LMFDB - Embedded newform 315.3.ca.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.52852 + 0.945463i) q^{2} +(8.09242 - 4.67216i) q^{4} +(-3.83301 - 3.21062i) q^{5} +(-6.80203 + 1.65300i) q^{7} +(-13.8047 + 13.8047i) q^{8} +O(q^{10})$	\(q+(-3.52852 + 0.945463i) q^{2} +(8.09242 - 4.67216i) q^{4} +(-3.83301 - 3.21062i) q^{5} +(-6.80203 + 1.65300i) q^{7} +(-13.8047 + 13.8047i) q^{8} +(16.5603 + 7.70474i) q^{10} +(7.38858 + 12.7974i) q^{11} +(-7.90282 + 7.90282i) q^{13} +(22.4382 - 12.2637i) q^{14} +(16.9695 - 29.3921i) q^{16} +(2.21369 - 8.26159i) q^{17} +(7.14233 + 4.12363i) q^{19} +(-46.0188 - 8.07322i) q^{20} +(-38.1702 - 38.1702i) q^{22} +(-4.87235 - 18.1839i) q^{23} +(4.38389 + 24.6126i) q^{25} +(20.4134 - 35.3570i) q^{26} +(-47.3218 + 45.1569i) q^{28} -5.44111i q^{29} +(-26.5427 - 45.9734i) q^{31} +(-11.8767 + 44.3244i) q^{32} +31.2441i q^{34} +(31.3794 + 15.5027i) q^{35} +(34.5256 - 9.25110i) q^{37} +(-29.1006 - 7.79747i) q^{38} +(97.2348 - 8.59191i) q^{40} +40.8709 q^{41} +(53.7395 - 53.7395i) q^{43} +(119.583 + 69.0412i) q^{44} +(34.3844 + 59.5555i) q^{46} +(-40.2908 + 10.7959i) q^{47} +(43.5352 - 22.4875i) q^{49} +(-38.7390 - 82.7012i) q^{50} +(-27.0297 + 100.876i) q^{52} +(55.5377 + 14.8813i) q^{53} +(12.7670 - 72.7744i) q^{55} +(71.0806 - 116.719i) q^{56} +(5.14437 + 19.1990i) q^{58} +(14.5251 - 8.38608i) q^{59} +(46.7481 - 80.9701i) q^{61} +(137.123 + 137.123i) q^{62} -31.8720i q^{64} +(55.6645 - 4.91865i) q^{65} +(-28.2333 + 105.368i) q^{67} +(-20.6854 - 77.1989i) q^{68} +(-125.380 - 25.0336i) q^{70} -51.0976 q^{71} +(42.2429 + 11.3190i) q^{73} +(-113.077 + 65.2853i) q^{74} +77.0650 q^{76} +(-71.4114 - 74.8349i) q^{77} +(-24.7788 - 14.3061i) q^{79} +(-159.411 + 58.1774i) q^{80} +(-144.213 + 38.6419i) q^{82} +(34.5883 - 34.5883i) q^{83} +(-35.0099 + 24.5594i) q^{85} +(-138.812 + 240.429i) q^{86} +(-278.660 - 74.6669i) q^{88} +(-45.7486 - 26.4130i) q^{89} +(40.6919 - 66.8186i) q^{91} +(-124.387 - 124.387i) q^{92} +(131.960 - 76.1869i) q^{94} +(-14.1372 - 38.7372i) q^{95} +(-33.9979 - 33.9979i) q^{97} +(-132.353 + 120.508i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−3.52852	+	0.945463i	−1.76426	+	0.472731i	−0.987573	−	0.157159i	$-0.949767\pi$
$2$	−3.52852	+	0.945463i	−1.76426	+	0.472731i	−0.776684	+	0.629890i	$0.783100\pi$
$3$		0			0
$3$		0			0
$4$	8.09242	−	4.67216i	2.02310	−	1.16804i
$5$	−3.83301	−	3.21062i	−0.766602	−	0.642123i
$5$	−3.83301	−	3.21062i	−0.766602	−	0.642123i
$6$		0			0
$7$	−6.80203	+	1.65300i	−0.971718	+	0.236143i
$7$	−6.80203	+	1.65300i	−0.971718	+	0.236143i
$8$	−13.8047	+	13.8047i	−1.72558	+	1.72558i
$9$		0			0
$10$	16.5603	+	7.70474i	1.65603	+	0.770474i
$11$	7.38858	+	12.7974i	0.671689	+	1.16340i	0.977425	+	0.211283i	$0.0677642\pi$
$11$	7.38858	+	12.7974i	0.671689	+	1.16340i	−0.305736	+	0.952116i	$0.598902\pi$
$12$		0			0
$13$	−7.90282	+	7.90282i	−0.607909	+	0.607909i	−0.942399	−	0.334490i	$-0.891436\pi$
$13$	−7.90282	+	7.90282i	−0.607909	+	0.607909i	0.334490	+	0.942399i	$0.391436\pi$
$14$	22.4382	−	12.2637i	1.60273	−	0.875978i
$15$		0			0
$16$	16.9695	−	29.3921i	1.06060	−	1.83700i
$17$	2.21369	−	8.26159i	0.130217	−	0.485976i	−0.869755	−	0.493484i	$-0.835723\pi$
$17$	2.21369	−	8.26159i	0.130217	−	0.485976i	0.999972	+	0.00750800i	$0.00238989\pi$
$18$		0			0
$19$	7.14233	+	4.12363i	0.375912	+	0.217033i	0.676038	−	0.736867i	$-0.263695\pi$
$19$	7.14233	+	4.12363i	0.375912	+	0.217033i	−0.300126	+	0.953900i	$0.597029\pi$
$20$	−46.0188	−	8.07322i	−2.30094	−	0.403661i
$21$		0			0
$22$	−38.1702	−	38.1702i	−1.73501	−	1.73501i
$23$	−4.87235	−	18.1839i	−0.211842	−	0.790603i	−0.987255	−	0.159149i	$-0.949125\pi$
$23$	−4.87235	−	18.1839i	−0.211842	−	0.790603i	0.775413	−	0.631454i	$-0.217542\pi$
$24$		0			0
$25$	4.38389	+	24.6126i	0.175356	+	0.984505i
$26$	20.4134	−	35.3570i	0.785131	−	1.35989i
$27$		0			0
$28$	−47.3218	+	45.1569i	−1.69006	+	1.61275i
$29$		−	5.44111i		−	0.187624i	−0.995590	−	0.0938122i	$-0.970095\pi$
$29$		−	5.44111i		−	0.187624i	0.995590	−	0.0938122i	$-0.0299053\pi$
$30$		0			0
$31$	−26.5427	−	45.9734i	−0.856217	−	1.48301i	−0.875511	−	0.483198i	$-0.839475\pi$
$31$	−26.5427	−	45.9734i	−0.856217	−	1.48301i	0.0192943	−	0.999814i	$-0.493858\pi$
$32$	−11.8767	+	44.3244i	−0.371146	+	1.38514i
$33$		0			0
$34$			31.2441i			0.918944i
$35$	31.3794	+	15.5027i	0.896553	+	0.442935i
$36$		0			0
$37$	34.5256	−	9.25110i	0.933124	−	0.250030i	0.239938	−	0.970788i	$-0.422873\pi$
$37$	34.5256	−	9.25110i	0.933124	−	0.250030i	0.693186	+	0.720758i	$0.256206\pi$
$38$	−29.1006	−	7.79747i	−0.765804	−	0.205197i
$39$		0			0
$40$	97.2348	−	8.59191i	2.43087	−	0.214798i
$41$	40.8709			0.996850			0.498425	−	0.866933i	$-0.333912\pi$
$41$	40.8709			0.996850			0.498425	+	0.866933i	$0.333912\pi$
$42$		0			0
$43$	53.7395	−	53.7395i	1.24976	−	1.24976i	0.293927	−	0.955828i	$-0.405038\pi$
$43$	53.7395	−	53.7395i	1.24976	−	1.24976i	0.955828	−	0.293927i	$-0.0949624\pi$
$44$	119.583	+	69.0412i	2.71779	+	1.56912i
$45$		0			0
$46$	34.3844	+	59.5555i	0.747486	+	1.29468i
$47$	−40.2908	+	10.7959i	−0.857251	+	0.229700i	−0.660567	−	0.750767i	$-0.729684\pi$
$47$	−40.2908	+	10.7959i	−0.857251	+	0.229700i	−0.196684	+	0.980467i	$0.563017\pi$
$48$		0			0
$49$	43.5352	−	22.4875i	0.888473	−	0.458928i
$50$	−38.7390	−	82.7012i	−0.774779	−	1.65402i
$51$		0			0
$52$	−27.0297	+	100.876i	−0.519802	+	1.93993i
$53$	55.5377	+	14.8813i	1.04788	+	0.280779i	0.741376	−	0.671090i	$-0.234174\pi$
$53$	55.5377	+	14.8813i	1.04788	+	0.280779i	0.306505	+	0.951869i	$0.400840\pi$
$54$		0			0
$55$	12.7670	−	72.7744i	0.232128	−	1.32317i
$56$	71.0806	−	116.719i	1.26930	−	2.08426i
$57$		0			0
$58$	5.14437	+	19.1990i	0.0886959	+	0.331018i
$59$	14.5251	−	8.38608i	0.246188	−	0.142137i	−0.371829	−	0.928301i	$-0.621269\pi$
$59$	14.5251	−	8.38608i	0.246188	−	0.142137i	0.618018	+	0.786164i	$0.287936\pi$
$60$		0			0
$61$	46.7481	−	80.9701i	0.766363	−	1.32738i	−0.173161	−	0.984894i	$-0.555398\pi$
$61$	46.7481	−	80.9701i	0.766363	−	1.32738i	0.939523	−	0.342485i	$-0.111269\pi$
$62$	137.123	+	137.123i	2.21165	+	2.21165i
$63$		0			0
$64$		−	31.8720i		−	0.498000i
$65$	55.6645	−	4.91865i	0.856377	−	0.0756716i
$66$		0			0
$67$	−28.2333	+	105.368i	−0.421393	+	1.57266i	0.350284	+	0.936644i	$0.386085\pi$
$67$	−28.2333	+	105.368i	−0.421393	+	1.57266i	−0.771677	+	0.636015i	$0.780582\pi$
$68$	−20.6854	−	77.1989i	−0.304197	−	1.13528i
$69$		0			0
$70$	−125.380	−	25.0336i	−1.79114	−	0.357623i
$71$	−51.0976			−0.719685			−0.359842	−	0.933013i	$-0.617170\pi$
$71$	−51.0976			−0.719685			−0.359842	+	0.933013i	$0.617170\pi$
$72$		0			0
$73$	42.2429	+	11.3190i	0.578670	+	0.155054i	0.536270	−	0.844046i	$-0.319833\pi$
$73$	42.2429	+	11.3190i	0.578670	+	0.155054i	0.0424003	+	0.999101i	$0.486500\pi$
$74$	−113.077	+	65.2853i	−1.52807	+	0.882234i
$75$		0			0
$76$	77.0650			1.01401
$77$	−71.4114	−	74.8349i	−0.927421	−	0.971882i
$78$		0			0
$79$	−24.7788	−	14.3061i	−0.313656	−	0.181089i	0.334905	−	0.942252i	$-0.391296\pi$
$79$	−24.7788	−	14.3061i	−0.313656	−	0.181089i	−0.648561	+	0.761162i	$0.724629\pi$
$80$	−159.411	+	58.1774i	−1.99264	+	0.727218i
$81$		0			0
$82$	−144.213	+	38.6419i	−1.75870	+	0.471242i
$83$	34.5883	−	34.5883i	0.416726	−	0.416726i	−0.467348	−	0.884074i	$-0.654790\pi$
$83$	34.5883	−	34.5883i	0.416726	−	0.416726i	0.884074	+	0.467348i	$0.154790\pi$
$84$		0			0
$85$	−35.0099	+	24.5594i	−0.411881	+	0.288935i
$86$	−138.812	+	240.429i	−1.61409	+	2.79569i
$87$		0			0
$88$	−278.660	−	74.6669i	−3.16660	−	0.848487i
$89$	−45.7486	−	26.4130i	−0.514029	−	0.296775i	0.220459	−	0.975396i	$-0.429244\pi$
$89$	−45.7486	−	26.4130i	−0.514029	−	0.296775i	−0.734488	+	0.678621i	$0.762578\pi$
$90$		0			0
$91$	40.6919	−	66.8186i	0.447163	−	0.734270i
$92$	−124.387	−	124.387i	−1.35203	−	1.35203i
$93$		0			0
$94$	131.960	−	76.1869i	1.40383	−	0.810499i
$95$	−14.1372	−	38.7372i	−0.148813	−	0.407760i
$96$		0			0
$97$	−33.9979	−	33.9979i	−0.350494	−	0.350494i	0.509799	−	0.860293i	$-0.329720\pi$
$97$	−33.9979	−	33.9979i	−0.350494	−	0.350494i	−0.860293	+	0.509799i	$0.829720\pi$
$98$	−132.353	+	120.508i	−1.35055	+	1.22968i
$99$		0			0
$100$	150.470	+	178.693i	1.50470	+	1.78693i
$101$	9.50773	+	16.4679i	0.0941360	+	0.163048i	0.909248	−	0.416256i	$-0.136658\pi$
$101$	9.50773	+	16.4679i	0.0941360	+	0.163048i	−0.815112	+	0.579304i	$0.803324\pi$
$102$		0			0
$103$	−8.35972	−	31.1989i	−0.0811623	−	0.302902i	0.913398	−	0.407069i	$-0.133449\pi$
$103$	−8.35972	−	31.1989i	−0.0811623	−	0.302902i	−0.994560	+	0.104167i	$0.966782\pi$
$104$		−	218.192i		−	2.09800i
$105$		0			0
$106$	−210.035			−1.98146
$107$	143.921	−	38.5636i	1.34506	−	0.360408i	0.486750	−	0.873541i	$-0.338182\pi$
$107$	143.921	−	38.5636i	1.34506	−	0.360408i	0.858309	+	0.513134i	$0.171515\pi$
$108$		0			0
$109$	111.636	−	64.4531i	1.02418	−	0.591313i	0.108871	−	0.994056i	$-0.465276\pi$
$109$	111.636	−	64.4531i	1.02418	−	0.591313i	0.915313	+	0.402743i	$0.131943\pi$
$110$	23.7568	+	268.856i	0.215971	+	2.44415i
$111$		0			0
$112$	−66.8421	+	227.976i	−0.596804	+	2.03550i
$113$	60.2587	−	60.2587i	0.533263	−	0.533263i	−0.388279	−	0.921542i	$-0.626930\pi$
$113$	60.2587	−	60.2587i	0.533263	−	0.533263i	0.921542	+	0.388279i	$0.126930\pi$
$114$		0			0
$115$	−39.7057	+	85.3422i	−0.345267	+	0.742106i
$116$	−25.4217	−	44.0317i	−0.219153	−	0.379584i
$117$		0			0
$118$	−43.3234	+	43.3234i	−0.367147	+	0.367147i
$119$	−1.40116	+	59.8548i	−0.0117744	+	0.502981i
$120$		0			0
$121$	−48.6822	+	84.3200i	−0.402332	+	0.696859i
$122$	−88.3972	+	329.903i	−0.724567	+	2.70412i
$123$		0			0
$124$	−429.590	−	248.024i	−3.46443	−	2.00019i
$125$	62.2182	−	108.415i	0.497746	−	0.867323i
$126$		0			0
$127$	66.3619	+	66.3619i	0.522534	+	0.522534i	0.918336	−	0.395802i	$-0.129533\pi$
$127$	66.3619	+	66.3619i	0.522534	+	0.522534i	−0.395802	+	0.918336i	$0.629533\pi$
$128$	−17.3729	−	64.8366i	−0.135726	−	0.506536i
$129$		0			0
$130$	−191.763	+	69.9842i	−1.47510	+	0.538340i
$131$	−0.764516	+	1.32418i	−0.00583600	+	0.0101082i	−0.868929	−	0.494937i	$-0.835191\pi$
$131$	−0.764516	+	1.32418i	−0.00583600	+	0.0101082i	0.863093	+	0.505046i	$0.168524\pi$
$132$		0			0
$133$	−55.3987	−	16.2428i	−0.416531	−	0.122126i
$134$		−	398.487i		−	2.97378i
$135$		0			0
$136$	83.4892	+	144.608i	0.613891	+	1.06329i
$137$	12.7240	−	47.4866i	0.0928759	−	0.346618i	−0.903813	−	0.427928i	$-0.859244\pi$
$137$	12.7240	−	47.4866i	0.0928759	−	0.346618i	0.996689	+	0.0813101i	$0.0259104\pi$
$138$		0			0
$139$			63.4936i			0.456789i	0.973569	+	0.228394i	$0.0733476\pi$
$139$			63.4936i			0.456789i	−0.973569	+	0.228394i	$0.926652\pi$
$140$	326.366	−	21.1548i	2.33119	−	0.151106i
$141$		0			0
$142$	180.299	−	48.3109i	1.26971	−	0.340218i
$143$	−159.526	−	42.7449i	−1.11557	−	0.298915i
$144$		0			0
$145$	−17.4693	+	20.8558i	−0.120478	+	0.143833i
$146$	−159.757			−1.09422
$147$		0			0
$148$	236.173	−	236.173i	1.59576	−	1.59576i
$149$	−30.8385	−	17.8046i	−0.206970	−	0.119494i	0.392932	−	0.919567i	$-0.371461\pi$
$149$	−30.8385	−	17.8046i	−0.206970	−	0.119494i	−0.599902	+	0.800073i	$0.704794\pi$
$150$		0			0
$151$	21.9235	+	37.9726i	0.145189	+	0.251474i	0.929443	−	0.368965i	$-0.120288\pi$
$151$	21.9235	+	37.9726i	0.145189	+	0.251474i	−0.784255	+	0.620439i	$0.786954\pi$
$152$	−155.523	+	41.6722i	−1.02318	+	0.274159i
$153$		0			0
$154$	322.730	+	196.539i	2.09565	+	1.27623i
$155$	−45.8643	+	261.435i	−0.295899	+	1.68668i
$156$		0			0
$157$	−20.5032	+	76.5190i	−0.130594	+	0.487382i	−0.999977	−	0.00675588i	$-0.997850\pi$
$157$	−20.5032	+	76.5190i	−0.130594	+	0.487382i	0.869384	+	0.494138i	$0.164516\pi$
$158$	100.958	+	27.0517i	0.638977	+	0.171213i
$159$		0			0
$160$	187.832	−	131.764i	1.17395	−	0.823526i
$161$	63.1998	+	115.633i	0.392546	+	0.718219i
$162$		0			0
$163$	−23.5853	−	88.0217i	−0.144695	−	0.540010i	−0.999769	−	0.0215035i	$-0.993155\pi$
$163$	−23.5853	−	88.0217i	−0.144695	−	0.540010i	0.855073	−	0.518507i	$-0.173512\pi$
$164$	330.744	−	190.955i	2.01673	−	1.16436i
$165$		0			0
$166$	−89.3433	+	154.747i	−0.538213	+	0.932212i
$167$	189.696	+	189.696i	1.13590	+	1.13590i	0.989177	+	0.146725i	$0.0468731\pi$
$167$	189.696	+	189.696i	1.13590	+	1.13590i	0.146725	+	0.989177i	$0.453127\pi$
$168$		0			0
$169$			44.0909i			0.260893i
$170$	100.313	−	119.759i	0.590075	−	0.704464i
$171$		0			0
$172$	183.803	−	685.962i	1.06862	−	3.98815i
$173$	−57.5035	−	214.606i	−0.332390	−	1.24050i	−0.906671	−	0.421839i	$-0.861385\pi$
$173$	−57.5035	−	214.606i	−0.332390	−	1.24050i	0.574280	−	0.818659i	$-0.305282\pi$
$174$		0			0
$175$	−70.5040	−	160.169i	−0.402880	−	0.915253i
$176$	501.523			2.84956
$177$		0			0
$178$	186.397	+	49.9449i	1.04717	+	0.280589i
$179$	−3.21768	+	1.85773i	−0.0179759	+	0.0103784i	−0.508961	−	0.860790i	$-0.669970\pi$
$179$	−3.21768	+	1.85773i	−0.0179759	+	0.0103784i	0.490985	+	0.871168i	$0.336637\pi$
$180$		0			0
$181$	−127.476			−0.704286			−0.352143	−	0.935946i	$-0.614547\pi$
$181$	−127.476			−0.704286			−0.352143	+	0.935946i	$0.614547\pi$
$182$	−80.4074	+	274.243i	−0.441799	+	1.50683i
$183$		0			0
$184$	318.283	+	183.761i	1.72980	+	0.998701i
$185$	−162.039	−	75.3888i	−0.875884	−	0.407507i
$186$		0			0
$187$	122.083	−	32.7120i	0.652849	−	0.174930i
$188$	−275.610	+	275.610i	−1.46601	+	1.46601i
$189$		0			0
$190$	86.5080	+	123.318i	0.455305	+	0.649045i
$191$	91.2245	−	158.005i	0.477615	−	0.827254i	−0.522056	−	0.852911i	$-0.674835\pi$
$191$	91.2245	−	158.005i	0.477615	−	0.827254i	0.999671	+	0.0256577i	$0.00816800\pi$
$192$		0			0
$193$	−42.4123	−	11.3644i	−0.219753	−	0.0588827i	0.147263	−	0.989097i	$-0.452954\pi$
$193$	−42.4123	−	11.3644i	−0.219753	−	0.0588827i	−0.367016	+	0.930215i	$0.619620\pi$
$194$	152.106	+	87.8185i	0.784052	+	0.452673i
$195$		0			0
$196$	247.240	−	385.382i	1.26143	−	1.96623i
$197$	−101.036	−	101.036i	−0.512872	−	0.512872i	0.402533	−	0.915405i	$-0.368130\pi$
$197$	−101.036	−	101.036i	−0.512872	−	0.512872i	−0.915405	+	0.402533i	$0.868130\pi$
$198$		0			0
$199$	−147.574	+	85.2021i	−0.741580	+	0.428151i	−0.822644	−	0.568558i	$-0.807502\pi$
$199$	−147.574	+	85.2021i	−0.741580	+	0.428151i	0.0810635	+	0.996709i	$0.474168\pi$
$200$	−400.287	−	279.251i	−2.00144	−	1.39625i
$201$		0			0
$202$	−49.1179	−	49.1179i	−0.243158	−	0.243158i
$203$	8.99415	+	37.0106i	0.0443061	+	0.182318i
$204$		0			0
$205$	−156.658	−	131.221i	−0.764187	−	0.640101i
$206$	58.9948	+	102.182i	0.286382	+	0.496029i
$207$		0			0
$208$	98.1732	+	366.387i	0.471987	+	1.76148i
$209$			121.871i			0.583115i
$210$		0			0
$211$	−97.2989			−0.461132			−0.230566	−	0.973057i	$-0.574058\pi$
$211$	−97.2989			−0.461132			−0.230566	+	0.973057i	$0.574058\pi$
$212$	518.962	−	139.055i	2.44793	−	0.655922i
$213$		0			0
$214$	−471.368	+	272.145i	−2.20266	+	1.27170i
$215$	−378.521	+	33.4470i	−1.76056	+	0.155568i
$216$		0			0
$217$	256.538	+	268.837i	1.18220	+	1.23888i
$218$	−332.972	+	332.972i	−1.52739	+	1.52739i
$219$		0			0
$220$	−236.697	−	648.570i	−1.07590	−	2.94805i
$221$	47.7955	+	82.7842i	0.216269	+	0.374589i
$222$		0			0
$223$	46.8438	−	46.8438i	0.210062	−	0.210062i	−0.594232	−	0.804294i	$-0.702544\pi$
$223$	46.8438	−	46.8438i	0.210062	−	0.210062i	0.804294	+	0.594232i	$0.202544\pi$
$224$	7.51737	−	321.128i	0.0335597	−	1.43361i
$225$		0			0
$226$	−155.652	+	269.596i	−0.688723	+	1.19290i
$227$	35.8205	−	133.684i	0.157799	−	0.588916i	−0.841050	−	0.540958i	$-0.818062\pi$
$227$	35.8205	−	133.684i	0.157799	−	0.588916i	0.998849	−	0.0479581i	$-0.0152714\pi$
$228$		0			0
$229$	261.304	+	150.864i	1.14106	+	0.658793i	0.946694	−	0.322135i	$-0.104401\pi$
$229$	261.304	+	150.864i	1.14106	+	0.658793i	0.194370	+	0.980928i	$0.437734\pi$
$230$	59.4142	−	338.671i	0.258322	−	1.47248i
$231$		0			0
$232$	75.1126	+	75.1126i	0.323761	+	0.323761i
$233$	61.4371	+	229.286i	0.263679	+	0.984062i	0.963054	+	0.269307i	$0.0867948\pi$
$233$	61.4371	+	229.286i	0.263679	+	0.984062i	−0.699376	+	0.714754i	$0.746539\pi$
$234$		0			0
$235$	189.096	+	87.9775i	0.804665	+	0.374372i
$236$	78.3622	−	135.727i	0.332043	−	0.575116i
$237$		0			0
$238$	−51.6465	−	212.523i	−0.217002	−	0.892955i
$239$			414.515i			1.73437i	0.497984	+	0.867186i	$0.334074\pi$
$239$			414.515i			1.73437i	−0.497984	+	0.867186i	$0.665926\pi$
$240$		0			0
$241$	−48.5940	−	84.1673i	−0.201635	−	0.349242i	0.747420	−	0.664351i	$-0.231292\pi$
$241$	−48.5940	−	84.1673i	−0.201635	−	0.349242i	−0.949055	+	0.315109i	$0.897959\pi$
$242$	92.0544	−	343.552i	0.380390	−	1.41963i
$243$		0			0
$244$		−	873.659i		−	3.58057i
$245$	−239.069	−	53.5800i	−0.975794	−	0.218694i
$246$		0			0
$247$	−89.0328	+	23.8563i	−0.360457	+	0.0965841i
$248$	1001.06	+	268.233i	4.03653	+	1.08159i
$249$		0			0
$250$	−117.035	+	441.370i	−0.468140	+	1.76548i
$251$	−183.078			−0.729394			−0.364697	−	0.931126i	$-0.618827\pi$
$251$	−183.078			−0.729394			−0.364697	+	0.931126i	$0.618827\pi$
$252$		0			0
$253$	196.706	−	196.706i	0.777496	−	0.777496i
$254$	−296.902	−	171.416i	−1.16890	−	0.674867i
$255$		0			0
$256$	186.345	+	322.759i	0.727911	+	1.26078i
$257$	157.493	−	42.2001i	0.612813	−	0.164203i	0.0609543	−	0.998141i	$-0.480586\pi$
$257$	157.493	−	42.2001i	0.612813	−	0.164203i	0.551858	+	0.833938i	$0.313919\pi$
$258$		0			0
$259$	−219.552	+	119.997i	−0.847691	+	0.463309i
$260$	427.480	−	299.877i	1.64415	−	1.15337i
$261$		0			0
$262$	1.44564	−	5.39521i	0.00551772	−	0.0205924i
$263$	396.959	+	106.365i	1.50935	+	0.404429i	0.916219	−	0.400679i	$-0.131226\pi$
$263$	396.959	+	106.365i	1.50935	+	0.404429i	0.593129	+	0.805107i	$0.297892\pi$
$264$		0			0
$265$	−165.098	−	235.350i	−0.623012	−	0.888114i
$266$	210.832	+	4.93542i	0.792602	+	0.0185542i
$267$		0			0
$268$	263.821	+	984.594i	0.984407	+	3.67386i
$269$	−63.6605	+	36.7544i	−0.236656	+	0.136633i	−0.613639	−	0.789587i	$-0.710295\pi$
$269$	−63.6605	+	36.7544i	−0.236656	+	0.136633i	0.376983	+	0.926220i	$0.376962\pi$
$270$		0			0
$271$	208.069	−	360.386i	0.767782	−	1.32984i	−0.170981	−	0.985274i	$-0.554694\pi$
$271$	208.069	−	360.386i	0.767782	−	1.32984i	0.938763	−	0.344563i	$-0.111973\pi$
$272$	−205.260	−	205.260i	−0.754632	−	0.754632i
$273$		0			0
$274$			179.587i			0.655428i
$275$	−282.587	+	237.955i	−1.02759	+	0.865290i
$276$		0			0
$277$	80.0217	−	298.645i	0.288887	−	1.07814i	−0.657065	−	0.753834i	$-0.728202\pi$
$277$	80.0217	−	298.645i	0.288887	−	1.07814i	0.945952	−	0.324307i	$-0.105131\pi$
$278$	−60.0309	−	224.038i	−0.215938	−	0.805893i
$279$		0			0
$280$	−647.192	+	219.172i	−2.31140	+	0.782755i
$281$	−61.2527			−0.217981			−0.108991	−	0.994043i	$-0.534762\pi$
$281$	−61.2527			−0.217981			−0.108991	+	0.994043i	$0.534762\pi$
$282$		0			0
$283$	−152.506	−	40.8640i	−0.538892	−	0.144396i	−0.0209006	−	0.999782i	$-0.506653\pi$
$283$	−152.506	−	40.8640i	−0.538892	−	0.144396i	−0.517991	+	0.855386i	$0.673320\pi$
$284$	−413.503	+	238.736i	−1.45600	+	0.840621i
$285$		0			0
$286$	603.304			2.10945
$287$	−278.005	+	67.5595i	−0.968658	+	0.235399i
$288$		0			0
$289$	186.928	+	107.923i	0.646809	+	0.373436i
$290$	41.9223	−	90.1066i	0.144560	−	0.310712i
$291$		0			0
$292$	394.732	−	105.768i	1.35182	−	0.362219i
$293$	−37.4650	+	37.4650i	−0.127867	+	0.127867i	−0.768144	−	0.640277i	$-0.778820\pi$
$293$	−37.4650	+	37.4650i	−0.127867	+	0.127867i	0.640277	+	0.768144i	$0.278820\pi$
$294$		0			0
$295$	−82.5994	−	14.4907i	−0.279998	−	0.0491209i
$296$	−348.906	+	604.322i	−1.17874	+	2.04163i
$297$		0			0
$298$	125.648	+	33.6672i	0.421637	+	0.112977i
$299$	182.209	+	105.199i	0.609395	+	0.351835i
$300$		0			0
$301$	−276.706	+	454.369i	−0.919289	+	1.50953i
$302$	−113.259	−	113.259i	−0.375030	−	0.375030i
$303$		0			0
$304$	242.404	−	139.952i	0.797381	−	0.460368i
$305$	−439.150	+	160.269i	−1.43984	+	0.525472i
$306$		0			0
$307$	293.400	+	293.400i	0.955699	+	0.955699i	0.999059	−	0.0433607i	$-0.0138065\pi$
$307$	293.400	+	293.400i	0.955699	+	0.955699i	−0.0433607	+	0.999059i	$0.513806\pi$
$308$	−927.532	−	271.950i	−3.01147	−	0.882955i
$309$		0			0
$310$	−85.3440	−	965.839i	−0.275303	−	3.11561i
$311$	−133.293	−	230.871i	−0.428596	−	0.742351i	0.568152	−	0.822923i	$-0.307658\pi$
$311$	−133.293	−	230.871i	−0.428596	−	0.742351i	−0.996749	+	0.0805727i	$0.974325\pi$
$312$		0			0
$313$	−57.2788	−	213.767i	−0.182999	−	0.682963i	−0.995050	−	0.0993760i	$-0.968315\pi$
$313$	−57.2788	−	213.767i	−0.182999	−	0.682963i	0.812051	−	0.583587i	$-0.198351\pi$
$314$		−	289.383i		−	0.921603i
$315$		0			0
$316$	−267.361			−0.846079
$317$	−446.075	+	119.525i	−1.40718	+	0.377052i	−0.880917	−	0.473272i	$-0.843073\pi$
$317$	−446.075	+	119.525i	−1.40718	+	0.377052i	−0.526260	+	0.850324i	$0.676406\pi$
$318$		0			0
$319$	69.6320	−	40.2020i	0.218282	−	0.126025i
$320$	−102.329	+	122.166i	−0.319777	+	0.381768i
$321$		0			0
$322$	−332.329	−	348.261i	−1.03208	−	1.08155i
$323$	49.8786	−	49.8786i	0.154423	−	0.154423i
$324$		0			0
$325$	−229.154	−	159.864i	−0.705090	−	0.491889i
$326$	166.442	+	288.287i	0.510560	+	0.884315i
$327$		0			0
$328$	−564.208	+	564.208i	−1.72015	+	1.72015i
$329$	256.214	−	140.035i	0.778764	−	0.425637i
$330$		0			0
$331$	−228.038	+	394.974i	−0.688937	+	1.19327i	0.283245	+	0.959048i	$0.408589\pi$
$331$	−228.038	+	394.974i	−0.688937	+	1.19327i	−0.972182	+	0.234226i	$0.924744\pi$
$332$	118.301	−	441.505i	0.356328	−	1.32983i
$333$		0			0
$334$	−848.694	−	489.994i	−2.54100	−	1.46705i
$335$	446.515	−	313.231i	1.33288	−	0.935017i
$336$		0			0
$337$	−334.947	−	334.947i	−0.993908	−	0.993908i	0.00607399	−	0.999982i	$-0.498067\pi$
$337$	−334.947	−	334.947i	−0.993908	−	0.993908i	−0.999982	+	0.00607399i	$0.998067\pi$
$338$	−41.6863	−	155.575i	−0.123332	−	0.460282i
$339$		0			0
$340$	−168.569	+	362.317i	−0.495791	+	1.06564i
$341$	392.226	−	679.355i	1.15022	−	1.99224i
$342$		0			0
$343$	−258.956	+	224.924i	−0.754973	+	0.655756i
$344$			1483.71i			4.31311i
$345$		0			0
$346$	405.804	+	702.874i	1.17284	+	2.03143i
$347$	−21.8916	+	81.7004i	−0.0630881	+	0.235448i	−0.990269	−	0.139166i	$-0.955558\pi$
$347$	−21.8916	+	81.7004i	−0.0630881	+	0.235448i	0.927181	+	0.374614i	$0.122225\pi$
$348$		0			0
$349$			1.96290i			0.00562435i	0.999996	+	0.00281218i	$0.000895145\pi$
$349$			1.96290i			0.00562435i	−0.999996	+	0.00281218i	$0.999105\pi$
$350$	400.209	+	498.501i	1.14345	+	1.42429i
$351$		0			0
$352$	−654.988	+	175.504i	−1.86076	+	0.498590i
$353$	424.231	+	113.672i	1.20179	+	0.322018i	0.803535	−	0.595258i	$-0.202950\pi$
$353$	424.231	+	113.672i	1.20179	+	0.322018i	0.398253	+	0.917276i	$0.369617\pi$
$354$		0			0
$355$	195.858	+	164.055i	0.551711	+	0.462126i
$356$	−493.622			−1.38658
$357$		0			0
$358$	9.59723	−	9.59723i	0.0268079	−	0.0268079i
$359$	206.235	+	119.070i	0.574471	+	0.331671i	0.758933	−	0.651169i	$-0.225721\pi$
$359$	206.235	+	119.070i	0.574471	+	0.331671i	−0.184462	+	0.982840i	$0.559054\pi$
$360$		0			0
$361$	−146.491	−	253.731i	−0.405793	−	0.702855i
$362$	449.800	−	120.524i	1.24254	−	0.332938i
$363$		0			0
$364$	17.1085	−	730.843i	0.0470014	−	2.00781i
$365$	−125.577	−	179.012i	−0.344046	−	0.490443i
$366$		0			0
$367$	99.8556	−	372.666i	0.272086	−	1.01544i	−0.685683	−	0.727901i	$-0.740496\pi$
$367$	99.8556	−	372.666i	0.272086	−	1.01544i	0.957769	−	0.287539i	$-0.0928371\pi$
$368$	−617.143	−	165.363i	−1.67702	−	0.449356i
$369$		0			0
$370$	643.033	+	112.809i	1.73793	+	0.304890i
$371$	−402.368	−	9.41913i	−1.08455	−	0.0253885i
$372$		0			0
$373$	−46.0346	−	171.804i	−0.123417	−	0.460599i	0.876361	−	0.481655i	$-0.159964\pi$
$373$	−46.0346	−	171.804i	−0.123417	−	0.460599i	−0.999778	+	0.0210554i	$0.993297\pi$
$374$	−399.843	+	230.849i	−1.06910	+	0.617245i
$375$		0			0
$376$	407.167	−	705.234i	1.08289	−	1.87562i
$377$	43.0001	+	43.0001i	0.114059	+	0.114059i
$378$		0			0
$379$			530.767i			1.40044i	0.713927	+	0.700220i	$0.246915\pi$
$379$			530.767i			1.40044i	−0.713927	+	0.700220i	$0.753085\pi$
$380$	−295.391	−	247.426i	−0.777344	−	0.651121i
$381$		0			0
$382$	−172.499	+	643.774i	−0.451567	+	1.68527i
$383$	24.7833	+	92.4927i	0.0647085	+	0.241495i	0.990703	−	0.136041i	$-0.0434380\pi$
$383$	24.7833	+	92.4927i	0.0647085	+	0.241495i	−0.925995	+	0.377536i	$0.876771\pi$
$384$		0			0
$385$	33.4543	+	516.117i	0.0868942	+	1.34056i
$386$	160.397			0.415537
$387$		0			0
$388$	−433.969	−	116.282i	−1.11848	−	0.299695i
$389$	275.146	−	158.856i	0.707317	−	0.408370i	−0.102750	−	0.994707i	$-0.532764\pi$
$389$	275.146	−	158.856i	0.707317	−	0.408370i	0.810067	+	0.586337i	$0.199431\pi$
$390$		0			0
$391$	−161.014			−0.411799
$392$	−290.556	+	911.421i	−0.741215	+	2.32505i
$393$		0			0
$394$	452.032	+	260.981i	1.14729	+	0.662388i
$395$	49.0462	+	134.391i	0.124168	+	0.340229i
$396$		0			0
$397$	271.959	−	72.8713i	0.685036	−	0.183555i	0.100518	−	0.994935i	$-0.467950\pi$
$397$	271.959	−	72.8713i	0.685036	−	0.183555i	0.584519	+	0.811380i	$0.301283\pi$
$398$	440.163	−	440.163i	1.10594	−	1.10594i
$399$		0			0
$400$	797.809	+	288.813i	1.99452	+	0.722032i
$401$	196.938	−	341.107i	0.491118	−	0.850642i	−0.508829	−	0.860867i	$-0.669922\pi$
$401$	196.938	−	341.107i	0.491118	−	0.850642i	0.999948	+	0.0102254i	$0.00325490\pi$
$402$		0			0
$403$	573.082	+	153.557i	1.42204	+	0.381034i
$404$	153.881	+	88.8433i	0.380894	+	0.219909i
$405$		0			0
$406$	−66.7281	−	122.089i	−0.164355	−	0.300711i
$407$	373.485	+	373.485i	0.917654	+	0.917654i
$408$		0			0
$409$	261.465	−	150.957i	0.639280	−	0.369088i	−0.145057	−	0.989423i	$-0.546337\pi$
$409$	261.465	−	150.957i	0.639280	−	0.369088i	0.784337	+	0.620335i	$0.213003\pi$
$410$	676.836	+	314.899i	1.65082	+	0.768047i
$411$		0			0
$412$	−213.417	−	213.417i	−0.518001	−	0.518001i
$413$	−84.9381	+	81.0524i	−0.205661	+	0.196253i
$414$		0			0
$415$	−243.627	+	21.5275i	−0.587052	+	0.0518734i
$416$	−256.428	−	444.147i	−0.616414	−	1.06766i
$417$		0			0
$418$	−115.224	−	430.023i	−0.275657	−	1.02876i
$419$		−	439.671i		−	1.04934i	−0.851307	−	0.524668i	$-0.824190\pi$
$419$		−	439.671i		−	1.04934i	0.851307	−	0.524668i	$-0.175810\pi$
$420$		0			0
$421$	−134.308			−0.319020			−0.159510	−	0.987196i	$-0.550991\pi$
$421$	−134.308			−0.319020			−0.159510	+	0.987196i	$0.550991\pi$
$422$	343.321	−	91.9925i	0.813556	−	0.217992i
$423$		0			0
$424$	−972.110	+	561.248i	−2.29271	+	1.32370i
$425$	213.044	+	18.2667i	0.501280	+	0.0429805i
$426$		0			0
$427$	−184.139	+	628.036i	−0.431238	+	1.47081i
$428$	984.496	−	984.496i	2.30023	−	2.30023i
$429$		0			0
$430$	1303.99	−	475.895i	3.03254	−	1.10673i
$431$	369.794	+	640.501i	0.857990	+	1.48608i	0.873843	+	0.486208i	$0.161620\pi$
$431$	369.794	+	640.501i	0.857990	+	1.48608i	−0.0158536	+	0.999874i	$0.505047\pi$
$432$		0			0
$433$	419.987	−	419.987i	0.969947	−	0.969947i	−0.0296144	−	0.999561i	$-0.509428\pi$
$433$	419.987	−	419.987i	0.969947	−	0.969947i	0.999561	+	0.0296144i	$0.00942795\pi$
$434$	−1159.37	−	706.048i	−2.67137	−	1.62684i
$435$		0			0
$436$	602.271	−	1043.16i	1.38136	−	2.39258i
$437$	40.1835	−	149.967i	0.0919532	−	0.343174i
$438$		0			0
$439$	−160.861	−	92.8731i	−0.366426	−	0.211556i	0.305470	−	0.952202i	$-0.401186\pi$
$439$	−160.861	−	92.8731i	−0.366426	−	0.211556i	−0.671896	+	0.740646i	$0.734520\pi$
$440$	828.381	+	1180.87i	1.88268	+	2.68380i
$441$		0			0
$442$	−246.917	−	246.917i	−0.558635	−	0.558635i
$443$	−213.428	−	796.525i	−0.481779	−	1.79802i	−0.594145	−	0.804358i	$-0.702509\pi$
$443$	−213.428	−	796.525i	−0.481779	−	1.79802i	0.112366	−	0.993667i	$-0.464157\pi$
$444$		0			0
$445$	90.5528	+	248.122i	0.203489	+	0.557578i
$446$	−121.000	+	209.578i	−0.271301	+	0.469907i
$447$		0			0
$448$	52.6844	+	216.794i	0.117599	+	0.483916i
$449$			116.438i			0.259328i	0.991558	+	0.129664i	$0.0413898\pi$
$449$			116.438i			0.259328i	−0.991558	+	0.129664i	$0.958610\pi$
$450$		0			0
$451$	301.978	+	523.040i	0.669573	+	1.15973i
$452$	206.101	−	769.178i	0.455975	−	1.70172i
$453$		0			0
$454$			505.572i			1.11360i
$455$	−370.501	+	125.470i	−0.814288	+	0.275759i
$456$		0			0
$457$	85.9655	−	23.0344i	0.188108	−	0.0504035i	−0.163535	−	0.986538i	$-0.552290\pi$
$457$	85.9655	−	23.0344i	0.188108	−	0.0504035i	0.351643	+	0.936134i	$0.385623\pi$
$458$	−1064.65	−	285.272i	−2.32456	−	0.622865i
$459$		0			0
$460$	77.4175	+	876.136i	0.168299	+	1.90464i
$461$	−556.638			−1.20746			−0.603729	−	0.797190i	$-0.706319\pi$
$461$	−556.638			−1.20746			−0.603729	+	0.797190i	$0.706319\pi$
$462$		0			0
$463$	−154.534	+	154.534i	−0.333767	+	0.333767i	−0.854015	−	0.520248i	$-0.825840\pi$
$463$	−154.534	+	154.534i	−0.333767	+	0.333767i	0.520248	+	0.854015i	$0.325840\pi$
$464$	−159.925	−	92.3330i	−0.344667	−	0.198994i
$465$		0			0
$466$	−433.563	−	750.954i	−0.930394	−	1.61149i
$467$	0.763909	−	0.204689i	0.00163578	−	0.000438306i	−0.258001	−	0.966145i	$-0.583064\pi$
$467$	0.763909	−	0.204689i	0.00163578	−	0.000438306i	0.259637	+	0.965706i	$0.416397\pi$
$468$		0			0
$469$	17.8703	−	763.387i	0.0381030	−	1.62769i
$470$	−750.409	−	131.647i	−1.59661	−	0.280099i
$471$		0			0
$472$	−84.7473	+	316.281i	−0.179549	+	0.670088i
$473$	1084.78	+	290.667i	2.29341	+	0.614518i
$474$		0			0
$475$	−70.1821	+	193.869i	−0.147752	+	0.408145i
$476$	268.312	+	490.916i	0.563681	+	1.03134i
$477$		0			0
$478$	−391.909	−	1462.62i	−0.819892	−	3.05988i
$479$	758.464	−	437.899i	1.58343	−	0.914195i	0.589079	−	0.808076i	$-0.299491\pi$
$479$	758.464	−	437.899i	1.58343	−	0.914195i	0.994353	−	0.106119i	$-0.0338426\pi$
$480$		0			0
$481$	−199.740	+	345.959i	−0.415259	+	0.719250i
$482$	251.042	+	251.042i	0.520834	+	0.520834i
$483$		0			0
$484$			909.804i			1.87976i
$485$	21.1600	+	239.469i	0.0436290	+	0.493750i
$486$		0			0
$487$	−144.993	+	541.121i	−0.297727	+	1.11113i	0.641301	+	0.767289i	$0.278395\pi$
$487$	−144.993	+	541.121i	−0.297727	+	1.11113i	−0.939028	+	0.343841i	$0.888272\pi$
$488$	472.423	+	1763.11i	0.968080	+	3.61292i
$489$		0			0
$490$	894.218	−	36.9733i	1.82493	−	0.0754558i
$491$	−383.827			−0.781726			−0.390863	−	0.920449i	$-0.627823\pi$
$491$	−383.827			−0.781726			−0.390863	+	0.920449i	$0.627823\pi$
$492$		0			0
$493$	−44.9522	−	12.0449i	−0.0911809	−	0.0244319i
$494$	291.598	−	168.354i	0.590280	−	0.340798i
$495$		0			0
$496$	−1801.67			−3.63240
$497$	347.567	−	84.4643i	0.699331	−	0.169948i
$498$		0			0
$499$	−10.5456	−	6.08851i	−0.0211335	−	0.0122014i	0.489396	−	0.872062i	$-0.337217\pi$
$499$	−10.5456	−	6.08851i	−0.0211335	−	0.0122014i	−0.510530	+	0.859860i	$0.670551\pi$
$500$	−3.03844	−	1168.04i	−0.00607689	−	2.33607i
$501$		0			0
$502$	645.993	−	173.093i	1.28684	−	0.344808i
$503$	−250.202	+	250.202i	−0.497420	+	0.497420i	−0.910634	−	0.413214i	$-0.864406\pi$
$503$	−250.202	+	250.202i	−0.497420	+	0.497420i	0.413214	+	0.910634i	$0.364406\pi$
$504$		0			0
$505$	16.4288	−	93.6472i	0.0325323	−	0.185440i
$506$	−508.103	+	880.060i	−1.00416	+	1.73925i
$507$		0			0
$508$	847.081	+	226.975i	1.66748	+	0.446801i
$509$	−536.048	−	309.488i	−1.05314	−	0.608031i	−0.129613	−	0.991565i	$-0.541374\pi$
$509$	−536.048	−	309.488i	−1.05314	−	0.608031i	−0.923527	+	0.383534i	$0.874707\pi$
$510$		0			0
$511$	−306.048	−	7.16436i	−0.598920	−	0.0140203i
$512$	−772.824	−	772.824i	−1.50942	−	1.50942i
$513$		0			0
$514$	−515.817	+	297.807i	−1.00354	+	0.579392i
$515$	−68.1248	+	146.425i	−0.132281	+	0.284321i
$516$		0			0
$517$	−435.851	−	435.851i	−0.843038	−	0.843038i
$518$	661.240	−	630.990i	1.27652	−	1.21813i
$519$		0			0
$520$	−700.529	+	836.330i	−1.34717	+	1.60833i
$521$	−234.346	−	405.900i	−0.449801	−	0.779078i	0.548572	−	0.836104i	$-0.315172\pi$
$521$	−234.346	−	405.900i	−0.449801	−	0.779078i	−0.998373	+	0.0570252i	$0.981838\pi$
$522$		0			0
$523$	−4.04502	−	15.0962i	−0.00773427	−	0.0288647i	0.961951	−	0.273222i	$-0.0880895\pi$
$523$	−4.04502	−	15.0962i	−0.00773427	−	0.0288647i	−0.969685	+	0.244358i	$0.921423\pi$
$524$			14.2878i			0.0272667i
$525$		0			0
$526$	−1501.24			−2.85407
$527$	−438.570	+	117.515i	−0.832202	+	0.222988i
$528$		0			0
$529$	151.214	−	87.3034i	0.285849	−	0.165035i
$530$	805.067	+	674.342i	1.51899	+	1.27234i
$531$		0			0
$532$	−524.198	+	127.388i	−0.985335	+	0.239452i
$533$	−322.995	+	322.995i	−0.605994	+	0.605994i
$534$		0			0
$535$	−675.465	−	314.262i	−1.26255	−	0.587405i
$536$	−1064.82	−	1844.32i	−1.98660	−	3.44090i
$537$		0			0
$538$	189.877	−	189.877i	0.352931	−	0.352931i
$539$	609.444	+	390.986i	1.13069	+	0.725392i
$540$		0			0
$541$	364.758	−	631.779i	0.674229	−	1.16780i	−0.302465	−	0.953161i	$-0.597810\pi$
$541$	364.758	−	631.779i	0.674229	−	1.16780i	0.976694	−	0.214638i	$-0.0688571\pi$
$542$	−393.443	+	1468.35i	−0.725909	+	2.70913i
$543$		0			0
$544$	339.898	+	196.240i	0.624813	+	0.360736i
$545$	−634.836	−	111.371i	−1.16484	−	0.204351i
$546$		0			0
$547$	464.863	+	464.863i	0.849841	+	0.849841i	0.990113	−	0.140272i	$-0.0447977\pi$
$547$	464.863	+	464.863i	0.849841	+	0.849841i	−0.140272	+	0.990113i	$0.544798\pi$
$548$	−118.897	−	443.730i	−0.216966	−	0.809727i
$549$		0			0
$550$	772.134	−	1106.80i	1.40388	−	2.01237i
$551$	22.4371	−	38.8622i	0.0407207	−	0.0705303i
$552$		0			0
$553$	192.194	+	56.3509i	0.347548	+	0.101900i
$554$			1129.43i			2.03868i
$555$		0			0
$556$	296.653	+	513.817i	0.533548	+	0.924132i
$557$	−98.6198	+	368.054i	−0.177055	+	0.660779i	0.819137	+	0.573598i	$0.194453\pi$
$557$	−98.6198	+	368.054i	−0.177055	+	0.660779i	−0.996192	+	0.0871816i	$0.972214\pi$
$558$		0			0
$559$			849.387i			1.51948i
$560$	988.151	−	659.231i	1.76455	−	1.17720i
$561$		0			0
$562$	216.131	−	57.9121i	0.384575	−	0.103046i
$563$	−762.882	−	204.414i	−1.35503	−	0.363079i	−0.493041	−	0.870006i	$-0.664115\pi$
$563$	−762.882	−	204.414i	−1.35503	−	0.363079i	−0.861989	+	0.506927i	$0.830781\pi$
$564$		0			0
$565$	−424.440	+	37.5046i	−0.751221	+	0.0663798i
$566$	576.757			1.01900
$567$		0			0
$568$	705.385	−	705.385i	1.24188	−	1.24188i
$569$	271.365	+	156.673i	0.476916	+	0.275347i	0.719130	−	0.694875i	$-0.244540\pi$
$569$	271.365	+	156.673i	0.476916	+	0.275347i	−0.242215	+	0.970223i	$0.577874\pi$
$570$		0			0
$571$	−385.124	−	667.054i	−0.674472	−	1.16822i	−0.976623	−	0.214960i	$-0.931038\pi$
$571$	−385.124	−	667.054i	−0.674472	−	1.16822i	0.302151	−	0.953260i	$-0.402295\pi$
$572$	−1490.66	+	399.422i	−2.60605	+	0.698290i
$573$		0			0
$574$	917.069	−	501.228i	1.59768	−	0.873219i
$575$	426.193	−	199.638i	0.741205	−	0.347196i
$576$		0			0
$577$	217.694	−	812.444i	0.377286	−	1.40805i	−0.472691	−	0.881228i	$-0.656717\pi$
$577$	217.694	−	812.444i	0.377286	−	1.40805i	0.849976	−	0.526821i	$-0.176616\pi$
$578$	−761.615	−	204.074i	−1.31767	−	0.353069i
$579$		0			0
$580$	−43.9273	+	250.393i	−0.0757367	+	0.431713i
$581$	−178.096	+	292.445i	−0.306533	+	0.503347i
$582$		0			0
$583$	219.903	+	820.689i	0.377192	+	1.40770i
$584$	−739.404	+	426.895i	−1.26610	+	0.730985i
$585$		0			0
$586$	96.7740	−	167.618i	0.165143	−	0.286037i
$587$	−300.621	−	300.621i	−0.512131	−	0.512131i	0.403048	−	0.915179i	$-0.367951\pi$
$587$	−300.621	−	300.621i	−0.512131	−	0.512131i	−0.915179	+	0.403048i	$0.867951\pi$
$588$		0			0
$589$		−	437.809i		−	0.743309i
$590$	305.154	−	26.9641i	0.517209	−	0.0457019i
$591$		0			0
$592$	313.974	−	1171.77i	0.530361	−	1.97933i
$593$	−88.7777	−	331.323i	−0.149709	−	0.558723i	−0.999500	−	0.0316034i	$-0.989939\pi$
$593$	−88.7777	−	331.323i	−0.149709	−	0.558723i	0.849791	−	0.527120i	$-0.176728\pi$
$594$		0			0
$595$	197.541	−	224.925i	0.332002	−	0.378026i
$596$	−332.744			−0.558296
$597$		0			0
$598$	−742.389	−	198.923i	−1.24145	−	0.332647i
$599$	−407.516	+	235.280i	−0.680328	+	0.392787i	−0.799978	−	0.600029i	$-0.795156\pi$
$599$	−407.516	+	235.280i	−0.680328	+	0.392787i	0.119651	+	0.992816i	$0.461822\pi$
$600$		0			0
$601$	1180.46			1.96417			0.982083	−	0.188450i	$-0.0603464\pi$
$601$	1180.46			1.96417			0.982083	+	0.188450i	$0.0603464\pi$
$602$	546.773	−	1864.86i	0.908261	−	3.09778i
$603$		0			0
$604$	354.828	+	204.860i	0.587464	+	0.339173i
$605$	457.318	−	166.899i	0.755898	−	0.275867i
$606$		0			0
$607$	−834.313	+	223.553i	−1.37449	+	0.368292i	−0.869115	−	0.494610i	$-0.835311\pi$
$607$	−834.313	+	223.553i	−1.37449	+	0.368292i	−0.505371	+	0.862902i	$0.668644\pi$
$608$	−267.604	+	267.604i	−0.440139	+	0.440139i
$609$		0			0
$610$	1398.02	−	980.711i	2.29183	−	1.60772i
$611$	233.093	−	403.729i	0.381494	−	0.660767i
$612$		0			0
$613$	−478.615	−	128.245i	−0.780775	−	0.209208i	−0.153649	−	0.988126i	$-0.549102\pi$
$613$	−478.615	−	128.245i	−0.780775	−	0.209208i	−0.627126	+	0.778918i	$0.715769\pi$
$614$	−1312.66	−	757.866i	−2.13789	−	1.23431i
$615$		0			0
$616$	2018.88	+	47.2605i	3.27740	+	0.0767216i
$617$	−13.0926	−	13.0926i	−0.0212197	−	0.0212197i	0.696417	−	0.717637i	$-0.254776\pi$
$617$	−13.0926	−	13.0926i	−0.0212197	−	0.0212197i	−0.717637	+	0.696417i	$0.754776\pi$
$618$		0			0
$619$	386.935	−	223.397i	0.625096	−	0.360899i	−0.153754	−	0.988109i	$-0.549136\pi$
$619$	386.935	−	223.397i	0.625096	−	0.360899i	0.778850	+	0.627210i	$0.215803\pi$
$620$	850.312	+	2329.92i	1.37147	+	3.75794i
$621$		0			0
$622$	688.608	+	688.608i	1.10709	+	1.10709i
$623$	354.844	+	104.039i	0.569573	+	0.166997i
$624$		0			0
$625$	−586.563	+	215.798i	−0.938501	+	0.345277i
$626$	404.218	+	700.127i	0.645716	+	1.11841i
$627$		0			0
$628$	191.588	+	715.018i	0.305077	+	1.13856i
$629$		−	305.715i		−	0.486034i
$630$		0			0
$631$	905.125			1.43443			0.717215	−	0.696852i	$-0.245417\pi$
$631$	905.125			1.43443			0.717215	+	0.696852i	$0.245417\pi$
$632$	539.554	−	144.573i	0.853724	−	0.228755i
$633$		0			0
$634$	1460.98	−	843.495i	2.30438	−	1.33043i
$635$	−41.3031	−	467.428i	−0.0650443	−	0.736107i
$636$		0			0
$637$	−166.336	+	521.765i	−0.261124	+	0.819098i
$638$	−207.688	+	207.688i	−0.325530	+	0.325530i
$639$		0			0
$640$	−141.575	+	304.297i	−0.221211	+	0.475464i
$641$	−112.385	−	194.656i	−0.175327	−	0.303675i	0.764947	−	0.644093i	$-0.222765\pi$
$641$	−112.385	−	194.656i	−0.175327	−	0.303675i	−0.940274	+	0.340417i	$0.889432\pi$
$642$		0			0
$643$	−115.806	+	115.806i	−0.180102	+	0.180102i	−0.791400	−	0.611298i	$-0.790648\pi$
$643$	−115.806	+	115.806i	−0.180102	+	0.180102i	0.611298	+	0.791400i	$0.290648\pi$
$644$	1051.70	+	640.473i	1.63307	+	0.994523i
$645$		0			0
$646$	−128.839	+	223.156i	−0.199441	+	0.345442i
$647$	−122.458	+	457.021i	−0.189271	+	0.706369i	0.804405	+	0.594082i	$0.202484\pi$
$647$	−122.458	+	457.021i	−0.189271	+	0.706369i	−0.993676	+	0.112288i	$0.964182\pi$
$648$		0			0
$649$	214.640	+	123.922i	0.330724	+	0.190944i
$650$	959.720	+	347.426i	1.47649	+	0.534501i
$651$		0			0
$652$	−602.114	−	602.114i	−0.923488	−	0.923488i
$653$	272.625	+	1017.45i	0.417497	+	1.55812i	0.779782	+	0.626051i	$0.215330\pi$
$653$	272.625	+	1017.45i	0.417497	+	1.55812i	−0.362285	+	0.932067i	$0.618003\pi$
$654$		0			0
$655$	7.18183	−	2.62103i	0.0109646	−	0.00400157i
$656$	693.559	−	1201.28i	1.05725	−	1.83122i
$657$		0			0
$658$	−771.656	+	736.354i	−1.17273	+	1.11908i
$659$			77.0532i			0.116924i	0.998290	+	0.0584622i	$0.0186197\pi$
$659$			77.0532i			0.116924i	−0.998290	+	0.0584622i	$0.981380\pi$
$660$		0			0
$661$	−321.259	−	556.436i	−0.486019	−	0.841810i	0.513852	−	0.857879i	$-0.328218\pi$
$661$	−321.259	−	556.436i	−0.486019	−	0.841810i	−0.999871	+	0.0160692i	$0.994885\pi$
$662$	431.203	−	1609.27i	0.651364	−	2.43093i
$663$		0			0
$664$			954.958i			1.43819i
$665$	160.194	+	240.122i	0.240894	+	0.361086i
$666$		0			0
$667$	−98.9404	+	26.5110i	−0.148336	+	0.0397466i
$668$	2421.38	+	648.808i	3.62483	+	0.971270i
$669$		0			0
$670$	−1279.39	+	1527.40i	−1.90953	+	2.27970i
$671$	1381.61			2.05903
$672$		0			0
$673$	−321.230	+	321.230i	−0.477310	+	0.477310i	−0.904270	−	0.426960i	$-0.859584\pi$
$673$	−321.230	+	321.230i	−0.477310	+	0.477310i	0.426960	+	0.904270i	$0.359584\pi$
$674$	1498.54	+	865.185i	2.22336	+	1.28366i
$675$		0			0
$676$	206.000	+	356.802i	0.304733	+	0.527813i
$677$	1088.09	−	291.552i	1.60722	−	0.430654i	0.660008	−	0.751259i	$-0.270553\pi$
$677$	1088.09	−	291.552i	1.60722	−	0.430654i	0.947213	+	0.320605i	$0.103886\pi$
$678$		0			0
$679$	287.454	+	175.056i	0.423348	+	0.257815i
$680$	144.265	−	822.334i	0.212154	−	1.20931i
$681$		0			0
$682$	−741.670	+	2767.95i	−1.08749	+	4.05858i
$683$	−1059.34	−	283.849i	−1.55101	−	0.415592i	−0.621206	−	0.783648i	$-0.713357\pi$
$683$	−1059.34	−	283.849i	−1.55101	−	0.415592i	−0.929804	+	0.368056i	$0.880023\pi$
$684$		0			0
$685$	−201.233	+	141.165i	−0.293770	+	0.206080i
$686$	701.072	−	1038.48i	1.02197	−	1.51382i
$687$		0			0
$688$	−667.581	−	2491.45i	−0.970322	−	3.62129i
$689$	−556.508	+	321.300i	−0.807704	+	0.466328i
$690$		0			0
$691$	−47.8948	+	82.9562i	−0.0693123	+	0.120052i	−0.898599	−	0.438771i	$-0.855414\pi$
$691$	−47.8948	+	82.9562i	−0.0693123	+	0.120052i	0.829286	+	0.558824i	$0.188747\pi$
$692$	−1468.02	−	1468.02i	−2.12141	−	2.12141i
$693$		0			0
$694$		−	308.979i		−	0.445214i
$695$	203.854	−	243.372i	0.293315	−	0.350175i
$696$		0			0
$697$	90.4752	−	337.658i	0.129807	−	0.484445i
$698$	−1.85585	−	6.92612i	−0.00265881	−	0.00992281i
$699$		0			0
$700$	−1318.88	−	966.750i	−1.88412	−	1.38107i
$701$	518.219			0.739257			0.369628	−	0.929180i	$-0.379485\pi$
$701$	518.219			0.739257			0.369628	+	0.929180i	$0.379485\pi$
$702$		0			0
$703$	284.741	+	76.2962i	0.405037	+	0.108529i
$704$	407.879	−	235.489i	0.579373	−	0.334501i
$705$		0			0
$706$	−1604.38			−2.27249
$707$	−91.8932	−	96.2987i	−0.129976	−	0.136207i
$708$		0			0
$709$	−382.186	−	220.655i	−0.539049	−	0.311220i	0.205645	−	0.978627i	$-0.434071\pi$
$709$	−382.186	−	220.655i	−0.539049	−	0.311220i	−0.744693	+	0.667407i	$0.767404\pi$
$710$	−846.194	−	393.694i	−1.19182	−	0.554498i
$711$		0			0
$712$	996.165	−	266.922i	1.39911	−	0.374890i
$713$	−706.648	+	706.648i	−0.991091	+	0.991091i
$714$		0			0
$715$	474.227	+	676.018i	0.663255	+	0.945480i
$716$	−17.3592	+	30.0671i	−0.0242447	+	0.0419931i
$717$		0			0
$718$	−840.279	−	225.152i	−1.17031	−	0.313582i
$719$	−922.670	−	532.704i	−1.28327	−	0.740896i	−0.305825	−	0.952088i	$-0.598932\pi$
$719$	−922.670	−	532.704i	−1.28327	−	0.740896i	−0.977445	+	0.211192i	$0.932265\pi$
$720$		0			0
$721$	108.435	+	198.397i	0.150395	+	0.275169i
$722$	756.790	+	756.790i	1.04819	+	1.04819i
$723$		0			0
$724$	−1031.59	+	595.587i	−1.42484	+	0.822634i
$725$	133.920	−	23.8532i	0.184717	−	0.0329010i
$726$		0			0
$727$	−1013.20	−	1013.20i	−1.39367	−	1.39367i	−0.816917	−	0.576755i	$-0.804319\pi$
$727$	−1013.20	−	1013.20i	−1.39367	−	1.39367i	−0.576755	−	0.816917i	$-0.695681\pi$
$728$	360.670	+	1484.14i	0.495426	+	2.03866i
$729$		0			0
$730$	612.348	+	512.917i	0.838833	+	0.702626i
$731$	−325.011	−	562.936i	−0.444612	−	0.770090i
$732$		0			0
$733$	−131.207	−	489.670i	−0.178999	−	0.668035i	−0.995836	−	0.0911656i	$-0.970941\pi$
$733$	−131.207	−	489.670i	−0.178999	−	0.668035i	0.816836	−	0.576870i	$-0.195726\pi$
$734$			1409.37i			1.92012i
$735$		0			0
$736$	863.856			1.17372
$737$	−1557.04	+	417.208i	−2.11267	+	0.566090i
$738$		0			0
$739$	−436.379	+	251.943i	−0.590499	+	0.340925i	−0.765295	−	0.643680i	$-0.777407\pi$
$739$	−436.379	+	251.943i	−0.590499	+	0.340925i	0.174796	+	0.984605i	$0.444073\pi$
$740$	−1663.51	+	146.992i	−2.24799	+	0.198638i
$741$		0			0
$742$	1428.67	−	347.188i	1.92543	−	0.467908i
$743$	93.7564	−	93.7564i	0.126186	−	0.126186i	−0.641193	−	0.767380i	$-0.721560\pi$
$743$	93.7564	−	93.7564i	0.126186	−	0.126186i	0.767380	+	0.641193i	$0.221560\pi$
$744$		0			0
$745$	61.0405	+	167.256i	0.0819335	+	0.224505i
$746$	324.868	+	562.687i	0.435480	+	0.754273i
$747$		0			0
$748$	835.109	−	835.109i	1.11646	−	1.11646i
$749$	−915.211	+	500.213i	−1.22191	+	0.667841i
$750$		0			0
$751$	236.900	−	410.323i	0.315446	−	0.546369i	−0.664086	−	0.747656i	$-0.731179\pi$
$751$	236.900	−	410.323i	0.315446	−	0.546369i	0.979532	+	0.201287i	$0.0645125\pi$
$752$	−366.402	+	1367.43i	−0.487237	+	1.81839i
$753$		0			0
$754$	−192.381	−	111.072i	−0.255148	−	0.147310i
$755$	37.8825	−	215.937i	0.0501755	−	0.286010i
$756$		0			0
$757$	−119.279	−	119.279i	−0.157568	−	0.157568i	0.623920	−	0.781488i	$-0.285539\pi$
$757$	−119.279	−	119.279i	−0.157568	−	0.157568i	−0.781488	+	0.623920i	$0.785539\pi$
$758$	−501.821	−	1872.82i	−0.662032	−	2.47074i
$759$		0			0
$760$	729.913	+	339.594i	0.960412	+	0.446834i
$761$	−378.809	+	656.117i	−0.497778	+	0.862177i	−0.999997	−	0.00256378i	$-0.999184\pi$
$761$	−378.809	+	656.117i	−0.497778	+	0.862177i	0.502219	+	0.864741i	$0.332517\pi$
$762$		0			0
$763$	−652.811	+	622.947i	−0.855585	+	0.816444i
$764$		−	1704.86i		−	2.23149i
$765$		0			0
$766$	−174.897	−	302.930i	−0.228325	−	0.395470i
$767$	−48.5157	+	181.063i	−0.0632539	+	0.236067i
$768$		0			0
$769$			885.349i			1.15130i	0.817696	+	0.575650i	$0.195251\pi$
$769$			885.349i			1.15130i	−0.817696	+	0.575650i	$0.804749\pi$
$770$	−606.014	−	1789.50i	−0.787031	−	2.32402i
$771$		0			0
$772$	−396.314	+	106.192i	−0.513361	+	0.137555i
$773$	476.974	+	127.805i	0.617042	+	0.165336i	0.553783	−	0.832661i	$-0.313184\pi$
$773$	476.974	+	127.805i	0.617042	+	0.165336i	0.0632594	+	0.997997i	$0.479850\pi$
$774$		0			0
$775$	1015.16	−	854.829i	1.30989	−	1.10300i
$776$	938.660			1.20961
$777$		0			0
$778$	−820.666	+	820.666i	−1.05484	+	1.05484i
$779$	291.913	+	168.536i	0.374728	+	0.216349i
$780$		0			0
$781$	−377.539	−	653.916i	−0.483404	−	0.837281i
$782$	568.139	−	152.232i	0.726520	−	0.194671i
$783$		0			0
$784$	77.8172	−	1661.19i	0.0992566	−	2.11887i
$785$	324.262	−	227.470i	0.413072	−	0.289771i
$786$		0			0
$787$	−127.645	+	476.379i	−0.162192	+	0.605310i	0.836189	+	0.548441i	$0.184779\pi$
$787$	−127.645	+	476.379i	−0.162192	+	0.605310i	−0.998382	+	0.0568694i	$0.981888\pi$
$788$	−1289.68	−	345.569i	−1.63665	−	0.438539i
$789$		0			0
$790$	−300.121	−	427.828i	−0.379901	−	0.541554i
$791$	−310.274	+	509.489i	−0.392255	+	0.644108i
$792$		0			0
$793$	270.450	+	1009.33i	0.341047	+	1.27280i
$794$	−890.716	+	514.255i	−1.12181	+	0.647677i
$795$		0			0
$796$	−796.156	+	1378.98i	−1.00020	+	1.73239i
$797$	813.338	+	813.338i	1.02050	+	1.02050i	0.999785	+	0.0207143i	$0.00659405\pi$
$797$	813.338	+	813.338i	1.02050	+	1.02050i	0.0207143	+	0.999785i	$0.493406\pi$
$798$		0			0
$799$			356.765i			0.446514i
$800$	−1143.01	−	98.0029i	−1.42876	−	0.122504i
$801$		0			0
$802$	−372.396	+	1389.80i	−0.464334	+	1.73292i
$803$	167.262	+	624.231i	0.208296	+	0.777373i
$804$		0			0
$805$	129.008	−	646.133i	0.160259	−	0.802650i
$806$	−2167.31			−2.68897
$807$		0			0
$808$	−358.584	−	96.0824i	−0.443793	−	0.118914i
$809$	1172.08	−	676.703i	1.44881	−	0.836469i	0.450396	−	0.892829i	$-0.351283\pi$
$809$	1172.08	−	676.703i	1.44881	−	0.836469i	0.998411	+	0.0563600i	$0.0179494\pi$
$810$		0			0
$811$	148.433			0.183024			0.0915122	−	0.995804i	$-0.470830\pi$
$811$	148.433			0.183024			0.0915122	+	0.995804i	$0.470830\pi$
$812$	245.704	+	257.483i	0.302591	+	0.317097i
$813$		0			0
$814$	−1670.96	−	964.731i	−2.05278	−	1.18517i
$815$	−192.201	+	413.111i	−0.235830	+	0.506885i
$816$		0			0
$817$	605.427	−	162.224i	0.741036	−	0.198560i
$818$	−779.860	+	779.860i	−0.953375	+	0.953375i
$819$		0			0
$820$	−1880.83	−	329.959i	−2.29369	−	0.402390i
$821$	435.634	−	754.541i	0.530614	−	0.919051i	−0.468747	−	0.883332i	$-0.655295\pi$
$821$	435.634	−	754.541i	0.530614	−	0.919051i	0.999362	−	0.0357189i	$-0.0113721\pi$
$822$		0			0
$823$	1219.61	+	326.794i	1.48191	+	0.397076i	0.906996	−	0.421139i	$-0.138369\pi$
$823$	1219.61	+	326.794i	1.48191	+	0.397076i	0.574913	+	0.818215i	$0.305036\pi$
$824$	546.093	+	315.287i	0.662734	+	0.382630i
$825$		0			0
$826$	223.073	−	366.300i	0.270065	−	0.443463i
$827$	−621.888	−	621.888i	−0.751980	−	0.751980i	0.222868	−	0.974849i	$-0.428458\pi$
$827$	−621.888	−	621.888i	−0.751980	−	0.751980i	−0.974849	+	0.222868i	$0.928458\pi$
$828$		0			0
$829$	557.418	−	321.825i	0.672398	−	0.388209i	−0.124587	−	0.992209i	$-0.539760\pi$
$829$	557.418	−	321.825i	0.672398	−	0.388209i	0.796985	+	0.603999i	$0.206427\pi$
$830$	839.287	−	306.300i	1.01119	−	0.369036i
$831$		0			0
$832$	251.879	+	251.879i	0.302739	+	0.302739i
$833$	−89.4092	−	409.450i	−0.107334	−	0.491537i
$834$		0			0
$835$	−118.065	−	1336.14i	−0.141395	−	1.60017i
$836$	569.401	+	986.231i	0.681101	+	1.17970i
$837$		0			0
$838$	415.693	+	1551.39i	0.496054	+	1.85130i
$839$			669.803i			0.798335i	0.916878	+	0.399168i	$0.130701\pi$
$839$			669.803i			0.798335i	−0.916878	+	0.399168i	$0.869299\pi$
$840$		0			0
$841$	811.394			0.964797
$842$	473.906	−	126.983i	0.562834	−	0.150811i
$843$		0			0
$844$	−787.384	+	454.596i	−0.932919	+	0.538621i
$845$	141.559	−	169.001i	0.167525	−	0.200001i
$846$		0			0
$847$	191.757	−	654.019i	0.226395	−	0.772159i
$848$	1379.84	−	1379.84i	1.62717	−	1.62717i
$849$		0			0
$850$	−768.999	+	136.971i	−0.904705	+	0.161142i
$851$	−336.442	−	582.734i	−0.395349	−	0.684764i
$852$		0			0
$853$	102.971	−	102.971i	0.120716	−	0.120716i	−0.644168	−	0.764884i	$-0.722796\pi$
$853$	102.971	−	102.971i	0.120716	−	0.120716i	0.764884	+	0.644168i	$0.222796\pi$
$854$	55.9512	−	2390.13i	0.0655166	−	2.79875i
$855$		0			0
$856$	−1454.43	+	2519.14i	−1.69910	+	2.94292i
$857$	−286.339	+	1068.63i	−0.334118	+	1.24694i	0.570705	+	0.821156i	$0.306670\pi$
$857$	−286.339	+	1068.63i	−0.334118	+	1.24694i	−0.904822	+	0.425789i	$0.859996\pi$
$858$		0			0
$859$	−1331.23	−	768.585i	−1.54974	−	0.894744i	−0.998161	−	0.0606233i	$-0.980691\pi$
$859$	−1331.23	−	768.585i	−1.54974	−	0.894744i	−0.551582	−	0.834121i	$-0.685975\pi$
$860$	−2906.88	+	2039.18i	−3.38009	+	2.37113i
$861$		0			0
$862$	−1910.39	−	1910.39i	−2.21623	−	2.21623i
$863$	−113.614	−	424.014i	−0.131650	−	0.491326i	0.868339	−	0.495971i	$-0.165188\pi$
$863$	−113.614	−	424.014i	−0.131650	−	0.491326i	−0.999989	+	0.00464550i	$0.998521\pi$
$864$		0			0
$865$	−468.606	+	1007.21i	−0.541741	+	1.16440i
$866$	−1084.85	+	1879.01i	−1.25271	+	2.16976i
$867$		0			0
$868$	3332.06	+	976.953i	3.83878	+	1.12552i
$869$		−	422.806i		−	0.486543i
$870$		0			0
$871$	−609.583	−	1055.83i	−0.699865	−	1.21220i
$872$	−651.345	+	2430.85i	−0.746955	+	2.78768i
$873$		0			0
$874$			567.153i			0.648916i
$875$	−243.999	+	840.291i	−0.278856	+	0.960333i
$876$		0			0
$877$	711.560	−	190.662i	0.811357	−	0.217402i	0.170792	−	0.985307i	$-0.445367\pi$
$877$	711.560	−	190.662i	0.811357	−	0.217402i	0.640564	+	0.767905i	$0.278701\pi$
$878$	655.409	+	175.616i	0.746479	+	0.200018i
$879$		0			0
$880$	−1922.34	−	1610.20i	−2.18448	−	1.82977i
$881$	−226.230			−0.256788			−0.128394	−	0.991723i	$-0.540982\pi$
$881$	−226.230			−0.256788			−0.128394	+	0.991723i	$0.540982\pi$
$882$		0			0
$883$	1050.50	−	1050.50i	1.18970	−	1.18970i	0.212546	−	0.977151i	$-0.431824\pi$
$883$	1050.50	−	1050.50i	1.18970	−	1.18970i	0.977151	−	0.212546i	$-0.0681757\pi$
$884$	773.562	+	446.616i	0.875070	+	0.505222i
$885$		0			0
$886$	1506.17	+	2608.76i	1.69997	+	2.94443i
$887$	1177.61	−	315.539i	1.32763	−	0.355737i	0.475799	−	0.879554i	$-0.342159\pi$
$887$	1177.61	−	315.539i	1.32763	−	0.355737i	0.851831	+	0.523817i	$0.175492\pi$
$888$		0			0
$889$	−561.092	−	341.699i	−0.631149	−	0.384364i
$890$	−554.107	−	789.888i	−0.622592	−	0.887515i
$891$		0			0
$892$	160.218	−	597.942i	0.179617	−	0.670339i
$893$	−332.288	−	89.0364i	−0.372103	−	0.0997048i
$894$		0			0
$895$	18.2979	+	3.21005i	0.0204445	+	0.00358665i
$896$	225.346	+	412.303i	0.251502	+	0.460160i
$897$		0			0
$898$	−110.088	−	410.854i	−0.122592	−	0.457521i
$899$	−250.146	+	144.422i	−0.278249	+	0.160647i
$900$		0			0
$901$	245.886	−	425.887i	0.272903	−	0.472682i
$902$	−1560.05	−	1560.05i	−1.72954	−	1.72954i
$903$		0			0
$904$			1663.70i			1.84038i
$905$	488.616	+	409.276i	0.539907	+	0.452238i
$906$		0			0
$907$	−112.523	+	419.940i	−0.124060	+	0.462999i	−0.999804	−	0.0197764i	$-0.993705\pi$
$907$	−112.523	+	419.940i	−0.124060	+	0.462999i	0.875744	+	0.482775i	$0.160371\pi$
$908$	−334.718	−	1249.18i	−0.368632	−	1.37575i
$909$		0			0
$910$	1188.69	−	793.018i	1.30625	−	0.871449i
$911$	−529.083			−0.580771			−0.290386	−	0.956910i	$-0.593784\pi$
$911$	−529.083			−0.580771			−0.290386	+	0.956910i	$0.593784\pi$
$912$		0			0
$913$	698.198	+	187.081i	0.764729	+	0.204909i
$914$	−281.552	+	162.554i	−0.308044	+	0.177849i
$915$		0			0
$916$	2819.44			3.07799
$917$	3.01139	−	10.2709i	0.00328396	−	0.0112005i
$918$		0			0
$919$	741.713	+	428.228i	0.807087	+	0.465972i	0.845943	−	0.533273i	$-0.179038\pi$
$919$	741.713	+	428.228i	0.807087	+	0.465972i	−0.0388560	+	0.999245i	$0.512371\pi$
$920$	−629.997	−	1726.24i	−0.684779	−	1.87635i
$921$		0			0
$922$	1964.10	−	526.280i	2.13027	−	0.570803i
$923$	403.815	−	403.815i	0.437503	−	0.437503i
$924$		0			0
$925$	379.050	+	809.210i	0.409784	+	0.874821i
$926$	399.170	−	691.383i	0.431069	−	0.746634i
$927$		0			0
$928$	241.174	+	64.6223i	0.259885	+	0.0696361i
$929$	127.324	+	73.5105i	0.137055	+	0.0791286i	0.566960	−	0.823746i	$-0.308120\pi$
$929$	127.324	+	73.5105i	0.137055	+	0.0791286i	−0.429905	+	0.902874i	$0.641453\pi$
$930$		0			0
$931$	403.673	+	18.9097i	0.433590	+	0.0203112i
$932$	1568.44	+	1568.44i	1.68287	+	1.68287i
$933$		0			0
$934$	−2.50194	+	1.44449i	−0.00267873	+	0.00154657i
$935$	−572.970	−	266.576i	−0.612802	−	0.285108i
$936$		0			0
$937$	−456.315	−	456.315i	−0.486996	−	0.486996i	0.420361	−	0.907357i	$-0.361903\pi$
$937$	−456.315	−	456.315i	−0.486996	−	0.486996i	−0.907357	+	0.420361i	$0.861903\pi$
$938$	658.698	+	2710.52i	0.702237	+	2.88968i
$939$		0			0
$940$	1941.29	−	171.537i	2.06520	−	0.182487i
$941$	−549.211	−	951.261i	−0.583646	−	1.01090i	−0.995043	−	0.0994480i	$-0.968292\pi$
$941$	−549.211	−	951.261i	−0.583646	−	1.01090i	0.411397	−	0.911456i	$-0.365041\pi$
$942$		0			0
$943$	−199.137	−	743.191i	−0.211174	−	0.788113i
$944$		−	569.231i		−	0.602999i
$945$		0			0
$946$	−4102.49			−4.33667
$947$	27.5184	−	7.37353i	0.0290585	−	0.00778620i	−0.244261	−	0.969710i	$-0.578545\pi$
$947$	27.5184	−	7.37353i	0.0290585	−	0.00778620i	0.273319	+	0.961923i	$0.411879\pi$
$948$		0			0
$949$	−423.290	+	244.387i	−0.446038	+	0.257520i
$950$	64.3425	−	750.424i	0.0677289	−	0.789920i
$951$		0			0
$952$	−806.932	−	845.617i	−0.847618	−	0.888254i
$953$	−0.329346	+	0.329346i	−0.000345589	+	0.000345589i	−0.707280	−	0.706934i	$-0.750078\pi$
$953$	−0.329346	+	0.329346i	−0.000345589	+	0.000345589i	0.706934	+	0.707280i	$0.250078\pi$
$954$		0			0
$955$	−856.959	+	312.749i	−0.897339	+	0.327486i
$956$	1936.68	+	3354.43i	2.02582	+	3.50882i
$957$		0			0
$958$	−2262.23	+	2262.23i	−2.36141	+	2.36141i
$959$	−8.05368	+	344.038i	−0.00839800	+	0.358747i
$960$		0			0
$961$	−928.533	+	1608.27i	−0.966215	+	1.67353i
$962$	377.693	−	1409.57i	0.392612	−	1.46525i
$963$		0			0
$964$	−786.486	−	454.078i	−0.815857	−	0.471035i
$965$	126.080	+	179.729i	0.130653	+	0.186248i
$966$		0			0
$967$	215.333	+	215.333i	0.222682	+	0.222682i	0.809627	−	0.586945i	$-0.199669\pi$
$967$	215.333	+	215.333i	0.222682	+	0.222682i	−0.586945	+	0.809627i	$0.699669\pi$
$968$	−491.968	−	1836.05i	−0.508231	−	1.89675i
$969$		0			0
$970$	−301.072	−	824.963i	−0.310384	−	0.850477i
$971$	−645.827	+	1118.61i	−0.665116	+	1.15201i	0.314138	+	0.949377i	$0.398284\pi$
$971$	−645.827	+	1118.61i	−0.665116	+	1.15201i	−0.979254	+	0.202637i	$0.935049\pi$
$972$		0			0
$973$	−104.955	−	431.886i	−0.107867	−	0.443870i
$974$		−	2046.44i		−	2.10107i
$975$		0			0
$976$	−1586.59	−	2748.05i	−1.62560	−	2.81562i
$977$	49.0310	−	182.986i	0.0501852	−	0.187294i	−0.936283	−	0.351247i	$-0.885758\pi$
$977$	49.0310	−	182.986i	0.0501852	−	0.187294i	0.986468	+	0.163953i	$0.0524245\pi$
$978$		0			0
$979$		−	780.617i		−	0.797361i
$980$	−2184.98	+	683.379i	−2.22958	+	0.697325i
$981$		0			0
$982$	1354.34	−	362.895i	1.37917	−	0.369546i
$983$	−748.302	−	200.507i	−0.761243	−	0.203974i	−0.142744	−	0.989760i	$-0.545592\pi$
$983$	−748.302	−	200.507i	−0.761243	−	0.203974i	−0.618499	+	0.785785i	$0.712259\pi$
$984$		0			0
$985$	62.8839	+	711.659i	0.0638415	+	0.722496i
$986$	170.003			0.172416
$987$		0			0
$988$	−609.031	+	609.031i	−0.616428	+	0.616428i
$989$	−1239.03	−	715.354i	−1.25281	−	0.723311i
$990$		0			0
$991$	−38.1160	−	66.0188i	−0.0384621	−	0.0666184i	0.846154	−	0.532939i	$-0.178913\pi$
$991$	−38.1160	−	66.0188i	−0.0384621	−	0.0666184i	−0.884616	+	0.466321i	$0.845579\pi$
$992$	2352.98	−	630.479i	2.37196	−	0.635563i
$993$		0			0
$994$	−1146.54	+	626.646i	−1.15346	+	0.630428i
$995$	839.205	+	147.224i	0.843422	+	0.147964i
$996$		0			0
$997$	−17.0560	+	63.6540i	−0.0171074	+	0.0638455i	−0.973952	−	0.226755i	$-0.927188\pi$
$997$	−17.0560	+	63.6540i	−0.0171074	+	0.0638455i	0.956844	+	0.290600i	$0.0938550\pi$
$998$	42.9668	+	11.5129i	0.0430529	+	0.0115360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.1		64
3.2	odd	2		105.3.v.a.37.16	✓	64
5.3	odd	4	inner	315.3.ca.b.163.16		64
7.4	even	3	inner	315.3.ca.b.172.16		64
15.8	even	4		105.3.v.a.58.1	yes	64
21.11	odd	6		105.3.v.a.67.1	yes	64
35.18	odd	12	inner	315.3.ca.b.298.1		64
105.53	even	12		105.3.v.a.88.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.16	✓	64	3.2	odd	2
105.3.v.a.58.1	yes	64	15.8	even	4
105.3.v.a.67.1	yes	64	21.11	odd	6
105.3.v.a.88.16	yes	64	105.53	even	12
315.3.ca.b.37.1		64	1.1	even	1	trivial
315.3.ca.b.163.16		64	5.3	odd	4	inner
315.3.ca.b.172.16		64	7.4	even	3	inner
315.3.ca.b.298.1		64	35.18	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.52852 + 0.945463i) q^{2} +(8.09242 - 4.67216i) q^{4} +(-3.83301 - 3.21062i) q^{5} +(-6.80203 + 1.65300i) q^{7} +(-13.8047 + 13.8047i) q^{8} +O(q^{10})\)	\(q+(-3.52852 + 0.945463i) q^{2} +(8.09242 - 4.67216i) q^{4} +(-3.83301 - 3.21062i) q^{5} +(-6.80203 + 1.65300i) q^{7} +(-13.8047 + 13.8047i) q^{8} +(16.5603 + 7.70474i) q^{10} +(7.38858 + 12.7974i) q^{11} +(-7.90282 + 7.90282i) q^{13} +(22.4382 - 12.2637i) q^{14} +(16.9695 - 29.3921i) q^{16} +(2.21369 - 8.26159i) q^{17} +(7.14233 + 4.12363i) q^{19} +(-46.0188 - 8.07322i) q^{20} +(-38.1702 - 38.1702i) q^{22} +(-4.87235 - 18.1839i) q^{23} +(4.38389 + 24.6126i) q^{25} +(20.4134 - 35.3570i) q^{26} +(-47.3218 + 45.1569i) q^{28} -5.44111i q^{29} +(-26.5427 - 45.9734i) q^{31} +(-11.8767 + 44.3244i) q^{32} +31.2441i q^{34} +(31.3794 + 15.5027i) q^{35} +(34.5256 - 9.25110i) q^{37} +(-29.1006 - 7.79747i) q^{38} +(97.2348 - 8.59191i) q^{40} +40.8709 q^{41} +(53.7395 - 53.7395i) q^{43} +(119.583 + 69.0412i) q^{44} +(34.3844 + 59.5555i) q^{46} +(-40.2908 + 10.7959i) q^{47} +(43.5352 - 22.4875i) q^{49} +(-38.7390 - 82.7012i) q^{50} +(-27.0297 + 100.876i) q^{52} +(55.5377 + 14.8813i) q^{53} +(12.7670 - 72.7744i) q^{55} +(71.0806 - 116.719i) q^{56} +(5.14437 + 19.1990i) q^{58} +(14.5251 - 8.38608i) q^{59} +(46.7481 - 80.9701i) q^{61} +(137.123 + 137.123i) q^{62} -31.8720i q^{64} +(55.6645 - 4.91865i) q^{65} +(-28.2333 + 105.368i) q^{67} +(-20.6854 - 77.1989i) q^{68} +(-125.380 - 25.0336i) q^{70} -51.0976 q^{71} +(42.2429 + 11.3190i) q^{73} +(-113.077 + 65.2853i) q^{74} +77.0650 q^{76} +(-71.4114 - 74.8349i) q^{77} +(-24.7788 - 14.3061i) q^{79} +(-159.411 + 58.1774i) q^{80} +(-144.213 + 38.6419i) q^{82} +(34.5883 - 34.5883i) q^{83} +(-35.0099 + 24.5594i) q^{85} +(-138.812 + 240.429i) q^{86} +(-278.660 - 74.6669i) q^{88} +(-45.7486 - 26.4130i) q^{89} +(40.6919 - 66.8186i) q^{91} +(-124.387 - 124.387i) q^{92} +(131.960 - 76.1869i) q^{94} +(-14.1372 - 38.7372i) q^{95} +(-33.9979 - 33.9979i) q^{97} +(-132.353 + 120.508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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