LMFDB - Embedded newform 45.4.l.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	45.23
Dual form			45.4.l.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.429078 + 1.60134i) q^{2} +(-4.91725 - 1.67949i) q^{3} +(4.54802 + 2.62580i) q^{4} +(-7.92902 + 7.88230i) q^{5} +(4.79931 - 7.15356i) q^{6} +(-30.4193 - 8.15082i) q^{7} +(-15.5344 + 15.5344i) q^{8} +(21.3587 + 16.5169i) q^{9} +O(q^{10})$	\(q+(-0.429078 + 1.60134i) q^{2} +(-4.91725 - 1.67949i) q^{3} +(4.54802 + 2.62580i) q^{4} +(-7.92902 + 7.88230i) q^{5} +(4.79931 - 7.15356i) q^{6} +(-30.4193 - 8.15082i) q^{7} +(-15.5344 + 15.5344i) q^{8} +(21.3587 + 16.5169i) q^{9} +(-9.22008 - 16.0792i) q^{10} +(-31.0214 + 17.9102i) q^{11} +(-17.9537 - 20.5500i) q^{12} +(53.6997 - 14.3888i) q^{13} +(26.1045 - 45.2143i) q^{14} +(52.2272 - 25.4426i) q^{15} +(2.79604 + 4.84288i) q^{16} +(29.9510 + 29.9510i) q^{17} +(-35.6137 + 27.1155i) q^{18} +17.7095i q^{19} +(-56.7587 + 15.0288i) q^{20} +(135.890 + 91.1683i) q^{21} +(-15.3698 - 57.3607i) q^{22} +(27.3107 + 101.925i) q^{23} +(102.476 - 50.2966i) q^{24} +(0.738685 - 124.998i) q^{25} +92.1654i q^{26} +(-77.2859 - 117.089i) q^{27} +(-116.945 - 116.945i) q^{28} +(-26.5786 - 46.0355i) q^{29} +(18.3327 + 94.5503i) q^{30} +(-19.1014 + 33.0846i) q^{31} +(-178.717 + 47.8872i) q^{32} +(182.620 - 35.9690i) q^{33} +(-60.8131 + 35.1104i) q^{34} +(305.442 - 175.146i) q^{35} +(53.7695 + 131.203i) q^{36} +(-75.1697 + 75.1697i) q^{37} +(-28.3590 - 7.59877i) q^{38} +(-288.220 - 19.4346i) q^{39} +(0.725746 - 245.619i) q^{40} +(-126.863 - 73.2444i) q^{41} +(-204.299 + 178.488i) q^{42} +(-140.961 + 526.075i) q^{43} -188.114 q^{44} +(-299.544 + 37.3926i) q^{45} -174.935 q^{46} +(43.2145 - 161.279i) q^{47} +(-5.61527 - 28.5095i) q^{48} +(561.849 + 324.384i) q^{49} +(199.847 + 54.8167i) q^{50} +(-96.9742 - 197.579i) q^{51} +(282.009 + 75.5641i) q^{52} +(-170.746 + 170.746i) q^{53} +(220.661 - 73.5208i) q^{54} +(104.796 - 386.530i) q^{55} +(599.162 - 345.926i) q^{56} +(29.7429 - 87.0821i) q^{57} +(85.1228 - 22.8086i) q^{58} +(28.0525 - 48.5883i) q^{59} +(304.337 + 21.4248i) q^{60} +(187.285 + 324.386i) q^{61} +(-44.7838 - 44.7838i) q^{62} +(-515.089 - 676.522i) q^{63} -261.998i q^{64} +(-312.369 + 537.366i) q^{65} +(-20.7596 + 307.870i) q^{66} +(-29.6904 - 110.806i) q^{67} +(57.5724 + 214.863i) q^{68} +(36.8879 - 547.058i) q^{69} +(149.410 + 564.268i) q^{70} -921.281i q^{71} +(-588.372 + 75.2138i) q^{72} +(373.434 + 373.434i) q^{73} +(-88.1187 - 152.626i) q^{74} +(-213.564 + 613.405i) q^{75} +(-46.5016 + 80.5432i) q^{76} +(1089.63 - 291.966i) q^{77} +(154.791 - 453.200i) q^{78} +(-492.922 + 284.589i) q^{79} +(-60.3429 - 16.3601i) q^{80} +(183.385 + 705.557i) q^{81} +(171.723 - 171.723i) q^{82} +(439.165 + 117.674i) q^{83} +(378.640 + 771.455i) q^{84} +(-473.565 - 1.39927i) q^{85} +(-781.941 - 451.454i) q^{86} +(53.3777 + 271.006i) q^{87} +(203.674 - 760.121i) q^{88} -148.257 q^{89} +(68.6496 - 495.717i) q^{90} -1750.79 q^{91} +(-143.425 + 535.269i) q^{92} +(149.492 - 130.605i) q^{93} +(239.720 + 138.402i) q^{94} +(-139.592 - 140.419i) q^{95} +(959.224 + 64.6801i) q^{96} +(-312.391 - 83.7049i) q^{97} +(-760.526 + 760.526i) q^{98} +(-958.396 - 129.839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.429078	+	1.60134i	−0.151702	+	0.566160i	0.847663	+	0.530535i	$0.178009\pi$
$2$	−0.429078	+	1.60134i	−0.151702	+	0.566160i	−0.999365	+	0.0356249i	$0.988658\pi$
$3$	−4.91725	−	1.67949i	−0.946325	−	0.323217i
$3$	−4.91725	−	1.67949i	−0.946325	−	0.323217i
$4$	4.54802	+	2.62580i	0.568502	+	0.328225i
$5$	−7.92902	+	7.88230i	−0.709193	+	0.705014i
$5$	−7.92902	+	7.88230i	−0.709193	+	0.705014i
$6$	4.79931	−	7.15356i	0.326552	−	0.486738i
$7$	−30.4193	−	8.15082i	−1.64249	−	0.440103i	−0.684991	−	0.728552i	$-0.740194\pi$
$7$	−30.4193	−	8.15082i	−1.64249	−	0.440103i	−0.957495	+	0.288449i	$0.906860\pi$
$8$	−15.5344	+	15.5344i	−0.686528	+	0.686528i
$9$	21.3587	+	16.5169i	0.791061	+	0.611737i
$10$	−9.22008	−	16.0792i	−0.291565	−	0.508469i
$11$	−31.0214	+	17.9102i	−0.850300	+	0.490921i	−0.860752	−	0.509025i	$-0.830006\pi$
$11$	−31.0214	+	17.9102i	−0.850300	+	0.490921i	0.0104522	+	0.999945i	$0.496673\pi$
$12$	−17.9537	−	20.5500i	−0.431900	−	0.494357i
$13$	53.6997	−	14.3888i	1.14566	−	0.306979i	0.364437	−	0.931228i	$-0.381261\pi$
$13$	53.6997	−	14.3888i	1.14566	−	0.306979i	0.781226	+	0.624249i	$0.214595\pi$
$14$	26.1045	−	45.2143i	0.498337	−	0.863145i
$15$	52.2272	−	25.4426i	0.899000	−	0.437949i
$16$	2.79604	+	4.84288i	0.0436881	+	0.0756700i
$17$	29.9510	+	29.9510i	0.427305	+	0.427305i	0.887709	−	0.460404i	$-0.152296\pi$
$17$	29.9510	+	29.9510i	0.427305	+	0.427305i	−0.460404	+	0.887709i	$0.652296\pi$
$18$	−35.6137	+	27.1155i	−0.466346	+	0.355065i
$19$			17.7095i			0.213834i	0.994268	+	0.106917i	$0.0340979\pi$
$19$			17.7095i			0.213834i	−0.994268	+	0.106917i	$0.965902\pi$
$20$	−56.7587	+	15.0288i	−0.634581	+	0.168027i
$21$	135.890	+	91.1683i	1.41208	+	0.947360i
$22$	−15.3698	−	57.3607i	−0.148947	−	0.555879i
$23$	27.3107	+	101.925i	0.247595	+	0.924036i	0.972062	+	0.234726i	$0.0754193\pi$
$23$	27.3107	+	101.925i	0.247595	+	0.924036i	−0.724467	+	0.689310i	$0.757914\pi$
$24$	102.476	−	50.2966i	0.871576	−	0.427781i
$25$	0.738685	−	124.998i	0.00590948	−	0.999983i
$26$			92.1654i			0.695197i
$27$	−77.2859	−	117.089i	−0.550877	−	0.834586i
$28$	−116.945	−	116.945i	−0.789304	−	0.789304i
$29$	−26.5786	−	46.0355i	−0.170190	−	0.294779i	0.768296	−	0.640095i	$-0.221105\pi$
$29$	−26.5786	−	46.0355i	−0.170190	−	0.294779i	−0.938486	+	0.345316i	$0.887772\pi$
$30$	18.3327	+	94.5503i	0.111569	+	0.575415i
$31$	−19.1014	+	33.0846i	−0.110668	+	0.191683i	−0.916040	−	0.401087i	$-0.868632\pi$
$31$	−19.1014	+	33.0846i	−0.110668	+	0.191683i	0.805372	+	0.592770i	$0.201966\pi$
$32$	−178.717	+	47.8872i	−0.987284	+	0.264542i
$33$	182.620	−	35.9690i	0.963334	−	0.189739i
$34$	−60.8131	+	35.1104i	−0.306746	+	0.177100i
$35$	305.442	−	175.146i	1.47512	−	0.845858i
$36$	53.7695	+	131.203i	0.248933	+	0.607420i
$37$	−75.1697	+	75.1697i	−0.333995	+	0.333995i	−0.854102	−	0.520106i	$-0.825892\pi$
$37$	−75.1697	+	75.1697i	−0.333995	+	0.333995i	0.520106	+	0.854102i	$0.325892\pi$
$38$	−28.3590	−	7.59877i	−0.121064	−	0.0324390i
$39$	−288.220	−	19.4346i	−1.18339	−	0.0797955i
$40$	0.725746	−	245.619i	0.00286876	−	0.970893i
$41$	−126.863	−	73.2444i	−0.483236	−	0.278996i	0.238528	−	0.971136i	$-0.423335\pi$
$41$	−126.863	−	73.2444i	−0.483236	−	0.278996i	−0.721764	+	0.692139i	$0.756668\pi$
$42$	−204.299	+	178.488i	−0.750572	+	0.655744i
$43$	−140.961	+	526.075i	−0.499916	+	1.86571i	0.000626116		1.00000i	$0.499801\pi$
$43$	−140.961	+	526.075i	−0.499916	+	1.86571i	−0.500542	+	0.865712i	$0.666866\pi$
$44$	−188.114			−0.644530
$45$	−299.544	+	37.3926i	−0.992298	+	0.123870i
$46$	−174.935			−0.560712
$47$	43.2145	−	161.279i	0.134117	−	0.500530i	−0.865883	−	0.500246i	$-0.833243\pi$
$47$	43.2145	−	161.279i	0.134117	−	0.500530i	1.00000		0.000284175i	$-9.04559e-5\pi$
$48$	−5.61527	−	28.5095i	−0.0168853	−	0.0857291i
$49$	561.849	+	324.384i	1.63804	+	0.945725i
$50$	199.847	+	54.8167i	0.565253	+	0.155045i
$51$	−96.9742	−	197.579i	−0.266257	−	0.542481i
$52$	282.009	+	75.5641i	0.752070	+	0.201517i
$53$	−170.746	+	170.746i	−0.442525	+	0.442525i	−0.892860	−	0.450335i	$-0.851305\pi$
$53$	−170.746	+	170.746i	−0.442525	+	0.442525i	0.450335	+	0.892860i	$0.351305\pi$
$54$	220.661	−	73.5208i	0.556078	−	0.185276i
$55$	104.796	−	386.530i	0.256920	−	0.947631i
$56$	599.162	−	345.926i	1.42976	−	0.825470i
$57$	29.7429	−	87.0821i	0.0691147	−	0.202356i
$58$	85.1228	−	22.8086i	0.192710	−	0.0516365i
$59$	28.0525	−	48.5883i	0.0619004	−	0.107215i	−0.833414	−	0.552648i	$-0.813617\pi$
$59$	28.0525	−	48.5883i	0.0619004	−	0.107215i	0.895315	+	0.445434i	$0.146951\pi$
$60$	304.337	+	21.4248i	0.654829	+	0.0460989i
$61$	187.285	+	324.386i	0.393104	+	0.680876i	0.992857	−	0.119309i	$-0.0380679\pi$
$61$	187.285	+	324.386i	0.393104	+	0.680876i	−0.599753	+	0.800185i	$0.704735\pi$
$62$	−44.7838	−	44.7838i	−0.0917346	−	0.0917346i
$63$	−515.089	−	676.522i	−1.03008	−	1.35292i
$64$		−	261.998i		−	0.511716i
$65$	−312.369	+	537.366i	−0.596071	+	1.02542i
$66$	−20.7596	+	307.870i	−0.0387170	+	0.574185i
$67$	−29.6904	−	110.806i	−0.0541382	−	0.202046i	0.933559	−	0.358423i	$-0.116685\pi$
$67$	−29.6904	−	110.806i	−0.0541382	−	0.202046i	−0.987698	+	0.156376i	$0.950019\pi$
$68$	57.5724	+	214.863i	0.102672	+	0.383176i
$69$	36.8879	−	547.058i	0.0643592	−	0.954465i
$70$	149.410	+	564.268i	0.255112	+	0.963471i
$71$		−	921.281i		−	1.53994i	−0.638079	−	0.769971i	$-0.720271\pi$
$71$		−	921.281i		−	1.53994i	0.638079	−	0.769971i	$-0.279729\pi$
$72$	−588.372	+	75.2138i	−0.963060	+	0.123111i
$73$	373.434	+	373.434i	0.598729	+	0.598729i	0.939974	−	0.341246i	$-0.110849\pi$
$73$	373.434	+	373.434i	0.598729	+	0.598729i	−0.341246	+	0.939974i	$0.610849\pi$
$74$	−88.1187	−	152.626i	−0.138427	−	0.239762i
$75$	−213.564	+	613.405i	−0.328804	+	0.944398i
$76$	−46.5016	+	80.5432i	−0.0701856	+	0.121565i
$77$	1089.63	−	291.966i	1.61266	−	0.432111i
$78$	154.791	−	453.200i	0.224700	−	0.657883i
$79$	−492.922	+	284.589i	−0.702000	+	0.405300i	−0.808092	−	0.589056i	$-0.799500\pi$
$79$	−492.922	+	284.589i	−0.702000	+	0.405300i	0.106092	+	0.994356i	$0.466166\pi$
$80$	−60.3429	−	16.3601i	−0.0843317	−	0.0228639i
$81$	183.385	+	705.557i	0.251556	+	0.967843i
$82$	171.723	−	171.723i	0.231264	−	0.231264i
$83$	439.165	+	117.674i	0.580779	+	0.155619i	0.537235	−	0.843432i	$-0.319469\pi$
$83$	439.165	+	117.674i	0.580779	+	0.155619i	0.0435432	+	0.999052i	$0.486135\pi$
$84$	378.640	+	771.455i	0.491822	+	1.00205i
$85$	−473.565	−	1.39927i	−0.604298	−	0.00178556i
$86$	−781.941	−	451.454i	−0.980452	−	0.566065i
$87$	53.3777	+	271.006i	0.0657780	+	0.333965i
$88$	203.674	−	760.121i	0.246724	−	0.920786i
$89$	−148.257			−0.176575			−0.0882874	−	0.996095i	$-0.528139\pi$
$89$	−148.257			−0.176575			−0.0882874	+	0.996095i	$0.528139\pi$
$90$	68.6496	−	495.717i	0.0804033	−	0.580591i
$91$	−1750.79			−2.01684
$92$	−143.425	+	535.269i	−0.162533	+	0.606583i
$93$	149.492	−	130.605i	0.166683	−	0.145625i
$94$	239.720	+	138.402i	0.263034	+	0.151863i
$95$	−139.592	−	140.419i	−0.150756	−	0.151649i
$96$	959.224	+	64.6801i	1.01980	+	0.0687644i
$97$	−312.391	−	83.7049i	−0.326995	−	0.0876180i	0.0915871	−	0.995797i	$-0.470806\pi$
$97$	−312.391	−	83.7049i	−0.326995	−	0.0876180i	−0.418582	+	0.908179i	$0.637473\pi$
$98$	−760.526	+	760.526i	−0.783926	+	0.783926i
$99$	−958.396	−	129.839i	−0.972954	−	0.131811i
$100$	331.579	−	566.553i	0.331579	−	0.566553i
$101$	−225.111	+	129.968i	−0.221776	+	0.128043i	−0.606773	−	0.794875i	$-0.707536\pi$
$101$	−225.111	+	129.968i	−0.221776	+	0.128043i	0.384996	+	0.922918i	$0.374203\pi$
$102$	358.000	−	70.5121i	0.347523	−	0.0684484i
$103$	1135.69	−	304.307i	1.08643	−	0.291109i	0.329205	−	0.944259i	$-0.393219\pi$
$103$	1135.69	−	304.307i	1.08643	−	0.291109i	0.757229	+	0.653149i	$0.226553\pi$
$104$	−610.670	+	1057.71i	−0.575780	+	0.997280i
$105$	−1796.09	+	348.250i	−1.66934	+	0.323673i
$106$	−200.160	−	346.687i	−0.183408	−	0.317671i
$107$	832.828	+	832.828i	0.752453	+	0.752453i	0.974937	−	0.222483i	$-0.0714162\pi$
$107$	832.828	+	832.828i	0.752453	+	0.752453i	−0.222483	+	0.974937i	$0.571416\pi$
$108$	−44.0451	−	735.461i	−0.0392430	−	0.655276i
$109$			494.550i			0.434581i	0.976107	+	0.217290i	$0.0697219\pi$
$109$			494.550i			0.434581i	−0.976107	+	0.217290i	$0.930278\pi$
$110$	574.001	+	333.665i	0.497535	+	0.289216i
$111$	495.874	−	243.382i	0.424021	−	0.208115i
$112$	−45.5800	−	170.107i	−0.0384545	−	0.143514i
$113$	−426.881	−	1593.14i	−0.355377	−	1.32629i	−0.880009	−	0.474957i	$-0.842464\pi$
$113$	−426.881	−	1593.14i	−0.355377	−	1.32629i	0.524632	−	0.851329i	$-0.324203\pi$
$114$	126.686	+	84.9935i	0.104081	+	0.0698278i
$115$	−1019.95	−	592.894i	−0.827051	−	0.480762i
$116$		−	279.160i		−	0.223443i
$117$	1384.61	+	579.627i	1.09408	+	0.458004i
$118$	65.7698	+	65.7698i	0.0513102	+	0.0513102i
$119$	−666.962	−	1155.21i	−0.513784	−	0.889900i
$120$	−416.082	+	1206.55i	−0.316524	+	0.917853i
$121$	−23.9492	+	41.4813i	−0.0179934	+	0.0311655i
$122$	−599.813	+	160.719i	−0.445119	+	0.119269i
$123$	500.804	+	573.225i	0.367122	+	0.420211i
$124$	−173.747	+	100.313i	−0.125830	+	0.0726482i
$125$	979.413	+	996.933i	0.700811	+	0.713347i
$126$	1304.36	−	534.552i	0.922232	−	0.377950i
$127$	944.231	−	944.231i	0.659740	−	0.659740i	−0.295579	−	0.955318i	$-0.595512\pi$
$127$	944.231	−	944.231i	0.659740	−	0.659740i	0.955318	+	0.295579i	$0.0955124\pi$
$128$	−1010.19	−	270.680i	−0.697571	−	0.186914i
$129$	1576.68	−	2350.10i	1.07611	−	1.60399i
$130$	−726.476	−	730.782i	−0.490124	−	0.493029i
$131$	1480.35	+	854.679i	0.987317	+	0.570028i	0.904471	−	0.426535i	$-0.140266\pi$
$131$	1480.35	+	854.679i	0.987317	+	0.570028i	0.0828457	+	0.996562i	$0.473599\pi$
$132$	925.005	+	315.935i	0.609935	+	0.208323i
$133$	144.347	−	538.711i	0.0941089	−	0.351219i
$134$	190.178			0.122603
$135$	1535.73	+	319.211i	0.979074	+	0.203506i
$136$	−930.539			−0.586714
$137$	−369.776	+	1380.02i	−0.230599	+	0.860608i	0.749484	+	0.662022i	$0.230302\pi$
$137$	−369.776	+	1380.02i	−0.230599	+	0.860608i	−0.980083	+	0.198586i	$0.936365\pi$
$138$	860.199	+	293.801i	0.530616	+	0.181232i
$139$	304.149	+	175.600i	0.185594	+	0.107153i	0.589918	−	0.807463i	$-0.299160\pi$
$139$	304.149	+	175.600i	0.185594	+	0.107153i	−0.404324	+	0.914616i	$0.632493\pi$
$140$	1849.05	+	5.46352i	1.11624	+	0.00329823i
$141$	−483.362	+	720.469i	−0.288698	+	0.430315i
$142$	1475.28	+	395.301i	0.871853	+	0.233612i
$143$	−1408.13	+	1408.13i	−0.823454	+	0.823454i
$144$	−20.2697	+	149.619i	−0.0117301	+	0.0865852i
$145$	573.608	+	155.516i	0.328521	+	0.0890681i
$146$	−758.228	+	437.763i	−0.429804	+	0.248148i
$147$	−2217.95	−	2538.69i	−1.24445	−	1.42441i
$148$	−539.254	+	144.493i	−0.299503	+	0.0802515i
$149$	−817.396	+	1415.77i	−0.449421	+	0.778419i	−0.998348	−	0.0574504i	$-0.981703\pi$
$149$	−817.396	+	1415.77i	−0.449421	+	0.778419i	0.548928	+	0.835870i	$0.315036\pi$
$150$	−890.634	−	605.188i	−0.484800	−	0.329423i
$151$	−238.948	−	413.869i	−0.128777	−	0.223048i	0.794426	−	0.607361i	$-0.207772\pi$
$151$	−238.948	−	413.869i	−0.128777	−	0.223048i	−0.923203	+	0.384313i	$0.874438\pi$
$152$	−275.106	−	275.106i	−0.146803	−	0.146803i
$153$	145.016	+	1134.41i	0.0766263	+	0.599423i
$154$			1870.15i			0.978576i
$155$	−109.327	−	412.892i	−0.0566542	−	0.213963i
$156$	−1259.80	−	845.198i	−0.646569	−	0.433782i
$157$	−447.091	−	1668.57i	−0.227272	−	0.848192i	−0.981481	−	0.191557i	$-0.938646\pi$
$157$	−447.091	−	1668.57i	−0.227272	−	0.848192i	0.754209	−	0.656634i	$-0.228020\pi$
$158$	−244.221	−	911.447i	−0.122970	−	0.458929i
$159$	1126.37	−	552.836i	0.561804	−	0.275741i
$160$	1039.59	−	1788.40i	0.513669	−	0.883661i
$161$		−	3323.09i		−	1.62668i
$162$	−1208.52	−	9.07787i	−0.586115	−	0.00440262i
$163$	2222.14	+	2222.14i	1.06780	+	1.06780i	0.997528	+	0.0702721i	$0.0223867\pi$
$163$	2222.14	+	2222.14i	1.06780	+	1.06780i	0.0702721	+	0.997528i	$0.477613\pi$
$164$	−384.650	−	666.234i	−0.183147	−	0.317220i
$165$	−1164.48	+	1724.66i	−0.549421	+	0.813726i
$166$	−376.872	+	652.762i	−0.176211	+	0.305206i
$167$	−1630.68	+	436.939i	−0.755603	+	0.202463i	−0.616002	−	0.787744i	$-0.711249\pi$
$167$	−1630.68	+	436.939i	−0.755603	+	0.202463i	−0.139601	+	0.990208i	$0.544582\pi$
$168$	−3527.20	+	694.721i	−1.61982	+	0.319041i
$169$	773.962	−	446.847i	0.352281	−	0.203390i
$170$	205.437	−	757.738i	0.0926841	−	0.341858i
$171$	−292.506	+	378.252i	−0.130810	+	0.169156i
$172$	−2022.46	+	2022.46i	−0.896576	+	0.896576i
$173$	2637.73	+	706.777i	1.15921	+	0.310609i	0.786649	−	0.617400i	$-0.211814\pi$
$173$	2637.73	+	706.777i	1.15921	+	0.310609i	0.372558	+	0.928009i	$0.378481\pi$
$174$	−456.877	−	30.8070i	−0.199056	−	0.0134223i
$175$	−1041.30	+	3796.32i	−0.449801	+	1.63986i
$176$	−173.474	−	100.155i	−0.0742959	−	0.0428948i
$177$	−219.544	+	191.807i	−0.0932315	+	0.0814526i
$178$	63.6136	−	237.409i	0.0267868	−	0.0999696i
$179$	484.184			0.202177			0.101088	−	0.994877i	$-0.467768\pi$
$179$	484.184			0.202177			0.101088	+	0.994877i	$0.467768\pi$
$180$	−1460.52	−	616.481i	−0.604781	−	0.255277i
$181$	2651.62			1.08891			0.544456	−	0.838789i	$-0.316736\pi$
$181$	2651.62			1.08891			0.544456	+	0.838789i	$0.316736\pi$
$182$	751.224	−	2803.61i	0.305958	−	1.14185i
$183$	−376.123	−	1909.63i	−0.151933	−	0.771388i
$184$	−2007.59	−	1159.08i	−0.804357	−	0.464396i
$185$	3.51183	−	1188.53i	0.00139565	−	0.472339i
$186$	144.999	+	295.427i	0.0571606	+	0.116461i
$187$	−1465.55	−	392.693i	−0.573110	−	0.153564i
$188$	620.026	−	620.026i	0.240532	−	0.240532i
$189$	1396.61	+	4191.71i	0.537505	+	1.61324i
$190$	284.755	−	163.283i	0.108728	−	0.0623464i
$191$	785.170	−	453.318i	0.297450	−	0.171733i	−0.343847	−	0.939026i	$-0.611730\pi$
$191$	785.170	−	453.318i	0.297450	−	0.171733i	0.641297	+	0.767293i	$0.278397\pi$
$192$	−440.022	+	1288.31i	−0.165395	+	0.484249i
$193$	−2622.33	+	702.651i	−0.978028	+	0.262062i	−0.712214	−	0.701963i	$-0.752307\pi$
$193$	−2622.33	+	702.651i	−0.978028	+	0.262062i	−0.265814	+	0.964024i	$0.585641\pi$
$194$	268.080	−	464.328i	0.0992115	−	0.171839i
$195$	2438.49	−	2117.74i	0.895509	−	0.777717i
$196$	1703.53	+	2950.61i	0.620821	+	1.07529i
$197$	749.196	+	749.196i	0.270954	+	0.270954i	0.829484	−	0.558530i	$-0.188634\pi$
$197$	749.196	+	749.196i	0.270954	+	0.270954i	−0.558530	+	0.829484i	$0.688634\pi$
$198$	619.143	−	1479.01i	0.222225	−	0.530851i
$199$		−	4679.84i		−	1.66706i	−0.552473	−	0.833531i	$-0.686316\pi$
$199$		−	4679.84i		−	1.66706i	0.552473	−	0.833531i	$-0.313684\pi$
$200$	1930.29	+	1953.24i	0.682459	+	0.690573i
$201$	−40.1021	+	594.725i	−0.0140726	+	0.208700i
$202$	−111.533	−	416.247i	−0.0388487	−	0.144985i
$203$	433.275	+	1617.00i	0.149803	+	0.559071i
$204$	77.7616	−	1153.23i	0.0266882	−	0.395794i
$205$	1583.23	−	419.216i	0.539404	−	0.142826i
$206$			1949.20i			0.659257i
$207$	−1100.16	+	2628.07i	−0.369404	+	0.882432i
$208$	219.830	+	219.830i	0.0732809	+	0.0732809i
$209$	−317.181	−	549.374i	−0.104975	−	0.181823i
$210$	212.996	−	3025.58i	0.0699910	−	0.994213i
$211$	−2264.65	+	3922.50i	−0.738887	+	1.27979i	0.214109	+	0.976810i	$0.431315\pi$
$211$	−2264.65	+	3922.50i	−0.738887	+	1.27979i	−0.952997	+	0.302981i	$0.902018\pi$
$212$	−1224.90	+	328.212i	−0.396824	+	0.106329i
$213$	−1547.28	+	4530.17i	−0.497736	+	1.45729i
$214$	−1690.99	+	976.293i	−0.540157	+	0.311860i
$215$	−3028.99	−	5282.35i	−0.960817	−	1.67560i
$216$	3019.49	+	618.318i	0.951160	+	0.194774i
$217$	850.718	−	850.718i	0.266131	−	0.266131i
$218$	−791.944	−	212.201i	−0.246042	−	0.0659268i
$219$	−1209.09	−	2463.45i	−0.373072	−	0.760111i
$220$	1491.56	−	1482.77i	0.457096	−	0.454403i
$221$	2039.32	+	1177.40i	0.620721	+	0.358373i
$222$	176.968	+	898.494i	0.0535015	+	0.271635i
$223$	81.6646	−	304.776i	0.0245232	−	0.0915217i	−0.952580	−	0.304289i	$-0.901581\pi$
$223$	81.6646	−	304.776i	0.0245232	−	0.0915217i	0.977103	+	0.212768i	$0.0682477\pi$
$224$	5826.77			1.73803
$225$	2080.35	−	2657.58i	0.616401	−	0.787433i
$226$	2734.33			0.804801
$227$	1211.60	−	4521.76i	0.354259	−	1.32211i	−0.527156	−	0.849769i	$-0.676742\pi$
$227$	1211.60	−	4521.76i	0.354259	−	1.32211i	0.881415	−	0.472343i	$-0.156592\pi$
$228$	363.931	−	317.952i	0.105710	−	0.0923548i
$229$	3088.47	+	1783.13i	0.891231	+	0.514552i	0.874345	−	0.485305i	$-0.161291\pi$
$229$	3088.47	+	1783.13i	0.891231	+	0.514552i	0.0168860	+	0.999857i	$0.494625\pi$
$230$	1387.06	−	1378.89i	0.397653	−	0.395310i
$231$	−5848.34	−	394.351i	−1.66577	−	0.112322i
$232$	1128.01	+	302.250i	0.319214	+	0.0855332i
$233$	−32.0022	+	32.0022i	−0.00899801	+	0.00899801i	−0.711591	−	0.702593i	$-0.752025\pi$
$233$	−32.0022	+	32.0022i	−0.00899801	+	0.00899801i	0.702593	+	0.711591i	$0.252025\pi$
$234$	−1522.29	+	1968.53i	−0.425278	+	0.549944i
$235$	928.599	+	1619.41i	0.257766	+	0.449527i
$236$	255.166	−	147.320i	0.0703810	−	0.0406345i
$237$	2901.78	−	571.538i	0.795320	−	0.156647i
$238$	2136.07	−	572.358i	0.581768	−	0.155884i
$239$	−171.781	+	297.534i	−0.0464921	+	0.0805267i	−0.888335	−	0.459196i	$-0.848138\pi$
$239$	−171.781	+	297.534i	−0.0464921	+	0.0805267i	0.841843	+	0.539723i	$0.181471\pi$
$240$	269.244	+	181.791i	0.0724152	+	0.0488941i
$241$	−2279.51	−	3948.22i	−0.609277	−	1.05530i	−0.991360	−	0.131171i	$-0.958126\pi$
$241$	−2279.51	−	3948.22i	−0.609277	−	1.05530i	0.382082	−	0.924128i	$-0.375207\pi$
$242$	−56.1496	−	56.1496i	−0.0149150	−	0.0149150i
$243$	283.226	−	3777.39i	0.0747692	−	0.997201i
$244$			1967.09i			0.516106i
$245$	−7011.80	+	1856.62i	−1.82844	+	0.484143i
$246$	−1132.81	+	556.000i	−0.293600	+	0.144103i
$247$	254.819	+	950.996i	0.0656426	+	0.244981i
$248$	−217.220	−	810.677i	−0.0556189	−	0.207573i
$249$	−1961.85	−	1316.20i	−0.499306	−	0.334984i
$250$	−2016.67	+	1140.61i	−0.510183	+	0.288555i
$251$			6166.99i			1.55083i	0.631455	+	0.775413i	$0.282458\pi$
$251$			6166.99i			1.55083i	−0.631455	+	0.775413i	$0.717542\pi$
$252$	−566.220	−	4429.35i	−0.141542	−	1.10723i
$253$	−2672.71	−	2672.71i	−0.664158	−	0.664158i
$254$	1106.89	+	1917.18i	0.273434	+	0.473602i
$255$	2326.29	+	802.226i	0.571285	+	0.197009i
$256$	1914.90	−	3316.70i	0.467504	−	0.809740i
$257$	−5581.97	+	1495.68i	−1.35484	+	0.363028i	−0.861919	−	0.507047i	$-0.830737\pi$
$257$	−5581.97	+	1495.68i	−1.35484	+	0.363028i	−0.492920	+	0.870075i	$0.664071\pi$
$258$	3086.79	+	3533.17i	0.744865	+	0.852580i
$259$	2899.30	−	1673.91i	0.695575	−	0.401590i
$260$	−2831.68	+	1623.73i	−0.675435	+	0.387306i
$261$	192.680	−	1422.25i	0.0456957	−	0.337300i
$262$	−2003.82	+	2003.82i	−0.472505	+	0.472505i
$263$	2387.18	+	639.642i	0.559694	+	0.149970i	0.527566	−	0.849514i	$-0.323105\pi$
$263$	2387.18	+	639.642i	0.559694	+	0.149970i	0.0321282	+	0.999484i	$0.489772\pi$
$264$	−2278.13	+	3395.64i	−0.531095	+	0.791617i
$265$	7.97705	−	2699.72i	0.00184916	−	0.625822i
$266$	800.723	+	462.298i	0.184570	+	0.106561i
$267$	729.014	+	248.995i	0.167097	+	0.0570720i
$268$	155.922	−	581.909i	0.0355390	−	0.132633i
$269$	−5983.06			−1.35611			−0.678055	−	0.735012i	$-0.737177\pi$
$269$	−5983.06			−1.35611			−0.678055	+	0.735012i	$0.737177\pi$
$270$	−1170.12	+	2322.27i	−0.263744	+	0.523440i
$271$	228.531			0.0512260			0.0256130	−	0.999672i	$-0.491846\pi$
$271$	228.531			0.0512260			0.0256130	+	0.999672i	$0.491846\pi$
$272$	−61.3049	+	228.793i	−0.0136660	+	0.0510023i
$273$	8609.05	+	2940.42i	1.90858	+	0.651876i
$274$	−2051.22	−	1184.28i	−0.452259	−	0.261112i
$275$	2215.82	+	3890.84i	0.485887	+	0.853186i
$276$	1604.23	−	2391.17i	0.349867	−	0.521491i
$277$	−3273.32	−	877.084i	−0.710017	−	0.190249i	−0.114304	−	0.993446i	$-0.536464\pi$
$277$	−3273.32	−	877.084i	−0.710017	−	0.190249i	−0.595713	+	0.803197i	$0.703131\pi$
$278$	−411.700	+	411.700i	−0.0888206	+	0.0888206i
$279$	−954.436	+	391.147i	−0.204805	+	0.0839332i
$280$	−2024.07	+	7465.63i	−0.432005	+	1.59342i
$281$	−7217.53	+	4167.04i	−1.53225	+	0.884644i	−0.532990	+	0.846122i	$0.678932\pi$
$281$	−7217.53	+	4167.04i	−1.53225	+	0.884644i	−0.999258	+	0.0385220i	$0.987735\pi$
$282$	−946.317	−	1083.16i	−0.199831	−	0.228729i
$283$	−8023.23	+	2149.82i	−1.68527	+	0.451567i	−0.969162	−	0.246423i	$-0.920745\pi$
$283$	−8023.23	+	2149.82i	−1.68527	+	0.451567i	−0.716107	+	0.697990i	$0.754078\pi$
$284$	2419.10	−	4190.00i	0.505447	−	0.875461i
$285$	450.575	+	924.918i	0.0936484	+	0.192237i
$286$	−1650.70	−	2859.10i	−0.341287	−	0.591126i
$287$	3262.08	+	3262.08i	0.670921	+	0.670921i
$288$	−4608.11	−	1929.05i	−0.942832	−	0.394689i
$289$		−	3118.88i		−	0.634821i
$290$	−495.156	+	851.813i	−0.100264	+	0.172483i
$291$	1395.52	+	936.254i	0.281124	+	0.188605i
$292$	717.822	+	2678.95i	0.143861	+	0.536896i
$293$	−2384.38	−	8898.62i	−0.475416	−	1.77428i	−0.619806	−	0.784755i	$-0.712789\pi$
$293$	−2384.38	−	8898.62i	−0.475416	−	1.77428i	0.144390	−	0.989521i	$-0.453878\pi$
$294$	5016.99	−	2462.40i	0.995227	−	0.488470i
$295$	160.559	+	606.376i	0.0316885	+	0.119677i
$296$		−	2335.43i		−	0.458594i
$297$	4494.61	+	2248.06i	0.878127	+	0.439211i
$298$	−1916.41	−	1916.41i	−0.372532	−	0.372532i
$299$	2933.15	+	5080.37i	0.567320	+	0.982627i
$300$	−2581.97	+	2229.00i	−0.496901	+	0.428971i
$301$	8575.88	−	14853.9i	1.64221	−	2.84439i
$302$	765.273	−	205.054i	0.145816	−	0.0390714i
$303$	1325.21	−	261.014i	0.251258	−	0.0494881i
$304$	−85.7651	+	49.5165i	−0.0161808	+	0.00934199i
$305$	−4041.89	−	1095.83i	−0.758814	−	0.205729i
$306$	−1878.80	−	254.531i	−0.350993	−	0.0475509i
$307$	−1803.17	+	1803.17i	−0.335219	+	0.335219i	−0.854564	−	0.519346i	$-0.826176\pi$
$307$	−1803.17	+	1803.17i	−0.335219	+	0.335219i	0.519346	+	0.854564i	$0.326176\pi$
$308$	5722.30	+	1533.29i	1.05863	+	0.283659i
$309$	−6095.54	−	411.020i	−1.12221	−	0.0756702i
$310$	708.091	+	2.09224i	0.129732	+	0.000383327i
$311$	−250.629	−	144.701i	−0.0456974	−	0.0263834i	0.476977	−	0.878916i	$-0.341732\pi$
$311$	−250.629	−	144.701i	−0.0456974	−	0.0263834i	−0.522675	+	0.852532i	$0.675066\pi$
$312$	4779.22	−	4175.42i	0.867213	−	0.757649i
$313$	−505.039	+	1884.83i	−0.0912028	+	0.340373i	−0.996416	−	0.0845834i	$-0.973044\pi$
$313$	−505.039	+	1884.83i	−0.0912028	+	0.340373i	0.905214	+	0.424957i	$0.139711\pi$
$314$	2863.78			0.514690
$315$	9416.70	+	1304.08i	1.68435	+	0.233258i
$316$	−2989.09			−0.532118
$317$	1160.15	−	4329.75i	0.205554	−	0.767139i	−0.783726	−	0.621107i	$-0.786683\pi$
$317$	1160.15	−	4329.75i	0.205554	−	0.767139i	0.989280	−	0.146032i	$-0.0466502\pi$
$318$	401.979	+	2040.91i	0.0708864	+	0.359901i
$319$	1649.01	+	952.056i	0.289426	+	0.167100i
$320$	2065.15	+	2077.39i	0.360767	+	0.362905i
$321$	−2696.50	−	5493.94i	−0.468860	−	0.955271i
$322$	5321.40	+	1425.86i	0.920962	+	0.246771i
$323$	−530.418	+	530.418i	−0.0913722	+	0.0913722i
$324$	−1018.62	+	3690.42i	−0.174660	+	0.632788i
$325$	−1758.90	−	6722.97i	−0.300204	−	1.14746i
$326$	−4511.87	+	2604.93i	−0.766533	+	0.442558i
$327$	830.590	−	2431.83i	0.140464	−	0.411255i
$328$	3108.54	−	832.931i	0.523294	−	0.140216i
$329$	−2629.11	+	4553.75i	−0.440570	+	0.763089i
$330$	−2262.12	−	2604.74i	−0.377351	−	0.434504i
$331$	4301.37	+	7450.20i	0.714274	+	1.23716i	0.963239	+	0.268647i	$0.0865765\pi$
$331$	4301.37	+	7450.20i	0.714274	+	1.23716i	−0.248964	+	0.968513i	$0.580090\pi$
$332$	1688.34	+	1688.34i	0.279096	+	0.279096i
$333$	−2847.09	+	363.954i	−0.468528	+	0.0598936i
$334$		−	2798.76i		−	0.458506i
$335$	1108.82	+	644.555i	0.180840	+	0.105122i
$336$	−61.5638	+	913.008i	−0.00999577	+	0.148240i
$337$	1745.21	+	6513.21i	0.282100	+	1.05281i	0.950933	+	0.309397i	$0.100127\pi$
$337$	1745.21	+	6513.21i	0.282100	+	1.05281i	−0.668833	+	0.743412i	$0.733206\pi$
$338$	383.465	+	1431.11i	0.0617093	+	0.230302i
$339$	−576.579	+	8550.82i	−0.0923760	+	1.36996i
$340$	−2150.11	−	1249.85i	−0.342959	−	0.199361i
$341$		−	1368.44i		−	0.217317i
$342$	−480.202	−	630.702i	−0.0759250	−	0.0997206i
$343$	−6808.97	−	6808.97i	−1.07187	−	1.07187i
$344$	−5982.49	−	10362.0i	−0.937657	−	1.62407i
$345$	4019.59	+	4628.40i	0.627268	+	0.722274i
$346$	−2263.58	+	3920.64i	−0.351708	+	0.609176i
$347$	11379.2	−	3049.05i	1.76043	−	0.471705i	0.773626	−	0.633643i	$-0.218441\pi$
$347$	11379.2	−	3049.05i	1.76043	−	0.471705i	0.986801	+	0.161938i	$0.0517744\pi$
$348$	−468.846	+	1372.70i	−0.0722206	+	0.211450i
$349$	−6061.28	+	3499.48i	−0.929664	+	0.536742i	−0.886705	−	0.462335i	$-0.847012\pi$
$349$	−6061.28	+	3499.48i	−0.929664	+	0.536742i	−0.0429588	+	0.999077i	$0.513678\pi$
$350$	−5632.40	−	3296.40i	−0.860185	−	0.503429i
$351$	−5835.00	−	5175.60i	−0.887320	−	0.787046i
$352$	4686.39	−	4686.39i	0.709618	−	0.709618i
$353$	6870.23	+	1840.87i	1.03588	+	0.277563i	0.736405	−	0.676541i	$-0.236522\pi$
$353$	6870.23	+	1840.87i	1.03588	+	0.277563i	0.299475	+	0.954104i	$0.403189\pi$
$354$	−212.947	−	433.866i	−0.0319718	−	0.0651404i
$355$	7261.81	+	7304.85i	1.08568	+	1.09212i
$356$	−674.273	−	389.292i	−0.100383	−	0.0579563i
$357$	1339.46	+	6800.62i	0.198576	+	1.00820i
$358$	−207.753	+	775.344i	−0.0306706	+	0.114464i
$359$	10744.0			1.57951			0.789755	−	0.613422i	$-0.210208\pi$
$359$	10744.0			1.57951			0.789755	+	0.613422i	$0.210208\pi$
$360$	4072.36	−	5234.10i	0.596200	−	0.766281i
$361$	6545.37			0.954275
$362$	−1137.75	+	4246.15i	−0.165190	+	0.616498i
$363$	187.432	−	163.751i	0.0271009	−	0.0236769i
$364$	−7962.60	−	4597.21i	−1.14658	−	0.661976i
$365$	−5904.49	−	17.4464i	−0.846726	−	0.00250188i
$366$	3219.36	+	217.080i	0.459777	+	0.0310026i
$367$	−1991.06	−	533.504i	−0.283195	−	0.0758820i	0.114425	−	0.993432i	$-0.463497\pi$
$367$	−1991.06	−	533.504i	−0.283195	−	0.0758820i	−0.397621	+	0.917550i	$0.630164\pi$
$368$	−417.248	+	417.248i	−0.0591048	+	0.0591048i
$369$	−1499.85	−	3659.78i	−0.211597	−	0.516316i
$370$	1901.74	+	515.597i	0.267207	+	0.0724449i
$371$	6585.70	−	3802.25i	0.921597	−	0.532084i
$372$	1022.83	−	201.458i	0.142557	−	0.0280783i
$373$	7625.58	−	2043.27i	1.05855	−	0.283637i	0.312767	−	0.949830i	$-0.398744\pi$
$373$	7625.58	−	2043.27i	1.05855	−	0.283637i	0.745779	+	0.666193i	$0.232077\pi$
$374$	1257.67	−	2178.35i	0.173884	−	0.301176i
$375$	−3141.68	−	6547.08i	−0.432629	−	0.901572i
$376$	1834.05	+	3176.67i	0.251553	+	0.435703i
$377$	−2089.66	−	2089.66i	−0.285472	−	0.285472i
$378$	−7311.61	+	437.876i	−0.994891	+	0.0595818i
$379$			7547.27i			1.02289i	0.859315	+	0.511447i	$0.170890\pi$
$379$			7547.27i			1.02289i	−0.859315	+	0.511447i	$0.829110\pi$
$380$	−266.153	−	1005.17i	−0.0359299	−	0.135695i
$381$	−6228.84	+	3057.20i	−0.837567	+	0.411089i
$382$	389.018	+	1451.83i	0.0521044	+	0.194456i
$383$	−1444.78	−	5392.00i	−0.192754	−	0.719369i	−0.992837	−	0.119479i	$-0.961878\pi$
$383$	−1444.78	−	5392.00i	−0.192754	−	0.719369i	0.800082	−	0.599890i	$-0.204789\pi$
$384$	4512.76	+	3027.60i	0.599715	+	0.402348i
$385$	−6338.34	+	10903.8i	−0.839043	+	1.44340i
$386$		−	4500.74i		−	0.593475i
$387$	−11699.9	+	8908.00i	−1.53679	+	1.17008i
$388$	−1200.97	−	1200.97i	−0.157139	−	0.157139i
$389$	−3919.49	−	6788.76i	−0.510864	−	0.884842i	−0.999921	−	0.0125902i	$-0.995992\pi$
$389$	−3919.49	−	6788.76i	−0.510864	−	0.884842i	0.489057	−	0.872252i	$-0.337341\pi$
$390$	2344.92	+	4813.54i	0.304461	+	0.624982i
$391$	−2234.77	+	3870.74i	−0.289047	+	0.500643i
$392$	−13767.1	+	3688.87i	−1.77383	+	0.475297i
$393$	−5843.81	−	6688.89i	−0.750080	−	0.858549i
$394$	−1521.18	+	878.255i	−0.194508	+	0.112299i
$395$	1665.17	−	6141.87i	0.212111	−	0.782356i
$396$	−4017.87	−	3107.06i	−0.509863	−	0.394283i
$397$	488.460	−	488.460i	0.0617509	−	0.0617509i	−0.675557	−	0.737308i	$-0.736097\pi$
$397$	488.460	−	488.460i	0.0617509	−	0.0617509i	0.737308	+	0.675557i	$0.236097\pi$
$398$	7494.03	+	2008.02i	0.943823	+	0.252897i
$399$	−1614.55	+	2406.55i	−0.202578	+	0.301950i
$400$	607.415	−	345.921i	0.0759268	−	0.0432401i
$401$	7854.07	+	4534.55i	0.978088	+	0.564699i	0.901692	−	0.432378i	$-0.142325\pi$
$401$	7854.07	+	4534.55i	0.978088	+	0.564699i	0.0763957	+	0.997078i	$0.475659\pi$
$402$	−935.151	−	319.401i	−0.116023	−	0.0396275i
$403$	−549.693	+	2051.48i	−0.0679458	+	0.253577i
$404$	−1365.08			−0.168107
$405$	−7015.47	−	4148.88i	−0.860745	−	0.509036i
$406$	−2775.28			−0.339249
$407$	985.563	−	3678.17i	0.120031	−	0.447961i
$408$	4575.69	+	1562.83i	0.555222	+	0.189636i
$409$	1057.59	+	610.597i	0.127859	+	0.0738193i	0.562565	−	0.826753i	$-0.309815\pi$
$409$	1057.59	+	610.597i	0.127859	+	0.0738193i	−0.434706	+	0.900572i	$0.643148\pi$
$410$	−8.02270	+	2715.17i	−0.000966373	+	0.327056i
$411$	4136.01	−	6164.88i	0.496385	−	0.739881i
$412$	5964.18	+	1598.10i	0.713189	+	0.191098i
$413$	−1249.37	+	1249.37i	−0.148856	+	0.148856i
$414$	−3736.38	−	2889.38i	−0.443558	−	0.343008i
$415$	−4409.69	+	2528.59i	−0.521598	+	0.299093i
$416$	−8908.03	+	5143.06i	−1.04989	+	0.606152i
$417$	−1200.66	−	1374.28i	−0.140999	−	0.161389i
$418$	1015.83	−	272.191i	0.118866	−	0.0318500i
$419$	−8196.06	+	14196.0i	−0.955618	+	1.65518i	−0.222670	+	0.974894i	$0.571477\pi$
$419$	−8196.06	+	14196.0i	−0.955618	+	1.65518i	−0.732948	+	0.680285i	$0.761856\pi$
$420$	−9083.08	−	3132.32i	−1.05526	−	0.363909i
$421$	−815.167	−	1411.91i	−0.0943677	−	0.163450i	0.814977	−	0.579494i	$-0.196750\pi$
$421$	−815.167	−	1411.91i	−0.0943677	−	0.163450i	−0.909345	+	0.416044i	$0.863416\pi$
$422$	−5309.54	−	5309.54i	−0.612475	−	0.612475i
$423$	3586.83	−	2730.93i	0.412287	−	0.313906i
$424$		−	5304.87i		−	0.607611i
$425$	3765.93	−	3721.68i	0.429823	−	0.424772i
$426$	−6590.44	−	4421.51i	−0.749549	−	0.502871i
$427$	−3053.05	−	11394.1i	−0.346012	−	1.29134i
$428$	1600.88	+	5974.55i	0.180797	+	0.674745i
$429$	9289.08	−	4559.20i	1.04541	−	0.513101i
$430$	9758.53	−	2583.91i	1.09441	−	0.289784i
$431$			9676.25i			1.08141i	0.841212	+	0.540706i	$0.181843\pi$
$431$			9676.25i			1.08141i	−0.841212	+	0.540706i	$0.818157\pi$
$432$	350.954	−	701.672i	0.0390863	−	0.0781463i
$433$	6547.86	+	6547.86i	0.726720	+	0.726720i	0.969965	−	0.243245i	$-0.0782118\pi$
$433$	6547.86	+	6547.86i	0.726720	+	0.726720i	−0.243245	+	0.969965i	$0.578212\pi$
$434$	997.265	+	1727.31i	0.110300	+	0.191045i
$435$	−2559.39	−	1728.08i	−0.282099	−	0.190471i
$436$	−1298.59	+	2249.22i	−0.142640	+	0.247060i
$437$	−1805.04	+	483.660i	−0.197590	+	0.0529441i
$438$	4463.61	−	879.158i	0.486940	−	0.0959082i
$439$	14231.6	−	8216.60i	1.54723	−	0.893296i	0.548882	−	0.835900i	$-0.315054\pi$
$439$	14231.6	−	8216.60i	1.54723	−	0.893296i	0.998352	−	0.0573956i	$-0.0182796\pi$
$440$	4376.57	+	7632.43i	0.474192	+	0.826959i
$441$	6642.53	+	16208.4i	0.717259	+	1.75018i
$442$	−2760.45	+	2760.45i	−0.297061	+	0.297061i
$443$	−6857.35	−	1837.42i	−0.735446	−	0.197062i	−0.128393	−	0.991723i	$-0.540982\pi$
$443$	−6857.35	−	1837.42i	−0.735446	−	0.197062i	−0.607053	+	0.794661i	$0.707648\pi$
$444$	2894.32	+	195.163i	0.309365	+	0.0208604i
$445$	1175.53	−	1168.60i	0.125226	−	0.124488i
$446$	453.010	+	261.546i	0.0480957	+	0.0277680i
$447$	6397.11	−	5588.89i	0.676896	−	0.591377i
$448$	−2135.50	+	7969.80i	−0.225207	+	0.840486i
$449$	15813.2			1.66207			0.831037	−	0.556218i	$-0.187748\pi$
$449$	15813.2			1.66207			0.831037	+	0.556218i	$0.187748\pi$
$450$	3363.07	+	4471.67i	0.352303	+	0.468436i
$451$	5247.29			0.547861
$452$	2241.81	−	8366.55i	0.233287	−	0.870640i
$453$	479.877	+	2436.41i	0.0497717	+	0.252698i
$454$	6721.00	+	3880.37i	0.694785	+	0.401134i
$455$	13882.0	−	13800.2i	1.43033	−	1.42190i
$456$	890.728	+	1814.80i	0.0914741	+	0.186373i
$457$	−11690.9	−	3132.55i	−1.19666	−	0.320645i	−0.395147	−	0.918618i	$-0.629306\pi$
$457$	−11690.9	−	3132.55i	−1.19666	−	0.320645i	−0.801516	+	0.597973i	$0.795973\pi$
$458$	−4180.59	+	4180.59i	−0.426520	+	0.426520i
$459$	1192.15	−	5821.73i	0.121230	−	0.592015i
$460$	−3081.93	−	5374.68i	−0.312382	−	0.544773i
$461$	8677.59	−	5010.01i	0.876693	−	0.506159i	0.00712658	−	0.999975i	$-0.497732\pi$
$461$	8677.59	−	5010.01i	0.876693	−	0.506159i	0.869567	+	0.493816i	$0.164398\pi$
$462$	3140.88	−	9195.97i	0.316292	−	0.926051i
$463$	−8700.34	+	2331.25i	−0.873303	+	0.234001i	−0.667515	−	0.744596i	$-0.732642\pi$
$463$	−8700.34	+	2331.25i	−0.873303	+	0.234001i	−0.205787	+	0.978597i	$0.565975\pi$
$464$	148.630	−	257.434i	0.0148706	−	0.0257566i
$465$	−155.855	+	2213.91i	−0.0155433	+	0.220790i
$466$	−37.5150	−	64.9780i	−0.00372929	−	0.00645933i
$467$	−2385.09	−	2385.09i	−0.236336	−	0.236336i	0.578995	−	0.815331i	$-0.303445\pi$
$467$	−2385.09	−	2385.09i	−0.236336	−	0.236336i	−0.815331	+	0.578995i	$0.803445\pi$
$468$	4775.25	+	6271.86i	0.471659	+	0.619481i
$469$			3612.64i			0.355685i
$470$	−2991.67	+	792.149i	−0.293608	+	0.0777428i
$471$	−603.875	+	8955.64i	−0.0590767	+	0.876123i
$472$	319.011	+	1190.57i	0.0311095	+	0.116102i
$473$	−5049.29	−	18844.2i	−0.490838	−	1.83183i
$474$	−329.864	+	4891.98i	−0.0319645	+	0.474042i
$475$	2213.65	+	13.0818i	0.213830	+	0.00126365i
$476$		−	7005.24i		−	0.674547i
$477$	−6467.11	+	826.714i	−0.620773	+	0.0793556i
$478$	−402.746	−	402.746i	−0.0385380	−	0.0385380i
$479$	−49.6552	−	86.0054i	−0.00473654	−	0.00820394i	0.863647	−	0.504096i	$-0.168174\pi$
$479$	−49.6552	−	86.0054i	−0.00473654	−	0.00820394i	−0.868384	+	0.495892i	$0.834841\pi$
$480$	−8115.53	+	7048.04i	−0.771712	+	0.670203i
$481$	−2954.99	+	5118.19i	−0.280116	+	0.485176i
$482$	7300.53	−	1956.17i	0.689897	−	0.184857i
$483$	−5581.08	+	16340.4i	−0.525772	+	1.53937i
$484$	−217.843	+	125.772i	−0.0204586	+	0.0118118i
$485$	3136.74	−	1798.66i	0.293674	−	0.168398i
$486$	5927.37	+	2074.34i	0.553232	+	0.193609i
$487$	−752.120	+	752.120i	−0.0699831	+	0.0699831i	−0.741232	−	0.671249i	$-0.765758\pi$
$487$	−752.120	+	752.120i	−0.0699831	+	0.0699831i	0.671249	+	0.741232i	$0.265758\pi$
$488$	−7948.48	−	2129.79i	−0.737317	−	0.197564i
$489$	−7194.76	−	14658.9i	−0.665354	−	1.35562i
$490$	35.5308	−	12024.9i	0.00327575	−	1.10863i
$491$	−3533.78	−	2040.23i	−0.324801	−	0.187524i	0.328729	−	0.944424i	$-0.393380\pi$
$491$	−3533.78	−	2040.23i	−0.324801	−	0.187524i	−0.653531	+	0.756900i	$0.726713\pi$
$492$	772.491	+	3922.05i	0.0707857	+	0.359390i
$493$	582.753	−	2174.86i	0.0532371	−	0.198684i
$494$	−1632.21			−0.148657
$495$	8622.57	−	6524.87i	0.782941	−	0.592467i
$496$	−213.633			−0.0193395
$497$	−7509.19	+	28024.7i	−0.677733	+	2.52933i
$498$	2949.48	−	2576.84i	0.265400	−	0.231869i
$499$	−4377.28	−	2527.22i	−0.392693	−	0.226722i	0.290633	−	0.956835i	$-0.406134\pi$
$499$	−4377.28	−	2527.22i	−0.392693	−	0.226722i	−0.683326	+	0.730113i	$0.739467\pi$
$500$	1836.64	+	7105.81i	0.164274	+	0.635563i
$501$	8752.29	+	590.163i	0.780486	+	0.0526279i
$502$	−9875.46	−	2646.12i	−0.878014	−	0.235263i
$503$	−4080.19	+	4080.19i	−0.361683	+	0.361683i	−0.864432	−	0.502749i	$-0.832322\pi$
$503$	−4080.19	+	4080.19i	−0.361683	+	0.361683i	0.502749	+	0.864432i	$0.332322\pi$
$504$	18510.9	+	2507.77i	1.63600	+	0.221637i
$505$	760.465	−	2804.92i	0.0670104	−	0.247163i
$506$	5426.73	−	3133.12i	0.476774	−	0.275265i
$507$	−4556.24	+	897.401i	−0.399112	+	0.0786094i
$508$	6773.74	−	1815.02i	0.591607	−	0.158521i
$509$	−3668.96	+	6354.83i	−0.319497	+	0.553385i	−0.980383	−	0.197101i	$-0.936847\pi$
$509$	−3668.96	+	6354.83i	−0.319497	+	0.553385i	0.660886	+	0.750486i	$0.270181\pi$
$510$	−2282.79	+	3380.96i	−0.198204	+	0.293552i
$511$	−8315.80	−	14403.4i	−0.719901	−	1.24691i
$512$	−1426.57	−	1426.57i	−0.123137	−	0.123137i
$513$	2073.59	−	1368.70i	0.178463	−	0.117796i
$514$		−	9580.40i		−	0.822127i
$515$	−6606.26	+	11364.7i	−0.565255	+	0.972404i
$516$	13341.6	−	6548.25i	1.13824	−	0.558664i
$517$	1547.96	+	5777.07i	0.131681	+	0.491441i
$518$	1436.48	+	5361.01i	0.121844	+	0.454728i
$519$	−11783.3	−	7905.43i	−0.996592	−	0.668612i
$520$	−3495.18	−	13200.1i	−0.294758	−	1.11320i
$521$			4773.62i			0.401412i	0.979651	+	0.200706i	$0.0643237\pi$
$521$			4773.62i			0.401412i	−0.979651	+	0.200706i	$0.935676\pi$
$522$	2194.84	+	918.804i	0.184033	+	0.0770401i
$523$	3198.98	+	3198.98i	0.267460	+	0.267460i	0.828076	−	0.560616i	$-0.189436\pi$
$523$	3198.98	+	3198.98i	0.267460	+	0.267460i	−0.560616	+	0.828076i	$0.689436\pi$
$524$	4488.43	+	7774.19i	0.374195	+	0.648124i
$525$	11496.2	−	16918.6i	0.955688	−	1.40645i
$526$	−2048.57	+	3548.23i	−0.169813	+	0.294125i
$527$	−1563.02	+	418.811i	−0.129196	+	0.0346180i
$528$	684.805	+	783.835i	0.0564438	+	0.0646061i
$529$	894.110	−	516.215i	0.0734865	−	0.0424274i
$530$	4319.76	+	1171.17i	0.354034	+	0.0959853i
$531$	1401.69	−	574.442i	0.114554	−	0.0469466i
$532$	2071.04	−	2071.04i	0.168780	−	0.168780i
$533$	−7866.40	−	2107.80i	−0.639272	−	0.171292i
$534$	−711.529	+	1060.56i	−0.0576608	+	0.0859457i
$535$	−13168.1	−	38.9087i	−1.06413	−	0.00314424i
$536$	2182.52	+	1260.08i	0.175878	+	0.101543i
$537$	−2380.85	−	813.181i	−0.191325	−	0.0653470i
$538$	2567.20	−	9580.91i	0.205724	−	0.767774i
$539$	−23239.1			−1.85711
$540$	6146.36	+	5484.31i	0.489810	+	0.437050i
$541$	−24284.5			−1.92989			−0.964945	−	0.262452i	$-0.915469\pi$
$541$	−24284.5			−1.92989			−0.964945	+	0.262452i	$0.915469\pi$
$542$	−98.0575	+	365.955i	−0.00777109	+	0.0290021i
$543$	−13038.7	−	4453.35i	−1.03047	−	0.351955i
$544$	−6787.03	−	3918.50i	−0.534911	−	0.308831i
$545$	−3898.19	−	3921.30i	−0.306386	−	0.308202i
$546$	−8402.57	+	12524.4i	−0.658602	+	0.981672i
$547$	−3858.66	−	1033.92i	−0.301617	−	0.0808180i	0.104837	−	0.994489i	$-0.466568\pi$
$547$	−3858.66	−	1033.92i	−0.301617	−	0.0808180i	−0.406454	+	0.913671i	$0.633235\pi$
$548$	−5305.41	+	5305.41i	−0.413569	+	0.413569i
$549$	−1357.71	+	10021.8i	−0.105547	+	0.779091i
$550$	−7181.31	+	1878.81i	−0.556750	+	0.145660i
$551$	815.267	−	470.694i	0.0630336	−	0.0363925i
$552$	7925.17	+	9071.23i	0.611083	+	0.699451i
$553$	17313.9	−	4639.26i	1.33140	−	0.356747i
$554$	2809.02	−	4865.37i	0.215422	−	0.373122i
$555$	−2013.39	+	5838.41i	−0.153989	+	0.446535i
$556$	922.183	+	1597.27i	0.0703404	+	0.121833i
$557$	12226.1	+	12226.1i	0.930051	+	0.930051i	0.997709	−	0.0676576i	$-0.0215526\pi$
$557$	12226.1	+	12226.1i	0.930051	+	0.930051i	−0.0676576	+	0.997709i	$0.521553\pi$
$558$	−216.833	−	1696.21i	−0.0164503	−	0.128685i
$559$			30278.3i			2.29094i
$560$	1702.24	+	989.505i	0.128451	+	0.0746682i
$561$	6546.95	+	4392.34i	0.492714	+	0.330561i
$562$	−3575.97	−	13345.7i	−0.268404	−	1.00170i
$563$	3386.78	+	12639.6i	0.253527	+	0.946176i	0.968904	+	0.247437i	$0.0795884\pi$
$563$	3386.78	+	12639.6i	0.253527	+	0.946176i	−0.715377	+	0.698739i	$0.753745\pi$
$564$	−4090.15	+	2007.50i	−0.305366	+	0.149877i
$565$	15942.4	+	9267.25i	1.18708	+	0.690047i
$566$		−	13770.4i		−	1.02264i
$567$	172.444	−	22957.3i	0.0127724	−	1.70038i
$568$	14311.5	+	14311.5i	1.05721	+	1.05721i
$569$	−4163.99	−	7212.24i	−0.306790	−	0.531376i	0.670868	−	0.741577i	$-0.265922\pi$
$569$	−4163.99	−	7212.24i	−0.306790	−	0.531376i	−0.977658	+	0.210201i	$0.932588\pi$
$570$	−1674.44	+	324.663i	−0.123043	+	0.0238573i
$571$	−4453.29	+	7713.32i	−0.326382	+	0.565311i	−0.981791	−	0.189964i	$-0.939163\pi$
$571$	−4453.29	+	7713.32i	−0.326382	+	0.565311i	0.655409	+	0.755274i	$0.272496\pi$
$572$	−10101.7	+	2706.74i	−0.738414	+	0.197857i
$573$	−4622.22	+	910.396i	−0.336991	+	0.0663741i
$574$	−6623.39	+	3824.01i	−0.481629	+	0.278068i
$575$	12760.6	−	3338.49i	0.925483	−	0.242130i
$576$	4327.40	−	5595.93i	0.313035	−	0.404798i
$577$	11134.8	−	11134.8i	0.803374	−	0.803374i	−0.180248	−	0.983621i	$-0.557690\pi$
$577$	11134.8	−	11134.8i	0.803374	−	0.803374i	0.983621	+	0.180248i	$0.0576899\pi$
$578$	4994.38	+	1338.24i	0.359410	+	0.0963036i
$579$	14074.7	+	949.054i	1.01023	+	0.0681198i
$580$	2200.43	+	2213.47i	0.157531	+	0.158464i
$581$	−12399.9	−	7159.11i	−0.885432	−	0.511205i
$582$	−2098.05	+	1832.98i	−0.149428	+	0.130549i
$583$	2238.68	−	8354.89i	0.159034	−	0.593523i
$584$	−11602.1			−0.822088
$585$	−15547.4	+	6318.05i	−1.09881	+	0.446529i
$586$	15272.8			1.07664
$587$	4519.05	−	16865.3i	0.317753	−	1.18587i	−0.603646	−	0.797253i	$-0.706286\pi$
$587$	4519.05	−	16865.3i	0.317753	−	1.18587i	0.921399	−	0.388618i	$-0.127048\pi$
$588$	−3421.20	−	17369.9i	−0.239945	−	1.21824i
$589$	−585.913	−	338.277i	−0.0409883	−	0.0236646i
$590$	−1039.91	−	3.07268i	−0.0725632	−	0.000214407i
$591$	−2425.72	−	4942.25i	−0.168834	−	0.343988i
$592$	−574.215	−	153.860i	−0.0398650	−	0.0106818i
$593$	−4464.48	+	4464.48i	−0.309164	+	0.309164i	−0.844585	−	0.535421i	$-0.820153\pi$
$593$	−4464.48	+	4464.48i	−0.309164	+	0.309164i	0.535421	+	0.844585i	$0.320153\pi$
$594$	−5528.45	+	6232.81i	−0.381877	+	0.430531i
$595$	14394.1	+	3902.50i	0.991765	+	0.268886i
$596$	−7435.06	+	4292.63i	−0.510993	+	0.295022i
$597$	−7859.73	+	23011.9i	−0.538823	+	1.57758i
$598$	−9393.96	+	2517.10i	−0.642387	+	0.172127i
$599$	7836.14	−	13572.6i	0.534517	−	0.925811i	−0.464669	−	0.885484i	$-0.653827\pi$
$599$	7836.14	−	13572.6i	0.534517	−	0.925811i	0.999187	−	0.0403269i	$-0.0128399\pi$
$600$	−6211.26	−	12846.4i	−0.422623	−	0.874089i
$601$	−3405.59	−	5898.65i	−0.231143	−	0.400351i	0.727002	−	0.686635i	$-0.240913\pi$
$601$	−3405.59	−	5898.65i	−0.231143	−	0.400351i	−0.958145	+	0.286284i	$0.907580\pi$
$602$	20106.4	+	20106.4i	1.36125	+	1.36125i
$603$	1196.02	−	2857.06i	0.0807726	−	0.192949i
$604$		−	2509.71i		−	0.169071i
$605$	−137.074	−	517.681i	−0.00921133	−	0.0347880i
$606$	−150.645	+	2234.11i	−0.0100982	+	0.149760i
$607$	223.118	+	832.687i	0.0149194	+	0.0556800i	0.972984	−	0.230872i	$-0.0741577\pi$
$607$	223.118	+	832.687i	0.0149194	+	0.0556800i	−0.958065	+	0.286552i	$0.907491\pi$
$608$	−848.059	−	3165.00i	−0.0565680	−	0.211115i
$609$	585.214	−	8678.89i	0.0389393	−	0.577481i
$610$	3489.09	−	6002.25i	0.231589	−	0.398400i
$611$		−	9282.42i		−	0.614610i
$612$	−2319.20	+	5540.10i	−0.153183	+	0.365924i
$613$	2254.58	+	2254.58i	0.148551	+	0.148551i	0.777470	−	0.628920i	$-0.216503\pi$
$613$	2254.58	+	2254.58i	0.148551	+	0.148551i	−0.628920	+	0.777470i	$0.716503\pi$
$614$	−2113.79	−	3661.18i	−0.138934	−	0.240641i
$615$	−8489.22	−	597.627i	−0.556615	−	0.0391848i
$616$	−12391.2	+	21462.2i	−0.810481	+	1.40379i
$617$	21865.6	−	5858.87i	1.42670	−	0.382284i	0.538847	−	0.842404i	$-0.318860\pi$
$617$	21865.6	−	5858.87i	1.42670	−	0.382284i	0.887857	+	0.460120i	$0.152194\pi$
$618$	3273.65	−	9584.68i	0.213083	−	0.623871i
$619$	4224.11	−	2438.79i	0.274283	−	0.158357i	−0.356549	−	0.934276i	$-0.616047\pi$
$619$	4224.11	−	2438.79i	0.274283	−	0.158357i	0.630832	+	0.775919i	$0.282714\pi$
$620$	586.948	−	2164.91i	0.0380200	−	0.140234i
$621$	9823.58	−	11075.2i	0.634793	−	0.715669i
$622$	339.255	−	339.255i	0.0218696	−	0.0218696i
$623$	4509.86	+	1208.41i	0.290022	+	0.0777111i
$624$	−711.756	−	1450.16i	−0.0456619	−	0.0930332i
$625$	−15623.9	−	184.668i	−0.999930	−	0.0118188i
$626$	−2801.55	−	1617.48i	−0.178870	−	0.103271i
$627$	636.993	+	3234.11i	0.0405727	+	0.205993i
$628$	2347.94	−	8762.64i	0.149193	−	0.556795i
$629$	−4502.81			−0.285436
$630$	−6128.77	+	14519.8i	−0.387581	+	0.918226i
$631$	3038.06			0.191669			0.0958346	−	0.995397i	$-0.469448\pi$
$631$	3038.06			0.191669			0.0958346	+	0.995397i	$0.469448\pi$
$632$	3236.32	−	12078.1i	0.203693	−	0.760193i
$633$	17723.6	−	15484.4i	1.11288	−	0.972276i
$634$	6435.61	+	3715.60i	0.403140	+	0.232753i
$635$	−44.1133	+	14929.5i	−0.00275682	+	0.933009i
$636$	6574.38	+	443.308i	0.409891	+	0.0276388i
$637$	34838.6	+	9334.98i	2.16696	+	0.580636i
$638$	−2232.12	+	2232.12i	−0.138512	+	0.138512i
$639$	15216.7	−	19677.3i	0.942039	−	1.21819i
$640$	10143.4	−	5816.40i	0.626489	−	0.359240i
$641$	18662.9	−	10775.1i	1.14999	−	0.663946i	0.201104	−	0.979570i	$-0.435547\pi$
$641$	18662.9	−	10775.1i	1.14999	−	0.663946i	0.948884	+	0.315624i	$0.102214\pi$
$642$	9954.69	−	1960.68i	0.611963	−	0.120533i
$643$	−8185.22	+	2193.22i	−0.502012	+	0.134514i	−0.500933	−	0.865486i	$-0.667010\pi$
$643$	−8185.22	+	2193.22i	−0.502012	+	0.134514i	−0.00107824	+	0.999999i	$0.500343\pi$
$644$	8725.76	−	15113.5i	0.533918	−	0.924773i
$645$	6022.68	+	31061.8i	0.367663	+	1.89621i
$646$	−621.789	−	1076.97i	−0.0378699	−	0.0655926i
$647$	−23205.8	−	23205.8i	−1.41007	−	1.41007i	−0.759118	−	0.650953i	$-0.774370\pi$
$647$	−23205.8	−	23205.8i	−1.41007	−	1.41007i	−0.650953	−	0.759118i	$-0.725630\pi$
$648$	−13809.1	−	8111.62i	−0.837152	−	0.491751i
$649$			2009.70i			0.121553i
$650$	11520.5	+	68.0812i	0.695185	+	0.00410825i
$651$	−5611.96	+	2754.42i	−0.337865	+	0.165829i
$652$	4271.44	+	15941.2i	0.256568	+	0.957525i
$653$	6103.35	+	22778.0i	0.365762	+	1.36504i	0.866385	+	0.499377i	$0.166438\pi$
$653$	6103.35	+	22778.0i	0.365762	+	1.36504i	−0.500623	+	0.865666i	$0.666896\pi$
$654$	3537.79	+	2373.50i	0.211527	+	0.141913i
$655$	−18474.5	+	4891.78i	−1.10208	+	0.291813i
$656$		−	819.176i		−	0.0487553i
$657$	1808.08	+	14144.0i	0.107367	+	0.839895i
$658$	−6164.01	−	6164.01i	−0.365195	−	0.365195i
$659$	11587.9	+	20070.8i	0.684976	+	1.18641i	0.973444	+	0.228923i	$0.0735205\pi$
$659$	11587.9	+	20070.8i	0.684976	+	1.18641i	−0.288469	+	0.957489i	$0.593146\pi$
$660$	−9824.68	+	4786.11i	−0.579432	+	0.282271i
$661$	7538.30	−	13056.7i	0.443580	−	0.768302i	−0.554373	−	0.832269i	$-0.687042\pi$
$661$	7538.30	−	13056.7i	0.443580	−	0.768302i	0.997952	+	0.0639664i	$0.0203750\pi$
$662$	−13775.9	+	3691.25i	−0.808787	+	0.216714i
$663$	−8050.40	−	9214.58i	−0.471571	−	0.539765i
$664$	−8650.14	+	4994.16i	−0.505558	+	0.291884i
$665$	3101.75	+	5409.23i	0.180873	+	0.315430i
$666$	638.811	−	4715.33i	0.0371673	−	0.274348i
$667$	3966.29	−	3966.29i	0.230248	−	0.230248i
$668$	−8563.67	−	2294.63i	−0.496016	−	0.132907i
$669$	−913.432	+	1361.51i	−0.0527882	+	0.0786829i
$670$	−1507.92	+	1499.04i	−0.0869495	+	0.0864372i
$671$	−11619.7	−	6708.61i	−0.668512	−	0.385966i
$672$	−28651.7	−	9785.98i	−1.64474	−	0.561760i
$673$	−3781.35	+	14112.2i	−0.216583	+	0.808298i	0.769021	+	0.639224i	$0.220744\pi$
$673$	−3781.35	+	14112.2i	−0.216583	+	0.808298i	−0.985603	+	0.169074i	$0.945922\pi$
$674$	−11178.7			−0.638853
$675$	−14693.0	+	9574.08i	−0.837827	+	0.545936i
$676$	4693.32			0.267030
$677$	−2647.83	+	9881.83i	−0.150317	+	0.560989i	0.849144	+	0.528161i	$0.177118\pi$
$677$	−2647.83	+	9881.83i	−0.150317	+	0.560989i	−0.999461	+	0.0328285i	$0.989548\pi$
$678$	−13445.4	−	4592.27i	−0.761603	−	0.260125i
$679$	8820.44	+	5092.48i	0.498523	+	0.287823i
$680$	7378.26	−	7334.79i	0.416093	−	0.413642i
$681$	−13552.0	+	20199.7i	−0.762573	+	1.13665i
$682$	2191.34	+	587.168i	0.123036	+	0.0329675i
$683$	21858.2	−	21858.2i	1.22457	−	1.22457i	0.258579	−	0.965990i	$-0.416746\pi$
$683$	21858.2	−	21858.2i	1.22457	−	1.22457i	0.965990	−	0.258579i	$-0.0832541\pi$
$684$	−2323.54	+	952.232i	−0.129887	+	0.0532303i
$685$	−7945.79	−	13856.9i	−0.443202	−	0.772913i
$686$	13825.1	−	7981.91i	0.769451	−	0.444243i
$687$	−12192.0	−	13955.1i	−0.677082	−	0.774995i
$688$	−2941.85	+	788.266i	−0.163019	+	0.0436807i
$689$	−6712.19	+	11625.9i	−0.371138	+	0.642830i
$690$	−9136.36	+	4450.79i	−0.504080	+	0.245564i
$691$	7416.99	+	12846.6i	0.408329	+	0.707247i	0.994703	−	0.102794i	$-0.0327782\pi$
$691$	7416.99	+	12846.6i	0.408329	+	0.707247i	−0.586373	+	0.810041i	$0.699445\pi$
$692$	10140.6	+	10140.6i	0.557062	+	0.557062i
$693$	28095.4	+	11761.3i	1.54005	+	0.644698i
$694$			19530.3i			1.06824i
$695$	−3795.74	+	1005.05i	−0.207166	+	0.0548545i
$696$	−5039.10	−	3380.72i	−0.274435	−	0.184118i
$697$	−1605.93	−	5993.42i	−0.0872725	−	0.325706i
$698$	−3003.10	−	11207.7i	−0.162850	−	0.607763i
$699$	211.110	−	103.616i	0.0114233	−	0.00560673i
$700$	−14704.2	+	14531.5i	−0.793955	+	0.784626i
$701$		−	29266.1i		−	1.57684i	−0.615136	−	0.788421i	$-0.710899\pi$
$701$		−	29266.1i		−	1.57684i	0.615136	−	0.788421i	$-0.289101\pi$
$702$	10791.6	−	7123.09i	0.580202	−	0.382968i
$703$	−1331.22	−	1331.22i	−0.0714195	−	0.0714195i
$704$	4692.44	+	8127.55i	0.251212	+	0.435112i
$705$	−1846.37	−	9522.62i	−0.0986360	−	0.508713i
$706$	−5895.73	+	10211.7i	−0.314290	+	0.544366i
$707$	7907.07	−	2118.69i	0.420617	−	0.112704i
$708$	−1502.14	+	295.863i	−0.0797371	+	0.0157051i
$709$	10569.7	−	6102.42i	0.559878	−	0.323246i	−0.193219	−	0.981156i	$-0.561893\pi$
$709$	10569.7	−	6102.42i	0.559878	−	0.323246i	0.753096	+	0.657910i	$0.228559\pi$
$710$	−14813.4	+	8494.29i	−0.783012	+	0.448993i
$711$	−15228.7	−	2063.11i	−0.803262	−	0.108822i
$712$	2303.07	−	2303.07i	0.121224	−	0.121224i
$713$	−3893.82	−	1043.35i	−0.204523	−	0.0548017i
$714$	−11464.8	−	773.070i	−0.600926	−	0.0405202i
$715$	65.7862	−	22264.4i	0.00344093	−	1.16454i
$716$	2202.08	+	1271.37i	0.114938	+	0.0663595i
$717$	1344.40	−	1174.54i	0.0700243	−	0.0611774i
$718$	−4609.99	+	17204.7i	−0.239615	+	0.894255i
$719$	−12947.9			−0.671592			−0.335796	−	0.941935i	$-0.609005\pi$
$719$	−12947.9			−0.671592			−0.335796	+	0.941935i	$0.609005\pi$
$720$	−1018.62	−	1346.11i	−0.0527249	−	0.0696755i
$721$	−37027.2			−1.91257
$722$	−2808.48	+	10481.4i	−0.144765	+	0.540272i
$723$	4577.92	+	23242.8i	0.235484	+	1.19559i
$724$	12059.6	+	6962.62i	0.619049	+	0.357408i
$725$	−5773.97	+	3288.26i	−0.295779	+	0.168445i
$726$	181.799	+	370.404i	0.00929367	+	0.0189352i
$727$	3951.09	+	1058.69i	0.201565	+	0.0540091i	0.358189	−	0.933649i	$-0.383394\pi$
$727$	3951.09	+	1058.69i	0.201565	+	0.0540091i	−0.156624	+	0.987658i	$0.550061\pi$
$728$	27197.3	−	27197.3i	1.38462	−	1.38462i
$729$	−7736.76	+	18098.7i	−0.393068	+	0.919509i
$730$	2561.42	−	9447.62i	0.129867	−	0.479003i
$731$	−19978.4	+	11534.5i	−1.01084	+	0.583611i
$732$	3303.69	−	9672.66i	0.166814	−	0.488404i
$733$	−8630.30	+	2312.48i	−0.434881	+	0.116526i	−0.469616	−	0.882871i	$-0.655608\pi$
$733$	−8630.30	+	2312.48i	−0.434881	+	0.116526i	0.0347357	+	0.999397i	$0.488941\pi$
$734$	1708.64	−	2959.46i	0.0859226	−	0.148822i
$735$	37596.9	+	2646.76i	1.88678	+	0.132826i
$736$	−9761.80	−	16907.9i	−0.488892	−	0.846786i
$737$	2905.60	+	2905.60i	0.145223	+	0.145223i
$738$	6504.12	−	831.445i	0.324417	−	0.0414714i
$739$		−	10810.9i		−	0.538140i	−0.963121	−	0.269070i	$-0.913284\pi$
$739$		−	10810.9i		−	0.538140i	0.963121	−	0.269070i	$-0.0867163\pi$
$740$	3136.82	−	5396.24i	0.155827	−	0.268067i
$741$	344.177	−	5104.25i	0.0170630	−	0.253049i
$742$	3262.93	+	12177.4i	0.161436	+	0.602489i
$743$	3801.46	+	14187.3i	0.187701	+	0.700511i	0.994036	+	0.109052i	$0.0347814\pi$
$743$	3801.46	+	14187.3i	0.187701	+	0.700511i	−0.806335	+	0.591460i	$0.798552\pi$
$744$	−293.394	+	4351.12i	−0.0144575	+	0.214408i
$745$	−4678.39	−	17668.6i	−0.230071	−	0.868898i
$746$			13087.9i			0.642334i
$747$	7436.37	+	9767.00i	0.364234	+	0.478388i
$748$	−5634.21	−	5634.21i	−0.275411	−	0.275411i
$749$	−18545.8	−	32122.2i	−0.904737	−	1.56705i
$750$	11832.1	−	2221.70i	0.576064	−	0.108167i
$751$	10459.1	−	18115.7i	0.508201	−	0.880229i	−0.491754	−	0.870734i	$-0.663644\pi$
$751$	10459.1	−	18115.7i	0.508201	−	0.880229i	0.999955	−	0.00949541i	$-0.00302253\pi$
$752$	901.883	−	241.659i	0.0437344	−	0.0117186i
$753$	10357.4	−	30324.6i	0.501253	−	1.46758i
$754$	4242.88	−	2449.63i	0.204929	−	0.118316i
$755$	5156.86	+	1398.12i	0.248579	+	0.0673945i
$756$	−4654.79	+	22731.2i	−0.223933	+	1.09355i
$757$	−18342.1	+	18342.1i	−0.880653	+	0.880653i	−0.993601	−	0.112948i	$-0.963971\pi$
$757$	−18342.1	+	18342.1i	−0.880653	+	0.880653i	0.112948	+	0.993601i	$0.463971\pi$
$758$	−12085.7	−	3238.37i	−0.579121	−	0.155175i
$759$	8653.61	+	17631.2i	0.413842	+	0.843177i
$760$	4349.79	+	12.8526i	0.207610	+	0.000613438i
$761$	9287.39	+	5362.08i	0.442402	+	0.255421i	0.704616	−	0.709589i	$-0.251119\pi$
$761$	9287.39	+	5362.08i	0.442402	+	0.255421i	−0.262214	+	0.965010i	$0.584453\pi$
$762$	−2222.96	−	11286.3i	−0.105681	−	0.536560i
$763$	4030.99	−	15043.9i	0.191260	−	0.713793i
$764$	4761.29			0.225468
$765$	−10091.6	−	7851.70i	−0.476944	−	0.371084i
$766$	9254.36			0.436519
$767$	807.283	−	3012.82i	0.0380043	−	0.141834i
$768$	−14986.4	+	13093.0i	−0.704132	+	0.615172i
$769$	−19273.4	−	11127.5i	−0.903793	−	0.521805i	−0.0253640	−	0.999678i	$-0.508074\pi$
$769$	−19273.4	−	11127.5i	−0.903793	−	0.521805i	−0.878429	+	0.477873i	$0.841408\pi$
$770$	−14741.1	−	14828.4i	−0.689910	−	0.693999i
$771$	29959.9	+	2020.18i	1.39945	+	0.0943647i
$772$	−13771.4	−	3690.04i	−0.642026	−	0.172030i
$773$	−20786.4	+	20786.4i	−0.967184	+	0.967184i	−0.999478	−	0.0322943i	$-0.989719\pi$
$773$	−20786.4	+	20786.4i	−0.967184	+	0.967184i	0.0322943	+	0.999478i	$0.489719\pi$
$774$	−9244.60	−	22557.7i	−0.429316	−	1.04757i
$775$	4121.40	+	2412.08i	0.191026	+	0.111799i
$776$	6153.09	−	3552.49i	0.284643	−	0.164339i
$777$	−17067.9	+	3361.71i	−0.788040	+	0.155213i
$778$	12552.9	−	3363.53i	0.578461	−	0.154998i
$779$	1297.12	−	2246.68i	0.0596589	−	0.103332i
$780$	16651.1	−	3228.53i	0.764365	−	0.148205i
$781$	16500.3	+	28579.4i	0.755990	+	1.30941i
$782$	−5239.48	−	5239.48i	−0.239595	−	0.239595i
$783$	−3336.11	+	6669.96i	−0.152264	+	0.304425i
$784$			3627.96i			0.165268i
$785$	16697.1	+	9705.99i	0.759167	+	0.441301i
$786$	13218.6	−	6487.88i	0.599864	−	0.294421i
$787$	−4496.33	−	16780.5i	−0.203656	−	0.760053i	−0.989855	−	0.142080i	$-0.954621\pi$
$787$	−4496.33	−	16780.5i	−0.203656	−	0.760053i	0.786200	−	0.617973i	$-0.212046\pi$
$788$	1440.12	+	5374.60i	0.0651042	+	0.242972i
$789$	−10664.1	−	7154.50i	−0.481180	−	0.322823i
$790$	9120.73	+	5301.85i	0.410761	+	0.238774i
$791$			51941.7i			2.33481i
$792$	16905.0	−	12871.1i	0.758452	−	0.577468i
$793$	14724.7	+	14724.7i	0.659379	+	0.659379i
$794$	572.604	+	991.779i	0.0255931	+	0.0443286i
$795$	−4573.37	+	13261.8i	−0.204026	+	0.591633i
$796$	12288.3	−	21284.0i	0.547171	−	0.947728i
$797$	22854.4	−	6123.82i	1.01574	−	0.272167i	0.287714	−	0.957716i	$-0.407105\pi$
$797$	22854.4	−	6123.82i	1.01574	−	0.272167i	0.728026	+	0.685550i	$0.240438\pi$
$798$	−3160.93	−	3618.04i	−0.140220	−	0.160498i
$799$	6124.78	−	3536.14i	0.271188	−	0.156570i
$800$	5853.78	+	22374.7i	0.258703	+	0.988830i
$801$	−3166.56	−	2448.74i	−0.139682	−	0.108017i
$802$	−10631.4	+	10631.4i	−0.468088	+	0.468088i
$803$	−18272.7	−	4896.16i	−0.803027	−	0.215170i
$804$	−1744.01	+	2599.52i	−0.0765008	+	0.114027i
$805$	26193.6	+	26348.8i	1.14683	+	1.15363i
$806$	−3049.26	−	1760.49i	−0.133258	−	0.0769363i
$807$	29420.2	+	10048.5i	1.28332	+	0.438318i
$808$	1477.99	−	5515.93i	0.0643509	−	0.240161i
$809$	30629.1			1.33110			0.665552	−	0.746352i	$-0.268196\pi$
$809$	30629.1			1.33110			0.665552	+	0.746352i	$0.268196\pi$
$810$	9653.97	−	9453.97i	0.418773	−	0.410097i
$811$	16552.9			0.716709			0.358354	−	0.933586i	$-0.383338\pi$
$811$	16552.9			0.716709			0.358354	+	0.933586i	$0.383338\pi$
$812$	−2275.38	+	8491.85i	−0.0983379	+	0.367002i
$813$	−1123.74	−	383.814i	−0.0484764	−	0.0165571i
$814$	5467.13	+	3156.45i	0.235409	+	0.135913i
$815$	−35135.0	−	103.816i	−1.51009	−	0.00446196i
$816$	685.706	−	1022.07i	0.0294173	−	0.0438476i
$817$	−9316.53	−	2496.36i	−0.398952	−	0.106899i
$818$	−1431.56	+	1431.56i	−0.0611899	+	0.0611899i
$819$	−37394.4	−	28917.5i	−1.59544	−	1.23377i
$820$	8301.35	+	2250.65i	0.353531	+	0.0958489i
$821$	−12828.3	+	7406.41i	−0.545323	+	0.314842i	−0.747234	−	0.664562i	$-0.768618\pi$
$821$	−12828.3	+	7406.41i	−0.545323	+	0.314842i	0.201910	+	0.979404i	$0.435285\pi$
$822$	8097.41	+	9268.38i	0.343588	+	0.393275i
$823$	5249.91	−	1406.71i	0.222358	−	0.0595806i	−0.145920	−	0.989296i	$-0.546614\pi$
$823$	5249.91	−	1406.71i	0.222358	−	0.0595806i	0.368278	+	0.929716i	$0.379948\pi$
$824$	−12915.0	+	22369.4i	−0.546013	+	0.945722i
$825$	−4361.14	−	22853.6i	−0.184043	−	0.964438i
$826$	−1464.59	−	2536.75i	−0.0616945	−	0.106858i
$827$	−9704.44	−	9704.44i	−0.408049	−	0.408049i	0.473009	−	0.881058i	$-0.343168\pi$
$827$	−9704.44	−	9704.44i	−0.408049	−	0.408049i	−0.881058	+	0.473009i	$0.843168\pi$
$828$	−11904.3	+	9063.69i	−0.499643	+	0.380417i
$829$		−	44654.1i		−	1.87081i	−0.353581	−	0.935404i	$-0.615036\pi$
$829$		−	44654.1i		−	1.87081i	0.353581	−	0.935404i	$-0.384964\pi$
$830$	−2157.04	−	8146.38i	−0.0902071	−	0.340681i
$831$	14622.7	+	9810.33i	0.610415	+	0.409527i
$832$	−3769.84	−	14069.2i	−0.157086	−	0.586253i
$833$	7112.33	+	26543.6i	0.295831	+	1.10406i
$834$	2715.87	−	1332.99i	0.112761	−	0.0553448i
$835$	9485.60	−	16318.0i	0.393129	−	0.676297i
$836$		−	3331.42i		−	0.137822i
$837$	5350.12	−	320.407i	0.220941	−	0.0132316i
$838$	−19215.9	−	19215.9i	−0.792126	−	0.792126i
$839$	7021.07	+	12160.9i	0.288909	+	0.500404i	0.973549	−	0.228476i	$-0.0733743\pi$
$839$	7021.07	+	12160.9i	0.288909	+	0.500404i	−0.684641	+	0.728880i	$0.740041\pi$
$840$	22491.3	−	33310.9i	0.923836	−	1.36826i
$841$	10781.7	−	18674.4i	0.442070	−	0.765688i
$842$	2610.72	−	699.541i	0.106854	−	0.0286316i
$843$	42488.9	−	8368.65i	1.73594	−	0.341912i
$844$	−20599.4	+	11893.1i	−0.840118	+	0.485042i
$845$	−2614.58	+	9643.66i	−0.106443	+	0.392606i
$846$	2834.12	+	6915.52i	0.115176	+	0.281041i
$847$	1066.63	−	1066.63i	0.0432700	−	0.0432700i
$848$	−1304.32	−	349.491i	−0.0528189	−	0.0141528i
$849$	43062.8	+	2903.71i	1.74077	+	0.117379i
$850$	4343.81	+	7627.44i	0.175284	+	0.307787i
$851$	−9714.61	−	5608.73i	−0.391319	−	0.225928i
$852$	−18932.4	+	16540.4i	−0.761281	+	0.665101i
$853$	−2278.33	+	8502.85i	−0.0914521	+	0.341304i	−0.996458	−	0.0840959i	$-0.973200\pi$
$853$	−2278.33	+	8502.85i	−0.0914521	+	0.341304i	0.905006	+	0.425400i	$0.139866\pi$
$854$	19555.9			0.783593
$855$	−662.205	−	5304.79i	−0.0264877	−	0.212187i
$856$	−25874.9			−1.03316
$857$	1190.94	−	4444.64i	0.0474699	−	0.177160i	−0.938121	−	0.346308i	$-0.887435\pi$
$857$	1190.94	−	4444.64i	0.0474699	−	0.177160i	0.985591	+	0.169148i	$0.0541017\pi$
$858$	3315.10	+	16831.2i	0.131906	+	0.669707i
$859$	−2297.03	−	1326.19i	−0.0912382	−	0.0526764i	0.453687	−	0.891161i	$-0.350109\pi$
$859$	−2297.03	−	1326.19i	−0.0912382	−	0.0526764i	−0.544925	+	0.838485i	$0.683442\pi$
$860$	94.4868	−	31977.8i	0.00374648	−	1.26795i
$861$	−10561.8	−	21519.1i	−0.418056	−	0.851763i
$862$	−15495.0	−	4151.87i	−0.612252	−	0.164052i
$863$	−11554.8	+	11554.8i	−0.455770	+	0.455770i	−0.897264	−	0.441494i	$-0.854449\pi$
$863$	−11554.8	+	11554.8i	−0.455770	+	0.455770i	0.441494	+	0.897264i	$0.354449\pi$
$864$	19419.4	+	17224.9i	0.764655	+	0.678243i
$865$	−26485.6	+	15187.3i	−1.04108	+	0.596976i
$866$	−13294.9	+	7675.81i	−0.521685	+	0.301195i
$867$	−5238.11	+	15336.3i	−0.205185	+	0.600747i
$868$	6102.90	−	1635.27i	0.238647	−	0.0639453i
$869$	10194.1	−	17656.7i	0.397941	−	0.689253i
$870$	3865.41	−	3356.97i	0.150632	−	0.130818i
$871$	−3188.73	−	5523.04i	−0.124048	−	0.214858i
$872$	−7682.52	−	7682.52i	−0.298352	−	0.298352i
$873$	−5289.71	−	6947.55i	−0.205074	−	0.269346i
$874$		−	3098.02i		−	0.119899i
$875$	−21667.2	−	38309.0i	−0.837126	−	1.48009i
$876$	969.546	−	14378.6i	0.0373949	−	0.554576i
$877$	−1586.40	−	5920.54i	−0.0610821	−	0.227962i	0.928636	−	0.370992i	$-0.120982\pi$
$877$	−1586.40	−	5920.54i	−0.0610821	−	0.227962i	−0.989718	+	0.143030i	$0.954315\pi$
$878$	7051.12	+	26315.1i	0.271029	+	1.01150i
$879$	−3220.52	+	47761.2i	−0.123579	+	1.83270i
$880$	2164.93	−	573.241i	0.0829316	−	0.0219590i
$881$			2309.20i			0.0883075i	0.999025	+	0.0441537i	$0.0140591\pi$
$881$			2309.20i			0.0883075i	−0.999025	+	0.0441537i	$0.985941\pi$
$882$	−28805.4	+	3682.29i	−1.09969	+	0.140577i
$883$	−19660.7	−	19660.7i	−0.749303	−	0.749303i	0.225045	−	0.974348i	$-0.427747\pi$
$883$	−19660.7	−	19660.7i	−0.749303	−	0.749303i	−0.974348	+	0.225045i	$0.927747\pi$
$884$	6183.24	+	10709.7i	0.235254	+	0.407472i
$885$	228.890	−	3251.36i	0.00869386	−	0.123495i
$886$	5884.68	−	10192.6i	0.223137	−	0.386485i
$887$	−28356.7	+	7598.16i	−1.07342	+	0.287623i	−0.751898	−	0.659279i	$-0.770862\pi$
$887$	−28356.7	+	7598.16i	−1.07342	+	0.287623i	−0.321524	+	0.946902i	$0.604195\pi$
$888$	−3922.31	+	11483.9i	−0.148226	+	0.433979i
$889$	−36419.1	+	21026.6i	−1.37397	+	0.793260i
$890$	1366.94	+	2383.84i	0.0514830	+	0.0897828i
$891$	−18325.5	−	18602.9i	−0.689032	−	0.699462i
$892$	1171.69	−	1171.69i	0.0439812	−	0.0439812i
$893$	2856.17	+	765.308i	0.107030	+	0.0286787i
$894$	6204.87	+	12642.0i	0.232127	+	0.472944i
$895$	−3839.11	+	3816.49i	−0.143382	+	0.142538i
$896$	28523.0	+	16467.8i	1.06349	+	0.614006i
$897$	−5890.64	−	29907.6i	−0.219267	−	1.11325i
$898$	−6785.10	+	25322.3i	−0.252140	+	0.940999i
$899$	2030.76			0.0753387
$900$	16439.8	−	6624.15i	0.608880	−	0.245339i
$901$	−10228.0			−0.378186
$902$	−2251.50	+	8402.70i	−0.0831116	+	0.310177i
$903$	−67116.5	+	58637.0i	−2.47342	+	2.16093i
$904$	31379.8	+	18117.1i	1.15451	+	0.666556i
$905$	−21024.7	+	20900.9i	−0.772249	+	0.767699i
$906$	−4107.42	−	276.962i	−0.150618	−	0.0101561i
$907$	−32801.4	−	8789.11i	−1.20083	−	0.321761i	−0.397672	−	0.917528i	$-0.630182\pi$
$907$	−32801.4	−	8789.11i	−1.20083	−	0.321761i	−0.803158	+	0.595766i	$0.796848\pi$
$908$	17383.6	−	17383.6i	0.635347	−	0.635347i
$909$	−6954.75	−	942.196i	−0.253767	−	0.0343792i
$910$	16142.4	+	28151.2i	0.588039	+	1.02550i
$911$	−5799.18	+	3348.16i	−0.210906	+	0.121767i	−0.601732	−	0.798698i	$-0.705523\pi$
$911$	−5799.18	+	3348.16i	−0.210906	+	0.121767i	0.390826	+	0.920464i	$0.372189\pi$
$912$	504.890	−	99.4437i	0.0183318	−	0.00361065i
$913$	−15731.1	+	4215.13i	−0.570233	+	0.152793i
$914$	10032.6	−	17376.9i	0.363072	−	0.628860i
$915$	18034.6	+	12176.8i	0.651589	+	0.439948i
$916$	9364.28	+	16219.4i	0.337778	+	0.585048i
$917$	−38064.7	−	38064.7i	−1.37078	−	1.37078i
$918$	8811.05	+	4407.01i	0.316784	+	0.158446i
$919$		−	50724.3i		−	1.82072i	−0.413820	−	0.910359i	$-0.635806\pi$
$919$		−	50724.3i		−	1.82072i	0.413820	−	0.910359i	$-0.364194\pi$
$920$	25054.5	−	6634.05i	0.897850	−	0.237737i
$921$	11895.0	−	5838.23i	0.425574	−	0.208877i
$922$	4299.37	+	16045.5i	0.153571	+	0.573134i
$923$	−13256.1	−	49472.5i	−0.472731	−	1.76425i
$924$	−25562.8	−	17150.1i	−0.910125	−	0.610602i
$925$	9340.52	+	9451.58i	0.332016	+	0.335963i
$926$		−	14932.5i		−	0.529927i
$927$	29283.0	+	12258.5i	1.03752	+	0.434326i
$928$	6954.57	+	6954.57i	0.246008	+	0.246008i
$929$	18550.3	+	32130.0i	0.655128	+	1.13472i	0.981862	+	0.189599i	$0.0607188\pi$
$929$	18550.3	+	32130.0i	0.655128	+	1.13472i	−0.326733	+	0.945117i	$0.605948\pi$
$930$	−3478.34	−	1199.52i	−0.122645	−	0.0422943i
$931$	−5744.68	+	9950.08i	−0.202228	+	0.350269i
$932$	−229.578	+	61.5153i	−0.00806876	+	0.00216202i
$933$	989.384	+	1132.46i	0.0347170	+	0.0397374i
$934$	4842.73	−	2795.95i	0.169656	−	0.0979511i
$935$	14715.7	−	8438.23i	0.514711	−	0.295144i
$936$	−30513.2	+	12504.9i	−1.06555	+	0.436684i
$937$	1098.31	−	1098.31i	0.0382927	−	0.0382927i	−0.687701	−	0.725994i	$-0.741380\pi$
$937$	1098.31	−	1098.31i	0.0382927	−	0.0382927i	0.725994	+	0.687701i	$0.241380\pi$
$938$	−5785.07	−	1550.10i	−0.201374	−	0.0539581i
$939$	5648.94	−	8419.97i	0.196322	−	0.292626i
$940$	−28.9668	+	9803.43i	−0.00100510	+	0.340162i
$941$	24281.2	+	14018.8i	0.841175	+	0.485653i	0.857664	−	0.514211i	$-0.171915\pi$
$941$	24281.2	+	14018.8i	0.841175	+	0.485653i	−0.0164881	+	0.999864i	$0.505249\pi$
$942$	−14081.9	−	4809.68i	−0.487064	−	0.166356i
$943$	4000.71	−	14930.9i	0.138156	−	0.515605i
$944$	313.743			0.0108172
$945$	−44114.1	−	22227.7i	−1.51855	−	0.765149i
$946$	32342.5			1.11157
$947$	−6441.22	+	24038.9i	−0.221026	+	0.824879i	0.762932	+	0.646479i	$0.223759\pi$
$947$	−6441.22	+	24038.9i	−0.221026	+	0.824879i	−0.983958	+	0.178401i	$0.942908\pi$
$948$	14698.1	+	5020.13i	0.503557	+	0.171990i
$949$	25426.6	+	14680.0i	0.869738	+	0.502144i
$950$	−970.778	+	3539.20i	−0.0331539	+	0.120870i
$951$	−12976.5	+	19342.0i	−0.442474	+	0.659524i
$952$	28306.3	+	7584.65i	0.963669	+	0.258214i
$953$	34055.7	−	34055.7i	1.15758	−	1.15758i	0.172583	−	0.984995i	$-0.444789\pi$
$953$	34055.7	−	34055.7i	1.15758	−	1.15758i	0.984995	−	0.172583i	$-0.0552112\pi$
$954$	1451.04	−	10710.8i	0.0492445	−	0.363495i
$955$	−2652.44	+	9783.31i	−0.0898753	+	0.331498i
$956$	−1562.53	+	902.127i	−0.0528617	+	0.0305197i
$957$	−6509.63	−	7450.99i	−0.219881	−	0.251678i
$958$	159.030	−	42.6119i	0.00536328	−	0.00143709i
$959$	22496.6	−	38965.3i	0.757512	−	1.31205i
$960$	−6665.91	−	13683.4i	−0.224105	−	0.460032i
$961$	14165.8	+	24535.8i	0.475505	+	0.823599i
$962$	−6928.05	−	6928.05i	−0.232193	−	0.232193i
$963$	4032.36	+	31543.8i	0.134933	+	1.05554i
$964$		−	23942.1i		−	0.799920i
$965$	15254.0	−	26241.3i	0.508853	−	0.875376i
$966$	−23771.9	−	15948.5i	−0.791769	−	0.531196i
$967$	4004.02	+	14943.2i	0.133155	+	0.496940i	0.999999	−	0.00163930i	$-0.000521807\pi$
$967$	4004.02	+	14943.2i	0.133155	+	0.496940i	−0.866844	+	0.498580i	$0.833855\pi$
$968$	−272.349	−	1016.42i	−0.00904302	−	0.0337490i
$969$	3499.02	−	1717.37i	0.116001	−	0.0569348i
$970$	1534.36	+	5794.76i	0.0507891	+	0.191813i
$971$			42148.6i			1.39301i	0.717552	+	0.696505i	$0.245263\pi$
$971$			42148.6i			1.39301i	−0.717552	+	0.696505i	$0.754737\pi$
$972$	11206.8	−	16436.0i	0.369813	−	0.542370i
$973$	−7820.70	−	7820.70i	−0.257677	−	0.257677i
$974$	−881.682	−	1527.12i	−0.0290050	−	0.0502382i
$975$	−2642.19	+	36012.6i	−0.0867874	+	1.18290i
$976$	−1047.31	+	1813.99i	−0.0343479	+	0.0594923i
$977$	8214.17	−	2200.98i	0.268981	−	0.0720733i	−0.121807	−	0.992554i	$-0.538869\pi$
$977$	8214.17	−	2200.98i	0.268981	−	0.0720733i	0.390789	+	0.920480i	$0.372202\pi$
$978$	26561.0	−	5231.47i	0.868431	−	0.171047i
$979$	4599.12	−	2655.30i	0.150142	−	0.0866843i
$980$	−36764.9	−	9967.65i	−1.19838	−	0.324903i
$981$	−8168.43	+	10562.9i	−0.265849	+	0.343780i
$982$	4783.38	−	4783.38i	0.155442	−	0.155442i
$983$	41929.5	+	11235.0i	1.36047	+	0.364537i	0.863990	−	0.503510i	$-0.167958\pi$
$983$	41929.5	+	11235.0i	1.36047	+	0.364537i	0.496482	+	0.868047i	$0.334625\pi$
$984$	−16684.4	−	1125.02i	−0.540526	−	0.0364475i
$985$	−11845.8	−	35.0015i	−0.383186	−	0.00113222i
$986$	3232.65	+	1866.37i	0.104410	+	0.0602814i
$987$	20575.9	−	17976.4i	0.663565	−	0.579730i
$988$	−1338.20	+	4994.25i	−0.0430911	+	0.160818i
$989$	−57469.9			−1.84776
$990$	6748.79	+	16607.4i	0.216657	+	0.533148i
$991$	39569.0			1.26837			0.634183	−	0.773183i	$-0.281337\pi$
$991$	39569.0			1.26837			0.634183	+	0.773183i	$0.281337\pi$
$992$	1829.43	−	6827.52i	0.0585528	−	0.218522i
$993$	−8638.42	−	43858.6i	−0.276064	−	1.40162i
$994$	−41655.1	−	24049.6i	−1.32919	−	0.767410i
$995$	36887.9	+	37106.6i	1.17530	+	1.18227i
$996$	−5466.45	−	11137.5i	−0.173907	−	0.354324i
$997$	54073.3	+	14488.9i	1.71767	+	0.460249i	0.977284	−	0.211933i	$-0.0679757\pi$
$997$	54073.3	+	14488.9i	1.71767	+	0.460249i	0.740387	+	0.672181i	$0.234642\pi$
$998$	5925.14	−	5925.14i	0.187933	−	0.187933i
$999$	14611.1	+	2992.00i	0.462738	+	0.0947574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.23.7	yes	64
3.2	odd	2		135.4.m.a.98.10		64
5.2	odd	4	inner	45.4.l.a.32.7	yes	64
5.3	odd	4		225.4.p.b.32.10		64
5.4	even	2		225.4.p.b.68.10		64
9.2	odd	6	inner	45.4.l.a.38.7	yes	64
9.7	even	3		135.4.m.a.8.10		64
15.2	even	4		135.4.m.a.17.10		64
45.2	even	12	inner	45.4.l.a.2.7	✓	64
45.7	odd	12		135.4.m.a.62.10		64
45.29	odd	6		225.4.p.b.218.10		64
45.38	even	12		225.4.p.b.182.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.7	✓	64	45.2	even	12	inner
45.4.l.a.23.7	yes	64	1.1	even	1	trivial
45.4.l.a.32.7	yes	64	5.2	odd	4	inner
45.4.l.a.38.7	yes	64	9.2	odd	6	inner
135.4.m.a.8.10		64	9.7	even	3
135.4.m.a.17.10		64	15.2	even	4
135.4.m.a.62.10		64	45.7	odd	12
135.4.m.a.98.10		64	3.2	odd	2
225.4.p.b.32.10		64	5.3	odd	4
225.4.p.b.68.10		64	5.4	even	2
225.4.p.b.182.10		64	45.38	even	12
225.4.p.b.218.10		64	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.429078 + 1.60134i) q^{2} +(-4.91725 - 1.67949i) q^{3} +(4.54802 + 2.62580i) q^{4} +(-7.92902 + 7.88230i) q^{5} +(4.79931 - 7.15356i) q^{6} +(-30.4193 - 8.15082i) q^{7} +(-15.5344 + 15.5344i) q^{8} +(21.3587 + 16.5169i) q^{9} +O(q^{10})\)	\(q+(-0.429078 + 1.60134i) q^{2} +(-4.91725 - 1.67949i) q^{3} +(4.54802 + 2.62580i) q^{4} +(-7.92902 + 7.88230i) q^{5} +(4.79931 - 7.15356i) q^{6} +(-30.4193 - 8.15082i) q^{7} +(-15.5344 + 15.5344i) q^{8} +(21.3587 + 16.5169i) q^{9} +(-9.22008 - 16.0792i) q^{10} +(-31.0214 + 17.9102i) q^{11} +(-17.9537 - 20.5500i) q^{12} +(53.6997 - 14.3888i) q^{13} +(26.1045 - 45.2143i) q^{14} +(52.2272 - 25.4426i) q^{15} +(2.79604 + 4.84288i) q^{16} +(29.9510 + 29.9510i) q^{17} +(-35.6137 + 27.1155i) q^{18} +17.7095i q^{19} +(-56.7587 + 15.0288i) q^{20} +(135.890 + 91.1683i) q^{21} +(-15.3698 - 57.3607i) q^{22} +(27.3107 + 101.925i) q^{23} +(102.476 - 50.2966i) q^{24} +(0.738685 - 124.998i) q^{25} +92.1654i q^{26} +(-77.2859 - 117.089i) q^{27} +(-116.945 - 116.945i) q^{28} +(-26.5786 - 46.0355i) q^{29} +(18.3327 + 94.5503i) q^{30} +(-19.1014 + 33.0846i) q^{31} +(-178.717 + 47.8872i) q^{32} +(182.620 - 35.9690i) q^{33} +(-60.8131 + 35.1104i) q^{34} +(305.442 - 175.146i) q^{35} +(53.7695 + 131.203i) q^{36} +(-75.1697 + 75.1697i) q^{37} +(-28.3590 - 7.59877i) q^{38} +(-288.220 - 19.4346i) q^{39} +(0.725746 - 245.619i) q^{40} +(-126.863 - 73.2444i) q^{41} +(-204.299 + 178.488i) q^{42} +(-140.961 + 526.075i) q^{43} -188.114 q^{44} +(-299.544 + 37.3926i) q^{45} -174.935 q^{46} +(43.2145 - 161.279i) q^{47} +(-5.61527 - 28.5095i) q^{48} +(561.849 + 324.384i) q^{49} +(199.847 + 54.8167i) q^{50} +(-96.9742 - 197.579i) q^{51} +(282.009 + 75.5641i) q^{52} +(-170.746 + 170.746i) q^{53} +(220.661 - 73.5208i) q^{54} +(104.796 - 386.530i) q^{55} +(599.162 - 345.926i) q^{56} +(29.7429 - 87.0821i) q^{57} +(85.1228 - 22.8086i) q^{58} +(28.0525 - 48.5883i) q^{59} +(304.337 + 21.4248i) q^{60} +(187.285 + 324.386i) q^{61} +(-44.7838 - 44.7838i) q^{62} +(-515.089 - 676.522i) q^{63} -261.998i q^{64} +(-312.369 + 537.366i) q^{65} +(-20.7596 + 307.870i) q^{66} +(-29.6904 - 110.806i) q^{67} +(57.5724 + 214.863i) q^{68} +(36.8879 - 547.058i) q^{69} +(149.410 + 564.268i) q^{70} -921.281i q^{71} +(-588.372 + 75.2138i) q^{72} +(373.434 + 373.434i) q^{73} +(-88.1187 - 152.626i) q^{74} +(-213.564 + 613.405i) q^{75} +(-46.5016 + 80.5432i) q^{76} +(1089.63 - 291.966i) q^{77} +(154.791 - 453.200i) q^{78} +(-492.922 + 284.589i) q^{79} +(-60.3429 - 16.3601i) q^{80} +(183.385 + 705.557i) q^{81} +(171.723 - 171.723i) q^{82} +(439.165 + 117.674i) q^{83} +(378.640 + 771.455i) q^{84} +(-473.565 - 1.39927i) q^{85} +(-781.941 - 451.454i) q^{86} +(53.3777 + 271.006i) q^{87} +(203.674 - 760.121i) q^{88} -148.257 q^{89} +(68.6496 - 495.717i) q^{90} -1750.79 q^{91} +(-143.425 + 535.269i) q^{92} +(149.492 - 130.605i) q^{93} +(239.720 + 138.402i) q^{94} +(-139.592 - 140.419i) q^{95} +(959.224 + 64.6801i) q^{96} +(-312.391 - 83.7049i) q^{97} +(-760.526 + 760.526i) q^{98} +(-958.396 - 129.839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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