LMFDB - Embedded newform 525.3.l.e.232.2

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			232.2
Character	$\chi$	$=$	525.232
Dual form			525.3.l.e.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41688 - 2.41688i) q^{2} +(-1.22474 + 1.22474i) q^{3} +7.68258i q^{4} +5.92011 q^{6} +(1.87083 + 1.87083i) q^{7} +(8.90034 - 8.90034i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-2.41688 - 2.41688i) q^{2} +(-1.22474 + 1.22474i) q^{3} +7.68258i q^{4} +5.92011 q^{6} +(1.87083 + 1.87083i) q^{7} +(8.90034 - 8.90034i) q^{8} -3.00000i q^{9} -20.9312 q^{11} +(-9.40920 - 9.40920i) q^{12} +(9.34319 - 9.34319i) q^{13} -9.04312i q^{14} -12.2917 q^{16} +(-7.08868 - 7.08868i) q^{17} +(-7.25063 + 7.25063i) q^{18} -14.9507i q^{19} -4.58258 q^{21} +(50.5882 + 50.5882i) q^{22} +(-12.9691 + 12.9691i) q^{23} +21.8013i q^{24} -45.1627 q^{26} +(3.67423 + 3.67423i) q^{27} +(-14.3728 + 14.3728i) q^{28} +39.6296i q^{29} +12.8776 q^{31} +(-5.89378 - 5.89378i) q^{32} +(25.6354 - 25.6354i) q^{33} +34.2649i q^{34} +23.0477 q^{36} +(31.7205 + 31.7205i) q^{37} +(-36.1341 + 36.1341i) q^{38} +22.8861i q^{39} +69.4519 q^{41} +(11.0755 + 11.0755i) q^{42} +(-4.46880 + 4.46880i) q^{43} -160.806i q^{44} +62.6895 q^{46} +(4.41044 + 4.41044i) q^{47} +(15.0542 - 15.0542i) q^{48} +7.00000i q^{49} +17.3636 q^{51} +(71.7798 + 71.7798i) q^{52} +(48.5314 - 48.5314i) q^{53} -17.7603i q^{54} +33.3020 q^{56} +(18.3108 + 18.3108i) q^{57} +(95.7797 - 95.7797i) q^{58} +29.4254i q^{59} +7.09295 q^{61} +(-31.1235 - 31.1235i) q^{62} +(5.61249 - 5.61249i) q^{63} +77.6560i q^{64} -123.915 q^{66} +(1.39800 + 1.39800i) q^{67} +(54.4593 - 54.4593i) q^{68} -31.7677i q^{69} -15.9437 q^{71} +(-26.7010 - 26.7010i) q^{72} +(-32.4160 + 32.4160i) q^{73} -153.329i q^{74} +114.860 q^{76} +(-39.1588 - 39.1588i) q^{77} +(55.3128 - 55.3128i) q^{78} -66.1155i q^{79} -9.00000 q^{81} +(-167.857 - 167.857i) q^{82} +(83.6744 - 83.6744i) q^{83} -35.2060i q^{84} +21.6011 q^{86} +(-48.5361 - 48.5361i) q^{87} +(-186.295 + 186.295i) q^{88} +62.7487i q^{89} +34.9590 q^{91} +(-99.6363 - 99.6363i) q^{92} +(-15.7717 + 15.7717i) q^{93} -21.3190i q^{94} +14.4368 q^{96} +(85.4547 + 85.4547i) q^{97} +(16.9181 - 16.9181i) q^{98} +62.7937i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.41688	−	2.41688i	−1.20844	−	1.20844i	−0.971533	−	0.236905i	$-0.923867\pi$
$2$	−2.41688	−	2.41688i	−1.20844	−	1.20844i	−0.236905	−	0.971533i	$-0.576133\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			7.68258i			1.92065i
$5$		0			0
$5$		0			0
$6$	5.92011			0.986686
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	8.90034	−	8.90034i	1.11254	−	1.11254i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−20.9312			−1.90284			−0.951420	−	0.307897i	$-0.900375\pi$
$11$	−20.9312			−1.90284			−0.951420	+	0.307897i	$0.900375\pi$
$12$	−9.40920	−	9.40920i	−0.784100	−	0.784100i
$13$	9.34319	−	9.34319i	0.718707	−	0.718707i	−0.249633	−	0.968340i	$-0.580310\pi$
$13$	9.34319	−	9.34319i	0.718707	−	0.718707i	0.968340	+	0.249633i	$0.0803101\pi$
$14$		−	9.04312i		−	0.645937i
$15$		0			0
$16$	−12.2917			−0.768233
$17$	−7.08868	−	7.08868i	−0.416981	−	0.416981i	0.467181	−	0.884162i	$-0.345270\pi$
$17$	−7.08868	−	7.08868i	−0.416981	−	0.416981i	−0.884162	+	0.467181i	$0.845270\pi$
$18$	−7.25063	+	7.25063i	−0.402813	+	0.402813i
$19$		−	14.9507i		−	0.786881i	−0.919350	−	0.393440i	$-0.871285\pi$
$19$		−	14.9507i		−	0.786881i	0.919350	−	0.393440i	$-0.128715\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	50.5882	+	50.5882i	2.29946	+	2.29946i
$23$	−12.9691	+	12.9691i	−0.563874	+	0.563874i	−0.930406	−	0.366531i	$-0.880545\pi$
$23$	−12.9691	+	12.9691i	−0.563874	+	0.563874i	0.366531	+	0.930406i	$0.380545\pi$
$24$			21.8013i			0.908388i
$25$		0			0
$26$	−45.1627			−1.73703
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−14.3728	+	14.3728i	−0.513314	+	0.513314i
$29$			39.6296i			1.36654i	0.730168	+	0.683268i	$0.239442\pi$
$29$			39.6296i			1.36654i	−0.730168	+	0.683268i	$0.760558\pi$
$30$		0			0
$31$	12.8776			0.415405			0.207703	−	0.978192i	$-0.433401\pi$
$31$	12.8776			0.415405			0.207703	+	0.978192i	$0.433401\pi$
$32$	−5.89378	−	5.89378i	−0.184181	−	0.184181i
$33$	25.6354	−	25.6354i	0.776831	−	0.776831i
$34$			34.2649i			1.00779i
$35$		0			0
$36$	23.0477			0.640215
$37$	31.7205	+	31.7205i	0.857312	+	0.857312i	0.991021	−	0.133709i	$-0.0426887\pi$
$37$	31.7205	+	31.7205i	0.857312	+	0.857312i	−0.133709	+	0.991021i	$0.542689\pi$
$38$	−36.1341	+	36.1341i	−0.950897	+	0.950897i
$39$			22.8861i			0.586822i
$40$		0			0
$41$	69.4519			1.69395			0.846974	−	0.531634i	$-0.178422\pi$
$41$	69.4519			1.69395			0.846974	+	0.531634i	$0.178422\pi$
$42$	11.0755	+	11.0755i	0.263703	+	0.263703i
$43$	−4.46880	+	4.46880i	−0.103926	+	0.103926i	−0.757158	−	0.653232i	$-0.773413\pi$
$43$	−4.46880	+	4.46880i	−0.103926	+	0.103926i	0.653232	+	0.757158i	$0.273413\pi$
$44$		−	160.806i		−	3.65468i
$45$		0			0
$46$	62.6895			1.36281
$47$	4.41044	+	4.41044i	0.0938392	+	0.0938392i	0.752468	−	0.658629i	$-0.228863\pi$
$47$	4.41044	+	4.41044i	0.0938392	+	0.0938392i	−0.658629	+	0.752468i	$0.728863\pi$
$48$	15.0542	−	15.0542i	0.313630	−	0.313630i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	17.3636			0.340464
$52$	71.7798	+	71.7798i	1.38038	+	1.38038i
$53$	48.5314	−	48.5314i	0.915687	−	0.915687i	−0.0810246	−	0.996712i	$-0.525819\pi$
$53$	48.5314	−	48.5314i	0.915687	−	0.915687i	0.996712	+	0.0810246i	$0.0258192\pi$
$54$		−	17.7603i		−	0.328895i
$55$		0			0
$56$	33.3020			0.594679
$57$	18.3108	+	18.3108i	0.321243	+	0.321243i
$58$	95.7797	−	95.7797i	1.65137	−	1.65137i
$59$			29.4254i			0.498736i	0.968409	+	0.249368i	$0.0802229\pi$
$59$			29.4254i			0.498736i	−0.968409	+	0.249368i	$0.919777\pi$
$60$		0			0
$61$	7.09295			0.116278			0.0581389	−	0.998309i	$-0.481483\pi$
$61$	7.09295			0.116278			0.0581389	+	0.998309i	$0.481483\pi$
$62$	−31.1235	−	31.1235i	−0.501992	−	0.501992i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$			77.6560i			1.21338i
$65$		0			0
$66$	−123.915			−1.87750
$67$	1.39800	+	1.39800i	0.0208657	+	0.0208657i	0.717463	−	0.696597i	$-0.245303\pi$
$67$	1.39800	+	1.39800i	0.0208657	+	0.0208657i	−0.696597	+	0.717463i	$0.745303\pi$
$68$	54.4593	−	54.4593i	0.800873	−	0.800873i
$69$		−	31.7677i		−	0.460402i
$70$		0			0
$71$	−15.9437			−0.224559			−0.112279	−	0.993677i	$-0.535815\pi$
$71$	−15.9437			−0.224559			−0.112279	+	0.993677i	$0.535815\pi$
$72$	−26.7010	−	26.7010i	−0.370848	−	0.370848i
$73$	−32.4160	+	32.4160i	−0.444055	+	0.444055i	−0.893372	−	0.449317i	$-0.851667\pi$
$73$	−32.4160	+	32.4160i	−0.444055	+	0.444055i	0.449317	+	0.893372i	$0.351667\pi$
$74$		−	153.329i		−	2.07202i
$75$		0			0
$76$	114.860			1.51132
$77$	−39.1588	−	39.1588i	−0.508555	−	0.508555i
$78$	55.3128	−	55.3128i	0.709138	−	0.709138i
$79$		−	66.1155i		−	0.836905i	−0.908239	−	0.418453i	$-0.862573\pi$
$79$		−	66.1155i		−	0.836905i	0.908239	−	0.418453i	$-0.137427\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−167.857	−	167.857i	−2.04703	−	2.04703i
$83$	83.6744	−	83.6744i	1.00812	−	1.00812i	0.00815803	−	0.999967i	$-0.497403\pi$
$83$	83.6744	−	83.6744i	1.00812	−	1.00812i	0.999967	−	0.00815803i	$-0.00259681\pi$
$84$		−	35.2060i		−	0.419119i
$85$		0			0
$86$	21.6011			0.251175
$87$	−48.5361	−	48.5361i	−0.557886	−	0.557886i
$88$	−186.295	+	186.295i	−2.11699	+	2.11699i
$89$			62.7487i			0.705042i	0.935804	+	0.352521i	$0.114675\pi$
$89$			62.7487i			0.705042i	−0.935804	+	0.352521i	$0.885325\pi$
$90$		0			0
$91$	34.9590			0.384165
$92$	−99.6363	−	99.6363i	−1.08300	−	1.08300i
$93$	−15.7717	+	15.7717i	−0.169589	+	0.169589i
$94$		−	21.3190i		−	0.226798i
$95$		0			0
$96$	14.4368			0.150383
$97$	85.4547	+	85.4547i	0.880976	+	0.880976i	0.993634	−	0.112658i	$-0.0359364\pi$
$97$	85.4547	+	85.4547i	0.880976	+	0.880976i	−0.112658	+	0.993634i	$0.535936\pi$
$98$	16.9181	−	16.9181i	0.172634	−	0.172634i
$99$			62.7937i			0.634280i
$100$		0			0
$101$	145.641			1.44199			0.720997	−	0.692938i	$-0.243684\pi$
$101$	145.641			1.44199			0.720997	+	0.692938i	$0.243684\pi$
$102$	−41.9658	−	41.9658i	−0.411429	−	0.411429i
$103$	−62.2547	+	62.2547i	−0.604414	+	0.604414i	−0.941481	−	0.337067i	$-0.890565\pi$
$103$	−62.2547	+	62.2547i	−0.604414	+	0.604414i	0.337067	+	0.941481i	$0.390565\pi$
$104$		−	166.315i		−	1.59918i
$105$		0			0
$106$	−234.589			−2.21310
$107$	4.15809	+	4.15809i	0.0388607	+	0.0388607i	0.726270	−	0.687409i	$-0.241252\pi$
$107$	4.15809	+	4.15809i	0.0388607	+	0.0388607i	−0.687409	+	0.726270i	$0.741252\pi$
$108$	−28.2276	+	28.2276i	−0.261367	+	0.261367i
$109$			78.6347i			0.721419i	0.932678	+	0.360710i	$0.117465\pi$
$109$			78.6347i			0.721419i	−0.932678	+	0.360710i	$0.882535\pi$
$110$		0			0
$111$	−77.6991			−0.699992
$112$	−22.9957	−	22.9957i	−0.205319	−	0.205319i
$113$	107.343	−	107.343i	0.949938	−	0.949938i	−0.0488672	−	0.998805i	$-0.515561\pi$
$113$	107.343	−	107.343i	0.949938	−	0.949938i	0.998805	+	0.0488672i	$0.0155611\pi$
$114$		−	88.5100i		−	0.776404i
$115$		0			0
$116$	−304.457			−2.62463
$117$	−28.0296	−	28.0296i	−0.239569	−	0.239569i
$118$	71.1176	−	71.1176i	0.602692	−	0.602692i
$119$		−	26.5234i		−	0.222886i
$120$		0			0
$121$	317.117			2.62080
$122$	−17.1428	−	17.1428i	−0.140515	−	0.140515i
$123$	−85.0608	+	85.0608i	−0.691552	+	0.691552i
$124$			98.9329i			0.797846i
$125$		0			0
$126$	−27.1294			−0.215312
$127$	116.651	+	116.651i	0.918514	+	0.918514i	0.996921	−	0.0784074i	$-0.0249835\pi$
$127$	116.651	+	116.651i	0.918514	+	0.918514i	−0.0784074	+	0.996921i	$0.524983\pi$
$128$	164.110	−	164.110i	1.28211	−	1.28211i
$129$		−	10.9463i		−	0.0848548i
$130$		0			0
$131$	139.820			1.06733			0.533664	−	0.845697i	$-0.320815\pi$
$131$	139.820			1.06733			0.533664	+	0.845697i	$0.320815\pi$
$132$	196.946	+	196.946i	1.49202	+	1.49202i
$133$	27.9703	−	27.9703i	0.210303	−	0.210303i
$134$		−	6.75760i		−	0.0504298i
$135$		0			0
$136$	−126.183			−0.927819
$137$	161.119	+	161.119i	1.17605	+	1.17605i	0.980741	+	0.195313i	$0.0625723\pi$
$137$	161.119	+	161.119i	1.17605	+	1.17605i	0.195313	+	0.980741i	$0.437428\pi$
$138$	−76.7786	+	76.7786i	−0.556367	+	0.556367i
$139$		−	201.129i		−	1.44697i	−0.690340	−	0.723485i	$-0.742539\pi$
$139$		−	201.129i		−	1.44697i	0.690340	−	0.723485i	$-0.257461\pi$
$140$		0			0
$141$	−10.8033			−0.0766194
$142$	38.5339	+	38.5339i	0.271365	+	0.271365i
$143$	−195.565	+	195.565i	−1.36758	+	1.36758i
$144$			36.8752i			0.256078i
$145$		0			0
$146$	156.691			1.07323
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−243.696	+	243.696i	−1.64659	+	1.64659i
$149$			23.2371i			0.155954i	0.996955	+	0.0779768i	$0.0248460\pi$
$149$			23.2371i			0.155954i	−0.996955	+	0.0779768i	$0.975154\pi$
$150$		0			0
$151$	−39.3517			−0.260607			−0.130304	−	0.991474i	$-0.541595\pi$
$151$	−39.3517			−0.260607			−0.130304	+	0.991474i	$0.541595\pi$
$152$	−133.067	−	133.067i	−0.875439	−	0.875439i
$153$	−21.2660	+	21.2660i	−0.138994	+	0.138994i
$154$			189.284i			1.22912i
$155$		0			0
$156$	−175.824			−1.12708
$157$	−51.1623	−	51.1623i	−0.325874	−	0.325874i	0.525141	−	0.851015i	$-0.324013\pi$
$157$	−51.1623	−	51.1623i	−0.325874	−	0.325874i	−0.851015	+	0.525141i	$0.824013\pi$
$158$	−159.793	+	159.793i	−1.01135	+	1.01135i
$159$			118.877i			0.747656i
$160$		0			0
$161$	−48.5260			−0.301404
$162$	21.7519	+	21.7519i	0.134271	+	0.134271i
$163$	40.2804	−	40.2804i	0.247119	−	0.247119i	−0.572668	−	0.819787i	$-0.694092\pi$
$163$	40.2804	−	40.2804i	0.247119	−	0.247119i	0.819787	+	0.572668i	$0.194092\pi$
$164$			533.570i			3.25347i
$165$		0			0
$166$	−404.461			−2.43651
$167$	66.9974	+	66.9974i	0.401182	+	0.401182i	0.878649	−	0.477467i	$-0.158445\pi$
$167$	66.9974	+	66.9974i	0.401182	+	0.401182i	−0.477467	+	0.878649i	$0.658445\pi$
$168$	−40.7865	+	40.7865i	−0.242777	+	0.242777i
$169$		−	5.59045i		−	0.0330796i
$170$		0			0
$171$	−44.8522			−0.262294
$172$	−34.3319	−	34.3319i	−0.199604	−	0.199604i
$173$	−221.843	+	221.843i	−1.28233	+	1.28233i	−0.342991	+	0.939339i	$0.611440\pi$
$173$	−221.843	+	221.843i	−1.28233	+	1.28233i	−0.939339	+	0.342991i	$0.888560\pi$
$174$			234.611i			1.34834i
$175$		0			0
$176$	257.281			1.46182
$177$	−36.0387	−	36.0387i	−0.203608	−	0.203608i
$178$	151.656	−	151.656i	0.851999	−	0.851999i
$179$			129.207i			0.721827i	0.932599	+	0.360914i	$0.117535\pi$
$179$			129.207i			0.721827i	−0.932599	+	0.360914i	$0.882465\pi$
$180$		0			0
$181$	28.8400			0.159337			0.0796685	−	0.996821i	$-0.474614\pi$
$181$	28.8400			0.159337			0.0796685	+	0.996821i	$0.474614\pi$
$182$	−84.4916	−	84.4916i	−0.464240	−	0.464240i
$183$	−8.68705	+	8.68705i	−0.0474702	+	0.0474702i
$184$			230.859i			1.25467i
$185$		0			0
$186$	76.2366			0.409874
$187$	148.375	+	148.375i	0.793448	+	0.793448i
$188$	−33.8836	+	33.8836i	−0.180232	+	0.180232i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	29.9221			0.156660			0.0783302	−	0.996927i	$-0.475041\pi$
$191$	29.9221			0.156660			0.0783302	+	0.996927i	$0.475041\pi$
$192$	−95.1088	−	95.1088i	−0.495358	−	0.495358i
$193$	42.5417	−	42.5417i	0.220423	−	0.220423i	−0.588253	−	0.808677i	$-0.700184\pi$
$193$	42.5417	−	42.5417i	0.220423	−	0.220423i	0.808677	+	0.588253i	$0.200184\pi$
$194$		−	413.067i		−	2.12921i
$195$		0			0
$196$	−53.7781			−0.274378
$197$	−249.093	−	249.093i	−1.26443	−	1.26443i	−0.948922	−	0.315509i	$-0.897825\pi$
$197$	−249.093	−	249.093i	−1.26443	−	1.26443i	−0.315509	−	0.948922i	$-0.602175\pi$
$198$	151.765	−	151.765i	0.766488	−	0.766488i
$199$			16.7548i			0.0841949i	0.999114	+	0.0420974i	$0.0134040\pi$
$199$			16.7548i			0.0841949i	−0.999114	+	0.0420974i	$0.986596\pi$
$200$		0			0
$201$	−3.42439			−0.0170368
$202$	−351.997	−	351.997i	−1.74256	−	1.74256i
$203$	−74.1401	+	74.1401i	−0.365222	+	0.365222i
$204$			133.398i			0.653910i
$205$		0			0
$206$	300.924			1.46079
$207$	38.9073	+	38.9073i	0.187958	+	0.187958i
$208$	−114.844	+	114.844i	−0.552135	+	0.552135i
$209$			312.937i			1.49731i
$210$		0			0
$211$	77.0276			0.365060			0.182530	−	0.983200i	$-0.441571\pi$
$211$	77.0276			0.365060			0.182530	+	0.983200i	$0.441571\pi$
$212$	372.847	+	372.847i	1.75871	+	1.75871i
$213$	19.5269	−	19.5269i	0.0916758	−	0.0916758i
$214$		−	20.0992i		−	0.0939214i
$215$		0			0
$216$	65.4039			0.302796
$217$	24.0917	+	24.0917i	0.111022	+	0.111022i
$218$	190.050	−	190.050i	0.871791	−	0.871791i
$219$		−	79.4027i		−	0.362570i
$220$		0			0
$221$	−132.462			−0.599374
$222$	187.789	+	187.789i	0.845897	+	0.845897i
$223$	44.1625	−	44.1625i	0.198038	−	0.198038i	−0.601120	−	0.799158i	$-0.705279\pi$
$223$	44.1625	−	44.1625i	0.198038	−	0.198038i	0.799158	+	0.601120i	$0.205279\pi$
$224$		−	22.0525i		−	0.0984487i
$225$		0			0
$226$	−518.869			−2.29588
$227$	176.500	+	176.500i	0.777533	+	0.777533i	0.979411	−	0.201878i	$-0.0647044\pi$
$227$	176.500	+	176.500i	0.777533	+	0.777533i	−0.201878	+	0.979411i	$0.564704\pi$
$228$	−140.674	+	140.674i	−0.616993	+	0.616993i
$229$			296.743i			1.29582i	0.761716	+	0.647911i	$0.224357\pi$
$229$			296.743i			1.29582i	−0.761716	+	0.647911i	$0.775643\pi$
$230$		0			0
$231$	95.9190			0.415234
$232$	352.717	+	352.717i	1.52033	+	1.52033i
$233$	88.1651	−	88.1651i	0.378391	−	0.378391i	−0.492131	−	0.870521i	$-0.663782\pi$
$233$	88.1651	−	88.1651i	0.378391	−	0.378391i	0.870521	+	0.492131i	$0.163782\pi$
$234$			135.488i			0.579009i
$235$		0			0
$236$	−226.063			−0.957895
$237$	80.9746	+	80.9746i	0.341665	+	0.341665i
$238$	−64.1038	+	64.1038i	−0.269344	+	0.269344i
$239$		−	370.319i		−	1.54945i	−0.632297	−	0.774726i	$-0.717888\pi$
$239$		−	370.319i		−	1.54945i	0.632297	−	0.774726i	$-0.282112\pi$
$240$		0			0
$241$	−202.313			−0.839471			−0.419736	−	0.907646i	$-0.637877\pi$
$241$	−202.313			−0.839471			−0.419736	+	0.907646i	$0.637877\pi$
$242$	−766.431	−	766.431i	−3.16707	−	3.16707i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			54.4921i			0.223328i
$245$		0			0
$246$	411.163			1.67139
$247$	−139.688	−	139.688i	−0.565537	−	0.565537i
$248$	114.615	−	114.615i	0.462156	−	0.462156i
$249$			204.959i			0.823130i
$250$		0			0
$251$	−358.910			−1.42992			−0.714960	−	0.699165i	$-0.753555\pi$
$251$	−358.910			−1.42992			−0.714960	+	0.699165i	$0.753555\pi$
$252$	43.1184	+	43.1184i	0.171105	+	0.171105i
$253$	271.459	−	271.459i	1.07296	−	1.07296i
$254$		−	563.863i		−	2.21993i
$255$		0			0
$256$	−482.642			−1.88532
$257$	157.946	+	157.946i	0.614576	+	0.614576i	0.944135	−	0.329559i	$-0.106900\pi$
$257$	157.946	+	157.946i	0.614576	+	0.614576i	−0.329559	+	0.944135i	$0.606900\pi$
$258$	−26.4558	+	26.4558i	−0.102542	+	0.102542i
$259$			118.687i			0.458252i
$260$		0			0
$261$	118.889			0.455512
$262$	−337.927	−	337.927i	−1.28980	−	1.28980i
$263$	−9.79809	+	9.79809i	−0.0372551	+	0.0372551i	−0.725489	−	0.688234i	$-0.758386\pi$
$263$	−9.79809	+	9.79809i	−0.0372551	+	0.0372551i	0.688234	+	0.725489i	$0.258386\pi$
$264$		−	456.328i		−	1.72852i
$265$		0			0
$266$	−135.201			−0.508276
$267$	−76.8512	−	76.8512i	−0.287832	−	0.287832i
$268$	−10.7403	+	10.7403i	−0.0400756	+	0.0400756i
$269$		−	143.504i		−	0.533473i	−0.963770	−	0.266736i	$-0.914055\pi$
$269$		−	143.504i		−	0.533473i	0.963770	−	0.266736i	$-0.0859453\pi$
$270$		0			0
$271$	−29.4732			−0.108757			−0.0543785	−	0.998520i	$-0.517318\pi$
$271$	−29.4732			−0.108757			−0.0543785	+	0.998520i	$0.517318\pi$
$272$	87.1321	+	87.1321i	0.320339	+	0.320339i
$273$	−42.8159	+	42.8159i	−0.156835	+	0.156835i
$274$		−	778.811i		−	2.84238i
$275$		0			0
$276$	244.058			0.884268
$277$	−189.827	−	189.827i	−0.685295	−	0.685295i	0.275894	−	0.961188i	$-0.411026\pi$
$277$	−189.827	−	189.827i	−0.685295	−	0.685295i	−0.961188	+	0.275894i	$0.911026\pi$
$278$	−486.103	+	486.103i	−1.74857	+	1.74857i
$279$		−	38.6327i		−	0.138468i
$280$		0			0
$281$	−61.2502			−0.217972			−0.108986	−	0.994043i	$-0.534760\pi$
$281$	−61.2502			−0.217972			−0.108986	+	0.994043i	$0.534760\pi$
$282$	26.1103	+	26.1103i	0.0925898	+	0.0925898i
$283$	176.415	−	176.415i	0.623375	−	0.623375i	−0.323018	−	0.946393i	$-0.604697\pi$
$283$	176.415	−	176.415i	0.623375	−	0.623375i	0.946393	+	0.323018i	$0.104697\pi$
$284$		−	122.489i		−	0.431298i
$285$		0			0
$286$	945.310			3.30528
$287$	129.933	+	129.933i	0.452727	+	0.452727i
$288$	−17.6813	+	17.6813i	−0.0613935	+	0.0613935i
$289$		−	188.501i		−	0.652254i
$290$		0			0
$291$	−209.320			−0.719314
$292$	−249.039	−	249.039i	−0.852873	−	0.852873i
$293$	92.7415	−	92.7415i	0.316524	−	0.316524i	−0.530907	−	0.847430i	$-0.678148\pi$
$293$	92.7415	−	92.7415i	0.316524	−	0.316524i	0.847430	+	0.530907i	$0.178148\pi$
$294$			41.4408i			0.140955i
$295$		0			0
$296$	564.647			1.90759
$297$	−76.9063	−	76.9063i	−0.258944	−	0.258944i
$298$	56.1612	−	56.1612i	0.188460	−	0.188460i
$299$			242.346i			0.810521i
$300$		0			0
$301$	−16.7207			−0.0555505
$302$	95.1081	+	95.1081i	0.314927	+	0.314927i
$303$	−178.374	+	178.374i	−0.588692	+	0.588692i
$304$			183.770i			0.604508i
$305$		0			0
$306$	102.795			0.335931
$307$	228.867	+	228.867i	0.745494	+	0.745494i	0.973629	−	0.228135i	$-0.0732628\pi$
$307$	228.867	+	228.867i	0.745494	+	0.745494i	−0.228135	+	0.973629i	$0.573263\pi$
$308$	300.840	−	300.840i	0.976754	−	0.976754i
$309$		−	152.492i		−	0.493502i
$310$		0			0
$311$	291.118			0.936070			0.468035	−	0.883710i	$-0.344962\pi$
$311$	291.118			0.936070			0.468035	+	0.883710i	$0.344962\pi$
$312$	203.694	+	203.694i	0.652864	+	0.652864i
$313$	−251.667	+	251.667i	−0.804049	+	0.804049i	−0.983726	−	0.179677i	$-0.942495\pi$
$313$	−251.667	+	251.667i	−0.804049	+	0.804049i	0.179677	+	0.983726i	$0.442495\pi$
$314$			247.306i			0.787598i
$315$		0			0
$316$	507.938			1.60740
$317$	−30.4080	−	30.4080i	−0.0959244	−	0.0959244i	0.657516	−	0.753440i	$-0.271607\pi$
$317$	−30.4080	−	30.4080i	−0.0959244	−	0.0959244i	−0.753440	+	0.657516i	$0.771607\pi$
$318$	287.312	−	287.312i	0.903496	−	0.903496i
$319$		−	829.495i		−	2.60030i
$320$		0			0
$321$	−10.1852			−0.0317296
$322$	117.281	+	117.281i	0.364228	+	0.364228i
$323$	−105.981	+	105.981i	−0.328114	+	0.328114i
$324$		−	69.1432i		−	0.213405i
$325$		0			0
$326$	−194.705			−0.597255
$327$	−96.3075	−	96.3075i	−0.294518	−	0.294518i
$328$	618.146	−	618.146i	1.88459	−	1.88459i
$329$			16.5024i			0.0501592i
$330$		0			0
$331$	−600.898			−1.81540			−0.907701	−	0.419617i	$-0.862164\pi$
$331$	−600.898			−1.81540			−0.907701	+	0.419617i	$0.862164\pi$
$332$	642.835	+	642.835i	1.93625	+	1.93625i
$333$	95.1616	−	95.1616i	0.285771	−	0.285771i
$334$		−	323.849i		−	0.969607i
$335$		0			0
$336$	56.3278			0.167642
$337$	18.3744	+	18.3744i	0.0545235	+	0.0545235i	0.733843	−	0.679319i	$-0.237725\pi$
$337$	18.3744	+	18.3744i	0.0545235	+	0.0545235i	−0.679319	+	0.733843i	$0.737725\pi$
$338$	−13.5114	+	13.5114i	−0.0399746	+	0.0399746i
$339$			262.936i			0.775621i
$340$		0			0
$341$	−269.543			−0.790450
$342$	108.402	+	108.402i	0.316966	+	0.316966i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			79.5477i			0.231243i
$345$		0			0
$346$	1072.33			3.09923
$347$	−274.252	−	274.252i	−0.790351	−	0.790351i	0.191200	−	0.981551i	$-0.438762\pi$
$347$	−274.252	−	274.252i	−0.790351	−	0.790351i	−0.981551	+	0.191200i	$0.938762\pi$
$348$	372.882	−	372.882i	1.07150	−	1.07150i
$349$		−	218.995i		−	0.627494i	−0.949507	−	0.313747i	$-0.898416\pi$
$349$		−	218.995i		−	0.627494i	0.949507	−	0.313747i	$-0.101584\pi$
$350$		0			0
$351$	68.6582			0.195607
$352$	123.364	+	123.364i	0.350466	+	0.350466i
$353$	−77.0417	+	77.0417i	−0.218248	+	0.218248i	−0.807760	−	0.589512i	$-0.799320\pi$
$353$	−77.0417	+	77.0417i	−0.218248	+	0.218248i	0.589512	+	0.807760i	$0.299320\pi$
$354$			174.202i			0.492096i
$355$		0			0
$356$	−482.072			−1.35413
$357$	32.4844	+	32.4844i	0.0909927	+	0.0909927i
$358$	312.277	−	312.277i	0.872283	−	0.872283i
$359$			532.713i			1.48388i	0.670466	+	0.741940i	$0.266094\pi$
$359$			532.713i			1.48388i	−0.670466	+	0.741940i	$0.733906\pi$
$360$		0			0
$361$	137.476			0.380819
$362$	−69.7027	−	69.7027i	−0.192549	−	0.192549i
$363$	−388.387	+	388.387i	−1.06994	+	1.06994i
$364$			268.576i			0.737845i
$365$		0			0
$366$	41.9910			0.114730
$367$	−367.459	−	367.459i	−1.00125	−	1.00125i	−0.999999	−	0.00125078i	$-0.999602\pi$
$367$	−367.459	−	367.459i	−1.00125	−	1.00125i	−0.00125078	−	0.999999i	$-0.500398\pi$
$368$	159.413	−	159.413i	0.433187	−	0.433187i
$369$		−	208.356i		−	0.564649i
$370$		0			0
$371$	181.588			0.489456
$372$	−121.168	−	121.168i	−0.325719	−	0.325719i
$373$	−30.1723	+	30.1723i	−0.0808908	+	0.0808908i	−0.746395	−	0.665504i	$-0.768217\pi$
$373$	−30.1723	+	30.1723i	−0.0808908	+	0.0808908i	0.665504	+	0.746395i	$0.268217\pi$
$374$		−	717.207i		−	1.91767i
$375$		0			0
$376$	78.5089			0.208800
$377$	370.267	+	370.267i	0.982139	+	0.982139i
$378$	33.2266	−	33.2266i	0.0879009	−	0.0879009i
$379$			254.898i			0.672555i	0.941763	+	0.336277i	$0.109168\pi$
$379$			254.898i			0.672555i	−0.941763	+	0.336277i	$0.890832\pi$
$380$		0			0
$381$	−285.736			−0.749964
$382$	−72.3181	−	72.3181i	−0.189314	−	0.189314i
$383$	−104.737	+	104.737i	−0.273465	+	0.273465i	−0.830493	−	0.557028i	$-0.811941\pi$
$383$	−104.737	+	104.737i	−0.273465	+	0.273465i	0.557028	+	0.830493i	$0.311941\pi$
$384$			401.985i			1.04684i
$385$		0			0
$386$	−205.636			−0.532736
$387$	13.4064	+	13.4064i	0.0346418	+	0.0346418i
$388$	−656.512	+	656.512i	−1.69204	+	1.69204i
$389$		−	667.039i		−	1.71475i	−0.514689	−	0.857377i	$-0.672092\pi$
$389$		−	667.039i		−	1.71475i	0.514689	−	0.857377i	$-0.327908\pi$
$390$		0			0
$391$	183.868			0.470250
$392$	62.3024	+	62.3024i	0.158935	+	0.158935i
$393$	−171.244	+	171.244i	−0.435735	+	0.435735i
$394$			1204.05i			3.05598i
$395$		0			0
$396$	−482.418			−1.21823
$397$	171.665	+	171.665i	0.432406	+	0.432406i	0.889446	−	0.457040i	$-0.151090\pi$
$397$	171.665	+	171.665i	0.432406	+	0.432406i	−0.457040	+	0.889446i	$0.651090\pi$
$398$	40.4942	−	40.4942i	0.101744	−	0.101744i
$399$			68.5129i			0.171711i
$400$		0			0
$401$	686.098			1.71097			0.855484	−	0.517829i	$-0.173260\pi$
$401$	686.098			1.71097			0.855484	+	0.517829i	$0.173260\pi$
$402$	8.27633	+	8.27633i	0.0205879	+	0.0205879i
$403$	120.318	−	120.318i	0.298555	−	0.298555i
$404$			1118.90i			2.76956i
$405$		0			0
$406$	358.375			0.882697
$407$	−663.950	−	663.950i	−1.63133	−	1.63133i
$408$	154.542	−	154.542i	0.378780	−	0.378780i
$409$		−	556.252i		−	1.36003i	−0.733198	−	0.680015i	$-0.761973\pi$
$409$		−	556.252i		−	1.36003i	0.733198	−	0.680015i	$-0.238027\pi$
$410$		0			0
$411$	−394.660			−0.960244
$412$	−478.277	−	478.277i	−1.16087	−	1.16087i
$413$	−55.0499	+	55.0499i	−0.133293	+	0.133293i
$414$		−	188.068i		−	0.454272i
$415$		0			0
$416$	−110.133			−0.264744
$417$	246.331	+	246.331i	0.590723	+	0.590723i
$418$	756.331	−	756.331i	1.80940	−	1.80940i
$419$			143.631i			0.342794i	0.985202	+	0.171397i	$0.0548280\pi$
$419$			143.631i			0.342794i	−0.985202	+	0.171397i	$0.945172\pi$
$420$		0			0
$421$	110.369			0.262159			0.131080	−	0.991372i	$-0.458156\pi$
$421$	110.369			0.262159			0.131080	+	0.991372i	$0.458156\pi$
$422$	−186.166	−	186.166i	−0.441152	−	0.441152i
$423$	13.2313	−	13.2313i	0.0312797	−	0.0312797i
$424$		−	863.893i		−	2.03748i
$425$		0			0
$426$	−94.3884			−0.221569
$427$	13.2697	+	13.2697i	0.0310766	+	0.0310766i
$428$	−31.9449	+	31.9449i	−0.0746376	+	0.0746376i
$429$		−	479.033i		−	1.11663i
$430$		0			0
$431$	439.840			1.02051			0.510255	−	0.860023i	$-0.329551\pi$
$431$	439.840			1.02051			0.510255	+	0.860023i	$0.329551\pi$
$432$	−45.1627	−	45.1627i	−0.104543	−	0.104543i
$433$	118.543	−	118.543i	0.273770	−	0.273770i	−0.556846	−	0.830616i	$-0.687989\pi$
$433$	118.543	−	118.543i	0.273770	−	0.273770i	0.830616	+	0.556846i	$0.187989\pi$
$434$		−	116.453i		−	0.268326i
$435$		0			0
$436$	−604.118			−1.38559
$437$	193.898	+	193.898i	0.443702	+	0.443702i
$438$	−191.907	+	191.907i	−0.438143	+	0.438143i
$439$			351.519i			0.800727i	0.916356	+	0.400363i	$0.131116\pi$
$439$			351.519i			0.800727i	−0.916356	+	0.400363i	$0.868884\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	320.144	+	320.144i	0.724307	+	0.724307i
$443$	41.1332	−	41.1332i	0.0928514	−	0.0928514i	−0.659155	−	0.752007i	$-0.729086\pi$
$443$	41.1332	−	41.1332i	0.0928514	−	0.0928514i	0.752007	+	0.659155i	$0.229086\pi$
$444$		−	596.930i		−	1.34444i
$445$		0			0
$446$	−213.470			−0.478633
$447$	−28.4595	−	28.4595i	−0.0636678	−	0.0636678i
$448$	−145.281	+	145.281i	−0.324288	+	0.324288i
$449$			209.909i			0.467503i	0.972296	+	0.233751i	$0.0751002\pi$
$449$			209.909i			0.467503i	−0.972296	+	0.233751i	$0.924900\pi$
$450$		0			0
$451$	−1453.71			−3.22331
$452$	824.671	+	824.671i	1.82449	+	1.82449i
$453$	48.1957	−	48.1957i	0.106392	−	0.106392i
$454$		−	853.157i		−	1.87920i
$455$		0			0
$456$	325.945			0.714793
$457$	156.842	+	156.842i	0.343199	+	0.343199i	0.857568	−	0.514370i	$-0.171974\pi$
$457$	156.842	+	156.842i	0.343199	+	0.343199i	−0.514370	+	0.857568i	$0.671974\pi$
$458$	717.192	−	717.192i	1.56592	−	1.56592i
$459$		−	52.0909i		−	0.113488i
$460$		0			0
$461$	274.147			0.594680			0.297340	−	0.954772i	$-0.403901\pi$
$461$	274.147			0.594680			0.297340	+	0.954772i	$0.403901\pi$
$462$	−231.824	−	231.824i	−0.501784	−	0.501784i
$463$	−483.190	+	483.190i	−1.04361	+	1.04361i	−0.0446032	+	0.999005i	$0.514202\pi$
$463$	−483.190	+	483.190i	−1.04361	+	1.04361i	−0.999005	+	0.0446032i	$0.985798\pi$
$464$		−	487.116i		−	1.04982i
$465$		0			0
$466$	−426.168			−0.914524
$467$	−8.70901	−	8.70901i	−0.0186489	−	0.0186489i	0.697721	−	0.716370i	$-0.254198\pi$
$467$	−8.70901	−	8.70901i	−0.0186489	−	0.0186489i	−0.716370	+	0.697721i	$0.754198\pi$
$468$	215.339	−	215.339i	0.460127	−	0.460127i
$469$			5.23085i			0.0111532i
$470$		0			0
$471$	125.321			0.266075
$472$	261.896	+	261.896i	0.554865	+	0.554865i
$473$	93.5374	−	93.5374i	0.197754	−	0.197754i
$474$		−	391.411i		−	0.825762i
$475$		0			0
$476$	203.768			0.428084
$477$	−145.594	−	145.594i	−0.305229	−	0.305229i
$478$	−895.015	+	895.015i	−1.87242	+	1.87242i
$479$			806.280i			1.68326i	0.540056	+	0.841629i	$0.318403\pi$
$479$			806.280i			1.68326i	−0.540056	+	0.841629i	$0.681597\pi$
$480$		0			0
$481$	592.742			1.23231
$482$	488.965	+	488.965i	1.01445	+	1.01445i
$483$	59.4319	−	59.4319i	0.123047	−	0.123047i
$484$			2436.27i			5.03362i
$485$		0			0
$486$	−53.2810			−0.109632
$487$	153.496	+	153.496i	0.315186	+	0.315186i	0.846915	−	0.531729i	$-0.178457\pi$
$487$	153.496	+	153.496i	0.315186	+	0.315186i	−0.531729	+	0.846915i	$0.678457\pi$
$488$	63.1297	−	63.1297i	0.129364	−	0.129364i
$489$			98.6663i			0.201772i
$490$		0			0
$491$	−180.954			−0.368543			−0.184271	−	0.982875i	$-0.558993\pi$
$491$	−180.954			−0.368543			−0.184271	+	0.982875i	$0.558993\pi$
$492$	−653.487	−	653.487i	−1.32823	−	1.32823i
$493$	280.921	−	280.921i	0.569820	−	0.569820i
$494$			675.215i			1.36683i
$495$		0			0
$496$	−158.288			−0.319128
$497$	−29.8279	−	29.8279i	−0.0600159	−	0.0600159i
$498$	495.362	−	495.362i	0.994702	−	0.994702i
$499$			13.9603i			0.0279765i	0.999902	+	0.0139883i	$0.00445275\pi$
$499$			13.9603i			0.0279765i	−0.999902	+	0.0139883i	$0.995547\pi$
$500$		0			0
$501$	−164.109			−0.327564
$502$	867.441	+	867.441i	1.72797	+	1.72797i
$503$	−358.510	+	358.510i	−0.712743	+	0.712743i	−0.967108	−	0.254365i	$-0.918134\pi$
$503$	−358.510	+	358.510i	−0.712743	+	0.712743i	0.254365	+	0.967108i	$0.418134\pi$
$504$		−	99.9061i		−	0.198226i
$505$		0			0
$506$	−1312.17			−2.59322
$507$	6.84688	+	6.84688i	0.0135047	+	0.0135047i
$508$	−896.183	+	896.183i	−1.76414	+	1.76414i
$509$		−	446.506i		−	0.877223i	−0.898677	−	0.438611i	$-0.855470\pi$
$509$		−	446.506i		−	0.877223i	0.898677	−	0.438611i	$-0.144530\pi$
$510$		0			0
$511$	−121.290			−0.237357
$512$	510.047	+	510.047i	0.996186	+	0.996186i
$513$	54.9325	−	54.9325i	0.107081	−	0.107081i
$514$		−	763.472i		−	1.48535i
$515$		0			0
$516$	84.0956			0.162976
$517$	−92.3160	−	92.3160i	−0.178561	−	0.178561i
$518$	286.853	−	286.853i	0.553770	−	0.553770i
$519$		−	543.402i		−	1.04702i
$520$		0			0
$521$	−682.112			−1.30924			−0.654618	−	0.755960i	$-0.727171\pi$
$521$	−682.112			−1.30924			−0.654618	+	0.755960i	$0.727171\pi$
$522$	−287.339	−	287.339i	−0.550458	−	0.550458i
$523$	252.224	−	252.224i	0.482263	−	0.482263i	−0.423591	−	0.905854i	$-0.639231\pi$
$523$	252.224	−	252.224i	0.482263	−	0.482263i	0.905854	+	0.423591i	$0.139231\pi$
$524$			1074.18i			2.04996i
$525$		0			0
$526$	47.3615			0.0900410
$527$	−91.2849	−	91.2849i	−0.173216	−	0.173216i
$528$	−315.104	+	315.104i	−0.596787	+	0.596787i
$529$			192.604i			0.364091i
$530$		0			0
$531$	88.2763			0.166245
$532$	214.884	+	214.884i	0.403917	+	0.403917i
$533$	648.902	−	648.902i	1.21745	−	1.21745i
$534$			371.479i			0.695654i
$535$		0			0
$536$	24.8854			0.0464280
$537$	−158.246	−	158.246i	−0.294685	−	0.294685i
$538$	−346.832	+	346.832i	−0.644669	+	0.644669i
$539$		−	146.519i		−	0.271834i
$540$		0			0
$541$	225.356			0.416554			0.208277	−	0.978070i	$-0.433214\pi$
$541$	225.356			0.416554			0.208277	+	0.978070i	$0.433214\pi$
$542$	71.2330	+	71.2330i	0.131426	+	0.131426i
$543$	−35.3217	+	35.3217i	−0.0650491	+	0.0650491i
$544$			83.5582i			0.153600i
$545$		0			0
$546$	206.961			0.379050
$547$	−211.802	−	211.802i	−0.387207	−	0.387207i	0.486483	−	0.873690i	$-0.338280\pi$
$547$	−211.802	−	211.802i	−0.387207	−	0.387207i	−0.873690	+	0.486483i	$0.838280\pi$
$548$	−1237.81	+	1237.81i	−2.25878	+	2.25878i
$549$		−	21.2788i		−	0.0387593i
$550$		0			0
$551$	592.491			1.07530
$552$	−282.743	−	282.743i	−0.512216	−	0.512216i
$553$	123.691	−	123.691i	0.223672	−	0.223672i
$554$			917.575i			1.65627i
$555$		0			0
$556$	1545.19			2.77912
$557$	74.4003	+	74.4003i	0.133573	+	0.133573i	0.770732	−	0.637159i	$-0.219891\pi$
$557$	74.4003	+	74.4003i	0.133573	+	0.133573i	−0.637159	+	0.770732i	$0.719891\pi$
$558$	−93.3704	+	93.3704i	−0.167331	+	0.167331i
$559$			83.5057i			0.149384i
$560$		0			0
$561$	−363.442			−0.647848
$562$	148.034	+	148.034i	0.263406	+	0.263406i
$563$	340.172	−	340.172i	0.604214	−	0.604214i	−0.337214	−	0.941428i	$-0.609485\pi$
$563$	340.172	−	340.172i	0.604214	−	0.604214i	0.941428	+	0.337214i	$0.109485\pi$
$564$		−	82.9975i		−	0.147159i
$565$		0			0
$566$	−852.747			−1.50662
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	−141.904	+	141.904i	−0.249831	+	0.249831i
$569$			672.360i			1.18165i	0.806799	+	0.590826i	$0.201198\pi$
$569$			672.360i			1.18165i	−0.806799	+	0.590826i	$0.798802\pi$
$570$		0			0
$571$	613.562			1.07454			0.537269	−	0.843411i	$-0.319456\pi$
$571$	613.562			1.07454			0.537269	+	0.843411i	$0.319456\pi$
$572$	−1502.44	−	1502.44i	−2.62664	−	2.62664i
$573$	−36.6470	+	36.6470i	−0.0639563	+	0.0639563i
$574$		−	628.062i		−	1.09418i
$575$		0			0
$576$	232.968			0.404458
$577$	81.3337	+	81.3337i	0.140960	+	0.140960i	0.774065	−	0.633106i	$-0.218220\pi$
$577$	81.3337	+	81.3337i	0.140960	+	0.140960i	−0.633106	+	0.774065i	$0.718220\pi$
$578$	−455.584	+	455.584i	−0.788208	+	0.788208i
$579$			104.205i			0.179975i
$580$		0			0
$581$	313.081			0.538865
$582$	505.901	+	505.901i	0.869246	+	0.869246i
$583$	−1015.82	+	1015.82i	−1.74241	+	1.74241i
$584$			577.028i			0.988061i
$585$		0			0
$586$	−448.289			−0.764999
$587$	−819.321	−	819.321i	−1.39578	−	1.39578i	−0.811694	−	0.584082i	$-0.801454\pi$
$587$	−819.321	−	819.321i	−1.39578	−	1.39578i	−0.584082	−	0.811694i	$-0.698546\pi$
$588$	65.8644	−	65.8644i	0.112014	−	0.112014i
$589$		−	192.529i		−	0.326874i
$590$		0			0
$591$	610.151			1.03240
$592$	−389.900	−	389.900i	−0.658615	−	0.658615i
$593$	308.110	−	308.110i	0.519578	−	0.519578i	−0.397865	−	0.917444i	$-0.630249\pi$
$593$	308.110	−	308.110i	0.519578	−	0.519578i	0.917444	+	0.397865i	$0.130249\pi$
$594$			371.746i			0.625835i
$595$		0			0
$596$	−178.521			−0.299532
$597$	−20.5203	−	20.5203i	−0.0343724	−	0.0343724i
$598$	585.720	−	585.720i	0.979464	−	0.979464i
$599$			458.753i			0.765864i	0.923776	+	0.382932i	$0.125086\pi$
$599$			458.753i			0.765864i	−0.923776	+	0.382932i	$0.874914\pi$
$600$		0			0
$601$	829.765			1.38064			0.690320	−	0.723504i	$-0.257470\pi$
$601$	829.765			1.38064			0.690320	+	0.723504i	$0.257470\pi$
$602$	40.4119	+	40.4119i	0.0671294	+	0.0671294i
$603$	4.19401	−	4.19401i	0.00695524	−	0.00695524i
$604$		−	302.322i		−	0.500534i
$605$		0			0
$606$	862.214			1.42279
$607$	249.775	+	249.775i	0.411490	+	0.411490i	0.882258	−	0.470767i	$-0.156023\pi$
$607$	249.775	+	249.775i	0.411490	+	0.411490i	−0.470767	+	0.882258i	$0.656023\pi$
$608$	−88.1163	+	88.1163i	−0.144928	+	0.144928i
$609$		−	181.605i		−	0.298203i
$610$		0			0
$611$	82.4152			0.134886
$612$	−163.378	−	163.378i	−0.266958	−	0.266958i
$613$	−90.9769	+	90.9769i	−0.148413	+	0.148413i	−0.777409	−	0.628996i	$-0.783466\pi$
$613$	−90.9769	+	90.9769i	−0.148413	+	0.148413i	0.628996	+	0.777409i	$0.283466\pi$
$614$		−	1106.29i		−	1.80177i
$615$		0			0
$616$	−697.053			−1.13158
$617$	445.593	+	445.593i	0.722193	+	0.722193i	0.969052	−	0.246858i	$-0.0793983\pi$
$617$	445.593	+	445.593i	0.722193	+	0.722193i	−0.246858	+	0.969052i	$0.579398\pi$
$618$	−368.555	+	368.555i	−0.596367	+	0.596367i
$619$			943.969i			1.52499i	0.646994	+	0.762495i	$0.276026\pi$
$619$			943.969i			1.52499i	−0.646994	+	0.762495i	$0.723974\pi$
$620$		0			0
$621$	−95.3031			−0.153467
$622$	−703.595	−	703.595i	−1.13118	−	1.13118i
$623$	−117.392	+	117.392i	−0.188430	+	0.188430i
$624$		−	281.309i		−	0.450816i
$625$		0			0
$626$	1216.50			1.94329
$627$	−383.268	−	383.268i	−0.611273	−	0.611273i
$628$	393.058	−	393.058i	0.625889	−	0.625889i
$629$		−	449.713i		−	0.714965i
$630$		0			0
$631$	−1001.49			−1.58714			−0.793570	−	0.608478i	$-0.791780\pi$
$631$	−1001.49			−1.58714			−0.793570	+	0.608478i	$0.791780\pi$
$632$	−588.451	−	588.451i	−0.931093	−	0.931093i
$633$	−94.3392	+	94.3392i	−0.149035	+	0.149035i
$634$			146.985i			0.231837i
$635$		0			0
$636$	−913.284			−1.43598
$637$	65.4023	+	65.4023i	0.102672	+	0.102672i
$638$	−2004.79	+	2004.79i	−3.14230	+	3.14230i
$639$			47.8310i			0.0748529i
$640$		0			0
$641$	−878.051			−1.36981			−0.684907	−	0.728630i	$-0.740157\pi$
$641$	−878.051			−1.36981			−0.684907	+	0.728630i	$0.740157\pi$
$642$	24.6164	+	24.6164i	0.0383433	+	0.0383433i
$643$	551.380	−	551.380i	0.857511	−	0.857511i	−0.133533	−	0.991044i	$-0.542632\pi$
$643$	551.380	−	551.380i	0.857511	−	0.857511i	0.991044	+	0.133533i	$0.0426323\pi$
$644$		−	372.805i		−	0.578889i
$645$		0			0
$646$	512.286			0.793012
$647$	−315.391	−	315.391i	−0.487466	−	0.487466i	0.420039	−	0.907506i	$-0.362016\pi$
$647$	−315.391	−	315.391i	−0.487466	−	0.487466i	−0.907506	+	0.420039i	$0.862016\pi$
$648$	−80.1031	+	80.1031i	−0.123616	+	0.123616i
$649$		−	615.911i		−	0.949015i
$650$		0			0
$651$	−59.0124			−0.0906489
$652$	309.457	+	309.457i	0.474628	+	0.474628i
$653$	825.176	−	825.176i	1.26367	−	1.26367i	0.314368	−	0.949301i	$-0.398207\pi$
$653$	825.176	−	825.176i	1.26367	−	1.26367i	0.949301	−	0.314368i	$-0.101793\pi$
$654$			465.526i			0.711814i
$655$		0			0
$656$	−853.684			−1.30135
$657$	97.2481	+	97.2481i	0.148018	+	0.148018i
$658$	39.8842	−	39.8842i	0.0606143	−	0.0606143i
$659$		−	956.471i		−	1.45140i	−0.688012	−	0.725699i	$-0.741517\pi$
$659$		−	956.471i		−	1.45140i	0.688012	−	0.725699i	$-0.258483\pi$
$660$		0			0
$661$	18.2815			0.0276573			0.0138286	−	0.999904i	$-0.495598\pi$
$661$	18.2815			0.0276573			0.0138286	+	0.999904i	$0.495598\pi$
$662$	1452.30	+	1452.30i	2.19380	+	2.19380i
$663$	162.232	−	162.232i	0.244694	−	0.244694i
$664$		−	1489.46i		−	2.24316i
$665$		0			0
$666$	−459.988			−0.690672
$667$	−513.960	−	513.960i	−0.770555	−	0.770555i
$668$	−514.713	+	514.713i	−0.770528	+	0.770528i
$669$			108.176i			0.161697i
$670$		0			0
$671$	−148.464			−0.221258
$672$	27.0087	+	27.0087i	0.0401915	+	0.0401915i
$673$	829.059	−	829.059i	1.23189	−	1.23189i	0.268647	−	0.963239i	$-0.413424\pi$
$673$	829.059	−	829.059i	1.23189	−	1.23189i	0.963239	−	0.268647i	$-0.0865764\pi$
$674$		−	88.8173i		−	0.131776i
$675$		0			0
$676$	42.9491			0.0635342
$677$	421.712	+	421.712i	0.622913	+	0.622913i	0.946275	−	0.323362i	$-0.104813\pi$
$677$	421.712	+	421.712i	0.622913	+	0.622913i	−0.323362	+	0.946275i	$0.604813\pi$
$678$	635.483	−	635.483i	0.937290	−	0.937290i
$679$			319.742i			0.470901i
$680$		0			0
$681$	−432.335			−0.634853
$682$	651.453	+	651.453i	0.955209	+	0.955209i
$683$	40.2821	−	40.2821i	0.0589782	−	0.0589782i	−0.677003	−	0.735981i	$-0.736721\pi$
$683$	40.2821	−	40.2821i	0.0589782	−	0.0589782i	0.735981	+	0.677003i	$0.236721\pi$
$684$		−	344.581i		−	0.503773i
$685$		0			0
$686$	63.3019			0.0922768
$687$	−363.435	−	363.435i	−0.529017	−	0.529017i
$688$	54.9293	−	54.9293i	0.0798390	−	0.0798390i
$689$		−	906.877i		−	1.31622i
$690$		0			0
$691$	499.429			0.722763			0.361381	−	0.932418i	$-0.382305\pi$
$691$	499.429			0.722763			0.361381	+	0.932418i	$0.382305\pi$
$692$	−1704.33	−	1704.33i	−2.46290	−	2.46290i
$693$	−117.476	+	117.476i	−0.169518	+	0.169518i
$694$			1325.67i			1.91018i
$695$		0			0
$696$	−863.976			−1.24134
$697$	−492.322	−	492.322i	−0.706344	−	0.706344i
$698$	−529.285	+	529.285i	−0.758287	+	0.758287i
$699$			215.959i			0.308955i
$700$		0			0
$701$	29.9935			0.0427867			0.0213934	−	0.999771i	$-0.493190\pi$
$701$	29.9935			0.0427867			0.0213934	+	0.999771i	$0.493190\pi$
$702$	−165.938	−	165.938i	−0.236379	−	0.236379i
$703$	474.245	−	474.245i	0.674602	−	0.674602i
$704$		−	1625.44i		−	2.30886i
$705$		0			0
$706$	372.401			0.527480
$707$	272.470	+	272.470i	0.385389	+	0.385389i
$708$	276.870	−	276.870i	0.391059	−	0.391059i
$709$		−	983.508i		−	1.38718i	−0.720372	−	0.693588i	$-0.756029\pi$
$709$		−	983.508i		−	1.38718i	0.720372	−	0.693588i	$-0.243971\pi$
$710$		0			0
$711$	−198.347			−0.278968
$712$	558.485	+	558.485i	0.784389	+	0.784389i
$713$	−167.011	+	167.011i	−0.234236	+	0.234236i
$714$		−	157.022i		−	0.219918i
$715$		0			0
$716$	−992.644			−1.38637
$717$	453.546	+	453.546i	0.632561	+	0.632561i
$718$	1287.50	−	1287.50i	1.79318	−	1.79318i
$719$			59.3020i			0.0824784i	0.999149	+	0.0412392i	$0.0131306\pi$
$719$			59.3020i			0.0824784i	−0.999149	+	0.0412392i	$0.986869\pi$
$720$		0			0
$721$	−232.936			−0.323073
$722$	−332.261	−	332.261i	−0.460196	−	0.460196i
$723$	247.781	−	247.781i	0.342713	−	0.342713i
$724$			221.566i			0.306030i
$725$		0			0
$726$	1877.37			2.58590
$727$	25.0937	+	25.0937i	0.0345168	+	0.0345168i	0.724155	−	0.689638i	$-0.242230\pi$
$727$	25.0937	+	25.0937i	0.0345168	+	0.0345168i	−0.689638	+	0.724155i	$0.742230\pi$
$728$	311.147	−	311.147i	0.427400	−	0.427400i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	63.3557			0.0866699
$732$	−66.7390	−	66.7390i	−0.0911734	−	0.0911734i
$733$	−611.839	+	611.839i	−0.834706	+	0.834706i	−0.988156	−	0.153451i	$-0.950961\pi$
$733$	−611.839	+	611.839i	−0.834706	+	0.834706i	0.153451	+	0.988156i	$0.450961\pi$
$734$			1776.20i			2.41990i
$735$		0			0
$736$	152.874			0.207709
$737$	−29.2619	−	29.2619i	−0.0397041	−	0.0397041i
$738$	−503.570	+	503.570i	−0.682344	+	0.682344i
$739$			566.278i			0.766277i	0.923691	+	0.383138i	$0.125157\pi$
$739$			566.278i			0.766277i	−0.923691	+	0.383138i	$0.874843\pi$
$740$		0			0
$741$	342.163			0.461759
$742$	−438.876	−	438.876i	−0.591477	−	0.591477i
$743$	−65.5539	+	65.5539i	−0.0882287	+	0.0882287i	−0.749844	−	0.661615i	$-0.769871\pi$
$743$	−65.5539	+	65.5539i	−0.0882287	+	0.0882287i	0.661615	+	0.749844i	$0.269871\pi$
$744$			280.748i			0.377349i
$745$		0			0
$746$	145.845			0.195503
$747$	−251.023	−	251.023i	−0.336042	−	0.336042i
$748$	−1139.90	+	1139.90i	−1.52393	+	1.52393i
$749$			15.5582i			0.0207719i
$750$		0			0
$751$	−99.3347			−0.132270			−0.0661350	−	0.997811i	$-0.521067\pi$
$751$	−99.3347			−0.132270			−0.0661350	+	0.997811i	$0.521067\pi$
$752$	−54.2120	−	54.2120i	−0.0720904	−	0.0720904i
$753$	439.573	−	439.573i	0.583763	−	0.583763i
$754$		−	1789.78i		−	2.37371i
$755$		0			0
$756$	−105.618			−0.139706
$757$	−605.866	−	605.866i	−0.800351	−	0.800351i	0.182799	−	0.983150i	$-0.441484\pi$
$757$	−605.866	−	605.866i	−0.800351	−	0.800351i	−0.983150	+	0.182799i	$0.941484\pi$
$758$	616.058	−	616.058i	0.812741	−	0.812741i
$759$			664.937i			0.876070i
$760$		0			0
$761$	126.096			0.165698			0.0828489	−	0.996562i	$-0.473598\pi$
$761$	126.096			0.165698			0.0828489	+	0.996562i	$0.473598\pi$
$762$	690.589	+	690.589i	0.906285	+	0.906285i
$763$	−147.112	+	147.112i	−0.192807	+	0.192807i
$764$			229.879i			0.300889i
$765$		0			0
$766$	506.273			0.660931
$767$	274.927	+	274.927i	0.358445	+	0.358445i
$768$	591.114	−	591.114i	0.769679	−	0.769679i
$769$			115.901i			0.150716i	0.997157	+	0.0753582i	$0.0240100\pi$
$769$			115.901i			0.150716i	−0.997157	+	0.0753582i	$0.975990\pi$
$770$		0			0
$771$	−386.887			−0.501799
$772$	326.830	+	326.830i	0.423355	+	0.423355i
$773$	−325.618	+	325.618i	−0.421240	+	0.421240i	−0.885630	−	0.464391i	$-0.846273\pi$
$773$	−325.618	+	325.618i	−0.421240	+	0.421240i	0.464391	+	0.885630i	$0.346273\pi$
$774$		−	64.8032i		−	0.0837250i
$775$		0			0
$776$	1521.15			1.96025
$777$	−145.362	−	145.362i	−0.187081	−	0.187081i
$778$	−1612.15	+	1612.15i	−2.07217	+	2.07217i
$779$		−	1038.36i		−	1.33294i
$780$		0			0
$781$	333.721			0.427299
$782$	−444.385	−	444.385i	−0.568268	−	0.568268i
$783$	−145.608	+	145.608i	−0.185962	+	0.185962i
$784$		−	86.0421i		−	0.109748i
$785$		0			0
$786$	827.750			1.05312
$787$	140.660	+	140.660i	0.178730	+	0.178730i	0.790802	−	0.612072i	$-0.209664\pi$
$787$	140.660	+	140.660i	0.178730	+	0.178730i	−0.612072	+	0.790802i	$0.709664\pi$
$788$	1913.68	−	1913.68i	2.42852	−	2.42852i
$789$		−	24.0003i		−	0.0304187i
$790$		0			0
$791$	401.641			0.507763
$792$	558.886	+	558.886i	0.705664	+	0.705664i
$793$	66.2708	−	66.2708i	0.0835697	−	0.0835697i
$794$		−	829.788i		−	1.04507i
$795$		0			0
$796$	−128.720			−0.161709
$797$	533.305	+	533.305i	0.669141	+	0.669141i	0.957517	−	0.288376i	$-0.0931154\pi$
$797$	533.305	+	533.305i	0.669141	+	0.669141i	−0.288376	+	0.957517i	$0.593115\pi$
$798$	165.587	−	165.587i	0.207503	−	0.207503i
$799$		−	62.5284i		−	0.0782584i
$800$		0			0
$801$	188.246			0.235014
$802$	−1658.21	−	1658.21i	−2.06760	−	2.06760i
$803$	678.507	−	678.507i	0.844966	−	0.844966i
$804$		−	26.3082i		−	0.0327216i
$805$		0			0
$806$	−581.585			−0.721570
$807$	175.756	+	175.756i	0.217789	+	0.217789i
$808$	1296.26	−	1296.26i	1.60428	−	1.60428i
$809$			651.161i			0.804896i	0.915443	+	0.402448i	$0.131841\pi$
$809$			651.161i			0.804896i	−0.915443	+	0.402448i	$0.868159\pi$
$810$		0			0
$811$	94.9703			0.117103			0.0585513	−	0.998284i	$-0.481352\pi$
$811$	94.9703			0.117103			0.0585513	+	0.998284i	$0.481352\pi$
$812$	−569.587	−	569.587i	−0.701462	−	0.701462i
$813$	36.0971	−	36.0971i	0.0443999	−	0.0443999i
$814$			3209.37i			3.94271i
$815$		0			0
$816$	−213.429			−0.261555
$817$	66.8118	+	66.8118i	0.0817770	+	0.0817770i
$818$	−1344.39	+	1344.39i	−1.64351	+	1.64351i
$819$		−	104.877i		−	0.128055i
$820$		0			0
$821$	−368.589			−0.448952			−0.224476	−	0.974480i	$-0.572067\pi$
$821$	−368.589			−0.448952			−0.224476	+	0.974480i	$0.572067\pi$
$822$	953.845	+	953.845i	1.16040	+	1.16040i
$823$	−494.462	+	494.462i	−0.600804	+	0.600804i	−0.940526	−	0.339722i	$-0.889667\pi$
$823$	−494.462	+	494.462i	−0.600804	+	0.600804i	0.339722	+	0.940526i	$0.389667\pi$
$824$			1108.18i			1.34487i
$825$		0			0
$826$	266.098			0.322152
$827$	191.666	+	191.666i	0.231761	+	0.231761i	0.813427	−	0.581666i	$-0.197599\pi$
$827$	191.666	+	191.666i	0.231761	+	0.231761i	−0.581666	+	0.813427i	$0.697599\pi$
$828$	−298.909	+	298.909i	−0.361001	+	0.361001i
$829$			110.729i			0.133569i	0.997767	+	0.0667847i	$0.0212741\pi$
$829$			110.729i			0.133569i	−0.997767	+	0.0667847i	$0.978726\pi$
$830$		0			0
$831$	464.978			0.559541
$832$	725.555	+	725.555i	0.872061	+	0.872061i
$833$	49.6207	−	49.6207i	0.0595687	−	0.0595687i
$834$		−	1190.71i		−	1.42770i
$835$		0			0
$836$	−2404.17			−2.87580
$837$	47.3152	+	47.3152i	0.0565295	+	0.0565295i
$838$	347.137	−	347.137i	0.414245	−	0.414245i
$839$			184.793i			0.220254i	0.993918	+	0.110127i	$0.0351258\pi$
$839$			184.793i			0.220254i	−0.993918	+	0.110127i	$0.964874\pi$
$840$		0			0
$841$	−729.502			−0.867422
$842$	−266.748	−	266.748i	−0.316803	−	0.316803i
$843$	75.0159	−	75.0159i	0.0889869	−	0.0889869i
$844$			591.771i			0.701150i
$845$		0			0
$846$	−63.9570			−0.0755993
$847$	593.271	+	593.271i	0.700438	+	0.700438i
$848$	−596.535	+	596.535i	−0.703462	+	0.703462i
$849$			432.127i			0.508984i
$850$		0			0
$851$	−822.774			−0.966832
$852$	150.017	+	150.017i	0.176077	+	0.176077i
$853$	−3.11065	+	3.11065i	−0.00364672	+	0.00364672i	−0.708928	−	0.705281i	$-0.750821\pi$
$853$	−3.11065	+	3.11065i	−0.00364672	+	0.00364672i	0.705281	+	0.708928i	$0.250821\pi$
$854$		−	64.1424i		−	0.0751082i
$855$		0			0
$856$	74.0169			0.0864683
$857$	−141.310	−	141.310i	−0.164889	−	0.164889i	0.619840	−	0.784729i	$-0.287198\pi$
$857$	−141.310	−	141.310i	−0.164889	−	0.164889i	−0.784729	+	0.619840i	$0.787198\pi$
$858$	−1157.76	+	1157.76i	−1.34938	+	1.34938i
$859$			1054.78i			1.22792i	0.789338	+	0.613959i	$0.210424\pi$
$859$			1054.78i			1.22792i	−0.789338	+	0.613959i	$0.789576\pi$
$860$		0			0
$861$	−318.269			−0.369650
$862$	−1063.04	−	1063.04i	−1.23322	−	1.23322i
$863$	227.600	−	227.600i	0.263732	−	0.263732i	−0.562837	−	0.826568i	$-0.690290\pi$
$863$	227.600	−	227.600i	0.263732	−	0.263732i	0.826568	+	0.562837i	$0.190290\pi$
$864$		−	43.3103i		−	0.0501276i
$865$		0			0
$866$	−573.005			−0.661669
$867$	230.866	+	230.866i	0.266281	+	0.266281i
$868$	−185.087	+	185.087i	−0.213233	+	0.213233i
$869$			1383.88i			1.59250i
$870$		0			0
$871$	26.1236			0.0299927
$872$	699.876	+	699.876i	0.802610	+	0.802610i
$873$	256.364	−	256.364i	0.293659	−	0.293659i
$874$		−	937.254i		−	1.07237i
$875$		0			0
$876$	610.018			0.696368
$877$	71.4976	+	71.4976i	0.0815252	+	0.0815252i	0.746693	−	0.665168i	$-0.231640\pi$
$877$	71.4976	+	71.4976i	0.0815252	+	0.0815252i	−0.665168	+	0.746693i	$0.731640\pi$
$878$	849.578	−	849.578i	0.967629	−	0.967629i
$879$			227.169i			0.258441i
$880$		0			0
$881$	932.073			1.05797			0.528986	−	0.848631i	$-0.322572\pi$
$881$	932.073			1.05797			0.528986	+	0.848631i	$0.322572\pi$
$882$	−50.7544	−	50.7544i	−0.0575447	−	0.0575447i
$883$	616.640	−	616.640i	0.698346	−	0.698346i	−0.265708	−	0.964054i	$-0.585606\pi$
$883$	616.640	−	616.640i	0.698346	−	0.698346i	0.964054	+	0.265708i	$0.0856056\pi$
$884$		−	1017.65i		−	1.15119i
$885$		0			0
$886$	−198.828			−0.224410
$887$	990.320	+	990.320i	1.11648	+	1.11648i	0.992254	+	0.124229i	$0.0396459\pi$
$887$	990.320	+	990.320i	1.11648	+	1.11648i	0.124229	+	0.992254i	$0.460354\pi$
$888$	−691.549	+	691.549i	−0.778771	+	0.778771i
$889$			436.469i			0.490966i
$890$		0			0
$891$	188.381			0.211427
$892$	339.282	+	339.282i	0.380361	+	0.380361i
$893$	65.9394	−	65.9394i	0.0738403	−	0.0738403i
$894$			137.566i			0.153877i
$895$		0			0
$896$	614.043			0.685316
$897$	−296.812	−	296.812i	−0.330894	−	0.330894i
$898$	507.323	−	507.323i	0.564948	−	0.564948i
$899$			510.332i			0.567666i
$900$		0			0
$901$	−688.047			−0.763649
$902$	3513.45	+	3513.45i	3.89517	+	3.89517i
$903$	20.4786	−	20.4786i	0.0226784	−	0.0226784i
$904$		−	1910.78i		−	2.11369i
$905$		0			0
$906$	−232.966			−0.257137
$907$	449.584	+	449.584i	0.495682	+	0.495682i	0.910091	−	0.414409i	$-0.136012\pi$
$907$	449.584	+	449.584i	0.495682	+	0.495682i	−0.414409	+	0.910091i	$0.636012\pi$
$908$	−1355.98	+	1355.98i	−1.49336	+	1.49336i
$909$		−	436.924i		−	0.480665i
$910$		0			0
$911$	1065.29			1.16936			0.584680	−	0.811264i	$-0.301220\pi$
$911$	1065.29			1.16936			0.584680	+	0.811264i	$0.301220\pi$
$912$	−225.072	−	225.072i	−0.246789	−	0.246789i
$913$	−1751.41	+	1751.41i	−1.91830	+	1.91830i
$914$		−	758.134i		−	0.829468i
$915$		0			0
$916$	−2279.75			−2.48881
$917$	261.579	+	261.579i	0.285255	+	0.285255i
$918$	−125.897	+	125.897i	−0.137143	+	0.137143i
$919$			1080.05i			1.17525i	0.809135	+	0.587623i	$0.199936\pi$
$919$			1080.05i			1.17525i	−0.809135	+	0.587623i	$0.800064\pi$
$920$		0			0
$921$	−560.607			−0.608694
$922$	−662.580	−	662.580i	−0.718634	−	0.718634i
$923$	−148.965	+	148.965i	−0.161392	+	0.161392i
$924$			736.905i			0.797516i
$925$		0			0
$926$	2335.62			2.52227
$927$	186.764	+	186.764i	0.201471	+	0.201471i
$928$	233.568	−	233.568i	0.251690	−	0.251690i
$929$			1513.19i			1.62884i	0.580278	+	0.814419i	$0.302944\pi$
$929$			1513.19i			1.62884i	−0.580278	+	0.814419i	$0.697056\pi$
$930$		0			0
$931$	104.655			0.112412
$932$	677.335	+	677.335i	0.726755	+	0.726755i
$933$	−356.545	+	356.545i	−0.382149	+	0.382149i
$934$			42.0972i			0.0450720i
$935$		0			0
$936$	−498.946			−0.533062
$937$	−754.545	−	754.545i	−0.805278	−	0.805278i	0.178637	−	0.983915i	$-0.442831\pi$
$937$	−754.545	−	754.545i	−0.805278	−	0.805278i	−0.983915	+	0.178637i	$0.942831\pi$
$938$	12.6423	−	12.6423i	0.0134779	−	0.0134779i
$939$		−	616.457i		−	0.656503i
$940$		0			0
$941$	1377.61			1.46399			0.731993	−	0.681312i	$-0.238590\pi$
$941$	1377.61			1.46399			0.731993	+	0.681312i	$0.238590\pi$
$942$	−302.886	−	302.886i	−0.321535	−	0.321535i
$943$	−900.729	+	900.729i	−0.955174	+	0.955174i
$944$		−	361.690i		−	0.383146i
$945$		0			0
$946$	−452.137			−0.477946
$947$	−133.593	−	133.593i	−0.141070	−	0.141070i	0.633045	−	0.774115i	$-0.281805\pi$
$947$	−133.593	−	133.593i	−0.141070	−	0.141070i	−0.774115	+	0.633045i	$0.781805\pi$
$948$	−622.094	+	622.094i	−0.656217	+	0.656217i
$949$			605.738i			0.638291i
$950$		0			0
$951$	74.4842			0.0783219
$952$	−236.067	−	236.067i	−0.247970	−	0.247970i
$953$	498.927	−	498.927i	0.523533	−	0.523533i	−0.395104	−	0.918636i	$-0.629291\pi$
$953$	498.927	−	498.927i	0.523533	−	0.523533i	0.918636	+	0.395104i	$0.129291\pi$
$954$			703.767i			0.737701i
$955$		0			0
$956$	2845.01			2.97595
$957$	1015.92	+	1015.92i	1.06157	+	1.06157i
$958$	1948.68	−	1948.68i	2.03411	−	2.03411i
$959$			602.854i			0.628627i
$960$		0			0
$961$	−795.168			−0.827438
$962$	−1432.58	−	1432.58i	−1.48917	−	1.48917i
$963$	12.4743	−	12.4743i	0.0129536	−	0.0129536i
$964$		−	1554.28i		−	1.61233i
$965$		0			0
$966$	−287.279			−0.297391
$967$	−506.991	−	506.991i	−0.524293	−	0.524293i	0.394572	−	0.918865i	$-0.370893\pi$
$967$	−506.991	−	506.991i	−0.524293	−	0.524293i	−0.918865	+	0.394572i	$0.870893\pi$
$968$	2822.45	−	2822.45i	2.91575	−	2.91575i
$969$		−	259.599i		−	0.267904i
$970$		0			0
$971$	−74.6256			−0.0768543			−0.0384272	−	0.999261i	$-0.512235\pi$
$971$	−74.6256			−0.0768543			−0.0384272	+	0.999261i	$0.512235\pi$
$972$	84.6828	+	84.6828i	0.0871222	+	0.0871222i
$973$	376.277	−	376.277i	0.386719	−	0.386719i
$974$		−	741.960i		−	0.761766i
$975$		0			0
$976$	−87.1846			−0.0893285
$977$	291.427	+	291.427i	0.298288	+	0.298288i	0.840343	−	0.542055i	$-0.182354\pi$
$977$	291.427	+	291.427i	0.298288	+	0.298288i	−0.542055	+	0.840343i	$0.682354\pi$
$978$	238.464	−	238.464i	0.243829	−	0.243829i
$979$		−	1313.41i		−	1.34158i
$980$		0			0
$981$	235.904			0.240473
$982$	437.345	+	437.345i	0.445361	+	0.445361i
$983$	932.709	−	932.709i	0.948839	−	0.948839i	−0.0499141	−	0.998754i	$-0.515895\pi$
$983$	932.709	−	932.709i	0.948839	−	0.948839i	0.998754	+	0.0499141i	$0.0158948\pi$
$984$			1514.14i			1.53876i
$985$		0			0
$986$	−1357.90			−1.37718
$987$	−20.2112	−	20.2112i	−0.0204774	−	0.0204774i
$988$	1073.16	−	1073.16i	1.08620	−	1.08620i
$989$		−	115.913i		−	0.117202i
$990$		0			0
$991$	294.340			0.297013			0.148507	−	0.988911i	$-0.452553\pi$
$991$	294.340			0.297013			0.148507	+	0.988911i	$0.452553\pi$
$992$	−75.8975	−	75.8975i	−0.0765096	−	0.0765096i
$993$	735.947	−	735.947i	0.741135	−	0.741135i
$994$			144.181i			0.145051i
$995$		0			0
$996$	−1574.62			−1.58094
$997$	−678.292	−	678.292i	−0.680333	−	0.680333i	0.279742	−	0.960075i	$-0.409751\pi$
$997$	−678.292	−	678.292i	−0.680333	−	0.680333i	−0.960075	+	0.279742i	$0.909751\pi$
$998$	33.7403	−	33.7403i	0.0338079	−	0.0338079i
$999$			233.097i			0.233331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.232.2		24
5.2	odd	4		105.3.l.a.43.11	yes	24
5.3	odd	4	inner	525.3.l.e.43.2		24
5.4	even	2		105.3.l.a.22.11	✓	24
15.2	even	4		315.3.o.b.253.2		24
15.14	odd	2		315.3.o.b.127.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.11	✓	24	5.4	even	2
105.3.l.a.43.11	yes	24	5.2	odd	4
315.3.o.b.127.2		24	15.14	odd	2
315.3.o.b.253.2		24	15.2	even	4
525.3.l.e.43.2		24	5.3	odd	4	inner
525.3.l.e.232.2		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)

\(f(q)\)	\(=\)	\(q+(-2.41688 - 2.41688i) q^{2} +(-1.22474 + 1.22474i) q^{3} +7.68258i q^{4} +5.92011 q^{6} +(1.87083 + 1.87083i) q^{7} +(8.90034 - 8.90034i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-2.41688 - 2.41688i) q^{2} +(-1.22474 + 1.22474i) q^{3} +7.68258i q^{4} +5.92011 q^{6} +(1.87083 + 1.87083i) q^{7} +(8.90034 - 8.90034i) q^{8} -3.00000i q^{9} -20.9312 q^{11} +(-9.40920 - 9.40920i) q^{12} +(9.34319 - 9.34319i) q^{13} -9.04312i q^{14} -12.2917 q^{16} +(-7.08868 - 7.08868i) q^{17} +(-7.25063 + 7.25063i) q^{18} -14.9507i q^{19} -4.58258 q^{21} +(50.5882 + 50.5882i) q^{22} +(-12.9691 + 12.9691i) q^{23} +21.8013i q^{24} -45.1627 q^{26} +(3.67423 + 3.67423i) q^{27} +(-14.3728 + 14.3728i) q^{28} +39.6296i q^{29} +12.8776 q^{31} +(-5.89378 - 5.89378i) q^{32} +(25.6354 - 25.6354i) q^{33} +34.2649i q^{34} +23.0477 q^{36} +(31.7205 + 31.7205i) q^{37} +(-36.1341 + 36.1341i) q^{38} +22.8861i q^{39} +69.4519 q^{41} +(11.0755 + 11.0755i) q^{42} +(-4.46880 + 4.46880i) q^{43} -160.806i q^{44} +62.6895 q^{46} +(4.41044 + 4.41044i) q^{47} +(15.0542 - 15.0542i) q^{48} +7.00000i q^{49} +17.3636 q^{51} +(71.7798 + 71.7798i) q^{52} +(48.5314 - 48.5314i) q^{53} -17.7603i q^{54} +33.3020 q^{56} +(18.3108 + 18.3108i) q^{57} +(95.7797 - 95.7797i) q^{58} +29.4254i q^{59} +7.09295 q^{61} +(-31.1235 - 31.1235i) q^{62} +(5.61249 - 5.61249i) q^{63} +77.6560i q^{64} -123.915 q^{66} +(1.39800 + 1.39800i) q^{67} +(54.4593 - 54.4593i) q^{68} -31.7677i q^{69} -15.9437 q^{71} +(-26.7010 - 26.7010i) q^{72} +(-32.4160 + 32.4160i) q^{73} -153.329i q^{74} +114.860 q^{76} +(-39.1588 - 39.1588i) q^{77} +(55.3128 - 55.3128i) q^{78} -66.1155i q^{79} -9.00000 q^{81} +(-167.857 - 167.857i) q^{82} +(83.6744 - 83.6744i) q^{83} -35.2060i q^{84} +21.6011 q^{86} +(-48.5361 - 48.5361i) q^{87} +(-186.295 + 186.295i) q^{88} +62.7487i q^{89} +34.9590 q^{91} +(-99.6363 - 99.6363i) q^{92} +(-15.7717 + 15.7717i) q^{93} -21.3190i q^{94} +14.4368 q^{96} +(85.4547 + 85.4547i) q^{97} +(16.9181 - 16.9181i) q^{98} +62.7937i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 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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