LMFDB - Embedded newform 74.4.f.b.33.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.f (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.5
Character	$\chi$	$=$	74.33
Dual form			74.4.f.b.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(1.33010 + 7.54337i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-4.89924 + 4.11095i) q^{5} +15.3195 q^{6} +(-6.34775 + 5.32640i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-29.7615 + 10.8323i) q^{9} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(1.33010 + 7.54337i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-4.89924 + 4.11095i) q^{5} +15.3195 q^{6} +(-6.34775 + 5.32640i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-29.7615 + 10.8323i) q^{9} +(6.39551 + 11.0773i) q^{10} +(-32.5912 + 56.4496i) q^{11} +(5.32040 - 30.1735i) q^{12} +(24.8424 + 9.04190i) q^{13} +(8.28640 + 14.3525i) q^{14} +(-37.5269 - 31.4888i) q^{15} +(12.2567 + 10.2846i) q^{16} +(96.1207 - 34.9851i) q^{17} +(10.9994 + 62.3808i) q^{18} +(-11.5967 - 65.7679i) q^{19} +(24.0392 - 8.74957i) q^{20} +(-48.6221 - 40.7988i) q^{21} +(99.8652 + 83.7968i) q^{22} +(41.4085 + 71.7217i) q^{23} +(-57.5824 - 20.9583i) q^{24} +(-14.6034 + 82.8199i) q^{25} +(26.4367 - 45.7898i) q^{26} +(-17.8914 - 30.9888i) q^{27} +(31.1467 - 11.3365i) q^{28} +(113.346 - 196.321i) q^{29} +(-75.0538 + 62.9776i) q^{30} -94.8681 q^{31} +(24.5134 - 20.5692i) q^{32} +(-469.169 - 170.764i) q^{33} +(-35.5248 - 201.471i) q^{34} +(9.20261 - 52.1906i) q^{35} +126.686 q^{36} +(93.2459 - 204.837i) q^{37} -133.565 q^{38} +(-35.1635 + 199.422i) q^{39} +(-8.88454 - 50.3868i) q^{40} +(-37.3117 - 13.5803i) q^{41} +(-97.2442 + 81.5976i) q^{42} -48.1559 q^{43} +(199.730 - 167.594i) q^{44} +(101.278 - 175.418i) q^{45} +(155.645 - 56.6502i) q^{46} +(95.8190 + 165.963i) q^{47} +(-61.2779 + 106.136i) q^{48} +(-47.6379 + 270.168i) q^{49} +(158.052 + 57.5261i) q^{50} +(391.755 + 678.540i) q^{51} +(-81.0069 - 67.9729i) q^{52} +(242.959 + 203.867i) q^{53} +(-67.2497 + 24.4769i) q^{54} +(-72.3894 - 410.541i) q^{55} +(-11.5113 - 65.2841i) q^{56} +(480.687 - 174.956i) q^{57} +(-347.313 - 291.430i) q^{58} +(319.785 + 268.331i) q^{59} +(97.9758 + 169.699i) q^{60} +(44.1852 + 16.0821i) q^{61} +(-32.9474 + 186.854i) q^{62} +(131.222 - 227.282i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-158.880 + 57.8275i) q^{65} +(-499.280 + 864.778i) q^{66} +(221.866 - 186.168i) q^{67} -409.158 q^{68} +(-485.946 + 407.757i) q^{69} +(-99.5994 - 36.2512i) q^{70} +(99.1058 + 562.057i) q^{71} +(43.9977 - 249.523i) q^{72} -955.693 q^{73} +(-371.066 - 254.798i) q^{74} -644.165 q^{75} +(-46.3866 + 263.072i) q^{76} +(-93.7921 - 531.921i) q^{77} +(380.573 + 138.517i) q^{78} +(396.441 - 332.653i) q^{79} -102.328 q^{80} +(-445.106 + 373.488i) q^{81} +(-39.7063 + 68.7733i) q^{82} +(1208.19 - 439.746i) q^{83} +(126.943 + 219.872i) q^{84} +(-327.096 + 566.548i) q^{85} +(-16.7244 + 94.8487i) q^{86} +(1631.69 + 593.885i) q^{87} +(-260.729 - 451.597i) q^{88} +(-143.735 - 120.608i) q^{89} +(-310.333 - 260.400i) q^{90} +(-205.854 + 74.9248i) q^{91} +(-57.5241 - 326.236i) q^{92} +(-126.184 - 715.625i) q^{93} +(360.162 - 131.088i) q^{94} +(327.184 + 274.540i) q^{95} +(187.766 + 157.555i) q^{96} +(-617.359 - 1069.30i) q^{97} +(515.582 + 187.657i) q^{98} +(358.484 - 2033.06i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) $ 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$	1.33010	+	7.54337i	0.255978	+	1.45172i	0.793551	+	0.608504i	$0.208230\pi$
$3$	1.33010	+	7.54337i	0.255978	+	1.45172i	−0.537573	+	0.843217i	$0.680659\pi$
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	−4.89924	+	4.11095i	−0.438202	+	0.367695i	−0.835036	−	0.550196i	$-0.814553\pi$
$5$	−4.89924	+	4.11095i	−0.438202	+	0.367695i	0.396834	+	0.917890i	$0.370109\pi$
$6$	15.3195			1.04236
$7$	−6.34775	+	5.32640i	−0.342746	+	0.287598i	−0.797870	−	0.602830i	$-0.794040\pi$
$7$	−6.34775	+	5.32640i	−0.342746	+	0.287598i	0.455123	+	0.890428i	$0.349595\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	−29.7615	+	10.8323i	−1.10228	+	0.401197i
$10$	6.39551	+	11.0773i	0.202244	+	0.350296i
$11$	−32.5912	+	56.4496i	−0.893328	+	1.54729i	−0.0574679	+	0.998347i	$0.518303\pi$
$11$	−32.5912	+	56.4496i	−0.893328	+	1.54729i	−0.835860	+	0.548942i	$0.815031\pi$
$12$	5.32040	−	30.1735i	0.127989	−	0.725861i
$13$	24.8424	+	9.04190i	0.530004	+	0.192906i	0.593140	−	0.805099i	$-0.297888\pi$
$13$	24.8424	+	9.04190i	0.530004	+	0.192906i	−0.0631363	+	0.998005i	$0.520110\pi$
$14$	8.28640	+	14.3525i	0.158188	+	0.273990i
$15$	−37.5269	−	31.4888i	−0.645960	−	0.542025i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	96.1207	−	34.9851i	1.37133	−	0.499125i	0.451795	−	0.892122i	$-0.350784\pi$
$17$	96.1207	−	34.9851i	1.37133	−	0.499125i	0.919540	+	0.392997i	$0.128562\pi$
$18$	10.9994	+	62.3808i	0.144033	+	0.816849i
$19$	−11.5967	−	65.7679i	−0.140024	−	0.794115i	−0.971229	−	0.238149i	$-0.923459\pi$
$19$	−11.5967	−	65.7679i	−0.140024	−	0.794115i	0.831205	−	0.555966i	$-0.187652\pi$
$20$	24.0392	−	8.74957i	0.268767	−	0.0978231i
$21$	−48.6221	−	40.7988i	−0.505248	−	0.423954i
$22$	99.8652	+	83.7968i	0.967787	+	0.812070i
$23$	41.4085	+	71.7217i	0.375403	+	0.650218i	0.990387	−	0.138322i	$-0.0441708\pi$
$23$	41.4085	+	71.7217i	0.375403	+	0.650218i	−0.614984	+	0.788540i	$0.710838\pi$
$24$	−57.5824	−	20.9583i	−0.489748	−	0.178254i
$25$	−14.6034	+	82.8199i	−0.116827	+	0.662559i
$26$	26.4367	−	45.7898i	0.199411	−	0.345389i
$27$	−17.8914	−	30.9888i	−0.127526	−	0.220882i
$28$	31.1467	−	11.3365i	0.210220	−	0.0765140i
$29$	113.346	−	196.321i	0.725788	−	1.25710i	−0.232860	−	0.972510i	$-0.574808\pi$
$29$	113.346	−	196.321i	0.725788	−	1.25710i	0.958649	−	0.284592i	$-0.0918582\pi$
$30$	−75.0538	+	62.9776i	−0.456763	+	0.383270i
$31$	−94.8681			−0.549639			−0.274820	−	0.961496i	$-0.588618\pi$
$31$	−94.8681			−0.549639			−0.274820	+	0.961496i	$0.588618\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$	−469.169	−	170.764i	−2.47491	−	0.900792i
$34$	−35.5248	−	201.471i	−0.179190	−	1.01623i
$35$	9.20261	−	52.1906i	0.0444436	−	0.252052i
$36$	126.686			0.586510
$37$	93.2459	−	204.837i	0.414312	−	0.910135i
$37$	93.2459	−	204.837i	0.414312	−	0.910135i
$38$	−133.565			−0.570187
$39$	−35.1635	+	199.422i	−0.144376	+	0.818797i
$40$	−8.88454	−	50.3868i	−0.0351192	−	0.199171i
$41$	−37.3117	−	13.5803i	−0.142125	−	0.0517291i	0.269978	−	0.962866i	$-0.412983\pi$
$41$	−37.3117	−	13.5803i	−0.142125	−	0.0517291i	−0.412103	+	0.911137i	$0.635206\pi$
$42$	−97.2442	+	81.5976i	−0.357264	+	0.299780i
$43$	−48.1559			−0.170784			−0.0853920	−	0.996347i	$-0.527214\pi$
$43$	−48.1559			−0.170784			−0.0853920	+	0.996347i	$0.527214\pi$
$44$	199.730	−	167.594i	0.684329	−	0.574220i
$45$	101.278	−	175.418i	0.335502	−	0.581107i
$46$	155.645	−	56.6502i	0.498883	−	0.181579i
$47$	95.8190	+	165.963i	0.297375	+	0.515069i	0.975535	−	0.219846i	$-0.0705554\pi$
$47$	95.8190	+	165.963i	0.297375	+	0.515069i	−0.678159	+	0.734915i	$0.737222\pi$
$48$	−61.2779	+	106.136i	−0.184265	+	0.319156i
$49$	−47.6379	+	270.168i	−0.138886	+	0.787661i
$50$	158.052	+	57.5261i	0.447037	+	0.162708i
$51$	391.755	+	678.540i	1.07562	+	1.86303i
$52$	−81.0069	−	67.9729i	−0.216031	−	0.181272i
$53$	242.959	+	203.867i	0.629679	+	0.528364i	0.900829	−	0.434173i	$-0.142959\pi$
$53$	242.959	+	203.867i	0.629679	+	0.528364i	−0.271150	+	0.962537i	$0.587404\pi$
$54$	−67.2497	+	24.4769i	−0.169473	+	0.0616831i
$55$	−72.3894	−	410.541i	−0.177473	−	1.00650i
$56$	−11.5113	−	65.2841i	−0.0274691	−	0.155785i
$57$	480.687	−	174.956i	1.11699	−	0.406552i
$58$	−347.313	−	291.430i	−0.786283	−	0.659770i
$59$	319.785	+	268.331i	0.705634	+	0.592097i	0.923370	−	0.383910i	$-0.125423\pi$
$59$	319.785	+	268.331i	0.705634	+	0.592097i	−0.217736	+	0.976008i	$0.569867\pi$
$60$	97.9758	+	169.699i	0.210810	+	0.365134i
$61$	44.1852	+	16.0821i	0.0927433	+	0.0337558i	0.387975	−	0.921670i	$-0.373175\pi$
$61$	44.1852	+	16.0821i	0.0927433	+	0.0337558i	−0.295232	+	0.955426i	$0.595397\pi$
$62$	−32.9474	+	186.854i	−0.0674890	+	0.382749i
$63$	131.222	−	227.282i	0.262419	−	0.454522i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−158.880	+	57.8275i	−0.303179	+	0.110348i
$66$	−499.280	+	864.778i	−0.931168	+	1.61283i
$67$	221.866	−	186.168i	0.404556	−	0.339463i	−0.417696	−	0.908587i	$-0.637162\pi$
$67$	221.866	−	186.168i	0.404556	−	0.339463i	0.822251	+	0.569124i	$0.192718\pi$
$68$	−409.158			−0.729672
$69$	−485.946	+	407.757i	−0.847840	+	0.711423i
$70$	−99.5994	−	36.2512i	−0.170063	−	0.0618978i
$71$	99.1058	+	562.057i	0.165658	+	0.939492i	0.948384	+	0.317125i	$0.102718\pi$
$71$	99.1058	+	562.057i	0.165658	+	0.939492i	−0.782726	+	0.622367i	$0.786171\pi$
$72$	43.9977	−	249.523i	0.0720163	−	0.408425i
$73$	−955.693			−1.53227			−0.766133	−	0.642682i	$-0.777822\pi$
$73$	−955.693			−1.53227			−0.766133	+	0.642682i	$0.777822\pi$
$74$	−371.066	−	254.798i	−0.582913	−	0.400265i
$75$	−644.165			−0.991756
$76$	−46.3866	+	263.072i	−0.0700120	+	0.397058i
$77$	−93.7921	−	531.921i	−0.138813	−	0.787248i
$78$	380.573	+	138.517i	0.552454	+	0.201077i
$79$	396.441	−	332.653i	0.564596	−	0.473752i	−0.315252	−	0.949008i	$-0.602089\pi$
$79$	396.441	−	332.653i	0.564596	−	0.473752i	0.879848	+	0.475256i	$0.157645\pi$
$80$	−102.328			−0.143008
$81$	−445.106	+	373.488i	−0.610571	+	0.512330i
$82$	−39.7063	+	68.7733i	−0.0534735	+	0.0926188i
$83$	1208.19	−	439.746i	1.59779	−	0.581547i	0.618815	−	0.785536i	$-0.287613\pi$
$83$	1208.19	−	439.746i	1.59779	−	0.581547i	0.978973	+	0.203989i	$0.0653907\pi$
$84$	126.943	+	219.872i	0.164889	+	0.285596i
$85$	−327.096	+	566.548i	−0.417395	+	0.722950i
$86$	−16.7244	+	94.8487i	−0.0209702	+	0.118928i
$87$	1631.69	+	593.885i	2.01075	+	0.731853i
$88$	−260.729	−	451.597i	−0.315839	−	0.547050i
$89$	−143.735	−	120.608i	−0.171190	−	0.143645i	0.553167	−	0.833070i	$-0.313419\pi$
$89$	−143.735	−	120.608i	−0.171190	−	0.143645i	−0.724357	+	0.689425i	$0.757863\pi$
$90$	−310.333	−	260.400i	−0.363467	−	0.304985i
$91$	−205.854	+	74.9248i	−0.237136	+	0.0863105i
$92$	−57.5241	−	326.236i	−0.0651881	−	0.369700i
$93$	−126.184	−	715.625i	−0.140695	−	0.797923i
$94$	360.162	−	131.088i	0.395190	−	0.143837i
$95$	327.184	+	274.540i	0.353351	+	0.296496i
$96$	187.766	+	157.555i	0.199623	+	0.167504i
$97$	−617.359	−	1069.30i	−0.646219	−	1.11928i	−0.984018	−	0.178066i	$-0.943016\pi$
$97$	−617.359	−	1069.30i	−0.646219	−	1.11928i	0.337799	−	0.941218i	$-0.390318\pi$
$98$	515.582	+	187.657i	0.531446	+	0.193430i
$99$	358.484	−	2033.06i	0.363929	−	2.06394i
$100$	168.195	−	291.322i	0.168195	−	0.291322i
$101$	754.093	+	1306.13i	0.742921	+	1.28678i	0.951160	+	0.308699i	$0.0998936\pi$
$101$	754.093	+	1306.13i	0.742921	+	1.28678i	−0.208239	+	0.978078i	$0.566773\pi$
$102$	1472.52	−	535.953i	1.42942	−	0.520267i
$103$	−629.686	+	1090.65i	−0.602377	+	1.04335i	0.390083	+	0.920780i	$0.372446\pi$
$103$	−629.686	+	1090.65i	−0.602377	+	1.04335i	−0.992460	+	0.122568i	$0.960887\pi$
$104$	−162.014	+	135.946i	−0.152757	+	0.128179i
$105$	405.933			0.377286
$106$	485.918	−	407.734i	0.445251	−	0.373610i
$107$	−1700.13	−	618.797i	−1.53605	−	0.559078i	−0.570959	−	0.820978i	$-0.693429\pi$
$107$	−1700.13	−	618.797i	−1.53605	−	0.559078i	−0.965095	+	0.261900i	$0.915651\pi$
$108$	24.8545	+	140.957i	0.0221447	+	0.125589i
$109$	251.494	−	1426.29i	0.220998	−	1.25334i	−0.649192	−	0.760625i	$-0.724893\pi$
$109$	251.494	−	1426.29i	0.220998	−	1.25334i	0.870190	−	0.492717i	$-0.163996\pi$
$110$	−833.748			−0.722680
$111$	1669.19	+	430.934i	1.42732	+	0.368491i
$112$	−132.582			−0.111856
$113$	−399.398	+	2265.10i	−0.332497	+	1.88569i	0.118171	+	0.992993i	$0.462297\pi$
$113$	−399.398	+	2265.10i	−0.332497	+	1.88569i	−0.450668	+	0.892692i	$0.648814\pi$
$114$	−177.655	−	1007.53i	−0.145955	−	0.827752i
$115$	−497.715	−	181.153i	−0.403584	−	0.146893i
$116$	−694.626	+	582.860i	−0.555986	+	0.466528i
$117$	−837.293			−0.661605
$118$	639.569	−	536.662i	0.498959	−	0.418676i
$119$	−423.806	+	734.053i	−0.326472	+	0.565467i
$120$	368.268	−	134.039i	0.280151	−	0.101967i
$121$	−1458.87	−	2526.84i	−1.09607	−	1.89845i
$122$	47.0209	−	81.4427i	0.0348941	−	0.0604383i
$123$	52.8133	−	299.519i	0.0387156	−	0.219567i
$124$	356.588	+	129.787i	0.258246	+	0.0939939i
$125$	−668.642	−	1158.12i	−0.478441	−	0.828685i
$126$	−402.086	−	337.390i	−0.284291	−	0.238549i
$127$	−527.302	−	442.459i	−0.368429	−	0.309149i	0.439711	−	0.898140i	$-0.355081\pi$
$127$	−527.302	−	442.459i	−0.368429	−	0.309149i	−0.808140	+	0.588991i	$0.799525\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$	−64.0522	−	363.258i	−0.0437169	−	0.247931i
$130$	58.7196	+	333.015i	0.0396158	+	0.224672i
$131$	191.576	−	69.7280i	0.127772	−	0.0465051i	−0.277343	−	0.960771i	$-0.589454\pi$
$131$	191.576	−	69.7280i	0.127772	−	0.0465051i	0.405115	+	0.914266i	$0.367232\pi$
$132$	1529.88	+	1283.72i	1.00878	+	0.846468i
$133$	423.919	+	355.710i	0.276379	+	0.231910i
$134$	−289.625	−	501.646i	−0.186715	−	0.323400i
$135$	215.048	+	78.2711i	0.137099	+	0.0499000i
$136$	−142.099	+	805.884i	−0.0895948	+	0.508117i
$137$	−67.1795	+	116.358i	−0.0418944	+	0.0725632i	−0.886212	−	0.463279i	$-0.846673\pi$
$137$	−67.1795	+	116.358i	−0.0418944	+	0.0725632i	0.844318	+	0.535843i	$0.180006\pi$
$138$	634.357	+	1098.74i	0.391305	+	0.677760i
$139$	1665.35	−	606.136i	1.01621	−	0.369869i	0.220394	−	0.975411i	$-0.429266\pi$
$139$	1665.35	−	606.136i	1.01621	−	0.369869i	0.795813	+	0.605542i	$0.207044\pi$
$140$	−105.991	+	183.583i	−0.0639851	+	0.110825i
$141$	−1124.47	+	943.546i	−0.671615	+	0.563552i
$142$	1141.46			0.674569
$143$	−1320.06	+	1107.66i	−0.771948	+	0.647741i
$144$	−476.184	−	173.317i	−0.275570	−	0.100299i
$145$	251.757	+	1427.79i	0.144188	+	0.817733i
$146$	−331.909	+	1882.35i	−0.188144	+	1.06702i
$147$	−2101.34			−1.17902
$148$	−630.723	+	642.367i	−0.350305	+	0.356772i
$149$	3134.12			1.72320			0.861600	−	0.507588i	$-0.169463\pi$
$149$	3134.12			1.72320			0.861600	+	0.507588i	$0.169463\pi$
$150$	−223.716	+	1268.76i	−0.121776	+	0.690624i
$151$	83.8196	+	475.365i	0.0451731	+	0.256190i	0.999028	−	0.0440782i	$-0.0140351\pi$
$151$	83.8196	+	475.365i	0.0451731	+	0.256190i	−0.953855	+	0.300268i	$0.902924\pi$
$152$	502.040	+	182.728i	0.267900	+	0.0975077i
$153$	−2481.73	+	2082.42i	−1.31135	+	1.10035i
$154$	−1080.25			−0.565256
$155$	464.782	−	389.998i	0.240853	−	0.202099i
$156$	404.997	−	701.475i	0.207857	−	0.360019i
$157$	2418.68	−	880.327i	1.22950	−	0.447501i	0.356074	−	0.934458i	$-0.384115\pi$
$157$	2418.68	−	880.327i	1.22950	−	0.447501i	0.873426	+	0.486957i	$0.161893\pi$
$158$	−517.517	−	896.365i	−0.260579	−	0.451335i
$159$	−1214.68	+	2103.89i	−0.605853	+	1.04937i
$160$	−35.5382	+	201.547i	−0.0175596	+	0.0995856i
$161$	−644.869	−	234.713i	−0.315670	−	0.114894i
$162$	581.045	+	1006.40i	0.281797	+	0.488088i
$163$	860.767	+	722.269i	0.413623	+	0.347071i	0.825731	−	0.564064i	$-0.190763\pi$
$163$	860.767	+	722.269i	0.413623	+	0.347071i	−0.412108	+	0.911135i	$0.635207\pi$
$164$	121.667	+	102.091i	0.0579305	+	0.0486095i
$165$	3000.58	−	1092.12i	1.41572	−	0.515281i
$166$	−446.530	−	2532.40i	−0.208780	−	1.18405i
$167$	−365.997	−	2075.67i	−0.169591	−	0.961799i	−0.944203	−	0.329363i	$-0.893166\pi$
$167$	−365.997	−	2075.67i	−0.169591	−	0.961799i	0.774612	−	0.632436i	$-0.217945\pi$
$168$	477.151	−	173.669i	0.219125	−	0.0797549i
$169$	−1147.61	−	962.959i	−0.522353	−	0.438306i
$170$	1002.28	+	841.014i	0.452185	+	0.379429i
$171$	1057.55	+	1831.73i	0.472942	+	0.819159i
$172$	181.007	+	65.8812i	0.0802422	+	0.0292058i
$173$	486.703	−	2760.23i	0.213892	−	1.21304i	−0.668927	−	0.743328i	$-0.733246\pi$
$173$	486.703	−	2760.23i	0.213892	−	1.21304i	0.882819	−	0.469714i	$-0.155643\pi$
$174$	1736.40	−	3007.54i	0.756531	−	1.31035i
$175$	−348.433	−	603.503i	−0.150509	−	0.260689i
$176$	−980.022	+	356.699i	−0.419727	+	0.152768i
$177$	−1598.78	+	2769.16i	−0.678934	+	1.17595i
$178$	−287.471	+	241.216i	−0.121050	+	0.101573i
$179$	−3199.04			−1.33580			−0.667898	−	0.744253i	$-0.732806\pi$
$179$	−3199.04			−1.33580			−0.667898	+	0.744253i	$0.732806\pi$
$180$	−620.666	+	520.801i	−0.257010	+	0.215657i
$181$	−1170.56	−	426.049i	−0.480702	−	0.174961i	0.0902924	−	0.995915i	$-0.471220\pi$
$181$	−1170.56	−	426.049i	−0.480702	−	0.174961i	−0.570994	+	0.820954i	$0.693442\pi$
$182$	76.0807	+	431.475i	0.0309861	+	0.175731i
$183$	−62.5425	+	354.696i	−0.0252638	+	0.143278i
$184$	−662.537			−0.265450
$185$	385.241	+	1386.88i	0.153100	+	0.551163i
$186$	−1453.33			−0.572921
$187$	−1157.79	+	6566.17i	−0.452761	+	2.56773i
$188$	−133.110	−	754.906i	−0.0516387	−	0.292857i
$189$	278.629	+	101.413i	0.107234	+	0.0390301i
$190$	654.367	−	549.079i	0.249857	−	0.209655i
$191$	4870.80			1.84523			0.922614	−	0.385725i	$-0.126049\pi$
$191$	4870.80			1.84523			0.922614	+	0.385725i	$0.126049\pi$
$192$	375.533	−	315.109i	0.141155	−	0.118443i
$193$	1880.84	−	3257.71i	0.701482	−	1.21500i	−0.266464	−	0.963845i	$-0.585855\pi$
$193$	1880.84	−	3257.71i	0.701482	−	1.21500i	0.967946	−	0.251157i	$-0.0808112\pi$
$194$	−2320.51	+	844.596i	−0.858778	+	0.312569i
$195$	−647.540	−	1121.57i	−0.237802	−	0.411885i
$196$	548.671	−	950.326i	0.199953	−	0.346329i
$197$	759.721	−	4308.59i	0.274761	−	1.55825i	−0.464960	−	0.885332i	$-0.653931\pi$
$197$	759.721	−	4308.59i	0.274761	−	1.55825i	0.739721	−	0.672914i	$-0.234958\pi$
$198$	−3879.85	−	1412.15i	−1.39257	−	0.506854i
$199$	793.187	+	1373.84i	0.282550	+	0.489392i	0.972012	−	0.234930i	$-0.0754862\pi$
$199$	793.187	+	1373.84i	0.282550	+	0.489392i	−0.689462	+	0.724322i	$0.742153\pi$
$200$	−515.379	−	432.455i	−0.182214	−	0.152896i
$201$	1699.43	+	1425.99i	0.596362	+	0.500407i
$202$	2834.46	−	1031.66i	0.987287	−	0.359343i
$203$	326.192	+	1849.93i	0.112779	+	0.639603i
$204$	−544.221	−	3086.43i	−0.186780	−	1.05928i
$205$	238.627	−	86.8532i	0.0812998	−	0.0295907i
$206$	1929.47	+	1619.02i	0.652586	+	0.547584i
$207$	−2009.29	−	1686.00i	−0.674664	−	0.566111i
$208$	211.494	+	366.318i	0.0705023	+	0.122113i
$209$	4090.52	+	1488.83i	1.35381	+	0.492748i
$210$	140.979	−	799.533i	0.0463261	−	0.262729i
$211$	1530.43	−	2650.79i	0.499334	−	0.864871i	−0.500666	−	0.865641i	$-0.666912\pi$
$211$	1530.43	−	2650.79i	0.499334	−	0.864871i	1.00000		0.000769239i	$0.000244856\pi$
$212$	−634.321	−	1098.68i	−0.205497	−	0.355931i
$213$	−4107.98	+	1495.18i	−1.32148	+	0.480978i
$214$	−1809.24	+	3133.70i	−0.577931	+	1.00101i
$215$	235.928	−	197.967i	0.0748378	−	0.0627964i
$216$	286.263			0.0901746
$217$	602.199	−	505.305i	0.188387	−	0.158075i
$218$	−2721.91	−	990.694i	−0.845646	−	0.307790i
$219$	−1271.17	−	7209.14i	−0.392226	−	2.22442i
$220$	−289.558	+	1642.16i	−0.0887363	+	0.503248i
$221$	2704.20			0.823096
$222$	1428.48	−	3137.99i	0.431861	−	0.948687i
$223$	−2097.48			−0.629854			−0.314927	−	0.949116i	$-0.601980\pi$
$223$	−2097.48			−0.629854			−0.314927	+	0.949116i	$0.601980\pi$
$224$	−46.0454	+	261.136i	−0.0137345	+	0.0778925i
$225$	−462.512	−	2623.03i	−0.137040	−	0.777195i
$226$	4322.66	+	1573.32i	1.27230	+	0.463078i
$227$	−3037.54	+	2548.80i	−0.888144	+	0.745241i	−0.967837	−	0.251578i	$-0.919050\pi$
$227$	−3037.54	+	2548.80i	−0.888144	+	0.745241i	0.0796933	+	0.996819i	$0.474606\pi$
$228$	−2046.14			−0.594339
$229$	−354.195	+	297.205i	−0.102209	+	0.0857636i	−0.692460	−	0.721456i	$-0.743473\pi$
$229$	−354.195	+	297.205i	−0.102209	+	0.0857636i	0.590251	+	0.807220i	$0.299029\pi$
$230$	−529.657	+	917.393i	−0.151846	+	0.263005i
$231$	3887.73	−	1415.02i	1.10733	−	0.403036i
$232$	906.770	+	1570.57i	0.256605	+	0.444453i
$233$	2344.62	−	4060.99i	0.659231	−	1.14182i	−0.321584	−	0.946881i	$-0.604215\pi$
$233$	2344.62	−	4060.99i	0.659231	−	1.14182i	0.980815	−	0.194941i	$-0.0624515\pi$
$234$	−290.789	+	1649.14i	−0.0812370	+	0.460718i
$235$	−1151.71	−	419.187i	−0.319698	−	0.116361i
$236$	−834.898	−	1446.09i	−0.230285	−	0.398865i
$237$	3036.63	+	2548.04i	0.832280	+	0.698366i
$238$	1298.62	+	1089.67i	0.353684	+	0.296776i
$239$	687.799	−	250.338i	0.186151	−	0.0677534i	−0.247263	−	0.968948i	$-0.579531\pi$
$239$	687.799	−	250.338i	0.186151	−	0.0677534i	0.433414	+	0.901195i	$0.357309\pi$
$240$	−136.107	−	771.898i	−0.0366068	−	0.207608i
$241$	52.2511	+	296.331i	0.0139659	+	0.0792048i	0.990994	−	0.133905i	$-0.0427518\pi$
$241$	52.2511	+	296.331i	0.0139659	+	0.0792048i	−0.977028	+	0.213110i	$0.931641\pi$
$242$	−5483.56	+	1995.85i	−1.45660	+	0.530158i
$243$	−4149.50	−	3481.84i	−1.09543	−	0.919178i
$244$	−144.081	−	120.898i	−0.0378025	−	0.0317201i
$245$	−877.257	−	1519.45i	−0.228759	−	0.396222i
$246$	−571.596	−	208.044i	−0.148145	−	0.0539203i
$247$	306.578	−	1738.69i	0.0789760	−	0.447895i
$248$	379.472	−	657.266i	0.0971634	−	0.168292i
$249$	4924.19	+	8528.94i	1.25324	+	2.17068i
$250$	−2513.27	+	914.756i	−0.635813	+	0.231417i
$251$	3008.37	−	5210.65i	0.756520	−	1.31033i	−0.188095	−	0.982151i	$-0.560231\pi$
$251$	3008.37	−	5210.65i	0.756520	−	1.31033i	0.944615	−	0.328181i	$-0.106435\pi$
$252$	−804.173	+	674.781i	−0.201024	+	0.168679i
$253$	−5398.21			−1.34143
$254$	−1054.60	+	884.919i	−0.260519	+	0.218601i
$255$	−4708.75	−	1713.84i	−1.15637	−	0.420883i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	−816.809	+	4632.35i	−0.198253	+	1.12435i	0.709456	+	0.704750i	$0.248941\pi$
$257$	−816.809	+	4632.35i	−0.198253	+	1.12435i	−0.907709	+	0.419600i	$0.862170\pi$
$258$	−737.723			−0.178018
$259$	499.141	+	1796.92i	0.119750	+	0.431101i
$260$	676.306			0.161318
$261$	−1246.74	+	7070.63i	−0.295676	+	1.67686i
$262$	−70.8037	−	401.548i	−0.0166957	−	0.0946858i
$263$	3181.58	+	1158.00i	0.745949	+	0.271503i	0.686900	−	0.726752i	$-0.258971\pi$
$263$	3181.58	+	1158.00i	0.745949	+	0.271503i	0.0590492	+	0.998255i	$0.481193\pi$
$264$	3059.76	−	2567.45i	0.713316	−	0.598543i
$265$	−2028.40			−0.470203
$266$	847.837	−	711.420i	0.195429	−	0.163985i
$267$	718.610	−	1244.67i	0.164712	−	0.285290i
$268$	−1088.64	+	396.231i	−0.248130	+	0.0903121i
$269$	3257.76	+	5642.61i	0.738399	+	1.27894i	0.953216	+	0.302290i	$0.0977510\pi$
$269$	3257.76	+	5642.61i	0.738399	+	1.27894i	−0.214817	+	0.976654i	$0.568916\pi$
$270$	228.849	−	396.379i	0.0515827	−	0.0893439i
$271$	78.7811	−	446.790i	0.0176591	−	0.100150i	−0.974704	−	0.223498i	$-0.928252\pi$
$271$	78.7811	−	446.790i	0.0176591	−	0.100150i	0.992363	+	0.123349i	$0.0393634\pi$
$272$	1537.93	+	559.761i	0.342834	+	0.124781i
$273$	−838.992	−	1453.18i	−0.186000	−	0.322162i
$274$	205.850	+	172.729i	0.0453863	+	0.0380836i
$275$	−4199.21	−	3523.55i	−0.920806	−	0.772648i
$276$	2384.40	−	867.852i	0.520015	−	0.189270i
$277$	1413.46	+	8016.16i	0.306595	+	1.73879i	0.615899	+	0.787825i	$0.288793\pi$
$277$	1413.46	+	8016.16i	0.306595	+	1.73879i	−0.309304	+	0.950963i	$0.600096\pi$
$278$	−615.487	−	3490.60i	−0.132786	−	0.753066i
$279$	2823.42	−	1027.64i	0.605856	−	0.220513i
$280$	324.777	+	272.520i	0.0693183	+	0.0581650i
$281$	−1588.17	−	1332.63i	−0.337160	−	0.282911i	0.458449	−	0.888720i	$-0.348405\pi$
$281$	−1588.17	−	1332.63i	−0.337160	−	0.282911i	−0.795610	+	0.605809i	$0.792849\pi$
$282$	1467.90	+	2542.47i	0.309971	+	0.536886i
$283$	−2414.99	−	878.985i	−0.507267	−	0.184630i	0.0756929	−	0.997131i	$-0.475883\pi$
$283$	−2414.99	−	878.985i	−0.507267	−	0.184630i	−0.582959	+	0.812501i	$0.698105\pi$
$284$	396.423	−	2248.23i	0.0828289	−	0.469746i
$285$	−1635.77	+	2833.23i	−0.339980	+	0.588863i
$286$	1723.21	+	2984.69i	0.356278	+	0.617092i
$287$	309.180	−	112.532i	0.0635899	−	0.0231448i
$288$	−506.745	+	877.708i	−0.103681	+	0.179581i
$289$	4251.65	−	3567.56i	0.865388	−	0.726147i
$290$	2899.63			0.587144
$291$	7244.95	−	6079.23i	1.45947	−	1.22464i
$292$	3592.23	+	1307.47i	0.719930	+	0.262033i
$293$	431.162	+	2445.24i	0.0859684	+	0.487551i	0.997143	+	0.0755316i	$0.0240654\pi$
$293$	431.162	+	2445.24i	0.0859684	+	0.487551i	−0.911175	+	0.412020i	$0.864824\pi$
$294$	−729.787	+	4138.83i	−0.144769	+	0.821025i
$295$	−2669.80			−0.526921
$296$	1046.17	+	1465.37i	0.205430	+	0.287747i
$297$	2332.41			0.455691
$298$	1088.47	−	6173.00i	0.211588	−	1.19997i
$299$	380.188	+	2156.15i	0.0735346	+	0.417035i
$300$	2421.27	+	881.269i	0.465973	+	0.169600i
$301$	305.682	−	256.498i	0.0585356	−	0.0491172i
$302$	965.396			0.183948
$303$	−8849.58	+	7425.68i	−1.67787	+	1.40790i
$304$	534.260	−	925.365i	0.100796	−	0.174583i
$305$	−282.587	+	102.853i	−0.0530521	+	0.0193094i
$306$	3239.67	+	5611.27i	0.605227	+	1.04828i
$307$	−4792.06	+	8300.09i	−0.890871	+	1.54303i	−0.0520377	+	0.998645i	$0.516572\pi$
$307$	−4792.06	+	8300.09i	−0.890871	+	1.54303i	−0.838833	+	0.544389i	$0.816762\pi$
$308$	−375.168	+	2127.69i	−0.0694065	+	0.393624i
$309$	−9064.71	−	3299.28i	−1.66885	−	0.607410i
$310$	−606.730	−	1050.89i	−0.111161	−	0.192537i
$311$	207.036	+	173.724i	0.0377490	+	0.0316752i	0.661467	−	0.749974i	$-0.269934\pi$
$311$	207.036	+	173.724i	0.0377490	+	0.0316752i	−0.623718	+	0.781649i	$0.714379\pi$
$312$	−1240.98	−	1041.31i	−0.225182	−	0.188950i
$313$	−3052.68	+	1111.08i	−0.551271	+	0.200646i	−0.602611	−	0.798035i	$-0.705873\pi$
$313$	−3052.68	+	1111.08i	−0.551271	+	0.200646i	0.0513403	+	0.998681i	$0.483651\pi$
$314$	−893.907	−	5069.60i	−0.160656	−	0.911127i
$315$	291.461	+	1652.96i	0.0521332	+	0.295662i
$316$	−1945.23	+	708.005i	−0.346290	+	0.126039i
$317$	−5650.80	−	4741.59i	−1.00120	−	0.840108i	−0.0140507	−	0.999901i	$-0.504473\pi$
$317$	−5650.80	−	4741.59i	−1.00120	−	0.840108i	−0.987150	+	0.159794i	$0.948917\pi$
$318$	3722.01	+	3123.13i	0.656351	+	0.550744i
$319$	7388.17	+	12796.7i	1.29673	+	2.24601i
$320$	384.628	+	139.993i	0.0671917	+	0.0244558i
$321$	2406.47	−	13647.8i	0.418430	−	2.37304i
$322$	−686.256	+	1188.63i	−0.118769	+	0.205714i
$323$	−3415.57	−	5915.94i	−0.588382	−	1.01911i
$324$	2184.01	−	794.916i	0.374488	−	0.136302i
$325$	−1111.63	+	1925.40i	−0.189730	+	0.328622i
$326$	1721.53	−	1444.54i	0.292475	−	0.245416i
$327$	11093.6			1.87607
$328$	243.334	−	204.182i	0.0409631	−	0.0343721i
$329$	−1492.22	−	543.124i	−0.250057	−	0.0910134i
$330$	−1108.97	−	6289.27i	−0.184990	−	1.04913i
$331$	236.795	−	1342.93i	0.0393215	−	0.223003i	−0.958814	−	0.284033i	$-0.908327\pi$
$331$	236.795	−	1342.93i	0.0393215	−	0.223003i	0.998136	+	0.0610300i	$0.0194385\pi$
$332$	−5142.93			−0.850166
$333$	−556.282	+	7106.33i	−0.0915437	+	1.16944i
$334$	−4215.39			−0.690586
$335$	−321.649	+	1824.16i	−0.0524583	+	0.297506i
$336$	−176.348	−	1000.12i	−0.0286326	−	0.162384i
$337$	1230.66	+	447.923i	0.198927	+	0.0724034i	0.439562	−	0.898212i	$-0.355134\pi$
$337$	1230.66	+	447.923i	0.198927	+	0.0724034i	−0.240635	+	0.970616i	$0.577356\pi$
$338$	−2295.22	+	1925.92i	−0.369359	+	0.309929i
$339$	−17617.7			−2.82260
$340$	2004.56	−	1682.03i	0.319743	−	0.268296i
$341$	3091.86	−	5355.27i	0.491008	−	0.850451i
$342$	3975.10	−	1446.82i	0.628505	−	0.228757i
$343$	−2557.75	−	4430.14i	−0.402639	−	0.697392i
$344$	192.624	−	333.634i	0.0301906	−	0.0522917i
$345$	704.497	−	3995.40i	0.109939	−	0.623493i
$346$	−5267.56	−	1917.24i	−0.818456	−	0.297894i
$347$	−4844.35	−	8390.66i	−0.749448	−	1.29808i	−0.948088	−	0.318009i	$-0.896986\pi$
$347$	−4844.35	−	8390.66i	−0.749448	−	1.29808i	0.198640	−	0.980072i	$-0.436347\pi$
$348$	−5320.65	−	4464.56i	−0.819589	−	0.687717i
$349$	123.592	+	103.706i	0.0189562	+	0.0159061i	0.652216	−	0.758033i	$-0.273839\pi$
$349$	123.592	+	103.706i	0.0189562	+	0.0159061i	−0.633260	+	0.773939i	$0.718284\pi$
$350$	−1309.68	+	476.684i	−0.200015	+	0.0727996i
$351$	−164.268	−	931.610i	−0.0249800	−	0.141669i
$352$	362.202	+	2054.15i	0.0548449	+	0.311041i
$353$	2856.12	−	1039.54i	0.430640	−	0.156740i	−0.117600	−	0.993061i	$-0.537520\pi$
$353$	2856.12	−	1039.54i	0.430640	−	0.156740i	0.548240	+	0.836321i	$0.315298\pi$
$354$	4898.93	+	4110.69i	0.735523	+	0.617177i
$355$	−2796.13	−	2346.23i	−0.418038	−	0.350775i
$356$	375.266	+	649.980i	0.0558682	+	0.0967665i
$357$	−6100.94	−	2220.56i	−0.904470	−	0.329200i
$358$	−1111.02	+	6300.88i	−0.164019	+	0.930201i
$359$	−4373.13	+	7574.48i	−0.642911	+	1.11355i	0.341869	+	0.939748i	$0.388940\pi$
$359$	−4373.13	+	7574.48i	−0.642911	+	1.11355i	−0.984780	+	0.173807i	$0.944393\pi$
$360$	810.222	+	1403.35i	0.118618	+	0.205452i
$361$	2254.42	−	820.541i	0.328680	−	0.119630i
$362$	−1245.68	+	2157.59i	−0.180861	+	0.313260i
$363$	17120.4	−	14365.7i	2.47545	−	2.07715i
$364$	876.262			0.126178
$365$	4682.17	−	3928.81i	0.671441	−	0.563406i
$366$	676.894	+	246.369i	0.0966717	+	0.0351856i
$367$	−493.748	−	2800.19i	−0.0702274	−	0.398279i	−0.999577	−	0.0290787i	$-0.990743\pi$
$367$	−493.748	−	2800.19i	−0.0702274	−	0.398279i	0.929350	−	0.369201i	$-0.120368\pi$
$368$	−230.097	+	1304.94i	−0.0325941	+	0.184850i
$369$	1257.56			0.177414
$370$	2865.40	−	277.120i	0.402609	−	0.0389372i
$371$	−2628.12			−0.367777
$372$	−504.736	+	2862.50i	−0.0703477	+	0.398962i
$373$	1898.42	+	10766.5i	0.263530	+	1.49455i	0.773190	+	0.634175i	$0.218660\pi$
$373$	1898.42	+	10766.5i	0.263530	+	1.49455i	−0.509660	+	0.860376i	$0.670229\pi$
$374$	12530.7	+	4560.82i	1.73248	+	0.630573i
$375$	7846.78	−	6584.23i	1.08055	−	0.906689i
$376$	−1533.10			−0.210276
$377$	4590.91	−	3852.23i	0.627173	−	0.526260i
$378$	296.511	−	513.572i	0.0403462	−	0.0698817i
$379$	4844.90	−	1763.40i	0.656638	−	0.238997i	0.00785376	−	0.999969i	$-0.497500\pi$
$379$	4844.90	−	1763.40i	0.656638	−	0.238997i	0.648784	+	0.760973i	$0.275278\pi$
$380$	−854.215	−	1479.54i	−0.115317	−	0.199734i
$381$	2636.27	−	4566.15i	0.354489	−	0.613992i
$382$	1691.61	−	9593.60i	0.226571	−	1.28495i
$383$	−3607.65	−	1313.08i	−0.481312	−	0.175183i	0.0899579	−	0.995946i	$-0.471327\pi$
$383$	−3607.65	−	1313.08i	−0.481312	−	0.175183i	−0.571270	+	0.820762i	$0.693549\pi$
$384$	−490.223	−	849.091i	−0.0651474	−	0.112839i
$385$	2646.21	+	2220.44i	0.350295	+	0.293932i
$386$	−5763.24	−	4835.93i	−0.759951	−	0.637674i
$387$	1433.19	−	521.640i	0.188251	−	0.0685179i
$388$	857.626	+	4863.84i	0.112215	+	0.636402i
$389$	−545.686	−	3094.74i	−0.0711243	−	0.403366i	−0.999497	−	0.0317153i	$-0.989903\pi$
$389$	−545.686	−	3094.74i	−0.0711243	−	0.403366i	0.928373	−	0.371651i	$-0.121208\pi$
$390$	−2433.96	+	885.887i	−0.316021	+	0.115022i
$391$	6489.40	+	5445.26i	0.839343	+	0.704293i
$392$	−1681.23	−	1410.72i	−0.216619	−	0.181765i
$393$	780.799	+	1352.38i	0.100219	+	0.173585i
$394$	−8222.42	−	2992.72i	−1.05137	−	0.382667i
$395$	−574.738	+	3259.50i	−0.0732106	+	0.415198i
$396$	−4128.85	+	7151.38i	−0.523946	+	0.907501i
$397$	1067.62	+	1849.18i	0.134968	+	0.233772i	0.925585	−	0.378539i	$-0.123573\pi$
$397$	1067.62	+	1849.18i	0.134968	+	0.233772i	−0.790617	+	0.612311i	$0.790240\pi$
$398$	2981.41	−	1085.14i	0.375488	−	0.136667i
$399$	−2119.40	+	3670.90i	−0.265921	+	0.460589i
$400$	−1030.76	+	864.909i	−0.128845	+	0.108114i
$401$	2830.20			0.352453			0.176226	−	0.984350i	$-0.443611\pi$
$401$	2830.20			0.352453			0.176226	+	0.984350i	$0.443611\pi$
$402$	3398.87	−	2851.99i	0.421692	−	0.353841i
$403$	−2356.75	−	857.788i	−0.291311	−	0.106028i
$404$	−1047.57	−	5941.09i	−0.129007	−	0.731634i
$405$	645.290	−	3659.62i	0.0791721	−	0.449007i
$406$	3756.93			0.459245
$407$	8523.97	+	11939.6i	1.03813	+	1.45411i
$408$	−6268.08			−0.760579
$409$	1070.42	−	6070.65i	0.129410	−	0.733923i	−0.849180	−	0.528104i	$-0.822903\pi$
$409$	1070.42	−	6070.65i	0.129410	−	0.733923i	0.978590	−	0.205819i	$-0.0659857\pi$
$410$	−88.1931	−	500.168i	−0.0106233	−	0.0602476i
$411$	−967.089	−	351.991i	−0.116066	−	0.0422444i
$412$	3858.94	−	3238.04i	0.461448	−	0.387201i
$413$	−3459.15			−0.412140
$414$	−4018.59	+	3371.99i	−0.477060	+	0.400301i
$415$	−4111.46	+	7121.25i	−0.486321	+	0.842333i
$416$	794.957	−	289.341i	0.0936923	−	0.0341012i
$417$	6787.38	+	11756.1i	0.797073	+	1.38057i
$418$	4353.04	−	7539.68i	0.509364	−	0.882244i
$419$	−1362.81	+	7728.91i	−0.158897	+	0.901150i	0.796239	+	0.604982i	$0.206820\pi$
$419$	−1362.81	+	7728.91i	−0.158897	+	0.901150i	−0.955136	+	0.296168i	$0.904291\pi$
$420$	−1525.81	−	555.350i	−0.177266	−	0.0645197i
$421$	3937.37	+	6819.73i	0.455810	+	0.789485i	0.998734	−	0.0502960i	$-0.0160165\pi$
$421$	3937.37	+	6819.73i	0.455810	+	0.789485i	−0.542925	+	0.839781i	$0.682683\pi$
$422$	−4689.52	−	3934.98i	−0.540953	−	0.453914i
$423$	−4649.49	−	3901.38i	−0.534434	−	0.448444i
$424$	−2384.27	+	867.803i	−0.273090	+	0.0993968i
$425$	1493.77	+	8471.60i	0.170491	+	0.966901i
$426$	1518.25	+	8610.42i	0.172675	+	0.979287i
$427$	−366.137	+	133.263i	−0.0414955	+	0.0151031i
$428$	5543.84	+	4651.83i	0.626102	+	0.525362i
$429$	−10111.3	−	8484.37i	−1.13794	−	0.954846i
$430$	−307.982	−	533.440i	−0.0345400	−	0.0598250i
$431$	−11115.7	−	4045.79i	−1.24228	−	0.452155i	−0.364497	−	0.931205i	$-0.618759\pi$
$431$	−11115.7	−	4045.79i	−1.24228	−	0.452155i	−0.877788	+	0.479050i	$0.840981\pi$
$432$	99.4180	−	563.828i	0.0110723	−	0.0627944i
$433$	−3387.15	+	5866.71i	−0.375926	+	0.651123i	−0.990465	−	0.137763i	$-0.956009\pi$
$433$	−3387.15	+	5866.71i	−0.375926	+	0.651123i	0.614539	+	0.788886i	$0.289342\pi$
$434$	−786.115	−	1361.59i	−0.0869464	−	0.150596i
$435$	−10435.5	+	3798.20i	−1.15021	+	0.418643i
$436$	−2896.59	+	5017.05i	−0.318169	+	0.551085i
$437$	4236.79	−	3555.08i	0.463782	−	0.389160i
$438$	−14640.7			−1.59717
$439$	1940.59	−	1628.35i	0.210978	−	0.177032i	−0.531175	−	0.847262i	$-0.678249\pi$
$439$	1940.59	−	1628.35i	0.210978	−	0.177032i	0.742153	+	0.670231i	$0.233805\pi$
$440$	3133.87	+	1140.63i	0.339548	+	0.123586i
$441$	−1508.77	−	8556.63i	−0.162916	−	0.923943i
$442$	939.159	−	5326.24i	0.101066	−	0.573175i
$443$	1724.85			0.184989			0.0924943	−	0.995713i	$-0.470516\pi$
$443$	1724.85			0.184989			0.0924943	+	0.995713i	$0.470516\pi$
$444$	−5684.54	−	3903.37i	−0.607604	−	0.417220i
$445$	1200.01			0.127833
$446$	−728.446	+	4131.22i	−0.0773384	+	0.438608i
$447$	4168.68	+	23641.8i	0.441101	+	2.50161i
$448$	498.347	+	181.383i	0.0525551	+	0.0191285i
$449$	−2020.51	+	1695.41i	−0.212369	+	0.178199i	−0.742767	−	0.669550i	$-0.766487\pi$
$449$	−2020.51	+	1695.41i	−0.212369	+	0.178199i	0.530398	+	0.847749i	$0.322043\pi$
$450$	−5327.00			−0.558038
$451$	1982.64	−	1663.63i	0.207004	−	0.173697i
$452$	4600.08	−	7967.57i	0.478694	−	0.829122i
$453$	−3474.36	+	1264.56i	−0.360353	+	0.131158i
$454$	3965.23	+	6867.97i	0.409906	+	0.709978i
$455$	700.518	−	1213.33i	0.0721775	−	0.125015i
$456$	−710.618	+	4030.12i	−0.0729775	+	0.413876i
$457$	−3252.41	−	1183.78i	−0.332913	−	0.121171i	0.170155	−	0.985417i	$-0.445573\pi$
$457$	−3252.41	−	1183.78i	−0.332913	−	0.121171i	−0.503068	+	0.864247i	$0.667796\pi$
$458$	462.369	+	800.847i	0.0471727	+	0.0817055i
$459$	−2803.88	−	2352.74i	−0.285129	−	0.239251i
$460$	1622.96	+	1361.83i	0.164502	+	0.138034i
$461$	−7040.02	+	2562.36i	−0.711250	+	0.258874i	−0.672207	−	0.740364i	$-0.734653\pi$
$461$	−7040.02	+	2562.36i	−0.711250	+	0.258874i	−0.0390434	+	0.999238i	$0.512431\pi$
$462$	−1436.85	−	8148.76i	−0.144693	−	0.820594i
$463$	−2808.12	−	15925.6i	−0.281867	−	1.59855i	−0.716267	−	0.697826i	$-0.754151\pi$
$463$	−2808.12	−	15925.6i	−0.281867	−	1.59855i	0.434401	−	0.900720i	$-0.356960\pi$
$464$	3408.34	−	1240.53i	0.341009	−	0.124117i
$465$	3560.11	+	2987.28i	0.355045	+	0.297918i
$466$	−7184.32	−	6028.36i	−0.714178	−	0.599267i
$467$	4554.33	+	7888.32i	0.451283	+	0.781645i	0.998466	−	0.0553682i	$-0.0176333\pi$
$467$	4554.33	+	7888.32i	0.451283	+	0.781645i	−0.547183	+	0.837013i	$0.684300\pi$
$468$	3147.19	+	1145.48i	0.310853	+	0.113141i
$469$	−416.747	+	2363.49i	−0.0410311	+	0.232699i
$470$	−1225.62	+	2122.84i	−0.120285	+	0.208339i
$471$	9857.71	+	17074.0i	0.964372	+	1.67034i
$472$	−3138.19	+	1142.21i	−0.306032	+	0.111386i
$473$	1569.46	−	2718.38i	0.152566	−	0.264252i
$474$	6073.26	−	5096.07i	0.588511	−	0.493819i
$475$	5616.24			0.542507
$476$	2597.23	−	2179.34i	0.250092	−	0.209852i
$477$	−9439.19	−	3435.58i	−0.906060	−	0.329779i
$478$	−254.200	−	1441.64i	−0.0243240	−	0.137948i
$479$	−1056.57	+	5992.10i	−0.100785	+	0.571578i	0.892036	+	0.451965i	$0.149277\pi$
$479$	−1056.57	+	5992.10i	−0.100785	+	0.571578i	−0.992821	+	0.119614i	$0.961834\pi$
$480$	−1567.61			−0.149065
$481$	4168.57	−	4245.53i	0.395157	−	0.402452i
$482$	601.805			0.0568702
$483$	912.788	−	5176.68i	0.0859903	−	0.487675i
$484$	2026.64	+	11493.6i	0.190331	+	1.07942i
$485$	7420.42	+	2700.81i	0.694729	+	0.252861i
$486$	−8299.00	+	6963.69i	−0.774589	+	0.649957i
$487$	15263.3			1.42022			0.710111	−	0.704089i	$-0.248645\pi$
$487$	15263.3			1.42022			0.710111	+	0.704089i	$0.248645\pi$
$488$	−288.161	+	241.796i	−0.0267304	+	0.0224295i
$489$	−4303.44	+	7453.77i	−0.397972	+	0.689307i
$490$	−3297.41	+	1200.16i	−0.304004	+	0.110648i
$491$	7547.41	+	13072.5i	0.693706	+	1.20153i	0.970615	+	0.240638i	$0.0773567\pi$
$491$	7547.41	+	13072.5i	0.693706	+	1.20153i	−0.276909	+	0.960896i	$0.589310\pi$
$492$	−608.279	+	1053.57i	−0.0557385	+	0.0965419i
$493$	4026.60	−	22836.0i	0.367848	−	2.08617i
$494$	−3318.08	−	1207.68i	−0.302201	−	0.109992i
$495$	6601.53	+	11434.2i	0.599427	+	1.03824i
$496$	−1162.77	−	975.681i	−0.105262	−	0.0883253i
$497$	−3622.84	−	3039.92i	−0.326975	−	0.274365i
$498$	18508.9	−	6736.68i	1.66547	−	0.606181i
$499$	−769.972	−	4366.73i	−0.0690755	−	0.391747i	−0.999670	−	0.0256945i	$-0.991820\pi$
$499$	−769.972	−	4366.73i	−0.0690755	−	0.391747i	0.930594	−	0.366052i	$-0.119291\pi$
$500$	928.868	+	5267.87i	0.0830805	+	0.471173i
$501$	15170.8	−	5521.71i	1.35285	−	0.492398i
$502$	−9218.18	−	7734.97i	−0.819577	−	0.687706i
$503$	−5574.89	−	4677.89i	−0.494179	−	0.414666i	0.361342	−	0.932433i	$-0.382319\pi$
$503$	−5574.89	−	4677.89i	−0.494179	−	0.414666i	−0.855521	+	0.517768i	$0.826763\pi$
$504$	1049.77	+	1818.26i	0.0927790	+	0.160698i
$505$	−9063.91	−	3298.99i	−0.798690	−	0.290699i
$506$	−1874.78	+	10632.4i	−0.164712	+	0.934126i
$507$	5737.52	−	9937.67i	0.502588	−	0.870508i
$508$	1376.69	+	2384.50i	0.120238	+	0.208258i
$509$	−10439.3	+	3799.59i	−0.909063	+	0.330872i	−0.753878	−	0.657014i	$-0.771819\pi$
$509$	−10439.3	+	3799.59i	−0.909063	+	0.330872i	−0.155184	+	0.987886i	$0.549597\pi$
$510$	−5010.95	+	8679.21i	−0.435075	+	0.753572i
$511$	6066.50	−	5090.40i	0.525179	−	0.440677i
$512$	512.000			0.0441942
$513$	−1830.59	+	1536.05i	−0.157549	+	0.132199i
$514$	8840.28	+	3217.60i	0.758615	+	0.276113i
$515$	−1398.62	−	7931.96i	−0.119671	−	0.678688i
$516$	−256.209	+	1453.03i	−0.0218584	+	0.123965i
$517$	−12491.4			−1.06261
$518$	3712.59	−	359.053i	0.314907	−	0.0304554i
$519$	21468.8			1.81575
$520$	234.878	−	1332.06i	0.0198079	−	0.112336i
$521$	1731.48	+	9819.70i	0.145600	+	0.825737i	0.966884	+	0.255217i	$0.0821470\pi$
$521$	1731.48	+	9819.70i	0.145600	+	0.825737i	−0.821284	+	0.570519i	$0.806742\pi$
$522$	13493.4	+	4911.20i	1.13140	+	0.411796i
$523$	3555.15	−	2983.13i	0.297239	−	0.249413i	−0.481955	−	0.876196i	$-0.660073\pi$
$523$	3555.15	−	2983.13i	0.297239	−	0.249413i	0.779194	+	0.626783i	$0.215629\pi$
$524$	−815.484			−0.0679859
$525$	4089.00	−	3431.08i	0.339921	−	0.285228i
$526$	3385.77	−	5864.32i	0.280659	−	0.486115i
$527$	−9118.79	+	3318.97i	−0.753739	+	0.274339i
$528$	−3994.24	−	6918.22i	−0.329218	−	0.570221i
$529$	2654.16	−	4597.15i	0.218145	−	0.377837i
$530$	−704.457	+	3995.17i	−0.0577352	+	0.327433i
$531$	−12423.9	−	4521.94i	−1.01535	−	0.369558i
$532$	−1106.77	−	1916.99i	−0.0901968	−	0.156225i
$533$	−804.121	−	674.737i	−0.0653477	−	0.0548333i
$534$	−2201.95	−	1847.65i	−0.178441	−	0.149730i
$535$	10873.2	−	3957.52i	0.878671	−	0.319810i
$536$	402.343	+	2281.80i	0.0324227	+	0.183878i
$537$	−4255.04	−	24131.5i	−0.341934	−	1.93920i
$538$	12245.2	−	4456.88i	0.981277	−	0.357156i
$539$	−13698.3	−	11494.2i	−1.09467	−	0.918537i
$540$	−701.235	−	588.406i	−0.0558821	−	0.0468907i
$541$	−7978.35	−	13818.9i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$541$	−7978.35	−	13818.9i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$542$	−852.644	−	310.337i	−0.0675723	−	0.0245943i
$543$	1656.88	−	9396.65i	0.130946	−	0.742631i
$544$	1636.63	−	2834.73i	0.128989	−	0.223415i
$545$	4631.30	+	8021.64i	0.364005	+	0.630476i
$546$	−3153.58	+	1147.81i	−0.247181	+	0.0899664i
$547$	2601.47	−	4505.87i	0.203347	−	0.352207i	−0.746258	−	0.665657i	$-0.768151\pi$
$547$	2601.47	−	4505.87i	0.203347	−	0.352207i	0.949605	+	0.313450i	$0.101485\pi$
$548$	411.700	−	345.457i	0.0320930	−	0.0269292i
$549$	−1489.23			−0.115772
$550$	−8398.41	+	7047.10i	−0.651108	+	0.546345i
$551$	−14226.1	−	5177.87i	−1.09991	−	0.400335i
$552$	−881.240	−	4997.76i	−0.0679494	−	0.385360i
$553$	−744.664	+	4223.20i	−0.0572628	+	0.324754i
$554$	16279.6			1.24848
$555$	−9949.30	+	4750.70i	−0.760945	+	0.363344i
$556$	−7088.90			−0.540713
$557$	460.913	−	2613.97i	0.0350620	−	0.198846i	−0.962245	−	0.272184i	$-0.912254\pi$
$557$	460.913	−	2613.97i	0.0350620	−	0.198846i	0.997307	+	0.0733378i	$0.0233651\pi$
$558$	−1043.49	−	5917.95i	−0.0791660	−	0.448973i
$559$	−1196.31	−	435.421i	−0.0905161	−	0.0329452i
$560$	649.553	−	545.040i	0.0490154	−	0.0411288i
$561$	−51071.0			−3.84353
$562$	−3176.33	+	2665.26i	−0.238408	+	0.200048i
$563$	−2784.99	+	4823.75i	−0.208479	+	0.361095i	−0.951235	−	0.308466i	$-0.900184\pi$
$563$	−2784.99	+	4823.75i	−0.208479	+	0.361095i	0.742757	+	0.669561i	$0.233518\pi$
$564$	5517.49	−	2008.20i	0.411929	−	0.149930i
$565$	−7354.96	−	12739.2i	−0.547656	−	0.948568i
$566$	−2569.98	+	4451.34i	−0.190856	+	0.330572i
$567$	836.076	−	4741.62i	0.0619257	−	0.351198i
$568$	−4290.47	−	1561.60i	−0.316944	−	0.115358i
$569$	−1917.68	−	3321.53i	−0.141289	−	0.244720i	0.786693	−	0.617344i	$-0.211791\pi$
$569$	−1917.68	−	3321.53i	−0.141289	−	0.244720i	−0.927982	+	0.372624i	$0.878458\pi$
$570$	5012.28	+	4205.80i	0.368318	+	0.309055i
$571$	−588.452	−	493.769i	−0.0431277	−	0.0361885i	0.620969	−	0.783835i	$-0.286739\pi$
$571$	−588.452	−	493.769i	−0.0431277	−	0.0361885i	−0.664097	+	0.747647i	$0.731184\pi$
$572$	6477.15	−	2357.49i	0.473467	−	0.172328i
$573$	6478.64	+	36742.2i	0.472337	+	2.67876i
$574$	−114.268	−	648.047i	−0.00830917	−	0.0471236i
$575$	−6544.69	+	2382.07i	−0.474665	+	0.172764i
$576$	1552.76	+	1302.92i	0.112323	+	0.0942504i
$577$	3360.50	+	2819.79i	0.242460	+	0.203448i	0.755917	−	0.654667i	$-0.227191\pi$
$577$	3360.50	+	2819.79i	0.242460	+	0.203448i	−0.513457	+	0.858115i	$0.671636\pi$
$578$	−5550.14	−	9613.12i	−0.399403	−	0.691787i
$579$	27075.8	+	9854.80i	1.94341	+	0.707343i
$580$	1007.03	−	5711.15i	0.0720942	−	0.408866i
$581$	−5327.05	+	9226.72i	−0.380384	+	0.658845i
$582$	−9457.61	−	16381.1i	−0.673592	−	1.16670i
$583$	−19426.5	+	7070.68i	−1.38004	+	0.502294i
$584$	3822.77	−	6621.24i	0.270869	−	0.469159i
$585$	4102.10	−	3442.07i	0.289916	−	0.243269i
$586$	4965.93			0.350069
$587$	12770.6	−	10715.8i	0.897953	−	0.753472i	−0.0718363	−	0.997416i	$-0.522886\pi$
$587$	12770.6	−	10715.8i	0.897953	−	0.753472i	0.969789	+	0.243944i	$0.0784415\pi$
$588$	7898.45	+	2874.80i	0.553957	+	0.201624i
$589$	1100.15	+	6239.28i	0.0769627	+	0.436477i
$590$	−927.211	+	5258.48i	−0.0646995	+	0.366929i
$591$	33511.8			2.33247
$592$	3249.56	−	1551.63i	0.225601	−	0.107722i
$593$	−6291.75			−0.435702			−0.217851	−	0.975982i	$-0.569905\pi$
$593$	−6291.75			−0.435702			−0.217851	+	0.975982i	$0.569905\pi$
$594$	810.037	−	4593.95i	0.0559533	−	0.317327i
$595$	−941.330	−	5338.55i	−0.0648585	−	0.367831i
$596$	−11780.4	−	4287.72i	−0.809639	−	0.294684i
$597$	−9308.36	+	7810.64i	−0.638134	+	0.535458i
$598$	4378.83			0.299438
$599$	12260.3	−	10287.6i	0.836299	−	0.701738i	−0.120429	−	0.992722i	$-0.538427\pi$
$599$	12260.3	−	10287.6i	0.836299	−	0.701738i	0.956728	+	0.290984i	$0.0939826\pi$
$600$	2576.66	−	4462.90i	0.175319	−	0.303662i
$601$	501.386	−	182.490i	0.0340299	−	0.0123859i	−0.324949	−	0.945732i	$-0.605347\pi$
$601$	501.386	−	182.490i	0.0340299	−	0.0123859i	0.358979	+	0.933346i	$0.383125\pi$
$602$	−399.039	−	691.156i	−0.0270160	−	0.0467931i
$603$	−4586.44	+	7943.95i	−0.309742	+	0.536489i
$604$	335.279	−	1901.46i	0.0225866	−	0.128095i
$605$	17535.1	+	6382.24i	1.17835	+	0.428884i
$606$	11552.3	+	20009.2i	0.774390	+	1.34128i
$607$	−15747.0	−	13213.3i	−1.05297	−	0.883545i	−0.0595653	−	0.998224i	$-0.518971\pi$
$607$	−15747.0	−	13213.3i	−1.05297	−	0.883545i	−0.993403	+	0.114680i	$0.963416\pi$
$608$	−1637.07	−	1373.66i	−0.109197	−	0.0916272i
$609$	−13520.8	+	4921.17i	−0.899657	+	0.327448i
$610$	104.440	+	592.308i	0.00693221	+	0.0393145i
$611$	879.751	+	4989.32i	0.0582503	+	0.330354i
$612$	12177.2	−	4432.12i	0.804302	−	0.292742i
$613$	3250.64	+	2727.61i	0.214180	+	0.179718i	0.743565	−	0.668663i	$-0.233133\pi$
$613$	3250.64	+	2727.61i	0.214180	+	0.179718i	−0.529386	+	0.848381i	$0.677578\pi$
$614$	14683.7	+	12321.1i	0.965125	+	0.809836i
$615$	972.564	+	1684.53i	0.0637684	+	0.110450i
$616$	4060.43	+	1477.88i	0.265583	+	0.0966644i
$617$	−3013.95	+	17092.9i	−0.196656	+	1.11529i	0.713384	+	0.700773i	$0.247162\pi$
$617$	−3013.95	+	17092.9i	−0.196656	+	1.11529i	−0.910040	+	0.414520i	$0.863950\pi$
$618$	−9646.46	+	16708.2i	−0.627893	+	1.08754i
$619$	1103.47	+	1911.27i	0.0716515	+	0.124104i	0.899625	−	0.436663i	$-0.143840\pi$
$619$	1103.47	+	1911.27i	0.0716515	+	0.124104i	−0.827974	+	0.560767i	$0.810506\pi$
$620$	−2280.56	+	830.055i	−0.147725	+	0.0537674i
$621$	1481.72	−	2566.41i	0.0957475	−	0.165840i
$622$	414.073	−	347.448i	0.0266926	−	0.0223978i
$623$	1554.80			0.0999869
$624$	−2481.97	+	2082.62i	−0.159228	+	0.133608i
$625$	−1841.40	−	670.215i	−0.117850	−	0.0428937i
$626$	1128.23	+	6398.48i	0.0720335	+	0.408522i
$627$	−5789.97	+	32836.6i	−0.368787	+	2.09149i
$628$	−10295.6			−0.654203
$629$	1796.62	−	22951.3i	0.113889	−	1.45489i
$630$	3356.91			0.212290
$631$	−4064.03	+	23048.3i	−0.256397	+	1.45410i	0.536064	+	0.844177i	$0.319911\pi$
$631$	−4064.03	+	23048.3i	−0.256397	+	1.45410i	−0.792461	+	0.609922i	$0.791201\pi$
$632$	718.927	+	4077.24i	0.0452490	+	0.256620i
$633$	22031.5	+	8018.81i	1.38337	+	0.503506i
$634$	−11301.6	+	9483.17i	−0.707956	+	0.594046i
$635$	4402.31			0.275119
$636$	7444.01	−	6246.27i	0.464111	−	0.389435i
$637$	−3626.27	+	6280.88i	−0.225554	+	0.390671i
$638$	27770.4	−	10107.6i	1.72326	−	0.627217i
$639$	−9037.92	−	15654.1i	−0.559522	−	0.969120i
$640$	409.312	−	708.950i	0.0252805	−	0.0437870i
$641$	2622.07	−	14870.5i	0.161569	−	0.916301i	−0.790964	−	0.611863i	$-0.790420\pi$
$641$	2622.07	−	14870.5i	0.161569	−	0.916301i	0.952532	−	0.304438i	$-0.0984686\pi$
$642$	−26045.1	−	9479.64i	−1.60112	−	0.582760i
$643$	−1789.32	−	3099.20i	−0.109742	−	0.190078i	0.805924	−	0.592019i	$-0.201669\pi$
$643$	−1789.32	−	3099.20i	−0.109742	−	0.190078i	−0.915666	+	0.401941i	$0.868336\pi$
$644$	2102.81	+	1764.47i	0.128668	+	0.107965i
$645$	1807.14	+	1516.37i	0.110320	+	0.0925692i
$646$	−12838.4	+	4672.78i	−0.781917	+	0.284594i
$647$	−4468.84	−	25344.0i	−0.271543	−	1.53999i	−0.749734	−	0.661739i	$-0.769819\pi$
$647$	−4468.84	−	25344.0i	−0.271543	−	1.53999i	0.478192	−	0.878255i	$-0.341292\pi$
$648$	−807.179	−	4577.74i	−0.0489336	−	0.277516i
$649$	−25569.3	+	9306.48i	−1.54651	+	0.562883i
$650$	3406.24	+	2858.17i	0.205544	+	0.172472i
$651$	4612.69	+	3870.50i	0.277704	+	0.233022i
$652$	−2247.30	−	3892.44i	−0.134987	−	0.233803i
$653$	5979.41	+	2176.33i	0.358335	+	0.130423i	0.514913	−	0.857242i	$-0.327824\pi$
$653$	5979.41	+	2176.33i	0.358335	+	0.130423i	−0.156579	+	0.987666i	$0.550046\pi$
$654$	3852.76	−	21850.1i	0.230359	−	1.30643i
$655$	−651.929	+	1129.17i	−0.0388901	+	0.0673595i
$656$	−317.650	−	550.186i	−0.0189057	−	0.0327457i
$657$	28442.9	−	10352.4i	1.68898	−	0.614740i
$658$	−1587.99	+	2750.48i	−0.0940825	+	0.162956i
$659$	−17213.9	+	14444.2i	−1.01754	+	0.853817i	−0.989316	−	0.145784i	$-0.953429\pi$
$659$	−17213.9	+	14444.2i	−1.01754	+	0.853817i	−0.0282234	+	0.999602i	$0.508985\pi$
$660$	−12772.6			−0.753291
$661$	16834.8	−	14126.0i	0.990615	−	0.831225i	0.00495850	−	0.999988i	$-0.498422\pi$
$661$	16834.8	−	14126.0i	0.990615	−	0.831225i	0.985657	+	0.168763i	$0.0539772\pi$
$662$	−2562.82	−	932.789i	−0.150463	−	0.0547641i
$663$	3596.86	+	20398.8i	0.210694	+	1.19491i
$664$	−1786.12	+	10129.6i	−0.104390	+	0.592025i
$665$	−3539.19			−0.206382
$666$	13803.5	+	3563.66i	0.803118	+	0.207341i
$667$	18774.0			1.08985
$668$	−1463.99	+	8302.70i	−0.0847956	+	0.480900i
$669$	−2789.85	−	15822.0i	−0.161229	−	0.914373i
$670$	3481.19	+	1267.05i	0.200731	+	0.0730602i
$671$	−2347.88	+	1970.10i	−0.135080	+	0.113346i
$672$	−2031.09			−0.116594
$673$	−1952.49	+	1638.33i	−0.111832	+	0.0938380i	−0.696989	−	0.717082i	$-0.745477\pi$
$673$	−1952.49	+	1638.33i	−0.111832	+	0.0938380i	0.585157	+	0.810920i	$0.301033\pi$
$674$	1309.64	−	2268.36i	0.0748449	−	0.129635i
$675$	2827.77	−	1029.22i	0.161246	−	0.0586886i
$676$	2996.20	+	5189.56i	0.170471	+	0.295264i
$677$	−10464.6	+	18125.2i	−0.594071	+	1.02896i	0.399606	+	0.916687i	$0.369147\pi$
$677$	−10464.6	+	18125.2i	−0.594071	+	1.02896i	−0.993677	+	0.112275i	$0.964186\pi$
$678$	−6118.56	+	34700.1i	−0.346581	+	1.96556i
$679$	9614.34	+	3499.33i	0.543394	+	0.197779i
$680$	−2616.77	−	4532.38i	−0.147571	−	0.255601i
$681$	−23266.8	−	19523.1i	−1.30923	−	1.09857i
$682$	−9474.02	−	7949.65i	−0.531934	−	0.446346i
$683$	2574.24	−	936.947i	0.144218	−	0.0524909i	−0.268903	−	0.963167i	$-0.586661\pi$
$683$	2574.24	−	936.947i	0.144218	−	0.0524909i	0.413120	+	0.910676i	$0.364439\pi$
$684$	−1469.14	−	8331.89i	−0.0821255	−	0.465757i
$685$	−149.215	−	846.239i	−0.00832293	−	0.0472017i
$686$	−9613.98	+	3499.20i	−0.535078	+	0.194752i
$687$	−2713.04	−	2276.51i	−0.150668	−	0.126426i
$688$	−590.233	−	495.265i	−0.0327070	−	0.0274445i
$689$	4192.35	+	7261.36i	0.231808	+	0.401503i
$690$	−7624.73	−	2775.17i	−0.420679	−	0.153115i
$691$	2820.86	−	15997.9i	0.155297	−	0.880735i	−0.803216	−	0.595688i	$-0.796880\pi$
$691$	2820.86	−	15997.9i	0.155297	−	0.880735i	0.958513	−	0.285047i	$-0.0920093\pi$
$692$	−5605.62	+	9709.22i	−0.307939	+	0.533366i
$693$	8553.33	+	14814.8i	0.468852	+	0.812075i
$694$	−18208.8	+	6627.46i	−0.995960	+	0.362500i
$695$	−5667.14	+	9815.77i	−0.309305	+	0.535731i
$696$	−10641.3	+	8929.11i	−0.579537	+	0.486289i
$697$	−4061.54			−0.220720
$698$	247.183	−	207.411i	0.0134040	−	0.0112473i
$699$	33752.1	+	12284.8i	1.82636	+	0.664739i
$700$	484.038	+	2745.12i	0.0261356	+	0.148222i
$701$	−221.942	+	1258.70i	−0.0119581	+	0.0678178i	−0.990203	−	0.139636i	$-0.955407\pi$
$701$	−221.942	+	1258.70i	−0.0119581	+	0.0678178i	0.978245	+	0.207454i	$0.0665178\pi$
$702$	−1891.96			−0.101720
$703$	−14553.0	−	3757.16i	−0.780766	−	0.201570i
$704$	4171.67			0.223332
$705$	1630.20	−	9245.32i	0.0870877	−	0.493899i
$706$	−1055.58	−	5986.48i	−0.0562709	−	0.319128i
$707$	−11743.7	−	4274.37i	−0.624709	−	0.227375i
$708$	9797.86	−	8221.38i	0.520094	−	0.436410i
$709$	18302.2			0.969467			0.484734	−	0.874662i	$-0.338917\pi$
$709$	18302.2			0.969467			0.484734	+	0.874662i	$0.338917\pi$
$710$	−5592.27	+	4692.47i	−0.295597	+	0.248036i
$711$	−8195.28	+	14194.6i	−0.432274	+	0.748721i
$712$	1410.54	−	513.394i	0.0742446	−	0.0270228i
$713$	−3928.35	−	6804.10i	−0.206336	−	0.357385i
$714$	−6492.48	+	11245.3i	−0.340301	+	0.589419i
$715$	1913.74	−	10853.4i	0.100098	−	0.567682i
$716$	12024.5	+	4376.55i	0.627619	+	0.228435i
$717$	2803.24	+	4855.35i	0.146009	+	0.252896i
$718$	13400.0	+	11244.0i	0.696498	+	0.584431i
$719$	−20098.1	−	16864.3i	−1.04247	−	0.874732i	−0.0501838	−	0.998740i	$-0.515981\pi$
$719$	−20098.1	−	16864.3i	−1.04247	−	0.874732i	−0.992281	+	0.124008i	$0.960425\pi$
$720$	3045.44	−	1108.45i	0.157635	−	0.0573743i
$721$	−1812.14	−	10277.1i	−0.0936026	−	0.530846i
$722$	−833.199	−	4725.31i	−0.0429480	−	0.243570i
$723$	−2165.83	+	788.299i	−0.111408	+	0.0405493i
$724$	3816.99	+	3202.84i	0.195936	+	0.164410i
$725$	14604.1	+	12254.3i	0.748113	+	0.627741i
$726$	−22349.1	−	38709.8i	−1.14250	−	1.97886i
$727$	31272.2	+	11382.1i	1.59535	+	0.580661i	0.978469	−	0.206394i	$-0.0661728\pi$
$727$	31272.2	+	11382.1i	1.59535	+	0.580661i	0.616883	+	0.787055i	$0.288395\pi$
$728$	304.323	−	1725.90i	0.0154931	−	0.0878655i
$729$	12901.5	−	22346.0i	0.655463	−	1.13529i
$730$	−6112.14	−	10586.5i	−0.309891	−	0.536747i
$731$	−4628.78	+	1684.74i	−0.234202	+	0.0852425i
$732$	720.336	−	1247.66i	0.0363721	−	0.0629983i
$733$	26187.0	−	21973.5i	1.31956	−	1.10724i	0.333163	−	0.942869i	$-0.391884\pi$
$733$	26187.0	−	21973.5i	1.31956	−	1.10724i	0.986398	−	0.164374i	$-0.0525605\pi$
$734$	−5686.77			−0.285971
$735$	10295.0	−	8638.50i	0.516647	−	0.433518i
$736$	2490.32	+	906.404i	0.124721	+	0.0453947i
$737$	3278.21	+	18591.7i	0.163846	+	0.929216i
$738$	436.746	−	2476.91i	0.0217843	−	0.123545i
$739$	−23223.6			−1.15601			−0.578007	−	0.816032i	$-0.696169\pi$
$739$	−23223.6			−1.15601			−0.578007	+	0.816032i	$0.696169\pi$
$740$	449.325	−	5739.99i	0.0223210	−	0.285143i
$741$	13523.4			0.670436
$742$	−912.737	+	5176.39i	−0.0451585	+	0.256107i
$743$	−925.295	−	5247.61i	−0.0456875	−	0.259107i	0.953405	−	0.301692i	$-0.0975515\pi$
$743$	−925.295	−	5247.61i	−0.0456875	−	0.259107i	−0.999093	+	0.0425858i	$0.986440\pi$
$744$	5462.73	+	1988.27i	0.269185	+	0.0979752i
$745$	−15354.8	+	12884.2i	−0.755109	+	0.633611i
$746$	21865.1			1.07311
$747$	−31194.2	+	26175.0i	−1.52789	+	1.28205i
$748$	13334.9	−	23096.8i	0.651836	−	1.12901i
$749$	14088.0	−	5127.60i	0.687267	−	0.250145i
$750$	−10243.2	−	17741.8i	−0.498707	−	0.863786i
$751$	10840.4	−	18776.1i	0.526725	−	0.912314i	−0.472790	−	0.881175i	$-0.656753\pi$
$751$	10840.4	−	18776.1i	0.526725	−	0.912314i	0.999515	−	0.0311394i	$-0.00991357\pi$
$752$	−532.441	+	3019.63i	−0.0258193	+	0.146429i
$753$	43307.3	+	15762.6i	2.09589	+	0.762841i
$754$	−5993.01	−	10380.2i	−0.289460	−	0.501359i
$755$	−2364.85	−	1984.35i	−0.113995	−	0.0956528i
$756$	−908.562	−	762.374i	−0.0437091	−	0.0366763i
$757$	6627.05	−	2412.05i	0.318183	−	0.115809i	−0.177992	−	0.984032i	$-0.556960\pi$
$757$	6627.05	−	2412.05i	0.318183	−	0.115809i	0.496174	+	0.868223i	$0.334738\pi$
$758$	−1790.60	−	10155.0i	−0.0858016	−	0.486605i
$759$	−7180.16	−	40720.7i	−0.343377	−	1.94739i
$760$	−3210.80	+	1168.64i	−0.153247	+	0.0557775i
$761$	18606.0	+	15612.3i	0.886290	+	0.743685i	0.967462	−	0.253015i	$-0.0814221\pi$
$761$	18606.0	+	15612.3i	0.886290	+	0.743685i	−0.0811727	+	0.996700i	$0.525867\pi$
$762$	−8078.00	−	6778.24i	−0.384035	−	0.322244i
$763$	6000.59	+	10393.3i	0.284713	+	0.493137i
$764$	−18308.2	−	6663.64i	−0.866973	−	0.315552i
$765$	3597.87	−	20404.5i	0.170041	−	0.964350i
$766$	−3839.18	+	6649.66i	−0.181091	+	0.313658i
$767$	5518.00	+	9557.46i	0.259770	+	0.449934i
$768$	−1842.64	+	670.665i	−0.0865760	+	0.0315111i
$769$	−17854.7	+	30925.3i	−0.837267	+	1.45019i	0.0549039	+	0.998492i	$0.482515\pi$
$769$	−17854.7	+	30925.3i	−0.837267	+	1.45019i	−0.892171	+	0.451698i	$0.850819\pi$
$770$	5292.43	−	4440.87i	0.247696	−	0.207842i
$771$	−36030.0			−1.68299
$772$	−11526.5	+	9671.86i	−0.537366	+	0.450904i
$773$	−21218.5	−	7722.90i	−0.987292	−	0.359345i	−0.202621	−	0.979257i	$-0.564946\pi$
$773$	−21218.5	−	7722.90i	−0.987292	−	0.359345i	−0.784671	+	0.619912i	$0.787168\pi$
$774$	−529.687	−	3004.00i	−0.0245985	−	0.139505i
$775$	1385.40	−	7856.97i	0.0642127	−	0.364168i
$776$	9877.74			0.456946
$777$	−12890.9	+	6155.29i	−0.595185	+	0.284195i
$778$	−6284.96			−0.289623
$779$	−460.460	+	2611.40i	−0.0211780	+	0.120107i
$780$	899.553	+	5101.62i	0.0412938	+	0.234189i
$781$	−34957.9	−	12723.6i	−1.60165	−	0.582954i
$782$	12978.8	−	10890.5i	0.593505	−	0.498010i
$783$	−8111.70			−0.370228
$784$	−3362.45	+	2821.43i	−0.153173	+	0.128527i
$785$	−8230.70	+	14256.0i	−0.374225	+	0.648176i
$786$	2934.84	−	1068.20i	0.133184	−	0.0484749i
$787$	−4971.20	−	8610.37i	−0.225164	−	0.389996i	0.731205	−	0.682158i	$-0.238958\pi$
$787$	−4971.20	−	8610.37i	−0.225164	−	0.389996i	−0.956369	+	0.292163i	$0.905625\pi$
$788$	−8750.12	+	15155.6i	−0.395571	+	0.685149i
$789$	−4503.41	+	25540.1i	−0.203201	+	1.15241i
$790$	6220.35	+	2264.02i	0.280140	+	0.101962i
$791$	−9529.53	−	16505.6i	−0.428358	−	0.741937i
$792$	12651.5	+	10615.9i	0.567617	+	0.476287i
$793$	952.255	+	799.037i	0.0426426	+	0.0357814i
$794$	4012.95	−	1460.59i	0.179363	−	0.0652828i
$795$	−2697.98	−	15301.0i	−0.120362	−	0.682604i
$796$	−1101.88	−	6249.09i	−0.0490643	−	0.278258i
$797$	23916.1	−	8704.75i	1.06293	−	0.386874i	0.249399	−	0.968401i	$-0.419767\pi$
$797$	23916.1	−	8704.75i	1.06293	−	0.386874i	0.813527	+	0.581527i	$0.197545\pi$
$798$	6494.21	+	5449.29i	0.288086	+	0.241733i
$799$	15016.4	+	12600.3i	0.664885	+	0.557905i
$800$	1345.56	+	2330.58i	0.0594659	+	0.102998i
$801$	5584.24	+	2032.50i	0.246329	+	0.0896565i
$802$	982.918	−	5574.41i	0.0432769	−	0.245435i
$803$	31147.2	−	53948.5i	1.36882	−	2.37086i
$804$	−4436.91	−	7684.95i	−0.194624	−	0.337099i
$805$	4124.27	−	1501.11i	0.180573	−	0.0657232i
$806$	−2508.00	+	4343.99i	−0.109604	+	0.189839i
$807$	−38231.1	+	32079.7i	−1.66766	+	1.39933i
$808$	−12065.5			−0.525325
$809$	16518.4	−	13860.6i	0.717870	−	0.602364i	−0.208925	−	0.977932i	$-0.566997\pi$
$809$	16518.4	−	13860.6i	0.717870	−	0.602364i	0.926795	+	0.375567i	$0.122552\pi$
$810$	−6983.94	−	2541.95i	−0.302951	−	0.110265i
$811$	3025.75	+	17159.9i	0.131009	+	0.742989i	0.977556	+	0.210675i	$0.0675663\pi$
$811$	3025.75	+	17159.9i	0.131009	+	0.742989i	−0.846547	+	0.532314i	$0.821323\pi$
$812$	1304.77	−	7399.71i	0.0563896	−	0.319801i
$813$	3475.09			0.149910
$814$	26476.7	−	12642.4i	1.14006	−	0.544367i
$815$	−7186.32			−0.308866
$816$	−2176.88	+	12345.7i	−0.0933899	+	0.529640i
$817$	558.448	+	3167.11i	0.0239138	+	0.135622i
$818$	−11585.1	−	4216.63i	−0.495187	−	0.180233i
$819$	5314.93	−	4459.75i	0.226763	−	0.190276i
$820$	−1015.77			−0.0432587
$821$	28717.8	−	24097.1i	1.22078	−	1.02435i	0.221993	−	0.975048i	$-0.428744\pi$
$821$	28717.8	−	24097.1i	1.22078	−	1.02435i	0.998784	−	0.0493050i	$-0.0157006\pi$
$822$	−1029.15	+	1782.55i	−0.0436690	+	0.0756368i
$823$	8889.75	−	3235.60i	0.376521	−	0.137043i	−0.146825	−	0.989162i	$-0.546906\pi$
$823$	8889.75	−	3235.60i	0.376521	−	0.137043i	0.523347	+	0.852120i	$0.324683\pi$
$824$	−5037.49	−	8725.19i	−0.212972	−	0.368879i
$825$	20994.1	−	36362.8i	0.885964	−	1.53453i
$826$	−1201.35	+	6813.20i	−0.0506057	+	0.286999i
$827$	−25763.3	−	9377.07i	−1.08329	−	0.394284i	−0.262156	−	0.965025i	$-0.584434\pi$
$827$	−25763.3	−	9377.07i	−1.08329	−	0.394284i	−0.821130	+	0.570742i	$0.806656\pi$
$828$	5245.89	+	9086.15i	0.220178	+	0.381359i
$829$	−18820.5	−	15792.3i	−0.788495	−	0.661626i	0.156878	−	0.987618i	$-0.449857\pi$
$829$	−18820.5	−	15792.3i	−0.788495	−	0.661626i	−0.945372	+	0.325992i	$0.894302\pi$
$830$	12598.2	+	10571.2i	0.526857	+	0.442085i
$831$	−58588.8	+	21324.6i	−2.44575	+	0.890182i
$832$	−293.804	−	1666.25i	−0.0122426	−	0.0694312i
$833$	4872.85	+	27635.3i	0.202682	+	1.14947i
$834$	25512.2	−	9285.69i	1.05925	−	0.385536i
$835$	10326.1	+	8664.63i	0.427964	+	0.359104i
$836$	−13338.5	−	11192.3i	−0.551820	−	0.463032i
$837$	1697.33	+	2939.85i	0.0700934	+	0.121405i
$838$	14749.7	+	5368.44i	0.608018	+	0.221300i
$839$	−4757.19	+	26979.4i	−0.195753	+	1.11017i	0.715590	+	0.698521i	$0.246158\pi$
$839$	−4757.19	+	26979.4i	−0.195753	+	1.11017i	−0.911343	+	0.411649i	$0.864953\pi$
$840$	−1623.73	+	2812.39i	−0.0666954	+	0.115520i
$841$	−13500.2	−	23383.1i	−0.553538	−	0.958756i
$842$	14799.7	−	5386.64i	0.605737	−	0.220470i
$843$	7940.10	−	13752.7i	0.324403	−	0.561882i
$844$	−9379.04	+	7869.95i	−0.382512	+	0.320965i
$845$	9581.10			0.390059
$846$	−9298.97	+	7802.76i	−0.377902	+	0.317098i
$847$	22719.5	+	8269.21i	0.921665	+	0.335459i
$848$	881.190	+	4997.48i	0.0356842	+	0.202375i
$849$	3418.33	−	19386.3i	0.138182	−	0.783671i
$850$	17204.6			0.694250
$851$	18552.4	−	1794.25i	0.747320	−	0.0722751i
$852$	17486.5			0.703143
$853$	−4783.01	+	27125.8i	−0.191990	+	1.08883i	0.724651	+	0.689116i	$0.242001\pi$
$853$	−4783.01	+	27125.8i	−0.191990	+	1.08883i	−0.916641	+	0.399712i	$0.869110\pi$
$854$	135.319	+	767.430i	0.00542214	+	0.0307505i
$855$	−12711.4	−	4626.56i	−0.508444	−	0.185059i
$856$	11087.7	−	9303.66i	0.442721	−	0.371487i
$857$	−35304.1			−1.40719			−0.703596	−	0.710600i	$-0.748424\pi$
$857$	−35304.1			−1.40719			−0.703596	+	0.710600i	$0.748424\pi$
$858$	−20222.5	+	16968.7i	−0.804646	+	0.675178i
$859$	−19842.6	+	34368.3i	−0.788149	+	1.36511i	0.138951	+	0.990299i	$0.455627\pi$
$859$	−19842.6	+	34368.3i	−0.788149	+	1.36511i	−0.927100	+	0.374815i	$0.877706\pi$
$860$	−1157.63	+	421.344i	−0.0459011	+	0.0167066i
$861$	1260.11	+	2182.58i	0.0498775	+	0.0863903i
$862$	−11829.1	+	20488.6i	−0.467402	+	0.809563i
$863$	4132.94	−	23439.1i	0.163021	−	0.924536i	−0.788061	−	0.615597i	$-0.788915\pi$
$863$	4132.94	−	23439.1i	0.163021	−	0.924536i	0.951082	−	0.308939i	$-0.0999740\pi$
$864$	−1076.00	−	391.630i	−0.0423682	−	0.0154208i
$865$	8962.69	+	15523.8i	0.352301	+	0.610204i
$866$	10378.8	+	8708.87i	0.407260	+	0.341731i
$867$	32566.5	+	27326.6i	1.27568	+	1.07043i
$868$	−2954.83	+	1075.47i	−0.115545	+	0.0420551i
$869$	5857.67	+	33220.5i	0.228663	+	1.29681i
$870$	3856.79	+	21872.9i	0.150296	+	0.852370i
$871$	7194.99	−	2618.76i	0.279900	−	0.101875i
$872$	8875.68	+	7447.58i	0.344689	+	0.289228i
$873$	29956.5	+	25136.5i	1.16137	+	0.974502i
$874$	−5530.73	−	9579.51i	−0.214050	−	0.370746i
$875$	10413.0	+	3790.02i	0.402312	+	0.146430i
$876$	−5084.67	+	28836.6i	−0.196113	+	1.11221i
$877$	14213.6	−	24618.7i	0.547273	−	0.947905i	−0.451187	−	0.892430i	$-0.648999\pi$
$877$	14213.6	−	24618.7i	0.547273	−	0.947905i	0.998460	−	0.0554756i	$-0.0176675\pi$
$878$	−2533.26	−	4387.74i	−0.0973730	−	0.168655i
$879$	−17871.9	+	6504.83i	−0.685783	+	0.249605i
$880$	3334.99	−	5776.38i	0.127753	−	0.221275i
$881$	−12872.5	+	10801.3i	−0.492266	+	0.413060i	−0.854838	−	0.518896i	$-0.826343\pi$
$881$	−12872.5	+	10801.3i	−0.492266	+	0.413060i	0.362571	+	0.931956i	$0.381899\pi$
$882$	−17377.3			−0.663405
$883$	−3026.62	+	2539.63i	−0.115350	+	0.0967899i	−0.698638	−	0.715475i	$-0.746210\pi$
$883$	−3026.62	+	2539.63i	−0.115350	+	0.0967899i	0.583288	+	0.812265i	$0.301766\pi$
$884$	−10164.5	−	3699.56i	−0.386729	−	0.140758i
$885$	−3551.10	−	20139.3i	−0.134880	−	0.764943i
$886$	599.033	−	3397.29i	0.0227143	−	0.128819i
$887$	−42013.1			−1.59037			−0.795186	−	0.606365i	$-0.792627\pi$
$887$	−42013.1			−1.59037			−0.795186	+	0.606365i	$0.792627\pi$
$888$	−9662.35	+	9840.73i	−0.365143	+	0.371884i
$889$	5703.90			0.215189
$890$	416.759	−	2363.55i	0.0156964	−	0.0890186i
$891$	−6576.73	−	37298.5i	−0.247282	−	1.40241i
$892$	7883.93	+	2869.52i	0.295935	+	0.107711i
$893$	9803.88	−	8226.43i	0.367385	−	0.308272i
$894$	48013.0			1.79619
$895$	15672.9	−	13151.1i	0.585348	−	0.491165i
$896$	530.330	−	918.558i	0.0197735	−	0.0342487i
$897$	−15759.0	+	5735.79i	−0.586596	+	0.213503i
$898$	2637.59	+	4568.43i	0.0980149	+	0.169767i
$899$	−10752.9	+	18624.6i	−0.398922	+	0.690953i
$900$	−1850.05	+	10492.1i	−0.0685202	+	0.388598i
$901$	30485.7	+	11095.9i	1.12722	+	0.410275i
$902$	−2588.15	−	4482.81i	−0.0955387	−	0.165478i
$903$	2341.44	+	1964.70i	0.0862883	+	0.0724045i
$904$	−14095.5	−	11827.5i	−0.518593	−	0.435151i
$905$	7486.32	−	2724.80i	0.274976	−	0.100083i
$906$	1284.07	+	7282.34i	0.0470866	+	0.267041i
$907$	1873.81	+	10626.9i	0.0685987	+	0.389042i	0.999705	+	0.0242941i	$0.00773381\pi$
$907$	1873.81	+	10626.9i	0.0685987	+	0.389042i	−0.931106	+	0.364748i	$0.881155\pi$
$908$	14904.4	−	5424.75i	0.544735	−	0.198267i
$909$	−36591.3	−	30703.8i	−1.33516	−	1.12033i
$910$	−2146.51	−	1801.14i	−0.0781935	−	0.0656122i
$911$	12223.4	+	21171.5i	0.444543	+	0.769971i	0.998020	−	0.0628930i	$-0.0200327\pi$
$911$	12223.4	+	21171.5i	0.444543	+	0.769971i	−0.553477	+	0.832864i	$0.686699\pi$
$912$	7690.99	+	2799.29i	0.279248	+	0.101638i
$913$	−14552.9	+	82533.9i	−0.527527	+	2.99175i
$914$	−3461.15	+	5994.88i	−0.125257	+	0.216951i
$915$	−1151.73	−	1994.85i	−0.0416120	−	0.0720741i
$916$	1737.94	−	632.558i	0.0626890	−	0.0228169i
$917$	−844.679	+	1463.03i	−0.0304185	+	0.0526864i
$918$	−5607.76	+	4705.47i	−0.201616	+	0.169176i
$919$	12721.5			0.456632			0.228316	−	0.973587i	$-0.426678\pi$
$919$	12721.5			0.456632			0.228316	+	0.973587i	$0.426678\pi$
$920$	3245.93	−	2723.66i	0.116321	−	0.0976047i
$921$	−68984.6	−	25108.3i	−2.46810	−	0.898314i
$922$	2601.88	+	14756.0i	0.0929376	+	0.527076i
$923$	−2620.04	+	14859.0i	−0.0934340	+	0.529890i
$924$	−16548.9			−0.589199
$925$	15602.9	+	10713.9i	0.554615	+	0.380834i
$926$	−32342.6			−1.14778
$927$	6926.18	−	39280.3i	0.245400	−	1.39173i
$928$	−1259.67	−	7143.95i	−0.0445590	−	0.252707i
$929$	−26066.3	−	9487.35i	−0.920567	−	0.335059i	−0.162103	−	0.986774i	$-0.551828\pi$
$929$	−26066.3	−	9487.35i	−0.920567	−	0.335059i	−0.758464	+	0.651715i	$0.774050\pi$
$930$	7120.21	−	5974.57i	0.251055	−	0.210660i
$931$	18320.8			0.644941
$932$	−14368.6	+	12056.7i	−0.505000	+	0.423746i
$933$	−1035.09	+	1792.82i	−0.0363207	+	0.0629093i
$934$	17118.7	−	6230.68i	0.599721	−	0.218281i
$935$	−21320.9	−	36928.9i	−0.745742	−	1.29166i
$936$	3349.17	−	5800.93i	0.116956	−	0.202574i
$937$	−1956.94	+	11098.4i	−0.0682289	+	0.386945i	0.931502	+	0.363737i	$0.118499\pi$
$937$	−1956.94	+	11098.4i	−0.0682289	+	0.386945i	−0.999731	+	0.0232084i	$0.992612\pi$
$938$	4510.43	+	1641.66i	0.157005	+	0.0571452i
$939$	−12441.7	−	21549.6i	−0.432395	−	0.748931i
$940$	3755.52	+	3151.26i	0.130310	+	0.109343i
$941$	3083.10	+	2587.03i	0.106808	+	0.0896224i	0.694628	−	0.719370i	$-0.255569\pi$
$941$	3083.10	+	2587.03i	0.106808	+	0.0896224i	−0.587820	+	0.808992i	$0.700014\pi$
$942$	37052.9	−	13486.1i	1.28158	−	0.466457i
$943$	−571.018	−	3238.40i	−0.0197189	−	0.111831i
$944$	1159.83	+	6577.71i	0.0399886	+	0.226786i
$945$	−1781.97	+	648.586i	−0.0613414	+	0.0223265i
$946$	−4809.10	−	4035.31i	−0.165283	−	0.138689i
$947$	−19881.9	−	16682.9i	−0.682234	−	0.572462i	0.234424	−	0.972134i	$-0.424680\pi$
$947$	−19881.9	−	16682.9i	−0.682234	−	0.572462i	−0.916658	+	0.399672i	$0.869124\pi$
$948$	−7928.08	−	13731.8i	−0.271616	−	0.470453i
$949$	−23741.7	−	8641.28i	−0.812107	−	0.295583i
$950$	1950.50	−	11061.8i	0.0666132	−	0.377782i
$951$	28251.4	−	48932.9i	0.963317	−	1.66851i
$952$	−3390.45	−	5872.43i	−0.115425	−	0.199923i
$953$	40707.0	−	14816.1i	1.38366	−	0.503611i	0.460374	−	0.887725i	$-0.347715\pi$
$953$	40707.0	−	14816.1i	1.38366	−	0.503611i	0.923286	+	0.384114i	$0.125493\pi$
$954$	−10045.0	+	17398.4i	−0.340899	+	0.590455i
$955$	−23863.2	+	20023.6i	−0.808581	+	0.678480i
$956$	−2927.76			−0.0990488
$957$	−86703.1	+	72752.6i	−2.92865	+	2.45743i
$958$	11435.2	+	4162.07i	0.385651	+	0.140366i
$959$	−193.332	−	1096.44i	−0.00650991	−	0.0369195i
$960$	−544.426	+	3087.59i	−0.0183034	+	0.103804i
$961$	−20791.0			−0.697897
$962$	−6914.33	−	9684.93i	−0.231733	−	0.324589i
$963$	57301.5			1.91746
$964$	209.005	−	1185.32i	0.00698297	−	0.0396024i
$965$	4177.61	+	23692.4i	0.139359	+	0.790347i
$966$	−9879.06	−	3595.68i	−0.329041	−	0.119761i
$967$	−22458.8	+	18845.2i	−0.746874	+	0.626702i	−0.934674	−	0.355505i	$-0.884309\pi$
$967$	−22458.8	+	18845.2i	−0.746874	+	0.626702i	0.187800	+	0.982207i	$0.439864\pi$
$968$	23341.9			0.775039
$969$	40083.1	−	33633.7i	1.32885	−	1.11504i
$970$	7896.64	−	13677.4i	0.261388	−	0.452736i
$971$	−11937.6	+	4344.94i	−0.394538	+	0.143600i	−0.531668	−	0.846953i	$-0.678434\pi$
$971$	−11937.6	+	4344.94i	−0.394538	+	0.143600i	0.137130	+	0.990553i	$0.456212\pi$
$972$	10833.6	+	18764.3i	0.357497	+	0.619203i
$973$	−7342.68	+	12717.9i	−0.241928	+	0.419031i
$974$	5300.91	−	30062.9i	0.174386	−	0.988992i
$975$	−16002.6	−	5824.47i	−0.525634	−	0.191315i
$976$	376.168	+	651.541i	0.0123369	+	0.0213682i
$977$	9568.57	+	8028.98i	0.313332	+	0.262917i	0.785868	−	0.618395i	$-0.212217\pi$
$977$	9568.57	+	8028.98i	0.313332	+	0.262917i	−0.472535	+	0.881312i	$0.656661\pi$
$978$	13186.5	+	11064.8i	0.431143	+	0.361772i
$979$	11492.8	−	4183.03i	0.375190	−	0.136558i
$980$	1218.67	+	6911.44i	0.0397236	+	0.225283i
$981$	7965.21	+	45173.0i	0.259235	+	1.47020i
$982$	28369.0	−	10325.5i	0.921884	−	0.335538i
$983$	−26645.6	−	22358.3i	−0.864559	−	0.725451i	0.0983863	−	0.995148i	$-0.468632\pi$
$983$	−26645.6	−	22358.3i	−0.864559	−	0.725451i	−0.962945	+	0.269697i	$0.913076\pi$
$984$	1863.88	+	1563.98i	0.0603843	+	0.0506685i
$985$	13990.4	+	24232.0i	0.452558	+	0.783854i
$986$	−43579.7	−	15861.7i	−1.40756	−	0.512312i
$987$	2112.18	−	11978.8i	0.0681171	−	0.386311i
$988$	−3531.02	+	6115.91i	−0.113701	+	0.196936i
$989$	−1994.07	−	3453.83i	−0.0641129	−	0.111047i
$990$	24813.6	−	9031.42i	0.796595	−	0.289937i
$991$	13337.7	−	23101.5i	0.427533	−	0.740509i	−0.569120	−	0.822254i	$-0.692716\pi$
$991$	13337.7	−	23101.5i	0.427533	−	0.740509i	0.996653	+	0.0817452i	$0.0260494\pi$
$992$	−2325.54	+	1951.36i	−0.0744315	+	0.0624554i
$993$	10445.2			0.333804
$994$	−7245.68	+	6079.85i	−0.231206	+	0.194005i
$995$	−9533.80	−	3470.02i	−0.303761	−	0.110560i
$996$	−6840.61	−	38795.0i	−0.217623	−	1.23420i
$997$	8089.70	−	45879.0i	0.256974	−	1.45737i	−0.533979	−	0.845498i	$-0.679304\pi$
$997$	8089.70	−	45879.0i	0.256974	−	1.45737i	0.790953	−	0.611877i	$-0.209585\pi$
$998$	−8868.18			−0.281280
$999$	−8015.96	+	775.243i	−0.253868	+	0.0245521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.f.b.33.5	yes	30
37.9	even	9	inner	74.4.f.b.9.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.f.b.9.5	✓	30	37.9	even	9	inner
74.4.f.b.33.5	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(1.33010 + 7.54337i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-4.89924 + 4.11095i) q^{5} +15.3195 q^{6} +(-6.34775 + 5.32640i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-29.7615 + 10.8323i) q^{9} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(1.33010 + 7.54337i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-4.89924 + 4.11095i) q^{5} +15.3195 q^{6} +(-6.34775 + 5.32640i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-29.7615 + 10.8323i) q^{9} +(6.39551 + 11.0773i) q^{10} +(-32.5912 + 56.4496i) q^{11} +(5.32040 - 30.1735i) q^{12} +(24.8424 + 9.04190i) q^{13} +(8.28640 + 14.3525i) q^{14} +(-37.5269 - 31.4888i) q^{15} +(12.2567 + 10.2846i) q^{16} +(96.1207 - 34.9851i) q^{17} +(10.9994 + 62.3808i) q^{18} +(-11.5967 - 65.7679i) q^{19} +(24.0392 - 8.74957i) q^{20} +(-48.6221 - 40.7988i) q^{21} +(99.8652 + 83.7968i) q^{22} +(41.4085 + 71.7217i) q^{23} +(-57.5824 - 20.9583i) q^{24} +(-14.6034 + 82.8199i) q^{25} +(26.4367 - 45.7898i) q^{26} +(-17.8914 - 30.9888i) q^{27} +(31.1467 - 11.3365i) q^{28} +(113.346 - 196.321i) q^{29} +(-75.0538 + 62.9776i) q^{30} -94.8681 q^{31} +(24.5134 - 20.5692i) q^{32} +(-469.169 - 170.764i) q^{33} +(-35.5248 - 201.471i) q^{34} +(9.20261 - 52.1906i) q^{35} +126.686 q^{36} +(93.2459 - 204.837i) q^{37} -133.565 q^{38} +(-35.1635 + 199.422i) q^{39} +(-8.88454 - 50.3868i) q^{40} +(-37.3117 - 13.5803i) q^{41} +(-97.2442 + 81.5976i) q^{42} -48.1559 q^{43} +(199.730 - 167.594i) q^{44} +(101.278 - 175.418i) q^{45} +(155.645 - 56.6502i) q^{46} +(95.8190 + 165.963i) q^{47} +(-61.2779 + 106.136i) q^{48} +(-47.6379 + 270.168i) q^{49} +(158.052 + 57.5261i) q^{50} +(391.755 + 678.540i) q^{51} +(-81.0069 - 67.9729i) q^{52} +(242.959 + 203.867i) q^{53} +(-67.2497 + 24.4769i) q^{54} +(-72.3894 - 410.541i) q^{55} +(-11.5113 - 65.2841i) q^{56} +(480.687 - 174.956i) q^{57} +(-347.313 - 291.430i) q^{58} +(319.785 + 268.331i) q^{59} +(97.9758 + 169.699i) q^{60} +(44.1852 + 16.0821i) q^{61} +(-32.9474 + 186.854i) q^{62} +(131.222 - 227.282i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-158.880 + 57.8275i) q^{65} +(-499.280 + 864.778i) q^{66} +(221.866 - 186.168i) q^{67} -409.158 q^{68} +(-485.946 + 407.757i) q^{69} +(-99.5994 - 36.2512i) q^{70} +(99.1058 + 562.057i) q^{71} +(43.9977 - 249.523i) q^{72} -955.693 q^{73} +(-371.066 - 254.798i) q^{74} -644.165 q^{75} +(-46.3866 + 263.072i) q^{76} +(-93.7921 - 531.921i) q^{77} +(380.573 + 138.517i) q^{78} +(396.441 - 332.653i) q^{79} -102.328 q^{80} +(-445.106 + 373.488i) q^{81} +(-39.7063 + 68.7733i) q^{82} +(1208.19 - 439.746i) q^{83} +(126.943 + 219.872i) q^{84} +(-327.096 + 566.548i) q^{85} +(-16.7244 + 94.8487i) q^{86} +(1631.69 + 593.885i) q^{87} +(-260.729 - 451.597i) q^{88} +(-143.735 - 120.608i) q^{89} +(-310.333 - 260.400i) q^{90} +(-205.854 + 74.9248i) q^{91} +(-57.5241 - 326.236i) q^{92} +(-126.184 - 715.625i) q^{93} +(360.162 - 131.088i) q^{94} +(327.184 + 274.540i) q^{95} +(187.766 + 157.555i) q^{96} +(-617.359 - 1069.30i) q^{97} +(515.582 + 187.657i) q^{98} +(358.484 - 2033.06i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

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