LMFDB - Embedded newform 525.3.l.e.232.1

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			232.1
Character	$\chi$	$=$	525.232
Dual form			525.3.l.e.43.1

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.74240	−	2.74240i	−1.37120	−	1.37120i	−0.858671	−	0.512527i	$-0.828709\pi$
$2$	−2.74240	−	2.74240i	−1.37120	−	1.37120i	−0.512527	−	0.858671i	$-0.671291\pi$
$3$	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	−0.946419	−	0.322940i	$-0.895329\pi$
$13$	−8.10523	+	8.10523i	−0.623479	+	0.623479i	0.322940	+	0.946419i	$0.395329\pi$
$14$			10.2611i			0.732936i
$15$		0			0
$16$	−61.7483			−3.85927
$17$	5.51018	+	5.51018i	0.324128	+	0.324128i	0.850348	−	0.526220i	$-0.176391\pi$
$17$	5.51018	+	5.51018i	0.324128	+	0.324128i	−0.526220	+	0.850348i	$0.676391\pi$
$18$	−8.22719	+	8.22719i	−0.457066	+	0.457066i
$19$			12.1318i			0.638513i	0.947668	+	0.319257i	$0.103433\pi$
$19$			12.1318i			0.638513i	−0.947668	+	0.319257i	$0.896567\pi$
$20$		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	−0.0591858	+	0.998247i	$0.518850\pi$
$23$	−24.3210	+	24.3210i	−1.05743	+	1.05743i	−0.998247	+	0.0591858i	$0.981150\pi$
$24$		−	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	$0.0821389\pi$
$29$			14.8012i			0.510385i	−0.966890	+	0.255193i	$0.917861\pi$
$30$		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	0.998072	−	0.0620735i	$-0.0197713\pi$
$37$	34.6319	+	34.6319i	0.935998	+	0.935998i	−0.0620735	+	0.998072i	$0.519771\pi$
$38$	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	−0.538657	−	0.842525i	$-0.681068\pi$
$43$	13.0663	−	13.0663i	0.303868	−	0.303868i	0.842525	+	0.538657i	$0.181068\pi$
$44$			120.717i			2.74358i
$45$		0			0
$46$	133.395			2.89990
$47$	54.1653	+	54.1653i	1.15245	+	1.15245i	0.986059	+	0.166394i	$0.0532124\pi$
$47$	54.1653	+	54.1653i	1.15245	+	1.15245i	0.166394	+	0.986059i	$0.446788\pi$
$48$	−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	−0.768045	−	0.640396i	$-0.778770\pi$
$53$	−6.76541	+	6.76541i	−0.127649	+	0.127649i	0.640396	+	0.768045i	$0.278770\pi$
$54$			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	$-0.877159\pi$
$59$		−	44.4162i		−	0.752816i	0.926454	−	0.376408i	$-0.122841\pi$
$60$		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	0.702150	−	0.712029i	$-0.252224\pi$
$67$	−0.661895	−	0.661895i	−0.00987903	−	0.00987903i	−0.712029	+	0.702150i	$0.752224\pi$
$68$	−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	−0.219486	−	0.975616i	$-0.570438\pi$
$73$	55.1974	−	55.1974i	0.756129	−	0.756129i	0.975616	+	0.219486i	$0.0704382\pi$
$74$		−	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	$0.143408\pi$
$79$			68.8001i			0.870887i	−0.900216	+	0.435444i	$0.856592\pi$
$80$		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	−0.130688	−	0.991423i	$-0.541719\pi$
$83$	71.4410	−	71.4410i	0.860735	−	0.860735i	0.991423	+	0.130688i	$0.0417188\pi$
$84$		−	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	$0.0751917\pi$
$89$			41.6575i			0.468062i	−0.972229	+	0.234031i	$0.924808\pi$
$90$		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	0.564865	−	0.825183i	$-0.308928\pi$
$97$	−25.2508	−	25.2508i	−0.260318	−	0.260318i	−0.825183	+	0.564865i	$0.808928\pi$
$98$	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	−0.872985	−	0.487746i	$-0.837819\pi$
$103$	−39.6796	+	39.6796i	−0.385239	+	0.385239i	0.487746	+	0.872985i	$0.337819\pi$
$104$			313.032i			3.00993i
$105$		0			0
$106$	37.1069			0.350065
$107$	68.3716	+	68.3716i	0.638987	+	0.638987i	0.950306	−	0.311318i	$-0.100771\pi$
$107$	68.3716	+	68.3716i	0.638987	+	0.638987i	−0.311318	+	0.950306i	$0.600771\pi$
$108$	40.5690	−	40.5690i	0.375639	−	0.375639i
$109$			135.475i			1.24289i	0.783458	+	0.621445i	$0.213454\pi$
$109$			135.475i			1.24289i	−0.783458	+	0.621445i	$0.786546\pi$
$110$		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	−0.734646	−	0.678451i	$-0.762652\pi$
$113$	−6.34998	+	6.34998i	−0.0561945	+	0.0561945i	0.678451	+	0.734646i	$0.262652\pi$
$114$		−	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	0.622734	−	0.782434i	$-0.286022\pi$
$127$	−20.2819	−	20.2819i	−0.159700	−	0.159700i	−0.782434	+	0.622734i	$0.786022\pi$
$128$	−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	−0.997195	−	0.0748506i	$-0.976152\pi$
$137$	−146.870	−	146.870i	−1.07205	−	1.07205i	−0.0748506	−	0.997195i	$-0.523848\pi$
$138$	163.375	−	163.375i	1.18388	−	1.18388i
$139$			146.322i			1.05268i	0.850275	+	0.526339i	$0.176436\pi$
$139$			146.322i			1.05268i	−0.850275	+	0.526339i	$0.823564\pi$
$140$		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	$-0.840414\pi$
$149$		−	143.223i		−	0.961228i	0.876932	−	0.480614i	$-0.159586\pi$
$150$		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	0.996868	+	0.0790870i	$0.0252005\pi$
$157$	168.925	+	168.925i	1.07595	+	1.07595i	0.0790870	+	0.996868i	$0.474800\pi$
$158$	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	−0.0271997	+	0.999630i	$0.508659\pi$
$163$	−167.373	+	167.373i	−1.02683	+	1.02683i	−0.999630	+	0.0271997i	$0.991341\pi$
$164$			354.404i			2.16100i
$165$		0			0
$166$	−391.839			−2.36048
$167$	−80.3381	−	80.3381i	−0.481066	−	0.481066i	0.424406	−	0.905472i	$-0.360483\pi$
$167$	−80.3381	−	80.3381i	−0.481066	−	0.481066i	−0.905472	+	0.424406i	$0.860483\pi$
$168$	−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	−0.452355	−	0.891838i	$-0.649416\pi$
$173$	76.0306	−	76.0306i	0.439483	−	0.439483i	0.891838	+	0.452355i	$0.149416\pi$
$174$		−	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	$-0.934813\pi$
$179$		−	72.8033i		−	0.406722i	0.979104	−	0.203361i	$-0.0651865\pi$
$180$		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	−0.694017	−	0.719959i	$-0.744161\pi$
$193$	5.00682	−	5.00682i	0.0259421	−	0.0259421i	0.719959	+	0.694017i	$0.244161\pi$
$194$			138.495i			0.713894i
$195$		0			0
$196$	−77.2903			−0.394338
$197$	207.221	+	207.221i	1.05188	+	1.05188i	0.998578	+	0.0533056i	$0.0169757\pi$
$197$	207.221	+	207.221i	1.05188	+	1.05188i	0.0533056	+	0.998578i	$0.483024\pi$
$198$	−89.9486	+	89.9486i	−0.454286	+	0.454286i
$199$			115.701i			0.581414i	0.956812	+	0.290707i	$0.0938905\pi$
$199$			115.701i			0.581414i	−0.956812	+	0.290707i	$0.906109\pi$
$200$		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	−0.582499	−	0.812831i	$-0.697925\pi$
$223$	51.3641	−	51.3641i	0.230332	−	0.230332i	0.812831	+	0.582499i	$0.197925\pi$
$224$		−	344.593i		−	1.53836i
$225$		0			0
$226$	34.8283			0.154108
$227$	106.842	+	106.842i	0.470670	+	0.470670i	0.902132	−	0.431461i	$-0.142002\pi$
$227$	106.842	+	106.842i	0.470670	+	0.470670i	−0.431461	+	0.902132i	$0.642002\pi$
$228$	−164.058	+	164.058i	−0.719551	+	0.719551i
$229$		−	88.3402i		−	0.385765i	−0.981222	−	0.192883i	$-0.938216\pi$
$229$		−	88.3402i		−	0.385765i	0.981222	−	0.192883i	$-0.0617836\pi$
$230$		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	0.126242	−	0.991999i	$-0.459708\pi$
$233$	260.550	−	260.550i	1.11824	−	1.11824i	0.991999	−	0.126242i	$-0.0402915\pi$
$234$		−	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	$0.113114\pi$
$239$			166.308i			0.695851i	−0.937522	+	0.347925i	$0.886886\pi$
$240$		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	0.461703	−	0.887035i	$-0.347239\pi$
$257$	−109.310	−	109.310i	−0.425332	−	0.425332i	−0.887035	+	0.461703i	$0.847239\pi$
$258$	−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	−0.981290	−	0.192536i	$-0.938329\pi$
$263$	−207.442	+	207.442i	−0.788754	+	0.788754i	0.192536	+	0.981290i	$0.438329\pi$
$264$		−	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	$-0.981342\pi$
$269$		−	31.5174i		−	0.117165i	0.998283	−	0.0585825i	$-0.0186581\pi$
$270$		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	0.757716	−	0.652585i	$-0.226315\pi$
$277$	29.1214	+	29.1214i	0.105131	+	0.105131i	−0.652585	+	0.757716i	$0.726315\pi$
$278$	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	−0.965720	−	0.259585i	$-0.916414\pi$
$283$	−199.836	+	199.836i	−0.706135	+	0.706135i	0.259585	+	0.965720i	$0.416414\pi$
$284$			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	−0.475011	−	0.879980i	$-0.657556\pi$
$293$	118.656	−	118.656i	0.404969	−	0.404969i	0.879980	+	0.475011i	$0.157556\pi$
$294$		−	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	−0.999597	−	0.0283934i	$-0.990961\pi$
$307$	−315.593	−	315.593i	−1.02799	−	1.02799i	−0.0283934	−	0.999597i	$-0.509039\pi$
$308$	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	−0.966634	−	0.256160i	$-0.917543\pi$
$313$	−222.379	+	222.379i	−0.710475	+	0.710475i	0.256160	+	0.966634i	$0.417543\pi$
$314$		−	926.518i		−	2.95069i
$315$		0			0
$316$	−759.655			−2.40397
$317$	183.394	+	183.394i	0.578530	+	0.578530i	0.934498	−	0.355968i	$-0.115849\pi$
$317$	183.394	+	183.394i	0.578530	+	0.578530i	−0.355968	+	0.934498i	$0.615849\pi$
$318$	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	0.976927	+	0.213571i	$0.0685095\pi$
$337$	401.198	+	401.198i	1.19050	+	1.19050i	0.213571	+	0.976927i	$0.431490\pi$
$338$	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	0.861271	−	0.508145i	$-0.169669\pi$
$347$	122.535	+	122.535i	0.353126	+	0.353126i	−0.508145	+	0.861271i	$0.669669\pi$
$348$	−200.156	+	200.156i	−0.575161	+	0.575161i
$349$			18.8032i			0.0538774i	0.999637	+	0.0269387i	$0.00857589\pi$
$349$			18.8032i			0.0538774i	−0.999637	+	0.0269387i	$0.991424\pi$
$350$		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	−0.961429	−	0.275052i	$-0.911305\pi$
$353$	−242.291	+	242.291i	−0.686377	+	0.686377i	0.275052	+	0.961429i	$0.411305\pi$
$354$			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	$0.103056\pi$
$359$			228.420i			0.636268i	−0.948046	+	0.318134i	$0.896944\pi$
$360$		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	−0.899735	−	0.436437i	$-0.856240\pi$
$367$	−490.375	−	490.375i	−1.33617	−	1.33617i	−0.436437	−	0.899735i	$-0.643760\pi$
$368$	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	−0.975695	−	0.219133i	$-0.929677\pi$
$373$	−282.198	+	282.198i	−0.756562	+	0.756562i	0.219133	+	0.975695i	$0.429677\pi$
$374$		−	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	$0.172012\pi$
$379$			389.970i			1.02895i	−0.857507	+	0.514473i	$0.827988\pi$
$380$		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	−0.991726	−	0.128376i	$-0.959024\pi$
$383$	−330.663	+	330.663i	−0.863350	+	0.863350i	0.128376	+	0.991726i	$0.459024\pi$
$384$			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	$-0.782185\pi$
$389$		−	491.789i		−	1.26424i	0.774871	−	0.632119i	$-0.217815\pi$
$390$		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	−0.852333	−	0.523000i	$-0.824813\pi$
$397$	−546.007	−	546.007i	−1.37533	−	1.37533i	−0.523000	−	0.852333i	$-0.675187\pi$
$398$	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	$0.0281505\pi$
$409$			72.2476i			0.176645i	−0.996092	+	0.0883223i	$0.971849\pi$
$410$		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	$-0.869443\pi$
$419$		−	334.155i		−	0.797506i	0.917058	−	0.398753i	$-0.130557\pi$
$420$		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	−0.691770	−	0.722118i	$-0.743169\pi$
$433$	13.1404	−	13.1404i	0.0303474	−	0.0303474i	0.722118	+	0.691770i	$0.243169\pi$
$434$		−	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	$0.161446\pi$
$439$			426.469i			0.971457i	−0.874110	+	0.485728i	$0.838554\pi$
$440$		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	−0.975290	−	0.220930i	$-0.929091\pi$
$443$	−334.181	+	334.181i	−0.754360	+	0.754360i	0.220930	+	0.975290i	$0.429091\pi$
$444$			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	$-0.827445\pi$
$449$		−	463.309i		−	1.03187i	0.856628	−	0.515935i	$-0.172555\pi$
$450$		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	0.198901	−	0.980020i	$-0.436263\pi$
$457$	−356.971	−	356.971i	−0.781119	−	0.781119i	−0.980020	+	0.198901i	$0.936263\pi$
$458$	−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	−0.662483	−	0.749077i	$-0.730497\pi$
$463$	40.0934	−	40.0934i	0.0865947	−	0.0865947i	0.749077	+	0.662483i	$0.230497\pi$
$464$		−	913.947i		−	1.96971i
$465$		0			0
$466$	−1429.06			−3.06666
$467$	−494.819	−	494.819i	−1.05957	−	1.05957i	−0.998110	−	0.0614589i	$-0.980425\pi$
$467$	−494.819	−	494.819i	−1.05957	−	1.05957i	−0.0614589	−	0.998110i	$-0.519575\pi$
$468$	−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	$0.350311\pi$
$479$			854.008i			1.78290i	−0.453121	+	0.891449i	$0.649689\pi$
$480$		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	0.162007	−	0.986790i	$-0.448203\pi$
$487$	−401.669	−	401.669i	−0.824782	−	0.824782i	−0.986790	+	0.162007i	$0.948203\pi$
$488$	−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	$0.0951125\pi$
$499$			293.789i			0.588756i	−0.955689	+	0.294378i	$0.904888\pi$
$500$		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	−0.340246	−	0.940336i	$-0.610510\pi$
$503$	301.845	−	301.845i	0.600090	−	0.600090i	0.940336	+	0.340246i	$0.110510\pi$
$504$			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	$-0.838169\pi$
$509$		−	495.550i		−	0.973575i	0.873520	−	0.486787i	$-0.161831\pi$
$510$		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	0.344314	−	0.938855i	$-0.388111\pi$
$523$	671.097	−	671.097i	1.28317	−	1.28317i	0.938855	−	0.344314i	$-0.111889\pi$
$524$			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	0.974326	+	0.225141i	$0.0722841\pi$
$547$	656.108	+	656.108i	1.19947	+	1.19947i	0.225141	+	0.974326i	$0.427716\pi$
$548$	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	0.634522	−	0.772905i	$-0.281197\pi$
$557$	−77.0795	−	77.0795i	−0.138383	−	0.138383i	−0.772905	+	0.634522i	$0.781197\pi$
$558$	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	−0.790373	−	0.612626i	$-0.790113\pi$
$563$	−100.072	+	100.072i	−0.177747	+	0.177747i	0.612626	+	0.790373i	$0.290113\pi$
$564$			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	$0.0205440\pi$
$569$			73.3966i			0.128992i	−0.997918	+	0.0644961i	$0.979456\pi$
$570$		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	0.997704	+	0.0677285i	$0.0215752\pi$
$577$	614.754	+	614.754i	1.06543	+	1.06543i	0.0677285	+	0.997704i	$0.478425\pi$
$578$	−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	0.929204	−	0.369568i	$-0.120494\pi$
$587$	328.506	+	328.506i	0.559636	+	0.559636i	−0.369568	+	0.929204i	$0.620494\pi$
$588$	−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	−0.666856	−	0.745186i	$-0.732361\pi$
$593$	46.4495	−	46.4495i	0.0783298	−	0.0783298i	0.745186	+	0.666856i	$0.232361\pi$
$594$			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	$0.0685724\pi$
$599$			256.090i			0.427529i	−0.976885	+	0.213764i	$0.931428\pi$
$600$		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	−0.929215	−	0.369540i	$-0.879515\pi$
$607$	−788.344	−	788.344i	−1.29875	−	1.29875i	−0.369540	−	0.929215i	$-0.620485\pi$
$608$	−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	−0.814656	−	0.579944i	$-0.803074\pi$
$613$	−143.879	+	143.879i	−0.234712	+	0.234712i	0.579944	+	0.814656i	$0.303074\pi$
$614$			1730.96i			2.81916i
$615$		0			0
$616$	−789.952			−1.28239
$617$	280.216	+	280.216i	0.454159	+	0.454159i	0.896732	−	0.442573i	$-0.145934\pi$
$617$	280.216	+	280.216i	0.454159	+	0.454159i	−0.442573	+	0.896732i	$0.645934\pi$
$618$	266.547	−	266.547i	0.431305	−	0.431305i
$619$		−	438.884i		−	0.709020i	−0.935052	−	0.354510i	$-0.884648\pi$
$619$		−	438.884i		−	0.709020i	0.935052	−	0.354510i	$-0.115352\pi$
$620$		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	−0.567920	−	0.823084i	$-0.692252\pi$
$643$	164.070	−	164.070i	0.255163	−	0.255163i	0.823084	+	0.567920i	$0.192252\pi$
$644$			1004.78i			1.56022i
$645$		0			0
$646$	366.648			0.567566
$647$	−495.936	−	495.936i	−0.766517	−	0.766517i	0.210975	−	0.977491i	$-0.432336\pi$
$647$	−495.936	−	495.936i	−0.766517	−	0.766517i	−0.977491	+	0.210975i	$0.932336\pi$
$648$	−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	0.286982	−	0.957936i	$-0.407348\pi$
$653$	812.931	−	812.931i	1.24492	−	1.24492i	0.957936	−	0.286982i	$-0.0926519\pi$
$654$		−	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	$0.0326808\pi$
$659$			135.081i			0.204979i	−0.994734	+	0.102490i	$0.967319\pi$
$660$		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	−0.526765	−	0.850011i	$-0.676595\pi$
$673$	217.545	−	217.545i	0.323246	−	0.323246i	0.850011	+	0.526765i	$0.176595\pi$
$674$		−	2200.49i		−	3.26482i
$675$		0			0
$676$	−415.276			−0.614313
$677$	601.143	+	601.143i	0.887952	+	0.887952i	0.994326	−	0.106374i	$-0.0339242\pi$
$677$	601.143	+	601.143i	0.887952	+	0.887952i	−0.106374	+	0.994326i	$0.533924\pi$
$678$	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	−0.694823	−	0.719181i	$-0.744517\pi$
$683$	16.6370	−	16.6370i	0.0243587	−	0.0243587i	0.719181	+	0.694823i	$0.244517\pi$
$684$			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	$0.184235\pi$
$709$			775.664i			1.09402i	−0.837125	+	0.547012i	$0.815765\pi$
$710$		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	$-0.956661\pi$
$719$		−	195.183i		−	0.271464i	0.990746	−	0.135732i	$-0.0433386\pi$
$720$		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	0.789288	−	0.614023i	$-0.210450\pi$
$727$	127.418	+	127.418i	0.175265	+	0.175265i	−0.614023	+	0.789288i	$0.710450\pi$
$728$	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	−0.0986932	−	0.995118i	$-0.531466\pi$
$733$	657.079	−	657.079i	0.896425	−	0.896425i	0.995118	+	0.0986932i	$0.0314662\pi$
$734$			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	$0.298466\pi$
$739$			1191.53i			1.61235i	−0.591676	+	0.806176i	$0.701534\pi$
$740$		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	−0.780408	−	0.625270i	$-0.784989\pi$
$743$	−115.268	+	115.268i	−0.155138	+	0.155138i	0.625270	+	0.780408i	$0.284989\pi$
$744$			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	0.625476	−	0.780243i	$-0.284905\pi$
$757$	−117.159	−	117.159i	−0.154767	−	0.154767i	−0.780243	+	0.625476i	$0.784905\pi$
$758$	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	$-0.565022\pi$
$769$		−	1506.02i		−	1.95842i	0.202857	−	0.979208i	$-0.434978\pi$
$770$		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	−0.224094	−	0.974568i	$-0.571942\pi$
$773$	580.116	−	580.116i	0.750474	−	0.750474i	0.974568	+	0.224094i	$0.0719422\pi$
$774$			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	0.789598	−	0.613625i	$-0.210289\pi$
$787$	138.491	+	138.491i	0.175973	+	0.175973i	−0.613625	+	0.789598i	$0.710289\pi$
$788$	−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	−0.768811	−	0.639475i	$-0.779152\pi$
$797$	−1122.40	−	1122.40i	−1.40829	−	1.40829i	−0.639475	−	0.768811i	$-0.720848\pi$
$798$	−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	$0.00595744\pi$
$809$			30.2805i			0.0374295i	−0.999825	+	0.0187147i	$0.994043\pi$
$810$		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	−0.584437	−	0.811439i	$-0.698685\pi$
$823$	186.823	−	186.823i	0.227002	−	0.227002i	0.811439	+	0.584437i	$0.198685\pi$
$824$			1532.47i			1.85979i
$825$		0			0
$826$	455.759			0.551766
$827$	−59.3982	−	59.3982i	−0.0718237	−	0.0718237i	0.670282	−	0.742106i	$-0.266173\pi$
$827$	−59.3982	−	59.3982i	−0.0718237	−	0.0718237i	−0.742106	+	0.670282i	$0.766173\pi$
$828$	−805.618	+	805.618i	−0.972968	+	0.972968i
$829$		−	1486.79i		−	1.79347i	−0.442564	−	0.896737i	$-0.645931\pi$
$829$		−	1486.79i		−	1.79347i	0.442564	−	0.896737i	$-0.354069\pi$
$830$		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	$-0.912882\pi$
$839$		−	453.536i		−	0.540568i	0.962781	−	0.270284i	$-0.0871176\pi$
$840$		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	−0.0298251	−	0.999555i	$-0.509495\pi$
$853$	827.180	−	827.180i	0.969730	−	0.969730i	0.999555	+	0.0298251i	$0.00949502\pi$
$854$		−	866.493i		−	1.01463i
$855$		0			0
$856$	2640.58			3.08479
$857$	264.140	+	264.140i	0.308215	+	0.308215i	0.844217	−	0.536002i	$-0.180066\pi$
$857$	264.140	+	264.140i	0.308215	+	0.308215i	−0.536002	+	0.844217i	$0.680066\pi$
$858$	595.270	−	595.270i	0.693788	−	0.693788i
$859$		−	710.066i		−	0.826619i	−0.910591	−	0.413310i	$-0.864373\pi$
$859$		−	710.066i		−	0.826619i	0.910591	−	0.413310i	$-0.135627\pi$
$860$		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	−0.128190	+	0.991750i	$0.540917\pi$
$863$	−966.508	+	966.508i	−1.11994	+	1.11994i	−0.991750	+	0.128190i	$0.959083\pi$
$864$		−	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	0.984608	+	0.174779i	$0.0559212\pi$
$877$	1016.78	+	1016.78i	1.15939	+	1.15939i	0.174779	+	0.984608i	$0.444079\pi$
$878$	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	−0.448017	−	0.894025i	$-0.647870\pi$
$883$	393.825	−	393.825i	0.446008	−	0.446008i	0.894025	+	0.448017i	$0.147870\pi$
$884$		−	986.252i		−	1.11567i
$885$		0			0
$886$	1832.92			2.06875
$887$	−1046.82	−	1046.82i	−1.18018	−	1.18018i	−0.979697	−	0.200486i	$-0.935748\pi$
$887$	−1046.82	−	1046.82i	−1.18018	−	1.18018i	−0.200486	−	0.979697i	$-0.564252\pi$
$888$	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	0.870666	−	0.491875i	$-0.163688\pi$
$907$	343.564	+	343.564i	0.378791	+	0.378791i	−0.491875	+	0.870666i	$0.663688\pi$
$908$	−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	$-0.960200\pi$
$919$		−	229.218i		−	0.249422i	0.992193	−	0.124711i	$-0.0398003\pi$
$920$		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	$-0.811505\pi$
$929$		−	1037.08i		−	1.11634i	0.829728	−	0.558168i	$-0.188495\pi$
$930$		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	0.781255	−	0.624212i	$-0.214580\pi$
$937$	147.149	+	147.149i	0.157043	+	0.157043i	−0.624212	+	0.781255i	$0.714580\pi$
$938$	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	0.625026	−	0.780604i	$-0.285089\pi$
$947$	−147.333	−	147.333i	−0.155579	−	0.155579i	−0.780604	+	0.625026i	$0.785089\pi$
$948$	−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	−0.750539	−	0.660826i	$-0.770206\pi$
$953$	−85.4967	+	85.4967i	−0.0897132	+	0.0897132i	0.660826	+	0.750539i	$0.270206\pi$
$954$		−	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	0.853919	−	0.520406i	$-0.174219\pi$
$967$	322.508	+	322.508i	0.333514	+	0.333514i	−0.520406	+	0.853919i	$0.674219\pi$
$968$	−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	0.686174	−	0.727437i	$-0.259289\pi$
$977$	−40.3145	−	40.3145i	−0.0412635	−	0.0412635i	−0.727437	+	0.686174i	$0.759289\pi$
$978$	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	−0.0828047	+	0.996566i	$0.526388\pi$
$983$	−1061.02	+	1061.02i	−1.07937	+	1.07937i	−0.996566	+	0.0828047i	$0.973612\pi$
$984$		−	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	0.830891	−	0.556435i	$-0.187831\pi$
$997$	273.633	+	273.633i	0.274456	+	0.274456i	−0.556435	+	0.830891i	$0.687831\pi$
$998$	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.232.1		24
5.2	odd	4		105.3.l.a.43.12	yes	24
5.3	odd	4	inner	525.3.l.e.43.1		24
5.4	even	2		105.3.l.a.22.12	✓	24
15.2	even	4		315.3.o.b.253.1		24
15.14	odd	2		315.3.o.b.127.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.12	✓	24	5.4	even	2
105.3.l.a.43.12	yes	24	5.2	odd	4
315.3.o.b.127.1		24	15.14	odd	2
315.3.o.b.253.1		24	15.2	even	4
525.3.l.e.43.1		24	5.3	odd	4	inner
525.3.l.e.232.1		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)

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