LMFDB - Embedded newform 114.4.i.c.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1488 x^{16} + 4798 x^{15} + 939930 x^{14} - 421443 x^{13} - 319752461 x^{12} + \cdots + 20\!\cdots\!49 $ x^18 - 6x^17 - 1488x^16 + 4798x^15 + 939930x^14 - 421443x^13 - 319752461x^12 - 722235969x^11 + 60651236964x^10 + 300466233870x^9 - 5754248160525x^8 - 46793226683178x^7 + 141508710385350x^6 + 2567891527205481x^5 + 9930325439050983x^4 + 15397443154057401x^3 + 9475016573038698x^2 + 12035110299066666*x + 20915625186935649
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$16.8282 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.4.i.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-11.5845 + 9.72055i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(-2.24091 + 3.88137i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})$	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-11.5845 + 9.72055i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(-2.24091 + 3.88137i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(-28.4210 + 10.3444i) q^{10} +(-24.0527 - 41.6606i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-13.5692 + 76.9550i) q^{13} +(-6.86654 + 5.76171i) q^{14} +(-34.7535 - 29.1616i) q^{15} +(2.77837 + 15.7569i) q^{16} +(31.2438 + 11.3718i) q^{17} -18.0000 q^{18} +(81.5073 + 14.6822i) q^{19} -60.4900 q^{20} +(-12.6346 - 4.59861i) q^{21} +(-16.7069 - 94.7493i) q^{22} +(47.5868 + 39.9301i) q^{23} +(-18.3851 + 15.4269i) q^{24} +(18.0055 - 102.114i) q^{25} +(-78.1421 + 135.346i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(-16.8461 + 6.13149i) q^{28} +(100.483 - 36.5729i) q^{29} +(-45.3675 - 78.5788i) q^{30} +(-149.032 + 258.132i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(110.553 - 92.7648i) q^{33} +(50.9404 + 42.7441i) q^{34} +(-11.7692 - 66.7466i) q^{35} +(-33.8289 - 12.3127i) q^{36} +159.613 q^{37} +(143.140 + 83.3478i) q^{38} -234.426 q^{39} +(-113.684 - 41.3776i) q^{40} +(-13.5496 - 76.8437i) q^{41} +(-20.5996 - 17.2851i) q^{42} +(356.922 - 299.493i) q^{43} +(33.4137 - 189.499i) q^{44} +(68.0512 - 117.868i) q^{45} +(62.1201 + 107.595i) q^{46} +(231.920 - 84.4118i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(161.457 + 279.651i) q^{49} +(103.690 - 179.596i) q^{50} +(-17.3209 + 98.2316i) q^{51} +(-239.441 + 200.915i) q^{52} +(-223.991 - 187.951i) q^{53} +(-9.37700 - 53.1796i) q^{54} +(683.603 + 248.811i) q^{55} -35.8545 q^{56} +(-0.916742 + 248.456i) q^{57} +213.864 q^{58} +(-376.675 - 137.099i) q^{59} +(-31.5119 - 178.713i) q^{60} +(-369.724 - 310.235i) q^{61} +(-456.662 + 383.185i) q^{62} +(7.00433 - 39.7235i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-590.852 - 1023.39i) q^{65} +(271.226 - 98.7183i) q^{66} +(832.540 - 303.020i) q^{67} +(66.4980 + 115.178i) q^{68} +(-93.1802 + 161.393i) q^{69} +(23.5384 - 133.493i) q^{70} +(-119.216 + 100.034i) q^{71} +(-55.1552 - 46.2807i) q^{72} +(148.457 + 841.940i) q^{73} +(299.974 + 109.182i) q^{74} +311.069 q^{75} +(212.003 + 254.556i) q^{76} +215.600 q^{77} +(-440.578 - 160.357i) q^{78} +(40.1809 + 227.877i) q^{79} +(-185.352 - 155.529i) q^{80} +(62.0496 - 52.0658i) q^{81} +(27.0992 - 153.687i) q^{82} +(-292.160 + 506.036i) q^{83} +(-26.8909 - 46.5764i) q^{84} +(-472.485 + 171.970i) q^{85} +(875.660 - 318.714i) q^{86} +(160.398 + 277.817i) q^{87} +(192.422 - 333.285i) q^{88} +(129.234 - 732.920i) q^{89} +(208.521 - 174.970i) q^{90} +(-268.283 - 225.116i) q^{91} +(43.1482 + 244.706i) q^{92} +(-840.268 - 305.832i) q^{93} +493.607 q^{94} +(-1086.94 + 622.209i) q^{95} -96.0000 q^{96} +(-1233.20 - 448.847i) q^{97} +(112.147 + 636.015i) q^{98} +(331.658 + 278.294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) $ 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$4$	3.06418	+	2.57115i	0.383022	+	0.321394i
$5$	−11.5845	+	9.72055i	−1.03615	+	0.869432i	−0.991570	−	0.129573i	$-0.958639\pi$
$5$	−11.5845	+	9.72055i	−1.03615	+	0.869432i	−0.0445793	+	0.999006i	$0.514195\pi$
$6$	−1.04189	+	5.90885i	−0.0708916	+	0.402046i
$7$	−2.24091	+	3.88137i	−0.120998	+	0.209574i	−0.920161	−	0.391539i	$-0.871943\pi$
$7$	−2.24091	+	3.88137i	−0.120998	+	0.209574i	0.799164	+	0.601113i	$0.205276\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	−8.45723	+	3.07818i	−0.313231	+	0.114007i
$10$	−28.4210	+	10.3444i	−0.898750	+	0.327118i
$11$	−24.0527	−	41.6606i	−0.659289	−	1.14192i	−0.980800	−	0.195016i	$-0.937524\pi$
$11$	−24.0527	−	41.6606i	−0.659289	−	1.14192i	0.321511	−	0.946906i	$-0.395809\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	−13.5692	+	76.9550i	−0.289495	+	1.64181i	0.399279	+	0.916829i	$0.369260\pi$
$13$	−13.5692	+	76.9550i	−0.289495	+	1.64181i	−0.688774	+	0.724976i	$0.741851\pi$
$14$	−6.86654	+	5.76171i	−0.131083	+	0.109992i
$15$	−34.7535	−	29.1616i	−0.598221	−	0.501967i
$16$	2.77837	+	15.7569i	0.0434120	+	0.246202i
$17$	31.2438	+	11.3718i	0.445750	+	0.162240i	0.555136	−	0.831760i	$-0.312666\pi$
$17$	31.2438	+	11.3718i	0.445750	+	0.162240i	−0.109386	+	0.993999i	$0.534889\pi$
$18$	−18.0000			−0.235702
$19$	81.5073	+	14.6822i	0.984160	+	0.177281i
$19$	81.5073	+	14.6822i	0.984160	+	0.177281i
$20$	−60.4900			−0.676298
$21$	−12.6346	−	4.59861i	−0.131290	−	0.0477857i
$22$	−16.7069	−	94.7493i	−0.161905	−	0.918210i
$23$	47.5868	+	39.9301i	0.431414	+	0.362000i	0.832485	−	0.554047i	$-0.186917\pi$
$23$	47.5868	+	39.9301i	0.431414	+	0.362000i	−0.401071	+	0.916047i	$0.631362\pi$
$24$	−18.3851	+	15.4269i	−0.156368	+	0.131208i
$25$	18.0055	−	102.114i	0.144044	−	0.816916i
$26$	−78.1421	+	135.346i	−0.589420	+	1.02091i
$27$	−13.5000	−	23.3827i	−0.0962250	−	0.166667i
$28$	−16.8461	+	6.13149i	−0.113701	+	0.0413836i
$29$	100.483	−	36.5729i	0.643422	−	0.234186i	0.000359298	−	1.00000i	$-0.499886\pi$
$29$	100.483	−	36.5729i	0.643422	−	0.234186i	0.643063	+	0.765813i	$0.277663\pi$
$30$	−45.3675	−	78.5788i	−0.276098	−	0.478215i
$31$	−149.032	+	258.132i	−0.863452	+	1.49554i	0.00512500	+	0.999987i	$0.498369\pi$
$31$	−149.032	+	258.132i	−0.863452	+	1.49554i	−0.868577	+	0.495555i	$0.834965\pi$
$32$	−5.55674	+	31.5138i	−0.0306970	+	0.174091i
$33$	110.553	−	92.7648i	0.583175	−	0.489342i
$34$	50.9404	+	42.7441i	0.256947	+	0.215604i
$35$	−11.7692	−	66.7466i	−0.0568389	−	0.322349i
$36$	−33.8289	−	12.3127i	−0.156615	−	0.0570034i
$37$	159.613			0.709194			0.354597	−	0.935019i	$-0.384618\pi$
$37$	159.613			0.709194			0.354597	+	0.935019i	$0.384618\pi$
$38$	143.140	+	83.3478i	0.611064	+	0.355810i
$39$	−234.426			−0.962520
$40$	−113.684	−	41.3776i	−0.449375	−	0.163559i
$41$	−13.5496	−	76.8437i	−0.0516121	−	0.292707i	0.948066	−	0.318073i	$-0.103036\pi$
$41$	−13.5496	−	76.8437i	−0.0516121	−	0.292707i	−0.999678	+	0.0253666i	$0.991925\pi$
$42$	−20.5996	−	17.2851i	−0.0756807	−	0.0635037i
$43$	356.922	−	299.493i	1.26582	−	1.06215i	0.270781	−	0.962641i	$-0.412718\pi$
$43$	356.922	−	299.493i	1.26582	−	1.06215i	0.995037	−	0.0995059i	$-0.0317262\pi$
$44$	33.4137	−	189.499i	0.114484	−	0.649273i
$45$	68.0512	−	117.868i	0.225433	−	0.390461i
$46$	62.1201	+	107.595i	0.199111	+	0.344871i
$47$	231.920	−	84.4118i	0.719765	−	0.261973i	0.0439388	−	0.999034i	$-0.486009\pi$
$47$	231.920	−	84.4118i	0.719765	−	0.261973i	0.675826	+	0.737061i	$0.263787\pi$
$48$	−45.1052	+	16.4170i	−0.135633	+	0.0493664i
$49$	161.457	+	279.651i	0.470719	+	0.815309i
$50$	103.690	−	179.596i	0.293279	−	0.507974i
$51$	−17.3209	+	98.2316i	−0.0475570	+	0.269709i
$52$	−239.441	+	200.915i	−0.638549	+	0.535806i
$53$	−223.991	−	187.951i	−0.580519	−	0.487113i	0.304599	−	0.952481i	$-0.401478\pi$
$53$	−223.991	−	187.951i	−0.580519	−	0.487113i	−0.885118	+	0.465368i	$0.845922\pi$
$54$	−9.37700	−	53.1796i	−0.0236305	−	0.134015i
$55$	683.603	+	248.811i	1.67594	+	0.609994i
$56$	−35.8545			−0.0855583
$57$	−0.916742	+	248.456i	−0.00213027	+	0.577346i
$58$	213.864			0.484167
$59$	−376.675	−	137.099i	−0.831169	−	0.302521i	−0.108830	−	0.994060i	$-0.534711\pi$
$59$	−376.675	−	137.099i	−0.831169	−	0.302521i	−0.722339	+	0.691540i	$0.756933\pi$
$60$	−31.5119	−	178.713i	−0.0678028	−	0.384529i
$61$	−369.724	−	310.235i	−0.776038	−	0.651173i	0.166209	−	0.986090i	$-0.446847\pi$
$61$	−369.724	−	310.235i	−0.776038	−	0.651173i	−0.942248	+	0.334917i	$0.891292\pi$
$62$	−456.662	+	383.185i	−0.935421	+	0.784911i
$63$	7.00433	−	39.7235i	0.0140073	−	0.0794396i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−590.852	−	1023.39i	−1.12748	−	1.95285i
$66$	271.226	−	98.7183i	0.505843	−	0.184112i
$67$	832.540	−	303.020i	1.51807	−	0.552534i	0.557407	−	0.830239i	$-0.311796\pi$
$67$	832.540	−	303.020i	1.51807	−	0.552534i	0.960666	+	0.277705i	$0.0895739\pi$
$68$	66.4980	+	115.178i	0.118589	+	0.205403i
$69$	−93.1802	+	161.393i	−0.162574	+	0.281586i
$70$	23.5384	−	133.493i	0.0401912	−	0.227935i
$71$	−119.216	+	100.034i	−0.199272	+	0.167209i	−0.736963	−	0.675933i	$-0.763741\pi$
$71$	−119.216	+	100.034i	−0.199272	+	0.167209i	0.537692	+	0.843142i	$0.319296\pi$
$72$	−55.1552	−	46.2807i	−0.0902792	−	0.0757532i
$73$	148.457	+	841.940i	0.238021	+	1.34989i	0.836157	+	0.548490i	$0.184797\pi$
$73$	148.457	+	841.940i	0.238021	+	1.34989i	−0.598136	+	0.801395i	$0.704092\pi$
$74$	299.974	+	109.182i	0.471233	+	0.171515i
$75$	311.069			0.478922
$76$	212.003	+	254.556i	0.319978	+	0.384205i
$77$	215.600			0.319090
$78$	−440.578	−	160.357i	−0.639559	−	0.232780i
$79$	40.1809	+	227.877i	0.0572241	+	0.324534i	0.999959	−	0.00900769i	$-0.00286727\pi$
$79$	40.1809	+	227.877i	0.0572241	+	0.324534i	−0.942735	+	0.333542i	$0.891756\pi$
$80$	−185.352	−	155.529i	−0.259037	−	0.217358i
$81$	62.0496	−	52.0658i	0.0851160	−	0.0714208i
$82$	27.0992	−	153.687i	0.0364953	−	0.206975i
$83$	−292.160	+	506.036i	−0.386370	+	0.669213i	−0.991958	−	0.126566i	$-0.959605\pi$
$83$	−292.160	+	506.036i	−0.386370	+	0.669213i	0.605588	+	0.795778i	$0.292938\pi$
$84$	−26.8909	−	46.5764i	−0.0349290	−	0.0604988i
$85$	−472.485	+	171.970i	−0.602919	+	0.219445i
$86$	875.660	−	318.714i	1.09796	−	0.399626i
$87$	160.398	+	277.817i	0.197660	+	0.342358i
$88$	192.422	−	333.285i	0.233094	−	0.403730i
$89$	129.234	−	732.920i	0.153918	−	0.872915i	−0.805850	−	0.592120i	$-0.798291\pi$
$89$	129.234	−	732.920i	0.153918	−	0.872915i	0.959768	−	0.280794i	$-0.0905979\pi$
$90$	208.521	−	174.970i	0.244223	−	0.204927i
$91$	−268.283	−	225.116i	−0.309052	−	0.259325i
$92$	43.1482	+	244.706i	0.0488968	+	0.277308i
$93$	−840.268	−	305.832i	−0.936900	−	0.341004i
$94$	493.607			0.541614
$95$	−1086.94	+	622.209i	−1.17387	+	0.671972i
$96$	−96.0000			−0.102062
$97$	−1233.20	−	448.847i	−1.29085	−	0.469830i	−0.396842	−	0.917887i	$-0.629894\pi$
$97$	−1233.20	−	448.847i	−1.29085	−	0.469830i	−0.894005	+	0.448057i	$0.852116\pi$
$98$	112.147	+	636.015i	0.115597	+	0.655584i
$99$	331.658	+	278.294i	0.336696	+	0.282522i
$100$	317.724	−	266.602i	0.317724	−	0.266602i
$101$	−88.0495	+	499.353i	−0.0867451	+	0.491956i	0.910221	+	0.414122i	$0.135911\pi$
$101$	−88.0495	+	499.353i	−0.0867451	+	0.491956i	−0.996966	+	0.0778335i	$0.975200\pi$
$102$	−99.7470	+	172.767i	−0.0968277	+	0.167710i
$103$	537.019	+	930.144i	0.513728	+	0.889804i	0.999873	+	0.0159254i	$0.00506943\pi$
$103$	537.019	+	930.144i	0.513728	+	0.889804i	−0.486145	+	0.873878i	$0.661597\pi$
$104$	−587.437	+	213.809i	−0.553874	+	0.201594i
$105$	191.066	−	69.5425i	0.177583	−	0.0646348i
$106$	−292.399	−	506.450i	−0.267928	−	0.464064i
$107$	−289.766	+	501.890i	−0.261801	+	0.453453i	−0.966721	−	0.255834i	$-0.917650\pi$
$107$	−289.766	+	501.890i	−0.261801	+	0.453453i	0.704919	+	0.709287i	$0.250983\pi$
$108$	18.7540	−	106.359i	0.0167093	−	0.0947632i
$109$	−682.174	+	572.412i	−0.599453	+	0.503001i	−0.891270	−	0.453473i	$-0.850185\pi$
$109$	−682.174	+	572.412i	−0.599453	+	0.503001i	0.291817	+	0.956474i	$0.405740\pi$
$110$	1114.56	+	935.224i	0.966080	+	0.810637i
$111$	83.1494	+	471.564i	0.0711008	+	0.403233i
$112$	−67.3845	−	24.5259i	−0.0568503	−	0.0206918i
$113$	−2069.33			−1.72271			−0.861356	−	0.508002i	$-0.830384\pi$
$113$	−2069.33			−1.72271			−0.861356	+	0.508002i	$0.830384\pi$
$114$	−171.677	+	466.317i	−0.141044	+	0.383110i
$115$	−939.411			−0.761744
$116$	401.932	+	146.291i	0.321711	+	0.117093i
$117$	−122.123	−	692.595i	−0.0964982	−	0.547268i
$118$	−614.137	−	515.322i	−0.479118	−	0.402028i
$119$	−114.153	+	95.7856i	−0.0879359	+	0.0737870i
$120$	63.0238	−	357.426i	0.0479439	−	0.271903i
$121$	−491.569	+	851.422i	−0.369323	+	0.639686i
$122$	−482.641	−	835.958i	−0.358166	−	0.620361i
$123$	219.970	−	80.0626i	0.161252	−	0.0586911i
$124$	−1120.36	+	407.776i	−0.811379	+	0.295318i
$125$	−161.132	−	279.089i	−0.115297	−	0.199700i
$126$	40.3363	−	69.8646i	0.0285194	−	0.0493971i
$127$	−99.4902	+	564.237i	−0.0695144	+	0.394236i	0.930121	+	0.367252i	$0.119701\pi$
$127$	−99.4902	+	564.237i	−0.0695144	+	0.394236i	−0.999636	+	0.0269837i	$0.991410\pi$
$128$	−98.0537	+	82.2768i	−0.0677094	+	0.0568149i
$129$	1070.77	+	898.480i	0.730820	+	0.613231i
$130$	−410.401	−	2327.50i	−0.276881	−	1.57027i
$131$	2129.46	+	775.060i	1.42024	+	0.516926i	0.934118	−	0.356964i	$-0.116188\pi$
$131$	2129.46	+	775.060i	1.42024	+	0.516926i	0.486124	+	0.873890i	$0.338410\pi$
$132$	577.266			0.380640
$133$	−239.637	+	283.458i	−0.156235	+	0.184804i
$134$	1771.94			1.14233
$135$	383.683	+	139.649i	0.244609	+	0.0890304i
$136$	46.1890	+	261.951i	0.0291226	+	0.165163i
$137$	660.325	+	554.079i	0.411791	+	0.345534i	0.825030	−	0.565089i	$-0.191158\pi$
$137$	660.325	+	554.079i	0.411791	+	0.345534i	−0.413239	+	0.910623i	$0.635603\pi$
$138$	−285.521	+	239.580i	−0.176124	+	0.147786i
$139$	444.232	−	2519.36i	0.271074	−	1.53734i	−0.480089	−	0.877220i	$-0.659396\pi$
$139$	444.232	−	2519.36i	0.271074	−	1.53734i	0.751163	−	0.660117i	$-0.229493\pi$
$140$	135.552	−	234.784i	0.0818305	−	0.141735i
$141$	370.205	+	641.215i	0.221113	+	0.382979i
$142$	−292.479	+	106.454i	−0.172847	+	0.0629112i
$143$	3532.37	−	1285.68i	2.06567	−	0.751844i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−808.538	+	1400.43i	−0.463072	+	0.802064i
$146$	−296.913	+	1683.88i	−0.168306	+	0.954513i
$147$	−742.098	+	622.694i	−0.416376	+	0.349381i
$148$	489.082	+	410.388i	0.271637	+	0.227930i
$149$	−449.757	−	2550.70i	−0.247286	−	1.40243i	−0.815124	−	0.579286i	$-0.803331\pi$
$149$	−449.757	−	2550.70i	−0.247286	−	1.40243i	0.567838	−	0.823140i	$-0.307780\pi$
$150$	584.619	+	212.784i	0.318226	+	0.115825i
$151$	737.454			0.397438			0.198719	−	0.980057i	$-0.436322\pi$
$151$	737.454			0.397438			0.198719	+	0.980057i	$0.436322\pi$
$152$	224.308	+	623.428i	0.119696	+	0.332675i
$153$	−299.241			−0.158119
$154$	405.195	+	147.479i	0.212023	+	0.0771701i
$155$	−782.716	−	4439.00i	−0.405608	−	2.30032i
$156$	−718.324	−	602.746i	−0.368666	−	0.309348i
$157$	2188.29	−	1836.20i	1.11239	−	0.933404i	0.114193	−	0.993459i	$-0.463572\pi$
$157$	2188.29	−	1836.20i	1.11239	−	0.933404i	0.998195	+	0.0600542i	$0.0191274\pi$
$158$	−80.3618	+	455.755i	−0.0404636	+	0.229480i
$159$	438.599	−	759.676i	0.218762	−	0.378907i
$160$	−241.960	−	419.087i	−0.119554	−	0.207073i
$161$	−261.621	+	95.2222i	−0.128066	+	0.0466122i
$162$	152.230	−	55.4073i	0.0738292	−	0.0268716i
$163$	−1207.13	−	2090.82i	−0.580062	−	1.00470i	−0.995471	−	0.0950618i	$-0.969695\pi$
$163$	−1207.13	−	2090.82i	−0.580062	−	1.00470i	0.415410	−	0.909634i	$-0.363638\pi$
$164$	156.058	−	270.301i	0.0743055	−	0.128701i
$165$	−378.974	+	2149.27i	−0.178807	+	1.01406i
$166$	−895.230	+	751.187i	−0.418574	+	0.351226i
$167$	1091.04	+	915.495i	0.505554	+	0.424211i	0.859562	−	0.511032i	$-0.170737\pi$
$167$	1091.04	+	915.495i	0.505554	+	0.424211i	−0.354007	+	0.935243i	$0.615181\pi$
$168$	−18.6782	−	105.929i	−0.00857771	−	0.0486466i
$169$	−3673.44	−	1337.02i	−1.67203	−	0.608567i
$170$	−1005.62			−0.453689
$171$	−734.520	+	126.723i	−0.328481	+	0.0566711i
$172$	1863.72			0.826204
$173$	3537.18	+	1287.43i	1.55449	+	0.565788i	0.969466	−	0.245227i	$-0.0788624\pi$
$173$	3537.18	+	1287.43i	1.55449	+	0.565788i	0.585025	+	0.811015i	$0.301085\pi$
$174$	111.411	+	631.844i	0.0485406	+	0.275287i
$175$	355.995	+	298.715i	0.153775	+	0.129033i
$176$	589.615	−	494.746i	0.252522	−	0.211891i
$177$	208.820	−	1184.28i	0.0886774	−	0.502915i
$178$	744.227	−	1289.04i	0.313383	−	0.542795i
$179$	1728.46	+	2993.77i	0.721736	+	1.25008i	0.960303	+	0.278958i	$0.0899890\pi$
$179$	1728.46	+	2993.77i	0.721736	+	1.25008i	−0.238567	+	0.971126i	$0.576678\pi$
$180$	511.578	−	186.199i	0.211838	−	0.0771026i
$181$	1963.61	−	714.696i	0.806376	−	0.293497i	0.0942502	−	0.995549i	$-0.469955\pi$
$181$	1963.61	−	714.696i	0.806376	−	0.293497i	0.712126	+	0.702052i	$0.247732\pi$
$182$	−350.219	−	606.597i	−0.142637	−	0.247055i
$183$	723.961	−	1253.94i	0.292441	−	0.506523i
$184$	−86.2964	+	489.411i	−0.0345753	+	0.196086i
$185$	−1849.03	+	1551.52i	−0.734831	+	0.616596i
$186$	−1369.98	−	1149.55i	−0.540065	−	0.453169i
$187$	−277.743	−	1575.16i	−0.108613	−	0.615974i
$188$	927.678	+	337.647i	0.359882	+	0.130986i
$189$	121.009			0.0465720
$190$	−2468.40	+	425.860i	−0.942506	+	0.162606i
$191$	−1067.13			−0.404266			−0.202133	−	0.979358i	$-0.564787\pi$
$191$	−1067.13			−0.404266			−0.202133	+	0.979358i	$0.564787\pi$
$192$	−180.421	−	65.6679i	−0.0678165	−	0.0246832i
$193$	−550.887	−	3124.24i	−0.205460	−	1.16522i	−0.896715	−	0.442609i	$-0.854053\pi$
$193$	−550.887	−	3124.24i	−0.205460	−	1.16522i	0.691255	−	0.722611i	$-0.257058\pi$
$194$	−2010.62	−	1687.11i	−0.744094	−	0.624369i
$195$	2715.71	−	2278.75i	0.997314	−	0.836846i
$196$	−224.293	+	1272.03i	−0.0817395	+	0.463568i
$197$	94.7618	−	164.132i	0.0342716	−	0.0593601i	−0.848381	−	0.529386i	$-0.822422\pi$
$197$	94.7618	−	164.132i	0.0342716	−	0.0593601i	0.882652	+	0.470026i	$0.155756\pi$
$198$	432.949	+	749.890i	0.155396	+	0.269153i
$199$	966.166	−	351.656i	0.344169	−	0.125267i	−0.164152	−	0.986435i	$-0.552489\pi$
$199$	966.166	−	351.656i	0.344169	−	0.125267i	0.508321	+	0.861168i	$0.330266\pi$
$200$	779.492	−	283.712i	0.275592	−	0.100307i
$201$	1328.96	+	2301.82i	0.466355	+	0.807750i
$202$	−507.057	+	878.248i	−0.176616	+	0.305908i
$203$	−83.2207	+	471.968i	−0.0287731	+	0.163181i
$204$	−305.643	+	256.465i	−0.104898	+	0.0880201i
$205$	903.929	+	758.486i	0.307967	+	0.258415i
$206$	373.009	+	2115.44i	0.126159	+	0.715484i
$207$	−525.364	−	191.217i	−0.176403	−	0.0642053i
$208$	−1250.27			−0.416783
$209$	−1348.80	−	3748.79i	−0.446405	−	1.24071i
$210$	406.657			0.133629
$211$	2376.57	+	865.000i	0.775401	+	0.282223i	0.699254	−	0.714874i	$-0.253516\pi$
$211$	2376.57	+	865.000i	0.775401	+	0.282223i	0.0761475	+	0.997097i	$0.475738\pi$
$212$	−203.098	−	1151.83i	−0.0657965	−	0.373150i
$213$	−357.647	−	300.101i	−0.115050	−	0.0965380i
$214$	−887.895	+	745.032i	−0.283623	+	0.237988i
$215$	−1223.53	+	6938.96i	−0.388111	+	2.20109i
$216$	108.000	−	187.061i	0.0340207	−	0.0589256i
$217$	−667.936	−	1156.90i	−0.208951	−	0.361914i
$218$	−1673.62	+	609.148i	−0.519963	+	0.189251i
$219$	−2410.11	+	877.208i	−0.743653	+	0.270668i
$220$	1454.95	+	2520.05i	0.445876	+	0.772280i
$221$	−1299.07	+	2250.06i	−0.395408	+	0.684867i
$222$	−166.299	+	943.127i	−0.0502759	+	0.285129i
$223$	−66.7645	+	56.0221i	−0.0200488	+	0.0168229i	−0.652757	−	0.757567i	$-0.726388\pi$
$223$	−66.7645	+	56.0221i	−0.0200488	+	0.0168229i	0.632708	+	0.774390i	$0.281943\pi$
$224$	−109.865	−	92.1874i	−0.0327707	−	0.0274979i
$225$	162.050	+	919.030i	0.0480147	+	0.272305i
$226$	−3889.07	−	1415.51i	−1.14468	−	0.416629i
$227$	2926.99			0.855820			0.427910	−	0.903821i	$-0.359250\pi$
$227$	2926.99			0.855820			0.427910	+	0.903821i	$0.359250\pi$
$228$	−641.626	+	758.955i	−0.186371	+	0.220452i
$229$	1877.74			0.541853			0.270927	−	0.962600i	$-0.412670\pi$
$229$	1877.74			0.541853			0.270927	+	0.962600i	$0.412670\pi$
$230$	−1765.52	−	642.595i	−0.506151	−	0.184224i
$231$	112.316	+	636.974i	0.0319906	+	0.181428i
$232$	655.317	+	549.876i	0.185447	+	0.155608i
$233$	393.765	−	330.408i	0.110714	−	0.0929001i	−0.585750	−	0.810492i	$-0.699200\pi$
$233$	393.765	−	330.408i	0.110714	−	0.0929001i	0.696464	+	0.717592i	$0.254756\pi$
$234$	244.246	−	1385.19i	0.0682345	−	0.386977i
$235$	−1866.14	+	3232.25i	−0.518016	+	0.897230i
$236$	−801.699	−	1388.58i	−0.221128	−	0.383005i
$237$	−652.314	+	237.423i	−0.178786	+	0.0650729i
$238$	−280.058	+	101.933i	−0.0762751	+	0.0277619i
$239$	2006.48	+	3475.33i	0.543049	+	0.940588i	0.998727	+	0.0504433i	$0.0160634\pi$
$239$	2006.48	+	3475.33i	0.543049	+	0.940588i	−0.455678	+	0.890145i	$0.650603\pi$
$240$	362.940	−	628.630i	0.0976153	−	0.169075i
$241$	−1109.87	+	6294.41i	−0.296653	+	1.68240i	0.363756	+	0.931494i	$0.381494\pi$
$241$	−1109.87	+	6294.41i	−0.296653	+	1.68240i	−0.660409	+	0.750906i	$0.729617\pi$
$242$	−1506.25	+	1263.90i	−0.400106	+	0.335729i
$243$	186.149	+	156.197i	0.0491418	+	0.0412348i
$244$	−335.239	−	1901.23i	−0.0879568	−	0.498828i
$245$	−4588.76	−	1670.17i	−1.19659	−	0.435524i
$246$	468.175			0.121340
$247$	−2235.86	+	6073.16i	−0.575969	+	1.56448i
$248$	−2384.52			−0.610552
$249$	−1647.24	−	599.548i	−0.419236	−	0.152589i
$250$	−111.921	−	634.737i	−0.0283141	−	0.160577i
$251$	−3560.34	−	2987.48i	−0.895324	−	0.751266i	0.0739466	−	0.997262i	$-0.476441\pi$
$251$	−3560.34	−	2987.48i	−0.895324	−	0.751266i	−0.969271	+	0.245996i	$0.920885\pi$
$252$	123.598	−	103.711i	0.0308965	−	0.0259253i
$253$	518.916	−	2942.92i	0.128949	−	0.731304i
$254$	−572.941	+	992.363i	−0.141534	+	0.245143i
$255$	−754.211	−	1306.33i	−0.185218	−	0.320807i
$256$	−240.561	+	87.5572i	−0.0587308	+	0.0213763i
$257$	2801.52	−	1019.67i	0.679977	−	0.247491i	0.0211394	−	0.999777i	$-0.493271\pi$
$257$	2801.52	−	1019.67i	0.679977	−	0.247491i	0.658838	+	0.752285i	$0.271048\pi$
$258$	1397.79	+	2421.04i	0.337296	+	0.584214i
$259$	−357.677	+	619.516i	−0.0858108	+	0.148629i
$260$	820.803	−	4655.00i	0.195785	−	1.11035i
$261$	−737.231	+	618.610i	−0.174841	+	0.146709i
$262$	3471.90	+	2913.27i	0.818683	+	0.686956i
$263$	−641.953	−	3640.70i	−0.150511	−	0.853593i	−0.962775	−	0.270303i	$-0.912876\pi$
$263$	−641.953	−	3640.70i	−0.150511	−	0.853593i	0.812264	−	0.583290i	$-0.198235\pi$
$264$	1084.90	+	394.873i	0.252922	+	0.0920559i
$265$	4421.80			1.02502
$266$	−644.268	+	368.805i	−0.148506	+	0.0850109i
$267$	2232.68			0.511752
$268$	3330.16	+	1212.08i	0.759037	+	0.276267i
$269$	−1041.80	−	5908.34i	−0.236133	−	1.33918i	−0.840215	−	0.542253i	$-0.817571\pi$
$269$	−1041.80	−	5908.34i	−0.236133	−	1.33918i	0.604082	−	0.796922i	$-0.293540\pi$
$270$	625.563	+	524.910i	0.141002	+	0.118315i
$271$	−231.484	+	194.238i	−0.0518880	+	0.0435392i	−0.668363	−	0.743835i	$-0.733005\pi$
$271$	−231.484	+	194.238i	−0.0518880	+	0.0435392i	0.616475	+	0.787375i	$0.288560\pi$
$272$	−92.3780	+	523.902i	−0.0205928	+	0.116788i
$273$	525.328	−	909.895i	0.116463	−	0.201719i
$274$	861.993	+	1493.02i	0.190054	+	0.329184i
$275$	−4687.23	+	1706.01i	−1.02782	+	0.374096i
$276$	−700.486	+	254.956i	−0.152769	+	0.0556034i
$277$	52.1673	+	90.3564i	0.0113156	+	0.0195992i	0.871628	−	0.490168i	$-0.163065\pi$
$277$	52.1673	+	90.3564i	0.0113156	+	0.0195992i	−0.860312	+	0.509768i	$0.829731\pi$
$278$	2558.23	−	4430.98i	0.551915	−	0.955945i
$279$	465.825	−	2641.83i	0.0999579	−	0.566889i
$280$	415.357	−	348.526i	0.0886511	−	0.0743871i
$281$	2281.93	+	1914.76i	0.484443	+	0.406496i	0.852030	−	0.523494i	$-0.175372\pi$
$281$	2281.93	+	1914.76i	0.484443	+	0.406496i	−0.367587	+	0.929989i	$0.619816\pi$
$282$	257.142	+	1458.32i	0.0542999	+	0.307950i
$283$	−326.597	−	118.871i	−0.0686012	−	0.0249688i	0.307492	−	0.951551i	$-0.400510\pi$
$283$	−326.597	−	118.871i	−0.0686012	−	0.0249688i	−0.376093	+	0.926582i	$0.622733\pi$
$284$	−622.500			−0.130065
$285$	−2404.50	−	2887.14i	−0.499756	−	0.600069i
$286$	7518.13			1.55439
$287$	328.622	+	119.609i	0.0675887	+	0.0246003i
$288$	−50.0107	−	283.625i	−0.0102323	−	0.0580304i
$289$	−2916.72	−	2447.42i	−0.593673	−	0.498151i
$290$	−2477.50	+	2078.87i	−0.501669	+	0.420950i
$291$	683.657	−	3877.21i	0.137721	−	0.781052i
$292$	−1709.86	+	2961.56i	−0.342677	+	0.593535i
$293$	−3068.99	−	5315.65i	−0.611920	−	1.05988i	−0.990917	−	0.134478i	$-0.957064\pi$
$293$	−3068.99	−	5315.65i	−0.611920	−	1.05988i	0.378997	−	0.925398i	$-0.376269\pi$
$294$	−1820.64	+	662.657i	−0.361162	+	0.131452i
$295$	5696.27	−	2073.27i	1.12424	−	0.409189i
$296$	638.451	+	1105.83i	0.125369	+	0.217145i
$297$	−649.424	+	1124.84i	−0.126880	+	0.219763i
$298$	899.515	−	5101.40i	0.174857	−	0.991665i
$299$	−3718.53	+	3120.22i	−0.719225	+	0.603502i
$300$	953.171	+	799.806i	0.183438	+	0.153923i
$301$	362.614	+	2056.48i	0.0694375	+	0.393800i
$302$	1385.96	+	504.448i	0.264083	+	0.0961183i
$303$	−1521.17			−0.288412
$304$	−4.88929	+	1325.10i	−0.000922435	+	0.249998i
$305$	7298.73			1.37024
$306$	−562.389	−	204.693i	−0.105064	−	0.0382402i
$307$	−452.062	−	2563.77i	−0.0840408	−	0.476619i	−0.997559	−	0.0698223i	$-0.977757\pi$
$307$	−452.062	−	2563.77i	−0.0840408	−	0.476619i	0.913519	−	0.406797i	$-0.133354\pi$
$308$	660.637	+	554.340i	0.122218	+	0.102553i
$309$	−2468.28	+	2071.13i	−0.454419	+	0.381303i
$310$	1565.43	−	8878.00i	0.286808	−	1.62657i
$311$	1606.90	−	2783.23i	0.292987	−	0.507468i	−0.681528	−	0.731792i	$-0.738684\pi$
$311$	1606.90	−	2783.23i	0.292987	−	0.507468i	0.974515	+	0.224324i	$0.0720175\pi$
$312$	−937.706	−	1624.15i	−0.170151	−	0.294710i
$313$	−5157.16	+	1877.05i	−0.931309	+	0.338969i	−0.762728	−	0.646719i	$-0.776141\pi$
$313$	−5157.16	+	1877.05i	−0.931309	+	0.338969i	−0.168581	+	0.985688i	$0.553918\pi$
$314$	5368.68	−	1954.04i	0.964880	−	0.351187i
$315$	304.993	+	528.263i	0.0545537	+	0.0944897i
$316$	−462.785	+	801.568i	−0.0823851	+	0.142695i
$317$	−977.915	+	5546.03i	−0.173265	+	0.982637i	0.766861	+	0.641813i	$0.221817\pi$
$317$	−977.915	+	5546.03i	−0.173265	+	0.982637i	−0.940127	+	0.340825i	$0.889294\pi$
$318$	1343.94	−	1127.70i	0.236996	−	0.198863i
$319$	−3940.54	−	3306.51i	−0.691623	−	0.580341i
$320$	−168.064	−	953.136i	−0.0293595	−	0.166506i
$321$	−1633.75	−	594.635i	−0.284071	−	0.103393i
$322$	−556.822			−0.0963680
$323$	2379.64	+	1385.62i	0.409927	+	0.238693i
$324$	324.000			0.0555556
$325$	7613.89	+	2771.23i	1.29952	+	0.472985i
$326$	−838.467	−	4755.18i	−0.142449	−	0.807868i
$327$	−2046.52	−	1717.24i	−0.346095	−	0.290408i
$328$	478.191	−	401.249i	0.0804989	−	0.0675466i
$329$	−192.077	+	1089.32i	−0.0321871	+	0.182542i
$330$	−2182.42	+	3780.07i	−0.364056	+	0.630564i
$331$	4004.61	+	6936.19i	0.664995	+	1.15181i	0.979287	+	0.202479i	$0.0648999\pi$
$331$	4004.61	+	6936.19i	0.664995	+	1.15181i	−0.314291	+	0.949327i	$0.601767\pi$
$332$	−2196.32	+	799.397i	−0.363069	+	0.132146i
$333$	−1349.88	+	491.317i	−0.222141	+	0.0808529i
$334$	1424.26	+	2466.89i	0.233329	+	0.404138i
$335$	−6699.04	+	11603.1i	−1.09256	+	1.89237i
$336$	37.3564	−	211.859i	0.00606536	−	0.0343984i
$337$	7862.45	−	6597.38i	1.27090	−	1.06642i	0.276474	−	0.961021i	$-0.410834\pi$
$337$	7862.45	−	6597.38i	1.27090	−	1.06642i	0.994431	−	0.105394i	$-0.0336104\pi$
$338$	−5989.23	−	5025.56i	−0.963820	−	0.808741i
$339$	−1078.01	−	6113.68i	−0.172712	−	0.979498i
$340$	−1889.94	−	687.881i	−0.301460	−	0.109722i
$341$	14338.5			2.27706
$342$	−1467.13	−	264.280i	−0.231969	−	0.0417855i
$343$	−2984.50			−0.469819
$344$	3502.64	+	1274.86i	0.548982	+	0.199813i
$345$	−489.381	−	2775.42i	−0.0763693	−	0.433112i
$346$	5767.07	+	4839.15i	0.896069	+	0.751891i
$347$	−4259.76	+	3574.36i	−0.659008	+	0.552974i	−0.909789	−	0.415070i	$-0.863757\pi$
$347$	−4259.76	+	3574.36i	−0.659008	+	0.552974i	0.250781	+	0.968044i	$0.419313\pi$
$348$	−222.822	+	1263.69i	−0.0343234	+	0.194657i
$349$	−4154.60	+	7195.98i	−0.637223	+	1.10370i	0.348817	+	0.937191i	$0.386584\pi$
$349$	−4154.60	+	7195.98i	−0.637223	+	1.10370i	−0.986040	+	0.166511i	$0.946750\pi$
$350$	464.718	+	804.916i	0.0709721	+	0.122927i
$351$	1982.60	−	721.607i	0.301491	−	0.109734i
$352$	1446.54	−	526.497i	0.219036	−	0.0797228i
$353$	−204.299	−	353.856i	−0.0308038	−	0.0533537i	0.850213	−	0.526440i	$-0.176473\pi$
$353$	−204.299	−	353.856i	−0.0308038	−	0.0533537i	−0.881016	+	0.473086i	$0.843140\pi$
$354$	1202.55	−	2082.88i	0.180550	−	0.312722i
$355$	408.670	−	2317.68i	0.0610984	−	0.346506i
$356$	2280.44	−	1913.52i	0.339504	−	0.284877i
$357$	−342.458	−	287.357i	−0.0507698	−	0.0426009i
$358$	1200.57	+	6808.78i	0.177241	+	1.00518i
$359$	10482.9	+	3815.46i	1.54113	+	0.560925i	0.966316	−	0.257360i	$-0.0828526\pi$
$359$	10482.9	+	3815.46i	1.54113	+	0.560925i	0.574813	+	0.818285i	$0.305075\pi$
$360$	1088.82			0.159405
$361$	6427.86	+	2393.42i	0.937143	+	0.348945i
$362$	4179.26			0.606788
$363$	−2771.54	−	1008.76i	−0.400739	−	0.145857i
$364$	−243.259	−	1379.59i	−0.0350282	−	0.198655i
$365$	−9903.92	−	8310.37i	−1.42026	−	1.19174i
$366$	2218.34	−	1861.41i	0.316816	−	0.265840i
$367$	2062.58	−	11697.5i	0.293368	−	1.66377i	−0.380396	−	0.924824i	$-0.624212\pi$
$367$	2062.58	−	11697.5i	0.293368	−	1.66377i	0.673764	−	0.738947i	$-0.264677\pi$
$368$	−496.961	+	860.762i	−0.0703964	+	0.121930i
$369$	351.131	+	608.177i	0.0495370	+	0.0858007i
$370$	−4536.35	+	1651.10i	−0.637388	+	0.231990i
$371$	1231.45	−	448.210i	0.172328	−	0.0627222i
$372$	−1788.39	−	3097.58i	−0.249257	−	0.431726i
$373$	−2087.79	+	3616.16i	−0.289817	+	0.501978i	−0.973766	−	0.227552i	$-0.926928\pi$
$373$	−2087.79	+	3616.16i	−0.289817	+	0.501978i	0.683949	+	0.729530i	$0.260261\pi$
$374$	555.486	−	3150.32i	0.0768008	−	0.435559i
$375$	740.607	−	621.443i	0.101986	−	0.0855765i
$376$	1512.50	+	1269.14i	0.207450	+	0.174071i
$377$	1450.98	+	8228.94i	0.198221	+	1.12417i
$378$	227.423	+	82.7751i	0.0309454	+	0.0112632i
$379$	−10079.1			−1.36604			−0.683022	−	0.730398i	$-0.739335\pi$
$379$	−10079.1			−1.36604			−0.683022	+	0.730398i	$0.739335\pi$
$380$	−4930.37	−	888.127i	−0.665586	−	0.119895i
$381$	−1718.82			−0.231123
$382$	−2005.55	−	729.960i	−0.268620	−	0.0977696i
$383$	−1007.45	−	5713.52i	−0.134408	−	0.762265i	−0.975270	−	0.221016i	$-0.929063\pi$
$383$	−1007.45	−	5713.52i	−0.134408	−	0.762265i	0.840862	−	0.541249i	$-0.182048\pi$
$384$	−294.161	−	246.830i	−0.0390920	−	0.0328021i
$385$	−2497.62	+	2095.75i	−0.330624	+	0.277427i
$386$	1101.77	−	6248.47i	0.145282	−	0.823935i
$387$	−2096.68	+	3631.56i	−0.275401	+	0.477009i
$388$	−2624.68	−	4546.08i	−0.343423	−	0.594826i
$389$	2128.54	−	774.725i	0.277432	−	0.100977i	−0.199557	−	0.979886i	$-0.563950\pi$
$389$	2128.54	−	774.725i	0.277432	−	0.100977i	0.476989	+	0.878909i	$0.341728\pi$
$390$	6662.63	−	2425.00i	0.865065	−	0.314858i
$391$	1032.72	+	1788.72i	0.133572	+	0.231354i
$392$	−1291.65	+	2237.21i	−0.166424	+	0.288255i
$393$	−1180.52	+	6695.09i	−0.151526	+	0.859345i
$394$	290.367	−	243.647i	0.0371281	−	0.0311542i
$395$	−2680.57	−	2249.26i	−0.341453	−	0.286513i
$396$	300.723	+	1705.49i	0.0381614	+	0.216424i
$397$	10477.6	+	3813.52i	1.32457	+	0.482104i	0.904920	−	0.425582i	$-0.139931\pi$
$397$	10477.6	+	3813.52i	1.32457	+	0.482104i	0.419650	+	0.907686i	$0.362153\pi$
$398$	2056.34			0.258983
$399$	−962.293	−	560.324i	−0.120739	−	0.0703040i
$400$	1659.04			0.207379
$401$	8238.42	+	2998.54i	1.02595	+	0.373416i	0.799538	−	0.600615i	$-0.205078\pi$
$401$	8238.42	+	2998.54i	1.02595	+	0.373416i	0.226414	+	0.974031i	$0.427300\pi$
$402$	923.083	+	5235.06i	0.114525	+	0.649506i
$403$	−17842.3	−	14971.4i	−2.20542	−	1.85057i
$404$	−1553.71	+	1303.72i	−0.191337	+	0.160551i
$405$	−212.705	+	1206.31i	−0.0260973	+	0.148005i
$406$	−479.249	+	830.084i	−0.0585831	+	0.101469i
$407$	−3839.12	−	6649.56i	−0.467563	−	0.809844i
$408$	−749.852	+	272.924i	−0.0909883	+	0.0331170i
$409$	−10073.5	+	3666.47i	−1.21786	+	0.443264i	−0.869423	−	0.494068i	$-0.835509\pi$
$409$	−10073.5	+	3666.47i	−1.21786	+	0.443264i	−0.348436	+	0.937333i	$0.613287\pi$
$410$	1180.00	+	2043.81i	0.142136	+	0.246187i
$411$	−1292.99	+	2239.52i	−0.155179	+	0.268778i
$412$	−746.019	+	4230.88i	−0.0892080	+	0.505924i
$413$	1376.23	−	1154.79i	0.163970	−	0.137587i
$414$	−856.562	−	718.741i	−0.101685	−	0.0853241i
$415$	−1534.42	−	8702.13i	−0.181498	−	1.02933i
$416$	−2349.75	−	855.238i	−0.276937	−	0.100797i
$417$	7674.69			0.901274
$418$	29.4002	−	7968.05i	0.00344022	−	0.932369i
$419$	−12190.4			−1.42134			−0.710671	−	0.703525i	$-0.751608\pi$
$419$	−12190.4			−1.42134			−0.710671	+	0.703525i	$0.751608\pi$
$420$	764.266	+	278.170i	0.0887913	+	0.0323174i
$421$	−1297.52	−	7358.59i	−0.150207	−	0.851867i	−0.963038	−	0.269367i	$-0.913186\pi$
$421$	−1297.52	−	7358.59i	−0.150207	−	0.851867i	0.812831	−	0.582500i	$-0.197925\pi$
$422$	3874.79	+	3251.34i	0.446971	+	0.375053i
$423$	−1701.56	+	1427.78i	−0.195586	+	0.164116i
$424$	406.197	−	2303.66i	0.0465251	−	0.263857i
$425$	1723.79	−	2985.69i	0.196744	−	0.340770i
$426$	−466.875	−	808.651i	−0.0530989	−	0.0919701i
$427$	2032.66	−	739.826i	0.230368	−	0.0838470i
$428$	−2178.33	+	792.847i	−0.246013	+	0.0895413i
$429$	5638.60	+	9766.34i	0.634578	+	1.09912i
$430$	−7046.01	+	12204.0i	−0.790206	+	1.36868i
$431$	−2579.09	+	14626.7i	−0.288237	+	1.63467i	0.405251	+	0.914206i	$0.367184\pi$
$431$	−2579.09	+	14626.7i	−0.288237	+	1.63467i	−0.693488	+	0.720468i	$0.743927\pi$
$432$	330.931	−	277.684i	0.0368563	−	0.0309261i
$433$	1925.20	+	1615.43i	0.213670	+	0.179290i	0.743341	−	0.668913i	$-0.233240\pi$
$433$	1925.20	+	1615.43i	0.213670	+	0.179290i	−0.529671	+	0.848203i	$0.677685\pi$
$434$	−463.943	−	2631.15i	−0.0513133	−	0.291012i
$435$	−4558.66	−	1659.22i	−0.502463	−	0.182881i
$436$	−3562.06			−0.391265
$437$	3292.41	+	3953.27i	0.360405	+	0.432747i
$438$	−5129.57			−0.559590
$439$	5686.39	+	2069.68i	0.618215	+	0.225012i	0.632094	−	0.774892i	$-0.282196\pi$
$439$	5686.39	+	2069.68i	0.618215	+	0.225012i	−0.0138788	+	0.999904i	$0.504418\pi$
$440$	1010.60	+	5731.38i	0.109496	+	0.620984i
$441$	−2226.29	−	1868.08i	−0.240395	−	0.201715i
$442$	−3980.59	+	3340.11i	−0.428365	+	0.359441i
$443$	948.486	−	5379.13i	0.101724	−	0.576908i	−0.890754	−	0.454486i	$-0.849823\pi$
$443$	948.486	−	5379.13i	0.101724	−	0.576908i	0.992478	−	0.122422i	$-0.0390660\pi$
$444$	−957.676	+	1658.74i	−0.102363	+	0.177298i
$445$	5627.28	+	9746.74i	0.599458	+	1.03829i
$446$	−163.798	+	59.6175i	−0.0173902	+	0.00632953i
$447$	7301.55	−	2657.55i	0.772598	−	0.281203i
$448$	−143.418	−	248.407i	−0.0151247	−	0.0261968i
$449$	7576.33	−	13122.6i	0.796323	−	1.37927i	−0.125673	−	0.992072i	$-0.540109\pi$
$449$	7576.33	−	13122.6i	0.796323	−	1.37927i	0.921996	−	0.387200i	$-0.126558\pi$
$450$	−324.100	+	1838.06i	−0.0339516	+	0.192549i
$451$	−2875.45	+	2412.79i	−0.300221	+	0.251915i
$452$	−6340.80	−	5320.56i	−0.659837	−	0.553669i
$453$	384.172	+	2178.75i	0.0398455	+	0.225975i
$454$	5500.94	+	2002.18i	0.568661	+	0.206976i
$455$	5296.18			0.545689
$456$	−1725.02	+	987.471i	−0.177152	+	0.101409i
$457$	−10196.7			−1.04373			−0.521863	−	0.853029i	$-0.674763\pi$
$457$	−10196.7			−1.04373			−0.521863	+	0.853029i	$0.674763\pi$
$458$	3528.99	+	1284.45i	0.360042	+	0.131044i
$459$	−155.888	−	884.085i	−0.0158523	−	0.0899031i
$460$	−2878.52	−	2415.37i	−0.291765	−	0.244820i
$461$	−7843.64	+	6581.60i	−0.792440	+	0.664936i	−0.946348	−	0.323149i	$-0.895259\pi$
$461$	−7843.64	+	6581.60i	−0.792440	+	0.664936i	0.153908	+	0.988085i	$0.450814\pi$
$462$	−224.631	+	1273.95i	−0.0226208	+	0.128289i
$463$	2462.89	−	4265.86i	0.247215	−	0.428188i	−0.715537	−	0.698575i	$-0.753818\pi$
$463$	2462.89	−	4265.86i	0.247215	−	0.428188i	0.962752	+	0.270386i	$0.0871514\pi$
$464$	855.455	+	1481.69i	0.0855894	+	0.148245i
$465$	12706.9	−	4624.95i	1.26725	−	0.461240i
$466$	966.048	−	351.613i	0.0960328	−	0.0349531i
$467$	7528.37	+	13039.5i	0.745977	+	1.29207i	0.949737	+	0.313049i	$0.101350\pi$
$467$	7528.37	+	13039.5i	0.745977	+	1.29207i	−0.203760	+	0.979021i	$0.565316\pi$
$468$	1406.56	−	2436.23i	0.138928	−	0.240630i
$469$	−689.515	+	3910.43i	−0.0678866	+	0.385004i
$470$	−5718.19	+	4798.13i	−0.561193	+	0.470897i
$471$	6564.88	+	5508.59i	0.642238	+	0.538901i
$472$	−556.854	−	3158.08i	−0.0543036	−	0.307971i
$473$	−21062.0	−	7665.95i	−2.04743	−	0.745203i
$474$	−1388.36			−0.134534
$475$	2966.85	−	8058.71i	0.286586	−	0.778440i
$476$	−596.064			−0.0573961
$477$	2472.89	+	900.058i	0.237371	+	0.0863958i
$478$	1393.69	+	7904.00i	0.133360	+	0.756319i
$479$	13654.7	+	11457.7i	1.30251	+	1.09293i	0.989706	+	0.143113i	$0.0457111\pi$
$479$	13654.7	+	11457.7i	1.30251	+	1.09293i	0.312799	+	0.949819i	$0.398733\pi$
$480$	1112.11	−	933.173i	0.105752	−	0.0887361i
$481$	−2165.82	+	12283.0i	−0.205308	+	1.16436i
$482$	−6391.51	+	11070.4i	−0.603994	+	1.04615i
$483$	−417.617	−	723.333i	−0.0393421	−	0.0681424i
$484$	−3695.39	+	1345.01i	−0.347050	+	0.126316i
$485$	18649.0	−	6787.68i	1.74600	−	0.635490i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−1906.74	+	3302.57i	−0.177418	+	0.307297i	−0.940996	−	0.338419i	$-0.890108\pi$
$487$	−1906.74	+	3302.57i	−0.177418	+	0.307297i	0.763577	+	0.645716i	$0.223441\pi$
$488$	670.477	−	3802.47i	0.0621948	−	0.352724i
$489$	5548.31	−	4655.59i	0.513095	−	0.430538i
$490$	−7481.58	−	6277.79i	−0.689762	−	0.578779i
$491$	182.943	+	1037.52i	0.0168148	+	0.0953617i	0.992060	−	0.125764i	$-0.0401381\pi$
$491$	182.943	+	1037.52i	0.0168148	+	0.0953617i	−0.975245	+	0.221125i	$0.929027\pi$
$492$	879.881	+	320.251i	0.0806262	+	0.0293456i
$493$	3555.38			0.324799
$494$	−8356.33	+	9884.39i	−0.761071	+	0.900243i
$495$	−6547.27			−0.594501
$496$	−4481.43	−	1631.11i	−0.405690	−	0.147659i
$497$	−121.116	−	686.886i	−0.0109312	−	0.0619940i
$498$	−2685.69	−	2253.56i	−0.241664	−	0.202780i
$499$	4586.21	−	3848.29i	0.411437	−	0.345237i	−0.413458	−	0.910523i	$-0.635679\pi$
$499$	4586.21	−	3848.29i	0.411437	−	0.345237i	0.824894	+	0.565287i	$0.191235\pi$
$500$	223.843	−	1269.47i	0.0200211	−	0.113545i
$501$	−2136.39	+	3700.33i	−0.190512	+	0.329977i
$502$	−4647.69	−	8050.03i	−0.413220	−	0.715718i
$503$	−10100.1	+	3676.14i	−0.895312	+	0.325867i	−0.748373	−	0.663278i	$-0.769164\pi$
$503$	−10100.1	+	3676.14i	−0.895312	+	0.325867i	−0.146940	+	0.989145i	$0.546942\pi$
$504$	303.230	−	110.367i	0.0267995	−	0.00975422i
$505$	−3833.98	−	6640.65i	−0.337841	−	0.585158i
$506$	2988.32	−	5175.92i	0.262543	−	0.454739i
$507$	2036.47	−	11549.4i	0.178388	−	1.01169i
$508$	−1755.59	+	1473.12i	−0.153330	+	0.128660i
$509$	−14223.8	−	11935.2i	−1.23862	−	1.03933i	−0.997630	−	0.0688017i	$-0.978082\pi$
$509$	−14223.8	−	11935.2i	−1.23862	−	1.03933i	−0.240993	−	0.970527i	$-0.577473\pi$
$510$	−523.870	−	2971.01i	−0.0454850	−	0.257958i
$511$	−3600.56	−	1310.50i	−0.311701	−	0.113450i
$512$	−512.000			−0.0441942
$513$	−757.038	−	2104.07i	−0.0651541	−	0.181086i
$514$	5962.63			0.511674
$515$	−15262.6	−	5555.13i	−1.30592	−	0.475317i
$516$	970.893	+	5506.21i	0.0828317	+	0.469762i
$517$	−9094.95	−	7631.57i	−0.773685	−	0.649199i
$518$	−1095.99	+	919.643i	−0.0929632	+	0.0780054i
$519$	−1960.93	+	11121.0i	−0.165849	+	0.940575i
$520$	4726.81	−	8187.08i	0.398624	−	0.690437i
$521$	7516.41	+	13018.8i	0.632053	+	1.09475i	0.987131	+	0.159912i	$0.0511210\pi$
$521$	7516.41	+	13018.8i	0.632053	+	1.09475i	−0.355078	+	0.934837i	$0.615546\pi$
$522$	−1808.70	+	658.311i	−0.151656	+	0.0551983i
$523$	16936.7	−	6164.46i	1.41604	−	0.515398i	0.483147	−	0.875539i	$-0.339494\pi$
$523$	16936.7	−	6164.46i	1.41604	−	0.515398i	0.932898	+	0.360142i	$0.117272\pi$
$524$	4532.25	+	7850.08i	0.377848	+	0.654451i
$525$	−697.077	+	1207.37i	−0.0579485	+	0.100370i
$526$	1283.91	−	7281.39i	0.106428	−	0.603581i
$527$	−7591.77	+	6370.25i	−0.627519	+	0.526551i
$528$	1768.85	+	1484.24i	0.145794	+	0.122335i
$529$	−1442.68	−	8181.87i	−0.118574	−	0.672464i
$530$	8310.27	+	3024.69i	0.681085	+	0.247895i
$531$	3607.65			0.294837
$532$	−1463.10	+	252.422i	−0.119236	+	0.0205712i
$533$	6097.37			0.495509
$534$	4196.07	+	1527.24i	0.340040	+	0.123765i
$535$	−1521.85	−	8630.82i	−0.122982	−	0.697464i
$536$	5429.54	+	4555.93i	0.437538	+	0.367138i
$537$	−7944.44	+	6666.18i	−0.638413	+	0.535692i
$538$	2083.60	−	11816.7i	0.166971	−	0.946940i
$539$	7766.95	−	13452.8i	0.620680	−	1.07505i
$540$	816.614	+	1414.42i	0.0650768	+	0.112716i
$541$	−11964.9	+	4354.85i	−0.950849	+	0.346081i	−0.770441	−	0.637511i	$-0.779964\pi$
$541$	−11964.9	+	4354.85i	−0.950849	+	0.346081i	−0.180408	+	0.983592i	$0.557742\pi$
$542$	−567.914	+	206.704i	−0.0450074	+	0.0163813i
$543$	3134.45	+	5429.02i	0.247720	+	0.429064i
$544$	−531.984	+	921.423i	−0.0419276	+	0.0726208i
$545$	2338.49	−	13262.2i	0.183798	−	1.04237i
$546$	1609.70	−	1350.70i	0.126170	−	0.105869i
$547$	5114.60	+	4291.66i	0.399789	+	0.335462i	0.820412	−	0.571773i	$-0.193744\pi$
$547$	5114.60	+	4291.66i	0.399789	+	0.335462i	−0.420623	+	0.907235i	$0.638189\pi$
$548$	598.734	+	3395.59i	0.0466727	+	0.264694i
$549$	4081.80	+	1485.66i	0.317317	+	0.115494i
$550$	−9976.09			−0.773422
$551$	8727.07	−	1505.64i	0.674747	−	0.116411i
$552$	−1490.88			−0.114957
$553$	−974.517	−	354.695i	−0.0749379	−	0.0272752i
$554$	36.2350	+	205.499i	0.00277884	+	0.0157596i
$555$	−5547.10	−	4654.57i	−0.424255	−	0.355992i
$556$	7838.87	−	6577.59i	0.597918	−	0.501712i
$557$	1578.11	−	8949.92i	0.120048	−	0.680826i	−0.864078	−	0.503357i	$-0.832098\pi$
$557$	1578.11	−	8949.92i	0.120048	−	0.680826i	0.984126	−	0.177469i	$-0.0567910\pi$
$558$	2682.58	−	4646.37i	0.203517	−	0.352503i
$559$	18204.3	+	31530.9i	1.37739	+	2.38571i
$560$	1019.02	−	370.893i	0.0768955	−	0.0279877i
$561$	4509.00	−	1641.14i	0.339341	−	0.123510i
$562$	2978.84	+	5159.51i	0.223585	+	0.387261i
$563$	7465.04	−	12929.8i	0.558817	−	0.967900i	−0.438779	−	0.898595i	$-0.644589\pi$
$563$	7465.04	−	12929.8i	0.558817	−	0.967900i	0.997596	−	0.0693043i	$-0.0220779\pi$
$564$	−514.284	+	2916.65i	−0.0383959	+	0.217754i
$565$	23972.2	−	20115.0i	1.78499	−	1.49778i
$566$	−532.488	−	446.810i	−0.0395444	−	0.0331817i
$567$	63.0390	+	357.512i	0.00466912	+	0.0264799i
$568$	−1169.92	−	425.815i	−0.0864236	−	0.0314556i
$569$	21984.2			1.61973			0.809865	−	0.586616i	$-0.199540\pi$
$569$	21984.2			1.61973			0.809865	+	0.586616i	$0.199540\pi$
$570$	−2544.07	−	7070.83i	−0.186946	−	0.519587i
$571$	−5475.75			−0.401319			−0.200659	−	0.979661i	$-0.564308\pi$
$571$	−5475.75			−0.401319			−0.200659	+	0.979661i	$0.564308\pi$
$572$	14129.5	+	5142.70i	1.03284	+	0.375922i
$573$	−555.916	−	3152.75i	−0.0405300	−	0.229857i
$574$	535.791	+	449.582i	0.0389607	+	0.0326919i
$575$	4934.26	−	4140.34i	0.357866	−	0.300285i
$576$	100.021	−	567.249i	0.00723534	−	0.0410337i
$577$	806.684	−	1397.22i	0.0582022	−	0.100809i	−0.835456	−	0.549557i	$-0.814797\pi$
$577$	806.684	−	1397.22i	0.0582022	−	0.100809i	0.893658	+	0.448748i	$0.148130\pi$
$578$	−3807.50	−	6594.79i	−0.273999	−	0.474580i
$579$	8943.34	−	3255.11i	0.641921	−	0.233640i
$580$	−6078.22	+	2212.29i	−0.435145	+	0.158380i
$581$	−1309.41	−	2267.96i	−0.0934998	−	0.161946i
$582$	3937.02	−	6819.12i	0.280403	−	0.485673i
$583$	−2442.54	+	13852.3i	−0.173515	+	0.984055i
$584$	−5239.30	+	4396.30i	−0.371240	+	0.311507i
$585$	8147.14	+	6836.26i	0.575799	+	0.483153i
$586$	−2131.70	−	12089.5i	−0.150273	−	0.852238i
$587$	−21376.9	−	7780.56i	−1.50310	−	0.547084i	−0.546239	−	0.837629i	$-0.683941\pi$
$587$	−21376.9	−	7780.56i	−1.50310	−	0.547084i	−0.956861	+	0.290546i	$0.906163\pi$
$588$	−3874.96			−0.271770
$589$	−15937.2	+	18851.5i	−1.11491	+	1.31878i
$590$	12123.7			0.845974
$591$	534.282	+	194.463i	0.0371868	+	0.0135349i
$592$	443.463	+	2515.01i	0.0307876	+	0.174605i
$593$	−2211.96	−	1856.05i	−0.153177	−	0.128531i	0.562978	−	0.826472i	$-0.309655\pi$
$593$	−2211.96	−	1856.05i	−0.153177	−	0.128531i	−0.716156	+	0.697941i	$0.754100\pi$
$594$	−1989.95	+	1669.77i	−0.137456	+	0.115339i
$595$	391.315	−	2219.26i	0.0269619	−	0.152909i
$596$	5180.10	−	8972.19i	0.356015	−	0.616637i
$597$	1542.26	+	2671.27i	0.105729	+	0.183129i
$598$	−9122.91	+	3320.47i	−0.623852	+	0.227064i
$599$	−16642.7	+	6057.43i	−1.13523	+	0.413188i	−0.840187	−	0.542297i	$-0.817555\pi$
$599$	−16642.7	+	6057.43i	−1.13523	+	0.413188i	−0.295039	+	0.955485i	$0.595333\pi$
$600$	1244.28	+	2155.15i	0.0846623	+	0.146639i
$601$	6070.54	−	10514.5i	0.412017	−	0.713635i	−0.583093	−	0.812405i	$-0.698158\pi$
$601$	6070.54	−	10514.5i	0.412017	−	0.713635i	0.995110	+	0.0987707i	$0.0314910\pi$
$602$	−725.227	+	4112.97i	−0.0490998	+	0.278459i
$603$	−6108.24	+	5125.42i	−0.412515	+	0.346141i
$604$	2259.69	+	1896.10i	0.152228	+	0.127734i
$605$	−2581.71	−	14641.6i	−0.173490	−	0.983912i
$606$	−2858.87	−	1040.54i	−0.191639	−	0.0697510i
$607$	−8397.60			−0.561529			−0.280765	−	0.959777i	$-0.590588\pi$
$607$	−8397.60			−0.561529			−0.280765	+	0.959777i	$0.590588\pi$
$608$	−915.608	+	2487.02i	−0.0610737	+	0.165892i
$609$	−1437.75			−0.0956658
$610$	13717.1	+	4992.62i	0.910475	+	0.331386i
$611$	3348.94	+	18992.8i	0.221741	+	1.25755i
$612$	−916.928	−	769.394i	−0.0605631	−	0.0508185i
$613$	5284.58	−	4434.29i	0.348193	−	0.292169i	−0.451871	−	0.892083i	$-0.649243\pi$
$613$	5284.58	−	4434.29i	0.348193	−	0.292169i	0.800064	+	0.599915i	$0.204799\pi$
$614$	904.124	−	5127.54i	0.0594258	−	0.337021i
$615$	−1769.99	+	3065.72i	−0.116054	+	0.201011i
$616$	862.400	+	1493.72i	0.0564076	+	0.0977008i
$617$	−9868.07	+	3591.69i	−0.643880	+	0.234353i	−0.643261	−	0.765647i	$-0.722419\pi$
$617$	−9868.07	+	3591.69i	−0.643880	+	0.234353i	−0.000618400		1.00000i	$0.500197\pi$
$618$	−6055.59	+	2204.05i	−0.394161	+	0.143463i
$619$	−10319.8	−	17874.4i	−0.670093	−	1.16064i	−0.977877	−	0.209179i	$-0.932921\pi$
$619$	−10319.8	−	17874.4i	−0.670093	−	1.16064i	0.307784	−	0.951456i	$-0.400413\pi$
$620$	9014.96	−	15614.4i	0.583951	−	1.01143i
$621$	291.250	−	1651.76i	0.0188204	−	0.106736i
$622$	4923.82	−	4131.58i	0.317407	−	0.266336i
$623$	2555.13	+	2144.01i	0.164317	+	0.137878i
$624$	−651.323	−	3693.84i	−0.0417849	−	0.236974i
$625$	16759.1	+	6099.81i	1.07258	+	0.390388i
$626$	−10976.3			−0.700798
$627$	10372.9	−	5937.85i	0.660689	−	0.378205i
$628$	11426.5			0.726060
$629$	4986.91	+	1815.09i	0.316123	+	0.115059i
$630$	211.846	+	1201.44i	0.0133971	+	0.0759785i
$631$	17331.7	+	14543.0i	1.09345	+	0.917511i	0.996967	−	0.0778241i	$-0.0247973\pi$
$631$	17331.7	+	14543.0i	1.09345	+	0.917511i	0.0964797	+	0.995335i	$0.469242\pi$
$632$	−1418.06	+	1189.89i	−0.0892520	+	0.0748913i
$633$	−1317.52	+	7472.00i	−0.0827276	+	0.469171i
$634$	−5631.59	+	9754.19i	−0.352774	+	0.611023i
$635$	−4332.15	−	7503.50i	−0.270734	−	0.468925i
$636$	3297.18	−	1200.08i	0.205569	−	0.0748210i
$637$	−23711.4	+	8630.24i	−1.47485	+	0.536802i
$638$	−5144.01	−	8909.69i	−0.319206	−	0.552881i
$639$	700.312	−	1212.98i	0.0433551	−	0.0750932i
$640$	336.127	−	1906.27i	0.0207603	−	0.117737i
$641$	−13341.9	+	11195.2i	−0.822111	+	0.689833i	−0.953465	−	0.301502i	$-0.902512\pi$
$641$	−13341.9	+	11195.2i	−0.822111	+	0.689833i	0.131354	+	0.991335i	$0.458067\pi$
$642$	−2663.68	−	2235.10i	−0.163750	−	0.137402i
$643$	−4892.03	−	27744.1i	−0.300036	−	1.70159i	−0.645999	−	0.763338i	$-0.723559\pi$
$643$	−4892.03	−	27744.1i	−0.300036	−	1.70159i	0.345963	−	0.938248i	$-0.387552\pi$
$644$	−1046.48	−	380.889i	−0.0640329	−	0.0233061i
$645$	−21138.0			−1.29040
$646$	3524.44	+	4231.87i	0.214655	+	0.257741i
$647$	−4309.66			−0.261871			−0.130935	−	0.991391i	$-0.541798\pi$
$647$	−4309.66			−0.261871			−0.130935	+	0.991391i	$0.541798\pi$
$648$	608.921	+	221.629i	0.0369146	+	0.0134358i
$649$	3348.47	+	18990.1i	0.202525	+	1.14858i
$650$	12413.8	+	10416.4i	0.749092	+	0.628562i
$651$	3070.01	−	2576.04i	0.184828	−	0.155089i
$652$	1676.93	−	9510.36i	0.100727	−	0.571249i
$653$	2119.42	−	3670.95i	0.127013	−	0.219993i	−0.795505	−	0.605947i	$-0.792794\pi$
$653$	2119.42	−	3670.95i	0.127013	−	0.219993i	0.922518	+	0.385954i	$0.126128\pi$
$654$	−2671.54	−	4627.25i	−0.159733	−	0.276666i
$655$	−32202.7	+	11720.8i	−1.92101	+	0.699192i
$656$	1173.18	−	427.001i	0.0698244	−	0.0254140i
$657$	−3847.18	−	6663.51i	−0.228452	−	0.395690i
$658$	−1106.13	+	1915.87i	−0.0655340	+	0.113508i
$659$	3332.32	−	18898.5i	0.196978	−	1.11712i	−0.712595	−	0.701576i	$-0.752480\pi$
$659$	3332.32	−	18898.5i	0.196978	−	1.11712i	0.909573	−	0.415544i	$-0.136409\pi$
$660$	−6687.34	+	5611.34i	−0.394400	+	0.330941i
$661$	6075.58	+	5098.01i	0.357508	+	0.299985i	0.803796	−	0.594904i	$-0.202810\pi$
$661$	6075.58	+	5098.01i	0.357508	+	0.299985i	−0.446289	+	0.894889i	$0.647255\pi$
$662$	2781.58	+	15775.1i	0.163307	+	0.926158i
$663$	−7324.38	−	2665.86i	−0.429043	−	0.156159i
$664$	−4674.56			−0.273205
$665$	20.7111	−	5613.13i	0.00120773	−	0.327320i
$666$	−2873.03			−0.167159
$667$	6242.02	+	2271.91i	0.362357	+	0.131887i
$668$	989.279	+	5610.48i	0.0572999	+	0.324964i
$669$	−200.294	−	168.066i	−0.0115752	−	0.00971273i
$670$	−20527.1	+	17224.2i	−1.18363	+	0.993180i
$671$	−4031.70	+	22864.9i	−0.231956	+	1.31549i
$672$	215.127	−	372.611i	0.0123493	−	0.0213896i
$673$	−2962.37	−	5130.97i	−0.169674	−	0.293885i	0.768631	−	0.639692i	$-0.220938\pi$
$673$	−2962.37	−	5130.97i	−0.169674	−	0.293885i	−0.938305	+	0.345808i	$0.887605\pi$
$674$	19289.4	−	7020.78i	1.10238	−	0.401232i
$675$	−2630.78	+	957.527i	−0.150013	+	0.0546004i
$676$	−7818.39	−	13541.8i	−0.444833	−	0.770473i
$677$	−13425.9	+	23254.4i	−0.762186	+	1.32014i	0.179536	+	0.983751i	$0.442540\pi$
$677$	−13425.9	+	23254.4i	−0.762186	+	1.32014i	−0.941722	+	0.336393i	$0.890793\pi$
$678$	2156.01	−	12227.4i	0.122126	−	0.692609i
$679$	4505.62	−	3780.66i	0.254654	−	0.213680i
$680$	−3081.38	−	2585.59i	−0.173773	−	0.145813i
$681$	1524.80	+	8647.57i	0.0858009	+	0.486601i
$682$	26947.7	+	9808.14i	1.51302	+	0.550694i
$683$	−9910.91			−0.555242			−0.277621	−	0.960691i	$-0.589546\pi$
$683$	−9910.91			−0.555242			−0.277621	+	0.960691i	$0.589546\pi$
$684$	−2576.53	−	1500.26i	−0.144029	−	0.0838653i
$685$	−13035.5			−0.727095
$686$	−5609.03	−	2041.52i	−0.312177	−	0.113623i
$687$	978.197	+	5547.63i	0.0543240	+	0.308086i
$688$	5710.76	+	4791.90i	0.316454	+	0.265537i
$689$	17503.1	−	14686.9i	0.967802	−	0.812083i
$690$	978.762	−	5550.84i	0.0540012	−	0.306256i
$691$	8640.26	−	14965.4i	0.475674	−	0.823892i	−0.523938	−	0.851757i	$-0.675537\pi$
$691$	8640.26	−	14965.4i	0.475674	−	0.823892i	0.999612	+	0.0278649i	$0.00887081\pi$
$692$	7528.38	+	13039.5i	0.413564	+	0.716313i
$693$	−1823.38	+	663.656i	−0.0999487	+	0.0363784i
$694$	−10450.7	+	3803.76i	−0.571621	+	0.208053i
$695$	19343.4	+	33503.8i	1.05574	+	1.82859i
$696$	−1283.18	+	2222.54i	−0.0698835	+	0.121042i
$697$	450.511	−	2554.98i	0.0244825	−	0.138847i
$698$	−12730.4	+	10682.1i	−0.690336	+	0.579260i
$699$	1181.29	+	991.223i	0.0639208	+	0.0536359i
$700$	322.790	+	1830.63i	0.0174290	+	0.0988449i
$701$	−6716.58	−	2444.64i	−0.361886	−	0.131716i	0.154677	−	0.987965i	$-0.450566\pi$
$701$	−6716.58	−	2444.64i	−0.361886	−	0.131716i	−0.516562	+	0.856250i	$0.672789\pi$
$702$	4219.68			0.226868
$703$	13009.6	+	2343.47i	0.697960	+	0.125726i
$704$	3078.75			0.164822
$705$	−10521.6	−	3829.55i	−0.562080	−	0.204580i
$706$	−141.904	−	804.780i	−0.00756465	−	0.0429013i
$707$	−1740.86	−	1460.76i	−0.0926052	−	0.0777050i
$708$	3684.82	−	3091.93i	0.195599	−	0.164127i
$709$	−3707.92	+	21028.7i	−0.196409	+	1.11389i	0.713989	+	0.700157i	$0.246887\pi$
$709$	−3707.92	+	21028.7i	−0.196409	+	1.11389i	−0.910398	+	0.413733i	$0.864225\pi$
$710$	2353.44	−	4076.27i	0.124398	−	0.215464i
$711$	−1041.27	−	1803.53i	−0.0549234	−	0.0951302i
$712$	5594.76	−	2036.32i	0.294484	−	0.107183i
$713$	−17399.2	+	6332.78i	−0.913891	+	0.332629i
$714$	−447.048	−	774.309i	−0.0234318	−	0.0405852i
$715$	−28423.2	+	49230.5i	−1.48667	+	2.57499i
$716$	−2401.14	+	13617.6i	−0.125328	+	0.710771i
$717$	−9222.33	+	7738.46i	−0.480355	+	0.403065i
$718$	17091.4	+	14341.4i	0.888366	+	0.745428i
$719$	1443.14	+	8184.46i	0.0748541	+	0.424519i	0.999088	+	0.0426926i	$0.0135936\pi$
$719$	1443.14	+	8184.46i	0.0748541	+	0.424519i	−0.924234	+	0.381826i	$0.875295\pi$
$720$	2046.31	+	744.796i	0.105919	+	0.0385513i
$721$	−4813.64			−0.248640
$722$	10443.2	+	8895.07i	0.538306	+	0.458504i
$723$	−19174.5			−0.986319
$724$	7854.45	+	2858.79i	0.403188	+	0.146748i
$725$	−1925.37	−	10919.3i	−0.0986293	−	0.559355i
$726$	−4518.76	−	3791.69i	−0.231001	−	0.193833i
$727$	1118.35	−	938.403i	0.0570525	−	0.0478727i	−0.613816	−	0.789449i	$-0.710366\pi$
$727$	1118.35	−	938.403i	0.0570525	−	0.0478727i	0.670868	+	0.741577i	$0.265922\pi$
$728$	486.519	−	2759.18i	0.0247687	−	0.140470i
$729$	−364.500	+	631.333i	−0.0185185	+	0.0320750i
$730$	−12928.6	−	22393.1i	−0.655494	−	1.13535i
$731$	14557.4	−	5298.46i	0.736560	−	0.268086i
$732$	5442.41	−	1980.87i	0.274805	−	0.100021i
$733$	−9073.19	−	15715.2i	−0.457198	−	0.791890i	0.541614	−	0.840627i	$-0.317813\pi$
$733$	−9073.19	−	15715.2i	−0.457198	−	0.791890i	−0.998812	+	0.0487378i	$0.984480\pi$
$734$	11877.9	−	20573.2i	0.597306	−	1.03456i
$735$	2543.90	−	14427.2i	0.127664	−	0.724021i
$736$	−1522.78	+	1277.76i	−0.0762640	+	0.0639931i
$737$	−32648.8	−	27395.6i	−1.63180	−	1.36924i
$738$	243.893	+	1383.19i	0.0121651	+	0.0689916i
$739$	−3372.08	−	1227.34i	−0.167854	−	0.0610938i	0.256726	−	0.966484i	$-0.417356\pi$
$739$	−3372.08	−	1227.34i	−0.167854	−	0.0610938i	−0.424580	+	0.905390i	$0.639578\pi$
$740$	−9654.97			−0.479627
$741$	−19107.5	−	3441.90i	−0.947274	−	0.170636i
$742$	2620.96			0.129674
$743$	−23354.2	−	8500.22i	−1.15314	−	0.419708i	−0.306496	−	0.951872i	$-0.599157\pi$
$743$	−23354.2	−	8500.22i	−1.15314	−	0.419708i	−0.846641	+	0.532164i	$0.821379\pi$
$744$	−1242.20	−	7044.87i	−0.0612114	−	0.347147i
$745$	30004.4	+	25176.7i	1.47554	+	1.23812i
$746$	−6397.37	+	5368.03i	−0.313973	+	0.263455i
$747$	913.195	−	5178.99i	0.0447283	−	0.253667i
$748$	3198.92	−	5540.69i	0.156369	−	0.270839i
$749$	−1298.68	−	2249.38i	−0.0633547	−	0.109734i
$750$	1816.98	−	661.326i	0.0884622	−	0.0321976i
$751$	22078.4	−	8035.89i	1.07277	−	0.390458i	0.255560	−	0.966793i	$-0.417740\pi$
$751$	22078.4	−	8035.89i	1.07277	−	0.390458i	0.817213	+	0.576335i	$0.195518\pi$
$752$	1974.43	+	3419.81i	0.0957447	+	0.165835i
$753$	6971.53	−	12075.0i	0.337393	−	0.584381i
$754$	−2901.97	+	16457.9i	−0.140164	+	0.794908i
$755$	−8543.03	+	7168.45i	−0.411805	+	0.345545i
$756$	370.793	+	311.132i	0.0178381	+	0.0149680i
$757$	83.9922	+	476.343i	0.00403269	+	0.0228705i	0.986758	−	0.162201i	$-0.0518594\pi$
$757$	83.9922	+	476.343i	0.00403269	+	0.0228705i	−0.982725	+	0.185072i	$0.940748\pi$
$758$	−18942.6	−	6894.54i	−0.907686	−	0.330371i
$759$	8964.96			0.428732
$760$	−8658.55	−	5041.71i	−0.413261	−	0.240634i
$761$	−25304.2			−1.20536			−0.602679	−	0.797984i	$-0.705900\pi$
$761$	−25304.2			−1.20536			−0.602679	+	0.797984i	$0.705900\pi$
$762$	−3230.33	−	1175.74i	−0.153573	−	0.0558960i
$763$	−693.051	−	3930.49i	−0.0328835	−	0.186492i
$764$	−3269.88	−	2743.75i	−0.154843	−	0.129929i
$765$	3466.56	−	2908.79i	0.163835	−	0.137474i
$766$	2014.90	−	11427.0i	0.0950407	−	0.539003i
$767$	15661.6	−	27126.7i	0.737299	−	1.27704i
$768$	−384.000	−	665.108i	−0.0180422	−	0.0312500i
$769$	24857.9	−	9047.55i	1.16567	−	0.424269i	0.314551	−	0.949241i	$-0.398146\pi$
$769$	24857.9	−	9047.55i	1.16567	−	0.424269i	0.851120	+	0.524971i	$0.175924\pi$
$770$	−6127.56	+	2230.25i	−0.286782	+	0.104380i
$771$	4471.98	+	7745.69i	0.208890	+	0.361808i
$772$	6344.87	−	10989.6i	0.295799	−	0.512339i
$773$	−4899.76	+	27787.9i	−0.227984	+	1.29296i	0.628912	+	0.777476i	$0.283500\pi$
$773$	−4899.76	+	27787.9i	−0.227984	+	1.29296i	−0.856897	+	0.515488i	$0.827611\pi$
$774$	−6424.60	+	5390.88i	−0.298356	+	0.250350i
$775$	23675.6	+	19866.1i	1.09736	+	0.920791i
$776$	−1823.08	−	10339.2i	−0.0843362	−	0.478295i
$777$	−2016.64	−	733.997i	−0.0931102	−	0.0338893i
$778$	4530.29			0.208764
$779$	23.8442	−	6462.26i	0.00109667	−	0.297220i
$780$	14180.4			0.650950
$781$	7034.92	+	2560.50i	0.322317	+	0.117314i
$782$	717.317	+	4068.11i	0.0328021	+	0.186030i
$783$	−2211.69	−	1855.83i	−0.100944	−	0.0847024i
$784$	−3957.86	+	3321.03i	−0.180296	+	0.151286i
$785$	−7501.45	+	42542.9i	−0.341068	+	1.93429i
$786$	−6798.37	+	11775.1i	−0.308511	+	0.534357i
$787$	4604.37	+	7975.01i	0.208549	+	0.361218i	0.951258	−	0.308397i	$-0.0997925\pi$
$787$	4604.37	+	7975.01i	0.208549	+	0.361218i	−0.742709	+	0.669615i	$0.766459\pi$
$788$	712.376	−	259.284i	0.0322048	−	0.0117216i
$789$	10421.7	−	3793.20i	0.470245	−	0.171155i
$790$	−3499.23	−	6060.85i	−0.157591	−	0.272956i
$791$	4637.18	−	8031.84i	0.208444	−	0.361036i
$792$	−601.447	+	3410.98i	−0.0269842	+	0.153035i
$793$	28891.0	−	24242.5i	1.29376	−	1.08559i
$794$	17082.8	+	14334.2i	0.763533	+	0.640681i
$795$	2303.51	+	13063.9i	0.102764	+	0.582803i
$796$	3864.66	+	1406.62i	0.172085	+	0.0626337i
$797$	36127.2			1.60564			0.802818	−	0.596224i	$-0.203333\pi$
$797$	36127.2			1.60564			0.802818	+	0.596224i	$0.203333\pi$
$798$	−1425.23	−	1711.31i	−0.0632240	−	0.0759145i
$799$	8205.97			0.363337
$800$	3117.97	+	1134.85i	0.137796	+	0.0501536i
$801$	1163.10	+	6596.28i	0.0513061	+	0.290972i
$802$	13432.0	+	11270.8i	0.591399	+	0.496242i
$803$	31504.9	−	26435.8i	1.38454	−	1.16177i
$804$	−1846.17	+	10470.1i	−0.0809817	+	0.459270i
$805$	2105.13	−	3646.20i	0.0921692	−	0.159642i
$806$	−23291.4	−	40341.9i	−1.01787	−	1.76301i
$807$	16913.0	−	6155.84i	0.737753	−	0.268520i
$808$	−3811.82	+	1387.39i	−0.165965	+	0.0604062i
$809$	−17485.6	−	30285.9i	−0.759902	−	1.31619i	−0.942900	−	0.333076i	$-0.891913\pi$
$809$	−17485.6	−	30285.9i	−0.759902	−	1.31619i	0.182998	−	0.983113i	$-0.441420\pi$
$810$	−1224.92	+	2121.63i	−0.0531350	+	0.0920325i
$811$	2329.96	−	13213.9i	0.100883	−	0.572136i	−0.891902	−	0.452228i	$-0.850629\pi$
$811$	2329.96	−	13213.9i	0.100883	−	0.572136i	0.992785	−	0.119907i	$-0.0382597\pi$
$812$	−1468.50	+	1232.22i	−0.0634660	+	0.0532543i
$813$	−694.452	−	582.714i	−0.0299575	−	0.0251374i
$814$	−2666.63	−	15123.2i	−0.114822	−	0.651189i
$815$	34307.9	+	12487.1i	1.47455	+	0.536691i
$816$	−1595.95			−0.0684675
$817$	33489.0	−	19170.5i	1.43407	−	0.820918i
$818$	−21440.1			−0.916423
$819$	2961.88	+	1078.04i	0.126369	+	0.0459947i
$820$	819.616	+	4648.27i	0.0349052	+	0.197957i
$821$	−30337.8	−	25456.4i	−1.28964	−	1.08214i	−0.991837	−	0.127513i	$-0.959301\pi$
$821$	−30337.8	−	25456.4i	−1.28964	−	1.08214i	−0.297806	−	0.954626i	$-0.596255\pi$
$822$	−3961.95	+	3324.47i	−0.168113	+	0.141064i
$823$	1733.03	−	9828.50i	0.0734017	−	0.416282i	−0.925860	−	0.377866i	$-0.876658\pi$
$823$	1733.03	−	9828.50i	0.0734017	−	0.416282i	0.999262	−	0.0384155i	$-0.0122310\pi$
$824$	−4296.15	+	7441.15i	−0.181630	+	0.314593i
$825$	−7482.07	−	12959.3i	−0.315748	−	0.546892i
$826$	3376.38	−	1228.90i	0.142227	−	0.0517663i
$827$	17261.5	−	6282.68i	0.725807	−	0.264172i	0.0474179	−	0.998875i	$-0.484901\pi$
$827$	17261.5	−	6282.68i	0.725807	−	0.264172i	0.678389	+	0.734703i	$0.262679\pi$
$828$	−1118.16	−	1936.71i	−0.0469310	−	0.0812868i
$829$	−4960.49	+	8591.82i	−0.207823	+	0.359959i	−0.951028	−	0.309104i	$-0.899971\pi$
$829$	−4960.49	+	8591.82i	−0.207823	+	0.359959i	0.743206	+	0.669063i	$0.233304\pi$
$830$	3068.84	−	17404.3i	0.128339	−	0.727844i
$831$	−239.775	+	201.195i	−0.0100093	+	0.00839877i
$832$	−3831.06	−	3214.64i	−0.159637	−	0.133952i
$833$	1864.38	+	10573.4i	0.0775474	+	0.439793i
$834$	14423.7	+	5249.80i	0.598863	+	0.217968i
$835$	−21538.3			−0.892652
$836$	5505.72	−	14954.9i	0.227774	−	0.618692i
$837$	8047.75			0.332343
$838$	−22910.5	−	8338.75i	−0.944429	−	0.343744i
$839$	−4472.12	−	25362.7i	−0.184022	−	1.04364i	−0.927205	−	0.374554i	$-0.877796\pi$
$839$	−4472.12	−	25362.7i	−0.184022	−	1.04364i	0.743183	−	0.669089i	$-0.233315\pi$
$840$	1246.07	+	1045.58i	0.0511828	+	0.0429474i
$841$	−9923.78	+	8327.04i	−0.406896	+	0.341426i
$842$	2595.04	−	14717.2i	0.106212	−	0.602361i
$843$	−4468.27	+	7739.26i	−0.182557	+	0.316197i
$844$	5058.18	+	8761.02i	0.206291	+	0.357307i
$845$	55551.6	−	20219.1i	2.26158	−	0.823146i
$846$	−4174.55	+	1519.41i	−0.169650	+	0.0617476i
$847$	−2203.12	−	3815.92i	−0.0893744	−	0.154801i
$848$	2339.19	−	4051.60i	0.0947267	−	0.164071i
$849$	181.058	−	1026.83i	0.00731907	−	0.0415085i
$850$	5282.00	−	4432.12i	0.213142	−	0.178848i
$851$	7595.46	+	6373.34i	0.305956	+	0.256728i
$852$	−324.288	−	1839.13i	−0.0130398	−	0.0739524i
$853$	−23591.3	−	8586.54i	−0.946954	−	0.344663i	−0.178046	−	0.984022i	$-0.556978\pi$
$853$	−23591.3	−	8586.54i	−0.946954	−	0.344663i	−0.768908	+	0.639359i	$0.779200\pi$
$854$	4326.21			0.173349
$855$	7277.23	−	8607.97i	0.291083	−	0.344311i
$856$	−4636.26			−0.185121
$857$	−40261.4	−	14654.0i	−1.60479	−	0.584095i	−0.624389	−	0.781114i	$-0.714652\pi$
$857$	−40261.4	−	14654.0i	−1.60479	−	0.584095i	−0.980400	+	0.197019i	$0.936874\pi$
$858$	3916.53	+	22211.7i	0.155837	+	0.883795i
$859$	11700.9	+	9818.19i	0.464759	+	0.389979i	0.844879	−	0.534958i	$-0.179673\pi$
$859$	11700.9	+	9818.19i	0.464759	+	0.389979i	−0.380119	+	0.924937i	$0.624117\pi$
$860$	−21590.2	+	18116.3i	−0.856070	+	0.718328i
$861$	−182.181	+	1033.20i	−0.00721104	+	0.0408958i
$862$	−14852.4	+	25725.0i	−0.586860	+	1.01647i
$863$	7809.81	+	13527.0i	0.308052	+	0.533562i	0.977936	−	0.208904i	$-0.0669895\pi$
$863$	7809.81	+	13527.0i	0.308052	+	0.533562i	−0.669884	+	0.742466i	$0.733656\pi$
$864$	811.894	−	295.505i	0.0319690	−	0.0116358i
$865$	−53491.0	+	19469.1i	−2.10260	+	0.765284i
$866$	2513.16	+	4352.93i	0.0986152	+	0.170807i
$867$	5711.26	−	9892.19i	0.223719	−	0.387493i
$868$	927.886	−	5262.30i	0.0362840	−	0.205777i
$869$	8527.04	−	7155.03i	0.332865	−	0.279307i
$870$	−7432.51	−	6236.62i	−0.289639	−	0.243036i
$871$	12021.9	+	68179.8i	0.467679	+	2.65234i
$872$	−6694.48	−	2436.59i	−0.259981	−	0.0946255i
$873$	11811.1			0.457897
$874$	3483.50	+	9681.85i	0.134818	+	0.374707i
$875$	1444.33			0.0558026
$876$	−9640.44	−	3508.83i	−0.371827	−	0.135334i
$877$	−7103.05	−	40283.4i	−0.273493	−	1.55105i	−0.743709	−	0.668503i	$-0.766935\pi$
$877$	−7103.05	−	40283.4i	−0.273493	−	1.55105i	0.470217	−	0.882551i	$-0.344176\pi$
$878$	9271.17	+	7779.43i	0.356363	+	0.299024i
$879$	14105.9	−	11836.3i	0.541275	−	0.454183i
$880$	−2021.19	+	11462.8i	−0.0774255	+	0.439102i
$881$	−19014.8	+	32934.6i	−0.727156	+	1.25947i	0.230924	+	0.972972i	$0.425825\pi$
$881$	−19014.8	+	32934.6i	−0.727156	+	1.25947i	−0.958080	+	0.286500i	$0.907508\pi$
$882$	−2906.22	−	5033.72i	−0.110950	−	0.192170i
$883$	4791.98	−	1744.14i	0.182631	−	0.0664722i	−0.249086	−	0.968481i	$-0.580130\pi$
$883$	4791.98	−	1744.14i	0.182631	−	0.0664722i	0.431717	+	0.902009i	$0.357908\pi$
$884$	−9765.84	+	3554.48i	−0.371562	+	0.135237i
$885$	9092.77	+	15749.1i	0.345367	+	0.598194i
$886$	5462.11	−	9460.65i	0.207114	−	0.358732i
$887$	3958.74	−	22451.1i	0.149855	−	0.849871i	−0.813485	−	0.581586i	$-0.802432\pi$
$887$	3958.74	−	22451.1i	0.149855	−	0.849871i	0.963340	−	0.268284i	$-0.0864566\pi$
$888$	−2934.49	+	2462.33i	−0.110895	+	0.0930522i
$889$	−1967.06	−	1650.56i	−0.0742105	−	0.0622700i
$890$	3908.67	+	22167.2i	0.147212	+	0.834882i
$891$	−3661.55	−	1332.70i	−0.137673	−	0.0501089i
$892$	−348.620			−0.0130859
$893$	20142.5	−	3475.08i	0.754807	−	0.130223i
$894$	15540.3			0.581371
$895$	−49124.4	−	17879.8i	−1.83469	−	0.667773i
$896$	−99.6172	−	564.957i	−0.00371426	−	0.0210646i
$897$	−11155.6	−	9360.66i	−0.415245	−	0.348432i
$898$	23215.2	−	19479.9i	0.862697	−	0.723888i
$899$	−5534.62	+	31388.4i	−0.205328	+	1.16447i
$900$	−1866.41	+	3232.73i	−0.0691265	+	0.119731i
$901$	−4860.99	−	8419.48i	−0.179737	−	0.311314i
$902$	−7054.52	+	2567.64i	−0.260410	+	0.0947815i
$903$	−5886.82	+	2142.63i	−0.216945	+	0.0789615i
$904$	−8277.33	−	14336.8i	−0.304535	−	0.527470i
$905$	−15800.2	+	27366.8i	−0.580350	+	1.00520i
$906$	−768.345	+	4357.50i	−0.0281750	+	0.159788i
$907$	28631.8	−	24024.9i	1.04818	−	0.879531i	0.0552824	−	0.998471i	$-0.482394\pi$
$907$	28631.8	−	24024.9i	1.04818	−	0.879531i	0.992901	+	0.118940i	$0.0379497\pi$
$908$	8968.82	+	7525.73i	0.327798	+	0.275055i
$909$	−792.445	−	4494.18i	−0.0289150	−	0.163985i
$910$	9953.56	+	3622.80i	0.362590	+	0.131972i
$911$	2115.74			0.0769456			0.0384728	−	0.999260i	$-0.487751\pi$
$911$	2115.74			0.0769456			0.0384728	+	0.999260i	$0.487751\pi$
$912$	−3917.44	+	675.857i	−0.142236	+	0.0245393i
$913$	28109.0			1.01892
$914$	−19163.6	−	6974.97i	−0.693517	−	0.252420i
$915$	3802.23	+	21563.5i	0.137375	+	0.779091i
$916$	5753.72	+	4827.95i	0.207542	+	0.174148i
$917$	−7780.21	+	6528.37i	−0.280180	+	0.235099i
$918$	311.776	−	1768.17i	0.0112093	−	0.0635711i
$919$	12487.5	−	21629.1i	0.448233	−	0.776362i	−0.550038	−	0.835139i	$-0.685387\pi$
$919$	12487.5	−	21629.1i	0.448233	−	0.776362i	0.998271	+	0.0587775i	$0.0187202\pi$
$920$	−3757.64	−	6508.43i	−0.134659	−	0.233235i
$921$	7338.96	−	2671.16i	0.262570	−	0.0955677i
$922$	−19243.3	+	7003.99i	−0.687359	+	0.250178i
$923$	−6080.43	−	10531.6i	−0.216836	−	0.375571i
$924$	−1293.60	+	2240.58i	−0.0460566	+	0.0797724i
$925$	2873.91	−	16298.8i	0.102155	−	0.579351i
$926$	7546.74	−	6332.47i	0.267820	−	0.224728i
$927$	−7404.84	−	6213.40i	−0.262359	−	0.220146i
$928$	594.193	+	3369.83i	0.0210187	+	0.119203i
$929$	4814.97	+	1752.51i	0.170047	+	0.0618922i	0.425641	−	0.904892i	$-0.360049\pi$
$929$	4814.97	+	1752.51i	0.170047	+	0.0618922i	−0.255594	+	0.966784i	$0.582271\pi$
$930$	27044.9			0.953588
$931$	9053.99	+	25164.1i	0.318724	+	0.885845i
$932$	2056.09			0.0722635
$933$	9059.94	+	3297.55i	0.317909	+	0.115709i
$934$	5229.15	+	29656.0i	0.183194	+	1.03894i
$935$	18528.9	+	15547.6i	0.648087	+	0.543809i
$936$	4309.94	−	3616.47i	0.150507	−	0.126291i
$937$	5988.80	−	33964.2i	0.208800	−	1.18416i	−0.682547	−	0.730842i	$-0.739128\pi$
$937$	5988.80	−	33964.2i	0.208800	−	1.18416i	0.891347	−	0.453322i	$-0.149761\pi$
$938$	−3970.76	+	6877.55i	−0.138219	+	0.239403i
$939$	−8232.20	−	14258.6i	−0.286100	−	0.495539i
$940$	−14028.8	+	5106.07i	−0.486776	+	0.177172i
$941$	10430.7	−	3796.47i	0.361351	−	0.131521i	−0.154963	−	0.987920i	$-0.549526\pi$
$941$	10430.7	−	3796.47i	0.361351	−	0.131521i	0.516314	+	0.856399i	$0.327304\pi$
$942$	8569.85	+	14843.4i	0.296413	+	0.513402i
$943$	2423.59	−	4197.78i	0.0836935	−	0.144961i
$944$	1113.71	−	6316.16i	0.0383984	−	0.217768i
$945$	−1401.83	+	1176.27i	−0.0482556	+	0.0404912i
$946$	−34339.9	−	28814.6i	−1.18022	−	0.990319i
$947$	5934.20	+	33654.5i	0.203628	+	1.15483i	0.899584	+	0.436747i	$0.143870\pi$
$947$	5934.20	+	33654.5i	0.203628	+	1.15483i	−0.695956	+	0.718084i	$0.745019\pi$
$948$	−2609.26	−	949.691i	−0.0893931	−	0.0325364i
$949$	−66805.9			−2.28515
$950$	11088.3	−	13116.0i	0.378687	−	0.447935i
$951$	−16894.8			−0.576078
$952$	−1120.23	−	407.732i	−0.0381376	−	0.0138809i
$953$	7914.50	+	44885.4i	0.269020	+	1.52569i	0.757339	+	0.653022i	$0.226499\pi$
$953$	7914.50	+	44885.4i	0.269020	+	1.52569i	−0.488319	+	0.872665i	$0.662390\pi$
$954$	4031.83	+	3383.11i	0.136830	+	0.114814i
$955$	12362.2	−	10373.1i	0.418880	−	0.351482i
$956$	−2787.38	+	15808.0i	−0.0942994	+	0.534799i
$957$	7716.01	−	13364.5i	0.260630	−	0.451425i
$958$	17825.0	+	30873.8i	0.601147	+	1.04122i
$959$	−3630.31	+	1321.33i	−0.122241	+	0.0444920i
$960$	2728.41	−	993.062i	0.0917283	−	0.0333864i
$961$	−29525.8	−	51140.1i	−0.991097	−	1.71663i
$962$	−12472.5	+	21603.0i	−0.418013	+	0.724020i
$963$	905.712	−	5136.55i	0.0303075	−	0.171883i
$964$	−19584.7	+	16433.5i	−0.654338	+	0.549055i
$965$	36751.1	+	30837.8i	1.22597	+	1.02871i
$966$	−290.073	−	1645.09i	−0.00966145	−	0.0547928i
$967$	32450.4	+	11811.0i	1.07915	+	0.392777i	0.819589	−	0.572951i	$-0.194202\pi$
$967$	32450.4	+	11811.0i	1.07915	+	0.392777i	0.259556	+	0.965728i	$0.416424\pi$
$968$	−7865.10			−0.261151
$969$	−2854.04	+	7752.28i	−0.0946180	+	0.257006i
$970$	39691.7			1.31384
$971$	−17316.2	−	6302.60i	−0.572302	−	0.208301i	0.0396260	−	0.999215i	$-0.487383\pi$
$971$	−17316.2	−	6302.60i	−0.572302	−	0.208301i	−0.611927	+	0.790914i	$0.709606\pi$
$972$	168.786	+	957.233i	0.00556977	+	0.0315877i
$973$	8783.10	+	7369.89i	0.289387	+	0.242824i
$974$	−5842.59	+	4902.52i	−0.192206	+	0.161280i
$975$	−4220.97	+	23938.3i	−0.138645	+	0.786297i
$976$	3861.12	−	6687.66i	0.126631	−	0.219331i
$977$	5730.64	+	9925.75i	0.187655	+	0.325029i	0.944468	−	0.328603i	$-0.106578\pi$
$977$	5730.64	+	9925.75i	0.187655	+	0.325029i	−0.756813	+	0.653632i	$0.773245\pi$
$978$	13612.0	−	4954.37i	0.445056	−	0.161987i
$979$	−33642.3	+	12244.8i	−1.09828	+	0.399740i
$980$	−9766.51	−	16916.1i	−0.318347	−	0.551392i
$981$	4007.32	−	6940.88i	0.130422	−	0.225897i
$982$	−365.885	+	2075.04i	−0.0118899	+	0.0674309i
$983$	24105.8	−	20227.1i	0.782151	−	0.656303i	−0.161638	−	0.986850i	$-0.551678\pi$
$983$	24105.8	−	20227.1i	0.782151	−	0.656303i	0.943789	+	0.330547i	$0.107233\pi$
$984$	1434.57	+	1203.75i	0.0464761	+	0.0389981i
$985$	497.688	+	2822.53i	0.0160991	+	0.0913028i
$986$	6681.92	+	2432.02i	0.215817	+	0.0785511i
$987$	−3318.39			−0.107017
$988$	−22466.1	+	12860.5i	−0.723423	+	0.414117i
$989$	28943.6			0.930589
$990$	−12304.8	−	4478.60i	−0.395024	−	0.143777i
$991$	−4306.52	−	24423.5i	−0.138044	−	0.782884i	−0.972692	−	0.232101i	$-0.925440\pi$
$991$	−4306.52	−	24423.5i	−0.138044	−	0.782884i	0.834648	−	0.550784i	$-0.185671\pi$
$992$	−7306.59	−	6130.95i	−0.233855	−	0.196228i
$993$	−18406.3	+	15444.7i	−0.588223	+	0.493578i
$994$	242.233	−	1373.77i	0.00772954	−	0.0438364i
$995$	−7774.26	+	13465.4i	−0.247699	+	0.429027i
$996$	−3505.92	−	6072.43i	−0.111535	−	0.193185i
$997$	−32630.4	+	11876.5i	−1.03653	+	0.377265i	−0.803562	−	0.595221i	$-0.797065\pi$
$997$	−32630.4	+	11876.5i	−1.03653	+	0.377265i	−0.232964	+	0.972485i	$0.574842\pi$
$998$	11251.6	−	4095.26i	0.356878	−	0.129893i
$999$	−2154.77	−	3732.17i	−0.0682422	−	0.118199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.c.61.1	yes	18
19.5	even	9	inner	114.4.i.c.43.1	✓	18
19.9	even	9		2166.4.a.bk.1.3		9
19.10	odd	18		2166.4.a.bl.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.c.43.1	✓	18	19.5	even	9	inner
114.4.i.c.61.1	yes	18	1.1	even	1	trivial
2166.4.a.bk.1.3		9	19.9	even	9
2166.4.a.bl.1.3		9	19.10	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-11.5845 + 9.72055i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(-2.24091 + 3.88137i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-11.5845 + 9.72055i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(-2.24091 + 3.88137i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(-28.4210 + 10.3444i) q^{10} +(-24.0527 - 41.6606i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-13.5692 + 76.9550i) q^{13} +(-6.86654 + 5.76171i) q^{14} +(-34.7535 - 29.1616i) q^{15} +(2.77837 + 15.7569i) q^{16} +(31.2438 + 11.3718i) q^{17} -18.0000 q^{18} +(81.5073 + 14.6822i) q^{19} -60.4900 q^{20} +(-12.6346 - 4.59861i) q^{21} +(-16.7069 - 94.7493i) q^{22} +(47.5868 + 39.9301i) q^{23} +(-18.3851 + 15.4269i) q^{24} +(18.0055 - 102.114i) q^{25} +(-78.1421 + 135.346i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(-16.8461 + 6.13149i) q^{28} +(100.483 - 36.5729i) q^{29} +(-45.3675 - 78.5788i) q^{30} +(-149.032 + 258.132i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(110.553 - 92.7648i) q^{33} +(50.9404 + 42.7441i) q^{34} +(-11.7692 - 66.7466i) q^{35} +(-33.8289 - 12.3127i) q^{36} +159.613 q^{37} +(143.140 + 83.3478i) q^{38} -234.426 q^{39} +(-113.684 - 41.3776i) q^{40} +(-13.5496 - 76.8437i) q^{41} +(-20.5996 - 17.2851i) q^{42} +(356.922 - 299.493i) q^{43} +(33.4137 - 189.499i) q^{44} +(68.0512 - 117.868i) q^{45} +(62.1201 + 107.595i) q^{46} +(231.920 - 84.4118i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(161.457 + 279.651i) q^{49} +(103.690 - 179.596i) q^{50} +(-17.3209 + 98.2316i) q^{51} +(-239.441 + 200.915i) q^{52} +(-223.991 - 187.951i) q^{53} +(-9.37700 - 53.1796i) q^{54} +(683.603 + 248.811i) q^{55} -35.8545 q^{56} +(-0.916742 + 248.456i) q^{57} +213.864 q^{58} +(-376.675 - 137.099i) q^{59} +(-31.5119 - 178.713i) q^{60} +(-369.724 - 310.235i) q^{61} +(-456.662 + 383.185i) q^{62} +(7.00433 - 39.7235i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-590.852 - 1023.39i) q^{65} +(271.226 - 98.7183i) q^{66} +(832.540 - 303.020i) q^{67} +(66.4980 + 115.178i) q^{68} +(-93.1802 + 161.393i) q^{69} +(23.5384 - 133.493i) q^{70} +(-119.216 + 100.034i) q^{71} +(-55.1552 - 46.2807i) q^{72} +(148.457 + 841.940i) q^{73} +(299.974 + 109.182i) q^{74} +311.069 q^{75} +(212.003 + 254.556i) q^{76} +215.600 q^{77} +(-440.578 - 160.357i) q^{78} +(40.1809 + 227.877i) q^{79} +(-185.352 - 155.529i) q^{80} +(62.0496 - 52.0658i) q^{81} +(27.0992 - 153.687i) q^{82} +(-292.160 + 506.036i) q^{83} +(-26.8909 - 46.5764i) q^{84} +(-472.485 + 171.970i) q^{85} +(875.660 - 318.714i) q^{86} +(160.398 + 277.817i) q^{87} +(192.422 - 333.285i) q^{88} +(129.234 - 732.920i) q^{89} +(208.521 - 174.970i) q^{90} +(-268.283 - 225.116i) q^{91} +(43.1482 + 244.706i) q^{92} +(-840.268 - 305.832i) q^{93} +493.607 q^{94} +(-1086.94 + 622.209i) q^{95} -96.0000 q^{96} +(-1233.20 - 448.847i) q^{97} +(112.147 + 636.015i) q^{98} +(331.658 + 278.294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

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