LMFDB - Embedded newform 315.3.w.a.271.3

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			271.3
Root			$-0.336732 + 0.583237i$ of defining polynomial
Character	$\chi$	$=$	315.271
Dual form			315.3.w.a.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.336732 - 0.583237i) q^{2} +(1.77322 + 3.07131i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +O(q^{10})$	\(q+(0.336732 - 0.583237i) q^{2} +(1.77322 + 3.07131i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(-1.30416 + 0.752955i) q^{10} +(-0.0223800 - 0.0387632i) q^{11} +23.0010i q^{13} +(-1.38970 + 4.50476i) q^{14} +(-5.38154 + 9.32109i) q^{16} +(8.16292 - 4.71286i) q^{17} +(0.991050 + 0.572183i) q^{19} -7.93010i q^{20} -0.0301442 q^{22} +(-22.1202 + 38.3133i) q^{23} +(2.50000 + 4.33013i) q^{25} +(13.4150 + 7.74518i) q^{26} +(-16.8848 - 18.1987i) q^{28} -53.0004 q^{29} +(19.5690 - 11.2982i) q^{31} +(13.7888 + 23.8829i) q^{32} -6.34788i q^{34} +(14.9569 + 4.61414i) q^{35} +(-21.1418 + 36.6186i) q^{37} +(0.667436 - 0.385344i) q^{38} +(-9.84175 - 5.68214i) q^{40} -38.2787i q^{41} +76.5222 q^{43} +(0.0793693 - 0.137472i) q^{44} +(14.8971 + 25.8026i) q^{46} +(23.5070 + 13.5718i) q^{47} +(44.1489 - 21.2574i) q^{49} +3.36732 q^{50} +(-70.6434 + 40.7860i) q^{52} +(9.49388 + 16.4439i) q^{53} +0.100086i q^{55} +(-34.6841 + 7.91521i) q^{56} +(-17.8469 + 30.9118i) q^{58} +(4.21731 - 2.43486i) q^{59} +(-33.6432 - 19.4239i) q^{61} -15.2178i q^{62} -24.4798 q^{64} +(25.7159 - 44.5413i) q^{65} +(3.50439 + 6.06978i) q^{67} +(28.9494 + 16.7139i) q^{68} +(7.72761 - 7.16970i) q^{70} +46.8735 q^{71} +(72.3956 - 41.7976i) q^{73} +(14.2382 + 24.6613i) q^{74} +4.05843i q^{76} +(0.213104 + 0.229686i) q^{77} +(-10.2397 + 17.7357i) q^{79} +(20.8426 - 12.0335i) q^{80} +(-22.3256 - 12.8897i) q^{82} -125.683i q^{83} -21.0766 q^{85} +(25.7674 - 44.6305i) q^{86} +(-0.113741 - 0.197005i) q^{88} +(-40.4455 - 23.3512i) q^{89} +(-35.8223 - 156.972i) q^{91} -156.896 q^{92} +(15.8311 - 9.14010i) q^{94} +(-1.27944 - 2.21606i) q^{95} +3.11494i q^{97} +(2.46826 - 32.9073i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.336732	−	0.583237i	0.168366	−	0.291618i	−0.769480	−	0.638671i	$-0.779484\pi$
$2$	0.336732	−	0.583237i	0.168366	−	0.291618i	0.937845	+	0.347053i	$0.112818\pi$
$3$		0			0
$3$		0			0
$4$	1.77322	+	3.07131i	0.443306	+	0.767828i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$		0			0
$7$	−6.82455	+	1.55742i	−0.974935	+	0.222489i
$7$	−6.82455	+	1.55742i	−0.974935	+	0.222489i
$8$	5.08226			0.635282
$9$		0			0
$10$	−1.30416	+	0.752955i	−0.130416	+	0.0752955i
$11$	−0.0223800	−	0.0387632i	−0.00203454	−	0.00352393i	0.865006	−	0.501761i	$-0.167314\pi$
$11$	−0.0223800	−	0.0387632i	−0.00203454	−	0.00352393i	−0.867041	+	0.498237i	$0.833981\pi$
$12$		0			0
$13$			23.0010i			1.76931i	0.466246	+	0.884655i	$0.345606\pi$
$13$			23.0010i			1.76931i	−0.466246	+	0.884655i	$0.654394\pi$
$14$	−1.38970	+	4.50476i	−0.0992641	+	0.321768i
$15$		0			0
$16$	−5.38154	+	9.32109i	−0.336346	+	0.582568i
$17$	8.16292	−	4.71286i	0.480172	−	0.277227i	−0.240316	−	0.970695i	$-0.577251\pi$
$17$	8.16292	−	4.71286i	0.480172	−	0.277227i	0.720488	+	0.693467i	$0.243918\pi$
$18$		0			0
$19$	0.991050	+	0.572183i	0.0521605	+	0.0301149i	0.525853	−	0.850575i	$-0.323746\pi$
$19$	0.991050	+	0.572183i	0.0521605	+	0.0301149i	−0.473693	+	0.880690i	$0.657079\pi$
$20$		−	7.93010i		−	0.396505i
$21$		0			0
$22$	−0.0301442			−0.00137019
$23$	−22.1202	+	38.3133i	−0.961748	+	1.66580i	−0.243637	+	0.969866i	$0.578341\pi$
$23$	−22.1202	+	38.3133i	−0.961748	+	1.66580i	−0.718110	+	0.695929i	$0.754993\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	13.4150	+	7.74518i	0.515963	+	0.297891i
$27$		0			0
$28$	−16.8848	−	18.1987i	−0.603028	−	0.649952i
$29$	−53.0004			−1.82760			−0.913799	−	0.406166i	$-0.866866\pi$
$29$	−53.0004			−1.82760			−0.913799	+	0.406166i	$0.866866\pi$
$30$		0			0
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	−0.149981	−	0.988689i	$-0.547921\pi$
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	0.781239	+	0.624232i	$0.214588\pi$
$32$	13.7888	+	23.8829i	0.430899	+	0.746340i
$33$		0			0
$34$		−	6.34788i		−	0.186702i
$35$	14.9569	+	4.61414i	0.427341	+	0.131833i
$36$		0			0
$37$	−21.1418	+	36.6186i	−0.571400	+	0.989693i	0.425023	+	0.905183i	$0.360266\pi$
$37$	−21.1418	+	36.6186i	−0.571400	+	0.989693i	−0.996423	+	0.0845106i	$0.973067\pi$
$38$	0.667436	−	0.385344i	0.0175641	−	0.0101406i
$39$		0			0
$40$	−9.84175	−	5.68214i	−0.246044	−	0.142053i
$41$		−	38.2787i		−	0.933628i	−0.884356	−	0.466814i	$-0.845402\pi$
$41$		−	38.2787i		−	0.933628i	0.884356	−	0.466814i	$-0.154598\pi$
$42$		0			0
$43$	76.5222			1.77959			0.889793	−	0.456365i	$-0.150849\pi$
$43$	76.5222			1.77959			0.889793	+	0.456365i	$0.150849\pi$
$44$	0.0793693	−	0.137472i	0.00180385	−	0.00312436i
$45$		0			0
$46$	14.8971	+	25.8026i	0.323851	+	0.560926i
$47$	23.5070	+	13.5718i	0.500149	+	0.288761i	0.728775	−	0.684753i	$-0.240090\pi$
$47$	23.5070	+	13.5718i	0.500149	+	0.288761i	−0.228626	+	0.973514i	$0.573423\pi$
$48$		0			0
$49$	44.1489	−	21.2574i	0.900998	−	0.433824i
$50$	3.36732			0.0673464
$51$		0			0
$52$	−70.6434	+	40.7860i	−1.35853	+	0.784345i
$53$	9.49388	+	16.4439i	0.179130	+	0.310262i	0.941583	−	0.336782i	$-0.109338\pi$
$53$	9.49388	+	16.4439i	0.179130	+	0.310262i	−0.762453	+	0.647044i	$0.776005\pi$
$54$		0			0
$55$			0.100086i			0.00181975i
$56$	−34.6841	+	7.91521i	−0.619359	+	0.141343i
$57$		0			0
$58$	−17.8469	+	30.9118i	−0.307705	+	0.532961i
$59$	4.21731	−	2.43486i	0.0714798	−	0.0412689i	−0.463834	−	0.885922i	$-0.653527\pi$
$59$	4.21731	−	2.43486i	0.0714798	−	0.0412689i	0.535314	+	0.844653i	$0.320193\pi$
$60$		0			0
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	0.198210	−	0.980160i	$-0.436487\pi$
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	−0.749738	+	0.661735i	$0.769821\pi$
$62$		−	15.2178i		−	0.245449i
$63$		0			0
$64$	−24.4798			−0.382497
$65$	25.7159	−	44.5413i	0.395630	−	0.685251i
$66$		0			0
$67$	3.50439	+	6.06978i	0.0523043	+	0.0905938i	0.890992	−	0.454019i	$-0.150010\pi$
$67$	3.50439	+	6.06978i	0.0523043	+	0.0905938i	−0.838688	+	0.544612i	$0.816677\pi$
$68$	28.9494	+	16.7139i	0.425726	+	0.245793i
$69$		0			0
$70$	7.72761	−	7.16970i	0.110394	−	0.102424i
$71$	46.8735			0.660190			0.330095	−	0.943948i	$-0.392919\pi$
$71$	46.8735			0.660190			0.330095	+	0.943948i	$0.392919\pi$
$72$		0			0
$73$	72.3956	−	41.7976i	0.991720	−	0.572570i	0.0859319	−	0.996301i	$-0.472613\pi$
$73$	72.3956	−	41.7976i	0.991720	−	0.572570i	0.905788	+	0.423731i	$0.139280\pi$
$74$	14.2382	+	24.6613i	0.192408	+	0.333261i
$75$		0			0
$76$			4.05843i			0.0534004i
$77$	0.213104	+	0.229686i	0.00276758	+	0.00298294i
$78$		0			0
$79$	−10.2397	+	17.7357i	−0.129617	+	0.224502i	−0.923528	−	0.383531i	$-0.874708\pi$
$79$	−10.2397	+	17.7357i	−0.129617	+	0.224502i	0.793912	+	0.608033i	$0.208041\pi$
$80$	20.8426	−	12.0335i	0.260533	−	0.150419i
$81$		0			0
$82$	−22.3256	−	12.8897i	−0.272263	−	0.157191i
$83$		−	125.683i		−	1.51425i	−0.653271	−	0.757124i	$-0.726604\pi$
$83$		−	125.683i		−	1.51425i	0.653271	−	0.757124i	$-0.273396\pi$
$84$		0			0
$85$	−21.0766			−0.247960
$86$	25.7674	−	44.6305i	0.299621	−	0.518960i
$87$		0			0
$88$	−0.113741	−	0.197005i	−0.00129251	−	0.00223869i
$89$	−40.4455	−	23.3512i	−0.454444	−	0.262373i	0.255261	−	0.966872i	$-0.417838\pi$
$89$	−40.4455	−	23.3512i	−0.454444	−	0.262373i	−0.709705	+	0.704499i	$0.751172\pi$
$90$		0			0
$91$	−35.8223	−	156.972i	−0.393651	−	1.72496i
$92$	−156.896			−1.70539
$93$		0			0
$94$	15.8311	−	9.14010i	0.168416	−	0.0972351i
$95$	−1.27944	−	2.21606i	−0.0134678	−	0.0233269i
$96$		0			0
$97$			3.11494i			0.0321128i	0.999871	+	0.0160564i	$0.00511112\pi$
$97$			3.11494i			0.0321128i	−0.999871	+	0.0160564i	$0.994889\pi$
$98$	2.46826	−	32.9073i	0.0251863	−	0.335789i
$99$		0			0
$100$	−8.86612	+	15.3566i	−0.0886612	+	0.153566i
$101$	77.4555	−	44.7189i	0.766886	−	0.442762i	−0.0648768	−	0.997893i	$-0.520665\pi$
$101$	77.4555	−	44.7189i	0.766886	−	0.442762i	0.831763	+	0.555132i	$0.187332\pi$
$102$		0			0
$103$	−79.1385	−	45.6906i	−0.768335	−	0.443598i	0.0639453	−	0.997953i	$-0.479632\pi$
$103$	−79.1385	−	45.6906i	−0.768335	−	0.443598i	−0.832280	+	0.554355i	$0.812965\pi$
$104$			116.897i			1.12401i
$105$		0			0
$106$	12.7876			0.120637
$107$	−52.5515	+	91.0219i	−0.491136	+	0.850672i	−0.999948	−	0.0102057i	$-0.996751\pi$
$107$	−52.5515	+	91.0219i	−0.491136	+	0.850672i	0.508812	+	0.860877i	$0.330085\pi$
$108$		0			0
$109$	−27.8507	−	48.2388i	−0.255511	−	0.442558i	0.709523	−	0.704682i	$-0.248910\pi$
$109$	−27.8507	−	48.2388i	−0.255511	−	0.442558i	−0.965034	+	0.262124i	$0.915577\pi$
$110$	0.0583739	+	0.0337022i	0.000530672	+	0.000306384i
$111$		0			0
$112$	22.2097	−	71.9936i	0.198301	−	0.642800i
$113$	5.25425			0.0464978			0.0232489	−	0.999730i	$-0.492599\pi$
$113$	5.25425			0.0464978			0.0232489	+	0.999730i	$0.492599\pi$
$114$		0			0
$115$	85.6711	−	49.4623i	0.744967	−	0.430107i
$116$	−93.9815	−	162.781i	−0.810185	−	1.40328i
$117$		0			0
$118$		−	3.27958i		−	0.0277931i
$119$	−48.3683	+	44.8763i	−0.406457	+	0.377111i
$120$		0			0
$121$	60.4990	−	104.787i	0.499992	−	0.866011i
$122$	−22.6575	+	13.0813i	−0.185717	+	0.107224i
$123$		0			0
$124$	69.4005	+	40.0684i	0.559681	+	0.323132i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−5.54989			−0.0436999			−0.0218500	−	0.999761i	$-0.506956\pi$
$127$	−5.54989			−0.0436999			−0.0218500	+	0.999761i	$0.506956\pi$
$128$	−63.3983	+	109.809i	−0.495299	+	0.857883i
$129$		0			0
$130$	−17.3187	−	29.9969i	−0.133221	−	0.230746i
$131$	144.212	+	83.2606i	1.10085	+	0.635577i	0.936445	−	0.350815i	$-0.114096\pi$
$131$	144.212	+	83.2606i	1.10085	+	0.635577i	0.164407	+	0.986393i	$0.447429\pi$
$132$		0			0
$133$	−7.65460	−	2.36141i	−0.0575534	−	0.0177550i
$134$	4.72016			0.0352251
$135$		0			0
$136$	41.4861	−	23.9520i	0.305045	−	0.176118i
$137$	36.4731	+	63.1733i	0.266227	+	0.461119i	0.967884	−	0.251395i	$-0.0808895\pi$
$137$	36.4731	+	63.1733i	0.266227	+	0.461119i	−0.701657	+	0.712515i	$0.747556\pi$
$138$		0			0
$139$			114.994i			0.827292i	0.910438	+	0.413646i	$0.135745\pi$
$139$			114.994i			0.827292i	−0.910438	+	0.413646i	$0.864255\pi$
$140$	12.3505	+	54.1193i	0.0882178	+	0.386567i
$141$		0			0
$142$	15.7838	−	27.3383i	0.111153	−	0.192523i
$143$	0.891594	−	0.514762i	0.00623492	−	0.00359973i
$144$		0			0
$145$	102.635	+	59.2562i	0.707826	+	0.408664i
$146$		−	56.2983i		−	0.385605i
$147$		0			0
$148$	−149.956			−1.01322
$149$	36.3729	−	62.9997i	0.244113	−	0.422817i	−0.717769	−	0.696282i	$-0.754836\pi$
$149$	36.3729	−	62.9997i	0.244113	−	0.422817i	0.961882	+	0.273465i	$0.0881698\pi$
$150$		0			0
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	0.996033	−	0.0889823i	$-0.0283615\pi$
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	−0.575078	+	0.818099i	$0.695028\pi$
$152$	5.03677	+	2.90798i	0.0331366	+	0.0191315i
$153$		0			0
$154$	0.205720	−	0.0469471i	0.00133585	−	0.000304851i
$155$	−50.5270			−0.325980
$156$		0			0
$157$	130.826	−	75.5327i	0.833290	−	0.481100i	−0.0216880	−	0.999765i	$-0.506904\pi$
$157$	130.826	−	75.5327i	0.833290	−	0.481100i	0.854978	+	0.518665i	$0.173571\pi$
$158$	6.89607	+	11.9443i	0.0436460	+	0.0755971i
$159$		0			0
$160$		−	61.6653i		−	0.385408i
$161$	91.2904	−	295.921i	0.567021	−	1.83802i
$162$		0			0
$163$	29.9639	−	51.8990i	0.183828	−	0.318399i	−0.759353	−	0.650679i	$-0.774485\pi$
$163$	29.9639	−	51.8990i	0.183828	−	0.318399i	0.943181	+	0.332280i	$0.107818\pi$
$164$	117.566	−	67.8768i	0.716866	−	0.413883i
$165$		0			0
$166$	−73.3027	−	42.3213i	−0.441582	−	0.254948i
$167$			224.089i			1.34185i	0.741526	+	0.670924i	$0.234102\pi$
$167$			224.089i			1.34185i	−0.741526	+	0.670924i	$0.765898\pi$
$168$		0			0
$169$	−360.047			−2.13046
$170$	−7.09715	+	12.2926i	−0.0417479	+	0.0723096i
$171$		0			0
$172$	135.691	+	235.024i	0.788901	+	1.36642i
$173$	−165.080	−	95.3092i	−0.954221	−	0.550920i	−0.0598317	−	0.998208i	$-0.519056\pi$
$173$	−165.080	−	95.3092i	−0.954221	−	0.550920i	−0.894390	+	0.447288i	$0.852390\pi$
$174$		0			0
$175$	−23.8052	−	25.6576i	−0.136030	−	0.146615i
$176$	0.481754			0.00273724
$177$		0			0
$178$	−27.2386	+	15.7262i	−0.153026	+	0.0883494i
$179$	108.931	+	188.674i	0.608553	+	1.05404i	0.991479	+	0.130265i	$0.0415829\pi$
$179$	108.931	+	188.674i	0.608553	+	1.05404i	−0.382926	+	0.923779i	$0.625084\pi$
$180$		0			0
$181$			39.0804i			0.215914i	0.994156	+	0.107957i	$0.0344309\pi$
$181$			39.0804i			0.215914i	−0.994156	+	0.107957i	$0.965569\pi$
$182$	−103.614	−	31.9645i	−0.569308	−	0.175629i
$183$		0			0
$184$	−112.421	+	194.718i	−0.610981	+	1.05825i
$185$	81.8818	−	47.2745i	0.442604	−	0.255538i
$186$		0			0
$187$	−0.365372	−	0.210947i	−0.00195386	−	0.00112806i
$188$			96.2632i			0.512038i
$189$		0			0
$190$	−1.72331			−0.00907006
$191$	94.7586	−	164.127i	0.496118	−	0.859302i	−0.503872	−	0.863778i	$-0.668092\pi$
$191$	94.7586	−	164.127i	0.496118	−	0.859302i	0.999990	+	0.00447651i	$0.00142492\pi$
$192$		0			0
$193$	136.570	+	236.547i	0.707619	+	1.22563i	0.965738	+	0.259519i	$0.0835640\pi$
$193$	136.570	+	236.547i	0.707619	+	1.22563i	−0.258119	+	0.966113i	$0.583103\pi$
$194$	1.81675	+	1.04890i	0.00936467	+	0.00540669i
$195$		0			0
$196$	143.574	+	97.9010i	0.732520	+	0.499495i
$197$	−198.898			−1.00963			−0.504817	−	0.863226i	$-0.668440\pi$
$197$	−198.898			−1.00963			−0.504817	+	0.863226i	$0.668440\pi$
$198$		0			0
$199$	33.2334	−	19.1873i	0.167002	−	0.0964185i	−0.414170	−	0.910200i	$-0.635928\pi$
$199$	33.2334	−	19.1873i	0.167002	−	0.0964185i	0.581171	+	0.813781i	$0.302595\pi$
$200$	12.7056	+	22.0068i	0.0635282	+	0.110034i
$201$		0			0
$202$		−	60.2331i		−	0.298184i
$203$	361.704	−	82.5438i	1.78179	−	0.406620i
$204$		0			0
$205$	−42.7969	+	74.1265i	−0.208766	+	0.361593i
$206$	−53.2969	+	30.7710i	−0.258723	+	0.149374i
$207$		0			0
$208$	−214.395	−	123.781i	−1.03074	−	0.595100i
$209$		−	0.0512217i		−	0.000245080i
$210$		0			0
$211$	−127.283			−0.603238			−0.301619	−	0.953429i	$-0.597527\pi$
$211$	−127.283			−0.603238			−0.301619	+	0.953429i	$0.597527\pi$
$212$	−33.6695	+	58.3173i	−0.158819	+	0.275082i
$213$		0			0
$214$	35.3915	+	61.2999i	0.165381	+	0.286448i
$215$	−148.185	−	85.5544i	−0.689230	−	0.397927i
$216$		0			0
$217$	−115.954	+	107.582i	−0.534349	+	0.495770i
$218$	−37.5129			−0.172077
$219$		0			0
$220$	−0.307396	+	0.177475i	−0.00139725	+	0.000806705i
$221$	108.401	+	187.756i	0.490501	+	0.849573i
$222$		0			0
$223$			293.558i			1.31641i	0.752841	+	0.658203i	$0.228683\pi$
$223$			293.558i			1.31641i	−0.752841	+	0.658203i	$0.771317\pi$
$224$	−131.298	−	141.515i	−0.586151	−	0.631763i
$225$		0			0
$226$	1.76927	−	3.06447i	0.00782864	−	0.0135596i
$227$	−186.611	+	107.740i	−0.822077	+	0.474626i	−0.851132	−	0.524952i	$-0.824083\pi$
$227$	−186.611	+	107.740i	−0.822077	+	0.474626i	0.0290554	+	0.999578i	$0.490750\pi$
$228$		0			0
$229$	124.938	+	72.1332i	0.545582	+	0.314992i	0.747338	−	0.664444i	$-0.231332\pi$
$229$	124.938	+	72.1332i	0.545582	+	0.314992i	−0.201756	+	0.979436i	$0.564665\pi$
$230$		−	66.6221i		−	0.289661i
$231$		0			0
$232$	−269.361			−1.16104
$233$	−143.216	+	248.058i	−0.614662	+	1.06463i	0.375781	+	0.926708i	$0.377374\pi$
$233$	−143.216	+	248.058i	−0.614662	+	1.06463i	−0.990444	+	0.137918i	$0.955959\pi$
$234$		0			0
$235$	−30.3474	−	52.5633i	−0.129138	−	0.223673i
$236$	14.9565	+	8.63511i	0.0633748	+	0.0365895i
$237$		0			0
$238$	9.88632	+	43.3214i	0.0415392	+	0.182023i
$239$	413.420			1.72979			0.864895	−	0.501954i	$-0.167385\pi$
$239$	413.420			1.72979			0.864895	+	0.501954i	$0.167385\pi$
$240$		0			0
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.136948	−	0.990578i	$-0.456271\pi$
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.926340	+	0.376689i	$0.122937\pi$
$242$	−40.7439	−	70.5705i	−0.168363	−	0.291613i
$243$		0			0
$244$		−	137.772i		−	0.564639i
$245$	−109.260	−	8.19523i	−0.445961	−	0.0334499i
$246$		0			0
$247$	−13.1608	+	22.7952i	−0.0532826	+	0.0922881i
$248$	99.4547	−	57.4202i	0.401027	−	0.231533i
$249$		0			0
$250$	−6.52078	−	3.76478i	−0.0260831	−	0.0150591i
$251$			311.712i			1.24188i	0.783858	+	0.620940i	$0.213249\pi$
$251$			311.712i			1.24188i	−0.783858	+	0.620940i	$0.786751\pi$
$252$		0			0
$253$	1.98020			0.00782686
$254$	−1.86882	+	3.23690i	−0.00735758	+	0.0127437i
$255$		0			0
$256$	−6.26320	−	10.8482i	−0.0244656	−	0.0423757i
$257$	125.335	+	72.3619i	0.487683	+	0.281564i	0.723613	−	0.690206i	$-0.242480\pi$
$257$	125.335	+	72.3619i	0.487683	+	0.281564i	−0.235930	+	0.971770i	$0.575814\pi$
$258$		0			0
$259$	87.2525	−	282.832i	0.336882	−	1.09202i
$260$	182.400			0.701540
$261$		0			0
$262$	97.1213	−	56.0730i	0.370692	−	0.214019i
$263$	−114.833	−	198.896i	−0.436626	−	0.756258i	0.560801	−	0.827950i	$-0.310493\pi$
$263$	−114.833	−	198.896i	−0.436626	−	0.756258i	−0.997427	+	0.0716928i	$0.977160\pi$
$264$		0			0
$265$		−	42.4579i		−	0.160219i
$266$	−3.95481	+	3.66928i	−0.0148677	+	0.0137943i
$267$		0			0
$268$	−12.4281	+	21.5262i	−0.0463736	+	0.0803215i
$269$	−367.508	+	212.181i	−1.36620	+	0.788776i	−0.990440	−	0.137941i	$-0.955952\pi$
$269$	−367.508	+	212.181i	−1.36620	+	0.788776i	−0.375760	+	0.926717i	$0.622618\pi$
$270$		0			0
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.887604	−	0.460607i	$-0.152368\pi$
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.0449051	+	0.998991i	$0.485701\pi$
$272$			101.450i			0.372977i
$273$		0			0
$274$	49.1267			0.179294
$275$	0.111900	−	0.193816i	0.000406908	−	0.000704786i
$276$		0			0
$277$	101.450	+	175.717i	0.366247	+	0.634358i	0.988975	−	0.148080i	$-0.0473092\pi$
$277$	101.450	+	175.717i	0.366247	+	0.634358i	−0.622729	+	0.782438i	$0.713976\pi$
$278$	67.0684	+	38.7220i	0.241253	+	0.139288i
$279$		0			0
$280$	76.0149	+	23.4503i	0.271482	+	0.0837510i
$281$	−254.325			−0.905071			−0.452536	−	0.891746i	$-0.649480\pi$
$281$	−254.325			−0.905071			−0.452536	+	0.891746i	$0.649480\pi$
$282$		0			0
$283$	384.259	−	221.852i	1.35781	−	0.783930i	0.368478	−	0.929636i	$-0.379879\pi$
$283$	384.259	−	221.852i	1.35781	−	0.783930i	0.989328	+	0.145706i	$0.0465455\pi$
$284$	83.1172	+	143.963i	0.292666	+	0.506912i
$285$		0			0
$286$		−	0.693347i		−	0.00242429i
$287$	59.6161	+	261.235i	0.207722	+	0.910227i
$288$		0			0
$289$	−100.078	+	173.340i	−0.346290	+	0.599792i
$290$	69.1208	−	39.9069i	0.238348	−	0.137610i
$291$		0			0
$292$	256.747	+	148.233i	0.879270	+	0.507647i
$293$			223.513i			0.762845i	0.924401	+	0.381422i	$0.124566\pi$
$293$			223.513i			0.762845i	−0.924401	+	0.381422i	$0.875434\pi$
$294$		0			0
$295$	−10.8890			−0.0369120
$296$	−107.448	+	186.105i	−0.363000	+	0.628734i
$297$		0			0
$298$	−24.4958	−	42.4280i	−0.0822007	−	0.142376i
$299$	−881.245	−	508.787i	−2.94731	−	1.70163i
$300$		0			0
$301$	−522.229	+	119.177i	−1.73498	+	0.395937i
$302$	85.6165			0.283498
$303$		0			0
$304$	−10.6667	+	6.15845i	−0.0350880	+	0.0202580i
$305$	43.4332	+	75.2285i	0.142404	+	0.246651i
$306$		0			0
$307$		−	47.3887i		−	0.154361i	−0.997017	−	0.0771803i	$-0.975408\pi$
$307$		−	47.3887i		−	0.154361i	0.997017	−	0.0771803i	$-0.0245917\pi$
$308$	−0.327559	+	1.06179i	−0.00106350	+	0.00344738i
$309$		0			0
$310$	−17.0140	+	29.4692i	−0.0548840	+	0.0950619i
$311$	313.595	−	181.054i	1.00834	−	0.582167i	0.0976367	−	0.995222i	$-0.468872\pi$
$311$	313.595	−	181.054i	1.00834	−	0.582167i	0.910706	+	0.413055i	$0.135538\pi$
$312$		0			0
$313$	−340.880	−	196.807i	−1.08907	−	0.628777i	−0.155744	−	0.987797i	$-0.549778\pi$
$313$	−340.880	−	196.807i	−1.08907	−	0.628777i	−0.933330	+	0.359020i	$0.883111\pi$
$314$		−	101.737i		−	0.324003i
$315$		0			0
$316$	−72.6291			−0.229839
$317$	288.788	−	500.196i	0.911004	−	1.57791i	0.0983557	−	0.995151i	$-0.468642\pi$
$317$	288.788	−	500.196i	0.911004	−	1.57791i	0.812648	−	0.582754i	$-0.198025\pi$
$318$		0			0
$319$	1.18615	+	2.05446i	0.00371833	+	0.00644033i
$320$	47.4049	+	27.3693i	0.148140	+	0.0855289i
$321$		0			0
$322$	−141.852	−	152.890i	−0.440533	−	0.474814i
$323$	10.7865			0.0333947
$324$		0			0
$325$	−99.5974	+	57.5026i	−0.306453	+	0.176931i
$326$	−20.1796	−	34.9521i	−0.0619006	−	0.107215i
$327$		0			0
$328$		−	194.542i		−	0.593117i
$329$	−181.562	−	56.0109i	−0.551859	−	0.170246i
$330$		0			0
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	−0.693388	−	0.720565i	$-0.743883\pi$
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	0.970721	+	0.240209i	$0.0772160\pi$
$332$	386.011	−	222.863i	1.16268	−	0.671275i
$333$		0			0
$334$	130.697	+	75.4578i	0.391307	+	0.225921i
$335$		−	15.6721i		−	0.0467824i
$336$		0			0
$337$	−205.885			−0.610934			−0.305467	−	0.952203i	$-0.598813\pi$
$337$	−205.885			−0.610934			−0.305467	+	0.952203i	$0.598813\pi$
$338$	−121.239	+	209.993i	−0.358696	+	0.621280i
$339$		0			0
$340$	−37.3735	−	64.7327i	−0.109922	−	0.190390i
$341$	−0.875907	−	0.505705i	−0.00256864	−	0.00148301i
$342$		0			0
$343$	−268.190	+	213.830i	−0.781894	+	0.623412i
$344$	388.905			1.13054
$345$		0			0
$346$	−111.176	+	64.1872i	−0.321317	+	0.185512i
$347$	99.7256	+	172.730i	0.287394	+	0.497780i	0.973187	−	0.230016i	$-0.0738779\pi$
$347$	99.7256	+	172.730i	0.287394	+	0.497780i	−0.685793	+	0.727796i	$0.740545\pi$
$348$		0			0
$349$		−	391.231i		−	1.12101i	−0.828152	−	0.560503i	$-0.810608\pi$
$349$		−	391.231i		−	1.12101i	0.828152	−	0.560503i	$-0.189392\pi$
$350$	−22.9804	+	5.24433i	−0.0656583	+	0.0149838i
$351$		0			0
$352$	0.617185	−	1.06900i	0.00175337	−	0.00303692i
$353$	81.1020	−	46.8243i	0.229751	−	0.132647i	−0.380706	−	0.924696i	$-0.624319\pi$
$353$	81.1020	−	46.8243i	0.229751	−	0.132647i	0.610457	+	0.792049i	$0.290986\pi$
$354$		0			0
$355$	−90.7701	−	52.4061i	−0.255690	−	0.147623i
$356$		−	165.628i		−	0.465246i
$357$		0			0
$358$	146.722			0.409838
$359$	73.8759	−	127.957i	0.205782	−	0.356426i	−0.744599	−	0.667512i	$-0.767359\pi$
$359$	73.8759	−	127.957i	0.205782	−	0.356426i	0.950382	+	0.311086i	$0.100693\pi$
$360$		0			0
$361$	−179.845	−	311.501i	−0.498186	−	0.862884i
$362$	22.7931	+	13.1596i	0.0629644	+	0.0363525i
$363$		0			0
$364$	418.588	−	388.367i	1.14997	−	1.06694i
$365$	−186.925			−0.512122
$366$		0			0
$367$	−71.5485	+	41.3085i	−0.194955	+	0.112557i	−0.594300	−	0.804243i	$-0.702571\pi$
$367$	−71.5485	+	41.3085i	−0.194955	+	0.112557i	0.399345	+	0.916801i	$0.369238\pi$
$368$	−238.081	−	412.369i	−0.646960	−	1.12057i
$369$		0			0
$370$		−	63.6753i		−	0.172095i
$371$	−90.4014	−	97.4361i	−0.243670	−	0.262631i
$372$		0			0
$373$	171.325	−	296.744i	0.459318	−	0.795561i	−0.539607	−	0.841917i	$-0.681427\pi$
$373$	171.325	−	296.744i	0.459318	−	0.795561i	0.998925	+	0.0463554i	$0.0147607\pi$
$374$	−0.246064	+	0.142065i	−0.000657926	+	0.000379854i
$375$		0			0
$376$	119.469	+	68.9752i	0.317736	+	0.183445i
$377$		−	1219.06i		−	3.23359i
$378$		0			0
$379$	355.679			0.938467			0.469233	−	0.883074i	$-0.344530\pi$
$379$	355.679			0.938467			0.469233	+	0.883074i	$0.344530\pi$
$380$	4.53747	−	7.85912i	0.0119407	−	0.0206819i
$381$		0			0
$382$	−63.8164	−	110.533i	−0.167059	−	0.289354i
$383$	144.616	+	83.4939i	0.377586	+	0.218000i	0.676768	−	0.736197i	$-0.263380\pi$
$383$	144.616	+	83.4939i	0.377586	+	0.218000i	−0.299181	+	0.954196i	$0.596714\pi$
$384$		0			0
$385$	−0.155876	−	0.683043i	−0.000404873	−	0.00177414i
$386$	183.950			0.476556
$387$		0			0
$388$	−9.56695	+	5.52348i	−0.0246571	+	0.0142358i
$389$	79.6452	+	137.950i	0.204744	+	0.354626i	0.950051	−	0.312095i	$-0.101031\pi$
$389$	79.6452	+	137.950i	0.204744	+	0.354626i	−0.745307	+	0.666721i	$0.767697\pi$
$390$		0			0
$391$			416.998i			1.06649i
$392$	224.376	−	108.035i	0.572388	−	0.275601i
$393$		0			0
$394$	−66.9753	+	116.005i	−0.169988	+	0.294428i
$395$	39.6582	−	22.8967i	0.100401	−	0.0579663i
$396$		0			0
$397$	−510.352	−	294.652i	−1.28552	−	0.742196i	−0.307669	−	0.951494i	$-0.599549\pi$
$397$	−510.352	−	294.652i	−1.28552	−	0.742196i	−0.977852	+	0.209298i	$0.932882\pi$
$398$		−	25.8439i		−	0.0649344i
$399$		0			0
$400$	−53.8154			−0.134538
$401$	−83.1535	+	144.026i	−0.207365	+	0.359167i	−0.950884	−	0.309548i	$-0.899822\pi$
$401$	−83.1535	+	144.026i	−0.207365	+	0.359167i	0.743518	+	0.668716i	$0.233156\pi$
$402$		0			0
$403$	259.870	+	450.107i	0.644838	+	1.11689i
$404$	274.692	+	158.593i	0.679930	+	0.392558i
$405$		0			0
$406$	73.6545	−	238.754i	0.181415	−	0.588064i
$407$	1.89261			0.00465014
$408$		0			0
$409$	−189.742	+	109.548i	−0.463917	+	0.267843i	−0.713690	−	0.700462i	$-0.752977\pi$
$409$	−189.742	+	109.548i	−0.463917	+	0.267843i	0.249773	+	0.968304i	$0.419644\pi$
$410$	28.8222	+	49.9215i	0.0702980	+	0.121760i
$411$		0			0
$412$		−	324.079i		−	0.786599i
$413$	−24.9891	+	23.1850i	−0.0605063	+	0.0561379i
$414$		0			0
$415$	−140.517	+	243.383i	−0.338596	+	0.586466i
$416$	−549.331	+	317.156i	−1.32051	+	0.762395i
$417$		0			0
$418$	−0.0298744	−	0.0172480i	−7.14698e−5	−	4.12631e-5i
$419$			554.704i			1.32388i	0.749558	+	0.661938i	$0.230266\pi$
$419$			554.704i			1.32388i	−0.749558	+	0.661938i	$0.769734\pi$
$420$		0			0
$421$	642.342			1.52575			0.762876	−	0.646545i	$-0.223787\pi$
$421$	642.342			1.52575			0.762876	+	0.646545i	$0.223787\pi$
$422$	−42.8603	+	74.2362i	−0.101565	+	0.175915i
$423$		0			0
$424$	48.2503	+	83.5720i	0.113798	+	0.197104i
$425$	40.8146	+	23.5643i	0.0960344	+	0.0554455i
$426$		0			0
$427$	259.851	+	80.1629i	0.608550	+	0.187735i
$428$	−372.742			−0.870893
$429$		0			0
$430$	−99.7969	+	57.6178i	−0.232086	+	0.133995i
$431$	37.6661	+	65.2395i	0.0873923	+	0.151368i	0.906408	−	0.422403i	$-0.138813\pi$
$431$	37.6661	+	65.2395i	0.0873923	+	0.151368i	−0.819016	+	0.573771i	$0.805480\pi$
$432$		0			0
$433$		−	353.064i		−	0.815391i	−0.913118	−	0.407695i	$-0.866333\pi$
$433$		−	353.064i		−	0.815391i	0.913118	−	0.407695i	$-0.133667\pi$
$434$	23.7005	+	103.855i	0.0546095	+	0.239297i
$435$		0			0
$436$	98.7710	−	171.076i	0.226539	−	0.392377i
$437$	−43.8444	+	25.3136i	−0.100331	+	0.0579259i
$438$		0			0
$439$	−235.512	−	135.973i	−0.536473	−	0.309733i	0.207175	−	0.978304i	$-0.433573\pi$
$439$	−235.512	−	135.973i	−0.536473	−	0.309733i	−0.743648	+	0.668571i	$0.766906\pi$
$440$			0.508664i			0.00115605i
$441$		0			0
$442$	146.008			0.330335
$443$	−55.1204	+	95.4714i	−0.124425	+	0.215511i	−0.921508	−	0.388359i	$-0.873042\pi$
$443$	−55.1204	+	95.4714i	−0.124425	+	0.215511i	0.797083	+	0.603870i	$0.206375\pi$
$444$		0			0
$445$	52.2149	+	90.4389i	0.117337	+	0.203233i
$446$	171.214	+	98.8504i	0.383888	+	0.221638i
$447$		0			0
$448$	167.064	−	38.1253i	0.372910	−	0.0851012i
$449$	−59.1007			−0.131627			−0.0658137	−	0.997832i	$-0.520964\pi$
$449$	−59.1007			−0.131627			−0.0658137	+	0.997832i	$0.520964\pi$
$450$		0			0
$451$	−1.48381	+	0.856677i	−0.00329004	+	0.00189950i
$452$	9.31696	+	16.1375i	0.0206127	+	0.0357023i
$453$		0			0
$454$			145.118i			0.319643i
$455$	−106.130	+	344.025i	−0.233253	+	0.756098i
$456$		0			0
$457$	102.638	−	177.775i	0.224592	−	0.389004i	−0.731605	−	0.681729i	$-0.761228\pi$
$457$	102.638	−	177.775i	0.224592	−	0.389004i	0.956197	+	0.292724i	$0.0945618\pi$
$458$	84.1414	−	48.5791i	0.183715	−	0.106068i
$459$		0			0
$460$	303.828	+	175.415i	0.660496	+	0.381338i
$461$			466.172i			1.01122i	0.862762	+	0.505610i	$0.168732\pi$
$461$			466.172i			1.01122i	−0.862762	+	0.505610i	$0.831268\pi$
$462$		0			0
$463$	191.705			0.414051			0.207025	−	0.978336i	$-0.433622\pi$
$463$	191.705			0.414051			0.207025	+	0.978336i	$0.433622\pi$
$464$	285.223	−	494.021i	0.614706	−	1.06470i
$465$		0			0
$466$	96.4510	+	167.058i	0.206976	+	0.358493i
$467$	730.261	+	421.617i	1.56373	+	0.902819i	0.996874	+	0.0790015i	$0.0251732\pi$
$467$	730.261	+	421.617i	1.56373	+	0.902819i	0.566855	+	0.823818i	$0.308160\pi$
$468$		0			0
$469$	−33.3691	−	35.9657i	−0.0711494	−	0.0766859i
$470$	−40.8758			−0.0869697
$471$		0			0
$472$	21.4334	−	12.3746i	0.0454098	−	0.0262174i
$473$	−1.71256	−	2.96625i	−0.00362064	−	0.00627113i
$474$		0			0
$475$			5.72183i			0.0120460i
$476$	−223.597	−	68.9786i	−0.469741	−	0.144913i
$477$		0			0
$478$	139.212	−	241.121i	0.291237	−	0.504438i
$479$	246.540	−	142.340i	0.514698	−	0.297161i	−0.220065	−	0.975485i	$-0.570627\pi$
$479$	246.540	−	142.340i	0.514698	−	0.297161i	0.734763	+	0.678324i	$0.237293\pi$
$480$		0			0
$481$	−842.267	−	486.283i	−1.75107	−	1.01098i
$482$		−	199.274i		−	0.413432i
$483$		0			0
$484$	429.113			0.886597
$485$	3.48261	−	6.03205i	0.00718063	−	0.0124372i
$486$		0			0
$487$	97.8228	+	169.434i	0.200868	+	0.347914i	0.948808	−	0.315852i	$-0.102290\pi$
$487$	97.8228	+	169.434i	0.200868	+	0.347914i	−0.747940	+	0.663766i	$0.768957\pi$
$488$	−170.984	−	98.7174i	−0.350376	−	0.202290i
$489$		0			0
$490$	−41.5712	+	60.9651i	−0.0848392	+	0.124419i
$491$	−745.464			−1.51826			−0.759128	−	0.650941i	$-0.774375\pi$
$491$	−745.464			−1.51826			−0.759128	+	0.650941i	$0.774375\pi$
$492$		0			0
$493$	−432.638	+	249.784i	−0.877562	+	0.506660i
$494$	8.86332	+	15.3517i	0.0179419	+	0.0310763i
$495$		0			0
$496$			243.206i			0.490335i
$497$	−319.890	+	73.0017i	−0.643642	+	0.146885i
$498$		0			0
$499$	−45.9747	+	79.6306i	−0.0921337	+	0.159580i	−0.908409	−	0.418083i	$-0.862702\pi$
$499$	−45.9747	+	79.6306i	−0.0921337	+	0.159580i	0.816275	+	0.577663i	$0.196035\pi$
$500$	34.3383	−	19.8252i	0.0686766	−	0.0396505i
$501$		0			0
$502$	181.802	+	104.963i	0.362155	+	0.209090i
$503$		−	672.220i		−	1.33642i	−0.743972	−	0.668211i	$-0.767060\pi$
$503$		−	672.220i		−	1.33642i	0.743972	−	0.668211i	$-0.232940\pi$
$504$		0			0
$505$	−199.989			−0.396018
$506$	0.666795	−	1.15492i	0.00131778	−	0.00228246i
$507$		0			0
$508$	−9.84119	−	17.0454i	−0.0193724	−	0.0335540i
$509$	−282.238	−	162.950i	−0.554495	−	0.320138i	0.196438	−	0.980516i	$-0.437063\pi$
$509$	−282.238	−	162.950i	−0.554495	−	0.320138i	−0.750933	+	0.660378i	$0.770396\pi$
$510$		0			0
$511$	−428.970	+	398.000i	−0.839473	+	0.778865i
$512$	−515.622			−1.00707
$513$		0			0
$514$	84.4082	−	48.7331i	0.164218	−	0.0948115i
$515$	102.167	+	176.959i	0.198383	+	0.343610i
$516$		0			0
$517$		−	1.21494i		−	0.00234999i
$518$	−135.577	−	146.127i	−0.261733	−	0.282099i
$519$		0			0
$520$	130.695	−	226.370i	0.251336	−	0.435328i
$521$	−515.449	+	297.595i	−0.989346	+	0.571199i	−0.905079	−	0.425244i	$-0.860188\pi$
$521$	−515.449	+	297.595i	−0.989346	+	0.571199i	−0.0842672	+	0.996443i	$0.526855\pi$
$522$		0			0
$523$	−43.6490	−	25.2007i	−0.0834588	−	0.0481850i	0.457690	−	0.889112i	$-0.348677\pi$
$523$	−43.6490	−	25.2007i	−0.0834588	−	0.0481850i	−0.541149	+	0.840927i	$0.682010\pi$
$524$			590.559i			1.12702i
$525$		0			0
$526$	−154.671			−0.294051
$527$	106.494	−	184.452i	0.202075	−	0.350004i
$528$		0			0
$529$	−714.106	−	1236.87i	−1.34992	−	2.33812i
$530$	−24.7630	−	14.2969i	−0.0467227	−	0.0269753i
$531$		0			0
$532$	−6.32068	−	27.6970i	−0.0118810	−	0.0520620i
$533$	880.451			1.65188
$534$		0			0
$535$	203.531	−	117.509i	0.380432	−	0.219642i
$536$	17.8102	+	30.8482i	0.0332280	+	0.0575526i
$537$		0			0
$538$			285.792i			0.531212i
$539$	−1.81205	−	1.23561i	−0.00336188	−	0.00229242i
$540$		0			0
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	0.000512769		1.00000i	$0.499837\pi$
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	−0.866282	+	0.499556i	$0.833497\pi$
$542$	170.191	−	98.2598i	0.314006	−	0.181291i
$543$		0			0
$544$	225.113	+	129.969i	0.413812	+	0.238914i
$545$			124.552i			0.228536i
$546$		0			0
$547$	−3.89041			−0.00711227			−0.00355613	−	0.999994i	$-0.501132\pi$
$547$	−3.89041			−0.00711227			−0.00355613	+	0.999994i	$0.501132\pi$
$548$	−129.350	+	224.041i	−0.236040	+	0.408834i
$549$		0			0
$550$	−0.0753604	−	0.130528i	−0.000137019	−	0.000237324i
$551$	−52.5260	−	30.3259i	−0.0953285	−	0.0550379i
$552$		0			0
$553$	42.2594	−	136.986i	0.0764185	−	0.247714i
$554$	136.646			0.246654
$555$		0			0
$556$	−353.181	+	203.909i	−0.635218	+	0.366743i
$557$	193.381	+	334.945i	0.347183	+	0.601338i	0.985748	−	0.168230i	$-0.0538051\pi$
$557$	193.381	+	334.945i	0.347183	+	0.601338i	−0.638565	+	0.769568i	$0.720472\pi$
$558$		0			0
$559$			1760.09i			3.14864i
$560$	−123.500	+	114.584i	−0.220536	+	0.204614i
$561$		0			0
$562$	−85.6393	+	148.332i	−0.152383	+	0.263935i
$563$	105.001	−	60.6226i	0.186503	−	0.107678i	−0.403841	−	0.914829i	$-0.632325\pi$
$563$	105.001	−	60.6226i	0.186503	−	0.107678i	0.590345	+	0.807151i	$0.298992\pi$
$564$		0			0
$565$	−10.1748	−	5.87443i	−0.0180085	−	0.0103972i
$566$		−	298.819i		−	0.527948i
$567$		0			0
$568$	238.223			0.419407
$569$	204.955	−	354.993i	0.360202	−	0.623889i	−0.627792	−	0.778381i	$-0.716041\pi$
$569$	204.955	−	354.993i	0.360202	−	0.623889i	0.987994	+	0.154493i	$0.0493743\pi$
$570$		0			0
$571$	287.861	+	498.591i	0.504136	+	0.873188i	0.999989	+	0.00478199i	$0.00152216\pi$
$571$	287.861	+	498.591i	0.504136	+	0.873188i	−0.495853	+	0.868406i	$0.665145\pi$
$572$	3.16199	+	1.82558i	0.00552796	+	0.00319157i
$573$		0			0
$574$	172.436	+	53.1959i	0.300412	+	0.0926758i
$575$	−221.202			−0.384699
$576$		0			0
$577$	−202.254	+	116.772i	−0.350527	+	0.202377i	−0.664917	−	0.746917i	$-0.731533\pi$
$577$	−202.254	+	116.772i	−0.350527	+	0.202377i	0.314390	+	0.949294i	$0.398200\pi$
$578$	67.3988	+	116.738i	0.116607	+	0.201969i
$579$		0			0
$580$			420.298i			0.724652i
$581$	195.741	+	857.727i	0.336903	+	1.47629i
$582$		0			0
$583$	0.424945	−	0.736027i	0.000728894	−	0.00126248i
$584$	367.933	−	212.426i	0.630022	−	0.363743i
$585$		0			0
$586$	130.361	+	75.2641i	0.222459	+	0.128437i
$587$		−	606.882i		−	1.03387i	−0.856024	−	0.516935i	$-0.827073\pi$
$587$		−	606.882i		−	1.03387i	0.856024	−	0.516935i	$-0.172927\pi$
$588$		0			0
$589$	25.8585			0.0439024
$590$	−3.66668	+	6.35088i	−0.00621472	+	0.0107642i
$591$		0			0
$592$	−227.551	−	394.129i	−0.384376	−	0.665759i
$593$	701.998	+	405.299i	1.18381	+	0.683472i	0.956892	−	0.290443i	$-0.0938026\pi$
$593$	701.998	+	405.299i	1.18381	+	0.683472i	0.226915	+	0.973914i	$0.427136\pi$
$594$		0			0
$595$	143.838	−	32.8251i	0.241745	−	0.0551682i
$596$	257.989			0.432867
$597$		0			0
$598$	−593.487	+	342.650i	−0.992453	+	0.572993i
$599$	−511.389	−	885.752i	−0.853738	−	1.47872i	−0.877811	−	0.479007i	$-0.840997\pi$
$599$	−511.389	−	885.752i	−0.853738	−	1.47872i	0.0240732	−	0.999710i	$-0.492337\pi$
$600$		0			0
$601$			147.884i			0.246063i	0.992403	+	0.123032i	$0.0392617\pi$
$601$			147.884i			0.246063i	−0.992403	+	0.123032i	$0.960738\pi$
$602$	−106.343	+	344.714i	−0.176649	+	0.572614i
$603$		0			0
$604$	−225.427	+	390.452i	−0.373224	+	0.646443i
$605$	−234.312	+	135.280i	−0.387292	+	0.223603i
$606$		0			0
$607$	815.490	+	470.823i	1.34348	+	0.775656i	0.987316	−	0.158769i	$-0.0507524\pi$
$607$	815.490	+	470.823i	1.34348	+	0.775656i	0.356160	+	0.934425i	$0.384086\pi$
$608$			31.5588i			0.0519060i
$609$		0			0
$610$	58.5014			0.0959039
$611$	−312.165	+	540.685i	−0.510908	+	0.884919i
$612$		0			0
$613$	−180.068	−	311.886i	−0.293748	−	0.508786i	0.680945	−	0.732335i	$-0.261569\pi$
$613$	−180.068	−	311.886i	−0.293748	−	0.508786i	−0.974693	+	0.223548i	$0.928236\pi$
$614$	−27.6388	−	15.9573i	−0.0450144	−	0.0259891i
$615$		0			0
$616$	1.08305	+	1.16733i	0.00175819	+	0.00189501i
$617$	−769.687			−1.24747			−0.623734	−	0.781637i	$-0.714385\pi$
$617$	−769.687			−1.24747			−0.623734	+	0.781637i	$0.714385\pi$
$618$		0			0
$619$	−853.542	+	492.793i	−1.37890	+	0.796111i	−0.992028	−	0.126020i	$-0.959780\pi$
$619$	−853.542	+	492.793i	−1.37890	+	0.796111i	−0.386877	+	0.922131i	$0.626446\pi$
$620$	−89.5956	−	155.184i	−0.144509	−	0.250297i
$621$		0			0
$622$		−	243.866i		−	0.392068i
$623$	312.390	+	96.3709i	0.501428	+	0.154688i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−229.570	+	132.542i	−0.366726	+	0.211729i
$627$		0			0
$628$	463.969	+	267.873i	0.738804	+	0.426549i
$629$			398.554i			0.633630i
$630$		0			0
$631$	−89.7688			−0.142264			−0.0711322	−	0.997467i	$-0.522661\pi$
$631$	−89.7688			−0.142264			−0.0711322	+	0.997467i	$0.522661\pi$
$632$	−52.0408	+	90.1373i	−0.0823431	+	0.142622i
$633$		0			0
$634$	−194.488	−	336.864i	−0.306764	−	0.531331i
$635$	10.7473	+	6.20497i	0.0169249	+	0.00977160i
$636$		0			0
$637$	488.941	+	1015.47i	0.767569	+	1.59414i
$638$	1.59765			0.00250416
$639$		0			0
$640$	245.540	−	141.763i	0.383657	−	0.221504i
$641$	−214.166	−	370.947i	−0.334113	−	0.578701i	0.649201	−	0.760617i	$-0.275103\pi$
$641$	−214.166	−	370.947i	−0.334113	−	0.578701i	−0.983314	+	0.181916i	$0.941770\pi$
$642$		0			0
$643$			111.498i			0.173403i	0.996234	+	0.0867015i	$0.0276326\pi$
$643$			111.498i			0.173403i	−0.996234	+	0.0867015i	$0.972367\pi$
$644$	1070.75	−	244.353i	1.66265	−	0.379431i
$645$		0			0
$646$	3.63215	−	6.29107i	0.00562253	−	0.00973850i
$647$	250.033	−	144.357i	0.386450	−	0.223117i	−0.294171	−	0.955753i	$-0.595043\pi$
$647$	250.033	−	144.357i	0.386450	−	0.223117i	0.680621	+	0.732636i	$0.261710\pi$
$648$		0			0
$649$	−0.188766	−	0.108984i	−0.000290857	−	0.000167926i
$650$			77.4518i			0.119157i
$651$		0			0
$652$	212.531			0.325967
$653$	426.848	−	739.322i	0.653672	−	1.13219i	−0.328553	−	0.944485i	$-0.606561\pi$
$653$	426.848	−	739.322i	0.653672	−	1.13219i	0.982225	−	0.187707i	$-0.0601056\pi$
$654$		0			0
$655$	−186.176	−	322.467i	−0.284239	−	0.492316i
$656$	356.800	+	205.998i	0.543902	+	0.314022i
$657$		0			0
$658$	−93.8052	+	87.0327i	−0.142561	+	0.132269i
$659$	288.693			0.438077			0.219039	−	0.975716i	$-0.429708\pi$
$659$	288.693			0.438077			0.219039	+	0.975716i	$0.429708\pi$
$660$		0			0
$661$	182.367	−	105.289i	0.275895	−	0.159288i	−0.355668	−	0.934612i	$-0.615747\pi$
$661$	182.367	−	105.289i	0.275895	−	0.159288i	0.631564	+	0.775324i	$0.282413\pi$
$662$	−61.8222	−	107.079i	−0.0933870	−	0.161751i
$663$		0			0
$664$		−	638.751i		−	0.961974i
$665$	12.1829	+	13.1309i	0.0183202	+	0.0197458i
$666$		0			0
$667$	1172.38	−	2030.62i	1.75769	−	3.04441i
$668$	−688.246	+	397.359i	−1.03031	+	0.594849i
$669$		0			0
$670$	−9.14055	−	5.27730i	−0.0136426	−	0.00787656i
$671$			1.73883i			0.00259140i
$672$		0			0
$673$	760.139			1.12948			0.564739	−	0.825269i	$-0.308977\pi$
$673$	760.139			1.12948			0.564739	+	0.825269i	$0.308977\pi$
$674$	−69.3279	+	120.080i	−0.102860	+	0.178160i
$675$		0			0
$676$	−638.444	−	1105.82i	−0.944444	−	1.63583i
$677$	−163.263	−	94.2600i	−0.241157	−	0.139232i	0.374552	−	0.927206i	$-0.377797\pi$
$677$	−163.263	−	94.2600i	−0.241157	−	0.139232i	−0.615708	+	0.787974i	$0.711130\pi$
$678$		0			0
$679$	−4.85126	−	21.2580i	−0.00714472	−	0.0313079i
$680$	−107.117			−0.157524
$681$		0			0
$682$	−0.589892	+	0.340574i	−0.000864944	+	0.000499375i
$683$	260.243	+	450.754i	0.381029	+	0.659962i	0.991210	−	0.132301i	$-0.0422364\pi$
$683$	260.243	+	450.754i	0.381029	+	0.659962i	−0.610181	+	0.792262i	$0.708903\pi$
$684$		0			0
$685$		−	163.113i		−	0.238121i
$686$	34.4057	+	228.421i	0.0501541	+	0.332976i
$687$		0			0
$688$	−411.807	+	713.270i	−0.598556	+	1.03673i
$689$	−378.226	+	218.369i	−0.548949	+	0.316936i
$690$		0			0
$691$	590.615	+	340.991i	0.854724	+	0.493475i	0.862242	−	0.506496i	$-0.169060\pi$
$691$	590.615	+	340.991i	0.854724	+	0.493475i	−0.00751772	+	0.999972i	$0.502393\pi$
$692$		−	676.018i		−	0.976904i
$693$		0			0
$694$	134.323			0.193549
$695$	128.567	−	222.684i	0.184988	−	0.320409i
$696$		0			0
$697$	−180.403	−	312.466i	−0.258827	−	0.448302i
$698$	−228.180	−	131.740i	−0.326906	−	0.188739i
$699$		0			0
$700$	36.5906	−	118.610i	0.0522723	−	0.169443i
$701$	946.473			1.35018			0.675088	−	0.737737i	$-0.264106\pi$
$701$	946.473			1.35018			0.675088	+	0.737737i	$0.264106\pi$
$702$		0			0
$703$	−41.9051	+	24.1939i	−0.0596090	+	0.0344153i
$704$	0.547857	+	0.948916i	0.000778206	+	0.00134789i
$705$		0			0
$706$		−	63.0689i		−	0.0893327i
$707$	−458.952	+	425.817i	−0.649155	+	0.602287i
$708$		0			0
$709$	504.785	−	874.313i	0.711967	−	1.23316i	−0.252150	−	0.967688i	$-0.581138\pi$
$709$	504.785	−	874.313i	0.711967	−	1.23316i	0.964118	−	0.265475i	$-0.0855289\pi$
$710$	−61.1304	+	35.2936i	−0.0860991	+	0.0497093i
$711$		0			0
$712$	−205.554	−	118.677i	−0.288700	−	0.166681i
$713$			999.671i			1.40206i
$714$		0			0
$715$	−2.30209			−0.00321970
$716$	−386.318	+	669.122i	−0.539550	+	0.934528i
$717$		0			0
$718$	−49.7527	−	86.1742i	−0.0692935	−	0.120020i
$719$	−783.382	−	452.286i	−1.08954	−	0.629049i	−0.156089	−	0.987743i	$-0.549889\pi$
$719$	−783.382	−	452.286i	−1.08954	−	0.629049i	−0.933455	+	0.358694i	$0.883222\pi$
$720$		0			0
$721$	611.244	+	188.566i	0.847773	+	0.261534i
$722$	−242.238			−0.335510
$723$		0			0
$724$	−120.028	+	69.2983i	−0.165785	+	0.0957159i
$725$	−132.501	−	229.498i	−0.182760	−	0.316549i
$726$		0			0
$727$		−	535.515i		−	0.736609i	−0.929705	−	0.368304i	$-0.879938\pi$
$727$		−	535.515i		−	0.736609i	0.929705	−	0.368304i	$-0.120062\pi$
$728$	−182.058	−	797.770i	−0.250080	−	1.09584i
$729$		0			0
$730$	−62.9434	+	109.021i	−0.0862239	+	0.149344i
$731$	624.644	−	360.639i	0.854507	−	0.493350i
$732$		0			0
$733$	−652.583	−	376.769i	−0.890290	−	0.514009i	−0.0162527	−	0.999868i	$-0.505174\pi$
$733$	−652.583	−	376.769i	−0.890290	−	0.514009i	−0.874037	+	0.485859i	$0.838507\pi$
$734$			55.6396i			0.0758033i
$735$		0			0
$736$	−1220.04			−1.65767
$737$	0.156856	−	0.271683i	0.000212831	−	0.000368634i
$738$		0			0
$739$	546.157	+	945.972i	0.739049	+	1.28007i	0.952924	+	0.303209i	$0.0980580\pi$
$739$	546.157	+	945.972i	0.739049	+	1.28007i	−0.213875	+	0.976861i	$0.568609\pi$
$740$	290.389	+	167.656i	0.392418	+	0.226563i
$741$		0			0
$742$	−87.2693	+	19.9156i	−0.117614	+	0.0268404i
$743$	362.303			0.487622			0.243811	−	0.969823i	$-0.421602\pi$
$743$	362.303			0.487622			0.243811	+	0.969823i	$0.421602\pi$
$744$		0			0
$745$	−140.872	+	81.3322i	−0.189089	+	0.109171i
$746$	−115.381	−	199.847i	−0.154667	−	0.267891i
$747$		0			0
$748$		−	1.49623i		−	0.00200030i
$749$	216.881	−	703.028i	0.289561	−	0.938622i
$750$		0			0
$751$	336.270	−	582.437i	0.447763	−	0.775548i	−0.550477	−	0.834850i	$-0.685554\pi$
$751$	336.270	−	582.437i	0.447763	−	0.775548i	0.998240	+	0.0593020i	$0.0188875\pi$
$752$	−253.008	+	146.074i	−0.336446	+	0.194247i
$753$		0			0
$754$	−711.002	−	410.497i	−0.942974	−	0.544426i
$755$		−	284.268i		−	0.376514i
$756$		0			0
$757$	−368.166			−0.486349			−0.243174	−	0.969983i	$-0.578189\pi$
$757$	−368.166			−0.486349			−0.243174	+	0.969983i	$0.578189\pi$
$758$	119.768	−	207.445i	0.158006	−	0.273674i
$759$		0			0
$760$	−6.50244	−	11.2626i	−0.00855585	−	0.0148192i
$761$	−565.660	−	326.584i	−0.743312	−	0.429151i	0.0799606	−	0.996798i	$-0.474521\pi$
$761$	−565.660	−	326.584i	−0.743312	−	0.429151i	−0.823272	+	0.567647i	$0.807854\pi$
$762$		0			0
$763$	265.197	+	285.833i	0.347571	+	0.374617i
$764$	672.113			0.879728
$765$		0			0
$766$	97.3933	−	56.2301i	0.127145	−	0.0734074i
$767$	56.0043	+	97.0024i	0.0730174	+	0.126470i
$768$		0			0
$769$		−	1393.19i		−	1.81170i	−0.423602	−	0.905848i	$-0.639235\pi$
$769$		−	1393.19i		−	1.81170i	0.423602	−	0.905848i	$-0.360765\pi$
$770$	−0.450864	−	0.139090i	−0.000585538	−	0.000180636i
$771$		0			0
$772$	−484.340	+	838.901i	−0.627383	+	1.08666i
$773$	−1129.82	+	652.302i	−1.46160	+	0.843858i	−0.999086	−	0.0427514i	$-0.986388\pi$
$773$	−1129.82	+	652.302i	−1.46160	+	0.843858i	−0.462519	+	0.886609i	$0.653054\pi$
$774$		0			0
$775$	97.8451	+	56.4909i	0.126252	+	0.0728914i
$776$			15.8309i			0.0204007i
$777$		0			0
$778$	107.276			0.137887
$779$	21.9024	−	37.9362i	0.0281161	−	0.0486985i
$780$		0			0
$781$	−1.04903	−	1.81697i	−0.00134318	−	0.00232646i
$782$	243.208	+	140.416i	0.311008	+	0.179561i
$783$		0			0
$784$	−39.4469	+	525.913i	−0.0503149	+	0.670808i
$785$	−337.793			−0.430309
$786$		0			0
$787$	182.275	−	105.237i	0.231607	−	0.133719i	−0.379706	−	0.925107i	$-0.623975\pi$
$787$	182.275	−	105.237i	0.231607	−	0.133719i	0.611313	+	0.791389i	$0.290642\pi$
$788$	−352.691	−	610.878i	−0.447577	−	0.775226i
$789$		0			0
$790$		−	30.8402i		−	0.0390382i
$791$	−35.8579	+	8.18308i	−0.0453323	+	0.0103452i
$792$		0			0
$793$	446.770	−	773.829i	0.563393	−	0.975825i
$794$	−343.703	+	198.437i	−0.432876	+	0.249921i
$795$		0			0
$796$	117.860	+	68.0467i	0.148066	+	0.0854858i
$797$		−	254.794i		−	0.319691i	−0.987142	−	0.159845i	$-0.948900\pi$
$797$		−	254.794i		−	0.319691i	0.987142	−	0.159845i	$-0.0510996\pi$
$798$		0			0
$799$	255.848			0.320210
$800$	−68.9439	+	119.414i	−0.0861799	+	0.149268i
$801$		0			0
$802$	56.0009	+	96.9964i	0.0698265	+	0.120943i
$803$	−3.24042	−	1.87086i	−0.00403539	−	0.00232983i
$804$		0			0
$805$	−507.633	+	470.983i	−0.630600	+	0.585073i
$806$	350.025			0.434275
$807$		0			0
$808$	393.649	−	227.273i	0.487189	−	0.281279i
$809$	−114.683	−	198.637i	−0.141759	−	0.245533i	0.786400	−	0.617717i	$-0.211942\pi$
$809$	−114.683	−	198.637i	−0.141759	−	0.245533i	−0.928159	+	0.372184i	$0.878609\pi$
$810$		0			0
$811$		−	1108.59i		−	1.36694i	−0.729978	−	0.683470i	$-0.760470\pi$
$811$		−	1108.59i		−	1.36694i	0.729978	−	0.683470i	$-0.239530\pi$
$812$	894.899	+	964.536i	1.10209	+	1.18785i
$813$		0			0
$814$	0.637302	−	1.10384i	0.000782926	−	0.00135607i
$815$	−116.050	+	67.0013i	−0.142392	+	0.0822102i
$816$		0			0
$817$	75.8373	+	43.7847i	0.0928241	+	0.0535920i
$818$			147.553i			0.180382i
$819$		0			0
$820$	−303.554			−0.370188
$821$	433.762	−	751.297i	0.528333	−	0.915100i	−0.471121	−	0.882069i	$-0.656150\pi$
$821$	433.762	−	751.297i	0.528333	−	0.915100i	0.999454	−	0.0330318i	$-0.0105162\pi$
$822$		0			0
$823$	−492.440	−	852.931i	−0.598348	−	1.03637i	−0.993065	−	0.117566i	$-0.962491\pi$
$823$	−492.440	−	852.931i	−0.598348	−	1.03637i	0.394718	−	0.918802i	$-0.370842\pi$
$824$	−402.202	−	232.212i	−0.488110	−	0.281810i
$825$		0			0
$826$	5.10769	+	22.3817i	0.00618364	+	0.0270964i
$827$	767.641			0.928224			0.464112	−	0.885777i	$-0.346374\pi$
$827$	767.641			0.928224			0.464112	+	0.885777i	$0.346374\pi$
$828$		0			0
$829$	−153.578	+	88.6684i	−0.185257	+	0.106958i	−0.589760	−	0.807578i	$-0.700778\pi$
$829$	−153.578	+	88.6684i	−0.185257	+	0.106958i	0.404503	+	0.914537i	$0.367444\pi$
$830$	94.6333	+	163.910i	0.114016	+	0.197482i
$831$		0			0
$832$		−	563.061i		−	0.676756i
$833$	260.201	−	381.590i	0.312366	−	0.458091i
$834$		0			0
$835$	250.539	−	433.946i	0.300046	−	0.519696i
$836$	0.157318	−	0.0908275i	0.000188179	−	0.000108645i
$837$		0			0
$838$	323.524	+	186.787i	0.386067	+	0.222896i
$839$			15.9176i			0.0189721i	0.999955	+	0.00948606i	$0.00301955\pi$
$839$			15.9176i			0.0189721i	−0.999955	+	0.00948606i	$0.996980\pi$
$840$		0			0
$841$	1968.04			2.34012
$842$	216.297	−	374.637i	0.256885	−	0.444937i
$843$		0			0
$844$	−225.701	−	390.926i	−0.267419	−	0.463183i
$845$	697.229	+	402.545i	0.825123	+	0.476385i
$846$		0			0
$847$	−249.680	+	809.348i	−0.294782	+	0.955547i
$848$	−204.367			−0.240998
$849$		0			0
$850$	27.4871	−	15.8697i	0.0323378	−	0.0186702i
$851$	−935.321	−	1620.02i	−1.09908	−	1.90367i
$852$		0			0
$853$			694.629i			0.814336i	0.913353	+	0.407168i	$0.133484\pi$
$853$			694.629i			0.814336i	−0.913353	+	0.407168i	$0.866516\pi$
$854$	134.254	−	124.561i	0.157206	−	0.145856i
$855$		0			0
$856$	−267.080	+	462.597i	−0.312010	+	0.540417i
$857$	1301.17	−	751.232i	1.51829	−	0.876583i	0.518518	−	0.855067i	$-0.326484\pi$
$857$	1301.17	−	751.232i	1.51829	−	0.876583i	0.999769	−	0.0215161i	$-0.00684933\pi$
$858$		0			0
$859$	−254.436	−	146.898i	−0.296200	−	0.171011i	0.344535	−	0.938774i	$-0.388037\pi$
$859$	−254.436	−	146.898i	−0.296200	−	0.171011i	−0.640734	+	0.767763i	$0.721370\pi$
$860$		−	606.828i		−	0.705614i
$861$		0			0
$862$	50.7334			0.0588555
$863$	−129.059	+	223.537i	−0.149547	+	0.259023i	−0.931060	−	0.364866i	$-0.881115\pi$
$863$	−129.059	+	223.537i	−0.149547	+	0.259023i	0.781513	+	0.623889i	$0.214448\pi$
$864$		0			0
$865$	213.118	+	369.131i	0.246379	+	0.426741i
$866$	−205.920	−	118.888i	−0.237783	−	0.137284i
$867$		0			0
$868$	−536.030	−	165.363i	−0.617546	−	0.190510i
$869$	0.916657			0.00105484
$870$		0			0
$871$	−139.611	+	80.6046i	−0.160288	+	0.0925426i
$872$	−141.544	−	245.162i	−0.162322	−	0.281149i
$873$		0			0
$874$			34.0956i			0.0390109i
$875$	17.4125	+	76.3008i	0.0199000	+	0.0872009i
$876$		0			0
$877$	−668.747	+	1158.30i	−0.762539	+	1.32076i	0.178999	+	0.983849i	$0.442714\pi$
$877$	−668.747	+	1158.30i	−0.762539	+	1.32076i	−0.941538	+	0.336907i	$0.890619\pi$
$878$	−158.609	+	91.5727i	−0.180648	+	0.104297i
$879$		0			0
$880$	−0.932913	−	0.538618i	−0.00106013	−	0.000612065i
$881$			606.188i			0.688069i	0.938957	+	0.344034i	$0.111794\pi$
$881$			606.188i			0.688069i	−0.938957	+	0.344034i	$0.888206\pi$
$882$		0			0
$883$	−862.650			−0.976953			−0.488477	−	0.872577i	$-0.662447\pi$
$883$	−862.650			−0.976953			−0.488477	+	0.872577i	$0.662447\pi$
$884$	−384.437	+	665.865i	−0.434884	+	0.753241i
$885$		0			0
$886$	37.1216	+	64.2965i	0.0418980	+	0.0725694i
$887$	799.662	+	461.685i	0.901536	+	0.520502i	0.877698	−	0.479214i	$-0.159078\pi$
$887$	799.662	+	461.685i	0.901536	+	0.520502i	0.0238378	+	0.999716i	$0.492411\pi$
$888$		0			0
$889$	37.8755	−	8.64351i	0.0426046	−	0.00972273i
$890$	70.3297			0.0790221
$891$		0			0
$892$	−901.610	+	520.545i	−1.01077	+	0.583570i
$893$	15.5311	+	26.9006i	0.0173920	+	0.0301239i
$894$		0			0
$895$		−	487.154i		−	0.544306i
$896$	261.646	−	848.134i	0.292015	−	0.946579i
$897$		0			0
$898$	−19.9011	+	34.4697i	−0.0221616	+	0.0383850i
$899$	−1037.16	+	598.807i	−1.15369	+	0.666082i
$900$		0			0
$901$	154.996	+	89.4867i	0.172026	+	0.0993193i
$902$			1.15388i			0.00127925i
$903$		0			0
$904$	26.7035			0.0295392
$905$	43.6932	−	75.6789i	0.0482798	−	0.0836231i
$906$		0			0
$907$	47.3567	+	82.0242i	0.0522125	+	0.0904346i	0.890950	−	0.454101i	$-0.150039\pi$
$907$	47.3567	+	82.0242i	0.0522125	+	0.0904346i	−0.838738	+	0.544535i	$0.816706\pi$
$908$	−661.807	−	382.095i	−0.728863	−	0.420809i
$909$		0			0
$910$	164.910	+	177.743i	0.181220	+	0.195322i
$911$	556.948			0.611359			0.305679	−	0.952134i	$-0.401116\pi$
$911$	556.948			0.611359			0.305679	+	0.952134i	$0.401116\pi$
$912$		0			0
$913$	−4.87186	+	2.81277i	−0.00533610	+	0.00308080i
$914$	−69.1233	−	119.725i	−0.0756272	−	0.130990i
$915$		0			0
$916$			511.633i			0.558551i
$917$	−1113.85	−	343.618i	−1.21467	−	0.374720i
$918$		0			0
$919$	478.581	−	828.926i	0.520762	−	0.901987i	−0.478946	−	0.877844i	$-0.658981\pi$
$919$	478.581	−	828.926i	0.520762	−	0.901987i	0.999709	−	0.0241428i	$-0.00768562\pi$
$920$	435.403	−	251.380i	0.473264	−	0.273239i
$921$		0			0
$922$	271.889	+	156.975i	0.294890	+	0.170255i
$923$			1078.14i			1.16808i
$924$		0			0
$925$	−211.418			−0.228560
$926$	64.5533	−	111.810i	0.0697120	−	0.120745i
$927$		0			0
$928$	−730.811	−	1265.80i	−0.787511	−	1.36401i
$929$	990.414	+	571.816i	1.06611	+	0.615517i	0.927115	−	0.374776i	$-0.122280\pi$
$929$	990.414	+	571.816i	1.06611	+	0.615517i	0.138992	+	0.990294i	$0.455614\pi$
$930$		0			0
$931$	55.9169	+	4.19412i	0.0600611	+	0.00450497i
$932$	−1015.82			−1.08993
$933$		0			0
$934$	491.804	−	283.943i	0.526557	−	0.304008i
$935$	0.471693	+	0.816996i	0.000504484	+	0.000873792i
$936$		0			0
$937$		−	578.660i		−	0.617567i	−0.951132	−	0.308783i	$-0.900078\pi$
$937$		−	578.660i		−	0.617567i	0.951132	−	0.308783i	$-0.0999218\pi$
$938$	−32.2129	+	7.35127i	−0.0343422	+	0.00783717i
$939$		0			0
$940$	107.625	−	186.413i	0.114495	−	0.198312i
$941$	1086.18	−	627.108i	1.15428	−	0.666427i	0.204357	−	0.978896i	$-0.434490\pi$
$941$	1086.18	−	627.108i	1.15428	−	0.666427i	0.949928	+	0.312470i	$0.101156\pi$
$942$		0			0
$943$	1466.59	+	846.733i	1.55523	+	0.897915i
$944$			52.4132i			0.0555225i
$945$		0			0
$946$	−2.30670			−0.00243837
$947$	−878.012	+	1520.76i	−0.927151	+	1.60587i	−0.139086	+	0.990280i	$0.544417\pi$
$947$	−878.012	+	1520.76i	−0.927151	+	1.60587i	−0.788065	+	0.615592i	$0.788917\pi$
$948$		0			0
$949$	961.388	+	1665.17i	1.01305	+	1.75466i
$950$	3.33718	+	1.92672i	0.00351282	+	0.00202813i
$951$		0			0
$952$	−245.820	+	228.073i	−0.258215	+	0.239572i
$953$	1048.32			1.10002			0.550011	−	0.835157i	$-0.314624\pi$
$953$	1048.32			1.10002			0.550011	+	0.835157i	$0.314624\pi$
$954$		0			0
$955$	−366.998	+	211.887i	−0.384292	+	0.221871i
$956$	733.085	+	1269.74i	0.766826	+	1.32818i
$957$		0			0
$958$		−	191.722i		−	0.200127i
$959$	−347.300	−	374.325i	−0.362148	−	0.390329i
$960$		0			0
$961$	−225.203	+	390.062i	−0.234342	+	0.405892i
$962$	−567.236	+	327.494i	−0.589642	+	0.340430i
$963$		0			0
$964$	908.785	+	524.688i	0.942723	+	0.544282i
$965$		−	610.762i		−	0.632914i
$966$		0			0
$967$	−1770.86			−1.83130			−0.915648	−	0.401982i	$-0.868321\pi$
$967$	−1770.86			−1.83130			−0.915648	+	0.401982i	$0.868321\pi$
$968$	307.471	−	532.556i	0.317636	−	0.550161i
$969$		0			0
$970$	−2.34541	−	4.06237i	−0.00241795	−	0.00418801i
$971$	−834.000	−	481.510i	−0.858908	−	0.495891i	0.00473848	−	0.999989i	$-0.498492\pi$
$971$	−834.000	−	481.510i	−0.858908	−	0.495891i	−0.863646	+	0.504098i	$0.831825\pi$
$972$		0			0
$973$	−179.093	−	784.779i	−0.184063	−	0.806556i
$974$	131.760			0.135277
$975$		0			0
$976$	362.105	−	209.061i	0.371009	−	0.214202i
$977$	−269.150	−	466.182i	−0.275487	−	0.477157i	0.694771	−	0.719231i	$-0.255506\pi$
$977$	−269.150	−	466.182i	−0.275487	−	0.477157i	−0.970258	+	0.242074i	$0.922172\pi$
$978$		0			0
$979$			2.09040i			0.00213524i
$980$	−168.573	−	350.105i	−0.172013	−	0.357250i
$981$		0			0
$982$	−251.021	+	434.782i	−0.255623	+	0.442751i
$983$	586.233	−	338.462i	0.596371	−	0.344315i	−0.171241	−	0.985229i	$-0.554778\pi$
$983$	586.233	−	338.462i	0.596371	−	0.344315i	0.767613	+	0.640914i	$0.221444\pi$
$984$		0			0
$985$	385.164	+	222.375i	0.391030	+	0.225761i
$986$			336.440i			0.341217i
$987$		0			0
$988$	−93.3481			−0.0944819
$989$	−1692.69	+	2931.82i	−1.71151	+	2.96443i
$990$		0			0
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	−0.994204	−	0.107514i	$-0.965711\pi$
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	0.403992	−	0.914763i	$-0.367622\pi$
$992$	539.666	+	311.576i	0.544018	+	0.314089i
$993$		0			0
$994$	−65.1400	+	211.154i	−0.0655332	+	0.212428i
$995$	−85.8082			−0.0862394
$996$		0			0
$997$	523.016	−	301.963i	0.524590	−	0.302872i	−0.214221	−	0.976785i	$-0.568721\pi$
$997$	523.016	−	301.963i	0.524590	−	0.302872i	0.738810	+	0.673913i	$0.235388\pi$
$998$	30.9623	+	53.6283i	0.0310244	+	0.0537358i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.w.a.271.3		8
3.2	odd	2		105.3.n.a.61.2	yes	8
7.3	odd	6	inner	315.3.w.a.136.3		8
15.2	even	4		525.3.s.h.124.4		16
15.8	even	4		525.3.s.h.124.5		16
15.14	odd	2		525.3.o.l.376.3		8
21.2	odd	6		735.3.h.a.391.5		8
21.5	even	6		735.3.h.a.391.6		8
21.17	even	6		105.3.n.a.31.2	✓	8
105.17	odd	12		525.3.s.h.199.5		16
105.38	odd	12		525.3.s.h.199.4		16
105.59	even	6		525.3.o.l.451.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.2	✓	8	21.17	even	6
105.3.n.a.61.2	yes	8	3.2	odd	2
315.3.w.a.136.3		8	7.3	odd	6	inner
315.3.w.a.271.3		8	1.1	even	1	trivial
525.3.o.l.376.3		8	15.14	odd	2
525.3.o.l.451.3		8	105.59	even	6
525.3.s.h.124.4		16	15.2	even	4
525.3.s.h.124.5		16	15.8	even	4
525.3.s.h.199.4		16	105.38	odd	12
525.3.s.h.199.5		16	105.17	odd	12
735.3.h.a.391.5		8	21.2	odd	6
735.3.h.a.391.6		8	21.5	even	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)

\(f(q)\)	\(=\)	\(q+(0.336732 - 0.583237i) q^{2} +(1.77322 + 3.07131i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +O(q^{10})\)	\(q+(0.336732 - 0.583237i) q^{2} +(1.77322 + 3.07131i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(-1.30416 + 0.752955i) q^{10} +(-0.0223800 - 0.0387632i) q^{11} +23.0010i q^{13} +(-1.38970 + 4.50476i) q^{14} +(-5.38154 + 9.32109i) q^{16} +(8.16292 - 4.71286i) q^{17} +(0.991050 + 0.572183i) q^{19} -7.93010i q^{20} -0.0301442 q^{22} +(-22.1202 + 38.3133i) q^{23} +(2.50000 + 4.33013i) q^{25} +(13.4150 + 7.74518i) q^{26} +(-16.8848 - 18.1987i) q^{28} -53.0004 q^{29} +(19.5690 - 11.2982i) q^{31} +(13.7888 + 23.8829i) q^{32} -6.34788i q^{34} +(14.9569 + 4.61414i) q^{35} +(-21.1418 + 36.6186i) q^{37} +(0.667436 - 0.385344i) q^{38} +(-9.84175 - 5.68214i) q^{40} -38.2787i q^{41} +76.5222 q^{43} +(0.0793693 - 0.137472i) q^{44} +(14.8971 + 25.8026i) q^{46} +(23.5070 + 13.5718i) q^{47} +(44.1489 - 21.2574i) q^{49} +3.36732 q^{50} +(-70.6434 + 40.7860i) q^{52} +(9.49388 + 16.4439i) q^{53} +0.100086i q^{55} +(-34.6841 + 7.91521i) q^{56} +(-17.8469 + 30.9118i) q^{58} +(4.21731 - 2.43486i) q^{59} +(-33.6432 - 19.4239i) q^{61} -15.2178i q^{62} -24.4798 q^{64} +(25.7159 - 44.5413i) q^{65} +(3.50439 + 6.06978i) q^{67} +(28.9494 + 16.7139i) q^{68} +(7.72761 - 7.16970i) q^{70} +46.8735 q^{71} +(72.3956 - 41.7976i) q^{73} +(14.2382 + 24.6613i) q^{74} +4.05843i q^{76} +(0.213104 + 0.229686i) q^{77} +(-10.2397 + 17.7357i) q^{79} +(20.8426 - 12.0335i) q^{80} +(-22.3256 - 12.8897i) q^{82} -125.683i q^{83} -21.0766 q^{85} +(25.7674 - 44.6305i) q^{86} +(-0.113741 - 0.197005i) q^{88} +(-40.4455 - 23.3512i) q^{89} +(-35.8223 - 156.972i) q^{91} -156.896 q^{92} +(15.8311 - 9.14010i) q^{94} +(-1.27944 - 2.21606i) q^{95} +3.11494i q^{97} +(2.46826 - 32.9073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more