LMFDB - Embedded newform 325.3.g.b.99.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(99,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.99"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.g (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,0,0,-16,-12] 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:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.1
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	325.99
Dual form			325.3.g.b.174.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.581139 + 0.581139i) q^{2} +4.16228i q^{3} +3.32456i q^{4} +(-2.41886 - 2.41886i) q^{6} +(-4.58114 - 4.58114i) q^{7} +(-4.25658 - 4.25658i) q^{8} -8.32456 q^{9} +(5.32456 - 5.32456i) q^{11} -13.8377 q^{12} +(-11.5811 + 5.90569i) q^{13} +5.32456 q^{14} -8.35089 q^{16} -21.9737 q^{17} +(4.83772 - 4.83772i) q^{18} +(-3.16228 - 3.16228i) q^{19} +(19.0680 - 19.0680i) q^{21} +6.18861i q^{22} +8.51317 q^{23} +(17.7171 - 17.7171i) q^{24} +(3.29822 - 10.1623i) q^{26} +2.81139i q^{27} +(15.2302 - 15.2302i) q^{28} +5.81139 q^{29} +(0.513167 + 0.513167i) q^{31} +(21.8794 - 21.8794i) q^{32} +(22.1623 + 22.1623i) q^{33} +(12.7698 - 12.7698i) q^{34} -27.6754i q^{36} +(24.2302 + 24.2302i) q^{37} +3.67544 q^{38} +(-24.5811 - 48.2039i) q^{39} +(4.83772 + 4.83772i) q^{41} +22.1623i q^{42} -30.4868 q^{43} +(17.7018 + 17.7018i) q^{44} +(-4.94733 + 4.94733i) q^{46} +(-37.3662 - 37.3662i) q^{47} -34.7587i q^{48} -7.02633i q^{49} -91.4605i q^{51} +(-19.6338 - 38.5021i) q^{52} +35.8114i q^{53} +(-1.63381 - 1.63381i) q^{54} +39.0000i q^{56} +(13.1623 - 13.1623i) q^{57} +(-3.37722 + 3.37722i) q^{58} +(-58.2719 + 58.2719i) q^{59} -80.3246 q^{61} -0.596443 q^{62} +(38.1359 + 38.1359i) q^{63} -7.97367i q^{64} -25.7587 q^{66} +(-39.0833 + 39.0833i) q^{67} -73.0527i q^{68} +35.4342i q^{69} +(91.5548 + 91.5548i) q^{71} +(35.4342 + 35.4342i) q^{72} +(-31.6228 - 31.6228i) q^{73} -28.1623 q^{74} +(10.5132 - 10.5132i) q^{76} -48.7851 q^{77} +(42.2982 + 13.7281i) q^{78} +18.7851 q^{79} -86.6228 q^{81} -5.62278 q^{82} +(-44.6228 + 44.6228i) q^{83} +(63.3925 + 63.3925i) q^{84} +(17.7171 - 17.7171i) q^{86} +24.1886i q^{87} -45.3288 q^{88} +(-8.89039 + 8.89039i) q^{89} +(80.1096 + 26.0000i) q^{91} +28.3025i q^{92} +(-2.13594 + 2.13594i) q^{93} +43.4299 q^{94} +(91.0680 + 91.0680i) q^{96} +(121.355 - 121.355i) q^{97} +(4.08328 + 4.08328i) q^{98} +(-44.3246 + 44.3246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 16 q^{6} - 12 q^{7} - 36 q^{8} - 8 q^{9} - 4 q^{11} - 68 q^{12} - 40 q^{13} - 4 q^{14} - 84 q^{16} - 12 q^{17} + 32 q^{18} + 32 q^{21} + 72 q^{23} - 24 q^{24} - 88 q^{26} + 4 q^{28} - 40 q^{29}+ \cdots - 152 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 16 * q^6 - 12 * q^7 - 36 * q^8 - 8 * q^9 - 4 * q^11 - 68 * q^12 - 40 * q^13 - 4 * q^14 - 84 * q^16 - 12 * q^17 + 32 * q^18 + 32 * q^21 + 72 * q^23 - 24 * q^24 - 88 * q^26 + 4 * q^28 - 40 * q^29 + 40 * q^31 - 20 * q^32 + 76 * q^33 + 108 * q^34 + 40 * q^37 + 40 * q^38 - 92 * q^39 + 32 * q^41 - 84 * q^43 + 172 * q^44 + 132 * q^46 - 4 * q^47 - 224 * q^52 - 152 * q^54 + 40 * q^57 - 140 * q^58 - 56 * q^59 - 296 * q^61 + 200 * q^62 + 64 * q^63 + 112 * q^66 + 84 * q^67 + 284 * q^71 - 48 * q^72 - 100 * q^74 + 80 * q^76 - 56 * q^77 + 68 * q^78 - 64 * q^79 - 220 * q^81 + 104 * q^82 - 52 * q^83 + 184 * q^84 - 24 * q^86 + 312 * q^88 - 200 * q^89 + 156 * q^91 + 80 * q^93 + 452 * q^94 + 320 * q^96 + 68 * q^97 - 224 * q^98 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.581139	+	0.581139i	−0.290569	+	0.290569i	−0.837305	−	0.546736i	$-0.815870\pi$
$2$	−0.581139	+	0.581139i	−0.290569	+	0.290569i	0.546736	+	0.837305i	$0.315870\pi$
$3$			4.16228i			1.38743i	0.720252	+	0.693713i	$0.244026\pi$
$3$			4.16228i			1.38743i	−0.720252	+	0.693713i	$0.755974\pi$
$4$			3.32456i			0.831139i
$5$		0			0
$5$		0			0
$6$	−2.41886	−	2.41886i	−0.403144	−	0.403144i
$7$	−4.58114	−	4.58114i	−0.654448	−	0.654448i	0.299613	−	0.954061i	$-0.403143\pi$
$7$	−4.58114	−	4.58114i	−0.654448	−	0.654448i	−0.954061	+	0.299613i	$0.903143\pi$
$8$	−4.25658	−	4.25658i	−0.532073	−	0.532073i
$9$	−8.32456			−0.924951
$10$		0			0
$11$	5.32456	−	5.32456i	0.484050	−	0.484050i	−0.422372	−	0.906423i	$-0.638802\pi$
$11$	5.32456	−	5.32456i	0.484050	−	0.484050i	0.906423	+	0.422372i	$0.138802\pi$
$12$	−13.8377			−1.15314
$13$	−11.5811	+	5.90569i	−0.890857	+	0.454284i
$13$	−11.5811	+	5.90569i	−0.890857	+	0.454284i
$14$	5.32456			0.380325
$15$		0			0
$16$	−8.35089			−0.521931
$17$	−21.9737			−1.29257			−0.646284	−	0.763097i	$-0.723678\pi$
$17$	−21.9737			−1.29257			−0.646284	+	0.763097i	$0.723678\pi$
$18$	4.83772	−	4.83772i	0.268762	−	0.268762i
$19$	−3.16228	−	3.16228i	−0.166436	−	0.166436i	0.618975	−	0.785411i	$-0.287548\pi$
$19$	−3.16228	−	3.16228i	−0.166436	−	0.166436i	−0.785411	+	0.618975i	$0.787548\pi$
$20$		0			0
$21$	19.0680	−	19.0680i	0.907999	−	0.907999i
$22$			6.18861i			0.281301i
$23$	8.51317			0.370138			0.185069	−	0.982726i	$-0.440749\pi$
$23$	8.51317			0.370138			0.185069	+	0.982726i	$0.440749\pi$
$24$	17.7171	−	17.7171i	0.738212	−	0.738212i
$25$		0			0
$26$	3.29822	−	10.1623i	0.126855	−	0.390857i
$27$			2.81139i			0.104125i
$28$	15.2302	−	15.2302i	0.543937	−	0.543937i
$29$	5.81139			0.200393			0.100196	−	0.994968i	$-0.468053\pi$
$29$	5.81139			0.200393			0.100196	+	0.994968i	$0.468053\pi$
$30$		0			0
$31$	0.513167	+	0.513167i	0.0165538	+	0.0165538i	0.715335	−	0.698781i	$-0.246274\pi$
$31$	0.513167	+	0.513167i	0.0165538	+	0.0165538i	−0.698781	+	0.715335i	$0.746274\pi$
$32$	21.8794	−	21.8794i	0.683730	−	0.683730i
$33$	22.1623	+	22.1623i	0.671584	+	0.671584i
$34$	12.7698	−	12.7698i	0.375581	−	0.375581i
$35$		0			0
$36$		−	27.6754i		−	0.768762i
$37$	24.2302	+	24.2302i	0.654872	+	0.654872i	0.954162	−	0.299290i	$-0.0967499\pi$
$37$	24.2302	+	24.2302i	0.654872	+	0.654872i	−0.299290	+	0.954162i	$0.596750\pi$
$38$	3.67544			0.0967222
$39$	−24.5811	−	48.2039i	−0.630286	−	1.23600i
$40$		0			0
$41$	4.83772	+	4.83772i	0.117993	+	0.117993i	0.763638	−	0.645645i	$-0.223411\pi$
$41$	4.83772	+	4.83772i	0.117993	+	0.117993i	−0.645645	+	0.763638i	$0.723411\pi$
$42$			22.1623i			0.527673i
$43$	−30.4868			−0.708996			−0.354498	−	0.935057i	$-0.615348\pi$
$43$	−30.4868			−0.708996			−0.354498	+	0.935057i	$0.615348\pi$
$44$	17.7018	+	17.7018i	0.402313	+	0.402313i
$45$		0			0
$46$	−4.94733	+	4.94733i	−0.107551	+	0.107551i
$47$	−37.3662	−	37.3662i	−0.795025	−	0.795025i	0.187281	−	0.982306i	$-0.440033\pi$
$47$	−37.3662	−	37.3662i	−0.795025	−	0.795025i	−0.982306	+	0.187281i	$0.940033\pi$
$48$		−	34.7587i		−	0.724140i
$49$		−	7.02633i		−	0.143395i
$50$		0			0
$51$		−	91.4605i		−	1.79334i
$52$	−19.6338	−	38.5021i	−0.377573	−	0.740426i
$53$			35.8114i			0.675687i	0.941202	+	0.337843i	$0.109697\pi$
$53$			35.8114i			0.675687i	−0.941202	+	0.337843i	$0.890303\pi$
$54$	−1.63381	−	1.63381i	−0.0302557	−	0.0302557i
$55$		0			0
$56$			39.0000i			0.696429i
$57$	13.1623	−	13.1623i	0.230917	−	0.230917i
$58$	−3.37722	+	3.37722i	−0.0582280	+	0.0582280i
$59$	−58.2719	+	58.2719i	−0.987659	+	0.987659i	−0.999925	−	0.0122657i	$-0.996096\pi$
$59$	−58.2719	+	58.2719i	−0.987659	+	0.987659i	0.0122657	+	0.999925i	$0.496096\pi$
$60$		0			0
$61$	−80.3246			−1.31680			−0.658398	−	0.752670i	$-0.728766\pi$
$61$	−80.3246			−1.31680			−0.658398	+	0.752670i	$0.728766\pi$
$62$	−0.596443			−0.00962004
$63$	38.1359	+	38.1359i	0.605332	+	0.605332i
$64$		−	7.97367i		−	0.124589i
$65$		0			0
$66$	−25.7587			−0.390284
$67$	−39.0833	+	39.0833i	−0.583332	+	0.583332i	−0.935817	−	0.352485i	$-0.885337\pi$
$67$	−39.0833	+	39.0833i	−0.583332	+	0.583332i	0.352485	+	0.935817i	$0.385337\pi$
$68$		−	73.0527i		−	1.07430i
$69$			35.4342i			0.513539i
$70$		0			0
$71$	91.5548	+	91.5548i	1.28950	+	1.28950i	0.935088	+	0.354417i	$0.115321\pi$
$71$	91.5548	+	91.5548i	1.28950	+	1.28950i	0.354417	+	0.935088i	$0.384679\pi$
$72$	35.4342	+	35.4342i	0.492141	+	0.492141i
$73$	−31.6228	−	31.6228i	−0.433189	−	0.433189i	0.456523	−	0.889712i	$-0.349095\pi$
$73$	−31.6228	−	31.6228i	−0.433189	−	0.433189i	−0.889712	+	0.456523i	$0.849095\pi$
$74$	−28.1623			−0.380571
$75$		0			0
$76$	10.5132	−	10.5132i	0.138331	−	0.138331i
$77$	−48.7851			−0.633572
$78$	42.2982	+	13.7281i	0.542285	+	0.176001i
$79$	18.7851			0.237785			0.118893	−	0.992907i	$-0.462066\pi$
$79$	18.7851			0.237785			0.118893	+	0.992907i	$0.462066\pi$
$80$		0			0
$81$	−86.6228			−1.06942
$82$	−5.62278			−0.0685704
$83$	−44.6228	+	44.6228i	−0.537624	+	0.537624i	−0.922830	−	0.385207i	$-0.874130\pi$
$83$	−44.6228	+	44.6228i	−0.537624	+	0.537624i	0.385207	+	0.922830i	$0.374130\pi$
$84$	63.3925	+	63.3925i	0.754673	+	0.754673i
$85$		0			0
$86$	17.7171	−	17.7171i	0.206013	−	0.206013i
$87$			24.1886i			0.278030i
$88$	−45.3288			−0.515100
$89$	−8.89039	+	8.89039i	−0.0998920	+	0.0998920i	−0.755287	−	0.655395i	$-0.772502\pi$
$89$	−8.89039	+	8.89039i	−0.0998920	+	0.0998920i	0.655395	+	0.755287i	$0.272502\pi$
$90$		0			0
$91$	80.1096	+	26.0000i	0.880325	+	0.285714i
$92$			28.3025i			0.307636i
$93$	−2.13594	+	2.13594i	−0.0229671	+	0.0229671i
$94$	43.4299			0.462020
$95$		0			0
$96$	91.0680	+	91.0680i	0.948625	+	0.948625i
$97$	121.355	−	121.355i	1.25108	−	1.25108i	0.295850	−	0.955235i	$-0.404397\pi$
$97$	121.355	−	121.355i	1.25108	−	1.25108i	0.955235	−	0.295850i	$-0.0956027\pi$
$98$	4.08328	+	4.08328i	0.0416661	+	0.0416661i
$99$	−44.3246	+	44.3246i	−0.447723	+	0.447723i
$100$		0			0
$101$			104.921i			1.03882i	0.854525	+	0.519411i	$0.173849\pi$
$101$			104.921i			1.03882i	−0.854525	+	0.519411i	$0.826151\pi$
$102$	53.1512	+	53.1512i	0.521091	+	0.521091i
$103$	−35.4342			−0.344021			−0.172011	−	0.985095i	$-0.555026\pi$
$103$	−35.4342			−0.344021			−0.172011	+	0.985095i	$0.555026\pi$
$104$	74.4342	+	24.1580i	0.715713	+	0.232289i
$105$		0			0
$106$	−20.8114	−	20.8114i	−0.196334	−	0.196334i
$107$		−	4.42989i		−	0.0414009i	−0.999786	−	0.0207004i	$-0.993410\pi$
$107$		−	4.42989i		−	0.0414009i	0.999786	−	0.0207004i	$-0.00658962\pi$
$108$	−9.34662			−0.0865427
$109$	−120.774	−	120.774i	−1.10802	−	1.10802i	−0.993411	−	0.114608i	$-0.963439\pi$
$109$	−120.774	−	120.774i	−1.10802	−	1.10802i	−0.114608	−	0.993411i	$-0.536561\pi$
$110$		0			0
$111$	−100.853	+	100.853i	−0.908586	+	0.908586i
$112$	38.2566	+	38.2566i	0.341577	+	0.341577i
$113$		−	68.5438i		−	0.606582i	−0.952898	−	0.303291i	$-0.901915\pi$
$113$		−	68.5438i		−	0.606582i	0.952898	−	0.303291i	$-0.0980854\pi$
$114$			15.2982i			0.134195i
$115$		0			0
$116$			19.3203i			0.166554i
$117$	96.4078	−	49.1623i	0.823999	−	0.420190i
$118$		−	67.7281i		−	0.573967i
$119$	100.664	+	100.664i	0.845919	+	0.845919i
$120$		0			0
$121$			64.2982i			0.531390i
$122$	46.6797	−	46.6797i	0.382621	−	0.382621i
$123$	−20.1359	+	20.1359i	−0.163707	+	0.163707i
$124$	−1.70605	+	1.70605i	−0.0137585	+	0.0137585i
$125$		0			0
$126$	−44.3246			−0.351782
$127$	101.162			0.796553			0.398277	−	0.917265i	$-0.369608\pi$
$127$	101.162			0.796553			0.398277	+	0.917265i	$0.369608\pi$
$128$	92.1512	+	92.1512i	0.719932	+	0.719932i
$129$		−	126.895i		−	0.983680i
$130$		0			0
$131$	−257.732			−1.96742			−0.983711	−	0.179755i	$-0.942469\pi$
$131$	−257.732			−1.96742			−0.983711	+	0.179755i	$0.942469\pi$
$132$	−73.6797	+	73.6797i	−0.558180	+	0.558180i
$133$			28.9737i			0.217847i
$134$		−	45.4256i		−	0.338997i
$135$		0			0
$136$	93.5327	+	93.5327i	0.687741	+	0.687741i
$137$	175.272	+	175.272i	1.27936	+	1.27936i	0.941028	+	0.338329i	$0.109862\pi$
$137$	175.272	+	175.272i	1.27936	+	1.27936i	0.338329	+	0.941028i	$0.390138\pi$
$138$	−20.5922	−	20.5922i	−0.149219	−	0.149219i
$139$	−135.460			−0.974536			−0.487268	−	0.873252i	$-0.662007\pi$
$139$	−135.460			−0.974536			−0.487268	+	0.873252i	$0.662007\pi$
$140$		0			0
$141$	155.528	−	155.528i	1.10304	−	1.10304i
$142$	−106.412			−0.749381
$143$	−30.2192	+	93.1096i	−0.211323	+	0.651116i
$144$	69.5174			0.482760
$145$		0			0
$146$	36.7544			0.251743
$147$	29.2456			0.198949
$148$	−80.5548	+	80.5548i	−0.544289	+	0.544289i
$149$	−36.2192	−	36.2192i	−0.243082	−	0.243082i	0.575042	−	0.818124i	$-0.304986\pi$
$149$	−36.2192	−	36.2192i	−0.243082	−	0.243082i	−0.818124	+	0.575042i	$0.804986\pi$
$150$		0			0
$151$	−75.1776	+	75.1776i	−0.497865	+	0.497865i	−0.910773	−	0.412908i	$-0.864513\pi$
$151$	−75.1776	+	75.1776i	−0.497865	+	0.497865i	0.412908	+	0.910773i	$0.364513\pi$
$152$			26.9210i			0.177112i
$153$	182.921			1.19556
$154$	28.3509	−	28.3509i	0.184097	−	0.184097i
$155$		0			0
$156$	160.257	−	81.7214i	1.02729	−	0.523855i
$157$			55.4562i			0.353224i	0.984281	+	0.176612i	$0.0565138\pi$
$157$			55.4562i			0.353224i	−0.984281	+	0.176612i	$0.943486\pi$
$158$	−10.9167	+	10.9167i	−0.0690932	+	0.0690932i
$159$	−149.057			−0.937465
$160$		0			0
$161$	−39.0000	−	39.0000i	−0.242236	−	0.242236i
$162$	50.3399	−	50.3399i	0.310740	−	0.310740i
$163$	45.4605	+	45.4605i	0.278899	+	0.278899i	0.832669	−	0.553771i	$-0.186812\pi$
$163$	45.4605	+	45.4605i	0.278899	+	0.278899i	−0.553771	+	0.832669i	$0.686812\pi$
$164$	−16.0833	+	16.0833i	−0.0980688	+	0.0980688i
$165$		0			0
$166$		−	51.8641i		−	0.312434i
$167$	−137.215	−	137.215i	−0.821646	−	0.821646i	0.164698	−	0.986344i	$-0.447335\pi$
$167$	−137.215	−	137.215i	−0.821646	−	0.821646i	−0.986344	+	0.164698i	$0.947335\pi$
$168$	−162.329			−0.966243
$169$	99.2456	−	136.789i	0.587252	−	0.809404i
$170$		0			0
$171$	26.3246	+	26.3246i	0.153945	+	0.153945i
$172$		−	101.355i		−	0.589274i
$173$	79.3815			0.458853			0.229426	−	0.973326i	$-0.426315\pi$
$173$	79.3815			0.458853			0.229426	+	0.973326i	$0.426315\pi$
$174$	−14.0569	−	14.0569i	−0.0807870	−	0.0807870i
$175$		0			0
$176$	−44.4648	+	44.4648i	−0.252641	+	0.252641i
$177$	−242.544	−	242.544i	−1.37030	−	1.37030i
$178$		−	10.3331i		−	0.0580511i
$179$			318.329i			1.77837i	0.457545	+	0.889187i	$0.348729\pi$
$179$			318.329i			1.77837i	−0.457545	+	0.889187i	$0.651271\pi$
$180$		0			0
$181$		−	238.144i		−	1.31572i	−0.753142	−	0.657858i	$-0.771463\pi$
$181$		−	238.144i		−	1.31572i	0.753142	−	0.657858i	$-0.228537\pi$
$182$	−61.6644	+	31.4452i	−0.338815	+	0.172776i
$183$		−	334.333i		−	1.82696i
$184$	−36.2370	−	36.2370i	−0.196940	−	0.196940i
$185$		0			0
$186$		−	2.48256i		−	0.0133471i
$187$	−117.000	+	117.000i	−0.625668	+	0.625668i
$188$	124.226	−	124.226i	0.660776	−	0.660776i
$189$	12.8794	−	12.8794i	0.0681448	−	0.0681448i
$190$		0			0
$191$	−3.70605			−0.0194034			−0.00970171	−	0.999953i	$-0.503088\pi$
$191$	−3.70605			−0.0194034			−0.00970171	+	0.999953i	$0.503088\pi$
$192$	33.1886			0.172857
$193$	−43.1359	−	43.1359i	−0.223502	−	0.223502i	0.586469	−	0.809972i	$-0.300517\pi$
$193$	−43.1359	−	43.1359i	−0.223502	−	0.223502i	−0.809972	+	0.586469i	$0.800517\pi$
$194$			141.048i			0.727054i
$195$		0			0
$196$	23.3594			0.119181
$197$	−126.094	+	126.094i	−0.640073	+	0.640073i	−0.950573	−	0.310501i	$-0.899503\pi$
$197$	−126.094	+	126.094i	−0.640073	+	0.640073i	0.310501	+	0.950573i	$0.399503\pi$
$198$		−	51.5174i		−	0.260189i
$199$			152.241i			0.765032i	0.923949	+	0.382516i	$0.124942\pi$
$199$			152.241i			0.765032i	−0.923949	+	0.382516i	$0.875058\pi$
$200$		0			0
$201$	−162.675	−	162.675i	−0.809331	−	0.809331i
$202$	−60.9737	−	60.9737i	−0.301850	−	0.301850i
$203$	−26.6228	−	26.6228i	−0.131147	−	0.131147i
$204$	304.065			1.49052
$205$		0			0
$206$	20.5922	−	20.5922i	0.0999620	−	0.0999620i
$207$	−70.8683			−0.342359
$208$	96.7128	−	49.3178i	0.464965	−	0.237105i
$209$	−33.6754			−0.161127
$210$		0			0
$211$	−47.5744			−0.225471			−0.112736	−	0.993625i	$-0.535961\pi$
$211$	−47.5744			−0.225471			−0.112736	+	0.993625i	$0.535961\pi$
$212$	−119.057			−0.561589
$213$	−381.077	+	381.077i	−1.78909	+	1.78909i
$214$	2.57438	+	2.57438i	0.0120298	+	0.0120298i
$215$		0			0
$216$	11.9669	−	11.9669i	0.0554024	−	0.0554024i
$217$		−	4.70178i		−	0.0216672i
$218$	140.373			0.643913
$219$	131.623	−	131.623i	0.601017	−	0.601017i
$220$		0			0
$221$	254.480	−	129.770i	1.15149	−	0.587193i
$222$		−	117.219i		−	0.528015i
$223$	−38.2260	+	38.2260i	−0.171417	+	0.171417i	−0.787602	−	0.616185i	$-0.788677\pi$
$223$	−38.2260	+	38.2260i	−0.171417	+	0.171417i	0.616185	+	0.787602i	$0.288677\pi$
$224$	−200.465			−0.894932
$225$		0			0
$226$	39.8334	+	39.8334i	0.176254	+	0.176254i
$227$	−44.7324	+	44.7324i	−0.197059	+	0.197059i	−0.798738	−	0.601679i	$-0.794499\pi$
$227$	−44.7324	+	44.7324i	−0.197059	+	0.197059i	0.601679	+	0.798738i	$0.294499\pi$
$228$	43.7587	+	43.7587i	0.191924	+	0.191924i
$229$	167.634	−	167.634i	0.732025	−	0.732025i	−0.238995	−	0.971021i	$-0.576818\pi$
$229$	167.634	−	167.634i	0.732025	−	0.732025i	0.971021	+	0.238995i	$0.0768181\pi$
$230$		0			0
$231$		−	203.057i		−	0.879034i
$232$	−24.7367	−	24.7367i	−0.106624	−	0.106624i
$233$	292.789			1.25661			0.628303	−	0.777969i	$-0.283750\pi$
$233$	292.789			1.25661			0.628303	+	0.777969i	$0.283750\pi$
$234$	−27.4562	+	84.5964i	−0.117334	+	0.361523i
$235$		0			0
$236$	−193.728	−	193.728i	−0.820882	−	0.820882i
$237$			78.1886i			0.329910i
$238$	−117.000			−0.491597
$239$	−0.0153037	−	0.0153037i	−6.40324e−5	−	6.40324e-5i	0.707075	−	0.707139i	$-0.250014\pi$
$239$	−0.0153037	−	0.0153037i	−6.40324e−5	−	6.40324e-5i	−0.707139	+	0.707075i	$0.750014\pi$
$240$		0			0
$241$	240.197	−	240.197i	0.996669	−	0.996669i	−0.00332576	−	0.999994i	$-0.501059\pi$
$241$	240.197	−	240.197i	0.996669	−	0.996669i	0.999994	+	0.00332576i	$0.00105862\pi$
$242$	−37.3662	−	37.3662i	−0.154406	−	0.154406i
$243$		−	335.246i		−	1.37961i
$244$		−	267.043i		−	1.09444i
$245$		0			0
$246$		−	23.4036i		−	0.0951364i
$247$	55.2982	+	17.9473i	0.223879	+	0.0726613i
$248$		−	4.36868i		−	0.0176156i
$249$	−185.732	−	185.732i	−0.745913	−	0.745913i
$250$		0			0
$251$			131.842i			0.525267i	0.964896	+	0.262633i	$0.0845910\pi$
$251$			131.842i			0.525267i	−0.964896	+	0.262633i	$0.915409\pi$
$252$	−126.785	+	126.785i	−0.503115	+	0.503115i
$253$	45.3288	−	45.3288i	0.179165	−	0.179165i
$254$	−58.7893	+	58.7893i	−0.231454	+	0.231454i
$255$		0			0
$256$	−75.2107			−0.293792
$257$	156.579			0.609255			0.304628	−	0.952471i	$-0.401468\pi$
$257$	156.579			0.609255			0.304628	+	0.952471i	$0.401468\pi$
$258$	73.7434	+	73.7434i	0.285827	+	0.285827i
$259$		−	222.004i		−	0.857159i
$260$		0			0
$261$	−48.3772			−0.185353
$262$	149.778	−	149.778i	0.571673	−	0.571673i
$263$			338.982i			1.28891i	0.764644	+	0.644453i	$0.222915\pi$
$263$			338.982i			1.28891i	−0.764644	+	0.644453i	$0.777085\pi$
$264$		−	188.671i		−	0.714664i
$265$		0			0
$266$	−16.8377	−	16.8377i	−0.0632997	−	0.0632997i
$267$	−37.0043	−	37.0043i	−0.138593	−	0.138593i
$268$	−129.935	−	129.935i	−0.484830	−	0.484830i
$269$	222.061			0.825506			0.412753	−	0.910843i	$-0.364567\pi$
$269$	222.061			0.825506			0.412753	+	0.910843i	$0.364567\pi$
$270$		0			0
$271$	39.0722	−	39.0722i	0.144178	−	0.144178i	−0.631333	−	0.775511i	$-0.717492\pi$
$271$	39.0722	−	39.0722i	0.144178	−	0.144178i	0.775511	+	0.631333i	$0.217492\pi$
$272$	183.500			0.674631
$273$	−108.219	+	333.438i	−0.396407	+	1.22139i
$274$	−203.715			−0.743484
$275$		0			0
$276$	−117.803			−0.426822
$277$	−112.053			−0.404522			−0.202261	−	0.979332i	$-0.564829\pi$
$277$	−112.053			−0.404522			−0.202261	+	0.979332i	$0.564829\pi$
$278$	78.7214	−	78.7214i	0.283170	−	0.283170i
$279$	−4.27189	−	4.27189i	−0.0153114	−	0.0153114i
$280$		0			0
$281$	−174.846	+	174.846i	−0.622229	+	0.622229i	−0.946101	−	0.323872i	$-0.895015\pi$
$281$	−174.846	+	174.846i	−0.622229	+	0.622229i	0.323872	+	0.946101i	$0.395015\pi$
$282$			180.767i			0.641019i
$283$	271.201			0.958309			0.479154	−	0.877731i	$-0.340943\pi$
$283$	271.201			0.958309			0.479154	+	0.877731i	$0.340943\pi$
$284$	−304.379	+	304.379i	−1.07176	+	1.07176i
$285$		0			0
$286$	−36.5480	−	71.6712i	−0.127790	−	0.250599i
$287$		−	44.3246i		−	0.154441i
$288$	−182.136	+	182.136i	−0.632416	+	0.632416i
$289$	193.842			0.670734
$290$		0			0
$291$	505.114	+	505.114i	1.73579	+	1.73579i
$292$	105.132	−	105.132i	0.360040	−	0.360040i
$293$	240.156	+	240.156i	0.819643	+	0.819643i	0.986056	−	0.166413i	$-0.0532184\pi$
$293$	240.156	+	240.156i	0.819643	+	0.819643i	−0.166413	+	0.986056i	$0.553218\pi$
$294$	−16.9957	+	16.9957i	−0.0578086	+	0.0578086i
$295$		0			0
$296$		−	206.276i		−	0.696879i
$297$	14.9694	+	14.9694i	0.0504020	+	0.0504020i
$298$	42.0968			0.141264
$299$	−98.5922	+	50.2762i	−0.329740	+	0.168148i
$300$		0			0
$301$	139.664	+	139.664i	0.464001	+	0.464001i
$302$		−	87.3772i		−	0.289329i
$303$	−436.710			−1.44129
$304$	26.4078	+	26.4078i	0.0868679	+	0.0868679i
$305$		0			0
$306$	−106.302	+	106.302i	−0.347394	+	0.347394i
$307$	219.684	+	219.684i	0.715583	+	0.715583i	0.967697	−	0.252114i	$-0.0811259\pi$
$307$	219.684	+	219.684i	0.715583	+	0.715583i	−0.252114	+	0.967697i	$0.581126\pi$
$308$		−	162.189i		−	0.526586i
$309$		−	147.487i		−	0.477304i
$310$		0			0
$311$			341.684i			1.09866i	0.835605	+	0.549331i	$0.185117\pi$
$311$			341.684i			1.09866i	−0.835605	+	0.549331i	$0.814883\pi$
$312$	−100.552	+	309.816i	−0.322283	+	0.992999i
$313$		−	438.517i		−	1.40101i	−0.713645	−	0.700507i	$-0.752957\pi$
$313$		−	438.517i		−	1.40101i	0.713645	−	0.700507i	$-0.247043\pi$
$314$	−32.2278	−	32.2278i	−0.102636	−	0.102636i
$315$		0			0
$316$			62.4520i			0.197633i
$317$	−153.140	+	153.140i	−0.483092	+	0.483092i	−0.906118	−	0.423026i	$-0.860968\pi$
$317$	−153.140	+	153.140i	−0.483092	+	0.483092i	0.423026	+	0.906118i	$0.360968\pi$
$318$	86.6228	−	86.6228i	0.272399	−	0.272399i
$319$	30.9431	−	30.9431i	0.0970002	−	0.0970002i
$320$		0			0
$321$	18.4384			0.0574406
$322$	45.3288			0.140773
$323$	69.4868	+	69.4868i	0.215130	+	0.215130i
$324$		−	287.982i		−	0.888834i
$325$		0			0
$326$	−52.8377			−0.162079
$327$	502.695	−	502.695i	1.53729	−	1.53729i
$328$		−	41.1843i		−	0.125562i
$329$			342.359i			1.04061i
$330$		0			0
$331$	−195.982	−	195.982i	−0.592091	−	0.592091i	0.346105	−	0.938196i	$-0.387504\pi$
$331$	−195.982	−	195.982i	−0.592091	−	0.592091i	−0.938196	+	0.346105i	$0.887504\pi$
$332$	−148.351	−	148.351i	−0.446840	−	0.446840i
$333$	−201.706	−	201.706i	−0.605724	−	0.605724i
$334$	159.482			0.477491
$335$		0			0
$336$	−159.235	+	159.235i	−0.473912	+	0.473912i
$337$	7.32456			0.0217346			0.0108673	−	0.999941i	$-0.496541\pi$
$337$	7.32456			0.0217346			0.0108673	+	0.999941i	$0.496541\pi$
$338$	21.8181	+	137.169i	0.0645507	+	0.405826i
$339$	285.298			0.841588
$340$		0			0
$341$	5.46477			0.0160257
$342$	−30.5964			−0.0894633
$343$	−256.664	+	256.664i	−0.748293	+	0.748293i
$344$	129.770	+	129.770i	0.377238	+	0.377238i
$345$		0			0
$346$	−46.1317	+	46.1317i	−0.133329	+	0.133329i
$347$		−	154.759i		−	0.445991i	−0.974820	−	0.222995i	$-0.928417\pi$
$347$		−	154.759i		−	0.445991i	0.974820	−	0.222995i	$-0.0715835\pi$
$348$	−80.4164			−0.231082
$349$	−220.419	+	220.419i	−0.631573	+	0.631573i	−0.948462	−	0.316890i	$-0.897361\pi$
$349$	−220.419	+	220.419i	−0.631573	+	0.631573i	0.316890	+	0.948462i	$0.397361\pi$
$350$		0			0
$351$	−16.6032	−	32.5591i	−0.0473026	−	0.0927609i
$352$		−	232.996i		−	0.661920i
$353$	331.680	−	331.680i	0.939603	−	0.939603i	−0.0586746	−	0.998277i	$-0.518687\pi$
$353$	331.680	−	331.680i	0.939603	−	0.939603i	0.998277	+	0.0586746i	$0.0186874\pi$
$354$	281.903			0.796337
$355$		0			0
$356$	−29.5566	−	29.5566i	−0.0830241	−	0.0830241i
$357$	−418.993	+	418.993i	−1.17365	+	1.17365i
$358$	−184.993	−	184.993i	−0.516741	−	0.516741i
$359$	−132.785	+	132.785i	−0.369875	+	0.369875i	−0.867431	−	0.497557i	$-0.834231\pi$
$359$	−132.785	+	132.785i	−0.369875	+	0.369875i	0.497557	+	0.867431i	$0.334231\pi$
$360$		0			0
$361$		−	341.000i		−	0.944598i
$362$	138.395	+	138.395i	0.382307	+	0.382307i
$363$	−267.627			−0.737265
$364$	−86.4384	+	266.329i	−0.237468	+	0.731673i
$365$		0			0
$366$	194.294	+	194.294i	0.530858	+	0.530858i
$367$			282.416i			0.769527i	0.923015	+	0.384763i	$0.125717\pi$
$367$			282.416i			0.769527i	−0.923015	+	0.384763i	$0.874283\pi$
$368$	−71.0925			−0.193186
$369$	−40.2719	−	40.2719i	−0.109138	−	0.109138i
$370$		0			0
$371$	164.057	−	164.057i	0.442202	−	0.442202i
$372$	−7.10106	−	7.10106i	−0.0190889	−	0.0190889i
$373$			648.877i			1.73962i	0.493390	+	0.869808i	$0.335758\pi$
$373$			648.877i			1.73962i	−0.493390	+	0.869808i	$0.664242\pi$
$374$		−	135.986i		−	0.363600i
$375$		0			0
$376$			318.105i			0.846023i
$377$	−67.3025	+	34.3203i	−0.178521	+	0.0910352i
$378$			14.9694i			0.0396016i
$379$	429.302	+	429.302i	1.13272	+	1.13272i	0.989722	+	0.143002i	$0.0456755\pi$
$379$	429.302	+	429.302i	1.13272	+	1.13272i	0.143002	+	0.989722i	$0.454325\pi$
$380$		0			0
$381$			421.065i			1.10516i
$382$	2.15373	−	2.15373i	0.00563804	−	0.00563804i
$383$	132.739	−	132.739i	0.346577	−	0.346577i	−0.512256	−	0.858833i	$-0.671190\pi$
$383$	132.739	−	132.739i	0.346577	−	0.346577i	0.858833	+	0.512256i	$0.171190\pi$
$384$	−383.559	+	383.559i	−0.998852	+	0.998852i
$385$		0			0
$386$	50.1359			0.129886
$387$	253.789			0.655786
$388$	403.452	+	403.452i	1.03982	+	1.03982i
$389$			510.342i			1.31193i	0.754790	+	0.655966i	$0.227739\pi$
$389$			510.342i			1.31193i	−0.754790	+	0.655966i	$0.772261\pi$
$390$		0			0
$391$	−187.065			−0.478428
$392$	−29.9082	+	29.9082i	−0.0762964	+	0.0762964i
$393$		−	1072.75i		−	2.72965i
$394$		−	146.557i		−	0.371971i
$395$		0			0
$396$	−147.359	−	147.359i	−0.372120	−	0.372120i
$397$	−142.061	−	142.061i	−0.357837	−	0.357837i	0.505178	−	0.863015i	$-0.331427\pi$
$397$	−142.061	−	142.061i	−0.357837	−	0.357837i	−0.863015	+	0.505178i	$0.831427\pi$
$398$	−88.4733	−	88.4733i	−0.222295	−	0.222295i
$399$	−120.596			−0.302247
$400$		0			0
$401$	144.298	−	144.298i	0.359846	−	0.359846i	−0.503910	−	0.863756i	$-0.668106\pi$
$401$	144.298	−	144.298i	0.359846	−	0.359846i	0.863756	+	0.503910i	$0.168106\pi$
$402$	189.074			0.470333
$403$	−8.97367	−	2.91245i	−0.0222672	−	0.00722693i
$404$	−348.816			−0.863405
$405$		0			0
$406$	30.9431			0.0762144
$407$	258.031			0.633982
$408$	−389.309	+	389.309i	−0.954189	+	0.954189i
$409$	−91.8598	−	91.8598i	−0.224596	−	0.224596i	0.585835	−	0.810431i	$-0.300767\pi$
$409$	−91.8598	−	91.8598i	−0.224596	−	0.224596i	−0.810431	+	0.585835i	$0.800767\pi$
$410$		0			0
$411$	−729.530	+	729.530i	−1.77501	+	1.77501i
$412$		−	117.803i		−	0.285929i
$413$	533.903			1.29274
$414$	41.1843	−	41.1843i	0.0994791	−	0.0994791i
$415$		0			0
$416$	−124.175	+	382.601i	−0.298498	+	0.919713i
$417$		−	563.824i		−	1.35210i
$418$	19.5701	−	19.5701i	0.0468184	−	0.0468184i
$419$	83.2327			0.198646			0.0993231	−	0.995055i	$-0.468332\pi$
$419$	83.2327			0.198646			0.0993231	+	0.995055i	$0.468332\pi$
$420$		0			0
$421$	68.3135	+	68.3135i	0.162265	+	0.162265i	0.783569	−	0.621304i	$-0.213397\pi$
$421$	68.3135	+	68.3135i	0.162265	+	0.162265i	−0.621304	+	0.783569i	$0.713397\pi$
$422$	27.6473	−	27.6473i	0.0655150	−	0.0655150i
$423$	311.057	+	311.057i	0.735359	+	0.735359i
$424$	152.434	−	152.434i	0.359515	−	0.359515i
$425$		0			0
$426$		−	442.917i		−	1.03971i
$427$	367.978	+	367.978i	0.861775	+	0.861775i
$428$	14.7274			0.0344099
$429$	−387.548	−	125.781i	−0.903375	−	0.293195i
$430$		0			0
$431$	469.963	+	469.963i	1.09040	+	1.09040i	0.995485	+	0.0949152i	$0.0302580\pi$
$431$	469.963	+	469.963i	1.09040	+	1.09040i	0.0949152	+	0.995485i	$0.469742\pi$
$432$		−	23.4776i		−	0.0543463i
$433$	−122.140			−0.282079			−0.141040	−	0.990004i	$-0.545044\pi$
$433$	−122.140			−0.282079			−0.141040	+	0.990004i	$0.545044\pi$
$434$	2.73239	+	2.73239i	0.00629582	+	0.00629582i
$435$		0			0
$436$	401.520	−	401.520i	0.920917	−	0.920917i
$437$	−26.9210	−	26.9210i	−0.0616041	−	0.0616041i
$438$			152.982i			0.349274i
$439$		−	31.2897i		−	0.0712749i	−0.999365	−	0.0356374i	$-0.988654\pi$
$439$		−	31.2897i		−	0.0712749i	0.999365	−	0.0356374i	$-0.0113462\pi$
$440$		0			0
$441$			58.4911i			0.132633i
$442$	−72.4740	+	223.302i	−0.163968	+	0.505209i
$443$		−	567.372i		−	1.28075i	−0.768062	−	0.640375i	$-0.778779\pi$
$443$		−	567.372i		−	1.28075i	0.768062	−	0.640375i	$-0.221221\pi$
$444$	−335.291	−	335.291i	−0.755161	−	0.755161i
$445$		0			0
$446$		−	44.4292i		−	0.0996170i
$447$	150.754	−	150.754i	0.337258	−	0.337258i
$448$	−36.5285	+	36.5285i	−0.0815368	+	0.0815368i
$449$	530.873	−	530.873i	1.18234	−	1.18234i	0.203209	−	0.979135i	$-0.434863\pi$
$449$	530.873	−	530.873i	1.18234	−	1.18234i	0.979135	−	0.203209i	$-0.0651371\pi$
$450$		0			0
$451$	51.5174			0.114229
$452$	227.878			0.504154
$453$	−312.910	−	312.910i	−0.690750	−	0.690750i
$454$		−	51.9915i		−	0.114519i
$455$		0			0
$456$	−112.053			−0.245730
$457$	−232.092	+	232.092i	−0.507860	+	0.507860i	−0.913869	−	0.406009i	$-0.866920\pi$
$457$	−232.092	+	232.092i	−0.507860	+	0.507860i	0.406009	+	0.913869i	$0.366920\pi$
$458$			194.837i			0.425408i
$459$		−	61.7765i		−	0.134589i
$460$		0			0
$461$	−209.748	−	209.748i	−0.454984	−	0.454984i	0.442021	−	0.897005i	$-0.354262\pi$
$461$	−209.748	−	209.748i	−0.454984	−	0.454984i	−0.897005	+	0.442021i	$0.854262\pi$
$462$	118.004	+	118.004i	0.255421	+	0.255421i
$463$	−127.645	−	127.645i	−0.275691	−	0.275691i	0.555695	−	0.831386i	$-0.312452\pi$
$463$	−127.645	−	127.645i	−0.275691	−	0.275691i	−0.831386	+	0.555695i	$0.812452\pi$
$464$	−48.5303			−0.104591
$465$		0			0
$466$	−170.151	+	170.151i	−0.365131	+	0.365131i
$467$	687.737			1.47267			0.736335	−	0.676617i	$-0.236555\pi$
$467$	687.737			1.47267			0.736335	+	0.676617i	$0.236555\pi$
$468$	163.443	+	320.513i	0.349237	+	0.684857i
$469$	358.092			0.763522
$470$		0			0
$471$	−230.824			−0.490073
$472$	496.078			1.05101
$473$	−162.329	+	162.329i	−0.343190	+	0.343190i
$474$	−45.4384	−	45.4384i	−0.0958617	−	0.0958617i
$475$		0			0
$476$	−334.664	+	334.664i	−0.703077	+	0.703077i
$477$		−	298.114i		−	0.624977i
$478$	0.0177872			3.72117e−5
$479$	318.642	−	318.642i	0.665224	−	0.665224i	−0.291383	−	0.956607i	$-0.594115\pi$
$479$	318.642	−	318.642i	0.665224	−	0.665224i	0.956607	+	0.291383i	$0.0941152\pi$
$480$		0			0
$481$	−423.710	−	137.517i	−0.880895	−	0.285899i
$482$			279.176i			0.579203i
$483$	162.329	−	162.329i	0.336085	−	0.336085i
$484$	−213.763			−0.441659
$485$		0			0
$486$	194.824	+	194.824i	0.400873	+	0.400873i
$487$	−557.065	+	557.065i	−1.14387	+	1.14387i	−0.156136	+	0.987736i	$0.549904\pi$
$487$	−557.065	+	557.065i	−1.14387	+	1.14387i	−0.987736	+	0.156136i	$0.950096\pi$
$488$	341.908	+	341.908i	0.700632	+	0.700632i
$489$	−189.219	+	189.219i	−0.386951	+	0.386951i
$490$		0			0
$491$		−	400.698i		−	0.816085i	−0.912963	−	0.408042i	$-0.866212\pi$
$491$		−	400.698i		−	0.816085i	0.912963	−	0.408042i	$-0.133788\pi$
$492$	−66.9431	−	66.9431i	−0.136063	−	0.136063i
$493$	−127.698			−0.259021
$494$	−42.5658	+	21.7061i	−0.0861657	+	0.0439394i
$495$		0			0
$496$	−4.28540	−	4.28540i	−0.00863992	−	0.00863992i
$497$		−	838.851i		−	1.68783i
$498$	215.873			0.433479
$499$	−102.671	−	102.671i	−0.205754	−	0.205754i	0.596706	−	0.802460i	$-0.296476\pi$
$499$	−102.671	−	102.671i	−0.205754	−	0.205754i	−0.802460	+	0.596706i	$0.796476\pi$
$500$		0			0
$501$	571.127	−	571.127i	1.13997	−	1.13997i
$502$	−76.6185	−	76.6185i	−0.152627	−	0.152627i
$503$			46.2719i			0.0919918i	0.998942	+	0.0459959i	$0.0146461\pi$
$503$			46.2719i			0.0919918i	−0.998942	+	0.0459959i	$0.985354\pi$
$504$		−	324.658i		−	0.644162i
$505$		0			0
$506$			52.6847i			0.104120i
$507$	569.355	+	413.088i	1.12299	+	0.814768i
$508$			336.320i			0.662046i
$509$	372.280	+	372.280i	0.731396	+	0.731396i	0.970896	−	0.239500i	$-0.0769837\pi$
$509$	372.280	+	372.280i	0.731396	+	0.731396i	−0.239500	+	0.970896i	$0.576984\pi$
$510$		0			0
$511$			289.737i			0.566999i
$512$	−324.897	+	324.897i	−0.634565	+	0.634565i
$513$	8.89039	−	8.89039i	0.0173302	−	0.0173302i
$514$	−90.9939	+	90.9939i	−0.177031	+	0.177031i
$515$		0			0
$516$	421.868			0.817574
$517$	−397.917			−0.769665
$518$	129.015	+	129.015i	0.249064	+	0.249064i
$519$			330.408i			0.636624i
$520$		0			0
$521$	27.1224			0.0520584			0.0260292	−	0.999661i	$-0.491714\pi$
$521$	27.1224			0.0520584			0.0260292	+	0.999661i	$0.491714\pi$
$522$	28.1139	−	28.1139i	0.0538580	−	0.0538580i
$523$		−	473.851i		−	0.906024i	−0.891504	−	0.453012i	$-0.850349\pi$
$523$		−	473.851i		−	0.906024i	0.891504	−	0.453012i	$-0.149651\pi$
$524$		−	856.846i		−	1.63520i
$525$		0			0
$526$	−196.996	−	196.996i	−0.374517	−	0.374517i
$527$	−11.2762	−	11.2762i	−0.0213969	−	0.0213969i
$528$	−185.075	−	185.075i	−0.350520	−	0.350520i
$529$	−456.526			−0.862998
$530$		0			0
$531$	485.088	−	485.088i	0.913536	−	0.913536i
$532$	−96.3246			−0.181061
$533$	−84.5964	−	27.4562i	−0.158718	−	0.0515126i
$534$	43.0092			0.0805416
$535$		0			0
$536$	332.722			0.620751
$537$	−1324.97			−2.46736
$538$	−129.048	+	129.048i	−0.239867	+	0.239867i
$539$	−37.4121	−	37.4121i	−0.0694102	−	0.0694102i
$540$		0			0
$541$	531.379	−	531.379i	0.982216	−	0.982216i	−0.0176283	−	0.999845i	$-0.505612\pi$
$541$	531.379	−	531.379i	0.982216	−	0.982216i	0.999845	+	0.0176283i	$0.00561156\pi$
$542$			45.4128i			0.0837874i
$543$	991.223			1.82546
$544$	−480.770	+	480.770i	−0.883768	+	0.883768i
$545$		0			0
$546$	−130.884	−	256.664i	−0.239714	−	0.470081i
$547$		−	716.223i		−	1.30937i	−0.755903	−	0.654683i	$-0.772802\pi$
$547$		−	716.223i		−	1.30937i	0.755903	−	0.654683i	$-0.227198\pi$
$548$	−582.701	+	582.701i	−1.06332	+	1.06332i
$549$	668.666			1.21797
$550$		0			0
$551$	−18.3772	−	18.3772i	−0.0333525	−	0.0333525i
$552$	150.828	−	150.828i	0.273240	−	0.273240i
$553$	−86.0569	−	86.0569i	−0.155618	−	0.155618i
$554$	65.1182	−	65.1182i	0.117542	−	0.117542i
$555$		0			0
$556$		−	450.346i		−	0.809975i
$557$	−248.577	−	248.577i	−0.446278	−	0.446278i	0.447837	−	0.894115i	$-0.352194\pi$
$557$	−248.577	−	248.577i	−0.446278	−	0.446278i	−0.894115	+	0.447837i	$0.852194\pi$
$558$	4.96512			0.00889806
$559$	353.072	−	180.046i	0.631614	−	0.322086i
$560$		0			0
$561$	−486.986	−	486.986i	−0.868069	−	0.868069i
$562$		−	203.220i		−	0.361601i
$563$	−708.329			−1.25813			−0.629066	−	0.777352i	$-0.716563\pi$
$563$	−708.329			−1.25813			−0.629066	+	0.777352i	$0.716563\pi$
$564$	517.063	+	517.063i	0.916778	+	0.916778i
$565$		0			0
$566$	−157.606	+	157.606i	−0.278455	+	0.278455i
$567$	396.831	+	396.831i	0.699878	+	0.699878i
$568$		−	779.421i		−	1.37222i
$569$			349.394i			0.614050i	0.951701	+	0.307025i	$0.0993335\pi$
$569$			349.394i			0.614050i	−0.951701	+	0.307025i	$0.900667\pi$
$570$		0			0
$571$			906.285i			1.58719i	0.608447	+	0.793594i	$0.291793\pi$
$571$			906.285i			1.58719i	−0.608447	+	0.793594i	$0.708207\pi$
$572$	−309.548	−	100.465i	−0.541168	−	0.175639i
$573$		−	15.4256i		−	0.0269208i
$574$	25.7587	+	25.7587i	0.0448758	+	0.0448758i
$575$		0			0
$576$			66.3772i			0.115238i
$577$	−357.842	+	357.842i	−0.620177	+	0.620177i	−0.945577	−	0.325400i	$-0.894501\pi$
$577$	−357.842	+	357.842i	−0.620177	+	0.620177i	0.325400	+	0.945577i	$0.394501\pi$
$578$	−112.649	+	112.649i	−0.194895	+	0.194895i
$579$	179.544	−	179.544i	0.310093	−	0.310093i
$580$		0			0
$581$	408.846			0.703694
$582$	−587.083			−1.00873
$583$	190.680	+	190.680i	0.327066	+	0.327066i
$584$			269.210i			0.460976i
$585$		0			0
$586$	−279.127			−0.476327
$587$	−405.311	+	405.311i	−0.690479	+	0.690479i	−0.962337	−	0.271858i	$-0.912362\pi$
$587$	−405.311	+	405.311i	−0.690479	+	0.690479i	0.271858	+	0.962337i	$0.412362\pi$
$588$			97.2285i			0.165355i
$589$		−	3.24555i		−	0.00551028i
$590$		0			0
$591$	−524.840	−	524.840i	−0.888053	−	0.888053i
$592$	−202.344	−	202.344i	−0.341798	−	0.341798i
$593$	−550.285	−	550.285i	−0.927967	−	0.927967i	0.0696070	−	0.997574i	$-0.477825\pi$
$593$	−550.285	−	550.285i	−0.927967	−	0.927967i	−0.997574	+	0.0696070i	$0.977825\pi$
$594$	−17.3986			−0.0292906
$595$		0			0
$596$	120.413	−	120.413i	0.202035	−	0.202035i
$597$	−633.670			−1.06142
$598$	28.0783	−	86.5132i	0.0469537	−	0.144671i
$599$	−235.228			−0.392702			−0.196351	−	0.980534i	$-0.562909\pi$
$599$	−235.228			−0.392702			−0.196351	+	0.980534i	$0.562909\pi$
$600$		0			0
$601$	−559.298			−0.930612			−0.465306	−	0.885150i	$-0.654056\pi$
$601$	−559.298			−0.930612			−0.465306	+	0.885150i	$0.654056\pi$
$602$	−162.329			−0.269649
$603$	325.351	−	325.351i	0.539554	−	0.539554i
$604$	−249.932	−	249.932i	−0.413795	−	0.413795i
$605$		0			0
$606$	253.789	−	253.789i	0.418794	−	0.418794i
$607$		−	507.912i		−	0.836757i	−0.908273	−	0.418379i	$-0.862598\pi$
$607$		−	507.912i		−	0.836757i	0.908273	−	0.418379i	$-0.137402\pi$
$608$	−138.377			−0.227594
$609$	110.811	−	110.811i	0.181956	−	0.181956i
$610$		0			0
$611$	653.416	+	212.070i	1.06942	+	0.347086i
$612$			608.131i			0.993678i
$613$	−231.540	+	231.540i	−0.377715	+	0.377715i	−0.870277	−	0.492562i	$-0.836060\pi$
$613$	−231.540	+	231.540i	−0.377715	+	0.377715i	0.492562	+	0.870277i	$0.336060\pi$
$614$	−255.334			−0.415853
$615$		0			0
$616$	207.658	+	207.658i	0.337107	+	0.337107i
$617$	271.412	−	271.412i	0.439890	−	0.439890i	−0.452085	−	0.891975i	$-0.649320\pi$
$617$	271.412	−	271.412i	0.439890	−	0.439890i	0.891975	+	0.452085i	$0.149320\pi$
$618$	85.7103	+	85.7103i	0.138690	+	0.138690i
$619$	235.048	−	235.048i	0.379723	−	0.379723i	−0.491279	−	0.871002i	$-0.663471\pi$
$619$	235.048	−	235.048i	0.379723	−	0.379723i	0.871002	+	0.491279i	$0.163471\pi$
$620$		0			0
$621$			23.9338i			0.0385408i
$622$	−198.566	−	198.566i	−0.319238	−	0.319238i
$623$	81.4562			0.130748
$624$	205.274	+	402.546i	0.328965	+	0.645105i
$625$		0			0
$626$	254.840	+	254.840i	0.407092	+	0.407092i
$627$		−	140.167i		−	0.223551i
$628$	−184.367			−0.293578
$629$	−532.427	−	532.427i	−0.846466	−	0.846466i
$630$		0			0
$631$	−95.4630	+	95.4630i	−0.151288	+	0.151288i	−0.778693	−	0.627405i	$-0.784117\pi$
$631$	−95.4630	+	95.4630i	−0.151288	+	0.151288i	0.627405	+	0.778693i	$0.284117\pi$
$632$	−79.9602	−	79.9602i	−0.126519	−	0.126519i
$633$		−	198.018i		−	0.312824i
$634$		−	177.991i		−	0.280744i
$635$		0			0
$636$		−	495.548i		−	0.779164i
$637$	41.4954	+	81.3729i	0.0651419	+	0.127744i
$638$			35.9644i			0.0563706i
$639$	−762.153	−	762.153i	−1.19273	−	1.19273i
$640$		0			0
$641$		−	904.710i		−	1.41140i	−0.708508	−	0.705702i	$-0.750632\pi$
$641$		−	904.710i		−	1.41140i	0.708508	−	0.705702i	$-0.249368\pi$
$642$	−10.7153	+	10.7153i	−0.0166905	+	0.0166905i
$643$	−108.312	+	108.312i	−0.168447	+	0.168447i	−0.786297	−	0.617849i	$-0.788004\pi$
$643$	−108.312	+	108.312i	−0.168447	+	0.168447i	0.617849	+	0.786297i	$0.288004\pi$
$644$	129.658	−	129.658i	0.201332	−	0.201332i
$645$		0			0
$646$	−80.7630			−0.125020
$647$	−306.474			−0.473685			−0.236842	−	0.971548i	$-0.576112\pi$
$647$	−306.474			−0.473685			−0.236842	+	0.971548i	$0.576112\pi$
$648$	368.717	+	368.717i	0.569008	+	0.569008i
$649$			620.544i			0.956154i
$650$		0			0
$651$	19.5701			0.0300616
$652$	−151.136	+	151.136i	−0.231804	+	0.231804i
$653$			1009.69i			1.54624i	0.634262	+	0.773118i	$0.281304\pi$
$653$			1009.69i			1.54624i	−0.634262	+	0.773118i	$0.718696\pi$
$654$			584.271i			0.893381i
$655$		0			0
$656$	−40.3993	−	40.3993i	−0.0615843	−	0.0615843i
$657$	263.246	+	263.246i	0.400678	+	0.400678i
$658$	−198.958	−	198.958i	−0.302368	−	0.302368i
$659$	211.009			0.320196			0.160098	−	0.987101i	$-0.448819\pi$
$659$	211.009			0.320196			0.160098	+	0.987101i	$0.448819\pi$
$660$		0			0
$661$	−61.5922	+	61.5922i	−0.0931803	+	0.0931803i	−0.752160	−	0.658980i	$-0.770988\pi$
$661$	−61.5922	+	61.5922i	−0.0931803	+	0.0931803i	0.658980	+	0.752160i	$0.270988\pi$
$662$	227.786			0.344087
$663$	540.138	+	1059.22i	0.814687	+	1.59761i
$664$	379.881			0.572110
$665$		0			0
$666$	234.438			0.352010
$667$	49.4733			0.0741729
$668$	456.179	−	456.179i	0.682902	−	0.682902i
$669$	−159.107	−	159.107i	−0.237828	−	0.237828i
$670$		0			0
$671$	−427.693	+	427.693i	−0.637396	+	0.637396i
$672$		−	834.390i		−	1.24165i
$673$	105.500			0.156760			0.0783801	−	0.996924i	$-0.475025\pi$
$673$	105.500			0.156760			0.0783801	+	0.996924i	$0.475025\pi$
$674$	−4.25658	+	4.25658i	−0.00631541	+	0.00631541i
$675$		0			0
$676$	454.764	+	329.947i	0.672727	+	0.488088i
$677$		−	215.969i		−	0.319009i	−0.987197	−	0.159505i	$-0.949010\pi$
$677$		−	215.969i		−	0.319009i	0.987197	−	0.159505i	$-0.0509897\pi$
$678$	−165.798	+	165.798i	−0.244540	+	0.244540i
$679$	−1111.89			−1.63754
$680$		0			0
$681$	−186.189	−	186.189i	−0.273405	−	0.273405i
$682$	−3.17579	+	3.17579i	−0.00465659	+	0.00465659i
$683$	−672.956	−	672.956i	−0.985294	−	0.985294i	0.0145993	−	0.999893i	$-0.495353\pi$
$683$	−672.956	−	672.956i	−0.985294	−	0.985294i	−0.999893	+	0.0145993i	$0.995353\pi$
$684$	−87.5174	+	87.5174i	−0.127949	+	0.127949i
$685$		0			0
$686$		−	298.315i		−	0.434862i
$687$	697.738	+	697.738i	1.01563	+	1.01563i
$688$	254.592			0.370047
$689$	−211.491	−	414.737i	−0.306954	−	0.601940i
$690$		0			0
$691$	−563.105	−	563.105i	−0.814913	−	0.814913i	0.170453	−	0.985366i	$-0.445477\pi$
$691$	−563.105	−	563.105i	−0.814913	−	0.814913i	−0.985366	+	0.170453i	$0.945477\pi$
$692$			263.908i			0.381370i
$693$	406.114			0.586023
$694$	89.9363	+	89.9363i	0.129591	+	0.129591i
$695$		0			0
$696$	102.961	−	102.961i	0.147932	−	0.147932i
$697$	−106.302	−	106.302i	−0.152514	−	0.152514i
$698$		−	256.188i		−	0.367031i
$699$			1218.67i			1.74345i
$700$		0			0
$701$		−	179.934i		−	0.256682i	−0.991730	−	0.128341i	$-0.959035\pi$
$701$		−	179.934i		−	0.256682i	0.991730	−	0.128341i	$-0.0409651\pi$
$702$	28.5701	+	9.27258i	0.0406982	+	0.0132088i
$703$		−	153.246i		−	0.217988i
$704$	−42.4562	−	42.4562i	−0.0603071	−	0.0603071i
$705$		0			0
$706$			385.504i			0.546040i
$707$	480.658	−	480.658i	0.679855	−	0.679855i
$708$	806.350	−	806.350i	1.13891	−	1.13891i
$709$	291.315	−	291.315i	0.410882	−	0.410882i	−0.471164	−	0.882046i	$-0.656166\pi$
$709$	291.315	−	291.315i	0.410882	−	0.410882i	0.882046	+	0.471164i	$0.156166\pi$
$710$		0			0
$711$	−156.377			−0.219940
$712$	75.6854			0.106300
$713$	4.36868	+	4.36868i	0.00612718	+	0.00612718i
$714$		−	486.986i		−	0.682054i
$715$		0			0
$716$	−1058.30			−1.47808
$717$	0.0636984	−	0.0636984i	8.88401e−5	−	8.88401e-5i
$718$		−	154.333i		−	0.214949i
$719$		−	487.565i		−	0.678116i	−0.940766	−	0.339058i	$-0.889892\pi$
$719$		−	487.565i		−	0.678116i	0.940766	−	0.339058i	$-0.110108\pi$
$720$		0			0
$721$	162.329	+	162.329i	0.225144	+	0.225144i
$722$	198.168	+	198.168i	0.274471	+	0.274471i
$723$	999.767	+	999.767i	1.38280	+	1.38280i
$724$	791.725			1.09354
$725$		0			0
$726$	155.528	−	155.528i	0.214227	−	0.214227i
$727$	277.337			0.381482			0.190741	−	0.981640i	$-0.438911\pi$
$727$	277.337			0.381482			0.190741	+	0.981640i	$0.438911\pi$
$728$	−230.322	−	451.664i	−0.316376	−	0.620418i
$729$	615.780			0.844691
$730$		0			0
$731$	669.907			0.916426
$732$	1111.51			1.51845
$733$	−235.559	+	235.559i	−0.321363	+	0.321363i	−0.849290	−	0.527927i	$-0.822970\pi$
$733$	−235.559	+	235.559i	−0.321363	+	0.321363i	0.527927	+	0.849290i	$0.322970\pi$
$734$	−164.123	−	164.123i	−0.223601	−	0.223601i
$735$		0			0
$736$	186.263	−	186.263i	0.253074	−	0.253074i
$737$			416.202i			0.564725i
$738$	46.8071			0.0634243
$739$	667.732	−	667.732i	0.903561	−	0.903561i	−0.0921811	−	0.995742i	$-0.529384\pi$
$739$	667.732	−	667.732i	0.903561	−	0.903561i	0.995742	+	0.0921811i	$0.0293839\pi$
$740$		0			0
$741$	−74.7018	+	230.167i	−0.100812	+	0.310616i
$742$			190.680i			0.256981i
$743$	335.358	−	335.358i	0.451356	−	0.451356i	−0.444448	−	0.895804i	$-0.646600\pi$
$743$	335.358	−	335.358i	0.451356	−	0.451356i	0.895804	+	0.444448i	$0.146600\pi$
$744$	18.1836			0.0244404
$745$		0			0
$746$	−377.088	−	377.088i	−0.505479	−	0.505479i
$747$	371.465	−	371.465i	0.497275	−	0.497275i
$748$	−388.973	−	388.973i	−0.520017	−	0.520017i
$749$	−20.2939	+	20.2939i	−0.0270947	+	0.0270947i
$750$		0			0
$751$			1300.24i			1.73134i	0.500615	+	0.865670i	$0.333107\pi$
$751$			1300.24i			1.73134i	−0.500615	+	0.865670i	$0.666893\pi$
$752$	312.041	+	312.041i	0.414948	+	0.414948i
$753$	−548.763			−0.728769
$754$	19.1672	−	59.0569i	0.0254207	−	0.0783249i
$755$		0			0
$756$	42.8181	+	42.8181i	0.0566378	+	0.0566378i
$757$			1155.45i			1.52636i	0.646188	+	0.763178i	$0.276362\pi$
$757$			1155.45i			1.52636i	−0.646188	+	0.763178i	$0.723638\pi$
$758$	−498.969			−0.658270
$759$	188.671	+	188.671i	0.248579	+	0.248579i
$760$		0			0
$761$	−205.412	+	205.412i	−0.269924	+	0.269924i	−0.829069	−	0.559146i	$-0.811129\pi$
$761$	−205.412	+	205.412i	−0.269924	+	0.269924i	0.559146	+	0.829069i	$0.311129\pi$
$762$	−244.698	−	244.698i	−0.321125	−	0.321125i
$763$			1106.57i			1.45028i
$764$		−	12.3210i		−	0.0161269i
$765$		0			0
$766$			154.280i			0.201410i
$767$	330.719	−	1018.99i	0.431185	−	1.32854i
$768$		−	313.048i		−	0.407614i
$769$	−62.0527	−	62.0527i	−0.0806927	−	0.0806927i	0.665608	−	0.746301i	$-0.268172\pi$
$769$	−62.0527	−	62.0527i	−0.0806927	−	0.0806927i	−0.746301	+	0.665608i	$0.768172\pi$
$770$		0			0
$771$			651.724i			0.845297i
$772$	143.408	−	143.408i	0.185761	−	0.185761i
$773$	−318.813	+	318.813i	−0.412436	+	0.412436i	−0.882586	−	0.470150i	$-0.844200\pi$
$773$	−318.813	+	318.813i	−0.412436	+	0.412436i	0.470150	+	0.882586i	$0.344200\pi$
$774$	−147.487	+	147.487i	−0.190551	+	0.190551i
$775$		0			0
$776$	−1033.12			−1.33134
$777$	924.043			1.18925
$778$	−296.579	−	296.579i	−0.381207	−	0.381207i
$779$		−	30.5964i		−	0.0392766i
$780$		0			0
$781$	974.977			1.24837
$782$	108.711	−	108.711i	0.139017	−	0.139017i
$783$			16.3381i			0.0208660i
$784$			58.6761i			0.0748420i
$785$		0			0
$786$	623.419	+	623.419i	0.793154	+	0.793154i
$787$	634.566	+	634.566i	0.806310	+	0.806310i	0.984073	−	0.177763i	$-0.0568862\pi$
$787$	634.566	+	634.566i	0.806310	+	0.806310i	−0.177763	+	0.984073i	$0.556886\pi$
$788$	−419.207	−	419.207i	−0.531989	−	0.531989i
$789$	−1410.94			−1.78826
$790$		0			0
$791$	−314.009	+	314.009i	−0.396977	+	0.396977i
$792$	377.342			0.476442
$793$	930.250	−	474.372i	1.17308	−	0.598200i
$794$	165.115			0.207953
$795$		0			0
$796$	−506.135			−0.635847
$797$	−407.026			−0.510698			−0.255349	−	0.966849i	$-0.582190\pi$
$797$	−407.026			−0.510698			−0.255349	+	0.966849i	$0.582190\pi$
$798$	70.0833	−	70.0833i	0.0878237	−	0.0878237i
$799$	821.072	+	821.072i	1.02762	+	1.02762i
$800$		0			0
$801$	74.0085	−	74.0085i	0.0923952	−	0.0923952i
$802$			167.715i			0.209120i
$803$	−336.754			−0.419370
$804$	540.824	−	540.824i	0.672666	−	0.672666i
$805$		0			0
$806$	6.90748	−	3.52241i	0.00857008	−	0.00437023i
$807$			924.280i			1.14533i
$808$	446.605	−	446.605i	0.552729	−	0.552729i
$809$	647.641			0.800545			0.400272	−	0.916396i	$-0.368916\pi$
$809$	647.641			0.800545			0.400272	+	0.916396i	$0.368916\pi$
$810$		0			0
$811$	850.386	+	850.386i	1.04856	+	1.04856i	0.998759	+	0.0498055i	$0.0158601\pi$
$811$	850.386	+	850.386i	1.04856	+	1.04856i	0.0498055	+	0.998759i	$0.484140\pi$
$812$	88.5089	−	88.5089i	0.109001	−	0.109001i
$813$	162.630	+	162.630i	0.200036	+	0.200036i
$814$	−149.952	+	149.952i	−0.184216	+	0.184216i
$815$		0			0
$816$			763.777i			0.936001i
$817$	96.4078	+	96.4078i	0.118002	+	0.118002i
$818$	106.767			0.130521
$819$	−666.877	−	216.438i	−0.814257	−	0.264272i
$820$		0			0
$821$	330.186	+	330.186i	0.402176	+	0.402176i	0.878999	−	0.476824i	$-0.158212\pi$
$821$	330.186	+	330.186i	0.402176	+	0.402176i	−0.476824	+	0.878999i	$0.658212\pi$
$822$		−	847.917i		−	1.03153i
$823$	−507.579			−0.616742			−0.308371	−	0.951266i	$-0.599784\pi$
$823$	−507.579			−0.616742			−0.308371	+	0.951266i	$0.599784\pi$
$824$	150.828	+	150.828i	0.183044	+	0.183044i
$825$		0			0
$826$	−310.272	+	310.272i	−0.375632	+	0.375632i
$827$	−488.452	−	488.452i	−0.590631	−	0.590631i	0.347171	−	0.937802i	$-0.387142\pi$
$827$	−488.452	−	488.452i	−0.590631	−	0.590631i	−0.937802	+	0.347171i	$0.887142\pi$
$828$		−	235.606i		−	0.284548i
$829$			1391.89i			1.67900i	0.543361	+	0.839499i	$0.317152\pi$
$829$			1391.89i			1.67900i	−0.543361	+	0.839499i	$0.682848\pi$
$830$		0			0
$831$		−	466.394i		−	0.561245i
$832$	47.0900	+	92.3441i	0.0565986	+	0.110991i
$833$			154.394i			0.185347i
$834$	327.660	+	327.660i	0.392878	+	0.392878i
$835$		0			0
$836$		−	111.956i		−	0.133919i
$837$	−1.44271	+	1.44271i	−0.00172367	+	0.00172367i
$838$	−48.3698	+	48.3698i	−0.0577205	+	0.0577205i
$839$	128.794	−	128.794i	0.153508	−	0.153508i	−0.626174	−	0.779683i	$-0.715380\pi$
$839$	128.794	−	128.794i	0.153508	−	0.153508i	0.779683	+	0.626174i	$0.215380\pi$
$840$		0			0
$841$	−807.228			−0.959843
$842$	−79.3993			−0.0942984
$843$	−727.759	−	727.759i	−0.863296	−	0.863296i
$844$		−	158.164i		−	0.187398i
$845$		0			0
$846$	−361.535			−0.427346
$847$	294.559	−	294.559i	0.347768	−	0.347768i
$848$		−	299.057i		−	0.352661i
$849$			1128.82i			1.32958i
$850$		0			0
$851$	206.276	+	206.276i	0.242393	+	0.242393i
$852$	−1266.91	−	1266.91i	−1.48698	−	1.48698i
$853$	485.546	+	485.546i	0.569221	+	0.569221i	0.931910	−	0.362689i	$-0.118141\pi$
$853$	485.546	+	485.546i	0.569221	+	0.569221i	−0.362689	+	0.931910i	$0.618141\pi$
$854$	−427.693			−0.500811
$855$		0			0
$856$	−18.8562	+	18.8562i	−0.0220283	+	0.0220283i
$857$	−1245.24			−1.45302			−0.726509	−	0.687157i	$-0.758859\pi$
$857$	−1245.24			−1.45302			−0.726509	+	0.687157i	$0.758859\pi$
$858$	298.315	−	152.123i	0.347687	−	0.177300i
$859$	−1194.94			−1.39108			−0.695540	−	0.718487i	$-0.744835\pi$
$859$	−1194.94			−1.39108			−0.695540	+	0.718487i	$0.744835\pi$
$860$		0			0
$861$	184.491			0.214275
$862$	−546.227			−0.633674
$863$	−604.195	+	604.195i	−0.700111	+	0.700111i	−0.964434	−	0.264324i	$-0.914851\pi$
$863$	−604.195	+	604.195i	−0.700111	+	0.700111i	0.264324	+	0.964434i	$0.414851\pi$
$864$	61.5114	+	61.5114i	0.0711937	+	0.0711937i
$865$		0			0
$866$	70.9804	−	70.9804i	0.0819635	−	0.0819635i
$867$			806.824i			0.930593i
$868$	15.6313			0.0180084
$869$	100.022	−	100.022i	0.115100	−	0.115100i
$870$		0			0
$871$	221.815	−	683.443i	0.254667	−	0.784664i
$872$			1028.17i			1.17909i
$873$	−1010.23	+	1010.23i	−1.15719	+	1.15719i
$874$	31.2897			0.0358005
$875$		0			0
$876$	437.587	+	437.587i	0.499529	+	0.499529i
$877$	1065.53	−	1065.53i	1.21497	−	1.21497i	0.245603	−	0.969370i	$-0.421014\pi$
$877$	1065.53	−	1065.53i	1.21497	−	1.21497i	0.969370	−	0.245603i	$-0.0789861\pi$
$878$	18.1836	+	18.1836i	0.0207103	+	0.0207103i
$879$	−999.594	+	999.594i	−1.13719	+	1.13719i
$880$		0			0
$881$			821.315i			0.932253i	0.884718	+	0.466126i	$0.154351\pi$
$881$			821.315i			0.932253i	−0.884718	+	0.466126i	$0.845649\pi$
$882$	−33.9915	−	33.9915i	−0.0385391	−	0.0385391i
$883$	1091.97			1.23666			0.618329	−	0.785920i	$-0.287810\pi$
$883$	1091.97			1.23666			0.618329	+	0.785920i	$0.287810\pi$
$884$	431.427	+	846.033i	0.488039	+	0.957051i
$885$		0			0
$886$	329.722	+	329.722i	0.372147	+	0.372147i
$887$			1478.73i			1.66711i	0.552436	+	0.833555i	$0.313698\pi$
$887$			1478.73i			1.66711i	−0.552436	+	0.833555i	$0.686302\pi$
$888$	858.579			0.966868
$889$	−463.438	−	463.438i	−0.521303	−	0.521303i
$890$		0			0
$891$	−461.228	+	461.228i	−0.517652	+	0.517652i
$892$	−127.084	−	127.084i	−0.142471	−	0.142471i
$893$			236.325i			0.264641i
$894$			175.219i			0.195994i
$895$		0			0
$896$		−	844.315i		−	0.942316i
$897$	−209.263	−	410.368i	−0.233292	−	0.457489i
$898$			617.021i			0.687106i
$899$	2.98221	+	2.98221i	0.00331726	+	0.00331726i
$900$		0			0
$901$		−	786.907i		−	0.873371i
$902$	−29.9388	+	29.9388i	−0.0331916	+	0.0331916i
$903$	−581.322	+	581.322i	−0.643768	+	0.643768i
$904$	−291.762	+	291.762i	−0.322746	+	0.322746i
$905$		0			0
$906$	363.688			0.401422
$907$	−1460.57			−1.61033			−0.805167	−	0.593048i	$-0.797925\pi$
$907$	−1460.57			−1.61033			−0.805167	+	0.593048i	$0.797925\pi$
$908$	−148.715	−	148.715i	−0.163783	−	0.163783i
$909$		−	873.421i		−	0.960859i
$910$		0			0
$911$	287.689			0.315795			0.157897	−	0.987456i	$-0.449528\pi$
$911$	287.689			0.315795			0.157897	+	0.987456i	$0.449528\pi$
$912$	−109.917	+	109.917i	−0.120523	+	0.120523i
$913$			475.193i			0.520474i
$914$		−	269.755i		−	0.295137i
$915$		0			0
$916$	557.308	+	557.308i	0.608415	+	0.608415i
$917$	1180.71	+	1180.71i	1.28758	+	1.28758i
$918$	35.9007	+	35.9007i	0.0391075	+	0.0391075i
$919$	−1696.20			−1.84570			−0.922851	−	0.385156i	$-0.874148\pi$
$919$	−1696.20			−1.84570			−0.922851	+	0.385156i	$0.874148\pi$
$920$		0			0
$921$	−914.386	+	914.386i	−0.992818	+	0.992818i
$922$	243.785			0.264409
$923$	−1601.00	−	519.614i	−1.73457	−	0.562962i
$924$	675.074			0.730600
$925$		0			0
$926$	148.359			0.160215
$927$	294.974			0.318202
$928$	127.149	−	127.149i	0.137015	−	0.137015i
$929$	−912.403	−	912.403i	−0.982134	−	0.982134i	0.0177088	−	0.999843i	$-0.494363\pi$
$929$	−912.403	−	912.403i	−0.982134	−	0.982134i	−0.999843	+	0.0177088i	$0.994363\pi$
$930$		0			0
$931$	−22.2192	+	22.2192i	−0.0238660	+	0.0238660i
$932$			973.394i			1.04441i
$933$	−1422.18			−1.52431
$934$	−399.670	+	399.670i	−0.427913	+	0.427913i
$935$		0			0
$936$	−619.631	−	201.105i	−0.661999	−	0.214855i
$937$		−	1041.30i		−	1.11131i	−0.831413	−	0.555655i	$-0.812467\pi$
$937$		−	1041.30i		−	1.11131i	0.831413	−	0.555655i	$-0.187533\pi$
$938$	−208.101	+	208.101i	−0.221856	+	0.221856i
$939$	1825.23			1.94380
$940$		0			0
$941$	−502.392	−	502.392i	−0.533891	−	0.533891i	0.387837	−	0.921728i	$-0.373222\pi$
$941$	−502.392	−	502.392i	−0.533891	−	0.533891i	−0.921728	+	0.387837i	$0.873222\pi$
$942$	134.141	−	134.141i	0.142400	−	0.142400i
$943$	41.1843	+	41.1843i	0.0436737	+	0.0436737i
$944$	486.622	−	486.622i	0.515489	−	0.515489i
$945$		0			0
$946$		−	188.671i		−	0.199441i
$947$	−683.569	−	683.569i	−0.721826	−	0.721826i	0.247151	−	0.968977i	$-0.420506\pi$
$947$	−683.569	−	683.569i	−0.721826	−	0.721826i	−0.968977	+	0.247151i	$0.920506\pi$
$948$	−259.942			−0.274201
$949$	552.982	+	179.473i	0.582700	+	0.189118i
$950$		0			0
$951$	−637.412	−	637.412i	−0.670255	−	0.670255i
$952$		−	856.973i		−	0.900182i
$953$	694.290			0.728531			0.364265	−	0.931295i	$-0.381320\pi$
$953$	694.290			0.728531			0.364265	+	0.931295i	$0.381320\pi$
$954$	173.246	+	173.246i	0.181599	+	0.181599i
$955$		0			0
$956$	0.0508781	−	0.0508781i	5.32198e−5	−	5.32198e-5i
$957$	128.794	+	128.794i	0.134581	+	0.134581i
$958$			370.351i			0.386588i
$959$		−	1605.89i		−	1.67455i
$960$		0			0
$961$		−	960.473i		−	0.999452i
$962$	326.151	−	166.318i	0.339035	−	0.172888i
$963$			36.8769i			0.0382937i
$964$	798.549	+	798.549i	0.828370	+	0.828370i
$965$		0			0
$966$			188.671i			0.195312i
$967$	616.081	−	616.081i	0.637106	−	0.637106i	−0.312735	−	0.949841i	$-0.601245\pi$
$967$	616.081	−	616.081i	0.637106	−	0.637106i	0.949841	+	0.312735i	$0.101245\pi$
$968$	273.691	−	273.691i	0.282738	−	0.282738i
$969$	−289.223	+	289.223i	−0.298476	+	0.298476i
$970$		0			0
$971$	−473.890			−0.488044			−0.244022	−	0.969770i	$-0.578467\pi$
$971$	−473.890			−0.488044			−0.244022	+	0.969770i	$0.578467\pi$
$972$	1114.54			1.14665
$973$	620.563	+	620.563i	0.637784	+	0.637784i
$974$		−	647.465i		−	0.664748i
$975$		0			0
$976$	670.781			0.687276
$977$	−9.56087	+	9.56087i	−0.00978594	+	0.00978594i	−0.711983	−	0.702197i	$-0.752203\pi$
$977$	−9.56087	+	9.56087i	−0.00978594	+	0.00978594i	0.702197	+	0.711983i	$0.252203\pi$
$978$		−	219.925i		−	0.224872i
$979$			94.6748i			0.0967056i
$980$		0			0
$981$	1005.39	+	1005.39i	1.02486	+	1.02486i
$982$	232.861	+	232.861i	0.237129	+	0.237129i
$983$	−695.475	−	695.475i	−0.707503	−	0.707503i	0.258507	−	0.966009i	$-0.416770\pi$
$983$	−695.475	−	695.475i	−0.707503	−	0.707503i	−0.966009	+	0.258507i	$0.916770\pi$
$984$	171.421			0.174208
$985$		0			0
$986$	74.2100	−	74.2100i	0.0752637	−	0.0752637i
$987$	−1425.00			−1.44376
$988$	−59.6669	+	183.842i	−0.0603916	+	0.186075i
$989$	−259.540			−0.262426
$990$		0			0
$991$	−1625.34			−1.64010			−0.820051	−	0.572291i	$-0.806055\pi$
$991$	−1625.34			−1.64010			−0.820051	+	0.572291i	$0.806055\pi$
$992$	22.4555			0.0226366
$993$	815.732	−	815.732i	0.821483	−	0.821483i
$994$	487.489	+	487.489i	0.490431	+	0.490431i
$995$		0			0
$996$	617.478	−	617.478i	0.619957	−	0.619957i
$997$		−	31.3986i		−	0.0314931i	−0.999876	−	0.0157465i	$-0.994988\pi$
$997$		−	31.3986i		−	0.0314931i	0.999876	−	0.0157465i	$-0.00501248\pi$
$998$	119.332			0.119572
$999$	−68.1206	+	68.1206i	−0.0681888	+	0.0681888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.g.b.99.1		4
5.2	odd	4		325.3.j.a.151.1		4
5.3	odd	4		13.3.d.a.8.2	yes	4
5.4	even	2		325.3.g.a.99.2		4
13.5	odd	4		325.3.g.a.174.2		4
15.8	even	4		117.3.j.a.73.1		4
20.3	even	4		208.3.t.c.177.2		4
65.3	odd	12		169.3.f.f.150.1		8
65.8	even	4		169.3.d.d.70.1		4
65.18	even	4		13.3.d.a.5.2	✓	4
65.23	odd	12		169.3.f.d.150.2		8
65.28	even	12		169.3.f.f.19.2		8
65.33	even	12		169.3.f.d.80.2		8
65.38	odd	4		169.3.d.d.99.1		4
65.43	odd	12		169.3.f.d.89.1		8
65.44	odd	4	inner	325.3.g.b.174.1		4
65.48	odd	12		169.3.f.f.89.2		8
65.57	even	4		325.3.j.a.226.1		4
65.58	even	12		169.3.f.f.80.1		8
65.63	even	12		169.3.f.d.19.1		8
195.83	odd	4		117.3.j.a.109.1		4
260.83	odd	4		208.3.t.c.161.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.2	✓	4	65.18	even	4
13.3.d.a.8.2	yes	4	5.3	odd	4
117.3.j.a.73.1		4	15.8	even	4
117.3.j.a.109.1		4	195.83	odd	4
169.3.d.d.70.1		4	65.8	even	4
169.3.d.d.99.1		4	65.38	odd	4
169.3.f.d.19.1		8	65.63	even	12
169.3.f.d.80.2		8	65.33	even	12
169.3.f.d.89.1		8	65.43	odd	12
169.3.f.d.150.2		8	65.23	odd	12
169.3.f.f.19.2		8	65.28	even	12
169.3.f.f.80.1		8	65.58	even	12
169.3.f.f.89.2		8	65.48	odd	12
169.3.f.f.150.1		8	65.3	odd	12
208.3.t.c.161.2		4	260.83	odd	4
208.3.t.c.177.2		4	20.3	even	4
325.3.g.a.99.2		4	5.4	even	2
325.3.g.a.174.2		4	13.5	odd	4
325.3.g.b.99.1		4	1.1	even	1	trivial
325.3.g.b.174.1		4	65.44	odd	4	inner
325.3.j.a.151.1		4	5.2	odd	4
325.3.j.a.226.1		4	65.57	even	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.581139 + 0.581139i) q^{2} +4.16228i q^{3} +3.32456i q^{4} +(-2.41886 - 2.41886i) q^{6} +(-4.58114 - 4.58114i) q^{7} +(-4.25658 - 4.25658i) q^{8} -8.32456 q^{9} +(5.32456 - 5.32456i) q^{11} -13.8377 q^{12} +(-11.5811 + 5.90569i) q^{13} +5.32456 q^{14} -8.35089 q^{16} -21.9737 q^{17} +(4.83772 - 4.83772i) q^{18} +(-3.16228 - 3.16228i) q^{19} +(19.0680 - 19.0680i) q^{21} +6.18861i q^{22} +8.51317 q^{23} +(17.7171 - 17.7171i) q^{24} +(3.29822 - 10.1623i) q^{26} +2.81139i q^{27} +(15.2302 - 15.2302i) q^{28} +5.81139 q^{29} +(0.513167 + 0.513167i) q^{31} +(21.8794 - 21.8794i) q^{32} +(22.1623 + 22.1623i) q^{33} +(12.7698 - 12.7698i) q^{34} -27.6754i q^{36} +(24.2302 + 24.2302i) q^{37} +3.67544 q^{38} +(-24.5811 - 48.2039i) q^{39} +(4.83772 + 4.83772i) q^{41} +22.1623i q^{42} -30.4868 q^{43} +(17.7018 + 17.7018i) q^{44} +(-4.94733 + 4.94733i) q^{46} +(-37.3662 - 37.3662i) q^{47} -34.7587i q^{48} -7.02633i q^{49} -91.4605i q^{51} +(-19.6338 - 38.5021i) q^{52} +35.8114i q^{53} +(-1.63381 - 1.63381i) q^{54} +39.0000i q^{56} +(13.1623 - 13.1623i) q^{57} +(-3.37722 + 3.37722i) q^{58} +(-58.2719 + 58.2719i) q^{59} -80.3246 q^{61} -0.596443 q^{62} +(38.1359 + 38.1359i) q^{63} -7.97367i q^{64} -25.7587 q^{66} +(-39.0833 + 39.0833i) q^{67} -73.0527i q^{68} +35.4342i q^{69} +(91.5548 + 91.5548i) q^{71} +(35.4342 + 35.4342i) q^{72} +(-31.6228 - 31.6228i) q^{73} -28.1623 q^{74} +(10.5132 - 10.5132i) q^{76} -48.7851 q^{77} +(42.2982 + 13.7281i) q^{78} +18.7851 q^{79} -86.6228 q^{81} -5.62278 q^{82} +(-44.6228 + 44.6228i) q^{83} +(63.3925 + 63.3925i) q^{84} +(17.7171 - 17.7171i) q^{86} +24.1886i q^{87} -45.3288 q^{88} +(-8.89039 + 8.89039i) q^{89} +(80.1096 + 26.0000i) q^{91} +28.3025i q^{92} +(-2.13594 + 2.13594i) q^{93} +43.4299 q^{94} +(91.0680 + 91.0680i) q^{96} +(121.355 - 121.355i) q^{97} +(4.08328 + 4.08328i) q^{98} +(-44.3246 + 44.3246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 16 q^{6} - 12 q^{7} - 36 q^{8} - 8 q^{9} - 4 q^{11} - 68 q^{12} - 40 q^{13} - 4 q^{14} - 84 q^{16} - 12 q^{17} + 32 q^{18} + 32 q^{21} + 72 q^{23} - 24 q^{24} - 88 q^{26} + 4 q^{28} - 40 q^{29}+ \cdots - 152 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 16 * q^6 - 12 * q^7 - 36 * q^8 - 8 * q^9 - 4 * q^11 - 68 * q^12 - 40 * q^13 - 4 * q^14 - 84 * q^16 - 12 * q^17 + 32 * q^18 + 32 * q^21 + 72 * q^23 - 24 * q^24 - 88 * q^26 + 4 * q^28 - 40 * q^29 + 40 * q^31 - 20 * q^32 + 76 * q^33 + 108 * q^34 + 40 * q^37 + 40 * q^38 - 92 * q^39 + 32 * q^41 - 84 * q^43 + 172 * q^44 + 132 * q^46 - 4 * q^47 - 224 * q^52 - 152 * q^54 + 40 * q^57 - 140 * q^58 - 56 * q^59 - 296 * q^61 + 200 * q^62 + 64 * q^63 + 112 * q^66 + 84 * q^67 + 284 * q^71 - 48 * q^72 - 100 * q^74 + 80 * q^76 - 56 * q^77 + 68 * q^78 - 64 * q^79 - 220 * q^81 + 104 * q^82 - 52 * q^83 + 184 * q^84 - 24 * q^86 + 312 * q^88 - 200 * q^89 + 156 * q^91 + 80 * q^93 + 452 * q^94 + 320 * q^96 + 68 * q^97 - 224 * q^98 - 152 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more