LMFDB - Embedded newform 114.4.i.d.73.3

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			73.3
Root			$-5.58864 + 9.67980i$ of defining polynomial
Character	$\chi$	$=$	114.73
Dual form			114.4.i.d.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53209 + 1.28558i) q^{2} +(-2.81908 + 1.02606i) q^{3} +(0.694593 + 3.93923i) q^{4} +(2.52217 - 14.3039i) q^{5} +(-5.63816 - 2.05212i) q^{6} +(-11.3921 - 19.7317i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(6.89440 - 5.78509i) q^{9} +O(q^{10})$	\(q+(1.53209 + 1.28558i) q^{2} +(-2.81908 + 1.02606i) q^{3} +(0.694593 + 3.93923i) q^{4} +(2.52217 - 14.3039i) q^{5} +(-5.63816 - 2.05212i) q^{6} +(-11.3921 - 19.7317i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(6.89440 - 5.78509i) q^{9} +(22.2529 - 18.6724i) q^{10} +(16.6031 - 28.7575i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(-9.41284 - 3.42599i) q^{13} +(7.91289 - 44.8762i) q^{14} +(7.56650 + 42.9117i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(39.2507 + 32.9352i) q^{17} +18.0000 q^{18} +(40.8106 - 72.0659i) q^{19} +58.0983 q^{20} +(52.3613 + 43.9363i) q^{21} +(62.4074 - 22.7144i) q^{22} +(-17.8534 - 101.251i) q^{23} +(4.16756 - 23.6354i) q^{24} +(-80.7789 - 29.4011i) q^{25} +(-10.0169 - 17.3498i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(69.8150 - 58.5817i) q^{28} +(-165.651 + 138.998i) q^{29} +(-43.5737 + 75.4719i) q^{30} +(-42.4191 - 73.4720i) q^{31} +(-30.0702 - 10.9446i) q^{32} +(-17.2986 + 98.1054i) q^{33} +(17.7948 + 100.919i) q^{34} +(-310.974 + 113.185i) q^{35} +(27.5776 + 23.1404i) q^{36} +269.416 q^{37} +(155.172 - 57.9462i) q^{38} +30.0508 q^{39} +(89.0117 + 74.6897i) q^{40} +(-446.122 + 162.375i) q^{41} +(23.7387 + 134.629i) q^{42} +(6.57266 - 37.2754i) q^{43} +(124.815 + 45.4289i) q^{44} +(-65.3606 - 113.208i) q^{45} +(102.813 - 178.078i) q^{46} +(225.040 - 188.831i) q^{47} +(36.7701 - 30.8538i) q^{48} +(-88.0611 + 152.526i) q^{49} +(-85.9631 - 148.893i) q^{50} +(-144.444 - 52.5734i) q^{51} +(6.95769 - 39.4590i) q^{52} +(91.1586 + 516.986i) q^{53} +(-50.7434 + 18.4691i) q^{54} +(-369.468 - 310.021i) q^{55} +182.274 q^{56} +(-41.1043 + 245.034i) q^{57} -432.484 q^{58} +(488.363 + 409.785i) q^{59} +(-163.784 + 59.6123i) q^{60} +(-78.7080 - 446.375i) q^{61} +(29.4640 - 167.098i) q^{62} +(-192.692 - 70.1341i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-72.7458 + 125.999i) q^{65} +(-152.625 + 128.067i) q^{66} +(54.1731 - 45.4566i) q^{67} +(-102.476 + 177.494i) q^{68} +(154.220 + 267.117i) q^{69} +(-621.948 - 226.370i) q^{70} +(-50.0088 + 283.614i) q^{71} +(12.5027 + 70.9062i) q^{72} +(956.123 - 348.000i) q^{73} +(412.769 + 346.354i) q^{74} +257.889 q^{75} +(312.231 + 110.706i) q^{76} -756.580 q^{77} +(46.0405 + 38.6326i) q^{78} +(-571.491 + 208.006i) q^{79} +(40.3546 + 228.863i) q^{80} +(14.0655 - 79.7694i) q^{81} +(-892.244 - 324.750i) q^{82} +(99.7089 + 172.701i) q^{83} +(-136.706 + 236.781i) q^{84} +(570.099 - 478.370i) q^{85} +(57.9903 - 48.6596i) q^{86} +(324.363 - 561.813i) q^{87} +(132.825 + 230.060i) q^{88} +(1042.46 + 379.426i) q^{89} +(45.3990 - 257.470i) q^{90} +(39.6314 + 224.761i) q^{91} +(386.452 - 140.657i) q^{92} +(194.969 + 163.599i) q^{93} +587.537 q^{94} +(-927.893 - 765.513i) q^{95} +96.0000 q^{96} +(1128.01 + 946.510i) q^{97} +(-331.002 + 120.475i) q^{98} +(-51.8959 - 294.316i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.53209	+	1.28558i	0.541675	+	0.454519i
$2$	1.53209	+	1.28558i	0.541675	+	0.454519i
$3$	−2.81908	+	1.02606i	−0.542532	+	0.197465i
$3$	−2.81908	+	1.02606i	−0.542532	+	0.197465i
$4$	0.694593	+	3.93923i	0.0868241	+	0.492404i
$5$	2.52217	−	14.3039i	0.225589	−	1.27938i	−0.635966	−	0.771717i	$-0.719398\pi$
$5$	2.52217	−	14.3039i	0.225589	−	1.27938i	0.861555	−	0.507664i	$-0.169491\pi$
$6$	−5.63816	−	2.05212i	−0.383628	−	0.139629i
$7$	−11.3921	−	19.7317i	−0.615117	−	1.06541i	−0.990364	−	0.138489i	$-0.955775\pi$
$7$	−11.3921	−	19.7317i	−0.615117	−	1.06541i	0.375247	−	0.926925i	$-0.377558\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	6.89440	−	5.78509i	0.255348	−	0.214263i
$10$	22.2529	−	18.6724i	0.703700	−	0.590474i
$11$	16.6031	−	28.7575i	0.455094	−	0.788246i	−0.543600	−	0.839345i	$-0.682939\pi$
$11$	16.6031	−	28.7575i	0.455094	−	0.788246i	0.998694	+	0.0510987i	$0.0162723\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	−9.41284	−	3.42599i	−0.200819	−	0.0730923i	0.239652	−	0.970859i	$-0.422967\pi$
$13$	−9.41284	−	3.42599i	−0.200819	−	0.0730923i	−0.440472	+	0.897767i	$0.645189\pi$
$14$	7.91289	−	44.8762i	0.151058	−	0.856691i
$15$	7.56650	+	42.9117i	0.130244	+	0.738651i
$16$	−15.0351	+	5.47232i	−0.234923	+	0.0855050i
$17$	39.2507	+	32.9352i	0.559982	+	0.469881i	0.878304	−	0.478102i	$-0.158675\pi$
$17$	39.2507	+	32.9352i	0.559982	+	0.469881i	−0.318323	+	0.947982i	$0.603119\pi$
$18$	18.0000			0.235702
$19$	40.8106	−	72.0659i	0.492768	−	0.870161i
$19$	40.8106	−	72.0659i	0.492768	−	0.870161i
$20$	58.0983			0.649559
$21$	52.3613	+	43.9363i	0.544103	+	0.456557i
$22$	62.4074	−	22.7144i	0.604786	−	0.220124i
$23$	−17.8534	−	101.251i	−0.161856	−	0.917930i	−0.952247	−	0.305328i	$-0.901234\pi$
$23$	−17.8534	−	101.251i	−0.161856	−	0.917930i	0.790391	−	0.612602i	$-0.209877\pi$
$24$	4.16756	−	23.6354i	0.0354458	−	0.201023i
$25$	−80.7789	−	29.4011i	−0.646231	−	0.235209i
$26$	−10.0169	−	17.3498i	−0.0755570	−	0.130869i
$27$	−13.5000	+	23.3827i	−0.0962250	+	0.166667i
$28$	69.8150	−	58.5817i	0.471207	−	0.395390i
$29$	−165.651	+	138.998i	−1.06071	+	0.890043i	−0.994179	−	0.107742i	$-0.965638\pi$
$29$	−165.651	+	138.998i	−1.06071	+	0.890043i	−0.0665325	+	0.997784i	$0.521194\pi$
$30$	−43.5737	+	75.4719i	−0.265181	+	0.459307i
$31$	−42.4191	−	73.4720i	−0.245764	−	0.425676i	0.716582	−	0.697503i	$-0.245706\pi$
$31$	−42.4191	−	73.4720i	−0.245764	−	0.425676i	−0.962346	+	0.271827i	$0.912372\pi$
$32$	−30.0702	−	10.9446i	−0.166116	−	0.0604612i
$33$	−17.2986	+	98.1054i	−0.0912517	+	0.517514i
$34$	17.7948	+	100.919i	0.0897584	+	0.509045i
$35$	−310.974	+	113.185i	−1.50183	+	0.546623i
$36$	27.5776	+	23.1404i	0.127674	+	0.107131i
$37$	269.416			1.19707			0.598537	−	0.801095i	$-0.295749\pi$
$37$	269.416			1.19707			0.598537	+	0.801095i	$0.295749\pi$
$38$	155.172	−	57.9462i	0.662425	−	0.247372i
$39$	30.0508			0.123384
$40$	89.0117	+	74.6897i	0.351850	+	0.295237i
$41$	−446.122	+	162.375i	−1.69933	+	0.618506i	−0.995749	−	0.0921088i	$-0.970639\pi$
$41$	−446.122	+	162.375i	−1.69933	+	0.618506i	−0.703582	+	0.710615i	$0.748417\pi$
$42$	23.7387	+	134.629i	0.0872132	+	0.494611i
$43$	6.57266	−	37.2754i	0.0233098	−	0.132197i	−0.970932	−	0.239355i	$-0.923064\pi$
$43$	6.57266	−	37.2754i	0.0233098	−	0.132197i	0.994242	+	0.107158i	$0.0341752\pi$
$44$	124.815	+	45.4289i	0.427648	+	0.155651i
$45$	−65.3606	−	113.208i	−0.216520	−	0.375023i
$46$	102.813	−	178.078i	0.329544	−	0.570787i
$47$	225.040	−	188.831i	0.698413	−	0.586038i	−0.222909	−	0.974839i	$-0.571555\pi$
$47$	225.040	−	188.831i	0.698413	−	0.586038i	0.921322	+	0.388801i	$0.127111\pi$
$48$	36.7701	−	30.8538i	0.110569	−	0.0927784i
$49$	−88.0611	+	152.526i	−0.256738	+	0.444683i
$50$	−85.9631	−	148.893i	−0.243140	−	0.421132i
$51$	−144.444	−	52.5734i	−0.396593	−	0.144348i
$52$	6.95769	−	39.4590i	0.0185550	−	0.105230i
$53$	91.1586	+	516.986i	0.236256	+	1.33988i	0.839951	+	0.542662i	$0.182583\pi$
$53$	91.1586	+	516.986i	0.236256	+	1.33988i	−0.603695	+	0.797215i	$0.706305\pi$
$54$	−50.7434	+	18.4691i	−0.127876	+	0.0465430i
$55$	−369.468	−	310.021i	−0.905802	−	0.760058i
$56$	182.274			0.434953
$57$	−41.1043	+	245.034i	−0.0955158	+	0.569394i
$58$	−432.484			−0.979103
$59$	488.363	+	409.785i	1.07762	+	0.904229i	0.995721	−	0.0924117i	$-0.0294576\pi$
$59$	488.363	+	409.785i	1.07762	+	0.904229i	0.0818974	+	0.996641i	$0.473902\pi$
$60$	−163.784	+	59.6123i	−0.352406	+	0.128265i
$61$	−78.7080	−	446.375i	−0.165205	−	0.936927i	−0.948852	−	0.315720i	$-0.897754\pi$
$61$	−78.7080	−	446.375i	−0.165205	−	0.936927i	0.783647	−	0.621206i	$-0.213357\pi$
$62$	29.4640	−	167.098i	0.0603537	−	0.342283i
$63$	−192.692	−	70.1341i	−0.385347	−	0.140255i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−72.7458	+	125.999i	−0.138816	+	0.240436i
$66$	−152.625	+	128.067i	−0.284649	+	0.238849i
$67$	54.1731	−	45.4566i	0.0987805	−	0.0828867i	−0.592060	−	0.805894i	$-0.701685\pi$
$67$	54.1731	−	45.4566i	0.0987805	−	0.0828867i	0.690840	+	0.723007i	$0.257241\pi$
$68$	−102.476	+	177.494i	−0.182751	+	0.316534i
$69$	154.220	+	267.117i	0.269071	+	0.466045i
$70$	−621.948	−	226.370i	−1.06196	−	0.386521i
$71$	−50.0088	+	283.614i	−0.0835909	+	0.474068i	0.914061	+	0.405577i	$0.132929\pi$
$71$	−50.0088	+	283.614i	−0.0835909	+	0.474068i	−0.997652	+	0.0684905i	$0.978182\pi$
$72$	12.5027	+	70.9062i	0.0204646	+	0.116061i
$73$	956.123	−	348.000i	1.53296	−	0.557950i	0.568612	−	0.822606i	$-0.307480\pi$
$73$	956.123	−	348.000i	1.53296	−	0.557950i	0.964343	+	0.264655i	$0.0852582\pi$
$74$	412.769	+	346.354i	0.648425	+	0.544093i
$75$	257.889			0.397047
$76$	312.231	+	110.706i	0.471255	+	0.167090i
$77$	−756.580			−1.11974
$78$	46.0405	+	38.6326i	0.0668341	+	0.0560805i
$79$	−571.491	+	208.006i	−0.813896	+	0.296234i	−0.715232	−	0.698887i	$-0.753679\pi$
$79$	−571.491	+	208.006i	−0.813896	+	0.296234i	−0.0986640	+	0.995121i	$0.531457\pi$
$80$	40.3546	+	228.863i	0.0563973	+	0.319845i
$81$	14.0655	−	79.7694i	0.0192942	−	0.109423i
$82$	−892.244	−	324.750i	−1.20161	−	0.437350i
$83$	99.7089	+	172.701i	0.131861	+	0.228390i	0.924394	−	0.381439i	$-0.124571\pi$
$83$	99.7089	+	172.701i	0.131861	+	0.228390i	−0.792533	+	0.609829i	$0.791238\pi$
$84$	−136.706	+	236.781i	−0.177569	+	0.307559i
$85$	570.099	−	478.370i	0.727482	−	0.610430i
$86$	57.9903	−	48.6596i	0.0727122	−	0.0610128i
$87$	324.363	−	561.813i	0.399717	−	0.692330i
$88$	132.825	+	230.060i	0.160900	+	0.278687i
$89$	1042.46	+	379.426i	1.24158	+	0.451899i	0.877549	−	0.479486i	$-0.159177\pi$
$89$	1042.46	+	379.426i	1.24158	+	0.451899i	0.364034	+	0.931386i	$0.381399\pi$
$90$	45.3990	−	257.470i	0.0531719	−	0.301553i
$91$	39.6314	+	224.761i	0.0456539	+	0.258916i
$92$	386.452	−	140.657i	0.437939	−	0.159397i
$93$	194.969	+	163.599i	0.217391	+	0.182413i
$94$	587.537			0.644679
$95$	−927.893	−	765.513i	−1.00210	−	0.826737i
$96$	96.0000			0.102062
$97$	1128.01	+	946.510i	1.18074	+	0.990758i	0.999974	+	0.00723213i	$0.00230208\pi$
$97$	1128.01	+	946.510i	1.18074	+	0.990758i	0.180766	+	0.983526i	$0.442142\pi$
$98$	−331.002	+	120.475i	−0.341186	+	0.124181i
$99$	−51.8959	−	294.316i	−0.0526842	−	0.298787i
$100$	59.7094	−	338.629i	0.0597094	−	0.338629i
$101$	345.595	+	125.786i	0.340475	+	0.123923i	0.506598	−	0.862182i	$-0.330903\pi$
$101$	345.595	+	125.786i	0.340475	+	0.123923i	−0.166123	+	0.986105i	$0.553125\pi$
$102$	−153.714	−	266.241i	−0.149216	−	0.258449i
$103$	672.860	−	1165.43i	0.643678	−	1.11488i	−0.340927	−	0.940090i	$-0.610741\pi$
$103$	672.860	−	1165.43i	0.643678	−	1.11488i	0.984605	−	0.174793i	$-0.0559258\pi$
$104$	61.3873	−	51.5101i	0.0578800	−	0.0485671i
$105$	760.525	−	638.156i	0.706853	−	0.593120i
$106$	−524.961	+	909.260i	−0.481026	+	0.833161i
$107$	−748.276	−	1296.05i	−0.676062	−	1.17097i	−0.976157	−	0.217064i	$-0.930352\pi$
$107$	−748.276	−	1296.05i	−0.676062	−	1.17097i	0.300096	−	0.953909i	$-0.402981\pi$
$108$	−101.487	−	36.9382i	−0.0904220	−	0.0329109i
$109$	272.105	−	1543.18i	0.239109	−	1.35606i	−0.594675	−	0.803966i	$-0.702719\pi$
$109$	272.105	−	1543.18i	0.239109	−	1.35606i	0.833784	−	0.552090i	$-0.186170\pi$
$110$	−167.503	−	949.959i	−0.145189	−	0.823410i
$111$	−759.505	+	276.437i	−0.649450	+	0.236381i
$112$	279.260	+	234.327i	0.235604	+	0.197695i
$113$	−428.237			−0.356505			−0.178253	−	0.983985i	$-0.557044\pi$
$113$	−428.237			−0.356505			−0.178253	+	0.983985i	$0.557044\pi$
$114$	−377.985	+	322.570i	−0.310539	+	0.265013i
$115$	−1493.32			−1.21089
$116$	−662.604	−	555.991i	−0.530356	−	0.445021i
$117$	−84.7156	+	30.8339i	−0.0669398	+	0.0243641i
$118$	221.406	+	1255.66i	0.172729	+	0.979597i
$119$	202.721	−	1149.69i	0.156163	−	0.885644i
$120$	−327.567	−	119.225i	−0.249189	−	0.0906973i
$121$	114.172	+	197.751i	0.0857789	+	0.148573i
$122$	453.262	−	785.072i	0.336364	−	0.582599i
$123$	1091.05	−	915.496i	0.799807	−	0.671118i
$124$	259.959	−	218.132i	0.188266	−	0.157974i
$125$	283.497	−	491.031i	0.202854	−	0.351353i
$126$	−205.058	−	355.171i	−0.144984	−	0.251120i
$127$	1162.30	+	423.044i	0.812109	+	0.295583i	0.714495	−	0.699641i	$-0.246657\pi$
$127$	1162.30	+	423.044i	0.812109	+	0.295583i	0.0976140	+	0.995224i	$0.468879\pi$
$128$	22.2270	−	126.055i	0.0153485	−	0.0870455i
$129$	19.7180	+	111.826i	0.0134579	+	0.0763237i
$130$	−273.435	+	99.5222i	−0.184476	+	0.0671436i
$131$	1844.64	+	1547.84i	1.23028	+	1.03233i	0.998221	+	0.0596293i	$0.0189919\pi$
$131$	1844.64	+	1547.84i	1.23028	+	1.03233i	0.232063	+	0.972701i	$0.425453\pi$
$132$	−398.475			−0.262749
$133$	−1886.91	+	15.7193i	−1.23019	+	0.0102484i
$134$	141.436			0.0911806
$135$	300.415	+	252.078i	0.191523	+	0.160707i
$136$	−385.185	+	140.196i	−0.242863	+	0.0883948i
$137$	213.103	+	1208.57i	0.132895	+	0.753684i	0.976303	+	0.216410i	$0.0694348\pi$
$137$	213.103	+	1208.57i	0.132895	+	0.753684i	−0.843408	+	0.537274i	$0.819454\pi$
$138$	−107.120	+	607.509i	−0.0660774	+	0.374743i
$139$	329.723	+	120.009i	0.201200	+	0.0732307i	0.440654	−	0.897677i	$-0.354746\pi$
$139$	329.723	+	120.009i	0.201200	+	0.0732307i	−0.239455	+	0.970908i	$0.576969\pi$
$140$	−661.863	−	1146.38i	−0.399555	−	0.692049i
$141$	−440.653	+	763.233i	−0.263189	+	0.455857i
$142$	−441.225	+	370.232i	−0.260752	+	0.218797i
$143$	−254.806	+	213.807i	−0.149006	+	0.125031i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	1570.41	+	2720.03i	0.899418	+	1.55784i
$146$	1912.25	+	696.001i	1.08396	+	0.394530i
$147$	91.7499	−	520.340i	0.0514790	−	0.291952i
$148$	187.134	+	1061.29i	0.103935	+	0.589443i
$149$	36.6965	−	13.3564i	0.0201765	−	0.00734364i	−0.331912	−	0.943310i	$-0.607694\pi$
$149$	36.6965	−	13.3564i	0.0201765	−	0.00734364i	0.352089	+	0.935967i	$0.385472\pi$
$150$	395.110	+	331.536i	0.215070	+	0.180465i
$151$	−1441.23			−0.776728			−0.388364	−	0.921506i	$-0.626960\pi$
$151$	−1441.23			−0.776728			−0.388364	+	0.921506i	$0.626960\pi$
$152$	336.045	+	571.008i	0.179321	+	0.304703i
$153$	461.143			0.243668
$154$	−1159.15	−	972.641i	−0.606538	−	0.508946i
$155$	−1157.92	+	421.450i	−0.600043	+	0.218398i
$156$	20.8731	+	118.377i	0.0107127	+	0.0607548i
$157$	−496.042	+	2813.19i	−0.252156	+	1.43005i	0.551114	+	0.834430i	$0.314203\pi$
$157$	−496.042	+	2813.19i	−0.252156	+	1.43005i	−0.803270	+	0.595616i	$0.796908\pi$
$158$	−1142.98	−	416.012i	−0.575512	−	0.209469i
$159$	−787.442	−	1363.89i	−0.392756	−	0.680273i
$160$	−232.393	+	402.517i	−0.114827	+	0.198886i
$161$	−1794.48	+	1505.75i	−0.878415	+	0.737078i
$162$	124.099	−	104.132i	0.0601861	−	0.0505022i
$163$	−1206.67	+	2090.01i	−0.579837	+	1.00431i	0.415661	+	0.909520i	$0.363550\pi$
$163$	−1206.67	+	2090.01i	−0.579837	+	1.00431i	−0.995498	+	0.0947871i	$0.969783\pi$
$164$	−949.506	−	1644.59i	−0.452097	−	0.783056i
$165$	1359.66	+	494.876i	0.641512	+	0.233491i
$166$	−69.2570	+	392.776i	−0.0323819	+	0.183647i
$167$	−281.594	−	1597.00i	−0.130481	−	0.739996i	−0.977900	−	0.209071i	$-0.932956\pi$
$167$	−281.594	−	1597.00i	−0.130481	−	0.739996i	0.847419	−	0.530924i	$-0.178155\pi$
$168$	−513.845	+	187.024i	−0.235976	+	0.0858883i
$169$	−1606.14	−	1347.71i	−0.731059	−	0.613431i
$170$	1488.42			0.671511
$171$	−135.543	−	732.944i	−0.0606154	−	0.327776i
$172$	151.402			0.0671179
$173$	−867.399	−	727.834i	−0.381197	−	0.319862i	0.431975	−	0.901886i	$-0.357817\pi$
$173$	−867.399	−	727.834i	−0.381197	−	0.319862i	−0.813172	+	0.582023i	$0.802261\pi$
$174$	1219.21	−	443.755i	0.531194	−	0.193339i
$175$	340.108	+	1928.85i	0.146913	+	0.833185i
$176$	−92.2593	+	523.229i	−0.0395131	+	0.224090i
$177$	−1797.20	−	654.127i	−0.763196	−	0.277781i
$178$	1109.37	+	1921.48i	0.467138	+	0.809107i
$179$	−460.427	+	797.482i	−0.192256	+	0.332998i	−0.945998	−	0.324173i	$-0.894914\pi$
$179$	−460.427	+	797.482i	−0.192256	+	0.332998i	0.753741	+	0.657171i	$0.228247\pi$
$180$	400.553	−	336.104i	0.165864	−	0.139176i
$181$	−2991.84	+	2510.45i	−1.22863	+	1.03094i	−0.230301	+	0.973120i	$0.573971\pi$
$181$	−2991.84	+	2510.45i	−1.22863	+	1.03094i	−0.998327	+	0.0578213i	$0.981585\pi$
$182$	−228.228	+	395.303i	−0.0929528	+	0.160999i
$183$	679.892	+	1177.61i	0.274640	+	0.475690i
$184$	772.904	+	281.314i	0.309670	+	0.112711i
$185$	679.512	−	3853.70i	0.270047	−	1.53151i
$186$	88.3919	+	501.295i	0.0348452	+	0.197617i
$187$	1598.82	−	581.923i	0.625226	−	0.227564i
$188$	900.159	+	755.323i	0.349207	+	0.293019i
$189$	615.175			0.236759
$190$	−437.489	−	2365.71i	−0.167046	−	0.903298i
$191$	−4321.73			−1.63722			−0.818610	−	0.574349i	$-0.805255\pi$
$191$	−4321.73			−1.63722			−0.818610	+	0.574349i	$0.805255\pi$
$192$	147.081	+	123.415i	0.0552845	+	0.0463892i
$193$	3770.48	−	1372.34i	1.40624	−	0.511831i	0.476219	−	0.879327i	$-0.342007\pi$
$193$	3770.48	−	1372.34i	1.40624	−	0.511831i	0.930025	+	0.367496i	$0.119785\pi$
$194$	511.397	+	2900.28i	0.189259	+	1.07334i
$195$	75.7931	−	429.844i	0.0278341	−	0.157855i
$196$	−662.003	−	240.949i	−0.241255	−	0.0878096i
$197$	66.8935	+	115.863i	0.0241927	+	0.0419030i	0.877868	−	0.478902i	$-0.158965\pi$
$197$	66.8935	+	115.863i	0.0241927	+	0.0419030i	−0.853676	+	0.520805i	$0.825632\pi$
$198$	298.856	−	517.635i	0.107267	−	0.185791i
$199$	3090.17	−	2592.96i	1.10079	−	0.923670i	0.103309	−	0.994649i	$-0.467057\pi$
$199$	3090.17	−	2592.96i	1.10079	−	0.923670i	0.997478	+	0.0709794i	$0.0226125\pi$
$200$	526.813	−	442.048i	0.186256	−	0.156288i
$201$	−106.077	+	183.731i	−0.0372243	+	0.0644744i
$202$	367.775	+	637.004i	0.128102	+	0.221879i
$203$	4629.79	+	1685.10i	1.60073	+	0.582616i
$204$	106.769	−	605.517i	0.0366437	−	0.207817i
$205$	1197.41	+	6790.83i	0.407953	+	2.31362i
$206$	2529.13	−	920.526i	0.855401	−	0.311340i
$207$	−708.837	−	594.785i	−0.238008	−	0.199712i
$208$	160.271			0.0534269
$209$	−1394.85	−	2370.13i	−0.461645	−	0.784427i
$210$	1985.59			0.652470
$211$	−2832.79	−	2377.00i	−0.924254	−	0.775541i	0.0505230	−	0.998723i	$-0.483911\pi$
$211$	−2832.79	−	2377.00i	−0.924254	−	0.775541i	−0.974777	+	0.223182i	$0.928356\pi$
$212$	−1973.21	+	718.189i	−0.639248	+	0.232667i
$213$	−150.026	−	850.842i	−0.0482612	−	0.273703i
$214$	519.747	−	2947.63i	0.166024	−	0.941570i
$215$	−516.607	−	188.030i	−0.163871	−	0.0596442i
$216$	−108.000	−	187.061i	−0.0340207	−	0.0589256i
$217$	−966.487	+	1674.00i	−0.302347	+	0.523681i
$218$	2400.77	−	2014.48i	0.745874	−	0.625862i
$219$	−2338.32	+	1962.08i	−0.721501	+	0.605411i
$220$	964.614	−	1670.76i	0.295610	−	0.512012i
$221$	−256.625	−	444.487i	−0.0781106	−	0.135291i
$222$	−1519.01	−	552.874i	−0.459231	−	0.167146i
$223$	878.543	−	4982.47i	0.263819	−	1.49619i	−0.508559	−	0.861027i	$-0.669822\pi$
$223$	878.543	−	4982.47i	0.263819	−	1.49619i	0.772378	−	0.635164i	$-0.219067\pi$
$224$	126.606	+	718.020i	0.0377644	+	0.214173i
$225$	−727.010	+	264.610i	−0.215410	+	0.0784030i
$226$	−656.096	−	550.530i	−0.193110	−	0.162039i
$227$	−3124.48			−0.913563			−0.456781	−	0.889579i	$-0.650998\pi$
$227$	−3124.48			−0.913563			−0.456781	+	0.889579i	$0.650998\pi$
$228$	−993.794	+	8.27906i	−0.288665	+	0.00240480i
$229$	−2197.05			−0.633997			−0.316998	−	0.948426i	$-0.602675\pi$
$229$	−2197.05			−0.633997			−0.316998	+	0.948426i	$0.602675\pi$
$230$	−2287.90	−	1919.78i	−0.655912	−	0.550375i
$231$	2132.86	−	776.297i	0.607497	−	0.221111i
$232$	−300.400	−	1703.66i	−0.0850097	−	0.482114i
$233$	−304.536	+	1727.11i	−0.0856259	+	0.485609i	0.911594	+	0.411092i	$0.134853\pi$
$233$	−304.536	+	1727.11i	−0.0856259	+	0.485609i	−0.997220	+	0.0745167i	$0.976259\pi$
$234$	−169.431	−	61.6679i	−0.0473336	−	0.0172280i
$235$	−2133.43	−	3695.21i	−0.592211	−	1.02574i
$236$	−1275.03	+	2208.41i	−0.351683	+	0.609132i
$237$	1397.65	−	1172.77i	0.383069	−	0.321433i
$238$	1788.60	−	1500.81i	0.487132	−	0.408752i
$239$	1824.68	−	3160.44i	0.493844	−	0.855364i	−0.506130	−	0.862457i	$-0.668925\pi$
$239$	1824.68	−	3160.44i	0.493844	−	0.855364i	0.999975	+	0.00709327i	$0.00225788\pi$
$240$	−348.590	−	603.775i	−0.0937557	−	0.162390i
$241$	−1446.83	−	526.602i	−0.386715	−	0.140753i	0.141344	−	0.989961i	$-0.454858\pi$
$241$	−1446.83	−	526.602i	−0.386715	−	0.140753i	−0.528059	+	0.849208i	$0.677080\pi$
$242$	−79.3028	+	449.749i	−0.0210652	+	0.119467i
$243$	42.1965	+	239.308i	0.0111395	+	0.0631754i
$244$	1703.71	−	620.098i	0.447002	−	0.162696i
$245$	1959.62	+	1644.32i	0.511002	+	0.428781i
$246$	2848.52			0.738272
$247$	−631.041	+	538.528i	−0.162559	+	0.138728i
$248$	678.705			0.173781
$249$	−458.289	−	384.550i	−0.116638	−	0.0978709i
$250$	1065.60	−	387.846i	0.269578	−	0.0981183i
$251$	1293.96	+	7338.40i	0.325394	+	1.84540i	0.506893	+	0.862009i	$0.330794\pi$
$251$	1293.96	+	7338.40i	0.325394	+	1.84540i	−0.181499	+	0.983391i	$0.558095\pi$
$252$	142.432	−	807.772i	0.0356047	−	0.201924i
$253$	−3208.16	−	1167.67i	−0.797214	−	0.290162i
$254$	1236.90	+	2142.37i	0.305551	+	0.529229i
$255$	−1116.32	+	1933.52i	−0.274143	+	0.474830i
$256$	196.107	−	164.554i	0.0478778	−	0.0401742i
$257$	4920.60	−	4128.87i	1.19431	−	1.00215i	0.194538	−	0.980895i	$-0.437679\pi$
$257$	4920.60	−	4128.87i	1.19431	−	1.00215i	0.999774	−	0.0212522i	$-0.00676530\pi$
$258$	−113.551	+	196.677i	−0.0274008	+	0.0474595i
$259$	−3069.22	−	5316.05i	−0.736340	−	1.27538i
$260$	−546.870	−	199.044i	−0.130444	−	0.0474777i
$261$	−337.950	+	1916.61i	−0.0801479	+	0.454541i
$262$	836.293	+	4742.85i	0.197200	+	1.11838i
$263$	4451.91	−	1620.36i	1.04379	−	0.379909i	0.237474	−	0.971394i	$-0.423680\pi$
$263$	4451.91	−	1620.36i	1.04379	−	0.379909i	0.806316	+	0.591485i	$0.201458\pi$
$264$	−610.500	−	512.270i	−0.142324	−	0.119424i
$265$	7624.84			1.76751
$266$	−2911.12	−	2401.68i	−0.671022	−	0.553595i
$267$	−3328.10			−0.762833
$268$	216.692	+	181.826i	0.0493903	+	0.0414433i
$269$	5275.93	−	1920.28i	1.19583	−	0.435248i	0.334065	−	0.942550i	$-0.391579\pi$
$269$	5275.93	−	1920.28i	1.19583	−	0.435248i	0.861768	+	0.507302i	$0.169357\pi$
$270$	136.197	+	772.411i	0.0306988	+	0.174102i
$271$	−908.312	+	5151.30i	−0.203602	+	1.15468i	0.696023	+	0.718019i	$0.254951\pi$
$271$	−908.312	+	5151.30i	−0.203602	+	1.15468i	−0.899625	+	0.436663i	$0.856160\pi$
$272$	−770.370	−	280.392i	−0.171730	−	0.0625046i
$273$	−342.343	−	592.955i	−0.0758957	−	0.131455i
$274$	−1227.21	+	2125.59i	−0.270578	+	0.468655i
$275$	−2186.69	+	1834.85i	−0.479499	+	0.402347i
$276$	−945.116	+	793.047i	−0.206121	+	0.172956i
$277$	3619.95	−	6269.94i	0.785205	−	1.36002i	−0.143671	−	0.989626i	$-0.545891\pi$
$277$	3619.95	−	6269.94i	0.785205	−	1.36002i	0.928876	−	0.370390i	$-0.120776\pi$
$278$	350.884	+	607.749i	0.0757001	+	0.131116i
$279$	−717.496	−	261.147i	−0.153962	−	0.0560375i
$280$	459.725	−	2607.23i	0.0981208	−	0.556471i
$281$	−320.226	−	1816.09i	−0.0679825	−	0.385548i	−0.999747	−	0.0224851i	$-0.992842\pi$
$281$	−320.226	−	1816.09i	−0.0679825	−	0.385548i	0.931765	−	0.363063i	$-0.118269\pi$
$282$	−1656.31	+	602.849i	−0.349759	+	0.127302i
$283$	−1068.58	−	896.646i	−0.224454	−	0.188339i	0.523625	−	0.851949i	$-0.324579\pi$
$283$	−1068.58	−	896.646i	−0.224454	−	0.188339i	−0.748079	+	0.663609i	$0.769024\pi$
$284$	−1151.96			−0.240690
$285$	3401.27	+	1205.97i	0.706925	+	0.250650i
$286$	−665.250			−0.137542
$287$	8286.22	+	6952.97i	1.70425	+	1.43004i
$288$	−270.631	+	98.5018i	−0.0553719	+	0.0201537i
$289$	−397.247	−	2252.90i	−0.0808563	−	0.458559i
$290$	−1090.80	+	6186.22i	−0.220875	+	1.25265i
$291$	−4151.12	−	1510.88i	−0.836229	−	0.304363i
$292$	2034.97	+	3524.67i	0.407834	+	0.706390i
$293$	−2293.53	+	3972.51i	−0.457301	+	0.792069i	−0.998817	−	0.0486212i	$-0.984517\pi$
$293$	−2293.53	+	3972.51i	−0.457301	+	0.792069i	0.541516	+	0.840691i	$0.317851\pi$
$294$	809.505	−	679.255i	0.160583	−	0.134745i
$295$	7093.27	−	5951.96i	1.39995	−	1.17470i
$296$	−1077.66	+	1866.57i	−0.211615	+	0.366527i
$297$	448.285	+	776.452i	0.0875829	+	0.151698i
$298$	73.3930	+	26.7129i	0.0142669	+	0.00519274i
$299$	−178.836	+	1014.23i	−0.0345898	+	0.196169i
$300$	179.128	+	1015.89i	0.0344732	+	0.195507i
$301$	−810.386	+	294.956i	−0.155182	+	0.0564817i
$302$	−2208.10	−	1852.81i	−0.420734	−	0.353038i
$303$	−1103.32			−0.209189
$304$	−219.223	+	1306.85i	−0.0413596	+	0.246555i
$305$	−6583.43			−1.23595
$306$	706.512	+	592.834i	0.131989	+	0.110752i
$307$	−5705.87	+	2076.77i	−1.06075	+	0.386082i	−0.812711	−	0.582667i	$-0.802009\pi$
$307$	−5705.87	+	2076.77i	−1.06075	+	0.386082i	−0.248042	+	0.968749i	$0.579787\pi$
$308$	−525.515	−	2980.34i	−0.0972208	−	0.551366i
$309$	−701.045	+	3975.83i	−0.129065	+	0.731964i
$310$	−2315.85	−	842.900i	−0.424295	−	0.154431i
$311$	−1320.06	−	2286.40i	−0.240687	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$311$	−1320.06	−	2286.40i	−0.240687	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$312$	−120.203	+	208.198i	−0.0218114	+	0.0377785i
$313$	2902.71	−	2435.66i	0.524187	−	0.439845i	−0.341901	−	0.939736i	$-0.611071\pi$
$313$	2902.71	−	2435.66i	0.524187	−	0.439845i	0.866089	+	0.499891i	$0.166626\pi$
$314$	−4376.55	+	3672.36i	−0.786570	+	0.660011i
$315$	−1489.19	+	2579.36i	−0.266370	+	0.461366i
$316$	−1216.34	−	2106.76i	−0.216533	−	0.375045i
$317$	−764.168	−	278.134i	−0.135394	−	0.0492795i	0.273434	−	0.961891i	$-0.411840\pi$
$317$	−764.168	−	278.134i	−0.135394	−	0.0492795i	−0.408829	+	0.912611i	$0.634063\pi$
$318$	546.951	−	3101.92i	0.0964513	−	0.547003i
$319$	1246.90	+	7071.51i	0.218849	+	1.24115i
$320$	−873.512	+	317.933i	−0.152596	+	0.0555405i
$321$	3439.28	+	2885.90i	0.598012	+	0.501791i
$322$	−4685.06			−0.810832
$323$	3975.35	−	1484.53i	0.684813	−	0.255732i
$324$	324.000			0.0555556
$325$	659.631	+	553.496i	0.112584	+	0.0944691i
$326$	−4535.58	+	1650.82i	−0.770560	+	0.280461i
$327$	816.315	+	4629.55i	0.138050	+	0.782920i
$328$	659.520	−	3740.32i	0.111024	−	0.629649i
$329$	−6289.64	−	2289.24i	−1.05398	−	0.383617i
$330$	1446.92	+	2506.14i	0.241365	+	0.418056i
$331$	−791.486	+	1370.89i	−0.131432	+	0.227647i	−0.924229	−	0.381839i	$-0.875291\pi$
$331$	−791.486	+	1370.89i	−0.131432	+	0.227647i	0.792797	+	0.609486i	$0.208624\pi$
$332$	−611.051	+	512.733i	−0.101011	+	0.0847587i
$333$	1857.46	−	1558.60i	0.305670	−	0.256488i
$334$	1621.63	−	2808.75i	0.265664	−	0.460144i
$335$	−513.574	−	889.536i	−0.0837598	−	0.145076i
$336$	−1027.69	−	374.048i	−0.166860	−	0.0607322i
$337$	−1260.51	+	7148.72i	−0.203752	+	1.15554i	0.695639	+	0.718391i	$0.255121\pi$
$337$	−1260.51	+	7148.72i	−0.203752	+	1.15554i	−0.899392	+	0.437144i	$0.855990\pi$
$338$	−728.163	−	4129.62i	−0.117180	−	0.664561i
$339$	1207.23	−	439.397i	0.193415	−	0.0703975i
$340$	2280.40	+	1913.48i	0.363741	+	0.305215i
$341$	−2817.16			−0.447383
$342$	734.591	−	1297.19i	0.116147	−	0.205099i
$343$	−3802.18			−0.598538
$344$	231.961	+	194.638i	0.0363561	+	0.0305064i
$345$	4209.79	−	1532.24i	0.656949	−	0.239110i
$346$	−393.247	−	2230.21i	−0.0611014	−	0.346523i
$347$	−139.995	+	793.953i	−0.0216580	+	0.122829i	−0.993720	−	0.111896i	$-0.964308\pi$
$347$	−139.995	+	793.953i	−0.0216580	+	0.122829i	0.972062	+	0.234725i	$0.0754188\pi$
$348$	2438.41	+	887.510i	0.375611	+	0.136711i
$349$	−3953.67	−	6847.96i	−0.606404	−	1.05032i	−0.991828	−	0.127583i	$-0.959278\pi$
$349$	−3953.67	−	6847.96i	−0.606404	−	1.05032i	0.385424	−	0.922740i	$-0.374055\pi$
$350$	−1958.61	+	3392.41i	−0.299120	+	0.518091i
$351$	207.182	−	173.847i	0.0315059	−	0.0264366i
$352$	−813.999	+	683.027i	−0.123257	+	0.103425i
$353$	−2783.79	+	4821.66i	−0.419734	+	0.727000i	−0.995912	−	0.0903235i	$-0.971210\pi$
$353$	−2783.79	+	4821.66i	−0.419734	+	0.727000i	0.576179	+	0.817324i	$0.304543\pi$
$354$	−1912.54	−	3312.61i	−0.287148	−	0.497354i
$355$	3930.66	+	1430.64i	0.587656	+	0.213889i
$356$	−770.558	+	4370.05i	−0.114718	+	0.650596i
$357$	608.163	+	3449.06i	0.0901607	+	0.511327i
$358$	−1730.64	+	629.901i	−0.255495	+	0.0929924i
$359$	7356.36	+	6172.72i	1.08149	+	0.907476i	0.996043	−	0.0888674i	$-0.0283248\pi$
$359$	7356.36	+	6172.72i	1.08149	+	0.907476i	0.0854438	+	0.996343i	$0.472769\pi$
$360$	1045.77			0.153102
$361$	−3527.99	−	5882.11i	−0.514359	−	0.857575i
$362$	−7811.13			−1.13410
$363$	−524.763	−	440.329i	−0.0758759	−	0.0636674i
$364$	−857.858	+	312.235i	−0.123527	+	0.0449603i
$365$	−2566.27	−	14554.0i	−0.368012	−	2.08710i
$366$	−472.248	+	2678.25i	−0.0674448	+	0.382499i
$367$	567.860	+	206.684i	0.0807685	+	0.0293973i	0.382088	−	0.924126i	$-0.375205\pi$
$367$	567.860	+	206.684i	0.0807685	+	0.0293973i	−0.301320	+	0.953523i	$0.597427\pi$
$368$	822.508	+	1424.62i	0.116511	+	0.201804i
$369$	−2136.39	+	3700.33i	−0.301398	+	0.522037i
$370$	5995.29	−	5030.65i	0.842380	−	0.706841i
$371$	9162.55	−	7688.29i	1.28220	−	1.07589i
$372$	−509.029	+	881.664i	−0.0709460	+	0.122882i
$373$	−1065.33	−	1845.21i	−0.147884	−	0.256143i	0.782561	−	0.622574i	$-0.213913\pi$
$373$	−1065.33	−	1845.21i	−0.147884	−	0.256143i	−0.930445	+	0.366431i	$0.880580\pi$
$374$	3197.64	+	1163.85i	0.442101	+	0.160912i
$375$	−295.372	+	1675.14i	−0.0406745	+	0.230677i
$376$	408.099	+	2314.44i	0.0559737	+	0.317442i
$377$	2035.45	−	740.844i	0.278067	−	0.101208i
$378$	942.503	+	790.854i	0.128246	+	0.107611i
$379$	2326.95			0.315376			0.157688	−	0.987489i	$-0.449596\pi$
$379$	2326.95			0.315376			0.157688	+	0.987489i	$0.449596\pi$
$380$	2371.03	−	4186.90i	0.320082	−	0.565220i
$381$	−3710.69			−0.498962
$382$	−6621.27	−	5555.90i	−0.886842	−	0.744149i
$383$	6034.51	−	2196.38i	0.805089	−	0.293028i	0.0934952	−	0.995620i	$-0.470196\pi$
$383$	6034.51	−	2196.38i	0.805089	−	0.293028i	0.711594	+	0.702591i	$0.247974\pi$
$384$	66.6809	+	378.166i	0.00886145	+	0.0502558i
$385$	−1908.22	+	10822.1i	−0.252602	+	1.43258i
$386$	7540.96	+	2744.69i	0.994365	+	0.361919i
$387$	−170.327	−	295.015i	−0.0223726	−	0.0387506i
$388$	−2945.02	+	5100.92i	−0.385337	+	0.667423i
$389$	−6307.78	+	5292.85i	−0.822152	+	0.689867i	−0.953475	−	0.301472i	$-0.902522\pi$
$389$	−6307.78	+	5292.85i	−0.822152	+	0.689867i	0.131323	+	0.991340i	$0.458077\pi$
$390$	668.718	−	561.121i	0.0868253	−	0.0728551i
$391$	2633.98	−	4562.20i	0.340681	−	0.590077i
$392$	−704.489	−	1220.21i	−0.0907706	−	0.157219i
$393$	−6788.36	−	2470.76i	−0.871317	−	0.317134i
$394$	−46.4637	+	263.509i	−0.00594114	+	0.0336939i
$395$	1533.90	+	8699.19i	0.195390	+	1.10811i
$396$	1123.33	−	408.860i	0.142549	−	0.0518838i
$397$	7600.18	+	6377.31i	0.960812	+	0.806217i	0.981085	−	0.193578i	$-0.0620092\pi$
$397$	7600.18	+	6377.31i	0.960812	+	0.806217i	−0.0202733	+	0.999794i	$0.506454\pi$
$398$	8067.87			1.01609
$399$	5303.20	−	1980.39i	0.665394	−	0.248480i
$400$	1375.41			0.171926
$401$	−8507.85	−	7138.93i	−1.05951	−	0.889031i	−0.0654447	−	0.997856i	$-0.520847\pi$
$401$	−8507.85	−	7138.93i	−1.05951	−	0.889031i	−0.994061	+	0.108825i	$0.965291\pi$
$402$	−398.719	+	145.122i	−0.0494684	+	0.0180050i
$403$	147.569	+	836.907i	0.0182406	+	0.103447i
$404$	−255.454	+	1448.75i	−0.0314586	+	0.178411i
$405$	−1105.54	−	402.383i	−0.135641	−	0.0493694i
$406$	4926.92	+	8533.67i	0.602263	+	1.04315i
$407$	4473.15	−	7747.72i	0.544781	−	0.943588i
$408$	942.017	−	790.446i	0.114306	−	0.0959140i
$409$	5963.41	−	5003.89i	0.720957	−	0.604955i	−0.206693	−	0.978406i	$-0.566270\pi$
$409$	5963.41	−	5003.89i	0.720957	−	0.604955i	0.927650	+	0.373451i	$0.121826\pi$
$410$	−6895.58	+	11943.5i	−0.830606	+	1.43865i
$411$	−1840.81	−	3188.38i	−0.220926	−	0.382655i
$412$	5058.25	+	1841.05i	0.604860	+	0.220151i
$413$	2522.28	−	14304.6i	0.300517	−	1.70432i
$414$	−321.361	−	1822.53i	−0.0381498	−	0.216358i
$415$	2721.78	−	990.647i	0.321944	−	0.117178i
$416$	245.549	+	206.040i	0.0289400	+	0.0242836i
$417$	−1052.65			−0.123618
$418$	909.948	−	5424.43i	0.106476	−	0.634731i
$419$	−12224.7			−1.42534			−0.712669	−	0.701500i	$-0.752514\pi$
$419$	−12224.7			−1.42534			−0.712669	+	0.701500i	$0.752514\pi$
$420$	3042.10	+	2552.62i	0.353427	+	0.296560i
$421$	−8639.85	+	3144.65i	−1.00019	+	0.364040i	−0.789658	−	0.613547i	$-0.789742\pi$
$421$	−8639.85	+	3144.65i	−1.00019	+	0.364040i	−0.210533	+	0.977587i	$0.567520\pi$
$422$	−1284.28	−	7283.54i	−0.148147	−	0.840183i
$423$	459.111	−	2603.75i	0.0527725	−	0.299288i
$424$	−3946.42	−	1436.38i	−0.452017	−	0.164521i
$425$	−2202.30	−	3814.49i	−0.251358	−	0.435364i
$426$	863.968	−	1496.44i	0.0982614	−	0.170194i
$427$	−7911.11	+	6638.21i	−0.896594	+	0.752332i
$428$	4585.70	−	3847.86i	0.517893	−	0.434564i
$429$	498.938	−	864.185i	0.0561514	−	0.0972570i
$430$	−549.762	−	952.215i	−0.0616555	−	0.106790i
$431$	12908.6	+	4698.36i	1.44266	+	0.525086i	0.940531	−	0.339707i	$-0.110328\pi$
$431$	12908.6	+	4698.36i	1.44266	+	0.525086i	0.502130	+	0.864792i	$0.332550\pi$
$432$	75.0160	−	425.437i	0.00835465	−	0.0473816i
$433$	138.682	+	786.506i	0.0153918	+	0.0872912i	0.991536	−	0.129832i	$-0.0414438\pi$
$433$	138.682	+	786.506i	0.0153918	+	0.0872912i	−0.976144	+	0.217123i	$0.930333\pi$
$434$	−3632.80	+	1322.23i	−0.401797	+	0.146242i
$435$	−7218.03	−	6056.65i	−0.795582	−	0.667572i
$436$	6267.96			0.688488
$437$	−8025.39	−	2845.52i	−0.878504	−	0.311486i
$438$	−6104.91			−0.665991
$439$	8192.23	+	6874.10i	0.890646	+	0.747341i	0.968340	−	0.249636i	$-0.0803111\pi$
$439$	8192.23	+	6874.10i	0.890646	+	0.747341i	−0.0776933	+	0.996977i	$0.524756\pi$
$440$	3625.76	−	1319.67i	0.392844	−	0.142984i
$441$	275.250	+	1561.02i	0.0297214	+	0.168558i
$442$	178.250	−	1010.90i	0.0191820	−	0.108787i
$443$	8906.33	+	3241.64i	0.955198	+	0.347664i	0.772150	−	0.635441i	$-0.219181\pi$
$443$	8906.33	+	3241.64i	0.955198	+	0.347664i	0.183048	+	0.983104i	$0.441404\pi$
$444$	−1616.50	−	2799.85i	−0.172783	−	0.299268i
$445$	8056.54	−	13954.3i	0.858239	−	1.48651i
$446$	7751.34	−	6504.15i	0.822952	−	0.690539i
$447$	−89.7458	+	75.3057i	−0.00949627	+	0.00796831i
$448$	−729.096	+	1262.83i	−0.0768896	+	0.133177i
$449$	1620.70	+	2807.14i	0.170347	+	0.295049i	0.938541	−	0.345168i	$-0.112178\pi$
$449$	1620.70	+	2807.14i	0.170347	+	0.295049i	−0.768195	+	0.640217i	$0.778845\pi$
$450$	−1454.02	−	529.220i	−0.152318	−	0.0554393i
$451$	−2737.53	+	15525.3i	−0.285821	+	1.62097i
$452$	−297.450	−	1686.92i	−0.0309533	−	0.175545i
$453$	4062.95	−	1478.79i	0.421400	−	0.153377i
$454$	−4786.97	−	4016.75i	−0.494854	−	0.415232i
$455$	3314.92			0.341551
$456$	−1533.22	−	1264.91i	−0.157456	−	0.129901i
$457$	3617.76			0.370310			0.185155	−	0.982709i	$-0.440721\pi$
$457$	3617.76			0.370310			0.185155	+	0.982709i	$0.440721\pi$
$458$	−3366.08	−	2824.47i	−0.343420	−	0.288164i
$459$	−1300.00	+	473.161i	−0.132198	+	0.0481160i
$460$	−1037.25	−	5882.54i	−0.105135	−	0.596249i
$461$	−1026.15	+	5819.60i	−0.103672	+	0.587951i	0.888071	+	0.459707i	$0.152045\pi$
$461$	−1026.15	+	5819.60i	−0.103672	+	0.587951i	−0.991743	+	0.128245i	$0.959066\pi$
$462$	4265.72	+	1552.59i	0.429565	+	0.156349i
$463$	2536.99	+	4394.20i	0.254653	+	0.441071i	0.964801	−	0.262981i	$-0.0847056\pi$
$463$	2536.99	+	4394.20i	0.254653	+	0.441071i	−0.710149	+	0.704052i	$0.751372\pi$
$464$	1729.94	−	2996.34i	0.173083	−	0.299788i
$465$	2831.85	−	2376.20i	0.282417	−	0.236976i
$466$	−2686.91	+	2254.58i	−0.267100	+	0.224124i
$467$	−9467.95	+	16399.0i	−0.938169	+	1.62496i	−0.169284	+	0.985567i	$0.554146\pi$
$467$	−9467.95	+	16399.0i	−0.938169	+	1.62496i	−0.768884	+	0.639388i	$0.779188\pi$
$468$	−180.305	−	312.297i	−0.0178090	−	0.0308460i
$469$	−1514.08	−	551.082i	−0.149070	−	0.0542571i
$470$	1481.87	−	8404.08i	0.145433	−	0.824790i
$471$	−1488.12	−	8439.58i	−0.145582	−	0.825637i
$472$	−4792.53	+	1744.34i	−0.467360	+	0.170105i
$473$	−962.821	−	807.902i	−0.0935952	−	0.0785357i
$474$	3649.01			0.353596
$475$	−5415.46	+	4621.53i	−0.523112	+	0.446422i
$476$	4669.69			0.449653
$477$	3619.29	+	3036.95i	0.347413	+	0.291514i
$478$	6858.56	−	2496.31i	0.656283	−	0.238867i
$479$	1085.60	+	6156.75i	0.103554	+	0.587284i	0.991788	+	0.127893i	$0.0408213\pi$
$479$	1085.60	+	6156.75i	0.103554	+	0.587284i	−0.888234	+	0.459391i	$0.848068\pi$
$480$	242.128	−	1373.18i	0.0230241	−	0.130576i
$481$	−2535.97	−	923.017i	−0.240395	−	0.0874968i
$482$	−1539.68	−	2666.81i	−0.145499	−	0.252012i
$483$	3513.79	−	6086.07i	0.331021	−	0.573345i
$484$	−699.685	+	587.105i	−0.0657104	+	0.0551376i
$485$	16383.8	−	13747.7i	1.53392	−	1.28711i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	−7192.13	−	12457.1i	−0.669212	−	1.15911i	−0.978125	−	0.208019i	$-0.933298\pi$
$487$	−7192.13	−	12457.1i	−0.669212	−	1.15911i	0.308913	−	0.951090i	$-0.400035\pi$
$488$	3407.41	+	1240.20i	0.316078	+	0.115043i
$489$	1257.21	−	7130.01i	0.116264	−	0.659366i
$490$	888.419	+	5038.47i	0.0819075	+	0.464521i
$491$	−15369.6	+	5594.08i	−1.41267	+	0.514170i	−0.931912	−	0.362683i	$-0.881861\pi$
$491$	−15369.6	+	5594.08i	−1.41267	+	0.514170i	−0.480758	+	0.876853i	$0.659638\pi$
$492$	4364.18	+	3661.98i	0.399904	+	0.335559i
$493$	−11079.8			−1.01219
$494$	−1659.13	+	13.8218i	−0.151109	+	0.00125885i
$495$	−4340.76			−0.394147
$496$	1039.84	+	872.526i	0.0941331	+	0.0789871i
$497$	6165.91	−	2244.21i	0.556496	−	0.202548i
$498$	−207.771	−	1178.33i	−0.0186957	−	0.106028i
$499$	−3477.05	+	19719.3i	−0.311932	+	1.76906i	0.276997	+	0.960871i	$0.410661\pi$
$499$	−3477.05	+	19719.3i	−0.311932	+	1.76906i	−0.588929	+	0.808185i	$0.700450\pi$
$500$	2131.20	+	775.693i	0.190620	+	0.0693801i
$501$	2432.45	+	4213.13i	0.216914	+	0.375706i
$502$	−7451.60	+	12906.6i	−0.662513	+	1.14751i
$503$	2300.81	−	1930.61i	0.203952	−	0.171136i	−0.535091	−	0.844795i	$-0.679723\pi$
$503$	2300.81	−	1930.61i	0.203952	−	0.171136i	0.739043	+	0.673658i	$0.235278\pi$
$504$	1256.67	−	1054.47i	0.111065	−	0.0931942i
$505$	2670.88	−	4626.11i	0.235352	−	0.407642i
$506$	−3414.05	−	5913.31i	−0.299947	−	0.519523i
$507$	5910.65	+	2151.30i	0.517754	+	0.188447i
$508$	−859.140	+	4872.43i	−0.0750358	+	0.425549i
$509$	539.644	+	3060.47i	0.0469927	+	0.266509i	0.999247	−	0.0387966i	$-0.0123524\pi$
$509$	539.644	+	3060.47i	0.0469927	+	0.266509i	−0.952254	+	0.305306i	$0.901241\pi$
$510$	−4195.98	+	1527.21i	−0.364316	+	0.132600i
$511$	−17758.9	−	14901.5i	−1.53740	−	1.29003i
$512$	512.000			0.0441942
$513$	1134.15	+	1927.15i	0.0976101	+	0.165859i
$514$	12846.8			1.10242
$515$	−14973.1	−	12563.9i	−1.28115	−	1.07502i
$516$	−426.814	+	155.347i	−0.0364136	+	0.0132535i
$517$	−1693.93	−	9606.76i	−0.144099	−	0.817224i
$518$	2131.86	−	12090.4i	0.180827	−	1.02552i
$519$	3192.07	+	1161.82i	0.269973	+	0.0982622i
$520$	−581.967	−	1008.00i	−0.0490787	−	0.0850068i
$521$	−9902.54	+	17151.7i	−0.832703	+	1.44228i	0.0631839	+	0.998002i	$0.479875\pi$
$521$	−9902.54	+	17151.7i	−0.832703	+	1.44228i	−0.895887	+	0.444282i	$0.853459\pi$
$522$	−2981.72	+	2501.96i	−0.250012	+	0.209785i
$523$	9786.35	−	8211.72i	0.818216	−	0.686565i	−0.134337	−	0.990936i	$-0.542891\pi$
$523$	9786.35	−	8211.72i	0.818216	−	0.686565i	0.952554	+	0.304371i	$0.0984462\pi$
$524$	−4816.02	+	8341.59i	−0.401505	+	0.695427i
$525$	−2937.91	−	5088.61i	−0.244230	−	0.423019i
$526$	8903.83	+	3240.73i	0.738071	+	0.268636i
$527$	754.839	−	4280.91i	0.0623934	−	0.353851i
$528$	−276.778	−	1569.69i	−0.0228129	−	0.129378i
$529$	1500.12	−	545.999i	0.123294	−	0.0448754i
$530$	11681.9	+	9802.30i	0.957416	+	0.803368i
$531$	5737.62			0.468910
$532$	−1372.55	−	7422.04i	−0.111857	−	0.604861i
$533$	4755.57			0.386466
$534$	−5098.95	−	4278.52i	−0.413208	−	0.346722i
$535$	−20425.9	+	7434.42i	−1.65063	+	0.600781i
$536$	98.2403	+	557.148i	0.00791667	+	0.0448977i
$537$	479.714	−	2720.59i	0.0385497	−	0.218626i
$538$	10551.9	+	3840.56i	0.845582	+	0.307767i
$539$	2924.18	+	5064.83i	0.233680	+	0.404745i
$540$	−784.327	+	1358.49i	−0.0625038	+	0.108260i
$541$	413.852	−	347.263i	0.0328889	−	0.0275971i	−0.626195	−	0.779666i	$-0.715389\pi$
$541$	413.852	−	347.263i	0.0328889	−	0.0275971i	0.659084	+	0.752069i	$0.270944\pi$
$542$	−8013.99	+	6724.54i	−0.635112	+	0.532922i
$543$	5858.35	−	10147.0i	0.462994	−	0.801930i
$544$	−819.810	−	1419.95i	−0.0646123	−	0.111912i
$545$	−21387.3	−	7784.33i	−1.68097	−	0.611824i
$546$	237.789	−	1348.57i	0.0186381	−	0.105702i
$547$	708.143	+	4016.08i	0.0553529	+	0.313922i	0.999895	−	0.0144675i	$-0.00460532\pi$
$547$	708.143	+	4016.08i	0.0553529	+	0.313922i	−0.944542	+	0.328389i	$0.893494\pi$
$548$	−4612.80	+	1678.92i	−0.359578	+	0.130876i
$549$	−3124.97	−	2622.16i	−0.242933	−	0.203845i
$550$	−5709.03			−0.442607
$551$	3256.68	+	17610.4i	0.251795	+	1.36157i
$552$	−2467.52			−0.190262
$553$	10614.8	+	8906.89i	0.816253	+	0.684918i
$554$	13606.6	−	4952.39i	1.04348	−	0.379796i
$555$	2038.53	+	11561.1i	0.155912	+	0.884219i
$556$	−243.722	+	1382.21i	−0.0185901	+	0.105430i
$557$	−7019.31	−	2554.82i	−0.533964	−	0.194347i	0.0609435	−	0.998141i	$-0.480589\pi$
$557$	−7019.31	−	2554.82i	−0.533964	−	0.194347i	−0.594907	+	0.803794i	$0.702811\pi$
$558$	−763.543	−	1322.50i	−0.0579272	−	0.100333i
$559$	−189.573	+	328.350i	−0.0143436	+	0.0248439i
$560$	4056.13	−	3403.50i	0.306077	−	0.256829i
$561$	−3910.11	+	3280.97i	−0.294269	+	0.246921i
$562$	1844.11	−	3194.09i	0.138415	−	0.239741i
$563$	9890.35	+	17130.6i	0.740371	+	1.28236i	0.952327	+	0.305080i	$0.0986834\pi$
$563$	9890.35	+	17130.6i	0.740371	+	1.28236i	−0.211956	+	0.977279i	$0.567983\pi$
$564$	−3312.63	−	1205.70i	−0.247317	−	0.0900160i
$565$	−1080.08	+	6125.46i	−0.0804238	+	0.456106i
$566$	−484.455	−	2747.48i	−0.0359773	−	0.204038i
$567$	−1734.23	+	631.207i	−0.128449	+	0.0467517i
$568$	−1764.90	−	1480.93i	−0.130376	−	0.109398i
$569$	−7544.98			−0.555891			−0.277945	−	0.960597i	$-0.589653\pi$
$569$	−7544.98			−0.555891			−0.277945	+	0.960597i	$0.589653\pi$
$570$	3660.68	+	6220.23i	0.268998	+	0.457082i
$571$	1405.02			0.102974			0.0514871	−	0.998674i	$-0.483604\pi$
$571$	1405.02			0.102974			0.0514871	+	0.998674i	$0.483604\pi$
$572$	−1019.22	−	855.229i	−0.0745032	−	0.0625156i
$573$	12183.3	−	4434.35i	0.888244	−	0.323294i
$574$	3756.67	+	21305.1i	0.273171	+	1.54923i
$575$	−1534.73	+	8703.90i	−0.111309	+	0.631265i
$576$	−541.263	−	197.004i	−0.0391539	−	0.0142508i
$577$	10494.7	+	18177.3i	0.757191	+	1.31149i	0.944278	+	0.329150i	$0.106762\pi$
$577$	10494.7	+	18177.3i	0.757191	+	1.31149i	−0.187087	+	0.982343i	$0.559905\pi$
$578$	2287.65	−	3962.33i	0.164626	−	0.285141i
$579$	−9221.17	+	7737.48i	−0.661863	+	0.555369i
$580$	−9624.04	+	8075.53i	−0.688994	+	0.578135i
$581$	2271.79	−	3934.86i	0.162220	−	0.280973i
$582$	−4417.53	−	7651.38i	−0.314626	−	0.544948i
$583$	16380.7	+	5962.10i	1.16367	+	0.423542i
$584$	−1413.48	+	8016.22i	−0.100154	+	0.568002i
$585$	227.379	+	1289.53i	0.0160700	+	0.0911377i
$586$	−8620.84	+	3137.73i	−0.607720	+	0.221192i
$587$	−5605.64	−	4703.69i	−0.394156	−	0.330736i	0.424074	−	0.905628i	$-0.360600\pi$
$587$	−5605.64	−	4703.69i	−0.394156	−	0.330736i	−0.818230	+	0.574892i	$0.805044\pi$
$588$	2113.47			0.148228
$589$	−7025.97	+	58.5316i	−0.491511	+	0.00409466i
$590$	18519.2			1.29224
$591$	−307.460	−	257.990i	−0.0213997	−	0.0179565i
$592$	−4050.69	+	1474.33i	−0.281220	+	0.102356i
$593$	1117.71	+	6338.87i	0.0774014	+	0.438965i	0.998739	+	0.0502019i	$0.0159865\pi$
$593$	1117.71	+	6338.87i	0.0774014	+	0.438965i	−0.921338	+	0.388763i	$0.872902\pi$
$594$	−311.375	+	1765.90i	−0.0215082	+	0.121979i
$595$	−15933.7	−	5799.40i	−1.09785	−	0.399584i
$596$	78.1032	+	135.279i	0.00536784	+	0.00929737i
$597$	−6050.90	+	10480.5i	−0.414819	+	0.718488i
$598$	−1577.86	+	1323.98i	−0.107899	+	0.0905379i
$599$	1324.81	−	1111.65i	0.0903678	−	0.0758276i	−0.596485	−	0.802625i	$-0.703436\pi$
$599$	1324.81	−	1111.65i	0.0903678	−	0.0758276i	0.686852	+	0.726797i	$0.258992\pi$
$600$	−1031.56	+	1786.71i	−0.0701886	+	0.121570i
$601$	3155.29	+	5465.12i	0.214155	+	0.370926i	0.953011	−	0.302937i	$-0.0979671\pi$
$601$	3155.29	+	5465.12i	0.214155	+	0.370926i	−0.738856	+	0.673863i	$0.764634\pi$
$602$	−1620.77	−	589.913i	−0.109730	−	0.0399386i
$603$	110.520	−	626.792i	0.00746391	−	0.0423299i
$604$	−1001.07	−	5677.35i	−0.0674387	−	0.382464i
$605$	3116.57	−	1134.34i	0.209433	−	0.0762272i
$606$	−1690.39	−	1418.41i	−0.113313	−	0.0950805i
$607$	−777.764			−0.0520074			−0.0260037	−	0.999662i	$-0.508278\pi$
$607$	−777.764			−0.0520074			−0.0260037	+	0.999662i	$0.508278\pi$
$608$	−2015.92	+	1720.38i	−0.134468	+	0.114754i
$609$	−14780.7			−0.983491
$610$	−10086.4	−	8463.49i	−0.669486	−	0.561765i
$611$	−2765.20	+	1006.45i	−0.183090	+	0.0666392i
$612$	320.307	+	1816.55i	0.0211563	+	0.119983i
$613$	−4876.77	+	27657.6i	−0.321323	+	1.82231i	0.213022	+	0.977047i	$0.431669\pi$
$613$	−4876.77	+	27657.6i	−0.321323	+	1.82231i	−0.534345	+	0.845266i	$0.679442\pi$
$614$	−11411.7	−	4153.53i	−0.750065	−	0.273001i
$615$	−10343.4	−	17915.3i	−0.678187	−	1.17465i
$616$	3026.32	−	5241.74i	0.197945	−	0.342850i
$617$	7927.46	−	6651.93i	0.517257	−	0.434030i	−0.346417	−	0.938080i	$-0.612602\pi$
$617$	7927.46	−	6651.93i	0.517257	−	0.434030i	0.863674	+	0.504051i	$0.168157\pi$
$618$	−6185.29	+	5190.07i	−0.402603	+	0.337824i
$619$	10279.8	−	17805.1i	0.667495	−	1.15614i	−0.311107	−	0.950375i	$-0.600700\pi$
$619$	10279.8	−	17805.1i	0.667495	−	1.15614i	0.978602	−	0.205761i	$-0.0659668\pi$
$620$	−2464.47	−	4268.59i	−0.159638	−	0.276501i
$621$	2608.55	+	949.435i	0.168563	+	0.0613519i
$622$	916.901	−	5200.01i	0.0591067	−	0.335211i
$623$	−4389.15	−	24892.1i	−0.282259	−	1.60077i
$624$	−451.816	+	164.448i	−0.0289858	+	0.0105500i
$625$	−14540.1	−	12200.6i	−0.930565	−	0.780837i
$626$	7578.43			0.483858
$627$	6364.09	+	5250.38i	0.405354	+	0.334418i
$628$	−11426.4			−0.726053
$629$	10574.8	+	8873.28i	0.670339	+	0.562481i
$630$	−5597.53	+	2037.33i	−0.353986	+	0.128840i
$631$	1786.38	+	10131.1i	0.112701	+	0.639162i	0.987863	+	0.155330i	$0.0496442\pi$
$631$	1786.38	+	10131.1i	0.112701	+	0.639162i	−0.875161	+	0.483832i	$0.839245\pi$
$632$	844.859	−	4791.43i	0.0531751	−	0.301571i
$633$	10424.8	+	3794.32i	0.654580	+	0.238248i
$634$	−813.211	−	1408.52i	−0.0509412	−	0.0882328i
$635$	8982.71	−	15558.5i	0.561367	−	0.972315i
$636$	4825.72	−	4049.26i	0.300869	−	0.252459i
$637$	1351.46	−	1134.01i	0.0840609	−	0.0705355i
$638$	−7180.59	+	12437.2i	−0.445584	+	0.771774i
$639$	1295.95	+	2244.65i	0.0802301	+	0.138963i
$640$	−1747.02	−	635.865i	−0.107902	−	0.0392731i
$641$	−206.316	+	1170.08i	−0.0127130	+	0.0720988i	−0.990504	−	0.137482i	$-0.956099\pi$
$641$	−206.316	+	1170.08i	−0.0127130	+	0.0720988i	0.977791	+	0.209581i	$0.0672101\pi$
$642$	1559.24	+	8842.90i	0.0958541	+	0.543616i
$643$	16932.3	−	6162.86i	1.03848	−	0.377978i	0.234179	−	0.972193i	$-0.424760\pi$
$643$	16932.3	−	6162.86i	1.03848	−	0.377978i	0.804306	+	0.594216i	$0.202537\pi$
$644$	−7177.92	−	6022.99i	−0.439208	−	0.368539i
$645$	1649.29			0.100683
$646$	7999.07	+	2836.18i	0.487181	+	0.172737i
$647$	3288.22			0.199804			0.0999019	−	0.994997i	$-0.468147\pi$
$647$	3288.22			0.199804			0.0999019	+	0.994997i	$0.468147\pi$
$648$	496.397	+	416.526i	0.0300931	+	0.0252511i
$649$	19892.8	−	7240.37i	1.20317	−	0.437919i
$650$	299.052	+	1696.01i	0.0180458	+	0.102343i
$651$	1006.97	−	5710.82i	0.0606242	−	0.343817i
$652$	−9071.16	−	3301.63i	−0.544868	−	0.198316i
$653$	−7079.79	−	12262.6i	−0.424278	−	0.734872i	0.572074	−	0.820202i	$-0.306139\pi$
$653$	−7079.79	−	12262.6i	−0.424278	−	0.734872i	−0.996353	+	0.0853301i	$0.972805\pi$
$654$	−4700.97	+	8142.32i	−0.281074	+	0.486835i
$655$	26792.6	−	22481.7i	1.59828	−	1.34112i
$656$	5818.91	−	4882.65i	0.346327	−	0.290603i
$657$	4578.68	−	7930.51i	0.271890	−	0.470926i
$658$	−6693.30	−	11593.1i	−0.396553	−	0.686850i
$659$	10018.5	+	3646.45i	0.592210	+	0.215547i	0.620701	−	0.784047i	$-0.286848\pi$
$659$	10018.5	+	3646.45i	0.592210	+	0.215547i	−0.0284909	+	0.999594i	$0.509070\pi$
$660$	−1005.02	+	5699.75i	−0.0592733	+	0.336156i
$661$	−540.983	−	3068.06i	−0.0318333	−	0.180535i	0.964745	−	0.263185i	$-0.0847729\pi$
$661$	−540.983	−	3068.06i	−0.0318333	−	0.180535i	−0.996579	+	0.0826495i	$0.973662\pi$
$662$	−2975.02	+	1082.82i	−0.174664	+	0.0635723i
$663$	1179.51	+	989.730i	0.0690928	+	0.0579758i
$664$	−1595.34			−0.0932399
$665$	−4534.24	+	27029.8i	−0.264406	+	1.57619i
$666$	4849.49			0.282153
$667$	17031.2	+	14290.8i	0.988679	+	0.829600i
$668$	6095.35	−	2218.52i	0.353048	−	0.128499i
$669$	2635.63	+	14947.4i	0.152316	+	0.863826i
$670$	356.725	−	2023.09i	0.0205694	−	0.116655i
$671$	−14143.4	−	5147.79i	−0.813713	−	0.296167i
$672$	−1093.64	−	1894.25i	−0.0627801	−	0.108738i
$673$	13641.0	−	23626.9i	0.781309	−	1.35327i	−0.149870	−	0.988706i	$-0.547886\pi$
$673$	13641.0	−	23626.9i	0.781309	−	1.35327i	0.931179	−	0.364561i	$-0.118781\pi$
$674$	−11121.4	+	9331.98i	−0.635581	+	0.533315i
$675$	1777.99	−	1491.91i	0.101385	−	0.0850722i
$676$	4193.32	−	7263.05i	0.238582	−	0.413237i
$677$	1004.64	+	1740.09i	0.0570333	+	0.0987847i	0.893132	−	0.449794i	$-0.148503\pi$
$677$	1004.64	+	1740.09i	0.0570333	+	0.0987847i	−0.836099	+	0.548578i	$0.815169\pi$
$678$	2414.46	+	878.793i	0.136765	+	0.0497785i
$679$	5825.90	−	33040.3i	0.329275	−	1.86741i
$680$	1033.85	+	5863.25i	0.0583033	+	0.330655i
$681$	8808.14	−	3205.90i	0.495637	−	0.180397i
$682$	−4316.14	−	3621.67i	−0.242336	−	0.203344i
$683$	−19205.3			−1.07595			−0.537973	−	0.842962i	$-0.680810\pi$
$683$	−19205.3			−1.07595			−0.537973	+	0.842962i	$0.680810\pi$
$684$	2793.09	−	1043.03i	0.156135	−	0.0583061i
$685$	17824.7			0.994228
$686$	−5825.28	−	4887.99i	−0.324213	−	0.272047i
$687$	6193.66	−	2254.31i	0.343963	−	0.125192i
$688$	105.163	+	596.407i	0.00582745	+	0.0330491i
$689$	913.130	−	5178.61i	0.0504898	−	0.286342i
$690$	8419.58	+	3064.48i	0.464533	+	0.169076i
$691$	−671.978	−	1163.90i	−0.0369946	−	0.0640765i	0.846935	−	0.531696i	$-0.178445\pi$
$691$	−671.978	−	1163.90i	−0.0369946	−	0.0640765i	−0.883930	+	0.467619i	$0.845112\pi$
$692$	2264.62	−	3922.43i	0.124404	−	0.215475i
$693$	−5216.17	+	4376.88i	−0.285925	+	0.239919i
$694$	−1235.17	+	1036.43i	−0.0675597	+	0.0566893i
$695$	2548.22	−	4413.65i	0.139078	−	0.240891i
$696$	2594.91	+	4494.51i	0.141321	+	0.244776i
$697$	−22858.5	−	8319.80i	−1.24222	−	0.452130i
$698$	2746.19	−	15574.4i	0.148918	−	0.844556i
$699$	−913.609	−	5181.33i	−0.0494361	−	0.280366i
$700$	−7361.95	+	2679.53i	−0.397508	+	0.144681i
$701$	−9252.69	−	7763.93i	−0.498530	−	0.418316i	0.358542	−	0.933514i	$-0.383274\pi$
$701$	−9252.69	−	7763.93i	−0.498530	−	0.418316i	−0.857071	+	0.515198i	$0.827718\pi$
$702$	540.914			0.0290819
$703$	10995.0	−	19415.7i	0.589880	−	1.04165i
$704$	−2125.20			−0.113774
$705$	9805.82	+	8228.06i	0.523842	+	0.439555i
$706$	−10463.6	+	3808.44i	−0.557795	+	0.203021i
$707$	−1455.08	−	8252.17i	−0.0774030	−	0.438974i
$708$	1328.44	−	7533.93i	0.0705165	−	0.399919i
$709$	26092.2	+	9496.79i	1.38211	+	0.503046i	0.922816	−	0.385241i	$-0.125882\pi$
$709$	26092.2	+	9496.79i	1.38211	+	0.503046i	0.459290	+	0.888286i	$0.348104\pi$
$710$	4182.92	+	7245.03i	0.221102	+	0.382959i
$711$	−2736.76	+	4740.20i	−0.144355	+	0.250030i
$712$	−6798.59	+	5704.70i	−0.357848	+	0.300270i
$713$	−6681.82	+	5606.71i	−0.350962	+	0.294492i
$714$	−3502.27	+	6066.11i	−0.183570	+	0.317953i
$715$	2415.62	+	4183.97i	0.126348	+	0.218842i
$716$	−3461.28	−	1259.80i	−0.180662	−	0.0657556i
$717$	−1901.12	+	10781.8i	−0.0990216	+	0.561579i
$718$	3335.10	+	18914.3i	0.173350	+	0.983114i
$719$	11892.6	−	4328.57i	0.616858	−	0.224518i	−0.0146435	−	0.999893i	$-0.504661\pi$
$719$	11892.6	−	4328.57i	0.616858	−	0.224518i	0.631501	+	0.775375i	$0.282439\pi$
$720$	1602.21	+	1344.41i	0.0829318	+	0.0695880i
$721$	−30661.2			−1.58375
$722$	2156.70	−	13547.4i	0.111169	−	0.698313i
$723$	4619.04			0.237599
$724$	−11967.4	−	10041.8i	−0.614314	−	0.515470i
$725$	17467.8	−	6357.76i	0.894811	−	0.325685i
$726$	−237.908	−	1349.25i	−0.0121620	−	0.0689741i
$727$	6488.92	−	36800.5i	0.331033	−	1.87738i	−0.132322	−	0.991207i	$-0.542243\pi$
$727$	6488.92	−	36800.5i	0.331033	−	1.87738i	0.463355	−	0.886173i	$-0.346645\pi$
$728$	−1715.72	−	624.470i	−0.0873471	−	0.0317917i
$729$	−364.500	−	631.333i	−0.0185185	−	0.0320750i
$730$	14778.5	−	25597.2i	0.749285	−	1.29780i
$731$	1485.66	−	1246.61i	0.0751696	−	0.0630748i
$732$	−4166.62	+	3496.21i	−0.210386	+	0.176535i
$733$	12239.3	−	21199.0i	0.616736	−	1.06822i	−0.373341	−	0.927694i	$-0.621788\pi$
$733$	12239.3	−	21199.0i	0.616736	−	1.06822i	0.990077	−	0.140524i	$-0.0448787\pi$
$734$	604.304	+	1046.68i	0.0303886	+	0.0526347i
$735$	−7211.48	−	2624.77i	−0.361904	−	0.131722i
$736$	−571.308	+	3240.05i	−0.0286123	+	0.162269i
$737$	−407.774	−	2312.60i	−0.0203807	−	0.115585i
$738$	−8030.20	+	2922.75i	−0.400536	+	0.145783i
$739$	−18144.2	−	15224.8i	−0.903173	−	0.757852i	0.0676349	−	0.997710i	$-0.478455\pi$
$739$	−18144.2	−	15224.8i	−0.903173	−	0.757852i	−0.970808	+	0.239858i	$0.922899\pi$
$740$	15652.6			0.777569
$741$	1226.39	−	2165.64i	0.0607998	−	0.107364i
$742$	23921.7			1.18355
$743$	−4756.59	−	3991.25i	−0.234862	−	0.197072i	0.517759	−	0.855526i	$-0.326766\pi$
$743$	−4756.59	−	3991.25i	−0.234862	−	0.197072i	−0.752621	+	0.658454i	$0.771211\pi$
$744$	−1913.32	+	696.392i	−0.0942820	+	0.0343158i
$745$	−98.4946	−	558.591i	−0.00484371	−	0.0274700i
$746$	739.972	−	4196.59i	0.0363168	−	0.205963i
$747$	1686.52	+	613.844i	0.0826059	+	0.0300661i
$748$	3402.86	+	5893.92i	0.166338	+	0.288106i
$749$	−17048.9	+	29529.6i	−0.831714	+	1.44057i
$750$	−2606.05	+	2186.74i	−0.126880	+	0.106465i
$751$	−21504.3	+	18044.2i	−1.04488	+	0.876754i	−0.992545	−	0.121875i	$-0.961109\pi$
$751$	−21504.3	+	18044.2i	−1.04488	+	0.876754i	−0.0523299	+	0.998630i	$0.516665\pi$
$752$	−2350.15	+	4070.58i	−0.113964	+	0.197392i
$753$	−11177.4	−	19359.8i	−0.540939	−	0.936934i
$754$	4070.90	+	1481.69i	0.196623	+	0.0715648i
$755$	−3635.03	+	20615.3i	−0.175222	+	0.993731i
$756$	427.296	+	2423.32i	0.0205564	+	0.116581i
$757$	3308.09	−	1204.05i	0.158830	−	0.0578095i	−0.261381	−	0.965236i	$-0.584178\pi$
$757$	3308.09	−	1204.05i	0.158830	−	0.0578095i	0.420212	+	0.907426i	$0.361956\pi$
$758$	3565.10	+	2991.47i	0.170832	+	0.143345i
$759$	10242.2			0.489811
$760$	9015.20	−	3366.58i	0.430284	−	0.160682i
$761$	−23591.6			−1.12378			−0.561890	−	0.827212i	$-0.689926\pi$
$761$	−23591.6			−1.12378			−0.561890	+	0.827212i	$0.689926\pi$
$762$	−5685.11	−	4770.38i	−0.270275	−	0.226788i
$763$	−33549.6	+	12211.0i	−1.59184	+	0.579383i
$764$	−3001.84	−	17024.3i	−0.142150	−	0.806174i
$765$	1163.08	−	6596.15i	0.0549689	−	0.311744i
$766$	12069.0	+	4392.76i	0.569284	+	0.207202i
$767$	−3192.96	−	5530.37i	−0.150314	−	0.260352i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−22864.4	+	19185.5i	−1.07218	+	0.899670i	−0.995249	−	0.0973665i	$-0.968958\pi$
$769$	−22864.4	+	19185.5i	−1.07218	+	0.899670i	−0.0769358	+	0.997036i	$0.524514\pi$
$770$	−16836.1	+	14127.2i	−0.787964	+	0.661180i
$771$	−9635.07	+	16688.4i	−0.450063	+	0.779532i
$772$	8024.92	+	13899.6i	0.374123	+	0.648001i
$773$	17183.6	+	6254.32i	0.799548	+	0.291012i	0.709299	−	0.704907i	$-0.249011\pi$
$773$	17183.6	+	6254.32i	0.799548	+	0.291012i	0.0902491	+	0.995919i	$0.471234\pi$
$774$	118.308	−	670.958i	0.00549418	−	0.0311590i
$775$	1266.41	+	7182.15i	0.0586977	+	0.332891i
$776$	−11069.6	+	4029.02i	−0.512084	+	0.186383i
$777$	14107.0	+	11837.1i	0.651331	+	0.546532i
$778$	−16468.4			−0.758897
$779$	−6504.80	+	38776.8i	−0.299177	+	1.78347i
$780$	1745.90			0.0801452
$781$	7325.72	+	6147.01i	0.335640	+	0.281635i
$782$	9900.54	−	3603.50i	0.452740	−	0.164784i
$783$	−1013.85	−	5749.84i	−0.0462734	−	0.262430i
$784$	489.333	−	2775.15i	0.0222910	−	0.126419i
$785$	38988.5	+	14190.7i	1.77269	+	0.645206i
$786$	−7224.03	−	12512.4i	−0.327828	−	0.567814i
$787$	710.957	−	1231.41i	0.0322019	−	0.0557753i	−0.849475	−	0.527628i	$-0.823081\pi$
$787$	710.957	−	1231.41i	0.0322019	−	0.0557753i	0.881677	+	0.471853i	$0.156415\pi$
$788$	−409.947	+	343.986i	−0.0185327	+	0.0155508i
$789$	−10887.7	+	9135.87i	−0.491270	+	0.412225i
$790$	−8833.39	+	15299.9i	−0.397820	+	0.689044i
$791$	4878.52	+	8449.85i	0.219293	+	0.379826i
$792$	2246.67	+	817.719i	0.100798	+	0.0366874i
$793$	−788.413	+	4471.31i	−0.0353056	+	0.200228i
$794$	3445.64	+	19541.2i	0.154007	+	0.873415i
$795$	−21495.0	+	7823.54i	−0.958930	+	0.349022i
$796$	12360.7	+	10371.9i	0.550393	+	0.461835i
$797$	14172.5			0.629881			0.314941	−	0.949111i	$-0.398015\pi$
$797$	14172.5			0.629881			0.314941	+	0.949111i	$0.398015\pi$
$798$	10670.9	+	3783.53i	0.473367	+	0.167839i
$799$	15052.2			0.666467
$800$	2107.25	+	1768.19i	0.0931282	+	0.0781438i
$801$	9382.17	−	3414.83i	0.413861	−	0.150633i
$802$	−3857.15	−	21875.0i	−0.169826	−	0.963132i
$803$	5867.03	−	33273.6i	0.257837	−	1.46227i
$804$	−797.437	−	290.243i	−0.0349794	−	0.0127315i
$805$	17012.1	+	29465.8i	0.744842	+	1.29010i
$806$	−849.818	+	1471.93i	−0.0371384	+	0.0643256i
$807$	−12902.9	+	10826.9i	−0.562831	+	0.472272i
$808$	−2253.85	+	1891.21i	−0.0981315	+	0.0823421i
$809$	587.160	−	1016.99i	0.0255172	−	0.0441971i	−0.852985	−	0.521936i	$-0.825210\pi$
$809$	587.160	−	1016.99i	0.0255172	−	0.0441971i	0.878502	+	0.477739i	$0.158543\pi$
$810$	−1176.49	−	2037.74i	−0.0510341	−	0.0883937i
$811$	−6863.27	−	2498.03i	−0.297166	−	0.108160i	0.189134	−	0.981951i	$-0.439432\pi$
$811$	−6863.27	−	2498.03i	−0.297166	−	0.108160i	−0.486301	+	0.873791i	$0.661654\pi$
$812$	−3422.20	+	19408.3i	−0.147901	+	0.838789i
$813$	−2724.94	−	15453.9i	−0.117549	−	0.666656i
$814$	16813.5	−	6119.63i	0.723973	−	0.263505i
$815$	26851.9	+	22531.4i	1.15409	+	0.968393i
$816$	2459.43			0.105511
$817$	−2418.05	−	1994.90i	−0.103546	−	0.0854255i
$818$	15569.4			0.665489
$819$	1573.50	+	1320.32i	0.0671337	+	0.0563318i
$820$	−25918.9	+	9433.72i	−1.10381	+	0.401756i
$821$	154.966	+	878.858i	0.00658753	+	0.0373597i	0.987924	−	0.154937i	$-0.0495175\pi$
$821$	154.966	+	878.858i	0.00658753	+	0.0373597i	−0.981337	+	0.192297i	$0.938406\pi$
$822$	1278.62	−	7251.39i	0.0542541	−	0.307690i
$823$	−32118.8	−	11690.3i	−1.36038	−	0.495136i	−0.444206	−	0.895925i	$-0.646514\pi$
$823$	−32118.8	−	11690.3i	−1.36038	−	0.495136i	−0.916171	+	0.400788i	$0.868736\pi$
$824$	5382.88	+	9323.42i	0.227575	+	0.394171i
$825$	4281.77	−	7416.25i	0.180694	−	0.312970i
$826$	22254.0	−	18673.3i	0.937428	−	0.786595i
$827$	1172.05	−	983.465i	0.0492819	−	0.0413524i	−0.617814	−	0.786324i	$-0.711982\pi$
$827$	1172.05	−	983.465i	0.0492819	−	0.0413524i	0.667096	+	0.744972i	$0.267537\pi$
$828$	1850.64	−	3205.41i	0.0776742	−	0.134536i
$829$	18228.0	+	31571.9i	0.763673	+	1.32272i	0.940945	+	0.338559i	$0.109940\pi$
$829$	18228.0	+	31571.9i	0.763673	+	1.32272i	−0.177272	+	0.984162i	$0.556727\pi$
$830$	5443.56	+	1981.29i	0.227649	+	0.0828575i
$831$	−3771.59	+	21389.7i	−0.157443	+	0.892903i
$832$	111.323	+	631.344i	0.00463874	+	0.0263076i
$833$	−8479.95	+	3086.45i	−0.352717	+	0.128378i
$834$	−1612.76	−	1353.26i	−0.0669607	−	0.0561867i
$835$	−23553.5			−0.976171
$836$	8367.64	−	7140.91i	0.346173	−	0.295423i
$837$	2290.63			0.0945947
$838$	−18729.4	−	15715.8i	−0.772071	−	0.647844i
$839$	−15355.8	+	5589.04i	−0.631871	+	0.229982i	−0.638046	−	0.769999i	$-0.720257\pi$
$839$	−15355.8	+	5589.04i	−0.631871	+	0.229982i	0.00617438	+	0.999981i	$0.498035\pi$
$840$	1379.18	+	7821.69i	0.0566501	+	0.321279i
$841$	3884.80	−	22031.8i	0.159285	−	0.903349i
$842$	−17279.7	−	6289.30i	−0.707242	−	0.257415i
$843$	2766.16	+	4791.13i	0.113015	+	0.195748i
$844$	7395.90	−	12810.1i	0.301632	−	0.522442i
$845$	−23328.4	+	19574.9i	−0.949731	+	0.796919i
$846$	4050.72	−	3398.95i	0.164618	−	0.138131i
$847$	2601.32	−	4505.61i	0.105528	−	0.182780i
$848$	−4199.69	−	7274.08i	−0.170068	−	0.294567i
$849$	3932.43	+	1431.29i	0.158964	+	0.0578582i
$850$	1529.70	−	8675.35i	0.0617273	−	0.350073i
$851$	−4809.98	−	27278.8i	−0.193753	−	1.09883i
$852$	3247.46	−	1181.98i	0.130582	−	0.0475280i
$853$	−56.4449	−	47.3629i	−0.00226570	−	0.00190114i	0.641654	−	0.766994i	$-0.278249\pi$
$853$	−56.4449	−	47.3629i	−0.00226570	−	0.00190114i	−0.643920	+	0.765093i	$0.722693\pi$
$854$	−20654.5			−0.827612
$855$	−10825.8	+	90.1873i	−0.433024	+	0.00360742i
$856$	11972.4			0.478048
$857$	25217.5	+	21160.0i	1.00515	+	0.843419i	0.987689	−	0.156428i	$-0.0499980\pi$
$857$	25217.5	+	21160.0i	1.00515	+	0.843419i	0.0174588	+	0.999848i	$0.494442\pi$
$858$	1875.39	−	682.587i	0.0746210	−	0.0271598i
$859$	−6842.73	−	38807.0i	−0.271794	−	1.54142i	−0.748965	−	0.662609i	$-0.769449\pi$
$859$	−6842.73	−	38807.0i	−0.271794	−	1.54142i	0.477171	−	0.878810i	$-0.341662\pi$
$860$	381.861	−	2165.64i	0.0151411	−	0.0858694i
$861$	−30493.7	−	11098.8i	−1.20699	−	0.439310i
$862$	13737.1	+	23793.3i	0.542792	+	0.940143i
$863$	1690.76	−	2928.49i	0.0666910	−	0.115512i	−0.830752	−	0.556643i	$-0.812089\pi$
$863$	1690.76	−	2928.49i	0.0666910	−	0.115512i	0.897443	+	0.441131i	$0.145423\pi$
$864$	661.862	−	555.368i	0.0260614	−	0.0218681i
$865$	−12598.6	+	10571.5i	−0.495220	+	0.415539i
$866$	−798.640	+	1383.28i	−0.0313382	+	0.0542793i
$867$	3431.48	+	5943.50i	0.134417	+	0.232816i
$868$	−7265.60	−	2644.46i	−0.284114	−	0.103409i
$869$	−3506.83	+	19888.2i	−0.136894	+	0.776365i
$870$	−3272.39	−	18558.6i	−0.127522	−	0.723215i
$871$	−665.656	+	242.279i	−0.0258954	+	0.00942516i
$872$	9603.07	+	8057.93i	0.372937	+	0.312931i
$873$	13252.6			0.513782
$874$	−8637.48	−	14676.8i	−0.334287	−	0.568022i
$875$	−12918.5			−0.499115
$876$	−9353.27	−	7848.32i	−0.360751	−	0.302706i
$877$	−28827.5	+	10492.4i	−1.10996	+	0.403993i	−0.830979	−	0.556304i	$-0.812219\pi$
$877$	−28827.5	+	10492.4i	−1.10996	+	0.403993i	−0.278982	+	0.960296i	$0.589997\pi$
$878$	3714.05	+	21063.5i	0.142760	+	0.809632i
$879$	2389.60	−	13552.1i	0.0916943	−	0.520024i
$880$	7251.52	+	2639.34i	0.277783	+	0.101105i
$881$	−25365.3	−	43934.0i	−0.970010	−	1.68011i	−0.695506	−	0.718521i	$-0.744820\pi$
$881$	−25365.3	−	43934.0i	−0.970010	−	1.68011i	−0.274504	−	0.961586i	$-0.588514\pi$
$882$	−1585.10	+	2745.47i	−0.0605137	+	0.104813i
$883$	−24485.5	+	20545.8i	−0.933185	+	0.783035i	−0.976386	−	0.216031i	$-0.930689\pi$
$883$	−24485.5	+	20545.8i	−0.933185	+	0.783035i	0.0432014	+	0.999066i	$0.486244\pi$
$884$	1572.69	−	1319.64i	0.0598362	−	0.0502085i
$885$	−13889.4	+	24057.1i	−0.527556	+	0.913754i
$886$	9477.92	+	16416.2i	0.359387	+	0.622477i
$887$	−43498.1	−	15832.0i	−1.64659	−	0.599309i	−0.658415	−	0.752655i	$-0.728773\pi$
$887$	−43498.1	−	15832.0i	−1.64659	−	0.599309i	−0.988173	+	0.153346i	$0.950995\pi$
$888$	1122.81	−	6367.75i	0.0424312	−	0.240639i
$889$	−4893.72	−	27753.7i	−0.184623	−	1.04705i
$890$	30282.7	−	11022.0i	1.14054	−	0.415121i
$891$	−2060.44	−	1728.91i	−0.0774716	−	0.0650064i
$892$	20237.3			0.759636
$893$	−4424.25	−	23924.0i	−0.165792	−	0.896513i
$894$	−234.310			−0.00876565
$895$	10245.8	+	8597.28i	0.382660	+	0.321090i
$896$	−2740.51	+	997.462i	−0.102181	+	0.0371907i
$897$	−536.508	−	3042.69i	−0.0199704	−	0.113258i
$898$	−1125.73	+	6384.31i	−0.0418329	+	0.237246i
$899$	17239.2	+	6274.56i	0.639555	+	0.232779i
$900$	−1547.34	−	2680.07i	−0.0573088	−	0.0992617i
$901$	−13449.0	+	23294.4i	−0.497283	+	0.861319i
$902$	−24153.0	+	20266.8i	−0.891584	+	0.748128i
$903$	1981.90	−	1663.01i	0.0730381	−	0.0612863i
$904$	1712.95	−	2966.91i	0.0630218	−	0.109157i
$905$	28363.3	+	49126.8i	1.04180	+	1.80445i
$906$	8125.90	+	2957.59i	0.297975	+	0.108454i
$907$	405.069	−	2297.26i	0.0148292	−	0.0841007i	−0.976495	−	0.215540i	$-0.930849\pi$
$907$	405.069	−	2297.26i	0.0148292	−	0.0841007i	0.991324	+	0.131439i	$0.0419599\pi$
$908$	−2170.24	−	12308.0i	−0.0793192	−	0.449842i
$909$	3110.36	−	1132.08i	0.113492	−	0.0413076i
$910$	5078.75	+	4261.58i	0.185010	+	0.155242i
$911$	1536.03			0.0558629			0.0279314	−	0.999610i	$-0.491108\pi$
$911$	1536.03			0.0558629			0.0279314	+	0.999610i	$0.491108\pi$
$912$	−722.896	−	3909.04i	−0.0262472	−	0.141931i
$913$	6621.92			0.240037
$914$	5542.74	+	4650.91i	0.200588	+	0.168313i
$915$	18559.2	−	6755.00i	0.670544	−	0.244058i
$916$	−1526.06	−	8654.69i	−0.0550462	−	0.312182i
$917$	9527.15	−	54031.2i	0.343091	−	1.94576i
$918$	−2600.00	−	946.322i	−0.0934779	−	0.0340232i
$919$	7804.44	+	13517.7i	0.280136	+	0.485209i	0.971418	−	0.237375i	$-0.0762872\pi$
$919$	7804.44	+	13517.7i	0.280136	+	0.485209i	−0.691282	+	0.722585i	$0.742954\pi$
$920$	5973.28	−	10346.0i	0.214058	−	0.370759i
$921$	13954.4	−	11709.1i	0.499254	−	0.418924i
$922$	−9053.68	+	7596.94i	−0.323392	+	0.271358i
$923$	1442.38	−	2498.28i	0.0514373	−	0.0890921i
$924$	4539.48	+	7862.61i	0.161621	+	0.279936i
$925$	−21763.1	−	7921.13i	−0.773586	−	0.281562i
$926$	−1762.18	+	9993.81i	−0.0625365	+	0.354662i
$927$	−2103.14	−	11927.5i	−0.0745157	−	0.422599i
$928$	6502.44	−	2366.69i	0.230014	−	0.0837182i
$929$	28579.9	+	23981.4i	1.00934	+	0.846937i	0.988251	−	0.152841i	$-0.0488422\pi$
$929$	28579.9	+	23981.4i	1.00934	+	0.846937i	0.0210890	+	0.999778i	$0.493287\pi$
$930$	7393.42			0.260688
$931$	7398.12	+	12570.9i	0.260434	+	0.442529i
$932$	−7015.02			−0.246550
$933$	6067.33	+	5091.09i	0.212900	+	0.178644i
$934$	−35587.9	+	12952.9i	−1.24676	+	0.453782i
$935$	−4291.28	−	24337.1i	−0.150096	−	0.851238i
$936$	125.238	−	710.262i	0.00437345	−	0.0248030i
$937$	21162.1	+	7702.36i	0.737817	+	0.268543i	0.683470	−	0.729979i	$-0.260470\pi$
$937$	21162.1	+	7702.36i	0.737817	+	0.268543i	0.0543469	+	0.998522i	$0.482692\pi$
$938$	−1611.26	−	2790.78i	−0.0560867	−	0.0971451i
$939$	−5683.82	+	9844.66i	−0.197534	+	0.342139i
$940$	13074.4	−	10970.7i	0.453660	−	0.380666i
$941$	6334.47	−	5315.25i	0.219445	−	0.184136i	−0.526437	−	0.850214i	$-0.676473\pi$
$941$	6334.47	−	5315.25i	0.219445	−	0.184136i	0.745882	+	0.666078i	$0.232028\pi$
$942$	8569.77	−	14843.3i	0.296410	−	0.513397i
$943$	24405.5	+	42271.6i	0.842792	+	1.45976i
$944$	−9585.06	−	3488.68i	−0.330474	−	0.120283i
$945$	1551.57	−	8799.41i	0.0534102	−	0.302904i
$946$	−436.507	−	2475.56i	−0.0150022	−	0.0850817i
$947$	1833.58	−	667.369i	0.0629180	−	0.0229003i	−0.310369	−	0.950616i	$-0.600453\pi$
$947$	1833.58	−	667.369i	0.0629180	−	0.0229003i	0.373287	+	0.927716i	$0.378231\pi$
$948$	5590.61	+	4691.08i	0.191534	+	0.160716i
$949$	−10192.1			−0.348629
$950$	−14238.3	+	118.616i	−0.486264	+	0.00405095i
$951$	2439.63			0.0831866
$952$	7154.38	+	6003.24i	0.243566	+	0.204376i
$953$	−26094.3	+	9497.56i	−0.886966	+	0.322829i	−0.745017	−	0.667045i	$-0.767559\pi$
$953$	−26094.3	+	9497.56i	−0.886966	+	0.322829i	−0.141948	+	0.989874i	$0.545337\pi$
$954$	1640.85	+	9305.75i	0.0556862	+	0.315812i
$955$	−10900.1	+	61817.6i	−0.369339	+	2.09463i
$956$	13717.1	+	4992.62i	0.464062	+	0.168905i
$957$	−10770.9	−	18655.7i	−0.363818	−	0.630151i
$958$	−6251.73	+	10828.3i	−0.210839	+	0.365185i
$959$	21419.4	−	17973.0i	0.721240	−	0.605192i
$960$	2136.28	−	1792.55i	0.0718210	−	0.0602650i
$961$	11296.7	−	19566.5i	0.379200	−	0.656794i
$962$	−2698.72	−	4674.32i	−0.0904473	−	0.156659i
$963$	−12656.7	−	4606.66i	−0.423527	−	0.154151i
$964$	1069.45	−	6065.16i	0.0357310	−	0.202641i
$965$	−10120.1	−	57393.9i	−0.337593	−	1.91458i
$966$	13207.5	−	4807.15i	0.439902	−	0.160111i
$967$	20136.8	+	16896.7i	0.669653	+	0.561906i	0.912963	−	0.408043i	$-0.133789\pi$
$967$	20136.8	+	16896.7i	0.669653	+	0.561906i	−0.243310	+	0.969949i	$0.578233\pi$
$968$	−1826.75			−0.0606548
$969$	−9683.61	+	8263.95i	−0.321034	+	0.273970i
$970$	42775.1			1.41590
$971$	−7254.39	−	6087.15i	−0.239757	−	0.201180i	0.514989	−	0.857196i	$-0.327796\pi$
$971$	−7254.39	−	6087.15i	−0.239757	−	0.201180i	−0.754747	+	0.656016i	$0.772240\pi$
$972$	−913.381	+	332.444i	−0.0301407	+	0.0109703i
$973$	−1388.25	−	7873.18i	−0.0457403	−	0.259406i
$974$	4995.60	−	28331.4i	0.164342	−	0.932031i
$975$	−2427.47	−	883.527i	−0.0797347	−	0.0290210i
$976$	3626.09	+	6280.58i	0.118923	+	0.205980i
$977$	3707.48	−	6421.55i	0.121405	−	0.210280i	−0.798917	−	0.601442i	$-0.794593\pi$
$977$	3707.48	−	6421.55i	0.121405	−	0.210280i	0.920322	+	0.391161i	$0.127927\pi$
$978$	11092.3	−	9307.56i	0.362672	−	0.304318i
$979$	28219.5	−	23679.0i	0.921245	−	0.773017i
$980$	−5116.20	+	8861.52i	−0.166766	+	0.288848i
$981$	−7051.45	−	12213.5i	−0.229496	−	0.397499i
$982$	−30739.2	−	11188.2i	−0.998909	−	0.363573i
$983$	298.382	−	1692.21i	0.00968150	−	0.0549065i	−0.979584	−	0.201034i	$-0.935570\pi$
$983$	298.382	−	1692.21i	0.00968150	−	0.0549065i	0.989266	+	0.146127i	$0.0466810\pi$
$984$	1978.56	+	11221.0i	0.0640998	+	0.363528i
$985$	1826.01	−	664.613i	0.0590675	−	0.0214988i
$986$	−16975.3	−	14244.0i	−0.548280	−	0.460061i
$987$	20079.9			0.647568
$988$	−2559.70	−	2111.76i	−0.0824241	−	0.0680000i
$989$	−3891.54			−0.125120
$990$	−6650.43	−	5580.38i	−0.213500	−	0.179147i
$991$	−11969.8	+	4356.63i	−0.383685	+	0.139650i	−0.526659	−	0.850077i	$-0.676556\pi$
$991$	−11969.8	+	4356.63i	−0.383685	+	0.139650i	0.142974	+	0.989726i	$0.454333\pi$
$992$	471.423	+	2673.58i	0.0150884	+	0.0855707i
$993$	824.641	−	4676.77i	0.0263537	−	0.149459i
$994$	12331.8	+	4488.41i	0.393502	+	0.143223i
$995$	−29295.6	−	50741.4i	−0.933400	−	1.61670i
$996$	1196.51	−	2072.41i	0.0380650	−	0.0659305i
$997$	−3642.53	+	3056.44i	−0.115707	+	0.0970897i	−0.698805	−	0.715312i	$-0.746285\pi$
$997$	−3642.53	+	3056.44i	−0.115707	+	0.0970897i	0.583098	+	0.812402i	$0.301840\pi$
$998$	−30677.8	+	25741.8i	−0.973036	+	0.816474i
$999$	−3637.12	+	6299.67i	−0.115188	+	0.199512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.d.73.3	yes	18
19.5	even	9		2166.4.a.bm.1.7		9
19.6	even	9	inner	114.4.i.d.25.3	✓	18
19.14	odd	18		2166.4.a.bj.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.25.3	✓	18	19.6	even	9	inner
114.4.i.d.73.3	yes	18	1.1	even	1	trivial
2166.4.a.bj.1.7		9	19.14	odd	18
2166.4.a.bm.1.7		9	19.5	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)

\(f(q)\)	\(=\)	\(q+(1.53209 + 1.28558i) q^{2} +(-2.81908 + 1.02606i) q^{3} +(0.694593 + 3.93923i) q^{4} +(2.52217 - 14.3039i) q^{5} +(-5.63816 - 2.05212i) q^{6} +(-11.3921 - 19.7317i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(6.89440 - 5.78509i) q^{9} +O(q^{10})\)	\(q+(1.53209 + 1.28558i) q^{2} +(-2.81908 + 1.02606i) q^{3} +(0.694593 + 3.93923i) q^{4} +(2.52217 - 14.3039i) q^{5} +(-5.63816 - 2.05212i) q^{6} +(-11.3921 - 19.7317i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(6.89440 - 5.78509i) q^{9} +(22.2529 - 18.6724i) q^{10} +(16.6031 - 28.7575i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(-9.41284 - 3.42599i) q^{13} +(7.91289 - 44.8762i) q^{14} +(7.56650 + 42.9117i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(39.2507 + 32.9352i) q^{17} +18.0000 q^{18} +(40.8106 - 72.0659i) q^{19} +58.0983 q^{20} +(52.3613 + 43.9363i) q^{21} +(62.4074 - 22.7144i) q^{22} +(-17.8534 - 101.251i) q^{23} +(4.16756 - 23.6354i) q^{24} +(-80.7789 - 29.4011i) q^{25} +(-10.0169 - 17.3498i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(69.8150 - 58.5817i) q^{28} +(-165.651 + 138.998i) q^{29} +(-43.5737 + 75.4719i) q^{30} +(-42.4191 - 73.4720i) q^{31} +(-30.0702 - 10.9446i) q^{32} +(-17.2986 + 98.1054i) q^{33} +(17.7948 + 100.919i) q^{34} +(-310.974 + 113.185i) q^{35} +(27.5776 + 23.1404i) q^{36} +269.416 q^{37} +(155.172 - 57.9462i) q^{38} +30.0508 q^{39} +(89.0117 + 74.6897i) q^{40} +(-446.122 + 162.375i) q^{41} +(23.7387 + 134.629i) q^{42} +(6.57266 - 37.2754i) q^{43} +(124.815 + 45.4289i) q^{44} +(-65.3606 - 113.208i) q^{45} +(102.813 - 178.078i) q^{46} +(225.040 - 188.831i) q^{47} +(36.7701 - 30.8538i) q^{48} +(-88.0611 + 152.526i) q^{49} +(-85.9631 - 148.893i) q^{50} +(-144.444 - 52.5734i) q^{51} +(6.95769 - 39.4590i) q^{52} +(91.1586 + 516.986i) q^{53} +(-50.7434 + 18.4691i) q^{54} +(-369.468 - 310.021i) q^{55} +182.274 q^{56} +(-41.1043 + 245.034i) q^{57} -432.484 q^{58} +(488.363 + 409.785i) q^{59} +(-163.784 + 59.6123i) q^{60} +(-78.7080 - 446.375i) q^{61} +(29.4640 - 167.098i) q^{62} +(-192.692 - 70.1341i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-72.7458 + 125.999i) q^{65} +(-152.625 + 128.067i) q^{66} +(54.1731 - 45.4566i) q^{67} +(-102.476 + 177.494i) q^{68} +(154.220 + 267.117i) q^{69} +(-621.948 - 226.370i) q^{70} +(-50.0088 + 283.614i) q^{71} +(12.5027 + 70.9062i) q^{72} +(956.123 - 348.000i) q^{73} +(412.769 + 346.354i) q^{74} +257.889 q^{75} +(312.231 + 110.706i) q^{76} -756.580 q^{77} +(46.0405 + 38.6326i) q^{78} +(-571.491 + 208.006i) q^{79} +(40.3546 + 228.863i) q^{80} +(14.0655 - 79.7694i) q^{81} +(-892.244 - 324.750i) q^{82} +(99.7089 + 172.701i) q^{83} +(-136.706 + 236.781i) q^{84} +(570.099 - 478.370i) q^{85} +(57.9903 - 48.6596i) q^{86} +(324.363 - 561.813i) q^{87} +(132.825 + 230.060i) q^{88} +(1042.46 + 379.426i) q^{89} +(45.3990 - 257.470i) q^{90} +(39.6314 + 224.761i) q^{91} +(386.452 - 140.657i) q^{92} +(194.969 + 163.599i) q^{93} +587.537 q^{94} +(-927.893 - 765.513i) q^{95} +96.0000 q^{96} +(1128.01 + 946.510i) q^{97} +(-331.002 + 120.475i) q^{98} +(-51.8959 - 294.316i) 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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