LMFDB - Embedded newform 684.3.g.b.343.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.9
Root			$-0.0607713 + 1.99908i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0607713 - 1.99908i) q^{2} +(-3.99261 - 0.242973i) q^{4} +5.82257 q^{5} -5.45132i q^{7} +(-0.728358 + 7.96677i) q^{8} +O(q^{10})$	\(q+(0.0607713 - 1.99908i) q^{2} +(-3.99261 - 0.242973i) q^{4} +5.82257 q^{5} -5.45132i q^{7} +(-0.728358 + 7.96677i) q^{8} +(0.353845 - 11.6398i) q^{10} +1.60915i q^{11} +23.5274 q^{13} +(-10.8976 - 0.331284i) q^{14} +(15.8819 + 1.94019i) q^{16} +5.92676 q^{17} +4.35890i q^{19} +(-23.2473 - 1.41473i) q^{20} +(3.21681 + 0.0977900i) q^{22} +26.6121i q^{23} +8.90234 q^{25} +(1.42979 - 47.0331i) q^{26} +(-1.32452 + 21.7650i) q^{28} +1.49241 q^{29} -31.3933i q^{31} +(4.84376 - 31.6313i) q^{32} +(0.360177 - 11.8480i) q^{34} -31.7407i q^{35} +26.8255 q^{37} +(8.71377 + 0.264896i) q^{38} +(-4.24092 + 46.3871i) q^{40} +44.0382 q^{41} -27.8586i q^{43} +(0.390980 - 6.42471i) q^{44} +(53.1996 + 1.61725i) q^{46} -32.5166i q^{47} +19.2831 q^{49} +(0.541007 - 17.7965i) q^{50} +(-93.9360 - 5.71653i) q^{52} -76.7637 q^{53} +9.36938i q^{55} +(43.4294 + 3.97051i) q^{56} +(0.0906959 - 2.98345i) q^{58} -33.8895i q^{59} +53.0162 q^{61} +(-62.7575 - 1.90781i) q^{62} +(-62.9390 - 11.6053i) q^{64} +136.990 q^{65} -76.1917i q^{67} +(-23.6632 - 1.44004i) q^{68} +(-63.4521 - 1.92892i) q^{70} +59.9326i q^{71} -49.8188 q^{73} +(1.63022 - 53.6263i) q^{74} +(1.05909 - 17.4034i) q^{76} +8.77198 q^{77} +23.3990i q^{79} +(92.4737 + 11.2969i) q^{80} +(2.67626 - 88.0358i) q^{82} -137.116i q^{83} +34.5090 q^{85} +(-55.6915 - 1.69300i) q^{86} +(-12.8197 - 1.17204i) q^{88} -116.608 q^{89} -128.256i q^{91} +(6.46602 - 106.252i) q^{92} +(-65.0032 - 1.97608i) q^{94} +25.3800i q^{95} -65.7341 q^{97} +(1.17186 - 38.5484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.0607713	−	1.99908i	0.0303857	−	0.999538i
$2$	0.0607713	−	1.99908i	0.0303857	−	0.999538i
$3$		0			0
$3$		0			0
$4$	−3.99261	−	0.242973i	−0.998153	−	0.0607433i
$5$	5.82257			1.16451			0.582257	−	0.813005i	$-0.302170\pi$
$5$	5.82257			1.16451			0.582257	+	0.813005i	$0.302170\pi$
$6$		0			0
$7$		−	5.45132i		−	0.778760i	−0.921077	−	0.389380i	$-0.872689\pi$
$7$		−	5.45132i		−	0.778760i	0.921077	−	0.389380i	$-0.127311\pi$
$8$	−0.728358	+	7.96677i	−0.0910448	+	0.995847i
$9$		0			0
$10$	0.353845	−	11.6398i	0.0353845	−	1.16398i
$11$			1.60915i			0.146286i	0.997321	+	0.0731431i	$0.0233030\pi$
$11$			1.60915i			0.146286i	−0.997321	+	0.0731431i	$0.976697\pi$
$12$		0			0
$13$	23.5274			1.80980			0.904901	−	0.425622i	$-0.139945\pi$
$13$	23.5274			1.80980			0.904901	+	0.425622i	$0.139945\pi$
$14$	−10.8976	−	0.331284i	−0.778401	−	0.0236631i
$15$		0			0
$16$	15.8819	+	1.94019i	0.992621	+	0.121262i
$17$	5.92676			0.348633			0.174316	−	0.984690i	$-0.444228\pi$
$17$	5.92676			0.348633			0.174316	+	0.984690i	$0.444228\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−23.2473	−	1.41473i	−1.16236	−	0.0707364i
$21$		0			0
$22$	3.21681	+	0.0977900i	0.146219	+	0.00444500i
$23$			26.6121i			1.15705i	0.815665	+	0.578524i	$0.196371\pi$
$23$			26.6121i			1.15705i	−0.815665	+	0.578524i	$0.803629\pi$
$24$		0			0
$25$	8.90234			0.356094
$26$	1.42979	−	47.0331i	0.0549920	−	1.80897i
$27$		0			0
$28$	−1.32452	+	21.7650i	−0.0473044	+	0.777322i
$29$	1.49241			0.0514625			0.0257313	−	0.999669i	$-0.491809\pi$
$29$	1.49241			0.0514625			0.0257313	+	0.999669i	$0.491809\pi$
$30$		0			0
$31$		−	31.3933i		−	1.01269i	−0.862332	−	0.506343i	$-0.830997\pi$
$31$		−	31.3933i		−	1.01269i	0.862332	−	0.506343i	$-0.169003\pi$
$32$	4.84376	−	31.6313i	0.151368	−	0.988478i
$33$		0			0
$34$	0.360177	−	11.8480i	0.0105934	−	0.348472i
$35$		−	31.7407i		−	0.906877i
$36$		0			0
$37$	26.8255			0.725015			0.362507	−	0.931981i	$-0.381921\pi$
$37$	26.8255			0.725015			0.362507	+	0.931981i	$0.381921\pi$
$38$	8.71377	+	0.264896i	0.229310	+	0.00697095i
$39$		0			0
$40$	−4.24092	+	46.3871i	−0.106023	+	1.15968i
$41$	44.0382			1.07410			0.537051	−	0.843550i	$-0.319538\pi$
$41$	44.0382			1.07410			0.537051	+	0.843550i	$0.319538\pi$
$42$		0			0
$43$		−	27.8586i		−	0.647875i	−0.946079	−	0.323937i	$-0.894993\pi$
$43$		−	27.8586i		−	0.647875i	0.946079	−	0.323937i	$-0.105007\pi$
$44$	0.390980	−	6.42471i	0.00888590	−	0.146016i
$45$		0			0
$46$	53.1996	+	1.61725i	1.15651	+	0.0351577i
$47$		−	32.5166i		−	0.691843i	−0.938264	−	0.345921i	$-0.887566\pi$
$47$		−	32.5166i		−	0.691843i	0.938264	−	0.345921i	$-0.112434\pi$
$48$		0			0
$49$	19.2831			0.393533
$50$	0.541007	−	17.7965i	0.0108201	−	0.355929i
$51$		0			0
$52$	−93.9360	−	5.71653i	−1.80646	−	0.109933i
$53$	−76.7637			−1.44837			−0.724186	−	0.689605i	$-0.757784\pi$
$53$	−76.7637			−1.44837			−0.724186	+	0.689605i	$0.757784\pi$
$54$		0			0
$55$			9.36938i			0.170352i
$56$	43.4294	+	3.97051i	0.775526	+	0.0709020i
$57$		0			0
$58$	0.0906959	−	2.98345i	0.00156372	−	0.0514388i
$59$		−	33.8895i		−	0.574398i	−0.957871	−	0.287199i	$-0.907276\pi$
$59$		−	33.8895i		−	0.574398i	0.957871	−	0.287199i	$-0.0927241\pi$
$60$		0			0
$61$	53.0162			0.869118			0.434559	−	0.900643i	$-0.356904\pi$
$61$	53.0162			0.869118			0.434559	+	0.900643i	$0.356904\pi$
$62$	−62.7575	−	1.90781i	−1.01222	−	0.0307711i
$63$		0			0
$64$	−62.9390	−	11.6053i	−0.983422	−	0.181333i
$65$	136.990			2.10754
$66$		0			0
$67$		−	76.1917i		−	1.13719i	−0.822618	−	0.568594i	$-0.807487\pi$
$67$		−	76.1917i		−	1.13719i	0.822618	−	0.568594i	$-0.192513\pi$
$68$	−23.6632	−	1.44004i	−0.347989	−	0.0211771i
$69$		0			0
$70$	−63.4521	−	1.92892i	−0.906459	−	0.0275561i
$71$			59.9326i			0.844121i	0.906568	+	0.422060i	$0.138693\pi$
$71$			59.9326i			0.844121i	−0.906568	+	0.422060i	$0.861307\pi$
$72$		0			0
$73$	−49.8188			−0.682450			−0.341225	−	0.939982i	$-0.610842\pi$
$73$	−49.8188			−0.682450			−0.341225	+	0.939982i	$0.610842\pi$
$74$	1.63022	−	53.6263i	0.0220301	−	0.724680i
$75$		0			0
$76$	1.05909	−	17.4034i	0.0139355	−	0.228992i
$77$	8.77198			0.113922
$78$		0			0
$79$			23.3990i			0.296190i	0.988973	+	0.148095i	$0.0473141\pi$
$79$			23.3990i			0.296190i	−0.988973	+	0.148095i	$0.952686\pi$
$80$	92.4737	+	11.2969i	1.15592	+	0.141212i
$81$		0			0
$82$	2.67626	−	88.0358i	0.0326373	−	1.07361i
$83$		−	137.116i		−	1.65200i	−0.563667	−	0.826002i	$-0.690610\pi$
$83$		−	137.116i		−	1.65200i	0.563667	−	0.826002i	$-0.309390\pi$
$84$		0			0
$85$	34.5090			0.405988
$86$	−55.6915	−	1.69300i	−0.647576	−	0.0196861i
$87$		0			0
$88$	−12.8197	−	1.17204i	−0.145679	−	0.0133186i
$89$	−116.608			−1.31020			−0.655101	−	0.755541i	$-0.727374\pi$
$89$	−116.608			−1.31020			−0.655101	+	0.755541i	$0.727374\pi$
$90$		0			0
$91$		−	128.256i		−	1.40940i
$92$	6.46602	−	106.252i	0.0702828	−	1.15491i
$93$		0			0
$94$	−65.0032	−	1.97608i	−0.691523	−	0.0210221i
$95$			25.3800i			0.267158i
$96$		0			0
$97$	−65.7341			−0.677671			−0.338836	−	0.940846i	$-0.610033\pi$
$97$	−65.7341			−0.677671			−0.338836	+	0.940846i	$0.610033\pi$
$98$	1.17186	−	38.5484i	0.0119577	−	0.393351i
$99$		0			0
$100$	−35.5436	−	2.16303i	−0.355436	−	0.0216303i
$101$	−1.81406			−0.0179609			−0.00898047	−	0.999960i	$-0.502859\pi$
$101$	−1.81406			−0.0179609			−0.00898047	+	0.999960i	$0.502859\pi$
$102$		0			0
$103$			0.494673i			0.00480265i	0.999997	+	0.00240133i	$0.000764367\pi$
$103$			0.494673i			0.00480265i	−0.999997	+	0.00240133i	$0.999236\pi$
$104$	−17.1364	+	187.438i	−0.164773	+	1.80229i
$105$		0			0
$106$	−4.66503	+	153.457i	−0.0440097	+	1.44770i
$107$		−	11.7361i		−	0.109684i	−0.998495	−	0.0548418i	$-0.982535\pi$
$107$		−	11.7361i		−	0.109684i	0.998495	−	0.0548418i	$-0.0174654\pi$
$108$		0			0
$109$	−28.9819			−0.265889			−0.132945	−	0.991123i	$-0.542443\pi$
$109$	−28.9819			−0.265889			−0.132945	+	0.991123i	$0.542443\pi$
$110$	18.7301	+	0.569390i	0.170274	+	0.00517627i
$111$		0			0
$112$	10.5766	−	86.5775i	0.0944341	−	0.773013i
$113$	140.725			1.24536			0.622678	−	0.782478i	$-0.286045\pi$
$113$	140.725			1.24536			0.622678	+	0.782478i	$0.286045\pi$
$114$		0			0
$115$			154.951i			1.34740i
$116$	−5.95863	−	0.362616i	−0.0513675	−	0.00312600i
$117$		0			0
$118$	−67.7477	−	2.05951i	−0.574133	−	0.0174535i
$119$		−	32.3086i		−	0.271501i
$120$		0			0
$121$	118.411			0.978600
$122$	3.22186	−	105.983i	0.0264087	−	0.868716i
$123$		0			0
$124$	−7.62772	+	125.341i	−0.0615138	+	1.01082i
$125$	−93.7298			−0.749838
$126$		0			0
$127$			50.4262i			0.397056i	0.980095	+	0.198528i	$0.0636161\pi$
$127$			50.4262i			0.397056i	−0.980095	+	0.198528i	$0.936384\pi$
$128$	−27.0248	+	125.115i	−0.211131	+	0.977458i
$129$		0			0
$130$	8.32507	−	273.854i	0.0640390	−	2.10657i
$131$			124.954i			0.953847i	0.878945	+	0.476924i	$0.158248\pi$
$131$			124.954i			0.953847i	−0.878945	+	0.476924i	$0.841752\pi$
$132$		0			0
$133$	23.7618			0.178660
$134$	−152.313	−	4.63027i	−1.13666	−	0.0345542i
$135$		0			0
$136$	−4.31680	+	47.2171i	−0.0317412	+	0.347185i
$137$	−137.151			−1.00110			−0.500551	−	0.865707i	$-0.666869\pi$
$137$	−137.151			−1.00110			−0.500551	+	0.865707i	$0.666869\pi$
$138$		0			0
$139$			89.6885i			0.645241i	0.946528	+	0.322621i	$0.104564\pi$
$139$			89.6885i			0.645241i	−0.946528	+	0.322621i	$0.895436\pi$
$140$	−7.71214	+	126.728i	−0.0550867	+	0.905203i
$141$		0			0
$142$	119.810	+	3.64218i	0.843731	+	0.0256492i
$143$			37.8591i			0.264749i
$144$		0			0
$145$	8.68969			0.0599289
$146$	−3.02756	+	99.5917i	−0.0207367	+	0.682135i
$147$		0			0
$148$	−107.104	−	6.51788i	−0.723676	−	0.0440398i
$149$	−18.9194			−0.126976			−0.0634878	−	0.997983i	$-0.520222\pi$
$149$	−18.9194			−0.126976			−0.0634878	+	0.997983i	$0.520222\pi$
$150$		0			0
$151$			269.061i			1.78186i	0.454141	+	0.890930i	$0.349946\pi$
$151$			269.061i			1.78186i	−0.454141	+	0.890930i	$0.650054\pi$
$152$	−34.7264	−	3.17484i	−0.228463	−	0.0208871i
$153$		0			0
$154$	0.533085	−	17.5359i	0.00346159	−	0.113869i
$155$		−	182.790i		−	1.17929i
$156$		0			0
$157$	11.4972			0.0732305			0.0366153	−	0.999329i	$-0.488342\pi$
$157$	11.4972			0.0732305			0.0366153	+	0.999329i	$0.488342\pi$
$158$	46.7764	+	1.42199i	0.296053	+	0.00899993i
$159$		0			0
$160$	28.2032	−	184.175i	0.176270	−	1.15110i
$161$	145.071			0.901063
$162$		0			0
$163$			126.564i			0.776465i	0.921562	+	0.388232i	$0.126914\pi$
$163$			126.564i			0.776465i	−0.921562	+	0.388232i	$0.873086\pi$
$164$	−175.828	−	10.7001i	−1.07212	−	0.0652445i
$165$		0			0
$166$	−274.106	−	8.33274i	−1.65124	−	0.0501972i
$167$		−	14.2424i		−	0.0852836i	−0.999090	−	0.0426418i	$-0.986423\pi$
$167$		−	14.2424i		−	0.0852836i	0.999090	−	0.0426418i	$-0.0135774\pi$
$168$		0			0
$169$	384.540			2.27539
$170$	2.09715	−	68.9860i	0.0123362	−	0.405800i
$171$		0			0
$172$	−6.76889	+	111.229i	−0.0393540	+	0.646678i
$173$	217.817			1.25906			0.629528	−	0.776978i	$-0.283248\pi$
$173$	217.817			1.25906			0.629528	+	0.776978i	$0.283248\pi$
$174$		0			0
$175$		−	48.5295i		−	0.277312i
$176$	−3.12206	+	25.5564i	−0.0177390	+	0.145207i
$177$		0			0
$178$	−7.08642	+	233.108i	−0.0398114	+	1.30960i
$179$			180.223i			1.00684i	0.864043	+	0.503418i	$0.167924\pi$
$179$			180.223i			1.00684i	−0.864043	+	0.503418i	$0.832076\pi$
$180$		0			0
$181$	−95.0637			−0.525214			−0.262607	−	0.964903i	$-0.584582\pi$
$181$	−95.0637			−0.525214			−0.262607	+	0.964903i	$0.584582\pi$
$182$	−256.393	−	7.79426i	−1.40875	−	0.0428256i
$183$		0			0
$184$	−212.013	−	19.3831i	−1.15224	−	0.105343i
$185$	156.194			0.844290
$186$		0			0
$187$			9.53703i			0.0510001i
$188$	−7.90066	+	129.826i	−0.0420248	+	0.690565i
$189$		0			0
$190$	50.7366	+	1.54238i	0.267035	+	0.00811777i
$191$		−	25.4789i		−	0.133397i	−0.997773	−	0.0666987i	$-0.978753\pi$
$191$		−	25.4789i		−	0.133397i	0.997773	−	0.0666987i	$-0.0212466\pi$
$192$		0			0
$193$	339.566			1.75941			0.879705	−	0.475520i	$-0.157740\pi$
$193$	339.566			1.75941			0.879705	+	0.475520i	$0.157740\pi$
$194$	−3.99475	+	131.407i	−0.0205915	+	0.677358i
$195$		0			0
$196$	−76.9900	−	4.68527i	−0.392806	−	0.0239045i
$197$	−136.859			−0.694717			−0.347358	−	0.937732i	$-0.612921\pi$
$197$	−136.859			−0.694717			−0.347358	+	0.937732i	$0.612921\pi$
$198$		0			0
$199$		−	199.411i		−	1.00207i	−0.865428	−	0.501034i	$-0.832953\pi$
$199$		−	199.411i		−	1.00207i	0.865428	−	0.501034i	$-0.167047\pi$
$200$	−6.48409	+	70.9230i	−0.0324205	+	0.354615i
$201$		0			0
$202$	−0.110243	+	3.62644i	−0.000545755	+	0.0179527i
$203$		−	8.13563i		−	0.0400770i
$204$		0			0
$205$	256.416			1.25081
$206$	0.988890	+	0.0300619i	0.00480044	+	0.000145932i
$207$		0			0
$208$	373.661	+	45.6478i	1.79645	+	0.219461i
$209$	−7.01411			−0.0335604
$210$		0			0
$211$		−	363.655i		−	1.72348i	−0.507347	−	0.861742i	$-0.669374\pi$
$211$		−	363.655i		−	1.72348i	0.507347	−	0.861742i	$-0.330626\pi$
$212$	306.488	+	18.6515i	1.44570	+	0.0879788i
$213$		0			0
$214$	−23.4614	−	0.713221i	−0.109633	−	0.00333281i
$215$		−	162.209i		−	0.754460i
$216$		0			0
$217$	−171.135			−0.788640
$218$	−1.76127	+	57.9371i	−0.00807922	+	0.265766i
$219$		0			0
$220$	2.27651	−	37.4083i	0.0103478	−	0.170038i
$221$	139.441			0.630956
$222$		0			0
$223$			268.968i			1.20614i	0.797690	+	0.603068i	$0.206055\pi$
$223$			268.968i			1.20614i	−0.797690	+	0.603068i	$0.793945\pi$
$224$	−172.432	−	26.4049i	−0.769787	−	0.117879i
$225$		0			0
$226$	8.55206	−	281.320i	0.0378410	−	1.24478i
$227$			79.9913i			0.352384i	0.984356	+	0.176192i	$0.0563780\pi$
$227$			79.9913i			0.352384i	−0.984356	+	0.176192i	$0.943622\pi$
$228$		0			0
$229$	297.342			1.29843			0.649217	−	0.760603i	$-0.275097\pi$
$229$	297.342			1.29843			0.649217	+	0.760603i	$0.275097\pi$
$230$	309.759	+	9.41657i	1.34678	+	0.0409416i
$231$		0			0
$232$	−1.08701	+	11.8897i	−0.00468539	+	0.0512488i
$233$	255.975			1.09860			0.549302	−	0.835624i	$-0.314894\pi$
$233$	255.975			1.09860			0.549302	+	0.835624i	$0.314894\pi$
$234$		0			0
$235$		−	189.330i		−	0.805661i
$236$	−8.23423	+	135.308i	−0.0348908	+	0.573337i
$237$		0			0
$238$	−64.5875	−	1.96344i	−0.271376	−	0.00824974i
$239$			148.674i			0.622067i	0.950399	+	0.311034i	$0.100675\pi$
$239$			148.674i			0.622067i	−0.950399	+	0.311034i	$0.899325\pi$
$240$		0			0
$241$	−330.295			−1.37052			−0.685259	−	0.728299i	$-0.740311\pi$
$241$	−330.295			−1.37052			−0.685259	+	0.728299i	$0.740311\pi$
$242$	7.19597	−	236.712i	0.0297354	−	0.978148i
$243$		0			0
$244$	−211.673	−	12.8815i	−0.867513	−	0.0527930i
$245$	112.277			0.458274
$246$		0			0
$247$			102.554i			0.415197i
$248$	250.103	+	22.8655i	1.00848	+	0.0921997i
$249$		0			0
$250$	−5.69608	+	187.373i	−0.0227843	+	0.749492i
$251$			253.493i			1.00993i	0.863139	+	0.504966i	$0.168495\pi$
$251$			253.493i			1.00993i	−0.863139	+	0.504966i	$0.831505\pi$
$252$		0			0
$253$	−42.8228			−0.169260
$254$	100.806	+	3.06446i	0.396873	+	0.0120648i
$255$		0			0
$256$	248.471	+	61.6281i	0.970591	+	0.240735i
$257$	−254.160			−0.988950			−0.494475	−	0.869192i	$-0.664640\pi$
$257$	−254.160			−0.988950			−0.494475	+	0.869192i	$0.664640\pi$
$258$		0			0
$259$		−	146.235i		−	0.564613i
$260$	−546.949	−	33.2849i	−2.10365	−	0.128019i
$261$		0			0
$262$	249.793	+	7.59362i	0.953407	+	0.0289833i
$263$			190.047i			0.722613i	0.932447	+	0.361306i	$0.117669\pi$
$263$			190.047i			0.722613i	−0.932447	+	0.361306i	$0.882331\pi$
$264$		0			0
$265$	−446.962			−1.68665
$266$	1.44403	−	47.5016i	0.00542870	−	0.178577i
$267$		0			0
$268$	−18.5125	+	304.204i	−0.0690766	+	1.13509i
$269$	−233.427			−0.867758			−0.433879	−	0.900971i	$-0.642855\pi$
$269$	−233.427			−0.867758			−0.433879	+	0.900971i	$0.642855\pi$
$270$		0			0
$271$			2.73196i			0.0100810i	0.999987	+	0.00504051i	$0.00160445\pi$
$271$			2.73196i			0.0100810i	−0.999987	+	0.00504051i	$0.998396\pi$
$272$	94.1283	+	11.4991i	0.346060	+	0.0422760i
$273$		0			0
$274$	−8.33485	+	274.175i	−0.0304192	+	1.00064i
$275$			14.3252i			0.0520916i
$276$		0			0
$277$	−20.4896			−0.0739697			−0.0369848	−	0.999316i	$-0.511775\pi$
$277$	−20.4896			−0.0739697			−0.0369848	+	0.999316i	$0.511775\pi$
$278$	179.294	+	5.45049i	0.644943	+	0.0196061i
$279$		0			0
$280$	252.871	+	23.1186i	0.903111	+	0.0825664i
$281$	285.339			1.01544			0.507721	−	0.861522i	$-0.330488\pi$
$281$	285.339			1.01544			0.507721	+	0.861522i	$0.330488\pi$
$282$		0			0
$283$			4.45505i			0.0157422i	0.999969	+	0.00787112i	$0.00250548\pi$
$283$			4.45505i			0.0157422i	−0.999969	+	0.00787112i	$0.997495\pi$
$284$	14.5620	−	239.288i	0.0512746	−	0.842562i
$285$		0			0
$286$	75.6833	+	2.30075i	0.264627	+	0.00804458i
$287$		−	240.066i		−	0.836468i
$288$		0			0
$289$	−253.874			−0.878455
$290$	0.528084	−	17.3713i	0.00182098	−	0.0599012i
$291$		0			0
$292$	198.907	+	12.1046i	0.681190	+	0.0414542i
$293$	−326.981			−1.11598			−0.557988	−	0.829849i	$-0.688426\pi$
$293$	−326.981			−1.11598			−0.557988	+	0.829849i	$0.688426\pi$
$294$		0			0
$295$		−	197.324i		−	0.668895i
$296$	−19.5386	+	213.713i	−0.0660088	+	0.722004i
$297$		0			0
$298$	−1.14975	+	37.8213i	−0.00385824	+	0.126917i
$299$			626.114i			2.09403i
$300$		0			0
$301$	−151.866			−0.504539
$302$	537.873	+	16.3512i	1.78104	+	0.0541430i
$303$		0			0
$304$	−8.45711	+	69.2277i	−0.0278195	+	0.227723i
$305$	308.690			1.01210
$306$		0			0
$307$			352.091i			1.14688i	0.819249	+	0.573438i	$0.194391\pi$
$307$			352.091i			1.14688i	−0.819249	+	0.573438i	$0.805609\pi$
$308$	−35.0231	−	2.13136i	−0.113711	−	0.00691998i
$309$		0			0
$310$	−365.410	−	11.1084i	−1.17874	−	0.0358334i
$311$		−	75.4387i		−	0.242568i	−0.992618	−	0.121284i	$-0.961299\pi$
$311$		−	75.4387i		−	0.242568i	0.992618	−	0.121284i	$-0.0387012\pi$
$312$		0			0
$313$	−13.1951			−0.0421569			−0.0210784	−	0.999778i	$-0.506710\pi$
$313$	−13.1951			−0.0421569			−0.0210784	+	0.999778i	$0.506710\pi$
$314$	0.698699	−	22.9838i	0.00222516	−	0.0731967i
$315$		0			0
$316$	5.68533	−	93.4232i	0.0179915	−	0.295643i
$317$	−276.427			−0.872011			−0.436005	−	0.899944i	$-0.643607\pi$
$317$	−276.427			−0.872011			−0.436005	+	0.899944i	$0.643607\pi$
$318$		0			0
$319$			2.40151i			0.00752826i
$320$	−366.467	−	67.5729i	−1.14521	−	0.211165i
$321$		0			0
$322$	8.81616	−	290.008i	0.0273794	−	0.900647i
$323$			25.8341i			0.0799818i
$324$		0			0
$325$	209.449			0.644459
$326$	253.011	+	7.69145i	0.776106	+	0.0235934i
$327$		0			0
$328$	−32.0756	+	350.843i	−0.0977914	+	1.06964i
$329$	−177.258			−0.538779
$330$		0			0
$331$			550.110i			1.66196i	0.556301	+	0.830981i	$0.312220\pi$
$331$			550.110i			1.66196i	−0.556301	+	0.830981i	$0.687780\pi$
$332$	−33.3156	+	547.453i	−0.100348	+	1.64895i
$333$		0			0
$334$	−28.4716	−	0.865527i	−0.0852442	−	0.00259140i
$335$		−	443.631i		−	1.32427i
$336$		0			0
$337$	−179.034			−0.531259			−0.265630	−	0.964075i	$-0.585580\pi$
$337$	−179.034			−0.531259			−0.265630	+	0.964075i	$0.585580\pi$
$338$	23.3690	−	768.725i	0.0691391	−	2.27433i
$339$		0			0
$340$	−137.781	−	8.38475i	−0.405238	−	0.0246610i
$341$	50.5164			0.148142
$342$		0			0
$343$		−	372.233i		−	1.08523i
$344$	221.943	+	20.2910i	0.645184	+	0.0589856i
$345$		0			0
$346$	13.2370	−	435.432i	0.0382573	−	1.25848i
$347$		−	161.757i		−	0.466157i	−0.972458	−	0.233079i	$-0.925120\pi$
$347$		−	161.757i		−	0.466157i	0.972458	−	0.233079i	$-0.0748800\pi$
$348$		0			0
$349$	−472.810			−1.35476			−0.677378	−	0.735635i	$-0.736884\pi$
$349$	−472.810			−1.35476			−0.677378	+	0.735635i	$0.736884\pi$
$350$	−97.0142	−	2.94920i	−0.277184	−	0.00842629i
$351$		0			0
$352$	50.8994	+	7.79433i	0.144601	+	0.0221430i
$353$	−319.200			−0.904249			−0.452125	−	0.891955i	$-0.649334\pi$
$353$	−319.200			−0.904249			−0.452125	+	0.891955i	$0.649334\pi$
$354$		0			0
$355$			348.962i			0.982991i
$356$	465.571	+	28.3326i	1.30778	+	0.0795860i
$357$		0			0
$358$	360.281	+	10.9524i	1.00637	+	0.0305933i
$359$			545.770i			1.52025i	0.649776	+	0.760126i	$0.274863\pi$
$359$			545.770i			1.52025i	−0.649776	+	0.760126i	$0.725137\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−5.77715	+	190.040i	−0.0159590	+	0.524971i
$363$		0			0
$364$	−31.1626	+	512.075i	−0.0856117	+	1.40680i
$365$	−290.074			−0.794723
$366$		0			0
$367$		−	90.4491i		−	0.246455i	−0.992378	−	0.123228i	$-0.960675\pi$
$367$		−	90.4491i		−	0.246455i	0.992378	−	0.123228i	$-0.0393246\pi$
$368$	−51.6327	+	422.651i	−0.140306	+	1.14851i
$369$		0			0
$370$	9.49210	−	312.243i	0.0256543	−	0.843900i
$371$			418.464i			1.12793i
$372$		0			0
$373$	468.975			1.25731			0.628653	−	0.777686i	$-0.283606\pi$
$373$	468.975			1.25731			0.628653	+	0.777686i	$0.283606\pi$
$374$	19.0652	+	0.579578i	0.0509766	+	0.00154967i
$375$		0			0
$376$	259.052	+	23.6837i	0.688969	+	0.0629886i
$377$	35.1127			0.0931370
$378$		0			0
$379$		−	196.529i		−	0.518545i	−0.965804	−	0.259273i	$-0.916517\pi$
$379$		−	196.529i		−	0.518545i	0.965804	−	0.259273i	$-0.0834828\pi$
$380$	6.16666	−	101.333i	0.0162280	−	0.266665i
$381$		0			0
$382$	−50.9342	−	1.54839i	−0.133336	−	0.00405337i
$383$			24.8045i			0.0647637i	0.999476	+	0.0323819i	$0.0103093\pi$
$383$			24.8045i			0.0647637i	−0.999476	+	0.0323819i	$0.989691\pi$
$384$		0			0
$385$	51.0755			0.132664
$386$	20.6359	−	678.819i	0.0534608	−	1.75860i
$387$		0			0
$388$	262.451	+	15.9716i	0.676420	+	0.0411639i
$389$	126.462			0.325095			0.162547	−	0.986701i	$-0.448029\pi$
$389$	126.462			0.325095			0.162547	+	0.986701i	$0.448029\pi$
$390$		0			0
$391$			157.723i			0.403385i
$392$	−14.0450	+	153.624i	−0.0358291	+	0.391898i
$393$		0			0
$394$	−8.31712	+	273.592i	−0.0211094	+	0.694396i
$395$			136.242i			0.344917i
$396$		0			0
$397$	403.878			1.01732			0.508662	−	0.860966i	$-0.330140\pi$
$397$	403.878			1.01732			0.508662	+	0.860966i	$0.330140\pi$
$398$	−398.639	−	12.1185i	−1.00160	−	0.0304485i
$399$		0			0
$400$	141.386	+	17.2723i	0.353466	+	0.0431807i
$401$	−345.608			−0.861865			−0.430933	−	0.902384i	$-0.641815\pi$
$401$	−345.608			−0.861865			−0.430933	+	0.902384i	$0.641815\pi$
$402$		0			0
$403$		−	738.603i		−	1.83276i
$404$	7.24282	+	0.440767i	0.0179278	+	0.00109101i
$405$		0			0
$406$	−16.2637	−	0.494413i	−0.0400585	−	0.00121777i
$407$			43.1663i			0.106060i
$408$		0			0
$409$	−429.506			−1.05014			−0.525069	−	0.851060i	$-0.675960\pi$
$409$	−429.506			−1.05014			−0.525069	+	0.851060i	$0.675960\pi$
$410$	15.5827	−	512.595i	0.0380066	−	1.25023i
$411$		0			0
$412$	0.120192	−	1.97504i	0.000291729	−	0.00479378i
$413$	−184.742			−0.447318
$414$		0			0
$415$		−	798.370i		−	1.92378i
$416$	113.961	−	744.203i	0.273945	−	1.78895i
$417$		0			0
$418$	−0.426257	+	14.0218i	−0.00101975	+	0.0335449i
$419$		−	345.206i		−	0.823881i	−0.911211	−	0.411940i	$-0.864851\pi$
$419$		−	345.206i		−	0.823881i	0.911211	−	0.411940i	$-0.135149\pi$
$420$		0			0
$421$	−195.468			−0.464295			−0.232148	−	0.972681i	$-0.574575\pi$
$421$	−195.468			−0.464295			−0.232148	+	0.972681i	$0.574575\pi$
$422$	−726.974	−	22.0998i	−1.72269	−	0.0523692i
$423$		0			0
$424$	55.9115	−	611.559i	0.131867	−	1.44236i
$425$	52.7620			0.124146
$426$		0			0
$427$		−	289.008i		−	0.676834i
$428$	−2.85157	+	46.8579i	−0.00666254	+	0.109481i
$429$		0			0
$430$	−324.268	−	9.85764i	−0.754111	−	0.0229247i
$431$		−	643.698i		−	1.49350i	−0.665106	−	0.746749i	$-0.731614\pi$
$431$		−	643.698i		−	1.49350i	0.665106	−	0.746749i	$-0.268386\pi$
$432$		0			0
$433$	−755.385			−1.74454			−0.872269	−	0.489026i	$-0.837352\pi$
$433$	−755.385			−1.74454			−0.872269	+	0.489026i	$0.837352\pi$
$434$	−10.4001	+	342.112i	−0.0239633	+	0.788275i
$435$		0			0
$436$	115.714	+	7.04183i	0.265398	+	0.0161510i
$437$	−115.999			−0.265445
$438$		0			0
$439$			522.862i			1.19103i	0.803345	+	0.595514i	$0.203052\pi$
$439$			522.862i			1.19103i	−0.803345	+	0.595514i	$0.796948\pi$
$440$	−74.6437	−	6.82426i	−0.169645	−	0.0155097i
$441$		0			0
$442$	8.47403	−	278.754i	0.0191720	−	0.630665i
$443$		−	5.86286i		−	0.0132345i	−0.999978	−	0.00661723i	$-0.997894\pi$
$443$		−	5.86286i		−	0.0132345i	0.999978	−	0.00661723i	$-0.00210634\pi$
$444$		0			0
$445$	−678.959			−1.52575
$446$	537.688	+	16.3455i	1.20558	+	0.0366492i
$447$		0			0
$448$	−63.2644	+	343.101i	−0.141215	+	0.765850i
$449$	−626.982			−1.39640			−0.698199	−	0.715904i	$-0.746015\pi$
$449$	−626.982			−1.39640			−0.698199	+	0.715904i	$0.746015\pi$
$450$		0			0
$451$			70.8640i			0.157126i
$452$	−561.861	−	34.1924i	−1.24306	−	0.0756470i
$453$		0			0
$454$	159.909	+	4.86117i	0.352222	+	0.0107074i
$455$		−	746.777i		−	1.64127i
$456$		0			0
$457$	−451.537			−0.988046			−0.494023	−	0.869449i	$-0.664474\pi$
$457$	−451.537			−0.988046			−0.494023	+	0.869449i	$0.664474\pi$
$458$	18.0698	−	594.408i	0.0394538	−	1.29784i
$459$		0			0
$460$	37.6489	−	618.659i	0.0818454	−	1.34491i
$461$	−50.7723			−0.110135			−0.0550675	−	0.998483i	$-0.517537\pi$
$461$	−50.7723			−0.110135			−0.0550675	+	0.998483i	$0.517537\pi$
$462$		0			0
$463$			69.7862i			0.150726i	0.997156	+	0.0753631i	$0.0240116\pi$
$463$			69.7862i			0.150726i	−0.997156	+	0.0753631i	$0.975988\pi$
$464$	23.7024	+	2.89557i	0.0510828	+	0.00624046i
$465$		0			0
$466$	15.5559	−	511.713i	0.0333818	−	1.09810i
$467$		−	461.829i		−	0.988927i	−0.869198	−	0.494464i	$-0.835365\pi$
$467$		−	461.829i		−	0.988927i	0.869198	−	0.494464i	$-0.164635\pi$
$468$		0			0
$469$	−415.345			−0.885597
$470$	−378.486	−	11.5058i	−0.805289	−	0.0244805i
$471$		0			0
$472$	269.990	+	24.6837i	0.572012	+	0.0522959i
$473$	44.8286			0.0947751
$474$		0			0
$475$			38.8044i			0.0816935i
$476$	−7.85013	+	128.996i	−0.0164919	+	0.271000i
$477$		0			0
$478$	297.211	+	9.03512i	0.621780	+	0.0189019i
$479$		−	814.201i		−	1.69979i	−0.526949	−	0.849897i	$-0.676664\pi$
$479$		−	814.201i		−	1.69979i	0.526949	−	0.849897i	$-0.323336\pi$
$480$		0			0
$481$	631.136			1.31213
$482$	−20.0725	+	660.285i	−0.0416441	+	1.36989i
$483$		0			0
$484$	−472.768	−	28.7706i	−0.976793	−	0.0594434i
$485$	−382.742			−0.789158
$486$		0			0
$487$		−	149.015i		−	0.305986i	−0.988227	−	0.152993i	$-0.951109\pi$
$487$		−	149.015i		−	0.305986i	0.988227	−	0.152993i	$-0.0488912\pi$
$488$	−38.6148	+	422.368i	−0.0791286	+	0.865508i
$489$		0			0
$490$	6.82323	−	224.451i	0.0139250	−	0.458063i
$491$		−	367.294i		−	0.748053i	−0.927418	−	0.374027i	$-0.877977\pi$
$491$		−	367.294i		−	0.748053i	0.927418	−	0.374027i	$-0.122023\pi$
$492$		0			0
$493$	8.84517			0.0179415
$494$	205.013	+	6.23232i	0.415005	+	0.0126160i
$495$		0			0
$496$	60.9091	−	498.586i	0.122801	−	1.00521i
$497$	326.712			0.657368
$498$		0			0
$499$			138.107i			0.276767i	0.990379	+	0.138384i	$0.0441907\pi$
$499$			138.107i			0.276767i	−0.990379	+	0.138384i	$0.955809\pi$
$500$	374.227	+	22.7738i	0.748454	+	0.0455476i
$501$		0			0
$502$	506.752	+	15.4051i	1.00947	+	0.0306875i
$503$			31.6936i			0.0630092i	0.999504	+	0.0315046i	$0.0100299\pi$
$503$			31.6936i			0.0630092i	−0.999504	+	0.0315046i	$0.989970\pi$
$504$		0			0
$505$	−10.5625			−0.0209158
$506$	−2.60240	+	85.6061i	−0.00514308	+	0.169182i
$507$		0			0
$508$	12.2522	−	201.332i	0.0241185	−	0.396323i
$509$	564.839			1.10970			0.554852	−	0.831949i	$-0.312775\pi$
$509$	564.839			1.10970			0.554852	+	0.831949i	$0.312775\pi$
$510$		0			0
$511$			271.578i			0.531465i
$512$	138.299	−	492.968i	0.270116	−	0.962828i
$513$		0			0
$514$	−15.4457	+	508.086i	−0.0300499	+	0.988494i
$515$			2.88027i			0.00559276i
$516$		0			0
$517$	52.3240			0.101207
$518$	−292.334	−	8.88687i	−0.564352	−	0.0171561i
$519$		0			0
$520$	−99.7779	+	1091.37i	−0.191881	+	2.09879i
$521$	304.845			0.585114			0.292557	−	0.956248i	$-0.405494\pi$
$521$	304.845			0.585114			0.292557	+	0.956248i	$0.405494\pi$
$522$		0			0
$523$			812.948i			1.55439i	0.629257	+	0.777197i	$0.283359\pi$
$523$			812.948i			1.55439i	−0.629257	+	0.777197i	$0.716641\pi$
$524$	30.3604	−	498.893i	0.0579398	−	0.952086i
$525$		0			0
$526$	379.919	+	11.5494i	0.722279	+	0.0219571i
$527$		−	186.060i		−	0.353055i
$528$		0			0
$529$	−179.204			−0.338759
$530$	−27.1625	+	893.512i	−0.0512500	+	1.68587i
$531$		0			0
$532$	−94.8715	−	5.77347i	−0.178330	−	0.0108524i
$533$	1036.11			1.94391
$534$		0			0
$535$		−	68.3345i		−	0.127728i
$536$	607.002	+	55.4948i	1.13247	+	0.103535i
$537$		0			0
$538$	−14.1857	+	466.638i	−0.0263674	+	0.867357i
$539$			31.0294i			0.0575684i
$540$		0			0
$541$	−396.300			−0.732532			−0.366266	−	0.930510i	$-0.619364\pi$
$541$	−396.300			−0.732532			−0.366266	+	0.930510i	$0.619364\pi$
$542$	5.46139	+	0.166025i	0.0100764	+	0.000306319i
$543$		0			0
$544$	28.7078	−	187.471i	0.0527717	−	0.344616i
$545$	−168.749			−0.309632
$546$		0			0
$547$			526.396i			0.962333i	0.876629	+	0.481167i	$0.159787\pi$
$547$			526.396i			0.962333i	−0.876629	+	0.481167i	$0.840213\pi$
$548$	547.591	+	33.3240i	0.999254	+	0.0608102i
$549$		0			0
$550$	28.6371	+	0.870560i	0.0520675	+	0.00158284i
$551$			6.50528i			0.0118063i
$552$		0			0
$553$	127.555			0.230661
$554$	−1.24518	+	40.9603i	−0.00224762	+	0.0739355i
$555$		0			0
$556$	21.7919	−	358.092i	0.0391940	−	0.644050i
$557$	−68.8105			−0.123538			−0.0617688	−	0.998090i	$-0.519674\pi$
$557$	−68.8105			−0.123538			−0.0617688	+	0.998090i	$0.519674\pi$
$558$		0			0
$559$		−	655.442i		−	1.17253i
$560$	61.5832	−	504.104i	0.109970	−	0.900185i
$561$		0			0
$562$	17.3404	−	570.415i	0.0308549	−	1.01497i
$563$			588.997i			1.04618i	0.852279	+	0.523088i	$0.175220\pi$
$563$			588.997i			1.04618i	−0.852279	+	0.523088i	$0.824780\pi$
$564$		0			0
$565$	819.383			1.45023
$566$	8.90599	+	0.270739i	0.0157350	+	0.000478338i
$567$		0			0
$568$	−477.469	−	43.6524i	−0.840615	−	0.0768528i
$569$	421.857			0.741401			0.370700	−	0.928752i	$-0.379118\pi$
$569$	421.857			0.741401			0.370700	+	0.928752i	$0.379118\pi$
$570$		0			0
$571$		−	393.676i		−	0.689451i	−0.938704	−	0.344725i	$-0.887972\pi$
$571$		−	393.676i		−	0.689451i	0.938704	−	0.344725i	$-0.112028\pi$
$572$	9.19875	−	151.157i	0.0160817	−	0.264260i
$573$		0			0
$574$	−479.911	−	14.5892i	−0.836082	−	0.0254166i
$575$			236.910i			0.412017i
$576$		0			0
$577$	703.416			1.21909			0.609546	−	0.792751i	$-0.291352\pi$
$577$	703.416			1.21909			0.609546	+	0.792751i	$0.291352\pi$
$578$	−15.4282	+	507.513i	−0.0266924	+	0.878050i
$579$		0			0
$580$	−34.6946	−	2.11136i	−0.0598182	−	0.00364027i
$581$	−747.465			−1.28651
$582$		0			0
$583$		−	123.524i		−	0.211877i
$584$	36.2860	−	396.895i	0.0621335	−	0.679615i
$585$		0			0
$586$	−19.8711	+	653.660i	−0.0339097	+	1.11546i
$587$		−	56.2392i		−	0.0958078i	−0.998852	−	0.0479039i	$-0.984746\pi$
$587$		−	56.2392i		−	0.0958078i	0.998852	−	0.0479039i	$-0.0152541\pi$
$588$		0			0
$589$	136.840			0.232326
$590$	−394.466	−	11.9916i	−0.668586	−	0.0203248i
$591$		0			0
$592$	426.041	+	52.0468i	0.719665	+	0.0879169i
$593$	−553.916			−0.934090			−0.467045	−	0.884233i	$-0.654681\pi$
$593$	−553.916			−0.934090			−0.467045	+	0.884233i	$0.654681\pi$
$594$		0			0
$595$		−	188.119i		−	0.316167i
$596$	75.5377	+	4.59690i	0.126741	+	0.00771291i
$597$		0			0
$598$	1251.65	+	38.0498i	2.09306	+	0.0636284i
$599$			724.179i			1.20898i	0.796613	+	0.604490i	$0.206623\pi$
$599$			724.179i			1.20898i	−0.796613	+	0.604490i	$0.793377\pi$
$600$		0			0
$601$	−393.734			−0.655132			−0.327566	−	0.944828i	$-0.606228\pi$
$601$	−393.734			−0.655132			−0.327566	+	0.944828i	$0.606228\pi$
$602$	−9.22911	+	303.592i	−0.0153308	+	0.504306i
$603$		0			0
$604$	65.3745	−	1074.26i	0.108236	−	1.77857i
$605$	689.454			1.13959
$606$		0			0
$607$			860.362i			1.41740i	0.705510	+	0.708700i	$0.250718\pi$
$607$			860.362i			1.41740i	−0.705510	+	0.708700i	$0.749282\pi$
$608$	137.878	+	21.1135i	0.226772	+	0.0347261i
$609$		0			0
$610$	18.7595	−	617.096i	0.0307533	−	1.01163i
$611$		−	765.032i		−	1.25210i
$612$		0			0
$613$	563.747			0.919652			0.459826	−	0.888009i	$-0.347912\pi$
$613$	563.747			0.919652			0.459826	+	0.888009i	$0.347912\pi$
$614$	703.856	+	21.3970i	1.14635	+	0.0348486i
$615$		0			0
$616$	−6.38914	+	69.8844i	−0.0103720	+	0.113449i
$617$	677.849			1.09862			0.549310	−	0.835619i	$-0.314891\pi$
$617$	677.849			1.09862			0.549310	+	0.835619i	$0.314891\pi$
$618$		0			0
$619$			997.063i			1.61076i	0.592756	+	0.805382i	$0.298040\pi$
$619$			997.063i			1.61076i	−0.592756	+	0.805382i	$0.701960\pi$
$620$	−44.4129	+	729.808i	−0.0716338	+	1.17711i
$621$		0			0
$622$	−150.808	−	4.58451i	−0.242456	−	0.00737060i
$623$			635.668i			1.02033i
$624$		0			0
$625$	−768.307			−1.22929
$626$	−0.801884	+	26.3780i	−0.00128096	+	0.0421374i
$627$		0			0
$628$	−45.9038	−	2.79351i	−0.0730953	−	0.00444826i
$629$	158.988			0.252764
$630$		0			0
$631$		−	1071.78i		−	1.69854i	−0.527959	−	0.849270i	$-0.677042\pi$
$631$		−	1071.78i		−	1.69854i	0.527959	−	0.849270i	$-0.322958\pi$
$632$	−186.415	−	17.0429i	−0.294960	−	0.0269665i
$633$		0			0
$634$	−16.7989	+	552.599i	−0.0264966	+	0.871608i
$635$			293.610i			0.462378i
$636$		0			0
$637$	453.682			0.712216
$638$	4.80081	+	0.145943i	0.00752478	+	0.000228751i
$639$		0			0
$640$	−157.354	+	728.489i	−0.245866	+	1.13826i
$641$	627.241			0.978536			0.489268	−	0.872134i	$-0.337264\pi$
$641$	627.241			0.978536			0.489268	+	0.872134i	$0.337264\pi$
$642$		0			0
$643$		−	620.131i		−	0.964433i	−0.876052	−	0.482217i	$-0.839832\pi$
$643$		−	620.131i		−	0.964433i	0.876052	−	0.482217i	$-0.160168\pi$
$644$	−579.213	−	35.2484i	−0.899399	−	0.0547335i
$645$		0			0
$646$	51.6444	+	1.56997i	0.0799449	+	0.00243030i
$647$		−	1270.23i		−	1.96327i	−0.190778	−	0.981633i	$-0.561101\pi$
$647$		−	1270.23i		−	1.96327i	0.190778	−	0.981633i	$-0.438899\pi$
$648$		0			0
$649$	54.5332			0.0840265
$650$	12.7285	−	418.705i	0.0195823	−	0.644162i
$651$		0			0
$652$	30.7516	−	505.320i	0.0471650	−	0.775031i
$653$	−775.383			−1.18742			−0.593708	−	0.804681i	$-0.702337\pi$
$653$	−775.383			−1.18742			−0.593708	+	0.804681i	$0.702337\pi$
$654$		0			0
$655$			727.554i			1.11077i
$656$	699.412	+	85.4427i	1.06618	+	0.130248i
$657$		0			0
$658$	−10.7722	+	354.353i	−0.0163712	+	0.538531i
$659$			516.735i			0.784119i	0.919940	+	0.392060i	$0.128237\pi$
$659$			516.735i			0.784119i	−0.919940	+	0.392060i	$0.871763\pi$
$660$		0			0
$661$	−987.675			−1.49421			−0.747107	−	0.664704i	$-0.768558\pi$
$661$	−987.675			−1.49421			−0.747107	+	0.664704i	$0.768558\pi$
$662$	1099.71	+	33.4309i	1.66119	+	0.0504998i
$663$		0			0
$664$	1092.37	+	99.8698i	1.64514	+	0.150406i
$665$	138.355			0.208052
$666$		0			0
$667$			39.7163i			0.0595446i
$668$	−3.46051	+	56.8643i	−0.00518041	+	0.0851261i
$669$		0			0
$670$	−886.853	−	26.9601i	−1.32366	−	0.0402389i
$671$			85.3109i			0.127140i
$672$		0			0
$673$	−237.022			−0.352187			−0.176094	−	0.984373i	$-0.556346\pi$
$673$	−237.022			−0.352187			−0.176094	+	0.984373i	$0.556346\pi$
$674$	−10.8802	+	357.904i	−0.0161427	+	0.531014i
$675$		0			0
$676$	−1535.32	−	93.4329i	−2.27118	−	0.138214i
$677$	−894.692			−1.32155			−0.660777	−	0.750582i	$-0.729773\pi$
$677$	−894.692			−1.32155			−0.660777	+	0.750582i	$0.729773\pi$
$678$		0			0
$679$			358.338i			0.527743i
$680$	−25.1349	+	274.925i	−0.0369631	+	0.404302i
$681$		0			0
$682$	3.06995	−	100.986i	0.00450139	−	0.148074i
$683$			1327.94i			1.94427i	0.234421	+	0.972135i	$0.424680\pi$
$683$			1327.94i			1.94427i	−0.234421	+	0.972135i	$0.575320\pi$
$684$		0			0
$685$	−798.572			−1.16580
$686$	−744.122	−	22.6211i	−1.08473	−	0.0329754i
$687$		0			0
$688$	54.0511	−	442.449i	0.0785627	−	0.643094i
$689$	−1806.05			−2.62127
$690$		0			0
$691$			552.974i			0.800252i	0.916460	+	0.400126i	$0.131034\pi$
$691$			552.974i			0.800252i	−0.916460	+	0.400126i	$0.868966\pi$
$692$	−869.658	−	52.9236i	−1.25673	−	0.0764792i
$693$		0			0
$694$	−323.364	−	9.83016i	−0.465942	−	0.0141645i
$695$			522.218i			0.751393i
$696$		0			0
$697$	261.004			0.374467
$698$	−28.7333	+	945.183i	−0.0411652	+	1.35413i
$699$		0			0
$700$	−11.7914	+	193.760i	−0.0168448	+	0.276799i
$701$	−815.608			−1.16349			−0.581746	−	0.813370i	$-0.697630\pi$
$701$	−815.608			−1.16349			−0.581746	+	0.813370i	$0.697630\pi$
$702$		0			0
$703$			116.930i			0.166330i
$704$	18.6747	−	101.278i	0.0265266	−	0.143861i
$705$		0			0
$706$	−19.3982	+	638.105i	−0.0274762	+	0.903832i
$707$			9.88900i			0.0139873i
$708$		0			0
$709$	764.747			1.07863			0.539314	−	0.842105i	$-0.318684\pi$
$709$	764.747			1.07863			0.539314	+	0.842105i	$0.318684\pi$
$710$	697.601	+	21.2069i	0.982537	+	0.0298688i
$711$		0			0
$712$	84.9324	−	928.990i	0.119287	−	1.30476i
$713$	835.441			1.17173
$714$		0			0
$715$			220.437i			0.308304i
$716$	43.7894	−	719.563i	0.0611584	−	1.00498i
$717$		0			0
$718$	1091.04	+	33.1672i	1.51955	+	0.0461938i
$719$		−	713.170i		−	0.991892i	−0.868353	−	0.495946i	$-0.834821\pi$
$719$		−	713.170i		−	0.991892i	0.868353	−	0.495946i	$-0.165179\pi$
$720$		0			0
$721$	2.69662			0.00374011
$722$	−1.15465	+	37.9825i	−0.00159925	+	0.0526073i
$723$		0			0
$724$	379.553	+	23.0979i	0.524244	+	0.0319032i
$725$	13.2860			0.0183255
$726$		0			0
$727$		−	890.749i		−	1.22524i	−0.790378	−	0.612619i	$-0.790116\pi$
$727$		−	890.749i		−	1.22524i	0.790378	−	0.612619i	$-0.209884\pi$
$728$	1021.78	+	93.4160i	1.40355	+	0.128319i
$729$		0			0
$730$	−17.6282	+	579.880i	−0.0241482	+	0.794356i
$731$		−	165.111i		−	0.225870i
$732$		0			0
$733$	−221.785			−0.302572			−0.151286	−	0.988490i	$-0.548341\pi$
$733$	−221.785			−0.302572			−0.151286	+	0.988490i	$0.548341\pi$
$734$	−180.815	−	5.49671i	−0.246342	−	0.00748871i
$735$		0			0
$736$	841.775	+	128.903i	1.14372	+	0.175140i
$737$	122.604			0.166355
$738$		0			0
$739$		−	635.372i		−	0.859772i	−0.902883	−	0.429886i	$-0.858554\pi$
$739$		−	635.372i		−	0.859772i	0.902883	−	0.429886i	$-0.141446\pi$
$740$	−623.621	−	37.9508i	−0.842731	−	0.0512849i
$741$		0			0
$742$	836.541	+	25.4306i	1.12741	+	0.0342730i
$743$		−	795.274i		−	1.07036i	−0.844740	−	0.535178i	$-0.820245\pi$
$743$		−	795.274i		−	1.07036i	0.844740	−	0.535178i	$-0.179755\pi$
$744$		0			0
$745$	−110.159			−0.147865
$746$	28.5002	−	937.518i	0.0382041	−	1.25673i
$747$		0			0
$748$	2.31724	−	38.0777i	0.00309791	−	0.0509060i
$749$	−63.9775			−0.0854172
$750$		0			0
$751$		−	84.7437i		−	0.112841i	−0.998407	−	0.0564206i	$-0.982031\pi$
$751$		−	84.7437i		−	0.112841i	0.998407	−	0.0564206i	$-0.0179688\pi$
$752$	63.0885	−	516.426i	0.0838943	−	0.686737i
$753$		0			0
$754$	2.13384	−	70.1929i	0.00283003	−	0.0930940i
$755$			1566.63i			2.07500i
$756$		0			0
$757$	1207.44			1.59503			0.797514	−	0.603301i	$-0.206148\pi$
$757$	1207.44			1.59503			0.797514	+	0.603301i	$0.206148\pi$
$758$	−392.876	−	11.9433i	−0.518306	−	0.0157563i
$759$		0			0
$760$	−202.197	−	18.4857i	−0.266048	−	0.0243233i
$761$	−524.706			−0.689495			−0.344748	−	0.938695i	$-0.612035\pi$
$761$	−524.706			−0.689495			−0.344748	+	0.938695i	$0.612035\pi$
$762$		0			0
$763$			157.990i			0.207064i
$764$	−6.19068	+	101.727i	−0.00810299	+	0.133151i
$765$		0			0
$766$	49.5861	+	1.50740i	0.0647338	+	0.00196789i
$767$		−	797.332i		−	1.03955i
$768$		0			0
$769$	531.656			0.691360			0.345680	−	0.938352i	$-0.387648\pi$
$769$	531.656			0.691360			0.345680	+	0.938352i	$0.387648\pi$
$770$	3.10393	−	102.104i	0.00403107	−	0.132602i
$771$		0			0
$772$	−1355.76	−	82.5054i	−1.75616	−	0.106872i
$773$	249.261			0.322459			0.161229	−	0.986917i	$-0.448454\pi$
$773$	249.261			0.322459			0.161229	+	0.986917i	$0.448454\pi$
$774$		0			0
$775$		−	279.474i		−	0.360611i
$776$	47.8780	−	523.689i	0.0616984	−	0.674857i
$777$		0			0
$778$	7.68525	−	252.807i	0.00987821	−	0.324944i
$779$			191.958i			0.246416i
$780$		0			0
$781$	−96.4404			−0.123483
$782$	315.301	+	9.58506i	0.403198	+	0.0122571i
$783$		0			0
$784$	306.253	+	37.4130i	0.390629	+	0.0477206i
$785$	66.9432			0.0852780
$786$		0			0
$787$		−	226.270i		−	0.287509i	−0.989613	−	0.143755i	$-0.954082\pi$
$787$		−	226.270i		−	0.287509i	0.989613	−	0.143755i	$-0.0459176\pi$
$788$	546.426	+	33.2531i	0.693434	+	0.0421994i
$789$		0			0
$790$	272.359	+	8.27963i	0.344758	+	0.0104805i
$791$		−	767.138i		−	0.969833i
$792$		0			0
$793$	1247.33			1.57293
$794$	24.5442	−	807.383i	0.0309121	−	1.01685i
$795$		0			0
$796$	−48.4516	+	796.173i	−0.0608688	+	1.00022i
$797$	874.323			1.09702			0.548509	−	0.836145i	$-0.315196\pi$
$797$	874.323			1.09702			0.548509	+	0.836145i	$0.315196\pi$
$798$		0			0
$799$		−	192.718i		−	0.241199i
$800$	43.1208	−	281.592i	0.0539010	−	0.351991i
$801$		0			0
$802$	−21.0031	+	690.897i	−0.0261883	+	0.861467i
$803$		−	80.1659i		−	0.0998330i
$804$		0			0
$805$	844.687			1.04930
$806$	−1476.52	−	44.8859i	−1.83192	−	0.0556897i
$807$		0			0
$808$	1.32128	−	14.4522i	0.00163525	−	0.0178864i
$809$	314.242			0.388433			0.194216	−	0.980959i	$-0.437784\pi$
$809$	314.242			0.388433			0.194216	+	0.980959i	$0.437784\pi$
$810$		0			0
$811$			1244.45i			1.53446i	0.641371	+	0.767231i	$0.278366\pi$
$811$			1244.45i			1.53446i	−0.641371	+	0.767231i	$0.721634\pi$
$812$	−1.97674	+	32.4824i	−0.00243441	+	0.0400030i
$813$		0			0
$814$	86.2927	+	2.62327i	0.106011	+	0.00322269i
$815$			736.927i			0.904204i
$816$		0			0
$817$	121.433			0.148633
$818$	−26.1017	+	858.616i	−0.0319091	+	1.04965i
$819$		0			0
$820$	−1023.77	−	62.3021i	−1.24850	−	0.0759782i
$821$	−406.689			−0.495358			−0.247679	−	0.968842i	$-0.579668\pi$
$821$	−406.689			−0.495358			−0.247679	+	0.968842i	$0.579668\pi$
$822$		0			0
$823$		−	1354.51i		−	1.64582i	−0.568171	−	0.822910i	$-0.692349\pi$
$823$		−	1354.51i		−	1.64582i	0.568171	−	0.822910i	$-0.307651\pi$
$824$	−3.94095	−	0.360299i	−0.00478271	−	0.000437256i
$825$		0			0
$826$	−11.2270	+	369.314i	−0.0135921	+	0.447112i
$827$			465.660i			0.563072i	0.959551	+	0.281536i	$0.0908439\pi$
$827$			465.660i			0.563072i	−0.959551	+	0.281536i	$0.909156\pi$
$828$		0			0
$829$	−1349.16			−1.62745			−0.813727	−	0.581248i	$-0.802565\pi$
$829$	−1349.16			−1.62745			−0.813727	+	0.581248i	$0.802565\pi$
$830$	−1596.00	−	48.5180i	−1.92289	−	0.0584554i
$831$		0			0
$832$	−1480.79	−	273.044i	−1.77980	−	0.328177i
$833$	114.286			0.137198
$834$		0			0
$835$		−	82.9272i		−	0.0993140i
$836$	28.0046	+	1.70424i	0.0334984	+	0.00203857i
$837$		0			0
$838$	−690.093	−	20.9786i	−0.823500	−	0.0250342i
$839$			860.694i			1.02586i	0.858431	+	0.512929i	$0.171439\pi$
$839$			860.694i			1.02586i	−0.858431	+	0.512929i	$0.828561\pi$
$840$		0			0
$841$	−838.773			−0.997352
$842$	−11.8789	+	390.756i	−0.0141079	+	0.464081i
$843$		0			0
$844$	−88.3584	+	1451.93i	−0.104690	+	1.72030i
$845$	2239.01			2.64972
$846$		0			0
$847$		−	645.494i		−	0.762095i
$848$	−1219.16	−	148.937i	−1.43768	−	0.175633i
$849$		0			0
$850$	3.20642	−	105.475i	0.00377225	−	0.124089i
$851$			713.884i			0.838877i
$852$		0			0
$853$	−279.325			−0.327462			−0.163731	−	0.986505i	$-0.552353\pi$
$853$	−279.325			−0.327462			−0.163731	+	0.986505i	$0.552353\pi$
$854$	−577.749	−	17.5634i	−0.676522	−	0.0205660i
$855$		0			0
$856$	93.4992	+	8.54811i	0.109228	+	0.00998611i
$857$	−548.748			−0.640313			−0.320157	−	0.947365i	$-0.603736\pi$
$857$	−548.748			−0.640313			−0.320157	+	0.947365i	$0.603736\pi$
$858$		0			0
$859$			241.447i			0.281079i	0.990075	+	0.140539i	$0.0448837\pi$
$859$			241.447i			0.281079i	−0.990075	+	0.140539i	$0.955116\pi$
$860$	−39.4124	+	647.637i	−0.0458283	+	0.753066i
$861$		0			0
$862$	−1286.80	−	39.1184i	−1.49281	−	0.0453809i
$863$			316.519i			0.366766i	0.983042	+	0.183383i	$0.0587048\pi$
$863$			316.519i			0.366766i	−0.983042	+	0.183383i	$0.941295\pi$
$864$		0			0
$865$	1268.25			1.46619
$866$	−45.9058	+	1510.07i	−0.0530090	+	1.74373i
$867$		0			0
$868$	683.275	+	41.5811i	0.787183	+	0.0479045i
$869$	−37.6525			−0.0433285
$870$		0			0
$871$		−	1792.59i		−	2.05809i
$872$	21.1092	−	230.892i	0.0242078	−	0.264785i
$873$		0			0
$874$	−7.04944	+	231.892i	−0.00806572	+	0.265322i
$875$			510.951i			0.583944i
$876$		0			0
$877$	883.893			1.00786			0.503930	−	0.863744i	$-0.331887\pi$
$877$	883.893			1.00786			0.503930	+	0.863744i	$0.331887\pi$
$878$	1045.24	+	31.7750i	1.19048	+	0.0361902i
$879$		0			0
$880$	−18.1784	+	148.804i	−0.0206573	+	0.169095i
$881$	823.058			0.934231			0.467116	−	0.884196i	$-0.345293\pi$
$881$	823.058			0.934231			0.467116	+	0.884196i	$0.345293\pi$
$882$		0			0
$883$			1295.31i			1.46694i	0.679721	+	0.733470i	$0.262101\pi$
$883$			1295.31i			1.46694i	−0.679721	+	0.733470i	$0.737899\pi$
$884$	−556.735	−	33.8805i	−0.629791	−	0.0383263i
$885$		0			0
$886$	−11.7203	−	0.356294i	−0.0132283	−	0.000402138i
$887$			229.109i			0.258297i	0.991625	+	0.129148i	$0.0412244\pi$
$887$			229.109i			0.258297i	−0.991625	+	0.129148i	$0.958776\pi$
$888$		0			0
$889$	274.889			0.309212
$890$	−41.2612	+	1357.29i	−0.0463609	+	1.52505i
$891$		0			0
$892$	65.3520	−	1073.89i	0.0732646	−	1.20391i
$893$	141.737			0.158720
$894$		0			0
$895$			1049.36i			1.17247i
$896$	682.040	+	147.321i	0.761205	+	0.164421i
$897$		0			0
$898$	−38.1025	+	1253.39i	−0.0424304	+	1.39575i
$899$		−	46.8517i		−	0.0521154i
$900$		0			0
$901$	−454.960			−0.504950
$902$	141.663	+	4.30650i	0.157054	+	0.00477439i
$903$		0			0
$904$	−102.498	+	1121.13i	−0.113383	+	1.24018i
$905$	−553.515			−0.611619
$906$		0			0
$907$			1024.23i			1.12925i	0.825347	+	0.564626i	$0.190980\pi$
$907$			1024.23i			1.12925i	−0.825347	+	0.564626i	$0.809020\pi$
$908$	19.4357	−	319.374i	0.0214050	−	0.351734i
$909$		0			0
$910$	−1492.87	−	45.3826i	−1.64051	−	0.0498710i
$911$			596.394i			0.654659i	0.944910	+	0.327329i	$0.106149\pi$
$911$			596.394i			0.654659i	−0.944910	+	0.327329i	$0.893851\pi$
$912$		0			0
$913$	220.640			0.241665
$914$	−27.4405	+	902.657i	−0.0300224	+	0.987590i
$915$		0			0
$916$	−1187.17	−	72.2460i	−1.29604	−	0.0788711i
$917$	681.164			0.742818
$918$		0			0
$919$		−	1761.71i		−	1.91699i	−0.285116	−	0.958493i	$-0.592032\pi$
$919$		−	1761.71i		−	1.91699i	0.285116	−	0.958493i	$-0.407968\pi$
$920$	−1234.46	−	112.860i	−1.34180	−	0.122674i
$921$		0			0
$922$	−3.08550	+	101.498i	−0.00334653	+	0.110084i
$923$			1410.06i			1.52769i
$924$		0			0
$925$	238.810			0.258173
$926$	139.508	+	4.24100i	0.150657	+	0.00457991i
$927$		0			0
$928$	7.22890	−	47.2070i	0.00778976	−	0.0508696i
$929$	−146.570			−0.157771			−0.0788857	−	0.996884i	$-0.525136\pi$
$929$	−146.570			−0.157771			−0.0788857	+	0.996884i	$0.525136\pi$
$930$		0			0
$931$			84.0531i			0.0902826i
$932$	−1022.01	−	62.1950i	−1.09658	−	0.0667328i
$933$		0			0
$934$	−923.232	−	28.0660i	−0.988471	−	0.0300492i
$935$			55.5300i			0.0593904i
$936$		0			0
$937$	813.237			0.867915			0.433958	−	0.900933i	$-0.357117\pi$
$937$	813.237			0.867915			0.433958	+	0.900933i	$0.357117\pi$
$938$	−25.2411	+	830.307i	−0.0269095	+	0.885188i
$939$		0			0
$940$	−46.0021	+	755.922i	−0.0489384	+	0.804173i
$941$	−573.885			−0.609867			−0.304934	−	0.952374i	$-0.598634\pi$
$941$	−573.885			−0.609867			−0.304934	+	0.952374i	$0.598634\pi$
$942$		0			0
$943$			1171.95i			1.24279i
$944$	65.7522	−	538.230i	0.0696527	−	0.570159i
$945$		0			0
$946$	2.72430	−	89.6159i	0.00287981	−	0.0947314i
$947$		−	1186.01i		−	1.25239i	−0.779666	−	0.626195i	$-0.784611\pi$
$947$		−	1186.01i		−	1.25239i	0.779666	−	0.626195i	$-0.215389\pi$
$948$		0			0
$949$	−1172.11			−1.23510
$950$	77.5730	+	2.35819i	0.0816558	+	0.00248231i
$951$		0			0
$952$	257.396	+	23.5323i	0.270374	+	0.0247188i
$953$	−132.421			−0.138951			−0.0694757	−	0.997584i	$-0.522133\pi$
$953$	−132.421			−0.138951			−0.0694757	+	0.997584i	$0.522133\pi$
$954$		0			0
$955$		−	148.353i		−	0.155343i
$956$	36.1238	−	593.598i	0.0377864	−	0.620918i
$957$		0			0
$958$	−1627.65	−	49.4801i	−1.69901	−	0.0516493i
$959$			747.654i			0.779619i
$960$		0			0
$961$	−24.5372			−0.0255330
$962$	38.3550	−	1261.69i	0.0398700	−	1.31153i
$963$		0			0
$964$	1318.74	+	80.2528i	1.36799	+	0.0832498i
$965$	1977.15			2.04886
$966$		0			0
$967$			949.146i			0.981536i	0.871290	+	0.490768i	$0.163284\pi$
$967$			949.146i			0.981536i	−0.871290	+	0.490768i	$0.836716\pi$
$968$	−86.2453	+	943.351i	−0.0890964	+	0.974536i
$969$		0			0
$970$	−23.2597	+	765.130i	−0.0239791	+	0.788793i
$971$			1700.58i			1.75137i	0.482883	+	0.875685i	$0.339590\pi$
$971$			1700.58i			1.75137i	−0.482883	+	0.875685i	$0.660410\pi$
$972$		0			0
$973$	488.921			0.502488
$974$	−297.893	−	9.05585i	−0.305845	−	0.00929759i
$975$		0			0
$976$	841.999	+	102.862i	0.862704	+	0.105391i
$977$	−1288.94			−1.31929			−0.659643	−	0.751579i	$-0.729293\pi$
$977$	−1288.94			−1.31929			−0.659643	+	0.751579i	$0.729293\pi$
$978$		0			0
$979$		−	187.640i		−	0.191665i
$980$	−448.280	−	27.2803i	−0.457428	−	0.0278371i
$981$		0			0
$982$	−734.249	−	22.3209i	−0.747708	−	0.0227301i
$983$		−	1526.52i		−	1.55292i	−0.630168	−	0.776459i	$-0.717014\pi$
$983$		−	1526.52i		−	1.55292i	0.630168	−	0.776459i	$-0.282986\pi$
$984$		0			0
$985$	−796.873			−0.809008
$986$	0.537533	−	17.6822i	0.000545165	−	0.0179332i
$987$		0			0
$988$	24.9178	−	409.457i	0.0252204	−	0.414430i
$989$	741.376			0.749622
$990$		0			0
$991$		−	613.326i		−	0.618896i	−0.950916	−	0.309448i	$-0.899856\pi$
$991$		−	613.326i		−	0.618896i	0.950916	−	0.309448i	$-0.100144\pi$
$992$	−993.009	−	152.062i	−1.00102	−	0.153288i
$993$		0			0
$994$	19.8547	−	653.122i	0.0199745	−	0.657064i
$995$		−	1161.09i		−	1.16692i
$996$		0			0
$997$	−34.6625			−0.0347668			−0.0173834	−	0.999849i	$-0.505534\pi$
$997$	−34.6625			−0.0347668			−0.0173834	+	0.999849i	$0.505534\pi$
$998$	276.086	+	8.39293i	0.276639	+	0.00840975i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.9		14
3.2	odd	2		76.3.b.b.39.6	yes	14
4.3	odd	2	inner	684.3.g.b.343.10		14
12.11	even	2		76.3.b.b.39.5	✓	14
24.5	odd	2		1216.3.d.d.191.14		14
24.11	even	2		1216.3.d.d.191.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.5	✓	14	12.11	even	2
76.3.b.b.39.6	yes	14	3.2	odd	2
684.3.g.b.343.9		14	1.1	even	1	trivial
684.3.g.b.343.10		14	4.3	odd	2	inner
1216.3.d.d.191.1		14	24.11	even	2
1216.3.d.d.191.14		14	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0607713 - 1.99908i) q^{2} +(-3.99261 - 0.242973i) q^{4} +5.82257 q^{5} -5.45132i q^{7} +(-0.728358 + 7.96677i) q^{8} +O(q^{10})\)	\(q+(0.0607713 - 1.99908i) q^{2} +(-3.99261 - 0.242973i) q^{4} +5.82257 q^{5} -5.45132i q^{7} +(-0.728358 + 7.96677i) q^{8} +(0.353845 - 11.6398i) q^{10} +1.60915i q^{11} +23.5274 q^{13} +(-10.8976 - 0.331284i) q^{14} +(15.8819 + 1.94019i) q^{16} +5.92676 q^{17} +4.35890i q^{19} +(-23.2473 - 1.41473i) q^{20} +(3.21681 + 0.0977900i) q^{22} +26.6121i q^{23} +8.90234 q^{25} +(1.42979 - 47.0331i) q^{26} +(-1.32452 + 21.7650i) q^{28} +1.49241 q^{29} -31.3933i q^{31} +(4.84376 - 31.6313i) q^{32} +(0.360177 - 11.8480i) q^{34} -31.7407i q^{35} +26.8255 q^{37} +(8.71377 + 0.264896i) q^{38} +(-4.24092 + 46.3871i) q^{40} +44.0382 q^{41} -27.8586i q^{43} +(0.390980 - 6.42471i) q^{44} +(53.1996 + 1.61725i) q^{46} -32.5166i q^{47} +19.2831 q^{49} +(0.541007 - 17.7965i) q^{50} +(-93.9360 - 5.71653i) q^{52} -76.7637 q^{53} +9.36938i q^{55} +(43.4294 + 3.97051i) q^{56} +(0.0906959 - 2.98345i) q^{58} -33.8895i q^{59} +53.0162 q^{61} +(-62.7575 - 1.90781i) q^{62} +(-62.9390 - 11.6053i) q^{64} +136.990 q^{65} -76.1917i q^{67} +(-23.6632 - 1.44004i) q^{68} +(-63.4521 - 1.92892i) q^{70} +59.9326i q^{71} -49.8188 q^{73} +(1.63022 - 53.6263i) q^{74} +(1.05909 - 17.4034i) q^{76} +8.77198 q^{77} +23.3990i q^{79} +(92.4737 + 11.2969i) q^{80} +(2.67626 - 88.0358i) q^{82} -137.116i q^{83} +34.5090 q^{85} +(-55.6915 - 1.69300i) q^{86} +(-12.8197 - 1.17204i) q^{88} -116.608 q^{89} -128.256i q^{91} +(6.46602 - 106.252i) q^{92} +(-65.0032 - 1.97608i) q^{94} +25.3800i q^{95} -65.7341 q^{97} +(1.17186 - 38.5484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Introduction

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