LMFDB - Embedded newform 315.3.w.a.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("315.136");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			136.2
Root			$0.836732 + 1.44926i$ of defining polynomial
Character	$\chi$	$=$	315.136
Dual form			315.3.w.a.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.836732 - 1.44926i) q^{2} +(0.599760 - 1.03881i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.76104 + 5.13152i) q^{7} -8.70121 q^{8} +O(q^{10})$	\(q+(-0.836732 - 1.44926i) q^{2} +(0.599760 - 1.03881i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.76104 + 5.13152i) q^{7} -8.70121 q^{8} +(3.24065 + 1.87099i) q^{10} +(-6.91411 + 11.9756i) q^{11} +6.12052i q^{13} +(3.45321 - 11.1937i) q^{14} +(4.88154 + 8.45507i) q^{16} +(2.14655 + 1.23931i) q^{17} +(-24.2290 + 13.9886i) q^{19} +2.68221i q^{20} +23.1410 q^{22} +(6.62020 + 11.4665i) q^{23} +(2.50000 - 4.33013i) q^{25} +(8.87024 - 5.12123i) q^{26} +(8.18618 - 1.86816i) q^{28} +27.6516 q^{29} +(-16.2122 - 9.36010i) q^{31} +(-9.23334 + 15.9926i) q^{32} -4.14789i q^{34} +(-14.9569 - 4.61414i) q^{35} +(20.5067 + 35.5187i) q^{37} +(40.5463 + 23.4094i) q^{38} +(16.8498 - 9.72824i) q^{40} +22.5351i q^{41} +7.60485 q^{43} +(8.29361 + 14.3650i) q^{44} +(11.0787 - 19.1888i) q^{46} +(11.9214 - 6.88283i) q^{47} +(-3.66502 + 48.8627i) q^{49} -8.36732 q^{50} +(6.35808 + 3.67084i) q^{52} +(46.2995 - 80.1930i) q^{53} -30.9208i q^{55} +(-41.4268 - 44.6504i) q^{56} +(-23.1370 - 40.0744i) q^{58} +(61.5680 + 35.5463i) q^{59} +(-100.214 + 57.8584i) q^{61} +31.3276i q^{62} +69.9556 q^{64} +(-6.84295 - 11.8523i) q^{65} +(5.70227 - 9.87662i) q^{67} +(2.57483 - 1.48658i) q^{68} +(5.82783 + 25.5373i) q^{70} -99.4924 q^{71} +(90.1276 + 52.0352i) q^{73} +(34.3172 - 59.4392i) q^{74} +33.5592i q^{76} +(-94.3714 + 21.5364i) q^{77} +(-64.4982 - 111.714i) q^{79} +(-18.9061 - 10.9154i) q^{80} +(32.6592 - 18.8558i) q^{82} +30.3382i q^{83} -5.54238 q^{85} +(-6.36322 - 11.0214i) q^{86} +(60.1611 - 104.202i) q^{88} +(-93.9587 + 54.2471i) q^{89} +(-31.4076 + 29.1400i) q^{91} +15.8821 q^{92} +(-19.9501 - 11.5182i) q^{94} +(31.2794 - 54.1776i) q^{95} -153.154i q^{97} +(73.8816 - 35.5734i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8	$ 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8} - 20 q^{11} + 16 q^{14} - 2 q^{16} + 18 q^{17} - 16 q^{22} - 62 q^{23} + 20 q^{25} - 120 q^{26} - 120 q^{28} + 100 q^{29} - 126 q^{31} - 36 q^{32} - 80 q^{37} - 114 q^{38} + 90 q^{40} + 352 q^{43} + 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} - 20 q^{50} - 48 q^{52} + 76 q^{53} - 196 q^{56} - 40 q^{58} + 54 q^{59} - 396 q^{61} - 4 q^{64} + 60 q^{65} + 184 q^{67} + 312 q^{68} - 164 q^{71} + 348 q^{73} + 140 q^{74} - 152 q^{77} - 206 q^{79} + 204 q^{82} - 60 q^{85} - 178 q^{86} + 124 q^{88} - 282 q^{89} - 114 q^{91} + 288 q^{92} + 30 q^{94} + 120 q^{95} + 592 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8 - 20 * q^11 + 16 * q^14 - 2 * q^16 + 18 * q^17 - 16 * q^22 - 62 * q^23 + 20 * q^25 - 120 * q^26 - 120 * q^28 + 100 * q^29 - 126 * q^31 - 36 * q^32 - 80 * q^37 - 114 * q^38 + 90 * q^40 + 352 * q^43 + 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 - 20 * q^50 - 48 * q^52 + 76 * q^53 - 196 * q^56 - 40 * q^58 + 54 * q^59 - 396 * q^61 - 4 * q^64 + 60 * q^65 + 184 * q^67 + 312 * q^68 - 164 * q^71 + 348 * q^73 + 140 * q^74 - 152 * q^77 - 206 * q^79 + 204 * q^82 - 60 * q^85 - 178 * q^86 + 124 * q^88 - 282 * q^89 - 114 * q^91 + 288 * q^92 + 30 * q^94 + 120 * q^95 + 592 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.836732	−	1.44926i	−0.418366	−	0.724631i	0.577409	−	0.816455i	$-0.304064\pi$
$2$	−0.836732	−	1.44926i	−0.418366	−	0.724631i	−0.995775	+	0.0918238i	$0.970730\pi$
$3$		0			0
$3$		0			0
$4$	0.599760	−	1.03881i	0.149940	−	0.259704i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	4.76104	+	5.13152i	0.680148	+	0.733074i
$7$	4.76104	+	5.13152i	0.680148	+	0.733074i
$8$	−8.70121			−1.08765
$9$		0			0
$10$	3.24065	+	1.87099i	0.324065	+	0.187099i
$11$	−6.91411	+	11.9756i	−0.628556	+	1.08869i	0.359286	+	0.933227i	$0.383020\pi$
$11$	−6.91411	+	11.9756i	−0.628556	+	1.08869i	−0.987842	+	0.155463i	$0.950313\pi$
$12$		0			0
$13$			6.12052i			0.470809i	0.971897	+	0.235405i	$0.0756415\pi$
$13$			6.12052i			0.470809i	−0.971897	+	0.235405i	$0.924358\pi$
$14$	3.45321	−	11.1937i	0.246658	−	0.799550i
$15$		0			0
$16$	4.88154	+	8.45507i	0.305096	+	0.528442i
$17$	2.14655	+	1.23931i	0.126268	+	0.0729008i	0.561804	−	0.827271i	$-0.310108\pi$
$17$	2.14655	+	1.23931i	0.126268	+	0.0729008i	−0.435536	+	0.900171i	$0.643441\pi$
$18$		0			0
$19$	−24.2290	+	13.9886i	−1.27521	+	0.736242i	−0.975963	−	0.217935i	$-0.930068\pi$
$19$	−24.2290	+	13.9886i	−1.27521	+	0.736242i	−0.299245	+	0.954176i	$0.596735\pi$
$20$			2.68221i			0.134110i
$21$		0			0
$22$	23.1410			1.05186
$23$	6.62020	+	11.4665i	0.287835	+	0.498544i	0.973293	−	0.229568i	$-0.0737313\pi$
$23$	6.62020	+	11.4665i	0.287835	+	0.498544i	−0.685458	+	0.728112i	$0.740398\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	8.87024	−	5.12123i	0.341163	−	0.196970i
$27$		0			0
$28$	8.18618	−	1.86816i	0.292364	−	0.0667199i
$29$	27.6516			0.953503			0.476751	−	0.879038i	$-0.341814\pi$
$29$	27.6516			0.953503			0.476751	+	0.879038i	$0.341814\pi$
$30$		0			0
$31$	−16.2122	−	9.36010i	−0.522973	−	0.301939i	0.215177	−	0.976575i	$-0.430967\pi$
$31$	−16.2122	−	9.36010i	−0.522973	−	0.301939i	−0.738150	+	0.674636i	$0.764300\pi$
$32$	−9.23334	+	15.9926i	−0.288542	+	0.499769i
$33$		0			0
$34$		−	4.14789i		−	0.121997i
$35$	−14.9569	−	4.61414i	−0.427341	−	0.131833i
$36$		0			0
$37$	20.5067	+	35.5187i	0.554235	+	0.959964i	0.997963	+	0.0638017i	$0.0203225\pi$
$37$	20.5067	+	35.5187i	0.554235	+	0.959964i	−0.443727	+	0.896162i	$0.646344\pi$
$38$	40.5463	+	23.4094i	1.06701	+	0.616037i
$39$		0			0
$40$	16.8498	−	9.72824i	0.421245	−	0.243206i
$41$			22.5351i			0.549636i	0.961496	+	0.274818i	$0.0886176\pi$
$41$			22.5351i			0.549636i	−0.961496	+	0.274818i	$0.911382\pi$
$42$		0			0
$43$	7.60485			0.176857			0.0884285	−	0.996083i	$-0.471816\pi$
$43$	7.60485			0.176857			0.0884285	+	0.996083i	$0.471816\pi$
$44$	8.29361	+	14.3650i	0.188491	+	0.326476i
$45$		0			0
$46$	11.0787	−	19.1888i	0.240840	−	0.417148i
$47$	11.9214	−	6.88283i	0.253647	−	0.146443i	−0.367786	−	0.929910i	$-0.619884\pi$
$47$	11.9214	−	6.88283i	0.253647	−	0.146443i	0.621433	+	0.783467i	$0.286551\pi$
$48$		0			0
$49$	−3.66502	+	48.8627i	−0.0747963	+	0.997199i
$50$	−8.36732			−0.167346
$51$		0			0
$52$	6.35808	+	3.67084i	0.122271	+	0.0705931i
$53$	46.2995	−	80.1930i	0.873575	−	1.51308i	0.0153016	−	0.999883i	$-0.495129\pi$
$53$	46.2995	−	80.1930i	0.873575	−	1.51308i	0.858273	−	0.513193i	$-0.171537\pi$
$54$		0			0
$55$		−	30.9208i		−	0.562197i
$56$	−41.4268	−	44.6504i	−0.739764	−	0.797329i
$57$		0			0
$58$	−23.1370	−	40.0744i	−0.398913	−	0.690938i
$59$	61.5680	+	35.5463i	1.04352	+	0.602479i	0.920830	−	0.389965i	$-0.127513\pi$
$59$	61.5680	+	35.5463i	1.04352	+	0.602479i	0.122695	+	0.992444i	$0.460846\pi$
$60$		0			0
$61$	−100.214	+	57.8584i	−1.64285	+	0.948498i	−0.663031	+	0.748592i	$0.730730\pi$
$61$	−100.214	+	57.8584i	−1.64285	+	0.948498i	−0.979815	+	0.199906i	$0.935936\pi$
$62$			31.3276i			0.505283i
$63$		0			0
$64$	69.9556			1.09306
$65$	−6.84295	−	11.8523i	−0.105276	−	0.182344i
$66$		0			0
$67$	5.70227	−	9.87662i	0.0851085	−	0.147412i	−0.820329	−	0.571892i	$-0.806210\pi$
$67$	5.70227	−	9.87662i	0.0851085	−	0.147412i	0.905437	+	0.424480i	$0.139543\pi$
$68$	2.57483	−	1.48658i	0.0378652	−	0.0218615i
$69$		0			0
$70$	5.82783	+	25.5373i	0.0832547	+	0.364819i
$71$	−99.4924			−1.40130			−0.700651	−	0.713504i	$-0.747107\pi$
$71$	−99.4924			−1.40130			−0.700651	+	0.713504i	$0.747107\pi$
$72$		0			0
$73$	90.1276	+	52.0352i	1.23462	+	0.712811i	0.967991	−	0.250987i	$-0.0807550\pi$
$73$	90.1276	+	52.0352i	1.23462	+	0.712811i	0.266634	+	0.963798i	$0.414088\pi$
$74$	34.3172	−	59.4392i	0.463746	−	0.803232i
$75$		0			0
$76$			33.5592i			0.441568i
$77$	−94.3714	+	21.5364i	−1.22560	+	0.279693i
$78$		0			0
$79$	−64.4982	−	111.714i	−0.816433	−	1.41410i	−0.908294	−	0.418331i	$-0.862615\pi$
$79$	−64.4982	−	111.714i	−0.816433	−	1.41410i	0.0918616	−	0.995772i	$-0.470718\pi$
$80$	−18.9061	−	10.9154i	−0.236326	−	0.136443i
$81$		0			0
$82$	32.6592	−	18.8558i	0.398283	−	0.229949i
$83$			30.3382i			0.365520i	0.983158	+	0.182760i	$0.0585032\pi$
$83$			30.3382i			0.365520i	−0.983158	+	0.182760i	$0.941497\pi$
$84$		0			0
$85$	−5.54238			−0.0652045
$86$	−6.36322	−	11.0214i	−0.0739909	−	0.128156i
$87$		0			0
$88$	60.1611	−	104.202i	0.683649	−	1.18411i
$89$	−93.9587	+	54.2471i	−1.05572	+	0.609518i	−0.924244	−	0.381802i	$-0.875304\pi$
$89$	−93.9587	+	54.2471i	−1.05572	+	0.609518i	−0.131472	+	0.991320i	$0.541970\pi$
$90$		0			0
$91$	−31.4076	+	29.1400i	−0.345138	+	0.320220i
$92$	15.8821			0.172632
$93$		0			0
$94$	−19.9501	−	11.5182i	−0.212235	−	0.122534i
$95$	31.2794	−	54.1776i	0.329257	−	0.570290i
$96$		0			0
$97$		−	153.154i		−	1.57890i	−0.613812	−	0.789452i	$-0.710365\pi$
$97$		−	153.154i		−	1.57890i	0.613812	−	0.789452i	$-0.289635\pi$
$98$	73.8816	−	35.5734i	0.753893	−	0.362994i
$99$		0			0
$100$	−2.99880	−	5.19407i	−0.0299880	−	0.0519407i
$101$	−98.9544	−	57.1314i	−0.979747	−	0.565657i	−0.0775531	−	0.996988i	$-0.524711\pi$
$101$	−98.9544	−	57.1314i	−0.979747	−	0.565657i	−0.902194	+	0.431331i	$0.858044\pi$
$102$		0			0
$103$	−48.4794	+	27.9896i	−0.470674	+	0.271744i	−0.716522	−	0.697565i	$-0.754267\pi$
$103$	−48.4794	+	27.9896i	−0.470674	+	0.271744i	0.245848	+	0.969308i	$0.420934\pi$
$104$		−	53.2559i		−	0.512076i
$105$		0			0
$106$	−154.961			−1.46190
$107$	49.3529	+	85.4817i	0.461242	+	0.798895i	0.999023	−	0.0441897i	$-0.0140706\pi$
$107$	49.3529	+	85.4817i	0.461242	+	0.798895i	−0.537781	+	0.843085i	$0.680737\pi$
$108$		0			0
$109$	−26.3791	+	45.6900i	−0.242010	+	0.419174i	−0.961287	−	0.275550i	$-0.911140\pi$
$109$	−26.3791	+	45.6900i	−0.242010	+	0.419174i	0.719276	+	0.694724i	$0.244473\pi$
$110$	−44.8124	+	25.8725i	−0.407386	+	0.235204i
$111$		0			0
$112$	−20.1462	+	65.3046i	−0.179877	+	0.583077i
$113$	−106.206			−0.939875			−0.469937	−	0.882700i	$-0.655724\pi$
$113$	−106.206			−0.939875			−0.469937	+	0.882700i	$0.655724\pi$
$114$		0			0
$115$	−25.6399	−	14.8032i	−0.222956	−	0.128724i
$116$	16.5843	−	28.7249i	0.142968	−	0.247628i
$117$		0			0
$118$		−	118.971i		−	1.00823i
$119$	3.86026	+	16.9155i	0.0324392	+	0.142147i
$120$		0			0
$121$	−35.1099	−	60.8121i	−0.290164	−	0.502579i
$122$	167.704	+	96.8239i	1.37462	+	0.793638i
$123$		0			0
$124$	−19.4468	+	11.2276i	−0.156829	+	0.0905453i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−197.402			−1.55434			−0.777172	−	0.629288i	$-0.783347\pi$
$127$	−197.402			−1.55434			−0.777172	+	0.629288i	$0.783347\pi$
$128$	−21.6007	−	37.4135i	−0.168756	−	0.292293i
$129$		0			0
$130$	−11.4514	+	19.8344i	−0.0880879	+	0.152573i
$131$	−127.379	+	73.5423i	−0.972358	+	0.561391i	−0.899954	−	0.435984i	$-0.856400\pi$
$131$	−127.379	+	73.5423i	−0.972358	+	0.561391i	−0.0724040	+	0.997375i	$0.523067\pi$
$132$		0			0
$133$	−187.138	−	57.7311i	−1.40705	−	0.434069i
$134$	−19.0851			−0.142426
$135$		0			0
$136$	−18.6776	−	10.7835i	−0.137335	−	0.0792906i
$137$	124.296	−	215.287i	0.907270	−	1.57144i	0.0894293	−	0.995993i	$-0.471496\pi$
$137$	124.296	−	215.287i	0.907270	−	1.57144i	0.817841	−	0.575445i	$-0.195171\pi$
$138$		0			0
$139$		−	15.7344i		−	0.113197i	−0.998397	−	0.0565985i	$-0.981974\pi$
$139$		−	15.7344i		−	0.113197i	0.998397	−	0.0565985i	$-0.0180255\pi$
$140$	−13.7638	+	12.7701i	−0.0983129	+	0.0912150i
$141$		0			0
$142$	83.2485	+	144.191i	0.586257	+	1.01543i
$143$	−73.2968	−	42.3180i	−0.512565	−	0.295930i
$144$		0			0
$145$	−53.5471	+	30.9154i	−0.369290	+	0.213210i
$146$		−	174.158i		−	1.19286i
$147$		0			0
$148$	49.1964			0.332408
$149$	92.1029	+	159.527i	0.618140	+	1.07065i	0.989825	+	0.142291i	$0.0454470\pi$
$149$	92.1029	+	159.527i	0.618140	+	1.07065i	−0.371684	+	0.928359i	$0.621220\pi$
$150$		0			0
$151$	131.625	−	227.982i	0.871690	−	1.50981i	0.0114426	−	0.999935i	$-0.496358\pi$
$151$	131.625	−	227.982i	0.871690	−	1.50981i	0.860247	−	0.509877i	$-0.170309\pi$
$152$	210.821	−	121.718i	1.38698	−	0.800774i
$153$		0			0
$154$	110.175	+	118.749i	0.715424	+	0.771095i
$155$	41.8596			0.270062
$156$		0			0
$157$	187.600	+	108.311i	1.19490	+	0.689878i	0.959415	−	0.281999i	$-0.0909975\pi$
$157$	187.600	+	108.311i	1.19490	+	0.689878i	0.235489	+	0.971877i	$0.424331\pi$
$158$	−107.935	+	186.950i	−0.683135	+	1.18323i
$159$		0			0
$160$		−	41.2928i		−	0.258080i
$161$	−27.3217	+	88.5642i	−0.169700	+	0.550088i
$162$		0			0
$163$	86.2901	+	149.459i	0.529387	+	0.916926i	0.999413	+	0.0342728i	$0.0109115\pi$
$163$	86.2901	+	149.459i	0.529387	+	0.916926i	−0.470025	+	0.882653i	$0.655755\pi$
$164$	23.4098	+	13.5156i	0.142743	+	0.0824124i
$165$		0			0
$166$	43.9680	−	25.3849i	0.264867	−	0.152921i
$167$			156.923i			0.939658i	0.882758	+	0.469829i	$0.155684\pi$
$167$			156.923i			0.939658i	−0.882758	+	0.469829i	$0.844316\pi$
$168$		0			0
$169$	131.539			0.778339
$170$	4.63748	+	8.03236i	0.0272793	+	0.0472492i
$171$		0			0
$172$	4.56108	−	7.90003i	0.0265179	−	0.0459304i
$173$	41.2245	−	23.8010i	0.238292	−	0.137578i	−0.376100	−	0.926579i	$-0.622735\pi$
$173$	41.2245	−	23.8010i	0.238292	−	0.137578i	0.614391	+	0.789001i	$0.289402\pi$
$174$		0			0
$175$	34.1227	−	7.78710i	0.194987	−	0.0444977i
$176$	−135.006			−0.767079
$177$		0			0
$178$	157.237	+	90.7805i	0.883351	+	0.510003i
$179$	14.7747	−	25.5905i	0.0825402	−	0.142964i	−0.821800	−	0.569776i	$-0.807030\pi$
$179$	14.7747	−	25.5905i	0.0825402	−	0.142964i	0.904340	+	0.426812i	$0.140363\pi$
$180$		0			0
$181$		−	10.3249i		−	0.0570439i	−0.999593	−	0.0285219i	$-0.990920\pi$
$181$		−	10.3249i		−	0.0570439i	0.999593	−	0.0285219i	$-0.00908005\pi$
$182$	68.5112	+	21.1354i	0.376435	+	0.116129i
$183$		0			0
$184$	−57.6037	−	99.7725i	−0.313064	−	0.542242i
$185$	−79.4221	−	45.8544i	−0.429309	−	0.247862i
$186$		0			0
$187$	−29.6830	+	17.1375i	−0.158733	+	0.0916444i
$188$		−	16.5122i		−	0.0878308i
$189$		0			0
$190$	−104.690			−0.551000
$191$	−59.5045	−	103.065i	−0.311542	−	0.539607i	0.667154	−	0.744920i	$-0.267512\pi$
$191$	−59.5045	−	103.065i	−0.311542	−	0.539607i	−0.978696	+	0.205313i	$0.934179\pi$
$192$		0			0
$193$	−4.95254	+	8.57805i	−0.0256608	+	0.0444459i	−0.878571	−	0.477612i	$-0.841502\pi$
$193$	−4.95254	+	8.57805i	−0.0256608	+	0.0444459i	0.852910	+	0.522058i	$0.174836\pi$
$194$	−221.960	+	128.149i	−1.14412	+	0.660560i
$195$		0			0
$196$	48.5612	+	33.1132i	0.247761	+	0.168945i
$197$	290.342			1.47382			0.736908	−	0.675994i	$-0.236285\pi$
$197$	290.342			1.47382			0.736908	+	0.675994i	$0.236285\pi$
$198$		0			0
$199$	294.002	+	169.742i	1.47740	+	0.852977i	0.999674	−	0.0255322i	$-0.00812803\pi$
$199$	294.002	+	169.742i	1.47740	+	0.852977i	0.477725	+	0.878509i	$0.341461\pi$
$200$	−21.7530	+	37.6773i	−0.108765	+	0.188387i
$201$		0			0
$202$			191.215i			0.946607i
$203$	131.650	+	141.895i	0.648523	+	0.698989i
$204$		0			0
$205$	−25.1950	−	43.6390i	−0.122902	−	0.212873i
$206$	81.1285	+	46.8396i	0.393828	+	0.227377i
$207$		0			0
$208$	−51.7494	+	29.8775i	−0.248795	+	0.143642i
$209$		−	386.875i		−	1.85108i
$210$		0			0
$211$	11.1098			0.0526531			0.0263265	−	0.999653i	$-0.491619\pi$
$211$	11.1098			0.0526531			0.0263265	+	0.999653i	$0.491619\pi$
$212$	−55.5371	−	96.1931i	−0.261968	−	0.453741i
$213$		0			0
$214$	82.5903	−	143.051i	0.385936	−	0.668461i
$215$	−14.7267	+	8.50248i	−0.0684964	+	0.0395464i
$216$		0			0
$217$	−29.1552	−	127.757i	−0.134356	−	0.588741i
$218$	88.2890			0.404996
$219$		0			0
$220$	−32.1210	−	18.5451i	−0.146005	−	0.0842958i
$221$	−7.58524	+	13.1380i	−0.0343224	+	0.0594481i
$222$		0			0
$223$			359.376i			1.61155i	0.592220	+	0.805776i	$0.298252\pi$
$223$			359.376i			1.61155i	−0.592220	+	0.805776i	$0.701748\pi$
$224$	−126.027	+	28.7604i	−0.562619	+	0.128395i
$225$		0			0
$226$	88.8658	+	153.920i	0.393212	+	0.681062i
$227$	64.3040	+	37.1259i	0.283277	+	0.163550i	0.634906	−	0.772589i	$-0.281039\pi$
$227$	64.3040	+	37.1259i	0.283277	+	0.163550i	−0.351629	+	0.936140i	$0.614372\pi$
$228$		0			0
$229$	288.608	−	166.628i	1.26030	−	0.727633i	0.287165	−	0.957881i	$-0.407287\pi$
$229$	288.608	−	166.628i	1.26030	−	0.727633i	0.973132	+	0.230248i	$0.0739538\pi$
$230$			49.5453i			0.215414i
$231$		0			0
$232$	−240.602			−1.03708
$233$	−132.338	−	229.216i	−0.567975	−	0.983761i	−0.996766	−	0.0803575i	$-0.974394\pi$
$233$	−132.338	−	229.216i	−0.567975	−	0.983761i	0.428791	−	0.903404i	$-0.358940\pi$
$234$		0			0
$235$	−15.3905	+	26.6571i	−0.0654914	+	0.113434i
$236$	73.8520	−	42.6385i	0.312932	−	0.180671i
$237$		0			0
$238$	21.2850	−	19.7483i	0.0894328	−	0.0829759i
$239$	266.197			1.11380			0.556898	−	0.830581i	$-0.311991\pi$
$239$	266.197			1.11380			0.556898	+	0.830581i	$0.311991\pi$
$240$		0			0
$241$	−29.4197	−	16.9855i	−0.122074	−	0.0704792i	0.437720	−	0.899111i	$-0.355786\pi$
$241$	−29.4197	−	16.9855i	−0.122074	−	0.0704792i	−0.559793	+	0.828632i	$0.689120\pi$
$242$	−58.7551	+	101.767i	−0.242790	+	0.420524i
$243$		0			0
$244$			138.805i			0.568871i
$245$	−47.5329	−	98.7199i	−0.194012	−	0.402938i
$246$		0			0
$247$	−85.6174	−	148.294i	−0.346629	−	0.600380i
$248$	141.065	+	81.4441i	0.568812	+	0.328404i
$249$		0			0
$250$	16.2032	−	9.35495i	0.0648130	−	0.0374198i
$251$			84.6771i			0.337359i	0.985671	+	0.168680i	$0.0539503\pi$
$251$			84.6771i			0.337359i	−0.985671	+	0.168680i	$0.946050\pi$
$252$		0			0
$253$	−183.091			−0.723680
$254$	165.172	+	286.087i	0.650285	+	1.12633i
$255$		0			0
$256$	103.763	−	179.723i	0.405325	−	0.702044i
$257$	−27.6440	+	15.9603i	−0.107564	+	0.0621022i	−0.552817	−	0.833303i	$-0.686447\pi$
$257$	−27.6440	+	15.9603i	−0.107564	+	0.0621022i	0.445253	+	0.895405i	$0.353114\pi$
$258$		0			0
$259$	−84.6315	+	274.336i	−0.326763	+	1.05921i
$260$	−16.4165			−0.0631404
$261$		0			0
$262$	213.164	+	123.070i	0.813603	+	0.469734i
$263$	−74.0405	+	128.242i	−0.281523	+	0.487612i	−0.971760	−	0.235971i	$-0.924173\pi$
$263$	−74.0405	+	128.242i	−0.281523	+	0.487612i	0.690237	+	0.723583i	$0.257506\pi$
$264$		0			0
$265$			207.057i			0.781349i
$266$	72.9165	+	319.517i	0.274122	+	1.20119i
$267$		0			0
$268$	−6.83998	−	11.8472i	−0.0255223	−	0.0442060i
$269$	78.8909	+	45.5477i	0.293275	+	0.169322i	0.639418	−	0.768859i	$-0.279175\pi$
$269$	78.8909	+	45.5477i	0.293275	+	0.169322i	−0.346143	+	0.938182i	$0.612509\pi$
$270$		0			0
$271$	−108.045	+	62.3797i	−0.398689	+	0.230183i	−0.685918	−	0.727679i	$-0.740599\pi$
$271$	−108.045	+	62.3797i	−0.398689	+	0.230183i	0.287229	+	0.957862i	$0.407266\pi$
$272$			24.1990i			0.0889670i
$273$		0			0
$274$	−416.010			−1.51828
$275$	34.5706	+	59.8780i	0.125711	+	0.217738i
$276$		0			0
$277$	61.9619	−	107.321i	0.223689	−	0.387441i	−0.732236	−	0.681051i	$-0.761523\pi$
$277$	61.9619	−	107.321i	0.223689	−	0.387441i	0.955925	+	0.293610i	$0.0948566\pi$
$278$	−22.8033	+	13.1655i	−0.0820261	+	0.0473578i
$279$		0			0
$280$	130.143	+	40.1486i	0.464798	+	0.143388i
$281$	17.8049			0.0633627			0.0316814	−	0.999498i	$-0.489914\pi$
$281$	17.8049			0.0633627			0.0316814	+	0.999498i	$0.489914\pi$
$282$		0			0
$283$	−96.2623	−	55.5770i	−0.340149	−	0.196385i	0.320189	−	0.947354i	$-0.396254\pi$
$283$	−96.2623	−	55.5770i	−0.340149	−	0.196385i	−0.660338	+	0.750968i	$0.729587\pi$
$284$	−59.6716	+	103.354i	−0.210111	+	0.363923i
$285$		0			0
$286$			141.635i			0.495228i
$287$	−115.639	+	107.290i	−0.402924	+	0.373834i
$288$		0			0
$289$	−141.428	−	244.961i	−0.489371	−	0.847615i
$290$	89.6091	+	51.7358i	0.308997	+	0.178399i
$291$		0			0
$292$	108.110	−	62.4173i	0.370239	−	0.213758i
$293$			76.6488i			0.261600i	0.991409	+	0.130800i	$0.0417546\pi$
$293$			76.6488i			0.261600i	−0.991409	+	0.130800i	$0.958245\pi$
$294$		0			0
$295$	−158.968			−0.538874
$296$	−178.433	−	309.055i	−0.602814	−	1.04411i
$297$		0			0
$298$	154.131	−	266.963i	0.517218	−	0.895847i
$299$	−70.1810	+	40.5190i	−0.234719	+	0.135515i
$300$		0			0
$301$	36.2070	+	39.0244i	0.120289	+	0.129649i
$302$	−440.540			−1.45874
$303$		0			0
$304$	−236.549	−	136.572i	−0.778122	−	0.449249i
$305$	129.375	−	224.084i	0.424181	−	0.734703i
$306$		0			0
$307$		−	357.562i		−	1.16470i	−0.812939	−	0.582349i	$-0.802134\pi$
$307$		−	357.562i		−	1.16470i	0.812939	−	0.582349i	$-0.197866\pi$
$308$	−34.2279	+	110.951i	−0.111129	+	0.360230i
$309$		0			0
$310$	−35.0253	−	60.6656i	−0.112985	−	0.195695i
$311$	−272.856	−	157.533i	−0.877349	−	0.506538i	−0.00756579	−	0.999971i	$-0.502408\pi$
$311$	−272.856	−	157.533i	−0.877349	−	0.506538i	−0.869784	+	0.493434i	$0.835742\pi$
$312$		0			0
$313$	−227.260	+	131.209i	−0.726070	+	0.419197i	−0.816983	−	0.576662i	$-0.804355\pi$
$313$	−227.260	+	131.209i	−0.726070	+	0.419197i	0.0909126	+	0.995859i	$0.471022\pi$
$314$		−	362.508i		−	1.15449i
$315$		0			0
$316$	−154.734			−0.489664
$317$	−154.797	−	268.117i	−0.488320	−	0.845795i	0.511590	−	0.859230i	$-0.329057\pi$
$317$	−154.797	−	268.117i	−0.488320	−	0.845795i	−0.999910	+	0.0134349i	$0.995723\pi$
$318$		0			0
$319$	−191.186	+	331.144i	−0.599330	+	1.03807i
$320$	−135.468	+	78.2127i	−0.423339	+	0.244415i
$321$		0			0
$322$	151.214	−	34.5082i	0.469607	−	0.107168i
$323$	−69.3450			−0.214690
$324$		0			0
$325$	26.5026	+	15.3013i	0.0815465	+	0.0470809i
$326$	144.403	−	250.114i	0.442955	−	0.767221i
$327$		0			0
$328$		−	196.082i		−	0.597812i
$329$	92.0778	+	28.4056i	0.279872	+	0.0863391i
$330$		0			0
$331$	43.4062	+	75.1818i	0.131137	+	0.227135i	0.924115	−	0.382115i	$-0.124804\pi$
$331$	43.4062	+	75.1818i	0.131137	+	0.227135i	−0.792978	+	0.609250i	$0.791471\pi$
$332$	31.5157	+	18.1956i	0.0949269	+	0.0548061i
$333$		0			0
$334$	227.422	−	131.302i	0.680905	−	0.393121i
$335$			25.5013i			0.0761233i
$336$		0			0
$337$	373.915			1.10954			0.554770	−	0.832004i	$-0.312806\pi$
$337$	373.915			1.10954			0.554770	+	0.832004i	$0.312806\pi$
$338$	−110.063	−	190.635i	−0.325630	−	0.564008i
$339$		0			0
$340$	−3.32410	+	5.75750i	−0.00977675	+	0.0169338i
$341$	224.185	−	129.433i	0.657435	−	0.379570i
$342$		0			0
$343$	−268.190	+	213.830i	−0.781894	+	0.623412i
$344$	−66.1714			−0.192359
$345$		0			0
$346$	−68.9877	−	39.8301i	−0.199386	−	0.115116i
$347$	−165.439	+	286.549i	−0.476770	+	0.825790i	−0.999646	−	0.0266188i	$-0.991526\pi$
$347$	−165.439	+	286.549i	−0.476770	+	0.825790i	0.522875	+	0.852409i	$0.324859\pi$
$348$		0			0
$349$		−	250.907i		−	0.718932i	−0.933158	−	0.359466i	$-0.882959\pi$
$349$		−	250.907i		−	0.718932i	0.933158	−	0.359466i	$-0.117041\pi$
$350$	−39.8371	−	42.9371i	−0.113820	−	0.122677i
$351$		0			0
$352$	−127.681	−	221.149i	−0.362729	−	0.628265i
$353$	108.875	+	62.8589i	0.308427	+	0.178071i	0.646222	−	0.763149i	$-0.276348\pi$
$353$	108.875	+	62.8589i	0.308427	+	0.178071i	−0.337795	+	0.941220i	$0.609681\pi$
$354$		0			0
$355$	192.666	−	111.236i	0.542722	−	0.313341i
$356$			130.141i			0.365564i
$357$		0			0
$358$	−49.4498			−0.138128
$359$	−178.790	−	309.674i	−0.498023	−	0.862601i	0.501975	−	0.864882i	$-0.332607\pi$
$359$	−178.790	−	309.674i	−0.498023	−	0.862601i	−0.999997	+	0.00228149i	$0.999274\pi$
$360$		0			0
$361$	210.861	−	365.223i	0.584103	−	1.01170i
$362$	−14.9636	+	8.63921i	−0.0413358	+	0.0238652i
$363$		0			0
$364$	11.4341	+	50.1037i	0.0314123	+	0.137647i
$365$	−232.709			−0.637558
$366$		0			0
$367$	603.879	+	348.650i	1.64545	+	0.949999i	0.978850	+	0.204582i	$0.0655834\pi$
$367$	603.879	+	348.650i	1.64545	+	0.949999i	0.666598	+	0.745418i	$0.267750\pi$
$368$	−64.6334	+	111.948i	−0.175634	+	0.304208i
$369$		0			0
$370$			153.471i			0.414787i
$371$	631.946	−	144.215i	1.70336	−	0.388721i
$372$		0			0
$373$	72.6433	+	125.822i	0.194754	+	0.337324i	0.946820	−	0.321764i	$-0.104276\pi$
$373$	72.6433	+	125.822i	0.194754	+	0.337324i	−0.752066	+	0.659088i	$0.770942\pi$
$374$	49.6735	+	28.6790i	0.132817	+	0.0766818i
$375$		0			0
$376$	−103.731	+	59.8890i	−0.275880	+	0.159279i
$377$			169.242i			0.448918i
$378$		0			0
$379$	−222.630			−0.587415			−0.293708	−	0.955895i	$-0.594889\pi$
$379$	−222.630			−0.587415			−0.293708	+	0.955895i	$0.594889\pi$
$380$	−37.5203	−	64.9871i	−0.0987377	−	0.171019i
$381$		0			0
$382$	−99.5787	+	172.475i	−0.260677	+	0.451506i
$383$	30.1012	−	17.3789i	0.0785932	−	0.0453758i	−0.460188	−	0.887821i	$-0.652218\pi$
$383$	30.1012	−	17.3789i	0.0785932	−	0.0453758i	0.538782	+	0.842445i	$0.318885\pi$
$384$		0			0
$385$	158.671	−	147.215i	0.412132	−	0.382378i
$386$	16.5758			0.0429425
$387$		0			0
$388$	−159.098	−	91.8555i	−0.410047	−	0.236741i
$389$	276.283	−	478.537i	0.710240	−	1.23017i	−0.254528	−	0.967066i	$-0.581920\pi$
$389$	276.283	−	478.537i	0.710240	−	1.23017i	0.964767	−	0.263105i	$-0.0847467\pi$
$390$		0			0
$391$			32.8180i			0.0839335i
$392$	31.8901	−	425.165i	0.0813523	−	1.08460i
$393$		0			0
$394$	−242.938	−	420.781i	−0.616594	−	1.06797i
$395$	249.800	+	144.222i	0.632406	+	0.365120i
$396$		0			0
$397$	49.9274	−	28.8256i	0.125762	−	0.0726085i	−0.435799	−	0.900044i	$-0.643534\pi$
$397$	49.9274	−	28.8256i	0.125762	−	0.0726085i	0.561561	+	0.827435i	$0.310201\pi$
$398$		−	568.115i		−	1.42743i
$399$		0			0
$400$	48.8154			0.122038
$401$	281.160	+	486.983i	0.701146	+	1.21442i	0.968064	+	0.250701i	$0.0806612\pi$
$401$	281.160	+	486.983i	0.701146	+	1.21442i	−0.266918	+	0.963719i	$0.586005\pi$
$402$		0			0
$403$	57.2886	−	99.2268i	0.142155	−	0.246220i
$404$	−118.698	+	68.5302i	−0.293806	+	0.169629i
$405$		0			0
$406$	95.4866	−	309.524i	0.235189	−	0.762373i
$407$	−567.143			−1.39347
$408$		0			0
$409$	−174.709	−	100.869i	−0.427163	−	0.246622i	0.270975	−	0.962587i	$-0.412654\pi$
$409$	−174.709	−	100.869i	−0.427163	−	0.246622i	−0.698137	+	0.715964i	$0.745987\pi$
$410$	−42.1629	+	73.0283i	−0.102836	+	0.178118i
$411$		0			0
$412$			67.1482i			0.162981i
$413$	110.721	+	485.175i	0.268090	+	1.17476i
$414$		0			0
$415$	−33.9191	−	58.7496i	−0.0817328	−	0.141565i
$416$	−97.8831	−	56.5128i	−0.235296	−	0.135848i
$417$		0			0
$418$	−560.683	+	323.710i	−1.34135	+	0.774427i
$419$			304.381i			0.726447i	0.931702	+	0.363223i	$0.118324\pi$
$419$			304.381i			0.726447i	−0.931702	+	0.363223i	$0.881676\pi$
$420$		0			0
$421$	556.622			1.32214			0.661071	−	0.750323i	$-0.270102\pi$
$421$	556.622			1.32214			0.661071	+	0.750323i	$0.270102\pi$
$422$	−9.29592	−	16.1010i	−0.0220283	−	0.0381541i
$423$		0			0
$424$	−402.861	+	697.776i	−0.950144	+	1.64570i
$425$	10.7328	−	6.19657i	0.0252536	−	0.0145802i
$426$		0			0
$427$	−774.022	−	238.782i	−1.81270	−	0.559209i
$428$	118.400			0.276635
$429$		0			0
$430$	24.6446	+	14.2286i	0.0573131	+	0.0330897i
$431$	−90.2225	+	156.270i	−0.209333	+	0.362575i	−0.951505	−	0.307634i	$-0.900463\pi$
$431$	−90.2225	+	156.270i	−0.209333	+	0.362575i	0.742172	+	0.670210i	$0.233796\pi$
$432$		0			0
$433$		−	724.048i		−	1.67217i	−0.548603	−	0.836083i	$-0.684840\pi$
$433$		−	724.048i		−	1.67217i	0.548603	−	0.836083i	$-0.315160\pi$
$434$	−160.758	+	149.152i	−0.370410	+	0.343668i
$435$		0			0
$436$	31.6423	+	54.8061i	0.0725741	+	0.125702i
$437$	−320.801	−	185.214i	−0.734098	−	0.423832i
$438$		0			0
$439$	354.272	−	204.539i	0.806997	−	0.465920i	−0.0389147	−	0.999243i	$-0.512390\pi$
$439$	354.272	−	204.539i	0.806997	−	0.465920i	0.845912	+	0.533322i	$0.179057\pi$
$440$			269.049i			0.611474i
$441$		0			0
$442$	25.3873			0.0574372
$443$	−199.400	−	345.370i	−0.450112	−	0.779617i	0.548280	−	0.836295i	$-0.315283\pi$
$443$	−199.400	−	345.370i	−0.450112	−	0.779617i	−0.998393	+	0.0566775i	$0.981949\pi$
$444$		0			0
$445$	121.300	−	210.098i	0.272585	−	0.472131i
$446$	520.830	−	300.702i	1.16778	−	0.674219i
$447$		0			0
$448$	333.061	+	358.979i	0.743441	+	0.801292i
$449$	519.843			1.15778			0.578889	−	0.815406i	$-0.303486\pi$
$449$	519.843			1.15778			0.578889	+	0.815406i	$0.303486\pi$
$450$		0			0
$451$	−269.871	−	155.810i	−0.598384	−	0.345477i
$452$	−63.6980	+	110.328i	−0.140925	+	0.244089i
$453$		0			0
$454$		−	124.258i		−	0.273695i
$455$	28.2410	−	91.5442i	0.0620680	−	0.201196i
$456$		0			0
$457$	−116.891	−	202.462i	−0.255780	−	0.443024i	0.709327	−	0.704880i	$-0.248999\pi$
$457$	−116.891	−	202.462i	−0.255780	−	0.443024i	−0.965107	+	0.261856i	$0.915666\pi$
$458$	−482.975	−	278.846i	−1.05453	−	0.608834i
$459$		0			0
$460$	−30.7556	+	17.7567i	−0.0668599	+	0.0386016i
$461$			745.085i			1.61624i	0.589021	+	0.808118i	$0.299514\pi$
$461$			745.085i			1.61624i	−0.589021	+	0.808118i	$0.700486\pi$
$462$		0			0
$463$	742.448			1.60356			0.801779	−	0.597620i	$-0.203887\pi$
$463$	742.448			1.60356			0.801779	+	0.597620i	$0.203887\pi$
$464$	134.982	+	233.796i	0.290910	+	0.503871i
$465$		0			0
$466$	−221.463	+	383.585i	−0.475242	+	0.823144i
$467$	524.404	−	302.765i	1.12292	−	0.648318i	0.180776	−	0.983524i	$-0.442139\pi$
$467$	524.404	−	302.765i	1.12292	−	0.648318i	0.942145	+	0.335206i	$0.108806\pi$
$468$		0			0
$469$	77.8308	−	17.7617i	0.165951	−	0.0378713i
$470$	51.5108			0.109598
$471$		0			0
$472$	−535.716	−	309.296i	−1.13499	−	0.655287i
$473$	−52.5808	+	91.0726i	−0.111164	+	0.192542i
$474$		0			0
$475$			139.886i			0.294497i
$476$	19.8873	+	6.13515i	0.0417801	+	0.0128890i
$477$		0			0
$478$	−222.736	−	385.790i	−0.465974	−	0.807091i
$479$	−260.542	−	150.424i	−0.543930	−	0.314038i	0.202740	−	0.979233i	$-0.435015\pi$
$479$	−260.542	−	150.424i	−0.543930	−	0.314038i	−0.746670	+	0.665194i	$0.768349\pi$
$480$		0			0
$481$	−217.393	+	125.512i	−0.451960	+	0.260939i
$482$			56.8492i			0.117944i
$483$		0			0
$484$	−84.2300			−0.174029
$485$	171.231	+	296.581i	0.353054	+	0.611507i
$486$		0			0
$487$	−295.602	+	511.998i	−0.606986	+	1.05133i	0.384748	+	0.923021i	$0.374288\pi$
$487$	−295.602	+	511.998i	−0.606986	+	1.05133i	−0.991734	+	0.128309i	$0.959045\pi$
$488$	871.979	−	503.438i	1.78684	−	1.03163i
$489$		0			0
$490$	−103.299	+	151.490i	−0.210814	+	0.309163i
$491$	308.637			0.628589			0.314295	−	0.949325i	$-0.398232\pi$
$491$	308.637			0.628589			0.314295	+	0.949325i	$0.398232\pi$
$492$		0			0
$493$	59.3556	+	34.2690i	0.120397	+	0.0695111i
$494$	−143.278	+	248.164i	−0.290036	+	0.502357i
$495$		0			0
$496$		−	182.767i		−	0.368481i
$497$	−473.687	−	510.548i	−0.953093	−	1.02726i
$498$		0			0
$499$	447.344	+	774.822i	0.896480	+	1.55275i	0.831962	+	0.554833i	$0.187218\pi$
$499$	447.344	+	774.822i	0.896480	+	1.55275i	0.0645183	+	0.997917i	$0.479449\pi$
$500$	11.6143	+	6.70552i	0.0232286	+	0.0134110i
$501$		0			0
$502$	122.719	−	70.8520i	0.244461	−	0.141140i
$503$			609.546i			1.21182i	0.795533	+	0.605911i	$0.207191\pi$
$503$			609.546i			1.21182i	−0.795533	+	0.605911i	$0.792809\pi$
$504$		0			0
$505$	255.499			0.505939
$506$	153.198	+	265.347i	0.302763	+	0.524401i
$507$		0			0
$508$	−118.394	+	205.064i	−0.233058	+	0.403669i
$509$	−205.570	+	118.686i	−0.403871	+	0.233175i	−0.688153	−	0.725566i	$-0.741578\pi$
$509$	−205.570	+	118.686i	−0.403871	+	0.233175i	0.284282	+	0.958741i	$0.408245\pi$
$510$		0			0
$511$	162.081	+	710.233i	0.317185	+	1.38989i
$512$	−520.094			−1.01581
$513$		0			0
$514$	46.2612	+	26.7089i	0.0900023	+	0.0519629i
$515$	62.5867	−	108.403i	0.121527	−	0.210492i
$516$		0			0
$517$			190.355i			0.368191i
$518$	468.399	−	106.893i	0.904245	−	0.206356i
$519$		0			0
$520$	59.5419	+	103.130i	0.114504	+	0.198326i
$521$	32.6670	+	18.8603i	0.0627006	+	0.0362002i	0.531023	−	0.847358i	$-0.321808\pi$
$521$	32.6670	+	18.8603i	0.0627006	+	0.0362002i	−0.468322	+	0.883558i	$0.655141\pi$
$522$		0			0
$523$	40.5068	−	23.3866i	0.0774509	−	0.0447163i	−0.460774	−	0.887517i	$-0.652428\pi$
$523$	40.5068	−	23.3866i	0.0774509	−	0.0447163i	0.538225	+	0.842801i	$0.319095\pi$
$524$			176.431i			0.336700i
$525$		0			0
$526$	247.808			0.471118
$527$	−23.2002	−	40.1839i	−0.0440231	−	0.0762503i
$528$		0			0
$529$	176.846	−	306.306i	0.334303	−	0.579029i
$530$	300.081	−	173.252i	0.566190	−	0.326890i
$531$		0			0
$532$	−172.210	+	159.777i	−0.323702	+	0.300332i
$533$	−137.926			−0.258774
$534$		0			0
$535$	−191.143	−	110.356i	−0.357277	−	0.206274i
$536$	−49.6166	+	85.9385i	−0.0925683	+	0.160333i
$537$		0			0
$538$		−	152.445i		−	0.283355i
$539$	−559.820	−	381.733i	−1.03863	−	0.708225i
$540$		0			0
$541$	195.629	+	338.839i	0.361606	+	0.626320i	0.988225	−	0.153005i	$-0.0488951\pi$
$541$	195.629	+	338.839i	0.361606	+	0.626320i	−0.626619	+	0.779326i	$0.715562\pi$
$542$	180.809	+	104.390i	0.333596	+	0.192602i
$543$		0			0
$544$	−39.6397	+	22.8860i	−0.0728671	+	0.0420699i
$545$		−	117.971i		−	0.216461i
$546$		0			0
$547$	−389.827			−0.712664			−0.356332	−	0.934359i	$-0.615973\pi$
$547$	−389.827			−0.712664			−0.356332	+	0.934359i	$0.615973\pi$
$548$	−149.096	−	258.241i	−0.272072	−	0.471243i
$549$		0			0
$550$	57.8526	−	100.204i	0.105186	−	0.182188i
$551$	−669.969	+	386.807i	−1.21591	+	0.702009i
$552$		0			0
$553$	266.185	−	862.849i	0.481347	−	1.56031i
$554$	−207.382			−0.374336
$555$		0			0
$556$	−16.3451	−	9.43686i	−0.0293977	−	0.0169728i
$557$	89.4085	−	154.860i	0.160518	−	0.278025i	−0.774537	−	0.632529i	$-0.782017\pi$
$557$	89.4085	−	154.860i	0.160518	−	0.278025i	0.935055	+	0.354504i	$0.115350\pi$
$558$		0			0
$559$			46.5456i			0.0832659i
$560$	−33.9999	−	148.986i	−0.0607141	−	0.266046i
$561$		0			0
$562$	−14.8979	−	25.8040i	−0.0265088	−	0.0459146i
$563$	139.571	+	80.5815i	0.247906	+	0.143129i	0.618805	−	0.785545i	$-0.287617\pi$
$563$	139.571	+	80.5815i	0.247906	+	0.143129i	−0.370899	+	0.928673i	$0.620950\pi$
$564$		0			0
$565$	205.667	−	118.742i	0.364012	−	0.210162i
$566$			186.012i			0.328644i
$567$		0			0
$568$	865.704			1.52413
$569$	6.24946	+	10.8244i	0.0109832	+	0.0190235i	0.871465	−	0.490458i	$-0.163171\pi$
$569$	6.24946	+	10.8244i	0.0109832	+	0.0190235i	−0.860482	+	0.509482i	$0.829837\pi$
$570$		0			0
$571$	−61.6982	+	106.864i	−0.108053	+	0.187153i	−0.914981	−	0.403496i	$-0.867795\pi$
$571$	−61.6982	+	106.864i	−0.108053	+	0.187153i	0.806929	+	0.590649i	$0.201128\pi$
$572$	−87.9210	+	50.7612i	−0.153708	+	0.0887434i
$573$		0			0
$574$	252.251	+	77.8183i	0.439462	+	0.135572i
$575$	66.2020			0.115134
$576$		0			0
$577$	−143.692	−	82.9608i	−0.249033	−	0.143779i	0.370288	−	0.928917i	$-0.379259\pi$
$577$	−143.692	−	82.9608i	−0.249033	−	0.143779i	−0.619322	+	0.785137i	$0.712592\pi$
$578$	−236.675	+	409.933i	−0.409472	+	0.709227i
$579$		0			0
$580$			74.1673i			0.127875i
$581$	−155.681	+	144.441i	−0.267954	+	0.248608i
$582$		0			0
$583$	640.239	+	1108.93i	1.09818	+	1.90210i
$584$	−784.219	−	452.769i	−1.34284	−	0.775290i
$585$		0			0
$586$	111.084	−	64.1345i	0.189564	−	0.109445i
$587$			186.037i			0.316929i	0.987365	+	0.158465i	$0.0506544\pi$
$587$			186.037i			0.316929i	−0.987365	+	0.158465i	$0.949346\pi$
$588$		0			0
$589$	523.738			0.889199
$590$	133.013	+	230.386i	0.225446	+	0.390485i
$591$		0			0
$592$	−200.208	+	346.771i	−0.338190	+	0.585762i
$593$	−494.838	+	285.695i	−0.834465	+	0.481779i	−0.855379	−	0.518003i	$-0.826676\pi$
$593$	−494.838	+	285.695i	−0.834465	+	0.481779i	0.0209140	+	0.999781i	$0.493342\pi$
$594$		0			0
$595$	−26.3875	−	28.4408i	−0.0443487	−	0.0477997i
$596$	220.959			0.370736
$597$		0			0
$598$	117.445	+	67.8071i	0.196397	+	0.113390i
$599$	87.2619	−	151.142i	0.145679	−	0.252324i	−0.783947	−	0.620828i	$-0.786797\pi$
$599$	87.2619	−	151.142i	0.145679	−	0.252324i	0.929626	+	0.368504i	$0.120130\pi$
$600$		0			0
$601$			667.415i			1.11051i	0.831681	+	0.555254i	$0.187379\pi$
$601$			667.415i			1.11051i	−0.831681	+	0.555254i	$0.812621\pi$
$602$	26.2611	−	85.1264i	0.0436231	−	0.141406i
$603$		0			0
$604$	−157.887	−	273.468i	−0.261402	−	0.452762i
$605$	135.980	+	78.5081i	0.224760	+	0.129765i
$606$		0			0
$607$	23.3123	−	13.4594i	0.0384057	−	0.0221736i	−0.480674	−	0.876899i	$-0.659608\pi$
$607$	23.3123	−	13.4594i	0.0384057	−	0.0221736i	0.519080	+	0.854726i	$0.326275\pi$
$608$		−	516.646i		−	0.849746i
$609$		0			0
$610$	−433.009			−0.709852
$611$	42.1265	+	72.9653i	0.0689468	+	0.119419i
$612$		0			0
$613$	32.7197	−	56.6723i	0.0533764	−	0.0924507i	−0.838103	−	0.545513i	$-0.816335\pi$
$613$	32.7197	−	56.6723i	0.0533764	−	0.0924507i	0.891479	+	0.453062i	$0.149668\pi$
$614$	−518.201	+	299.183i	−0.843976	+	0.487270i
$615$		0			0
$616$	821.145	−	187.392i	1.33303	−	0.304208i
$617$	−1059.51			−1.71720			−0.858601	−	0.512644i	$-0.828666\pi$
$617$	−1059.51			−1.71720			−0.858601	+	0.512644i	$0.828666\pi$
$618$		0			0
$619$	139.355	+	80.4565i	0.225129	+	0.129978i	0.608323	−	0.793690i	$-0.291843\pi$
$619$	139.355	+	80.4565i	0.225129	+	0.129978i	−0.383194	+	0.923668i	$0.625176\pi$
$620$	25.1057	−	43.4844i	0.0404931	−	0.0701361i
$621$		0			0
$622$			527.252i			0.847673i
$623$	−725.711	−	223.879i	−1.16487	−	0.359356i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	380.311	+	219.573i	0.607526	+	0.350755i
$627$		0			0
$628$	225.030	−	129.921i	0.358328	−	0.206881i
$629$			101.657i			0.161617i
$630$		0			0
$631$	−45.2151			−0.0716562			−0.0358281	−	0.999358i	$-0.511407\pi$
$631$	−45.2151			−0.0716562			−0.0358281	+	0.999358i	$0.511407\pi$
$632$	561.212	+	972.048i	0.887994	+	1.53805i
$633$		0			0
$634$	−259.048	+	448.684i	−0.408593	+	0.707703i
$635$	382.267	−	220.702i	0.601995	−	0.347562i
$636$		0			0
$637$	−299.065	−	22.4318i	−0.469490	−	0.0352148i
$638$	639.886			1.00296
$639$		0			0
$640$	83.6592	+	48.3007i	0.130718	+	0.0754698i
$641$	161.675	−	280.030i	0.252224	−	0.436865i	−0.711914	−	0.702267i	$-0.752171\pi$
$641$	161.675	−	280.030i	0.252224	−	0.436865i	0.964138	+	0.265402i	$0.0855047\pi$
$642$		0			0
$643$		−	363.744i		−	0.565698i	−0.959164	−	0.282849i	$-0.908720\pi$
$643$		−	363.744i		−	0.565698i	0.959164	−	0.282849i	$-0.0912795\pi$
$644$	75.6153	+	81.4994i	0.117415	+	0.126552i
$645$		0			0
$646$	58.0232	+	100.499i	0.0898191	+	0.155571i
$647$	1114.98	+	643.737i	1.72331	+	0.994956i	0.911812	+	0.410608i	$0.134683\pi$
$647$	1114.98	+	643.737i	1.72331	+	0.994956i	0.811503	+	0.584348i	$0.198650\pi$
$648$		0			0
$649$	−851.376	+	491.542i	−1.31183	+	0.757384i
$650$		−	51.2123i		−	0.0787882i
$651$		0			0
$652$	207.013			0.317505
$653$	308.886	+	535.007i	0.473026	+	0.819306i	0.999523	−	0.0308714i	$-0.00982823\pi$
$653$	308.886	+	535.007i	0.473026	+	0.819306i	−0.526497	+	0.850177i	$0.676495\pi$
$654$		0			0
$655$	164.446	−	284.828i	0.251062	−	0.434852i
$656$	−190.536	+	110.006i	−0.290451	+	0.167692i
$657$		0			0
$658$	−35.8773	−	157.213i	−0.0545247	−	0.238925i
$659$	1229.62			1.86589			0.932945	−	0.360019i	$-0.117230\pi$
$659$	1229.62			1.86589			0.932945	+	0.360019i	$0.117230\pi$
$660$		0			0
$661$	−606.437	−	350.127i	−0.917454	−	0.529692i	−0.0346322	−	0.999400i	$-0.511026\pi$
$661$	−606.437	−	350.127i	−0.917454	−	0.529692i	−0.882822	+	0.469708i	$0.844359\pi$
$662$	72.6387	−	125.814i	0.109726	−	0.190051i
$663$		0			0
$664$		−	263.979i		−	0.397558i
$665$	426.936	−	97.4304i	0.642009	−	0.146512i
$666$		0			0
$667$	183.059	+	317.067i	0.274451	+	0.475363i
$668$	163.014	+	94.1160i	0.244032	+	0.140892i
$669$		0			0
$670$	36.9581	−	21.3378i	0.0551613	−	0.0318474i
$671$		−	1600.16i		−	2.38473i
$672$		0			0
$673$	−121.032			−0.179840			−0.0899201	−	0.995949i	$-0.528661\pi$
$673$	−121.032			−0.179840			−0.0899201	+	0.995949i	$0.528661\pi$
$674$	−312.867	−	541.901i	−0.464194	−	0.804007i
$675$		0			0
$676$	78.8920	−	136.645i	0.116704	−	0.202137i
$677$	851.854	−	491.818i	1.25828	−	0.726467i	0.285538	−	0.958367i	$-0.407828\pi$
$677$	851.854	−	491.818i	1.25828	−	0.726467i	0.972739	+	0.231901i	$0.0744944\pi$
$678$		0			0
$679$	785.912	−	729.171i	1.15745	−	1.07389i
$680$	48.2254			0.0709197
$681$		0			0
$682$	−375.166	−	216.602i	−0.550097	−	0.317599i
$683$	56.5263	−	97.9064i	0.0827618	−	0.143348i	−0.821674	−	0.569958i	$-0.806959\pi$
$683$	56.5263	−	97.9064i	0.0827618	−	0.143348i	0.904435	+	0.426611i	$0.140293\pi$
$684$		0			0
$685$			555.869i			0.811487i
$686$	534.299	+	209.758i	0.778861	+	0.305770i
$687$		0			0
$688$	37.1234	+	64.2995i	0.0539584	+	0.0934586i
$689$	490.823	+	283.377i	0.712370	+	0.411287i
$690$		0			0
$691$	−771.062	+	445.173i	−1.11586	+	0.644244i	−0.940342	−	0.340231i	$-0.889495\pi$
$691$	−771.062	+	445.173i	−1.11586	+	0.644244i	−0.175522	+	0.984475i	$0.556161\pi$
$692$		−	57.0995i		−	0.0825137i
$693$		0			0
$694$	553.713			0.797858
$695$	17.5916	+	30.4695i	0.0253116	+	0.0438410i
$696$		0			0
$697$	−27.9280	+	48.3728i	−0.0400689	+	0.0694014i
$698$	−363.630	+	209.942i	−0.520960	+	0.300776i
$699$		0			0
$700$	12.3761	−	40.1176i	0.0176801	−	0.0573108i
$701$	730.892			1.04264			0.521321	−	0.853361i	$-0.325440\pi$
$701$	730.892			1.04264			0.521321	+	0.853361i	$0.325440\pi$
$702$		0			0
$703$	−993.712	−	573.720i	−1.41353	−	0.816102i
$704$	−483.681	+	837.760i	−0.687047	+	1.19000i
$705$		0			0
$706$		−	210.384i		−	0.297995i
$707$	−177.955	−	779.791i	−0.251704	−	1.10296i
$708$		0			0
$709$	−576.325	−	998.224i	−0.812870	−	1.40793i	−0.910847	−	0.412744i	$-0.864570\pi$
$709$	−576.325	−	998.224i	−0.812870	−	1.40793i	0.0979765	−	0.995189i	$-0.468763\pi$
$710$	−322.420	−	186.149i	−0.454113	−	0.262182i
$711$		0			0
$712$	817.554	−	472.015i	1.14825	−	0.662943i
$713$		−	247.863i		−	0.347633i
$714$		0			0
$715$	189.252			0.264688
$716$	−17.7225	−	30.6963i	−0.0247521	−	0.0428720i
$717$		0			0
$718$	−299.199	+	518.228i	−0.416712	+	0.721766i
$719$	−688.275	+	397.376i	−0.957267	+	0.552678i	−0.895331	−	0.445402i	$-0.853061\pi$
$719$	−688.275	+	397.376i	−0.957267	+	0.552678i	−0.0619361	+	0.998080i	$0.519727\pi$
$720$		0			0
$721$	−374.442	−	115.514i	−0.519336	−	0.160213i
$722$	−705.738			−0.977476
$723$		0			0
$724$	−10.7257	−	6.19249i	−0.0148145	−	0.00855316i
$725$	69.1290	−	119.735i	0.0953503	−	0.165152i
$726$		0			0
$727$		−	312.108i		−	0.429310i	−0.976690	−	0.214655i	$-0.931137\pi$
$727$		−	312.108i		−	0.429310i	0.976690	−	0.214655i	$-0.0688626\pi$
$728$	273.284	−	253.553i	0.375390	−	0.348288i
$729$		0			0
$730$	194.715	+	337.256i	0.266732	+	0.461994i
$731$	16.3242	+	9.42479i	0.0223314	+	0.0128930i
$732$		0			0
$733$	215.629	−	124.493i	0.294173	−	0.169841i	−0.345649	−	0.938364i	$-0.612341\pi$
$733$	215.629	−	124.493i	0.294173	−	0.169841i	0.639822	+	0.768523i	$0.279008\pi$
$734$		−	1166.91i		−	1.58979i
$735$		0			0
$736$	−244.506			−0.332209
$737$	78.8522	+	136.576i	0.106991	+	0.185314i
$738$		0			0
$739$	−152.219	+	263.652i	−0.205980	+	0.356768i	−0.950445	−	0.310894i	$-0.899372\pi$
$739$	−152.219	+	263.652i	−0.205980	+	0.356768i	0.744464	+	0.667662i	$0.232705\pi$
$740$	−95.2684	+	55.0032i	−0.128741	+	0.0743287i
$741$		0			0
$742$	−737.775	−	795.185i	−0.994306	−	1.07168i
$743$	235.455			0.316898			0.158449	−	0.987367i	$-0.449351\pi$
$743$	235.455			0.316898			0.158449	+	0.987367i	$0.449351\pi$
$744$		0			0
$745$	−356.713	−	205.948i	−0.478810	−	0.276441i
$746$	121.566	−	210.558i	0.162957	−	0.282250i
$747$		0			0
$748$			41.1136i			0.0549646i
$749$	−203.680	+	660.237i	−0.271936	+	0.881492i
$750$		0			0
$751$	387.921	+	671.900i	0.516540	+	0.894673i	0.999816	+	0.0192050i	$0.00611351\pi$
$751$	387.921	+	671.900i	0.516540	+	0.894673i	−0.483276	+	0.875468i	$0.660553\pi$
$752$	116.390	+	67.1976i	0.154774	+	0.0893585i
$753$		0			0
$754$	245.276	−	141.610i	0.325300	−	0.187812i
$755$			588.646i			0.779663i
$756$		0			0
$757$	−194.342			−0.256727			−0.128363	−	0.991727i	$-0.540972\pi$
$757$	−194.342			−0.256727			−0.128363	+	0.991727i	$0.540972\pi$
$758$	186.282	+	322.650i	0.245755	+	0.425659i
$759$		0			0
$760$	−272.169	+	471.410i	−0.358117	+	0.620277i
$761$	441.278	−	254.772i	0.579866	−	0.334786i	−0.181214	−	0.983444i	$-0.558003\pi$
$761$	441.278	−	254.772i	0.579866	−	0.334786i	0.761080	+	0.648658i	$0.224669\pi$
$762$		0			0
$763$	−360.051	+	82.1668i	−0.471889	+	0.107689i
$764$	−142.754			−0.186850
$765$		0			0
$766$	−50.3732	−	29.0830i	−0.0657614	−	0.0379674i
$767$	−217.562	+	376.828i	−0.283653	+	0.491301i
$768$		0			0
$769$		−	1174.80i		−	1.52769i	−0.645398	−	0.763846i	$-0.723308\pi$
$769$		−	1174.80i		−	1.52769i	0.645398	−	0.763846i	$-0.276692\pi$
$770$	−346.119	−	106.776i	−0.449505	−	0.138670i
$771$		0			0
$772$	5.94067	+	10.2895i	0.00769517	+	0.0133284i
$773$	−996.623	−	575.401i	−1.28929	−	0.744373i	−0.310764	−	0.950487i	$-0.600585\pi$
$773$	−996.623	−	575.401i	−1.28929	−	0.744373i	−0.978528	+	0.206114i	$0.933918\pi$
$774$		0			0
$775$	−81.0608	+	46.8005i	−0.104595	+	0.0603877i
$776$			1332.62i			1.71730i
$777$		0			0
$778$	−924.700			−1.18856
$779$	−315.234	−	546.001i	−0.404665	−	0.700900i
$780$		0			0
$781$	687.902	−	1191.48i	0.880796	−	1.52558i
$782$	47.5619	−	27.4599i	0.0608208	−	0.0351149i
$783$		0			0
$784$	−431.029	+	207.537i	−0.549782	+	0.264716i
$785$	−484.381			−0.617046
$786$		0			0
$787$	−199.749	−	115.325i	−0.253810	−	0.146538i	0.367697	−	0.929946i	$-0.380146\pi$
$787$	−199.749	−	115.325i	−0.253810	−	0.146538i	−0.621508	+	0.783408i	$0.713480\pi$
$788$	174.135	−	301.611i	0.220984	−	0.382755i
$789$		0			0
$790$		−	482.702i		−	0.611015i
$791$	−505.650	−	544.998i	−0.639254	−	0.688998i
$792$		0			0
$793$	−354.123	−	613.359i	−0.446561	−	0.773467i
$794$	−83.5517	−	48.2386i	−0.105229	−	0.0607539i
$795$		0			0
$796$	352.662	−	203.609i	0.443042	−	0.255791i
$797$		−	246.018i		−	0.308680i	−0.988018	−	0.154340i	$-0.950675\pi$
$797$		−	246.018i		−	0.308680i	0.988018	−	0.154340i	$-0.0493251\pi$
$798$		0			0
$799$	34.1200			0.0427033
$800$	46.1667	+	79.9631i	0.0577084	+	0.0999538i
$801$		0			0
$802$	470.510	−	814.948i	0.586671	−	1.01614i
$803$	−1246.30	+	719.554i	−1.55206	+	0.896083i
$804$		0			0
$805$	−46.1096	−	202.050i	−0.0572790	−	0.250994i
$806$	−191.741			−0.237892
$807$		0			0
$808$	861.023	+	497.112i	1.06562	+	0.615237i
$809$	120.772	−	209.183i	0.149285	−	0.258569i	−0.781678	−	0.623682i	$-0.785636\pi$
$809$	120.772	−	209.183i	0.149285	−	0.258569i	0.930963	+	0.365112i	$0.118969\pi$
$810$		0			0
$811$			626.619i			0.772650i	0.922363	+	0.386325i	$0.126256\pi$
$811$			626.619i			0.772650i	−0.922363	+	0.386325i	$0.873744\pi$
$812$	226.361	−	51.6575i	0.278770	−	0.0636176i
$813$		0			0
$814$	474.546	+	821.938i	0.582981	+	1.00975i
$815$	−334.200	−	192.951i	−0.410062	−	0.236749i
$816$		0			0
$817$	−184.258	+	106.381i	−0.225529	+	0.130209i
$818$			337.600i			0.412714i
$819$		0			0
$820$	−60.4438			−0.0737119
$821$	−49.3857	−	85.5386i	−0.0601532	−	0.104188i	0.834381	−	0.551189i	$-0.185826\pi$
$821$	−49.3857	−	85.5386i	−0.0601532	−	0.104188i	−0.894534	+	0.447000i	$0.852492\pi$
$822$		0			0
$823$	−391.560	+	678.202i	−0.475772	+	0.824061i	−0.999615	−	0.0277542i	$-0.991164\pi$
$823$	−391.560	+	678.202i	−0.475772	+	0.824061i	0.523843	+	0.851815i	$0.324498\pi$
$824$	421.829	−	243.543i	0.511929	−	0.295562i
$825$		0			0
$826$	610.501	−	566.425i	0.739106	−	0.685744i
$827$	1131.53			1.36823			0.684116	−	0.729373i	$-0.260188\pi$
$827$	1131.53			1.36823			0.684116	+	0.729373i	$0.260188\pi$
$828$		0			0
$829$	164.501	+	94.9749i	0.198434	+	0.114566i	0.595925	−	0.803040i	$-0.296786\pi$
$829$	164.501	+	94.9749i	0.198434	+	0.114566i	−0.397491	+	0.917606i	$0.630119\pi$
$830$	−56.7624	+	98.3154i	−0.0683884	+	0.118452i
$831$		0			0
$832$			428.165i			0.514621i
$833$	−68.4234	+	100.344i	−0.0821410	+	0.120461i
$834$		0			0
$835$	−175.445	−	303.880i	−0.210114	−	0.363928i
$836$	−401.891	−	232.032i	−0.480731	−	0.277550i
$837$		0			0
$838$	441.128	−	254.685i	0.526406	−	0.303921i
$839$		−	1431.33i		−	1.70599i	−0.521919	−	0.852995i	$-0.674784\pi$
$839$		−	1431.33i		−	1.70599i	0.521919	−	0.852995i	$-0.325216\pi$
$840$		0			0
$841$	−76.3899			−0.0908322
$842$	−465.743	−	806.691i	−0.553139	−	0.958065i
$843$		0			0
$844$	6.66321	−	11.5410i	0.00789480	−	0.0136742i
$845$	−254.725	+	147.065i	−0.301449	+	0.174042i
$846$		0			0
$847$	144.899	−	469.696i	0.171073	−	0.554541i
$848$	904.050			1.06610
$849$		0			0
$850$	−17.9609	−	10.3697i	−0.0211305	−	0.0121997i
$851$	−271.517	+	470.281i	−0.319056	+	0.552621i
$852$		0			0
$853$			1123.73i			1.31739i	0.752412	+	0.658693i	$0.228890\pi$
$853$			1123.73i			1.31739i	−0.752412	+	0.658693i	$0.771110\pi$
$854$	301.591	+	1321.56i	0.353151	+	1.54749i
$855$		0			0
$856$	−429.430	−	743.794i	−0.501670	−	0.868919i
$857$	−1300.05	−	750.584i	−1.51698	−	0.875827i	−0.999801	−	0.0199480i	$-0.993650\pi$
$857$	−1300.05	−	750.584i	−1.51698	−	0.875827i	−0.517176	−	0.855879i	$-0.673017\pi$
$858$		0			0
$859$	−1203.93	+	695.091i	−1.40155	+	0.809186i	−0.994552	−	0.104242i	$-0.966758\pi$
$859$	−1203.93	+	695.091i	−1.40155	+	0.809186i	−0.407000	+	0.913428i	$0.633425\pi$
$860$			20.3978i			0.0237184i
$861$		0			0
$862$	301.968			0.350311
$863$	133.534	+	231.288i	0.154732	+	0.268004i	0.932962	−	0.359976i	$-0.117215\pi$
$863$	133.534	+	231.288i	0.154732	+	0.268004i	−0.778229	+	0.627980i	$0.783882\pi$
$864$		0			0
$865$	−53.2206	+	92.1808i	−0.0615267	+	0.106567i
$866$	−1049.33	+	605.834i	−1.21170	+	0.699577i
$867$		0			0
$868$	−150.202	−	46.3366i	−0.173044	−	0.0533832i
$869$	1783.79			2.05269
$870$		0			0
$871$	60.4500	+	34.9008i	0.0694030	+	0.0400699i
$872$	229.530	−	397.558i	0.263223	−	0.455915i
$873$		0			0
$874$			619.899i			0.709267i
$875$	−57.3722	+	53.2300i	−0.0655682	+	0.0608343i
$876$		0			0
$877$	499.609	+	865.348i	0.569679	+	0.986714i	0.996597	+	0.0824232i	$0.0262659\pi$
$877$	499.609	+	865.348i	0.569679	+	0.986714i	−0.426918	+	0.904290i	$0.640401\pi$
$878$	−592.861	−	342.288i	−0.675240	−	0.389850i
$879$		0			0
$880$	261.438	−	150.941i	0.297089	−	0.171524i
$881$		−	94.1956i		−	0.106919i	−0.998570	−	0.0534595i	$-0.982975\pi$
$881$		−	94.1956i		−	0.106919i	0.998570	−	0.0534595i	$-0.0170248\pi$
$882$		0			0
$883$	−389.465			−0.441070			−0.220535	−	0.975379i	$-0.570780\pi$
$883$	−389.465			−0.441070			−0.220535	+	0.975379i	$0.570780\pi$
$884$	9.09865	+	15.7593i	0.0102926	+	0.0178273i
$885$		0			0
$886$	−333.688	+	577.965i	−0.376623	+	0.652330i
$887$	−638.869	+	368.851i	−0.720258	+	0.415841i	−0.814848	−	0.579675i	$-0.803179\pi$
$887$	−638.869	+	368.851i	−0.720258	+	0.415841i	0.0945896	+	0.995516i	$0.469846\pi$
$888$		0			0
$889$	−939.837	−	1012.97i	−1.05718	−	1.13945i
$890$	−405.983			−0.456161
$891$		0			0
$892$	373.325	+	215.539i	0.418526	+	0.241636i
$893$	−192.562	+	333.528i	−0.215635	+	0.373491i
$894$		0			0
$895$			66.0744i			0.0738262i
$896$	89.1465	−	288.972i	0.0994939	−	0.322513i
$897$		0			0
$898$	−434.969	−	753.388i	−0.484375	−	0.838962i
$899$	−448.292	−	258.821i	−0.498656	−	0.287899i
$900$		0			0
$901$	198.769	−	114.759i	0.220609	−	0.127369i
$902$			521.485i			0.578143i
$903$		0			0
$904$	924.119			1.02226
$905$	11.5436	+	19.9942i	0.0127554	+	0.0220930i
$906$		0			0
$907$	−64.2146	+	111.223i	−0.0707989	+	0.122627i	−0.899252	−	0.437432i	$-0.855888\pi$
$907$	−64.2146	+	111.223i	−0.0707989	+	0.122627i	0.828453	+	0.560059i	$0.189222\pi$
$908$	77.1339	−	44.5333i	0.0849492	−	0.0490454i
$909$		0			0
$910$	−156.302	+	35.6694i	−0.171760	+	0.0391971i
$911$	−851.535			−0.934725			−0.467363	−	0.884066i	$-0.654796\pi$
$911$	−851.535			−0.934725			−0.467363	+	0.884066i	$0.654796\pi$
$912$		0			0
$913$	−363.318	−	209.762i	−0.397938	−	0.229750i
$914$	−195.614	+	338.813i	−0.214019	+	0.370692i
$915$		0			0
$916$		−	399.747i		−	0.436405i
$917$	−983.840	−	303.510i	−1.07289	−	0.330982i
$918$		0			0
$919$	755.722	+	1308.95i	0.822330	+	1.42432i	0.903943	+	0.427654i	$0.140660\pi$
$919$	755.722	+	1308.95i	0.822330	+	1.42432i	−0.0816123	+	0.996664i	$0.526007\pi$
$920$	223.098	+	128.806i	0.242498	+	0.140006i
$921$		0			0
$922$	1079.82	−	623.436i	1.17117	−	0.676178i
$923$		−	608.945i		−	0.659746i
$924$		0			0
$925$	205.067			0.221694
$926$	−621.230	−	1076.00i	−0.670874	−	1.16199i
$927$		0			0
$928$	−255.316	+	442.221i	−0.275126	+	0.476531i
$929$	44.6801	−	25.7961i	0.0480949	−	0.0277676i	−0.475760	−	0.879575i	$-0.657827\pi$
$929$	44.6801	−	25.7961i	0.0480949	−	0.0277676i	0.523855	+	0.851808i	$0.324494\pi$
$930$		0			0
$931$	−594.721	−	1235.16i	−0.638798	−	1.32670i
$932$	−317.484			−0.340648
$933$		0			0
$934$	−877.571	−	506.666i	−0.939583	−	0.542469i
$935$	38.3206	−	66.3733i	0.0409846	−	0.0709875i
$936$		0			0
$937$			1321.41i			1.41026i	0.709080	+	0.705128i	$0.249110\pi$
$937$			1321.41i			1.41026i	−0.709080	+	0.705128i	$0.750890\pi$
$938$	−90.8648	−	97.9355i	−0.0968708	−	0.104409i
$939$		0			0
$940$	18.4612	+	31.9757i	0.0196396	+	0.0340167i
$941$	−708.633	−	409.129i	−0.753063	−	0.434781i	0.0737363	−	0.997278i	$-0.476508\pi$
$941$	−708.633	−	409.129i	−0.753063	−	0.434781i	−0.826800	+	0.562496i	$0.809841\pi$
$942$		0			0
$943$	−258.399	+	149.187i	−0.274018	+	0.158204i
$944$			694.082i			0.735256i
$945$		0			0
$946$	175.984			0.186030
$947$	716.084	+	1240.29i	0.756160	+	1.30971i	0.944796	+	0.327661i	$0.106260\pi$
$947$	716.084	+	1240.29i	0.756160	+	1.30971i	−0.188635	+	0.982047i	$0.560406\pi$
$948$		0			0
$949$	−318.482	+	551.628i	−0.335598	+	0.581273i
$950$	202.731	−	117.047i	0.213401	−	0.123207i
$951$		0			0
$952$	−33.5889	−	147.185i	−0.0352825	−	0.154606i
$953$	864.220			0.906841			0.453421	−	0.891297i	$-0.350204\pi$
$953$	864.220			0.906841			0.453421	+	0.891297i	$0.350204\pi$
$954$		0			0
$955$	230.460	+	133.056i	0.241319	+	0.139326i
$956$	159.654	−	276.530i	0.167003	−	0.289257i
$957$		0			0
$958$			503.459i			0.525531i
$959$	1696.53	−	387.162i	1.76906	−	0.403714i
$960$		0			0
$961$	−305.277	−	528.756i	−0.317666	−	0.550214i
$962$	363.799	+	210.039i	0.378169	+	0.218336i
$963$		0			0
$964$	−35.2895	+	20.3744i	−0.0366074	+	0.0211353i
$965$		−	22.1484i		−	0.0229517i
$966$		0			0
$967$	−247.825			−0.256282			−0.128141	−	0.991756i	$-0.540901\pi$
$967$	−247.825			−0.256282			−0.128141	+	0.991756i	$0.540901\pi$
$968$	305.498	+	529.139i	0.315597	+	0.546631i
$969$		0			0
$970$	286.549	−	496.317i	0.295411	−	0.511667i
$971$	−119.734	+	69.1286i	−0.123310	+	0.0711932i	−0.560386	−	0.828231i	$-0.689347\pi$
$971$	−119.734	+	69.1286i	−0.123310	+	0.0711932i	0.437076	+	0.899424i	$0.356014\pi$
$972$		0			0
$973$	80.7414	−	74.9120i	0.0829819	−	0.0769908i
$974$	989.359			1.01577
$975$		0			0
$976$	−978.393	−	564.875i	−1.00245	−	0.578766i
$977$	89.6857	−	155.340i	0.0917971	−	0.158997i	−0.816470	−	0.577387i	$-0.804072\pi$
$977$	89.6857	−	155.340i	0.0917971	−	0.158997i	0.908267	+	0.418390i	$0.137406\pi$
$978$		0			0
$979$		−	1500.28i		−	1.53246i
$980$	−131.060	−	9.83034i	−0.133735	−	0.0100310i
$981$		0			0
$982$	−258.247	−	447.296i	−0.262980	−	0.455495i
$983$	670.259	+	386.974i	0.681850	+	0.393666i	0.800552	−	0.599264i	$-0.204540\pi$
$983$	670.259	+	386.974i	0.681850	+	0.393666i	−0.118702	+	0.992930i	$0.537873\pi$
$984$		0			0
$985$	−562.244	+	324.612i	−0.570806	+	0.329555i
$986$		−	114.696i		−	0.116324i
$987$		0			0
$988$	−205.400			−0.207894
$989$	50.3456	+	87.2011i	0.0509055	+	0.0881710i
$990$		0			0
$991$	314.025	−	543.907i	0.316877	−	0.548847i	−0.662958	−	0.748657i	$-0.730699\pi$
$991$	314.025	−	543.907i	0.316877	−	0.548847i	0.979835	+	0.199810i	$0.0640324\pi$
$992$	299.385	−	172.850i	0.301799	−	0.174244i
$993$		0			0
$994$	−343.568	+	1113.69i	−0.345642	+	1.12041i
$995$	−759.111			−0.762926
$996$		0			0
$997$	1245.49	+	719.086i	1.24924	+	0.721250i	0.970958	−	0.239250i	$-0.0769015\pi$
$997$	1245.49	+	719.086i	1.24924	+	0.721250i	0.278283	+	0.960499i	$0.410235\pi$
$998$	748.613	−	1296.64i	0.750113	−	1.29923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.w.a.136.2		8
3.2	odd	2		105.3.n.a.31.3	✓	8
7.5	odd	6	inner	315.3.w.a.271.2		8
15.2	even	4		525.3.s.h.199.3		16
15.8	even	4		525.3.s.h.199.6		16
15.14	odd	2		525.3.o.l.451.2		8
21.5	even	6		105.3.n.a.61.3	yes	8
21.11	odd	6		735.3.h.a.391.4		8
21.17	even	6		735.3.h.a.391.3		8
105.47	odd	12		525.3.s.h.124.6		16
105.68	odd	12		525.3.s.h.124.3		16
105.89	even	6		525.3.o.l.376.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.3	✓	8	3.2	odd	2
105.3.n.a.61.3	yes	8	21.5	even	6
315.3.w.a.136.2		8	1.1	even	1	trivial
315.3.w.a.271.2		8	7.5	odd	6	inner
525.3.o.l.376.2		8	105.89	even	6
525.3.o.l.451.2		8	15.14	odd	2
525.3.s.h.124.3		16	105.68	odd	12
525.3.s.h.124.6		16	105.47	odd	12
525.3.s.h.199.3		16	15.2	even	4
525.3.s.h.199.6		16	15.8	even	4
735.3.h.a.391.3		8	21.17	even	6
735.3.h.a.391.4		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.836732 - 1.44926i) q^{2} +(0.599760 - 1.03881i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.76104 + 5.13152i) q^{7} -8.70121 q^{8} +O(q^{10})\)	\(q+(-0.836732 - 1.44926i) q^{2} +(0.599760 - 1.03881i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(4.76104 + 5.13152i) q^{7} -8.70121 q^{8} +(3.24065 + 1.87099i) q^{10} +(-6.91411 + 11.9756i) q^{11} +6.12052i q^{13} +(3.45321 - 11.1937i) q^{14} +(4.88154 + 8.45507i) q^{16} +(2.14655 + 1.23931i) q^{17} +(-24.2290 + 13.9886i) q^{19} +2.68221i q^{20} +23.1410 q^{22} +(6.62020 + 11.4665i) q^{23} +(2.50000 - 4.33013i) q^{25} +(8.87024 - 5.12123i) q^{26} +(8.18618 - 1.86816i) q^{28} +27.6516 q^{29} +(-16.2122 - 9.36010i) q^{31} +(-9.23334 + 15.9926i) q^{32} -4.14789i q^{34} +(-14.9569 - 4.61414i) q^{35} +(20.5067 + 35.5187i) q^{37} +(40.5463 + 23.4094i) q^{38} +(16.8498 - 9.72824i) q^{40} +22.5351i q^{41} +7.60485 q^{43} +(8.29361 + 14.3650i) q^{44} +(11.0787 - 19.1888i) q^{46} +(11.9214 - 6.88283i) q^{47} +(-3.66502 + 48.8627i) q^{49} -8.36732 q^{50} +(6.35808 + 3.67084i) q^{52} +(46.2995 - 80.1930i) q^{53} -30.9208i q^{55} +(-41.4268 - 44.6504i) q^{56} +(-23.1370 - 40.0744i) q^{58} +(61.5680 + 35.5463i) q^{59} +(-100.214 + 57.8584i) q^{61} +31.3276i q^{62} +69.9556 q^{64} +(-6.84295 - 11.8523i) q^{65} +(5.70227 - 9.87662i) q^{67} +(2.57483 - 1.48658i) q^{68} +(5.82783 + 25.5373i) q^{70} -99.4924 q^{71} +(90.1276 + 52.0352i) q^{73} +(34.3172 - 59.4392i) q^{74} +33.5592i q^{76} +(-94.3714 + 21.5364i) q^{77} +(-64.4982 - 111.714i) q^{79} +(-18.9061 - 10.9154i) q^{80} +(32.6592 - 18.8558i) q^{82} +30.3382i q^{83} -5.54238 q^{85} +(-6.36322 - 11.0214i) q^{86} +(60.1611 - 104.202i) q^{88} +(-93.9587 + 54.2471i) q^{89} +(-31.4076 + 29.1400i) q^{91} +15.8821 q^{92} +(-19.9501 - 11.5182i) q^{94} +(31.2794 - 54.1776i) q^{95} -153.154i q^{97} +(73.8816 - 35.5734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8	\( 8 q - 2 q^{2} - 6 q^{4} - 16 q^{7} + 32 q^{8} - 20 q^{11} + 16 q^{14} - 2 q^{16} + 18 q^{17} - 16 q^{22} - 62 q^{23} + 20 q^{25} - 120 q^{26} - 120 q^{28} + 100 q^{29} - 126 q^{31} - 36 q^{32} - 80 q^{37} - 114 q^{38} + 90 q^{40} + 352 q^{43} + 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} - 20 q^{50} - 48 q^{52} + 76 q^{53} - 196 q^{56} - 40 q^{58} + 54 q^{59} - 396 q^{61} - 4 q^{64} + 60 q^{65} + 184 q^{67} + 312 q^{68} - 164 q^{71} + 348 q^{73} + 140 q^{74} - 152 q^{77} - 206 q^{79} + 204 q^{82} - 60 q^{85} - 178 q^{86} + 124 q^{88} - 282 q^{89} - 114 q^{91} + 288 q^{92} + 30 q^{94} + 120 q^{95} + 592 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 6 * q^4 - 16 * q^7 + 32 * q^8 - 20 * q^11 + 16 * q^14 - 2 * q^16 + 18 * q^17 - 16 * q^22 - 62 * q^23 + 20 * q^25 - 120 * q^26 - 120 * q^28 + 100 * q^29 - 126 * q^31 - 36 * q^32 - 80 * q^37 - 114 * q^38 + 90 * q^40 + 352 * q^43 + 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 - 20 * q^50 - 48 * q^52 + 76 * q^53 - 196 * q^56 - 40 * q^58 + 54 * q^59 - 396 * q^61 - 4 * q^64 + 60 * q^65 + 184 * q^67 + 312 * q^68 - 164 * q^71 + 348 * q^73 + 140 * q^74 - 152 * q^77 - 206 * q^79 + 204 * q^82 - 60 * q^85 - 178 * q^86 + 124 * q^88 - 282 * q^89 - 114 * q^91 + 288 * q^92 + 30 * q^94 + 120 * q^95 + 592 * q^98

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