LMFDB - Embedded newform 525.3.l.e.43.1

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			43.1
Character	$\chi$	$=$	525.43
Dual form			525.3.l.e.232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74240 + 2.74240i) q^{2} +(1.22474 + 1.22474i) q^{3} -11.0415i q^{4} -6.71747 q^{6} +(-1.87083 + 1.87083i) q^{7} +(19.3105 + 19.3105i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-2.74240 + 2.74240i) q^{2} +(1.22474 + 1.22474i) q^{3} -11.0415i q^{4} -6.71747 q^{6} +(-1.87083 + 1.87083i) q^{7} +(19.3105 + 19.3105i) q^{8} +3.00000i q^{9} +10.9331 q^{11} +(13.5230 - 13.5230i) q^{12} +(-8.10523 - 8.10523i) q^{13} -10.2611i q^{14} -61.7483 q^{16} +(5.51018 - 5.51018i) q^{17} +(-8.22719 - 8.22719i) q^{18} -12.1318i q^{19} -4.58258 q^{21} +(-29.9829 + 29.9829i) q^{22} +(-24.3210 - 24.3210i) q^{23} +47.3009i q^{24} +44.4555 q^{26} +(-3.67423 + 3.67423i) q^{27} +(20.6567 + 20.6567i) q^{28} -14.8012i q^{29} -8.07276 q^{31} +(92.0962 - 92.0962i) q^{32} +(13.3902 + 13.3902i) q^{33} +30.2222i q^{34} +33.1244 q^{36} +(34.6319 - 34.6319i) q^{37} +(33.2701 + 33.2701i) q^{38} -19.8537i q^{39} +32.0975 q^{41} +(12.5672 - 12.5672i) q^{42} +(13.0663 + 13.0663i) q^{43} -120.717i q^{44} +133.395 q^{46} +(54.1653 - 54.1653i) q^{47} +(-75.6259 - 75.6259i) q^{48} -7.00000i q^{49} +13.4971 q^{51} +(-89.4937 + 89.4937i) q^{52} +(-6.76541 - 6.76541i) q^{53} -20.1524i q^{54} -72.2534 q^{56} +(14.8583 - 14.8583i) q^{57} +(40.5907 + 40.5907i) q^{58} +44.4162i q^{59} -84.4444 q^{61} +(22.1387 - 22.1387i) q^{62} +(-5.61249 - 5.61249i) q^{63} +258.136i q^{64} -73.4427 q^{66} +(-0.661895 + 0.661895i) q^{67} +(-60.8405 - 60.8405i) q^{68} -59.5739i q^{69} +103.429 q^{71} +(-57.9316 + 57.9316i) q^{72} +(55.1974 + 55.1974i) q^{73} +189.949i q^{74} -133.952 q^{76} +(-20.4539 + 20.4539i) q^{77} +(54.4467 + 54.4467i) q^{78} -68.8001i q^{79} -9.00000 q^{81} +(-88.0241 + 88.0241i) q^{82} +(71.4410 + 71.4410i) q^{83} +50.5984i q^{84} -71.6660 q^{86} +(18.1277 - 18.1277i) q^{87} +(211.124 + 211.124i) q^{88} -41.6575i q^{89} +30.3270 q^{91} +(-268.539 + 268.539i) q^{92} +(-9.88708 - 9.88708i) q^{93} +297.086i q^{94} +225.589 q^{96} +(-25.2508 + 25.2508i) q^{97} +(19.1968 + 19.1968i) q^{98} +32.7993i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.74240	+	2.74240i	−1.37120	+	1.37120i	−0.512527	+	0.858671i	$0.671291\pi$
$2$	−2.74240	+	2.74240i	−1.37120	+	1.37120i	−0.858671	+	0.512527i	$0.828709\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	11.0415i		−	2.76037i
$5$		0			0
$5$		0			0
$6$	−6.71747			−1.11958
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	19.3105	+	19.3105i	2.41382	+	2.41382i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	10.9331			0.993917			0.496958	−	0.867774i	$-0.334450\pi$
$11$	10.9331			0.993917			0.496958	+	0.867774i	$0.334450\pi$
$12$	13.5230	−	13.5230i	1.12692	−	1.12692i
$13$	−8.10523	−	8.10523i	−0.623479	−	0.623479i	0.322940	−	0.946419i	$-0.395329\pi$
$13$	−8.10523	−	8.10523i	−0.623479	−	0.623479i	−0.946419	+	0.322940i	$0.895329\pi$
$14$		−	10.2611i		−	0.732936i
$15$		0			0
$16$	−61.7483			−3.85927
$17$	5.51018	−	5.51018i	0.324128	−	0.324128i	−0.526220	−	0.850348i	$-0.676391\pi$
$17$	5.51018	−	5.51018i	0.324128	−	0.324128i	0.850348	+	0.526220i	$0.176391\pi$
$18$	−8.22719	−	8.22719i	−0.457066	−	0.457066i
$19$		−	12.1318i		−	0.638513i	−0.947668	−	0.319257i	$-0.896567\pi$
$19$		−	12.1318i		−	0.638513i	0.947668	−	0.319257i	$-0.103433\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	−29.9829	+	29.9829i	−1.36286	+	1.36286i
$23$	−24.3210	−	24.3210i	−1.05743	−	1.05743i	−0.998247	−	0.0591858i	$-0.981150\pi$
$23$	−24.3210	−	24.3210i	−1.05743	−	1.05743i	−0.0591858	−	0.998247i	$-0.518850\pi$
$24$			47.3009i			1.97087i
$25$		0			0
$26$	44.4555			1.70983
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	20.6567	+	20.6567i	0.737740	+	0.737740i
$29$		−	14.8012i		−	0.510385i	−0.966890	−	0.255193i	$-0.917861\pi$
$29$		−	14.8012i		−	0.510385i	0.966890	−	0.255193i	$-0.0821389\pi$
$30$		0			0
$31$	−8.07276			−0.260412			−0.130206	−	0.991487i	$-0.541564\pi$
$31$	−8.07276			−0.260412			−0.130206	+	0.991487i	$0.541564\pi$
$32$	92.0962	−	92.0962i	2.87801	−	2.87801i
$33$	13.3902	+	13.3902i	0.405765	+	0.405765i
$34$			30.2222i			0.888888i
$35$		0			0
$36$	33.1244			0.920123
$37$	34.6319	−	34.6319i	0.935998	−	0.935998i	−0.0620735	−	0.998072i	$-0.519771\pi$
$37$	34.6319	−	34.6319i	0.935998	−	0.935998i	0.998072	+	0.0620735i	$0.0197713\pi$
$38$	33.2701	+	33.2701i	0.875528	+	0.875528i
$39$		−	19.8537i		−	0.509069i
$40$		0			0
$41$	32.0975			0.782866			0.391433	−	0.920207i	$-0.371979\pi$
$41$	32.0975			0.782866			0.391433	+	0.920207i	$0.371979\pi$
$42$	12.5672	−	12.5672i	0.299220	−	0.299220i
$43$	13.0663	+	13.0663i	0.303868	+	0.303868i	0.842525	−	0.538657i	$-0.181068\pi$
$43$	13.0663	+	13.0663i	0.303868	+	0.303868i	−0.538657	+	0.842525i	$0.681068\pi$
$44$		−	120.717i		−	2.74358i
$45$		0			0
$46$	133.395			2.89990
$47$	54.1653	−	54.1653i	1.15245	−	1.15245i	0.166394	−	0.986059i	$-0.446788\pi$
$47$	54.1653	−	54.1653i	1.15245	−	1.15245i	0.986059	−	0.166394i	$-0.0532124\pi$
$48$	−75.6259	−	75.6259i	−1.57554	−	1.57554i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	13.4971			0.264649
$52$	−89.4937	+	89.4937i	−1.72103	+	1.72103i
$53$	−6.76541	−	6.76541i	−0.127649	−	0.127649i	0.640396	−	0.768045i	$-0.278770\pi$
$53$	−6.76541	−	6.76541i	−0.127649	−	0.127649i	−0.768045	+	0.640396i	$0.778770\pi$
$54$		−	20.1524i		−	0.373193i
$55$		0			0
$56$	−72.2534			−1.29024
$57$	14.8583	−	14.8583i	0.260672	−	0.260672i
$58$	40.5907	+	40.5907i	0.699839	+	0.699839i
$59$			44.4162i			0.752816i	0.926454	+	0.376408i	$0.122841\pi$
$59$			44.4162i			0.752816i	−0.926454	+	0.376408i	$0.877159\pi$
$60$		0			0
$61$	−84.4444			−1.38433			−0.692167	−	0.721737i	$-0.743344\pi$
$61$	−84.4444			−1.38433			−0.692167	+	0.721737i	$0.743344\pi$
$62$	22.1387	−	22.1387i	0.357076	−	0.357076i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			258.136i			4.03337i
$65$		0			0
$66$	−73.4427			−1.11277
$67$	−0.661895	+	0.661895i	−0.00987903	+	0.00987903i	−0.712029	−	0.702150i	$-0.752224\pi$
$67$	−0.661895	+	0.661895i	−0.00987903	+	0.00987903i	0.702150	+	0.712029i	$0.252224\pi$
$68$	−60.8405	−	60.8405i	−0.894713	−	0.894713i
$69$		−	59.5739i		−	0.863390i
$70$		0			0
$71$	103.429			1.45675			0.728373	−	0.685181i	$-0.240277\pi$
$71$	103.429			1.45675			0.728373	+	0.685181i	$0.240277\pi$
$72$	−57.9316	+	57.9316i	−0.804605	+	0.804605i
$73$	55.1974	+	55.1974i	0.756129	+	0.756129i	0.975616	−	0.219486i	$-0.0704382\pi$
$73$	55.1974	+	55.1974i	0.756129	+	0.756129i	−0.219486	+	0.975616i	$0.570438\pi$
$74$			189.949i			2.56688i
$75$		0			0
$76$	−133.952			−1.76253
$77$	−20.4539	+	20.4539i	−0.265635	+	0.265635i
$78$	54.4467	+	54.4467i	0.698034	+	0.698034i
$79$		−	68.8001i		−	0.870887i	−0.900216	−	0.435444i	$-0.856592\pi$
$79$		−	68.8001i		−	0.870887i	0.900216	−	0.435444i	$-0.143408\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−88.0241	+	88.0241i	−1.07346	+	1.07346i
$83$	71.4410	+	71.4410i	0.860735	+	0.860735i	0.991423	−	0.130688i	$-0.0417188\pi$
$83$	71.4410	+	71.4410i	0.860735	+	0.860735i	−0.130688	+	0.991423i	$0.541719\pi$
$84$			50.5984i			0.602362i
$85$		0			0
$86$	−71.6660			−0.833326
$87$	18.1277	−	18.1277i	0.208364	−	0.208364i
$88$	211.124	+	211.124i	2.39913	+	2.39913i
$89$		−	41.6575i		−	0.468062i	−0.972229	−	0.234031i	$-0.924808\pi$
$89$		−	41.6575i		−	0.468062i	0.972229	−	0.234031i	$-0.0751917\pi$
$90$		0			0
$91$	30.3270			0.333264
$92$	−268.539	+	268.539i	−2.91890	+	2.91890i
$93$	−9.88708	−	9.88708i	−0.106313	−	0.106313i
$94$			297.086i			3.16048i
$95$		0			0
$96$	225.589			2.34988
$97$	−25.2508	+	25.2508i	−0.260318	+	0.260318i	−0.825183	−	0.564865i	$-0.808928\pi$
$97$	−25.2508	+	25.2508i	−0.260318	+	0.260318i	0.564865	+	0.825183i	$0.308928\pi$
$98$	19.1968	+	19.1968i	0.195885	+	0.195885i
$99$			32.7993i			0.331306i
$100$		0			0
$101$	53.7274			0.531955			0.265977	−	0.963979i	$-0.414305\pi$
$101$	53.7274			0.531955			0.265977	+	0.963979i	$0.414305\pi$
$102$	−37.0145	+	37.0145i	−0.362887	+	0.362887i
$103$	−39.6796	−	39.6796i	−0.385239	−	0.385239i	0.487746	−	0.872985i	$-0.337819\pi$
$103$	−39.6796	−	39.6796i	−0.385239	−	0.385239i	−0.872985	+	0.487746i	$0.837819\pi$
$104$		−	313.032i		−	3.00993i
$105$		0			0
$106$	37.1069			0.350065
$107$	68.3716	−	68.3716i	0.638987	−	0.638987i	−0.311318	−	0.950306i	$-0.600771\pi$
$107$	68.3716	−	68.3716i	0.638987	−	0.638987i	0.950306	+	0.311318i	$0.100771\pi$
$108$	40.5690	+	40.5690i	0.375639	+	0.375639i
$109$		−	135.475i		−	1.24289i	−0.783458	−	0.621445i	$-0.786546\pi$
$109$		−	135.475i		−	1.24289i	0.783458	−	0.621445i	$-0.213454\pi$
$110$		0			0
$111$	84.8306			0.764239
$112$	115.520	−	115.520i	1.03143	−	1.03143i
$113$	−6.34998	−	6.34998i	−0.0561945	−	0.0561945i	0.678451	−	0.734646i	$-0.262652\pi$
$113$	−6.34998	−	6.34998i	−0.0561945	−	0.0561945i	−0.734646	+	0.678451i	$0.762652\pi$
$114$			81.4947i			0.714866i
$115$		0			0
$116$	−163.427			−1.40885
$117$	24.3157	−	24.3157i	0.207826	−	0.207826i
$118$	−121.807	−	121.807i	−1.03226	−	1.03226i
$119$			20.6172i			0.173254i
$120$		0			0
$121$	−1.46766			−0.0121294
$122$	231.580	−	231.580i	1.89820	−	1.89820i
$123$	39.3113	+	39.3113i	0.319604	+	0.319604i
$124$			89.1352i			0.718833i
$125$		0			0
$126$	30.7833			0.244312
$127$	−20.2819	+	20.2819i	−0.159700	+	0.159700i	−0.782434	−	0.622734i	$-0.786022\pi$
$127$	−20.2819	+	20.2819i	−0.159700	+	0.159700i	0.622734	+	0.782434i	$0.286022\pi$
$128$	−339.525	−	339.525i	−2.65254	−	2.65254i
$129$			32.0058i			0.248107i
$130$		0			0
$131$	77.7144			0.593240			0.296620	−	0.954996i	$-0.404141\pi$
$131$	77.7144			0.593240			0.296620	+	0.954996i	$0.404141\pi$
$132$	147.848	−	147.848i	1.12006	−	1.12006i
$133$	22.6964	+	22.6964i	0.170650	+	0.170650i
$134$		−	3.63036i		−	0.0270922i
$135$		0			0
$136$	212.809			1.56477
$137$	−146.870	+	146.870i	−1.07205	+	1.07205i	−0.0748506	+	0.997195i	$0.523848\pi$
$137$	−146.870	+	146.870i	−1.07205	+	1.07205i	−0.997195	+	0.0748506i	$0.976152\pi$
$138$	163.375	+	163.375i	1.18388	+	1.18388i
$139$		−	146.322i		−	1.05268i	−0.850275	−	0.526339i	$-0.823564\pi$
$139$		−	146.322i		−	1.05268i	0.850275	−	0.526339i	$-0.176436\pi$
$140$		0			0
$141$	132.677			0.940974
$142$	−283.643	+	283.643i	−1.99749	+	1.99749i
$143$	−88.6152	−	88.6152i	−0.619686	−	0.619686i
$144$		−	185.245i		−	1.28642i
$145$		0			0
$146$	−302.746			−2.07361
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	−382.388	−	382.388i	−2.58370	−	2.58370i
$149$			143.223i			0.961228i	0.876932	+	0.480614i	$0.159586\pi$
$149$			143.223i			0.961228i	−0.876932	+	0.480614i	$0.840414\pi$
$150$		0			0
$151$	204.429			1.35384			0.676919	−	0.736058i	$-0.263315\pi$
$151$	204.429			1.35384			0.676919	+	0.736058i	$0.263315\pi$
$152$	234.270	−	234.270i	1.54125	−	1.54125i
$153$	16.5305	+	16.5305i	0.108043	+	0.108043i
$154$		−	112.186i		−	0.728478i
$155$		0			0
$156$	−219.214			−1.40522
$157$	168.925	−	168.925i	1.07595	−	1.07595i	0.0790870	−	0.996868i	$-0.474800\pi$
$157$	168.925	−	168.925i	1.07595	−	1.07595i	0.996868	−	0.0790870i	$-0.0252005\pi$
$158$	188.677	+	188.677i	1.19416	+	1.19416i
$159$		−	16.5718i		−	0.104225i
$160$		0			0
$161$	91.0007			0.565222
$162$	24.6816	−	24.6816i	0.152355	−	0.152355i
$163$	−167.373	−	167.373i	−1.02683	−	1.02683i	−0.999630	−	0.0271997i	$-0.991341\pi$
$163$	−167.373	−	167.373i	−1.02683	−	1.02683i	−0.0271997	−	0.999630i	$-0.508659\pi$
$164$		−	354.404i		−	2.16100i
$165$		0			0
$166$	−391.839			−2.36048
$167$	−80.3381	+	80.3381i	−0.481066	+	0.481066i	−0.905472	−	0.424406i	$-0.860483\pi$
$167$	−80.3381	+	80.3381i	−0.481066	+	0.481066i	0.424406	+	0.905472i	$0.360483\pi$
$168$	−88.4919	−	88.4919i	−0.526738	−	0.526738i
$169$		−	37.6105i		−	0.222547i
$170$		0			0
$171$	36.3953			0.212838
$172$	144.271	−	144.271i	0.838787	−	0.838787i
$173$	76.0306	+	76.0306i	0.439483	+	0.439483i	0.891838	−	0.452355i	$-0.149416\pi$
$173$	76.0306	+	76.0306i	0.439483	+	0.439483i	−0.452355	+	0.891838i	$0.649416\pi$
$174$			99.4265i			0.571417i
$175$		0			0
$176$	−675.099			−3.83579
$177$	−54.3985	+	54.3985i	−0.307336	+	0.307336i
$178$	114.241	+	114.241i	0.641806	+	0.641806i
$179$			72.8033i			0.406722i	0.979104	+	0.203361i	$0.0651865\pi$
$179$			72.8033i			0.406722i	−0.979104	+	0.203361i	$0.934813\pi$
$180$		0			0
$181$	116.021			0.641000			0.320500	−	0.947249i	$-0.396149\pi$
$181$	116.021			0.641000			0.320500	+	0.947249i	$0.396149\pi$
$182$	−83.1686	+	83.1686i	−0.456971	+	0.456971i
$183$	−103.423	−	103.423i	−0.565152	−	0.565152i
$184$		−	939.301i		−	5.10489i
$185$		0			0
$186$	54.2286			0.291551
$187$	60.2432	−	60.2432i	0.322156	−	0.322156i
$188$	−598.065	−	598.065i	−3.18120	−	3.18120i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	−134.337			−0.703336			−0.351668	−	0.936125i	$-0.614385\pi$
$191$	−134.337			−0.703336			−0.351668	+	0.936125i	$0.614385\pi$
$192$	−316.150	+	316.150i	−1.64662	+	1.64662i
$193$	5.00682	+	5.00682i	0.0259421	+	0.0259421i	0.719959	−	0.694017i	$-0.244161\pi$
$193$	5.00682	+	5.00682i	0.0259421	+	0.0259421i	−0.694017	+	0.719959i	$0.744161\pi$
$194$		−	138.495i		−	0.713894i
$195$		0			0
$196$	−77.2903			−0.394338
$197$	207.221	−	207.221i	1.05188	−	1.05188i	0.0533056	−	0.998578i	$-0.483024\pi$
$197$	207.221	−	207.221i	1.05188	−	1.05188i	0.998578	−	0.0533056i	$-0.0169757\pi$
$198$	−89.9486	−	89.9486i	−0.454286	−	0.454286i
$199$		−	115.701i		−	0.581414i	−0.956812	−	0.290707i	$-0.906109\pi$
$199$		−	115.701i		−	0.581414i	0.956812	−	0.290707i	$-0.0938905\pi$
$200$		0			0
$201$	−1.62130			−0.00806619
$202$	−147.342	+	147.342i	−0.729416	+	0.729416i
$203$	27.6905	+	27.6905i	0.136406	+	0.136406i
$204$		−	149.028i		−	0.730530i
$205$		0			0
$206$	217.634			1.05648
$207$	72.9629	−	72.9629i	0.352478	−	0.352478i
$208$	500.484	+	500.484i	2.40617	+	2.40617i
$209$		−	132.637i		−	0.634629i
$210$		0			0
$211$	66.2124			0.313803			0.156901	−	0.987614i	$-0.449850\pi$
$211$	66.2124			0.313803			0.156901	+	0.987614i	$0.449850\pi$
$212$	−74.7001	+	74.7001i	−0.352359	+	0.352359i
$213$	126.674	+	126.674i	0.594714	+	0.594714i
$214$			375.004i			1.75236i
$215$		0			0
$216$	−141.903			−0.656957
$217$	15.1028	−	15.1028i	0.0695980	−	0.0695980i
$218$	371.526	+	371.526i	1.70425	+	1.70425i
$219$			135.206i			0.617377i
$220$		0			0
$221$	−89.3225			−0.404174
$222$	−232.639	+	232.639i	−1.04792	+	1.04792i
$223$	51.3641	+	51.3641i	0.230332	+	0.230332i	0.812831	−	0.582499i	$-0.197925\pi$
$223$	51.3641	+	51.3641i	0.230332	+	0.230332i	−0.582499	+	0.812831i	$0.697925\pi$
$224$			344.593i			1.53836i
$225$		0			0
$226$	34.8283			0.154108
$227$	106.842	−	106.842i	0.470670	−	0.470670i	−0.431461	−	0.902132i	$-0.642002\pi$
$227$	106.842	−	106.842i	0.470670	−	0.470670i	0.902132	+	0.431461i	$0.142002\pi$
$228$	−164.058	−	164.058i	−0.719551	−	0.719551i
$229$			88.3402i			0.385765i	0.981222	+	0.192883i	$0.0617836\pi$
$229$			88.3402i			0.385765i	−0.981222	+	0.192883i	$0.938216\pi$
$230$		0			0
$231$	−50.1017			−0.216890
$232$	285.818	−	285.818i	1.23198	−	1.23198i
$233$	260.550	+	260.550i	1.11824	+	1.11824i	0.991999	+	0.126242i	$0.0402915\pi$
$233$	260.550	+	260.550i	1.11824	+	1.11824i	0.126242	+	0.991999i	$0.459708\pi$
$234$			133.367i			0.569942i
$235$		0			0
$236$	490.420			2.07805
$237$	84.2626	−	84.2626i	0.355538	−	0.355538i
$238$	−56.5405	−	56.5405i	−0.237565	−	0.237565i
$239$		−	166.308i		−	0.695851i	−0.937522	−	0.347925i	$-0.886886\pi$
$239$		−	166.308i		−	0.695851i	0.937522	−	0.347925i	$-0.113114\pi$
$240$		0			0
$241$	−309.962			−1.28615			−0.643075	−	0.765804i	$-0.722342\pi$
$241$	−309.962			−1.28615			−0.643075	+	0.765804i	$0.722342\pi$
$242$	4.02490	−	4.02490i	0.0166318	−	0.0166318i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			932.391i			3.82127i
$245$		0			0
$246$	−215.614			−0.876480
$247$	−98.3306	+	98.3306i	−0.398100	+	0.398100i
$248$	−155.889	−	155.889i	−0.628586	−	0.628586i
$249$			174.994i			0.702787i
$250$		0			0
$251$	−403.709			−1.60840			−0.804201	−	0.594358i	$-0.797406\pi$
$251$	−403.709			−1.60840			−0.804201	+	0.594358i	$0.797406\pi$
$252$	−61.9701	+	61.9701i	−0.245913	+	0.245913i
$253$	−265.903	−	265.903i	−1.05100	−	1.05100i
$254$		−	111.242i		−	0.437960i
$255$		0			0
$256$	829.683			3.24095
$257$	−109.310	+	109.310i	−0.425332	+	0.425332i	−0.887035	−	0.461703i	$-0.847239\pi$
$257$	−109.310	+	109.310i	−0.425332	+	0.425332i	0.461703	+	0.887035i	$0.347239\pi$
$258$	−87.7726	−	87.7726i	−0.340204	−	0.340204i
$259$			129.581i			0.500312i
$260$		0			0
$261$	44.4035			0.170128
$262$	−213.124	+	213.124i	−0.813449	+	0.813449i
$263$	−207.442	−	207.442i	−0.788754	−	0.788754i	0.192536	−	0.981290i	$-0.438329\pi$
$263$	−207.442	−	207.442i	−0.788754	−	0.788754i	−0.981290	+	0.192536i	$0.938329\pi$
$264$			517.145i			1.95888i
$265$		0			0
$266$	−124.485			−0.467989
$267$	51.0198	−	51.0198i	0.191086	−	0.191086i
$268$	7.30830	+	7.30830i	0.0272698	+	0.0272698i
$269$			31.5174i			0.117165i	0.998283	+	0.0585825i	$0.0186581\pi$
$269$			31.5174i			0.117165i	−0.998283	+	0.0585825i	$0.981342\pi$
$270$		0			0
$271$	−92.6505			−0.341884			−0.170942	−	0.985281i	$-0.554681\pi$
$271$	−92.6505			−0.341884			−0.170942	+	0.985281i	$0.554681\pi$
$272$	−340.244	+	340.244i	−1.25090	+	1.25090i
$273$	37.1428	+	37.1428i	0.136054	+	0.136054i
$274$		−	805.553i		−	2.93997i
$275$		0			0
$276$	−657.784			−2.38328
$277$	29.1214	−	29.1214i	0.105131	−	0.105131i	−0.652585	−	0.757716i	$-0.726315\pi$
$277$	29.1214	−	29.1214i	0.105131	−	0.105131i	0.757716	+	0.652585i	$0.226315\pi$
$278$	401.274	+	401.274i	1.44343	+	1.44343i
$279$		−	24.2183i		−	0.0868039i
$280$		0			0
$281$	−186.605			−0.664075			−0.332038	−	0.943266i	$-0.607736\pi$
$281$	−186.605			−0.664075			−0.332038	+	0.943266i	$0.607736\pi$
$282$	−363.854	+	363.854i	−1.29026	+	1.29026i
$283$	−199.836	−	199.836i	−0.706135	−	0.706135i	0.259585	−	0.965720i	$-0.416414\pi$
$283$	−199.836	−	199.836i	−0.706135	−	0.706135i	−0.965720	+	0.259585i	$0.916414\pi$
$284$		−	1142.01i		−	4.02115i
$285$		0			0
$286$	486.036			1.69943
$287$	−60.0489	+	60.0489i	−0.209230	+	0.209230i
$288$	276.289	+	276.289i	0.959336	+	0.959336i
$289$			228.276i			0.789882i
$290$		0			0
$291$	−61.8516			−0.212548
$292$	609.461	−	609.461i	2.08720	−	2.08720i
$293$	118.656	+	118.656i	0.404969	+	0.404969i	0.879980	−	0.475011i	$-0.157556\pi$
$293$	118.656	+	118.656i	0.404969	+	0.404969i	−0.475011	+	0.879980i	$0.657556\pi$
$294$			47.0223i			0.159940i
$295$		0			0
$296$	1337.52			4.51865
$297$	−40.1707	+	40.1707i	−0.135255	+	0.135255i
$298$	−392.774	−	392.774i	−1.31803	−	1.31803i
$299$			394.254i			1.31857i
$300$		0			0
$301$	−48.8897			−0.162424
$302$	−560.626	+	560.626i	−1.85638	+	1.85638i
$303$	65.8024	+	65.8024i	0.217170	+	0.217170i
$304$			749.115i			2.46419i
$305$		0			0
$306$	−90.6665			−0.296296
$307$	−315.593	+	315.593i	−1.02799	+	1.02799i	−0.0283934	+	0.999597i	$0.509039\pi$
$307$	−315.593	+	315.593i	−1.02799	+	1.02799i	−0.999597	+	0.0283934i	$0.990961\pi$
$308$	225.842	+	225.842i	0.733252	+	0.733252i
$309$		−	97.1948i		−	0.314546i
$310$		0			0
$311$	569.702			1.83184			0.915919	−	0.401362i	$-0.131463\pi$
$311$	569.702			1.83184			0.915919	+	0.401362i	$0.131463\pi$
$312$	383.385	−	383.385i	1.22880	−	1.22880i
$313$	−222.379	−	222.379i	−0.710475	−	0.710475i	0.256160	−	0.966634i	$-0.417543\pi$
$313$	−222.379	−	222.379i	−0.710475	−	0.710475i	−0.966634	+	0.256160i	$0.917543\pi$
$314$			926.518i			2.95069i
$315$		0			0
$316$	−759.655			−2.40397
$317$	183.394	−	183.394i	0.578530	−	0.578530i	−0.355968	−	0.934498i	$-0.615849\pi$
$317$	183.394	−	183.394i	0.578530	−	0.578530i	0.934498	+	0.355968i	$0.115849\pi$
$318$	45.4464	+	45.4464i	0.142913	+	0.142913i
$319$		−	161.822i		−	0.507281i
$320$		0			0
$321$	167.476			0.521731
$322$	−249.560	+	249.560i	−0.775031	+	0.775031i
$323$	−66.8481	−	66.8481i	−0.206960	−	0.206960i
$324$			99.3733i			0.306708i
$325$		0			0
$326$	918.008			2.81597
$327$	165.922	−	165.922i	0.507408	−	0.507408i
$328$	619.819	+	619.819i	1.88969	+	1.88969i
$329$			202.668i			0.616012i
$330$		0			0
$331$	−215.246			−0.650291			−0.325146	−	0.945664i	$-0.605413\pi$
$331$	−215.246			−0.650291			−0.325146	+	0.945664i	$0.605413\pi$
$332$	788.814	−	788.814i	2.37595	−	2.37595i
$333$	103.896	+	103.896i	0.311999	+	0.311999i
$334$		−	440.638i		−	1.31927i
$335$		0			0
$336$	282.966			0.842161
$337$	401.198	−	401.198i	1.19050	−	1.19050i	0.213571	−	0.976927i	$-0.431490\pi$
$337$	401.198	−	401.198i	1.19050	−	1.19050i	0.976927	−	0.213571i	$-0.0685095\pi$
$338$	103.143	+	103.143i	0.305157	+	0.305157i
$339$		−	15.5542i		−	0.0458827i
$340$		0			0
$341$	−88.2602			−0.258828
$342$	−99.8102	+	99.8102i	−0.291843	+	0.291843i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$			504.635i			1.46696i
$345$		0			0
$346$	−417.012			−1.20524
$347$	122.535	−	122.535i	0.353126	−	0.353126i	−0.508145	−	0.861271i	$-0.669669\pi$
$347$	122.535	−	122.535i	0.353126	−	0.353126i	0.861271	+	0.508145i	$0.169669\pi$
$348$	−200.156	−	200.156i	−0.575161	−	0.575161i
$349$		−	18.8032i		−	0.0538774i	−0.999637	−	0.0269387i	$-0.991424\pi$
$349$		−	18.8032i		−	0.0538774i	0.999637	−	0.0269387i	$-0.00857589\pi$
$350$		0			0
$351$	59.5610			0.169690
$352$	1006.90	−	1006.90i	2.86050	−	2.86050i
$353$	−242.291	−	242.291i	−0.686377	−	0.686377i	0.275052	−	0.961429i	$-0.411305\pi$
$353$	−242.291	−	242.291i	−0.686377	−	0.686377i	−0.961429	+	0.275052i	$0.911305\pi$
$354$		−	298.364i		−	0.842837i
$355$		0			0
$356$	−459.961			−1.29202
$357$	−25.2508	+	25.2508i	−0.0707305	+	0.0707305i
$358$	−199.655	−	199.655i	−0.557697	−	0.557697i
$359$		−	228.420i		−	0.636268i	−0.948046	−	0.318134i	$-0.896944\pi$
$359$		−	228.420i		−	0.636268i	0.948046	−	0.318134i	$-0.103056\pi$
$360$		0			0
$361$	213.821			0.592301
$362$	−318.176	+	318.176i	−0.878938	+	0.878938i
$363$	−1.79750	−	1.79750i	−0.00495180	−	0.00495180i
$364$		−	334.855i		−	0.919931i
$365$		0			0
$366$	567.253			1.54987
$367$	−490.375	+	490.375i	−1.33617	+	1.33617i	−0.436437	+	0.899735i	$0.643760\pi$
$367$	−490.375	+	490.375i	−1.33617	+	1.33617i	−0.899735	+	0.436437i	$0.856240\pi$
$368$	1501.78	+	1501.78i	4.08092	+	4.08092i
$369$			96.2925i			0.260955i
$370$		0			0
$371$	25.3138			0.0682314
$372$	−109.168	+	109.168i	−0.293462	+	0.293462i
$373$	−282.198	−	282.198i	−0.756562	−	0.756562i	0.219133	−	0.975695i	$-0.429677\pi$
$373$	−282.198	−	282.198i	−0.756562	−	0.756562i	−0.975695	+	0.219133i	$0.929677\pi$
$374$			330.422i			0.883480i
$375$		0			0
$376$	2091.92			5.56362
$377$	−119.967	+	119.967i	−0.318215	+	0.318215i
$378$	37.7017	+	37.7017i	0.0997400	+	0.0997400i
$379$		−	389.970i		−	1.02895i	−0.857507	−	0.514473i	$-0.827988\pi$
$379$		−	389.970i		−	1.02895i	0.857507	−	0.514473i	$-0.172012\pi$
$380$		0			0
$381$	−49.6802			−0.130394
$382$	368.406	−	368.406i	0.964412	−	0.964412i
$383$	−330.663	−	330.663i	−0.863350	−	0.863350i	0.128376	−	0.991726i	$-0.459024\pi$
$383$	−330.663	−	330.663i	−0.863350	−	0.863350i	−0.991726	+	0.128376i	$0.959024\pi$
$384$		−	831.663i		−	2.16579i
$385$		0			0
$386$	−27.4614			−0.0711435
$387$	−39.1989	+	39.1989i	−0.101289	+	0.101289i
$388$	278.806	+	278.806i	0.718572	+	0.718572i
$389$			491.789i			1.26424i	0.774871	+	0.632119i	$0.217815\pi$
$389$			491.789i			1.26424i	−0.774871	+	0.632119i	$0.782185\pi$
$390$		0			0
$391$	−268.025			−0.685487
$392$	135.174	−	135.174i	0.344831	−	0.344831i
$393$	95.1803	+	95.1803i	0.242189	+	0.242189i
$394$			1136.56i			2.88468i
$395$		0			0
$396$	362.152			0.914526
$397$	−546.007	+	546.007i	−1.37533	+	1.37533i	−0.523000	+	0.852333i	$0.675187\pi$
$397$	−546.007	+	546.007i	−1.37533	+	1.37533i	−0.852333	+	0.523000i	$0.824813\pi$
$398$	317.299	+	317.299i	0.797234	+	0.797234i
$399$			55.5947i			0.139335i
$400$		0			0
$401$	−631.914			−1.57585			−0.787923	−	0.615774i	$-0.788843\pi$
$401$	−631.914			−1.57585			−0.787923	+	0.615774i	$0.788843\pi$
$402$	4.44626	−	4.44626i	0.0110603	−	0.0110603i
$403$	65.4316	+	65.4316i	0.162361	+	0.162361i
$404$		−	593.230i		−	1.46839i
$405$		0			0
$406$	−151.876			−0.374080
$407$	378.634	−	378.634i	0.930304	−	0.930304i
$408$	260.636	+	260.636i	0.638815	+	0.638815i
$409$		−	72.2476i		−	0.176645i	−0.996092	−	0.0883223i	$-0.971849\pi$
$409$		−	72.2476i		−	0.176645i	0.996092	−	0.0883223i	$-0.0281505\pi$
$410$		0			0
$411$	−359.757			−0.875321
$412$	−438.121	+	438.121i	−1.06340	+	1.06340i
$413$	−83.0950	−	83.0950i	−0.201199	−	0.201199i
$414$			400.186i			0.966633i
$415$		0			0
$416$	−1492.92			−3.58876
$417$	179.207	−	179.207i	0.429754	−	0.429754i
$418$	363.744	+	363.744i	0.870202	+	0.870202i
$419$			334.155i			0.797506i	0.917058	+	0.398753i	$0.130557\pi$
$419$			334.155i			0.797506i	−0.917058	+	0.398753i	$0.869443\pi$
$420$		0			0
$421$	316.485			0.751746			0.375873	−	0.926671i	$-0.377343\pi$
$421$	316.485			0.751746			0.375873	+	0.926671i	$0.377343\pi$
$422$	−181.581	+	181.581i	−0.430286	+	0.430286i
$423$	162.496	+	162.496i	0.384151	+	0.384151i
$424$		−	261.287i		−	0.616243i
$425$		0			0
$426$	−694.781			−1.63094
$427$	157.981	−	157.981i	0.369979	−	0.369979i
$428$	−754.924	−	754.924i	−1.76384	−	1.76384i
$429$		−	217.062i		−	0.505972i
$430$		0			0
$431$	−431.234			−1.00054			−0.500272	−	0.865869i	$-0.666766\pi$
$431$	−431.234			−1.00054			−0.500272	+	0.865869i	$0.666766\pi$
$432$	226.878	−	226.878i	0.525180	−	0.525180i
$433$	13.1404	+	13.1404i	0.0303474	+	0.0303474i	0.722118	−	0.691770i	$-0.243169\pi$
$433$	13.1404	+	13.1404i	0.0303474	+	0.0303474i	−0.691770	+	0.722118i	$0.743169\pi$
$434$			82.8355i			0.190865i
$435$		0			0
$436$	−1495.84			−3.43084
$437$	−295.056	+	295.056i	−0.675185	+	0.675185i
$438$	−370.787	−	370.787i	−0.846546	−	0.846546i
$439$		−	426.469i		−	0.971457i	−0.874110	−	0.485728i	$-0.838554\pi$
$439$		−	426.469i		−	0.971457i	0.874110	−	0.485728i	$-0.161446\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	244.958	−	244.958i	0.554203	−	0.554203i
$443$	−334.181	−	334.181i	−0.754360	−	0.754360i	0.220930	−	0.975290i	$-0.429091\pi$
$443$	−334.181	−	334.181i	−0.754360	−	0.754360i	−0.975290	+	0.220930i	$0.929091\pi$
$444$		−	936.655i		−	2.10958i
$445$		0			0
$446$	−281.721			−0.631662
$447$	−175.412	+	175.412i	−0.392420	+	0.392420i
$448$	−482.927	−	482.927i	−1.07796	−	1.07796i
$449$			463.309i			1.03187i	0.856628	+	0.515935i	$0.172555\pi$
$449$			463.309i			1.03187i	−0.856628	+	0.515935i	$0.827445\pi$
$450$		0			0
$451$	350.925			0.778104
$452$	−70.1132	+	70.1132i	−0.155118	+	0.155118i
$453$	250.374	+	250.374i	0.552702	+	0.552702i
$454$			586.007i			1.29076i
$455$		0			0
$456$	573.843			1.25843
$457$	−356.971	+	356.971i	−0.781119	+	0.781119i	−0.980020	−	0.198901i	$-0.936263\pi$
$457$	−356.971	+	356.971i	−0.781119	+	0.781119i	0.198901	+	0.980020i	$0.436263\pi$
$458$	−242.264	−	242.264i	−0.528960	−	0.528960i
$459$			40.4914i			0.0882165i
$460$		0			0
$461$	−126.296			−0.273960			−0.136980	−	0.990574i	$-0.543740\pi$
$461$	−126.296			−0.273960			−0.136980	+	0.990574i	$0.543740\pi$
$462$	137.399	−	137.399i	0.297400	−	0.297400i
$463$	40.0934	+	40.0934i	0.0865947	+	0.0865947i	0.749077	−	0.662483i	$-0.230497\pi$
$463$	40.0934	+	40.0934i	0.0865947	+	0.0865947i	−0.662483	+	0.749077i	$0.730497\pi$
$464$			913.947i			1.96971i
$465$		0			0
$466$	−1429.06			−3.06666
$467$	−494.819	+	494.819i	−1.05957	+	1.05957i	−0.0614589	+	0.998110i	$0.519575\pi$
$467$	−494.819	+	494.819i	−1.05957	+	1.05957i	−0.998110	+	0.0614589i	$0.980425\pi$
$468$	−268.481	−	268.481i	−0.573678	−	0.573678i
$469$		−	2.47658i		−	0.00528056i
$470$		0			0
$471$	413.780			0.878513
$472$	−857.699	+	857.699i	−1.81716	+	1.81716i
$473$	142.855	+	142.855i	0.302019	+	0.302019i
$474$			462.163i			0.975027i
$475$		0			0
$476$	227.644			0.478244
$477$	20.2962	−	20.2962i	0.0425497	−	0.0425497i
$478$	456.083	+	456.083i	0.954149	+	0.954149i
$479$		−	854.008i		−	1.78290i	−0.453121	−	0.891449i	$-0.649689\pi$
$479$		−	854.008i		−	1.78290i	0.453121	−	0.891449i	$-0.350311\pi$
$480$		0			0
$481$	−561.399			−1.16715
$482$	850.039	−	850.039i	1.76357	−	1.76357i
$483$	111.453	+	111.453i	0.230751	+	0.230751i
$484$			16.2051i			0.0334816i
$485$		0			0
$486$	60.4572			0.124398
$487$	−401.669	+	401.669i	−0.824782	+	0.824782i	−0.986790	−	0.162007i	$-0.948203\pi$
$487$	−401.669	+	401.669i	−0.824782	+	0.824782i	0.162007	+	0.986790i	$0.448203\pi$
$488$	−1630.66	−	1630.66i	−3.34153	−	3.34153i
$489$		−	409.979i		−	0.838403i
$490$		0			0
$491$	−250.314			−0.509805			−0.254903	−	0.966967i	$-0.582043\pi$
$491$	−250.314			−0.509805			−0.254903	+	0.966967i	$0.582043\pi$
$492$	434.054	−	434.054i	0.882224	−	0.882224i
$493$	−81.5571	−	81.5571i	−0.165430	−	0.165430i
$494$		−	539.323i		−	1.09175i
$495$		0			0
$496$	498.480			1.00500
$497$	−193.498	+	193.498i	−0.389332	+	0.389332i
$498$	−479.903	−	479.903i	−0.963661	−	0.963661i
$499$		−	293.789i		−	0.588756i	−0.955689	−	0.294378i	$-0.904888\pi$
$499$		−	293.789i		−	0.588756i	0.955689	−	0.294378i	$-0.0951125\pi$
$500$		0			0
$501$	−196.787			−0.392789
$502$	1107.13	−	1107.13i	2.20544	−	2.20544i
$503$	301.845	+	301.845i	0.600090	+	0.600090i	0.940336	−	0.340246i	$-0.110510\pi$
$503$	301.845	+	301.845i	0.600090	+	0.600090i	−0.340246	+	0.940336i	$0.610510\pi$
$504$		−	216.760i		−	0.430079i
$505$		0			0
$506$	1458.42			2.88226
$507$	46.0633	−	46.0633i	0.0908546	−	0.0908546i
$508$	223.942	+	223.942i	0.440830	+	0.440830i
$509$			495.550i			0.973575i	0.873520	+	0.486787i	$0.161831\pi$
$509$			495.550i			0.973575i	−0.873520	+	0.486787i	$0.838169\pi$
$510$		0			0
$511$	−206.530			−0.404168
$512$	−917.219	+	917.219i	−1.79144	+	1.79144i
$513$	44.5749	+	44.5749i	0.0868906	+	0.0868906i
$514$		−	599.544i		−	1.16643i
$515$		0			0
$516$	353.391			0.684867
$517$	592.194	−	592.194i	1.14544	−	1.14544i
$518$	−355.362	−	355.362i	−0.686027	−	0.686027i
$519$			186.236i			0.358837i
$520$		0			0
$521$	375.437			0.720609			0.360304	−	0.932835i	$-0.382673\pi$
$521$	375.437			0.720609			0.360304	+	0.932835i	$0.382673\pi$
$522$	−121.772	+	121.772i	−0.233280	+	0.233280i
$523$	671.097	+	671.097i	1.28317	+	1.28317i	0.938855	+	0.344314i	$0.111889\pi$
$523$	671.097	+	671.097i	1.28317	+	1.28317i	0.344314	+	0.938855i	$0.388111\pi$
$524$		−	858.082i		−	1.63756i
$525$		0			0
$526$	1137.78			2.16308
$527$	−44.4824	+	44.4824i	−0.0844068	+	0.0844068i
$528$	−826.825	−	826.825i	−1.56596	−	1.56596i
$529$			654.018i			1.23633i
$530$		0			0
$531$	−133.248			−0.250939
$532$	250.602	−	250.602i	0.471057	−	0.471057i
$533$	−260.158	−	260.158i	−0.488101	−	0.488101i
$534$			279.833i			0.524032i
$535$		0			0
$536$	−25.5631			−0.0476923
$537$	−89.1654	+	89.1654i	−0.166044	+	0.166044i
$538$	−86.4331	−	86.4331i	−0.160656	−	0.160656i
$539$		−	76.5316i		−	0.141988i
$540$		0			0
$541$	557.721			1.03091			0.515454	−	0.856917i	$-0.327623\pi$
$541$	557.721			1.03091			0.515454	+	0.856917i	$0.327623\pi$
$542$	254.084	−	254.084i	0.468790	−	0.468790i
$543$	142.096	+	142.096i	0.261687	+	0.261687i
$544$		−	1014.93i		−	1.86569i
$545$		0			0
$546$	−203.721			−0.373115
$547$	656.108	−	656.108i	1.19947	−	1.19947i	0.225141	−	0.974326i	$-0.427716\pi$
$547$	656.108	−	656.108i	1.19947	−	1.19947i	0.974326	−	0.225141i	$-0.0722841\pi$
$548$	1621.66	+	1621.66i	2.95924	+	2.95924i
$549$		−	253.333i		−	0.461445i
$550$		0			0
$551$	−179.564			−0.325888
$552$	1150.40	−	1150.40i	2.08406	−	2.08406i
$553$	128.713	+	128.713i	0.232754	+	0.232754i
$554$			159.725i			0.288312i
$555$		0			0
$556$	−1615.61			−2.90578
$557$	−77.0795	+	77.0795i	−0.138383	+	0.138383i	−0.772905	−	0.634522i	$-0.781197\pi$
$557$	−77.0795	+	77.0795i	−0.138383	+	0.138383i	0.634522	+	0.772905i	$0.281197\pi$
$558$	66.4162	+	66.4162i	0.119025	+	0.119025i
$559$		−	211.811i		−	0.378910i
$560$		0			0
$561$	147.565			0.263040
$562$	511.745	−	511.745i	0.910579	−	0.910579i
$563$	−100.072	−	100.072i	−0.177747	−	0.177747i	0.612626	−	0.790373i	$-0.290113\pi$
$563$	−100.072	−	100.072i	−0.177747	−	0.177747i	−0.790373	+	0.612626i	$0.790113\pi$
$564$		−	1464.95i		−	2.59744i
$565$		0			0
$566$	1096.06			1.93650
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	1997.27	+	1997.27i	3.51631	+	3.51631i
$569$		−	73.3966i		−	0.128992i	−0.997918	−	0.0644961i	$-0.979456\pi$
$569$		−	73.3966i		−	0.128992i	0.997918	−	0.0644961i	$-0.0205440\pi$
$570$		0			0
$571$	−131.618			−0.230504			−0.115252	−	0.993336i	$-0.536768\pi$
$571$	−131.618			−0.230504			−0.115252	+	0.993336i	$0.536768\pi$
$572$	−978.442	+	978.442i	−1.71056	+	1.71056i
$573$	−164.529	−	164.529i	−0.287136	−	0.287136i
$574$		−	329.356i		−	0.573791i
$575$		0			0
$576$	−774.407			−1.34446
$577$	614.754	−	614.754i	1.06543	−	1.06543i	0.0677285	−	0.997704i	$-0.478425\pi$
$577$	614.754	−	614.754i	1.06543	−	1.06543i	0.997704	−	0.0677285i	$-0.0215752\pi$
$578$	−626.023	−	626.023i	−1.08308	−	1.08308i
$579$			12.2642i			0.0211816i
$580$		0			0
$581$	−267.308			−0.460082
$582$	169.622	−	169.622i	0.291446	−	0.291446i
$583$	−73.9668	−	73.9668i	−0.126873	−	0.126873i
$584$			2131.78i			3.65031i
$585$		0			0
$586$	−650.803			−1.11059
$587$	328.506	−	328.506i	0.559636	−	0.559636i	−0.369568	−	0.929204i	$-0.620494\pi$
$587$	328.506	−	328.506i	0.559636	−	0.559636i	0.929204	+	0.369568i	$0.120494\pi$
$588$	−94.6609	−	94.6609i	−0.160988	−	0.160988i
$589$			97.9368i			0.166276i
$590$		0			0
$591$	507.586			0.858860
$592$	−2138.46	+	2138.46i	−3.61227	+	3.61227i
$593$	46.4495	+	46.4495i	0.0783298	+	0.0783298i	0.745186	−	0.666856i	$-0.232361\pi$
$593$	46.4495	+	46.4495i	0.0783298	+	0.0783298i	−0.666856	+	0.745186i	$0.732361\pi$
$594$		−	220.328i		−	0.370923i
$595$		0			0
$596$	1581.39			2.65334
$597$	141.705	−	141.705i	0.237361	−	0.237361i
$598$	−1081.20	−	1081.20i	−1.80803	−	1.80803i
$599$		−	256.090i		−	0.427529i	−0.976885	−	0.213764i	$-0.931428\pi$
$599$		−	256.090i		−	0.427529i	0.976885	−	0.213764i	$-0.0685724\pi$
$600$		0			0
$601$	433.545			0.721372			0.360686	−	0.932687i	$-0.382543\pi$
$601$	433.545			0.721372			0.360686	+	0.932687i	$0.382543\pi$
$602$	134.075	−	134.075i	0.222716	−	0.222716i
$603$	−1.98568	−	1.98568i	−0.00329301	−	0.00329301i
$604$		−	2257.20i		−	3.73709i
$605$		0			0
$606$	−360.913			−0.595565
$607$	−788.344	+	788.344i	−1.29875	+	1.29875i	−0.369540	+	0.929215i	$0.620485\pi$
$607$	−788.344	+	788.344i	−1.29875	+	1.29875i	−0.929215	+	0.369540i	$0.879515\pi$
$608$	−1117.29	−	1117.29i	−1.83765	−	1.83765i
$609$			67.8275i			0.111375i
$610$		0			0
$611$	−878.045			−1.43706
$612$	182.521	−	182.521i	0.298238	−	0.298238i
$613$	−143.879	−	143.879i	−0.234712	−	0.234712i	0.579944	−	0.814656i	$-0.303074\pi$
$613$	−143.879	−	143.879i	−0.234712	−	0.234712i	−0.814656	+	0.579944i	$0.803074\pi$
$614$		−	1730.96i		−	2.81916i
$615$		0			0
$616$	−789.952			−1.28239
$617$	280.216	−	280.216i	0.454159	−	0.454159i	−0.442573	−	0.896732i	$-0.645934\pi$
$617$	280.216	−	280.216i	0.454159	−	0.454159i	0.896732	+	0.442573i	$0.145934\pi$
$618$	266.547	+	266.547i	0.431305	+	0.431305i
$619$			438.884i			0.709020i	0.935052	+	0.354510i	$0.115352\pi$
$619$			438.884i			0.709020i	−0.935052	+	0.354510i	$0.884648\pi$
$620$		0			0
$621$	178.722			0.287797
$622$	−1562.35	+	1562.35i	−2.51181	+	2.51181i
$623$	77.9341	+	77.9341i	0.125095	+	0.125095i
$624$			1225.93i			1.96463i
$625$		0			0
$626$	1219.70			1.94840
$627$	162.447	−	162.447i	0.259086	−	0.259086i
$628$	−1865.18	−	1865.18i	−2.97003	−	2.97003i
$629$		−	381.656i		−	0.606766i
$630$		0			0
$631$	601.250			0.952852			0.476426	−	0.879215i	$-0.341932\pi$
$631$	601.250			0.952852			0.476426	+	0.879215i	$0.341932\pi$
$632$	1328.57	−	1328.57i	2.10216	−	2.10216i
$633$	81.0933	+	81.0933i	0.128109	+	0.128109i
$634$			1005.88i			1.58656i
$635$		0			0
$636$	−182.977			−0.287700
$637$	−56.7366	+	56.7366i	−0.0890685	+	0.0890685i
$638$	443.781	+	443.781i	0.695582	+	0.695582i
$639$			310.287i			0.485582i
$640$		0			0
$641$	803.007			1.25274			0.626371	−	0.779525i	$-0.284540\pi$
$641$	803.007			1.25274			0.626371	+	0.779525i	$0.284540\pi$
$642$	−459.285	+	459.285i	−0.715397	+	0.715397i
$643$	164.070	+	164.070i	0.255163	+	0.255163i	0.823084	−	0.567920i	$-0.192252\pi$
$643$	164.070	+	164.070i	0.255163	+	0.255163i	−0.567920	+	0.823084i	$0.692252\pi$
$644$		−	1004.78i		−	1.56022i
$645$		0			0
$646$	366.648			0.567566
$647$	−495.936	+	495.936i	−0.766517	+	0.766517i	−0.977491	−	0.210975i	$-0.932336\pi$
$647$	−495.936	+	495.936i	−0.766517	+	0.766517i	0.210975	+	0.977491i	$0.432336\pi$
$648$	−173.795	−	173.795i	−0.268202	−	0.268202i
$649$			485.606i			0.748237i
$650$		0			0
$651$	36.9941			0.0568265
$652$	−1848.05	+	1848.05i	−2.83443	+	2.83443i
$653$	812.931	+	812.931i	1.24492	+	1.24492i	0.957936	+	0.286982i	$0.0926519\pi$
$653$	812.931	+	812.931i	1.24492	+	1.24492i	0.286982	+	0.957936i	$0.407348\pi$
$654$			910.050i			1.39151i
$655$		0			0
$656$	−1981.97			−3.02129
$657$	−165.592	+	165.592i	−0.252043	+	0.252043i
$658$	−555.796	−	555.796i	−0.844675	−	0.844675i
$659$		−	135.081i		−	0.204979i	−0.994734	−	0.102490i	$-0.967319\pi$
$659$		−	135.081i		−	0.204979i	0.994734	−	0.102490i	$-0.0326808\pi$
$660$		0			0
$661$	−128.892			−0.194996			−0.0974980	−	0.995236i	$-0.531084\pi$
$661$	−128.892			−0.194996			−0.0974980	+	0.995236i	$0.531084\pi$
$662$	590.291	−	590.291i	0.891678	−	0.891678i
$663$	−109.397	−	109.397i	−0.165003	−	0.165003i
$664$			2759.13i			4.15531i
$665$		0			0
$666$	−569.847			−0.855626
$667$	−359.979	+	359.979i	−0.539698	+	0.539698i
$668$	887.051	+	887.051i	1.32792	+	1.32792i
$669$			125.816i			0.188065i
$670$		0			0
$671$	−923.237			−1.37591
$672$	−422.038	+	422.038i	−0.628033	+	0.628033i
$673$	217.545	+	217.545i	0.323246	+	0.323246i	0.850011	−	0.526765i	$-0.176595\pi$
$673$	217.545	+	217.545i	0.323246	+	0.323246i	−0.526765	+	0.850011i	$0.676595\pi$
$674$			2200.49i			3.26482i
$675$		0			0
$676$	−415.276			−0.614313
$677$	601.143	−	601.143i	0.887952	−	0.887952i	−0.106374	−	0.994326i	$-0.533924\pi$
$677$	601.143	−	601.143i	0.887952	−	0.887952i	0.994326	+	0.106374i	$0.0339242\pi$
$678$	42.6558	+	42.6558i	0.0629142	+	0.0629142i
$679$		−	94.4798i		−	0.139146i
$680$		0			0
$681$	261.709			0.384301
$682$	242.045	−	242.045i	0.354904	−	0.354904i
$683$	16.6370	+	16.6370i	0.0243587	+	0.0243587i	0.719181	−	0.694823i	$-0.244517\pi$
$683$	16.6370	+	16.6370i	0.0243587	+	0.0243587i	−0.694823	+	0.719181i	$0.744517\pi$
$684$		−	401.857i		−	0.587511i
$685$		0			0
$686$	−71.8278			−0.104705
$687$	−108.194	+	108.194i	−0.157488	+	0.157488i
$688$	−806.823	−	806.823i	−1.17271	−	1.17271i
$689$			109.670i			0.159173i
$690$		0			0
$691$	333.673			0.482884			0.241442	−	0.970415i	$-0.422380\pi$
$691$	333.673			0.482884			0.241442	+	0.970415i	$0.422380\pi$
$692$	839.490	−	839.490i	1.21314	−	1.21314i
$693$	−61.3618	−	61.3618i	−0.0885451	−	0.0885451i
$694$			672.077i			0.968411i
$695$		0			0
$696$	700.109			1.00590
$697$	176.863	−	176.863i	0.253749	−	0.253749i
$698$	51.5659	+	51.5659i	0.0738766	+	0.0738766i
$699$			638.215i			0.913040i
$700$		0			0
$701$	978.544			1.39593			0.697963	−	0.716134i	$-0.254090\pi$
$701$	978.544			1.39593			0.697963	+	0.716134i	$0.254090\pi$
$702$	−163.340	+	163.340i	−0.232678	+	0.232678i
$703$	−420.146	−	420.146i	−0.597647	−	0.597647i
$704$			2822.22i			4.00883i
$705$		0			0
$706$	1328.92			1.88232
$707$	−100.515	+	100.515i	−0.142171	+	0.142171i
$708$	600.639	+	600.639i	0.848361	+	0.848361i
$709$		−	775.664i		−	1.09402i	−0.837125	−	0.547012i	$-0.815765\pi$
$709$		−	775.664i		−	1.09402i	0.837125	−	0.547012i	$-0.184235\pi$
$710$		0			0
$711$	206.400			0.290296
$712$	804.428	−	804.428i	1.12982	−	1.12982i
$713$	196.337	+	196.337i	0.275368	+	0.275368i
$714$		−	138.495i		−	0.193971i
$715$		0			0
$716$	803.856			1.12270
$717$	203.685	−	203.685i	0.284080	−	0.284080i
$718$	626.419	+	626.419i	0.872450	+	0.872450i
$719$			195.183i			0.271464i	0.990746	+	0.135732i	$0.0433386\pi$
$719$			195.183i			0.271464i	−0.990746	+	0.135732i	$0.956661\pi$
$720$		0			0
$721$	148.467			0.205919
$722$	−586.381	+	586.381i	−0.812162	+	0.812162i
$723$	−379.624	−	379.624i	−0.525068	−	0.525068i
$724$		−	1281.04i		−	1.76940i
$725$		0			0
$726$	9.85894			0.0135798
$727$	127.418	−	127.418i	0.175265	−	0.175265i	−0.614023	−	0.789288i	$-0.710450\pi$
$727$	127.418	−	127.418i	0.175265	−	0.175265i	0.789288	+	0.614023i	$0.210450\pi$
$728$	585.630	+	585.630i	0.804437	+	0.804437i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	143.995			0.196984
$732$	−1141.94	+	1141.94i	−1.56003	+	1.56003i
$733$	657.079	+	657.079i	0.896425	+	0.896425i	0.995118	−	0.0986932i	$-0.0314662\pi$
$733$	657.079	+	657.079i	0.896425	+	0.896425i	−0.0986932	+	0.995118i	$0.531466\pi$
$734$		−	2689.61i		−	3.66431i
$735$		0			0
$736$	−4479.74			−6.08660
$737$	−7.23655	+	7.23655i	−0.00981893	+	0.00981893i
$738$	−264.072	−	264.072i	−0.357821	−	0.357821i
$739$		−	1191.53i		−	1.61235i	−0.591676	−	0.806176i	$-0.701534\pi$
$739$		−	1191.53i		−	1.61235i	0.591676	−	0.806176i	$-0.298466\pi$
$740$		0			0
$741$	−240.860			−0.325047
$742$	−69.4206	+	69.4206i	−0.0935588	+	0.0935588i
$743$	−115.268	−	115.268i	−0.155138	−	0.155138i	0.625270	−	0.780408i	$-0.284989\pi$
$743$	−115.268	−	115.268i	−0.155138	−	0.155138i	−0.780408	+	0.625270i	$0.784989\pi$
$744$		−	381.849i		−	0.513238i
$745$		0			0
$746$	1547.79			2.07479
$747$	−214.323	+	214.323i	−0.286912	+	0.286912i
$748$	−665.174	−	665.174i	−0.889270	−	0.889270i
$749$			255.823i			0.341553i
$750$		0			0
$751$	−627.744			−0.835878			−0.417939	−	0.908475i	$-0.637247\pi$
$751$	−627.744			−0.835878			−0.417939	+	0.908475i	$0.637247\pi$
$752$	−3344.62	+	3344.62i	−4.44763	+	4.44763i
$753$	−494.440	−	494.440i	−0.656627	−	0.656627i
$754$		−	657.994i		−	0.872671i
$755$		0			0
$756$	−151.795			−0.200787
$757$	−117.159	+	117.159i	−0.154767	+	0.154767i	−0.780243	−	0.625476i	$-0.784905\pi$
$757$	−117.159	+	117.159i	−0.154767	+	0.154767i	0.625476	+	0.780243i	$0.284905\pi$
$758$	1069.45	+	1069.45i	1.41089	+	1.41089i
$759$		−	651.327i		−	0.858138i
$760$		0			0
$761$	1272.61			1.67229			0.836145	−	0.548509i	$-0.184804\pi$
$761$	1272.61			1.67229			0.836145	+	0.548509i	$0.184804\pi$
$762$	136.243	−	136.243i	0.178796	−	0.178796i
$763$	253.451	+	253.451i	0.332176	+	0.332176i
$764$			1483.28i			1.94147i
$765$		0			0
$766$	1813.62			2.36765
$767$	360.003	−	360.003i	0.469365	−	0.469365i
$768$	1016.15	+	1016.15i	1.32311	+	1.32311i
$769$			1506.02i			1.95842i	0.202857	+	0.979208i	$0.434978\pi$
$769$			1506.02i			1.95842i	−0.202857	+	0.979208i	$0.565022\pi$
$770$		0			0
$771$	−267.754			−0.347282
$772$	55.2827	−	55.2827i	0.0716097	−	0.0716097i
$773$	580.116	+	580.116i	0.750474	+	0.750474i	0.974568	−	0.224094i	$-0.0719422\pi$
$773$	580.116	+	580.116i	0.750474	+	0.750474i	−0.224094	+	0.974568i	$0.571942\pi$
$774$		−	214.998i		−	0.277775i
$775$		0			0
$776$	−975.212			−1.25672
$777$	−158.703	+	158.703i	−0.204252	+	0.204252i
$778$	−1348.68	−	1348.68i	−1.73352	−	1.73352i
$779$		−	389.399i		−	0.499870i
$780$		0			0
$781$	1130.80			1.44788
$782$	735.032	−	735.032i	0.939939	−	0.939939i
$783$	54.3830	+	54.3830i	0.0694546	+	0.0694546i
$784$			432.238i			0.551324i
$785$		0			0
$786$	−522.044			−0.664179
$787$	138.491	−	138.491i	0.175973	−	0.175973i	−0.613625	−	0.789598i	$-0.710289\pi$
$787$	138.491	−	138.491i	0.175973	−	0.175973i	0.789598	+	0.613625i	$0.210289\pi$
$788$	−2288.03	−	2288.03i	−2.90359	−	2.90359i
$789$		−	508.128i		−	0.644015i
$790$		0			0
$791$	23.7595			0.0300372
$792$	−633.371	+	633.371i	−0.799710	+	0.799710i
$793$	684.441	+	684.441i	0.863103	+	0.863103i
$794$		−	2994.74i		−	3.77171i
$795$		0			0
$796$	−1277.51			−1.60492
$797$	−1122.40	+	1122.40i	−1.40829	+	1.40829i	−0.639475	+	0.768811i	$0.720848\pi$
$797$	−1122.40	+	1122.40i	−1.40829	+	1.40829i	−0.768811	+	0.639475i	$0.779152\pi$
$798$	−152.463	−	152.463i	−0.191056	−	0.191056i
$799$		−	596.921i		−	0.747085i
$800$		0			0
$801$	124.973			0.156021
$802$	1732.96	−	1732.96i	2.16080	−	2.16080i
$803$	603.478	+	603.478i	0.751529	+	0.751529i
$804$			17.9016i			0.0222657i
$805$		0			0
$806$	−358.879			−0.445259
$807$	−38.6007	+	38.6007i	−0.0478324	+	0.0478324i
$808$	1037.50	+	1037.50i	1.28404	+	1.28404i
$809$		−	30.2805i		−	0.0374295i	−0.999825	−	0.0187147i	$-0.994043\pi$
$809$		−	30.2805i		−	0.0374295i	0.999825	−	0.0187147i	$-0.00595744\pi$
$810$		0			0
$811$	−1118.58			−1.37926			−0.689629	−	0.724163i	$-0.742226\pi$
$811$	−1118.58			−1.37926			−0.689629	+	0.724163i	$0.742226\pi$
$812$	305.744	−	305.744i	0.376532	−	0.376532i
$813$	−113.473	−	113.473i	−0.139573	−	0.139573i
$814$			2076.73i			2.55126i
$815$		0			0
$816$	−833.424			−1.02135
$817$	158.517	−	158.517i	0.194024	−	0.194024i
$818$	198.132	+	198.132i	0.242215	+	0.242215i
$819$			90.9810i			0.111088i
$820$		0			0
$821$	−923.859			−1.12528			−0.562642	−	0.826700i	$-0.690215\pi$
$821$	−923.859			−1.12528			−0.562642	+	0.826700i	$0.690215\pi$
$822$	986.597	−	986.597i	1.20024	−	1.20024i
$823$	186.823	+	186.823i	0.227002	+	0.227002i	0.811439	−	0.584437i	$-0.198685\pi$
$823$	186.823	+	186.823i	0.227002	+	0.227002i	−0.584437	+	0.811439i	$0.698685\pi$
$824$		−	1532.47i		−	1.85979i
$825$		0			0
$826$	455.759			0.551766
$827$	−59.3982	+	59.3982i	−0.0718237	+	0.0718237i	−0.742106	−	0.670282i	$-0.766173\pi$
$827$	−59.3982	+	59.3982i	−0.0718237	+	0.0718237i	0.670282	+	0.742106i	$0.266173\pi$
$828$	−805.618	−	805.618i	−0.972968	−	0.972968i
$829$			1486.79i			1.79347i	0.442564	+	0.896737i	$0.354069\pi$
$829$			1486.79i			1.79347i	−0.442564	+	0.896737i	$0.645931\pi$
$830$		0			0
$831$	71.3326			0.0858394
$832$	2092.25	−	2092.25i	2.51472	−	2.51472i
$833$	−38.5712	−	38.5712i	−0.0463040	−	0.0463040i
$834$			982.916i			1.17856i
$835$		0			0
$836$	−1464.51			−1.75181
$837$	29.6612	−	29.6612i	0.0354376	−	0.0354376i
$838$	−916.386	−	916.386i	−1.09354	−	1.09354i
$839$			453.536i			0.540568i	0.962781	+	0.270284i	$0.0871176\pi$
$839$			453.536i			0.540568i	−0.962781	+	0.270284i	$0.912882\pi$
$840$		0			0
$841$	621.925			0.739507
$842$	−867.927	+	867.927i	−1.03079	+	1.03079i
$843$	−228.544	−	228.544i	−0.271108	−	0.271108i
$844$		−	731.082i		−	0.866211i
$845$		0			0
$846$	−891.257			−1.05349
$847$	2.74573	−	2.74573i	0.00324172	−	0.00324172i
$848$	417.753	+	417.753i	0.492633	+	0.492633i
$849$		−	489.497i		−	0.576557i
$850$		0			0
$851$	−1684.56			−1.97951
$852$	1398.67	−	1398.67i	1.64163	−	1.64163i
$853$	827.180	+	827.180i	0.969730	+	0.969730i	0.999555	−	0.0298251i	$-0.00949502\pi$
$853$	827.180	+	827.180i	0.969730	+	0.969730i	−0.0298251	+	0.999555i	$0.509495\pi$
$854$			866.493i			1.01463i
$855$		0			0
$856$	2640.58			3.08479
$857$	264.140	−	264.140i	0.308215	−	0.308215i	−0.536002	−	0.844217i	$-0.680066\pi$
$857$	264.140	−	264.140i	0.308215	−	0.308215i	0.844217	+	0.536002i	$0.180066\pi$
$858$	595.270	+	595.270i	0.693788	+	0.693788i
$859$			710.066i			0.826619i	0.910591	+	0.413310i	$0.135627\pi$
$859$			710.066i			0.826619i	−0.910591	+	0.413310i	$0.864373\pi$
$860$		0			0
$861$	−147.089			−0.170835
$862$	1182.61	−	1182.61i	1.37194	−	1.37194i
$863$	−966.508	−	966.508i	−1.11994	−	1.11994i	−0.991750	−	0.128190i	$-0.959083\pi$
$863$	−966.508	−	966.508i	−1.11994	−	1.11994i	−0.128190	−	0.991750i	$-0.540917\pi$
$864$			676.766i			0.783294i
$865$		0			0
$866$	−72.0725			−0.0832246
$867$	−279.580	+	279.580i	−0.322468	+	0.322468i
$868$	−166.757	−	166.757i	−0.192116	−	0.192116i
$869$		−	752.197i		−	0.865590i
$870$		0			0
$871$	10.7296			0.0123187
$872$	2616.09	−	2616.09i	3.00011	−	3.00011i
$873$	−75.7524	−	75.7524i	−0.0867725	−	0.0867725i
$874$		−	1618.32i		−	1.85162i
$875$		0			0
$876$	1492.87			1.70419
$877$	1016.78	−	1016.78i	1.15939	−	1.15939i	0.174779	−	0.984608i	$-0.444079\pi$
$877$	1016.78	−	1016.78i	1.15939	−	1.15939i	0.984608	−	0.174779i	$-0.0559212\pi$
$878$	1169.55	+	1169.55i	1.33206	+	1.33206i
$879$			290.646i			0.330656i
$880$		0			0
$881$	615.784			0.698961			0.349480	−	0.936944i	$-0.386358\pi$
$881$	615.784			0.698961			0.349480	+	0.936944i	$0.386358\pi$
$882$	−57.5903	+	57.5903i	−0.0652952	+	0.0652952i
$883$	393.825	+	393.825i	0.446008	+	0.446008i	0.894025	−	0.448017i	$-0.147870\pi$
$883$	393.825	+	393.825i	0.446008	+	0.446008i	−0.448017	+	0.894025i	$0.647870\pi$
$884$			986.252i			1.11567i
$885$		0			0
$886$	1832.92			2.06875
$887$	−1046.82	+	1046.82i	−1.18018	+	1.18018i	−0.200486	+	0.979697i	$0.564252\pi$
$887$	−1046.82	+	1046.82i	−1.18018	+	1.18018i	−0.979697	+	0.200486i	$0.935748\pi$
$888$	1638.12	+	1638.12i	1.84473	+	1.84473i
$889$		−	75.8878i		−	0.0853631i
$890$		0			0
$891$	−98.3978			−0.110435
$892$	567.135	−	567.135i	0.635802	−	0.635802i
$893$	−657.120	−	657.120i	−0.735857	−	0.735857i
$894$		−	962.096i		−	1.07617i
$895$		0			0
$896$	1270.39			1.41784
$897$	−482.860	+	482.860i	−0.538306	+	0.538306i
$898$	−1270.58	−	1270.58i	−1.41490	−	1.41490i
$899$			119.486i			0.132910i
$900$		0			0
$901$	−74.5572			−0.0827494
$902$	−962.375	+	962.375i	−1.06693	+	1.06693i
$903$	−59.8774	−	59.8774i	−0.0663094	−	0.0663094i
$904$		−	245.243i		−	0.271286i
$905$		0			0
$906$	−1373.25			−1.51573
$907$	343.564	−	343.564i	0.378791	−	0.378791i	−0.491875	−	0.870666i	$-0.663688\pi$
$907$	343.564	−	343.564i	0.378791	−	0.378791i	0.870666	+	0.491875i	$0.163688\pi$
$908$	−1179.70	−	1179.70i	−1.29922	−	1.29922i
$909$			161.182i			0.177318i
$910$		0			0
$911$	313.466			0.344090			0.172045	−	0.985089i	$-0.444963\pi$
$911$	313.466			0.344090			0.172045	+	0.985089i	$0.444963\pi$
$912$	−917.475	+	917.475i	−1.00600	+	1.00600i
$913$	781.071	+	781.071i	0.855499	+	0.855499i
$914$		−	1957.91i		−	2.14214i
$915$		0			0
$916$	975.406			1.06485
$917$	−145.390	+	145.390i	−0.158550	+	0.158550i
$918$	−111.043	−	111.043i	−0.120962	−	0.120962i
$919$			229.218i			0.249422i	0.992193	+	0.124711i	$0.0398003\pi$
$919$			229.218i			0.249422i	−0.992193	+	0.124711i	$0.960200\pi$
$920$		0			0
$921$	−773.042			−0.839351
$922$	346.352	−	346.352i	0.375653	−	0.375653i
$923$	−838.315	−	838.315i	−0.908250	−	0.908250i
$924$			553.197i			0.598698i
$925$		0			0
$926$	−219.904			−0.237477
$927$	119.039	−	119.039i	0.128413	−	0.128413i
$928$	−1363.13	−	1363.13i	−1.46889	−	1.46889i
$929$			1037.08i			1.11634i	0.829728	+	0.558168i	$0.188495\pi$
$929$			1037.08i			1.11634i	−0.829728	+	0.558168i	$0.811505\pi$
$930$		0			0
$931$	−84.9223			−0.0912162
$932$	2876.86	−	2876.86i	3.08676	−	3.08676i
$933$	697.739	+	697.739i	0.747845	+	0.747845i
$934$		−	2713.98i		−	2.90576i
$935$		0			0
$936$	939.097			1.00331
$937$	147.149	−	147.149i	0.157043	−	0.157043i	−0.624212	−	0.781255i	$-0.714580\pi$
$937$	147.149	−	147.149i	0.157043	−	0.157043i	0.781255	+	0.624212i	$0.214580\pi$
$938$	6.79177	+	6.79177i	0.00724070	+	0.00724070i
$939$		−	544.714i		−	0.580100i
$940$		0			0
$941$	−1810.77			−1.92431			−0.962154	−	0.272505i	$-0.912148\pi$
$941$	−1810.77			−1.92431			−0.962154	+	0.272505i	$0.912148\pi$
$942$	−1134.75	+	1134.75i	−1.20462	+	1.20462i
$943$	−780.642	−	780.642i	−0.827828	−	0.827828i
$944$		−	2742.62i		−	2.90532i
$945$		0			0
$946$	−783.531			−0.828257
$947$	−147.333	+	147.333i	−0.155579	+	0.155579i	−0.780604	−	0.625026i	$-0.785089\pi$
$947$	−147.333	+	147.333i	−0.155579	+	0.155579i	0.625026	+	0.780604i	$0.285089\pi$
$948$	−930.383	−	930.383i	−0.981417	−	0.981417i
$949$		−	894.776i		−	0.942861i
$950$		0			0
$951$	449.222			0.472368
$952$	−398.129	+	398.129i	−0.418202	+	0.418202i
$953$	−85.4967	−	85.4967i	−0.0897132	−	0.0897132i	0.660826	−	0.750539i	$-0.270206\pi$
$953$	−85.4967	−	85.4967i	−0.0897132	−	0.0897132i	−0.750539	+	0.660826i	$0.770206\pi$
$954$			111.321i			0.116688i
$955$		0			0
$956$	−1836.29			−1.92081
$957$	198.191	−	198.191i	0.207096	−	0.207096i
$958$	2342.03	+	2342.03i	2.44471	+	2.44471i
$959$		−	549.538i		−	0.573032i
$960$		0			0
$961$	−895.830			−0.932186
$962$	1539.58	−	1539.58i	1.60039	−	1.60039i
$963$	205.115	+	205.115i	0.212996	+	0.212996i
$964$			3422.44i			3.55025i
$965$		0			0
$966$	−611.295			−0.632810
$967$	322.508	−	322.508i	0.333514	−	0.333514i	−0.520406	−	0.853919i	$-0.674219\pi$
$967$	322.508	−	322.508i	0.333514	−	0.333514i	0.853919	+	0.520406i	$0.174219\pi$
$968$	−28.3412	−	28.3412i	−0.0292781	−	0.0292781i
$969$		−	163.744i		−	0.168982i
$970$		0			0
$971$	−1373.43			−1.41445			−0.707223	−	0.706991i	$-0.750052\pi$
$971$	−1373.43			−1.41445			−0.707223	+	0.706991i	$0.750052\pi$
$972$	−121.707	+	121.707i	−0.125213	+	0.125213i
$973$	273.744	+	273.744i	0.281340	+	0.281340i
$974$		−	2203.07i		−	2.26188i
$975$		0			0
$976$	5214.30			5.34252
$977$	−40.3145	+	40.3145i	−0.0412635	+	0.0412635i	−0.727437	−	0.686174i	$-0.759289\pi$
$977$	−40.3145	+	40.3145i	−0.0412635	+	0.0412635i	0.686174	+	0.727437i	$0.259289\pi$
$978$	1124.33	+	1124.33i	1.14962	+	1.14962i
$979$		−	455.445i		−	0.465215i
$980$		0			0
$981$	406.425			0.414297
$982$	686.461	−	686.461i	0.699044	−	0.699044i
$983$	−1061.02	−	1061.02i	−1.07937	−	1.07937i	−0.996566	−	0.0828047i	$-0.973612\pi$
$983$	−1061.02	−	1061.02i	−1.07937	−	1.07937i	−0.0828047	−	0.996566i	$-0.526388\pi$
$984$			1518.24i			1.54293i
$985$		0			0
$986$	447.324			0.453675
$987$	−248.217	+	248.217i	−0.251486	+	0.251486i
$988$	1085.72	+	1085.72i	1.09890	+	1.09890i
$989$		−	635.570i		−	0.642640i
$990$		0			0
$991$	1624.85			1.63960			0.819802	−	0.572647i	$-0.194083\pi$
$991$	1624.85			1.63960			0.819802	+	0.572647i	$0.194083\pi$
$992$	−743.471	+	743.471i	−0.749467	+	0.749467i
$993$	−263.622	−	263.622i	−0.265480	−	0.265480i
$994$		−	1061.30i		−	1.06770i
$995$		0			0
$996$	1932.19			1.93995
$997$	273.633	−	273.633i	0.274456	−	0.274456i	−0.556435	−	0.830891i	$-0.687831\pi$
$997$	273.633	−	273.633i	0.274456	−	0.274456i	0.830891	+	0.556435i	$0.187831\pi$
$998$	805.687	+	805.687i	0.807301	+	0.807301i
$999$			254.492i			0.254746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.43.1		24
5.2	odd	4	inner	525.3.l.e.232.1		24
5.3	odd	4		105.3.l.a.22.12	✓	24
5.4	even	2		105.3.l.a.43.12	yes	24
15.8	even	4		315.3.o.b.127.1		24
15.14	odd	2		315.3.o.b.253.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.12	✓	24	5.3	odd	4
105.3.l.a.43.12	yes	24	5.4	even	2
315.3.o.b.127.1		24	15.8	even	4
315.3.o.b.253.1		24	15.14	odd	2
525.3.l.e.43.1		24	1.1	even	1	trivial
525.3.l.e.232.1		24	5.2	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-2.74240 + 2.74240i) q^{2} +(1.22474 + 1.22474i) q^{3} -11.0415i q^{4} -6.71747 q^{6} +(-1.87083 + 1.87083i) q^{7} +(19.3105 + 19.3105i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-2.74240 + 2.74240i) q^{2} +(1.22474 + 1.22474i) q^{3} -11.0415i q^{4} -6.71747 q^{6} +(-1.87083 + 1.87083i) q^{7} +(19.3105 + 19.3105i) q^{8} +3.00000i q^{9} +10.9331 q^{11} +(13.5230 - 13.5230i) q^{12} +(-8.10523 - 8.10523i) q^{13} -10.2611i q^{14} -61.7483 q^{16} +(5.51018 - 5.51018i) q^{17} +(-8.22719 - 8.22719i) q^{18} -12.1318i q^{19} -4.58258 q^{21} +(-29.9829 + 29.9829i) q^{22} +(-24.3210 - 24.3210i) q^{23} +47.3009i q^{24} +44.4555 q^{26} +(-3.67423 + 3.67423i) q^{27} +(20.6567 + 20.6567i) q^{28} -14.8012i q^{29} -8.07276 q^{31} +(92.0962 - 92.0962i) q^{32} +(13.3902 + 13.3902i) q^{33} +30.2222i q^{34} +33.1244 q^{36} +(34.6319 - 34.6319i) q^{37} +(33.2701 + 33.2701i) q^{38} -19.8537i q^{39} +32.0975 q^{41} +(12.5672 - 12.5672i) q^{42} +(13.0663 + 13.0663i) q^{43} -120.717i q^{44} +133.395 q^{46} +(54.1653 - 54.1653i) q^{47} +(-75.6259 - 75.6259i) q^{48} -7.00000i q^{49} +13.4971 q^{51} +(-89.4937 + 89.4937i) q^{52} +(-6.76541 - 6.76541i) q^{53} -20.1524i q^{54} -72.2534 q^{56} +(14.8583 - 14.8583i) q^{57} +(40.5907 + 40.5907i) q^{58} +44.4162i q^{59} -84.4444 q^{61} +(22.1387 - 22.1387i) q^{62} +(-5.61249 - 5.61249i) q^{63} +258.136i q^{64} -73.4427 q^{66} +(-0.661895 + 0.661895i) q^{67} +(-60.8405 - 60.8405i) q^{68} -59.5739i q^{69} +103.429 q^{71} +(-57.9316 + 57.9316i) q^{72} +(55.1974 + 55.1974i) q^{73} +189.949i q^{74} -133.952 q^{76} +(-20.4539 + 20.4539i) q^{77} +(54.4467 + 54.4467i) q^{78} -68.8001i q^{79} -9.00000 q^{81} +(-88.0241 + 88.0241i) q^{82} +(71.4410 + 71.4410i) q^{83} +50.5984i q^{84} -71.6660 q^{86} +(18.1277 - 18.1277i) q^{87} +(211.124 + 211.124i) q^{88} -41.6575i q^{89} +30.3270 q^{91} +(-268.539 + 268.539i) q^{92} +(-9.88708 - 9.88708i) q^{93} +297.086i q^{94} +225.589 q^{96} +(-25.2508 + 25.2508i) q^{97} +(19.1968 + 19.1968i) q^{98} +32.7993i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 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

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