LMFDB - Embedded newform 121.4.c.h.27.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,4,Mod(3,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.3"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.2
Root			$2.86504 + 2.08157i$ of defining polynomial
Character	$\chi$	$=$	121.27
Dual form			121.4.c.h.9.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59435 + 4.90690i) q^{2} +(-3.67405 - 2.66936i) q^{3} +(-15.0635 + 10.9443i) q^{4} +(-2.66846 + 8.21268i) q^{5} +(7.24054 - 22.2841i) q^{6} +(-1.34505 + 0.977239i) q^{7} +(-44.3266 - 32.2052i) q^{8} +(-1.97025 - 6.06380i) q^{9} -44.5532 q^{10} +84.5585 q^{12} +(-8.84517 - 27.2226i) q^{13} +(-6.93969 - 5.04198i) q^{14} +(31.7267 - 23.0508i) q^{15} +(41.3254 - 127.186i) q^{16} +(2.42938 - 7.47686i) q^{17} +(26.6132 - 19.3356i) q^{18} +(-38.8386 - 28.2179i) q^{19} +(-49.6856 - 152.917i) q^{20} +7.55040 q^{21} -153.265 q^{23} +(76.8914 + 236.647i) q^{24} +(40.7996 + 29.6427i) q^{25} +(119.476 - 86.8047i) q^{26} +(-46.8385 + 144.154i) q^{27} +(9.56608 - 29.4414i) q^{28} +(-196.131 + 142.497i) q^{29} +(163.691 + 118.928i) q^{30} +(51.2794 + 157.822i) q^{31} +251.651 q^{32} +40.5614 q^{34} +(-4.43653 - 13.6542i) q^{35} +(96.0430 + 69.7793i) q^{36} +(55.6391 - 40.4242i) q^{37} +(76.5400 - 235.566i) q^{38} +(-40.1693 + 123.628i) q^{39} +(382.775 - 278.102i) q^{40} +(-248.811 - 180.772i) q^{41} +(12.0380 + 37.0490i) q^{42} -52.9746 q^{43} +55.0576 q^{45} +(-244.358 - 752.056i) q^{46} +(44.1194 + 32.0546i) q^{47} +(-491.338 + 356.978i) q^{48} +(-105.139 + 323.584i) q^{49} +(-80.4047 + 247.460i) q^{50} +(-28.8841 + 20.9855i) q^{51} +(431.173 + 313.265i) q^{52} +(77.3290 + 237.994i) q^{53} -782.025 q^{54} +91.0939 q^{56} +(67.3715 + 207.348i) q^{57} +(-1011.92 - 735.203i) q^{58} +(-306.711 + 222.839i) q^{59} +(-225.641 + 694.453i) q^{60} +(215.861 - 664.351i) q^{61} +(-692.657 + 503.245i) q^{62} +(8.57587 + 6.23074i) q^{63} +(70.6167 + 217.336i) q^{64} +247.174 q^{65} -278.021 q^{67} +(45.2340 + 139.216i) q^{68} +(563.105 + 409.120i) q^{69} +(59.9265 - 43.5392i) q^{70} +(-47.8053 + 147.130i) q^{71} +(-107.951 + 332.240i) q^{72} +(769.534 - 559.099i) q^{73} +(287.065 + 208.565i) q^{74} +(-70.7732 - 217.818i) q^{75} +893.872 q^{76} -670.675 q^{78} +(0.686168 + 2.11181i) q^{79} +(934.267 + 678.784i) q^{80} +(417.615 - 303.415i) q^{81} +(490.337 - 1509.10i) q^{82} +(-234.738 + 722.450i) q^{83} +(-113.736 + 82.6339i) q^{84} +(54.9224 + 39.9035i) q^{85} +(-84.4599 - 259.941i) q^{86} +1100.97 q^{87} +1157.64 q^{89} +(87.7809 + 270.162i) q^{90} +(38.5003 + 27.9721i) q^{91} +(2308.72 - 1677.38i) q^{92} +(232.879 - 716.728i) q^{93} +(-86.9470 + 267.595i) q^{94} +(335.384 - 243.671i) q^{95} +(-924.581 - 671.747i) q^{96} +(228.566 + 703.454i) q^{97} -1755.42 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 3 q^{3} - 17 q^{4} + 18 q^{5} - 14 q^{6} + 10 q^{7} - 113 q^{8} + 31 q^{9} + 40 q^{10} + 190 q^{12} + 40 q^{13} + 64 q^{14} + 119 q^{15} + 343 q^{16} - 201 q^{17} + 53 q^{18} - 302 q^{19}+ \cdots + 2740 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 - 3 * q^3 - 17 * q^4 + 18 * q^5 - 14 * q^6 + 10 * q^7 - 113 * q^8 + 31 * q^9 + 40 * q^10 + 190 * q^12 + 40 * q^13 + 64 * q^14 + 119 * q^15 + 343 * q^16 - 201 * q^17 + 53 * q^18 - 302 * q^19 - 88 * q^20 + 334 * q^21 - 12 * q^23 + 348 * q^24 + 214 * q^25 + 340 * q^26 + 72 * q^27 + 18 * q^28 - 164 * q^29 + 306 * q^30 + 324 * q^31 + 324 * q^32 - 298 * q^34 - 593 * q^35 - 125 * q^36 - 174 * q^37 - 327 * q^38 - 125 * q^39 + 282 * q^40 - 121 * q^41 - 590 * q^42 - 650 * q^43 + 452 * q^45 + 54 * q^46 + 12 * q^47 - 991 * q^48 - 1130 * q^49 + 1163 * q^50 + 194 * q^51 + 1600 * q^52 + 682 * q^53 - 3100 * q^54 - 1560 * q^56 - 333 * q^57 - 2348 * q^58 - 854 * q^59 - 502 * q^60 + 630 * q^61 - 2114 * q^62 + 67 * q^63 - 1289 * q^64 + 1790 * q^65 + 86 * q^67 - 575 * q^68 + 1198 * q^69 + 166 * q^70 - 1772 * q^71 + 104 * q^72 + 2425 * q^73 + 1274 * q^74 + 975 * q^75 - 242 * q^76 - 1340 * q^78 - 116 * q^79 + 1794 * q^80 - 26 * q^81 + 2708 * q^82 - 1738 * q^83 - 174 * q^84 - 1662 * q^85 - 784 * q^86 + 2310 * q^87 + 3782 * q^89 + 2658 * q^90 - 55 * q^91 + 5900 * q^92 + 2743 * q^93 - 1458 * q^94 - 487 * q^95 - 2383 * q^96 + 3116 * q^97 + 2740 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	1.59435	+	4.90690i	0.563687	+	1.73485i	0.671821	+	0.740713i	$0.265512\pi$
$2$	1.59435	+	4.90690i	0.563687	+	1.73485i	−0.108135	+	0.994136i	$0.534488\pi$
$3$	−3.67405	−	2.66936i	−0.707072	−	0.513718i	0.175156	−	0.984541i	$-0.443957\pi$
$3$	−3.67405	−	2.66936i	−0.707072	−	0.513718i	−0.882228	+	0.470823i	$0.843957\pi$
$4$	−15.0635	+	10.9443i	−1.88294	+	1.36804i
$5$	−2.66846	+	8.21268i	−0.238675	+	0.734565i	0.757938	+	0.652326i	$0.226207\pi$
$5$	−2.66846	+	8.21268i	−0.238675	+	0.734565i	−0.996613	+	0.0822383i	$0.973793\pi$
$6$	7.24054	−	22.2841i	0.492656	−	1.51624i
$7$	−1.34505	+	0.977239i	−0.0726261	+	0.0527660i	−0.623506	−	0.781819i	$-0.714292\pi$
$7$	−1.34505	+	0.977239i	−0.0726261	+	0.0527660i	0.550880	+	0.834585i	$0.314292\pi$
$8$	−44.3266	−	32.2052i	−1.95898	−	1.42328i
$9$	−1.97025	−	6.06380i	−0.0729721	−	0.224585i
$10$	−44.5532			−1.40890
$11$		0			0
$11$		0			0
$12$	84.5585			2.03416
$13$	−8.84517	−	27.2226i	−0.188708	−	0.580785i	0.811284	−	0.584652i	$-0.198769\pi$
$13$	−8.84517	−	27.2226i	−0.188708	−	0.580785i	−0.999993	+	0.00386737i	$0.998769\pi$
$14$	−6.93969	−	5.04198i	−0.132479	−	0.0962519i
$15$	31.7267	−	23.0508i	0.546119	−	0.396779i
$16$	41.3254	−	127.186i	0.645709	−	1.98729i
$17$	2.42938	−	7.47686i	0.0346595	−	0.106671i	−0.932230	−	0.361866i	$-0.882140\pi$
$17$	2.42938	−	7.47686i	0.0346595	−	0.106671i	0.966890	+	0.255195i	$0.0821397\pi$
$18$	26.6132	−	19.3356i	0.348488	−	0.253191i
$19$	−38.8386	−	28.2179i	−0.468957	−	0.340717i	0.328078	−	0.944651i	$-0.393599\pi$
$19$	−38.8386	−	28.2179i	−0.468957	−	0.340717i	−0.797035	+	0.603934i	$0.793599\pi$
$20$	−49.6856	−	152.917i	−0.555502	−	1.70966i
$21$	7.55040			0.0784587
$22$		0			0
$23$	−153.265			−1.38948			−0.694739	−	0.719262i	$-0.744480\pi$
$23$	−153.265			−1.38948			−0.694739	+	0.719262i	$0.744480\pi$
$24$	76.8914	+	236.647i	0.653974	+	2.01273i
$25$	40.7996	+	29.6427i	0.326397	+	0.237141i
$26$	119.476	−	86.8047i	0.901202	−	0.654761i
$27$	−46.8385	+	144.154i	−0.333854	+	1.02750i
$28$	9.56608	−	29.4414i	0.0645650	−	0.198711i
$29$	−196.131	+	142.497i	−1.25588	+	0.912452i	−0.998548	−	0.0538706i	$-0.982844\pi$
$29$	−196.131	+	142.497i	−1.25588	+	0.912452i	−0.257334	+	0.966322i	$0.582844\pi$
$30$	163.691	+	118.928i	0.996192	+	0.723776i
$31$	51.2794	+	157.822i	0.297098	+	0.914374i	0.982509	+	0.186217i	$0.0596228\pi$
$31$	51.2794	+	157.822i	0.297098	+	0.914374i	−0.685410	+	0.728157i	$0.740377\pi$
$32$	251.651			1.39019
$33$		0			0
$34$	40.5614			0.204595
$35$	−4.43653	−	13.6542i	−0.0214260	−	0.0659425i
$36$	96.0430	+	69.7793i	0.444644	+	0.323052i
$37$	55.6391	−	40.4242i	0.247216	−	0.179613i	−0.457276	−	0.889325i	$-0.651175\pi$
$37$	55.6391	−	40.4242i	0.247216	−	0.179613i	0.704492	+	0.709712i	$0.251175\pi$
$38$	76.5400	−	235.566i	0.326748	−	1.00563i
$39$	−40.1693	+	123.628i	−0.164929	+	0.507600i
$40$	382.775	−	278.102i	1.51305	−	1.09930i
$41$	−248.811	−	180.772i	−0.947750	−	0.688580i	0.00252390	−	0.999997i	$-0.499197\pi$
$41$	−248.811	−	180.772i	−0.947750	−	0.688580i	−0.950274	+	0.311416i	$0.899197\pi$
$42$	12.0380	+	37.0490i	0.0442261	+	0.136114i
$43$	−52.9746			−0.187873			−0.0939367	−	0.995578i	$-0.529945\pi$
$43$	−52.9746			−0.187873			−0.0939367	+	0.995578i	$0.529945\pi$
$44$		0			0
$45$	55.0576			0.182389
$46$	−244.358	−	752.056i	−0.783231	−	2.41054i
$47$	44.1194	+	32.0546i	0.136925	+	0.0994818i	0.654139	−	0.756374i	$-0.273031\pi$
$47$	44.1194	+	32.0546i	0.136925	+	0.0994818i	−0.517214	+	0.855856i	$0.673031\pi$
$48$	−491.338	+	356.978i	−1.47747	+	1.07344i
$49$	−105.139	+	323.584i	−0.306527	+	0.943392i
$50$	−80.4047	+	247.460i	−0.227419	+	0.699923i
$51$	−28.8841	+	20.9855i	−0.0793055	+	0.0576188i
$52$	431.173	+	313.265i	1.14986	+	0.835424i
$53$	77.3290	+	237.994i	0.200414	+	0.616811i	0.999871	+	0.0160872i	$0.00512095\pi$
$53$	77.3290	+	237.994i	0.200414	+	0.616811i	−0.799456	+	0.600724i	$0.794879\pi$
$54$	−782.025			−1.97074
$55$		0			0
$56$	91.0939			0.217374
$57$	67.3715	+	207.348i	0.156554	+	0.481823i
$58$	−1011.92	−	735.203i	−2.29089	−	1.66443i
$59$	−306.711	+	222.839i	−0.676786	+	0.491714i	−0.872290	−	0.488989i	$-0.837366\pi$
$59$	−306.711	+	222.839i	−0.676786	+	0.491714i	0.195504	+	0.980703i	$0.437366\pi$
$60$	−225.641	+	694.453i	−0.485503	+	1.49422i
$61$	215.861	−	664.351i	0.453084	−	1.39445i	−0.420285	−	0.907392i	$-0.638070\pi$
$61$	215.861	−	664.351i	0.453084	−	1.39445i	0.873369	−	0.487058i	$-0.161930\pi$
$62$	−692.657	+	503.245i	−1.41883	+	1.03084i
$63$	8.57587	+	6.23074i	0.0171501	+	0.0124603i
$64$	70.6167	+	217.336i	0.137923	+	0.424484i
$65$	247.174			0.471664
$66$		0			0
$67$	−278.021			−0.506949			−0.253475	−	0.967342i	$-0.581573\pi$
$67$	−278.021			−0.506949			−0.253475	+	0.967342i	$0.581573\pi$
$68$	45.2340	+	139.216i	0.0806680	+	0.248271i
$69$	563.105	+	409.120i	0.982462	+	0.713800i
$70$	59.9265	−	43.5392i	0.102323	−	0.0743418i
$71$	−47.8053	+	147.130i	−0.0799077	+	0.245931i	−0.983028	−	0.183458i	$-0.941271\pi$
$71$	−47.8053	+	147.130i	−0.0799077	+	0.245931i	0.903120	+	0.429388i	$0.141271\pi$
$72$	−107.951	+	332.240i	−0.176697	+	0.543818i
$73$	769.534	−	559.099i	1.23380	−	0.896406i	0.236628	−	0.971600i	$-0.423958\pi$
$73$	769.534	−	559.099i	1.23380	−	0.896406i	0.997169	+	0.0751945i	$0.0239578\pi$
$74$	287.065	+	208.565i	0.450955	+	0.327638i
$75$	−70.7732	−	217.818i	−0.108963	−	0.335352i
$76$	893.872			1.34913
$77$		0			0
$78$	−670.675			−0.973577
$79$	0.686168	+	2.11181i	0.000977215	+	0.00300756i	0.951544	−	0.307513i	$-0.0994967\pi$
$79$	0.686168	+	2.11181i	0.000977215	+	0.00300756i	−0.950567	+	0.310520i	$0.899497\pi$
$80$	934.267	+	678.784i	1.30568	+	0.948630i
$81$	417.615	−	303.415i	0.572860	−	0.416207i
$82$	490.337	−	1509.10i	0.660349	−	2.03235i
$83$	−234.738	+	722.450i	−0.310432	+	0.955412i	0.667162	+	0.744913i	$0.267509\pi$
$83$	−234.738	+	722.450i	−0.310432	+	0.955412i	−0.977594	+	0.210499i	$0.932491\pi$
$84$	−113.736	+	82.6339i	−0.147733	+	0.107335i
$85$	54.9224	+	39.9035i	0.0700843	+	0.0509193i
$86$	−84.4599	−	259.941i	−0.105902	−	0.325932i
$87$	1100.97			1.35674
$88$		0			0
$89$	1157.64			1.37876			0.689382	−	0.724398i	$-0.257882\pi$
$89$	1157.64			1.37876			0.689382	+	0.724398i	$0.257882\pi$
$90$	87.7809	+	270.162i	0.102810	+	0.316417i
$91$	38.5003	+	27.9721i	0.0443508	+	0.0322228i
$92$	2308.72	−	1677.38i	2.61631	−	1.90086i
$93$	232.879	−	716.728i	0.259661	−	0.799153i
$94$	−86.9470	+	267.595i	−0.0954032	+	0.293621i
$95$	335.384	−	243.671i	0.362207	−	0.263159i
$96$	−924.581	−	671.747i	−0.982965	−	0.714166i
$97$	228.566	+	703.454i	0.239251	+	0.736339i	0.996529	+	0.0832464i	$0.0265288\pi$
$97$	228.566	+	703.454i	0.239251	+	0.736339i	−0.757278	+	0.653093i	$0.773471\pi$
$98$	−1755.42			−1.80943
$99$		0			0
$100$	−939.006			−0.939006
$101$	190.422	+	586.057i	0.187600	+	0.577375i	0.999983	−	0.00574932i	$-0.00183008\pi$
$101$	190.422	+	586.057i	0.187600	+	0.577375i	−0.812383	+	0.583124i	$0.801830\pi$
$102$	−149.025	−	108.273i	−0.144663	−	0.105104i
$103$	−1235.79	+	897.853i	−1.18219	+	0.858914i	−0.992417	−	0.122914i	$-0.960776\pi$
$103$	−1235.79	+	897.853i	−1.18219	+	0.858914i	−0.189776	+	0.981827i	$0.560776\pi$
$104$	−484.634	+	1491.55i	−0.456945	+	1.40633i
$105$	−20.1480	+	62.0091i	−0.0187261	+	0.0576330i
$106$	−1044.52	+	758.890i	−0.957104	+	0.695377i
$107$	60.3407	+	43.8401i	0.0545174	+	0.0396092i	0.614710	−	0.788753i	$-0.289273\pi$
$107$	60.3407	+	43.8401i	0.0545174	+	0.0396092i	−0.560193	+	0.828362i	$0.689273\pi$
$108$	−872.112	−	2684.08i	−0.777028	−	2.39145i
$109$	583.022			0.512325			0.256162	−	0.966634i	$-0.417542\pi$
$109$	583.022			0.512325			0.256162	+	0.966634i	$0.417542\pi$
$110$		0			0
$111$	−312.328			−0.267070
$112$	68.7067	+	211.457i	0.0579658	+	0.178400i
$113$	147.565	+	107.212i	0.122847	+	0.0892536i	0.647512	−	0.762055i	$-0.275809\pi$
$113$	147.565	+	107.212i	0.122847	+	0.0892536i	−0.524665	+	0.851309i	$0.675809\pi$
$114$	−910.022	+	661.169i	−0.747643	+	0.543195i
$115$	408.983	−	1258.72i	0.331633	−	1.02066i
$116$	1394.89	−	4293.03i	1.11649	−	3.43619i
$117$	−147.645	+	107.271i	−0.116665	+	0.0847622i
$118$	−1582.45	−	1149.72i	−1.23455	−	0.896950i
$119$	4.03903	+	12.4309i	0.00311141	+	0.00957593i
$120$	−2148.69			−1.63456
$121$		0			0
$122$	3604.06			2.67456
$123$	431.601	+	1328.33i	0.316391	+	0.973752i
$124$	−2499.70	−	1816.14i	−1.81032	−	1.31527i
$125$	−1225.58	+	890.439i	−0.876957	+	0.637146i
$126$	−16.9007	+	52.0149i	−0.0119494	+	0.0367766i
$127$	−44.8164	+	137.931i	−0.0313135	+	0.0963730i	−0.965492	−	0.260434i	$-0.916134\pi$
$127$	−44.8164	+	137.931i	−0.0313135	+	0.0963730i	0.934178	+	0.356807i	$0.116134\pi$
$128$	674.865	−	490.318i	0.466017	−	0.338582i
$129$	194.632	+	141.408i	0.132840	+	0.0965139i
$130$	394.081	+	1212.86i	0.265871	+	0.818266i
$131$	−2.12942			−0.00142022			−0.000710109	−	1.00000i	$-0.500226\pi$
$131$	−2.12942			−0.00142022			−0.000710109		1.00000i	$0.500226\pi$
$132$		0			0
$133$	79.8156			0.0520368
$134$	−443.261	−	1364.22i	−0.285761	−	0.879481i
$135$	−1058.90	−	769.339i	−0.675081	−	0.490475i
$136$	−348.480	+	253.186i	−0.219720	+	0.159636i
$137$	−122.960	+	378.432i	−0.0766803	+	0.235998i	−0.982048	−	0.188631i	$-0.939595\pi$
$137$	−122.960	+	378.432i	−0.0766803	+	0.235998i	0.905368	+	0.424628i	$0.139595\pi$
$138$	−1109.72	+	3415.37i	−0.684535	+	2.10678i
$139$	−211.328	+	153.539i	−0.128954	+	0.0936907i	−0.650393	−	0.759598i	$-0.725396\pi$
$139$	−211.328	+	153.539i	−0.128954	+	0.0936907i	0.521438	+	0.853289i	$0.325396\pi$
$140$	216.266	+	157.126i	0.130556	+	0.0948543i
$141$	−76.5318	−	235.541i	−0.0457102	−	0.140682i
$142$	−798.168			−0.471695
$143$		0			0
$144$	−852.654			−0.493434
$145$	−646.918	−	1991.01i	−0.370508	−	1.14031i
$146$	3970.35	+	2884.63i	2.25060	+	1.63516i
$147$	1250.05	−	908.211i	0.701374	−	0.509578i
$148$	−395.707	+	1217.86i	−0.219777	+	0.676403i
$149$	292.953	−	901.617i	0.161072	−	0.495727i	−0.837654	−	0.546202i	$-0.816073\pi$
$149$	292.953	−	901.617i	0.161072	−	0.495727i	0.998725	+	0.0504743i	$0.0160733\pi$
$150$	955.971	−	694.554i	0.520365	−	0.378067i
$151$	−1468.52	−	1066.94i	−0.791434	−	0.575010i	0.116955	−	0.993137i	$-0.462687\pi$
$151$	−1468.52	−	1066.94i	−0.791434	−	0.575010i	−0.908389	+	0.418127i	$0.862687\pi$
$152$	812.822	+	2501.61i	0.433740	+	1.33492i
$153$	−50.1247			−0.0264859
$154$		0			0
$155$	−1432.98			−0.742577
$156$	−747.935	−	2301.91i	−0.383864	−	1.18141i
$157$	747.989	+	543.446i	0.380229	+	0.276253i	0.761440	−	0.648235i	$-0.224493\pi$
$157$	747.989	+	543.446i	0.380229	+	0.276253i	−0.381211	+	0.924488i	$0.624493\pi$
$158$	−9.26844	+	6.73391i	−0.00466682	+	0.00339064i
$159$	351.180	−	1080.82i	0.175160	−	0.539086i
$160$	−671.522	+	2066.73i	−0.331803	+	1.02119i
$161$	206.150	−	149.777i	0.100912	−	0.0733172i
$162$	2154.65	+	1565.44i	1.04497	+	0.759215i
$163$	−906.046	−	2788.52i	−0.435380	−	1.33996i	−0.892696	−	0.450659i	$-0.851189\pi$
$163$	−906.046	−	2788.52i	−0.435380	−	1.33996i	0.457316	−	0.889304i	$-0.348811\pi$
$164$	5726.40			2.72656
$165$		0			0
$166$	−3919.24			−1.83248
$167$	340.142	+	1046.85i	0.157611	+	0.485076i	0.998416	−	0.0562619i	$-0.0179182\pi$
$167$	340.142	+	1046.85i	0.157611	+	0.485076i	−0.840805	+	0.541337i	$0.817918\pi$
$168$	−334.684	−	243.162i	−0.153699	−	0.111669i
$169$	1114.58	−	809.786i	0.507317	−	0.368587i
$170$	−108.237	+	333.118i	−0.0488316	+	0.150288i
$171$	−94.5859	+	291.106i	−0.0422992	+	0.130184i
$172$	797.986	−	579.770i	0.353755	−	0.257018i
$173$	2920.84	+	2122.11i	1.28363	+	0.932609i	0.999656	−	0.0262248i	$-0.00834856\pi$
$173$	2920.84	+	2122.11i	1.28363	+	0.932609i	0.283969	+	0.958833i	$0.408349\pi$
$174$	1755.33	+	5402.35i	0.764778	+	2.35374i
$175$	−83.8457			−0.0362179
$176$		0			0
$177$	1721.71			0.731139
$178$	1845.69	+	5680.44i	0.777191	+	2.39195i
$179$	−2775.32	−	2016.39i	−1.15887	−	0.841967i	−0.169233	−	0.985576i	$-0.554129\pi$
$179$	−2775.32	−	2016.39i	−1.15887	−	0.841967i	−0.989634	+	0.143609i	$0.954129\pi$
$180$	−829.363	+	602.567i	−0.343428	+	0.249515i
$181$	−1145.06	+	3524.14i	−0.470231	+	1.44722i	0.382051	+	0.924141i	$0.375218\pi$
$181$	−1145.06	+	3524.14i	−0.470231	+	1.44722i	−0.852282	+	0.523082i	$0.824782\pi$
$182$	−75.8733	+	233.514i	−0.0309017	+	0.0951055i
$183$	−2566.48	+	1864.65i	−1.03672	+	0.753220i
$184$	6793.73	+	4935.94i	2.72196	+	1.97762i
$185$	183.520	+	564.817i	0.0729333	+	0.224466i
$186$	3888.20			1.53278
$187$		0			0
$188$	−1015.41			−0.393917
$189$	−77.8726	−	239.667i	−0.0299704	−	0.0922393i
$190$	1730.38	+	1257.20i	0.660712	+	0.480035i
$191$	2458.79	−	1786.41i	0.931474	−	0.676755i	−0.0148796	−	0.999889i	$-0.504736\pi$
$191$	2458.79	−	1786.41i	0.931474	−	0.676755i	0.946353	+	0.323134i	$0.104736\pi$
$192$	320.697	−	987.005i	0.120543	−	0.370994i
$193$	−216.124	+	665.161i	−0.0806059	+	0.248080i	−0.983236	−	0.182338i	$-0.941634\pi$
$193$	−216.124	+	665.161i	−0.0806059	+	0.248080i	0.902630	+	0.430417i	$0.141634\pi$
$194$	−3087.36	+	2243.10i	−1.14257	+	0.830129i
$195$	−908.131	−	659.795i	−0.333500	−	0.242302i
$196$	−1957.64	−	6024.98i	−0.713424	−	2.19569i
$197$	−4239.08			−1.53311			−0.766553	−	0.642181i	$-0.778030\pi$
$197$	−4239.08			−1.53311			−0.766553	+	0.642181i	$0.778030\pi$
$198$		0			0
$199$	−2020.32			−0.719680			−0.359840	−	0.933014i	$-0.617169\pi$
$199$	−2020.32			−0.719680			−0.359840	+	0.933014i	$0.617169\pi$
$200$	−853.863	−	2627.92i	−0.301886	−	0.929110i
$201$	1021.46	+	742.136i	0.358450	+	0.260429i
$202$	−2572.12	+	1868.76i	−0.895911	+	0.650917i
$203$	124.553	−	383.334i	0.0430634	−	0.132536i
$204$	205.425	−	632.232i	0.0705030	−	0.216986i
$205$	2148.56	−	1561.02i	0.732011	−	0.531837i
$206$	−6375.95	−	4632.40i	−2.15647	−	1.56677i
$207$	301.970	+	929.370i	0.101393	+	0.312056i
$208$	−3827.88			−1.27604
$209$		0			0
$210$	−336.395			−0.110540
$211$	−1708.15	−	5257.15i	−0.557317	−	1.71525i	−0.689744	−	0.724053i	$-0.742277\pi$
$211$	−1708.15	−	5257.15i	−0.557317	−	1.71525i	0.132427	−	0.991193i	$-0.457723\pi$
$212$	−3769.53	−	2738.72i	−1.22119	−	0.887246i
$213$	568.381	−	412.953i	0.182839	−	0.132841i
$214$	−118.915	+	365.982i	−0.0379853	+	0.116907i
$215$	141.361	−	435.064i	0.0448406	−	0.138005i
$216$	6718.70	−	4881.42i	2.11643	−	1.53768i
$217$	−223.203	−	162.166i	−0.0698249	−	0.0507308i
$218$	929.539	+	2860.83i	0.288791	+	0.888806i
$219$	−4319.75			−1.33288
$220$		0			0
$221$	−225.028			−0.0684934
$222$	−497.958	−	1532.56i	−0.150544	−	0.463327i
$223$	2647.49	+	1923.51i	0.795018	+	0.577614i	0.909448	−	0.415817i	$-0.136504\pi$
$223$	2647.49	+	1923.51i	0.795018	+	0.577614i	−0.114430	+	0.993431i	$0.536504\pi$
$224$	−338.485	+	245.924i	−0.100964	+	0.0733547i
$225$	99.3618	−	305.804i	0.0294405	−	0.0906087i
$226$	−290.809	+	895.017i	−0.0855943	+	0.263432i
$227$	−4562.93	+	3315.16i	−1.33415	+	0.969317i	−0.334512	+	0.942391i	$0.608572\pi$
$227$	−4562.93	+	3315.16i	−1.33415	+	0.969317i	−0.999637	+	0.0269252i	$0.991428\pi$
$228$	−3284.13	−	2386.06i	−0.953934	−	0.693074i
$229$	337.455	+	1038.58i	0.0973784	+	0.299700i	0.987866	−	0.155307i	$-0.0496367\pi$
$229$	337.455	+	1038.58i	0.0973784	+	0.299700i	−0.890488	+	0.455007i	$0.849637\pi$
$230$	6828.46			1.95763
$231$		0			0
$232$	13283.0			3.75892
$233$	−508.566	−	1565.21i	−0.142993	−	0.440086i	0.853755	−	0.520675i	$-0.174320\pi$
$233$	−508.566	−	1565.21i	−0.142993	−	0.440086i	−0.996747	+	0.0805894i	$0.974320\pi$
$234$	−761.764	−	553.454i	−0.212812	−	0.154617i
$235$	−380.985	+	276.802i	−0.105756	+	0.0768365i
$236$	2181.34	−	6713.48i	0.601666	−	1.85174i
$237$	3.11615	−	9.59053i	0.000854075	−	0.00262857i
$238$	−54.5574	+	39.6382i	−0.0148589	+	0.0107957i
$239$	−659.274	−	478.991i	−0.178430	−	0.129637i	0.494985	−	0.868901i	$-0.335174\pi$
$239$	−659.274	−	478.991i	−0.178430	−	0.129637i	−0.673416	+	0.739264i	$0.735174\pi$
$240$	−1620.63	−	4987.78i	−0.435880	−	1.34150i
$241$	−6368.48			−1.70220			−0.851100	−	0.525004i	$-0.824064\pi$
$241$	−6368.48			−1.70220			−0.851100	+	0.525004i	$0.824064\pi$
$242$		0			0
$243$	1748.19			0.461509
$244$	4019.24	+	12369.9i	1.05453	+	3.24551i
$245$	−2376.93	−	1726.94i	−0.619823	−	0.450327i
$246$	−5829.86	+	4235.64i	−1.51097	+	1.09778i
$247$	−424.631	+	1306.88i	−0.109387	+	0.336659i
$248$	2809.63	−	8647.16i	0.719403	−	2.21409i
$249$	2790.92	−	2027.72i	0.710310	−	0.516071i
$250$	−6323.30	−	4594.14i	−1.59968	−	1.16224i
$251$	−195.714	−	602.345i	−0.0492165	−	0.151473i	0.923428	−	0.383772i	$-0.125375\pi$
$251$	−195.714	−	602.345i	−0.0492165	−	0.151473i	−0.972644	+	0.232299i	$0.925375\pi$
$252$	−197.374			−0.0493389
$253$		0			0
$254$	−748.264			−0.184844
$255$	−95.2713	−	293.215i	−0.0233966	−	0.0720072i
$256$	4960.93	+	3604.32i	1.21116	+	0.879962i
$257$	−369.839	+	268.704i	−0.0897663	+	0.0652190i	−0.631763	−	0.775162i	$-0.717668\pi$
$257$	−369.839	+	268.704i	−0.0897663	+	0.0652190i	0.541997	+	0.840381i	$0.317668\pi$
$258$	−383.565	+	1180.49i	−0.0925570	+	0.284861i
$259$	−35.3335	+	108.745i	−0.00847690	+	0.0260892i
$260$	−3723.32	+	2705.15i	−0.888116	+	0.645254i
$261$	1250.50	+	908.543i	0.296568	+	0.215469i
$262$	−3.39504	−	10.4489i	−0.000800558	−	0.00246386i
$263$	6954.78			1.63061			0.815305	−	0.579032i	$-0.196570\pi$
$263$	6954.78			1.63061			0.815305	+	0.579032i	$0.196570\pi$
$264$		0			0
$265$	−2160.92			−0.500922
$266$	127.254	+	391.647i	0.0293324	+	0.0902760i
$267$	−4253.25	−	3090.16i	−0.974886	−	0.708296i
$268$	4187.98	−	3042.74i	0.954557	−	0.693526i
$269$	−1366.25	+	4204.88i	−0.309671	+	0.953071i	0.668221	+	0.743963i	$0.267056\pi$
$269$	−1366.25	+	4204.88i	−0.309671	+	0.953071i	−0.977893	+	0.209108i	$0.932944\pi$
$270$	2086.81	−	6422.53i	0.470366	−	1.44764i
$271$	−2827.80	+	2054.52i	−0.633863	+	0.460528i	−0.857736	−	0.514090i	$-0.828130\pi$
$271$	−2827.80	+	2054.52i	−0.633863	+	0.460528i	0.223873	+	0.974618i	$0.428130\pi$
$272$	−850.560	−	617.968i	−0.189606	−	0.137757i
$273$	−66.7846	−	205.542i	−0.0148058	−	0.0455676i
$274$	−2052.97			−0.452644
$275$		0			0
$276$	−12959.9			−2.82643
$277$	847.902	+	2609.57i	0.183919	+	0.566043i	0.999928	−	0.0119952i	$-0.00381829\pi$
$277$	847.902	+	2609.57i	0.183919	+	0.566043i	−0.816009	+	0.578039i	$0.803818\pi$
$278$	−1090.33	−	792.171i	−0.235229	−	0.170904i
$279$	855.966	−	621.895i	0.183675	−	0.133448i
$280$	−243.081	+	748.126i	−0.0518816	+	0.159675i
$281$	−540.634	+	1663.90i	−0.114774	+	0.353239i	−0.991900	−	0.127022i	$-0.959458\pi$
$281$	−540.634	+	1663.90i	−0.114774	+	0.353239i	0.877126	+	0.480261i	$0.159458\pi$
$282$	1033.76	−	751.067i	0.218295	−	0.158601i
$283$	1678.00	+	1219.14i	0.352463	+	0.256079i	0.749902	−	0.661549i	$-0.230101\pi$
$283$	1678.00	+	1219.14i	0.352463	+	0.256079i	−0.397439	+	0.917629i	$0.630101\pi$
$284$	−890.114	−	2739.49i	−0.185981	−	0.572390i
$285$	−1882.66			−0.391296
$286$		0			0
$287$	511.321			0.105165
$288$	−495.816	−	1525.96i	−0.101445	−	0.312216i
$289$	3924.70	+	2851.46i	0.798840	+	0.580391i
$290$	8738.26	−	6348.72i	1.76941	−	1.28555i
$291$	1038.01	−	3194.65i	0.209103	−	0.643553i
$292$	−5472.96	+	16844.0i	−1.09685	+	3.37576i
$293$	2849.04	−	2069.95i	0.568064	−	0.412723i	−0.266337	−	0.963880i	$-0.585814\pi$
$293$	2849.04	−	2069.95i	0.568064	−	0.412723i	0.834401	+	0.551157i	$0.185814\pi$
$294$	6449.50	+	4685.84i	1.27940	+	0.929536i
$295$	−1011.66	−	3113.56i	−0.199664	−	0.614503i
$296$	−3768.16			−0.739932
$297$		0			0
$298$	4891.21			0.950806
$299$	1355.66	+	4172.28i	0.262206	+	0.806988i
$300$	3449.96	+	2506.54i	0.663945	+	0.482384i
$301$	71.2537	−	51.7689i	0.0136445	−	0.00991332i
$302$	2894.05	−	8906.96i	0.551436	−	1.69714i
$303$	864.777	−	2661.51i	0.163961	−	0.504619i
$304$	−5193.95	+	3773.62i	−0.979912	+	0.711948i
$305$	4880.09	+	3545.59i	0.916175	+	0.665640i
$306$	−79.9161	−	245.956i	−0.0149297	−	0.0459490i
$307$	6944.40			1.29100			0.645501	−	0.763759i	$-0.276648\pi$
$307$	6944.40			1.29100			0.645501	+	0.763759i	$0.276648\pi$
$308$		0			0
$309$	6937.05			1.27714
$310$	−2284.66	−	7031.46i	−0.418581	−	1.28826i
$311$	−1852.70	−	1346.06i	−0.337803	−	0.245428i	0.405931	−	0.913904i	$-0.366947\pi$
$311$	−1852.70	−	1346.06i	−0.337803	−	0.245428i	−0.743734	+	0.668475i	$0.766947\pi$
$312$	5762.05	−	4186.37i	1.04555	−	0.759637i
$313$	2447.15	−	7531.54i	0.441920	−	1.36009i	−0.443907	−	0.896073i	$-0.646408\pi$
$313$	2447.15	−	7531.54i	0.441920	−	1.36009i	0.885827	−	0.464016i	$-0.153592\pi$
$314$	−1474.08	+	4536.74i	−0.264927	+	0.815361i
$315$	−74.0555	+	53.8044i	−0.0132462	+	0.00962393i
$316$	−33.4484	−	24.3017i	−0.00595449	−	0.00432619i
$317$	−428.726	−	1319.48i	−0.0759610	−	0.233784i	0.905865	−	0.423566i	$-0.139222\pi$
$317$	−428.726	−	1319.48i	−0.0759610	−	0.233784i	−0.981826	+	0.189782i	$0.939222\pi$
$318$	5863.38			1.03397
$319$		0			0
$320$	−1973.35			−0.344730
$321$	−104.670	−	322.142i	−0.0181998	−	0.0560131i
$322$	1063.61	+	772.761i	0.184077	+	0.133740i
$323$	−305.335	+	221.839i	−0.0525984	+	0.0382150i
$324$	−2970.09	+	9141.01i	−0.509275	+	1.56739i
$325$	446.072	−	1372.87i	0.0761342	−	0.234317i
$326$	12238.4	−	8891.75i	2.07922	−	1.51064i
$327$	−2142.05	−	1556.29i	−0.362250	−	0.263190i
$328$	5207.17	+	16026.0i	0.876578	+	2.69783i
$329$	−90.6680			−0.0151936
$330$		0			0
$331$	−11641.4			−1.93315			−0.966574	−	0.256389i	$-0.917467\pi$
$331$	−11641.4			−1.93315			−0.966574	+	0.256389i	$0.917467\pi$
$332$	−4370.72	−	13451.7i	−0.722514	−	2.22367i
$333$	−354.747	−	257.739i	−0.0583784	−	0.0424144i
$334$	−4594.47	+	3338.08i	−0.752690	+	0.546861i
$335$	741.888	−	2283.29i	0.120996	−	0.372387i
$336$	312.023	−	960.309i	0.0506615	−	0.155920i
$337$	6858.29	−	4982.84i	1.10859	−	0.805438i	0.126149	−	0.992011i	$-0.459738\pi$
$337$	6858.29	−	4982.84i	1.10859	−	0.805438i	0.982441	+	0.186574i	$0.0597383\pi$
$338$	5750.56	+	4178.02i	0.925411	+	0.672351i
$339$	−255.973	−	787.805i	−0.0410105	−	0.126217i
$340$	−1264.04			−0.201624
$341$		0			0
$342$	−1579.23			−0.249692
$343$	−351.023	−	1080.34i	−0.0552579	−	0.170066i
$344$	2348.19	+	1706.06i	0.368040	+	0.267397i
$345$	−4862.59	+	3532.88i	−0.758821	+	0.551316i
$346$	−5756.16	+	17715.6i	−0.894373	+	2.75260i
$347$	−590.536	+	1817.48i	−0.0913591	+	0.281175i	−0.986288	−	0.165035i	$-0.947226\pi$
$347$	−590.536	+	1817.48i	−0.0913591	+	0.281175i	0.894929	+	0.446209i	$0.147226\pi$
$348$	−16584.5	+	12049.4i	−2.55467	+	1.85608i
$349$	−6978.67	−	5070.30i	−1.07037	−	0.777671i	−0.0943926	−	0.995535i	$-0.530091\pi$
$349$	−6978.67	−	5070.30i	−1.07037	−	0.777671i	−0.975979	+	0.217865i	$0.930091\pi$
$350$	−133.679	−	411.422i	−0.0204156	−	0.0628327i
$351$	4338.55			0.659756
$352$		0			0
$353$	6345.10			0.956702			0.478351	−	0.878169i	$-0.341235\pi$
$353$	6345.10			0.956702			0.478351	+	0.878169i	$0.341235\pi$
$354$	2745.00	+	8448.25i	0.412133	+	1.26842i
$355$	−1080.76	−	785.220i	−0.161580	−	0.117395i
$356$	−17438.2	+	12669.6i	−2.59613	+	1.88620i
$357$	18.3428	−	56.4533i	0.00271934	−	0.00836926i
$358$	5469.39	−	16833.0i	0.807447	−	2.48507i
$359$	−3699.07	+	2687.53i	−0.543814	+	0.395104i	−0.825500	−	0.564403i	$-0.809107\pi$
$359$	−3699.07	+	2687.53i	−0.543814	+	0.395104i	0.281685	+	0.959507i	$0.409107\pi$
$360$	−2440.52	−	1773.14i	−0.357296	−	0.259591i
$361$	−1407.36	−	4331.41i	−0.205185	−	0.631493i
$362$	−19118.2			−2.77578
$363$		0			0
$364$	−886.085			−0.127592
$365$	2538.23	+	7811.88i	0.363992	+	1.12025i
$366$	−13241.5	−	9620.52i	−1.89111	−	1.37397i
$367$	−1153.15	+	837.814i	−0.164016	+	0.119165i	−0.666766	−	0.745267i	$-0.732322\pi$
$367$	−1153.15	+	837.814i	−0.164016	+	0.119165i	0.502749	+	0.864432i	$0.332322\pi$
$368$	−6333.74	+	19493.3i	−0.897199	+	2.76129i
$369$	−605.944	+	1864.90i	−0.0854856	+	0.263098i
$370$	−2478.90	+	1801.03i	−0.348303	+	0.253057i
$371$	−336.589	−	244.546i	−0.0471019	−	0.0342216i
$372$	4336.11	+	13345.2i	0.604346	+	1.85999i
$373$	8121.64			1.12741			0.563703	−	0.825977i	$-0.309376\pi$
$373$	8121.64			1.12741			0.563703	+	0.825977i	$0.309376\pi$
$374$		0			0
$375$	6879.76			0.947385
$376$	−923.339	−	2841.75i	−0.126643	−	0.389766i
$377$	5613.97	+	4078.79i	0.766934	+	0.557210i
$378$	1051.87	−	764.226i	0.143127	−	0.103988i
$379$	1636.89	−	5037.82i	0.221850	−	0.682785i	−0.776746	−	0.629814i	$-0.783131\pi$
$379$	1636.89	−	5037.82i	0.221850	−	0.682785i	0.998596	−	0.0529706i	$-0.0168690\pi$
$380$	−2385.26	+	7341.09i	−0.322004	+	0.991026i
$381$	532.844	−	387.134i	0.0716494	−	0.0520564i
$382$	12685.9	+	9216.84i	1.69913	+	1.23449i
$383$	3410.71	+	10497.1i	0.455037	+	1.40046i	0.871092	+	0.491120i	$0.163412\pi$
$383$	3410.71	+	10497.1i	0.455037	+	1.40046i	−0.416055	+	0.909340i	$0.636588\pi$
$384$	−3788.33			−0.503443
$385$		0			0
$386$	−3608.45			−0.475817
$387$	104.373	+	321.227i	0.0137095	+	0.0421936i
$388$	−11141.8	−	8095.01i	−1.45784	−	1.05918i
$389$	−8996.72	+	6536.50i	−1.17263	+	0.851963i	−0.991321	−	0.131464i	$-0.958032\pi$
$389$	−8996.72	+	6536.50i	−1.17263	+	0.851963i	−0.181306	+	0.983427i	$0.558032\pi$
$390$	1789.67	−	5508.04i	0.232368	−	0.715156i
$391$	−372.339	+	1145.94i	−0.0481586	+	0.148217i
$392$	15081.5	−	10957.4i	1.94319	−	1.41181i
$393$	7.82361	+	5.68419i	0.00100420	+	0.000729591i
$394$	−6758.56	−	20800.7i	−0.864192	−	2.65971i
$395$	−19.1746			−0.00244248
$396$		0			0
$397$	−2320.56			−0.293364			−0.146682	−	0.989184i	$-0.546859\pi$
$397$	−2320.56			−0.293364			−0.146682	+	0.989184i	$0.546859\pi$
$398$	−3221.08	−	9913.48i	−0.405674	−	1.24854i
$399$	−293.247	−	213.056i	−0.0367938	−	0.0267322i
$400$	5456.20	−	3964.16i	0.682026	−	0.495521i
$401$	150.709	−	463.834i	0.0187682	−	0.0577625i	−0.941234	−	0.337756i	$-0.890332\pi$
$401$	150.709	−	463.834i	0.0187682	−	0.0577625i	0.960002	+	0.279993i	$0.0903322\pi$
$402$	−2013.02	+	6195.43i	−0.249752	+	0.768657i
$403$	3842.75	−	2791.92i	0.474990	−	0.345100i
$404$	−9282.41	−	6744.07i	−1.14311	−	0.830519i
$405$	1377.46	+	4239.39i	0.169004	+	0.520141i
$406$	2079.56			0.254204
$407$		0			0
$408$	1956.18			0.237366
$409$	−3107.35	−	9563.43i	−0.375668	−	1.15619i	−0.943027	−	0.332717i	$-0.892034\pi$
$409$	−3107.35	−	9563.43i	−0.375668	−	1.15619i	0.567358	−	0.823471i	$-0.307966\pi$
$410$	11085.3	+	8053.97i	1.33528	+	0.970139i
$411$	1461.93	−	1062.16i	0.175455	−	0.127475i
$412$	8788.98	−	27049.7i	1.05098	−	3.23457i
$413$	194.776	−	599.460i	0.0232066	−	0.0714225i
$414$	−4078.87	+	2963.47i	−0.484217	+	0.351804i
$415$	−5306.86	−	3855.66i	−0.627720	−	0.456065i
$416$	−2225.90	−	6850.61i	−0.262341	−	0.807402i
$417$	1186.28			0.139310
$418$		0			0
$419$	1237.92			0.144335			0.0721675	−	0.997393i	$-0.477008\pi$
$419$	1237.92			0.144335			0.0721675	+	0.997393i	$0.477008\pi$
$420$	−375.146	−	1154.58i	−0.0435840	−	0.134138i
$421$	3204.91	+	2328.50i	0.371016	+	0.269559i	0.757632	−	0.652682i	$-0.226356\pi$
$421$	3204.91	+	2328.50i	0.371016	+	0.269559i	−0.386616	+	0.922241i	$0.626356\pi$
$422$	23072.9	−	16763.4i	2.66154	−	1.93372i
$423$	107.447	−	330.687i	0.0123504	−	0.0380107i
$424$	4236.91	−	13039.9i	0.485289	−	1.49357i
$425$	320.752	−	233.040i	0.0366088	−	0.0265979i
$426$	2932.51	+	2130.59i	0.333523	+	0.242318i
$427$	358.886	+	1104.54i	0.0406738	+	0.125181i
$428$	−1388.74			−0.156840
$429$		0			0
$430$	2360.19			0.264694
$431$	2630.51	+	8095.89i	0.293985	+	0.904792i	0.983561	+	0.180579i	$0.0577970\pi$
$431$	2630.51	+	8095.89i	0.293985	+	0.904792i	−0.689576	+	0.724214i	$0.742203\pi$
$432$	16398.8	+	11914.4i	1.82636	+	1.32693i
$433$	8741.61	−	6351.15i	0.970196	−	0.704889i	0.0146998	−	0.999892i	$-0.495321\pi$
$433$	8741.61	−	6351.15i	0.970196	−	0.704889i	0.955496	+	0.295003i	$0.0953207\pi$
$434$	439.871	−	1353.78i	0.0486509	−	0.149732i
$435$	−2937.90	+	9041.93i	−0.323820	+	0.996615i
$436$	−8782.38	+	6380.77i	−0.964678	+	0.700880i
$437$	5952.60	+	4324.82i	0.651605	+	0.473419i
$438$	−6887.17	−	21196.5i	−0.751329	−	2.31235i
$439$	3175.21			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$439$	3175.21			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$440$		0			0
$441$	2169.29			0.234240
$442$	−358.773	−	1104.19i	−0.0386088	−	0.118826i
$443$	1921.62	+	1396.14i	0.206093	+	0.149735i	0.686044	−	0.727560i	$-0.259346\pi$
$443$	1921.62	+	1396.14i	0.206093	+	0.149735i	−0.479951	+	0.877295i	$0.659346\pi$
$444$	4704.76	−	3418.21i	0.502878	−	0.365363i
$445$	−3089.13	+	9507.36i	−0.329076	+	1.01279i
$446$	−5217.46	+	16057.7i	−0.553933	+	1.70483i
$447$	−3483.06	+	2530.59i	−0.368553	+	0.267770i
$448$	−307.372	−	223.319i	−0.0324151	−	0.0235510i
$449$	2524.68	+	7770.18i	0.265361	+	0.816698i	0.991610	+	0.129266i	$0.0412621\pi$
$449$	2524.68	+	7770.18i	0.265361	+	0.816698i	−0.726249	+	0.687432i	$0.758738\pi$
$450$	1658.97			0.173788
$451$		0			0
$452$	−3396.21			−0.353416
$453$	2547.37	+	7840.01i	0.264208	+	0.813148i
$454$	−23542.0	−	17104.3i	−2.43366	−	1.76816i
$455$	−332.462	+	241.548i	−0.0342551	+	0.0248878i
$456$	3691.33	−	11360.8i	0.379084	−	1.16670i
$457$	2847.29	−	8763.05i	0.291445	−	0.896976i	−0.692947	−	0.720989i	$-0.743688\pi$
$457$	2847.29	−	8763.05i	0.291445	−	0.896976i	0.984392	−	0.175988i	$-0.0563120\pi$
$458$	−4558.18	+	3311.71i	−0.465043	+	0.337874i
$459$	964.031	+	700.410i	0.0980329	+	0.0712251i
$460$	7615.08	+	23436.8i	0.771858	+	2.37554i
$461$	−4588.84			−0.463609			−0.231804	−	0.972762i	$-0.574463\pi$
$461$	−4588.84			−0.463609			−0.231804	+	0.972762i	$0.574463\pi$
$462$		0			0
$463$	−11230.6			−1.12728			−0.563639	−	0.826021i	$-0.690599\pi$
$463$	−11230.6			−1.12728			−0.563639	+	0.826021i	$0.690599\pi$
$464$	10018.6	+	30833.9i	1.00237	+	3.08498i
$465$	5264.83	+	3825.12i	0.525055	+	0.381475i
$466$	6869.47	−	4990.96i	0.682880	−	0.496141i
$467$	−4036.13	+	12421.9i	−0.399935	+	1.23087i	0.525116	+	0.851031i	$0.324022\pi$
$467$	−4036.13	+	12421.9i	−0.399935	+	1.23087i	−0.925051	+	0.379843i	$0.875978\pi$
$468$	1050.06	−	3231.75i	0.103716	−	0.319205i
$469$	373.953	−	271.693i	0.0368178	−	0.0267497i
$470$	−1965.66	−	1428.14i	−0.192913	−	0.140160i
$471$	−1297.50	−	3993.30i	−0.126934	−	0.390661i
$472$	20772.0			2.02566
$473$		0			0
$474$	52.0280			0.00504161
$475$	−748.146	−	2302.56i	−0.0722680	−	0.222418i
$476$	−196.889	−	143.049i	−0.0189588	−	0.0137744i
$477$	1290.79	−	937.815i	0.123902	−	0.0900201i
$478$	1299.25	−	3998.67i	0.124322	−	0.382625i
$479$	4931.85	−	15178.7i	0.470442	−	1.44787i	−0.381564	−	0.924342i	$-0.624615\pi$
$479$	4931.85	−	15178.7i	0.470442	−	1.44787i	0.852007	−	0.523531i	$-0.175385\pi$
$480$	7984.06	−	5800.76i	0.759210	−	0.551598i
$481$	−1592.59	−	1157.08i	−0.150968	−	0.109685i
$482$	−10153.6	−	31249.5i	−0.959507	−	2.95306i
$483$	−1157.21			−0.109017
$484$		0			0
$485$	−6387.16			−0.597992
$486$	2787.23	+	8578.21i	0.260147	+	0.800649i
$487$	3515.59	+	2554.22i	0.327118	+	0.237665i	0.739207	−	0.673479i	$-0.235201\pi$
$487$	3515.59	+	2554.22i	0.327118	+	0.237665i	−0.412089	+	0.911144i	$0.635201\pi$
$488$	−30964.0	+	22496.6i	−2.87228	+	2.08683i
$489$	−4114.70	+	12663.7i	−0.380518	+	1.17111i
$490$	4684.27	−	14416.7i	0.431865	−	1.32914i
$491$	−2352.29	+	1709.04i	−0.216206	+	0.157083i	−0.690617	−	0.723221i	$-0.742661\pi$
$491$	−2352.29	+	1709.04i	−0.216206	+	0.157083i	0.474411	+	0.880303i	$0.342661\pi$
$492$	−21039.1	−	15285.8i	−1.92788	−	1.40068i
$493$	588.957	+	1812.62i	0.0538038	+	0.165591i
$494$	−7089.74			−0.645713
$495$		0			0
$496$	22191.9			2.00896
$497$	−79.4801	−	244.614i	−0.00717338	−	0.0220774i
$498$	14399.5	+	10461.9i	1.29570	+	0.941379i
$499$	−12828.9	+	9320.75i	−1.15090	+	0.836181i	−0.988601	−	0.150560i	$-0.951892\pi$
$499$	−12828.9	+	9320.75i	−1.15090	+	0.836181i	−0.162303	+	0.986741i	$0.551892\pi$
$500$	8716.40	−	26826.3i	0.779619	−	2.39942i
$501$	1544.71	−	4754.14i	0.137750	−	0.423951i
$502$	2643.61	−	1920.69i	0.235040	−	0.170766i
$503$	−1550.57	−	1126.55i	−0.137448	−	0.0998619i	0.516937	−	0.856024i	$-0.327072\pi$
$503$	−1550.57	−	1126.55i	−0.137448	−	0.0998619i	−0.654385	+	0.756162i	$0.727072\pi$
$504$	−179.478	−	552.375i	−0.0158622	−	0.0488190i
$505$	−5321.24			−0.468895
$506$		0			0
$507$	−6256.62			−0.548060
$508$	−834.462	−	2568.21i	−0.0728804	−	0.224303i
$509$	−7186.63	−	5221.39i	−0.625819	−	0.454684i	0.229130	−	0.973396i	$-0.426412\pi$
$509$	−7186.63	−	5221.39i	−0.625819	−	0.454684i	−0.854949	+	0.518712i	$0.826412\pi$
$510$	1286.88	−	934.973i	0.111733	−	0.0811790i
$511$	−488.692	+	1504.04i	−0.0423061	+	0.130205i
$512$	−7714.40	+	23742.5i	−0.665882	+	2.04937i
$513$	5886.86	−	4277.05i	0.506649	−	0.368102i
$514$	−1908.15	−	1386.35i	−0.163745	−	0.118968i
$515$	−4076.13	−	12545.0i	−0.348768	−	1.07340i
$516$	−4479.46			−0.382165
$517$		0			0
$518$	−589.936			−0.0500392
$519$	−5066.64	−	15593.5i	−0.428518	−	1.31884i
$520$	−10956.4	−	7960.29i	−0.923980	−	0.671311i
$521$	11343.5	−	8241.50i	0.953869	−	0.693026i	0.00215031	−	0.999998i	$-0.499316\pi$
$521$	11343.5	−	8241.50i	0.953869	−	0.693026i	0.951719	+	0.306971i	$0.0993155\pi$
$522$	−2464.39	+	7584.62i	−0.206635	+	0.635957i
$523$	−4674.70	+	14387.2i	−0.390842	+	1.20289i	0.541311	+	0.840822i	$0.317928\pi$
$523$	−4674.70	+	14387.2i	−0.390842	+	1.20289i	−0.932153	+	0.362065i	$0.882072\pi$
$524$	32.0766	−	23.3050i	0.00267419	−	0.00194291i
$525$	308.054	+	223.814i	0.0256087	+	0.0186058i
$526$	11088.3	+	34126.4i	0.919153	+	2.82886i
$527$	1304.59			0.107834
$528$		0			0
$529$	11323.2			0.930650
$530$	−3445.26	−	10603.4i	−0.282363	−	0.869024i
$531$	1955.55	+	1420.79i	0.159818	+	0.116115i
$532$	−1202.31	+	873.526i	−0.0979823	+	0.0711883i
$533$	−2720.31	+	8372.25i	−0.221069	+	0.680379i
$534$	8381.96	−	25797.0i	0.679257	−	2.09054i
$535$	−521.062	+	378.574i	−0.0421074	+	0.0305928i
$536$	12323.7	+	8953.71i	0.993104	+	0.721532i
$537$	4814.22	+	14816.6i	0.386870	+	1.19066i
$538$	−22811.2			−1.82799
$539$		0			0
$540$	24370.7			1.94213
$541$	−3697.53	−	11379.8i	−0.293843	−	0.904356i	−0.983608	−	0.180322i	$-0.942286\pi$
$541$	−3697.53	−	11379.8i	−0.293843	−	0.904356i	0.689764	−	0.724034i	$-0.257714\pi$
$542$	−14589.8	−	10600.1i	−1.15625	−	0.840063i
$543$	13614.2	−	9891.31i	1.07595	−	0.781725i
$544$	611.357	−	1881.56i	0.0481833	−	0.148293i
$545$	−1555.77	+	4788.18i	−0.122279	+	0.376336i
$546$	902.095	−	655.410i	0.0707071	−	0.0513717i
$547$	−12618.2	−	9167.63i	−0.986313	−	0.716598i	−0.0272026	−	0.999630i	$-0.508660\pi$
$547$	−12618.2	−	9167.63i	−0.986313	−	0.716598i	−0.959111	+	0.283031i	$0.908660\pi$
$548$	−2289.46	−	7046.25i	−0.178469	−	0.549272i
$549$	−4453.79			−0.346235
$550$		0			0
$551$	11638.4			0.899843
$552$	−11784.8	−	36269.8i	−0.908683	−	2.79664i
$553$	−2.98668	−	2.16995i	−0.000229668	−	0.000166864i
$554$	−11453.1	+	8321.13i	−0.878328	+	0.638142i
$555$	833.434	−	2565.05i	0.0637429	−	0.196181i
$556$	1502.97	−	4625.68i	0.114641	−	0.352828i
$557$	−15094.9	+	10967.1i	−1.14828	+	0.834272i	−0.988251	−	0.152841i	$-0.951158\pi$
$557$	−15094.9	+	10967.1i	−1.14828	+	0.834272i	−0.160026	+	0.987113i	$0.551158\pi$
$558$	4416.28	+	3208.62i	0.335047	+	0.243426i
$559$	468.570	+	1442.11i	0.0354533	+	0.109114i
$560$	−1919.97			−0.144882
$561$		0			0
$562$	−9026.55			−0.677512
$563$	4624.62	+	14233.1i	0.346189	+	1.06546i	0.960944	+	0.276742i	$0.0892548\pi$
$563$	4624.62	+	14233.1i	0.346189	+	1.06546i	−0.614755	+	0.788718i	$0.710745\pi$
$564$	3730.67	+	2710.49i	0.278528	+	0.202362i
$565$	−1274.27	+	925.810i	−0.0948830	+	0.0689365i
$566$	−3306.88	+	10177.5i	−0.245580	+	0.755819i
$567$	−265.206	+	816.219i	−0.0196430	+	0.0604550i
$568$	6857.38	−	4982.18i	0.506566	−	0.368042i
$569$	−10572.6	−	7681.42i	−0.778954	−	0.565943i	0.125711	−	0.992067i	$-0.459879\pi$
$569$	−10572.6	−	7681.42i	−0.778954	−	0.565943i	−0.904665	+	0.426124i	$0.859879\pi$
$570$	−3001.62	−	9238.03i	−0.220568	−	0.678839i
$571$	−13852.7			−1.01527			−0.507633	−	0.861573i	$-0.669480\pi$
$571$	−13852.7			−1.01527			−0.507633	+	0.861573i	$0.669480\pi$
$572$		0			0
$573$	−13802.3			−1.00628
$574$	815.224	+	2509.00i	0.0592801	+	0.182445i
$575$	−6253.16	−	4543.19i	−0.453522	−	0.329503i
$576$	1178.75	−	856.411i	0.0852683	−	0.0619510i
$577$	3956.75	−	12177.6i	0.285479	−	0.878615i	−0.700775	−	0.713382i	$-0.747162\pi$
$577$	3956.75	−	12177.6i	0.285479	−	0.878615i	0.986255	−	0.165233i	$-0.0528376\pi$
$578$	−7734.49	+	23804.3i	−0.556596	+	1.71303i
$579$	2569.60	−	1866.93i	0.184437	−	0.134001i
$580$	31535.1	+	22911.6i	2.25763	+	1.64026i
$581$	−390.271	−	1201.13i	−0.0278677	−	0.0857681i
$582$	17330.8			1.23434
$583$		0			0
$584$	−52116.8			−3.69282
$585$	−486.994	−	1498.81i	−0.0344183	−	0.105929i
$586$	14699.4	+	10679.7i	1.03622	+	0.752859i
$587$	−9763.07	+	7093.29i	−0.686482	+	0.498759i	−0.875502	−	0.483215i	$-0.839469\pi$
$587$	−9763.07	+	7093.29i	−0.686482	+	0.498759i	0.189019	+	0.981973i	$0.439469\pi$
$588$	−8890.37	+	27361.8i	−0.623525	+	1.91901i
$589$	2461.77	−	7576.56i	0.172217	−	0.530028i
$590$	13665.0	−	9928.19i	0.953522	−	0.692774i
$591$	15574.6	+	11315.6i	1.08402	+	0.787584i
$592$	−2842.10	−	8747.08i	−0.197313	−	0.607268i
$593$	10537.6			0.729729			0.364864	−	0.931061i	$-0.381115\pi$
$593$	10537.6			0.729729			0.364864	+	0.931061i	$0.381115\pi$
$594$		0			0
$595$	−112.869			−0.00777676
$596$	5454.66	+	16787.7i	0.374885	+	1.15378i
$597$	7422.75	+	5392.94i	0.508866	+	0.369713i
$598$	−18311.6	+	13304.1i	−1.25220	+	0.909777i
$599$	1692.20	−	5208.05i	0.115428	−	0.355251i	−0.876608	−	0.481205i	$-0.840199\pi$
$599$	1692.20	−	5208.05i	0.115428	−	0.355251i	0.992036	+	0.125954i	$0.0401993\pi$
$600$	−3877.72	+	11934.4i	−0.263845	+	0.812032i
$601$	−13837.4	+	10053.5i	−0.939170	+	0.682347i	−0.948221	−	0.317612i	$-0.897119\pi$
$601$	−13837.4	+	10053.5i	−0.939170	+	0.682347i	0.00905088	+	0.999959i	$0.497119\pi$
$602$	367.628	+	267.097i	0.0248893	+	0.0180832i
$603$	547.769	+	1685.86i	0.0369932	+	0.113853i
$604$	33798.1			2.27686
$605$		0			0
$606$	14438.5			0.967861
$607$	503.344	+	1549.13i	0.0336575	+	0.103587i	0.966474	−	0.256765i	$-0.0826566\pi$
$607$	503.344	+	1549.13i	0.0336575	+	0.103587i	−0.932816	+	0.360352i	$0.882657\pi$
$608$	−9773.78	−	7101.07i	−0.651939	−	0.473662i
$609$	−1480.87	+	1075.91i	−0.0985349	+	0.0715898i
$610$	−9617.30	+	29599.0i	−0.638349	+	1.96464i
$611$	482.367	−	1484.57i	0.0319386	−	0.0982970i
$612$	755.055	−	548.580i	0.0498714	−	0.0362337i
$613$	12796.4	+	9297.14i	0.843136	+	0.612574i	0.923245	−	0.384212i	$-0.125527\pi$
$613$	12796.4	+	9297.14i	0.843136	+	0.612574i	−0.0801088	+	0.996786i	$0.525527\pi$
$614$	11071.8	+	34075.5i	0.727721	+	2.23970i
$615$	−12060.9			−0.790799
$616$		0			0
$617$	−9377.02			−0.611839			−0.305919	−	0.952057i	$-0.598964\pi$
$617$	−9377.02			−0.611839			−0.305919	+	0.952057i	$0.598964\pi$
$618$	11060.1	+	34039.4i	0.719904	+	2.21564i
$619$	−5169.71	−	3756.01i	−0.335684	−	0.243888i	0.407155	−	0.913359i	$-0.366521\pi$
$619$	−5169.71	−	3756.01i	−0.335684	−	0.243888i	−0.742838	+	0.669471i	$0.766521\pi$
$620$	21585.7	−	15682.9i	1.39823	−	1.01587i
$621$	7178.71	−	22093.8i	0.463884	−	1.42769i
$622$	3651.15	−	11237.1i	0.235366	−	0.724383i
$623$	−1557.09	+	1131.29i	−0.100134	+	0.0727518i
$624$	14063.8	+	10218.0i	0.902250	+	0.655523i
$625$	−2094.46	−	6446.08i	−0.134045	−	0.412549i
$626$	40858.1			2.60865
$627$		0			0
$628$	−17215.0			−1.09387
$629$	−167.077	−	514.211i	−0.0105911	−	0.0325961i
$630$	−382.083	−	277.599i	−0.0241628	−	0.0175553i
$631$	14323.9	−	10406.9i	0.903683	−	0.656564i	−0.0357261	−	0.999362i	$-0.511374\pi$
$631$	14323.9	−	10406.9i	0.903683	−	0.656564i	0.939409	+	0.342797i	$0.111374\pi$
$632$	37.5957	−	115.708i	0.00236626	−	0.00728260i
$633$	−7757.36	+	23874.7i	−0.487089	+	1.49911i
$634$	5791.02	−	4207.43i	0.362762	−	0.263562i
$635$	−1013.19	−	736.126i	−0.0633185	−	0.0460036i
$636$	6538.82	+	20124.4i	0.407675	+	1.25469i
$637$	9738.77			0.605752
$638$		0			0
$639$	986.352			0.0610634
$640$	2225.98	+	6850.85i	0.137484	+	0.423131i
$641$	−14700.4	−	10680.5i	−0.905819	−	0.658116i	0.0341348	−	0.999417i	$-0.489132\pi$
$641$	−14700.4	−	10680.5i	−0.905819	−	0.658116i	−0.939954	+	0.341301i	$0.889132\pi$
$642$	1413.84	−	1027.21i	0.0869153	−	0.0631477i
$643$	1687.38	−	5193.23i	0.103490	−	0.318509i	−0.885883	−	0.463908i	$-0.846447\pi$
$643$	1687.38	−	5193.23i	0.103490	−	0.318509i	0.989373	+	0.145399i	$0.0464467\pi$
$644$	−1466.15	+	4512.34i	−0.0897117	+	0.276104i
$645$	−1680.71	+	1221.11i	−0.102601	+	0.0745442i
$646$	−1575.35	−	1144.56i	−0.0959462	−	0.0697090i
$647$	−3478.81	−	10706.7i	−0.211385	−	0.650577i	−0.999391	−	0.0349083i	$-0.988886\pi$
$647$	−3478.81	−	10706.7i	−0.211385	−	0.650577i	0.788005	−	0.615668i	$-0.211114\pi$
$648$	−28283.0			−1.71460
$649$		0			0
$650$	7447.71			0.449421
$651$	387.180	+	1191.62i	0.0233099	+	0.0717406i
$652$	44166.7	+	32089.0i	2.65292	+	1.92746i
$653$	−1860.98	+	1352.08i	−0.111525	+	0.0810274i	−0.642150	−	0.766579i	$-0.721957\pi$
$653$	−1860.98	+	1352.08i	−0.111525	+	0.0810274i	0.530625	+	0.847607i	$0.321957\pi$
$654$	4221.39	−	12992.1i	0.252400	−	0.776807i
$655$	5.68228	−	17.4883i	0.000338970	−	0.00104324i
$656$	−33273.9	+	24174.9i	−1.98038	+	1.43883i
$657$	−4906.44	−	3564.74i	−0.291352	−	0.211680i
$658$	−144.556	−	444.898i	−0.00856442	−	0.0263586i
$659$	−8719.26			−0.515408			−0.257704	−	0.966224i	$-0.582966\pi$
$659$	−8719.26			−0.515408			−0.257704	+	0.966224i	$0.582966\pi$
$660$		0			0
$661$	22031.4			1.29640			0.648201	−	0.761469i	$-0.275522\pi$
$661$	22031.4			1.29640			0.648201	+	0.761469i	$0.275522\pi$
$662$	−18560.5	−	57123.4i	−1.08969	−	3.35372i
$663$	826.766	+	600.680i	0.0484297	+	0.0351863i
$664$	33671.8	−	24464.0i	1.96795	−	1.42980i
$665$	−212.985	+	655.500i	−0.0124199	+	0.0382244i
$666$	699.107	−	2151.63i	0.0406754	−	0.125186i
$667$	30060.0	−	21839.9i	1.74502	−	1.26783i
$668$	−16580.8	−	12046.6i	−0.960374	−	0.697752i
$669$	−4592.48	−	14134.2i	−0.265404	−	0.816830i
$670$	12386.7			0.714240
$671$		0			0
$672$	1900.07			0.109073
$673$	−2749.68	−	8462.64i	−0.157492	−	0.484711i	0.840913	−	0.541171i	$-0.182019\pi$
$673$	−2749.68	−	8462.64i	−0.157492	−	0.484711i	−0.998405	+	0.0564597i	$0.982019\pi$
$674$	35384.8	+	25708.5i	2.02221	+	1.46922i
$675$	−6184.10	+	4493.01i	−0.352631	+	0.256202i
$676$	−7926.91	+	24396.5i	−0.451007	+	1.38806i
$677$	5639.74	−	17357.3i	0.320167	−	0.985371i	−0.653409	−	0.757005i	$-0.726662\pi$
$677$	5639.74	−	17357.3i	0.320167	−	0.985371i	0.973575	−	0.228366i	$-0.0733383\pi$
$678$	3457.57	−	2512.07i	0.195851	−	0.142294i
$679$	−994.876	−	722.820i	−0.0562295	−	0.0408531i
$680$	−1149.43	−	3537.57i	−0.0648213	−	0.199500i
$681$	25613.8			1.44130
$682$		0			0
$683$	−17118.2			−0.959018			−0.479509	−	0.877537i	$-0.659185\pi$
$683$	−17118.2			−0.959018			−0.479509	+	0.877537i	$0.659185\pi$
$684$	−1761.15	−	5420.26i	−0.0984491	−	0.302995i
$685$	−2779.83	−	2019.67i	−0.155054	−	0.112653i
$686$	4741.45	−	3444.86i	0.263891	−	0.191728i
$687$	1532.51	−	4716.59i	0.0851077	−	0.261934i
$688$	−2189.20	+	6737.65i	−0.121311	+	0.373358i
$689$	5794.84	−	4210.20i	0.320415	−	0.232795i
$690$	−25088.1	−	18227.6i	−1.38419	−	1.00567i
$691$	−1474.22	−	4537.18i	−0.0811606	−	0.249787i	0.902240	−	0.431234i	$-0.141922\pi$
$691$	−1474.22	−	4537.18i	−0.0811606	−	0.249787i	−0.983401	+	0.181448i	$0.941922\pi$
$692$	−67223.2			−3.69284
$693$		0			0
$694$	−9859.71			−0.539293
$695$	−697.045	−	2145.28i	−0.0380438	−	0.117087i
$696$	−48802.4	−	35457.0i	−2.65783	−	1.93103i
$697$	−1956.06	+	1421.16i	−0.106300	+	0.0772315i
$698$	13753.0	−	42327.4i	0.745787	−	2.29530i
$699$	−2309.59	+	7108.19i	−0.124974	+	0.384630i
$700$	1263.01	−	917.633i	0.0681963	−	0.0495475i
$701$	9334.96	+	6782.24i	0.502962	+	0.365423i	0.810147	−	0.586226i	$-0.199387\pi$
$701$	9334.96	+	6782.24i	0.502962	+	0.365423i	−0.307185	+	0.951650i	$0.599387\pi$
$702$	6917.15	+	21288.8i	0.371896	+	1.14458i
$703$	−3301.63			−0.177131
$704$		0			0
$705$	2138.64			0.114250
$706$	10116.3	+	31134.8i	0.539280	+	1.65973i
$707$	−828.845	−	602.191i	−0.0440904	−	0.0320336i
$708$	−25935.0	+	18842.9i	−1.37669	+	1.00023i
$709$	1775.80	−	5465.34i	0.0940640	−	0.289499i	−0.892945	−	0.450167i	$-0.851365\pi$
$709$	1775.80	−	5465.34i	0.0940640	−	0.289499i	0.987009	+	0.160667i	$0.0513646\pi$
$710$	2129.88	−	6555.10i	0.112582	−	0.346491i
$711$	11.4537	−	8.32158i	0.000604144	−	0.000438936i
$712$	−51314.5	−	37282.1i	−2.70097	−	1.96237i
$713$	−7859.34	−	24188.6i	−0.412812	−	1.27050i
$714$	306.255			0.0160523
$715$		0			0
$716$	63874.2			3.33392
$717$	1143.61	+	3519.67i	0.0595662	+	0.183326i
$718$	−19085.0	−	13866.1i	−0.991988	−	0.720721i
$719$	−15519.5	+	11275.6i	−0.804981	+	0.584853i	−0.912371	−	0.409364i	$-0.865751\pi$
$719$	−15519.5	+	11275.6i	−0.804981	+	0.584853i	0.107390	+	0.994217i	$0.465751\pi$
$720$	2275.28	−	7002.58i	0.117770	−	0.362459i
$721$	784.786	−	2415.32i	0.0405367	−	0.124759i
$722$	19010.0	−	13811.5i	0.979886	−	0.711929i
$723$	23398.2	+	16999.8i	1.20358	+	0.874450i
$724$	−21320.6	−	65618.0i	−1.09444	−	3.36833i
$725$	−12226.1			−0.626296
$726$		0			0
$727$	35335.6			1.80265			0.901323	−	0.433148i	$-0.142597\pi$
$727$	35335.6			1.80265			0.901323	+	0.433148i	$0.142597\pi$
$728$	−805.741	−	2479.82i	−0.0410203	−	0.126247i
$729$	−17698.6	−	12858.8i	−0.899180	−	0.653293i
$730$	−34285.2	+	24909.7i	−1.73829	+	1.26294i
$731$	−128.695	+	396.084i	−0.00651159	+	0.0200406i
$732$	18252.9	−	56176.6i	0.921647	−	2.83654i
$733$	−12118.0	+	8804.22i	−0.610624	+	0.443644i	−0.849634	−	0.527373i	$-0.823177\pi$
$733$	−12118.0	+	8804.22i	−0.610624	+	0.443644i	0.239010	+	0.971017i	$0.423177\pi$
$734$	−5949.59	−	4322.63i	−0.299187	−	0.217372i
$735$	4123.15	+	12689.8i	0.206918	+	0.636828i
$736$	−38569.4			−1.93164
$737$		0			0
$738$	−10117.0			−0.504622
$739$	6633.42	+	20415.6i	0.330196	+	1.01624i	0.969041	+	0.246902i	$0.0794125\pi$
$739$	6633.42	+	20415.6i	0.330196	+	1.01624i	−0.638845	+	0.769335i	$0.720587\pi$
$740$	−8945.99	−	6499.64i	−0.444407	−	0.322880i
$741$	5048.65	−	3668.06i	0.250292	−	0.181848i
$742$	663.323	−	2041.50i	0.0328185	−	0.101005i
$743$	7917.85	−	24368.6i	0.390952	−	1.20323i	−0.541117	−	0.840947i	$-0.681998\pi$
$743$	7917.85	−	24368.6i	0.390952	−	1.20323i	0.932069	−	0.362280i	$-0.118002\pi$
$744$	−33405.1	+	24270.2i	−1.64609	+	1.19595i
$745$	6622.96	+	4811.86i	0.325700	+	0.236635i
$746$	12948.7	+	39852.0i	0.635504	+	1.95588i
$747$	4843.28			0.237224
$748$		0			0
$749$	−124.004			−0.00604940
$750$	10968.7	+	33758.3i	0.534028	+	1.64357i
$751$	820.808	+	596.352i	0.0398824	+	0.0289763i	0.607548	−	0.794283i	$-0.292153\pi$
$751$	820.808	+	596.352i	0.0398824	+	0.0289763i	−0.567665	+	0.823259i	$0.692153\pi$
$752$	5900.16	−	4286.72i	0.286113	−	0.207873i
$753$	−888.810	+	2735.48i	−0.0430147	+	0.132386i
$754$	−11063.6	+	34050.1i	−0.534365	+	1.64461i
$755$	12681.2	−	9213.40i	0.611278	−	0.444119i
$756$	3796.03	+	2757.98i	0.182619	+	0.132681i
$757$	−1496.88	−	4606.93i	−0.0718693	−	0.221191i	0.908670	−	0.417516i	$-0.137099\pi$
$757$	−1496.88	−	4606.93i	−0.0718693	−	0.221191i	−0.980539	+	0.196325i	$0.937099\pi$
$758$	27329.8			1.30958
$759$		0			0
$760$	−22713.9			−1.08410
$761$	6120.48	+	18836.9i	0.291547	+	0.897290i	0.984359	+	0.176172i	$0.0563715\pi$
$761$	6120.48	+	18836.9i	0.291547	+	0.897290i	−0.692812	+	0.721118i	$0.743629\pi$
$762$	2749.16	+	1997.38i	0.130698	+	0.0949575i
$763$	−784.196	+	569.752i	−0.0372081	+	0.0270333i
$764$	−17487.0	+	53819.4i	−0.828085	+	2.54858i
$765$	133.756	−	411.658i	0.00632151	−	0.0194556i
$766$	−46070.3	+	33472.0i	−2.17309	+	1.57884i
$767$	8779.17	+	6378.44i	0.413295	+	0.300277i
$768$	−8605.49	−	26485.0i	−0.404328	−	1.24439i
$769$	−30538.7			−1.43206			−0.716030	−	0.698069i	$-0.754043\pi$
$769$	−30538.7			−1.43206			−0.716030	+	0.698069i	$0.754043\pi$
$770$		0			0
$771$	2076.08			0.0969754
$772$	−4024.13	−	12385.0i	−0.187606	−	0.577392i
$773$	−1906.94	−	1385.47i	−0.0887293	−	0.0644656i	0.542536	−	0.840032i	$-0.317464\pi$
$773$	−1906.94	−	1385.47i	−0.0887293	−	0.0644656i	−0.631265	+	0.775567i	$0.717464\pi$
$774$	−1409.82	+	1024.30i	−0.0654716	+	0.0475679i
$775$	−2586.08	+	7959.12i	−0.119864	+	0.368903i
$776$	12523.3	−	38542.8i	0.579330	−	1.78300i
$777$	420.098	−	305.219i	0.0193963	−	0.0140922i
$778$	−46417.8	−	33724.5i	−2.13902	−	1.55409i
$779$	4562.47	+	14041.8i	0.209843	+	0.645829i
$780$	20900.7			0.959441
$781$		0			0
$782$	−6216.66			−0.284280
$783$	−11355.1	−	34947.4i	−0.518261	−	1.59504i
$784$	36810.5	+	26744.4i	1.67686	+	1.21831i
$785$	−6459.13	+	4692.83i	−0.293677	+	0.213369i
$786$	−15.4182	+	47.4522i	−0.000699679	+	0.00215339i
$787$	−8101.71	+	24934.5i	−0.366957	+	1.12938i	0.581790	+	0.813339i	$0.302353\pi$
$787$	−8101.71	+	24934.5i	−0.366957	+	1.12938i	−0.948747	+	0.316037i	$0.897647\pi$
$788$	63855.6	−	46393.8i	2.88675	−	2.09735i
$789$	−25552.2	−	18564.8i	−1.15296	−	0.837673i
$790$	−30.5710	−	94.0879i	−0.00137680	−	0.00423734i
$791$	−303.254			−0.0136314
$792$		0			0
$793$	−19994.7			−0.895376
$794$	−3699.78	−	11386.8i	−0.165366	−	0.508943i
$795$	7939.34	+	5768.27i	0.354188	+	0.257332i
$796$	30433.1	−	22110.9i	1.35512	−	0.984550i
$797$	5614.34	−	17279.1i	0.249523	−	0.767953i	−0.745336	−	0.666689i	$-0.767711\pi$
$797$	5614.34	−	17279.1i	0.249523	−	0.767953i	0.994860	−	0.101265i	$-0.0322889\pi$
$798$	577.908	−	1778.62i	0.0256362	−	0.0789002i
$799$	346.850	−	252.002i	0.0153576	−	0.0111579i
$800$	10267.3	+	7459.62i	0.453754	+	0.329672i
$801$	−2280.85	−	7019.72i	−0.100611	−	0.309650i
$802$	2516.27			0.110789
$803$		0			0
$804$	−23509.0			−1.03122
$805$	679.966	+	2092.72i	0.0297710	+	0.0916257i
$806$	19826.3	+	14404.7i	0.866442	+	0.629507i
$807$	16244.0	−	11802.0i	0.708570	−	0.514806i
$808$	10433.3	−	32110.5i	0.454262	−	1.39807i
$809$	−960.631	+	2956.52i	−0.0417478	+	0.128487i	−0.969758	−	0.244068i	$-0.921518\pi$
$809$	−960.631	+	2956.52i	−0.0417478	+	0.128487i	0.928010	+	0.372554i	$0.121518\pi$
$810$	−18606.1	+	13518.1i	−0.807101	+	0.586393i
$811$	16792.4	+	12200.4i	0.727078	+	0.528253i	0.888638	−	0.458610i	$-0.151652\pi$
$811$	16792.4	+	12200.4i	0.727078	+	0.528253i	−0.161560	+	0.986863i	$0.551652\pi$
$812$	2319.12	+	7137.50i	0.100228	+	0.308470i
$813$	15873.8			0.684769
$814$		0			0
$815$	25319.0			1.08820
$816$	1475.43	+	4540.90i	0.0632969	+	0.194808i
$817$	2057.46	+	1494.83i	0.0881045	+	0.0640117i
$818$	41972.6	−	30494.8i	1.79405	−	1.30346i
$819$	93.7620	−	288.570i	0.00400038	−	0.0123119i
$820$	−15280.7	+	47029.1i	−0.650761	+	2.00284i
$821$	6405.05	−	4653.54i	0.272275	−	0.197819i	−0.443266	−	0.896390i	$-0.646180\pi$
$821$	6405.05	−	4653.54i	0.272275	−	0.197819i	0.715541	+	0.698571i	$0.246180\pi$
$822$	7542.72	+	5480.11i	0.320052	+	0.232531i
$823$	9044.36	+	27835.7i	0.383070	+	1.17897i	0.937871	+	0.346985i	$0.112795\pi$
$823$	9044.36	+	27835.7i	0.383070	+	1.17897i	−0.554801	+	0.831983i	$0.687205\pi$
$824$	83693.9			3.53837
$825$		0			0
$826$	3252.03			0.136989
$827$	−4296.40	−	13223.0i	−0.180654	−	0.555995i	0.819193	−	0.573518i	$-0.194422\pi$
$827$	−4296.40	−	13223.0i	−0.180654	−	0.555995i	−0.999846	+	0.0175235i	$0.994422\pi$
$828$	−14720.1	−	10694.7i	−0.617823	−	0.448874i
$829$	7656.49	−	5562.76i	0.320773	−	0.233055i	−0.415732	−	0.909487i	$-0.636475\pi$
$829$	7656.49	−	5562.76i	0.320773	−	0.233055i	0.736505	+	0.676432i	$0.236475\pi$
$830$	10458.3	−	32187.5i	0.437367	−	1.34608i
$831$	3850.64	−	11851.1i	0.160743	−	0.494716i
$832$	5291.84	−	3844.75i	0.220507	−	0.160207i
$833$	2163.97	+	1572.21i	0.0900084	+	0.0653949i
$834$	1891.34	+	5820.96i	0.0785275	+	0.241683i
$835$	−9505.10			−0.393937
$836$		0			0
$837$	−25152.5			−1.03871
$838$	1973.68	+	6074.35i	0.0813598	+	0.250400i
$839$	30868.8	+	22427.5i	1.27021	+	0.922864i	0.999211	−	0.0397149i	$-0.0126450\pi$
$839$	30868.8	+	22427.5i	1.27021	+	0.922864i	0.271002	+	0.962579i	$0.412645\pi$
$840$	2890.11	−	2099.79i	0.118712	−	0.0862494i
$841$	10625.2	−	32701.0i	0.435655	−	1.34081i
$842$	−6315.98	+	19438.6i	−0.258507	+	0.795603i
$843$	6427.87	−	4670.12i	0.262619	−	0.190804i
$844$	83266.6	+	60496.7i	3.39592	+	2.46728i
$845$	3676.32	+	11314.5i	0.149668	+	0.460630i
$846$	1793.95			0.0729046
$847$		0			0
$848$	33465.3			1.35519
$849$	−2910.76	−	8958.38i	−0.117664	−	0.362133i
$850$	1654.89	+	1202.35i	0.0667792	+	0.0485179i
$851$	−8527.54	+	6195.62i	−0.343502	+	0.249569i
$852$	−4042.35	+	12441.1i	−0.162545	+	0.500263i
$853$	−12688.9	+	39052.3i	−0.509330	+	1.56756i	0.284039	+	0.958813i	$0.408326\pi$
$853$	−12688.9	+	39052.3i	−0.509330	+	1.56756i	−0.793368	+	0.608742i	$0.791674\pi$
$854$	−4847.66	+	3522.03i	−0.194243	+	0.141126i
$855$	−2138.36	−	1553.61i	−0.0855326	−	0.0621430i
$856$	−1262.82	−	3886.57i	−0.0504234	−	0.155187i
$857$	2923.27			0.116519			0.0582596	−	0.998301i	$-0.481445\pi$
$857$	2923.27			0.116519			0.0582596	+	0.998301i	$0.481445\pi$
$858$		0			0
$859$	18049.4			0.716924			0.358462	−	0.933544i	$-0.383301\pi$
$859$	18049.4			0.716924			0.358462	+	0.933544i	$0.383301\pi$
$860$	2632.08	+	8100.70i	0.104364	+	0.321199i
$861$	−1878.62	−	1364.90i	−0.0743592	−	0.0540251i
$862$	−35531.7	+	25815.3i	−1.40396	+	1.02004i
$863$	−10813.1	+	33279.3i	−0.426515	+	1.31268i	0.475020	+	0.879975i	$0.342441\pi$
$863$	−10813.1	+	33279.3i	−0.426515	+	1.31268i	−0.901536	+	0.432704i	$0.857559\pi$
$864$	−11787.0	+	36276.6i	−0.464121	+	1.42842i
$865$	−25222.4	+	18325.1i	−0.991430	+	0.720316i
$866$	45101.6	+	32768.2i	1.76976	+	1.28581i
$867$	−6807.99	−	20952.8i	−0.266680	−	0.820757i
$868$	5137.03			0.200878
$869$		0			0
$870$	−49051.9			−1.91151
$871$	2459.14	+	7568.45i	0.0956656	+	0.294429i
$872$	−25843.4	−	18776.3i	−1.00363	−	0.729182i
$873$	3815.27	−	2771.96i	0.147912	−	0.107464i
$874$	−11730.9	+	36104.1i	−0.454009	+	1.39730i
$875$	778.305	−	2395.38i	0.0300703	−	0.0925469i
$876$	65070.7	−	47276.6i	2.50974	−	1.82344i
$877$	−24528.0	−	17820.6i	−0.944415	−	0.686158i	0.00506422	−	0.999987i	$-0.498388\pi$
$877$	−24528.0	−	17820.6i	−0.944415	−	0.686158i	−0.949479	+	0.313829i	$0.898388\pi$
$878$	5062.39	+	15580.4i	0.194587	+	0.598877i
$879$	−15993.0			−0.613685
$880$		0			0
$881$	−33005.5			−1.26218			−0.631092	−	0.775708i	$-0.717393\pi$
$881$	−33005.5			−1.26218			−0.631092	+	0.775708i	$0.717393\pi$
$882$	3458.61	+	10644.5i	0.132038	+	0.406371i
$883$	11176.2	+	8119.96i	0.425943	+	0.309466i	0.780025	−	0.625749i	$-0.215206\pi$
$883$	11176.2	+	8119.96i	0.425943	+	0.309466i	−0.354081	+	0.935215i	$0.615206\pi$
$884$	3389.72	−	2462.78i	0.128969	−	0.0937015i
$885$	−4594.32	+	14139.9i	−0.174504	+	0.537069i
$886$	−3786.98	+	11655.1i	−0.143596	+	0.441943i
$887$	−17035.6	+	12377.1i	−0.644871	+	0.468526i	−0.861520	−	0.507723i	$-0.830487\pi$
$887$	−17035.6	+	12377.1i	−0.644871	+	0.468526i	0.216649	+	0.976249i	$0.430487\pi$
$888$	13844.4	+	10058.6i	0.523186	+	0.380117i
$889$	−74.5108	−	229.321i	−0.00281104	−	0.00865148i
$890$	−51576.8			−1.94254
$891$		0			0
$892$	−60932.1			−2.28717
$893$	−809.021	−	2489.91i	−0.0303167	−	0.0933053i
$894$	−17970.6	−	13056.4i	−0.672289	−	0.488446i
$895$	23965.8	−	17412.2i	0.895071	−	0.650307i
$896$	−428.572	+	1319.01i	−0.0159795	+	0.0491797i
$897$	6156.56	−	18947.9i	0.229165	−	0.705299i
$898$	−34102.2	+	24776.7i	−1.26727	+	0.920724i
$899$	−32546.6	−	23646.5i	−1.20744	−	0.877258i
$900$	1850.07	+	5693.94i	0.0685213	+	0.210887i
$901$	1967.31			0.0727421
$902$		0			0
$903$	−399.980			−0.0147403
$904$	−3088.26	−	9504.69i	−0.113622	−	0.349692i
$905$	−25887.1	−	18808.1i	−0.950847	−	0.690831i
$906$	−34408.7	+	24999.4i	−1.26176	+	0.916721i
$907$	−11776.1	+	36243.2i	−0.431113	+	1.32683i	0.465904	+	0.884835i	$0.345729\pi$
$907$	−11776.1	+	36243.2i	−0.431113	+	1.32683i	−0.897017	+	0.441995i	$0.854271\pi$
$908$	32451.7	−	99876.1i	1.18607	−	3.65034i
$909$	3178.56	−	2309.36i	0.115980	−	0.0842646i
$910$	−1715.31	−	1246.25i	−0.0624857	−	0.0453985i
$911$	−193.786	−	596.413i	−0.00704767	−	0.0216905i	0.947471	−	0.319842i	$-0.103630\pi$
$911$	−193.786	−	596.413i	−0.00704767	−	0.0216905i	−0.954519	+	0.298152i	$0.903630\pi$
$912$	29156.0			1.05861
$913$		0			0
$914$	47538.9			1.72040
$915$	−8465.27	−	26053.4i	−0.305850	−	0.941311i
$916$	−16449.8	−	11951.5i	−0.593359	−	0.431100i
$917$	2.86419	−	2.08095i	0.000103145	−	7.49391e-5i
$918$	−1899.84	+	5847.10i	−0.0683050	+	0.210221i
$919$	15106.5	−	46493.0i	0.542238	−	1.66884i	−0.185230	−	0.982695i	$-0.559303\pi$
$919$	15106.5	−	46493.0i	0.542238	−	1.66884i	0.727468	−	0.686142i	$-0.240697\pi$
$920$	−58666.1	+	42623.4i	−2.10235	+	1.52745i
$921$	−25514.1	−	18537.1i	−0.912832	−	0.663211i
$922$	−7316.21	−	22517.0i	−0.261330	−	0.804292i
$923$	4428.10			0.157912
$924$		0			0
$925$	3468.33			0.123284
$926$	−17905.4	−	55107.3i	−0.635431	−	1.95566i
$927$	7879.21	+	5724.58i	0.279166	+	0.202826i
$928$	−49356.6	+	35859.7i	−1.74592	+	1.26848i
$929$	−9954.76	+	30637.6i	−0.351566	+	1.08201i	0.606408	+	0.795154i	$0.292610\pi$
$929$	−9954.76	+	30637.6i	−0.351566	+	1.08201i	−0.957974	+	0.286856i	$0.907390\pi$
$930$	−10375.5	+	31932.6i	−0.365835	+	1.12592i
$931$	13214.3	−	9600.73i	0.465178	−	0.337971i
$932$	24790.9	+	18011.6i	0.871301	+	0.633037i
$933$	3213.79	+	9891.02i	0.112770	+	0.347071i
$934$	−67388.0			−2.36082
$935$		0			0
$936$	9999.30			0.349185
$937$	14040.7	+	43212.9i	0.489531	+	1.50662i	0.825310	+	0.564680i	$0.191000\pi$
$937$	14040.7	+	43212.9i	0.489531	+	1.50662i	−0.335779	+	0.941941i	$0.609000\pi$
$938$	1929.38	+	1401.77i	0.0671603	+	0.0487948i
$939$	−29095.3	+	21139.0i	−1.01117	+	0.734659i
$940$	2709.58	−	8339.24i	0.0940179	−	0.289357i
$941$	−12930.8	+	39797.0i	−0.447963	+	1.37869i	0.431239	+	0.902238i	$0.358077\pi$
$941$	−12930.8	+	39797.0i	−0.447963	+	1.37869i	−0.879202	+	0.476450i	$0.841923\pi$
$942$	17526.0	−	12733.4i	0.606188	−	0.440421i
$943$	38134.1	+	27706.0i	1.31688	+	0.956768i
$944$	15667.1	+	48218.4i	0.540170	+	1.66247i
$945$	2176.11			0.0749089
$946$		0			0
$947$	−24265.2			−0.832644			−0.416322	−	0.909217i	$-0.636681\pi$
$947$	−24265.2			−0.832644			−0.416322	+	0.909217i	$0.636681\pi$
$948$	58.0214	+	178.572i	0.00198781	+	0.00611786i
$949$	−22026.8	−	16003.4i	−0.753447	−	0.547411i
$950$	10105.6	−	7342.15i	0.345125	−	0.250748i
$951$	−1947.01	+	5992.27i	−0.0663891	+	0.204325i
$952$	221.302	−	681.097i	0.00753406	−	0.0231875i
$953$	−36696.1	+	26661.2i	−1.24733	+	0.906235i	−0.998064	−	0.0622005i	$-0.980188\pi$
$953$	−36696.1	+	26661.2i	−1.24733	+	0.906235i	−0.249262	+	0.968436i	$0.580188\pi$
$954$	6659.73	+	4838.58i	0.226013	+	0.164208i
$955$	8110.06	+	24960.2i	0.274801	+	0.845752i
$956$	15173.2			0.513323
$957$		0			0
$958$	82343.2			2.77702
$959$	−204.431	−	629.174i	−0.00688365	−	0.0211857i
$960$	7250.19	+	5267.57i	0.243749	+	0.177094i
$961$	1823.33	−	1324.73i	0.0612042	−	0.0444675i
$962$	3138.55	−	9659.46i	0.105188	−	0.323736i
$963$	146.951	−	452.270i	0.00491739	−	0.0151342i
$964$	95931.9	−	69698.6i	3.20514	−	2.32867i
$965$	−4886.04	−	3549.92i	−0.162992	−	0.118421i
$966$	−1845.00	−	5678.33i	−0.0614513	−	0.189128i
$967$	22874.2			0.760687			0.380343	−	0.924845i	$-0.375806\pi$
$967$	22874.2			0.760687			0.380343	+	0.924845i	$0.375806\pi$
$968$		0			0
$969$	1713.98			0.0568226
$970$	−10183.4	−	31341.1i	−0.337080	−	1.03743i
$971$	−75.2596	−	54.6793i	−0.00248733	−	0.00180715i	0.586541	−	0.809920i	$-0.300489\pi$
$971$	−75.2596	−	54.6793i	−0.00248733	−	0.00180715i	−0.589028	+	0.808112i	$0.700489\pi$
$972$	−26334.0	+	19132.8i	−0.868996	+	0.631362i
$973$	134.204	−	413.036i	0.00442176	−	0.0136088i
$974$	−6928.24	+	21322.9i	−0.227921	+	0.701469i
$975$	−5303.57	+	3853.27i	−0.174205	+	0.126568i
$976$	−75575.9	−	54909.1i	−2.47861	−	1.80082i
$977$	−1606.98	−	4945.78i	−0.0526222	−	0.161954i	0.921292	−	0.388872i	$-0.127135\pi$
$977$	−1606.98	−	4945.78i	−0.0526222	−	0.161954i	−0.973914	+	0.226918i	$0.927135\pi$
$978$	−68699.9			−2.24620
$979$		0			0
$980$	54705.2			1.78316
$981$	−1148.70	−	3535.33i	−0.0373854	−	0.115061i
$982$	−12136.4	−	8817.63i	−0.394388	−	0.286539i
$983$	37174.8	−	27009.1i	1.20620	−	0.876355i	0.211319	−	0.977417i	$-0.432224\pi$
$983$	37174.8	−	27009.1i	1.20620	−	0.876355i	0.994880	+	0.101062i	$0.0322242\pi$
$984$	23647.7	−	72780.2i	0.766120	−	2.35787i
$985$	11311.8	−	34814.2i	0.365913	−	1.12617i
$986$	−7955.35	+	5779.90i	−0.256947	+	0.186683i
$987$	333.119	+	242.025i	0.0107430	+	0.00780521i
$988$	−7906.45	−	24333.5i	−0.254593	−	0.783556i
$989$	8119.17			0.261046
$990$		0			0
$991$	22935.6			0.735191			0.367595	−	0.929986i	$-0.380181\pi$
$991$	22935.6			0.735191			0.367595	+	0.929986i	$0.380181\pi$
$992$	12904.5	+	39716.0i	0.413023	+	1.27115i
$993$	42771.3	+	31075.2i	1.36687	+	0.993093i
$994$	1073.58	−	780.001i	0.0342574	−	0.0248895i
$995$	5391.14	−	16592.2i	0.171769	−	0.528652i
$996$	−19849.1	+	61089.3i	−0.631469	+	1.94346i
$997$	3248.78	−	2360.38i	0.103199	−	0.0749788i	−0.534989	−	0.844859i	$-0.679684\pi$
$997$	3248.78	−	2360.38i	0.103199	−	0.0749788i	0.638188	+	0.769880i	$0.279684\pi$
$998$	−66189.7	−	48089.6i	−2.09940	−	1.52530i
$999$	3221.25	+	9914.00i	0.102018	+	0.313979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.h.27.2		8
11.2	odd	10		121.4.c.b.9.1		8
11.3	even	5		121.4.a.g.1.4		4
11.4	even	5		11.4.c.a.3.1	✓	8
11.5	even	5		11.4.c.a.4.1	yes	8
11.6	odd	10		121.4.c.i.81.2		8
11.7	odd	10		121.4.c.i.3.2		8
11.8	odd	10		121.4.a.f.1.1		4
11.9	even	5	inner	121.4.c.h.9.2		8
11.10	odd	2		121.4.c.b.27.1		8
33.5	odd	10		99.4.f.c.37.2		8
33.8	even	10		1089.4.a.bh.1.4		4
33.14	odd	10		1089.4.a.y.1.1		4
33.26	odd	10		99.4.f.c.91.2		8
44.3	odd	10		1936.4.a.bk.1.1		4
44.15	odd	10		176.4.m.c.113.1		8
44.19	even	10		1936.4.a.bl.1.1		4
44.27	odd	10		176.4.m.c.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.1	✓	8	11.4	even	5
11.4.c.a.4.1	yes	8	11.5	even	5
99.4.f.c.37.2		8	33.5	odd	10
99.4.f.c.91.2		8	33.26	odd	10
121.4.a.f.1.1		4	11.8	odd	10
121.4.a.g.1.4		4	11.3	even	5
121.4.c.b.9.1		8	11.2	odd	10
121.4.c.b.27.1		8	11.10	odd	2
121.4.c.h.9.2		8	11.9	even	5	inner
121.4.c.h.27.2		8	1.1	even	1	trivial
121.4.c.i.3.2		8	11.7	odd	10
121.4.c.i.81.2		8	11.6	odd	10
176.4.m.c.81.1		8	44.27	odd	10
176.4.m.c.113.1		8	44.15	odd	10
1089.4.a.y.1.1		4	33.14	odd	10
1089.4.a.bh.1.4		4	33.8	even	10
1936.4.a.bk.1.1		4	44.3	odd	10
1936.4.a.bl.1.1		4	44.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.59435 + 4.90690i) q^{2} +(-3.67405 - 2.66936i) q^{3} +(-15.0635 + 10.9443i) q^{4} +(-2.66846 + 8.21268i) q^{5} +(7.24054 - 22.2841i) q^{6} +(-1.34505 + 0.977239i) q^{7} +(-44.3266 - 32.2052i) q^{8} +(-1.97025 - 6.06380i) q^{9} -44.5532 q^{10} +84.5585 q^{12} +(-8.84517 - 27.2226i) q^{13} +(-6.93969 - 5.04198i) q^{14} +(31.7267 - 23.0508i) q^{15} +(41.3254 - 127.186i) q^{16} +(2.42938 - 7.47686i) q^{17} +(26.6132 - 19.3356i) q^{18} +(-38.8386 - 28.2179i) q^{19} +(-49.6856 - 152.917i) q^{20} +7.55040 q^{21} -153.265 q^{23} +(76.8914 + 236.647i) q^{24} +(40.7996 + 29.6427i) q^{25} +(119.476 - 86.8047i) q^{26} +(-46.8385 + 144.154i) q^{27} +(9.56608 - 29.4414i) q^{28} +(-196.131 + 142.497i) q^{29} +(163.691 + 118.928i) q^{30} +(51.2794 + 157.822i) q^{31} +251.651 q^{32} +40.5614 q^{34} +(-4.43653 - 13.6542i) q^{35} +(96.0430 + 69.7793i) q^{36} +(55.6391 - 40.4242i) q^{37} +(76.5400 - 235.566i) q^{38} +(-40.1693 + 123.628i) q^{39} +(382.775 - 278.102i) q^{40} +(-248.811 - 180.772i) q^{41} +(12.0380 + 37.0490i) q^{42} -52.9746 q^{43} +55.0576 q^{45} +(-244.358 - 752.056i) q^{46} +(44.1194 + 32.0546i) q^{47} +(-491.338 + 356.978i) q^{48} +(-105.139 + 323.584i) q^{49} +(-80.4047 + 247.460i) q^{50} +(-28.8841 + 20.9855i) q^{51} +(431.173 + 313.265i) q^{52} +(77.3290 + 237.994i) q^{53} -782.025 q^{54} +91.0939 q^{56} +(67.3715 + 207.348i) q^{57} +(-1011.92 - 735.203i) q^{58} +(-306.711 + 222.839i) q^{59} +(-225.641 + 694.453i) q^{60} +(215.861 - 664.351i) q^{61} +(-692.657 + 503.245i) q^{62} +(8.57587 + 6.23074i) q^{63} +(70.6167 + 217.336i) q^{64} +247.174 q^{65} -278.021 q^{67} +(45.2340 + 139.216i) q^{68} +(563.105 + 409.120i) q^{69} +(59.9265 - 43.5392i) q^{70} +(-47.8053 + 147.130i) q^{71} +(-107.951 + 332.240i) q^{72} +(769.534 - 559.099i) q^{73} +(287.065 + 208.565i) q^{74} +(-70.7732 - 217.818i) q^{75} +893.872 q^{76} -670.675 q^{78} +(0.686168 + 2.11181i) q^{79} +(934.267 + 678.784i) q^{80} +(417.615 - 303.415i) q^{81} +(490.337 - 1509.10i) q^{82} +(-234.738 + 722.450i) q^{83} +(-113.736 + 82.6339i) q^{84} +(54.9224 + 39.9035i) q^{85} +(-84.4599 - 259.941i) q^{86} +1100.97 q^{87} +1157.64 q^{89} +(87.7809 + 270.162i) q^{90} +(38.5003 + 27.9721i) q^{91} +(2308.72 - 1677.38i) q^{92} +(232.879 - 716.728i) q^{93} +(-86.9470 + 267.595i) q^{94} +(335.384 - 243.671i) q^{95} +(-924.581 - 671.747i) q^{96} +(228.566 + 703.454i) q^{97} -1755.42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 3 q^{3} - 17 q^{4} + 18 q^{5} - 14 q^{6} + 10 q^{7} - 113 q^{8} + 31 q^{9} + 40 q^{10} + 190 q^{12} + 40 q^{13} + 64 q^{14} + 119 q^{15} + 343 q^{16} - 201 q^{17} + 53 q^{18} - 302 q^{19}+ \cdots + 2740 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 - 3 * q^3 - 17 * q^4 + 18 * q^5 - 14 * q^6 + 10 * q^7 - 113 * q^8 + 31 * q^9 + 40 * q^10 + 190 * q^12 + 40 * q^13 + 64 * q^14 + 119 * q^15 + 343 * q^16 - 201 * q^17 + 53 * q^18 - 302 * q^19 - 88 * q^20 + 334 * q^21 - 12 * q^23 + 348 * q^24 + 214 * q^25 + 340 * q^26 + 72 * q^27 + 18 * q^28 - 164 * q^29 + 306 * q^30 + 324 * q^31 + 324 * q^32 - 298 * q^34 - 593 * q^35 - 125 * q^36 - 174 * q^37 - 327 * q^38 - 125 * q^39 + 282 * q^40 - 121 * q^41 - 590 * q^42 - 650 * q^43 + 452 * q^45 + 54 * q^46 + 12 * q^47 - 991 * q^48 - 1130 * q^49 + 1163 * q^50 + 194 * q^51 + 1600 * q^52 + 682 * q^53 - 3100 * q^54 - 1560 * q^56 - 333 * q^57 - 2348 * q^58 - 854 * q^59 - 502 * q^60 + 630 * q^61 - 2114 * q^62 + 67 * q^63 - 1289 * q^64 + 1790 * q^65 + 86 * q^67 - 575 * q^68 + 1198 * q^69 + 166 * q^70 - 1772 * q^71 + 104 * q^72 + 2425 * q^73 + 1274 * q^74 + 975 * q^75 - 242 * q^76 - 1340 * q^78 - 116 * q^79 + 1794 * q^80 - 26 * q^81 + 2708 * q^82 - 1738 * q^83 - 174 * q^84 - 1662 * q^85 - 784 * q^86 + 2310 * q^87 + 3782 * q^89 + 2658 * q^90 - 55 * q^91 + 5900 * q^92 + 2743 * q^93 - 1458 * q^94 - 487 * q^95 - 2383 * q^96 + 3116 * q^97 + 2740 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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