LMFDB - Embedded newform 201.4.m.b.4.16

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			4.16
Character	$\chi$	$=$	201.4
Dual form			201.4.m.b.151.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.21003 + 0.402009i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(9.70733 + 1.87093i) q^{4} +(-0.265215 - 1.84461i) q^{5} +(-9.97308 - 7.84292i) q^{6} +(17.7472 - 24.9224i) q^{7} +(7.65306 + 2.24714i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})$	\(q+(4.21003 + 0.402009i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(9.70733 + 1.87093i) q^{4} +(-0.265215 - 1.84461i) q^{5} +(-9.97308 - 7.84292i) q^{6} +(17.7472 - 24.9224i) q^{7} +(7.65306 + 2.24714i) q^{8} +(3.73874 + 8.18669i) q^{9} +(-0.375013 - 7.87250i) q^{10} +(1.61925 - 1.27339i) q^{11} +(-21.4645 - 20.4663i) q^{12} +(2.52071 - 10.3905i) q^{13} +(84.7352 - 97.7896i) q^{14} +(-2.32248 + 5.08552i) q^{15} +(-42.1064 - 16.8568i) q^{16} +(74.1341 - 14.2882i) q^{17} +(12.4491 + 35.9692i) q^{18} +(-59.2415 - 83.1930i) q^{19} +(0.876617 - 18.4025i) q^{20} +(-85.2118 + 34.1137i) q^{21} +(7.32901 - 4.71007i) q^{22} +(79.8142 - 41.1471i) q^{23} +(-15.6698 - 18.0839i) q^{24} +(116.604 - 34.2381i) q^{25} +(14.7894 - 42.7311i) q^{26} +(3.84250 - 26.7252i) q^{27} +(218.906 - 208.726i) q^{28} +(91.4718 + 158.434i) q^{29} +(-11.8221 + 20.4765i) q^{30} +(39.9618 + 164.725i) q^{31} +(-227.208 - 117.134i) q^{32} +(-6.15194 + 0.587440i) q^{33} +(317.851 - 30.3511i) q^{34} +(-50.6790 - 26.1268i) q^{35} +(20.9764 + 86.4658i) q^{36} +(-199.312 + 345.219i) q^{37} +(-215.964 - 374.061i) q^{38} +(-23.2143 + 22.1348i) q^{39} +(2.11540 - 14.7129i) q^{40} +(16.7987 - 48.5367i) q^{41} +(-372.459 + 109.364i) q^{42} +(-166.317 - 191.941i) q^{43} +(18.1010 - 9.33173i) q^{44} +(14.1097 - 9.06775i) q^{45} +(352.562 - 141.144i) q^{46} +(-17.6689 + 370.915i) q^{47} +(78.9259 + 110.836i) q^{48} +(-193.980 - 560.469i) q^{49} +(504.672 - 97.2676i) q^{50} +(-210.271 - 84.1798i) q^{51} +(43.9094 - 96.1481i) q^{52} +(-265.559 + 306.471i) q^{53} +(26.9208 - 110.969i) q^{54} +(-2.77837 - 2.64917i) q^{55} +(191.824 - 150.852i) q^{56} +(14.5787 + 306.044i) q^{57} +(321.407 + 703.784i) q^{58} +(-500.387 - 146.927i) q^{59} +(-32.0597 + 45.0216i) q^{60} +(535.886 + 421.425i) q^{61} +(102.020 + 709.562i) q^{62} +(270.384 + 52.1122i) q^{63} +(-604.223 - 388.311i) q^{64} +(-19.8350 - 1.89402i) q^{65} -26.1360 q^{66} +(-445.783 + 319.438i) q^{67} +746.376 q^{68} +(-268.169 - 25.6071i) q^{69} +(-202.857 - 130.368i) q^{70} +(371.373 + 71.5762i) q^{71} +(10.2161 + 71.0546i) q^{72} +(248.522 + 195.440i) q^{73} +(-977.893 + 1373.26i) q^{74} +(-349.813 - 102.714i) q^{75} +(-419.428 - 918.418i) q^{76} +(-2.99890 - 62.9547i) q^{77} +(-106.631 + 83.8558i) q^{78} +(201.509 + 192.139i) q^{79} +(-19.9271 + 82.1406i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(90.2354 - 197.588i) q^{82} +(520.980 + 208.569i) q^{83} +(-891.003 + 171.727i) q^{84} +(-46.0176 - 132.959i) q^{85} +(-623.040 - 874.937i) q^{86} +(26.1144 - 548.209i) q^{87} +(15.2537 - 6.10666i) q^{88} +(1253.07 - 805.302i) q^{89} +(63.0476 - 32.5033i) q^{90} +(-214.221 - 247.225i) q^{91} +(851.766 - 250.101i) q^{92} +(166.317 - 480.541i) q^{93} +(-223.498 + 1554.46i) q^{94} +(-137.747 + 131.342i) q^{95} +(383.437 + 664.133i) q^{96} +(-335.457 + 581.028i) q^{97} +(-591.349 - 2437.58i) q^{98} +(16.4788 + 8.49542i) 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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

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

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 $

$2$	4.21003	+	0.402009i	1.48847	+	0.142132i	0.807365	−	0.590053i	$-0.200893\pi$
$2$	4.21003	+	0.402009i	1.48847	+	0.142132i	0.681106	+	0.732185i	$0.261499\pi$
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$4$	9.70733	+	1.87093i	1.21342	+	0.233867i
$5$	−0.265215	−	1.84461i	−0.0237216	−	0.164987i	0.974517	−	0.224313i	$-0.0720139\pi$
$5$	−0.265215	−	1.84461i	−0.0237216	−	0.164987i	−0.998239	+	0.0593262i	$0.981105\pi$
$6$	−9.97308	−	7.84292i	−0.678582	−	0.533643i
$7$	17.7472	−	24.9224i	0.958257	−	1.34568i	0.0199795	−	0.999800i	$-0.493640\pi$
$7$	17.7472	−	24.9224i	0.958257	−	1.34568i	0.938278	−	0.345883i	$-0.112421\pi$
$8$	7.65306	+	2.24714i	0.338220	+	0.0993105i
$9$	3.73874	+	8.18669i	0.138472	+	0.303211i
$10$	−0.375013	−	7.87250i	−0.0118590	−	0.248950i
$11$	1.61925	−	1.27339i	0.0443839	−	0.0349038i	−0.595721	−	0.803192i	$-0.703133\pi$
$11$	1.61925	−	1.27339i	0.0443839	−	0.0349038i	0.640105	+	0.768288i	$0.278891\pi$
$12$	−21.4645	−	20.4663i	−0.516355	−	0.492343i
$13$	2.52071	−	10.3905i	0.0537785	−	0.221678i	−0.938581	−	0.345059i	$-0.887859\pi$
$13$	2.52071	−	10.3905i	0.0537785	−	0.221678i	0.992359	+	0.123382i	$0.0393739\pi$
$14$	84.7352	−	97.7896i	1.61760	−	1.86681i
$15$	−2.32248	+	5.08552i	−0.0399774	+	0.0875383i
$16$	−42.1064	−	16.8568i	−0.657912	−	0.263388i
$17$	74.1341	−	14.2882i	1.05766	−	0.203847i	0.369368	−	0.929283i	$-0.379574\pi$
$17$	74.1341	−	14.2882i	1.05766	−	0.203847i	0.688289	+	0.725437i	$0.258362\pi$
$18$	12.4491	+	35.9692i	0.163015	+	0.471001i
$19$	−59.2415	−	83.1930i	−0.715312	−	1.00451i	−0.998960	−	0.0455864i	$-0.985484\pi$
$19$	−59.2415	−	83.1930i	−0.715312	−	1.00451i	0.283649	−	0.958928i	$-0.408455\pi$
$20$	0.876617	−	18.4025i	0.00980087	−	0.205746i
$21$	−85.2118	+	34.1137i	−0.885464	+	0.354486i
$22$	7.32901	−	4.71007i	0.0710250	−	0.0456450i
$23$	79.8142	−	41.1471i	0.723583	−	0.373033i	−0.0567574	−	0.998388i	$-0.518076\pi$
$23$	79.8142	−	41.1471i	0.723583	−	0.373033i	0.780340	+	0.625355i	$0.215046\pi$
$24$	−15.6698	−	18.0839i	−0.133274	−	0.153807i
$25$	116.604	−	34.2381i	0.932835	−	0.273905i
$26$	14.7894	−	42.7311i	0.111555	−	0.322318i
$27$	3.84250	−	26.7252i	0.0273885	−	0.190491i
$28$	218.906	−	208.726i	1.47747	−	1.40877i
$29$	91.4718	+	158.434i	0.585720	+	1.01450i	0.994785	+	0.101992i	$0.0325215\pi$
$29$	91.4718	+	158.434i	0.585720	+	1.01450i	−0.409065	+	0.912505i	$0.634145\pi$
$30$	−11.8221	+	20.4765i	−0.0719472	+	0.124616i
$31$	39.9618	+	164.725i	0.231528	+	0.954370i	0.962352	+	0.271805i	$0.0876205\pi$
$31$	39.9618	+	164.725i	0.231528	+	0.954370i	−0.730825	+	0.682565i	$0.760864\pi$
$32$	−227.208	−	117.134i	−1.25516	−	0.647080i
$33$	−6.15194	+	0.587440i	−0.0324520	+	0.00309879i
$34$	317.851	−	30.3511i	1.60326	−	0.153093i
$35$	−50.6790	−	26.1268i	−0.244752	−	0.126178i
$36$	20.9764	+	86.4658i	0.0971128	+	0.400305i
$37$	−199.312	+	345.219i	−0.885588	+	1.53388i	−0.0405500	+	0.999178i	$0.512911\pi$
$37$	−199.312	+	345.219i	−0.885588	+	1.53388i	−0.845038	+	0.534706i	$0.820422\pi$
$38$	−215.964	−	374.061i	−0.921947	−	1.59686i
$39$	−23.2143	+	22.1348i	−0.0953145	+	0.0908822i
$40$	2.11540	−	14.7129i	0.00836183	−	0.0581578i
$41$	16.7987	−	48.5367i	0.0639883	−	0.184882i	−0.908474	−	0.417940i	$-0.862752\pi$
$41$	16.7987	−	48.5367i	0.0639883	−	0.184882i	0.972463	+	0.233058i	$0.0748733\pi$
$42$	−372.459	+	109.364i	−1.36837	+	0.401790i
$43$	−166.317	−	191.941i	−0.589841	−	0.680713i	0.379850	−	0.925048i	$-0.375976\pi$
$43$	−166.317	−	191.941i	−0.589841	−	0.680713i	−0.969691	+	0.244335i	$0.921430\pi$
$44$	18.1010	−	9.33173i	0.0620189	−	0.0319730i
$45$	14.1097	−	9.06775i	0.0467411	−	0.0300387i
$46$	352.562	−	141.144i	1.13005	−	0.452405i
$47$	−17.6689	+	370.915i	−0.0548355	+	1.15114i	0.788950	+	0.614458i	$0.210625\pi$
$47$	−17.6689	+	370.915i	−0.0548355	+	1.15114i	−0.843785	+	0.536681i	$0.819678\pi$
$48$	78.9259	+	110.836i	0.237333	+	0.333287i
$49$	−193.980	−	560.469i	−0.565540	−	1.63402i
$50$	504.672	−	97.2676i	1.42743	−	0.275114i
$51$	−210.271	−	84.1798i	−0.577330	−	0.231128i
$52$	43.9094	−	96.1481i	0.117099	−	0.256411i
$53$	−265.559	+	306.471i	−0.688251	+	0.794284i	−0.987115	−	0.160011i	$-0.948847\pi$
$53$	−265.559	+	306.471i	−0.688251	+	0.794284i	0.298864	+	0.954296i	$0.403392\pi$
$54$	26.9208	−	110.969i	0.0678418	−	0.279648i
$55$	−2.77837	−	2.64917i	−0.00681154	−	0.00649479i
$56$	191.824	−	150.852i	0.457743	−	0.359973i
$57$	14.5787	+	306.044i	0.0338771	+	0.711167i
$58$	321.407	+	703.784i	0.727635	+	1.59330i
$59$	−500.387	−	146.927i	−1.10415	−	0.324207i	−0.321650	−	0.946859i	$-0.604237\pi$
$59$	−500.387	−	146.927i	−1.10415	−	0.324207i	−0.782499	+	0.622651i	$0.786055\pi$
$60$	−32.0597	+	45.0216i	−0.0689815	+	0.0968710i
$61$	535.886	+	421.425i	1.12481	+	0.884556i	0.994271	−	0.106887i	$-0.0340884\pi$
$61$	535.886	+	421.425i	1.12481	+	0.884556i	0.130534	+	0.991444i	$0.458331\pi$
$62$	102.020	+	709.562i	0.208976	+	1.45346i
$63$	270.384	+	52.1122i	0.540717	+	0.104215i
$64$	−604.223	−	388.311i	−1.18012	−	0.758419i
$65$	−19.8350	−	1.89402i	−0.0378497	−	0.00361421i
$66$	−26.1360			−0.0487443
$67$	−445.783	+	319.438i	−0.812852	+	0.582471i
$67$	−445.783	+	319.438i	−0.812852	+	0.582471i
$68$	746.376			1.33105
$69$	−268.169	−	25.6071i	−0.467881	−	0.0446772i
$70$	−202.857	−	130.368i	−0.346372	−	0.222600i
$71$	371.373	+	71.5762i	0.620758	+	0.119641i	0.489927	−	0.871763i	$-0.337023\pi$
$71$	371.373	+	71.5762i	0.620758	+	0.119641i	0.130831	+	0.991405i	$0.458235\pi$
$72$	10.2161	+	71.0546i	0.0167220	+	0.116304i
$73$	248.522	+	195.440i	0.398457	+	0.313350i	0.797203	−	0.603712i	$-0.206312\pi$
$73$	248.522	+	195.440i	0.398457	+	0.313350i	−0.398746	+	0.917061i	$0.630555\pi$
$74$	−977.893	+	1373.26i	−1.53619	+	2.15727i
$75$	−349.813	−	102.714i	−0.538572	−	0.158139i
$76$	−419.428	−	918.418i	−0.633048	−	1.38618i
$77$	−2.99890	−	62.9547i	−0.00443840	−	0.0931735i
$78$	−106.631	+	83.8558i	−0.154790	+	0.121728i
$79$	201.509	+	192.139i	0.286982	+	0.273637i	0.819871	−	0.572548i	$-0.194045\pi$
$79$	201.509	+	192.139i	0.286982	+	0.273637i	−0.532889	+	0.846185i	$0.678894\pi$
$80$	−19.9271	+	82.1406i	−0.0278490	+	0.114795i
$81$	−53.0437	+	61.2157i	−0.0727623	+	0.0839722i
$82$	90.2354	−	197.588i	0.121522	−	0.266097i
$83$	520.980	+	208.569i	0.688975	+	0.275824i	0.689616	−	0.724176i	$-0.257780\pi$
$83$	520.980	+	208.569i	0.688975	+	0.275824i	−0.000640105		1.00000i	$0.500204\pi$
$84$	−891.003	+	171.727i	−1.15734	+	0.223059i
$85$	−46.0176	−	132.959i	−0.0587213	−	0.169664i
$86$	−623.040	−	874.937i	−0.781210	−	1.09706i
$87$	26.1144	−	548.209i	0.0321811	−	0.675565i
$88$	15.2537	−	6.10666i	0.0184778	−	0.00739741i
$89$	1253.07	−	805.302i	1.49242	−	0.959121i	0.496583	−	0.867989i	$-0.334588\pi$
$89$	1253.07	−	805.302i	1.49242	−	0.959121i	0.995839	−	0.0911325i	$-0.0290487\pi$
$90$	63.0476	−	32.5033i	0.0738422	−	0.0380683i
$91$	−214.221	−	247.225i	−0.246775	−	0.284793i
$92$	851.766	−	250.101i	0.965247	−	0.283422i
$93$	166.317	−	480.541i	0.185444	−	0.535804i
$94$	−223.498	+	1554.46i	−0.245234	+	1.70564i
$95$	−137.747	+	131.342i	−0.148764	+	0.141846i
$96$	383.437	+	664.133i	0.407650	+	0.706070i
$97$	−335.457	+	581.028i	−0.351139	+	0.608191i	−0.986449	−	0.164066i	$-0.947539\pi$
$97$	−335.457	+	581.028i	−0.351139	+	0.608191i	0.635310	+	0.772257i	$0.280872\pi$
$98$	−591.349	−	2437.58i	−0.609544	−	2.51257i
$99$	16.4788	+	8.49542i	0.0167291	+	0.00862446i
$100$	1195.97	−	114.202i	1.19597	−	0.114202i
$101$	455.477	−	43.4928i	0.448729	−	0.0428485i	0.131754	−	0.991282i	$-0.457939\pi$
$101$	455.477	−	43.4928i	0.448729	−	0.0428485i	0.316975	+	0.948434i	$0.397333\pi$
$102$	−851.407	−	438.931i	−0.826488	−	0.426084i
$103$	−395.419	−	1629.94i	−0.378270	−	1.55925i	−0.769310	−	0.638876i	$-0.779400\pi$
$103$	−395.419	−	1629.94i	−0.378270	−	1.55925i	0.391040	−	0.920374i	$-0.372116\pi$
$104$	42.6401	−	73.8549i	0.0402039	−	0.0696353i
$105$	85.5260	+	148.135i	0.0794903	+	0.137681i
$106$	−1241.22	+	1183.50i	−1.13734	+	1.08445i
$107$	68.2500	−	474.689i	0.0616633	−	0.428878i	−0.935482	−	0.353374i	$-0.885034\pi$
$107$	68.2500	−	474.689i	0.0616633	−	0.428878i	0.997145	−	0.0755040i	$-0.0240566\pi$
$108$	87.3014	−	252.241i	0.0777832	−	0.224740i
$109$	641.779	−	188.443i	0.563956	−	0.165593i	0.0126865	−	0.999920i	$-0.495962\pi$
$109$	641.779	−	188.443i	0.563956	−	0.165593i	0.551270	+	0.834327i	$0.314143\pi$
$110$	−10.6320	−	12.2700i	−0.00921567	−	0.0106354i
$111$	1062.94	−	547.981i	0.908913	−	0.468577i
$112$	−1167.38	+	750.231i	−0.984886	+	0.632948i
$113$	829.951	−	332.262i	0.690931	−	0.276607i	0.000494271	−	1.00000i	$-0.499843\pi$
$113$	829.951	−	332.262i	0.690931	−	0.276607i	0.690437	+	0.723393i	$0.257418\pi$
$114$	−61.6559	+	1294.32i	−0.0506544	+	1.06337i
$115$	−97.0683	−	136.313i	−0.0787102	−	0.110533i
$116$	591.527	+	1709.11i	0.473465	+	1.36799i
$117$	94.4883	−	18.2111i	0.0746619	−	0.0143899i
$118$	−2047.58	−	819.726i	−1.59741	−	0.639508i
$119$	959.574	−	2101.17i	0.739194	−	1.61861i
$120$	−29.2019	+	33.7008i	−0.0222147	+	0.0256371i
$121$	−312.795	+	1289.36i	−0.235007	+	0.968713i
$122$	2086.68	+	1989.64i	1.54852	+	1.47651i
$123$	−121.119	+	95.2488i	−0.0887879	+	0.0698236i
$124$	79.7331	+	1673.80i	0.0577439	+	1.21219i
$125$	−190.851	−	417.906i	−0.136562	−	0.299029i
$126$	1117.38	+	328.091i	0.790030	+	0.231974i
$127$	−461.557	+	648.166i	−0.322492	+	0.452877i	−0.943716	−	0.330756i	$-0.892696\pi$
$127$	−461.557	+	648.166i	−0.322492	+	0.452877i	0.621224	+	0.783633i	$0.286636\pi$
$128$	−780.218	−	613.570i	−0.538767	−	0.423691i
$129$	108.433	+	754.166i	0.0740075	+	0.514733i
$130$	−82.7447	−	15.9477i	−0.0558245	−	0.0107593i
$131$	1107.28	+	711.603i	0.738498	+	0.474604i	0.855027	−	0.518584i	$-0.173541\pi$
$131$	1107.28	+	711.603i	0.738498	+	0.474604i	−0.116529	+	0.993187i	$0.537177\pi$
$132$	−60.8180	−	5.80741i	−0.0401025	−	0.00382932i
$133$	−3124.74			−2.03721
$134$	−2005.18	+	1165.63i	−1.29269	+	0.751459i
$135$	−50.3167			−0.0320783
$136$	599.460	+	57.2415i	0.377965	+	0.0360913i
$137$	−757.563	−	486.856i	−0.472431	−	0.303613i	0.282675	−	0.959216i	$-0.408778\pi$
$137$	−757.563	−	486.856i	−0.472431	−	0.303613i	−0.755106	+	0.655603i	$0.772415\pi$
$138$	−1118.71	−	215.613i	−0.690077	−	0.133001i
$139$	93.6106	+	651.076i	0.0571219	+	0.397292i	0.998245	+	0.0592264i	$0.0188634\pi$
$139$	93.6106	+	651.076i	0.0571219	+	0.397292i	−0.941123	+	0.338065i	$0.890228\pi$
$140$	−443.076	−	348.439i	−0.267477	−	0.210346i
$141$	646.187	−	907.443i	0.385949	−	0.541989i
$142$	1534.72	+	450.634i	0.906976	+	0.266312i
$143$	−9.14955	−	20.0347i	−0.00535052	−	0.0117160i
$144$	−19.4228	−	407.735i	−0.0112401	−	0.235958i
$145$	267.989	−	210.749i	0.153485	−	0.120702i
$146$	967.718	+	922.717i	0.548554	+	0.523045i
$147$	−419.478	+	1729.11i	−0.235360	+	0.970168i
$148$	−2580.67	+	2978.26i	−1.43331	+	1.65413i
$149$	−299.586	+	656.001i	−0.164718	+	0.360683i	−0.973935	−	0.226828i	$-0.927165\pi$
$149$	−299.586	+	656.001i	−0.164718	+	0.360683i	0.809217	+	0.587510i	$0.199892\pi$
$150$	−1431.43	−	573.059i	−0.779173	−	0.311934i
$151$	−659.881	+	127.182i	−0.355631	+	0.0685423i	−0.363938	−	0.931423i	$-0.618568\pi$
$151$	−659.881	+	127.182i	−0.355631	+	0.0685423i	0.00830666	+	0.999965i	$0.497356\pi$
$152$	−266.432	−	769.804i	−0.142174	−	0.410785i
$153$	394.141	+	553.493i	0.208264	+	0.292466i
$154$	12.6829	−	266.247i	0.00663648	−	0.139317i
$155$	293.255	−	117.402i	0.151967	−	0.0608382i
$156$	−266.762	+	171.437i	−0.136910	+	0.0879870i
$157$	−1705.46	+	879.225i	−0.866945	+	0.446941i	−0.833513	−	0.552500i	$-0.813674\pi$
$157$	−1705.46	+	879.225i	−0.866945	+	0.446941i	−0.0334320	+	0.999441i	$0.510644\pi$
$158$	771.120	+	889.919i	0.388272	+	0.448090i
$159$	1167.28	−	342.744i	0.582209	−	0.170952i
$160$	−155.808	+	450.177i	−0.0769856	+	0.222435i
$161$	390.992	−	2719.41i	0.191394	−	1.33118i
$162$	−247.925	+	236.396i	−0.120240	+	0.114648i
$163$	−353.359	−	612.036i	−0.169799	−	0.294100i	0.768550	−	0.639789i	$-0.220978\pi$
$163$	−353.359	−	612.036i	−0.169799	−	0.294100i	−0.938349	+	0.345689i	$0.887645\pi$
$164$	253.880	−	439.732i	0.120882	−	0.209374i
$165$	2.71519	+	11.1922i	0.00128107	+	0.00528066i
$166$	2109.50	+	1087.52i	0.986317	+	0.508482i
$167$	2698.68	−	257.692i	1.25048	−	0.119406i	0.551271	−	0.834326i	$-0.314143\pi$
$167$	2698.68	−	257.692i	1.25048	−	0.119406i	0.699206	+	0.714920i	$0.253537\pi$
$168$	−728.789	+	69.5909i	−0.334686	+	0.0319587i
$169$	1851.16	+	954.341i	0.842586	+	0.434384i
$170$	−140.285	−	578.262i	−0.0632903	−	0.260886i
$171$	459.587	−	796.028i	0.205529	−	0.355987i
$172$	−1255.39	−	2174.40i	−0.556526	−	0.963932i
$173$	830.843	−	792.208i	0.365132	−	0.348153i	−0.485196	−	0.874405i	$-0.661252\pi$
$173$	830.843	−	792.208i	0.365132	−	0.348153i	0.850328	+	0.526253i	$0.176403\pi$
$174$	330.328	−	2297.48i	0.143920	−	1.00099i
$175$	1216.10	−	3513.69i	0.525306	−	1.51777i
$176$	−89.6461	+	26.3225i	−0.0383939	+	0.0112735i
$177$	1024.55	+	1182.40i	0.435085	+	0.502115i
$178$	5599.22	−	2886.60i	2.35775	−	1.21550i
$179$	3332.53	−	2141.69i	1.39154	−	0.894287i	0.391869	−	0.920021i	$-0.371829\pi$
$179$	3332.53	−	2141.69i	1.39154	−	0.894287i	0.999669	+	0.0257342i	$0.00819236\pi$
$180$	153.933	−	61.6253i	0.0637414	−	0.0255182i
$181$	30.3198	−	636.490i	0.0124511	−	0.261381i	−0.984055	−	0.177863i	$-0.943082\pi$
$181$	30.3198	−	636.490i	0.0124511	−	0.261381i	0.996506	−	0.0835175i	$-0.0266155\pi$
$182$	−802.492	−	1126.94i	−0.326839	−	0.458981i
$183$	−668.928	−	1932.74i	−0.270211	−	0.780723i
$184$	703.286	−	135.547i	0.281777	−	0.0543080i
$185$	689.656	+	276.097i	0.274079	+	0.109725i
$186$	893.381	−	1956.23i	0.352182	−	0.771172i
$187$	101.847	−	117.538i	0.0398278	−	0.0459638i
$188$	−865.475	+	3567.53i	−0.335751	+	1.38399i
$189$	−597.862	−	570.061i	−0.230096	−	0.219396i
$190$	−632.720	+	497.577i	−0.241591	+	0.189989i
$191$	26.1957	+	549.915i	0.00992384	+	0.208327i	0.998383	+	0.0568410i	$0.0181028\pi$
$191$	26.1957	+	549.915i	0.00992384	+	0.208327i	−0.988459	+	0.151486i	$0.951594\pi$
$192$	895.105	+	1960.01i	0.336451	+	0.736726i
$193$	−4760.76	−	1397.88i	−1.77558	−	0.521357i	−0.780926	−	0.624623i	$-0.785252\pi$
$193$	−4760.76	−	1397.88i	−1.77558	−	0.521357i	−0.994654	+	0.103266i	$0.967071\pi$
$194$	−1645.86	+	2311.29i	−0.609103	+	0.855366i
$195$	46.9869	+	36.9509i	0.0172554	+	0.0135698i
$196$	−834.429	−	5803.58i	−0.304092	−	2.11501i
$197$	−4641.69	−	894.612i	−1.67871	−	0.323545i	−0.741145	−	0.671345i	$-0.765717\pi$
$197$	−4641.69	−	894.612i	−1.67871	−	0.323545i	−0.937569	+	0.347800i	$0.886929\pi$
$198$	65.9611	+	42.3906i	0.0236750	+	0.0152150i
$199$	−1278.20	−	122.053i	−0.455323	−	0.0434780i	−0.135124	−	0.990829i	$-0.543143\pi$
$199$	−1278.20	−	122.053i	−0.455323	−	0.0434780i	−0.320198	+	0.947351i	$0.603749\pi$
$200$	969.318			0.342706
$201$	1643.15	−	83.1589i	0.576612	−	0.0291820i
$202$	1935.06			0.674011
$203$	5571.92	+	532.054i	1.92646	+	0.183955i
$204$	−1883.67	−	1210.56i	−0.646488	−	0.415473i
$205$	−93.9867	−	18.1145i	−0.0320211	−	0.00617155i
$206$	−1009.48	−	7021.06i	−0.341425	−	2.37466i
$207$	635.262	+	499.576i	0.213303	+	0.167744i
$208$	−281.290	+	395.016i	−0.0937689	+	0.131680i
$209$	−201.864	−	59.2726i	−0.0668097	−	0.0196171i
$210$	300.515	+	658.037i	0.0987501	+	0.216233i
$211$	−114.031	−	2393.79i	−0.0372047	−	0.781022i	−0.937970	−	0.346716i	$-0.887297\pi$
$211$	−114.031	−	2393.79i	−0.0372047	−	0.781022i	0.900765	−	0.434306i	$-0.143006\pi$
$212$	−3151.25	+	2478.17i	−1.02089	+	0.802838i
$213$	−821.165	−	782.979i	−0.264156	−	0.251873i
$214$	478.164	−	1971.02i	0.152741	−	0.629608i
$215$	−309.946	+	357.697i	−0.0983169	+	0.113464i
$216$	89.4621	−	195.895i	0.0281811	−	0.0617081i
$217$	4814.55	+	1927.46i	1.50614	+	0.602969i
$218$	2777.66	−	535.351i	0.862969	−	0.166324i
$219$	−310.222	−	896.328i	−0.0957208	−	0.276567i
$220$	−22.0141	−	30.9145i	−0.00674632	−	0.00947387i
$221$	38.4092	−	806.309i	0.0116909	−	0.245422i
$222$	4695.29	−	1879.71i	1.41949	−	0.568278i
$223$	3062.75	−	1968.31i	0.919717	−	0.591066i	0.00714137	−	0.999975i	$-0.497727\pi$
$223$	3062.75	−	1968.31i	0.919717	−	0.591066i	0.912575	+	0.408908i	$0.134090\pi$
$224$	−6951.57	+	3583.78i	−2.07353	+	1.06898i
$225$	716.250	+	826.596i	0.212222	+	0.244917i
$226$	3627.69	−	1065.19i	1.06775	−	0.313518i
$227$	−365.313	+	1055.50i	−0.106814	+	0.308617i	−0.985724	−	0.168369i	$-0.946150\pi$
$227$	−365.313	+	1055.50i	−0.106814	+	0.308617i	0.878910	+	0.476987i	$0.158271\pi$
$228$	−431.068	+	2998.15i	−0.125211	+	0.870865i
$229$	−2280.50	+	2174.45i	−0.658077	+	0.627475i	−0.943675	−	0.330875i	$-0.892656\pi$
$229$	−2280.50	+	2174.45i	−0.658077	+	0.627475i	0.285598	+	0.958350i	$0.407808\pi$
$230$	−353.861	−	612.906i	−0.101448	−	0.175712i
$231$	−94.5392	+	163.747i	−0.0269274	+	0.0466396i
$232$	344.016	+	1418.05i	0.0973523	+	0.401292i
$233$	−5014.75	−	2585.29i	−1.40999	−	0.726900i	−0.425932	−	0.904755i	$-0.640054\pi$
$233$	−5014.75	−	2585.29i	−1.40999	−	0.726900i	−0.984057	+	0.177855i	$0.943084\pi$
$234$	405.120	−	38.6842i	0.113177	−	0.0108071i
$235$	688.880	−	65.7801i	0.191224	−	0.0182597i
$236$	−4582.53	−	2362.46i	−1.26397	−	0.651622i
$237$	−196.927	−	811.745i	−0.0539738	−	0.222483i
$238$	4884.53	−	8460.26i	1.33032	−	2.30419i
$239$	721.300	+	1249.33i	0.195218	+	0.338127i	0.946972	−	0.321317i	$-0.104125\pi$
$239$	721.300	+	1249.33i	0.195218	+	0.338127i	−0.751754	+	0.659443i	$0.770792\pi$
$240$	183.517	−	174.983i	0.0493582	−	0.0470629i
$241$	−217.897	+	1515.50i	−0.0582405	+	0.405071i	0.939758	+	0.341839i	$0.111050\pi$
$241$	−217.897	+	1515.50i	−0.0582405	+	0.405071i	−0.997999	+	0.0632319i	$0.979859\pi$
$242$	−1835.21	+	5302.49i	−0.487486	+	1.40850i
$243$	233.157	−	68.4610i	0.0615515	−	0.0180732i
$244$	4413.56	+	5093.52i	1.15799	+	1.33639i
$245$	−982.402	+	506.463i	−0.256177	+	0.132068i
$246$	−548.205	+	352.310i	−0.142082	+	0.0913108i
$247$	−1013.75	+	405.844i	−0.261147	+	0.104548i
$248$	−64.3298	+	1350.45i	−0.0164716	+	0.345781i
$249$	−976.546	−	1371.37i	−0.248538	−	0.349023i
$250$	−635.488	−	1836.12i	−0.160767	−	0.464506i
$251$	1616.20	−	311.496i	0.406428	−	0.0783326i	0.0180599	−	0.999837i	$-0.494251\pi$
$251$	1616.20	−	311.496i	0.406428	−	0.0783326i	0.388368	+	0.921504i	$0.373039\pi$
$252$	2527.21	+	1011.74i	0.631742	+	0.252911i
$253$	76.8428	−	168.262i	0.0190951	−	0.0418125i
$254$	−2203.74	+	2543.25i	−0.544389	+	0.628258i
$255$	−99.5120	+	410.194i	−0.0244380	+	0.100735i
$256$	1120.45	+	1068.34i	0.273547	+	0.260826i
$257$	−2586.06	+	2033.70i	−0.627680	+	0.493613i	−0.880591	−	0.473876i	$-0.842854\pi$
$257$	−2586.06	+	2033.70i	−0.627680	+	0.493613i	0.252911	+	0.967489i	$0.418612\pi$
$258$	153.323	+	3218.65i	0.0369980	+	0.776684i
$259$	5066.46	+	11094.0i	1.21550	+	2.66158i
$260$	−189.001	−	55.4958i	−0.0450822	−	0.0132373i
$261$	−955.059	+	1341.19i	−0.226501	+	0.318076i
$262$	4375.60	+	3441.01i	1.03178	+	0.811398i
$263$	774.703	+	5388.18i	0.181636	+	1.26331i	0.852895	+	0.522083i	$0.174845\pi$
$263$	774.703	+	5388.18i	0.181636	+	1.26331i	−0.671259	+	0.741223i	$0.734246\pi$
$264$	−48.4012	−	9.32857i	−0.0112837	−	0.00217475i
$265$	635.751	+	408.572i	0.147373	+	0.0947109i
$266$	−13155.2	−	1256.17i	−3.03233	−	0.289552i
$267$	−4468.60			−1.02425
$268$	−4925.01	+	2266.86i	−1.12255	+	0.516680i
$269$	2667.59			0.604632			0.302316	−	0.953208i	$-0.402240\pi$
$269$	2667.59			0.604632			0.302316	+	0.953208i	$0.402240\pi$
$270$	−211.835	−	20.2278i	−0.0477476	−	0.00455934i
$271$	−1322.49	−	849.911i	−0.296441	−	0.190511i	0.383963	−	0.923349i	$-0.374559\pi$
$271$	−1322.49	−	849.911i	−0.296441	−	0.190511i	−0.680403	+	0.732838i	$0.738195\pi$
$272$	−3362.37	−	648.044i	−0.749536	−	0.144461i
$273$	139.664	+	971.387i	0.0309629	+	0.215352i
$274$	−2993.64	−	2354.23i	−0.660046	−	0.519066i
$275$	145.213	−	203.923i	0.0318425	−	0.0447165i
$276$	−2555.30	−	750.303i	−0.557286	−	0.163634i
$277$	−453.348	−	992.695i	−0.0983360	−	0.215326i	0.854070	−	0.520158i	$-0.174127\pi$
$277$	−453.348	−	992.695i	−0.0983360	−	0.215326i	−0.952406	+	0.304832i	$0.901400\pi$
$278$	132.365	+	2778.68i	0.0285566	+	0.599476i
$279$	−1199.14	+	943.018i	−0.257315	+	0.202355i
$280$	−329.139	−	313.833i	−0.0702493	−	0.0669825i
$281$	−2013.57	+	8300.05i	−0.427471	+	1.76206i	0.196389	+	0.980526i	$0.437078\pi$
$281$	−2013.57	+	8300.05i	−0.427471	+	1.76206i	−0.623861	+	0.781535i	$0.714437\pi$
$282$	3085.27	−	3560.59i	0.651507	−	0.751880i
$283$	3599.63	−	7882.08i	0.756098	−	1.65562i	0.00100920	−	0.999999i	$-0.499679\pi$
$283$	3599.63	−	7882.08i	0.756098	−	1.65562i	0.755088	−	0.655623i	$-0.227594\pi$
$284$	3471.12	+	1389.63i	0.725258	+	0.290349i
$285$	560.666	−	108.060i	0.116530	−	0.0224593i
$286$	−30.4658	−	88.0250i	−0.00629887	−	0.0181994i
$287$	−911.522	−	1280.05i	−0.187475	−	0.263272i
$288$	109.468	−	2298.02i	0.0223975	−	0.470180i
$289$	730.640	−	292.504i	0.148716	−	0.0595367i
$290$	1212.97	−	779.526i	0.245613	−	0.157846i
$291$	1789.00	−	922.292i	0.360388	−	0.185793i
$292$	2046.83	+	2362.17i	0.410211	+	0.473409i
$293$	3344.31	−	981.977i	0.666814	−	0.195794i	0.0692302	−	0.997601i	$-0.477946\pi$
$293$	3344.31	−	981.977i	0.666814	−	0.195794i	0.597584	+	0.801806i	$0.296128\pi$
$294$	−2461.13	+	7110.98i	−0.488218	+	1.41061i
$295$	−138.313	+	961.987i	−0.0272979	+	0.189861i
$296$	−2301.11	+	2194.10i	−0.451855	+	0.430843i
$297$	−27.8097	−	48.1678i	−0.00543327	−	0.00941070i
$298$	−1524.98	+	2641.35i	−0.296443	+	0.513454i
$299$	−226.351	−	933.031i	−0.0437800	−	0.180464i
$300$	−3203.58	−	1651.56i	−0.616529	−	0.317843i
$301$	−7735.28	+	738.630i	−1.48124	+	0.141442i
$302$	−2829.25	+	270.160i	−0.539089	+	0.0514768i
$303$	−1220.06	−	628.983i	−0.231322	−	0.119255i
$304$	1092.07	+	4501.58i	0.206035	+	0.849287i
$305$	635.241	−	1100.27i	0.119258	−	0.206561i
$306$	1436.83	+	2488.67i	0.268426	+	0.464928i
$307$	−2939.73	+	2803.02i	−0.546512	+	0.521098i	−0.912258	−	0.409617i	$-0.865662\pi$
$307$	−2939.73	+	2803.02i	−0.546512	+	0.521098i	0.365746	+	0.930715i	$0.380814\pi$
$308$	88.6728	−	616.733i	0.0164046	−	0.114096i
$309$	−1645.69	+	4754.92i	−0.302978	+	0.875397i
$310$	1281.81	−	376.373i	0.234845	−	0.0689567i
$311$	−938.164	−	1082.70i	−0.171056	−	0.197409i	0.663748	−	0.747956i	$-0.268965\pi$
$311$	−938.164	−	1082.70i	−0.171056	−	0.197409i	−0.834804	+	0.550547i	$0.814419\pi$
$312$	−227.400	+	117.233i	−0.0412629	+	0.0212725i
$313$	962.651	−	618.658i	0.173841	−	0.111721i	−0.450827	−	0.892612i	$-0.648871\pi$
$313$	962.651	−	618.658i	0.173841	−	0.111721i	0.624668	+	0.780891i	$0.285234\pi$
$314$	−7533.49	+	3015.95i	−1.35395	+	0.542039i
$315$	24.4169	−	512.575i	0.00436742	−	0.0916835i
$316$	1596.64	+	2242.17i	0.284234	+	0.399151i
$317$	526.940	+	1522.49i	0.0933624	+	0.269753i	0.982007	−	0.188843i	$-0.0604737\pi$
$317$	526.940	+	1522.49i	0.0933624	+	0.269753i	−0.888645	+	0.458596i	$0.848353\pi$
$318$	5052.07	−	973.707i	0.890900	−	0.171707i
$319$	349.864	+	140.064i	0.0614064	+	0.0245834i
$320$	−556.034	+	1217.54i	−0.0971351	+	0.212696i
$321$	−942.156	+	1087.31i	−0.163819	+	0.189058i
$322$	2739.31	−	11291.6i	0.474087	−	1.95421i
$323$	−5580.49	−	5320.98i	−0.961321	−	0.916618i
$324$	−629.443	+	495.000i	−0.107929	+	0.0848765i
$325$	−61.8259	−	1297.89i	−0.0105523	−	0.221519i
$326$	−1241.61	−	2718.74i	−0.210940	−	0.461894i
$327$	−1925.34	−	565.330i	−0.325600	−	0.0956049i
$328$	237.630	−	333.705i	0.0400029	−	0.0561762i
$329$	8930.52	+	7023.04i	1.49652	+	1.17688i
$330$	6.93168	+	48.2109i	0.00115629	+	0.00804218i
$331$	−10210.6	−	1967.93i	−1.69554	−	0.326789i	−0.752281	−	0.658843i	$-0.771046\pi$
$331$	−10210.6	−	1967.93i	−1.69554	−	0.326789i	−0.943260	+	0.332054i	$0.892258\pi$
$332$	4667.10	+	2999.36i	0.771508	+	0.495818i
$333$	−3571.38	−	341.025i	−0.587719	−	0.0561203i
$334$	11465.1			1.87827
$335$	707.467	+	737.577i	0.115382	+	0.120293i
$336$	4163.01			0.675925
$337$	−11063.3	−	1056.42i	−1.78829	−	0.170761i	−0.852365	−	0.522948i	$-0.824832\pi$
$337$	−11063.3	−	1056.42i	−1.78829	−	0.170761i	−0.935930	+	0.352186i	$0.885438\pi$
$338$	7409.80	+	4761.99i	1.19243	+	0.766326i
$339$	−2633.50	−	507.566i	−0.421924	−	0.0813191i
$340$	−197.950	−	1376.77i	−0.0315746	−	0.219606i
$341$	274.468	+	215.844i	0.0435873	+	0.0342774i
$342$	2254.89	−	3166.54i	0.356521	−	0.500664i
$343$	−7341.66	−	2155.71i	−1.15572	−	0.339350i
$344$	−841.519	−	1842.67i	−0.131894	−	0.288808i
$345$	23.8875	+	501.460i	0.00372770	+	0.0782541i
$346$	3816.35	−	3001.21i	0.592972	−	0.466318i
$347$	961.006	+	916.317i	0.148673	+	0.141759i	0.760766	−	0.649027i	$-0.224824\pi$
$347$	961.006	+	916.317i	0.148673	+	0.141759i	−0.612093	+	0.790786i	$0.709672\pi$
$348$	1279.16	−	5272.79i	0.197041	−	0.812215i
$349$	−3854.19	+	4447.97i	−0.591146	+	0.682218i	−0.969963	−	0.243253i	$-0.921785\pi$
$349$	−3854.19	+	4447.97i	−0.591146	+	0.682218i	0.378817	+	0.925472i	$0.376331\pi$
$350$	6532.36	−	14303.9i	0.997626	−	2.18450i
$351$	−268.003	−	107.292i	−0.0407548	−	0.0163158i
$352$	−517.065	+	99.6561i	−0.0782945	+	0.0150900i
$353$	2461.67	+	7112.52i	0.371165	+	1.07241i	0.963728	+	0.266887i	$0.0859950\pi$
$353$	2461.67	+	7112.52i	0.371165	+	1.07241i	−0.592563	+	0.805524i	$0.701884\pi$
$354$	3838.06	+	5389.81i	0.576245	+	0.809223i
$355$	33.5367	−	704.022i	0.00501392	−	0.105255i
$356$	13670.7	−	5472.91i	2.03524	−	0.814785i
$357$	−5829.68	+	3746.51i	−0.864256	+	0.555424i
$358$	14891.0	−	7676.87i	2.19837	−	1.13334i
$359$	−6107.41	−	7048.33i	−0.897874	−	1.03620i	−0.999145	−	0.0413431i	$-0.986836\pi$
$359$	−6107.41	−	7048.33i	−0.897874	−	1.03620i	0.101271	−	0.994859i	$-0.467709\pi$
$360$	128.359	−	37.6895i	0.0187920	−	0.00551781i
$361$	−1168.16	+	3375.19i	−0.170311	+	0.492081i
$362$	383.522	−	2667.45i	0.0556836	−	0.387288i
$363$	2880.66	−	2746.70i	0.416516	−	0.397147i
$364$	−1616.98	−	2800.68i	−0.232837	−	0.403285i
$365$	294.599	−	510.261i	0.0422466	−	0.0731733i
$366$	−2039.23	−	8405.81i	−0.291235	−	1.20049i
$367$	5853.87	+	3017.88i	0.832614	+	0.429243i	0.821164	−	0.570692i	$-0.193325\pi$
$367$	5853.87	+	3017.88i	0.832614	+	0.429243i	0.0114501	+	0.999934i	$0.496355\pi$
$368$	−4054.29	+	387.138i	−0.574306	+	0.0548396i
$369$	460.161	−	43.9400i	0.0649188	−	0.00619899i
$370$	2792.48	+	1439.62i	0.392363	+	0.202277i
$371$	2925.09	+	12057.4i	0.409334	+	1.68730i
$372$	2513.55	−	4353.60i	0.350327	−	0.606784i
$373$	3776.11	+	6540.42i	0.524181	+	0.907908i	0.999604	+	0.0281508i	$0.00896188\pi$
$373$	3776.11	+	6540.42i	0.524181	+	0.907908i	−0.475422	+	0.879758i	$0.657705\pi$
$374$	476.031	−	453.895i	0.0658155	−	0.0627549i
$375$	−196.148	+	1364.24i	−0.0270108	+	0.187864i
$376$	−968.718	+	2798.93i	−0.132867	+	0.383893i
$377$	1876.78	−	551.074i	0.256391	−	0.0752831i
$378$	−2287.85	−	2640.32i	−0.311308	−	0.359268i
$379$	−10775.4	+	5555.09i	−1.46041	+	0.752892i	−0.991469	−	0.130340i	$-0.958393\pi$
$379$	−10775.4	+	5555.09i	−1.46041	+	0.752892i	−0.468937	+	0.883232i	$0.655363\pi$
$380$	−1582.89	+	1017.26i	−0.213685	+	0.137327i
$381$	2216.13	−	887.206i	0.297995	−	0.119299i
$382$	−110.786	+	2325.69i	−0.0148385	+	0.311499i
$383$	470.009	+	660.036i	0.0627059	+	0.0880581i	0.844738	−	0.535180i	$-0.179756\pi$
$383$	470.009	+	660.036i	0.0627059	+	0.0880581i	−0.782032	+	0.623238i	$0.785817\pi$
$384$	973.920	+	2813.96i	0.129427	+	0.373956i
$385$	−115.332	+	22.2284i	−0.0152671	+	0.00294250i
$386$	−19481.0	−	7799.01i	−2.56880	−	1.02839i
$387$	949.540	−	2079.20i	0.124723	−	0.273106i
$388$	−4343.46	+	5012.61i	−0.568313	+	0.655868i
$389$	3062.59	−	12624.2i	0.399176	−	1.64543i	−0.317676	−	0.948199i	$-0.602902\pi$
$389$	3062.59	−	12624.2i	0.399176	−	1.64543i	0.716852	−	0.697226i	$-0.245583\pi$
$390$	182.962	+	174.454i	0.0237555	+	0.0226508i
$391$	5329.03	−	4190.80i	0.689261	−	0.542040i
$392$	−225.089	−	4725.20i	−0.0290018	−	0.608823i
$393$	−1640.34	−	3591.83i	−0.210544	−	0.461028i
$394$	−19182.0	−	5632.35i	−2.45273	−	0.720187i
$395$	300.978	−	422.665i	0.0383389	−	0.0538395i
$396$	144.071	+	113.299i	0.0182824	+	0.0143774i
$397$	770.958	+	5362.13i	0.0974642	+	0.677878i	0.978714	+	0.205228i	$0.0657936\pi$
$397$	770.958	+	5362.13i	0.0974642	+	0.677878i	−0.881250	+	0.472650i	$0.843297\pi$
$398$	−5332.20	−	1027.70i	−0.671555	−	0.129432i
$399$	7886.09	+	5068.08i	0.989469	+	0.635893i
$400$	−5486.93	−	523.939i	−0.685867	−	0.0654923i
$401$	3871.58			0.482138			0.241069	−	0.970508i	$-0.422502\pi$
$401$	3871.58			0.482138			0.241069	+	0.970508i	$0.422502\pi$
$402$	6951.16	+	310.461i	0.862418	+	0.0385184i
$403$	1812.31			0.224014
$404$	4502.84	+	429.969i	0.554516	+	0.0529499i
$405$	126.987	+	81.6098i	0.0155804	+	0.0100129i
$406$	23244.1	+	4479.92i	2.84134	+	0.547623i
$407$	116.863	+	812.799i	0.0142326	+	0.0989901i
$408$	−1420.05	−	1116.74i	−0.172311	−	0.135507i
$409$	133.005	−	186.779i	0.0160799	−	0.0225810i	−0.806458	−	0.591292i	$-0.798618\pi$
$409$	133.005	−	186.779i	0.0160799	−	0.0225810i	0.822538	+	0.568711i	$0.192558\pi$
$410$	−388.405	−	114.046i	−0.0467852	−	0.0137374i
$411$	1122.26	+	2457.42i	0.134689	+	0.294928i
$412$	−788.953	−	16562.2i	−0.0943420	−	1.98048i
$413$	−12542.2	+	9863.31i	−1.49434	+	1.17516i
$414$	2473.64	+	2358.61i	0.293654	+	0.279999i
$415$	246.557	−	1016.32i	0.0291639	−	0.120215i
$416$	−1789.81	+	2065.55i	−0.210944	+	0.243442i
$417$	819.744	−	1794.99i	0.0962663	−	0.210794i
$418$	−826.026	−	330.691i	−0.0966561	−	0.0386953i
$419$	12921.3	−	2490.37i	1.50655	−	0.290364i	0.631875	−	0.775071i	$-0.282286\pi$
$419$	12921.3	−	2490.37i	1.50655	−	0.290364i	0.874677	+	0.484707i	$0.161074\pi$
$420$	553.077	+	1598.01i	0.0642557	+	0.185655i
$421$	−8436.89	−	11848.0i	−0.976695	−	1.37158i	−0.927925	−	0.372767i	$-0.878409\pi$
$421$	−8436.89	−	11848.0i	−0.976695	−	1.37158i	−0.0487703	−	0.998810i	$-0.515530\pi$
$422$	482.256	−	10123.8i	0.0556300	−	1.16782i
$423$	−3102.62	+	1242.10i	−0.356631	+	0.142773i
$424$	−2721.02	+	1748.69i	−0.311661	+	0.200293i
$425$	8155.16	−	4204.28i	0.930784	−	0.479853i
$426$	−3142.37	−	3626.48i	−0.357390	−	0.412450i
$427$	20013.4	−	5876.46i	2.26819	−	0.665999i
$428$	1550.64	−	4480.27i	0.175124	−	0.505986i
$429$	−9.40349	+	65.4027i	−0.00105829	+	0.00736054i
$430$	−1448.68	+	1381.31i	−0.162469	+	0.154914i
$431$	−4519.98	−	7828.84i	−0.505150	−	0.874946i	−0.999982	−	0.00595751i	$-0.998104\pi$
$431$	−4519.98	−	7828.84i	−0.505150	−	0.874946i	0.494832	−	0.868989i	$-0.335230\pi$
$432$	−612.296	+	1060.53i	−0.0681924	+	0.118113i
$433$	2115.87	+	8721.75i	0.234832	+	0.967992i	0.960129	+	0.279556i	$0.0901872\pi$
$433$	2115.87	+	8721.75i	0.234832	+	0.967992i	−0.725297	+	0.688436i	$0.758298\pi$
$434$	19494.6	+	10050.1i	2.15615	+	1.11157i
$435$	−1018.16	+	97.2224i	−0.112223	+	0.0107160i
$436$	6582.52	−	628.554i	0.723040	−	0.0690420i
$437$	−8151.46	−	4202.37i	−0.892304	−	0.460015i
$438$	−945.712	−	3898.28i	−0.103169	−	0.425267i
$439$	748.630	−	1296.67i	0.0813899	−	0.140971i	−0.822457	−	0.568827i	$-0.807397\pi$
$439$	748.630	−	1296.67i	0.0813899	−	0.140971i	0.903847	+	0.427855i	$0.140731\pi$
$440$	−15.3099	−	26.5176i	−0.00165880	−	0.00287313i
$441$	3863.15	−	3683.50i	0.417141	−	0.397743i
$442$	485.848	−	3379.14i	0.0522837	−	0.363641i
$443$	1076.71	−	3110.96i	0.115477	−	0.333648i	−0.872421	−	0.488755i	$-0.837451\pi$
$443$	1076.71	−	3110.96i	0.115477	−	0.333648i	0.987898	+	0.155107i	$0.0495723\pi$
$444$	11343.5	−	3330.75i	1.21247	−	0.356015i
$445$	−1817.80	−	2097.86i	−0.193645	−	0.223479i
$446$	13685.5	−	7055.39i	1.45298	−	0.749064i
$447$	1820.07	−	1169.69i	0.192587	−	0.123768i
$448$	−20400.9	+	8167.29i	−2.15145	+	0.861312i
$449$	−459.863	+	9653.72i	−0.0483347	+	1.01467i	0.836267	+	0.548323i	$0.184734\pi$
$449$	−459.863	+	9653.72i	−0.0483347	+	1.01467i	−0.884601	+	0.466348i	$0.845569\pi$
$450$	2683.13	+	3767.94i	0.281076	+	0.394716i
$451$	−34.6050	−	99.9845i	−0.00361305	−	0.0104392i
$452$	8678.24	−	1672.59i	0.903076	−	0.174054i
$453$	1871.66	+	749.300i	0.194124	+	0.0777156i
$454$	−1962.30	+	4296.84i	−0.202853	+	0.444187i
$455$	−399.219	+	460.723i	−0.0411333	+	0.0474704i
$456$	−576.153	+	2374.93i	−0.0591685	+	0.243896i
$457$	−6846.89	−	6528.49i	−0.700840	−	0.668249i	0.253376	−	0.967368i	$-0.418459\pi$
$457$	−6846.89	−	6528.49i	−0.700840	−	0.668249i	−0.954216	+	0.299118i	$0.903307\pi$
$458$	−10475.1	+	8237.73i	−1.06871	+	0.840445i
$459$	−96.9937	−	2036.15i	−0.00986336	−	0.207057i
$460$	−687.241	−	1504.85i	−0.0696582	−	0.152530i
$461$	−7774.16	−	2282.70i	−0.785420	−	0.230620i	−0.135656	−	0.990756i	$-0.543314\pi$
$461$	−7774.16	−	2282.70i	−0.785420	−	0.230620i	−0.649764	+	0.760136i	$0.725132\pi$
$462$	−463.841	+	651.373i	−0.0467096	+	0.0655944i
$463$	3872.16	+	3045.10i	0.388671	+	0.305654i	0.793305	−	0.608824i	$-0.208359\pi$
$463$	3872.16	+	3045.10i	0.388671	+	0.305654i	−0.404634	+	0.914479i	$0.632601\pi$
$464$	−1180.85	−	8213.00i	−0.118146	−	0.821721i
$465$	−930.522	−	179.343i	−0.0927998	−	0.0178857i
$466$	−20073.0	−	12900.1i	−1.99541	−	1.28237i
$467$	785.531	+	75.0091i	0.0778373	+	0.00743256i	0.133902	−	0.990995i	$-0.457249\pi$
$467$	785.531	+	75.0091i	0.0778373	+	0.00743256i	−0.0560647	+	0.998427i	$0.517855\pi$
$468$	951.300			0.0939613
$469$	49.7719	+	16779.1i	0.00490032	+	1.65200i
$470$	2926.65			0.287226
$471$	5730.20	+	547.168i	0.560581	+	0.0535290i
$472$	−3499.32	−	2248.88i	−0.341249	−	0.219307i
$473$	−513.725	−	99.0124i	−0.0499389	−	0.00962494i
$474$	−502.741	−	3496.64i	−0.0487166	−	0.338831i
$475$	−9756.18	−	7672.35i	−0.942409	−	0.741119i
$476$	13246.1	−	18601.5i	1.27549	−	1.79117i
$477$	−3501.84	−	1028.23i	−0.336139	−	0.0986993i
$478$	2534.45	+	5549.68i	0.242517	+	0.531039i
$479$	−271.562	−	5700.78i	−0.0259039	−	0.543790i	−0.974102	−	0.226110i	$-0.927399\pi$
$479$	−271.562	−	5700.78i	−0.0259039	−	0.543790i	0.948198	−	0.317680i	$-0.102904\pi$
$480$	1123.37	−	883.431i	0.106822	−	0.0840061i
$481$	3084.60	+	2941.16i	0.292403	+	0.278805i
$482$	−1526.60	+	6292.72i	−0.144263	+	0.594659i
$483$	−5397.43	+	6228.97i	−0.508472	+	0.586807i
$484$	−5448.70	+	11931.0i	−0.511711	+	1.12049i
$485$	1160.74	+	464.690i	0.108673	+	0.0435062i
$486$	1009.12	−	194.492i	0.0941864	−	0.0181529i
$487$	3969.74	+	11469.8i	0.369376	+	1.06724i	0.964608	+	0.263688i	$0.0849390\pi$
$487$	3969.74	+	11469.8i	0.369376	+	1.06724i	−0.595232	+	0.803554i	$0.702940\pi$
$488$	3154.16	+	4429.40i	0.292586	+	0.410880i
$489$	−100.881	+	2117.75i	−0.00932924	+	0.195845i
$490$	−4339.55	+	1737.29i	−0.400083	+	0.160169i
$491$	−16378.3	+	10525.7i	−1.50538	+	0.967450i	−0.511231	+	0.859443i	$0.670810\pi$
$491$	−16378.3	+	10525.7i	−1.50538	+	0.967450i	−0.994150	+	0.108006i	$0.965553\pi$
$492$	−1353.94	+	698.006i	−0.124066	+	0.0639605i
$493$	9044.91	+	10438.4i	0.826292	+	0.953592i
$494$	−4431.07	+	1301.08i	−0.403569	+	0.118499i
$495$	11.3003	−	32.6501i	0.00102608	−	0.00296468i
$496$	1094.09	−	7609.60i	0.0990450	−	0.688873i
$497$	8374.67	−	7985.23i	0.755846	−	0.720697i
$498$	−3559.99	−	6166.08i	−0.320335	−	0.554836i
$499$	−388.926	+	673.639i	−0.0348912	+	0.0604333i	−0.882944	−	0.469479i	$-0.844442\pi$
$499$	−388.926	+	673.639i	−0.0348912	+	0.0604333i	0.848053	+	0.529912i	$0.177775\pi$
$500$	−1070.78	−	4413.82i	−0.0957736	−	0.394784i
$501$	−7228.77	−	3726.69i	−0.644626	−	0.332328i
$502$	6929.46	−	661.683i	0.616090	−	0.0588294i
$503$	−8977.74	+	857.270i	−0.795821	+	0.0759916i	−0.485042	−	0.874491i	$-0.661196\pi$
$503$	−8977.74	+	857.270i	−0.795821	+	0.0759916i	−0.310778	+	0.950482i	$0.600590\pi$
$504$	1952.16	+	1006.41i	0.172532	+	0.0889464i
$505$	−201.027	−	828.644i	−0.0177140	−	0.0730181i
$506$	391.153	−	677.498i	0.0343654	−	0.0595226i
$507$	−3124.02	−	5410.97i	−0.273654	−	0.473983i
$508$	−5693.16	+	5428.42i	−0.497230	+	0.474108i
$509$	−886.787	+	6167.74i	−0.0772223	+	0.537093i	0.914085	+	0.405523i	$0.132911\pi$
$509$	−886.787	+	6167.74i	−0.0772223	+	0.537093i	−0.991307	+	0.131570i	$0.957998\pi$
$510$	−583.851	+	1686.93i	−0.0506928	+	0.146467i
$511$	9281.40	−	2725.27i	0.803493	−	0.235927i
$512$	9487.63	+	10949.3i	0.818941	+	0.945109i
$513$	−2450.98	+	1263.57i	−0.210943	+	0.108748i
$514$	−11704.9	+	7522.31i	−1.00444	+	0.645515i
$515$	−2901.74	+	1161.68i	−0.248283	+	0.0993975i
$516$	−358.403	+	7523.80i	−0.0305772	+	0.641893i
$517$	443.710	+	623.104i	0.0377453	+	0.0530059i
$518$	16870.1	+	48742.9i	1.43094	+	4.13444i
$519$	−3381.75	+	651.779i	−0.286016	+	0.0551251i
$520$	−147.542	−	59.0671i	−0.0124426	−	0.00498127i
$521$	7924.45	−	17352.1i	0.666366	−	1.45914i	−0.210103	−	0.977679i	$-0.567380\pi$
$521$	7924.45	−	17352.1i	0.666366	−	1.45914i	0.876469	−	0.481458i	$-0.159893\pi$
$522$	−4560.00	+	5262.52i	−0.382348	+	0.441253i
$523$	4132.50	−	17034.4i	0.345509	−	1.42421i	−0.488550	−	0.872536i	$-0.662474\pi$
$523$	4132.50	−	17034.4i	0.345509	−	1.42421i	0.834060	−	0.551674i	$-0.186011\pi$
$524$	9417.33	+	8979.41i	0.785111	+	0.748601i
$525$	−8768.08	+	6895.30i	−0.728896	+	0.573210i
$526$	1095.43	+	22995.8i	0.0908040	+	1.90621i
$527$	5316.15	+	11640.7i	0.439422	+	0.962199i
$528$	268.938	+	78.9674i	0.0221667	+	0.00650874i
$529$	−2380.33	+	3342.71i	−0.195638	+	0.274736i
$530$	2512.28	+	1975.68i	0.205899	+	0.161921i
$531$	−667.969	−	4645.83i	−0.0545902	−	0.379683i
$532$	−30332.8	−	5846.18i	−2.47198	−	0.476436i
$533$	−461.977	−	296.895i	−0.0375431	−	0.0241275i
$534$	−18812.9	−	1796.42i	−1.52456	−	0.145578i
$535$	−893.719			−0.0722221
$536$	−4129.42	+	1442.94i	−0.332769	+	0.116279i
$537$	−11884.2			−0.955009
$538$	11230.6	+	1072.40i	0.899977	+	0.0859374i
$539$	−1027.80	−	660.527i	−0.0821345	−	0.0527846i
$540$	−488.440	−	94.1392i	−0.0389243	−	0.00750205i
$541$	−1382.74	−	9617.15i	−0.109886	−	0.764276i	−0.968024	−	0.250857i	$-0.919288\pi$
$541$	−1382.74	−	9617.15i	−0.109886	−	0.764276i	0.858138	−	0.513419i	$-0.171621\pi$
$542$	−5226.04	−	4109.81i	−0.414166	−	0.325703i
$543$	−1108.86	+	1557.17i	−0.0876347	+	0.123066i
$544$	−18517.5	−	5437.23i	−1.45943	−	0.428528i
$545$	−517.814	−	1133.85i	−0.0406986	−	0.0891174i
$546$	197.485	+	4145.71i	0.0154791	+	0.324945i
$547$	−11122.6	+	8746.93i	−0.869414	+	0.683715i	−0.949735	−	0.313055i	$-0.898648\pi$
$547$	−11122.6	+	8746.93i	−0.869414	+	0.683715i	0.0803214	+	0.996769i	$0.474405\pi$
$548$	−6443.04	−	6143.42i	−0.502250	−	0.478894i
$549$	−1446.54	+	5962.72i	−0.112453	+	0.463539i
$550$	693.331	−	800.146i	0.0537522	−	0.0620334i
$551$	7761.66	−	16995.7i	0.600105	−	1.31405i
$552$	−1994.77	−	798.586i	−0.153810	−	0.0615762i
$553$	8364.79	−	1612.18i	0.643231	−	0.123973i
$554$	−1509.54	−	4361.53i	−0.115766	−	0.334483i
$555$	−1292.72	−	1815.37i	−0.0988701	−	0.138844i
$556$	−309.412	+	6495.35i	−0.0236007	+	0.495439i
$557$	21565.8	−	8633.65i	1.64052	−	0.656767i	0.646201	−	0.763167i	$-0.276357\pi$
$557$	21565.8	−	8633.65i	1.64052	−	0.656767i	0.994323	+	0.106400i	$0.0339323\pi$
$558$	−5427.54	+	3488.07i	−0.411767	+	0.264627i
$559$	−2413.60	+	1244.30i	−0.182620	+	0.0941470i
$560$	1693.49	+	1954.39i	0.127791	+	0.147479i
$561$	−447.675	+	131.449i	−0.0336914	+	0.00989268i
$562$	−11813.9	+	34134.0i	−0.886724	+	2.56202i
$563$	−2234.78	+	15543.3i	−0.167291	+	1.16353i	0.717162	+	0.696906i	$0.245441\pi$
$563$	−2234.78	+	15543.3i	−0.167291	+	1.16353i	−0.884453	+	0.466629i	$0.845468\pi$
$564$	7970.52	−	7599.87i	0.595070	−	0.567398i
$565$	−833.010	−	1442.82i	−0.0620266	−	0.107433i
$566$	18323.2	−	31736.7i	1.36075	−	2.35688i
$567$	584.267	+	2408.38i	0.0432750	+	0.178382i
$568$	2681.30	+	1382.30i	0.198072	+	0.102113i
$569$	−25012.7	+	2388.42i	−1.84286	+	0.175971i	−0.957403	−	0.288756i	$-0.906759\pi$
$569$	−25012.7	+	2388.42i	−1.84286	+	0.175971i	−0.885454	+	0.464727i	$0.846152\pi$
$570$	2403.86	−	229.541i	0.176644	−	0.0168674i
$571$	22080.2	+	11383.1i	1.61826	+	0.834272i	0.998786	+	0.0492565i	$0.0156852\pi$
$571$	22080.2	+	11383.1i	1.61826	+	0.834272i	0.619476	+	0.785016i	$0.287345\pi$
$572$	−51.3340	−	211.602i	−0.00375242	−	0.0154677i
$573$	825.808	−	1430.34i	0.0602070	−	0.104282i
$574$	−3322.94	−	5755.51i	−0.241632	−	0.418520i
$575$	7897.88	−	7530.62i	0.572808	−	0.546171i
$576$	919.948	−	6398.38i	0.0665472	−	0.462846i
$577$	7022.06	−	20288.9i	0.506641	−	1.46384i	−0.344439	−	0.938809i	$-0.611931\pi$
$577$	7022.06	−	20288.9i	0.506641	−	1.46384i	0.851080	−	0.525035i	$-0.175948\pi$
$578$	3193.61	−	937.727i	0.229821	−	0.0674815i
$579$	9747.75	+	11249.5i	0.699660	+	0.807450i
$580$	2995.76	−	1544.42i	0.214469	−	0.110566i
$581$	14444.0	−	9282.57i	1.03139	−	0.662833i
$582$	7902.50	−	3163.68i	0.562834	−	0.225325i
$583$	−39.7481	+	834.415i	−0.00282366	+	0.0592760i
$584$	1462.77	+	2054.18i	0.103647	+	0.145552i
$585$	−58.6522	−	169.464i	−0.00414525	−	0.0119769i
$586$	14474.4	−	2789.71i	1.02036	−	0.196659i
$587$	−8737.58	−	3498.00i	−0.614376	−	0.245959i	0.0435386	−	0.999052i	$-0.486137\pi$
$587$	−8737.58	−	3498.00i	−0.614376	−	0.245959i	−0.657914	+	0.753093i	$0.728561\pi$
$588$	−7307.06	+	16000.2i	−0.512480	+	1.12217i
$589$	11336.6	−	13083.1i	0.793064	−	0.915245i
$590$	−969.029	+	3994.39i	−0.0676174	+	0.278723i
$591$	10263.5	+	9786.24i	0.714356	+	0.681137i
$592$	14211.6	−	11176.1i	0.986646	−	0.775907i
$593$	−339.408	−	7125.06i	−0.0235039	−	0.493408i	−0.979674	−	0.200596i	$-0.935712\pi$
$593$	−339.408	−	7125.06i	−0.0235039	−	0.493408i	0.956170	−	0.292812i	$-0.0945910\pi$
$594$	−97.7157	−	213.968i	−0.00674971	−	0.0147798i
$595$	−4130.35	−	1212.78i	−0.284584	−	0.0835615i
$596$	−4135.51	+	5807.51i	−0.284223	+	0.399136i
$597$	3027.91	+	2381.17i	0.207578	+	0.163241i
$598$	−577.857	−	4019.09i	−0.0395156	−	0.274837i
$599$	23418.8	+	4513.60i	1.59744	+	0.307881i	0.908802	−	0.417227i	$-0.136998\pi$
$599$	23418.8	+	4513.60i	1.59744	+	0.307881i	0.688635	+	0.725108i	$0.258210\pi$
$600$	−2446.33	−	1572.16i	−0.166451	−	0.106972i
$601$	−18832.6	−	1798.30i	−1.27820	−	0.122053i	−0.566222	−	0.824253i	$-0.691595\pi$
$601$	−18832.6	−	1798.30i	−1.27820	−	0.122053i	−0.711980	+	0.702200i	$0.752201\pi$
$602$	−32862.7			−2.22489
$603$	−4281.80	−	2455.19i	−0.289168	−	0.165810i
$604$	−6643.63			−0.447558
$605$	2461.32	+	235.028i	0.165400	+	0.0157938i
$606$	−4883.62	−	3138.51i	−0.327366	−	0.210385i
$607$	14620.5	+	2817.87i	0.977639	+	0.188424i	0.652954	−	0.757398i	$-0.273530\pi$
$607$	14620.5	+	2817.87i	0.977639	+	0.188424i	0.324685	+	0.945822i	$0.394742\pi$
$608$	3715.42	+	25841.3i	0.247829	+	1.72369i
$609$	−13199.2	−	10380.0i	−0.878259	−	0.690671i
$610$	3116.70	−	4376.80i	0.206871	−	0.290510i
$611$	3809.46	+	1118.56i	0.252233	+	0.0740623i
$612$	2790.50	+	6110.35i	0.184313	+	0.403588i
$613$	−361.087	−	7580.14i	−0.0237914	−	0.499444i	−0.979044	−	0.203651i	$-0.934719\pi$
$613$	−361.087	−	7580.14i	−0.0237914	−	0.499444i	0.955252	−	0.295793i	$-0.0955838\pi$
$614$	−13503.2	+	10619.0i	−0.887531	+	0.697962i
$615$	207.820	+	198.156i	0.0136262	+	0.0129925i
$616$	118.517	−	488.535i	0.00775195	−	0.0319540i
$617$	11068.0	−	12773.2i	0.722174	−	0.833433i	−0.269393	−	0.963030i	$-0.586823\pi$
$617$	11068.0	−	12773.2i	0.722174	−	0.833433i	0.991567	+	0.129598i	$0.0413685\pi$
$618$	−8839.94	+	19356.8i	−0.575396	+	1.25994i
$619$	−8789.45	−	3518.76i	−0.570723	−	0.228483i	0.0683074	−	0.997664i	$-0.478240\pi$
$619$	−8789.45	−	3518.76i	−0.570723	−	0.228483i	−0.639031	+	0.769181i	$0.720664\pi$
$620$	3066.37	−	590.995i	0.198627	−	0.0382821i
$621$	−792.977	−	2291.16i	−0.0512416	−	0.148053i
$622$	−3514.45	−	4935.35i	−0.226554	−	0.318150i
$623$	2168.45	−	45521.5i	0.139450	−	2.92741i
$624$	1350.59	−	540.696i	0.0866458	−	0.0346878i
$625$	12059.1	−	7749.93i	0.771784	−	0.495996i
$626$	4301.50	−	2217.58i	0.274637	−	0.141585i
$627$	413.321	+	476.998i	0.0263261	+	0.0303819i
$628$	−18200.4	+	5344.12i	−1.15649	+	0.339576i
$629$	−9843.29	+	28440.3i	−0.623971	+	1.80285i
$630$	308.856	−	2148.14i	0.0195319	−	0.135847i
$631$	13663.9	−	13028.5i	0.862046	−	0.821959i	−0.123328	−	0.992366i	$-0.539357\pi$
$631$	13663.9	−	13028.5i	0.862046	−	0.821959i	0.985374	+	0.170407i	$0.0545081\pi$
$632$	1110.40	+	1923.27i	0.0698882	+	0.121050i
$633$	−3594.76	+	6226.31i	−0.225717	+	0.390954i
$634$	1606.38	+	6621.58i	0.100627	+	0.414789i
$635$	1318.03	+	679.490i	0.0823690	+	0.0424642i
$636$	11972.4	−	1143.23i	0.746442	−	0.0712766i
$637$	−6312.54	+	602.774i	−0.392640	+	0.0374926i
$638$	1416.63	+	730.324i	0.0879075	+	0.0453195i
$639$	802.492	+	3307.92i	0.0496809	+	0.204788i
$640$	−924.873	+	1601.93i	−0.0571231	+	0.0989402i
$641$	5632.13	+	9755.13i	0.347045	+	0.601099i	0.985723	−	0.168375i	$-0.0538519\pi$
$641$	5632.13	+	9755.13i	0.347045	+	0.601099i	−0.638678	+	0.769474i	$0.720519\pi$
$642$	−4403.61	+	4198.84i	−0.270711	+	0.258123i
$643$	2785.44	−	19373.2i	0.170835	−	1.18818i	−0.706290	−	0.707923i	$-0.749632\pi$
$643$	2785.44	−	19373.2i	0.170835	−	1.18818i	0.877125	−	0.480262i	$-0.159458\pi$
$644$	8883.31	−	25666.6i	0.543558	−	1.57051i
$645$	1362.39	−	400.032i	0.0831688	−	0.0244206i
$646$	−21354.9	−	24644.9i	−1.30062	−	1.50099i
$647$	−10455.0	+	5389.94i	−0.635285	+	0.327512i	−0.745609	−	0.666383i	$-0.767841\pi$
$647$	−10455.0	+	5389.94i	−0.635285	+	0.327512i	0.110324	+	0.993896i	$0.464811\pi$
$648$	−543.507	+	349.291i	−0.0329490	+	0.0211750i
$649$	−997.347	+	399.277i	−0.0603225	+	0.0241495i
$650$	261.473	−	5488.99i	0.0157782	−	0.331225i
$651$	−9024.59	−	12673.3i	−0.543320	−	0.762987i
$652$	−2285.09	−	6602.34i	−0.137256	−	0.396576i
$653$	−30247.3	+	5829.69i	−1.81266	+	0.349362i	−0.979150	−	0.203140i	$-0.934885\pi$
$653$	−30247.3	+	5829.69i	−1.81266	+	0.349362i	−0.833512	+	0.552501i	$0.813673\pi$
$654$	−7878.46	−	3154.06i	−0.471058	−	0.188583i
$655$	1018.97	−	2231.22i	0.0607852	−	0.133101i
$656$	−1525.51	+	1760.53i	−0.0907944	+	0.104782i
$657$	−670.848	+	2765.27i	−0.0398360	+	0.164206i
$658$	34774.5	+	33157.4i	2.06026	+	1.96445i
$659$	20824.9	−	16376.9i	1.23099	−	0.968062i	0.231003	−	0.972953i	$-0.425799\pi$
$659$	20824.9	−	16376.9i	1.23099	−	0.968062i	0.999988	+	0.00489079i	$0.00155679\pi$
$660$	5.41743	+	113.726i	0.000319505	+	0.00670723i
$661$	7031.47	+	15396.8i	0.413756	+	0.905999i	0.995688	+	0.0927619i	$0.0295696\pi$
$661$	7031.47	+	15396.8i	0.413756	+	0.905999i	−0.581932	+	0.813237i	$0.697703\pi$
$662$	−42195.7	−	12389.8i	−2.47732	−	0.727406i
$663$	−1404.71	+	1972.63i	−0.0822839	+	0.115552i
$664$	3518.40	+	2766.90i	0.205633	+	0.161712i
$665$	828.728	+	5763.93i	0.0483259	+	0.336114i
$666$	−14898.5	−	2871.45i	−0.866826	−	0.167067i
$667$	13819.8	+	8881.47i	0.802258	+	0.515580i
$668$	26679.0	+	2547.54i	1.54527	+	0.147556i
$669$	−10922.1			−0.631199
$670$	2681.95	+	3389.63i	0.154646	+	0.195452i
$671$	1404.37			0.0807976
$672$	23356.7	+	2230.30i	1.34078	+	0.128029i
$673$	5345.82	+	3435.55i	0.306191	+	0.196777i	0.684708	−	0.728817i	$-0.259930\pi$
$673$	5345.82	+	3435.55i	0.306191	+	0.196777i	−0.378518	+	0.925594i	$0.623566\pi$
$674$	−46152.1	−	8895.08i	−2.63755	−	0.508347i
$675$	−466.968	−	3247.83i	−0.0266276	−	0.185199i
$676$	16184.3	+	12727.5i	0.920820	+	0.724141i
$677$	−15230.2	+	21387.9i	−0.864617	+	1.21418i	0.110805	+	0.993842i	$0.464657\pi$
$677$	−15230.2	+	21387.9i	−0.864617	+	1.21418i	−0.975423	+	0.220343i	$0.929282\pi$
$678$	−10883.1	−	3195.56i	−0.616463	−	0.181010i
$679$	8527.22	+	18672.0i	0.481951	+	1.05533i
$680$	−53.3975	−	1120.95i	−0.00301133	−	0.0632155i
$681$	2633.91	−	2071.33i	0.148211	−	0.116554i
$682$	1068.75	+	1019.05i	0.0600065	+	0.0572161i
$683$	−6865.70	+	28300.8i	−0.384639	+	1.58550i	0.369785	+	0.929117i	$0.379431\pi$
$683$	−6865.70	+	28300.8i	−0.384639	+	1.58550i	−0.754424	+	0.656387i	$0.772084\pi$
$684$	5950.68	−	6867.45i	0.332646	−	0.383894i
$685$	−697.144	+	1526.53i	−0.0388854	+	0.0851471i
$686$	−30042.0	−	12027.0i	−1.67202	−	0.669378i
$687$	9282.22	−	1789.00i	0.515486	−	0.0993518i
$688$	3767.51	+	10885.5i	0.208772	+	0.603206i
$689$	2515.00	+	3531.82i	0.139062	+	0.195286i
$690$	−101.024	+	2120.76i	−0.00557382	+	0.117009i
$691$	−6691.37	+	2678.82i	−0.368382	+	0.147478i	−0.548465	−	0.836174i	$-0.684788\pi$
$691$	−6691.37	+	2678.82i	−0.368382	+	0.147478i	0.180083	+	0.983651i	$0.442363\pi$
$692$	9547.44	−	6135.76i	0.524478	−	0.337062i
$693$	504.179	−	259.922i	0.0276366	−	0.0142477i
$694$	3677.50	+	4244.06i	0.201147	+	0.232136i
$695$	1176.16	−	345.351i	0.0641930	−	0.0188488i
$696$	1431.76	−	4136.79i	0.0779750	−	0.225294i
$697$	551.857	−	3838.25i	0.0299901	−	0.208585i
$698$	−18014.4	+	17176.7i	−0.976868	+	0.931442i
$699$	8462.91	+	14658.2i	0.457935	+	0.793167i
$700$	18379.0	−	31833.3i	0.992371	−	1.71884i
$701$	7412.28	+	30553.8i	0.399369	+	1.64622i	0.716313	+	0.697779i	$0.245828\pi$
$701$	7412.28	+	30553.8i	0.399369	+	1.64622i	−0.316944	+	0.948444i	$0.602657\pi$
$702$	−1085.17	−	559.443i	−0.0583433	−	0.0300781i
$703$	40527.4	−	3869.90i	2.17428	−	0.207619i
$704$	−1472.86	+	140.641i	−0.0788502	+	0.00752928i
$705$	−1845.26	−	951.297i	−0.0985766	−	0.0508198i
$706$	7504.39	+	30933.5i	0.400045	+	1.64901i
$707$	6999.48	−	12123.5i	0.372338	−	0.644908i
$708$	7733.48	+	13394.8i	0.410511	+	0.711026i
$709$	14140.5	−	13483.0i	0.749025	−	0.714193i	−0.215988	−	0.976396i	$-0.569297\pi$
$709$	14140.5	−	13483.0i	0.749025	−	0.714193i	0.965013	+	0.262203i	$0.0844488\pi$
$710$	424.214	−	2950.47i	0.0224232	−	0.155957i
$711$	−819.591	+	2368.05i	−0.0432307	+	0.124907i
$712$	11399.5	−	3347.19i	0.600019	−	0.176181i
$713$	9967.47	+	11503.1i	0.523541	+	0.604198i
$714$	−26049.3	+	13429.3i	−1.36536	+	0.703894i
$715$	−34.5297	+	22.1909i	−0.00180607	+	0.00116069i
$716$	36356.9	−	14555.1i	1.89766	−	0.759707i
$717$	205.925	−	4322.90i	0.0107258	−	0.225163i
$718$	−22878.9	−	32128.9i	−1.18918	−	1.66997i
$719$	−8086.47	−	23364.3i	−0.419436	−	1.21188i	−0.934882	−	0.354959i	$-0.884495\pi$
$719$	−8086.47	−	23364.3i	−0.419436	−	1.21188i	0.515446	−	0.856922i	$-0.327626\pi$
$720$	−746.962	+	143.965i	−0.0386634	+	0.00745175i
$721$	−47639.6	−	19072.0i	−2.46074	−	0.985131i
$722$	−6274.86	+	13740.0i	−0.323443	+	0.708242i
$723$	3007.95	−	3471.36i	0.154726	−	0.178563i
$724$	1485.15	−	6121.89i	0.0762366	−	0.314252i
$725$	16090.5	+	15342.2i	0.824256	+	0.785927i
$726$	13231.9	−	10405.6i	0.676419	−	0.531942i
$727$	−1294.17	−	27167.9i	−0.0660220	−	1.38597i	−0.752390	−	0.658718i	$-0.771099\pi$
$727$	−1294.17	−	27167.9i	−0.0660220	−	1.38597i	0.686368	−	0.727254i	$-0.259204\pi$
$728$	−1083.90	−	2373.41i	−0.0551813	−	0.120830i
$729$	−699.470	−	205.383i	−0.0355368	−	0.0104345i
$730$	1445.40	−	2029.78i	0.0732832	−	0.102912i
$731$	−15072.3	−	11853.0i	−0.762610	−	0.599723i
$732$	−2877.47	−	20013.3i	−0.145293	−	1.01053i
$733$	−13783.6	−	2656.57i	−0.694556	−	0.133865i	−0.170258	−	0.985400i	$-0.554460\pi$
$733$	−13783.6	−	2656.57i	−0.694556	−	0.133865i	−0.524298	+	0.851535i	$0.675672\pi$
$734$	23431.8	+	15058.7i	1.17831	+	0.757256i
$735$	3300.79	+	315.187i	0.165648	+	0.0158175i
$736$	−22954.2			−1.14960
$737$	−315.065	+	1084.91i	−0.0157470	+	0.0542239i
$738$	1954.96			0.0975108
$739$	−5108.99	−	487.849i	−0.254313	−	0.0242839i	−0.0328790	−	0.999459i	$-0.510468\pi$
$739$	−5108.99	−	487.849i	−0.254313	−	0.0242839i	−0.221434	+	0.975175i	$0.571074\pi$
$740$	6178.16	+	3970.46i	0.306910	+	0.197239i
$741$	3216.71	+	619.970i	0.159472	+	0.0307357i
$742$	7467.53	+	51937.8i	0.369463	+	2.56967i
$743$	−8799.81	−	6920.24i	−0.434500	−	0.341695i	0.376831	−	0.926282i	$-0.377014\pi$
$743$	−8799.81	−	6920.24i	−0.434500	−	0.341695i	−0.811331	+	0.584588i	$0.801256\pi$
$744$	2352.68	−	3303.87i	0.115932	−	0.162803i
$745$	1289.52	+	378.638i	0.0634154	+	0.0186204i
$746$	13268.2	+	29053.4i	0.651186	+	1.42590i
$747$	240.317	+	5044.88i	0.0117708	+	0.247099i
$748$	1208.57	−	950.430i	0.0590771	−	0.0464588i
$749$	−10619.2	−	10125.3i	−0.518045	−	0.493955i
$750$	−1374.23	+	5664.64i	−0.0669063	+	0.275791i
$751$	−11699.3	+	13501.7i	−0.568460	+	0.656038i	−0.965083	−	0.261944i	$-0.915636\pi$
$751$	−11699.3	+	13501.7i	−0.568460	+	0.656038i	0.396623	+	0.917981i	$0.370182\pi$
$752$	6996.43	−	15320.0i	0.339273	−	0.742905i
$753$	−4584.12	−	1835.20i	−0.221852	−	0.0888161i
$754$	8122.86	−	1565.55i	0.392330	−	0.0756155i
$755$	409.611	+	1183.49i	0.0197447	+	0.0570487i
$756$	−4737.10	−	6652.33i	−0.227892	−	0.320030i
$757$	704.270	−	14784.5i	0.0338139	−	0.709841i	−0.916778	−	0.399398i	$-0.869219\pi$
$757$	704.270	−	14784.5i	0.0338139	−	0.709841i	0.950592	−	0.310444i	$-0.100478\pi$
$758$	−47597.9	+	19055.3i	−2.28078	+	0.913087i
$759$	−466.841	+	300.020i	−0.0223258	+	0.0143479i
$760$	−1349.33	+	695.627i	−0.0644017	+	0.0332014i
$761$	14397.4	+	16615.5i	0.685817	+	0.791475i	0.986763	−	0.162166i	$-0.0518480\pi$
$761$	14397.4	+	16615.5i	0.685817	+	0.791475i	−0.300947	+	0.953641i	$0.597303\pi$
$762$	9686.66	−	2844.26i	0.460513	−	0.135219i
$763$	6693.30	−	19339.0i	0.317580	−	0.917587i
$764$	−774.565	+	5387.22i	−0.0366790	+	0.255108i
$765$	916.448	−	873.831i	0.0433127	−	0.0412986i
$766$	1713.41	+	2967.72i	0.0808200	+	0.139984i
$767$	−2787.98	+	4828.92i	−0.131249	+	0.227330i
$768$	−1094.97	−	4513.52i	−0.0514470	−	0.212067i
$769$	−30626.1	−	15788.9i	−1.43616	−	0.740392i	−0.448031	−	0.894018i	$-0.647875\pi$
$769$	−30626.1	−	15788.9i	−1.43616	−	0.740392i	−0.988129	+	0.153626i	$0.950905\pi$
$770$	−494.486	+	47.2177i	−0.0231429	+	0.00220988i
$771$	9825.09	−	938.182i	0.458939	−	0.0438233i
$772$	−43598.9	−	22476.8i	−2.03259	−	1.04787i
$773$	5951.76	+	24533.5i	0.276934	+	1.14154i	0.925004	+	0.379956i	$0.124061\pi$
$773$	5951.76	+	24533.5i	0.276934	+	1.14154i	−0.648071	+	0.761580i	$0.724424\pi$
$774$	4833.45	−	8371.79i	0.224464	−	0.388783i
$775$	10299.6	+	17839.4i	0.477384	+	0.826853i
$776$	−3872.92	+	3692.82i	−0.179162	+	0.170831i
$777$	5207.08	−	36216.0i	0.240416	−	1.67213i
$778$	17968.6	−	51916.9i	0.828029	−	2.39243i
$779$	−5033.10	+	1477.85i	−0.231488	+	0.0679711i
$780$	386.984	+	446.604i	0.0177644	+	0.0205013i
$781$	692.490	−	357.004i	0.0317276	−	0.0163567i
$782$	24120.1	−	15501.1i	1.10299	−	0.708846i
$783$	4585.65	−	1835.82i	0.209295	−	0.0837890i
$784$	−1279.94	+	26869.2i	−0.0583062	+	1.22400i
$785$	2074.14	+	2912.73i	0.0943049	+	0.132433i
$786$	−5461.91	−	15781.2i	−0.247863	−	0.716152i
$787$	19685.1	−	3793.99i	0.891611	−	0.171844i	0.277183	−	0.960817i	$-0.410599\pi$
$787$	19685.1	−	3793.99i	0.891611	−	0.171844i	0.614428	+	0.788973i	$0.289387\pi$
$788$	−43384.6	−	17368.6i	−1.96131	−	0.785190i
$789$	6784.04	−	14855.0i	0.306107	−	0.670281i
$790$	1437.04	−	1658.44i	0.0647186	−	0.0746893i
$791$	6448.50	−	26581.1i	0.289864	−	1.19484i
$792$	107.023	+	102.046i	0.00480163	+	0.00457835i
$793$	5729.64	−	4505.84i	0.256577	−	0.201774i
$794$	1090.13	+	22884.7i	0.0487246	+	1.02286i
$795$	−941.811	−	2062.28i	−0.0420158	−	0.0920018i
$796$	−12179.6	−	3576.24i	−0.542328	−	0.159242i
$797$	10243.0	−	14384.3i	0.455240	−	0.639295i	−0.521620	−	0.853178i	$-0.674672\pi$
$797$	10243.0	−	14384.3i	0.455240	−	0.639295i	0.976859	+	0.213884i	$0.0686113\pi$
$798$	31163.3	+	24507.1i	1.38242	+	1.08714i
$799$	3989.83	+	27749.9i	0.176658	+	1.22869i
$800$	−30503.9	−	5879.15i	−1.34810	−	0.259824i
$801$	11277.7	+	7247.72i	0.497474	+	0.319707i
$802$	16299.5	+	1556.41i	0.717649	+	0.0685271i
$803$	651.292			0.0286221
$804$	16106.2	+	2266.98i	0.706495	+	0.0994406i
$805$	−5119.95			−0.224167
$806$	7629.88	+	728.566i	0.333438	+	0.0318395i
$807$	−6732.36	−	4326.63i	−0.293668	−	0.188729i
$808$	3583.53	+	690.668i	0.156025	+	0.0300713i
$809$	631.365	+	4391.24i	0.0274383	+	0.190838i	0.998931	−	0.0462331i	$-0.0147217\pi$
$809$	631.365	+	4391.24i	0.0274383	+	0.190838i	−0.971492	+	0.237071i	$0.923813\pi$
$810$	501.813	+	394.630i	0.0217678	+	0.0171184i
$811$	2564.48	−	3601.31i	0.111037	−	0.155930i	−0.755318	−	0.655359i	$-0.772517\pi$
$811$	2564.48	−	3601.31i	0.111037	−	0.155930i	0.866355	+	0.499429i	$0.166457\pi$
$812$	53093.0	+	15589.5i	2.29458	+	0.673749i
$813$	1959.15	+	4289.95i	0.0845147	+	0.185061i
$814$	165.244	+	3468.89i	0.00711522	+	0.149367i
$815$	−1035.25	+	814.132i	−0.0444949	+	0.0349911i
$816$	7434.74	+	7089.01i	0.318956	+	0.304124i
$817$	−6115.22	+	25207.3i	−0.261866	+	1.07943i
$818$	635.042	−	732.877i	0.0271439	−	0.0313257i
$819$	1223.03	−	2678.07i	0.0521810	−	0.114261i
$820$	−878.469	−	351.686i	−0.0374115	−	0.0149773i
$821$	10906.8	−	2102.12i	0.463644	−	0.0893600i	0.0479204	−	0.998851i	$-0.484741\pi$
$821$	10906.8	−	2102.12i	0.463644	−	0.0893600i	0.415723	+	0.909491i	$0.363528\pi$
$822$	3736.87	+	10797.0i	0.158562	+	0.458136i
$823$	−8307.46	−	11666.2i	−0.351859	−	0.494116i	0.600277	−	0.799792i	$-0.295057\pi$
$823$	−8307.46	−	11666.2i	−0.351859	−	0.494116i	−0.952136	+	0.305676i	$0.901118\pi$
$824$	636.538	−	13362.6i	0.0269112	−	0.564936i
$825$	−697.231	+	279.129i	−0.0294236	+	0.0117794i
$826$	−56768.3	+	36482.8i	−2.39131	+	1.53680i
$827$	−20874.9	+	10761.8i	−0.877742	+	0.452507i	−0.837344	−	0.546676i	$-0.815893\pi$
$827$	−20874.9	+	10761.8i	−0.877742	+	0.452507i	−0.0403978	+	0.999184i	$0.512863\pi$
$828$	5232.02	+	6038.08i	0.219596	+	0.253427i
$829$	−772.755	+	226.901i	−0.0323750	+	0.00950616i	−0.297880	−	0.954603i	$-0.596280\pi$
$829$	−772.755	+	226.901i	−0.0323750	+	0.00950616i	0.265505	+	0.964109i	$0.414461\pi$
$830$	1446.58	−	4179.63i	0.0604959	−	0.174792i
$831$	−465.931	+	3240.62i	−0.0194500	+	0.135278i
$832$	−5557.83	+	5299.38i	−0.231590	+	0.220821i
$833$	−22388.6	−	38778.3i	−0.931237	−	1.61295i
$834$	4172.75	−	7227.42i	0.173250	−	0.300078i
$835$	−1191.07	−	4909.67i	−0.0493638	−	0.203480i
$836$	−1848.67	−	953.053i	−0.0764802	−	0.0394283i
$837$	4555.86	−	435.031i	0.188140	−	0.0179652i
$838$	55400.1	−	5290.07i	2.28373	−	0.218070i
$839$	−16547.8	−	8530.99i	−0.680922	−	0.351040i	0.0828169	−	0.996565i	$-0.473608\pi$
$839$	−16547.8	−	8530.99i	−0.680922	−	0.351040i	−0.763739	+	0.645525i	$0.776639\pi$
$840$	321.654	+	1325.88i	0.0132121	+	0.0544608i
$841$	−4539.67	+	7862.94i	−0.186136	+	0.322397i
$842$	−30756.6	−	53272.0i	−1.25884	−	2.18037i
$843$	18543.8	−	17681.5i	0.757630	−	0.722399i
$844$	3371.70	−	23450.7i	0.137510	−	0.956405i
$845$	1269.43	−	3667.78i	0.0516802	−	0.149320i
$846$	−13561.5	+	3982.01i	−0.551127	+	0.161825i
$847$	26582.7	+	30678.0i	1.07838	+	1.24452i
$848$	16347.9	−	8427.91i	0.662014	−	0.341292i
$849$	−21868.7	+	14054.2i	−0.884020	+	0.568125i
$850$	36023.6	−	14421.7i	1.45365	−	0.581953i
$851$	−1703.20	+	35754.5i	−0.0686073	+	1.44025i
$852$	−6506.41	−	9136.98i	−0.261627	−	0.367403i
$853$	4423.02	+	12779.5i	0.177540	+	0.512968i	0.998299	−	0.0583071i	$-0.0185703\pi$
$853$	4423.02	+	12779.5i	0.177540	+	0.512968i	−0.820759	+	0.571275i	$0.806449\pi$
$854$	86619.3	−	16694.5i	3.47079	−	0.668940i
$855$	−1590.25	−	636.641i	−0.0636087	−	0.0254651i
$856$	1589.01	−	3479.46i	0.0634479	−	0.138931i
$857$	−5232.18	+	6038.26i	−0.208551	+	0.240680i	−0.850382	−	0.526165i	$-0.823629\pi$
$857$	−5232.18	+	6038.26i	−0.208551	+	0.240680i	0.641832	+	0.766846i	$0.278175\pi$
$858$	−65.8815	+	271.567i	−0.00262140	+	0.0108055i
$859$	8077.67	+	7702.04i	0.320846	+	0.305926i	0.833336	−	0.552768i	$-0.186428\pi$
$859$	8077.67	+	7702.04i	0.320846	+	0.305926i	−0.512490	+	0.858693i	$0.671277\pi$
$860$	−3677.97	+	2892.39i	−0.145835	+	0.114686i
$861$	224.316	+	4708.97i	0.00887882	+	0.186389i
$862$	−15882.0	−	34776.7i	−0.627544	−	1.37413i
$863$	−27305.3	−	8017.56i	−1.07704	−	0.316247i	−0.305344	−	0.952242i	$-0.598771\pi$
$863$	−27305.3	−	8017.56i	−1.07704	−	0.316247i	−0.771693	+	0.635996i	$0.780590\pi$
$864$	−4003.48	+	5622.10i	−0.157640	+	0.221375i
$865$	−1681.67	−	1322.48i	−0.0661022	−	0.0519834i
$866$	5401.67	+	37569.4i	0.211959	+	1.47420i
$867$	−2318.38	−	446.831i	−0.0908146	−	0.0175031i
$868$	43130.3	+	27718.1i	1.68656	+	1.08389i
$869$	570.963	+	54.5203i	0.0222884	+	0.00212828i
$870$	−4325.57			−0.168564
$871$	2195.43	+	5437.13i	0.0854070	+	0.211516i
$872$	5335.03			0.207187
$873$	−6010.88	−	573.970i	−0.233033	−	0.0222519i
$874$	−32628.5	−	20969.1i	−1.26279	−	0.811544i
$875$	−13802.3	−	2660.17i	−0.533260	−	0.102777i
$876$	−1334.46	−	9281.35i	−0.0514693	−	0.357977i
$877$	−5121.93	−	4027.93i	−0.197212	−	0.155090i	0.514670	−	0.857389i	$-0.327915\pi$
$877$	−5121.93	−	4027.93i	−0.197212	−	0.155090i	−0.711882	+	0.702299i	$0.752157\pi$
$878$	3673.03	−	5158.05i	0.141183	−	0.198264i
$879$	−10032.9	−	2945.93i	−0.384985	−	0.113042i
$880$	72.3303	+	158.381i	0.00277074	+	0.00606708i
$881$	−864.648	−	18151.2i	−0.0330655	−	0.694131i	−0.953166	−	0.302448i	$-0.902196\pi$
$881$	−864.648	−	18151.2i	−0.0330655	−	0.694131i	0.920100	−	0.391683i	$-0.128107\pi$
$882$	17744.8	−	13954.6i	0.677435	−	0.532741i
$883$	−19963.2	−	19034.8i	−0.760832	−	0.725451i	0.206644	−	0.978416i	$-0.433746\pi$
$883$	−19963.2	−	19034.8i	−0.760832	−	0.725451i	−0.967475	+	0.252965i	$0.918594\pi$
$884$	1881.40	−	7755.24i	0.0715818	−	0.295064i
$885$	1909.34	−	2203.49i	0.0725216	−	0.0836944i
$886$	5783.63	−	12664.4i	0.219306	−	0.480213i
$887$	−15696.5	−	6283.92i	−0.594178	−	0.237873i	0.0550288	−	0.998485i	$-0.482475\pi$
$887$	−15696.5	−	6283.92i	−0.594178	−	0.237873i	−0.649207	+	0.760612i	$0.724899\pi$
$888$	9366.10	−	1805.17i	0.353948	−	0.0682178i
$889$	7962.53	+	23006.2i	0.300399	+	0.867946i
$890$	−6809.65	−	9562.82i	−0.256472	−	0.360165i
$891$	−7.93943	+	166.669i	−0.000298519	+	0.00626669i
$892$	33413.7	−	13376.8i	1.25423	−	0.502118i
$893$	31904.2	−	20503.6i	1.19556	−	0.768340i
$894$	8132.76	−	4192.73i	0.304251	−	0.156852i
$895$	−4834.42	−	5579.22i	−0.180555	−	0.208372i
$896$	−29138.3	+	8555.78i	−1.08643	+	0.319005i
$897$	−942.049	+	2721.87i	−0.0350659	+	0.101316i
$898$	−5816.92	+	40457.6i	−0.216162	+	1.50344i
$899$	−22442.6	+	21399.0i	−0.832595	+	0.793878i
$900$	5406.36	+	9364.10i	0.200236	+	0.346818i
$901$	−15308.1	+	26514.3i	−0.566021	+	0.980377i
$902$	−105.493	−	434.849i	−0.00389417	−	0.0160520i
$903$	20720.0	+	10681.9i	0.763586	+	0.393656i
$904$	7098.30	−	677.805i	0.261157	−	0.0249375i
$905$	−1182.12	+	112.879i	−0.0434198	+	0.00414609i
$906$	7578.52	+	3907.00i	0.277902	+	0.143269i
$907$	−9185.02	−	37861.2i	−0.336255	−	1.38606i	−0.849395	−	0.527758i	$-0.823033\pi$
$907$	−9185.02	−	37861.2i	−0.336255	−	1.38606i	0.513139	−	0.858305i	$-0.328482\pi$
$908$	−5520.99	+	9562.63i	−0.201785	+	0.349501i
$909$	2058.97	+	3566.24i	0.0751284	+	0.130126i
$910$	−1865.94	+	1779.17i	−0.0679728	+	0.0648120i
$911$	1578.85	−	10981.1i	0.0574199	−	0.399365i	−0.940761	−	0.339071i	$-0.889887\pi$
$911$	1578.85	−	10981.1i	0.0574199	−	0.399365i	0.998181	−	0.0602934i	$-0.0192036\pi$
$912$	4545.08	−	13132.2i	0.165025	−	0.476808i
$913$	1109.19	−	325.687i	0.0402067	−	0.0118058i
$914$	−26201.1	−	30237.7i	−0.948200	−	1.09428i
$915$	−3387.75	+	1746.51i	−0.122399	+	0.0631013i
$916$	−26205.8	+	16841.4i	−0.945266	+	0.607486i
$917$	37385.9	−	14967.1i	1.34634	−	0.538992i
$918$	410.204	−	8611.24i	0.0147481	−	0.309601i
$919$	−14790.0	−	20769.7i	−0.530880	−	0.745517i	0.458843	−	0.888518i	$-0.348264\pi$
$919$	−14790.0	−	20769.7i	−0.530880	−	0.745517i	−0.989723	+	0.143001i	$0.954325\pi$
$920$	−436.554	−	1261.34i	−0.0156443	−	0.0452012i
$921$	11965.5	−	2306.15i	0.428095	−	0.0825085i
$922$	−31811.8	−	12735.5i	−1.13630	−	0.454904i
$923$	1679.84	−	3678.34i	0.0599053	−	0.131174i
$924$	−1224.08	+	1412.67i	−0.0435815	+	0.0502958i
$925$	−11421.0	+	47078.2i	−0.405969	+	1.67343i
$926$	15077.8	+	14376.6i	0.535083	+	0.510200i
$927$	11865.4	−	9331.09i	0.420402	−	0.330607i
$928$	−2225.16	−	46711.9i	−0.0787118	−	1.65236i
$929$	−12441.7	−	27243.6i	−0.439398	−	0.962147i	−0.991708	−	0.128508i	$-0.958981\pi$
$929$	−12441.7	−	27243.6i	−0.439398	−	0.962147i	0.552311	−	0.833638i	$-0.313746\pi$
$930$	−3845.43	−	1129.12i	−0.135588	−	0.0398121i
$931$	−35135.4	+	49340.8i	−1.23686	+	1.73693i
$932$	−43843.0	−	34478.5i	−1.54091	−	1.21178i
$933$	611.648	+	4254.10i	0.0214624	+	0.149274i
$934$	3276.95	+	631.581i	0.114802	+	0.0221263i
$935$	−243.823	−	156.696i	−0.00852821	−	0.00548075i
$936$	764.047	+	72.9576i	0.0266813	+	0.00254775i
$937$	−9703.86			−0.338326			−0.169163	−	0.985588i	$-0.554106\pi$
$937$	−9703.86			−0.338326			−0.169163	+	0.985588i	$0.554106\pi$
$938$	−6535.81	+	70660.6i	−0.227507	+	2.45965i
$939$	−3432.92			−0.119307
$940$	6810.26	+	650.301i	0.236304	+	0.0225643i
$941$	26308.8	+	16907.7i	0.911417	+	0.585732i	0.910155	−	0.414267i	$-0.135962\pi$
$941$	26308.8	+	16907.7i	0.911417	+	0.585732i	0.00126154	+	0.999999i	$0.499598\pi$
$942$	23904.4	+	4607.19i	0.826801	+	0.159353i
$943$	−656.368	−	4565.14i	−0.0226662	−	0.157647i
$944$	18592.7	+	14621.5i	0.641040	+	0.504120i
$945$	−892.979	+	1254.01i	−0.0307393	+	0.0431672i
$946$	−2123.00	−	623.368i	−0.0729646	−	0.0214243i
$947$	2258.04	+	4944.42i	0.0774830	+	0.169664i	0.944409	−	0.328773i	$-0.106635\pi$
$947$	2258.04	+	4944.42i	0.0774830	+	0.169664i	−0.866926	+	0.498437i	$0.833908\pi$
$948$	−392.916	−	8248.31i	−0.0134613	−	0.282587i
$949$	2657.18	−	2089.63i	0.0908911	−	0.0714776i
$950$	−37989.5	−	36222.9i	−1.29741	−	1.23708i
$951$	1139.50	−	4697.06i	0.0388545	−	0.160161i
$952$	12065.3	−	13924.1i	0.410755	−	0.474037i
$953$	−4563.82	+	9993.38i	−0.155128	+	0.339682i	−0.971199	−	0.238269i	$-0.923420\pi$
$953$	−4563.82	+	9993.38i	−0.155128	+	0.339682i	0.816072	+	0.577951i	$0.196147\pi$
$954$	−14329.5	−	5736.66i	−0.486305	−	0.194687i
$955$	1007.43	−	194.167i	0.0341359	−	0.00657915i
$956$	4664.48	+	13477.1i	0.157804	+	0.455943i
$957$	−655.800	−	920.942i	−0.0221515	−	0.0311074i
$958$	1148.48	−	24109.6i	0.0387326	−	0.813097i
$959$	−25578.2	+	10240.0i	−0.861277	+	0.344803i
$960$	3378.06	−	2170.95i	0.113569	−	0.0729864i
$961$	941.956	−	485.612i	0.0316188	−	0.0163006i
$962$	11803.9	+	13622.4i	0.395606	+	0.456553i
$963$	4141.30	−	1216.00i	0.138579	−	0.0406905i
$964$	−4950.60	+	14303.8i	−0.165403	+	0.477899i
$965$	−1315.93	+	9152.49i	−0.0438977	+	0.305315i
$966$	−25227.5	+	24054.3i	−0.840249	+	0.801176i
$967$	4750.71	+	8228.47i	0.157986	+	0.273640i	0.934142	−	0.356901i	$-0.116167\pi$
$967$	4750.71	+	8228.47i	0.157986	+	0.273640i	−0.776156	+	0.630541i	$0.782833\pi$
$968$	−5291.20	+	9164.63i	−0.175688	+	0.304300i
$969$	5453.59	+	22480.0i	0.180799	+	0.745265i
$970$	4699.94	+	2422.99i	0.155573	+	0.0802036i
$971$	−12697.1	+	1212.43i	−0.419639	+	0.0400706i	−0.302740	−	0.953073i	$-0.597901\pi$
$971$	−12697.1	+	1212.43i	−0.419639	+	0.0400706i	−0.116899	+	0.993144i	$0.537295\pi$
$972$	2391.42	−	228.352i	0.0789143	−	0.00753540i
$973$	17887.7	+	9221.76i	0.589367	+	0.303840i
$974$	12101.8	+	49884.2i	0.398117	+	1.64106i
$975$	−1949.04	+	3375.83i	−0.0640196	+	0.110885i
$976$	−15460.3	−	26778.0i	−0.507041	−	0.878221i
$977$	31496.2	−	30031.6i	1.03138	−	0.983415i	0.0315053	−	0.999504i	$-0.489970\pi$
$977$	31496.2	−	30031.6i	1.03138	−	0.983415i	0.999871	+	0.0160887i	$0.00512141\pi$
$978$	−1276.07	+	8875.25i	−0.0417221	+	0.290183i
$979$	1003.58	−	2899.64i	0.0327624	−	0.0946608i
$980$	−10484.1	+	3078.40i	−0.341736	+	0.100343i
$981$	3942.17	+	4549.50i	0.128301	+	0.148068i
$982$	−73184.6	+	37729.3i	−2.37822	+	1.22606i
$983$	−34244.5	+	22007.6i	−1.11112	+	0.714073i	−0.961537	−	0.274676i	$-0.911429\pi$
$983$	−34244.5	+	22007.6i	−1.11112	+	0.714073i	−0.149583	+	0.988749i	$0.547793\pi$
$984$	−1140.97	+	456.774i	−0.0369641	+	0.0147982i
$985$	−419.166	+	8799.38i	−0.0135591	+	0.284641i
$986$	33883.0	+	47582.0i	1.09438	+	1.53684i
$987$	−11147.7	−	32209.1i	−0.359508	−	1.03873i
$988$	−10600.1	+	2043.00i	−0.341330	+	0.0657860i
$989$	−21172.3	−	8476.10i	−0.680727	−	0.272522i
$990$	60.7004	−	132.915i	0.00194867	−	0.00426700i
$991$	−30527.3	+	35230.4i	−0.978538	+	1.12929i	0.0130570	+	0.999915i	$0.495844\pi$
$991$	−30527.3	+	35230.4i	−0.978538	+	1.12929i	−0.991595	+	0.129379i	$0.958702\pi$
$992$	10215.2	−	42107.8i	0.326950	−	1.34770i
$993$	22577.2	+	21527.3i	0.721517	+	0.687965i
$994$	38467.8	−	30251.4i	1.22749	−	0.965307i
$995$	113.857	+	2390.15i	0.00362765	+	0.0761537i
$996$	−6913.91	−	15139.4i	−0.219956	−	0.481635i
$997$	−21618.9	−	6347.87i	−0.686736	−	0.201644i	−0.0802936	−	0.996771i	$-0.525586\pi$
$997$	−21618.9	−	6347.87i	−0.686736	−	0.201644i	−0.606443	+	0.795127i	$0.707404\pi$
$998$	−1908.20	+	2679.69i	−0.0605240	+	0.0849941i
$999$	8460.19	+	6653.17i	0.267936	+	0.210708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.m.b.4.16	✓	360
67.17	even	33	inner	201.4.m.b.151.16	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.m.b.4.16	✓	360	1.1	even	1	trivial
201.4.m.b.151.16	yes	360	67.17	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)

\(f(q)\)	\(=\)	\(q+(4.21003 + 0.402009i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(9.70733 + 1.87093i) q^{4} +(-0.265215 - 1.84461i) q^{5} +(-9.97308 - 7.84292i) q^{6} +(17.7472 - 24.9224i) q^{7} +(7.65306 + 2.24714i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})\)	\(q+(4.21003 + 0.402009i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(9.70733 + 1.87093i) q^{4} +(-0.265215 - 1.84461i) q^{5} +(-9.97308 - 7.84292i) q^{6} +(17.7472 - 24.9224i) q^{7} +(7.65306 + 2.24714i) q^{8} +(3.73874 + 8.18669i) q^{9} +(-0.375013 - 7.87250i) q^{10} +(1.61925 - 1.27339i) q^{11} +(-21.4645 - 20.4663i) q^{12} +(2.52071 - 10.3905i) q^{13} +(84.7352 - 97.7896i) q^{14} +(-2.32248 + 5.08552i) q^{15} +(-42.1064 - 16.8568i) q^{16} +(74.1341 - 14.2882i) q^{17} +(12.4491 + 35.9692i) q^{18} +(-59.2415 - 83.1930i) q^{19} +(0.876617 - 18.4025i) q^{20} +(-85.2118 + 34.1137i) q^{21} +(7.32901 - 4.71007i) q^{22} +(79.8142 - 41.1471i) q^{23} +(-15.6698 - 18.0839i) q^{24} +(116.604 - 34.2381i) q^{25} +(14.7894 - 42.7311i) q^{26} +(3.84250 - 26.7252i) q^{27} +(218.906 - 208.726i) q^{28} +(91.4718 + 158.434i) q^{29} +(-11.8221 + 20.4765i) q^{30} +(39.9618 + 164.725i) q^{31} +(-227.208 - 117.134i) q^{32} +(-6.15194 + 0.587440i) q^{33} +(317.851 - 30.3511i) q^{34} +(-50.6790 - 26.1268i) q^{35} +(20.9764 + 86.4658i) q^{36} +(-199.312 + 345.219i) q^{37} +(-215.964 - 374.061i) q^{38} +(-23.2143 + 22.1348i) q^{39} +(2.11540 - 14.7129i) q^{40} +(16.7987 - 48.5367i) q^{41} +(-372.459 + 109.364i) q^{42} +(-166.317 - 191.941i) q^{43} +(18.1010 - 9.33173i) q^{44} +(14.1097 - 9.06775i) q^{45} +(352.562 - 141.144i) q^{46} +(-17.6689 + 370.915i) q^{47} +(78.9259 + 110.836i) q^{48} +(-193.980 - 560.469i) q^{49} +(504.672 - 97.2676i) q^{50} +(-210.271 - 84.1798i) q^{51} +(43.9094 - 96.1481i) q^{52} +(-265.559 + 306.471i) q^{53} +(26.9208 - 110.969i) q^{54} +(-2.77837 - 2.64917i) q^{55} +(191.824 - 150.852i) q^{56} +(14.5787 + 306.044i) q^{57} +(321.407 + 703.784i) q^{58} +(-500.387 - 146.927i) q^{59} +(-32.0597 + 45.0216i) q^{60} +(535.886 + 421.425i) q^{61} +(102.020 + 709.562i) q^{62} +(270.384 + 52.1122i) q^{63} +(-604.223 - 388.311i) q^{64} +(-19.8350 - 1.89402i) q^{65} -26.1360 q^{66} +(-445.783 + 319.438i) q^{67} +746.376 q^{68} +(-268.169 - 25.6071i) q^{69} +(-202.857 - 130.368i) q^{70} +(371.373 + 71.5762i) q^{71} +(10.2161 + 71.0546i) q^{72} +(248.522 + 195.440i) q^{73} +(-977.893 + 1373.26i) q^{74} +(-349.813 - 102.714i) q^{75} +(-419.428 - 918.418i) q^{76} +(-2.99890 - 62.9547i) q^{77} +(-106.631 + 83.8558i) q^{78} +(201.509 + 192.139i) q^{79} +(-19.9271 + 82.1406i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(90.2354 - 197.588i) q^{82} +(520.980 + 208.569i) q^{83} +(-891.003 + 171.727i) q^{84} +(-46.0176 - 132.959i) q^{85} +(-623.040 - 874.937i) q^{86} +(26.1144 - 548.209i) q^{87} +(15.2537 - 6.10666i) q^{88} +(1253.07 - 805.302i) q^{89} +(63.0476 - 32.5033i) q^{90} +(-214.221 - 247.225i) q^{91} +(851.766 - 250.101i) q^{92} +(166.317 - 480.541i) q^{93} +(-223.498 + 1554.46i) q^{94} +(-137.747 + 131.342i) q^{95} +(383.437 + 664.133i) q^{96} +(-335.457 + 581.028i) q^{97} +(-591.349 - 2437.58i) q^{98} +(16.4788 + 8.49542i) 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

Modular forms

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