LMFDB - Embedded newform 44.4.g.a.7.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [44,4,Mod(7,44)] 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("44.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	44.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.59608404025$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.14
Character	$\chi$	$=$	44.7
Dual form			44.4.g.a.19.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.10599 - 1.88807i) q^{2} +(5.25156 + 1.70634i) q^{3} +(0.870417 - 7.95251i) q^{4} +(-3.44642 + 2.50397i) q^{5} +(14.2814 - 6.32176i) q^{6} +(3.17779 + 9.78024i) q^{7} +(-13.1818 - 18.3913i) q^{8} +(2.82388 + 2.05167i) q^{9} +(-2.53048 + 11.7804i) q^{10} +(-26.0814 + 25.5100i) q^{11} +(18.1407 - 40.2779i) q^{12} +(22.7250 - 31.2782i) q^{13} +(25.1581 + 14.5972i) q^{14} +(-22.3717 + 7.26902i) q^{15} +(-62.4847 - 13.8440i) q^{16} +(-1.50760 - 2.07503i) q^{17} +(9.82077 - 1.01087i) q^{18} +(-25.8272 + 79.4879i) q^{19} +(16.9130 + 29.5872i) q^{20} +56.7839i q^{21} +(-6.76265 + 102.967i) q^{22} +70.0868i q^{23} +(-37.8431 - 119.076i) q^{24} +(-33.0192 + 101.623i) q^{25} +(-11.1967 - 108.778i) q^{26} +(-76.3035 - 105.023i) q^{27} +(80.5434 - 16.7585i) q^{28} +(135.711 - 44.0953i) q^{29} +(-33.3904 + 57.5478i) q^{30} +(174.122 - 239.658i) q^{31} +(-157.731 + 88.8199i) q^{32} +(-180.497 + 89.4639i) q^{33} +(-7.09277 - 1.52355i) q^{34} +(-35.4415 - 25.7497i) q^{35} +(18.7739 - 20.6711i) q^{36} +(-130.196 - 400.703i) q^{37} +(95.6865 + 216.164i) q^{38} +(172.713 - 125.483i) q^{39} +(91.4814 + 30.3775i) q^{40} +(99.0076 + 32.1695i) q^{41} +(107.212 + 119.587i) q^{42} +364.837 q^{43} +(180.167 + 229.617i) q^{44} -14.8696 q^{45} +(132.329 + 147.602i) q^{46} +(-175.569 - 57.0459i) q^{47} +(-304.520 - 179.323i) q^{48} +(191.938 - 139.451i) q^{49} +(122.332 + 276.359i) q^{50} +(-4.37654 - 13.4696i) q^{51} +(-228.960 - 207.945i) q^{52} +(-62.5214 - 45.4245i) q^{53} +(-358.984 - 77.1112i) q^{54} +(26.0111 - 153.225i) q^{55} +(137.983 - 187.365i) q^{56} +(-271.266 + 373.366i) q^{57} +(202.552 - 349.096i) q^{58} +(-699.233 + 227.195i) q^{59} +(38.3342 + 184.239i) q^{60} +(230.570 + 317.352i) q^{61} +(-85.7909 - 833.472i) q^{62} +(-11.0921 + 34.1380i) q^{63} +(-164.482 + 484.860i) q^{64} +164.701i q^{65} +(-211.211 + 529.200i) q^{66} +514.238i q^{67} +(-17.8139 + 10.1830i) q^{68} +(-119.592 + 368.065i) q^{69} +(-123.257 + 12.6870i) q^{70} +(-74.1139 - 102.009i) q^{71} +(0.509209 - 78.9796i) q^{72} +(498.791 - 162.067i) q^{73} +(-1030.75 - 598.059i) q^{74} +(-346.805 + 477.336i) q^{75} +(609.647 + 274.578i) q^{76} +(-332.375 - 174.017i) q^{77} +(126.811 - 590.360i) q^{78} +(326.213 + 237.007i) q^{79} +(250.014 - 108.748i) q^{80} +(-250.631 - 771.364i) q^{81} +(269.248 - 119.184i) q^{82} +(-495.576 + 360.057i) q^{83} +(451.575 + 49.4257i) q^{84} +(10.3916 + 3.37644i) q^{85} +(768.345 - 688.837i) q^{86} +787.938 q^{87} +(812.962 + 143.405i) q^{88} +745.456 q^{89} +(-31.3153 + 28.0748i) q^{90} +(378.123 + 122.860i) q^{91} +(557.366 + 61.0048i) q^{92} +(1323.35 - 961.470i) q^{93} +(-477.454 + 211.348i) q^{94} +(-110.024 - 338.620i) q^{95} +(-979.890 + 197.302i) q^{96} +(-1106.98 - 804.268i) q^{97} +(140.927 - 656.075i) q^{98} +(-125.989 + 18.5269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 5 q^{2} + 7 q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} + 122 q^{9} - 38 q^{12} - 10 q^{13} + 66 q^{14} - 73 q^{16} - 10 q^{17} - 230 q^{18} - 180 q^{20} - 747 q^{22} - 455 q^{24} - 374 q^{25} + 330 q^{26}+ \cdots + 3904 q^{97}+O(q^{100}) $ 64 * q - 5 * q^2 + 7 * q^4 - 6 * q^5 - 5 * q^6 - 5 * q^8 + 122 * q^9 - 38 * q^12 - 10 * q^13 + 66 * q^14 - 73 * q^16 - 10 * q^17 - 230 * q^18 - 180 * q^20 - 747 * q^22 - 455 * q^24 - 374 * q^25 + 330 * q^26 + 520 * q^28 - 10 * q^29 + 880 * q^30 + 776 * q^33 - 846 * q^34 - 206 * q^36 - 30 * q^37 + 1016 * q^38 + 1080 * q^40 - 750 * q^41 + 1114 * q^42 + 1584 * q^44 - 1592 * q^45 + 1330 * q^46 + 68 * q^48 - 766 * q^49 + 655 * q^50 + 1610 * q^52 + 526 * q^53 + 1284 * q^56 + 1380 * q^57 - 2208 * q^58 - 4412 * q^60 - 10 * q^61 - 3980 * q^62 - 2825 * q^64 - 1694 * q^66 - 3840 * q^68 + 824 * q^69 - 1916 * q^70 - 5555 * q^72 - 2470 * q^73 - 1890 * q^74 + 714 * q^77 - 880 * q^78 + 6756 * q^80 + 2996 * q^81 + 6849 * q^82 + 6530 * q^84 + 3230 * q^85 + 1883 * q^86 + 3147 * q^88 + 1428 * q^89 + 10080 * q^90 + 2820 * q^92 + 130 * q^93 + 7280 * q^94 + 5720 * q^96 + 3904 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.10599	−	1.88807i	0.744581	−	0.667532i
$2$	2.10599	−	1.88807i	0.744581	−	0.667532i
$3$	5.25156	+	1.70634i	1.01066	+	0.328385i	0.767119	−	0.641505i	$-0.221690\pi$
$3$	5.25156	+	1.70634i	1.01066	+	0.328385i	0.243545	+	0.969890i	$0.421690\pi$
$4$	0.870417	−	7.95251i	0.108802	−	0.994063i
$5$	−3.44642	+	2.50397i	−0.308258	+	0.223962i	−0.731148	−	0.682218i	$-0.761015\pi$
$5$	−3.44642	+	2.50397i	−0.308258	+	0.223962i	0.422891	+	0.906181i	$0.361015\pi$
$6$	14.2814	−	6.32176i	0.971729	−	0.430142i
$7$	3.17779	+	9.78024i	0.171585	+	0.528083i	0.999461	−	0.0328274i	$-0.0104512\pi$
$7$	3.17779	+	9.78024i	0.171585	+	0.528083i	−0.827876	+	0.560911i	$0.810451\pi$
$8$	−13.1818	−	18.3913i	−0.582557	−	0.812790i
$9$	2.82388	+	2.05167i	0.104588	+	0.0759878i
$10$	−2.53048	+	11.7804i	−0.0800208	+	0.372530i
$11$	−26.0814	+	25.5100i	−0.714894	+	0.699233i
$11$	−26.0814	+	25.5100i	−0.714894	+	0.699233i
$12$	18.1407	−	40.2779i	0.436398	−	0.968935i
$13$	22.7250	−	31.2782i	0.484828	−	0.667309i	−0.494596	−	0.869123i	$-0.664684\pi$
$13$	22.7250	−	31.2782i	0.484828	−	0.667309i	0.979424	+	0.201814i	$0.0646838\pi$
$14$	25.1581	+	14.5972i	0.480271	+	0.278663i
$15$	−22.3717	+	7.26902i	−0.385091	+	0.125124i
$16$	−62.4847	−	13.8440i	−0.976324	−	0.216312i
$17$	−1.50760	−	2.07503i	−0.0215086	−	0.0296040i	0.798127	−	0.602489i	$-0.205824\pi$
$17$	−1.50760	−	2.07503i	−0.0215086	−	0.0296040i	−0.819636	+	0.572885i	$0.805824\pi$
$18$	9.82077	−	1.01087i	0.128599	−	0.0132369i
$19$	−25.8272	+	79.4879i	−0.311851	+	0.959777i	0.665181	+	0.746682i	$0.268354\pi$
$19$	−25.8272	+	79.4879i	−0.311851	+	0.959777i	−0.977031	+	0.213095i	$0.931646\pi$
$20$	16.9130	+	29.5872i	0.189094	+	0.330795i
$21$			56.7839i			0.590060i
$22$	−6.76265	+	102.967i	−0.0655364	+	0.997850i
$23$			70.0868i			0.635396i	0.948192	+	0.317698i	$0.102910\pi$
$23$			70.0868i			0.635396i	−0.948192	+	0.317698i	$0.897090\pi$
$24$	−37.8431	−	119.076i	−0.321862	−	1.01276i
$25$	−33.0192	+	101.623i	−0.264153	+	0.812980i
$26$	−11.1967	−	108.778i	−0.0844560	−	0.820504i
$27$	−76.3035	−	105.023i	−0.543874	−	0.748579i
$28$	80.5434	−	16.7585i	0.543617	−	0.113109i
$29$	135.711	−	44.0953i	0.868999	−	0.282355i	0.159617	−	0.987179i	$-0.448974\pi$
$29$	135.711	−	44.0953i	0.868999	−	0.282355i	0.709382	+	0.704824i	$0.248974\pi$
$30$	−33.3904	+	57.5478i	−0.203207	+	0.350225i
$31$	174.122	−	239.658i	1.00881	−	1.38851i	0.0890555	−	0.996027i	$-0.471615\pi$
$31$	174.122	−	239.658i	1.00881	−	1.38851i	0.919758	−	0.392486i	$-0.128385\pi$
$32$	−157.731	+	88.8199i	−0.871348	+	0.490666i
$33$	−180.497	+	89.4639i	−0.952135	+	0.471929i
$34$	−7.09277	−	1.52355i	−0.0357765	−	0.00768492i
$35$	−35.4415	−	25.7497i	−0.171163	−	0.124357i
$36$	18.7739	−	20.6711i	0.0869161	−	0.0956997i
$37$	−130.196	−	400.703i	−0.578491	−	1.78041i	−0.623973	−	0.781446i	$-0.714482\pi$
$37$	−130.196	−	400.703i	−0.578491	−	1.78041i	0.0454820	−	0.998965i	$-0.485518\pi$
$38$	95.6865	+	216.164i	0.408484	+	0.922802i
$39$	172.713	−	125.483i	0.709132	−	0.515215i
$40$	91.4814	+	30.3775i	0.361612	+	0.120078i
$41$	99.0076	+	32.1695i	0.377131	+	0.122537i	0.491448	−	0.870907i	$-0.336468\pi$
$41$	99.0076	+	32.1695i	0.377131	+	0.122537i	−0.114316	+	0.993444i	$0.536468\pi$
$42$	107.212	+	119.587i	0.393884	+	0.439348i
$43$	364.837			1.29389			0.646944	−	0.762538i	$-0.276047\pi$
$43$	364.837			1.29389			0.646944	+	0.762538i	$0.276047\pi$
$44$	180.167	+	229.617i	0.617300	+	0.786728i
$45$	−14.8696			−0.0492585
$46$	132.329	+	147.602i	0.424147	+	0.473104i
$47$	−175.569	−	57.0459i	−0.544881	−	0.177043i	0.0236261	−	0.999721i	$-0.492479\pi$
$47$	−175.569	−	57.0459i	−0.544881	−	0.177043i	−0.568507	+	0.822678i	$0.692479\pi$
$48$	−304.520	−	179.323i	−0.915702	−	0.539229i
$49$	191.938	−	139.451i	0.559586	−	0.406563i
$50$	122.332	+	276.359i	0.346007	+	0.781661i
$51$	−4.37654	−	13.4696i	−0.0120164	−	0.0369828i
$52$	−228.960	−	207.945i	−0.610597	−	0.554555i
$53$	−62.5214	−	45.4245i	−0.162037	−	0.117727i	0.503812	−	0.863813i	$-0.331931\pi$
$53$	−62.5214	−	45.4245i	−0.162037	−	0.117727i	−0.665849	+	0.746086i	$0.731931\pi$
$54$	−358.984	−	77.1112i	−0.904659	−	0.194324i
$55$	26.0111	−	153.225i	0.0637698	−	0.375653i
$56$	137.983	−	187.365i	0.329263	−	0.447101i
$57$	−271.266	+	373.366i	−0.630352	+	0.867605i
$58$	202.552	−	349.096i	0.458559	−	0.790320i
$59$	−699.233	+	227.195i	−1.54292	+	0.501326i	−0.952181	−	0.305535i	$-0.901165\pi$
$59$	−699.233	+	227.195i	−1.54292	+	0.501326i	−0.590741	+	0.806861i	$0.701165\pi$
$60$	38.3342	+	184.239i	0.0824820	+	0.396418i
$61$	230.570	+	317.352i	0.483958	+	0.666111i	0.979259	−	0.202610i	$-0.0649425\pi$
$61$	230.570	+	317.352i	0.483958	+	0.666111i	−0.495302	+	0.868721i	$0.664943\pi$
$62$	−85.7909	−	833.472i	−0.175733	−	1.70728i
$63$	−11.0921	+	34.1380i	−0.0221821	+	0.0682696i
$64$	−164.482	+	484.860i	−0.321254	+	0.946993i
$65$			164.701i			0.314286i
$66$	−211.211	+	529.200i	−0.393914	+	0.986970i
$67$			514.238i			0.937674i	0.883285	+	0.468837i	$0.155327\pi$
$67$			514.238i			0.937674i	−0.883285	+	0.468837i	$0.844673\pi$
$68$	−17.8139	+	10.1830i	−0.0317684	+	0.0181599i
$69$	−119.592	+	368.065i	−0.208654	+	0.642172i
$70$	−123.257	+	12.6870i	−0.210457	+	0.0216627i
$71$	−74.1139	−	102.009i	−0.123883	−	0.170510i	0.742571	−	0.669768i	$-0.233606\pi$
$71$	−74.1139	−	102.009i	−0.123883	−	0.170510i	−0.866454	+	0.499257i	$0.833606\pi$
$72$	0.509209	−	78.9796i	0.000833483	−	0.129275i
$73$	498.791	−	162.067i	0.799713	−	0.259843i	0.119478	−	0.992837i	$-0.461878\pi$
$73$	498.791	−	162.067i	0.799713	−	0.259843i	0.680235	+	0.732994i	$0.261878\pi$
$74$	−1030.75	−	598.059i	−1.61921	−	0.939500i
$75$	−346.805	+	477.336i	−0.533941	+	0.734906i
$76$	609.647	+	274.578i	0.920149	+	0.414425i
$77$	−332.375	−	174.017i	−0.491918	−	0.257546i
$78$	126.811	−	590.360i	0.184084	−	0.856988i
$79$	326.213	+	237.007i	0.464580	+	0.337537i	0.795325	−	0.606183i	$-0.207300\pi$
$79$	326.213	+	237.007i	0.464580	+	0.337537i	−0.330745	+	0.943720i	$0.607300\pi$
$80$	250.014	−	108.748i	0.349405	−	0.151980i
$81$	−250.631	−	771.364i	−0.343802	−	1.05811i
$82$	269.248	−	119.184i	0.362603	−	0.160508i
$83$	−495.576	+	360.057i	−0.655380	+	0.476161i	−0.865100	−	0.501600i	$-0.832745\pi$
$83$	−495.576	+	360.057i	−0.655380	+	0.476161i	0.209720	+	0.977762i	$0.432745\pi$
$84$	451.575	+	49.4257i	0.586557	+	0.0641998i
$85$	10.3916	+	3.37644i	0.0132604	+	0.00430855i
$86$	768.345	−	688.837i	0.963405	−	0.863712i
$87$	787.938			0.970987
$88$	812.962	+	143.405i	0.984796	+	0.173716i
$89$	745.456			0.887845			0.443922	−	0.896065i	$-0.353587\pi$
$89$	745.456			0.887845			0.443922	+	0.896065i	$0.353587\pi$
$90$	−31.3153	+	28.0748i	−0.0366770	+	0.0328816i
$91$	378.123	+	122.860i	0.435584	+	0.141530i
$92$	557.366	+	61.0048i	0.631624	+	0.0691324i
$93$	1323.35	−	961.470i	1.47554	−	1.07204i
$94$	−477.454	+	211.348i	−0.523890	+	0.231903i
$95$	−110.024	−	338.620i	−0.118824	−	0.365701i
$96$	−979.890	+	197.302i	−1.04177	+	0.209761i
$97$	−1106.98	−	804.268i	−1.15873	−	0.841866i	−0.169112	−	0.985597i	$-0.554090\pi$
$97$	−1106.98	−	804.268i	−1.15873	−	0.841866i	−0.989617	+	0.143731i	$0.954090\pi$
$98$	140.927	−	656.075i	0.145263	−	0.676261i
$99$	−125.989	+	18.5269i	−0.127903	+	0.0188083i
$100$	779.414	+	351.039i	0.779414	+	0.351039i
$101$	−1037.83	+	1428.45i	−1.02246	+	1.40729i	−0.111989	+	0.993709i	$0.535722\pi$
$101$	−1037.83	+	1428.45i	−1.02246	+	1.40729i	−0.910467	+	0.413581i	$0.864278\pi$
$102$	−34.6485	−	20.1037i	−0.0336344	−	0.0195153i
$103$	530.466	−	172.359i	0.507460	−	0.164884i	−0.0440870	−	0.999028i	$-0.514038\pi$
$103$	530.466	−	172.359i	0.507460	−	0.164884i	0.551547	+	0.834144i	$0.314038\pi$
$104$	−874.803	−	5.64015i	−0.824822	−	0.00531791i
$105$	−142.185	−	195.702i	−0.132151	−	0.181891i
$106$	−217.434	+	22.3809i	−0.199236	+	0.0205078i
$107$	−147.768	+	454.784i	−0.133508	+	0.410894i	−0.995355	−	0.0962737i	$-0.969308\pi$
$107$	−147.768	+	454.784i	−0.133508	+	0.410894i	0.861847	+	0.507168i	$0.169308\pi$
$108$	−901.610	+	515.390i	−0.803310	+	0.459199i
$109$			1752.35i			1.53986i	0.638126	+	0.769932i	$0.279710\pi$
$109$			1752.35i			1.53986i	−0.638126	+	0.769932i	$0.720290\pi$
$110$	−234.520	−	371.803i	−0.203279	−	0.322273i
$111$		−	2326.48i		−	1.98937i
$112$	−63.1660	−	655.109i	−0.0532913	−	0.552696i
$113$	−370.314	+	1139.71i	−0.308285	+	0.948803i	0.670146	+	0.742229i	$0.266231\pi$
$113$	−370.314	+	1139.71i	−0.308285	+	0.948803i	−0.978431	+	0.206574i	$0.933769\pi$
$114$	133.654	+	1298.47i	0.109806	+	1.06678i
$115$	−175.496	−	241.549i	−0.142305	−	0.195866i
$116$	−232.543	−	1117.63i	−0.186130	−	0.894561i
$117$	128.345	−	41.7019i	0.101415	−	0.0329516i
$118$	−1043.62	+	1798.67i	−0.814180	+	1.40323i
$119$	15.5034	−	21.3386i	0.0119428	−	0.0164379i
$120$	428.586	+	315.628i	0.326036	+	0.240106i
$121$	29.4779	−	1330.67i	0.0221472	−	0.999755i
$122$	1084.76	+	233.010i	0.804996	+	0.172916i
$123$	465.053	+	337.881i	0.340914	+	0.247688i
$124$	−1754.33	−	1593.31i	−1.27051	−	1.15390i
$125$	−305.214	−	939.353i	−0.218394	−	0.672146i
$126$	41.0949	+	92.8371i	0.0290558	+	0.0656396i
$127$	658.463	−	478.401i	0.460072	−	0.334262i	−0.333488	−	0.942754i	$-0.608226\pi$
$127$	658.463	−	478.401i	0.460072	−	0.334262i	0.793559	+	0.608493i	$0.208226\pi$
$128$	569.050	+	1331.67i	0.392948	+	0.919561i
$129$	1915.97	+	622.535i	1.30769	+	0.424893i
$130$	310.966	+	346.859i	0.209796	+	0.234012i
$131$	−2673.84			−1.78331			−0.891657	−	0.452712i	$-0.850457\pi$
$131$	−2673.84			−1.78331			−0.891657	+	0.452712i	$0.850457\pi$
$132$	554.355	+	1513.27i	0.365533	+	0.997829i
$133$	−859.484			−0.560351
$134$	970.915	+	1082.98i	0.625928	+	0.698175i
$135$	525.948	+	170.891i	0.335307	+	0.108948i
$136$	−18.2897	+	55.0792i	−0.0115319	+	0.0347280i
$137$	1019.60	−	740.786i	0.635845	−	0.461968i	−0.222575	−	0.974915i	$-0.571446\pi$
$137$	1019.60	−	740.786i	0.635845	−	0.461968i	0.858420	+	0.512947i	$0.171446\pi$
$138$	443.072	+	1000.94i	0.273310	+	0.617433i
$139$	−246.957	−	760.055i	−0.150695	−	0.463791i	0.847004	−	0.531586i	$-0.178404\pi$
$139$	−246.957	−	760.055i	−0.150695	−	0.463791i	−0.997699	+	0.0677946i	$0.978404\pi$
$140$	−235.624	+	259.436i	−0.142242	+	0.156617i
$141$	−824.674	−	599.161i	−0.492554	−	0.357861i
$142$	−348.683	−	74.8984i	−0.206062	−	0.0442629i
$143$	205.209	+	1395.49i	0.120003	+	0.816063i
$144$	−148.046	−	167.292i	−0.0856749	−	0.0968125i
$145$	−357.305	+	491.789i	−0.204639	+	0.281661i
$146$	744.457	−	1283.06i	0.421998	−	0.727308i
$147$	1245.93	−	404.826i	0.699063	−	0.227139i
$148$	−3299.92	+	686.609i	−1.83278	+	0.381344i
$149$	−715.120	−	984.279i	−0.393188	−	0.541176i	0.565830	−	0.824522i	$-0.308556\pi$
$149$	−715.120	−	984.279i	−0.393188	−	0.541176i	−0.959018	+	0.283345i	$0.908556\pi$
$150$	170.873	+	1660.06i	0.0930113	+	0.903620i
$151$	978.075	−	3010.21i	0.527117	−	1.62230i	−0.232975	−	0.972483i	$-0.574846\pi$
$151$	978.075	−	3010.21i	0.527117	−	1.62230i	0.760092	−	0.649816i	$-0.225154\pi$
$152$	1802.34	−	572.794i	0.961768	−	0.305656i
$153$		−	8.95272i		−	0.00473062i
$154$	−1028.54	+	261.068i	−0.538193	+	0.136607i
$155$			1261.96i			0.653956i
$156$	−847.573	−	1482.72i	−0.435001	−	0.760979i
$157$	−267.862	+	824.394i	−0.136164	+	0.419069i	−0.995769	−	0.0918894i	$-0.970709\pi$
$157$	−267.862	+	824.394i	−0.136164	+	0.419069i	0.859605	+	0.510958i	$0.170709\pi$
$158$	1134.49	−	116.775i	0.571234	−	0.0587982i
$159$	−250.826	−	345.232i	−0.125106	−	0.172193i
$160$	321.205	−	701.065i	0.158709	−	0.346400i
$161$	−685.466	+	222.721i	−0.335542	+	0.109024i
$162$	−1984.21	−	1151.28i	−0.962312	−	0.558352i
$163$	−1257.52	+	1730.83i	−0.604273	+	0.831711i	−0.996091	−	0.0883321i	$-0.971846\pi$
$163$	−1257.52	+	1730.83i	−0.604273	+	0.831711i	0.391818	+	0.920043i	$0.371846\pi$
$164$	342.006	−	759.358i	0.162843	−	0.361560i
$165$	398.053	−	760.290i	0.187809	−	0.358718i
$166$	−363.869	+	1693.96i	−0.170131	+	0.792028i
$167$	939.960	+	682.921i	0.435546	+	0.316443i	0.783863	−	0.620934i	$-0.213247\pi$
$167$	939.960	+	682.921i	0.435546	+	0.316443i	−0.348316	+	0.937377i	$0.613247\pi$
$168$	1044.33	−	748.512i	0.479595	−	0.343744i
$169$	217.007	+	667.880i	0.0987743	+	0.303996i
$170$	28.2596	−	12.5093i	0.0127495	−	0.00564365i
$171$	−236.016	+	171.476i	−0.105547	+	0.0766846i
$172$	317.561	−	2901.37i	0.140778	−	1.28621i
$173$	3746.39	+	1217.27i	1.64643	+	0.534958i	0.977962	−	0.208783i	$-0.0669501\pi$
$173$	3746.39	+	1217.27i	1.64643	+	0.534958i	0.668469	+	0.743740i	$0.266950\pi$
$174$	1659.39	−	1487.68i	0.722978	−	0.648165i
$175$	−1098.82			−0.474646
$176$	1982.85	−	1232.92i	0.849221	−	0.528037i
$177$	−4059.74			−1.72400
$178$	1569.93	−	1407.47i	0.661073	−	0.592665i
$179$	1937.76	+	629.615i	0.809133	+	0.262903i	0.684230	−	0.729266i	$-0.260138\pi$
$179$	1937.76	+	629.615i	0.809133	+	0.262903i	0.124902	+	0.992169i	$0.460138\pi$
$180$	−12.9428	+	118.251i	−0.00535943	+	0.0489661i
$181$	716.172	−	520.329i	0.294103	−	0.213678i	−0.430942	−	0.902379i	$-0.641819\pi$
$181$	716.172	−	520.329i	0.294103	−	0.213678i	0.725045	+	0.688701i	$0.241819\pi$
$182$	1028.29	−	455.180i	0.418803	−	0.185386i
$183$	669.342	+	2060.02i	0.270378	+	0.832138i
$184$	1288.99	−	923.868i	0.516444	−	0.370155i
$185$	1452.06	+	1054.99i	0.577069	+	0.419265i
$186$	971.648	−	4523.42i	0.383036	−	1.78319i
$187$	92.2542	+	15.6608i	0.0360764	+	0.00612423i
$188$	−606.477	+	1346.56i	−0.235276	+	0.522384i
$189$	784.670	−	1080.01i	0.301991	−	0.415656i
$190$	−871.046	−	505.398i	−0.332591	−	0.192976i
$191$	−2116.73	+	687.766i	−0.801889	+	0.260550i	−0.681159	−	0.732136i	$-0.738524\pi$
$191$	−2116.73	+	687.766i	−0.801889	+	0.260550i	−0.120730	+	0.992685i	$0.538524\pi$
$192$	−1691.12	+	2265.61i	−0.635658	+	0.851597i
$193$	495.341	+	681.779i	0.184743	+	0.254277i	0.891336	−	0.453343i	$-0.149769\pi$
$193$	495.341	+	681.779i	0.184743	+	0.254277i	−0.706593	+	0.707620i	$0.749769\pi$
$194$	−3849.80	+	396.267i	−1.42474	+	0.146651i
$195$	−281.035	+	864.936i	−0.103207	+	0.317638i
$196$	−941.921	−	1647.77i	−0.343266	−	0.600499i
$197$		−	1317.25i		−	0.476398i	−0.971216	−	0.238199i	$-0.923443\pi$
$197$		−	1317.25i		−	0.476398i	0.971216	−	0.238199i	$-0.0765570\pi$
$198$	−230.352	+	276.893i	−0.0826788	+	0.0993834i
$199$			2308.07i			0.822185i	0.911594	+	0.411093i	$0.134853\pi$
$199$			2308.07i			0.822185i	−0.911594	+	0.411093i	$0.865147\pi$
$200$	2304.22	−	732.298i	0.814667	−	0.258906i
$201$	−877.463	+	2700.55i	−0.307918	+	0.947674i
$202$	511.346	+	4967.81i	0.178110	+	1.73036i
$203$	862.525	+	1187.16i	0.298214	+	0.410456i
$204$	−110.927	+	23.0803i	−0.0380706	+	0.00792129i
$205$	−421.774	+	137.043i	−0.143697	+	0.0466901i
$206$	791.733	−	1364.54i	0.267780	−	0.461515i
$207$	−143.795	+	197.917i	−0.0482824	+	0.0664550i
$208$	−1852.98	+	1639.81i	−0.617697	+	0.546635i
$209$	−1354.13	−	2732.01i	−0.448168	−	0.904195i
$210$	−668.939	−	143.691i	−0.219815	−	0.0472171i
$211$	−4123.30	−	2995.75i	−1.34531	−	0.977422i	−0.999231	−	0.0392156i	$-0.987514\pi$
$211$	−4123.30	−	2995.75i	−1.34531	−	0.977422i	−0.346076	−	0.938207i	$-0.612486\pi$
$212$	−415.658	+	457.664i	−0.134658	+	0.148266i
$213$	−215.152	−	662.170i	−0.0692111	−	0.213010i
$214$	547.463	+	1236.77i	0.174878	+	0.395065i
$215$	−1257.38	+	913.543i	−0.398851	+	0.289782i
$216$	−925.693	+	2787.71i	−0.291599	+	0.878145i
$217$	2897.24	+	941.370i	0.906347	+	0.294490i
$218$	3308.56	+	3690.45i	1.02791	+	1.14655i
$219$	2895.97			0.893570
$220$	−1195.89	−	340.224i	−0.366485	−	0.104263i
$221$	−99.1632			−0.0301830
$222$	−4392.54	−	4899.55i	−1.32796	−	1.48124i
$223$	−3405.49	−	1106.51i	−1.02264	−	0.332275i	−0.250762	−	0.968049i	$-0.580681\pi$
$223$	−3405.49	−	1106.51i	−1.02264	−	0.332275i	−0.771876	+	0.635773i	$0.780681\pi$
$224$	−1369.92	−	1260.39i	−0.408622	−	0.375954i
$225$	−301.738	+	219.226i	−0.0894039	+	0.0649558i
$226$	1371.97	+	3099.39i	0.403813	+	0.912251i
$227$	−303.461	−	933.958i	−0.0887288	−	0.273079i	0.896840	−	0.442355i	$-0.145857\pi$
$227$	−303.461	−	933.958i	−0.0887288	−	0.273079i	−0.985569	+	0.169276i	$0.945857\pi$
$228$	2733.08	+	2482.23i	0.793871	+	0.721007i
$229$	−1828.84	−	1328.73i	−0.527744	−	0.383428i	0.291769	−	0.956489i	$-0.405756\pi$
$229$	−1828.84	−	1328.73i	−0.527744	−	0.383428i	−0.819513	+	0.573060i	$0.805756\pi$
$230$	−825.653	−	177.353i	−0.236704	−	0.0508449i
$231$	−1448.56	−	1481.00i	−0.412590	−	0.421831i
$232$	−2599.89	−	1914.66i	−0.735736	−	0.541825i
$233$	776.406	−	1068.63i	0.218301	−	0.300465i	−0.685795	−	0.727794i	$-0.740545\pi$
$233$	776.406	−	1068.63i	0.218301	−	0.300465i	0.904096	+	0.427329i	$0.140545\pi$
$234$	191.558	−	330.148i	0.0535152	−	0.0922327i
$235$	747.928	−	243.017i	0.207615	−	0.0674581i
$236$	1198.14	+	5758.41i	0.330476	+	1.58831i
$237$	1308.71	+	1801.29i	0.358692	+	0.493697i
$238$	−7.63863	−	74.2106i	−0.00208042	−	0.0202116i
$239$	1058.31	−	3257.14i	0.286428	−	0.881534i	−0.699539	−	0.714594i	$-0.746611\pi$
$239$	1058.31	−	3257.14i	0.286428	−	0.881534i	0.985967	−	0.166940i	$-0.0533886\pi$
$240$	1498.52	−	144.489i	0.403039	−	0.0388613i
$241$		−	209.827i		−	0.0560836i	−0.999607	−	0.0280418i	$-0.991073\pi$
$241$		−	209.827i		−	0.0560836i	0.999607	−	0.0280418i	$-0.00892715\pi$
$242$	−2450.32	−	2858.05i	−0.650878	−	0.759182i
$243$		−	973.519i		−	0.257001i
$244$	2724.43	−	1557.38i	0.714812	−	0.408610i
$245$	−312.318	+	961.216i	−0.0814419	+	0.250652i
$246$	1617.34	−	166.476i	0.419178	−	0.0431468i
$247$	1899.32	+	2614.19i	0.489274	+	0.673428i
$248$	−6702.87	−	43.2157i	−1.71626	−	0.0110653i
$249$	−3216.93	+	1045.24i	−0.818733	+	0.266022i
$250$	−2416.34	−	1402.01i	−0.611291	−	0.354683i
$251$	3299.16	−	4540.91i	0.829647	−	1.14191i	−0.158342	−	0.987384i	$-0.550615\pi$
$251$	3299.16	−	4540.91i	0.829647	−	1.14191i	0.987989	−	0.154527i	$-0.0493852\pi$
$252$	261.828	+	117.924i	0.0654509	+	0.0294783i
$253$	−1787.92	−	1827.96i	−0.444290	−	0.454241i
$254$	483.465	−	2250.73i	0.119430	−	0.555997i
$255$	48.8109	+	35.4632i	0.0119869	+	0.00870899i
$256$	3712.69	+	1730.08i	0.906418	+	0.422382i
$257$	894.774	+	2753.83i	0.217177	+	0.668401i	0.998992	+	0.0448911i	$0.0142941\pi$
$257$	894.774	+	2753.83i	0.217177	+	0.668401i	−0.781815	+	0.623510i	$0.785706\pi$
$258$	5210.40	−	2306.42i	1.25731	−	0.556555i
$259$	3505.24	−	2546.70i	0.840945	−	0.610982i
$260$	1309.78	+	143.358i	0.312420	+	0.0341950i
$261$	473.702	+	153.915i	0.112343	+	0.0365023i
$262$	−5631.08	+	5048.38i	−1.32782	+	1.19042i
$263$	3991.57			0.935857			0.467929	−	0.883766i	$-0.345000\pi$
$263$	3991.57			0.935857			0.467929	+	0.883766i	$0.345000\pi$
$264$	4024.63	+	2140.28i	0.938252	+	0.498960i
$265$	329.217			0.0763156
$266$	−1810.07	+	1622.76i	−0.417227	+	0.374052i
$267$	3914.81	+	1272.00i	0.897313	+	0.291555i
$268$	4089.48	+	447.601i	0.932108	+	0.102021i
$269$	−1079.24	+	784.113i	−0.244618	+	0.177726i	−0.703338	−	0.710855i	$-0.748308\pi$
$269$	−1079.24	+	784.113i	−0.244618	+	0.177726i	0.458720	+	0.888581i	$0.348308\pi$
$270$	1430.30	−	633.130i	0.322389	−	0.142708i
$271$	556.370	+	1712.33i	0.124713	+	0.383826i	0.993849	−	0.110747i	$-0.0353244\pi$
$271$	556.370	+	1712.33i	0.124713	+	0.383826i	−0.869136	+	0.494573i	$0.835324\pi$
$272$	65.4751	+	150.529i	0.0145956	+	0.0335557i
$273$	1776.10	+	1290.41i	0.393753	+	0.286078i
$274$	748.628	−	3485.17i	0.165059	−	0.768419i
$275$	−1731.21	−	3492.78i	−0.379621	−	0.765900i
$276$	2822.95	+	1271.42i	0.615658	+	0.277285i
$277$	1165.40	−	1604.03i	0.252787	−	0.347931i	−0.663698	−	0.748001i	$-0.731014\pi$
$277$	1165.40	−	1604.03i	0.252787	−	0.347931i	0.916485	+	0.400070i	$0.131014\pi$
$278$	−1955.12	−	1134.40i	−0.421800	−	0.244737i
$279$	983.400	−	319.526i	0.211020	−	0.0685646i
$280$	−6.39088	+	991.243i	−0.00136403	+	0.211565i
$281$	−3383.47	−	4656.95i	−0.718296	−	0.988649i	−0.999579	−	0.0290242i	$-0.990760\pi$
$281$	−3383.47	−	4656.95i	−0.718296	−	0.988649i	0.281283	−	0.959625i	$-0.409240\pi$
$282$	−2868.01	+	295.210i	−0.605630	+	0.0623386i
$283$	−783.661	+	2411.86i	−0.164607	+	0.506609i	−0.999007	−	0.0445508i	$-0.985814\pi$
$283$	−783.661	+	2411.86i	−0.164607	+	0.506609i	0.834400	+	0.551159i	$0.185814\pi$
$284$	−875.737	+	500.601i	−0.182977	+	0.104596i
$285$		−	1966.02i		−	0.408621i
$286$	3066.95	+	2551.45i	0.634100	+	0.527519i
$287$			1070.55i			0.220182i
$288$	−627.643	−	72.7947i	−0.128417	−	0.0148940i
$289$	1516.17	−	4666.28i	0.308603	−	0.949783i
$290$	176.046	+	1710.32i	0.0356476	+	0.346322i
$291$	−4441.02	−	6112.54i	−0.894630	−	1.23135i
$292$	−854.683	−	4107.70i	−0.171290	−	0.823237i
$293$	−2675.93	+	869.461i	−0.533547	+	0.173360i	−0.563384	−	0.826195i	$-0.690501\pi$
$293$	−2675.93	+	869.461i	−0.533547	+	0.173360i	0.0298376	+	0.999555i	$0.490501\pi$
$294$	1859.57	−	3204.95i	0.368886	−	0.635771i
$295$	1840.96	−	2533.87i	0.363339	−	0.500094i
$296$	−5653.25	+	7676.46i	−1.11010	+	1.50738i
$297$	4669.23	+	792.635i	0.912243	+	0.154860i
$298$	−3364.42	−	722.691i	−0.654013	−	0.140484i
$299$	2192.19	+	1592.72i	0.424006	+	0.308058i
$300$	3494.15	+	3173.45i	0.672449	+	0.610730i
$301$	1159.38	+	3568.20i	0.222011	+	0.683280i
$302$	−3623.65	−	8186.14i	−0.690455	−	1.55980i
$303$	−7887.66	+	5730.72i	−1.49549	+	1.08654i
$304$	2714.23	−	4609.23i	0.512079	−	0.869597i
$305$	−1589.28	−	516.389i	−0.298367	−	0.0969454i
$306$	−16.9033	−	18.8544i	−0.00315784	−	0.00352233i
$307$	93.9236			0.0174609			0.00873046	−	0.999962i	$-0.497221\pi$
$307$	93.9236			0.0174609			0.00873046	+	0.999962i	$0.497221\pi$
$308$	−1673.17	+	2491.75i	−0.309539	+	0.460976i
$309$	3079.88			0.567016
$310$	2382.66	+	2657.68i	0.436536	+	0.486923i
$311$	−6931.21	−	2252.09i	−1.26377	−	0.410624i	−0.400935	−	0.916107i	$-0.631315\pi$
$311$	−6931.21	−	2252.09i	−1.26377	−	0.410624i	−0.862837	+	0.505482i	$0.831315\pi$
$312$	−4584.46	−	1522.33i	−0.831872	−	0.276233i
$313$	−3924.78	+	2851.52i	−0.708759	+	0.514943i	−0.882773	−	0.469800i	$-0.844326\pi$
$313$	−3924.78	+	2851.52i	−0.708759	+	0.514943i	0.174014	+	0.984743i	$0.444326\pi$
$314$	992.395	+	2241.91i	0.178357	+	0.402925i
$315$	−47.2526	−	145.428i	−0.00845200	−	0.0260126i
$316$	2168.74	−	2387.91i	0.386080	−	0.425097i
$317$	−1842.71	−	1338.81i	−0.326489	−	0.237208i	0.412451	−	0.910980i	$-0.364673\pi$
$317$	−1842.71	−	1338.81i	−0.326489	−	0.237208i	−0.738939	+	0.673772i	$0.764673\pi$
$318$	−1180.06	−	253.481i	−0.208096	−	0.0446997i
$319$	−2414.67	+	4612.07i	−0.423810	+	0.809486i
$320$	−647.202	−	2082.89i	−0.113062	−	0.363867i
$321$	−1552.03	+	2136.19i	−0.269863	+	0.371434i
$322$	−1023.07	+	1763.25i	−0.177061	+	0.305162i
$323$	203.876	−	66.2435i	0.0351207	−	0.0114114i
$324$	−6352.43	+	1321.74i	−1.08924	+	0.226636i
$325$	2428.21	+	3342.15i	0.414440	+	0.570428i
$326$	619.587	+	6019.39i	0.105263	+	1.02265i
$327$	−2990.11	+	9202.60i	−0.505667	+	1.55628i
$328$	−713.454	−	2244.93i	−0.120103	−	0.377914i
$329$		−	1898.39i		−	0.318120i
$330$	−597.179	−	2352.72i	−0.0996171	−	0.392463i
$331$			6621.40i			1.09953i	0.835319	+	0.549766i	$0.185283\pi$
$331$			6621.40i			1.09953i	−0.835319	+	0.549766i	$0.814717\pi$
$332$	2432.00	+	4254.47i	0.402028	+	0.703297i
$333$	454.452	−	1398.66i	0.0747862	−	0.230168i
$334$	3268.95	−	336.479i	0.535536	−	0.0551237i
$335$	−1287.64	−	1772.28i	−0.210004	−	0.289045i
$336$	786.116	−	3548.13i	0.127637	−	0.576090i
$337$	7657.13	−	2487.95i	1.23772	−	0.402158i	0.384212	−	0.923245i	$-0.374473\pi$
$337$	7657.13	−	2487.95i	1.23772	−	0.402158i	0.853504	+	0.521087i	$0.174473\pi$
$338$	1718.02	+	996.826i	0.276473	+	0.160415i
$339$	−3889.45	+	5353.37i	−0.623145	+	0.857685i
$340$	35.8962	−	79.7006i	0.00572573	−	0.0127129i
$341$	1572.34	+	10692.5i	0.249699	+	1.69803i
$342$	−173.291	+	806.740i	−0.0273991	+	0.127554i
$343$	4827.42	+	3507.32i	0.759930	+	0.552122i
$344$	−4809.20	−	6709.85i	−0.753764	−	1.05166i
$345$	−509.462	−	1567.96i	−0.0795030	−	0.244685i
$346$	10188.2	−	4509.85i	1.58300	−	0.700726i
$347$	8840.51	−	6423.01i	1.36768	−	0.993675i	0.369761	−	0.929127i	$-0.379440\pi$
$347$	8840.51	−	6423.01i	1.36768	−	0.993675i	0.997915	−	0.0645477i	$-0.0205605\pi$
$348$	685.835	−	6266.08i	0.105645	−	0.965222i
$349$	−9043.01	−	2938.25i	−1.38700	−	0.450662i	−0.482033	−	0.876153i	$-0.660101\pi$
$349$	−9043.01	−	2938.25i	−1.38700	−	0.450662i	−0.904963	+	0.425491i	$0.860101\pi$
$350$	−2314.11	+	2074.65i	−0.353412	+	0.316841i
$351$	−5018.91			−0.763219
$352$	1848.04	−	6340.26i	0.279832	−	0.960049i
$353$	5205.14			0.784821			0.392410	−	0.919790i	$-0.371641\pi$
$353$	5205.14			0.784821			0.392410	+	0.919790i	$0.371641\pi$
$354$	−8549.78	+	7665.05i	−1.28366	+	1.15083i
$355$	510.856	+	165.987i	0.0763758	+	0.0248160i
$356$	648.858	−	5928.25i	0.0965994	−	0.882574i
$357$	117.828	−	85.6072i	0.0174681	−	0.0126914i
$358$	5269.66	−	2332.65i	0.777961	−	0.344369i
$359$	1980.90	+	6096.59i	0.291220	+	0.896283i	0.984465	+	0.175581i	$0.0561804\pi$
$359$	1980.90	+	6096.59i	0.291220	+	0.896283i	−0.693245	+	0.720702i	$0.743820\pi$
$360$	196.008	+	273.472i	0.0286959	+	0.0400368i
$361$	−102.231	−	74.2753i	−0.0149047	−	0.0108289i
$362$	525.837	−	2447.99i	0.0763464	−	0.355424i
$363$	2425.38	−	6937.82i	0.350687	−	1.00314i
$364$	1306.17	−	2900.09i	0.188082	−	0.417599i
$365$	−1313.23	+	1807.51i	−0.188323	+	0.259204i
$366$	5299.09	+	3074.63i	0.756797	+	0.439108i
$367$	−2365.09	+	768.463i	−0.336394	+	0.109301i	−0.472343	−	0.881415i	$-0.656592\pi$
$367$	−2365.09	+	768.463i	−0.336394	+	0.109301i	0.135949	+	0.990716i	$0.456592\pi$
$368$	970.282	−	4379.36i	0.137444	−	0.620353i
$369$	213.585	+	293.974i	0.0301322	+	0.0414734i
$370$	5049.92	−	519.797i	0.709548	−	0.0730351i
$371$	245.582	−	755.824i	0.0343665	−	0.105769i
$372$	−6494.23	−	11360.8i	−0.905135	−	1.58342i
$373$			4847.13i			0.672854i	0.941710	+	0.336427i	$0.109219\pi$
$373$			4847.13i			0.672854i	−0.941710	+	0.336427i	$0.890781\pi$
$374$	223.855	−	141.200i	0.0309500	−	0.0195222i
$375$		−	5453.87i		−	0.751031i
$376$	1265.16	+	3980.92i	0.173526	+	0.546011i
$377$	1704.81	−	5246.87i	0.232897	−	0.716784i
$378$	−386.612	−	3756.00i	−0.0526062	−	0.511078i
$379$	2441.50	+	3360.44i	0.330901	+	0.455447i	0.941756	−	0.336296i	$-0.109174\pi$
$379$	2441.50	+	3360.44i	0.330901	+	0.455447i	−0.610855	+	0.791742i	$0.709174\pi$
$380$	−2788.64	+	580.228i	−0.376459	+	0.0783291i
$381$	4274.27	−	1388.79i	0.574744	−	0.186746i
$382$	−3159.26	+	5444.95i	−0.423146	+	0.729287i
$383$	1511.98	−	2081.06i	0.201720	−	0.277643i	−0.696158	−	0.717889i	$-0.745109\pi$
$383$	1511.98	−	2081.06i	0.201720	−	0.277643i	0.897877	+	0.440246i	$0.145109\pi$
$384$	716.130	+	7964.32i	0.0951689	+	1.05840i
$385$	1581.24	−	232.524i	0.209318	−	0.0307805i
$386$	2330.43	+	500.585i	0.307295	+	0.0660080i
$387$	1030.26	+	748.526i	0.135325	+	0.0983197i
$388$	−7359.48	+	8103.21i	−0.962940	+	1.06025i
$389$	−767.770	−	2362.95i	−0.100071	−	0.307986i	0.888471	−	0.458932i	$-0.151768\pi$
$389$	−767.770	−	2362.95i	−0.100071	−	0.307986i	−0.988542	+	0.150946i	$0.951768\pi$
$390$	1041.20	+	2352.16i	0.135188	+	0.305401i
$391$	145.432	−	105.663i	0.0188103	−	0.0136665i
$392$	−5094.78	−	1691.79i	−0.656442	−	0.217980i
$393$	−14041.8	−	4562.46i	−1.80233	−	0.585613i
$394$	−2487.06	−	2774.12i	−0.318011	−	0.354717i
$395$	−1717.73			−0.218806
$396$	37.6722	+	1018.05i	0.00478055	+	0.129190i
$397$	1316.80			0.166469			0.0832344	−	0.996530i	$-0.473475\pi$
$397$	1316.80			0.166469			0.0832344	+	0.996530i	$0.473475\pi$
$398$	4357.79	+	4860.78i	0.548835	+	0.612184i
$399$	−4513.63	−	1466.57i	−0.566327	−	0.184011i
$400$	3470.06	−	5892.74i	0.433757	−	0.736593i
$401$	−128.351	+	93.2525i	−0.0159839	+	0.0116130i	−0.595749	−	0.803171i	$-0.703145\pi$
$401$	−128.351	+	93.2525i	−0.0159839	+	0.0116130i	0.579765	+	0.814784i	$0.303145\pi$
$402$	3250.89	+	7344.06i	0.403333	+	0.911165i
$403$	−3539.17	−	10892.4i	−0.437465	−	1.34638i
$404$	10456.4	+	9496.71i	1.28769	+	1.16950i
$405$	2795.26	+	2030.87i	0.342957	+	0.249173i
$406$	4057.91	+	871.655i	0.496037	+	0.106551i
$407$	13617.7	+	7129.59i	1.65848	+	0.868306i
$408$	−190.033	+	258.044i	−0.0230590	+	0.0313114i
$409$	−1347.94	+	1855.29i	−0.162962	+	0.224298i	−0.882687	−	0.469961i	$-0.844268\pi$
$409$	−1347.94	+	1855.29i	−0.162962	+	0.224298i	0.719725	+	0.694259i	$0.244268\pi$
$410$	−629.508	+	1084.95i	−0.0758272	+	0.130687i
$411$	6618.55	−	2150.50i	0.794329	−	0.258093i
$412$	−908.958	−	4368.56i	−0.108692	−	0.522387i
$413$	−4444.03	−	6116.69i	−0.529483	−	0.728771i
$414$	70.8487	+	688.306i	0.00841068	+	0.0817111i
$415$	806.392	−	2481.82i	0.0953837	−	0.293561i
$416$	−806.297	+	6951.97i	−0.0950287	+	0.819347i
$417$		−	4412.87i		−	0.518223i
$418$	−8009.99	−	3196.90i	−0.937276	−	0.374081i
$419$		−	12386.5i		−	1.44420i	−0.691791	−	0.722098i	$-0.743178\pi$
$419$		−	12386.5i		−	1.44420i	0.691791	−	0.722098i	$-0.256822\pi$
$420$	−1680.08	+	960.389i	−0.195189	+	0.111577i
$421$	2547.72	−	7841.09i	0.294937	−	0.907723i	−0.688306	−	0.725421i	$-0.741645\pi$
$421$	2547.72	−	7841.09i	0.294937	−	0.907723i	0.983243	−	0.182302i	$-0.0583548\pi$
$422$	−14339.8	+	1476.02i	−1.65415	+	0.170265i
$423$	−378.748	−	521.301i	−0.0435351	−	0.0599209i
$424$	−11.2740	+	1748.63i	−0.00129131	+	0.200285i
$425$	260.649	−	84.6900i	0.0297490	−	0.00966605i
$426$	−1703.33	−	988.304i	−0.193724	−	0.112403i
$427$	−2371.07	+	3263.50i	−0.268722	+	0.369864i
$428$	3488.06	+	1570.98i	0.393929	+	0.177421i
$429$	−1303.51	+	7678.68i	−0.146699	+	0.864173i
$430$	−923.214	+	4297.94i	−0.103538	+	0.482012i
$431$	−9322.79	−	6773.40i	−1.04191	−	0.756992i	−0.0712523	−	0.997458i	$-0.522700\pi$
$431$	−9322.79	−	6773.40i	−1.04191	−	0.756992i	−0.970657	+	0.240467i	$0.922700\pi$
$432$	3313.87	+	7618.66i	0.369071	+	0.848502i
$433$	908.270	+	2795.37i	0.100805	+	0.310247i	0.988723	−	0.149756i	$-0.0478487\pi$
$433$	908.270	+	2795.37i	0.100805	+	0.310247i	−0.887918	+	0.460002i	$0.847849\pi$
$434$	7878.93	−	3487.66i	0.871430	−	0.385744i
$435$	−2715.57	+	1972.98i	−0.299314	+	0.217464i
$436$	13935.6	+	1525.28i	1.53072	+	0.167540i
$437$	−5571.05	−	1810.14i	−0.609839	−	0.198149i
$438$	6098.90	−	5467.79i	0.665335	−	0.596486i
$439$	3546.14			0.385531			0.192765	−	0.981245i	$-0.438254\pi$
$439$	3546.14			0.385531			0.192765	+	0.981245i	$0.438254\pi$
$440$	−3160.89	+	1541.40i	−0.342477	+	0.167008i
$441$	828.119			0.0894200
$442$	−208.837	+	187.227i	−0.0224737	+	0.0201481i
$443$	11129.6	+	3616.23i	1.19364	+	0.387838i	0.837418	−	0.546563i	$-0.184064\pi$
$443$	11129.6	+	3616.23i	1.19364	+	0.387838i	0.356224	+	0.934401i	$0.384064\pi$
$444$	−18501.3	−	2025.01i	−1.97756	−	0.216447i
$445$	−2569.16	+	1866.60i	−0.273685	+	0.198844i
$446$	−9261.10	+	4099.48i	−0.983241	+	0.435238i
$447$	−2075.99	−	6389.24i	−0.219667	−	0.676064i
$448$	−5264.74	−	67.8900i	−0.555213	−	0.00715960i
$449$	11933.7	+	8670.32i	1.25431	+	0.911308i	0.998464	−	0.0554095i	$-0.0176464\pi$
$449$	11933.7	+	8670.32i	1.25431	+	0.911308i	0.255845	+	0.966718i	$0.417646\pi$
$450$	−221.546	+	1031.39i	−0.0232084	+	0.108045i
$451$	−3402.90	+	1686.66i	−0.355291	+	0.176101i
$452$	8741.21	+	3936.94i	0.909628	+	0.409686i
$453$	10272.8	−	14139.4i	1.06548	−	1.46650i
$454$	−2402.46	−	1393.95i	−0.248355	−	0.144100i
$455$	−1610.81	+	523.384i	−0.165969	+	0.0539267i
$456$	10442.5	+	67.3261i	1.07240	+	0.00691411i
$457$	5991.32	+	8246.34i	0.613265	+	0.844086i	0.996841	−	0.0794227i	$-0.0253077\pi$
$457$	5991.32	+	8246.34i	0.613265	+	0.844086i	−0.383576	+	0.923509i	$0.625308\pi$
$458$	−6360.26	+	654.674i	−0.648899	+	0.0667924i
$459$	−102.890	+	316.664i	−0.0104630	+	0.0322017i
$460$	−2073.67	+	1185.38i	−0.210186	+	0.120149i
$461$			5980.69i			0.604227i	0.953272	+	0.302113i	$0.0976922\pi$
$461$			5980.69i			0.604227i	−0.953272	+	0.302113i	$0.902308\pi$
$462$	−5846.89	−	384.010i	−0.588792	−	0.0386705i
$463$		−	7335.59i		−	0.736315i	−0.929763	−	0.368157i	$-0.879989\pi$
$463$		−	7335.59i		−	0.736315i	0.929763	−	0.368157i	$-0.120011\pi$
$464$	−9090.34	+	876.496i	−0.909501	+	0.0876946i
$465$	−2153.33	+	6627.27i	−0.214749	+	0.660929i
$466$	−382.540	−	3716.44i	−0.0380275	−	0.369443i
$467$	6706.54	+	9230.77i	0.664544	+	0.914666i	0.999621	−	0.0275247i	$-0.00876249\pi$
$467$	6706.54	+	9230.77i	0.664544	+	0.914666i	−0.335077	+	0.942191i	$0.608762\pi$
$468$	−219.921	−	1056.96i	−0.0217219	−	0.104398i
$469$	−5029.37	+	1634.14i	−0.495170	+	0.160890i
$470$	1116.30	−	1923.93i	0.109556	−	0.188817i
$471$	−2813.39	+	3872.30i	−0.275232	+	0.378824i
$472$	13395.5	+	9865.00i	1.30631	+	0.962020i
$473$	−9515.47	+	9307.01i	−0.924993	+	0.904729i
$474$	6157.09	+	1322.57i	0.596634	+	0.128159i
$475$	−7224.97	−	5249.25i	−0.697904	−	0.507057i
$476$	−156.201	−	141.865i	−0.0150409	−	0.0136604i
$477$	−83.3571	−	256.547i	−0.00800138	−	0.0246257i
$478$	−3920.90	−	8857.66i	−0.375184	−	0.847573i
$479$	−7895.13	+	5736.15i	−0.753106	+	0.547164i	−0.896788	−	0.442460i	$-0.854106\pi$
$479$	−7895.13	+	5736.15i	−0.753106	+	0.547164i	0.143682	+	0.989624i	$0.454106\pi$
$480$	2883.08	−	3133.61i	0.274154	−	0.297977i
$481$	−15492.0	−	5033.65i	−1.46855	−	0.477162i
$482$	−396.167	−	441.894i	−0.0374376	−	0.0417588i
$483$	−3979.81			−0.374922
$484$	−10556.5	−	1392.66i	−0.991410	−	0.130791i
$485$	5828.99			0.545733
$486$	−1838.07	−	2050.22i	−0.171556	−	0.191358i
$487$	3095.46	+	1005.78i	0.288026	+	0.0935855i	0.449467	−	0.893297i	$-0.351614\pi$
$487$	3095.46	+	1005.78i	0.288026	+	0.0935855i	−0.161440	+	0.986882i	$0.551614\pi$
$488$	2797.21	−	8423.74i	0.259475	−	0.781403i
$489$	−9557.32	+	6943.80i	−0.883838	+	0.642146i
$490$	1157.10	+	2613.99i	0.106678	+	0.240996i
$491$	798.970	+	2458.98i	0.0734359	+	0.226012i	0.981037	−	0.193822i	$-0.0620883\pi$
$491$	798.970	+	2458.98i	0.0734359	+	0.226012i	−0.907601	+	0.419834i	$0.862088\pi$
$492$	3091.79	−	3404.24i	0.283310	−	0.311941i
$493$	−296.097	−	215.127i	−0.0270497	−	0.0196528i
$494$	8935.70	+	1919.42i	0.813839	+	0.174816i
$495$	387.821	−	379.324i	0.0352146	−	0.0344432i
$496$	−14197.8	+	12564.4i	−1.28528	+	1.13742i
$497$	762.154	−	1049.01i	0.0687872	−	0.0946775i
$498$	−4801.34	+	8275.05i	−0.432035	+	0.744606i
$499$	−14248.4	+	4629.60i	−1.27825	+	0.415329i	−0.867964	−	0.496627i	$-0.834572\pi$
$499$	−14248.4	+	4629.60i	−1.27825	+	0.415329i	−0.410287	+	0.911956i	$0.634572\pi$
$500$	−7735.87	+	1609.59i	−0.691918	+	0.143966i
$501$	3770.97	+	5190.29i	0.336276	+	0.462844i
$502$	−1625.52	−	15792.2i	−0.144523	−	1.40406i
$503$	4616.75	−	14208.9i	0.409246	−	1.25953i	−0.508052	−	0.861326i	$-0.669634\pi$
$503$	4616.75	−	14208.9i	0.409246	−	1.25953i	0.917298	−	0.398202i	$-0.130366\pi$
$504$	774.057	−	246.001i	0.0684112	−	0.0217415i
$505$		−	7521.76i		−	0.662800i
$506$	−7216.65	−	473.973i	−0.634030	−	0.0416416i
$507$			3877.70i			0.339674i
$508$	−3231.35	−	5652.84i	−0.282220	−	0.493709i
$509$	6630.07	−	20405.3i	0.577353	−	1.77691i	−0.0506708	−	0.998715i	$-0.516136\pi$
$509$	6630.07	−	20405.3i	0.577353	−	1.77691i	0.628024	−	0.778194i	$-0.283864\pi$
$510$	169.752	−	17.4729i	0.0147388	−	0.00151709i
$511$	3170.11	+	4363.28i	0.274437	+	0.377730i
$512$	11085.4	−	3366.27i	0.956855	−	0.290565i
$513$	10318.7	−	3352.76i	0.888076	−	0.288554i
$514$	7083.80	+	4110.16i	0.607885	+	0.352707i
$515$	−1396.63	+	1922.29i	−0.119501	+	0.164478i
$516$	6618.41	−	14694.9i	0.564649	−	1.25369i
$517$	6034.33	−	2990.94i	0.513326	−	0.254432i
$518$	2573.66	−	11981.5i	0.218302	−	1.01628i
$519$	17597.3	+	12785.2i	1.48832	+	1.08133i
$520$	3029.06	−	2171.05i	0.255449	−	0.183090i
$521$	−1847.98	−	5687.51i	−0.155397	−	0.478262i	0.842804	−	0.538220i	$-0.180903\pi$
$521$	−1847.98	−	5687.51i	−0.155397	−	0.478262i	−0.998201	+	0.0599585i	$0.980903\pi$
$522$	1288.21	−	570.236i	0.108015	−	0.0478133i
$523$	6436.84	−	4676.64i	0.538171	−	0.391004i	−0.285235	−	0.958458i	$-0.592072\pi$
$523$	6436.84	−	4676.64i	0.538171	−	0.391004i	0.823405	+	0.567454i	$0.192072\pi$
$524$	−2327.35	+	21263.7i	−0.194028	+	1.77273i
$525$	−5770.53	−	1874.96i	−0.479708	−	0.155866i
$526$	8406.21	−	7536.34i	0.696822	−	0.624715i
$527$	−759.803			−0.0628037
$528$	12516.8	−	3091.33i	1.03168	−	0.254797i
$529$	7254.84			0.596272
$530$	693.329	−	621.583i	0.0568232	−	0.0509431i
$531$	−2440.68	−	793.025i	−0.199466	−	0.0648105i
$532$	−748.109	+	6835.05i	−0.0609674	+	0.557024i
$533$	3256.15	−	2365.73i	0.264614	−	0.192254i
$534$	10646.2	−	4712.60i	0.862744	−	0.381899i
$535$	−629.496	−	1937.39i	−0.0508700	−	0.156562i
$536$	9457.52	−	6778.56i	0.762132	−	0.546249i
$537$	9101.92	+	6612.93i	0.731428	+	0.531413i
$538$	−792.413	+	3689.01i	−0.0635006	+	0.295622i
$539$	−1448.61	+	8533.43i	−0.115763	+	0.681931i
$540$	1816.81	−	4033.86i	0.144783	−	0.321462i
$541$	2307.56	−	3176.09i	0.183382	−	0.252404i	−0.707422	−	0.706792i	$-0.750142\pi$
$541$	2307.56	−	3176.09i	0.183382	−	0.252404i	0.890804	+	0.454387i	$0.150142\pi$
$542$	4404.71	+	2555.70i	0.349075	+	0.202540i
$543$	4648.88	−	1510.51i	0.367408	−	0.119378i
$544$	422.098	+	193.391i	0.0332671	+	0.0152419i
$545$	−4387.85	−	6039.36i	−0.344871	−	0.474675i
$546$	6176.84	−	635.794i	0.484147	−	0.0498342i
$547$	−7769.21	+	23911.2i	−0.607289	+	1.86904i	−0.127076	+	0.991893i	$0.540559\pi$
$547$	−7769.21	+	23911.2i	−0.607289	+	1.86904i	−0.480214	+	0.877152i	$0.659441\pi$
$548$	−5003.63	−	8753.21i	−0.390044	−	0.682333i
$549$			1369.22i			0.106442i
$550$	−10240.5	−	4087.13i	−0.793921	−	0.316865i
$551$			11926.3i			0.922098i
$552$	8345.64	−	2652.30i	0.643504	−	0.204510i
$553$	−1281.35	+	3943.60i	−0.0985328	+	0.303253i
$554$	−574.198	−	5578.42i	−0.0440349	−	0.427806i
$555$	5825.44	+	8018.03i	0.445543	+	0.613237i
$556$	−6259.29	+	1302.36i	−0.477434	+	0.0993388i
$557$	−15535.4	+	5047.77i	−1.18179	+	0.383987i	−0.833031	−	0.553226i	$-0.813397\pi$
$557$	−15535.4	+	5047.77i	−1.18179	+	0.383987i	−0.348759	+	0.937213i	$0.613397\pi$
$558$	1467.75	−	2529.64i	0.111353	−	0.191915i
$559$	8290.91	−	11411.5i	0.627313	−	0.863423i
$560$	1858.07	+	2099.62i	0.140211	+	0.158438i
$561$	457.756	+	239.660i	0.0344500	+	0.0180365i
$562$	−15918.2	−	3419.29i	−1.19478	−	0.256644i
$563$	−9320.88	−	6772.02i	−0.697741	−	0.506939i	0.181455	−	0.983399i	$-0.441919\pi$
$563$	−9320.88	−	6772.02i	−0.697741	−	0.506939i	−0.879196	+	0.476461i	$0.841919\pi$
$564$	−5482.64	+	6036.71i	−0.409328	+	0.450694i
$565$	−1577.54	−	4855.17i	−0.117465	−	0.361520i
$566$	2903.37	+	6558.97i	0.215614	+	0.487092i
$567$	6747.67	−	4902.47i	0.499780	−	0.363112i
$568$	−899.130	+	2707.71i	−0.0664201	+	0.200023i
$569$	16408.2	+	5331.36i	1.20891	+	0.392798i	0.843031	−	0.537865i	$-0.180769\pi$
$569$	16408.2	+	5331.36i	1.20891	+	0.392798i	0.365878	+	0.930663i	$0.380769\pi$
$570$	−3711.98	−	4140.43i	−0.272768	−	0.304252i
$571$	−12867.6			−0.943070			−0.471535	−	0.881847i	$-0.656300\pi$
$571$	−12867.6			−0.943070			−0.471535	+	0.881847i	$0.656300\pi$
$572$	11276.3	−	417.269i	0.824275	−	0.0305016i
$573$	−12289.7			−0.896001
$574$	2021.26	+	2254.56i	0.146979	+	0.163944i
$575$	−7122.40	−	2314.21i	−0.516565	−	0.167842i
$576$	−1459.25	+	1031.73i	−0.105559	+	0.0746329i
$577$	−15293.0	+	11111.0i	−1.10339	+	0.801660i	−0.981610	−	0.190898i	$-0.938860\pi$
$577$	−15293.0	+	11111.0i	−1.10339	+	0.801660i	−0.121780	+	0.992557i	$0.538860\pi$
$578$	−5617.21	−	12689.8i	−0.404230	−	0.913193i
$579$	1437.97	+	4425.62i	0.103213	+	0.317656i
$580$	3599.95	+	3269.54i	0.257724	+	0.234069i
$581$	−5096.28	−	3702.66i	−0.363906	−	0.264393i
$582$	−20893.6	−	4488.03i	−1.48809	−	0.319648i
$583$	2789.42	−	410.189i	0.198158	−	0.0291395i
$584$	−9555.57	−	7037.10i	−0.677076	−	0.498626i
$585$	−337.912	+	465.095i	−0.0238819	+	0.0328706i
$586$	−3993.88	+	6883.40i	−0.281546	+	0.485240i
$587$	−2813.20	+	914.063i	−0.197808	+	0.0642716i	−0.406245	−	0.913764i	$-0.633162\pi$
$587$	−2813.20	+	914.063i	−0.197808	+	0.0642716i	0.208438	+	0.978036i	$0.433162\pi$
$588$	−2134.91	−	10260.6i	−0.149731	−	0.719626i
$589$	14552.8	+	20030.3i	1.01806	+	1.40124i
$590$	−907.054	−	8812.18i	−0.0632929	−	0.614901i
$591$	2247.68	−	6917.63i	0.156442	−	0.481478i
$592$	2587.96	+	26840.3i	0.179669	+	1.86339i
$593$		−	2570.29i		−	0.177992i	−0.996032	−	0.0889961i	$-0.971634\pi$
$593$		−	2570.29i		−	0.177992i	0.996032	−	0.0889961i	$-0.0283659\pi$
$594$	11329.9	−	7146.53i	0.782613	−	0.493646i
$595$			112.362i			0.00774185i
$596$	−8449.94	+	4830.27i	−0.580743	+	0.331972i
$597$	−3938.35	+	12121.0i	−0.269993	+	0.830953i
$598$	7623.90	−	784.742i	0.521345	−	0.0536630i
$599$	−8743.46	−	12034.3i	−0.596407	−	0.820884i	0.398966	−	0.916966i	$-0.369369\pi$
$599$	−8743.46	−	12034.3i	−0.596407	−	0.820884i	−0.995373	+	0.0960813i	$0.969369\pi$
$600$	13350.3	+	86.0742i	0.908375	+	0.00585660i
$601$	8656.49	−	2812.66i	0.587530	−	0.190900i	−0.000141221	−	1.00000i	$-0.500045\pi$
$601$	8656.49	−	2812.66i	0.587530	−	0.190900i	0.587671	+	0.809100i	$0.300045\pi$
$602$	9178.63	+	5325.62i	0.621417	+	0.360558i
$603$	−1055.05	+	1452.15i	−0.0712518	+	0.0980697i
$604$	−23087.4	−	10398.3i	−1.55532	−	0.700497i
$605$	3230.38	+	4659.88i	0.217080	+	0.313142i
$606$	−5791.39	+	26961.3i	−0.388216	+	1.80731i
$607$	−9474.97	−	6883.97i	−0.633571	−	0.460316i	0.224065	−	0.974574i	$-0.428067\pi$
$607$	−9474.97	−	6883.97i	−0.633571	−	0.460316i	−0.857635	+	0.514258i	$0.828067\pi$
$608$	−2986.37	−	14831.7i	−0.199199	−	0.989314i
$609$	2503.90	+	7706.22i	0.166606	+	0.512762i
$610$	−4321.99	+	1913.16i	−0.286873	+	0.126986i
$611$	−5774.10	+	4195.13i	−0.382316	+	0.277769i
$612$	−71.1966	−	7.79260i	−0.00470254	−	0.000514701i
$613$	9675.27	+	3143.69i	0.637488	+	0.207133i	0.609889	−	0.792487i	$-0.291214\pi$
$613$	9675.27	+	3143.69i	0.637488	+	0.207133i	0.0275990	+	0.999619i	$0.491214\pi$
$614$	197.802	−	177.334i	0.0130011	−	0.0116557i
$615$	−2448.81			−0.160562
$616$	1180.89	+	8406.67i	0.0772396	+	0.549861i
$617$	−8549.84			−0.557866			−0.278933	−	0.960310i	$-0.589981\pi$
$617$	−8549.84			−0.557866			−0.278933	+	0.960310i	$0.589981\pi$
$618$	6486.20	−	5815.01i	0.422190	−	0.378502i
$619$	−3124.76	−	1015.30i	−0.202899	−	0.0659259i	0.205804	−	0.978593i	$-0.434019\pi$
$619$	−3124.76	−	1015.30i	−0.202899	−	0.0659259i	−0.408703	+	0.912667i	$0.634019\pi$
$620$	10035.8	+	1098.43i	0.650073	+	0.0711518i
$621$	7360.71	−	5347.87i	0.475644	−	0.345576i
$622$	−18849.2	+	8343.70i	−1.21509	+	0.537865i
$623$	2368.90	+	7290.74i	0.152341	+	0.468856i
$624$	−12529.1	+	5449.75i	−0.803790	+	0.349623i
$625$	−7401.65	−	5377.61i	−0.473706	−	0.344167i
$626$	−2881.70	+	13415.5i	−0.183987	+	0.856536i
$627$	−2449.57	−	16657.9i	−0.156023	−	1.06101i
$628$	6322.85	+	2847.74i	0.401766	+	0.180951i
$629$	−635.187	+	874.260i	−0.0402648	+	0.0554197i
$630$	−374.092	−	217.055i	−0.0236574	−	0.0137265i
$631$	20412.0	−	6632.25i	1.28778	−	0.418424i	0.416464	−	0.909152i	$-0.363269\pi$
$631$	20412.0	−	6632.25i	1.28778	−	0.418424i	0.871313	+	0.490728i	$0.163269\pi$
$632$	58.8234	−	9123.66i	0.00370232	−	0.574240i
$633$	−16542.0	−	22768.1i	−1.03868	−	1.42962i
$634$	−6408.49	+	659.638i	−0.401441	+	0.0413211i
$635$	−1071.44	+	3297.55i	−0.0669586	+	0.206077i
$636$	−2963.78	+	1694.20i	−0.184783	+	0.105628i
$637$		−	9172.50i		−	0.570530i
$638$	3622.60	+	14272.0i	0.224797	+	0.885635i
$639$		−	440.119i		−	0.0272470i
$640$	−5295.64	−	3164.60i	−0.327076	−	0.195456i
$641$	3086.62	−	9499.63i	0.190193	−	0.585355i	−0.809806	−	0.586698i	$-0.800427\pi$
$641$	3086.62	−	9499.63i	0.190193	−	0.585355i	0.999999	+	0.00134290i	$0.000427459\pi$
$642$	764.695	+	7429.13i	0.0470095	+	0.456705i
$643$	−12551.8	−	17276.1i	−0.769824	−	1.05957i	−0.996333	−	0.0855624i	$-0.972731\pi$
$643$	−12551.8	−	17276.1i	−0.769824	−	1.05957i	0.226509	−	0.974009i	$-0.427269\pi$
$644$	1174.55	+	5645.03i	0.0718693	+	0.345412i
$645$	−8162.05	+	2652.01i	−0.498264	+	0.161896i
$646$	304.290	−	524.440i	0.0185327	−	0.0319409i
$647$	9425.80	−	12973.5i	0.572745	−	0.788316i	−0.420131	−	0.907463i	$-0.638016\pi$
$647$	9425.80	−	12973.5i	0.572745	−	0.788316i	0.992877	+	0.119147i	$0.0380160\pi$
$648$	−10882.6	+	14777.4i	−0.659739	+	0.895849i
$649$	12441.2	−	23763.0i	0.752482	−	1.43726i
$650$	11424.0	+	2453.92i	0.689363	+	0.148078i
$651$	13608.7	+	9887.33i	0.819306	+	0.595261i
$652$	12669.8	+	11507.0i	0.761027	+	0.691178i
$653$	8686.81	+	26735.2i	0.520584	+	1.60219i	0.772887	+	0.634544i	$0.218812\pi$
$653$	8686.81	+	26735.2i	0.520584	+	1.60219i	−0.252304	+	0.967648i	$0.581188\pi$
$654$	11078.0	+	25026.1i	0.662359	+	1.49633i
$655$	9215.17	−	6695.21i	0.549720	−	0.399395i
$656$	−5741.11	−	3380.77i	−0.341696	−	0.201214i
$657$	1741.04	+	565.697i	0.103385	+	0.0335920i
$658$	−3584.28	−	3998.00i	−0.212356	−	0.236866i
$659$	14722.1			0.870248			0.435124	−	0.900371i	$-0.356705\pi$
$659$	14722.1			0.870248			0.435124	+	0.900371i	$0.356705\pi$
$660$	−5699.74	−	3827.29i	−0.336154	−	0.225723i
$661$	−2312.93			−0.136101			−0.0680504	−	0.997682i	$-0.521678\pi$
$661$	−2312.93			−0.136101			−0.0680504	+	0.997682i	$0.521678\pi$
$662$	12501.6	+	13944.6i	0.733972	+	0.818690i
$663$	−520.762	−	169.206i	−0.0305048	−	0.00991162i
$664$	13154.5	+	4368.12i	0.768815	+	0.255295i
$665$	2962.15	−	2152.12i	0.172732	−	0.125497i
$666$	−1683.69	−	3803.60i	−0.0979603	−	0.221301i
$667$	3090.50	+	9511.58i	0.179407	+	0.552159i
$668$	6249.09	−	6880.61i	0.361953	−	0.398531i
$669$	−15996.1	−	11621.8i	−0.924429	−	0.671637i
$670$	−6057.94	−	1301.27i	−0.349312	−	0.0750335i
$671$	−14109.2	−	2395.14i	−0.811745	−	0.137799i
$672$	−5043.55	−	8956.58i	−0.289522	−	0.514148i
$673$	−6732.83	+	9266.94i	−0.385634	+	0.530779i	−0.957066	−	0.289870i	$-0.906388\pi$
$673$	−6732.83	+	9266.94i	−0.385634	+	0.530779i	0.571432	+	0.820649i	$0.306388\pi$
$674$	11428.4	−	19696.8i	0.653126	−	1.12565i
$675$	13192.2	−	4286.39i	0.752246	−	0.244420i
$676$	5500.20	−	1144.42i	0.312938	−	0.0651125i
$677$	−12679.0	−	17451.2i	−0.719786	−	0.990701i	−0.999531	−	0.0306264i	$-0.990250\pi$
$677$	−12679.0	−	17451.2i	−0.719786	−	0.990701i	0.279745	−	0.960074i	$-0.409750\pi$
$678$	1916.36	+	18617.7i	0.108550	+	1.05459i
$679$	4348.18	−	13382.3i	0.245755	−	0.756357i
$680$	−74.8827	−	235.623i	−0.00422297	−	0.0132879i
$681$		−	5422.54i		−	0.305128i
$682$	23499.4	+	19549.6i	1.31941	+	1.09764i
$683$			18505.0i			1.03671i	0.855165	+	0.518356i	$0.173456\pi$
$683$			18505.0i			1.03671i	−0.855165	+	0.518356i	$0.826544\pi$
$684$	1158.23	+	2026.17i	0.0647456	+	0.113264i
$685$	−1659.08	+	5106.13i	−0.0925405	+	0.284810i
$686$	16788.6	−	1728.08i	0.934388	−	0.0961784i
$687$	−7337.02	−	10098.5i	−0.407460	−	0.560820i
$688$	−22796.8	−	5050.81i	−1.26325	−	0.279884i
$689$	−2841.59	+	923.289i	−0.157121	+	0.0510516i
$690$	−4033.34	−	2340.22i	−0.222532	−	0.129117i
$691$	−4127.65	+	5681.22i	−0.227241	+	0.312770i	−0.907379	−	0.420314i	$-0.861920\pi$
$691$	−4127.65	+	5681.22i	−0.227241	+	0.312770i	0.680138	+	0.733084i	$0.261920\pi$
$692$	12941.3	−	28733.6i	0.710917	−	1.57845i
$693$	−581.564	−	1173.33i	−0.0318785	−	0.0643160i
$694$	6491.00	−	30218.3i	0.355036	−	1.65284i
$695$	2754.27	+	2001.10i	0.150325	+	0.109217i
$696$	−10386.4	−	14491.2i	−0.565655	−	0.789208i
$697$	−82.5108	−	253.942i	−0.00448396	−	0.0138002i
$698$	−24592.1	+	10885.9i	−1.33356	+	0.590309i
$699$	5900.79	−	4287.18i	0.319297	−	0.231983i
$700$	−956.432	+	8738.38i	−0.0516425	+	0.471828i
$701$	26717.4	+	8681.00i	1.43952	+	0.467727i	0.921747	−	0.387792i	$-0.126762\pi$
$701$	26717.4	+	8681.00i	1.43952	+	0.467727i	0.517770	+	0.855520i	$0.326762\pi$
$702$	−10569.8	+	9476.04i	−0.568278	+	0.509473i
$703$	35213.7			1.88920
$704$	−8078.87	−	16841.8i	−0.432506	−	0.901631i
$705$	4342.46			0.231981
$706$	10962.0	−	9827.65i	0.584363	−	0.523893i
$707$	−17268.6	−	5610.92i	−0.918604	−	0.298473i
$708$	−3533.66	+	32285.1i	−0.187575	+	1.71377i
$709$	−6409.80	+	4656.99i	−0.339528	+	0.246681i	−0.744463	−	0.667664i	$-0.767294\pi$
$709$	−6409.80	+	4656.99i	−0.339528	+	0.246681i	0.404935	+	0.914346i	$0.367294\pi$
$710$	1389.25	−	614.961i	0.0734334	−	0.0325058i
$711$	434.925	+	1338.56i	0.0229409	+	0.0706048i
$712$	−9826.43	−	13709.9i	−0.517220	−	0.721631i
$713$	16796.9	+	12203.7i	0.882256	+	0.640996i
$714$	86.5134	−	402.756i	0.00453457	−	0.0211103i
$715$	−4201.52	−	4295.62i	−0.219759	−	0.224681i
$716$	6693.68	−	14862.0i	0.349378	−	0.775725i
$717$	11115.5	−	15299.2i	0.578965	−	0.796876i
$718$	15682.5	+	9099.31i	0.815135	+	0.472957i
$719$	−11234.1	+	3650.19i	−0.582702	+	0.189331i	−0.585511	−	0.810665i	$-0.699106\pi$
$719$	−11234.1	+	3650.19i	−0.582702	+	0.189331i	0.00280855	+	0.999996i	$0.499106\pi$
$720$	929.125	+	205.855i	0.0480923	+	0.0106552i
$721$	3371.42	+	4640.36i	0.174145	+	0.239689i
$722$	−355.535	+	36.5959i	−0.0183264	+	0.00188637i
$723$	358.035	−	1101.92i	0.0184170	−	0.0566816i
$724$	−3514.55	−	6148.26i	−0.180411	−	0.315605i
$725$			15247.3i			0.781064i
$726$	−7991.22	−	19190.3i	−0.408515	−	0.981017i
$727$		−	9071.88i		−	0.462802i	−0.972858	−	0.231401i	$-0.925669\pi$
$727$		−	9071.88i		−	0.462802i	0.972858	−	0.231401i	$-0.0743310\pi$
$728$	−2724.78	−	8573.70i	−0.138718	−	0.436487i
$729$	−5105.90	+	15714.3i	−0.259406	+	0.798371i
$730$	647.038	+	6286.08i	0.0328054	+	0.318710i
$731$	−550.027	−	757.047i	−0.0278297	−	0.0383043i
$732$	16965.0	−	3529.87i	0.856616	−	0.178235i
$733$	−26167.9	+	8502.47i	−1.31860	+	0.428439i	−0.882014	−	0.471223i	$-0.843813\pi$
$733$	−26167.9	+	8502.47i	−1.31860	+	0.428439i	−0.436586	+	0.899662i	$0.643813\pi$
$734$	−3529.95	+	6083.81i	−0.177510	+	0.305937i
$735$	−3280.32	+	4514.97i	−0.164621	+	0.226581i
$736$	−6225.11	−	11054.9i	−0.311767	−	0.553651i
$737$	−13118.2	−	13412.0i	−0.655653	−	0.670338i
$738$	1004.85	+	215.846i	0.0501206	+	0.0107661i
$739$	−329.521	−	239.411i	−0.0164028	−	0.0119173i	0.579554	−	0.814934i	$-0.303227\pi$
$739$	−329.521	−	239.411i	−0.0164028	−	0.0119173i	−0.595956	+	0.803017i	$0.703227\pi$
$740$	9653.68	−	10629.3i	0.479563	−	0.528026i
$741$	5513.70	+	16969.4i	0.273348	+	0.841279i
$742$	−909.851	−	2055.44i	−0.0450157	−	0.101695i
$743$	−26055.9	+	18930.7i	−1.28654	+	0.934726i	−0.999729	−	0.0232611i	$-0.992595\pi$
$743$	−26055.9	+	18930.7i	−1.28654	+	0.934726i	−0.286811	+	0.957987i	$0.592595\pi$
$744$	−35126.8	−	11664.3i	−1.73093	−	0.574777i
$745$	4929.22	+	1601.60i	0.242406	+	0.0787625i
$746$	9151.69	+	10208.0i	0.449152	+	0.500995i
$747$	−2138.17			−0.104727
$748$	204.842	−	720.021i	0.0100131	−	0.0351959i
$749$	−4917.48			−0.239894
$750$	−10297.3	−	11485.8i	−0.501337	−	0.559204i
$751$	21409.0	+	6956.21i	1.04025	+	0.337997i	0.778834	−	0.627230i	$-0.215811\pi$
$751$	21409.0	+	6956.21i	1.04025	+	0.337997i	0.261414	+	0.965227i	$0.415811\pi$
$752$	10180.7	+	5995.08i	0.493684	+	0.290716i
$753$	25074.1	−	18217.4i	1.21348	−	0.881645i
$754$	−6316.11	−	14268.7i	−0.305065	−	0.689170i
$755$	4166.61	+	12823.5i	0.200846	+	0.618140i
$756$	−7905.77	−	7180.15i	−0.380331	−	0.345423i
$757$	−26881.7	−	19530.7i	−1.29066	−	0.937720i	−0.290842	−	0.956771i	$-0.593936\pi$
$757$	−26881.7	−	19530.7i	−1.29066	−	0.937720i	−0.999819	+	0.0190510i	$0.993936\pi$
$758$	11486.5	+	2467.35i	0.550408	+	0.118230i
$759$	−6270.24	−	12650.4i	−0.299862	−	0.604983i
$760$	−4777.35	+	6487.09i	−0.228017	+	0.309621i
$761$	−21407.3	+	29464.6i	−1.01973	+	1.40353i	−0.107332	+	0.994223i	$0.534231\pi$
$761$	−21407.3	+	29464.6i	−1.01973	+	1.40353i	−0.912395	+	0.409311i	$0.865769\pi$
$762$	6379.45	−	10994.9i	0.303285	−	0.522707i
$763$	−17138.4	+	5568.62i	−0.813176	+	0.264217i
$764$	3627.03	+	17431.9i	0.171756	+	0.825477i
$765$	22.4174	+	30.8549i	0.00105948	+	0.00145825i
$766$	−744.962	−	7237.42i	−0.0351391	−	0.341382i
$767$	−8783.80	+	27033.7i	−0.413513	+	1.27266i
$768$	16545.3	+	15420.7i	0.777380	+	0.724540i
$769$		−	11220.0i		−	0.526145i	−0.964776	−	0.263072i	$-0.915264\pi$
$769$		−	11220.0i		−	0.526145i	0.964776	−	0.263072i	$-0.0847358\pi$
$770$	2891.06	−	3475.18i	0.135307	−	0.162645i
$771$			15988.7i			0.746847i
$772$	5853.01	−	3345.77i	0.272868	−	0.155981i
$773$	−2372.86	+	7302.92i	−0.110409	+	0.339803i	−0.990962	−	0.134145i	$-0.957171\pi$
$773$	−2372.86	+	7302.92i	−0.110409	+	0.339803i	0.880553	+	0.473948i	$0.157171\pi$
$774$	3582.98	−	368.803i	0.166392	−	0.0171271i
$775$	18605.3	+	25608.0i	0.862352	+	1.18693i
$776$	−199.613	+	30960.5i	−0.00923413	+	1.43224i
$777$	22753.5	−	7393.06i	1.05055	−	0.341344i
$778$	−6078.33	−	3526.77i	−0.280101	−	0.162520i
$779$	−5114.17	+	7039.06i	−0.235217	+	0.323749i
$780$	6633.79	+	2987.79i	0.304523	+	0.137154i
$781$	4535.24	+	769.890i	0.207790	+	0.0352738i
$782$	106.781	−	497.110i	0.00488297	−	0.0227322i
$783$	−14986.3	−	10888.1i	−0.683991	−	0.496949i
$784$	−13923.8	+	6056.38i	−0.634282	+	0.275892i
$785$	−1141.10	−	3511.93i	−0.0518821	−	0.159677i
$786$	−38186.2	+	16903.4i	−1.73290	+	0.767077i
$787$	−20587.1	+	14957.4i	−0.932465	+	0.677476i	−0.946595	−	0.322425i	$-0.895502\pi$
$787$	−20587.1	+	14957.4i	−0.932465	+	0.677476i	0.0141300	+	0.999900i	$0.495502\pi$
$788$	−10475.5	−	1146.56i	−0.473569	−	0.0518331i
$789$	20962.0	+	6810.95i	0.945837	+	0.307321i
$790$	−3617.52	+	3243.18i	−0.162919	+	0.146060i
$791$	−12323.4			−0.553944
$792$	2001.49	+	2072.89i	0.0897978	+	0.0930011i
$793$	15165.9			0.679138
$794$	2773.16	−	2486.20i	0.123949	−	0.111123i
$795$	1728.90	+	561.755i	0.0771295	+	0.0250609i
$796$	18355.0	+	2008.98i	0.817304	+	0.0894555i
$797$	29793.3	−	21646.1i	1.32413	−	0.962039i	0.324262	−	0.945967i	$-0.394884\pi$
$797$	29793.3	−	21646.1i	1.32413	−	0.962039i	0.999871	−	0.0160716i	$-0.00511598\pi$
$798$	−12274.7	+	5433.45i	−0.544509	+	0.241030i
$799$	146.316	+	450.313i	0.00647844	+	0.0199386i
$800$	−3817.97	−	18961.8i	−0.168732	−	0.838000i
$801$	2105.08	+	1529.43i	0.0928581	+	0.0674654i
$802$	−94.2396	+	438.724i	−0.00414927	+	0.0193166i
$803$	−8874.83	+	16951.1i	−0.390020	+	0.744946i
$804$	20712.4	+	9328.64i	0.908546	+	0.409199i
$805$	1804.72	−	2483.98i	0.0790161	−	0.108756i
$806$	−28019.1	−	16257.2i	−1.22448	−	0.710467i
$807$	−7005.65	+	2276.27i	−0.305589	+	0.0992920i
$808$	39951.6	+	257.582i	1.73947	+	0.0112150i
$809$	−5619.50	−	7734.58i	−0.244216	−	0.336135i	0.669259	−	0.743029i	$-0.266612\pi$
$809$	−5619.50	−	7734.58i	−0.244216	−	0.336135i	−0.913475	+	0.406894i	$0.866612\pi$
$810$	9721.22	−	1000.62i	0.421690	−	0.0434053i
$811$	8788.66	−	27048.7i	0.380532	−	1.17116i	−0.559138	−	0.829075i	$-0.688868\pi$
$811$	8788.66	−	27048.7i	0.380532	−	1.17116i	0.939670	−	0.342083i	$-0.111132\pi$
$812$	10191.7	−	5825.91i	0.440465	−	0.251785i
$813$			9941.78i			0.428872i
$814$	42139.8	−	10696.2i	1.81450	−	0.460565i
$815$		−	9113.96i		−	0.391715i
$816$	86.9939	+	902.234i	0.00373210	+	0.0387065i
$817$	−9422.72	+	29000.1i	−0.403500	+	1.24184i
$818$	664.140	+	6452.22i	0.0283877	+	0.275791i
$819$	815.709	+	1122.73i	0.0348024	+	0.0479014i
$820$	722.714	+	3473.44i	0.0307784	+	0.147924i
$821$	8966.68	−	2913.45i	0.381169	−	0.123849i	−0.112164	−	0.993690i	$-0.535778\pi$
$821$	8966.68	−	2913.45i	0.381169	−	0.123849i	0.493333	+	0.869840i	$0.335778\pi$
$822$	9878.34	−	17025.2i	0.419157	−	0.722411i
$823$	−8874.77	+	12215.1i	−0.375887	+	0.517364i	−0.954489	−	0.298246i	$-0.903598\pi$
$823$	−8874.77	+	12215.1i	−0.375887	+	0.517364i	0.578602	+	0.815610i	$0.303598\pi$
$824$	−10162.4	−	7483.98i	−0.429640	−	0.316404i
$825$	−3131.69	−	21296.6i	−0.132159	−	0.898729i
$826$	−20907.8	−	4491.08i	−0.880722	−	0.189182i
$827$	5573.65	+	4049.50i	0.234359	+	0.170272i	0.698766	−	0.715350i	$-0.253733\pi$
$827$	5573.65	+	4049.50i	0.234359	+	0.170272i	−0.464407	+	0.885622i	$0.653733\pi$
$828$	1448.77	+	1315.80i	0.0608072	+	0.0552262i
$829$	−12586.7	−	38738.0i	−0.527329	−	1.62295i	−0.759665	−	0.650315i	$-0.774637\pi$
$829$	−12586.7	−	38738.0i	−0.527329	−	1.62295i	0.232336	−	0.972636i	$-0.425363\pi$
$830$	−2987.58	−	6749.21i	−0.124940	−	0.282251i
$831$	8857.17	−	6435.11i	0.369738	−	0.268630i
$832$	11427.7	+	16163.1i	0.476184	+	0.673505i
$833$	−578.730	−	188.041i	−0.0240718	−	0.00782140i
$834$	−8331.78	−	9293.47i	−0.345930	−	0.385859i
$835$	−4949.52			−0.205132
$836$	−22905.0	+	8390.73i	−0.947589	+	0.347129i
$837$	−38455.7			−1.58808
$838$	−23386.4	−	26085.8i	−0.964047	−	1.07532i
$839$	−5978.25	−	1942.45i	−0.245998	−	0.0799295i	0.183423	−	0.983034i	$-0.441282\pi$
$839$	−5978.25	−	1942.45i	−0.245998	−	0.0799295i	−0.429421	+	0.903105i	$0.641282\pi$
$840$	−1724.96	+	5194.67i	−0.0708532	+	0.213373i
$841$	−3257.94	+	2367.03i	−0.133582	+	0.0970533i
$842$	−9439.00	−	21323.5i	−0.386329	−	0.872753i
$843$	−9822.20	−	30229.6i	−0.401298	−	1.23507i
$844$	−27412.7	+	30183.0i	−1.11799	+	1.23097i
$845$	−2420.25	−	1758.42i	−0.0985316	−	0.0715874i
$846$	−1781.89	−	382.757i	−0.0724145	−	0.0155549i
$847$	13108.0	−	3940.30i	0.531754	−	0.159847i
$848$	3277.78	+	3703.88i	0.132735	+	0.149990i
$849$	−8230.89	+	11328.8i	−0.332725	+	0.457957i
$850$	389.025	−	670.479i	0.0156982	−	0.0270556i
$851$	28084.0	−	9125.05i	1.13127	−	0.367571i
$852$	−5453.18	+	1134.63i	−0.219276	+	0.0456243i
$853$	15646.8	+	21536.0i	0.628061	+	0.864452i	0.997909	−	0.0646404i	$-0.0205900\pi$
$853$	15646.8	+	21536.0i	0.628061	+	0.864452i	−0.369847	+	0.929093i	$0.620590\pi$
$854$	1168.24	+	11349.7i	0.0468108	+	0.454775i
$855$	384.040	−	1181.96i	0.0153613	−	0.0472772i
$856$	10311.9	−	3277.20i	0.411746	−	0.130856i
$857$			17221.4i			0.686433i	0.939256	+	0.343216i	$0.111516\pi$
$857$			17221.4i			0.686433i	−0.939256	+	0.343216i	$0.888484\pi$
$858$	11752.7	+	18632.4i	0.467633	+	0.741373i
$859$		−	11261.5i		−	0.447309i	−0.974668	−	0.223655i	$-0.928201\pi$
$859$		−	11261.5i		−	0.447309i	0.974668	−	0.223655i	$-0.0717988\pi$
$860$	6170.51	+	10794.5i	0.244666	+	0.428012i
$861$	−1826.71	+	5622.04i	−0.0723045	+	0.222530i
$862$	−32422.4	+	3337.30i	−1.28110	+	0.131866i
$863$	4185.38	+	5760.68i	0.165089	+	0.227226i	0.883544	−	0.468348i	$-0.155150\pi$
$863$	4185.38	+	5760.68i	0.165089	+	0.227226i	−0.718455	+	0.695573i	$0.755150\pi$
$864$	21363.5	+	9788.05i	0.841206	+	0.385412i
$865$	−15959.7	+	5185.61i	−0.627335	+	0.203834i
$866$	7190.65	+	4172.15i	0.282157	+	0.163713i
$867$	15924.5	−	21918.2i	0.623788	−	0.858571i
$868$	10008.1	−	22220.9i	0.391354	−	0.868925i
$869$	−14554.1	+	2140.21i	−0.568142	+	0.0835462i
$870$	−1993.86	+	9282.25i	−0.0776991	+	0.361722i
$871$	16084.4	+	11686.0i	0.625718	+	0.454611i
$872$	32228.1	−	23099.1i	1.25159	−	0.897058i
$873$	−1475.89	−	4542.31i	−0.0572179	−	0.176099i
$874$	−15150.3	+	6706.36i	−0.586345	+	0.259549i
$875$	8217.19	−	5970.14i	0.317476	−	0.230660i
$876$	2520.70	−	23030.3i	0.0972223	−	0.888265i
$877$	41406.0	+	13453.6i	1.59428	+	0.518012i	0.965683	−	0.259723i	$-0.0836313\pi$
$877$	41406.0	+	13453.6i	1.59428	+	0.518012i	0.628593	+	0.777735i	$0.283631\pi$
$878$	7468.15	−	6695.35i	0.287059	−	0.257354i
$879$	−15536.4			−0.596165
$880$	−3746.55	+	9214.16i	−0.143518	+	0.352965i
$881$	−44373.0			−1.69689			−0.848447	−	0.529280i	$-0.822462\pi$
$881$	−44373.0			−1.69689			−0.848447	+	0.529280i	$0.822462\pi$
$882$	1744.01	−	1563.54i	0.0665805	−	0.0596907i
$883$	29955.5	+	9733.13i	1.14166	+	0.370947i	0.817994	−	0.575226i	$-0.195086\pi$
$883$	29955.5	+	9733.13i	1.14166	+	0.370947i	0.323662	+	0.946173i	$0.395086\pi$
$884$	−86.3133	+	788.596i	−0.00328397	+	0.0300038i
$885$	13991.6	−	10165.5i	0.531437	−	0.386112i
$886$	30266.6	−	13397.7i	1.14766	−	0.508018i
$887$	−10707.5	−	32954.2i	−0.405323	−	1.24745i	−0.920626	−	0.390447i	$-0.872321\pi$
$887$	−10707.5	−	32954.2i	−0.405323	−	1.24745i	0.515303	−	0.857008i	$-0.327679\pi$
$888$	−42787.0	+	30667.1i	−1.61694	+	1.15892i
$889$	6771.33	+	4919.66i	0.255459	+	0.185602i
$890$	−1886.36	+	8781.79i	−0.0710461	+	0.330749i
$891$	26214.3	+	13724.6i	0.985649	+	0.516041i
$892$	−11763.7	+	26119.0i	−0.441568	+	0.980415i
$893$	9068.92	−	12482.3i	0.339843	−	0.467754i
$894$	−16435.3	−	9536.09i	−0.614854	−	0.356750i
$895$	−8254.87	+	2682.17i	−0.308302	+	0.100173i
$896$	−11215.7	+	9797.20i	−0.418181	+	0.365292i
$897$	8794.71	+	12104.9i	0.327366	+	0.450580i
$898$	41502.3	−	4271.92i	1.54226	−	0.158748i
$899$	13062.5	−	40202.3i	0.484604	−	1.49146i
$900$	1480.76	+	2590.39i	0.0548428	+	0.0959405i
$901$			198.215i			0.00732909i
$902$	−3981.96	+	9977.00i	−0.146990	+	0.368290i
$903$			20716.9i			0.763472i
$904$	25842.1	−	8212.80i	0.950771	−	0.302161i
$905$	−1165.34	+	3586.55i	−0.0428036	+	0.131736i
$906$	−5061.49	−	49173.2i	−0.185604	−	1.80317i
$907$	−4216.80	−	5803.93i	−0.154373	−	0.212477i	0.724825	−	0.688934i	$-0.241921\pi$
$907$	−4216.80	−	5803.93i	−0.154373	−	0.212477i	−0.879198	+	0.476457i	$0.841921\pi$
$908$	−7691.44	+	1600.35i	−0.281112	+	0.0584904i
$909$	−5861.43	+	1904.49i	−0.213874	+	0.0694918i
$910$	−2404.17	+	4143.56i	−0.0875798	+	0.150943i
$911$	−6257.09	+	8612.14i	−0.227559	+	0.313209i	−0.907495	−	0.420063i	$-0.862008\pi$
$911$	−6257.09	+	8612.14i	−0.227559	+	0.313209i	0.679935	+	0.733272i	$0.262008\pi$
$912$	22118.9	−	19574.3i	0.803102	−	0.710711i
$913$	3740.25	−	22032.9i	0.135580	−	0.798668i
$914$	28187.3	+	6054.74i	1.02008	+	0.219117i
$915$	−7465.08	−	5423.70i	−0.269714	−	0.195958i
$916$	−12158.6	+	13387.3i	−0.438572	+	0.482893i
$917$	−8496.89	−	26150.7i	−0.305989	−	0.941738i
$918$	381.195	+	861.155i	0.0137051	+	0.0309612i
$919$	41351.8	−	30043.9i	1.48430	−	1.07841i	0.508159	−	0.861263i	$-0.330326\pi$
$919$	41351.8	−	30043.9i	1.48430	−	1.07841i	0.976140	−	0.217143i	$-0.0696739\pi$
$920$	−2129.07	+	6411.64i	−0.0762970	+	0.229767i
$921$	493.246	+	160.265i	0.0176471	+	0.00573390i
$922$	11291.9	+	12595.3i	0.403341	+	0.449896i
$923$	−4874.89			−0.173845
$924$	−13038.5	+	10230.6i	−0.464217	+	0.364244i
$925$	45019.5			1.60025
$926$	−13850.1	−	15448.7i	−0.491514	−	0.548246i
$927$	1851.60	+	601.620i	0.0656034	+	0.0213159i
$928$	−17489.3	+	19009.1i	−0.618659	+	0.672417i
$929$	−17003.4	+	12353.7i	−0.600499	+	0.436288i	−0.846056	−	0.533094i	$-0.821029\pi$
$929$	−17003.4	+	12353.7i	−0.600499	+	0.436288i	0.245557	+	0.969382i	$0.421029\pi$
$930$	7977.82	+	18022.6i	0.281293	+	0.635467i
$931$	6127.46	+	18858.4i	0.215703	+	0.663865i
$932$	−7822.50	−	7104.53i	−0.274930	−	0.249696i
$933$	−32556.9	−	23654.0i	−1.14241	−	0.830006i
$934$	31552.2	+	6777.54i	1.10538	+	0.237439i
$935$	−357.161	+	177.028i	−0.0124924	+	0.00619192i
$936$	−2458.77	−	1810.73i	−0.0858626	−	0.0632326i
$937$	−13864.7	+	19083.1i	−0.483393	+	0.665333i	−0.979153	−	0.203126i	$-0.934890\pi$
$937$	−13864.7	+	19083.1i	−0.483393	+	0.665333i	0.495760	+	0.868460i	$0.334890\pi$
$938$	−7506.45	+	12937.3i	−0.261295	+	0.450338i
$939$	−25476.9	+	8277.93i	−0.885416	+	0.287689i
$940$	−1281.58	−	6159.43i	−0.0444687	−	0.213722i
$941$	−3131.35	−	4309.93i	−0.108479	−	0.149309i	0.751326	−	0.659932i	$-0.229415\pi$
$941$	−3131.35	−	4309.93i	−0.108479	−	0.149309i	−0.859805	+	0.510623i	$0.829415\pi$
$942$	1386.17	+	13466.9i	0.0479448	+	0.465791i
$943$	−2254.66	+	6939.13i	−0.0778598	+	0.239628i
$944$	46836.7	−	4516.02i	1.61483	−	0.155703i
$945$			5686.95i			0.195764i
$946$	−2467.27	+	37566.3i	−0.0847968	+	1.29111i
$947$		−	49718.2i		−	1.70605i	−0.521873	−	0.853023i	$-0.674767\pi$
$947$		−	49718.2i		−	1.70605i	0.521873	−	0.853023i	$-0.325233\pi$
$948$	15463.9	−	8839.67i	0.529793	−	0.302847i
$949$	6265.83	−	19284.3i	0.214328	−	0.659635i
$950$	−25126.7	+	2586.33i	−0.858123	+	0.0883282i
$951$	−7392.65	−	10175.1i	−0.252075	−	0.346951i
$952$	−596.809	−	3.84783i	−0.0203179	−	0.000130997i
$953$	46993.8	−	15269.2i	1.59736	−	0.519012i	0.630904	−	0.775861i	$-0.282684\pi$
$953$	46993.8	−	15269.2i	1.59736	−	0.519012i	0.966451	+	0.256849i	$0.0826844\pi$
$954$	−659.927	−	382.902i	−0.0223961	−	0.0129947i
$955$	5572.99	−	7670.56i	0.188835	−	0.259909i
$956$	−24981.2	−	11251.3i	−0.845137	−	0.380640i
$957$	−20550.5	+	20100.3i	−0.694153	+	0.678946i
$958$	−5796.87	+	26986.8i	−0.195499	+	0.910130i
$959$	10485.2	+	7617.91i	0.353059	+	0.256512i
$960$	155.295	−	12042.8i	0.00522095	−	0.404875i
$961$	−17911.7	−	55126.6i	−0.601246	−	1.85044i
$962$	−42129.9	+	18649.1i	−1.41198	+	0.625020i
$963$	−1350.35	+	981.086i	−0.0451863	+	0.0328297i
$964$	−1668.65	−	182.637i	−0.0557506	−	0.00610201i
$965$	−3414.31	−	1109.38i	−0.113897	−	0.0370074i
$966$	−8381.44	+	7514.13i	−0.279160	+	0.250273i
$967$	−58669.9			−1.95108			−0.975542	−	0.219813i	$-0.929455\pi$
$967$	−58669.9			−1.95108			−0.975542	+	0.219813i	$0.929455\pi$
$968$	−24861.4	+	16998.5i	−0.825492	+	0.564413i
$969$	1183.70			0.0392426
$970$	12275.8	−	11005.5i	0.406343	−	0.364294i
$971$	−5650.40	−	1835.93i	−0.186746	−	0.0606774i	0.214151	−	0.976801i	$-0.431301\pi$
$971$	−5650.40	−	1835.93i	−0.186746	−	0.0606774i	−0.400897	+	0.916123i	$0.631301\pi$
$972$	−7741.91	−	847.367i	−0.255475	−	0.0279623i
$973$	6648.74	−	4830.59i	0.219063	−	0.159159i
$974$	8418.00	−	3726.28i	0.276930	−	0.122585i
$975$	7049.08	+	21694.9i	0.231540	+	0.712606i
$976$	−10013.7	−	23021.7i	−0.328412	−	0.755026i
$977$	40358.9	+	29322.5i	1.32159	+	0.960194i	0.999911	+	0.0133458i	$0.00424822\pi$
$977$	40358.9	+	29322.5i	1.32159	+	0.960194i	0.321682	+	0.946848i	$0.395752\pi$
$978$	−7017.30	+	32668.4i	−0.229436	+	1.06812i
$979$	−19442.5	+	19016.6i	−0.634715	+	0.620810i
$980$	7372.23	+	3320.37i	0.240303	+	0.108230i
$981$	−3595.25	+	4948.44i	−0.117011	+	0.161052i
$982$	6325.34	+	3670.08i	0.205549	+	0.119264i
$983$	−15019.1	+	4879.99i	−0.487318	+	0.158339i	−0.542362	−	0.840145i	$-0.682470\pi$
$983$	−15019.1	+	4879.99i	−0.487318	+	0.158339i	0.0550444	+	0.998484i	$0.482470\pi$
$984$	83.8593	−	13006.8i	0.00271681	−	0.421384i
$985$	3298.36	+	4539.81i	0.106695	+	0.146853i
$986$	−1029.75	+	105.994i	−0.0332596	+	0.00342347i
$987$	3239.29	−	9969.52i	0.104466	−	0.321513i
$988$	22442.5	−	12828.9i	0.722664	−	0.413099i
$989$			25570.3i			0.822131i
$990$	100.558	−	1531.09i	0.00322823	−	0.0491526i
$991$		−	1687.53i		−	0.0540931i	−0.999634	−	0.0270465i	$-0.991390\pi$
$991$		−	1687.53i		−	0.0540931i	0.999634	−	0.0270465i	$-0.00861023\pi$
$992$	−6177.96	+	53267.0i	−0.197732	+	1.70487i
$993$	−11298.3	+	34772.7i	−0.361069	+	1.11126i
$994$	−375.518	−	3648.21i	−0.0119826	−	0.116413i
$995$	−5779.35	−	7954.59i	−0.184138	−	0.253445i
$996$	5512.24	+	26492.4i	0.175363	+	0.842816i
$997$	−22933.3	+	7451.47i	−0.728490	+	0.236701i	−0.649700	−	0.760191i	$-0.725106\pi$
$997$	−22933.3	+	7451.47i	−0.728490	+	0.236701i	−0.0787895	+	0.996891i	$0.525106\pi$
$998$	−21266.1	+	36651.9i	−0.674516	+	1.16252i
$999$	−32148.5	+	44248.6i	−1.01815	+	1.40137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.4.g.a.7.14	yes	64
4.3	odd	2	inner	44.4.g.a.7.11	✓	64
11.8	odd	10	inner	44.4.g.a.19.11	yes	64
44.19	even	10	inner	44.4.g.a.19.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.g.a.7.11	✓	64	4.3	odd	2	inner
44.4.g.a.7.14	yes	64	1.1	even	1	trivial
44.4.g.a.19.11	yes	64	11.8	odd	10	inner
44.4.g.a.19.14	yes	64	44.19	even	10	inner

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:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	44.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10599 - 1.88807i) q^{2} +(5.25156 + 1.70634i) q^{3} +(0.870417 - 7.95251i) q^{4} +(-3.44642 + 2.50397i) q^{5} +(14.2814 - 6.32176i) q^{6} +(3.17779 + 9.78024i) q^{7} +(-13.1818 - 18.3913i) q^{8} +(2.82388 + 2.05167i) q^{9} +(-2.53048 + 11.7804i) q^{10} +(-26.0814 + 25.5100i) q^{11} +(18.1407 - 40.2779i) q^{12} +(22.7250 - 31.2782i) q^{13} +(25.1581 + 14.5972i) q^{14} +(-22.3717 + 7.26902i) q^{15} +(-62.4847 - 13.8440i) q^{16} +(-1.50760 - 2.07503i) q^{17} +(9.82077 - 1.01087i) q^{18} +(-25.8272 + 79.4879i) q^{19} +(16.9130 + 29.5872i) q^{20} +56.7839i q^{21} +(-6.76265 + 102.967i) q^{22} +70.0868i q^{23} +(-37.8431 - 119.076i) q^{24} +(-33.0192 + 101.623i) q^{25} +(-11.1967 - 108.778i) q^{26} +(-76.3035 - 105.023i) q^{27} +(80.5434 - 16.7585i) q^{28} +(135.711 - 44.0953i) q^{29} +(-33.3904 + 57.5478i) q^{30} +(174.122 - 239.658i) q^{31} +(-157.731 + 88.8199i) q^{32} +(-180.497 + 89.4639i) q^{33} +(-7.09277 - 1.52355i) q^{34} +(-35.4415 - 25.7497i) q^{35} +(18.7739 - 20.6711i) q^{36} +(-130.196 - 400.703i) q^{37} +(95.6865 + 216.164i) q^{38} +(172.713 - 125.483i) q^{39} +(91.4814 + 30.3775i) q^{40} +(99.0076 + 32.1695i) q^{41} +(107.212 + 119.587i) q^{42} +364.837 q^{43} +(180.167 + 229.617i) q^{44} -14.8696 q^{45} +(132.329 + 147.602i) q^{46} +(-175.569 - 57.0459i) q^{47} +(-304.520 - 179.323i) q^{48} +(191.938 - 139.451i) q^{49} +(122.332 + 276.359i) q^{50} +(-4.37654 - 13.4696i) q^{51} +(-228.960 - 207.945i) q^{52} +(-62.5214 - 45.4245i) q^{53} +(-358.984 - 77.1112i) q^{54} +(26.0111 - 153.225i) q^{55} +(137.983 - 187.365i) q^{56} +(-271.266 + 373.366i) q^{57} +(202.552 - 349.096i) q^{58} +(-699.233 + 227.195i) q^{59} +(38.3342 + 184.239i) q^{60} +(230.570 + 317.352i) q^{61} +(-85.7909 - 833.472i) q^{62} +(-11.0921 + 34.1380i) q^{63} +(-164.482 + 484.860i) q^{64} +164.701i q^{65} +(-211.211 + 529.200i) q^{66} +514.238i q^{67} +(-17.8139 + 10.1830i) q^{68} +(-119.592 + 368.065i) q^{69} +(-123.257 + 12.6870i) q^{70} +(-74.1139 - 102.009i) q^{71} +(0.509209 - 78.9796i) q^{72} +(498.791 - 162.067i) q^{73} +(-1030.75 - 598.059i) q^{74} +(-346.805 + 477.336i) q^{75} +(609.647 + 274.578i) q^{76} +(-332.375 - 174.017i) q^{77} +(126.811 - 590.360i) q^{78} +(326.213 + 237.007i) q^{79} +(250.014 - 108.748i) q^{80} +(-250.631 - 771.364i) q^{81} +(269.248 - 119.184i) q^{82} +(-495.576 + 360.057i) q^{83} +(451.575 + 49.4257i) q^{84} +(10.3916 + 3.37644i) q^{85} +(768.345 - 688.837i) q^{86} +787.938 q^{87} +(812.962 + 143.405i) q^{88} +745.456 q^{89} +(-31.3153 + 28.0748i) q^{90} +(378.123 + 122.860i) q^{91} +(557.366 + 61.0048i) q^{92} +(1323.35 - 961.470i) q^{93} +(-477.454 + 211.348i) q^{94} +(-110.024 - 338.620i) q^{95} +(-979.890 + 197.302i) q^{96} +(-1106.98 - 804.268i) q^{97} +(140.927 - 656.075i) q^{98} +(-125.989 + 18.5269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} + 7 q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} + 122 q^{9} - 38 q^{12} - 10 q^{13} + 66 q^{14} - 73 q^{16} - 10 q^{17} - 230 q^{18} - 180 q^{20} - 747 q^{22} - 455 q^{24} - 374 q^{25} + 330 q^{26}+ \cdots + 3904 q^{97}+O(q^{100}) \) 64 * q - 5 * q^2 + 7 * q^4 - 6 * q^5 - 5 * q^6 - 5 * q^8 + 122 * q^9 - 38 * q^12 - 10 * q^13 + 66 * q^14 - 73 * q^16 - 10 * q^17 - 230 * q^18 - 180 * q^20 - 747 * q^22 - 455 * q^24 - 374 * q^25 + 330 * q^26 + 520 * q^28 - 10 * q^29 + 880 * q^30 + 776 * q^33 - 846 * q^34 - 206 * q^36 - 30 * q^37 + 1016 * q^38 + 1080 * q^40 - 750 * q^41 + 1114 * q^42 + 1584 * q^44 - 1592 * q^45 + 1330 * q^46 + 68 * q^48 - 766 * q^49 + 655 * q^50 + 1610 * q^52 + 526 * q^53 + 1284 * q^56 + 1380 * q^57 - 2208 * q^58 - 4412 * q^60 - 10 * q^61 - 3980 * q^62 - 2825 * q^64 - 1694 * q^66 - 3840 * q^68 + 824 * q^69 - 1916 * q^70 - 5555 * q^72 - 2470 * q^73 - 1890 * q^74 + 714 * q^77 - 880 * q^78 + 6756 * q^80 + 2996 * q^81 + 6849 * q^82 + 6530 * q^84 + 3230 * q^85 + 1883 * q^86 + 3147 * q^88 + 1428 * q^89 + 10080 * q^90 + 2820 * q^92 + 130 * q^93 + 7280 * q^94 + 5720 * q^96 + 3904 * q^97

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