LMFDB - Embedded newform 845.2.m.h.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.5
Root			$0.583700 - 2.17840i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.h.316.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80664 - 1.04307i) q^{2} +(1.54307 + 2.67267i) q^{3} +(1.17597 - 2.03684i) q^{4} +1.00000i q^{5} +(5.57553 + 3.21903i) q^{6} +(-1.17081 - 0.675970i) q^{7} -0.734191i q^{8} +(-3.26210 + 5.65012i) q^{9} +(1.04307 + 1.80664i) q^{10} +(3.23390 - 1.86710i) q^{11} +7.25839 q^{12} -2.82032 q^{14} +(-2.67267 + 1.54307i) q^{15} +(1.58613 + 2.74726i) q^{16} +(-1.35194 + 2.34163i) q^{17} +13.6103i q^{18} +(-0.379379 - 0.219035i) q^{19} +(2.03684 + 1.17597i) q^{20} -4.17226i q^{21} +(3.89500 - 6.74635i) q^{22} +(-2.54307 - 4.40472i) q^{23} +(1.96225 - 1.13290i) q^{24} -1.00000 q^{25} -10.8761 q^{27} +(-2.75368 + 1.58984i) q^{28} +(0.675970 + 1.17081i) q^{29} +(-3.21903 + 5.57553i) q^{30} -6.43807i q^{31} +(7.00279 + 4.04307i) q^{32} +(9.98025 + 5.76210i) q^{33} +5.64064i q^{34} +(0.675970 - 1.17081i) q^{35} +(7.67226 + 13.2887i) q^{36} +(6.36697 - 3.67597i) q^{37} -0.913870 q^{38} +0.734191 q^{40} +(5.95491 - 3.43807i) q^{41} +(-4.35194 - 7.53778i) q^{42} +(-0.104996 + 0.181858i) q^{43} -8.78259i q^{44} +(-5.65012 - 3.26210i) q^{45} +(-9.18882 - 5.30516i) q^{46} -1.35194i q^{47} +(-4.89500 + 8.47840i) q^{48} +(-2.58613 - 4.47931i) q^{49} +(-1.80664 + 1.04307i) q^{50} -8.34452 q^{51} -1.46838 q^{53} +(-19.6493 + 11.3445i) q^{54} +(1.86710 + 3.23390i) q^{55} +(-0.496291 + 0.859601i) q^{56} -1.35194i q^{57} +(2.44247 + 1.41016i) q^{58} +(1.96225 + 1.13290i) q^{59} +7.25839i q^{60} +(-1.76210 + 3.05205i) q^{61} +(-6.71533 - 11.6313i) q^{62} +(7.63862 - 4.41016i) q^{63} +10.5242 q^{64} +24.0410 q^{66} +(-9.98025 + 5.76210i) q^{67} +(3.17968 + 5.50737i) q^{68} +(7.84823 - 13.5935i) q^{69} -2.82032i q^{70} +(-0.379379 - 0.219035i) q^{71} +(4.14827 + 2.39500i) q^{72} -3.69646i q^{73} +(7.66855 - 13.2823i) q^{74} +(-1.54307 - 2.67267i) q^{75} +(-0.892277 + 0.515156i) q^{76} -5.04840 q^{77} +15.0484 q^{79} +(-2.74726 + 1.58613i) q^{80} +(-6.99629 - 12.1179i) q^{81} +(7.17226 - 12.4227i) q^{82} -0.475800i q^{83} +(-8.49822 - 4.90645i) q^{84} +(-2.34163 - 1.35194i) q^{85} +0.438069i q^{86} +(-2.08613 + 3.61328i) q^{87} +(-1.37080 - 2.37430i) q^{88} +(-9.56819 + 5.52420i) q^{89} -13.6103 q^{90} -11.9623 q^{92} +(17.2068 - 9.93436i) q^{93} +(-1.41016 - 2.44247i) q^{94} +(0.219035 - 0.379379i) q^{95} +24.9549i q^{96} +(-2.85453 - 1.64806i) q^{97} +(-9.34442 - 5.39500i) q^{98} +24.3626i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 10 q^{4} - 6 q^{9} - 2 q^{10} + 16 q^{14} - 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} - 12 q^{25} - 56 q^{27} + 4 q^{29} - 20 q^{30} + 4 q^{35} + 34 q^{36} - 40 q^{38} - 12 q^{40} - 44 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) $ 12 * q + 4 * q^3 + 10 * q^4 - 6 * q^9 - 2 * q^10 + 16 * q^14 - 10 * q^16 - 8 * q^17 + 24 * q^22 - 16 * q^23 - 12 * q^25 - 56 * q^27 + 4 * q^29 - 20 * q^30 + 4 * q^35 + 34 * q^36 - 40 * q^38 - 12 * q^40 - 44 * q^42 - 24 * q^43 - 36 * q^48 - 2 * q^49 + 16 * q^51 + 24 * q^53 + 12 * q^55 + 48 * q^56 + 12 * q^61 - 8 * q^62 + 60 * q^64 + 48 * q^66 + 88 * q^68 + 32 * q^69 - 20 * q^74 - 4 * q^75 + 72 * q^77 + 48 * q^79 - 30 * q^81 + 28 * q^82 + 4 * q^87 - 60 * q^88 - 68 * q^90 - 40 * q^92 + 8 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.80664	−	1.04307i	1.27749	−	0.737558i	0.301103	−	0.953592i	$-0.402645\pi$
$2$	1.80664	−	1.04307i	1.27749	−	0.737558i	0.976386	+	0.216033i	$0.0693120\pi$
$3$	1.54307	+	2.67267i	0.890889	+	1.54307i	0.838811	+	0.544422i	$0.183251\pi$
$3$	1.54307	+	2.67267i	0.890889	+	1.54307i	0.0520776	+	0.998643i	$0.483416\pi$
$4$	1.17597	−	2.03684i	0.587985	−	1.01842i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	5.57553	+	3.21903i	2.27620	+	1.31417i
$7$	−1.17081	−	0.675970i	−0.442526	−	0.255492i	0.262143	−	0.965029i	$-0.415571\pi$
$7$	−1.17081	−	0.675970i	−0.442526	−	0.255492i	−0.704669	+	0.709537i	$0.748904\pi$
$8$		−	0.734191i		−	0.259576i
$9$	−3.26210	+	5.65012i	−1.08737	+	1.88337i
$10$	1.04307	+	1.80664i	0.329846	+	0.571310i
$11$	3.23390	−	1.86710i	0.975059	−	0.562950i	0.0742841	−	0.997237i	$-0.476333\pi$
$11$	3.23390	−	1.86710i	0.975059	−	0.562950i	0.900775	+	0.434287i	$0.143000\pi$
$12$	7.25839			2.09532
$13$		0			0
$13$		0			0
$14$	−2.82032			−0.753763
$15$	−2.67267	+	1.54307i	−0.690080	+	0.398418i
$16$	1.58613	+	2.74726i	0.396533	+	0.686815i
$17$	−1.35194	+	2.34163i	−0.327893	+	0.567928i	−0.982094	−	0.188393i	$-0.939672\pi$
$17$	−1.35194	+	2.34163i	−0.327893	+	0.567928i	0.654200	+	0.756321i	$0.273005\pi$
$18$			13.6103i			3.20799i
$19$	−0.379379	−	0.219035i	−0.0870356	−	0.0502500i	0.455851	−	0.890056i	$-0.349335\pi$
$19$	−0.379379	−	0.219035i	−0.0870356	−	0.0502500i	−0.542886	+	0.839806i	$0.682668\pi$
$20$	2.03684	+	1.17597i	0.455451	+	0.262955i
$21$		−	4.17226i		−	0.910462i
$22$	3.89500	−	6.74635i	0.830418	−	1.43833i
$23$	−2.54307	−	4.40472i	−0.530266	−	0.918447i	−0.999376	−	0.0353078i	$-0.988759\pi$
$23$	−2.54307	−	4.40472i	−0.530266	−	0.918447i	0.469111	−	0.883139i	$-0.344575\pi$
$24$	1.96225	−	1.13290i	0.400542	−	0.231253i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−10.8761			−2.09311
$28$	−2.75368	+	1.58984i	−0.520397	+	0.300451i
$29$	0.675970	+	1.17081i	0.125524	+	0.217415i	0.921938	−	0.387338i	$-0.126605\pi$
$29$	0.675970	+	1.17081i	0.125524	+	0.217415i	−0.796413	+	0.604753i	$0.793272\pi$
$30$	−3.21903	+	5.57553i	−0.587713	+	1.01795i
$31$		−	6.43807i		−	1.15631i	−0.815926	−	0.578156i	$-0.803773\pi$
$31$		−	6.43807i		−	1.15631i	0.815926	−	0.578156i	$-0.196227\pi$
$32$	7.00279	+	4.04307i	1.23793	+	0.714720i
$33$	9.98025	+	5.76210i	1.73734	+	1.00305i
$34$			5.64064i			0.967362i
$35$	0.675970	−	1.17081i	0.114260	−	0.197904i
$36$	7.67226	+	13.2887i	1.27871	+	2.21479i
$37$	6.36697	−	3.67597i	1.04672	−	0.604326i	0.124993	−	0.992158i	$-0.460109\pi$
$37$	6.36697	−	3.67597i	1.04672	−	0.604326i	0.921730	+	0.387832i	$0.126776\pi$
$38$	−0.913870			−0.148249
$39$		0			0
$40$	0.734191			0.116086
$41$	5.95491	−	3.43807i	0.930001	−	0.536936i	0.0431890	−	0.999067i	$-0.486248\pi$
$41$	5.95491	−	3.43807i	0.930001	−	0.536936i	0.886812	+	0.462131i	$0.152915\pi$
$42$	−4.35194	−	7.53778i	−0.671519	−	1.16310i
$43$	−0.104996	+	0.181858i	−0.0160117	+	0.0277331i	−0.873920	−	0.486069i	$-0.838430\pi$
$43$	−0.104996	+	0.181858i	−0.0160117	+	0.0277331i	0.857909	+	0.513802i	$0.171764\pi$
$44$		−	8.78259i		−	1.32403i
$45$	−5.65012	−	3.26210i	−0.842271	−	0.486285i
$46$	−9.18882	−	5.30516i	−1.35482	−	0.782204i
$47$		−	1.35194i		−	0.197201i	−0.995127	−	0.0986003i	$-0.968563\pi$
$47$		−	1.35194i		−	0.197201i	0.995127	−	0.0986003i	$-0.0314365\pi$
$48$	−4.89500	+	8.47840i	−0.706533	+	1.22375i
$49$	−2.58613	−	4.47931i	−0.369447	−	0.639901i
$50$	−1.80664	+	1.04307i	−0.255498	+	0.147512i
$51$	−8.34452			−1.16847
$52$		0			0
$53$	−1.46838			−0.201698			−0.100849	−	0.994902i	$-0.532156\pi$
$53$	−1.46838			−0.201698			−0.100849	+	0.994902i	$0.532156\pi$
$54$	−19.6493	+	11.3445i	−2.67393	+	1.54379i
$55$	1.86710	+	3.23390i	0.251759	+	0.436060i
$56$	−0.496291	+	0.859601i	−0.0663196	+	0.114869i
$57$		−	1.35194i		−	0.179069i
$58$	2.44247	+	1.41016i	0.320712	+	0.185163i
$59$	1.96225	+	1.13290i	0.255463	+	0.147492i	0.622263	−	0.782808i	$-0.286213\pi$
$59$	1.96225	+	1.13290i	0.255463	+	0.147492i	−0.366800	+	0.930300i	$0.619547\pi$
$60$			7.25839i			0.937054i
$61$	−1.76210	+	3.05205i	−0.225614	+	0.390774i	−0.956503	−	0.291721i	$-0.905772\pi$
$61$	−1.76210	+	3.05205i	−0.225614	+	0.390774i	0.730890	+	0.682496i	$0.239105\pi$
$62$	−6.71533	−	11.6313i	−0.852847	−	1.47717i
$63$	7.63862	−	4.41016i	0.962376	−	0.555628i
$64$	10.5242			1.31552
$65$		0			0
$66$	24.0410			2.95924
$67$	−9.98025	+	5.76210i	−1.21928	+	0.703953i	−0.964764	−	0.263116i	$-0.915250\pi$
$67$	−9.98025	+	5.76210i	−1.21928	+	0.703953i	−0.254517	+	0.967068i	$0.581917\pi$
$68$	3.17968	+	5.50737i	0.385593	+	0.667866i
$69$	7.84823	−	13.5935i	0.944816	−	1.63647i
$70$		−	2.82032i		−	0.337093i
$71$	−0.379379	−	0.219035i	−0.0450240	−	0.0259946i	0.477319	−	0.878730i	$-0.341609\pi$
$71$	−0.379379	−	0.219035i	−0.0450240	−	0.0259946i	−0.522343	+	0.852735i	$0.674942\pi$
$72$	4.14827	+	2.39500i	0.488878	+	0.282254i
$73$		−	3.69646i		−	0.432638i	−0.976323	−	0.216319i	$-0.930595\pi$
$73$		−	3.69646i		−	0.432638i	0.976323	−	0.216319i	$-0.0694051\pi$
$74$	7.66855	−	13.2823i	0.891451	−	1.54404i
$75$	−1.54307	−	2.67267i	−0.178178	−	0.308613i
$76$	−0.892277	+	0.515156i	−0.102351	+	0.0590925i
$77$	−5.04840			−0.575318
$78$		0			0
$79$	15.0484			1.69308			0.846539	−	0.532327i	$-0.178682\pi$
$79$	15.0484			1.69308			0.846539	+	0.532327i	$0.178682\pi$
$80$	−2.74726	+	1.58613i	−0.307153	+	0.177335i
$81$	−6.99629	−	12.1179i	−0.777366	−	1.34644i
$82$	7.17226	−	12.4227i	0.792044	−	1.37186i
$83$		−	0.475800i		−	0.0522259i	−0.999659	−	0.0261129i	$-0.991687\pi$
$83$		−	0.475800i		−	0.0522259i	0.999659	−	0.0261129i	$-0.00831295\pi$
$84$	−8.49822	−	4.90645i	−0.927232	−	0.535338i
$85$	−2.34163	−	1.35194i	−0.253985	−	0.146638i
$86$			0.438069i			0.0472382i
$87$	−2.08613	+	3.61328i	−0.223657	+	0.387385i
$88$	−1.37080	−	2.37430i	−0.146128	−	0.253102i
$89$	−9.56819	+	5.52420i	−1.01423	+	0.585564i	−0.912426	−	0.409241i	$-0.865794\pi$
$89$	−9.56819	+	5.52420i	−1.01423	+	0.585564i	−0.101800	+	0.994805i	$0.532460\pi$
$90$	−13.6103			−1.43465
$91$		0			0
$92$	−11.9623			−1.24715
$93$	17.2068	−	9.93436i	1.78426	−	1.03015i
$94$	−1.41016	−	2.44247i	−0.145447	−	0.251922i
$95$	0.219035	−	0.379379i	0.0224725	−	0.0389235i
$96$			24.9549i			2.54694i
$97$	−2.85453	−	1.64806i	−0.289833	−	0.167335i	0.348033	−	0.937482i	$-0.386850\pi$
$97$	−2.85453	−	1.64806i	−0.289833	−	0.167335i	−0.637867	+	0.770147i	$0.720183\pi$
$98$	−9.34442	−	5.39500i	−0.943929	−	0.544978i
$99$			24.3626i			2.44853i
$100$	−1.17597	+	2.03684i	−0.117597	+	0.203684i
$101$	8.08613	+	14.0056i	0.804600	+	1.39361i	0.916561	+	0.399895i	$0.130954\pi$
$101$	8.08613	+	14.0056i	0.804600	+	1.39361i	−0.111961	+	0.993713i	$0.535713\pi$
$102$	−15.0756	+	8.70388i	−1.49270	+	0.861812i
$103$	−10.5545			−1.03997			−0.519983	−	0.854176i	$-0.674062\pi$
$103$	−10.5545			−1.03997			−0.519983	+	0.854176i	$0.674062\pi$
$104$		0			0
$105$	4.17226			0.407171
$106$	−2.65284	+	1.53162i	−0.257667	+	0.148764i
$107$	−6.71533	−	11.6313i	−0.649195	−	1.12444i	−0.983315	−	0.181908i	$-0.941773\pi$
$107$	−6.71533	−	11.6313i	−0.649195	−	1.12444i	0.334120	−	0.942530i	$-0.391561\pi$
$108$	−12.7900	+	22.1529i	−1.23072	+	2.13167i
$109$		−	11.6406i		−	1.11497i	−0.830187	−	0.557486i	$-0.811766\pi$
$109$		−	11.6406i		−	1.11497i	0.830187	−	0.557486i	$-0.188234\pi$
$110$	6.74635	+	3.89500i	0.643239	+	0.371374i
$111$	19.6493	+	11.3445i	1.86503	+	1.07677i
$112$		−	4.28870i		−	0.405244i
$113$	6.87614	−	11.9098i	0.646853	−	1.12038i	−0.337018	−	0.941498i	$-0.609418\pi$
$113$	6.87614	−	11.9098i	0.646853	−	1.12038i	0.983870	−	0.178883i	$-0.0572485\pi$
$114$	−1.41016	−	2.44247i	−0.132074	−	0.228758i
$115$	4.40472	−	2.54307i	0.410742	−	0.237142i
$116$	3.17968			0.295226
$117$		0			0
$118$	4.72677			0.435135
$119$	3.16574	−	1.82774i	0.290203	−	0.167549i
$120$	1.13290	+	1.96225i	0.103420	+	0.179128i
$121$	1.47209	−	2.54974i	0.133826	−	0.231794i
$122$			7.35194i			0.665613i
$123$	18.3776	+	10.6103i	1.65706	+	0.956701i
$124$	−13.1133	−	7.57097i	−1.17761	−	0.679894i
$125$		−	1.00000i		−	0.0894427i
$126$	9.20017	−	15.9352i	0.819616	−	1.41962i
$127$	−1.98113	−	3.43143i	−0.175797	−	0.304490i	0.764640	−	0.644458i	$-0.222917\pi$
$127$	−1.98113	−	3.43143i	−0.175797	−	0.304490i	−0.940437	+	0.339968i	$0.889584\pi$
$128$	5.00787	−	2.89130i	0.442637	−	0.255557i
$129$	−0.648061			−0.0570586
$130$		0			0
$131$	−11.0484			−0.965303			−0.482652	−	0.875812i	$-0.660326\pi$
$131$	−11.0484			−0.965303			−0.482652	+	0.875812i	$0.660326\pi$
$132$	23.4729	−	13.5521i	2.04306	−	1.17956i
$133$	0.296122	+	0.512898i	0.0256770	+	0.0444739i
$134$	−12.0205	+	20.8201i	−1.03841	+	1.79858i
$135$		−	10.8761i		−	0.936069i
$136$	1.71920	+	0.992582i	0.147420	+	0.0851132i
$137$	−10.8399	−	6.25839i	−0.926111	−	0.534690i	−0.0405314	−	0.999178i	$-0.512905\pi$
$137$	−10.8399	−	6.25839i	−0.926111	−	0.534690i	−0.885579	+	0.464488i	$0.846238\pi$
$138$		−	32.7449i		−	2.78743i
$139$	−0.820321	+	1.42084i	−0.0695787	+	0.120514i	−0.898716	−	0.438531i	$-0.855499\pi$
$139$	−0.820321	+	1.42084i	−0.0695787	+	0.120514i	0.829137	+	0.559045i	$0.188832\pi$
$140$	−1.58984	−	2.75368i	−0.134366	−	0.232729i
$141$	3.61328	−	2.08613i	0.304293	−	0.175684i
$142$	−0.913870			−0.0766903
$143$		0			0
$144$	−20.6965			−1.72470
$145$	−1.17081	+	0.675970i	−0.0972308	+	0.0561362i
$146$	−3.85565	−	6.67818i	−0.319096	−	0.552690i
$147$	7.98113	−	13.8237i	0.658273	−	1.14016i
$148$		−	17.2913i		−	1.42134i
$149$	−2.85453	−	1.64806i	−0.233852	−	0.135014i	0.378496	−	0.925603i	$-0.376441\pi$
$149$	−2.85453	−	1.64806i	−0.233852	−	0.135014i	−0.612348	+	0.790589i	$0.709775\pi$
$150$	−5.57553	−	3.21903i	−0.455240	−	0.262833i
$151$		−	9.65873i		−	0.786016i	−0.919535	−	0.393008i	$-0.871434\pi$
$151$		−	9.65873i		−	0.786016i	0.919535	−	0.393008i	$-0.128566\pi$
$152$	−0.160813	+	0.278537i	−0.0130437	+	0.0225923i
$153$	−8.82032	−	15.2772i	−0.713081	−	1.23509i
$154$	−9.12065	+	5.26581i	−0.734963	+	0.424331i
$155$	6.43807			0.517118
$156$		0			0
$157$	11.5800			0.924186			0.462093	−	0.886831i	$-0.347099\pi$
$157$	11.5800			0.924186			0.462093	+	0.886831i	$0.347099\pi$
$158$	27.1871	−	15.6965i	2.16289	−	1.24874i
$159$	−2.26581	−	3.92450i	−0.179690	−	0.311233i
$160$	−4.04307	+	7.00279i	−0.319632	+	0.553619i
$161$			6.87614i			0.541916i
$162$	−25.2796	−	14.5952i	−1.98615	−	1.14671i
$163$	−16.4481	−	9.49629i	−1.28831	−	0.743807i	−0.309958	−	0.950750i	$-0.600315\pi$
$163$	−16.4481	−	9.49629i	−1.28831	−	0.743807i	−0.978353	+	0.206943i	$0.933648\pi$
$164$		−	16.1723i		−	1.26284i
$165$	−5.76210	+	9.98025i	−0.448579	+	0.776961i
$166$	−0.496291	−	0.859601i	−0.0385196	−	0.0667180i
$167$	14.6635	−	8.46598i	1.13470	−	0.655117i	0.189584	−	0.981864i	$-0.439286\pi$
$167$	14.6635	−	8.46598i	1.13470	−	0.655117i	0.945112	+	0.326747i	$0.105953\pi$
$168$	−3.06324			−0.236334
$169$		0			0
$170$	−5.64064			−0.432618
$171$	2.47515	−	1.42903i	0.189279	−	0.109280i
$172$	0.246944	+	0.427719i	0.0188293	+	0.0326132i
$173$	−5.38225	+	9.32233i	−0.409205	+	0.708764i	−0.994801	−	0.101839i	$-0.967527\pi$
$173$	−5.38225	+	9.32233i	−0.409205	+	0.708764i	0.585596	+	0.810603i	$0.300861\pi$
$174$			8.70388i			0.659839i
$175$	1.17081	+	0.675970i	0.0885052	+	0.0510985i
$176$	10.2588	+	5.92291i	0.773285	+	0.446456i
$177$			6.99258i			0.525595i
$178$	−11.5242	+	19.9605i	−0.863775	+	1.49610i
$179$	9.25839	+	16.0360i	0.692005	+	1.19859i	0.971180	+	0.238347i	$0.0766056\pi$
$179$	9.25839	+	16.0360i	0.692005	+	1.19859i	−0.279175	+	0.960240i	$0.590061\pi$
$180$	−13.2887	+	7.67226i	−0.990485	+	0.571857i
$181$	12.2887			0.913412			0.456706	−	0.889618i	$-0.349029\pi$
$181$	12.2887			0.913412			0.456706	+	0.889618i	$0.349029\pi$
$182$		0			0
$183$	−10.8761			−0.803987
$184$	−3.23390	+	1.86710i	−0.238407	+	0.137644i
$185$	3.67597	+	6.36697i	0.270263	+	0.468109i
$186$	20.7244	−	35.8957i	1.51958	−	2.63200i
$187$			10.0968i			0.738351i
$188$	−2.75368	−	1.58984i	−0.200833	−	0.115951i
$189$	12.7339	+	7.35194i	0.926257	+	0.534775i
$190$		−	0.913870i		−	0.0662991i
$191$	−2.70388	+	4.68325i	−0.195646	+	0.338868i	−0.947112	−	0.320903i	$-0.896014\pi$
$191$	−2.70388	+	4.68325i	−0.195646	+	0.338868i	0.751466	+	0.659772i	$0.229347\pi$
$192$	16.2395	+	28.1277i	1.17199	+	2.02994i
$193$	−16.5489	+	9.55451i	−1.19122	+	0.687749i	−0.958582	−	0.284816i	$-0.908068\pi$
$193$	−16.5489	+	9.55451i	−1.19122	+	0.687749i	−0.232634	+	0.972564i	$0.574734\pi$
$194$	−6.87614			−0.493678
$195$		0			0
$196$	−12.1648			−0.868917
$197$	−10.6382	+	6.14195i	−0.757938	+	0.437596i	−0.828555	−	0.559908i	$-0.810837\pi$
$197$	−10.6382	+	6.14195i	−0.757938	+	0.437596i	0.0706170	+	0.997504i	$0.477503\pi$
$198$	25.4118	+	44.0145i	1.80594	+	3.12797i
$199$	0.382252	−	0.662080i	0.0270971	−	0.0469336i	−0.852159	−	0.523283i	$-0.824707\pi$
$199$	0.382252	−	0.662080i	0.0270971	−	0.0469336i	0.879256	+	0.476350i	$0.158040\pi$
$200$			0.734191i			0.0519151i
$201$	−30.8003	−	17.7826i	−2.17249	−	1.25429i
$202$	29.2175	+	16.8687i	2.05573	+	1.18688i
$203$		−	1.82774i		−	0.128282i
$204$	−9.81290	+	16.9964i	−0.687041	+	1.18999i
$205$	3.43807	+	5.95491i	0.240125	+	0.415909i
$206$	−19.0682	+	11.0090i	−1.32855	+	0.767036i
$207$	33.1829			2.30637
$208$		0			0
$209$	−1.63583			−0.113153
$210$	7.53778	−	4.35194i	0.520156	−	0.300312i
$211$	3.96227	+	6.86285i	0.272774	+	0.472458i	0.969571	−	0.244810i	$-0.0787256\pi$
$211$	3.96227	+	6.86285i	0.272774	+	0.472458i	−0.696797	+	0.717268i	$0.745392\pi$
$212$	−1.72677	+	2.99086i	−0.118595	+	0.205413i
$213$		−	1.35194i		−	0.0926333i
$214$	−24.2644	−	14.0090i	−1.65868	−	0.957638i
$215$	−0.181858	−	0.104996i	−0.0124026	−	0.00716065i
$216$			7.98516i			0.543322i
$217$	−4.35194	+	7.53778i	−0.295429	+	0.511698i
$218$	−12.1419	−	21.0305i	−0.822356	−	1.42436i
$219$	9.87941	−	5.70388i	0.667588	−	0.385432i
$220$	8.78259			0.592122
$221$		0			0
$222$	47.3323			3.17674
$223$	−3.71413	+	2.14435i	−0.248716	+	0.143596i	−0.619176	−	0.785252i	$-0.712533\pi$
$223$	−3.71413	+	2.14435i	−0.248716	+	0.143596i	0.370460	+	0.928848i	$0.379200\pi$
$224$	−5.46598	−	9.46735i	−0.365211	−	0.632564i
$225$	3.26210	−	5.65012i	0.217473	−	0.376675i
$226$		−	28.6890i		−	1.90837i
$227$	22.0918	+	12.7547i	1.46628	+	0.846558i	0.999289	−	0.0377034i	$-0.0120042\pi$
$227$	22.0918	+	12.7547i	1.46628	+	0.846558i	0.466992	+	0.884261i	$0.345338\pi$
$228$	−2.75368	−	1.58984i	−0.182367	−	0.105290i
$229$			25.1090i			1.65925i	0.558320	+	0.829626i	$0.311446\pi$
$229$			25.1090i			1.65925i	−0.558320	+	0.829626i	$0.688554\pi$
$230$	5.30516	−	9.18882i	0.349812	−	0.605893i
$231$	−7.79001	−	13.4927i	−0.512545	−	0.887754i
$232$	0.859601	−	0.496291i	0.0564356	−	0.0325831i
$233$	−15.2961			−1.00208			−0.501041	−	0.865423i	$-0.667049\pi$
$233$	−15.2961			−1.00208			−0.501041	+	0.865423i	$0.667049\pi$
$234$		0			0
$235$	1.35194			0.0881908
$236$	4.61509	−	2.66452i	0.300417	−	0.173446i
$237$	23.2207	+	40.2194i	1.50834	+	2.61253i
$238$	3.81290	−	6.60414i	0.247154	−	0.428083i
$239$		−	13.6736i		−	0.884469i	−0.896899	−	0.442235i	$-0.854186\pi$
$239$		−	13.6736i		−	0.884469i	0.896899	−	0.442235i	$-0.145814\pi$
$240$	−8.47840	−	4.89500i	−0.547278	−	0.315971i
$241$	−10.8399	−	6.25839i	−0.698256	−	0.403138i	0.108441	−	0.994103i	$-0.465414\pi$
$241$	−10.8399	−	6.25839i	−0.698256	−	0.403138i	−0.806698	+	0.590964i	$0.798747\pi$
$242$		−	6.14195i		−	0.394819i
$243$	5.27726	−	9.14048i	0.338536	−	0.586362i
$244$	4.14435	+	7.17823i	0.265315	+	0.459539i
$245$	4.47931	−	2.58613i	0.286173	−	0.165222i
$246$	44.2691			2.82249
$247$		0			0
$248$	−4.72677			−0.300150
$249$	1.27166	−	0.734191i	0.0805879	−	0.0465275i
$250$	−1.04307	−	1.80664i	−0.0659692	−	0.114262i
$251$	−7.31421	+	12.6686i	−0.461669	+	0.799634i	−0.999044	−	0.0437094i	$-0.986082\pi$
$251$	−7.31421	+	12.6686i	−0.461669	+	0.799634i	0.537376	+	0.843343i	$0.319416\pi$
$252$		−	20.7449i		−	1.30680i
$253$	−16.4481	−	9.49629i	−1.03408	−	0.597027i
$254$	−7.15840	−	4.13290i	−0.449158	−	0.259321i
$255$		−	8.34452i		−	0.522554i
$256$	−4.49258	+	7.78138i	−0.280786	+	0.486336i
$257$	14.0484	+	24.3325i	0.876315	+	1.51782i	0.855355	+	0.518042i	$0.173339\pi$
$257$	14.0484	+	24.3325i	0.876315	+	1.51782i	0.0209598	+	0.999780i	$0.493328\pi$
$258$	−1.17081	+	0.675970i	−0.0728917	+	0.0420840i
$259$	−9.93937			−0.617603
$260$		0			0
$261$	−8.82032			−0.545964
$262$	−19.9605	+	11.5242i	−1.23316	+	0.711967i
$263$	−7.88759	−	13.6617i	−0.486369	−	0.842416i	0.513508	−	0.858085i	$-0.328346\pi$
$263$	−7.88759	−	13.6617i	−0.486369	−	0.842416i	−0.999877	+	0.0156684i	$0.995012\pi$
$264$	4.23048	−	7.32741i	0.260368	−	0.450971i
$265$		−	1.46838i		−	0.0902020i
$266$	1.06997	+	0.617748i	0.0656041	+	0.0378766i
$267$	−29.5287	−	17.0484i	−1.80713	−	1.04335i
$268$			27.1042i			1.65565i
$269$	2.08613	−	3.61328i	0.127194	−	0.220306i	−0.795395	−	0.606092i	$-0.792736\pi$
$269$	2.08613	−	3.61328i	0.127194	−	0.220306i	0.922588	+	0.385786i	$0.126070\pi$
$270$	−11.3445	−	19.6493i	−0.690406	−	1.19582i
$271$	5.26432	−	3.03936i	0.319785	−	0.184628i	−0.331512	−	0.943451i	$-0.607559\pi$
$271$	5.26432	−	3.03936i	0.319785	−	0.184628i	0.651297	+	0.758823i	$0.274225\pi$
$272$	−8.57741			−0.520082
$273$		0			0
$274$	−26.1116			−1.57746
$275$	−3.23390	+	1.86710i	−0.195012	+	0.112590i
$276$	−18.4586	−	31.9712i	−1.11107	−	1.92444i
$277$	−13.0787	+	22.6530i	−0.785824	+	1.36109i	0.142682	+	0.989769i	$0.454427\pi$
$277$	−13.0787	+	22.6530i	−0.785824	+	1.36109i	−0.928506	+	0.371318i	$0.878906\pi$
$278$			3.42259i			0.205274i
$279$	36.3759	+	21.0016i	2.17777	+	1.25733i
$280$	−0.859601	−	0.496291i	−0.0513710	−	0.0296590i
$281$			6.64325i			0.396303i	0.980171	+	0.198152i	$0.0634938\pi$
$281$			6.64325i			0.396303i	−0.980171	+	0.198152i	$0.936506\pi$
$282$	4.35194	−	7.53778i	0.259154	−	0.448868i
$283$	8.77114	+	15.1921i	0.521390	+	0.903075i	0.999690	+	0.0248781i	$0.00791977\pi$
$283$	8.77114	+	15.1921i	0.521390	+	0.903075i	−0.478300	+	0.878196i	$0.658747\pi$
$284$	−0.892277	+	0.515156i	−0.0529469	+	0.0305689i
$285$	1.35194			0.0800820
$286$		0			0
$287$	−9.29612			−0.548733
$288$	−45.6876	+	26.3778i	−2.69217	+	1.55432i
$289$	4.84452	+	8.39096i	0.284972	+	0.493586i
$290$	−1.41016	+	2.44247i	−0.0828075	+	0.143427i
$291$		−	10.1723i		−	0.596308i
$292$	−7.52909	−	4.34692i	−0.440607	−	0.254385i
$293$	12.0760	+	6.97209i	0.705488	+	0.407314i	0.809388	−	0.587274i	$-0.199799\pi$
$293$	12.0760	+	6.97209i	0.705488	+	0.407314i	−0.103900	+	0.994588i	$0.533132\pi$
$294$		−	33.2994i		−	1.94206i
$295$	−1.13290	+	1.96225i	−0.0659603	+	0.114247i
$296$	−2.69886	−	4.67457i	−0.156868	−	0.271704i
$297$	−35.1724	+	20.3068i	−2.04091	+	1.17832i
$298$	−6.87614			−0.398324
$299$		0			0
$300$	−7.25839			−0.419063
$301$	0.245861	−	0.141948i	0.0141712	−	0.00818174i
$302$	−10.0747	−	17.4499i	−0.579733	−	1.00413i
$303$	−24.9549	+	43.2231i	−1.43362	+	2.48310i
$304$		−	1.38967i		−	0.0797031i
$305$	−3.05205	−	1.76210i	−0.174760	−	0.100898i
$306$	−31.8703	−	18.4003i	−1.82190	−	1.05188i
$307$			28.2132i			1.61021i	0.593129	+	0.805107i	$0.297892\pi$
$307$			28.2132i			1.61021i	−0.593129	+	0.805107i	$0.702108\pi$
$308$	−5.93676	+	10.2828i	−0.338279	+	0.585916i
$309$	−16.2863	−	28.2087i	−0.926495	−	1.60474i
$310$	11.6313	−	6.71533i	0.660613	−	0.381405i
$311$	−7.23550			−0.410287			−0.205144	−	0.978732i	$-0.565766\pi$
$311$	−7.23550			−0.410287			−0.205144	+	0.978732i	$0.565766\pi$
$312$		0			0
$313$	−21.7523			−1.22951			−0.614756	−	0.788718i	$-0.710745\pi$
$313$	−21.7523			−1.22951			−0.614756	+	0.788718i	$0.710745\pi$
$314$	20.9209	−	12.0787i	1.18064	−	0.681641i
$315$	4.41016	+	7.63862i	0.248484	+	0.430388i
$316$	17.6965	−	30.6512i	0.995504	−	1.72426i
$317$		−	14.7449i		−	0.828154i	−0.910242	−	0.414077i	$-0.864104\pi$
$317$		−	14.7449i		−	0.828154i	0.910242	−	0.414077i	$-0.135896\pi$
$318$	−8.18701	−	4.72677i	−0.459105	−	0.265064i
$319$	4.37204	+	2.52420i	0.244787	+	0.141328i
$320$			10.5242i			0.588321i
$321$	20.7244	−	35.8957i	1.15672	−	2.00350i
$322$	7.17226	+	12.4227i	0.399694	+	0.692291i
$323$	1.02580	−	0.592243i	0.0570768	−	0.0329533i
$324$	−32.9097			−1.82832
$325$		0			0
$326$	−39.6210			−2.19440
$327$	31.1116	−	17.9623i	1.72047	−	0.993316i
$328$	−2.52420	−	4.37204i	−0.139376	−	0.241406i
$329$	−0.913870	+	1.58287i	−0.0503833	+	0.0872664i
$330$			24.0410i			1.32341i
$331$	29.4605	+	17.0090i	1.61930	+	0.934902i	0.987102	+	0.160092i	$0.0511792\pi$
$331$	29.4605	+	17.0090i	1.61930	+	0.934902i	0.632195	+	0.774809i	$0.282154\pi$
$332$	−0.969129	−	0.559527i	−0.0531879	−	0.0307080i
$333$			47.9655i			2.62849i
$334$	17.6611	−	30.5900i	0.966374	−	1.67381i
$335$	−5.76210	−	9.98025i	−0.314817	−	0.545279i
$336$	11.4623	−	6.61775i	0.625318	−	0.361028i
$337$	−15.3929			−0.838506			−0.419253	−	0.907869i	$-0.637708\pi$
$337$	−15.3929			−0.838506			−0.419253	+	0.907869i	$0.637708\pi$
$338$		0			0
$339$	42.4413			2.30510
$340$	−5.50737	+	3.17968i	−0.298679	+	0.172442i
$341$	−12.0205	−	20.8201i	−0.650946	−	1.12747i
$342$	2.98113	−	5.16348i	0.161201	−	0.279209i
$343$			16.4562i			0.888549i
$344$	0.133518	+	0.0770869i	0.00719883	+	0.00415625i
$345$	13.5935	+	7.84823i	0.731851	+	0.422534i
$346$			22.4562i			1.20725i
$347$	1.44952	−	2.51064i	0.0778141	−	0.134778i	−0.824492	−	0.565873i	$-0.808539\pi$
$347$	1.44952	−	2.51064i	0.0778141	−	0.134778i	0.902307	+	0.431095i	$0.141873\pi$
$348$	4.90645	+	8.49822i	0.263013	+	0.455553i
$349$	−15.8343	+	9.14195i	−0.847592	+	0.489357i	−0.859838	−	0.510568i	$-0.829435\pi$
$349$	−15.8343	+	9.14195i	−0.847592	+	0.489357i	0.0122459	+	0.999925i	$0.496102\pi$
$350$	2.82032			0.150753
$351$		0			0
$352$	30.1952			1.60941
$353$	−18.2768	+	10.5521i	−0.972775	+	0.561632i	−0.900081	−	0.435722i	$-0.856493\pi$
$353$	−18.2768	+	10.5521i	−0.972775	+	0.561632i	−0.0726941	+	0.997354i	$0.523160\pi$
$354$	7.29372	+	12.6331i	0.387657	+	0.671441i
$355$	0.219035	−	0.379379i	0.0116252	−	0.0201354i
$356$			25.9852i			1.37721i
$357$	9.76988	+	5.64064i	0.517077	+	0.298534i
$358$	33.4532	+	19.3142i	1.76806	+	1.02079i
$359$		−	34.5349i		−	1.82268i	−0.411654	−	0.911340i	$-0.635049\pi$
$359$		−	34.5349i		−	1.82268i	0.411654	−	0.911340i	$-0.364951\pi$
$360$	−2.39500	+	4.14827i	−0.126228	+	0.218633i
$361$	−9.40405	−	16.2883i	−0.494950	−	0.857278i
$362$	22.2013	−	12.8179i	1.16687	−	0.673695i
$363$	9.08613			0.476898
$364$		0			0
$365$	3.69646			0.193482
$366$	−19.6493	+	11.3445i	−1.02708	+	0.592988i
$367$	−0.801456	−	1.38816i	−0.0418356	−	0.0724615i	0.844349	−	0.535793i	$-0.179987\pi$
$367$	−0.801456	−	1.38816i	−0.0418356	−	0.0724615i	−0.886185	+	0.463332i	$0.846654\pi$
$368$	8.06726	−	13.9729i	0.420535	−	0.728388i
$369$			44.8613i			2.33539i
$370$	13.2823	+	7.66855i	0.690515	+	0.398669i
$371$	1.71920	+	0.992582i	0.0892565	+	0.0515323i
$372$		−	46.7300i		−	2.42284i
$373$	−9.79001	+	16.9568i	−0.506907	+	0.877989i	0.493061	+	0.869995i	$0.335878\pi$
$373$	−9.79001	+	16.9568i	−0.506907	+	0.877989i	−0.999968	+	0.00799446i	$0.997455\pi$
$374$	10.5316	+	18.2413i	0.544577	+	0.943235i
$375$	2.67267	−	1.54307i	0.138016	−	0.0796835i
$376$	−0.992582			−0.0511885
$377$		0			0
$378$	30.6742			1.57771
$379$	5.51018	−	3.18130i	0.283039	−	0.163413i	−0.351759	−	0.936090i	$-0.614416\pi$
$379$	5.51018	−	3.18130i	0.283039	−	0.163413i	0.634798	+	0.772678i	$0.281083\pi$
$380$	−0.515156	−	0.892277i	−0.0264270	−	0.0457728i
$381$	6.11404	−	10.5898i	0.313232	−	0.542533i
$382$			11.2813i			0.577201i
$383$	−13.8394	−	7.99018i	−0.707160	−	0.408279i	0.102849	−	0.994697i	$-0.467204\pi$
$383$	−13.8394	−	7.99018i	−0.707160	−	0.408279i	−0.810009	+	0.586418i	$0.800538\pi$
$384$	15.4549	+	8.92291i	0.788682	+	0.455346i
$385$		−	5.04840i		−	0.257290i
$386$	−19.9320	+	34.5232i	−1.01451	+	1.75718i
$387$	−0.685013	−	1.18648i	−0.0348212	−	0.0603120i
$388$	−6.71367	+	3.87614i	−0.340835	+	0.196781i
$389$	21.5046			1.09032			0.545162	−	0.838331i	$-0.316468\pi$
$389$	21.5046			1.09032			0.545162	+	0.838331i	$0.316468\pi$
$390$		0			0
$391$	13.7523			0.695483
$392$	−3.28867	+	1.89871i	−0.166103	+	0.0958995i
$393$	−17.0484	−	29.5287i	−0.859978	−	1.48953i
$394$	−12.8129	+	22.1926i	−0.645505	+	1.11805i
$395$			15.0484i			0.757167i
$396$	49.6227	+	28.6497i	2.49364	+	1.43970i
$397$	13.3918	+	7.73179i	0.672118	+	0.388047i	0.796879	−	0.604140i	$-0.206483\pi$
$397$	13.3918	+	7.73179i	0.672118	+	0.388047i	−0.124761	+	0.992187i	$0.539816\pi$
$398$		−	1.59485i		−	0.0799428i
$399$	−0.913870	+	1.58287i	−0.0457507	+	0.0792426i
$400$	−1.58613	−	2.74726i	−0.0793065	−	0.137363i
$401$	22.3021	−	12.8761i	1.11372	−	0.643004i	0.173926	−	0.984759i	$-0.444355\pi$
$401$	22.3021	−	12.8761i	1.11372	−	0.643004i	0.939789	+	0.341755i	$0.111021\pi$
$402$	−74.1936			−3.70044
$403$		0			0
$404$	38.0362			1.89237
$405$	12.1179	−	6.99629i	0.602145	−	0.347648i
$406$	−1.90645	−	3.30207i	−0.0946156	−	0.163879i
$407$	13.7268	−	23.7755i	0.680411	−	1.17851i
$408$			6.12647i			0.303306i
$409$	−9.12065	−	5.26581i	−0.450987	−	0.260377i	0.257260	−	0.966342i	$-0.417180\pi$
$409$	−9.12065	−	5.26581i	−0.450987	−	0.260377i	−0.708247	+	0.705965i	$0.750514\pi$
$410$	12.4227	+	7.17226i	0.613514	+	0.354213i
$411$		−	38.6284i		−	1.90540i
$412$	−12.4118	+	21.4978i	−0.611485	+	1.05912i
$413$	−1.53162	−	2.65284i	−0.0753660	−	0.130538i
$414$	59.9497	−	34.6120i	2.94637	−	1.70108i
$415$	0.475800			0.0233561
$416$		0			0
$417$	−5.06324			−0.247948
$418$	−2.95537	+	1.70628i	−0.144552	+	0.0834570i
$419$	−3.73419	−	6.46781i	−0.182427	−	0.315973i	0.760279	−	0.649596i	$-0.225062\pi$
$419$	−3.73419	−	6.46781i	−0.182427	−	0.315973i	−0.942707	+	0.333623i	$0.891729\pi$
$420$	4.90645	−	8.49822i	0.239410	−	0.414671i
$421$		−	35.4897i		−	1.72966i	−0.502062	−	0.864832i	$-0.667425\pi$
$421$		−	35.4897i		−	1.72966i	0.502062	−	0.864832i	$-0.332575\pi$
$422$	14.3168	+	8.26581i	0.696931	+	0.402373i
$423$	7.63862	+	4.41016i	0.371403	+	0.214429i
$424$			1.07807i			0.0523558i
$425$	1.35194	−	2.34163i	0.0655787	−	0.113586i
$426$	−1.41016	−	2.44247i	−0.0683225	−	0.118338i
$427$	4.12618	−	2.38225i	0.199680	−	0.115285i
$428$	−31.5881			−1.52687
$429$		0			0
$430$	−0.438069			−0.0211256
$431$	0.133518	−	0.0770869i	0.00643136	−	0.00371315i	−0.496781	−	0.867876i	$-0.665485\pi$
$431$	0.133518	−	0.0770869i	0.00643136	−	0.00371315i	0.503212	+	0.864163i	$0.332151\pi$
$432$	−17.2510	−	29.8796i	−0.829988	−	1.43758i
$433$	2.82774	−	4.89779i	0.135892	−	0.235373i	−0.790046	−	0.613048i	$-0.789943\pi$
$433$	2.82774	−	4.89779i	0.135892	−	0.235373i	0.925938	+	0.377675i	$0.123276\pi$
$434$			18.1574i			0.871584i
$435$	−3.61328	−	2.08613i	−0.173244	−	0.100022i
$436$	−23.7101	−	13.6890i	−1.13551	−	0.655586i
$437$			2.22808i			0.106583i
$438$	11.8990	−	20.6097i	0.568558	−	0.984771i
$439$	13.4865	+	23.3592i	0.643674	+	1.11488i	0.984606	+	0.174788i	$0.0559241\pi$
$439$	13.4865	+	23.3592i	0.643674	+	1.11488i	−0.340932	+	0.940088i	$0.610743\pi$
$440$	2.37430	−	1.37080i	0.113190	−	0.0653506i
$441$	33.7449			1.60690
$442$		0			0
$443$	29.3700			1.39541			0.697706	−	0.716384i	$-0.254204\pi$
$443$	29.3700			1.39541			0.697706	+	0.716384i	$0.254204\pi$
$444$	46.2139	−	26.6816i	2.19322	−	1.26625i
$445$	−5.52420	−	9.56819i	−0.261872	−	0.453576i
$446$	−4.47340	+	7.74815i	−0.211821	+	0.366886i
$447$		−	10.1723i		−	0.481131i
$448$	−12.3219	−	7.11404i	−0.582154	−	0.336107i
$449$	−27.4329	−	15.8384i	−1.29464	−	0.747461i	−0.315167	−	0.949036i	$-0.602061\pi$
$449$	−27.4329	−	15.8384i	−1.29464	−	0.747461i	−0.979473	+	0.201576i	$0.935394\pi$
$450$		−	13.6103i		−	0.641597i
$451$	12.8384	−	22.2368i	0.604537	−	1.04709i
$452$	−16.1723	−	28.0112i	−0.760679	−	1.31753i
$453$	25.8146	−	14.9040i	1.21287	−	0.700253i
$454$	53.2159			2.49754
$455$		0			0
$456$	−0.992582			−0.0464819
$457$	−18.3335	+	10.5848i	−0.857603	+	0.495137i	−0.863209	−	0.504847i	$-0.831549\pi$
$457$	−18.3335	+	10.5848i	−0.857603	+	0.495137i	0.00560598	+	0.999984i	$0.498216\pi$
$458$	26.1903	+	45.3630i	1.22379	+	2.11967i
$459$	14.7039	−	25.4679i	0.686318	−	1.18874i
$460$		−	11.9623i		−	0.557744i
$461$	−30.4891	−	17.6029i	−1.42002	−	0.819849i	−0.423721	−	0.905793i	$-0.639276\pi$
$461$	−30.4891	−	17.6029i	−1.42002	−	0.819849i	−0.996300	+	0.0859436i	$0.972610\pi$
$462$	−28.1475	−	16.2510i	−1.30954	−	0.756064i
$463$		−	1.35194i		−	0.0628299i	−0.999506	−	0.0314150i	$-0.989999\pi$
$463$		−	1.35194i		−	0.0628299i	0.999506	−	0.0314150i	$-0.0100013\pi$
$464$	−2.14435	+	3.71413i	−0.0995490	+	0.172424i
$465$	9.93436	+	17.2068i	0.460695	+	0.797947i
$466$	−27.6346	+	15.9549i	−1.28015	+	0.739094i
$467$	31.6635			1.46521			0.732607	−	0.680652i	$-0.238303\pi$
$467$	31.6635			1.46521			0.732607	+	0.680652i	$0.238303\pi$
$468$		0			0
$469$	15.5800			0.719418
$470$	2.44247	−	1.41016i	0.112663	−	0.0650459i
$471$	17.8687	+	30.9495i	0.823347	+	1.42608i
$472$	0.831768	−	1.44066i	0.0382852	−	0.0663120i
$473$			0.784148i			0.0360552i
$474$	83.9028	+	48.4413i	3.85378	+	2.22498i
$475$	0.379379	+	0.219035i	0.0174071	+	0.0100500i
$476$		−	8.59746i		−	0.394064i
$477$	4.79001	−	8.29654i	0.219319	−	0.379872i
$478$	−14.2624	−	24.7032i	−0.652348	−	1.12990i
$479$	11.5304	−	6.65710i	0.526839	−	0.304171i	−0.212889	−	0.977076i	$-0.568287\pi$
$479$	11.5304	−	6.65710i	0.526839	−	0.304171i	0.739728	+	0.672906i	$0.234954\pi$
$480$	−24.9549			−1.13903
$481$		0			0
$482$	−26.1116			−1.18935
$483$	−18.3776	+	10.6103i	−0.836211	+	0.482787i
$484$	−3.46227	−	5.99683i	−0.157376	−	0.272583i
$485$	1.64806	−	2.85453i	0.0748346	−	0.129617i
$486$		−	22.0181i		−	0.998761i
$487$	7.70397	+	4.44789i	0.349100	+	0.201553i	0.664289	−	0.747476i	$-0.268734\pi$
$487$	7.70397	+	4.44789i	0.349100	+	0.201553i	−0.315189	+	0.949029i	$0.602068\pi$
$488$	2.24078	+	1.29372i	0.101436	+	0.0585639i
$489$		−	58.6136i		−	2.65060i
$490$	5.39500	−	9.34442i	0.243721	−	0.422138i
$491$	−4.76450	−	8.25236i	−0.215019	−	0.372424i	0.738259	−	0.674517i	$-0.235648\pi$
$491$	−4.76450	−	8.25236i	−0.215019	−	0.372424i	−0.953278	+	0.302093i	$0.902315\pi$
$492$	43.2231	−	24.9549i	1.94865	−	1.12505i
$493$	−3.65548			−0.164635
$494$		0			0
$495$	−24.3626			−1.09502
$496$	17.6870	−	10.2116i	0.794171	−	0.458515i
$497$	0.296122	+	0.512898i	0.0132829	+	0.0230066i
$498$	1.53162	−	2.65284i	0.0686334	−	0.118877i
$499$			25.4716i			1.14027i	0.821552	+	0.570133i	$0.193109\pi$
$499$			25.4716i			1.14027i	−0.821552	+	0.570133i	$0.806891\pi$
$500$	−2.03684	−	1.17597i	−0.0910902	−	0.0525910i
$501$	45.2535	+	26.1271i	2.02178	+	1.16727i
$502$			30.5168i			1.36203i
$503$	16.3331	−	28.2897i	0.728256	−	1.26138i	−0.229364	−	0.973341i	$-0.573665\pi$
$503$	16.3331	−	28.2897i	0.728256	−	1.26138i	0.957620	−	0.288035i	$-0.0930020\pi$
$504$	−3.23790	−	5.60821i	−0.144228	−	0.249809i
$505$	−14.0056	+	8.08613i	−0.623241	+	0.359828i
$506$	−39.6210			−1.76137
$507$		0			0
$508$	−9.31902			−0.413464
$509$	−7.29192	+	4.20999i	−0.323209	+	0.186605i	−0.652822	−	0.757511i	$-0.726415\pi$
$509$	−7.29192	+	4.20999i	−0.323209	+	0.186605i	0.329613	+	0.944116i	$0.393082\pi$
$510$	−8.70388	−	15.0756i	−0.385414	−	0.667557i
$511$	−2.49869	+	4.32787i	−0.110536	+	0.191454i
$512$			30.3094i			1.33950i
$513$	4.12618	+	2.38225i	0.182175	+	0.105179i
$514$	50.7608	+	29.3068i	2.23897	+	1.29267i
$515$		−	10.5545i		−	0.465087i
$516$	−0.762100	+	1.32000i	−0.0335496	+	0.0581096i
$517$	−2.52420	−	4.37204i	−0.111014	−	0.192282i
$518$	−17.9569	+	10.3674i	−0.788980	+	0.455518i
$519$	−33.2207			−1.45823
$520$		0			0
$521$	27.3371			1.19766			0.598830	−	0.800876i	$-0.295632\pi$
$521$	27.3371			1.19766			0.598830	+	0.800876i	$0.295632\pi$
$522$	−15.9352	+	9.20017i	−0.697463	+	0.402680i
$523$	3.88759	+	6.73350i	0.169992	+	0.294435i	0.938417	−	0.345505i	$-0.112292\pi$
$523$	3.88759	+	6.73350i	0.169992	+	0.294435i	−0.768425	+	0.639940i	$0.778959\pi$
$524$	−12.9926	+	22.5038i	−0.567584	+	0.983084i
$525$			4.17226i			0.182092i
$526$	−28.5001	−	16.4545i	−1.24266	−	0.717452i
$527$	15.0756	+	8.70388i	0.656702	+	0.379147i
$528$			36.5578i			1.59097i
$529$	−1.43436	+	2.48438i	−0.0623635	+	0.108017i
$530$	−1.53162	−	2.65284i	−0.0665292	−	0.115232i
$531$	−12.8021	+	7.39130i	−0.555564	+	0.320755i
$532$	1.39292			0.0603907
$533$		0			0
$534$	−71.1304			−3.07811
$535$	11.6313	−	6.71533i	0.502864	−	0.290329i
$536$	4.23048	+	7.32741i	0.182729	+	0.316496i
$537$	−28.5726	+	49.4892i	−1.23300	+	2.13562i
$538$		−	8.70388i		−	0.375251i
$539$	−16.7266	−	9.65710i	−0.720465	−	0.415961i
$540$	−22.1529	−	12.7900i	−0.953311	−	0.550394i
$541$			2.77934i			0.119493i	0.998214	+	0.0597466i	$0.0190293\pi$
$541$			2.77934i			0.119493i	−0.998214	+	0.0597466i	$0.980971\pi$
$542$	6.34049	−	10.9821i	0.272347	−	0.471720i
$543$	18.9623	+	32.8436i	0.813749	+	1.40945i
$544$	−18.9347	+	10.9320i	−0.811819	+	0.468704i
$545$	11.6406			0.498630
$546$		0			0
$547$	−38.4184			−1.64265			−0.821327	−	0.570458i	$-0.806766\pi$
$547$	−38.4184			−1.64265			−0.821327	+	0.570458i	$0.806766\pi$
$548$	−25.4947	+	14.7194i	−1.08908	+	0.628780i
$549$	−11.4963	−	19.9122i	−0.490650	−	0.849830i
$550$	−3.89500	+	6.74635i	−0.166084	+	0.287665i
$551$		−	0.592243i		−	0.0252304i
$552$	−9.98025	−	5.76210i	−0.424788	−	0.245251i
$553$	−17.6189	−	10.1723i	−0.749231	−	0.432569i
$554$			54.5678i			2.31836i
$555$	−11.3445	+	19.6493i	−0.481548	+	0.834066i
$556$	1.92935	+	3.34172i	0.0818225	+	0.141721i
$557$	−6.16528	+	3.55953i	−0.261231	+	0.150822i	−0.624896	−	0.780708i	$-0.714859\pi$
$557$	−6.16528	+	3.55953i	−0.261231	+	0.150822i	0.363665	+	0.931530i	$0.381525\pi$
$558$	87.6242			3.70943
$559$		0			0
$560$	4.28870			0.181231
$561$	−26.9854	+	15.5800i	−1.13932	+	0.657789i
$562$	6.92935	+	12.0020i	0.292297	+	0.506273i
$563$	16.4118	−	28.4260i	0.691674	−	1.19802i	−0.279615	−	0.960112i	$-0.590207\pi$
$563$	16.4118	−	28.4260i	0.691674	−	1.19802i	0.971289	−	0.237903i	$-0.0764599\pi$
$564$		−	9.81290i		−	0.413198i
$565$	11.9098	+	6.87614i	0.501050	+	0.289281i
$566$	31.6926	+	18.2977i	1.33214	+	0.769112i
$567$			18.9171i			0.794444i
$568$	−0.160813	+	0.278537i	−0.00674758	+	0.0116871i
$569$	7.70628	+	13.3477i	0.323064	+	0.559564i	0.981119	−	0.193407i	$-0.0619537\pi$
$569$	7.70628	+	13.3477i	0.323064	+	0.559564i	−0.658055	+	0.752970i	$0.728620\pi$
$570$	2.44247	−	1.41016i	0.102304	−	0.0590651i
$571$	−31.5142			−1.31883			−0.659413	−	0.751780i	$-0.729195\pi$
$571$	−31.5142			−1.31883			−0.659413	+	0.751780i	$0.729195\pi$
$572$		0			0
$573$	−16.6890			−0.697195
$574$	−16.7948	+	9.69646i	−0.701000	+	0.404722i
$575$	2.54307	+	4.40472i	0.106053	+	0.183689i
$576$	−34.3310	+	59.4630i	−1.43046	+	2.47763i
$577$			44.3855i			1.84779i	0.382643	+	0.923896i	$0.375014\pi$
$577$			44.3855i			1.84779i	−0.382643	+	0.923896i	$0.624986\pi$
$578$	17.5046	+	10.1063i	0.728096	+	0.420367i
$579$	−51.0721	−	29.4865i	−2.12248	−	1.22542i
$580$			3.17968i			0.132029i
$581$	−0.321627	+	0.557074i	−0.0133433	+	0.0231113i
$582$	−10.6103	−	18.3776i	−0.439812	−	0.761777i
$583$	−4.74861	+	2.74161i	−0.196667	+	0.113546i
$584$	−2.71391			−0.112302
$585$		0			0
$586$	29.0894			1.20167
$587$	11.5631	−	6.67597i	0.477261	−	0.275547i	−0.242013	−	0.970273i	$-0.577808\pi$
$587$	11.5631	−	6.67597i	0.477261	−	0.275547i	0.719274	+	0.694726i	$0.244474\pi$
$588$	−18.7711	−	32.5126i	−0.774109	−	1.34080i
$589$	−1.41016	+	2.44247i	−0.0581047	+	0.100640i
$590$			4.72677i			0.194598i
$591$	−32.8308	−	18.9549i	−1.35048	−	0.779698i
$592$	20.1977	+	11.6611i	0.830119	+	0.479270i
$593$		−	37.3929i		−	1.53554i	−0.640724	−	0.767772i	$-0.721366\pi$
$593$		−	37.3929i		−	1.53554i	0.640724	−	0.767772i	$-0.278634\pi$
$594$	−42.3626	+	73.3742i	−1.73816	+	3.01058i
$595$	1.82774	+	3.16574i	0.0749300	+	0.129783i
$596$	−6.71367	+	3.87614i	−0.275003	+	0.158773i
$597$	2.35936			0.0965621
$598$		0			0
$599$	13.8277			0.564986			0.282493	−	0.959269i	$-0.408839\pi$
$599$	13.8277			0.564986			0.282493	+	0.959269i	$0.408839\pi$
$600$	−1.96225	+	1.13290i	−0.0801084	+	0.0462506i
$601$	−3.17226	−	5.49452i	−0.129399	−	0.224126i	0.794045	−	0.607859i	$-0.207972\pi$
$601$	−3.17226	−	5.49452i	−0.129399	−	0.224126i	−0.923444	+	0.383733i	$0.874638\pi$
$602$	0.296122	−	0.512898i	0.0120690	−	0.0209041i
$603$		−	75.1862i		−	3.06182i
$604$	−19.6733	−	11.3584i	−0.800494	−	0.462166i
$605$	2.54974	+	1.47209i	0.103662	+	0.0598490i
$606$			104.118i			4.22951i
$607$	8.12308	−	14.0696i	0.329706	−	0.571067i	−0.652748	−	0.757575i	$-0.726384\pi$
$607$	8.12308	−	14.0696i	0.329706	−	0.571067i	0.982453	+	0.186508i	$0.0597171\pi$
$608$	−1.77114	−	3.06771i	−0.0718293	−	0.124412i
$609$	4.88494	−	2.82032i	0.197948	−	0.114285i
$610$	−7.35194			−0.297671
$611$		0			0
$612$	−41.4897			−1.67712
$613$	−19.6493	+	11.3445i	−0.793627	+	0.458201i	−0.841238	−	0.540665i	$-0.818173\pi$
$613$	−19.6493	+	11.3445i	−0.793627	+	0.458201i	0.0476107	+	0.998866i	$0.484839\pi$
$614$	29.4282	+	50.9712i	1.18763	+	2.05703i
$615$	−10.6103	+	18.3776i	−0.427850	+	0.741058i
$616$			3.70649i			0.149339i
$617$	−7.80482	−	4.50611i	−0.314210	−	0.181409i	0.334599	−	0.942361i	$-0.391399\pi$
$617$	−7.80482	−	4.50611i	−0.314210	−	0.181409i	−0.648809	+	0.760951i	$0.724733\pi$
$618$	−58.8470	−	33.9753i	−2.36717	−	1.36669i
$619$		−	3.45030i		−	0.138679i	−0.997593	−	0.0693395i	$-0.977911\pi$
$619$		−	3.45030i		−	0.138679i	0.997593	−	0.0693395i	$-0.0220892\pi$
$620$	7.57097	−	13.1133i	0.304058	−	0.526643i
$621$	27.6587	+	47.9063i	1.10991	+	1.92241i
$622$	−13.0719	+	7.54709i	−0.524137	+	0.302611i
$623$	14.9368			0.598429
$624$		0			0
$625$	1.00000			0.0400000
$626$	−39.2986	+	22.6890i	−1.57069	+	0.906836i
$627$	−2.52420	−	4.37204i	−0.100807	−	0.174603i
$628$	13.6177	−	23.5866i	0.543407	−	0.941209i
$629$			19.8787i			0.792618i
$630$	15.9352	+	9.20017i	0.634872	+	0.366544i
$631$	−21.6115	−	12.4774i	−0.860342	−	0.496718i	0.00378506	−	0.999993i	$-0.498795\pi$
$631$	−21.6115	−	12.4774i	−0.860342	−	0.496718i	−0.864127	+	0.503274i	$0.832129\pi$
$632$		−	11.0484i		−	0.439482i
$633$	−12.2281	+	21.1797i	−0.486022	+	0.841816i
$634$	−15.3798	−	26.6387i	−0.610812	−	1.05796i
$635$	3.43143	−	1.98113i	0.136172	−	0.0786189i
$636$	−10.6581			−0.422621
$637$		0			0
$638$	10.5316			0.416951
$639$	2.47515	−	1.42903i	0.0979153	−	0.0565314i
$640$	2.89130	+	5.00787i	0.114288	+	0.197953i
$641$	20.5652	−	35.6199i	0.812276	−	1.40690i	−0.0989918	−	0.995088i	$-0.531562\pi$
$641$	20.5652	−	35.6199i	0.812276	−	1.40690i	0.911268	−	0.411815i	$-0.135105\pi$
$642$		−	86.4675i		−	3.41260i
$643$	−6.25744	−	3.61273i	−0.246769	−	0.142472i	0.371515	−	0.928427i	$-0.378839\pi$
$643$	−6.25744	−	3.61273i	−0.246769	−	0.142472i	−0.618284	+	0.785955i	$0.712172\pi$
$644$	14.0056	+	8.08613i	0.551897	+	0.318638i
$645$		−	0.648061i		−	0.0255174i
$646$	1.23550	−	2.13994i	0.0486100	−	0.0841949i
$647$	−4.22886	−	7.32460i	−0.166254	−	0.287960i	0.770846	−	0.637021i	$-0.219834\pi$
$647$	−4.22886	−	7.32460i	−0.166254	−	0.287960i	−0.937100	+	0.349062i	$0.886500\pi$
$648$	−8.89688	+	5.13661i	−0.349502	+	0.201785i
$649$	8.46096			0.332122
$650$		0			0
$651$	−26.8613			−1.05278
$652$	−38.6848	+	22.3347i	−1.51501	+	0.874694i
$653$	8.19035	+	14.1861i	0.320513	+	0.555145i	0.980594	−	0.196050i	$-0.0628114\pi$
$653$	8.19035	+	14.1861i	0.320513	+	0.555145i	−0.660081	+	0.751194i	$0.729478\pi$
$654$	37.4716	−	64.9028i	1.46526	−	2.53790i
$655$		−	11.0484i		−	0.431697i
$656$	18.8905	+	10.9065i	0.737551	+	0.425825i
$657$	20.8855	+	12.0582i	0.814819	+	0.470436i
$658$			3.81290i			0.148642i
$659$	0.154174	−	0.267037i	0.00600576	−	0.0104023i	−0.863007	−	0.505192i	$-0.831422\pi$
$659$	0.154174	−	0.267037i	0.00600576	−	0.0104023i	0.869013	+	0.494790i	$0.164755\pi$
$660$	13.5521	+	23.4729i	0.527515	+	0.913683i
$661$	28.3934	−	16.3929i	1.10437	−	0.637611i	0.167008	−	0.985956i	$-0.446590\pi$
$661$	28.3934	−	16.3929i	1.10437	−	0.637611i	0.937366	+	0.348345i	$0.113256\pi$
$662$	70.9662			2.75818
$663$		0			0
$664$	−0.349328			−0.0135566
$665$	−0.512898	+	0.296122i	−0.0198893	+	0.0114831i
$666$	50.0312	+	86.6565i	1.93867	+	3.35787i
$667$	3.43807	−	5.95491i	0.133123	−	0.230575i
$668$		−	39.8229i		−	1.54080i
$669$	−11.4623	−	6.61775i	−0.443157	−	0.255857i
$670$	−20.8201	−	12.0205i	−0.804351	−	0.464392i
$671$			13.1600i			0.508037i
$672$	16.8687	−	29.2175i	0.650725	−	1.12709i
$673$	−10.8761	−	18.8380i	−0.419244	−	0.726152i	0.576619	−	0.817013i	$-0.304372\pi$
$673$	−10.8761	−	18.8380i	−0.419244	−	0.726152i	−0.995864	+	0.0908605i	$0.971038\pi$
$674$	−27.8095	+	16.0558i	−1.07118	+	0.618447i
$675$	10.8761			0.418623
$676$		0			0
$677$	−14.4200			−0.554205			−0.277102	−	0.960840i	$-0.589374\pi$
$677$	−14.4200			−0.554205			−0.277102	+	0.960840i	$0.589374\pi$
$678$	76.6763	−	44.2691i	2.94473	−	1.70014i
$679$	2.22808	+	3.85914i	0.0855058	+	0.148100i
$680$	−0.992582	+	1.71920i	−0.0380638	+	0.0659284i
$681$			78.7252i			3.01676i
$682$	−43.4334	−	25.0763i	−1.66315	−	0.960221i
$683$	−33.9306	−	19.5898i	−1.29832	−	0.749584i	−0.318205	−	0.948022i	$-0.603080\pi$
$683$	−33.9306	−	19.5898i	−1.29832	−	0.749584i	−0.980114	+	0.198438i	$0.936413\pi$
$684$		−	6.72197i		−	0.257021i
$685$	6.25839	−	10.8399i	0.239121	−	0.414169i
$686$	17.1648	+	29.7304i	0.655357	+	1.13511i
$687$	−67.1081	+	38.7449i	−2.56033	+	1.47821i
$688$	−0.666147			−0.0253966
$689$		0			0
$690$	32.7449			1.24658
$691$	−4.81677	+	2.78097i	−0.183239	+	0.105793i	−0.588813	−	0.808269i	$-0.700405\pi$
$691$	−4.81677	+	2.78097i	−0.183239	+	0.105793i	0.405575	+	0.914062i	$0.367071\pi$
$692$	12.6587	+	21.9256i	0.481213	+	0.833485i
$693$	16.4684	−	28.5241i	0.625582	−	1.08354i
$694$		−	6.04776i		−	0.229570i
$695$	−1.42084	−	0.820321i	−0.0538955	−	0.0311166i
$696$	2.65284	+	1.53162i	0.100556	+	0.0580558i
$697$			18.5922i			0.704231i
$698$	−19.0713	+	33.0324i	−0.721859	+	1.25030i
$699$	−23.6029	−	40.8814i	−0.892744	−	1.54628i
$700$	2.75368	−	1.58984i	0.104079	−	0.0600903i
$701$	9.58002			0.361832			0.180916	−	0.983499i	$-0.442094\pi$
$701$	9.58002			0.361832			0.180916	+	0.983499i	$0.442094\pi$
$702$		0			0
$703$	−3.22066			−0.121469
$704$	34.0343	−	19.6497i	1.28271	−	0.740575i
$705$	2.08613	+	3.61328i	0.0785682	+	0.136084i
$706$	−22.0131	+	38.1278i	−0.828473	+	1.43496i
$707$		−	21.8639i		−	0.822277i
$708$	14.2428	+	8.22306i	0.535276	+	0.309042i
$709$	10.5286	+	6.07871i	0.395411	+	0.228291i	0.684502	−	0.729011i	$-0.260020\pi$
$709$	10.5286	+	6.07871i	0.395411	+	0.228291i	−0.289091	+	0.957302i	$0.593353\pi$
$710$		−	0.913870i		−	0.0342969i
$711$	−49.0894	+	85.0253i	−1.84100	+	3.18870i
$712$	4.05582	+	7.02488i	0.151998	+	0.263269i
$713$	−28.3579	+	16.3724i	−1.06201	+	0.613152i
$714$	23.5342			0.880746
$715$		0			0
$716$	43.5503			1.62755
$717$	36.5449	−	21.0992i	1.36479	−	0.787964i
$718$	−36.0221	−	62.3921i	−1.34433	−	2.32845i
$719$	10.5726	−	18.3123i	0.394291	−	0.682933i	−0.598719	−	0.800959i	$-0.704323\pi$
$719$	10.5726	−	18.3123i	0.394291	−	0.682933i	0.993010	+	0.118026i	$0.0376567\pi$
$720$		−	20.6965i		−	0.771312i
$721$	12.3574	+	7.13453i	0.460212	+	0.265704i
$722$	−33.9795	−	19.6181i	−1.26459	−	0.730109i
$723$		−	38.6284i		−	1.43661i
$724$	14.4511	−	25.0301i	0.537072	−	0.930237i
$725$	−0.675970	−	1.17081i	−0.0251049	−	0.0434829i
$726$	16.4154	−	9.47743i	0.609232	−	0.351740i
$727$	9.72938			0.360843			0.180421	−	0.983589i	$-0.442254\pi$
$727$	9.72938			0.360843			0.180421	+	0.983589i	$0.442254\pi$
$728$		0			0
$729$	−9.40515			−0.348339
$730$	6.67818	−	3.85565i	0.247170	−	0.142704i
$731$	−0.283896	−	0.491722i	−0.0105003	−	0.0181870i
$732$	−12.7900	+	22.1529i	−0.472732	+	0.818796i
$733$		−	4.40515i		−	0.162708i	−0.996685	−	0.0813539i	$-0.974076\pi$
$733$		−	4.40515i		−	0.162708i	0.996685	−	0.0813539i	$-0.0259244\pi$
$734$	−2.89589	−	1.67194i	−0.106889	−	0.0617125i
$735$	13.8237	+	7.98113i	0.509896	+	0.294389i
$736$		−	41.1271i		−	1.51597i
$737$	−21.5168	+	37.2682i	−0.792581	+	1.37279i
$738$	46.7933	+	81.0483i	1.72248	+	2.98343i
$739$	10.8159	−	6.24454i	0.397868	−	0.229709i	−0.287696	−	0.957722i	$-0.592889\pi$
$739$	10.8159	−	6.24454i	0.397868	−	0.229709i	0.685564	+	0.728013i	$0.259556\pi$
$740$	17.2913			0.635641
$741$		0			0
$742$	4.14131			0.152032
$743$	20.5742	−	11.8785i	0.754796	−	0.435781i	−0.0726284	−	0.997359i	$-0.523139\pi$
$743$	20.5742	−	11.8785i	0.754796	−	0.435781i	0.827424	+	0.561578i	$0.189805\pi$
$744$	−7.29372	−	12.6331i	−0.267401	−	0.463152i
$745$	1.64806	−	2.85453i	0.0603803	−	0.104582i
$746$			40.8465i			1.49550i
$747$	2.68833	+	1.55211i	0.0983609	+	0.0567887i
$748$	20.5656	+	11.8735i	0.751951	+	0.434139i
$749$			18.1574i			0.663458i
$750$	3.21903	−	5.57553i	0.117543	−	0.203590i
$751$	−16.0787	−	27.8491i	−0.586721	−	1.01623i	−0.994659	−	0.103220i	$-0.967085\pi$
$751$	−16.0787	−	27.8491i	−0.586721	−	1.01623i	0.407938	−	0.913010i	$-0.366248\pi$
$752$	3.71413	−	2.14435i	0.135440	−	0.0781965i
$753$	−45.1452			−1.64518
$754$		0			0
$755$	9.65873			0.351517
$756$	29.9494	−	17.2913i	1.08925	−	0.628879i
$757$	18.0861	+	31.3261i	0.657352	+	1.13857i	0.981299	+	0.192491i	$0.0616567\pi$
$757$	18.0861	+	31.3261i	0.657352	+	1.13857i	−0.323947	+	0.946075i	$0.605010\pi$
$758$	6.63661	−	11.4950i	0.241053	−	0.417515i
$759$		−	58.6136i		−	2.12754i
$760$	−0.278537	−	0.160813i	−0.0101036	−	0.00583331i
$761$	29.3270	+	16.9320i	1.06310	+	0.613783i	0.926289	−	0.376814i	$-0.122980\pi$
$761$	29.3270	+	16.9320i	1.06310	+	0.613783i	0.136814	+	0.990597i	$0.456314\pi$
$762$		−	25.5094i		−	0.924107i
$763$	−7.86872	+	13.6290i	−0.284867	+	0.493404i
$764$	6.35936	+	11.0147i	0.230073	+	0.398499i
$765$	15.2772	−	8.82032i	0.552350	−	0.318899i
$766$	−33.3371			−1.20452
$767$		0			0
$768$	−27.7294			−1.00060
$769$	−18.9347	+	10.9320i	−0.682803	+	0.394216i	−0.800910	−	0.598784i	$-0.795651\pi$
$769$	−18.9347	+	10.9320i	−0.682803	+	0.394216i	0.118107	+	0.993001i	$0.462317\pi$
$770$	−5.26581	−	9.12065i	−0.189767	−	0.328685i
$771$	−43.3552	+	75.0934i	−1.56140	+	2.70442i
$772$			44.9433i			1.61754i
$773$	19.1719	+	11.0689i	0.689565	+	0.398120i	0.803449	−	0.595374i	$-0.202996\pi$
$773$	19.1719	+	11.0689i	0.689565	+	0.398120i	−0.113884	+	0.993494i	$0.536329\pi$
$774$	−2.47515	−	1.42903i	−0.0889673	−	0.0513653i
$775$			6.43807i			0.231262i
$776$	−1.20999	+	2.09577i	−0.0434362	+	0.0752336i
$777$	−15.3371	−	26.5646i	−0.550215	−	0.953001i
$778$	38.8510	−	22.4307i	1.39288	−	0.804178i
$779$	−3.01223			−0.107924
$780$		0			0
$781$	−1.63583			−0.0585348
$782$	24.8454	−	14.3445i	0.888471	−	0.512959i
$783$	−7.35194	−	12.7339i	−0.262737	−	0.455074i
$784$	8.20388	−	14.2095i	0.292996	−	0.507483i
$785$			11.5800i			0.413309i
$786$	−61.6007	−	35.5652i	−2.19722	−	1.26857i
$787$	13.2170	+	7.63082i	0.471134	+	0.272009i	0.716714	−	0.697367i	$-0.245645\pi$
$787$	13.2170	+	7.63082i	0.471134	+	0.272009i	−0.245580	+	0.969376i	$0.578978\pi$
$788$			28.8910i			1.02920i
$789$	24.3421	−	42.1618i	0.866602	−	1.50100i
$790$	15.6965	+	27.1871i	0.558455	+	0.967272i
$791$	−16.1014	+	9.29612i	−0.572498	+	0.330532i
$792$	17.8868			0.635580
$793$		0			0
$794$	32.2590			1.14483
$795$	3.92450	−	2.26581i	0.139188	−	0.0803600i
$796$	−0.899033	−	1.55717i	−0.0318654	−	0.0551925i
$797$	4.61033	−	7.98533i	0.163306	−	0.282855i	−0.772746	−	0.634715i	$-0.781117\pi$
$797$	4.61033	−	7.98533i	0.163306	−	0.282855i	0.936053	+	0.351860i	$0.114451\pi$
$798$			3.81290i			0.134975i
$799$	3.16574	+	1.82774i	0.111996	+	0.0646608i
$800$	−7.00279	−	4.04307i	−0.247586	−	0.142944i
$801$		−	72.0820i		−	2.54689i
$802$	26.8613	−	46.5251i	0.948506	−	1.64286i
$803$	−6.90164	−	11.9540i	−0.243554	−	0.421847i
$804$	−72.4405	+	41.8236i	−2.55478	+	1.47500i
$805$	−6.87614			−0.242352
$806$		0			0
$807$	12.8761			0.453262
$808$	10.2828	−	5.93676i	0.361747	−	0.208855i
$809$	−0.0837264	−	0.145018i	−0.00294366	−	0.00509858i	0.864550	−	0.502547i	$-0.167604\pi$
$809$	−0.0837264	−	0.145018i	−0.00294366	−	0.00509858i	−0.867493	+	0.497449i	$0.834270\pi$
$810$	14.5952	−	25.2796i	0.512822	−	0.888234i
$811$		−	36.0032i		−	1.26425i	−0.774868	−	0.632123i	$-0.782184\pi$
$811$		−	36.0032i		−	1.26425i	0.774868	−	0.632123i	$-0.217816\pi$
$812$	−3.72281	−	2.14937i	−0.130645	−	0.0754280i
$813$	16.2464	+	9.37985i	0.569785	+	0.328966i
$814$		−	57.2717i		−	2.00737i
$815$	9.49629	−	16.4481i	0.332641	−	0.576150i
$816$	−13.2355	−	22.9246i	−0.463335	−	0.802520i
$817$	0.0796664	−	0.0459954i	0.00278717	−	0.00160918i
$818$	−21.9703			−0.768174
$819$		0			0
$820$	16.1723			0.564760
$821$	−4.37204	+	2.52420i	−0.152585	+	0.0880952i	−0.574349	−	0.818611i	$-0.694745\pi$
$821$	−4.37204	+	2.52420i	−0.152585	+	0.0880952i	0.421763	+	0.906706i	$0.361411\pi$
$822$	−40.2920	−	69.7877i	−1.40534	−	2.43413i
$823$	−5.65470	+	9.79423i	−0.197110	+	0.341405i	−0.947590	−	0.319488i	$-0.896489\pi$
$823$	−5.65470	+	9.79423i	−0.197110	+	0.341405i	0.750480	+	0.660893i	$0.229822\pi$
$824$			7.74903i			0.269950i
$825$	−9.98025	−	5.76210i	−0.347468	−	0.200611i
$826$	−5.53417	−	3.19515i	−0.192558	−	0.111174i
$827$		−	43.8687i		−	1.52546i	−0.646714	−	0.762732i	$-0.723857\pi$
$827$		−	43.8687i		−	1.52546i	0.646714	−	0.762732i	$-0.276143\pi$
$828$	39.0221	−	67.5883i	1.35611	−	2.34886i
$829$	−22.2231	−	38.4915i	−0.771839	−	1.33686i	−0.936554	−	0.350523i	$-0.886004\pi$
$829$	−22.2231	−	38.4915i	−0.771839	−	1.33686i	0.164715	−	0.986341i	$-0.447329\pi$
$830$	0.859601	−	0.496291i	0.0298372	−	0.0172265i
$831$	−80.7252			−2.80033
$832$		0			0
$833$	13.9852			0.484557
$834$	−9.14745	+	5.28128i	−0.316750	+	0.182876i
$835$	8.46598	+	14.6635i	0.292977	+	0.507451i
$836$	−1.92369	+	3.33193i	−0.0665323	+	0.115237i
$837$			70.0213i			2.42029i
$838$	−13.4927	−	7.79001i	−0.466097	−	0.269101i
$839$	1.24767	+	0.720340i	0.0430742	+	0.0248689i	0.521382	−	0.853323i	$-0.325416\pi$
$839$	1.24767	+	0.720340i	0.0430742	+	0.0248689i	−0.478308	+	0.878192i	$0.658750\pi$
$840$		−	3.06324i		−	0.105692i
$841$	13.5861	−	23.5319i	0.468487	−	0.811444i
$842$	−37.0181	−	64.1172i	−1.27573	−	2.20962i
$843$	−17.7552	+	10.2510i	−0.611522	+	0.353062i
$844$	18.6380			0.641548
$845$		0			0
$846$	18.4003			0.632617
$847$	−3.44709	+	1.99018i	−0.118443	+	0.0683833i
$848$	−2.32905	−	4.03402i	−0.0799797	−	0.138529i
$849$	−27.0689	+	46.8847i	−0.929002	+	1.60908i
$850$		−	5.64064i		−	0.193472i
$851$	−32.3832	−	18.6965i	−1.11008	−	0.640906i
$852$	−2.75368	−	1.58984i	−0.0943396	−	0.0544670i
$853$			0.992582i			0.0339853i	0.999856	+	0.0169927i	$0.00540920\pi$
$853$			0.992582i			0.0339853i	−0.999856	+	0.0169927i	$0.994591\pi$
$854$	4.96969	−	8.60775i	0.170059	−	0.294551i
$855$	1.42903	+	2.47515i	0.0488717	+	0.0846482i
$856$	−8.53958	+	4.93033i	−0.291877	+	0.168515i
$857$	10.6071			0.362331			0.181165	−	0.983453i	$-0.442013\pi$
$857$	10.6071			0.362331			0.181165	+	0.983453i	$0.442013\pi$
$858$		0			0
$859$	−40.9123			−1.39591			−0.697955	−	0.716142i	$-0.745906\pi$
$859$	−40.9123			−1.39591			−0.697955	+	0.716142i	$0.745906\pi$
$860$	−0.427719	+	0.246944i	−0.0145851	+	0.00842070i
$861$	−14.3445	−	24.8454i	−0.488860	−	0.846730i
$862$	0.160813	−	0.278537i	0.00547732	−	0.00948700i
$863$			48.2494i			1.64243i	0.570619	+	0.821215i	$0.306703\pi$
$863$			48.2494i			1.64243i	−0.570619	+	0.821215i	$0.693297\pi$
$864$	−76.1634	−	43.9729i	−2.59113	−	1.49599i
$865$	−9.32233	−	5.38225i	−0.316969	−	0.183002i
$866$		−	11.7981i		−	0.400915i
$867$	−14.9508	+	25.8956i	−0.507757	+	0.879460i
$868$	10.2355	+	17.7284i	0.347415	+	0.601741i
$869$	48.6651	−	28.0968i	1.65085	−	0.953119i
$870$	−8.70388			−0.295089
$871$		0			0
$872$	−8.54645			−0.289419
$873$	18.6235	−	10.7523i	0.630310	−	0.363909i
$874$	2.32403	+	4.02534i	0.0786115	+	0.136159i
$875$	−0.675970	+	1.17081i	−0.0228519	+	0.0395807i
$876$		−	26.8304i		−	0.906514i
$877$	−4.17036	−	2.40776i	−0.140823	−	0.0813042i	0.427933	−	0.903810i	$-0.359242\pi$
$877$	−4.17036	−	2.40776i	−0.140823	−	0.0813042i	−0.568756	+	0.822506i	$0.692575\pi$
$878$	48.7304	+	28.1345i	1.64457	+	0.949494i
$879$			43.0336i			1.45149i
$880$	−5.92291	+	10.2588i	−0.199661	+	0.345824i
$881$	10.8105	+	18.7243i	0.364215	+	0.630839i	0.988650	−	0.150238i	$-0.0480040\pi$
$881$	10.8105	+	18.7243i	0.364215	+	0.630839i	−0.624435	+	0.781077i	$0.714671\pi$
$882$	60.9649	−	35.1981i	2.05279	−	1.18518i
$883$	21.1616			0.712144			0.356072	−	0.934458i	$-0.384116\pi$
$883$	21.1616			0.712144			0.356072	+	0.934458i	$0.384116\pi$
$884$		0			0
$885$	−6.99258			−0.235053
$886$	53.0611	−	30.6348i	1.78262	−	1.02920i
$887$	4.55048	+	7.88167i	0.152790	+	0.264641i	0.932252	−	0.361809i	$-0.117841\pi$
$887$	4.55048	+	7.88167i	0.152790	+	0.264641i	−0.779462	+	0.626450i	$0.784507\pi$
$888$	8.32905	−	14.4263i	0.279504	−	0.484116i
$889$			5.35675i			0.179660i
$890$	−19.9605	−	11.5242i	−0.669077	−	0.386292i
$891$	−45.2507	−	26.1255i	−1.51595	−	0.875237i
$892$			10.0868i			0.337730i
$893$	−0.296122	+	0.512898i	−0.00990933	+	0.0171635i
$894$	−10.6103	−	18.3776i	−0.354863	−	0.614640i
$895$	−16.0360	+	9.25839i	−0.536024	+	0.309474i
$896$	−7.81771			−0.261171
$897$		0			0
$898$	−66.0820			−2.20518
$899$	7.53778	−	4.35194i	0.251399	−	0.145145i
$900$	−7.67226	−	13.2887i	−0.255742	−	0.442958i
$901$	1.98516	−	3.43840i	0.0661354	−	0.114550i
$902$		−	53.5652i		−	1.78353i
$903$	0.758758	+	0.438069i	0.0252499	+	0.0145780i
$904$	−8.74408	−	5.04840i	−0.290824	−	0.167907i
$905$			12.2887i			0.408490i
$906$	31.0918	−	53.8525i	1.03296	−	1.78913i
$907$	21.6218	+	37.4500i	0.717939	+	1.24351i	0.961815	+	0.273701i	$0.0882478\pi$
$907$	21.6218	+	37.4500i	0.717939	+	1.24351i	−0.243876	+	0.969807i	$0.578419\pi$
$908$	51.9585	−	29.9982i	1.72430	−	0.995526i
$909$	−105.511			−3.49958
$910$		0			0
$911$	23.2058			0.768843			0.384422	−	0.923158i	$-0.374401\pi$
$911$	23.2058			0.768843			0.384422	+	0.923158i	$0.374401\pi$
$912$	3.71413	−	2.14435i	0.122987	−	0.0710066i
$913$	−0.888365	−	1.53869i	−0.0294006	−	0.0509233i
$914$	−22.0813	+	38.2460i	−0.730385	+	1.26506i
$915$		−	10.8761i		−	0.359554i
$916$	51.1430	+	29.5274i	1.68981	+	0.975614i
$917$	12.9356	+	7.46838i	0.427172	+	0.246628i
$918$		−	61.3484i		−	2.02480i
$919$	−0.209991	+	0.363716i	−0.00692698	+	0.0119979i	−0.869468	−	0.493989i	$-0.835538\pi$
$919$	−0.209991	+	0.363716i	−0.00692698	+	0.0119979i	0.862541	+	0.505987i	$0.168872\pi$
$920$	−1.86710	−	3.23390i	−0.0615563	−	0.106619i
$921$	−75.4046	+	43.5349i	−2.48467	+	1.43452i
$922$	−73.4439			−2.41875
$923$		0			0
$924$	−36.6433			−1.20547
$925$	−6.36697	+	3.67597i	−0.209345	+	0.120865i
$926$	−1.41016	−	2.44247i	−0.0463408	−	0.0802645i
$927$	34.4299	−	59.6343i	1.13083	−	1.95865i
$928$			10.9320i			0.358859i
$929$	33.9661	+	19.6103i	1.11439	+	0.643394i	0.939963	−	0.341276i	$-0.110859\pi$
$929$	33.9661	+	19.6103i	1.11439	+	0.643394i	0.174428	+	0.984670i	$0.444192\pi$
$930$	35.8957	+	20.7244i	1.17707	+	0.679579i
$931$			2.26581i			0.0742589i
$932$	−17.9878	+	31.1557i	−0.589209	+	1.02054i
$933$	−11.1648	−	19.3381i	−0.365521	−	0.633100i
$934$	57.2047	−	33.0271i	1.87179	−	1.08068i
$935$	−10.0968			−0.330201
$936$		0			0
$937$	−22.5774			−0.737572			−0.368786	−	0.929514i	$-0.620226\pi$
$937$	−22.5774			−0.737572			−0.368786	+	0.929514i	$0.620226\pi$
$938$	28.1475	−	16.2510i	0.919049	−	0.530613i
$939$	−33.5652	−	58.1366i	−1.09536	−	1.89722i
$940$	1.58984	−	2.75368i	0.0518548	−	0.0898152i
$941$		−	18.0510i		−	0.588446i	−0.955737	−	0.294223i	$-0.904939\pi$
$941$		−	18.0510i		−	0.588446i	0.955737	−	0.294223i	$-0.0950609\pi$
$942$	64.5648	+	37.2765i	2.10363	+	1.21453i
$943$	−30.2875	−	17.4865i	−0.986295	−	0.569438i
$944$			7.18774i			0.233941i
$945$	−7.35194	+	12.7339i	−0.239159	+	0.414235i
$946$	0.817917	+	1.41667i	0.0265928	+	0.0460601i
$947$	−21.2676	+	12.2789i	−0.691106	+	0.399010i	−0.804026	−	0.594594i	$-0.797313\pi$
$947$	−21.2676	+	12.2789i	−0.691106	+	0.399010i	0.112920	+	0.993604i	$0.463979\pi$
$948$	109.227			3.54753
$949$		0			0
$950$	0.913870			0.0296499
$951$	39.4081	−	22.7523i	1.27790	−	0.737793i
$952$	−1.34191	−	2.32426i	−0.0434916	−	0.0753296i
$953$	17.4610	−	30.2433i	0.565616	−	0.979676i	−0.431376	−	0.902172i	$-0.641972\pi$
$953$	17.4610	−	30.2433i	0.565616	−	0.979676i	0.996992	−	0.0775036i	$-0.0246949\pi$
$954$		−	19.9852i		−	0.647044i
$955$	−4.68325	−	2.70388i	−0.151547	−	0.0874955i
$956$	−27.8509	−	16.0797i	−0.900761	−	0.520055i
$957$			15.5800i			0.503630i
$958$	13.8876	−	24.0540i	0.448688	−	0.777150i
$959$	8.46096	+	14.6548i	0.273219	+	0.473229i
$960$	−28.1277	+	16.2395i	−0.907817	+	0.524128i
$961$	−10.4487			−0.337056
$962$		0			0
$963$	87.6242			2.82365
$964$	−25.4947	+	14.7194i	−0.821128	+	0.474078i
$965$	−9.55451	−	16.5489i	−0.307571	−	0.532728i
$966$	−22.1345	+	38.3381i	−0.712167	+	1.23351i
$967$		−	5.16484i		−	0.166090i	−0.996546	−	0.0830451i	$-0.973535\pi$
$967$		−	5.16484i		−	0.166090i	0.996546	−	0.0830451i	$-0.0264645\pi$
$968$	−1.87199	−	1.08080i	−0.0601682	−	0.0347381i
$969$	3.16574	+	1.82774i	0.101698	+	0.0587155i
$970$		−	6.87614i		−	0.220780i
$971$	−7.14676	+	12.3785i	−0.229350	+	0.397246i	−0.957616	−	0.288049i	$-0.906993\pi$
$971$	−7.14676	+	12.3785i	−0.229350	+	0.397246i	0.728265	+	0.685295i	$0.240327\pi$
$972$	−12.4118	−	21.4978i	−0.398108	−	0.689544i
$973$	1.92089	−	1.10902i	0.0615808	−	0.0355537i
$974$	18.5578			0.594629
$975$		0			0
$976$	−11.1797			−0.357853
$977$	−0.367879	+	0.212395i	−0.0117695	+	0.00679512i	−0.505873	−	0.862608i	$-0.668830\pi$
$977$	−0.367879	+	0.212395i	−0.0117695	+	0.00679512i	0.494104	+	0.869403i	$0.335496\pi$
$978$	−61.1378	−	105.894i	−1.95497	−	3.38611i
$979$	−20.6284	+	35.7295i	−0.659287	+	1.14192i
$980$		−	12.1648i		−	0.388592i
$981$	65.7711	+	37.9729i	2.09991	+	1.21238i
$982$	−17.2155	−	9.93937i	−0.549369	−	0.317178i
$983$			17.8081i			0.567990i	0.958826	+	0.283995i	$0.0916599\pi$
$983$			17.8081i			0.567990i	−0.958826	+	0.283995i	$0.908340\pi$
$984$	7.79001	−	13.4927i	0.248336	−	0.430131i
$985$	−6.14195	−	10.6382i	−0.195699	−	0.338960i
$986$	−6.60414	+	3.81290i	−0.210319	+	0.121428i
$987$	−5.64064			−0.179544
$988$		0			0
$989$	1.06804			0.0339618
$990$	−44.0145	+	25.4118i	−1.39887	+	0.807640i
$991$	17.3748	+	30.0941i	0.551930	+	0.955970i	0.998135	+	0.0610399i	$0.0194417\pi$
$991$	17.3748	+	30.0941i	0.551930	+	0.955970i	−0.446206	+	0.894931i	$0.647225\pi$
$992$	26.0295	−	45.0845i	0.826439	−	1.43143i
$993$			104.984i			3.33157i
$994$	1.06997	+	0.617748i	0.0339374	+	0.0195938i
$995$	0.662080	+	0.382252i	0.0209893	+	0.0121182i
$996$		−	3.45355i		−	0.109430i
$997$	−24.0107	+	41.5877i	−0.760425	+	1.31710i	0.182206	+	0.983260i	$0.441676\pi$
$997$	−24.0107	+	41.5877i	−0.760425	+	1.31710i	−0.942631	+	0.333835i	$0.891657\pi$
$998$	26.5686	+	46.0181i	0.841013	+	1.45668i
$999$	−69.2480	+	39.9804i	−2.19091	+	1.26492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.h.361.5		12
13.2	odd	12		845.2.a.i.1.3		3
13.3	even	3		65.2.c.a.51.5	yes	6
13.4	even	6	inner	845.2.m.h.316.5		12
13.5	odd	4		845.2.e.k.146.1		6
13.6	odd	12		845.2.e.k.191.1		6
13.7	odd	12		845.2.e.i.191.3		6
13.8	odd	4		845.2.e.i.146.3		6
13.9	even	3	inner	845.2.m.h.316.2		12
13.10	even	6		65.2.c.a.51.2	✓	6
13.11	odd	12		845.2.a.k.1.1		3
13.12	even	2	inner	845.2.m.h.361.2		12
39.2	even	12		7605.2.a.cc.1.1		3
39.11	even	12		7605.2.a.bs.1.3		3
39.23	odd	6		585.2.b.g.181.5		6
39.29	odd	6		585.2.b.g.181.2		6
52.3	odd	6		1040.2.k.d.961.6		6
52.23	odd	6		1040.2.k.d.961.5		6
65.3	odd	12		325.2.d.e.324.5		6
65.23	odd	12		325.2.d.f.324.1		6
65.24	odd	12		4225.2.a.bc.1.3		3
65.29	even	6		325.2.c.g.51.2		6
65.42	odd	12		325.2.d.f.324.2		6
65.49	even	6		325.2.c.g.51.5		6
65.54	odd	12		4225.2.a.be.1.1		3
65.62	odd	12		325.2.d.e.324.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.2	✓	6	13.10	even	6
65.2.c.a.51.5	yes	6	13.3	even	3
325.2.c.g.51.2		6	65.29	even	6
325.2.c.g.51.5		6	65.49	even	6
325.2.d.e.324.5		6	65.3	odd	12
325.2.d.e.324.6		6	65.62	odd	12
325.2.d.f.324.1		6	65.23	odd	12
325.2.d.f.324.2		6	65.42	odd	12
585.2.b.g.181.2		6	39.29	odd	6
585.2.b.g.181.5		6	39.23	odd	6
845.2.a.i.1.3		3	13.2	odd	12
845.2.a.k.1.1		3	13.11	odd	12
845.2.e.i.146.3		6	13.8	odd	4
845.2.e.i.191.3		6	13.7	odd	12
845.2.e.k.146.1		6	13.5	odd	4
845.2.e.k.191.1		6	13.6	odd	12
845.2.m.h.316.2		12	13.9	even	3	inner
845.2.m.h.316.5		12	13.4	even	6	inner
845.2.m.h.361.2		12	13.12	even	2	inner
845.2.m.h.361.5		12	1.1	even	1	trivial
1040.2.k.d.961.5		6	52.23	odd	6
1040.2.k.d.961.6		6	52.3	odd	6
4225.2.a.bc.1.3		3	65.24	odd	12
4225.2.a.be.1.1		3	65.54	odd	12
7605.2.a.bs.1.3		3	39.11	even	12
7605.2.a.cc.1.1		3	39.2	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80664 - 1.04307i) q^{2} +(1.54307 + 2.67267i) q^{3} +(1.17597 - 2.03684i) q^{4} +1.00000i q^{5} +(5.57553 + 3.21903i) q^{6} +(-1.17081 - 0.675970i) q^{7} -0.734191i q^{8} +(-3.26210 + 5.65012i) q^{9} +(1.04307 + 1.80664i) q^{10} +(3.23390 - 1.86710i) q^{11} +7.25839 q^{12} -2.82032 q^{14} +(-2.67267 + 1.54307i) q^{15} +(1.58613 + 2.74726i) q^{16} +(-1.35194 + 2.34163i) q^{17} +13.6103i q^{18} +(-0.379379 - 0.219035i) q^{19} +(2.03684 + 1.17597i) q^{20} -4.17226i q^{21} +(3.89500 - 6.74635i) q^{22} +(-2.54307 - 4.40472i) q^{23} +(1.96225 - 1.13290i) q^{24} -1.00000 q^{25} -10.8761 q^{27} +(-2.75368 + 1.58984i) q^{28} +(0.675970 + 1.17081i) q^{29} +(-3.21903 + 5.57553i) q^{30} -6.43807i q^{31} +(7.00279 + 4.04307i) q^{32} +(9.98025 + 5.76210i) q^{33} +5.64064i q^{34} +(0.675970 - 1.17081i) q^{35} +(7.67226 + 13.2887i) q^{36} +(6.36697 - 3.67597i) q^{37} -0.913870 q^{38} +0.734191 q^{40} +(5.95491 - 3.43807i) q^{41} +(-4.35194 - 7.53778i) q^{42} +(-0.104996 + 0.181858i) q^{43} -8.78259i q^{44} +(-5.65012 - 3.26210i) q^{45} +(-9.18882 - 5.30516i) q^{46} -1.35194i q^{47} +(-4.89500 + 8.47840i) q^{48} +(-2.58613 - 4.47931i) q^{49} +(-1.80664 + 1.04307i) q^{50} -8.34452 q^{51} -1.46838 q^{53} +(-19.6493 + 11.3445i) q^{54} +(1.86710 + 3.23390i) q^{55} +(-0.496291 + 0.859601i) q^{56} -1.35194i q^{57} +(2.44247 + 1.41016i) q^{58} +(1.96225 + 1.13290i) q^{59} +7.25839i q^{60} +(-1.76210 + 3.05205i) q^{61} +(-6.71533 - 11.6313i) q^{62} +(7.63862 - 4.41016i) q^{63} +10.5242 q^{64} +24.0410 q^{66} +(-9.98025 + 5.76210i) q^{67} +(3.17968 + 5.50737i) q^{68} +(7.84823 - 13.5935i) q^{69} -2.82032i q^{70} +(-0.379379 - 0.219035i) q^{71} +(4.14827 + 2.39500i) q^{72} -3.69646i q^{73} +(7.66855 - 13.2823i) q^{74} +(-1.54307 - 2.67267i) q^{75} +(-0.892277 + 0.515156i) q^{76} -5.04840 q^{77} +15.0484 q^{79} +(-2.74726 + 1.58613i) q^{80} +(-6.99629 - 12.1179i) q^{81} +(7.17226 - 12.4227i) q^{82} -0.475800i q^{83} +(-8.49822 - 4.90645i) q^{84} +(-2.34163 - 1.35194i) q^{85} +0.438069i q^{86} +(-2.08613 + 3.61328i) q^{87} +(-1.37080 - 2.37430i) q^{88} +(-9.56819 + 5.52420i) q^{89} -13.6103 q^{90} -11.9623 q^{92} +(17.2068 - 9.93436i) q^{93} +(-1.41016 - 2.44247i) q^{94} +(0.219035 - 0.379379i) q^{95} +24.9549i q^{96} +(-2.85453 - 1.64806i) q^{97} +(-9.34442 - 5.39500i) q^{98} +24.3626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 10 q^{4} - 6 q^{9} - 2 q^{10} + 16 q^{14} - 10 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} - 12 q^{25} - 56 q^{27} + 4 q^{29} - 20 q^{30} + 4 q^{35} + 34 q^{36} - 40 q^{38} - 12 q^{40} - 44 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) \) 12 * q + 4 * q^3 + 10 * q^4 - 6 * q^9 - 2 * q^10 + 16 * q^14 - 10 * q^16 - 8 * q^17 + 24 * q^22 - 16 * q^23 - 12 * q^25 - 56 * q^27 + 4 * q^29 - 20 * q^30 + 4 * q^35 + 34 * q^36 - 40 * q^38 - 12 * q^40 - 44 * q^42 - 24 * q^43 - 36 * q^48 - 2 * q^49 + 16 * q^51 + 24 * q^53 + 12 * q^55 + 48 * q^56 + 12 * q^61 - 8 * q^62 + 60 * q^64 + 48 * q^66 + 88 * q^68 + 32 * q^69 - 20 * q^74 - 4 * q^75 + 72 * q^77 + 48 * q^79 - 30 * q^81 + 28 * q^82 + 4 * q^87 - 60 * q^88 - 68 * q^90 - 40 * q^92 + 8 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

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Database

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