LMFDB - Embedded newform 230.4.g.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	230.31
Dual form			230.4.g.b.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.284630 - 1.97964i) q^{2} +(-1.76914 - 3.87387i) q^{3} +(-3.83797 - 1.12693i) q^{4} +(-3.27430 - 3.77875i) q^{5} +(-8.17242 + 2.39964i) q^{6} +(-26.5942 - 17.0910i) q^{7} +(-3.32332 + 7.27706i) q^{8} +(5.80424 - 6.69844i) q^{9} +O(q^{10})$	\(q+(0.284630 - 1.97964i) q^{2} +(-1.76914 - 3.87387i) q^{3} +(-3.83797 - 1.12693i) q^{4} +(-3.27430 - 3.77875i) q^{5} +(-8.17242 + 2.39964i) q^{6} +(-26.5942 - 17.0910i) q^{7} +(-3.32332 + 7.27706i) q^{8} +(5.80424 - 6.69844i) q^{9} +(-8.41254 + 5.40641i) q^{10} +(2.31578 + 16.1066i) q^{11} +(2.42432 + 16.8615i) q^{12} +(-2.85088 + 1.83215i) q^{13} +(-41.4036 + 47.7823i) q^{14} +(-8.84568 + 19.3693i) q^{15} +(13.4601 + 8.65025i) q^{16} +(19.9821 - 5.86727i) q^{17} +(-11.6085 - 13.3969i) q^{18} +(52.6683 + 15.4648i) q^{19} +(8.30830 + 18.1926i) q^{20} +(-19.1597 + 133.259i) q^{21} +32.5444 q^{22} +(-77.0352 + 78.9467i) q^{23} +34.0698 q^{24} +(-3.55787 + 24.7455i) q^{25} +(2.81556 + 6.16522i) q^{26} +(-146.545 - 43.0295i) q^{27} +(82.8072 + 95.5646i) q^{28} +(-13.8771 + 4.07468i) q^{29} +(35.8266 + 23.0244i) q^{30} +(-3.19871 + 7.00419i) q^{31} +(20.9555 - 24.1840i) q^{32} +(58.2979 - 37.4658i) q^{33} +(-5.92760 - 41.2274i) q^{34} +(22.4947 + 156.454i) q^{35} +(-29.8252 + 19.1675i) q^{36} +(87.6813 - 101.190i) q^{37} +(45.6057 - 99.8627i) q^{38} +(12.1411 + 7.80262i) q^{39} +(38.3797 - 11.2693i) q^{40} +(177.057 + 204.335i) q^{41} +(258.351 + 75.8587i) q^{42} +(80.9235 + 177.198i) q^{43} +(9.26311 - 64.4264i) q^{44} -44.3166 q^{45} +(134.360 + 174.973i) q^{46} -374.802 q^{47} +(9.69726 - 67.4459i) q^{48} +(272.659 + 597.039i) q^{49} +(47.9746 + 14.0866i) q^{50} +(-58.0800 - 67.0279i) q^{51} +(13.0063 - 3.81900i) q^{52} +(-249.519 - 160.356i) q^{53} +(-126.894 + 277.859i) q^{54} +(53.2802 - 61.4886i) q^{55} +(212.753 - 136.728i) q^{56} +(-33.2688 - 231.389i) q^{57} +(4.11658 + 28.6315i) q^{58} +(-211.554 + 135.958i) q^{59} +(55.7774 - 64.3705i) q^{60} +(305.937 - 669.909i) q^{61} +(12.9554 + 8.32590i) q^{62} +(-268.842 + 78.9391i) q^{63} +(-41.9111 - 48.3680i) q^{64} +(16.2579 + 4.77375i) q^{65} +(-57.5755 - 126.073i) q^{66} +(-15.3596 + 106.828i) q^{67} -83.3026 q^{68} +(442.115 + 158.757i) q^{69} +316.125 q^{70} +(67.3543 - 468.460i) q^{71} +(29.4556 + 64.4988i) q^{72} +(-1137.06 - 333.871i) q^{73} +(-175.363 - 202.379i) q^{74} +(102.155 - 29.9955i) q^{75} +(-184.712 - 118.707i) q^{76} +(213.692 - 467.920i) q^{77} +(18.9021 - 21.8142i) q^{78} +(-1134.53 + 729.116i) q^{79} +(-11.3852 - 79.1857i) q^{80} +(58.5102 + 406.948i) q^{81} +(454.905 - 292.350i) q^{82} +(-358.620 + 413.870i) q^{83} +(223.707 - 489.851i) q^{84} +(-87.5983 - 56.2960i) q^{85} +(373.821 - 109.764i) q^{86} +(40.3353 + 46.5494i) q^{87} +(-124.905 - 36.6753i) q^{88} +(-74.3745 - 162.857i) q^{89} +(-12.6138 + 87.7310i) q^{90} +107.130 q^{91} +(384.626 - 216.182i) q^{92} +32.7923 q^{93} +(-106.680 + 741.975i) q^{94} +(-114.014 - 249.657i) q^{95} +(-130.759 - 38.3942i) q^{96} +(-673.651 - 777.434i) q^{97} +(1259.53 - 369.832i) q^{98} +(121.330 + 77.9743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{2} - 3 q^{3} - 24 q^{4} - 30 q^{5} + 6 q^{6} + 100 q^{7} + 48 q^{8} + 69 q^{9}+O(q^{10}) $ 60 * q + 12 * q^2 - 3 * q^3 - 24 * q^4 - 30 * q^5 + 6 * q^6 + 100 * q^7 + 48 * q^8 + 69 * q^9	\( 60 q + 12 q^{2} - 3 q^{3} - 24 q^{4} - 30 q^{5} + 6 q^{6} + 100 q^{7} + 48 q^{8} + 69 q^{9} + 60 q^{10} - 51 q^{11} + 120 q^{12} + 184 q^{13} + 20 q^{14} - 15 q^{15} - 96 q^{16} - 334 q^{17} - 138 q^{18} + 258 q^{19} - 120 q^{20} + 716 q^{21} + 344 q^{22} - 288 q^{23} + 288 q^{24} - 150 q^{25} + 336 q^{26} - 813 q^{27} - 40 q^{28} + 1462 q^{29} + 30 q^{30} - 481 q^{31} + 192 q^{32} + 269 q^{33} - 168 q^{34} - 380 q^{35} + 12 q^{36} - 787 q^{37} - 978 q^{38} + 2065 q^{39} + 240 q^{40} - 1843 q^{41} + 724 q^{42} + 128 q^{43} - 204 q^{44} + 2380 q^{45} + 92 q^{46} - 1838 q^{47} + 480 q^{48} - 606 q^{49} + 300 q^{50} + 2320 q^{51} - 12 q^{52} - 3284 q^{53} + 636 q^{54} - 200 q^{55} - 800 q^{56} - 2710 q^{57} - 856 q^{58} - 2708 q^{59} - 60 q^{60} + 437 q^{61} + 962 q^{62} + 6063 q^{63} - 384 q^{64} - 15 q^{65} + 1090 q^{66} + 2804 q^{67} + 600 q^{68} + 7900 q^{69} - 120 q^{70} + 2676 q^{71} + 1384 q^{72} + 876 q^{73} + 1574 q^{74} - 75 q^{75} + 20 q^{76} + 9310 q^{77} - 2612 q^{78} - 1233 q^{79} - 480 q^{80} - 6030 q^{81} - 1132 q^{82} - 9923 q^{83} - 964 q^{84} + 1300 q^{85} + 5222 q^{86} - 5719 q^{87} - 1176 q^{88} - 1827 q^{89} + 190 q^{90} - 7626 q^{91} + 564 q^{92} + 230 q^{93} - 1142 q^{94} + 2445 q^{95} + 96 q^{96} + 939 q^{97} - 5916 q^{98} - 10589 q^{99}+O(q^{100}) \) 60 * q + 12 * q^2 - 3 * q^3 - 24 * q^4 - 30 * q^5 + 6 * q^6 + 100 * q^7 + 48 * q^8 + 69 * q^9 + 60 * q^10 - 51 * q^11 + 120 * q^12 + 184 * q^13 + 20 * q^14 - 15 * q^15 - 96 * q^16 - 334 * q^17 - 138 * q^18 + 258 * q^19 - 120 * q^20 + 716 * q^21 + 344 * q^22 - 288 * q^23 + 288 * q^24 - 150 * q^25 + 336 * q^26 - 813 * q^27 - 40 * q^28 + 1462 * q^29 + 30 * q^30 - 481 * q^31 + 192 * q^32 + 269 * q^33 - 168 * q^34 - 380 * q^35 + 12 * q^36 - 787 * q^37 - 978 * q^38 + 2065 * q^39 + 240 * q^40 - 1843 * q^41 + 724 * q^42 + 128 * q^43 - 204 * q^44 + 2380 * q^45 + 92 * q^46 - 1838 * q^47 + 480 * q^48 - 606 * q^49 + 300 * q^50 + 2320 * q^51 - 12 * q^52 - 3284 * q^53 + 636 * q^54 - 200 * q^55 - 800 * q^56 - 2710 * q^57 - 856 * q^58 - 2708 * q^59 - 60 * q^60 + 437 * q^61 + 962 * q^62 + 6063 * q^63 - 384 * q^64 - 15 * q^65 + 1090 * q^66 + 2804 * q^67 + 600 * q^68 + 7900 * q^69 - 120 * q^70 + 2676 * q^71 + 1384 * q^72 + 876 * q^73 + 1574 * q^74 - 75 * q^75 + 20 * q^76 + 9310 * q^77 - 2612 * q^78 - 1233 * q^79 - 480 * q^80 - 6030 * q^81 - 1132 * q^82 - 9923 * q^83 - 964 * q^84 + 1300 * q^85 + 5222 * q^86 - 5719 * q^87 - 1176 * q^88 - 1827 * q^89 + 190 * q^90 - 7626 * q^91 + 564 * q^92 + 230 * q^93 - 1142 * q^94 + 2445 * q^95 + 96 * q^96 + 939 * q^97 - 5916 * q^98 - 10589 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.284630	−	1.97964i	0.100632	−	0.699909i
$2$	0.284630	−	1.97964i	0.100632	−	0.699909i
$3$	−1.76914	−	3.87387i	−0.340470	−	0.745526i	0.659511	−	0.751695i	$-0.270764\pi$
$3$	−1.76914	−	3.87387i	−0.340470	−	0.745526i	−0.999981	+	0.00616918i	$0.998036\pi$
$4$	−3.83797	−	1.12693i	−0.479746	−	0.140866i
$5$	−3.27430	−	3.77875i	−0.292863	−	0.337981i
$5$	−3.27430	−	3.77875i	−0.292863	−	0.337981i
$6$	−8.17242	+	2.39964i	−0.556063	+	0.163275i
$7$	−26.5942	−	17.0910i	−1.43595	−	0.922829i	−0.999736	−	0.0229855i	$-0.992683\pi$
$7$	−26.5942	−	17.0910i	−1.43595	−	0.922829i	−0.436214	−	0.899843i	$-0.643681\pi$
$8$	−3.32332	+	7.27706i	−0.146871	+	0.321603i
$9$	5.80424	−	6.69844i	0.214972	−	0.248091i
$10$	−8.41254	+	5.40641i	−0.266028	+	0.170966i
$11$	2.31578	+	16.1066i	0.0634758	+	0.441484i	0.996631	+	0.0820111i	$0.0261343\pi$
$11$	2.31578	+	16.1066i	0.0634758	+	0.441484i	−0.933156	+	0.359473i	$0.882957\pi$
$12$	2.42432	+	16.8615i	0.0583200	+	0.405624i
$13$	−2.85088	+	1.83215i	−0.0608225	+	0.0390883i	−0.570699	−	0.821160i	$-0.693328\pi$
$13$	−2.85088	+	1.83215i	−0.0608225	+	0.0390883i	0.509876	+	0.860248i	$0.329691\pi$
$14$	−41.4036	+	47.7823i	−0.790399	+	0.912169i
$15$	−8.84568	+	19.3693i	−0.152263	+	0.333409i
$16$	13.4601	+	8.65025i	0.210313	+	0.135160i
$17$	19.9821	−	5.86727i	0.285080	−	0.0837071i	−0.136066	−	0.990700i	$-0.543446\pi$
$17$	19.9821	−	5.86727i	0.285080	−	0.0837071i	0.421146	+	0.906993i	$0.361628\pi$
$18$	−11.6085	−	13.3969i	−0.152008	−	0.175427i
$19$	52.6683	+	15.4648i	0.635944	+	0.186730i	0.583784	−	0.811909i	$-0.301571\pi$
$19$	52.6683	+	15.4648i	0.635944	+	0.186730i	0.0521596	+	0.998639i	$0.483390\pi$
$20$	8.30830	+	18.1926i	0.0928896	+	0.203400i
$21$	−19.1597	+	133.259i	−0.199095	+	1.38473i
$22$	32.5444			0.315386
$23$	−77.0352	+	78.9467i	−0.698389	+	0.715718i
$23$	−77.0352	+	78.9467i	−0.698389	+	0.715718i
$24$	34.0698			0.289769
$25$	−3.55787	+	24.7455i	−0.0284630	+	0.197964i
$26$	2.81556	+	6.16522i	0.0212376	+	0.0465038i
$27$	−146.545	−	43.0295i	−1.04454	−	0.306705i
$28$	82.8072	+	95.5646i	0.558896	+	0.645001i
$29$	−13.8771	+	4.07468i	−0.0888591	+	0.0260914i	−0.325860	−	0.945418i	$-0.605654\pi$
$29$	−13.8771	+	4.07468i	−0.0888591	+	0.0260914i	0.237001	+	0.971509i	$0.423836\pi$
$30$	35.8266	+	23.0244i	0.218034	+	0.140122i
$31$	−3.19871	+	7.00419i	−0.0185324	+	0.0405803i	−0.918672	−	0.395021i	$-0.870737\pi$
$31$	−3.19871	+	7.00419i	−0.0185324	+	0.0405803i	0.900139	+	0.435602i	$0.143464\pi$
$32$	20.9555	−	24.1840i	0.115764	−	0.133599i
$33$	58.2979	−	37.4658i	0.307526	−	0.197635i
$34$	−5.92760	−	41.2274i	−0.0298993	−	0.207954i
$35$	22.4947	+	156.454i	0.108637	+	0.755586i
$36$	−29.8252	+	19.1675i	−0.138080	+	0.0887383i
$37$	87.6813	−	101.190i	0.389587	−	0.449608i	−0.526747	−	0.850022i	$-0.676588\pi$
$37$	87.6813	−	101.190i	0.389587	−	0.449608i	0.916334	+	0.400415i	$0.131134\pi$
$38$	45.6057	−	99.8627i	0.194690	−	0.426312i
$39$	12.1411	+	7.80262i	0.0498496	+	0.0320364i
$40$	38.3797	−	11.2693i	0.151709	−	0.0445458i
$41$	177.057	+	204.335i	0.674431	+	0.778335i	0.985063	−	0.172196i	$-0.0550861\pi$
$41$	177.057	+	204.335i	0.674431	+	0.778335i	−0.310632	+	0.950530i	$0.600541\pi$
$42$	258.351	+	75.8587i	0.949153	+	0.278696i
$43$	80.9235	+	177.198i	0.286993	+	0.628428i	0.997136	−	0.0756301i	$-0.0240968\pi$
$43$	80.9235	+	177.198i	0.286993	+	0.628428i	−0.710143	+	0.704058i	$0.751370\pi$
$44$	9.26311	−	64.4264i	0.0317379	−	0.220742i
$45$	−44.3166			−0.146807
$46$	134.360	+	174.973i	0.430658	+	0.560833i
$47$	−374.802			−1.16320			−0.581601	−	0.813474i	$-0.697574\pi$
$47$	−374.802			−1.16320			−0.581601	+	0.813474i	$0.697574\pi$
$48$	9.69726	−	67.4459i	0.0291600	−	0.202812i
$49$	272.659	+	597.039i	0.794923	+	1.74064i
$50$	47.9746	+	14.0866i	0.135693	+	0.0398430i
$51$	−58.0800	−	67.0279i	−0.159467	−	0.184035i
$52$	13.0063	−	3.81900i	0.0346856	−	0.0101846i
$53$	−249.519	−	160.356i	−0.646681	−	0.415596i	0.175771	−	0.984431i	$-0.443758\pi$
$53$	−249.519	−	160.356i	−0.646681	−	0.415596i	−0.822452	+	0.568835i	$0.807394\pi$
$54$	−126.894	+	277.859i	−0.319780	+	0.700220i
$55$	53.2802	−	61.4886i	0.130624	−	0.150748i
$56$	212.753	−	136.728i	0.507685	−	0.326269i
$57$	−33.2688	−	231.389i	−0.0773080	−	0.537689i
$58$	4.11658	+	28.6315i	0.00931955	+	0.0648189i
$59$	−211.554	+	135.958i	−0.466814	+	0.300003i	−0.752822	−	0.658224i	$-0.771308\pi$
$59$	−211.554	+	135.958i	−0.466814	+	0.300003i	0.286008	+	0.958227i	$0.407672\pi$
$60$	55.7774	−	64.3705i	0.120014	−	0.138503i
$61$	305.937	−	669.909i	0.642152	−	1.40612i	−0.256107	−	0.966648i	$-0.582440\pi$
$61$	305.937	−	669.909i	0.642152	−	1.40612i	0.898259	−	0.439467i	$-0.144833\pi$
$62$	12.9554	+	8.32590i	0.0265376	+	0.0170547i
$63$	−268.842	+	78.9391i	−0.537634	+	0.157863i
$64$	−41.9111	−	48.3680i	−0.0818576	−	0.0944687i
$65$	16.2579	+	4.77375i	0.0310238	+	0.00910940i
$66$	−57.5755	−	126.073i	−0.107380	−	0.235129i
$67$	−15.3596	+	106.828i	−0.0280071	+	0.194794i	−0.999021	−	0.0442274i	$-0.985917\pi$
$67$	−15.3596	+	106.828i	−0.0280071	+	0.194794i	0.971014	+	0.239021i	$0.0768265\pi$
$68$	−83.3026			−0.148558
$69$	442.115	+	158.757i	0.771367	+	0.276986i
$70$	316.125			0.539774
$71$	67.3543	−	468.460i	0.112584	−	0.783041i	−0.852805	−	0.522229i	$-0.825101\pi$
$71$	67.3543	−	468.460i	0.112584	−	0.783041i	0.965390	−	0.260812i	$-0.0839903\pi$
$72$	29.4556	+	64.4988i	0.0482136	+	0.105573i
$73$	−1137.06	−	333.871i	−1.82305	−	0.535297i	−0.823563	−	0.567224i	$-0.808017\pi$
$73$	−1137.06	−	333.871i	−1.82305	−	0.535297i	−0.999490	+	0.0319274i	$0.989835\pi$
$74$	−175.363	−	202.379i	−0.275480	−	0.317921i
$75$	102.155	−	29.9955i	0.157278	−	0.0461811i
$76$	−184.712	−	118.707i	−0.278788	−	0.179166i
$77$	213.692	−	467.920i	0.316266	−	0.692525i
$78$	18.9021	−	21.8142i	0.0274390	−	0.0316663i
$79$	−1134.53	+	729.116i	−1.61575	+	1.03838i	−0.657096	+	0.753807i	$0.728215\pi$
$79$	−1134.53	+	729.116i	−1.61575	+	1.03838i	−0.958655	+	0.284572i	$0.908148\pi$
$80$	−11.3852	−	79.1857i	−0.0159113	−	0.110665i
$81$	58.5102	+	406.948i	0.0802609	+	0.558227i
$82$	454.905	−	292.350i	0.612633	−	0.393715i
$83$	−358.620	+	413.870i	−0.474261	+	0.547327i	−0.941592	−	0.336756i	$-0.890670\pi$
$83$	−358.620	+	413.870i	−0.474261	+	0.547327i	0.467331	+	0.884083i	$0.345216\pi$
$84$	223.707	−	489.851i	0.290577	−	0.636275i
$85$	−87.5983	−	56.2960i	−0.111781	−	0.0718372i
$86$	373.821	−	109.764i	0.468723	−	0.137630i
$87$	40.3353	+	46.5494i	0.0497057	+	0.0573634i
$88$	−124.905	−	36.6753i	−0.151305	−	0.0444273i
$89$	−74.3745	−	162.857i	−0.0885807	−	0.193965i	0.860157	−	0.510030i	$-0.170366\pi$
$89$	−74.3745	−	162.857i	−0.0885807	−	0.193965i	−0.948738	+	0.316065i	$0.897638\pi$
$90$	−12.6138	+	87.7310i	−0.0147735	+	0.102752i
$91$	107.130			0.123410
$92$	384.626	−	216.182i	0.435870	−	0.244984i
$93$	32.7923			0.0365634
$94$	−106.680	+	741.975i	−0.117055	+	0.814137i
$95$	−114.014	−	249.657i	−0.123133	−	0.269624i
$96$	−130.759	−	38.3942i	−0.139016	−	0.0408187i
$97$	−673.651	−	777.434i	−0.705143	−	0.813778i	0.284295	−	0.958737i	$-0.408241\pi$
$97$	−673.651	−	777.434i	−0.705143	−	0.813778i	−0.989438	+	0.144959i	$0.953695\pi$
$98$	1259.53	−	369.832i	1.29828	−	0.381211i
$99$	121.330	+	77.9743i	0.123173	+	0.0791587i
$100$	41.5415	−	90.9632i	0.0415415	−	0.0909632i
$101$	−282.454	+	325.969i	−0.278270	+	0.321140i	−0.877630	−	0.479339i	$-0.840876\pi$
$101$	−282.454	+	325.969i	−0.278270	+	0.321140i	0.599360	+	0.800480i	$0.295422\pi$
$102$	−149.223	+	95.8995i	−0.144855	+	0.0930928i
$103$	−72.3745	−	503.375i	−0.0692356	−	0.481544i	−0.994709	−	0.102732i	$-0.967242\pi$
$103$	−72.3745	−	503.375i	−0.0692356	−	0.481544i	0.925473	−	0.378812i	$-0.123667\pi$
$104$	−3.85827	−	26.8349i	−0.00363783	−	0.0253017i
$105$	566.285	−	363.929i	0.526322	−	0.338246i
$106$	−388.468	+	448.316i	−0.355956	+	0.410796i
$107$	376.723	−	824.909i	0.340366	−	0.745299i	−0.659614	−	0.751605i	$-0.729280\pi$
$107$	376.723	−	824.909i	0.340366	−	0.745299i	0.999980	+	0.00630627i	$0.00200736\pi$
$108$	513.945	+	330.292i	0.457911	+	0.294281i
$109$	−1505.35	+	442.012i	−1.32281	+	0.388414i	−0.865508	−	0.500895i	$-0.833004\pi$
$109$	−1505.35	+	442.012i	−1.32281	+	0.388414i	−0.457307	+	0.889309i	$0.651186\pi$
$110$	−106.560	−	122.977i	−0.0923648	−	0.106595i
$111$	−547.116	−	160.648i	−0.467837	−	0.137369i
$112$	−210.117	−	460.092i	−0.177270	−	0.388166i
$113$	−86.3274	+	600.420i	−0.0718672	+	0.499848i	0.921816	+	0.387627i	$0.126705\pi$
$113$	−86.3274	+	600.420i	−0.0718672	+	0.499848i	−0.993683	+	0.112220i	$0.964204\pi$
$114$	−467.537			−0.384113
$115$	550.556	+	32.6011i	0.446432	+	0.0264354i
$116$	57.8518			0.0463052
$117$	−4.27463	+	29.7307i	−0.00337769	+	0.0234924i
$118$	208.933	+	457.500i	0.162999	+	0.356918i
$119$	−631.684	−	185.479i	−0.486608	−	0.142881i
$120$	−111.555	−	128.741i	−0.0848625	−	0.0979366i
$121$	1023.03	−	300.387i	0.768614	−	0.225686i
$122$	−1239.10	−	796.322i	−0.919533	−	0.590948i
$123$	478.328	−	1047.39i	0.350645	−	0.767806i
$124$	20.1698	−	23.2772i	0.0146073	−	0.0168577i
$125$	105.157	−	67.5801i	0.0752440	−	0.0483564i
$126$	79.7509	+	554.680i	0.0563871	+	0.392181i
$127$	−246.783	−	1716.41i	−0.172429	−	1.19927i	−0.873733	−	0.486405i	$-0.838308\pi$
$127$	−246.783	−	1716.41i	−0.172429	−	1.19927i	0.701305	−	0.712862i	$-0.252601\pi$
$128$	−107.680	+	69.2020i	−0.0743570	+	0.0477863i
$129$	543.276	−	626.974i	0.370797	−	0.427922i
$130$	14.0778	−	30.8261i	0.00949773	−	0.0207971i
$131$	138.076	+	88.7363i	0.0920900	+	0.0591827i	0.585875	−	0.810401i	$-0.300751\pi$
$131$	138.076	+	88.7363i	0.0920900	+	0.0591827i	−0.493785	+	0.869584i	$0.664387\pi$
$132$	−265.967	+	78.0949i	−0.175375	+	0.0514946i
$133$	−1136.36	−	1311.43i	−0.740863	−	0.855002i
$134$	207.110	+	60.8131i	0.133519	+	0.0392048i
$135$	317.235	+	694.649i	0.202246	+	0.442858i
$136$	−23.7104	+	164.909i	−0.0149496	+	0.103977i
$137$	2388.43			1.48947			0.744733	−	0.667362i	$-0.232577\pi$
$137$	2388.43			1.48947			0.744733	+	0.667362i	$0.232577\pi$
$138$	440.120	−	830.042i	0.271489	−	0.512014i
$139$	−741.931			−0.452732			−0.226366	−	0.974042i	$-0.572685\pi$
$139$	−741.931			−0.452732			−0.226366	+	0.974042i	$0.572685\pi$
$140$	89.9786	−	625.815i	0.0543185	−	0.377793i
$141$	663.076	+	1451.93i	0.396036	+	0.867198i
$142$	−908.212	−	266.675i	−0.536728	−	0.157598i
$143$	−36.1117	−	41.6752i	−0.0211176	−	0.0243710i
$144$	136.069	−	39.9533i	0.0787434	−	0.0231211i
$145$	60.8350	+	39.0963i	0.0348419	+	0.0223915i
$146$	−984.587	+	2155.94i	−0.558116	+	1.22210i
$147$	1830.48	−	2112.49i	1.02704	−	1.18527i
$148$	−450.552	+	289.552i	−0.250238	+	0.160818i
$149$	−295.113	−	2052.56i	−0.162259	−	1.12854i	−0.894362	−	0.447343i	$-0.852370\pi$
$149$	−295.113	−	2052.56i	−0.162259	−	1.12854i	0.732103	−	0.681194i	$-0.238539\pi$
$150$	−30.3039	−	210.769i	−0.0164954	−	0.114728i
$151$	−2822.79	+	1814.10i	−1.52129	+	0.977675i	−0.529713	+	0.848177i	$0.677700\pi$
$151$	−2822.79	+	1814.10i	−1.52129	+	0.977675i	−0.991580	+	0.129498i	$0.958663\pi$
$152$	−287.572	+	331.876i	−0.153455	+	0.177096i
$153$	76.6791	−	167.904i	0.0405172	−	0.0887204i
$154$	−865.492	−	556.218i	−0.452879	−	0.291047i
$155$	36.9406	−	10.8467i	0.0191429	−	0.00562085i
$156$	−37.8043	−	43.6284i	−0.0194023	−	0.0223915i
$157$	1214.75	+	356.682i	0.617499	+	0.181314i	0.575498	−	0.817803i	$-0.304808\pi$
$157$	1214.75	+	356.682i	0.617499	+	0.181314i	0.0420015	+	0.999118i	$0.486627\pi$
$158$	1120.47	+	2453.49i	0.564176	+	1.23537i
$159$	−179.765	+	1250.30i	−0.0896624	+	0.623615i
$160$	−160.000			−0.0790569
$161$	3397.97	−	782.910i	1.66334	−	0.383242i
$162$	822.265			0.398785
$163$	−457.040	+	3178.78i	−0.219620	+	1.52749i	0.519823	+	0.854274i	$0.325998\pi$
$163$	−457.040	+	3178.78i	−0.219620	+	1.52749i	−0.739443	+	0.673219i	$0.764911\pi$
$164$	−449.269	−	983.762i	−0.213915	−	0.468408i
$165$	−332.459	−	97.6186i	−0.156860	−	0.0460582i
$166$	717.241	+	827.740i	0.335353	+	0.387019i
$167$	1659.67	−	487.322i	0.769035	−	0.225809i	0.126398	−	0.991980i	$-0.459659\pi$
$167$	1659.67	−	487.322i	0.769035	−	0.225809i	0.642637	+	0.766171i	$0.277840\pi$
$168$	−906.056	−	582.287i	−0.416094	−	0.267407i
$169$	−907.896	+	1988.01i	−0.413244	+	0.904877i
$170$	−136.379	+	157.390i	−0.0615282	+	0.0710073i
$171$	409.289	−	263.034i	0.183036	−	0.117630i
$172$	−110.893	−	771.275i	−0.0491598	−	0.341914i
$173$	282.815	+	1967.02i	0.124289	+	0.864450i	0.952610	+	0.304195i	$0.0983875\pi$
$173$	282.815	+	1967.02i	0.124289	+	0.864450i	−0.828321	+	0.560254i	$0.810703\pi$
$174$	103.632	−	66.6001i	0.0451512	−	0.0290169i
$175$	517.545	−	597.279i	0.223558	−	0.258000i
$176$	−108.156	+	236.828i	−0.0463212	+	0.101429i
$177$	900.951	+	579.006i	0.382597	+	0.245880i
$178$	−343.569	+	100.881i	−0.144672	+	0.0424794i
$179$	−672.800	−	776.453i	−0.280936	−	0.324217i	0.597691	−	0.801727i	$-0.296085\pi$
$179$	−672.800	−	776.453i	−0.280936	−	0.324217i	−0.878626	+	0.477510i	$0.841540\pi$
$180$	170.086	+	49.9417i	0.0704302	+	0.0206802i
$181$	303.485	+	664.538i	0.124629	+	0.272899i	0.961654	−	0.274265i	$-0.0884346\pi$
$181$	303.485	+	664.538i	0.124629	+	0.272899i	−0.837025	+	0.547164i	$0.815707\pi$
$182$	30.4924	−	212.080i	0.0124190	−	0.0863757i
$183$	−3136.38			−1.26693
$184$	−318.487	−	822.954i	−0.127604	−	0.329723i
$185$	−669.466			−0.266055
$186$	9.33365	−	64.9170i	0.00367944	−	0.0255911i
$187$	140.776	+	308.256i	0.0550510	+	0.120545i
$188$	1438.48	+	422.376i	0.558042	+	0.163856i
$189$	3161.82	+	3648.94i	1.21687	+	1.40435i
$190$	−526.683	+	154.648i	−0.201103	+	0.0590492i
$191$	431.884	+	277.555i	0.163613	+	0.105148i	0.619885	−	0.784693i	$-0.287179\pi$
$191$	431.884	+	277.555i	0.163613	+	0.105148i	−0.456272	+	0.889840i	$0.650816\pi$
$192$	−113.225	+	247.927i	−0.0425588	+	0.0931908i
$193$	1204.31	−	1389.85i	0.449162	−	0.518360i	−0.485337	−	0.874327i	$-0.661303\pi$
$193$	1204.31	−	1389.85i	0.449162	−	0.518360i	0.934498	+	0.355967i	$0.115849\pi$
$194$	−1730.78	+	1112.31i	−0.640531	+	0.411644i
$195$	−10.2696	−	71.4264i	−0.00377138	−	0.0262305i
$196$	−373.635	−	2598.69i	−0.136164	−	0.947043i
$197$	−176.801	+	113.623i	−0.0639420	+	0.0410930i	−0.572221	−	0.820099i	$-0.693918\pi$
$197$	−176.801	+	113.623i	−0.0639420	+	0.0410930i	0.508279	+	0.861192i	$0.330282\pi$
$198$	188.896	−	217.997i	0.0677991	−	0.0782443i
$199$	28.6382	−	62.7090i	0.0102016	−	0.0223383i	−0.904463	−	0.426553i	$-0.859728\pi$
$199$	28.6382	−	62.7090i	0.0102016	−	0.0223383i	0.914664	+	0.404215i	$0.132455\pi$
$200$	−168.251	−	108.128i	−0.0594856	−	0.0382291i
$201$	441.012	−	129.493i	0.154759	−	0.0454414i
$202$	564.908	+	651.939i	0.196766	+	0.227081i
$203$	438.690	+	128.811i	0.151675	+	0.0445358i
$204$	147.374	+	322.703i	0.0505795	+	0.110754i
$205$	192.391	−	1338.11i	0.0655471	−	0.455890i
$206$	−1017.10			−0.344005
$207$	81.6898	+	974.241i	0.0274291	+	0.327123i
$208$	−54.2216			−0.0180750
$209$	−127.117	+	884.120i	−0.0420712	+	0.292612i
$210$	−559.269	−	1224.63i	−0.183777	−	0.402416i
$211$	−4216.19	−	1237.98i	−1.37561	−	0.403916i	−0.491373	−	0.870949i	$-0.663505\pi$
$211$	−4216.19	−	1237.98i	−1.37561	−	0.403916i	−0.884240	+	0.467033i	$0.845323\pi$
$212$	776.937	+	896.633i	0.251699	+	0.290476i
$213$	−1933.91	+	567.847i	−0.622109	+	0.182668i
$214$	−1525.80	−	980.571i	−0.487390	−	0.313226i
$215$	404.617	−	885.988i	0.128347	−	0.281041i
$216$	800.144	−	923.416i	0.252051	−	0.290882i
$217$	204.776	−	131.601i	0.0640603	−	0.0411691i
$218$	446.557	+	3105.87i	0.138737	+	0.964937i
$219$	718.242	+	4995.49i	0.221618	+	1.54139i
$220$	−273.781	+	175.949i	−0.0839015	+	0.0539202i
$221$	−46.2169	+	53.3371i	−0.0140673	+	0.0162346i
$222$	−473.750	+	1037.37i	−0.143225	+	0.313620i
$223$	2688.37	+	1727.71i	0.807294	+	0.518816i	0.877989	−	0.478682i	$-0.158885\pi$
$223$	2688.37	+	1727.71i	0.807294	+	0.518816i	−0.0706946	+	0.997498i	$0.522522\pi$
$224$	−970.624	+	285.001i	−0.289520	+	0.0850108i
$225$	145.106	+	167.461i	0.0429943	+	0.0496181i
$226$	1164.05	+	341.795i	0.342616	+	0.100601i
$227$	−551.549	−	1207.72i	−0.161267	−	0.353125i	0.811698	−	0.584077i	$-0.198543\pi$
$227$	−551.549	−	1207.72i	−0.161267	−	0.353125i	−0.972965	+	0.230952i	$0.925816\pi$
$228$	−133.075	+	925.557i	−0.0386540	+	0.268844i
$229$	4847.87			1.39894			0.699468	−	0.714664i	$-0.253420\pi$
$229$	4847.87			1.39894			0.699468	+	0.714664i	$0.253420\pi$
$230$	221.243	−	1080.63i	0.0634276	−	0.309801i
$231$	−2190.71			−0.623975
$232$	16.4663	−	114.526i	0.00465978	−	0.0324095i
$233$	1677.87	+	3674.02i	0.471763	+	1.03302i	0.984647	+	0.174558i	$0.0558497\pi$
$233$	1677.87	+	3674.02i	0.471763	+	1.03302i	−0.512884	+	0.858458i	$0.671423\pi$
$234$	57.6396	+	16.9245i	0.0161026	+	0.00472816i
$235$	1227.22	+	1416.28i	0.340659	+	0.393141i
$236$	965.155	−	283.395i	0.266213	−	0.0781672i
$237$	4831.63	+	3105.10i	1.32425	+	0.851046i
$238$	−546.978	+	1197.72i	−0.148972	+	0.326203i
$239$	−1108.33	+	1279.08i	−0.299966	+	0.346179i	−0.885644	−	0.464364i	$-0.846283\pi$
$239$	−1108.33	+	1279.08i	−0.299966	+	0.346179i	0.585678	+	0.810544i	$0.300828\pi$
$240$	−286.613	+	184.195i	−0.0770866	+	0.0495406i
$241$	−101.549	−	706.289i	−0.0271425	−	0.188780i	0.971739	−	0.236056i	$-0.0758550\pi$
$241$	−101.549	−	706.289i	−0.0271425	−	0.188780i	−0.998882	+	0.0472761i	$0.984946\pi$
$242$	−303.476	−	2110.72i	−0.0806124	−	0.560672i
$243$	−1996.18	+	1282.87i	−0.526975	+	0.338666i
$244$	−1929.12	+	2226.32i	−0.506144	+	0.584122i
$245$	1363.29	−	2985.19i	0.355500	−	0.778437i
$246$	−1937.31	−	1245.04i	−0.502108	−	0.322685i
$247$	−178.485	+	52.4080i	−0.0459787	+	0.0135006i
$248$	−40.3396	−	46.5544i	−0.0103289	−	0.0119202i
$249$	2237.73	+	657.055i	0.569518	+	0.167226i
$250$	−103.854	−	227.408i	−0.0262732	−	0.0575302i
$251$	605.532	−	4211.57i	0.152274	−	1.05909i	−0.760121	−	0.649781i	$-0.774861\pi$
$251$	605.532	−	4211.57i	0.152274	−	1.05909i	0.912396	−	0.409309i	$-0.134230\pi$
$252$	1120.77			0.280165
$253$	−1449.96	−	1057.95i	−0.360309	−	0.262896i
$254$	−3468.12			−0.856730
$255$	−63.1100	+	438.939i	−0.0154984	+	0.107794i
$256$	106.346	+	232.866i	0.0259634	+	0.0568520i
$257$	3534.54	+	1037.83i	0.857893	+	0.251900i	0.680958	−	0.732322i	$-0.261564\pi$
$257$	3534.54	+	1037.83i	0.857893	+	0.251900i	0.176935	+	0.984223i	$0.443382\pi$
$258$	−1086.55	−	1253.95i	−0.262193	−	0.302587i
$259$	−4061.25	+	1192.49i	−0.974338	+	0.286091i
$260$	−57.0177	−	36.6430i	−0.0136003	−	0.00874040i
$261$	−53.2519	+	116.605i	−0.0126292	+	0.0276540i
$262$	214.967	−	248.085i	0.0506897	−	0.0584990i
$263$	3798.44	−	2441.11i	0.890576	−	0.572339i	−0.0134051	−	0.999910i	$-0.504267\pi$
$263$	3798.44	−	2441.11i	0.890576	−	0.572339i	0.903982	+	0.427571i	$0.140631\pi$
$264$	78.8980	+	548.748i	0.0183933	+	0.127928i
$265$	211.056	+	1467.92i	0.0489247	+	0.340279i
$266$	−2919.60	+	1876.31i	−0.672978	+	0.432497i
$267$	−499.309	+	576.234i	−0.114447	+	0.132078i
$268$	179.338	−	392.695i	0.0408761	−	0.0895063i
$269$	2544.06	+	1634.97i	0.576632	+	0.370579i	0.796214	−	0.605015i	$-0.206833\pi$
$269$	2544.06	+	1634.97i	0.576632	+	0.370579i	−0.219582	+	0.975594i	$0.570469\pi$
$270$	1465.45	−	430.295i	0.330313	−	0.0969886i
$271$	−3738.91	−	4314.93i	−0.838091	−	0.967209i	0.161716	−	0.986837i	$-0.448297\pi$
$271$	−3738.91	−	4314.93i	−0.838091	−	0.967209i	−0.999807	+	0.0196285i	$0.993752\pi$
$272$	319.713	+	93.8762i	0.0712701	+	0.0209268i
$273$	−189.528	−	415.008i	−0.0420174	−	0.0920053i
$274$	679.817	−	4728.23i	0.149888	−	1.04249i
$275$	−406.805			−0.0892047
$276$	−1517.92	−	1107.54i	−0.331043	−	0.241543i
$277$	−4840.37			−1.04993			−0.524963	−	0.851125i	$-0.675921\pi$
$277$	−4840.37			−1.04993			−0.524963	+	0.851125i	$0.675921\pi$
$278$	−211.176	+	1468.76i	−0.0455593	+	0.316872i
$279$	28.3511	+	62.0804i	0.00608365	+	0.0133213i
$280$	−1213.28	−	356.251i	−0.258955	−	0.0760360i
$281$	1978.17	+	2282.93i	0.419957	+	0.484656i	0.925824	−	0.377956i	$-0.123373\pi$
$281$	1978.17	+	2282.93i	0.419957	+	0.484656i	−0.505867	+	0.862611i	$0.668827\pi$
$282$	3063.04	−	899.390i	0.646814	−	0.189922i
$283$	−6142.86	−	3947.77i	−1.29030	−	0.829226i	−0.298179	−	0.954510i	$-0.596379\pi$
$283$	−6142.86	−	3947.77i	−1.29030	−	0.829226i	−0.992121	+	0.125284i	$0.960016\pi$
$284$	−786.425	+	1722.03i	−0.164316	+	0.359802i
$285$	−765.430	+	883.353i	−0.159088	+	0.183598i
$286$	−92.7804	+	59.6264i	−0.0191826	+	0.0123279i
$287$	−1216.39	−	8460.20i	−0.250179	−	1.74003i
$288$	−40.3642	−	280.739i	−0.00825862	−	0.0574400i
$289$	−3768.22	+	2421.69i	−0.766990	+	0.492914i
$290$	94.7122	−	109.304i	0.0191782	−	0.0221329i
$291$	−1819.90	+	3985.02i	−0.366613	+	0.802770i
$292$	3987.76	+	2562.78i	0.799198	+	0.513614i
$293$	−4780.09	+	1403.56i	−0.953092	+	0.279853i	−0.721074	−	0.692859i	$-0.756351\pi$
$293$	−4780.09	+	1403.56i	−0.953092	+	0.279853i	−0.232018	+	0.972711i	$0.574533\pi$
$294$	−3660.96	−	4224.97i	−0.726229	−	0.838113i
$295$	1206.44	+	354.244i	0.238108	+	0.0699148i
$296$	444.970	+	974.348i	0.0873761	+	0.191327i
$297$	353.693	−	2459.99i	0.0691022	−	0.480616i
$298$	−4147.33			−0.806202
$299$	74.9760	−	366.208i	0.0145016	−	0.0708306i
$300$	−425.872			−0.0819591
$301$	876.399	−	6095.49i	0.167823	−	1.16724i
$302$	2787.81	+	6104.46i	0.531194	+	1.16315i
$303$	1762.46	+	517.506i	0.334161	+	0.0981185i
$304$	575.144	+	663.751i	0.108509	+	0.125226i
$305$	−3533.15	+	1037.43i	−0.663303	+	0.194763i
$306$	−310.564	−	199.588i	−0.0580189	−	0.0372865i
$307$	833.186	−	1824.42i	0.154894	−	0.339170i	−0.816237	−	0.577717i	$-0.803944\pi$
$307$	833.186	−	1824.42i	0.154894	−	0.339170i	0.971131	+	0.238547i	$0.0766710\pi$
$308$	−1347.46	+	1555.05i	−0.249281	+	0.287685i
$309$	−1821.97	+	1170.91i	−0.335431	+	0.215568i
$310$	−10.9583	−	76.2165i	−0.00200771	−	0.0139639i
$311$	−1066.15	−	7415.24i	−0.194392	−	1.35203i	−0.820213	−	0.572059i	$-0.806145\pi$
$311$	−1066.15	−	7415.24i	−0.194392	−	1.35203i	0.625821	−	0.779967i	$-0.284764\pi$
$312$	−97.1289	+	62.4210i	−0.0176245	+	0.0113266i
$313$	6755.42	−	7796.17i	1.21993	−	1.40788i	0.334960	−	0.942232i	$-0.391277\pi$
$313$	6755.42	−	7796.17i	1.21993	−	1.40788i	0.884972	−	0.465644i	$-0.154177\pi$
$314$	1051.86	−	2303.24i	0.189044	−	0.413948i
$315$	1178.56	+	757.415i	0.210808	+	0.135478i
$316$	5175.95	−	1519.79i	0.921423	−	0.270554i
$317$	−6040.47	−	6971.08i	−1.07024	−	1.23513i	−0.970751	−	0.240087i	$-0.922824\pi$
$317$	−6040.47	−	6971.08i	−1.07024	−	1.23513i	−0.0994905	−	0.995039i	$-0.531721\pi$
$318$	2423.97	+	711.742i	0.427451	+	0.125511i
$319$	−97.7655	−	214.077i	−0.0171593	−	0.0375736i
$320$	−45.5407	+	316.743i	−0.00795564	+	0.0553327i
$321$	−3862.06			−0.671524
$322$	−582.721	−	6949.60i	−0.100850	−	1.20275i
$323$	1143.16			0.196926
$324$	234.041	−	1627.79i	0.0401305	−	0.279114i
$325$	−35.1945	−	77.0652i	−0.00600689	−	0.0131533i
$326$	6162.76	+	1809.55i	1.04701	+	0.307429i
$327$	4375.47	+	5049.56i	0.739952	+	0.853950i
$328$	−2075.37	+	609.384i	−0.349370	+	0.102584i
$329$	9967.55	+	6405.76i	1.67030	+	1.07344i
$330$	−287.878	+	630.364i	−0.0480216	+	0.105153i
$331$	−1705.31	+	1968.03i	−0.283179	+	0.326806i	−0.879463	−	0.475968i	$-0.842098\pi$
$331$	−1705.31	+	1968.03i	−0.283179	+	0.326806i	0.596284	+	0.802774i	$0.296643\pi$
$332$	1842.78	−	1184.28i	0.304625	−	0.195771i
$333$	−168.890	−	1174.66i	−0.0277932	−	0.193306i
$334$	−492.333	−	3424.25i	−0.0806565	−	0.560978i
$335$	453.970	−	291.749i	0.0740388	−	0.0475819i
$336$	−1410.61	+	1627.93i	−0.229033	+	0.264318i
$337$	−395.705	+	866.474i	−0.0639627	+	0.140059i	−0.938914	−	0.344153i	$-0.888166\pi$
$337$	−395.705	+	866.474i	−0.0639627	+	0.140059i	0.874951	+	0.484212i	$0.160893\pi$
$338$	3677.15	+	2363.16i	0.591747	+	0.380292i
$339$	2478.67	−	727.804i	0.397118	−	0.116604i
$340$	272.758	+	314.780i	0.0435070	+	0.0502098i
$341$	−120.221	−	35.3001i	−0.0190919	−	0.00560589i
$342$	−404.218	−	885.114i	−0.0639111	−	0.139946i
$343$	1409.75	−	9805.03i	0.221922	−	1.54350i
$344$	−1558.41			−0.244256
$345$	−847.717	−	2190.46i	−0.132288	−	0.341827i
$346$	3974.50			0.617544
$347$	537.350	−	3737.35i	0.0831310	−	0.578189i	−0.905098	−	0.425204i	$-0.860202\pi$
$347$	537.350	−	3737.35i	0.0831310	−	0.578189i	0.988229	−	0.152985i	$-0.0488885\pi$
$348$	−102.348	−	224.110i	−0.0157656	−	0.0345217i
$349$	5044.99	+	1481.34i	0.773788	+	0.227205i	0.644707	−	0.764430i	$-0.276979\pi$
$349$	5044.99	+	1481.34i	0.773788	+	0.227205i	0.129080	+	0.991634i	$0.458797\pi$
$350$	−1035.09	−	1194.56i	−0.158080	−	0.182434i
$351$	496.620	−	145.821i	0.0755202	−	0.0221747i
$352$	438.050	+	281.518i	0.0663299	+	0.0426277i
$353$	436.060	−	954.837i	0.0657482	−	0.143968i	−0.873905	−	0.486096i	$-0.838420\pi$
$353$	436.060	−	954.837i	0.0657482	−	0.143968i	0.939653	+	0.342128i	$0.111148\pi$
$354$	1402.66	−	1618.76i	0.210595	−	0.243040i
$355$	−1990.73	+	1279.36i	−0.297625	+	0.191272i
$356$	101.918	+	708.857i	0.0151732	+	0.105532i
$357$	399.013	+	2775.20i	0.0591541	+	0.411426i
$358$	−1728.60	+	1110.90i	−0.255194	+	0.164003i
$359$	7015.53	−	8096.36i	1.03138	−	1.19028i	0.0498928	−	0.998755i	$-0.484112\pi$
$359$	7015.53	−	8096.36i	1.03138	−	1.19028i	0.981488	−	0.191523i	$-0.0613425\pi$
$360$	147.278	−	322.494i	0.0215618	−	0.0472137i
$361$	−3235.37	−	2079.25i	−0.471697	−	0.303141i
$362$	1401.93	−	411.644i	0.203546	−	0.0597666i
$363$	−2973.53	−	3431.64i	−0.429945	−	0.496183i
$364$	−411.163	−	120.728i	−0.0592055	−	0.0173843i
$365$	2461.47	+	5389.86i	0.352984	+	0.772927i
$366$	−892.708	+	6208.92i	−0.127493	+	0.886736i
$367$	−6641.97			−0.944708			−0.472354	−	0.881409i	$-0.656596\pi$
$367$	−6641.97			−0.944708			−0.472354	+	0.881409i	$0.656596\pi$
$368$	−1719.81	+	396.253i	−0.243617	+	0.0561308i
$369$	2396.41			0.338081
$370$	−190.550	+	1325.30i	−0.0267735	+	0.186214i
$371$	3895.10	+	8529.07i	0.545076	+	1.19355i
$372$	−125.856	−	36.9546i	−0.0175412	−	0.00515055i
$373$	−6799.52	−	7847.07i	−0.943877	−	1.08929i	−0.995883	−	0.0906452i	$-0.971107\pi$
$373$	−6799.52	−	7847.07i	−0.943877	−	1.08929i	0.0520064	−	0.998647i	$-0.483438\pi$
$374$	650.305	−	190.947i	0.0899104	−	0.0264001i
$375$	−447.833	−	287.805i	−0.0616693	−	0.0396325i
$376$	1245.59	−	2727.46i	0.170841	−	0.374090i
$377$	32.0966	−	37.0414i	0.00438477	−	0.00506029i
$378$	8123.54	−	5220.69i	1.10537	−	0.710378i
$379$	−746.366	−	5191.09i	−0.101156	−	0.703558i	−0.975780	−	0.218755i	$-0.929800\pi$
$379$	−746.366	−	5191.09i	−0.101156	−	0.703558i	0.874624	−	0.484803i	$-0.161109\pi$
$380$	156.238	+	1086.66i	0.0210917	+	0.146696i
$381$	−6212.56	+	3992.57i	−0.835378	+	0.536865i
$382$	672.387	−	775.976i	0.0900584	−	0.103933i
$383$	1697.22	−	3716.39i	0.226433	−	0.495819i	−0.761981	−	0.647599i	$-0.775773\pi$
$383$	1697.22	−	3716.39i	0.226433	−	0.495819i	0.988414	+	0.151780i	$0.0485005\pi$
$384$	458.581	+	294.712i	0.0609423	+	0.0391653i
$385$	−2467.84	+	724.625i	−0.326683	+	0.0959228i
$386$	−2408.62	−	2779.70i	−0.317605	−	0.366536i
$387$	1656.65	+	486.436i	0.217602	+	0.0638938i
$388$	1709.34	+	3742.93i	0.223656	+	0.489738i
$389$	−32.0521	+	222.927i	−0.00417765	+	0.0290562i	−0.991804	−	0.127771i	$-0.959218\pi$
$389$	−32.0521	+	222.927i	−0.00417765	+	0.0290562i	0.987626	+	0.156828i	$0.0501267\pi$
$390$	−144.322			−0.0187385
$391$	−1076.12	+	2029.50i	−0.139186	+	0.262497i
$392$	−5250.82			−0.676547
$393$	99.4768	−	691.876i	0.0127683	−	0.0888054i
$394$	174.611	+	382.344i	0.0223268	+	0.0488889i
$395$	6469.93	+	1899.74i	0.824146	+	0.241991i
$396$	−377.791	−	435.994i	−0.0479412	−	0.0553271i
$397$	−5774.39	+	1695.51i	−0.729996	+	0.214346i	−0.625550	−	0.780184i	$-0.715125\pi$
$397$	−5774.39	+	1695.51i	−0.729996	+	0.214346i	−0.104446	+	0.994531i	$0.533307\pi$
$398$	−115.990	−	74.5423i	−0.0146082	−	0.00938811i
$399$	−3069.93	+	6722.20i	−0.385184	+	0.843436i
$400$	−261.944	+	302.300i	−0.0327430	+	0.0377875i
$401$	−7157.43	+	4599.80i	−0.891334	+	0.572825i	−0.904208	−	0.427092i	$-0.859538\pi$
$401$	−7157.43	+	4599.80i	−0.891334	+	0.572825i	0.0128747	+	0.999917i	$0.495902\pi$
$402$	−130.825	−	909.904i	−0.0162312	−	0.112890i
$403$	−3.71360	−	25.8287i	−0.000459027	−	0.00319260i
$404$	1451.40	−	932.756i	0.178737	−	0.114867i
$405$	1346.17	−	1553.57i	0.165165	−	0.190611i
$406$	379.864	−	831.787i	0.0464343	−	0.101677i
$407$	1832.87	+	1177.91i	0.223224	+	0.143457i
$408$	680.784	−	199.896i	0.0826074	−	0.0242557i
$409$	−2381.91	−	2748.87i	−0.287966	−	0.332330i	0.593273	−	0.805001i	$-0.297835\pi$
$409$	−2381.91	−	2748.87i	−0.287966	−	0.332330i	−0.881239	+	0.472671i	$0.843290\pi$
$410$	−2594.22	−	761.730i	−0.312486	−	0.0917541i
$411$	−4225.45	−	9252.44i	−0.507119	−	1.11044i
$412$	−289.498	+	2013.50i	−0.0346178	+	0.240772i
$413$	7949.77			0.947173
$414$	1951.90	+	115.581i	0.231717	+	0.0137211i
$415$	2738.14			0.323880
$416$	−15.4331	+	107.339i	−0.00181892	+	0.0126508i
$417$	1312.58	+	2874.14i	0.154142	+	0.337524i
$418$	1714.06	+	503.293i	0.200568	+	0.0588921i
$419$	−1510.35	−	1743.03i	−0.176098	−	0.203228i	0.660838	−	0.750529i	$-0.270201\pi$
$419$	−1510.35	−	1743.03i	−0.176098	−	0.203228i	−0.836936	+	0.547300i	$0.815656\pi$
$420$	−2583.51	+	758.587i	−0.300148	+	0.0881315i
$421$	−1115.70	−	717.014i	−0.129158	−	0.0830051i	0.474466	−	0.880274i	$-0.342641\pi$
$421$	−1115.70	−	717.014i	−0.129158	−	0.0830051i	−0.603625	+	0.797269i	$0.706277\pi$
$422$	−3650.82	+	7994.18i	−0.421135	+	0.922158i
$423$	−2175.44	+	2510.59i	−0.250056	+	0.288580i
$424$	1996.15	−	1282.85i	0.228636	−	0.146936i
$425$	74.0950	+	515.342i	0.00845679	+	0.0588183i
$426$	573.686	+	3990.07i	0.0652469	+	0.453802i
$427$	−19585.6	+	12586.9i	−2.21970	+	1.42652i
$428$	−2375.47	+	2741.44i	−0.268277	+	0.309608i
$429$	−97.5575	+	213.621i	−0.0109793	+	0.0240413i
$430$	−1638.77	−	1053.18i	−0.183788	−	0.118113i
$431$	11920.2	−	3500.10i	1.33220	−	0.391169i	0.463319	−	0.886192i	$-0.346659\pi$
$431$	11920.2	−	3500.10i	1.33220	−	0.391169i	0.868880	+	0.495023i	$0.164840\pi$
$432$	−1600.29	−	1846.83i	−0.178227	−	0.205685i
$433$	−2117.71	−	621.817i	−0.235037	−	0.0690129i	0.162093	−	0.986775i	$-0.448175\pi$
$433$	−2117.71	−	621.817i	−0.235037	−	0.0690129i	−0.397130	+	0.917763i	$0.629994\pi$
$434$	−202.239	−	442.841i	−0.0223681	−	0.0489793i
$435$	43.8284	−	304.834i	0.00483083	−	0.0335992i
$436$	6275.63			0.689330
$437$	−5278.21	+	2966.65i	−0.577782	+	0.324747i
$438$	10093.7			1.10113
$439$	−1159.04	+	8061.31i	−0.126009	+	0.876413i	0.824532	+	0.565815i	$0.191438\pi$
$439$	−1159.04	+	8061.31i	−0.126009	+	0.876413i	−0.950541	+	0.310598i	$0.899471\pi$
$440$	270.389	+	592.069i	0.0292961	+	0.0641495i
$441$	5581.81	+	1638.97i	0.602722	+	0.176975i
$442$	92.4337	+	106.674i	0.00994711	+	0.0114796i
$443$	−17659.5	+	5185.29i	−1.89397	+	0.556119i	−0.901639	+	0.432490i	$0.857635\pi$
$443$	−17659.5	+	5185.29i	−1.89397	+	0.556119i	−0.992329	+	0.123629i	$0.960547\pi$
$444$	1918.78	+	1233.12i	0.205092	+	0.131805i
$445$	−371.872	+	814.287i	−0.0396145	+	0.0867436i
$446$	4185.44	−	4830.25i	0.444364	−	0.512823i
$447$	−7429.24	+	4774.48i	−0.786110	+	0.505202i
$448$	287.932	+	2002.61i	0.0303649	+	0.211193i
$449$	621.505	+	4322.66i	0.0653243	+	0.454341i	0.996062	+	0.0886544i	$0.0282567\pi$
$449$	621.505	+	4322.66i	0.0653243	+	0.454341i	−0.930738	+	0.365686i	$0.880834\pi$
$450$	372.815	−	239.593i	0.0390548	−	0.0250990i
$451$	−2881.11	+	3324.98i	−0.300812	+	0.347156i
$452$	1007.95	−	2207.11i	0.104890	−	0.229676i
$453$	12021.5	+	7725.72i	1.24684	+	0.801294i
$454$	−2547.85	+	748.115i	−0.263384	+	0.0773366i
$455$	−350.777	−	404.818i	−0.0361421	−	0.0417103i
$456$	1794.40	+	526.882i	0.184277	+	0.0541086i
$457$	6054.97	+	13258.5i	0.619780	+	1.35713i	0.915679	+	0.401911i	$0.131654\pi$
$457$	6054.97	+	13258.5i	0.619780	+	1.35713i	−0.295898	+	0.955219i	$0.595619\pi$
$458$	1379.85	−	9597.05i	0.140777	−	0.979128i
$459$	−3180.74			−0.323451
$460$	−2076.28	−	745.560i	−0.210450	−	0.0755694i
$461$	−4965.63			−0.501676			−0.250838	−	0.968029i	$-0.580706\pi$
$461$	−4965.63			−0.501676			−0.250838	+	0.968029i	$0.580706\pi$
$462$	−623.541	+	4336.82i	−0.0627917	+	0.436726i
$463$	−281.855	−	617.176i	−0.0282914	−	0.0619494i	0.894959	−	0.446149i	$-0.147205\pi$
$463$	−281.855	−	617.176i	−0.0282914	−	0.0619494i	−0.923250	+	0.384199i	$0.874478\pi$
$464$	−222.034	−	65.1949i	−0.0222148	−	0.00652284i
$465$	−107.372	−	123.914i	−0.0107081	−	0.0123578i
$466$	7750.81	−	2275.84i	0.770492	−	0.226237i
$467$	2102.31	+	1351.07i	0.208315	+	0.133876i	0.640638	−	0.767843i	$-0.278670\pi$
$467$	2102.31	+	1351.07i	0.208315	+	0.133876i	−0.432323	+	0.901719i	$0.642306\pi$
$468$	49.9104	−	109.289i	0.00492972	−	0.0107946i
$469$	2234.28	−	2578.50i	0.219978	−	0.253868i
$470$	3153.04	−	2026.33i	0.309444	−	0.198868i
$471$	−767.314	−	5336.79i	−0.0750658	−	0.522094i
$472$	−286.309	−	1991.32i	−0.0279205	−	0.194191i
$473$	−2666.65	+	1713.75i	−0.259223	+	0.166593i
$474$	7522.22	−	8681.10i	0.728918	−	0.841216i
$475$	−570.072	+	1248.28i	−0.0550667	+	0.120579i
$476$	2215.36	+	1423.73i	0.213321	+	0.137093i
$477$	−2522.40	+	740.645i	−0.242124	+	0.0710939i
$478$	2216.66	+	2558.16i	0.212108	+	0.244786i
$479$	−1831.40	−	537.747i	−0.174694	−	0.0512949i	0.193215	−	0.981156i	$-0.438108\pi$
$479$	−1831.40	−	537.747i	−0.174694	−	0.0512949i	−0.367910	+	0.929861i	$0.619927\pi$
$480$	283.062	+	619.819i	0.0269165	+	0.0589390i
$481$	−64.5745	+	449.126i	−0.00612130	+	0.0425746i
$482$	−1427.10			−0.134861
$483$	−9044.35	−	11778.2i	−0.852034	−	1.10958i
$484$	−4264.86			−0.400532
$485$	−731.991	+	5091.11i	−0.0685320	+	0.476651i
$486$	1971.44	+	4316.86i	0.184005	+	0.402915i
$487$	−6858.99	−	2013.98i	−0.638215	−	0.187397i	−0.0534123	−	0.998573i	$-0.517010\pi$
$487$	−6858.99	−	2013.98i	−0.638215	−	0.187397i	−0.584802	+	0.811176i	$0.698828\pi$
$488$	3858.24	+	4452.64i	0.357898	+	0.413036i
$489$	13122.7	−	3853.18i	1.21356	−	0.356333i
$490$	−5521.59	−	3548.51i	−0.509061	−	0.327154i
$491$	−5058.80	+	11077.2i	−0.464970	+	1.01814i	0.521356	+	0.853339i	$0.325426\pi$
$491$	−5058.80	+	11077.2i	−0.464970	+	1.01814i	−0.986326	+	0.164804i	$0.947301\pi$
$492$	−3016.14	+	3480.82i	−0.276379	+	0.318958i
$493$	−253.386	+	162.841i	−0.0231479	+	0.0148763i
$494$	52.9469	+	368.254i	0.00482225	+	0.0335395i
$495$	−102.627	−	713.789i	−0.00931870	−	0.0648130i
$496$	−103.643	+	66.6072i	−0.00938246	+	0.00602974i
$497$	−9797.68	+	11307.1i	−0.884278	+	1.02051i
$498$	1937.66	−	4242.88i	0.174354	−	0.381783i
$499$	−16244.6	−	10439.8i	−1.45733	−	0.936571i	−0.998854	−	0.0478663i	$-0.984758\pi$
$499$	−16244.6	−	10439.8i	−1.45733	−	0.936571i	−0.458480	−	0.888705i	$-0.651606\pi$
$500$	−479.746	+	140.866i	−0.0429098	+	0.0125995i
$501$	−4823.99	−	5567.19i	−0.430180	−	0.496454i
$502$	−8165.04	−	2397.47i	−0.725944	−	0.213156i
$503$	7953.78	+	17416.4i	0.705053	+	1.54385i	0.833735	+	0.552165i	$0.186198\pi$
$503$	7953.78	+	17416.4i	0.705053	+	1.54385i	−0.128682	+	0.991686i	$0.541075\pi$
$504$	319.004	−	2218.72i	0.0281935	−	0.196090i
$505$	2156.60			0.190034
$506$	−2507.07	+	2569.28i	−0.220262	+	0.225728i
$507$	9307.50			0.815307
$508$	−987.131	+	6865.65i	−0.0862143	+	0.599633i
$509$	1584.20	+	3468.91i	0.137953	+	0.302076i	0.965982	−	0.258611i	$-0.0832646\pi$
$509$	1584.20	+	3468.91i	0.137953	+	0.302076i	−0.828028	+	0.560686i	$0.810537\pi$
$510$	850.980	+	249.870i	0.0738863	+	0.0216950i
$511$	24533.0	+	28312.6i	2.12383	+	2.45103i
$512$	491.260	−	144.247i	0.0424040	−	0.0124509i
$513$	−7052.83	−	4532.58i	−0.606999	−	0.390094i
$514$	3060.58	−	6701.73i	0.262639	−	0.575098i
$515$	−1665.15	+	1921.69i	−0.142476	+	0.164427i
$516$	−2791.63	+	1794.07i	−0.238168	+	0.153061i
$517$	−867.959	−	6036.79i	−0.0738352	−	0.513535i
$518$	1204.75	+	8379.24i	0.102189	+	0.710738i
$519$	7119.64	−	4575.51i	0.602153	−	0.386980i
$520$	−88.7691	+	102.445i	−0.00748612	+	0.00863944i
$521$	8455.13	−	18514.2i	0.710991	−	1.55685i	−0.115125	−	0.993351i	$-0.536727\pi$
$521$	8455.13	−	18514.2i	0.710991	−	1.55685i	0.826115	−	0.563501i	$-0.190546\pi$
$522$	215.680	+	138.609i	0.0180844	+	0.0116221i
$523$	−13646.4	+	4006.94i	−1.14094	+	0.335012i	−0.797001	−	0.603978i	$-0.793581\pi$
$523$	−13646.4	+	4006.94i	−1.14094	+	0.335012i	−0.343944	+	0.938990i	$0.611763\pi$
$524$	−429.934	−	496.170i	−0.0358430	−	0.0413650i
$525$	−3229.39	−	948.234i	−0.268461	−	0.0788272i
$526$	−3751.37	−	8214.36i	−0.310965	−	0.680918i
$527$	−22.8213	+	158.726i	−0.00188636	+	0.0131199i
$528$	1108.78			0.0913892
$529$	−298.162	−	12163.3i	−0.0245058	−	0.999700i
$530$	2966.04			0.243088
$531$	−317.206	+	2206.22i	−0.0259239	+	0.180304i
$532$	2883.43	+	6313.82i	0.234986	+	0.514547i
$533$	−879.141	−	258.139i	−0.0714444	−	0.0209780i
$534$	998.619	+	1152.47i	0.0809260	+	0.0933935i
$535$	−4350.63	+	1277.46i	−0.351578	+	0.103233i
$536$	−726.351	−	466.798i	−0.0585328	−	0.0376168i
$537$	−1817.60	+	3979.99i	−0.146062	+	0.319831i
$538$	3960.77	−	4570.97i	0.317399	−	0.366298i
$539$	−8984.84	+	5774.21i	−0.718005	+	0.461434i
$540$	−434.720	−	3023.54i	−0.0346433	−	0.240949i
$541$	−1924.68	−	13386.4i	−0.152955	−	1.06382i	−0.911233	−	0.411892i	$-0.864868\pi$
$541$	−1924.68	−	13386.4i	−0.152955	−	1.06382i	0.758278	−	0.651931i	$-0.226041\pi$
$542$	−9606.23	+	6173.55i	−0.761297	+	0.489256i
$543$	2037.43	−	2351.32i	0.161021	−	0.185828i
$544$	276.841	−	606.198i	0.0218189	−	0.0477767i
$545$	6599.24	+	4241.07i	0.518680	+	0.333335i
$546$	−875.513	+	257.074i	−0.0686237	+	0.0201497i
$547$	11581.1	+	13365.3i	0.905254	+	1.04472i	0.998794	+	0.0491031i	$0.0156363\pi$
$547$	11581.1	+	13365.3i	0.905254	+	1.04472i	−0.0935399	+	0.995616i	$0.529818\pi$
$548$	−9166.71	−	2691.59i	−0.714567	−	0.209816i
$549$	−2711.62	−	5937.61i	−0.210800	−	0.461587i
$550$	−115.789	+	805.330i	−0.00897683	+	0.0624352i
$551$	−793.897			−0.0613814
$552$	−2624.57	+	2689.69i	−0.202372	+	0.207393i
$553$	42633.1			3.27838
$554$	−1377.71	+	9582.20i	−0.105656	+	0.734853i
$555$	1184.38	+	2593.42i	0.0905837	+	0.198351i
$556$	2847.51	+	836.105i	0.217197	+	0.0637747i
$557$	1787.33	+	2062.69i	0.135963	+	0.156910i	0.819648	−	0.572868i	$-0.194169\pi$
$557$	1787.33	+	2062.69i	0.135963	+	0.156910i	−0.683685	+	0.729778i	$0.739624\pi$
$558$	130.967	−	38.4552i	0.00993594	−	0.00291746i
$559$	−555.357	−	356.906i	−0.0420198	−	0.0270045i
$560$	−1050.59	+	2300.46i	−0.0792774	+	0.173593i
$561$	945.090	−	1090.69i	0.0711261	−	0.0820839i
$562$	5082.43	−	3266.28i	0.381476	−	0.245160i
$563$	−1616.19	−	11240.9i	−0.120985	−	0.841467i	−0.956444	−	0.291915i	$-0.905708\pi$
$563$	−1616.19	−	11240.9i	−0.120985	−	0.841467i	0.835460	−	0.549552i	$-0.185201\pi$
$564$	−908.639	−	6319.72i	−0.0678380	−	0.471823i
$565$	2551.50	−	1639.75i	0.189986	−	0.122097i
$566$	−9563.62	+	11037.0i	−0.710228	+	0.819647i
$567$	5399.12	−	11822.4i	0.399897	−	0.875653i
$568$	3185.17	+	2046.98i	0.235293	+	0.151214i
$569$	16876.7	−	4955.45i	1.24342	−	0.365102i	0.407123	−	0.913373i	$-0.366532\pi$
$569$	16876.7	−	4955.45i	1.24342	−	0.365102i	0.836301	+	0.548271i	$0.184714\pi$
$570$	1530.86	+	1766.71i	0.112492	+	0.129823i
$571$	15329.4	+	4501.11i	1.12349	+	0.329887i	0.790147	−	0.612918i	$-0.210004\pi$
$571$	15329.4	+	4501.11i	1.12349	+	0.329887i	0.333345	+	0.942805i	$0.391822\pi$
$572$	91.6308	+	200.644i	0.00669804	+	0.0146667i
$573$	311.150	−	2164.09i	0.0226849	−	0.157777i
$574$	−17094.4			−1.24304
$575$	−1679.50	−	2187.16i	−0.121808	−	0.158628i
$576$	−567.252			−0.0410339
$577$	1791.48	−	12460.0i	0.129256	−	0.898992i	−0.817245	−	0.576290i	$-0.804500\pi$
$577$	1791.48	−	12460.0i	0.129256	−	0.898992i	0.946501	−	0.322702i	$-0.104591\pi$
$578$	3721.53	+	8149.01i	0.267812	+	0.586426i
$579$	−7514.68	−	2206.51i	−0.539377	−	0.158375i
$580$	−189.424	−	218.607i	−0.0135611	−	0.0156503i
$581$	16610.7	−	4877.33i	1.18610	−	0.348272i
$582$	7370.92	+	4737.00i	0.524973	+	0.337380i
$583$	2004.96	−	4390.25i	0.142430	−	0.311879i
$584$	6208.42	−	7164.89i	0.439908	−	0.507681i
$585$	126.341	−	81.1947i	0.00892919	−	0.00573844i
$586$	1417.99	+	9862.37i	0.0999604	+	0.695240i
$587$	3032.93	+	21094.5i	0.213258	+	1.48324i	0.762179	+	0.647366i	$0.224130\pi$
$587$	3032.93	+	21094.5i	0.213258	+	1.48324i	−0.548921	+	0.835874i	$0.684961\pi$
$588$	−9405.95	+	6044.84i	−0.659685	+	0.423954i
$589$	−276.789	+	319.432i	−0.0193631	+	0.0223463i
$590$	1044.67	−	2287.50i	0.0728953	−	0.159618i
$591$	752.947	+	483.890i	0.0524063	+	0.0336795i
$592$	2055.51	−	603.553i	0.142704	−	0.0419018i
$593$	2853.65	+	3293.29i	0.197615	+	0.228060i	0.845905	−	0.533334i	$-0.179061\pi$
$593$	2853.65	+	3293.29i	0.197615	+	0.228060i	−0.648290	+	0.761393i	$0.724516\pi$
$594$	−4769.23	−	1400.37i	−0.329434	−	0.0967305i
$595$	1367.45	+	2994.29i	0.0942182	+	0.206309i
$596$	−1180.45	+	8210.23i	−0.0811296	+	0.564269i
$597$	−293.591			−0.0201271
$598$	−703.621	−	252.659i	−0.0481157	−	0.0172776i
$599$	20202.3			1.37803			0.689016	−	0.724746i	$-0.258043\pi$
$599$	20202.3			1.37803			0.689016	+	0.724746i	$0.258043\pi$
$600$	−121.216	+	843.074i	−0.00824769	+	0.0573639i
$601$	3263.91	+	7146.96i	0.221527	+	0.485076i	0.987465	−	0.157838i	$-0.0504525\pi$
$601$	3263.91	+	7146.96i	0.221527	+	0.485076i	−0.765938	+	0.642914i	$0.777725\pi$
$602$	−11817.4	−	3469.91i	−0.800071	−	0.234922i
$603$	626.433	+	722.943i	0.0423057	+	0.0488234i
$604$	12878.1	−	3781.36i	0.867556	−	0.254738i
$605$	−4484.79	−	2882.20i	−0.301376	−	0.193683i
$606$	1526.13	−	3341.75i	0.102301	−	0.224009i
$607$	19025.3	−	21956.4i	1.27218	−	1.46818i	0.456444	−	0.889752i	$-0.349123\pi$
$607$	19025.3	−	21956.4i	1.27218	−	1.46818i	0.815737	−	0.578423i	$-0.196332\pi$
$608$	1477.69	−	949.656i	0.0985664	−	0.0633448i
$609$	−277.106	−	1927.31i	−0.0184382	−	0.128241i
$610$	1048.09	+	7289.66i	0.0695674	+	0.483852i
$611$	1068.52	−	686.695i	0.0707490	−	0.0454676i
$612$	−483.508	+	557.998i	−0.0319357	+	0.0368558i
$613$	5651.35	−	12374.7i	0.372358	−	0.815351i	−0.626982	−	0.779034i	$-0.715710\pi$
$613$	5651.35	−	12374.7i	0.372358	−	0.815351i	0.999340	−	0.0363175i	$-0.0115628\pi$
$614$	−3374.55	−	2168.69i	−0.221801	−	0.142543i
$615$	−5524.02	+	1622.00i	−0.362195	+	0.106350i
$616$	2694.91	+	3110.10i	0.176268	+	0.203424i
$617$	−28925.9	−	8493.41i	−1.88738	−	0.554184i	−0.994612	−	0.103665i	$-0.966943\pi$
$617$	−28925.9	−	8493.41i	−1.88738	−	0.554184i	−0.892767	−	0.450520i	$-0.851239\pi$
$618$	1799.39	+	3940.12i	0.117123	+	0.256464i
$619$	2274.65	−	15820.6i	0.147700	−	1.02727i	−0.772273	−	0.635290i	$-0.780880\pi$
$619$	2274.65	−	15820.6i	0.147700	−	1.02727i	0.919973	−	0.391982i	$-0.128211\pi$
$620$	−154.001			−0.00997550
$621$	14686.2	−	8254.46i	0.949010	−	0.533398i
$622$	−14983.0			−0.965857
$623$	−805.474	+	5602.19i	−0.0517987	+	0.360268i
$624$	95.9255	+	210.047i	0.00615399	+	0.0134754i
$625$	−599.683	−	176.083i	−0.0383797	−	0.0112693i
$626$	−13510.8	−	15592.3i	−0.862622	−	0.995519i
$627$	3649.85	−	1071.69i	0.232474	−	0.0682604i
$628$	−4260.21	−	2737.87i	−0.270702	−	0.173970i
$629$	1158.35	−	2536.43i	0.0734282	−	0.160785i
$630$	1834.87	−	2117.55i	0.116036	−	0.133913i
$631$	−22067.2	+	14181.7i	−1.39221	+	0.894716i	−0.999687	−	0.0250283i	$-0.992032\pi$
$631$	−22067.2	+	14181.7i	−1.39221	+	0.894716i	−0.392518	+	0.919744i	$0.628396\pi$
$632$	−1535.42	−	10679.1i	−0.0966390	−	0.672139i
$633$	2663.22	+	18523.1i	0.167225	+	1.16308i
$634$	−15519.5	+	9973.80i	−0.972176	+	0.624780i
$635$	−5677.84	+	6552.58i	−0.354832	+	0.409498i
$636$	2098.93	−	4596.01i	0.130862	−	0.286547i
$637$	−1871.18	−	1202.54i	−0.116388	−	0.0747979i
$638$	−451.622	+	132.608i	−0.0280249	+	0.00822886i
$639$	−2747.01	−	3170.22i	−0.170063	−	0.196263i
$640$	614.076	+	180.309i	0.0379273	+	0.0111365i
$641$	−4109.73	−	8999.06i	−0.253237	−	0.554511i	0.739730	−	0.672904i	$-0.234953\pi$
$641$	−4109.73	−	8999.06i	−0.253237	−	0.554511i	−0.992967	+	0.118393i	$0.962226\pi$
$642$	−1099.26	+	7645.50i	−0.0675767	+	0.470006i
$643$	2849.16			0.174743			0.0873715	−	0.996176i	$-0.472153\pi$
$643$	2849.16			0.174743			0.0873715	+	0.996176i	$0.472153\pi$
$644$	−13923.6	−	824.482i	−0.851966	−	0.0504490i
$645$	−4148.02			−0.253222
$646$	325.377	−	2263.04i	0.0198170	−	0.137830i
$647$	−11649.7	−	25509.2i	−0.707876	−	1.55003i	−0.830152	−	0.557537i	$-0.811746\pi$
$647$	−11649.7	−	25509.2i	−0.707876	−	1.55003i	0.122276	−	0.992496i	$-0.460981\pi$
$648$	−3155.83	−	926.635i	−0.191316	−	0.0561754i
$649$	−2679.73	−	3092.57i	−0.162078	−	0.187048i
$650$	−162.579	+	47.7375i	−0.00981058	+	0.00288064i
$651$	−872.083	−	560.453i	−0.0525032	−	0.0337418i
$652$	5336.37	−	11685.0i	0.320534	−	0.701872i
$653$	−8090.37	+	9336.78i	−0.484840	+	0.559535i	−0.944479	−	0.328570i	$-0.893433\pi$
$653$	−8090.37	+	9336.78i	−0.484840	+	0.559535i	0.459640	+	0.888106i	$0.347979\pi$
$654$	11241.7	−	7224.62i	0.672150	−	0.431965i
$655$	−116.792	−	812.306i	−0.00696708	−	0.0484571i
$656$	615.651	+	4281.94i	0.0366420	+	0.254850i
$657$	−8836.19	+	5678.67i	−0.524707	+	0.337209i
$658$	15518.2	−	17908.9i	0.919394	−	1.06104i
$659$	10543.7	−	23087.4i	0.623252	−	1.36473i	−0.289878	−	0.957064i	$-0.593615\pi$
$659$	10543.7	−	23087.4i	0.623252	−	1.36473i	0.913130	−	0.407668i	$-0.133658\pi$
$660$	1165.96	+	749.315i	0.0687649	+	0.0441925i
$661$	−23015.0	+	6757.82i	−1.35428	+	0.397653i	−0.876744	−	0.480958i	$-0.840289\pi$
$661$	−23015.0	+	6757.82i	−1.35428	+	0.397653i	−0.477538	+	0.878611i	$0.658471\pi$
$662$	3410.61	+	3936.06i	0.200238	+	0.231087i
$663$	288.385	+	84.6774i	0.0168928	+	0.00496018i
$664$	−1819.94	−	3985.12i	−0.106367	−	0.232911i
$665$	−1234.77	+	8588.03i	−0.0720036	+	0.500796i
$666$	−2373.47			−0.138093
$667$	747.342	−	1409.45i	0.0433841	−	0.0818200i
$668$	−6918.93			−0.400751
$669$	1936.83	−	13470.9i	0.111931	−	0.778500i
$670$	−448.345	−	981.738i	−0.0258523	−	0.0566087i
$671$	11498.4	+	3376.24i	0.661538	+	0.194245i
$672$	2821.22	+	3255.86i	0.161951	+	0.186901i
$673$	−20203.8	+	5932.37i	−1.15720	+	0.339786i	−0.803346	−	0.595513i	$-0.796949\pi$
$673$	−20203.8	+	5932.37i	−1.15720	+	0.339786i	−0.353859	+	0.935299i	$0.615131\pi$
$674$	1602.68	+	1029.98i	0.0915918	+	0.0588625i
$675$	1586.18	−	3473.24i	0.0904474	−	0.198052i
$676$	5724.83	−	6606.81i	0.325719	−	0.375900i
$677$	−19006.8	+	12214.9i	−1.07901	+	0.693438i	−0.954329	−	0.298758i	$-0.903428\pi$
$677$	−19006.8	+	12214.9i	−1.07901	+	0.693438i	−0.124682	+	0.992197i	$0.539791\pi$
$678$	−735.288	−	5114.04i	−0.0416498	−	0.289681i
$679$	4628.02	+	32188.6i	0.261572	+	1.81927i
$680$	700.786	−	450.368i	0.0395205	−	0.0253983i
$681$	−3702.79	+	4273.25i	−0.208357	+	0.240457i
$682$	−104.100	+	227.948i	−0.00584487	+	0.0127985i
$683$	−27764.3	−	17843.0i	−1.55545	−	0.999625i	−0.983830	−	0.179105i	$-0.942680\pi$
$683$	−27764.3	−	17843.0i	−1.55545	−	0.999625i	−0.571617	−	0.820520i	$-0.693684\pi$
$684$	−1867.26	+	548.278i	−0.104381	+	0.0306490i
$685$	−7820.43	−	9025.26i	−0.436209	−	0.503412i
$686$	−19009.2	−	5581.60i	−1.05798	−	0.310651i
$687$	−8576.54	−	18780.0i	−0.476296	−	1.04294i
$688$	−443.570	+	3085.10i	−0.0245799	+	0.170957i
$689$	1005.15			0.0555777
$690$	−4577.61	+	1054.71i	−0.252560	+	0.0581913i
$691$	16369.5			0.901192			0.450596	−	0.892728i	$-0.351212\pi$
$691$	16369.5			0.901192			0.450596	+	0.892728i	$0.351212\pi$
$692$	1131.26	−	7868.08i	0.0621445	−	0.432225i
$693$	−1894.02	−	4147.32i	−0.103821	−	0.227336i
$694$	−7245.67	−	2127.52i	−0.396314	−	0.116368i
$695$	2429.31	+	2803.57i	0.132588	+	0.153015i
$696$	−472.789	+	138.823i	−0.0257486	+	0.00756047i
$697$	4736.85	+	3044.19i	0.257419	+	0.165433i
$698$	4368.48	−	9565.64i	0.236890	−	0.518717i
$699$	11264.3	−	12999.7i	0.609519	−	0.703423i
$700$	−2659.42	+	1709.10i	−0.143595	+	0.0922829i
$701$	−4160.49	−	28936.8i	−0.224165	−	1.55910i	−0.722039	−	0.691852i	$-0.756795\pi$
$701$	−4160.49	−	28936.8i	−0.224165	−	1.55910i	0.497875	−	0.867249i	$-0.334114\pi$
$702$	−147.320	−	1024.63i	−0.00792057	−	0.0550888i
$703$	6182.90	−	3973.51i	0.331711	−	0.213178i
$704$	681.986	−	787.054i	0.0365104	−	0.0421353i
$705$	3315.38	−	7259.67i	0.177113	−	0.387823i
$706$	−1766.12	−	1135.02i	−0.0941485	−	0.0605056i
$707$	13082.8	−	3841.45i	0.695939	−	0.204346i
$708$	−2805.33	−	3237.52i	−0.148913	−	0.171855i
$709$	−7156.44	−	2101.32i	−0.379077	−	0.111307i	0.0866423	−	0.996239i	$-0.472386\pi$
$709$	−7156.44	−	2101.32i	−0.379077	−	0.111307i	−0.465720	+	0.884932i	$0.654204\pi$
$710$	1966.06	+	4305.08i	0.103923	+	0.227559i
$711$	−1701.12	+	11831.5i	−0.0897284	+	0.624075i
$712$	1432.29			0.0753897
$713$	−306.545	−	792.097i	−0.0161013	−	0.0416048i
$714$	5607.47			0.293914
$715$	−39.2392	+	272.914i	−0.00205239	+	0.0142747i
$716$	1707.18	+	3738.20i	0.0891066	+	0.195116i
$717$	6915.77	+	2030.65i	0.360215	+	0.105769i
$718$	−14031.1	−	16192.7i	−0.729296	−	0.841653i
$719$	23725.9	−	6966.56i	1.23064	−	0.361348i	0.399147	−	0.916887i	$-0.369306\pi$
$719$	23725.9	−	6966.56i	1.23064	−	0.361348i	0.831490	+	0.555539i	$0.187488\pi$
$720$	−596.503	−	383.349i	−0.0308755	−	0.0198425i
$721$	−6678.46	+	14623.8i	−0.344964	+	0.755366i
$722$	−5037.05	+	5813.06i	−0.259639	+	0.299640i
$723$	−2556.42	+	1642.91i	−0.131500	+	0.0845096i
$724$	−415.877	−	2892.49i	−0.0213480	−	0.148478i
$725$	−51.4573	−	357.893i	−0.00263597	−	0.0183336i
$726$	−7639.78	+	4909.79i	−0.390549	+	0.250991i
$727$	−15103.7	+	17430.6i	−0.770517	+	0.889224i	−0.996387	−	0.0849338i	$-0.972932\pi$
$727$	−15103.7	+	17430.6i	−0.770517	+	0.889224i	0.225870	+	0.974157i	$0.427478\pi$
$728$	−356.028	+	779.593i	−0.0181254	+	0.0396890i
$729$	17839.6	+	11464.8i	0.906343	+	0.582471i
$730$	11370.6	−	3338.71i	0.576500	−	0.169276i
$731$	2656.68	+	3065.98i	0.134420	+	0.155129i
$732$	12037.4	+	3534.48i	0.607805	+	0.178468i
$733$	−1097.47	−	2403.13i	−0.0553017	−	0.121094i	0.879964	−	0.475041i	$-0.157567\pi$
$733$	−1097.47	−	2403.13i	−0.0553017	−	0.121094i	−0.935266	+	0.353947i	$0.884839\pi$
$734$	−1890.50	+	13148.7i	−0.0950677	+	0.661210i
$735$	−13976.1			−0.701382
$736$	294.932	+	3517.39i	0.0147708	+	0.176159i
$737$	−1756.21			−0.0877759
$738$	682.088	−	4744.03i	0.0340217	−	0.236626i
$739$	5073.41	+	11109.2i	0.252542	+	0.552989i	0.992863	−	0.119265i	$-0.0380537\pi$
$739$	5073.41	+	11109.2i	0.252542	+	0.552989i	−0.740321	+	0.672254i	$0.765326\pi$
$740$	2569.39	+	754.441i	0.127639	+	0.0374781i
$741$	518.786	+	598.711i	0.0257194	+	0.0296818i
$742$	17993.2	−	5283.27i	0.890229	−	0.261395i
$743$	−7984.31	−	5131.20i	−0.394234	−	0.253359i	0.328473	−	0.944513i	$-0.393466\pi$
$743$	−7984.31	−	5131.20i	−0.394234	−	0.253359i	−0.722707	+	0.691155i	$0.757102\pi$
$744$	−108.979	+	238.631i	−0.00537012	+	0.0117589i
$745$	−6789.81	+	7835.86i	−0.333905	+	0.385347i
$746$	−17469.7	+	11227.1i	−0.857390	+	0.551011i
$747$	690.768	+	4804.40i	0.0338338	+	0.235320i
$748$	−192.910	−	1341.72i	−0.00942982	−	0.0655858i
$749$	−24117.2	+	15499.2i	−1.17653	+	0.756111i
$750$	−697.217	+	804.631i	−0.0339450	+	0.0391746i
$751$	9287.05	−	20335.8i	0.451251	−	0.988101i	−0.538144	−	0.842853i	$-0.680875\pi$
$751$	9287.05	−	20335.8i	0.451251	−	0.988101i	0.989395	−	0.145249i	$-0.0463982\pi$
$752$	−5044.86	−	3242.13i	−0.244637	−	0.157219i
$753$	−17386.3	+	5105.08i	−0.841424	+	0.247064i
$754$	−64.1931	−	74.0828i	−0.00310050	−	0.00357817i
$755$	16097.7	+	4726.70i	0.775966	+	0.227844i
$756$	−8022.89	−	17567.7i	−0.385965	−	0.845146i
$757$	−3135.10	+	21805.1i	−0.150525	+	1.04692i	0.764818	+	0.644247i	$0.222829\pi$
$757$	−3135.10	+	21805.1i	−0.150525	+	1.04692i	−0.915343	+	0.402676i	$0.868080\pi$
$758$	−10488.9			−0.502606
$759$	−1533.19	+	7488.61i	−0.0733218	+	0.358128i
$760$	2195.67			0.104797
$761$	3870.27	−	26918.3i	0.184359	−	1.28224i	−0.661949	−	0.749549i	$-0.730270\pi$
$761$	3870.27	−	26918.3i	0.184359	−	1.28224i	0.846307	−	0.532695i	$-0.178821\pi$
$762$	6135.58	+	13435.0i	0.291691	+	0.638714i
$763$	47588.1	+	13973.1i	2.25793	+	0.662989i
$764$	−1344.77	−	1551.95i	−0.0636809	−	0.0734917i
$765$	−885.537	+	260.017i	−0.0418518	+	0.0122888i
$766$	−6874.05	−	4417.68i	−0.324242	−	0.208378i
$767$	354.022	−	775.200i	0.0166662	−	0.0364939i
$768$	713.950	−	823.942i	0.0335449	−	0.0387128i
$769$	−17750.8	+	11407.8i	−0.832395	+	0.534948i	−0.886038	−	0.463612i	$-0.846553\pi$
$769$	−17750.8	+	11407.8i	−0.832395	+	0.534948i	0.0536429	+	0.998560i	$0.482917\pi$
$770$	732.076	+	5091.70i	0.0342626	+	0.238302i
$771$	−2232.65	−	15528.4i	−0.104289	−	0.725346i
$772$	−6188.37	+	3977.03i	−0.288503	+	0.185410i
$773$	22683.0	−	26177.6i	1.05544	−	1.21804i	0.0802213	−	0.996777i	$-0.474437\pi$
$773$	22683.0	−	26177.6i	1.05544	−	1.21804i	0.975215	−	0.221261i	$-0.0710172\pi$
$774$	1434.50	−	3141.12i	0.0666176	−	0.145872i
$775$	−161.942	−	104.074i	−0.00750597	−	0.00482379i
$776$	7896.19	−	2318.53i	0.365279	−	0.107256i
$777$	11804.4	+	13623.1i	0.545022	+	0.628989i
$778$	432.193	+	126.903i	0.0199163	+	0.00584796i
$779$	6165.29	+	13500.1i	0.283562	+	0.620914i
$780$	−41.0782	+	285.705i	−0.00188569	+	0.0131153i
$781$	7701.26			0.352846
$782$	3711.40	+	2707.99i	0.169718	+	0.123833i
$783$	2208.95			0.100819
$784$	−1494.54	+	10394.7i	−0.0680821	+	0.473521i
$785$	−2629.64	−	5758.11i	−0.119562	−	0.261803i
$786$	−1341.35	−	393.857i	−0.0608709	−	0.0178733i
$787$	25021.9	+	28876.8i	1.13334	+	1.30794i	0.945457	+	0.325746i	$0.105615\pi$
$787$	25021.9	+	28876.8i	1.13334	+	1.30794i	0.187878	+	0.982192i	$0.439839\pi$
$788$	806.604	−	236.840i	0.0364646	−	0.0107070i
$789$	−16176.5	−	10396.0i	−0.729908	−	0.469084i
$790$	5602.35	−	12267.4i	0.252307	−	0.552476i
$791$	12557.6	−	14492.2i	0.564471	−	0.651435i
$792$	−970.643	+	623.795i	−0.0435484	+	0.0279868i
$793$	355.184	+	2470.36i	0.0159054	+	0.110624i
$794$	1712.95	+	11913.8i	0.0765621	+	0.532501i
$795$	5313.16	−	3414.56i	0.237029	−	0.152329i
$796$	−180.581	+	208.402i	−0.00804087	+	0.00927966i
$797$	4083.87	−	8942.43i	0.181503	−	0.397437i	−0.796909	−	0.604099i	$-0.793533\pi$
$797$	4083.87	−	8942.43i	0.181503	−	0.397437i	0.978412	+	0.206663i	$0.0662603\pi$
$798$	12433.8	+	7990.69i	0.551567	+	0.354471i
$799$	−7489.33	+	2199.06i	−0.331606	+	0.0973683i
$800$	523.889	+	604.600i	0.0231528	+	0.0267198i
$801$	−1522.58	−	447.069i	−0.0671631	−	0.0197209i
$802$	7068.74	+	15478.4i	0.311229	+	0.681497i
$803$	2744.35	−	19087.3i	0.120605	−	0.838827i
$804$	−1838.52			−0.0806464
$805$	−14084.4	−	10276.6i	−0.616658	−	0.449940i
$806$	−52.1885			−0.00228072
$807$	1832.86	−	12747.8i	0.0799501	−	0.556065i
$808$	−1433.41	−	3138.74i	−0.0624100	−	0.136659i
$809$	24142.6	+	7088.92i	1.04921	+	0.308076i	0.760498	−	0.649341i	$-0.224955\pi$
$809$	24142.6	+	7088.92i	1.04921	+	0.308076i	0.288711	+	0.957416i	$0.406773\pi$
$810$	−2692.34	−	3107.13i	−0.116789	−	0.134782i
$811$	12737.5	−	3740.07i	0.551510	−	0.161938i	0.00590846	−	0.999983i	$-0.498119\pi$
$811$	12737.5	−	3740.07i	0.551510	−	0.161938i	0.545602	+	0.838044i	$0.316301\pi$
$812$	−1538.52	−	988.747i	−0.0664919	−	0.0427318i
$813$	−10100.8	+	22117.8i	−0.435734	+	0.954125i
$814$	2853.54	−	3293.16i	0.122870	−	0.141800i
$815$	13508.3	−	8681.26i	0.580583	−	0.373118i
$816$	−201.952	−	1404.61i	−0.00866388	−	0.0602586i
$817$	1521.77	+	10584.2i	0.0651654	+	0.453235i
$818$	−6119.75	+	3932.92i	−0.261579	+	0.168107i
$819$	621.809	−	717.606i	0.0265296	−	0.0306168i
$820$	−2246.34	+	4918.81i	−0.0956656	+	0.209478i
$821$	−35684.7	−	22933.2i	−1.51694	−	0.974876i	−0.992341	−	0.123525i	$-0.960580\pi$
$821$	−35684.7	−	22933.2i	−1.51694	−	0.974876i	−0.524596	−	0.851352i	$-0.675783\pi$
$822$	−19519.2	+	5731.36i	−0.828237	+	0.243192i
$823$	9611.33	+	11092.1i	0.407084	+	0.469800i	0.921859	−	0.387525i	$-0.126670\pi$
$823$	9611.33	+	11092.1i	0.407084	+	0.469800i	−0.514775	+	0.857325i	$0.672125\pi$
$824$	3903.61	+	1146.20i	0.165035	+	0.0484586i
$825$	719.694	+	1575.91i	0.0303716	+	0.0665044i
$826$	2262.74	−	15737.7i	0.0953158	−	0.662936i
$827$	30117.8			1.26638			0.633191	−	0.773996i	$-0.281745\pi$
$827$	30117.8			1.26638			0.633191	+	0.773996i	$0.281745\pi$
$828$	784.379	−	3831.17i	0.0329216	−	0.160800i
$829$	−2737.08			−0.114671			−0.0573357	−	0.998355i	$-0.518261\pi$
$829$	−2737.08			−0.114671			−0.0573357	+	0.998355i	$0.518261\pi$
$830$	779.356	−	5420.54i	0.0325926	−	0.226687i
$831$	8563.27	+	18750.9i	0.357469	+	0.782748i
$832$	208.101	+	61.1040i	0.00867141	+	0.00254615i
$833$	8951.27	+	10330.3i	0.372321	+	0.429681i
$834$	6063.38	−	1780.37i	0.251748	−	0.0739198i
$835$	−7275.72	−	4675.82i	−0.301541	−	0.193788i
$836$	1484.21	−	3249.97i	0.0614026	−	0.134453i
$837$	770.142	−	888.791i	0.0318041	−	0.0367038i
$838$	−3880.47	+	2493.83i	−0.159963	+	0.102802i
$839$	354.973	+	2468.89i	0.0146067	+	0.101592i	0.995821	−	0.0913314i	$-0.0291122\pi$
$839$	354.973	+	2468.89i	0.0146067	+	0.101592i	−0.981214	+	0.192923i	$0.938203\pi$
$840$	766.388	+	5330.34i	0.0314796	+	0.218946i
$841$	−20341.4	+	13072.6i	−0.834038	+	0.536004i
$842$	−1736.99	+	2004.60i	−0.0710935	+	0.0820462i
$843$	5344.12	−	11702.0i	0.218341	−	0.478099i
$844$	14786.5	+	9502.70i	0.603047	+	0.387555i
$845$	10484.9	−	3078.65i	0.426855	−	0.125336i
$846$	4350.88	+	5021.18i	0.176816	+	0.204057i
$847$	−32340.4	−	9496.01i	−1.31196	−	0.385226i
$848$	−1971.42	−	4316.80i	−0.0798335	−	0.174811i
$849$	−4425.61	+	30780.8i	−0.178900	+	1.24428i
$850$	1041.28			0.0420185
$851$	1234.04	+	14717.3i	0.0497090	+	0.592836i
$852$	8062.21			0.324186
$853$	−1856.12	+	12909.6i	−0.0745046	+	0.518191i	0.918057	+	0.396448i	$0.129757\pi$
$853$	−1856.12	+	12909.6i	−0.0745046	+	0.518191i	−0.992562	+	0.121743i	$0.961152\pi$
$854$	19342.9	+	42355.0i	0.775059	+	1.69714i
$855$	−2334.08	−	685.347i	−0.0933611	−	0.0274133i
$856$	4750.94	+	5482.87i	0.189701	+	0.218926i
$857$	25818.8	−	7581.09i	1.02912	−	0.302176i	0.276766	−	0.960937i	$-0.410737\pi$
$857$	25818.8	−	7581.09i	1.02912	−	0.302176i	0.752352	+	0.658761i	$0.228919\pi$
$858$	395.126	+	253.932i	0.0157219	+	0.0101038i
$859$	3136.75	−	6868.53i	0.124592	−	0.272819i	−0.837050	−	0.547127i	$-0.815722\pi$
$859$	3136.75	−	6868.53i	0.124592	−	0.272819i	0.961642	+	0.274308i	$0.0884488\pi$
$860$	−2551.36	+	2944.42i	−0.101163	+	0.116749i
$861$	−30621.7	+	19679.4i	−1.21206	+	0.778945i
$862$	−3536.09	−	24594.0i	−0.139721	−	0.971782i
$863$	6660.98	+	46328.1i	0.262737	+	1.82738i	0.512049	+	0.858956i	$0.328887\pi$
$863$	6660.98	+	46328.1i	0.262737	+	1.82738i	−0.249312	+	0.968423i	$0.580204\pi$
$864$	−4111.56	+	2642.34i	−0.161896	+	0.104044i
$865$	6506.85	−	7509.31i	0.255768	−	0.295172i
$866$	−1833.74	+	4015.33i	−0.0719550	+	0.157559i
$867$	16047.8	+	10313.3i	0.628618	+	0.403988i
$868$	−934.229	+	274.314i	−0.0365320	+	0.0107268i
$869$	−14370.9	−	16584.9i	−0.560989	−	0.647415i
$870$	−590.987	−	173.529i	−0.0230303	−	0.00676229i
$871$	−151.937	−	332.697i	−0.00591068	−	0.0129426i
$872$	1786.23	−	12423.5i	0.0693685	−	0.482469i
$873$	−9117.63			−0.353476
$874$	4370.58	+	11293.4i	0.169150	+	0.437075i
$875$	−3951.57			−0.152671
$876$	2872.97	−	19981.9i	0.110809	−	0.770693i
$877$	5251.81	+	11499.9i	0.202213	+	0.442785i	0.983385	−	0.181531i	$-0.0581052\pi$
$877$	5251.81	+	11499.9i	0.202213	+	0.442785i	−0.781172	+	0.624316i	$0.785378\pi$
$878$	15628.6	+	4588.98i	0.600729	+	0.176390i
$879$	13893.8	+	16034.3i	0.533137	+	0.615273i
$880$	1249.05	−	366.753i	0.0478470	−	0.0140491i
$881$	−14339.7	−	9215.59i	−0.548374	−	0.352419i	0.236932	−	0.971526i	$-0.423858\pi$
$881$	−14339.7	−	9215.59i	−0.548374	−	0.352419i	−0.785306	+	0.619107i	$0.787495\pi$
$882$	4833.32	−	10583.5i	0.184520	−	0.404041i
$883$	29449.3	−	33986.3i	1.12237	−	1.29528i	0.171669	−	0.985155i	$-0.445084\pi$
$883$	29449.3	−	33986.3i	1.12237	−	1.29528i	0.950696	−	0.310124i	$-0.100370\pi$
$884$	237.486	−	152.623i	0.00903566	−	0.00580687i
$885$	−762.069	−	5300.31i	−0.0289454	−	0.201320i
$886$	5238.61	+	36435.4i	0.198640	+	1.38157i
$887$	25350.0	−	16291.4i	0.959604	−	0.616700i	0.0357153	−	0.999362i	$-0.488629\pi$
$887$	25350.0	−	16291.4i	0.959604	−	0.616700i	0.923888	+	0.382662i	$0.124993\pi$
$888$	2987.28	−	3447.51i	0.112890	−	0.130282i
$889$	−22772.3	+	49864.3i	−0.859119	+	1.88121i
$890$	1506.15	+	967.945i	0.0567262	+	0.0364557i
$891$	−6419.04	+	1884.80i	−0.241353	+	0.0708678i
$892$	−8370.88	−	9660.51i	−0.314213	−	0.362621i
$893$	−19740.2	−	5796.24i	−0.739732	−	0.217205i
$894$	7337.19	+	16066.2i	0.274488	+	0.601045i
$895$	−731.068	+	5084.69i	−0.0273038	+	0.189902i
$896$	4046.40			0.150872
$897$	−1551.28	+	357.425i	−0.0577434	+	0.0133044i
$898$	8734.23			0.324571
$899$	15.8489	−	110.232i	0.000587976	−	0.00408947i
$900$	−368.195	−	806.235i	−0.0136369	−	0.0298606i
$901$	−5926.76	−	1740.25i	−0.219144	−	0.0643465i
$902$	5762.22	+	6649.96i	0.212706	+	0.245476i
$903$	−25163.6	+	7388.69i	−0.927344	+	0.272293i
$904$	−4082.40	−	2623.60i	−0.150197	−	0.0965261i
$905$	1517.42	−	3322.69i	0.0557357	−	0.122044i
$906$	18715.8	−	21599.2i	0.686305	−	0.792038i
$907$	6676.17	−	4290.52i	0.244409	−	0.157072i	−0.412702	−	0.910866i	$-0.635415\pi$
$907$	6676.17	−	4290.52i	0.244409	−	0.157072i	0.657111	+	0.753794i	$0.271778\pi$
$908$	755.809	+	5256.76i	0.0276238	+	0.192128i
$909$	544.058	+	3784.01i	0.0198518	+	0.138072i
$910$	−901.237	+	579.190i	−0.0328304	+	0.0210988i
$911$	−4564.49	+	5267.71i	−0.166003	+	0.191577i	−0.832656	−	0.553791i	$-0.813181\pi$
$911$	−4564.49	+	5267.71i	−0.166003	+	0.191577i	0.666653	+	0.745368i	$0.267726\pi$
$912$	1553.78	−	3402.30i	0.0564152	−	0.123532i
$913$	−7496.52	−	4817.72i	−0.271740	−	0.174637i
$914$	27970.6	−	8212.91i	1.01224	−	0.297220i
$915$	10269.5	+	11851.6i	0.371036	+	0.428199i
$916$	−18606.0	−	5463.21i	−0.671134	−	0.197063i
$917$	−2155.43	−	4719.73i	−0.0776211	−	0.169967i
$918$	−905.333	+	6296.73i	−0.0325495	+	0.226387i
$919$	−37255.8			−1.33727			−0.668637	−	0.743589i	$-0.733122\pi$
$919$	−37255.8			−1.33727			−0.668637	+	0.743589i	$0.733122\pi$
$920$	−2066.91	+	3898.08i	−0.0740697	+	0.139691i
$921$	−8541.59			−0.305597
$922$	−1413.37	+	9830.17i	−0.0504845	+	0.351127i
$923$	666.270	+	1458.93i	0.0237601	+	0.0520273i
$924$	8407.89	+	2468.78i	0.299350	+	0.0878970i
$925$	2192.03	+	2529.74i	0.0779174	+	0.0899215i
$926$	−1302.01	+	382.305i	−0.0462060	+	0.0135673i
$927$	−3791.91	−	2436.91i	−0.134350	−	0.0863417i
$928$	−192.260	+	420.991i	−0.00680091	+	0.0148919i
$929$	2763.37	−	3189.10i	0.0975922	−	0.112627i	−0.704852	−	0.709354i	$-0.748987\pi$
$929$	2763.37	−	3189.10i	0.0975922	−	0.112627i	0.802445	+	0.596726i	$0.203532\pi$
$930$	−275.866	+	177.288i	−0.00972689	+	0.00625109i
$931$	5127.37	+	35661.6i	0.180497	+	1.25538i
$932$	−2299.25	−	15991.6i	−0.0808093	−	0.562041i
$933$	−26839.5	+	17248.7i	−0.941786	+	0.605249i
$934$	3273.01	−	3777.26i	0.114664	−	0.132329i
$935$	703.878	−	1541.28i	0.0246196	−	0.0539093i
$936$	−202.146	−	129.912i	−0.00705914	−	0.00453663i
$937$	32077.7	−	9418.85i	1.11839	−	0.328389i	0.330255	−	0.943892i	$-0.392865\pi$
$937$	32077.7	−	9418.85i	1.11839	−	0.328389i	0.788135	+	0.615503i	$0.211047\pi$
$938$	−4468.57	−	5157.00i	−0.155548	−	0.179512i
$939$	−42152.6	−	12377.1i	−1.46496	−	0.430151i
$940$	−3113.97	−	6818.64i	−0.108049	−	0.236595i
$941$	5207.42	−	36218.4i	0.180401	−	1.25471i	−0.675417	−	0.737436i	$-0.736036\pi$
$941$	5207.42	−	36218.4i	0.180401	−	1.25471i	0.855818	−	0.517277i	$-0.173054\pi$
$942$	−10783.3			−0.372972
$943$	−29771.2	−	1762.89i	−1.02808	−	0.0608777i
$944$	−4023.60			−0.138726
$945$	3435.65	−	23895.5i	0.118266	−	0.822560i
$946$	2633.61	+	5766.80i	0.0905137	+	0.198197i
$947$	1212.10	+	355.904i	0.0415922	+	0.0122126i	0.302462	−	0.953161i	$-0.402191\pi$
$947$	1212.10	+	355.904i	0.0415922	+	0.0122126i	−0.260870	+	0.965374i	$0.584009\pi$
$948$	−15044.4	−	17362.2i	−0.515423	−	0.594829i
$949$	3853.33	−	1131.44i	0.131807	−	0.0387019i
$950$	2308.90	+	1483.84i	0.0788531	+	0.0506758i
$951$	−16318.6	+	35732.8i	−0.556432	+	1.21842i
$952$	3449.03	−	3980.39i	0.117420	−	0.135510i
$953$	−19397.0	+	12465.7i	−0.659318	+	0.423718i	−0.827061	−	0.562113i	$-0.809989\pi$
$953$	−19397.0	+	12465.7i	−0.659318	+	0.423718i	0.167742	+	0.985831i	$0.446352\pi$
$954$	748.261	+	5204.27i	0.0253940	+	0.176619i
$955$	−365.309	−	2540.78i	−0.0123781	−	0.0860919i
$956$	5695.17	−	3660.06i	0.192673	−	0.123823i
$957$	−656.344	+	757.461i	−0.0221699	+	0.0255854i
$958$	−1585.82	+	3472.45i	−0.0534816	+	0.117108i
$959$	−63518.2	−	40820.6i	−2.13880	−	1.37452i
$960$	1307.59	−	383.942i	0.0439606	−	0.0129080i
$961$	19470.1	+	22469.7i	0.653557	+	0.754245i
$962$	870.729	+	255.669i	0.0291823	+	0.00856871i
$963$	−3339.02	−	7311.42i	−0.111732	−	0.244660i
$964$	−406.196	+	2825.16i	−0.0135713	+	0.0943902i
$965$	−9195.17			−0.306739
$966$	−25890.9	+	14552.2i	−0.862346	+	0.484688i
$967$	−5458.17			−0.181513			−0.0907564	−	0.995873i	$-0.528928\pi$
$967$	−5458.17			−0.181513			−0.0907564	+	0.995873i	$0.528928\pi$
$968$	−1213.91	+	8442.90i	−0.0403062	+	0.280336i
$969$	−2022.40	−	4428.44i	−0.0670473	−	0.146813i
$970$	9870.24	+	2898.16i	0.326716	+	0.0959324i
$971$	16430.4	+	18961.7i	0.543024	+	0.626683i	0.959243	−	0.282581i	$-0.0911907\pi$
$971$	16430.4	+	18961.7i	0.543024	+	0.626683i	−0.416220	+	0.909264i	$0.636645\pi$
$972$	9106.97	−	2674.05i	0.300521	−	0.0882409i
$973$	19731.0	+	12680.4i	0.650101	+	0.417794i
$974$	−5939.24	+	13005.1i	−0.195385	+	0.427834i
$975$	−236.277	+	272.678i	−0.00776093	+	0.00895659i
$976$	9912.82	−	6370.58i	0.325104	−	0.208932i
$977$	−2287.95	−	15913.0i	−0.0749211	−	0.521088i	−0.992376	−	0.123248i	$-0.960669\pi$
$977$	−2287.95	−	15913.0i	−0.0749211	−	0.521088i	0.917455	−	0.397840i	$-0.130240\pi$
$978$	−3892.81	−	27075.1i	−0.127278	−	0.885240i
$979$	2450.84	−	1575.06i	0.0800095	−	0.0514190i
$980$	−8596.39	+	9920.76i	−0.280206	+	0.323374i
$981$	−5776.64	+	12649.1i	−0.188006	+	0.411676i
$982$	20489.1	+	13167.5i	0.665817	+	0.427895i
$983$	33044.9	−	9702.86i	1.07220	−	0.314825i	0.302443	−	0.953167i	$-0.402198\pi$
$983$	33044.9	−	9702.86i	1.07220	−	0.314825i	0.769753	+	0.638342i	$0.220379\pi$
$984$	6032.29	+	6961.63i	0.195429	+	0.225537i
$985$	1008.25	+	296.050i	0.0326149	+	0.00957660i
$986$	250.246	+	547.963i	0.00808262	+	0.0176985i
$987$	7181.09	−	49945.6i	0.231587	−	1.61073i
$988$	744.081			0.0239599
$989$	−20223.1	−	7261.82i	−0.650210	−	0.233481i
$990$	−1442.26			−0.0463010
$991$	2205.37	−	15338.7i	0.0706920	−	0.491674i	−0.923461	−	0.383692i	$-0.874652\pi$
$991$	2205.37	−	15338.7i	0.0706920	−	0.491674i	0.994153	−	0.107981i	$-0.0344386\pi$
$992$	102.359	+	224.134i	0.00327610	+	0.00717366i
$993$	10640.8	+	3124.42i	0.340056	+	0.0998495i
$994$	19595.4	+	22614.3i	0.625279	+	0.721610i
$995$	−330.732	+	97.1115i	−0.0105376	+	0.00309411i
$996$	−7847.87	−	5043.52i	−0.249668	−	0.160452i
$997$	9607.60	−	21037.7i	0.305191	−	0.668276i	−0.693444	−	0.720511i	$-0.743907\pi$
$997$	9607.60	−	21037.7i	0.305191	−	0.668276i	0.998635	+	0.0522353i	$0.0166346\pi$
$998$	−25290.8	+	29187.1i	−0.802169	+	0.925753i
$999$	−17203.4	+	11056.0i	−0.544837	+	0.350145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.g.b.31.2	✓	60
23.3	even	11	inner	230.4.g.b.141.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.g.b.31.2	✓	60	1.1	even	1	trivial
230.4.g.b.141.2	yes	60	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.284630 - 1.97964i) q^{2} +(-1.76914 - 3.87387i) q^{3} +(-3.83797 - 1.12693i) q^{4} +(-3.27430 - 3.77875i) q^{5} +(-8.17242 + 2.39964i) q^{6} +(-26.5942 - 17.0910i) q^{7} +(-3.32332 + 7.27706i) q^{8} +(5.80424 - 6.69844i) q^{9} +O(q^{10})\)	\(q+(0.284630 - 1.97964i) q^{2} +(-1.76914 - 3.87387i) q^{3} +(-3.83797 - 1.12693i) q^{4} +(-3.27430 - 3.77875i) q^{5} +(-8.17242 + 2.39964i) q^{6} +(-26.5942 - 17.0910i) q^{7} +(-3.32332 + 7.27706i) q^{8} +(5.80424 - 6.69844i) q^{9} +(-8.41254 + 5.40641i) q^{10} +(2.31578 + 16.1066i) q^{11} +(2.42432 + 16.8615i) q^{12} +(-2.85088 + 1.83215i) q^{13} +(-41.4036 + 47.7823i) q^{14} +(-8.84568 + 19.3693i) q^{15} +(13.4601 + 8.65025i) q^{16} +(19.9821 - 5.86727i) q^{17} +(-11.6085 - 13.3969i) q^{18} +(52.6683 + 15.4648i) q^{19} +(8.30830 + 18.1926i) q^{20} +(-19.1597 + 133.259i) q^{21} +32.5444 q^{22} +(-77.0352 + 78.9467i) q^{23} +34.0698 q^{24} +(-3.55787 + 24.7455i) q^{25} +(2.81556 + 6.16522i) q^{26} +(-146.545 - 43.0295i) q^{27} +(82.8072 + 95.5646i) q^{28} +(-13.8771 + 4.07468i) q^{29} +(35.8266 + 23.0244i) q^{30} +(-3.19871 + 7.00419i) q^{31} +(20.9555 - 24.1840i) q^{32} +(58.2979 - 37.4658i) q^{33} +(-5.92760 - 41.2274i) q^{34} +(22.4947 + 156.454i) q^{35} +(-29.8252 + 19.1675i) q^{36} +(87.6813 - 101.190i) q^{37} +(45.6057 - 99.8627i) q^{38} +(12.1411 + 7.80262i) q^{39} +(38.3797 - 11.2693i) q^{40} +(177.057 + 204.335i) q^{41} +(258.351 + 75.8587i) q^{42} +(80.9235 + 177.198i) q^{43} +(9.26311 - 64.4264i) q^{44} -44.3166 q^{45} +(134.360 + 174.973i) q^{46} -374.802 q^{47} +(9.69726 - 67.4459i) q^{48} +(272.659 + 597.039i) q^{49} +(47.9746 + 14.0866i) q^{50} +(-58.0800 - 67.0279i) q^{51} +(13.0063 - 3.81900i) q^{52} +(-249.519 - 160.356i) q^{53} +(-126.894 + 277.859i) q^{54} +(53.2802 - 61.4886i) q^{55} +(212.753 - 136.728i) q^{56} +(-33.2688 - 231.389i) q^{57} +(4.11658 + 28.6315i) q^{58} +(-211.554 + 135.958i) q^{59} +(55.7774 - 64.3705i) q^{60} +(305.937 - 669.909i) q^{61} +(12.9554 + 8.32590i) q^{62} +(-268.842 + 78.9391i) q^{63} +(-41.9111 - 48.3680i) q^{64} +(16.2579 + 4.77375i) q^{65} +(-57.5755 - 126.073i) q^{66} +(-15.3596 + 106.828i) q^{67} -83.3026 q^{68} +(442.115 + 158.757i) q^{69} +316.125 q^{70} +(67.3543 - 468.460i) q^{71} +(29.4556 + 64.4988i) q^{72} +(-1137.06 - 333.871i) q^{73} +(-175.363 - 202.379i) q^{74} +(102.155 - 29.9955i) q^{75} +(-184.712 - 118.707i) q^{76} +(213.692 - 467.920i) q^{77} +(18.9021 - 21.8142i) q^{78} +(-1134.53 + 729.116i) q^{79} +(-11.3852 - 79.1857i) q^{80} +(58.5102 + 406.948i) q^{81} +(454.905 - 292.350i) q^{82} +(-358.620 + 413.870i) q^{83} +(223.707 - 489.851i) q^{84} +(-87.5983 - 56.2960i) q^{85} +(373.821 - 109.764i) q^{86} +(40.3353 + 46.5494i) q^{87} +(-124.905 - 36.6753i) q^{88} +(-74.3745 - 162.857i) q^{89} +(-12.6138 + 87.7310i) q^{90} +107.130 q^{91} +(384.626 - 216.182i) q^{92} +32.7923 q^{93} +(-106.680 + 741.975i) q^{94} +(-114.014 - 249.657i) q^{95} +(-130.759 - 38.3942i) q^{96} +(-673.651 - 777.434i) q^{97} +(1259.53 - 369.832i) q^{98} +(121.330 + 77.9743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{2} - 3 q^{3} - 24 q^{4} - 30 q^{5} + 6 q^{6} + 100 q^{7} + 48 q^{8} + 69 q^{9}+O(q^{10}) \) 60 * q + 12 * q^2 - 3 * q^3 - 24 * q^4 - 30 * q^5 + 6 * q^6 + 100 * q^7 + 48 * q^8 + 69 * q^9	\( 60 q + 12 q^{2} - 3 q^{3} - 24 q^{4} - 30 q^{5} + 6 q^{6} + 100 q^{7} + 48 q^{8} + 69 q^{9} + 60 q^{10} - 51 q^{11} + 120 q^{12} + 184 q^{13} + 20 q^{14} - 15 q^{15} - 96 q^{16} - 334 q^{17} - 138 q^{18} + 258 q^{19} - 120 q^{20} + 716 q^{21} + 344 q^{22} - 288 q^{23} + 288 q^{24} - 150 q^{25} + 336 q^{26} - 813 q^{27} - 40 q^{28} + 1462 q^{29} + 30 q^{30} - 481 q^{31} + 192 q^{32} + 269 q^{33} - 168 q^{34} - 380 q^{35} + 12 q^{36} - 787 q^{37} - 978 q^{38} + 2065 q^{39} + 240 q^{40} - 1843 q^{41} + 724 q^{42} + 128 q^{43} - 204 q^{44} + 2380 q^{45} + 92 q^{46} - 1838 q^{47} + 480 q^{48} - 606 q^{49} + 300 q^{50} + 2320 q^{51} - 12 q^{52} - 3284 q^{53} + 636 q^{54} - 200 q^{55} - 800 q^{56} - 2710 q^{57} - 856 q^{58} - 2708 q^{59} - 60 q^{60} + 437 q^{61} + 962 q^{62} + 6063 q^{63} - 384 q^{64} - 15 q^{65} + 1090 q^{66} + 2804 q^{67} + 600 q^{68} + 7900 q^{69} - 120 q^{70} + 2676 q^{71} + 1384 q^{72} + 876 q^{73} + 1574 q^{74} - 75 q^{75} + 20 q^{76} + 9310 q^{77} - 2612 q^{78} - 1233 q^{79} - 480 q^{80} - 6030 q^{81} - 1132 q^{82} - 9923 q^{83} - 964 q^{84} + 1300 q^{85} + 5222 q^{86} - 5719 q^{87} - 1176 q^{88} - 1827 q^{89} + 190 q^{90} - 7626 q^{91} + 564 q^{92} + 230 q^{93} - 1142 q^{94} + 2445 q^{95} + 96 q^{96} + 939 q^{97} - 5916 q^{98} - 10589 q^{99}+O(q^{100}) \) 60 * q + 12 * q^2 - 3 * q^3 - 24 * q^4 - 30 * q^5 + 6 * q^6 + 100 * q^7 + 48 * q^8 + 69 * q^9 + 60 * q^10 - 51 * q^11 + 120 * q^12 + 184 * q^13 + 20 * q^14 - 15 * q^15 - 96 * q^16 - 334 * q^17 - 138 * q^18 + 258 * q^19 - 120 * q^20 + 716 * q^21 + 344 * q^22 - 288 * q^23 + 288 * q^24 - 150 * q^25 + 336 * q^26 - 813 * q^27 - 40 * q^28 + 1462 * q^29 + 30 * q^30 - 481 * q^31 + 192 * q^32 + 269 * q^33 - 168 * q^34 - 380 * q^35 + 12 * q^36 - 787 * q^37 - 978 * q^38 + 2065 * q^39 + 240 * q^40 - 1843 * q^41 + 724 * q^42 + 128 * q^43 - 204 * q^44 + 2380 * q^45 + 92 * q^46 - 1838 * q^47 + 480 * q^48 - 606 * q^49 + 300 * q^50 + 2320 * q^51 - 12 * q^52 - 3284 * q^53 + 636 * q^54 - 200 * q^55 - 800 * q^56 - 2710 * q^57 - 856 * q^58 - 2708 * q^59 - 60 * q^60 + 437 * q^61 + 962 * q^62 + 6063 * q^63 - 384 * q^64 - 15 * q^65 + 1090 * q^66 + 2804 * q^67 + 600 * q^68 + 7900 * q^69 - 120 * q^70 + 2676 * q^71 + 1384 * q^72 + 876 * q^73 + 1574 * q^74 - 75 * q^75 + 20 * q^76 + 9310 * q^77 - 2612 * q^78 - 1233 * q^79 - 480 * q^80 - 6030 * q^81 - 1132 * q^82 - 9923 * q^83 - 964 * q^84 + 1300 * q^85 + 5222 * q^86 - 5719 * q^87 - 1176 * q^88 - 1827 * q^89 + 190 * q^90 - 7626 * q^91 + 564 * q^92 + 230 * q^93 - 1142 * q^94 + 2445 * q^95 + 96 * q^96 + 939 * q^97 - 5916 * q^98 - 10589 * q^99

Introduction

L-functions

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