LMFDB - Embedded newform 315.3.o.b.253.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (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:	$8.58312832735$
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			253.8
Character	$\chi$	$=$	315.253
Dual form			315.3.o.b.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.867675 - 0.867675i) q^{2} +2.49428i q^{4} +(4.93004 - 0.833478i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(5.63493 + 5.63493i) q^{8} +O(q^{10})$	\(q+(0.867675 - 0.867675i) q^{2} +2.49428i q^{4} +(4.93004 - 0.833478i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(5.63493 + 5.63493i) q^{8} +(3.55449 - 5.00086i) q^{10} +1.49884 q^{11} +(2.15706 + 2.15706i) q^{13} +3.24654i q^{14} -0.198550 q^{16} +(2.96697 - 2.96697i) q^{17} +34.8524i q^{19} +(2.07893 + 12.2969i) q^{20} +(1.30051 - 1.30051i) q^{22} +(7.50682 + 7.50682i) q^{23} +(23.6106 - 8.21817i) q^{25} +3.74326 q^{26} +(-4.66637 - 4.66637i) q^{28} -37.1782i q^{29} +47.0705 q^{31} +(-22.7120 + 22.7120i) q^{32} -5.14873i q^{34} +(-7.66397 + 10.7826i) q^{35} +(16.3936 - 16.3936i) q^{37} +(30.2406 + 30.2406i) q^{38} +(32.4770 + 23.0838i) q^{40} -73.4639 q^{41} +(-0.244769 - 0.244769i) q^{43} +3.73853i q^{44} +13.0270 q^{46} +(38.9392 - 38.9392i) q^{47} -7.00000i q^{49} +(13.3557 - 27.6171i) q^{50} +(-5.38032 + 5.38032i) q^{52} +(33.0957 + 33.0957i) q^{53} +(7.38936 - 1.24925i) q^{55} -21.0840 q^{56} +(-32.2586 - 32.2586i) q^{58} -31.6176i q^{59} -106.415 q^{61} +(40.8419 - 40.8419i) q^{62} +38.6190i q^{64} +(12.4323 + 8.83655i) q^{65} +(28.6607 - 28.6607i) q^{67} +(7.40045 + 7.40045i) q^{68} +(2.70592 + 16.0056i) q^{70} -15.8493 q^{71} +(-26.2684 - 26.2684i) q^{73} -28.4486i q^{74} -86.9316 q^{76} +(-2.80408 + 2.80408i) q^{77} -73.8402i q^{79} +(-0.978860 + 0.165487i) q^{80} +(-63.7428 + 63.7428i) q^{82} +(-58.6690 - 58.6690i) q^{83} +(12.1544 - 17.1002i) q^{85} -0.424760 q^{86} +(8.44587 + 8.44587i) q^{88} -83.2528i q^{89} -8.07100 q^{91} +(-18.7241 + 18.7241i) q^{92} -67.5732i q^{94} +(29.0487 + 171.824i) q^{95} +(-103.272 + 103.272i) q^{97} +(-6.07373 - 6.07373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.867675	−	0.867675i	0.433838	−	0.433838i	−0.456094	−	0.889932i	$-0.650752\pi$
$2$	0.867675	−	0.867675i	0.433838	−	0.433838i	0.889932	+	0.456094i	$0.150752\pi$
$3$		0			0
$3$		0			0
$4$			2.49428i			0.623570i
$5$	4.93004	−	0.833478i	0.986008	−	0.166696i
$5$	4.93004	−	0.833478i	0.986008	−	0.166696i
$6$		0			0
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	5.63493	+	5.63493i	0.704366	+	0.704366i
$9$		0			0
$10$	3.55449	−	5.00086i	0.355449	−	0.500086i
$11$	1.49884			0.136258			0.0681292	−	0.997677i	$-0.478297\pi$
$11$	1.49884			0.136258			0.0681292	+	0.997677i	$0.478297\pi$
$12$		0			0
$13$	2.15706	+	2.15706i	0.165928	+	0.165928i	0.785187	−	0.619259i	$-0.212567\pi$
$13$	2.15706	+	2.15706i	0.165928	+	0.165928i	−0.619259	+	0.785187i	$0.712567\pi$
$14$			3.24654i			0.231896i
$15$		0			0
$16$	−0.198550			−0.0124094
$17$	2.96697	−	2.96697i	0.174528	−	0.174528i	−0.614438	−	0.788965i	$-0.710617\pi$
$17$	2.96697	−	2.96697i	0.174528	−	0.174528i	0.788965	+	0.614438i	$0.210617\pi$
$18$		0			0
$19$			34.8524i			1.83434i	0.398501	+	0.917168i	$0.369531\pi$
$19$			34.8524i			1.83434i	−0.398501	+	0.917168i	$0.630469\pi$
$20$	2.07893	+	12.2969i	0.103946	+	0.614845i
$21$		0			0
$22$	1.30051	−	1.30051i	0.0591140	−	0.0591140i
$23$	7.50682	+	7.50682i	0.326383	+	0.326383i	0.851209	−	0.524826i	$-0.175870\pi$
$23$	7.50682	+	7.50682i	0.326383	+	0.326383i	−0.524826	+	0.851209i	$0.675870\pi$
$24$		0			0
$25$	23.6106	−	8.21817i	0.944425	−	0.328727i
$26$	3.74326			0.143972
$27$		0			0
$28$	−4.66637	−	4.66637i	−0.166656	−	0.166656i
$29$		−	37.1782i		−	1.28201i	−0.767538	−	0.641004i	$-0.778518\pi$
$29$		−	37.1782i		−	1.28201i	0.767538	−	0.641004i	$-0.221482\pi$
$30$		0			0
$31$	47.0705			1.51840			0.759201	−	0.650856i	$-0.225590\pi$
$31$	47.0705			1.51840			0.759201	+	0.650856i	$0.225590\pi$
$32$	−22.7120	+	22.7120i	−0.709749	+	0.709749i
$33$		0			0
$34$		−	5.14873i		−	0.151433i
$35$	−7.66397	+	10.7826i	−0.218971	+	0.308073i
$36$		0			0
$37$	16.3936	−	16.3936i	0.443070	−	0.443070i	−0.449972	−	0.893043i	$-0.648566\pi$
$37$	16.3936	−	16.3936i	0.443070	−	0.443070i	0.893043	+	0.449972i	$0.148566\pi$
$38$	30.2406	+	30.2406i	0.795804	+	0.795804i
$39$		0			0
$40$	32.4770	+	23.0838i	0.811925	+	0.577096i
$41$	−73.4639			−1.79180			−0.895902	−	0.444252i	$-0.853469\pi$
$41$	−73.4639			−1.79180			−0.895902	+	0.444252i	$0.853469\pi$
$42$		0			0
$43$	−0.244769	−	0.244769i	−0.00569230	−	0.00569230i	0.704255	−	0.709947i	$-0.251281\pi$
$43$	−0.244769	−	0.244769i	−0.00569230	−	0.00569230i	−0.709947	+	0.704255i	$0.751281\pi$
$44$			3.73853i			0.0849667i
$45$		0			0
$46$	13.0270			0.283195
$47$	38.9392	−	38.9392i	0.828494	−	0.828494i	−0.158814	−	0.987308i	$-0.550767\pi$
$47$	38.9392	−	38.9392i	0.828494	−	0.828494i	0.987308	+	0.158814i	$0.0507671\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	13.3557	−	27.6171i	0.267113	−	0.552341i
$51$		0			0
$52$	−5.38032	+	5.38032i	−0.103468	+	0.103468i
$53$	33.0957	+	33.0957i	0.624447	+	0.624447i	0.946665	−	0.322218i	$-0.104429\pi$
$53$	33.0957	+	33.0957i	0.624447	+	0.624447i	−0.322218	+	0.946665i	$0.604429\pi$
$54$		0			0
$55$	7.38936	−	1.24925i	0.134352	−	0.0227137i
$56$	−21.0840			−0.376499
$57$		0			0
$58$	−32.2586	−	32.2586i	−0.556183	−	0.556183i
$59$		−	31.6176i		−	0.535891i	−0.963434	−	0.267946i	$-0.913655\pi$
$59$		−	31.6176i		−	0.535891i	0.963434	−	0.267946i	$-0.0863447\pi$
$60$		0			0
$61$	−106.415			−1.74451			−0.872256	−	0.489049i	$-0.837344\pi$
$61$	−106.415			−1.74451			−0.872256	+	0.489049i	$0.837344\pi$
$62$	40.8419	−	40.8419i	0.658740	−	0.658740i
$63$		0			0
$64$			38.6190i			0.603422i
$65$	12.4323	+	8.83655i	0.191266	+	0.135947i
$66$		0			0
$67$	28.6607	−	28.6607i	0.427771	−	0.427771i	−0.460097	−	0.887868i	$-0.652186\pi$
$67$	28.6607	−	28.6607i	0.427771	−	0.427771i	0.887868	+	0.460097i	$0.152186\pi$
$68$	7.40045	+	7.40045i	0.108830	+	0.108830i
$69$		0			0
$70$	2.70592	+	16.0056i	0.0386560	+	0.228651i
$71$	−15.8493			−0.223229			−0.111615	−	0.993752i	$-0.535602\pi$
$71$	−15.8493			−0.223229			−0.111615	+	0.993752i	$0.535602\pi$
$72$		0			0
$73$	−26.2684	−	26.2684i	−0.359841	−	0.359841i	0.503913	−	0.863754i	$-0.331893\pi$
$73$	−26.2684	−	26.2684i	−0.359841	−	0.359841i	−0.863754	+	0.503913i	$0.831893\pi$
$74$		−	28.4486i		−	0.384441i
$75$		0			0
$76$	−86.9316			−1.14384
$77$	−2.80408	+	2.80408i	−0.0364166	+	0.0364166i
$78$		0			0
$79$		−	73.8402i		−	0.934686i	−0.884076	−	0.467343i	$-0.845211\pi$
$79$		−	73.8402i		−	0.934686i	0.884076	−	0.467343i	$-0.154789\pi$
$80$	−0.978860	+	0.165487i	−0.0122358	+	0.00206859i
$81$		0			0
$82$	−63.7428	+	63.7428i	−0.777352	+	0.777352i
$83$	−58.6690	−	58.6690i	−0.706856	−	0.706856i	0.259017	−	0.965873i	$-0.416601\pi$
$83$	−58.6690	−	58.6690i	−0.706856	−	0.706856i	−0.965873	+	0.259017i	$0.916601\pi$
$84$		0			0
$85$	12.1544	−	17.1002i	0.142993	−	0.201179i
$86$	−0.424760			−0.00493907
$87$		0			0
$88$	8.44587	+	8.44587i	0.0959758	+	0.0959758i
$89$		−	83.2528i		−	0.935424i	−0.883881	−	0.467712i	$-0.845078\pi$
$89$		−	83.2528i		−	0.935424i	0.883881	−	0.467712i	$-0.154922\pi$
$90$		0			0
$91$	−8.07100			−0.0886923
$92$	−18.7241	+	18.7241i	−0.203523	+	0.203523i
$93$		0			0
$94$		−	67.5732i		−	0.718864i
$95$	29.0487	+	171.824i	0.305776	+	1.80867i
$96$		0			0
$97$	−103.272	+	103.272i	−1.06466	+	1.06466i	−0.0669049	+	0.997759i	$0.521312\pi$
$97$	−103.272	+	103.272i	−1.06466	+	1.06466i	−0.997759	+	0.0669049i	$0.978688\pi$
$98$	−6.07373	−	6.07373i	−0.0619768	−	0.0619768i
$99$		0			0
$100$	20.4984	+	58.8915i	0.204984	+	0.588915i
$101$	−88.5891			−0.877120			−0.438560	−	0.898702i	$-0.644511\pi$
$101$	−88.5891			−0.877120			−0.438560	+	0.898702i	$0.644511\pi$
$102$		0			0
$103$	22.0312	+	22.0312i	0.213895	+	0.213895i	0.805920	−	0.592025i	$-0.201671\pi$
$103$	22.0312	+	22.0312i	0.213895	+	0.213895i	−0.592025	+	0.805920i	$0.701671\pi$
$104$			24.3098i			0.233748i
$105$		0			0
$106$	57.4326			0.541817
$107$	−108.746	+	108.746i	−1.01632	+	1.01632i	−0.0164543	+	0.999865i	$0.505238\pi$
$107$	−108.746	+	108.746i	−1.01632	+	1.01632i	−0.999865	+	0.0164543i	$0.994762\pi$
$108$		0			0
$109$		−	75.8376i		−	0.695758i	−0.937539	−	0.347879i	$-0.886902\pi$
$109$		−	75.8376i		−	0.695758i	0.937539	−	0.347879i	$-0.113098\pi$
$110$	5.32762	−	7.49551i	0.0484329	−	0.0681410i
$111$		0			0
$112$	0.371453	−	0.371453i	0.00331655	−	0.00331655i
$113$	22.0544	+	22.0544i	0.195171	+	0.195171i	0.797926	−	0.602755i	$-0.205930\pi$
$113$	22.0544	+	22.0544i	0.195171	+	0.195171i	−0.602755	+	0.797926i	$0.705930\pi$
$114$		0			0
$115$	43.2657	+	30.7522i	0.376223	+	0.267410i
$116$	92.7329			0.799421
$117$		0			0
$118$	−27.4338	−	27.4338i	−0.232490	−	0.232490i
$119$			11.1014i			0.0932890i
$120$		0			0
$121$	−118.753			−0.981434
$122$	−92.3339	+	92.3339i	−0.756835	+	0.756835i
$123$		0			0
$124$			117.407i			0.946830i
$125$	109.552	−	60.1948i	0.876414	−	0.481559i
$126$		0			0
$127$	168.587	−	168.587i	1.32746	−	1.32746i	0.419880	−	0.907579i	$-0.362072\pi$
$127$	168.587	−	168.587i	1.32746	−	1.32746i	0.907579	−	0.419880i	$-0.137928\pi$
$128$	−57.3391	−	57.3391i	−0.447962	−	0.447962i
$129$		0			0
$130$	18.4544	−	3.11993i	0.141957	−	0.0239994i
$131$	−21.2016			−0.161845			−0.0809223	−	0.996720i	$-0.525787\pi$
$131$	−21.2016			−0.161845			−0.0809223	+	0.996720i	$0.525787\pi$
$132$		0			0
$133$	−65.2028	−	65.2028i	−0.490247	−	0.490247i
$134$		−	49.7363i		−	0.371166i
$135$		0			0
$136$	33.4373			0.245863
$137$	104.237	−	104.237i	0.760851	−	0.760851i	−0.215625	−	0.976476i	$-0.569179\pi$
$137$	104.237	−	104.237i	0.760851	−	0.760851i	0.976476	+	0.215625i	$0.0691790\pi$
$138$		0			0
$139$		−	120.516i		−	0.867019i	−0.901149	−	0.433509i	$-0.857275\pi$
$139$		−	120.516i		−	0.867019i	0.901149	−	0.433509i	$-0.142725\pi$
$140$	−26.8947	−	19.1161i	−0.192105	−	0.136543i
$141$		0			0
$142$	−13.7520	+	13.7520i	−0.0968452	+	0.0968452i
$143$	3.23310	+	3.23310i	0.0226091	+	0.0226091i
$144$		0			0
$145$	−30.9872	−	183.290i	−0.213705	−	1.26407i
$146$	−45.5849			−0.312225
$147$		0			0
$148$	40.8902	+	40.8902i	0.276285	+	0.276285i
$149$			11.2725i			0.0756543i	0.999284	+	0.0378272i	$0.0120436\pi$
$149$			11.2725i			0.0756543i	−0.999284	+	0.0378272i	$0.987956\pi$
$150$		0			0
$151$	−19.8815			−0.131666			−0.0658328	−	0.997831i	$-0.520970\pi$
$151$	−19.8815			−0.131666			−0.0658328	+	0.997831i	$0.520970\pi$
$152$	−196.391	+	196.391i	−1.29204	+	1.29204i
$153$		0			0
$154$			4.86606i			0.0315978i
$155$	232.059	−	39.2322i	1.49716	−	0.253111i
$156$		0			0
$157$	−35.1027	+	35.1027i	−0.223584	+	0.223584i	−0.810006	−	0.586422i	$-0.800536\pi$
$157$	−35.1027	+	35.1027i	−0.223584	+	0.223584i	0.586422	+	0.810006i	$0.300536\pi$
$158$	−64.0693	−	64.0693i	−0.405502	−	0.405502i
$159$		0			0
$160$	−93.0411	+	130.901i	−0.581507	+	0.818131i
$161$	−28.0879			−0.174459
$162$		0			0
$163$	172.736	+	172.736i	1.05973	+	1.05973i	0.998099	+	0.0616300i	$0.0196299\pi$
$163$	172.736	+	172.736i	1.05973	+	1.05973i	0.0616300	+	0.998099i	$0.480370\pi$
$164$		−	183.240i		−	1.11731i
$165$		0			0
$166$	−101.811			−0.613321
$167$	−173.446	+	173.446i	−1.03860	+	1.03860i	−0.0393730	+	0.999225i	$0.512536\pi$
$167$	−173.446	+	173.446i	−1.03860	+	1.03860i	−0.999225	+	0.0393730i	$0.987464\pi$
$168$		0			0
$169$		−	159.694i		−	0.944936i
$170$	−4.29136	−	25.3835i	−0.0252433	−	0.149315i
$171$		0			0
$172$	0.610522	−	0.610522i	0.00354955	−	0.00354955i
$173$	−13.5601	−	13.5601i	−0.0783823	−	0.0783823i	0.666829	−	0.745211i	$-0.267651\pi$
$173$	−13.5601	−	13.5601i	−0.0783823	−	0.0783823i	−0.745211	+	0.666829i	$0.767651\pi$
$174$		0			0
$175$	−28.7967	+	59.5462i	−0.164552	+	0.340264i
$176$	−0.297595			−0.00169088
$177$		0			0
$178$	−72.2364	−	72.2364i	−0.405822	−	0.405822i
$179$		−	288.985i		−	1.61444i	−0.590249	−	0.807222i	$-0.700970\pi$
$179$		−	288.985i		−	1.61444i	0.590249	−	0.807222i	$-0.299030\pi$
$180$		0			0
$181$	20.6446			0.114059			0.0570293	−	0.998373i	$-0.481837\pi$
$181$	20.6446			0.114059			0.0570293	+	0.998373i	$0.481837\pi$
$182$	−7.00300	+	7.00300i	−0.0384780	+	0.0384780i
$183$		0			0
$184$			84.6007i			0.459786i
$185$	67.1575	−	94.4849i	0.363013	−	0.510729i
$186$		0			0
$187$	4.44702	−	4.44702i	0.0237809	−	0.0237809i
$188$	97.1253	+	97.1253i	0.516624	+	0.516624i
$189$		0			0
$190$	174.292	+	123.882i	0.917326	+	0.652012i
$191$	140.214			0.734104			0.367052	−	0.930200i	$-0.380367\pi$
$191$	140.214			0.734104			0.367052	+	0.930200i	$0.380367\pi$
$192$		0			0
$193$	196.589	+	196.589i	1.01860	+	1.01860i	0.999824	+	0.0187736i	$0.00597619\pi$
$193$	196.589	+	196.589i	1.01860	+	1.01860i	0.0187736	+	0.999824i	$0.494024\pi$
$194$			179.214i			0.923783i
$195$		0			0
$196$	17.4600			0.0890814
$197$	206.963	−	206.963i	1.05057	−	1.05057i	0.0519216	−	0.998651i	$-0.483465\pi$
$197$	206.963	−	206.963i	1.05057	−	1.05057i	0.998651	−	0.0519216i	$-0.0165346\pi$
$198$		0			0
$199$		−	160.567i		−	0.806869i	−0.915009	−	0.403435i	$-0.867816\pi$
$199$		−	160.567i		−	0.806869i	0.915009	−	0.403435i	$-0.132184\pi$
$200$	179.353	+	86.7354i	0.896764	+	0.433677i
$201$		0			0
$202$	−76.8666	+	76.8666i	−0.380528	+	0.380528i
$203$	69.5541	+	69.5541i	0.342631	+	0.342631i
$204$		0			0
$205$	−362.180	+	61.2306i	−1.76673	+	0.298686i
$206$	38.2318			0.185591
$207$		0			0
$208$	−0.428285	−	0.428285i	−0.00205906	−	0.00205906i
$209$			52.2383i			0.249944i
$210$		0			0
$211$	265.902			1.26020			0.630099	−	0.776515i	$-0.283014\pi$
$211$	265.902			1.26020			0.630099	+	0.776515i	$0.283014\pi$
$212$	−82.5499	+	82.5499i	−0.389386	+	0.389386i
$213$		0			0
$214$			188.713i			0.881835i
$215$	−1.41073	−	1.00271i	−0.00656154	−	0.00466377i
$216$		0			0
$217$	−88.0608	+	88.0608i	−0.405810	+	0.405810i
$218$	−65.8024	−	65.8024i	−0.301846	−	0.301846i
$219$		0			0
$220$	3.11599	+	18.4311i	0.0141636	+	0.0837779i
$221$	12.7999			0.0579181
$222$		0			0
$223$	143.987	+	143.987i	0.645683	+	0.645683i	0.951947	−	0.306264i	$-0.0990789\pi$
$223$	143.987	+	143.987i	0.645683	+	0.645683i	−0.306264	+	0.951947i	$0.599079\pi$
$224$		−	84.9804i		−	0.379377i
$225$		0			0
$226$	38.2720			0.169345
$227$	174.471	−	174.471i	0.768596	−	0.768596i	−0.209264	−	0.977859i	$-0.567107\pi$
$227$	174.471	−	174.471i	0.768596	−	0.768596i	0.977859	+	0.209264i	$0.0671067\pi$
$228$		0			0
$229$		−	41.2978i		−	0.180340i	−0.995926	−	0.0901700i	$-0.971259\pi$
$229$		−	41.2978i		−	0.180340i	0.995926	−	0.0901700i	$-0.0287410\pi$
$230$	64.2234	−	10.8577i	0.279232	−	0.0472073i
$231$		0			0
$232$	209.497	−	209.497i	0.903002	−	0.903002i
$233$	72.8228	+	72.8228i	0.312544	+	0.312544i	0.845894	−	0.533350i	$-0.179067\pi$
$233$	72.8228	+	72.8228i	0.312544	+	0.312544i	−0.533350	+	0.845894i	$0.679067\pi$
$234$		0			0
$235$	159.517	−	224.427i	0.678796	−	0.955008i
$236$	78.8631			0.334166
$237$		0			0
$238$	9.63240	+	9.63240i	0.0404723	+	0.0404723i
$239$			418.650i			1.75168i	0.482606	+	0.875838i	$0.339690\pi$
$239$			418.650i			1.75168i	−0.482606	+	0.875838i	$0.660310\pi$
$240$		0			0
$241$	371.820			1.54282			0.771410	−	0.636338i	$-0.219552\pi$
$241$	371.820			1.54282			0.771410	+	0.636338i	$0.219552\pi$
$242$	−103.039	+	103.039i	−0.425783	+	0.425783i
$243$		0			0
$244$		−	265.429i		−	1.08783i
$245$	−5.83435	−	34.5103i	−0.0238137	−	0.140858i
$246$		0			0
$247$	−75.1788	+	75.1788i	−0.304368	+	0.304368i
$248$	265.238	+	265.238i	1.06951	+	1.06951i
$249$		0			0
$250$	42.8257	−	147.285i	0.171303	−	0.589140i
$251$	−469.550			−1.87072			−0.935358	−	0.353702i	$-0.884923\pi$
$251$	−469.550			−1.87072			−0.935358	+	0.353702i	$0.884923\pi$
$252$		0			0
$253$	11.2515	+	11.2515i	0.0444725	+	0.0444725i
$254$		−	292.558i		−	1.15180i
$255$		0			0
$256$	−253.980			−0.992108
$257$	−215.003	+	215.003i	−0.836589	+	0.836589i	−0.988408	−	0.151819i	$-0.951487\pi$
$257$	−215.003	+	215.003i	−0.836589	+	0.836589i	0.151819	+	0.988408i	$0.451487\pi$
$258$		0			0
$259$			61.3393i			0.236831i
$260$	−22.0408	+	31.0096i	−0.0847724	+	0.119268i
$261$		0			0
$262$	−18.3961	+	18.3961i	−0.0702142	+	0.0702142i
$263$	−95.9799	−	95.9799i	−0.364943	−	0.364943i	0.500686	−	0.865629i	$-0.333081\pi$
$263$	−95.9799	−	95.9799i	−0.364943	−	0.364943i	−0.865629	+	0.500686i	$0.833081\pi$
$264$		0			0
$265$	190.748	+	135.579i	0.719803	+	0.511617i
$266$	−113.150			−0.425375
$267$		0			0
$268$	71.4877	+	71.4877i	0.266745	+	0.266745i
$269$			53.9055i			0.200392i	0.994968	+	0.100196i	$0.0319470\pi$
$269$			53.9055i			0.200392i	−0.994968	+	0.100196i	$0.968053\pi$
$270$		0			0
$271$	−163.641			−0.603843			−0.301921	−	0.953333i	$-0.597628\pi$
$271$	−163.641			−0.603843			−0.301921	+	0.953333i	$0.597628\pi$
$272$	−0.589092	+	0.589092i	−0.00216578	+	0.00216578i
$273$		0			0
$274$		−	180.887i		−	0.660171i
$275$	35.3886	−	12.3177i	0.128686	−	0.0447918i
$276$		0			0
$277$	25.4139	−	25.4139i	0.0917470	−	0.0917470i	−0.659744	−	0.751491i	$-0.729335\pi$
$277$	25.4139	−	25.4139i	0.0917470	−	0.0917470i	0.751491	+	0.659744i	$0.229335\pi$
$278$	−104.568	−	104.568i	−0.376145	−	0.376145i
$279$		0			0
$280$	−103.945	+	17.5730i	−0.371231	+	0.0627608i
$281$	−113.158			−0.402698			−0.201349	−	0.979520i	$-0.564532\pi$
$281$	−113.158			−0.402698			−0.201349	+	0.979520i	$0.564532\pi$
$282$		0			0
$283$	351.039	+	351.039i	1.24042	+	1.24042i	0.959827	+	0.280593i	$0.0905312\pi$
$283$	351.039	+	351.039i	1.24042	+	1.24042i	0.280593	+	0.959827i	$0.409469\pi$
$284$		−	39.5325i		−	0.139199i
$285$		0			0
$286$	5.61056			0.0196174
$287$	137.438	−	137.438i	0.478880	−	0.478880i
$288$		0			0
$289$			271.394i			0.939080i
$290$	−185.923	−	132.149i	−0.641115	−	0.455688i
$291$		0			0
$292$	65.5207	−	65.5207i	0.224386	−	0.224386i
$293$	86.4775	+	86.4775i	0.295145	+	0.295145i	0.839109	−	0.543964i	$-0.183077\pi$
$293$	86.4775	+	86.4775i	0.295145	+	0.295145i	−0.543964	+	0.839109i	$0.683077\pi$
$294$		0			0
$295$	−26.3526	−	155.876i	−0.0893307	−	0.528393i
$296$	184.753			0.624167
$297$		0			0
$298$	9.78086	+	9.78086i	0.0328217	+	0.0328217i
$299$			32.3854i			0.108312i
$300$		0			0
$301$	0.915841			0.00304266
$302$	−17.2507	+	17.2507i	−0.0571215	+	0.0571215i
$303$		0			0
$304$		−	6.91994i		−	0.0227630i
$305$	−524.632	+	88.6948i	−1.72010	+	0.290803i
$306$		0			0
$307$	−113.083	+	113.083i	−0.368348	+	0.368348i	−0.866874	−	0.498526i	$-0.833875\pi$
$307$	−113.083	+	113.083i	−0.368348	+	0.368348i	0.498526	+	0.866874i	$0.333875\pi$
$308$	−6.99416	−	6.99416i	−0.0227083	−	0.0227083i
$309$		0			0
$310$	167.311	−	235.393i	0.539714	−	0.759332i
$311$	73.9659			0.237832			0.118916	−	0.992904i	$-0.462058\pi$
$311$	73.9659			0.237832			0.118916	+	0.992904i	$0.462058\pi$
$312$		0			0
$313$	−324.281	−	324.281i	−1.03604	−	1.03604i	−0.999326	−	0.0367164i	$-0.988310\pi$
$313$	−324.281	−	324.281i	−1.03604	−	1.03604i	−0.0367164	−	0.999326i	$-0.511690\pi$
$314$			60.9154i			0.193998i
$315$		0			0
$316$	184.178			0.582842
$317$	151.033	−	151.033i	0.476445	−	0.476445i	−0.427547	−	0.903993i	$-0.640622\pi$
$317$	151.033	−	151.033i	0.476445	−	0.476445i	0.903993	+	0.427547i	$0.140622\pi$
$318$		0			0
$319$		−	55.7243i		−	0.174684i
$320$	32.1881	+	190.393i	0.100588	+	0.594980i
$321$		0			0
$322$	−24.3712	+	24.3712i	−0.0756870	+	0.0756870i
$323$	103.406	+	103.406i	0.320142	+	0.320142i
$324$		0			0
$325$	68.6568	+	33.2025i	0.211252	+	0.102162i
$326$	299.757			0.919501
$327$		0			0
$328$	−413.964	−	413.964i	−1.26208	−	1.26208i
$329$			145.697i			0.442849i
$330$		0			0
$331$	−181.099			−0.547128			−0.273564	−	0.961854i	$-0.588202\pi$
$331$	−181.099			−0.547128			−0.273564	+	0.961854i	$0.588202\pi$
$332$	146.337	−	146.337i	0.440774	−	0.440774i
$333$		0			0
$334$			300.989i			0.901165i
$335$	117.410	−	165.186i	0.350478	−	0.493093i
$336$		0			0
$337$	−388.741	+	388.741i	−1.15353	+	1.15353i	−0.167693	+	0.985839i	$0.553632\pi$
$337$	−388.741	+	388.741i	−1.15353	+	1.15353i	−0.985839	+	0.167693i	$0.946368\pi$
$338$	−138.563	−	138.563i	−0.409949	−	0.409949i
$339$		0			0
$340$	42.6527	+	30.3164i	0.125449	+	0.0891660i
$341$	70.5512			0.206895
$342$		0			0
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	2.75851i		−	0.00801892i
$345$		0			0
$346$	−23.5316			−0.0680104
$347$	−16.1754	+	16.1754i	−0.0466151	+	0.0466151i	−0.730030	−	0.683415i	$-0.760494\pi$
$347$	−16.1754	+	16.1754i	−0.0466151	+	0.0466151i	0.683415	+	0.730030i	$0.260494\pi$
$348$		0			0
$349$			249.140i			0.713868i	0.934130	+	0.356934i	$0.116178\pi$
$349$			249.140i			0.713868i	−0.934130	+	0.356934i	$0.883822\pi$
$350$	26.6806	+	76.6529i	0.0762304	+	0.219008i
$351$		0			0
$352$	−34.0417	+	34.0417i	−0.0967094	+	0.0967094i
$353$	315.334	+	315.334i	0.893298	+	0.893298i	0.994832	−	0.101534i	$-0.0323750\pi$
$353$	315.334	+	315.334i	0.893298	+	0.893298i	−0.101534	+	0.994832i	$0.532375\pi$
$354$		0			0
$355$	−78.1376	+	13.2100i	−0.220106	+	0.0372113i
$356$	207.656			0.583302
$357$		0			0
$358$	−250.745	−	250.745i	−0.700406	−	0.700406i
$359$			84.4547i			0.235250i	0.993058	+	0.117625i	$0.0375281\pi$
$359$			84.4547i			0.235250i	−0.993058	+	0.117625i	$0.962472\pi$
$360$		0			0
$361$	−853.689			−2.36479
$362$	17.9128	−	17.9128i	0.0494829	−	0.0494829i
$363$		0			0
$364$		−	20.1313i		−	0.0553058i
$365$	−151.398	−	107.610i	−0.414790	−	0.294822i
$366$		0			0
$367$	−199.907	+	199.907i	−0.544707	+	0.544707i	−0.924905	−	0.380198i	$-0.875856\pi$
$367$	−199.907	+	199.907i	−0.544707	+	0.544707i	0.380198	+	0.924905i	$0.375856\pi$
$368$	−1.49048	−	1.49048i	−0.00405021	−	0.00405021i
$369$		0			0
$370$	−23.7113	−	140.253i	−0.0640847	−	0.379062i
$371$	−123.833			−0.333781
$372$		0			0
$373$	−392.541	−	392.541i	−1.05239	−	1.05239i	−0.998550	−	0.0538401i	$-0.982854\pi$
$373$	−392.541	−	392.541i	−1.05239	−	1.05239i	−0.0538401	−	0.998550i	$-0.517146\pi$
$374$		−	7.71714i		−	0.0206341i
$375$		0			0
$376$	438.839			1.16713
$377$	80.1958	−	80.1958i	0.212721	−	0.212721i
$378$		0			0
$379$			360.732i			0.951798i	0.879500	+	0.475899i	$0.157877\pi$
$379$			360.732i			0.951798i	−0.879500	+	0.475899i	$0.842123\pi$
$380$	−428.576	+	72.4556i	−1.12783	+	0.190673i
$381$		0			0
$382$	121.660	−	121.660i	0.318482	−	0.318482i
$383$	−337.526	−	337.526i	−0.881268	−	0.881268i	0.112395	−	0.993664i	$-0.464148\pi$
$383$	−337.526	−	337.526i	−0.881268	−	0.881268i	−0.993664	+	0.112395i	$0.964148\pi$
$384$		0			0
$385$	−11.4871	+	16.1614i	−0.0298366	+	0.0419776i
$386$	341.151			0.883812
$387$		0			0
$388$	−257.590	−	257.590i	−0.663893	−	0.663893i
$389$		−	585.722i		−	1.50571i	−0.658185	−	0.752856i	$-0.728676\pi$
$389$		−	585.722i		−	1.50571i	0.658185	−	0.752856i	$-0.271324\pi$
$390$		0			0
$391$	44.5450			0.113926
$392$	39.4445	−	39.4445i	0.100624	−	0.100624i
$393$		0			0
$394$		−	359.153i		−	0.911556i
$395$	−61.5442	−	364.035i	−0.155808	−	0.921608i
$396$		0			0
$397$	−165.106	+	165.106i	−0.415883	+	0.415883i	−0.883782	−	0.467899i	$-0.845011\pi$
$397$	−165.106	+	165.106i	−0.415883	+	0.415883i	0.467899	+	0.883782i	$0.345011\pi$
$398$	−139.320	−	139.320i	−0.350050	−	0.350050i
$399$		0			0
$400$	−4.68789	+	1.63172i	−0.0117197	+	0.00407929i
$401$	−593.726			−1.48061			−0.740307	−	0.672269i	$-0.765320\pi$
$401$	−593.726			−1.48061			−0.740307	+	0.672269i	$0.765320\pi$
$402$		0			0
$403$	101.534	+	101.534i	0.251945	+	0.251945i
$404$		−	220.966i		−	0.546946i
$405$		0			0
$406$	120.701			0.297292
$407$	24.5714	−	24.5714i	0.0603721	−	0.0603721i
$408$		0			0
$409$		−	354.736i		−	0.867324i	−0.901076	−	0.433662i	$-0.857221\pi$
$409$		−	354.736i		−	0.867324i	0.901076	−	0.433662i	$-0.142779\pi$
$410$	−261.127	+	367.383i	−0.636894	+	0.896056i
$411$		0			0
$412$	−54.9519	+	54.9519i	−0.133378	+	0.133378i
$413$	59.1511	+	59.1511i	0.143223	+	0.143223i
$414$		0			0
$415$	−338.140	−	240.341i	−0.814795	−	0.579136i
$416$	−97.9824			−0.235535
$417$		0			0
$418$	45.3258	+	45.3258i	0.108435	+	0.108435i
$419$			107.473i			0.256498i	0.991742	+	0.128249i	$0.0409356\pi$
$419$			107.473i			0.256498i	−0.991742	+	0.128249i	$0.959064\pi$
$420$		0			0
$421$	572.426			1.35968			0.679841	−	0.733359i	$-0.262049\pi$
$421$	572.426			1.35968			0.679841	+	0.733359i	$0.262049\pi$
$422$	230.716	−	230.716i	0.546721	−	0.546721i
$423$		0			0
$424$			372.984i			0.879678i
$425$	45.6690	−	94.4351i	0.107456	−	0.222200i
$426$		0			0
$427$	199.085	−	199.085i	0.466241	−	0.466241i
$428$	−271.243	−	271.243i	−0.633746	−	0.633746i
$429$		0			0
$430$	−2.09408	+	0.354028i	−0.00486996	+	0.000823321i
$431$	−346.647			−0.804285			−0.402142	−	0.915577i	$-0.631734\pi$
$431$	−346.647			−0.804285			−0.402142	+	0.915577i	$0.631734\pi$
$432$		0			0
$433$	−103.330	−	103.330i	−0.238637	−	0.238637i	0.577649	−	0.816285i	$-0.303970\pi$
$433$	−103.330	−	103.330i	−0.238637	−	0.238637i	−0.816285	+	0.577649i	$0.803970\pi$
$434$			152.816i			0.352111i
$435$		0			0
$436$	189.160			0.433854
$437$	−261.630	+	261.630i	−0.598697	+	0.598697i
$438$		0			0
$439$			324.757i			0.739766i	0.929078	+	0.369883i	$0.120602\pi$
$439$			324.757i			0.739766i	−0.929078	+	0.369883i	$0.879398\pi$
$440$	48.6779	+	34.5990i	0.110632	+	0.0786342i
$441$		0			0
$442$	11.1061	−	11.1061i	0.0251270	−	0.0251270i
$443$	226.450	+	226.450i	0.511173	+	0.511173i	0.914886	−	0.403713i	$-0.132280\pi$
$443$	226.450	+	226.450i	0.511173	+	0.511173i	−0.403713	+	0.914886i	$0.632280\pi$
$444$		0			0
$445$	−69.3894	−	410.440i	−0.155931	−	0.922336i
$446$	249.868			0.560243
$447$		0			0
$448$	−72.2496	−	72.2496i	−0.161271	−	0.161271i
$449$			221.579i			0.493494i	0.969080	+	0.246747i	$0.0793617\pi$
$449$			221.579i			0.493494i	−0.969080	+	0.246747i	$0.920638\pi$
$450$		0			0
$451$	−110.111			−0.244148
$452$	−55.0097	+	55.0097i	−0.121703	+	0.121703i
$453$		0			0
$454$		−	302.769i		−	0.666891i
$455$	−39.7903	+	6.72700i	−0.0874513	+	0.0147846i
$456$		0			0
$457$	631.757	−	631.757i	1.38240	−	1.38240i	0.542064	−	0.840337i	$-0.317643\pi$
$457$	631.757	−	631.757i	1.38240	−	1.38240i	0.840337	−	0.542064i	$-0.182357\pi$
$458$	−35.8331	−	35.8331i	−0.0782382	−	0.0782382i
$459$		0			0
$460$	−76.7045	+	107.917i	−0.166749	+	0.234602i
$461$	−10.7536			−0.0233266			−0.0116633	−	0.999932i	$-0.503713\pi$
$461$	−10.7536			−0.0233266			−0.0116633	+	0.999932i	$0.503713\pi$
$462$		0			0
$463$	−87.0943	−	87.0943i	−0.188109	−	0.188109i	0.606769	−	0.794878i	$-0.292465\pi$
$463$	−87.0943	−	87.0943i	−0.188109	−	0.188109i	−0.794878	+	0.606769i	$0.792465\pi$
$464$			7.38174i			0.0159089i
$465$		0			0
$466$	126.373			0.271187
$467$	168.883	−	168.883i	0.361633	−	0.361633i	−0.502781	−	0.864414i	$-0.667690\pi$
$467$	168.883	−	168.883i	0.361633	−	0.361633i	0.864414	+	0.502781i	$0.167690\pi$
$468$		0			0
$469$			107.238i			0.228653i
$470$	−56.3208	−	333.139i	−0.119831	−	0.708806i
$471$		0			0
$472$	178.163	−	178.163i	0.377463	−	0.377463i
$473$	−0.366870	−	0.366870i	−0.000775624	−	0.000775624i
$474$		0			0
$475$	286.423	+	822.887i	0.602995	+	1.73239i
$476$	−27.6900			−0.0581722
$477$		0			0
$478$	363.253	+	363.253i	0.759943	+	0.759943i
$479$			591.385i			1.23462i	0.786718	+	0.617312i	$0.211779\pi$
$479$			591.385i			1.23462i	−0.786718	+	0.617312i	$0.788221\pi$
$480$		0			0
$481$	70.7241			0.147036
$482$	322.619	−	322.619i	0.669334	−	0.669334i
$483$		0			0
$484$		−	296.204i		−	0.611992i
$485$	−423.062	+	595.213i	−0.872293	+	1.22724i
$486$		0			0
$487$	454.628	−	454.628i	0.933527	−	0.933527i	−0.0643972	−	0.997924i	$-0.520512\pi$
$487$	454.628	−	454.628i	0.933527	−	0.933527i	0.997924	+	0.0643972i	$0.0205125\pi$
$488$	−599.642	−	599.642i	−1.22877	−	1.22877i
$489$		0			0
$490$	−35.0060	−	24.8814i	−0.0714409	−	0.0507784i
$491$	267.659			0.545130			0.272565	−	0.962137i	$-0.412128\pi$
$491$	267.659			0.545130			0.272565	+	0.962137i	$0.412128\pi$
$492$		0			0
$493$	−110.307	−	110.307i	−0.223746	−	0.223746i
$494$			130.462i			0.264092i
$495$		0			0
$496$	−9.34584			−0.0188424
$497$	29.6513	−	29.6513i	0.0596605	−	0.0596605i
$498$		0			0
$499$			598.541i			1.19948i	0.800194	+	0.599741i	$0.204730\pi$
$499$			598.541i			1.19948i	−0.800194	+	0.599741i	$0.795270\pi$
$500$	150.143	+	273.253i	0.300286	+	0.546505i
$501$		0			0
$502$	−407.417	+	407.417i	−0.811587	+	0.811587i
$503$	597.424	+	597.424i	1.18772	+	1.18772i	0.977696	+	0.210027i	$0.0673552\pi$
$503$	597.424	+	597.424i	1.18772	+	1.18772i	0.210027	+	0.977696i	$0.432645\pi$
$504$		0			0
$505$	−436.748	+	73.8371i	−0.864848	+	0.146212i
$506$	19.5254			0.0385877
$507$		0			0
$508$	420.504	+	420.504i	0.827764	+	0.827764i
$509$			734.407i			1.44284i	0.692496	+	0.721422i	$0.256511\pi$
$509$			734.407i			1.44284i	−0.692496	+	0.721422i	$0.743489\pi$
$510$		0			0
$511$	98.2873			0.192343
$512$	8.98472	−	8.98472i	0.0175483	−	0.0175483i
$513$		0			0
$514$			373.106i			0.725888i
$515$	126.977	+	90.2521i	0.246557	+	0.175247i
$516$		0			0
$517$	58.3638	−	58.3638i	0.112889	−	0.112889i
$518$	53.2225	+	53.2225i	0.102746	+	0.102746i
$519$		0			0
$520$	20.2617	+	119.848i	0.0389648	+	0.230477i
$521$	−207.188			−0.397674			−0.198837	−	0.980033i	$-0.563716\pi$
$521$	−207.188			−0.397674			−0.198837	+	0.980033i	$0.563716\pi$
$522$		0			0
$523$	143.359	+	143.359i	0.274110	+	0.274110i	0.830752	−	0.556642i	$-0.187911\pi$
$523$	143.359	+	143.359i	0.274110	+	0.274110i	−0.556642	+	0.830752i	$0.687911\pi$
$524$		−	52.8828i		−	0.100921i
$525$		0			0
$526$	−166.559			−0.316652
$527$	139.657	−	139.657i	0.265003	−	0.265003i
$528$		0			0
$529$		−	416.295i		−	0.786948i
$530$	283.145	−	47.8688i	0.534236	−	0.0903186i
$531$		0			0
$532$	162.634	−	162.634i	0.305703	−	0.305703i
$533$	−158.466	−	158.466i	−0.297310	−	0.297310i
$534$		0			0
$535$	−445.485	+	626.760i	−0.832683	+	1.17151i
$536$	323.001			0.602614
$537$		0			0
$538$	46.7724	+	46.7724i	0.0869376	+	0.0869376i
$539$		−	10.4919i		−	0.0194655i
$540$		0			0
$541$	−22.1387			−0.0409219			−0.0204609	−	0.999791i	$-0.506513\pi$
$541$	−22.1387			−0.0409219			−0.0204609	+	0.999791i	$0.506513\pi$
$542$	−141.988	+	141.988i	−0.261970	+	0.261970i
$543$		0			0
$544$			134.772i			0.247742i
$545$	−63.2090	−	373.883i	−0.115980	−	0.686023i
$546$		0			0
$547$	113.508	−	113.508i	0.207509	−	0.207509i	−0.595699	−	0.803208i	$-0.703125\pi$
$547$	113.508	−	113.508i	0.207509	−	0.207509i	0.803208	+	0.595699i	$0.203125\pi$
$548$	259.995	+	259.995i	0.474444	+	0.474444i
$549$		0			0
$550$	20.0180	−	41.3936i	0.0363964	−	0.0752612i
$551$	1295.75			2.35163
$552$		0			0
$553$	138.142	+	138.142i	0.249805	+	0.249805i
$554$		−	44.1020i		−	0.0796066i
$555$		0			0
$556$	300.600			0.540647
$557$	229.622	−	229.622i	0.412248	−	0.412248i	−0.470273	−	0.882521i	$-0.655845\pi$
$557$	229.622	−	229.622i	0.412248	−	0.412248i	0.882521	+	0.470273i	$0.155845\pi$
$558$		0			0
$559$		−	1.05596i		−	0.00188902i
$560$	1.52168	−	2.14088i	0.00271729	−	0.00382300i
$561$		0			0
$562$	−98.1844	+	98.1844i	−0.174705	+	0.174705i
$563$	−92.9885	−	92.9885i	−0.165166	−	0.165166i	0.619685	−	0.784851i	$-0.287260\pi$
$563$	−92.9885	−	92.9885i	−0.165166	−	0.165166i	−0.784851	+	0.619685i	$0.787260\pi$
$564$		0			0
$565$	127.111	+	90.3471i	0.224975	+	0.159906i
$566$	609.175			1.07628
$567$		0			0
$568$	−89.3094	−	89.3094i	−0.157235	−	0.157235i
$569$			388.149i			0.682160i	0.940034	+	0.341080i	$0.110793\pi$
$569$			388.149i			0.682160i	−0.940034	+	0.341080i	$0.889207\pi$
$570$		0			0
$571$	−488.529			−0.855568			−0.427784	−	0.903881i	$-0.640706\pi$
$571$	−488.529			−0.855568			−0.427784	+	0.903881i	$0.640706\pi$
$572$	−8.06426	+	8.06426i	−0.0140984	+	0.0140984i
$573$		0			0
$574$		−	238.504i		−	0.415512i
$575$	238.933	+	115.548i	0.415536	+	0.200954i
$576$		0			0
$577$	365.601	−	365.601i	0.633624	−	0.633624i	−0.315351	−	0.948975i	$-0.602122\pi$
$577$	365.601	−	365.601i	0.633624	−	0.633624i	0.948975	+	0.315351i	$0.102122\pi$
$578$	235.482	+	235.482i	0.407408	+	0.407408i
$579$		0			0
$580$	457.177	−	77.2909i	0.788236	−	0.133260i
$581$	219.519			0.377830
$582$		0			0
$583$	49.6053	+	49.6053i	0.0850862	+	0.0850862i
$584$		−	296.041i		−	0.506919i
$585$		0			0
$586$	150.069			0.256090
$587$	−410.771	+	410.771i	−0.699780	+	0.699780i	−0.964363	−	0.264583i	$-0.914766\pi$
$587$	−410.771	+	410.771i	−0.699780	+	0.699780i	0.264583	+	0.964363i	$0.414766\pi$
$588$		0			0
$589$			1640.52i			2.78526i
$590$	−158.115	−	112.384i	−0.267992	−	0.190482i
$591$		0			0
$592$	−3.25495	+	3.25495i	−0.00549823	+	0.00549823i
$593$	−776.361	−	776.361i	−1.30921	−	1.30921i	−0.921986	−	0.387224i	$-0.873434\pi$
$593$	−776.361	−	776.361i	−1.30921	−	1.30921i	−0.387224	−	0.921986i	$-0.626566\pi$
$594$		0			0
$595$	9.25277	+	54.7303i	0.0155509	+	0.0919837i
$596$	−28.1167			−0.0471757
$597$		0			0
$598$	28.1000	+	28.1000i	0.0469899	+	0.0469899i
$599$			573.555i			0.957521i	0.877946	+	0.478760i	$0.158914\pi$
$599$			573.555i			0.957521i	−0.877946	+	0.478760i	$0.841086\pi$
$600$		0			0
$601$	345.953			0.575628			0.287814	−	0.957686i	$-0.407071\pi$
$601$	345.953			0.575628			0.287814	+	0.957686i	$0.407071\pi$
$602$	0.794653	−	0.794653i	0.00132002	−	0.00132002i
$603$		0			0
$604$		−	49.5901i		−	0.0821028i
$605$	−585.460	+	98.9784i	−0.967702	+	0.163601i
$606$		0			0
$607$	627.891	−	627.891i	1.03442	−	1.03442i	0.0350309	−	0.999386i	$-0.488847\pi$
$607$	627.891	−	627.891i	1.03442	−	1.03442i	0.999386	−	0.0350309i	$-0.0111530\pi$
$608$	−791.567	−	791.567i	−1.30192	−	1.30192i
$609$		0			0
$610$	−378.252	+	532.168i	−0.620085	+	0.872407i
$611$	167.989			0.274941
$612$		0			0
$613$	114.845	+	114.845i	0.187349	+	0.187349i	0.794549	−	0.607200i	$-0.207707\pi$
$613$	114.845	+	114.845i	0.187349	+	0.187349i	−0.607200	+	0.794549i	$0.707707\pi$
$614$			196.238i			0.319606i
$615$		0			0
$616$	−31.6016			−0.0513012
$617$	271.304	−	271.304i	0.439715	−	0.439715i	−0.452201	−	0.891916i	$-0.649361\pi$
$617$	271.304	−	271.304i	0.439715	−	0.439715i	0.891916	+	0.452201i	$0.149361\pi$
$618$		0			0
$619$		−	346.221i		−	0.559323i	−0.960099	−	0.279662i	$-0.909778\pi$
$619$		−	346.221i		−	0.559323i	0.960099	−	0.279662i	$-0.0902223\pi$
$620$	97.8561	+	578.821i	0.157832	+	0.933582i
$621$		0			0
$622$	64.1784	−	64.1784i	0.103181	−	0.103181i
$623$	155.752	+	155.752i	0.250003	+	0.250003i
$624$		0			0
$625$	489.923	−	388.072i	0.783878	−	0.620915i
$626$	−562.741			−0.898948
$627$		0			0
$628$	−87.5558	−	87.5558i	−0.139420	−	0.139420i
$629$		−	97.2787i		−	0.154656i
$630$		0			0
$631$	−828.209			−1.31253			−0.656267	−	0.754528i	$-0.727866\pi$
$631$	−828.209			−1.31253			−0.656267	+	0.754528i	$0.727866\pi$
$632$	416.084	−	416.084i	0.658361	−	0.658361i
$633$		0			0
$634$		−	262.096i		−	0.413400i
$635$	690.629	−	971.657i	1.08760	−	1.53017i
$636$		0			0
$637$	15.0994	−	15.0994i	0.0237040	−	0.0237040i
$638$	−48.3506	−	48.3506i	−0.0757847	−	0.0757847i
$639$		0			0
$640$	−330.475	−	234.893i	−0.516368	−	0.367021i
$641$	167.603			0.261471			0.130736	−	0.991417i	$-0.458266\pi$
$641$	167.603			0.261471			0.130736	+	0.991417i	$0.458266\pi$
$642$		0			0
$643$	442.638	+	442.638i	0.688395	+	0.688395i	0.961877	−	0.273482i	$-0.0881755\pi$
$643$	442.638	+	442.638i	0.688395	+	0.688395i	−0.273482	+	0.961877i	$0.588176\pi$
$644$		−	70.0592i		−	0.108788i
$645$		0			0
$646$	179.446			0.277780
$647$	494.631	−	494.631i	0.764500	−	0.764500i	−0.212632	−	0.977132i	$-0.568204\pi$
$647$	494.631	−	494.631i	0.764500	−	0.764500i	0.977132	+	0.212632i	$0.0682037\pi$
$648$		0			0
$649$		−	47.3898i		−	0.0730197i
$650$	88.3808	−	30.7627i	0.135970	−	0.0473273i
$651$		0			0
$652$	−430.851	+	430.851i	−0.660815	+	0.660815i
$653$	106.722	+	106.722i	0.163434	+	0.163434i	0.784086	−	0.620652i	$-0.213132\pi$
$653$	106.722	+	106.722i	0.163434	+	0.163434i	−0.620652	+	0.784086i	$0.713132\pi$
$654$		0			0
$655$	−104.525	+	17.6711i	−0.159580	+	0.0269788i
$656$	14.5863			0.0222352
$657$		0			0
$658$	126.418	+	126.418i	0.192124	+	0.192124i
$659$			712.593i			1.08132i	0.841240	+	0.540662i	$0.181826\pi$
$659$			712.593i			1.08132i	−0.841240	+	0.540662i	$0.818174\pi$
$660$		0			0
$661$	−1217.06			−1.84123			−0.920617	−	0.390466i	$-0.872314\pi$
$661$	−1217.06			−1.84123			−0.920617	+	0.390466i	$0.872314\pi$
$662$	−157.135	+	157.135i	−0.237365	+	0.237365i
$663$		0			0
$664$		−	661.191i		−	0.995770i
$665$	−375.798	−	267.108i	−0.565110	−	0.401666i
$666$		0			0
$667$	279.090	−	279.090i	0.418426	−	0.418426i
$668$	−432.622	−	432.622i	−0.647638	−	0.647638i
$669$		0			0
$670$	−41.4541	−	245.202i	−0.0618718	−	0.365973i
$671$	−159.500			−0.237705
$672$		0			0
$673$	−545.679	−	545.679i	−0.810816	−	0.810816i	0.173940	−	0.984756i	$-0.444350\pi$
$673$	−545.679	−	545.679i	−0.810816	−	0.810816i	−0.984756	+	0.173940i	$0.944350\pi$
$674$			674.601i			1.00089i
$675$		0			0
$676$	398.322			0.589234
$677$	−297.552	+	297.552i	−0.439515	+	0.439515i	−0.891849	−	0.452333i	$-0.850592\pi$
$677$	−297.552	+	297.552i	−0.439515	+	0.439515i	0.452333	+	0.891849i	$0.350592\pi$
$678$		0			0
$679$		−	386.410i		−	0.569087i
$680$	164.847	−	27.8693i	0.242423	−	0.0409842i
$681$		0			0
$682$	61.2155	−	61.2155i	0.0897589	−	0.0897589i
$683$	−156.734	−	156.734i	−0.229479	−	0.229479i	0.582996	−	0.812475i	$-0.301880\pi$
$683$	−156.734	−	156.734i	−0.229479	−	0.229479i	−0.812475	+	0.582996i	$0.801880\pi$
$684$		0			0
$685$	427.012	−	600.770i	0.623375	−	0.877036i
$686$	22.7258			0.0331280
$687$		0			0
$688$	0.0485989	+	0.0485989i	7.06379e−5	+	7.06379e-5i
$689$			142.779i			0.207227i
$690$		0			0
$691$	330.267			0.477955			0.238977	−	0.971025i	$-0.423188\pi$
$691$	330.267			0.477955			0.238977	+	0.971025i	$0.423188\pi$
$692$	33.8228	−	33.8228i	0.0488769	−	0.0488769i
$693$		0			0
$694$			28.0700i			0.0404468i
$695$	−100.447	−	594.147i	−0.144528	−	0.854888i
$696$		0			0
$697$	−217.965	+	217.965i	−0.312719	+	0.312719i
$698$	216.172	+	216.172i	0.309703	+	0.309703i
$699$		0			0
$700$	−148.525	−	71.8269i	−0.212178	−	0.102610i
$701$	−1362.28			−1.94334			−0.971671	−	0.236336i	$-0.924054\pi$
$701$	−1362.28			−1.94334			−0.971671	+	0.236336i	$0.924054\pi$
$702$		0			0
$703$	571.356	+	571.356i	0.812740	+	0.812740i
$704$			57.8839i			0.0822214i
$705$		0			0
$706$	547.215			0.775093
$707$	165.735	−	165.735i	0.234420	−	0.234420i
$708$		0			0
$709$			370.256i			0.522222i	0.965309	+	0.261111i	$0.0840889\pi$
$709$			370.256i			0.522222i	−0.965309	+	0.261111i	$0.915911\pi$
$710$	−56.3360	+	79.2600i	−0.0793465	+	0.111634i
$711$		0			0
$712$	469.123	−	469.123i	0.658881	−	0.658881i
$713$	353.349	+	353.349i	0.495581	+	0.495581i
$714$		0			0
$715$	18.6340	+	13.2446i	0.0260616	+	0.0185239i
$716$	720.810			1.00672
$717$		0			0
$718$	73.2793	+	73.2793i	0.102060	+	0.102060i
$719$			883.893i			1.22934i	0.788786	+	0.614668i	$0.210710\pi$
$719$			883.893i			1.22934i	−0.788786	+	0.614668i	$0.789290\pi$
$720$		0			0
$721$	−82.4331			−0.114332
$722$	−740.725	+	740.725i	−1.02593	+	1.02593i
$723$		0			0
$724$			51.4934i			0.0711235i
$725$	−305.537	−	877.801i	−0.421430	−	1.21076i
$726$		0			0
$727$	−264.156	+	264.156i	−0.363351	+	0.363351i	−0.865045	−	0.501694i	$-0.832710\pi$
$727$	−264.156	+	264.156i	−0.363351	+	0.363351i	0.501694	+	0.865045i	$0.332710\pi$
$728$	−45.4795	−	45.4795i	−0.0624718	−	0.0624718i
$729$		0			0
$730$	−224.735	+	37.9940i	−0.307857	+	0.0520466i
$731$	−1.45244			−0.00198693
$732$		0			0
$733$	−335.629	−	335.629i	−0.457884	−	0.457884i	0.440076	−	0.897960i	$-0.354951\pi$
$733$	−335.629	−	335.629i	−0.457884	−	0.457884i	−0.897960	+	0.440076i	$0.854951\pi$
$734$			346.909i			0.472628i
$735$		0			0
$736$	−340.989			−0.463301
$737$	42.9578	−	42.9578i	0.0582874	−	0.0582874i
$738$		0			0
$739$		−	622.823i		−	0.842791i	−0.906877	−	0.421396i	$-0.861540\pi$
$739$		−	622.823i		−	0.842791i	0.906877	−	0.421396i	$-0.138460\pi$
$740$	235.672	+	167.509i	0.318475	+	0.226364i
$741$		0			0
$742$	−107.447	+	107.447i	−0.144807	+	0.144807i
$743$	−626.571	−	626.571i	−0.843299	−	0.843299i	0.145988	−	0.989286i	$-0.453364\pi$
$743$	−626.571	−	626.571i	−0.843299	−	0.843299i	−0.989286	+	0.145988i	$0.953364\pi$
$744$		0			0
$745$	9.39538	+	55.5739i	0.0126112	+	0.0745958i
$746$	−681.197			−0.913132
$747$		0			0
$748$	11.0921	+	11.0921i	0.0148290	+	0.0148290i
$749$		−	406.891i		−	0.543245i
$750$		0			0
$751$	953.276			1.26934			0.634671	−	0.772783i	$-0.281136\pi$
$751$	953.276			1.26934			0.634671	+	0.772783i	$0.281136\pi$
$752$	−7.73138	+	7.73138i	−0.0102811	+	0.0102811i
$753$		0			0
$754$		−	139.168i		−	0.184573i
$755$	−98.0167	+	16.5708i	−0.129823	+	0.0219481i
$756$		0			0
$757$	−202.867	+	202.867i	−0.267988	+	0.267988i	−0.828289	−	0.560301i	$-0.810685\pi$
$757$	−202.867	+	202.867i	−0.267988	+	0.267988i	0.560301	+	0.828289i	$0.310685\pi$
$758$	312.998	+	312.998i	0.412926	+	0.412926i
$759$		0			0
$760$	−804.527	+	1131.90i	−1.05859	+	1.48934i
$761$	721.550			0.948160			0.474080	−	0.880482i	$-0.342781\pi$
$761$	721.550			0.948160			0.474080	+	0.880482i	$0.342781\pi$
$762$		0			0
$763$	141.879	+	141.879i	0.185949	+	0.185949i
$764$			349.733i			0.457765i
$765$		0			0
$766$	−585.725			−0.764655
$767$	68.2011	−	68.2011i	0.0889193	−	0.0889193i
$768$		0			0
$769$		−	266.011i		−	0.345918i	−0.984929	−	0.172959i	$-0.944667\pi$
$769$		−	266.011i		−	0.345918i	0.984929	−	0.172959i	$-0.0553329\pi$
$770$	4.05575	+	23.9899i	0.00526721	+	0.0311557i
$771$		0			0
$772$	−490.349	+	490.349i	−0.635167	+	0.635167i
$773$	−97.5944	−	97.5944i	−0.126254	−	0.126254i	0.641156	−	0.767410i	$-0.278455\pi$
$773$	−97.5944	−	97.5944i	−0.126254	−	0.126254i	−0.767410	+	0.641156i	$0.778455\pi$
$774$		0			0
$775$	1111.36	−	386.833i	1.43402	−	0.499139i
$776$	−1163.86			−1.49983
$777$		0			0
$778$	−508.216	−	508.216i	−0.653234	−	0.653234i
$779$		−	2560.39i		−	3.28677i
$780$		0			0
$781$	−23.7556			−0.0304169
$782$	38.6506	−	38.6506i	0.0494253	−	0.0494253i
$783$		0			0
$784$			1.38985i			0.00177277i
$785$	−143.800	+	202.315i	−0.183185	+	0.257726i
$786$		0			0
$787$	−475.724	+	475.724i	−0.604477	+	0.604477i	−0.941497	−	0.337020i	$-0.890581\pi$
$787$	−475.724	+	475.724i	−0.604477	+	0.604477i	0.337020	+	0.941497i	$0.390581\pi$
$788$	516.223	+	516.223i	0.655106	+	0.655106i
$789$		0			0
$790$	−369.265	−	262.464i	−0.467424	−	0.332233i
$791$	−82.5199			−0.104323
$792$		0			0
$793$	−229.545	−	229.545i	−0.289464	−	0.289464i
$794$			286.516i			0.360851i
$795$		0			0
$796$	400.499			0.503139
$797$	195.835	−	195.835i	0.245715	−	0.245715i	−0.573495	−	0.819209i	$-0.694413\pi$
$797$	195.835	−	195.835i	0.245715	−	0.245715i	0.819209	+	0.573495i	$0.194413\pi$
$798$		0			0
$799$		−	231.063i		−	0.289190i
$800$	−349.593	+	722.895i	−0.436992	+	0.903619i
$801$		0			0
$802$	−515.161	+	515.161i	−0.642346	+	0.642346i
$803$	−39.3722	−	39.3722i	−0.0490314	−	0.0490314i
$804$		0			0
$805$	−138.475	+	23.4107i	−0.172018	+	0.0290816i
$806$	176.197			0.218607
$807$		0			0
$808$	−499.193	−	499.193i	−0.617813	−	0.617813i
$809$		−	1068.26i		−	1.32046i	−0.751062	−	0.660232i	$-0.770458\pi$
$809$		−	1068.26i		−	1.32046i	0.751062	−	0.660232i	$-0.229542\pi$
$810$		0			0
$811$	−705.937			−0.870453			−0.435226	−	0.900321i	$-0.643332\pi$
$811$	−705.937			−0.870453			−0.435226	+	0.900321i	$0.643332\pi$
$812$	−173.487	+	173.487i	−0.213654	+	0.213654i
$813$		0			0
$814$		−	42.6401i		−	0.0523834i
$815$	995.567	+	707.623i	1.22155	+	0.868250i
$816$		0			0
$817$	8.53078	−	8.53078i	0.0104416	−	0.0104416i
$818$	−307.795	−	307.795i	−0.376278	−	0.376278i
$819$		0			0
$820$	−152.726	−	903.379i	−0.186252	−	1.10168i
$821$	−471.239			−0.573982			−0.286991	−	0.957933i	$-0.592655\pi$
$821$	−471.239			−0.573982			−0.286991	+	0.957933i	$0.592655\pi$
$822$		0			0
$823$	−394.220	−	394.220i	−0.479004	−	0.479004i	0.425809	−	0.904813i	$-0.359990\pi$
$823$	−394.220	−	394.220i	−0.479004	−	0.479004i	−0.904813	+	0.425809i	$0.859990\pi$
$824$			248.288i			0.301320i
$825$		0			0
$826$	102.648			0.124271
$827$	−1059.35	+	1059.35i	−1.28095	+	1.28095i	−0.340825	+	0.940127i	$0.610706\pi$
$827$	−1059.35	+	1059.35i	−1.28095	+	1.28095i	−0.940127	+	0.340825i	$0.889294\pi$
$828$		0			0
$829$			82.5862i			0.0996215i	0.998759	+	0.0498107i	$0.0158618\pi$
$829$			82.5862i			0.0996215i	−0.998759	+	0.0498107i	$0.984138\pi$
$830$	−501.934	+	84.8575i	−0.604740	+	0.102238i
$831$		0			0
$832$	−83.3037	+	83.3037i	−0.100125	+	0.100125i
$833$	−20.7688	−	20.7688i	−0.0249325	−	0.0249325i
$834$		0			0
$835$	−710.532	+	999.658i	−0.850936	+	1.19720i
$836$	−130.297			−0.155857
$837$		0			0
$838$	93.2512	+	93.2512i	0.111278	+	0.111278i
$839$		−	340.123i		−	0.405391i	−0.979242	−	0.202696i	$-0.935030\pi$
$839$		−	340.123i		−	0.405391i	0.979242	−	0.202696i	$-0.0649702\pi$
$840$		0			0
$841$	−541.220			−0.643544
$842$	496.680	−	496.680i	0.589881	−	0.589881i
$843$		0			0
$844$			663.234i			0.785822i
$845$	−133.102	−	787.299i	−0.157517	−	0.931715i
$846$		0			0
$847$	222.167	−	222.167i	0.262299	−	0.262299i
$848$	−6.57115	−	6.57115i	−0.00774900	−	0.00774900i
$849$		0			0
$850$	−42.3131	−	121.565i	−0.0497802	−	0.143017i
$851$	246.128			0.289222
$852$		0			0
$853$	−111.572	−	111.572i	−0.130800	−	0.130800i	0.638676	−	0.769476i	$-0.279482\pi$
$853$	−111.572	−	111.572i	−0.130800	−	0.130800i	−0.769476	+	0.638676i	$0.779482\pi$
$854$		−	345.482i		−	0.404545i
$855$		0			0
$856$	−1225.55			−1.43172
$857$	396.513	−	396.513i	0.462675	−	0.462675i	−0.436856	−	0.899531i	$-0.643908\pi$
$857$	396.513	−	396.513i	0.462675	−	0.462675i	0.899531	+	0.436856i	$0.143908\pi$
$858$		0			0
$859$		−	581.785i		−	0.677281i	−0.940916	−	0.338641i	$-0.890033\pi$
$859$		−	581.785i		−	0.677281i	0.940916	−	0.338641i	$-0.109967\pi$
$860$	2.50104	−	3.51876i	0.00290819	−	0.00409158i
$861$		0			0
$862$	−300.777	+	300.777i	−0.348929	+	0.348929i
$863$	1069.82	+	1069.82i	1.23965	+	1.23965i	0.960145	+	0.279504i	$0.0901700\pi$
$863$	1069.82	+	1069.82i	1.23965	+	1.23965i	0.279504	+	0.960145i	$0.409830\pi$
$864$		0			0
$865$	−78.1542	−	55.5500i	−0.0903517	−	0.0642197i
$866$	−179.313			−0.207059
$867$		0			0
$868$	−219.648	−	219.648i	−0.253051	−	0.253051i
$869$		−	110.675i		−	0.127359i
$870$		0			0
$871$	123.646			0.141958
$872$	427.339	−	427.339i	0.490068	−	0.490068i
$873$		0			0
$874$			454.021i			0.519474i
$875$	−92.3383	+	317.567i	−0.105529	+	0.362933i
$876$		0			0
$877$	826.081	−	826.081i	0.941939	−	0.941939i	−0.0564653	−	0.998405i	$-0.517983\pi$
$877$	826.081	−	826.081i	0.941939	−	0.941939i	0.998405	+	0.0564653i	$0.0179830\pi$
$878$	281.784	+	281.784i	0.320938	+	0.320938i
$879$		0			0
$880$	−1.46716	+	0.248039i	−0.00166722	+	0.000281863i
$881$	1184.11			1.34406			0.672029	−	0.740525i	$-0.265423\pi$
$881$	1184.11			1.34406			0.672029	+	0.740525i	$0.265423\pi$
$882$		0			0
$883$	376.671	+	376.671i	0.426581	+	0.426581i	0.887462	−	0.460881i	$-0.152467\pi$
$883$	376.671	+	376.671i	0.426581	+	0.426581i	−0.460881	+	0.887462i	$0.652467\pi$
$884$			31.9265i			0.0361160i
$885$		0			0
$886$	392.970			0.443532
$887$	−727.292	+	727.292i	−0.819946	+	0.819946i	−0.986100	−	0.166154i	$-0.946865\pi$
$887$	−727.292	+	727.292i	−0.819946	+	0.819946i	0.166154	+	0.986100i	$0.446865\pi$
$888$		0			0
$889$			630.796i			0.709557i
$890$	−416.336	−	295.921i	−0.467793	−	0.332495i
$891$		0			0
$892$	−359.145	+	359.145i	−0.402629	+	0.402629i
$893$	1357.12	+	1357.12i	1.51974	+	1.51974i
$894$		0			0
$895$	−240.863	−	1424.71i	−0.269121	−	1.59185i
$896$	214.543			0.239446
$897$		0			0
$898$	192.258	+	192.258i	0.214096	+	0.214096i
$899$		−	1750.00i		−	1.94660i
$900$		0			0
$901$	196.388			0.217967
$902$	−95.5405	+	95.5405i	−0.105921	+	0.105921i
$903$		0			0
$904$			248.549i			0.274944i
$905$	101.779	−	17.2068i	0.112463	−	0.0190131i
$906$		0			0
$907$	−302.758	+	302.758i	−0.333801	+	0.333801i	−0.854028	−	0.520227i	$-0.825847\pi$
$907$	−302.758	+	302.758i	−0.333801	+	0.333801i	0.520227	+	0.854028i	$0.325847\pi$
$908$	435.180	+	435.180i	0.479273	+	0.479273i
$909$		0			0
$910$	−28.6882	+	40.3619i	−0.0315255	+	0.0443538i
$911$	111.452			0.122340			0.0611701	−	0.998127i	$-0.480517\pi$
$911$	111.452			0.122340			0.0611701	+	0.998127i	$0.480517\pi$
$912$		0			0
$913$	−87.9357	−	87.9357i	−0.0963151	−	0.0963151i
$914$		−	1096.32i		−	1.19948i
$915$		0			0
$916$	103.008			0.112455
$917$	39.6646	−	39.6646i	0.0432548	−	0.0432548i
$918$		0			0
$919$		−	568.949i		−	0.619095i	−0.950884	−	0.309548i	$-0.899822\pi$
$919$		−	568.949i		−	0.619095i	0.950884	−	0.309548i	$-0.100178\pi$
$920$	70.5128	+	417.085i	0.0766444	+	0.453353i
$921$		0			0
$922$	−9.33059	+	9.33059i	−0.0101199	+	0.0101199i
$923$	−34.1879	−	34.1879i	−0.0370400	−	0.0370400i
$924$		0			0
$925$	252.338	−	521.789i	0.272798	−	0.564096i
$926$	−151.139			−0.163217
$927$		0			0
$928$	844.391	+	844.391i	0.909904	+	0.909904i
$929$			1231.06i			1.32515i	0.748997	+	0.662574i	$0.230536\pi$
$929$			1231.06i			1.32515i	−0.748997	+	0.662574i	$0.769464\pi$
$930$		0			0
$931$	243.967			0.262048
$932$	−181.640	+	181.640i	−0.194893	+	0.194893i
$933$		0			0
$934$		−	293.071i		−	0.313780i
$935$	18.2175	−	25.6305i	0.0194840	−	0.0274123i
$936$		0			0
$937$	−160.482	+	160.482i	−0.171272	+	0.171272i	−0.787538	−	0.616266i	$-0.788645\pi$
$937$	−160.482	+	160.482i	−0.171272	+	0.171272i	0.616266	+	0.787538i	$0.288645\pi$
$938$	93.0481	+	93.0481i	0.0991984	+	0.0991984i
$939$		0			0
$940$	559.784	+	397.880i	0.595515	+	0.423277i
$941$	−149.861			−0.159258			−0.0796288	−	0.996825i	$-0.525373\pi$
$941$	−149.861			−0.159258			−0.0796288	+	0.996825i	$0.525373\pi$
$942$		0			0
$943$	−551.480	−	551.480i	−0.584815	−	0.584815i
$944$			6.27767i			0.00665008i
$945$		0			0
$946$	−0.636648			−0.000672990
$947$	−128.238	+	128.238i	−0.135415	+	0.135415i	−0.771565	−	0.636150i	$-0.780526\pi$
$947$	−128.238	+	128.238i	−0.135415	+	0.135415i	0.636150	+	0.771565i	$0.280526\pi$
$948$		0			0
$949$		−	113.325i		−	0.119415i
$950$	962.520	+	465.477i	1.01318	+	0.489975i
$951$		0			0
$952$	−62.5555	+	62.5555i	−0.0657095	+	0.0657095i
$953$	361.782	+	361.782i	0.379625	+	0.379625i	0.870967	−	0.491342i	$-0.163494\pi$
$953$	361.782	+	361.782i	0.379625	+	0.379625i	−0.491342	+	0.870967i	$0.663494\pi$
$954$		0			0
$955$	691.260	−	116.865i	0.723833	−	0.122372i
$956$	−1044.23			−1.09229
$957$		0			0
$958$	513.130	+	513.130i	0.535627	+	0.535627i
$959$			390.017i			0.406692i
$960$		0			0
$961$	1254.63			1.30554
$962$	61.3656	−	61.3656i	0.0637896	−	0.0637896i
$963$		0			0
$964$			927.423i			0.962057i
$965$	1133.05	+	805.341i	1.17414	+	0.834550i
$966$		0			0
$967$	−187.671	+	187.671i	−0.194075	+	0.194075i	−0.797454	−	0.603379i	$-0.793821\pi$
$967$	−187.671	+	187.671i	−0.194075	+	0.194075i	0.603379	+	0.797454i	$0.293821\pi$
$968$	−669.167	−	669.167i	−0.691288	−	0.691288i
$969$		0			0
$970$	149.371	+	883.532i	0.153991	+	0.910858i
$971$	−1651.98			−1.70132			−0.850659	−	0.525718i	$-0.823797\pi$
$971$	−1651.98			−1.70132			−0.850659	+	0.525718i	$0.823797\pi$
$972$		0			0
$973$	225.464	+	225.464i	0.231721	+	0.231721i
$974$		−	788.938i		−	0.809998i
$975$		0			0
$976$	21.1288			0.0216483
$977$	772.134	−	772.134i	0.790311	−	0.790311i	−0.191234	−	0.981545i	$-0.561249\pi$
$977$	772.134	−	772.134i	0.790311	−	0.790311i	0.981545	+	0.191234i	$0.0612488\pi$
$978$		0			0
$979$		−	124.783i		−	0.127459i
$980$	86.0783	−	14.5525i	0.0878350	−	0.0148495i
$981$		0			0
$982$	232.241	−	232.241i	0.236498	−	0.236498i
$983$	−235.236	−	235.236i	−0.239304	−	0.239304i	0.577258	−	0.816562i	$-0.304123\pi$
$983$	−235.236	−	235.236i	−0.239304	−	0.239304i	−0.816562	+	0.577258i	$0.804123\pi$
$984$		0			0
$985$	847.836	−	1192.83i	0.860748	−	1.21100i
$986$	−191.421			−0.194139
$987$		0			0
$988$	−187.517	−	187.517i	−0.189795	−	0.189795i
$989$		−	3.67487i		−	0.00371574i
$990$		0			0
$991$	308.024			0.310822			0.155411	−	0.987850i	$-0.450330\pi$
$991$	308.024			0.310822			0.155411	+	0.987850i	$0.450330\pi$
$992$	−1069.06	+	1069.06i	−1.07768	+	1.07768i
$993$		0			0
$994$		−	51.4553i		−	0.0517659i
$995$	−133.829	−	791.602i	−0.134502	−	0.795580i
$996$		0			0
$997$	−663.237	+	663.237i	−0.665232	+	0.665232i	−0.956609	−	0.291376i	$-0.905887\pi$
$997$	−663.237	+	663.237i	−0.665232	+	0.665232i	0.291376	+	0.956609i	$0.405887\pi$
$998$	519.339	+	519.339i	0.520380	+	0.520380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.253.8		24
3.2	odd	2		105.3.l.a.43.5	yes	24
5.2	odd	4	inner	315.3.o.b.127.8		24
15.2	even	4		105.3.l.a.22.5	✓	24
15.8	even	4		525.3.l.e.232.8		24
15.14	odd	2		525.3.l.e.43.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.5	✓	24	15.2	even	4
105.3.l.a.43.5	yes	24	3.2	odd	2
315.3.o.b.127.8		24	5.2	odd	4	inner
315.3.o.b.253.8		24	1.1	even	1	trivial
525.3.l.e.43.8		24	15.14	odd	2
525.3.l.e.232.8		24	15.8	even	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.867675 - 0.867675i) q^{2} +2.49428i q^{4} +(4.93004 - 0.833478i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(5.63493 + 5.63493i) q^{8} +O(q^{10})\)	\(q+(0.867675 - 0.867675i) q^{2} +2.49428i q^{4} +(4.93004 - 0.833478i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(5.63493 + 5.63493i) q^{8} +(3.55449 - 5.00086i) q^{10} +1.49884 q^{11} +(2.15706 + 2.15706i) q^{13} +3.24654i q^{14} -0.198550 q^{16} +(2.96697 - 2.96697i) q^{17} +34.8524i q^{19} +(2.07893 + 12.2969i) q^{20} +(1.30051 - 1.30051i) q^{22} +(7.50682 + 7.50682i) q^{23} +(23.6106 - 8.21817i) q^{25} +3.74326 q^{26} +(-4.66637 - 4.66637i) q^{28} -37.1782i q^{29} +47.0705 q^{31} +(-22.7120 + 22.7120i) q^{32} -5.14873i q^{34} +(-7.66397 + 10.7826i) q^{35} +(16.3936 - 16.3936i) q^{37} +(30.2406 + 30.2406i) q^{38} +(32.4770 + 23.0838i) q^{40} -73.4639 q^{41} +(-0.244769 - 0.244769i) q^{43} +3.73853i q^{44} +13.0270 q^{46} +(38.9392 - 38.9392i) q^{47} -7.00000i q^{49} +(13.3557 - 27.6171i) q^{50} +(-5.38032 + 5.38032i) q^{52} +(33.0957 + 33.0957i) q^{53} +(7.38936 - 1.24925i) q^{55} -21.0840 q^{56} +(-32.2586 - 32.2586i) q^{58} -31.6176i q^{59} -106.415 q^{61} +(40.8419 - 40.8419i) q^{62} +38.6190i q^{64} +(12.4323 + 8.83655i) q^{65} +(28.6607 - 28.6607i) q^{67} +(7.40045 + 7.40045i) q^{68} +(2.70592 + 16.0056i) q^{70} -15.8493 q^{71} +(-26.2684 - 26.2684i) q^{73} -28.4486i q^{74} -86.9316 q^{76} +(-2.80408 + 2.80408i) q^{77} -73.8402i q^{79} +(-0.978860 + 0.165487i) q^{80} +(-63.7428 + 63.7428i) q^{82} +(-58.6690 - 58.6690i) q^{83} +(12.1544 - 17.1002i) q^{85} -0.424760 q^{86} +(8.44587 + 8.44587i) q^{88} -83.2528i q^{89} -8.07100 q^{91} +(-18.7241 + 18.7241i) q^{92} -67.5732i q^{94} +(29.0487 + 171.824i) q^{95} +(-103.272 + 103.272i) q^{97} +(-6.07373 - 6.07373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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