LMFDB - Embedded newform 525.3.l.e.232.3

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			232.3
Character	$\chi$	$=$	525.232
Dual form			525.3.l.e.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24469 - 2.24469i) q^{2} +(-1.22474 + 1.22474i) q^{3} +6.07726i q^{4} +5.49834 q^{6} +(-1.87083 - 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-2.24469 - 2.24469i) q^{2} +(-1.22474 + 1.22474i) q^{3} +6.07726i q^{4} +5.49834 q^{6} +(-1.87083 - 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} -3.00000i q^{9} +3.94671 q^{11} +(-7.44309 - 7.44309i) q^{12} +(-8.57045 + 8.57045i) q^{13} +8.39886i q^{14} +3.37595 q^{16} +(17.2039 + 17.2039i) q^{17} +(-6.73407 + 6.73407i) q^{18} -24.3758i q^{19} +4.58258 q^{21} +(-8.85913 - 8.85913i) q^{22} +(19.6705 - 19.6705i) q^{23} +11.4215i q^{24} +38.4760 q^{26} +(3.67423 + 3.67423i) q^{27} +(11.3695 - 11.3695i) q^{28} +17.5580i q^{29} -43.8736 q^{31} +(-26.2292 - 26.2292i) q^{32} +(-4.83371 + 4.83371i) q^{33} -77.2348i q^{34} +18.2318 q^{36} +(-32.9598 - 32.9598i) q^{37} +(-54.7160 + 54.7160i) q^{38} -20.9932i q^{39} +22.4582 q^{41} +(-10.2865 - 10.2865i) q^{42} +(-14.3533 + 14.3533i) q^{43} +23.9852i q^{44} -88.3085 q^{46} +(-38.7355 - 38.7355i) q^{47} +(-4.13468 + 4.13468i) q^{48} +7.00000i q^{49} -42.1407 q^{51} +(-52.0849 - 52.0849i) q^{52} +(-9.01352 + 9.01352i) q^{53} -16.4950i q^{54} -17.4466 q^{56} +(29.8541 + 29.8541i) q^{57} +(39.4121 - 39.4121i) q^{58} +58.0335i q^{59} -89.2995 q^{61} +(98.4827 + 98.4827i) q^{62} +(-5.61249 + 5.61249i) q^{63} +104.249i q^{64} +21.7004 q^{66} +(21.2058 + 21.2058i) q^{67} +(-104.552 + 104.552i) q^{68} +48.1828i q^{69} -78.8147 q^{71} +(-13.9884 - 13.9884i) q^{72} +(18.2694 - 18.2694i) q^{73} +147.969i q^{74} +148.138 q^{76} +(-7.38362 - 7.38362i) q^{77} +(-47.1233 + 47.1233i) q^{78} -112.267i q^{79} -9.00000 q^{81} +(-50.4118 - 50.4118i) q^{82} +(12.9380 - 12.9380i) q^{83} +27.8495i q^{84} +64.4373 q^{86} +(-21.5040 - 21.5040i) q^{87} +(18.4027 - 18.4027i) q^{88} +22.2193i q^{89} +32.0677 q^{91} +(119.543 + 119.543i) q^{92} +(53.7340 - 53.7340i) q^{93} +173.898i q^{94} +64.2481 q^{96} +(-90.6427 - 90.6427i) q^{97} +(15.7128 - 15.7128i) q^{98} -11.8401i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.24469	−	2.24469i	−1.12234	−	1.12234i	−0.991388	−	0.130957i	$-0.958195\pi$
$2$	−2.24469	−	2.24469i	−1.12234	−	1.12234i	−0.130957	−	0.991388i	$-0.541805\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			6.07726i			1.51932i
$5$		0			0
$5$		0			0
$6$	5.49834			0.916391
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	4.66280	−	4.66280i	0.582850	−	0.582850i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	3.94671			0.358792			0.179396	−	0.983777i	$-0.442586\pi$
$11$	3.94671			0.358792			0.179396	+	0.983777i	$0.442586\pi$
$12$	−7.44309	−	7.44309i	−0.620258	−	0.620258i
$13$	−8.57045	+	8.57045i	−0.659265	+	0.659265i	−0.955206	−	0.295941i	$-0.904367\pi$
$13$	−8.57045	+	8.57045i	−0.659265	+	0.659265i	0.295941	+	0.955206i	$0.404367\pi$
$14$			8.39886i			0.599918i
$15$		0			0
$16$	3.37595			0.210997
$17$	17.2039	+	17.2039i	1.01199	+	1.01199i	0.999927	+	0.0120660i	$0.00384082\pi$
$17$	17.2039	+	17.2039i	1.01199	+	1.01199i	0.0120660	+	0.999927i	$0.496159\pi$
$18$	−6.73407	+	6.73407i	−0.374115	+	0.374115i
$19$		−	24.3758i		−	1.28294i	−0.767150	−	0.641468i	$-0.778326\pi$
$19$		−	24.3758i		−	1.28294i	0.767150	−	0.641468i	$-0.221674\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	−8.85913	−	8.85913i	−0.402688	−	0.402688i
$23$	19.6705	−	19.6705i	0.855240	−	0.855240i	−0.135533	−	0.990773i	$-0.543275\pi$
$23$	19.6705	−	19.6705i	0.855240	−	0.855240i	0.990773	+	0.135533i	$0.0432745\pi$
$24$			11.4215i			0.475895i
$25$		0			0
$26$	38.4760			1.47985
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	11.3695	−	11.3695i	0.406054	−	0.406054i
$29$			17.5580i			0.605447i	0.953078	+	0.302723i	$0.0978958\pi$
$29$			17.5580i			0.605447i	−0.953078	+	0.302723i	$0.902104\pi$
$30$		0			0
$31$	−43.8736			−1.41528			−0.707639	−	0.706574i	$-0.750240\pi$
$31$	−43.8736			−1.41528			−0.707639	+	0.706574i	$0.750240\pi$
$32$	−26.2292	−	26.2292i	−0.819662	−	0.819662i
$33$	−4.83371	+	4.83371i	−0.146476	+	0.146476i
$34$		−	77.2348i		−	2.27161i
$35$		0			0
$36$	18.2318			0.506438
$37$	−32.9598	−	32.9598i	−0.890805	−	0.890805i	0.103794	−	0.994599i	$-0.466902\pi$
$37$	−32.9598	−	32.9598i	−0.890805	−	0.890805i	−0.994599	+	0.103794i	$0.966902\pi$
$38$	−54.7160	+	54.7160i	−1.43990	+	1.43990i
$39$		−	20.9932i		−	0.538288i
$40$		0			0
$41$	22.4582			0.547762			0.273881	−	0.961764i	$-0.411693\pi$
$41$	22.4582			0.547762			0.273881	+	0.961764i	$0.411693\pi$
$42$	−10.2865	−	10.2865i	−0.244916	−	0.244916i
$43$	−14.3533	+	14.3533i	−0.333797	+	0.333797i	−0.854026	−	0.520230i	$-0.825846\pi$
$43$	−14.3533	+	14.3533i	−0.333797	+	0.333797i	0.520230	+	0.854026i	$0.325846\pi$
$44$			23.9852i			0.545118i
$45$		0			0
$46$	−88.3085			−1.91975
$47$	−38.7355	−	38.7355i	−0.824159	−	0.824159i	0.162542	−	0.986702i	$-0.448031\pi$
$47$	−38.7355	−	38.7355i	−0.824159	−	0.824159i	−0.986702	+	0.162542i	$0.948031\pi$
$48$	−4.13468	+	4.13468i	−0.0861391	+	0.0861391i
$49$			7.00000i			0.142857i
$50$		0			0
$51$	−42.1407			−0.826289
$52$	−52.0849	−	52.0849i	−1.00163	−	1.00163i
$53$	−9.01352	+	9.01352i	−0.170067	+	0.170067i	−0.787009	−	0.616942i	$-0.788371\pi$
$53$	−9.01352	+	9.01352i	−0.170067	+	0.170067i	0.616942	+	0.787009i	$0.288371\pi$
$54$		−	16.4950i		−	0.305464i
$55$		0			0
$56$	−17.4466			−0.311547
$57$	29.8541	+	29.8541i	0.523756	+	0.523756i
$58$	39.4121	−	39.4121i	0.679520	−	0.679520i
$59$			58.0335i			0.983618i	0.870703	+	0.491809i	$0.163664\pi$
$59$			58.0335i			0.983618i	−0.870703	+	0.491809i	$0.836336\pi$
$60$		0			0
$61$	−89.2995			−1.46393			−0.731963	−	0.681344i	$-0.761396\pi$
$61$	−89.2995			−1.46393			−0.731963	+	0.681344i	$0.761396\pi$
$62$	98.4827	+	98.4827i	1.58843	+	1.58843i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$			104.249i			1.62889i
$65$		0			0
$66$	21.7004			0.328793
$67$	21.2058	+	21.2058i	0.316505	+	0.316505i	0.847423	−	0.530918i	$-0.178153\pi$
$67$	21.2058	+	21.2058i	0.316505	+	0.316505i	−0.530918	+	0.847423i	$0.678153\pi$
$68$	−104.552	+	104.552i	−1.53754	+	1.53754i
$69$			48.1828i			0.698301i
$70$		0			0
$71$	−78.8147			−1.11007			−0.555033	−	0.831828i	$-0.687294\pi$
$71$	−78.8147			−1.11007			−0.555033	+	0.831828i	$0.687294\pi$
$72$	−13.9884	−	13.9884i	−0.194283	−	0.194283i
$73$	18.2694	−	18.2694i	0.250266	−	0.250266i	−0.570814	−	0.821080i	$-0.693372\pi$
$73$	18.2694	−	18.2694i	0.250266	−	0.250266i	0.821080	+	0.570814i	$0.193372\pi$
$74$			147.969i			1.99958i
$75$		0			0
$76$	148.138			1.94918
$77$	−7.38362	−	7.38362i	−0.0958911	−	0.0958911i
$78$	−47.1233	+	47.1233i	−0.604145	+	0.604145i
$79$		−	112.267i		−	1.42110i	−0.703646	−	0.710551i	$-0.748446\pi$
$79$		−	112.267i		−	1.42110i	0.703646	−	0.710551i	$-0.251554\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−50.4118	−	50.4118i	−0.614777	−	0.614777i
$83$	12.9380	−	12.9380i	0.155879	−	0.155879i	−0.624859	−	0.780738i	$-0.714843\pi$
$83$	12.9380	−	12.9380i	0.155879	−	0.155879i	0.780738	+	0.624859i	$0.214843\pi$
$84$			27.8495i			0.331542i
$85$		0			0
$86$	64.4373			0.749270
$87$	−21.5040	−	21.5040i	−0.247173	−	0.247173i
$88$	18.4027	−	18.4027i	0.209122	−	0.209122i
$89$			22.2193i			0.249655i	0.992178	+	0.124827i	$0.0398377\pi$
$89$			22.2193i			0.249655i	−0.992178	+	0.124827i	$0.960162\pi$
$90$		0			0
$91$	32.0677			0.352392
$92$	119.543	+	119.543i	1.29938	+	1.29938i
$93$	53.7340	−	53.7340i	0.577785	−	0.577785i
$94$			173.898i			1.84998i
$95$		0			0
$96$	64.2481			0.669251
$97$	−90.6427	−	90.6427i	−0.934461	−	0.934461i	0.0635195	−	0.997981i	$-0.479767\pi$
$97$	−90.6427	−	90.6427i	−0.934461	−	0.934461i	−0.997981	+	0.0635195i	$0.979767\pi$
$98$	15.7128	−	15.7128i	0.160335	−	0.160335i
$99$		−	11.8401i		−	0.119597i
$100$		0			0
$101$	−180.124			−1.78341			−0.891703	−	0.452621i	$-0.850489\pi$
$101$	−180.124			−1.78341			−0.891703	+	0.452621i	$0.850489\pi$
$102$	94.5929	+	94.5929i	0.927381	+	0.927381i
$103$	−137.374	+	137.374i	−1.33373	+	1.33373i	−0.431729	+	0.902003i	$0.642096\pi$
$103$	−137.374	+	137.374i	−1.33373	+	1.33373i	−0.902003	+	0.431729i	$0.857904\pi$
$104$			79.9247i			0.768506i
$105$		0			0
$106$	40.4651			0.381746
$107$	102.254	+	102.254i	0.955648	+	0.955648i	0.999057	−	0.0434091i	$-0.0138219\pi$
$107$	102.254	+	102.254i	0.955648	+	0.955648i	−0.0434091	+	0.999057i	$0.513822\pi$
$108$	−22.3293	+	22.3293i	−0.206753	+	0.206753i
$109$			58.4672i			0.536396i	0.963364	+	0.268198i	$0.0864282\pi$
$109$			58.4672i			0.536396i	−0.963364	+	0.268198i	$0.913572\pi$
$110$		0			0
$111$	80.7347			0.727340
$112$	−6.31582	−	6.31582i	−0.0563913	−	0.0563913i
$113$	−39.8190	+	39.8190i	−0.352381	+	0.352381i	−0.860995	−	0.508614i	$-0.830158\pi$
$113$	−39.8190	+	39.8190i	−0.352381	+	0.352381i	0.508614	+	0.860995i	$0.330158\pi$
$114$		−	134.026i		−	1.17567i
$115$		0			0
$116$	−106.704			−0.919864
$117$	25.7113	+	25.7113i	0.219755	+	0.219755i
$118$	130.267	−	130.267i	1.10396	−	1.10396i
$119$		−	64.3710i		−	0.540933i
$120$		0			0
$121$	−105.423			−0.871269
$122$	200.450	+	200.450i	1.64303	+	1.64303i
$123$	−27.5056	+	27.5056i	−0.223623	+	0.223623i
$124$		−	266.631i		−	2.15025i
$125$		0			0
$126$	25.1966			0.199973
$127$	−28.1517	−	28.1517i	−0.221667	−	0.221667i	0.587533	−	0.809200i	$-0.300099\pi$
$127$	−28.1517	−	28.1517i	−0.221667	−	0.221667i	−0.809200	+	0.587533i	$0.800099\pi$
$128$	129.090	−	129.090i	1.00851	−	1.00851i
$129$		−	35.1582i		−	0.272544i
$130$		0			0
$131$	−32.5463			−0.248445			−0.124223	−	0.992254i	$-0.539644\pi$
$131$	−32.5463			−0.248445			−0.124223	+	0.992254i	$0.539644\pi$
$132$	−29.3757	−	29.3757i	−0.222543	−	0.222543i
$133$	−45.6029	+	45.6029i	−0.342879	+	0.342879i
$134$		−	95.2009i		−	0.710454i
$135$		0			0
$136$	160.437			1.17968
$137$	−184.159	−	184.159i	−1.34423	−	1.34423i	−0.891804	−	0.452422i	$-0.850560\pi$
$137$	−184.159	−	184.159i	−1.34423	−	1.34423i	−0.452422	−	0.891804i	$-0.649440\pi$
$138$	108.155	−	108.155i	0.783734	−	0.783734i
$139$		−	76.2552i		−	0.548599i	−0.961644	−	0.274299i	$-0.911554\pi$
$139$		−	76.2552i		−	0.548599i	0.961644	−	0.274299i	$-0.0884459\pi$
$140$		0			0
$141$	94.8822			0.672923
$142$	176.914	+	176.914i	1.24588	+	1.24588i
$143$	−33.8251	+	33.8251i	−0.236539	+	0.236539i
$144$		−	10.1278i		−	0.0703323i
$145$		0			0
$146$	−82.0184			−0.561770
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	200.305	−	200.305i	1.35341	−	1.35341i
$149$		−	232.403i		−	1.55975i	−0.625933	−	0.779877i	$-0.715282\pi$
$149$		−	232.403i		−	1.55975i	0.625933	−	0.779877i	$-0.284718\pi$
$150$		0			0
$151$	170.930			1.13199			0.565994	−	0.824409i	$-0.308492\pi$
$151$	170.930			1.13199			0.565994	+	0.824409i	$0.308492\pi$
$152$	−113.659	−	113.659i	−0.747760	−	0.747760i
$153$	51.6117	−	51.6117i	0.337331	−	0.337331i
$154$			33.1478i			0.215246i
$155$		0			0
$156$	127.581			0.817829
$157$	−199.875	−	199.875i	−1.27309	−	1.27309i	−0.944457	−	0.328635i	$-0.893411\pi$
$157$	−199.875	−	199.875i	−1.27309	−	1.27309i	−0.328635	−	0.944457i	$-0.606589\pi$
$158$	−252.005	+	252.005i	−1.59497	+	1.59497i
$159$		−	22.0785i		−	0.138859i
$160$		0			0
$161$	−73.6004			−0.457145
$162$	20.2022	+	20.2022i	0.124705	+	0.124705i
$163$	147.090	−	147.090i	0.902392	−	0.902392i	−0.0932506	−	0.995643i	$-0.529726\pi$
$163$	147.090	−	147.090i	0.902392	−	0.902392i	0.995643	+	0.0932506i	$0.0297258\pi$
$164$			136.485i			0.832223i
$165$		0			0
$166$	−58.0834			−0.349900
$167$	−43.6355	−	43.6355i	−0.261290	−	0.261290i	0.564288	−	0.825578i	$-0.309151\pi$
$167$	−43.6355	−	43.6355i	−0.261290	−	0.261290i	−0.825578	+	0.564288i	$0.809151\pi$
$168$	21.3677	−	21.3677i	0.127188	−	0.127188i
$169$			22.0948i			0.130738i
$170$		0			0
$171$	−73.1273			−0.427645
$172$	−87.2285	−	87.2285i	−0.507143	−	0.507143i
$173$	79.6322	−	79.6322i	0.460302	−	0.460302i	−0.438453	−	0.898754i	$-0.644473\pi$
$173$	79.6322	−	79.6322i	0.460302	−	0.460302i	0.898754	+	0.438453i	$0.144473\pi$
$174$			96.5397i			0.554826i
$175$		0			0
$176$	13.3239			0.0757039
$177$	−71.0762	−	71.0762i	−0.401560	−	0.401560i
$178$	49.8754	−	49.8754i	0.280199	−	0.280199i
$179$		−	189.993i		−	1.06141i	−0.847555	−	0.530707i	$-0.821926\pi$
$179$		−	189.993i		−	1.06141i	0.847555	−	0.530707i	$-0.178074\pi$
$180$		0			0
$181$	193.279			1.06784			0.533920	−	0.845535i	$-0.320718\pi$
$181$	193.279			1.06784			0.533920	+	0.845535i	$0.320718\pi$
$182$	−71.9820	−	71.9820i	−0.395505	−	0.395505i
$183$	109.369	−	109.369i	0.597646	−	0.597646i
$184$		−	183.440i		−	0.996955i
$185$		0			0
$186$	−241.232			−1.29695
$187$	67.8987	+	67.8987i	0.363095	+	0.363095i
$188$	235.406	−	235.406i	1.25216	−	1.25216i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	236.062			1.23593			0.617963	−	0.786207i	$-0.287958\pi$
$191$	236.062			1.23593			0.617963	+	0.786207i	$0.287958\pi$
$192$	−127.678	−	127.678i	−0.664991	−	0.664991i
$193$	−126.994	+	126.994i	−0.658001	+	0.658001i	−0.954907	−	0.296906i	$-0.904045\pi$
$193$	−126.994	+	126.994i	−0.658001	+	0.658001i	0.296906	+	0.954907i	$0.404045\pi$
$194$			406.930i			2.09757i
$195$		0			0
$196$	−42.5408			−0.217045
$197$	−123.086	−	123.086i	−0.624804	−	0.624804i	0.321952	−	0.946756i	$-0.395661\pi$
$197$	−123.086	−	123.086i	−0.624804	−	0.624804i	−0.946756	+	0.321952i	$0.895661\pi$
$198$	−26.5774	+	26.5774i	−0.134229	+	0.134229i
$199$		−	27.6913i		−	0.139152i	−0.997577	−	0.0695761i	$-0.977835\pi$
$199$		−	27.6913i		−	0.139152i	0.997577	−	0.0695761i	$-0.0221647\pi$
$200$		0			0
$201$	−51.9434			−0.258425
$202$	404.322	+	404.322i	2.00160	+	2.00160i
$203$	32.8479	−	32.8479i	0.161812	−	0.161812i
$204$		−	256.100i		−	1.25539i
$205$		0			0
$206$	616.726			2.99381
$207$	−59.0116	−	59.0116i	−0.285080	−	0.285080i
$208$	−28.9334	+	28.9334i	−0.139103	+	0.139103i
$209$		−	96.2041i		−	0.460307i
$210$		0			0
$211$	−171.536			−0.812965			−0.406483	−	0.913658i	$-0.633245\pi$
$211$	−171.536			−0.812965			−0.406483	+	0.913658i	$0.633245\pi$
$212$	−54.7775	−	54.7775i	−0.258385	−	0.258385i
$213$	96.5278	−	96.5278i	0.453182	−	0.453182i
$214$		−	459.059i		−	2.14513i
$215$		0			0
$216$	34.2645			0.158632
$217$	82.0801	+	82.0801i	0.378249	+	0.378249i
$218$	131.241	−	131.241i	0.602021	−	0.602021i
$219$			44.7508i			0.204341i
$220$		0			0
$221$	−294.890			−1.33434
$222$	−181.224	−	181.224i	−0.816326	−	0.816326i
$223$	−6.27227	+	6.27227i	−0.0281268	+	0.0281268i	−0.721030	−	0.692904i	$-0.756331\pi$
$223$	−6.27227	+	6.27227i	−0.0281268	+	0.0281268i	0.692904	+	0.721030i	$0.256331\pi$
$224$			98.1406i			0.438128i
$225$		0			0
$226$	178.763			0.790985
$227$	155.382	+	155.382i	0.684501	+	0.684501i	0.961011	−	0.276510i	$-0.0891779\pi$
$227$	155.382	+	155.382i	0.684501	+	0.684501i	−0.276510	+	0.961011i	$0.589178\pi$
$228$	−181.431	+	181.431i	−0.795751	+	0.795751i
$229$			283.171i			1.23656i	0.785960	+	0.618278i	$0.212169\pi$
$229$			283.171i			1.23656i	−0.785960	+	0.618278i	$0.787831\pi$
$230$		0			0
$231$	18.0861			0.0782948
$232$	81.8693	+	81.8693i	0.352885	+	0.352885i
$233$	−18.5950	+	18.5950i	−0.0798069	+	0.0798069i	−0.745883	−	0.666077i	$-0.767972\pi$
$233$	−18.5950	+	18.5950i	−0.0798069	+	0.0798069i	0.666077	+	0.745883i	$0.267972\pi$
$234$		−	115.428i		−	0.493282i
$235$		0			0
$236$	−352.684			−1.49443
$237$	137.499	+	137.499i	0.580162	+	0.580162i
$238$	−144.493	+	144.493i	−0.607113	+	0.607113i
$239$		−	265.031i		−	1.10892i	−0.832211	−	0.554459i	$-0.812925\pi$
$239$		−	265.031i		−	1.10892i	0.832211	−	0.554459i	$-0.187075\pi$
$240$		0			0
$241$	127.492			0.529011			0.264506	−	0.964384i	$-0.414791\pi$
$241$	127.492			0.529011			0.264506	+	0.964384i	$0.414791\pi$
$242$	236.643	+	236.643i	0.977864	+	0.977864i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	542.696i		−	2.22417i
$245$		0			0
$246$	123.483			0.501964
$247$	208.911	+	208.911i	0.845795	+	0.845795i
$248$	−204.574	+	204.574i	−0.824896	+	0.824896i
$249$			31.6914i			0.127275i
$250$		0			0
$251$	31.9519			0.127298			0.0636492	−	0.997972i	$-0.479726\pi$
$251$	31.9519			0.127298			0.0636492	+	0.997972i	$0.479726\pi$
$252$	−34.1085	−	34.1085i	−0.135351	−	0.135351i
$253$	77.6338	−	77.6338i	0.306853	−	0.306853i
$254$			126.383i			0.497573i
$255$		0			0
$256$	−162.537			−0.634910
$257$	138.387	+	138.387i	0.538470	+	0.538470i	0.923079	−	0.384610i	$-0.125664\pi$
$257$	138.387	+	138.387i	0.538470	+	0.538470i	−0.384610	+	0.923079i	$0.625664\pi$
$258$	−78.9192	+	78.9192i	−0.305888	+	0.305888i
$259$			123.324i			0.476155i
$260$		0			0
$261$	52.6739			0.201816
$262$	73.0564	+	73.0564i	0.278841	+	0.278841i
$263$	230.486	−	230.486i	0.876373	−	0.876373i	−0.116785	−	0.993157i	$-0.537259\pi$
$263$	230.486	−	230.486i	0.876373	−	0.876373i	0.993157	+	0.116785i	$0.0372587\pi$
$264$			45.0773i			0.170747i
$265$		0			0
$266$	204.729			0.769657
$267$	−27.2129	−	27.2129i	−0.101921	−	0.101921i
$268$	−128.873	+	128.873i	−0.480870	+	0.480870i
$269$			332.673i			1.23670i	0.785901	+	0.618352i	$0.212199\pi$
$269$			332.673i			1.23670i	−0.785901	+	0.618352i	$0.787801\pi$
$270$		0			0
$271$	−253.724			−0.936251			−0.468126	−	0.883662i	$-0.655071\pi$
$271$	−253.724			−0.936251			−0.468126	+	0.883662i	$0.655071\pi$
$272$	58.0794	+	58.0794i	0.213527	+	0.213527i
$273$	−39.2747	+	39.2747i	−0.143863	+	0.143863i
$274$			826.759i			3.01737i
$275$		0			0
$276$	−292.819			−1.06094
$277$	−252.491	−	252.491i	−0.911521	−	0.911521i	0.0848711	−	0.996392i	$-0.472952\pi$
$277$	−252.491	−	252.491i	−0.911521	−	0.911521i	−0.996392	+	0.0848711i	$0.972952\pi$
$278$	−171.169	+	171.169i	−0.615717	+	0.615717i
$279$			131.621i			0.471759i
$280$		0			0
$281$	−3.26524			−0.0116201			−0.00581004	−	0.999983i	$-0.501849\pi$
$281$	−3.26524			−0.0116201			−0.00581004	+	0.999983i	$0.501849\pi$
$282$	−212.981	−	212.981i	−0.755252	−	0.755252i
$283$	−61.6256	+	61.6256i	−0.217758	+	0.217758i	−0.807553	−	0.589795i	$-0.799209\pi$
$283$	−61.6256	+	61.6256i	−0.217758	+	0.217758i	0.589795	+	0.807553i	$0.299209\pi$
$284$		−	478.977i		−	1.68654i
$285$		0			0
$286$	151.854			0.530956
$287$	−42.0155	−	42.0155i	−0.146395	−	0.146395i
$288$	−78.6875	+	78.6875i	−0.273221	+	0.273221i
$289$			302.947i			1.04826i
$290$		0			0
$291$	222.028			0.762984
$292$	111.028	+	111.028i	0.380233	+	0.380233i
$293$	−150.796	+	150.796i	−0.514663	+	0.514663i	−0.915952	−	0.401289i	$-0.868562\pi$
$293$	−150.796	+	150.796i	−0.514663	+	0.514663i	0.401289	+	0.915952i	$0.368562\pi$
$294$			38.4884i			0.130913i
$295$		0			0
$296$	−307.370			−1.03841
$297$	14.5011	+	14.5011i	0.0488254	+	0.0488254i
$298$	−521.673	+	521.673i	−1.75058	+	1.75058i
$299$			337.171i			1.12766i
$300$		0			0
$301$	53.7050			0.178422
$302$	−383.685	−	383.685i	−1.27048	−	1.27048i
$303$	220.606	−	220.606i	0.728072	−	0.728072i
$304$		−	82.2914i		−	0.270695i
$305$		0			0
$306$	−231.704			−0.757203
$307$	−37.6731	−	37.6731i	−0.122714	−	0.122714i	0.643083	−	0.765797i	$-0.277655\pi$
$307$	−37.6731	−	37.6731i	−0.122714	−	0.122714i	−0.765797	+	0.643083i	$0.777655\pi$
$308$	44.8722	−	44.8722i	0.145689	−	0.145689i
$309$		−	336.497i		−	1.08899i
$310$		0			0
$311$	208.646			0.670888			0.335444	−	0.942060i	$-0.391114\pi$
$311$	208.646			0.670888			0.335444	+	0.942060i	$0.391114\pi$
$312$	−97.8873	−	97.8873i	−0.313741	−	0.313741i
$313$	25.0439	−	25.0439i	0.0800125	−	0.0800125i	−0.665968	−	0.745980i	$-0.731981\pi$
$313$	25.0439	−	25.0439i	0.0800125	−	0.0800125i	0.745980	+	0.665968i	$0.231981\pi$
$314$			897.316i			2.85770i
$315$		0			0
$316$	682.276			2.15910
$317$	164.900	+	164.900i	0.520188	+	0.520188i	0.917628	−	0.397440i	$-0.130101\pi$
$317$	164.900	+	164.900i	0.520188	+	0.520188i	−0.397440	+	0.917628i	$0.630101\pi$
$318$	−49.5595	+	49.5595i	−0.155847	+	0.155847i
$319$			69.2961i			0.217229i
$320$		0			0
$321$	−250.471			−0.780284
$322$	165.210	+	165.210i	0.513074	+	0.513074i
$323$	419.358	−	419.358i	1.29832	−	1.29832i
$324$		−	54.6953i		−	0.168813i
$325$		0			0
$326$	−660.342			−2.02559
$327$	−71.6074	−	71.6074i	−0.218983	−	0.218983i
$328$	104.718	−	104.718i	0.319263	−	0.319263i
$329$			144.935i			0.440532i
$330$		0			0
$331$	−324.395			−0.980045			−0.490023	−	0.871710i	$-0.663011\pi$
$331$	−324.395			−0.980045			−0.490023	+	0.871710i	$0.663011\pi$
$332$	78.6273	+	78.6273i	0.236829	+	0.236829i
$333$	−98.8794	+	98.8794i	−0.296935	+	0.296935i
$334$			195.896i			0.586516i
$335$		0			0
$336$	15.4705			0.0460433
$337$	27.1490	+	27.1490i	0.0805607	+	0.0805607i	0.746239	−	0.665678i	$-0.231858\pi$
$337$	27.1490	+	27.1490i	0.0805607	+	0.0805607i	−0.665678	+	0.746239i	$0.731858\pi$
$338$	49.5959	−	49.5959i	0.146734	−	0.146734i
$339$		−	97.5362i		−	0.287718i
$340$		0			0
$341$	−173.156			−0.507790
$342$	164.148	+	164.148i	0.479965	+	0.479965i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			133.853i			0.389107i
$345$		0			0
$346$	−357.499			−1.03323
$347$	0.188420	+	0.188420i	0.000542997	+	0.000542997i	0.707378	−	0.706835i	$-0.249878\pi$
$347$	0.188420	+	0.188420i	0.000542997	+	0.000542997i	−0.706835	+	0.707378i	$0.749878\pi$
$348$	130.685	−	130.685i	0.375533	−	0.375533i
$349$			222.903i			0.638690i	0.947638	+	0.319345i	$0.103463\pi$
$349$			222.903i			0.638690i	−0.947638	+	0.319345i	$0.896537\pi$
$350$		0			0
$351$	−62.9797			−0.179429
$352$	−103.519	−	103.519i	−0.294088	−	0.294088i
$353$	−10.0036	+	10.0036i	−0.0283387	+	0.0283387i	−0.721134	−	0.692795i	$-0.756379\pi$
$353$	−10.0036	+	10.0036i	−0.0283387	+	0.0283387i	0.692795	+	0.721134i	$0.256379\pi$
$354$			319.088i			0.901378i
$355$		0			0
$356$	−135.032			−0.379304
$357$	78.8381	+	78.8381i	0.220835	+	0.220835i
$358$	−426.476	+	426.476i	−1.19127	+	1.19127i
$359$		−	605.191i		−	1.68577i	−0.538096	−	0.842884i	$-0.680856\pi$
$359$		−	605.191i		−	1.68577i	0.538096	−	0.842884i	$-0.319144\pi$
$360$		0			0
$361$	−233.179			−0.645924
$362$	−433.851	−	433.851i	−1.19848	−	1.19848i
$363$	129.117	−	129.117i	0.355694	−	0.355694i
$364$			194.884i			0.535395i
$365$		0			0
$366$	−490.999			−1.34153
$367$	−259.533	−	259.533i	−0.707174	−	0.707174i	0.258766	−	0.965940i	$-0.416684\pi$
$367$	−259.533	−	259.533i	−0.707174	−	0.707174i	−0.965940	+	0.258766i	$0.916684\pi$
$368$	66.4067	−	66.4067i	0.180453	−	0.180453i
$369$		−	67.3747i		−	0.182587i
$370$		0			0
$371$	33.7255			0.0909044
$372$	326.556	+	326.556i	0.877837	+	0.877837i
$373$	−446.882	+	446.882i	−1.19807	+	1.19807i	−0.223332	+	0.974742i	$0.571693\pi$
$373$	−446.882	+	446.882i	−1.19807	+	1.19807i	−0.974742	+	0.223332i	$0.928307\pi$
$374$		−	304.823i		−	0.815035i
$375$		0			0
$376$	−361.232			−0.960724
$377$	−150.480	−	150.480i	−0.399150	−	0.399150i
$378$	−30.8594	+	30.8594i	−0.0816386	+	0.0816386i
$379$		−	51.1198i		−	0.134881i	−0.997723	−	0.0674404i	$-0.978517\pi$
$379$		−	51.1198i		−	0.134881i	0.997723	−	0.0674404i	$-0.0214832\pi$
$380$		0			0
$381$	68.9572			0.180990
$382$	−529.886	−	529.886i	−1.38714	−	1.38714i
$383$	−405.345	+	405.345i	−1.05834	+	1.05834i	−0.0601525	+	0.998189i	$0.519159\pi$
$383$	−405.345	+	405.345i	−1.05834	+	1.05834i	−0.998189	+	0.0601525i	$0.980841\pi$
$384$			316.204i			0.823448i
$385$		0			0
$386$	570.125			1.47701
$387$	43.0598	+	43.0598i	0.111266	+	0.111266i
$388$	550.859	−	550.859i	1.41974	−	1.41974i
$389$		−	47.3061i		−	0.121609i	−0.998150	−	0.0608047i	$-0.980633\pi$
$389$		−	47.3061i		−	0.121609i	0.998150	−	0.0608047i	$-0.0193667\pi$
$390$		0			0
$391$	676.819			1.73099
$392$	32.6396	+	32.6396i	0.0832644	+	0.0832644i
$393$	39.8610	−	39.8610i	0.101427	−	0.101427i
$394$			552.581i			1.40249i
$395$		0			0
$396$	71.9555			0.181706
$397$	338.755	+	338.755i	0.853287	+	0.853287i	0.990537	−	0.137249i	$-0.0438261\pi$
$397$	338.755	+	338.755i	0.853287	+	0.853287i	−0.137249	+	0.990537i	$0.543826\pi$
$398$	−62.1583	+	62.1583i	−0.156177	+	0.156177i
$399$		−	111.704i		−	0.279960i
$400$		0			0
$401$	351.967			0.877723			0.438861	−	0.898555i	$-0.355382\pi$
$401$	351.967			0.877723			0.438861	+	0.898555i	$0.355382\pi$
$402$	116.597	+	116.597i	0.290042	+	0.290042i
$403$	376.017	−	376.017i	0.933044	−	0.933044i
$404$		−	1094.66i		−	2.70955i
$405$		0			0
$406$	−147.467			−0.363219
$407$	−130.083	−	130.083i	−0.319614	−	0.319614i
$408$	−196.494	+	196.494i	−0.481603	+	0.481603i
$409$			34.7110i			0.0848681i	0.999099	+	0.0424340i	$0.0135112\pi$
$409$			34.7110i			0.0848681i	−0.999099	+	0.0424340i	$0.986489\pi$
$410$		0			0
$411$	451.096			1.09756
$412$	−834.860	−	834.860i	−2.02636	−	2.02636i
$413$	108.571	−	108.571i	0.262883	−	0.262883i
$414$			264.925i			0.639916i
$415$		0			0
$416$	449.592			1.08075
$417$	93.3932	+	93.3932i	0.223964	+	0.223964i
$418$	−215.948	+	215.948i	−0.516623	+	0.516623i
$419$			522.337i			1.24663i	0.781972	+	0.623313i	$0.214214\pi$
$419$			522.337i			1.24663i	−0.781972	+	0.623313i	$0.785786\pi$
$420$		0			0
$421$	150.337			0.357096			0.178548	−	0.983931i	$-0.442860\pi$
$421$	150.337			0.357096			0.178548	+	0.983931i	$0.442860\pi$
$422$	385.044	+	385.044i	0.912427	+	0.912427i
$423$	−116.206	+	116.206i	−0.274720	+	0.274720i
$424$			84.0566i			0.198247i
$425$		0			0
$426$	−433.350			−1.01725
$427$	167.064	+	167.064i	0.391251	+	0.391251i
$428$	−621.426	+	621.426i	−1.45193	+	1.45193i
$429$		−	82.8542i		−	0.193133i
$430$		0			0
$431$	−165.122			−0.383113			−0.191557	−	0.981482i	$-0.561354\pi$
$431$	−165.122			−0.383113			−0.191557	+	0.981482i	$0.561354\pi$
$432$	12.4040	+	12.4040i	0.0287130	+	0.0287130i
$433$	173.796	−	173.796i	0.401377	−	0.401377i	−0.477341	−	0.878718i	$-0.658399\pi$
$433$	173.796	−	173.796i	0.401377	−	0.401377i	0.878718	+	0.477341i	$0.158399\pi$
$434$		−	368.488i		−	0.849052i
$435$		0			0
$436$	−355.320			−0.814955
$437$	−479.484	−	479.484i	−1.09722	−	1.09722i
$438$	100.452	−	100.452i	0.229342	−	0.229342i
$439$			140.286i			0.319558i	0.987153	+	0.159779i	$0.0510782\pi$
$439$			140.286i			0.319558i	−0.987153	+	0.159779i	$0.948922\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	661.937	+	661.937i	1.49759	+	1.49759i
$443$	−548.196	+	548.196i	−1.23746	+	1.23746i	−0.276429	+	0.961034i	$0.589151\pi$
$443$	−548.196	+	548.196i	−1.23746	+	1.23746i	−0.961034	+	0.276429i	$0.910849\pi$
$444$			490.646i			1.10506i
$445$		0			0
$446$	28.1586			0.0631359
$447$	284.635	+	284.635i	0.636767	+	0.636767i
$448$	195.032	−	195.032i	0.435339	−	0.435339i
$449$		−	693.773i		−	1.54515i	−0.634923	−	0.772576i	$-0.718968\pi$
$449$		−	693.773i		−	1.54515i	0.634923	−	0.772576i	$-0.281032\pi$
$450$		0			0
$451$	88.6361			0.196532
$452$	−241.990	−	241.990i	−0.535377	−	0.535377i
$453$	−209.346	+	209.346i	−0.462132	+	0.462132i
$454$		−	697.568i		−	1.53649i
$455$		0			0
$456$	278.408			0.610543
$457$	−327.671	−	327.671i	−0.717004	−	0.717004i	0.250987	−	0.967990i	$-0.419245\pi$
$457$	−327.671	−	327.671i	−0.717004	−	0.717004i	−0.967990	+	0.250987i	$0.919245\pi$
$458$	635.632	−	635.632i	1.38784	−	1.38784i
$459$			126.422i			0.275430i
$460$		0			0
$461$	93.1493			0.202059			0.101030	−	0.994883i	$-0.467786\pi$
$461$	93.1493			0.202059			0.101030	+	0.994883i	$0.467786\pi$
$462$	−40.5977	−	40.5977i	−0.0878737	−	0.0878737i
$463$	498.598	−	498.598i	1.07689	−	1.07689i	0.0800990	−	0.996787i	$-0.474476\pi$
$463$	498.598	−	498.598i	1.07689	−	1.07689i	0.996787	−	0.0800990i	$-0.0255236\pi$
$464$			59.2747i			0.127747i
$465$		0			0
$466$	83.4800			0.179142
$467$	308.256	+	308.256i	0.660078	+	0.660078i	0.955398	−	0.295320i	$-0.0954264\pi$
$467$	308.256	+	308.256i	0.660078	+	0.660078i	−0.295320	+	0.955398i	$0.595426\pi$
$468$	−156.255	+	156.255i	−0.333877	+	0.333877i
$469$		−	79.3449i		−	0.169179i
$470$		0			0
$471$	489.593			1.03948
$472$	270.599	+	270.599i	0.573302	+	0.573302i
$473$	−56.6482	+	56.6482i	−0.119764	+	0.119764i
$474$		−	617.283i		−	1.30228i
$475$		0			0
$476$	391.200			0.821848
$477$	27.0406	+	27.0406i	0.0566888	+	0.0566888i
$478$	−594.913	+	594.913i	−1.24459	+	1.24459i
$479$			178.073i			0.371760i	0.982572	+	0.185880i	$0.0595136\pi$
$479$			178.073i			0.371760i	−0.982572	+	0.185880i	$0.940486\pi$
$480$		0			0
$481$	564.961			1.17455
$482$	−286.179	−	286.179i	−0.593733	−	0.593733i
$483$	90.1417	−	90.1417i	0.186629	−	0.186629i
$484$		−	640.686i		−	1.32373i
$485$		0			0
$486$	−49.4851			−0.101821
$487$	330.361	+	330.361i	0.678359	+	0.678359i	0.959629	−	0.281270i	$-0.0907555\pi$
$487$	330.361	+	330.361i	0.678359	+	0.678359i	−0.281270	+	0.959629i	$0.590756\pi$
$488$	−416.386	+	416.386i	−0.853250	+	0.853250i
$489$			360.295i			0.736800i
$490$		0			0
$491$	−729.372			−1.48548			−0.742741	−	0.669578i	$-0.766475\pi$
$491$	−729.372			−1.48548			−0.742741	+	0.669578i	$0.766475\pi$
$492$	−167.159	−	167.159i	−0.339753	−	0.339753i
$493$	−302.065	+	302.065i	−0.612708	+	0.612708i
$494$		−	937.882i		−	1.89855i
$495$		0			0
$496$	−148.115			−0.298619
$497$	147.449	+	147.449i	0.296678	+	0.296678i
$498$	71.1373	−	71.1373i	0.142846	−	0.142846i
$499$			385.715i			0.772976i	0.922294	+	0.386488i	$0.126312\pi$
$499$			385.715i			0.772976i	−0.922294	+	0.386488i	$0.873688\pi$
$500$		0			0
$501$	106.885			0.213343
$502$	−71.7220	−	71.7220i	−0.142873	−	0.142873i
$503$	139.070	−	139.070i	0.276482	−	0.276482i	−0.555221	−	0.831703i	$-0.687366\pi$
$503$	139.070	−	139.070i	0.276482	−	0.276482i	0.831703	+	0.555221i	$0.187366\pi$
$504$			52.3398i			0.103849i
$505$		0			0
$506$	−348.528			−0.688790
$507$	−27.0605	−	27.0605i	−0.0533737	−	0.0533737i
$508$	171.085	−	171.085i	0.336781	−	0.336781i
$509$		−	337.164i		−	0.662404i	−0.943560	−	0.331202i	$-0.892546\pi$
$509$		−	337.164i		−	0.662404i	0.943560	−	0.331202i	$-0.107454\pi$
$510$		0			0
$511$	−68.3579			−0.133773
$512$	−151.514	−	151.514i	−0.295926	−	0.295926i
$513$	89.5623	−	89.5623i	0.174585	−	0.174585i
$514$		−	621.270i		−	1.20870i
$515$		0			0
$516$	213.665			0.414080
$517$	−152.878	−	152.878i	−0.295702	−	0.295702i
$518$	276.825	−	276.825i	0.534411	−	0.534411i
$519$			195.058i			0.375835i
$520$		0			0
$521$	−346.121			−0.664340			−0.332170	−	0.943220i	$-0.607781\pi$
$521$	−346.121			−0.664340			−0.332170	+	0.943220i	$0.607781\pi$
$522$	−118.236	−	118.236i	−0.226507	−	0.226507i
$523$	295.339	−	295.339i	0.564702	−	0.564702i	−0.365938	−	0.930639i	$-0.619252\pi$
$523$	295.339	−	295.339i	0.564702	−	0.564702i	0.930639	+	0.365938i	$0.119252\pi$
$524$		−	197.793i		−	0.377467i
$525$		0			0
$526$	−1034.74			−1.96718
$527$	−754.797	−	754.797i	−1.43225	−	1.43225i
$528$	−16.3184	+	16.3184i	−0.0309060	+	0.0309060i
$529$		−	244.859i		−	0.462872i
$530$		0			0
$531$	174.100			0.327873
$532$	−277.141	−	277.141i	−0.520941	−	0.520941i
$533$	−192.477	+	192.477i	−0.361120	+	0.361120i
$534$			122.169i			0.228781i
$535$		0			0
$536$	197.757			0.368950
$537$	232.693	+	232.693i	0.433321	+	0.433321i
$538$	746.748	−	746.748i	1.38801	−	1.38801i
$539$			27.6270i			0.0512560i
$540$		0			0
$541$	−734.168			−1.35706			−0.678529	−	0.734574i	$-0.737382\pi$
$541$	−734.168			−1.35706			−0.678529	+	0.734574i	$0.737382\pi$
$542$	569.532	+	569.532i	1.05080	+	1.05080i
$543$	−236.718	+	236.718i	−0.435944	+	0.435944i
$544$		−	902.487i		−	1.65898i
$545$		0			0
$546$	176.319			0.322929
$547$	−124.027	−	124.027i	−0.226740	−	0.226740i	0.584589	−	0.811329i	$-0.301256\pi$
$547$	−124.027	−	124.027i	−0.226740	−	0.226740i	−0.811329	+	0.584589i	$0.801256\pi$
$548$	1119.18	−	1119.18i	2.04230	−	2.04230i
$549$			267.899i			0.487976i
$550$		0			0
$551$	427.989			0.776749
$552$	224.667	+	224.667i	0.407005	+	0.407005i
$553$	−210.032	+	210.032i	−0.379805	+	0.379805i
$554$			1133.53i			2.04608i
$555$		0			0
$556$	463.423			0.833494
$557$	436.412	+	436.412i	0.783504	+	0.783504i	0.980420	−	0.196916i	$-0.0630926\pi$
$557$	436.412	+	436.412i	0.783504	+	0.783504i	−0.196916	+	0.980420i	$0.563093\pi$
$558$	295.448	−	295.448i	0.529477	−	0.529477i
$559$		−	246.028i		−	0.440121i
$560$		0			0
$561$	−166.317			−0.296466
$562$	7.32946	+	7.32946i	0.0130417	+	0.0130417i
$563$	259.609	−	259.609i	0.461117	−	0.461117i	−0.437905	−	0.899021i	$-0.644279\pi$
$563$	259.609	−	259.609i	0.461117	−	0.461117i	0.899021	+	0.437905i	$0.144279\pi$
$564$			576.624i			1.02238i
$565$		0			0
$566$	276.661			0.488800
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−367.497	+	367.497i	−0.647002	+	0.647002i
$569$			151.092i			0.265539i	0.991147	+	0.132770i	$0.0423870\pi$
$569$			151.092i			0.265539i	−0.991147	+	0.132770i	$0.957613\pi$
$570$		0			0
$571$	−502.406			−0.879871			−0.439935	−	0.898029i	$-0.644999\pi$
$571$	−502.406			−0.879871			−0.439935	+	0.898029i	$0.644999\pi$
$572$	−205.564	−	205.564i	−0.359377	−	0.359377i
$573$	−289.116	+	289.116i	−0.504565	+	0.504565i
$574$			188.624i			0.328612i
$575$		0			0
$576$	312.747			0.542963
$577$	−81.3805	−	81.3805i	−0.141041	−	0.141041i	0.633061	−	0.774102i	$-0.281798\pi$
$577$	−81.3805	−	81.3805i	−0.141041	−	0.141041i	−0.774102	+	0.633061i	$0.781798\pi$
$578$	680.023	−	680.023i	1.17651	−	1.17651i
$579$		−	311.071i		−	0.537255i
$580$		0			0
$581$	−48.4094			−0.0833208
$582$	−498.385	−	498.385i	−0.856331	−	0.856331i
$583$	−35.5738	+	35.5738i	−0.0610185	+	0.0610185i
$584$		−	170.374i		−	0.291736i
$585$		0			0
$586$	676.981			1.15526
$587$	283.065	+	283.065i	0.482224	+	0.482224i	0.905841	−	0.423617i	$-0.139240\pi$
$587$	283.065	+	283.065i	0.482224	+	0.482224i	−0.423617	+	0.905841i	$0.639240\pi$
$588$	52.1017	−	52.1017i	0.0886083	−	0.0886083i
$589$			1069.45i			1.81571i
$590$		0			0
$591$	301.499			0.510150
$592$	−111.271	−	111.271i	−0.187957	−	0.187957i
$593$	−5.75309	+	5.75309i	−0.00970167	+	0.00970167i	−0.711941	−	0.702239i	$-0.752184\pi$
$593$	−5.75309	+	5.75309i	−0.00970167	+	0.00970167i	0.702239	+	0.711941i	$0.252184\pi$
$594$		−	65.1011i		−	0.109598i
$595$		0			0
$596$	1412.38			2.36976
$597$	33.9148	+	33.9148i	0.0568086	+	0.0568086i
$598$	756.843	−	756.843i	1.26562	−	1.26562i
$599$			619.287i			1.03387i	0.856025	+	0.516934i	$0.172927\pi$
$599$			619.287i			1.03387i	−0.856025	+	0.516934i	$0.827073\pi$
$600$		0			0
$601$	457.367			0.761011			0.380505	−	0.924779i	$-0.375750\pi$
$601$	457.367			0.761011			0.380505	+	0.924779i	$0.375750\pi$
$602$	−120.551	−	120.551i	−0.200251	−	0.200251i
$603$	63.6174	−	63.6174i	0.105502	−	0.105502i
$604$			1038.79i			1.71985i
$605$		0			0
$606$	−990.383			−1.63430
$607$	25.5979	+	25.5979i	0.0421713	+	0.0421713i	0.727878	−	0.685707i	$-0.240507\pi$
$607$	25.5979	+	25.5979i	0.0421713	+	0.0421713i	−0.685707	+	0.727878i	$0.740507\pi$
$608$	−639.356	+	639.356i	−1.05157	+	1.05157i
$609$			80.4606i			0.132119i
$610$		0			0
$611$	663.961			1.08668
$612$	313.657	+	313.657i	0.512512	+	0.512512i
$613$	308.221	−	308.221i	0.502808	−	0.502808i	−0.409501	−	0.912309i	$-0.634297\pi$
$613$	308.221	−	308.221i	0.502808	−	0.502808i	0.912309	+	0.409501i	$0.134297\pi$
$614$			169.129i			0.275454i
$615$		0			0
$616$	−68.8567			−0.111780
$617$	−21.2194	−	21.2194i	−0.0343913	−	0.0343913i	0.689702	−	0.724093i	$-0.257742\pi$
$617$	−21.2194	−	21.2194i	−0.0343913	−	0.0343913i	−0.724093	+	0.689702i	$0.757742\pi$
$618$	−755.332	+	755.332i	−1.22222	+	1.22222i
$619$		−	794.043i		−	1.28278i	−0.767213	−	0.641392i	$-0.778357\pi$
$619$		−	794.043i		−	1.28278i	0.767213	−	0.641392i	$-0.221643\pi$
$620$		0			0
$621$	144.548			0.232767
$622$	−468.346	−	468.346i	−0.752968	−	0.752968i
$623$	41.5685	−	41.5685i	0.0667230	−	0.0667230i
$624$		−	70.8721i		−	0.113577i
$625$		0			0
$626$	−112.432			−0.179603
$627$	117.825	+	117.825i	0.187919	+	0.187919i
$628$	1214.69	−	1214.69i	1.93423	−	1.93423i
$629$		−	1134.07i		−	1.80298i
$630$		0			0
$631$	−365.937			−0.579932			−0.289966	−	0.957037i	$-0.593644\pi$
$631$	−365.937			−0.579932			−0.289966	+	0.957037i	$0.593644\pi$
$632$	−523.479	−	523.479i	−0.828290	−	0.828290i
$633$	210.087	−	210.087i	0.331892	−	0.331892i
$634$		−	740.297i		−	1.16766i
$635$		0			0
$636$	134.177			0.210970
$637$	−59.9931	−	59.9931i	−0.0941808	−	0.0941808i
$638$	155.548	−	155.548i	0.243806	−	0.243806i
$639$			236.444i			0.370022i
$640$		0			0
$641$	610.251			0.952029			0.476014	−	0.879437i	$-0.342081\pi$
$641$	610.251			0.952029			0.476014	+	0.879437i	$0.342081\pi$
$642$	562.230	+	562.230i	0.875747	+	0.875747i
$643$	18.4704	−	18.4704i	0.0287253	−	0.0287253i	−0.692598	−	0.721324i	$-0.743534\pi$
$643$	18.4704	−	18.4704i	0.0287253	−	0.0287253i	0.721324	+	0.692598i	$0.243534\pi$
$644$		−	447.289i		−	0.694548i
$645$		0			0
$646$	−1882.66			−2.91433
$647$	633.369	+	633.369i	0.978931	+	0.978931i	0.999783	−	0.0208512i	$-0.00663764\pi$
$647$	633.369	+	633.369i	0.978931	+	0.978931i	−0.0208512	+	0.999783i	$0.506638\pi$
$648$	−41.9652	+	41.9652i	−0.0647612	+	0.0647612i
$649$			229.041i			0.352914i
$650$		0			0
$651$	−201.054			−0.308839
$652$	893.904	+	893.904i	1.37102	+	1.37102i
$653$	−345.393	+	345.393i	−0.528933	+	0.528933i	−0.920254	−	0.391321i	$-0.872018\pi$
$653$	−345.393	+	345.393i	−0.528933	+	0.528933i	0.391321	+	0.920254i	$0.372018\pi$
$654$			321.473i			0.491548i
$655$		0			0
$656$	75.8178			0.115576
$657$	−54.8083	−	54.8083i	−0.0834221	−	0.0834221i
$658$	325.334	−	325.334i	0.494428	−	0.494428i
$659$			347.238i			0.526917i	0.964671	+	0.263458i	$0.0848632\pi$
$659$			347.238i			0.526917i	−0.964671	+	0.263458i	$0.915137\pi$
$660$		0			0
$661$	−482.959			−0.730649			−0.365324	−	0.930880i	$-0.619042\pi$
$661$	−482.959			−0.730649			−0.365324	+	0.930880i	$0.619042\pi$
$662$	728.166	+	728.166i	1.09995	+	1.09995i
$663$	361.165	−	361.165i	0.544744	−	0.544744i
$664$		−	120.654i		−	0.181708i
$665$		0			0
$666$	443.907			0.666527
$667$	345.374	+	345.374i	0.517802	+	0.517802i
$668$	265.184	−	265.184i	0.396982	−	0.396982i
$669$		−	15.3639i		−	0.0229654i
$670$		0			0
$671$	−352.439			−0.525245
$672$	−120.197	−	120.197i	−0.178865	−	0.178865i
$673$	−769.503	+	769.503i	−1.14339	+	1.14339i	−0.155566	+	0.987825i	$0.549720\pi$
$673$	−769.503	+	769.503i	−1.14339	+	1.14339i	−0.987825	+	0.155566i	$0.950280\pi$
$674$		−	121.882i		−	0.180834i
$675$		0			0
$676$	−134.276			−0.198633
$677$	−265.615	−	265.615i	−0.392341	−	0.392341i	0.483180	−	0.875521i	$-0.339482\pi$
$677$	−265.615	−	265.615i	−0.392341	−	0.392341i	−0.875521	+	0.483180i	$0.839482\pi$
$678$	−218.939	+	218.939i	−0.322918	+	0.322918i
$679$			339.154i			0.499490i
$680$		0			0
$681$	−380.606			−0.558893
$682$	388.682	+	388.682i	0.569916	+	0.569916i
$683$	−346.533	+	346.533i	−0.507369	+	0.507369i	−0.913718	−	0.406349i	$-0.866802\pi$
$683$	−346.533	+	346.533i	−0.507369	+	0.507369i	0.406349	+	0.913718i	$0.366802\pi$
$684$		−	444.414i		−	0.649728i
$685$		0			0
$686$	−58.7920			−0.0857026
$687$	−346.813	−	346.813i	−0.504822	−	0.504822i
$688$	−48.4559	+	48.4559i	−0.0704301	+	0.0704301i
$689$		−	154.500i		−	0.224238i
$690$		0			0
$691$	−330.788			−0.478709			−0.239355	−	0.970932i	$-0.576936\pi$
$691$	−330.788			−0.478709			−0.239355	+	0.970932i	$0.576936\pi$
$692$	483.946	+	483.946i	0.699343	+	0.699343i
$693$	−22.1508	+	22.1508i	−0.0319637	+	0.0319637i
$694$		−	0.845888i		−	0.00121886i
$695$		0			0
$696$	−200.538			−0.288129
$697$	386.369	+	386.369i	0.554331	+	0.554331i
$698$	500.348	−	500.348i	0.716830	−	0.716830i
$699$		−	45.5483i		−	0.0651620i
$700$		0			0
$701$	−595.747			−0.849853			−0.424926	−	0.905228i	$-0.639700\pi$
$701$	−595.747			−0.849853			−0.424926	+	0.905228i	$0.639700\pi$
$702$	141.370	+	141.370i	0.201382	+	0.201382i
$703$	−803.421	+	803.421i	−1.14285	+	1.14285i
$704$			411.440i			0.584432i
$705$		0			0
$706$	44.9098			0.0636116
$707$	336.981	+	336.981i	0.476635	+	0.476635i
$708$	431.948	−	431.948i	0.610097	−	0.610097i
$709$			546.791i			0.771215i	0.922663	+	0.385608i	$0.126008\pi$
$709$			546.791i			0.771215i	−0.922663	+	0.385608i	$0.873992\pi$
$710$		0			0
$711$	−336.801			−0.473701
$712$	103.604	+	103.604i	0.145511	+	0.145511i
$713$	−863.018	+	863.018i	−1.21040	+	1.21040i
$714$		−	353.934i		−	0.495706i
$715$		0			0
$716$	1154.64			1.61262
$717$	324.596	+	324.596i	0.452714	+	0.452714i
$718$	−1358.46	+	1358.46i	−1.89201	+	1.89201i
$719$		−	383.796i		−	0.533791i	−0.963725	−	0.266896i	$-0.914002\pi$
$719$		−	383.796i		−	0.533791i	0.963725	−	0.266896i	$-0.0859979\pi$
$720$		0			0
$721$	514.008			0.712910
$722$	523.413	+	523.413i	0.724949	+	0.724949i
$723$	−156.145	+	156.145i	−0.215968	+	0.215968i
$724$			1174.61i			1.62239i
$725$		0			0
$726$	−579.655			−0.798422
$727$	331.503	+	331.503i	0.455988	+	0.455988i	0.897336	−	0.441348i	$-0.145500\pi$
$727$	331.503	+	331.503i	0.455988	+	0.455988i	−0.441348	+	0.897336i	$0.645500\pi$
$728$	149.525	−	149.525i	0.205392	−	0.205392i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−493.864			−0.675600
$732$	664.665	+	664.665i	0.908012	+	0.908012i
$733$	−771.577	+	771.577i	−1.05263	+	1.05263i	−0.0540934	+	0.998536i	$0.517227\pi$
$733$	−771.577	+	771.577i	−1.05263	+	1.05263i	−0.998536	+	0.0540934i	$0.982773\pi$
$734$			1165.14i			1.58739i
$735$		0			0
$736$	−1031.88			−1.40202
$737$	83.6931	+	83.6931i	0.113559	+	0.113559i
$738$	−151.235	+	151.235i	−0.204926	+	0.204926i
$739$		−	644.895i		−	0.872658i	−0.899787	−	0.436329i	$-0.856278\pi$
$739$		−	644.895i		−	0.872658i	0.899787	−	0.436329i	$-0.143722\pi$
$740$		0			0
$741$	−511.726			−0.690589
$742$	−75.7033	−	75.7033i	−0.102026	−	0.102026i
$743$	−351.711	+	351.711i	−0.473366	+	0.473366i	−0.903002	−	0.429636i	$-0.858642\pi$
$743$	−351.711	+	351.711i	−0.473366	+	0.473366i	0.429636	+	0.903002i	$0.358642\pi$
$744$		−	501.102i		−	0.673525i
$745$		0			0
$746$	2006.22			2.68930
$747$	−38.8139	−	38.8139i	−0.0519597	−	0.0519597i
$748$	−412.638	+	412.638i	−0.551655	+	0.551655i
$749$		−	382.601i		−	0.510815i
$750$		0			0
$751$	1346.30			1.79268			0.896339	−	0.443369i	$-0.146217\pi$
$751$	1346.30			1.79268			0.896339	+	0.443369i	$0.146217\pi$
$752$	−130.769	−	130.769i	−0.173895	−	0.173895i
$753$	−39.1329	+	39.1329i	−0.0519693	+	0.0519693i
$754$			675.560i			0.895968i
$755$		0			0
$756$	83.5485			0.110514
$757$	−391.030	−	391.030i	−0.516553	−	0.516553i	0.399974	−	0.916527i	$-0.369019\pi$
$757$	−391.030	−	391.030i	−0.516553	−	0.516553i	−0.916527	+	0.399974i	$0.869019\pi$
$758$	−114.748	+	114.748i	−0.151383	+	0.151383i
$759$			190.163i			0.250545i
$760$		0			0
$761$	−385.783			−0.506943			−0.253471	−	0.967343i	$-0.581572\pi$
$761$	−385.783			−0.506943			−0.253471	+	0.967343i	$0.581572\pi$
$762$	−154.788	−	154.788i	−0.203133	−	0.203133i
$763$	109.382	−	109.382i	0.143358	−	0.143358i
$764$			1434.61i			1.87776i
$765$		0			0
$766$	1819.75			2.37565
$767$	−497.373	−	497.373i	−0.648465	−	0.648465i
$768$	199.066	−	199.066i	0.259201	−	0.259201i
$769$		−	1014.63i		−	1.31941i	−0.751525	−	0.659705i	$-0.770681\pi$
$769$		−	1014.63i		−	1.31941i	0.751525	−	0.659705i	$-0.229319\pi$
$770$		0			0
$771$	−338.977			−0.439659
$772$	−771.776	−	771.776i	−0.999710	−	0.999710i
$773$	833.644	−	833.644i	1.07845	−	1.07845i	0.0818044	−	0.996648i	$-0.473932\pi$
$773$	833.644	−	833.644i	1.07845	−	1.07845i	0.996648	−	0.0818044i	$-0.0260683\pi$
$774$		−	193.312i		−	0.249757i
$775$		0			0
$776$	−845.299			−1.08930
$777$	−151.041	−	151.041i	−0.194390	−	0.194390i
$778$	−106.187	+	106.187i	−0.136488	+	0.136488i
$779$		−	547.437i		−	0.702743i
$780$		0			0
$781$	−311.058			−0.398282
$782$	−1519.25	−	1519.25i	−1.94277	−	1.94277i
$783$	−64.5120	+	64.5120i	−0.0823909	+	0.0823909i
$784$			23.6316i			0.0301424i
$785$		0			0
$786$	−178.951			−0.227673
$787$	204.794	+	204.794i	0.260221	+	0.260221i	0.825144	−	0.564923i	$-0.191094\pi$
$787$	204.794	+	204.794i	0.260221	+	0.260221i	−0.564923	+	0.825144i	$0.691094\pi$
$788$	748.028	−	748.028i	0.949274	−	0.949274i
$789$			564.573i			0.715555i
$790$		0			0
$791$	148.989			0.188355
$792$	−55.2082	−	55.2082i	−0.0697073	−	0.0697073i
$793$	765.337	−	765.337i	0.965116	−	0.965116i
$794$		−	1520.80i		−	1.91537i
$795$		0			0
$796$	168.287			0.211416
$797$	813.821	+	813.821i	1.02111	+	1.02111i	0.999772	+	0.0213333i	$0.00679110\pi$
$797$	813.821	+	813.821i	1.02111	+	1.02111i	0.0213333	+	0.999772i	$0.493209\pi$
$798$	−250.740	+	250.740i	−0.314211	+	0.314211i
$799$		−	1332.80i		−	1.66809i
$800$		0			0
$801$	66.6578			0.0832183
$802$	−790.056	−	790.056i	−0.985108	−	0.985108i
$803$	72.1041	−	72.1041i	0.0897934	−	0.0897934i
$804$		−	315.674i		−	0.392629i
$805$		0			0
$806$	−1688.08			−2.09439
$807$	−407.440	−	407.440i	−0.504882	−	0.504882i
$808$	−839.883	+	839.883i	−1.03946	+	1.03946i
$809$			288.800i			0.356984i	0.983941	+	0.178492i	$0.0571219\pi$
$809$			288.800i			0.356984i	−0.983941	+	0.178492i	$0.942878\pi$
$810$		0			0
$811$	929.694			1.14635			0.573177	−	0.819431i	$-0.305711\pi$
$811$	929.694			1.14635			0.573177	+	0.819431i	$0.305711\pi$
$812$	199.625	+	199.625i	0.245844	+	0.245844i
$813$	310.747	−	310.747i	0.382223	−	0.382223i
$814$			583.991i			0.717433i
$815$		0			0
$816$	−142.265			−0.174344
$817$	349.872	+	349.872i	0.428240	+	0.428240i
$818$	77.9155	−	77.9155i	0.0952512	−	0.0952512i
$819$		−	96.2031i		−	0.117464i
$820$		0			0
$821$	−257.969			−0.314214			−0.157107	−	0.987582i	$-0.550217\pi$
$821$	−257.969			−0.314214			−0.157107	+	0.987582i	$0.550217\pi$
$822$	−1012.57	−	1012.57i	−1.23184	−	1.23184i
$823$	1099.78	−	1099.78i	1.33631	−	1.33631i	0.436703	−	0.899606i	$-0.356146\pi$
$823$	1099.78	−	1099.78i	1.33631	−	1.33631i	0.899606	−	0.436703i	$-0.143854\pi$
$824$			1281.10i			1.55473i
$825$		0			0
$826$	−487.415			−0.590091
$827$	−145.623	−	145.623i	−0.176086	−	0.176086i	0.613561	−	0.789647i	$-0.289736\pi$
$827$	−145.623	−	145.623i	−0.176086	−	0.176086i	−0.789647	+	0.613561i	$0.789736\pi$
$828$	358.629	−	358.629i	0.433127	−	0.433127i
$829$			1281.05i			1.54530i	0.634835	+	0.772648i	$0.281068\pi$
$829$			1281.05i			1.54530i	−0.634835	+	0.772648i	$0.718932\pi$
$830$		0			0
$831$	618.475			0.744254
$832$	−893.460	−	893.460i	−1.07387	−	1.07387i
$833$	−120.427	+	120.427i	−0.144570	+	0.144570i
$834$		−	419.277i		−	0.502731i
$835$		0			0
$836$	584.657			0.699351
$837$	−161.202	−	161.202i	−0.192595	−	0.192595i
$838$	1172.48	−	1172.48i	1.39915	−	1.39915i
$839$			303.598i			0.361858i	0.983496	+	0.180929i	$0.0579103\pi$
$839$			303.598i			0.361858i	−0.983496	+	0.180929i	$0.942090\pi$
$840$		0			0
$841$	532.718			0.633434
$842$	−337.461	−	337.461i	−0.400785	−	0.400785i
$843$	3.99909	−	3.99909i	0.00474388	−	0.00474388i
$844$		−	1042.47i		−	1.23515i
$845$		0			0
$846$	521.695			0.616661
$847$	197.229	+	197.229i	0.232856	+	0.232856i
$848$	−30.4292	+	30.4292i	−0.0358835	+	0.0358835i
$849$		−	150.951i		−	0.177799i
$850$		0			0
$851$	−1296.67			−1.52371
$852$	586.625	+	586.625i	0.688527	+	0.688527i
$853$	−39.5202	+	39.5202i	−0.0463309	+	0.0463309i	−0.729893	−	0.683562i	$-0.760430\pi$
$853$	−39.5202	+	39.5202i	−0.0463309	+	0.0463309i	0.683562	+	0.729893i	$0.260430\pi$
$854$		−	750.014i		−	0.878237i
$855$		0			0
$856$	953.584			1.11400
$857$	−388.871	−	388.871i	−0.453758	−	0.453758i	0.442842	−	0.896600i	$-0.353970\pi$
$857$	−388.871	−	388.871i	−0.453758	−	0.453758i	−0.896600	+	0.442842i	$0.853970\pi$
$858$	−185.982	+	185.982i	−0.216762	+	0.216762i
$859$		−	375.068i		−	0.436633i	−0.975878	−	0.218317i	$-0.929943\pi$
$859$		−	375.068i		−	0.436633i	0.975878	−	0.218317i	$-0.0700565\pi$
$860$		0			0
$861$	102.917			0.119531
$862$	370.647	+	370.647i	0.429985	+	0.429985i
$863$	374.656	−	374.656i	0.434132	−	0.434132i	−0.455899	−	0.890031i	$-0.650682\pi$
$863$	374.656	−	374.656i	0.434132	−	0.434132i	0.890031	+	0.455899i	$0.150682\pi$
$864$		−	192.744i		−	0.223084i
$865$		0			0
$866$	−780.236			−0.900966
$867$	−371.033	−	371.033i	−0.427951	−	0.427951i
$868$	−498.822	+	498.822i	−0.574680	+	0.574680i
$869$		−	443.085i		−	0.509880i
$870$		0			0
$871$	−363.487			−0.417321
$872$	272.621	+	272.621i	0.312639	+	0.312639i
$873$	−271.928	+	271.928i	−0.311487	+	0.311487i
$874$			2152.59i			2.46291i
$875$		0			0
$876$	−271.962			−0.310459
$877$	−281.962	−	281.962i	−0.321507	−	0.321507i	0.527838	−	0.849345i	$-0.323003\pi$
$877$	−281.962	−	281.962i	−0.321507	−	0.321507i	−0.849345	+	0.527838i	$0.823003\pi$
$878$	314.899	−	314.899i	0.358654	−	0.358654i
$879$		−	369.374i		−	0.420220i
$880$		0			0
$881$	−950.305			−1.07867			−0.539333	−	0.842092i	$-0.681324\pi$
$881$	−950.305			−1.07867			−0.539333	+	0.842092i	$0.681324\pi$
$882$	−47.1385	−	47.1385i	−0.0534450	−	0.0534450i
$883$	891.004	−	891.004i	1.00907	−	1.00907i	0.00910653	−	0.999959i	$-0.497101\pi$
$883$	891.004	−	891.004i	1.00907	−	1.00907i	0.999959	−	0.00910653i	$-0.00289874\pi$
$884$		−	1792.12i		−	2.02729i
$885$		0			0
$886$	2461.06			2.77772
$887$	−316.251	−	316.251i	−0.356540	−	0.356540i	0.505996	−	0.862536i	$-0.331125\pi$
$887$	−316.251	−	316.251i	−0.356540	−	0.356540i	−0.862536	+	0.505996i	$0.831125\pi$
$888$	376.450	−	376.450i	0.423930	−	0.423930i
$889$			105.334i			0.118486i
$890$		0			0
$891$	−35.5204			−0.0398657
$892$	−38.1182	−	38.1182i	−0.0427334	−	0.0427334i
$893$	−944.208	+	944.208i	−1.05734	+	1.05734i
$894$		−	1277.83i		−	1.42934i
$895$		0			0
$896$	−483.009			−0.539073
$897$	−412.948	−	412.948i	−0.460366	−	0.460366i
$898$	−1557.30	+	1557.30i	−1.73419	+	1.73419i
$899$		−	770.331i		−	0.856876i
$900$		0			0
$901$	−310.135			−0.344212
$902$	−198.961	−	198.961i	−0.220577	−	0.220577i
$903$	−65.7749	+	65.7749i	−0.0728405	+	0.0728405i
$904$			371.336i			0.410770i
$905$		0			0
$906$	939.833			1.03734
$907$	407.150	+	407.150i	0.448897	+	0.448897i	0.894988	−	0.446091i	$-0.147184\pi$
$907$	407.150	+	407.150i	0.448897	+	0.448897i	−0.446091	+	0.894988i	$0.647184\pi$
$908$	−944.295	+	944.295i	−1.03997	+	1.03997i
$909$			540.372i			0.594468i
$910$		0			0
$911$	637.398			0.699668			0.349834	−	0.936812i	$-0.386238\pi$
$911$	637.398			0.699668			0.349834	+	0.936812i	$0.386238\pi$
$912$	100.786	+	100.786i	0.110511	+	0.110511i
$913$	51.0623	−	51.0623i	0.0559281	−	0.0559281i
$914$			1471.04i			1.60945i
$915$		0			0
$916$	−1720.91			−1.87872
$917$	60.8886	+	60.8886i	0.0663998	+	0.0663998i
$918$	283.779	−	283.779i	0.309127	−	0.309127i
$919$		−	1104.07i		−	1.20138i	−0.799483	−	0.600689i	$-0.794893\pi$
$919$		−	1104.07i		−	1.20138i	0.799483	−	0.600689i	$-0.205107\pi$
$920$		0			0
$921$	92.2800			0.100195
$922$	−209.091	−	209.091i	−0.226780	−	0.226780i
$923$	675.477	−	675.477i	0.731828	−	0.731828i
$924$			109.914i			0.118954i
$925$		0			0
$926$	−2238.40			−2.41727
$927$	412.123	+	412.123i	0.444577	+	0.444577i
$928$	460.531	−	460.531i	0.496261	−	0.496261i
$929$			1765.37i			1.90029i	0.311814	+	0.950143i	$0.399063\pi$
$929$			1765.37i			1.90029i	−0.311814	+	0.950143i	$0.600937\pi$
$930$		0			0
$931$	170.630			0.183277
$932$	−113.007	−	113.007i	−0.121252	−	0.121252i
$933$	−255.538	+	255.538i	−0.273889	+	0.273889i
$934$		−	1383.88i		−	1.48167i
$935$		0			0
$936$	239.774			0.256169
$937$	−867.153	−	867.153i	−0.925457	−	0.925457i	0.0719509	−	0.997408i	$-0.477077\pi$
$937$	−867.153	−	867.153i	−0.925457	−	0.925457i	−0.997408	+	0.0719509i	$0.977077\pi$
$938$	−178.105	+	178.105i	−0.189877	+	0.189877i
$939$			61.3448i			0.0653299i
$940$		0			0
$941$	−1390.62			−1.47781			−0.738907	−	0.673807i	$-0.764658\pi$
$941$	−1390.62			−1.47781			−0.738907	+	0.673807i	$0.764658\pi$
$942$	−1098.98	−	1098.98i	−1.16665	−	1.16665i
$943$	441.765	−	441.765i	0.468468	−	0.468468i
$944$			195.918i			0.207540i
$945$		0			0
$946$	254.315			0.268832
$947$	55.6539	+	55.6539i	0.0587686	+	0.0587686i	0.735880	−	0.677112i	$-0.236769\pi$
$947$	55.6539	+	55.6539i	0.0587686	+	0.0587686i	−0.677112	+	0.735880i	$0.736769\pi$
$948$	−835.614	+	835.614i	−0.881450	+	0.881450i
$949$			313.154i			0.329984i
$950$		0			0
$951$	−403.920			−0.424732
$952$	−300.150	−	300.150i	−0.315283	−	0.315283i
$953$	−222.327	+	222.327i	−0.233292	+	0.233292i	−0.814065	−	0.580773i	$-0.802750\pi$
$953$	−222.327	+	222.327i	−0.233292	+	0.233292i	0.580773	+	0.814065i	$0.302750\pi$
$954$		−	121.395i		−	0.127249i
$955$		0			0
$956$	1610.66			1.68479
$957$	−84.8701	−	84.8701i	−0.0886835	−	0.0886835i
$958$	399.719	−	399.719i	0.417243	−	0.417243i
$959$			689.060i			0.718519i
$960$		0			0
$961$	963.896			1.00301
$962$	−1268.16	−	1268.16i	−1.31825	−	1.31825i
$963$	306.763	−	306.763i	0.318549	−	0.318549i
$964$			774.800i			0.803735i
$965$		0			0
$966$	−404.680			−0.418924
$967$	−807.256	−	807.256i	−0.834805	−	0.834805i	0.153365	−	0.988170i	$-0.450989\pi$
$967$	−807.256	−	807.256i	−0.834805	−	0.834805i	−0.988170	+	0.153365i	$0.950989\pi$
$968$	−491.569	+	491.569i	−0.507819	+	0.507819i
$969$			1027.21i			1.06008i
$970$		0			0
$971$	458.168			0.471852			0.235926	−	0.971771i	$-0.424188\pi$
$971$	458.168			0.471852			0.235926	+	0.971771i	$0.424188\pi$
$972$	66.9878	+	66.9878i	0.0689175	+	0.0689175i
$973$	−142.660	+	142.660i	−0.146619	+	0.146619i
$974$		−	1483.12i		−	1.52271i
$975$		0			0
$976$	−301.471			−0.308884
$977$	−921.703	−	921.703i	−0.943401	−	0.943401i	0.0550806	−	0.998482i	$-0.482458\pi$
$977$	−921.703	−	921.703i	−0.943401	−	0.943401i	−0.998482	+	0.0550806i	$0.982458\pi$
$978$	808.751	−	808.751i	0.826944	−	0.826944i
$979$			87.6930i			0.0895741i
$980$		0			0
$981$	175.402			0.178799
$982$	1637.21	+	1637.21i	1.66722	+	1.66722i
$983$	−398.575	+	398.575i	−0.405468	+	0.405468i	−0.880155	−	0.474687i	$-0.842561\pi$
$983$	−398.575	+	398.575i	−0.405468	+	0.405468i	0.474687	+	0.880155i	$0.342561\pi$
$984$			256.506i			0.260677i
$985$		0			0
$986$	1356.08			1.37534
$987$	−177.508	−	177.508i	−0.179846	−	0.179846i
$988$	−1269.61	+	1269.61i	−1.28503	+	1.28503i
$989$			564.673i			0.570953i
$990$		0			0
$991$	861.216			0.869037			0.434519	−	0.900663i	$-0.356918\pi$
$991$	861.216			0.869037			0.434519	+	0.900663i	$0.356918\pi$
$992$	1150.77	+	1150.77i	1.16005	+	1.16005i
$993$	397.301	−	397.301i	0.400102	−	0.400102i
$994$		−	661.953i		−	0.665949i
$995$		0			0
$996$	−192.597			−0.193370
$997$	1147.18	+	1147.18i	1.15063	+	1.15063i	0.986426	+	0.164209i	$0.0525072\pi$
$997$	1147.18	+	1147.18i	1.15063	+	1.15063i	0.164209	+	0.986426i	$0.447493\pi$
$998$	865.811	−	865.811i	0.867546	−	0.867546i
$999$		−	242.204i		−	0.242447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.l.e.232.3		24
5.2	odd	4		105.3.l.a.43.10	yes	24
5.3	odd	4	inner	525.3.l.e.43.3		24
5.4	even	2		105.3.l.a.22.10	✓	24
15.2	even	4		315.3.o.b.253.3		24
15.14	odd	2		315.3.o.b.127.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.10	✓	24	5.4	even	2
105.3.l.a.43.10	yes	24	5.2	odd	4
315.3.o.b.127.3		24	15.14	odd	2
315.3.o.b.253.3		24	15.2	even	4
525.3.l.e.43.3		24	5.3	odd	4	inner
525.3.l.e.232.3		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)

\(f(q)\)	\(=\)	\(q+(-2.24469 - 2.24469i) q^{2} +(-1.22474 + 1.22474i) q^{3} +6.07726i q^{4} +5.49834 q^{6} +(-1.87083 - 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-2.24469 - 2.24469i) q^{2} +(-1.22474 + 1.22474i) q^{3} +6.07726i q^{4} +5.49834 q^{6} +(-1.87083 - 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} -3.00000i q^{9} +3.94671 q^{11} +(-7.44309 - 7.44309i) q^{12} +(-8.57045 + 8.57045i) q^{13} +8.39886i q^{14} +3.37595 q^{16} +(17.2039 + 17.2039i) q^{17} +(-6.73407 + 6.73407i) q^{18} -24.3758i q^{19} +4.58258 q^{21} +(-8.85913 - 8.85913i) q^{22} +(19.6705 - 19.6705i) q^{23} +11.4215i q^{24} +38.4760 q^{26} +(3.67423 + 3.67423i) q^{27} +(11.3695 - 11.3695i) q^{28} +17.5580i q^{29} -43.8736 q^{31} +(-26.2292 - 26.2292i) q^{32} +(-4.83371 + 4.83371i) q^{33} -77.2348i q^{34} +18.2318 q^{36} +(-32.9598 - 32.9598i) q^{37} +(-54.7160 + 54.7160i) q^{38} -20.9932i q^{39} +22.4582 q^{41} +(-10.2865 - 10.2865i) q^{42} +(-14.3533 + 14.3533i) q^{43} +23.9852i q^{44} -88.3085 q^{46} +(-38.7355 - 38.7355i) q^{47} +(-4.13468 + 4.13468i) q^{48} +7.00000i q^{49} -42.1407 q^{51} +(-52.0849 - 52.0849i) q^{52} +(-9.01352 + 9.01352i) q^{53} -16.4950i q^{54} -17.4466 q^{56} +(29.8541 + 29.8541i) q^{57} +(39.4121 - 39.4121i) q^{58} +58.0335i q^{59} -89.2995 q^{61} +(98.4827 + 98.4827i) q^{62} +(-5.61249 + 5.61249i) q^{63} +104.249i q^{64} +21.7004 q^{66} +(21.2058 + 21.2058i) q^{67} +(-104.552 + 104.552i) q^{68} +48.1828i q^{69} -78.8147 q^{71} +(-13.9884 - 13.9884i) q^{72} +(18.2694 - 18.2694i) q^{73} +147.969i q^{74} +148.138 q^{76} +(-7.38362 - 7.38362i) q^{77} +(-47.1233 + 47.1233i) q^{78} -112.267i q^{79} -9.00000 q^{81} +(-50.4118 - 50.4118i) q^{82} +(12.9380 - 12.9380i) q^{83} +27.8495i q^{84} +64.4373 q^{86} +(-21.5040 - 21.5040i) q^{87} +(18.4027 - 18.4027i) q^{88} +22.2193i q^{89} +32.0677 q^{91} +(119.543 + 119.543i) q^{92} +(53.7340 - 53.7340i) q^{93} +173.898i q^{94} +64.2481 q^{96} +(-90.6427 - 90.6427i) q^{97} +(15.7128 - 15.7128i) q^{98} -11.8401i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8	\( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^6 + 48 * q^8 + 48 * q^12 - 64 * q^13 - 184 * q^16 - 24 * q^17 - 24 * q^18 - 8 * q^22 - 8 * q^23 - 80 * q^26 + 96 * q^31 - 56 * q^32 + 72 * q^33 + 168 * q^36 - 8 * q^37 - 56 * q^38 + 320 * q^41 + 112 * q^43 + 320 * q^46 - 64 * q^47 - 192 * q^48 - 192 * q^51 - 96 * q^52 + 72 * q^53 - 336 * q^56 - 48 * q^57 + 512 * q^58 - 496 * q^61 + 776 * q^62 - 192 * q^66 + 192 * q^67 - 568 * q^68 - 144 * q^71 - 144 * q^72 - 224 * q^73 + 416 * q^76 - 112 * q^77 + 216 * q^78 - 216 * q^81 - 352 * q^82 + 32 * q^83 + 240 * q^86 - 384 * q^87 - 216 * q^88 - 1304 * q^92 + 168 * q^96 + 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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