LMFDB - Embedded newform 120.4.w.c.53.29

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			53.29
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.445660 + 2.79310i) q^{2} +(-2.14982 - 4.73057i) q^{3} +(-7.60277 - 2.48954i) q^{4} +(-4.08469 + 10.4075i) q^{5} +(14.1710 - 3.89642i) q^{6} +(13.5500 - 13.5500i) q^{7} +(10.3418 - 20.1258i) q^{8} +(-17.7566 + 20.3397i) q^{9} +(-27.2487 - 16.0471i) q^{10} +23.6403 q^{11} +(4.56760 + 41.3175i) 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} +(-48.8974 - 58.6604i) q^{18} +105.429 q^{19} +(56.9648 - 68.9566i) q^{20} +(-93.2295 - 34.9693i) q^{21} +(-10.5355 + 66.0296i) q^{22} +(-6.66319 + 6.66319i) q^{23} +(-117.439 - 5.65583i) q^{24} +(-91.6306 - 85.0226i) q^{25} +(51.6292 + 71.2327i) q^{26} +(134.392 + 40.2721i) q^{27} +(-136.751 + 69.2844i) q^{28} -190.191i q^{29} +(-17.3325 + 163.400i) q^{30} -30.1383 q^{31} +(-128.730 + 127.265i) q^{32} +(-50.8223 - 111.832i) q^{33} +(-299.216 + 216.870i) q^{34} +(85.6738 + 196.369i) q^{35} +(185.636 - 110.432i) q^{36} +(203.258 + 203.258i) q^{37} +(-46.9856 + 294.474i) q^{38} +(-151.326 - 56.7607i) q^{39} +(167.215 + 189.839i) q^{40} -348.549i q^{41} +(139.221 - 244.814i) 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} +(68.1354 - 325.499i) q^{48} -24.2070i q^{49} +(278.312 - 218.042i) q^{50} +(238.426 - 635.652i) q^{51} +(-221.969 + 112.460i) q^{52} +(-195.204 - 195.204i) q^{53} +(-172.377 + 357.422i) q^{54} +(-96.5634 + 246.036i) q^{55} +(-132.573 - 412.837i) q^{56} +(-226.653 - 498.740i) q^{57} +(531.222 + 84.7607i) q^{58} -343.492i q^{59} +(-448.668 - 121.232i) q^{60} +232.915i q^{61} +(13.4314 - 84.1792i) q^{62} +(35.0015 + 516.206i) q^{63} +(-298.095 - 416.273i) q^{64} +(139.062 + 318.738i) q^{65} +(335.007 - 92.1125i) q^{66} +(397.741 + 397.741i) q^{67} +(-472.391 - 932.390i) q^{68} +(45.8453 + 17.1961i) q^{69} +(-586.660 + 151.781i) q^{70} +834.762i q^{71} +(225.718 + 567.714i) 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} +(225.978 - 397.373i) q^{78} -906.479i q^{79} +(-604.761 + 382.445i) q^{80} +(-98.4075 - 722.327i) q^{81} +(973.530 + 155.334i) q^{82} +(690.879 + 690.879i) q^{83} +(621.745 + 497.963i) q^{84} +(-1338.87 + 584.136i) q^{85} +(72.0092 + 99.3510i) q^{86} +(-899.713 + 408.876i) q^{87} +(244.483 - 475.780i) q^{88} +1288.76 q^{89} +(810.237 - 269.288i) q^{90} -596.035i q^{91} +(67.2471 - 34.0704i) q^{92} +(64.7918 + 142.571i) q^{93} +(215.858 - 156.453i) q^{94} +(-430.646 + 1097.25i) q^{95} +(878.785 + 335.371i) q^{96} +(-688.583 + 688.583i) q^{97} +(67.6124 + 10.7881i) 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 $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.445660	+	2.79310i	−0.157565	+	0.987509i
$2$	−0.445660	+	2.79310i	−0.157565	+	0.987509i
$3$	−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
$6$	14.1710	−	3.89642i	0.964216	−	0.265117i
$7$	13.5500	−	13.5500i	0.731633	−	0.731633i	−0.239310	−	0.970943i	$-0.576921\pi$
$7$	13.5500	−	13.5500i	0.731633	−	0.731633i	0.970943	+	0.239310i	$0.0769212\pi$
$8$	10.3418	−	20.1258i	0.457047	−	0.889443i
$9$	−17.7566	+	20.3397i	−0.657651	+	0.753323i
$10$	−27.2487	−	16.0471i	−0.861678	−	0.507455i
$11$	23.6403			0.647984			0.323992	−	0.946060i	$-0.394975\pi$
$11$	23.6403			0.647984			0.323992	+	0.946060i	$0.394975\pi$
$12$	4.56760	+	41.3175i	0.109879	+	0.993945i
$13$	21.9939	−	21.9939i	0.469231	−	0.469231i	−0.432435	−	0.901665i	$-0.642345\pi$
$13$	21.9939	−	21.9939i	0.469231	−	0.469231i	0.901665	+	0.432435i	$0.142345\pi$
$14$	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	0.915314	+	0.402740i	$0.131942\pi$
$17$	92.3861	+	92.3861i	1.31805	+	1.31805i	0.402740	+	0.915314i	$0.368058\pi$
$18$	−48.8974	−	58.6604i	−0.640290	−	0.768133i
$19$	105.429			1.27301			0.636503	−	0.771274i	$-0.280380\pi$
$19$	105.429			1.27301			0.636503	+	0.771274i	$0.280380\pi$
$20$	56.9648	−	68.9566i	0.636886	−	0.770958i
$21$	−93.2295	−	34.9693i	−0.968778	−	0.363378i
$22$	−10.5355	+	66.0296i	−0.102099	+	0.639889i
$23$	−6.66319	+	6.66319i	−0.0604075	+	0.0604075i	−0.736665	−	0.676258i	$-0.763601\pi$
$23$	−6.66319	+	6.66319i	−0.0604075	+	0.0604075i	0.676258	+	0.736665i	$0.263601\pi$
$24$	−117.439	−	5.65583i	−0.998842	−	0.0481038i
$25$	−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
$28$	−136.751	+	69.2844i	−0.922984	+	0.467626i
$29$		−	190.191i		−	1.21785i	−0.793228	−	0.608924i	$-0.791601\pi$
$29$		−	190.191i		−	1.21785i	0.793228	−	0.608924i	$-0.208399\pi$
$30$	−17.3325	+	163.400i	−0.105482	+	0.994421i
$31$	−30.1383			−0.174613			−0.0873064	−	0.996182i	$-0.527826\pi$
$31$	−30.1383			−0.174613			−0.0873064	+	0.996182i	$0.527826\pi$
$32$	−128.730	+	127.265i	−0.711141	+	0.703049i
$33$	−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
$36$	185.636	−	110.432i	0.859425	−	0.511261i
$37$	203.258	+	203.258i	0.903119	+	0.903119i	0.995705	−	0.0925854i	$-0.0295131\pi$
$37$	203.258	+	203.258i	0.903119	+	0.903119i	−0.0925854	+	0.995705i	$0.529513\pi$
$38$	−46.9856	+	294.474i	−0.200581	+	1.25711i
$39$	−151.326	−	56.7607i	−0.621323	−	0.233051i
$40$	167.215	+	189.839i	0.660977	+	0.750406i
$41$		−	348.549i		−	1.32766i	−0.747882	−	0.663831i	$-0.768929\pi$
$41$		−	348.549i		−	1.32766i	0.747882	−	0.663831i	$-0.231071\pi$
$42$	139.221	−	244.814i	0.511484	−	0.899421i
$43$	30.6757	−	30.6757i	0.108791	−	0.108791i	−0.650616	−	0.759407i	$-0.725489\pi$
$43$	30.6757	−	30.6757i	0.108791	−	0.108791i	0.759407	+	0.650616i	$0.225489\pi$
$44$	−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	0.596080	−	0.802925i	$-0.296724\pi$
$47$	−66.6485	−	66.6485i	−0.206844	−	0.206844i	−0.802925	+	0.596080i	$0.796724\pi$
$48$	68.1354	−	325.499i	0.204885	−	0.978786i
$49$		−	24.2070i		−	0.0705743i
$50$	278.312	−	218.042i	0.787186	−	0.616715i
$51$	238.426	−	635.652i	0.654633	−	1.74528i
$52$	−221.969	+	112.460i	−0.591953	+	0.299910i
$53$	−195.204	−	195.204i	−0.505911	−	0.505911i	0.407358	−	0.913269i	$-0.366450\pi$
$53$	−195.204	−	195.204i	−0.505911	−	0.505911i	−0.913269	+	0.407358i	$0.866450\pi$
$54$	−172.377	+	357.422i	−0.434399	+	0.900721i
$55$	−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
$58$	531.222	+	84.7607i	1.20264	+	0.191890i
$59$		−	343.492i		−	0.757946i	−0.925408	−	0.378973i	$-0.876277\pi$
$59$		−	343.492i		−	0.757946i	0.925408	−	0.378973i	$-0.123723\pi$
$60$	−448.668	−	121.232i	−0.965379	−	0.260850i
$61$			232.915i			0.488880i	0.969664	+	0.244440i	$0.0786041\pi$
$61$			232.915i			0.488880i	−0.969664	+	0.244440i	$0.921396\pi$
$62$	13.4314	−	84.1792i	0.0275128	−	0.172432i
$63$	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
$66$	335.007	−	92.1125i	0.624796	−	0.171792i
$67$	397.741	+	397.741i	0.725251	+	0.725251i	0.969670	−	0.244418i	$-0.0785971\pi$
$67$	397.741	+	397.741i	0.725251	+	0.725251i	−0.244418	+	0.969670i	$0.578597\pi$
$68$	−472.391	−	932.390i	−0.842439	−	1.66278i
$69$	45.8453	+	17.1961i	0.0799874	+	0.0300024i
$70$	−586.660	+	151.781i	−1.00170	+	0.259162i
$71$			834.762i			1.39533i	0.716427	+	0.697663i	$0.245776\pi$
$71$			834.762i			1.39533i	−0.716427	+	0.697663i	$0.754224\pi$
$72$	225.718	+	567.714i	0.369460	+	0.929247i
$73$	334.976	+	334.976i	0.537067	+	0.537067i	0.922666	−	0.385599i	$-0.126005\pi$
$73$	334.976	+	334.976i	0.537067	+	0.537067i	−0.385599	+	0.922666i	$0.626005\pi$
$74$	−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
$78$	225.978	−	397.373i	0.328038	−	0.576841i
$79$		−	906.479i		−	1.29097i	−0.763771	−	0.645487i	$-0.776655\pi$
$79$		−	906.479i		−	1.29097i	0.763771	−	0.645487i	$-0.223345\pi$
$80$	−604.761	+	382.445i	−0.845179	+	0.534483i
$81$	−98.4075	−	722.327i	−0.134990	−	0.990847i
$82$	973.530	+	155.334i	1.31108	+	0.209193i
$83$	690.879	+	690.879i	0.913660	+	0.913660i	0.996558	−	0.0828977i	$-0.0264175\pi$
$83$	690.879	+	690.879i	0.913660	+	0.913660i	−0.0828977	+	0.996558i	$0.526417\pi$
$84$	621.745	+	497.963i	0.807595	+	0.646812i
$85$	−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
$88$	244.483	−	475.780i	0.296159	−	0.576344i
$89$	1288.76			1.53493			0.767465	−	0.641091i	$-0.221518\pi$
$89$	1288.76			1.53493			0.767465	+	0.641091i	$0.221518\pi$
$90$	810.237	−	269.288i	0.948961	−	0.315393i
$91$		−	596.035i		−	0.686609i
$92$	67.2471	−	34.0704i	0.0762064	−	0.0386097i
$93$	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
$96$	878.785	+	335.371i	0.934277	+	0.356548i
$97$	−688.583	+	688.583i	−0.720773	+	0.720773i	−0.968763	−	0.247989i	$-0.920230\pi$
$97$	−688.583	+	688.583i	−0.720773	+	0.720773i	0.247989	+	0.968763i	$0.420230\pi$
$98$	67.6124	+	10.7881i	0.0696927	+	0.0111200i
$99$	−419.771	+	480.837i	−0.426147	+	0.488141i
$100$	484.979	+	874.526i	0.484979	+	0.874526i
$101$	−1938.57			−1.90985			−0.954925	−	0.296848i	$-0.904064\pi$
$101$	−1938.57			−1.90985			−0.954925	+	0.296848i	$0.904064\pi$
$102$	1669.18	+	949.231i	1.62033	+	0.921450i
$103$	280.520	+	280.520i	0.268354	+	0.268354i	0.828437	−	0.560083i	$-0.189231\pi$
$103$	280.520	+	280.520i	0.268354	+	0.268354i	−0.560083	+	0.828437i	$0.689231\pi$
$104$	−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	$-0.768953\pi$
$107$	−93.1446	+	93.1446i	−0.0841555	+	0.0841555i	0.663776	+	0.747931i	$0.268953\pi$
$108$	−921.491	−	640.754i	−0.821023	−	0.570894i
$109$	−1161.91			−1.02101			−0.510507	−	0.859874i	$-0.670542\pi$
$109$	−1161.91			−1.02101			−0.510507	+	0.859874i	$0.670542\pi$
$110$	−644.167	−	379.359i	−0.558353	−	0.328823i
$111$	524.559	−	1398.49i	0.448549	−	1.19585i
$112$	1212.18	−	186.306i	1.02268	−	0.157181i
$113$	61.0136	−	61.0136i	0.0507936	−	0.0507936i	−0.681254	−	0.732047i	$-0.738565\pi$
$113$	61.0136	−	61.0136i	0.0507936	−	0.0507936i	0.732047	+	0.681254i	$0.238565\pi$
$114$	1494.04	−	410.796i	1.22745	−	0.337496i
$115$	−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
$118$	959.405	+	153.081i	0.748478	+	0.119426i
$119$	2503.67			1.92866
$120$	538.567	−	1199.14i	0.409702	−	0.912220i
$121$	−772.136			−0.580117
$122$	−650.553	−	103.801i	−0.482773	−	0.0770302i
$123$	−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
$126$	−1457.41	−	132.290i	−1.03045	−	0.0935345i
$127$	728.509	−	728.509i	0.509014	−	0.509014i	−0.405210	−	0.914224i	$-0.632802\pi$
$127$	728.509	−	728.509i	0.509014	−	0.509014i	0.914224	+	0.405210i	$0.132802\pi$
$128$	1295.54	−	647.091i	0.894615	−	0.446838i
$129$	−211.060	−	79.1664i	−0.144053	−	0.0540326i
$130$	−952.241	+	246.365i	−0.642439	+	0.166212i
$131$	1108.11			0.739052			0.369526	−	0.929220i	$-0.379520\pi$
$131$	1108.11			0.739052			0.369526	+	0.929220i	$0.379520\pi$
$132$	107.979	+	976.759i	0.0712000	+	0.644060i
$133$	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	0.754411	−	0.656403i	$-0.227923\pi$
$137$	157.161	+	157.161i	0.0980083	+	0.0980083i	−0.656403	+	0.754411i	$0.727923\pi$
$138$	−68.4617	+	120.387i	−0.0422308	+	0.0742609i
$139$	−1006.99			−0.614471			−0.307236	−	0.951633i	$-0.599404\pi$
$139$	−1006.99			−0.614471			−0.307236	+	0.951633i	$0.599404\pi$
$140$	−162.488	−	1706.24i	−0.0980912	−	1.03003i
$141$	−172.003	+	458.567i	−0.102733	+	0.273889i
$142$	−2331.57	−	372.021i	−1.37790	−	0.219854i
$143$	519.941	−	519.941i	0.304054	−	0.304054i
$144$	−1686.27	+	377.444i	−0.975853	+	0.218428i
$145$	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
$148$	−1039.30	−	2051.34i	−0.577232	−	1.13932i
$149$			1884.11i			1.03592i	0.855405	+	0.517960i	$0.173309\pi$
$149$			1884.11i			1.03592i	−0.855405	+	0.517960i	$0.826691\pi$
$150$	−1629.78	−	847.826i	−0.887141	−	0.461498i
$151$	34.3422			0.0185081			0.00925407	−	0.999957i	$-0.497054\pi$
$151$	34.3422			0.0185081			0.00925407	+	0.999957i	$0.497054\pi$
$152$	1090.33	−	2121.85i	0.581824	−	1.13227i
$153$	−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
$156$	1009.19	+	808.272i	0.517948	+	0.414831i
$157$	−1860.87	−	1860.87i	−0.945945	−	0.945945i	0.0526676	−	0.998612i	$-0.483228\pi$
$157$	−1860.87	−	1860.87i	−0.945945	−	0.945945i	−0.998612	+	0.0526676i	$0.983228\pi$
$158$	2531.88	+	403.982i	1.27485	+	0.203412i
$159$	−503.773	+	1343.08i	−0.251269	+	0.669892i
$160$	−798.687	−	1859.60i	−0.394636	−	0.918838i
$161$			180.573i			0.0883922i
$162$	2061.39	+	47.0510i	0.999740	+	0.0228190i
$163$	1488.97	−	1488.97i	0.715493	−	0.715493i	−0.252186	−	0.967679i	$-0.581149\pi$
$163$	1488.97	−	1488.97i	0.715493	−	0.715493i	0.967679	+	0.252186i	$0.0811494\pi$
$164$	−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	0.109972	−	0.993935i	$-0.464924\pi$
$167$	−1907.69	−	1907.69i	−0.883963	−	0.883963i	−0.993935	+	0.109972i	$0.964924\pi$
$168$	−1667.94	+	1514.67i	−0.765981	+	0.695592i
$169$			1229.54i			0.559645i
$170$	−1034.87	−	3999.93i	−0.466886	−	1.80459i
$171$	−1872.06	+	2144.40i	−0.837194	+	0.958985i
$172$	−309.589	+	156.852i	−0.137244	+	0.0695339i
$173$	657.105	+	657.105i	0.288779	+	0.288779i	0.836597	−	0.547818i	$-0.184541\pi$
$173$	657.105	+	657.105i	0.288779	+	0.288779i	−0.547818	+	0.836597i	$0.684541\pi$
$174$	−741.064	−	2695.20i	−0.322873	−	1.17427i
$175$	−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
$178$	−574.351	+	3599.64i	−0.241851	+	1.51576i
$179$		−	2226.47i		−	0.929687i	−0.885393	−	0.464843i	$-0.846111\pi$
$179$		−	2226.47i		−	0.929687i	0.885393	−	0.464843i	$-0.153889\pi$
$180$	391.055	+	2383.08i	0.161931	+	0.986802i
$181$			759.935i			0.312075i	0.987751	+	0.156037i	$0.0498721\pi$
$181$			759.935i			0.312075i	−0.987751	+	0.156037i	$0.950128\pi$
$182$	1664.78	+	265.629i	0.678033	+	0.108185i
$183$	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
$186$	−427.091	+	117.431i	−0.168365	+	0.0462929i
$187$	2184.04	+	2184.04i	0.854078	+	0.854078i
$188$	340.789	+	672.638i	0.132205	+	0.260942i
$189$	2366.70	−	1275.33i	0.910859	−	0.490827i
$190$	−2872.81	−	1691.84i	−1.09692	−	0.645994i
$191$		−	109.634i		−	0.0415333i	−0.999784	−	0.0207667i	$-0.993389\pi$
$191$		−	109.634i		−	0.0415333i	0.999784	−	0.0207667i	$-0.00661071\pi$
$192$	−1328.36	+	2305.07i	−0.499303	+	0.866427i
$193$	857.642	+	857.642i	0.319868	+	0.319868i	0.848716	−	0.528849i	$-0.177376\pi$
$193$	857.642	+	857.642i	0.319868	+	0.319868i	−0.528849	+	0.848716i	$0.677376\pi$
$194$	−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	$-0.687712\pi$
$197$	760.319	−	760.319i	0.274977	−	0.274977i	0.831100	+	0.556123i	$0.187712\pi$
$198$	−1155.95	−	1386.75i	−0.414897	−	0.497738i
$199$		−	5232.87i		−	1.86406i	−0.362378	−	0.932031i	$-0.618035\pi$
$199$		−	5232.87i		−	1.86406i	0.362378	−	0.932031i	$-0.381965\pi$
$200$	−2658.77	+	964.851i	−0.940017	+	0.341126i
$201$	1026.47	−	2736.61i	0.360208	−	0.960328i
$202$	863.943	−	5414.61i	0.300925	−	1.88599i
$203$	−2577.10	−	2577.10i	−0.891019	−	0.891019i
$204$	−3395.18	+	4239.15i	−1.16525	+	1.45490i
$205$	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
$208$	1967.55	−	302.403i	0.655891	−	0.100807i
$209$	2492.38			0.824888
$210$	1979.22	+	2448.93i	0.650377	+	0.804726i
$211$		−	2462.42i		−	0.803414i	−0.915768	−	0.401707i	$-0.868417\pi$
$211$		−	2462.42i		−	0.803414i	0.915768	−	0.401707i	$-0.131583\pi$
$212$	998.121	+	1970.06i	0.323355	+	0.638227i
$213$	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
$216$	2200.36	−	2288.25i	0.693128	−	0.720815i
$217$	−408.375	+	408.375i	−0.127753	+	0.127753i
$218$	517.816	−	3245.32i	0.160876	−	1.00826i
$219$	864.489	−	2304.76i	0.266743	−	0.711147i
$220$	1346.67	−	1630.15i	0.412692	−	0.499568i
$221$	4063.85			1.23694
$222$	3672.35	+	2088.40i	1.11023	+	0.631369i
$223$	181.463	+	181.463i	0.0544919	+	0.0544919i	0.733828	−	0.679336i	$-0.237732\pi$
$223$	181.463	+	181.463i	0.0544919	+	0.0544919i	−0.679336	+	0.733828i	$0.737732\pi$
$224$	−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	$-0.928861\pi$
$227$	−2577.03	+	2577.03i	−0.753496	+	0.753496i	0.221634	+	0.975130i	$0.428861\pi$
$228$	481.559	+	4356.07i	0.139877	+	1.26530i
$229$	−2690.23			−0.776313			−0.388156	−	0.921593i	$-0.626888\pi$
$229$	−2690.23			−0.776313			−0.388156	+	0.921593i	$0.626888\pi$
$230$	288.488	−	74.6379i	0.0827059	−	0.0213977i
$231$	−2203.97	−	826.685i	−0.627752	−	0.235463i
$232$	−3827.75	−	1966.92i	−1.08321	−	0.556614i
$233$	−2252.87	+	2252.87i	−0.633435	+	0.633435i	−0.948928	−	0.315493i	$-0.897830\pi$
$233$	−2252.87	+	2252.87i	−0.633435	+	0.633435i	0.315493	+	0.948928i	$0.397830\pi$
$234$	−2365.61	−	214.728i	−0.660875	−	0.0599880i
$235$	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
$238$	−1115.79	+	6992.99i	−0.303890	+	1.90457i
$239$	3833.40			1.03750			0.518749	−	0.854927i	$-0.326398\pi$
$239$	3833.40			1.03750			0.518749	+	0.854927i	$0.326398\pi$
$240$	3109.31	+	2038.68i	0.836270	+	0.548318i
$241$	1641.79			0.438826			0.219413	−	0.975632i	$-0.429586\pi$
$241$	1641.79			0.438826			0.219413	+	0.975632i	$0.429586\pi$
$242$	344.110	−	2156.65i	0.0914060	−	0.572871i
$243$	−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
$246$	−1358.09	−	4939.29i	−0.351987	−	1.28015i
$247$	2318.80	−	2318.80i	0.597334	−	0.597334i
$248$	−311.684	+	606.557i	−0.0798063	+	0.155308i
$249$	1782.99	−	4753.51i	0.453784	−	1.20981i
$250$	1132.44	+	3787.16i	0.286487	+	0.958084i
$251$	−4943.40			−1.24313			−0.621564	−	0.783364i	$-0.713502\pi$
$251$	−4943.40			−1.24313			−0.621564	+	0.783364i	$0.713502\pi$
$252$	1019.01	−	4011.74i	0.254729	−	1.00284i
$253$	−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	0.506033	−	0.862514i	$-0.331111\pi$
$257$	−1468.71	−	1468.71i	−0.356481	−	0.356481i	−0.862514	+	0.506033i	$0.831111\pi$
$258$	315.181	−	554.231i	0.0760554	−	0.133740i
$259$	5508.31			1.32150
$260$	−263.744	−	2769.50i	−0.0629104	−	0.660604i
$261$	3868.43	+	3377.15i	0.917433	+	0.800920i
$262$	−493.840	+	3095.05i	−0.116449	+	0.729821i
$263$	−538.864	+	538.864i	−0.126341	+	0.126341i	−0.767450	−	0.641109i	$-0.778475\pi$
$263$	−538.864	+	538.864i	−0.126341	+	0.126341i	0.641109	+	0.767450i	$0.278475\pi$
$264$	−2776.30	−	133.706i	−0.647234	−	0.0311705i
$265$	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
$268$	−2033.74	−	4014.13i	−0.463547	−	0.914933i
$269$			402.369i			0.0912004i	0.998960	+	0.0456002i	$0.0145200\pi$
$269$			402.369i			0.0912004i	−0.998960	+	0.0456002i	$0.985480\pi$
$270$	−3015.74	−	3253.96i	−0.679749	−	0.733444i
$271$	−8159.60			−1.82900			−0.914502	−	0.404581i	$-0.867418\pi$
$271$	−8159.60			−1.82900			−0.914502	+	0.404581i	$0.867418\pi$
$272$	1270.26	+	8264.79i	0.283164	+	1.84238i
$273$	−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
$276$	−305.741	−	244.872i	−0.0666792	−	0.0534042i
$277$	333.740	+	333.740i	0.0723916	+	0.0723916i	0.742376	−	0.669984i	$-0.233699\pi$
$277$	333.740	+	333.740i	0.0723916	+	0.0723916i	−0.669984	+	0.742376i	$0.733699\pi$
$278$	448.774	−	2812.61i	0.0968190	−	0.606796i
$279$	535.153	−	613.004i	0.114834	−	0.131540i
$280$	4838.11	+	306.558i	1.03261	+	0.0654298i
$281$			985.762i			0.209273i	0.994511	+	0.104636i	$0.0333679\pi$
$281$			985.762i			0.209273i	−0.994511	+	0.104636i	$0.966632\pi$
$282$	−1204.17	−	684.787i	−0.254281	−	0.144605i
$283$	−5012.19	+	5012.19i	−1.05280	+	1.05280i	−0.0542790	+	0.998526i	$0.517286\pi$
$283$	−5012.19	+	5012.19i	−1.05280	+	1.05280i	−0.998526	+	0.0542790i	$0.982714\pi$
$284$	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
$288$	−302.731	−	4878.14i	−0.0619396	−	0.998080i
$289$			12157.4i			2.47453i
$290$	−3052.02	+	5182.45i	−0.618003	+	1.04939i
$291$	4737.72	+	1777.06i	0.954398	+	0.357984i
$292$	−1712.81	−	3380.68i	−0.343269	−	0.677532i
$293$	−684.466	−	684.466i	−0.136474	−	0.136474i	0.635569	−	0.772044i	$-0.280765\pi$
$293$	−684.466	−	684.466i	−0.136474	−	0.136474i	−0.772044	+	0.635569i	$0.780765\pi$
$294$	−94.3204	−	343.038i	−0.0187105	−	0.0680489i
$295$	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
$298$	−5262.50	−	839.672i	−1.02298	−	0.163225i
$299$			293.099i			0.0566901i
$300$	3094.39	−	4174.30i	0.595516	−	0.803344i
$301$		−	831.313i		−	0.159190i
$302$	−15.3050	+	95.9211i	−0.00291623	+	0.0182769i
$303$	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
$306$	901.974	−	9936.85i	0.168505	−	1.85638i
$307$	1726.29	+	1726.29i	0.320926	+	0.320926i	0.849122	−	0.528196i	$-0.177131\pi$
$307$	1726.29	+	1726.29i	0.320926	+	0.320926i	−0.528196	+	0.849122i	$0.677131\pi$
$308$	−3232.84	+	1637.91i	−0.598079	+	0.303014i
$309$	723.953	−	1930.09i	0.133282	−	0.355336i
$310$	821.228	+	483.633i	0.150460	+	0.0886082i
$311$		−	4178.94i		−	0.761949i	−0.924585	−	0.380975i	$-0.875589\pi$
$311$		−	4178.94i		−	0.761949i	0.924585	−	0.380975i	$-0.124411\pi$
$312$	−2707.34	+	2458.55i	−0.491259	+	0.446116i
$313$	−7559.82	−	7559.82i	−1.36520	−	1.36520i	−0.867152	−	0.498043i	$-0.834052\pi$
$313$	−7559.82	−	7559.82i	−1.36520	−	1.36520i	−0.498043	−	0.867152i	$-0.665948\pi$
$314$	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	$-0.865466\pi$
$317$	−2832.31	+	2832.31i	−0.501825	+	0.501825i	0.410180	+	0.912005i	$0.365466\pi$
$318$	−3526.83	−	2005.64i	−0.621933	−	0.353682i
$319$		−	4496.18i		−	0.789146i
$320$	5549.98	−	1402.06i	0.969541	−	0.244930i
$321$	640.871	+	240.383i	0.111433	+	0.0417972i
$322$	−504.358	−	80.4742i	−0.0872881	−	0.0139275i
$323$	9740.20	+	9740.20i	1.67789	+	1.67789i
$324$	−1050.10	+	5736.68i	−0.180058	+	0.983656i
$325$	−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
$328$	−7014.82	−	3604.62i	−1.18088	−	0.606804i
$329$	−1806.18			−0.302668
$330$	−409.745	+	3862.83i	−0.0683507	+	0.644369i
$331$			1899.46i			0.315419i	0.987486	+	0.157709i	$0.0504109\pi$
$331$			1899.46i			0.315419i	−0.987486	+	0.157709i	$0.949589\pi$
$332$	−3532.62	−	6972.57i	−0.583969	−	1.15262i
$333$	−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
$336$	−3487.29	−	5333.76i	−0.566211	−	0.866013i
$337$	−5416.63	+	5416.63i	−0.875556	+	0.875556i	−0.993071	−	0.117515i	$-0.962507\pi$
$337$	−5416.63	+	5416.63i	−0.875556	+	0.875556i	0.117515	+	0.993071i	$0.462507\pi$
$338$	−3434.23	−	547.958i	−0.552655	−	0.0881804i
$339$	−419.797	−	157.461i	−0.0672573	−	0.0252275i
$340$	11633.4	−	1107.87i	1.85562	−	0.176714i
$341$	−712.479			−0.113146
$342$	−5155.21	−	6184.53i	−0.815093	−	0.977839i
$343$	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	$-0.590243\pi$
$347$	4397.76	−	4397.76i	0.680357	−	0.680357i	0.960081	+	0.279723i	$0.0902428\pi$
$348$	7858.23	−	868.717i	1.21047	−	0.133816i
$349$	−11672.4			−1.79028			−0.895139	−	0.445787i	$-0.852924\pi$
$349$	−11672.4			−1.79028			−0.895139	+	0.445787i	$0.852924\pi$
$350$	816.669	−	6725.62i	0.124722	−	1.02714i
$351$	3841.53	−	2070.05i	0.584176	−	0.314790i
$352$	−3043.22	+	3008.59i	−0.460808	+	0.455564i
$353$	5095.42	−	5095.42i	0.768277	−	0.768277i	−0.209526	−	0.977803i	$-0.567192\pi$
$353$	5095.42	−	5095.42i	0.768277	−	0.768277i	0.977803	+	0.209526i	$0.0671921\pi$
$354$	−1338.39	−	4867.63i	−0.200945	−	0.730824i
$355$	−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
$358$	6218.74	+	992.248i	0.918074	+	0.146486i
$359$	−10047.6			−1.47714			−0.738571	−	0.674176i	$-0.764499\pi$
$359$	−10047.6			−1.47714			−0.738571	+	0.674176i	$0.764499\pi$
$360$	−6830.45	+	30.2108i	−0.999990	+	0.00442291i
$361$	4256.33			0.620546
$362$	−2122.57	−	338.673i	−0.308177	−	0.0491720i
$363$	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
$366$	907.532	+	3300.64i	0.129611	+	0.471386i
$367$	5113.00	−	5113.00i	0.727238	−	0.727238i	−0.242831	−	0.970069i	$-0.578076\pi$
$367$	5113.00	−	5113.00i	0.727238	−	0.727238i	0.970069	+	0.242831i	$0.0780759\pi$
$368$	−596.084	+	91.6152i	−0.0844376	+	0.0129776i
$369$	7089.38	+	6189.04i	1.00016	+	0.873139i
$370$	−2276.80	−	8800.22i	−0.319906	−	1.23649i
$371$	−5290.03			−0.740283
$372$	−137.660	−	1245.24i	−0.0191864	−	0.173556i
$373$	−829.354	+	829.354i	−0.115127	+	0.115127i	−0.762323	−	0.647196i	$-0.775941\pi$
$373$	−829.354	+	829.354i	−0.115127	+	0.115127i	0.647196	+	0.762323i	$0.275941\pi$
$374$	−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
$378$	2507.36	+	7178.79i	0.341176	+	0.976818i
$379$	7284.09			0.987226			0.493613	−	0.869682i	$-0.335676\pi$
$379$	7284.09			0.987226			0.493613	+	0.869682i	$0.335676\pi$
$380$	6005.76	−	7270.04i	0.810761	−	0.981434i
$381$	−5012.42	−	1880.10i	−0.674001	−	0.252810i
$382$	306.219	+	48.8597i	0.0410145	+	0.00654419i
$383$	7765.66	−	7765.66i	1.03605	−	1.03605i	0.0367230	−	0.999325i	$-0.488308\pi$
$383$	7765.66	−	7765.66i	1.03605	−	1.03605i	0.999325	−	0.0367230i	$-0.0116919\pi$
$384$	−5846.28	−	4737.52i	−0.776932	−	0.629585i
$385$	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
$388$	6949.40	−	3520.88i	0.909284	−	0.460685i
$389$			524.755i			0.0683962i	0.999415	+	0.0341981i	$0.0108877\pi$
$389$			524.755i			0.0683962i	−0.999415	+	0.0341981i	$0.989112\pi$
$390$	3212.59	+	3975.01i	0.417117	+	0.516108i
$391$	−1231.17			−0.159241
$392$	−487.184	−	250.344i	−0.0627718	−	0.0322558i
$393$	−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
$396$	4388.49	−	2610.66i	0.556894	−	0.331289i
$397$	7963.26	+	7963.26i	1.00671	+	1.00671i	0.999977	+	0.00673471i	$0.00214374\pi$
$397$	7963.26	+	7963.26i	1.00671	+	1.00671i	0.00673471	+	0.999977i	$0.497856\pi$
$398$	14615.9	+	2332.08i	1.84078	+	0.293711i
$399$	−9829.11	−	3686.79i	−1.23326	−	0.462582i
$400$	−1510.01	−	7856.20i	−0.188752	−	0.982025i
$401$			2609.86i			0.325012i	0.986708	+	0.162506i	$0.0519577\pi$
$401$			2609.86i			0.325012i	−0.986708	+	0.162506i	$0.948042\pi$
$402$	7186.17	+	4086.64i	0.891576	+	0.507022i
$403$	−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
$408$	−10327.2	−	11372.3i	−1.25313	−	1.37993i
$409$		−	9324.88i		−	1.12735i	−0.825997	−	0.563675i	$-0.809387\pi$
$409$		−	9324.88i		−	1.12735i	0.825997	−	0.563675i	$-0.190613\pi$
$410$	−5593.21	+	9497.49i	−0.673729	+	1.14402i
$411$	405.593	−	1081.33i	0.0486774	−	0.129776i
$412$	−1434.36	−	2831.10i	−0.171519	−	0.338539i
$413$	−4654.32	−	4654.32i	−0.554538	−	0.554538i
$414$	716.678	+	65.0533i	0.0850793	+	0.00772270i
$415$	−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
$418$	−1110.75	+	6961.46i	−0.129973	+	0.814584i
$419$			321.911i			0.0375332i	0.999824	+	0.0187666i	$0.00597394\pi$
$419$			321.911i			0.0375332i	−0.999824	+	0.0187666i	$0.994026\pi$
$420$	−7722.17	+	4436.76i	−0.897150	+	0.515457i
$421$		−	2975.11i		−	0.344413i	−0.985061	−	0.172207i	$-0.944910\pi$
$421$		−	2975.11i		−	0.344413i	0.985061	−	0.172207i	$-0.0550897\pi$
$422$	6877.79	+	1097.41i	0.793378	+	0.126590i
$423$	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
$426$	3252.58	+	11829.4i	0.369925	+	1.34539i
$427$	3156.00	+	3156.00i	0.357681	+	0.357681i
$428$	940.045	−	476.270i	0.106165	−	0.0537883i
$429$	−3577.40	−	1341.84i	−0.402607	−	0.151013i
$430$	−1328.13	+	343.614i	−0.148949	+	0.0385362i
$431$			17559.0i			1.96238i	0.193043	+	0.981190i	$0.438164\pi$
$431$			17559.0i			1.96238i	−0.193043	+	0.981190i	$0.561836\pi$
$432$	5410.70	+	7165.60i	0.602599	+	0.798044i
$433$	−4103.34	−	4103.34i	−0.455413	−	0.455413i	0.441733	−	0.897146i	$-0.354364\pi$
$433$	−4103.34	−	4103.34i	−0.455413	−	0.455413i	−0.897146	+	0.441733i	$0.854364\pi$
$434$	−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
$438$	6052.15	+	3441.74i	0.660235	+	0.375463i
$439$			10896.8i			1.18469i	0.805685	+	0.592344i	$0.201797\pi$
$439$			10896.8i			1.18469i	−0.805685	+	0.592344i	$0.798203\pi$
$440$	3953.02	+	4487.86i	0.428302	+	0.486251i
$441$	492.363	+	429.833i	0.0531652	+	0.0464133i
$442$	−1811.10	+	11350.7i	−0.194899	+	1.22149i
$443$	3646.95	+	3646.95i	0.391133	+	0.391133i	0.875091	−	0.483958i	$-0.160801\pi$
$443$	3646.95	+	3646.95i	0.391133	+	0.391133i	−0.483958	+	0.875091i	$0.660801\pi$
$444$	−7469.72	+	9326.52i	−0.798417	+	0.996885i
$445$	−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
$448$	−9679.71	−	1601.33i	−1.02081	−	0.168874i
$449$	1995.96			0.209789			0.104895	−	0.994483i	$-0.466549\pi$
$449$	1995.96			0.209789			0.104895	+	0.994483i	$0.466549\pi$
$450$	−506.970	+	9532.47i	−0.0531084	+	0.998589i
$451$		−	8239.80i		−	0.860304i
$452$	−615.768	+	311.976i	−0.0640781	+	0.0324649i
$453$	−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
$456$	−12381.5	−	596.290i	−1.27153	−	0.0612365i
$457$	3478.05	−	3478.05i	0.356009	−	0.356009i	−0.506330	−	0.862340i	$-0.668998\pi$
$457$	3478.05	−	3478.05i	0.356009	−	0.356009i	0.862340	+	0.506330i	$0.168998\pi$
$458$	1198.93	−	7514.08i	0.122320	−	0.766616i
$459$	8695.35	+	16136.5i	0.884236	+	1.64093i
$460$	79.9031	+	839.039i	0.00809892	+	0.0850443i
$461$	−858.652			−0.0867493			−0.0433746	−	0.999059i	$-0.513811\pi$
$461$	−858.652			−0.0867493			−0.0433746	+	0.999059i	$0.513811\pi$
$462$	3291.23	−	5787.49i	0.331433	−	0.582810i
$463$	2288.18	+	2288.18i	0.229678	+	0.229678i	0.812558	−	0.582880i	$-0.198074\pi$
$463$	2288.18	+	2288.18i	0.229678	+	0.229678i	−0.582880	+	0.812558i	$0.698074\pi$
$464$	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	$-0.753099\pi$
$467$	−138.937	+	138.937i	−0.0137671	+	0.0137671i	0.700190	+	0.713957i	$0.253099\pi$
$468$	1654.01	−	6511.68i	0.163369	−	0.643168i
$469$	10778.8			1.06124
$470$	746.565	+	2885.60i	0.0732691	+	0.283197i
$471$	−4802.44	+	12803.5i	−0.469819	+	1.25255i
$472$	−6913.04	−	3552.32i	−0.674149	−	0.346417i
$473$	725.182	−	725.182i	0.0704945	−	0.0704945i
$474$	−3532.02	−	12845.7i	−0.342260	−	1.24478i
$475$	−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
$478$	−1708.39	+	10707.1i	−0.163473	+	1.02454i
$479$	−4176.86			−0.398425			−0.199213	−	0.979956i	$-0.563838\pi$
$479$	−4176.86			−0.398425			−0.199213	+	0.979956i	$0.563838\pi$
$480$	−7079.92	+	7776.03i	−0.673235	+	0.739429i
$481$	8940.86			0.847542
$482$	−731.682	+	4585.68i	−0.0691436	+	0.433345i
$483$	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
$486$	−4209.02	−	9852.68i	−0.392850	−	0.919602i
$487$	−29.3477	+	29.3477i	−0.00273074	+	0.00273074i	−0.708471	−	0.705740i	$-0.750615\pi$
$487$	−29.3477	+	29.3477i	−0.00273074	+	0.00273074i	0.705740	+	0.708471i	$0.250615\pi$
$488$	4687.59	+	2408.75i	0.434830	+	0.223441i
$489$	−10244.7	−	3842.67i	−0.947407	−	0.355361i
$490$	−388.453	+	659.608i	−0.0358133	+	0.0608123i
$491$	1350.17			0.124098			0.0620491	−	0.998073i	$-0.480236\pi$
$491$	1350.17			0.124098			0.0620491	+	0.998073i	$0.480236\pi$
$492$	14401.2	−	1592.03i	1.31962	−	0.145883i
$493$	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
$498$	12482.4	+	7098.51i	1.12319	+	0.638739i
$499$	−6077.90			−0.545259			−0.272629	−	0.962119i	$-0.587893\pi$
$499$	−6077.90			−0.545259			−0.272629	+	0.962119i	$0.587893\pi$
$500$	−11082.6	+	1475.23i	−0.991257	+	0.131949i
$501$	−4923.29	+	13125.7i	−0.439035	+	1.17048i
$502$	2203.08	−	13807.4i	0.195873	−	1.22760i
$503$	−11674.3	+	11674.3i	−1.03485	+	1.03485i	−0.0354794	+	0.999370i	$0.511296\pi$
$503$	−11674.3	+	11674.3i	−1.03485	+	1.03485i	−0.999370	+	0.0354794i	$0.988704\pi$
$504$	10751.0	+	4634.06i	0.950177	+	0.409559i
$505$	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
$508$	−7352.34	+	3725.03i	−0.642141	+	0.325338i
$509$			403.668i			0.0351518i	0.999846	+	0.0175759i	$0.00559487\pi$
$509$			403.668i			0.0351518i	−0.999846	+	0.0175759i	$0.994405\pi$
$510$	−16697.2	+	13494.6i	−1.44973	+	1.17167i
$511$	9077.86			0.785873
$512$	−11460.7	+	1694.38i	−0.989247	+	0.146253i
$513$	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
$516$	1407.56	+	1127.33i	0.120086	+	0.0961780i
$517$	−1575.59	−	1575.59i	−0.134032	−	0.134032i
$518$	−2454.83	+	15385.2i	−0.208222	+	1.30500i
$519$	1695.83	−	4521.14i	0.143427	−	0.382381i
$520$	7853.01	+	497.592i	0.662264	+	0.0419632i
$521$			12374.1i			1.04054i	0.854003	+	0.520268i	$0.174168\pi$
$521$			12374.1i			1.04054i	−0.854003	+	0.520268i	$0.825832\pi$
$522$	−11156.7	+	9299.85i	−0.935470	+	0.779776i
$523$	15850.3	−	15850.3i	1.32521	−	1.32521i	0.415716	−	0.909495i	$-0.363531\pi$
$523$	15850.3	−	15850.3i	1.32521	−	1.32521i	0.909495	−	0.415716i	$-0.136469\pi$
$524$	−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
$528$	1610.74	−	7694.89i	0.132762	−	0.634237i
$529$			12078.2i			0.992702i
$530$	2186.58	+	8451.50i	0.179205	+	0.692660i
$531$	6986.52	+	6099.24i	0.570978	+	0.498464i
$532$	−14417.6	+	7304.61i	−1.17497	+	0.595291i
$533$	−7665.93	−	7665.93i	−0.622980	−	0.622980i
$534$	18263.1	−	5021.56i	1.48000	−	0.406937i
$535$	−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
$538$	−1123.86	−	179.320i	−0.0900612	−	0.0143700i
$539$		−	572.260i		−	0.0457310i
$540$	10432.6	−	6973.10i	0.831387	−	0.555694i
$541$		−	14672.6i		−	1.16604i	−0.812459	−	0.583018i	$-0.801872\pi$
$541$		−	14672.6i		−	1.16604i	0.812459	−	0.583018i	$-0.198128\pi$
$542$	3636.41	−	22790.5i	0.288187	−	1.80616i
$543$	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
$546$	−2322.40	−	8446.43i	−0.182032	−	0.662040i
$547$	14666.6	+	14666.6i	1.14643	+	1.14643i	0.987249	+	0.159182i	$0.0508857\pi$
$547$	14666.6	+	14666.6i	1.14643	+	1.14643i	0.159182	+	0.987249i	$0.449114\pi$
$548$	−803.598	−	1586.11i	−0.0626423	−	0.123641i
$549$	−4737.42	−	4135.77i	−0.368284	−	0.321512i
$550$	6579.39	−	5154.57i	0.510084	−	0.399621i
$551$		−	20051.7i		−	1.55033i
$552$	820.207	−	744.835i	0.0632434	−	0.0574317i
$553$	−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	$-0.693791\pi$
$557$	3265.81	−	3265.81i	0.248432	−	0.248432i	0.820327	+	0.571895i	$0.193791\pi$
$558$	1473.68	+	1767.93i	0.111803	+	0.134126i
$559$		−	1349.35i		−	0.102096i
$560$	−3012.40	+	13376.7i	−0.227316	+	1.00941i
$561$	5636.46	−	15027.0i	0.424192	−	1.13091i
$562$	−2753.33	−	439.315i	−0.206659	−	0.0329740i
$563$	−15854.6	−	15854.6i	−1.18684	−	1.18684i	−0.977936	−	0.208905i	$-0.933010\pi$
$563$	−15854.6	−	15854.6i	−1.18684	−	1.18684i	−0.208905	−	0.977936i	$-0.566990\pi$
$564$	2449.33	−	3058.17i	0.182864	−	0.228320i
$565$	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
$568$	16800.3	+	8632.94i	1.24106	+	0.637729i
$569$	−15762.7			−1.16135			−0.580674	−	0.814136i	$-0.697211\pi$
$569$	−15762.7			−1.16135			−0.580674	+	0.814136i	$0.697211\pi$
$570$	−1827.35	+	17227.1i	−0.134280	+	1.26590i
$571$		−	16858.9i		−	1.23559i	−0.786339	−	0.617795i	$-0.788026\pi$
$571$		−	16858.9i		−	1.23559i	0.786339	−	0.617795i	$-0.211974\pi$
$572$	−5247.41	+	2658.58i	−0.383576	+	0.194337i
$573$	−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
$576$	13760.0	+	1328.44i	0.995372	+	0.0960963i
$577$	−6369.66	+	6369.66i	−0.459571	+	0.459571i	−0.898515	−	0.438944i	$-0.855353\pi$
$577$	−6369.66	+	6369.66i	−0.459571	+	0.459571i	0.438944	+	0.898515i	$0.355353\pi$
$578$	−33956.8	−	5418.07i	−2.44362	−	0.389899i
$579$	2213.36	−	5900.91i	0.158867	−	0.423547i
$580$	−13114.9	−	10834.2i	−0.938910	−	0.775631i
$581$	18722.9			1.33693
$582$	−7074.92	+	12440.9i	−0.503892	+	0.886071i
$583$	−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	$-0.626637\pi$
$587$	7601.19	−	7601.19i	0.534471	−	0.534471i	0.921900	+	0.387428i	$0.126637\pi$
$588$	1000.17	−	110.568i	0.0701469	−	0.00775466i
$589$	−3177.46			−0.222283
$590$	−5512.06	+	9359.69i	−0.384623	+	0.653105i
$591$	−5231.29	−	1962.20i	−0.364106	−	0.136572i
$592$	2794.69	+	18183.3i	0.194022	+	1.26238i
$593$	−5652.89	+	5652.89i	−0.391461	+	0.391461i	−0.875208	−	0.483747i	$-0.839276\pi$
$593$	−5652.89	+	5652.89i	−0.391461	+	0.391461i	0.483747	+	0.875208i	$0.339276\pi$
$594$	−4075.05	+	8449.55i	−0.281483	+	0.583652i
$595$	−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
$598$	−818.653	−	130.622i	−0.0559819	−	0.00893235i
$599$	7162.66			0.488578			0.244289	−	0.969702i	$-0.421445\pi$
$599$	7162.66			0.488578			0.244289	+	0.969702i	$0.421445\pi$
$600$	10280.2	+	10503.2i	0.699477	+	0.714656i
$601$	−21472.0			−1.45734			−0.728671	−	0.684864i	$-0.759862\pi$
$601$	−21472.0			−1.45734			−0.728671	+	0.684864i	$0.759862\pi$
$602$	2321.94	+	370.483i	0.157201	+	0.0250827i
$603$	−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
$606$	−27471.5	+	7553.47i	−1.84151	+	0.506334i
$607$	874.002	−	874.002i	0.0584426	−	0.0584426i	−0.677281	−	0.735724i	$-0.736842\pi$
$607$	874.002	−	874.002i	0.0584426	−	0.0584426i	0.735724	+	0.677281i	$0.236842\pi$
$608$	−13571.9	+	13417.5i	−0.905288	+	0.894986i
$609$	−6650.85	+	17731.4i	−0.442539	+	1.17983i
$610$	3737.61	−	6346.61i	0.248084	−	0.421257i
$611$	−2931.71			−0.194115
$612$	27352.6	+	6947.76i	1.80664	+	0.458899i
$613$	4069.30	−	4069.30i	0.268120	−	0.268120i	−0.560222	−	0.828342i	$-0.689284\pi$
$613$	4069.30	−	4069.30i	0.268120	−	0.268120i	0.828342	+	0.560222i	$0.189284\pi$
$614$	−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	0.992468	+	0.122508i	$0.0390937\pi$
$617$	17088.1	+	17088.1i	1.11498	+	1.11498i	0.122508	+	0.992468i	$0.460906\pi$
$618$	5068.28	+	2882.23i	0.329897	+	0.187606i
$619$	−24760.0			−1.60773			−0.803867	−	0.594808i	$-0.797228\pi$
$619$	−24760.0			−1.60773			−0.803867	+	0.594808i	$0.797228\pi$
$620$	−1716.82	+	2078.23i	−0.111209	+	0.134619i
$621$	−1163.82	+	627.138i	−0.0752053	+	0.0405252i
$622$	11672.2	+	1862.39i	0.752431	+	0.120056i
$623$	17462.8	−	17462.8i	1.12301	−	1.12301i
$624$	−5660.42	−	8657.54i	−0.363138	−	0.555415i
$625$	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
$628$	9515.04	+	18780.5i	0.604604	+	1.19335i
$629$			37556.4i			2.38072i
$630$	7329.89	−	14627.6i	0.463539	−	0.925044i
$631$	9465.71			0.597185			0.298593	−	0.954381i	$-0.403483\pi$
$631$	9465.71			0.597185			0.298593	+	0.954381i	$0.403483\pi$
$632$	−18243.6	−	9374.62i	−1.14825	−	0.590036i
$633$	−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
$636$	7173.72	−	8956.94i	0.447259	−	0.558437i
$637$	−532.405	−	532.405i	−0.0331156	−	0.0331156i
$638$	12558.3	+	2003.77i	0.779289	+	0.124342i
$639$	−16978.8	−	14822.5i	−1.05113	−	0.917637i
$640$	1442.68	+	16126.5i	0.0891048	+	0.996022i
$641$			2756.35i			0.169843i	0.996388	+	0.0849214i	$0.0270639\pi$
$641$			2756.35i			0.169843i	−0.996388	+	0.0849214i	$0.972936\pi$
$642$	−957.025	+	1682.89i	−0.0588330	+	0.103455i
$643$	−15387.1	+	15387.1i	−0.943717	+	0.943717i	−0.998498	−	0.0547818i	$-0.982554\pi$
$643$	−15387.1	+	15387.1i	−0.943717	+	0.943717i	0.0547818	+	0.998498i	$0.482554\pi$
$644$	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	0.997713	+	0.0675938i	$0.0215322\pi$
$647$	17532.0	+	17532.0i	1.06531	+	1.06531i	0.0675938	+	0.997713i	$0.478468\pi$
$648$	−15555.1	−	5489.63i	−0.942998	−	0.332798i
$649$		−	8120.25i		−	0.491137i
$650$	1325.58	−	10916.7i	0.0799902	−	0.658754i
$651$	2809.78	+	1053.92i	0.169161	+	0.0634504i
$652$	−15027.2	+	7613.46i	−0.902623	+	0.457310i
$653$	8681.37	+	8681.37i	0.520258	+	0.520258i	0.917649	−	0.397391i	$-0.130084\pi$
$653$	8681.37	+	8681.37i	0.520258	+	0.520258i	−0.397391	+	0.917649i	$0.630084\pi$
$654$	−16465.4	+	4527.27i	−0.984478	+	0.270689i
$655$	−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
$658$	804.942	−	5044.83i	0.0476898	−	0.298887i
$659$		−	13562.6i		−	0.801707i	−0.916142	−	0.400853i	$-0.868714\pi$
$659$		−	13562.6i		−	0.801707i	0.916142	−	0.400853i	$-0.131286\pi$
$660$	−10606.6	−	2865.97i	−0.625550	−	0.169027i
$661$			4458.07i			0.262328i	0.991361	+	0.131164i	$0.0418714\pi$
$661$			4458.07i			0.262328i	−0.991361	+	0.131164i	$0.958129\pi$
$662$	−5305.37	−	846.513i	−0.311479	−	0.0496989i
$663$	−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
$666$	1984.43	−	21862.0i	0.115458	−	1.27197i
$667$	1267.28	+	1267.28i	0.0735672	+	0.0735672i
$668$	9754.48	+	19253.1i	0.564988	+	1.11515i
$669$	468.312	−	1248.54i	0.0270643	−	0.0721544i
$670$	−4455.31	−	17220.5i	−0.256901	−	0.992966i
$671$			5506.17i			0.316786i
$672$	16451.8	−	7363.28i	0.944410	−	0.422686i
$673$	8098.65	+	8098.65i	0.463864	+	0.463864i	0.899920	−	0.436056i	$-0.143625\pi$
$673$	8098.65	+	8098.65i	0.463864	+	0.463864i	−0.436056	+	0.899920i	$0.643625\pi$
$674$	−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	0.239337	−	0.970936i	$-0.423070\pi$
$677$	21319.0	−	21319.0i	1.21027	−	1.21027i	0.970936	−	0.239337i	$-0.0769302\pi$
$678$	626.890	−	1102.36i	0.0355097	−	0.0624422i
$679$			18660.7i			1.05468i
$680$	−2090.16	+	32986.9i	−0.117873	+	1.86028i
$681$	17731.0	+	6650.68i	0.997727	+	0.374236i
$682$	317.523	−	1990.02i	0.0178279	−	0.111733i
$683$	−2724.01	−	2724.01i	−0.152608	−	0.152608i	0.626674	−	0.779282i	$-0.284416\pi$
$683$	−2724.01	−	2724.01i	−0.152608	−	0.152608i	−0.779282	+	0.626674i	$0.784416\pi$
$684$	19571.5	−	11642.8i	1.09405	−	0.650839i
$685$	−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
$688$	2744.22	−	421.774i	0.152068	−	0.0233720i
$689$	−8586.56			−0.474778
$690$	−973.277	−	1204.26i	−0.0536986	−	0.0664424i
$691$		−	2093.61i		−	0.115260i	−0.998338	−	0.0576301i	$-0.981646\pi$
$691$		−	2093.61i		−	0.115260i	0.998338	−	0.0576301i	$-0.0183544\pi$
$692$	−3359.93	−	6631.72i	−0.184574	−	0.364306i
$693$	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
$696$	−1075.69	+	22335.9i	−0.0585832	+	1.21644i
$697$	32201.1	−	32201.1i	1.74993	−	1.74993i
$698$	5201.91	−	32602.0i	0.282085	−	1.76791i
$699$	15500.6	+	5814.10i	0.838751	+	0.314606i
$700$	18421.3	+	5278.37i	0.994659	+	0.285005i
$701$	12609.8			0.679411			0.339706	−	0.940532i	$-0.389673\pi$
$701$	12609.8			0.679411			0.339706	+	0.940532i	$0.389673\pi$
$702$	4069.84	+	11652.3i	0.218812	+	0.626479i
$703$	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
$708$	14192.2	−	1568.93i	0.753356	−	0.0832826i
$709$	−4224.57			−0.223776			−0.111888	−	0.993721i	$-0.535690\pi$
$709$	−4224.57			−0.223776			−0.111888	+	0.993721i	$0.535690\pi$
$710$	13395.5	−	22746.2i	0.708065	−	1.20232i
$711$	18437.5	+	16096.0i	0.972519	+	0.849010i
$712$	13328.1	−	25937.4i	0.701535	−	1.36523i
$713$	200.817	−	200.817i	0.0105479	−	0.0105479i
$714$	35479.6	−	9755.34i	1.85965	−	0.511323i
$715$	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
$718$	4477.83	−	28064.0i	0.232745	−	1.45869i
$719$	3475.57			0.180274			0.0901369	−	0.995929i	$-0.471270\pi$
$719$	3475.57			0.180274			0.0901369	+	0.995929i	$0.471270\pi$
$720$	2959.68	−	19091.6i	0.153196	−	0.988196i
$721$	7602.12			0.392673
$722$	−1896.88	+	11888.3i	−0.0977762	+	0.612795i
$723$	−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
$726$	−10942.0	+	3008.56i	−0.559358	+	0.153799i
$727$	−4473.63	+	4473.63i	−0.228223	+	0.228223i	−0.811950	−	0.583727i	$-0.801594\pi$
$727$	−4473.63	+	4473.63i	−0.228223	+	0.228223i	0.583727	+	0.811950i	$0.301594\pi$
$728$	−11995.7	−	6164.07i	−0.610700	−	0.313813i
$729$	16439.3	+	10824.5i	0.835204	+	0.549941i
$730$	−3752.24	−	14503.0i	−0.190242	−	0.735317i
$731$	5668.01			0.286784
$732$	−9623.45	+	1063.86i	−0.485920	+	0.0537178i
$733$	−302.954	+	302.954i	−0.0152658	+	0.0152658i	−0.714698	−	0.699433i	$-0.753436\pi$
$733$	−302.954	+	302.954i	−0.0152658	+	0.0152658i	0.699433	+	0.714698i	$0.253436\pi$
$734$	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
$738$	−20446.0	+	17043.1i	−1.01982	+	0.850089i
$739$	−20265.7			−1.00878			−0.504389	−	0.863477i	$-0.668282\pi$
$739$	−20265.7			−1.00878			−0.504389	+	0.863477i	$0.668282\pi$
$740$	25594.5	−	2437.41i	1.27145	−	0.121083i
$741$	−15954.2	−	5984.24i	−0.790948	−	0.296676i
$742$	2357.56	−	14775.6i	0.116642	−	0.731036i
$743$	−1627.48	+	1627.48i	−0.0803585	+	0.0803585i	−0.746144	−	0.665785i	$-0.768097\pi$
$743$	−1627.48	+	1627.48i	−0.0803585	+	0.0803585i	0.665785	+	0.746144i	$0.268097\pi$
$744$	3539.42	+	170.457i	0.174411	+	0.00839955i
$745$	−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
$748$	−11167.5	−	22042.0i	−0.545887	−	1.07745i
$749$			2524.23i			0.123142i
$750$	15480.9	−	13498.8i	0.753709	−	0.657208i
$751$	−34918.2			−1.69665			−0.848324	−	0.529478i	$-0.822388\pi$
$751$	−34918.2			−1.69665			−0.848324	+	0.529478i	$0.822388\pi$
$752$	−916.380	−	5962.32i	−0.0444374	−	0.289127i
$753$	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
$756$	−21168.5	+	3804.00i	−1.01837	+	0.183003i
$757$	20575.8	+	20575.8i	0.987899	+	0.987899i	0.999928	−	0.0120287i	$-0.00382895\pi$
$757$	20575.8	+	20575.8i	0.987899	+	0.987899i	−0.0120287	+	0.999928i	$0.503829\pi$
$758$	−3246.23	+	20345.2i	−0.155552	+	0.974894i
$759$	1083.80	+	406.520i	0.0518305	+	0.0194410i
$760$	17629.4	+	20014.6i	0.841428	+	0.955272i
$761$		−	14836.5i		−	0.706729i	−0.935486	−	0.353365i	$-0.885038\pi$
$761$		−	14836.5i		−	0.706729i	0.935486	−	0.353365i	$-0.114962\pi$
$762$	7485.15	−	13162.3i	0.355851	−	0.625747i
$763$	−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
$768$	15837.8	−	14217.9i	0.744138	−	0.668026i
$769$		−	5513.84i		−	0.258562i	−0.991608	−	0.129281i	$-0.958733\pi$
$769$		−	5513.84i		−	0.258562i	0.991608	−	0.129281i	$-0.0412669\pi$
$770$	−13868.8	+	3588.15i	−0.649087	+	0.167932i
$771$	−3790.38	+	10105.3i	−0.177052	+	0.472027i
$772$	−4385.32	−	8655.60i	−0.204445	−	0.403526i
$773$	6649.85	+	6649.85i	0.309416	+	0.309416i	0.844683	−	0.535267i	$-0.179789\pi$
$773$	6649.85	+	6649.85i	0.309416	+	0.309416i	−0.535267	+	0.844683i	$0.679789\pi$
$774$	−3299.41	−	299.489i	−0.153223	−	0.0139082i
$775$	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
$778$	−1465.69	−	233.862i	−0.0675419	−	0.0107768i
$779$		−	36747.2i		−	1.69012i
$780$	−12534.3	+	7201.57i	−0.575384	+	0.330587i
$781$			19734.0i			0.904148i
$782$	548.685	−	3438.78i	0.0250907	−	0.157252i
$783$	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
$786$	15703.0	−	4317.65i	0.712606	−	0.195936i
$787$	−17933.4	−	17933.4i	−0.812271	−	0.812271i	0.172703	−	0.984974i	$-0.444750\pi$
$787$	−17933.4	−	17933.4i	−0.812271	−	0.812271i	−0.984974	+	0.172703i	$0.944750\pi$
$788$	−7673.39	+	3887.69i	−0.346895	+	0.175753i
$789$	3707.59	+	1390.68i	0.167293	+	0.0627495i
$790$	−14546.4	+	24700.3i	−0.655111	+	1.11240i
$791$		−	1653.47i		−	0.0743245i
$792$	5336.04	+	13420.9i	0.239404	+	0.602137i
$793$	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	$-0.797269\pi$
$797$	−4707.94	+	4707.94i	−0.209239	+	0.209239i	0.594705	+	0.803944i	$0.297269\pi$
$798$	14678.0	−	25810.6i	0.651122	−	1.14497i
$799$		−	12314.8i		−	0.545264i
$800$	22616.1	−	716.418i	0.999499	−	0.0316615i
$801$	−22884.1	+	26213.1i	−1.00945	+	1.15630i
$802$	−7289.58	−	1163.11i	−0.320953	−	0.0512105i
$803$	7918.92	+	7918.92i	0.348011	+	0.348011i
$804$	−14617.0	+	18250.4i	−0.641170	+	0.800550i
$805$	−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
$808$	−20048.3	+	39015.2i	−0.872891	+	1.69870i
$809$	−39244.1			−1.70550			−0.852749	−	0.522320i	$-0.825067\pi$
$809$	−39244.1			−1.70550			−0.852749	+	0.522320i	$0.825067\pi$
$810$	−8909.81	+	21261.6i	−0.386492	+	0.922293i
$811$			16408.3i			0.710448i	0.934781	+	0.355224i	$0.115595\pi$
$811$			16408.3i			0.710448i	−0.934781	+	0.355224i	$0.884405\pi$
$812$	13177.3	+	26008.9i	0.569498	+	1.12406i
$813$	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
$816$	36366.3	−	23776.8i	1.56014	−	1.02004i
$817$	3234.11	−	3234.11i	0.138491	−	0.138491i
$818$	26045.3	+	4155.73i	1.11327	+	0.177630i
$819$	12123.2	+	10583.5i	0.517238	+	0.451549i
$820$	−24034.7	−	19855.0i	−1.02357	−	0.845570i
$821$	−7023.21			−0.298553			−0.149276	−	0.988796i	$-0.547694\pi$
$821$	−7023.21			−0.298553			−0.149276	+	0.988796i	$0.547694\pi$
$822$	2839.49	+	1614.76i	0.120485	+	0.0685175i
$823$	−26346.4	−	26346.4i	−1.11589	−	1.11589i	−0.992338	−	0.123552i	$-0.960571\pi$
$823$	−26346.4	−	26346.4i	−1.11589	−	1.11589i	−0.123552	−	0.992338i	$-0.539429\pi$
$824$	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	$-0.759527\pi$
$827$	−1006.50	+	1006.50i	−0.0423209	+	0.0423209i	0.685630	+	0.727951i	$0.259527\pi$
$828$	−501.095	+	1972.76i	−0.0210317	+	0.0827997i
$829$	21920.6			0.918376			0.459188	−	0.888339i	$-0.348140\pi$
$829$	21920.6			0.918376			0.459188	+	0.888339i	$0.348140\pi$
$830$	−7738.90	−	29912.2i	−0.323640	−	1.25092i
$831$	861.300	−	2296.26i	0.0359545	−	0.0958560i
$832$	−15711.7	−	2599.21i	−0.654694	−	0.108307i
$833$	2236.39	−	2236.39i	0.0930207	−	0.0930207i
$834$	−14270.0	+	3923.64i	−0.592483	+	0.162907i
$835$	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
$838$	−899.130	−	143.463i	−0.0370643	−	0.00591391i
$839$	31047.8			1.27758			0.638790	−	0.769381i	$-0.279435\pi$
$839$	31047.8			1.27758			0.638790	+	0.769381i	$0.279435\pi$
$840$	−8950.84	−	23546.0i	−0.367659	−	0.967161i
$841$	−11783.7			−0.483156
$842$	8309.77	+	1325.89i	0.340111	+	0.0542674i
$843$	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
$846$	−650.695	+	7168.56i	−0.0264437	+	0.291324i
$847$	−10462.5	+	10462.5i	−0.424433	+	0.424433i
$848$	−2683.94	−	17462.8i	−0.108687	−	0.707163i
$849$	34485.8	+	12935.2i	1.39405	+	0.522893i
$850$	45856.2	+	5568.16i	1.85042	+	0.224690i
$851$	−2708.69			−0.109110
$852$	−34490.3	+	3812.86i	−1.38688	+	0.153317i
$853$	−1829.37	+	1829.37i	−0.0734308	+	0.0734308i	−0.742868	−	0.669438i	$-0.766535\pi$
$853$	−1829.37	+	1829.37i	−0.0734308	+	0.0734308i	0.669438	+	0.742868i	$0.266535\pi$
$854$	−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	0.189170	−	0.981944i	$-0.439420\pi$
$857$	−19889.3	−	19889.3i	−0.792774	−	0.792774i	−0.981944	+	0.189170i	$0.939420\pi$
$858$	5342.20	−	9394.01i	0.212564	−	0.373784i
$859$	19612.5			0.779011			0.389505	−	0.921024i	$-0.372646\pi$
$859$	19612.5			0.779011			0.389505	+	0.921024i	$0.372646\pi$
$860$	−367.854	−	3862.72i	−0.0145857	−	0.153160i
$861$	−12188.5	+	32495.0i	−0.482443	+	1.28621i
$862$	−49043.9	−	7825.34i	−1.93787	−	0.309202i
$863$	−29168.7	+	29168.7i	−1.15054	+	1.15054i	−0.164093	+	0.986445i	$0.552470\pi$
$863$	−29168.7	+	29168.7i	−1.15054	+	1.15054i	−0.986445	+	0.164093i	$0.947530\pi$
$864$	−22425.6	+	11919.2i	−0.883024	+	0.469328i
$865$	−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
$868$	4121.45	−	2088.12i	0.161165	−	0.0816535i
$869$		−	21429.4i		−	0.836530i
$870$	31077.3	+	3296.49i	1.21105	+	0.128461i
$871$	17495.7			0.680620
$872$	−12016.2	+	23384.3i	−0.466651	+	0.908133i
$873$	−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
$876$	−12310.3	+	15370.4i	−0.474803	+	0.592828i
$877$	1922.31	+	1922.31i	0.0740158	+	0.0740158i	0.743146	−	0.669130i	$-0.233333\pi$
$877$	1922.31	+	1922.31i	0.0740158	+	0.0740158i	−0.669130	+	0.743146i	$0.733333\pi$
$878$	−30435.9	−	4856.29i	−1.16989	−	0.186665i
$879$	−1766.44	+	4709.39i	−0.0677821	+	0.180710i
$880$	−14296.7	+	9041.11i	−0.547662	+	0.346336i
$881$		−	3232.94i		−	0.123633i	−0.998088	−	0.0618163i	$-0.980311\pi$
$881$		−	3232.94i		−	0.123633i	0.998088	−	0.0618163i	$-0.0196893\pi$
$882$	−1419.99	+	1183.66i	−0.0542105	+	0.0451880i
$883$	16301.2	−	16301.2i	0.621269	−	0.621269i	−0.324587	−	0.945856i	$-0.605225\pi$
$883$	16301.2	−	16301.2i	0.621269	−	0.621269i	0.945856	+	0.324587i	$0.105225\pi$
$884$	−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	0.0158243	−	0.999875i	$-0.494963\pi$
$887$	−25995.8	−	25995.8i	−0.984051	−	0.984051i	−0.999875	+	0.0158243i	$0.994963\pi$
$888$	−22720.9	−	25020.1i	−0.858630	−	0.945517i
$889$		−	19742.6i		−	0.744822i
$890$	−35117.1	−	20681.0i	−1.32262	−	0.778908i
$891$	−2326.38	−	17076.0i	−0.0874712	−	0.642053i
$892$	−927.864	−	1831.39i	−0.0348287	−	0.0687437i
$893$	−7026.70	−	7026.70i	−0.263314	−	0.263314i
$894$	7341.27	+	26699.7i	0.274641	+	0.998851i
$895$	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
$898$	−889.522	+	5574.92i	−0.0330554	+	0.207169i
$899$			5732.04i			0.212652i
$900$	−26399.2	−	5664.26i	−0.977747	−	0.209787i
$901$		−	36068.2i		−	1.33364i
$902$	23014.6	+	3672.15i	0.849558	+	0.135554i
$903$	−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
$906$	486.664	−	133.811i	0.0178458	−	0.00490683i
$907$	1900.65	+	1900.65i	0.0695812	+	0.0695812i	0.741041	−	0.671460i	$-0.234332\pi$
$907$	1900.65	+	1900.65i	0.0695812	+	0.0695812i	−0.671460	+	0.741041i	$0.734332\pi$
$908$	26008.2	−	13176.9i	0.950565	−	0.481599i
$909$	34422.4	−	39429.9i	1.25601	−	1.43873i
$910$	−9564.66	+	16241.2i	−0.348423	+	0.591636i
$911$		−	21899.8i		−	0.796456i	−0.917286	−	0.398228i	$-0.869625\pi$
$911$		−	21899.8i		−	0.796456i	0.917286	−	0.398228i	$-0.130375\pi$
$912$	7183.46	−	34317.1i	0.260820	−	1.24600i
$913$	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
$918$	−48946.0	+	17095.5i	−1.75976	+	0.614637i
$919$			6800.64i			0.244105i	0.992524	+	0.122052i	$0.0389476\pi$
$919$			6800.64i			0.244105i	−0.992524	+	0.122052i	$0.961052\pi$
$920$	−2379.13	−	150.749i	−0.0852581	−	0.00540223i
$921$	4455.12	−	11877.5i	0.159393	−	0.424948i
$922$	382.667	−	2398.30i	0.0136686	−	0.0856656i
$923$	18359.6	+	18359.6i	0.654729	+	0.654729i
$924$	14698.2	+	11772.0i	0.523308	+	0.419123i
$925$	−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
$928$	24204.8	+	24483.4i	0.856207	+	0.866063i
$929$	3940.14			0.139151			0.0695757	−	0.997577i	$-0.477835\pi$
$929$	3940.14			0.139151			0.0695757	+	0.997577i	$0.477835\pi$
$930$	522.372	−	4924.60i	0.0184185	−	0.173639i
$931$		−	2552.12i		−	0.0898415i
$932$	22736.7	−	11519.4i	0.799104	−	0.404862i
$933$	−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
$936$	17450.6	+	7521.82i	0.609393	+	0.262669i
$937$	−13351.3	+	13351.3i	−0.465492	+	0.465492i	−0.900451	−	0.434958i	$-0.856763\pi$
$937$	−13351.3	+	13351.3i	−0.465492	+	0.465492i	0.434958	+	0.900451i	$0.356763\pi$
$938$	−4803.69	+	30106.3i	−0.167213	+	1.04798i
$939$	−19510.0	+	52014.5i	−0.678047	+	1.80770i
$940$	−8392.47	+	799.230i	−0.291204	+	0.0277319i
$941$	−43783.5			−1.51679			−0.758395	−	0.651795i	$-0.774016\pi$
$941$	−43783.5			−1.51679			−0.758395	+	0.651795i	$0.774016\pi$
$942$	−33621.1	−	19119.7i	−1.16288	−	0.661309i
$943$	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	$-0.930392\pi$
$947$	−22126.2	+	22126.2i	−0.759245	+	0.759245i	0.216940	+	0.976185i	$0.430392\pi$
$948$	37453.5	−	4140.44i	1.28316	−	0.141851i
$949$	14734.8			0.504017
$950$	29342.3	−	22988.0i	1.00209	−	0.785083i
$951$	19487.4	+	7309.50i	0.664482	+	0.249239i
$952$	25892.4	−	50388.3i	0.881490	−	1.71544i
$953$	−3751.04	+	3751.04i	−0.127501	+	0.127501i	−0.767977	−	0.640477i	$-0.778737\pi$
$953$	−3751.04	+	3751.04i	−0.127501	+	0.127501i	0.640477	+	0.767977i	$0.278737\pi$
$954$	−1905.79	+	20995.7i	−0.0646774	+	0.712537i
$955$	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
$958$	1861.46	−	11666.4i	0.0627778	−	0.393448i
$959$	4259.06			0.143412
$960$	−18564.0	−	23240.4i	−0.624114	−	0.781333i
$961$	−28882.7			−0.969510
$962$	−3984.58	+	24972.7i	−0.133543	+	0.836955i
$963$	−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
$966$	703.587	+	2558.90i	0.0234343	+	0.0852292i
$967$	−3625.15	+	3625.15i	−0.120555	+	0.120555i	−0.764811	−	0.644255i	$-0.777167\pi$
$967$	−3625.15	+	3625.15i	−0.120555	+	0.120555i	0.644255	+	0.764811i	$0.277167\pi$
$968$	−7985.27	+	15539.8i	−0.265141	+	0.515981i
$969$	25137.1	−	67016.3i	0.833353	−	2.22175i
$970$	29812.8	−	7713.18i	0.986835	−	0.255315i
$971$	6376.71			0.210750			0.105375	−	0.994433i	$-0.466396\pi$
$971$	6376.71			0.210750			0.105375	+	0.994433i	$0.466396\pi$
$972$	29395.3	−	7365.26i	0.970015	−	0.243046i
$973$	−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	0.586945	−	0.809627i	$-0.300330\pi$
$977$	−6800.26	−	6800.26i	−0.222681	−	0.222681i	−0.809627	+	0.586945i	$0.800330\pi$
$978$	15298.6	−	26901.9i	0.500200	−	0.879580i
$979$	30466.8			0.994609
$980$	−1669.23	−	1378.95i	−0.0544098	−	0.0449478i
$981$	20631.5	−	23632.9i	0.671471	−	0.769153i
$982$	−601.716	+	3771.15i	−0.0195535	+	0.122548i
$983$	−33279.1	+	33279.1i	−1.07979	+	1.07979i	−0.0832671	+	0.996527i	$0.526535\pi$
$983$	−33279.1	+	33279.1i	−1.07979	+	1.07979i	−0.996527	+	0.0832671i	$0.973465\pi$
$984$	−1971.33	+	40933.4i	−0.0638657	+	1.32613i
$985$	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
$988$	−23402.0	+	11856.5i	−0.753560	+	0.381788i
$989$			408.796i			0.0131435i
$990$	19154.3	−	6366.04i	0.614911	−	0.204370i
$991$	36313.9			1.16402			0.582012	−	0.813180i	$-0.302266\pi$
$991$	36313.9			1.16402			0.582012	+	0.813180i	$0.302266\pi$
$992$	3879.71	−	3835.56i	0.124174	−	0.122761i
$993$	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
$996$	−25389.7	+	31701.1i	−0.807736	+	1.00852i
$997$	−10579.3	−	10579.3i	−0.336058	−	0.336058i	0.518823	−	0.854881i	$-0.326370\pi$
$997$	−10579.3	−	10579.3i	−0.336058	−	0.336058i	−0.854881	+	0.518823i	$0.826370\pi$
$998$	2708.68	−	16976.2i	0.0859135	−	0.538448i
$999$	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.53.29	yes	128
3.2	odd	2	inner	120.4.w.c.53.36	yes	128
5.2	odd	4	inner	120.4.w.c.77.4	yes	128
8.5	even	2	inner	120.4.w.c.53.61	yes	128
15.2	even	4	inner	120.4.w.c.77.61	yes	128
24.5	odd	2	inner	120.4.w.c.53.4	✓	128
40.37	odd	4	inner	120.4.w.c.77.36	yes	128
120.77	even	4	inner	120.4.w.c.77.29	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.4	✓	128	24.5	odd	2	inner
120.4.w.c.53.29	yes	128	1.1	even	1	trivial
120.4.w.c.53.36	yes	128	3.2	odd	2	inner
120.4.w.c.53.61	yes	128	8.5	even	2	inner
120.4.w.c.77.4	yes	128	5.2	odd	4	inner
120.4.w.c.77.29	yes	128	120.77	even	4	inner
120.4.w.c.77.36	yes	128	40.37	odd	4	inner
120.4.w.c.77.61	yes	128	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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+(-0.445660 + 2.79310i) q^{2} +(-2.14982 - 4.73057i) q^{3} +(-7.60277 - 2.48954i) q^{4} +(-4.08469 + 10.4075i) q^{5} +(14.1710 - 3.89642i) q^{6} +(13.5500 - 13.5500i) q^{7} +(10.3418 - 20.1258i) q^{8} +(-17.7566 + 20.3397i) q^{9} +(-27.2487 - 16.0471i) q^{10} +23.6403 q^{11} +(4.56760 + 41.3175i) 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} +(-48.8974 - 58.6604i) q^{18} +105.429 q^{19} +(56.9648 - 68.9566i) q^{20} +(-93.2295 - 34.9693i) q^{21} +(-10.5355 + 66.0296i) q^{22} +(-6.66319 + 6.66319i) q^{23} +(-117.439 - 5.65583i) q^{24} +(-91.6306 - 85.0226i) q^{25} +(51.6292 + 71.2327i) q^{26} +(134.392 + 40.2721i) q^{27} +(-136.751 + 69.2844i) q^{28} -190.191i q^{29} +(-17.3325 + 163.400i) q^{30} -30.1383 q^{31} +(-128.730 + 127.265i) q^{32} +(-50.8223 - 111.832i) q^{33} +(-299.216 + 216.870i) q^{34} +(85.6738 + 196.369i) q^{35} +(185.636 - 110.432i) q^{36} +(203.258 + 203.258i) q^{37} +(-46.9856 + 294.474i) q^{38} +(-151.326 - 56.7607i) q^{39} +(167.215 + 189.839i) q^{40} -348.549i q^{41} +(139.221 - 244.814i) 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} +(68.1354 - 325.499i) q^{48} -24.2070i q^{49} +(278.312 - 218.042i) q^{50} +(238.426 - 635.652i) q^{51} +(-221.969 + 112.460i) q^{52} +(-195.204 - 195.204i) q^{53} +(-172.377 + 357.422i) q^{54} +(-96.5634 + 246.036i) q^{55} +(-132.573 - 412.837i) q^{56} +(-226.653 - 498.740i) q^{57} +(531.222 + 84.7607i) q^{58} -343.492i q^{59} +(-448.668 - 121.232i) q^{60} +232.915i q^{61} +(13.4314 - 84.1792i) q^{62} +(35.0015 + 516.206i) q^{63} +(-298.095 - 416.273i) q^{64} +(139.062 + 318.738i) q^{65} +(335.007 - 92.1125i) q^{66} +(397.741 + 397.741i) q^{67} +(-472.391 - 932.390i) q^{68} +(45.8453 + 17.1961i) q^{69} +(-586.660 + 151.781i) q^{70} +834.762i q^{71} +(225.718 + 567.714i) 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} +(225.978 - 397.373i) q^{78} -906.479i q^{79} +(-604.761 + 382.445i) q^{80} +(-98.4075 - 722.327i) q^{81} +(973.530 + 155.334i) q^{82} +(690.879 + 690.879i) q^{83} +(621.745 + 497.963i) q^{84} +(-1338.87 + 584.136i) q^{85} +(72.0092 + 99.3510i) q^{86} +(-899.713 + 408.876i) q^{87} +(244.483 - 475.780i) q^{88} +1288.76 q^{89} +(810.237 - 269.288i) q^{90} -596.035i q^{91} +(67.2471 - 34.0704i) q^{92} +(64.7918 + 142.571i) q^{93} +(215.858 - 156.453i) q^{94} +(-430.646 + 1097.25i) q^{95} +(878.785 + 335.371i) q^{96} +(-688.583 + 688.583i) q^{97} +(67.6124 + 10.7881i) 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

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