LMFDB - Embedded newform 120.4.w.c.77.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.61
Character	$\chi$	$=$	120.77
Dual form			120.4.w.c.53.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.79310 + 0.445660i) q^{2} +(2.14982 - 4.73057i) q^{3} +(7.60277 + 2.48954i) q^{4} +(4.08469 + 10.4075i) q^{5} +(8.11287 - 12.2548i) q^{6} +(13.5500 + 13.5500i) q^{7} +(20.1258 + 10.3418i) q^{8} +(-17.7566 - 20.3397i) q^{9} +(6.77075 + 30.8894i) q^{10} -23.6403 q^{11} +(28.1215 - 30.6134i) q^{12} +(-21.9939 - 21.9939i) q^{13} +(31.8078 + 43.8853i) q^{14} +(58.0146 + 3.05120i) q^{15} +(51.6043 + 37.8549i) q^{16} +(92.3861 - 92.3861i) q^{17} +(-40.5312 - 64.7242i) q^{18} -105.429 q^{19} +(5.14516 + 89.2946i) q^{20} +(93.2295 - 34.9693i) q^{21} +(-66.0296 - 10.5355i) q^{22} +(-6.66319 - 6.66319i) q^{23} +(92.1893 - 72.9735i) q^{24} +(-91.6306 + 85.0226i) q^{25} +(-51.6292 - 71.2327i) q^{26} +(-134.392 + 40.2721i) q^{27} +(69.2844 + 136.751i) q^{28} -190.191i q^{29} +(160.680 + 34.3771i) q^{30} -30.1383 q^{31} +(127.265 + 128.730i) q^{32} +(-50.8223 + 111.832i) q^{33} +(299.216 - 216.870i) q^{34} +(-85.6738 + 196.369i) q^{35} +(-84.3627 - 198.844i) q^{36} +(-203.258 + 203.258i) q^{37} +(-294.474 - 46.9856i) q^{38} +(-151.326 + 56.7607i) q^{39} +(-25.4242 + 251.701i) q^{40} +348.549i q^{41} +(275.983 - 56.1240i) q^{42} +(-30.6757 - 30.6757i) q^{43} +(-179.732 - 58.8536i) q^{44} +(139.155 - 267.882i) q^{45} +(-15.6414 - 21.5805i) q^{46} +(-66.6485 + 66.6485i) q^{47} +(290.015 - 162.737i) q^{48} +24.2070i q^{49} +(-293.824 + 196.640i) q^{50} +(-238.426 - 635.652i) q^{51} +(-112.460 - 221.969i) q^{52} +(195.204 - 195.204i) q^{53} +(-393.317 + 52.5908i) q^{54} +(-96.5634 - 246.036i) q^{55} +(132.573 + 412.837i) q^{56} +(-226.653 + 498.740i) q^{57} +(84.7607 - 531.222i) q^{58} -343.492i q^{59} +(433.476 + 167.627i) q^{60} +232.915i q^{61} +(-84.1792 - 13.4314i) q^{62} +(35.0015 - 516.206i) q^{63} +(298.095 + 416.273i) q^{64} +(139.062 - 318.738i) q^{65} +(-191.791 + 289.708i) q^{66} +(-397.741 + 397.741i) q^{67} +(932.390 - 472.391i) q^{68} +(-45.8453 + 17.1961i) q^{69} +(-326.809 + 510.297i) q^{70} -834.762i q^{71} +(-147.016 - 592.988i) q^{72} +(334.976 - 334.976i) q^{73} +(-658.303 + 477.135i) q^{74} +(205.216 + 616.248i) q^{75} +(-801.555 - 262.471i) q^{76} +(-320.327 - 320.327i) q^{77} +(-447.965 + 91.0981i) q^{78} +906.479i q^{79} +(-183.185 + 691.696i) q^{80} +(-98.4075 + 722.327i) q^{81} +(-155.334 + 973.530i) q^{82} +(-690.879 + 690.879i) q^{83} +(795.860 - 33.7648i) q^{84} +(1338.87 + 584.136i) q^{85} +(-72.0092 - 99.3510i) q^{86} +(-899.713 - 408.876i) q^{87} +(-475.780 - 244.483i) q^{88} +1288.76 q^{89} +(508.057 - 686.206i) q^{90} -596.035i q^{91} +(-34.0704 - 67.2471i) q^{92} +(-64.7918 + 142.571i) q^{93} +(-215.858 + 156.453i) q^{94} +(-430.646 - 1097.25i) q^{95} +(882.565 - 325.292i) q^{96} +(-688.583 - 688.583i) q^{97} +(-10.7881 + 67.6124i) q^{98} +(419.771 + 480.837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) $ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.79310	+	0.445660i	0.987509	+	0.157565i
$2$	2.79310	+	0.445660i	0.987509	+	0.157565i
$3$	2.14982	−	4.73057i	0.413732	−	0.910399i
$3$	2.14982	−	4.73057i	0.413732	−	0.910399i
$4$	7.60277	+	2.48954i	0.950347	+	0.311193i
$5$	4.08469	+	10.4075i	0.365346	+	0.930872i
$5$	4.08469	+	10.4075i	0.365346	+	0.930872i
$6$	8.11287	−	12.2548i	0.552011	−	0.833837i
$7$	13.5500	+	13.5500i	0.731633	+	0.731633i	0.970943	−	0.239310i	$-0.0769212\pi$
$7$	13.5500	+	13.5500i	0.731633	+	0.731633i	−0.239310	+	0.970943i	$0.576921\pi$
$8$	20.1258	+	10.3418i	0.889443	+	0.457047i
$9$	−17.7566	−	20.3397i	−0.657651	−	0.753323i
$10$	6.77075	+	30.8894i	0.214110	+	0.976810i
$11$	−23.6403			−0.647984			−0.323992	−	0.946060i	$-0.605025\pi$
$11$	−23.6403			−0.647984			−0.323992	+	0.946060i	$0.605025\pi$
$12$	28.1215	−	30.6134i	0.676499	−	0.736444i
$13$	−21.9939	−	21.9939i	−0.469231	−	0.469231i	0.432435	−	0.901665i	$-0.357655\pi$
$13$	−21.9939	−	21.9939i	−0.469231	−	0.469231i	−0.901665	+	0.432435i	$0.857655\pi$
$14$	31.8078	+	43.8853i	0.607215	+	0.837774i
$15$	58.0146	+	3.05120i	0.998620	+	0.0525212i
$16$	51.6043	+	37.8549i	0.806318	+	0.591483i
$17$	92.3861	−	92.3861i	1.31805	−	1.31805i	0.402740	−	0.915314i	$-0.368058\pi$
$17$	92.3861	−	92.3861i	1.31805	−	1.31805i	0.915314	−	0.402740i	$-0.131942\pi$
$18$	−40.5312	−	64.7242i	−0.530739	−	0.847535i
$19$	−105.429			−1.27301			−0.636503	−	0.771274i	$-0.719620\pi$
$19$	−105.429			−1.27301			−0.636503	+	0.771274i	$0.719620\pi$
$20$	5.14516	+	89.2946i	0.0575246	+	0.998344i
$21$	93.2295	−	34.9693i	0.968778	−	0.363378i
$22$	−66.0296	−	10.5355i	−0.639889	−	0.102099i
$23$	−6.66319	−	6.66319i	−0.0604075	−	0.0604075i	0.676258	−	0.736665i	$-0.263601\pi$
$23$	−6.66319	−	6.66319i	−0.0604075	−	0.0604075i	−0.736665	+	0.676258i	$0.763601\pi$
$24$	92.1893	−	72.9735i	0.784086	−	0.620652i
$25$	−91.6306	+	85.0226i	−0.733045	+	0.680181i
$26$	−51.6292	−	71.2327i	−0.389435	−	0.537303i
$27$	−134.392	+	40.2721i	−0.957915	+	0.287051i
$28$	69.2844	+	136.751i	0.467626	+	0.922984i
$29$		−	190.191i		−	1.21785i	−0.793228	−	0.608924i	$-0.791601\pi$
$29$		−	190.191i		−	1.21785i	0.793228	−	0.608924i	$-0.208399\pi$
$30$	160.680	+	34.3771i	0.977870	+	0.209212i
$31$	−30.1383			−0.174613			−0.0873064	−	0.996182i	$-0.527826\pi$
$31$	−30.1383			−0.174613			−0.0873064	+	0.996182i	$0.527826\pi$
$32$	127.265	+	128.730i	0.703049	+	0.711141i
$33$	−50.8223	+	111.832i	−0.268092	+	0.589923i
$34$	299.216	−	216.870i	1.50927	−	1.09391i
$35$	−85.6738	+	196.369i	−0.413757	+	0.948356i
$36$	−84.3627	−	198.844i	−0.390568	−	0.920574i
$37$	−203.258	+	203.258i	−0.903119	+	0.903119i	−0.995705	−	0.0925854i	$-0.970487\pi$
$37$	−203.258	+	203.258i	−0.903119	+	0.903119i	0.0925854	+	0.995705i	$0.470487\pi$
$38$	−294.474	−	46.9856i	−1.25711	−	0.200581i
$39$	−151.326	+	56.7607i	−0.621323	+	0.233051i
$40$	−25.4242	+	251.701i	−0.100498	+	0.994937i
$41$			348.549i			1.32766i	0.747882	+	0.663831i	$0.231071\pi$
$41$			348.549i			1.32766i	−0.747882	+	0.663831i	$0.768929\pi$
$42$	275.983	−	56.1240i	1.01393	−	0.206193i
$43$	−30.6757	−	30.6757i	−0.108791	−	0.108791i	0.650616	−	0.759407i	$-0.274511\pi$
$43$	−30.6757	−	30.6757i	−0.108791	−	0.108791i	−0.759407	+	0.650616i	$0.774511\pi$
$44$	−179.732	−	58.8536i	−0.615809	−	0.201648i
$45$	139.155	−	267.882i	0.460976	−	0.887412i
$46$	−15.6414	−	21.5805i	−0.0501348	−	0.0691710i
$47$	−66.6485	+	66.6485i	−0.206844	+	0.206844i	−0.802925	−	0.596080i	$-0.796724\pi$
$47$	−66.6485	+	66.6485i	−0.206844	+	0.206844i	0.596080	+	0.802925i	$0.296724\pi$
$48$	290.015	−	162.737i	0.872085	−	0.489355i
$49$			24.2070i			0.0705743i
$50$	−293.824	+	196.640i	−0.831060	+	0.556182i
$51$	−238.426	−	635.652i	−0.654633	−	1.74528i
$52$	−112.460	−	221.969i	−0.299910	−	0.591953i
$53$	195.204	−	195.204i	0.505911	−	0.505911i	−0.407358	−	0.913269i	$-0.633550\pi$
$53$	195.204	−	195.204i	0.505911	−	0.505911i	0.913269	+	0.407358i	$0.133550\pi$
$54$	−393.317	+	52.5908i	−0.991179	+	0.132532i
$55$	−96.5634	−	246.036i	−0.236738	−	0.603190i
$56$	132.573	+	412.837i	0.316355	+	0.985136i
$57$	−226.653	+	498.740i	−0.526684	+	1.15894i
$58$	84.7607	−	531.222i	0.191890	−	1.20264i
$59$		−	343.492i		−	0.757946i	−0.925408	−	0.378973i	$-0.876277\pi$
$59$		−	343.492i		−	0.757946i	0.925408	−	0.378973i	$-0.123723\pi$
$60$	433.476	+	167.627i	0.932691	+	0.360677i
$61$			232.915i			0.488880i	0.969664	+	0.244440i	$0.0786041\pi$
$61$			232.915i			0.488880i	−0.969664	+	0.244440i	$0.921396\pi$
$62$	−84.1792	−	13.4314i	−0.172432	−	0.0275128i
$63$	35.0015	−	516.206i	0.0699963	−	1.03232i
$64$	298.095	+	416.273i	0.582216	+	0.813034i
$65$	139.062	−	318.738i	0.265362	−	0.608225i
$66$	−191.791	+	289.708i	−0.357694	+	0.540313i
$67$	−397.741	+	397.741i	−0.725251	+	0.725251i	−0.969670	−	0.244418i	$-0.921403\pi$
$67$	−397.741	+	397.741i	−0.725251	+	0.725251i	0.244418	+	0.969670i	$0.421403\pi$
$68$	932.390	−	472.391i	1.66278	−	0.842439i
$69$	−45.8453	+	17.1961i	−0.0799874	+	0.0300024i
$70$	−326.809	+	510.297i	−0.558016	+	0.871316i
$71$		−	834.762i		−	1.39533i	−0.716427	−	0.697663i	$-0.754224\pi$
$71$		−	834.762i		−	1.39533i	0.716427	−	0.697663i	$-0.245776\pi$
$72$	−147.016	−	592.988i	−0.240639	−	0.970615i
$73$	334.976	−	334.976i	0.537067	−	0.537067i	−0.385599	−	0.922666i	$-0.626005\pi$
$73$	334.976	−	334.976i	0.537067	−	0.537067i	0.922666	+	0.385599i	$0.126005\pi$
$74$	−658.303	+	477.135i	−1.03414	+	0.749538i
$75$	205.216	+	616.248i	0.315951	+	0.948775i
$76$	−801.555	−	262.471i	−1.20980	−	0.396151i
$77$	−320.327	−	320.327i	−0.474086	−	0.474086i
$78$	−447.965	+	91.0981i	−0.650282	+	0.132241i
$79$			906.479i			1.29097i	0.763771	+	0.645487i	$0.223345\pi$
$79$			906.479i			1.29097i	−0.763771	+	0.645487i	$0.776655\pi$
$80$	−183.185	+	691.696i	−0.256009	+	0.966674i
$81$	−98.4075	+	722.327i	−0.134990	+	0.990847i
$82$	−155.334	+	973.530i	−0.209193	+	1.31108i
$83$	−690.879	+	690.879i	−0.913660	+	0.913660i	−0.996558	−	0.0828977i	$-0.973583\pi$
$83$	−690.879	+	690.879i	−0.913660	+	0.913660i	0.0828977	+	0.996558i	$0.473583\pi$
$84$	795.860	−	33.7648i	1.03376	−	0.0438576i
$85$	1338.87	+	584.136i	1.70849	+	0.745394i
$86$	−72.0092	−	99.3510i	−0.0902901	−	0.124573i
$87$	−899.713	−	408.876i	−1.10873	−	0.503863i
$88$	−475.780	−	244.483i	−0.576344	−	0.296159i
$89$	1288.76			1.53493			0.767465	−	0.641091i	$-0.221518\pi$
$89$	1288.76			1.53493			0.767465	+	0.641091i	$0.221518\pi$
$90$	508.057	−	686.206i	0.595043	−	0.803694i
$91$		−	596.035i		−	0.686609i
$92$	−34.0704	−	67.2471i	−0.0386097	−	0.0762064i
$93$	−64.7918	+	142.571i	−0.0722430	+	0.158967i
$94$	−215.858	+	156.453i	−0.236852	+	0.171669i
$95$	−430.646	−	1097.25i	−0.465088	−	1.18501i
$96$	882.565	−	325.292i	0.938296	−	0.345833i
$97$	−688.583	−	688.583i	−0.720773	−	0.720773i	0.247989	−	0.968763i	$-0.420230\pi$
$97$	−688.583	−	688.583i	−0.720773	−	0.720773i	−0.968763	+	0.247989i	$0.920230\pi$
$98$	−10.7881	+	67.6124i	−0.0111200	+	0.0696927i
$99$	419.771	+	480.837i	0.426147	+	0.488141i
$100$	−908.314	+	418.289i	−0.908314	+	0.418289i
$101$	1938.57			1.90985			0.954925	−	0.296848i	$-0.0959356\pi$
$101$	1938.57			1.90985			0.954925	+	0.296848i	$0.0959356\pi$
$102$	−382.661	−	1881.69i	−0.371462	−	1.82662i
$103$	280.520	−	280.520i	0.268354	−	0.268354i	−0.560083	−	0.828437i	$-0.689231\pi$
$103$	280.520	−	280.520i	0.268354	−	0.268354i	0.828437	+	0.560083i	$0.189231\pi$
$104$	−215.188	−	670.100i	−0.202893	−	0.631814i
$105$	744.756	+	827.443i	0.692197	+	0.769050i
$106$	632.217	−	458.228i	0.579305	−	0.419878i
$107$	93.1446	+	93.1446i	0.0841555	+	0.0841555i	0.747931	−	0.663776i	$-0.231047\pi$
$107$	93.1446	+	93.1446i	0.0841555	+	0.0841555i	−0.663776	+	0.747931i	$0.731047\pi$
$108$	−1122.01	−	28.3945i	−0.999680	−	0.0252988i
$109$	1161.91			1.02101			0.510507	−	0.859874i	$-0.329458\pi$
$109$	1161.91			1.02101			0.510507	+	0.859874i	$0.329458\pi$
$110$	−160.063	−	730.236i	−0.138740	−	0.632957i
$111$	524.559	+	1398.49i	0.448549	+	1.19585i
$112$	186.306	+	1212.18i	0.157181	+	1.02268i
$113$	61.0136	+	61.0136i	0.0507936	+	0.0507936i	0.732047	−	0.681254i	$-0.238565\pi$
$113$	61.0136	+	61.0136i	0.0507936	+	0.0507936i	−0.681254	+	0.732047i	$0.738565\pi$
$114$	−855.334	+	1292.02i	−0.702714	+	1.06148i
$115$	42.1298	−	96.5640i	0.0341620	−	0.0783012i
$116$	473.489	−	1445.98i	0.378986	−	1.15738i
$117$	−56.8129	+	837.884i	−0.0448919	+	0.662072i
$118$	153.081	−	959.405i	0.119426	−	0.748478i
$119$	2503.67			1.92866
$120$	1136.03	+	661.382i	0.864210	+	0.503131i
$121$	−772.136			−0.580117
$122$	−103.801	+	650.553i	−0.0770302	+	0.482773i
$123$	1648.83	+	749.316i	1.20870	+	0.549297i
$124$	−229.135	−	75.0306i	−0.165943	−	0.0543383i
$125$	−1259.15	−	606.351i	−0.900976	−	0.433869i
$126$	327.815	−	1426.21i	0.231778	−	1.00839i
$127$	728.509	+	728.509i	0.509014	+	0.509014i	0.914224	−	0.405210i	$-0.132802\pi$
$127$	728.509	+	728.509i	0.509014	+	0.509014i	−0.405210	+	0.914224i	$0.632802\pi$
$128$	647.091	+	1295.54i	0.446838	+	0.894615i
$129$	−211.060	+	79.1664i	−0.144053	+	0.0540326i
$130$	530.463	−	828.293i	0.357882	−	0.558816i
$131$	−1108.11			−0.739052			−0.369526	−	0.929220i	$-0.620480\pi$
$131$	−1108.11			−0.739052			−0.369526	+	0.929220i	$0.620480\pi$
$132$	−664.802	+	723.710i	−0.438360	+	0.477203i
$133$	−1428.57	−	1428.57i	−0.931374	−	0.931374i
$134$	−1288.19	+	933.672i	−0.830466	+	0.601918i
$135$	−968.080	−	1234.18i	−0.617178	−	0.786823i
$136$	2814.78	−	903.905i	1.77475	−	0.569921i
$137$	157.161	−	157.161i	0.0980083	−	0.0980083i	−0.656403	−	0.754411i	$-0.727923\pi$
$137$	157.161	−	157.161i	0.0980083	−	0.0980083i	0.754411	+	0.656403i	$0.227923\pi$
$138$	−135.714	+	27.5988i	−0.0837156	+	0.0170244i
$139$	1006.99			0.614471			0.307236	−	0.951633i	$-0.400596\pi$
$139$	1006.99			0.614471			0.307236	+	0.951633i	$0.400596\pi$
$140$	−1140.23	+	1279.66i	−0.688335	+	0.772509i
$141$	172.003	+	458.567i	0.102733	+	0.273889i
$142$	372.021	−	2331.57i	0.219854	−	1.37790i
$143$	519.941	+	519.941i	0.304054	+	0.304054i
$144$	−146.359	−	1721.79i	−0.0846986	−	0.996407i
$145$	1979.41	−	776.873i	1.13366	−	0.444936i
$146$	1084.90	−	786.334i	0.614982	−	0.445736i
$147$	114.513	+	52.0405i	0.0642507	+	0.0291989i
$148$	−2051.34	+	1039.30i	−1.13932	+	0.577232i
$149$			1884.11i			1.03592i	0.855405	+	0.517960i	$0.173309\pi$
$149$			1884.11i			1.03592i	−0.855405	+	0.517960i	$0.826691\pi$
$150$	298.552	+	1812.70i	0.162511	+	0.986707i
$151$	34.3422			0.0185081			0.00925407	−	0.999957i	$-0.497054\pi$
$151$	34.3422			0.0185081			0.00925407	+	0.999957i	$0.497054\pi$
$152$	−2121.85	−	1090.33i	−1.13227	−	0.581824i
$153$	−3519.57	−	238.645i	−1.85974	−	0.126100i
$154$	−751.947	−	1037.46i	−0.393465	−	0.542864i
$155$	−123.106	−	313.663i	−0.0637941	−	0.162542i
$156$	−1291.81	+	54.8056i	−0.662996	+	0.0281280i
$157$	1860.87	−	1860.87i	0.945945	−	0.945945i	−0.0526676	−	0.998612i	$-0.516772\pi$
$157$	1860.87	−	1860.87i	0.945945	−	0.945945i	0.998612	+	0.0526676i	$0.0167724\pi$
$158$	−403.982	+	2531.88i	−0.203412	+	1.27485i
$159$	−503.773	−	1343.08i	−0.251269	−	0.669892i
$160$	−819.916	+	1850.33i	−0.405125	+	0.914261i
$161$		−	180.573i		−	0.0883922i
$162$	−596.774	+	1973.67i	−0.289426	+	0.957200i
$163$	−1488.97	−	1488.97i	−0.715493	−	0.715493i	0.252186	−	0.967679i	$-0.418851\pi$
$163$	−1488.97	−	1488.97i	−0.715493	−	0.715493i	−0.967679	+	0.252186i	$0.918851\pi$
$164$	−867.728	+	2649.94i	−0.413160	+	1.26174i
$165$	−1371.48	−	72.1314i	−0.647089	−	0.0340328i
$166$	−2237.59	+	1621.79i	−1.04621	+	0.758287i
$167$	−1907.69	+	1907.69i	−0.883963	+	0.883963i	−0.993935	−	0.109972i	$-0.964924\pi$
$167$	−1907.69	+	1907.69i	−0.883963	+	0.883963i	0.109972	+	0.993935i	$0.464924\pi$
$168$	2237.96	+	260.375i	1.02775	+	0.119574i
$169$		−	1229.54i		−	0.559645i
$170$	3479.28	+	2228.23i	1.56970	+	1.00528i
$171$	1872.06	+	2144.40i	0.837194	+	0.958985i
$172$	−156.852	−	309.589i	−0.0695339	−	0.137244i
$173$	−657.105	+	657.105i	−0.288779	+	0.288779i	−0.836597	−	0.547818i	$-0.815459\pi$
$173$	−657.105	+	657.105i	−0.288779	+	0.288779i	0.547818	+	0.836597i	$0.315459\pi$
$174$	−2330.76	−	1543.00i	−1.01549	−	0.672266i
$175$	−2393.66	−	89.5384i	−1.03396	−	0.0386769i
$176$	−1219.94	−	894.901i	−0.522481	−	0.383271i
$177$	−1624.91	−	738.444i	−0.690033	−	0.313587i
$178$	3599.64	+	574.351i	1.51576	+	0.241851i
$179$		−	2226.47i		−	0.929687i	−0.885393	−	0.464843i	$-0.846111\pi$
$179$		−	2226.47i		−	0.929687i	0.885393	−	0.464843i	$-0.153889\pi$
$180$	1724.87	−	1690.22i	0.714244	−	0.699897i
$181$			759.935i			0.312075i	0.987751	+	0.156037i	$0.0498721\pi$
$181$			759.935i			0.312075i	−0.987751	+	0.156037i	$0.950128\pi$
$182$	265.629	−	1664.78i	0.108185	−	0.678033i
$183$	1101.82	+	500.724i	0.445075	+	0.202265i
$184$	−65.1926	−	203.011i	−0.0261199	−	0.0813380i
$185$	−2945.65	−	1285.15i	−1.17064	−	0.510737i
$186$	−244.508	+	369.340i	−0.0963882	+	0.145599i
$187$	−2184.04	+	2184.04i	−0.854078	+	0.854078i
$188$	−672.638	+	340.789i	−0.260942	+	0.132205i
$189$	−2366.70	−	1275.33i	−0.910859	−	0.490827i
$190$	−713.835	−	3256.65i	−0.272563	−	1.24349i
$191$			109.634i			0.0415333i	0.999784	+	0.0207667i	$0.00661071\pi$
$191$			109.634i			0.0415333i	−0.999784	+	0.0207667i	$0.993389\pi$
$192$	2610.06	−	515.246i	0.981067	−	0.193670i
$193$	857.642	−	857.642i	0.319868	−	0.319868i	−0.528849	−	0.848716i	$-0.677376\pi$
$193$	857.642	−	857.642i	0.319868	−	0.319868i	0.848716	+	0.528849i	$0.177376\pi$
$194$	−1616.40	−	2230.15i	−0.598201	−	0.825338i
$195$	−1208.86	−	1343.07i	−0.443938	−	0.493228i
$196$	−60.2643	+	184.040i	−0.0219622	+	0.0670700i
$197$	−760.319	−	760.319i	−0.274977	−	0.274977i	0.556123	−	0.831100i	$-0.312288\pi$
$197$	−760.319	−	760.319i	−0.274977	−	0.274977i	−0.831100	+	0.556123i	$0.812288\pi$
$198$	958.171	+	1530.10i	0.343910	+	0.549189i
$199$			5232.87i			1.86406i	0.362378	+	0.932031i	$0.381965\pi$
$199$			5232.87i			1.86406i	−0.362378	+	0.932031i	$0.618035\pi$
$200$	−2723.42	+	763.522i	−0.962876	+	0.269946i
$201$	1026.47	+	2736.61i	0.360208	+	0.960328i
$202$	5414.61	+	863.943i	1.88599	+	0.300925i
$203$	2577.10	−	2577.10i	0.891019	−	0.891019i
$204$	−230.213	−	5426.29i	−0.0790106	−	1.86234i
$205$	−3627.51	+	1423.72i	−1.23588	+	0.485056i
$206$	908.536	−	658.503i	0.307285	−	0.222719i
$207$	−17.2119	+	253.843i	−0.00577926	+	0.0852334i
$208$	−302.403	−	1967.55i	−0.100807	−	0.655891i
$209$	2492.38			0.824888
$210$	1711.42	+	2643.04i	0.562376	+	0.868509i
$211$		−	2462.42i		−	0.803414i	−0.915768	−	0.401707i	$-0.868417\pi$
$211$		−	2462.42i		−	0.803414i	0.915768	−	0.401707i	$-0.131583\pi$
$212$	1970.06	−	998.121i	0.638227	−	0.323355i
$213$	−3948.90	−	1794.59i	−1.27030	−	0.577291i
$214$	218.651	+	301.673i	0.0698443	+	0.0963642i
$215$	193.955	−	444.557i	0.0615239	−	0.141016i
$216$	−3121.23	−	579.344i	−0.983206	−	0.182497i
$217$	−408.375	−	408.375i	−0.127753	−	0.127753i
$218$	3245.32	+	517.816i	1.00826	+	0.160876i
$219$	−864.489	−	2304.76i	−0.266743	−	0.711147i
$220$	−121.633	−	2110.95i	−0.0372750	−	0.646911i
$221$	−4063.85			−1.23694
$222$	841.890	+	4139.90i	0.254522	+	1.25159i
$223$	181.463	−	181.463i	0.0544919	−	0.0544919i	−0.679336	−	0.733828i	$-0.737732\pi$
$223$	181.463	−	181.463i	0.0544919	−	0.0544919i	0.733828	+	0.679336i	$0.237732\pi$
$224$	−19.8494	+	3468.75i	−0.00592073	+	1.03467i
$225$	3356.38	+	354.028i	0.994483	+	0.104897i
$226$	143.225	+	197.608i	0.0421558	+	0.0581624i
$227$	2577.03	+	2577.03i	0.753496	+	0.753496i	0.975130	−	0.221634i	$-0.0711391\pi$
$227$	2577.03	+	2577.03i	0.753496	+	0.753496i	−0.221634	+	0.975130i	$0.571139\pi$
$228$	−2964.83	+	3227.55i	−0.861188	+	0.937498i
$229$	2690.23			0.776313			0.388156	−	0.921593i	$-0.373112\pi$
$229$	2690.23			0.776313			0.388156	+	0.921593i	$0.373112\pi$
$230$	160.707	−	250.937i	0.0460728	−	0.0719404i
$231$	−2203.97	+	826.685i	−0.627752	+	0.235463i
$232$	1966.92	−	3827.75i	0.556614	−	1.08321i
$233$	−2252.87	−	2252.87i	−0.633435	−	0.633435i	0.315493	−	0.948928i	$-0.397830\pi$
$233$	−2252.87	−	2252.87i	−0.633435	−	0.633435i	−0.948928	+	0.315493i	$0.897830\pi$
$234$	−532.096	+	2314.97i	−0.148650	+	0.646729i
$235$	−965.880	−	421.403i	−0.268115	−	0.116976i
$236$	855.138	−	2611.49i	0.235867	−	0.720311i
$237$	4288.16	+	1948.76i	1.17530	+	0.534117i
$238$	6992.99	+	1115.79i	1.90457	+	0.303890i
$239$	3833.40			1.03750			0.518749	−	0.854927i	$-0.326398\pi$
$239$	3833.40			1.03750			0.518749	+	0.854927i	$0.326398\pi$
$240$	2878.30	+	2353.59i	0.774140	+	0.633015i
$241$	1641.79			0.438826			0.219413	−	0.975632i	$-0.429586\pi$
$241$	1641.79			0.438826			0.219413	+	0.975632i	$0.429586\pi$
$242$	−2156.65	−	344.110i	−0.572871	−	0.0914060i
$243$	3205.46	+	2018.39i	0.846216	+	0.532840i
$244$	−579.851	+	1770.80i	−0.152136	+	0.464605i
$245$	−251.933	+	98.8781i	−0.0656956	+	0.0257840i
$246$	4271.41	+	2827.73i	1.10705	+	0.732884i
$247$	2318.80	+	2318.80i	0.597334	+	0.597334i
$248$	−606.557	−	311.684i	−0.155308	−	0.0798063i
$249$	1782.99	+	4753.51i	0.453784	+	1.20981i
$250$	−3246.71	−	2254.75i	−0.821359	−	0.570412i
$251$	4943.40			1.24313			0.621564	−	0.783364i	$-0.286498\pi$
$251$	4943.40			1.24313			0.621564	+	0.783364i	$0.286498\pi$
$252$	1551.23	−	3837.46i	0.387770	−	0.959275i
$253$	157.520	+	157.520i	0.0391431	+	0.0391431i
$254$	1710.13	+	2359.46i	0.422453	+	0.582858i
$255$	5641.63	−	5077.85i	1.38546	−	1.24701i
$256$	1230.01	+	3906.95i	0.300297	+	0.953846i
$257$	−1468.71	+	1468.71i	−0.356481	+	0.356481i	−0.862514	−	0.506033i	$-0.831111\pi$
$257$	−1468.71	+	1468.71i	−0.356481	+	0.356481i	0.506033	+	0.862514i	$0.331111\pi$
$258$	−624.794	+	127.058i	−0.150767	+	0.0306600i
$259$	−5508.31			−1.32150
$260$	1850.77	−	2077.09i	0.441461	−	0.495446i
$261$	−3868.43	+	3377.15i	−0.917433	+	0.800920i
$262$	−3095.05	−	493.840i	−0.729821	−	0.116449i
$263$	−538.864	−	538.864i	−0.126341	−	0.126341i	0.641109	−	0.767450i	$-0.278475\pi$
$263$	−538.864	−	538.864i	−0.126341	−	0.126341i	−0.767450	+	0.641109i	$0.778475\pi$
$264$	−2179.38	+	1725.12i	−0.508075	+	0.402172i
$265$	2828.92	+	1234.23i	0.655771	+	0.286106i
$266$	−3353.48	−	4626.79i	−0.772988	−	1.06649i
$267$	2770.61	−	6096.59i	0.635050	−	1.39740i
$268$	−4014.13	+	2033.74i	−0.914933	+	0.463547i
$269$			402.369i			0.0912004i	0.998960	+	0.0456002i	$0.0145200\pi$
$269$			402.369i			0.0912004i	−0.998960	+	0.0456002i	$0.985480\pi$
$270$	−2153.92	−	3878.61i	−0.485493	−	0.874240i
$271$	−8159.60			−1.82900			−0.914502	−	0.404581i	$-0.867418\pi$
$271$	−8159.60			−1.82900			−0.914502	+	0.404581i	$0.867418\pi$
$272$	8264.79	−	1270.26i	1.84238	−	0.283164i
$273$	−2819.59	−	1281.37i	−0.625088	−	0.284072i
$274$	509.005	−	368.924i	0.112227	−	0.0813414i
$275$	2166.17	−	2009.96i	0.475001	−	0.440746i
$276$	−391.362	+	16.6037i	−0.0853523	+	0.00362112i
$277$	−333.740	+	333.740i	−0.0723916	+	0.0723916i	−0.742376	−	0.669984i	$-0.766301\pi$
$277$	−333.740	+	333.740i	−0.0723916	+	0.0723916i	0.669984	+	0.742376i	$0.266301\pi$
$278$	2812.61	+	448.774i	0.606796	+	0.0968190i
$279$	535.153	+	613.004i	0.114834	+	0.131540i
$280$	−3755.06	+	3066.07i	−0.801457	+	0.654402i
$281$		−	985.762i		−	0.209273i	−0.994511	−	0.104636i	$-0.966632\pi$
$281$		−	985.762i		−	0.209273i	0.994511	−	0.104636i	$-0.0333679\pi$
$282$	276.057	+	1357.48i	0.0582941	+	0.286655i
$283$	5012.19	+	5012.19i	1.05280	+	1.05280i	0.998526	+	0.0542790i	$0.0172860\pi$
$283$	5012.19	+	5012.19i	1.05280	+	1.05280i	0.0542790	+	0.998526i	$0.482714\pi$
$284$	2078.18	−	6346.51i	0.434216	−	1.32604i
$285$	−6116.43	−	321.686i	−1.27125	−	0.0668598i
$286$	1220.53	+	1683.96i	0.252348	+	0.348164i
$287$	−4722.85	+	4722.85i	−0.971362	+	0.971362i
$288$	358.538	−	4874.35i	0.0733579	−	0.997306i
$289$		−	12157.4i		−	2.47453i
$290$	5874.90	−	1287.74i	1.18961	−	0.260753i
$291$	−4737.72	+	1777.06i	−0.954398	+	0.357984i
$292$	3380.68	−	1712.81i	0.677532	−	0.343269i
$293$	684.466	−	684.466i	0.136474	−	0.136474i	−0.635569	−	0.772044i	$-0.719235\pi$
$293$	684.466	−	684.466i	0.136474	−	0.136474i	0.772044	+	0.635569i	$0.219235\pi$
$294$	296.653	+	196.388i	0.0588474	+	0.0389578i
$295$	3574.88	−	1403.06i	0.705550	−	0.276913i
$296$	−6192.78	+	1988.68i	−1.21604	+	0.390505i
$297$	3177.06	−	952.045i	0.620713	−	0.186004i
$298$	−839.672	+	5262.50i	−0.163225	+	1.02298i
$299$			293.099i			0.0566901i
$300$	26.0380	+	5196.09i	0.00501101	+	0.999987i
$301$		−	831.313i		−	0.159190i
$302$	95.9211	+	15.3050i	0.0182769	+	0.00291623i
$303$	4167.57	−	9170.53i	0.790166	−	1.73872i
$304$	−5440.61	−	3991.01i	−1.02645	−	0.752961i
$305$	−2424.05	+	951.385i	−0.455084	+	0.178610i
$306$	−9724.14	−	2235.09i	−1.81664	−	0.417554i
$307$	−1726.29	+	1726.29i	−0.320926	+	0.320926i	−0.849122	−	0.528196i	$-0.822869\pi$
$307$	−1726.29	+	1726.29i	−0.320926	+	0.320926i	0.528196	+	0.849122i	$0.322869\pi$
$308$	−1637.91	−	3232.84i	−0.303014	−	0.598079i
$309$	−723.953	−	1930.09i	−0.133282	−	0.355336i
$310$	−204.059	−	930.955i	−0.0373863	−	0.170564i
$311$			4178.94i			0.761949i	0.924585	+	0.380975i	$0.124411\pi$
$311$			4178.94i			0.761949i	−0.924585	+	0.380975i	$0.875589\pi$
$312$	−3632.57	−	422.630i	−0.659146	−	0.0766882i
$313$	−7559.82	+	7559.82i	−1.36520	+	1.36520i	−0.498043	+	0.867152i	$0.665948\pi$
$313$	−7559.82	+	7559.82i	−1.36520	+	1.36520i	−0.867152	+	0.498043i	$0.834052\pi$
$314$	6026.89	−	4368.26i	1.08318	−	0.785081i
$315$	5515.37	−	1744.27i	0.986526	−	0.311995i
$316$	−2256.72	+	6891.76i	−0.401742	+	1.22687i
$317$	2832.31	+	2832.31i	0.501825	+	0.501825i	0.912005	−	0.410180i	$-0.134534\pi$
$317$	2832.31	+	2832.31i	0.501825	+	0.501825i	−0.410180	+	0.912005i	$0.634534\pi$
$318$	−808.529	−	3975.85i	−0.142579	−	0.701116i
$319$			4496.18i			0.789146i
$320$	−3114.73	+	4802.76i	−0.544120	+	0.839007i
$321$	640.871	−	240.383i	0.111433	−	0.0417972i
$322$	80.4742	−	504.358i	0.0139275	−	0.0872881i
$323$	−9740.20	+	9740.20i	−1.67789	+	1.67789i
$324$	−2546.44	+	5246.70i	−0.436632	+	0.899640i
$325$	3885.28	+	145.335i	0.663129	+	0.0248053i
$326$	−3495.27	−	4822.42i	−0.593819	−	0.819292i
$327$	2497.89	−	5496.48i	0.422426	−	0.929530i
$328$	−3604.62	+	7014.82i	−0.606804	+	1.18088i
$329$	−1806.18			−0.302668
$330$	−3798.54	−	812.685i	−0.633644	−	0.135566i
$331$			1899.46i			0.315419i	0.987486	+	0.157709i	$0.0504109\pi$
$331$			1899.46i			0.315419i	−0.987486	+	0.157709i	$0.949589\pi$
$332$	−6972.57	+	3532.62i	−1.15262	+	0.583969i
$333$	7743.38	+	525.041i	1.27428	+	0.0864026i
$334$	−6178.56	+	4478.19i	−1.01220	+	0.733640i
$335$	−5764.13	−	2514.83i	−0.940084	−	0.410148i
$336$	6134.80	+	1724.62i	0.996074	+	0.280018i
$337$	−5416.63	−	5416.63i	−0.875556	−	0.875556i	0.117515	−	0.993071i	$-0.462507\pi$
$337$	−5416.63	−	5416.63i	−0.875556	−	0.875556i	−0.993071	+	0.117515i	$0.962507\pi$
$338$	547.958	−	3434.23i	0.0881804	−	0.552655i
$339$	419.797	−	157.461i	0.0672573	−	0.0252275i
$340$	8724.92	+	7774.24i	1.39169	+	1.24005i
$341$	712.479			0.113146
$342$	4273.18	+	6823.82i	0.675635	+	1.07892i
$343$	4319.66	−	4319.66i	0.679999	−	0.679999i
$344$	−300.131	−	934.614i	−0.0470406	−	0.146485i
$345$	−366.232	−	406.893i	−0.0571514	−	0.0634968i
$346$	−2128.20	+	1542.51i	−0.330673	+	0.239671i
$347$	−4397.76	−	4397.76i	−0.680357	−	0.680357i	0.279723	−	0.960081i	$-0.409757\pi$
$347$	−4397.76	−	4397.76i	−0.680357	−	0.680357i	−0.960081	+	0.279723i	$0.909757\pi$
$348$	−5822.40	−	5348.47i	−0.896877	−	0.823873i
$349$	11672.4			1.79028			0.895139	−	0.445787i	$-0.147076\pi$
$349$	11672.4			1.79028			0.895139	+	0.445787i	$0.147076\pi$
$350$	−6645.81	−	1316.85i	−1.01495	−	0.201110i
$351$	3841.53	+	2070.05i	0.584176	+	0.314790i
$352$	−3008.59	−	3043.22i	−0.455564	−	0.460808i
$353$	5095.42	+	5095.42i	0.768277	+	0.768277i	0.977803	−	0.209526i	$-0.0671921\pi$
$353$	5095.42	+	5095.42i	0.768277	+	0.768277i	−0.209526	+	0.977803i	$0.567192\pi$
$354$	−4209.44	−	2786.70i	−0.632003	−	0.418394i
$355$	8687.76	−	3409.75i	1.29887	−	0.509777i
$356$	9798.18	+	3208.44i	1.45872	+	0.477660i
$357$	5382.43	−	11843.8i	0.797951	−	1.75585i
$358$	992.248	−	6218.74i	0.146486	−	0.918074i
$359$	−10047.6			−1.47714			−0.738571	−	0.674176i	$-0.764499\pi$
$359$	−10047.6			−1.47714			−0.738571	+	0.674176i	$0.764499\pi$
$360$	5570.98	−	3952.24i	0.815601	−	0.578614i
$361$	4256.33			0.620546
$362$	−338.673	+	2122.57i	−0.0491720	+	0.308177i
$363$	−1659.95	+	3652.64i	−0.240013	+	0.528138i
$364$	1483.86	−	4531.52i	0.213668	−	0.652517i
$365$	4854.52	+	2117.97i	0.696156	+	0.303725i
$366$	2854.33	+	1889.61i	0.407646	+	0.269867i
$367$	5113.00	+	5113.00i	0.727238	+	0.727238i	0.970069	−	0.242831i	$-0.0780759\pi$
$367$	5113.00	+	5113.00i	0.727238	+	0.727238i	−0.242831	+	0.970069i	$0.578076\pi$
$368$	−91.6152	−	596.084i	−0.0129776	−	0.0844376i
$369$	7089.38	−	6189.04i	1.00016	−	0.873139i
$370$	−7654.73	−	4902.32i	−1.07554	−	0.688809i
$371$	5290.03			0.740283
$372$	−847.535	+	922.636i	−0.118125	+	0.128593i
$373$	829.354	+	829.354i	0.115127	+	0.115127i	0.762323	−	0.647196i	$-0.224059\pi$
$373$	829.354	+	829.354i	0.115127	+	0.115127i	−0.647196	+	0.762323i	$0.724059\pi$
$374$	−7073.56	+	5126.88i	−0.977982	+	0.708837i
$375$	−5575.33	+	4652.97i	−0.767757	+	0.640742i
$376$	−2030.62	+	652.088i	−0.278514	+	0.0894385i
$377$	−4183.04	+	4183.04i	−0.571452	+	0.571452i
$378$	−6042.07	−	4616.85i	−0.822144	−	0.628215i
$379$	−7284.09			−0.987226			−0.493613	−	0.869682i	$-0.664324\pi$
$379$	−7284.09			−0.987226			−0.493613	+	0.869682i	$0.664324\pi$
$380$	−542.450	−	9414.26i	−0.0732292	−	1.27090i
$381$	5012.42	−	1880.10i	0.674001	−	0.252810i
$382$	−48.8597	+	306.219i	−0.00654419	+	0.0410145i
$383$	7765.66	+	7765.66i	1.03605	+	1.03605i	0.999325	+	0.0367230i	$0.0116919\pi$
$383$	7765.66	+	7765.66i	1.03605	+	1.03605i	0.0367230	+	0.999325i	$0.488308\pi$
$384$	7519.77	−	275.933i	0.999327	−	0.0366696i
$385$	2025.35	−	4642.23i	0.268108	−	0.614519i
$386$	2777.70	−	2013.26i	0.366272	−	0.265472i
$387$	−79.2391	+	1168.63i	−0.0104081	+	0.153501i
$388$	−3520.88	−	6949.40i	−0.460685	−	0.909284i
$389$			524.755i			0.0683962i	0.999415	+	0.0341981i	$0.0108877\pi$
$389$			524.755i			0.0683962i	−0.999415	+	0.0341981i	$0.989112\pi$
$390$	−2777.90	−	4290.07i	−0.360678	−	0.557015i
$391$	−1231.17			−0.159241
$392$	−250.344	+	487.184i	−0.0322558	+	0.0627718i
$393$	−2382.23	+	5241.98i	−0.305770	+	0.672832i
$394$	−1784.80	−	2462.49i	−0.228216	−	0.314869i
$395$	−9434.15	+	3702.69i	−1.20173	+	0.471652i
$396$	1994.36	+	4700.73i	0.253082	+	0.596517i
$397$	−7963.26	+	7963.26i	−1.00671	+	1.00671i	−0.00673471	+	0.999977i	$0.502144\pi$
$397$	−7963.26	+	7963.26i	−1.00671	+	1.00671i	−0.999977	+	0.00673471i	$0.997856\pi$
$398$	−2332.08	+	14615.9i	−0.293711	+	1.84078i
$399$	−9829.11	+	3686.79i	−1.23326	+	0.462582i
$400$	−7947.05	+	918.869i	−0.993382	+	0.114859i
$401$		−	2609.86i		−	0.325012i	−0.986708	−	0.162506i	$-0.948042\pi$
$401$		−	2609.86i		−	0.325012i	0.986708	−	0.162506i	$-0.0519577\pi$
$402$	1647.44	+	8101.08i	0.204395	+	1.00509i
$403$	662.857	+	662.857i	0.0819337	+	0.0819337i
$404$	14738.5	+	4826.15i	1.81502	+	0.594332i
$405$	−7919.56	+	1926.31i	−0.971669	+	0.236344i
$406$	8346.59	−	6049.57i	1.02028	−	0.739495i
$407$	4805.08	−	4805.08i	0.585207	−	0.585207i
$408$	1775.27	−	15258.8i	0.215415	−	1.85152i
$409$			9324.88i			1.12735i	0.825997	+	0.563675i	$0.190613\pi$
$409$			9324.88i			1.12735i	−0.825997	+	0.563675i	$0.809387\pi$
$410$	−10766.5	+	2359.94i	−1.29687	+	0.284266i
$411$	−405.593	−	1081.33i	−0.0486774	−	0.129776i
$412$	2831.10	−	1434.36i	0.338539	−	0.171519i
$413$	4654.32	−	4654.32i	0.554538	−	0.554538i
$414$	−161.202	+	701.337i	−0.0191368	+	0.0832581i
$415$	−10012.3	−	4368.27i	−1.18430	−	0.516698i
$416$	32.2187	−	5630.33i	0.00379724	−	0.663581i
$417$	2164.84	−	4763.62i	0.254227	−	0.559414i
$418$	6961.46	+	1110.75i	0.814584	+	0.129973i
$419$			321.911i			0.0375332i	0.999824	+	0.0187666i	$0.00597394\pi$
$419$			321.911i			0.0375332i	−0.999824	+	0.0187666i	$0.994026\pi$
$420$	3602.25	+	8144.97i	0.418504	+	0.946271i
$421$		−	2975.11i		−	0.344413i	−0.985061	−	0.172207i	$-0.944910\pi$
$421$		−	2975.11i		−	0.344413i	0.985061	−	0.172207i	$-0.0550897\pi$
$422$	1097.41	−	6877.79i	0.126590	−	0.793378i
$423$	2539.06	+	172.161i	0.291852	+	0.0197891i
$424$	5947.38	−	1909.87i	0.681204	−	0.218754i
$425$	−610.486	+	16320.3i	−0.0696774	+	1.86271i
$426$	−10229.9	−	6772.32i	−1.16347	−	0.770235i
$427$	−3156.00	+	3156.00i	−0.357681	+	0.357681i
$428$	476.270	+	940.045i	0.0537883	+	0.106165i
$429$	3577.40	−	1341.84i	0.402607	−	0.151013i
$430$	739.857	−	1155.25i	0.0829746	−	0.129561i
$431$		−	17559.0i		−	1.96238i	−0.193043	−	0.981190i	$-0.561836\pi$
$431$		−	17559.0i		−	1.96238i	0.193043	−	0.981190i	$-0.438164\pi$
$432$	−8459.70	−	3009.17i	−0.942170	−	0.335136i
$433$	−4103.34	+	4103.34i	−0.455413	+	0.455413i	−0.897146	−	0.441733i	$-0.854364\pi$
$433$	−4103.34	+	4103.34i	−0.455413	+	0.455413i	0.441733	+	0.897146i	$0.354364\pi$
$434$	−958.634	−	1322.63i	−0.106027	−	0.146286i
$435$	580.312	−	11033.9i	0.0639628	−	1.21617i
$436$	8833.72	+	2892.62i	0.970317	+	0.317732i
$437$	702.495	+	702.495i	0.0768991	+	0.0768991i
$438$	−1387.46	−	6822.69i	−0.151360	−	0.744294i
$439$		−	10896.8i		−	1.18469i	−0.805685	−	0.592344i	$-0.798203\pi$
$439$		−	10896.8i		−	1.18469i	0.805685	−	0.592344i	$-0.201797\pi$
$440$	601.035	−	5950.30i	0.0651209	−	0.644703i
$441$	492.363	−	429.833i	0.0531652	−	0.0464133i
$442$	−11350.7	−	1811.10i	−1.22149	−	0.194899i
$443$	−3646.95	+	3646.95i	−0.391133	+	0.391133i	−0.875091	−	0.483958i	$-0.839199\pi$
$443$	−3646.95	+	3646.95i	−0.391133	+	0.391133i	0.483958	+	0.875091i	$0.339199\pi$
$444$	506.491	+	11938.3i	0.0541374	+	1.27606i
$445$	5264.21	+	13412.8i	0.560781	+	1.42882i
$446$	587.716	−	425.974i	0.0623972	−	0.0452252i
$447$	8912.91	+	4050.49i	0.943101	+	0.428594i
$448$	−1601.33	+	9679.71i	−0.168874	+	1.02081i
$449$	1995.96			0.209789			0.104895	−	0.994483i	$-0.466549\pi$
$449$	1995.96			0.209789			0.104895	+	0.994483i	$0.466549\pi$
$450$	9216.92	+	2484.64i	0.965533	+	0.260282i
$451$		−	8239.80i		−	0.860304i
$452$	311.976	+	615.768i	0.0324649	+	0.0640781i
$453$	73.8294	−	162.458i	0.00765741	−	0.0168498i
$454$	6049.41	+	8346.37i	0.625359	+	0.862808i
$455$	6203.21	−	2434.62i	0.639145	−	0.250850i
$456$	−9719.45	+	7693.54i	−0.998147	+	0.790094i
$457$	3478.05	+	3478.05i	0.356009	+	0.356009i	0.862340	−	0.506330i	$-0.168998\pi$
$457$	3478.05	+	3478.05i	0.356009	+	0.356009i	−0.506330	+	0.862340i	$0.668998\pi$
$458$	7514.08	+	1198.93i	0.766616	+	0.122320i
$459$	−8695.35	+	16136.5i	−0.884236	+	1.64093i
$460$	560.704	−	629.270i	0.0568325	−	0.0637824i
$461$	858.652			0.0867493			0.0433746	−	0.999059i	$-0.486189\pi$
$461$	858.652			0.0867493			0.0433746	+	0.999059i	$0.486189\pi$
$462$	−6524.33	+	1326.79i	−0.657012	+	0.133610i
$463$	2288.18	−	2288.18i	0.229678	−	0.229678i	−0.582880	−	0.812558i	$-0.698074\pi$
$463$	2288.18	−	2288.18i	0.229678	−	0.229678i	0.812558	+	0.582880i	$0.198074\pi$
$464$	7199.67	−	9814.69i	0.720336	−	0.981973i
$465$	−1748.46	−	91.9581i	−0.174372	−	0.00917087i
$466$	−5288.47	−	7296.50i	−0.525716	−	0.725330i
$467$	138.937	+	138.937i	0.0137671	+	0.0137671i	0.713957	−	0.700190i	$-0.246901\pi$
$467$	138.937	+	138.937i	0.0137671	+	0.0137671i	−0.700190	+	0.713957i	$0.746901\pi$
$468$	−2517.89	+	6228.81i	−0.248695	+	0.615228i
$469$	−10778.8			−1.06124
$470$	−2509.99	−	1607.47i	−0.246335	−	0.157760i
$471$	−4802.44	−	12803.5i	−0.469819	−	1.25255i
$472$	3552.32	−	6913.04i	0.346417	−	0.674149i
$473$	725.182	+	725.182i	0.0704945	+	0.0704945i
$474$	11108.8	+	7354.15i	1.07646	+	0.712631i
$475$	9660.54	−	8963.87i	0.933171	−	0.865875i
$476$	19034.8	+	6233.00i	1.83290	+	0.600187i
$477$	−7436.54	−	504.236i	−0.713827	−	0.0484012i
$478$	10707.1	+	1708.39i	1.02454	+	0.163473i
$479$	−4176.86			−0.398425			−0.199213	−	0.979956i	$-0.563838\pi$
$479$	−4176.86			−0.398425			−0.199213	+	0.979956i	$0.563838\pi$
$480$	6990.47	+	7856.55i	0.664729	+	0.747085i
$481$	8940.86			0.847542
$482$	4585.68	+	731.682i	0.433345	+	0.0691436i
$483$	−854.213	−	388.199i	−0.0804722	−	0.0365707i
$484$	−5870.38	−	1922.27i	−0.551312	−	0.180528i
$485$	4353.75	−	9979.05i	0.407616	−	0.934279i
$486$	8053.65	+	7066.12i	0.751689	+	0.659518i
$487$	−29.3477	−	29.3477i	−0.00273074	−	0.00273074i	0.705740	−	0.708471i	$-0.250615\pi$
$487$	−29.3477	−	29.3477i	−0.00273074	−	0.00273074i	−0.708471	+	0.705740i	$0.750615\pi$
$488$	−2408.75	+	4687.59i	−0.223441	+	0.434830i
$489$	−10244.7	+	3842.67i	−0.947407	+	0.355361i
$490$	−747.740	+	163.899i	−0.0689376	+	0.0151106i
$491$	−1350.17			−0.124098			−0.0620491	−	0.998073i	$-0.519764\pi$
$491$	−1350.17			−0.124098			−0.0620491	+	0.998073i	$0.519764\pi$
$492$	10670.3	+	9801.73i	0.977749	+	0.898162i
$493$	−17571.0	−	17571.0i	−1.60519	−	1.60519i
$494$	5443.22	+	7510.01i	0.495753	+	0.683991i
$495$	−3289.66	+	6332.82i	−0.298705	+	0.575029i
$496$	−1555.27	−	1140.88i	−0.140793	−	0.103280i
$497$	11311.1	−	11311.1i	1.02087	−	1.02087i
$498$	2861.61	+	14071.6i	0.257493	+	1.26619i
$499$	6077.90			0.545259			0.272629	−	0.962119i	$-0.412107\pi$
$499$	6077.90			0.545259			0.272629	+	0.962119i	$0.412107\pi$
$500$	−8063.51	−	7744.66i	−0.721222	−	0.692704i
$501$	4923.29	+	13125.7i	0.439035	+	1.17048i
$502$	13807.4	+	2203.08i	1.22760	+	0.195873i
$503$	−11674.3	−	11674.3i	−1.03485	−	1.03485i	−0.999370	−	0.0354794i	$-0.988704\pi$
$503$	−11674.3	−	11674.3i	−1.03485	−	1.03485i	−0.0354794	−	0.999370i	$-0.511296\pi$
$504$	6042.93	−	10027.1i	0.534074	−	0.886194i
$505$	7918.46	+	20175.6i	0.697756	+	1.77782i
$506$	369.768	+	510.169i	0.0324865	+	0.0448217i
$507$	−5816.43	−	2643.29i	−0.509500	−	0.231543i
$508$	3725.03	+	7352.34i	0.325338	+	0.642141i
$509$			403.668i			0.0351518i	0.999846	+	0.0175759i	$0.00559487\pi$
$509$			403.668i			0.0351518i	−0.999846	+	0.0175759i	$0.994405\pi$
$510$	18020.6	−	11668.7i	1.56464	−	1.01313i
$511$	9077.86			0.785873
$512$	1694.38	+	11460.7i	0.146253	+	0.989247i
$513$	14168.8	−	4245.86i	1.21943	−	0.365418i
$514$	−4756.79	+	3447.70i	−0.408196	+	0.295859i
$515$	4065.34	+	1773.66i	0.347845	+	0.151761i
$516$	−1801.73	+	76.4395i	−0.153715	+	0.00652144i
$517$	1575.59	−	1575.59i	0.134032	−	0.134032i
$518$	−15385.2	−	2454.83i	−1.30500	−	0.208222i
$519$	1695.83	+	4521.14i	0.143427	+	0.382381i
$520$	6095.06	−	4976.71i	0.514012	−	0.419698i
$521$		−	12374.1i		−	1.04054i	−0.854003	−	0.520268i	$-0.825832\pi$
$521$		−	12374.1i		−	1.04054i	0.854003	−	0.520268i	$-0.174168\pi$
$522$	−12310.0	+	7708.68i	−1.03217	+	0.646360i
$523$	−15850.3	−	15850.3i	−1.32521	−	1.32521i	−0.909495	−	0.415716i	$-0.863531\pi$
$523$	−15850.3	−	15850.3i	−1.32521	−	1.32521i	−0.415716	−	0.909495i	$-0.636469\pi$
$524$	−8424.70	−	2758.68i	−0.702356	−	0.229988i
$525$	−5569.49	+	11130.9i	−0.462995	+	0.925316i
$526$	−1264.95	−	1745.25i	−0.104856	−	0.144670i
$527$	−2784.36	+	2784.36i	−0.230149	+	0.230149i
$528$	−6856.04	+	3847.15i	−0.565097	+	0.317094i
$529$		−	12078.2i		−	0.992702i
$530$	7351.41	+	4708.06i	0.602499	+	0.385858i
$531$	−6986.52	+	6099.24i	−0.570978	+	0.498464i
$532$	−7304.61	−	14417.6i	−0.595291	−	1.17497i
$533$	7665.93	−	7665.93i	0.622980	−	0.622980i
$534$	10455.6	−	15793.6i	0.847298	−	1.27988i
$535$	−588.932	+	1349.87i	−0.0475921	+	0.109084i
$536$	−12118.2	+	3891.50i	−0.976543	+	0.313595i
$537$	−10532.5	−	4786.49i	−0.846386	−	0.384641i
$538$	−179.320	+	1123.86i	−0.0143700	+	0.0900612i
$539$		−	572.260i		−	0.0457310i
$540$	−4287.55	−	11793.3i	−0.341679	−	0.939817i
$541$		−	14672.6i		−	1.16604i	−0.812459	−	0.583018i	$-0.801872\pi$
$541$		−	14672.6i		−	1.16604i	0.812459	−	0.583018i	$-0.198128\pi$
$542$	−22790.5	−	3636.41i	−1.80616	−	0.288187i
$543$	3594.93	+	1633.72i	0.284113	+	0.129115i
$544$	23650.5	+	135.336i	1.86398	+	0.0106663i
$545$	4746.03	+	12092.5i	0.373023	+	0.950433i
$546$	−7304.32	−	4835.56i	−0.572520	−	0.379016i
$547$	−14666.6	+	14666.6i	−1.14643	+	1.14643i	−0.159182	+	0.987249i	$0.550886\pi$
$547$	−14666.6	+	14666.6i	−1.14643	+	1.14643i	−0.987249	+	0.159182i	$0.949114\pi$
$548$	1586.11	−	803.598i	0.123641	−	0.0626423i
$549$	4737.42	−	4135.77i	0.368284	−	0.321512i
$550$	6946.09	−	4648.63i	0.538513	−	0.360397i
$551$			20051.7i			1.55033i
$552$	−1100.51	−	128.039i	−0.0848567	−	0.00987262i
$553$	−12282.8	+	12282.8i	−0.944519	+	0.944519i
$554$	−1080.90	+	783.433i	−0.0828937	+	0.0600810i
$555$	−12412.1	+	11171.7i	−0.949306	+	0.854440i
$556$	7655.89	+	2506.94i	0.583961	+	0.191219i
$557$	−3265.81	−	3265.81i	−0.248432	−	0.248432i	0.571895	−	0.820327i	$-0.306209\pi$
$557$	−3265.81	−	3265.81i	−0.248432	−	0.248432i	−0.820327	+	0.571895i	$0.806209\pi$
$558$	1221.54	+	1950.68i	0.0926739	+	0.147991i
$559$			1349.35i			0.102096i
$560$	−11854.7	+	6890.33i	−0.894556	+	0.519946i
$561$	5636.46	+	15027.0i	0.424192	+	1.13091i
$562$	439.315	−	2753.33i	0.0329740	−	0.206659i
$563$	15854.6	−	15854.6i	1.18684	−	1.18684i	0.208905	−	0.977936i	$-0.433010\pi$
$563$	15854.6	−	15854.6i	1.18684	−	1.18684i	0.977936	−	0.208905i	$-0.0669898\pi$
$564$	166.079	+	3914.59i	0.0123992	+	0.292259i
$565$	−385.775	+	884.218i	−0.0287251	+	0.0658395i
$566$	11765.8	+	16233.3i	0.873769	+	1.20554i
$567$	−11121.0	+	8454.14i	−0.823700	+	0.626174i
$568$	8632.94	−	16800.3i	0.637729	−	1.24106i
$569$	−15762.7			−1.16135			−0.580674	−	0.814136i	$-0.697211\pi$
$569$	−15762.7			−1.16135			−0.580674	+	0.814136i	$0.697211\pi$
$570$	−16940.4	−	3624.35i	−1.24484	−	0.266329i
$571$		−	16858.9i		−	1.23559i	−0.786339	−	0.617795i	$-0.788026\pi$
$571$		−	16858.9i		−	1.23559i	0.786339	−	0.617795i	$-0.211974\pi$
$572$	2658.58	+	5247.41i	0.194337	+	0.383576i
$573$	518.633	+	235.694i	0.0378119	+	0.0171837i
$574$	−15296.2	+	11086.6i	−1.11228	+	0.806176i
$575$	1177.07	+	44.0302i	0.0853694	+	0.00319337i
$576$	3173.74	−	13454.8i	0.229582	−	0.973289i
$577$	−6369.66	−	6369.66i	−0.459571	−	0.459571i	0.438944	−	0.898515i	$-0.355353\pi$
$577$	−6369.66	−	6369.66i	−0.459571	−	0.459571i	−0.898515	+	0.438944i	$0.855353\pi$
$578$	5418.07	−	33956.8i	0.389899	−	2.44362i
$579$	−2213.36	−	5900.91i	−0.158867	−	0.423547i
$580$	16983.0	−	978.563i	1.21583	−	0.0700562i
$581$	−18722.9			−1.33693
$582$	−14024.9	+	2852.10i	−0.998882	+	0.203133i
$583$	−4614.67	+	4614.67i	−0.327822	+	0.327822i
$584$	10205.9	−	3277.40i	0.723156	−	0.232226i
$585$	−8952.31	+	2831.22i	−0.632705	+	0.200097i
$586$	2216.82	−	1606.74i	0.156273	−	0.113266i
$587$	−7601.19	−	7601.19i	−0.534471	−	0.534471i	0.387428	−	0.921900i	$-0.373363\pi$
$587$	−7601.19	−	7601.19i	−0.534471	−	0.534471i	−0.921900	+	0.387428i	$0.873363\pi$
$588$	741.058	+	680.737i	0.0519740	+	0.0477434i
$589$	3177.46			0.222283
$590$	10610.3	−	2325.70i	0.740369	−	0.162284i
$591$	−5231.29	+	1962.20i	−0.364106	+	0.136572i
$592$	−18183.3	+	2794.69i	−1.26238	+	0.194022i
$593$	−5652.89	−	5652.89i	−0.391461	−	0.391461i	0.483747	−	0.875208i	$-0.339276\pi$
$593$	−5652.89	−	5652.89i	−0.391461	−	0.391461i	−0.875208	+	0.483747i	$0.839276\pi$
$594$	9298.13	−	1243.26i	0.642268	−	0.0858783i
$595$	10226.7	+	26056.9i	0.704630	+	1.79534i
$596$	−4690.57	+	14324.4i	−0.322371	+	0.984484i
$597$	24754.5	+	11249.7i	1.69704	+	0.771223i
$598$	−130.622	+	818.653i	−0.00893235	+	0.0559819i
$599$	7162.66			0.488578			0.244289	−	0.969702i	$-0.421445\pi$
$599$	7162.66			0.488578			0.244289	+	0.969702i	$0.421445\pi$
$600$	−2242.96	+	14524.8i	−0.152614	+	0.988286i
$601$	−21472.0			−1.45734			−0.728671	−	0.684864i	$-0.759862\pi$
$601$	−21472.0			−1.45734			−0.728671	+	0.684864i	$0.759862\pi$
$602$	370.483	−	2321.94i	0.0250827	−	0.157201i
$603$	15152.5	+	1027.42i	1.02331	+	0.0693858i
$604$	261.096	+	85.4964i	0.0175891	+	0.00575960i
$605$	−3153.94	−	8035.98i	−0.211944	−	0.540015i
$606$	15727.4	−	23756.9i	1.05426	−	1.59250i
$607$	874.002	+	874.002i	0.0584426	+	0.0584426i	0.735724	−	0.677281i	$-0.236842\pi$
$607$	874.002	+	874.002i	0.0584426	+	0.0584426i	−0.677281	+	0.735724i	$0.736842\pi$
$608$	−13417.5	−	13571.9i	−0.894986	−	0.905288i
$609$	−6650.85	−	17731.4i	−0.442539	−	1.17983i
$610$	−7194.60	+	1577.01i	−0.477542	+	0.104674i
$611$	2931.71			0.194115
$612$	−26164.4	−	10576.5i	−1.72816	−	0.698577i
$613$	−4069.30	−	4069.30i	−0.268120	−	0.268120i	0.560222	−	0.828342i	$-0.310716\pi$
$613$	−4069.30	−	4069.30i	−0.268120	−	0.268120i	−0.828342	+	0.560222i	$0.810716\pi$
$614$	−5591.02	+	4052.34i	−0.367484	+	0.266351i
$615$	−1063.49	+	20220.9i	−0.0697304	+	1.32583i
$616$	−3134.08	−	9759.59i	−0.204993	−	0.638352i
$617$	17088.1	−	17088.1i	1.11498	−	1.11498i	0.122508	−	0.992468i	$-0.460906\pi$
$617$	17088.1	−	17088.1i	1.11498	−	1.11498i	0.992468	−	0.122508i	$-0.0390937\pi$
$618$	−1161.91	−	5713.55i	−0.0756291	−	0.371898i
$619$	24760.0			1.60773			0.803867	−	0.594808i	$-0.202772\pi$
$619$	24760.0			1.60773			0.803867	+	0.594808i	$0.202772\pi$
$620$	−155.066	−	2691.19i	−0.0100445	−	0.174324i
$621$	1163.82	+	627.138i	0.0752053	+	0.0405252i
$622$	−1862.39	+	11672.2i	−0.120056	+	0.752431i
$623$	17462.8	+	17462.8i	1.12301	+	1.12301i
$624$	−9957.76	−	2799.34i	−0.638829	−	0.179588i
$625$	1167.32	−	15581.3i	0.0747085	−	0.997205i
$626$	−24484.4	+	17746.2i	−1.56325	+	1.13304i
$627$	5358.16	−	11790.4i	0.341283	−	0.750976i
$628$	18780.5	−	9515.04i	1.19335	−	0.604604i
$629$			37556.4i			2.38072i
$630$	16182.3	−	2413.93i	1.02336	−	0.152656i
$631$	9465.71			0.597185			0.298593	−	0.954381i	$-0.403483\pi$
$631$	9465.71			0.597185			0.298593	+	0.954381i	$0.403483\pi$
$632$	−9374.62	+	18243.6i	−0.590036	+	1.14825i
$633$	−11648.7	−	5293.76i	−0.731427	−	0.332398i
$634$	6648.67	+	9173.17i	0.416486	+	0.574626i
$635$	−4606.19	+	10557.7i	−0.287860	+	0.659792i
$636$	−486.420	−	11465.3i	−0.0303268	−	0.714823i
$637$	532.405	−	532.405i	0.0331156	−	0.0331156i
$638$	−2003.77	+	12558.3i	−0.124342	+	0.779289i
$639$	−16978.8	+	14822.5i	−1.05113	+	0.917637i
$640$	−10840.1	+	12026.5i	−0.669521	+	0.742793i
$641$		−	2756.35i		−	0.169843i	−0.996388	−	0.0849214i	$-0.972936\pi$
$641$		−	2756.35i		−	0.169843i	0.996388	−	0.0849214i	$-0.0270639\pi$
$642$	1897.14	−	385.803i	0.116627	−	0.0237172i
$643$	15387.1	+	15387.1i	0.943717	+	0.943717i	0.998498	−	0.0547818i	$-0.0174463\pi$
$643$	15387.1	+	15387.1i	0.943717	+	0.943717i	−0.0547818	+	0.998498i	$0.517446\pi$
$644$	449.545	−	1372.86i	0.0275070	−	0.0840033i
$645$	−1686.04	−	1873.23i	−0.102927	−	0.114354i
$646$	−31546.1	+	22864.5i	−1.92131	+	1.39256i
$647$	17532.0	−	17532.0i	1.06531	−	1.06531i	0.0675938	−	0.997713i	$-0.478468\pi$
$647$	17532.0	−	17532.0i	1.06531	−	1.06531i	0.997713	−	0.0675938i	$-0.0215322\pi$
$648$	−9450.69	+	13519.7i	−0.572929	+	0.819605i
$649$			8120.25i			0.491137i
$650$	10787.2	+	2137.45i	0.650937	+	0.128981i
$651$	−2809.78	+	1053.92i	−0.169161	+	0.0634504i
$652$	−7613.46	−	15027.2i	−0.457310	−	0.902623i
$653$	−8681.37	+	8681.37i	−0.520258	+	0.520258i	−0.917649	−	0.397391i	$-0.869916\pi$
$653$	−8681.37	+	8681.37i	−0.520258	+	0.520258i	0.397391	+	0.917649i	$0.369916\pi$
$654$	9426.40	−	14239.0i	0.563611	−	0.851359i
$655$	−4526.28	−	11532.6i	−0.270010	−	0.687963i
$656$	−13194.3	+	17986.6i	−0.785290	+	1.07052i
$657$	−12761.3	−	865.284i	−0.757788	−	0.0513820i
$658$	−5044.83	−	804.942i	−0.298887	−	0.0476898i
$659$		−	13562.6i		−	0.801707i	−0.916142	−	0.400853i	$-0.868714\pi$
$659$		−	13562.6i		−	0.801707i	0.916142	−	0.400853i	$-0.131286\pi$
$660$	−10247.5	−	3962.76i	−0.604368	−	0.233713i
$661$			4458.07i			0.262328i	0.991361	+	0.131164i	$0.0418714\pi$
$661$			4458.07i			0.262328i	−0.991361	+	0.131164i	$0.958129\pi$
$662$	−846.513	+	5305.37i	−0.0496989	+	0.311479i
$663$	−8736.54	+	19224.3i	−0.511763	+	1.12611i
$664$	−21049.4	+	6759.56i	−1.23023	+	0.395063i
$665$	9032.52	−	20703.1i	0.526716	−	1.20726i
$666$	21394.0	+	4917.41i	1.24475	+	0.286105i
$667$	−1267.28	+	1267.28i	−0.0735672	+	0.0735672i
$668$	−19253.1	+	9754.48i	−1.11515	+	0.564988i
$669$	−468.312	−	1248.54i	−0.0270643	−	0.0721544i
$670$	−14979.0	−	9593.00i	−0.863716	−	0.553149i
$671$		−	5506.17i		−	0.316786i
$672$	16366.5	+	7551.08i	0.939511	+	0.433466i
$673$	8098.65	−	8098.65i	0.463864	−	0.463864i	−0.436056	−	0.899920i	$-0.643625\pi$
$673$	8098.65	−	8098.65i	0.463864	−	0.463864i	0.899920	+	0.436056i	$0.143625\pi$
$674$	−12715.2	−	17543.1i	−0.726663	−	1.00258i
$675$	8890.36	−	15116.5i	0.506948	−	0.861977i
$676$	3061.00	−	9347.92i	0.174158	−	0.531857i
$677$	−21319.0	−	21319.0i	−1.21027	−	1.21027i	−0.970936	−	0.239337i	$-0.923070\pi$
$677$	−21319.0	−	21319.0i	−1.21027	−	1.21027i	−0.239337	−	0.970936i	$-0.576930\pi$
$678$	1242.71	−	252.717i	0.0703921	−	0.0143149i
$679$		−	18660.7i		−	1.05468i
$680$	20904.9	+	25602.6i	1.17892	+	1.44384i
$681$	17731.0	−	6650.68i	0.997727	−	0.374236i
$682$	1990.02	+	317.523i	0.111733	+	0.0178279i
$683$	2724.01	−	2724.01i	0.152608	−	0.152608i	−0.626674	−	0.779282i	$-0.715584\pi$
$683$	2724.01	−	2724.01i	0.152608	−	0.152608i	0.779282	+	0.626674i	$0.215584\pi$
$684$	8894.29	+	20964.0i	0.497196	+	1.17190i
$685$	2277.60	+	993.690i	0.127040	+	0.0554262i
$686$	13990.3	−	10140.1i	0.778648	−	0.564361i
$687$	5783.51	−	12726.3i	0.321186	−	0.706754i
$688$	−421.774	−	2744.22i	−0.0233720	−	0.152068i
$689$	−8586.56			−0.474778
$690$	−841.584	−	1299.71i	−0.0464327	−	0.0717087i
$691$		−	2093.61i		−	0.115260i	−0.998338	−	0.0576301i	$-0.981646\pi$
$691$		−	2093.61i		−	0.115260i	0.998338	−	0.0576301i	$-0.0183544\pi$
$692$	−6631.72	+	3359.93i	−0.364306	+	0.184574i
$693$	−827.445	+	12203.3i	−0.0453565	+	0.668923i
$694$	−10323.5	−	14243.3i	−0.564658	−	0.779059i
$695$	4113.23	+	10480.2i	0.224495	+	0.571994i
$696$	−13878.9	−	17533.6i	−0.755861	−	0.954898i
$697$	32201.1	+	32201.1i	1.74993	+	1.74993i
$698$	32602.0	+	5201.91i	1.76791	+	0.282085i
$699$	−15500.6	+	5814.10i	−0.838751	+	0.314606i
$700$	−17975.5	−	6639.85i	−0.970587	−	0.358518i
$701$	−12609.8			−0.679411			−0.339706	−	0.940532i	$-0.610327\pi$
$701$	−12609.8			−0.679411			−0.339706	+	0.940532i	$0.610327\pi$
$702$	9807.23	+	7493.88i	0.527279	+	0.402904i
$703$	21429.3	−	21429.3i	1.14968	−	1.14968i
$704$	−7047.05	−	9840.83i	−0.377267	−	0.526833i
$705$	−4069.94	+	3663.22i	−0.217422	+	0.195695i
$706$	11961.2	+	16502.8i	0.637627	+	0.879734i
$707$	26267.7	+	26267.7i	1.39731	+	1.39731i
$708$	−10515.4	−	9659.51i	−0.558184	−	0.512749i
$709$	4224.57			0.223776			0.111888	−	0.993721i	$-0.464310\pi$
$709$	4224.57			0.223776			0.111888	+	0.993721i	$0.464310\pi$
$710$	25785.3	−	5651.97i	1.36297	−	0.298753i
$711$	18437.5	−	16096.0i	0.972519	−	0.849010i
$712$	25937.4	+	13328.1i	1.36523	+	0.701535i
$713$	200.817	+	200.817i	0.0105479	+	0.0105479i
$714$	20312.0	−	30682.1i	1.06464	−	1.60819i
$715$	−3287.47	+	7535.07i	−0.171950	+	0.394120i
$716$	5542.89	−	16927.3i	0.289312	−	0.883525i
$717$	8241.10	−	18134.2i	0.429246	−	0.944536i
$718$	−28064.0	−	4477.83i	−1.45869	−	0.232745i
$719$	3475.57			0.180274			0.0901369	−	0.995929i	$-0.471270\pi$
$719$	3475.57			0.180274			0.0901369	+	0.995929i	$0.471270\pi$
$720$	17321.6	−	8556.21i	0.896582	−	0.442877i
$721$	7602.12			0.392673
$722$	11888.3	+	1896.88i	0.612795	+	0.0977762i
$723$	3529.55	−	7766.61i	0.181557	−	0.399507i
$724$	−1891.89	+	5777.62i	−0.0971155	+	0.296579i
$725$	16170.5	+	17427.3i	0.828357	+	0.892737i
$726$	−6264.24	+	9462.41i	−0.320231	+	0.483723i
$727$	−4473.63	−	4473.63i	−0.228223	−	0.228223i	0.583727	−	0.811950i	$-0.301594\pi$
$727$	−4473.63	−	4473.63i	−0.228223	−	0.228223i	−0.811950	+	0.583727i	$0.801594\pi$
$728$	6164.07	−	11995.7i	0.313813	−	0.610700i
$729$	16439.3	−	10824.5i	0.835204	−	0.549941i
$730$	12615.2	+	8079.17i	0.639604	+	0.409621i
$731$	−5668.01			−0.286784
$732$	7130.31	+	6549.92i	0.360032	+	0.330727i
$733$	302.954	+	302.954i	0.0152658	+	0.0152658i	0.714698	−	0.699433i	$-0.246564\pi$
$733$	302.954	+	302.954i	0.0152658	+	0.0152658i	−0.699433	+	0.714698i	$0.746564\pi$
$734$	12002.4	+	16559.8i	0.603567	+	0.832741i
$735$	−73.8604	+	1404.36i	−0.00370664	+	0.0704769i
$736$	9.76089	−	1705.75i	0.000488847	−	0.0854277i
$737$	9402.73	−	9402.73i	0.469951	−	0.469951i
$738$	22559.5	−	14127.1i	1.12524	−	0.704643i
$739$	20265.7			1.00878			0.504389	−	0.863477i	$-0.331718\pi$
$739$	20265.7			1.00878			0.504389	+	0.863477i	$0.331718\pi$
$740$	−19195.6	−	17104.1i	−0.953575	−	0.849672i
$741$	15954.2	−	5984.24i	0.790948	−	0.296676i
$742$	14775.6	+	2357.56i	0.731036	+	0.116642i
$743$	−1627.48	−	1627.48i	−0.0803585	−	0.0803585i	0.665785	−	0.746144i	$-0.268097\pi$
$743$	−1627.48	−	1627.48i	−0.0803585	−	0.0803585i	−0.746144	+	0.665785i	$0.768097\pi$
$744$	−2778.43	+	2199.30i	−0.136912	+	0.108374i
$745$	−19608.8	+	7696.00i	−0.964309	+	0.378470i
$746$	1946.86	+	2686.08i	0.0955489	+	0.131829i
$747$	26319.9	+	1784.63i	1.28915	+	0.0874111i
$748$	−22042.0	+	11167.5i	−1.07745	+	0.545887i
$749$			2524.23i			0.123142i
$750$	−17646.1	+	10511.5i	−0.859125	+	0.511766i
$751$	−34918.2			−1.69665			−0.848324	−	0.529478i	$-0.822388\pi$
$751$	−34918.2			−1.69665			−0.848324	+	0.529478i	$0.822388\pi$
$752$	−5962.32	+	916.380i	−0.289127	+	0.0444374i
$753$	10627.4	−	23385.1i	0.514322	−	1.13174i
$754$	−13547.8	+	9819.41i	−0.654354	+	0.474273i
$755$	140.277	+	357.415i	0.00676187	+	0.0172287i
$756$	−14818.5	−	15588.0i	−0.712890	−	0.749908i
$757$	−20575.8	+	20575.8i	−0.987899	+	0.987899i	−0.999928	−	0.0120287i	$-0.996171\pi$
$757$	−20575.8	+	20575.8i	−0.987899	+	0.987899i	0.0120287	+	0.999928i	$0.496171\pi$
$758$	−20345.2	−	3246.23i	−0.974894	−	0.155552i
$759$	1083.80	−	406.520i	0.0518305	−	0.0194410i
$760$	2680.45	−	26536.7i	0.127934	−	1.26656i
$761$			14836.5i			0.706729i	0.935486	+	0.353365i	$0.114962\pi$
$761$			14836.5i			0.706729i	−0.935486	+	0.353365i	$0.885038\pi$
$762$	14838.1	−	3017.47i	0.705415	−	0.143453i
$763$	15743.9	+	15743.9i	0.747008	+	0.747008i
$764$	−272.940	+	833.525i	−0.0129249	+	0.0394711i
$765$	−11892.7	−	37604.6i	−0.562066	−	1.77725i
$766$	18229.4	+	25151.1i	0.859862	+	1.18635i
$767$	−7554.71	+	7554.71i	−0.355651	+	0.355651i
$768$	21126.4	+	2580.56i	0.992622	+	0.121247i
$769$			5513.84i			0.258562i	0.991608	+	0.129281i	$0.0412669\pi$
$769$			5513.84i			0.258562i	−0.991608	+	0.129281i	$0.958733\pi$
$770$	7725.87	−	12063.6i	0.361586	−	0.564599i
$771$	3790.38	+	10105.3i	0.177052	+	0.472027i
$772$	8655.60	−	4385.32i	0.403526	−	0.204445i
$773$	−6649.85	+	6649.85i	−0.309416	+	0.309416i	−0.844683	−	0.535267i	$-0.820211\pi$
$773$	−6649.85	+	6649.85i	−0.309416	+	0.309416i	0.535267	+	0.844683i	$0.320211\pi$
$774$	−742.134	+	3228.78i	−0.0344644	+	0.149943i
$775$	2761.59	−	2562.44i	0.127999	−	0.118768i
$776$	−6737.09	−	20979.5i	−0.311659	−	0.970514i
$777$	−11841.8	+	26057.4i	−0.546749	+	1.20310i
$778$	−233.862	+	1465.69i	−0.0107768	+	0.0675419i
$779$		−	36747.2i		−	1.69012i
$780$	−5847.02	−	13220.6i	−0.268406	−	0.606888i
$781$			19734.0i			0.904148i
$782$	−3438.78	−	548.685i	−0.157252	−	0.0250907i
$783$	7659.40	+	25560.1i	0.349585	+	1.16660i
$784$	−916.352	+	1249.18i	−0.0417435	+	0.0569053i
$785$	26968.0	+	11765.8i	1.22615	+	0.534956i
$786$	−8989.94	+	13579.7i	−0.407965	+	0.616249i
$787$	17933.4	−	17933.4i	0.812271	−	0.812271i	−0.172703	−	0.984974i	$-0.555250\pi$
$787$	17933.4	−	17933.4i	0.812271	−	0.812271i	0.984974	+	0.172703i	$0.0552501\pi$
$788$	−3887.69	−	7673.39i	−0.175753	−	0.346895i
$789$	−3707.59	+	1390.68i	−0.167293	+	0.0627495i
$790$	−28000.6	+	6137.54i	−1.26104	+	0.276410i
$791$			1653.47i			0.0743245i
$792$	3475.51	+	14018.4i	0.155930	+	0.628942i
$793$	5122.69	−	5122.69i	0.229397	−	0.229397i
$794$	−25791.1	+	18693.2i	−1.15276	+	0.835515i
$795$	11920.3	−	10729.1i	0.531784	−	0.478642i
$796$	−13027.5	+	39784.3i	−0.580083	+	1.77151i
$797$	4707.94	+	4707.94i	0.209239	+	0.209239i	0.803944	−	0.594705i	$-0.202731\pi$
$797$	4707.94	+	4707.94i	0.209239	+	0.209239i	−0.594705	+	0.803944i	$0.702731\pi$
$798$	−29096.7	+	5917.11i	−1.29074	+	0.262485i
$799$			12314.8i			0.545264i
$800$	−22606.4	−	975.197i	−0.999071	−	0.0430980i
$801$	−22884.1	−	26213.1i	−1.00945	−	1.15630i
$802$	1163.11	−	7289.58i	0.0512105	−	0.320953i
$803$	−7918.92	+	7918.92i	−0.348011	+	0.348011i
$804$	991.116	+	23361.3i	0.0434751	+	1.02474i
$805$	1879.31	−	737.585i	0.0822818	−	0.0322937i
$806$	1556.02	+	2146.83i	0.0680004	+	0.0938201i
$807$	1903.44	+	865.020i	0.0830287	+	0.0377325i
$808$	39015.2	+	20048.3i	1.69870	+	0.872891i
$809$	−39244.1			−1.70550			−0.852749	−	0.522320i	$-0.825067\pi$
$809$	−39244.1			−1.70550			−0.852749	+	0.522320i	$0.825067\pi$
$810$	−22978.6	+	1850.94i	−0.996771	+	0.0802908i
$811$			16408.3i			0.710448i	0.934781	+	0.355224i	$0.115595\pi$
$811$			16408.3i			0.710448i	−0.934781	+	0.355224i	$0.884405\pi$
$812$	26008.9	−	13177.3i	1.12406	−	0.569498i
$813$	−17541.6	+	38599.5i	−0.756718	+	1.66512i
$814$	15562.5	−	11279.6i	0.670104	−	0.485689i
$815$	9414.43	−	21578.4i	0.404630	−	0.927435i
$816$	11758.7	−	41828.0i	0.504458	−	1.79445i
$817$	3234.11	+	3234.11i	0.138491	+	0.138491i
$818$	−4155.73	+	26045.3i	−0.177630	+	1.11327i
$819$	−12123.2	+	10583.5i	−0.517238	+	0.451549i
$820$	−31123.5	+	1793.34i	−1.32546	+	0.0763733i
$821$	7023.21			0.298553			0.149276	−	0.988796i	$-0.452306\pi$
$821$	7023.21			0.298553			0.149276	+	0.988796i	$0.452306\pi$
$822$	−650.956	−	3201.00i	−0.0276213	−	0.135825i
$823$	−26346.4	+	26346.4i	−1.11589	+	1.11589i	−0.123552	+	0.992338i	$0.539429\pi$
$823$	−26346.4	+	26346.4i	−1.11589	+	1.11589i	−0.992338	+	0.123552i	$0.960571\pi$
$824$	8546.77	−	2744.61i	0.361336	−	0.116035i
$825$	−4851.38	−	14568.3i	−0.204731	−	0.614791i
$826$	15074.2	−	10925.7i	0.634987	−	0.460236i
$827$	1006.50	+	1006.50i	0.0423209	+	0.0423209i	0.727951	−	0.685630i	$-0.240473\pi$
$827$	1006.50	+	1006.50i	0.0423209	+	0.0423209i	−0.685630	+	0.727951i	$0.740473\pi$
$828$	−762.811	+	1887.06i	−0.0320163	+	0.0792028i
$829$	−21920.6			−0.918376			−0.459188	−	0.888339i	$-0.651860\pi$
$829$	−21920.6			−0.918376			−0.459188	+	0.888339i	$0.651860\pi$
$830$	−26018.6	−	16663.1i	−1.08810	−	0.696849i
$831$	861.300	+	2296.26i	0.0359545	+	0.0958560i
$832$	2599.21	−	15711.7i	0.108307	−	0.654694i
$833$	2236.39	+	2236.39i	0.0930207	+	0.0930207i
$834$	8169.55	−	12340.5i	0.339195	−	0.512369i
$835$	−27646.6	−	12061.9i	−1.14581	−	0.499904i
$836$	18949.0	+	6204.89i	0.783929	+	0.256699i
$837$	4050.34	−	1213.73i	0.167264	−	0.0501228i
$838$	−143.463	+	899.130i	−0.00591391	+	0.0370643i
$839$	31047.8			1.27758			0.638790	−	0.769381i	$-0.279435\pi$
$839$	31047.8			1.27758			0.638790	+	0.769381i	$0.279435\pi$
$840$	6431.54	+	24355.1i	0.264178	+	1.00039i
$841$	−11783.7			−0.483156
$842$	1325.89	−	8309.77i	0.0542674	−	0.340111i
$843$	−4663.22	−	2119.21i	−0.190522	−	0.0865829i
$844$	6130.32	−	18721.3i	0.250017	−	0.763522i
$845$	12796.4	−	5022.30i	0.520958	−	0.204464i
$846$	7015.11	+	1612.42i	0.285088	+	0.0655274i
$847$	−10462.5	−	10462.5i	−0.424433	−	0.424433i
$848$	17462.8	−	2683.94i	0.707163	−	0.108687i
$849$	34485.8	−	12935.2i	1.39405	−	0.522893i
$850$	−8978.46	+	45312.1i	−0.362304	+	1.82846i
$851$	2708.69			0.109110
$852$	−25554.9	−	23474.8i	−1.02758	−	0.943936i
$853$	1829.37	+	1829.37i	0.0734308	+	0.0734308i	0.742868	−	0.669438i	$-0.233465\pi$
$853$	1829.37	+	1829.37i	0.0734308	+	0.0734308i	−0.669438	+	0.742868i	$0.733465\pi$
$854$	−10221.5	+	7408.51i	−0.409571	+	0.296855i
$855$	−14671.0	+	28242.6i	−0.586826	+	1.12968i
$856$	911.327	+	2837.89i	0.0363884	+	0.113314i
$857$	−19889.3	+	19889.3i	−0.792774	+	0.792774i	−0.981944	−	0.189170i	$-0.939420\pi$
$857$	−19889.3	+	19889.3i	−0.792774	+	0.792774i	0.189170	+	0.981944i	$0.439420\pi$
$858$	10590.0	−	2153.59i	0.421372	−	0.0856902i
$859$	−19612.5			−0.779011			−0.389505	−	0.921024i	$-0.627354\pi$
$859$	−19612.5			−0.779011			−0.389505	+	0.921024i	$0.627354\pi$
$860$	2581.34	−	2897.00i	0.102352	−	0.114869i
$861$	12188.5	+	32495.0i	0.482443	+	1.28621i
$862$	7825.34	−	49043.9i	0.309202	−	1.93787i
$863$	−29168.7	−	29168.7i	−1.15054	−	1.15054i	−0.986445	−	0.164093i	$-0.947530\pi$
$863$	−29168.7	−	29168.7i	−1.15054	−	1.15054i	−0.164093	−	0.986445i	$-0.552470\pi$
$864$	−22287.7	−	12175.1i	−0.877595	−	0.479402i
$865$	−9522.88	−	4154.73i	−0.374321	−	0.163312i
$866$	−13289.7	+	9632.33i	−0.521482	+	0.377967i
$867$	−57511.4	−	26136.2i	−2.25281	−	1.02379i
$868$	−2088.12	−	4121.45i	−0.0816535	−	0.161165i
$869$		−	21429.4i		−	0.836530i
$870$	6538.22	−	30560.0i	0.254789	−	1.19090i
$871$	17495.7			0.680620
$872$	23384.3	+	12016.2i	0.908133	+	0.466651i
$873$	−1778.70	+	26232.5i	−0.0689574	+	1.01699i
$874$	1649.06	+	2275.21i	0.0638220	+	0.0880551i
$875$	−8845.49	−	25277.6i	−0.341751	−	0.976617i
$876$	−834.712	−	19674.8i	−0.0321944	−	0.758845i
$877$	−1922.31	+	1922.31i	−0.0740158	+	0.0740158i	−0.743146	−	0.669130i	$-0.766667\pi$
$877$	−1922.31	+	1922.31i	−0.0740158	+	0.0740158i	0.669130	+	0.743146i	$0.266667\pi$
$878$	4856.29	−	30435.9i	0.186665	−	1.16989i
$879$	−1766.44	−	4709.39i	−0.0677821	−	0.180710i
$880$	4330.56	−	16351.9i	0.165890	−	0.626389i
$881$			3232.94i			0.123633i	0.998088	+	0.0618163i	$0.0196893\pi$
$881$			3232.94i			0.123633i	−0.998088	+	0.0618163i	$0.980311\pi$
$882$	1566.78	−	981.139i	0.0598142	−	0.0374565i
$883$	−16301.2	−	16301.2i	−0.621269	−	0.621269i	0.324587	−	0.945856i	$-0.394775\pi$
$883$	−16301.2	−	16301.2i	−0.621269	−	0.621269i	−0.945856	+	0.324587i	$0.894775\pi$
$884$	−30896.6	−	10117.1i	−1.17552	−	0.384928i
$885$	1048.06	−	19927.5i	0.0398082	−	0.756900i
$886$	−11811.6	+	8560.99i	−0.447876	+	0.324619i
$887$	−25995.8	+	25995.8i	−0.984051	+	0.984051i	−0.999875	−	0.0158243i	$-0.994963\pi$
$887$	−25995.8	+	25995.8i	−0.984051	+	0.984051i	0.0158243	+	0.999875i	$0.494963\pi$
$888$	−3905.77	+	33570.7i	−0.147600	+	1.26865i
$889$			19742.6i			0.744822i
$890$	8725.90	+	39809.2i	0.328644	+	1.49933i
$891$	2326.38	−	17076.0i	0.0874712	−	0.642053i
$892$	1831.39	−	927.864i	0.0687437	−	0.0348287i
$893$	7026.70	−	7026.70i	0.263314	−	0.263314i
$894$	23089.5	+	15285.5i	0.863789	+	0.571839i
$895$	23171.9	−	9094.43i	0.865419	−	0.339657i
$896$	−8786.52	+	26322.7i	−0.327608	+	0.981451i
$897$	1386.52	+	630.108i	0.0516106	+	0.0234545i
$898$	5574.92	+	889.522i	0.207169	+	0.0330554i
$899$			5732.04i			0.212652i
$900$	24636.4	+	11047.5i	0.912460	+	0.409165i
$901$		−	36068.2i		−	1.33364i
$902$	3672.15	−	23014.6i	0.135554	−	0.849558i
$903$	−3932.58	−	1787.17i	−0.144926	−	0.0658619i
$904$	596.956	+	1858.94i	0.0219629	+	0.0683930i
$905$	−7909.00	+	3104.10i	−0.290502	+	0.114015i
$906$	278.614	−	420.858i	0.0102167	−	0.0154328i
$907$	−1900.65	+	1900.65i	−0.0695812	+	0.0695812i	−0.741041	−	0.671460i	$-0.765668\pi$
$907$	−1900.65	+	1900.65i	−0.0695812	+	0.0695812i	0.671460	+	0.741041i	$0.265668\pi$
$908$	13176.9	+	26008.2i	0.481599	+	0.950565i
$909$	−34422.4	−	39429.9i	−1.25601	−	1.43873i
$910$	18411.2	−	4035.60i	0.670687	−	0.147010i
$911$			21899.8i			0.796456i	0.917286	+	0.398228i	$0.130375\pi$
$911$			21899.8i			0.796456i	−0.917286	+	0.398228i	$0.869625\pi$
$912$	−30576.1	+	17157.2i	−1.11017	+	0.622952i
$913$	16332.6	−	16332.6i	0.592037	−	0.592037i
$914$	8164.49	+	11264.5i	0.295468	+	0.407657i
$915$	−710.670	+	13512.4i	−0.0256765	+	0.488205i
$916$	20453.2	+	6697.46i	0.737766	+	0.241583i
$917$	−15014.9	−	15014.9i	−0.540715	−	0.540715i
$918$	−31478.4	+	41195.7i	−1.13174	+	1.48111i
$919$		−	6800.64i		−	0.244105i	−0.992524	−	0.122052i	$-0.961052\pi$
$919$		−	6800.64i		−	0.244105i	0.992524	−	0.122052i	$-0.0389476\pi$
$920$	1846.54	−	1507.73i	0.0661725	−	0.0540308i
$921$	4455.12	+	11877.5i	0.159393	+	0.424948i
$922$	2398.30	+	382.667i	0.0856656	+	0.0136686i
$923$	−18359.6	+	18359.6i	−0.654729	+	0.654729i
$924$	−18814.4	+	798.210i	−0.669857	+	0.0284190i
$925$	1343.12	−	35906.2i	0.0477424	−	1.27631i
$926$	7410.85	−	5371.35i	0.262998	−	0.190619i
$927$	−10686.8	−	724.619i	−0.378641	−	0.0256738i
$928$	24483.4	−	24204.8i	0.866063	−	0.856207i
$929$	3940.14			0.139151			0.0695757	−	0.997577i	$-0.477835\pi$
$929$	3940.14			0.139151			0.0695757	+	0.997577i	$0.477835\pi$
$930$	−4842.64	−	1036.07i	−0.170749	−	0.0365312i
$931$		−	2552.12i		−	0.0898415i
$932$	−11519.4	−	22736.7i	−0.404862	−	0.799104i
$933$	19768.8	+	8983.96i	0.693678	+	0.315243i
$934$	326.145	+	449.983i	0.0114259	+	0.0157643i
$935$	−31651.4	−	13809.2i	−1.10707	−	0.483003i
$936$	−9808.63	+	16275.5i	−0.342527	+	0.568357i
$937$	−13351.3	−	13351.3i	−0.465492	−	0.465492i	0.434958	−	0.900451i	$-0.356763\pi$
$937$	−13351.3	−	13351.3i	−0.465492	−	0.465492i	−0.900451	+	0.434958i	$0.856763\pi$
$938$	−30106.3	−	4803.69i	−1.04798	−	0.167213i
$939$	19510.0	+	52014.5i	0.678047	+	1.80770i
$940$	−6294.27	−	5608.43i	−0.218400	−	0.194603i
$941$	43783.5			1.51679			0.758395	−	0.651795i	$-0.225984\pi$
$941$	43783.5			1.51679			0.758395	+	0.651795i	$0.225984\pi$
$942$	−7707.67	−	37901.6i	−0.266592	−	1.31094i
$943$	2322.45	−	2322.45i	0.0802008	−	0.0802008i
$944$	13002.8	−	17725.7i	0.448312	−	0.611145i
$945$	3605.64	−	29840.7i	0.124118	−	1.02721i
$946$	1702.32	+	2348.69i	0.0585065	+	0.0807214i
$947$	22126.2	+	22126.2i	0.759245	+	0.759245i	0.976185	−	0.216940i	$-0.0696076\pi$
$947$	22126.2	+	22126.2i	0.759245	+	0.759245i	−0.216940	+	0.976185i	$0.569608\pi$
$948$	27750.4	+	25491.6i	0.950729	+	0.873342i
$949$	−14734.8			−0.504017
$950$	30977.7	−	20731.6i	1.05795	−	0.708024i
$951$	19487.4	−	7309.50i	0.664482	−	0.249239i
$952$	50388.3	+	25892.4i	1.71544	+	0.881490i
$953$	−3751.04	−	3751.04i	−0.127501	−	0.127501i	0.640477	−	0.767977i	$-0.278737\pi$
$953$	−3751.04	−	3751.04i	−0.127501	−	0.127501i	−0.767977	+	0.640477i	$0.778737\pi$
$954$	−20546.2	−	4722.55i	−0.697284	−	0.160271i
$955$	−1141.02	+	447.823i	−0.0386622	+	0.0151740i
$956$	29144.5	+	9543.42i	0.985983	+	0.322862i
$957$	21269.5	+	9665.95i	0.718438	+	0.326495i
$958$	−11666.4	−	1861.46i	−0.393448	−	0.0627778i
$959$	4259.06			0.143412
$960$	16023.7	+	25059.5i	0.538711	+	0.842491i
$961$	−28882.7			−0.969510
$962$	24972.7	+	3984.58i	0.836955	+	0.133543i
$963$	240.604	−	3548.47i	0.00805127	−	0.118741i
$964$	12482.2	+	4087.32i	0.417037	+	0.136560i
$965$	12429.1	+	5422.68i	0.414618	+	0.180893i
$966$	−2212.90	−	1464.97i	−0.0737047	−	0.0487935i
$967$	−3625.15	−	3625.15i	−0.120555	−	0.120555i	0.644255	−	0.764811i	$-0.277167\pi$
$967$	−3625.15	−	3625.15i	−0.120555	−	0.120555i	−0.764811	+	0.644255i	$0.777167\pi$
$968$	−15539.8	−	7985.27i	−0.515981	−	0.265141i
$969$	25137.1	+	67016.3i	0.833353	+	2.22175i
$970$	16607.7	−	25932.2i	0.549734	−	0.858383i
$971$	−6376.71			−0.210750			−0.105375	−	0.994433i	$-0.533604\pi$
$971$	−6376.71			−0.210750			−0.105375	+	0.994433i	$0.533604\pi$
$972$	19345.5	+	23325.5i	0.638383	+	0.769719i
$973$	13644.7	+	13644.7i	0.449567	+	0.449567i
$974$	−68.8919	−	95.0501i	−0.00226636	−	0.00312690i
$975$	9040.16	−	18067.2i	0.296940	−	0.593448i
$976$	−8816.96	+	12019.4i	−0.289164	+	0.394192i
$977$	−6800.26	+	6800.26i	−0.222681	+	0.222681i	−0.809627	−	0.586945i	$-0.800330\pi$
$977$	−6800.26	+	6800.26i	−0.222681	+	0.222681i	0.586945	+	0.809627i	$0.300330\pi$
$978$	−30327.0	+	6167.30i	−0.991565	+	0.201645i
$979$	−30466.8			−0.994609
$980$	−2161.55	+	124.549i	−0.0704574	+	0.00405976i
$981$	−20631.5	−	23632.9i	−0.671471	−	0.769153i
$982$	−3771.15	−	601.716i	−0.122548	−	0.0195535i
$983$	−33279.1	−	33279.1i	−1.07979	−	1.07979i	−0.996527	−	0.0832671i	$-0.973465\pi$
$983$	−33279.1	−	33279.1i	−1.07979	−	1.07979i	−0.0832671	−	0.996527i	$-0.526535\pi$
$984$	25434.8	+	32132.5i	0.824017	+	1.04100i
$985$	4807.32	−	11018.7i	0.155507	−	0.356430i
$986$	−41246.9	−	56908.3i	−1.33222	−	1.83806i
$987$	−3882.95	+	8544.25i	−0.125224	+	0.275549i
$988$	11856.5	+	23402.0i	0.381788	+	0.753560i
$989$			408.796i			0.0131435i
$990$	−12010.6	+	16222.1i	−0.385578	+	0.520780i
$991$	36313.9			1.16402			0.582012	−	0.813180i	$-0.302266\pi$
$991$	36313.9			1.16402			0.582012	+	0.813180i	$0.302266\pi$
$992$	−3835.56	−	3879.71i	−0.122761	−	0.124174i
$993$	8985.52	+	4083.48i	0.287157	+	0.130499i
$994$	36633.8	−	26552.0i	1.16897	−	0.847262i
$995$	−54460.9	+	21374.7i	−1.73520	+	0.681028i
$996$	1721.57	+	40578.7i	0.0547692	+	1.29095i
$997$	10579.3	−	10579.3i	0.336058	−	0.336058i	−0.518823	−	0.854881i	$-0.673630\pi$
$997$	10579.3	−	10579.3i	0.336058	−	0.336058i	0.854881	+	0.518823i	$0.173630\pi$
$998$	16976.2	+	2708.68i	0.538448	+	0.0859135i
$999$	19130.6	−	35501.8i	0.605871	−	1.12435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.77.61	yes	128
3.2	odd	2	inner	120.4.w.c.77.4	yes	128
5.3	odd	4	inner	120.4.w.c.53.36	yes	128
8.5	even	2	inner	120.4.w.c.77.29	yes	128
15.8	even	4	inner	120.4.w.c.53.29	yes	128
24.5	odd	2	inner	120.4.w.c.77.36	yes	128
40.13	odd	4	inner	120.4.w.c.53.4	✓	128
120.53	even	4	inner	120.4.w.c.53.61	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.4	✓	128	40.13	odd	4	inner
120.4.w.c.53.29	yes	128	15.8	even	4	inner
120.4.w.c.53.36	yes	128	5.3	odd	4	inner
120.4.w.c.53.61	yes	128	120.53	even	4	inner
120.4.w.c.77.4	yes	128	3.2	odd	2	inner
120.4.w.c.77.29	yes	128	8.5	even	2	inner
120.4.w.c.77.36	yes	128	24.5	odd	2	inner
120.4.w.c.77.61	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.79310 + 0.445660i) q^{2} +(2.14982 - 4.73057i) q^{3} +(7.60277 + 2.48954i) q^{4} +(4.08469 + 10.4075i) q^{5} +(8.11287 - 12.2548i) q^{6} +(13.5500 + 13.5500i) q^{7} +(20.1258 + 10.3418i) q^{8} +(-17.7566 - 20.3397i) q^{9} +(6.77075 + 30.8894i) q^{10} -23.6403 q^{11} +(28.1215 - 30.6134i) q^{12} +(-21.9939 - 21.9939i) q^{13} +(31.8078 + 43.8853i) q^{14} +(58.0146 + 3.05120i) q^{15} +(51.6043 + 37.8549i) q^{16} +(92.3861 - 92.3861i) q^{17} +(-40.5312 - 64.7242i) q^{18} -105.429 q^{19} +(5.14516 + 89.2946i) q^{20} +(93.2295 - 34.9693i) q^{21} +(-66.0296 - 10.5355i) q^{22} +(-6.66319 - 6.66319i) q^{23} +(92.1893 - 72.9735i) q^{24} +(-91.6306 + 85.0226i) q^{25} +(-51.6292 - 71.2327i) q^{26} +(-134.392 + 40.2721i) q^{27} +(69.2844 + 136.751i) q^{28} -190.191i q^{29} +(160.680 + 34.3771i) q^{30} -30.1383 q^{31} +(127.265 + 128.730i) q^{32} +(-50.8223 + 111.832i) q^{33} +(299.216 - 216.870i) q^{34} +(-85.6738 + 196.369i) q^{35} +(-84.3627 - 198.844i) q^{36} +(-203.258 + 203.258i) q^{37} +(-294.474 - 46.9856i) q^{38} +(-151.326 + 56.7607i) q^{39} +(-25.4242 + 251.701i) q^{40} +348.549i q^{41} +(275.983 - 56.1240i) q^{42} +(-30.6757 - 30.6757i) q^{43} +(-179.732 - 58.8536i) q^{44} +(139.155 - 267.882i) q^{45} +(-15.6414 - 21.5805i) q^{46} +(-66.6485 + 66.6485i) q^{47} +(290.015 - 162.737i) q^{48} +24.2070i q^{49} +(-293.824 + 196.640i) q^{50} +(-238.426 - 635.652i) q^{51} +(-112.460 - 221.969i) q^{52} +(195.204 - 195.204i) q^{53} +(-393.317 + 52.5908i) q^{54} +(-96.5634 - 246.036i) q^{55} +(132.573 + 412.837i) q^{56} +(-226.653 + 498.740i) q^{57} +(84.7607 - 531.222i) q^{58} -343.492i q^{59} +(433.476 + 167.627i) q^{60} +232.915i q^{61} +(-84.1792 - 13.4314i) q^{62} +(35.0015 - 516.206i) q^{63} +(298.095 + 416.273i) q^{64} +(139.062 - 318.738i) q^{65} +(-191.791 + 289.708i) q^{66} +(-397.741 + 397.741i) q^{67} +(932.390 - 472.391i) q^{68} +(-45.8453 + 17.1961i) q^{69} +(-326.809 + 510.297i) q^{70} -834.762i q^{71} +(-147.016 - 592.988i) q^{72} +(334.976 - 334.976i) q^{73} +(-658.303 + 477.135i) q^{74} +(205.216 + 616.248i) q^{75} +(-801.555 - 262.471i) q^{76} +(-320.327 - 320.327i) q^{77} +(-447.965 + 91.0981i) q^{78} +906.479i q^{79} +(-183.185 + 691.696i) q^{80} +(-98.4075 + 722.327i) q^{81} +(-155.334 + 973.530i) q^{82} +(-690.879 + 690.879i) q^{83} +(795.860 - 33.7648i) q^{84} +(1338.87 + 584.136i) q^{85} +(-72.0092 - 99.3510i) q^{86} +(-899.713 - 408.876i) q^{87} +(-475.780 - 244.483i) q^{88} +1288.76 q^{89} +(508.057 - 686.206i) q^{90} -596.035i q^{91} +(-34.0704 - 67.2471i) q^{92} +(-64.7918 + 142.571i) q^{93} +(-215.858 + 156.453i) q^{94} +(-430.646 - 1097.25i) q^{95} +(882.565 - 325.292i) q^{96} +(-688.583 - 688.583i) q^{97} +(-10.7881 + 67.6124i) q^{98} +(419.771 + 480.837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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