LMFDB - Embedded newform 750.3.f.b.193.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,3,Mod(193,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.193"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	750.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-16,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$20.4360198270$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6879707136000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{12} + 86x^{8} + 36x^{4} + 1 $ x^16 + 21x^12 + 86x^8 + 36*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.7
Root			$-1.05097 - 1.05097i$ of defining polynomial
Character	$\chi$	$=$	750.193
Dual form			750.3.f.b.307.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(2.54205 - 2.54205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -11.6397 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.97542 - 2.97542i) q^{13} +5.08411i q^{14} -4.00000 q^{16} +(-1.63878 + 1.63878i) q^{17} +(-3.00000 - 3.00000i) q^{18} +2.25042i q^{19} +6.22673 q^{21} +(11.6397 - 11.6397i) q^{22} +(-28.6600 - 28.6600i) q^{23} +4.89898i q^{24} +5.95083 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-5.08411 - 5.08411i) q^{28} +49.9726i q^{29} -19.5918 q^{31} +(4.00000 - 4.00000i) q^{32} +(-14.2556 - 14.2556i) q^{33} -3.27757i q^{34} +6.00000 q^{36} +(10.2972 - 10.2972i) q^{37} +(-2.25042 - 2.25042i) q^{38} -7.28825i q^{39} -43.8211 q^{41} +(-6.22673 + 6.22673i) q^{42} +(-10.4466 - 10.4466i) q^{43} +23.2794i q^{44} +57.3200 q^{46} +(-46.2319 + 46.2319i) q^{47} +(-4.89898 - 4.89898i) q^{48} +36.0759i q^{49} -4.01419 q^{51} +(-5.95083 + 5.95083i) q^{52} +(-40.8055 - 40.8055i) q^{53} -7.34847i q^{54} +10.1682 q^{56} +(-2.75619 + 2.75619i) q^{57} +(-49.9726 - 49.9726i) q^{58} -28.5724i q^{59} -14.8072 q^{61} +(19.5918 - 19.5918i) q^{62} +(7.62616 + 7.62616i) q^{63} +8.00000i q^{64} +28.5113 q^{66} +(13.4721 - 13.4721i) q^{67} +(3.27757 + 3.27757i) q^{68} -70.2024i q^{69} +3.29816 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-85.4956 - 85.4956i) q^{73} +20.5944i q^{74} +4.50083 q^{76} +(-29.5887 + 29.5887i) q^{77} +(7.28825 + 7.28825i) q^{78} -22.2942i q^{79} -9.00000 q^{81} +(43.8211 - 43.8211i) q^{82} +(-21.6882 - 21.6882i) q^{83} -12.4535i q^{84} +20.8931 q^{86} +(-61.2036 + 61.2036i) q^{87} +(-23.2794 - 23.2794i) q^{88} +113.653i q^{89} -15.1273 q^{91} +(-57.3200 + 57.3200i) q^{92} +(-23.9950 - 23.9950i) q^{93} -92.4638i q^{94} +9.79796 q^{96} +(50.8871 - 50.8871i) q^{97} +(-36.0759 - 36.0759i) q^{98} -34.9191i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	2.54205	−	2.54205i	0.363151	−	0.363151i	−0.501821	−	0.864972i	$-0.667336\pi$
$7$	2.54205	−	2.54205i	0.363151	−	0.363151i	0.864972	+	0.501821i	$0.167336\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−11.6397			−1.05815			−0.529077	−	0.848574i	$-0.677462\pi$
$11$	−11.6397			−1.05815			−0.529077	+	0.848574i	$0.677462\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−2.97542	−	2.97542i	−0.228878	−	0.228878i	0.583346	−	0.812224i	$-0.301743\pi$
$13$	−2.97542	−	2.97542i	−0.228878	−	0.228878i	−0.812224	+	0.583346i	$0.801743\pi$
$14$			5.08411i			0.363151i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−1.63878	+	1.63878i	−0.0963991	+	0.0963991i	−0.753662	−	0.657263i	$-0.771714\pi$
$17$	−1.63878	+	1.63878i	−0.0963991	+	0.0963991i	0.657263	+	0.753662i	$0.271714\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			2.25042i			0.118443i	0.998245	+	0.0592215i	$0.0188618\pi$
$19$			2.25042i			0.118443i	−0.998245	+	0.0592215i	$0.981138\pi$
$20$		0			0
$21$	6.22673			0.296511
$22$	11.6397	−	11.6397i	0.529077	−	0.529077i
$23$	−28.6600	−	28.6600i	−1.24609	−	1.24609i	−0.957434	−	0.288653i	$-0.906793\pi$
$23$	−28.6600	−	28.6600i	−1.24609	−	1.24609i	−0.288653	−	0.957434i	$-0.593207\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	5.95083			0.228878
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−5.08411	−	5.08411i	−0.181575	−	0.181575i
$29$			49.9726i			1.72319i	0.507595	+	0.861596i	$0.330535\pi$
$29$			49.9726i			1.72319i	−0.507595	+	0.861596i	$0.669465\pi$
$30$		0			0
$31$	−19.5918			−0.631995			−0.315998	−	0.948760i	$-0.602339\pi$
$31$	−19.5918			−0.631995			−0.315998	+	0.948760i	$0.602339\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−14.2556	−	14.2556i	−0.431989	−	0.431989i
$34$		−	3.27757i		−	0.0963991i
$35$		0			0
$36$	6.00000			0.166667
$37$	10.2972	−	10.2972i	0.278302	−	0.278302i	−0.554129	−	0.832431i	$-0.686948\pi$
$37$	10.2972	−	10.2972i	0.278302	−	0.278302i	0.832431	+	0.554129i	$0.186948\pi$
$38$	−2.25042	−	2.25042i	−0.0592215	−	0.0592215i
$39$		−	7.28825i		−	0.186878i
$40$		0			0
$41$	−43.8211			−1.06881			−0.534403	−	0.845230i	$-0.679464\pi$
$41$	−43.8211			−1.06881			−0.534403	+	0.845230i	$0.679464\pi$
$42$	−6.22673	+	6.22673i	−0.148256	+	0.148256i
$43$	−10.4466	−	10.4466i	−0.242944	−	0.242944i	0.575123	−	0.818067i	$-0.304954\pi$
$43$	−10.4466	−	10.4466i	−0.242944	−	0.242944i	−0.818067	+	0.575123i	$0.804954\pi$
$44$			23.2794i			0.529077i
$45$		0			0
$46$	57.3200			1.24609
$47$	−46.2319	+	46.2319i	−0.983657	+	0.983657i	−0.999869	−	0.0162113i	$-0.994840\pi$
$47$	−46.2319	+	46.2319i	−0.983657	+	0.983657i	0.0162113	+	0.999869i	$0.494840\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			36.0759i			0.736243i
$50$		0			0
$51$	−4.01419			−0.0787095
$52$	−5.95083	+	5.95083i	−0.114439	+	0.114439i
$53$	−40.8055	−	40.8055i	−0.769916	−	0.769916i	0.208176	−	0.978091i	$-0.433247\pi$
$53$	−40.8055	−	40.8055i	−0.769916	−	0.769916i	−0.978091	+	0.208176i	$0.933247\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	10.1682			0.181575
$57$	−2.75619	+	2.75619i	−0.0483541	+	0.0483541i
$58$	−49.9726	−	49.9726i	−0.861596	−	0.861596i
$59$		−	28.5724i		−	0.484278i	−0.970242	−	0.242139i	$-0.922151\pi$
$59$		−	28.5724i		−	0.484278i	0.970242	−	0.242139i	$-0.0778490\pi$
$60$		0			0
$61$	−14.8072			−0.242741			−0.121370	−	0.992607i	$-0.538729\pi$
$61$	−14.8072			−0.242741			−0.121370	+	0.992607i	$0.538729\pi$
$62$	19.5918	−	19.5918i	0.315998	−	0.315998i
$63$	7.62616	+	7.62616i	0.121050	+	0.121050i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	28.5113			0.431989
$67$	13.4721	−	13.4721i	0.201076	−	0.201076i	−0.599385	−	0.800461i	$-0.704588\pi$
$67$	13.4721	−	13.4721i	0.201076	−	0.201076i	0.800461	+	0.599385i	$0.204588\pi$
$68$	3.27757	+	3.27757i	0.0481995	+	0.0481995i
$69$		−	70.2024i		−	1.01743i
$70$		0			0
$71$	3.29816			0.0464529			0.0232265	−	0.999730i	$-0.492606\pi$
$71$	3.29816			0.0464529			0.0232265	+	0.999730i	$0.492606\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−85.4956	−	85.4956i	−1.17117	−	1.17117i	−0.981931	−	0.189241i	$-0.939397\pi$
$73$	−85.4956	−	85.4956i	−1.17117	−	1.17117i	−0.189241	−	0.981931i	$-0.560603\pi$
$74$			20.5944i			0.278302i
$75$		0			0
$76$	4.50083			0.0592215
$77$	−29.5887	+	29.5887i	−0.384269	+	0.384269i
$78$	7.28825	+	7.28825i	0.0934391	+	0.0934391i
$79$		−	22.2942i		−	0.282205i	−0.989995	−	0.141103i	$-0.954935\pi$
$79$		−	22.2942i		−	0.282205i	0.989995	−	0.141103i	$-0.0450648\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	43.8211	−	43.8211i	0.534403	−	0.534403i
$83$	−21.6882	−	21.6882i	−0.261304	−	0.261304i	0.564280	−	0.825584i	$-0.309154\pi$
$83$	−21.6882	−	21.6882i	−0.261304	−	0.261304i	−0.825584	+	0.564280i	$0.809154\pi$
$84$		−	12.4535i		−	0.148256i
$85$		0			0
$86$	20.8931			0.242944
$87$	−61.2036	+	61.2036i	−0.703490	+	0.703490i
$88$	−23.2794	−	23.2794i	−0.264538	−	0.264538i
$89$			113.653i			1.27700i	0.769621	+	0.638501i	$0.220445\pi$
$89$			113.653i			1.27700i	−0.769621	+	0.638501i	$0.779555\pi$
$90$		0			0
$91$	−15.1273			−0.166234
$92$	−57.3200	+	57.3200i	−0.623043	+	0.623043i
$93$	−23.9950	−	23.9950i	−0.258011	−	0.258011i
$94$		−	92.4638i		−	0.983657i
$95$		0			0
$96$	9.79796			0.102062
$97$	50.8871	−	50.8871i	0.524609	−	0.524609i	−0.394351	−	0.918960i	$-0.629031\pi$
$97$	50.8871	−	50.8871i	0.524609	−	0.524609i	0.918960	+	0.394351i	$0.129031\pi$
$98$	−36.0759	−	36.0759i	−0.368122	−	0.368122i
$99$		−	34.9191i		−	0.352718i
$100$		0			0
$101$	32.8309			0.325058			0.162529	−	0.986704i	$-0.448035\pi$
$101$	32.8309			0.325058			0.162529	+	0.986704i	$0.448035\pi$
$102$	4.01419	−	4.01419i	0.0393548	−	0.0393548i
$103$	56.2840	+	56.2840i	0.546446	+	0.546446i	0.925411	−	0.378965i	$-0.123720\pi$
$103$	56.2840	+	56.2840i	0.546446	+	0.546446i	−0.378965	+	0.925411i	$0.623720\pi$
$104$		−	11.9017i		−	0.114439i
$105$		0			0
$106$	81.6111			0.769916
$107$	121.285	−	121.285i	1.13350	−	1.13350i	0.143915	−	0.989590i	$-0.454031\pi$
$107$	121.285	−	121.285i	1.13350	−	1.13350i	0.989590	−	0.143915i	$-0.0459692\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	163.809i		−	1.50284i	−0.659826	−	0.751418i	$-0.729370\pi$
$109$		−	163.809i		−	1.50284i	0.659826	−	0.751418i	$-0.270630\pi$
$110$		0			0
$111$	25.2228			0.227233
$112$	−10.1682	+	10.1682i	−0.0907876	+	0.0907876i
$113$	−34.2754	−	34.2754i	−0.303322	−	0.303322i	0.538990	−	0.842312i	$-0.318806\pi$
$113$	−34.2754	−	34.2754i	−0.303322	−	0.303322i	−0.842312	+	0.538990i	$0.818806\pi$
$114$		−	5.51237i		−	0.0483541i
$115$		0			0
$116$	99.9451			0.861596
$117$	8.92625	−	8.92625i	0.0762927	−	0.0762927i
$118$	28.5724	+	28.5724i	0.242139	+	0.242139i
$119$			8.33176i			0.0700148i
$120$		0			0
$121$	14.4823			0.119688
$122$	14.8072	−	14.8072i	0.121370	−	0.121370i
$123$	−53.6696	−	53.6696i	−0.436338	−	0.436338i
$124$			39.1837i			0.315998i
$125$		0			0
$126$	−15.2523			−0.121050
$127$	18.5651	−	18.5651i	0.146182	−	0.146182i	−0.630228	−	0.776410i	$-0.717039\pi$
$127$	18.5651	−	18.5651i	0.146182	−	0.146182i	0.776410	+	0.630228i	$0.217039\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	25.5888i		−	0.198363i
$130$		0			0
$131$	−245.921			−1.87726			−0.938630	−	0.344927i	$-0.887904\pi$
$131$	−245.921			−1.87726			−0.938630	+	0.344927i	$0.887904\pi$
$132$	−28.5113	+	28.5113i	−0.215995	+	0.215995i
$133$	5.72068	+	5.72068i	0.0430126	+	0.0430126i
$134$			26.9442i			0.201076i
$135$		0			0
$136$	−6.55514			−0.0481995
$137$	−22.3515	+	22.3515i	−0.163150	+	0.163150i	−0.783961	−	0.620811i	$-0.786804\pi$
$137$	−22.3515	+	22.3515i	−0.163150	+	0.163150i	0.620811	+	0.783961i	$0.286804\pi$
$138$	70.2024	+	70.2024i	0.508713	+	0.508713i
$139$		−	118.418i		−	0.851931i	−0.904740	−	0.425965i	$-0.859935\pi$
$139$		−	118.418i		−	0.851931i	0.904740	−	0.425965i	$-0.140065\pi$
$140$		0			0
$141$	−113.245			−0.803153
$142$	−3.29816	+	3.29816i	−0.0232265	+	0.0232265i
$143$	34.6329	+	34.6329i	0.242188	+	0.242188i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	170.991			1.17117
$147$	−44.1838	+	44.1838i	−0.300570	+	0.300570i
$148$	−20.5944	−	20.5944i	−0.139151	−	0.139151i
$149$			246.854i			1.65674i	0.560182	+	0.828370i	$0.310731\pi$
$149$			246.854i			1.65674i	−0.560182	+	0.828370i	$0.689269\pi$
$150$		0			0
$151$	−139.432			−0.923394			−0.461697	−	0.887038i	$-0.652759\pi$
$151$	−139.432			−0.923394			−0.461697	+	0.887038i	$0.652759\pi$
$152$	−4.50083	+	4.50083i	−0.0296107	+	0.0296107i
$153$	−4.91635	−	4.91635i	−0.0321330	−	0.0321330i
$154$		−	59.1774i		−	0.384269i
$155$		0			0
$156$	−14.5765			−0.0934391
$157$	115.745	−	115.745i	0.737229	−	0.737229i	−0.234812	−	0.972041i	$-0.575447\pi$
$157$	115.745	−	115.745i	0.737229	−	0.737229i	0.972041	+	0.234812i	$0.0754474\pi$
$158$	22.2942	+	22.2942i	0.141103	+	0.141103i
$159$		−	99.9527i		−	0.628633i
$160$		0			0
$161$	−145.710			−0.905034
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−5.71791	−	5.71791i	−0.0350792	−	0.0350792i	0.689350	−	0.724429i	$-0.257896\pi$
$163$	−5.71791	−	5.71791i	−0.0350792	−	0.0350792i	−0.724429	+	0.689350i	$0.757896\pi$
$164$			87.6421i			0.534403i
$165$		0			0
$166$	43.3765			0.261304
$167$	−74.0063	+	74.0063i	−0.443152	+	0.443152i	−0.893070	−	0.449918i	$-0.851453\pi$
$167$	−74.0063	+	74.0063i	−0.443152	+	0.443152i	0.449918	+	0.893070i	$0.351453\pi$
$168$	12.4535	+	12.4535i	0.0741278	+	0.0741278i
$169$		−	151.294i		−	0.895230i
$170$		0			0
$171$	−6.75125			−0.0394810
$172$	−20.8931	+	20.8931i	−0.121472	+	0.121472i
$173$	−13.4974	−	13.4974i	−0.0780196	−	0.0780196i	0.667020	−	0.745040i	$-0.267570\pi$
$173$	−13.4974	−	13.4974i	−0.0780196	−	0.0780196i	−0.745040	+	0.667020i	$0.767570\pi$
$174$		−	122.407i		−	0.703490i
$175$		0			0
$176$	46.5587			0.264538
$177$	34.9939	−	34.9939i	0.197706	−	0.197706i
$178$	−113.653	−	113.653i	−0.638501	−	0.638501i
$179$			173.811i			0.971012i	0.874233	+	0.485506i	$0.161365\pi$
$179$			173.811i			0.971012i	−0.874233	+	0.485506i	$0.838635\pi$
$180$		0			0
$181$	−209.024			−1.15483			−0.577414	−	0.816451i	$-0.695938\pi$
$181$	−209.024			−1.15483			−0.577414	+	0.816451i	$0.695938\pi$
$182$	15.1273	−	15.1273i	0.0831172	−	0.0831172i
$183$	−18.1350	−	18.1350i	−0.0990986	−	0.0990986i
$184$		−	114.640i		−	0.623043i
$185$		0			0
$186$	47.9900			0.258011
$187$	19.0749	−	19.0749i	0.102005	−	0.102005i
$188$	92.4638	+	92.4638i	0.491829	+	0.491829i
$189$			18.6802i			0.0988371i
$190$		0			0
$191$	250.977			1.31401			0.657007	−	0.753885i	$-0.271822\pi$
$191$	250.977			1.31401			0.657007	+	0.753885i	$0.271822\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	243.593	+	243.593i	1.26214	+	1.26214i	0.950053	+	0.312087i	$0.101028\pi$
$193$	243.593	+	243.593i	1.26214	+	1.26214i	0.312087	+	0.950053i	$0.398972\pi$
$194$			101.774i			0.524609i
$195$		0			0
$196$	72.1519			0.368122
$197$	−139.759	+	139.759i	−0.709435	+	0.709435i	−0.966416	−	0.256981i	$-0.917272\pi$
$197$	−139.759	+	139.759i	−0.709435	+	0.709435i	0.256981	+	0.966416i	$0.417272\pi$
$198$	34.9191	+	34.9191i	0.176359	+	0.176359i
$199$		−	181.419i		−	0.911653i	−0.890069	−	0.455827i	$-0.849344\pi$
$199$		−	181.419i		−	0.911653i	0.890069	−	0.455827i	$-0.150656\pi$
$200$		0			0
$201$	32.9998			0.164178
$202$	−32.8309	+	32.8309i	−0.162529	+	0.162529i
$203$	127.033	+	127.033i	0.625778	+	0.625778i
$204$			8.02837i			0.0393548i
$205$		0			0
$206$	−112.568			−0.546446
$207$	85.9800	−	85.9800i	0.415362	−	0.415362i
$208$	11.9017	+	11.9017i	0.0572195	+	0.0572195i
$209$		−	26.1941i		−	0.125331i
$210$		0			0
$211$	−321.973			−1.52594			−0.762969	−	0.646435i	$-0.776259\pi$
$211$	−321.973			−1.52594			−0.762969	+	0.646435i	$0.776259\pi$
$212$	−81.6111	+	81.6111i	−0.384958	+	0.384958i
$213$	4.03940	+	4.03940i	0.0189643	+	0.0189643i
$214$			242.570i			1.13350i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−49.8035	+	49.8035i	−0.229509	+	0.229509i
$218$	163.809	+	163.809i	0.751418	+	0.751418i
$219$		−	209.420i		−	0.956258i
$220$		0			0
$221$	9.75213			0.0441273
$222$	−25.2228	+	25.2228i	−0.113616	+	0.113616i
$223$	255.414	+	255.414i	1.14535	+	1.14535i	0.987456	+	0.157897i	$0.0504713\pi$
$223$	255.414	+	255.414i	1.14535	+	1.14535i	0.157897	+	0.987456i	$0.449529\pi$
$224$		−	20.3364i		−	0.0907876i
$225$		0			0
$226$	68.5509			0.303322
$227$	154.685	−	154.685i	0.681431	−	0.681431i	−0.278891	−	0.960323i	$-0.589967\pi$
$227$	154.685	−	154.685i	0.681431	−	0.681431i	0.960323	+	0.278891i	$0.0899669\pi$
$228$	5.51237	+	5.51237i	0.0241771	+	0.0241771i
$229$			339.723i			1.48351i	0.670673	+	0.741753i	$0.266005\pi$
$229$			339.723i			1.48351i	−0.670673	+	0.741753i	$0.733995\pi$
$230$		0			0
$231$	−72.4772			−0.313754
$232$	−99.9451	+	99.9451i	−0.430798	+	0.430798i
$233$	47.4440	+	47.4440i	0.203622	+	0.203622i	0.801550	−	0.597928i	$-0.204009\pi$
$233$	47.4440	+	47.4440i	0.203622	+	0.203622i	−0.597928	+	0.801550i	$0.704009\pi$
$234$			17.8525i			0.0762927i
$235$		0			0
$236$	−57.1448			−0.242139
$237$	27.3047	−	27.3047i	0.115210	−	0.115210i
$238$	−8.33176	−	8.33176i	−0.0350074	−	0.0350074i
$239$			417.452i			1.74666i	0.487129	+	0.873330i	$0.338044\pi$
$239$			417.452i			1.74666i	−0.487129	+	0.873330i	$0.661956\pi$
$240$		0			0
$241$	225.983			0.937691			0.468845	−	0.883280i	$-0.344670\pi$
$241$	225.983			0.937691			0.468845	+	0.883280i	$0.344670\pi$
$242$	−14.4823	+	14.4823i	−0.0598441	+	0.0598441i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			29.6144i			0.121370i
$245$		0			0
$246$	107.339			0.436338
$247$	6.69592	−	6.69592i	0.0271090	−	0.0271090i
$248$	−39.1837	−	39.1837i	−0.157999	−	0.157999i
$249$		−	53.1251i		−	0.213354i
$250$		0			0
$251$	286.437			1.14118			0.570592	−	0.821234i	$-0.306714\pi$
$251$	286.437			1.14118			0.570592	+	0.821234i	$0.306714\pi$
$252$	15.2523	−	15.2523i	0.0605251	−	0.0605251i
$253$	333.593	+	333.593i	1.31855	+	1.31855i
$254$			37.1303i			0.146182i
$255$		0			0
$256$	16.0000			0.0625000
$257$	25.3011	−	25.3011i	0.0984478	−	0.0984478i	−0.656167	−	0.754615i	$-0.727824\pi$
$257$	25.3011	−	25.3011i	0.0984478	−	0.0984478i	0.754615	+	0.656167i	$0.227824\pi$
$258$	25.5888	+	25.5888i	0.0991813	+	0.0991813i
$259$		−	52.3520i		−	0.202131i
$260$		0			0
$261$	−149.918			−0.574397
$262$	245.921	−	245.921i	0.938630	−	0.938630i
$263$	181.190	+	181.190i	0.688934	+	0.688934i	0.961996	−	0.273062i	$-0.0880364\pi$
$263$	181.190	+	181.190i	0.688934	+	0.688934i	−0.273062	+	0.961996i	$0.588036\pi$
$264$		−	57.0226i		−	0.215995i
$265$		0			0
$266$	−11.4414			−0.0430126
$267$	−139.196	+	139.196i	−0.521334	+	0.521334i
$268$	−26.9442	−	26.9442i	−0.100538	−	0.100538i
$269$			292.747i			1.08828i	0.838995	+	0.544139i	$0.183143\pi$
$269$			292.747i			1.08828i	−0.838995	+	0.544139i	$0.816857\pi$
$270$		0			0
$271$	522.222			1.92702			0.963509	−	0.267678i	$-0.0862562\pi$
$271$	522.222			1.92702			0.963509	+	0.267678i	$0.0862562\pi$
$272$	6.55514	−	6.55514i	0.0240998	−	0.0240998i
$273$	−18.5271	−	18.5271i	−0.0678649	−	0.0678649i
$274$		−	44.7031i		−	0.163150i
$275$		0			0
$276$	−140.405			−0.508713
$277$	−301.603	+	301.603i	−1.08882	+	1.08882i	−0.0931698	+	0.995650i	$0.529700\pi$
$277$	−301.603	+	301.603i	−1.08882	+	1.08882i	−0.995650	+	0.0931698i	$0.970300\pi$
$278$	118.418	+	118.418i	0.425965	+	0.425965i
$279$		−	58.7755i		−	0.210665i
$280$		0			0
$281$	−213.384			−0.759374			−0.379687	−	0.925115i	$-0.623968\pi$
$281$	−213.384			−0.759374			−0.379687	+	0.925115i	$0.623968\pi$
$282$	113.245	−	113.245i	0.401576	−	0.401576i
$283$	207.552	+	207.552i	0.733399	+	0.733399i	0.971292	−	0.237892i	$-0.0764565\pi$
$283$	207.552	+	207.552i	0.733399	+	0.733399i	−0.237892	+	0.971292i	$0.576457\pi$
$284$		−	6.59632i		−	0.0232265i
$285$		0			0
$286$	−69.2658			−0.242188
$287$	−111.395	+	111.395i	−0.388138	+	0.388138i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			283.629i			0.981414i
$290$		0			0
$291$	124.647			0.428341
$292$	−170.991	+	170.991i	−0.585586	+	0.585586i
$293$	−341.524	−	341.524i	−1.16561	−	1.16561i	−0.983227	−	0.182385i	$-0.941618\pi$
$293$	−341.524	−	341.524i	−1.16561	−	1.16561i	−0.182385	−	0.983227i	$-0.558382\pi$
$294$		−	88.3676i		−	0.300570i
$295$		0			0
$296$	41.1887			0.139151
$297$	42.7669	−	42.7669i	0.143996	−	0.143996i
$298$	−246.854	−	246.854i	−0.828370	−	0.828370i
$299$			170.551i			0.570404i
$300$		0			0
$301$	−53.1115			−0.176450
$302$	139.432	−	139.432i	0.461697	−	0.461697i
$303$	40.2095	+	40.2095i	0.132704	+	0.132704i
$304$		−	9.00166i		−	0.0296107i
$305$		0			0
$306$	9.83271			0.0321330
$307$	−114.470	+	114.470i	−0.372866	+	0.372866i	−0.868520	−	0.495654i	$-0.834928\pi$
$307$	−114.470	+	114.470i	−0.372866	+	0.372866i	0.495654	+	0.868520i	$0.334928\pi$
$308$	59.1774	+	59.1774i	0.192134	+	0.192134i
$309$			137.867i			0.446172i
$310$		0			0
$311$	−177.510			−0.570773			−0.285387	−	0.958413i	$-0.592122\pi$
$311$	−177.510			−0.570773			−0.285387	+	0.958413i	$0.592122\pi$
$312$	14.5765	−	14.5765i	0.0467196	−	0.0467196i
$313$	−330.021	−	330.021i	−1.05438	−	1.05438i	−0.998434	−	0.0559462i	$-0.982182\pi$
$313$	−330.021	−	330.021i	−1.05438	−	1.05438i	−0.0559462	−	0.998434i	$-0.517818\pi$
$314$			231.490i			0.737229i
$315$		0			0
$316$	−44.5884			−0.141103
$317$	260.894	−	260.894i	0.823008	−	0.823008i	−0.163530	−	0.986538i	$-0.552288\pi$
$317$	260.894	−	260.894i	0.823008	−	0.823008i	0.986538	+	0.163530i	$0.0522881\pi$
$318$	99.9527	+	99.9527i	0.314317	+	0.314317i
$319$		−	581.665i		−	1.82340i
$320$		0			0
$321$	297.086			0.925503
$322$	145.710	−	145.710i	0.452517	−	0.452517i
$323$	−3.68795	−	3.68795i	−0.0114178	−	0.0114178i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	11.4358			0.0350792
$327$	200.624	−	200.624i	0.613530	−	0.613530i
$328$	−87.6421	−	87.6421i	−0.267202	−	0.267202i
$329$			235.048i			0.714431i
$330$		0			0
$331$	−307.794			−0.929891			−0.464945	−	0.885339i	$-0.653926\pi$
$331$	−307.794			−0.929891			−0.464945	+	0.885339i	$0.653926\pi$
$332$	−43.3765	+	43.3765i	−0.130652	+	0.130652i
$333$	30.8915	+	30.8915i	0.0927674	+	0.0927674i
$334$		−	148.013i		−	0.443152i
$335$		0			0
$336$	−24.9069			−0.0741278
$337$	−83.2426	+	83.2426i	−0.247011	+	0.247011i	−0.819743	−	0.572732i	$-0.805884\pi$
$337$	−83.2426	+	83.2426i	−0.247011	+	0.247011i	0.572732	+	0.819743i	$0.305884\pi$
$338$	151.294	+	151.294i	0.447615	+	0.447615i
$339$		−	83.9573i		−	0.247662i
$340$		0			0
$341$	228.043			0.668748
$342$	6.75125	−	6.75125i	0.0197405	−	0.0197405i
$343$	216.268	+	216.268i	0.630518	+	0.630518i
$344$		−	41.7863i		−	0.121472i
$345$		0			0
$346$	26.9948			0.0780196
$347$	−13.5122	+	13.5122i	−0.0389402	+	0.0389402i	−0.726309	−	0.687369i	$-0.758766\pi$
$347$	−13.5122	+	13.5122i	−0.0389402	+	0.0389402i	0.687369	+	0.726309i	$0.258766\pi$
$348$	122.407	+	122.407i	0.351745	+	0.351745i
$349$			163.810i			0.469370i	0.972071	+	0.234685i	$0.0754059\pi$
$349$			163.810i			0.469370i	−0.972071	+	0.234685i	$0.924594\pi$
$350$		0			0
$351$	21.8648			0.0622927
$352$	−46.5587	+	46.5587i	−0.132269	+	0.132269i
$353$	235.132	+	235.132i	0.666096	+	0.666096i	0.956810	−	0.290714i	$-0.0938927\pi$
$353$	235.132	+	235.132i	0.666096	+	0.666096i	−0.290714	+	0.956810i	$0.593893\pi$
$354$			69.9878i			0.197706i
$355$		0			0
$356$	227.306			0.638501
$357$	−10.2043	+	10.2043i	−0.0285834	+	0.0285834i
$358$	−173.811	−	173.811i	−0.485506	−	0.485506i
$359$		−	653.313i		−	1.81981i	−0.414814	−	0.909906i	$-0.636154\pi$
$359$		−	653.313i		−	1.81981i	0.414814	−	0.909906i	$-0.363846\pi$
$360$		0			0
$361$	355.936			0.985971
$362$	209.024	−	209.024i	0.577414	−	0.577414i
$363$	17.7371	+	17.7371i	0.0488625	+	0.0488625i
$364$			30.2547i			0.0831172i
$365$		0			0
$366$	36.2701			0.0990986
$367$	283.950	−	283.950i	0.773707	−	0.773707i	−0.205046	−	0.978752i	$-0.565734\pi$
$367$	283.950	−	283.950i	0.773707	−	0.773707i	0.978752	+	0.205046i	$0.0657343\pi$
$368$	114.640	+	114.640i	0.311522	+	0.311522i
$369$		−	131.463i		−	0.356269i
$370$		0			0
$371$	−207.460			−0.559191
$372$	−47.9900	+	47.9900i	−0.129005	+	0.129005i
$373$	119.395	+	119.395i	0.320094	+	0.320094i	0.848803	−	0.528709i	$-0.177324\pi$
$373$	119.395	+	119.395i	0.320094	+	0.320094i	−0.528709	+	0.848803i	$0.677324\pi$
$374$			38.1499i			0.102005i
$375$		0			0
$376$	−184.928			−0.491829
$377$	148.689	−	148.689i	0.394401	−	0.394401i
$378$	−18.6802	−	18.6802i	−0.0494185	−	0.0494185i
$379$		−	584.256i		−	1.54157i	−0.637094	−	0.770786i	$-0.719864\pi$
$379$		−	584.256i		−	1.54157i	0.637094	−	0.770786i	$-0.280136\pi$
$380$		0			0
$381$	45.4751			0.119357
$382$	−250.977	+	250.977i	−0.657007	+	0.657007i
$383$	−366.757	−	366.757i	−0.957590	−	0.957590i	0.0415468	−	0.999137i	$-0.486771\pi$
$383$	−366.757	−	366.757i	−0.957590	−	0.957590i	−0.999137	+	0.0415468i	$0.986771\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−487.186			−1.26214
$387$	31.3397	−	31.3397i	0.0809812	−	0.0809812i
$388$	−101.774	−	101.774i	−0.262304	−	0.262304i
$389$			548.426i			1.40984i	0.709289	+	0.704918i	$0.249016\pi$
$389$			548.426i			1.40984i	−0.709289	+	0.704918i	$0.750984\pi$
$390$		0			0
$391$	93.9351			0.240243
$392$	−72.1519	+	72.1519i	−0.184061	+	0.184061i
$393$	−301.190	−	301.190i	−0.766388	−	0.766388i
$394$		−	279.517i		−	0.709435i
$395$		0			0
$396$	−69.8381			−0.176359
$397$	−441.773	+	441.773i	−1.11278	+	1.11278i	−0.120004	+	0.992773i	$0.538291\pi$
$397$	−441.773	+	441.773i	−1.11278	+	1.11278i	−0.992773	+	0.120004i	$0.961709\pi$
$398$	181.419	+	181.419i	0.455827	+	0.455827i
$399$			14.0127i			0.0351197i
$400$		0			0
$401$	117.473			0.292951			0.146476	−	0.989214i	$-0.453207\pi$
$401$	117.473			0.292951			0.146476	+	0.989214i	$0.453207\pi$
$402$	−32.9998	+	32.9998i	−0.0820890	+	0.0820890i
$403$	58.2939	+	58.2939i	0.144650	+	0.144650i
$404$		−	65.6618i		−	0.162529i
$405$		0			0
$406$	−254.066			−0.625778
$407$	−119.856	+	119.856i	−0.294486	+	0.294486i
$408$	−8.02837	−	8.02837i	−0.0196774	−	0.0196774i
$409$			12.4587i			0.0304615i	0.999884	+	0.0152307i	$0.00484828\pi$
$409$			12.4587i			0.0304615i	−0.999884	+	0.0152307i	$0.995152\pi$
$410$		0			0
$411$	−54.7499			−0.133211
$412$	112.568	−	112.568i	0.273223	−	0.273223i
$413$	−72.6326	−	72.6326i	−0.175866	−	0.175866i
$414$			171.960i			0.415362i
$415$		0			0
$416$	−23.8033			−0.0572195
$417$	145.032	−	145.032i	0.347799	−	0.347799i
$418$	26.1941	+	26.1941i	0.0626654	+	0.0626654i
$419$		−	683.009i		−	1.63009i	−0.579396	−	0.815046i	$-0.696712\pi$
$419$		−	683.009i		−	1.63009i	0.579396	−	0.815046i	$-0.303288\pi$
$420$		0			0
$421$	238.737			0.567071			0.283535	−	0.958962i	$-0.408493\pi$
$421$	238.737			0.567071			0.283535	+	0.958962i	$0.408493\pi$
$422$	321.973	−	321.973i	0.762969	−	0.762969i
$423$	−138.696	−	138.696i	−0.327886	−	0.327886i
$424$		−	163.222i		−	0.384958i
$425$		0			0
$426$	−8.07880			−0.0189643
$427$	−37.6407	+	37.6407i	−0.0881515	+	0.0881515i
$428$	−242.570	−	242.570i	−0.566752	−	0.566752i
$429$			84.8329i			0.197746i
$430$		0			0
$431$	−224.817			−0.521617			−0.260809	−	0.965391i	$-0.583989\pi$
$431$	−224.817			−0.521617			−0.260809	+	0.965391i	$0.583989\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	222.884	+	222.884i	0.514744	+	0.514744i	0.915976	−	0.401232i	$-0.131418\pi$
$433$	222.884	+	222.884i	0.514744	+	0.514744i	−0.401232	+	0.915976i	$0.631418\pi$
$434$		−	99.6071i		−	0.229509i
$435$		0			0
$436$	−327.618			−0.751418
$437$	64.4969	−	64.4969i	0.147590	−	0.147590i
$438$	209.420	+	209.420i	0.478129	+	0.478129i
$439$			407.104i			0.927345i	0.886007	+	0.463672i	$0.153469\pi$
$439$			407.104i			0.927345i	−0.886007	+	0.463672i	$0.846531\pi$
$440$		0			0
$441$	−108.228			−0.245414
$442$	−9.75213	+	9.75213i	−0.0220636	+	0.0220636i
$443$	−496.036	−	496.036i	−1.11972	−	1.11972i	−0.991782	−	0.127938i	$-0.959164\pi$
$443$	−496.036	−	496.036i	−1.11972	−	1.11972i	−0.127938	−	0.991782i	$-0.540836\pi$
$444$		−	50.4457i		−	0.113616i
$445$		0			0
$446$	−510.827			−1.14535
$447$	−302.333	+	302.333i	−0.676361	+	0.676361i
$448$	20.3364	+	20.3364i	0.0453938	+	0.0453938i
$449$			239.876i			0.534245i	0.963663	+	0.267123i	$0.0860729\pi$
$449$			239.876i			0.534245i	−0.963663	+	0.267123i	$0.913927\pi$
$450$		0			0
$451$	510.063			1.13096
$452$	−68.5509	+	68.5509i	−0.151661	+	0.151661i
$453$	−170.769	−	170.769i	−0.376974	−	0.376974i
$454$			309.370i			0.681431i
$455$		0			0
$456$	−11.0247			−0.0241771
$457$	−403.772	+	403.772i	−0.883527	+	0.883527i	−0.993891	−	0.110364i	$-0.964798\pi$
$457$	−403.772	+	403.772i	−0.883527	+	0.883527i	0.110364	+	0.993891i	$0.464798\pi$
$458$	−339.723	−	339.723i	−0.741753	−	0.741753i
$459$		−	12.0426i		−	0.0262365i
$460$		0			0
$461$	20.4304			0.0443177			0.0221588	−	0.999754i	$-0.492946\pi$
$461$	20.4304			0.0443177			0.0221588	+	0.999754i	$0.492946\pi$
$462$	72.4772	−	72.4772i	0.156877	−	0.156877i
$463$	−445.994	−	445.994i	−0.963271	−	0.963271i	0.0360784	−	0.999349i	$-0.488513\pi$
$463$	−445.994	−	445.994i	−0.963271	−	0.963271i	−0.999349	+	0.0360784i	$0.988513\pi$
$464$		−	199.890i		−	0.430798i
$465$		0			0
$466$	−94.8881			−0.203622
$467$	−87.9123	+	87.9123i	−0.188249	+	0.188249i	−0.794939	−	0.606690i	$-0.792497\pi$
$467$	−87.9123	+	87.9123i	−0.188249	+	0.188249i	0.606690	+	0.794939i	$0.292497\pi$
$468$	−17.8525	−	17.8525i	−0.0381464	−	0.0381464i
$469$		−	68.4936i		−	0.146042i
$470$		0			0
$471$	283.516			0.601945
$472$	57.1448	−	57.1448i	0.121070	−	0.121070i
$473$	121.595	+	121.595i	0.257071	+	0.257071i
$474$			54.6095i			0.115210i
$475$		0			0
$476$	16.6635			0.0350074
$477$	122.417	−	122.417i	0.256639	−	0.256639i
$478$	−417.452	−	417.452i	−0.873330	−	0.873330i
$479$		−	716.386i		−	1.49559i	−0.663931	−	0.747793i	$-0.731113\pi$
$479$		−	716.386i		−	1.49559i	0.663931	−	0.747793i	$-0.268887\pi$
$480$		0			0
$481$	−61.2768			−0.127395
$482$	−225.983	+	225.983i	−0.468845	+	0.468845i
$483$	−178.458	−	178.458i	−0.369479	−	0.369479i
$484$		−	28.9645i		−	0.0598441i
$485$		0			0
$486$	22.0454			0.0453609
$487$	−183.244	+	183.244i	−0.376271	+	0.376271i	−0.869755	−	0.493484i	$-0.835723\pi$
$487$	−183.244	+	183.244i	−0.376271	+	0.376271i	0.493484	+	0.869755i	$0.335723\pi$
$488$	−29.6144	−	29.6144i	−0.0606852	−	0.0606852i
$489$		−	14.0060i		−	0.0286421i
$490$		0			0
$491$	796.428			1.62205			0.811027	−	0.585009i	$-0.198909\pi$
$491$	796.428			1.62205			0.811027	+	0.585009i	$0.198909\pi$
$492$	−107.339	+	107.339i	−0.218169	+	0.218169i
$493$	−81.8943	−	81.8943i	−0.166114	−	0.166114i
$494$			13.3918i			0.0271090i
$495$		0			0
$496$	78.3674			0.157999
$497$	8.38409	−	8.38409i	0.0168694	−	0.0168694i
$498$	53.1251	+	53.1251i	0.106677	+	0.106677i
$499$		−	41.7756i		−	0.0837186i	−0.999124	−	0.0418593i	$-0.986672\pi$
$499$		−	41.7756i		−	0.0837186i	0.999124	−	0.0418593i	$-0.0133281\pi$
$500$		0			0
$501$	−181.278			−0.361832
$502$	−286.437	+	286.437i	−0.570592	+	0.570592i
$503$	−73.7531	−	73.7531i	−0.146626	−	0.146626i	0.629983	−	0.776609i	$-0.283062\pi$
$503$	−73.7531	−	73.7531i	−0.146626	−	0.146626i	−0.776609	+	0.629983i	$0.783062\pi$
$504$			30.5046i			0.0605251i
$505$		0			0
$506$	−667.187			−1.31855
$507$	185.296	−	185.296i	0.365476	−	0.365476i
$508$	−37.1303	−	37.1303i	−0.0730910	−	0.0730910i
$509$		−	727.395i		−	1.42907i	−0.699601	−	0.714533i	$-0.746639\pi$
$509$		−	727.395i		−	1.42907i	0.699601	−	0.714533i	$-0.253361\pi$
$510$		0			0
$511$	−434.669			−0.850623
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−8.26856	−	8.26856i	−0.0161180	−	0.0161180i
$514$			50.6022i			0.0984478i
$515$		0			0
$516$	−51.1775			−0.0991813
$517$	538.125	−	538.125i	1.04086	−	1.04086i
$518$	52.3520	+	52.3520i	0.101066	+	0.101066i
$519$		−	33.0617i		−	0.0637027i
$520$		0			0
$521$	440.977			0.846405			0.423203	−	0.906035i	$-0.360906\pi$
$521$	440.977			0.846405			0.423203	+	0.906035i	$0.360906\pi$
$522$	149.918	−	149.918i	0.287199	−	0.287199i
$523$	−335.394	−	335.394i	−0.641288	−	0.641288i	0.309584	−	0.950872i	$-0.399810\pi$
$523$	−335.394	−	335.394i	−0.641288	−	0.641288i	−0.950872	+	0.309584i	$0.899810\pi$
$524$			491.842i			0.938630i
$525$		0			0
$526$	−362.379			−0.688934
$527$	32.1068	−	32.1068i	0.0609237	−	0.0609237i
$528$	57.0226	+	57.0226i	0.107997	+	0.107997i
$529$			1113.79i			2.10546i
$530$		0			0
$531$	85.7172			0.161426
$532$	11.4414	−	11.4414i	0.0215063	−	0.0215063i
$533$	130.386	+	130.386i	0.244626	+	0.244626i
$534$		−	278.392i		−	0.521334i
$535$		0			0
$536$	53.8884			0.100538
$537$	−212.874	+	212.874i	−0.396414	+	0.396414i
$538$	−292.747	−	292.747i	−0.544139	−	0.544139i
$539$		−	419.912i		−	0.779058i
$540$		0			0
$541$	−323.177			−0.597369			−0.298685	−	0.954352i	$-0.596548\pi$
$541$	−323.177			−0.597369			−0.298685	+	0.954352i	$0.596548\pi$
$542$	−522.222	+	522.222i	−0.963509	+	0.963509i
$543$	−256.001	−	256.001i	−0.471457	−	0.471457i
$544$			13.1103i			0.0240998i
$545$		0			0
$546$	37.0543			0.0678649
$547$	622.399	−	622.399i	1.13784	−	1.13784i	0.149005	−	0.988836i	$-0.452393\pi$
$547$	622.399	−	622.399i	1.13784	−	1.13784i	0.988836	−	0.149005i	$-0.0476072\pi$
$548$	44.7031	+	44.7031i	0.0815750	+	0.0815750i
$549$		−	44.4216i		−	0.0809137i
$550$		0			0
$551$	−112.459			−0.204100
$552$	140.405	−	140.405i	0.254356	−	0.254356i
$553$	−56.6731	−	56.6731i	−0.102483	−	0.102483i
$554$		−	603.206i		−	1.08882i
$555$		0			0
$556$	−236.837			−0.425965
$557$	402.619	−	402.619i	0.722835	−	0.722835i	−0.246347	−	0.969182i	$-0.579230\pi$
$557$	402.619	−	402.619i	0.722835	−	0.722835i	0.969182	+	0.246347i	$0.0792301\pi$
$558$	58.7755	+	58.7755i	0.105333	+	0.105333i
$559$			62.1658i			0.111209i
$560$		0			0
$561$	46.7239			0.0832867
$562$	213.384	−	213.384i	0.379687	−	0.379687i
$563$	−611.068	−	611.068i	−1.08538	−	1.08538i	−0.995998	−	0.0893800i	$-0.971511\pi$
$563$	−611.068	−	611.068i	−1.08538	−	1.08538i	−0.0893800	−	0.995998i	$-0.528489\pi$
$564$			226.489i			0.401576i
$565$		0			0
$566$	−415.104			−0.733399
$567$	−22.8785	+	22.8785i	−0.0403501	+	0.0403501i
$568$	6.59632	+	6.59632i	0.0116132	+	0.0116132i
$569$			402.379i			0.707168i	0.935403	+	0.353584i	$0.115037\pi$
$569$			402.379i			0.707168i	−0.935403	+	0.353584i	$0.884963\pi$
$570$		0			0
$571$	402.798			0.705426			0.352713	−	0.935731i	$-0.385259\pi$
$571$	402.798			0.705426			0.352713	+	0.935731i	$0.385259\pi$
$572$	69.2658	−	69.2658i	0.121094	−	0.121094i
$573$	307.382	+	307.382i	0.536444	+	0.536444i
$574$		−	222.791i		−	0.388138i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−222.528	+	222.528i	−0.385663	+	0.385663i	−0.873137	−	0.487474i	$-0.837918\pi$
$577$	−222.528	+	222.528i	−0.385663	+	0.385663i	0.487474	+	0.873137i	$0.337918\pi$
$578$	−283.629	−	283.629i	−0.490707	−	0.490707i
$579$			596.679i			1.03053i
$580$		0			0
$581$	−110.265			−0.189785
$582$	−124.647	+	124.647i	−0.214171	+	0.214171i
$583$	474.963	+	474.963i	0.814689	+	0.814689i
$584$		−	341.982i		−	0.585586i
$585$		0			0
$586$	683.049			1.16561
$587$	−495.692	+	495.692i	−0.844450	+	0.844450i	−0.989434	−	0.144984i	$-0.953687\pi$
$587$	−495.692	+	495.692i	−0.844450	+	0.844450i	0.144984	+	0.989434i	$0.453687\pi$
$588$	88.3676	+	88.3676i	0.150285	+	0.150285i
$589$		−	44.0898i		−	0.0748554i
$590$		0			0
$591$	−342.337			−0.579251
$592$	−41.1887	+	41.1887i	−0.0695756	+	0.0695756i
$593$	−429.389	−	429.389i	−0.724096	−	0.724096i	0.245341	−	0.969437i	$-0.421100\pi$
$593$	−429.389	−	429.389i	−0.724096	−	0.724096i	−0.969437	+	0.245341i	$0.921100\pi$
$594$			85.5339i			0.143996i
$595$		0			0
$596$	493.708			0.828370
$597$	222.192	−	222.192i	0.372181	−	0.372181i
$598$	−170.551	−	170.551i	−0.285202	−	0.285202i
$599$		−	239.308i		−	0.399513i	−0.979846	−	0.199756i	$-0.935985\pi$
$599$		−	239.308i		−	0.399513i	0.979846	−	0.199756i	$-0.0640150\pi$
$600$		0			0
$601$	709.983			1.18134			0.590668	−	0.806915i	$-0.298864\pi$
$601$	709.983			1.18134			0.590668	+	0.806915i	$0.298864\pi$
$602$	53.1115	−	53.1115i	0.0882251	−	0.0882251i
$603$	40.4163	+	40.4163i	0.0670254	+	0.0670254i
$604$			278.865i			0.461697i
$605$		0			0
$606$	−80.4189			−0.132704
$607$	−419.632	+	419.632i	−0.691321	+	0.691321i	−0.962523	−	0.271202i	$-0.912579\pi$
$607$	−419.632	+	419.632i	−0.691321	+	0.691321i	0.271202	+	0.962523i	$0.412579\pi$
$608$	9.00166	+	9.00166i	0.0148054	+	0.0148054i
$609$			311.166i			0.510946i
$610$		0			0
$611$	275.118			0.450275
$612$	−9.83271	+	9.83271i	−0.0160665	+	0.0160665i
$613$	−151.090	−	151.090i	−0.246477	−	0.246477i	0.573046	−	0.819523i	$-0.305762\pi$
$613$	−151.090	−	151.090i	−0.246477	−	0.246477i	−0.819523	+	0.573046i	$0.805762\pi$
$614$		−	228.940i		−	0.372866i
$615$		0			0
$616$	−118.355			−0.192134
$617$	216.560	−	216.560i	0.350988	−	0.350988i	−0.509489	−	0.860477i	$-0.670166\pi$
$617$	216.560	−	216.560i	0.350988	−	0.350988i	0.860477	+	0.509489i	$0.170166\pi$
$618$	−137.867	−	137.867i	−0.223086	−	0.223086i
$619$			29.2443i			0.0472444i	0.999721	+	0.0236222i	$0.00751989\pi$
$619$			29.2443i			0.0472444i	−0.999721	+	0.0236222i	$0.992480\pi$
$620$		0			0
$621$	210.607			0.339142
$622$	177.510	−	177.510i	0.285387	−	0.285387i
$623$	288.913	+	288.913i	0.463744	+	0.463744i
$624$			29.1530i			0.0467196i
$625$		0			0
$626$	660.042			1.05438
$627$	32.0811	−	32.0811i	0.0511661	−	0.0511661i
$628$	−231.490	−	231.490i	−0.368614	−	0.368614i
$629$			33.7497i			0.0536562i
$630$		0			0
$631$	633.546			1.00403			0.502017	−	0.864857i	$-0.332591\pi$
$631$	633.546			1.00403			0.502017	+	0.864857i	$0.332591\pi$
$632$	44.5884	−	44.5884i	0.0705513	−	0.0705513i
$633$	−394.335	−	394.335i	−0.622962	−	0.622962i
$634$			521.787i			0.823008i
$635$		0			0
$636$	−199.905			−0.314317
$637$	107.341	−	107.341i	0.168510	−	0.168510i
$638$	581.665	+	581.665i	0.911700	+	0.911700i
$639$			9.89447i			0.0154843i
$640$		0			0
$641$	504.266			0.786687			0.393343	−	0.919392i	$-0.371318\pi$
$641$	504.266			0.786687			0.393343	+	0.919392i	$0.371318\pi$
$642$	−297.086	+	297.086i	−0.462751	+	0.462751i
$643$	5.84791	+	5.84791i	0.00909472	+	0.00909472i	0.711640	−	0.702545i	$-0.247953\pi$
$643$	5.84791	+	5.84791i	0.00909472	+	0.00909472i	−0.702545	+	0.711640i	$0.747953\pi$
$644$			291.421i			0.452517i
$645$		0			0
$646$	7.37589			0.0114178
$647$	−405.598	+	405.598i	−0.626891	+	0.626891i	−0.947284	−	0.320394i	$-0.896185\pi$
$647$	−405.598	+	405.598i	−0.626891	+	0.626891i	0.320394	+	0.947284i	$0.396185\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			332.574i			0.512440i
$650$		0			0
$651$	−121.993			−0.187394
$652$	−11.4358	+	11.4358i	−0.0175396	+	0.0175396i
$653$	−839.625	−	839.625i	−1.28580	−	1.28580i	−0.937316	−	0.348481i	$-0.886698\pi$
$653$	−839.625	−	839.625i	−1.28580	−	1.28580i	−0.348481	−	0.937316i	$-0.613302\pi$
$654$			401.249i			0.613530i
$655$		0			0
$656$	175.284			0.267202
$657$	256.487	−	256.487i	0.390391	−	0.390391i
$658$	−235.048	−	235.048i	−0.357216	−	0.357216i
$659$		−	549.929i		−	0.834491i	−0.908794	−	0.417245i	$-0.862996\pi$
$659$		−	549.929i		−	0.834491i	0.908794	−	0.417245i	$-0.137004\pi$
$660$		0			0
$661$	−532.250			−0.805219			−0.402610	−	0.915372i	$-0.631897\pi$
$661$	−532.250			−0.805219			−0.402610	+	0.915372i	$0.631897\pi$
$662$	307.794	−	307.794i	0.464945	−	0.464945i
$663$	11.9439	+	11.9439i	0.0180149	+	0.0180149i
$664$		−	86.7530i		−	0.130652i
$665$		0			0
$666$	−61.7831			−0.0927674
$667$	1432.21	−	1432.21i	2.14725	−	2.14725i
$668$	148.013	+	148.013i	0.221576	+	0.221576i
$669$			625.633i			0.935176i
$670$		0			0
$671$	172.351			0.256857
$672$	24.9069	−	24.9069i	0.0370639	−	0.0370639i
$673$	400.025	+	400.025i	0.594390	+	0.594390i	0.938814	−	0.344424i	$-0.111926\pi$
$673$	400.025	+	400.025i	0.594390	+	0.594390i	−0.344424	+	0.938814i	$0.611926\pi$
$674$		−	166.485i		−	0.247011i
$675$		0			0
$676$	−302.588			−0.447615
$677$	109.403	−	109.403i	0.161600	−	0.161600i	−0.621675	−	0.783275i	$-0.713548\pi$
$677$	109.403	−	109.403i	0.161600	−	0.161600i	0.783275	+	0.621675i	$0.213548\pi$
$678$	83.9573	+	83.9573i	0.123831	+	0.123831i
$679$		−	258.715i		−	0.381024i
$680$		0			0
$681$	378.899			0.556386
$682$	−228.043	+	228.043i	−0.334374	+	0.334374i
$683$	215.650	+	215.650i	0.315740	+	0.315740i	0.847128	−	0.531388i	$-0.178329\pi$
$683$	215.650	+	215.650i	0.315740	+	0.315740i	−0.531388	+	0.847128i	$0.678329\pi$
$684$			13.5025i			0.0197405i
$685$		0			0
$686$	−432.535			−0.630518
$687$	−416.074	+	416.074i	−0.605639	+	0.605639i
$688$	41.7863	+	41.7863i	0.0607359	+	0.0607359i
$689$			242.827i			0.352434i
$690$		0			0
$691$	−250.249			−0.362156			−0.181078	−	0.983469i	$-0.557959\pi$
$691$	−250.249			−0.362156			−0.181078	+	0.983469i	$0.557959\pi$
$692$	−26.9948	+	26.9948i	−0.0390098	+	0.0390098i
$693$	−88.7661	−	88.7661i	−0.128090	−	0.128090i
$694$		−	27.0245i		−	0.0389402i
$695$		0			0
$696$	−244.815			−0.351745
$697$	71.8133	−	71.8133i	0.103032	−	0.103032i
$698$	−163.810	−	163.810i	−0.234685	−	0.234685i
$699$			116.214i			0.166257i
$700$		0			0
$701$	−325.266			−0.464003			−0.232002	−	0.972715i	$-0.574527\pi$
$701$	−325.266			−0.464003			−0.232002	+	0.972715i	$0.574527\pi$
$702$	−21.8648	+	21.8648i	−0.0311464	+	0.0311464i
$703$	23.1729	+	23.1729i	0.0329629	+	0.0329629i
$704$		−	93.1175i		−	0.132269i
$705$		0			0
$706$	−470.264			−0.666096
$707$	83.4579	−	83.4579i	0.118045	−	0.118045i
$708$	−69.9878	−	69.9878i	−0.0988528	−	0.0988528i
$709$			650.495i			0.917482i	0.888570	+	0.458741i	$0.151699\pi$
$709$			650.495i			0.917482i	−0.888570	+	0.458741i	$0.848301\pi$
$710$		0			0
$711$	66.8827			0.0940684
$712$	−227.306	+	227.306i	−0.319251	+	0.319251i
$713$	561.502	+	561.502i	0.787521	+	0.787521i
$714$		−	20.4086i		−	0.0285834i
$715$		0			0
$716$	347.622			0.485506
$717$	−511.272	+	511.272i	−0.713071	+	0.713071i
$718$	653.313	+	653.313i	0.909906	+	0.909906i
$719$			96.3152i			0.133957i	0.997754	+	0.0669786i	$0.0213359\pi$
$719$			96.3152i			0.133957i	−0.997754	+	0.0669786i	$0.978664\pi$
$720$		0			0
$721$	286.154			0.396885
$722$	−355.936	+	355.936i	−0.492986	+	0.492986i
$723$	276.772	+	276.772i	0.382811	+	0.382811i
$724$			418.048i			0.577414i
$725$		0			0
$726$	−35.4742			−0.0488625
$727$	−78.7155	+	78.7155i	−0.108274	+	0.108274i	−0.759169	−	0.650894i	$-0.774394\pi$
$727$	−78.7155	+	78.7155i	−0.108274	+	0.108274i	0.650894	+	0.759169i	$0.274394\pi$
$728$	−30.2547	−	30.2547i	−0.0415586	−	0.0415586i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	34.2394			0.0468391
$732$	−36.2701	+	36.2701i	−0.0495493	+	0.0495493i
$733$	643.982	+	643.982i	0.878556	+	0.878556i	0.993385	−	0.114829i	$-0.0366320\pi$
$733$	643.982	+	643.982i	0.878556	+	0.878556i	−0.114829	+	0.993385i	$0.536632\pi$
$734$			567.901i			0.773707i
$735$		0			0
$736$	−229.280			−0.311522
$737$	−156.811	+	156.811i	−0.212769	+	0.212769i
$738$	131.463	+	131.463i	0.178134	+	0.178134i
$739$			199.954i			0.270573i	0.990806	+	0.135287i	$0.0431956\pi$
$739$			199.954i			0.270573i	−0.990806	+	0.135287i	$0.956804\pi$
$740$		0			0
$741$	16.4016			0.0221344
$742$	207.460	−	207.460i	0.279595	−	0.279595i
$743$	−57.5163	−	57.5163i	−0.0774109	−	0.0774109i	0.667341	−	0.744752i	$-0.267432\pi$
$743$	−57.5163	−	57.5163i	−0.0774109	−	0.0774109i	−0.744752	+	0.667341i	$0.767432\pi$
$744$		−	95.9801i		−	0.129005i
$745$		0			0
$746$	−238.790			−0.320094
$747$	65.0647	−	65.0647i	0.0871014	−	0.0871014i
$748$	−38.1499	−	38.1499i	−0.0510025	−	0.0510025i
$749$		−	616.626i		−	0.823266i
$750$		0			0
$751$	−1245.32			−1.65822			−0.829110	−	0.559086i	$-0.811152\pi$
$751$	−1245.32			−1.65822			−0.829110	+	0.559086i	$0.811152\pi$
$752$	184.928	−	184.928i	0.245914	−	0.245914i
$753$	350.812	+	350.812i	0.465886	+	0.465886i
$754$			297.378i			0.394401i
$755$		0			0
$756$	37.3604			0.0494185
$757$	−371.768	+	371.768i	−0.491107	+	0.491107i	−0.908655	−	0.417548i	$-0.862890\pi$
$757$	−371.768	+	371.768i	−0.491107	+	0.491107i	0.417548	+	0.908655i	$0.362890\pi$
$758$	584.256	+	584.256i	0.770786	+	0.770786i
$759$			817.133i			1.07659i
$760$		0			0
$761$	705.973			0.927692			0.463846	−	0.885916i	$-0.346469\pi$
$761$	705.973			0.927692			0.463846	+	0.885916i	$0.346469\pi$
$762$	−45.4751	+	45.4751i	−0.0596786	+	0.0596786i
$763$	−416.412	−	416.412i	−0.545756	−	0.545756i
$764$		−	501.953i		−	0.657007i
$765$		0			0
$766$	733.514			0.957590
$767$	−85.0148	+	85.0148i	−0.110841	+	0.110841i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$			337.427i			0.438787i	0.975636	+	0.219394i	$0.0704079\pi$
$769$			337.427i			0.438787i	−0.975636	+	0.219394i	$0.929592\pi$
$770$		0			0
$771$	61.9747			0.0803823
$772$	487.186	−	487.186i	0.631070	−	0.631070i
$773$	453.969	+	453.969i	0.587282	+	0.587282i	0.936894	−	0.349613i	$-0.113687\pi$
$773$	453.969	+	453.969i	0.587282	+	0.587282i	−0.349613	+	0.936894i	$0.613687\pi$
$774$			62.6794i			0.0809812i
$775$		0			0
$776$	203.548			0.262304
$777$	64.1178	−	64.1178i	0.0825197	−	0.0825197i
$778$	−548.426	−	548.426i	−0.704918	−	0.704918i
$779$		−	98.6156i		−	0.126593i
$780$		0			0
$781$	−38.3895			−0.0491543
$782$	−93.9351	+	93.9351i	−0.120122	+	0.120122i
$783$	−183.611	−	183.611i	−0.234497	−	0.234497i
$784$		−	144.304i		−	0.184061i
$785$		0			0
$786$	602.381			0.766388
$787$	124.228	−	124.228i	0.157851	−	0.157851i	−0.623763	−	0.781614i	$-0.714397\pi$
$787$	124.228	−	124.228i	0.157851	−	0.157851i	0.781614	+	0.623763i	$0.214397\pi$
$788$	279.517	+	279.517i	0.354717	+	0.354717i
$789$			443.822i			0.562513i
$790$		0			0
$791$	−174.260			−0.220303
$792$	69.8381	−	69.8381i	0.0881794	−	0.0881794i
$793$	44.0576	+	44.0576i	0.0555581	+	0.0555581i
$794$		−	883.545i		−	1.11278i
$795$		0			0
$796$	−362.838			−0.455827
$797$	−109.273	+	109.273i	−0.137106	+	0.137106i	−0.772329	−	0.635223i	$-0.780908\pi$
$797$	−109.273	+	109.273i	−0.137106	+	0.137106i	0.635223	+	0.772329i	$0.280908\pi$
$798$	−14.0127	−	14.0127i	−0.0175598	−	0.0175598i
$799$		−	151.528i		−	0.189647i
$800$		0			0
$801$	−340.960			−0.425667
$802$	−117.473	+	117.473i	−0.146476	+	0.146476i
$803$	995.141	+	995.141i	1.23928	+	1.23928i
$804$		−	65.9996i		−	0.0820890i
$805$		0			0
$806$	−116.588			−0.144650
$807$	−358.540	+	358.540i	−0.444287	+	0.444287i
$808$	65.6618	+	65.6618i	0.0812646	+	0.0812646i
$809$		−	1034.43i		−	1.27866i	−0.768933	−	0.639329i	$-0.779212\pi$
$809$		−	1034.43i		−	1.27866i	0.768933	−	0.639329i	$-0.220788\pi$
$810$		0			0
$811$	1192.69			1.47065			0.735323	−	0.677717i	$-0.237030\pi$
$811$	1192.69			1.47065			0.735323	+	0.677717i	$0.237030\pi$
$812$	254.066	−	254.066i	0.312889	−	0.312889i
$813$	639.588	+	639.588i	0.786701	+	0.786701i
$814$		−	239.712i		−	0.294486i
$815$		0			0
$816$	16.0567			0.0196774
$817$	23.5091	−	23.5091i	0.0287749	−	0.0287749i
$818$	−12.4587	−	12.4587i	−0.0152307	−	0.0152307i
$819$		−	45.3820i		−	0.0554115i
$820$		0			0
$821$	−1557.52			−1.89710			−0.948551	−	0.316626i	$-0.897450\pi$
$821$	−1557.52			−1.89710			−0.948551	+	0.316626i	$0.897450\pi$
$822$	54.7499	−	54.7499i	0.0666057	−	0.0666057i
$823$	−596.826	−	596.826i	−0.725184	−	0.725184i	0.244472	−	0.969656i	$-0.421385\pi$
$823$	−596.826	−	596.826i	−0.725184	−	0.725184i	−0.969656	+	0.244472i	$0.921385\pi$
$824$			225.136i			0.273223i
$825$		0			0
$826$	145.265			0.175866
$827$	−389.334	+	389.334i	−0.470779	+	0.470779i	−0.902167	−	0.431388i	$-0.858024\pi$
$827$	−389.334	+	389.334i	−0.470779	+	0.470779i	0.431388	+	0.902167i	$0.358024\pi$
$828$	−171.960	−	171.960i	−0.207681	−	0.207681i
$829$		−	204.337i		−	0.246486i	−0.992377	−	0.123243i	$-0.960671\pi$
$829$		−	204.337i		−	0.246486i	0.992377	−	0.123243i	$-0.0393295\pi$
$830$		0			0
$831$	−738.774			−0.889018
$832$	23.8033	−	23.8033i	0.0286098	−	0.0286098i
$833$	−59.1207	−	59.1207i	−0.0709732	−	0.0709732i
$834$			290.065i			0.347799i
$835$		0			0
$836$	−52.3883			−0.0626654
$837$	71.9850	−	71.9850i	0.0860036	−	0.0860036i
$838$	683.009	+	683.009i	0.815046	+	0.815046i
$839$		−	1420.49i		−	1.69307i	−0.532330	−	0.846537i	$-0.678684\pi$
$839$		−	1420.49i		−	1.69307i	0.532330	−	0.846537i	$-0.321316\pi$
$840$		0			0
$841$	−1656.26			−1.96939
$842$	−238.737	+	238.737i	−0.283535	+	0.283535i
$843$	−261.341	−	261.341i	−0.310013	−	0.310013i
$844$			643.946i			0.762969i
$845$		0			0
$846$	277.391			0.327886
$847$	36.8147	−	36.8147i	0.0434648	−	0.0434648i
$848$	163.222	+	163.222i	0.192479	+	0.192479i
$849$			508.396i			0.598818i
$850$		0			0
$851$	−590.234			−0.693577
$852$	8.07880	−	8.07880i	0.00948216	−	0.00948216i
$853$	436.949	+	436.949i	0.512250	+	0.512250i	0.915215	−	0.402965i	$-0.132021\pi$
$853$	436.949	+	436.949i	0.512250	+	0.512250i	−0.402965	+	0.915215i	$0.632021\pi$
$854$		−	75.2814i		−	0.0881515i
$855$		0			0
$856$	485.140			0.566752
$857$	624.433	−	624.433i	0.728627	−	0.728627i	−0.241719	−	0.970346i	$-0.577711\pi$
$857$	624.433	−	624.433i	0.728627	−	0.728627i	0.970346	+	0.241719i	$0.0777112\pi$
$858$	−84.8329	−	84.8329i	−0.0988729	−	0.0988729i
$859$			393.615i			0.458225i	0.973400	+	0.229112i	$0.0735823\pi$
$859$			393.615i			0.458225i	−0.973400	+	0.229112i	$0.926418\pi$
$860$		0			0
$861$	−272.862			−0.316913
$862$	224.817	−	224.817i	0.260809	−	0.260809i
$863$	−279.850	−	279.850i	−0.324275	−	0.324275i	0.526129	−	0.850405i	$-0.323643\pi$
$863$	−279.850	−	279.850i	−0.324275	−	0.324275i	−0.850405	+	0.526129i	$0.823643\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−445.768			−0.514744
$867$	−347.373	+	347.373i	−0.400661	+	0.400661i
$868$	99.6071	+	99.6071i	0.114755	+	0.114755i
$869$			259.498i			0.298616i
$870$		0			0
$871$	−80.1702			−0.0920439
$872$	327.618	−	327.618i	0.375709	−	0.375709i
$873$	152.661	+	152.661i	0.174870	+	0.174870i
$874$			128.994i			0.147590i
$875$		0			0
$876$	−418.841			−0.478129
$877$	−808.189	+	808.189i	−0.921538	+	0.921538i	−0.997138	−	0.0756004i	$-0.975913\pi$
$877$	−808.189	+	808.189i	−0.921538	+	0.921538i	0.0756004	+	0.997138i	$0.475913\pi$
$878$	−407.104	−	407.104i	−0.463672	−	0.463672i
$879$		−	836.560i		−	0.951718i
$880$		0			0
$881$	1029.03			1.16803			0.584015	−	0.811743i	$-0.301481\pi$
$881$	1029.03			1.16803			0.584015	+	0.811743i	$0.301481\pi$
$882$	108.228	−	108.228i	0.122707	−	0.122707i
$883$	1030.35	+	1030.35i	1.16687	+	1.16687i	0.982939	+	0.183932i	$0.0588825\pi$
$883$	1030.35	+	1030.35i	1.16687	+	1.16687i	0.183932	+	0.982939i	$0.441117\pi$
$884$		−	19.5043i		−	0.0220636i
$885$		0			0
$886$	992.072			1.11972
$887$	−723.194	+	723.194i	−0.815326	+	0.815326i	−0.985427	−	0.170100i	$-0.945591\pi$
$887$	−723.194	+	723.194i	−0.815326	+	0.815326i	0.170100	+	0.985427i	$0.445591\pi$
$888$	50.4457	+	50.4457i	0.0568082	+	0.0568082i
$889$		−	94.3871i		−	0.106172i
$890$		0			0
$891$	104.757			0.117573
$892$	510.827	−	510.827i	0.572676	−	0.572676i
$893$	−104.041	−	104.041i	−0.116507	−	0.116507i
$894$		−	604.667i		−	0.676361i
$895$		0			0
$896$	−40.6729			−0.0453938
$897$	−208.881	+	208.881i	−0.232866	+	0.232866i
$898$	−239.876	−	239.876i	−0.267123	−	0.267123i
$899$		−	979.055i		−	1.08905i
$900$		0			0
$901$	133.743			0.148438
$902$	−510.063	+	510.063i	−0.565480	+	0.565480i
$903$	−65.0480	−	65.0480i	−0.0720355	−	0.0720355i
$904$		−	137.102i		−	0.151661i
$905$		0			0
$906$	341.538			0.376974
$907$	545.990	−	545.990i	0.601974	−	0.601974i	−0.338862	−	0.940836i	$-0.610042\pi$
$907$	545.990	−	545.990i	0.601974	−	0.601974i	0.940836	+	0.338862i	$0.110042\pi$
$908$	−309.370	−	309.370i	−0.340716	−	0.340716i
$909$			98.4927i			0.108353i
$910$		0			0
$911$	−91.1835			−0.100092			−0.0500458	−	0.998747i	$-0.515937\pi$
$911$	−91.1835			−0.100092			−0.0500458	+	0.998747i	$0.515937\pi$
$912$	11.0247	−	11.0247i	0.0120885	−	0.0120885i
$913$	252.444	+	252.444i	0.276500	+	0.276500i
$914$		−	807.544i		−	0.883527i
$915$		0			0
$916$	679.446			0.741753
$917$	−625.144	+	625.144i	−0.681728	+	0.681728i
$918$	12.0426	+	12.0426i	0.0131183	+	0.0131183i
$919$			128.676i			0.140018i	0.997546	+	0.0700088i	$0.0223027\pi$
$919$			128.676i			0.140018i	−0.997546	+	0.0700088i	$0.977697\pi$
$920$		0			0
$921$	−280.393			−0.304444
$922$	−20.4304	+	20.4304i	−0.0221588	+	0.0221588i
$923$	−9.81339	−	9.81339i	−0.0106321	−	0.0106321i
$924$			144.954i			0.156877i
$925$		0			0
$926$	891.989			0.963271
$927$	−168.852	+	168.852i	−0.182149	+	0.182149i
$928$	199.890	+	199.890i	0.215399	+	0.215399i
$929$		−	358.400i		−	0.385791i	−0.981219	−	0.192896i	$-0.938212\pi$
$929$		−	358.400i		−	0.385791i	0.981219	−	0.192896i	$-0.0617879\pi$
$930$		0			0
$931$	−81.1858			−0.0872028
$932$	94.8881	−	94.8881i	0.101811	−	0.101811i
$933$	−217.405	−	217.405i	−0.233017	−	0.233017i
$934$		−	175.825i		−	0.188249i
$935$		0			0
$936$	35.7050			0.0381464
$937$	−8.25178	+	8.25178i	−0.00880660	+	0.00880660i	−0.711496	−	0.702690i	$-0.751982\pi$
$937$	−8.25178	+	8.25178i	−0.00880660	+	0.00880660i	0.702690	+	0.711496i	$0.251982\pi$
$938$	68.4936	+	68.4936i	0.0730209	+	0.0730209i
$939$		−	808.383i		−	0.860898i
$940$		0			0
$941$	−1285.16			−1.36573			−0.682867	−	0.730543i	$-0.739267\pi$
$941$	−1285.16			−1.36573			−0.682867	+	0.730543i	$0.739267\pi$
$942$	−283.516	+	283.516i	−0.300972	+	0.300972i
$943$	1255.91	+	1255.91i	1.33183	+	1.33183i
$944$			114.290i			0.121070i
$945$		0			0
$946$	−243.190			−0.257071
$947$	1014.57	−	1014.57i	1.07135	−	1.07135i	0.0740977	−	0.997251i	$-0.476392\pi$
$947$	1014.57	−	1014.57i	1.07135	−	1.07135i	0.997251	−	0.0740977i	$-0.0236077\pi$
$948$	−54.6095	−	54.6095i	−0.0576049	−	0.0576049i
$949$			508.770i			0.536111i
$950$		0			0
$951$	639.056			0.671983
$952$	−16.6635	+	16.6635i	−0.0175037	+	0.0175037i
$953$	1060.16	+	1060.16i	1.11244	+	1.11244i	0.992820	+	0.119622i	$0.0381682\pi$
$953$	1060.16	+	1060.16i	1.11244	+	1.11244i	0.119622	+	0.992820i	$0.461832\pi$
$954$			244.833i			0.256639i
$955$		0			0
$956$	834.903			0.873330
$957$	712.391	−	712.391i	0.744400	−	0.744400i
$958$	716.386	+	716.386i	0.747793	+	0.747793i
$959$			113.638i			0.118496i
$960$		0			0
$961$	−577.160			−0.600582
$962$	61.2768	−	61.2768i	0.0636973	−	0.0636973i
$963$	363.855	+	363.855i	0.377835	+	0.377835i
$964$		−	451.967i		−	0.468845i
$965$		0			0
$966$	356.916			0.369479
$967$	1009.61	−	1009.61i	1.04406	−	1.04406i	0.0450775	−	0.998983i	$-0.485647\pi$
$967$	1009.61	−	1009.61i	1.04406	−	1.04406i	0.998983	−	0.0450775i	$-0.0143535\pi$
$968$	28.9645	+	28.9645i	0.0299220	+	0.0299220i
$969$		−	9.03359i		−	0.00932259i
$970$		0			0
$971$	−1690.86			−1.74136			−0.870681	−	0.491849i	$-0.836321\pi$
$971$	−1690.86			−1.74136			−0.870681	+	0.491849i	$0.836321\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−301.026	−	301.026i	−0.309379	−	0.309379i
$974$		−	366.488i		−	0.376271i
$975$		0			0
$976$	59.2288			0.0606852
$977$	207.840	−	207.840i	0.212732	−	0.212732i	−0.592695	−	0.805427i	$-0.701936\pi$
$977$	207.840	−	207.840i	0.212732	−	0.212732i	0.805427	+	0.592695i	$0.201936\pi$
$978$	14.0060	+	14.0060i	0.0143210	+	0.0143210i
$979$		−	1322.89i		−	1.35126i
$980$		0			0
$981$	491.428			0.500946
$982$	−796.428	+	796.428i	−0.811027	+	0.811027i
$983$	−68.4345	−	68.4345i	−0.0696180	−	0.0696180i	0.671440	−	0.741059i	$-0.265676\pi$
$983$	−68.4345	−	68.4345i	−0.0696180	−	0.0696180i	−0.741059	+	0.671440i	$0.765676\pi$
$984$		−	214.678i		−	0.218169i
$985$		0			0
$986$	163.789			0.166114
$987$	−287.874	+	287.874i	−0.291665	+	0.291665i
$988$	−13.3918	−	13.3918i	−0.0135545	−	0.0135545i
$989$			598.797i			0.605457i
$990$		0			0
$991$	947.411			0.956015			0.478008	−	0.878356i	$-0.341359\pi$
$991$	947.411			0.956015			0.478008	+	0.878356i	$0.341359\pi$
$992$	−78.3674	+	78.3674i	−0.0789994	+	0.0789994i
$993$	−376.969	−	376.969i	−0.379626	−	0.379626i
$994$			16.7682i			0.0168694i
$995$		0			0
$996$	−106.250			−0.106677
$997$	−771.330	+	771.330i	−0.773651	+	0.773651i	−0.978743	−	0.205092i	$-0.934251\pi$
$997$	−771.330	+	771.330i	−0.773651	+	0.773651i	0.205092	+	0.978743i	$0.434251\pi$
$998$	41.7756	+	41.7756i	0.0418593	+	0.0418593i
$999$			75.6685i			0.0757443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.3.f.b.193.7	✓	16
5.2	odd	4	inner	750.3.f.b.307.7	yes	16
5.3	odd	4		750.3.f.c.307.2	yes	16
5.4	even	2		750.3.f.c.193.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.3.f.b.193.7	✓	16	1.1	even	1	trivial
750.3.f.b.307.7	yes	16	5.2	odd	4	inner
750.3.f.c.193.2	yes	16	5.4	even	2
750.3.f.c.307.2	yes	16	5.3	odd	4

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	750.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(2.54205 - 2.54205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -11.6397 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.97542 - 2.97542i) q^{13} +5.08411i q^{14} -4.00000 q^{16} +(-1.63878 + 1.63878i) q^{17} +(-3.00000 - 3.00000i) q^{18} +2.25042i q^{19} +6.22673 q^{21} +(11.6397 - 11.6397i) q^{22} +(-28.6600 - 28.6600i) q^{23} +4.89898i q^{24} +5.95083 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-5.08411 - 5.08411i) q^{28} +49.9726i q^{29} -19.5918 q^{31} +(4.00000 - 4.00000i) q^{32} +(-14.2556 - 14.2556i) q^{33} -3.27757i q^{34} +6.00000 q^{36} +(10.2972 - 10.2972i) q^{37} +(-2.25042 - 2.25042i) q^{38} -7.28825i q^{39} -43.8211 q^{41} +(-6.22673 + 6.22673i) q^{42} +(-10.4466 - 10.4466i) q^{43} +23.2794i q^{44} +57.3200 q^{46} +(-46.2319 + 46.2319i) q^{47} +(-4.89898 - 4.89898i) q^{48} +36.0759i q^{49} -4.01419 q^{51} +(-5.95083 + 5.95083i) q^{52} +(-40.8055 - 40.8055i) q^{53} -7.34847i q^{54} +10.1682 q^{56} +(-2.75619 + 2.75619i) q^{57} +(-49.9726 - 49.9726i) q^{58} -28.5724i q^{59} -14.8072 q^{61} +(19.5918 - 19.5918i) q^{62} +(7.62616 + 7.62616i) q^{63} +8.00000i q^{64} +28.5113 q^{66} +(13.4721 - 13.4721i) q^{67} +(3.27757 + 3.27757i) q^{68} -70.2024i q^{69} +3.29816 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-85.4956 - 85.4956i) q^{73} +20.5944i q^{74} +4.50083 q^{76} +(-29.5887 + 29.5887i) q^{77} +(7.28825 + 7.28825i) q^{78} -22.2942i q^{79} -9.00000 q^{81} +(43.8211 - 43.8211i) q^{82} +(-21.6882 - 21.6882i) q^{83} -12.4535i q^{84} +20.8931 q^{86} +(-61.2036 + 61.2036i) q^{87} +(-23.2794 - 23.2794i) q^{88} +113.653i q^{89} -15.1273 q^{91} +(-57.3200 + 57.3200i) q^{92} +(-23.9950 - 23.9950i) q^{93} -92.4638i q^{94} +9.79796 q^{96} +(50.8871 - 50.8871i) q^{97} +(-36.0759 - 36.0759i) q^{98} -34.9191i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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