LMFDB - Embedded newform 315.3.w.a.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(136,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.136");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.w (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			136.4
Root			$-1.26021 - 2.18275i$ of defining polynomial
Character	$\chi$	$=$	315.136
Dual form			315.3.w.a.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26021 + 2.18275i) q^{2} +(-1.17628 + 2.03737i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.18050 + 3.28656i) q^{7} +4.15226 q^{8} +O(q^{10})$	\(q+(1.26021 + 2.18275i) q^{2} +(-1.17628 + 2.03737i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.18050 + 3.28656i) q^{7} +4.15226 q^{8} +(4.88079 + 2.81792i) q^{10} +(-4.36036 + 7.55236i) q^{11} +21.5286i q^{13} +(-14.9625 - 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(18.7862 + 10.8462i) q^{17} +(-2.71590 + 1.56803i) q^{19} +5.26047i q^{20} -21.9799 q^{22} +(2.05421 + 3.55799i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-46.9917 + 27.1307i) q^{26} +(0.574033 - 16.4579i) q^{28} +50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-16.7431 + 28.9999i) q^{32} +54.6743i q^{34} +(-8.29399 + 13.2744i) q^{35} +(-26.4906 - 45.8831i) q^{37} +(-6.84523 - 3.95209i) q^{38} +(8.04083 - 4.64237i) q^{40} -36.8122i q^{41} +17.6504 q^{43} +(-10.2580 - 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(3.49804 - 2.01959i) q^{47} +(27.3971 - 40.6251i) q^{49} +12.6021 q^{50} +(-43.8618 - 25.3236i) q^{52} +(2.22593 - 3.85542i) q^{53} +19.5001i q^{55} +(-25.6631 + 13.6467i) q^{56} +(64.0923 + 111.011i) q^{58} +(-81.5032 - 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} -98.7226i q^{62} -4.89677 q^{64} +(24.0697 + 41.6900i) q^{65} +(50.2661 - 87.0635i) q^{67} +(-44.1956 + 25.5164i) q^{68} +(-39.4270 - 1.37517i) q^{70} +56.6975 q^{71} +(64.8042 + 37.4147i) q^{73} +(66.7676 - 115.645i) q^{74} -7.37773i q^{76} +(2.12789 - 61.0079i) q^{77} +(-14.4903 - 25.0980i) q^{79} +(38.4891 + 22.2217i) q^{80} +(80.3519 - 46.3912i) q^{82} -21.1116i q^{83} +48.5058 q^{85} +(22.2433 + 38.5266i) q^{86} +(-18.1054 + 31.3594i) q^{88} +(-63.1066 + 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528 q^{92} +(8.81655 + 5.09024i) q^{94} +(-3.50621 + 6.07294i) q^{95} +73.7985i q^{97} +(123.201 + 8.60469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8	$ 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8} - 20 q^{11} + 16 q^{14} - 2 q^{16} + 18 q^{17} - 16 q^{22} - 62 q^{23} + 20 q^{25} - 120 q^{26} - 120 q^{28} + 100 q^{29} - 126 q^{31} - 36 q^{32} - 80 q^{37} - 114 q^{38} + 90 q^{40} + 352 q^{43} + 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} - 20 q^{50} - 48 q^{52} + 76 q^{53} - 196 q^{56} - 40 q^{58} + 54 q^{59} - 396 q^{61} - 4 q^{64} + 60 q^{65} + 184 q^{67} + 312 q^{68} - 164 q^{71} + 348 q^{73} + 140 q^{74} - 152 q^{77} - 206 q^{79} + 204 q^{82} - 60 q^{85} - 178 q^{86} + 124 q^{88} - 282 q^{89} - 114 q^{91} + 288 q^{92} + 30 q^{94} + 120 q^{95} + 592 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8 - 20 * q^11 + 16 * q^14 - 2 * q^16 + 18 * q^17 - 16 * q^22 - 62 * q^23 + 20 * q^25 - 120 * q^26 - 120 * q^28 + 100 * q^29 - 126 * q^31 - 36 * q^32 - 80 * q^37 - 114 * q^38 + 90 * q^40 + 352 * q^43 + 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 - 20 * q^50 - 48 * q^52 + 76 * q^53 - 196 * q^56 - 40 * q^58 + 54 * q^59 - 396 * q^61 - 4 * q^64 + 60 * q^65 + 184 * q^67 + 312 * q^68 - 164 * q^71 + 348 * q^73 + 140 * q^74 - 152 * q^77 - 206 * q^79 + 204 * q^82 - 60 * q^85 - 178 * q^86 + 124 * q^88 - 282 * q^89 - 114 * q^91 + 288 * q^92 + 30 * q^94 + 120 * q^95 + 592 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.26021	+	2.18275i	0.630107	+	1.09138i	0.987529	+	0.157434i	$0.0503223\pi$
$2$	1.26021	+	2.18275i	0.630107	+	1.09138i	−0.357423	+	0.933943i	$0.616344\pi$
$3$		0			0
$3$		0			0
$4$	−1.17628	+	2.03737i	−0.294069	+	0.509343i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−6.18050	+	3.28656i	−0.882928	+	0.469508i
$7$	−6.18050	+	3.28656i	−0.882928	+	0.469508i
$8$	4.15226			0.519033
$9$		0			0
$10$	4.88079	+	2.81792i	0.488079	+	0.281792i
$11$	−4.36036	+	7.55236i	−0.396396	+	0.686579i	−0.993278	−	0.115750i	$-0.963073\pi$
$11$	−4.36036	+	7.55236i	−0.396396	+	0.686579i	0.596882	+	0.802329i	$0.296406\pi$
$12$		0			0
$13$			21.5286i			1.65605i	0.560693	+	0.828024i	$0.310535\pi$
$13$			21.5286i			1.65605i	−0.560693	+	0.828024i	$0.689465\pi$
$14$	−14.9625	−	9.34874i	−1.06875	−	0.667767i
$15$		0			0
$16$	9.93785	+	17.2129i	0.621116	+	1.07580i
$17$	18.7862	+	10.8462i	1.10507	+	0.638013i	0.937548	−	0.347855i	$-0.113090\pi$
$17$	18.7862	+	10.8462i	1.10507	+	0.638013i	0.167523	+	0.985868i	$0.446423\pi$
$18$		0			0
$19$	−2.71590	+	1.56803i	−0.142942	+	0.0825276i	−0.569765	−	0.821807i	$-0.692966\pi$
$19$	−2.71590	+	1.56803i	−0.142942	+	0.0825276i	0.426823	+	0.904335i	$0.359633\pi$
$20$			5.26047i			0.263024i
$21$		0			0
$22$	−21.9799			−0.999088
$23$	2.05421	+	3.55799i	0.0893134	+	0.154695i	0.907221	−	0.420654i	$-0.138199\pi$
$23$	2.05421	+	3.55799i	0.0893134	+	0.154695i	−0.817908	+	0.575349i	$0.804866\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−46.9917	+	27.1307i	−1.80737	+	1.04349i
$27$		0			0
$28$	0.574033	−	16.4579i	0.0205012	−	0.587781i
$29$	50.8583			1.75373			0.876867	−	0.480732i	$-0.159629\pi$
$29$	50.8583			1.75373			0.876867	+	0.480732i	$0.159629\pi$
$30$		0			0
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.159536	−	0.987192i	$-0.551000\pi$
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.934701	+	0.355434i	$0.884333\pi$
$32$	−16.7431	+	28.9999i	−0.523222	+	0.906247i
$33$		0			0
$34$			54.6743i			1.60807i
$35$	−8.29399	+	13.2744i	−0.236971	+	0.379269i
$36$		0			0
$37$	−26.4906	−	45.8831i	−0.715962	−	1.24008i	−0.962587	−	0.270972i	$-0.912655\pi$
$37$	−26.4906	−	45.8831i	−0.715962	−	1.24008i	0.246625	−	0.969111i	$-0.420678\pi$
$38$	−6.84523	−	3.95209i	−0.180138	−	0.104002i
$39$		0			0
$40$	8.04083	−	4.64237i	0.201021	−	0.116059i
$41$		−	36.8122i		−	0.897857i	−0.893568	−	0.448929i	$-0.851806\pi$
$41$		−	36.8122i		−	0.897857i	0.893568	−	0.448929i	$-0.148194\pi$
$42$		0			0
$43$	17.6504			0.410475			0.205238	−	0.978712i	$-0.434203\pi$
$43$	17.6504			0.410475			0.205238	+	0.978712i	$0.434203\pi$
$44$	−10.2580	−	17.7674i	−0.233136	−	0.403804i
$45$		0			0
$46$	−5.17748	+	8.96766i	−0.112554	+	0.194949i
$47$	3.49804	−	2.01959i	0.0744263	−	0.0429701i	−0.462325	−	0.886711i	$-0.652985\pi$
$47$	3.49804	−	2.01959i	0.0744263	−	0.0429701i	0.536751	+	0.843740i	$0.319651\pi$
$48$		0			0
$49$	27.3971	−	40.6251i	0.559124	−	0.829084i
$50$	12.6021			0.252043
$51$		0			0
$52$	−43.8618	−	25.3236i	−0.843496	−	0.486993i
$53$	2.22593	−	3.85542i	0.0419986	−	0.0727438i	−0.844262	−	0.535931i	$-0.819961\pi$
$53$	2.22593	−	3.85542i	0.0419986	−	0.0727438i	0.886261	+	0.463187i	$0.153294\pi$
$54$		0			0
$55$			19.5001i			0.354548i
$56$	−25.6631	+	13.6467i	−0.458269	+	0.243690i
$57$		0			0
$58$	64.0923	+	111.011i	1.10504	+	1.91399i
$59$	−81.5032	−	47.0559i	−1.38141	−	0.797558i	−0.389084	−	0.921202i	$-0.627208\pi$
$59$	−81.5032	−	47.0559i	−1.38141	−	0.797558i	−0.992327	+	0.123644i	$0.960542\pi$
$60$		0			0
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.919546	−	0.392984i	$-0.871443\pi$
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.119439	+	0.992842i	$0.538110\pi$
$62$		−	98.7226i		−	1.59230i
$63$		0			0
$64$	−4.89677			−0.0765121
$65$	24.0697	+	41.6900i	0.370303	+	0.641384i
$66$		0			0
$67$	50.2661	−	87.0635i	0.750241	−	1.29946i	−0.197465	−	0.980310i	$-0.563271\pi$
$67$	50.2661	−	87.0635i	0.750241	−	1.29946i	0.947706	−	0.319145i	$-0.103396\pi$
$68$	−44.1956	+	25.5164i	−0.649936	+	0.375241i
$69$		0			0
$70$	−39.4270	−	1.37517i	−0.563242	−	0.0196453i
$71$	56.6975			0.798557			0.399278	−	0.916830i	$-0.369261\pi$
$71$	56.6975			0.798557			0.399278	+	0.916830i	$0.369261\pi$
$72$		0			0
$73$	64.8042	+	37.4147i	0.887729	+	0.512531i	0.873199	−	0.487364i	$-0.162041\pi$
$73$	64.8042	+	37.4147i	0.887729	+	0.512531i	0.0145299	+	0.999894i	$0.495375\pi$
$74$	66.7676	−	115.645i	0.902266	−	1.56277i
$75$		0			0
$76$		−	7.37773i		−	0.0970754i
$77$	2.12789	−	61.0079i	0.0276350	−	0.792311i
$78$		0			0
$79$	−14.4903	−	25.0980i	−0.183422	−	0.317696i	0.759622	−	0.650365i	$-0.225384\pi$
$79$	−14.4903	−	25.0980i	−0.183422	−	0.317696i	−0.943044	+	0.332669i	$0.892051\pi$
$80$	38.4891	+	22.2217i	0.481114	+	0.277771i
$81$		0			0
$82$	80.3519	−	46.3912i	0.979901	−	0.565746i
$83$		−	21.1116i		−	0.254357i	−0.991880	−	0.127179i	$-0.959408\pi$
$83$		−	21.1116i		−	0.254357i	0.991880	−	0.127179i	$-0.0405921\pi$
$84$		0			0
$85$	48.5058			0.570657
$86$	22.2433	+	38.5266i	0.258643	+	0.447983i
$87$		0			0
$88$	−18.1054	+	31.3594i	−0.205743	+	0.356357i
$89$	−63.1066	+	36.4346i	−0.709063	+	0.409378i	−0.810714	−	0.585442i	$-0.800921\pi$
$89$	−63.1066	+	36.4346i	−0.709063	+	0.409378i	0.101651	+	0.994820i	$0.467588\pi$
$90$		0			0
$91$	−70.7551	−	133.057i	−0.777528	−	1.46217i
$92$	−9.66528			−0.105057
$93$		0			0
$94$	8.81655	+	5.09024i	0.0937931	+	0.0541515i
$95$	−3.50621	+	6.07294i	−0.0369075	+	0.0639256i
$96$		0			0
$97$			73.7985i			0.760809i	0.924820	+	0.380405i	$0.124215\pi$
$97$			73.7985i			0.760809i	−0.924820	+	0.380405i	$0.875785\pi$
$98$	123.201	+	8.60469i	1.25715	+	0.0878030i
$99$		0			0
$100$	5.88139	+	10.1869i	0.0588139	+	0.101869i
$101$	92.6245	+	53.4768i	0.917075	+	0.529473i	0.882701	−	0.469936i	$-0.155723\pi$
$101$	92.6245	+	53.4768i	0.917075	+	0.529473i	0.0343741	+	0.999409i	$0.489056\pi$
$102$		0			0
$103$	18.6535	−	10.7696i	0.181102	−	0.104559i	−0.406708	−	0.913558i	$-0.633323\pi$
$103$	18.6535	−	10.7696i	0.181102	−	0.104559i	0.587810	+	0.808999i	$0.299990\pi$
$104$			89.3925i			0.859543i
$105$		0			0
$106$	11.2206			0.105855
$107$	44.8184	+	77.6277i	0.418863	+	0.725492i	0.995825	−	0.0912785i	$-0.0290953\pi$
$107$	44.8184	+	77.6277i	0.418863	+	0.725492i	−0.576962	+	0.816771i	$0.695762\pi$
$108$		0			0
$109$	−13.6751	+	23.6859i	−0.125459	+	0.217302i	−0.921912	−	0.387398i	$-0.873374\pi$
$109$	−13.6751	+	23.6859i	−0.125459	+	0.217302i	0.796453	+	0.604700i	$0.206707\pi$
$110$	−42.5640	+	24.5743i	−0.386945	+	0.223403i
$111$		0			0
$112$	−117.992	−	73.7227i	−1.05350	−	0.658238i
$113$	92.3372			0.817144			0.408572	−	0.912726i	$-0.366027\pi$
$113$	92.3372			0.817144			0.408572	+	0.912726i	$0.366027\pi$
$114$		0			0
$115$	7.95591	+	4.59335i	0.0691818	+	0.0399422i
$116$	−59.8235	+	103.617i	−0.515720	+	0.893253i
$117$		0			0
$118$		−	237.202i		−	2.01019i
$119$	−151.755	−	5.29305i	−1.27525	−	0.0444794i
$120$		0			0
$121$	22.4745	+	38.9270i	0.185740	+	0.321711i
$122$	−159.740	−	92.2258i	−1.30934	−	0.755949i
$123$		0			0
$124$	79.8019	−	46.0736i	0.643563	−	0.371562i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	191.591			1.50859			0.754297	−	0.656534i	$-0.227978\pi$
$127$	191.591			1.50859			0.754297	+	0.656534i	$0.227978\pi$
$128$	60.8015	+	105.311i	0.475011	+	0.822744i
$129$		0			0
$130$	−60.6660	+	105.077i	−0.466661	+	0.808281i
$131$	−50.9329	+	29.4062i	−0.388801	+	0.224474i	−0.681641	−	0.731687i	$-0.738733\pi$
$131$	−50.9329	+	29.4062i	−0.388801	+	0.224474i	0.292839	+	0.956162i	$0.405400\pi$
$132$		0			0
$133$	11.6322	−	18.6171i	0.0874601	−	0.139978i
$134$	253.384			1.89093
$135$		0			0
$136$	78.0054	+	45.0364i	0.573569	+	0.331150i
$137$	82.9571	−	143.686i	0.605526	−	1.04880i	−0.386442	−	0.922314i	$-0.626296\pi$
$137$	82.9571	−	143.686i	0.605526	−	1.04880i	0.991968	−	0.126488i	$-0.0403706\pi$
$138$		0			0
$139$		−	139.625i		−	1.00449i	−0.864724	−	0.502247i	$-0.832507\pi$
$139$		−	139.625i		−	1.00449i	0.864724	−	0.502247i	$-0.167493\pi$
$140$	−17.2889	−	32.5123i	−0.123492	−	0.232231i
$141$		0			0
$142$	71.4510	+	123.757i	0.503176	+	0.871527i
$143$	−162.592	−	93.8725i	−1.13701	−	0.656451i
$144$		0			0
$145$	98.4867	−	56.8613i	0.679219	−	0.392147i
$146$			188.602i			1.29180i
$147$		0			0
$148$	124.641			0.842171
$149$	−7.16861	−	12.4164i	−0.0481115	−	0.0833315i	0.840967	−	0.541087i	$-0.181987\pi$
$149$	−7.16861	−	12.4164i	−0.0481115	−	0.0833315i	−0.889078	+	0.457755i	$0.848654\pi$
$150$		0			0
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414925\pi$
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	−0.967328	+	0.253529i	$0.918409\pi$
$152$	−11.2771	+	6.51085i	−0.0741917	+	0.0428346i
$153$		0			0
$154$	135.847	−	72.2384i	0.882123	−	0.469080i
$155$	−87.5845			−0.565062
$156$		0			0
$157$	−210.373	−	121.459i	−1.33996	−	0.773624i	−0.353156	−	0.935565i	$-0.614891\pi$
$157$	−210.373	−	121.459i	−1.33996	−	0.773624i	−0.986801	+	0.161941i	$0.948225\pi$
$158$	36.5218	−	63.2577i	0.231151	−	0.400365i
$159$		0			0
$160$			74.8775i			0.467984i
$161$	−24.3896	−	15.2389i	−0.151488	−	0.0946514i
$162$		0			0
$163$	−6.61728	−	11.4615i	−0.0405968	−	0.0703157i	0.845013	−	0.534746i	$-0.179593\pi$
$163$	−6.61728	−	11.4615i	−0.0405968	−	0.0703157i	−0.885610	+	0.464430i	$0.846259\pi$
$164$	75.0001	+	43.3013i	0.457318	+	0.264032i
$165$		0			0
$166$	46.0815	−	26.6052i	0.277600	−	0.160272i
$167$		−	212.616i		−	1.27315i	−0.771216	−	0.636574i	$-0.780351\pi$
$167$		−	212.616i		−	1.27315i	0.771216	−	0.636574i	$-0.219649\pi$
$168$		0			0
$169$	−294.481			−1.74249
$170$	61.1277	+	105.876i	0.359575	+	0.622802i
$171$		0			0
$172$	−20.7618	+	35.9605i	−0.120708	+	0.209073i
$173$	215.456	−	124.393i	1.24541	−	0.719037i	0.275219	−	0.961382i	$-0.411250\pi$
$173$	215.456	−	124.393i	1.24541	−	0.719037i	0.970190	+	0.242345i	$0.0779164\pi$
$174$		0			0
$175$	−1.22002	+	34.9787i	−0.00697155	+	0.199878i
$176$	−173.330			−0.984832
$177$		0			0
$178$	−159.056	−	91.8308i	−0.893571	−	0.515903i
$179$	27.6352	−	47.8655i	0.154386	−	0.267405i	−0.778449	−	0.627708i	$-0.783993\pi$
$179$	27.6352	−	47.8655i	0.154386	−	0.267405i	0.932835	+	0.360303i	$0.117327\pi$
$180$		0			0
$181$			46.9001i			0.259117i	0.991572	+	0.129558i	$0.0413559\pi$
$181$			46.9001i			0.259117i	−0.991572	+	0.129558i	$0.958644\pi$
$182$	201.265	−	322.122i	1.10585	−	1.76990i
$183$		0			0
$184$	8.52961	+	14.7737i	0.0463566	+	0.0802920i
$185$	−102.598	−	59.2348i	−0.554582	−	0.320188i
$186$		0			0
$187$	−163.829	+	94.5869i	−0.876093	+	0.505812i
$188$			9.50241i			0.0505447i
$189$		0			0
$190$	−17.6743			−0.0930226
$191$	−10.0561	−	17.4177i	−0.0526499	−	0.0911923i	0.838499	−	0.544903i	$-0.183433\pi$
$191$	−10.0561	−	17.4177i	−0.0526499	−	0.0911923i	−0.891149	+	0.453710i	$0.850100\pi$
$192$		0			0
$193$	−14.3516	+	24.8578i	−0.0743609	+	0.128797i	−0.900808	−	0.434217i	$-0.857025\pi$
$193$	−14.3516	+	24.8578i	−0.0743609	+	0.128797i	0.826447	+	0.563014i	$0.190358\pi$
$194$	−161.084	+	93.0019i	−0.830330	+	0.479391i
$195$		0			0
$196$	50.5420	+	103.604i	0.257867	+	0.528594i
$197$	−224.436			−1.13927			−0.569636	−	0.821897i	$-0.692916\pi$
$197$	−224.436			−1.13927			−0.569636	+	0.821897i	$0.692916\pi$
$198$		0			0
$199$	−275.447	−	159.030i	−1.38416	−	0.799144i	−0.391509	−	0.920174i	$-0.628047\pi$
$199$	−275.447	−	159.030i	−1.38416	−	0.799144i	−0.992649	+	0.121030i	$0.961380\pi$
$200$	10.3807	−	17.9798i	0.0519033	−	0.0898992i
$201$		0			0
$202$			269.569i			1.33450i
$203$	−314.330	+	167.149i	−1.54842	+	0.823393i
$204$		0			0
$205$	−41.1572	−	71.2864i	−0.200767	−	0.347739i
$206$	47.0148	+	27.1440i	0.228227	+	0.131767i
$207$		0			0
$208$	−370.569	+	213.948i	−1.78158	+	1.02860i
$209$		−	27.3486i		−	0.130855i
$210$		0			0
$211$	285.317			1.35221			0.676107	−	0.736804i	$-0.263666\pi$
$211$	285.317			1.35221			0.676107	+	0.736804i	$0.263666\pi$
$212$	5.23662	+	9.07009i	0.0247010	+	0.0427835i
$213$		0			0
$214$	−112.961	+	195.655i	−0.527857	+	0.914276i
$215$	34.1799	−	19.7338i	0.158976	−	0.0917851i
$216$		0			0
$217$	274.016	+	9.55740i	1.26275	+	0.0440433i
$218$	−68.9341			−0.316211
$219$		0			0
$220$	−39.7290	−	22.9376i	−0.180586	−	0.104262i
$221$	−233.504	+	404.441i	−1.05658	+	1.83005i
$222$		0			0
$223$			57.0977i			0.256044i	0.991771	+	0.128022i	$0.0408627\pi$
$223$			57.0977i			0.256044i	−0.991771	+	0.128022i	$0.959137\pi$
$224$	8.17078	−	234.261i	0.0364767	−	1.04581i
$225$		0			0
$226$	116.365	+	201.549i	0.514888	+	0.891812i
$227$	158.185	+	91.3279i	0.696848	+	0.402325i	0.806172	−	0.591681i	$-0.201535\pi$
$227$	158.185	+	91.3279i	0.696848	+	0.402325i	−0.109324	+	0.994006i	$0.534869\pi$
$228$		0			0
$229$	−14.5347	+	8.39159i	−0.0634702	+	0.0366445i	−0.531399	−	0.847121i	$-0.678334\pi$
$229$	−14.5347	+	8.39159i	−0.0634702	+	0.0366445i	0.467929	+	0.883766i	$0.345000\pi$
$230$			23.1544i			0.100671i
$231$		0			0
$232$	211.177			0.910246
$233$	−133.203	−	230.715i	−0.571688	−	0.990193i	−0.996393	−	0.0848612i	$-0.972955\pi$
$233$	−133.203	−	230.715i	−0.571688	−	0.990193i	0.424704	−	0.905332i	$-0.360378\pi$
$234$		0			0
$235$	4.51595	−	7.82185i	0.0192168	−	0.0332845i
$236$	191.741	−	110.702i	0.812461	−	0.469075i
$237$		0			0
$238$	−179.690	−	337.914i	−0.755001	−	1.41981i
$239$	39.7012			0.166114			0.0830568	−	0.996545i	$-0.473532\pi$
$239$	39.7012			0.166114			0.0830568	+	0.996545i	$0.473532\pi$
$240$		0			0
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	0.642237	−	0.766506i	$-0.278006\pi$
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	−0.342695	+	0.939447i	$0.611340\pi$
$242$	−56.6454	+	98.1128i	−0.234072	+	0.405425i
$243$		0			0
$244$		−	172.166i		−	0.705600i
$245$	7.63390	−	109.301i	0.0311588	−	0.446127i
$246$		0			0
$247$	−33.7574	−	58.4695i	−0.136670	−	0.236719i
$248$	−140.850	−	81.3200i	−0.567945	−	0.327903i
$249$		0			0
$250$	24.4039	−	14.0896i	0.0976157	−	0.0563585i
$251$			111.464i			0.444079i	0.975038	+	0.222039i	$0.0712713\pi$
$251$			111.464i			0.444079i	−0.975038	+	0.222039i	$0.928729\pi$
$252$		0			0
$253$	−35.8283			−0.141614
$254$	241.446	+	418.197i	0.950575	+	1.64644i
$255$		0			0
$256$	−163.039	+	282.392i	−0.636872	+	1.10309i
$257$	193.043	−	111.454i	0.751141	−	0.433672i	−0.0749649	−	0.997186i	$-0.523884\pi$
$257$	193.043	−	111.454i	0.751141	−	0.433672i	0.826106	+	0.563515i	$0.190551\pi$
$258$		0			0
$259$	314.522	+	196.517i	1.21437	+	0.758754i
$260$	−113.251			−0.435580
$261$		0			0
$262$	−128.373	−	74.1161i	−0.489973	−	0.282886i
$263$	−213.250	+	369.360i	−0.810837	+	1.40441i	0.101442	+	0.994841i	$0.467654\pi$
$263$	−213.250	+	369.360i	−0.810837	+	1.40441i	−0.912279	+	0.409569i	$0.865679\pi$
$264$		0			0
$265$		−	9.95465i		−	0.0375647i
$266$	55.2957	+	1.92865i	0.207879	+	0.00725058i
$267$		0			0
$268$	118.254	+	204.822i	0.441246	+	0.764260i
$269$	51.5210	+	29.7457i	0.191528	+	0.110579i	0.592698	−	0.805425i	$-0.298063\pi$
$269$	51.5210	+	29.7457i	0.191528	+	0.110579i	−0.401170	+	0.916004i	$0.631396\pi$
$270$		0			0
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	−0.584519	−	0.811380i	$-0.698717\pi$
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	0.410416	+	0.911898i	$0.365383\pi$
$272$			431.153i			1.58512i
$273$		0			0
$274$	418.175			1.52618
$275$	21.8018	+	37.7618i	0.0792793	+	0.137316i
$276$		0			0
$277$	236.189	−	409.092i	0.852669	−	1.47687i	−0.0261222	−	0.999659i	$-0.508316\pi$
$277$	236.189	−	409.092i	0.852669	−	1.47687i	0.878791	−	0.477207i	$-0.158351\pi$
$278$	304.766	−	175.957i	1.09628	−	0.632939i
$279$		0			0
$280$	−34.4389	+	55.1188i	−0.122996	+	0.196853i
$281$	534.544			1.90229			0.951146	−	0.308743i	$-0.0999082\pi$
$281$	534.544			1.90229			0.951146	+	0.308743i	$0.0999082\pi$
$282$		0			0
$283$	−387.352	−	223.638i	−1.36873	−	0.790239i	−0.377967	−	0.925819i	$-0.623377\pi$
$283$	−387.352	−	223.638i	−1.36873	−	0.790239i	−0.990766	+	0.135580i	$0.956710\pi$
$284$	−66.6921	+	115.514i	−0.234831	+	0.406740i
$285$		0			0
$286$		−	473.198i		−	1.65454i
$287$	120.985	+	227.517i	0.421552	+	0.792743i
$288$		0			0
$289$	90.7814	+	157.238i	0.314122	+	0.544076i
$290$	248.229	+	143.315i	0.855961	+	0.494189i
$291$		0			0
$292$	−152.456	+	88.0202i	−0.522108	+	0.301439i
$293$			504.200i			1.72082i	0.509604	+	0.860409i	$0.329792\pi$
$293$			504.200i			1.72082i	−0.509604	+	0.860409i	$0.670208\pi$
$294$		0			0
$295$	−210.440			−0.713357
$296$	−109.996	−	190.519i	−0.371608	−	0.643644i
$297$		0			0
$298$	18.0680	−	31.2946i	0.0606308	−	0.105016i
$299$	−76.5986	+	44.2242i	−0.256183	+	0.147907i
$300$		0			0
$301$	−109.088	+	58.0092i	−0.362420	+	0.192722i
$302$	−535.274			−1.77243
$303$		0			0
$304$	−53.9804	−	31.1656i	−0.177567	−	0.102518i
$305$	−81.8207	+	141.718i	−0.268265	+	0.464648i
$306$		0			0
$307$			398.792i			1.29900i	0.760363	+	0.649499i	$0.225021\pi$
$307$			398.792i			1.29900i	−0.760363	+	0.649499i	$0.774979\pi$
$308$	121.793	+	76.0976i	0.395432	+	0.247070i
$309$		0			0
$310$	−110.375	−	191.176i	−0.356049	−	0.616695i
$311$	207.085	+	119.561i	0.665869	+	0.384440i	0.794510	−	0.607252i	$-0.207728\pi$
$311$	207.085	+	119.561i	0.665869	+	0.384440i	−0.128640	+	0.991691i	$0.541061\pi$
$312$		0			0
$313$	193.296	−	111.599i	0.617559	−	0.356548i	−0.158359	−	0.987382i	$-0.550620\pi$
$313$	193.296	−	111.599i	0.617559	−	0.356548i	0.775918	+	0.630834i	$0.217287\pi$
$314$		−	612.257i		−	1.94986i
$315$		0			0
$316$	68.1786			0.215755
$317$	−143.007	−	247.695i	−0.451126	−	0.781373i	0.547330	−	0.836917i	$-0.315644\pi$
$317$	−143.007	−	247.695i	−0.451126	−	0.781373i	−0.998456	+	0.0555434i	$0.982311\pi$
$318$		0			0
$319$	−221.761	+	384.100i	−0.695174	+	1.20408i
$320$	−9.48256	+	5.47476i	−0.0296330	+	0.0171086i
$321$		0			0
$322$	2.52665	−	72.4407i	0.00784675	−	0.224971i
$323$	−68.0286			−0.210615
$324$		0			0
$325$	93.2216	+	53.8215i	0.286836	+	0.165605i
$326$	16.6784	−	28.8878i	0.0511607	−	0.0886129i
$327$		0			0
$328$		−	152.854i		−	0.466018i
$329$	−14.9821	+	23.9786i	−0.0455383	+	0.0728833i
$330$		0			0
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	−0.909875	−	0.414882i	$-0.863823\pi$
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	0.0956391	−	0.995416i	$-0.469511\pi$
$332$	43.0123	+	24.8332i	0.129555	+	0.0747987i
$333$		0			0
$334$	464.088	−	267.941i	1.38948	−	0.802219i
$335$		−	224.797i		−	0.671036i
$336$		0			0
$337$	68.2484			0.202518			0.101259	−	0.994860i	$-0.467713\pi$
$337$	68.2484			0.202518			0.101259	+	0.994860i	$0.467713\pi$
$338$	−371.109	−	642.780i	−1.09796	−	1.90172i
$339$		0			0
$340$	−57.0563	+	98.8244i	−0.167813	+	0.290660i
$341$	295.819	−	170.791i	0.867503	−	0.500853i
$342$		0			0
$343$	−35.8105	+	341.126i	−0.104404	+	0.994535i
$344$	73.2893			0.213050
$345$		0			0
$346$	543.041	+	313.525i	1.56948	+	0.906141i
$347$	190.947	−	330.731i	0.550281	−	0.953114i	−0.447973	−	0.894047i	$-0.647854\pi$
$347$	190.947	−	330.731i	0.550281	−	0.953114i	0.998254	−	0.0590672i	$-0.0188126\pi$
$348$		0			0
$349$			301.869i			0.864953i	0.901645	+	0.432477i	$0.142360\pi$
$349$			301.869i			0.864953i	−0.901645	+	0.432477i	$0.857640\pi$
$350$	−77.8875	+	41.4177i	−0.222536	+	0.118336i
$351$		0			0
$352$	−146.012	−	252.900i	−0.414807	−	0.718466i
$353$	−110.891	−	64.0227i	−0.314138	−	0.181367i	0.334639	−	0.942346i	$-0.391386\pi$
$353$	−110.891	−	64.0227i	−0.314138	−	0.181367i	−0.648776	+	0.760979i	$0.724719\pi$
$354$		0			0
$355$	109.794	−	63.3898i	0.309280	−	0.178563i
$356$		−	171.429i		−	0.481542i
$357$		0			0
$358$	139.305			0.389120
$359$	−262.113	−	453.993i	−0.730119	−	1.26460i	−0.956832	−	0.290642i	$-0.906131\pi$
$359$	−262.113	−	453.993i	−0.730119	−	1.26460i	0.226713	−	0.973962i	$-0.427202\pi$
$360$		0			0
$361$	−175.583	+	304.118i	−0.486378	+	0.842432i
$362$	−102.371	+	59.1041i	−0.282794	+	0.163271i
$363$		0			0
$364$	354.315	+	12.3581i	0.973394	+	0.0339509i
$365$	167.324			0.458421
$366$		0			0
$367$	30.8202	+	17.7941i	0.0839789	+	0.0484852i	0.541401	−	0.840764i	$-0.317894\pi$
$367$	30.8202	+	17.7941i	0.0839789	+	0.0484852i	−0.457423	+	0.889249i	$0.651227\pi$
$368$	−40.8288	+	70.7176i	−0.110948	+	0.192167i
$369$		0			0
$370$		−	298.594i		−	0.807011i
$371$	−1.08627	+	31.1441i	−0.00292796	+	0.0839462i
$372$		0			0
$373$	133.546	+	231.308i	0.358031	+	0.620128i	0.987632	−	0.156791i	$-0.0501148\pi$
$373$	133.546	+	231.308i	0.358031	+	0.620128i	−0.629601	+	0.776919i	$0.716781\pi$
$374$	−412.920	−	238.399i	−1.10406	−	0.637432i
$375$		0			0
$376$	14.5248	−	8.38588i	0.0386297	−	0.0223029i
$377$			1094.91i			2.90427i
$378$		0			0
$379$	−125.687			−0.331627			−0.165813	−	0.986157i	$-0.553025\pi$
$379$	−125.687			−0.331627			−0.165813	+	0.986157i	$0.553025\pi$
$380$	−8.24856	−	14.2869i	−0.0217067	−	0.0375972i
$381$		0			0
$382$	25.3457	−	43.9001i	0.0663501	−	0.114922i
$383$	308.755	−	178.260i	0.806149	−	0.465430i	−0.0394677	−	0.999221i	$-0.512566\pi$
$383$	308.755	−	178.260i	0.806149	−	0.465430i	0.845617	+	0.533790i	$0.179233\pi$
$384$		0			0
$385$	−64.0883	−	120.520i	−0.166463	−	0.313040i
$386$	−72.3446			−0.187421
$387$		0			0
$388$	−150.355	−	86.8076i	−0.387513	−	0.223731i
$389$	223.316	−	386.795i	0.574078	−	0.994332i	−0.422064	−	0.906566i	$-0.638694\pi$
$389$	223.316	−	386.795i	0.574078	−	0.994332i	0.996141	−	0.0877654i	$-0.0279726\pi$
$390$		0			0
$391$			89.1216i			0.227933i
$392$	113.760	−	168.686i	0.290204	−	0.430322i
$393$		0			0
$394$	−282.838	−	489.890i	−0.717863	−	1.24337i
$395$	−56.1208	−	32.4014i	−0.142078	−	0.0820288i
$396$		0			0
$397$	525.089	−	303.160i	1.32264	−	0.763627i	0.338492	−	0.940969i	$-0.390083\pi$
$397$	525.089	−	303.160i	1.32264	−	0.763627i	0.984149	+	0.177342i	$0.0567499\pi$
$398$		−	801.645i		−	2.01418i
$399$		0			0
$400$	99.3785			0.248446
$401$	−364.402	−	631.163i	−0.908734	−	1.57397i	−0.815826	−	0.578298i	$-0.803717\pi$
$401$	−364.402	−	631.163i	−0.908734	−	1.57397i	−0.0929080	−	0.995675i	$-0.529616\pi$
$402$		0			0
$403$	421.627	−	730.280i	1.04622	−	1.81211i
$404$	−217.904	+	125.807i	−0.539367	+	0.311404i
$405$		0			0
$406$	−760.967	−	475.461i	−1.87430	−	1.17109i
$407$	462.034			1.13522
$408$		0			0
$409$	−459.563	−	265.329i	−1.12363	−	0.648725i	−0.181301	−	0.983428i	$-0.558031\pi$
$409$	−459.563	−	265.329i	−1.12363	−	0.648725i	−0.942324	+	0.334702i	$0.891364\pi$
$410$	103.734	−	179.672i	0.253009	−	0.438225i
$411$		0			0
$412$			50.6722i			0.122991i
$413$	658.382	+	22.9637i	1.59415	+	0.0556021i
$414$		0			0
$415$	−23.6035	−	40.8825i	−0.0568760	−	0.0985121i
$416$	−624.328	−	360.456i	−1.50079	−	0.866481i
$417$		0			0
$418$	59.6953	−	34.4651i	0.142812	−	0.0824524i
$419$			282.637i			0.674552i	0.941406	+	0.337276i	$0.109506\pi$
$419$			282.637i			0.674552i	−0.941406	+	0.337276i	$0.890494\pi$
$420$		0			0
$421$	440.590			1.04653			0.523267	−	0.852169i	$-0.324713\pi$
$421$	440.590			1.04653			0.523267	+	0.852169i	$0.324713\pi$
$422$	359.560	+	622.777i	0.852039	+	1.47577i
$423$		0			0
$424$	9.24264	−	16.0087i	0.0217987	−	0.0377564i
$425$	93.9311	−	54.2311i	0.221014	−	0.127603i
$426$		0			0
$427$	271.448	−	434.448i	0.635710	−	1.01744i
$428$	−210.875			−0.492700
$429$		0			0
$430$	86.1480	+	49.7376i	0.200344	+	0.115669i
$431$	−63.7174	+	110.362i	−0.147836	+	0.256060i	−0.930427	−	0.366476i	$-0.880564\pi$
$431$	−63.7174	+	110.362i	−0.147836	+	0.256060i	0.782591	+	0.622536i	$0.213897\pi$
$432$		0			0
$433$			433.284i			1.00066i	0.865836	+	0.500328i	$0.166787\pi$
$433$			433.284i			1.00066i	−0.865836	+	0.500328i	$0.833213\pi$
$434$	324.458	+	610.155i	0.747599	+	1.40589i
$435$		0			0
$436$	−32.1714	−	55.7225i	−0.0737876	−	0.127804i
$437$	−11.1580	−	6.44210i	−0.0255333	−	0.0147416i
$438$		0			0
$439$	−54.7578	+	31.6144i	−0.124733	+	0.0720146i	−0.561068	−	0.827770i	$-0.689609\pi$
$439$	−54.7578	+	31.6144i	−0.124733	+	0.0720146i	0.436335	+	0.899784i	$0.356276\pi$
$440$			80.9697i			0.184022i
$441$		0			0
$442$	−1177.06			−2.66303
$443$	219.190	+	379.648i	0.494785	+	0.856992i	0.999982	−	0.00601155i	$-0.00191355\pi$
$443$	219.190	+	379.648i	0.494785	+	0.856992i	−0.505197	+	0.863004i	$0.668580\pi$
$444$		0			0
$445$	−81.4703	+	141.111i	−0.183079	+	0.317103i
$446$	−124.630	+	71.9553i	−0.279440	+	0.161335i
$447$		0			0
$448$	30.2645	−	16.0935i	0.0675547	−	0.0359231i
$449$	−214.986			−0.478810			−0.239405	−	0.970920i	$-0.576952\pi$
$449$	−214.986			−0.478810			−0.239405	+	0.970920i	$0.576952\pi$
$450$		0			0
$451$	278.019	+	160.514i	0.616450	+	0.355907i
$452$	−108.614	+	188.125i	−0.240297	+	0.416207i
$453$		0			0
$454$			460.371i			1.01403i
$455$	−285.779	−	178.558i	−0.628087	−	0.392436i
$456$		0			0
$457$	120.600	+	208.885i	0.263894	+	0.457078i	0.967273	−	0.253737i	$-0.0816597\pi$
$457$	120.600	+	208.885i	0.263894	+	0.457078i	−0.703379	+	0.710815i	$0.748326\pi$
$458$	−36.6336	−	21.1504i	−0.0799860	−	0.0461799i
$459$		0			0
$460$	−18.7167	+	10.8061i	−0.0406885	+	0.0234915i
$461$		−	343.383i		−	0.744865i	−0.928059	−	0.372432i	$-0.878524\pi$
$461$		−	343.383i		−	0.744865i	0.928059	−	0.372432i	$-0.121476\pi$
$462$		0			0
$463$	74.7714			0.161493			0.0807467	−	0.996735i	$-0.474270\pi$
$463$	74.7714			0.161493			0.0807467	+	0.996735i	$0.474270\pi$
$464$	505.422	+	875.417i	1.08927	+	1.88667i
$465$		0			0
$466$	335.730	−	581.501i	0.720450	−	1.24786i
$467$	308.470	−	178.095i	0.660535	−	0.381360i	−0.131946	−	0.991257i	$-0.542122\pi$
$467$	308.470	−	178.095i	0.660535	−	0.381360i	0.792481	+	0.609897i	$0.208789\pi$
$468$		0			0
$469$	−24.5303	+	703.298i	−0.0523034	+	1.49957i
$470$	22.7642			0.0484345
$471$		0			0
$472$	−338.423	−	195.389i	−0.716998	−	0.413959i
$473$	−76.9623	+	133.303i	−0.162711	+	0.281824i
$474$		0			0
$475$			15.6803i			0.0330111i
$476$	189.290	−	302.955i	0.397668	−	0.636461i
$477$		0			0
$478$	50.0319	+	86.6579i	0.104669	+	0.181293i
$479$	−323.678	−	186.876i	−0.675737	−	0.390137i	0.122510	−	0.992467i	$-0.460906\pi$
$479$	−323.678	−	186.876i	−0.675737	−	0.390137i	−0.798247	+	0.602330i	$0.794239\pi$
$480$		0			0
$481$	987.799	−	570.306i	2.05364	−	1.18567i
$482$			210.096i			0.435884i
$483$		0			0
$484$	−105.745			−0.218482
$485$	82.5093	+	142.910i	0.170122	+	0.294660i
$486$		0			0
$487$	−388.781	+	673.389i	−0.798319	+	1.38273i	0.122391	+	0.992482i	$0.460944\pi$
$487$	−388.781	+	673.389i	−0.798319	+	1.38273i	−0.920710	+	0.390247i	$0.872390\pi$
$488$	−263.162	+	151.937i	−0.539267	+	0.311346i
$489$		0			0
$490$	248.198	−	121.080i	0.506526	−	0.247102i
$491$	−458.794			−0.934407			−0.467203	−	0.884150i	$-0.654738\pi$
$491$	−458.794			−0.934407			−0.467203	+	0.884150i	$0.654738\pi$
$492$		0			0
$493$	955.435	+	551.621i	1.93800	+	1.11891i
$494$	85.0831	−	147.368i	0.172233	−	0.298316i
$495$		0			0
$496$		−	778.511i		−	1.56958i
$497$	−350.419	+	186.340i	−0.705068	+	0.374929i
$498$		0			0
$499$	−317.772	−	550.396i	−0.636817	−	1.10300i	−0.986127	−	0.165992i	$-0.946917\pi$
$499$	−317.772	−	550.396i	−0.636817	−	1.10300i	0.349310	−	0.937007i	$-0.386416\pi$
$500$	22.7785	+	13.1512i	0.0455570	+	0.0263024i
$501$		0			0
$502$	−243.298	+	140.468i	−0.484657	+	0.279817i
$503$			10.6561i			0.0211852i	0.999944	+	0.0105926i	$0.00337179\pi$
$503$			10.6561i			0.0211852i	−0.999944	+	0.0105926i	$0.996628\pi$
$504$		0			0
$505$	239.156			0.473575
$506$	−45.1514	−	78.2045i	−0.0892319	−	0.154554i
$507$		0			0
$508$	−225.365	+	390.343i	−0.443631	+	0.768392i
$509$	−706.084	+	407.658i	−1.38720	+	0.800899i	−0.992999	−	0.118126i	$-0.962311\pi$
$509$	−706.084	+	407.658i	−1.38720	+	0.800899i	−0.394200	+	0.919025i	$0.628978\pi$
$510$		0			0
$511$	−523.488	−	18.2587i	−1.02444	−	0.0357313i
$512$	−335.445			−0.655167
$513$		0			0
$514$	486.552	+	280.911i	0.946599	+	0.546519i
$515$	24.0816	−	41.7105i	0.0467604	−	0.0809913i
$516$		0			0
$517$			35.2246i			0.0681327i
$518$	−32.5832	+	934.179i	−0.0629019	+	1.80343i
$519$		0			0
$520$	99.9438	+	173.108i	0.192200	+	0.332900i
$521$	383.930	+	221.662i	0.736911	+	0.425456i	0.820945	−	0.571007i	$-0.193447\pi$
$521$	383.930	+	221.662i	0.736911	+	0.425456i	−0.0840344	+	0.996463i	$0.526781\pi$
$522$		0			0
$523$	−549.148	+	317.051i	−1.05000	+	0.606216i	−0.922648	−	0.385642i	$-0.873980\pi$
$523$	−549.148	+	317.051i	−1.05000	+	0.606216i	−0.127348	+	0.991858i	$0.540646\pi$
$524$		−	138.359i		−	0.264044i
$525$		0			0
$526$	−1074.96			−2.04366
$527$	−424.836	−	735.837i	−0.806140	−	1.39628i
$528$		0			0
$529$	256.060	−	443.510i	0.484046	−	0.838393i
$530$	21.7286	−	12.5450i	0.0409973	−	0.0236698i
$531$		0			0
$532$	24.2474	+	45.5980i	0.0455777	+	0.0857106i
$533$	792.515			1.48689
$534$		0			0
$535$	173.581	+	100.217i	0.324450	+	0.187321i
$536$	208.718	−	361.511i	0.389400	−	0.674460i
$537$		0			0
$538$			149.944i			0.278706i
$539$	187.355	+	384.053i	0.347597	+	0.712528i
$540$		0			0
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	0.935542	−	0.353217i	$-0.114912\pi$
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	−0.773665	+	0.633594i	$0.781579\pi$
$542$	−118.919	−	68.6577i	−0.219407	−	0.126675i
$543$		0			0
$544$	−629.079	+	363.199i	−1.15640	+	0.667646i
$545$			61.1568i			0.112214i
$546$		0			0
$547$	−773.543			−1.41416			−0.707078	−	0.707136i	$-0.749987\pi$
$547$	−773.543			−1.41416			−0.707078	+	0.707136i	$0.749987\pi$
$548$	195.161	+	338.029i	0.356133	+	0.616841i
$549$		0			0
$550$	−54.9499	+	95.1759i	−0.0999088	+	0.173047i
$551$	−138.126	+	79.7471i	−0.250682	+	0.144732i
$552$		0			0
$553$	172.043	+	107.495i	0.311109	+	0.194385i
$554$	1190.60			2.14909
$555$		0			0
$556$	284.468	+	164.237i	0.511632	+	0.295391i
$557$	−378.264	+	655.173i	−0.679110	+	1.17625i	0.296140	+	0.955145i	$0.404301\pi$
$557$	−378.264	+	655.173i	−0.679110	+	1.17625i	−0.975249	+	0.221108i	$0.929033\pi$
$558$		0			0
$559$			379.989i			0.679766i
$560$	−310.915	−	10.8444i	−0.555205	−	0.0193650i
$561$		0			0
$562$	673.639	+	1166.78i	1.19865	+	2.07612i
$563$	451.185	+	260.492i	0.801394	+	0.462685i	0.843958	−	0.536409i	$-0.180219\pi$
$563$	451.185	+	260.492i	0.801394	+	0.462685i	−0.0425646	+	0.999094i	$0.513553\pi$
$564$		0			0
$565$	178.810	−	103.236i	0.316478	−	0.182719i
$566$		−	1127.32i		−	1.99174i
$567$		0			0
$568$	235.423			0.414477
$569$	−91.5332	−	158.540i	−0.160867	−	0.278629i	0.774313	−	0.632803i	$-0.218096\pi$
$569$	−91.5332	−	158.540i	−0.160867	−	0.278629i	−0.935180	+	0.354173i	$0.884762\pi$
$570$		0			0
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.0152618	+	0.999884i	$0.504858\pi$
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.858294	+	0.513159i	$0.828475\pi$
$572$	382.507	−	220.840i	0.668718	−	0.386084i
$573$		0			0
$574$	−344.147	+	550.802i	−0.599560	+	0.959585i
$575$	20.5421			0.0357254
$576$		0			0
$577$	279.135	+	161.158i	0.483769	+	0.279304i	0.721986	−	0.691908i	$-0.243230\pi$
$577$	279.135	+	161.158i	0.483769	+	0.279304i	−0.238217	+	0.971212i	$0.576563\pi$
$578$	−228.808	+	396.307i	−0.395861	+	0.685652i
$579$		0			0
$580$			267.539i			0.461274i
$581$	69.3847	+	130.480i	0.119423	+	0.224579i
$582$		0			0
$583$	19.4117	+	33.6220i	0.0332962	+	0.0576707i
$584$	269.084	+	155.356i	0.460761	+	0.266020i
$585$		0			0
$586$	−1100.54	+	635.400i	−1.87806	+	1.08430i
$587$			406.391i			0.692318i	0.938176	+	0.346159i	$0.112514\pi$
$587$			406.391i			0.692318i	−0.938176	+	0.346159i	$0.887486\pi$
$588$		0			0
$589$	122.836			0.208550
$590$	−265.200	−	459.340i	−0.449491	−	0.778542i
$591$		0			0
$592$	526.519	−	911.958i	0.889391	−	1.54047i
$593$	−333.688	+	192.655i	−0.562711	+	0.324881i	−0.754233	−	0.656607i	$-0.771991\pi$
$593$	−333.688	+	192.655i	−0.562711	+	0.324881i	0.191522	+	0.981488i	$0.438658\pi$
$594$		0			0
$595$	−299.790	+	159.417i	−0.503849	+	0.267928i
$596$	33.7291			0.0565925
$597$		0			0
$598$	−193.061	−	111.464i	−0.322845	−	0.186395i
$599$	−448.272	+	776.430i	−0.748367	+	1.29621i	0.200238	+	0.979747i	$0.435829\pi$
$599$	−448.272	+	776.430i	−0.748367	+	1.29621i	−0.948605	+	0.316463i	$0.897505\pi$
$600$		0			0
$601$		−	599.296i		−	0.997166i	−0.866842	−	0.498583i	$-0.833854\pi$
$601$		−	599.296i		−	0.997166i	0.866842	−	0.498583i	$-0.166146\pi$
$602$	−264.095	−	165.009i	−0.438695	−	0.274102i
$603$		0			0
$604$	−249.811	−	432.686i	−0.413595	−	0.716367i
$605$	87.0435	+	50.2546i	0.143874	+	0.0830654i
$606$		0			0
$607$	−426.925	+	246.485i	−0.703336	+	0.406071i	−0.808589	−	0.588374i	$-0.799768\pi$
$607$	−426.925	+	246.485i	−0.703336	+	0.406071i	0.105253	+	0.994445i	$0.466435\pi$
$608$		−	105.014i		−	0.172721i
$609$		0			0
$610$	−412.446			−0.676142
$611$	43.4790	+	75.3079i	0.0711604	+	0.123253i
$612$		0			0
$613$	70.4822	−	122.079i	0.114979	−	0.199150i	−0.802792	−	0.596259i	$-0.796653\pi$
$613$	70.4822	−	122.079i	0.114979	−	0.199150i	0.917771	+	0.397109i	$0.129987\pi$
$614$	−870.465	+	502.563i	−1.41770	+	0.818507i
$615$		0			0
$616$	8.83557	−	253.321i	0.0143435	−	0.411236i
$617$	−61.9853			−0.100462			−0.0502312	−	0.998738i	$-0.515996\pi$
$617$	−61.9853			−0.100462			−0.0502312	+	0.998738i	$0.515996\pi$
$618$		0			0
$619$	−549.456	−	317.228i	−0.887651	−	0.512485i	−0.0144774	−	0.999895i	$-0.504608\pi$
$619$	−549.456	−	317.228i	−0.887651	−	0.512485i	−0.873173	+	0.487410i	$0.837942\pi$
$620$	103.024	−	178.442i	0.166167	−	0.287810i
$621$		0			0
$622$			602.689i			0.968953i
$623$	270.286	−	432.588i	0.433845	−	0.694362i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	487.188	+	281.278i	0.778256	+	0.449326i
$627$		0			0
$628$	494.914	−	285.739i	0.788080	−	0.454998i
$629$		−	1149.29i		−	1.82717i
$630$		0			0
$631$	93.3216			0.147895			0.0739474	−	0.997262i	$-0.476440\pi$
$631$	93.3216			0.147895			0.0739474	+	0.997262i	$0.476440\pi$
$632$	−60.1677	−	104.213i	−0.0952020	−	0.164895i
$633$		0			0
$634$	360.439	−	624.298i	0.568515	−	0.984698i
$635$	371.015	−	214.206i	0.584276	−	0.337332i
$636$		0			0
$637$	874.603	+	589.821i	1.37300	+	0.925935i
$638$	−1117.86			−1.75214
$639$		0			0
$640$	235.483	+	135.956i	0.367942	+	0.212432i
$641$	153.961	−	266.668i	0.240188	−	0.416018i	−0.720579	−	0.693372i	$-0.756124\pi$
$641$	153.961	−	266.668i	0.240188	−	0.416018i	0.960768	+	0.277354i	$0.0894575\pi$
$642$		0			0
$643$			296.519i			0.461150i	0.973055	+	0.230575i	$0.0740607\pi$
$643$			296.519i			0.461150i	−0.973055	+	0.230575i	$0.925939\pi$
$644$	59.7362	−	31.7655i	0.0927581	−	0.0493253i
$645$		0			0
$646$	−85.7306	−	148.490i	−0.132710	−	0.229860i
$647$	−203.727	−	117.622i	−0.314880	−	0.181796i	0.334228	−	0.942492i	$-0.391524\pi$
$647$	−203.727	−	117.622i	−0.314880	−	0.181796i	−0.649108	+	0.760696i	$0.724858\pi$
$648$		0			0
$649$	710.767	−	410.361i	1.09517	−	0.632298i
$650$			271.307i			0.417395i
$651$		0			0
$652$	31.1350			0.0477531
$653$	148.823	+	257.769i	0.227906	+	0.394746i	0.957187	−	0.289469i	$-0.0934786\pi$
$653$	148.823	+	257.769i	0.227906	+	0.394746i	−0.729281	+	0.684214i	$0.760145\pi$
$654$		0			0
$655$	−65.7542	+	113.890i	−0.100388	+	0.173877i
$656$	633.643	−	365.834i	0.965919	−	0.557673i
$657$		0			0
$658$	−71.2200	−	2.48408i	−0.108237	−	0.00377519i
$659$	127.740			0.193839			0.0969197	−	0.995292i	$-0.469101\pi$
$659$	127.740			0.193839			0.0969197	+	0.995292i	$0.469101\pi$
$660$		0			0
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.275696	−	0.961245i	$-0.588908\pi$
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.970311	+	0.241863i	$0.922242\pi$
$662$	679.286	−	1176.56i	1.02611	−	1.77728i
$663$		0			0
$664$		−	87.6611i		−	0.132020i
$665$	1.71106	−	49.0571i	0.00257302	−	0.0737701i
$666$		0			0
$667$	104.474	+	180.953i	0.156632	+	0.271295i
$668$	433.178	+	250.095i	0.648469	+	0.374394i
$669$		0			0
$670$	490.677	−	283.292i	0.732353	−	0.422824i
$671$		−	638.206i		−	0.951126i
$672$		0			0
$673$	−1003.39			−1.49092			−0.745460	−	0.666550i	$-0.767770\pi$
$673$	−1003.39			−1.49092			−0.745460	+	0.666550i	$0.767770\pi$
$674$	86.0076	+	148.970i	0.127608	+	0.221023i
$675$		0			0
$676$	346.392	−	599.968i	0.512414	−	0.887526i
$677$	−408.603	+	235.907i	−0.603550	+	0.348460i	−0.770437	−	0.637516i	$-0.779962\pi$
$677$	−408.603	+	235.907i	−0.603550	+	0.348460i	0.166887	+	0.985976i	$0.446629\pi$
$678$		0			0
$679$	−242.543	−	456.111i	−0.357206	−	0.671740i
$680$	201.409			0.296190
$681$		0			0
$682$	745.589	+	430.466i	1.09324	+	0.631182i
$683$	208.614	−	361.330i	0.305438	−	0.529034i	−0.671921	−	0.740623i	$-0.734530\pi$
$683$	208.614	−	361.330i	0.305438	−	0.529034i	0.977359	+	0.211589i	$0.0678638\pi$
$684$		0			0
$685$		−	370.995i		−	0.541599i
$686$	−789.722	+	351.726i	−1.15120	+	0.512719i
$687$		0			0
$688$	175.407	+	303.815i	0.254953	+	0.441591i
$689$	83.0019	+	47.9211i	0.120467	+	0.0695517i
$690$		0			0
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	−0.379030	−	0.925384i	$-0.623742\pi$
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	0.611891	+	0.790942i	$0.290409\pi$
$692$			585.285i			0.845787i
$693$		0			0
$694$	962.538			1.38694
$695$	−156.105	−	270.382i	−0.224612	−	0.389039i
$696$		0			0
$697$	399.273	−	691.561i	0.572845	−	0.992197i
$698$	−658.905	+	380.419i	−0.943990	+	0.545013i
$699$		0			0
$700$	−69.8296	−	43.6303i	−0.0997566	−	0.0623291i
$701$	−1034.80			−1.47618			−0.738089	−	0.674704i	$-0.764271\pi$
$701$	−1034.80			−1.47618			−0.738089	+	0.674704i	$0.764271\pi$
$702$		0			0
$703$	143.892	+	83.0759i	0.204682	+	0.118173i
$704$	21.3517	−	36.9822i	0.0303291	−	0.0525316i
$705$		0			0
$706$		−	322.729i		−	0.457123i
$707$	−748.220	−	26.0971i	−1.05830	−	0.0369125i
$708$		0			0
$709$	108.321	+	187.618i	0.152780	+	0.264623i	0.932248	−	0.361819i	$-0.117844\pi$
$709$	108.321	+	187.618i	0.152780	+	0.264623i	−0.779468	+	0.626442i	$0.784511\pi$
$710$	276.729	+	159.769i	0.389759	+	0.225027i
$711$		0			0
$712$	−262.035	+	151.286i	−0.368027	+	0.212481i
$713$		−	160.923i		−	0.225698i
$714$		0			0
$715$	−419.811			−0.587148
$716$	65.0133	+	112.606i	0.0908007	+	0.157271i
$717$		0			0
$718$	660.636	−	1144.26i	0.920106	−	1.59367i
$719$	−0.325449	+	0.187898i	−0.000452641	+	0.000261332i	−0.500226	−	0.865895i	$-0.666750\pi$
$719$	−0.325449	+	0.187898i	−0.000452641	+	0.000261332i	0.499774	+	0.866156i	$0.333417\pi$
$720$		0			0
$721$	−79.8930	+	127.867i	−0.110809	+	0.177347i
$722$	−885.086			−1.22588
$723$		0			0
$724$	−95.5530	−	55.1675i	−0.131979	−	0.0761983i
$725$	127.146	−	220.223i	0.175373	−	0.303756i
$726$		0			0
$727$		−	174.857i		−	0.240518i	−0.992743	−	0.120259i	$-0.961627\pi$
$727$		−	174.857i		−	0.240518i	0.992743	−	0.120259i	$-0.0383726\pi$
$728$	−293.794	−	552.490i	−0.403563	−	0.758915i
$729$		0			0
$730$	210.864	+	365.227i	0.288854	+	0.500310i
$731$	331.585	+	191.441i	0.453605	+	0.261889i
$732$		0			0
$733$	−738.210	+	426.206i	−1.00711	+	0.581454i	−0.910344	−	0.413853i	$-0.864183\pi$
$733$	−738.210	+	426.206i	−1.00711	+	0.581454i	−0.0967645	+	0.995307i	$0.530849\pi$
$734$			89.6973i			0.122203i
$735$		0			0
$736$	−137.575			−0.186923
$737$	438.357	+	759.256i	0.594785	+	1.03020i
$738$		0			0
$739$	584.126	−	1011.74i	0.790428	−	1.36906i	−0.135275	−	0.990808i	$-0.543192\pi$
$739$	584.126	−	1011.74i	0.790428	−	1.36906i	0.925702	−	0.378253i	$-0.123475\pi$
$740$	241.367	−	139.353i	0.326171	−	0.188315i
$741$		0			0
$742$	−69.3488	+	36.8771i	−0.0934619	+	0.0496996i
$743$	558.877			0.752190			0.376095	−	0.926581i	$-0.377267\pi$
$743$	558.877			0.752190			0.376095	+	0.926581i	$0.377267\pi$
$744$		0			0
$745$	−27.7639	−	16.0295i	−0.0372670	−	0.0215161i
$746$	−336.592	+	582.995i	−0.451196	+	0.781494i
$747$		0			0
$748$		−	445.042i		−	0.594976i
$749$	−532.128	−	332.479i	−0.710451	−	0.443898i
$750$		0			0
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	−0.890102	−	0.455762i	$-0.849367\pi$
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	0.0503493	−	0.998732i	$-0.483967\pi$
$752$	69.5260	+	40.1408i	0.0924547	+	0.0533788i
$753$		0			0
$754$	−2389.92	+	1379.82i	−3.16965	+	1.83000i
$755$			474.883i			0.628985i
$756$		0			0
$757$	−1269.13			−1.67652			−0.838262	−	0.545268i	$-0.816428\pi$
$757$	−1269.13			−1.67652			−0.838262	+	0.545268i	$0.816428\pi$
$758$	−158.392	−	274.343i	−0.208960	−	0.361930i
$759$		0			0
$760$	−14.5587	+	25.2164i	−0.0191562	+	0.0331795i
$761$	157.718	−	91.0585i	0.207251	−	0.119656i	−0.392782	−	0.919632i	$-0.628487\pi$
$761$	157.718	−	91.0585i	0.207251	−	0.119656i	0.600033	+	0.799975i	$0.295154\pi$
$762$		0			0
$763$	6.67355	−	191.335i	0.00874646	−	0.250766i
$764$	47.3152			0.0619309
$765$		0			0
$766$	778.195	+	449.291i	1.01592	+	0.586542i
$767$	1013.05	−	1754.65i	1.32079	−	2.28768i
$768$		0			0
$769$		−	810.237i		−	1.05362i	−0.849982	−	0.526812i	$-0.823387\pi$
$769$		−	810.237i		−	1.05362i	0.849982	−	0.526812i	$-0.176613\pi$
$770$	182.301	−	291.771i	0.236755	−	0.378923i
$771$		0			0
$772$	−33.7630	−	58.4793i	−0.0437345	−	0.0757504i
$773$	−212.492	−	122.682i	−0.274893	−	0.158709i	0.356216	−	0.934404i	$-0.384067\pi$
$773$	−212.492	−	122.682i	−0.274893	−	0.158709i	−0.631109	+	0.775694i	$0.717400\pi$
$774$		0			0
$775$	−169.607	+	97.9225i	−0.218847	+	0.126352i
$776$			306.431i			0.394885i
$777$		0			0
$778$	1125.70			1.44692
$779$	57.7224	+	99.9781i	0.0740981	+	0.128342i
$780$		0			0
$781$	−247.222	+	428.200i	−0.316545	+	0.548272i
$782$	−194.531	+	112.312i	−0.248760	+	0.143622i
$783$		0			0
$784$	971.543	+	67.8553i	1.23921	+	0.0865501i
$785$	−543.181			−0.691950
$786$		0			0
$787$	−373.020	−	215.363i	−0.473977	−	0.273651i	0.243926	−	0.969794i	$-0.421565\pi$
$787$	−373.020	−	215.363i	−0.473977	−	0.273651i	−0.717903	+	0.696143i	$0.754898\pi$
$788$	264.000	−	457.261i	0.335025	−	0.580280i
$789$		0			0
$790$		−	163.331i		−	0.206748i
$791$	−570.690	+	303.472i	−0.721479	+	0.383656i
$792$		0			0
$793$	−787.761	−	1364.44i	−0.993393	−	1.72061i
$794$	1323.45	+	764.093i	1.66681	+	0.962334i
$795$		0			0
$796$	648.005	−	374.126i	0.814077	−	0.470008i
$797$			1137.61i			1.42737i	0.700468	+	0.713684i	$0.252975\pi$
$797$			1137.61i			1.42737i	−0.700468	+	0.713684i	$0.747025\pi$
$798$		0			0
$799$	87.6199			0.109662
$800$	83.7155	+	145.000i	0.104644	+	0.181249i
$801$		0			0
$802$	918.449	−	1590.80i	1.14520	−	1.98354i
$803$	−565.139	+	326.283i	−0.703785	+	0.406330i
$804$		0			0
$805$	−64.2678	−	2.24159i	−0.0798358	−	0.00278459i
$806$	2125.36			2.63692
$807$		0			0
$808$	384.602	+	222.050i	0.475992	+	0.274814i
$809$	455.336	−	788.665i	0.562838	−	0.974864i	−0.434409	−	0.900716i	$-0.643043\pi$
$809$	455.336	−	788.665i	0.562838	−	0.974864i	0.997247	−	0.0741482i	$-0.0236238\pi$
$810$		0			0
$811$			546.361i			0.673688i	0.941560	+	0.336844i	$0.109360\pi$
$811$			546.361i			0.673688i	−0.941560	+	0.336844i	$0.890640\pi$
$812$	29.1944	−	837.020i	0.0359537	−	1.03081i
$813$		0			0
$814$	582.262	+	1008.51i	0.715309	+	1.23895i
$815$	−25.6286	−	14.7967i	−0.0314462	−	0.0181554i
$816$		0			0
$817$	−47.9368	+	27.6763i	−0.0586742	+	0.0338756i
$818$		−	1337.48i		−	1.63507i
$819$		0			0
$820$	193.649			0.236158
$821$	322.150	+	557.980i	0.392388	+	0.679635i	0.992764	−	0.120082i	$-0.0383159\pi$
$821$	322.150	+	557.980i	0.392388	+	0.679635i	−0.600376	+	0.799718i	$0.704983\pi$
$822$		0			0
$823$	−384.661	+	666.252i	−0.467388	+	0.809540i	−0.999306	−	0.0372559i	$-0.988138\pi$
$823$	−384.661	+	666.252i	−0.467388	+	0.809540i	0.531917	+	0.846796i	$0.321472\pi$
$824$	77.4543	−	44.7183i	0.0939980	−	0.0542697i
$825$		0			0
$826$	779.579	+	1466.03i	0.943800	+	1.77485i
$827$	−715.404			−0.865060			−0.432530	−	0.901620i	$-0.642379\pi$
$827$	−715.404			−0.865060			−0.432530	+	0.901620i	$0.642379\pi$
$828$		0			0
$829$	68.2973	+	39.4315i	0.0823852	+	0.0475651i	0.540627	−	0.841263i	$-0.318187\pi$
$829$	68.2973	+	39.4315i	0.0823852	+	0.0475651i	−0.458241	+	0.888828i	$0.651521\pi$
$830$	59.4910	−	103.041i	0.0716759	−	0.124146i
$831$		0			0
$832$		−	105.421i		−	0.126708i
$833$	955.317	−	466.038i	1.14684	−	0.559469i
$834$		0			0
$835$	−237.712	−	411.729i	−0.284685	−	0.493088i
$836$	55.7193	+	32.1696i	0.0666499	+	0.0384803i
$837$		0			0
$838$	−616.928	+	356.184i	−0.736191	+	0.425040i
$839$			165.698i			0.197494i	0.995113	+	0.0987471i	$0.0314835\pi$
$839$			165.698i			0.197494i	−0.995113	+	0.0987471i	$0.968517\pi$
$840$		0			0
$841$	1745.57			2.07559
$842$	555.238	+	961.701i	0.659428	+	1.14216i
$843$		0			0
$844$	−335.612	+	581.297i	−0.397645	+	0.688741i
$845$	−570.260	+	329.240i	−0.674864	+	0.389633i
$846$		0			0
$847$	−266.840	−	166.724i	−0.315041	−	0.196841i
$848$	88.4838			0.104344
$849$		0			0
$850$	236.747	+	136.686i	0.278525	+	0.160807i
$851$	108.834	−	188.507i	0.127890	−	0.221512i
$852$		0			0
$853$		−	1066.17i		−	1.24991i	−0.780661	−	0.624955i	$-0.785117\pi$
$853$		−	1066.17i		−	1.24991i	0.780661	−	0.624955i	$-0.214883\pi$
$854$	1290.38	+	45.0070i	1.51098	+	0.0527014i
$855$		0			0
$856$	186.098	+	322.331i	0.217404	+	0.376555i
$857$	−192.821	−	111.325i	−0.224995	−	0.129901i	0.383266	−	0.923638i	$-0.374799\pi$
$857$	−192.821	−	111.325i	−0.224995	−	0.129901i	−0.608261	+	0.793737i	$0.708133\pi$
$858$		0			0
$859$	1313.46	−	758.329i	1.52906	−	0.882805i	0.529661	−	0.848209i	$-0.322319\pi$
$859$	1313.46	−	758.329i	1.52906	−	0.882805i	0.999401	−	0.0345956i	$-0.0110143\pi$
$860$			92.8497i			0.107965i
$861$		0			0
$862$	−321.190			−0.372610
$863$	69.0180	+	119.543i	0.0799745	+	0.138520i	0.903239	−	0.429139i	$-0.141183\pi$
$863$	69.0180	+	119.543i	0.0799745	+	0.138520i	−0.823264	+	0.567658i	$0.807849\pi$
$864$		0			0
$865$	278.152	−	481.774i	0.321563	−	0.556964i
$866$	−945.752	+	546.030i	−1.09209	+	0.630520i
$867$		0			0
$868$	−341.791	+	547.031i	−0.393769	+	0.630221i
$869$	252.732			0.290831
$870$		0			0
$871$	1874.36	+	1082.16i	2.15196	+	1.24243i
$872$	−56.7825	+	98.3502i	−0.0651176	+	0.112787i
$873$		0			0
$874$		−	32.4737i		−	0.0371552i
$875$	36.7448	+	69.1000i	0.0419941	+	0.0789715i
$876$		0			0
$877$	308.810	+	534.875i	0.352121	+	0.609892i	0.986621	−	0.163031i	$-0.0521271\pi$
$877$	308.810	+	534.875i	0.352121	+	0.609892i	−0.634500	+	0.772923i	$0.718794\pi$
$878$	−138.013	−	79.6818i	−0.157190	−	0.0907538i
$879$		0			0
$880$	−335.653	+	193.789i	−0.381424	+	0.220215i
$881$		−	425.629i		−	0.483120i	−0.970386	−	0.241560i	$-0.922341\pi$
$881$		−	425.629i		−	0.483120i	0.970386	−	0.241560i	$-0.0776591\pi$
$882$		0			0
$883$	295.270			0.334394			0.167197	−	0.985923i	$-0.446528\pi$
$883$	295.270			0.334394			0.167197	+	0.985923i	$0.446528\pi$
$884$	−549.332	−	951.471i	−0.621416	−	1.07632i
$885$		0			0
$886$	−552.452	+	956.874i	−0.623535	+	1.07999i
$887$	1463.38	−	844.884i	1.64981	−	0.952519i	0.672665	−	0.739947i	$-0.265150\pi$
$887$	1463.38	−	844.884i	1.64981	−	0.952519i	0.977146	−	0.212571i	$-0.0681838\pi$
$888$		0			0
$889$	−1184.13	+	629.676i	−1.33198	+	0.708297i
$890$	−410.680			−0.461438
$891$		0			0
$892$	−116.329	−	67.1628i	−0.130414	−	0.0752946i
$893$	−6.33354	+	10.9700i	−0.00709244	+	0.0122845i
$894$		0			0
$895$		−	123.588i		−	0.138087i
$896$	−721.895	−	451.048i	−0.805686	−	0.503402i
$897$		0			0
$898$	−270.928	−	469.261i	−0.301702	−	0.522563i
$899$	−1725.18	−	996.035i	−1.91900	−	1.10794i
$900$		0			0
$901$	83.6336	−	48.2859i	0.0928230	−	0.0535914i
$902$			809.129i			0.897039i
$903$		0			0
$904$	383.409			0.424124
$905$	52.4359	+	90.8216i	0.0579402	+	0.100355i
$906$		0			0
$907$	−221.038	+	382.848i	−0.243702	+	0.422104i	−0.961766	−	0.273873i	$-0.911695\pi$
$907$	−221.038	+	382.848i	−0.243702	+	0.422104i	0.718064	+	0.695977i	$0.245028\pi$
$908$	−372.138	+	214.854i	−0.409843	+	0.236623i
$909$		0			0
$910$	29.6055	−	848.808i	0.0325335	−	0.932756i
$911$	−998.378			−1.09591			−0.547957	−	0.836507i	$-0.684594\pi$
$911$	−998.378			−1.09591			−0.547957	+	0.836507i	$0.684594\pi$
$912$		0			0
$913$	159.443	+	92.0544i	0.174636	+	0.100826i
$914$	−303.963	+	526.479i	−0.332563	+	0.576016i
$915$		0			0
$916$		−	39.4834i		−	0.0431041i
$917$	218.146	−	349.139i	0.237891	−	0.380740i
$918$		0			0
$919$	−154.797	−	268.116i	−0.168441	−	0.291748i	0.769431	−	0.638730i	$-0.220540\pi$
$919$	−154.797	−	268.116i	−0.168441	−	0.291748i	−0.937872	+	0.346982i	$0.887206\pi$
$920$	33.0350	+	19.0728i	0.0359077	+	0.0207313i
$921$		0			0
$922$	749.520	−	432.736i	0.812928	−	0.469344i
$923$			1220.62i			1.32245i
$924$		0			0
$925$	−264.906			−0.286385
$926$	94.2280	+	163.208i	0.101758	+	0.176250i
$927$		0			0
$928$	−851.526	+	1474.89i	−0.917593	+	1.58932i
$929$	443.269	−	255.921i	0.477146	−	0.275480i	−0.242080	−	0.970256i	$-0.577830\pi$
$929$	443.269	−	255.921i	0.477146	−	0.275480i	0.719226	+	0.694776i	$0.244496\pi$
$930$		0			0
$931$	−10.7064	+	153.293i	−0.0114999	+	0.164654i
$932$	626.737			0.672464
$933$		0			0
$934$	777.476	+	448.876i	0.832415	+	0.480595i
$935$	−211.503	+	366.334i	−0.226206	+	0.391801i
$936$		0			0
$937$		−	592.935i		−	0.632801i	−0.948626	−	0.316401i	$-0.897526\pi$
$937$		−	592.935i		−	0.632801i	0.948626	−	0.316401i	$-0.102474\pi$
$938$	−1566.04	+	832.762i	−1.66955	+	0.887807i
$939$		0			0
$940$	10.6240	+	18.4013i	0.0113021	+	0.0195759i
$941$	549.458	+	317.230i	0.583909	+	0.337120i	0.762685	−	0.646770i	$-0.223881\pi$
$941$	549.458	+	317.230i	0.583909	+	0.337120i	−0.178777	+	0.983890i	$0.557214\pi$
$942$		0			0
$943$	130.977	−	75.6198i	0.138894	−	0.0801907i
$944$		−	1870.54i		−	1.98150i
$945$		0			0
$946$	−387.956			−0.410101
$947$	329.805	+	571.239i	0.348263	+	0.603209i	0.985941	−	0.167094i	$-0.0534384\pi$
$947$	329.805	+	571.239i	0.348263	+	0.603209i	−0.637678	+	0.770303i	$0.720105\pi$
$948$		0			0
$949$	−805.487	+	1395.14i	−0.848775	+	1.47012i
$950$	−34.2261	+	19.7605i	−0.0360275	+	0.0208005i
$951$		0			0
$952$	−630.127	−	21.9781i	−0.661898	−	0.0230863i
$953$	615.571			0.645930			0.322965	−	0.946411i	$-0.395320\pi$
$953$	615.571			0.645930			0.322965	+	0.946411i	$0.395320\pi$
$954$		0			0
$955$	−38.9472	−	22.4862i	−0.0407824	−	0.0235457i
$956$	−46.6996	+	80.8861i	−0.0488489	+	0.0846088i
$957$		0			0
$958$		−	942.013i		−	0.983312i
$959$	−40.4837	+	1160.69i	−0.0422145	+	1.21032i
$960$		0			0
$961$	286.605	+	496.415i	0.298237	+	0.516561i
$962$	2489.68	+	1437.41i	2.58802	+	1.49419i
$963$		0			0
$964$	−169.830	+	98.0515i	−0.176172	+	0.101713i
$965$			64.1825i			0.0665104i
$966$		0			0
$967$	386.702			0.399899			0.199949	−	0.979806i	$-0.435922\pi$
$967$	386.702			0.399899			0.199949	+	0.979806i	$0.435922\pi$
$968$	93.3202	+	161.635i	0.0964052	+	0.166979i
$969$		0			0
$970$	−207.959	+	360.195i	−0.214390	+	0.371335i
$971$	−487.138	+	281.249i	−0.501687	+	0.289649i	−0.729410	−	0.684077i	$-0.760205\pi$
$971$	−487.138	+	281.249i	−0.501687	+	0.289649i	0.227723	+	0.973726i	$0.426872\pi$
$972$		0			0
$973$	458.885	+	862.950i	0.471619	+	0.886896i
$974$	−1959.79			−2.01211
$975$		0			0
$976$	−1259.68	−	727.279i	−1.29066	−	0.745163i
$977$	356.041	−	616.682i	0.364423	−	0.631199i	−0.624260	−	0.781216i	$-0.714600\pi$
$977$	356.041	−	616.682i	0.364423	−	0.631199i	0.988683	+	0.150017i	$0.0479329\pi$
$978$		0			0
$979$		−	635.472i		−	0.649103i
$980$	213.707	+	144.122i	0.218069	+	0.147063i
$981$		0			0
$982$	−578.178	−	1001.43i	−0.588776	−	1.01979i
$983$	−1064.18	−	614.407i	−1.08259	−	0.625032i	−0.150995	−	0.988535i	$-0.548248\pi$
$983$	−1064.18	−	614.407i	−1.08259	−	0.625032i	−0.931593	+	0.363502i	$0.881581\pi$
$984$		0			0
$985$	−434.619	+	250.928i	−0.441238	+	0.254749i
$986$			2780.64i			2.82012i
$987$		0			0
$988$	158.832			0.160761
$989$	36.2577	+	62.8001i	0.0366609	+	0.0634986i
$990$		0			0
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	−0.361280	−	0.932457i	$-0.617660\pi$
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	0.988172	−	0.153351i	$-0.0490064\pi$
$992$	1135.90	−	655.811i	1.14506	−	0.661100i
$993$		0			0
$994$	−848.337	−	530.050i	−0.853457	−	0.533250i
$995$	−711.202			−0.714776
$996$		0			0
$997$	−694.350	−	400.883i	−0.696439	−	0.402089i	0.109581	−	0.993978i	$-0.465049\pi$
$997$	−694.350	−	400.883i	−0.696439	−	0.402089i	−0.806020	+	0.591889i	$0.798382\pi$
$998$	800.920	−	1387.23i	0.802525	−	1.39001i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.w.a.136.4		8
3.2	odd	2		105.3.n.a.31.1	✓	8
7.5	odd	6	inner	315.3.w.a.271.4		8
15.2	even	4		525.3.s.h.199.7		16
15.8	even	4		525.3.s.h.199.2		16
15.14	odd	2		525.3.o.l.451.4		8
21.5	even	6		105.3.n.a.61.1	yes	8
21.11	odd	6		735.3.h.a.391.8		8
21.17	even	6		735.3.h.a.391.7		8
105.47	odd	12		525.3.s.h.124.2		16
105.68	odd	12		525.3.s.h.124.7		16
105.89	even	6		525.3.o.l.376.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.1	✓	8	3.2	odd	2
105.3.n.a.61.1	yes	8	21.5	even	6
315.3.w.a.136.4		8	1.1	even	1	trivial
315.3.w.a.271.4		8	7.5	odd	6	inner
525.3.o.l.376.4		8	105.89	even	6
525.3.o.l.451.4		8	15.14	odd	2
525.3.s.h.124.2		16	105.47	odd	12
525.3.s.h.124.7		16	105.68	odd	12
525.3.s.h.199.2		16	15.8	even	4
525.3.s.h.199.7		16	15.2	even	4
735.3.h.a.391.7		8	21.17	even	6
735.3.h.a.391.8		8	21.11	odd	6

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.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26021 + 2.18275i) q^{2} +(-1.17628 + 2.03737i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.18050 + 3.28656i) q^{7} +4.15226 q^{8} +O(q^{10})\)	\(q+(1.26021 + 2.18275i) q^{2} +(-1.17628 + 2.03737i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.18050 + 3.28656i) q^{7} +4.15226 q^{8} +(4.88079 + 2.81792i) q^{10} +(-4.36036 + 7.55236i) q^{11} +21.5286i q^{13} +(-14.9625 - 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(18.7862 + 10.8462i) q^{17} +(-2.71590 + 1.56803i) q^{19} +5.26047i q^{20} -21.9799 q^{22} +(2.05421 + 3.55799i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-46.9917 + 27.1307i) q^{26} +(0.574033 - 16.4579i) q^{28} +50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-16.7431 + 28.9999i) q^{32} +54.6743i q^{34} +(-8.29399 + 13.2744i) q^{35} +(-26.4906 - 45.8831i) q^{37} +(-6.84523 - 3.95209i) q^{38} +(8.04083 - 4.64237i) q^{40} -36.8122i q^{41} +17.6504 q^{43} +(-10.2580 - 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(3.49804 - 2.01959i) q^{47} +(27.3971 - 40.6251i) q^{49} +12.6021 q^{50} +(-43.8618 - 25.3236i) q^{52} +(2.22593 - 3.85542i) q^{53} +19.5001i q^{55} +(-25.6631 + 13.6467i) q^{56} +(64.0923 + 111.011i) q^{58} +(-81.5032 - 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} -98.7226i q^{62} -4.89677 q^{64} +(24.0697 + 41.6900i) q^{65} +(50.2661 - 87.0635i) q^{67} +(-44.1956 + 25.5164i) q^{68} +(-39.4270 - 1.37517i) q^{70} +56.6975 q^{71} +(64.8042 + 37.4147i) q^{73} +(66.7676 - 115.645i) q^{74} -7.37773i q^{76} +(2.12789 - 61.0079i) q^{77} +(-14.4903 - 25.0980i) q^{79} +(38.4891 + 22.2217i) q^{80} +(80.3519 - 46.3912i) q^{82} -21.1116i q^{83} +48.5058 q^{85} +(22.2433 + 38.5266i) q^{86} +(-18.1054 + 31.3594i) q^{88} +(-63.1066 + 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528 q^{92} +(8.81655 + 5.09024i) q^{94} +(-3.50621 + 6.07294i) q^{95} +73.7985i q^{97} +(123.201 + 8.60469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8	\( 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8} - 20 q^{11} + 16 q^{14} - 2 q^{16} + 18 q^{17} - 16 q^{22} - 62 q^{23} + 20 q^{25} - 120 q^{26} - 120 q^{28} + 100 q^{29} - 126 q^{31} - 36 q^{32} - 80 q^{37} - 114 q^{38} + 90 q^{40} + 352 q^{43} + 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} - 20 q^{50} - 48 q^{52} + 76 q^{53} - 196 q^{56} - 40 q^{58} + 54 q^{59} - 396 q^{61} - 4 q^{64} + 60 q^{65} + 184 q^{67} + 312 q^{68} - 164 q^{71} + 348 q^{73} + 140 q^{74} - 152 q^{77} - 206 q^{79} + 204 q^{82} - 60 q^{85} - 178 q^{86} + 124 q^{88} - 282 q^{89} - 114 q^{91} + 288 q^{92} + 30 q^{94} + 120 q^{95} + 592 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8 - 20 * q^11 + 16 * q^14 - 2 * q^16 + 18 * q^17 - 16 * q^22 - 62 * q^23 + 20 * q^25 - 120 * q^26 - 120 * q^28 + 100 * q^29 - 126 * q^31 - 36 * q^32 - 80 * q^37 - 114 * q^38 + 90 * q^40 + 352 * q^43 + 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 - 20 * q^50 - 48 * q^52 + 76 * q^53 - 196 * q^56 - 40 * q^58 + 54 * q^59 - 396 * q^61 - 4 * q^64 + 60 * q^65 + 184 * q^67 + 312 * q^68 - 164 * q^71 + 348 * q^73 + 140 * q^74 - 152 * q^77 - 206 * q^79 + 204 * q^82 - 60 * q^85 - 178 * q^86 + 124 * q^88 - 282 * q^89 - 114 * q^91 + 288 * q^92 + 30 * q^94 + 120 * q^95 + 592 * q^98

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