LMFDB - Embedded newform 42.4.f.a.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,4,Mod(5,42)] 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("42.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, 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:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Root			$-0.0204843 - 2.99993i$ of defining polynomial
Character	$\chi$	$=$	42.17
Dual form			42.4.f.a.5.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-0.0354799 + 5.19603i) q^{3} +(2.00000 - 3.46410i) q^{4} +(5.27257 + 9.13236i) q^{5} +(5.13458 + 9.03527i) q^{6} +(17.7029 - 5.44135i) q^{7} -8.00000i q^{8} +(-26.9975 - 0.368709i) q^{9} +(18.2647 + 10.5451i) q^{10} +(-26.6918 - 15.4105i) q^{11} +(17.9286 + 10.5150i) q^{12} -19.8400i q^{13} +(25.2209 - 27.1276i) q^{14} +(-47.6391 + 27.0724i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(46.3453 - 80.2724i) q^{17} +(-47.1297 + 26.3589i) q^{18} +(-118.901 + 68.6474i) q^{19} +42.1806 q^{20} +(27.6454 + 92.1777i) q^{21} -61.6421 q^{22} +(-37.6697 + 21.7486i) q^{23} +(41.5683 + 0.283839i) q^{24} +(6.89995 - 11.9511i) q^{25} +(-19.8400 - 34.3640i) q^{26} +(2.87369 - 140.267i) q^{27} +(16.5563 - 72.2073i) q^{28} -134.318i q^{29} +(-55.4409 + 94.5300i) q^{30} +(144.963 + 83.6945i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(81.0206 - 138.145i) q^{33} -185.381i q^{34} +(143.032 + 132.979i) q^{35} +(-55.2722 + 92.7846i) q^{36} +(191.747 + 332.115i) q^{37} +(-137.295 + 237.802i) q^{38} +(103.089 + 0.703923i) q^{39} +(73.0589 - 42.1806i) q^{40} +107.887 q^{41} +(140.061 + 132.011i) q^{42} -285.480 q^{43} +(-106.767 + 61.6421i) q^{44} +(-138.979 - 248.495i) q^{45} +(-43.4973 + 75.3395i) q^{46} +(120.906 + 209.416i) q^{47} +(72.2822 - 41.0766i) q^{48} +(283.783 - 192.655i) q^{49} -27.5998i q^{50} +(415.453 + 243.660i) q^{51} +(-68.7279 - 39.6801i) q^{52} +(-432.694 - 249.816i) q^{53} +(-135.289 - 245.823i) q^{54} -325.013i q^{55} +(-43.5308 - 141.623i) q^{56} +(-352.476 - 620.248i) q^{57} +(-134.318 - 232.646i) q^{58} +(-366.212 + 634.299i) q^{59} +(-1.49656 + 219.172i) q^{60} +(-265.207 + 153.117i) q^{61} +334.778 q^{62} +(-479.939 + 140.376i) q^{63} -64.0000 q^{64} +(181.187 - 104.608i) q^{65} +(2.18706 - 320.294i) q^{66} +(-280.049 + 485.060i) q^{67} +(-185.381 - 321.089i) q^{68} +(-111.670 - 196.505i) q^{69} +(380.718 + 87.2945i) q^{70} +74.2161i q^{71} +(-2.94967 + 215.980i) q^{72} +(141.409 + 81.6426i) q^{73} +(664.230 + 383.494i) q^{74} +(61.8533 + 36.2764i) q^{75} +549.180i q^{76} +(-556.376 - 127.571i) q^{77} +(179.260 - 101.870i) q^{78} +(-437.160 - 757.183i) q^{79} +(84.3612 - 146.118i) q^{80} +(728.728 + 19.9084i) q^{81} +(186.866 - 107.887i) q^{82} +406.600 q^{83} +(374.604 + 88.5892i) q^{84} +977.435 q^{85} +(-494.466 + 285.480i) q^{86} +(697.922 + 4.76560i) q^{87} +(-123.284 + 213.535i) q^{88} +(526.091 + 911.216i) q^{89} +(-489.214 - 291.427i) q^{90} +(-107.957 - 351.226i) q^{91} +173.989i q^{92} +(-440.023 + 750.264i) q^{93} +(418.832 + 241.813i) q^{94} +(-1253.83 - 723.897i) q^{95} +(84.1197 - 143.429i) q^{96} +243.235i q^{97} +(298.872 - 617.472i) q^{98} +(714.930 + 425.887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−0.0354799	+	5.19603i	−0.00682811	+	0.999977i
$3$	−0.0354799	+	5.19603i	−0.00682811	+	0.999977i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	5.27257	+	9.13236i	0.471593	+	0.816823i	0.999472	−	0.0324964i	$-0.0103457\pi$
$5$	5.27257	+	9.13236i	0.471593	+	0.816823i	−0.527879	+	0.849320i	$0.677012\pi$
$6$	5.13458	+	9.03527i	0.349364	+	0.614772i
$7$	17.7029	−	5.44135i	0.955865	−	0.293806i
$7$	17.7029	−	5.44135i	0.955865	−	0.293806i
$8$		−	8.00000i		−	0.353553i
$9$	−26.9975	−	0.368709i	−0.999907	−	0.0136559i
$10$	18.2647	+	10.5451i	0.577581	+	0.333467i
$11$	−26.6918	−	15.4105i	−0.731626	−	0.422405i	0.0873906	−	0.996174i	$-0.472147\pi$
$11$	−26.6918	−	15.4105i	−0.731626	−	0.422405i	−0.819017	+	0.573770i	$0.805481\pi$
$12$	17.9286	+	10.5150i	0.431296	+	0.252951i
$13$		−	19.8400i		−	0.423280i	−0.977348	−	0.211640i	$-0.932120\pi$
$13$		−	19.8400i		−	0.423280i	0.977348	−	0.211640i	$-0.0678804\pi$
$14$	25.2209	−	27.1276i	0.481470	−	0.517868i
$15$	−47.6391	+	27.0724i	−0.820025	+	0.466005i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	46.3453	−	80.2724i	0.661199	−	1.14523i	−0.319102	−	0.947720i	$-0.603381\pi$
$17$	46.3453	−	80.2724i	0.661199	−	1.14523i	0.980301	−	0.197510i	$-0.0632854\pi$
$18$	−47.1297	+	26.3589i	−0.617143	+	0.345158i
$19$	−118.901	+	68.6474i	−1.43567	+	0.828884i	−0.997545	−	0.0700296i	$-0.977691\pi$
$19$	−118.901	+	68.6474i	−1.43567	+	0.828884i	−0.438125	+	0.898914i	$0.644357\pi$
$20$	42.1806			0.471593
$21$	27.6454	+	92.1777i	0.287272	+	0.957849i
$22$	−61.6421			−0.597370
$23$	−37.6697	+	21.7486i	−0.341508	+	0.197170i	−0.660939	−	0.750440i	$-0.729842\pi$
$23$	−37.6697	+	21.7486i	−0.341508	+	0.197170i	0.319431	+	0.947610i	$0.396508\pi$
$24$	41.5683	+	0.283839i	0.353545	+	0.00241410i
$25$	6.89995	−	11.9511i	0.0551996	−	0.0956085i
$26$	−19.8400	−	34.3640i	−0.149652	−	0.259205i
$27$	2.87369	−	140.267i	0.0204831	−	0.999790i
$28$	16.5563	−	72.2073i	0.111745	−	0.487353i
$29$		−	134.318i		−	0.860079i	−0.902810	−	0.430039i	$-0.858500\pi$
$29$		−	134.318i		−	0.860079i	0.902810	−	0.430039i	$-0.141500\pi$
$30$	−55.4409	+	94.5300i	−0.337403	+	0.575291i
$31$	144.963	+	83.6945i	0.839876	+	0.484903i	0.857222	−	0.514947i	$-0.172188\pi$
$31$	144.963	+	83.6945i	0.839876	+	0.484903i	−0.0173460	+	0.999850i	$0.505522\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	81.0206	−	138.145i	0.427390	−	0.728725i
$34$		−	185.381i		−	0.935076i
$35$	143.032	+	132.979i	0.690767	+	0.642216i
$36$	−55.2722	+	92.7846i	−0.255890	+	0.429558i
$37$	191.747	+	332.115i	0.851972	+	1.47566i	0.879426	+	0.476036i	$0.157927\pi$
$37$	191.747	+	332.115i	0.851972	+	1.47566i	−0.0274532	+	0.999623i	$0.508740\pi$
$38$	−137.295	+	237.802i	−0.586110	+	1.01517i
$39$	103.089	+	0.703923i	0.423270	+	0.00289020i
$40$	73.0589	−	42.1806i	0.288791	−	0.166733i
$41$	107.887			0.410954			0.205477	−	0.978662i	$-0.434125\pi$
$41$	107.887			0.410954			0.205477	+	0.978662i	$0.434125\pi$
$42$	140.061	+	132.011i	0.514568	+	0.484994i
$43$	−285.480			−1.01245			−0.506225	−	0.862402i	$-0.668959\pi$
$43$	−285.480			−1.01245			−0.506225	+	0.862402i	$0.668959\pi$
$44$	−106.767	+	61.6421i	−0.365813	+	0.211202i
$45$	−138.979	−	248.495i	−0.460395	−	0.823187i
$46$	−43.4973	+	75.3395i	−0.139420	+	0.241483i
$47$	120.906	+	209.416i	0.375234	+	0.649924i	0.990362	−	0.138503i	$-0.0442291\pi$
$47$	120.906	+	209.416i	0.375234	+	0.649924i	−0.615128	+	0.788427i	$0.710896\pi$
$48$	72.2822	−	41.0766i	0.217355	−	0.123519i
$49$	283.783	−	192.655i	0.827357	−	0.561677i
$50$		−	27.5998i		−	0.0780640i
$51$	415.453	+	243.660i	1.14069	+	0.669003i
$52$	−68.7279	−	39.6801i	−0.183286	−	0.105820i
$53$	−432.694	−	249.816i	−1.12142	−	0.647451i	−0.179655	−	0.983730i	$-0.557498\pi$
$53$	−432.694	−	249.816i	−1.12142	−	0.647451i	−0.941762	+	0.336279i	$0.890831\pi$
$54$	−135.289	−	245.823i	−0.340936	−	0.619486i
$55$		−	325.013i		−	0.796813i
$56$	−43.5308	−	141.623i	−0.103876	−	0.337949i
$57$	−352.476	−	620.248i	−0.819062	−	1.44130i
$58$	−134.318	−	232.646i	−0.304084	−	0.526689i
$59$	−366.212	+	634.299i	−0.808081	+	1.39964i	0.106110	+	0.994354i	$0.466161\pi$
$59$	−366.212	+	634.299i	−0.808081	+	1.39964i	−0.914191	+	0.405284i	$0.867173\pi$
$60$	−1.49656	+	219.172i	−0.00322009	+	0.471582i
$61$	−265.207	+	153.117i	−0.556661	+	0.321388i	−0.751804	−	0.659387i	$-0.770816\pi$
$61$	−265.207	+	153.117i	−0.556661	+	0.321388i	0.195143	+	0.980775i	$0.437483\pi$
$62$	334.778			0.685756
$63$	−479.939	+	140.376i	−0.959788	+	0.280725i
$64$	−64.0000			−0.125000
$65$	181.187	−	104.608i	0.345745	−	0.199616i
$66$	2.18706	−	320.294i	0.00407891	−	0.597356i
$67$	−280.049	+	485.060i	−0.510649	+	0.884470i	0.489275	+	0.872130i	$0.337261\pi$
$67$	−280.049	+	485.060i	−0.510649	+	0.884470i	−0.999924	+	0.0123404i	$0.996072\pi$
$68$	−185.381	−	321.089i	−0.330599	−	0.572615i
$69$	−111.670	−	196.505i	−0.194833	−	0.342846i
$70$	380.718	+	87.2945i	0.650064	+	0.149053i
$71$			74.2161i			0.124054i	0.998074	+	0.0620270i	$0.0197565\pi$
$71$			74.2161i			0.124054i	−0.998074	+	0.0620270i	$0.980244\pi$
$72$	−2.94967	+	215.980i	−0.00482809	+	0.353520i
$73$	141.409	+	81.6426i	0.226722	+	0.130898i	0.609059	−	0.793125i	$-0.291547\pi$
$73$	141.409	+	81.6426i	0.226722	+	0.130898i	−0.382337	+	0.924023i	$0.624881\pi$
$74$	664.230	+	383.494i	1.04345	+	0.602435i
$75$	61.8533	+	36.2764i	0.0952294	+	0.0558512i
$76$			549.180i			0.828884i
$77$	−556.376	−	127.571i	−0.823441	−	0.188806i
$78$	179.260	−	101.870i	0.260221	−	0.147879i
$79$	−437.160	−	757.183i	−0.622586	−	1.07835i	−0.989002	−	0.147900i	$-0.952749\pi$
$79$	−437.160	−	757.183i	−0.622586	−	1.07835i	0.366416	−	0.930451i	$-0.380585\pi$
$80$	84.3612	−	146.118i	0.117898	−	0.204206i
$81$	728.728	+	19.9084i	0.999627	+	0.0273093i
$82$	186.866	−	107.887i	0.251657	−	0.145294i
$83$	406.600			0.537712			0.268856	−	0.963180i	$-0.413354\pi$
$83$	406.600			0.537712			0.268856	+	0.963180i	$0.413354\pi$
$84$	374.604	+	88.5892i	0.486579	+	0.115070i
$85$	977.435			1.24727
$86$	−494.466	+	285.480i	−0.619996	+	0.357955i
$87$	697.922	+	4.76560i	0.860059	+	0.00587271i
$88$	−123.284	+	213.535i	−0.149343	+	0.258669i
$89$	526.091	+	911.216i	0.626579	+	1.08527i	0.988233	+	0.152954i	$0.0488786\pi$
$89$	526.091	+	911.216i	0.626579	+	1.08527i	−0.361655	+	0.932312i	$0.617788\pi$
$90$	−489.214	−	291.427i	−0.572974	−	0.341323i
$91$	−107.957	−	351.226i	−0.124362	−	0.404598i
$92$			173.989i			0.197170i
$93$	−440.023	+	750.264i	−0.490626	+	0.836546i
$94$	418.832	+	241.813i	0.459566	+	0.265330i
$95$	−1253.83	−	723.897i	−1.35410	−	0.781793i
$96$	84.1197	−	143.429i	0.0894316	−	0.152486i
$97$			243.235i			0.254606i	0.991864	+	0.127303i	$0.0406320\pi$
$97$			243.235i			0.254606i	−0.991864	+	0.127303i	$0.959368\pi$
$98$	298.872	−	617.472i	0.308068	−	0.636470i
$99$	714.930	+	425.887i	0.725790	+	0.432356i
$100$	−27.5998	−	47.8043i	−0.0275998	−	0.0478043i
$101$	106.008	−	183.612i	0.104438	−	0.180892i	−0.809070	−	0.587712i	$-0.800029\pi$
$101$	106.008	−	183.612i	0.104438	−	0.180892i	0.913508	+	0.406820i	$0.133362\pi$
$102$	963.246	+	6.57730i	0.935054	+	0.00638480i
$103$	−742.977	+	428.958i	−0.710754	+	0.410354i	−0.811340	−	0.584574i	$-0.801262\pi$
$103$	−742.977	+	428.958i	−0.710754	+	0.410354i	0.100586	+	0.994928i	$0.467928\pi$
$104$	−158.720			−0.149652
$105$	−696.038	+	738.481i	−0.646918	+	0.686366i
$106$	−999.264			−0.915633
$107$	1860.36	−	1074.08i	1.68082	−	0.970424i	0.719708	−	0.694276i	$-0.244275\pi$
$107$	1860.36	−	1074.08i	1.68082	−	0.970424i	0.961115	−	0.276148i	$-0.0890578\pi$
$108$	−480.151	−	290.488i	−0.427801	−	0.258817i
$109$	621.510	−	1076.49i	0.546145	−	0.945952i	−0.452388	−	0.891821i	$-0.649428\pi$
$109$	621.510	−	1076.49i	0.546145	−	0.945952i	0.998534	−	0.0541307i	$-0.0172388\pi$
$110$	−325.013	−	562.938i	−0.281716	−	0.487946i
$111$	−1732.48	+	984.539i	−1.48144	+	0.841877i
$112$	−217.021	−	201.767i	−0.183094	−	0.170225i
$113$			193.701i			0.161256i	0.996744	+	0.0806278i	$0.0256925\pi$
$113$			193.701i			0.161256i	−0.996744	+	0.0806278i	$0.974307\pi$
$114$	−1230.75	−	721.826i	−1.01115	−	0.593028i
$115$	−397.233	−	229.342i	−0.322106	−	0.185968i
$116$	−465.292	−	268.637i	−0.372425	−	0.215020i
$117$	−7.31521	+	535.631i	−0.00578027	+	0.423240i
$118$			1464.85i			1.14280i
$119$	383.654	−	1673.23i	0.295542	−	1.28895i
$120$	216.580	+	381.113i	0.164758	+	0.289922i
$121$	−190.531	−	330.009i	−0.143149	−	0.247941i
$122$	−306.235	+	530.414i	−0.227256	+	0.393618i
$123$	−3.82782	+	560.584i	−0.00280604	+	0.410944i
$124$	579.853	−	334.778i	0.419938	−	0.242451i
$125$	1463.67			1.04731
$126$	−690.903	+	723.077i	−0.488497	+	0.511245i
$127$	1010.51			0.706052			0.353026	−	0.935614i	$-0.385153\pi$
$127$	1010.51			0.706052			0.353026	+	0.935614i	$0.385153\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	10.1288	−	1483.36i	0.00691312	−	1.01243i
$130$	209.216	−	362.373i	0.141150	−	0.244479i
$131$	−179.314	−	310.581i	−0.119593	−	0.207142i	0.800013	−	0.599982i	$-0.204826\pi$
$131$	−179.314	−	310.581i	−0.119593	−	0.207142i	−0.919607	+	0.392841i	$0.871492\pi$
$132$	−316.506	−	556.953i	−0.208700	−	0.367247i
$133$	−1731.35	+	1862.24i	−1.12878	+	1.21411i
$134$			1120.20i			0.722167i
$135$	1296.12	−	713.323i	0.826312	−	0.454763i
$136$	−642.179	−	370.762i	−0.404900	−	0.233769i
$137$	−1194.04	−	689.378i	−0.744625	−	0.429909i	0.0791238	−	0.996865i	$-0.474788\pi$
$137$	−1194.04	−	689.378i	−0.744625	−	0.429909i	−0.823748	+	0.566956i	$0.808121\pi$
$138$	−389.923	−	228.686i	−0.240525	−	0.141066i
$139$		−	474.488i		−	0.289536i	−0.989466	−	0.144768i	$-0.953756\pi$
$139$		−	474.488i		−	0.289536i	0.989466	−	0.144768i	$-0.0462436\pi$
$140$	746.717	−	229.519i	0.450780	−	0.138557i
$141$	−1092.42	+	620.803i	−0.652471	+	0.370787i
$142$	74.2161	+	128.546i	0.0438597	+	0.0759672i
$143$	−305.746	+	529.567i	−0.178795	+	0.309683i
$144$	210.871	+	377.038i	0.122032	+	0.218193i
$145$	1226.64	−	708.203i	0.702533	−	0.405607i
$146$	326.570			0.185117
$147$	990.974	+	1481.38i	0.556015	+	0.831173i
$148$	1533.97			0.851972
$149$	−519.125	+	299.717i	−0.285426	+	0.164791i	−0.635877	−	0.771790i	$-0.719361\pi$
$149$	−519.125	+	299.717i	−0.285426	+	0.164791i	0.350451	+	0.936581i	$0.386028\pi$
$150$	143.409	+	0.979238i	0.0780622	+	0.000533030i
$151$	997.588	−	1727.87i	0.537633	−	0.931208i	−0.461398	−	0.887193i	$-0.652652\pi$
$151$	997.588	−	1727.87i	0.537633	−	0.931208i	0.999031	−	0.0440145i	$-0.0140148\pi$
$152$	549.180	+	951.207i	0.293055	+	0.507586i
$153$	−1280.80	+	2150.06i	−0.676776	+	1.13609i
$154$	−1091.24	+	335.417i	−0.571006	+	0.175511i
$155$			1765.14i			0.914707i
$156$	208.617	−	355.705i	0.107069	−	0.182559i
$157$	−765.966	−	442.231i	−0.389368	−	0.224802i	0.292518	−	0.956260i	$-0.405507\pi$
$157$	−765.966	−	442.231i	−0.389368	−	0.224802i	−0.681886	+	0.731458i	$0.738840\pi$
$158$	−1514.37	−	874.320i	−0.762510	−	0.440235i
$159$	1313.40	−	2239.43i	0.655093	−	1.11697i
$160$		−	337.445i		−	0.166733i
$161$	−548.520	+	589.988i	−0.268506	+	0.288805i
$162$	1282.10	−	694.246i	0.621799	−	0.336698i
$163$	338.492	+	586.286i	0.162655	+	0.281727i	0.935820	−	0.352478i	$-0.114661\pi$
$163$	338.492	+	586.286i	0.162655	+	0.281727i	−0.773165	+	0.634205i	$0.781328\pi$
$164$	215.774	−	373.731i	0.102739	−	0.177948i
$165$	1688.78	+	11.5314i	0.796794	+	0.00544072i
$166$	704.251	−	406.600i	0.329280	−	0.190110i
$167$	−3718.74			−1.72314			−0.861571	−	0.507637i	$-0.830519\pi$
$167$	−3718.74			−1.72314			−0.861571	+	0.507637i	$0.830519\pi$
$168$	737.422	−	221.163i	0.338651	−	0.101566i
$169$	1803.37			0.820834
$170$	1692.97	−	977.435i	0.763792	−	0.440976i
$171$	3235.34	−	1809.47i	1.44686	−	0.809202i
$172$	−570.961	+	988.933i	−0.253112	+	0.438404i
$173$	1318.97	+	2284.52i	0.579650	+	1.00398i	0.995519	+	0.0945591i	$0.0301441\pi$
$173$	1318.97	+	2284.52i	0.579650	+	1.00398i	−0.415869	+	0.909425i	$0.636523\pi$
$174$	1213.60	−	689.668i	0.528753	−	0.300480i
$175$	57.1190	−	249.113i	0.0246731	−	0.107607i
$176$			493.137i			0.211202i
$177$	−3282.84	−	1925.36i	−1.39409	−	0.817619i
$178$	1822.43	+	1052.18i	0.767399	+	0.443058i
$179$	2861.56	+	1652.12i	1.19488	+	0.689862i	0.959409	−	0.282020i	$-0.0910044\pi$
$179$	2861.56	+	1652.12i	1.19488	+	0.689862i	0.235468	+	0.971882i	$0.424338\pi$
$180$	−1138.77	−	15.5524i	−0.471549	−	0.00644003i
$181$			417.941i			0.171631i	0.996311	+	0.0858157i	$0.0273496\pi$
$181$			417.941i			0.171631i	−0.996311	+	0.0858157i	$0.972650\pi$
$182$	−538.212	−	500.384i	−0.219203	−	0.203796i
$183$	−786.193	−	1383.46i	−0.317580	−	0.558842i
$184$	173.989	+	301.358i	0.0697100	+	0.120741i
$185$	−2022.00	+	3502.20i	−0.803569	+	1.39182i
$186$	−11.8779	+	1739.52i	−0.00468242	+	0.685740i
$187$	−2474.08	+	1428.41i	−0.967501	+	0.558587i
$188$	967.250			0.375234
$189$	−712.368	−	2498.76i	−0.274165	−	0.961683i
$190$	−2895.59			−1.10562
$191$	−920.494	+	531.447i	−0.348715	+	0.201331i	−0.664119	−	0.747627i	$-0.731193\pi$
$191$	−920.494	+	531.447i	−0.348715	+	0.201331i	0.315404	+	0.948957i	$0.397860\pi$
$192$	2.27071	−	332.546i	0.000853514	−	0.124997i
$193$	−1945.03	+	3368.89i	−0.725420	+	1.25646i	0.233380	+	0.972386i	$0.425021\pi$
$193$	−1945.03	+	3368.89i	−0.725420	+	1.25646i	−0.958801	+	0.284079i	$0.908312\pi$
$194$	243.235	+	421.295i	0.0900167	+	0.155914i
$195$	537.118	+	945.162i	0.197250	+	0.347100i
$196$	−99.8105	−	1368.36i	−0.0363741	−	0.498675i
$197$		−	3227.57i		−	1.16728i	−0.812011	−	0.583642i	$-0.801627\pi$
$197$		−	3227.57i		−	1.16728i	0.812011	−	0.583642i	$-0.198373\pi$
$198$	1664.18	+	22.7280i	0.597315	+	0.00815763i
$199$	−2398.78	−	1384.94i	−0.854497	−	0.493344i	0.00766855	−	0.999971i	$-0.497559\pi$
$199$	−2398.78	−	1384.94i	−0.854497	−	0.493344i	−0.862166	+	0.506626i	$0.830892\pi$
$200$	−95.6085	−	55.1996i	−0.0338027	−	0.0195160i
$201$	−2510.45	−	1472.36i	−0.880963	−	0.516676i
$202$		−	424.034i		−	0.147698i
$203$	−730.874	−	2377.82i	−0.252696	−	0.822119i
$204$	1674.97	−	951.854i	0.574859	−	0.326682i
$205$	568.842	+	985.263i	0.193803	+	0.335677i
$206$	−857.916	+	1485.95i	−0.290164	+	0.502579i
$207$	1025.01	−	573.269i	0.344169	−	0.192488i
$208$	−274.912	+	158.720i	−0.0916428	+	0.0529100i
$209$	4231.58			1.40050
$210$	−467.093	+	1975.13i	−0.153488	+	0.649031i
$211$	−1978.76			−0.645610			−0.322805	−	0.946465i	$-0.604626\pi$
$211$	−1978.76			−0.645610			−0.322805	+	0.946465i	$0.604626\pi$
$212$	−1730.78	+	999.264i	−0.560709	+	0.323725i
$213$	−385.629	−	2.63318i	−0.124051	−	0.000847053i
$214$	2148.16	−	3720.73i	0.686193	−	1.18852i
$215$	−1505.22	−	2607.11i	−0.477464	−	0.826993i
$216$	−1122.13	−	22.9895i	−0.353479	−	0.00724185i
$217$	3021.68	+	692.838i	0.945275	+	0.216741i
$218$		−	2486.04i		−	0.772366i
$219$	−429.235	+	731.869i	−0.132443	+	0.225823i
$220$	−1125.88	−	650.025i	−0.345030	−	0.199203i
$221$	−1592.61	−	919.492i	−0.484753	−	0.279872i
$222$	−2016.21	+	3437.76i	−0.609546	+	1.03931i
$223$		−	2434.70i		−	0.731120i	−0.930788	−	0.365560i	$-0.880878\pi$
$223$		−	2434.70i		−	0.731120i	0.930788	−	0.365560i	$-0.119122\pi$
$224$	−577.658	−	132.451i	−0.172305	−	0.0395077i
$225$	−190.688	+	320.105i	−0.0565001	+	0.0948458i
$226$	193.701	+	335.500i	0.0570125	+	0.0987485i
$227$	165.862	−	287.281i	0.0484961	−	0.0839977i	−0.840758	−	0.541411i	$-0.817890\pi$
$227$	165.862	−	287.281i	0.0484961	−	0.0839977i	0.889254	+	0.457413i	$0.151224\pi$
$228$	−2853.55	−	19.4848i	−0.828865	−	0.00565971i
$229$	1842.29	−	1063.65i	0.531624	−	0.306933i	−0.210054	−	0.977690i	$-0.567364\pi$
$229$	1842.29	−	1063.65i	0.531624	−	0.306933i	0.741677	+	0.670757i	$0.234031\pi$
$230$	−917.370			−0.262998
$231$	682.603	−	2886.42i	0.194424	−	0.822132i
$232$	−1074.55			−0.304084
$233$	−809.394	+	467.304i	−0.227576	+	0.131391i	−0.609453	−	0.792822i	$-0.708611\pi$
$233$	−809.394	+	467.304i	−0.227576	+	0.131391i	0.381877	+	0.924213i	$0.375278\pi$
$234$	522.961	+	935.056i	0.146098	+	0.261224i
$235$	−1274.97	+	2208.32i	−0.353915	+	0.613000i
$236$	1464.85	+	2537.19i	0.404041	+	0.699819i
$237$	3949.86	−	2244.63i	1.08258	−	0.615209i
$238$	−1008.72	−	3281.78i	−0.274731	−	0.893807i
$239$			1923.73i			0.520651i	0.965521	+	0.260325i	$0.0838298\pi$
$239$			1923.73i			0.520651i	−0.965521	+	0.260325i	$0.916170\pi$
$240$	756.240	+	443.527i	0.203396	+	0.119290i
$241$	2846.13	+	1643.22i	0.760729	+	0.439207i	0.829557	−	0.558422i	$-0.188593\pi$
$241$	2846.13	+	1643.22i	0.760729	+	0.439207i	−0.0688286	+	0.997629i	$0.521926\pi$
$242$	−660.018	−	381.062i	−0.175321	−	0.101221i
$243$	−129.300	+	3785.79i	−0.0341342	+	0.999417i
$244$			1224.94i			0.321388i
$245$	3255.67	+	1575.82i	0.848967	+	0.410921i
$246$	553.954	+	974.788i	0.143572	+	0.252643i
$247$	1361.97	+	2359.00i	0.350850	+	0.607690i
$248$	669.556	−	1159.71i	0.171439	−	0.296941i
$249$	−14.4261	+	2112.70i	−0.00367156	+	0.537700i
$250$	2535.14	−	1463.67i	0.641346	−	0.370281i
$251$	4303.94			1.08232			0.541160	−	0.840919i	$-0.317985\pi$
$251$	4303.94			1.08232			0.541160	+	0.840919i	$0.317985\pi$
$252$	−473.603	+	1943.31i	−0.118390	+	0.485782i
$253$	1340.63			0.333142
$254$	1750.26	−	1010.51i	0.432366	−	0.249627i
$255$	−34.6793	+	5078.78i	−0.00851648	+	1.24724i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2345.95	−	4063.31i	−0.569403	−	0.986235i	−0.996625	−	0.0820884i	$-0.973841\pi$
$257$	−2345.95	−	4063.31i	−0.569403	−	0.986235i	0.427222	−	0.904147i	$-0.359492\pi$
$258$	−1465.82	−	2579.39i	−0.353713	−	0.622426i
$259$	5201.63	+	4836.03i	1.24793	+	1.16022i
$260$		−	836.865i		−	0.199616i
$261$	−49.5244	+	3626.26i	−0.0117451	+	0.859999i
$262$	−621.162	−	358.628i	−0.146471	−	0.0845653i
$263$	911.918	+	526.496i	0.213807	+	0.123442i	0.603079	−	0.797681i	$-0.293940\pi$
$263$	911.918	+	526.496i	0.213807	+	0.123442i	−0.389272	+	0.921123i	$0.627274\pi$
$264$	−1105.16	−	648.165i	−0.257643	−	0.151105i
$265$		−	5268.69i		−	1.22133i
$266$	−1136.55	+	4956.84i	−0.261979	+	1.14257i
$267$	−4753.37	+	2701.25i	−1.08952	+	0.619154i
$268$	1120.20	+	1940.24i	0.255325	+	0.442235i
$269$	1327.49	−	2299.28i	0.300887	−	0.521151i	−0.675450	−	0.737405i	$-0.736051\pi$
$269$	1327.49	−	2299.28i	0.300887	−	0.521151i	0.976337	+	0.216255i	$0.0693841\pi$
$270$	1531.62	−	2531.63i	0.345227	−	0.570630i
$271$	2347.45	−	1355.30i	0.526189	−	0.303795i	−0.213274	−	0.976992i	$-0.568413\pi$
$271$	2347.45	−	1355.30i	0.526189	−	0.303795i	0.739463	+	0.673197i	$0.235079\pi$
$272$	−1483.05			−0.330599
$273$	1828.81	−	548.485i	0.405438	−	0.121596i
$274$	−2757.51			−0.607983
$275$	−368.345	+	212.664i	−0.0807710	+	0.0466331i
$276$	−904.052	−	6.17311i	−0.197165	−	0.00134630i
$277$	−960.218	+	1663.15i	−0.208281	+	0.360754i	−0.951173	−	0.308658i	$-0.900120\pi$
$277$	−960.218	+	1663.15i	−0.208281	+	0.360754i	0.742892	+	0.669411i	$0.233454\pi$
$278$	−474.488	−	821.837i	−0.102367	−	0.177304i
$279$	−3882.78	−	2312.99i	−0.833176	−	0.496327i
$280$	1063.83	−	1144.26i	0.227058	−	0.244223i
$281$		−	5730.99i		−	1.21666i	−0.793683	−	0.608331i	$-0.791839\pi$
$281$		−	5730.99i		−	1.21666i	0.793683	−	0.608331i	$-0.208161\pi$
$282$	−1271.33	+	2167.68i	−0.268462	+	0.457743i
$283$	−1588.75	−	917.265i	−0.333715	−	0.192670i	0.323774	−	0.946134i	$-0.395048\pi$
$283$	−1588.75	−	917.265i	−0.333715	−	0.192670i	−0.657489	+	0.753464i	$0.728381\pi$
$284$	257.092	+	148.432i	0.0537169	+	0.0310135i
$285$	3805.88	−	6489.24i	0.791020	−	1.34873i
$286$			1222.98i			0.252855i
$287$	1909.91	−	587.051i	0.392817	−	0.120741i
$288$	742.277	+	442.178i	0.151872	+	0.0904707i
$289$	−1839.27	−	3185.71i	−0.374368	−	0.648424i
$290$	1416.41	−	2453.29i	0.286808	−	0.496766i
$291$	−1263.86	−	8.62995i	−0.254600	−	0.00173848i
$292$	565.636	−	326.570i	0.113361	−	0.0654489i
$293$	−1206.83			−0.240627			−0.120314	−	0.992736i	$-0.538390\pi$
$293$	−1206.83			−0.240627			−0.120314	+	0.992736i	$0.538390\pi$
$294$	3197.80	+	1574.86i	0.634352	+	0.312406i
$295$	−7723.53			−1.52434
$296$	2656.92	−	1533.97i	0.521724	−	0.301218i
$297$	−2238.29	+	3699.69i	−0.437302	+	0.722821i
$298$	−599.434	+	1038.25i	−0.116525	+	0.201826i
$299$	431.494	+	747.369i	0.0834580	+	0.144553i
$300$	249.372	−	141.713i	0.0479916	−	0.0272728i
$301$	−5053.82	+	1553.40i	−0.967765	+	0.297463i
$302$		−	3990.35i		−	0.760328i
$303$	950.293	+	557.338i	0.180175	+	0.105671i
$304$	1902.41	+	1098.36i	0.358917	+	0.207221i
$305$	−2796.65	−	1614.65i	−0.525035	−	0.303129i
$306$	−68.3517	+	5004.82i	−0.0127693	+	0.934989i
$307$		−	5508.71i		−	1.02410i	−0.858955	−	0.512050i	$-0.828886\pi$
$307$		−	5508.71i		−	1.02410i	0.858955	−	0.512050i	$-0.171114\pi$
$308$	−1554.67	+	1672.20i	−0.287616	+	0.309359i
$309$	−2202.52	−	3875.75i	−0.405491	−	0.713539i
$310$	1765.14	+	3057.32i	0.323398	+	0.560142i
$311$	2114.51	−	3662.44i	0.385540	−	0.667775i	−0.606304	−	0.795233i	$-0.707348\pi$
$311$	2114.51	−	3662.44i	0.385540	−	0.667775i	0.991844	+	0.127458i	$0.0406817\pi$
$312$	5.63138	−	824.716i	0.00102184	−	0.149649i
$313$	−4672.64	+	2697.75i	−0.843813	+	0.487176i	−0.858558	−	0.512716i	$-0.828640\pi$
$313$	−4672.64	+	2697.75i	−0.843813	+	0.487176i	0.0147455	+	0.999891i	$0.495306\pi$
$314$	−1768.92			−0.317917
$315$	−3812.48	−	3642.84i	−0.681932	−	0.651590i
$316$	−3497.28			−0.622586
$317$	−6169.57	+	3562.00i	−1.09312	+	0.631111i	−0.934404	−	0.356214i	$-0.884067\pi$
$317$	−6169.57	+	3562.00i	−1.09312	+	0.631111i	−0.158711	+	0.987325i	$0.550734\pi$
$318$	35.4538	−	5192.21i	0.00625204	−	0.915612i
$319$	−2069.92	+	3585.20i	−0.363301	+	0.629256i
$320$	−337.445	−	584.471i	−0.0589492	−	0.102103i
$321$	5514.96	+	9704.62i	0.958925	+	1.68741i
$322$	−360.078	+	1570.41i	−0.0623178	+	0.271787i
$323$			12725.9i			2.19223i
$324$	1526.42	−	2484.57i	0.261732	−	0.426024i
$325$	−237.110	−	136.895i	−0.0404692	−	0.0233649i
$326$	1172.57	+	676.984i	0.199211	+	0.115014i
$327$	5571.41	+	3267.58i	0.942200	+	0.552592i
$328$		−	863.096i		−	0.145294i
$329$	3279.89	+	3049.37i	0.549624	+	0.510994i
$330$	2936.58	−	1668.80i	0.489858	−	0.278377i
$331$	−886.224	−	1534.99i	−0.147164	−	0.254896i	0.783014	−	0.622004i	$-0.213681\pi$
$331$	−886.224	−	1534.99i	−0.147164	−	0.254896i	−0.930178	+	0.367108i	$0.880348\pi$
$332$	813.199	−	1408.50i	0.134428	−	0.232836i
$333$	−5054.23	−	9036.97i	−0.831741	−	1.48716i
$334$	−6441.05	+	3718.74i	−1.05520	+	0.609223i
$335$	−5906.32			−0.963275
$336$	1056.09	−	1120.49i	0.171471	−	0.181927i
$337$	7800.94			1.26096			0.630481	−	0.776205i	$-0.282858\pi$
$337$	7800.94			1.26096			0.630481	+	0.776205i	$0.282858\pi$
$338$	3123.53	−	1803.37i	0.502656	−	0.290209i
$339$	−1006.48	−	6.87250i	−0.161252	−	0.00110107i
$340$	1954.87	−	3385.94i	0.311817	−	0.540083i
$341$	−2579.56	−	4467.92i	−0.409650	−	0.709535i
$342$	3794.30	−	6369.43i	0.599918	−	1.00707i
$343$	3975.47	−	4954.72i	0.625818	−	0.779969i
$344$			2283.84i			0.357955i
$345$	1205.76	−	2055.90i	0.188163	−	0.320828i
$346$	4569.05	+	2637.94i	0.709924	+	0.409875i
$347$	6209.38	+	3584.99i	0.960625	+	0.554617i	0.896365	−	0.443316i	$-0.146198\pi$
$347$	6209.38	+	3584.99i	0.960625	+	0.554617i	0.0642596	+	0.997933i	$0.479531\pi$
$348$	1412.35	−	2408.14i	0.217558	−	0.370948i
$349$			5543.44i			0.850240i	0.905137	+	0.425120i	$0.139768\pi$
$349$			5543.44i			0.850240i	−0.905137	+	0.425120i	$0.860232\pi$
$350$	−150.180	−	488.596i	−0.0229356	−	0.0746187i
$351$	−2782.90	−	57.0142i	−0.423191	−	0.00867006i
$352$	493.137	+	854.138i	0.0746713	+	0.129334i
$353$	−15.4669	+	26.7895i	−0.00233207	+	0.00403926i	−0.867189	−	0.497979i	$-0.834076\pi$
$353$	−15.4669	+	26.7895i	−0.00233207	+	0.00403926i	0.864857	+	0.502018i	$0.167409\pi$
$354$	−7611.41	−	51.9727i	−1.14277	−	0.00780316i
$355$	−677.768	+	391.310i	−0.101330	+	0.0585030i
$356$	4208.72			0.626579
$357$	8680.56	+	2052.84i	1.28690	+	0.304336i
$358$	6608.48			0.975612
$359$	−5694.34	+	3287.63i	−0.837147	+	0.483327i	−0.856294	−	0.516489i	$-0.827239\pi$
$359$	−5694.34	+	3287.63i	−0.837147	+	0.483327i	0.0191462	+	0.999817i	$0.493905\pi$
$360$	−1987.96	+	1111.83i	−0.291041	+	0.162774i
$361$	5995.44	−	10384.4i	0.874099	−	1.51398i
$362$	417.941	+	723.895i	0.0606809	+	0.105102i
$363$	1721.50	−	978.296i	0.248912	−	0.141452i
$364$	−1432.60	−	328.478i	−0.206287	−	0.0472993i
$365$			1721.87i			0.246922i
$366$	−2745.18	−	1610.02i	−0.392058	−	0.229938i
$367$	2095.30	+	1209.72i	0.298021	+	0.172062i	0.641553	−	0.767078i	$-0.278290\pi$
$367$	2095.30	+	1209.72i	0.298021	+	0.172062i	−0.343533	+	0.939141i	$0.611624\pi$
$368$	602.716	+	347.978i	0.0853770	+	0.0492924i
$369$	−2912.68	−	39.7789i	−0.410916	−	0.00561195i
$370$			8087.99i			1.13642i
$371$	−9019.27	−	2068.02i	−1.26215	−	0.289397i
$372$	1718.94	+	3024.81i	0.239578	+	0.421584i
$373$	−4895.66	−	8479.53i	−0.679591	−	1.17709i	−0.975104	−	0.221748i	$-0.928824\pi$
$373$	−4895.66	−	8479.53i	−0.679591	−	1.17709i	0.295513	−	0.955339i	$-0.404510\pi$
$374$	−2856.82	+	4948.16i	−0.394981	+	0.684126i
$375$	−51.9307	+	7605.25i	−0.00715117	+	1.04729i
$376$	1675.33	−	967.250i	0.229783	−	0.132665i
$377$	−2664.88			−0.364054
$378$	−3732.62	−	3615.61i	−0.507897	−	0.491976i
$379$	12660.9			1.71595			0.857977	−	0.513689i	$-0.171721\pi$
$379$	12660.9			1.71595			0.857977	+	0.513689i	$0.171721\pi$
$380$	−5015.31	+	2895.59i	−0.677052	+	0.390896i
$381$	−35.8529	+	5250.66i	−0.00482100	+	0.706035i
$382$	−1062.89	+	1840.99i	−0.142362	+	0.246579i
$383$	4549.42	+	7879.82i	0.606957	+	1.05128i	0.991739	+	0.128272i	$0.0409431\pi$
$383$	4549.42	+	7879.82i	0.606957	+	1.05128i	−0.384782	+	0.923007i	$0.625724\pi$
$384$	−328.613	−	578.257i	−0.0436705	−	0.0768465i
$385$	−1768.51	−	5753.66i	−0.234108	−	0.761645i
$386$			7780.11i			1.02590i
$387$	7707.25	+	105.259i	1.01236	+	0.0138259i
$388$	842.590	+	486.470i	0.110248	+	0.0636514i
$389$	8450.00	+	4878.61i	1.10137	+	0.635875i	0.936580	−	0.350454i	$-0.113973\pi$
$389$	8450.00	+	4878.61i	1.10137	+	0.635875i	0.164787	+	0.986329i	$0.447306\pi$
$390$	1875.48	+	1099.95i	0.243509	+	0.142816i
$391$			4031.78i			0.521473i
$392$	−1541.24	−	2270.27i	−0.198583	−	0.292515i
$393$	1620.15	−	920.701i	0.207954	−	0.118176i
$394$	−3227.57	−	5590.32i	−0.412697	−	0.714813i
$395$	4609.91	−	7984.61i	0.587215	−	1.01709i
$396$	2905.18	−	1624.82i	0.368663	−	0.206187i
$397$	−7069.17	+	4081.39i	−0.893681	+	0.515967i	−0.875145	−	0.483861i	$-0.839234\pi$
$397$	−7069.17	+	4081.39i	−0.893681	+	0.515967i	−0.0185365	+	0.999828i	$0.505901\pi$
$398$	−5539.74			−0.697694
$399$	−9614.82	−	9062.23i	−1.20637	−	1.13704i
$400$	−220.798			−0.0275998
$401$	8885.22	−	5129.88i	1.10650	−	0.638838i	0.168579	−	0.985688i	$-0.446082\pi$
$401$	8885.22	−	5129.88i	1.10650	−	0.638838i	0.937921	+	0.346850i	$0.112749\pi$
$402$	−5820.58	−	39.7445i	−0.722150	−	0.00493103i
$403$	1660.50	−	2876.08i	0.205250	−	0.355503i
$404$	−424.034	−	734.448i	−0.0522190	−	0.0904459i
$405$	3660.46	+	6759.98i	0.449111	+	0.829398i
$406$	−3643.73	−	3387.63i	−0.445407	−	0.414102i
$407$		−	11819.7i		−	1.43951i
$408$	1949.28	−	3323.63i	0.236528	−	0.403294i
$409$	−1795.47	−	1036.61i	−0.217067	−	0.125323i	0.387525	−	0.921859i	$-0.373330\pi$
$409$	−1795.47	−	1036.61i	−0.217067	−	0.125323i	−0.604591	+	0.796536i	$0.706664\pi$
$410$	1970.53	+	1137.68i	0.237359	+	0.137040i
$411$	3624.40	−	6179.80i	0.434984	−	0.741672i
$412$			3431.66i			0.410354i
$413$	−3031.57	+	13221.6i	−0.361196	+	1.57528i
$414$	1202.09	−	2017.94i	0.142705	−	0.239556i
$415$	2143.83	+	3713.22i	0.253581	+	0.439216i
$416$	−317.441	+	549.823i	−0.0374130	+	0.0648012i
$417$	2465.45	+	16.8348i	0.289530	+	0.00197699i
$418$	7329.30	−	4231.58i	0.857627	−	0.495151i
$419$	−11576.2			−1.34973			−0.674863	−	0.737943i	$-0.735797\pi$
$419$	−11576.2			−1.34973			−0.674863	+	0.737943i	$0.735797\pi$
$420$	1166.10	+	3888.11i	0.135475	+	0.451715i
$421$	−1493.04			−0.172842			−0.0864208	−	0.996259i	$-0.527543\pi$
$421$	−1493.04			−0.172842			−0.0864208	+	0.996259i	$0.527543\pi$
$422$	−3427.32	+	1978.76i	−0.395354	+	0.228258i
$423$	−3186.95	−	5698.28i	−0.366324	−	0.654988i
$424$	−1998.53	+	3461.55i	−0.228908	+	0.396481i
$425$	−639.560	−	1107.75i	−0.0729958	−	0.126432i
$426$	−670.562	+	381.068i	−0.0762649	+	0.0433399i
$427$	−3861.76	+	4153.70i	−0.437667	+	0.470754i
$428$		−	8592.65i		−	0.970424i
$429$	−2740.80	−	1607.45i	−0.308455	−	0.180906i
$430$	−5214.22	−	3010.43i	−0.584772	−	0.337618i
$431$	3354.19	+	1936.54i	0.374862	+	0.216427i	0.675580	−	0.737286i	$-0.263893\pi$
$431$	3354.19	+	1936.54i	0.374862	+	0.216427i	−0.300719	+	0.953713i	$0.597226\pi$
$432$	−1966.58	+	1082.31i	−0.219021	+	0.120539i
$433$			5450.01i			0.604875i	0.953169	+	0.302437i	$0.0978003\pi$
$433$			5450.01i			0.604875i	−0.953169	+	0.302437i	$0.902200\pi$
$434$	5926.53	−	1821.65i	0.655490	−	0.201479i
$435$	3636.32	+	6398.81i	0.400801	+	0.705286i
$436$	−2486.04	−	4305.95i	−0.273073	−	0.472976i
$437$	2985.98	−	5171.86i	0.326862	−	0.566141i
$438$	−11.5867	+	1696.87i	−0.00126400	+	0.185113i
$439$	−2350.20	+	1356.89i	−0.255510	+	0.147519i	−0.622284	−	0.782791i	$-0.713795\pi$
$439$	−2350.20	+	1356.89i	−0.255510	+	0.147519i	0.366775	+	0.930310i	$0.380462\pi$
$440$	−2600.10			−0.281716
$441$	−7732.47	+	5096.57i	−0.834950	+	0.550326i
$442$	−3677.97			−0.395799
$443$	9583.65	−	5533.13i	1.02784	−	0.593424i	0.111475	−	0.993767i	$-0.464443\pi$
$443$	9583.65	−	5533.13i	1.02784	−	0.593424i	0.916365	+	0.400344i	$0.131109\pi$
$444$	−54.4252	+	7970.58i	−0.00581736	+	0.851953i
$445$	−5547.70	+	9608.90i	−0.590980	+	1.02361i
$446$	−2434.70	−	4217.03i	−0.258490	−	0.447718i
$447$	−1538.92	−	2708.03i	−0.162838	−	0.286544i
$448$	−1132.98	+	348.247i	−0.119483	+	0.0367257i
$449$		−	3599.14i		−	0.378294i	−0.981949	−	0.189147i	$-0.939428\pi$
$449$		−	3599.14i		−	0.378294i	0.981949	−	0.189147i	$-0.0605722\pi$
$450$	−10.1763	+	745.125i	−0.00106603	+	0.0780568i
$451$	−2879.70	−	1662.60i	−0.300665	−	0.173589i
$452$	671.001	+	387.402i	0.0698257	+	0.0403139i
$453$	8942.69	+	5244.81i	0.927515	+	0.543979i
$454$		−	663.446i		−	0.0685839i
$455$	2638.31	−	2837.76i	0.271837	−	0.292388i
$456$	−4961.99	+	2819.81i	−0.509575	+	0.289582i
$457$	−4157.54	−	7201.08i	−0.425562	−	0.737094i	0.570911	−	0.821012i	$-0.306590\pi$
$457$	−4157.54	−	7201.08i	−0.425562	−	0.737094i	−0.996473	+	0.0839176i	$0.973257\pi$
$458$	2127.29	−	3684.58i	0.217035	−	0.375915i
$459$	−11126.4	−	6731.38i	−1.13145	−	0.684518i
$460$	−1588.93	+	917.370i	−0.161053	+	0.0929839i
$461$	−5672.08			−0.573048			−0.286524	−	0.958073i	$-0.592500\pi$
$461$	−5672.08			−0.573048			−0.286524	+	0.958073i	$0.592500\pi$
$462$	−1704.12	−	5682.03i	−0.171608	−	0.572191i
$463$	6332.06			0.635585			0.317792	−	0.948160i	$-0.397058\pi$
$463$	6332.06			0.635585			0.317792	+	0.948160i	$0.397058\pi$
$464$	−1861.17	+	1074.55i	−0.186213	+	0.107510i
$465$	−9171.73	−	62.6271i	−0.914686	−	0.00624572i
$466$	−934.608	+	1618.79i	−0.0929074	+	0.160920i
$467$	−6469.64	−	11205.7i	−0.641069	−	1.11036i	−0.985195	−	0.171440i	$-0.945158\pi$
$467$	−6469.64	−	11205.7i	−0.641069	−	1.11036i	0.344126	−	0.938924i	$-0.388175\pi$
$468$	1840.85	+	1096.60i	0.181823	+	0.108313i
$469$	−2318.30	+	10110.8i	−0.228249	+	0.995466i
$470$			5099.90i			0.500512i
$471$	2325.02	−	3964.29i	0.227455	−	0.387824i
$472$	5074.39	+	2929.70i	0.494847	+	0.285700i
$473$	7619.99	+	4399.40i	0.740735	+	0.427663i
$474$	4596.72	−	7837.67i	0.445431	−	0.759486i
$475$			1894.66i			0.183016i
$476$	−5028.94	−	4675.48i	−0.484246	−	0.450211i
$477$	11589.5	+	6903.94i	1.11247	+	0.662704i
$478$	1923.73	+	3331.99i	0.184078	+	0.318832i
$479$	−1051.99	+	1822.10i	−0.100348	+	0.173808i	−0.911828	−	0.410572i	$-0.865329\pi$
$479$	−1051.99	+	1822.10i	−0.100348	+	0.173808i	0.811480	+	0.584380i	$0.198662\pi$
$480$	1753.37	+	11.9725i	0.166730	+	0.00113847i
$481$	6589.18	−	3804.26i	0.624617	−	0.360623i
$482$	6572.87			0.621132
$483$	−3046.13	−	2871.06i	−0.286964	−	0.270472i
$484$	−1524.25			−0.143149
$485$	−2221.31	+	1282.47i	−0.207968	+	0.120070i
$486$	3561.83	+	6686.48i	0.332445	+	0.624084i
$487$	6295.98	−	10905.0i	0.585828	−	1.01468i	−0.408944	−	0.912559i	$-0.634103\pi$
$487$	6295.98	−	10905.0i	0.585828	−	1.01468i	0.994772	−	0.102124i	$-0.0325638\pi$
$488$	1224.94	+	2121.66i	0.113628	+	0.196809i
$489$	−3058.37	+	1738.01i	−0.282831	+	0.160727i
$490$	7214.80	−	526.258i	0.665166	−	0.0485182i
$491$			1372.36i			0.126138i	0.998009	+	0.0630689i	$0.0200888\pi$
$491$			1372.36i			0.126138i	−0.998009	+	0.0630689i	$0.979911\pi$
$492$	1934.26	+	1134.43i	0.177243	+	0.103951i
$493$	−10782.0	−	6225.02i	−0.984988	−	0.568683i
$494$	4718.00	+	2723.94i	0.429702	+	0.248088i
$495$	−119.835	+	8774.52i	−0.0108812	+	0.796738i
$496$		−	2678.23i		−	0.242451i
$497$	403.836	+	1313.84i	0.0364477	+	0.118579i
$498$	2087.72	+	3673.74i	0.187857	+	0.330570i
$499$	4588.75	+	7947.95i	0.411665	+	0.713025i	0.995072	−	0.0991554i	$-0.0316141\pi$
$499$	4588.75	+	7947.95i	0.411665	+	0.713025i	−0.583407	+	0.812180i	$0.698281\pi$
$500$	2927.33	−	5070.28i	0.261828	−	0.453500i
$501$	131.941	−	19322.7i	0.0117658	−	1.72310i
$502$	7454.65	−	4303.94i	0.662783	−	0.382658i
$503$	−1025.01			−0.0908605			−0.0454302	−	0.998968i	$-0.514466\pi$
$503$	−1025.01			−0.0908605			−0.0454302	+	0.998968i	$0.514466\pi$
$504$	1123.01	+	3839.51i	0.0992512	+	0.339336i
$505$	2235.75			0.197009
$506$	2322.04	−	1340.63i	0.204007	−	0.117783i
$507$	−63.9835	+	9370.38i	−0.00560474	+	0.820815i
$508$	2021.03	−	3500.52i	0.176513	−	0.305729i
$509$	2308.88	+	3999.09i	0.201059	+	0.348245i	0.948870	−	0.315667i	$-0.102228\pi$
$509$	2308.88	+	3999.09i	0.201059	+	0.348245i	−0.747811	+	0.663912i	$0.768895\pi$
$510$	5018.72	+	8831.39i	0.435750	+	0.766785i
$511$	2947.59	+	675.851i	0.255174	+	0.0585086i
$512$			512.000i			0.0441942i
$513$	9287.27	+	16875.1i	0.799304	+	1.45235i
$514$	−8126.62	−	4691.91i	−0.697374	−	0.402629i
$515$	−7834.80	−	4523.42i	−0.670374	−	0.387040i
$516$	−5118.27	−	3001.82i	−0.436665	−	0.256100i
$517$		−	7452.92i		−	0.634002i
$518$	13845.5	+	3174.62i	1.17440	+	0.269276i
$519$	−11917.3	+	6772.36i	−1.00792	+	0.572781i
$520$	−836.865	−	1449.49i	−0.0705749	−	0.122239i
$521$	−6012.38	+	10413.7i	−0.505580	+	0.875690i	0.494399	+	0.869235i	$0.335388\pi$
$521$	−6012.38	+	10413.7i	−0.505580	+	0.875690i	−0.999979	+	0.00645499i	$0.997945\pi$
$522$	3540.48	+	6330.39i	0.296863	+	0.530792i
$523$	2045.16	−	1180.78i	0.170992	−	0.0987222i	−0.412062	−	0.911156i	$-0.635191\pi$
$523$	2045.16	−	1180.78i	0.170992	−	0.0987222i	0.583053	+	0.812434i	$0.301858\pi$
$524$	−1434.51			−0.119593
$525$	1292.37	+	305.630i	0.107436	+	0.0254073i
$526$	2105.98			0.174573
$527$	13436.7	−	7757.69i	1.11065	−	0.641234i
$528$	−2562.36	−	17.4964i	−0.211197	−	0.00144211i
$529$	−5137.49	+	8898.40i	−0.422248	+	0.731355i
$530$	−5268.69	−	9125.65i	−0.431807	−	0.747911i
$531$	10120.7	−	16989.4i	0.827119	−	1.38847i
$532$	2988.28	+	9722.06i	0.243531	+	0.792302i
$533$		−	2140.48i		−	0.173949i
$534$	−5531.83	+	9432.08i	−0.448287	+	0.764356i
$535$	19617.8	+	11326.3i	1.58533	+	0.915291i
$536$	3880.48	+	2240.40i	0.312707	+	0.180542i
$537$	−8686.00	+	14810.1i	−0.698005	+	1.19014i
$538$		−	5309.96i		−	0.425518i
$539$	−10543.6	+	769.067i	−0.842571	+	0.0614583i
$540$	121.214	−	5916.53i	0.00965967	−	0.471494i
$541$	1479.47	+	2562.52i	0.117574	+	0.203644i	0.918806	−	0.394710i	$-0.129155\pi$
$541$	1479.47	+	2562.52i	0.117574	+	0.203644i	−0.801232	+	0.598354i	$0.795822\pi$
$542$	2710.60	−	4694.89i	0.214816	−	0.372072i
$543$	−2171.63	−	14.8285i	−0.171627	−	0.00117192i
$544$	−2568.72	+	1483.05i	−0.202450	+	0.116885i
$545$	13107.8			1.03023
$546$	2619.11	−	2778.81i	0.205288	−	0.217806i
$547$	−8615.33			−0.673427			−0.336714	−	0.941607i	$-0.609315\pi$
$547$	−8615.33			−0.673427			−0.336714	+	0.941607i	$0.609315\pi$
$548$	−4776.15	+	2757.51i	−0.372312	+	0.214955i
$549$	7216.38	−	4036.00i	0.560997	−	0.313756i
$550$	−425.328	+	736.689i	−0.0329746	+	0.0571137i
$551$	9220.61	+	15970.6i	0.712906	+	1.23479i
$552$	−1572.04	+	893.360i	−0.121214	+	0.0688839i
$553$	−11859.1	−	11025.6i	−0.911934	−	0.847839i
$554$			3840.87i			0.294554i
$555$	−18125.8	−	10630.6i	−1.38630	−	0.813054i
$556$	−1643.67	−	948.976i	−0.125373	−	0.0723841i
$557$	−20665.9	−	11931.5i	−1.57207	−	0.907635i	−0.995915	−	0.0902950i	$-0.971219\pi$
$557$	−20665.9	−	11931.5i	−1.57207	−	0.907635i	−0.576155	−	0.817340i	$-0.695448\pi$
$558$	−9038.17	−	123.436i	−0.685692	−	0.00936461i
$559$			5663.94i			0.428550i
$560$	698.356	−	3045.74i	0.0526981	−	0.229832i
$561$	−7334.29	−	12906.1i	−0.551968	−	0.971292i
$562$	−5730.99	−	9926.36i	−0.430155	−	0.745050i
$563$	5552.10	−	9616.52i	0.415618	−	0.719872i	−0.579875	−	0.814705i	$-0.696899\pi$
$563$	5552.10	−	9616.52i	0.415618	−	0.719872i	0.995493	+	0.0948337i	$0.0302319\pi$
$564$	−34.3179	+	5025.86i	−0.00256214	+	0.375225i
$565$	−1768.95	+	1021.30i	−0.131717	+	0.0760470i
$566$	−3669.06			−0.272477
$567$	13008.9	−	3612.83i	0.963532	−	0.267592i
$568$	593.729			0.0438597
$569$	−20144.7	+	11630.5i	−1.48420	+	0.856903i	−0.999839	−	0.0179647i	$-0.994281\pi$
$569$	−20144.7	+	11630.5i	−1.48420	+	0.856903i	−0.484361	+	0.874868i	$0.660948\pi$
$570$	102.735	−	15045.6i	0.00754931	−	1.10560i
$571$	1521.55	−	2635.40i	0.111514	−	0.193149i	−0.804867	−	0.593456i	$-0.797763\pi$
$571$	1521.55	−	2635.40i	0.111514	−	0.193149i	0.916381	+	0.400307i	$0.131097\pi$
$572$	1222.98	+	2118.27i	0.0893977	+	0.154841i
$573$	−2728.76	−	4801.77i	−0.198945	−	0.350082i
$574$	2721.01	−	2926.71i	0.197862	−	0.212820i
$575$			600.258i			0.0435348i
$576$	1727.84	+	23.5974i	0.124988	+	0.00170699i
$577$	8570.32	+	4948.08i	0.618349	+	0.357004i	0.776226	−	0.630455i	$-0.217132\pi$
$577$	8570.32	+	4948.08i	0.618349	+	0.357004i	−0.157877	+	0.987459i	$0.550465\pi$
$578$	−6371.41	−	3678.54i	−0.458505	−	0.264718i
$579$	−17435.8	−	10226.0i	−1.25148	−	0.733983i
$580$		−	5665.63i		−	0.405607i
$581$	7197.98	−	2212.45i	0.513980	−	0.157983i
$582$	−2197.69	+	1248.91i	−0.156525	+	0.0889500i
$583$	7699.60	+	13336.1i	0.546972	+	0.947384i
$584$	653.141	−	1131.27i	0.0462794	−	0.0801582i
$585$	−4930.15	+	2757.35i	−0.348439	+	0.194876i
$586$	−2090.29	+	1206.83i	−0.147354	+	0.0850746i
$587$	−14853.9			−1.04444			−0.522219	−	0.852812i	$-0.674896\pi$
$587$	−14853.9			−1.04444			−0.522219	+	0.852812i	$0.674896\pi$
$588$	7113.61	−	470.069i	0.498912	−	0.0329682i
$589$	−22981.7			−1.60771
$590$	−13377.5	+	7723.53i	−0.933466	+	0.538937i
$591$	16770.6	+	114.514i	1.16726	+	0.00797034i
$592$	3067.95	−	5313.84i	0.212993	−	0.368915i
$593$	2072.42	+	3589.54i	0.143515	+	0.248575i	0.928818	−	0.370537i	$-0.120826\pi$
$593$	2072.42	+	3589.54i	0.143515	+	0.248575i	−0.785303	+	0.619111i	$0.787493\pi$
$594$	−177.141	+	8646.34i	−0.0122360	+	0.597245i
$595$	17303.4	−	5318.57i	1.19222	−	0.366454i
$596$			2397.74i			0.164791i
$597$	7281.28	−	12415.0i	0.499167	−	0.851109i
$598$	1494.74	+	862.987i	0.102215	+	0.0590137i
$599$	4311.66	+	2489.34i	0.294107	+	0.169802i	0.639792	−	0.768548i	$-0.279020\pi$
$599$	4311.66	+	2489.34i	0.294107	+	0.169802i	−0.345686	+	0.938350i	$0.612354\pi$
$600$	290.211	−	494.826i	0.0197464	−	0.0336687i
$601$		−	6641.45i		−	0.450766i	−0.974270	−	0.225383i	$-0.927637\pi$
$601$		−	6641.45i		−	0.450766i	0.974270	−	0.225383i	$-0.0723633\pi$
$602$	−7200.08	+	7744.39i	−0.487464	+	0.524315i
$603$	7739.48	−	12992.1i	0.522680	−	0.877414i
$604$	−3990.35	−	6911.50i	−0.268817	−	0.465604i
$605$	2009.18	−	3480.00i	0.135016	−	0.233854i
$606$	2203.29	+	15.0447i	0.147694	+	0.00100850i
$607$	−6658.36	+	3844.21i	−0.445230	+	0.257054i	−0.705814	−	0.708398i	$-0.749418\pi$
$607$	−6658.36	+	3844.21i	−0.445230	+	0.257054i	0.260583	+	0.965451i	$0.416085\pi$
$608$	4393.44			0.293055
$609$	12381.2	−	3713.28i	0.823826	−	0.247077i
$610$	−6458.58			−0.428689
$611$	4154.82	−	2398.79i	0.275100	−	0.158829i
$612$	4886.43	+	8736.96i	0.322749	+	0.577076i
$613$	−4708.37	+	8155.14i	−0.310227	+	0.537330i	−0.978411	−	0.206666i	$-0.933739\pi$
$613$	−4708.37	+	8155.14i	−0.310227	+	0.537330i	0.668184	+	0.743996i	$0.267072\pi$
$614$	−5508.71	−	9541.37i	−0.362074	−	0.627131i
$615$	−5139.64	+	2920.76i	−0.336992	+	0.191507i
$616$	−1020.57	+	4451.01i	−0.0667530	+	0.291130i
$617$		−	9209.91i		−	0.600935i	−0.953792	−	0.300468i	$-0.902857\pi$
$617$		−	9209.91i		−	0.600935i	0.953792	−	0.300468i	$-0.0971428\pi$
$618$	−7690.62	−	4510.48i	−0.500586	−	0.293589i
$619$	−8867.28	−	5119.53i	−0.575777	−	0.332425i	0.183676	−	0.982987i	$-0.441200\pi$
$619$	−8867.28	−	5119.53i	−0.575777	−	0.332425i	−0.759454	+	0.650562i	$0.774534\pi$
$620$	6114.63	+	3530.28i	0.396080	+	0.228677i
$621$	2942.36	+	5346.31i	0.190133	+	0.345475i
$622$		−	8458.05i		−	0.545236i
$623$	14271.6	+	13268.5i	0.917782	+	0.853276i
$624$	−814.962	−	1434.08i	−0.0522830	−	0.0920019i
$625$	6854.79	+	11872.8i	0.438706	+	0.759862i
$626$	−5395.50	+	9345.29i	−0.344485	+	0.596666i
$627$	−150.136	+	21987.4i	−0.00956276	+	1.40047i
$628$	−3063.86	+	1768.92i	−0.194684	+	0.112401i
$629$	35546.2			2.25329
$630$	−10246.2	−	2497.11i	−0.647968	−	0.157916i
$631$	−25041.7			−1.57987			−0.789934	−	0.613192i	$-0.789885\pi$
$631$	−25041.7			−1.57987			−0.789934	+	0.613192i	$0.789885\pi$
$632$	−6057.47	+	3497.28i	−0.381255	+	0.220118i
$633$	70.2063	−	10281.7i	0.00440830	−	0.645595i
$634$	−7124.01	+	12339.1i	−0.446263	+	0.772949i
$635$	5328.00	+	9228.37i	0.332969	+	0.576719i
$636$	−5130.80	−	9028.62i	−0.319889	−	0.562906i
$637$	−3822.29	−	5630.27i	−0.237747	−	0.350203i
$638$			8279.67i			0.513786i
$639$	27.3642	−	2003.65i	0.00169407	−	0.124042i
$640$	−1168.94	−	674.889i	−0.0721977	−	0.0416833i
$641$	545.089	+	314.707i	0.0335877	+	0.0193919i	0.516700	−	0.856167i	$-0.327160\pi$
$641$	545.089	+	314.707i	0.0335877	+	0.0193919i	−0.483112	+	0.875558i	$0.660494\pi$
$642$	19256.8	+	11293.9i	1.18381	+	0.694293i
$643$		−	11568.9i		−	0.709538i	−0.934954	−	0.354769i	$-0.884559\pi$
$643$		−	11568.9i		−	0.709538i	0.934954	−	0.354769i	$-0.115441\pi$
$644$	946.736	+	3080.11i	0.0579295	+	0.188468i
$645$	13600.0	−	7728.65i	0.830234	−	0.471807i
$646$	12725.9	+	22042.0i	0.775070	+	1.34246i
$647$	−9784.59	+	16947.4i	−0.594547	+	1.02979i	0.399064	+	0.916923i	$0.369335\pi$
$647$	−9784.59	+	16947.4i	−0.594547	+	1.02979i	−0.993611	+	0.112862i	$0.963998\pi$
$648$	159.268	−	5829.82i	0.00965528	−	0.353422i
$649$	19549.8	−	11287.1i	1.18243	−	0.682675i
$650$	−547.581			−0.0330429
$651$	−3707.21	+	15676.1i	−0.223191	+	0.943773i
$652$	2707.94			0.162655
$653$	−5834.29	+	3368.43i	−0.349638	+	0.201863i	−0.664526	−	0.747265i	$-0.731366\pi$
$653$	−5834.29	+	3368.43i	−0.349638	+	0.201863i	0.314888	+	0.949129i	$0.398033\pi$
$654$	12917.5	+	88.2044i	0.772348	+	0.00527380i
$655$	1890.89	−	3275.12i	0.112799	−	0.195373i
$656$	−863.096	−	1494.93i	−0.0513693	−	0.0889742i
$657$	−3787.59	−	2256.28i	−0.224913	−	0.133982i
$658$	8730.31	+	2001.77i	0.517238	+	0.118597i
$659$			3912.25i			0.231259i	0.993292	+	0.115629i	$0.0368885\pi$
$659$			3912.25i			0.231259i	−0.993292	+	0.115629i	$0.963112\pi$
$660$	3417.50	−	5827.03i	0.201554	−	0.343662i
$661$	24001.8	+	13857.5i	1.41235	+	0.815420i	0.995609	−	0.0936057i	$-0.0298393\pi$
$661$	24001.8	+	13857.5i	1.41235	+	0.815420i	0.416740	+	0.909026i	$0.363173\pi$
$662$	−3069.97	−	1772.45i	−0.180238	−	0.104061i
$663$	4834.22	−	8242.61i	0.283176	−	0.482830i
$664$		−	3252.80i		−	0.190110i
$665$	−26135.3	−	5992.54i	−1.52404	−	0.349445i
$666$	−17791.1	−	10598.3i	−1.03512	−	0.616629i
$667$	2921.24	+	5059.73i	0.169581	+	0.293724i
$668$	−7437.48	+	12882.1i	−0.430786	+	0.746143i
$669$	12650.8	+	86.3830i	0.731103	+	0.00499217i
$670$	−10230.1	+	5906.32i	−0.589883	+	0.340569i
$671$	9438.48			0.543023
$672$	708.713	−	2996.83i	0.0406833	−	0.172032i
$673$	27462.5			1.57296			0.786479	−	0.617617i	$-0.211902\pi$
$673$	27462.5			1.57296			0.786479	+	0.617617i	$0.211902\pi$
$674$	13511.6	−	7800.94i	0.772179	−	0.445817i
$675$	−1656.51	−	1002.18i	−0.0944578	−	0.0571464i
$676$	3606.75	−	6247.07i	0.205209	−	0.355432i
$677$	−4757.18	−	8239.68i	−0.270064	−	0.467765i	0.698814	−	0.715303i	$-0.253712\pi$
$677$	−4757.18	−	8239.68i	−0.270064	−	0.467765i	−0.968878	+	0.247539i	$0.920378\pi$
$678$	−1750.14	+	994.574i	−0.0991354	+	0.0563369i
$679$	1323.53	+	4305.96i	0.0748046	+	0.243369i
$680$		−	7819.48i		−	0.440976i
$681$	1486.83	+	872.014i	0.0836646	+	0.0490685i
$682$	−8935.84	−	5159.11i	−0.501717	−	0.289666i
$683$	−22760.4	−	13140.7i	−1.27511	−	0.736186i	−0.299166	−	0.954201i	$-0.596708\pi$
$683$	−22760.4	−	13140.7i	−1.27511	−	0.736186i	−0.975945	+	0.218015i	$0.930042\pi$
$684$	202.488	−	14826.5i	0.0113192	−	0.828807i
$685$		−	14539.2i		−	0.810969i
$686$	1931.01	−	12557.3i	0.107473	−	0.698892i
$687$	5461.37	+	9610.33i	0.303296	+	0.533707i
$688$	2283.84	+	3955.73i	0.126556	+	0.219202i
$689$	−4956.36	+	8584.67i	−0.274053	+	0.474673i
$690$	32.5482	−	4766.68i	0.00179578	−	0.262992i
$691$	−6698.34	+	3867.29i	−0.368765	+	0.212907i	−0.672919	−	0.739716i	$-0.734960\pi$
$691$	−6698.34	+	3867.29i	−0.368765	+	0.212907i	0.304154	+	0.952623i	$0.401626\pi$
$692$	10551.8			0.579650
$693$	14973.7	+	3649.24i	0.820786	+	0.200033i
$694$	14339.9			0.784347
$695$	4333.20	−	2501.77i	0.236500	−	0.136543i
$696$	38.1248	−	5583.38i	0.00207632	−	0.304077i
$697$	5000.05	−	8660.34i	0.271722	−	0.470637i
$698$	5543.44	+	9601.52i	0.300605	+	0.520663i
$699$	−2399.41	−	4222.22i	−0.129834	−	0.228468i
$700$	−748.716	−	696.092i	−0.0404269	−	0.0375855i
$701$			16405.7i			0.883929i	0.897033	+	0.441964i	$0.145718\pi$
$701$			16405.7i			0.883929i	−0.897033	+	0.441964i	$0.854282\pi$
$702$	−4877.13	+	2684.15i	−0.262216	+	0.144311i
$703$	−45597.7	−	26325.9i	−2.44630	−	1.41237i
$704$	1708.28	+	986.274i	0.0914533	+	0.0528006i
$705$	−11429.3	−	6703.16i	−0.610569	−	0.358093i
$706$			61.8677i			0.00329805i
$707$	877.556	−	3827.29i	0.0466816	−	0.203593i
$708$	−13235.3	+	7521.39i	−0.702562	+	0.399253i
$709$	5304.71	+	9188.03i	0.280991	+	0.486691i	0.971629	−	0.236510i	$-0.0760035\pi$
$709$	5304.71	+	9188.03i	0.280991	+	0.486691i	−0.690638	+	0.723201i	$0.742670\pi$
$710$	−782.619	+	1355.54i	−0.0413679	+	0.0716512i
$711$	11523.0	+	20603.2i	0.607803	+	1.08675i
$712$	7289.73	−	4208.72i	0.383699	−	0.221529i
$713$	−7280.97			−0.382432
$714$	17088.0	−	5124.93i	0.895662	−	0.268621i
$715$	−6448.26			−0.337275
$716$	11446.2	−	6608.48i	0.597438	−	0.344931i
$717$	−9995.74	−	68.2536i	−0.520638	−	0.00355506i
$718$	−6575.26	+	11388.7i	−0.341764	+	0.591953i
$719$	−10075.2	−	17450.8i	−0.522591	−	0.905153i	−0.999654	−	0.0262848i	$-0.991632\pi$
$719$	−10075.2	−	17450.8i	−0.522591	−	0.905153i	0.477064	−	0.878869i	$-0.341701\pi$
$720$	−2331.41	+	3913.71i	−0.120676	+	0.202577i
$721$	−10818.7	+	11636.6i	−0.558821	+	0.601067i
$722$		−	23981.8i		−	1.23616i
$723$	−8639.18	+	14730.3i	−0.444391	+	0.757712i
$724$	1447.79	+	835.881i	0.0743186	+	0.0429079i
$725$	−1605.25	−	926.790i	−0.0822309	−	0.0474760i
$726$	2003.43	−	3415.96i	0.102416	−	0.174625i
$727$			26758.5i			1.36509i	0.730846	+	0.682543i	$0.239126\pi$
$727$			26758.5i			1.36509i	−0.730846	+	0.682543i	$0.760874\pi$
$728$	−2809.81	+	863.654i	−0.143047	+	0.0439686i
$729$	−19666.5	−	806.167i	−0.999161	−	0.0409575i
$730$	1721.87	+	2982.36i	0.0873002	+	0.151208i
$731$	−13230.7	+	22916.2i	−0.669431	+	1.15949i
$732$	−6364.82	−	43.4607i	−0.321381	−	0.00219447i
$733$	7106.39	−	4102.88i	0.358091	−	0.206744i	−0.310152	−	0.950687i	$-0.600380\pi$
$733$	7106.39	−	4102.88i	0.358091	−	0.206744i	0.668243	+	0.743943i	$0.267047\pi$
$734$	4838.88			0.243333
$735$	−8303.54	+	16860.6i	−0.416709	+	0.846141i
$736$	1391.91			0.0697100
$737$	14950.1	−	8631.42i	0.747208	−	0.431401i
$738$	−5084.68	+	2843.78i	−0.253618	+	0.141844i
$739$	10324.9	−	17883.2i	0.513946	−	0.890180i	−0.485923	−	0.874001i	$-0.661517\pi$
$739$	10324.9	−	17883.2i	0.513946	−	0.890180i	0.999869	−	0.0161788i	$-0.00515010\pi$
$740$	8087.99	+	14008.8i	0.401784	+	0.695911i
$741$	−12305.8	+	6993.13i	−0.610072	+	0.346693i
$742$	−17689.8	+	5437.35i	−0.875222	+	0.269018i
$743$		−	8375.29i		−	0.413539i	−0.978390	−	0.206769i	$-0.933705\pi$
$743$		−	8375.29i		−	0.413539i	0.978390	−	0.206769i	$-0.0662950\pi$
$744$	6002.11	+	3520.18i	0.295764	+	0.173463i
$745$	−5474.25	−	3160.56i	−0.269210	−	0.155428i
$746$	−16959.1	−	9791.32i	−0.832326	−	0.480544i
$747$	−10977.2	−	149.917i	−0.537662	−	0.00734294i
$748$			11427.3i			0.558587i
$749$	27089.3	−	29137.2i	1.32152	−	1.42143i
$750$	7515.30	+	13224.6i	0.365893	+	0.643859i
$751$	−13298.8	−	23034.3i	−0.646181	−	1.11922i	−0.984028	−	0.178016i	$-0.943032\pi$
$751$	−13298.8	−	23034.3i	−0.646181	−	1.11922i	0.337847	−	0.941201i	$-0.390301\pi$
$752$	1934.50	−	3350.65i	0.0938085	−	0.162481i
$753$	−152.703	+	22363.4i	−0.00739020	+	1.08230i
$754$	−4615.71	+	2664.88i	−0.222937	+	0.128713i
$755$	21039.4			1.01418
$756$	−10080.7	−	2529.80i	−0.484962	−	0.121704i
$757$	−26633.6			−1.27875			−0.639376	−	0.768894i	$-0.720807\pi$
$757$	−26633.6			−1.27875			−0.639376	+	0.768894i	$0.720807\pi$
$758$	21929.3	−	12660.9i	1.05080	−	0.606681i
$759$	−47.5655	+	6965.97i	−0.00227473	+	0.333134i
$760$	−5791.18	+	10030.6i	−0.276405	+	0.478748i
$761$	−4243.87	−	7350.60i	−0.202155	−	0.350143i	0.747067	−	0.664748i	$-0.231461\pi$
$761$	−4243.87	−	7350.60i	−0.202155	−	0.350143i	−0.949223	+	0.314605i	$0.898128\pi$
$762$	5188.56	+	9130.26i	0.246669	+	0.434061i
$763$	5144.96	−	22438.8i	0.244116	−	1.06466i
$764$			4251.58i			0.201331i
$765$	−26388.3	−	360.389i	−1.24715	−	0.0170326i
$766$	15759.6	+	9098.83i	0.743367	+	0.429183i
$767$	12584.5	+	7265.67i	0.592439	+	0.342045i
$768$	−1147.43	−	672.958i	−0.0539119	−	0.0316189i
$769$		−	22673.5i		−	1.06324i	−0.846984	−	0.531618i	$-0.821584\pi$
$769$		−	22673.5i		−	1.06324i	0.846984	−	0.531618i	$-0.178416\pi$
$770$	−8816.80	−	8197.12i	−0.412644	−	0.383641i
$771$	21196.3	−	12045.5i	0.990100	−	0.562656i
$772$	7780.11	+	13475.5i	0.362710	+	0.628232i
$773$	18141.2	−	31421.4i	0.844103	−	1.46203i	−0.0422941	−	0.999105i	$-0.513467\pi$
$773$	18141.2	−	31421.4i	0.844103	−	1.46203i	0.886398	−	0.462925i	$-0.153200\pi$
$774$	13454.6	−	7524.94i	0.624827	−	0.349455i
$775$	2000.48	−	1154.98i	0.0927217	−	0.0535329i
$776$	1945.88			0.0900167
$777$	−25312.7	+	26856.2i	−1.16871	+	1.23998i
$778$	19514.4			0.899263
$779$	−12827.9	+	7406.17i	−0.589994	+	0.340633i
$780$	4348.37	+	29.6919i	0.199611	+	0.00136300i
$781$	1143.71	−	1980.96i	0.0524009	−	0.0907611i
$782$	4031.78	+	6983.26i	0.184369	+	0.319336i
$783$	−18840.4	−	385.990i	−0.859898	−	0.0176170i
$784$	−4939.78	−	2390.98i	−0.225026	−	0.108918i
$785$		−	9326.77i		−	0.424060i
$786$	1885.48	−	3214.85i	0.0855634	−	0.145891i
$787$	−1911.44	−	1103.57i	−0.0865763	−	0.0499849i	0.456087	−	0.889935i	$-0.349251\pi$
$787$	−1911.44	−	1103.57i	−0.0865763	−	0.0499849i	−0.542663	+	0.839950i	$0.682584\pi$
$788$	−11180.6	−	6455.14i	−0.505449	−	0.291821i
$789$	−2768.04	+	4719.67i	−0.124899	+	0.212959i
$790$		−	18439.7i		−	0.830448i
$791$	1054.00	+	3429.07i	0.0473778	+	0.154139i
$792$	3407.10	−	5719.44i	0.152861	−	0.256605i
$793$	3037.86	+	5261.72i	0.136037	+	0.235623i
$794$	−8162.78	+	14138.3i	−0.364844	+	0.631928i
$795$	27376.3	+	186.933i	1.22130	+	0.00833940i
$796$	−9595.12	+	5539.74i	−0.427249	+	0.246672i
$797$	−43496.3			−1.93315			−0.966574	−	0.256388i	$-0.917467\pi$
$797$	−43496.3			−1.93315			−0.966574	+	0.256388i	$0.917467\pi$
$798$	−25715.6	−	6081.42i	−1.14075	−	0.269774i
$799$	22413.7			0.992417
$800$	−382.434	+	220.798i	−0.0169014	+	0.00975801i
$801$	−13867.1	−	24794.5i	−0.611700	−	1.09372i
$802$	10259.8	−	17770.4i	0.451727	−	0.782414i
$803$	−2516.31	−	4358.38i	−0.110584	−	0.191537i
$804$	−10121.3	+	5751.74i	−0.443968	+	0.252299i
$805$	−8280.09	−	1898.54i	−0.362528	−	0.0831237i
$806$		−	6642.01i		−	0.290267i
$807$	11900.0	+	6979.26i	0.519084	+	0.304438i
$808$	−1468.90	−	848.068i	−0.0639549	−	0.0369244i
$809$	23156.7	+	13369.5i	1.00636	+	0.581024i	0.910125	−	0.414335i	$-0.135986\pi$
$809$	23156.7	+	13369.5i	1.00636	+	0.581024i	0.0962378	+	0.995358i	$0.469319\pi$
$810$	13100.1	+	8048.17i	0.568259	+	0.349116i
$811$			43614.5i			1.88842i	0.329338	+	0.944212i	$0.393174\pi$
$811$			43614.5i			1.88842i	−0.329338	+	0.944212i	$0.606826\pi$
$812$	−9698.76	−	2223.82i	−0.419162	−	0.0961093i
$813$	6958.89	+	12245.5i	0.300195	+	0.528251i
$814$	−11819.7	−	20472.3i	−0.508943	−	0.881515i
$815$	−3569.45	+	6182.47i	−0.153414	+	0.265721i
$816$	52.6184	−	7705.97i	0.00225737	−	0.330592i
$817$	33943.9	−	19597.5i	1.45354	−	0.839204i
$818$	−4146.46			−0.177234
$819$	2785.06	+	9522.02i	0.118825	+	0.406259i
$820$	4550.74			0.193803
$821$	3199.70	−	1847.35i	0.136017	−	0.0785297i	−0.430447	−	0.902616i	$-0.641644\pi$
$821$	3199.70	−	1847.35i	0.136017	−	0.0785297i	0.566465	+	0.824086i	$0.308311\pi$
$822$	97.8363	−	14328.1i	0.00415138	−	0.607969i
$823$	−8733.70	+	15127.2i	−0.369912	+	0.640706i	−0.989551	−	0.144180i	$-0.953945\pi$
$823$	−8733.70	+	15127.2i	−0.369912	+	0.640706i	0.619640	+	0.784887i	$0.287279\pi$
$824$	3431.66	+	5943.81i	0.145082	+	0.251289i
$825$	−1091.94	−	1921.48i	−0.0460805	−	0.0810875i
$826$	7970.77	+	25932.0i	0.335761	+	1.09236i
$827$			37321.1i			1.56926i	0.619962	+	0.784632i	$0.287148\pi$
$827$			37321.1i			1.56926i	−0.619962	+	0.784632i	$0.712852\pi$
$828$	64.1514	−	4697.27i	0.00269253	−	0.197151i
$829$	39701.3	+	22921.6i	1.66331	+	0.960313i	0.971118	+	0.238601i	$0.0766887\pi$
$829$	39701.3	+	22921.6i	1.66331	+	0.960313i	0.692193	+	0.721712i	$0.256645\pi$
$830$	7426.43	+	4287.65i	0.310573	+	0.179309i
$831$	−8607.69	−	5048.33i	−0.359323	−	0.210740i
$832$			1269.76i			0.0529100i
$833$	−2312.87	−	31708.6i	−0.0962020	−	1.31889i
$834$	4287.13	−	2436.30i	0.177999	−	0.101154i
$835$	−19607.3	−	33960.9i	−0.812622	−	1.40750i
$836$	8463.15	−	14658.6i	0.350125	−	0.606434i
$837$	12156.1	−	20093.0i	0.502004	−	0.829768i
$838$	−20050.6	+	11576.2i	−0.826536	+	0.477201i
$839$	11522.6			0.474141			0.237071	−	0.971492i	$-0.423813\pi$
$839$	11522.6			0.474141			0.237071	+	0.971492i	$0.423813\pi$
$840$	5907.85	+	5568.31i	0.242667	+	0.228720i
$841$	6347.59			0.260264
$842$	−2586.02	+	1493.04i	−0.105843	+	0.0611087i
$843$	29778.4	+	203.335i	1.21663	+	0.00830750i
$844$	−3957.53	+	6854.64i	−0.161403	+	0.279557i
$845$	9508.41	+	16469.1i	0.387100	+	0.670477i
$846$	−11218.2	−	6682.76i	−0.455900	−	0.271581i
$847$	−5168.64	−	4805.36i	−0.209677	−	0.194940i
$848$			7994.12i			0.323725i
$849$	4822.51	−	8222.65i	0.194945	−	0.332392i
$850$	−2215.50	−	1279.12i	−0.0894013	−	0.0516159i
$851$	−14446.1	−	8340.46i	−0.581911	−	0.335966i
$852$	−780.380	+	1330.59i	−0.0313795	+	0.0535039i
$853$			44074.7i			1.76915i	0.466395	+	0.884577i	$0.345553\pi$
$853$			44074.7i			1.76915i	−0.466395	+	0.884577i	$0.654447\pi$
$854$	−2535.06	+	11056.2i	−0.101579	+	0.443015i
$855$	33583.3	+	20005.7i	1.34330	+	0.800211i
$856$	−8592.65	−	14882.9i	−0.343097	−	0.594261i
$857$	−8037.61	+	13921.5i	−0.320373	+	0.554902i	−0.980565	−	0.196195i	$-0.937142\pi$
$857$	−8037.61	+	13921.5i	−0.320373	+	0.554902i	0.660192	+	0.751097i	$0.270475\pi$
$858$	−6354.66	−	43.3913i	−0.252849	−	0.00172652i
$859$	16666.7	−	9622.52i	0.662002	−	0.382207i	−0.131037	−	0.991377i	$-0.541831\pi$
$859$	16666.7	−	9622.52i	0.662002	−	0.382207i	0.793040	+	0.609170i	$0.208497\pi$
$860$	−12041.7			−0.477464
$861$	2982.57	+	9944.78i	0.118056	+	0.393632i
$862$	7746.16			0.306073
$863$	−10098.5	+	5830.35i	−0.398326	+	0.229974i	−0.685762	−	0.727826i	$-0.740531\pi$
$863$	−10098.5	+	5830.35i	−0.398326	+	0.229974i	0.287435	+	0.957800i	$0.407197\pi$
$864$	−2323.91	+	3841.21i	−0.0915056	+	0.151251i
$865$	−13908.7	+	24090.6i	−0.546718	+	0.946944i
$866$	5450.01	+	9439.69i	0.213855	+	0.370408i
$867$	16618.3	−	9443.87i	0.650965	−	0.369931i
$868$	8443.41	−	9081.72i	0.330171	−	0.355131i
$869$			26947.5i			1.05193i
$870$	12697.1	+	7446.73i	0.494796	+	0.290193i
$871$	9623.61	+	5556.19i	0.374378	+	0.216147i
$872$	−8611.89	−	4972.08i	−0.334444	−	0.193092i
$873$	89.6830	−	6566.73i	0.00347687	−	0.254582i
$874$		−	11943.9i		−	0.462252i
$875$	25911.1	−	7964.32i	1.00109	−	0.307707i
$876$	1676.80	+	2950.65i	0.0646733	+	0.113805i
$877$	−18913.9	−	32759.9i	−0.728254	−	1.26137i	−0.957621	−	0.288033i	$-0.906999\pi$
$877$	−18913.9	−	32759.9i	−0.728254	−	1.26137i	0.229367	−	0.973340i	$-0.426334\pi$
$878$	−2713.77	+	4700.39i	−0.104311	+	0.180673i
$879$	42.8182	−	6270.73i	0.00164303	−	0.240622i
$880$	−4503.51	+	2600.10i	−0.172515	+	0.0996016i
$881$	26234.8			1.00326			0.501631	−	0.865082i	$-0.332734\pi$
$881$	26234.8			1.00326			0.501631	+	0.865082i	$0.332734\pi$
$882$	−8296.46	+	16560.0i	−0.316730	+	0.632204i
$883$	−6803.07			−0.259277			−0.129639	−	0.991561i	$-0.541382\pi$
$883$	−6803.07			−0.259277			−0.129639	+	0.991561i	$0.541382\pi$
$884$	−6370.43	+	3677.97i	−0.242376	+	0.139936i
$885$	274.030	−	40131.7i	0.0104084	−	1.52431i
$886$	11066.3	−	19167.3i	0.419614	−	0.726793i
$887$	6115.02	+	10591.5i	0.231480	+	0.400934i	0.958244	−	0.285953i	$-0.0923100\pi$
$887$	6115.02	+	10591.5i	0.231480	+	0.400934i	−0.726764	+	0.686887i	$0.758977\pi$
$888$	7876.31	+	13859.9i	0.297648	+	0.523769i
$889$	17889.0	−	5498.56i	0.674890	−	0.207442i
$890$			22190.8i			0.835773i
$891$	−19144.3	−	11761.5i	−0.719818	−	0.442227i
$892$	−8434.06	−	4869.40i	−0.316584	−	0.182780i
$893$	−28751.7	−	16599.8i	−1.07742	−	0.622051i
$894$	−5373.52	−	3151.52i	−0.201026	−	0.117900i
$895$			34843.7i			1.30134i
$896$	−1614.14	+	1736.16i	−0.0601837	+	0.0647335i
$897$	−3898.66	+	2215.54i	−0.145120	+	0.0824690i
$898$	−3599.14	−	6233.89i	−0.133747	−	0.231657i
$899$	11241.7	−	19471.2i	0.417055	−	0.722360i
$900$	727.499	+	1300.77i	0.0269444	+	0.0481767i
$901$	−40106.7	+	23155.6i	−1.48296	+	0.856187i
$902$	−6650.38			−0.245492
$903$	−7892.20	−	26314.9i	−0.290848	−	0.969774i
$904$	1549.61			0.0570125
$905$	−3816.79	+	2203.62i	−0.140193	+	0.0809402i
$906$	20734.0	+	141.577i	0.760310	+	0.00519160i
$907$	9920.70	−	17183.2i	0.363188	−	0.629060i	−0.625296	−	0.780388i	$-0.715022\pi$
$907$	9920.70	−	17183.2i	0.363188	−	0.629060i	0.988484	+	0.151328i	$0.0483549\pi$
$908$	−663.446	−	1149.12i	−0.0242481	−	0.0419989i
$909$	−2929.66	+	4917.98i	−0.106898	+	0.179449i
$910$	1731.93	−	7553.46i	0.0630910	−	0.275159i
$911$		−	48153.2i		−	1.75125i	−0.482995	−	0.875623i	$-0.660451\pi$
$911$		−	48153.2i		−	1.75125i	0.482995	−	0.875623i	$-0.339549\pi$
$912$	−5774.61	+	9846.03i	−0.209667	+	0.357494i
$913$	−10852.9	−	6265.92i	−0.393404	−	0.227132i
$914$	−14402.2	−	8315.09i	−0.521204	−	0.300917i
$915$	8488.97	−	14474.2i	0.306707	−	0.522953i
$916$		−	8509.17i		−	0.306933i
$917$	−4864.35	−	4522.46i	−0.175175	−	0.162862i
$918$	−26002.8	−	532.728i	−0.934880	−	0.0191532i
$919$	−11559.8	−	20022.1i	−0.414932	−	0.718683i	0.580490	−	0.814268i	$-0.302861\pi$
$919$	−11559.8	−	20022.1i	−0.414932	−	0.718683i	−0.995421	+	0.0955849i	$0.969528\pi$
$920$	−1834.74	+	3177.86i	−0.0657495	+	0.113882i
$921$	28623.5	+	195.449i	1.02408	+	0.00699267i
$922$	−9824.34	+	5672.08i	−0.350919	+	0.202603i
$923$	1472.45			0.0525095
$924$	−8633.65	−	8137.45i	−0.307388	−	0.289721i
$925$	5292.17			0.188114
$926$	10967.5	−	6332.06i	0.389215	−	0.224713i
$927$	20216.7	−	11306.8i	0.716291	−	0.400610i
$928$	−2149.09	+	3722.34i	−0.0760209	+	0.131672i
$929$	16001.3	+	27715.1i	0.565109	+	0.978797i	0.997040	+	0.0768903i	$0.0244991\pi$
$929$	16001.3	+	27715.1i	0.565109	+	0.978797i	−0.431931	+	0.901907i	$0.642168\pi$
$930$	−15948.5	+	9063.26i	−0.562337	+	0.319566i
$931$	−20516.8	+	42387.9i	−0.722246	+	1.49217i
$932$			3738.43i			0.131391i
$933$	18955.2	+	11117.0i	0.665127	+	0.390091i
$934$	−22411.5	−	12939.3i	−0.785146	−	0.453304i
$935$	−26089.5	−	15062.8i	−0.912534	−	0.526852i
$936$	4285.05	+	58.5217i	0.149638	+	0.00204363i
$937$			22855.6i			0.796863i	0.917198	+	0.398431i	$0.130445\pi$
$937$			22855.6i			0.796863i	−0.917198	+	0.398431i	$0.869555\pi$
$938$	6095.39	+	19830.7i	0.212177	+	0.690294i
$939$	−13851.8	−	24374.9i	−0.481403	−	0.847120i
$940$	5099.90	+	8833.28i	0.176958	+	0.306500i
$941$	−27703.7	+	47984.2i	−0.959739	+	1.66232i	−0.236610	+	0.971605i	$0.576036\pi$
$941$	−27703.7	+	47984.2i	−0.959739	+	1.66232i	−0.723129	+	0.690713i	$0.757297\pi$
$942$	62.7612	−	9191.38i	0.00217077	−	0.317910i
$943$	−4064.07	+	2346.39i	−0.140344	+	0.0810277i
$944$	11718.8			0.404041
$945$	19063.6	−	19680.5i	0.656231	−	0.677467i
$946$	17597.6			0.604807
$947$	5965.73	−	3444.31i	0.204710	−	0.118189i	−0.394141	−	0.919050i	$-0.628958\pi$
$947$	5965.73	−	3444.31i	0.204710	−	0.118189i	0.598850	+	0.800861i	$0.295624\pi$
$948$	124.083	−	18172.0i	0.00425109	−	0.622572i
$949$	1619.79	−	2805.56i	0.0554064	−	0.0959667i
$950$	1894.66	+	3281.64i	0.0647061	+	0.112074i
$951$	−18289.4	−	32183.7i	−0.623632	−	1.09740i
$952$	−13385.9	−	3069.23i	−0.455712	−	0.104490i
$953$			50638.7i			1.72125i	0.509242	+	0.860623i	$0.329926\pi$
$953$			50638.7i			1.72125i	−0.509242	+	0.860623i	$0.670074\pi$
$954$	26977.6	+	368.438i	0.915548	+	0.0125038i
$955$	−9706.74	−	5604.19i	−0.328903	−	0.189892i
$956$	6663.98	+	3847.45i	0.225448	+	0.130163i
$957$	−18555.4	−	10882.6i	−0.626761	−	0.367589i
$958$			4207.97i			0.141914i
$959$	−24889.1	−	5706.79i	−0.838070	−	0.192160i
$960$	3048.90	−	1732.64i	0.102503	−	0.0582506i
$961$	−885.947	−	1534.51i	−0.0297387	−	0.0515090i
$962$	7608.53	−	13178.4i	0.254999	−	0.441671i
$963$	−50621.2	+	28311.6i	−1.69392	+	0.947380i
$964$	11384.5	−	6572.87i	0.380364	−	0.219603i
$965$	−41021.2			−1.36841
$966$	−8147.12	−	1926.69i	−0.271355	−	0.0641722i
$967$	−15112.3			−0.502562			−0.251281	−	0.967914i	$-0.580852\pi$
$967$	−15112.3			−0.502562			−0.251281	+	0.967914i	$0.580852\pi$
$968$	−2640.07	+	1524.25i	−0.0876603	+	0.0506107i
$969$	−66124.4	−	451.515i	−2.19218	−	0.0149688i
$970$	−2564.95	+	4442.62i	−0.0849026	+	0.147056i
$971$	−14046.2	−	24328.7i	−0.464226	−	0.804063i	0.534941	−	0.844890i	$-0.320334\pi$
$971$	−14046.2	−	24328.7i	−0.464226	−	0.804063i	−0.999166	+	0.0408272i	$0.987001\pi$
$972$	12855.8	+	8019.48i	0.424227	+	0.264635i
$973$	−2581.86	−	8399.80i	−0.0850674	−	0.276758i
$974$		−	25183.9i		−	0.828485i
$975$	719.725	−	1227.17i	0.0236407	−	0.0403087i
$976$	4243.31	+	2449.88i	0.139165	+	0.0803470i
$977$	34769.9	+	20074.4i	1.13857	+	0.657356i	0.946077	−	0.323941i	$-0.105008\pi$
$977$	34769.9	+	20074.4i	1.13857	+	0.657356i	0.192497	+	0.981298i	$0.438341\pi$
$978$	−3559.23	+	6068.70i	−0.116372	+	0.198421i
$979$		−	32429.3i		−	1.05868i
$980$	11970.1	−	8126.31i	0.390176	−	0.264883i
$981$	−17176.1	+	28833.3i	−0.559012	+	0.938405i
$982$	1372.36	+	2376.99i	0.0445964	+	0.0772433i
$983$	−7276.53	+	12603.3i	−0.236099	+	0.408935i	−0.959591	−	0.281397i	$-0.909202\pi$
$983$	−7276.53	+	12603.3i	−0.236099	+	0.408935i	0.723493	+	0.690332i	$0.242536\pi$
$984$	4484.67	+	30.6225i	0.145291	+	0.000992084i
$985$	29475.4	−	17017.6i	0.953465	−	0.550483i
$986$	−24900.1			−0.804239
$987$	−15961.0	+	16934.2i	−0.514735	+	0.546122i
$988$	10895.7			0.350850
$989$	10754.0	−	6208.81i	0.345760	−	0.199624i
$990$	8566.96	+	15317.8i	0.275026	+	0.491748i
$991$	16550.0	−	28665.4i	0.530503	−	0.918857i	−0.468864	−	0.883270i	$-0.655337\pi$
$991$	16550.0	−	28665.4i	0.530503	−	0.918857i	0.999367	−	0.0355870i	$-0.0113301\pi$
$992$	−2678.23	−	4638.82i	−0.0857195	−	0.148471i
$993$	8007.28	−	4550.39i	0.255894	−	0.145420i
$994$	2013.30	+	1871.80i	0.0642435	+	0.0597282i
$995$		−	29208.7i		−	0.930631i
$996$	7289.77	+	4275.38i	0.231913	+	0.136015i
$997$	43647.5	+	25199.9i	1.38649	+	0.800491i	0.992918	−	0.118803i	$-0.0379055\pi$
$997$	43647.5	+	25199.9i	1.38649	+	0.800491i	0.393573	+	0.919293i	$0.371239\pi$
$998$	15895.9	+	9177.51i	0.504184	+	0.291091i
$999$	47135.7	−	25941.3i	1.49280	−	0.821568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.f.a.17.6	yes	16
3.2	odd	2	inner	42.4.f.a.17.4	yes	16
4.3	odd	2		336.4.bc.e.17.5		16
7.2	even	3		294.4.f.a.215.1		16
7.3	odd	6		294.4.d.a.293.10		16
7.4	even	3		294.4.d.a.293.15		16
7.5	odd	6	inner	42.4.f.a.5.4	✓	16
7.6	odd	2		294.4.f.a.227.7		16
12.11	even	2		336.4.bc.e.17.2		16
21.2	odd	6		294.4.f.a.215.7		16
21.5	even	6	inner	42.4.f.a.5.6	yes	16
21.11	odd	6		294.4.d.a.293.2		16
21.17	even	6		294.4.d.a.293.7		16
21.20	even	2		294.4.f.a.227.1		16
28.19	even	6		336.4.bc.e.257.2		16
84.47	odd	6		336.4.bc.e.257.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.4	✓	16	7.5	odd	6	inner
42.4.f.a.5.6	yes	16	21.5	even	6	inner
42.4.f.a.17.4	yes	16	3.2	odd	2	inner
42.4.f.a.17.6	yes	16	1.1	even	1	trivial
294.4.d.a.293.2		16	21.11	odd	6
294.4.d.a.293.7		16	21.17	even	6
294.4.d.a.293.10		16	7.3	odd	6
294.4.d.a.293.15		16	7.4	even	3
294.4.f.a.215.1		16	7.2	even	3
294.4.f.a.215.7		16	21.2	odd	6
294.4.f.a.227.1		16	21.20	even	2
294.4.f.a.227.7		16	7.6	odd	2
336.4.bc.e.17.2		16	12.11	even	2
336.4.bc.e.17.5		16	4.3	odd	2
336.4.bc.e.257.2		16	28.19	even	6
336.4.bc.e.257.5		16	84.47	odd	6

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-0.0354799 + 5.19603i) q^{3} +(2.00000 - 3.46410i) q^{4} +(5.27257 + 9.13236i) q^{5} +(5.13458 + 9.03527i) q^{6} +(17.7029 - 5.44135i) q^{7} -8.00000i q^{8} +(-26.9975 - 0.368709i) q^{9} +(18.2647 + 10.5451i) q^{10} +(-26.6918 - 15.4105i) q^{11} +(17.9286 + 10.5150i) q^{12} -19.8400i q^{13} +(25.2209 - 27.1276i) q^{14} +(-47.6391 + 27.0724i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(46.3453 - 80.2724i) q^{17} +(-47.1297 + 26.3589i) q^{18} +(-118.901 + 68.6474i) q^{19} +42.1806 q^{20} +(27.6454 + 92.1777i) q^{21} -61.6421 q^{22} +(-37.6697 + 21.7486i) q^{23} +(41.5683 + 0.283839i) q^{24} +(6.89995 - 11.9511i) q^{25} +(-19.8400 - 34.3640i) q^{26} +(2.87369 - 140.267i) q^{27} +(16.5563 - 72.2073i) q^{28} -134.318i q^{29} +(-55.4409 + 94.5300i) q^{30} +(144.963 + 83.6945i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(81.0206 - 138.145i) q^{33} -185.381i q^{34} +(143.032 + 132.979i) q^{35} +(-55.2722 + 92.7846i) q^{36} +(191.747 + 332.115i) q^{37} +(-137.295 + 237.802i) q^{38} +(103.089 + 0.703923i) q^{39} +(73.0589 - 42.1806i) q^{40} +107.887 q^{41} +(140.061 + 132.011i) q^{42} -285.480 q^{43} +(-106.767 + 61.6421i) q^{44} +(-138.979 - 248.495i) q^{45} +(-43.4973 + 75.3395i) q^{46} +(120.906 + 209.416i) q^{47} +(72.2822 - 41.0766i) q^{48} +(283.783 - 192.655i) q^{49} -27.5998i q^{50} +(415.453 + 243.660i) q^{51} +(-68.7279 - 39.6801i) q^{52} +(-432.694 - 249.816i) q^{53} +(-135.289 - 245.823i) q^{54} -325.013i q^{55} +(-43.5308 - 141.623i) q^{56} +(-352.476 - 620.248i) q^{57} +(-134.318 - 232.646i) q^{58} +(-366.212 + 634.299i) q^{59} +(-1.49656 + 219.172i) q^{60} +(-265.207 + 153.117i) q^{61} +334.778 q^{62} +(-479.939 + 140.376i) q^{63} -64.0000 q^{64} +(181.187 - 104.608i) q^{65} +(2.18706 - 320.294i) q^{66} +(-280.049 + 485.060i) q^{67} +(-185.381 - 321.089i) q^{68} +(-111.670 - 196.505i) q^{69} +(380.718 + 87.2945i) q^{70} +74.2161i q^{71} +(-2.94967 + 215.980i) q^{72} +(141.409 + 81.6426i) q^{73} +(664.230 + 383.494i) q^{74} +(61.8533 + 36.2764i) q^{75} +549.180i q^{76} +(-556.376 - 127.571i) q^{77} +(179.260 - 101.870i) q^{78} +(-437.160 - 757.183i) q^{79} +(84.3612 - 146.118i) q^{80} +(728.728 + 19.9084i) q^{81} +(186.866 - 107.887i) q^{82} +406.600 q^{83} +(374.604 + 88.5892i) q^{84} +977.435 q^{85} +(-494.466 + 285.480i) q^{86} +(697.922 + 4.76560i) q^{87} +(-123.284 + 213.535i) q^{88} +(526.091 + 911.216i) q^{89} +(-489.214 - 291.427i) q^{90} +(-107.957 - 351.226i) q^{91} +173.989i q^{92} +(-440.023 + 750.264i) q^{93} +(418.832 + 241.813i) q^{94} +(-1253.83 - 723.897i) q^{95} +(84.1197 - 143.429i) q^{96} +243.235i q^{97} +(298.872 - 617.472i) q^{98} +(714.930 + 425.887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Introduction

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