LMFDB - Embedded newform 114.4.i.d.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 603 x^{16} - 1528 x^{15} + 240417 x^{14} - 786198 x^{13} + 54822410 x^{12} + \cdots + 11\!\cdots\!24 $ x^18 + 603x^16 - 1528x^15 + 240417x^14 - 786198x^13 + 54822410x^12 - 261322128x^11 + 9122210535x^10 - 45012474508x^9 + 1000170346788x^8 - 5035551052410x^7 + 79008124941737x^6 - 336274219954836x^5 + 3621639622047612x^4 - 11991799127581216x^3 + 107004711561222960x^2 - 278928948783924960x + 1161091951621493824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.3
Root			$4.63076 - 8.02071i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.4.i.d.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.64995 - 2.78435i) q^{5} +(4.59627 - 3.85673i) q^{6} +(15.4961 + 26.8400i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.64995 - 2.78435i) q^{5} +(4.59627 - 3.85673i) q^{6} +(15.4961 + 26.8400i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-2.82731 - 16.0344i) q^{10} +(9.20432 - 15.9423i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(9.78332 - 8.20918i) q^{13} +(58.2461 - 21.1999i) q^{14} +(22.9498 + 8.35306i) q^{15} +(12.2567 + 10.2846i) q^{16} +(6.17110 - 34.9981i) q^{17} +18.0000 q^{18} +(82.5293 - 6.92217i) q^{19} -32.5636 q^{20} +(-16.1452 + 91.5639i) q^{21} +(-28.2037 - 23.6657i) q^{22} +(75.4470 + 27.4605i) q^{23} +(-22.5526 + 8.20848i) q^{24} +(-44.9865 + 37.7482i) q^{25} +(-12.7712 - 22.1204i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-21.5269 - 122.085i) q^{28} +(-23.9096 - 135.598i) q^{29} +(24.4227 - 42.3014i) q^{30} +(-83.8800 - 145.284i) q^{31} +(24.5134 - 20.5692i) q^{32} +(51.8954 - 18.8884i) q^{33} +(-66.7895 - 24.3094i) q^{34} +(193.276 + 162.178i) q^{35} +(6.25133 - 35.4531i) q^{36} -300.898 q^{37} +(15.0281 - 164.955i) q^{38} +38.3137 q^{39} +(-11.3092 + 64.1378i) q^{40} +(262.285 + 220.083i) q^{41} +(174.738 + 63.5996i) q^{42} +(-449.845 + 163.730i) q^{43} +(-56.4073 + 47.3314i) q^{44} +(36.6341 + 63.4520i) q^{45} +(80.2890 - 139.065i) q^{46} +(12.6364 + 71.6645i) q^{47} +(8.33511 + 47.2708i) q^{48} +(-308.756 + 534.781i) q^{49} +(58.7257 + 101.716i) q^{50} +(81.6710 - 68.5301i) q^{51} +(-48.0041 + 17.4721i) q^{52} +(-435.535 - 158.522i) q^{53} +(41.3664 + 34.7105i) q^{54} +(26.0234 - 147.586i) q^{55} -247.937 q^{56} +(203.012 + 143.238i) q^{57} -275.380 q^{58} +(-56.7694 + 321.955i) q^{59} +(-74.8355 - 62.7944i) q^{60} +(-25.7174 - 9.36038i) q^{61} +(-315.286 + 114.755i) q^{62} +(-213.672 + 179.292i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(51.9846 - 90.0400i) q^{65} +(-19.1798 - 108.774i) q^{66} +(-154.563 - 876.572i) q^{67} +(-71.0759 + 123.107i) q^{68} +(120.434 + 208.597i) q^{69} +(386.552 - 324.356i) q^{70} +(382.004 - 139.038i) q^{71} +(-67.6579 - 24.6255i) q^{72} +(242.712 + 203.660i) q^{73} +(-104.501 + 592.652i) q^{74} -176.177 q^{75} +(-319.679 - 86.8879i) q^{76} +570.523 q^{77} +(13.3062 - 75.4632i) q^{78} +(90.9217 + 76.2924i) q^{79} +(122.399 + 44.5496i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(524.570 - 440.167i) q^{82} +(-640.778 - 1109.86i) q^{83} +(185.953 - 322.080i) q^{84} +(-50.2384 - 284.916i) q^{85} +(166.256 + 942.885i) q^{86} +(206.535 - 357.729i) q^{87} +(73.6345 + 127.539i) q^{88} +(31.2373 - 26.2112i) q^{89} +(137.699 - 50.1183i) q^{90} +(371.937 + 135.374i) q^{91} +(-246.020 - 206.435i) q^{92} +(87.3936 - 495.634i) q^{93} +145.540 q^{94} +(612.071 - 282.745i) q^{95} +96.0000 q^{96} +(156.265 - 886.225i) q^{97} +(946.083 + 793.858i) q^{98} +(155.686 + 56.6651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) $ 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	7.64995	−	2.78435i	0.684232	−	0.249040i	0.0235684	−	0.999722i	$-0.492497\pi$
$5$	7.64995	−	2.78435i	0.684232	−	0.249040i	0.660663	+	0.750682i	$0.270275\pi$
$6$	4.59627	−	3.85673i	0.312736	−	0.262417i
$7$	15.4961	+	26.8400i	0.836709	+	1.44922i	0.892632	+	0.450787i	$0.148857\pi$
$7$	15.4961	+	26.8400i	0.836709	+	1.44922i	−0.0559228	+	0.998435i	$0.517810\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	1.56283	+	8.86327i	0.0578827	+	0.328269i
$10$	−2.82731	−	16.0344i	−0.0894072	−	0.507054i
$11$	9.20432	−	15.9423i	0.252291	−	0.436982i	−0.711865	−	0.702316i	$-0.752149\pi$
$11$	9.20432	−	15.9423i	0.252291	−	0.436982i	0.964156	+	0.265335i	$0.0854825\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	9.78332	−	8.20918i	0.208724	−	0.175140i	−0.532433	−	0.846472i	$-0.678722\pi$
$13$	9.78332	−	8.20918i	0.208724	−	0.175140i	0.741156	+	0.671332i	$0.234278\pi$
$14$	58.2461	−	21.1999i	1.11192	−	0.404707i
$15$	22.9498	+	8.35306i	0.395041	+	0.143783i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	6.17110	−	34.9981i	0.0880419	−	0.499311i	−0.908617	−	0.417631i	$-0.862860\pi$
$17$	6.17110	−	34.9981i	0.0880419	−	0.499311i	0.996659	−	0.0816795i	$-0.0260284\pi$
$18$	18.0000			0.235702
$19$	82.5293	−	6.92217i	0.996501	−	0.0835818i
$19$	82.5293	−	6.92217i	0.996501	−	0.0835818i
$20$	−32.5636			−0.364072
$21$	−16.1452	+	91.5639i	−0.167770	+	0.951470i
$22$	−28.2037	−	23.6657i	−0.273320	−	0.229343i
$23$	75.4470	+	27.4605i	0.683991	+	0.248952i	0.660560	−	0.750773i	$-0.270319\pi$
$23$	75.4470	+	27.4605i	0.683991	+	0.248952i	0.0234306	+	0.999725i	$0.492541\pi$
$24$	−22.5526	+	8.20848i	−0.191814	+	0.0698146i
$25$	−44.9865	+	37.7482i	−0.359892	+	0.301985i
$26$	−12.7712	−	22.1204i	−0.0963324	−	0.166853i
$27$	−13.5000	+	23.3827i	−0.0962250	+	0.166667i
$28$	−21.5269	−	122.085i	−0.145293	−	0.823997i
$29$	−23.9096	−	135.598i	−0.153100	−	0.868274i	−0.960502	−	0.278273i	$-0.910238\pi$
$29$	−23.9096	−	135.598i	−0.153100	−	0.868274i	0.807402	−	0.590002i	$-0.200873\pi$
$30$	24.4227	−	42.3014i	0.148632	−	0.257438i
$31$	−83.8800	−	145.284i	−0.485977	−	0.841737i	0.513893	−	0.857854i	$-0.328203\pi$
$31$	−83.8800	−	145.284i	−0.485977	−	0.841737i	−0.999870	+	0.0161174i	$0.994869\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$	51.8954	−	18.8884i	0.273752	−	0.0996377i
$34$	−66.7895	−	24.3094i	−0.336892	−	0.122618i
$35$	193.276	+	162.178i	0.933417	+	0.783230i
$36$	6.25133	−	35.4531i	0.0289414	−	0.164135i
$37$	−300.898			−1.33695			−0.668476	−	0.743733i	$-0.733053\pi$
$37$	−300.898			−1.33695			−0.668476	+	0.743733i	$0.733053\pi$
$38$	15.0281	−	164.955i	0.0641548	−	0.704190i
$39$	38.3137			0.157310
$40$	−11.3092	+	64.1378i	−0.0447036	+	0.253527i
$41$	262.285	+	220.083i	0.999074	+	0.838323i	0.986856	−	0.161602i	$-0.0516662\pi$
$41$	262.285	+	220.083i	0.999074	+	0.838323i	0.0122184	+	0.999925i	$0.496111\pi$
$42$	174.738	+	63.5996i	0.641970	+	0.233658i
$43$	−449.845	+	163.730i	−1.59537	+	0.580666i	−0.978472	−	0.206381i	$-0.933832\pi$
$43$	−449.845	+	163.730i	−1.59537	+	0.580666i	−0.616894	+	0.787046i	$0.711609\pi$
$44$	−56.4073	+	47.3314i	−0.193266	+	0.162170i
$45$	36.6341	+	63.4520i	0.121357	+	0.210197i
$46$	80.2890	−	139.065i	0.257347	−	0.445738i
$47$	12.6364	+	71.6645i	0.0392171	+	0.222411i	0.998117	−	0.0613318i	$-0.0195348\pi$
$47$	12.6364	+	71.6645i	0.0392171	+	0.222411i	−0.958900	+	0.283743i	$0.908424\pi$
$48$	8.33511	+	47.2708i	0.0250640	+	0.142145i
$49$	−308.756	+	534.781i	−0.900163	+	1.55913i
$50$	58.7257	+	101.716i	0.166101	+	0.287696i
$51$	81.6710	−	68.5301i	0.224240	−	0.188159i
$52$	−48.0041	+	17.4721i	−0.128019	+	0.0465950i
$53$	−435.535	−	158.522i	−1.12878	−	0.410842i	−0.290931	−	0.956744i	$-0.593965\pi$
$53$	−435.535	−	158.522i	−1.12878	−	0.410842i	−0.837849	+	0.545902i	$0.816187\pi$
$54$	41.3664	+	34.7105i	0.104245	+	0.0874723i
$55$	26.0234	−	147.586i	0.0637999	−	0.361827i
$56$	−247.937			−0.591642
$57$	203.012	+	143.238i	0.471747	+	0.332849i
$58$	−275.380			−0.623434
$59$	−56.7694	+	321.955i	−0.125267	+	0.710423i	0.855882	+	0.517171i	$0.173015\pi$
$59$	−56.7694	+	321.955i	−0.125267	+	0.710423i	−0.981149	+	0.193253i	$0.938096\pi$
$60$	−74.8355	−	62.7944i	−0.161020	−	0.135112i
$61$	−25.7174	−	9.36038i	−0.0539800	−	0.0196471i	0.314889	−	0.949128i	$-0.398033\pi$
$61$	−25.7174	−	9.36038i	−0.0539800	−	0.0196471i	−0.368869	+	0.929481i	$0.620255\pi$
$62$	−315.286	+	114.755i	−0.645827	+	0.235062i
$63$	−213.672	+	179.292i	−0.427304	+	0.358551i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	51.9846	−	90.0400i	0.0991985	−	0.171817i
$66$	−19.1798	−	108.774i	−0.0357707	−	0.202866i
$67$	−154.563	−	876.572i	−0.281834	−	1.59836i	−0.716378	−	0.697712i	$-0.754202\pi$
$67$	−154.563	−	876.572i	−0.281834	−	1.59836i	0.434544	−	0.900651i	$-0.356910\pi$
$68$	−71.0759	+	123.107i	−0.126753	+	0.219543i
$69$	120.434	+	208.597i	0.210123	+	0.363944i
$70$	386.552	−	324.356i	0.660026	−	0.553827i
$71$	382.004	−	139.038i	0.638529	−	0.232406i	−0.00241026	−	0.999997i	$-0.500767\pi$
$71$	382.004	−	139.038i	0.638529	−	0.232406i	0.640939	+	0.767592i	$0.278545\pi$
$72$	−67.6579	−	24.6255i	−0.110744	−	0.0403075i
$73$	242.712	+	203.660i	0.389141	+	0.326528i	0.816279	−	0.577658i	$-0.196033\pi$
$73$	242.712	+	203.660i	0.389141	+	0.326528i	−0.427137	+	0.904187i	$0.640478\pi$
$74$	−104.501	+	592.652i	−0.164161	+	0.931006i
$75$	−176.177			−0.271242
$76$	−319.679	−	86.8879i	−0.482496	−	0.131141i
$77$	570.523			0.844378
$78$	13.3062	−	75.4632i	0.0193158	−	0.109545i
$79$	90.9217	+	76.2924i	0.129487	+	0.108653i	0.705231	−	0.708977i	$-0.250843\pi$
$79$	90.9217	+	76.2924i	0.129487	+	0.108653i	−0.575744	+	0.817630i	$0.695288\pi$
$80$	122.399	+	44.5496i	0.171058	+	0.0622600i
$81$	−76.1151	+	27.7036i	−0.104410	+	0.0380022i
$82$	524.570	−	440.167i	0.706452	−	0.592784i
$83$	−640.778	−	1109.86i	−0.847404	−	1.46775i	−0.883517	−	0.468399i	$-0.844831\pi$
$83$	−640.778	−	1109.86i	−0.847404	−	1.46775i	0.0361134	−	0.999348i	$-0.488502\pi$
$84$	185.953	−	322.080i	0.241537	−	0.418354i
$85$	−50.2384	−	284.916i	−0.0641072	−	0.363570i
$86$	166.256	+	942.885i	0.208463	+	1.18225i
$87$	206.535	−	357.729i	0.254516	−	0.440834i
$88$	73.6345	+	127.539i	0.0891985	+	0.154496i
$89$	31.2373	−	26.2112i	0.0372039	−	0.0312178i	−0.623996	−	0.781427i	$-0.714492\pi$
$89$	31.2373	−	26.2112i	0.0372039	−	0.0312178i	0.661200	+	0.750210i	$0.270047\pi$
$90$	137.699	−	50.1183i	0.161275	−	0.0586993i
$91$	371.937	+	135.374i	0.428457	+	0.155946i
$92$	−246.020	−	206.435i	−0.278797	−	0.233939i
$93$	87.3936	−	495.634i	0.0974440	−	0.552633i
$94$	145.540			0.159695
$95$	612.071	−	282.745i	0.661022	−	0.305358i
$96$	96.0000			0.102062
$97$	156.265	−	886.225i	0.163571	−	0.927655i	−0.786955	−	0.617010i	$-0.788344\pi$
$97$	156.265	−	886.225i	0.163571	−	0.927655i	0.950526	−	0.310645i	$-0.100545\pi$
$98$	946.083	+	793.858i	0.975192	+	0.818283i
$99$	155.686	+	56.6651i	0.158051	+	0.0575258i
$100$	220.737	−	80.3415i	0.220737	−	0.0803415i
$101$	700.646	−	587.912i	0.690266	−	0.579202i	−0.228720	−	0.973492i	$-0.573454\pi$
$101$	700.646	−	587.912i	0.690266	−	0.579202i	0.918986	+	0.394290i	$0.129009\pi$
$102$	−106.614	−	184.661i	−0.103494	−	0.179256i
$103$	−145.436	+	251.903i	−0.139129	+	0.240978i	−0.927167	−	0.374648i	$-0.877764\pi$
$103$	−145.436	+	251.903i	−0.139129	+	0.240978i	0.788038	+	0.615626i	$0.211097\pi$
$104$	17.7416	+	100.618i	0.0167279	+	0.0948689i
$105$	131.436	+	745.412i	0.122161	+	0.692808i
$106$	−463.487	+	802.782i	−0.424696	+	0.735595i
$107$	76.8061	+	133.032i	0.0693937	+	0.120193i	0.898635	−	0.438698i	$-0.144560\pi$
$107$	76.8061	+	133.032i	0.0693937	+	0.120193i	−0.829241	+	0.558891i	$0.811227\pi$
$108$	82.7328	−	69.4211i	0.0737127	−	0.0618523i
$109$	−1739.94	+	633.287i	−1.52896	+	0.556495i	−0.963366	−	0.268191i	$-0.913574\pi$
$109$	−1739.94	+	633.287i	−1.52896	+	0.556495i	−0.565591	+	0.824686i	$0.691352\pi$
$110$	−281.650	−	102.512i	−0.244130	−	0.0888560i
$111$	−691.503	−	580.240i	−0.591302	−	0.496161i
$112$	−86.1076	+	488.341i	−0.0726465	+	0.411999i
$113$	−229.292			−0.190885			−0.0954425	−	0.995435i	$-0.530427\pi$
$113$	−229.292			−0.190885			−0.0954425	+	0.995435i	$0.530427\pi$
$114$	352.630	−	350.109i	0.289709	−	0.287638i
$115$	653.625			0.530007
$116$	−95.6385	+	542.393i	−0.0765501	+	0.434137i
$117$	88.0499	+	73.8827i	0.0695745	+	0.0583799i
$118$	614.412	+	223.628i	0.479332	+	0.174463i
$119$	1034.97	−	376.700i	0.797277	−	0.290185i
$120$	−149.671	+	125.589i	−0.113859	+	0.0955387i
$121$	496.061	+	859.203i	0.372698	+	0.645532i
$122$	−27.3679	+	47.4026i	−0.0203096	+	0.0351773i
$123$	178.366	+	1011.56i	0.130754	+	0.741540i
$124$	116.525	+	660.845i	0.0843890	+	0.478594i
$125$	−747.847	+	1295.31i	−0.535115	+	0.926847i
$126$	278.929	+	483.119i	0.197214	+	0.341585i
$127$	1366.28	−	1146.45i	0.954630	−	0.801030i	−0.0254409	−	0.999676i	$-0.508099\pi$
$127$	1366.28	−	1146.45i	0.954630	−	0.801030i	0.980071	+	0.198646i	$0.0636545\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$	−1349.54	−	491.191i	−0.921085	−	0.335247i
$130$	−159.290	−	133.660i	−0.107467	−	0.0901753i
$131$	476.764	−	2703.86i	0.317978	−	1.80334i	−0.237036	−	0.971501i	$-0.576176\pi$
$131$	476.764	−	2703.86i	0.317978	−	1.80334i	0.555014	−	0.831841i	$-0.312713\pi$
$132$	−220.904			−0.145661
$133$	1464.67	+	2107.82i	0.954910	+	1.37422i
$134$	−1780.19			−1.14765
$135$	−38.1686	+	216.465i	−0.0243336	+	0.138003i
$136$	217.789	+	182.747i	0.137318	+	0.115224i
$137$	−243.111	−	88.4852i	−0.151609	−	0.0551810i	0.265101	−	0.964221i	$-0.414595\pi$
$137$	−243.111	−	88.4852i	−0.151609	−	0.0551810i	−0.416710	+	0.909040i	$0.636817\pi$
$138$	452.682	−	164.763i	0.279238	−	0.101634i
$139$	1446.94	−	1214.12i	0.882931	−	0.740867i	−0.0838483	−	0.996479i	$-0.526721\pi$
$139$	1446.94	−	1214.12i	0.882931	−	0.740867i	0.966780	+	0.255611i	$0.0822767\pi$
$140$	−504.608	−	874.006i	−0.304622	−	0.527621i
$141$	−109.155	+	189.062i	−0.0651951	+	0.112921i
$142$	−141.183	−	800.689i	−0.0834354	−	0.473185i
$143$	−40.8248	−	231.529i	−0.0238737	−	0.135395i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	−560.460	−	970.746i	−0.320991	−	0.555973i
$146$	485.425	−	407.320i	0.275165	−	0.230890i
$147$	−1740.81	+	633.605i	−0.976734	+	0.355502i
$148$	1131.00	+	411.652i	0.628162	+	0.228632i
$149$	−1637.47	−	1374.00i	−0.900316	−	0.755455i	0.0699359	−	0.997551i	$-0.477721\pi$
$149$	−1637.47	−	1374.00i	−0.900316	−	0.755455i	−0.970252	+	0.242096i	$0.922165\pi$
$150$	−61.1857	+	347.001i	−0.0333053	+	0.188884i
$151$	54.9452			0.0296117			0.0148059	−	0.999890i	$-0.495287\pi$
$151$	54.9452			0.0296117			0.0148059	+	0.999890i	$0.495287\pi$
$152$	−282.159	+	599.468i	−0.150567	+	0.319890i
$153$	319.842			0.169004
$154$	198.140	−	1123.71i	0.103679	−	0.587995i
$155$	−1046.20	−	877.866i	−0.542147	−	0.454915i
$156$	−144.012	−	52.4162i	−0.0739116	−	0.0269016i
$157$	569.725	−	207.363i	0.289611	−	0.105410i	−0.193129	−	0.981173i	$-0.561864\pi$
$157$	569.725	−	207.363i	0.289611	−	0.105410i	0.482741	+	0.875763i	$0.339641\pi$
$158$	181.843	−	152.585i	0.0915613	−	0.0768290i
$159$	−695.230	−	1204.17i	−0.346763	−	0.600611i
$160$	130.254	−	225.607i	0.0643595	−	0.111474i
$161$	432.093	+	2450.52i	0.211514	+	1.19955i
$162$	28.1310	+	159.539i	0.0136431	+	0.0773738i
$163$	−1905.96	+	3301.23i	−0.915869	+	1.58633i	−0.110244	+	0.993905i	$0.535163\pi$
$163$	−1905.96	+	3301.23i	−0.915869	+	1.58633i	−0.805625	+	0.592426i	$0.798170\pi$
$164$	−684.778	−	1186.07i	−0.326050	−	0.564735i
$165$	344.405	−	288.990i	0.162496	−	0.136351i
$166$	−2408.54	+	876.636i	−1.12614	+	0.409880i
$167$	−3312.30	−	1205.58i	−1.53481	−	0.558625i	−0.570016	−	0.821633i	$-0.693063\pi$
$167$	−3312.30	−	1205.58i	−1.53481	−	0.558625i	−0.964794	+	0.263008i	$0.915285\pi$
$168$	−569.792	−	478.113i	−0.261669	−	0.219567i
$169$	−353.182	+	2003.00i	−0.160757	+	0.911696i
$170$	−578.622			−0.261049
$171$	190.333	+	720.661i	0.0851175	+	0.322283i
$172$	1914.86			0.848876
$173$	−695.850	+	3946.36i	−0.305806	+	1.73431i	0.313879	+	0.949463i	$0.398371\pi$
$173$	−695.850	+	3946.36i	−0.305806	+	1.73431i	−0.619686	+	0.784850i	$0.712740\pi$
$174$	−632.860	−	531.033i	−0.275730	−	0.231365i
$175$	−1710.27	−	622.489i	−0.738769	−	0.268890i
$176$	276.775	−	100.738i	0.118538	−	0.0431444i
$177$	−751.310	+	630.424i	−0.319050	+	0.267715i
$178$	−40.7774	−	70.6286i	−0.0171708	−	0.0297407i
$179$	2262.63	−	3919.00i	0.944789	−	1.63642i	0.188616	−	0.982051i	$-0.439600\pi$
$179$	2262.63	−	3919.00i	0.944789	−	1.63642i	0.756173	−	0.654372i	$-0.227067\pi$
$180$	−50.8915	−	288.620i	−0.0210735	−	0.119514i
$181$	410.372	+	2327.34i	0.168523	+	0.955743i	0.945357	+	0.326037i	$0.105714\pi$
$181$	410.372	+	2327.34i	0.168523	+	0.955743i	−0.776834	+	0.629706i	$0.783175\pi$
$182$	395.807	−	685.558i	0.161204	−	0.279214i
$183$	−41.0519	−	71.1040i	−0.0165827	−	0.0287222i
$184$	−492.040	+	412.870i	−0.197139	+	0.165420i
$185$	−2301.85	+	837.805i	−0.914786	+	0.332955i
$186$	−945.857	−	344.264i	−0.372869	−	0.135713i
$187$	−501.151	−	420.515i	−0.195977	−	0.164445i
$188$	50.5455	−	286.658i	0.0196086	−	0.111206i
$189$	−836.787			−0.322049
$190$	−344.329	−	1303.74i	−0.131475	−	0.497807i
$191$	928.169			0.351623			0.175811	−	0.984424i	$-0.443745\pi$
$191$	928.169			0.351623			0.175811	+	0.984424i	$0.443745\pi$
$192$	33.3405	−	189.083i	0.0125320	−	0.0710724i
$193$	516.787	+	433.636i	0.192742	+	0.161729i	0.734052	−	0.679094i	$-0.237627\pi$
$193$	516.787	+	433.636i	0.192742	+	0.161729i	−0.541310	+	0.840823i	$0.682071\pi$
$194$	−1691.25	−	615.566i	−0.625901	−	0.227809i
$195$	293.097	−	106.679i	0.107637	−	0.0391765i
$196$	1892.17	−	1587.72i	0.689565	−	0.578614i
$197$	1986.18	+	3440.16i	0.718322	+	1.24417i	0.961664	+	0.274230i	$0.0884228\pi$
$197$	1986.18	+	3440.16i	0.718322	+	1.24417i	−0.243342	+	0.969940i	$0.578244\pi$
$198$	165.678	−	286.962i	0.0594657	−	0.102998i
$199$	340.507	+	1931.11i	0.121296	+	0.687904i	0.983439	+	0.181239i	$0.0580107\pi$
$199$	340.507	+	1931.11i	0.121296	+	0.687904i	−0.862143	+	0.506665i	$0.830878\pi$
$200$	−81.5809	−	462.668i	−0.0288432	−	0.163578i
$201$	1335.14	−	2312.53i	0.468525	−	0.811510i
$202$	−914.629	−	1584.18i	−0.318579	−	0.551796i
$203$	3268.95	−	2742.97i	1.13022	−	0.948369i
$204$	−400.737	+	145.856i	−0.137535	+	0.0500588i
$205$	2619.26	+	953.331i	0.892374	+	0.324798i
$206$	445.643	+	373.939i	0.150725	+	0.126474i
$207$	−125.478	+	711.623i	−0.0421321	+	0.238943i
$208$	204.340			0.0681173
$209$	649.270	−	1379.42i	0.214885	−	0.456540i
$210$	1513.82			0.497446
$211$	−229.321	+	1300.55i	−0.0748205	+	0.424328i	0.924272	+	0.381735i	$0.124673\pi$
$211$	−229.321	+	1300.55i	−0.0748205	+	0.424328i	−0.999092	+	0.0425936i	$0.986438\pi$
$212$	1420.21	+	1191.69i	0.460095	+	0.386065i
$213$	1146.01	+	417.115i	0.368655	+	0.134179i
$214$	288.697	−	105.077i	0.0922192	−	0.0335650i
$215$	−2985.41	+	2505.05i	−0.946991	+	0.794620i
$216$	−108.000	−	187.061i	−0.0340207	−	0.0589256i
$217$	2599.62	−	4502.67i	0.813242	−	1.40858i
$218$	643.057	+	3646.96i	0.199786	+	1.13304i
$219$	165.055	+	936.075i	0.0509288	+	0.288831i
$220$	−299.726	+	519.140i	−0.0918523	+	0.159093i
$221$	−226.932	−	393.057i	−0.0690727	−	0.119638i
$222$	−1383.01	+	1160.48i	−0.418114	+	0.350839i
$223$	514.878	−	187.400i	0.154613	−	0.0562747i	−0.263554	−	0.964645i	$-0.584895\pi$
$223$	514.878	−	187.400i	0.154613	−	0.0562747i	0.418167	+	0.908370i	$0.362673\pi$
$224$	931.938	+	339.198i	0.277981	+	0.101177i
$225$	−404.879	−	339.734i	−0.119964	−	0.100662i
$226$	−79.6324	+	451.618i	−0.0234384	+	0.132926i
$227$	4988.53			1.45859			0.729295	−	0.684199i	$-0.239848\pi$
$227$	4988.53			1.45859			0.729295	+	0.684199i	$0.239848\pi$
$228$	−567.113	−	816.137i	−0.164728	−	0.237061i
$229$	−1885.37			−0.544055			−0.272028	−	0.962289i	$-0.587694\pi$
$229$	−1885.37			−0.544055			−0.272028	+	0.962289i	$0.587694\pi$
$230$	227.002	−	1287.39i	0.0650784	−	0.369078i
$231$	1311.14	+	1100.17i	0.373448	+	0.313360i
$232$	1035.09	+	376.742i	0.292918	+	0.106613i
$233$	−5337.32	+	1942.63i	−1.50068	+	0.546205i	−0.956238	−	0.292591i	$-0.905483\pi$
$233$	−5337.32	+	1942.63i	−1.50068	+	0.546205i	−0.544447	+	0.838795i	$0.683260\pi$
$234$	176.100	−	147.765i	0.0491966	−	0.0412809i
$235$	296.207	+	513.045i	0.0822230	+	0.142414i
$236$	653.843	−	1132.49i	0.180346	−	0.312368i
$237$	61.8308	+	350.660i	0.0169466	+	0.0961089i
$238$	−382.511	−	2169.33i	−0.104179	−	0.590827i
$239$	−659.925	+	1143.02i	−0.178607	+	0.309356i	−0.941404	−	0.337282i	$-0.890492\pi$
$239$	−659.925	+	1143.02i	−0.178607	+	0.309356i	0.762797	+	0.646638i	$0.223826\pi$
$240$	195.382	+	338.411i	0.0525493	+	0.0910180i
$241$	3957.95	−	3321.11i	1.05790	−	0.887684i	0.0639981	−	0.997950i	$-0.479615\pi$
$241$	3957.95	−	3321.11i	1.05790	−	0.887684i	0.993902	+	0.110266i	$0.0351704\pi$
$242$	1864.58	−	678.651i	0.495288	−	0.180270i
$243$	−228.345	−	83.1109i	−0.0602813	−	0.0219406i
$244$	83.8602	+	70.3671i	0.0220025	+	0.0184623i
$245$	−872.947	+	4950.73i	−0.227635	+	1.29098i
$246$	2054.33			0.532437
$247$	750.585	−	745.220i	0.193355	−	0.191972i
$248$	1342.08			0.343638
$249$	667.619	−	3786.26i	0.169914	−	0.963632i
$250$	2291.53	+	1922.83i	0.579718	+	0.486441i
$251$	1200.32	+	436.881i	0.301847	+	0.109863i	0.488503	−	0.872562i	$-0.337543\pi$
$251$	1200.32	+	436.881i	0.301847	+	0.109863i	−0.186657	+	0.982425i	$0.559765\pi$
$252$	1048.43	−	381.598i	0.262083	−	0.0953904i
$253$	1132.22	−	950.047i	0.281353	−	0.236083i
$254$	−1783.56	−	3089.21i	−0.440592	−	0.763127i
$255$	433.967	−	751.652i	0.106573	−	0.184589i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−887.380	−	5032.58i	−0.215382	−	1.22149i	−0.880242	−	0.474525i	$-0.842620\pi$
$257$	−887.380	−	5032.58i	−0.215382	−	1.22149i	0.664860	−	0.746968i	$-0.268491\pi$
$258$	−1436.15	+	2487.48i	−0.346552	+	0.600246i
$259$	−4662.73	−	8076.08i	−1.11864	−	1.93754i
$260$	−318.580	+	267.321i	−0.0759904	+	0.0637635i
$261$	1164.48	−	423.835i	0.276166	−	0.100516i
$262$	−5160.00	−	1878.08i	−1.21674	−	0.442857i
$263$	4744.53	+	3981.13i	1.11240	+	0.933411i	0.998196	−	0.0600472i	$-0.0191251\pi$
$263$	4744.53	+	3981.13i	1.11240	+	0.933411i	0.114200	+	0.993458i	$0.463570\pi$
$264$	−76.7190	+	435.095i	−0.0178853	+	0.101433i
$265$	−3773.20			−0.874663
$266$	4660.26	−	2152.80i	1.07421	−	0.496228i
$267$	122.332			0.0280398
$268$	−618.253	+	3506.29i	−0.140917	+	0.799181i
$269$	1448.14	+	1215.13i	0.328232	+	0.275420i	0.791979	−	0.610548i	$-0.209051\pi$
$269$	1448.14	+	1215.13i	0.328232	+	0.275420i	−0.463747	+	0.885968i	$0.653495\pi$
$270$	413.097	+	150.355i	0.0931122	+	0.0338901i
$271$	−876.386	+	318.979i	−0.196445	+	0.0715002i	−0.438369	−	0.898795i	$-0.644444\pi$
$271$	−876.386	+	318.979i	−0.196445	+	0.0715002i	0.241924	+	0.970295i	$0.422222\pi$
$272$	435.579	−	365.494i	0.0970987	−	0.0814755i
$273$	593.711	+	1028.34i	0.131623	+	0.227977i
$274$	−258.714	+	448.105i	−0.0570418	+	0.0987993i
$275$	187.724	+	1064.64i	0.0411643	+	0.233455i
$276$	−167.304	−	948.831i	−0.0364875	−	0.206931i
$277$	1358.74	−	2353.41i	0.294725	−	0.510478i	−0.680196	−	0.733030i	$-0.738105\pi$
$277$	1358.74	−	2353.41i	0.294725	−	0.510478i	0.974921	+	0.222552i	$0.0714387\pi$
$278$	−1888.84	−	3271.57i	−0.407500	−	0.705811i
$279$	1156.60	−	970.506i	0.248187	−	0.208253i
$280$	−1896.70	+	690.344i	−0.404821	+	0.147343i
$281$	−4155.49	−	1512.47i	−0.882190	−	0.321091i	−0.139097	−	0.990279i	$-0.544420\pi$
$281$	−4155.49	−	1512.47i	−0.882190	−	0.321091i	−0.743093	+	0.669188i	$0.766642\pi$
$282$	334.470	+	280.654i	0.0706292	+	0.0592649i
$283$	−1237.89	+	7020.43i	−0.260018	+	1.47463i	0.522839	+	0.852431i	$0.324873\pi$
$283$	−1237.89	+	7020.43i	−0.260018	+	1.47463i	−0.782857	+	0.622202i	$0.786238\pi$
$284$	−1626.08			−0.339754
$285$	1951.85	+	530.509i	0.405677	+	0.110262i
$286$	−470.202			−0.0972154
$287$	−1842.64	+	10450.1i	−0.378982	+	2.14931i
$288$	220.621	+	185.123i	0.0451396	+	0.0378766i
$289$	3429.93	+	1248.39i	0.698133	+	0.254100i
$290$	−2106.64	+	766.755i	−0.426573	+	0.155260i
$291$	2068.08	−	1735.33i	0.416609	−	0.349576i
$292$	−633.677	−	1097.56i	−0.126997	−	0.219965i
$293$	3121.12	−	5405.93i	0.622312	−	1.07788i	−0.366742	−	0.930323i	$-0.619527\pi$
$293$	3121.12	−	5405.93i	0.622312	−	1.07788i	0.989054	−	0.147554i	$-0.0471400\pi$
$294$	643.379	+	3648.78i	0.127628	+	0.723814i
$295$	462.154	+	2621.00i	0.0912123	+	0.517291i
$296$	1203.59	−	2084.68i	0.236342	−	0.409356i
$297$	248.517	+	430.443i	0.0485535	+	0.0840972i
$298$	−3274.95	+	2748.01i	−0.636620	+	0.534187i
$299$	963.550	−	350.704i	0.186366	−	0.0678318i
$300$	662.210	+	241.025i	0.127442	+	0.0463852i
$301$	−11365.3	−	9536.65i	−2.17637	−	1.82619i
$302$	19.0823	−	108.221i	0.00363596	−	0.0206206i
$303$	2743.89			0.520238
$304$	1082.73	+	763.938i	0.204272	+	0.144128i
$305$	−222.800			−0.0418278
$306$	111.080	−	629.965i	0.0207517	−	0.117689i
$307$	−1674.05	−	1404.70i	−0.311216	−	0.261141i	0.473779	−	0.880644i	$-0.342890\pi$
$307$	−1674.05	−	1404.70i	−0.311216	−	0.261141i	−0.784994	+	0.619503i	$0.787334\pi$
$308$	−2144.46	−	780.521i	−0.396728	−	0.144397i
$309$	−819.993	+	298.453i	−0.150964	+	0.0549463i
$310$	−2092.40	+	1755.73i	−0.383356	+	0.321674i
$311$	528.745	+	915.813i	0.0964063	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$311$	528.745	+	915.813i	0.0964063	+	0.166981i	−0.813788	+	0.581161i	$0.802599\pi$
$312$	−153.255	+	265.445i	−0.0278088	+	0.0481662i
$313$	−669.836	−	3798.83i	−0.120963	−	0.686014i	−0.983624	−	0.180232i	$-0.942315\pi$
$313$	−669.836	−	3798.83i	−0.120963	−	0.686014i	0.862661	−	0.505782i	$-0.168796\pi$
$314$	−210.562	−	1194.16i	−0.0378430	−	0.214618i
$315$	−1135.37	+	1966.51i	−0.203082	+	0.351748i
$316$	−237.380	−	411.154i	−0.0422584	−	0.0731937i
$317$	188.001	−	157.752i	0.0333098	−	0.0279502i	−0.625981	−	0.779838i	$-0.715301\pi$
$317$	188.001	−	157.752i	0.0333098	−	0.0279502i	0.659291	+	0.751888i	$0.270857\pi$
$318$	−2613.21	+	951.131i	−0.460822	+	0.167726i
$319$	−2381.83	−	866.913i	−0.418046	−	0.152156i
$320$	−399.123	−	334.904i	−0.0697239	−	0.0585053i
$321$	−80.0235	+	453.836i	−0.0139143	+	0.0789117i
$322$	4976.65			0.861298
$323$	267.034	−	2931.08i	0.0460006	−	0.504922i
$324$	324.000			0.0555556
$325$	−130.236	+	738.605i	−0.0222283	+	0.126063i
$326$	5840.21	+	4900.52i	0.992207	+	0.832560i
$327$	−5219.83	−	1899.86i	−0.882744	−	0.321292i
$328$	−2573.92	+	936.831i	−0.433296	+	0.157707i
$329$	−1727.66	+	1449.68i	−0.289510	+	0.242928i
$330$	−449.589	−	778.710i	−0.0749971	−	0.129899i
$331$	1017.64	−	1762.60i	0.168986	−	0.292693i	−0.769077	−	0.639156i	$-0.779284\pi$
$331$	1017.64	−	1762.60i	0.168986	−	0.292693i	0.938064	+	0.346463i	$0.112617\pi$
$332$	890.159	+	5048.34i	0.147150	+	0.834530i
$333$	−470.253	−	2666.94i	−0.0773865	−	0.438880i
$334$	−3524.87	+	6105.26i	−0.577463	+	1.00019i
$335$	−3623.09	−	6275.37i	−0.590896	−	1.02346i
$336$	−1139.58	+	956.225i	−0.185028	+	0.155257i
$337$	−717.697	+	261.220i	−0.116010	+	0.0422242i	−0.399373	−	0.916789i	$-0.630772\pi$
$337$	−717.697	+	261.220i	−0.116010	+	0.0422242i	0.283363	+	0.959013i	$0.408550\pi$
$338$	3822.47	+	1391.27i	0.615134	+	0.223890i
$339$	−526.945	−	442.159i	−0.0844239	−	0.0708401i
$340$	−200.953	+	1139.66i	−0.0320536	+	0.181785i
$341$	−3088.23			−0.490431
$342$	1485.53	−	124.599i	0.234878	−	0.0197004i
$343$	−8507.71			−1.33928
$344$	665.024	−	3771.54i	0.104232	−	0.591127i
$345$	1502.12	+	1260.43i	0.234409	+	0.196693i
$346$	7531.14	+	2741.11i	1.17016	+	0.425905i
$347$	2946.72	−	1072.52i	0.455874	−	0.165925i	−0.103869	−	0.994591i	$-0.533122\pi$
$347$	2946.72	−	1072.52i	0.455874	−	0.165925i	0.559743	+	0.828666i	$0.310900\pi$
$348$	−1265.72	+	1062.07i	−0.194970	+	0.163600i
$349$	−838.497	−	1452.32i	−0.128607	−	0.222753i	0.794530	−	0.607224i	$-0.207717\pi$
$349$	−838.497	−	1452.32i	−0.128607	−	0.222753i	−0.923137	+	0.384471i	$0.874384\pi$
$350$	−1820.04	+	3152.39i	−0.277957	+	0.481436i
$351$	59.8779	+	339.584i	0.00910554	+	0.0516401i
$352$	−102.292	−	580.127i	−0.0154892	−	0.0878434i
$353$	−3726.94	+	6455.25i	−0.561940	+	0.973309i	0.435387	+	0.900244i	$0.356612\pi$
$353$	−3726.94	+	6455.25i	−0.561940	+	0.973309i	−0.997327	+	0.0730658i	$0.976722\pi$
$354$	980.765	+	1698.74i	0.147252	+	0.255047i
$355$	2535.18	−	2127.27i	0.379024	−	0.318039i
$356$	−153.273	+	55.7868i	−0.0228187	+	0.00830532i
$357$	3104.92	+	1130.10i	0.460308	+	0.167539i
$358$	−6933.11	−	5817.57i	−1.02354	−	0.858850i
$359$	−2060.53	+	11685.8i	−0.302926	+	1.71798i	0.330185	+	0.943916i	$0.392889\pi$
$359$	−2060.53	+	11685.8i	−0.302926	+	1.71798i	−0.633110	+	0.774062i	$0.718222\pi$
$360$	−586.145			−0.0858126
$361$	6763.17	−	1142.56i	0.986028	−	0.166579i
$362$	4726.48			0.686238
$363$	−516.841	+	2931.15i	−0.0747303	+	0.423817i
$364$	−1212.82	−	1017.68i	−0.174641	−	0.146541i
$365$	2423.80	+	882.190i	0.347582	+	0.126509i
$366$	−154.305	+	56.1623i	−0.0220372	+	0.00802090i
$367$	−7907.20	+	6634.93i	−1.12467	+	0.943707i	−0.998831	−	0.0483442i	$-0.984606\pi$
$367$	−7907.20	+	6634.93i	−1.12467	+	0.943707i	−0.125835	+	0.992051i	$0.540161\pi$
$368$	642.312	+	1112.52i	0.0909860	+	0.157592i
$369$	−1540.75	+	2668.66i	−0.217366	+	0.376490i
$370$	850.729	+	4824.72i	0.119533	+	0.677907i
$371$	−2494.36	−	14146.2i	−0.349058	−	1.97961i
$372$	−1006.56	+	1743.41i	−0.140289	+	0.242988i
$373$	1942.72	+	3364.89i	0.269679	+	0.467098i	0.968779	−	0.247926i	$-0.0797490\pi$
$373$	1942.72	+	3364.89i	0.269679	+	0.467098i	−0.699100	+	0.715024i	$0.746416\pi$
$374$	−1002.30	+	841.031i	−0.138577	+	0.116280i
$375$	−4216.48	+	1534.67i	−0.580634	+	0.211334i
$376$	−547.052	−	199.111i	−0.0750320	−	0.0273094i
$377$	−1347.07	−	1130.32i	−0.184025	−	0.154415i
$378$	−290.613	+	1648.15i	−0.0395437	+	0.224264i
$379$	13322.5			1.80563			0.902814	−	0.430031i	$-0.141498\pi$
$379$	13322.5			1.80563			0.902814	+	0.430031i	$0.141498\pi$
$380$	−2687.45	+	225.411i	−0.362798	+	0.0304298i
$381$	5350.67			0.719483
$382$	322.350	−	1828.14i	0.0431750	−	0.244858i
$383$	205.993	+	172.849i	0.0274824	+	0.0230605i	0.656425	−	0.754391i	$-0.272068\pi$
$383$	205.993	+	172.849i	0.0274824	+	0.0230605i	−0.628943	+	0.777451i	$0.716512\pi$
$384$	−360.842	−	131.336i	−0.0479535	−	0.0174536i
$385$	4364.47	−	1588.54i	0.577750	−	0.210284i
$386$	1033.57	−	867.272i	0.136289	−	0.114360i
$387$	−2154.22	−	3731.22i	−0.282959	−	0.490099i
$388$	−1799.79	+	3117.33i	−0.235491	+	0.407883i
$389$	−1397.19	−	7923.84i	−0.182109	−	1.03279i	−0.929614	−	0.368534i	$-0.879860\pi$
$389$	−1397.19	−	7923.84i	−0.182109	−	1.03279i	0.747506	−	0.664255i	$-0.231251\pi$
$390$	−108.324	−	614.338i	−0.0140647	−	0.0797647i
$391$	1426.65	−	2471.04i	0.184524	−	0.319606i
$392$	−2470.05	−	4278.25i	−0.318256	−	0.551235i
$393$	6309.70	−	5294.47i	0.809879	−	0.679569i
$394$	7465.59	−	2717.25i	0.954597	−	0.347445i
$395$	907.971	+	330.474i	0.115658	+	0.0420961i
$396$	−507.666	−	425.982i	−0.0644222	−	0.0540566i
$397$	−868.306	+	4924.41i	−0.109771	+	0.622541i	0.879436	+	0.476017i	$0.157920\pi$
$397$	−868.306	+	4924.41i	−0.109771	+	0.622541i	−0.989207	+	0.146525i	$0.953191\pi$
$398$	3921.80			0.493925
$399$	−698.630	+	7668.46i	−0.0876572	+	0.962163i
$400$	−939.612			−0.117451
$401$	1912.75	−	10847.8i	0.238200	−	1.35090i	−0.597568	−	0.801818i	$-0.703866\pi$
$401$	1912.75	−	10847.8i	0.238200	−	1.35090i	0.835769	−	0.549082i	$-0.185022\pi$
$402$	−4091.11	−	3432.85i	−0.507577	−	0.425908i
$403$	−2013.29	−	732.778i	−0.248856	−	0.0905763i
$404$	−3437.88	+	1251.29i	−0.423369	+	0.154094i
$405$	−505.140	+	423.863i	−0.0619768	+	0.0520047i
$406$	−4267.31	−	7391.19i	−0.521633	−	0.903494i
$407$	−2769.56	+	4797.01i	−0.337302	+	0.584224i
$408$	148.107	+	839.954i	0.0179715	+	0.101921i
$409$	1757.12	+	9965.12i	0.212430	+	1.20475i	0.885311	+	0.465000i	$0.153946\pi$
$409$	1757.12	+	9965.12i	0.212430	+	1.20475i	−0.672880	+	0.739751i	$0.734943\pi$
$410$	2787.35	−	4827.84i	0.335750	−	0.581536i
$411$	−388.070	−	672.157i	−0.0465744	−	0.0806693i
$412$	891.286	−	747.878i	0.106579	−	0.0894303i
$413$	−9520.97	+	3465.35i	−1.13437	+	0.412878i
$414$	1358.05	+	494.288i	0.161218	+	0.0586786i
$415$	−7992.16	−	6706.22i	−0.945348	−	0.793241i
$416$	70.9664	−	402.470i	0.00836397	−	0.0474345i
$417$	5666.52			0.665445
$418$	−2491.45	−	1757.88i	−0.291533	−	0.205696i
$419$	12647.7			1.47466			0.737328	−	0.675534i	$-0.236087\pi$
$419$	12647.7			1.47466			0.737328	+	0.675534i	$0.236087\pi$
$420$	525.745	−	2981.65i	0.0610803	−	0.346404i
$421$	−4655.65	−	3906.55i	−0.538960	−	0.452241i	0.332222	−	0.943201i	$-0.392202\pi$
$421$	−4655.65	−	3906.55i	−0.538960	−	0.452241i	−0.871182	+	0.490960i	$0.836646\pi$
$422$	2481.93	+	903.350i	0.286300	+	0.104205i
$423$	−615.433	+	223.999i	−0.0707409	+	0.0257476i
$424$	2840.41	−	2383.39i	0.325336	−	0.272989i
$425$	1043.50	+	1807.39i	0.119099	+	0.206285i
$426$	1219.56	−	2112.34i	0.138704	−	0.240243i
$427$	−147.287	−	835.304i	−0.0166925	−	0.0946679i
$428$	−106.698	−	605.114i	−0.0120501	−	0.0683395i
$429$	352.651	−	610.810i	0.0396880	−	0.0687417i
$430$	3897.17	+	6750.10i	0.437066	+	0.757020i
$431$	9367.57	−	7860.32i	1.04691	−	0.878465i	0.0541480	−	0.998533i	$-0.482756\pi$
$431$	9367.57	−	7860.32i	1.04691	−	0.878465i	0.992766	+	0.120068i	$0.0383113\pi$
$432$	−405.947	+	147.753i	−0.0452110	+	0.0164555i
$433$	−630.301	−	229.411i	−0.0699546	−	0.0254614i	0.306806	−	0.951772i	$-0.400740\pi$
$433$	−630.301	−	229.411i	−0.0699546	−	0.0254614i	−0.376760	+	0.926311i	$0.622962\pi$
$434$	−7965.69	−	6684.01i	−0.881026	−	0.739269i
$435$	583.938	−	3311.67i	0.0643624	−	0.365018i
$436$	7406.43			0.813541
$437$	6416.67	+	1744.04i	0.702405	+	0.190912i
$438$	1901.03			0.207385
$439$	−2667.68	+	15129.2i	−0.290027	+	1.64482i	0.396731	+	0.917935i	$0.370145\pi$
$439$	−2667.68	+	15129.2i	−0.290027	+	1.64482i	−0.686757	+	0.726887i	$0.740966\pi$
$440$	918.413	+	770.640i	0.0995082	+	0.0834973i
$441$	−5222.44	−	1900.81i	−0.563918	−	0.205249i
$442$	−852.984	+	310.461i	−0.0917926	+	0.0334098i
$443$	−4694.08	+	3938.80i	−0.503437	+	0.422434i	−0.858813	−	0.512290i	$-0.828797\pi$
$443$	−4694.08	+	3938.80i	−0.503437	+	0.422434i	0.355376	+	0.934724i	$0.384353\pi$
$444$	1805.39	+	3127.02i	0.192972	+	0.334238i
$445$	165.983	−	287.490i	0.0176816	−	0.0306255i
$446$	−190.291	−	1079.19i	−0.0202030	−	0.114577i
$447$	−1113.56	−	6315.29i	−0.117829	−	0.668239i
$448$	991.748	−	1717.76i	0.104589	−	0.181153i
$449$	2292.56	+	3970.83i	0.240964	+	0.417361i	0.960989	−	0.276586i	$-0.0892032\pi$
$449$	2292.56	+	3970.83i	0.240964	+	0.417361i	−0.720025	+	0.693948i	$0.755870\pi$
$450$	−809.757	+	679.467i	−0.0848274	+	0.0711786i
$451$	5922.80	−	2155.72i	0.618390	−	0.225075i
$452$	861.858	+	313.690i	0.0896867	+	0.0326433i
$453$	126.271	+	105.954i	0.0130966	+	0.0109893i
$454$	1732.50	−	9825.48i	0.179097	−	1.01571i
$455$	3222.23			0.332001
$456$	−1804.43	+	833.553i	−0.185308	+	0.0856024i
$457$	10683.5			1.09356			0.546778	−	0.837278i	$-0.315854\pi$
$457$	10683.5			1.09356			0.546778	+	0.837278i	$0.315854\pi$
$458$	−654.782	+	3713.45i	−0.0668034	+	0.378861i
$459$	735.039	+	616.771i	0.0747466	+	0.0627198i
$460$	−2456.83	−	894.212i	−0.249022	−	0.0906366i
$461$	−2775.62	+	1010.24i	−0.280420	+	0.102065i	−0.478401	−	0.878141i	$-0.658784\pi$
$461$	−2775.62	+	1010.24i	−0.280420	+	0.102065i	0.197981	+	0.980206i	$0.436561\pi$
$462$	2622.27	−	2200.35i	0.264068	−	0.221579i
$463$	4701.14	+	8142.62i	0.471880	+	0.817321i	0.999482	−	0.0321708i	$-0.0102421\pi$
$463$	4701.14	+	8142.62i	0.471880	+	0.817321i	−0.527602	+	0.849492i	$0.676909\pi$
$464$	1101.52	−	1907.89i	0.110209	−	0.190887i
$465$	−711.463	−	4034.91i	−0.0709533	−	0.402396i
$466$	1972.59	+	11187.1i	0.196092	+	1.11209i
$467$	−2203.68	+	3816.89i	−0.218360	+	0.378211i	−0.954307	−	0.298829i	$-0.903404\pi$
$467$	−2203.68	+	3816.89i	−0.218360	+	0.378211i	0.735947	+	0.677040i	$0.236737\pi$
$468$	−229.882	−	398.167i	−0.0227058	−	0.0393275i
$469$	21132.0	−	17731.9i	2.08057	−	1.74580i
$470$	1113.37	−	405.235i	0.109268	−	0.0397704i
$471$	1709.17	+	622.089i	0.167207	+	0.0608585i
$472$	−2003.49	−	1681.13i	−0.195378	−	0.163941i
$473$	−1530.27	+	8678.61i	−0.148757	+	0.843643i
$474$	712.139			0.0690076
$475$	−3451.41	+	3426.73i	−0.333392	+	0.331009i
$476$	−4405.59			−0.424222
$477$	724.353	−	4108.01i	0.0695300	−	0.394324i
$478$	2022.13	+	1696.77i	0.193494	+	0.162361i
$479$	−215.597	−	78.4708i	−0.0205655	−	0.00748522i	0.331717	−	0.943379i	$-0.392372\pi$
$479$	−215.597	−	78.4708i	−0.0205655	−	0.00748522i	−0.352282	+	0.935894i	$0.614594\pi$
$480$	734.395	−	267.298i	0.0698341	−	0.0254175i
$481$	−2943.78	+	2470.12i	−0.279053	+	0.234154i
$482$	−5166.74	−	8949.05i	−0.488254	−	0.845681i
$483$	−3732.49	+	6464.86i	−0.351624	+	0.609030i
$484$	−689.121	−	3908.20i	−0.0647183	−	0.367036i
$485$	−1272.14	−	7214.67i	−0.119103	−	0.675467i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	6735.11	+	11665.5i	0.626688	+	1.08545i	0.988212	+	0.153092i	$0.0489231\pi$
$487$	6735.11	+	11665.5i	0.626688	+	1.08545i	−0.361524	+	0.932363i	$0.617744\pi$
$488$	167.720	−	140.734i	0.0155581	−	0.0130548i
$489$	−10746.1	+	3911.27i	−0.993776	+	0.361705i
$490$	9447.86	+	3438.74i	0.871043	+	0.317034i
$491$	−1525.17	−	1279.77i	−0.140183	−	0.117627i	0.570000	−	0.821645i	$-0.306943\pi$
$491$	−1525.17	−	1279.77i	−0.140183	−	0.117627i	−0.710183	+	0.704017i	$0.751388\pi$
$492$	713.462	−	4046.25i	0.0653768	−	0.370770i
$493$	−4893.22			−0.447018
$494$	−1207.12	−	1737.18i	−0.109941	−	0.158217i
$495$	1348.77			0.122470
$496$	466.099	−	2643.38i	0.0421945	−	0.239297i
$497$	9651.34	+	8098.44i	0.871070	+	0.730915i
$498$	−7225.61	−	2629.91i	−0.650175	−	0.236645i
$499$	19869.2	−	7231.80i	1.78250	−	0.648777i	0.782854	−	0.622205i	$-0.213763\pi$
$499$	19869.2	−	7231.80i	1.78250	−	0.648777i	0.999647	−	0.0265719i	$-0.00845909\pi$
$500$	4583.07	−	3845.65i	0.409922	−	0.343966i
$501$	−5287.31	−	9157.89i	−0.471496	−	0.816655i
$502$	1277.35	−	2212.44i	0.113568	−	0.196705i
$503$	1678.87	+	9521.36i	0.148821	+	0.844009i	0.964219	+	0.265107i	$0.0854073\pi$
$503$	1678.87	+	9521.36i	0.148821	+	0.844009i	−0.815397	+	0.578901i	$0.803482\pi$
$504$	−387.484	−	2197.53i	−0.0342459	−	0.194218i
$505$	3722.95	−	6448.34i	0.328058	−	0.568213i
$506$	−1478.01	−	2559.99i	−0.129853	−	0.224912i
$507$	−4674.16	+	3922.09i	−0.409442	+	0.343562i
$508$	−6703.98	+	2440.05i	−0.585514	+	0.213110i
$509$	−12386.1	−	4508.16i	−1.07859	−	0.392575i	−0.259208	−	0.965821i	$-0.583462\pi$
$509$	−12386.1	−	4508.16i	−1.07859	−	0.392575i	−0.819383	+	0.573246i	$0.805684\pi$
$510$	−1329.75	−	1115.79i	−0.115456	−	0.0968788i
$511$	−1705.14	+	9670.32i	−0.147614	+	0.837162i
$512$	512.000			0.0441942
$513$	−952.287	+	2023.21i	−0.0819580	+	0.174126i
$514$	−10220.4			−0.877051
$515$	−411.193	+	2331.99i	−0.0351832	+	0.199534i
$516$	4400.60	+	3692.55i	0.375438	+	0.315030i
$517$	1258.81	+	458.169i	0.107084	+	0.0389753i
$518$	−17526.1	+	6378.99i	−1.48659	+	0.541074i
$519$	−9209.17	+	7727.41i	−0.778878	+	0.653556i
$520$	415.877	+	720.320i	0.0350720	+	0.0607464i
$521$	−9982.48	+	17290.2i	−0.839425	+	1.45393i	0.0509506	+	0.998701i	$0.483775\pi$
$521$	−9982.48	+	17290.2i	−0.839425	+	1.45393i	−0.890376	+	0.455226i	$0.849558\pi$
$522$	−430.373	−	2440.77i	−0.0360861	−	0.204654i
$523$	1695.79	+	9617.30i	0.141781	+	0.804082i	0.969895	+	0.243522i	$0.0783030\pi$
$523$	1695.79	+	9617.30i	0.141781	+	0.804082i	−0.828114	+	0.560560i	$0.810586\pi$
$524$	−5491.15	+	9510.95i	−0.457790	+	0.792916i
$525$	−2730.05	−	4728.59i	−0.226951	−	0.393091i
$526$	9489.05	−	7962.26i	0.786582	−	0.660021i
$527$	−5602.30	+	2039.07i	−0.463074	+	0.168545i
$528$	830.326	+	302.214i	0.0684381	+	0.0249094i
$529$	−4382.29	−	3677.18i	−0.360178	−	0.302226i
$530$	−1310.42	+	7431.75i	−0.107398	+	0.609084i
$531$	−2942.30			−0.240461
$532$	−2621.69	−	9926.59i	−0.213656	−	0.808970i
$533$	4372.72			0.355354
$534$	42.4856	−	240.948i	0.00344294	−	0.0195259i
$535$	957.971	+	803.833i	0.0774144	+	0.0649584i
$536$	6691.32	+	2435.44i	0.539218	+	0.196259i
$537$	12757.1	−	4643.20i	1.02516	−	0.373126i
$538$	2896.28	−	2430.26i	0.232095	−	0.194751i
$539$	5683.78	+	9844.59i	0.454207	+	0.786710i
$540$	439.609	−	761.425i	0.0350329	−	0.0606787i
$541$	524.373	+	2973.87i	0.0416720	+	0.236334i	0.998529	−	0.0542267i	$-0.0172694\pi$
$541$	524.373	+	2973.87i	0.0416720	+	0.236334i	−0.956857	+	0.290560i	$0.906158\pi$
$542$	323.899	+	1836.92i	0.0256691	+	0.145577i
$543$	−3544.86	+	6139.88i	−0.280156	+	0.485244i
$544$	−568.608	−	984.857i	−0.0448141	−	0.0776202i
$545$	−11547.2	+	9689.23i	−0.907572	+	0.761543i
$546$	2231.62	−	812.245i	0.174917	−	0.0636646i
$547$	−15955.3	−	5807.24i	−1.24716	−	0.453930i	−0.367721	−	0.929936i	$-0.619862\pi$
$547$	−15955.3	−	5807.24i	−1.24716	−	0.453930i	−0.879442	+	0.476006i	$0.842084\pi$
$548$	792.744	+	665.191i	0.0617963	+	0.0518532i
$549$	42.7715	−	242.569i	0.00332503	−	0.0188572i
$550$	2162.12			0.167624
$551$	−2911.88	−	11025.3i	−0.225136	−	0.852440i
$552$	−1926.94			−0.148579
$553$	−638.756	+	3622.57i	−0.0491188	+	0.278566i
$554$	−4163.42	−	3493.52i	−0.319290	−	0.267916i
$555$	−6905.55	−	2513.41i	−0.528152	−	0.192231i
$556$	−7099.72	+	2584.09i	−0.541538	+	0.197104i
$557$	2164.16	−	1815.94i	0.164629	−	0.138140i	−0.556751	−	0.830679i	$-0.687952\pi$
$557$	2164.16	−	1815.94i	0.164629	−	0.138140i	0.721380	+	0.692539i	$0.243508\pi$
$558$	−1509.84	−	2615.12i	−0.114546	−	0.198399i
$559$	−3056.89	+	5294.69i	−0.231293	+	0.400611i
$560$	700.994	+	3975.53i	0.0528971	+	0.299994i
$561$	−340.805	−	1932.80i	−0.0256485	−	0.145460i
$562$	−4422.18	+	7659.43i	−0.331919	+	0.574900i
$563$	−6238.82	−	10806.0i	−0.467025	−	0.808911i	0.532266	−	0.846577i	$-0.321341\pi$
$563$	−6238.82	−	10806.0i	−0.467025	−	0.808911i	−0.999290	+	0.0376668i	$0.988007\pi$
$564$	668.941	−	561.308i	0.0499424	−	0.0419066i
$565$	−1754.07	+	638.431i	−0.130610	+	0.0475380i
$566$	13397.6	+	4876.34i	0.994955	+	0.362134i
$567$	−1923.05	−	1613.63i	−0.142435	−	0.119517i
$568$	−564.732	+	3202.76i	−0.0417177	+	0.236593i
$569$	−12247.8			−0.902380			−0.451190	−	0.892428i	$-0.649000\pi$
$569$	−12247.8			−0.902380			−0.451190	+	0.892428i	$0.649000\pi$
$570$	1722.77	−	3660.16i	0.126595	−	0.268960i
$571$	−9943.88			−0.728789			−0.364394	−	0.931245i	$-0.618724\pi$
$571$	−9943.88			−0.728789			−0.364394	+	0.931245i	$0.618724\pi$
$572$	−163.299	+	926.116i	−0.0119369	+	0.0676973i
$573$	2133.06	+	1789.85i	0.155514	+	0.130492i
$574$	19942.8	+	7258.60i	1.45017	+	0.527819i
$575$	−4430.68	+	1612.64i	−0.321343	+	0.116959i
$576$	441.242	−	370.246i	0.0319185	−	0.0267828i
$577$	8659.87	+	14999.3i	0.624810	+	1.08220i	0.988578	+	0.150713i	$0.0481568\pi$
$577$	8659.87	+	14999.3i	0.624810	+	1.08220i	−0.363768	+	0.931490i	$0.618510\pi$
$578$	3650.05	−	6322.08i	0.262668	−	0.454955i
$579$	351.438	+	1993.11i	0.0252250	+	0.143058i
$580$	778.583	+	4415.57i	0.0557395	+	0.316114i
$581$	19859.1	−	34396.9i	1.41806	−	2.45615i
$582$	−2699.69	−	4676.00i	−0.192278	−	0.333035i
$583$	−6536.01	+	5484.37i	−0.464312	+	0.389604i
$584$	−2381.85	+	866.921i	−0.168770	+	0.0614271i
$585$	879.292	+	320.036i	0.0621440	+	0.0226186i
$586$	−9563.66	−	8024.86i	−0.674183	−	0.565706i
$587$	4763.18	−	27013.4i	0.334919	−	1.89942i	−0.0931083	−	0.995656i	$-0.529680\pi$
$587$	4763.18	−	27013.4i	0.334919	−	1.89942i	0.428028	−	0.903766i	$-0.359209\pi$
$588$	7410.14			0.519709
$589$	−7928.24	−	11409.6i	−0.554630	−	0.798173i
$590$	5322.88			0.371423
$591$	−2069.38	+	11736.0i	−0.144032	+	0.816845i
$592$	−3688.01	−	3094.61i	−0.256041	−	0.214844i
$593$	−17307.9	−	6299.57i	−1.19857	−	0.436243i	−0.335844	−	0.941918i	$-0.609022\pi$
$593$	−17307.9	−	6299.57i	−1.19857	−	0.436243i	−0.862724	+	0.505674i	$0.831244\pi$
$594$	934.117	−	339.991i	0.0645240	−	0.0234848i
$595$	6868.64	−	5763.47i	0.473255	−	0.397108i
$596$	4275.14	+	7404.76i	0.293820	+	0.508911i
$597$	−2941.35	+	5094.57i	−0.201644	+	0.349258i
$598$	−356.114	−	2019.62i	−0.0243521	−	0.138108i
$599$	−4592.81	−	26047.1i	−0.313284	−	1.77672i	−0.581686	−	0.813413i	$-0.697607\pi$
$599$	−4592.81	−	26047.1i	−0.313284	−	1.77672i	0.268403	−	0.963307i	$-0.413504\pi$
$600$	704.709	−	1220.59i	0.0479494	−	0.0830507i
$601$	−7987.37	−	13834.5i	−0.542116	−	0.938973i	−0.998782	−	0.0493345i	$-0.984290\pi$
$601$	−7987.37	−	13834.5i	−0.542116	−	0.938973i	0.456666	−	0.889638i	$-0.349043\pi$
$602$	−22730.7	+	19073.3i	−1.53893	+	1.29131i
$603$	7527.74	−	2739.87i	0.508380	−	0.185035i
$604$	−206.526	−	75.1694i	−0.0139130	−	0.00506391i
$605$	6187.16	+	5191.65i	0.415775	+	0.348877i
$606$	952.942	−	5404.40i	0.0638789	−	0.362275i
$607$	4071.27			0.272237			0.136119	−	0.990693i	$-0.456537\pi$
$607$	4071.27			0.272237			0.136119	+	0.990693i	$0.456537\pi$
$608$	1880.69	−	1867.25i	0.125448	−	0.124551i
$609$	12801.9			0.851823
$610$	−77.3775	+	438.830i	−0.00513594	+	0.0291274i
$611$	711.933	+	597.382i	0.0471387	+	0.0395540i
$612$	−1202.21	−	437.569i	−0.0794061	−	0.0289015i
$613$	−21828.8	+	7945.05i	−1.43827	+	0.523487i	−0.939289	−	0.343127i	$-0.888514\pi$
$613$	−21828.8	+	7945.05i	−1.43827	+	0.523487i	−0.498980	+	0.866614i	$0.666292\pi$
$614$	−3348.11	+	2809.39i	−0.220063	+	0.184655i
$615$	4181.03	+	7241.76i	0.274139	+	0.474823i
$616$	−2282.09	+	3952.70i	−0.149266	+	0.258537i
$617$	−2960.41	−	16789.3i	−0.193163	−	1.09548i	−0.915010	−	0.403430i	$-0.867818\pi$
$617$	−2960.41	−	16789.3i	−0.193163	−	1.09548i	0.721847	−	0.692052i	$-0.243293\pi$
$618$	303.057	+	1718.72i	0.0197261	+	0.111872i
$619$	−5591.82	+	9685.32i	−0.363093	+	0.628895i	−0.988468	−	0.151429i	$-0.951612\pi$
$619$	−5591.82	+	9685.32i	−0.363093	+	0.628895i	0.625376	+	0.780324i	$0.284946\pi$
$620$	2731.43	+	4730.98i	0.176931	+	0.306453i
$621$	−1660.63	+	1393.44i	−0.107309	+	0.0900430i
$622$	1987.43	−	723.366i	0.128117	−	0.0466307i
$623$	1187.56	+	432.238i	0.0763704	+	0.0277965i
$624$	469.600	+	394.041i	0.0301266	+	0.0252793i
$625$	−839.689	+	4762.11i	−0.0537401	+	0.304775i
$626$	−7714.86			−0.492569
$627$	4152.14	−	1918.07i	0.264467	−	0.122170i
$628$	−2425.15			−0.154099
$629$	−1856.87	+	10530.8i	−0.117708	+	0.667555i
$630$	3478.97	+	2919.20i	0.220009	+	0.184609i
$631$	−14053.4	−	5115.02i	−0.886620	−	0.322703i	−0.141742	−	0.989904i	$-0.545270\pi$
$631$	−14053.4	−	5115.02i	−0.886620	−	0.322703i	−0.744878	+	0.667200i	$0.767493\pi$
$632$	−892.256	+	324.754i	−0.0561583	+	0.0204399i
$633$	−3034.93	+	2546.61i	−0.190565	+	0.159903i
$634$	−245.418	−	425.077i	−0.0153735	−	0.0266277i
$635$	7259.88	−	12574.5i	0.453700	−	0.785831i
$636$	965.803	+	5477.34i	0.0602148	+	0.341495i
$637$	1369.46	+	7766.57i	0.0851802	+	0.483081i
$638$	−2534.69	+	4390.20i	−0.157287	+	0.272429i
$639$	1829.34	+	3168.51i	0.113251	+	0.196157i
$640$	−798.245	+	669.807i	−0.0493022	+	0.0413695i
$641$	19744.8	−	7186.51i	1.21665	−	0.442824i	0.347644	−	0.937627i	$-0.386982\pi$
$641$	19744.8	−	7186.51i	1.21665	−	0.442824i	0.869005	+	0.494803i	$0.164760\pi$
$642$	866.090	+	315.231i	0.0532428	+	0.0193788i
$643$	11820.7	+	9918.71i	0.724979	+	0.608329i	0.928758	−	0.370688i	$-0.120878\pi$
$643$	11820.7	+	9918.71i	0.724979	+	0.608329i	−0.203779	+	0.979017i	$0.565322\pi$
$644$	1728.37	−	9802.10i	0.105757	−	0.599777i
$645$	−11691.5			−0.713726
$646$	−5680.37	−	1543.91i	−0.345961	−	0.0940314i
$647$	22376.5			1.35968			0.679839	−	0.733361i	$-0.262050\pi$
$647$	22376.5			1.35968			0.679839	+	0.733361i	$0.262050\pi$
$648$	112.524	−	638.155i	0.00682154	−	0.0386869i
$649$	4610.20	+	3868.41i	0.278838	+	0.233973i
$650$	1409.54	+	513.030i	0.0850563	+	0.0309580i
$651$	14657.1	−	5334.73i	0.882420	−	0.321174i
$652$	11680.4	−	9801.04i	0.701596	−	0.588709i
$653$	12708.8	+	22012.2i	0.761611	+	1.31915i	0.942020	+	0.335557i	$0.108925\pi$
$653$	12708.8	+	22012.2i	0.761611	+	1.31915i	−0.180409	+	0.983592i	$0.557742\pi$
$654$	−5554.83	+	9621.24i	−0.332127	+	0.575260i
$655$	−3881.29	−	22011.9i	−0.231534	−	1.31309i
$656$	951.283	+	5395.00i	0.0566179	+	0.321096i
$657$	−1425.77	+	2469.51i	−0.0846647	+	0.146644i
$658$	2255.30	+	3906.29i	0.133618	+	0.231433i
$659$	4553.43	−	3820.78i	0.269160	−	0.225852i	−0.498210	−	0.867056i	$-0.666009\pi$
$659$	4553.43	−	3820.78i	0.269160	−	0.225852i	0.767370	+	0.641204i	$0.221565\pi$
$660$	−1689.90	+	615.074i	−0.0996656	+	0.0362753i
$661$	578.438	+	210.534i	0.0340373	+	0.0123885i	0.358983	−	0.933344i	$-0.383124\pi$
$661$	578.438	+	210.534i	0.0340373	+	0.0123885i	−0.324945	+	0.945733i	$0.605346\pi$
$662$	−3118.22	−	2616.50i	−0.183071	−	0.153615i
$663$	236.438	−	1340.90i	0.0138499	−	0.0785466i
$664$	10252.4			0.599205
$665$	17073.5	+	12046.5i	0.995615	+	0.702473i
$666$	−5416.16			−0.315123
$667$	1919.68	−	10887.0i	0.111440	−	0.632006i
$668$	10800.8	+	9062.98i	0.625594	+	0.524936i
$669$	1544.63	+	562.201i	0.0892661	+	0.0324902i
$670$	−13618.3	+	4956.67i	−0.785258	+	0.285810i
$671$	−385.938	+	323.840i	−0.0222041	+	0.0186315i
$672$	1487.62	+	2576.64i	0.0853962	+	0.147911i
$673$	5447.35	−	9435.08i	0.312006	−	0.540410i	−0.666791	−	0.745245i	$-0.732333\pi$
$673$	5447.35	−	9435.08i	0.312006	−	0.540410i	0.978796	+	0.204835i	$0.0656659\pi$
$674$	265.250	+	1504.31i	0.0151588	+	0.0859699i
$675$	−275.336	−	1561.51i	−0.0157003	−	0.0890406i
$676$	4067.79	−	7045.62i	0.231440	−	0.400866i
$677$	8078.27	+	13992.0i	0.458602	+	0.794321i	0.998887	−	0.0471604i	$-0.0150172\pi$
$677$	8078.27	+	13992.0i	0.458602	+	0.794321i	−0.540286	+	0.841482i	$0.681684\pi$
$678$	−1053.89	+	884.318i	−0.0596967	+	0.0500915i
$679$	26207.8	−	9538.84i	1.48124	−	0.539127i
$680$	2174.91	+	791.602i	0.122653	+	0.0446420i
$681$	11464.3	+	9619.69i	0.645100	+	0.541303i
$682$	−1072.53	+	6082.63i	−0.0602190	+	0.341519i
$683$	−15478.1			−0.867136			−0.433568	−	0.901121i	$-0.642746\pi$
$683$	−15478.1			−0.867136			−0.433568	+	0.901121i	$0.642746\pi$
$684$	270.506	−	2969.19i	0.0151214	−	0.165979i
$685$	−2106.16			−0.117478
$686$	−2954.70	+	16756.9i	−0.164447	+	0.932627i
$687$	−4332.83	−	3635.68i	−0.240623	−	0.201906i
$688$	−7197.52	−	2619.68i	−0.398841	−	0.145166i
$689$	−5562.31	+	2024.52i	−0.307558	+	0.111942i
$690$	3004.23	−	2520.85i	0.165753	−	0.139083i
$691$	−5693.33	−	9861.14i	−0.313436	−	0.542888i	0.665667	−	0.746249i	$-0.268147\pi$
$691$	−5693.33	−	9861.14i	−0.313436	−	0.542888i	−0.979104	+	0.203361i	$0.934814\pi$
$692$	8014.48	−	13881.5i	0.440267	−	0.762565i
$693$	891.632	+	5056.70i	0.0488749	+	0.277183i
$694$	−1089.06	−	6176.39i	−0.0595682	−	0.337828i
$695$	7688.43	−	13316.8i	0.419624	−	0.726810i
$696$	1652.28	+	2861.83i	0.0899849	+	0.155858i
$697$	9321.08	−	7821.31i	0.506544	−	0.425041i
$698$	−3151.72	+	1147.13i	−0.170909	+	0.0622057i
$699$	−16012.0	−	5827.88i	−0.866421	−	0.315351i
$700$	5576.91	+	4679.58i	0.301125	+	0.252674i
$701$	479.117	−	2717.21i	0.0258145	−	0.146402i	−0.969176	−	0.246369i	$-0.920763\pi$
$701$	479.117	−	2717.21i	0.0258145	−	0.146402i	0.994991	+	0.0999670i	$0.0318737\pi$
$702$	689.646			0.0370784
$703$	−24832.9	+	2082.86i	−1.33227	+	0.111745i
$704$	−1178.15			−0.0630729
$705$	−308.615	+	1750.24i	−0.0164867	+	0.0935005i
$706$	11420.0	+	9582.52i	0.608778	+	0.510826i
$707$	26636.8	+	9695.00i	1.41694	+	0.515726i
$708$	3686.47	−	1341.77i	0.195687	−	0.0712241i
$709$	925.320	−	776.436i	0.0490143	−	0.0411279i	−0.617951	−	0.786216i	$-0.712037\pi$
$709$	925.320	−	776.436i	0.0490143	−	0.0411279i	0.666966	+	0.745088i	$0.267593\pi$
$710$	−3309.44	−	5732.12i	−0.174931	−	0.302990i
$711$	−534.104	+	925.096i	−0.0281723	+	0.0487958i
$712$	56.6474	+	321.263i	0.00298167	+	0.0169099i
$713$	−2338.92	−	13264.6i	−0.122851	−	0.696725i
$714$	3304.19	−	5723.03i	0.173188	−	0.299971i
$715$	−956.966	−	1657.51i	−0.0500539	−	0.0866958i
$716$	−13866.2	+	11635.1i	−0.723750	+	0.607299i
$717$	−3720.76	+	1354.25i	−0.193800	+	0.0705373i
$718$	22301.0	+	8116.89i	1.15914	+	0.421893i
$719$	10757.2	+	9026.38i	0.557965	+	0.468188i	0.877627	−	0.479343i	$-0.159125\pi$
$719$	10757.2	+	9026.38i	0.557965	+	0.468188i	−0.319663	+	0.947531i	$0.603570\pi$
$720$	−203.566	+	1154.48i	−0.0105367	+	0.0597569i
$721$	−9014.77			−0.465641
$722$	98.4132	−	13717.6i	0.00507280	−	0.707089i
$723$	15500.2			0.797315
$724$	1641.49	−	9309.34i	0.0842617	−	0.477872i
$725$	6194.19	+	5197.55i	0.317306	+	0.266251i
$726$	5593.74	+	2035.95i	0.285955	+	0.104079i
$727$	−14109.7	+	5135.53i	−0.719809	+	0.261989i	−0.675845	−	0.737044i	$-0.736221\pi$
$727$	−14109.7	+	5135.53i	−0.719809	+	0.261989i	−0.0439646	+	0.999033i	$0.513999\pi$
$728$	−2425.65	+	2035.36i	−0.123490	+	0.103620i
$729$	−364.500	−	631.333i	−0.0185185	−	0.0320750i
$730$	2579.35	−	4467.57i	0.130775	−	0.226510i
$731$	2954.20	+	16754.1i	0.149473	+	0.847706i
$732$	57.0287	+	323.426i	0.00287956	+	0.0163308i
$733$	−6264.30	+	10850.1i	−0.315658	+	0.546736i	−0.979577	−	0.201069i	$-0.935559\pi$
$733$	−6264.30	+	10850.1i	−0.315658	+	0.546736i	0.663919	+	0.747804i	$0.268892\pi$
$734$	10322.1	+	17878.4i	0.519068	+	0.899053i
$735$	−11553.0	+	9694.08i	−0.579778	+	0.486492i
$736$	2414.30	−	878.735i	0.120914	−	0.0440090i
$737$	−15397.3	−	5604.14i	−0.769560	−	0.280097i
$738$	4721.13	+	3961.50i	0.235484	+	0.197595i
$739$	−1640.35	+	9302.91i	−0.0816528	+	0.463076i	0.916376	+	0.400319i	$0.131101\pi$
$739$	−1640.35	+	9302.91i	−0.0816528	+	0.463076i	−0.998029	+	0.0627574i	$0.980011\pi$
$740$	9798.31			0.486747
$741$	3162.00	−	265.214i	0.156760	−	0.0131483i
$742$	−28728.9			−1.42139
$743$	6154.67	−	34904.9i	0.303894	−	1.72347i	−0.324773	−	0.945792i	$-0.605288\pi$
$743$	6154.67	−	34904.9i	0.303894	−	1.72347i	0.628666	−	0.777675i	$-0.283601\pi$
$744$	3084.28	+	2588.02i	0.151983	+	0.127529i
$745$	−16352.3	−	5951.75i	−0.804164	−	0.292692i
$746$	7302.25	−	2657.80i	0.358384	−	0.130441i
$747$	8835.56	−	7413.91i	0.432766	−	0.363134i
$748$	1308.41	+	2266.23i	0.0639576	+	0.110778i
$749$	−2380.39	+	4122.95i	−0.116125	+	0.201134i
$750$	1558.35	+	8837.82i	0.0758703	+	0.430282i
$751$	5099.35	+	28919.8i	0.247774	+	1.40519i	0.813962	+	0.580918i	$0.197306\pi$
$751$	5099.35	+	28919.8i	0.247774	+	1.40519i	−0.566189	+	0.824276i	$0.691583\pi$
$752$	−582.160	+	1008.33i	−0.0282303	+	0.0488963i
$753$	1916.03	+	3318.66i	0.0927278	+	0.160609i
$754$	−2694.13	+	2260.65i	−0.130125	+	0.109188i
$755$	420.327	−	152.987i	0.0202613	−	0.00737451i
$756$	3145.29	+	1144.79i	0.151314	+	0.0550737i
$757$	11826.8	+	9923.89i	0.567838	+	0.476473i	0.880928	−	0.473251i	$-0.156920\pi$
$757$	11826.8	+	9923.89i	0.567838	+	0.476473i	−0.313089	+	0.949724i	$0.601364\pi$
$758$	4626.87	−	26240.3i	0.221709	−	1.25737i
$759$	4434.03			0.212049
$760$	−489.370	+	5371.53i	−0.0233570	+	0.256376i
$761$	−28960.0			−1.37950			−0.689751	−	0.724047i	$-0.742280\pi$
$761$	−28960.0			−1.37950			−0.689751	+	0.724047i	$0.742280\pi$
$762$	1858.27	−	10538.8i	0.0883438	−	0.501022i
$763$	−43959.7	−	36886.6i	−2.08578	−	1.75017i
$764$	−3488.78	−	1269.81i	−0.165209	−	0.0601311i
$765$	2446.77	−	890.552i	0.115638	−	0.0420889i
$766$	411.986	−	345.698i	0.0194330	−	0.0163062i
$767$	2087.60	+	3615.82i	0.0982773	+	0.170221i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−3883.73	−	22025.7i	−0.182121	−	1.03286i	−0.929599	−	0.368572i	$-0.879847\pi$
$769$	−3883.73	−	22025.7i	−0.182121	−	1.03286i	0.747479	−	0.664286i	$-0.231264\pi$
$770$	−1613.04	−	9148.02i	−0.0754935	−	0.428145i
$771$	7665.33	−	13276.7i	0.358054	−	0.620168i
$772$	−1349.24	−	2336.94i	−0.0629016	−	0.108949i
$773$	3610.70	−	3029.74i	0.168005	−	0.140973i	−0.554909	−	0.831911i	$-0.687247\pi$
$773$	3610.70	−	3029.74i	0.168005	−	0.140973i	0.722914	+	0.690938i	$0.242802\pi$
$774$	−8097.21	+	2947.14i	−0.376031	+	0.136864i
$775$	9257.68	+	3369.52i	0.429091	+	0.156177i
$776$	5514.89	+	4627.54i	0.255120	+	0.214071i
$777$	4858.04	−	27551.3i	0.224300	−	1.27207i
$778$	−16092.2			−0.741558
$779$	23169.7	+	16347.7i	1.06565	+	0.751885i
$780$	−1247.63			−0.0572723
$781$	1299.49	−	7369.80i	0.0595385	−	0.337659i
$782$	−4371.52	−	3668.14i	−0.199905	−	0.167740i
$783$	3493.43	+	1271.50i	0.159444	+	0.0580330i
$784$	−9284.34	+	3379.22i	−0.422938	+	0.153937i
$785$	3780.99	−	3172.63i	0.171910	−	0.144250i
$786$	−8236.73	−	14266.4i	−0.373784	−	0.647413i
$787$	18523.6	−	32083.9i	0.839004	−	1.45320i	−0.0517235	−	0.998661i	$-0.516471\pi$
$787$	18523.6	−	32083.9i	0.839004	−	1.45320i	0.890728	−	0.454537i	$-0.150195\pi$
$788$	−2759.17	−	15648.0i	−0.124735	−	0.707409i
$789$	3226.49	+	18298.3i	0.145584	+	0.825650i
$790$	966.242	−	1673.58i	0.0435156	−	0.0753713i
$791$	−3553.13	−	6154.20i	−0.159715	−	0.276635i
$792$	−1015.33	+	851.965i	−0.0455533	+	0.0382238i
$793$	−328.443	+	119.544i	−0.0147079	+	0.00535323i
$794$	9397.63	+	3420.46i	0.420037	+	0.152881i
$795$	−8671.31	−	7276.10i	−0.386843	−	0.324599i
$796$	1362.03	−	7724.45i	0.0606480	−	0.343952i
$797$	−20492.0			−0.910747			−0.455373	−	0.890301i	$-0.650494\pi$
$797$	−20492.0			−0.910747			−0.455373	+	0.890301i	$0.650494\pi$
$798$	14861.3	+	4039.26i	0.659253	+	0.179183i
$799$	2586.10			0.114505
$800$	−326.324	+	1850.67i	−0.0144216	+	0.0817890i
$801$	281.136	+	235.901i	0.0124013	+	0.0104059i
$802$	−20701.6	−	7534.77i	−0.911470	−	0.331748i
$803$	5480.82	−	1994.85i	0.240864	−	0.0876673i
$804$	−8182.22	+	6865.70i	−0.358911	+	0.301162i
$805$	10128.6	+	17543.3i	0.443462	+	0.768098i
$806$	−2142.50	+	3710.92i	−0.0936307	+	0.162173i
$807$	984.799	+	5585.07i	0.0429573	+	0.243623i
$808$	1270.59	+	7205.87i	0.0553207	+	0.313740i
$809$	−193.605	+	335.333i	−0.00841381	+	0.0145732i	−0.870202	−	0.492696i	$-0.836012\pi$
$809$	−193.605	+	335.333i	−0.00841381	+	0.0145732i	0.861788	+	0.507269i	$0.169345\pi$
$810$	659.413	+	1142.14i	0.0286042	+	0.0495439i
$811$	25180.3	−	21128.8i	1.09026	−	0.914837i	0.0935288	−	0.995617i	$-0.470185\pi$
$811$	25180.3	−	21128.8i	1.09026	−	0.914837i	0.996732	+	0.0807791i	$0.0257408\pi$
$812$	−16039.8	+	5838.02i	−0.693211	+	0.252308i
$813$	−2629.16	−	956.936i	−0.113418	−	0.0412807i
$814$	8486.41	+	7120.95i	0.365416	+	0.306620i
$815$	−5388.74	+	30561.1i	−0.231607	+	1.31351i
$816$	1705.82			0.0731811
$817$	−35992.0	+	16626.4i	−1.54125	+	0.711977i
$818$	20237.7			0.865030
$819$	−618.581	+	3508.15i	−0.0263919	+	0.149676i
$820$	−8540.95	−	7166.71i	−0.363735	−	0.305210i
$821$	−38467.5	−	14001.0i	−1.63523	−	0.595175i	−0.649035	−	0.760759i	$-0.724827\pi$
$821$	−38467.5	−	14001.0i	−1.63523	−	0.595175i	−0.986196	+	0.165584i	$0.947049\pi$
$822$	−1458.67	+	530.911i	−0.0618940	+	0.0225276i
$823$	5839.26	−	4899.72i	0.247320	−	0.207526i	−0.510698	−	0.859760i	$-0.670613\pi$
$823$	5839.26	−	4899.72i	0.247320	−	0.207526i	0.758017	+	0.652235i	$0.226168\pi$
$824$	−1163.49	−	2015.23i	−0.0491895	−	0.0851987i
$825$	−1621.59	+	2808.68i	−0.0684322	+	0.118528i
$826$	3518.81	+	19956.1i	0.148226	+	0.840633i
$827$	4256.42	+	24139.3i	0.178972	+	1.01500i	0.933458	+	0.358686i	$0.116775\pi$
$827$	4256.42	+	24139.3i	0.178972	+	1.01500i	−0.754486	+	0.656316i	$0.772114\pi$
$828$	1445.20	−	2503.16i	0.0606573	−	0.105062i
$829$	6732.50	+	11661.0i	0.282062	+	0.488546i	0.971893	−	0.235425i	$-0.0756482\pi$
$829$	6732.50	+	11661.0i	0.282062	+	0.488546i	−0.689830	+	0.723971i	$0.742315\pi$
$830$	−15984.3	+	13412.4i	−0.668462	+	0.560906i
$831$	7660.78	−	2788.30i	0.319795	−	0.116396i
$832$	−768.066	−	279.553i	−0.0320047	−	0.0116487i
$833$	16810.9	+	14106.1i	0.699237	+	0.586730i
$834$	1967.96	−	11160.9i	0.0817086	−	0.463392i
$835$	−28695.6			−1.18929
$836$	−4327.62	+	4296.69i	−0.179036	+	0.177756i
$837$	4529.52			0.187053
$838$	4392.51	−	24911.1i	0.181070	−	1.02690i
$839$	−23932.1	−	20081.4i	−0.984777	−	0.826326i	2.64785e−5	−	1.00000i	$-0.499992\pi$
$839$	−23932.1	−	20081.4i	−0.984777	−	0.826326i	−0.984803	+	0.173674i	$0.944436\pi$
$840$	−5690.11	−	2071.03i	−0.233723	−	0.0850683i
$841$	5102.96	−	1857.33i	0.209232	−	0.0761543i
$842$	−9311.29	+	7813.10i	−0.381102	+	0.319783i
$843$	−6633.26	−	11489.1i	−0.271010	−	0.469404i
$844$	2641.22	−	4574.72i	0.107719	−	0.186574i
$845$	2875.22	+	16306.2i	0.117054	+	0.663846i
$846$	227.455	+	1289.96i	0.00924357	+	0.0524229i
$847$	−15374.0	+	26628.5i	−0.623679	+	1.08024i
$848$	−3707.89	−	6422.26i	−0.150153	−	0.260072i
$849$	−16382.8	+	13746.8i	−0.662256	+	0.555699i
$850$	3922.26	−	1427.59i	0.158274	−	0.0576069i
$851$	−22701.8	−	8262.78i	−0.914463	−	0.332837i
$852$	−3736.95	−	3135.68i	−0.150265	−	0.126087i
$853$	−4361.33	+	24734.3i	−0.175064	+	0.992835i	0.763007	+	0.646390i	$0.223722\pi$
$853$	−4361.33	+	24734.3i	−0.175064	+	0.992835i	−0.938071	+	0.346444i	$0.887389\pi$
$854$	−1696.38			−0.0679730
$855$	3462.61	+	4983.07i	0.138501	+	0.199318i
$856$	−1228.90			−0.0490688
$857$	−5419.10	+	30733.2i	−0.216001	+	1.22500i	0.663160	+	0.748478i	$0.269215\pi$
$857$	−5419.10	+	30733.2i	−0.216001	+	1.22500i	−0.879161	+	0.476525i	$0.841896\pi$
$858$	−1080.59	−	906.719i	−0.0429960	−	0.0360780i
$859$	32481.2	+	11822.2i	1.29016	+	0.469579i	0.893779	−	0.448508i	$-0.148045\pi$
$859$	32481.2	+	11822.2i	1.29016	+	0.469579i	0.396378	+	0.918087i	$0.370267\pi$
$860$	14648.6	−	5331.65i	0.580828	−	0.211404i
$861$	−24386.3	+	20462.5i	−0.965254	+	0.809944i
$862$	−12228.5	−	21180.4i	−0.483183	−	0.836898i
$863$	−20334.1	+	35219.6i	−0.802062	+	1.38921i	0.116195	+	0.993226i	$0.462930\pi$
$863$	−20334.1	+	35219.6i	−0.802062	+	1.38921i	−0.918257	+	0.395985i	$0.870403\pi$
$864$	150.032	+	850.874i	0.00590763	+	0.0335038i
$865$	5664.84	+	32126.9i	0.222671	+	1.26283i
$866$	−670.752	+	1161.78i	−0.0263200	+	0.0455875i
$867$	5475.08	+	9483.11i	0.214468	+	0.371469i
$868$	−15931.4	+	13368.0i	−0.622980	+	0.522742i
$869$	2053.15	−	747.286i	0.0801477	−	0.0291714i
$870$	−6319.93	−	2300.27i	−0.246282	−	0.0896394i
$871$	−8708.08	−	7306.95i	−0.338762	−	0.284255i
$872$	2572.23	−	14587.8i	0.0998929	−	0.566521i
$873$	8099.07			0.313989
$874$	5663.57	−	12032.7i	0.219191	−	0.465688i
$875$	−46354.7			−1.79094
$876$	660.221	−	3744.30i	0.0254644	−	0.144416i
$877$	−18580.7	−	15591.0i	−0.715421	−	0.600310i	0.210693	−	0.977552i	$-0.432428\pi$
$877$	−18580.7	−	15591.0i	−0.715421	−	0.600310i	−0.926114	+	0.377243i	$0.876872\pi$
$878$	28872.2	+	10508.6i	1.10978	+	0.403928i
$879$	17597.3	−	6404.91i	0.675249	−	0.245770i
$880$	1836.83	−	1541.28i	0.0703630	−	0.0590415i
$881$	−6907.23	−	11963.7i	−0.264144	−	0.457510i	0.703195	−	0.710997i	$-0.251756\pi$
$881$	−6907.23	−	11963.7i	−0.264144	−	0.457510i	−0.967339	+	0.253487i	$0.918423\pi$
$882$	−5557.61	+	9626.06i	−0.212170	+	0.367490i
$883$	−7851.79	−	44529.7i	−0.299245	−	1.69711i	−0.649428	−	0.760423i	$-0.724991\pi$
$883$	−7851.79	−	44529.7i	−0.299245	−	1.69711i	0.350182	−	0.936682i	$-0.386120\pi$
$884$	315.250	+	1787.87i	0.0119944	+	0.0680234i
$885$	−3992.16	+	6914.62i	−0.151633	+	0.262635i
$886$	6127.69	+	10613.5i	0.232352	+	0.402445i
$887$	−16819.2	+	14112.9i	−0.636676	+	0.534235i	−0.902995	−	0.429650i	$-0.858637\pi$
$887$	−16819.2	+	14112.9i	−0.636676	+	0.534235i	0.266319	+	0.963885i	$0.414192\pi$
$888$	6786.03	−	2469.91i	0.256446	−	0.0933388i
$889$	51942.6	+	18905.6i	1.95962	+	0.713243i
$890$	−508.600	−	426.766i	−0.0191554	−	0.0160733i
$891$	−258.927	+	1468.45i	−0.00973555	+	0.0552130i
$892$	−2191.69			−0.0822680
$893$	1538.95	+	5826.95i	0.0576695	+	0.218355i
$894$	−12825.4			−0.479806
$895$	6397.16	−	36280.1i	0.238920	−	1.35498i
$896$	−3038.89	−	2549.93i	−0.113306	−	0.0950751i
$897$	2890.65	+	1052.11i	0.107599	+	0.0391627i
$898$	8617.21	−	3136.41i	0.320223	−	0.116552i
$899$	−17694.8	+	14847.7i	−0.656455	+	0.550831i
$900$	1057.06	+	1830.89i	0.0391505	+	0.0678106i
$901$	−8235.69	+	14264.6i	−0.304518	+	0.527440i
$902$	−2188.98	−	12414.3i	−0.0808038	−	0.458261i
$903$	−7728.94	−	43833.0i	−0.284832	−	1.61536i
$904$	917.170	−	1588.58i	0.0337440	−	0.0584464i
$905$	9619.45	+	16661.4i	0.353327	+	0.611981i
$906$	252.543	−	211.908i	0.00926067	−	0.00777062i
$907$	26780.7	−	9747.37i	0.980417	−	0.356843i	0.198415	−	0.980118i	$-0.436421\pi$
$907$	26780.7	−	9747.37i	0.980417	−	0.356843i	0.782002	+	0.623276i	$0.214199\pi$
$908$	−18750.7	−	6824.71i	−0.685314	−	0.249434i
$909$	6305.82	+	5291.21i	0.230089	+	0.193067i
$910$	1119.07	−	6346.55i	0.0407657	−	0.231194i
$911$	10983.9			0.399466			0.199733	−	0.979850i	$-0.435993\pi$
$911$	10983.9			0.399466			0.199733	+	0.979850i	$0.435993\pi$
$912$	1015.11	+	3843.53i	0.0368570	+	0.139552i
$913$	−23591.7			−0.855171
$914$	3710.35	−	21042.5i	0.134275	−	0.761513i
$915$	−512.023	−	429.638i	−0.0184994	−	0.0155229i
$916$	7086.67	+	2579.34i	0.255622	+	0.0930390i
$917$	79959.6	−	29102.9i	2.87950	−	1.04805i
$918$	1470.08	−	1233.54i	0.0528538	−	0.0443496i
$919$	10615.7	+	18386.9i	0.381044	+	0.659988i	0.991212	−	0.132285i	$-0.0422313\pi$
$919$	10615.7	+	18386.9i	0.381044	+	0.659988i	−0.610168	+	0.792272i	$0.708898\pi$
$920$	−2614.50	+	4528.45i	−0.0936929	+	0.162281i
$921$	−1138.43	−	6456.36i	−0.0407303	−	0.230993i
$922$	1025.83	+	5817.76i	0.0366419	+	0.207807i
$923$	2595.88	−	4496.20i	0.0925726	−	0.160340i
$924$	−3423.14	−	5929.05i	−0.121875	−	0.211095i
$925$	13536.3	−	11358.3i	0.481159	−	0.403740i
$926$	17670.5	−	6431.54i	0.627094	−	0.228244i
$927$	−2459.98	−	895.359i	−0.0871589	−	0.0317232i
$928$	−3375.25	−	2832.17i	−0.119395	−	0.100184i
$929$	3241.83	−	18385.3i	0.114490	−	0.649303i	−0.872512	−	0.488593i	$-0.837510\pi$
$929$	3241.83	−	18385.3i	0.114490	−	0.649303i	0.987002	−	0.160710i	$-0.0513785\pi$
$930$	−8194.30			−0.288927
$931$	−21779.6	+	46272.4i	−0.766699	+	1.62891i
$932$	22719.4			0.798498
$933$	−550.893	+	3124.27i	−0.0193306	+	0.109629i
$934$	6752.47	+	5666.00i	0.236561	+	0.198498i
$935$	−5004.64	−	1821.54i	−0.175047	−	0.0637120i
$936$	−864.074	+	314.497i	−0.0301743	+	0.0109825i
$937$	11806.5	−	9906.80i	0.411633	−	0.345401i	−0.413336	−	0.910578i	$-0.635637\pi$
$937$	11806.5	−	9906.80i	0.411633	−	0.345401i	0.824970	+	0.565177i	$0.191192\pi$
$938$	−27585.9	−	47780.2i	−0.960247	−	1.66320i
$939$	5786.15	−	10021.9i	0.201090	−	0.348299i
$940$	−411.486	−	2333.65i	−0.0142779	−	0.0809738i
$941$	5605.75	+	31791.8i	0.194200	+	1.10136i	0.913553	+	0.406719i	$0.133327\pi$
$941$	5605.75	+	31791.8i	0.194200	+	1.10136i	−0.719353	+	0.694645i	$0.755562\pi$
$942$	1818.87	−	3150.37i	0.0629107	−	0.108964i
$943$	13745.0	+	23807.1i	0.474655	+	0.822127i
$944$	−4006.99	+	3362.26i	−0.138153	+	0.115924i
$945$	−6401.38	+	2329.91i	−0.220356	+	0.0802032i
$946$	16562.1	+	6028.10i	0.569217	+	0.207178i
$947$	42461.6	+	35629.5i	1.45704	+	1.22260i	0.927235	+	0.374479i	$0.122178\pi$
$947$	42461.6	+	35629.5i	1.45704	+	1.22260i	0.529803	+	0.848121i	$0.322266\pi$
$948$	247.323	−	1402.64i	0.00847330	−	0.0480545i
$949$	4046.41			0.138411
$950$	5550.69	+	7988.03i	0.189566	+	0.272806i
$951$	736.254			0.0251048
$952$	−1530.05	+	8677.32i	−0.0520893	+	0.295413i
$953$	−9291.11	−	7796.16i	−0.315812	−	0.264997i	0.471078	−	0.882092i	$-0.343865\pi$
$953$	−9291.11	−	7796.16i	−0.315812	−	0.264997i	−0.786889	+	0.617094i	$0.788310\pi$
$954$	−7839.63	−	2853.39i	−0.266056	−	0.0968364i
$955$	7100.44	−	2584.35i	0.240592	−	0.0875682i
$956$	4044.26	−	3393.53i	0.136821	−	0.114806i
$957$	−3802.03	−	6585.31i	−0.128424	−	0.222438i
$958$	−229.433	+	397.390i	−0.00773763	+	0.0134020i
$959$	−1392.33	−	7896.27i	−0.0468827	−	0.265885i
$960$	−271.421	−	1539.31i	−0.00912509	−	0.0517510i
$961$	823.805	−	1426.87i	0.0276528	−	0.0478961i
$962$	3842.83	+	6655.98i	0.128792	+	0.223074i
$963$	−1059.06	+	888.661i	−0.0354391	+	0.0297370i
$964$	−19420.6	+	7068.51i	−0.648853	+	0.236163i
$965$	5160.79	+	1878.37i	0.172157	+	0.0626601i
$966$	11437.0	+	9596.80i	0.380932	+	0.319640i
$967$	2311.78	−	13110.7i	0.0768787	−	0.436001i	−0.921937	−	0.387341i	$-0.873394\pi$
$967$	2311.78	−	13110.7i	0.0768787	−	0.436001i	0.998815	−	0.0486602i	$-0.0154951\pi$
$968$	−7936.98			−0.263537
$969$	6265.87	−	6221.08i	0.207728	−	0.206243i
$970$	−14651.9			−0.484995
$971$	7301.25	−	41407.5i	0.241306	−	1.36852i	−0.587610	−	0.809144i	$-0.699931\pi$
$971$	7301.25	−	41407.5i	0.241306	−	1.36852i	0.828917	−	0.559372i	$-0.188958\pi$
$972$	744.595	+	624.790i	0.0245709	+	0.0206174i
$973$	55008.8	+	20021.6i	1.81244	+	0.659673i
$974$	25315.7	−	9214.17i	0.832821	−	0.303122i
$975$	−1723.60	+	1446.27i	−0.0566147	+	0.0475054i
$976$	−218.943	−	379.221i	−0.00718054	−	0.0124371i
$977$	−8645.46	+	14974.4i	−0.283104	+	0.490351i	−0.972148	−	0.234369i	$-0.924698\pi$
$977$	−8645.46	+	14974.4i	−0.283104	+	0.490351i	0.689044	+	0.724720i	$0.258031\pi$
$978$	3971.60	+	22524.1i	0.129855	+	0.736443i
$979$	−130.350	−	739.253i	−0.00425537	−	0.0241334i
$980$	10054.2	−	17414.4i	0.327724	−	0.567635i
$981$	−8332.24	−	14431.9i	−0.271180	−	0.469698i
$982$	−3050.33	+	2559.53i	−0.0991242	+	0.0831751i
$983$	7806.54	−	2841.35i	0.253296	−	0.0921921i	−0.212252	−	0.977215i	$-0.568080\pi$
$983$	7806.54	−	2841.35i	0.253296	−	0.0921921i	0.465548	+	0.885023i	$0.345857\pi$
$984$	−7721.77	−	2810.49i	−0.250164	−	0.0910521i
$985$	24772.8	+	20786.8i	0.801347	+	0.672410i
$986$	−1699.40	+	9637.77i	−0.0548883	+	0.311287i
$987$	−6765.89			−0.218197
$988$	−3840.80	+	1774.25i	−0.123676	+	0.0571320i
$989$	−38435.6			−1.23577
$990$	468.422	−	2656.55i	0.0150378	−	0.0852836i
$991$	−6288.87	−	5276.99i	−0.201587	−	0.169151i	0.536406	−	0.843960i	$-0.319782\pi$
$991$	−6288.87	−	5276.99i	−0.201587	−	0.169151i	−0.737993	+	0.674809i	$0.764226\pi$
$992$	−5044.57	−	1836.07i	−0.161457	−	0.0587655i
$993$	5737.60	−	2088.32i	0.183361	−	0.0667379i
$994$	19302.7	−	16196.9i	0.615940	−	0.516835i
$995$	7981.75	+	13824.8i	0.254310	+	0.440478i
$996$	−7689.33	+	13318.3i	−0.244624	+	0.423702i
$997$	−3764.63	−	21350.3i	−0.119586	−	0.678205i	−0.984377	−	0.176073i	$-0.943660\pi$
$997$	−3764.63	−	21350.3i	−0.119586	−	0.678205i	0.864791	−	0.502131i	$-0.167451\pi$
$998$	−7343.36	−	41646.3i	−0.232916	−	1.32093i
$999$	4062.12	−	7035.79i	0.128648	−	0.222825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.d.55.3	✓	18
19.3	odd	18		2166.4.a.bj.1.2		9
19.9	even	9	inner	114.4.i.d.85.3	yes	18
19.16	even	9		2166.4.a.bm.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.55.3	✓	18	1.1	even	1	trivial
114.4.i.d.85.3	yes	18	19.9	even	9	inner
2166.4.a.bj.1.2		9	19.3	odd	18
2166.4.a.bm.1.2		9	19.16	even	9

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.64995 - 2.78435i) q^{5} +(4.59627 - 3.85673i) q^{6} +(15.4961 + 26.8400i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.64995 - 2.78435i) q^{5} +(4.59627 - 3.85673i) q^{6} +(15.4961 + 26.8400i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-2.82731 - 16.0344i) q^{10} +(9.20432 - 15.9423i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(9.78332 - 8.20918i) q^{13} +(58.2461 - 21.1999i) q^{14} +(22.9498 + 8.35306i) q^{15} +(12.2567 + 10.2846i) q^{16} +(6.17110 - 34.9981i) q^{17} +18.0000 q^{18} +(82.5293 - 6.92217i) q^{19} -32.5636 q^{20} +(-16.1452 + 91.5639i) q^{21} +(-28.2037 - 23.6657i) q^{22} +(75.4470 + 27.4605i) q^{23} +(-22.5526 + 8.20848i) q^{24} +(-44.9865 + 37.7482i) q^{25} +(-12.7712 - 22.1204i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-21.5269 - 122.085i) q^{28} +(-23.9096 - 135.598i) q^{29} +(24.4227 - 42.3014i) q^{30} +(-83.8800 - 145.284i) q^{31} +(24.5134 - 20.5692i) q^{32} +(51.8954 - 18.8884i) q^{33} +(-66.7895 - 24.3094i) q^{34} +(193.276 + 162.178i) q^{35} +(6.25133 - 35.4531i) q^{36} -300.898 q^{37} +(15.0281 - 164.955i) q^{38} +38.3137 q^{39} +(-11.3092 + 64.1378i) q^{40} +(262.285 + 220.083i) q^{41} +(174.738 + 63.5996i) q^{42} +(-449.845 + 163.730i) q^{43} +(-56.4073 + 47.3314i) q^{44} +(36.6341 + 63.4520i) q^{45} +(80.2890 - 139.065i) q^{46} +(12.6364 + 71.6645i) q^{47} +(8.33511 + 47.2708i) q^{48} +(-308.756 + 534.781i) q^{49} +(58.7257 + 101.716i) q^{50} +(81.6710 - 68.5301i) q^{51} +(-48.0041 + 17.4721i) q^{52} +(-435.535 - 158.522i) q^{53} +(41.3664 + 34.7105i) q^{54} +(26.0234 - 147.586i) q^{55} -247.937 q^{56} +(203.012 + 143.238i) q^{57} -275.380 q^{58} +(-56.7694 + 321.955i) q^{59} +(-74.8355 - 62.7944i) q^{60} +(-25.7174 - 9.36038i) q^{61} +(-315.286 + 114.755i) q^{62} +(-213.672 + 179.292i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(51.9846 - 90.0400i) q^{65} +(-19.1798 - 108.774i) q^{66} +(-154.563 - 876.572i) q^{67} +(-71.0759 + 123.107i) q^{68} +(120.434 + 208.597i) q^{69} +(386.552 - 324.356i) q^{70} +(382.004 - 139.038i) q^{71} +(-67.6579 - 24.6255i) q^{72} +(242.712 + 203.660i) q^{73} +(-104.501 + 592.652i) q^{74} -176.177 q^{75} +(-319.679 - 86.8879i) q^{76} +570.523 q^{77} +(13.3062 - 75.4632i) q^{78} +(90.9217 + 76.2924i) q^{79} +(122.399 + 44.5496i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(524.570 - 440.167i) q^{82} +(-640.778 - 1109.86i) q^{83} +(185.953 - 322.080i) q^{84} +(-50.2384 - 284.916i) q^{85} +(166.256 + 942.885i) q^{86} +(206.535 - 357.729i) q^{87} +(73.6345 + 127.539i) q^{88} +(31.2373 - 26.2112i) q^{89} +(137.699 - 50.1183i) q^{90} +(371.937 + 135.374i) q^{91} +(-246.020 - 206.435i) q^{92} +(87.3936 - 495.634i) q^{93} +145.540 q^{94} +(612.071 - 282.745i) q^{95} +96.0000 q^{96} +(156.265 - 886.225i) q^{97} +(946.083 + 793.858i) q^{98} +(155.686 + 56.6651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) \) 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * q^99

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