LMFDB - Embedded newform 201.4.m.b.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(4,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.m (of order $33$, degree $20$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$18$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	201.10
Dual form			201.4.m.b.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.39327 - 3.23548i) q^{2} +(0.426945 + 2.96946i) q^{3} +(0.665321 + 13.9668i) q^{4} +(-1.46096 + 3.19905i) q^{5} +(8.15890 - 11.4576i) q^{6} +(3.19725 - 13.1792i) q^{7} +(18.3688 - 21.1988i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})$	\(q+(-3.39327 - 3.23548i) q^{2} +(0.426945 + 2.96946i) q^{3} +(0.665321 + 13.9668i) q^{4} +(-1.46096 + 3.19905i) q^{5} +(8.15890 - 11.4576i) q^{6} +(3.19725 - 13.1792i) q^{7} +(18.3688 - 21.1988i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(15.3079 - 6.12835i) q^{10} +(-21.2157 - 29.7933i) q^{11} +(-41.1899 + 7.93870i) q^{12} +(5.86180 - 16.9366i) q^{13} +(-53.4903 + 34.3761i) q^{14} +(-10.1232 - 2.97244i) q^{15} +(-19.5641 + 1.86815i) q^{16} +(-0.536777 + 11.2683i) q^{17} +(37.5063 + 19.3358i) q^{18} +(33.7667 + 139.188i) q^{19} +(-45.6525 - 18.2765i) q^{20} +(40.5003 + 3.86731i) q^{21} +(-24.4049 + 169.740i) q^{22} +(-29.4262 + 23.1410i) q^{23} +(70.7915 + 45.4949i) q^{24} +(73.7581 + 85.1214i) q^{25} +(-74.6886 + 38.5046i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(186.199 + 35.8869i) q^{28} +(-45.5920 + 78.9676i) q^{29} +(24.7335 + 42.8398i) q^{30} +(13.9190 + 40.2164i) q^{31} +(-103.960 - 81.7547i) q^{32} +(79.4121 - 75.7193i) q^{33} +(38.2799 - 36.4998i) q^{34} +(37.4900 + 29.4824i) q^{35} +(-41.1595 - 118.922i) q^{36} +(107.011 + 185.349i) q^{37} +(335.761 - 581.555i) q^{38} +(52.7952 + 10.1754i) q^{39} +(40.9798 + 89.7333i) q^{40} +(113.629 - 58.5796i) q^{41} +(-124.916 - 144.161i) q^{42} +(127.678 + 82.0536i) q^{43} +(402.001 - 316.137i) q^{44} +(4.50451 - 31.3296i) q^{45} +(174.723 + 16.6840i) q^{46} +(278.815 + 111.621i) q^{47} +(-13.9002 - 57.2973i) q^{48} +(141.401 + 72.8971i) q^{49} +(25.1271 - 527.483i) q^{50} +(-33.6901 + 3.21702i) q^{51} +(240.450 + 70.6024i) q^{52} +(-32.2834 + 20.7473i) q^{53} +(-41.4039 + 119.629i) q^{54} +(126.305 - 24.3433i) q^{55} +(-220.654 - 309.865i) q^{56} +(-398.898 + 159.695i) q^{57} +(410.204 - 120.447i) q^{58} +(-225.152 + 259.839i) q^{59} +(34.7803 - 143.366i) q^{60} +(-1.94132 + 2.72620i) q^{61} +(82.8882 - 181.500i) q^{62} +(5.80755 + 121.915i) q^{63} +(110.623 + 769.400i) q^{64} +(45.6170 + 43.4958i) q^{65} -514.455 q^{66} +(-411.067 + 363.024i) q^{67} -157.740 q^{68} +(-81.2797 - 77.5000i) q^{69} +(-31.8239 - 221.340i) q^{70} +(51.5791 + 1082.78i) q^{71} +(-104.872 + 229.637i) q^{72} +(264.424 - 371.331i) q^{73} +(236.574 - 975.171i) q^{74} +(-221.274 + 255.364i) q^{75} +(-1921.55 + 564.218i) q^{76} +(-460.484 + 184.350i) q^{77} +(-146.226 - 205.346i) q^{78} +(-333.699 + 64.3152i) q^{79} +(22.6060 - 65.3158i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-575.106 - 168.866i) q^{82} +(826.976 - 78.9666i) q^{83} +(-27.0683 + 568.233i) q^{84} +(-35.2638 - 18.1797i) q^{85} +(-167.763 - 691.530i) q^{86} +(-253.957 - 101.669i) q^{87} +(-1021.29 - 97.5212i) q^{88} +(-68.0564 + 473.343i) q^{89} +(-116.651 + 91.7356i) q^{90} +(-204.469 - 131.404i) q^{91} +(-342.783 - 395.593i) q^{92} +(-113.478 + 58.5022i) q^{93} +(-584.948 - 1280.86i) q^{94} +(-494.602 - 95.3267i) q^{95} +(198.383 - 343.609i) q^{96} +(654.245 + 1133.19i) q^{97} +(-243.954 - 704.859i) q^{98} +(258.750 + 203.483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9}+O(q^{10}) $ 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9} + 19 q^{10} + 192 q^{11} - 105 q^{12} + 46 q^{13} - 14 q^{14} + 54 q^{15} + 346 q^{16} + 228 q^{17} - 18 q^{18} + 88 q^{19} + 180 q^{20} + 66 q^{21} - 247 q^{22} + 676 q^{23} + 144 q^{24} - 1120 q^{25} + 333 q^{26} + 972 q^{27} - 3894 q^{28} - 2210 q^{29} + 702 q^{30} + 96 q^{31} - 1970 q^{32} - 708 q^{33} - 26 q^{34} + 1272 q^{35} + 315 q^{36} - 3616 q^{37} - 20 q^{38} - 138 q^{39} - 5357 q^{40} + 288 q^{41} - 618 q^{42} - 1680 q^{43} + 2951 q^{44} + 36 q^{45} - 1125 q^{46} - 40 q^{47} - 1038 q^{48} - 4954 q^{49} - 3590 q^{50} - 90 q^{51} + 9120 q^{52} + 3896 q^{53} + 54 q^{54} - 1076 q^{55} + 3557 q^{56} + 660 q^{57} + 3232 q^{58} + 116 q^{59} + 3618 q^{60} - 672 q^{61} + 3882 q^{62} - 1584 q^{63} - 11581 q^{64} - 15380 q^{65} - 5166 q^{66} - 288 q^{67} + 13898 q^{68} - 1632 q^{69} - 5058 q^{70} - 15102 q^{71} - 2016 q^{72} - 146 q^{73} - 3531 q^{74} + 3360 q^{75} + 10770 q^{76} + 3594 q^{77} + 1905 q^{78} + 2852 q^{79} + 27997 q^{80} - 2916 q^{81} + 8824 q^{82} + 5278 q^{83} + 6765 q^{84} - 5290 q^{85} + 5973 q^{86} + 228 q^{87} + 13872 q^{88} + 1462 q^{89} + 171 q^{90} + 74 q^{91} - 3144 q^{92} + 3144 q^{93} + 3262 q^{94} + 1600 q^{95} - 855 q^{96} + 6626 q^{97} + 15491 q^{98} + 144 q^{99}+O(q^{100}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9 + 19 * q^10 + 192 * q^11 - 105 * q^12 + 46 * q^13 - 14 * q^14 + 54 * q^15 + 346 * q^16 + 228 * q^17 - 18 * q^18 + 88 * q^19 + 180 * q^20 + 66 * q^21 - 247 * q^22 + 676 * q^23 + 144 * q^24 - 1120 * q^25 + 333 * q^26 + 972 * q^27 - 3894 * q^28 - 2210 * q^29 + 702 * q^30 + 96 * q^31 - 1970 * q^32 - 708 * q^33 - 26 * q^34 + 1272 * q^35 + 315 * q^36 - 3616 * q^37 - 20 * q^38 - 138 * q^39 - 5357 * q^40 + 288 * q^41 - 618 * q^42 - 1680 * q^43 + 2951 * q^44 + 36 * q^45 - 1125 * q^46 - 40 * q^47 - 1038 * q^48 - 4954 * q^49 - 3590 * q^50 - 90 * q^51 + 9120 * q^52 + 3896 * q^53 + 54 * q^54 - 1076 * q^55 + 3557 * q^56 + 660 * q^57 + 3232 * q^58 + 116 * q^59 + 3618 * q^60 - 672 * q^61 + 3882 * q^62 - 1584 * q^63 - 11581 * q^64 - 15380 * q^65 - 5166 * q^66 - 288 * q^67 + 13898 * q^68 - 1632 * q^69 - 5058 * q^70 - 15102 * q^71 - 2016 * q^72 - 146 * q^73 - 3531 * q^74 + 3360 * q^75 + 10770 * q^76 + 3594 * q^77 + 1905 * q^78 + 2852 * q^79 + 27997 * q^80 - 2916 * q^81 + 8824 * q^82 + 5278 * q^83 + 6765 * q^84 - 5290 * q^85 + 5973 * q^86 + 228 * q^87 + 13872 * q^88 + 1462 * q^89 + 171 * q^90 + 74 * q^91 - 3144 * q^92 + 3144 * q^93 + 3262 * q^94 + 1600 * q^95 - 855 * q^96 + 6626 * q^97 + 15491 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{8}{33}\right)$

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 $

$2$	−3.39327	−	3.23548i	−1.19970	−	1.14391i	−0.985952	−	0.167027i	$-0.946583\pi$
$2$	−3.39327	−	3.23548i	−1.19970	−	1.14391i	−0.213751	−	0.976888i	$-0.568568\pi$
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$4$	0.665321	+	13.9668i	0.0831651	+	1.74585i
$5$	−1.46096	+	3.19905i	−0.130672	+	0.286132i	−0.963647	−	0.267179i	$-0.913908\pi$
$5$	−1.46096	+	3.19905i	−0.130672	+	0.286132i	0.832975	+	0.553311i	$0.186636\pi$
$6$	8.15890	−	11.4576i	0.555143	−	0.779589i
$7$	3.19725	−	13.1792i	0.172635	−	0.711612i	−0.818016	−	0.575195i	$-0.804926\pi$
$7$	3.19725	−	13.1792i	0.172635	−	0.711612i	0.990652	−	0.136417i	$-0.0435587\pi$
$8$	18.3688	−	21.1988i	0.811796	−	0.936862i
$9$	−8.63544	+	2.53559i	−0.319831	+	0.0939109i
$10$	15.3079	−	6.12835i	0.484078	−	0.193796i
$11$	−21.2157	−	29.7933i	−0.581524	−	0.816637i	0.414085	−	0.910238i	$-0.364101\pi$
$11$	−21.2157	−	29.7933i	−0.581524	−	0.816637i	−0.995610	+	0.0936014i	$0.970162\pi$
$12$	−41.1899	+	7.93870i	−0.990874	+	0.190975i
$13$	5.86180	−	16.9366i	0.125059	−	0.361335i	−0.865040	−	0.501703i	$-0.832707\pi$
$13$	5.86180	−	16.9366i	0.125059	−	0.361335i	0.990099	+	0.140368i	$0.0448284\pi$
$14$	−53.4903	+	34.3761i	−1.02113	+	0.656243i
$15$	−10.1232	−	2.97244i	−0.174253	−	0.0511654i
$16$	−19.5641	+	1.86815i	−0.305689	+	0.0291898i
$17$	−0.536777	+	11.2683i	−0.00765810	+	0.160763i	0.991799	+	0.127809i	$0.0407945\pi$
$17$	−0.536777	+	11.2683i	−0.00765810	+	0.160763i	−0.999457	+	0.0329540i	$0.989509\pi$
$18$	37.5063	+	19.3358i	0.491128	+	0.253194i
$19$	33.7667	+	139.188i	0.407716	+	1.68063i	0.692006	+	0.721892i	$0.256727\pi$
$19$	33.7667	+	139.188i	0.407716	+	1.68063i	−0.284290	+	0.958738i	$0.591758\pi$
$20$	−45.6525	−	18.2765i	−0.510410	−	0.204337i
$21$	40.5003	+	3.86731i	0.420852	+	0.0401865i
$22$	−24.4049	+	169.740i	−0.236506	+	1.64494i
$23$	−29.4262	+	23.1410i	−0.266773	+	0.209793i	−0.742580	−	0.669757i	$-0.766398\pi$
$23$	−29.4262	+	23.1410i	−0.266773	+	0.209793i	0.475807	+	0.879549i	$0.342156\pi$
$24$	70.7915	+	45.4949i	0.602094	+	0.386942i
$25$	73.7581	+	85.1214i	0.590065	+	0.680971i
$26$	−74.6886	+	38.5046i	−0.563371	+	0.290438i
$27$	−11.2162	−	24.5601i	−0.0799467	−	0.175059i
$28$	186.199	+	35.8869i	1.25673	+	0.242214i
$29$	−45.5920	+	78.9676i	−0.291939	+	0.505652i	−0.974268	−	0.225392i	$-0.927634\pi$
$29$	−45.5920	+	78.9676i	−0.291939	+	0.505652i	0.682330	+	0.731045i	$0.260967\pi$
$30$	24.7335	+	42.8398i	0.150524	+	0.260714i
$31$	13.9190	+	40.2164i	0.0806429	+	0.233002i	0.978114	−	0.208072i	$-0.0667188\pi$
$31$	13.9190	+	40.2164i	0.0806429	+	0.233002i	−0.897471	+	0.441074i	$0.854598\pi$
$32$	−103.960	−	81.7547i	−0.574301	−	0.451635i
$33$	79.4121	−	75.7193i	0.418905	−	0.399425i
$34$	38.2799	−	36.4998i	0.193087	−	0.184108i
$35$	37.4900	+	29.4824i	0.181056	+	0.142384i
$36$	−41.1595	−	118.922i	−0.190553	−	0.550567i
$37$	107.011	+	185.349i	0.475473	+	0.823544i	0.999605	−	0.0280929i	$-0.00894343\pi$
$37$	107.011	+	185.349i	0.475473	+	0.823544i	−0.524132	+	0.851637i	$0.675610\pi$
$38$	335.761	−	581.555i	1.43336	−	2.48265i
$39$	52.7952	+	10.1754i	0.216769	+	0.0417788i
$40$	40.9798	+	89.7333i	0.161987	+	0.354702i
$41$	113.629	−	58.5796i	0.432824	−	0.223136i	−0.228025	−	0.973655i	$-0.573227\pi$
$41$	113.629	−	58.5796i	0.432824	−	0.223136i	0.660849	+	0.750519i	$0.270196\pi$
$42$	−124.916	−	144.161i	−0.458928	−	0.529631i
$43$	127.678	+	82.0536i	0.452807	+	0.291001i	0.747097	−	0.664715i	$-0.231447\pi$
$43$	127.678	+	82.0536i	0.452807	+	0.291001i	−0.294290	+	0.955716i	$0.595083\pi$
$44$	402.001	−	316.137i	1.37736	−	1.08317i
$45$	4.50451	−	31.3296i	0.0149221	−	0.103785i
$46$	174.723	+	16.6840i	0.560033	+	0.0534767i
$47$	278.815	+	111.621i	0.865304	+	0.346415i	0.761486	−	0.648181i	$-0.224470\pi$
$47$	278.815	+	111.621i	0.865304	+	0.346415i	0.103818	+	0.994596i	$0.466894\pi$
$48$	−13.9002	−	57.2973i	−0.0417983	−	0.172295i
$49$	141.401	+	72.8971i	0.412247	+	0.212528i
$50$	25.1271	−	527.483i	0.0710702	−	1.49195i
$51$	−33.6901	+	3.21702i	−0.0925012	+	0.00883279i
$52$	240.450	+	70.6024i	0.641238	+	0.188284i
$53$	−32.2834	+	20.7473i	−0.0836690	+	0.0537708i	−0.581806	−	0.813327i	$-0.697654\pi$
$53$	−32.2834	+	20.7473i	−0.0836690	+	0.0537708i	0.498137	+	0.867098i	$0.334018\pi$
$54$	−41.4039	+	119.629i	−0.104340	+	0.301471i
$55$	126.305	−	24.3433i	0.309654	−	0.0596810i
$56$	−220.654	−	309.865i	−0.526538	−	0.739419i
$57$	−398.898	+	159.695i	−0.926936	+	0.371089i
$58$	410.204	−	120.447i	0.928663	−	0.272680i
$59$	−225.152	+	259.839i	−0.496819	+	0.573359i	−0.947675	−	0.319237i	$-0.896573\pi$
$59$	−225.152	+	259.839i	−0.496819	+	0.573359i	0.450856	+	0.892597i	$0.351119\pi$
$60$	34.7803	−	143.366i	0.0748354	−	0.308476i
$61$	−1.94132	+	2.72620i	−0.00407476	+	0.00572220i	−0.816608	−	0.577192i	$-0.804148\pi$
$61$	−1.94132	+	2.72620i	−0.00407476	+	0.00572220i	0.812534	+	0.582914i	$0.198088\pi$
$62$	82.8882	−	181.500i	0.169787	−	0.371782i
$63$	5.80755	+	121.915i	0.0116140	+	0.243808i
$64$	110.623	+	769.400i	0.216060	+	1.50273i
$65$	45.6170	+	43.4958i	0.0870477	+	0.0829998i
$66$	−514.455			−0.959470
$67$	−411.067	+	363.024i	−0.749550	+	0.661948i
$67$	−411.067	+	363.024i	−0.749550	+	0.661948i
$68$	−157.740			−0.281305
$69$	−81.2797	−	77.5000i	−0.141810	−	0.135216i
$70$	−31.8239	−	221.340i	−0.0543383	−	0.377931i
$71$	51.5791	+	1082.78i	0.0862156	+	1.80989i	0.465970	+	0.884801i	$0.345706\pi$
$71$	51.5791	+	1082.78i	0.0862156	+	1.80989i	−0.379754	+	0.925088i	$0.623991\pi$
$72$	−104.872	+	229.637i	−0.171656	+	0.375874i
$73$	264.424	−	371.331i	0.423952	−	0.595357i	−0.546260	−	0.837616i	$-0.683949\pi$
$73$	264.424	−	371.331i	0.423952	−	0.595357i	0.970212	+	0.242259i	$0.0778883\pi$
$74$	236.574	−	975.171i	0.371637	−	1.53191i
$75$	−221.274	+	255.364i	−0.340674	+	0.393159i
$76$	−1921.55	+	564.218i	−2.90022	+	0.851582i
$77$	−460.484	+	184.350i	−0.681520	+	0.272839i
$78$	−146.226	−	205.346i	−0.212267	−	0.298088i
$79$	−333.699	+	64.3152i	−0.475242	+	0.0915953i	−0.421247	−	0.906946i	$-0.638407\pi$
$79$	−333.699	+	64.3152i	−0.475242	+	0.0915953i	−0.0539945	+	0.998541i	$0.517195\pi$
$80$	22.6060	−	65.3158i	0.0315929	−	0.0912817i
$81$	68.1415	−	43.7919i	0.0934726	−	0.0600712i
$82$	−575.106	−	168.866i	−0.774510	−	0.227417i
$83$	826.976	−	78.9666i	1.09364	−	0.104430i	0.467391	−	0.884051i	$-0.345194\pi$
$83$	826.976	−	78.9666i	1.09364	−	0.104430i	0.626252	+	0.779620i	$0.284588\pi$
$84$	−27.0683	+	568.233i	−0.0351594	+	0.738087i
$85$	−35.2638	−	18.1797i	−0.0449987	−	0.0231985i
$86$	−167.763	−	691.530i	−0.210353	−	0.867088i
$87$	−253.957	−	101.669i	−0.312954	−	0.125288i
$88$	−1021.29	−	97.5212i	−1.23716	−	0.118134i
$89$	−68.0564	+	473.343i	−0.0810558	+	0.563755i	0.908309	+	0.418300i	$0.137374\pi$
$89$	−68.0564	+	473.343i	−0.0810558	+	0.563755i	−0.989365	+	0.145456i	$0.953535\pi$
$90$	−116.651	+	91.7356i	−0.136624	+	0.107442i
$91$	−204.469	−	131.404i	−0.235541	−	0.151373i
$92$	−342.783	−	395.593i	−0.388453	−	0.448298i
$93$	−113.478	+	58.5022i	−0.126529	+	0.0652300i
$94$	−584.948	−	1280.86i	−0.641838	−	1.40543i
$95$	−494.602	−	95.3267i	−0.534159	−	0.102951i
$96$	198.383	−	343.609i	0.210910	−	0.365307i
$97$	654.245	+	1133.19i	0.684830	+	1.18616i	0.973490	+	0.228729i	$0.0734570\pi$
$97$	654.245	+	1133.19i	0.684830	+	1.18616i	−0.288660	+	0.957432i	$0.593210\pi$
$98$	−243.954	−	704.859i	−0.251460	−	0.726546i
$99$	258.750	+	203.483i	0.262681	+	0.206574i
$100$	−1139.80	+	1086.80i	−1.13980	+	1.08680i
$101$	185.668	−	177.034i	0.182918	−	0.174412i	−0.593088	−	0.805138i	$-0.702091\pi$
$101$	185.668	−	177.034i	0.182918	−	0.174412i	0.776006	+	0.630726i	$0.217243\pi$
$102$	124.728	+	98.0875i	0.121078	+	0.0952167i
$103$	−159.867	−	461.904i	−0.152933	−	0.441872i	0.842345	−	0.538939i	$-0.181175\pi$
$103$	−159.867	−	461.904i	−0.152933	−	0.441872i	−0.995278	+	0.0970679i	$0.969054\pi$
$104$	−251.360	−	435.368i	−0.236999	−	0.410494i
$105$	−71.5409	+	123.913i	−0.0664922	+	0.115168i
$106$	176.674	+	34.0510i	0.161887	+	0.0312012i
$107$	114.630	+	251.004i	0.103567	+	0.226780i	0.954320	−	0.298785i	$-0.0965813\pi$
$107$	114.630	+	251.004i	0.103567	+	0.226780i	−0.850754	+	0.525565i	$0.823854\pi$
$108$	335.563	−	172.995i	0.298978	−	0.154134i
$109$	−774.419	−	893.727i	−0.680513	−	0.785354i	0.305470	−	0.952202i	$-0.401186\pi$
$109$	−774.419	−	893.727i	−0.680513	−	0.785354i	−0.985983	+	0.166848i	$0.946641\pi$
$110$	−507.351	−	326.055i	−0.439764	−	0.282619i
$111$	−504.699	+	396.899i	−0.431566	+	0.339388i
$112$	−37.9306	+	263.813i	−0.0320009	+	0.222571i
$113$	−354.386	−	33.8397i	−0.295025	−	0.0281715i	−0.0535059	−	0.998568i	$-0.517040\pi$
$113$	−354.386	−	33.8397i	−0.295025	−	0.0281715i	−0.241519	+	0.970396i	$0.577646\pi$
$114$	1870.26	+	748.739i	1.53654	+	0.615139i
$115$	−31.0388	−	127.944i	−0.0251686	−	0.103746i
$116$	−1133.26	−	584.235i	−0.907072	−	0.467628i
$117$	−7.67498	+	161.118i	−0.00606455	+	0.127311i
$118$	1604.71	−	153.231i	1.25191	−	0.119543i
$119$	146.792	+	43.1020i	0.113079	+	0.0332030i
$120$	−248.964	+	159.999i	−0.189393	+	0.121716i
$121$	−2.20535	+	6.37195i	−0.00165691	+	0.00478734i
$122$	15.4080	−	2.96965i	0.0114342	−	0.00220377i
$123$	222.463	+	312.406i	0.163080	+	0.229014i
$124$	−552.433	+	221.161i	−0.400080	+	0.160168i
$125$	−801.865	+	235.449i	−0.573768	+	0.168473i
$126$	374.748	−	432.483i	0.264962	−	0.305783i
$127$	195.803	−	807.110i	0.136809	−	0.563933i	−0.861602	−	0.507584i	$-0.830539\pi$
$127$	195.803	−	807.110i	0.136809	−	0.563933i	0.998411	−	0.0563492i	$-0.0179460\pi$
$128$	1500.28	−	2106.85i	1.03599	−	1.45485i
$129$	−189.144	+	414.167i	−0.129094	+	0.282677i
$130$	−14.0614	−	295.186i	−0.00948669	−	0.199150i
$131$	−66.5307	−	462.731i	−0.0443726	−	0.308618i	−0.999906	−	0.0137344i	$-0.995628\pi$
$131$	−66.5307	−	462.731i	−0.0443726	−	0.308618i	0.955533	−	0.294884i	$-0.0952810\pi$
$132$	1110.39	+	1058.76i	0.732175	+	0.698127i
$133$	1942.36			1.26634
$134$	2569.42	+	98.1590i	1.65645	+	0.0632810i
$135$	94.9552			0.0605366
$136$	229.015	+	218.365i	0.144396	+	0.137681i
$137$	87.0602	+	605.517i	0.0542924	+	0.377612i	0.998794	+	0.0491040i	$0.0156366\pi$
$137$	87.0602	+	605.517i	0.0542924	+	0.377612i	−0.944501	+	0.328508i	$0.893454\pi$
$138$	25.0544	+	525.958i	0.0154549	+	0.324438i
$139$	−130.282	+	285.277i	−0.0794990	+	0.174078i	−0.945208	−	0.326470i	$-0.894141\pi$
$139$	−130.282	+	285.277i	−0.0794990	+	0.174078i	0.865709	+	0.500548i	$0.166868\pi$
$140$	−386.833	+	543.230i	−0.233524	+	0.327938i
$141$	−212.415	+	875.586i	−0.126869	+	0.522962i
$142$	3328.28	−	3841.04i	1.96693	−	2.26995i
$143$	−628.957	+	184.678i	−0.367804	+	0.107997i
$144$	164.208	−	65.7389i	0.0950277	−	0.0380433i
$145$	−186.013	−	261.219i	−0.106535	−	0.149607i
$146$	−2098.70	+	404.491i	−1.18965	+	0.229287i
$147$	−156.095	+	451.007i	−0.0875817	+	0.253051i
$148$	−2517.53	+	1617.92i	−1.39824	+	0.898596i
$149$	−1367.99	−	401.679i	−0.752151	−	0.220851i	−0.116885	−	0.993145i	$-0.537291\pi$
$149$	−1367.99	−	401.679i	−0.752151	−	0.220851i	−0.635265	+	0.772294i	$0.719109\pi$
$150$	1577.07	−	150.592i	0.858448	−	0.0819718i
$151$	59.3302	−	1245.49i	0.0319750	−	0.671238i	−0.924808	−	0.380435i	$-0.875774\pi$
$151$	59.3302	−	1245.49i	0.0319750	−	0.671238i	0.956783	−	0.290803i	$-0.0939226\pi$
$152$	3570.87	+	1840.91i	1.90550	+	0.982354i
$153$	−23.9366	−	98.6681i	−0.0126481	−	0.0521362i
$154$	2159.01	+	864.337i	1.12973	+	0.452274i
$155$	−148.989	−	14.2267i	−0.0772071	−	0.00737238i
$156$	−106.993	+	744.150i	−0.0549119	+	0.381921i
$157$	−1571.59	+	1235.91i	−0.798895	+	0.628258i	−0.931842	−	0.362865i	$-0.881799\pi$
$157$	−1571.59	+	1235.91i	−0.798895	+	0.628258i	0.132947	+	0.991123i	$0.457556\pi$
$158$	1340.42	+	861.438i	0.674926	+	0.433749i
$159$	−75.3914	−	87.0063i	−0.0376033	−	0.0433965i
$160$	413.418	−	213.132i	0.204272	−	0.105310i
$161$	210.898	+	461.802i	0.103237	+	0.226056i
$162$	−372.911	−	71.8727i	−0.180856	−	0.0348571i
$163$	1600.22	−	2771.67i	0.768952	−	1.33186i	−0.169180	−	0.985585i	$-0.554112\pi$
$163$	1600.22	−	2771.67i	0.768952	−	1.33186i	0.938132	−	0.346278i	$-0.112555\pi$
$164$	893.769	+	1548.05i	0.425559	+	0.737089i
$165$	126.212	+	364.666i	0.0595490	+	0.172056i
$166$	−3061.65	−	2407.71i	−1.43151	−	1.12575i
$167$	525.390	−	500.959i	0.243449	−	0.232128i	−0.558524	−	0.829488i	$-0.688632\pi$
$167$	525.390	−	500.959i	0.243449	−	0.232128i	0.801973	+	0.597360i	$0.203784\pi$
$168$	825.926	−	787.519i	0.379295	−	0.361657i
$169$	1474.47	+	1159.54i	0.671130	+	0.527782i
$170$	60.8395	+	175.784i	0.0274481	+	0.0793060i
$171$	−644.515	−	1116.33i	−0.288230	−	0.499229i
$172$	−1061.08	+	1837.84i	−0.470387	+	0.814734i
$173$	2528.71	+	487.368i	1.11130	+	0.214185i	0.711684	−	0.702500i	$-0.247933\pi$
$173$	2528.71	+	487.368i	1.11130	+	0.214185i	0.399611	+	0.916685i	$0.369145\pi$
$174$	532.797	+	1166.66i	0.232134	+	0.508302i
$175$	1357.66	−	699.921i	0.586453	−	0.302337i
$176$	470.724	+	543.245i	0.201603	+	0.232662i
$177$	−867.711	−	557.644i	−0.368481	−	0.236808i
$178$	1762.43	−	1385.99i	0.742131	−	0.583618i
$179$	638.556	−	4441.25i	0.266636	−	1.85450i	−0.213029	−	0.977046i	$-0.568333\pi$
$179$	638.556	−	4441.25i	0.266636	−	1.85450i	0.479666	−	0.877451i	$-0.340758\pi$
$180$	440.571	+	42.0694i	0.182435	+	0.0174204i
$181$	171.286	+	68.5725i	0.0703402	+	0.0281600i	0.406566	−	0.913622i	$-0.366726\pi$
$181$	171.286	+	68.5725i	0.0703402	+	0.0281600i	−0.336226	+	0.941781i	$0.609150\pi$
$182$	268.664	+	1107.45i	0.109421	+	0.451041i
$183$	−8.92419	−	4.60074i	−0.00360489	−	0.00185845i
$184$	−49.9639	+	1048.87i	−0.0200184	+	0.420238i
$185$	−749.278	+	71.5474i	−0.297773	+	0.0284339i
$186$	574.346	+	168.643i	0.226414	+	0.0664813i
$187$	347.109	−	223.073i	0.135738	−	0.0872338i
$188$	−1373.48	+	3968.41i	−0.532826	+	1.53950i
$189$	−359.544	+	69.2964i	−0.138376	+	0.0266697i
$190$	1369.89	+	1923.74i	0.523065	+	0.734542i
$191$	−3815.24	+	1527.39i	−1.44535	+	0.578629i	−0.955975	−	0.293448i	$-0.905197\pi$
$191$	−3815.24	+	1527.39i	−1.44535	+	0.578629i	−0.489370	+	0.872076i	$0.662773\pi$
$192$	−2237.47	+	656.982i	−0.841020	+	0.246946i
$193$	559.995	−	646.269i	0.208857	−	0.241033i	−0.641650	−	0.766997i	$-0.721750\pi$
$193$	559.995	−	646.269i	0.208857	−	0.241033i	0.850507	+	0.525964i	$0.176295\pi$
$194$	1446.37	−	5962.01i	0.535274	−	2.20643i
$195$	−109.683	+	154.028i	−0.0402799	+	0.0565652i
$196$	−924.063	+	2023.42i	−0.336758	+	0.737396i
$197$	192.612	+	4043.43i	0.0696603	+	1.46235i	0.715359	+	0.698757i	$0.246263\pi$
$197$	192.612	+	4043.43i	0.0696603	+	1.46235i	−0.645699	+	0.763592i	$0.723434\pi$
$198$	−219.644	−	1527.66i	−0.0788354	−	0.548312i
$199$	−2433.03	−	2319.89i	−0.866697	−	0.826394i	0.119352	−	0.992852i	$-0.461918\pi$
$199$	−2433.03	−	2319.89i	−0.866697	−	0.826394i	−0.986048	+	0.166458i	$0.946767\pi$
$200$	3159.32			1.11699
$201$	−1253.49	−	1065.66i	−0.439873	−	0.373959i
$202$	−1202.81			−0.418959
$203$	894.964	+	853.347i	0.309429	+	0.295040i
$204$	−67.3462	−	468.403i	−0.0231136	−	0.160759i
$205$	21.3926	+	449.086i	0.00728840	+	0.153002i
$206$	−952.011	+	2084.61i	−0.321989	+	0.705057i
$207$	195.432	−	274.445i	0.0656205	−	0.0921511i
$208$	−83.0409	+	342.299i	−0.0276820	+	0.114107i
$209$	3430.49	−	3958.99i	1.13537	−	1.31028i
$210$	643.675	−	189.000i	0.211513	−	0.0621059i
$211$	−4870.35	+	1949.80i	−1.58905	+	0.636158i	−0.986770	−	0.162128i	$-0.948164\pi$
$211$	−4870.35	+	1949.80i	−1.58905	+	0.636158i	−0.602277	+	0.798287i	$0.705740\pi$
$212$	−311.252	−	437.092i	−0.100834	−	0.141602i
$213$	−3193.25	+	615.448i	−1.02722	+	0.197980i
$214$	423.148	−	1222.61i	0.135167	−	0.390540i
$215$	−449.025	+	288.571i	−0.142434	+	0.0915367i
$216$	−726.672	−	213.370i	−0.228906	−	0.0672130i
$217$	574.523	−	54.8603i	0.179729	−	0.0171620i
$218$	−263.821	+	5538.28i	−0.0819642	+	1.72064i
$219$	1215.55	+	626.659i	0.375065	+	0.193359i
$220$	424.032	+	1747.88i	0.129947	+	0.535647i
$221$	187.700	+	75.1439i	0.0571317	+	0.0228721i
$222$	2996.74	+	286.154i	0.905982	+	0.0865108i
$223$	−354.911	+	2468.46i	−0.106577	+	0.741256i	0.864525	+	0.502590i	$0.167619\pi$
$223$	−354.911	+	2468.46i	−0.106577	+	0.741256i	−0.971102	+	0.238666i	$0.923290\pi$
$224$	−1409.85	+	1108.72i	−0.420533	+	0.330711i
$225$	−852.766	−	548.040i	−0.252671	−	0.162382i
$226$	1093.04	+	1261.44i	0.321717	+	0.371281i
$227$	−3255.48	+	1678.32i	−0.951867	+	0.490721i	−0.862934	−	0.505316i	$-0.831376\pi$
$227$	−3255.48	+	1678.32i	−0.951867	+	0.490721i	−0.0889324	+	0.996038i	$0.528346\pi$
$228$	−2495.82	−	5465.08i	−0.724955	−	1.58743i
$229$	−3368.11	−	649.150i	−0.971925	−	0.187323i	−0.321513	−	0.946905i	$-0.604192\pi$
$229$	−3368.11	−	649.150i	−0.971925	−	0.187323i	−0.650412	+	0.759582i	$0.725404\pi$
$230$	−308.636	+	534.574i	−0.0884820	+	0.153255i
$231$	−744.022	−	1288.68i	−0.211918	−	0.367053i
$232$	836.545	+	2417.04i	0.236732	+	0.683993i
$233$	3497.96	+	2750.83i	0.983515	+	0.773444i	0.974009	−	0.226510i	$-0.0727317\pi$
$233$	3497.96	+	2750.83i	0.983515	+	0.773444i	0.00950582	+	0.999955i	$0.496974\pi$
$234$	547.336	−	521.884i	0.152908	−	0.145798i
$235$	−764.416	+	728.869i	−0.212191	+	0.202324i
$236$	−3778.92	−	2971.78i	−1.04232	−	0.819688i
$237$	−333.453	−	963.449i	−0.0913928	−	0.264062i
$238$	−358.650	−	621.199i	−0.0976798	−	0.169186i
$239$	−1469.67	+	2545.55i	−0.397763	+	0.688946i	−0.993450	−	0.114271i	$-0.963547\pi$
$239$	−1469.67	+	2545.55i	−0.397763	+	0.688946i	0.595687	+	0.803217i	$0.296880\pi$
$240$	203.605	+	39.2416i	0.0547609	+	0.0105543i
$241$	−680.408	−	1489.89i	−0.181863	−	0.398224i	0.796641	−	0.604453i	$-0.206608\pi$
$241$	−680.408	−	1489.89i	−0.181863	−	0.398224i	−0.978504	+	0.206229i	$0.933881\pi$
$242$	28.0997	−	14.4864i	0.00746411	−	0.00384802i
$243$	159.131	+	183.647i	0.0420093	+	0.0484814i
$244$	−39.3679	−	25.3002i	−0.0103290	−	0.00663804i
$245$	−439.782	+	345.848i	−0.114680	+	0.0901854i
$246$	255.904	−	1779.85i	0.0663246	−	0.461298i
$247$	2555.30	+	244.002i	0.658259	+	0.0628561i
$248$	1108.21	+	443.662i	0.283757	+	0.113599i
$249$	587.561	+	2421.96i	0.149539	+	0.616408i
$250$	3482.74	+	1795.48i	0.881071	+	0.454224i
$251$	184.609	−	3875.42i	0.0464240	−	0.974559i	−0.848737	−	0.528815i	$-0.822636\pi$
$251$	184.609	−	3875.42i	0.0464240	−	0.974559i	0.895161	−	0.445743i	$-0.147061\pi$
$252$	−1698.90	+	162.226i	−0.424686	+	0.0405526i
$253$	1313.74	+	385.749i	0.326459	+	0.0958571i
$254$	−3275.80	+	2105.23i	−0.809221	+	0.520055i
$255$	38.9284	−	112.476i	0.00955997	−	0.0276217i
$256$	−5801.41	+	1118.13i	−1.41636	+	0.272981i
$257$	379.154	+	532.447i	0.0920271	+	0.129234i	0.858023	−	0.513612i	$-0.171693\pi$
$257$	379.154	+	532.447i	0.0920271	+	0.129234i	−0.765995	+	0.642846i	$0.777754\pi$
$258$	1981.85	−	793.412i	0.478234	−	0.191456i
$259$	2784.90	−	817.719i	0.668127	−	0.196180i
$260$	−577.147	+	666.063i	−0.137666	+	0.158875i
$261$	193.477	−	797.523i	0.0458847	−	0.189139i
$262$	−1271.40	+	1785.43i	−0.299799	+	0.421009i
$263$	879.669	−	1926.21i	0.206246	−	0.451616i	−0.778036	−	0.628220i	$-0.783784\pi$
$263$	879.669	−	1926.21i	0.206246	−	0.451616i	0.984282	+	0.176604i	$0.0565112\pi$
$264$	−146.448	−	3074.31i	−0.0341410	−	0.716708i
$265$	−19.2069	−	133.587i	−0.00445234	−	0.0309667i
$266$	−6590.94	−	6284.45i	−1.51924	−	1.44859i
$267$	−1434.63			−0.328831
$268$	−5343.78	−	5499.77i	−1.21800	−	1.25355i
$269$	4366.23			0.989643			0.494821	−	0.868995i	$-0.335233\pi$
$269$	4366.23			0.989643			0.494821	+	0.868995i	$0.335233\pi$
$270$	−322.209	−	307.226i	−0.0726260	−	0.0692488i
$271$	−30.7824	−	214.096i	−0.00689998	−	0.0479904i	0.986081	−	0.166268i	$-0.0531718\pi$
$271$	−30.7824	−	214.096i	−0.00689998	−	0.0479904i	−0.992981	+	0.118278i	$0.962263\pi$
$272$	−10.5493	−	221.458i	−0.00235165	−	0.0493671i
$273$	302.904	−	663.267i	0.0671523	−	0.147043i
$274$	1663.72	−	2336.37i	0.366821	−	0.515128i
$275$	971.214	−	4003.40i	0.212969	−	0.877869i
$276$	1028.35	−	1186.78i	0.224273	−	0.258825i
$277$	6919.21	−	2031.66i	1.50085	−	0.440689i	0.574863	−	0.818249i	$-0.305055\pi$
$277$	6919.21	−	2031.66i	1.50085	−	0.440689i	0.925985	+	0.377561i	$0.123237\pi$
$278$	1365.09	−	546.500i	0.294506	−	0.117902i
$279$	−222.169	−	311.993i	−0.0476735	−	0.0669481i
$280$	1313.64	−	253.183i	0.280375	−	0.0540378i
$281$	−69.0149	+	199.406i	−0.0146515	+	0.0423329i	−0.952090	−	0.305819i	$-0.901070\pi$
$281$	−69.0149	+	199.406i	−0.0146515	+	0.0423329i	0.937438	+	0.348152i	$0.113191\pi$
$282$	3553.72	−	2283.84i	0.750429	−	0.482272i
$283$	−3251.52	−	954.733i	−0.682978	−	0.200541i	−0.0782040	−	0.996937i	$-0.524919\pi$
$283$	−3251.52	−	954.733i	−0.682978	−	0.200541i	−0.604774	+	0.796397i	$0.706737\pi$
$284$	−15088.6	+	1440.79i	−3.15262	+	0.301039i
$285$	71.9016	−	1509.40i	0.0149442	−	0.313717i
$286$	2731.75	+	1408.31i	0.564796	+	0.291173i
$287$	−408.736	−	1684.83i	−0.0840659	−	0.346524i
$288$	1105.03	+	442.388i	0.226093	+	0.0905138i
$289$	4764.07	+	454.913i	0.969686	+	0.0925938i
$290$	−213.975	+	1488.23i	−0.0433278	+	0.301351i
$291$	−3085.63	+	2426.57i	−0.621590	+	0.488824i
$292$	5362.24	+	3446.10i	1.07466	+	0.690643i
$293$	3920.24	+	4524.19i	0.781647	+	0.902069i	0.997227	−	0.0744173i	$-0.0237097\pi$
$293$	3920.24	+	4524.19i	0.781647	+	0.902069i	−0.215580	+	0.976486i	$0.569164\pi$
$294$	1988.90	−	1025.35i	0.394541	−	0.203400i
$295$	−502.301	−	1099.89i	−0.0991360	−	0.217078i
$296$	5894.83	+	1136.14i	1.15753	+	0.223097i
$297$	−493.765	+	855.226i	−0.0964685	+	0.167088i
$298$	3342.35	+	5789.13i	0.649723	+	1.12535i
$299$	219.438	+	634.026i	0.0424430	+	0.122631i
$300$	−3713.84	−	2920.59i	−0.714728	−	0.562069i
$301$	1489.62	−	1420.35i	0.285250	−	0.271986i
$302$	−4231.10	+	4034.34i	−0.806200	+	0.768710i
$303$	604.968	+	475.752i	0.114701	+	0.0902021i
$304$	−920.639	−	2660.01i	−0.173692	−	0.501849i
$305$	−5.88507	−	10.1932i	−0.00110485	−	0.00191365i
$306$	−238.015	+	412.254i	−0.0444654	+	0.0770164i
$307$	4424.60	+	852.771i	0.822558	+	0.158535i	0.583130	−	0.812379i	$-0.301828\pi$
$307$	4424.60	+	852.771i	0.822558	+	0.158535i	0.239428	+	0.970914i	$0.423040\pi$
$308$	−2881.15	−	6308.84i	−0.533015	−	1.16714i
$309$	1303.35	−	671.926i	0.239952	−	0.123704i
$310$	459.531	+	530.327i	0.0841922	+	0.0971630i
$311$	−1799.72	−	1156.61i	−0.328145	−	0.210886i	0.366186	−	0.930542i	$-0.380663\pi$
$311$	−1799.72	−	1156.61i	−0.328145	−	0.210886i	−0.694331	+	0.719656i	$0.744300\pi$
$312$	1185.49	−	932.282i	0.215113	−	0.169167i
$313$	883.653	−	6145.94i	0.159575	−	1.10987i	−0.739843	−	0.672780i	$-0.765100\pi$
$313$	883.653	−	6145.94i	0.159575	−	1.10987i	0.899418	−	0.437090i	$-0.143991\pi$
$314$	9331.60	+	891.060i	1.67711	+	0.160145i
$315$	−398.498	−	159.534i	−0.0712788	−	0.0285357i
$316$	−1120.30	−	4617.92i	−0.199435	−	0.822083i
$317$	−1292.15	−	666.147i	−0.228940	−	0.118027i	0.339940	−	0.940447i	$-0.389593\pi$
$317$	−1292.15	−	666.147i	−0.228940	−	0.118027i	−0.568881	+	0.822420i	$0.692623\pi$
$318$	−25.6835	+	539.164i	−0.00452912	+	0.0950780i
$319$	3319.97	−	317.018i	0.582704	−	0.0556414i
$320$	−2622.96	−	770.171i	−0.458213	−	0.134543i
$321$	−696.406	+	447.553i	−0.121089	+	0.0778192i
$322$	778.517	−	2249.38i	0.134736	−	0.389294i
$323$	−1586.55	+	305.782i	−0.273306	+	0.0526754i
$324$	656.969	+	922.584i	0.112649	+	0.158193i
$325$	1874.02	−	750.244i	0.319852	−	0.128049i
$326$	−14397.7	+	4227.54i	−2.44605	+	0.718226i
$327$	2323.26	−	2681.18i	0.392894	−	0.453424i
$328$	845.409	−	3484.83i	0.142317	−	0.586638i
$329$	2362.51	−	3317.68i	0.395895	−	0.555957i
$330$	751.597	−	1645.77i	0.125376	−	0.274535i
$331$	276.367	+	5801.66i	0.0458928	+	0.963407i	0.897988	+	0.440020i	$0.145029\pi$
$331$	276.367	+	5801.66i	0.0458928	+	0.963407i	−0.852095	+	0.523387i	$0.824668\pi$
$332$	1653.12	+	11497.7i	0.273273	+	1.90065i
$333$	−1394.06	−	1329.23i	−0.229411	−	0.218743i
$334$	−3403.64			−0.557601
$335$	−560.781	−	1845.39i	−0.0914589	−	0.300968i
$336$	−799.578			−0.129823
$337$	6239.12	+	5948.99i	1.00851	+	0.961609i	0.999264	−	0.0383481i	$-0.0122096\pi$
$337$	6239.12	+	5948.99i	1.00851	+	0.961609i	0.00924225	+	0.999957i	$0.497058\pi$
$338$	−1251.63	−	8705.26i	−0.201419	−	1.40090i
$339$	−50.8172	−	1066.78i	−0.00814162	−	0.170914i
$340$	230.451	−	504.617i	0.0367587	−	0.0804904i
$341$	902.875	−	1267.91i	0.143382	−	0.201352i
$342$	−1424.86	+	5873.34i	−0.225285	+	0.928637i
$343$	4458.97	−	5145.93i	0.701929	−	0.810070i
$344$	4084.73	−	1199.39i	0.640215	−	0.187984i
$345$	366.672	−	146.794i	0.0572202	−	0.0229075i
$346$	−7003.73	−	9835.36i	−1.08822	−	1.52818i
$347$	−7895.63	+	1521.76i	−1.22150	+	0.235424i	−0.758937	−	0.651163i	$-0.774281\pi$
$347$	−7895.63	+	1521.76i	−1.22150	+	0.235424i	−0.462560	+	0.886588i	$0.653069\pi$
$348$	1251.03	−	3614.61i	0.192707	−	0.556791i
$349$	−7382.55	+	4744.48i	−1.13232	+	0.727696i	−0.966042	−	0.258383i	$-0.916810\pi$
$349$	−7382.55	+	4744.48i	−1.13232	+	0.727696i	−0.166275	+	0.986079i	$0.553174\pi$
$350$	−6871.48	−	2017.65i	−1.04942	−	0.308137i
$351$	−481.710	+	45.9977i	−0.0732529	+	0.00699481i
$352$	−230.166	+	4831.77i	−0.0348519	+	0.731632i
$353$	3247.62	+	1674.27i	0.489670	+	0.252442i	0.685334	−	0.728229i	$-0.259656\pi$
$353$	3247.62	+	1674.27i	0.489670	+	0.252442i	−0.195665	+	0.980671i	$0.562686\pi$
$354$	1140.14	+	4699.70i	0.171179	+	0.705611i
$355$	−3539.21	−	1416.89i	−0.529132	−	0.211833i
$356$	−6656.36	−	635.606i	−0.990974	−	0.0946265i
$357$	−65.3178	+	454.296i	−0.00968344	+	0.0673498i
$358$	−16536.4	+	13004.4i	−2.44127	+	1.91984i
$359$	10598.7	+	6811.34i	1.55815	+	1.00136i	0.983063	+	0.183270i	$0.0586682\pi$
$359$	10598.7	+	6811.34i	1.55815	+	1.00136i	0.575087	+	0.818092i	$0.304968\pi$
$360$	−581.406	−	670.978i	−0.0851188	−	0.0982324i
$361$	−12136.7	+	6256.88i	−1.76945	+	0.912215i
$362$	−359.355	−	786.877i	−0.0521747	−	0.114247i
$363$	−19.8628	−	3.82825i	−0.00287198	−	0.000553529i
$364$	1699.26	−	2943.21i	0.244686	−	0.423808i
$365$	801.595	+	1388.40i	0.114952	+	0.199102i
$366$	15.3966	+	44.4856i	0.00219889	+	0.00635328i
$367$	−5726.98	−	4503.74i	−0.814566	−	0.640582i	0.121427	−	0.992600i	$-0.461253\pi$
$367$	−5726.98	−	4503.74i	−0.814566	−	0.640582i	−0.935993	+	0.352018i	$0.885495\pi$
$368$	532.466	−	507.705i	0.0754258	−	0.0719184i
$369$	−832.698	+	793.976i	−0.117476	+	0.112013i
$370$	2774.00	+	2181.49i	0.389765	+	0.306515i
$371$	170.215	+	491.804i	0.0238197	+	0.0688226i
$372$	−892.588	−	1546.01i	−0.124405	−	0.215475i
$373$	1442.06	−	2497.72i	0.200180	−	0.346721i	−0.748407	−	0.663240i	$-0.769181\pi$
$373$	1442.06	−	2497.72i	0.200180	−	0.346721i	0.948586	+	0.316519i	$0.102514\pi$
$374$	−1899.58	−	366.115i	−0.262634	−	0.0506186i
$375$	−1041.51	−	2280.59i	−0.143422	−	0.314051i
$376$	7487.72	−	3860.19i	1.02699	−	0.529452i
$377$	1070.19	+	1235.06i	0.146200	+	0.168724i
$378$	1444.24	+	928.155i	0.196517	+	0.126294i
$379$	−10629.6	+	8359.17i	−1.44064	+	1.13293i	−0.472862	+	0.881136i	$0.656779\pi$
$379$	−10629.6	+	8359.17i	−1.44064	+	1.13293i	−0.967780	+	0.251797i	$0.918978\pi$
$380$	1002.34	−	6971.43i	0.135313	−	0.941123i
$381$	2480.28	+	236.838i	0.333514	+	0.0318467i
$382$	17888.0	+	7161.27i	2.39589	+	0.959169i
$383$	2197.17	+	9056.84i	0.293133	+	1.20831i	0.907759	+	0.419492i	$0.137792\pi$
$383$	2197.17	+	9056.84i	0.293133	+	1.20831i	−0.614626	+	0.788819i	$0.710693\pi$
$384$	6896.74	+	3555.52i	0.916531	+	0.472505i
$385$	83.0026	−	1742.44i	0.0109875	−	0.230657i
$386$	−3991.21	+	381.114i	−0.526288	+	0.0502544i
$387$	−1310.61	−	384.829i	−0.172150	−	0.0505478i
$388$	−15391.7	+	9891.65i	−2.01391	+	1.29426i
$389$	−3520.52	+	10171.9i	−0.458863	+	1.32580i	0.444061	+	0.895997i	$0.353537\pi$
$389$	−3520.52	+	10171.9i	−0.458863	+	1.32580i	−0.902924	+	0.429800i	$0.858584\pi$
$390$	870.541	−	167.783i	0.113030	−	0.0217847i
$391$	−244.965	−	344.006i	−0.0316840	−	0.0444939i
$392$	4142.70	−	1658.49i	0.533770	−	0.213689i
$393$	1345.66	−	395.121i	0.172721	−	0.0507156i
$394$	12428.9	−	14343.7i	1.58923	−	1.83407i
$395$	281.772	−	1161.48i	0.0358924	−	0.147951i
$396$	−2669.86	+	3749.29i	−0.338802	+	0.475781i
$397$	84.0157	−	183.969i	0.0106212	−	0.0232573i	−0.904247	−	0.427010i	$-0.859567\pi$
$397$	84.0157	−	183.969i	0.0106212	−	0.0232573i	0.914868	+	0.403752i	$0.132294\pi$
$398$	749.980	+	15744.0i	0.0944550	+	1.98285i
$399$	829.278	+	5767.75i	0.104050	+	0.723681i
$400$	−1602.03	−	1527.53i	−0.200254	−	0.190942i
$401$	13159.1			1.63874			0.819368	−	0.573267i	$-0.194324\pi$
$401$	13159.1			1.63874			0.819368	+	0.573267i	$0.194324\pi$
$402$	805.521	+	7671.72i	0.0999396	+	0.951817i
$403$	762.717			0.0942770
$404$	2596.13	+	2475.41i	0.319709	+	0.304842i
$405$	40.5406	+	281.966i	0.00497402	+	0.0345951i
$406$	−275.873	−	5791.28i	−0.0337225	−	0.707922i
$407$	3251.83	−	7120.51i	0.396037	−	0.867200i
$408$	−550.652	+	773.282i	−0.0668169	+	0.0938313i
$409$	−512.842	+	2113.96i	−0.0620010	+	0.255572i	−0.994374	−	0.105926i	$-0.966219\pi$
$409$	−512.842	+	2113.96i	−0.0620010	+	0.255572i	0.932373	+	0.361498i	$0.117734\pi$
$410$	1380.42	−	1593.09i	0.166278	−	0.191895i
$411$	−1760.89	+	517.044i	−0.211334	+	0.0620533i
$412$	6344.96	−	2540.14i	0.758723	−	0.303747i
$413$	2704.62	+	3798.10i	0.322241	+	0.452524i
$414$	−1551.12	+	298.953i	−0.184138	+	0.0354897i
$415$	−955.558	+	2760.90i	−0.113028	+	0.326572i
$416$	−1994.03	+	1281.49i	−0.235013	+	0.151034i
$417$	−902.744	−	265.070i	−0.106013	−	0.0311283i
$418$	−24449.8	+	2334.68i	−2.86096	+	0.273188i
$419$	631.061	−	13247.6i	0.0735784	−	1.54460i	−0.596683	−	0.802477i	$-0.703515\pi$
$419$	631.061	−	13247.6i	0.0735784	−	1.54460i	0.670262	−	0.742125i	$-0.266182\pi$
$420$	−1778.26	−	916.757i	−0.206596	−	0.106507i
$421$	−3270.18	−	13479.9i	−0.378572	−	1.56049i	−0.768623	−	0.639702i	$-0.779058\pi$
$421$	−3270.18	−	13479.9i	−0.378572	−	1.56049i	0.390052	−	0.920793i	$-0.372457\pi$
$422$	22835.0	+	9141.74i	2.63410	+	1.05453i
$423$	−2690.71	−	256.932i	−0.309283	−	0.0295330i
$424$	−153.192	+	1065.47i	−0.0175463	+	0.122037i
$425$	−998.768	+	785.440i	−0.113994	+	0.0896457i
$426$	12826.8	+	8243.31i	1.45883	+	0.937534i
$427$	29.7224	+	34.3015i	0.00336854	+	0.00388750i
$428$	−3429.45	+	1768.01i	−0.387310	+	0.199672i
$429$	−816.926	−	1788.82i	−0.0919384	−	0.201317i
$430$	2457.33	+	473.612i	0.275589	+	0.0531153i
$431$	−3176.52	+	5501.90i	−0.355006	+	0.614889i	−0.987119	−	0.159988i	$-0.948855\pi$
$431$	−3176.52	+	5501.90i	−0.355006	+	0.614889i	0.632113	+	0.774876i	$0.282188\pi$
$432$	265.317	+	459.542i	0.0295488	+	0.0511800i
$433$	−4433.60	−	12810.0i	−0.492067	−	1.42173i	−0.868684	−	0.495366i	$-0.835034\pi$
$433$	−4433.60	−	12810.0i	−0.492067	−	1.42173i	0.376617	−	0.926369i	$-0.377087\pi$
$434$	−2127.01	−	1672.70i	−0.235253	−	0.185005i
$435$	696.264	−	663.886i	0.0767432	−	0.0731745i
$436$	11967.3	−	11410.8i	1.31451	−	1.25339i
$437$	−4214.58	−	3314.38i	−0.461351	−	0.362811i
$438$	−2097.15	−	6059.31i	−0.228780	−	0.661016i
$439$	−7956.79	−	13781.6i	−0.865049	−	1.49831i	−0.866998	−	0.498311i	$-0.833954\pi$
$439$	−7956.79	−	13781.6i	−0.865049	−	1.49831i	0.00194891	−	0.999998i	$-0.499380\pi$
$440$	1804.03	−	3124.68i	0.195463	−	0.338552i
$441$	−1405.89	−	270.964i	−0.151808	−	0.0292586i
$442$	−393.792	−	862.285i	−0.0423774	−	0.0927935i
$443$	5837.23	−	3009.30i	0.626039	−	0.322745i	−0.115852	−	0.993267i	$-0.536960\pi$
$443$	5837.23	−	3009.30i	0.626039	−	0.322745i	0.741890	+	0.670521i	$0.233929\pi$
$444$	−5879.20	−	6784.96i	−0.628411	−	0.725225i
$445$	−1414.82	−	909.249i	−0.150717	−	0.0968597i
$446$	9190.95	−	7227.85i	0.975794	−	0.767373i
$447$	608.715	−	4233.70i	0.0644099	−	0.447981i
$448$	10493.8	+	1002.04i	1.10666	+	0.105673i
$449$	−3393.80	−	1358.67i	−0.356711	−	0.142805i	0.186384	−	0.982477i	$-0.440323\pi$
$449$	−3393.80	−	1358.67i	−0.356711	−	0.142805i	−0.543095	+	0.839672i	$0.682747\pi$
$450$	1120.50	+	4618.76i	0.117380	+	0.483845i
$451$	−4155.98	−	2142.56i	−0.433919	−	0.223701i
$452$	236.853	−	4972.15i	0.0246474	−	0.517412i
$453$	3723.78	−	355.578i	0.386222	−	0.0368797i
$454$	16476.9	+	4838.05i	1.70330	+	0.500134i
$455$	719.090	−	462.131i	0.0740911	−	0.0476155i
$456$	−3941.96	+	11389.6i	−0.404823	+	1.16966i
$457$	12594.2	−	2427.34i	1.28913	−	0.248460i	0.501798	−	0.864985i	$-0.332672\pi$
$457$	12594.2	−	2427.34i	1.28913	−	0.248460i	0.787335	+	0.616525i	$0.211460\pi$
$458$	9328.60	+	13100.2i	0.951740	+	1.33653i
$459$	282.772	−	113.205i	0.0287552	−	0.0115119i
$460$	1766.31	−	518.637i	0.179032	−	0.0525686i
$461$	8412.00	−	9707.96i	0.849861	−	0.980792i	−0.150108	−	0.988670i	$-0.547962\pi$
$461$	8412.00	−	9707.96i	0.849861	−	0.980792i	0.999969	+	0.00787804i	$0.00250769\pi$
$462$	−1644.84	+	6780.13i	−0.165638	+	0.682771i
$463$	−5456.84	+	7663.06i	−0.547734	+	0.769185i	−0.991936	−	0.126742i	$-0.959548\pi$
$463$	−5456.84	+	7663.06i	−0.547734	+	0.769185i	0.444202	+	0.895927i	$0.353487\pi$
$464$	744.443	−	1630.10i	0.0744826	−	0.163094i
$465$	−21.3643	−	448.492i	−0.00213064	−	0.0447276i
$466$	−2969.29	−	20651.9i	−0.295171	−	2.05296i
$467$	9972.36	+	9508.62i	0.988149	+	0.942198i	0.998331	−	0.0577499i	$-0.0183926\pi$
$467$	9972.36	+	9508.62i	0.988149	+	0.942198i	−0.0101820	+	0.999948i	$0.503241\pi$
$468$	−2255.41			−0.222770
$469$	3470.10	+	6578.23i	0.341651	+	0.647664i
$470$	4952.11			0.486008
$471$	−4340.98	−	4139.11i	−0.424674	−	0.404926i
$472$	1372.49	+	9545.90i	0.133843	+	0.930901i
$473$	−264.130	−	5544.76i	−0.0256759	−	0.539003i
$474$	−1985.72	+	4348.13i	−0.192420	+	0.421342i
$475$	−9357.32	+	13140.5i	−0.903881	+	1.26932i
$476$	−504.333	+	2078.89i	−0.0485632	+	0.200180i
$477$	226.174	−	261.019i	0.0217103	−	0.0250550i
$478$	13223.1	−	3882.65i	1.26529	−	0.371524i
$479$	−5233.89	+	2095.33i	−0.499254	+	0.199871i	−0.607602	−	0.794242i	$-0.707868\pi$
$479$	−5233.89	+	2095.33i	−0.499254	+	0.199871i	0.108348	+	0.994113i	$0.465444\pi$
$480$	809.393	+	1136.63i	0.0769658	+	0.108083i
$481$	3766.45	−	725.923i	0.357038	−	0.0688134i
$482$	−2511.69	+	7257.04i	−0.237353	+	0.685787i
$483$	−1281.26	+	823.417i	−0.120703	+	0.0775710i
$484$	−90.4630	−	26.5623i	−0.00849577	−	0.00249458i
$485$	−4580.94	+	437.427i	−0.428886	+	0.0409537i
$486$	54.2111	−	1138.03i	0.00505980	−	0.106218i
$487$	−5734.88	−	2956.54i	−0.533618	−	0.275099i	0.170285	−	0.985395i	$-0.445531\pi$
$487$	−5734.88	−	2956.54i	−0.533618	−	0.275099i	−0.703904	+	0.710295i	$0.748561\pi$
$488$	22.1323	+	91.2308i	0.00205304	+	0.00846275i
$489$	8913.57	+	3568.46i	0.824306	+	0.330002i
$490$	2611.28	+	249.347i	0.240747	+	0.0229885i
$491$	489.582	−	3405.12i	0.0449990	−	0.312975i	−0.954874	−	0.297013i	$-0.904010\pi$
$491$	489.582	−	3405.12i	0.0449990	−	0.312975i	0.999873	−	0.0159625i	$-0.00508123\pi$
$492$	−4215.30	+	3314.95i	−0.386261	+	0.303759i
$493$	−865.361	−	556.134i	−0.0790546	−	0.0508053i
$494$	−7881.38	−	9095.60i	−0.717814	−	0.828401i
$495$	−1028.98	+	530.474i	−0.0934324	+	0.0481678i
$496$	−347.443	−	760.795i	−0.0314529	−	0.0688723i
$497$	14435.1	+	2782.14i	1.30282	+	0.251098i
$498$	5842.45	−	10119.4i	0.525716	−	0.910566i
$499$	5695.79	+	9865.39i	0.510979	+	0.885041i	0.999919	+	0.0127240i	$0.00405028\pi$
$499$	5695.79	+	9865.39i	0.510979	+	0.885041i	−0.488940	+	0.872317i	$0.662616\pi$
$500$	−3821.97	−	11042.8i	−0.341847	−	0.987702i
$501$	1711.89	+	1346.25i	0.152658	+	0.120052i
$502$	−13165.3	+	12553.1i	−1.17051	+	1.11608i
$503$	9281.23	−	8849.63i	0.822722	−	0.784464i	−0.156409	−	0.987692i	$-0.549992\pi$
$503$	9281.23	−	8849.63i	0.822722	−	0.784464i	0.979131	+	0.203228i	$0.0651433\pi$
$504$	2691.13	+	2116.33i	0.237843	+	0.187041i
$505$	295.088	+	852.602i	0.0260025	+	0.0751293i
$506$	−3209.80	−	5559.54i	−0.282002	−	0.488442i
$507$	−2813.69	+	4873.45i	−0.246470	+	0.426899i
$508$	11403.0	+	2197.75i	0.995920	+	0.191948i
$509$	−6191.16	−	13556.7i	−0.539132	−	1.18053i	−0.961675	−	0.274192i	$-0.911590\pi$
$509$	−6191.16	−	13556.7i	−0.539132	−	1.18053i	0.422543	−	0.906343i	$-0.361138\pi$
$510$	−496.009	+	255.711i	−0.0430660	+	0.0222021i
$511$	−4048.44	−	4672.14i	−0.350474	−	0.404469i
$512$	5896.66	+	3789.56i	0.508981	+	0.327102i
$513$	3039.74	−	2390.48i	0.261613	−	0.205735i
$514$	436.149	−	3033.48i	0.0374275	−	0.260314i
$515$	1711.21	+	163.401i	0.146418	+	0.0139812i
$516$	−5910.43	−	2366.18i	−0.504249	−	0.201871i
$517$	−2589.70	−	10674.9i	−0.220300	−	0.908088i
$518$	−12095.6	−	6235.73i	−1.02597	−	0.528923i
$519$	−367.605	+	7716.98i	−0.0310907	+	0.652674i
$520$	1759.99	−	168.059i	0.148424	−	0.0141728i
$521$	20280.6	+	5954.92i	1.70539	+	0.500748i	0.981870	−	0.189553i	$-0.0607039\pi$
$521$	20280.6	+	5954.92i	1.70539	+	0.500748i	0.723522	+	0.690301i	$0.242522\pi$
$522$	−3236.89	+	2080.22i	−0.271408	+	0.174423i
$523$	−5750.98	+	16616.4i	−0.480827	+	1.38926i	0.400302	+	0.916383i	$0.368905\pi$
$523$	−5750.98	+	16616.4i	−0.480827	+	1.38926i	−0.881129	+	0.472876i	$0.843216\pi$
$524$	6418.61	−	1237.09i	0.535111	−	0.103134i
$525$	2658.03	+	3732.69i	0.220964	+	0.310301i
$526$	−9217.16	+	3689.99i	−0.764044	+	0.305877i
$527$	−460.643	+	135.257i	−0.0380758	+	0.0111801i
$528$	−1412.17	+	1629.73i	−0.116396	+	0.134328i
$529$	−2538.09	+	10462.1i	−0.208604	+	0.859878i
$530$	−367.043	+	515.440i	−0.0300818	+	0.0422440i
$531$	1285.44	−	2814.72i	0.105053	−	0.230035i
$532$	1292.29	+	27128.5i	0.105316	+	2.21084i
$533$	−326.069	−	2267.86i	−0.0264983	−	0.184300i
$534$	4868.10	+	4641.72i	0.394500	+	0.376155i
$535$	−970.442			−0.0784222
$536$	144.841	+	15382.5i	0.0116719	+	1.23959i
$537$	13460.8			1.08170
$538$	−14815.8	−	14126.9i	−1.18728	−	1.13207i
$539$	−828.069	−	5759.35i	−0.0661734	−	0.460246i
$540$	63.1757	+	1326.22i	0.00503454	+	0.105688i
$541$	−3308.50	+	7244.61i	−0.262927	+	0.575731i	−0.994345	−	0.106199i	$-0.966132\pi$
$541$	−3308.50	+	7244.61i	−0.262927	+	0.575731i	0.731418	+	0.681930i	$0.238859\pi$
$542$	−588.251	+	826.082i	−0.0466190	+	0.0654673i
$543$	−130.494	+	537.904i	−0.0103131	+	0.0425113i
$544$	977.043	−	1127.57i	0.0770044	−	0.0888678i
$545$	3990.47	−	1171.71i	0.313638	−	0.0920926i
$546$	−3173.82	+	1270.61i	−0.248767	+	0.0995915i
$547$	−9022.16	−	12669.8i	−0.705228	−	0.990354i	−0.999401	−	0.0346018i	$-0.988984\pi$
$547$	−9022.16	−	12669.8i	−0.705228	−	0.990354i	0.294173	−	0.955752i	$-0.404956\pi$
$548$	−8399.21	+	1618.82i	−0.654738	+	0.126190i
$549$	9.85160	−	28.4643i	0.000765858	−	0.00221280i
$550$	−16248.5	+	10442.3i	−1.25971	+	0.809565i
$551$	−12530.9	−	3679.39i	−0.968843	−	0.284478i
$552$	−3135.92	+	299.444i	−0.241800	+	0.0230891i
$553$	−219.293	+	4603.53i	−0.0168631	+	0.354000i
$554$	−30052.2	−	15493.0i	−2.30468	−	1.18815i
$555$	−532.358	−	2194.41i	−0.0407159	−	0.167833i
$556$	−4071.09	−	1629.82i	−0.310526	−	0.124316i
$557$	3362.50	+	321.080i	0.255787	+	0.0244247i	0.222162	−	0.975010i	$-0.428689\pi$
$557$	3362.50	+	321.080i	0.255787	+	0.0244247i	0.0336255	+	0.999435i	$0.489295\pi$
$558$	−255.566	+	1777.50i	−0.0193888	+	0.134852i
$559$	2138.13	−	1681.44i	0.161777	−	0.127223i
$560$	−788.536	−	506.761i	−0.0595031	−	0.0382403i
$561$	810.604	+	935.487i	0.0610049	+	0.0704034i
$562$	879.359	−	453.341i	0.0660027	−	0.0340268i
$563$	−5951.06	−	13031.0i	−0.445484	−	0.975473i	−0.990559	−	0.137086i	$-0.956226\pi$
$563$	−5951.06	−	13031.0i	−0.445484	−	0.975473i	0.545076	−	0.838387i	$-0.316501\pi$
$564$	−12370.5	−	2384.21i	−0.923564	−	0.178002i
$565$	625.997	−	1084.26i	0.0466122	−	0.0807348i
$566$	7944.28	+	13759.9i	0.589970	+	1.02186i
$567$	−359.278	−	1038.07i	−0.0266107	−	0.0768866i
$568$	23901.0	+	18796.0i	1.76561	+	1.38849i
$569$	−4973.80	+	4742.51i	−0.366454	+	0.349413i	−0.850825	−	0.525450i	$-0.823897\pi$
$569$	−4973.80	+	4742.51i	−0.366454	+	0.349413i	0.484371	+	0.874863i	$0.339049\pi$
$570$	−5127.62	+	4889.18i	−0.376794	+	0.359272i
$571$	−4725.30	−	3716.02i	−0.346318	−	0.272348i	0.429815	−	0.902917i	$-0.358579\pi$
$571$	−4725.30	−	3716.02i	−0.346318	−	0.272348i	−0.776133	+	0.630570i	$0.782821\pi$
$572$	−2997.83	−	8661.65i	−0.219135	−	0.633150i
$573$	−6164.43	−	10677.1i	−0.449429	−	0.778433i
$574$	−4064.29	+	7039.55i	−0.295540	+	0.511890i
$575$	−4140.21	−	797.960i	−0.300276	−	0.0578734i
$576$	−2906.16	−	6363.61i	−0.210226	−	0.460330i
$577$	15946.6	−	8221.04i	1.15055	−	0.593148i	0.225967	−	0.974135i	$-0.427446\pi$
$577$	15946.6	−	8221.04i	1.15055	−	0.593148i	0.924580	+	0.380987i	$0.124416\pi$
$578$	−14693.9	−	16957.7i	−1.05742	−	1.22032i
$579$	2158.16	+	1386.96i	0.154905	+	0.0995514i
$580$	3524.64	−	2771.81i	0.252332	−	0.198436i
$581$	1603.33	−	11151.4i	0.114487	−	0.796278i
$582$	18321.5	+	1749.49i	1.30490	+	0.124603i
$583$	1303.04	+	521.659i	0.0925668	+	0.0370582i
$584$	−3014.61	−	12426.4i	−0.213605	−	0.880493i
$585$	−504.211	−	259.939i	−0.0356351	−	0.0183712i
$586$	1335.50	−	28035.7i	0.0941453	−	1.97635i
$587$	−7170.38	+	684.688i	−0.504179	+	0.0481433i	−0.344047	−	0.938952i	$-0.611798\pi$
$587$	−7170.38	+	684.688i	−0.504179	+	0.0481433i	−0.160132	+	0.987096i	$0.551192\pi$
$588$	−6402.98	−	1880.09i	−0.449072	−	0.131860i
$589$	−5127.64	+	3295.34i	−0.358711	+	0.230530i
$590$	−1854.22	+	5357.40i	−0.129384	+	0.373832i
$591$	−11924.6	+	2298.28i	−0.829970	+	0.159964i
$592$	−2439.84	−	3426.27i	−0.169386	−	0.237870i
$593$	−21560.0	+	8631.33i	−1.49302	+	0.597717i	−0.967457	−	0.253035i	$-0.918571\pi$
$593$	−21560.0	+	8631.33i	−1.49302	+	0.597717i	−0.525568	+	0.850752i	$0.676147\pi$
$594$	4442.54	−	1304.45i	0.306868	−	0.0901047i
$595$	−352.342	+	406.624i	−0.0242767	+	0.0280168i
$596$	4700.02	−	19373.7i	0.323021	−	1.33151i
$597$	5850.05	−	8215.25i	0.401050	−	0.563195i
$598$	1306.76	−	2861.41i	0.0893604	−	0.195672i
$599$	−398.800	−	8371.84i	−0.0272029	−	0.571058i	−0.970790	−	0.239933i	$-0.922875\pi$
$599$	−398.800	−	8371.84i	−0.0272029	−	0.571058i	0.943587	−	0.331126i	$-0.107428\pi$
$600$	1348.85	+	9381.48i	0.0917779	+	0.638329i
$601$	10620.7	+	10126.8i	0.720844	+	0.687323i	0.958841	−	0.283942i	$-0.0916425\pi$
$601$	10620.7	+	10126.8i	0.720844	+	0.687323i	−0.237997	+	0.971266i	$0.576491\pi$
$602$	−9650.21			−0.653344
$603$	2629.26	−	4177.17i	0.177565	−	0.282102i
$604$	17435.1			1.17454
$605$	−17.1622	−	16.3642i	−0.00115330	−	0.00109967i
$606$	−513.535	−	3571.72i	−0.0344240	−	0.239424i
$607$	−418.915	−	8794.11i	−0.0280119	−	0.588043i	−0.968620	−	0.248548i	$-0.920047\pi$
$607$	−418.915	−	8794.11i	−0.0280119	−	0.588043i	0.940608	−	0.339495i	$-0.110256\pi$
$608$	7868.92	−	17230.5i	0.524880	−	1.14933i
$609$	−2151.88	+	3021.90i	−0.143183	+	0.201073i
$610$	−13.0104	+	53.6295i	−0.000863565	+	0.00355966i
$611$	3524.82	−	4067.86i	0.233386	−	0.269342i
$612$	1362.15	−	399.964i	0.0899702	−	0.0264176i
$613$	−14852.4	+	5946.00i	−0.978601	+	0.391773i	−0.805151	−	0.593070i	$-0.797916\pi$
$613$	−14852.4	+	5946.00i	−0.978601	+	0.391773i	−0.173450	+	0.984843i	$0.555492\pi$
$614$	−12254.8	−	17209.4i	−0.805475	−	1.13113i
$615$	−1324.41	+	255.259i	−0.0868380	+	0.0167367i
$616$	−4550.56	+	13148.0i	−0.297642	+	0.859980i
$617$	−5622.37	+	3613.28i	−0.366853	+	0.235762i	−0.711059	−	0.703132i	$-0.751784\pi$
$617$	−5622.37	+	3613.28i	−0.366853	+	0.235762i	0.344207	+	0.938894i	$0.388148\pi$
$618$	−6596.64	−	1936.95i	−0.429378	−	0.126077i
$619$	−27846.1	+	2658.98i	−1.80813	+	0.172655i	−0.943852	−	0.330368i	$-0.892827\pi$
$619$	−27846.1	+	2658.98i	−1.80813	+	0.172655i	−0.864273	+	0.503023i	$0.832221\pi$
$620$	99.5765	−	2090.37i	0.00645014	−	0.135405i
$621$	898.394	+	463.154i	0.0580536	+	0.0299287i
$622$	2364.76	+	9747.68i	0.152441	+	0.628370i
$623$	6020.70	+	2410.33i	0.387182	+	0.155004i
$624$	−1051.90	−	100.444i	−0.0674835	−	0.00644389i
$625$	−1585.37	+	11026.5i	−0.101464	+	0.705694i
$626$	−22883.5	+	17995.8i	−1.46104	+	1.14897i
$627$	13220.7	+	8496.44i	0.842081	+	0.541172i
$628$	−18307.3	−	21127.8i	−1.16328	−	1.34250i
$629$	−2146.01	+	1106.35i	−0.136037	+	0.0701319i
$630$	836.042	+	1830.68i	0.0528710	+	0.115771i
$631$	13224.6	+	2548.84i	0.834332	+	0.160804i	0.588489	−	0.808505i	$-0.299723\pi$
$631$	13224.6	+	2548.84i	0.834332	+	0.160804i	0.245843	+	0.969310i	$0.420935\pi$
$632$	−4766.26	+	8255.41i	−0.299987	+	0.519593i
$633$	−7869.22	−	13629.9i	−0.494113	−	0.855828i
$634$	2229.30	+	6441.13i	0.139648	+	0.403486i
$635$	2295.93	+	1805.54i	0.143482	+	0.112835i
$636$	1165.04	−	1110.86i	0.0726366	−	0.0692589i
$637$	2063.49	−	1967.53i	0.128349	−	0.122381i
$638$	−12291.3	−	9665.96i	−0.762721	−	0.599810i
$639$	−3190.89	−	9219.47i	−0.197543	−	0.570762i
$640$	4548.06	+	7877.48i	0.280903	+	0.486539i
$641$	−2638.01	+	4569.17i	−0.162551	+	0.281547i	−0.935783	−	0.352577i	$-0.885306\pi$
$641$	−2638.01	+	4569.17i	−0.162551	+	0.281547i	0.773232	+	0.634123i	$0.218639\pi$
$642$	3811.15	+	734.538i	0.234290	+	0.0451556i
$643$	8064.81	+	17659.5i	0.494627	+	1.08308i	0.978179	+	0.207766i	$0.0666193\pi$
$643$	8064.81	+	17659.5i	0.494627	+	1.08308i	−0.483552	+	0.875316i	$0.660653\pi$
$644$	−6309.58	+	3252.81i	−0.386075	+	0.199035i
$645$	−1048.61	−	1210.16i	−0.0640139	−	0.0738760i
$646$	6372.94	+	4095.64i	0.388142	+	0.249444i
$647$	−5398.69	+	4245.58i	−0.328044	+	0.257977i	−0.768574	−	0.639761i	$-0.779033\pi$
$647$	−5398.69	+	4245.58i	−0.328044	+	0.257977i	0.440530	+	0.897738i	$0.354791\pi$
$648$	323.346	−	2248.92i	0.0196022	−	0.136337i
$649$	12518.2	+	1195.34i	0.757138	+	0.0722980i
$650$	−8786.45	−	3517.57i	−0.530205	−	0.212262i
$651$	408.195	+	1682.60i	0.0245752	+	0.101300i
$652$	39776.0	+	20505.9i	2.38918	+	1.23171i
$653$	−568.161	+	11927.2i	−0.0340488	+	0.714773i	0.915719	+	0.401818i	$0.131622\pi$
$653$	−568.161	+	11927.2i	−0.0340488	+	0.714773i	−0.949768	+	0.312954i	$0.898681\pi$
$654$	−16558.4	+	1581.13i	−0.990035	+	0.0945369i
$655$	1577.50	+	463.195i	0.0941037	+	0.0276314i
$656$	−2113.61	+	1358.33i	−0.125796	+	0.0808445i
$657$	−1341.87	+	3877.08i	−0.0796824	+	0.230227i
$658$	−18751.0	+	3613.95i	−1.11092	+	0.214113i
$659$	−6140.93	−	8623.74i	−0.363000	−	0.509762i	0.592173	−	0.805811i	$-0.298270\pi$
$659$	−6140.93	−	8623.74i	−0.363000	−	0.509762i	−0.955173	+	0.296049i	$0.904331\pi$
$660$	−5009.24	+	2005.40i	−0.295431	+	0.118273i
$661$	15053.6	−	4420.12i	0.885803	−	0.260095i	0.192980	−	0.981203i	$-0.438185\pi$
$661$	15053.6	−	4420.12i	0.885803	−	0.260095i	0.692823	+	0.721108i	$0.256367\pi$
$662$	17833.4	−	20580.8i	1.04700	−	1.20830i
$663$	−143.000	+	589.452i	−0.00837653	+	0.0345285i
$664$	13516.6	−	18981.4i	0.789978	−	1.10937i
$665$	−2837.70	+	6213.69i	−0.165475	+	0.362341i
$666$	429.718	+	9020.88i	0.0250018	+	0.524853i
$667$	−485.792	−	3378.76i	−0.0282008	−	0.196141i
$668$	7346.34	+	7004.72i	0.425507	+	0.405720i
$669$	−7481.52			−0.432365
$670$	−4067.83	+	8076.30i	−0.234558	+	0.465694i
$671$	122.409			0.00704253
$672$	−3894.22	−	3713.14i	−0.223546	−	0.213151i
$673$	1414.48	+	9837.92i	0.0810166	+	0.563483i	0.989386	+	0.145313i	$0.0464190\pi$
$673$	1414.48	+	9837.92i	0.0810166	+	0.563483i	−0.908369	+	0.418169i	$0.862672\pi$
$674$	−1923.21	−	40373.1i	−0.109910	−	2.30729i
$675$	1263.30	−	2766.24i	0.0720362	−	0.157737i
$676$	−15214.0	+	21365.1i	−0.865614	+	1.21559i
$677$	−2533.17	+	10441.9i	−0.143808	+	0.592783i	0.853607	+	0.520918i	$0.174410\pi$
$677$	−2533.17	+	10441.9i	−0.143808	+	0.592783i	−0.997414	+	0.0718652i	$0.977105\pi$
$678$	−3279.12	+	3784.31i	−0.185743	+	0.214359i
$679$	17026.3	−	4999.38i	0.962312	−	0.282560i
$680$	−1033.14	+	413.608i	−0.0582636	+	0.0233252i
$681$	−6373.61	−	8950.48i	−0.358645	−	0.503646i
$682$	−7166.00	+	1381.13i	−0.402346	+	0.0775459i
$683$	−4763.39	+	13762.9i	−0.266861	+	0.771044i	0.729355	+	0.684135i	$0.239820\pi$
$683$	−4763.39	+	13762.9i	−0.266861	+	0.771044i	−0.996216	+	0.0869089i	$0.972301\pi$
$684$	15162.8	−	9744.53i	0.847608	−	0.544724i
$685$	−2064.27	−	606.124i	−0.115141	−	0.0338085i
$686$	−31780.1	+	3034.63i	−1.76876	+	0.168896i
$687$	489.631	−	10278.6i	0.0271916	−	0.570821i
$688$	−2651.19	−	1366.78i	−0.146912	−	0.0757386i
$689$	162.148	+	668.385i	0.00896570	+	0.0369571i
$690$	−1719.17	−	688.251i	−0.0948516	−	0.0379728i
$691$	−31837.2	−	3040.08i	−1.75274	−	0.167367i	−0.831285	−	0.555847i	$-0.812394\pi$
$691$	−31837.2	−	3040.08i	−1.75274	−	0.167367i	−0.921457	+	0.388480i	$0.873000\pi$
$692$	−5124.58	+	35642.2i	−0.281513	+	1.95797i
$693$	3509.04	−	2759.54i	0.192349	−	0.151265i
$694$	31715.7	+	20382.4i	1.73474	+	1.11485i
$695$	−722.280	−	833.556i	−0.0394211	−	0.0454943i
$696$	−6820.15	+	3516.03i	−0.371433	+	0.191487i
$697$	599.102	+	1311.85i	0.0325575	+	0.0712910i
$698$	40401.7	+	7786.78i	2.19087	+	0.422255i
$699$	−6675.04	+	11561.5i	−0.361192	+	0.625603i
$700$	10678.9	+	18496.5i	0.576608	+	0.998715i
$701$	3821.29	+	11040.9i	0.205889	+	0.594878i	0.999915	−	0.0130058i	$-0.00413998\pi$
$701$	3821.29	+	11040.9i	0.205889	+	0.594878i	−0.794026	+	0.607883i	$0.792019\pi$
$702$	1783.40	+	1402.48i	0.0958833	+	0.0754034i
$703$	−22184.9	+	21153.3i	−1.19021	+	1.13487i
$704$	20576.0	−	19619.2i	1.10154	−	1.05032i
$705$	−2490.71	−	1958.72i	−0.133058	−	0.104638i
$706$	−5603.02	−	16188.9i	−0.298686	−	0.862997i
$707$	−1739.55	−	3012.99i	−0.0925354	−	0.160276i
$708$	7211.20	−	12490.2i	0.382787	−	0.663007i
$709$	−13779.9	−	2655.86i	−0.729923	−	0.140681i	−0.189268	−	0.981926i	$-0.560611\pi$
$709$	−13779.9	−	2655.86i	−0.729923	−	0.140681i	−0.540655	+	0.841244i	$0.681824\pi$
$710$	7425.21	+	16258.9i	0.392483	+	0.859419i
$711$	2718.56	−	1401.52i	0.143395	−	0.0739254i
$712$	8784.17	+	10137.5i	0.462360	+	0.533592i
$713$	−1340.23	−	861.313i	−0.0703955	−	0.0452404i
$714$	1691.51	−	1330.21i	0.0886597	−	0.0697227i
$715$	328.084	−	2281.87i	0.0171603	−	0.119353i
$716$	62455.0	+	5963.73i	3.25985	+	0.311278i
$717$	−8186.39	−	3277.34i	−0.426397	−	0.170704i
$718$	−13926.2	−	57404.5i	−0.723845	−	2.98373i
$719$	2655.94	+	1369.23i	0.137761	+	0.0710205i	0.525729	−	0.850652i	$-0.323793\pi$
$719$	2655.94	+	1369.23i	0.137761	+	0.0710205i	−0.387968	+	0.921673i	$0.626823\pi$
$720$	−29.5986	+	621.350i	−0.00153205	+	0.0321616i
$721$	−6598.68	+	630.097i	−0.340843	+	0.0325465i
$722$	61427.0	+	18036.6i	3.16631	+	0.929713i
$723$	4133.67	−	2656.55i	0.212632	−	0.136650i
$724$	−843.778	+	2437.94i	−0.0433132	+	0.125145i
$725$	−10084.6	+	1943.65i	−0.516597	+	0.0995659i
$726$	55.0138	+	77.2561i	0.00281233	+	0.00394937i
$727$	−6087.67	+	2437.13i	−0.310563	+	0.124331i	−0.521708	−	0.853124i	$-0.674705\pi$
$727$	−6087.67	+	2437.13i	−0.310563	+	0.124331i	0.211145	+	0.977455i	$0.432281\pi$
$728$	−6541.48	+	1920.75i	−0.333026	+	0.0977854i
$729$	−477.393	+	550.941i	−0.0242541	+	0.0279907i
$730$	1772.12	−	7304.78i	0.0898481	−	0.370359i
$731$	−993.143	+	1394.67i	−0.0502499	+	0.0705662i
$732$	58.3202	−	127.703i	0.00294478	−	0.00644816i
$733$	82.7904	+	1737.98i	0.00417181	+	0.0875770i	0.999993	−	0.00374767i	$-0.00119292\pi$
$733$	82.7904	+	1737.98i	0.00417181	+	0.0875770i	−0.995821	+	0.0913247i	$0.970890\pi$
$734$	4861.43	+	33812.0i	0.244467	+	1.70030i
$735$	−1214.75	−	1158.26i	−0.0609613	−	0.0581265i
$736$	4951.01			0.247958
$737$	19536.7	+	4545.22i	0.976452	+	0.227172i
$738$	5394.47			0.269069
$739$	21225.1	+	20238.1i	1.05653	+	1.00740i	0.999959	+	0.00900482i	$0.00286636\pi$
$739$	21225.1	+	20238.1i	1.05653	+	1.00740i	0.0565746	+	0.998398i	$0.481982\pi$
$740$	−1497.80	−	10417.4i	−0.0744056	−	0.517503i
$741$	366.418	+	7692.06i	0.0181656	+	0.381342i
$742$	1013.64	−	2219.55i	0.0501506	−	0.109815i
$743$	19196.3	−	26957.4i	0.947836	−	1.33105i	0.00422639	−	0.999991i	$-0.498655\pi$
$743$	19196.3	−	26957.4i	0.947836	−	1.33105i	0.943610	−	0.331059i	$-0.107406\pi$
$744$	−844.292	+	3480.22i	−0.0416038	+	0.171493i
$745$	3283.57	−	3789.44i	0.161478	−	0.186355i
$746$	−12974.6	+	3809.69i	−0.636776	+	0.186974i
$747$	−6941.07	+	2778.79i	−0.339974	+	0.136105i
$748$	3346.56	+	4699.58i	0.163586	+	0.229724i
$749$	3674.54	−	708.209i	0.179259	−	0.0345492i
$750$	−3844.67	+	11108.4i	−0.187183	+	0.540830i
$751$	9730.82	−	6253.62i	0.472813	−	0.303859i	−0.282448	−	0.959283i	$-0.591146\pi$
$751$	9730.82	−	6253.62i	0.472813	−	0.303859i	0.755261	+	0.655424i	$0.227510\pi$
$752$	−5663.28	−	1662.89i	−0.274626	−	0.0806374i
$753$	11586.7	−	1106.40i	0.560749	−	0.0535450i
$754$	364.580	−	7653.48i	0.0176091	−	0.369660i
$755$	3897.72	+	2009.41i	0.187884	+	0.0968610i
$756$	−1207.06	−	4975.57i	−0.0580693	−	0.239365i
$757$	−2097.59	−	839.748i	−0.100711	−	0.0403186i	0.320760	−	0.947161i	$-0.396062\pi$
$757$	−2097.59	−	839.748i	−0.100711	−	0.0403186i	−0.421471	+	0.906842i	$0.638486\pi$
$758$	63114.9	+	6026.74i	3.02432	+	0.288788i
$759$	−584.574	+	4065.80i	−0.0279561	+	0.194439i
$760$	−11106.1	+	8733.91i	−0.530078	+	0.416858i
$761$	29164.4	+	18742.8i	1.38923	+	0.892806i	0.999603	−	0.0281648i	$-0.00896634\pi$
$761$	29164.4	+	18742.8i	1.38923	+	0.892806i	0.389631	+	0.920971i	$0.372603\pi$
$762$	−7649.99	−	8828.56i	−0.363688	−	0.419718i
$763$	−14254.7	+	7348.78i	−0.676347	+	0.348681i
$764$	−23871.1	−	52270.5i	−1.13040	−	2.47523i
$765$	350.614	+	67.5754i	0.0165706	+	0.00319372i
$766$	21847.7	−	37841.2i	1.03053	−	1.78493i
$767$	3080.99	+	5336.43i	0.145043	+	0.251222i
$768$	−5797.12	−	16749.7i	−0.272377	−	0.786982i
$769$	−17921.0	−	14093.2i	−0.840372	−	0.660876i	0.102242	−	0.994760i	$-0.467398\pi$
$769$	−17921.0	−	14093.2i	−0.840372	−	0.660876i	−0.942614	+	0.333884i	$0.891641\pi$
$770$	−5919.28	+	5644.02i	−0.277034	+	0.264151i
$771$	−1419.21	+	1353.21i	−0.0662924	+	0.0632097i
$772$	9398.88	+	7391.36i	0.438178	+	0.344587i
$773$	653.204	+	1887.31i	0.0303934	+	0.0878160i	0.959177	−	0.282807i	$-0.0912655\pi$
$773$	653.204	+	1887.31i	0.0303934	+	0.0878160i	−0.928784	+	0.370623i	$0.879144\pi$
$774$	3202.15	+	5546.28i	0.148706	+	0.257567i
$775$	−2396.63	+	4151.09i	−0.111083	+	0.192402i
$776$	36039.9	+	6946.12i	1.66721	+	0.321329i
$777$	3617.18	+	7920.53i	0.167009	+	0.365698i
$778$	44857.0	−	23125.4i	2.06710	−	1.06566i
$779$	11990.5	+	13837.7i	0.551479	+	0.636441i
$780$	−2224.26	−	1429.44i	−0.102104	−	0.0656184i
$781$	31165.2	−	24508.6i	1.42788	−	1.12290i
$782$	−281.789	+	1959.89i	−0.0128859	+	0.0896232i
$783$	2450.82	+	234.025i	0.111858	+	0.0106812i
$784$	−2902.56	−	1162.01i	−0.132223	−	0.0529341i
$785$	−1657.72	−	6833.21i	−0.0753713	−	0.310685i
$786$	−5844.60	−	3013.10i	−0.265229	−	0.136735i
$787$	−163.969	+	3442.13i	−0.00742677	+	0.155907i	0.992107	+	0.125390i	$0.0400183\pi$
$787$	−163.969	+	3442.13i	−0.00742677	+	0.155907i	−0.999534	+	0.0305167i	$0.990285\pi$
$788$	−56345.7	+	5380.36i	−2.54725	+	0.243233i
$789$	6095.37	+	1789.76i	0.275033	+	0.0807569i
$790$	−4714.08	+	3029.56i	−0.212303	+	0.136439i
$791$	−1579.04	+	4562.34i	−0.0709788	+	0.205080i
$792$	9066.54	−	1747.43i	0.406775	−	0.0783994i
$793$	34.7928	+	48.8597i	0.00155805	+	0.00218797i
$794$	−880.316	+	352.425i	−0.0393466	+	0.0157520i
$795$	388.481	−	114.068i	0.0173308	−	0.00508879i
$796$	30782.6	−	35525.1i	1.37068	−	1.58185i
$797$	−963.901	+	3973.25i	−0.0428396	+	0.176587i	−0.989212	−	0.146490i	$-0.953202\pi$
$797$	−963.901	+	3973.25i	−0.0428396	+	0.176587i	0.946373	+	0.323077i	$0.104717\pi$
$798$	15847.5	−	22254.7i	0.703001	−	0.987227i
$799$	−1407.44	+	3081.86i	−0.0623174	+	0.136456i
$800$	−708.786	−	14879.2i	−0.0313242	−	0.657576i
$801$	−612.508	−	4260.09i	−0.0270186	−	0.187918i
$802$	−44652.4	−	42576.0i	−1.96600	−	1.87458i
$803$	−16673.1			−0.732728
$804$	14049.9	−	18216.3i	0.616294	−	0.799052i
$805$	−1785.44			−0.0781720
$806$	−2588.11	−	2467.76i	−0.113104	−	0.107845i
$807$	1864.14	+	12965.4i	0.0813145	+	0.565555i
$808$	−342.400	−	7187.86i	−0.0149079	−	0.312955i
$809$	3097.65	−	6782.91i	0.134620	−	0.294777i	−0.830302	−	0.557314i	$-0.811832\pi$
$809$	3097.65	−	6782.91i	0.134620	−	0.294777i	0.964922	+	0.262537i	$0.0845592\pi$
$810$	774.731	−	1087.96i	0.0336065	−	0.0471937i
$811$	4968.17	−	20479.1i	0.215112	−	0.886705i	−0.757231	−	0.653148i	$-0.773448\pi$
$811$	4968.17	−	20479.1i	0.215112	−	0.886705i	0.972343	−	0.233558i	$-0.0750368\pi$
$812$	−11323.1	+	13067.5i	−0.489363	+	0.564754i
$813$	622.608	−	182.814i	0.0268583	−	0.00788632i
$814$	−34072.6	+	13640.6i	−1.46713	+	0.587350i
$815$	6528.84	+	9168.48i	0.280608	+	0.394059i
$816$	653.107	−	125.876i	0.0280188	−	0.00540018i
$817$	−7109.63	+	20541.9i	−0.304449	+	0.879647i
$818$	8579.90	−	5513.97i	0.366735	−	0.235686i
$819$	2098.87	+	616.284i	0.0895488	+	0.0262939i
$820$	−6258.06	+	597.572i	−0.266513	+	0.0254489i
$821$	−444.117	+	9323.17i	−0.0188792	+	0.396323i	0.969574	+	0.244797i	$0.0787215\pi$
$821$	−444.117	+	9323.17i	−0.0188792	+	0.396323i	−0.988453	+	0.151525i	$0.951582\pi$
$822$	7648.07	+	3942.86i	0.324522	+	0.167303i
$823$	−1210.83	−	4991.11i	−0.0512842	−	0.211396i	0.940404	−	0.340059i	$-0.110447\pi$
$823$	−1210.83	−	4991.11i	−0.0512842	−	0.211396i	−0.991688	+	0.128662i	$0.958932\pi$
$824$	−12728.4	−	5095.67i	−0.538123	−	0.215432i
$825$	12302.6	+	1174.76i	0.519178	+	0.0495755i
$826$	3111.18	−	21638.7i	0.131056	−	0.911511i
$827$	15747.8	−	12384.2i	0.662158	−	0.520727i	−0.229574	−	0.973291i	$-0.573733\pi$
$827$	15747.8	−	12384.2i	0.662158	−	0.520727i	0.891732	+	0.452565i	$0.149491\pi$
$828$	3963.15	+	2546.96i	0.166339	+	0.106900i
$829$	−1923.38	−	2219.70i	−0.0805811	−	0.0929956i	0.714027	−	0.700118i	$-0.246869\pi$
$829$	−1923.38	−	2219.70i	−0.0805811	−	0.0929956i	−0.794608	+	0.607122i	$0.792324\pi$
$830$	12175.3	−	6276.81i	0.509170	−	0.262496i
$831$	8987.07	+	19678.9i	0.375160	+	0.821486i
$832$	13679.4	+	2636.49i	0.570011	+	0.109861i
$833$	−897.330	+	1554.22i	−0.0373237	+	0.0646466i
$834$	2205.63	+	3820.26i	0.0915764	+	0.158615i
$835$	835.019	+	2412.63i	0.0346072	+	0.0999910i
$836$	57576.8	+	45278.9i	2.38198	+	1.87321i
$837$	831.598	−	792.927i	0.0343420	−	0.0327450i
$838$	−45003.7	+	42911.0i	−1.85517	+	1.76890i
$839$	−29968.4	−	23567.4i	−1.23316	−	0.969769i	−0.233166	−	0.972437i	$-0.574908\pi$
$839$	−29968.4	−	23567.4i	−1.23316	−	0.969769i	−0.999996	+	0.00266752i	$0.999151\pi$
$840$	1312.67	+	3792.71i	0.0539183	+	0.155787i
$841$	8037.24	+	13920.9i	0.329544	+	0.570787i
$842$	−32517.2	+	56321.5i	−1.33090	+	2.30518i
$843$	−621.593	−	119.802i	−0.0253960	−	0.00489467i
$844$	−30472.8	−	66726.0i	−1.24279	−	2.72133i
$845$	−5863.56	+	3022.87i	−0.238713	+	0.123065i
$846$	8299.02	+	9577.58i	0.337265	+	0.389224i
$847$	76.9263	+	49.4376i	0.00312068	+	0.00200554i
$848$	592.836	−	466.212i	0.0240072	−	0.0188794i
$849$	1446.83	−	10062.9i	0.0584864	−	0.406782i
$850$	5930.37	+	566.282i	0.239306	+	0.0228509i
$851$	−7438.08	−	2977.76i	−0.299617	−	0.119949i
$852$	−10720.4	−	44190.0i	−0.431073	−	1.77691i
$853$	26076.3	+	13443.2i	1.04670	+	0.539611i	0.893723	−	0.448619i	$-0.148084\pi$
$853$	26076.3	+	13443.2i	1.04670	+	0.539611i	0.152976	+	0.988230i	$0.451114\pi$
$854$	10.1255	−	212.560i	0.000405723	−	0.00851717i
$855$	4512.81	−	430.921i	0.180509	−	0.0172365i
$856$	7426.58	+	2180.64i	0.296537	+	0.0870710i
$857$	−24925.2	+	16018.5i	−0.993501	+	0.638484i	−0.933073	−	0.359688i	$-0.882883\pi$
$857$	−24925.2	+	16018.5i	−0.993501	+	0.638484i	−0.0604284	+	0.998173i	$0.519247\pi$
$858$	−3015.63	+	8713.10i	−0.119991	+	0.346690i
$859$	10168.3	−	1959.78i	0.403886	−	0.0778426i	0.0167372	−	0.999860i	$-0.494672\pi$
$859$	10168.3	−	1959.78i	0.403886	−	0.0778426i	0.387149	+	0.922017i	$0.373460\pi$
$860$	−4329.16	−	6079.46i	−0.171655	−	0.241056i
$861$	4828.54	−	1933.06i	0.191122	−	0.0765138i
$862$	28580.1	−	8391.87i	1.12928	−	0.331587i
$863$	13916.3	−	16060.2i	0.548917	−	0.633483i	−0.411714	−	0.911313i	$-0.635070\pi$
$863$	13916.3	−	16060.2i	0.548917	−	0.633483i	0.960630	+	0.277830i	$0.0896151\pi$
$864$	−841.869	+	3470.23i	−0.0331493	+	0.136643i
$865$	−5253.45	+	7377.43i	−0.206500	+	0.289989i
$866$	−26402.2	+	57812.8i	−1.03601	+	2.26854i
$867$	683.144	+	14340.9i	0.0267598	+	0.561758i
$868$	1148.47	+	7987.76i	0.0449095	+	0.312353i
$869$	8995.81	+	8577.49i	0.351165	+	0.334835i
$870$	−4510.60			−0.175774
$871$	3738.79	+	9090.04i	0.145447	+	0.353621i
$872$	−33171.1			−1.28821
$873$	−8522.99	−	8126.66i	−0.330423	−	0.315058i
$874$	3577.60	+	24882.8i	0.138460	+	0.963012i
$875$	539.274	+	11320.8i	0.0208352	+	0.437385i
$876$	−7943.70	+	17394.3i	−0.306384	+	0.670888i
$877$	−18355.5	+	25776.7i	−0.706752	+	0.992495i	0.292590	+	0.956238i	$0.405483\pi$
$877$	−18355.5	+	25776.7i	−0.706752	+	0.992495i	−0.999343	+	0.0362567i	$0.988457\pi$
$878$	−17590.4	+	72508.6i	−0.676136	+	2.78707i
$879$	−11760.7	+	13572.6i	−0.451284	+	0.520810i
$880$	−2425.57	+	712.213i	−0.0929160	+	0.0272826i
$881$	−19083.7	+	7639.96i	−0.729791	+	0.292164i	−0.706646	−	0.707568i	$-0.749792\pi$
$881$	−19083.7	+	7639.96i	−0.729791	+	0.292164i	−0.0231457	+	0.999732i	$0.507368\pi$
$882$	3893.89	+	5468.20i	0.148655	+	0.208757i
$883$	35178.3	−	6780.05i	1.34071	−	0.258400i	0.532065	−	0.846703i	$-0.321416\pi$
$883$	35178.3	−	6780.05i	1.34071	−	0.258400i	0.808640	+	0.588304i	$0.200204\pi$
$884$	−924.639	+	2671.57i	−0.0351798	+	0.101645i
$885$	3051.62	−	1961.16i	0.115909	−	0.0744899i
$886$	−29543.8	−	8674.86i	−1.12025	−	0.328936i
$887$	−30925.4	+	2953.02i	−1.17066	+	0.111784i	−0.662217	−	0.749312i	$-0.730384\pi$
$887$	−30925.4	+	2953.02i	−1.17066	+	0.111784i	−0.508442	+	0.861096i	$0.669778\pi$
$888$	−856.949	+	17989.6i	−0.0323844	+	0.679832i
$889$	−10011.1	−	5161.06i	−0.377683	−	0.194709i
$890$	1859.01	+	7662.95i	0.0700160	+	0.288610i
$891$	−2750.37	−	1101.08i	−0.103413	−	0.0414003i
$892$	−34712.6	−	3314.65i	−1.30299	−	0.124420i
$893$	−6121.61	+	42576.8i	−0.229398	+	1.59550i
$894$	−15763.6	+	12396.6i	−0.589725	+	0.463764i
$895$	13274.9	+	8531.25i	0.495788	+	0.318624i
$896$	−22969.9	−	26508.6i	−0.856439	−	0.988384i
$897$	−1789.03	+	922.308i	−0.0665930	+	0.0343311i
$898$	7120.13	+	15590.9i	0.264590	+	0.579371i
$899$	−3810.39	−	734.392i	−0.141361	−	0.0272451i
$900$	7087.00	−	12275.0i	0.262481	−	0.454631i
$901$	−216.458	−	374.917i	−0.00800363	−	0.0138627i
$902$	7170.18	+	20716.9i	0.264680	+	0.764742i
$903$	4853.67	+	3816.97i	0.178870	+	0.140665i
$904$	−7227.02	+	6890.95i	−0.265893	+	0.253528i
$905$	−469.608	+	447.770i	−0.0172489	+	0.0164468i
$906$	−13786.3	−	10841.7i	−0.505539	−	0.397561i
$907$	186.752	+	539.585i	0.00683683	+	0.0197537i	0.948368	−	0.317173i	$-0.102734\pi$
$907$	186.752	+	539.585i	0.00683683	+	0.0197537i	−0.941531	+	0.336927i	$0.890612\pi$
$908$	−25606.6	−	44352.0i	−0.935888	−	1.62101i
$909$	−1154.44	+	1999.55i	−0.0421236	+	0.0729602i
$910$	−3935.28	−	758.464i	−0.143355	−	0.0276295i
$911$	−12751.7	−	27922.4i	−0.463758	−	1.01549i	−0.986615	−	0.163067i	$-0.947861\pi$
$911$	−12751.7	−	27922.4i	−0.463758	−	1.01549i	0.522857	−	0.852420i	$-0.324866\pi$
$912$	7505.75	−	3869.48i	0.272522	−	0.140495i
$913$	−19897.5	−	22963.0i	−0.721262	−	0.832380i
$914$	−50589.3	−	32511.8i	−1.83079	−	1.17658i
$915$	27.7559	−	21.8275i	0.00100282	−	0.000788626i
$916$	6825.67	−	47473.6i	0.246208	−	1.71241i
$917$	−6311.16	−	602.643i	−0.227277	−	0.0217023i
$918$	−1325.79	−	530.768i	−0.0476664	−	0.0190827i
$919$	−8936.85	−	36838.2i	−0.320783	−	1.32228i	−0.872647	−	0.488351i	$-0.837599\pi$
$919$	−8936.85	−	36838.2i	−0.320783	−	1.32228i	0.551865	−	0.833934i	$-0.313917\pi$
$920$	−3282.40	−	1692.19i	−0.117628	−	0.0606413i
$921$	−643.216	+	13502.8i	−0.0230127	+	0.483096i
$922$	−59954.1	+	5724.93i	−2.14152	+	0.204491i
$923$	18640.9	+	5473.45i	0.664758	+	0.195191i
$924$	17503.8	−	11249.0i	0.623195	−	0.400503i
$925$	−7884.20	+	22779.9i	−0.280250	+	0.809728i
$926$	43310.2	−	8347.36i	1.53700	−	0.296233i
$927$	2551.72	+	3583.39i	0.0904093	+	0.126962i
$928$	11195.7	−	4482.08i	0.396031	−	0.158547i
$929$	−40611.9	+	11924.7i	−1.43427	+	0.421138i	−0.904306	−	0.426885i	$-0.859611\pi$
$929$	−40611.9	+	11924.7i	−1.43427	+	0.421138i	−0.529959	+	0.848023i	$0.677793\pi$
$930$	−1378.59	+	1590.98i	−0.0486084	+	0.0560971i
$931$	−5371.79	+	22142.8i	−0.189101	+	0.779486i
$932$	−36093.0	+	50685.5i	−1.26852	+	1.78139i
$933$	2666.14	−	5838.03i	0.0935535	−	0.204854i
$934$	−3073.98	−	64530.7i	−0.107691	−	2.26072i
$935$	206.511	+	1436.32i	0.00722315	+	0.0502381i
$936$	3274.52	+	3122.25i	0.114349	+	0.109032i
$937$	10283.2			0.358525			0.179263	−	0.983801i	$-0.442629\pi$
$937$	10283.2			0.358525			0.179263	+	0.983801i	$0.442629\pi$
$938$	9508.74	−	33549.2i	0.330993	−	1.16782i
$939$	18627.4			0.647373
$940$	−10688.5	−	10191.5i	−0.370874	−	0.353628i
$941$	768.899	+	5347.81i	0.0266370	+	0.185264i	0.998796	−	0.0490582i	$-0.0156220\pi$
$941$	768.899	+	5347.81i	0.0266370	+	0.185264i	−0.972159	+	0.234322i	$0.924713\pi$
$942$	1338.11	+	28090.3i	0.0462822	+	0.971583i
$943$	−1988.06	+	4353.25i	−0.0686535	+	0.150330i
$944$	3919.48	−	5504.14i	0.135136	−	0.189772i
$945$	303.595	−	1251.44i	0.0104508	−	0.0430786i
$946$	−17043.7	+	19669.5i	−0.585770	+	0.676015i
$947$	−46984.8	+	13796.0i	−1.61225	+	0.473400i	−0.958921	−	0.283673i	$-0.908447\pi$
$947$	−46984.8	+	13796.0i	−1.61225	+	0.473400i	−0.653330	+	0.757073i	$0.726629\pi$
$948$	13234.4	−	5298.27i	0.453412	−	0.181519i
$949$	−4739.08	−	6655.10i	−0.162104	−	0.227644i
$950$	74267.9	−	14314.0i	2.53639	−	0.488849i
$951$	1426.43	−	4121.39i	0.0486383	−	0.140531i
$952$	3610.11	−	2320.08i	0.122904	−	0.0789854i
$953$	−14097.8	−	4139.49i	−0.479195	−	0.140704i	0.0332098	−	0.999448i	$-0.489427\pi$
$953$	−14097.8	−	4139.49i	−0.479195	−	0.140704i	−0.512405	+	0.858744i	$0.671245\pi$
$954$	−1611.99	+	153.927i	−0.0547067	+	0.00522386i
$955$	687.699	−	14436.6i	0.0233020	−	0.489169i
$956$	−36531.0	−	18833.1i	−1.23588	−	0.637138i
$957$	2358.82	+	9723.17i	0.0796758	+	0.328428i
$958$	24539.4	+	9824.11i	0.827592	+	0.331318i
$959$	8258.60	+	788.601i	0.278086	+	0.0265540i
$960$	1167.14	−	8117.61i	0.0392387	−	0.272911i
$961$	21993.7	−	17296.0i	0.738266	−	0.580579i
$962$	−15129.3	−	9723.01i	−0.507056	−	0.325865i
$963$	−1626.32	−	1876.87i	−0.0544210	−	0.0628052i
$964$	20356.3	−	10494.4i	0.680115	−	0.350624i
$965$	1249.32	+	2735.62i	0.0416756	+	0.0912568i
$966$	7011.82	+	1351.42i	0.233542	+	0.0450116i
$967$	26729.5	−	46296.9i	0.888898	−	1.53962i	0.0477179	−	0.998861i	$-0.484805\pi$
$967$	26729.5	−	46296.9i	0.888898	−	1.53962i	0.841180	−	0.540755i	$-0.181862\pi$
$968$	94.5677	+	163.796i	0.00314000	+	0.00543864i
$969$	−1585.37	−	4580.64i	−0.0525589	−	0.151859i
$970$	16959.7	+	13337.2i	0.561384	+	0.441477i
$971$	−33640.5	+	32076.2i	−1.11182	+	1.06012i	−0.114041	+	0.993476i	$0.536380\pi$
$971$	−33640.5	+	32076.2i	−1.11182	+	1.06012i	−0.997777	+	0.0666404i	$0.978772\pi$
$972$	−2459.09	+	2344.74i	−0.0811475	+	0.0773740i
$973$	3343.19	+	2629.12i	0.110152	+	0.0866245i
$974$	9894.20	+	28587.4i	0.325494	+	0.940452i
$975$	3027.92	+	5244.52i	0.0994576	+	0.172266i
$976$	32.8872	−	56.9624i	0.00107858	−	0.00186816i
$977$	4672.32	+	900.515i	0.153000	+	0.0294883i	0.265176	−	0.964200i	$-0.414570\pi$
$977$	4672.32	+	900.515i	0.153000	+	0.0294883i	−0.112176	+	0.993688i	$0.535782\pi$
$978$	−18700.5	−	40948.4i	−0.611428	−	1.33884i
$979$	15546.3	−	8014.67i	0.507519	−	0.261644i
$980$	−5122.99	−	5912.24i	−0.166988	−	0.192714i
$981$	8953.58	+	5754.11i	0.291402	+	0.187273i
$982$	−12678.5	+	9970.46i	−0.412002	+	0.324002i
$983$	226.086	−	1572.47i	0.00733574	−	0.0510212i	−0.985825	−	0.167778i	$-0.946341\pi$
$983$	226.086	−	1572.47i	0.00733574	−	0.0510212i	0.993161	+	0.116757i	$0.0372499\pi$
$984$	10709.0	+	1022.59i	0.346942	+	0.0331289i
$985$	−13216.5	−	5291.10i	−0.427527	−	0.171156i
$986$	1137.05	+	4686.97i	0.0367251	+	0.151383i
$987$	10860.4	+	5598.93i	0.350244	+	0.180563i
$988$	−1707.83	+	35851.8i	−0.0549932	+	1.15445i
$989$	−5655.87	+	540.070i	−0.181847	+	0.0173642i
$990$	5207.94	+	1529.19i	0.167191	+	0.0490917i
$991$	46512.3	−	29891.6i	1.49093	−	0.958162i	0.494918	−	0.868940i	$-0.335198\pi$
$991$	46512.3	−	29891.6i	1.49093	−	0.958162i	0.996012	−	0.0892229i	$-0.0284383\pi$
$992$	1840.86	−	5318.82i	0.0589187	−	0.170235i
$993$	−17109.8	+	3297.65i	−0.546791	+	0.105385i
$994$	−39980.7	−	56145.0i	−1.27576	−	1.79156i
$995$	10976.0	−	4394.12i	0.349710	−	0.140003i
$996$	−33436.1	+	9817.73i	−1.06372	+	0.312336i
$997$	33899.0	−	39121.5i	1.07682	−	1.24272i	0.108214	−	0.994128i	$-0.465487\pi$
$997$	33899.0	−	39121.5i	1.07682	−	1.24272i	0.968608	−	0.248592i	$-0.0799678\pi$
$998$	12591.9	−	51904.6i	0.399389	−	1.64630i
$999$	3351.92	−	4707.11i	0.106156	−	0.149075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.m.b.10.2	✓	360
67.47	even	33	inner	201.4.m.b.181.2	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.m.b.10.2	✓	360	1.1	even	1	trivial
201.4.m.b.181.2	yes	360	67.47	even	33	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.39327 - 3.23548i) q^{2} +(0.426945 + 2.96946i) q^{3} +(0.665321 + 13.9668i) q^{4} +(-1.46096 + 3.19905i) q^{5} +(8.15890 - 11.4576i) q^{6} +(3.19725 - 13.1792i) q^{7} +(18.3688 - 21.1988i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)	\(q+(-3.39327 - 3.23548i) q^{2} +(0.426945 + 2.96946i) q^{3} +(0.665321 + 13.9668i) q^{4} +(-1.46096 + 3.19905i) q^{5} +(8.15890 - 11.4576i) q^{6} +(3.19725 - 13.1792i) q^{7} +(18.3688 - 21.1988i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(15.3079 - 6.12835i) q^{10} +(-21.2157 - 29.7933i) q^{11} +(-41.1899 + 7.93870i) q^{12} +(5.86180 - 16.9366i) q^{13} +(-53.4903 + 34.3761i) q^{14} +(-10.1232 - 2.97244i) q^{15} +(-19.5641 + 1.86815i) q^{16} +(-0.536777 + 11.2683i) q^{17} +(37.5063 + 19.3358i) q^{18} +(33.7667 + 139.188i) q^{19} +(-45.6525 - 18.2765i) q^{20} +(40.5003 + 3.86731i) q^{21} +(-24.4049 + 169.740i) q^{22} +(-29.4262 + 23.1410i) q^{23} +(70.7915 + 45.4949i) q^{24} +(73.7581 + 85.1214i) q^{25} +(-74.6886 + 38.5046i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(186.199 + 35.8869i) q^{28} +(-45.5920 + 78.9676i) q^{29} +(24.7335 + 42.8398i) q^{30} +(13.9190 + 40.2164i) q^{31} +(-103.960 - 81.7547i) q^{32} +(79.4121 - 75.7193i) q^{33} +(38.2799 - 36.4998i) q^{34} +(37.4900 + 29.4824i) q^{35} +(-41.1595 - 118.922i) q^{36} +(107.011 + 185.349i) q^{37} +(335.761 - 581.555i) q^{38} +(52.7952 + 10.1754i) q^{39} +(40.9798 + 89.7333i) q^{40} +(113.629 - 58.5796i) q^{41} +(-124.916 - 144.161i) q^{42} +(127.678 + 82.0536i) q^{43} +(402.001 - 316.137i) q^{44} +(4.50451 - 31.3296i) q^{45} +(174.723 + 16.6840i) q^{46} +(278.815 + 111.621i) q^{47} +(-13.9002 - 57.2973i) q^{48} +(141.401 + 72.8971i) q^{49} +(25.1271 - 527.483i) q^{50} +(-33.6901 + 3.21702i) q^{51} +(240.450 + 70.6024i) q^{52} +(-32.2834 + 20.7473i) q^{53} +(-41.4039 + 119.629i) q^{54} +(126.305 - 24.3433i) q^{55} +(-220.654 - 309.865i) q^{56} +(-398.898 + 159.695i) q^{57} +(410.204 - 120.447i) q^{58} +(-225.152 + 259.839i) q^{59} +(34.7803 - 143.366i) q^{60} +(-1.94132 + 2.72620i) q^{61} +(82.8882 - 181.500i) q^{62} +(5.80755 + 121.915i) q^{63} +(110.623 + 769.400i) q^{64} +(45.6170 + 43.4958i) q^{65} -514.455 q^{66} +(-411.067 + 363.024i) q^{67} -157.740 q^{68} +(-81.2797 - 77.5000i) q^{69} +(-31.8239 - 221.340i) q^{70} +(51.5791 + 1082.78i) q^{71} +(-104.872 + 229.637i) q^{72} +(264.424 - 371.331i) q^{73} +(236.574 - 975.171i) q^{74} +(-221.274 + 255.364i) q^{75} +(-1921.55 + 564.218i) q^{76} +(-460.484 + 184.350i) q^{77} +(-146.226 - 205.346i) q^{78} +(-333.699 + 64.3152i) q^{79} +(22.6060 - 65.3158i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-575.106 - 168.866i) q^{82} +(826.976 - 78.9666i) q^{83} +(-27.0683 + 568.233i) q^{84} +(-35.2638 - 18.1797i) q^{85} +(-167.763 - 691.530i) q^{86} +(-253.957 - 101.669i) q^{87} +(-1021.29 - 97.5212i) q^{88} +(-68.0564 + 473.343i) q^{89} +(-116.651 + 91.7356i) q^{90} +(-204.469 - 131.404i) q^{91} +(-342.783 - 395.593i) q^{92} +(-113.478 + 58.5022i) q^{93} +(-584.948 - 1280.86i) q^{94} +(-494.602 - 95.3267i) q^{95} +(198.383 - 343.609i) q^{96} +(654.245 + 1133.19i) q^{97} +(-243.954 - 704.859i) q^{98} +(258.750 + 203.483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9}+O(q^{10}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9} + 19 q^{10} + 192 q^{11} - 105 q^{12} + 46 q^{13} - 14 q^{14} + 54 q^{15} + 346 q^{16} + 228 q^{17} - 18 q^{18} + 88 q^{19} + 180 q^{20} + 66 q^{21} - 247 q^{22} + 676 q^{23} + 144 q^{24} - 1120 q^{25} + 333 q^{26} + 972 q^{27} - 3894 q^{28} - 2210 q^{29} + 702 q^{30} + 96 q^{31} - 1970 q^{32} - 708 q^{33} - 26 q^{34} + 1272 q^{35} + 315 q^{36} - 3616 q^{37} - 20 q^{38} - 138 q^{39} - 5357 q^{40} + 288 q^{41} - 618 q^{42} - 1680 q^{43} + 2951 q^{44} + 36 q^{45} - 1125 q^{46} - 40 q^{47} - 1038 q^{48} - 4954 q^{49} - 3590 q^{50} - 90 q^{51} + 9120 q^{52} + 3896 q^{53} + 54 q^{54} - 1076 q^{55} + 3557 q^{56} + 660 q^{57} + 3232 q^{58} + 116 q^{59} + 3618 q^{60} - 672 q^{61} + 3882 q^{62} - 1584 q^{63} - 11581 q^{64} - 15380 q^{65} - 5166 q^{66} - 288 q^{67} + 13898 q^{68} - 1632 q^{69} - 5058 q^{70} - 15102 q^{71} - 2016 q^{72} - 146 q^{73} - 3531 q^{74} + 3360 q^{75} + 10770 q^{76} + 3594 q^{77} + 1905 q^{78} + 2852 q^{79} + 27997 q^{80} - 2916 q^{81} + 8824 q^{82} + 5278 q^{83} + 6765 q^{84} - 5290 q^{85} + 5973 q^{86} + 228 q^{87} + 13872 q^{88} + 1462 q^{89} + 171 q^{90} + 74 q^{91} - 3144 q^{92} + 3144 q^{93} + 3262 q^{94} + 1600 q^{95} - 855 q^{96} + 6626 q^{97} + 15491 q^{98} + 144 q^{99}+O(q^{100}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9 + 19 * q^10 + 192 * q^11 - 105 * q^12 + 46 * q^13 - 14 * q^14 + 54 * q^15 + 346 * q^16 + 228 * q^17 - 18 * q^18 + 88 * q^19 + 180 * q^20 + 66 * q^21 - 247 * q^22 + 676 * q^23 + 144 * q^24 - 1120 * q^25 + 333 * q^26 + 972 * q^27 - 3894 * q^28 - 2210 * q^29 + 702 * q^30 + 96 * q^31 - 1970 * q^32 - 708 * q^33 - 26 * q^34 + 1272 * q^35 + 315 * q^36 - 3616 * q^37 - 20 * q^38 - 138 * q^39 - 5357 * q^40 + 288 * q^41 - 618 * q^42 - 1680 * q^43 + 2951 * q^44 + 36 * q^45 - 1125 * q^46 - 40 * q^47 - 1038 * q^48 - 4954 * q^49 - 3590 * q^50 - 90 * q^51 + 9120 * q^52 + 3896 * q^53 + 54 * q^54 - 1076 * q^55 + 3557 * q^56 + 660 * q^57 + 3232 * q^58 + 116 * q^59 + 3618 * q^60 - 672 * q^61 + 3882 * q^62 - 1584 * q^63 - 11581 * q^64 - 15380 * q^65 - 5166 * q^66 - 288 * q^67 + 13898 * q^68 - 1632 * q^69 - 5058 * q^70 - 15102 * q^71 - 2016 * q^72 - 146 * q^73 - 3531 * q^74 + 3360 * q^75 + 10770 * q^76 + 3594 * q^77 + 1905 * q^78 + 2852 * q^79 + 27997 * q^80 - 2916 * q^81 + 8824 * q^82 + 5278 * q^83 + 6765 * q^84 - 5290 * q^85 + 5973 * q^86 + 228 * q^87 + 13872 * q^88 + 1462 * q^89 + 171 * q^90 + 74 * q^91 - 3144 * q^92 + 3144 * q^93 + 3262 * q^94 + 1600 * q^95 - 855 * q^96 + 6626 * q^97 + 15491 * q^98 + 144 * q^99

Introduction

L-functions

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