LMFDB - Embedded newform 525.3.l.e.232.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(43,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			232.4
Character	$\chi$	$=$	525.232
Dual form			525.3.l.e.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08980 - 2.08980i) q^{2} +(1.22474 - 1.22474i) q^{3} +4.73454i q^{4} -5.11895 q^{6} +(1.87083 + 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-2.08980 - 2.08980i) q^{2} +(1.22474 - 1.22474i) q^{3} +4.73454i q^{4} -5.11895 q^{6} +(1.87083 + 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} -3.00000i q^{9} +2.70159 q^{11} +(5.79861 + 5.79861i) q^{12} +(2.37916 - 2.37916i) q^{13} -7.81932i q^{14} +12.5223 q^{16} +(-16.3715 - 16.3715i) q^{17} +(-6.26941 + 6.26941i) q^{18} -9.18722i q^{19} +4.58258 q^{21} +(-5.64579 - 5.64579i) q^{22} +(-21.4530 + 21.4530i) q^{23} -3.76010i q^{24} -9.94394 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-8.85752 + 8.85752i) q^{28} -52.3515i q^{29} -5.01849 q^{31} +(-32.3093 - 32.3093i) q^{32} +(3.30876 - 3.30876i) q^{33} +68.4262i q^{34} +14.2036 q^{36} +(-23.2257 - 23.2257i) q^{37} +(-19.1995 + 19.1995i) q^{38} -5.82772i q^{39} -60.5336 q^{41} +(-9.57668 - 9.57668i) q^{42} +(8.78639 - 8.78639i) q^{43} +12.7908i q^{44} +89.6651 q^{46} +(-2.24235 - 2.24235i) q^{47} +(15.3366 - 15.3366i) q^{48} +7.00000i q^{49} -40.1017 q^{51} +(11.2642 + 11.2642i) q^{52} +(25.6733 - 25.6733i) q^{53} +15.3568i q^{54} +5.74364 q^{56} +(-11.2520 - 11.2520i) q^{57} +(-109.404 + 109.404i) q^{58} -100.980i q^{59} -82.1567 q^{61} +(10.4877 + 10.4877i) q^{62} +(5.61249 - 5.61249i) q^{63} +84.9509i q^{64} -13.8293 q^{66} +(65.1606 + 65.1606i) q^{67} +(77.5114 - 77.5114i) q^{68} +52.5489i q^{69} -22.8905 q^{71} +(-4.60516 - 4.60516i) q^{72} +(5.38609 - 5.38609i) q^{73} +97.0741i q^{74} +43.4973 q^{76} +(5.05422 + 5.05422i) q^{77} +(-12.1788 + 12.1788i) q^{78} +117.836i q^{79} -9.00000 q^{81} +(126.503 + 126.503i) q^{82} +(-85.5086 + 85.5086i) q^{83} +21.6964i q^{84} -36.7236 q^{86} +(-64.1173 - 64.1173i) q^{87} +(4.14709 - 4.14709i) q^{88} +119.010i q^{89} +8.90199 q^{91} +(-101.570 - 101.570i) q^{92} +(-6.14637 + 6.14637i) q^{93} +9.37213i q^{94} -79.1412 q^{96} +(55.1059 + 55.1059i) q^{97} +(14.6286 - 14.6286i) q^{98} -8.10478i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8	$ 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8 + 48 * q^12 - 64 * q^13 - 184 * q^16 - 24 * q^17 - 24 * q^18 - 8 * q^22 - 8 * q^23 - 80 * q^26 + 96 * q^31 - 56 * q^32 + 72 * q^33 + 168 * q^36 - 8 * q^37 - 56 * q^38 + 320 * q^41 + 112 * q^43 + 320 * q^46 - 64 * q^47 - 192 * q^48 - 192 * q^51 - 96 * q^52 + 72 * q^53 - 336 * q^56 - 48 * q^57 + 512 * q^58 - 496 * q^61 + 776 * q^62 - 192 * q^66 + 192 * q^67 - 568 * q^68 - 144 * q^71 - 144 * q^72 - 224 * q^73 + 416 * q^76 - 112 * q^77 + 216 * q^78 - 216 * q^81 - 352 * q^82 + 32 * q^83 + 240 * q^86 - 384 * q^87 - 216 * q^88 - 1304 * q^92 + 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−2.08980	−	2.08980i	−1.04490	−	1.04490i	−0.998943	−	0.0459576i	$-0.985366\pi$
$2$	−2.08980	−	2.08980i	−1.04490	−	1.04490i	−0.0459576	−	0.998943i	$-0.514634\pi$
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			4.73454i			1.18364i
$5$		0			0
$5$		0			0
$6$	−5.11895			−0.853158
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	1.53505	−	1.53505i	0.191882	−	0.191882i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	2.70159			0.245599			0.122800	−	0.992431i	$-0.460813\pi$
$11$	2.70159			0.245599			0.122800	+	0.992431i	$0.460813\pi$
$12$	5.79861	+	5.79861i	0.483217	+	0.483217i
$13$	2.37916	−	2.37916i	0.183012	−	0.183012i	−0.609655	−	0.792667i	$-0.708692\pi$
$13$	2.37916	−	2.37916i	0.183012	−	0.183012i	0.792667	+	0.609655i	$0.208692\pi$
$14$		−	7.81932i		−	0.558523i
$15$		0			0
$16$	12.5223			0.782642
$17$	−16.3715	−	16.3715i	−0.963027	−	0.963027i	0.0363138	−	0.999340i	$-0.488438\pi$
$17$	−16.3715	−	16.3715i	−0.963027	−	0.963027i	−0.999340	+	0.0363138i	$0.988438\pi$
$18$	−6.26941	+	6.26941i	−0.348300	+	0.348300i
$19$		−	9.18722i		−	0.483538i	−0.970334	−	0.241769i	$-0.922272\pi$
$19$		−	9.18722i		−	0.483538i	0.970334	−	0.241769i	$-0.0777276\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−5.64579	−	5.64579i	−0.256627	−	0.256627i
$23$	−21.4530	+	21.4530i	−0.932740	+	0.932740i	−0.997876	−	0.0651365i	$-0.979252\pi$
$23$	−21.4530	+	21.4530i	−0.932740	+	0.932740i	0.0651365	+	0.997876i	$0.479252\pi$
$24$		−	3.76010i		−	0.156671i
$25$		0			0
$26$	−9.94394			−0.382459
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−8.85752	+	8.85752i	−0.316340	+	0.316340i
$29$		−	52.3515i		−	1.80523i	−0.430453	−	0.902613i	$-0.641646\pi$
$29$		−	52.3515i		−	1.80523i	0.430453	−	0.902613i	$-0.358354\pi$
$30$		0			0
$31$	−5.01849			−0.161887			−0.0809434	−	0.996719i	$-0.525793\pi$
$31$	−5.01849			−0.161887			−0.0809434	+	0.996719i	$0.525793\pi$
$32$	−32.3093	−	32.3093i	−1.00966	−	1.00966i
$33$	3.30876	−	3.30876i	0.100265	−	0.100265i
$34$			68.4262i			2.01253i
$35$		0			0
$36$	14.2036			0.394545
$37$	−23.2257	−	23.2257i	−0.627721	−	0.627721i	0.319773	−	0.947494i	$-0.396393\pi$
$37$	−23.2257	−	23.2257i	−0.627721	−	0.627721i	−0.947494	+	0.319773i	$0.896393\pi$
$38$	−19.1995	+	19.1995i	−0.505249	+	0.505249i
$39$		−	5.82772i		−	0.149429i
$40$		0			0
$41$	−60.5336			−1.47643			−0.738215	−	0.674566i	$-0.764331\pi$
$41$	−60.5336			−1.47643			−0.738215	+	0.674566i	$0.764331\pi$
$42$	−9.57668	−	9.57668i	−0.228016	−	0.228016i
$43$	8.78639	−	8.78639i	0.204335	−	0.204335i	−0.597520	−	0.801854i	$-0.703847\pi$
$43$	8.78639	−	8.78639i	0.204335	−	0.204335i	0.801854	+	0.597520i	$0.203847\pi$
$44$			12.7908i			0.290700i
$45$		0			0
$46$	89.6651			1.94924
$47$	−2.24235	−	2.24235i	−0.0477096	−	0.0477096i	0.682850	−	0.730559i	$-0.260740\pi$
$47$	−2.24235	−	2.24235i	−0.0477096	−	0.0477096i	−0.730559	+	0.682850i	$0.760740\pi$
$48$	15.3366	−	15.3366i	0.319512	−	0.319512i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	−40.1017			−0.786308
$52$	11.2642	+	11.2642i	0.216620	+	0.216620i
$53$	25.6733	−	25.6733i	0.484401	−	0.484401i	−0.422133	−	0.906534i	$-0.638718\pi$
$53$	25.6733	−	25.6733i	0.484401	−	0.484401i	0.906534	+	0.422133i	$0.138718\pi$
$54$			15.3568i			0.284386i
$55$		0			0
$56$	5.74364			0.102565
$57$	−11.2520	−	11.2520i	−0.197404	−	0.197404i
$58$	−109.404	+	109.404i	−1.88628	+	1.88628i
$59$		−	100.980i		−	1.71152i	−0.517374	−	0.855759i	$-0.673091\pi$
$59$		−	100.980i		−	1.71152i	0.517374	−	0.855759i	$-0.326909\pi$
$60$		0			0
$61$	−82.1567			−1.34683			−0.673415	−	0.739264i	$-0.735173\pi$
$61$	−82.1567			−1.34683			−0.673415	+	0.739264i	$0.735173\pi$
$62$	10.4877	+	10.4877i	0.169156	+	0.169156i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$			84.9509i			1.32736i
$65$		0			0
$66$	−13.8293			−0.209535
$67$	65.1606	+	65.1606i	0.972546	+	0.972546i	0.999633	−	0.0270874i	$-0.00862323\pi$
$67$	65.1606	+	65.1606i	0.972546	+	0.972546i	−0.0270874	+	0.999633i	$0.508623\pi$
$68$	77.5114	−	77.5114i	1.13987	−	1.13987i
$69$			52.5489i			0.761579i
$70$		0			0
$71$	−22.8905			−0.322402			−0.161201	−	0.986922i	$-0.551537\pi$
$71$	−22.8905			−0.322402			−0.161201	+	0.986922i	$0.551537\pi$
$72$	−4.60516	−	4.60516i	−0.0639605	−	0.0639605i
$73$	5.38609	−	5.38609i	0.0737820	−	0.0737820i	−0.669253	−	0.743035i	$-0.733386\pi$
$73$	5.38609	−	5.38609i	0.0737820	−	0.0737820i	0.743035	+	0.669253i	$0.233386\pi$
$74$			97.0741i			1.31181i
$75$		0			0
$76$	43.4973			0.572333
$77$	5.05422	+	5.05422i	0.0656392	+	0.0656392i
$78$	−12.1788	+	12.1788i	−0.156138	+	0.156138i
$79$			117.836i			1.49159i	0.666175	+	0.745795i	$0.267930\pi$
$79$			117.836i			1.49159i	−0.666175	+	0.745795i	$0.732070\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	126.503	+	126.503i	1.54272	+	1.54272i
$83$	−85.5086	+	85.5086i	−1.03022	+	1.03022i	−0.0306951	+	0.999529i	$0.509772\pi$
$83$	−85.5086	+	85.5086i	−1.03022	+	1.03022i	−0.999529	+	0.0306951i	$0.990228\pi$
$84$			21.6964i			0.258291i
$85$		0			0
$86$	−36.7236			−0.427019
$87$	−64.1173	−	64.1173i	−0.736980	−	0.736980i
$88$	4.14709	−	4.14709i	0.0471260	−	0.0471260i
$89$			119.010i			1.33719i	0.743629	+	0.668593i	$0.233103\pi$
$89$			119.010i			1.33719i	−0.743629	+	0.668593i	$0.766897\pi$
$90$		0			0
$91$	8.90199			0.0978241
$92$	−101.570	−	101.570i	−1.10402	−	1.10402i
$93$	−6.14637	+	6.14637i	−0.0660900	+	0.0660900i
$94$			9.37213i			0.0997035i
$95$		0			0
$96$	−79.1412			−0.824388
$97$	55.1059	+	55.1059i	0.568102	+	0.568102i	0.931596	−	0.363494i	$-0.118416\pi$
$97$	55.1059	+	55.1059i	0.568102	+	0.568102i	−0.363494	+	0.931596i	$0.618416\pi$
$98$	14.6286	−	14.6286i	0.149272	−	0.149272i
$99$		−	8.10478i		−	0.0818664i
$100$		0			0
$101$	128.322			1.27052			0.635259	−	0.772299i	$-0.280893\pi$
$101$	128.322			1.27052			0.635259	+	0.772299i	$0.280893\pi$
$102$	83.8046	+	83.8046i	0.821614	+	0.821614i
$103$	−10.5985	+	10.5985i	−0.102898	+	0.102898i	−0.756682	−	0.653783i	$-0.773181\pi$
$103$	−10.5985	+	10.5985i	−0.102898	+	0.102898i	0.653783	+	0.756682i	$0.273181\pi$
$104$		−	7.30426i		−	0.0702333i
$105$		0			0
$106$	−107.304			−1.01230
$107$	−138.356	−	138.356i	−1.29305	−	1.29305i	−0.932894	−	0.360151i	$-0.882725\pi$
$107$	−138.356	−	138.356i	−1.29305	−	1.29305i	−0.360151	−	0.932894i	$-0.617275\pi$
$108$	17.3958	−	17.3958i	0.161072	−	0.161072i
$109$		−	161.387i		−	1.48061i	−0.672271	−	0.740305i	$-0.734681\pi$
$109$		−	161.387i		−	1.48061i	0.672271	−	0.740305i	$-0.265319\pi$
$110$		0			0
$111$	−56.8911			−0.512532
$112$	23.4270	+	23.4270i	0.209170	+	0.209170i
$113$	34.2178	−	34.2178i	0.302812	−	0.302812i	−0.539301	−	0.842113i	$-0.681311\pi$
$113$	34.2178	−	34.2178i	0.302812	−	0.302812i	0.842113	+	0.539301i	$0.181311\pi$
$114$			47.0289i			0.412534i
$115$		0			0
$116$	247.861			2.13673
$117$	−7.13747	−	7.13747i	−0.0610040	−	0.0610040i
$118$	−211.027	+	211.027i	−1.78837	+	1.78837i
$119$		−	61.2564i		−	0.514759i
$120$		0			0
$121$	−113.701			−0.939681
$122$	171.691	+	171.691i	1.40730	+	1.40730i
$123$	−74.1383	+	74.1383i	−0.602750	+	0.602750i
$124$		−	23.7603i		−	0.191615i
$125$		0			0
$126$	−23.4580			−0.186174
$127$	13.3778	+	13.3778i	0.105337	+	0.105337i	0.757811	−	0.652474i	$-0.226269\pi$
$127$	13.3778	+	13.3778i	0.105337	+	0.105337i	−0.652474	+	0.757811i	$0.726269\pi$
$128$	48.2934	−	48.2934i	0.377292	−	0.377292i
$129$		−	21.5222i		−	0.166838i
$130$		0			0
$131$	27.9162			0.213101			0.106550	−	0.994307i	$-0.466019\pi$
$131$	27.9162			0.213101			0.106550	+	0.994307i	$0.466019\pi$
$132$	15.6655	+	15.6655i	0.118678	+	0.118678i
$133$	17.1877	−	17.1877i	0.129231	−	0.129231i
$134$		−	272.345i		−	2.03243i
$135$		0			0
$136$	−50.2621			−0.369574
$137$	−69.2726	−	69.2726i	−0.505639	−	0.505639i	0.407546	−	0.913185i	$-0.366385\pi$
$137$	−69.2726	−	69.2726i	−0.505639	−	0.505639i	−0.913185	+	0.407546i	$0.866385\pi$
$138$	109.817	−	109.817i	0.795775	−	0.795775i
$139$		−	233.891i		−	1.68267i	−0.540513	−	0.841335i	$-0.681770\pi$
$139$		−	233.891i		−	1.68267i	0.540513	−	0.841335i	$-0.318230\pi$
$140$		0			0
$141$	−5.49261			−0.0389547
$142$	47.8367	+	47.8367i	0.336878	+	0.336878i
$143$	6.42751	−	6.42751i	0.0449477	−	0.0449477i
$144$		−	37.5668i		−	0.260881i
$145$		0			0
$146$	−22.5117			−0.154190
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	109.963	−	109.963i	0.742993	−	0.742993i
$149$			127.594i			0.856336i	0.903699	+	0.428168i	$0.140841\pi$
$149$			127.594i			0.856336i	−0.903699	+	0.428168i	$0.859159\pi$
$150$		0			0
$151$	49.1914			0.325771			0.162886	−	0.986645i	$-0.447920\pi$
$151$	49.1914			0.325771			0.162886	+	0.986645i	$0.447920\pi$
$152$	−14.1029	−	14.1029i	−0.0927821	−	0.0927821i
$153$	−49.1144	+	49.1144i	−0.321009	+	0.321009i
$154$		−	21.1246i		−	0.137173i
$155$		0			0
$156$	27.5916			0.176869
$157$	−130.828	−	130.828i	−0.833301	−	0.833301i	0.154666	−	0.987967i	$-0.450570\pi$
$157$	−130.828	−	130.828i	−0.833301	−	0.833301i	−0.987967	+	0.154666i	$0.950570\pi$
$158$	246.253	−	246.253i	1.55856	−	1.55856i
$159$		−	62.8864i		−	0.395512i
$160$		0			0
$161$	−80.2698			−0.498570
$162$	18.8082	+	18.8082i	0.116100	+	0.116100i
$163$	35.5824	−	35.5824i	0.218297	−	0.218297i	−0.589483	−	0.807780i	$-0.700669\pi$
$163$	35.5824	−	35.5824i	0.218297	−	0.218297i	0.807780	+	0.589483i	$0.200669\pi$
$164$		−	286.599i		−	1.74756i
$165$		0			0
$166$	357.392			2.15296
$167$	−27.7479	−	27.7479i	−0.166155	−	0.166155i	0.619132	−	0.785287i	$-0.287485\pi$
$167$	−27.7479	−	27.7479i	−0.166155	−	0.166155i	−0.785287	+	0.619132i	$0.787485\pi$
$168$	7.03449	−	7.03449i	0.0418720	−	0.0418720i
$169$			157.679i			0.933013i
$170$		0			0
$171$	−27.5617			−0.161179
$172$	41.5995	+	41.5995i	0.241858	+	0.241858i
$173$	190.785	−	190.785i	1.10280	−	1.10280i	0.108732	−	0.994071i	$-0.465321\pi$
$173$	190.785	−	190.785i	1.10280	−	1.10280i	0.994071	−	0.108732i	$-0.0346790\pi$
$174$			267.985i			1.54014i
$175$		0			0
$176$	33.8301			0.192216
$177$	−123.674	−	123.674i	−0.698724	−	0.698724i
$178$	248.706	−	248.706i	1.39723	−	1.39723i
$179$		−	180.379i		−	1.00770i	−0.863791	−	0.503851i	$-0.831916\pi$
$179$		−	180.379i		−	1.00770i	0.863791	−	0.503851i	$-0.168084\pi$
$180$		0			0
$181$	−20.8061			−0.114951			−0.0574754	−	0.998347i	$-0.518305\pi$
$181$	−20.8061			−0.114951			−0.0574754	+	0.998347i	$0.518305\pi$
$182$	−18.6034	−	18.6034i	−0.102217	−	0.102217i
$183$	−100.621	+	100.621i	−0.549841	+	0.549841i
$184$			65.8630i			0.357951i
$185$		0			0
$186$	25.6894			0.138115
$187$	−44.2290	−	44.2290i	−0.236519	−	0.236519i
$188$	10.6165	−	10.6165i	0.0564708	−	0.0564708i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	221.603			1.16022			0.580112	−	0.814536i	$-0.303009\pi$
$191$	221.603			1.16022			0.580112	+	0.814536i	$0.303009\pi$
$192$	104.043	+	104.043i	0.541891	+	0.541891i
$193$	188.688	−	188.688i	0.977659	−	0.977659i	−0.0220973	−	0.999756i	$-0.507034\pi$
$193$	188.688	−	188.688i	0.977659	−	0.977659i	0.999756	+	0.0220973i	$0.00703437\pi$
$194$		−	230.321i		−	1.18722i
$195$		0			0
$196$	−33.1418			−0.169091
$197$	−85.7353	−	85.7353i	−0.435205	−	0.435205i	0.455190	−	0.890394i	$-0.349571\pi$
$197$	−85.7353	−	85.7353i	−0.435205	−	0.435205i	−0.890394	+	0.455190i	$0.849571\pi$
$198$	−16.9374	+	16.9374i	−0.0855423	+	0.0855423i
$199$		−	106.621i		−	0.535783i	−0.963449	−	0.267892i	$-0.913673\pi$
$199$		−	106.621i		−	0.535783i	0.963449	−	0.267892i	$-0.0863269\pi$
$200$		0			0
$201$	159.610			0.794080
$202$	−268.168	−	268.168i	−1.32756	−	1.32756i
$203$	97.9408	−	97.9408i	0.482467	−	0.482467i
$204$		−	189.863i		−	0.930703i
$205$		0			0
$206$	44.2976			0.215037
$207$	64.3590	+	64.3590i	0.310913	+	0.310913i
$208$	29.7924	−	29.7924i	0.143233	−	0.143233i
$209$		−	24.8201i		−	0.118757i
$210$		0			0
$211$	−210.119			−0.995827			−0.497913	−	0.867227i	$-0.665900\pi$
$211$	−210.119			−0.995827			−0.497913	+	0.867227i	$0.665900\pi$
$212$	121.551	+	121.551i	0.573355	+	0.573355i
$213$	−28.0351	+	28.0351i	−0.131620	+	0.131620i
$214$			578.273i			2.70221i
$215$		0			0
$216$	−11.2803			−0.0522235
$217$	−9.38874	−	9.38874i	−0.0432661	−	0.0432661i
$218$	−337.266	+	337.266i	−1.54709	+	1.54709i
$219$		−	13.1932i		−	0.0602428i
$220$		0			0
$221$	−77.9005			−0.352491
$222$	118.891	+	118.891i	0.535545	+	0.535545i
$223$	138.303	−	138.303i	0.620191	−	0.620191i	−0.325389	−	0.945580i	$-0.605495\pi$
$223$	138.303	−	138.303i	0.620191	−	0.620191i	0.945580	+	0.325389i	$0.105495\pi$
$224$		−	120.890i		−	0.539688i
$225$		0			0
$226$	−143.017			−0.632818
$227$	286.401	+	286.401i	1.26168	+	1.26168i	0.950280	+	0.311397i	$0.100797\pi$
$227$	286.401	+	286.401i	1.26168	+	1.26168i	0.311397	+	0.950280i	$0.399203\pi$
$228$	53.2731	−	53.2731i	0.233654	−	0.233654i
$229$		−	210.860i		−	0.920787i	−0.887715	−	0.460394i	$-0.847708\pi$
$229$		−	210.860i		−	0.920787i	0.887715	−	0.460394i	$-0.152292\pi$
$230$		0			0
$231$	12.3803			0.0535942
$232$	−80.3624	−	80.3624i	−0.346389	−	0.346389i
$233$	−217.881	+	217.881i	−0.935112	+	0.935112i	−0.998019	−	0.0629077i	$-0.979963\pi$
$233$	−217.881	+	217.881i	−0.935112	+	0.935112i	0.0629077	+	0.998019i	$0.479963\pi$
$234$			29.8318i			0.127486i
$235$		0			0
$236$	478.092			2.02581
$237$	144.319	+	144.319i	0.608939	+	0.608939i
$238$	−128.014	+	128.014i	−0.537873	+	0.537873i
$239$			103.424i			0.432737i	0.976312	+	0.216369i	$0.0694213\pi$
$239$			103.424i			0.432737i	−0.976312	+	0.216369i	$0.930579\pi$
$240$		0			0
$241$	−13.3346			−0.0553304			−0.0276652	−	0.999617i	$-0.508807\pi$
$241$	−13.3346			−0.0553304			−0.0276652	+	0.999617i	$0.508807\pi$
$242$	237.613	+	237.613i	0.981874	+	0.981874i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	388.974i		−	1.59416i
$245$		0			0
$246$	309.869			1.25963
$247$	−21.8579	−	21.8579i	−0.0884934	−	0.0884934i
$248$	−7.70365	+	7.70365i	−0.0310631	+	0.0310631i
$249$			209.452i			0.841174i
$250$		0			0
$251$	−324.833			−1.29416			−0.647078	−	0.762424i	$-0.724009\pi$
$251$	−324.833			−1.29416			−0.647078	+	0.762424i	$0.724009\pi$
$252$	26.5726	+	26.5726i	0.105447	+	0.105447i
$253$	−57.9573	+	57.9573i	−0.229080	+	0.229080i
$254$		−	55.9141i		−	0.220134i
$255$		0			0
$256$	137.956			0.538891
$257$	−45.5488	−	45.5488i	−0.177233	−	0.177233i	0.612916	−	0.790148i	$-0.289997\pi$
$257$	−45.5488	−	45.5488i	−0.177233	−	0.177233i	−0.790148	+	0.612916i	$0.789997\pi$
$258$	−44.9771	+	44.9771i	−0.174330	+	0.174330i
$259$		−	86.9025i		−	0.335531i
$260$		0			0
$261$	−157.055			−0.601742
$262$	−58.3393	−	58.3393i	−0.222669	−	0.222669i
$263$	186.483	−	186.483i	0.709062	−	0.709062i	−0.257276	−	0.966338i	$-0.582825\pi$
$263$	186.483	−	186.483i	0.709062	−	0.709062i	0.966338	+	0.257276i	$0.0828250\pi$
$264$		−	10.1582i		−	0.0384782i
$265$		0			0
$266$	−71.8379			−0.270067
$267$	145.756	+	145.756i	0.545904	+	0.545904i
$268$	−308.506	+	308.506i	−1.15114	+	1.15114i
$269$			489.403i			1.81934i	0.415330	+	0.909671i	$0.363666\pi$
$269$			489.403i			1.81934i	−0.415330	+	0.909671i	$0.636334\pi$
$270$		0			0
$271$	35.3651			0.130499			0.0652493	−	0.997869i	$-0.479216\pi$
$271$	35.3651			0.130499			0.0652493	+	0.997869i	$0.479216\pi$
$272$	−205.008	−	205.008i	−0.753705	−	0.753705i
$273$	10.9027	−	10.9027i	0.0399365	−	0.0399365i
$274$			289.532i			1.05669i
$275$		0			0
$276$	−248.795			−0.901432
$277$	88.7149	+	88.7149i	0.320270	+	0.320270i	0.848871	−	0.528600i	$-0.177283\pi$
$277$	88.7149	+	88.7149i	0.320270	+	0.320270i	−0.528600	+	0.848871i	$0.677283\pi$
$278$	−488.786	+	488.786i	−1.75822	+	1.75822i
$279$			15.0555i			0.0539623i
$280$		0			0
$281$	−31.7224			−0.112891			−0.0564456	−	0.998406i	$-0.517977\pi$
$281$	−31.7224			−0.112891			−0.0564456	+	0.998406i	$0.517977\pi$
$282$	11.4785	+	11.4785i	0.0407038	+	0.0407038i
$283$	111.462	−	111.462i	0.393859	−	0.393859i	−0.482202	−	0.876060i	$-0.660163\pi$
$283$	111.462	−	111.462i	0.393859	−	0.393859i	0.876060	+	0.482202i	$0.160163\pi$
$284$		−	108.376i		−	0.381607i
$285$		0			0
$286$	−26.8645			−0.0939317
$287$	−113.248	−	113.248i	−0.394593	−	0.394593i
$288$	−96.9278	+	96.9278i	−0.336555	+	0.336555i
$289$			247.049i			0.854841i
$290$		0			0
$291$	134.981			0.463854
$292$	25.5007	+	25.5007i	0.0873311	+	0.0873311i
$293$	−10.3345	+	10.3345i	−0.0352712	+	0.0352712i	−0.724522	−	0.689251i	$-0.757940\pi$
$293$	−10.3345	+	10.3345i	−0.0352712	+	0.0352712i	0.689251	+	0.724522i	$0.257940\pi$
$294$		−	35.8326i		−	0.121880i
$295$		0			0
$296$	−71.3053			−0.240896
$297$	−9.92628	−	9.92628i	−0.0334218	−	0.0334218i
$298$	266.646	−	266.646i	0.894786	−	0.894786i
$299$			102.080i			0.341405i
$300$		0			0
$301$	32.8756			0.109221
$302$	−102.800	−	102.800i	−0.340399	−	0.340399i
$303$	157.162	−	157.162i	0.518687	−	0.518687i
$304$		−	115.045i		−	0.378437i
$305$		0			0
$306$	205.279			0.670845
$307$	−296.667	−	296.667i	−0.966341	−	0.966341i	0.0331110	−	0.999452i	$-0.489459\pi$
$307$	−296.667	−	296.667i	−0.966341	−	0.966341i	−0.999452	+	0.0331110i	$0.989459\pi$
$308$	−23.9294	+	23.9294i	−0.0776929	+	0.0776929i
$309$			25.9610i			0.0840160i
$310$		0			0
$311$	−36.8400			−0.118457			−0.0592284	−	0.998244i	$-0.518864\pi$
$311$	−36.8400			−0.118457			−0.0592284	+	0.998244i	$0.518864\pi$
$312$	−8.94586	−	8.94586i	−0.0286726	−	0.0286726i
$313$	90.5345	−	90.5345i	0.289248	−	0.289248i	−0.547535	−	0.836783i	$-0.684434\pi$
$313$	90.5345	−	90.5345i	0.289248	−	0.289248i	0.836783	+	0.547535i	$0.184434\pi$
$314$			546.810i			1.74143i
$315$		0			0
$316$	−557.898			−1.76550
$317$	−2.40123	−	2.40123i	−0.00757485	−	0.00757485i	0.703309	−	0.710884i	$-0.251705\pi$
$317$	−2.40123	−	2.40123i	−0.00757485	−	0.00757485i	−0.710884	+	0.703309i	$0.751705\pi$
$318$	−131.420	+	131.420i	−0.413271	+	0.413271i
$319$		−	141.433i		−	0.443362i
$320$		0			0
$321$	−338.901			−1.05577
$322$	167.748	+	167.748i	0.520957	+	0.520957i
$323$	−150.408	+	150.408i	−0.465660	+	0.465660i
$324$		−	42.6109i		−	0.131515i
$325$		0			0
$326$	−148.720			−0.456198
$327$	−197.657	−	197.657i	−0.604457	−	0.604457i
$328$	−92.9223	+	92.9223i	−0.283300	+	0.283300i
$329$		−	8.39010i		−	0.0255018i
$330$		0			0
$331$	−288.021			−0.870154			−0.435077	−	0.900393i	$-0.643279\pi$
$331$	−288.021			−0.870154			−0.435077	+	0.900393i	$0.643279\pi$
$332$	−404.844	−	404.844i	−1.21941	−	1.21941i
$333$	−69.6770	+	69.6770i	−0.209240	+	0.209240i
$334$			115.975i			0.347232i
$335$		0			0
$336$	57.3842			0.170786
$337$	354.146	+	354.146i	1.05088	+	1.05088i	0.998634	+	0.0522432i	$0.0166371\pi$
$337$	354.146	+	354.146i	1.05088	+	1.05088i	0.0522432	+	0.998634i	$0.483363\pi$
$338$	329.518	−	329.518i	0.974906	−	0.974906i
$339$		−	83.8162i		−	0.247245i
$340$		0			0
$341$	−13.5579			−0.0397593
$342$	57.5984	+	57.5984i	0.168416	+	0.168416i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	26.9751i		−	0.0784161i
$345$		0			0
$346$	−797.405			−2.30464
$347$	440.033	+	440.033i	1.26811	+	1.26811i	0.947064	+	0.321044i	$0.104034\pi$
$347$	440.033	+	440.033i	1.26811	+	1.26811i	0.321044	+	0.947064i	$0.395966\pi$
$348$	303.566	−	303.566i	0.872316	−	0.872316i
$349$		−	429.577i		−	1.23088i	−0.788184	−	0.615440i	$-0.788978\pi$
$349$		−	429.577i		−	1.23088i	0.788184	−	0.615440i	$-0.211022\pi$
$350$		0			0
$351$	−17.4832			−0.0498096
$352$	−87.2865	−	87.2865i	−0.247973	−	0.247973i
$353$	−240.557	+	240.557i	−0.681463	+	0.681463i	−0.960330	−	0.278867i	$-0.910041\pi$
$353$	−240.557	+	240.557i	−0.681463	+	0.681463i	0.278867	+	0.960330i	$0.410041\pi$
$354$			516.909i			1.46020i
$355$		0			0
$356$	−563.456			−1.58274
$357$	−75.0234	−	75.0234i	−0.210150	−	0.210150i
$358$	−376.956	+	376.956i	−1.05295	+	1.05295i
$359$		−	53.5007i		−	0.149027i	−0.997220	−	0.0745135i	$-0.976260\pi$
$359$		−	53.5007i		−	0.149027i	0.997220	−	0.0745135i	$-0.0237404\pi$
$360$		0			0
$361$	276.595			0.766191
$362$	43.4806	+	43.4806i	0.120112	+	0.120112i
$363$	−139.255	+	139.255i	−0.383623	+	0.383623i
$364$			42.1469i			0.115788i
$365$		0			0
$366$	420.556			1.14906
$367$	−1.26172	−	1.26172i	−0.00343792	−	0.00343792i	0.705386	−	0.708824i	$-0.250774\pi$
$367$	−1.26172	−	1.26172i	−0.00343792	−	0.00343792i	−0.708824	+	0.705386i	$0.750774\pi$
$368$	−268.640	+	268.640i	−0.730001	+	0.730001i
$369$			181.601i			0.492143i
$370$		0			0
$371$	96.0606			0.258923
$372$	−29.1003	−	29.1003i	−0.0782266	−	0.0782266i
$373$	48.6449	−	48.6449i	0.130415	−	0.130415i	−0.638886	−	0.769301i	$-0.720604\pi$
$373$	48.6449	−	48.6449i	0.130415	−	0.130415i	0.769301	+	0.638886i	$0.220604\pi$
$374$			184.860i			0.494277i
$375$		0			0
$376$	−6.88425			−0.0183092
$377$	−124.553	−	124.553i	−0.330378	−	0.330378i
$378$	−28.7300	+	28.7300i	−0.0760054	+	0.0760054i
$379$			482.025i			1.27183i	0.771758	+	0.635917i	$0.219378\pi$
$379$			482.025i			1.27183i	−0.771758	+	0.635917i	$0.780622\pi$
$380$		0			0
$381$	32.7689			0.0860076
$382$	−463.106	−	463.106i	−1.21232	−	1.21232i
$383$	75.2958	−	75.2958i	0.196595	−	0.196595i	−0.601944	−	0.798539i	$-0.705607\pi$
$383$	75.2958	−	75.2958i	0.196595	−	0.196595i	0.798539	+	0.601944i	$0.205607\pi$
$384$		−	118.294i		−	0.308058i
$385$		0			0
$386$	−788.641			−2.04311
$387$	−26.3592	−	26.3592i	−0.0681115	−	0.0681115i
$388$	−260.901	+	260.901i	−0.672426	+	0.672426i
$389$			270.881i			0.696353i	0.937429	+	0.348176i	$0.113199\pi$
$389$			270.881i			0.696353i	−0.937429	+	0.348176i	$0.886801\pi$
$390$		0			0
$391$	702.434			1.79651
$392$	10.7454	+	10.7454i	0.0274117	+	0.0274117i
$393$	34.1902	−	34.1902i	0.0869979	−	0.0869979i
$394$			358.340i			0.909492i
$395$		0			0
$396$	38.3724			0.0969001
$397$	62.2126	+	62.2126i	0.156707	+	0.156707i	0.781106	−	0.624399i	$-0.214656\pi$
$397$	62.2126	+	62.2126i	0.156707	+	0.156707i	−0.624399	+	0.781106i	$0.714656\pi$
$398$	−222.817	+	222.817i	−0.559841	+	0.559841i
$399$		−	42.1012i		−	0.105517i
$400$		0			0
$401$	520.801			1.29876			0.649378	−	0.760466i	$-0.275029\pi$
$401$	520.801			1.29876			0.649378	+	0.760466i	$0.275029\pi$
$402$	−333.554	−	333.554i	−0.829735	−	0.829735i
$403$	−11.9398	+	11.9398i	−0.0296273	+	0.0296273i
$404$			607.547i			1.50383i
$405$		0			0
$406$	−409.354			−1.00826
$407$	−62.7463	−	62.7463i	−0.154168	−	0.154168i
$408$	−61.5582	+	61.5582i	−0.150878	+	0.150878i
$409$		−	575.516i		−	1.40713i	−0.710631	−	0.703564i	$-0.751591\pi$
$409$		−	575.516i		−	1.40713i	0.710631	−	0.703564i	$-0.248409\pi$
$410$		0			0
$411$	−169.682			−0.412853
$412$	−50.1791	−	50.1791i	−0.121794	−	0.121794i
$413$	188.916	−	188.916i	0.457423	−	0.457423i
$414$		−	268.995i		−	0.649747i
$415$		0			0
$416$	−153.738			−0.369562
$417$	−286.457	−	286.457i	−0.686947	−	0.686947i
$418$	−51.8692	+	51.8692i	−0.124089	+	0.124089i
$419$		−	113.474i		−	0.270822i	−0.990790	−	0.135411i	$-0.956765\pi$
$419$		−	113.474i		−	0.270822i	0.990790	−	0.135411i	$-0.0432355\pi$
$420$		0			0
$421$	737.737			1.75234			0.876172	−	0.481999i	$-0.160089\pi$
$421$	737.737			1.75234			0.876172	+	0.481999i	$0.160089\pi$
$422$	439.108	+	439.108i	1.04054	+	1.04054i
$423$	−6.72705	+	6.72705i	−0.0159032	+	0.0159032i
$424$		−	78.8196i		−	0.185895i
$425$		0			0
$426$	117.176			0.275060
$427$	−153.701	−	153.701i	−0.359956	−	0.359956i
$428$	655.052	−	655.052i	1.53049	−	1.53049i
$429$		−	15.7441i		−	0.0366996i
$430$		0			0
$431$	626.096			1.45266			0.726329	−	0.687347i	$-0.241225\pi$
$431$	626.096			1.45266			0.726329	+	0.687347i	$0.241225\pi$
$432$	−46.0097	−	46.0097i	−0.106504	−	0.106504i
$433$	−99.3139	+	99.3139i	−0.229362	+	0.229362i	−0.812426	−	0.583064i	$-0.801854\pi$
$433$	−99.3139	+	99.3139i	−0.229362	+	0.229362i	0.583064	+	0.812426i	$0.301854\pi$
$434$			39.2412i			0.0904176i
$435$		0			0
$436$	764.092			1.75250
$437$	197.094	+	197.094i	0.451015	+	0.451015i
$438$	−27.5711	+	27.5711i	−0.0629477	+	0.0629477i
$439$			249.762i			0.568933i	0.958686	+	0.284467i	$0.0918165\pi$
$439$			249.762i			0.568933i	−0.958686	+	0.284467i	$0.908183\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	162.797	+	162.797i	0.368318	+	0.368318i
$443$	213.838	−	213.838i	0.482704	−	0.482704i	−0.423290	−	0.905994i	$-0.639125\pi$
$443$	213.838	−	213.838i	0.482704	−	0.482704i	0.905994	+	0.423290i	$0.139125\pi$
$444$		−	269.353i		−	0.606651i
$445$		0			0
$446$	−578.050			−1.29608
$447$	156.270	+	156.270i	0.349598	+	0.349598i
$448$	−158.929	+	158.929i	−0.354751	+	0.354751i
$449$			540.540i			1.20387i	0.798544	+	0.601937i	$0.205604\pi$
$449$			540.540i			1.20387i	−0.798544	+	0.601937i	$0.794396\pi$
$450$		0			0
$451$	−163.537			−0.362610
$452$	162.006	+	162.006i	0.358420	+	0.358420i
$453$	60.2470	−	60.2470i	0.132995	−	0.132995i
$454$		−	1197.04i		−	2.63666i
$455$		0			0
$456$	−34.5448			−0.0757562
$457$	236.212	+	236.212i	0.516876	+	0.516876i	0.916625	−	0.399749i	$-0.130903\pi$
$457$	236.212	+	236.212i	0.516876	+	0.516876i	−0.399749	+	0.916625i	$0.630903\pi$
$458$	−440.656	+	440.656i	−0.962131	+	0.962131i
$459$			120.305i			0.262103i
$460$		0			0
$461$	156.987			0.340536			0.170268	−	0.985398i	$-0.445537\pi$
$461$	156.987			0.340536			0.170268	+	0.985398i	$0.445537\pi$
$462$	−25.8723	−	25.8723i	−0.0560006	−	0.0560006i
$463$	269.161	−	269.161i	0.581342	−	0.581342i	−0.353930	−	0.935272i	$-0.615155\pi$
$463$	269.161	−	269.161i	0.581342	−	0.581342i	0.935272	+	0.353930i	$0.115155\pi$
$464$		−	655.560i		−	1.41284i
$465$		0			0
$466$	910.656			1.95420
$467$	−114.700	−	114.700i	−0.245610	−	0.245610i	0.573556	−	0.819166i	$-0.305564\pi$
$467$	−114.700	−	114.700i	−0.245610	−	0.245610i	−0.819166	+	0.573556i	$0.805564\pi$
$468$	33.7927	−	33.7927i	0.0722066	−	0.0722066i
$469$			243.808i			0.519848i
$470$		0			0
$471$	−320.462			−0.680387
$472$	−155.009	−	155.009i	−0.328409	−	0.328409i
$473$	23.7372	−	23.7372i	0.0501844	−	0.0501844i
$474$		−	603.195i		−	1.27256i
$475$		0			0
$476$	290.021			0.609288
$477$	−77.0198	−	77.0198i	−0.161467	−	0.161467i
$478$	216.136	−	216.136i	0.452168	−	0.452168i
$479$		−	158.331i		−	0.330546i	−0.986248	−	0.165273i	$-0.947149\pi$
$479$		−	158.331i		−	0.330546i	0.986248	−	0.165273i	$-0.0528505\pi$
$480$		0			0
$481$	−110.515			−0.229761
$482$	27.8667	+	27.8667i	0.0578148	+	0.0578148i
$483$	−98.3101	+	98.3101i	−0.203541	+	0.203541i
$484$		−	538.324i		−	1.11224i
$485$		0			0
$486$	46.0705			0.0947953
$487$	−220.865	−	220.865i	−0.453521	−	0.453521i	0.443000	−	0.896521i	$-0.353914\pi$
$487$	−220.865	−	220.865i	−0.453521	−	0.453521i	−0.896521	+	0.443000i	$0.853914\pi$
$488$	−126.115	+	126.115i	−0.258432	+	0.258432i
$489$		−	87.1588i		−	0.178239i
$490$		0			0
$491$	925.802			1.88554			0.942772	−	0.333439i	$-0.108209\pi$
$491$	925.802			1.88554			0.942772	+	0.333439i	$0.108209\pi$
$492$	−351.011	−	351.011i	−0.713437	−	0.713437i
$493$	−857.071	+	857.071i	−1.73848	+	1.73848i
$494$			91.3572i			0.184934i
$495$		0			0
$496$	−62.8429			−0.126699
$497$	−42.8243	−	42.8243i	−0.0861656	−	0.0861656i
$498$	437.714	−	437.714i	0.878944	−	0.878944i
$499$		−	114.955i		−	0.230370i	−0.993344	−	0.115185i	$-0.963254\pi$
$499$		−	114.955i		−	0.230370i	0.993344	−	0.115185i	$-0.0367461\pi$
$500$		0			0
$501$	−67.9683			−0.135665
$502$	678.837	+	678.837i	1.35226	+	1.35226i
$503$	46.4397	−	46.4397i	0.0923254	−	0.0923254i	−0.659436	−	0.751761i	$-0.729205\pi$
$503$	46.4397	−	46.4397i	0.0923254	−	0.0923254i	0.751761	+	0.659436i	$0.229205\pi$
$504$		−	17.2309i		−	0.0341883i
$505$		0			0
$506$	242.239			0.478732
$507$	193.117	+	193.117i	0.380901	+	0.380901i
$508$	−63.3380	+	63.3380i	−0.124681	+	0.124681i
$509$		−	185.083i		−	0.363621i	−0.983334	−	0.181811i	$-0.941804\pi$
$509$		−	185.083i		−	0.363621i	0.983334	−	0.181811i	$-0.0581958\pi$
$510$		0			0
$511$	20.1529			0.0394381
$512$	−481.475	−	481.475i	−0.940380	−	0.940380i
$513$	−33.7560	+	33.7560i	−0.0658012	+	0.0658012i
$514$			190.376i			0.370381i
$515$		0			0
$516$	101.898			0.197476
$517$	−6.05791	−	6.05791i	−0.0117174	−	0.0117174i
$518$	−181.609	+	181.609i	−0.350597	+	0.350597i
$519$		−	467.326i		−	0.900435i
$520$		0			0
$521$	−275.217			−0.528248			−0.264124	−	0.964489i	$-0.585083\pi$
$521$	−275.217			−0.528248			−0.264124	+	0.964489i	$0.585083\pi$
$522$	328.213	+	328.213i	0.628761	+	0.628761i
$523$	424.281	−	424.281i	0.811245	−	0.811245i	−0.173576	−	0.984821i	$-0.555532\pi$
$523$	424.281	−	424.281i	0.811245	−	0.811245i	0.984821	+	0.173576i	$0.0555321\pi$
$524$			132.170i			0.252233i
$525$		0			0
$526$	−779.426			−1.48180
$527$	82.1600	+	82.1600i	0.155901	+	0.155901i
$528$	41.4332	−	41.4332i	0.0784719	−	0.0784719i
$529$		−	391.464i		−	0.740007i
$530$		0			0
$531$	−302.939			−0.570506
$532$	81.3760	+	81.3760i	0.152962	+	0.152962i
$533$	−144.019	+	144.019i	−0.270205	+	0.270205i
$534$		−	609.204i		−	1.14083i
$535$		0			0
$536$	200.050			0.373227
$537$	−220.918	−	220.918i	−0.411392	−	0.411392i
$538$	1022.76	−	1022.76i	1.90103	−	1.90103i
$539$			18.9111i			0.0350856i
$540$		0			0
$541$	−484.593			−0.895735			−0.447868	−	0.894100i	$-0.647816\pi$
$541$	−484.593			−0.895735			−0.447868	+	0.894100i	$0.647816\pi$
$542$	−73.9061	−	73.9061i	−0.136358	−	0.136358i
$543$	−25.4821	+	25.4821i	−0.0469284	+	0.0469284i
$544$			1057.90i			1.94467i
$545$		0			0
$546$	−45.5688			−0.0834594
$547$	367.275	+	367.275i	0.671436	+	0.671436i	0.958047	−	0.286611i	$-0.0925288\pi$
$547$	367.275	+	367.275i	0.671436	+	0.671436i	−0.286611	+	0.958047i	$0.592529\pi$
$548$	327.974	−	327.974i	0.598493	−	0.598493i
$549$			246.470i			0.448944i
$550$		0			0
$551$	−480.965			−0.872895
$552$	80.6654	+	80.6654i	0.146133	+	0.146133i
$553$	−220.450	+	220.450i	−0.398644	+	0.398644i
$554$		−	370.793i		−	0.669302i
$555$		0			0
$556$	1107.37			1.99167
$557$	−532.387	−	532.387i	−0.955811	−	0.955811i	0.0432528	−	0.999064i	$-0.486228\pi$
$557$	−532.387	−	532.387i	−0.955811	−	0.955811i	−0.999064	+	0.0432528i	$0.986228\pi$
$558$	31.4630	−	31.4630i	0.0563853	−	0.0563853i
$559$		−	41.8084i		−	0.0747914i
$560$		0			0
$561$	−108.338			−0.193117
$562$	66.2936	+	66.2936i	0.117960	+	0.117960i
$563$	724.535	−	724.535i	1.28692	−	1.28692i	0.350268	−	0.936649i	$-0.386090\pi$
$563$	724.535	−	724.535i	1.28692	−	1.28692i	0.936649	−	0.350268i	$-0.113910\pi$
$564$		−	26.0050i		−	0.0461082i
$565$		0			0
$566$	−465.867			−0.823087
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	−35.1382	+	35.1382i	−0.0618630	+	0.0618630i
$569$		−	63.5327i		−	0.111657i	−0.998440	−	0.0558284i	$-0.982220\pi$
$569$		−	63.5327i		−	0.111657i	0.998440	−	0.0558284i	$-0.0177800\pi$
$570$		0			0
$571$	186.947			0.327403			0.163701	−	0.986510i	$-0.447657\pi$
$571$	186.947			0.327403			0.163701	+	0.986510i	$0.447657\pi$
$572$	30.4314	+	30.4314i	0.0532017	+	0.0532017i
$573$	271.407	−	271.407i	0.473660	−	0.473660i
$574$			473.332i			0.824620i
$575$		0			0
$576$	254.853			0.442452
$577$	−650.925	−	650.925i	−1.12812	−	1.12812i	−0.990483	−	0.137637i	$-0.956049\pi$
$577$	−650.925	−	650.925i	−1.12812	−	1.12812i	−0.137637	−	0.990483i	$-0.543951\pi$
$578$	516.283	−	516.283i	0.893224	−	0.893224i
$579$		−	462.190i		−	0.798255i
$580$		0			0
$581$	−319.944			−0.550678
$582$	−282.084	−	282.084i	−0.484681	−	0.484681i
$583$	69.3587	−	69.3587i	0.118969	−	0.118969i
$584$		−	16.5359i		−	0.0283148i
$585$		0			0
$586$	43.1939			0.0737098
$587$	451.044	+	451.044i	0.768389	+	0.768389i	0.977823	−	0.209434i	$-0.0671621\pi$
$587$	451.044	+	451.044i	0.768389	+	0.768389i	−0.209434	+	0.977823i	$0.567162\pi$
$588$	−40.5903	+	40.5903i	−0.0690311	+	0.0690311i
$589$			46.1060i			0.0782785i
$590$		0			0
$591$	−210.008			−0.355343
$592$	−290.838	−	290.838i	−0.491281	−	0.491281i
$593$	−459.882	+	459.882i	−0.775518	+	0.775518i	−0.979065	−	0.203547i	$-0.934753\pi$
$593$	−459.882	+	459.882i	−0.775518	+	0.775518i	0.203547	+	0.979065i	$0.434753\pi$
$594$			41.4879i			0.0698450i
$595$		0			0
$596$	−604.100			−1.01359
$597$	−130.583	−	130.583i	−0.218733	−	0.218733i
$598$	213.327	−	213.327i	0.356735	−	0.356735i
$599$			415.835i			0.694216i	0.937825	+	0.347108i	$0.112836\pi$
$599$			415.835i			0.694216i	−0.937825	+	0.347108i	$0.887164\pi$
$600$		0			0
$601$	−693.471			−1.15386			−0.576931	−	0.816793i	$-0.695750\pi$
$601$	−693.471			−1.15386			−0.576931	+	0.816793i	$0.695750\pi$
$602$	−68.7036	−	68.7036i	−0.114126	−	0.114126i
$603$	195.482	−	195.482i	0.324182	−	0.324182i
$604$			232.899i			0.385594i
$605$		0			0
$606$	−656.875			−1.08395
$607$	−247.205	−	247.205i	−0.407257	−	0.407257i	0.473524	−	0.880781i	$-0.342982\pi$
$607$	−247.205	−	247.205i	−0.407257	−	0.407257i	−0.880781	+	0.473524i	$0.842982\pi$
$608$	−296.833	+	296.833i	−0.488211	+	0.488211i
$609$		−	239.905i		−	0.393933i
$610$		0			0
$611$	−10.6698			−0.0174629
$612$	−232.534	−	232.534i	−0.379958	−	0.379958i
$613$	−512.566	+	512.566i	−0.836159	+	0.836159i	−0.988351	−	0.152192i	$-0.951367\pi$
$613$	−512.566	+	512.566i	−0.836159	+	0.836159i	0.152192	+	0.988351i	$0.451367\pi$
$614$			1239.95i			2.01946i
$615$		0			0
$616$	15.5170			0.0251899
$617$	700.942	+	700.942i	1.13605	+	1.13605i	0.989152	+	0.146897i	$0.0469284\pi$
$617$	700.942	+	700.942i	1.13605	+	1.13605i	0.146897	+	0.989152i	$0.453072\pi$
$618$	54.2532	−	54.2532i	0.0877884	−	0.0877884i
$619$			354.521i			0.572732i	0.958120	+	0.286366i	$0.0924473\pi$
$619$			354.521i			0.572732i	−0.958120	+	0.286366i	$0.907553\pi$
$620$		0			0
$621$	157.647			0.253860
$622$	76.9884	+	76.9884i	0.123776	+	0.123776i
$623$	−222.646	+	222.646i	−0.357378	+	0.357378i
$624$		−	72.9763i		−	0.116949i
$625$		0			0
$626$	−378.398			−0.604470
$627$	−30.3983	−	30.3983i	−0.0484822	−	0.0484822i
$628$	619.412	−	619.412i	0.986325	−	0.986325i
$629$			760.476i			1.20902i
$630$		0			0
$631$	930.684			1.47494			0.737468	−	0.675383i	$-0.236021\pi$
$631$	930.684			1.47494			0.737468	+	0.675383i	$0.236021\pi$
$632$	180.884	+	180.884i	0.286209	+	0.286209i
$633$	−257.343	+	257.343i	−0.406545	+	0.406545i
$634$			10.0362i			0.0158299i
$635$		0			0
$636$	297.738			0.468142
$637$	16.6541	+	16.6541i	0.0261446	+	0.0261446i
$638$	−295.566	+	295.566i	−0.463270	+	0.463270i
$639$			68.6716i			0.107467i
$640$		0			0
$641$	−499.986			−0.780009			−0.390005	−	0.920813i	$-0.627527\pi$
$641$	−499.986			−0.780009			−0.390005	+	0.920813i	$0.627527\pi$
$642$	708.236	+	708.236i	1.10317	+	1.10317i
$643$	385.589	−	385.589i	0.599672	−	0.599672i	−0.340554	−	0.940225i	$-0.610614\pi$
$643$	385.589	−	385.589i	0.599672	−	0.599672i	0.940225	+	0.340554i	$0.110614\pi$
$644$		−	380.041i		−	0.590126i
$645$		0			0
$646$	628.647			0.973137
$647$	84.6226	+	84.6226i	0.130792	+	0.130792i	0.769472	−	0.638680i	$-0.220519\pi$
$647$	84.6226	+	84.6226i	0.130792	+	0.130792i	−0.638680	+	0.769472i	$0.720519\pi$
$648$	−13.8155	+	13.8155i	−0.0213202	+	0.0213202i
$649$		−	272.806i		−	0.420348i
$650$		0			0
$651$	−22.9976			−0.0353266
$652$	168.467	+	168.467i	0.258384	+	0.258384i
$653$	132.499	−	132.499i	0.202907	−	0.202907i	−0.598337	−	0.801244i	$-0.704172\pi$
$653$	132.499	−	132.499i	0.202907	−	0.202907i	0.801244	+	0.598337i	$0.204172\pi$
$654$			826.130i			1.26320i
$655$		0			0
$656$	−758.018			−1.15552
$657$	−16.1583	−	16.1583i	−0.0245940	−	0.0245940i
$658$	−17.5337	+	17.5337i	−0.0266469	+	0.0266469i
$659$		−	921.339i		−	1.39809i	−0.715080	−	0.699043i	$-0.753610\pi$
$659$		−	921.339i		−	1.39809i	0.715080	−	0.699043i	$-0.246390\pi$
$660$		0			0
$661$	705.918			1.06795			0.533977	−	0.845499i	$-0.320697\pi$
$661$	705.918			1.06795			0.533977	+	0.845499i	$0.320697\pi$
$662$	601.907	+	601.907i	0.909224	+	0.909224i
$663$	−95.4083	+	95.4083i	−0.143904	+	0.143904i
$664$			262.520i			0.395362i
$665$		0			0
$666$	291.222			0.437271
$667$	1123.10	+	1123.10i	1.68381	+	1.68381i
$668$	131.374	−	131.374i	0.196667	−	0.196667i
$669$		−	338.771i		−	0.506384i
$670$		0			0
$671$	−221.954			−0.330781
$672$	−148.060	−	148.060i	−0.220327	−	0.220327i
$673$	−480.376	+	480.376i	−0.713783	+	0.713783i	−0.967324	−	0.253542i	$-0.918405\pi$
$673$	−480.376	+	480.376i	−0.713783	+	0.713783i	0.253542	+	0.967324i	$0.418405\pi$
$674$		−	1480.19i		−	2.19613i
$675$		0			0
$676$	−746.539			−1.10435
$677$	−146.784	−	146.784i	−0.216815	−	0.216815i	0.590340	−	0.807155i	$-0.298994\pi$
$677$	−146.784	−	146.784i	−0.216815	−	0.216815i	−0.807155	+	0.590340i	$0.798994\pi$
$678$	−175.159	+	175.159i	−0.258347	+	0.258347i
$679$			206.187i			0.303663i
$680$		0			0
$681$	701.536			1.03016
$682$	28.3334	+	28.3334i	0.0415445	+	0.0415445i
$683$	88.7069	−	88.7069i	0.129878	−	0.129878i	−0.639179	−	0.769058i	$-0.720726\pi$
$683$	88.7069	−	88.7069i	0.129878	−	0.129878i	0.769058	+	0.639179i	$0.220726\pi$
$684$		−	130.492i		−	0.190778i
$685$		0			0
$686$	54.7353			0.0797890
$687$	−258.250	−	258.250i	−0.375910	−	0.375910i
$688$	110.025	−	110.025i	0.159921	−	0.159921i
$689$		−	122.161i		−	0.177303i
$690$		0			0
$691$	−664.952			−0.962304			−0.481152	−	0.876637i	$-0.659781\pi$
$691$	−664.952			−0.962304			−0.481152	+	0.876637i	$0.659781\pi$
$692$	903.280	+	903.280i	1.30532	+	1.30532i
$693$	15.1626	−	15.1626i	0.0218797	−	0.0218797i
$694$		−	1839.17i		−	2.65009i
$695$		0			0
$696$	−196.847			−0.282826
$697$	991.023	+	991.023i	1.42184	+	1.42184i
$698$	−897.731	+	897.731i	−1.28615	+	1.28615i
$699$			533.697i			0.763515i
$700$		0			0
$701$	−137.923			−0.196751			−0.0983757	−	0.995149i	$-0.531365\pi$
$701$	−137.923			−0.196751			−0.0983757	+	0.995149i	$0.531365\pi$
$702$	36.5364	+	36.5364i	0.0520461	+	0.0520461i
$703$	−213.380	+	213.380i	−0.303527	+	0.303527i
$704$			229.503i			0.325998i
$705$		0			0
$706$	1005.43			1.42412
$707$	240.069	+	240.069i	0.339560	+	0.339560i
$708$	585.541	−	585.541i	0.827035	−	0.827035i
$709$			371.525i			0.524013i	0.965066	+	0.262006i	$0.0843842\pi$
$709$			371.525i			0.524013i	−0.965066	+	0.262006i	$0.915616\pi$
$710$		0			0
$711$	353.507			0.497197
$712$	182.686	+	182.686i	0.256581	+	0.256581i
$713$	107.662	−	107.662i	0.150998	−	0.150998i
$714$			313.568i			0.439171i
$715$		0			0
$716$	854.010			1.19275
$717$	126.668	+	126.668i	0.176664	+	0.176664i
$718$	−111.806	+	111.806i	−0.155718	+	0.155718i
$719$			85.5943i			0.119046i	0.998227	+	0.0595232i	$0.0189580\pi$
$719$			85.5943i			0.119046i	−0.998227	+	0.0595232i	$0.981042\pi$
$720$		0			0
$721$	−39.6560			−0.0550014
$722$	−578.029	−	578.029i	−0.800594	−	0.800594i
$723$	−16.3315	+	16.3315i	−0.0225886	+	0.0225886i
$724$		−	98.5073i		−	0.136060i
$725$		0			0
$726$	582.032			0.801696
$727$	−589.673	−	589.673i	−0.811104	−	0.811104i	0.173695	−	0.984799i	$-0.444429\pi$
$727$	−589.673	−	589.673i	−0.811104	−	0.811104i	−0.984799	+	0.173695i	$0.944429\pi$
$728$	13.6650	−	13.6650i	0.0187706	−	0.0187706i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−287.692			−0.393559
$732$	−476.394	−	476.394i	−0.650812	−	0.650812i
$733$	−1019.17	+	1019.17i	−1.39040	+	1.39040i	−0.565992	+	0.824411i	$0.691507\pi$
$733$	−1019.17	+	1019.17i	−1.39040	+	1.39040i	−0.824411	+	0.565992i	$0.808493\pi$
$734$			5.27347i			0.00718457i
$735$		0			0
$736$	1386.26			1.88351
$737$	176.037	+	176.037i	0.238857	+	0.238857i
$738$	379.510	−	379.510i	0.514241	−	0.514241i
$739$			54.4746i			0.0737139i	0.999321	+	0.0368570i	$0.0117346\pi$
$739$			54.4746i			0.0737139i	−0.999321	+	0.0368570i	$0.988265\pi$
$740$		0			0
$741$	−53.5406			−0.0722545
$742$	−200.748	−	200.748i	−0.270549	−	0.270549i
$743$	−247.895	+	247.895i	−0.333641	+	0.333641i	−0.853968	−	0.520326i	$-0.825810\pi$
$743$	−247.895	+	247.895i	−0.333641	+	0.333641i	0.520326	+	0.853968i	$0.325810\pi$
$744$			18.8700i			0.0253629i
$745$		0			0
$746$	−203.316			−0.272542
$747$	256.526	+	256.526i	0.343408	+	0.343408i
$748$	209.404	−	209.404i	0.279952	−	0.279952i
$749$		−	517.680i		−	0.691162i
$750$		0			0
$751$	−1361.29			−1.81263			−0.906316	−	0.422600i	$-0.861117\pi$
$751$	−1361.29			−1.81263			−0.906316	+	0.422600i	$0.861117\pi$
$752$	−28.0793	−	28.0793i	−0.0373395	−	0.0373395i
$753$	−397.838	+	397.838i	−0.528337	+	0.528337i
$754$			520.580i			0.690425i
$755$		0			0
$756$	65.0892			0.0860969
$757$	−178.475	−	178.475i	−0.235767	−	0.235767i	0.579328	−	0.815095i	$-0.303315\pi$
$757$	−178.475	−	178.475i	−0.235767	−	0.235767i	−0.815095	+	0.579328i	$0.803315\pi$
$758$	1007.34	−	1007.34i	1.32894	−	1.32894i
$759$			141.966i			0.187043i
$760$		0			0
$761$	815.185			1.07120			0.535601	−	0.844471i	$-0.320085\pi$
$761$	815.185			1.07120			0.535601	+	0.844471i	$0.320085\pi$
$762$	−68.4805	−	68.4805i	−0.0898694	−	0.0898694i
$763$	301.927	−	301.927i	0.395710	−	0.395710i
$764$			1049.19i			1.37328i
$765$		0			0
$766$	−314.707			−0.410844
$767$	−240.246	−	240.246i	−0.313229	−	0.313229i
$768$	168.961	−	168.961i	0.220001	−	0.220001i
$769$			327.202i			0.425490i	0.977108	+	0.212745i	$0.0682403\pi$
$769$			327.202i			0.425490i	−0.977108	+	0.212745i	$0.931760\pi$
$770$		0			0
$771$	−111.571			−0.144710
$772$	893.352	+	893.352i	1.15719	+	1.15719i
$773$	−224.127	+	224.127i	−0.289944	+	0.289944i	−0.837058	−	0.547114i	$-0.815726\pi$
$773$	−224.127	+	224.127i	−0.289944	+	0.289944i	0.547114	+	0.837058i	$0.315726\pi$
$774$			110.171i			0.142340i
$775$		0			0
$776$	169.181			0.218017
$777$	−106.433	−	106.433i	−0.136980	−	0.136980i
$778$	566.088	−	566.088i	0.727620	−	0.727620i
$779$			556.136i			0.713910i
$780$		0			0
$781$	−61.8409			−0.0791817
$782$	−1467.95	−	1467.95i	−1.87717	−	1.87717i
$783$	−192.352	+	192.352i	−0.245660	+	0.245660i
$784$			87.6559i			0.111806i
$785$		0			0
$786$	−142.901			−0.181808
$787$	309.705	+	309.705i	0.393526	+	0.393526i	0.875942	−	0.482416i	$-0.160241\pi$
$787$	309.705	+	309.705i	0.393526	+	0.393526i	−0.482416	+	0.875942i	$0.660241\pi$
$788$	405.918	−	405.918i	0.515124	−	0.515124i
$789$		−	456.789i		−	0.578947i
$790$		0			0
$791$	128.031			0.161860
$792$	−12.4413	−	12.4413i	−0.0157087	−	0.0157087i
$793$	−195.464	+	195.464i	−0.246486	+	0.246486i
$794$		−	260.024i		−	0.327486i
$795$		0			0
$796$	504.801			0.634173
$797$	138.230	+	138.230i	0.173438	+	0.173438i	0.788488	−	0.615050i	$-0.210864\pi$
$797$	138.230	+	138.230i	0.173438	+	0.173438i	−0.615050	+	0.788488i	$0.710864\pi$
$798$	−87.9831	+	87.9831i	−0.110254	+	0.110254i
$799$			73.4210i			0.0918911i
$800$		0			0
$801$	357.029			0.445728
$802$	−1088.37	−	1088.37i	−1.35707	−	1.35707i
$803$	14.5510	−	14.5510i	0.0181208	−	0.0181208i
$804$			755.681i			0.939902i
$805$		0			0
$806$	49.9036			0.0619151
$807$	599.394	+	599.394i	0.742743	+	0.742743i
$808$	196.981	−	196.981i	0.243789	−	0.243789i
$809$			814.512i			1.00681i	0.864050	+	0.503407i	$0.167920\pi$
$809$			814.512i			1.00681i	−0.864050	+	0.503407i	$0.832080\pi$
$810$		0			0
$811$	255.277			0.314769			0.157384	−	0.987537i	$-0.449694\pi$
$811$	255.277			0.314769			0.157384	+	0.987537i	$0.449694\pi$
$812$	463.705	+	463.705i	0.571065	+	0.571065i
$813$	43.3133	−	43.3133i	0.0532759	−	0.0532759i
$814$			262.255i			0.322180i
$815$		0			0
$816$	−502.164			−0.615397
$817$	−80.7225	−	80.7225i	−0.0988036	−	0.0988036i
$818$	−1202.71	+	1202.71i	−1.47031	+	1.47031i
$819$		−	26.7060i		−	0.0326080i
$820$		0			0
$821$	−340.619			−0.414883			−0.207441	−	0.978247i	$-0.566514\pi$
$821$	−340.619			−0.414883			−0.207441	+	0.978247i	$0.566514\pi$
$822$	354.603	+	354.603i	0.431390	+	0.431390i
$823$	109.226	−	109.226i	0.132717	−	0.132717i	−0.637628	−	0.770345i	$-0.720084\pi$
$823$	109.226	−	109.226i	0.132717	−	0.132717i	0.770345	+	0.637628i	$0.220084\pi$
$824$			32.5385i			0.0394885i
$825$		0			0
$826$	−789.592			−0.955922
$827$	543.650	+	543.650i	0.657376	+	0.657376i	0.954758	−	0.297383i	$-0.0961137\pi$
$827$	543.650	+	543.650i	0.657376	+	0.657376i	−0.297383	+	0.954758i	$0.596114\pi$
$828$	−304.711	+	304.711i	−0.368008	+	0.368008i
$829$		−	419.953i		−	0.506578i	−0.967391	−	0.253289i	$-0.918488\pi$
$829$		−	419.953i		−	0.506578i	0.967391	−	0.253289i	$-0.0815123\pi$
$830$		0			0
$831$	217.306			0.261500
$832$	202.112	+	202.112i	0.242923	+	0.242923i
$833$	114.600	−	114.600i	0.137575	−	0.137575i
$834$			1197.28i			1.43558i
$835$		0			0
$836$	117.512			0.140565
$837$	18.4391	+	18.4391i	0.0220300	+	0.0220300i
$838$	−237.139	+	237.139i	−0.282982	+	0.282982i
$839$		−	762.801i		−	0.909178i	−0.890701	−	0.454589i	$-0.849786\pi$
$839$		−	762.801i		−	0.909178i	0.890701	−	0.454589i	$-0.150214\pi$
$840$		0			0
$841$	−1899.68			−2.25884
$842$	−1541.72	−	1541.72i	−1.83103	−	1.83103i
$843$	−38.8519	+	38.8519i	−0.0460876	+	0.0460876i
$844$		−	994.820i		−	1.17870i
$845$		0			0
$846$	28.1164			0.0332345
$847$	−212.716	−	212.716i	−0.251140	−	0.251140i
$848$	321.487	−	321.487i	0.379113	−	0.379113i
$849$		−	273.025i		−	0.321584i
$850$		0			0
$851$	996.522			1.17100
$852$	−132.733	−	132.733i	−0.155790	−	0.155790i
$853$	594.088	−	594.088i	0.696469	−	0.696469i	−0.267178	−	0.963647i	$-0.586091\pi$
$853$	594.088	−	594.088i	0.696469	−	0.696469i	0.963647	+	0.267178i	$0.0860911\pi$
$854$			642.410i			0.752236i
$855$		0			0
$856$	−424.767			−0.496223
$857$	−346.747	−	346.747i	−0.404605	−	0.404605i	0.475247	−	0.879852i	$-0.342359\pi$
$857$	−346.747	−	346.747i	−0.404605	−	0.404605i	−0.879852	+	0.475247i	$0.842359\pi$
$858$	−32.9021	+	32.9021i	−0.0383475	+	0.0383475i
$859$		−	1031.74i		−	1.20110i	−0.799588	−	0.600549i	$-0.794949\pi$
$859$		−	1031.74i		−	1.20110i	0.799588	−	0.600549i	$-0.205051\pi$
$860$		0			0
$861$	−277.400			−0.322183
$862$	−1308.42	−	1308.42i	−1.51788	−	1.51788i
$863$	695.429	−	695.429i	0.805828	−	0.805828i	−0.178172	−	0.983999i	$-0.557018\pi$
$863$	695.429	−	695.429i	0.805828	−	0.805828i	0.983999	+	0.178172i	$0.0570182\pi$
$864$			237.424i			0.274796i
$865$		0			0
$866$	415.093			0.479322
$867$	302.572	+	302.572i	0.348987	+	0.348987i
$868$	44.4514	−	44.4514i	0.0512113	−	0.0512113i
$869$			318.344i			0.366334i
$870$		0			0
$871$	310.055			0.355975
$872$	−247.737	−	247.737i	−0.284102	−	0.284102i
$873$	165.318	−	165.318i	0.189367	−	0.189367i
$874$		−	823.774i		−	0.942533i
$875$		0			0
$876$	62.4636			0.0713055
$877$	−1168.49	−	1168.49i	−1.33237	−	1.33237i	−0.903247	−	0.429121i	$-0.858823\pi$
$877$	−1168.49	−	1168.49i	−1.33237	−	1.33237i	−0.429121	−	0.903247i	$-0.641177\pi$
$878$	521.953	−	521.953i	0.594479	−	0.594479i
$879$			25.3141i			0.0287988i
$880$		0			0
$881$	−303.523			−0.344522			−0.172261	−	0.985051i	$-0.555107\pi$
$881$	−303.523			−0.344522			−0.172261	+	0.985051i	$0.555107\pi$
$882$	−43.8858	−	43.8858i	−0.0497572	−	0.0497572i
$883$	−720.863	+	720.863i	−0.816379	+	0.816379i	−0.985581	−	0.169202i	$-0.945881\pi$
$883$	−720.863	+	720.863i	−0.816379	+	0.816379i	0.169202	+	0.985581i	$0.445881\pi$
$884$		−	368.824i		−	0.417221i
$885$		0			0
$886$	−893.757			−1.00876
$887$	−975.650	−	975.650i	−1.09994	−	1.09994i	−0.994416	−	0.105527i	$-0.966347\pi$
$887$	−975.650	−	975.650i	−1.09994	−	1.09994i	−0.105527	−	0.994416i	$-0.533653\pi$
$888$	−87.3307	+	87.3307i	−0.0983454	+	0.0983454i
$889$			50.0553i			0.0563052i
$890$		0			0
$891$	−24.3143			−0.0272888
$892$	654.799	+	654.799i	0.734080	+	0.734080i
$893$	−20.6010	+	20.6010i	−0.0230694	+	0.0230694i
$894$		−	653.147i		−	0.730590i
$895$		0			0
$896$	180.697			0.201671
$897$	125.022	+	125.022i	0.139378	+	0.139378i
$898$	1129.62	−	1129.62i	1.25793	−	1.25793i
$899$			262.726i			0.292242i
$900$		0			0
$901$	−840.617			−0.932983
$902$	341.760	+	341.760i	0.378892	+	0.378892i
$903$	40.2643	−	40.2643i	0.0445895	−	0.0445895i
$904$		−	105.052i		−	0.116208i
$905$		0			0
$906$	−251.808			−0.277934
$907$	265.891	+	265.891i	0.293155	+	0.293155i	0.838325	−	0.545171i	$-0.183535\pi$
$907$	265.891	+	265.891i	0.293155	+	0.293155i	−0.545171	+	0.838325i	$0.683535\pi$
$908$	−1355.98	+	1355.98i	−1.49337	+	1.49337i
$909$		−	384.967i		−	0.423506i
$910$		0			0
$911$	916.932			1.00651			0.503256	−	0.864138i	$-0.332135\pi$
$911$	916.932			1.00651			0.503256	+	0.864138i	$0.332135\pi$
$912$	−140.901	−	140.901i	−0.154496	−	0.154496i
$913$	−231.009	+	231.009i	−0.253022	+	0.253022i
$914$		−	987.274i		−	1.08017i
$915$		0			0
$916$	998.327			1.08988
$917$	52.2264	+	52.2264i	0.0569535	+	0.0569535i
$918$	251.414	−	251.414i	0.273871	−	0.273871i
$919$		−	421.767i		−	0.458941i	−0.973316	−	0.229470i	$-0.926301\pi$
$919$		−	421.767i		−	0.458941i	0.973316	−	0.229470i	$-0.0736994\pi$
$920$		0			0
$921$	−726.682			−0.789014
$922$	−328.072	−	328.072i	−0.355827	−	0.355827i
$923$	−54.4602	+	54.4602i	−0.0590035	+	0.0590035i
$924$			58.6148i			0.0634360i
$925$		0			0
$926$	−1124.99			−1.21489
$927$	31.7955	+	31.7955i	0.0342994	+	0.0342994i
$928$	−1691.44	+	1691.44i	−1.82267	+	1.82267i
$929$			416.476i			0.448305i	0.974554	+	0.224153i	$0.0719614\pi$
$929$			416.476i			0.448305i	−0.974554	+	0.224153i	$0.928039\pi$
$930$		0			0
$931$	64.3106			0.0690769
$932$	−1031.57	−	1031.57i	−1.10683	−	1.10683i
$933$	−45.1196	+	45.1196i	−0.0483598	+	0.0483598i
$934$			479.401i			0.513277i
$935$		0			0
$936$	−21.9128			−0.0234111
$937$	−877.123	−	877.123i	−0.936097	−	0.936097i	0.0619806	−	0.998077i	$-0.480258\pi$
$937$	−877.123	−	877.123i	−0.936097	−	0.936097i	−0.998077	+	0.0619806i	$0.980258\pi$
$938$	509.511	−	509.511i	0.543189	−	0.543189i
$939$		−	221.763i		−	0.236170i
$940$		0			0
$941$	1322.22			1.40513			0.702563	−	0.711621i	$-0.252039\pi$
$941$	1322.22			1.40513			0.702563	+	0.711621i	$0.252039\pi$
$942$	669.703	+	669.703i	0.710937	+	0.710937i
$943$	1298.63	−	1298.63i	1.37713	−	1.37713i
$944$		−	1264.49i		−	1.33951i
$945$		0			0
$946$	−99.2122			−0.104876
$947$	445.898	+	445.898i	0.470853	+	0.470853i	0.902191	−	0.431338i	$-0.141958\pi$
$947$	445.898	+	445.898i	0.470853	+	0.470853i	−0.431338	+	0.902191i	$0.641958\pi$
$948$	−683.283	+	683.283i	−0.720763	+	0.720763i
$949$		−	25.6287i		−	0.0270060i
$950$		0			0
$951$	−5.88178			−0.00618484
$952$	−94.0317	−	94.0317i	−0.0987728	−	0.0987728i
$953$	−568.485	+	568.485i	−0.596521	+	0.596521i	−0.939385	−	0.342864i	$-0.888603\pi$
$953$	−568.485	+	568.485i	−0.596521	+	0.596521i	0.342864	+	0.939385i	$0.388603\pi$
$954$			321.912i			0.337434i
$955$		0			0
$956$	−489.667			−0.512204
$957$	−173.219	−	173.219i	−0.181002	−	0.181002i
$958$	−330.881	+	330.881i	−0.345388	+	0.345388i
$959$		−	259.194i		−	0.270275i
$960$		0			0
$961$	−935.815			−0.973793
$962$	230.955	+	230.955i	0.240078	+	0.240078i
$963$	−415.067	+	415.067i	−0.431015	+	0.431015i
$964$		−	63.1334i		−	0.0654911i
$965$		0			0
$966$	410.897			0.425359
$967$	721.223	+	721.223i	0.745836	+	0.745836i	0.973694	−	0.227858i	$-0.0731723\pi$
$967$	721.223	+	721.223i	0.745836	+	0.745836i	−0.227858	+	0.973694i	$0.573172\pi$
$968$	−174.538	+	174.538i	−0.180307	+	0.180307i
$969$			368.423i			0.380210i
$970$		0			0
$971$	670.576			0.690604			0.345302	−	0.938492i	$-0.387777\pi$
$971$	670.576			0.690604			0.345302	+	0.938492i	$0.387777\pi$
$972$	−52.1875	−	52.1875i	−0.0536908	−	0.0536908i
$973$	437.570	−	437.570i	0.449713	−	0.449713i
$974$			923.127i			0.947769i
$975$		0			0
$976$	−1028.79			−1.05409
$977$	787.654	+	787.654i	0.806196	+	0.806196i	0.984056	−	0.177860i	$-0.0569173\pi$
$977$	787.654	+	787.654i	0.806196	+	0.806196i	−0.177860	+	0.984056i	$0.556917\pi$
$978$	−182.145	+	182.145i	−0.186242	+	0.186242i
$979$			321.515i			0.328412i
$980$		0			0
$981$	−484.160			−0.493537
$982$	−1934.74	−	1934.74i	−1.97021	−	1.97021i
$983$	585.387	−	585.387i	0.595510	−	0.595510i	−0.343604	−	0.939115i	$-0.611648\pi$
$983$	585.387	−	585.387i	0.595510	−	0.595510i	0.939115	+	0.343604i	$0.111648\pi$
$984$			227.612i			0.231313i
$985$		0			0
$986$	3582.22			3.63308
$987$	−10.2757	−	10.2757i	−0.0104111	−	0.0104111i
$988$	103.487	−	103.487i	0.104744	−	0.104744i
$989$			376.989i			0.381182i
$990$		0			0
$991$	−1406.48			−1.41925			−0.709627	−	0.704577i	$-0.751137\pi$
$991$	−1406.48			−1.41925			−0.709627	+	0.704577i	$0.751137\pi$
$992$	162.144	+	162.144i	0.163451	+	0.163451i
$993$	−352.752	+	352.752i	−0.355239	+	0.355239i
$994$			178.989i			0.180069i
$995$		0			0
$996$	−991.662			−0.995644
$997$	−718.536	−	718.536i	−0.720698	−	0.720698i	0.248049	−	0.968747i	$-0.420211\pi$
$997$	−718.536	−	718.536i	−0.720698	−	0.720698i	−0.968747	+	0.248049i	$0.920211\pi$
$998$	−240.232	+	240.232i	−0.240714	+	0.240714i
$999$			170.673i			0.170844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.232.4		24
5.2	odd	4		105.3.l.a.43.9	yes	24
5.3	odd	4	inner	525.3.l.e.43.4		24
5.4	even	2		105.3.l.a.22.9	✓	24
15.2	even	4		315.3.o.b.253.4		24
15.14	odd	2		315.3.o.b.127.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.9	✓	24	5.4	even	2
105.3.l.a.43.9	yes	24	5.2	odd	4
315.3.o.b.127.4		24	15.14	odd	2
315.3.o.b.253.4		24	15.2	even	4
525.3.l.e.43.4		24	5.3	odd	4	inner
525.3.l.e.232.4		24	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08980 - 2.08980i) q^{2} +(1.22474 - 1.22474i) q^{3} +4.73454i q^{4} -5.11895 q^{6} +(1.87083 + 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-2.08980 - 2.08980i) q^{2} +(1.22474 - 1.22474i) q^{3} +4.73454i q^{4} -5.11895 q^{6} +(1.87083 + 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} -3.00000i q^{9} +2.70159 q^{11} +(5.79861 + 5.79861i) q^{12} +(2.37916 - 2.37916i) q^{13} -7.81932i q^{14} +12.5223 q^{16} +(-16.3715 - 16.3715i) q^{17} +(-6.26941 + 6.26941i) q^{18} -9.18722i q^{19} +4.58258 q^{21} +(-5.64579 - 5.64579i) q^{22} +(-21.4530 + 21.4530i) q^{23} -3.76010i q^{24} -9.94394 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-8.85752 + 8.85752i) q^{28} -52.3515i q^{29} -5.01849 q^{31} +(-32.3093 - 32.3093i) q^{32} +(3.30876 - 3.30876i) q^{33} +68.4262i q^{34} +14.2036 q^{36} +(-23.2257 - 23.2257i) q^{37} +(-19.1995 + 19.1995i) q^{38} -5.82772i q^{39} -60.5336 q^{41} +(-9.57668 - 9.57668i) q^{42} +(8.78639 - 8.78639i) q^{43} +12.7908i q^{44} +89.6651 q^{46} +(-2.24235 - 2.24235i) q^{47} +(15.3366 - 15.3366i) q^{48} +7.00000i q^{49} -40.1017 q^{51} +(11.2642 + 11.2642i) q^{52} +(25.6733 - 25.6733i) q^{53} +15.3568i q^{54} +5.74364 q^{56} +(-11.2520 - 11.2520i) q^{57} +(-109.404 + 109.404i) q^{58} -100.980i q^{59} -82.1567 q^{61} +(10.4877 + 10.4877i) q^{62} +(5.61249 - 5.61249i) q^{63} +84.9509i q^{64} -13.8293 q^{66} +(65.1606 + 65.1606i) q^{67} +(77.5114 - 77.5114i) q^{68} +52.5489i q^{69} -22.8905 q^{71} +(-4.60516 - 4.60516i) q^{72} +(5.38609 - 5.38609i) q^{73} +97.0741i q^{74} +43.4973 q^{76} +(5.05422 + 5.05422i) q^{77} +(-12.1788 + 12.1788i) q^{78} +117.836i q^{79} -9.00000 q^{81} +(126.503 + 126.503i) q^{82} +(-85.5086 + 85.5086i) q^{83} +21.6964i q^{84} -36.7236 q^{86} +(-64.1173 - 64.1173i) q^{87} +(4.14709 - 4.14709i) q^{88} +119.010i q^{89} +8.90199 q^{91} +(-101.570 - 101.570i) q^{92} +(-6.14637 + 6.14637i) q^{93} +9.37213i q^{94} -79.1412 q^{96} +(55.1059 + 55.1059i) q^{97} +(14.6286 - 14.6286i) q^{98} -8.10478i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8 + 48 * q^12 - 64 * q^13 - 184 * q^16 - 24 * q^17 - 24 * q^18 - 8 * q^22 - 8 * q^23 - 80 * q^26 + 96 * q^31 - 56 * q^32 + 72 * q^33 + 168 * q^36 - 8 * q^37 - 56 * q^38 + 320 * q^41 + 112 * q^43 + 320 * q^46 - 64 * q^47 - 192 * q^48 - 192 * q^51 - 96 * q^52 + 72 * q^53 - 336 * q^56 - 48 * q^57 + 512 * q^58 - 496 * q^61 + 776 * q^62 - 192 * q^66 + 192 * q^67 - 568 * q^68 - 144 * q^71 - 144 * q^72 - 224 * q^73 + 416 * q^76 - 112 * q^77 + 216 * q^78 - 216 * q^81 - 352 * q^82 + 32 * q^83 + 240 * q^86 - 384 * q^87 - 216 * q^88 - 1304 * q^92 + 168 * q^96 + 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more