LMFDB - Embedded newform 36.4.h.b.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, 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:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15223 + 1.83518i) q^{2} +(2.90476 - 4.30841i) q^{3} +(1.26420 + 7.89948i) q^{4} +(2.08666 - 1.20474i) q^{5} +(14.1584 - 3.94193i) q^{6} +(-2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(-10.1248 - 25.0298i) q^{9} +O(q^{10})$	\(q+(2.15223 + 1.83518i) q^{2} +(2.90476 - 4.30841i) q^{3} +(1.26420 + 7.89948i) q^{4} +(2.08666 - 1.20474i) q^{5} +(14.1584 - 3.94193i) q^{6} +(-2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(-10.1248 - 25.0298i) q^{9} +(6.70190 + 1.23654i) q^{10} +(-24.1428 + 41.8166i) q^{11} +(37.7064 + 17.4994i) q^{12} +(-20.3570 - 35.2594i) q^{13} +(-2.51714 - 7.09003i) q^{14} +(0.870754 - 12.4897i) q^{15} +(-60.8036 + 19.9731i) q^{16} -36.3729i q^{17} +(24.1433 - 72.4507i) q^{18} -125.173i q^{19} +(12.1548 + 14.9605i) q^{20} +(-12.4216 + 6.06163i) q^{21} +(-128.702 + 45.6925i) q^{22} +(97.0560 + 168.106i) q^{23} +(49.0383 + 106.861i) q^{24} +(-59.5972 + 103.225i) q^{25} +(20.8944 - 113.245i) q^{26} +(-137.248 - 29.0836i) q^{27} +(7.59405 - 19.8788i) q^{28} +(153.593 + 88.6772i) q^{29} +(24.7949 - 25.2827i) q^{30} +(152.058 - 87.7909i) q^{31} +(-167.518 - 68.5991i) q^{32} +(110.034 + 225.484i) q^{33} +(66.7510 - 78.2830i) q^{34} -6.40918 q^{35} +(184.922 - 111.623i) q^{36} +199.364 q^{37} +(229.716 - 269.402i) q^{38} +(-211.044 - 14.7136i) q^{39} +(-1.29548 + 54.5047i) q^{40} +(-201.816 + 116.518i) q^{41} +(-37.8585 - 9.74995i) q^{42} +(252.553 + 145.812i) q^{43} +(-360.851 - 137.851i) q^{44} +(-51.2813 - 40.0310i) q^{45} +(-99.6182 + 539.918i) q^{46} +(30.9476 - 53.6029i) q^{47} +(-90.5674 + 319.984i) q^{48} +(-167.962 - 290.919i) q^{49} +(-317.705 + 112.793i) q^{50} +(-156.709 - 105.655i) q^{51} +(252.795 - 205.385i) q^{52} -352.175i q^{53} +(-242.017 - 314.471i) q^{54} +116.343i q^{55} +(52.8254 - 28.8473i) q^{56} +(-539.298 - 363.598i) q^{57} +(167.830 + 472.726i) q^{58} +(-70.7911 - 122.614i) q^{59} +(99.7627 - 8.91095i) q^{60} +(-7.71518 + 13.3631i) q^{61} +(488.377 + 90.1086i) q^{62} +(-9.96583 + 71.1251i) q^{63} +(-234.645 - 455.067i) q^{64} +(-84.9565 - 49.0496i) q^{65} +(-176.986 + 687.228i) q^{66} +(-131.657 + 76.0120i) q^{67} +(287.327 - 45.9827i) q^{68} +(1006.19 + 70.1497i) q^{69} +(-13.7940 - 11.7620i) q^{70} -28.0331 q^{71} +(602.845 + 99.1275i) q^{72} +124.499 q^{73} +(429.078 + 365.870i) q^{74} +(271.622 + 556.614i) q^{75} +(988.804 - 158.244i) q^{76} +(111.232 - 64.2199i) q^{77} +(-427.213 - 418.971i) q^{78} +(-648.411 - 374.360i) q^{79} +(-102.814 + 114.929i) q^{80} +(-523.978 + 506.842i) q^{81} +(-648.187 - 119.595i) q^{82} +(174.444 - 302.146i) q^{83} +(-63.5872 - 90.4614i) q^{84} +(-43.8198 - 75.8981i) q^{85} +(275.962 + 777.302i) q^{86} +(828.210 - 404.158i) q^{87} +(-523.653 - 958.916i) q^{88} +416.864i q^{89} +(-36.9049 - 180.267i) q^{90} +108.299i q^{91} +(-1205.25 + 979.212i) q^{92} +(63.4532 - 910.140i) q^{93} +(164.978 - 58.5712i) q^{94} +(-150.801 - 261.195i) q^{95} +(-782.151 + 522.471i) q^{96} +(-752.565 + 1303.48i) q^{97} +(172.396 - 934.367i) q^{98} +(1291.10 + 180.905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.15223	+	1.83518i	0.760929	+	0.648835i
$2$	2.15223	+	1.83518i	0.760929	+	0.648835i
$3$	2.90476	−	4.30841i	0.559021	−	0.829154i
$3$	2.90476	−	4.30841i	0.559021	−	0.829154i
$4$	1.26420	+	7.89948i	0.158025	+	0.987435i
$5$	2.08666	−	1.20474i	0.186637	−	0.107755i	−0.403770	−	0.914860i	$-0.632301\pi$
$5$	2.08666	−	1.20474i	0.186637	−	0.107755i	0.590407	+	0.807106i	$0.298967\pi$
$6$	14.1584	−	3.94193i	0.963359	−	0.268215i
$7$	−2.30362	−	1.33000i	−0.124384	−	0.0718131i	0.436517	−	0.899696i	$-0.356212\pi$
$7$	−2.30362	−	1.33000i	−0.124384	−	0.0718131i	−0.560901	+	0.827883i	$0.689545\pi$
$8$	−11.7761	+	19.3216i	−0.520437	+	0.853900i
$9$	−10.1248	−	25.0298i	−0.374992	−	0.927028i
$10$	6.70190	+	1.23654i	0.211933	+	0.0391029i
$11$	−24.1428	+	41.8166i	−0.661758	+	1.14620i	0.318395	+	0.947958i	$0.396856\pi$
$11$	−24.1428	+	41.8166i	−0.661758	+	1.14620i	−0.980153	+	0.198241i	$0.936477\pi$
$12$	37.7064	+	17.4994i	0.907075	+	0.420969i
$13$	−20.3570	−	35.2594i	−0.434309	−	0.752245i	0.562930	−	0.826505i	$-0.309674\pi$
$13$	−20.3570	−	35.2594i	−0.434309	−	0.752245i	−0.997239	+	0.0742593i	$0.976341\pi$
$14$	−2.51714	−	7.09003i	−0.0480524	−	0.135349i
$15$	0.870754	−	12.4897i	0.0149885	−	0.214988i
$16$	−60.8036	+	19.9731i	−0.950056	+	0.312079i
$17$		−	36.3729i		−	0.518925i	−0.965753	−	0.259463i	$-0.916455\pi$
$17$		−	36.3729i		−	0.518925i	0.965753	−	0.259463i	$-0.0835455\pi$
$18$	24.1433	−	72.4507i	0.316146	−	0.948710i
$19$		−	125.173i		−	1.51141i	−0.654914	−	0.755703i	$-0.727295\pi$
$19$		−	125.173i		−	1.51141i	0.654914	−	0.755703i	$-0.272705\pi$
$20$	12.1548	+	14.9605i	0.135894	+	0.167264i
$21$	−12.4216	+	6.06163i	−0.129077	+	0.0629884i
$22$	−128.702	+	45.6925i	−1.24725	+	0.442804i
$23$	97.0560	+	168.106i	0.879894	+	1.52402i	0.851456	+	0.524426i	$0.175720\pi$
$23$	97.0560	+	168.106i	0.879894	+	1.52402i	0.0284384	+	0.999596i	$0.490947\pi$
$24$	49.0383	+	106.861i	0.417080	+	0.908870i
$25$	−59.5972	+	103.225i	−0.476778	+	0.825803i
$26$	20.8944	−	113.245i	0.157605	−	0.854200i
$27$	−137.248	−	29.0836i	−0.978277	−	0.207302i
$28$	7.59405	−	19.8788i	0.0512550	−	0.134169i
$29$	153.593	+	88.6772i	0.983503	+	0.567826i	0.903326	−	0.428955i	$-0.141118\pi$
$29$	153.593	+	88.6772i	0.983503	+	0.567826i	0.0801773	+	0.996781i	$0.474451\pi$
$30$	24.7949	−	25.2827i	0.150897	−	0.153865i
$31$	152.058	−	87.7909i	0.880983	−	0.508636i	0.0100006	−	0.999950i	$-0.496817\pi$
$31$	152.058	−	87.7909i	0.880983	−	0.508636i	0.870982	+	0.491314i	$0.163483\pi$
$32$	−167.518	−	68.5991i	−0.925413	−	0.378960i
$33$	110.034	+	225.484i	0.580439	+	1.18945i
$34$	66.7510	−	78.2830i	0.336697	−	0.394865i
$35$	−6.40918			−0.0309529
$36$	184.922	−	111.623i	0.856122	−	0.516774i
$37$	199.364			0.885818			0.442909	−	0.896566i	$-0.353946\pi$
$37$	199.364			0.885818			0.442909	+	0.896566i	$0.353946\pi$
$38$	229.716	−	269.402i	0.980654	−	1.15007i
$39$	−211.044	−	14.7136i	−0.866515	−	0.0604117i
$40$	−1.29548	+	54.5047i	−0.00512084	+	0.215449i
$41$	−201.816	+	116.518i	−0.768740	+	0.443832i	−0.832425	−	0.554138i	$-0.813048\pi$
$41$	−201.816	+	116.518i	−0.768740	+	0.443832i	0.0636849	+	0.997970i	$0.479715\pi$
$42$	−37.8585	−	9.74995i	−0.139088	−	0.0358202i
$43$	252.553	+	145.812i	0.895674	+	0.517118i	0.875794	−	0.482685i	$-0.160338\pi$
$43$	252.553	+	145.812i	0.895674	+	0.517118i	0.0198798	+	0.999802i	$0.493672\pi$
$44$	−360.851	−	137.851i	−1.23637	−	0.472315i
$45$	−51.2813	−	40.0310i	−0.169879	−	0.132610i
$46$	−99.6182	+	539.918i	−0.319302	+	1.73058i
$47$	30.9476	−	53.6029i	0.0960463	−	0.166357i	−0.813998	−	0.580867i	$-0.802714\pi$
$47$	30.9476	−	53.6029i	0.0960463	−	0.166357i	0.910045	+	0.414510i	$0.136047\pi$
$48$	−90.5674	+	319.984i	−0.272339	+	0.962201i
$49$	−167.962	−	290.919i	−0.489686	−	0.848161i
$50$	−317.705	+	112.793i	−0.898604	+	0.319027i
$51$	−156.709	−	105.655i	−0.430269	−	0.290090i
$52$	252.795	−	205.385i	0.674162	−	0.547726i
$53$		−	352.175i		−	0.912735i	−0.889791	−	0.456367i	$-0.849150\pi$
$53$		−	352.175i		−	0.912735i	0.889791	−	0.456367i	$-0.150850\pi$
$54$	−242.017	−	314.471i	−0.609894	−	0.792483i
$55$			116.343i			0.285231i
$56$	52.8254	−	28.8473i	0.126055	−	0.0688373i
$57$	−539.298	−	363.598i	−1.25319	−	0.844907i
$58$	167.830	+	472.726i	0.379950	+	1.07021i
$59$	−70.7911	−	122.614i	−0.156207	−	0.270559i	0.777291	−	0.629141i	$-0.216593\pi$
$59$	−70.7911	−	122.614i	−0.156207	−	0.270559i	−0.933498	+	0.358583i	$0.883260\pi$
$60$	99.7627	−	8.91095i	0.214655	−	0.0191733i
$61$	−7.71518	+	13.3631i	−0.0161939	+	0.0280486i	−0.874009	−	0.485910i	$-0.838488\pi$
$61$	−7.71518	+	13.3631i	−0.0161939	+	0.0280486i	0.857815	+	0.513959i	$0.171822\pi$
$62$	488.377	+	90.1086i	1.00039	+	0.184577i
$63$	−9.96583	+	71.1251i	−0.0199298	+	0.142237i
$64$	−234.645	−	455.067i	−0.458291	−	0.888802i
$65$	−84.9565	−	49.0496i	−0.162116	−	0.0935978i
$66$	−176.986	+	687.228i	−0.330084	+	1.28169i
$67$	−131.657	+	76.0120i	−0.240066	+	0.138602i	−0.615207	−	0.788366i	$-0.710928\pi$
$67$	−131.657	+	76.0120i	−0.240066	+	0.138602i	0.375141	+	0.926968i	$0.377594\pi$
$68$	287.327	−	45.9827i	0.512405	−	0.0820033i
$69$	1006.19	+	70.1497i	1.75553	+	0.122392i
$70$	−13.7940	−	11.7620i	−0.0235529	−	0.0200833i
$71$	−28.0331			−0.0468580			−0.0234290	−	0.999726i	$-0.507458\pi$
$71$	−28.0331			−0.0468580			−0.0234290	+	0.999726i	$0.507458\pi$
$72$	602.845	+	99.1275i	0.986749	+	0.162254i
$73$	124.499			0.199609			0.0998047	−	0.995007i	$-0.468178\pi$
$73$	124.499			0.199609			0.0998047	+	0.995007i	$0.468178\pi$
$74$	429.078	+	365.870i	0.674045	+	0.574750i
$75$	271.622	+	556.614i	0.418189	+	0.856963i
$76$	988.804	−	158.244i	1.49242	−	0.238840i
$77$	111.232	−	64.2199i	0.164624	−	0.0950459i
$78$	−427.213	−	418.971i	−0.620159	−	0.608194i
$79$	−648.411	−	374.360i	−0.923443	−	0.533150i	−0.0387108	−	0.999250i	$-0.512325\pi$
$79$	−648.411	−	374.360i	−0.923443	−	0.533150i	−0.884732	+	0.466101i	$0.845658\pi$
$80$	−102.814	+	114.929i	−0.143687	+	0.160619i
$81$	−523.978	+	506.842i	−0.718762	+	0.695256i
$82$	−648.187	−	119.595i	−0.872931	−	0.161061i
$83$	174.444	−	302.146i	0.230695	−	0.399576i	−0.727318	−	0.686301i	$-0.759233\pi$
$83$	174.444	−	302.146i	0.230695	−	0.399576i	0.958013	+	0.286725i	$0.0925667\pi$
$84$	−63.5872	−	90.4614i	−0.0825944	−	0.117502i
$85$	−43.8198	−	75.8981i	−0.0559167	−	0.0968506i
$86$	275.962	+	777.302i	0.346020	+	0.974635i
$87$	828.210	−	404.158i	1.02061	−	0.498049i
$88$	−523.653	−	958.916i	−0.634336	−	1.16160i
$89$			416.864i			0.496488i	0.968698	+	0.248244i	$0.0798535\pi$
$89$			416.864i			0.496488i	−0.968698	+	0.248244i	$0.920146\pi$
$90$	−36.9049	−	180.267i	−0.0432236	−	0.211131i
$91$			108.299i			0.124756i
$92$	−1205.25	+	979.212i	−1.36583	+	1.10967i
$93$	63.4532	−	910.140i	0.0707504	−	1.01481i
$94$	164.978	−	58.5712i	0.181023	−	0.0642677i
$95$	−150.801	−	261.195i	−0.162861	−	0.282084i
$96$	−782.151	+	522.471i	−0.831541	+	0.555463i
$97$	−752.565	+	1303.48i	−0.787747	+	1.36442i	0.139598	+	0.990208i	$0.455419\pi$
$97$	−752.565	+	1303.48i	−0.787747	+	1.36442i	−0.927344	+	0.374209i	$0.877914\pi$
$98$	172.396	−	934.367i	0.177701	−	0.963115i
$99$	1291.10	+	180.905i	1.31071	+	0.183653i
$100$	−890.770	−	340.289i	−0.890770	−	0.340289i
$101$	377.088	+	217.712i	0.371502	+	0.214487i	0.674114	−	0.738627i	$-0.264526\pi$
$101$	377.088	+	217.712i	0.371502	+	0.214487i	−0.302613	+	0.953114i	$0.597859\pi$
$102$	−143.380	−	514.984i	−0.139183	−	0.499912i
$103$	−1511.52	+	872.679i	−1.44597	+	0.834831i	−0.998238	−	0.0593366i	$-0.981101\pi$
$103$	−1511.52	+	872.679i	−1.44597	+	0.834831i	−0.447732	+	0.894168i	$0.647768\pi$
$104$	920.993	+	21.8904i	0.868373	+	0.0206397i
$105$	−18.6171	+	27.6134i	−0.0173033	+	0.0256647i
$106$	646.306	−	757.962i	0.592215	−	0.694526i
$107$	−783.805			−0.708161			−0.354081	−	0.935215i	$-0.615206\pi$
$107$	−783.805			−0.708161			−0.354081	+	0.935215i	$0.615206\pi$
$108$	56.2359	−	1120.96i	0.0501047	−	0.998744i
$109$	1581.89			1.39007			0.695035	−	0.718976i	$-0.255389\pi$
$109$	1581.89			1.39007			0.695035	+	0.718976i	$0.255389\pi$
$110$	−213.511	+	250.397i	−0.185068	+	0.217040i
$111$	579.105	−	858.943i	0.495191	−	0.734480i
$112$	166.633	+	34.8582i	0.140583	+	0.0294088i
$113$	−384.367	+	221.914i	−0.319984	+	0.184743i	−0.651386	−	0.758747i	$-0.725812\pi$
$113$	−384.367	+	221.914i	−0.319984	+	0.184743i	0.331401	+	0.943490i	$0.392479\pi$
$114$	−493.425	−	1772.26i	−0.405381	−	1.45603i
$115$	405.046	+	233.854i	0.328442	+	0.189626i
$116$	−506.331	+	1325.41i	−0.405273	+	1.06088i
$117$	−676.423	+	866.524i	−0.534490	+	0.684703i
$118$	72.6600	−	393.808i	0.0566855	−	0.307228i
$119$	−48.3759	+	83.7895i	−0.0372657	+	0.0645460i
$120$	231.066	+	163.904i	0.175778	+	0.124686i
$121$	−500.254	−	866.466i	−0.375848	−	0.650989i
$122$	−41.1286	+	14.6017i	−0.0305214	+	0.0108359i
$123$	−84.2167	+	1207.96i	−0.0617363	+	0.885515i
$124$	885.735	+	1090.20i	0.641462	+	0.789536i
$125$			588.380i			0.421010i
$126$	−151.976	+	134.788i	−0.107453	+	0.0953009i
$127$			425.829i			0.297529i	0.988873	+	0.148765i	$0.0475297\pi$
$127$			425.829i			0.297529i	−0.988873	+	0.148765i	$0.952470\pi$
$128$	330.121	−	1410.03i	0.227960	−	0.973671i
$129$	1361.82	−	664.555i	0.929470	−	0.453572i
$130$	−92.8309	−	261.477i	−0.0626293	−	0.176408i
$131$	−871.836	−	1510.06i	−0.581471	−	1.00714i	−0.995305	−	0.0967846i	$-0.969144\pi$
$131$	−871.836	−	1510.06i	−0.581471	−	1.00714i	0.413835	−	0.910352i	$-0.364189\pi$
$132$	−1642.10	+	1154.27i	−1.08278	+	0.761108i
$133$	−166.480	+	288.352i	−0.108539	+	0.187995i
$134$	−422.851	−	78.0187i	−0.272603	−	0.0502969i
$135$	−321.430	+	104.660i	−0.204920	+	0.0667239i
$136$	702.782	+	428.333i	0.443110	+	0.270068i
$137$	−1274.32	−	735.731i	−0.794692	−	0.458816i	0.0469195	−	0.998899i	$-0.485060\pi$
$137$	−1274.32	−	735.731i	−0.794692	−	0.458816i	−0.841612	+	0.540083i	$0.818393\pi$
$138$	2036.82	+	1997.53i	1.25642	+	1.23218i
$139$	1107.04	−	639.151i	0.675526	−	0.390015i	−0.122641	−	0.992451i	$-0.539136\pi$
$139$	1107.04	−	639.151i	0.675526	−	0.390015i	0.798167	+	0.602436i	$0.205803\pi$
$140$	−8.10250	−	50.6292i	−0.00489133	−	0.0305639i
$141$	−141.048	−	289.038i	−0.0842438	−	0.172634i
$142$	−60.3338	−	51.4459i	−0.0356556	−	0.0304031i
$143$	1965.90			1.14963
$144$	1115.54	+	1319.68i	0.645570	+	0.763701i
$145$	427.331			0.244744
$146$	267.950	+	228.478i	0.151889	+	0.129514i
$147$	−1741.29	−	121.399i	−0.977000	−	0.0681145i
$148$	252.037	+	1574.87i	0.139982	+	0.874688i
$149$	1861.15	−	1074.53i	1.02330	−	0.590800i	0.108239	−	0.994125i	$-0.465479\pi$
$149$	1861.15	−	1074.53i	1.02330	−	0.590800i	0.915057	+	0.403325i	$0.132146\pi$
$150$	−436.895	+	1696.44i	−0.237816	+	0.923424i
$151$	828.626	+	478.407i	0.446574	+	0.257829i	0.706382	−	0.707831i	$-0.250326\pi$
$151$	828.626	+	478.407i	0.446574	+	0.257829i	−0.259808	+	0.965660i	$0.583659\pi$
$152$	2418.54	+	1474.06i	1.29059	+	0.786592i
$153$	−910.406	+	368.268i	−0.481058	+	0.194593i
$154$	357.252	+	65.9152i	0.186936	+	0.0344909i
$155$	211.530	−	366.380i	0.109616	−	0.189860i
$156$	−150.573	−	1685.74i	−0.0772786	−	0.865174i
$157$	−1046.60	−	1812.77i	−0.532024	−	0.921493i	−0.999301	−	0.0373822i	$-0.988098\pi$
$157$	−1046.60	−	1812.77i	−0.532024	−	0.921493i	0.467277	−	0.884111i	$-0.345235\pi$
$158$	−708.511	−	1995.66i	−0.356748	−	1.00485i
$159$	−1517.31	−	1022.98i	−0.756798	−	0.510238i
$160$	−432.197	+	58.6713i	−0.213551	+	0.0289899i
$161$		−	516.337i		−	0.252752i
$162$	−2057.87	+	129.246i	−0.998034	+	0.0626821i
$163$		−	1468.60i		−	0.705703i	−0.935679	−	0.352851i	$-0.885212\pi$
$163$		−	1468.60i		−	0.705703i	0.935679	−	0.352851i	$-0.114788\pi$
$164$	−1175.57	−	1446.94i	−0.559736	−	0.688944i
$165$	501.253	+	337.948i	0.236500	+	0.159450i
$166$	929.936	−	330.151i	0.434801	−	0.154365i
$167$	1524.19	+	2639.98i	0.706261	+	1.22328i	0.966235	+	0.257664i	$0.0829527\pi$
$167$	1524.19	+	2639.98i	0.706261	+	1.22328i	−0.259974	+	0.965616i	$0.583714\pi$
$168$	29.1588	−	311.388i	0.0133908	−	0.143001i
$169$	269.685	−	467.108i	0.122751	−	0.212612i
$170$	44.9766	−	243.768i	0.0202915	−	0.109977i
$171$	−3133.06	+	1267.35i	−1.40112	+	0.566765i
$172$	−832.558	+	2179.37i	−0.369081	+	0.966137i
$173$	−2403.71	−	1387.79i	−1.05636	−	0.609892i	−0.131940	−	0.991258i	$-0.542121\pi$
$173$	−2403.71	−	1387.79i	−1.05636	−	0.609892i	−0.924424	+	0.381365i	$0.875454\pi$
$174$	2524.20	+	650.075i	1.09977	+	0.283230i
$175$	274.579	−	158.528i	0.118607	−	0.0684778i
$176$	632.765	−	3024.81i	0.271003	−	1.29547i
$177$	−733.901	−	51.1661i	−0.311658	−	0.0217281i
$178$	−765.021	+	897.187i	−0.322139	+	0.377792i
$179$	−477.618			−0.199435			−0.0997174	−	0.995016i	$-0.531794\pi$
$179$	−477.618			−0.199435			−0.0997174	+	0.995016i	$0.531794\pi$
$180$	251.394	−	455.703i	0.104099	−	0.188700i
$181$	−732.350			−0.300747			−0.150373	−	0.988629i	$-0.548048\pi$
$181$	−732.350			−0.300747			−0.150373	+	0.988629i	$0.548048\pi$
$182$	−198.749	+	233.085i	−0.0809463	+	0.0949307i
$183$	35.1629	+	72.0566i	0.0142039	+	0.0291070i
$184$	−4391.01	−	104.367i	−1.75929	−	0.0418153i
$185$	416.006	−	240.181i	0.165326	−	0.0954512i
$186$	1806.84	−	1842.38i	0.712280	−	0.726291i
$187$	1520.99	+	878.146i	0.594792	+	0.343403i
$188$	462.559	+	176.705i	0.179445	+	0.0685509i
$189$	277.488	+	249.538i	0.106795	+	0.0960381i
$190$	154.782	−	838.898i	0.0591003	−	0.320316i
$191$	−1543.00	+	2672.55i	−0.584542	+	1.01246i	0.410391	+	0.911910i	$0.365392\pi$
$191$	−1543.00	+	2672.55i	−0.584542	+	1.01246i	−0.994932	+	0.100546i	$0.967941\pi$
$192$	−2642.20	−	310.912i	−0.993148	−	0.116865i
$193$	817.160	+	1415.36i	0.304769	+	0.527876i	0.977210	−	0.212275i	$-0.0680873\pi$
$193$	817.160	+	1415.36i	0.304769	+	0.527876i	−0.672441	+	0.740151i	$0.734754\pi$
$194$	−4011.82	+	1424.30i	−1.48470	+	0.527106i
$195$	−458.104	+	223.550i	−0.168233	+	0.0820961i
$196$	2085.77	−	1694.59i	0.760121	−	0.617564i
$197$			3350.67i			1.21181i	0.795539	+	0.605903i	$0.207188\pi$
$197$			3350.67i			1.21181i	−0.795539	+	0.605903i	$0.792812\pi$
$198$	2446.75	+	2758.76i	0.878198	+	0.990184i
$199$		−	1046.61i		−	0.372826i	−0.982471	−	0.186413i	$-0.940314\pi$
$199$		−	1046.61i		−	0.372826i	0.982471	−	0.186413i	$-0.0596863\pi$
$200$	−1292.65	−	2367.11i	−0.457021	−	0.836899i
$201$	−54.9396	+	788.027i	−0.0192793	+	0.276533i
$202$	412.040	+	1160.59i	0.143520	+	0.404252i
$203$	−235.881	−	408.558i	−0.0815547	−	0.141257i
$204$	636.503	−	1371.49i	0.218452	−	0.470704i
$205$	−280.748	+	486.270i	−0.0956502	+	0.165671i
$206$	−4854.68	−	895.718i	−1.64195	−	0.302950i
$207$	3224.98	−	4131.32i	1.08286	−	1.38718i
$208$	1942.02	+	1737.30i	0.647378	+	0.579136i
$209$	5234.33	+	3022.04i	1.73237	+	1.00019i
$210$	−90.7440	+	25.2646i	−0.0298187	+	0.00830201i
$211$	4570.77	−	2638.94i	1.49130	−	0.861004i	0.491352	−	0.870961i	$-0.336503\pi$
$211$	4570.77	−	2638.94i	1.49130	−	0.861004i	0.999950	+	0.00995667i	$0.00316936\pi$
$212$	2782.00	−	445.220i	0.901266	−	0.144235i
$213$	−81.4294	+	120.778i	−0.0261946	+	0.0388525i
$214$	−1686.93	−	1438.43i	−0.538860	−	0.459480i
$215$	702.658			0.222888
$216$	2178.20	−	2309.36i	0.686147	−	0.727463i
$217$	−467.047			−0.146107
$218$	3404.60	+	2903.06i	1.05774	+	0.901927i
$219$	361.639	−	536.392i	0.111586	−	0.165507i
$220$	−919.050	+	147.081i	−0.281647	+	0.0450737i
$221$	−1282.49	+	740.444i	−0.390359	+	0.225374i
$222$	2822.68	−	785.881i	0.853361	−	0.237589i
$223$	−4122.02	−	2379.85i	−1.23781	−	0.714648i	−0.269161	−	0.963095i	$-0.586746\pi$
$223$	−4122.02	−	2379.85i	−1.23781	−	0.714648i	−0.968645	+	0.248447i	$0.920080\pi$
$224$	294.661	+	380.824i	0.0878923	+	0.113593i
$225$	3187.12	+	446.569i	0.944331	+	0.132317i
$226$	−1234.50	−	227.773i	−0.363353	−	0.0670409i
$227$	−1115.23	+	1931.63i	−0.326080	+	0.564788i	−0.981730	−	0.190277i	$-0.939061\pi$
$227$	−1115.23	+	1931.63i	−0.326080	+	0.564788i	0.655650	+	0.755065i	$0.272395\pi$
$228$	2190.45	−	4719.83i	0.636256	−	1.37096i
$229$	2917.29	+	5052.89i	0.841833	+	1.45810i	0.888343	+	0.459181i	$0.151857\pi$
$229$	2917.29	+	5052.89i	0.841833	+	1.45810i	−0.0465095	+	0.998918i	$0.514810\pi$
$230$	442.589	+	1246.64i	0.126885	+	0.357396i
$231$	46.4166	−	665.776i	0.0132207	−	0.189631i
$232$	−3522.12	+	1923.39i	−0.996718	+	0.544296i
$233$		−	3080.09i		−	0.866022i	−0.901389	−	0.433011i	$-0.857451\pi$
$233$		−	3080.09i		−	0.866022i	0.901389	−	0.433011i	$-0.142549\pi$
$234$	−3046.05	+	623.600i	−0.850968	+	0.174214i
$235$		−	149.135i		−	0.0413978i
$236$	879.091	−	714.221i	0.242474	−	0.196999i
$237$	−3496.37	+	1706.20i	−0.958287	+	0.467634i
$238$	−257.885	+	91.5558i	−0.0702362	+	0.0249356i
$239$	2645.73	+	4582.53i	0.716058	+	1.24025i	0.962550	+	0.271104i	$0.0873887\pi$
$239$	2645.73	+	4582.53i	0.716058	+	1.24025i	−0.246492	+	0.969145i	$0.579278\pi$
$240$	196.512	+	776.808i	0.0528533	+	0.208928i
$241$	2501.61	−	4332.91i	0.668642	−	1.15812i	−0.309642	−	0.950853i	$-0.600209\pi$
$241$	2501.61	−	4332.91i	0.668642	−	1.15812i	0.978284	−	0.207268i	$-0.0664573\pi$
$242$	513.461	−	2782.89i	0.136391	−	0.739220i
$243$	661.654	+	3729.76i	0.174671	+	0.984627i
$244$	−115.315	−	44.0523i	−0.0302553	−	0.0115580i
$245$	−700.961	−	404.700i	−0.182787	−	0.105532i
$246$	−2398.09	+	2445.26i	−0.621531	+	0.633757i
$247$	−4413.53	+	2548.15i	−1.13695	+	0.656417i
$248$	−94.4037	+	3971.84i	−0.0241719	+	1.01698i
$249$	−795.050	−	1629.23i	−0.202346	−	0.414653i
$250$	−1079.78	+	1266.33i	−0.273166	+	0.320359i
$251$	−2577.68			−0.648215			−0.324107	−	0.946020i	$-0.605064\pi$
$251$	−2577.68			−0.648215			−0.324107	+	0.946020i	$0.605064\pi$
$252$	−574.450	+	11.1915i	−0.143599	+	0.00279762i
$253$	−9372.83			−2.32911
$254$	−781.475	+	916.483i	−0.193048	+	0.226399i
$255$	−454.286	−	31.6719i	−0.111563	−	0.00777792i
$256$	3298.15	−	2428.87i	0.805213	−	0.592986i
$257$	−753.933	+	435.283i	−0.182992	+	0.105651i	−0.588698	−	0.808353i	$-0.700359\pi$
$257$	−753.933	+	435.283i	−0.182992	+	0.105651i	0.405705	+	0.914004i	$0.367026\pi$
$258$	4150.53	+	1068.92i	1.00155	+	0.257937i
$259$	−459.260	−	265.154i	−0.110182	−	0.0636134i
$260$	280.065	−	733.121i	0.0668033	−	0.174870i
$261$	664.469	−	4742.25i	0.157585	−	1.12467i
$262$	894.852	−	4849.99i	0.211008	−	1.14364i
$263$	2155.19	−	3732.90i	0.505304	−	0.875212i	−0.494677	−	0.869077i	$-0.664714\pi$
$263$	2155.19	−	3732.90i	0.505304	−	0.875212i	0.999981	−	0.00613515i	$-0.00195289\pi$
$264$	−5652.49	−	529.307i	−1.31775	−	0.123396i
$265$	−424.278	−	734.871i	−0.0983516	−	0.170350i
$266$	−887.483	+	315.079i	−0.204568	+	0.0726268i
$267$	1796.02	+	1210.89i	0.411665	+	0.277547i
$268$	−766.896	−	943.924i	−0.174797	−	0.215147i
$269$		−	5603.52i		−	1.27008i	−0.772478	−	0.635042i	$-0.780983\pi$
$269$		−	5603.52i		−	1.27008i	0.772478	−	0.635042i	$-0.219017\pi$
$270$	−883.862	−	364.629i	−0.199223	−	0.0821874i
$271$			2149.22i			0.481756i	0.970555	+	0.240878i	$0.0774353\pi$
$271$			2149.22i			0.481756i	−0.970555	+	0.240878i	$0.922565\pi$
$272$	726.479	+	2211.60i	0.161946	+	0.493008i
$273$	466.597	+	314.582i	0.103442	+	0.0697414i
$274$	−1392.44	−	3922.08i	−0.307008	−	0.864751i
$275$	−2877.69	−	4984.31i	−0.631023	−	1.09296i
$276$	717.884	+	8037.08i	0.156564	+	1.75281i
$277$	1604.99	−	2779.93i	0.348140	−	0.602995i	−0.637779	−	0.770219i	$-0.720147\pi$
$277$	1604.99	−	2779.93i	0.348140	−	0.602995i	0.985919	+	0.167224i	$0.0534802\pi$
$278$	3555.57	+	656.025i	0.767083	+	0.141531i
$279$	−3736.94	−	2917.12i	−0.801881	−	0.625962i
$280$	75.4755	−	123.835i	0.0161090	−	0.0264306i
$281$	−814.389	−	470.188i	−0.172891	−	0.0998187i	0.411057	−	0.911610i	$-0.365160\pi$
$281$	−814.389	−	470.188i	−0.172891	−	0.0998187i	−0.583948	+	0.811791i	$0.698493\pi$
$282$	226.871	−	880.926i	0.0479077	−	0.186023i
$283$	1775.44	−	1025.05i	0.372929	−	0.215310i	−0.301809	−	0.953369i	$-0.597590\pi$
$283$	1775.44	−	1025.05i	0.372929	−	0.215310i	0.674737	+	0.738058i	$0.264257\pi$
$284$	−35.4395	−	221.447i	−0.00740475	−	0.0462693i
$285$	−1563.37	−	108.995i	−0.324934	−	0.0226537i
$286$	4231.08	+	3607.80i	0.874787	+	0.745921i
$287$	619.877			0.127492
$288$	−20.9385	+	4887.48i	−0.00428407	+	0.999991i
$289$	3590.01			0.730716
$290$	919.715	+	784.230i	0.186233	+	0.158799i
$291$	3429.91	+	7028.65i	0.690945	+	1.41590i
$292$	157.392	+	983.476i	0.0315433	+	0.197101i
$293$	−3842.30	+	2218.35i	−0.766108	+	0.442312i	−0.831484	−	0.555548i	$-0.812508\pi$
$293$	−3842.30	+	2218.35i	−0.766108	+	0.442312i	0.0653767	+	0.997861i	$0.479175\pi$
$294$	−3524.87	−	3456.86i	−0.699232	−	0.685742i
$295$	−295.434	−	170.569i	−0.0583080	−	0.0336641i
$296$	−2347.74	+	3852.03i	−0.461013	+	0.756400i
$297$	4529.75	−	5037.11i	0.884992	−	0.984117i
$298$	5977.58	+	1102.90i	1.16199	+	0.214394i
$299$	3951.54	−	6844.26i	0.764292	−	1.32379i
$300$	−4053.58	+	2849.34i	−0.780111	+	0.548357i
$301$	−387.858	−	671.790i	−0.0742716	−	0.128642i
$302$	905.429	+	2550.32i	0.172522	+	0.485943i
$303$	2033.34	−	992.250i	0.385519	−	0.188130i
$304$	2500.09	+	7610.98i	0.471678	+	1.43592i
$305$			37.1790i			0.00697988i
$306$	−2635.24	−	878.164i	−0.492310	−	0.164056i
$307$			7392.80i			1.37436i	0.726486	+	0.687181i	$0.241152\pi$
$307$			7392.80i			1.37436i	−0.726486	+	0.687181i	$0.758848\pi$
$308$	647.923	+	797.489i	0.119866	+	0.147536i
$309$	−630.751	+	9047.19i	−0.116124	+	1.66562i
$310$	1127.64	−	400.339i	0.206598	−	0.0733475i
$311$	−2448.25	−	4240.50i	−0.446391	−	0.773172i	0.551757	−	0.834005i	$-0.313958\pi$
$311$	−2448.25	−	4240.50i	−0.446391	−	0.773172i	−0.998148	+	0.0608332i	$0.980624\pi$
$312$	2769.57	−	3904.43i	0.502552	−	0.708477i
$313$	−340.861	+	590.388i	−0.0615546	+	0.106616i	−0.895160	−	0.445744i	$-0.852939\pi$
$313$	−340.861	+	590.388i	−0.0615546	+	0.106616i	0.833606	+	0.552360i	$0.186273\pi$
$314$	1074.23	−	5822.20i	0.193065	−	1.04639i
$315$	64.8916	+	160.420i	0.0116071	+	0.0286942i
$316$	2137.53	−	5595.38i	0.380524	−	0.996091i
$317$	1344.13	+	776.034i	0.238151	+	0.137497i	0.614327	−	0.789052i	$-0.289428\pi$
$317$	1344.13	+	776.034i	0.238151	+	0.137497i	−0.376176	+	0.926548i	$0.622761\pi$
$318$	−1388.25	−	4986.24i	−0.244809	−	0.879291i
$319$	−7416.37	+	4281.84i	−1.30168	+	0.751527i
$320$	−1037.86	−	666.886i	−0.181307	−	0.116500i
$321$	−2276.76	+	3376.95i	−0.395877	+	0.587175i
$322$	947.573	−	1111.28i	0.163994	−	0.192326i
$323$	−4552.92			−0.784307
$324$	−4666.20	−	3498.40i	−0.800103	−	0.599863i
$325$	4852.88			0.828276
$326$	2695.15	−	3160.76i	0.457885	−	0.536990i
$327$	4595.01	−	6815.43i	0.777078	−	1.15258i
$328$	125.295	−	5271.53i	0.0210923	−	0.887414i
$329$	−142.583	+	82.3206i	−0.0238932	+	0.0137948i
$330$	458.617	+	1647.23i	0.0765031	+	0.274780i
$331$	6410.22	+	3700.94i	1.06446	+	0.614569i	0.926664	−	0.375891i	$-0.122663\pi$
$331$	6410.22	+	3700.94i	1.06446	+	0.614569i	0.137801	+	0.990460i	$0.455997\pi$
$332$	2607.33	+	996.043i	0.431011	+	0.164653i
$333$	−2018.52	−	4990.04i	−0.332175	−	0.821178i
$334$	−1564.43	+	8479.02i	−0.256293	+	1.38908i
$335$	−183.149	+	317.223i	−0.0298701	+	0.0517365i
$336$	634.211	−	616.667i	0.102973	−	0.100125i
$337$	4871.58	+	8437.83i	0.787454	+	1.36391i	0.927522	+	0.373769i	$0.121935\pi$
$337$	4871.58	+	8437.83i	0.787454	+	1.36391i	−0.140068	+	0.990142i	$0.544732\pi$
$338$	1437.65	−	510.403i	0.231355	−	0.0821368i
$339$	−160.394	+	2300.62i	−0.0256974	+	0.368591i
$340$	544.158	−	442.104i	0.0867975	−	0.0705190i
$341$			8478.09i			1.34638i
$342$	−9068.89	−	3022.10i	−1.43389	−	0.477826i
$343$			1805.94i			0.284290i
$344$	−5791.41	+	3162.62i	−0.907709	+	0.495689i
$345$	2184.10	−	1065.82i	0.340835	−	0.166324i
$346$	−2626.51	−	7398.09i	−0.408098	−	1.14949i
$347$	−3523.75	−	6103.31i	−0.545143	−	0.944216i	−0.998598	−	0.0529363i	$-0.983142\pi$
$347$	−3523.75	−	6103.31i	−0.545143	−	0.944216i	0.453455	−	0.891279i	$-0.350191\pi$
$348$	4239.66	+	6031.49i	0.653074	+	0.929085i
$349$	603.773	−	1045.77i	0.0926052	−	0.160397i	−0.816001	−	0.578050i	$-0.803814\pi$
$349$	603.773	−	1045.77i	0.0926052	−	0.160397i	0.908607	+	0.417653i	$0.137147\pi$
$350$	881.886	+	162.713i	0.134682	+	0.0248497i
$351$	1768.50	+	5431.35i	0.268933	+	0.825937i
$352$	6912.94	−	5348.85i	1.04676	−	0.809928i
$353$	1316.47	+	760.063i	0.198494	+	0.114601i	0.595953	−	0.803019i	$-0.296774\pi$
$353$	1316.47	+	760.063i	0.198494	+	0.114601i	−0.397459	+	0.917620i	$0.630108\pi$
$354$	−1485.63	−	1456.96i	−0.223051	−	0.218748i
$355$	−58.4957	+	33.7725i	−0.00874544	+	0.00504918i
$356$	−3293.01	+	527.000i	−0.490250	+	0.0784576i
$357$	220.479	+	451.811i	0.0326863	+	0.0669815i
$358$	−1027.94	−	876.517i	−0.151756	−	0.129400i
$359$	6515.20			0.957825			0.478912	−	0.877863i	$-0.341031\pi$
$359$	6515.20			0.957825			0.478912	+	0.877863i	$0.341031\pi$
$360$	1377.36	−	519.423i	0.201647	−	0.0760444i
$361$	−8809.35			−1.28435
$362$	−1576.19	−	1344.00i	−0.228847	−	0.195135i
$363$	−5186.21	−	361.572i	−0.749877	−	0.0522799i
$364$	−855.506	+	136.912i	−0.123189	+	0.0197146i
$365$	259.787	−	149.988i	0.0372545	−	0.0215089i
$366$	−56.5585	+	219.613i	−0.00807748	+	0.0313644i
$367$	−3492.35	−	2016.31i	−0.496729	−	0.286786i	0.230633	−	0.973041i	$-0.425920\pi$
$367$	−3492.35	−	2016.31i	−0.496729	−	0.286786i	−0.727362	+	0.686254i	$0.759254\pi$
$368$	−9258.94	−	8282.93i	−1.31156	−	1.17331i
$369$	4959.77	+	3871.68i	0.699716	+	0.546210i
$370$	1336.12	+	246.522i	0.187734	+	0.0346380i
$371$	−468.392	+	811.278i	−0.0655463	+	0.113530i
$372$	7269.85	−	649.354i	1.01324	−	0.0905039i
$373$	−1227.68	−	2126.40i	−0.170420	−	0.295176i	0.768147	−	0.640274i	$-0.221179\pi$
$373$	−1227.68	−	2126.40i	−0.170420	−	0.295176i	−0.938567	+	0.345098i	$0.887846\pi$
$374$	1661.97	+	4681.28i	0.229782	+	0.647228i
$375$	2534.98	+	1709.10i	0.349082	+	0.235353i
$376$	671.247	+	1229.19i	0.0920663	+	0.168592i
$377$		−	7220.81i		−	0.986448i
$378$	139.270	+	1046.30i	0.0189504	+	0.142371i
$379$		−	9518.27i		−	1.29003i	−0.764171	−	0.645014i	$-0.776851\pi$
$379$		−	9518.27i		−	1.29003i	0.764171	−	0.645014i	$-0.223149\pi$
$380$	1872.66	−	1521.45i	0.252804	−	0.205391i
$381$	1834.65	+	1236.93i	0.246698	+	0.166325i
$382$	−8225.52	+	2920.27i	−1.10171	+	0.391136i
$383$	4727.72	+	8188.65i	0.630744	+	1.09248i	0.987400	+	0.158245i	$0.0505837\pi$
$383$	4727.72	+	8188.65i	0.630744	+	1.09248i	−0.356655	+	0.934236i	$0.616083\pi$
$384$	−5116.05	−	5518.08i	−0.679888	−	0.733316i
$385$	154.736	−	268.011i	0.0204833	−	0.0354781i
$386$	−838.733	+	4545.83i	−0.110597	+	0.599421i
$387$	1092.58	−	7797.65i	0.143512	−	1.02423i
$388$	−11248.2	−	4297.01i	−1.47176	−	0.562236i
$389$	−2568.69	−	1483.04i	−0.334802	−	0.193298i	0.323169	−	0.946341i	$-0.395252\pi$
$389$	−2568.69	−	1483.04i	−0.334802	−	0.193298i	−0.657971	+	0.753043i	$0.728585\pi$
$390$	−1396.20	−	359.573i	−0.181280	−	0.0466864i
$391$	6114.50	−	3530.21i	0.790854	−	0.456600i
$392$	7598.96	+	180.614i	0.979095	+	0.0232714i
$393$	−9038.44	−	630.142i	−1.16013	−	0.0808816i
$394$	−6149.10	+	7211.43i	−0.786262	+	0.922097i
$395$	−1804.02			−0.229798
$396$	203.155	+	10427.7i	0.0257801	+	1.32327i
$397$	1296.85			0.163947			0.0819733	−	0.996635i	$-0.473878\pi$
$397$	1296.85			0.163947			0.0819733	+	0.996635i	$0.473878\pi$
$398$	1920.73	−	2252.55i	0.241903	−	0.283694i
$399$	758.754	+	1554.86i	0.0952011	+	0.195088i
$400$	1562.00	−	7466.82i	0.195250	−	0.933352i
$401$	−1782.15	+	1028.93i	−0.221936	+	0.128135i	−0.606847	−	0.794819i	$-0.707566\pi$
$401$	−1782.15	+	1028.93i	−0.221936	+	0.128135i	0.384910	+	0.922954i	$0.374232\pi$
$402$	−1564.42	+	1595.19i	−0.194095	+	0.197913i
$403$	−6190.90	−	3574.32i	−0.765238	−	0.441810i
$404$	−1243.10	+	3254.03i	−0.153085	+	0.400728i
$405$	−482.755	+	1688.86i	−0.0592303	+	0.207211i
$406$	242.108	−	1312.20i	0.0295951	−	0.160402i
$407$	−4813.22	+	8336.74i	−0.586198	+	1.01532i
$408$	3886.84	−	1783.67i	0.471636	−	0.216433i
$409$	−2897.54	−	5018.69i	−0.350304	−	0.606744i	0.635999	−	0.771690i	$-0.280588\pi$
$409$	−2897.54	−	5018.69i	−0.350304	−	0.606744i	−0.986303	+	0.164946i	$0.947255\pi$
$410$	−1496.63	+	531.341i	−0.180276	+	0.0640026i
$411$	−6871.43	+	3353.19i	−0.824678	+	0.402435i
$412$	−8804.58	−	10837.0i	−1.05284	−	1.29588i
$413$			376.608i			0.0448709i
$414$	14522.6	−	2973.14i	1.72403	−	0.352951i
$415$		−	840.635i		−	0.0994341i
$416$	991.398	+	7303.04i	0.116844	+	0.860723i
$417$	461.963	−	6626.17i	0.0542504	−	0.778141i
$418$	5719.48	+	16110.1i	0.669256	+	1.88509i
$419$	7052.61	+	12215.5i	0.822298	+	1.42426i	0.903967	+	0.427602i	$0.140641\pi$
$419$	7052.61	+	12215.5i	0.822298	+	1.42426i	−0.0816695	+	0.996659i	$0.526025\pi$
$420$	−241.667	−	112.157i	−0.0280766	−	0.0130302i
$421$	−3210.43	+	5560.63i	−0.371655	+	0.643726i	−0.989820	−	0.142323i	$-0.954543\pi$
$421$	−3210.43	+	5560.63i	−0.371655	+	0.643726i	0.618165	+	0.786048i	$0.287876\pi$
$422$	14680.3	+	2708.60i	1.69343	+	0.312447i
$423$	−1655.01	−	231.894i	−0.190234	−	0.0266551i
$424$	6804.57	+	4147.26i	0.779384	+	0.475021i
$425$	3754.61	+	2167.73i	0.428530	+	0.247412i
$426$	−396.905	+	110.505i	−0.0451411	+	0.0125680i
$427$	35.5457	−	20.5223i	0.00402852	−	0.00232587i
$428$	−990.887	−	6191.65i	−0.111907	−	0.699263i
$429$	5710.47	−	8469.92i	0.642667	−	0.953221i
$430$	1512.28	+	1289.51i	0.169602	+	0.144617i
$431$	−1119.73			−0.125140			−0.0625700	−	0.998041i	$-0.519930\pi$
$431$	−1119.73			−0.125140			−0.0625700	+	0.998041i	$0.519930\pi$
$432$	8926.09	−	972.884i	0.994113	−	0.108352i
$433$	−299.833			−0.0332773			−0.0166387	−	0.999862i	$-0.505296\pi$
$433$	−299.833			−0.0332773			−0.0166387	+	0.999862i	$0.505296\pi$
$434$	−1005.19	−	857.116i	−0.111177	−	0.0947993i
$435$	1241.29	−	1841.12i	0.136817	−	0.202930i
$436$	1999.83	+	12496.1i	0.219666	+	1.37260i
$437$	21042.4	−	12148.8i	2.30342	−	1.32988i
$438$	1762.71	−	490.766i	0.192296	−	0.0535382i
$439$	−2090.02	−	1206.67i	−0.227224	−	0.131188i	0.382067	−	0.924135i	$-0.375212\pi$
$439$	−2090.02	−	1206.67i	−0.227224	−	0.131188i	−0.609291	+	0.792947i	$0.708546\pi$
$440$	−2247.93	−	1370.07i	−0.243559	−	0.148445i
$441$	−5581.05	+	7149.55i	−0.602640	+	0.772006i
$442$	−4119.06	−	759.992i	−0.443266	−	0.0817853i
$443$	−2409.36	+	4173.14i	−0.258402	+	0.447566i	−0.965814	−	0.259236i	$-0.916529\pi$
$443$	−2409.36	+	4173.14i	−0.258402	+	0.447566i	0.707412	+	0.706802i	$0.249863\pi$
$444$	7517.31	+	3488.75i	0.803504	+	0.372902i
$445$	502.211	+	869.854i	0.0534990	+	0.0926630i
$446$	−4504.08	−	12686.7i	−0.478194	−	1.34693i
$447$	776.647	−	11139.8i	0.0821793	−	1.17874i
$448$	−64.7043	+	1360.38i	−0.00682364	+	0.143464i
$449$			8677.13i			0.912024i	0.889974	+	0.456012i	$0.150723\pi$
$449$			8677.13i			0.912024i	−0.889974	+	0.456012i	$0.849277\pi$
$450$	6039.88	+	6810.06i	0.632717	+	0.713399i
$451$		−	11252.3i		−	1.17484i
$452$	−2238.93	−	2755.76i	−0.232987	−	0.286770i
$453$	4468.13	−	2180.40i	0.463424	−	0.226146i
$454$	−5945.12	+	2110.67i	−0.614578	+	0.218191i
$455$	130.472	+	225.984i	0.0134431	+	0.0232841i
$456$	13376.1	−	6138.29i	1.37367	−	0.630377i
$457$	3460.04	−	5992.97i	0.354166	−	0.613434i	−0.632809	−	0.774308i	$-0.718098\pi$
$457$	3460.04	−	5992.97i	0.354166	−	0.613434i	0.986975	+	0.160874i	$0.0514313\pi$
$458$	−2994.30	+	16228.8i	−0.305491	+	1.65572i
$459$	−1057.86	+	4992.13i	−0.107574	+	0.507653i
$460$	−1335.26	+	3495.29i	−0.135341	+	0.354280i
$461$	−13470.8	−	7777.39i	−1.36095	−	0.785747i	−0.371203	−	0.928552i	$-0.621055\pi$
$461$	−13470.8	−	7777.39i	−1.36095	−	0.785747i	−0.989751	+	0.142805i	$0.954388\pi$
$462$	1321.72	−	1347.72i	0.133100	−	0.135718i
$463$	9994.39	−	5770.27i	1.00319	−	0.579194i	0.0940023	−	0.995572i	$-0.470034\pi$
$463$	9994.39	−	5770.27i	1.00319	−	0.579194i	0.909192	+	0.416378i	$0.136701\pi$
$464$	−11110.2	−	2324.16i	−1.11159	−	0.232535i
$465$	−964.074	−	1975.60i	−0.0961459	−	0.197024i
$466$	5652.53	−	6629.06i	0.561906	−	0.658981i
$467$	−7.01271			−0.000694881			−0.000347441	−	1.00000i	$-0.500111\pi$
$467$	−7.01271			−0.000694881			−0.000347441		1.00000i	$0.500111\pi$
$468$	−7700.23	−	4247.93i	−0.760562	−	0.419574i
$469$	404.383			0.0398138
$470$	273.690	−	320.973i	0.0268604	−	0.0315008i
$471$	−10850.3	−	756.458i	−1.06147	−	0.0740037i
$472$	3202.73	+	76.1234i	0.312326	+	0.00742344i
$473$	−12194.7	+	7040.61i	−1.18544	+	0.684414i
$474$	−10656.2	−	2744.36i	−1.03261	−	0.265934i
$475$	12921.1	+	7459.98i	1.24812	+	0.720605i
$476$	−723.051	−	276.218i	−0.0696239	−	0.0265975i
$477$	−8814.85	+	3565.69i	−0.846131	+	0.342268i
$478$	−2715.57	+	14718.1i	−0.259848	+	1.40834i
$479$	−2830.70	+	4902.92i	−0.270017	+	0.467683i	−0.968866	−	0.247586i	$-0.920363\pi$
$479$	−2830.70	+	4902.92i	−0.270017	+	0.467683i	0.698849	+	0.715269i	$0.253696\pi$
$480$	−1002.65	+	2032.51i	−0.0953424	+	0.193273i
$481$	−4058.46	−	7029.46i	−0.384719	−	0.666353i
$482$	13335.7	−	4734.52i	1.26022	−	0.447409i
$483$	−2224.59	−	1499.83i	−0.209570	−	0.141293i
$484$	6212.21	−	5047.14i	0.583415	−	0.473999i
$485$			3626.57i			0.339534i
$486$	−5420.76	+	9241.57i	−0.505948	+	0.862564i
$487$			9082.26i			0.845085i	0.906343	+	0.422542i	$0.138862\pi$
$487$			9082.26i			0.845085i	−0.906343	+	0.422542i	$0.861138\pi$
$488$	−167.340	−	306.435i	−0.0155228	−	0.0284255i
$489$	−6327.33	−	4265.92i	−0.585136	−	0.394502i
$490$	−765.932	−	2157.40i	−0.0706149	−	0.198901i
$491$	−5098.79	−	8831.36i	−0.468646	−	0.811718i	0.530712	−	0.847552i	$-0.321925\pi$
$491$	−5098.79	−	8831.36i	−0.468646	−	0.811718i	−0.999358	+	0.0358342i	$0.988591\pi$
$492$	−9648.75	+	861.840i	−0.884145	+	0.0789731i
$493$	3225.45	−	5586.65i	0.294659	−	0.510365i
$494$	−14175.3	−	2615.42i	−1.29104	−	0.238205i
$495$	2912.04	−	1177.95i	0.264417	−	0.106959i
$496$	−7492.24	+	8375.07i	−0.678249	+	0.758169i
$497$	64.5778	+	37.2840i	0.00582839	+	0.00336502i
$498$	1278.81	−	4965.55i	0.115070	−	0.446811i
$499$	2353.15	−	1358.59i	0.211105	−	0.121881i	−0.390720	−	0.920510i	$-0.627774\pi$
$499$	2353.15	−	1358.59i	0.211105	−	0.121881i	0.601825	+	0.798628i	$0.294441\pi$
$500$	−4647.89	+	743.831i	−0.415720	+	0.0665302i
$501$	15801.5	+	1101.65i	1.40910	+	0.0982397i
$502$	−5547.77	−	4730.52i	−0.493245	−	0.420585i
$503$	8294.45			0.735251			0.367626	−	0.929974i	$-0.380171\pi$
$503$	8294.45			0.735251			0.367626	+	0.929974i	$0.380171\pi$
$504$	−1256.89	−	1030.13i	−0.111084	−	0.0910433i
$505$	1049.14			0.0924479
$506$	−20172.5	−	17200.9i	−1.77229	−	1.51121i
$507$	−1229.12	−	2518.75i	−0.107667	−	0.220634i
$508$	−3363.83	+	538.334i	−0.293791	+	0.0470171i
$509$	2866.64	−	1655.05i	0.249629	−	0.144124i	−0.369965	−	0.929046i	$-0.620630\pi$
$509$	2866.64	−	1655.05i	0.249629	−	0.144124i	0.619595	+	0.784922i	$0.287297\pi$
$510$	−919.605	−	901.863i	−0.0798447	−	0.0783043i
$511$	−286.798	−	165.583i	−0.0248282	−	0.0143346i
$512$	11555.8	+	825.228i	0.997460	+	0.0712310i
$513$	−3640.49	+	17179.8i	−0.313317	+	1.47857i
$514$	−2421.46	−	446.775i	−0.207794	−	0.0383393i
$515$	−2102.70	+	3641.98i	−0.179914	+	0.311621i
$516$	6971.25	+	9917.55i	0.594753	+	0.846116i
$517$	1494.33	+	2588.25i	0.127119	+	0.220176i
$518$	−501.828	−	1413.50i	−0.0425657	−	0.119895i
$519$	−12961.4	+	6325.01i	−1.09622	+	0.534946i
$520$	1948.17	−	1063.88i	0.164294	−	0.0897193i
$521$		−	5030.71i		−	0.423031i	−0.977375	−	0.211516i	$-0.932160\pi$
$521$		−	5030.71i		−	0.423031i	0.977375	−	0.211516i	$-0.0678400\pi$
$522$	10133.0	−	8986.99i	0.849633	−	0.753544i
$523$			9680.16i			0.809338i	0.914463	+	0.404669i	$0.132613\pi$
$523$			9680.16i			0.809338i	−0.914463	+	0.404669i	$0.867387\pi$
$524$	10826.5	−	8796.08i	0.902595	−	0.733317i
$525$	114.580	−	1643.49i	0.00952515	−	0.136624i
$526$	11489.0	−	4078.90i	0.952369	−	0.338115i
$527$	−3193.21	−	5530.81i	−0.263944	−	0.457164i
$528$	−11194.1	−	11512.5i	−0.922652	−	0.948900i
$529$	−12756.2	+	22094.4i	−1.04843	+	1.81593i
$530$	435.479	−	2360.24i	0.0356905	−	0.193438i
$531$	−2352.25	+	3013.32i	−0.192239	+	0.246266i
$532$	−2488.30	−	950.571i	−0.202784	−	0.0774671i
$533$	8216.73	+	4743.93i	0.667742	+	0.385521i
$534$	1643.25	+	5902.13i	0.133165	+	0.478296i
$535$	−1635.54	+	944.278i	−0.132169	+	0.0763078i
$536$	81.7376	−	3438.94i	0.00658680	−	0.277126i
$537$	−1387.36	+	2057.77i	−0.111488	+	0.165362i
$538$	10283.5	−	12060.1i	0.824076	−	0.966443i
$539$	16220.3			1.29621
$540$	−1233.11	−	2406.81i	−0.0982681	−	0.191802i
$541$	18659.8			1.48290			0.741449	−	0.671009i	$-0.234139\pi$
$541$	18659.8			1.48290			0.741449	+	0.671009i	$0.234139\pi$
$542$	−3944.21	+	4625.62i	−0.312580	+	0.366582i
$543$	−2127.30	+	3155.26i	−0.168124	+	0.249365i
$544$	−2495.15	+	6093.11i	−0.196652	+	0.480220i
$545$	3300.88	−	1905.76i	0.259438	−	0.149787i
$546$	426.908	+	1533.34i	0.0334615	+	0.120185i
$547$	−3928.78	−	2268.28i	−0.307098	−	0.177303i	0.338529	−	0.940956i	$-0.390071\pi$
$547$	−3928.78	−	2268.28i	−0.307098	−	0.177303i	−0.645627	+	0.763653i	$0.723404\pi$
$548$	4200.89	−	10996.6i	0.327469	−	0.857212i
$549$	412.589	+	57.8108i	0.0320745	+	0.00449418i
$550$	2953.66	−	16008.5i	0.228990	−	1.24110i
$551$	11100.0	−	19225.8i	0.858216	−	1.48647i
$552$	−13204.5	+	18615.1i	−1.01815	+	1.43535i
$553$	995.797	+	1724.77i	0.0765743	+	0.132631i
$554$	8556.00	−	3037.59i	0.656154	−	0.232951i
$555$	173.597	−	2489.99i	0.0132771	−	0.190440i
$556$	6448.49	+	7937.04i	0.491865	+	0.605406i
$557$			17657.1i			1.34319i	0.740918	+	0.671596i	$0.234391\pi$
$557$			17657.1i			1.34319i	−0.740918	+	0.671596i	$0.765609\pi$
$558$	−2689.32	−	13136.3i	−0.204028	−	0.996601i
$559$		−	11873.1i		−	0.898355i
$560$	389.701	−	128.011i	0.0294069	−	0.00965974i
$561$	8201.53	−	4002.26i	0.617235	−	0.301204i
$562$	−889.873	−	2506.51i	−0.0667919	−	0.188133i
$563$	4972.47	+	8612.57i	0.372229	+	0.644719i	0.989908	−	0.141711i	$-0.0452604\pi$
$563$	4972.47	+	8612.57i	0.372229	+	0.644719i	−0.617679	+	0.786430i	$0.711927\pi$
$564$	2104.94	−	1479.61i	0.157152	−	0.110466i
$565$	−534.697	+	926.122i	−0.0398139	+	0.0689597i
$566$	5702.30	+	1052.11i	0.423473	+	0.0781334i
$567$	1881.15	−	470.683i	0.139331	−	0.0348622i
$568$	330.122	−	541.643i	0.0243866	−	0.0400121i
$569$	−4084.02	−	2357.91i	−0.300898	−	0.173724i	0.341948	−	0.939719i	$-0.388913\pi$
$569$	−4084.02	−	2357.91i	−0.300898	−	0.173724i	−0.642846	+	0.765995i	$0.722247\pi$
$570$	−3164.71	−	3103.66i	−0.232553	−	0.228067i
$571$	−7993.20	+	4614.88i	−0.585823	+	0.338225i	−0.763444	−	0.645874i	$-0.776493\pi$
$571$	−7993.20	+	4614.88i	−0.585823	+	0.338225i	0.177621	+	0.984099i	$0.443160\pi$
$572$	2485.30	+	15529.6i	0.181671	+	1.13519i
$573$	7032.41	+	14411.0i	0.512711	+	1.05066i
$574$	1334.12	+	1137.59i	0.0970123	+	0.0827213i
$575$	−23137.1			−1.67806
$576$	−9014.48	+	10480.6i	−0.652089	+	0.758142i
$577$	4076.34			0.294108			0.147054	−	0.989128i	$-0.453021\pi$
$577$	4076.34			0.294108			0.147054	+	0.989128i	$0.453021\pi$
$578$	7726.53	+	6588.33i	0.556023	+	0.474115i
$579$	8471.61	+	590.624i	0.608063	+	0.0423929i
$580$	540.232	+	3375.69i	0.0386757	+	0.241669i
$581$	−803.706	+	464.020i	−0.0573896	+	0.0331339i
$582$	−5516.91	+	21421.8i	−0.392926	+	1.52571i
$583$	14726.8	+	8502.51i	1.04618	+	0.604010i
$584$	−1466.12	+	2405.51i	−0.103884	+	0.170447i
$585$	−367.535	+	2623.06i	−0.0259755	+	0.185385i
$586$	−12340.6	−	2276.92i	−0.869941	−	0.160509i
$587$	4317.74	−	7478.55i	0.303599	−	0.525848i	−0.673350	−	0.739324i	$-0.735145\pi$
$587$	4317.74	−	7478.55i	0.303599	−	0.525848i	0.976948	+	0.213476i	$0.0684785\pi$
$588$	−1242.35	−	13908.7i	−0.0871320	−	0.975488i
$589$	−10989.1	−	19033.6i	−0.768755	−	1.33152i
$590$	−322.818	−	909.281i	−0.0225258	−	0.0634483i
$591$	14436.1	+	9732.89i	1.00477	+	0.677424i
$592$	−12122.1	+	3981.92i	−0.841577	+	0.276446i
$593$		−	24260.9i		−	1.68006i	−0.542537	−	0.840032i	$-0.682536\pi$
$593$		−	24260.9i		−	1.68006i	0.542537	−	0.840032i	$-0.317464\pi$
$594$	18993.1	−	2528.10i	1.31195	−	0.174628i
$595$			233.121i			0.0160622i
$596$	10841.1	+	13343.7i	0.745083	+	0.917076i
$597$	−4509.24	−	3040.16i	−0.309130	−	0.208418i
$598$	21065.1	−	7478.64i	1.44050	−	0.511412i
$599$	−7549.02	−	13075.3i	−0.514932	−	0.891889i	−0.999850	−	0.0173291i	$-0.994484\pi$
$599$	−7549.02	−	13075.3i	−0.514932	−	0.891889i	0.484917	−	0.874560i	$-0.338850\pi$
$600$	−13953.3	−	1306.61i	−0.949402	−	0.0889034i
$601$	−2964.13	+	5134.03i	−0.201180	+	0.348455i	−0.948909	−	0.315550i	$-0.897811\pi$
$601$	−2964.13	+	5134.03i	−0.201180	+	0.348455i	0.747729	+	0.664004i	$0.231144\pi$
$602$	398.097	−	2157.64i	0.0269522	−	0.146078i
$603$	3235.56	+	2525.73i	0.218511	+	0.170573i
$604$	−2731.62	+	7150.52i	−0.184020	+	0.481706i
$605$	−2087.73	−	1205.35i	−0.140294	−	0.0809990i
$606$	6197.18	+	1596.00i	0.415418	+	0.106985i
$607$	−16115.3	+	9304.20i	−1.07760	+	0.622151i	−0.930247	−	0.366933i	$-0.880408\pi$
$607$	−16115.3	+	9304.20i	−1.07760	+	0.622151i	−0.147350	+	0.989084i	$0.547074\pi$
$608$	−8586.77	+	20968.7i	−0.572762	+	1.39867i
$609$	−2445.41	−	170.489i	−0.162714	−	0.0113441i
$610$	−68.2303	+	80.0179i	−0.00452880	+	0.00531119i
$611$	−2520.01			−0.166855
$612$	−4060.06	−	6726.17i	−0.268167	−	0.444263i
$613$	7939.25			0.523105			0.261552	−	0.965189i	$-0.415766\pi$
$613$	7939.25			0.523105			0.261552	+	0.965189i	$0.415766\pi$
$614$	−13567.1	+	15911.0i	−0.891735	+	1.04579i
$615$	1279.54	+	2622.07i	0.0838963	+	0.171922i
$616$	−69.0572	+	2905.44i	−0.00451687	+	0.190038i
$617$	−25269.7	+	14589.5i	−1.64882	+	0.951946i	−0.671277	+	0.741206i	$0.734254\pi$
$617$	−25269.7	+	14589.5i	−1.64882	+	0.951946i	−0.977542	+	0.210740i	$0.932413\pi$
$618$	−17960.8	+	18314.1i	−1.16907	+	1.19207i
$619$	−14117.6	−	8150.83i	−0.916698	−	0.529256i	−0.0341179	−	0.999418i	$-0.510862\pi$
$619$	−14117.6	−	8150.83i	−0.916698	−	0.529256i	−0.882580	+	0.470162i	$0.844196\pi$
$620$	3161.63	+	1207.80i	0.204797	+	0.0782359i
$621$	−8431.65	−	25895.0i	−0.544848	−	1.67332i
$622$	2512.88	−	13619.5i	0.161990	−	0.877963i
$623$	554.427	−	960.297i	0.0356544	−	0.0617552i
$624$	13126.1	−	3320.56i	0.842091	−	0.213027i
$625$	−6740.81	−	11675.4i	−0.431412	−	0.747227i
$626$	−1817.08	+	645.110i	−0.116015	+	0.0411882i
$627$	28224.6	−	13773.3i	1.79774	−	0.877279i
$628$	12996.8	−	10559.3i	0.825842	−	0.670959i
$629$		−	7251.46i		−	0.459674i
$630$	−154.739	+	464.350i	−0.00978564	+	0.0293653i
$631$		−	2517.83i		−	0.158848i	−0.996841	−	0.0794242i	$-0.974692\pi$
$631$		−	2517.83i		−	0.158848i	0.996841	−	0.0794242i	$-0.0253082\pi$
$632$	14869.0	−	8119.79i	0.935850	−	0.511057i
$633$	1907.36	−	27358.2i	0.119764	−	1.71784i
$634$	1468.72	+	4136.93i	0.0920034	+	0.259146i
$635$	513.012	+	888.562i	0.0320602	+	0.0555300i
$636$	6162.84	−	13279.2i	0.384233	−	0.827919i
$637$	−6838.42	+	11844.5i	−0.425350	+	0.736728i
$638$	−23819.7	−	4394.88i	−1.47811	−	0.272720i
$639$	283.829	+	701.662i	0.0175714	+	0.0434387i
$640$	−1009.86	−	3339.96i	−0.0623720	−	0.206287i
$641$	14572.0	+	8413.13i	0.897907	+	0.518407i	0.876520	−	0.481365i	$-0.159859\pi$
$641$	14572.0	+	8413.13i	0.897907	+	0.518407i	0.0213863	+	0.999771i	$0.493192\pi$
$642$	−11097.4	+	3089.71i	−0.682214	+	0.189939i
$643$	−17687.6	+	10211.9i	−1.08481	+	0.626313i	−0.932189	−	0.361973i	$-0.882103\pi$
$643$	−17687.6	+	10211.9i	−1.08481	+	0.626313i	−0.152617	+	0.988285i	$0.548770\pi$
$644$	4078.79	−	652.754i	0.249576	−	0.0399412i
$645$	2041.05	−	3027.34i	0.124599	−	0.184808i
$646$	−9798.94	−	8355.44i	−0.596802	−	0.508886i
$647$	−21477.2			−1.30503			−0.652515	−	0.757776i	$-0.726286\pi$
$647$	−21477.2			−1.30503			−0.652515	+	0.757776i	$0.726286\pi$
$648$	−3622.53	−	16092.7i	−0.219609	−	0.975588i
$649$	6836.40			0.413485
$650$	10444.5	+	8905.93i	0.630259	+	0.537415i
$651$	−1356.66	+	2012.23i	−0.0816768	+	0.121145i
$652$	11601.2	−	1856.61i	0.696836	−	0.111519i
$653$	21836.5	−	12607.3i	1.30862	−	0.755533i	0.326756	−	0.945109i	$-0.394045\pi$
$653$	21836.5	−	12607.3i	1.30862	−	0.755533i	0.981866	+	0.189576i	$0.0607113\pi$
$654$	22397.1	−	6235.71i	1.33914	−	0.372837i
$655$	−3638.46	−	2100.66i	−0.217048	−	0.125313i
$656$	9943.90	−	11115.6i	0.591835	−	0.661573i
$657$	−1260.52	−	3116.18i	−0.0748519	−	0.185044i
$658$	−457.946	−	84.4938i	−0.0271316	−	0.00500595i
$659$	−6865.03	+	11890.6i	−0.405802	+	0.702870i	−0.994415	−	0.105545i	$-0.966341\pi$
$659$	−6865.03	+	11890.6i	−0.405802	+	0.702870i	0.588612	+	0.808416i	$0.299675\pi$
$660$	−2035.93	+	4386.88i	−0.120073	+	0.258726i
$661$	−772.039	−	1337.21i	−0.0454294	−	0.0786860i	0.842417	−	0.538827i	$-0.181132\pi$
$661$	−772.039	−	1337.21i	−0.0454294	−	0.0786860i	−0.887846	+	0.460141i	$0.847799\pi$
$662$	7004.37	+	19729.2i	0.411228	+	1.15831i
$663$	−535.175	+	7676.29i	−0.0313491	+	0.449657i
$664$	3783.65	+	6928.64i	0.221135	+	0.404945i
$665$			802.258i			0.0467823i
$666$	4813.32	−	14444.1i	0.280048	−	0.840385i
$667$			34426.6i			1.99851i
$668$	−18927.6	+	15377.8i	−1.09630	+	0.890696i
$669$	−22226.8	+	10846.5i	−1.28451	+	0.626829i
$670$	−976.341	+	346.626i	−0.0562975	+	0.0199870i
$671$	−372.533	−	645.246i	−0.0214329	−	0.0371229i
$672$	2496.67	−	163.318i	0.143320	−	0.00937518i
$673$	2684.11	−	4649.02i	0.153737	−	0.266280i	−0.778861	−	0.627196i	$-0.784202\pi$
$673$	2684.11	−	4649.02i	0.153737	−	0.266280i	0.932598	+	0.360916i	$0.117536\pi$
$674$	−5000.19	+	27100.4i	−0.285757	+	1.54877i
$675$	11181.8	−	12434.2i	0.637611	−	0.709028i
$676$	4030.84	+	1539.85i	0.229338	+	0.0876110i
$677$	−16713.8	−	9649.71i	−0.948838	−	0.547812i	−0.0561181	−	0.998424i	$-0.517872\pi$
$677$	−16713.8	−	9649.71i	−0.948838	−	0.547812i	−0.892720	+	0.450612i	$0.851206\pi$
$678$	−4567.26	+	4657.11i	−0.258709	+	0.263798i
$679$	3467.25	−	2001.82i	0.195966	−	0.113141i
$680$	1982.50	+	47.1205i	0.111802	+	0.00265734i
$681$	5082.79	+	10415.8i	0.286010	+	0.586099i
$682$	−15558.9	+	18246.8i	−0.873576	+	1.02450i
$683$	7466.11			0.418276			0.209138	−	0.977886i	$-0.432934\pi$
$683$	7466.11			0.418276			0.209138	+	0.977886i	$0.432934\pi$
$684$	−13972.2	−	23147.3i	−0.781055	−	1.29395i
$685$	−3545.45			−0.197759
$686$	−3314.22	+	3886.79i	−0.184457	+	0.216324i
$687$	30243.9	+	2108.55i	1.67959	+	0.117098i
$688$	−18268.4	−	3821.61i	−1.01232	−	0.211769i
$689$	−12417.5	+	7169.23i	−0.686600	+	0.396409i
$690$	6656.66	+	1714.33i	0.367268	+	0.0945849i
$691$	−20587.2	−	11886.0i	−1.13339	−	0.654364i	−0.188606	−	0.982053i	$-0.560397\pi$
$691$	−20587.2	−	11886.0i	−1.13339	−	0.654364i	−0.944786	+	0.327689i	$0.893730\pi$
$692$	7924.00	−	20742.5i	0.435297	−	1.13947i
$693$	−2733.61	−	2133.90i	−0.149843	−	0.116970i
$694$	3616.77	−	19602.5i	0.197825	−	1.07219i
$695$	1540.02	−	2667.39i	0.0840520	−	0.145582i
$696$	−1944.16	+	20761.7i	−0.105881	+	1.13071i
$697$	4238.12	+	7340.64i	0.230316	+	0.398919i
$698$	3218.63	−	1142.70i	0.174537	−	0.0619651i
$699$	−13270.3	−	8946.90i	−0.718066	−	0.484124i
$700$	1599.41	+	1968.62i	0.0863603	+	0.106296i
$701$			3501.89i			0.188680i	0.995540	+	0.0943399i	$0.0300740\pi$
$701$			3501.89i			0.188680i	−0.995540	+	0.0943399i	$0.969926\pi$
$702$	−6161.31	+	14935.0i	−0.331259	+	0.802973i
$703$		−	24955.1i		−	1.33883i
$704$	24694.4	+	1174.55i	1.32202	+	0.0628799i
$705$	−642.535	−	433.201i	−0.0343252	−	0.0231422i
$706$	1438.49	+	4051.79i	0.0766830	+	0.215993i
$707$	−579.113	−	1003.05i	−0.0308059	−	0.0533574i
$708$	−523.613	−	5862.12i	−0.0277946	−	0.311175i
$709$	−2079.38	+	3601.59i	−0.110145	+	0.190777i	−0.915829	−	0.401569i	$-0.868465\pi$
$709$	−2079.38	+	3601.59i	−0.110145	+	0.190777i	0.805684	+	0.592346i	$0.201798\pi$
$710$	−187.875	−	34.6641i	−0.00993074	−	0.00183228i
$711$	−2805.13	+	20019.9i	−0.147961	+	1.05598i
$712$	−8054.45	−	4909.04i	−0.423951	−	0.258391i
$713$	29516.3	+	17041.3i	1.55034	+	0.895091i
$714$	−354.634	+	1377.02i	−0.0185880	+	0.0721762i
$715$	4102.18	−	2368.40i	0.214564	−	0.123878i
$716$	−603.805	−	3772.93i	−0.0315157	−	0.196929i
$717$	27428.6	+	1912.27i	1.42865	+	0.0996025i
$718$	14022.2	+	11956.6i	0.728836	+	0.621470i
$719$	20077.1			1.04137			0.520687	−	0.853748i	$-0.325676\pi$
$719$	20077.1			1.04137			0.520687	+	0.853748i	$0.325676\pi$
$720$	3917.63	+	1409.78i	0.202780	+	0.0729716i
$721$	4642.64			0.239807
$722$	−18959.8	−	16166.8i	−0.977298	−	0.833331i
$723$	−11401.4	−	23364.0i	−0.586476	−	1.20182i
$724$	−925.838	−	5785.19i	−0.0475256	−	0.296968i
$725$	−18307.5	+	10569.8i	−0.937825	+	0.541454i
$726$	−10498.4	−	10295.8i	−0.536682	−	0.526328i
$727$	31220.9	+	18025.4i	1.59274	+	0.919566i	0.992835	+	0.119491i	$0.0381263\pi$
$727$	31220.9	+	18025.4i	1.59274	+	0.919566i	0.599900	+	0.800075i	$0.295207\pi$
$728$	−2092.51	−	1275.35i	−0.106529	−	0.0649278i
$729$	17991.3	+	7983.37i	0.914052	+	0.405597i
$730$	834.378	+	153.948i	0.0423037	+	0.00780530i
$731$	5303.59	−	9186.10i	0.268345	−	0.464788i
$732$	−524.757	+	368.863i	−0.0264967	+	0.0186251i
$733$	10850.9	+	18794.4i	0.546779	+	0.947049i	0.998493	+	0.0548859i	$0.0174795\pi$
$733$	10850.9	+	18794.4i	0.546779	+	0.947049i	−0.451714	+	0.892163i	$0.649187\pi$
$734$	−3816.05	−	10748.7i	−0.191898	−	0.540519i
$735$	−3779.74	+	1844.47i	−0.189684	+	0.0925638i
$736$	−4726.68	−	34818.7i	−0.236723	−	1.74379i
$737$		−	7340.58i		−	0.366884i
$738$	3569.33	+	17434.8i	0.178034	+	0.869628i
$739$		−	26112.0i		−	1.29979i	−0.760024	−	0.649895i	$-0.774813\pi$
$739$		−	26112.0i		−	1.29979i	0.760024	−	0.649895i	$-0.225187\pi$
$740$	2423.22	+	2982.60i	0.120378	+	0.148165i
$741$	−1841.74	+	26417.1i	−0.0913065	+	1.30966i
$742$	−2496.93	+	886.474i	−0.123538	+	0.0438591i
$743$	−2806.43	−	4860.88i	−0.138570	−	0.240011i	0.788385	−	0.615182i	$-0.210917\pi$
$743$	−2806.43	−	4860.88i	−0.138570	−	0.240011i	−0.926956	+	0.375171i	$0.877584\pi$
$744$	16838.1	+	11944.0i	0.829724	+	0.588557i
$745$	2589.06	−	4484.38i	0.127323	−	0.220530i
$746$	1260.09	−	6829.51i	0.0618432	−	0.335182i
$747$	−9328.84	−	1307.13i	−0.456927	−	0.0640232i
$748$	−5014.06	+	13125.2i	−0.245096	+	0.641585i
$749$	1805.59	+	1042.46i	0.0880839	+	0.0508553i
$750$	2319.35	+	8330.53i	0.112921	+	0.405584i
$751$	24027.9	−	13872.5i	1.16750	−	0.674056i	0.214409	−	0.976744i	$-0.431217\pi$
$751$	24027.9	−	13872.5i	1.16750	−	0.674056i	0.953090	+	0.302688i	$0.0978841\pi$
$752$	−811.113	+	3877.37i	−0.0393328	+	0.188023i
$753$	−7487.54	+	11105.7i	−0.362365	+	0.537470i
$754$	13251.5	−	15540.9i	0.640042	−	0.750616i
$755$	2305.42			0.111129
$756$	−1620.42	+	2507.47i	−0.0779551	+	0.120630i
$757$	−22792.6			−1.09433			−0.547167	−	0.837023i	$-0.684294\pi$
$757$	−22792.6			−1.09433			−0.547167	+	0.837023i	$0.684294\pi$
$758$	17467.8	−	20485.5i	0.837016	−	0.981620i
$759$	−27225.8	+	40382.0i	−1.30202	+	1.93119i
$760$	6822.54	+	162.160i	0.325631	+	0.00773968i
$761$	27979.1	−	16153.7i	1.33277	−	0.769477i	0.347049	−	0.937847i	$-0.387184\pi$
$761$	27979.1	−	16153.7i	1.33277	−	0.769477i	0.985724	+	0.168370i	$0.0538505\pi$
$762$	1678.59	+	6029.07i	0.0798017	+	0.286628i
$763$	−3644.08	−	2103.91i	−0.172902	−	0.0998253i
$764$	−23062.4	−	8810.24i	−1.09211	−	0.417203i
$765$	−1456.05	+	1865.25i	−0.0688149	+	0.0881546i
$766$	−4852.53	+	26300.1i	−0.228889	+	1.24055i
$767$	−2882.19	+	4992.10i	−0.135684	+	0.235012i
$768$	−884.232	−	21265.1i	−0.0415455	−	0.999137i
$769$	1200.97	+	2080.14i	0.0563174	+	0.0975446i	0.892810	−	0.450434i	$-0.148731\pi$
$769$	1200.97	+	2080.14i	0.0563174	+	0.0975446i	−0.836492	+	0.547979i	$0.815397\pi$
$770$	824.876	−	292.852i	0.0386058	−	0.0137060i
$771$	−314.612	+	4512.64i	−0.0146958	+	0.210790i
$772$	−10147.6	+	8244.44i	−0.473082	+	0.384358i
$773$			21135.4i			0.983424i	0.870758	+	0.491712i	$0.163629\pi$
$773$			21135.4i			0.983424i	−0.870758	+	0.491712i	$0.836371\pi$
$774$	16661.6	−	14777.3i	0.773759	−	0.686250i
$775$			20928.4i			0.970025i
$776$	−16323.0	−	29890.7i	−0.755103	−	1.38275i
$777$	−2476.43	+	1208.47i	−0.114339	+	0.0557963i
$778$	−2806.78	−	7905.87i	−0.129342	−	0.364318i
$779$	14585.0	+	25262.0i	0.670811	+	1.16188i
$780$	−2345.06	−	3336.17i	−0.107650	−	0.153146i
$781$	676.799	−	1172.25i	0.0310087	−	0.0537086i
$782$	19638.4	+	3623.41i	0.898041	+	0.165694i
$783$	−18501.4	−	16637.9i	−0.844427	−	0.759373i
$784$	16023.3	+	14334.2i	0.729922	+	0.652979i
$785$	−4367.81	−	2521.76i	−0.198591	−	0.114656i
$786$	−18296.4	−	17943.4i	−0.830294	−	0.814275i
$787$	−3776.51	+	2180.37i	−0.171052	+	0.0987570i	−0.583082	−	0.812413i	$-0.698153\pi$
$787$	−3776.51	+	2180.37i	−0.171052	+	0.0987570i	0.412030	+	0.911170i	$0.364820\pi$
$788$	−26468.6	+	4235.93i	−1.19658	+	0.191496i
$789$	−9822.57	−	20128.6i	−0.443210	−	0.908236i
$790$	−3882.67	−	3310.71i	−0.174860	−	0.149101i
$791$	1180.58			0.0530679
$792$	−18699.6	+	22815.7i	−0.838965	+	1.02364i
$793$	628.232			0.0281326
$794$	2791.11	+	2379.95i	0.124752	+	0.106374i
$795$	−4398.55	−	306.658i	−0.196227	−	0.0136805i
$796$	8267.70	−	1323.13i	0.368142	−	0.0589159i
$797$	−17755.1	+	10250.9i	−0.789106	+	0.455590i	−0.839648	−	0.543132i	$-0.817238\pi$
$797$	−17755.1	+	10250.9i	−0.789106	+	0.455590i	0.0505420	+	0.998722i	$0.483905\pi$
$798$	−1220.43	+	4738.87i	−0.0541389	+	0.210218i
$799$	−1949.69	−	1125.66i	−0.0863270	−	0.0498409i
$800$	17064.8	−	13203.8i	0.754163	−	0.583530i
$801$	10434.0	−	4220.65i	0.460258	−	0.186179i
$802$	−5723.88	−	1056.09i	−0.252016	−	0.0464985i
$803$	−3005.76	+	5206.12i	−0.132093	+	0.228792i
$804$	−6294.46	+	562.230i	−0.276105	+	0.0246621i
$805$	−622.050	−	1077.42i	−0.0272352	−	0.0471728i
$806$	−6764.72	−	19054.2i	−0.295629	−	0.832699i
$807$	−24142.3	−	16276.9i	−1.05309	−	0.710003i
$808$	−8647.18	+	4722.12i	−0.376493	+	0.205599i
$809$		−	34550.7i		−	1.50153i	−0.660568	−	0.750766i	$-0.729685\pi$
$809$		−	34550.7i		−	1.50153i	0.660568	−	0.750766i	$-0.270315\pi$
$810$	−4138.37	+	2748.88i	−0.179516	+	0.119242i
$811$			19709.5i			0.853384i	0.904397	+	0.426692i	$0.140321\pi$
$811$			19709.5i			0.853384i	−0.904397	+	0.426692i	$0.859679\pi$
$812$	2929.19	−	2379.84i	0.126594	−	0.102852i
$813$	9259.72	+	6242.96i	0.399449	+	0.269311i
$814$	−25658.6	+	9109.46i	−1.10483	+	0.392244i
$815$	−1769.27	−	3064.47i	−0.0760429	−	0.131710i
$816$	11638.7	+	3294.20i	0.499311	+	0.141324i
$817$	18251.7	−	31612.9i	0.781575	−	1.35373i
$818$	2974.03	−	16118.9i	0.127121	−	0.688978i
$819$	2710.70	−	1096.50i	0.115653	−	0.0467826i
$820$	−4196.20	−	1603.02i	−0.178704	−	0.0682682i
$821$	−28891.8	−	16680.7i	−1.22817	−	0.709086i	−0.261526	−	0.965196i	$-0.584226\pi$
$821$	−28891.8	−	16680.7i	−1.22817	−	0.709086i	−0.966648	+	0.256110i	$0.917559\pi$
$822$	−20942.6	−	5393.50i	−0.888635	−	0.228856i
$823$	36540.4	−	21096.6i	1.54765	−	0.893537i	0.549330	−	0.835605i	$-0.314883\pi$
$823$	36540.4	−	21096.6i	1.54765	−	0.893537i	0.998321	−	0.0579313i	$-0.0184504\pi$
$824$	938.413	−	39481.8i	0.0396738	−	1.66919i
$825$	−29833.5	−	2079.93i	−1.25899	−	0.0877743i
$826$	−691.145	+	810.548i	−0.0291138	+	0.0341435i
$827$	−13992.0			−0.588329			−0.294165	−	0.955755i	$-0.595041\pi$
$827$	−13992.0			−0.588329			−0.294165	+	0.955755i	$0.595041\pi$
$828$	36712.3	+	20252.8i	1.54087	+	0.850042i
$829$	−23454.8			−0.982653			−0.491327	−	0.870975i	$-0.663488\pi$
$829$	−23454.8			−0.982653			−0.491327	+	0.870975i	$0.663488\pi$
$830$	1542.72	−	1809.24i	0.0645164	−	0.0756623i
$831$	−7314.96	−	14990.0i	−0.305359	−	0.625748i
$832$	−11268.7	+	17537.2i	−0.469558	+	0.730762i
$833$	−10581.6	+	6109.28i	−0.440132	+	0.254110i
$834$	13154.5	−	13413.3i	0.546166	−	0.556910i
$835$	6360.95	+	3672.50i	0.263629	+	0.152206i
$836$	−17255.3	+	45168.9i	−0.713860	+	1.86866i
$837$	−23423.0	+	7626.76i	−0.967287	+	0.314957i
$838$	−7238.80	+	39233.4i	−0.298401	+	1.61730i
$839$	4579.55	−	7932.02i	0.188443	−	0.326393i	−0.756288	−	0.654238i	$-0.772989\pi$
$839$	4579.55	−	7932.02i	0.188443	−	0.326393i	0.944731	+	0.327846i	$0.106323\pi$
$840$	−314.296	−	684.891i	−0.0129098	−	0.0281321i
$841$	3532.81	+	6119.00i	0.144852	+	0.250892i
$842$	−17114.4	+	6076.03i	−0.700475	+	0.248686i
$843$	−4391.36	+	2142.94i	−0.179415	+	0.0875525i
$844$	26624.6	+	32770.6i	1.08585	+	1.33650i
$845$		−	1299.60i		−	0.0529082i
$846$	−3136.39	−	3536.33i	−0.127460	−	0.143713i
$847$			2661.35i			0.107963i
$848$	7034.01	+	21413.5i	0.284846	+	0.867149i
$849$	740.881	−	10626.8i	0.0299493	−	0.429578i
$850$	4102.62	+	11555.8i	0.165551	+	0.466309i
$851$	19349.5	+	33514.3i	0.779427	+	1.35001i
$852$	−1057.03	−	490.562i	−0.0425037	−	0.0197258i
$853$	16740.3	−	28995.1i	0.671955	−	1.16386i	−0.305394	−	0.952226i	$-0.598788\pi$
$853$	16740.3	−	28995.1i	0.671955	−	1.16386i	0.977349	−	0.211634i	$-0.0678784\pi$
$854$	114.165	+	21.0641i	0.00457452	+	0.000844028i
$855$	−5010.81	+	6419.04i	−0.200428	+	0.256756i
$856$	9230.20	−	15144.3i	0.368553	−	0.604699i
$857$	26803.0	+	15474.7i	1.06835	+	0.616811i	0.927730	−	0.373253i	$-0.121758\pi$
$857$	26803.0	+	15474.7i	1.06835	+	0.616811i	0.140618	+	0.990064i	$0.455091\pi$
$858$	27834.1	−	7749.46i	1.10751	−	0.308348i
$859$	5321.93	−	3072.62i	0.211388	−	0.122045i	−0.390568	−	0.920574i	$-0.627722\pi$
$859$	5321.93	−	3072.62i	0.211388	−	0.122045i	0.601956	+	0.798529i	$0.294388\pi$
$860$	888.301	+	5550.63i	0.0352219	+	0.220087i
$861$	1800.59	−	2670.68i	0.0712706	−	0.105710i
$862$	−2409.91	−	2054.91i	−0.0952227	−	0.0811953i
$863$	−13685.9			−0.539830			−0.269915	−	0.962884i	$-0.586996\pi$
$863$	−13685.9			−0.539830			−0.269915	+	0.962884i	$0.586996\pi$
$864$	20996.4	+	14287.1i	0.826751	+	0.562568i
$865$	−6687.66			−0.262875
$866$	−645.311	−	550.249i	−0.0253217	−	0.0215915i
$867$	10428.1	−	15467.2i	0.408486	−	0.605876i
$868$	−590.441	−	3689.43i	−0.0230886	−	0.144271i
$869$	31309.0	−	18076.3i	1.22219	−	0.705633i
$870$	6050.33	−	1684.51i	0.235776	−	0.0656439i
$871$	5360.27	+	3094.75i	0.208526	+	0.120392i
$872$	−18628.6	+	30564.6i	−0.723444	+	1.18698i
$873$	40245.4	+	5639.06i	1.56025	+	0.218618i
$874$	67583.3	+	12469.5i	2.61561	+	0.482595i
$875$	782.544	−	1355.41i	0.0302341	−	0.0523669i
$876$	4694.40	+	2178.65i	0.181061	+	0.0840295i
$877$	2574.73	+	4459.56i	0.0991361	+	0.171709i	0.911327	−	0.411683i	$-0.135059\pi$
$877$	2574.73	+	4459.56i	0.0991361	+	0.171709i	−0.812191	+	0.583391i	$0.801725\pi$
$878$	−2283.74	−	6432.61i	−0.0877819	−	0.247255i
$879$	−1603.37	+	22998.0i	−0.0615249	+	0.882483i
$880$	−2323.73	−	7074.07i	−0.0890146	−	0.270985i
$881$			26936.4i			1.03009i	0.857162	+	0.515046i	$0.172225\pi$
$881$			26936.4i			1.03009i	−0.857162	+	0.515046i	$0.827775\pi$
$882$	−25132.4	+	5145.22i	−0.959471	+	0.196427i
$883$		−	37301.8i		−	1.42164i	−0.703376	−	0.710818i	$-0.748325\pi$
$883$		−	37301.8i		−	1.42164i	0.703376	−	0.710818i	$-0.251675\pi$
$884$	−7470.44	−	9194.91i	−0.284229	−	0.349840i
$885$	−1593.05	+	777.391i	−0.0605081	+	0.0295274i
$886$	−12844.0	+	4559.94i	−0.487023	+	0.172905i
$887$	−17421.8	−	30175.4i	−0.659488	−	1.14227i	−0.980748	−	0.195276i	$-0.937440\pi$
$887$	−17421.8	−	30175.4i	−0.659488	−	1.14227i	0.321261	−	0.946991i	$-0.395893\pi$
$888$	9776.49	+	21304.2i	0.369457	+	0.805094i
$889$	566.352	−	980.950i	0.0213665	−	0.0370079i
$890$	−515.469	+	2793.78i	−0.0194141	+	0.105222i
$891$	−8544.11	−	34147.6i	−0.321255	−	1.28394i
$892$	13588.5	−	35570.4i	0.510064	−	1.33519i
$893$	−6709.65	−	3873.82i	−0.251433	−	0.145165i
$894$	22115.2	−	22550.2i	0.827340	−	0.843615i
$895$	−996.628	+	575.404i	−0.0372219	+	0.0214901i
$896$	−2635.80	+	2809.11i	−0.0982769	+	0.104739i
$897$	−18009.6	−	36905.8i	−0.670373	−	1.37374i
$898$	−15924.1	+	18675.2i	−0.591754	+	0.693985i
$899$	31140.2			1.15527
$900$	501.493	+	25741.1i	0.0185738	+	0.953375i
$901$	−12809.6			−0.473641
$902$	20650.1	−	24217.7i	0.762277	−	0.893969i
$903$	−4020.98	−	280.335i	−0.148184	−	0.0103311i
$904$	238.630	−	10039.9i	0.00877956	−	0.369382i
$905$	−1528.17	+	882.289i	−0.0561304	+	0.0324069i
$906$	13617.9	+	3507.11i	0.499364	+	0.128605i
$907$	7693.07	+	4441.59i	0.281636	+	0.162603i	0.634164	−	0.773199i	$-0.281344\pi$
$907$	7693.07	+	4441.59i	0.281636	+	0.162603i	−0.352528	+	0.935801i	$0.614678\pi$
$908$	−16668.8	−	6367.75i	−0.609220	−	0.232732i
$909$	1631.34	−	11642.7i	0.0595250	−	0.424823i
$910$	−133.916	+	725.809i	−0.00487833	+	0.0264399i
$911$	−22256.0	+	38548.6i	−0.809413	+	1.40194i	0.103858	+	0.994592i	$0.466881\pi$
$911$	−22256.0	+	38548.6i	−0.809413	+	1.40194i	−0.913271	+	0.407352i	$0.866452\pi$
$912$	40053.4	+	11336.6i	1.45428	+	0.411615i
$913$	8423.14	+	14589.3i	0.305329	+	0.528845i
$914$	18445.0	−	6548.45i	0.667513	−	0.236984i
$915$	160.182	+	107.996i	0.00578740	+	0.00390190i
$916$	−36227.2	+	29432.9i	−1.30675	+	1.06167i
$917$			4638.16i			0.167029i
$918$	−11438.2	+	8802.86i	−0.411239	+	0.316490i
$919$		−	7223.63i		−	0.259288i	−0.991561	−	0.129644i	$-0.958617\pi$
$919$		−	7223.63i		−	0.259288i	0.991561	−	0.129644i	$-0.0413834\pi$
$920$	−9288.30	+	5072.23i	−0.332855	+	0.181768i
$921$	31851.2	+	21474.3i	1.13956	+	0.768297i
$922$	−14719.4	−	41460.2i	−0.525768	−	1.48093i
$923$	570.670	+	988.430i	0.0203509	+	0.0352487i
$924$	5317.97	−	475.009i	0.189338	−	0.0169119i
$925$	−11881.6	+	20579.5i	−0.422339	+	0.731512i
$926$	32099.7	+	5922.60i	1.13916	+	0.210182i
$927$	37146.8	+	28997.4i	1.31614	+	1.02740i
$928$	−19646.4	−	25391.4i	−0.694964	−	0.898182i
$929$	−30912.2	−	17847.2i	−1.09171	−	0.630298i	−0.157677	−	0.987491i	$-0.550401\pi$
$929$	−30912.2	−	17847.2i	−1.09171	−	0.630298i	−0.934031	+	0.357193i	$0.883734\pi$
$930$	1550.68	−	6021.20i	0.0546762	−	0.212304i
$931$	−36415.3	+	21024.4i	−1.28192	+	0.740114i
$932$	24331.1	−	3893.85i	0.855141	−	0.136853i
$933$	−25381.4	−	1769.54i	−0.890620	−	0.0620922i
$934$	−15.0930	−	12.8696i	−0.000528755	−	0.000450864i
$935$	4231.74			0.148014
$936$	−8776.94	−	23273.9i	−0.306499	−	0.812746i
$937$	−4657.90			−0.162398			−0.0811991	−	0.996698i	$-0.525875\pi$
$937$	−4657.90			−0.162398			−0.0811991	+	0.996698i	$0.525875\pi$
$938$	870.326	+	742.117i	0.0302955	+	0.0258326i
$939$	1553.52	+	3183.50i	0.0539905	+	0.110639i
$940$	1178.09	−	188.537i	0.0408777	−	0.00654190i
$941$	22129.9	−	12776.7i	0.766645	−	0.442623i	−0.0650314	−	0.997883i	$-0.520715\pi$
$941$	22129.9	−	12776.7i	0.766645	−	0.442623i	0.831676	+	0.555260i	$0.187381\pi$
$942$	−21964.0	−	21540.3i	−0.759689	−	0.745032i
$943$	−39174.9	−	22617.6i	−1.35282	−	0.781051i
$944$	6753.33	+	6041.44i	0.232841	+	0.208297i
$945$	879.651	+	186.402i	0.0302805	+	0.00641658i
$946$	−39166.6	−	7226.48i	−1.34611	−	0.248365i
$947$	−26469.6	+	45846.6i	−0.908285	+	1.57319i	−0.0918380	+	0.995774i	$0.529274\pi$
$947$	−26469.6	+	45846.6i	−0.908285	+	1.57319i	−0.816447	+	0.577421i	$0.804059\pi$
$948$	−17898.2	−	25462.6i	−0.613192	−	0.872348i
$949$	−2534.42	−	4389.75i	−0.0866922	−	0.150155i
$950$	14118.7	+	39768.1i	0.482180	+	1.35816i
$951$	7247.85	−	3536.88i	0.247137	−	0.120600i
$952$	−1049.26	−	1921.42i	−0.0357214	−	0.0654133i
$953$			744.138i			0.0252938i	0.999920	+	0.0126469i	$0.00402574\pi$
$953$			744.138i			0.0252938i	−0.999920	+	0.0126469i	$0.995974\pi$
$954$	−25515.3	−	8502.67i	−0.865921	−	0.288558i
$955$			7435.63i			0.251949i
$956$	−32854.9	+	26693.1i	−1.11151	+	0.903051i
$957$	−3094.81	+	44390.5i	−0.104536	+	1.49941i
$958$	−15090.1	+	5357.36i	−0.508913	+	0.180677i
$959$	1957.04	+	3389.70i	0.0658980	+	0.114139i
$960$	−5887.95	+	2534.39i	−0.197951	+	0.0852051i
$961$	518.981	−	898.901i	0.0174207	−	0.0301736i
$962$	4165.60	−	22577.0i	0.139610	−	0.756666i
$963$	7935.85	+	19618.4i	0.265555	+	0.656486i
$964$	37390.3	+	14283.7i	1.24923	+	0.477228i
$965$	3410.28	+	1968.92i	0.113762	+	0.0656807i
$966$	−2035.37	−	7310.52i	−0.0677917	−	0.243491i
$967$	14044.5	−	8108.61i	0.467054	−	0.269654i	−0.247952	−	0.968772i	$-0.579757\pi$
$967$	14044.5	−	8108.61i	0.467054	−	0.269654i	0.715006	+	0.699119i	$0.246424\pi$
$968$	22632.5	+	537.936i	0.751485	+	0.0178615i
$969$	−13225.1	+	19615.8i	−0.438444	+	0.650311i
$970$	−6655.42	+	7805.22i	−0.220302	+	0.258361i
$971$	33620.7			1.11116			0.555582	−	0.831462i	$-0.312496\pi$
$971$	33620.7			1.11116			0.555582	+	0.831462i	$0.312496\pi$
$972$	−28626.7	+	9941.90i	−0.944653	+	0.328073i
$973$	−3400.28			−0.112033
$974$	−16667.6	+	19547.1i	−0.548321	+	0.643049i
$975$	14096.4	−	20908.2i	0.463023	−	0.686768i
$976$	202.209	−	966.619i	0.00663171	−	0.0317016i
$977$	18376.3	−	10609.6i	0.601751	−	0.347421i	−0.167979	−	0.985791i	$-0.553724\pi$
$977$	18376.3	−	10609.6i	0.601751	−	0.347421i	0.769730	+	0.638369i	$0.220391\pi$
$978$	−5789.12	−	20793.1i	−0.189280	−	0.679845i
$979$	−17431.8	−	10064.3i	−0.569074	−	0.328555i
$980$	2310.77	−	6048.85i	0.0753211	−	0.197167i
$981$	−16016.3	−	39594.4i	−0.521265	−	1.28863i
$982$	5233.39	−	28364.3i	0.170065	−	0.921733i
$983$	19149.3	−	33167.6i	0.621331	−	1.07618i	−0.367907	−	0.929862i	$-0.619926\pi$
$983$	19149.3	−	33167.6i	0.621331	−	1.07618i	0.989238	−	0.146314i	$-0.0467411\pi$
$984$	−22348.0	−	15852.3i	−0.724012	−	0.513571i
$985$	4036.68	+	6991.73i	0.130578	+	0.226168i
$986$	17194.4	−	6104.46i	0.555358	−	0.197166i
$987$	−59.4993	+	853.429i	−0.00191883	+	0.0275227i
$988$	−25708.7	−	31643.2i	−0.827836	−	1.01893i
$989$			56607.5i			1.82004i
$990$	8429.13	+	2808.91i	0.270601	+	0.0901747i
$991$		−	17803.2i		−	0.570674i	−0.958427	−	0.285337i	$-0.907894\pi$
$991$		−	17803.2i		−	0.570674i	0.958427	−	0.285337i	$-0.0921055\pi$
$992$	−31494.8	+	4275.47i	−1.00803	+	0.136841i
$993$	34565.3	−	16867.5i	1.10463	−	0.539048i
$994$	70.5633	+	198.756i	0.00225164	+	0.00634220i
$995$	−1260.89	−	2183.93i	−0.0401738	−	0.0695831i
$996$	11865.0	−	8340.16i	0.377467	−	0.265329i
$997$	−4517.89	+	7825.21i	−0.143513	+	0.248573i	−0.928817	−	0.370538i	$-0.879173\pi$
$997$	−4517.89	+	7825.21i	−0.143513	+	0.248573i	0.785304	+	0.619110i	$0.212507\pi$
$998$	7557.78	+	1394.46i	0.239717	+	0.0442292i
$999$	−27362.4	−	5798.24i	−0.866576	−	0.183632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.11.10	✓	24
3.2	odd	2		108.4.h.b.35.3		24
4.3	odd	2	inner	36.4.h.b.11.11	yes	24
9.2	odd	6		324.4.b.c.323.12		24
9.4	even	3		108.4.h.b.71.2		24
9.5	odd	6	inner	36.4.h.b.23.11	yes	24
9.7	even	3		324.4.b.c.323.13		24
12.11	even	2		108.4.h.b.35.2		24
36.7	odd	6		324.4.b.c.323.11		24
36.11	even	6		324.4.b.c.323.14		24
36.23	even	6	inner	36.4.h.b.23.10	yes	24
36.31	odd	6		108.4.h.b.71.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.10	✓	24	1.1	even	1	trivial
36.4.h.b.11.11	yes	24	4.3	odd	2	inner
36.4.h.b.23.10	yes	24	36.23	even	6	inner
36.4.h.b.23.11	yes	24	9.5	odd	6	inner
108.4.h.b.35.2		24	12.11	even	2
108.4.h.b.35.3		24	3.2	odd	2
108.4.h.b.71.2		24	9.4	even	3
108.4.h.b.71.3		24	36.31	odd	6
324.4.b.c.323.11		24	36.7	odd	6
324.4.b.c.323.12		24	9.2	odd	6
324.4.b.c.323.13		24	9.7	even	3
324.4.b.c.323.14		24	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15223 + 1.83518i) q^{2} +(2.90476 - 4.30841i) q^{3} +(1.26420 + 7.89948i) q^{4} +(2.08666 - 1.20474i) q^{5} +(14.1584 - 3.94193i) q^{6} +(-2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(-10.1248 - 25.0298i) q^{9} +O(q^{10})\)	\(q+(2.15223 + 1.83518i) q^{2} +(2.90476 - 4.30841i) q^{3} +(1.26420 + 7.89948i) q^{4} +(2.08666 - 1.20474i) q^{5} +(14.1584 - 3.94193i) q^{6} +(-2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(-10.1248 - 25.0298i) q^{9} +(6.70190 + 1.23654i) q^{10} +(-24.1428 + 41.8166i) q^{11} +(37.7064 + 17.4994i) q^{12} +(-20.3570 - 35.2594i) q^{13} +(-2.51714 - 7.09003i) q^{14} +(0.870754 - 12.4897i) q^{15} +(-60.8036 + 19.9731i) q^{16} -36.3729i q^{17} +(24.1433 - 72.4507i) q^{18} -125.173i q^{19} +(12.1548 + 14.9605i) q^{20} +(-12.4216 + 6.06163i) q^{21} +(-128.702 + 45.6925i) q^{22} +(97.0560 + 168.106i) q^{23} +(49.0383 + 106.861i) q^{24} +(-59.5972 + 103.225i) q^{25} +(20.8944 - 113.245i) q^{26} +(-137.248 - 29.0836i) q^{27} +(7.59405 - 19.8788i) q^{28} +(153.593 + 88.6772i) q^{29} +(24.7949 - 25.2827i) q^{30} +(152.058 - 87.7909i) q^{31} +(-167.518 - 68.5991i) q^{32} +(110.034 + 225.484i) q^{33} +(66.7510 - 78.2830i) q^{34} -6.40918 q^{35} +(184.922 - 111.623i) q^{36} +199.364 q^{37} +(229.716 - 269.402i) q^{38} +(-211.044 - 14.7136i) q^{39} +(-1.29548 + 54.5047i) q^{40} +(-201.816 + 116.518i) q^{41} +(-37.8585 - 9.74995i) q^{42} +(252.553 + 145.812i) q^{43} +(-360.851 - 137.851i) q^{44} +(-51.2813 - 40.0310i) q^{45} +(-99.6182 + 539.918i) q^{46} +(30.9476 - 53.6029i) q^{47} +(-90.5674 + 319.984i) q^{48} +(-167.962 - 290.919i) q^{49} +(-317.705 + 112.793i) q^{50} +(-156.709 - 105.655i) q^{51} +(252.795 - 205.385i) q^{52} -352.175i q^{53} +(-242.017 - 314.471i) q^{54} +116.343i q^{55} +(52.8254 - 28.8473i) q^{56} +(-539.298 - 363.598i) q^{57} +(167.830 + 472.726i) q^{58} +(-70.7911 - 122.614i) q^{59} +(99.7627 - 8.91095i) q^{60} +(-7.71518 + 13.3631i) q^{61} +(488.377 + 90.1086i) q^{62} +(-9.96583 + 71.1251i) q^{63} +(-234.645 - 455.067i) q^{64} +(-84.9565 - 49.0496i) q^{65} +(-176.986 + 687.228i) q^{66} +(-131.657 + 76.0120i) q^{67} +(287.327 - 45.9827i) q^{68} +(1006.19 + 70.1497i) q^{69} +(-13.7940 - 11.7620i) q^{70} -28.0331 q^{71} +(602.845 + 99.1275i) q^{72} +124.499 q^{73} +(429.078 + 365.870i) q^{74} +(271.622 + 556.614i) q^{75} +(988.804 - 158.244i) q^{76} +(111.232 - 64.2199i) q^{77} +(-427.213 - 418.971i) q^{78} +(-648.411 - 374.360i) q^{79} +(-102.814 + 114.929i) q^{80} +(-523.978 + 506.842i) q^{81} +(-648.187 - 119.595i) q^{82} +(174.444 - 302.146i) q^{83} +(-63.5872 - 90.4614i) q^{84} +(-43.8198 - 75.8981i) q^{85} +(275.962 + 777.302i) q^{86} +(828.210 - 404.158i) q^{87} +(-523.653 - 958.916i) q^{88} +416.864i q^{89} +(-36.9049 - 180.267i) q^{90} +108.299i q^{91} +(-1205.25 + 979.212i) q^{92} +(63.4532 - 910.140i) q^{93} +(164.978 - 58.5712i) q^{94} +(-150.801 - 261.195i) q^{95} +(-782.151 + 522.471i) q^{96} +(-752.565 + 1303.48i) q^{97} +(172.396 - 934.367i) q^{98} +(1291.10 + 180.905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

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