$613$	500.739	−	500.739i	0.816867	−	0.816867i	0.985653	+	0.168786i	$0.0539847\pi$
$614$			85.0240i			0.138476i
$615$		0			0
$616$	−86.1166			−0.139800
$617$	−122.242	−	122.242i	−0.198123	−	0.198123i	0.601072	−	0.799195i	$-0.294740\pi$
$617$	−122.242	−	122.242i	−0.198123	−	0.198123i	−0.799195	+	0.601072i	$0.794740\pi$
$618$	−138.121	+	138.121i	−0.223497	+	0.223497i
$619$		−	320.914i		−	0.518440i	−0.965818	−	0.259220i	$-0.916534\pi$
$619$		−	320.914i		−	0.518440i	0.965818	−	0.259220i	$-0.0834655\pi$
$620$		0			0
$621$	221.749			0.357083
$622$	−97.1353	−	97.1353i	−0.156166	−	0.156166i
$623$	−271.559	+	271.559i	−0.435889	+	0.435889i
$624$			75.4953i			0.120986i
$625$		0			0
$626$	188.983			0.301889
$627$	−339.913	−	339.913i	−0.542126	−	0.542126i
$628$	−199.590	+	199.590i	−0.317818	+	0.317818i
$629$		−	358.282i		−	0.569606i
$630$		0			0
$631$	−636.141			−1.00815			−0.504074	−	0.863661i	$-0.668166\pi$
$631$	−636.141			−1.00815			−0.504074	+	0.863661i	$0.668166\pi$
$632$	−2.12242	−	2.12242i	−0.00335827	−	0.00335827i
$633$	151.294	−	151.294i	0.239012	−	0.239012i
$634$		−	292.300i		−	0.461040i
$635$		0			0
$636$	−34.7106			−0.0545764
$637$	53.9365	+	53.9365i	0.0846726	+	0.0846726i
$638$	588.501	−	588.501i	0.922416	−	0.922416i
$639$			191.278i			0.299340i
$640$		0			0
$641$	−682.051			−1.06404			−0.532021	−	0.846731i	$-0.678567\pi$
$641$	−682.051			−1.06404			−0.532021	+	0.846731i	$0.678567\pi$
$642$	331.576	+	331.576i	0.516474	+	0.516474i
$643$	5.33298	−	5.33298i	0.00829390	−	0.00829390i	−0.702948	−	0.711242i	$-0.748133\pi$
$643$	5.33298	−	5.33298i	0.00829390	−	0.00829390i	0.711242	+	0.702948i	$0.248133\pi$
$644$			225.818i			0.350649i
$645$		0			0
$646$	1016.54			1.57359
$647$	−285.931	−	285.931i	−0.441933	−	0.441933i	0.450728	−	0.892661i	$-0.351164\pi$
$647$	−285.931	−	285.931i	−0.441933	−	0.441933i	−0.892661	+	0.450728i	$0.851164\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			1085.75i			1.67296i
$650$		0			0
$651$	215.313			0.330742
$652$	90.7768	+	90.7768i	0.139228	+	0.139228i
$653$	−199.462	+	199.462i	−0.305455	+	0.305455i	−0.843144	−	0.537689i	$-0.819298\pi$
$653$	−199.462	+	199.462i	−0.305455	+	0.305455i	0.537689	+	0.843144i	$0.319298\pi$
$654$		−	247.237i		−	0.378039i
$655$		0			0
$656$	−74.4355			−0.113469
$657$	150.565	+	150.565i	0.229170	+	0.229170i
$658$	−187.573	+	187.573i	−0.285066	+	0.285066i
$659$		−	204.685i		−	0.310599i	−0.987867	−	0.155300i	$-0.950366\pi$
$659$		−	204.685i		−	0.310599i	0.987867	−	0.155300i	$-0.0496343\pi$
$660$		0			0
$661$	143.044			0.216406			0.108203	−	0.994129i	$-0.465490\pi$
$661$	143.044			0.216406			0.108203	+	0.994129i	$0.465490\pi$
$662$	223.981	+	223.981i	0.338339	+	0.338339i
$663$	−397.765	+	397.765i	−0.599947	+	0.599947i
$664$		−	214.497i		−	0.323038i
$665$		0			0
$666$	51.0012			0.0765784
$667$	−1543.19	−	1543.19i	−2.31362	−	2.31362i
$668$	−198.500	+	198.500i	−0.297156	+	0.297156i
$669$		−	200.758i		−	0.300086i
$670$		0			0
$671$	−93.0986			−0.138746
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	317.527	−	317.527i	0.471808	−	0.471808i	−0.430691	−	0.902499i	$-0.641730\pi$
$673$	317.527	−	317.527i	0.471808	−	0.471808i	0.902499	+	0.430691i	$0.141730\pi$
$674$			83.4888i			0.123871i
$675$		0			0
$676$	−100.519			−0.148697
$677$	272.663	+	272.663i	0.402752	+	0.402752i	0.879202	−	0.476450i	$-0.158077\pi$
$677$	272.663	+	272.663i	0.402752	+	0.402752i	−0.476450	+	0.879202i	$0.658077\pi$
$678$	−62.0147	+	62.0147i	−0.0914671	+	0.0914671i
$679$			89.0035i			0.131080i
$680$		0			0
$681$	−229.294			−0.336702
$682$	540.697	+	540.697i	0.792812	+	0.792812i
$683$	449.231	−	449.231i	0.657732	−	0.657732i	−0.297111	−	0.954843i	$-0.596023\pi$
$683$	449.231	−	449.231i	0.657732	−	0.657732i	0.954843	+	0.297111i	$0.0960232\pi$
$684$			144.704i			0.211555i
$685$		0			0
$686$	26.1916			0.0381802
$687$	−427.403	−	427.403i	−0.622130	−	0.622130i
$688$	−104.553	+	104.553i	−0.151967	+	0.151967i
$689$			109.187i			0.158472i
$690$		0			0
$691$	1004.13			1.45316			0.726578	−	0.687084i	$-0.241109\pi$
$691$	1004.13			1.45316			0.726578	+	0.687084i	$0.241109\pi$
$692$	161.081	+	161.081i	0.232776	+	0.232776i
$693$	64.5875	−	64.5875i	0.0931998	−	0.0931998i
$694$		−	566.325i		−	0.816031i
$695$		0			0
$696$	−250.530			−0.359957
$697$	−392.181	−	392.181i	−0.562669	−	0.562669i
$698$	−73.8529	+	73.8529i	−0.105807	+	0.105807i
$699$			510.276i			0.730009i
$700$		0			0
$701$	−869.248			−1.24001			−0.620006	−	0.784597i	$-0.712870\pi$
$701$	−869.248			−1.24001			−0.620006	+	0.784597i	$0.712870\pi$
$702$	−56.6215	−	56.6215i	−0.0806574	−	0.0806574i
$703$	−205.002	+	205.002i	−0.291610	+	0.291610i
$704$			92.0626i			0.130771i
$705$		0			0
$706$	443.401			0.628047
$707$	−93.8159	−	93.8159i	−0.132696	−	0.132696i
$708$	231.106	−	231.106i	0.326421	−	0.326421i
$709$		−	79.6980i		−	0.112409i	−0.998419	−	0.0562045i	$-0.982100\pi$
$709$		−	79.6980i		−	0.112409i	0.998419	−	0.0562045i	$-0.0178999\pi$
$710$		0			0
$711$	3.18364			0.00447769
$712$	290.309	+	290.309i	0.407737	+	0.407737i
$713$	1417.83	−	1417.83i	1.98855	−	1.98855i
$714$			193.155i			0.270525i
$715$		0			0
$716$	−308.533			−0.430912
$717$	−405.136	−	405.136i	−0.565044	−	0.565044i
$718$	−351.735	+	351.735i	−0.489882	+	0.489882i
$719$		−	1081.03i		−	1.50351i	−0.659440	−	0.751757i	$-0.729207\pi$
$719$		−	1081.03i		−	1.50351i	0.659440	−	0.751757i	$-0.270793\pi$
$720$		0			0
$721$	210.983			0.292626
$722$	−220.645	−	220.645i	−0.305603	−	0.305603i
$723$	459.995	−	459.995i	0.636231	−	0.636231i
$724$			333.096i			0.460078i
$725$		0			0
$726$	27.9975			0.0385641
$727$	−281.701	−	281.701i	−0.387484	−	0.387484i	0.486305	−	0.873789i	$-0.338344\pi$
$727$	−281.701	−	281.701i	−0.387484	−	0.387484i	−0.873789	+	0.486305i	$0.838344\pi$
$728$	57.6605	−	57.6605i	0.0792040	−	0.0792040i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−1101.72			−1.50715
$732$	19.8164	+	19.8164i	0.0270716	+	0.0270716i
$733$	−1016.28	+	1016.28i	−1.38647	+	1.38647i	−0.553858	+	0.832611i	$0.686845\pi$
$733$	−1016.28	+	1016.28i	−1.38647	+	1.38647i	−0.832611	+	0.553858i	$0.813155\pi$
$734$		−	18.0753i		−	0.0246258i
$735$		0			0
$736$	241.409			0.328002
$737$	−237.601	−	237.601i	−0.322389	−	0.322389i
$738$	55.8266	−	55.8266i	0.0756458	−	0.0756458i
$739$		−	289.140i		−	0.391258i	−0.980678	−	0.195629i	$-0.937325\pi$
$739$		−	289.140i		−	0.391258i	0.980678	−	0.195629i	$-0.0626749\pi$
$740$		0			0
$741$	455.186			0.614286
$742$	26.5107	+	26.5107i	0.0357286	+	0.0357286i
$743$	−290.501	+	290.501i	−0.390984	+	0.390984i	−0.875038	−	0.484054i	$-0.839164\pi$
$743$	−290.501	+	290.501i	−0.390984	+	0.390984i	0.484054	+	0.875038i	$0.339164\pi$
$744$		−	230.180i		−	0.309381i
$745$		0			0
$746$	302.189			0.405079
$747$	160.873	+	160.873i	0.215358	+	0.215358i
$748$	−485.053	+	485.053i	−0.648467	+	0.648467i
$749$		−	506.491i		−	0.676223i
$750$		0			0
$751$	688.089			0.916231			0.458115	−	0.888893i	$-0.348525\pi$
$751$	688.089			0.916231			0.458115	+	0.888893i	$0.348525\pi$
$752$	200.524	+	200.524i	0.266655	+	0.266655i
$753$	50.5668	−	50.5668i	0.0671538	−	0.0671538i
$754$			788.077i			1.04520i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	−180.960	−	180.960i	−0.239049	−	0.239049i	0.577408	−	0.816456i	$-0.304064\pi$
$757$	−180.960	−	180.960i	−0.239049	−	0.239049i	−0.816456	+	0.577408i	$0.804064\pi$
$758$	−268.787	+	268.787i	−0.354601	+	0.354601i
$759$		−	850.614i		−	1.12070i
$760$		0			0
$761$	1096.09			1.44033			0.720163	−	0.693805i	$-0.244067\pi$
$761$	1096.09			1.44033			0.720163	+	0.693805i	$0.244067\pi$
$762$	−285.969	−	285.969i	−0.375287	−	0.375287i
$763$	−188.831	+	188.831i	−0.247484	+	0.247484i
$764$		−	471.291i		−	0.616873i
$765$		0			0
$766$	−608.682			−0.794625
$767$	−726.977	−	726.977i	−0.947818	−	0.947818i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			892.540i			1.16065i	0.814385	+	0.580325i	$0.197075\pi$
$769$			892.540i			1.16065i	−0.814385	+	0.580325i	$0.802925\pi$
$770$		0			0
$771$	248.306			0.322057
$772$	32.4422	+	32.4422i	0.0420235	+	0.0420235i
$773$	−836.773	+	836.773i	−1.08250	+	1.08250i	−0.0862244	+	0.996276i	$0.527480\pi$
$773$	−836.773	+	836.773i	−1.08250	+	1.08250i	−0.996276	+	0.0862244i	$0.972520\pi$
$774$		−	156.830i		−	0.202622i
$775$		0			0
$776$	95.1487			0.122614
$777$	−38.9528	−	38.9528i	−0.0501323	−	0.0501323i
$778$	50.0127	−	50.0127i	0.0642837	−	0.0642837i
$779$			448.796i			0.576118i
$780$		0			0
$781$	733.733			0.939479
$782$	1271.92	+	1271.92i	1.62650	+	1.62650i
$783$	187.898	−	187.898i	0.239971	−	0.239971i
$784$		−	28.0000i		−	0.0357143i
$785$		0			0
$786$	85.2431			0.108452
$787$	226.485	+	226.485i	0.287782	+	0.287782i	0.836203	−	0.548420i	$-0.184771\pi$
$787$	226.485	+	226.485i	0.287782	+	0.287782i	−0.548420	+	0.836203i	$0.684771\pi$
$788$	−13.3627	+	13.3627i	−0.0169577	+	0.0169577i
$789$			403.171i			0.510990i
$790$		0			0
$791$	94.7290			0.119759
$792$	−69.0469	−	69.0469i	−0.0871805	−	0.0871805i
$793$	62.3354	−	62.3354i	0.0786070	−	0.0786070i
$794$			650.003i			0.818644i
$795$		0			0
$796$	64.1423			0.0805808
$797$	728.914	+	728.914i	0.914572	+	0.914572i	0.996628	−	0.0820555i	$-0.0261485\pi$
$797$	728.914	+	728.914i	0.914572	+	0.914572i	−0.0820555	+	0.996628i	$0.526148\pi$
$798$	110.519	−	110.519i	0.138496	−	0.138496i
$799$			2113.02i			2.64458i
$800$		0			0
$801$	−435.463			−0.543649
$802$	−462.981	−	462.981i	−0.577283	−	0.577283i
$803$	577.558	−	577.558i	0.719250	−	0.719250i
$804$			101.149i			0.125807i
$805$		0			0
$806$	−724.062			−0.898340
$807$	311.267	+	311.267i	0.385708	+	0.385708i
$808$	−100.293	+	100.293i	−0.124126	+	0.124126i
$809$		−	1196.38i		−	1.47884i	−0.673247	−	0.739418i	$-0.735101\pi$
$809$		−	1196.38i		−	1.47884i	0.673247	−	0.739418i	$-0.264899\pi$
$810$		0			0
$811$	−1180.03			−1.45503			−0.727513	−	0.686094i	$-0.759324\pi$
$811$	−1180.03			−1.45503			−0.727513	+	0.686094i	$0.759324\pi$
$812$	191.346	+	191.346i	0.235647	+	0.235647i
$813$	27.5229	−	27.5229i	0.0338535	−	0.0338535i
$814$		−	195.638i		−	0.240341i
$815$		0			0
$816$	206.491			0.253053
$817$	630.385	+	630.385i	0.771585	+	0.771585i
$818$	−131.630	+	131.630i	−0.160917	+	0.160917i
$819$			86.4908i			0.105605i
$820$		0			0
$821$	35.8305			0.0436425			0.0218212	−	0.999762i	$-0.493054\pi$
$821$	35.8305			0.0436425			0.0218212	+	0.999762i	$0.493054\pi$
$822$	−322.236	−	322.236i	−0.392014	−	0.392014i
$823$	−448.829	+	448.829i	−0.545357	+	0.545357i	−0.925094	−	0.379737i	$-0.876014\pi$
$823$	−448.829	+	448.829i	−0.545357	+	0.545357i	0.379737	+	0.925094i	$0.376014\pi$
$824$		−	225.550i		−	0.273726i
$825$		0			0
$826$	−353.021			−0.427386
$827$	−874.926	−	874.926i	−1.05795	−	1.05795i	−0.998214	−	0.0597373i	$-0.980974\pi$
$827$	−874.926	−	874.926i	−1.05795	−	1.05795i	−0.0597373	−	0.998214i	$-0.519026\pi$
$828$	−181.057	+	181.057i	−0.218668	+	0.218668i
$829$			934.022i			1.12669i	0.826223	+	0.563343i	$0.190485\pi$
$829$			934.022i			1.12669i	−0.826223	+	0.563343i	$0.809515\pi$
$830$		0			0
$831$	−116.093			−0.139703
$832$	−61.6417	−	61.6417i	−0.0740886	−	0.0740886i
$833$	147.525	−	147.525i	0.177100	−	0.177100i
$834$			219.084i			0.262691i
$835$		0			0
$836$	555.076			0.663966
$837$	172.635	+	172.635i	0.206254	+	0.206254i
$838$	−536.418	+	536.418i	−0.640117	+	0.640117i
$839$		−	10.5147i		−	0.0125324i	−0.999980	−	0.00626621i	$-0.998005\pi$
$839$		−	10.5147i		−	0.0125324i	0.999980	−	0.00626621i	$-0.00199461\pi$
$840$		0			0
$841$	−1774.22			−2.10966
$842$	−508.770	−	508.770i	−0.604240	−	0.604240i
$843$	−23.1244	+	23.1244i	−0.0274310	+	0.0274310i
$844$			247.063i			0.292728i
$845$		0			0
$846$	−300.786			−0.355539
$847$	−21.3835	−	21.3835i	−0.0252461	−	0.0252461i
$848$	28.3411	−	28.3411i	0.0334211	−	0.0334211i
$849$		−	283.713i		−	0.334173i
$850$		0			0
$851$	−513.007			−0.602828
$852$	−156.178	−	156.178i	−0.183308	−	0.183308i
$853$	−1082.57	+	1082.57i	−1.26914	+	1.26914i	−0.322603	+	0.946534i	$0.604558\pi$
$853$	−1082.57	+	1082.57i	−1.26914	+	1.26914i	−0.946534	+	0.322603i	$0.895442\pi$
$854$		−	30.2701i		−	0.0354451i
$855$		0			0
$856$	−541.461			−0.632548
$857$	−506.843	−	506.843i	−0.591416	−	0.591416i	0.346598	−	0.938014i	$-0.387337\pi$
$857$	−506.843	−	506.843i	−0.591416	−	0.591416i	−0.938014	+	0.346598i	$0.887337\pi$
$858$	−217.197	+	217.197i	−0.253143	+	0.253143i
$859$		−	471.172i		−	0.548512i	−0.961657	−	0.274256i	$-0.911568\pi$
$859$		−	471.172i		−	0.548512i	0.961657	−	0.274256i	$-0.0884315\pi$
$860$		0			0
$861$	−85.2765			−0.0990436
$862$	467.561	+	467.561i	0.542414	+	0.542414i
$863$	−352.570	+	352.570i	−0.408540	+	0.408540i	−0.881229	−	0.472689i	$-0.843283\pi$
$863$	−352.570	+	352.570i	−0.408540	+	0.408540i	0.472689	+	0.881229i	$0.343283\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	258.782			0.298825
$867$	733.996	+	733.996i	0.846593	+	0.846593i
$868$	−175.803	+	175.803i	−0.202538	+	0.202538i
$869$		−	12.2122i		−	0.0140532i
$870$		0			0
$871$	318.178			0.365301
$872$	201.868	+	201.868i	0.231500	+	0.231500i
$873$	−71.3616	+	71.3616i	−0.0817429	+	0.0817429i
$874$		−	1455.54i		−	1.66537i
$875$		0			0
$876$	−245.872			−0.280675
$877$	1223.94	+	1223.94i	1.39560	+	1.39560i	0.812137	+	0.583467i	$0.198304\pi$
$877$	1223.94	+	1223.94i	1.39560	+	1.39560i	0.583467	+	0.812137i	$0.301696\pi$
$878$	51.7818	−	51.7818i	0.0589770	−	0.0589770i
$879$			549.790i			0.625472i
$880$		0			0
$881$	−635.103			−0.720889			−0.360444	−	0.932781i	$-0.617375\pi$
$881$	−635.103			−0.720889			−0.360444	+	0.932781i	$0.617375\pi$
$882$	21.0000	+	21.0000i	0.0238095	+	0.0238095i
$883$	230.546	−	230.546i	0.261094	−	0.261094i	−0.564405	−	0.825498i	$-0.690894\pi$
$883$	230.546	−	230.546i	0.261094	−	0.261094i	0.825498	+	0.564405i	$0.190894\pi$
$884$		−	649.547i		−	0.734782i
$885$		0			0
$886$	−715.028			−0.807029
$887$	1224.61	+	1224.61i	1.38062	+	1.38062i	0.843518	+	0.537101i	$0.180480\pi$
$887$	1224.61	+	1224.61i	1.38062	+	1.38062i	0.537101	+	0.843518i	$0.319520\pi$
$888$	−41.6423	+	41.6423i	−0.0468945	+	0.0468945i
$889$			436.824i			0.491366i
$890$		0			0
$891$	103.570			0.116241
$892$	163.918	+	163.918i	0.183765	+	0.183765i
$893$	1209.03	−	1209.03i	1.35389	−	1.35389i
$894$		−	136.534i		−	0.152723i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	569.540	+	569.540i	0.634938	+	0.634938i
$898$	615.742	−	615.742i	0.685681	−	0.685681i
$899$		−	2402.79i		−	2.67273i
$900$		0			0
$901$	298.643			0.331457
$902$	−214.148	−	214.148i	−0.237414	−	0.237414i
$903$	−119.781	+	119.781i	−0.132647	+	0.132647i
$904$		−	101.270i		−	0.112024i
$905$		0			0
$906$	203.226			0.224311
$907$	−766.713	−	766.713i	−0.845329	−	0.845329i	0.144217	−	0.989546i	$-0.453934\pi$
$907$	−766.713	−	766.713i	−0.845329	−	0.845329i	−0.989546	+	0.144217i	$0.953934\pi$
$908$	187.218	−	187.218i	0.206187	−	0.206187i
$909$		−	150.440i		−	0.165501i
$910$		0			0
$911$	−754.441			−0.828146			−0.414073	−	0.910244i	$-0.635894\pi$
$911$	−754.441			−0.828146			−0.414073	+	0.910244i	$0.635894\pi$
$912$	−118.150	−	118.150i	−0.129551	−	0.129551i
$913$	617.098	−	617.098i	0.675902	−	0.675902i
$914$			1004.29i			1.09878i
$915$		0			0
$916$	697.947			0.761950
$917$	−65.1055	−	65.1055i	−0.0709984	−	0.0709984i
$918$	−154.868	+	154.868i	−0.168702	+	0.168702i
$919$		−	858.117i		−	0.933750i	−0.884323	−	0.466875i	$-0.845380\pi$
$919$		−	858.117i		−	0.933750i	0.884323	−	0.466875i	$-0.154620\pi$
$920$		0			0
$921$	104.133			0.113065
$922$	100.965	+	100.965i	0.109506	+	0.109506i
$923$	−491.280	+	491.280i	−0.532265	+	0.532265i
$924$			105.471i			0.114146i
$925$		0			0
$926$	−624.471			−0.674374
$927$	169.163	+	169.163i	0.182484	+	0.182484i
$928$	204.557	−	204.557i	0.220428	−	0.220428i
$929$		−	631.542i		−	0.679809i	−0.940460	−	0.339904i	$-0.889605\pi$
$929$		−	631.542i		−	0.679809i	0.940460	−	0.339904i	$-0.110395\pi$
$930$		0			0
$931$	−168.821			−0.181333
$932$	−416.639	−	416.639i	−0.447037	−	0.447037i
$933$	−118.966	+	118.966i	−0.127509	+	0.127509i
$934$		−	1005.14i		−	1.07617i
$935$		0			0
$936$	92.4625			0.0987847
$937$	−1167.50	−	1167.50i	−1.24599	−	1.24599i	−0.957474	−	0.288519i	$-0.906837\pi$
$937$	−1167.50	−	1167.50i	−1.24599	−	1.24599i	−0.288519	−	0.957474i	$-0.593163\pi$
$938$	77.2537	−	77.2537i	0.0823600	−	0.0823600i
$939$		−	231.455i		−	0.246491i
$940$		0			0
$941$	−614.550			−0.653082			−0.326541	−	0.945183i	$-0.605883\pi$
$941$	−614.550			−0.653082			−0.326541	+	0.945183i	$0.605883\pi$
$942$	244.447	+	244.447i	0.259498	+	0.259498i
$943$	−561.544	+	561.544i	−0.595487	+	0.595487i
$944$			377.395i			0.399783i
$945$		0			0
$946$	−601.589			−0.635929
$947$	635.282	+	635.282i	0.670837	+	0.670837i	0.957909	−	0.287072i	$-0.0926820\pi$
$947$	635.282	+	635.282i	0.670837	+	0.670837i	−0.287072	+	0.957909i	$0.592682\pi$
$948$	−2.59943	+	2.59943i	−0.00274201	+	0.00274201i
$949$			773.423i			0.814987i
$950$		0			0
$951$	−357.992			−0.376438
$952$	−157.710	−	157.710i	−0.165662	−	0.165662i
$953$	−350.517	+	350.517i	−0.367803	+	0.367803i	−0.866676	−	0.498872i	$-0.833748\pi$
$953$	−350.517	+	350.517i	−0.367803	+	0.367803i	0.498872	+	0.866676i	$0.333748\pi$
$954$			42.5116i			0.0445614i
$955$		0			0
$956$	661.585			0.692035
$957$	−720.764	−	720.764i	−0.753149	−	0.753149i
$958$	−270.133	+	270.133i	−0.281976	+	0.281976i
$959$			492.223i			0.513267i
$960$		0			0
$961$	1246.61			1.29720
$962$	130.992	+	130.992i	0.136166	+	0.136166i
$963$	406.096	−	406.096i	0.421699	−	0.421699i
$964$			751.169i			0.779221i
$965$		0			0
$966$	276.569			0.286303
$967$	−435.204	−	435.204i	−0.450056	−	0.450056i	0.445317	−	0.895373i	$-0.353091\pi$
$967$	−435.204	−	435.204i	−0.450056	−	0.450056i	−0.895373	+	0.445317i	$0.853091\pi$
$968$	−22.8599	+	22.8599i	−0.0236156	+	0.0236156i
$969$		−	1245.00i		−	1.28483i
$970$		0			0
$971$	218.866			0.225403			0.112701	−	0.993629i	$-0.464050\pi$
$971$	218.866			0.225403			0.112701	+	0.993629i	$0.464050\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	167.328	−	167.328i	0.171971	−	0.171971i
$974$			455.264i			0.467417i
$975$		0			0
$976$	−32.3601			−0.0331559
$977$	−1000.73	−	1000.73i	−1.02429	−	1.02429i	−0.999698	−	0.0245886i	$-0.992172\pi$
$977$	−1000.73	−	1000.73i	−1.02429	−	1.02429i	−0.0245886	−	0.999698i	$-0.507828\pi$
$978$	111.178	−	111.178i	0.113679	−	0.113679i
$979$			1670.41i			1.70624i
$980$		0			0
$981$	−302.802			−0.308667
$982$	−23.2563	−	23.2563i	−0.0236826	−	0.0236826i
$983$	−915.596	+	915.596i	−0.931431	+	0.931431i	−0.997795	−	0.0663648i	$-0.978860\pi$
$983$	−915.596	+	915.596i	−0.931431	+	0.931431i	0.0663648	+	0.997795i	$0.478860\pi$
$984$			91.1645i			0.0926468i
$985$		0			0
$986$	2155.51			2.18612
$987$	229.729	+	229.729i	0.232755	+	0.232755i
$988$	−371.658	+	371.658i	−0.376172	+	0.376172i
$989$			1577.50i			1.59505i
$990$		0			0
$991$	−437.633			−0.441608			−0.220804	−	0.975318i	$-0.570868\pi$
$991$	−437.633			−0.441608			−0.220804	+	0.975318i	$0.570868\pi$
$992$	187.941	+	187.941i	0.189457	+	0.189457i
$993$	274.319	−	274.319i	0.276253	−	0.276253i
$994$			238.566i			0.240006i
$995$		0			0
$996$	−262.704			−0.263759
$997$	−180.748	−	180.748i	−0.181292	−	0.181292i	0.610627	−	0.791919i	$-0.290918\pi$
$997$	−180.748	−	180.748i	−0.181292	−	0.181292i	−0.791919	+	0.610627i	$0.790918\pi$
$998$	−319.077	+	319.077i	−0.319717	+	0.319717i
$999$		−	62.4634i		−	0.0625260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.h.757.5		16
5.2	odd	4		210.3.l.b.43.4	✓	16
5.3	odd	4	inner	1050.3.l.h.43.5		16
5.4	even	2		210.3.l.b.127.4	yes	16
15.2	even	4		630.3.o.f.253.1		16
15.14	odd	2		630.3.o.f.127.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.4	✓	16	5.2	odd	4
210.3.l.b.127.4	yes	16	5.4	even	2
630.3.o.f.127.1		16	15.14	odd	2
630.3.o.f.253.1		16	15.2	even	4
1050.3.l.h.43.5		16	5.3	odd	4	inner
1050.3.l.h.757.5		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -11.5078 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.70521 - 7.70521i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(-21.0749 - 21.0749i) q^{17} +(3.00000 - 3.00000i) q^{18} +24.1173i q^{19} -4.58258 q^{21} +(-11.5078 - 11.5078i) q^{22} +(-30.1762 + 30.1762i) q^{23} +4.89898i q^{24} +15.4104 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +51.1392i q^{29} -46.9852 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-14.0941 + 14.0941i) q^{33} -42.1499i q^{34} +6.00000 q^{36} +(8.50020 + 8.50020i) q^{37} +(-24.1173 + 24.1173i) q^{38} -18.8738i q^{39} +18.6089 q^{41} +(-4.58258 - 4.58258i) q^{42} +(26.1383 - 26.1383i) q^{43} -23.0156i q^{44} -60.3523 q^{46} +(-50.1311 - 50.1311i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} -51.6228 q^{51} +(15.4104 + 15.4104i) q^{52} +(-7.08527 + 7.08527i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(29.5376 + 29.5376i) q^{57} +(-51.1392 + 51.1392i) q^{58} -94.3487i q^{59} +8.09003 q^{61} +(-46.9852 - 46.9852i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} -28.1883 q^{66} +(20.6469 + 20.6469i) q^{67} +(42.1499 - 42.1499i) q^{68} +73.9162i q^{69} -63.7595 q^{71} +(6.00000 + 6.00000i) q^{72} +(-50.1883 + 50.1883i) q^{73} +17.0004i q^{74} -48.2346 q^{76} +(21.5292 + 21.5292i) q^{77} +(18.8738 - 18.8738i) q^{78} +1.06121i q^{79} -9.00000 q^{81} +(18.6089 + 18.6089i) q^{82} +(-53.6243 + 53.6243i) q^{83} -9.16515i q^{84} +52.2765 q^{86} +(62.6325 + 62.6325i) q^{87} +(23.0156 - 23.0156i) q^{88} -145.154i q^{89} -28.8303 q^{91} +(-60.3523 - 60.3523i) q^{92} +(-57.5449 + 57.5449i) q^{93} -100.262i q^{94} -9.79796 q^{96} +(-23.7872 - 23.7872i) q^{97} +(-7.00000 + 7.00000i) q^{98} +34.5235i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 - 32 * q^8	\( 16 q + 16 q^{2} - 32 q^{8} + 8 q^{11} + 32 q^{13} - 64 q^{16} - 56 q^{17} + 48 q^{18} + 8 q^{22} - 24 q^{23} + 64 q^{26} - 112 q^{31} - 64 q^{32} - 24 q^{33} + 96 q^{36} + 152 q^{37} - 48 q^{46} - 80 q^{47} - 72 q^{51} + 64 q^{52} - 48 q^{53} - 24 q^{57} - 96 q^{58} + 96 q^{61} - 112 q^{62} - 48 q^{66} + 80 q^{67} + 112 q^{68} + 536 q^{71} + 96 q^{72} + 168 q^{77} + 48 q^{78} - 144 q^{81} + 256 q^{83} + 144 q^{87} - 16 q^{88} - 48 q^{92} - 192 q^{93} - 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 - 32 * q^8 + 8 * q^11 + 32 * q^13 - 64 * q^16 - 56 * q^17 + 48 * q^18 + 8 * q^22 - 24 * q^23 + 64 * q^26 - 112 * q^31 - 64 * q^32 - 24 * q^33 + 96 * q^36 + 152 * q^37 - 48 * q^46 - 80 * q^47 - 72 * q^51 + 64 * q^52 - 48 * q^53 - 24 * q^57 - 96 * q^58 + 96 * q^61 - 112 * q^62 - 48 * q^66 + 80 * q^67 + 112 * q^68 + 536 * q^71 + 96 * q^72 + 168 * q^77 + 48 * q^78 - 144 * q^81 + 256 * q^83 + 144 * q^87 - 16 * q^88 - 48 * q^92 - 192 * q^93 - 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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