LMFDB - Embedded newform 425.3.u.e.401.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.7
Character	$\chi$	$=$	425.401
Dual form			425.3.u.e.301.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.369527 - 0.892116i) q^{2} +(-2.03052 - 1.35675i) q^{3} +(2.16911 + 2.16911i) q^{4} +(-1.96072 + 1.31011i) q^{6} +(-3.61453 - 0.718974i) q^{7} +(6.30510 - 2.61166i) q^{8} +(-1.16190 - 2.80507i) q^{9} +(2.67188 + 3.99876i) q^{11} +(-1.46148 - 7.34736i) q^{12} +(-1.64069 + 1.64069i) q^{13} +(-1.97707 + 2.95890i) q^{14} +5.68035i q^{16} +(2.30902 - 16.8425i) q^{17} -2.93181 q^{18} +(13.1725 - 31.8012i) q^{19} +(6.36391 + 6.36391i) q^{21} +(4.55469 - 0.905984i) q^{22} +(-2.03220 + 1.35787i) q^{23} +(-16.3460 - 3.25143i) q^{24} +(0.857405 + 2.06996i) q^{26} +(-5.73438 + 28.8287i) q^{27} +(-6.28076 - 9.39982i) q^{28} +(-10.1660 - 51.1081i) q^{29} +(8.78233 - 13.1437i) q^{31} +(30.2879 + 12.5457i) q^{32} -11.7447i q^{33} +(-14.1722 - 8.28365i) q^{34} +(3.56422 - 8.60478i) q^{36} +(-6.16017 - 4.11609i) q^{37} +(-23.5028 - 23.5028i) q^{38} +(5.55746 - 1.10545i) q^{39} +(13.6935 + 2.72380i) q^{41} +(8.02899 - 3.32572i) q^{42} +(-18.3147 - 44.2156i) q^{43} +(-2.87813 + 14.4693i) q^{44} +(0.460427 + 2.31472i) q^{46} +(23.0835 - 23.0835i) q^{47} +(7.70683 - 11.5341i) q^{48} +(-32.7222 - 13.5540i) q^{49} +(-27.5396 + 31.0663i) q^{51} -7.11764 q^{52} +(4.77734 - 11.5335i) q^{53} +(23.5995 + 15.7687i) q^{54} +(-24.6677 + 4.90671i) q^{56} +(-69.8934 + 46.7013i) q^{57} +(-49.3510 - 9.81653i) q^{58} +(-25.1448 + 10.4153i) q^{59} +(-13.3880 + 67.3061i) q^{61} +(-8.48040 - 12.6918i) q^{62} +(2.18294 + 10.9744i) q^{63} +(6.31796 - 6.31796i) q^{64} +(-10.4776 - 4.33997i) q^{66} -63.2487i q^{67} +(41.5416 - 31.5246i) q^{68} +5.96872 q^{69} +(-34.6942 - 23.1819i) q^{71} +(-14.6518 - 14.6518i) q^{72} +(-52.0944 + 10.3622i) q^{73} +(-5.94838 + 3.97458i) q^{74} +(97.5527 - 40.4076i) q^{76} +(-6.78259 - 16.3746i) q^{77} +(1.06744 - 5.36639i) q^{78} +(-36.8708 - 55.1810i) q^{79} +(31.4350 - 31.4350i) q^{81} +(7.49005 - 11.2097i) q^{82} +(109.522 + 45.3657i) q^{83} +27.6080i q^{84} -46.2132 q^{86} +(-48.6987 + 117.569i) q^{87} +(27.2899 + 18.2345i) q^{88} +(69.2116 + 69.2116i) q^{89} +(7.10991 - 4.75069i) q^{91} +(-7.35341 - 1.46268i) q^{92} +(-35.6655 + 14.7731i) q^{93} +(-12.0632 - 29.1231i) q^{94} +(-44.4790 - 66.5676i) q^{96} +(7.05322 + 35.4589i) q^{97} +(-24.1835 + 24.1835i) q^{98} +(8.11235 - 12.1410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	0.369527	−	0.892116i	0.184763	−	0.446058i	−0.804174	−	0.594394i	$-0.797392\pi$
$2$	0.369527	−	0.892116i	0.184763	−	0.446058i	0.988937	+	0.148336i	$0.0473918\pi$
$3$	−2.03052	−	1.35675i	−0.676842	−	0.452251i	0.169049	−	0.985608i	$-0.445930\pi$
$3$	−2.03052	−	1.35675i	−0.676842	−	0.452251i	−0.845891	+	0.533357i	$0.820930\pi$
$4$	2.16911	+	2.16911i	0.542276	+	0.542276i
$5$		0			0
$5$		0			0
$6$	−1.96072	+	1.31011i	−0.326786	+	0.218351i
$7$	−3.61453	−	0.718974i	−0.516361	−	0.102711i	−0.0699708	−	0.997549i	$-0.522291\pi$
$7$	−3.61453	−	0.718974i	−0.516361	−	0.102711i	−0.446390	+	0.894838i	$0.647291\pi$
$8$	6.30510	−	2.61166i	0.788138	−	0.326457i
$9$	−1.16190	−	2.80507i	−0.129100	−	0.311675i
$10$		0			0
$11$	2.67188	+	3.99876i	0.242898	+	0.363523i	0.932809	−	0.360372i	$-0.117350\pi$
$11$	2.67188	+	3.99876i	0.242898	+	0.363523i	−0.689910	+	0.723895i	$0.742350\pi$
$12$	−1.46148	−	7.34736i	−0.121790	−	0.612280i
$13$	−1.64069	+	1.64069i	−0.126207	+	0.126207i	−0.767389	−	0.641182i	$-0.778444\pi$
$13$	−1.64069	+	1.64069i	−0.126207	+	0.126207i	0.641182	+	0.767389i	$0.278444\pi$
$14$	−1.97707	+	2.95890i	−0.141219	+	0.211350i
$15$		0			0
$16$			5.68035i			0.355022i
$17$	2.30902	−	16.8425i	0.135825	−	0.990733i
$17$	2.30902	−	16.8425i	0.135825	−	0.990733i
$18$	−2.93181			−0.162878
$19$	13.1725	−	31.8012i	0.693289	−	1.67375i	−0.0447581	−	0.998998i	$-0.514252\pi$
$19$	13.1725	−	31.8012i	0.693289	−	1.67375i	0.738047	−	0.674749i	$-0.235748\pi$
$20$		0			0
$21$	6.36391	+	6.36391i	0.303044	+	0.303044i
$22$	4.55469	−	0.905984i	0.207031	−	0.0411811i
$23$	−2.03220	+	1.35787i	−0.0883563	+	0.0590378i	−0.598964	−	0.800776i	$-0.704421\pi$
$23$	−2.03220	+	1.35787i	−0.0883563	+	0.0590378i	0.510607	+	0.859814i	$0.329421\pi$
$24$	−16.3460	−	3.25143i	−0.681085	−	0.135476i
$25$		0			0
$26$	0.857405	+	2.06996i	0.0329771	+	0.0796138i
$27$	−5.73438	+	28.8287i	−0.212385	+	1.06773i
$28$	−6.28076	−	9.39982i	−0.224313	−	0.335708i
$29$	−10.1660	−	51.1081i	−0.350553	−	1.76235i	−0.605940	−	0.795510i	$-0.707203\pi$
$29$	−10.1660	−	51.1081i	−0.350553	−	1.76235i	0.255387	−	0.966839i	$-0.417797\pi$
$30$		0			0
$31$	8.78233	−	13.1437i	0.283301	−	0.423990i	−0.662339	−	0.749204i	$-0.730436\pi$
$31$	8.78233	−	13.1437i	0.283301	−	0.423990i	0.945640	+	0.325214i	$0.105436\pi$
$32$	30.2879	+	12.5457i	0.946498	+	0.392052i
$33$		−	11.7447i		−	0.355899i
$34$	−14.1722	−	8.28365i	−0.416829	−	0.243637i
$35$		0			0
$36$	3.56422	−	8.60478i	0.0990061	−	0.239022i
$37$	−6.16017	−	4.11609i	−0.166491	−	0.111246i	0.469533	−	0.882915i	$-0.344422\pi$
$37$	−6.16017	−	4.11609i	−0.166491	−	0.111246i	−0.636024	+	0.771669i	$0.719422\pi$
$38$	−23.5028	−	23.5028i	−0.618494	−	0.618494i
$39$	5.55746	−	1.10545i	0.142499	−	0.0283448i
$40$		0			0
$41$	13.6935	+	2.72380i	0.333987	+	0.0664342i	0.359235	−	0.933247i	$-0.383038\pi$
$41$	13.6935	+	2.72380i	0.333987	+	0.0664342i	−0.0252481	+	0.999681i	$0.508038\pi$
$42$	8.02899	−	3.32572i	0.191166	−	0.0791837i
$43$	−18.3147	−	44.2156i	−0.425923	−	1.02827i	−0.980568	−	0.196182i	$-0.937146\pi$
$43$	−18.3147	−	44.2156i	−0.425923	−	1.02827i	0.554645	−	0.832087i	$-0.312854\pi$
$44$	−2.87813	+	14.4693i	−0.0654120	+	0.328848i
$45$		0			0
$46$	0.460427	+	2.31472i	0.0100093	+	0.0503201i
$47$	23.0835	−	23.0835i	0.491138	−	0.491138i	−0.417527	−	0.908665i	$-0.637103\pi$
$47$	23.0835	−	23.0835i	0.491138	−	0.491138i	0.908665	+	0.417527i	$0.137103\pi$
$48$	7.70683	−	11.5341i	0.160559	−	0.240293i
$49$	−32.7222	−	13.5540i	−0.667800	−	0.276612i
$50$		0			0
$51$	−27.5396	+	31.0663i	−0.539992	+	0.609142i
$52$	−7.11764			−0.136878
$53$	4.77734	−	11.5335i	0.0901386	−	0.217614i	−0.872381	−	0.488827i	$-0.837425\pi$
$53$	4.77734	−	11.5335i	0.0901386	−	0.217614i	0.962519	+	0.271213i	$0.0874249\pi$
$54$	23.5995	+	15.7687i	0.437029	+	0.292013i
$55$		0			0
$56$	−24.6677	+	4.90671i	−0.440494	+	0.0876197i
$57$	−69.8934	+	46.7013i	−1.22620	+	0.819321i
$58$	−49.3510	−	9.81653i	−0.850880	−	0.169250i
$59$	−25.1448	+	10.4153i	−0.426183	+	0.176531i	−0.585457	−	0.810704i	$-0.699085\pi$
$59$	−25.1448	+	10.4153i	−0.426183	+	0.176531i	0.159274	+	0.987234i	$0.449085\pi$
$60$		0			0
$61$	−13.3880	+	67.3061i	−0.219476	+	1.10338i	0.701174	+	0.712990i	$0.252660\pi$
$61$	−13.3880	+	67.3061i	−0.219476	+	1.10338i	−0.920650	+	0.390389i	$0.872340\pi$
$62$	−8.48040	−	12.6918i	−0.136781	−	0.204707i
$63$	2.18294	+	10.9744i	0.0346499	+	0.174197i
$64$	6.31796	−	6.31796i	0.0987181	−	0.0987181i
$65$		0			0
$66$	−10.4776	−	4.33997i	−0.158752	−	0.0657571i
$67$		−	63.2487i		−	0.944011i	−0.881596	−	0.472005i	$-0.843530\pi$
$67$		−	63.2487i		−	0.944011i	0.881596	−	0.472005i	$-0.156470\pi$
$68$	41.5416	−	31.5246i	0.610906	−	0.463596i
$69$	5.96872			0.0865031
$70$		0			0
$71$	−34.6942	−	23.1819i	−0.488651	−	0.326506i	0.286717	−	0.958015i	$-0.407436\pi$
$71$	−34.6942	−	23.1819i	−0.488651	−	0.326506i	−0.775369	+	0.631509i	$0.782436\pi$
$72$	−14.6518	−	14.6518i	−0.203497	−	0.203497i
$73$	−52.0944	+	10.3622i	−0.713622	+	0.141948i	−0.538533	−	0.842604i	$-0.681021\pi$
$73$	−52.0944	+	10.3622i	−0.713622	+	0.141948i	−0.175089	+	0.984553i	$0.556021\pi$
$74$	−5.94838	+	3.97458i	−0.0803835	+	0.0537105i
$75$		0			0
$76$	97.5527	−	40.4076i	1.28359	−	0.531679i
$77$	−6.78259	−	16.3746i	−0.0880856	−	0.212657i
$78$	1.06744	−	5.36639i	0.0136852	−	0.0687999i
$79$	−36.8708	−	55.1810i	−0.466718	−	0.698494i	0.521206	−	0.853431i	$-0.325482\pi$
$79$	−36.8708	−	55.1810i	−0.466718	−	0.698494i	−0.987924	+	0.154937i	$0.950482\pi$
$80$		0			0
$81$	31.4350	−	31.4350i	0.388087	−	0.388087i
$82$	7.49005	−	11.2097i	0.0913421	−	0.136703i
$83$	109.522	+	45.3657i	1.31955	+	0.546574i	0.927655	−	0.373437i	$-0.121821\pi$
$83$	109.522	+	45.3657i	1.31955	+	0.546574i	0.391891	+	0.920012i	$0.371821\pi$
$84$			27.6080i			0.328667i
$85$		0			0
$86$	−46.2132			−0.537363
$87$	−48.6987	+	117.569i	−0.559755	+	1.35137i
$88$	27.2899	+	18.2345i	0.310112	+	0.207210i
$89$	69.2116	+	69.2116i	0.777658	+	0.777658i	0.979432	−	0.201774i	$-0.0646707\pi$
$89$	69.2116	+	69.2116i	0.777658	+	0.777658i	−0.201774	+	0.979432i	$0.564671\pi$
$90$		0			0
$91$	7.10991	−	4.75069i	0.0781309	−	0.0522054i
$92$	−7.35341	−	1.46268i	−0.0799283	−	0.0158987i
$93$	−35.6655	+	14.7731i	−0.383500	+	0.158851i
$94$	−12.0632	−	29.1231i	−0.128332	−	0.309820i
$95$		0			0
$96$	−44.4790	−	66.5676i	−0.463323	−	0.693412i
$97$	7.05322	+	35.4589i	0.0727136	+	0.365556i	0.999960	−	0.00889462i	$-0.00283128\pi$
$97$	7.05322	+	35.4589i	0.0727136	+	0.365556i	−0.927247	+	0.374451i	$0.877831\pi$
$98$	−24.1835	+	24.1835i	−0.246770	+	0.246770i
$99$	8.11235	−	12.1410i	0.0819429	−	0.122636i
$100$		0			0
$101$			124.397i			1.23166i	0.787880	+	0.615829i	$0.211179\pi$
$101$			124.397i			1.23166i	−0.787880	+	0.615829i	$0.788821\pi$
$102$	17.5381	+	36.0483i	0.171942	+	0.353415i
$103$	163.755			1.58985			0.794925	−	0.606707i	$-0.207510\pi$
$103$	163.755			1.58985			0.794925	+	0.606707i	$0.207510\pi$
$104$	−6.05978	+	14.6296i	−0.0582671	+	0.140669i
$105$		0			0
$106$	−8.52390	−	8.52390i	−0.0804141	−	0.0804141i
$107$	4.64598	−	0.924143i	0.0434204	−	0.00863685i	−0.173332	−	0.984863i	$-0.555453\pi$
$107$	4.64598	−	0.924143i	0.0434204	−	0.00863685i	0.216753	+	0.976227i	$0.430453\pi$
$108$	−74.9709	+	50.0940i	−0.694175	+	0.463833i
$109$	39.3336	+	7.82394i	0.360859	+	0.0717792i	0.372190	−	0.928157i	$-0.378607\pi$
$109$	39.3336	+	7.82394i	0.360859	+	0.0717792i	−0.0113314	+	0.999936i	$0.503607\pi$
$110$		0			0
$111$	6.92385	+	16.7156i	0.0623770	+	0.150591i
$112$	4.08402	−	20.5318i	0.0364645	−	0.183319i
$113$	64.0781	+	95.8997i	0.567063	+	0.848670i	0.998571	−	0.0534391i	$-0.0170183\pi$
$113$	64.0781	+	95.8997i	0.567063	+	0.848670i	−0.431508	+	0.902109i	$0.642018\pi$
$114$	15.8355	+	79.6105i	0.138908	+	0.698337i
$115$		0			0
$116$	88.8077	−	132.910i	0.765583	−	1.14578i
$117$	6.50856	+	2.69593i	0.0556287	+	0.0230422i
$118$			26.2808i			0.222719i
$119$	−20.4553	+	59.2174i	−0.171893	+	0.497625i
$120$		0			0
$121$	37.4536	−	90.4210i	0.309534	−	0.747281i
$122$	55.0977	+	36.8151i	0.451620	+	0.301763i
$123$	−24.1094	−	24.1094i	−0.196011	−	0.196011i
$124$	47.5599	−	9.46024i	0.383547	−	0.0762923i
$125$		0			0
$126$	10.5971	+	2.10789i	0.0841039	+	0.0167293i
$127$	221.668	−	91.8180i	1.74542	−	0.722976i	0.747120	−	0.664689i	$-0.231436\pi$
$127$	221.668	−	91.8180i	1.74542	−	0.722976i	0.998300	−	0.0582871i	$-0.0185639\pi$
$128$	46.8810	+	113.181i	0.366258	+	0.884225i
$129$	−22.8012	+	114.629i	−0.176753	+	0.888599i
$130$		0			0
$131$	42.5779	+	214.053i	0.325022	+	1.63400i	0.705147	+	0.709061i	$0.250881\pi$
$131$	42.5779	+	214.053i	0.325022	+	1.63400i	−0.380126	+	0.924935i	$0.624119\pi$
$132$	25.4754	−	25.4754i	0.192995	−	0.192995i
$133$	−70.4765	+	105.476i	−0.529899	+	0.793049i
$134$	−56.4252	−	23.3721i	−0.421084	−	0.174419i
$135$		0			0
$136$	−29.4281	−	112.224i	−0.216383	−	0.825175i
$137$	−153.897			−1.12334			−0.561668	−	0.827362i	$-0.689840\pi$
$137$	−153.897			−1.12334			−0.561668	+	0.827362i	$0.689840\pi$
$138$	2.20560	−	5.32479i	0.0159826	−	0.0385854i
$139$	152.360	+	101.804i	1.09611	+	0.732401i	0.965856	−	0.259079i	$-0.0834191\pi$
$139$	152.360	+	101.804i	1.09611	+	0.732401i	0.130259	+	0.991480i	$0.458419\pi$
$140$		0			0
$141$	−78.1901	+	15.5530i	−0.554540	+	0.110305i
$142$	−33.5014	+	22.3849i	−0.235926	+	0.157640i
$143$	−10.9444	−	2.17698i	−0.0765344	−	0.0152236i
$144$	15.9338	−	6.60000i	0.110651	−	0.0458333i
$145$		0			0
$146$	−10.0060	+	50.3034i	−0.0685341	+	0.344544i
$147$	48.0539	+	71.9177i	0.326897	+	0.489236i
$148$	−4.43381	−	22.2903i	−0.0299582	−	0.150610i
$149$	40.3951	−	40.3951i	0.271108	−	0.271108i	−0.558438	−	0.829546i	$-0.688599\pi$
$149$	40.3951	−	40.3951i	0.271108	−	0.271108i	0.829546	+	0.558438i	$0.188599\pi$
$150$		0			0
$151$	−54.5664	−	22.6021i	−0.361367	−	0.149683i	0.194610	−	0.980881i	$-0.437656\pi$
$151$	−54.5664	−	22.6021i	−0.361367	−	0.149683i	−0.555977	+	0.831198i	$0.687656\pi$
$152$		−	234.912i		−	1.54547i
$153$	−49.9272	+	13.0923i	−0.326322	+	0.0855704i
$154$	−17.1144			−0.111133
$155$		0			0
$156$	14.4525	+	9.65688i	0.0926445	+	0.0619031i
$157$	−3.65977	−	3.65977i	−0.0233107	−	0.0233107i	0.695355	−	0.718666i	$-0.255247\pi$
$157$	−3.65977	−	3.65977i	−0.0233107	−	0.0233107i	−0.718666	+	0.695355i	$0.755247\pi$
$158$	−62.8526	+	12.5022i	−0.397801	+	0.0791276i
$159$	−25.3487	+	16.9374i	−0.159426	+	0.106525i
$160$		0			0
$161$	8.32169	−	3.44696i	0.0516875	−	0.0214097i
$162$	−16.4276	−	39.6598i	−0.101405	−	0.244813i
$163$	21.4707	−	107.940i	0.131722	−	0.662211i	−0.857345	−	0.514743i	$-0.827887\pi$
$163$	21.4707	−	107.940i	0.131722	−	0.662211i	0.989067	−	0.147469i	$-0.0471125\pi$
$164$	23.7944	+	35.6108i	0.145088	+	0.217139i
$165$		0			0
$166$	80.9429	−	80.9429i	0.487608	−	0.487608i
$167$	−118.557	+	177.433i	−0.709923	+	1.06247i	0.284671	+	0.958625i	$0.408116\pi$
$167$	−118.557	+	177.433i	−0.709923	+	1.06247i	−0.994593	+	0.103849i	$0.966884\pi$
$168$	56.7455	+	23.5048i	0.337771	+	0.139909i
$169$			163.616i			0.968144i
$170$		0			0
$171$	−104.510			−0.611169
$172$	56.1817	−	135.635i	0.326638	−	0.788574i
$173$	−150.906	−	100.832i	−0.872287	−	0.582844i	0.0368589	−	0.999320i	$-0.488265\pi$
$173$	−150.906	−	100.832i	−0.872287	−	0.582844i	−0.909146	+	0.416477i	$0.863265\pi$
$174$	86.8898	+	86.8898i	0.499367	+	0.499367i
$175$		0			0
$176$	−22.7143	+	15.1772i	−0.129059	+	0.0862343i
$177$	65.1881	+	12.9667i	0.368295	+	0.0732583i
$178$	87.3203	−	36.1693i	0.490564	−	0.203198i
$179$	−13.9147	−	33.5930i	−0.0777356	−	0.187670i	0.880234	−	0.474540i	$-0.157385\pi$
$179$	−13.9147	−	33.5930i	−0.0777356	−	0.187670i	−0.957970	+	0.286869i	$0.907385\pi$
$180$		0			0
$181$	−115.240	−	172.469i	−0.636686	−	0.952868i	−0.999777	−	0.0211143i	$-0.993279\pi$
$181$	−115.240	−	172.469i	−0.636686	−	0.952868i	0.363091	−	0.931754i	$-0.381721\pi$
$182$	−1.61087	−	8.09838i	−0.00885092	−	0.0444966i
$183$	118.503	−	118.503i	0.647555	−	0.647555i
$184$	−9.26691	+	13.8689i	−0.0503636	+	0.0753745i
$185$		0			0
$186$			37.2768i			0.200413i
$187$	73.5183	−	35.7679i	0.393146	−	0.191272i
$188$	100.141			0.532665
$189$	41.4541	−	100.079i	0.219334	−	0.529519i
$190$		0			0
$191$	−131.649	−	131.649i	−0.689260	−	0.689260i	0.272808	−	0.962068i	$-0.412048\pi$
$191$	−131.649	−	131.649i	−0.689260	−	0.689260i	−0.962068	+	0.272808i	$0.912048\pi$
$192$	−21.4007	+	4.25686i	−0.111462	+	0.0221712i
$193$	−224.053	+	149.707i	−1.16089	+	0.775685i	−0.978237	−	0.207492i	$-0.933470\pi$
$193$	−224.053	+	149.707i	−1.16089	+	0.775685i	−0.182657	+	0.983177i	$0.558470\pi$
$194$	34.2399	+	6.81073i	0.176494	+	0.0351069i
$195$		0			0
$196$	−41.5779	−	100.378i	−0.212132	−	0.512133i
$197$	−42.9951	+	216.151i	−0.218249	+	1.09721i	0.703877	+	0.710322i	$0.251451\pi$
$197$	−42.9951	+	216.151i	−0.218249	+	1.09721i	−0.922126	+	0.386890i	$0.873549\pi$
$198$	−7.83344	−	11.7236i	−0.0395628	−	0.0592100i
$199$	−48.6247	−	244.453i	−0.244345	−	1.22841i	−0.886826	−	0.462104i	$-0.847095\pi$
$199$	−48.6247	−	244.453i	−0.244345	−	1.22841i	0.642480	−	0.766302i	$-0.277905\pi$
$200$		0			0
$201$	−85.8129	+	128.428i	−0.426930	+	0.638946i
$202$	110.977	+	45.9682i	0.549391	+	0.227565i
$203$			192.041i			0.946013i
$204$	−127.122	+	7.64973i	−0.623148	+	0.0374987i
$205$		0			0
$206$	60.5117	−	146.088i	0.293746	−	0.709166i
$207$	6.17013	+	4.12275i	0.0298074	+	0.0199167i
$208$	−9.31967	−	9.31967i	−0.0448061	−	0.0448061i
$209$	162.361	−	32.2955i	0.776845	−	0.154524i
$210$		0			0
$211$	9.91358	+	1.97193i	0.0469838	+	0.00934565i	0.218526	−	0.975831i	$-0.429875\pi$
$211$	9.91358	+	1.97193i	0.0469838	+	0.00934565i	−0.171542	+	0.985177i	$0.554875\pi$
$212$	35.3800	−	14.6549i	0.166887	−	0.0691268i
$213$	38.9953	+	94.1430i	0.183077	+	0.441986i
$214$	0.892371	−	4.48625i	0.00416996	−	0.0209638i
$215$		0			0
$216$	39.1348	+	196.744i	0.181180	+	0.910852i
$217$	−41.1939	+	41.1939i	−0.189834	+	0.189834i
$218$	21.5147	−	32.1990i	0.0986912	−	0.147702i
$219$	119.838	+	49.6385i	0.547206	+	0.226660i
$220$		0			0
$221$	23.8448	+	31.4216i	0.107895	+	0.142179i
$222$	17.4709			0.0786975
$223$	93.5097	−	225.752i	0.419326	−	1.01234i	−0.563217	−	0.826309i	$-0.690437\pi$
$223$	93.5097	−	225.752i	0.419326	−	1.01234i	0.982543	−	0.186034i	$-0.0595634\pi$
$224$	−100.457	−	67.1229i	−0.448467	−	0.299656i
$225$		0			0
$226$	109.232	−	21.7277i	0.483329	−	0.0961401i
$227$	−329.953	+	220.468i	−1.45354	+	0.971223i	−0.456880	+	0.889528i	$0.651033\pi$
$227$	−329.953	+	220.468i	−1.45354	+	0.971223i	−0.996657	+	0.0816943i	$0.973967\pi$
$228$	−252.906	−	50.3062i	−1.10924	−	0.220641i
$229$	−387.156	+	160.365i	−1.69064	+	0.700286i	−0.999743	−	0.0226689i	$-0.992784\pi$
$229$	−387.156	+	160.365i	−1.69064	+	0.700286i	−0.690896	+	0.722954i	$0.742784\pi$
$230$		0			0
$231$	−8.44410	+	42.4514i	−0.0365546	+	0.183772i
$232$	−197.575	−	295.692i	−0.851616	−	1.27453i
$233$	49.9022	+	250.875i	0.214172	+	1.07672i	0.926909	+	0.375286i	$0.122455\pi$
$233$	49.9022	+	250.875i	0.214172	+	1.07672i	−0.712737	+	0.701432i	$0.752545\pi$
$234$	4.81017	−	4.81017i	0.0205563	−	0.0205563i
$235$		0			0
$236$	−77.1336	−	31.9498i	−0.326837	−	0.135380i
$237$			162.071i			0.683843i
$238$	45.2700	+	40.1309i	0.190210	+	0.168617i
$239$	226.338			0.947021			0.473511	−	0.880788i	$-0.342987\pi$
$239$	226.338			0.947021			0.473511	+	0.880788i	$0.342987\pi$
$240$		0			0
$241$	380.956	+	254.547i	1.58073	+	1.05621i	0.962885	+	0.269911i	$0.0869943\pi$
$241$	380.956	+	254.547i	1.58073	+	1.05621i	0.617846	+	0.786299i	$0.288006\pi$
$242$	−66.8260	−	66.8260i	−0.276140	−	0.276140i
$243$	152.979	−	30.4294i	0.629543	−	0.125224i
$244$	−175.034	+	116.954i	−0.717353	+	0.479320i
$245$		0			0
$246$	−30.4175	+	12.5993i	−0.123648	+	0.0512168i
$247$	30.5639	+	73.7877i	0.123740	+	0.298736i
$248$	21.0467	−	105.809i	0.0848656	−	0.426648i
$249$	−160.838	−	240.711i	−0.645935	−	0.966710i
$250$		0			0
$251$	74.4069	−	74.4069i	0.296442	−	0.296442i	−0.543177	−	0.839618i	$-0.682779\pi$
$251$	74.4069	−	74.4069i	0.296442	−	0.296442i	0.839618	+	0.543177i	$0.182779\pi$
$252$	−19.0696	+	28.5396i	−0.0756729	+	0.113253i
$253$	−10.8596	−	4.49818i	−0.0429232	−	0.0177794i
$254$		−	231.683i		−	0.912138i
$255$		0			0
$256$	154.034			0.601695
$257$	31.6976	−	76.5248i	0.123337	−	0.297762i	−0.850136	−	0.526563i	$-0.823481\pi$
$257$	31.6976	−	76.5248i	0.123337	−	0.297762i	0.973473	+	0.228801i	$0.0734805\pi$
$258$	93.8371	+	62.6999i	0.363710	+	0.243023i
$259$	19.3067	+	19.3067i	0.0745433	+	0.0745433i
$260$		0			0
$261$	−131.550	+	87.8990i	−0.504023	+	0.336778i
$262$	206.694	+	41.1140i	0.788909	+	0.156924i
$263$	2.23755	−	0.926824i	0.00850780	−	0.00352405i	−0.378425	−	0.925632i	$-0.623534\pi$
$263$	2.23755	−	0.926824i	0.00850780	−	0.00352405i	0.386933	+	0.922108i	$0.373534\pi$
$264$	−30.6730	−	74.0513i	−0.116186	−	0.280497i
$265$		0			0
$266$	68.0535	+	101.849i	0.255840	+	0.382892i
$267$	−46.6328	−	234.439i	−0.174655	−	0.878048i
$268$	137.193	−	137.193i	0.511915	−	0.511915i
$269$	79.6966	−	119.274i	0.296270	−	0.443399i	−0.653233	−	0.757157i	$-0.726588\pi$
$269$	79.6966	−	119.274i	0.296270	−	0.443399i	0.949503	+	0.313757i	$0.101588\pi$
$270$		0			0
$271$		−	51.5741i		−	0.190310i	−0.995462	−	0.0951551i	$-0.969665\pi$
$271$		−	51.5741i		−	0.190310i	0.995462	−	0.0951551i	$-0.0303347\pi$
$272$	95.6710	+	13.1160i	0.351732	+	0.0482207i
$273$	−20.8824			−0.0764922
$274$	−56.8691	+	137.294i	−0.207552	+	0.501074i
$275$		0			0
$276$	12.9468	+	12.9468i	0.0469086	+	0.0469086i
$277$	350.729	−	69.7643i	1.26617	−	0.251857i	0.484080	−	0.875024i	$-0.339154\pi$
$277$	350.729	−	69.7643i	1.26617	−	0.251857i	0.782089	+	0.623167i	$0.214154\pi$
$278$	147.122	−	98.3037i	0.529215	−	0.353610i
$279$	−47.0732	−	9.36344i	−0.168721	−	0.0335607i
$280$		0			0
$281$	182.827	+	441.383i	0.650630	+	1.57076i	0.811866	+	0.583844i	$0.198452\pi$
$281$	182.827	+	441.383i	0.650630	+	1.57076i	−0.161236	+	0.986916i	$0.551548\pi$
$282$	−15.0183	+	75.5019i	−0.0532563	+	0.267737i
$283$	−122.046	−	182.654i	−0.431257	−	0.645422i	0.550661	−	0.834729i	$-0.314376\pi$
$283$	−122.046	−	182.654i	−0.431257	−	0.645422i	−0.981918	+	0.189307i	$0.939376\pi$
$284$	−24.9714	−	125.540i	−0.0879273	−	0.442041i
$285$		0			0
$286$	−5.98638	+	8.95925i	−0.0209314	+	0.0313260i
$287$	−47.5371	−	19.6905i	−0.165634	−	0.0686080i
$288$		−	99.5367i		−	0.345614i
$289$	−278.337	−	77.7792i	−0.963103	−	0.269132i
$290$		0			0
$291$	33.7873	−	81.5697i	0.116108	−	0.280308i
$292$	−135.475	−	90.5216i	−0.463956	−	0.310005i
$293$	−352.092	−	352.092i	−1.20168	−	1.20168i	−0.973656	−	0.228023i	$-0.926774\pi$
$293$	−352.092	−	352.092i	−1.20168	−	1.20168i	−0.228023	−	0.973656i	$-0.573226\pi$
$294$	81.9161	−	16.2941i	0.278626	−	0.0554222i
$295$		0			0
$296$	−49.5903	−	9.86412i	−0.167535	−	0.0333247i
$297$	−130.600	+	54.0965i	−0.439732	+	0.182143i
$298$	−21.1101	−	50.9642i	−0.0708392	−	0.171021i
$299$	1.10636	−	5.56203i	0.00370019	−	0.0186021i
$300$		0			0
$301$	34.4091	+	172.986i	0.114316	+	0.574705i
$302$	−40.3275	+	40.3275i	−0.133535	+	0.133535i
$303$	168.777	−	252.592i	0.557019	−	0.833637i
$304$	180.642	+	74.8243i	0.594217	+	0.246133i
$305$		0			0
$306$	−6.76960	+	49.3788i	−0.0221229	+	0.161369i
$307$	−153.821			−0.501046			−0.250523	−	0.968111i	$-0.580603\pi$
$307$	−153.821			−0.501046			−0.250523	+	0.968111i	$0.580603\pi$
$308$	20.8061	−	50.2304i	0.0675524	−	0.163086i
$309$	−332.508	−	222.175i	−1.07608	−	0.719012i
$310$		0			0
$311$	−301.680	+	60.0079i	−0.970032	+	0.192951i	−0.654582	−	0.755991i	$-0.727155\pi$
$311$	−301.680	+	60.0079i	−0.970032	+	0.192951i	−0.315450	+	0.948942i	$0.602155\pi$
$312$	32.1533	−	21.4841i	0.103055	−	0.0688594i
$313$	−234.843	−	46.7133i	−0.750299	−	0.149244i	−0.194894	−	0.980824i	$-0.562436\pi$
$313$	−234.843	−	46.7133i	−0.750299	−	0.149244i	−0.555404	+	0.831581i	$0.687436\pi$
$314$	−4.61733	+	1.91256i	−0.0147049	+	0.00609095i
$315$		0			0
$316$	39.7168	−	199.670i	0.125686	−	0.631867i
$317$	−163.783	−	245.119i	−0.516666	−	0.773245i	0.477782	−	0.878479i	$-0.341441\pi$
$317$	−163.783	−	245.119i	−0.516666	−	0.773245i	−0.994448	+	0.105233i	$0.966441\pi$
$318$	5.74316	+	28.8728i	0.0180602	+	0.0907950i
$319$	177.206	−	177.206i	0.555506	−	0.555506i
$320$		0			0
$321$	−10.6876	−	4.42695i	−0.0332947	−	0.0137911i
$322$		−	8.69766i		−	0.0270114i
$323$	−505.195	−	295.287i	−1.56407	−	0.914200i
$324$	136.372			0.420900
$325$		0			0
$326$	−88.3614	−	59.0412i	−0.271047	−	0.181108i
$327$	−69.2527	−	69.2527i	−0.211782	−	0.211782i
$328$	93.4524	−	18.5888i	0.284916	−	0.0566733i
$329$	−100.032	+	66.8394i	−0.304049	+	0.203159i
$330$		0			0
$331$	325.328	−	134.755i	0.982865	−	0.407116i	0.167379	−	0.985893i	$-0.446470\pi$
$331$	325.328	−	134.755i	0.982865	−	0.407116i	0.815486	+	0.578777i	$0.196470\pi$
$332$	139.163	+	335.968i	0.419165	+	1.01195i
$333$	−4.38845	+	22.0622i	−0.0131785	+	0.0662529i
$334$	114.481	+	171.333i	0.342758	+	0.512973i
$335$		0			0
$336$	−36.1492	+	36.1492i	−0.107587	+	0.107587i
$337$	104.502	−	156.398i	0.310095	−	0.464090i	−0.643386	−	0.765542i	$-0.722471\pi$
$337$	104.502	−	156.398i	0.310095	−	0.464090i	0.953482	+	0.301451i	$0.0974711\pi$
$338$	145.965	+	60.4606i	0.431849	+	0.178878i
$339$		−	281.665i		−	0.830870i
$340$		0			0
$341$	76.0238			0.222944
$342$	−38.6192	+	93.2349i	−0.112922	+	0.272617i
$343$	258.678	+	172.843i	0.754165	+	0.503917i
$344$	−230.952	−	230.952i	−0.671372	−	0.671372i
$345$		0			0
$346$	−145.718	+	97.3654i	−0.421149	+	0.281403i
$347$	355.397	+	70.6929i	1.02420	+	0.203726i	0.678485	−	0.734614i	$-0.262637\pi$
$347$	355.397	+	70.6929i	1.02420	+	0.203726i	0.345714	+	0.938340i	$0.387637\pi$
$348$	−360.652	+	149.387i	−1.03636	+	0.429273i
$349$	121.253	+	292.730i	0.347429	+	0.838767i	0.996922	+	0.0783995i	$0.0249810\pi$
$349$	121.253	+	292.730i	0.347429	+	0.838767i	−0.649493	+	0.760367i	$0.725019\pi$
$350$		0			0
$351$	−37.8905	−	56.7071i	−0.107950	−	0.161559i
$352$	30.7588	+	154.635i	0.0873828	+	0.439303i
$353$	77.6740	−	77.6740i	0.220040	−	0.220040i	−0.588475	−	0.808515i	$-0.700272\pi$
$353$	77.6740	−	77.6740i	0.220040	−	0.220040i	0.808515	+	0.588475i	$0.200272\pi$
$354$	35.6566	−	53.3639i	0.100725	−	0.150745i
$355$		0			0
$356$			300.254i			0.843411i
$357$	121.878	−	92.4896i	0.341396	−	0.259074i
$358$	−35.1107			−0.0980746
$359$	181.912	−	439.175i	0.506719	−	1.22333i	−0.439042	−	0.898467i	$-0.644682\pi$
$359$	181.912	−	439.175i	0.506719	−	1.22333i	0.945761	−	0.324862i	$-0.105318\pi$
$360$		0			0
$361$	−582.536	−	582.536i	−1.61367	−	1.61367i
$362$	−196.447	+	39.0757i	−0.542671	+	0.107944i
$363$	−198.729	+	132.787i	−0.547464	+	0.365804i
$364$	25.7269	+	5.11740i	0.0706783	+	0.0140588i
$365$		0			0
$366$	−61.9282	−	149.508i	−0.169203	−	0.408492i
$367$	25.3166	−	127.275i	0.0689824	−	0.346798i	−0.930844	−	0.365416i	$-0.880927\pi$
$367$	25.3166	−	127.275i	0.0689824	−	0.346798i	0.999827	+	0.0186181i	$0.00592667\pi$
$368$	−7.71317	−	11.5436i	−0.0209597	−	0.0313684i
$369$	−8.26998	−	41.5760i	−0.0224119	−	0.112672i
$370$		0			0
$371$	−25.5601	+	38.2535i	−0.0688953	+	0.103109i
$372$	−109.407	−	45.3177i	−0.294104	−	0.121822i
$373$			602.500i			1.61528i	0.589676	+	0.807640i	$0.299256\pi$
$373$			602.500i			1.61528i	−0.589676	+	0.807640i	$0.700744\pi$
$374$	−4.74213	−	78.8041i	−0.0126795	−	0.210706i
$375$		0			0
$376$	85.2575	−	205.830i	0.226749	−	0.547420i
$377$	100.532	+	67.1731i	0.266662	+	0.178178i
$378$	−73.9639	−	73.9639i	−0.195672	−	0.195672i
$379$	−345.346	+	68.6936i	−0.911203	+	0.181250i	−0.628365	−	0.777918i	$-0.716276\pi$
$379$	−345.346	+	68.6936i	−0.911203	+	0.181250i	−0.282838	+	0.959168i	$0.591276\pi$
$380$		0			0
$381$	−574.677	−	114.310i	−1.50834	−	0.300027i
$382$	−166.094	+	68.7983i	−0.434800	+	0.180100i
$383$	94.9085	+	229.129i	0.247803	+	0.598249i	0.998017	−	0.0629459i	$-0.0200495\pi$
$383$	94.9085	+	229.129i	0.247803	+	0.598249i	−0.750214	+	0.661195i	$0.770050\pi$
$384$	58.3653	−	293.422i	0.151993	−	0.764121i
$385$		0			0
$386$	50.7628	+	255.202i	0.131510	+	0.661144i
$387$	−102.748	+	102.748i	−0.265499	+	0.265499i
$388$	−61.6150	+	92.2134i	−0.158802	+	0.237663i
$389$	343.713	+	142.371i	0.883581	+	0.365991i	0.777885	−	0.628407i	$-0.216293\pi$
$389$	343.713	+	142.371i	0.883581	+	0.365991i	0.105697	+	0.994398i	$0.466293\pi$
$390$		0			0
$391$	18.1775	+	37.3625i	0.0464897	+	0.0955563i
$392$	−241.715			−0.616621
$393$	203.962	−	492.408i	0.518988	−	1.25295i
$394$	176.944	+	118.230i	0.449096	+	0.300077i
$395$		0			0
$396$	43.9316	−	8.73854i	0.110938	−	0.0220670i
$397$	629.967	−	420.930i	1.58682	−	1.06028i	0.627243	−	0.778824i	$-0.284183\pi$
$397$	629.967	−	420.930i	1.58682	−	1.06028i	0.959575	−	0.281454i	$-0.0908165\pi$
$398$	−236.049	−	46.9530i	−0.593087	−	0.117972i
$399$	286.209	−	118.552i	0.717315	−	0.297122i
$400$		0			0
$401$	78.7581	−	395.944i	0.196404	−	0.987391i	−0.749267	−	0.662268i	$-0.769594\pi$
$401$	78.7581	−	395.944i	0.196404	−	0.987391i	0.945672	−	0.325123i	$-0.105406\pi$
$402$	82.8627	+	124.013i	0.206126	+	0.308489i
$403$	7.15562	+	35.9737i	0.0177559	+	0.0892648i
$404$	−269.831	+	269.831i	−0.667899	+	0.667899i
$405$		0			0
$406$	171.323	+	70.9642i	0.421977	+	0.174789i
$407$		−	35.6307i		−	0.0875448i
$408$	−92.5054	+	267.800i	−0.226729	+	0.656372i
$409$	−439.976			−1.07574			−0.537868	−	0.843029i	$-0.680770\pi$
$409$	−439.976			−1.07574			−0.537868	+	0.843029i	$0.680770\pi$
$410$		0			0
$411$	312.492	+	208.800i	0.760321	+	0.508030i
$412$	355.201	+	355.201i	0.862138	+	0.862138i
$413$	98.3749	−	19.5680i	0.238196	−	0.0473801i
$414$	5.95800	−	3.98101i	0.0143913	−	0.00961596i
$415$		0			0
$416$	−70.2765	+	29.1095i	−0.168934	+	0.0699747i
$417$	−171.248	−	413.430i	−0.410667	−	0.991438i
$418$	31.1852	−	156.779i	0.0746058	−	0.375068i
$419$	353.408	+	528.913i	0.843457	+	1.26232i	0.963002	+	0.269493i	$0.0868562\pi$
$419$	353.408	+	528.913i	0.843457	+	1.26232i	−0.119546	+	0.992829i	$0.538144\pi$
$420$		0			0
$421$	466.115	−	466.115i	1.10716	−	1.10716i	0.113640	−	0.993522i	$-0.463749\pi$
$421$	466.115	−	466.115i	1.10716	−	1.10716i	0.993522	−	0.113640i	$-0.0362510\pi$
$422$	5.42253	−	8.11538i	0.0128496	−	0.0192308i
$423$	−91.5715	−	37.9302i	−0.216481	−	0.0896694i
$424$		−	85.1969i		−	0.200936i
$425$		0			0
$426$	98.3964			0.230977
$427$	96.7827	−	233.654i	0.226657	−	0.547199i
$428$	12.0822	+	8.07306i	0.0282294	+	0.0188623i
$429$	19.2693	+	19.2693i	0.0449168	+	0.0449168i
$430$		0			0
$431$	−30.0089	+	20.0513i	−0.0696262	+	0.0465227i	−0.589896	−	0.807479i	$-0.700831\pi$
$431$	−30.0089	+	20.0513i	−0.0696262	+	0.0465227i	0.520270	+	0.854002i	$0.325831\pi$
$432$	−163.757	−	32.5733i	−0.379067	−	0.0754011i
$433$	29.5441	−	12.2376i	0.0682312	−	0.0282623i	−0.348307	−	0.937381i	$-0.613243\pi$
$433$	29.5441	−	12.2376i	0.0682312	−	0.0282623i	0.416538	+	0.909118i	$0.363243\pi$
$434$	21.5275	+	51.9721i	0.0496026	+	0.119751i
$435$		0			0
$436$	68.3478	+	102.290i	0.156761	+	0.234609i
$437$	16.4128	+	82.5128i	0.0375579	+	0.188816i
$438$	88.5667	−	88.5667i	0.202207	−	0.202207i
$439$	−135.063	+	202.136i	−0.307661	+	0.460447i	−0.952792	−	0.303625i	$-0.901803\pi$
$439$	−135.063	+	202.136i	−0.307661	+	0.460447i	0.645131	+	0.764072i	$0.276803\pi$
$440$		0			0
$441$			107.537i			0.243847i
$442$	36.8430	−	9.66124i	0.0833552	−	0.0218580i
$443$	674.566			1.52272			0.761361	−	0.648328i	$-0.224531\pi$
$443$	674.566			1.52272			0.761361	+	0.648328i	$0.224531\pi$
$444$	−21.2394	+	51.2766i	−0.0478366	+	0.115488i
$445$		0			0
$446$	−166.843	−	166.843i	−0.374088	−	0.374088i
$447$	−136.830	+	27.2171i	−0.306106	+	0.0608883i
$448$	−27.3789	+	18.2940i	−0.0611136	+	0.0408348i
$449$	−514.273	−	102.295i	−1.14538	−	0.227829i	−0.414309	−	0.910136i	$-0.635977\pi$
$449$	−514.273	−	102.295i	−1.14538	−	0.227829i	−0.731066	+	0.682307i	$0.760977\pi$
$450$		0			0
$451$	25.6955	+	62.0345i	0.0569746	+	0.137549i
$452$	−69.0243	+	347.009i	−0.152709	+	0.767719i
$453$	80.1328	+	119.927i	0.176894	+	0.264740i
$454$	74.7563	+	375.825i	0.164661	+	0.827809i
$455$		0			0
$456$	−318.717	+	476.994i	−0.698942	+	1.04604i
$457$	−509.027	−	210.846i	−1.11384	−	0.461369i	−0.251584	−	0.967835i	$-0.580952\pi$
$457$	−509.027	−	210.846i	−1.11384	−	0.461369i	−0.862260	+	0.506466i	$0.830952\pi$
$458$			404.648i			0.883510i
$459$	472.305	+	163.147i	1.02899	+	0.355440i
$460$		0			0
$461$	−93.3130	+	225.278i	−0.202414	+	0.488672i	−0.992192	−	0.124722i	$-0.960196\pi$
$461$	−93.3130	+	225.278i	−0.202414	+	0.488672i	0.789777	+	0.613394i	$0.210196\pi$
$462$	34.7512	+	23.2200i	0.0752192	+	0.0502598i
$463$	260.222	+	260.222i	0.562035	+	0.562035i	0.929885	−	0.367850i	$-0.119906\pi$
$463$	260.222	+	260.222i	0.562035	+	0.562035i	−0.367850	+	0.929885i	$0.619906\pi$
$464$	290.312	−	57.7466i	0.625672	−	0.124454i
$465$		0			0
$466$	242.250	+	48.1865i	0.519850	+	0.103405i
$467$	−38.9983	+	16.1536i	−0.0835081	+	0.0345902i	−0.424046	−	0.905640i	$-0.639391\pi$
$467$	−38.9983	+	16.1536i	−0.0835081	+	0.0345902i	0.340538	+	0.940231i	$0.389391\pi$
$468$	8.26998	+	19.9655i	0.0176709	+	0.0426613i
$469$	−45.4742	+	228.614i	−0.0969599	+	0.487450i
$470$		0			0
$471$	2.46585	+	12.3967i	0.00523535	+	0.0263199i
$472$	−131.339	+	131.339i	−0.278261	+	0.278261i
$473$	127.873	−	191.375i	0.270344	−	0.404598i
$474$	144.586	+	59.8895i	0.305034	+	0.126349i
$475$		0			0
$476$	−172.818	+	84.0790i	−0.363064	+	0.176637i
$477$	−37.9032			−0.0794616
$478$	83.6380	−	201.920i	0.174975	−	0.422427i
$479$	49.4214	+	33.0224i	0.103176	+	0.0689402i	0.606088	−	0.795398i	$-0.292738\pi$
$479$	49.4214	+	33.0224i	0.103176	+	0.0689402i	−0.502912	+	0.864338i	$0.667738\pi$
$480$		0			0
$481$	16.8601	−	3.35368i	0.0350522	−	0.00697231i
$482$	367.859	−	245.795i	0.763193	−	0.509949i
$483$	−21.5741	−	4.29135i	−0.0446668	−	0.00888478i
$484$	277.373	−	114.892i	0.573086	−	0.237380i
$485$		0			0
$486$	29.3833	−	147.720i	0.0604594	−	0.303950i
$487$	314.829	+	471.175i	0.646466	+	0.967504i	0.999491	+	0.0318907i	$0.0101528\pi$
$487$	314.829	+	471.175i	0.646466	+	0.967504i	−0.353026	+	0.935614i	$0.614847\pi$
$488$	91.3678	+	459.337i	0.187229	+	0.941265i
$489$	−190.045	+	190.045i	−0.388641	+	0.388641i
$490$		0			0
$491$	457.623	+	189.554i	0.932022	+	0.386056i	0.796445	−	0.604711i	$-0.206711\pi$
$491$	457.623	+	189.554i	0.932022	+	0.386056i	0.135577	+	0.990767i	$0.456711\pi$
$492$		−	104.592i		−	0.212585i
$493$	−884.260	+	53.2114i	−1.79363	+	0.107934i
$494$	77.1214			0.156116
$495$		0			0
$496$	74.6607	+	49.8867i	0.150526	+	0.100578i
$497$	108.736	+	108.736i	0.218785	+	0.218785i
$498$	−274.176	+	54.5370i	−0.550554	+	0.109512i
$499$	199.361	−	133.209i	0.399522	−	0.266952i	−0.339537	−	0.940593i	$-0.610270\pi$
$499$	199.361	−	133.209i	0.399522	−	0.266952i	0.739059	+	0.673641i	$0.235270\pi$
$500$		0			0
$501$	481.466	−	199.430i	0.961010	−	0.398063i
$502$	−38.8843	−	93.8749i	−0.0774587	−	0.187002i
$503$	−39.5565	+	198.864i	−0.0786411	+	0.395355i	0.921337	+	0.388764i	$0.127098\pi$
$503$	−39.5565	+	198.864i	−0.0786411	+	0.395355i	−0.999978	+	0.00659103i	$0.997902\pi$
$504$	42.4250	+	63.4935i	0.0841767	+	0.125979i
$505$		0			0
$506$	−8.02581	+	8.02581i	−0.0158613	+	0.0158613i
$507$	221.987	−	332.227i	0.437844	−	0.655280i
$508$	679.985	+	281.659i	1.33855	+	0.554447i
$509$			979.909i			1.92516i	0.270990	+	0.962582i	$0.412649\pi$
$509$			979.909i			1.92516i	−0.270990	+	0.962582i	$0.587351\pi$
$510$		0			0
$511$	195.747			0.383066
$512$	−130.604	+	315.307i	−0.255087	+	0.615834i
$513$	841.251	+	562.106i	1.63986	+	1.09572i
$514$	−56.5559	−	56.5559i	−0.110031	−	0.110031i
$515$		0			0
$516$	−298.101	+	199.185i	−0.577716	+	0.386017i
$517$	153.981	+	30.6288i	0.297837	+	0.0592434i
$518$	24.3582	−	10.0895i	0.0470235	−	0.0194778i
$519$	169.614	+	409.484i	0.326809	+	0.788986i
$520$		0			0
$521$	171.777	+	257.082i	0.329706	+	0.493439i	0.958875	−	0.283829i	$-0.0916048\pi$
$521$	171.777	+	257.082i	0.329706	+	0.493439i	−0.629169	+	0.777268i	$0.716605\pi$
$522$	29.8048	+	149.839i	0.0570974	+	0.287048i
$523$	333.555	−	333.555i	0.637772	−	0.637772i	−0.312233	−	0.950005i	$-0.601077\pi$
$523$	333.555	−	333.555i	0.637772	−	0.637772i	0.950005	+	0.312233i	$0.101077\pi$
$524$	−371.949	+	556.660i	−0.709825	+	1.06233i
$525$		0			0
$526$		−	2.33864i		−	0.00444609i
$527$	−201.093	−	178.265i	−0.381582	−	0.338264i
$528$	66.7138			0.126352
$529$	−200.154	+	483.213i	−0.378362	+	0.913447i
$530$		0			0
$531$	58.4315	+	58.4315i	0.110040	+	0.110040i
$532$	−381.659	+	75.9166i	−0.717403	+	0.142700i
$533$	−26.9356	+	17.9978i	−0.0505358	+	0.0337669i
$534$	−226.379	−	45.0295i	−0.423930	−	0.0843250i
$535$		0			0
$536$	−165.184	−	398.790i	−0.308179	−	0.744011i
$537$	−17.3233	+	87.0902i	−0.0322594	+	0.162179i
$538$	−76.9567	−	115.174i	−0.143042	−	0.214078i
$539$	−33.2309	−	167.063i	−0.0616528	−	0.309950i
$540$		0			0
$541$	512.263	−	766.656i	0.946882	−	1.41711i	0.0383645	−	0.999264i	$-0.487785\pi$
$541$	512.263	−	766.656i	0.946882	−	1.41711i	0.908518	−	0.417846i	$-0.137215\pi$
$542$	−46.0101	−	19.0580i	−0.0848895	−	0.0351624i
$543$			506.555i			0.932883i
$544$	281.236	−	481.155i	0.516977	−	0.884477i
$545$		0			0
$546$	−7.71659	+	18.6295i	−0.0141330	+	0.0341200i
$547$	−487.252	−	325.572i	−0.890772	−	0.595195i	0.0237557	−	0.999718i	$-0.492438\pi$
$547$	−487.252	−	325.572i	−0.890772	−	0.595195i	−0.914528	+	0.404523i	$0.867438\pi$
$548$	−333.819	−	333.819i	−0.609159	−	0.609159i
$549$	204.354	−	40.6486i	0.372230	−	0.0740411i
$550$		0			0
$551$	−1759.21	−	349.929i	−3.19276	−	0.635080i
$552$	37.6334	−	15.5883i	0.0681764	−	0.0282396i
$553$	93.5966	+	225.962i	0.169252	+	0.408612i
$554$	67.3658	−	338.671i	0.121599	−	0.611319i
$555$		0			0
$556$	109.662	+	551.308i	0.197234	+	0.991561i
$557$	−195.753	+	195.753i	−0.351442	+	0.351442i	−0.860646	−	0.509204i	$-0.829940\pi$
$557$	−195.753	+	195.753i	−0.351442	+	0.351442i	0.509204	+	0.860646i	$0.329940\pi$
$558$	−25.7481	+	38.5347i	−0.0461435	+	0.0690587i
$559$	102.592	+	42.4952i	0.183529	+	0.0760200i
$560$		0			0
$561$	−197.809	−	27.1187i	−0.352601	−	0.0483399i
$562$	461.325			0.820863
$563$	96.5883	−	233.185i	0.171560	−	0.414183i	−0.814590	−	0.580037i	$-0.803038\pi$
$563$	96.5883	−	233.185i	0.171560	−	0.414183i	0.986150	+	0.165854i	$0.0530381\pi$
$564$	−203.339	−	135.867i	−0.360530	−	0.240898i
$565$		0			0
$566$	−208.048	+	41.3834i	−0.367576	+	0.0731155i
$567$	−136.224	+	91.0217i	−0.240253	+	0.160532i
$568$	−279.294	−	55.5550i	−0.491715	−	0.0978082i
$569$	−434.022	+	179.778i	−0.762781	+	0.315954i	−0.729944	−	0.683507i	$-0.760454\pi$
$569$	−434.022	+	179.778i	−0.762781	+	0.315954i	−0.0328365	+	0.999461i	$0.510454\pi$
$570$		0			0
$571$	158.498	−	796.824i	0.277580	−	1.39549i	−0.550479	−	0.834849i	$-0.685555\pi$
$571$	158.498	−	796.824i	0.277580	−	1.39549i	0.828059	−	0.560640i	$-0.189445\pi$
$572$	−19.0175	−	28.4617i	−0.0332474	−	0.0497582i
$573$	88.7012	+	445.931i	0.154801	+	0.778239i
$574$	−35.1324	+	35.1324i	−0.0612063	+	0.0612063i
$575$		0			0
$576$	−25.0632	−	10.3815i	−0.0435125	−	0.0180235i
$577$			834.634i			1.44651i	0.690583	+	0.723253i	$0.257354\pi$
$577$			834.634i			1.44651i	−0.690583	+	0.723253i	$0.742646\pi$
$578$	−172.241	+	219.567i	−0.297995	+	0.379874i
$579$	658.060			1.13655
$580$		0			0
$581$	−363.255	−	242.719i	−0.625223	−	0.417761i
$582$	−60.2844	−	60.2844i	−0.103581	−	0.103581i
$583$	58.8843	−	11.7128i	0.101002	−	0.0200906i
$584$	−301.398	+	201.388i	−0.516093	+	0.344842i
$585$		0			0
$586$	−444.214	+	184.000i	−0.758045	+	0.313993i
$587$	205.403	+	495.886i	0.349920	+	0.844781i	0.996629	+	0.0820440i	$0.0261448\pi$
$587$	205.403	+	495.886i	0.349920	+	0.844781i	−0.646709	+	0.762737i	$0.723855\pi$
$588$	−51.7632	+	260.231i	−0.0880326	+	0.442570i
$589$	−302.300	−	452.424i	−0.513243	−	0.768122i
$590$		0			0
$591$	380.566	−	380.566i	0.643936	−	0.643936i
$592$	23.3808	−	34.9919i	0.0394946	−	0.0591079i
$593$	−484.571	−	200.716i	−0.817152	−	0.338475i	−0.0653481	−	0.997863i	$-0.520816\pi$
$593$	−484.571	−	200.716i	−0.817152	−	0.338475i	−0.751803	+	0.659387i	$0.770816\pi$
$594$			136.501i			0.229800i
$595$		0			0
$596$	175.243			0.294031
$597$	−232.929	+	562.339i	−0.390165	+	0.941942i
$598$	−4.55315	−	3.04232i	−0.00761396	−	0.00508749i
$599$	−164.659	−	164.659i	−0.274890	−	0.274890i	0.556175	−	0.831065i	$-0.312268\pi$
$599$	−164.659	−	164.659i	−0.274890	−	0.274890i	−0.831065	+	0.556175i	$0.812268\pi$
$600$		0			0
$601$	127.119	−	84.9381i	0.211512	−	0.141328i	−0.445302	−	0.895380i	$-0.646904\pi$
$601$	127.119	−	84.9381i	0.211512	−	0.141328i	0.656814	+	0.754053i	$0.271904\pi$
$602$	167.039	+	33.2261i	0.277473	+	0.0551928i
$603$	−177.417	+	73.4887i	−0.294225	+	0.121872i
$604$	−69.3338	−	167.387i	−0.114791	−	0.277130i
$605$		0			0
$606$	−162.974	−	243.908i	−0.268934	−	0.402488i
$607$	−217.351	−	1092.70i	−0.358074	−	1.80016i	−0.568649	−	0.822580i	$-0.692534\pi$
$607$	−217.351	−	1092.70i	−0.358074	−	1.80016i	0.210576	−	0.977578i	$-0.432466\pi$
$608$	797.935	−	797.935i	1.31239	−	1.31239i
$609$	260.552	−	389.943i	0.427836	−	0.640301i
$610$		0			0
$611$			75.7454i			0.123970i
$612$	−136.696	−	79.8988i	−0.223359	−	0.130554i
$613$	−130.322			−0.212597			−0.106298	−	0.994334i	$-0.533900\pi$
$613$	−130.322			−0.212597			−0.106298	+	0.994334i	$0.533900\pi$
$614$	−56.8410	+	137.226i	−0.0925750	+	0.223496i
$615$		0			0
$616$	−85.5299	−	85.5299i	−0.138847	−	0.138847i
$617$	98.2934	−	19.5518i	0.159309	−	0.0316885i	−0.114792	−	0.993390i	$-0.536620\pi$
$617$	98.2934	−	19.5518i	0.159309	−	0.0316885i	0.274100	+	0.961701i	$0.411620\pi$
$618$	−321.076	+	214.536i	−0.519541	+	0.347146i
$619$	426.866	+	84.9089i	0.689606	+	0.137171i	0.527440	−	0.849592i	$-0.323152\pi$
$619$	426.866	+	84.9089i	0.689606	+	0.137171i	0.162166	+	0.986763i	$0.448152\pi$
$620$		0			0
$621$	−27.4922	−	66.3721i	−0.0442709	−	0.106879i
$622$	−57.9448	+	291.308i	−0.0931589	+	0.468341i
$623$	−200.406	−	299.928i	−0.321678	−	0.481426i
$624$	6.27932	+	31.5683i	0.0100630	+	0.0505902i
$625$		0			0
$626$	−128.455	+	192.246i	−0.205199	+	0.307102i
$627$	−373.494	−	154.706i	−0.595685	−	0.246741i
$628$		−	15.8769i		−	0.0252816i
$629$	−83.5490	+	94.2482i	−0.132828	+	0.149838i
$630$		0			0
$631$	46.4257	−	112.082i	0.0735748	−	0.177625i	−0.882813	−	0.469724i	$-0.844354\pi$
$631$	46.4257	−	112.082i	0.0735748	−	0.177625i	0.956388	+	0.292099i	$0.0943535\pi$
$632$	−376.588	−	251.628i	−0.595867	−	0.398145i
$633$	−17.4543	−	17.4543i	−0.0275740	−	0.0275740i
$634$	−279.197	+	55.5357i	−0.440373	+	0.0875957i
$635$		0			0
$636$	−91.7230	−	18.2448i	−0.144219	−	0.0286869i
$637$	75.9247	−	31.4490i	0.119191	−	0.0493706i
$638$	−92.6063	−	223.571i	−0.145151	−	0.350425i
$639$	−24.7159	+	124.255i	−0.0386790	+	0.194452i
$640$		0			0
$641$	−47.9641	−	241.132i	−0.0748270	−	0.376181i	0.925167	−	0.379560i	$-0.123924\pi$
$641$	−47.9641	−	241.132i	−0.0748270	−	0.376181i	−0.999994	+	0.00337889i	$0.998924\pi$
$642$	−7.89872	+	7.89872i	−0.0123033	+	0.0123033i
$643$	63.5318	−	95.0820i	0.0988052	−	0.147872i	−0.778773	−	0.627306i	$-0.784158\pi$
$643$	63.5318	−	95.0820i	0.0988052	−	0.147872i	0.877578	+	0.479433i	$0.159158\pi$
$644$	25.5274	+	10.5738i	0.0396389	+	0.0164190i
$645$		0			0
$646$	−450.113	+	341.576i	−0.696770	+	0.528756i
$647$	534.514			0.826143			0.413071	−	0.910699i	$-0.364456\pi$
$647$	534.514			0.826143			0.413071	+	0.910699i	$0.364456\pi$
$648$	116.103	−	280.299i	0.179172	−	0.432560i
$649$	−108.832	−	72.7194i	−0.167692	−	0.112048i
$650$		0			0
$651$	139.535	−	27.7553i	0.214340	−	0.0426349i
$652$	280.706	−	187.562i	0.430531	−	0.287672i
$653$	−788.185	−	156.780i	−1.20702	−	0.240092i	−0.449728	−	0.893166i	$-0.648479\pi$
$653$	−788.185	−	156.780i	−1.20702	−	0.240092i	−0.757294	+	0.653074i	$0.773479\pi$
$654$	−87.3722	+	36.1907i	−0.133597	+	0.0553375i
$655$		0			0
$656$	−15.4721	+	77.7837i	−0.0235856	+	0.118573i
$657$	89.5953	+	134.089i	0.136370	+	0.204093i
$658$	22.6639	+	113.939i	0.0344437	+	0.173160i
$659$	382.598	−	382.598i	0.580574	−	0.580574i	−0.354487	−	0.935061i	$-0.615344\pi$
$659$	382.598	−	382.598i	0.580574	−	0.580574i	0.935061	+	0.354487i	$0.115344\pi$
$660$		0			0
$661$	555.991	+	230.299i	0.841136	+	0.348410i	0.761301	−	0.648398i	$-0.224561\pi$
$661$	555.991	+	230.299i	0.841136	+	0.348410i	0.0798346	+	0.996808i	$0.474561\pi$
$662$		−	340.027i		−	0.513635i
$663$	−5.78616	−	96.1538i	−0.00872724	−	0.145028i
$664$	809.029			1.21842
$665$		0			0
$666$	18.0604	+	12.0676i	0.0271177	+	0.0181195i
$667$	90.0575	+	90.0575i	0.135019	+	0.135019i
$668$	−642.034	+	127.709i	−0.961129	+	0.191180i
$669$	−496.164	+	331.526i	−0.741650	+	0.495555i
$670$		0			0
$671$	−304.912	+	126.299i	−0.454414	+	0.188225i
$672$	112.910	+	272.589i	0.168021	+	0.405639i
$673$	212.613	−	1068.88i	0.315918	−	1.58823i	−0.417648	−	0.908609i	$-0.637146\pi$
$673$	212.613	−	1068.88i	0.315918	−	1.58823i	0.733566	−	0.679618i	$-0.237854\pi$
$674$	−100.909	−	151.021i	−0.149717	−	0.224067i
$675$		0			0
$676$	−354.901	+	354.901i	−0.525001	+	0.525001i
$677$	239.398	−	358.284i	0.353616	−	0.529223i	−0.611432	−	0.791297i	$-0.709406\pi$
$677$	239.398	−	358.284i	0.353616	−	0.529223i	0.965048	+	0.262074i	$0.0844063\pi$
$678$	−251.278	−	104.083i	−0.370616	−	0.153514i
$679$		−	133.238i		−	0.196227i
$680$		0			0
$681$	969.098			1.42305
$682$	28.0928	−	67.8221i	0.0411918	−	0.0994458i
$683$	448.957	+	299.984i	0.657331	+	0.439215i	0.838990	−	0.544147i	$-0.183147\pi$
$683$	448.957	+	299.984i	0.657331	+	0.439215i	−0.181659	+	0.983362i	$0.558147\pi$
$684$	−226.693	−	226.693i	−0.331422	−	0.331422i
$685$		0			0
$686$	249.785	−	166.901i	0.364118	−	0.243296i
$687$	1003.71	+	199.650i	1.46100	+	0.290611i
$688$	251.160	−	104.034i	0.365058	−	0.151212i
$689$	11.0848	+	26.7610i	0.0160882	+	0.0388404i
$690$		0			0
$691$	595.542	+	891.292i	0.861855	+	1.28986i	0.955721	+	0.294273i	$0.0950774\pi$
$691$	595.542	+	891.292i	0.861855	+	1.28986i	−0.0938662	+	0.995585i	$0.529923\pi$
$692$	−108.615	−	546.046i	−0.156958	−	0.789083i
$693$	−38.0513	+	38.0513i	−0.0549081	+	0.0549081i
$694$	194.395	−	290.933i	0.280108	−	0.419211i
$695$		0			0
$696$			868.470i			1.24780i
$697$	77.4940	−	224.342i	0.111182	−	0.321869i
$698$	305.955			0.438331
$699$	239.048	−	577.113i	0.341986	−	0.825627i
$700$		0			0
$701$	747.664	+	747.664i	1.06657	+	1.06657i	0.997620	+	0.0689480i	$0.0219642\pi$
$701$	747.664	+	747.664i	1.06657	+	1.06657i	0.0689480	+	0.997620i	$0.478036\pi$
$702$	−64.5909	+	12.8479i	−0.0920099	+	0.0183019i
$703$	−212.041	+	141.681i	−0.301624	+	0.201538i
$704$	42.1448	+	8.38313i	0.0598648	+	0.0119079i
$705$		0			0
$706$	−40.5916	−	97.9969i	−0.0574952	−	0.138806i
$707$	89.4385	−	449.638i	0.126504	−	0.635980i
$708$	113.274	+	169.526i	0.159991	+	0.239444i
$709$	−26.7092	−	134.276i	−0.0376716	−	0.189388i	0.957367	−	0.288873i	$-0.0932805\pi$
$709$	−26.7092	−	134.276i	−0.0376716	−	0.189388i	−0.995039	+	0.0994848i	$0.968281\pi$
$710$		0			0
$711$	−111.947	+	167.540i	−0.157450	+	0.235640i
$712$	617.143	+	255.629i	0.866774	+	0.359030i
$713$			38.6358i			0.0541877i
$714$	−37.4741	−	142.907i	−0.0524848	−	0.200150i
$715$		0			0
$716$	42.6843	−	103.049i	0.0596150	−	0.143923i
$717$	−459.585	−	307.085i	−0.640983	−	0.428291i
$718$	−324.574	−	324.574i	−0.452053	−	0.452053i
$719$	−178.522	+	35.5103i	−0.248292	+	0.0493884i	−0.317667	−	0.948202i	$-0.602900\pi$
$719$	−178.522	+	35.5103i	−0.248292	+	0.0493884i	0.0693750	+	0.997591i	$0.477900\pi$
$720$		0			0
$721$	−591.895	−	117.735i	−0.820937	−	0.163294i
$722$	−734.953	+	304.427i	−1.01794	+	0.421645i
$723$	−428.184	−	1033.73i	−0.592232	−	1.42977i
$724$	124.136	−	624.072i	0.171458	−	0.861977i
$725$		0			0
$726$	45.0254	+	226.358i	0.0620185	+	0.311788i
$727$	−235.573	+	235.573i	−0.324035	+	0.324035i	−0.850313	−	0.526278i	$-0.823587\pi$
$727$	−235.573	+	235.573i	−0.324035	+	0.324035i	0.526278	+	0.850313i	$0.323587\pi$
$728$	32.4215	−	48.5223i	0.0445351	−	0.0666514i
$729$	−721.559	−	298.880i	−0.989793	−	0.409986i
$730$		0			0
$731$	−786.988	+	206.370i	−1.07659	+	0.282312i
$732$	514.089			0.702307
$733$	258.816	−	624.836i	0.353091	−	0.852437i	−0.643144	−	0.765745i	$-0.722370\pi$
$733$	258.816	−	624.836i	0.353091	−	0.852437i	0.996235	−	0.0866918i	$-0.0276295\pi$
$734$	−104.189	−	69.6168i	−0.141947	−	0.0948458i
$735$		0			0
$736$	−78.5864	+	15.6318i	−0.106775	+	0.0212389i
$737$	252.916	−	168.993i	0.343170	−	0.229299i
$738$	−40.1466	−	7.98566i	−0.0543992	−	0.0108207i
$739$	−398.638	+	165.121i	−0.539429	+	0.223439i	−0.635727	−	0.771914i	$-0.719300\pi$
$739$	−398.638	+	165.121i	−0.539429	+	0.223439i	0.0962982	+	0.995353i	$0.469300\pi$
$740$		0			0
$741$	38.0510	−	191.295i	0.0513509	−	0.258158i
$742$	24.6814	+	36.9383i	0.0332633	+	0.0497821i
$743$	181.893	+	914.439i	0.244809	+	1.23074i	0.886119	+	0.463457i	$0.153391\pi$
$743$	181.893	+	914.439i	0.244809	+	1.23074i	−0.641310	+	0.767282i	$0.721609\pi$
$744$	−186.292	+	186.292i	−0.250393	+	0.250393i
$745$		0			0
$746$	537.500	+	222.640i	0.720509	+	0.298445i
$747$		−	359.929i		−	0.481832i
$748$	237.053	+	81.8847i	0.316916	+	0.109472i
$749$	−17.4574			−0.0233077
$750$		0			0
$751$	277.138	+	185.177i	0.369025	+	0.246574i	0.726231	−	0.687451i	$-0.241271\pi$
$751$	277.138	+	185.177i	0.369025	+	0.246574i	−0.357206	+	0.934026i	$0.616271\pi$
$752$	131.122	+	131.122i	0.174365	+	0.174365i
$753$	−252.037	+	50.1332i	−0.334710	+	0.0665780i
$754$	97.0753	−	64.8637i	0.128747	−	0.0860261i
$755$		0			0
$756$	307.001	−	127.164i	0.406086	−	0.168206i
$757$	−160.378	−	387.187i	−0.211860	−	0.511475i	0.781849	−	0.623468i	$-0.214277\pi$
$757$	−160.378	−	387.187i	−0.211860	−	0.511475i	−0.993709	+	0.111993i	$0.964277\pi$
$758$	−66.3319	+	333.473i	−0.0875091	+	0.439938i
$759$	15.9477	+	23.8674i	0.0210115	+	0.0314459i
$760$		0			0
$761$	947.231	−	947.231i	1.24472	−	1.24472i	0.286698	−	0.958021i	$-0.407442\pi$
$761$	947.231	−	947.231i	1.24472	−	1.24472i	0.958021	−	0.286698i	$-0.0925575\pi$
$762$	−314.337	+	470.438i	−0.412516	+	0.617373i
$763$	−136.547	−	56.5596i	−0.178961	−	0.0741280i
$764$		−	571.120i		−	0.747539i
$765$		0			0
$766$	239.481			0.312639
$767$	24.1664	−	58.3430i	0.0315077	−	0.0760664i
$768$	−312.770	−	208.986i	−0.407252	−	0.272117i
$769$	−420.026	−	420.026i	−0.546198	−	0.546198i	0.379141	−	0.925339i	$-0.376219\pi$
$769$	−420.026	−	420.026i	−0.546198	−	0.546198i	−0.925339	+	0.379141i	$0.876219\pi$
$770$		0			0
$771$	−168.188	+	112.380i	−0.218143	+	0.145758i
$772$	−810.724	−	161.263i	−1.05016	−	0.208890i
$773$	272.733	−	112.970i	0.352825	−	0.146145i	−0.199230	−	0.979953i	$-0.563844\pi$
$773$	272.733	−	112.970i	0.352825	−	0.146145i	0.552054	+	0.833808i	$0.313844\pi$
$774$	53.6951	+	129.631i	0.0693735	+	0.167483i
$775$		0			0
$776$	137.078	+	205.152i	0.176647	+	0.264371i
$777$	−13.0083	−	65.3972i	−0.0167417	−	0.0841663i
$778$	254.022	−	254.022i	0.326507	−	0.326507i
$779$	266.997	−	399.590i	0.342744	−	0.512952i
$780$		0			0
$781$		−	200.673i		−	0.256944i
$782$	40.0488	−	2.40998i	0.0512133	−	0.00308182i
$783$	1531.68			1.95616
$784$	76.9914	−	185.874i	0.0982033	−	0.237084i
$785$		0			0
$786$	−363.916	−	363.916i	−0.462998	−	0.462998i
$787$	816.561	−	162.424i	1.03756	−	0.206384i	0.353216	−	0.935542i	$-0.385088\pi$
$787$	816.561	−	162.424i	1.03756	−	0.206384i	0.684346	+	0.729158i	$0.260088\pi$
$788$	−562.115	+	375.593i	−0.713344	+	0.476641i
$789$	−5.80087	−	1.15387i	−0.00735218	−	0.00146244i
$790$		0			0
$791$	−162.663	−	392.703i	−0.205642	−	0.496463i
$792$	19.4411	−	97.7368i	0.0245468	−	0.123405i
$793$	−88.4627	−	132.394i	−0.111554	−	0.166953i
$794$	−142.729	−	717.548i	−0.179760	−	0.903713i
$795$		0			0
$796$	424.772	−	635.716i	0.533633	−	0.798638i
$797$	807.124	+	334.322i	1.01270	+	0.419475i	0.826440	−	0.563025i	$-0.190363\pi$
$797$	807.124	+	334.322i	1.01270	+	0.419475i	0.186263	+	0.982500i	$0.440363\pi$
$798$		−	299.139i		−	0.374861i
$799$	−335.482	−	442.083i	−0.419878	−	0.553295i
$800$		0			0
$801$	113.727	−	274.560i	0.141981	−	0.342772i
$802$	−324.125	−	216.573i	−0.404146	−	0.270041i
$803$	−180.626	−	180.626i	−0.224939	−	0.224939i
$804$	−464.711	+	92.4368i	−0.577999	+	0.114971i
$805$		0			0
$806$	34.7369	+	6.90960i	0.0430979	+	0.00857271i
$807$	−323.652	+	134.061i	−0.401056	+	0.166123i
$808$	324.884	+	784.339i	0.402084	+	0.970716i
$809$	−136.966	+	688.576i	−0.169303	+	0.851145i	0.798993	+	0.601340i	$0.205366\pi$
$809$	−136.966	+	688.576i	−0.169303	+	0.851145i	−0.968296	+	0.249805i	$0.919634\pi$
$810$		0			0
$811$	234.186	+	1177.33i	0.288762	+	1.45171i	0.803985	+	0.594650i	$0.202709\pi$
$811$	234.186	+	1177.33i	0.288762	+	1.45171i	−0.515222	+	0.857056i	$0.672291\pi$
$812$	−416.557	+	416.557i	−0.513001	+	0.513001i
$813$	−69.9733	+	104.722i	−0.0860680	+	0.128810i
$814$	−31.7867	−	13.1665i	−0.0390501	−	0.0161751i
$815$		0			0
$816$	−176.467	−	156.434i	−0.216259	−	0.191709i
$817$	−1647.36			−2.01635
$818$	−162.583	+	392.510i	−0.198757	+	0.479841i
$819$	−21.5870	−	14.4240i	−0.0263578	−	0.0176117i
$820$		0			0
$821$	−52.7387	+	10.4904i	−0.0642371	+	0.0127776i	−0.227104	−	0.973870i	$-0.572926\pi$
$821$	−52.7387	+	10.4904i	−0.0642371	+	0.0127776i	0.162867	+	0.986648i	$0.447926\pi$
$822$	301.748	−	201.622i	0.367091	−	0.245282i
$823$	−1145.72	−	227.898i	−1.39213	−	0.276911i	−0.558621	−	0.829423i	$-0.688669\pi$
$823$	−1145.72	−	227.898i	−1.39213	−	0.276911i	−0.833505	+	0.552512i	$0.813669\pi$
$824$	1032.49	−	427.671i	1.25302	−	0.519019i
$825$		0			0
$826$	18.8952	−	94.9927i	0.0228756	−	0.115003i
$827$	328.920	+	492.264i	0.397727	+	0.595241i	0.975242	−	0.221139i	$-0.0709776\pi$
$827$	328.920	+	492.264i	0.397727	+	0.595241i	−0.577515	+	0.816380i	$0.695978\pi$
$828$	4.44099	+	22.3263i	0.00536351	+	0.0269642i
$829$	565.240	−	565.240i	0.681833	−	0.681833i	−0.278580	−	0.960413i	$-0.589864\pi$
$829$	565.240	−	565.240i	0.681833	−	0.681833i	0.960413	+	0.278580i	$0.0898637\pi$
$830$		0			0
$831$	−806.817	−	334.194i	−0.970898	−	0.402159i
$832$			20.7316i			0.0249178i
$833$	−303.839	+	519.826i	−0.364752	+	0.624041i
$834$	−432.108			−0.518115
$835$		0			0
$836$	422.230	+	282.125i	0.505059	+	0.337470i
$837$	328.554	+	328.554i	0.392538	+	0.392538i
$838$	602.446	−	119.834i	0.718909	−	0.143000i
$839$	1264.66	−	845.022i	1.50735	−	1.00718i	0.519033	−	0.854754i	$-0.326292\pi$
$839$	1264.66	−	845.022i	1.50735	−	1.00718i	0.988315	−	0.152423i	$-0.0487077\pi$
$840$		0			0
$841$	−1731.71	+	717.297i	−2.05911	+	0.852910i
$842$	−243.587	−	588.071i	−0.289296	−	0.698422i
$843$	227.614	−	1144.29i	0.270004	−	1.35740i
$844$	17.2263	+	25.7809i	0.0204103	+	0.0305461i
$845$		0			0
$846$	−67.6762	+	67.6762i	−0.0799956	+	0.0799956i
$847$	−200.387	+	299.901i	−0.236585	+	0.354074i
$848$	65.5145	+	27.1370i	0.0772576	+	0.0320012i
$849$			536.470i			0.631885i
$850$		0			0
$851$	18.1078			0.0212782
$852$	−119.621	+	288.791i	−0.140400	+	0.338957i
$853$	−216.944	−	144.957i	−0.254330	−	0.169938i	0.421869	−	0.906657i	$-0.361374\pi$
$853$	−216.944	−	144.957i	−0.254330	−	0.169938i	−0.676199	+	0.736719i	$0.736374\pi$
$854$	−172.683	−	172.683i	−0.202205	−	0.202205i
$855$		0			0
$856$	26.8798	−	17.9605i	0.0314017	−	0.0209819i
$857$	−1194.09	−	237.520i	−1.39334	−	0.277153i	−0.559350	−	0.828932i	$-0.688949\pi$
$857$	−1194.09	−	237.520i	−1.39334	−	0.277153i	−0.833990	+	0.551779i	$0.813949\pi$
$858$	24.3110	−	10.0699i	0.0283345	−	0.0117365i
$859$	−137.942	−	333.021i	−0.160584	−	0.387685i	0.823023	−	0.568008i	$-0.192286\pi$
$859$	−137.942	−	333.021i	−0.160584	−	0.387685i	−0.983607	+	0.180323i	$0.942286\pi$
$860$		0			0
$861$	69.8100	+	104.478i	0.0810802	+	0.121345i
$862$	6.79900	+	34.1809i	0.00788747	+	0.0396530i
$863$	503.780	−	503.780i	0.583754	−	0.583754i	−0.352178	−	0.935933i	$-0.614559\pi$
$863$	503.780	−	503.780i	0.583754	−	0.583754i	0.935933	+	0.352178i	$0.114559\pi$
$864$	−535.358	+	801.220i	−0.619627	+	0.927338i
$865$		0			0
$866$		−	30.8789i		−	0.0356569i
$867$	459.643	+	535.567i	0.530153	+	0.617724i
$868$	−178.708			−0.205885
$869$	122.141	−	294.874i	0.140553	−	0.339326i
$870$		0			0
$871$	103.771	+	103.771i	0.119140	+	0.119140i
$872$	268.436	−	53.3952i	0.307839	−	0.0612330i
$873$	91.2698	−	60.9845i	0.104547	−	0.0698563i
$874$	79.6760	+	15.8485i	0.0911624	+	0.0181333i
$875$		0			0
$876$	152.270	+	367.613i	0.173824	+	0.419649i
$877$	142.612	−	716.957i	0.162613	−	0.817511i	−0.810242	−	0.586095i	$-0.800664\pi$
$877$	142.612	−	716.957i	0.162613	−	0.817511i	0.972855	−	0.231415i	$-0.0743356\pi$
$878$	130.420	+	195.187i	0.148542	+	0.222309i
$879$	237.229	+	1192.63i	0.269886	+	1.35681i
$880$		0			0
$881$	206.168	−	308.553i	0.234016	−	0.350230i	−0.695812	−	0.718224i	$-0.744955\pi$
$881$	206.168	−	308.553i	0.234016	−	0.350230i	0.929828	+	0.367994i	$0.119955\pi$
$882$	95.9352	+	39.7377i	0.108770	+	0.0450540i
$883$			1572.78i			1.78118i	0.454805	+	0.890591i	$0.349709\pi$
$883$			1572.78i			1.78118i	−0.454805	+	0.890591i	$0.650291\pi$
$884$	−16.4348	+	119.879i	−0.0185914	+	0.135609i
$885$		0			0
$886$	249.270	−	601.791i	0.281343	−	0.679223i
$887$	792.790	+	529.725i	0.893788	+	0.597210i	0.915395	−	0.402557i	$-0.131878\pi$
$887$	792.790	+	529.725i	0.893788	+	0.597210i	−0.0216074	+	0.999767i	$0.506878\pi$
$888$	87.3112	+	87.3112i	0.0983234	+	0.0983234i
$889$	−867.241	+	172.505i	−0.975524	+	0.194044i
$890$		0			0
$891$	209.692	+	41.7103i	0.235344	+	0.0468129i
$892$	692.513	−	286.848i	0.776360	−	0.321579i
$893$	−430.015	−	1038.15i	−0.481540	−	1.16254i
$894$	−26.2814	+	132.125i	−0.0293975	+	0.147791i
$895$		0			0
$896$	−88.0786	−	442.801i	−0.0983020	−	0.494198i
$897$	−9.79279	+	9.79279i	−0.0109173	+	0.0109173i
$898$	−281.297	+	420.991i	−0.313249	+	0.468810i
$899$	−761.031	−	315.229i	−0.846530	−	0.350644i
$900$		0			0
$901$	−183.222	−	107.093i	−0.203354	−	0.118861i
$902$	64.8372			0.0718816
$903$	164.831	−	397.937i	0.182537	−	0.440684i
$904$	654.477	+	437.307i	0.723979	+	0.483747i
$905$		0			0
$906$	136.600	−	27.1715i	0.150773	−	0.0299906i
$907$	−17.0762	+	11.4100i	−0.0188271	+	0.0125799i	−0.564948	−	0.825126i	$-0.691104\pi$
$907$	−17.0762	+	11.4100i	−0.0188271	+	0.0125799i	0.546121	+	0.837706i	$0.316104\pi$
$908$	−1193.92	−	237.485i	−1.31489	−	0.261548i
$909$	348.944	−	144.537i	0.383877	−	0.159007i
$910$		0			0
$911$	12.6018	−	63.3533i	0.0138329	−	0.0695426i	−0.973252	−	0.229739i	$-0.926213\pi$
$911$	12.6018	−	63.3533i	0.0138329	−	0.0695426i	0.987085	+	0.160196i	$0.0512128\pi$
$912$	−265.280	−	397.019i	−0.290877	−	0.435328i
$913$	111.225	+	559.165i	0.121823	+	0.612448i
$914$	−376.198	+	376.198i	−0.411595	+	0.411595i
$915$		0			0
$916$	−1187.63	−	491.933i	−1.29654	−	0.537045i
$917$		−	804.314i		−	0.877115i
$918$	320.076	−	361.064i	0.348666	−	0.393316i
$919$	−1708.90			−1.85952			−0.929760	−	0.368167i	$-0.879986\pi$
$919$	−1708.90			−1.85952			−0.929760	+	0.368167i	$0.879986\pi$
$920$		0			0
$921$	312.338	+	208.697i	0.339129	+	0.226599i
$922$	166.492	+	166.492i	0.180577	+	0.180577i
$923$	94.9566	−	18.8880i	0.102878	−	0.0204638i
$924$	−110.398	+	73.7654i	−0.119478	+	0.0798326i
$925$		0			0
$926$	328.307	−	135.989i	0.354544	−	0.146857i
$927$	−190.266	−	459.344i	−0.205250	−	0.495517i
$928$	333.278	−	1675.50i	0.359135	−	1.80550i
$929$	−71.3897	−	106.842i	−0.0768458	−	0.115008i	0.791056	−	0.611744i	$-0.209532\pi$
$929$	−71.3897	−	106.842i	−0.0768458	−	0.115008i	−0.867902	+	0.496736i	$0.834532\pi$
$930$		0			0
$931$	−862.066	+	862.066i	−0.925957	+	0.925957i
$932$	−435.931	+	652.418i	−0.467738	+	0.700019i
$933$	693.985	+	287.458i	0.743821	+	0.308101i
$934$			40.7602i			0.0436405i
$935$		0			0
$936$	48.0780			0.0513654
$937$	−479.379	+	1157.32i	−0.511610	+	1.23514i	0.431336	+	0.902191i	$0.358042\pi$
$937$	−479.379	+	1157.32i	−0.511610	+	1.23514i	−0.942946	+	0.332945i	$0.891958\pi$
$938$	187.147	+	125.047i	0.199517	+	0.133313i
$939$	413.477	+	413.477i	0.440338	+	0.440338i
$940$		0			0
$941$	−251.481	+	168.034i	−0.267249	+	0.178570i	−0.681973	−	0.731377i	$-0.738878\pi$
$941$	−251.481	+	168.034i	−0.267249	+	0.178570i	0.414725	+	0.909947i	$0.363878\pi$
$942$	11.9705	+	2.38107i	0.0127075	+	0.00252768i
$943$	−31.5264	+	13.0587i	−0.0334320	+	0.0138480i
$944$	−59.1626	−	142.831i	−0.0626723	−	0.151304i
$945$		0			0
$946$	−123.476	−	184.795i	−0.130525	−	0.195344i
$947$	−64.3908	−	323.715i	−0.0679946	−	0.341832i	0.931781	−	0.363021i	$-0.118255\pi$
$947$	−64.3908	−	323.715i	−0.0679946	−	0.341832i	−0.999775	+	0.0211894i	$0.993255\pi$
$948$	−351.549	+	351.549i	−0.370832	+	0.370832i
$949$	68.4694	−	102.472i	0.0721490	−	0.107979i
$950$		0			0
$951$			719.933i			0.757027i
$952$	25.6828	+	426.794i	0.0269777	+	0.448313i
$953$	−519.872			−0.545511			−0.272755	−	0.962083i	$-0.587935\pi$
$953$	−519.872			−0.545511			−0.272755	+	0.962083i	$0.587935\pi$
$954$	−14.0062	+	33.8141i	−0.0146816	+	0.0354445i
$955$		0			0
$956$	490.951	+	490.951i	0.513547	+	0.513547i
$957$	−600.247	+	119.397i	−0.627218	+	0.124761i
$958$	47.7223	−	31.8870i	0.0498145	−	0.0332850i
$959$	556.265	+	110.648i	0.580047	+	0.115379i
$960$		0			0
$961$	272.132	+	656.984i	0.283175	+	0.683646i
$962$	3.23838	−	16.2805i	0.00336630	−	0.0169235i
$963$	−7.99045	−	11.9586i	−0.00829746	−	0.0124180i
$964$	274.195	+	1378.47i	0.284435	+	1.42995i
$965$		0			0
$966$	−11.8006	+	17.6608i	−0.0122159	+	0.0182824i
$967$	−1113.70	−	461.309i	−1.15171	−	0.477052i	−0.276600	−	0.960985i	$-0.589208\pi$
$967$	−1113.70	−	461.309i	−1.15171	−	0.477052i	−0.875105	+	0.483933i	$0.839208\pi$
$968$		−	667.930i		−	0.690010i
$969$	625.179	+	1285.01i	0.645180	+	1.32612i
$970$		0			0
$971$	445.904	−	1076.51i	0.459222	−	1.10866i	−0.509491	−	0.860476i	$-0.670166\pi$
$971$	445.904	−	1076.51i	0.459222	−	1.10866i	0.968713	−	0.248184i	$-0.0798336\pi$
$972$	397.832	+	265.823i	0.409292	+	0.273480i
$973$	−477.515	−	477.515i	−0.490766	−	0.490766i
$974$	536.680	−	106.752i	0.551006	−	0.109602i
$975$		0			0
$976$	−382.322	−	76.0486i	−0.391724	−	0.0779187i
$977$	−496.049	+	205.470i	−0.507727	+	0.210307i	−0.621816	−	0.783163i	$-0.713605\pi$
$977$	−496.049	+	205.470i	−0.507727	+	0.210307i	0.114090	+	0.993470i	$0.463605\pi$
$978$	99.3157	+	239.769i	0.101550	+	0.245163i
$979$	−91.8349	+	461.685i	−0.0938048	+	0.471589i
$980$		0			0
$981$	−23.7550	−	119.424i	−0.0242150	−	0.121737i
$982$	338.208	−	338.208i	0.344407	−	0.344407i
$983$	247.073	−	369.770i	0.251345	−	0.376165i	−0.684245	−	0.729252i	$-0.739868\pi$
$983$	247.073	−	369.770i	0.251345	−	0.376165i	0.935590	+	0.353087i	$0.114868\pi$
$984$	−214.978	−	89.0467i	−0.218473	−	0.0904947i
$985$		0			0
$986$	−279.287	+	808.526i	−0.283252	+	0.820006i
$987$	293.802			0.297672
$988$	−93.7570	+	226.349i	−0.0948958	+	0.229099i
$989$	97.2580	+	64.9857i	0.0983397	+	0.0657085i
$990$		0			0
$991$	−1092.29	+	217.270i	−1.10221	+	0.219243i	−0.712484	−	0.701688i	$-0.752430\pi$
$991$	−1092.29	+	217.270i	−1.10221	+	0.219243i	−0.389725	+	0.920931i	$0.627430\pi$
$992$	430.895	−	287.915i	0.434370	−	0.290237i
$993$	−843.417	−	167.766i	−0.849363	−	0.168949i
$994$	137.186	−	56.8243i	0.138014	−	0.0571673i
$995$		0			0
$996$	173.253	−	871.002i	0.173949	−	0.874500i
$997$	906.023	+	1355.96i	0.908750	+	1.36004i	0.932825	+	0.360330i	$0.117336\pi$
$997$	906.023	+	1355.96i	0.908750	+	1.36004i	−0.0240755	+	0.999710i	$0.507664\pi$
$998$	−45.1686	−	227.078i	−0.0452591	−	0.227533i
$999$	153.986	−	153.986i	0.154140	−	0.154140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.e.401.7		96
5.2	odd	4		425.3.t.e.299.7		96
5.3	odd	4		425.3.t.h.299.6		96
5.4	even	2		85.3.q.a.61.6	yes	96
17.12	odd	16	inner	425.3.u.e.301.7		96
85.12	even	16		425.3.t.h.199.6		96
85.29	odd	16		85.3.q.a.46.6	✓	96
85.63	even	16		425.3.t.e.199.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.6	✓	96	85.29	odd	16
85.3.q.a.61.6	yes	96	5.4	even	2
425.3.t.e.199.7		96	85.63	even	16
425.3.t.e.299.7		96	5.2	odd	4
425.3.t.h.199.6		96	85.12	even	16
425.3.t.h.299.6		96	5.3	odd	4
425.3.u.e.301.7		96	17.12	odd	16	inner
425.3.u.e.401.7		96	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.369527 - 0.892116i) q^{2} +(-2.03052 - 1.35675i) q^{3} +(2.16911 + 2.16911i) q^{4} +(-1.96072 + 1.31011i) q^{6} +(-3.61453 - 0.718974i) q^{7} +(6.30510 - 2.61166i) q^{8} +(-1.16190 - 2.80507i) q^{9} +(2.67188 + 3.99876i) q^{11} +(-1.46148 - 7.34736i) q^{12} +(-1.64069 + 1.64069i) q^{13} +(-1.97707 + 2.95890i) q^{14} +5.68035i q^{16} +(2.30902 - 16.8425i) q^{17} -2.93181 q^{18} +(13.1725 - 31.8012i) q^{19} +(6.36391 + 6.36391i) q^{21} +(4.55469 - 0.905984i) q^{22} +(-2.03220 + 1.35787i) q^{23} +(-16.3460 - 3.25143i) q^{24} +(0.857405 + 2.06996i) q^{26} +(-5.73438 + 28.8287i) q^{27} +(-6.28076 - 9.39982i) q^{28} +(-10.1660 - 51.1081i) q^{29} +(8.78233 - 13.1437i) q^{31} +(30.2879 + 12.5457i) q^{32} -11.7447i q^{33} +(-14.1722 - 8.28365i) q^{34} +(3.56422 - 8.60478i) q^{36} +(-6.16017 - 4.11609i) q^{37} +(-23.5028 - 23.5028i) q^{38} +(5.55746 - 1.10545i) q^{39} +(13.6935 + 2.72380i) q^{41} +(8.02899 - 3.32572i) q^{42} +(-18.3147 - 44.2156i) q^{43} +(-2.87813 + 14.4693i) q^{44} +(0.460427 + 2.31472i) q^{46} +(23.0835 - 23.0835i) q^{47} +(7.70683 - 11.5341i) q^{48} +(-32.7222 - 13.5540i) q^{49} +(-27.5396 + 31.0663i) q^{51} -7.11764 q^{52} +(4.77734 - 11.5335i) q^{53} +(23.5995 + 15.7687i) q^{54} +(-24.6677 + 4.90671i) q^{56} +(-69.8934 + 46.7013i) q^{57} +(-49.3510 - 9.81653i) q^{58} +(-25.1448 + 10.4153i) q^{59} +(-13.3880 + 67.3061i) q^{61} +(-8.48040 - 12.6918i) q^{62} +(2.18294 + 10.9744i) q^{63} +(6.31796 - 6.31796i) q^{64} +(-10.4776 - 4.33997i) q^{66} -63.2487i q^{67} +(41.5416 - 31.5246i) q^{68} +5.96872 q^{69} +(-34.6942 - 23.1819i) q^{71} +(-14.6518 - 14.6518i) q^{72} +(-52.0944 + 10.3622i) q^{73} +(-5.94838 + 3.97458i) q^{74} +(97.5527 - 40.4076i) q^{76} +(-6.78259 - 16.3746i) q^{77} +(1.06744 - 5.36639i) q^{78} +(-36.8708 - 55.1810i) q^{79} +(31.4350 - 31.4350i) q^{81} +(7.49005 - 11.2097i) q^{82} +(109.522 + 45.3657i) q^{83} +27.6080i q^{84} -46.2132 q^{86} +(-48.6987 + 117.569i) q^{87} +(27.2899 + 18.2345i) q^{88} +(69.2116 + 69.2116i) q^{89} +(7.10991 - 4.75069i) q^{91} +(-7.35341 - 1.46268i) q^{92} +(-35.6655 + 14.7731i) q^{93} +(-12.0632 - 29.1231i) q^{94} +(-44.4790 - 66.5676i) q^{96} +(7.05322 + 35.4589i) q^{97} +(-24.1835 + 24.1835i) q^{98} +(8.11235 - 12.1410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Introduction

L-functions

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