LMFDB - Embedded newform 121.4.c.h.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$7.13923111069$
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			9.2
Root			$2.86504 - 2.08157i$ of defining polynomial
Character	$\chi$	$=$	121.9
Dual form			121.4.c.h.27.2

$q$-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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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	−0.108135	−	0.994136i	$-0.534488\pi$
$2$	1.59435	−	4.90690i	0.563687	−	1.73485i	0.671821	−	0.740713i	$-0.265512\pi$
$3$	−3.67405	+	2.66936i	−0.707072	+	0.513718i	−0.882228	−	0.470823i	$-0.843957\pi$
$3$	−3.67405	+	2.66936i	−0.707072	+	0.513718i	0.175156	+	0.984541i	$0.443957\pi$
$4$	−15.0635	−	10.9443i	−1.88294	−	1.36804i
$5$	−2.66846	−	8.21268i	−0.238675	−	0.734565i	−0.996613	−	0.0822383i	$-0.973793\pi$
$5$	−2.66846	−	8.21268i	−0.238675	−	0.734565i	0.757938	−	0.652326i	$-0.226207\pi$
$6$	7.24054	+	22.2841i	0.492656	+	1.51624i
$7$	−1.34505	−	0.977239i	−0.0726261	−	0.0527660i	0.550880	−	0.834585i	$-0.314292\pi$
$7$	−1.34505	−	0.977239i	−0.0726261	−	0.0527660i	−0.623506	+	0.781819i	$0.714292\pi$
$8$	−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	−0.999993	−	0.00386737i	$-0.998769\pi$
$13$	−8.84517	+	27.2226i	−0.188708	+	0.580785i	0.811284	+	0.584652i	$0.198769\pi$
$14$	−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	0.966890	−	0.255195i	$-0.0821397\pi$
$17$	2.42938	+	7.47686i	0.0346595	+	0.106671i	−0.932230	+	0.361866i	$0.882140\pi$
$18$	26.6132	+	19.3356i	0.348488	+	0.253191i
$19$	−38.8386	+	28.2179i	−0.468957	+	0.340717i	−0.797035	−	0.603934i	$-0.793599\pi$
$19$	−38.8386	+	28.2179i	−0.468957	+	0.340717i	0.328078	+	0.944651i	$0.393599\pi$
$20$	−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	−0.257334	−	0.966322i	$-0.582844\pi$
$29$	−196.131	−	142.497i	−1.25588	−	0.912452i	−0.998548	+	0.0538706i	$0.982844\pi$
$30$	163.691	−	118.928i	0.996192	−	0.723776i
$31$	51.2794	−	157.822i	0.297098	−	0.914374i	−0.685410	−	0.728157i	$-0.740377\pi$
$31$	51.2794	−	157.822i	0.297098	−	0.914374i	0.982509	−	0.186217i	$-0.0596228\pi$
$32$	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	0.704492	−	0.709712i	$-0.251175\pi$
$37$	55.6391	+	40.4242i	0.247216	+	0.179613i	−0.457276	+	0.889325i	$0.651175\pi$
$38$	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	−0.950274	−	0.311416i	$-0.899197\pi$
$41$	−248.811	+	180.772i	−0.947750	+	0.688580i	0.00252390	+	0.999997i	$0.499197\pi$
$42$	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	−0.517214	−	0.855856i	$-0.673031\pi$
$47$	44.1194	−	32.0546i	0.136925	−	0.0994818i	0.654139	+	0.756374i	$0.273031\pi$
$48$	−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	−0.799456	−	0.600724i	$-0.794879\pi$
$53$	77.3290	−	237.994i	0.200414	−	0.616811i	0.999871	−	0.0160872i	$-0.00512095\pi$
$54$	−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	0.195504	−	0.980703i	$-0.437366\pi$
$59$	−306.711	−	222.839i	−0.676786	−	0.491714i	−0.872290	+	0.488989i	$0.837366\pi$
$60$	−225.641	−	694.453i	−0.485503	−	1.49422i
$61$	215.861	+	664.351i	0.453084	+	1.39445i	0.873369	+	0.487058i	$0.161930\pi$
$61$	215.861	+	664.351i	0.453084	+	1.39445i	−0.420285	+	0.907392i	$0.638070\pi$
$62$	−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	0.903120	−	0.429388i	$-0.141271\pi$
$71$	−47.8053	−	147.130i	−0.0799077	−	0.245931i	−0.983028	+	0.183458i	$0.941271\pi$
$72$	−107.951	−	332.240i	−0.176697	−	0.543818i
$73$	769.534	+	559.099i	1.23380	+	0.896406i	0.997169	−	0.0751945i	$-0.0239578\pi$
$73$	769.534	+	559.099i	1.23380	+	0.896406i	0.236628	+	0.971600i	$0.423958\pi$
$74$	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	−0.950567	−	0.310520i	$-0.899497\pi$
$79$	0.686168	−	2.11181i	0.000977215	−	0.00300756i	0.951544	+	0.307513i	$0.0994967\pi$
$80$	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	−0.977594	−	0.210499i	$-0.932491\pi$
$83$	−234.738	−	722.450i	−0.310432	−	0.955412i	0.667162	−	0.744913i	$-0.267509\pi$
$84$	−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	−0.757278	−	0.653093i	$-0.773471\pi$
$97$	228.566	−	703.454i	0.239251	−	0.736339i	0.996529	−	0.0832464i	$-0.0265288\pi$
$98$	−1755.42			−1.80943
$99$		0			0
$100$	−939.006			−0.939006
$101$	190.422	−	586.057i	0.187600	−	0.577375i	−0.812383	−	0.583124i	$-0.801830\pi$
$101$	190.422	−	586.057i	0.187600	−	0.577375i	0.999983	+	0.00574932i	$0.00183008\pi$
$102$	−149.025	+	108.273i	−0.144663	+	0.105104i
$103$	−1235.79	−	897.853i	−1.18219	−	0.858914i	−0.189776	−	0.981827i	$-0.560776\pi$
$103$	−1235.79	−	897.853i	−1.18219	−	0.858914i	−0.992417	+	0.122914i	$0.960776\pi$
$104$	−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	−0.560193	−	0.828362i	$-0.689273\pi$
$107$	60.3407	−	43.8401i	0.0545174	−	0.0396092i	0.614710	+	0.788753i	$0.289273\pi$
$108$	−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	−0.524665	−	0.851309i	$-0.675809\pi$
$113$	147.565	−	107.212i	0.122847	−	0.0892536i	0.647512	+	0.762055i	$0.275809\pi$
$114$	−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	0.934178	−	0.356807i	$-0.116134\pi$
$127$	−44.8164	−	137.931i	−0.0313135	−	0.0963730i	−0.965492	+	0.260434i	$0.916134\pi$
$128$	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	0.905368	−	0.424628i	$-0.139595\pi$
$137$	−122.960	−	378.432i	−0.0766803	−	0.235998i	−0.982048	+	0.188631i	$0.939595\pi$
$138$	−1109.72	−	3415.37i	−0.684535	−	2.10678i
$139$	−211.328	−	153.539i	−0.128954	−	0.0936907i	0.521438	−	0.853289i	$-0.325396\pi$
$139$	−211.328	−	153.539i	−0.128954	−	0.0936907i	−0.650393	+	0.759598i	$0.725396\pi$
$140$	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	0.998725	−	0.0504743i	$-0.0160733\pi$
$149$	292.953	+	901.617i	0.161072	+	0.495727i	−0.837654	+	0.546202i	$0.816073\pi$
$150$	955.971	+	694.554i	0.520365	+	0.378067i
$151$	−1468.52	+	1066.94i	−0.791434	+	0.575010i	−0.908389	−	0.418127i	$-0.862687\pi$
$151$	−1468.52	+	1066.94i	−0.791434	+	0.575010i	0.116955	+	0.993137i	$0.462687\pi$
$152$	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	−0.381211	−	0.924488i	$-0.624493\pi$
$157$	747.989	−	543.446i	0.380229	−	0.276253i	0.761440	+	0.648235i	$0.224493\pi$
$158$	−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	0.457316	+	0.889304i	$0.348811\pi$
$163$	−906.046	+	2788.52i	−0.435380	+	1.33996i	−0.892696	+	0.450659i	$0.851189\pi$
$164$	5726.40			2.72656
$165$		0			0
$166$	−3919.24			−1.83248
$167$	340.142	−	1046.85i	0.157611	−	0.485076i	−0.840805	−	0.541337i	$-0.817918\pi$
$167$	340.142	−	1046.85i	0.157611	−	0.485076i	0.998416	+	0.0562619i	$0.0179182\pi$
$168$	−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	0.283969	−	0.958833i	$-0.408349\pi$
$173$	2920.84	−	2122.11i	1.28363	−	0.932609i	0.999656	+	0.0262248i	$0.00834856\pi$
$174$	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	−0.989634	−	0.143609i	$-0.954129\pi$
$179$	−2775.32	+	2016.39i	−1.15887	+	0.841967i	−0.169233	+	0.985576i	$0.554129\pi$
$180$	−829.363	−	602.567i	−0.343428	−	0.249515i
$181$	−1145.06	−	3524.14i	−0.470231	−	1.44722i	−0.852282	−	0.523082i	$-0.824782\pi$
$181$	−1145.06	−	3524.14i	−0.470231	−	1.44722i	0.382051	−	0.924141i	$-0.375218\pi$
$182$	−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	0.946353	−	0.323134i	$-0.104736\pi$
$191$	2458.79	+	1786.41i	0.931474	+	0.676755i	−0.0148796	+	0.999889i	$0.504736\pi$
$192$	320.697	+	987.005i	0.120543	+	0.370994i
$193$	−216.124	−	665.161i	−0.0806059	−	0.248080i	0.902630	−	0.430417i	$-0.141634\pi$
$193$	−216.124	−	665.161i	−0.0806059	−	0.248080i	−0.983236	+	0.182338i	$0.941634\pi$
$194$	−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	0.132427	+	0.991193i	$0.457723\pi$
$211$	−1708.15	+	5257.15i	−0.557317	+	1.71525i	−0.689744	+	0.724053i	$0.742277\pi$
$212$	−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	−0.114430	−	0.993431i	$-0.536504\pi$
$223$	2647.49	−	1923.51i	0.795018	−	0.577614i	0.909448	+	0.415817i	$0.136504\pi$
$224$	−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	−0.999637	−	0.0269252i	$-0.991428\pi$
$227$	−4562.93	−	3315.16i	−1.33415	−	0.969317i	−0.334512	−	0.942391i	$-0.608572\pi$
$228$	−3284.13	+	2386.06i	−0.953934	+	0.693074i
$229$	337.455	−	1038.58i	0.0973784	−	0.299700i	−0.890488	−	0.455007i	$-0.849637\pi$
$229$	337.455	−	1038.58i	0.0973784	−	0.299700i	0.987866	+	0.155307i	$0.0496367\pi$
$230$	6828.46			1.95763
$231$		0			0
$232$	13283.0			3.75892
$233$	−508.566	+	1565.21i	−0.142993	+	0.440086i	−0.996747	−	0.0805894i	$-0.974320\pi$
$233$	−508.566	+	1565.21i	−0.142993	+	0.440086i	0.853755	+	0.520675i	$0.174320\pi$
$234$	−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	−0.673416	−	0.739264i	$-0.735174\pi$
$239$	−659.274	+	478.991i	−0.178430	+	0.129637i	0.494985	+	0.868901i	$0.335174\pi$
$240$	−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	−0.972644	−	0.232299i	$-0.925375\pi$
$251$	−195.714	+	602.345i	−0.0492165	+	0.151473i	0.923428	+	0.383772i	$0.125375\pi$
$252$	−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	0.541997	−	0.840381i	$-0.317668\pi$
$257$	−369.839	−	268.704i	−0.0897663	−	0.0652190i	−0.631763	+	0.775162i	$0.717668\pi$
$258$	−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	−0.977893	−	0.209108i	$-0.932944\pi$
$269$	−1366.25	−	4204.88i	−0.309671	−	0.953071i	0.668221	−	0.743963i	$-0.267056\pi$
$270$	2086.81	+	6422.53i	0.470366	+	1.44764i
$271$	−2827.80	−	2054.52i	−0.633863	−	0.460528i	0.223873	−	0.974618i	$-0.428130\pi$
$271$	−2827.80	−	2054.52i	−0.633863	−	0.460528i	−0.857736	+	0.514090i	$0.828130\pi$
$272$	−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	−0.816009	−	0.578039i	$-0.803818\pi$
$277$	847.902	−	2609.57i	0.183919	−	0.566043i	0.999928	+	0.0119952i	$0.00381829\pi$
$278$	−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	0.877126	−	0.480261i	$-0.159458\pi$
$281$	−540.634	−	1663.90i	−0.114774	−	0.353239i	−0.991900	+	0.127022i	$0.959458\pi$
$282$	1033.76	+	751.067i	0.218295	+	0.158601i
$283$	1678.00	−	1219.14i	0.352463	−	0.256079i	−0.397439	−	0.917629i	$-0.630101\pi$
$283$	1678.00	−	1219.14i	0.352463	−	0.256079i	0.749902	+	0.661549i	$0.230101\pi$
$284$	−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	0.834401	−	0.551157i	$-0.185814\pi$
$293$	2849.04	+	2069.95i	0.568064	+	0.412723i	−0.266337	+	0.963880i	$0.585814\pi$
$294$	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	−0.743734	−	0.668475i	$-0.766947\pi$
$311$	−1852.70	+	1346.06i	−0.337803	+	0.245428i	0.405931	+	0.913904i	$0.366947\pi$
$312$	5762.05	+	4186.37i	1.04555	+	0.759637i
$313$	2447.15	+	7531.54i	0.441920	+	1.36009i	0.885827	+	0.464016i	$0.153592\pi$
$313$	2447.15	+	7531.54i	0.441920	+	1.36009i	−0.443907	+	0.896073i	$0.646408\pi$
$314$	−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	−0.981826	−	0.189782i	$-0.939222\pi$
$317$	−428.726	+	1319.48i	−0.0759610	+	0.233784i	0.905865	+	0.423566i	$0.139222\pi$
$318$	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	0.982441	−	0.186574i	$-0.0597383\pi$
$337$	6858.29	+	4982.84i	1.10859	+	0.805438i	0.126149	+	0.992011i	$0.459738\pi$
$338$	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	0.894929	−	0.446209i	$-0.147226\pi$
$347$	−590.536	−	1817.48i	−0.0913591	−	0.281175i	−0.986288	+	0.165035i	$0.947226\pi$
$348$	−16584.5	−	12049.4i	−2.55467	−	1.85608i
$349$	−6978.67	+	5070.30i	−1.07037	+	0.777671i	−0.975979	−	0.217865i	$-0.930091\pi$
$349$	−6978.67	+	5070.30i	−1.07037	+	0.777671i	−0.0943926	+	0.995535i	$0.530091\pi$
$350$	−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	0.281685	−	0.959507i	$-0.409107\pi$
$359$	−3699.07	−	2687.53i	−0.543814	−	0.395104i	−0.825500	+	0.564403i	$0.809107\pi$
$360$	−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	0.502749	−	0.864432i	$-0.332322\pi$
$367$	−1153.15	−	837.814i	−0.164016	−	0.119165i	−0.666766	+	0.745267i	$0.732322\pi$
$368$	−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	0.998596	+	0.0529706i	$0.0168690\pi$
$379$	1636.89	+	5037.82i	0.221850	+	0.682785i	−0.776746	+	0.629814i	$0.783131\pi$
$380$	−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	−0.416055	−	0.909340i	$-0.636588\pi$
$383$	3410.71	−	10497.1i	0.455037	−	1.40046i	0.871092	−	0.491120i	$-0.163412\pi$
$384$	−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	−0.181306	−	0.983427i	$-0.558032\pi$
$389$	−8996.72	−	6536.50i	−1.17263	−	0.851963i	−0.991321	+	0.131464i	$0.958032\pi$
$390$	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	0.960002	−	0.279993i	$-0.0903322\pi$
$401$	150.709	+	463.834i	0.0187682	+	0.0577625i	−0.941234	+	0.337756i	$0.890332\pi$
$402$	−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	0.567358	+	0.823471i	$0.307966\pi$
$409$	−3107.35	+	9563.43i	−0.375668	+	1.15619i	−0.943027	+	0.332717i	$0.892034\pi$
$410$	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	−0.386616	−	0.922241i	$-0.626356\pi$
$421$	3204.91	−	2328.50i	0.371016	−	0.269559i	0.757632	+	0.652682i	$0.226356\pi$
$422$	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	−0.689576	−	0.724214i	$-0.742203\pi$
$431$	2630.51	−	8095.89i	0.293985	−	0.904792i	0.983561	−	0.180579i	$-0.0577970\pi$
$432$	16398.8	−	11914.4i	1.82636	−	1.32693i
$433$	8741.61	+	6351.15i	0.970196	+	0.704889i	0.955496	−	0.295003i	$-0.0953207\pi$
$433$	8741.61	+	6351.15i	0.970196	+	0.704889i	0.0146998	+	0.999892i	$0.495321\pi$
$434$	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	−0.479951	−	0.877295i	$-0.659346\pi$
$443$	1921.62	−	1396.14i	0.206093	−	0.149735i	0.686044	+	0.727560i	$0.259346\pi$
$444$	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	−0.726249	−	0.687432i	$-0.758738\pi$
$449$	2524.68	−	7770.18i	0.265361	−	0.816698i	0.991610	−	0.129266i	$-0.0412621\pi$
$450$	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	0.984392	+	0.175988i	$0.0563120\pi$
$457$	2847.29	+	8763.05i	0.291445	+	0.896976i	−0.692947	+	0.720989i	$0.743688\pi$
$458$	−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	−0.925051	−	0.379843i	$-0.875978\pi$
$467$	−4036.13	−	12421.9i	−0.399935	−	1.23087i	0.525116	−	0.851031i	$-0.324022\pi$
$468$	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	0.852007	+	0.523531i	$0.175385\pi$
$479$	4931.85	+	15178.7i	0.470442	+	1.44787i	−0.381564	+	0.924342i	$0.624615\pi$
$480$	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	−0.412089	−	0.911144i	$-0.635201\pi$
$487$	3515.59	−	2554.22i	0.327118	−	0.237665i	0.739207	+	0.673479i	$0.235201\pi$
$488$	−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	0.474411	−	0.880303i	$-0.342661\pi$
$491$	−2352.29	−	1709.04i	−0.216206	−	0.157083i	−0.690617	+	0.723221i	$0.742661\pi$
$492$	−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	−0.162303	−	0.986741i	$-0.551892\pi$
$499$	−12828.9	−	9320.75i	−1.15090	−	0.836181i	−0.988601	+	0.150560i	$0.951892\pi$
$500$	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	−0.654385	−	0.756162i	$-0.727072\pi$
$503$	−1550.57	+	1126.55i	−0.137448	+	0.0998619i	0.516937	+	0.856024i	$0.327072\pi$
$504$	−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	−0.854949	−	0.518712i	$-0.826412\pi$
$509$	−7186.63	+	5221.39i	−0.625819	+	0.454684i	0.229130	+	0.973396i	$0.426412\pi$
$510$	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	0.951719	−	0.306971i	$-0.0993155\pi$
$521$	11343.5	+	8241.50i	0.953869	+	0.693026i	0.00215031	+	0.999998i	$0.499316\pi$
$522$	−2464.39	−	7584.62i	−0.206635	−	0.635957i
$523$	−4674.70	−	14387.2i	−0.390842	−	1.20289i	−0.932153	−	0.362065i	$-0.882072\pi$
$523$	−4674.70	−	14387.2i	−0.390842	−	1.20289i	0.541311	−	0.840822i	$-0.317928\pi$
$524$	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	0.689764	+	0.724034i	$0.257714\pi$
$541$	−3697.53	+	11379.8i	−0.293843	+	0.904356i	−0.983608	+	0.180322i	$0.942286\pi$
$542$	−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	−0.959111	−	0.283031i	$-0.908660\pi$
$547$	−12618.2	+	9167.63i	−0.986313	+	0.716598i	−0.0272026	+	0.999630i	$0.508660\pi$
$548$	−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	−0.160026	−	0.987113i	$-0.551158\pi$
$557$	−15094.9	−	10967.1i	−1.14828	−	0.834272i	−0.988251	+	0.152841i	$0.951158\pi$
$558$	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	−0.614755	−	0.788718i	$-0.710745\pi$
$563$	4624.62	−	14233.1i	0.346189	−	1.06546i	0.960944	−	0.276742i	$-0.0892548\pi$
$564$	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	−0.904665	−	0.426124i	$-0.859879\pi$
$569$	−10572.6	+	7681.42i	−0.778954	+	0.565943i	0.125711	+	0.992067i	$0.459879\pi$
$570$	−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	0.986255	+	0.165233i	$0.0528376\pi$
$577$	3956.75	+	12177.6i	0.285479	+	0.878615i	−0.700775	+	0.713382i	$0.747162\pi$
$578$	−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	0.189019	−	0.981973i	$-0.439469\pi$
$587$	−9763.07	−	7093.29i	−0.686482	−	0.498759i	−0.875502	+	0.483215i	$0.839469\pi$
$588$	−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	0.992036	−	0.125954i	$-0.0401993\pi$
$599$	1692.20	+	5208.05i	0.115428	+	0.355251i	−0.876608	+	0.481205i	$0.840199\pi$
$600$	−3877.72	−	11934.4i	−0.263845	−	0.812032i
$601$	−13837.4	−	10053.5i	−0.939170	−	0.682347i	0.00905088	−	0.999959i	$-0.497119\pi$
$601$	−13837.4	−	10053.5i	−0.939170	−	0.682347i	−0.948221	+	0.317612i	$0.897119\pi$
$602$	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	−0.932816	−	0.360352i	$-0.882657\pi$
$607$	503.344	−	1549.13i	0.0336575	−	0.103587i	0.966474	+	0.256765i	$0.0826566\pi$
$608$	−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	−0.0801088	−	0.996786i	$-0.525527\pi$
$613$	12796.4	−	9297.14i	0.843136	−	0.612574i	0.923245	+	0.384212i	$0.125527\pi$
$614$	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	−0.742838	−	0.669471i	$-0.766521\pi$
$619$	−5169.71	+	3756.01i	−0.335684	+	0.243888i	0.407155	+	0.913359i	$0.366521\pi$
$620$	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	0.939409	−	0.342797i	$-0.111374\pi$
$631$	14323.9	+	10406.9i	0.903683	+	0.656564i	−0.0357261	+	0.999362i	$0.511374\pi$
$632$	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	−0.939954	−	0.341301i	$-0.889132\pi$
$641$	−14700.4	+	10680.5i	−0.905819	+	0.658116i	0.0341348	+	0.999417i	$0.489132\pi$
$642$	1413.84	+	1027.21i	0.0869153	+	0.0631477i
$643$	1687.38	+	5193.23i	0.103490	+	0.318509i	0.989373	−	0.145399i	$-0.0464467\pi$
$643$	1687.38	+	5193.23i	0.103490	+	0.318509i	−0.885883	+	0.463908i	$0.846447\pi$
$644$	−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	0.788005	+	0.615668i	$0.211114\pi$
$647$	−3478.81	+	10706.7i	−0.211385	+	0.650577i	−0.999391	+	0.0349083i	$0.988886\pi$
$648$	−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	0.530625	−	0.847607i	$-0.321957\pi$
$653$	−1860.98	−	1352.08i	−0.111525	−	0.0810274i	−0.642150	+	0.766579i	$0.721957\pi$
$654$	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	−0.998405	−	0.0564597i	$-0.982019\pi$
$673$	−2749.68	+	8462.64i	−0.157492	+	0.484711i	0.840913	+	0.541171i	$0.182019\pi$
$674$	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	0.973575	+	0.228366i	$0.0733383\pi$
$677$	5639.74	+	17357.3i	0.320167	+	0.985371i	−0.653409	+	0.757005i	$0.726662\pi$
$678$	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	−0.983401	−	0.181448i	$-0.941922\pi$
$691$	−1474.22	+	4537.18i	−0.0811606	+	0.249787i	0.902240	+	0.431234i	$0.141922\pi$
$692$	−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	−0.307185	−	0.951650i	$-0.599387\pi$
$701$	9334.96	−	6782.24i	0.502962	−	0.365423i	0.810147	+	0.586226i	$0.199387\pi$
$702$	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	0.987009	−	0.160667i	$-0.0513646\pi$
$709$	1775.80	+	5465.34i	0.0940640	+	0.289499i	−0.892945	+	0.450167i	$0.851365\pi$
$710$	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	0.107390	−	0.994217i	$-0.465751\pi$
$719$	−15519.5	−	11275.6i	−0.804981	−	0.584853i	−0.912371	+	0.409364i	$0.865751\pi$
$720$	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	0.239010	−	0.971017i	$-0.423177\pi$
$733$	−12118.0	−	8804.22i	−0.610624	−	0.443644i	−0.849634	+	0.527373i	$0.823177\pi$
$734$	−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	−0.638845	−	0.769335i	$-0.720587\pi$
$739$	6633.42	−	20415.6i	0.330196	−	1.01624i	0.969041	−	0.246902i	$-0.0794125\pi$
$740$	−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	0.932069	+	0.362280i	$0.118002\pi$
$743$	7917.85	+	24368.6i	0.390952	+	1.20323i	−0.541117	+	0.840947i	$0.681998\pi$
$744$	−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	−0.567665	−	0.823259i	$-0.692153\pi$
$751$	820.808	−	596.352i	0.0398824	−	0.0289763i	0.607548	+	0.794283i	$0.292153\pi$
$752$	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	−0.980539	−	0.196325i	$-0.937099\pi$
$757$	−1496.88	+	4606.93i	−0.0718693	+	0.221191i	0.908670	+	0.417516i	$0.137099\pi$
$758$	27329.8			1.30958
$759$		0			0
$760$	−22713.9			−1.08410
$761$	6120.48	−	18836.9i	0.291547	−	0.897290i	−0.692812	−	0.721118i	$-0.743629\pi$
$761$	6120.48	−	18836.9i	0.291547	−	0.897290i	0.984359	−	0.176172i	$-0.0563715\pi$
$762$	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	−0.631265	−	0.775567i	$-0.717464\pi$
$773$	−1906.94	+	1385.47i	−0.0887293	+	0.0644656i	0.542536	+	0.840032i	$0.317464\pi$
$774$	−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	−0.948747	−	0.316037i	$-0.897647\pi$
$787$	−8101.71	−	24934.5i	−0.366957	−	1.12938i	0.581790	−	0.813339i	$-0.302353\pi$
$788$	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	0.994860	+	0.101265i	$0.0322889\pi$
$797$	5614.34	+	17279.1i	0.249523	+	0.767953i	−0.745336	+	0.666689i	$0.767711\pi$
$798$	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	0.928010	−	0.372554i	$-0.121518\pi$
$809$	−960.631	−	2956.52i	−0.0417478	−	0.128487i	−0.969758	+	0.244068i	$0.921518\pi$
$810$	−18606.1	−	13518.1i	−0.807101	−	0.586393i
$811$	16792.4	−	12200.4i	0.727078	−	0.528253i	−0.161560	−	0.986863i	$-0.551652\pi$
$811$	16792.4	−	12200.4i	0.727078	−	0.528253i	0.888638	+	0.458610i	$0.151652\pi$
$812$	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	0.715541	−	0.698571i	$-0.246180\pi$
$821$	6405.05	+	4653.54i	0.272275	+	0.197819i	−0.443266	+	0.896390i	$0.646180\pi$
$822$	7542.72	−	5480.11i	0.320052	−	0.232531i
$823$	9044.36	−	27835.7i	0.383070	−	1.17897i	−0.554801	−	0.831983i	$-0.687205\pi$
$823$	9044.36	−	27835.7i	0.383070	−	1.17897i	0.937871	−	0.346985i	$-0.112795\pi$
$824$	83693.9			3.53837
$825$		0			0
$826$	3252.03			0.136989
$827$	−4296.40	+	13223.0i	−0.180654	+	0.555995i	−0.999846	−	0.0175235i	$-0.994422\pi$
$827$	−4296.40	+	13223.0i	−0.180654	+	0.555995i	0.819193	+	0.573518i	$0.194422\pi$
$828$	−14720.1	+	10694.7i	−0.617823	+	0.448874i
$829$	7656.49	+	5562.76i	0.320773	+	0.233055i	0.736505	−	0.676432i	$-0.236475\pi$
$829$	7656.49	+	5562.76i	0.320773	+	0.233055i	−0.415732	+	0.909487i	$0.636475\pi$
$830$	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	0.271002	−	0.962579i	$-0.412645\pi$
$839$	30868.8	−	22427.5i	1.27021	−	0.922864i	0.999211	+	0.0397149i	$0.0126450\pi$
$840$	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	−0.793368	−	0.608742i	$-0.791674\pi$
$853$	−12688.9	−	39052.3i	−0.509330	−	1.56756i	0.284039	−	0.958813i	$-0.408326\pi$
$854$	−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	−0.901536	−	0.432704i	$-0.857559\pi$
$863$	−10813.1	−	33279.3i	−0.426515	−	1.31268i	0.475020	−	0.879975i	$-0.342441\pi$
$864$	−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	−0.949479	−	0.313829i	$-0.898388\pi$
$877$	−24528.0	+	17820.6i	−0.944415	+	0.686158i	0.00506422	+	0.999987i	$0.498388\pi$
$878$	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	−0.354081	−	0.935215i	$-0.615206\pi$
$883$	11176.2	−	8119.96i	0.425943	−	0.309466i	0.780025	+	0.625749i	$0.215206\pi$
$884$	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	0.216649	−	0.976249i	$-0.430487\pi$
$887$	−17035.6	−	12377.1i	−0.644871	−	0.468526i	−0.861520	+	0.507723i	$0.830487\pi$
$888$	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	−0.897017	−	0.441995i	$-0.854271\pi$
$907$	−11776.1	−	36243.2i	−0.431113	−	1.32683i	0.465904	−	0.884835i	$-0.345729\pi$
$908$	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	−0.954519	−	0.298152i	$-0.903630\pi$
$911$	−193.786	+	596.413i	−0.00704767	+	0.0216905i	0.947471	+	0.319842i	$0.103630\pi$
$912$	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	0.727468	+	0.686142i	$0.240697\pi$
$919$	15106.5	+	46493.0i	0.542238	+	1.66884i	−0.185230	+	0.982695i	$0.559303\pi$
$920$	−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	−0.957974	−	0.286856i	$-0.907390\pi$
$929$	−9954.76	−	30637.6i	−0.351566	−	1.08201i	0.606408	−	0.795154i	$-0.292610\pi$
$930$	−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	−0.335779	−	0.941941i	$-0.609000\pi$
$937$	14040.7	−	43212.9i	0.489531	−	1.50662i	0.825310	−	0.564680i	$-0.191000\pi$
$938$	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	−0.879202	−	0.476450i	$-0.841923\pi$
$941$	−12930.8	−	39797.0i	−0.447963	−	1.37869i	0.431239	−	0.902238i	$-0.358077\pi$
$942$	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	−0.249262	−	0.968436i	$-0.580188\pi$
$953$	−36696.1	−	26661.2i	−1.24733	−	0.906235i	−0.998064	+	0.0622005i	$0.980188\pi$
$954$	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	−0.589028	−	0.808112i	$-0.700489\pi$
$971$	−75.2596	+	54.6793i	−0.00248733	+	0.00180715i	0.586541	+	0.809920i	$0.300489\pi$
$972$	−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	−0.973914	−	0.226918i	$-0.927135\pi$
$977$	−1606.98	+	4945.78i	−0.0526222	+	0.161954i	0.921292	+	0.388872i	$0.127135\pi$
$978$	−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	0.994880	−	0.101062i	$-0.0322242\pi$
$983$	37174.8	+	27009.1i	1.20620	+	0.876355i	0.211319	+	0.977417i	$0.432224\pi$
$984$	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	0.638188	−	0.769880i	$-0.279684\pi$
$997$	3248.78	+	2360.38i	0.103199	+	0.0749788i	−0.534989	+	0.844859i	$0.679684\pi$
$998$	−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.9.2		8
11.2	odd	10		121.4.c.i.3.2		8
11.3	even	5		11.4.c.a.4.1	yes	8
11.4	even	5		121.4.a.g.1.4		4
11.5	even	5	inner	121.4.c.h.27.2		8
11.6	odd	10		121.4.c.b.27.1		8
11.7	odd	10		121.4.a.f.1.1		4
11.8	odd	10		121.4.c.i.81.2		8
11.9	even	5		11.4.c.a.3.1	✓	8
11.10	odd	2		121.4.c.b.9.1		8
33.14	odd	10		99.4.f.c.37.2		8
33.20	odd	10		99.4.f.c.91.2		8
33.26	odd	10		1089.4.a.y.1.1		4
33.29	even	10		1089.4.a.bh.1.4		4
44.3	odd	10		176.4.m.c.81.1		8
44.7	even	10		1936.4.a.bl.1.1		4
44.15	odd	10		1936.4.a.bk.1.1		4
44.31	odd	10		176.4.m.c.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.1	✓	8	11.9	even	5
11.4.c.a.4.1	yes	8	11.3	even	5
99.4.f.c.37.2		8	33.14	odd	10
99.4.f.c.91.2		8	33.20	odd	10
121.4.a.f.1.1		4	11.7	odd	10
121.4.a.g.1.4		4	11.4	even	5
121.4.c.b.9.1		8	11.10	odd	2
121.4.c.b.27.1		8	11.6	odd	10
121.4.c.h.9.2		8	1.1	even	1	trivial
121.4.c.h.27.2		8	11.5	even	5	inner
121.4.c.i.3.2		8	11.2	odd	10
121.4.c.i.81.2		8	11.8	odd	10
176.4.m.c.81.1		8	44.3	odd	10
176.4.m.c.113.1		8	44.31	odd	10
1089.4.a.y.1.1		4	33.26	odd	10
1089.4.a.bh.1.4		4	33.29	even	10
1936.4.a.bk.1.1		4	44.15	odd	10
1936.4.a.bl.1.1		4	44.7	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 $\F_{q}$

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

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Database

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