LMFDB - Embedded newform 304.3.r.b.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,3,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, 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("304.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not 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:	$8.28340003655$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.3.r.b.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.29225 - 1.90078i) q^{3} +(3.47303 + 6.01546i) q^{5} +1.22892 q^{7} +(2.72593 - 4.72145i) q^{9} +O(q^{10})$	\(q+(3.29225 - 1.90078i) q^{3} +(3.47303 + 6.01546i) q^{5} +1.22892 q^{7} +(2.72593 - 4.72145i) q^{9} +0.0363521 q^{11} +(14.6268 + 8.44481i) q^{13} +(22.8681 + 13.2029i) q^{15} +(-4.59329 - 7.95581i) q^{17} +(-12.7864 + 14.0537i) q^{19} +(4.04592 - 2.33591i) q^{21} +(4.87974 - 8.45195i) q^{23} +(-11.6238 + 20.1331i) q^{25} +13.4885i q^{27} +(4.50339 + 2.60003i) q^{29} -44.3727i q^{31} +(0.119680 - 0.0690974i) q^{33} +(4.26808 + 7.39254i) q^{35} -45.5661i q^{37} +64.2069 q^{39} +(50.0829 - 28.9153i) q^{41} +(-15.1574 - 26.2534i) q^{43} +37.8689 q^{45} +(-25.5066 + 44.1787i) q^{47} -47.4897 q^{49} +(-30.2445 - 17.4617i) q^{51} +(10.0847 + 5.82239i) q^{53} +(0.126252 + 0.218675i) q^{55} +(-15.3831 + 70.5725i) q^{57} +(17.7409 - 10.2427i) q^{59} +(-8.23849 + 14.2695i) q^{61} +(3.34996 - 5.80229i) q^{63} +117.316i q^{65} +(1.83276 + 1.05814i) q^{67} -37.1012i q^{69} +(33.7958 - 19.5120i) q^{71} +(-28.1064 - 48.6818i) q^{73} +88.3775i q^{75} +0.0446740 q^{77} +(-39.8385 + 23.0008i) q^{79} +(50.1720 + 86.9004i) q^{81} -65.3332 q^{83} +(31.9053 - 55.2615i) q^{85} +19.7684 q^{87} +(-134.435 - 77.6163i) q^{89} +(17.9753 + 10.3780i) q^{91} +(-84.3427 - 146.086i) q^{93} +(-128.947 - 28.1074i) q^{95} +(-98.8107 + 57.0484i) q^{97} +(0.0990933 - 0.171635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 - 2 * q^5 + 14 * q^9	$ 6 q + 9 q^{3} - 2 q^{5} + 14 q^{9} - 26 q^{11} + 30 q^{13} + 18 q^{15} - 42 q^{17} - 25 q^{19} - 102 q^{21} - 8 q^{23} - 17 q^{25} - 12 q^{29} + 123 q^{33} + 38 q^{35} + 44 q^{39} + 63 q^{41} + 34 q^{43} - 28 q^{45} - 58 q^{47} + 18 q^{49} - 132 q^{51} - 12 q^{53} + 28 q^{55} - 16 q^{57} + 147 q^{59} + 58 q^{61} - 86 q^{63} - 201 q^{67} + 102 q^{71} + 7 q^{73} - 376 q^{77} + 253 q^{81} - 146 q^{83} - 90 q^{85} + 568 q^{87} - 72 q^{89} + 216 q^{91} - 160 q^{93} - 558 q^{95} + 21 q^{97} + 56 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 - 2 * q^5 + 14 * q^9 - 26 * q^11 + 30 * q^13 + 18 * q^15 - 42 * q^17 - 25 * q^19 - 102 * q^21 - 8 * q^23 - 17 * q^25 - 12 * q^29 + 123 * q^33 + 38 * q^35 + 44 * q^39 + 63 * q^41 + 34 * q^43 - 28 * q^45 - 58 * q^47 + 18 * q^49 - 132 * q^51 - 12 * q^53 + 28 * q^55 - 16 * q^57 + 147 * q^59 + 58 * q^61 - 86 * q^63 - 201 * q^67 + 102 * q^71 + 7 * q^73 - 376 * q^77 + 253 * q^81 - 146 * q^83 - 90 * q^85 + 568 * q^87 - 72 * q^89 + 216 * q^91 - 160 * q^93 - 558 * q^95 + 21 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.29225	−	1.90078i	1.09742	−	0.633593i	0.161875	−	0.986811i	$-0.448246\pi$
$3$	3.29225	−	1.90078i	1.09742	−	0.633593i	0.935541	+	0.353218i	$0.114913\pi$
$4$		0			0
$5$	3.47303	+	6.01546i	0.694606	+	1.20309i	0.970313	+	0.241851i	$0.0777544\pi$
$5$	3.47303	+	6.01546i	0.694606	+	1.20309i	−0.275708	+	0.961241i	$0.588912\pi$
$6$		0			0
$7$	1.22892			0.175560			0.0877802	−	0.996140i	$-0.472023\pi$
$7$	1.22892			0.175560			0.0877802	+	0.996140i	$0.472023\pi$
$8$		0			0
$9$	2.72593	−	4.72145i	0.302881	−	0.524605i
$10$		0			0
$11$	0.0363521			0.00330474			0.00165237	−	0.999999i	$-0.499474\pi$
$11$	0.0363521			0.00330474			0.00165237	+	0.999999i	$0.499474\pi$
$12$		0			0
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.942708	−	0.333618i	$-0.108269\pi$
$13$	14.6268	+	8.44481i	1.12514	+	0.649601i	0.182433	+	0.983218i	$0.441603\pi$
$14$		0			0
$15$	22.8681	+	13.2029i	1.52454	+	0.880195i
$16$		0			0
$17$	−4.59329	−	7.95581i	−0.270194	−	0.467989i	0.698718	−	0.715398i	$-0.253754\pi$
$17$	−4.59329	−	7.95581i	−0.270194	−	0.467989i	−0.968911	+	0.247408i	$0.920421\pi$
$18$		0			0
$19$	−12.7864	+	14.0537i	−0.672971	+	0.739669i
$19$	−12.7864	+	14.0537i	−0.672971	+	0.739669i
$20$		0			0
$21$	4.04592	−	2.33591i	0.192663	−	0.111234i
$22$		0			0
$23$	4.87974	−	8.45195i	0.212162	−	0.367476i	−0.740229	−	0.672355i	$-0.765283\pi$
$23$	4.87974	−	8.45195i	0.212162	−	0.367476i	0.952391	+	0.304879i	$0.0986161\pi$
$24$		0			0
$25$	−11.6238	+	20.1331i	−0.464954	+	0.805323i
$26$		0			0
$27$			13.4885i			0.499573i
$28$		0			0
$29$	4.50339	+	2.60003i	0.155289	+	0.0896564i	0.575631	−	0.817710i	$-0.304756\pi$
$29$	4.50339	+	2.60003i	0.155289	+	0.0896564i	−0.420342	+	0.907366i	$0.638090\pi$
$30$		0			0
$31$		−	44.3727i		−	1.43138i	−0.698420	−	0.715689i	$-0.746113\pi$
$31$		−	44.3727i		−	1.43138i	0.698420	−	0.715689i	$-0.253887\pi$
$32$		0			0
$33$	0.119680	−	0.0690974i	0.00362667	−	0.00209386i
$34$		0			0
$35$	4.26808	+	7.39254i	0.121945	+	0.211215i
$36$		0			0
$37$		−	45.5661i		−	1.23152i	−0.787935	−	0.615758i	$-0.788850\pi$
$37$		−	45.5661i		−	1.23152i	0.787935	−	0.615758i	$-0.211150\pi$
$38$		0			0
$39$	64.2069			1.64633
$40$		0			0
$41$	50.0829	−	28.9153i	1.22153	−	0.705252i	0.256288	−	0.966600i	$-0.417500\pi$
$41$	50.0829	−	28.9153i	1.22153	−	0.705252i	0.965245	+	0.261348i	$0.0841670\pi$
$42$		0			0
$43$	−15.1574	−	26.2534i	−0.352497	−	0.610543i	0.634189	−	0.773178i	$-0.281334\pi$
$43$	−15.1574	−	26.2534i	−0.352497	−	0.610543i	−0.986686	+	0.162635i	$0.948001\pi$
$44$		0			0
$45$	37.8689			0.841531
$46$		0			0
$47$	−25.5066	+	44.1787i	−0.542693	+	0.939972i	0.456055	+	0.889951i	$0.349262\pi$
$47$	−25.5066	+	44.1787i	−0.542693	+	0.939972i	−0.998748	+	0.0500204i	$0.984071\pi$
$48$		0			0
$49$	−47.4897			−0.969179
$50$		0			0
$51$	−30.2445	−	17.4617i	−0.593029	−	0.342386i
$52$		0			0
$53$	10.0847	+	5.82239i	0.190277	+	0.109856i	0.592112	−	0.805856i	$-0.298294\pi$
$53$	10.0847	+	5.82239i	0.190277	+	0.109856i	−0.401835	+	0.915712i	$0.631628\pi$
$54$		0			0
$55$	0.126252	+	0.218675i	0.00229549	+	0.00397591i
$56$		0			0
$57$	−15.3831	+	70.5725i	−0.269879	+	1.23811i
$58$		0			0
$59$	17.7409	−	10.2427i	0.300694	−	0.173606i	−0.342061	−	0.939678i	$-0.611125\pi$
$59$	17.7409	−	10.2427i	0.300694	−	0.173606i	0.642754	+	0.766072i	$0.277792\pi$
$60$		0			0
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	−0.925619	−	0.378456i	$-0.876455\pi$
$61$	−8.23849	+	14.2695i	−0.135057	+	0.233926i	0.790562	+	0.612382i	$0.209788\pi$
$62$		0			0
$63$	3.34996	−	5.80229i	0.0531739	−	0.0920999i
$64$		0			0
$65$			117.316i			1.80486i
$66$		0			0
$67$	1.83276	+	1.05814i	0.0273546	+	0.0157932i	0.513615	−	0.858021i	$-0.328306\pi$
$67$	1.83276	+	1.05814i	0.0273546	+	0.0157932i	−0.486260	+	0.873814i	$0.661639\pi$
$68$		0			0
$69$		−	37.1012i		−	0.537699i
$70$		0			0
$71$	33.7958	−	19.5120i	0.475998	−	0.274817i	−0.242749	−	0.970089i	$-0.578049\pi$
$71$	33.7958	−	19.5120i	0.475998	−	0.274817i	0.718747	+	0.695272i	$0.244716\pi$
$72$		0			0
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	0.606752	−	0.794891i	$-0.292472\pi$
$73$	−28.1064	−	48.6818i	−0.385020	−	0.666874i	−0.991772	+	0.128017i	$0.959139\pi$
$74$		0			0
$75$			88.3775i			1.17837i
$76$		0			0
$77$	0.0446740			0.000580181
$78$		0			0
$79$	−39.8385	+	23.0008i	−0.504285	+	0.291149i	−0.730481	−	0.682933i	$-0.760704\pi$
$79$	−39.8385	+	23.0008i	−0.504285	+	0.291149i	0.226196	+	0.974082i	$0.427371\pi$
$80$		0			0
$81$	50.1720	+	86.9004i	0.619407	+	1.07284i
$82$		0			0
$83$	−65.3332			−0.787146			−0.393573	−	0.919293i	$-0.628761\pi$
$83$	−65.3332			−0.787146			−0.393573	+	0.919293i	$0.628761\pi$
$84$		0			0
$85$	31.9053	−	55.2615i	0.375356	−	0.650136i
$86$		0			0
$87$	19.7684			0.227223
$88$		0			0
$89$	−134.435	−	77.6163i	−1.51051	−	0.872093i	−0.999925	−	0.0122654i	$-0.996096\pi$
$89$	−134.435	−	77.6163i	−1.51051	−	0.872093i	−0.510585	−	0.859828i	$-0.670571\pi$
$90$		0			0
$91$	17.9753	+	10.3780i	0.197530	+	0.114044i
$92$		0			0
$93$	−84.3427	−	146.086i	−0.906911	−	1.57082i
$94$		0			0
$95$	−128.947	−	28.1074i	−1.35734	−	0.295868i
$96$		0			0
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.913718	−	0.406350i	$-0.866801\pi$
$97$	−98.8107	+	57.0484i	−1.01867	+	0.588128i	−0.104949	+	0.994478i	$0.533468\pi$
$98$		0			0
$99$	0.0990933	−	0.171635i	0.00100094	−	0.00173368i
$100$		0			0
$101$	85.7095	−	148.453i	0.848609	−	1.46983i	−0.0338413	−	0.999427i	$-0.510774\pi$
$101$	85.7095	−	148.453i	0.848609	−	1.46983i	0.882450	−	0.470406i	$-0.155893\pi$
$102$		0			0
$103$			121.297i			1.17764i	0.808264	+	0.588820i	$0.200407\pi$
$103$			121.297i			1.17764i	−0.808264	+	0.588820i	$0.799593\pi$
$104$		0			0
$105$	28.1032	+	16.2254i	0.267649	+	0.154527i
$106$		0			0
$107$		−	56.0566i		−	0.523893i	−0.965082	−	0.261947i	$-0.915636\pi$
$107$		−	56.0566i		−	0.523893i	0.965082	−	0.261947i	$-0.0843644\pi$
$108$		0			0
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	−0.696109	−	0.717936i	$-0.745087\pi$
$109$	−46.0431	+	26.5830i	−0.422414	+	0.243881i	0.273696	+	0.961816i	$0.411754\pi$
$110$		0			0
$111$	−86.6112	−	150.015i	−0.780281	−	1.35149i
$112$		0			0
$113$			136.946i			1.21191i	0.795497	+	0.605957i	$0.207210\pi$
$113$			136.946i			1.21191i	−0.795497	+	0.605957i	$0.792790\pi$
$114$		0			0
$115$	67.7898			0.589477
$116$		0			0
$117$	79.7434	−	46.0399i	0.681568	−	0.393503i
$118$		0			0
$119$	−5.64480	−	9.77708i	−0.0474353	−	0.0821603i
$120$		0			0
$121$	−120.999			−0.999989
$122$		0			0
$123$	109.923	−	190.393i	0.893686	−	1.54791i
$124$		0			0
$125$	12.1717			0.0973736
$126$		0			0
$127$	−136.758	−	78.9573i	−1.07684	−	0.621711i	−0.146794	−	0.989167i	$-0.546896\pi$
$127$	−136.758	−	78.9573i	−1.07684	−	0.621711i	−0.930041	+	0.367456i	$0.880229\pi$
$128$		0			0
$129$	−99.8037	−	57.6217i	−0.773672	−	0.446680i
$130$		0			0
$131$	−38.5396	−	66.7525i	−0.294195	−	0.509561i	0.680602	−	0.732653i	$-0.261718\pi$
$131$	−38.5396	−	66.7525i	−0.294195	−	0.509561i	−0.974797	+	0.223092i	$0.928385\pi$
$132$		0			0
$133$	−15.7136	+	17.2709i	−0.118147	+	0.129857i
$134$		0			0
$135$	−81.1394	+	46.8459i	−0.601033	+	0.347006i
$136$		0			0
$137$	45.3969	−	78.6298i	0.331364	−	0.573940i	−0.651415	−	0.758721i	$-0.725824\pi$
$137$	45.3969	−	78.6298i	0.331364	−	0.573940i	0.982780	+	0.184781i	$0.0591577\pi$
$138$		0			0
$139$	−45.7773	+	79.2886i	−0.329333	+	0.570421i	−0.982380	−	0.186896i	$-0.940157\pi$
$139$	−45.7773	+	79.2886i	−0.329333	+	0.570421i	0.653047	+	0.757318i	$0.273491\pi$
$140$		0			0
$141$			193.930i			1.37539i
$142$		0			0
$143$	0.531717	+	0.306987i	0.00371830	+	0.00214676i
$144$		0			0
$145$			36.1200i			0.249103i
$146$		0			0
$147$	−156.348	+	90.2676i	−1.06359	+	0.614065i
$148$		0			0
$149$	−12.0587	−	20.8863i	−0.0809308	−	0.140176i	0.822719	−	0.568448i	$-0.192456\pi$
$149$	−12.0587	−	20.8863i	−0.0809308	−	0.140176i	−0.903650	+	0.428272i	$0.859123\pi$
$150$		0			0
$151$			251.451i			1.66524i	0.553848	+	0.832618i	$0.313159\pi$
$151$			251.451i			1.66524i	−0.553848	+	0.832618i	$0.686841\pi$
$152$		0			0
$153$	−50.0839			−0.327346
$154$		0			0
$155$	266.922	−	154.108i	1.72208	−	0.994242i
$156$		0			0
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	0.971474	−	0.237144i	$-0.0762113\pi$
$157$	44.0172	+	76.2401i	0.280364	+	0.485605i	−0.691110	+	0.722750i	$0.742878\pi$
$158$		0			0
$159$	44.2684			0.278417
$160$		0			0
$161$	5.99682	−	10.3868i	0.0372473	−	0.0645143i
$162$		0			0
$163$	28.3608			0.173992			0.0869962	−	0.996209i	$-0.472273\pi$
$163$	28.3608			0.173992			0.0869962	+	0.996209i	$0.472273\pi$
$164$		0			0
$165$	0.831305	+	0.479954i	0.00503821	+	0.00290881i
$166$		0			0
$167$	52.1162	+	30.0893i	0.312073	+	0.180176i	0.647854	−	0.761765i	$-0.275667\pi$
$167$	52.1162	+	30.0893i	0.312073	+	0.180176i	−0.335781	+	0.941940i	$0.609000\pi$
$168$		0			0
$169$	58.1295	+	100.683i	0.343962	+	0.595759i
$170$		0			0
$171$	31.4989	+	98.6799i	0.184204	+	0.577076i
$172$		0			0
$173$	152.888	−	88.2699i	0.883745	−	0.510230i	0.0118536	−	0.999930i	$-0.496227\pi$
$173$	152.888	−	88.2699i	0.883745	−	0.510230i	0.871891	+	0.489699i	$0.162893\pi$
$174$		0			0
$175$	−14.2848	+	24.7420i	−0.0816275	+	0.141383i
$176$		0			0
$177$	38.9383	−	67.4432i	0.219991	−	0.381035i
$178$		0			0
$179$		−	0.226943i		−	0.00126784i	−1.00000		0.000633920i	$-0.999798\pi$
$179$		−	0.226943i		−	0.00126784i	1.00000		0.000633920i	$-0.000201783\pi$
$180$		0			0
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	0.812899	−	0.582405i	$-0.197888\pi$
$181$	129.410	+	74.7148i	0.714971	+	0.412789i	−0.0979279	+	0.995194i	$0.531221\pi$
$182$		0			0
$183$			62.6382i			0.342285i
$184$		0			0
$185$	274.101	−	158.252i	1.48163	−	0.855418i
$186$		0			0
$187$	−0.166976	−	0.289211i	−0.000892919	−	0.00154658i
$188$		0			0
$189$			16.5763i			0.0877053i
$190$		0			0
$191$	251.306			1.31574			0.657870	−	0.753132i	$-0.271458\pi$
$191$	251.306			1.31574			0.657870	+	0.753132i	$0.271458\pi$
$192$		0			0
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	−0.756703	−	0.653758i	$-0.773191\pi$
$193$	−109.795	+	63.3899i	−0.568884	+	0.328445i	0.187820	+	0.982204i	$0.439858\pi$
$194$		0			0
$195$	222.992	+	386.234i	1.14355	+	1.98069i
$196$		0			0
$197$	−285.803			−1.45077			−0.725387	−	0.688341i	$-0.758339\pi$
$197$	−285.803			−1.45077			−0.725387	+	0.688341i	$0.758339\pi$
$198$		0			0
$199$	77.0371	−	133.432i	0.387121	−	0.670514i	−0.604940	−	0.796271i	$-0.706803\pi$
$199$	77.0371	−	133.432i	0.387121	−	0.670514i	0.992061	+	0.125757i	$0.0401361\pi$
$200$		0			0
$201$	8.04520			0.0400259
$202$		0			0
$203$	5.53432	+	3.19524i	0.0272627	+	0.0157401i
$204$		0			0
$205$	347.878	+	200.848i	1.69697	+	0.979744i
$206$		0			0
$207$	−26.6036	−	46.0788i	−0.128520	−	0.222603i
$208$		0			0
$209$	−0.464815	+	0.510882i	−0.00222399	+	0.00244441i
$210$		0			0
$211$	138.091	−	79.7266i	0.654458	−	0.377851i	−0.135704	−	0.990749i	$-0.543330\pi$
$211$	138.091	−	79.7266i	0.654458	−	0.377851i	0.790162	+	0.612898i	$0.209996\pi$
$212$		0			0
$213$	74.1761	−	128.477i	0.348245	−	0.603178i
$214$		0			0
$215$	105.284	−	182.357i	0.489693	−	0.848173i
$216$		0			0
$217$		−	54.5306i		−	0.251293i
$218$		0			0
$219$	−185.067	−	106.848i	−0.845053	−	0.487892i
$220$		0			0
$221$		−	155.158i		−	0.702072i
$222$		0			0
$223$	161.907	−	93.4771i	0.726041	−	0.419180i	−0.0909314	−	0.995857i	$-0.528984\pi$
$223$	161.907	−	93.4771i	0.726041	−	0.419180i	0.816972	+	0.576677i	$0.195651\pi$
$224$		0			0
$225$	63.3715	+	109.763i	0.281651	+	0.487834i
$226$		0			0
$227$			8.87518i			0.0390977i	0.999809	+	0.0195489i	$0.00622299\pi$
$227$			8.87518i			0.0390977i	−0.999809	+	0.0195489i	$0.993777\pi$
$228$		0			0
$229$	265.920			1.16122			0.580611	−	0.814181i	$-0.302814\pi$
$229$	265.920			1.16122			0.580611	+	0.814181i	$0.302814\pi$
$230$		0			0
$231$	0.147078	−	0.0849154i	0.000636700	−	0.000367599i
$232$		0			0
$233$	4.52199	+	7.83232i	0.0194077	+	0.0336151i	0.875566	−	0.483098i	$-0.160489\pi$
$233$	4.52199	+	7.83232i	0.0194077	+	0.0336151i	−0.856158	+	0.516713i	$0.827155\pi$
$234$		0			0
$235$	−354.340			−1.50783
$236$		0			0
$237$	−87.4389	+	151.449i	−0.368940	+	0.639024i
$238$		0			0
$239$	48.3793			0.202424			0.101212	−	0.994865i	$-0.467728\pi$
$239$	48.3793			0.202424			0.101212	+	0.994865i	$0.467728\pi$
$240$		0			0
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	0.228883	−	0.973454i	$-0.426493\pi$
$241$	−120.431	−	69.5306i	−0.499712	−	0.288509i	−0.728594	+	0.684945i	$0.759826\pi$
$242$		0			0
$243$	225.225	+	130.034i	0.926851	+	0.535118i
$244$		0			0
$245$	−164.933	−	285.673i	−0.673197	−	1.16601i
$246$		0			0
$247$	−305.706	+	97.5823i	−1.23768	+	0.395070i
$248$		0			0
$249$	−215.093	+	124.184i	−0.863827	+	0.498731i
$250$		0			0
$251$	109.025	−	188.837i	0.434363	−	0.752340i	−0.562880	−	0.826539i	$-0.690307\pi$
$251$	109.025	−	188.837i	0.434363	−	0.752340i	0.997243	+	0.0741991i	$0.0236400\pi$
$252$		0			0
$253$	0.177389	−	0.307246i	0.000701142	−	0.00121441i
$254$		0			0
$255$		−	242.579i		−	0.951292i
$256$		0			0
$257$	192.080	+	110.898i	0.747394	+	0.431508i	0.824751	−	0.565495i	$-0.191315\pi$
$257$	192.080	+	110.898i	0.747394	+	0.431508i	−0.0773578	+	0.997003i	$0.524648\pi$
$258$		0			0
$259$		−	55.9973i		−	0.216206i
$260$		0			0
$261$	24.5518	−	14.1750i	0.0940684	−	0.0543104i
$262$		0			0
$263$	160.691	+	278.326i	0.610994	+	1.05827i	0.991073	+	0.133319i	$0.0425634\pi$
$263$	160.691	+	278.326i	0.610994	+	1.05827i	−0.380079	+	0.924954i	$0.624103\pi$
$264$		0			0
$265$			80.8853i			0.305228i
$266$		0			0
$267$	−590.126			−2.21021
$268$		0			0
$269$	−137.447	+	79.3552i	−0.510956	+	0.295001i	−0.733227	−	0.679984i	$-0.761987\pi$
$269$	−137.447	+	79.3552i	−0.510956	+	0.295001i	0.222270	+	0.974985i	$0.428653\pi$
$270$		0			0
$271$	244.649	+	423.745i	0.902765	+	1.56364i	0.823889	+	0.566751i	$0.191800\pi$
$271$	244.649	+	423.745i	0.902765	+	1.56364i	0.0788765	+	0.996884i	$0.474867\pi$
$272$		0			0
$273$	78.9053			0.289030
$274$		0			0
$275$	−0.422551	+	0.731881i	−0.00153655	+	0.00266138i
$276$		0			0
$277$	−183.051			−0.660835			−0.330417	−	0.943835i	$-0.607189\pi$
$277$	−183.051			−0.660835			−0.330417	+	0.943835i	$0.607189\pi$
$278$		0			0
$279$	−209.503	−	120.957i	−0.750908	−	0.433537i
$280$		0			0
$281$	230.908	+	133.315i	0.821736	+	0.474430i	0.851015	−	0.525142i	$-0.175988\pi$
$281$	230.908	+	133.315i	0.821736	+	0.474430i	−0.0292787	+	0.999571i	$0.509321\pi$
$282$		0			0
$283$	−178.014	−	308.329i	−0.629025	−	1.08950i	−0.987748	−	0.156059i	$-0.950121\pi$
$283$	−178.014	−	308.329i	−0.629025	−	1.08950i	0.358723	−	0.933444i	$-0.383212\pi$
$284$		0			0
$285$	−477.952	+	152.564i	−1.67703	+	0.535311i
$286$		0			0
$287$	61.5480	−	35.5347i	0.214453	−	0.123814i
$288$		0			0
$289$	102.303	−	177.195i	0.353991	−	0.613130i
$290$		0			0
$291$	−216.873	+	375.635i	−0.745267	+	1.29084i
$292$		0			0
$293$		−	357.755i		−	1.22101i	−0.792014	−	0.610503i	$-0.790967\pi$
$293$		−	357.755i		−	1.22101i	0.792014	−	0.610503i	$-0.209033\pi$
$294$		0			0
$295$	123.229	+	71.1465i	0.417727	+	0.241175i
$296$		0			0
$297$			0.490335i			0.00165096i
$298$		0			0
$299$	142.750	−	82.4169i	0.477425	−	0.275642i
$300$		0			0
$301$	−18.6273	−	32.2634i	−0.0618846	−	0.107187i
$302$		0			0
$303$		−	651.659i		−	2.15069i
$304$		0			0
$305$	−114.450			−0.375246
$306$		0			0
$307$	−125.866	+	72.6688i	−0.409987	+	0.236706i	−0.690784	−	0.723061i	$-0.742735\pi$
$307$	−125.866	+	72.6688i	−0.409987	+	0.236706i	0.280797	+	0.959767i	$0.409401\pi$
$308$		0			0
$309$	230.559	+	399.339i	0.746145	+	1.29236i
$310$		0			0
$311$	191.291			0.615084			0.307542	−	0.951534i	$-0.400494\pi$
$311$	191.291			0.615084			0.307542	+	0.951534i	$0.400494\pi$
$312$		0			0
$313$	156.376	−	270.851i	0.499603	−	0.865337i	−0.500397	−	0.865796i	$-0.666813\pi$
$313$	156.376	−	270.851i	0.499603	−	0.865337i	1.00000		0.000458751i	$0.000146025\pi$
$314$		0			0
$315$	46.5380			0.147740
$316$		0			0
$317$	78.3676	+	45.2456i	0.247217	+	0.142731i	0.618489	−	0.785793i	$-0.287745\pi$
$317$	78.3676	+	45.2456i	0.247217	+	0.142731i	−0.371273	+	0.928524i	$0.621078\pi$
$318$		0			0
$319$	0.163708	+	0.0945168i	0.000513191	+	0.000296291i
$320$		0			0
$321$	−106.551	−	184.552i	−0.331935	−	0.574928i
$322$		0			0
$323$	170.541	+	37.1738i	0.527989	+	0.115089i
$324$		0			0
$325$	−340.040	+	196.322i	−1.04628	+	0.604068i
$326$		0			0
$327$	−101.057	+	175.036i	−0.309042	+	0.535277i
$328$		0			0
$329$	−31.3456	+	54.2922i	−0.0952754	+	0.165022i
$330$		0			0
$331$		−	251.295i		−	0.759199i	−0.925151	−	0.379599i	$-0.876062\pi$
$331$		−	251.295i		−	0.759199i	0.925151	−	0.379599i	$-0.123938\pi$
$332$		0			0
$333$	−215.138	−	124.210i	−0.646060	−	0.373003i
$334$		0			0
$335$			14.6999i			0.0438802i
$336$		0			0
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	−0.796031	−	0.605256i	$-0.793071\pi$
$337$	−225.749	+	130.336i	−0.669879	+	0.386755i	0.126152	+	0.992011i	$0.459737\pi$
$338$		0			0
$339$	260.305	+	450.861i	0.767861	+	1.32997i
$340$		0			0
$341$		−	1.61304i		−	0.00473033i
$342$		0			0
$343$	−118.578			−0.345710
$344$		0			0
$345$	223.181	−	128.854i	0.646901	−	0.373489i
$346$		0			0
$347$	−169.713	−	293.952i	−0.489088	−	0.847125i	0.510833	−	0.859680i	$-0.329337\pi$
$347$	−169.713	−	293.952i	−0.489088	−	0.847125i	−0.999921	+	0.0125549i	$0.996004\pi$
$348$		0			0
$349$	−76.4095			−0.218938			−0.109469	−	0.993990i	$-0.534915\pi$
$349$	−76.4095			−0.218938			−0.109469	+	0.993990i	$0.534915\pi$
$350$		0			0
$351$	−113.908	+	197.294i	−0.324523	+	0.562090i
$352$		0			0
$353$	635.437			1.80010			0.900052	−	0.435783i	$-0.143528\pi$
$353$	635.437			1.80010			0.900052	+	0.435783i	$0.143528\pi$
$354$		0			0
$355$	234.748	+	135.532i	0.661261	+	0.381779i
$356$		0			0
$357$	−37.1682	−	21.4590i	−0.104112	−	0.0601094i
$358$		0			0
$359$	2.43138	+	4.21127i	0.00677264	+	0.0117306i	0.869392	−	0.494123i	$-0.164511\pi$
$359$	2.43138	+	4.21127i	0.00677264	+	0.0117306i	−0.862619	+	0.505854i	$0.831178\pi$
$360$		0			0
$361$	−34.0136	−	359.394i	−0.0942206	−	0.995551i
$362$		0			0
$363$	−398.358	+	229.992i	−1.09740	+	0.633586i
$364$		0			0
$365$	195.229	−	338.146i	0.534874	−	0.926428i
$366$		0			0
$367$	149.568	−	259.060i	0.407542	−	0.705884i	−0.587071	−	0.809535i	$-0.699719\pi$
$367$	149.568	−	259.060i	0.407542	−	0.705884i	0.994614	+	0.103651i	$0.0330525\pi$
$368$		0			0
$369$		−	315.285i		−	0.854430i
$370$		0			0
$371$	12.3933	+	7.15527i	0.0334051	+	0.0192864i
$372$		0			0
$373$			286.394i			0.767813i	0.923372	+	0.383907i	$0.125422\pi$
$373$			286.394i			0.767813i	−0.923372	+	0.383907i	$0.874578\pi$
$374$		0			0
$375$	40.0722	−	23.1357i	0.106859	−	0.0616952i
$376$		0			0
$377$	43.9136	+	76.0605i	0.116482	+	0.201752i
$378$		0			0
$379$			638.486i			1.68466i	0.538962	+	0.842330i	$0.318817\pi$
$379$			638.486i			1.68466i	−0.538962	+	0.842330i	$0.681183\pi$
$380$		0			0
$381$	−600.322			−1.57565
$382$		0			0
$383$	−297.246	+	171.615i	−0.776100	+	0.448082i	−0.835046	−	0.550180i	$-0.814559\pi$
$383$	−297.246	+	171.615i	−0.776100	+	0.448082i	0.0589464	+	0.998261i	$0.481226\pi$
$384$		0			0
$385$	0.155154	+	0.268734i	0.000402997	+	0.000698012i
$386$		0			0
$387$	−165.272			−0.427059
$388$		0			0
$389$	−176.043	+	304.915i	−0.452552	+	0.783843i	−0.998544	−	0.0539474i	$-0.982820\pi$
$389$	−176.043	+	304.915i	−0.452552	+	0.783843i	0.545992	+	0.837791i	$0.316153\pi$
$390$		0			0
$391$	−89.6562			−0.229300
$392$		0			0
$393$	−253.764	−	146.510i	−0.645709	−	0.372800i
$394$		0			0
$395$	−276.721	−	159.765i	−0.700559	−	0.404468i
$396$		0			0
$397$	205.686	+	356.259i	0.518101	+	0.897378i	0.999779	+	0.0210293i	$0.00669432\pi$
$397$	205.686	+	356.259i	0.518101	+	0.897378i	−0.481678	+	0.876349i	$0.659972\pi$
$398$		0			0
$399$	−18.9047	+	86.7282i	−0.0473801	+	0.217364i
$400$		0			0
$401$	−26.8409	+	15.4966i	−0.0669349	+	0.0386449i	−0.533094	−	0.846056i	$-0.678971\pi$
$401$	−26.8409	+	15.4966i	−0.0669349	+	0.0386449i	0.466159	+	0.884701i	$0.345637\pi$
$402$		0			0
$403$	374.719	−	649.032i	0.929823	−	1.61050i
$404$		0			0
$405$	−348.497	+	603.615i	−0.860487	+	1.49041i
$406$		0			0
$407$		−	1.65643i		−	0.00406984i
$408$		0			0
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	0.0279377	−	0.999610i	$-0.491106\pi$
$409$	−336.926	−	194.525i	−0.823781	−	0.475610i	−0.851719	+	0.524000i	$0.824439\pi$
$410$		0			0
$411$		−	345.158i		−	0.839801i
$412$		0			0
$413$	21.8022	−	12.5875i	0.0527899	−	0.0304783i
$414$		0			0
$415$	−226.904	−	393.009i	−0.546756	−	0.947010i
$416$		0			0
$417$			348.050i			0.834653i
$418$		0			0
$419$	−455.941			−1.08817			−0.544083	−	0.839032i	$-0.683122\pi$
$419$	−455.941			−1.08817			−0.544083	+	0.839032i	$0.683122\pi$
$420$		0			0
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	−0.694754	−	0.719248i	$-0.744487\pi$
$421$	−176.502	+	101.903i	−0.419244	+	0.242051i	0.275510	+	0.961298i	$0.411153\pi$
$422$		0			0
$423$	139.058	+	240.856i	0.328743	+	0.569399i
$424$		0			0
$425$	213.567			0.502510
$426$		0			0
$427$	−10.1245	+	17.5361i	−0.0237107	+	0.0410681i
$428$		0			0
$429$	2.33406			0.00544069
$430$		0			0
$431$	−609.299	−	351.779i	−1.41369	−	0.816193i	−0.417954	−	0.908468i	$-0.637253\pi$
$431$	−609.299	−	351.779i	−1.41369	−	0.816193i	−0.995734	+	0.0922756i	$0.970586\pi$
$432$		0			0
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	0.297295	−	0.954786i	$-0.403916\pi$
$433$	−164.941	−	95.2288i	−0.380927	−	0.219928i	−0.678221	+	0.734858i	$0.737249\pi$
$434$		0			0
$435$	68.6561	+	118.916i	0.157830	+	0.273370i
$436$		0			0
$437$	56.3868	+	176.649i	0.129032	+	0.404231i
$438$		0			0
$439$	−415.097	+	239.656i	−0.945551	+	0.545914i	−0.891696	−	0.452634i	$-0.850484\pi$
$439$	−415.097	+	239.656i	−0.945551	+	0.545914i	−0.0538552	+	0.998549i	$0.517151\pi$
$440$		0			0
$441$	−129.454	+	224.220i	−0.293546	+	0.508436i
$442$		0			0
$443$	383.888	−	664.914i	0.866565	−	1.50094i	0.00108097	−	0.999999i	$-0.499656\pi$
$443$	383.888	−	664.914i	0.866565	−	1.50094i	0.865484	−	0.500936i	$-0.167011\pi$
$444$		0			0
$445$		−	1078.25i		−	2.42304i
$446$		0			0
$447$	−79.4004	−	45.8418i	−0.177629	−	0.102554i
$448$		0			0
$449$		−	392.421i		−	0.873988i	−0.899464	−	0.436994i	$-0.856043\pi$
$449$		−	392.421i		−	0.873988i	0.899464	−	0.436994i	$-0.143957\pi$
$450$		0			0
$451$	1.82062	−	1.05113i	0.00403685	−	0.00233068i
$452$		0			0
$453$	477.952	+	827.837i	1.05508	+	1.82746i
$454$		0			0
$455$			144.173i			0.316863i
$456$		0			0
$457$	−695.090			−1.52099			−0.760493	−	0.649347i	$-0.775042\pi$
$457$	−695.090			−1.52099			−0.760493	+	0.649347i	$0.775042\pi$
$458$		0			0
$459$	107.312	−	61.9565i	0.233795	−	0.134981i
$460$		0			0
$461$	351.150	+	608.210i	0.761714	+	1.31933i	0.941967	+	0.335707i	$0.108975\pi$
$461$	351.150	+	608.210i	0.761714	+	1.31933i	−0.180253	+	0.983620i	$0.557692\pi$
$462$		0			0
$463$	14.4955			0.0313077			0.0156538	−	0.999877i	$-0.495017\pi$
$463$	14.4955			0.0313077			0.0156538	+	0.999877i	$0.495017\pi$
$464$		0			0
$465$	585.849	−	1014.72i	1.25989	−	2.18219i
$466$		0			0
$467$	863.890			1.84987			0.924935	−	0.380124i	$-0.124119\pi$
$467$	863.890			1.84987			0.924935	+	0.380124i	$0.124119\pi$
$468$		0			0
$469$	2.25232	+	1.30038i	0.00480239	+	0.00277266i
$470$		0			0
$471$	289.831	+	167.334i	0.615353	+	0.355274i
$472$		0			0
$473$	−0.551003	−	0.954366i	−0.00116491	−	0.00201769i
$474$		0			0
$475$	−134.317	−	420.789i	−0.282773	−	0.885871i
$476$		0			0
$477$	54.9802	−	31.7429i	0.115263	−	0.0665469i
$478$		0			0
$479$	198.015	−	342.972i	0.413393	−	0.716017i	−0.581866	−	0.813285i	$-0.697677\pi$
$479$	198.015	−	342.972i	0.413393	−	0.716017i	0.995258	+	0.0972678i	$0.0310103\pi$
$480$		0			0
$481$	384.797	−	666.488i	0.799994	−	1.38563i
$482$		0			0
$483$		−	45.5945i		−	0.0943986i
$484$		0			0
$485$	−686.345	−	396.261i	−1.41514	−	0.817033i
$486$		0			0
$487$			872.905i			1.79241i	0.443636	+	0.896207i	$0.353688\pi$
$487$			872.905i			1.79241i	−0.443636	+	0.896207i	$0.646312\pi$
$488$		0			0
$489$	93.3707	−	53.9076i	0.190942	−	0.110240i
$490$		0			0
$491$	350.193	+	606.552i	0.713224	+	1.23534i	0.963641	+	0.267201i	$0.0860989\pi$
$491$	350.193	+	606.552i	0.713224	+	1.23534i	−0.250417	+	0.968138i	$0.580568\pi$
$492$		0			0
$493$		−	47.7709i		−	0.0968983i
$494$		0			0
$495$	1.37662			0.00278104
$496$		0			0
$497$	41.5325	−	23.9788i	0.0835663	−	0.0482470i
$498$		0			0
$499$	76.5488	+	132.586i	0.153404	+	0.265704i	0.932477	−	0.361230i	$-0.117643\pi$
$499$	76.5488	+	132.586i	0.153404	+	0.265704i	−0.779073	+	0.626934i	$0.784310\pi$
$500$		0			0
$501$	228.773			0.456632
$502$		0			0
$503$	−203.824	+	353.033i	−0.405216	+	0.701855i	−0.994347	−	0.106183i	$-0.966137\pi$
$503$	−203.824	+	353.033i	−0.405216	+	0.701855i	0.589130	+	0.808038i	$0.299470\pi$
$504$		0			0
$505$	1190.69			2.35779
$506$		0			0
$507$	382.754	+	220.983i	0.754938	+	0.435864i
$508$		0			0
$509$	−171.070	−	98.7673i	−0.336090	−	0.194042i	0.322452	−	0.946586i	$-0.395493\pi$
$509$	−171.070	−	98.7673i	−0.336090	−	0.194042i	−0.658542	+	0.752544i	$0.728826\pi$
$510$		0			0
$511$	−34.5406	−	59.8261i	−0.0675942	−	0.117077i
$512$		0			0
$513$	−189.563	−	172.470i	−0.369519	−	0.336198i
$514$		0			0
$515$	−729.657	+	421.268i	−1.41681	+	0.817995i
$516$		0			0
$517$	−0.927218	+	1.60599i	−0.00179346	+	0.00310636i
$518$		0			0
$519$	335.563	−	581.212i	0.646557	−	1.11987i
$520$		0			0
$521$			698.844i			1.34135i	0.741751	+	0.670676i	$0.233996\pi$
$521$			698.844i			1.34135i	−0.741751	+	0.670676i	$0.766004\pi$
$522$		0			0
$523$	381.571	+	220.300i	0.729582	+	0.421224i	0.818269	−	0.574835i	$-0.194934\pi$
$523$	381.571	+	220.300i	0.729582	+	0.421224i	−0.0886874	+	0.996060i	$0.528267\pi$
$524$		0			0
$525$			108.609i			0.206874i
$526$		0			0
$527$	−353.021	+	203.817i	−0.669869	+	0.386749i
$528$		0			0
$529$	216.876	+	375.641i	0.409974	+	0.710096i
$530$		0			0
$531$		−	111.684i		−	0.210327i
$532$		0			0
$533$	976.738			1.83253
$534$		0			0
$535$	337.206	−	194.686i	0.630292	−	0.363899i
$536$		0			0
$537$	−0.431369	−	0.747153i	−0.000803295	−	0.00139135i
$538$		0			0
$539$	−1.72635			−0.00320288
$540$		0			0
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	0.0886479	+	0.996063i	$0.471745\pi$
$541$	−442.696	+	766.772i	−0.818292	+	1.41732i	−0.906940	+	0.421260i	$0.861588\pi$
$542$		0			0
$543$	568.065			1.04616
$544$		0			0
$545$	−319.818	−	184.647i	−0.586822	−	0.338802i
$546$		0			0
$547$	801.617	+	462.814i	1.46548	+	0.846095i	0.999256	−	0.0385725i	$-0.0122811\pi$
$547$	801.617	+	462.814i	1.46548	+	0.846095i	0.466223	+	0.884667i	$0.345614\pi$
$548$		0			0
$549$	44.9151	+	77.7952i	0.0818125	+	0.141703i
$550$		0			0
$551$	−94.1225	+	30.0442i	−0.170821	+	0.0545266i
$552$		0			0
$553$	−48.9585	+	28.2662i	−0.0885325	+	0.0511143i
$554$		0			0
$555$	601.606	−	1042.01i	1.08397	−	1.87750i
$556$		0			0
$557$	176.665	−	305.992i	0.317172	−	0.549358i	−0.662725	−	0.748863i	$-0.730600\pi$
$557$	176.665	−	305.992i	0.317172	−	0.549358i	0.979897	+	0.199505i	$0.0639335\pi$
$558$		0			0
$559$		−	512.005i		−	0.915930i
$560$		0			0
$561$	−1.09945	−	0.634769i	−0.00195981	−	0.00113150i
$562$		0			0
$563$			21.4065i			0.0380221i	0.999819	+	0.0190111i	$0.00605177\pi$
$563$			21.4065i			0.0380221i	−0.999819	+	0.0190111i	$0.993948\pi$
$564$		0			0
$565$	−823.795	+	475.618i	−1.45804	+	0.841802i
$566$		0			0
$567$	61.6575	+	106.794i	0.108743	+	0.188349i
$568$		0			0
$569$			378.852i			0.665821i	0.942958	+	0.332911i	$0.108031\pi$
$569$			378.852i			0.665821i	−0.942958	+	0.332911i	$0.891969\pi$
$570$		0			0
$571$	38.5842			0.0675730			0.0337865	−	0.999429i	$-0.489243\pi$
$571$	38.5842			0.0675730			0.0337865	+	0.999429i	$0.489243\pi$
$572$		0			0
$573$	827.362	−	477.678i	1.44391	−	0.833644i
$574$		0			0
$575$	113.443	+	196.488i	0.197291	+	0.341719i
$576$		0			0
$577$	399.348			0.692112			0.346056	−	0.938214i	$-0.387521\pi$
$577$	399.348			0.692112			0.346056	+	0.938214i	$0.387521\pi$
$578$		0			0
$579$	−240.981	+	417.391i	−0.416201	+	0.720882i
$580$		0			0
$581$	−80.2894			−0.138192
$582$		0			0
$583$	0.366600	+	0.211656i	0.000628816	+	0.000363047i
$584$		0			0
$585$	553.902	+	319.796i	0.946841	+	0.546659i
$586$		0			0
$587$	247.769	+	429.148i	0.422093	+	0.731087i	0.996144	−	0.0877330i	$-0.0279622\pi$
$587$	247.769	+	429.148i	0.422093	+	0.731087i	−0.574051	+	0.818820i	$0.694629\pi$
$588$		0			0
$589$	623.601	+	567.369i	1.05875	+	0.963275i
$590$		0			0
$591$	−940.933	+	543.248i	−1.59210	+	0.919201i
$592$		0			0
$593$	−114.717	+	198.696i	−0.193452	+	0.335069i	−0.946392	−	0.323020i	$-0.895302\pi$
$593$	−114.717	+	198.696i	−0.193452	+	0.335069i	0.752940	+	0.658089i	$0.228635\pi$
$594$		0			0
$595$	39.2091	−	67.9121i	0.0658976	−	0.114138i
$596$		0			0
$597$		−	585.723i		−	0.981110i
$598$		0			0
$599$	26.4546	+	15.2736i	0.0441646	+	0.0254984i	0.521920	−	0.852995i	$-0.325216\pi$
$599$	26.4546	+	15.2736i	0.0441646	+	0.0254984i	−0.477755	+	0.878493i	$0.658549\pi$
$600$		0			0
$601$			962.490i			1.60148i	0.599012	+	0.800740i	$0.295560\pi$
$601$			962.490i			1.60148i	−0.599012	+	0.800740i	$0.704440\pi$
$602$		0			0
$603$	9.99195	−	5.76885i	0.0165704	−	0.00956692i
$604$		0			0
$605$	−420.232	−	727.863i	−0.694598	−	1.20308i
$606$		0			0
$607$		−	249.770i		−	0.411483i	−0.978606	−	0.205741i	$-0.934039\pi$
$607$		−	249.770i		−	0.411483i	0.978606	−	0.205741i	$-0.0659606\pi$
$608$		0			0
$609$	24.2938			0.0398913
$610$		0			0
$611$	−746.161	+	430.796i	−1.22121	+	0.705067i
$612$		0			0
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	0.669655	−	0.742672i	$-0.266442\pi$
$613$	−189.015	−	327.384i	−0.308345	−	0.534069i	−0.978000	+	0.208603i	$0.933108\pi$
$614$		0			0
$615$	1527.07			2.48304
$616$		0			0
$617$	−259.371	+	449.243i	−0.420374	+	0.728109i	−0.995976	−	0.0896208i	$-0.971434\pi$
$617$	−259.371	+	449.243i	−0.420374	+	0.728109i	0.575602	+	0.817730i	$0.304768\pi$
$618$		0			0
$619$	−1035.34			−1.67261			−0.836303	−	0.548267i	$-0.815288\pi$
$619$	−1035.34			−1.67261			−0.836303	+	0.548267i	$0.815288\pi$
$620$		0			0
$621$	114.004	+	65.8202i	0.183581	+	0.105991i
$622$		0			0
$623$	−165.211	−	95.3844i	−0.265186	−	0.153105i
$624$		0			0
$625$	332.869	+	576.545i	0.532590	+	0.922473i
$626$		0			0
$627$	−0.559210	+	2.56546i	−0.000891881	+	0.00409165i
$628$		0			0
$629$	−362.516	+	209.298i	−0.576336	+	0.332748i
$630$		0			0
$631$	−528.945	+	916.160i	−0.838265	+	1.45192i	0.0530794	+	0.998590i	$0.483096\pi$
$631$	−528.945	+	916.160i	−0.838265	+	1.45192i	−0.891344	+	0.453327i	$0.850237\pi$
$632$		0			0
$633$	303.086	−	524.960i	0.478808	−	0.829320i
$634$		0			0
$635$		−	1096.88i		−	1.72738i
$636$		0			0
$637$	−694.625	−	401.042i	−1.09046	−	0.629579i
$638$		0			0
$639$		−	212.754i		−	0.332948i
$640$		0			0
$641$	−560.504	+	323.607i	−0.874421	+	0.504847i	−0.868815	−	0.495137i	$-0.835118\pi$
$641$	−560.504	+	323.607i	−0.874421	+	0.504847i	−0.00560636	+	0.999984i	$0.501785\pi$
$642$		0			0
$643$	−157.333	−	272.508i	−0.244685	−	0.423807i	0.717358	−	0.696705i	$-0.245351\pi$
$643$	−157.333	−	272.508i	−0.244685	−	0.423807i	−0.962043	+	0.272898i	$0.912018\pi$
$644$		0			0
$645$		−	800.487i		−	1.24107i
$646$		0			0
$647$	320.116			0.494769			0.247384	−	0.968917i	$-0.420429\pi$
$647$	320.116			0.494769			0.247384	+	0.968917i	$0.420429\pi$
$648$		0			0
$649$	0.644920	−	0.372345i	0.000993714	−	0.000573721i
$650$		0			0
$651$	−103.651	−	179.528i	−0.159218	−	0.275773i
$652$		0			0
$653$	131.969			0.202097			0.101049	−	0.994881i	$-0.467780\pi$
$653$	131.969			0.202097			0.101049	+	0.994881i	$0.467780\pi$
$654$		0			0
$655$	267.698	−	463.666i	0.408699	−	0.707888i
$656$		0			0
$657$	−306.465			−0.466460
$658$		0			0
$659$	635.205	+	366.736i	0.963892	+	0.556503i	0.897369	−	0.441281i	$-0.145476\pi$
$659$	635.205	+	366.736i	0.963892	+	0.556503i	0.0665235	+	0.997785i	$0.478809\pi$
$660$		0			0
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.874807	−	0.484472i	$-0.160988\pi$
$661$	590.038	+	340.659i	0.892644	+	0.515368i	0.0178378	+	0.999841i	$0.494322\pi$
$662$		0			0
$663$	−294.921	−	510.818i	−0.444828	−	0.770465i
$664$		0			0
$665$	−158.466	−	34.5419i	−0.238295	−	0.0519426i
$666$		0			0
$667$	43.9507	−	25.3750i	0.0658931	−	0.0380434i
$668$		0			0
$669$	355.359	−	615.499i	0.531179	−	0.920029i
$670$		0			0
$671$	−0.299487	+	0.518726i	−0.000446329	+	0.000773064i
$672$		0			0
$673$		−	710.831i		−	1.05621i	−0.849178	−	0.528107i	$-0.822902\pi$
$673$		−	710.831i		−	1.05621i	0.849178	−	0.528107i	$-0.177098\pi$
$674$		0			0
$675$	−271.565	−	156.788i	−0.402318	−	0.232278i
$676$		0			0
$677$		−	493.970i		−	0.729645i	−0.931077	−	0.364823i	$-0.881130\pi$
$677$		−	493.970i		−	0.729645i	0.931077	−	0.364823i	$-0.118870\pi$
$678$		0			0
$679$	−121.431	+	70.1081i	−0.178838	+	0.103252i
$680$		0			0
$681$	16.8698	+	29.2193i	0.0247721	+	0.0429065i
$682$		0			0
$683$		−	442.962i		−	0.648553i	−0.945962	−	0.324276i	$-0.894879\pi$
$683$		−	442.962i		−	0.648553i	0.945962	−	0.324276i	$-0.105121\pi$
$684$		0			0
$685$	630.659			0.920670
$686$		0			0
$687$	875.474	−	505.455i	1.27434	−	0.735743i
$688$		0			0
$689$	98.3380	+	170.326i	0.142726	+	0.247208i
$690$		0			0
$691$	−924.711			−1.33822			−0.669110	−	0.743163i	$-0.733325\pi$
$691$	−924.711			−1.33822			−0.669110	+	0.743163i	$0.733325\pi$
$692$		0			0
$693$	0.121778	−	0.210926i	0.000175726	−	0.000304366i
$694$		0			0
$695$	−635.943			−0.915026
$696$		0			0
$697$	−460.090	−	265.633i	−0.660101	−	0.381109i
$698$		0			0
$699$	29.7750	+	17.1906i	0.0425966	+	0.0245932i
$700$		0			0
$701$	−277.112	−	479.973i	−0.395310	−	0.684697i	0.597831	−	0.801622i	$-0.296030\pi$
$701$	−277.112	−	479.973i	−0.395310	−	0.684697i	−0.993141	+	0.116925i	$0.962696\pi$
$702$		0			0
$703$	640.373	+	582.629i	0.910915	+	0.828775i
$704$		0			0
$705$	−1166.58	+	673.523i	−1.65472	+	0.955351i
$706$		0			0
$707$	105.330	−	182.437i	0.148982	−	0.258045i
$708$		0			0
$709$	249.802	−	432.670i	0.352331	−	0.610254i	−0.634327	−	0.773065i	$-0.718723\pi$
$709$	249.802	−	432.670i	0.352331	−	0.610254i	0.986657	+	0.162811i	$0.0520560\pi$
$710$		0			0
$711$			250.794i			0.352734i
$712$		0			0
$713$	−375.036	−	216.527i	−0.525997	−	0.303684i
$714$		0			0
$715$			4.26469i			0.00596461i
$716$		0			0
$717$	159.277	−	91.9584i	0.222143	−	0.128254i
$718$		0			0
$719$	−174.396	−	302.062i	−0.242553	−	0.420114i	0.718888	−	0.695126i	$-0.244652\pi$
$719$	−174.396	−	302.062i	−0.242553	−	0.420114i	−0.961441	+	0.275012i	$0.911318\pi$
$720$		0			0
$721$			149.065i			0.206747i
$722$		0			0
$723$	−528.649			−0.731189
$724$		0			0
$725$	−104.693	+	60.4448i	−0.144405	+	0.0833721i
$726$		0			0
$727$	−41.3116	−	71.5538i	−0.0568247	−	0.0984233i	0.836214	−	0.548404i	$-0.184764\pi$
$727$	−41.3116	−	71.5538i	−0.0568247	−	0.0984233i	−0.893038	+	0.449980i	$0.851431\pi$
$728$		0			0
$729$	85.5657			0.117374
$730$		0			0
$731$	−139.245	+	241.179i	−0.190485	+	0.329930i
$732$		0			0
$733$	−981.828			−1.33947			−0.669733	−	0.742602i	$-0.733591\pi$
$733$	−981.828			−1.33947			−0.669733	+	0.742602i	$0.733591\pi$
$734$		0			0
$735$	−1086.00	−	627.003i	−1.47755	−	0.853066i
$736$		0			0
$737$	0.0666248	+	0.0384658i	9.03999e−5	+	5.21924e-5i
$738$		0			0
$739$	64.8765	+	112.369i	0.0877895	+	0.152056i	0.906576	−	0.422042i	$-0.138686\pi$
$739$	64.8765	+	112.369i	0.0877895	+	0.152056i	−0.818787	+	0.574097i	$0.805353\pi$
$740$		0			0
$741$	−820.978	+	902.345i	−1.10793	+	1.21774i
$742$		0			0
$743$	450.862	−	260.306i	0.606814	−	0.350344i	−0.164904	−	0.986310i	$-0.552731\pi$
$743$	450.862	−	260.306i	0.606814	−	0.350344i	0.771717	+	0.635966i	$0.219398\pi$
$744$		0			0
$745$	83.7603	−	145.077i	0.112430	−	0.194734i
$746$		0			0
$747$	−178.094	+	308.467i	−0.238412	+	0.412941i
$748$		0			0
$749$		−	68.8892i		−	0.0919749i
$750$		0			0
$751$	−880.913	−	508.595i	−1.17299	−	0.677224i	−0.218605	−	0.975813i	$-0.570151\pi$
$751$	−880.913	−	508.595i	−1.17299	−	0.677224i	−0.954382	+	0.298590i	$0.903484\pi$
$752$		0			0
$753$		−	828.932i		−	1.10084i
$754$		0			0
$755$	−1512.59	+	873.295i	−2.00343	+	1.15668i
$756$		0			0
$757$	155.490	+	269.317i	0.205403	+	0.355768i	0.950261	−	0.311455i	$-0.100816\pi$
$757$	155.490	+	269.317i	0.205403	+	0.355768i	−0.744858	+	0.667223i	$0.767483\pi$
$758$		0			0
$759$		−	1.34871i		−	0.00177695i
$760$		0			0
$761$	−1402.51			−1.84298			−0.921489	−	0.388404i	$-0.873027\pi$
$761$	−1402.51			−1.84298			−0.921489	+	0.388404i	$0.873027\pi$
$762$		0			0
$763$	−56.5834	+	32.6684i	−0.0741591	+	0.0428158i
$764$		0			0
$765$	−173.943	−	301.278i	−0.227376	−	0.393827i
$766$		0			0
$767$	345.991			0.451097
$768$		0			0
$769$	196.711	−	340.714i	0.255802	−	0.443061i	−0.709311	−	0.704895i	$-0.750994\pi$
$769$	196.711	−	340.714i	0.255802	−	0.443061i	0.965113	+	0.261834i	$0.0843273\pi$
$770$		0			0
$771$	843.167			1.09360
$772$		0			0
$773$	201.825	+	116.524i	0.261093	+	0.150742i	0.624833	−	0.780758i	$-0.285167\pi$
$773$	201.825	+	116.524i	0.261093	+	0.150742i	−0.363740	+	0.931501i	$0.618500\pi$
$774$		0			0
$775$	893.359	+	515.781i	1.15272	+	0.665524i
$776$		0			0
$777$	−106.438	−	184.357i	−0.136986	−	0.237267i
$778$		0			0
$779$	−234.014	+	1073.57i	−0.300403	+	1.37814i
$780$		0			0
$781$	1.22855	−	0.709304i	0.00157305	−	0.000908200i
$782$		0			0
$783$	−35.0705	+	60.7439i	−0.0447899	+	0.0775784i
$784$		0			0
$785$	−305.746	+	529.568i	−0.389485	+	0.674609i
$786$		0			0
$787$			193.205i			0.245495i	0.992438	+	0.122748i	$0.0391706\pi$
$787$			193.205i			0.245495i	−0.992438	+	0.122748i	$0.960829\pi$
$788$		0			0
$789$	1058.07	+	610.878i	1.34103	+	0.774243i
$790$		0			0
$791$			168.296i			0.212764i
$792$		0			0
$793$	−241.006	+	139.145i	−0.303917	+	0.175466i
$794$		0			0
$795$	153.745	+	266.295i	0.193390	+	0.334962i
$796$		0			0
$797$			255.622i			0.320730i	0.987058	+	0.160365i	$0.0512672\pi$
$797$			255.622i			0.320730i	−0.987058	+	0.160365i	$0.948733\pi$
$798$		0			0
$799$	468.636			0.586529
$800$		0			0
$801$	−732.922	+	423.153i	−0.915009	+	0.528281i
$802$		0			0
$803$	−1.02173	−	1.76969i	−0.00127239	−	0.00220384i
$804$		0			0
$805$	83.3085			0.103489
$806$		0			0
$807$	−301.674	+	522.514i	−0.373821	+	0.647477i
$808$		0			0
$809$	478.346			0.591281			0.295641	−	0.955299i	$-0.404467\pi$
$809$	478.346			0.591281			0.295641	+	0.955299i	$0.404467\pi$
$810$		0			0
$811$	−810.296	−	467.825i	−0.999132	−	0.576849i	−0.0911409	−	0.995838i	$-0.529051\pi$
$811$	−810.296	−	467.825i	−0.999132	−	0.576849i	−0.907991	+	0.418989i	$0.862385\pi$
$812$		0			0
$813$	1610.89	+	930.049i	1.98142	+	1.14397i
$814$		0			0
$815$	98.4977	+	170.603i	0.120856	+	0.209329i
$816$		0			0
$817$	562.766	+	122.670i	0.688820	+	0.150146i
$818$		0			0
$819$	97.9985	−	56.5795i	0.119656	−	0.0690836i
$820$		0			0
$821$	207.851	−	360.008i	0.253168	−	0.438500i	−0.711228	−	0.702961i	$-0.751861\pi$
$821$	207.851	−	360.008i	0.253168	−	0.438500i	0.964396	+	0.264461i	$0.0851941\pi$
$822$		0			0
$823$	571.455	−	989.790i	0.694356	−	1.20266i	−0.276041	−	0.961146i	$-0.589022\pi$
$823$	571.455	−	989.790i	0.694356	−	1.20266i	0.970397	−	0.241515i	$-0.0776442\pi$
$824$		0			0
$825$			3.21271i			0.00389419i
$826$		0			0
$827$	−943.619	−	544.799i	−1.14101	−	0.658765i	−0.194333	−	0.980936i	$-0.562254\pi$
$827$	−943.619	−	544.799i	−1.14101	−	0.658765i	−0.946682	+	0.322170i	$0.895588\pi$
$828$		0			0
$829$		−	242.265i		−	0.292237i	−0.989267	−	0.146119i	$-0.953322\pi$
$829$		−	242.265i		−	0.292237i	0.989267	−	0.146119i	$-0.0466781\pi$
$830$		0			0
$831$	−602.650	+	347.940i	−0.725210	+	0.418700i
$832$		0			0
$833$	218.134	+	377.820i	0.261866	+	0.453565i
$834$		0			0
$835$			418.004i			0.500604i
$836$		0			0
$837$	598.520			0.715078
$838$		0			0
$839$	1272.95	−	734.939i	1.51723	−	0.875971i	0.517431	−	0.855725i	$-0.326888\pi$
$839$	1272.95	−	734.939i	1.51723	−	0.875971i	0.999795	−	0.0202457i	$-0.00644485\pi$
$840$		0			0
$841$	−406.980	−	704.909i	−0.483923	−	0.838180i
$842$		0			0
$843$	1013.61			1.20238
$844$		0			0
$845$	−403.771	+	699.352i	−0.477836	+	0.827635i
$846$		0			0
$847$	−148.698			−0.175558
$848$		0			0
$849$	−1172.13	−	676.731i	−1.38060	−	0.797092i
$850$		0			0
$851$	−385.123	−	222.351i	−0.452553	−	0.261282i
$852$		0			0
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	−0.995619	−	0.0935062i	$-0.970192\pi$
$853$	−493.706	−	855.124i	−0.578788	−	1.00249i	0.416831	−	0.908984i	$-0.363141\pi$
$854$		0			0
$855$	−484.209	+	532.199i	−0.566326	+	0.622455i
$856$		0			0
$857$	−1279.05	+	738.461i	−1.49248	+	0.861681i	−0.999963	−	0.00862354i	$-0.997255\pi$
$857$	−1279.05	+	738.461i	−1.49248	+	0.861681i	−0.492513	+	0.870305i	$0.663922\pi$
$858$		0			0
$859$	−466.025	+	807.179i	−0.542520	+	0.939673i	0.456238	+	0.889858i	$0.349197\pi$
$859$	−466.025	+	807.179i	−0.542520	+	0.939673i	−0.998758	+	0.0498150i	$0.984137\pi$
$860$		0			0
$861$	135.087	−	233.978i	0.156896	−	0.271752i
$862$		0			0
$863$			1088.87i			1.26172i	0.775896	+	0.630861i	$0.217298\pi$
$863$			1088.87i			1.26172i	−0.775896	+	0.630861i	$0.782702\pi$
$864$		0			0
$865$	1061.97	+	613.127i	1.22771	+	0.708818i
$866$		0			0
$867$		−	777.825i		−	0.897145i
$868$		0			0
$869$	−1.44822	+	0.836128i	−0.00166653	+	0.000962172i
$870$		0			0
$871$	17.8717	+	30.9546i	0.0205185	+	0.0355392i
$872$		0			0
$873$			622.039i			0.712531i
$874$		0			0
$875$	14.9581			0.0170949
$876$		0			0
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	−0.610881	−	0.791723i	$-0.709184\pi$
$877$	−202.296	+	116.796i	−0.230669	+	0.133177i	0.380212	+	0.924899i	$0.375851\pi$
$878$		0			0
$879$	−680.013	−	1177.82i	−0.773621	−	1.33995i
$880$		0			0
$881$	488.267			0.554220			0.277110	−	0.960838i	$-0.410623\pi$
$881$	488.267			0.554220			0.277110	+	0.960838i	$0.410623\pi$
$882$		0			0
$883$	833.774	−	1444.14i	0.944252	−	1.63549i	0.187009	−	0.982358i	$-0.440121\pi$
$883$	833.774	−	1444.14i	0.944252	−	1.63549i	0.757243	−	0.653134i	$-0.226546\pi$
$884$		0			0
$885$	540.936			0.611227
$886$		0			0
$887$	−544.718	−	314.493i	−0.614113	−	0.354558i	0.160460	−	0.987042i	$-0.448702\pi$
$887$	−544.718	−	314.493i	−0.614113	−	0.354558i	−0.774573	+	0.632484i	$0.782035\pi$
$888$		0			0
$889$	−168.065	−	97.0325i	−0.189050	−	0.109148i
$890$		0			0
$891$	1.82386	+	3.15902i	0.00204698	+	0.00354547i
$892$		0			0
$893$	−294.736	−	923.350i	−0.330052	−	1.03399i
$894$		0			0
$895$	1.36517	−	0.788180i	0.00152533	−	0.000880648i
$896$		0			0
$897$	313.313	−	542.673i	0.349289	−	0.604987i
$898$		0			0
$899$	115.371	−	199.828i	0.128332	−	0.222278i
$900$		0			0
$901$		−	106.976i		−	0.118730i
$902$		0			0
$903$	−122.651	−	70.8126i	−0.135826	−	0.0784193i
$904$		0			0
$905$			1037.95i			1.14690i
$906$		0			0
$907$	1402.39	−	809.670i	1.54619	−	0.892690i	0.547757	−	0.836637i	$-0.315482\pi$
$907$	1402.39	−	809.670i	1.54619	−	0.892690i	0.998428	−	0.0560533i	$-0.0178517\pi$
$908$		0			0
$909$	−467.276	−	809.346i	−0.514055	−	0.890369i
$910$		0			0
$911$			895.922i			0.983449i	0.870751	+	0.491725i	$0.163633\pi$
$911$			895.922i			0.983449i	−0.870751	+	0.491725i	$0.836367\pi$
$912$		0			0
$913$	−2.37500			−0.00260131
$914$		0			0
$915$	−376.798	+	217.544i	−0.411801	+	0.237753i
$916$		0			0
$917$	−47.3621	−	82.0336i	−0.0516490	−	0.0894587i
$918$		0			0
$919$	−741.588			−0.806951			−0.403476	−	0.914990i	$-0.632198\pi$
$919$	−741.588			−0.806951			−0.403476	+	0.914990i	$0.632198\pi$
$920$		0			0
$921$	−276.255	+	478.487i	−0.299951	+	0.519530i
$922$		0			0
$923$	659.101			0.714086
$924$		0			0
$925$	917.387	+	529.653i	0.991769	+	0.572598i
$926$		0			0
$927$	572.697	+	330.647i	0.617796	+	0.356685i
$928$		0			0
$929$	657.059	+	1138.06i	0.707275	+	1.22504i	0.965864	+	0.259049i	$0.0834093\pi$
$929$	657.059	+	1138.06i	0.707275	+	1.22504i	−0.258589	+	0.965988i	$0.583257\pi$
$930$		0			0
$931$	607.225	−	667.407i	0.652229	−	0.716871i
$932$		0			0
$933$	629.778	−	363.602i	0.675003	−	0.389713i
$934$		0			0
$935$	1.15982	−	2.00887i	0.00124045	−	0.00214853i
$936$		0			0
$937$	392.873	−	680.475i	0.419288	−	0.726228i	−0.576580	−	0.817041i	$-0.695613\pi$
$937$	392.873	−	680.475i	0.419288	−	0.726228i	0.995868	+	0.0908128i	$0.0289465\pi$
$938$		0			0
$939$		−	1188.94i		−	1.26618i
$940$		0			0
$941$	−224.279	−	129.487i	−0.238341	−	0.137606i	0.376073	−	0.926590i	$-0.377274\pi$
$941$	−224.279	−	129.487i	−0.238341	−	0.137606i	−0.614414	+	0.788984i	$0.710608\pi$
$942$		0			0
$943$		−	564.397i		−	0.598512i
$944$		0			0
$945$	−99.7141	+	57.5699i	−0.105518	+	0.0609206i
$946$		0			0
$947$	211.830	+	366.901i	0.223686	+	0.387435i	0.955924	−	0.293613i	$-0.0948577\pi$
$947$	211.830	+	366.901i	0.223686	+	0.387435i	−0.732239	+	0.681048i	$0.761524\pi$
$948$		0			0
$949$		−	949.414i		−	1.00044i
$950$		0			0
$951$	344.008			0.361732
$952$		0			0
$953$	1077.21	−	621.927i	1.13034	−	0.652599i	0.186316	−	0.982490i	$-0.440345\pi$
$953$	1077.21	−	621.927i	1.13034	−	0.652599i	0.944019	+	0.329891i	$0.107012\pi$
$954$		0			0
$955$	872.794	+	1511.72i	0.913920	+	1.58296i
$956$		0			0
$957$	0.718623			0.000750912
$958$		0			0
$959$	55.7893	−	96.6299i	0.0581745	−	0.100761i
$960$		0			0
$961$	−1007.94			−1.04884
$962$		0			0
$963$	−264.668	−	152.806i	−0.274837	−	0.158677i
$964$		0			0
$965$	−762.639	−	440.310i	−0.790300	−	0.456280i
$966$		0			0
$967$	−120.498	−	208.709i	−0.124610	−	0.215832i	0.796970	−	0.604019i	$-0.206435\pi$
$967$	−120.498	−	208.709i	−0.124610	−	0.215832i	−0.921581	+	0.388187i	$0.873101\pi$
$968$		0			0
$969$	632.121	−	201.775i	0.652344	−	0.208230i
$970$		0			0
$971$	−94.1758	+	54.3724i	−0.0969885	+	0.0559963i	−0.547710	−	0.836668i	$-0.684500\pi$
$971$	−94.1758	+	54.3724i	−0.0969885	+	0.0559963i	0.450721	+	0.892665i	$0.351167\pi$
$972$		0			0
$973$	−56.2567	+	97.4395i	−0.0578178	+	0.100143i
$974$		0			0
$975$	−746.331	+	1292.68i	−0.765467	+	1.32583i
$976$		0			0
$977$			1730.59i			1.77133i	0.464323	+	0.885666i	$0.346298\pi$
$977$			1730.59i			1.77133i	−0.464323	+	0.885666i	$0.653702\pi$
$978$		0			0
$979$	−4.88701	−	2.82152i	−0.00499184	−	0.00288204i
$980$		0			0
$981$			289.853i			0.295467i
$982$		0			0
$983$	−1505.59	+	869.256i	−1.53163	+	0.884288i	−0.532346	+	0.846527i	$0.678689\pi$
$983$	−1505.59	+	869.256i	−1.53163	+	0.884288i	−0.999287	+	0.0377615i	$0.987977\pi$
$984$		0			0
$985$	−992.600	−	1719.23i	−1.00772	−	1.74542i
$986$		0			0
$987$			238.324i			0.241463i
$988$		0			0
$989$	−295.856			−0.299147
$990$		0			0
$991$	273.421	−	157.860i	0.275904	−	0.159293i	−0.355663	−	0.934614i	$-0.615745\pi$
$991$	273.421	−	157.860i	0.275904	−	0.159293i	0.631568	+	0.775321i	$0.282412\pi$
$992$		0			0
$993$	−477.656	−	827.325i	−0.481023	−	0.833157i
$994$		0			0
$995$	1070.21			1.07559
$996$		0			0
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	−0.345731	−	0.938334i	$-0.612369\pi$
$997$	637.836	−	1104.76i	0.639755	−	1.10809i	0.985486	−	0.169755i	$-0.0542976\pi$
$998$		0			0
$999$	614.618			0.615233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.3.r.b.145.2		6
4.3	odd	2		19.3.d.a.12.1	yes	6
12.11	even	2		171.3.p.d.145.3		6
19.8	odd	6	inner	304.3.r.b.65.2		6
76.3	even	18		361.3.f.h.127.3		18
76.7	odd	6		361.3.b.b.360.1		6
76.11	odd	6		361.3.d.c.293.3		6
76.15	even	18		361.3.f.i.116.3		18
76.23	odd	18		361.3.f.h.116.1		18
76.27	even	6		19.3.d.a.8.1	✓	6
76.31	even	6		361.3.b.b.360.6		6
76.35	odd	18		361.3.f.i.127.1		18
76.43	odd	18		361.3.f.i.262.1		18
76.47	odd	18		361.3.f.h.307.3		18
76.51	even	18		361.3.f.i.299.1		18
76.55	odd	18		361.3.f.i.333.3		18
76.59	even	18		361.3.f.h.333.1		18
76.63	odd	18		361.3.f.h.299.3		18
76.67	even	18		361.3.f.i.307.1		18
76.71	even	18		361.3.f.h.262.3		18
76.75	even	2		361.3.d.c.69.3		6
228.179	odd	6		171.3.p.d.46.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.1	✓	6	76.27	even	6
19.3.d.a.12.1	yes	6	4.3	odd	2
171.3.p.d.46.3		6	228.179	odd	6
171.3.p.d.145.3		6	12.11	even	2
304.3.r.b.65.2		6	19.8	odd	6	inner
304.3.r.b.145.2		6	1.1	even	1	trivial
361.3.b.b.360.1		6	76.7	odd	6
361.3.b.b.360.6		6	76.31	even	6
361.3.d.c.69.3		6	76.75	even	2
361.3.d.c.293.3		6	76.11	odd	6
361.3.f.h.116.1		18	76.23	odd	18
361.3.f.h.127.3		18	76.3	even	18
361.3.f.h.262.3		18	76.71	even	18
361.3.f.h.299.3		18	76.63	odd	18
361.3.f.h.307.3		18	76.47	odd	18
361.3.f.h.333.1		18	76.59	even	18
361.3.f.i.116.3		18	76.15	even	18
361.3.f.i.127.1		18	76.35	odd	18
361.3.f.i.262.1		18	76.43	odd	18
361.3.f.i.299.1		18	76.51	even	18
361.3.f.i.307.1		18	76.67	even	18
361.3.f.i.333.3		18	76.55	odd	18

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.29225 - 1.90078i) q^{3} +(3.47303 + 6.01546i) q^{5} +1.22892 q^{7} +(2.72593 - 4.72145i) q^{9} +O(q^{10})\)	\(q+(3.29225 - 1.90078i) q^{3} +(3.47303 + 6.01546i) q^{5} +1.22892 q^{7} +(2.72593 - 4.72145i) q^{9} +0.0363521 q^{11} +(14.6268 + 8.44481i) q^{13} +(22.8681 + 13.2029i) q^{15} +(-4.59329 - 7.95581i) q^{17} +(-12.7864 + 14.0537i) q^{19} +(4.04592 - 2.33591i) q^{21} +(4.87974 - 8.45195i) q^{23} +(-11.6238 + 20.1331i) q^{25} +13.4885i q^{27} +(4.50339 + 2.60003i) q^{29} -44.3727i q^{31} +(0.119680 - 0.0690974i) q^{33} +(4.26808 + 7.39254i) q^{35} -45.5661i q^{37} +64.2069 q^{39} +(50.0829 - 28.9153i) q^{41} +(-15.1574 - 26.2534i) q^{43} +37.8689 q^{45} +(-25.5066 + 44.1787i) q^{47} -47.4897 q^{49} +(-30.2445 - 17.4617i) q^{51} +(10.0847 + 5.82239i) q^{53} +(0.126252 + 0.218675i) q^{55} +(-15.3831 + 70.5725i) q^{57} +(17.7409 - 10.2427i) q^{59} +(-8.23849 + 14.2695i) q^{61} +(3.34996 - 5.80229i) q^{63} +117.316i q^{65} +(1.83276 + 1.05814i) q^{67} -37.1012i q^{69} +(33.7958 - 19.5120i) q^{71} +(-28.1064 - 48.6818i) q^{73} +88.3775i q^{75} +0.0446740 q^{77} +(-39.8385 + 23.0008i) q^{79} +(50.1720 + 86.9004i) q^{81} -65.3332 q^{83} +(31.9053 - 55.2615i) q^{85} +19.7684 q^{87} +(-134.435 - 77.6163i) q^{89} +(17.9753 + 10.3780i) q^{91} +(-84.3427 - 146.086i) q^{93} +(-128.947 - 28.1074i) q^{95} +(-98.8107 + 57.0484i) q^{97} +(0.0990933 - 0.171635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 - 2 * q^5 + 14 * q^9	\( 6 q + 9 q^{3} - 2 q^{5} + 14 q^{9} - 26 q^{11} + 30 q^{13} + 18 q^{15} - 42 q^{17} - 25 q^{19} - 102 q^{21} - 8 q^{23} - 17 q^{25} - 12 q^{29} + 123 q^{33} + 38 q^{35} + 44 q^{39} + 63 q^{41} + 34 q^{43} - 28 q^{45} - 58 q^{47} + 18 q^{49} - 132 q^{51} - 12 q^{53} + 28 q^{55} - 16 q^{57} + 147 q^{59} + 58 q^{61} - 86 q^{63} - 201 q^{67} + 102 q^{71} + 7 q^{73} - 376 q^{77} + 253 q^{81} - 146 q^{83} - 90 q^{85} + 568 q^{87} - 72 q^{89} + 216 q^{91} - 160 q^{93} - 558 q^{95} + 21 q^{97} + 56 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 - 2 * q^5 + 14 * q^9 - 26 * q^11 + 30 * q^13 + 18 * q^15 - 42 * q^17 - 25 * q^19 - 102 * q^21 - 8 * q^23 - 17 * q^25 - 12 * q^29 + 123 * q^33 + 38 * q^35 + 44 * q^39 + 63 * q^41 + 34 * q^43 - 28 * q^45 - 58 * q^47 + 18 * q^49 - 132 * q^51 - 12 * q^53 + 28 * q^55 - 16 * q^57 + 147 * q^59 + 58 * q^61 - 86 * q^63 - 201 * q^67 + 102 * q^71 + 7 * q^73 - 376 * q^77 + 253 * q^81 - 146 * q^83 - 90 * q^85 + 568 * q^87 - 72 * q^89 + 216 * q^91 - 160 * q^93 - 558 * q^95 + 21 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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