LMFDB - Embedded newform 128.4.k.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83459 - 2.15274i) q^{2} +(-7.96376 - 2.41578i) q^{3} +(-1.26855 + 7.89878i) q^{4} +(9.56707 + 0.942274i) q^{5} +(9.40970 + 21.5759i) q^{6} +(2.63589 + 3.94489i) q^{7} +(19.3313 - 11.7602i) q^{8} +(35.1358 + 23.4770i) q^{9} +O(q^{10})$	\(q+(-1.83459 - 2.15274i) q^{2} +(-7.96376 - 2.41578i) q^{3} +(-1.26855 + 7.89878i) q^{4} +(9.56707 + 0.942274i) q^{5} +(9.40970 + 21.5759i) q^{6} +(2.63589 + 3.94489i) q^{7} +(19.3313 - 11.7602i) q^{8} +(35.1358 + 23.4770i) q^{9} +(-15.5232 - 22.3241i) q^{10} +(17.2027 - 32.1840i) q^{11} +(29.1842 - 59.8395i) q^{12} +(4.18722 + 42.5135i) q^{13} +(3.65653 - 12.9116i) q^{14} +(-73.9135 - 30.6160i) q^{15} +(-60.7815 - 20.0401i) q^{16} +(-45.9844 + 19.0473i) q^{17} +(-13.9200 - 118.709i) q^{18} +(28.5922 - 34.8397i) q^{19} +(-19.5792 + 74.3729i) q^{20} +(-11.4616 - 37.7839i) q^{21} +(-100.844 + 22.0116i) q^{22} +(-36.4797 - 183.396i) q^{23} +(-182.360 + 46.9550i) q^{24} +(-31.9573 - 6.35670i) q^{25} +(83.8386 - 87.0089i) q^{26} +(-80.5520 - 98.1529i) q^{27} +(-34.5036 + 15.8160i) q^{28} +(216.890 - 115.930i) q^{29} +(69.6929 + 215.284i) q^{30} +(-74.5743 - 74.5743i) q^{31} +(68.3682 + 167.612i) q^{32} +(-214.748 + 214.748i) q^{33} +(125.366 + 64.0482i) q^{34} +(21.5006 + 40.2247i) q^{35} +(-230.012 + 247.749i) q^{36} +(157.468 - 129.231i) q^{37} +(-127.456 + 2.36509i) q^{38} +(69.3574 - 348.683i) q^{39} +(196.025 - 94.2949i) q^{40} +(314.762 - 62.6101i) q^{41} +(-60.3114 + 93.9918i) q^{42} +(-105.443 + 31.9859i) q^{43} +(232.392 + 176.708i) q^{44} +(314.025 + 257.714i) q^{45} +(-327.878 + 414.988i) q^{46} +(-74.4402 - 179.714i) q^{47} +(435.637 + 306.429i) q^{48} +(122.646 - 296.094i) q^{49} +(44.9442 + 80.4576i) q^{50} +(412.223 - 40.6004i) q^{51} +(-341.117 - 20.8568i) q^{52} +(-307.896 - 164.574i) q^{53} +(-63.5174 + 353.478i) q^{54} +(194.906 - 291.697i) q^{55} +(97.3477 + 45.2612i) q^{56} +(-311.867 + 208.383i) q^{57} +(-647.470 - 254.222i) q^{58} +(-44.5354 + 452.175i) q^{59} +(335.592 - 544.989i) q^{60} +(192.080 - 633.203i) q^{61} +(-23.7255 + 297.352i) q^{62} +200.490i q^{63} +(235.397 - 454.678i) q^{64} +410.675i q^{65} +(856.270 + 68.3213i) q^{66} +(122.506 - 403.849i) q^{67} +(-92.1172 - 387.383i) q^{68} +(-152.529 + 1548.65i) q^{69} +(47.1485 - 120.081i) q^{70} +(-319.508 + 213.489i) q^{71} +(955.315 + 40.6375i) q^{72} +(-292.462 + 437.700i) q^{73} +(-567.090 - 101.902i) q^{74} +(239.144 + 127.825i) q^{75} +(238.920 + 270.040i) q^{76} +(172.307 - 16.9707i) q^{77} +(-877.865 + 490.382i) q^{78} +(-56.3804 + 136.114i) q^{79} +(-562.618 - 248.998i) q^{80} +(-32.2429 - 77.8413i) q^{81} +(-712.243 - 562.736i) q^{82} +(999.656 + 820.396i) q^{83} +(312.986 - 42.6019i) q^{84} +(-457.883 + 138.897i) q^{85} +(262.303 + 168.311i) q^{86} +(-2007.32 + 399.281i) q^{87} +(-45.9389 - 824.465i) q^{88} +(134.295 - 675.147i) q^{89} +(-21.3176 - 1148.81i) q^{90} +(-156.674 + 128.579i) q^{91} +(1494.88 - 55.4976i) q^{92} +(413.737 + 774.047i) q^{93} +(-250.311 + 489.953i) q^{94} +(306.372 - 306.372i) q^{95} +(-139.554 - 1499.99i) q^{96} +(-997.565 - 997.565i) q^{97} +(-862.418 + 279.186i) q^{98} +(1360.02 - 726.944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.83459	−	2.15274i	−0.648626	−	0.761108i
$2$	−1.83459	−	2.15274i	−0.648626	−	0.761108i
$3$	−7.96376	−	2.41578i	−1.53263	−	0.464917i	−0.592451	−	0.805607i	$-0.701840\pi$
$3$	−7.96376	−	2.41578i	−1.53263	−	0.464917i	−0.940176	+	0.340689i	$0.889340\pi$
$4$	−1.26855	+	7.89878i	−0.158569	+	0.987348i
$5$	9.56707	+	0.942274i	0.855704	+	0.0842795i	0.516349	−	0.856379i	$-0.327291\pi$
$5$	9.56707	+	0.942274i	0.855704	+	0.0842795i	0.339356	+	0.940658i	$0.389791\pi$
$6$	9.40970	+	21.5759i	0.640249	+	1.46805i
$7$	2.63589	+	3.94489i	0.142325	+	0.213004i	0.895783	−	0.444492i	$-0.146616\pi$
$7$	2.63589	+	3.94489i	0.142325	+	0.213004i	−0.753458	+	0.657496i	$0.771616\pi$
$8$	19.3313	−	11.7602i	0.854330	−	0.519731i
$9$	35.1358	+	23.4770i	1.30133	+	0.869519i
$10$	−15.5232	−	22.3241i	−0.490886	−	0.705949i
$11$	17.2027	−	32.1840i	0.471528	−	0.882167i	−0.527931	−	0.849287i	$-0.677032\pi$
$11$	17.2027	−	32.1840i	0.471528	−	0.882167i	0.999459	−	0.0328802i	$-0.0104680\pi$
$12$	29.1842	−	59.8395i	0.702063	−	1.43951i
$13$	4.18722	+	42.5135i	0.0893327	+	0.907010i	0.930514	+	0.366257i	$0.119361\pi$
$13$	4.18722	+	42.5135i	0.0893327	+	0.907010i	−0.841181	+	0.540753i	$0.818139\pi$
$14$	3.65653	−	12.9116i	0.0698034	−	0.246484i
$15$	−73.9135	−	30.6160i	−1.27229	−	0.527001i
$16$	−60.7815	−	20.0401i	−0.949712	−	0.313126i
$17$	−45.9844	+	19.0473i	−0.656050	+	0.271745i	−0.685775	−	0.727813i	$-0.740537\pi$
$17$	−45.9844	+	19.0473i	−0.656050	+	0.271745i	0.0297255	+	0.999558i	$0.490537\pi$
$18$	−13.9200	−	118.709i	−0.182277	−	1.55444i
$19$	28.5922	−	34.8397i	0.345237	−	0.420672i	−0.571225	−	0.820793i	$-0.693532\pi$
$19$	28.5922	−	34.8397i	0.345237	−	0.420672i	0.916462	+	0.400121i	$0.131032\pi$
$20$	−19.5792	+	74.3729i	−0.218902	+	0.831514i
$21$	−11.4616	−	37.7839i	−0.119101	−	0.392625i
$22$	−100.844	+	22.0116i	−0.977270	+	0.213313i
$23$	−36.4797	−	183.396i	−0.330719	−	1.66264i	−0.685790	−	0.727799i	$-0.740543\pi$
$23$	−36.4797	−	183.396i	−0.330719	−	1.66264i	0.355071	−	0.934839i	$-0.384457\pi$
$24$	−182.360	+	46.9550i	−1.55100	+	0.399361i
$25$	−31.9573	−	6.35670i	−0.255658	−	0.0508536i
$26$	83.8386	−	87.0089i	0.632389	−	0.656302i
$27$	−80.5520	−	98.1529i	−0.574157	−	0.699612i
$28$	−34.5036	+	15.8160i	−0.232877	+	0.106748i
$29$	216.890	−	115.930i	1.38881	−	0.742333i	0.403800	−	0.914847i	$-0.367689\pi$
$29$	216.890	−	115.930i	1.38881	−	0.742333i	0.985007	+	0.172515i	$0.0551892\pi$
$30$	69.6929	+	215.284i	0.424137	+	1.31018i
$31$	−74.5743	−	74.5743i	−0.432062	−	0.432062i	0.457267	−	0.889329i	$-0.348828\pi$
$31$	−74.5743	−	74.5743i	−0.432062	−	0.432062i	−0.889329	+	0.457267i	$0.848828\pi$
$32$	68.3682	+	167.612i	0.377685	+	0.925934i
$33$	−214.748	+	214.748i	−1.13281	+	1.13281i
$34$	125.366	+	64.0482i	0.632358	+	0.323064i
$35$	21.5006	+	40.2247i	0.103836	+	0.194263i
$36$	−230.012	+	247.749i	−1.06487	+	1.14698i
$37$	157.468	−	129.231i	0.699666	−	0.574201i	−0.215877	−	0.976420i	$-0.569261\pi$
$37$	157.468	−	129.231i	0.699666	−	0.574201i	0.915543	+	0.402219i	$0.131761\pi$
$38$	−127.456	+	2.36509i	−0.544107	+	0.0100965i
$39$	69.3574	−	348.683i	0.284771	−	1.43164i
$40$	196.025	−	94.2949i	0.774857	−	0.372734i
$41$	314.762	−	62.6101i	1.19897	−	0.238489i	0.445078	−	0.895492i	$-0.353176\pi$
$41$	314.762	−	62.6101i	1.19897	−	0.238489i	0.753888	+	0.657003i	$0.228176\pi$
$42$	−60.3114	+	93.9918i	−0.221577	+	0.345315i
$43$	−105.443	+	31.9859i	−0.373953	+	0.113437i	−0.471666	−	0.881777i	$-0.656347\pi$
$43$	−105.443	+	31.9859i	−0.373953	+	0.113437i	0.0977132	+	0.995215i	$0.468847\pi$
$44$	232.392	+	176.708i	0.796236	+	0.605447i
$45$	314.025	+	257.714i	1.04027	+	0.853727i
$46$	−327.878	+	414.988i	−1.05093	+	1.33014i
$47$	−74.4402	−	179.714i	−0.231026	−	0.557746i	0.765273	−	0.643706i	$-0.222604\pi$
$47$	−74.4402	−	179.714i	−0.231026	−	0.557746i	−0.996299	+	0.0859605i	$0.972604\pi$
$48$	435.637	+	306.429i	1.30998	+	0.921443i
$49$	122.646	−	296.094i	0.357569	−	0.863248i
$50$	44.9442	+	80.4576i	0.127121	+	0.227568i
$51$	412.223	−	40.6004i	1.13182	−	0.111474i
$52$	−341.117	−	20.8568i	−0.909700	−	0.0556215i
$53$	−307.896	−	164.574i	−0.797976	−	0.426527i	0.0214090	−	0.999771i	$-0.493185\pi$
$53$	−307.896	−	164.574i	−0.797976	−	0.426527i	−0.819385	+	0.573244i	$0.805685\pi$
$54$	−63.5174	+	353.478i	−0.160067	+	0.890781i
$55$	194.906	−	291.697i	0.477838	−	0.715134i
$56$	97.3477	+	45.2612i	0.232297	+	0.108005i
$57$	−311.867	+	208.383i	−0.724697	+	0.484227i
$58$	−647.470	−	254.222i	−1.46581	−	0.575535i
$59$	−44.5354	+	452.175i	−0.0982714	+	0.997766i	0.811973	+	0.583695i	$0.198394\pi$
$59$	−44.5354	+	452.175i	−0.0982714	+	0.997766i	−0.910244	+	0.414071i	$0.864106\pi$
$60$	335.592	−	544.989i	0.722080	−	1.17263i
$61$	192.080	−	633.203i	0.403169	−	1.32907i	−0.486985	−	0.873410i	$-0.661903\pi$
$61$	192.080	−	633.203i	0.403169	−	1.32907i	0.890154	−	0.455660i	$-0.150597\pi$
$62$	−23.7255	+	297.352i	−0.0485991	+	0.609093i
$63$			200.490i			0.400942i
$64$	235.397	−	454.678i	0.459760	−	0.888043i
$65$			410.675i			0.783661i
$66$	856.270	+	68.3213i	1.59696	+	0.127421i
$67$	122.506	−	403.849i	0.223381	−	0.736388i	−0.771581	−	0.636131i	$-0.780534\pi$
$67$	122.506	−	403.849i	0.223381	−	0.736388i	0.994962	−	0.100257i	$-0.0319664\pi$
$68$	−92.1172	−	387.383i	−0.164277	−	0.690840i
$69$	−152.529	+	1548.65i	−0.266120	+	2.70196i
$70$	47.1485	−	120.081i	0.0805047	−	0.205035i
$71$	−319.508	+	213.489i	−0.534065	+	0.356851i	−0.793172	−	0.608998i	$-0.791572\pi$
$71$	−319.508	+	213.489i	−0.534065	+	0.356851i	0.259107	+	0.965849i	$0.416572\pi$
$72$	955.315	+	40.6375i	1.56368	+	0.0665163i
$73$	−292.462	+	437.700i	−0.468906	+	0.701767i	−0.988258	−	0.152793i	$-0.951173\pi$
$73$	−292.462	+	437.700i	−0.468906	+	0.701767i	0.519353	+	0.854560i	$0.326173\pi$
$74$	−567.090	−	101.902i	−0.890850	−	0.160079i
$75$	239.144	+	127.825i	0.368186	+	0.196800i
$76$	238.920	+	270.040i	0.360606	+	0.407575i
$77$	172.307	−	16.9707i	0.255015	−	0.0251168i
$78$	−877.865	+	490.382i	−1.27434	+	0.711857i
$79$	−56.3804	+	136.114i	−0.0802948	+	0.193849i	−0.958929	−	0.283647i	$-0.908456\pi$
$79$	−56.3804	+	136.114i	−0.0802948	+	0.193849i	0.878634	+	0.477496i	$0.158456\pi$
$80$	−562.618	−	248.998i	−0.786282	−	0.347985i
$81$	−32.2429	−	77.8413i	−0.0442290	−	0.106778i
$82$	−712.243	−	562.736i	−0.959196	−	0.757852i
$83$	999.656	+	820.396i	1.32201	+	1.08494i	0.989910	+	0.141696i	$0.0452556\pi$
$83$	999.656	+	820.396i	1.32201	+	1.08494i	0.332095	+	0.943246i	$0.392244\pi$
$84$	312.986	−	42.6019i	0.406543	−	0.0553363i
$85$	−457.883	+	138.897i	−0.584287	+	0.177242i
$86$	262.303	+	168.311i	0.328893	+	0.211040i
$87$	−2007.32	+	399.281i	−2.47365	+	0.492039i
$88$	−45.9389	−	824.465i	−0.0556489	−	0.998730i
$89$	134.295	−	675.147i	0.159947	−	0.804106i	−0.814618	−	0.579998i	$-0.803053\pi$
$89$	134.295	−	675.147i	0.159947	−	0.804106i	0.974564	−	0.224108i	$-0.0719468\pi$
$90$	−21.3176	−	1148.81i	−0.0249674	−	1.34551i
$91$	−156.674	+	128.579i	−0.180482	+	0.148118i
$92$	1494.88	−	55.4976i	1.69404	−	0.0628916i
$93$	413.737	+	774.047i	0.461317	+	0.863064i
$94$	−250.311	+	489.953i	−0.274655	+	0.537604i
$95$	306.372	−	306.372i	0.330875	−	0.330875i
$96$	−139.554	−	1499.99i	−0.148367	−	1.59470i
$97$	−997.565	−	997.565i	−1.04420	−	1.04420i	−0.998977	−	0.0452230i	$-0.985600\pi$
$97$	−997.565	−	997.565i	−1.04420	−	1.04420i	−0.0452230	−	0.998977i	$-0.514400\pi$
$98$	−862.418	+	279.186i	−0.888953	+	0.287776i
$99$	1360.02	−	726.944i	1.38067	−	0.737986i
$100$	90.7497	−	244.360i	0.0907497	−	0.244360i
$101$	1163.70	+	1417.97i	1.14646	+	1.39697i	0.904390	+	0.426706i	$0.140326\pi$
$101$	1163.70	+	1417.97i	1.14646	+	1.39697i	0.242069	+	0.970259i	$0.422174\pi$
$102$	−843.662	−	812.922i	−0.818970	−	0.789130i
$103$	314.025	+	62.4635i	0.300406	+	0.0597544i	0.342992	−	0.939338i	$-0.388560\pi$
$103$	314.025	+	62.4635i	0.300406	+	0.0597544i	−0.0425860	+	0.999093i	$0.513560\pi$
$104$	580.910	+	772.598i	0.547721	+	0.728457i
$105$	−74.0513	−	372.281i	−0.0688254	−	0.346008i
$106$	210.579	+	964.744i	0.192955	+	0.884002i
$107$	−530.741	−	1749.62i	−0.479521	−	1.58077i	−0.779230	−	0.626737i	$-0.784390\pi$
$107$	−530.741	−	1749.62i	−0.479521	−	1.58077i	0.299710	−	0.954030i	$-0.403110\pi$
$108$	877.473	−	511.750i	0.781804	−	0.455955i
$109$	823.887	−	1003.91i	0.723983	−	0.882175i	−0.272821	−	0.962065i	$-0.587957\pi$
$109$	823.887	−	1003.91i	0.723983	−	0.882175i	0.996804	+	0.0798894i	$0.0254567\pi$
$110$	−985.519	+	115.564i	−0.854232	+	0.100169i
$111$	−1566.23	+	648.756i	−1.33928	+	0.554749i
$112$	−81.1576	−	292.600i	−0.0684703	−	0.246858i
$113$	−864.234	−	357.977i	−0.719472	−	0.298015i	−0.00725399	−	0.999974i	$-0.502309\pi$
$113$	−864.234	−	357.977i	−0.719472	−	0.298015i	−0.712218	+	0.701959i	$0.752309\pi$
$114$	1020.74	+	289.070i	0.838606	+	0.237490i
$115$	−176.195	−	1788.93i	−0.142872	−	1.45060i
$116$	640.569	+	1860.23i	0.512718	+	1.48895i
$117$	−850.969	+	1592.05i	−0.672412	+	1.25799i
$118$	1055.12	−	733.683i	0.823149	−	0.572382i
$119$	−196.349	−	131.196i	−0.151255	−	0.101065i
$120$	−1788.89	+	277.389i	−1.36086	+	0.211017i
$121$	−0.412899	−	0.617947i	−0.000310217	−	0.000464273i
$122$	−1715.51	+	748.170i	−1.27307	+	0.555214i
$123$	−2657.94	−	261.785i	−1.94845	−	0.191905i
$124$	683.647	−	494.444i	0.495108	−	0.358084i
$125$	−1449.67	−	439.754i	−1.03730	−	0.314662i
$126$	431.602	−	367.817i	0.305160	−	0.260061i
$127$	−620.898			−0.433825			−0.216913	−	0.976191i	$-0.569599\pi$
$127$	−620.898			−0.433825			−0.216913	+	0.976191i	$0.569599\pi$
$128$	−1410.66	+	327.401i	−0.974108	+	0.226081i
$129$	916.997			0.625869
$130$	884.076	−	753.421i	0.596450	−	0.508303i
$131$	1890.34	+	573.429i	1.26076	+	0.382449i	0.848782	−	0.528743i	$-0.177337\pi$
$131$	1890.34	+	573.429i	1.26076	+	0.382449i	0.411982	+	0.911192i	$0.364837\pi$
$132$	−1423.83	−	1968.67i	−0.938850	−	1.29811i
$133$	212.805	+	20.9594i	0.138741	+	0.0136648i
$134$	−1094.13	+	477.174i	−0.705361	+	0.307623i
$135$	−678.159	−	1014.94i	−0.432346	−	0.647051i
$136$	−664.937	+	908.993i	−0.419249	+	0.573129i
$137$	1856.33	+	1240.36i	1.15764	+	0.773511i	0.977667	−	0.210160i	$-0.0673984\pi$
$137$	1856.33	+	1240.36i	1.15764	+	0.773511i	0.179975	+	0.983671i	$0.442398\pi$
$138$	3613.66	−	2512.78i	2.22910	−	1.55002i
$139$	919.785	−	1720.80i	0.561260	−	1.05004i	−0.427986	−	0.903785i	$-0.640777\pi$
$139$	919.785	−	1720.80i	0.561260	−	1.05004i	0.989246	−	0.146259i	$-0.0467232\pi$
$140$	−345.001	+	118.801i	−0.208271	+	0.0717180i
$141$	158.673	+	1611.03i	0.0947708	+	0.962224i
$142$	1045.75	+	296.153i	0.618011	+	0.175018i
$143$	1440.29	+	596.586i	0.842257	+	0.348874i
$144$	−1665.13	−	2131.09i	−0.963617	−	1.23327i
$145$	2184.24	−	904.740i	1.25097	−	0.518169i
$146$	1478.80	−	173.407i	0.838264	−	0.0982964i
$147$	−1692.02	+	2061.74i	−0.949359	+	1.15680i
$148$	821.010	+	1407.74i	0.455991	+	0.781864i
$149$	505.690	+	1667.04i	0.278039	+	0.916571i	0.979084	+	0.203454i	$0.0652169\pi$
$149$	505.690	+	1667.04i	0.278039	+	0.916571i	−0.701046	+	0.713116i	$0.747283\pi$
$150$	−163.557	−	749.320i	−0.0890293	−	0.407878i
$151$	268.084	+	1347.75i	0.144479	+	0.726347i	0.983308	+	0.181951i	$0.0582412\pi$
$151$	268.084	+	1347.75i	0.144479	+	0.726347i	−0.838828	+	0.544396i	$0.816759\pi$
$152$	143.003	−	1009.75i	0.0763098	−	0.538823i
$153$	−2062.87	−	410.331i	−1.09002	−	0.216819i
$154$	−352.646	−	339.797i	−0.184526	−	0.177803i
$155$	−643.188	−	783.726i	−0.333304	−	0.406132i
$156$	2666.19	+	990.162i	1.36837	+	0.508182i
$157$	−351.289	+	187.768i	−0.178573	+	0.0954491i	−0.558261	−	0.829665i	$-0.688531\pi$
$157$	−351.289	+	187.768i	−0.178573	+	0.0954491i	0.379688	+	0.925114i	$0.376031\pi$
$158$	396.453	−	128.342i	0.199621	−	0.0646224i
$159$	2054.43	+	2054.43i	1.02470	+	1.02470i
$160$	496.147	+	1667.98i	0.245149	+	0.824157i
$161$	627.320	−	627.320i	0.307079	−	0.307079i
$162$	−108.419	+	212.217i	−0.0525816	+	0.102922i
$163$	1542.90	+	2886.57i	0.741407	+	1.38708i	0.915489	+	0.402344i	$0.131804\pi$
$163$	1542.90	+	2886.57i	0.741407	+	1.38708i	−0.174081	+	0.984731i	$0.555696\pi$
$164$	95.2505	+	2565.66i	0.0453525	+	1.22161i
$165$	−2256.86	+	1852.16i	−1.06483	+	0.873879i
$166$	−67.8615	−	3657.09i	−0.0317294	−	1.70991i
$167$	548.279	−	2756.38i	0.254054	−	1.27722i	−0.617364	−	0.786678i	$-0.711799\pi$
$167$	548.279	−	2756.38i	0.254054	−	1.27722i	0.871419	−	0.490540i	$-0.163201\pi$
$168$	−665.912	−	595.620i	−0.305811	−	0.273530i
$169$	364.919	−	72.5869i	0.166099	−	0.0330391i
$170$	1139.04	+	730.882i	0.513884	+	0.329742i
$171$	1822.54	−	552.863i	0.815049	−	0.247242i
$172$	−118.889	−	873.451i	−0.0527047	−	0.387209i
$173$	146.564	+	120.282i	0.0644106	+	0.0528604i	0.666048	−	0.745909i	$-0.267985\pi$
$173$	146.564	+	120.282i	0.0644106	+	0.0528604i	−0.601637	+	0.798770i	$0.705485\pi$
$174$	4542.16	+	3588.71i	1.97896	+	1.56356i
$175$	−59.1594	−	142.823i	−0.0255545	−	0.0616939i
$176$	−1690.58	+	1611.45i	−0.724046	+	0.690157i
$177$	1447.03	−	3493.43i	0.614492	−	1.48352i
$178$	−1699.79	+	949.517i	−0.715757	+	0.399827i
$179$	−2941.75	+	289.737i	−1.22836	+	0.120983i	−0.691305	−	0.722563i	$-0.742964\pi$
$179$	−2941.75	+	289.737i	−1.22836	+	0.120983i	−0.537056	+	0.843546i	$0.680464\pi$
$180$	−2433.98	+	2153.49i	−1.00788	+	0.891733i
$181$	−3310.25	−	1769.36i	−1.35939	−	0.726607i	−0.379317	−	0.925267i	$-0.623841\pi$
$181$	−3310.25	−	1769.36i	−1.35939	−	0.726607i	−0.980068	+	0.198660i	$0.936341\pi$
$182$	564.229	+	101.388i	0.229799	+	0.0412933i
$183$	−3059.36	+	4578.65i	−1.23582	+	1.84953i
$184$	−2861.97	−	3116.27i	−1.14667	−	1.24856i
$185$	1628.28	−	1087.98i	0.647101	−	0.432379i
$186$	907.282	−	2310.73i	0.357662	−	0.910917i
$187$	−178.036	+	1807.63i	−0.0696217	+	0.706881i
$188$	1513.96	−	360.009i	0.587323	−	0.139662i
$189$	174.876	−	576.488i	0.0673034	−	0.221870i
$190$	−1221.61	−	97.4712i	−0.466445	−	0.0372174i
$191$			3793.28i			1.43703i	0.695513	+	0.718513i	$0.255177\pi$
$191$			3793.28i			1.43703i	−0.695513	+	0.718513i	$0.744823\pi$
$192$	−2973.05	+	3052.28i	−1.11751	+	1.14729i
$193$			2644.09i			0.986144i	0.869988	+	0.493072i	$0.164126\pi$
$193$			2644.09i			0.986144i	−0.869988	+	0.493072i	$0.835874\pi$
$194$	−317.372	+	3977.62i	−0.117453	+	1.47204i
$195$	992.101	−	3270.52i	0.364338	−	1.20106i
$196$	2183.20	+	1344.37i	0.795627	+	0.489930i
$197$	−62.4932	+	634.504i	−0.0226013	+	0.229475i	0.977248	+	0.212101i	$0.0680305\pi$
$197$	−62.4932	+	634.504i	−0.0226013	+	0.229475i	−0.999849	+	0.0173738i	$0.994469\pi$
$198$	−4059.99	−	1594.11i	−1.45723	−	0.572165i
$199$	−451.358	+	301.588i	−0.160783	+	0.107432i	−0.633359	−	0.773858i	$-0.718324\pi$
$199$	−451.358	+	301.588i	−0.160783	+	0.107432i	0.472576	+	0.881290i	$0.343324\pi$
$200$	−692.531	+	252.940i	−0.244847	+	0.0894278i
$201$	−1951.22	+	2920.21i	−0.684719	+	1.02475i
$202$	917.609	−	5106.54i	0.319617	−	1.77869i
$203$	1029.03	+	550.027i	0.355781	+	0.190169i
$204$	−202.233	+	3307.56i	−0.0694077	+	1.13517i
$205$	3070.35	−	302.403i	1.04606	−	0.103028i
$206$	−441.640	−	790.608i	−0.149371	−	0.267399i
$207$	3023.84	−	7300.21i	1.01532	−	2.45120i
$208$	597.469	−	2667.95i	0.199168	−	0.889370i
$209$	−629.418	−	1519.55i	−0.208315	−	0.502916i
$210$	−665.569	+	842.396i	−0.218708	+	0.276814i
$211$	−361.856	−	296.968i	−0.118063	−	0.0968915i	0.573509	−	0.819199i	$-0.305582\pi$
$211$	−361.856	−	296.968i	−0.118063	−	0.0968915i	−0.691572	+	0.722307i	$0.743082\pi$
$212$	1690.51	−	2223.23i	0.547665	−	0.720246i
$213$	3060.23	−	928.310i	0.984429	−	0.298623i
$214$	−2792.78	+	4352.38i	−0.892105	+	1.39029i
$215$	−1038.92	+	206.655i	−0.329554	+	0.0655523i
$216$	−2711.47	−	950.116i	−0.854129	−	0.299293i
$217$	97.6175	−	490.757i	0.0305378	−	0.153524i
$218$	−3672.65	+	68.1503i	−1.14102	+	0.0211730i
$219$	3386.49	−	2779.22i	1.04492	−	0.857544i
$220$	2056.80	+	1909.55i	0.630316	+	0.585190i
$221$	−1002.32	−	1875.20i	−0.305082	−	0.570768i
$222$	4270.00	+	2181.49i	1.29092	+	0.659514i
$223$	−2604.34	+	2604.34i	−0.782060	+	0.782060i	−0.980178	−	0.198118i	$-0.936517\pi$
$223$	−2604.34	+	2604.34i	−0.782060	+	0.782060i	0.198118	+	0.980178i	$0.436517\pi$
$224$	−480.999	+	711.512i	−0.143474	+	0.212232i
$225$	−973.610	−	973.610i	−0.288477	−	0.288477i
$226$	814.884	+	2517.21i	0.239846	+	0.740895i
$227$	2766.17	−	1478.55i	0.808799	−	0.432312i	−0.0145178	−	0.999895i	$-0.504621\pi$
$227$	2766.17	−	1478.55i	0.808799	−	0.432312i	0.823316	+	0.567583i	$0.192121\pi$
$228$	−1250.35	−	2727.71i	−0.363186	−	0.792312i
$229$	−643.602	−	784.232i	−0.185722	−	0.226303i	0.671823	−	0.740712i	$-0.265512\pi$
$229$	−643.602	−	784.232i	−0.185722	−	0.226303i	−0.857545	+	0.514408i	$0.828012\pi$
$230$	−3527.86	+	3661.26i	−1.01139	+	1.04964i
$231$	−1413.21	−	281.104i	−0.402520	−	0.0800663i
$232$	2829.40	−	4791.73i	0.800686	−	1.35600i
$233$	−1303.61	−	6553.68i	−0.366533	−	1.84268i	−0.519522	−	0.854457i	$-0.673890\pi$
$233$	−1303.61	−	6553.68i	−0.366533	−	1.84268i	0.152989	−	0.988228i	$-0.451110\pi$
$234$	4988.45	−	1088.85i	1.39361	−	0.304189i
$235$	−542.834	−	1789.48i	−0.150683	−	0.496736i
$236$	−3515.14	−	925.384i	−0.969559	−	0.255243i
$237$	777.823	−	947.780i	0.213186	−	0.259768i
$238$	77.7892	+	663.380i	0.0211862	+	0.180675i
$239$	−1600.42	+	662.916i	−0.433149	+	0.179416i	−0.588595	−	0.808428i	$-0.700319\pi$
$239$	−1600.42	+	662.916i	−0.433149	+	0.179416i	0.155446	+	0.987844i	$0.450319\pi$
$240$	3879.03	+	3342.12i	1.04329	+	0.898887i
$241$	−488.780	−	202.459i	−0.130643	−	0.0541143i	0.316404	−	0.948625i	$-0.397524\pi$
$241$	−488.780	−	202.459i	−0.130643	−	0.0541143i	−0.447047	+	0.894510i	$0.647524\pi$
$242$	−0.572777	+	2.02254i	−0.000152147	+	0.000537248i
$243$	404.762	+	4109.61i	0.106854	+	1.08490i
$244$	4757.87	+	2320.45i	1.24832	+	0.608818i
$245$	1452.37	−	2717.19i	0.378728	−	0.708549i
$246$	4312.69	+	6202.12i	1.11775	+	1.60745i
$247$	1600.88	+	1069.67i	0.412395	+	0.275554i
$248$	−2318.62	−	564.610i	−0.593680	−	0.144568i
$249$	−5979.12	−	8948.39i	−1.52173	−	2.27743i
$250$	1712.88	+	3927.53i	0.433329	+	0.993596i
$251$	5139.80	+	506.226i	1.29251	+	0.127302i	0.720795	−	0.693148i	$-0.243777\pi$
$251$	5139.80	+	506.226i	1.29251	+	0.127302i	0.571719	+	0.820450i	$0.306277\pi$
$252$	−1583.63	−	254.332i	−0.395869	−	0.0635771i
$253$	−6529.96	−	1980.84i	−1.62267	−	0.492231i
$254$	1139.09	+	1336.63i	0.281390	+	0.330187i
$255$	3982.02			0.977897
$256$	3292.79	+	2436.13i	0.803904	+	0.594759i
$257$	3689.56			0.895519			0.447760	−	0.894154i	$-0.352222\pi$
$257$	3689.56			0.895519			0.447760	+	0.894154i	$0.352222\pi$
$258$	−1682.31	−	1974.05i	−0.405955	−	0.476354i
$259$	924.871	+	280.556i	0.221887	+	0.0673086i
$260$	−3243.83	−	520.964i	−0.773746	−	0.124265i
$261$	10342.3	+	1018.63i	2.45277	+	0.241576i
$262$	−2233.56	−	5121.42i	−0.526679	−	1.20764i
$263$	2113.12	+	3162.51i	0.495440	+	0.741478i	0.991961	−	0.126547i	$-0.0403894\pi$
$263$	2113.12	+	3162.51i	0.495440	+	0.741478i	−0.496521	+	0.868025i	$0.665389\pi$
$264$	−1625.88	+	6676.82i	−0.379038	+	1.55655i
$265$	−2790.58	−	1864.61i	−0.646884	−	0.432234i
$266$	−345.289	−	496.564i	−0.0795904	−	0.114460i
$267$	−2700.50	+	5052.28i	−0.618981	+	1.15803i
$268$	3034.51	+	1479.95i	0.691650	+	0.337323i
$269$	−324.514	−	3294.84i	−0.0735538	−	0.746804i	−0.959254	−	0.282546i	$-0.908821\pi$
$269$	−324.514	−	3294.84i	−0.0735538	−	0.746804i	0.885700	−	0.464258i	$-0.153679\pi$
$270$	−940.748	+	3321.89i	−0.212045	+	0.748755i
$271$	1440.38	+	596.624i	0.322866	+	0.133736i	0.538229	−	0.842799i	$-0.319093\pi$
$271$	1440.38	+	596.624i	0.322866	+	0.133736i	−0.215363	+	0.976534i	$0.569093\pi$
$272$	3176.71	−	236.197i	0.708148	−	0.0526527i
$273$	1558.33	−	645.483i	0.345475	−	0.143100i
$274$	−735.436	−	6271.74i	−0.162151	−	1.38281i
$275$	−754.336	+	919.161i	−0.165412	+	0.201554i
$276$	−12038.9	−	3169.34i	−2.62558	−	0.691201i
$277$	274.448	+	904.735i	0.0595307	+	0.196246i	0.981662	−	0.190631i	$-0.0610535\pi$
$277$	274.448	+	904.735i	0.0595307	+	0.196246i	−0.922131	+	0.386878i	$0.873554\pi$
$278$	−5391.85	+	1176.90i	−1.16324	+	0.253906i
$279$	−869.448	−	4371.01i	−0.186568	−	0.937941i
$280$	888.683	+	524.745i	0.189675	+	0.111998i
$281$	−5825.67	−	1158.80i	−1.23676	−	0.246008i	−0.466954	−	0.884282i	$-0.654649\pi$
$281$	−5825.67	−	1158.80i	−1.23676	−	0.246008i	−0.769809	+	0.638274i	$0.779649\pi$
$282$	3177.03	−	3297.17i	0.670885	−	0.696254i
$283$	−2410.47	−	2937.17i	−0.506317	−	0.616950i	0.455635	−	0.890167i	$-0.349412\pi$
$283$	−2410.47	−	2937.17i	−0.506317	−	0.616950i	−0.961952	+	0.273217i	$0.911912\pi$
$284$	−1280.99	−	2794.55i	−0.267650	−	0.583894i
$285$	−3180.00	+	1699.75i	−0.660937	+	0.353278i
$286$	−1358.04	−	4195.05i	−0.280779	−	0.867337i
$287$	1076.67	+	1076.67i	0.221441	+	0.221441i
$288$	−1532.86	+	7494.27i	−0.313626	+	1.53335i
$289$	−1722.26	+	1722.26i	−0.350551	+	0.350551i
$290$	−5954.85	−	3042.26i	−1.20579	−	0.616026i
$291$	5534.47	+	10354.3i	1.11490	+	2.08584i
$292$	−3086.30	−	2865.34i	−0.618534	−	0.574252i
$293$	−2940.52	+	2413.23i	−0.586305	+	0.481168i	−0.880157	−	0.474683i	$-0.842563\pi$
$293$	−2940.52	+	2413.23i	−0.586305	+	0.481168i	0.293852	+	0.955851i	$0.405063\pi$
$294$	7542.55	−	139.961i	1.49623	−	0.0277642i
$295$	−852.146	+	4284.03i	−0.168183	+	0.845511i
$296$	1524.29	−	4350.05i	0.299316	−	0.854195i
$297$	−4544.66	+	903.990i	−0.887906	+	0.176616i
$298$	2660.96	−	4146.95i	0.517266	−	0.806129i
$299$	7644.06	−	2318.80i	1.47849	−	0.448494i
$300$	−1313.03	+	1726.79i	−0.252693	+	0.332321i
$301$	−404.118	−	331.651i	−0.0773853	−	0.0635085i
$302$	2409.53	−	3049.69i	0.459115	−	0.581092i
$303$	−5841.92	−	14103.6i	−1.10762	−	2.67404i
$304$	−2436.07	+	1544.62i	−0.459599	+	0.291415i
$305$	2434.29	−	5876.90i	0.457007	−	1.10331i
$306$	2901.19	+	5193.62i	0.541994	+	0.970259i
$307$	−5137.32	+	505.981i	−0.955056	+	0.0940648i	−0.563524	−	0.826100i	$-0.690555\pi$
$307$	−5137.32	+	505.981i	−0.955056	+	0.0940648i	−0.391532	+	0.920165i	$0.628055\pi$
$308$	−84.5324	+	1382.54i	−0.0156386	+	0.255771i
$309$	−2349.92	−	1256.06i	−0.432629	−	0.231245i
$310$	−507.171	+	2822.43i	−0.0929205	+	0.517107i
$311$	−4652.75	+	6963.34i	−0.848339	+	1.26963i	0.112815	+	0.993616i	$0.464013\pi$
$311$	−4652.75	+	6963.34i	−0.848339	+	1.26963i	−0.961154	+	0.276013i	$0.910987\pi$
$312$	−2759.80	−	7556.14i	−0.500779	−	1.37110i
$313$	−41.2885	+	27.5881i	−0.00745611	+	0.00498201i	−0.559293	−	0.828970i	$-0.688927\pi$
$313$	−41.2885	+	27.5881i	−0.00745611	+	0.00498201i	0.551837	+	0.833952i	$0.313927\pi$
$314$	1048.69	+	411.756i	0.188474	+	0.0740023i
$315$	−188.916	+	1918.10i	−0.0337912	+	0.343088i
$316$	−1003.62	−	618.005i	−0.178664	−	0.110017i
$317$	2504.25	−	8255.42i	0.443700	−	1.46268i	−0.395301	−	0.918552i	$-0.629360\pi$
$317$	2504.25	−	8255.42i	0.443700	−	1.46268i	0.839000	−	0.544131i	$-0.183140\pi$
$318$	653.611	−	8191.70i	0.115260	−	1.44455i
$319$		−	8974.69i		−	1.57519i
$320$	2680.49	−	4128.13i	0.468262	−	0.721154i
$321$			15215.7i			2.64566i
$322$	−2501.33	−	199.580i	−0.432899	−	0.0345408i
$323$	−651.190	+	2146.69i	−0.112177	+	0.369798i
$324$	655.753	−	155.934i	0.112441	−	0.0267376i
$325$	136.434	−	1385.23i	0.0232861	−	0.236427i
$326$	3383.42	−	8617.13i	0.574818	−	1.46398i
$327$	−8986.47	+	6004.57i	−1.51973	+	1.01545i
$328$	5348.45	−	4911.99i	0.900362	−	0.826888i
$329$	512.737	−	767.366i	0.0859213	−	0.128590i
$330$	8127.61	+	1460.47i	1.35579	+	0.243626i
$331$	−8003.54	−	4277.98i	−1.32905	−	0.710390i	−0.354602	−	0.935017i	$-0.615384\pi$
$331$	−8003.54	−	4277.98i	−1.32905	−	0.710390i	−0.974445	+	0.224627i	$0.927884\pi$
$332$	−7748.25	+	6855.35i	−1.28084	+	1.13324i
$333$	8566.74	−	843.750i	1.40977	−	0.138851i
$334$	−6939.64	+	3876.54i	−1.13689	+	0.635074i
$335$	1552.56	−	3748.21i	0.253210	−	0.611304i
$336$	−60.5372	+	2526.25i	−0.00982909	+	0.410174i
$337$	3774.51	+	9112.47i	0.610121	+	1.47296i	0.862868	+	0.505429i	$0.168666\pi$
$337$	3774.51	+	9112.47i	0.610121	+	1.47296i	−0.252748	+	0.967532i	$0.581334\pi$
$338$	−825.737	−	652.407i	−0.132882	−	0.104989i
$339$	6017.76	+	4938.65i	0.964129	+	0.791240i
$340$	−516.270	−	3792.92i	−0.0823491	−	0.605000i
$341$	−3682.98	+	1117.22i	−0.584881	+	0.177422i
$342$	−4533.79	−	2909.18i	−0.716840	−	0.459972i
$343$	3087.43	−	614.127i	0.486021	−	0.0966756i
$344$	−1662.20	+	1858.36i	−0.260522	+	0.291268i
$345$	−2918.50	+	14672.3i	−0.455440	+	2.28965i
$346$	−9.94946	−	536.181i	−0.00154591	−	0.0833100i
$347$	−4086.51	+	3353.71i	−0.632205	+	0.518838i	−0.895030	−	0.446006i	$-0.852846\pi$
$347$	−4086.51	+	3353.71i	−0.632205	+	0.518838i	0.262825	+	0.964844i	$0.415346\pi$
$348$	−607.437	−	16361.9i	−0.0935691	−	2.52037i
$349$	1942.09	+	3633.40i	0.297874	+	0.557282i	0.985683	−	0.168609i	$-0.0539275\pi$
$349$	1942.09	+	3633.40i	0.297874	+	0.557282i	−0.687809	+	0.725891i	$0.741428\pi$
$350$	−198.928	+	389.377i	−0.0303804	+	0.0594660i
$351$	3835.53	−	3835.53i	0.583264	−	0.583264i
$352$	6570.54	+	683.017i	0.994918	+	0.103423i
$353$	2046.37	+	2046.37i	0.308548	+	0.308548i	0.844346	−	0.535798i	$-0.179989\pi$
$353$	2046.37	+	2046.37i	0.308548	+	0.308548i	−0.535798	+	0.844346i	$0.679989\pi$
$354$	−10175.1	+	3293.95i	−1.52769	+	0.494552i
$355$	−3257.92	+	1741.40i	−0.487077	+	0.260348i
$356$	5162.48	+	1917.23i	0.768570	+	0.285430i
$357$	1246.74	+	1519.15i	0.184830	+	0.225216i
$358$	6020.63	+	5801.26i	0.888828	+	0.856442i
$359$	−9610.66	−	1911.68i	−1.41290	−	0.281043i	−0.571121	−	0.820866i	$-0.693491\pi$
$359$	−9610.66	−	1911.68i	−1.41290	−	0.281043i	−0.841779	+	0.539822i	$0.818491\pi$
$360$	9101.27	+	1288.95i	1.33244	+	0.188704i
$361$	941.834	+	4734.92i	0.137314	+	0.690322i
$362$	2263.97	+	10372.2i	0.328707	+	1.50593i
$363$	1.79541	+	5.91866i	0.000259599	+	0.000855782i
$364$	−816.868	−	1400.64i	−0.117625	−	0.201686i
$365$	−3210.44	+	3911.93i	−0.460389	+	0.560986i
$366$	15469.3	−	1813.96i	2.20927	−	0.259063i
$367$	3455.70	−	1431.40i	0.491516	−	0.203592i	−0.123138	−	0.992390i	$-0.539296\pi$
$367$	3455.70	−	1431.40i	0.491516	−	0.203592i	0.614654	+	0.788797i	$0.289296\pi$
$368$	−1457.97	+	11878.1i	−0.206528	+	1.68258i
$369$	12529.3	+	5189.82i	1.76762	+	0.732171i
$370$	−5329.37	−	1509.26i	−0.748813	−	0.212061i
$371$	−162.354	−	1648.41i	−0.0227197	−	0.230677i
$372$	−6638.88	+	2286.10i	−0.925295	+	0.318625i
$373$	−2099.05	+	3927.05i	−0.291380	+	0.545134i	−0.984435	−	0.175751i	$-0.943765\pi$
$373$	−2099.05	+	3927.05i	−0.291380	+	0.545134i	0.693054	+	0.720885i	$0.256265\pi$
$374$	4217.97	−	2932.99i	0.583171	−	0.405512i
$375$	10482.5	+	7004.19i	1.44351	+	0.964519i
$376$	−3552.50	−	2598.68i	−0.487250	−	0.356428i
$377$	5836.75	+	8735.32i	0.797369	+	1.19335i
$378$	−1561.85	+	681.159i	−0.212521	+	0.0926852i
$379$	−3896.29	−	383.751i	−0.528071	−	0.0520104i	−0.169531	−	0.985525i	$-0.554225\pi$
$379$	−3896.29	−	383.751i	−0.528071	−	0.0520104i	−0.358540	+	0.933514i	$0.616725\pi$
$380$	2031.32	+	2808.62i	0.274222	+	0.379155i
$381$	4944.68	+	1499.95i	0.664892	+	0.201693i
$382$	8165.93	−	6959.11i	1.09373	−	0.932092i
$383$	1804.88			0.240796			0.120398	−	0.992726i	$-0.461583\pi$
$383$	1804.88			0.240796			0.120398	+	0.992726i	$0.461583\pi$
$384$	12025.1	+	800.503i	1.59805	+	0.106381i
$385$	1664.46			0.220334
$386$	5692.03	−	4850.82i	0.750562	−	0.639639i
$387$	−4455.78	−	1351.65i	−0.585271	−	0.177540i
$388$	9145.02	−	6614.08i	1.19657	−	0.865410i
$389$	10916.4	+	1075.18i	1.42284	+	0.140138i	0.779961	−	0.625828i	$-0.215239\pi$
$389$	10916.4	+	1075.18i	1.42284	+	0.140138i	0.642881	+	0.765966i	$0.277739\pi$
$390$	−8860.67	+	3864.33i	−1.15045	+	0.501739i
$391$	5170.70	+	7738.50i	0.668782	+	1.00090i
$392$	−1111.21	−	7166.22i	−0.143175	−	0.923338i
$393$	−13669.0	−	9133.31i	−1.75447	−	1.17230i
$394$	1480.57	−	1029.52i	0.189315	−	0.131641i
$395$	−667.652	+	1249.09i	−0.0850461	+	0.159110i
$396$	4016.72	+	11664.6i	0.509716	+	1.48023i
$397$	770.544	+	7823.47i	0.0974119	+	0.989039i	0.912328	+	0.409460i	$0.134283\pi$
$397$	770.544	+	7823.47i	0.0974119	+	0.989039i	−0.814916	+	0.579579i	$0.803217\pi$
$398$	1477.30	+	418.365i	0.186056	+	0.0526903i
$399$	−1644.09	−	681.005i	−0.206285	−	0.0854459i
$400$	1815.02	+	1026.80i	0.226878	+	0.128350i
$401$	8029.74	−	3326.03i	0.999965	−	0.414199i	0.178181	−	0.983998i	$-0.442979\pi$
$401$	8029.74	−	3326.03i	0.999965	−	0.414199i	0.821784	+	0.569799i	$0.192979\pi$
$402$	9866.13	−	1156.92i	1.22407	−	0.143537i
$403$	2858.16	−	3482.67i	0.353288	−	0.430482i
$404$	−12676.5	+	7393.03i	−1.56108	+	0.910439i
$405$	−235.122	−	775.094i	−0.0288477	−	0.0950981i
$406$	−703.781	−	3224.30i	−0.0860298	−	0.394136i
$407$	−1450.29	−	7291.08i	−0.176629	−	0.887975i
$408$	7491.33	−	5632.67i	0.909010	−	0.683477i
$409$	1252.66	+	249.170i	0.151443	+	0.0301238i	0.270229	−	0.962796i	$-0.412900\pi$
$409$	1252.66	+	249.170i	0.151443	+	0.0301238i	−0.118787	+	0.992920i	$0.537900\pi$
$410$	−6283.82	−	6054.86i	−0.756917	−	0.729338i
$411$	−11786.9	−	14362.4i	−1.41461	−	1.72371i
$412$	−891.743	+	2401.18i	−0.106634	+	0.287130i
$413$	−1901.17	+	1016.20i	−0.226514	+	0.121075i
$414$	−21262.9	+	6883.35i	−2.52419	+	0.817145i
$415$	8790.73	+	8790.73i	1.03981	+	1.03981i
$416$	−6839.50	+	3608.40i	−0.806092	+	0.425280i
$417$	−11482.0	+	11482.0i	−1.34839	+	1.34839i
$418$	−2116.47	+	4142.72i	−0.247655	+	0.484754i
$419$	−4393.64	−	8219.93i	−0.512276	−	0.958400i	−0.996511	−	0.0834625i	$-0.973402\pi$
$419$	−4393.64	−	8219.93i	−0.512276	−	0.958400i	0.484235	−	0.874938i	$-0.339098\pi$
$420$	3034.50	−	112.656i	0.352544	−	0.0130882i
$421$	−10492.0	+	8610.53i	−1.21460	+	0.996797i	−0.214803	+	0.976657i	$0.568911\pi$
$421$	−10492.0	+	8610.53i	−1.21460	+	0.996797i	−0.999797	+	0.0201396i	$0.993589\pi$
$422$	24.5646	+	1323.80i	0.00283361	+	0.152705i
$423$	1603.64	−	8062.05i	0.184330	−	0.926691i
$424$	−7887.43	+	439.485i	−0.903414	+	0.0503379i
$425$	1590.61	−	316.393i	0.181544	−	0.0361113i
$426$	−7612.68	−	4884.80i	−0.865811	−	0.555562i
$427$	3004.21	−	911.318i	0.340478	−	0.103283i
$428$	14493.1	−	1972.72i	1.63681	−	0.222792i
$429$	−10028.9	−	8230.49i	−1.12867	−	0.926274i
$430$	2350.87	+	1857.40i	0.263649	+	0.208307i
$431$	2538.75	+	6129.08i	0.283729	+	0.684982i	0.999916	−	0.0129256i	$-0.00411446\pi$
$431$	2538.75	+	6129.08i	0.283729	+	0.684982i	−0.716187	+	0.697908i	$0.754114\pi$
$432$	2929.08	+	7580.15i	0.326216	+	0.844213i
$433$	3416.17	−	8247.35i	0.379147	−	0.915341i	−0.612980	−	0.790099i	$-0.710029\pi$
$433$	3416.17	−	8247.35i	0.379147	−	0.915341i	0.992126	−	0.125242i	$-0.0399707\pi$
$434$	−1235.56	+	690.192i	−0.136656	+	0.0763371i
$435$	−19580.4	+	1928.50i	−2.15818	+	0.212562i
$436$	6884.52	+	7781.22i	0.756213	+	0.854709i
$437$	−7432.50	−	3972.75i	−0.813603	−	0.434880i
$438$	−12195.7	−	2191.49i	−1.33045	−	0.239072i
$439$	5645.33	−	8448.83i	0.613751	−	0.918544i	−0.386241	−	0.922398i	$-0.626227\pi$
$439$	5645.33	−	8448.83i	0.613751	−	0.918544i	0.999993	+	0.00385394i	$0.00122675\pi$
$440$	337.371	−	7931.00i	0.0365535	−	0.859308i
$441$	11260.7	−	7524.15i	1.21593	−	0.812455i
$442$	−2197.98	+	5597.95i	−0.236532	+	0.602415i
$443$	−113.686	+	1154.28i	−0.0121928	+	0.123795i	−0.999354	−	0.0359297i	$-0.988561\pi$
$443$	−113.686	+	1154.28i	−0.0121928	+	0.123795i	0.987162	+	0.159725i	$0.0510607\pi$
$444$	−3137.53	−	13194.3i	−0.335361	−	1.41030i
$445$	1920.98	−	6332.63i	0.204637	−	0.674597i
$446$	10384.4	+	828.561i	1.10250	+	0.0879675i
$447$		−	14497.5i		−	1.53403i
$448$	2414.13	−	269.867i	0.254592	−	0.0284599i
$449$		−	11337.7i		−	1.19167i	−0.803108	−	0.595833i	$-0.796822\pi$
$449$		−	11337.7i		−	1.19167i	0.803108	−	0.595833i	$-0.203178\pi$
$450$	−309.751	+	3882.10i	−0.0324484	+	0.406676i
$451$	3399.72	−	11207.4i	0.354959	−	1.17014i
$452$	3923.91	−	6372.28i	0.408330	−	0.663113i
$453$	1120.91	−	11380.8i	0.116258	−	1.18039i
$454$	−8257.72	−	3242.31i	−0.853643	−	0.335174i
$455$	−1620.07	+	1082.49i	−0.166923	+	0.111534i
$456$	−3578.17	+	7695.91i	−0.367463	+	0.790338i
$457$	−6731.90	+	10075.0i	−0.689070	+	1.03127i	0.307741	+	0.951470i	$0.400427\pi$
$457$	−6731.90	+	10075.0i	−0.689070	+	1.03127i	−0.996811	+	0.0797961i	$0.974573\pi$
$458$	−507.498	+	2824.25i	−0.0517769	+	0.288141i
$459$	5573.68	+	2979.19i	0.566791	+	0.302956i
$460$	14353.9	+	877.638i	1.45490	+	0.0889567i
$461$	12665.1	−	1247.40i	1.27955	−	0.126024i	0.564695	−	0.825300i	$-0.308994\pi$
$461$	12665.1	−	1247.40i	1.27955	−	0.126024i	0.714852	+	0.699276i	$0.246494\pi$
$462$	1987.51	+	3557.98i	0.200146	+	0.358294i
$463$	−1335.70	+	3224.67i	−0.134072	+	0.323679i	−0.976630	−	0.214927i	$-0.931049\pi$
$463$	−1335.70	+	3224.67i	−0.134072	+	0.323679i	0.842558	+	0.538606i	$0.181049\pi$
$464$	−15506.1	+	2699.92i	−1.55141	+	0.270130i
$465$	3228.88	+	7795.21i	0.322013	+	0.777407i
$466$	−11716.8	+	14829.6i	−1.16474	+	1.47418i
$467$	8510.34	+	6984.25i	0.843279	+	0.692061i	0.953352	−	0.301862i	$-0.0976083\pi$
$467$	8510.34	+	6984.25i	0.843279	+	0.692061i	−0.110072	+	0.993924i	$0.535108\pi$
$468$	−11495.8	−	8741.23i	−1.13545	−	0.863383i
$469$	1916.05	−	581.228i	0.188646	−	0.0572252i
$470$	−2856.41	+	4451.55i	−0.280333	+	0.436882i
$471$	3251.19	−	646.702i	0.318061	−	0.0632664i
$472$	4456.73	+	9264.87i	0.434614	+	0.903496i
$473$	−784.478	+	3943.84i	−0.0762586	+	0.383378i
$474$	−3467.31	+	64.3399i	−0.335989	+	0.00623466i
$475$	−1135.19	+	931.630i	−0.109655	+	0.0899919i
$476$	1285.37	−	1384.49i	0.123771	−	0.133315i
$477$	−6954.47	−	13010.9i	−0.667555	−	1.24891i
$478$	4363.20	+	2229.11i	0.417507	+	0.213299i
$479$	−10944.2	+	10944.2i	−1.04396	+	1.04396i	−0.0449682	+	0.998988i	$0.514319\pi$
$479$	−10944.2	+	10944.2i	−1.04396	+	1.04396i	−0.998988	+	0.0449682i	$0.985681\pi$
$480$	78.2700	−	14482.0i	0.00744275	−	1.37710i
$481$	6153.42	+	6153.42i	0.583309	+	0.583309i
$482$	460.869	+	1423.64i	0.0435519	+	0.134534i
$483$	−6511.29	+	3480.36i	−0.613404	+	0.327871i
$484$	5.40482	−	2.47750i	0.000507590	−	0.000232673i
$485$	−8603.79	−	10483.8i	−0.805522	−	0.981531i
$486$	8104.34	−	8410.80i	0.756421	−	0.785024i
$487$	182.796	+	36.3604i	0.0170088	+	0.00338326i	0.203587	−	0.979057i	$-0.434740\pi$
$487$	182.796	+	36.3604i	0.0170088	+	0.00338326i	−0.186579	+	0.982440i	$0.559740\pi$
$488$	−3733.42	−	14499.5i	−0.346319	−	1.34500i
$489$	−5313.99	−	26715.2i	−0.491425	−	2.47056i
$490$	−8513.88	+	1858.36i	−0.784935	+	0.171331i
$491$	−2219.12	−	7315.45i	−0.203966	−	0.672386i	−0.997923	−	0.0644125i	$-0.979483\pi$
$491$	−2219.12	−	7315.45i	−0.203966	−	0.672386i	0.793957	−	0.607974i	$-0.208017\pi$
$492$	5439.53	−	20662.4i	0.498441	−	1.89336i
$493$	−7765.37	+	9462.14i	−0.709401	+	0.864408i
$494$	−634.233	−	5408.69i	−0.0577641	−	0.492608i
$495$	13696.3	−	5673.21i	1.24365	−	0.515135i
$496$	3038.26	+	6027.21i	0.275045	+	0.545625i
$497$	−1684.38	−	697.692i	−0.152021	−	0.0629693i
$498$	−8294.29	+	29288.1i	−0.746337	+	2.63541i
$499$	−1106.59	−	11235.4i	−0.0992738	−	1.00794i	−0.907777	−	0.419452i	$-0.862222\pi$
$499$	−1106.59	−	11235.4i	−0.0992738	−	1.00794i	0.808503	−	0.588491i	$-0.200278\pi$
$500$	5312.51	−	10892.8i	0.475165	−	0.974282i
$501$	−11025.2	+	20626.7i	−0.983171	+	1.83938i
$502$	−8339.65	−	11993.3i	−0.741468	−	1.06631i
$503$	13791.9	+	9215.47i	1.22257	+	0.816893i	0.987886	−	0.155179i	$-0.0495955\pi$
$503$	13791.9	+	9215.47i	1.22257	+	0.816893i	0.234681	+	0.972072i	$0.424596\pi$
$504$	2357.79	+	3875.72i	0.208382	+	0.342537i
$505$	9797.07	+	14662.4i	0.863295	+	1.29201i
$506$	7715.58	+	17691.3i	0.677864	+	1.55430i
$507$	−3081.48	−	303.499i	−0.269928	−	0.0265856i
$508$	787.643	−	4904.34i	0.0687913	−	0.428336i
$509$	−1743.07	−	528.755i	−0.151788	−	0.0460445i	0.213476	−	0.976948i	$-0.431521\pi$
$509$	−1743.07	−	528.755i	−0.151788	−	0.0460445i	−0.365265	+	0.930904i	$0.619021\pi$
$510$	−7305.37	−	8572.24i	−0.634289	−	0.744285i
$511$	−2497.58			−0.216216
$512$	−796.569	−	11557.8i	−0.0687572	−	0.997633i
$513$	−5722.77			−0.492528
$514$	−6768.83	−	7942.65i	−0.580857	−	0.681586i
$515$	2945.44	+	893.490i	0.252023	+	0.0764502i
$516$	−1163.26	+	7243.16i	−0.0992436	+	0.617951i
$517$	−7064.50	−	695.793i	−0.600960	−	0.0591894i
$518$	−1092.79	−	2505.71i	−0.0926924	−	0.212538i
$519$	−876.625	−	1311.96i	−0.0741417	−	0.110961i
$520$	4829.61	+	7938.88i	0.407293	+	0.669505i
$521$	11930.5	+	7971.70i	1.00323	+	0.670338i	0.944696	−	0.327947i	$-0.106357\pi$
$521$	11930.5	+	7971.70i	1.00323	+	0.670338i	0.0585362	+	0.998285i	$0.481357\pi$
$522$	−16781.0	−	24133.0i	−1.40706	−	2.02351i
$523$	−8465.47	+	15837.8i	−0.707781	+	1.32416i	0.228718	+	0.973493i	$0.426547\pi$
$523$	−8465.47	+	15837.8i	−0.707781	+	1.32416i	−0.936498	+	0.350672i	$0.885953\pi$
$524$	−6927.40	+	14204.0i	−0.577528	+	1.18417i
$525$	126.101	+	1280.33i	0.0104829	+	0.106434i
$526$	2931.34	−	10350.9i	0.242990	−	0.858025i
$527$	4849.69	+	2008.81i	0.400865	+	0.166044i
$528$	17356.3	−	8749.14i	1.43056	−	0.721132i
$529$	−21062.4	+	8724.35i	−1.73111	+	0.717050i
$530$	1105.57	+	9428.19i	0.0906090	+	0.772706i
$531$	−12180.5	+	14842.0i	−0.995460	+	1.21297i
$532$	−435.508	+	1654.31i	−0.0354919	+	0.134818i
$533$	3979.75	+	13119.5i	0.323419	+	1.06617i
$534$	15830.6	−	3455.40i	1.28287	−	0.280018i
$535$	−3429.02	−	17238.8i	−0.277102	−	1.39308i
$536$	−2381.13	−	9247.61i	−0.191883	−	0.745216i
$537$	24127.3	+	4799.23i	1.93887	+	0.385665i
$538$	−6497.58	+	6743.28i	−0.520689	+	0.540379i
$539$	−7419.65	−	9040.87i	−0.592925	−	0.722482i
$540$	8877.05	−	4069.13i	0.707421	−	0.324273i
$541$	4182.01	−	2235.33i	0.332345	−	0.177642i	−0.296781	−	0.954946i	$-0.595913\pi$
$541$	4182.01	−	2235.33i	0.332345	−	0.177642i	0.629126	+	0.777303i	$0.283413\pi$
$542$	−1358.13	−	4195.31i	−0.107632	−	0.332480i
$543$	22087.6	+	22087.6i	1.74562	+	1.74562i
$544$	−6336.43	−	6405.30i	−0.499398	−	0.504825i
$545$	8828.14	−	8828.14i	0.693864	−	0.693864i
$546$	−4248.46	−	2170.49i	−0.332999	−	0.170125i
$547$	2835.18	+	5304.25i	0.221615	+	0.414613i	0.968018	−	0.250882i	$-0.0807206\pi$
$547$	2835.18	+	5304.25i	0.221615	+	0.414613i	−0.746402	+	0.665495i	$0.768221\pi$
$548$	−12152.2	+	13089.3i	−0.947291	+	1.02034i
$549$	21614.6	−	17738.6i	1.68031	−	1.37899i
$550$	3362.61	−	62.3971i	0.260695	−	0.00483750i
$551$	2162.39	−	10871.1i	0.167189	−	0.840513i
$552$	15263.8	+	31731.1i	1.17694	+	2.44668i
$553$	−685.568	+	136.368i	−0.0527185	+	0.0104864i
$554$	1444.16	−	2250.63i	0.110751	−	0.172600i
$555$	−15595.6	+	4730.87i	−1.19278	+	0.361827i
$556$	12425.4	+	9448.11i	0.947760	+	0.720664i
$557$	−11437.4	−	9386.40i	−0.870048	−	0.714030i	0.0893759	−	0.995998i	$-0.471513\pi$
$557$	−11437.4	−	9386.40i	−0.870048	−	0.714030i	−0.959424	+	0.281968i	$0.909013\pi$
$558$	−7814.56	+	9890.71i	−0.592861	+	0.750371i
$559$	−1801.35	−	4348.84i	−0.136295	−	0.329045i
$560$	−500.731	−	2875.79i	−0.0377853	−	0.217008i
$561$	5784.66	−	13965.4i	0.435345	−	1.05102i
$562$	8193.14	+	14667.1i	0.614958	+	1.10088i
$563$	15308.2	−	1507.72i	1.14594	−	0.112865i	0.492826	−	0.870128i	$-0.335964\pi$
$563$	15308.2	−	1507.72i	1.14594	−	0.112865i	0.653110	+	0.757263i	$0.273464\pi$
$564$	−12926.5	−	790.361i	−0.965078	−	0.0590075i
$565$	−7930.87	−	4239.14i	−0.590538	−	0.315649i
$566$	−1900.72	+	10577.6i	−0.141154	+	0.785531i
$567$	222.086	−	332.376i	0.0164493	−	0.0246181i
$568$	−3665.84	+	7884.48i	−0.270802	+	0.582439i
$569$	7777.54	−	5196.78i	0.573025	−	0.382883i	−0.235032	−	0.971988i	$-0.575519\pi$
$569$	7777.54	−	5196.78i	0.573025	−	0.382883i	0.808057	+	0.589105i	$0.200519\pi$
$570$	9493.11	+	3727.37i	0.697584	+	0.273899i
$571$	2550.16	−	25892.2i	0.186901	−	1.89764i	−0.206768	−	0.978390i	$-0.566294\pi$
$571$	2550.16	−	25892.2i	0.186901	−	1.89764i	0.393669	−	0.919252i	$-0.371206\pi$
$572$	−6539.39	+	10619.7i	−0.478017	+	0.776280i
$573$	9163.73	−	30208.8i	0.668098	−	2.20243i
$574$	342.538	−	4293.03i	0.0249081	−	0.312173i
$575$			6092.73i			0.441886i
$576$	18945.4	−	10449.1i	1.37047	−	0.755866i
$577$			843.274i			0.0608422i	0.999537	+	0.0304211i	$0.00968483\pi$
$577$			843.274i			0.0608422i	−0.999537	+	0.0304211i	$0.990315\pi$
$578$	6867.20	+	547.930i	0.494183	+	0.0394306i
$579$	6387.55	−	21056.9i	0.458476	−	1.51139i
$580$	4375.52	+	18400.5i	0.313248	+	1.31731i
$581$	−601.389	+	6106.00i	−0.0429429	+	0.436006i
$582$	12136.5	−	30910.1i	0.864391	−	2.20149i
$583$	−10593.3	+	7078.20i	−0.752536	+	0.502829i
$584$	−506.236	+	11900.7i	−0.0358702	+	0.843245i
$585$	−9641.43	+	14429.4i	−0.681409	+	1.01980i
$586$	10589.7	+	1902.89i	0.746513	+	0.134143i
$587$	9222.20	+	4929.37i	0.648451	+	0.346604i	0.762610	−	0.646858i	$-0.223917\pi$
$587$	9222.20	+	4929.37i	0.648451	+	0.346604i	−0.114159	+	0.993462i	$0.536417\pi$
$588$	−14138.8	−	15980.4i	−0.991622	−	1.12078i
$589$	−4730.39	+	465.903i	−0.330921	+	0.0325928i
$590$	10785.7	−	6024.99i	0.752612	−	0.420415i
$591$	2030.50	−	4902.07i	0.141326	−	0.341191i
$592$	−12161.0	+	4699.18i	−0.844278	+	0.326242i
$593$	−1953.54	−	4716.27i	−0.135282	−	0.326600i	0.841692	−	0.539958i	$-0.181560\pi$
$593$	−1953.54	−	4716.27i	−0.135282	−	0.326600i	−0.976974	+	0.213358i	$0.931560\pi$
$594$	10283.6	+	8125.01i	0.710342	+	0.561235i
$595$	−1754.86	−	1440.18i	−0.120912	−	0.0992296i
$596$	−13809.1	+	1879.61i	−0.949062	+	0.129181i
$597$	4323.08	−	1311.39i	0.296368	−	0.0899023i
$598$	−19015.5	−	12201.6i	−1.30034	−	0.834382i
$599$	18508.4	−	3681.55i	1.26249	−	0.251125i	0.481933	−	0.876208i	$-0.339935\pi$
$599$	18508.4	−	3681.55i	1.26249	−	0.251125i	0.780558	+	0.625083i	$0.214935\pi$
$600$	6126.20	−	341.350i	0.416835	−	0.0232259i
$601$	−2840.96	+	14282.5i	−0.192820	+	0.969374i	0.756244	+	0.654290i	$0.227033\pi$
$601$	−2840.96	+	14282.5i	−0.192820	+	0.969374i	−0.949064	+	0.315083i	$0.897967\pi$
$602$	27.4335	+	1478.40i	0.00185732	+	0.100092i
$603$	13785.5	−	11313.5i	0.930995	−	0.764048i
$604$	−10985.7	+	407.844i	−0.740067	+	0.0274751i
$605$	−3.36796	−	6.30101i	−0.000226326	−	0.000423425i
$606$	−19643.9	+	38450.5i	−1.31680	+	2.57747i
$607$	−6216.50	+	6216.50i	−0.415683	+	0.415683i	−0.883713	−	0.468030i	$-0.844964\pi$
$607$	−6216.50	+	6216.50i	−0.415683	+	0.415683i	0.468030	+	0.883713i	$0.344964\pi$
$608$	7794.35	+	2410.47i	0.519906	+	0.160785i
$609$	−6866.19	−	6866.19i	−0.456867	−	0.456867i
$610$	−17117.3	+	5541.32i	−1.13617	+	0.367805i
$611$	7328.60	−	3917.22i	0.485243	−	0.259368i
$612$	5857.99	−	15773.7i	0.386920	−	1.04185i
$613$	1984.20	+	2417.76i	0.130736	+	0.159302i	0.834264	−	0.551365i	$-0.185893\pi$
$613$	1984.20	+	2417.76i	0.130736	+	0.159302i	−0.703528	+	0.710668i	$0.748393\pi$
$614$	10514.1	+	10131.0i	0.691067	+	0.665887i
$615$	−25182.1	−	5009.02i	−1.65112	−	0.328428i
$616$	3131.33	−	2354.42i	0.204813	−	0.153997i
$617$	−3338.48	−	16783.7i	−0.217832	−	1.09511i	−0.922624	−	0.385700i	$-0.873960\pi$
$617$	−3338.48	−	16783.7i	−0.217832	−	1.09511i	0.704792	−	0.709414i	$-0.251040\pi$
$618$	1607.18	+	7363.12i	0.104612	+	0.479269i
$619$	5970.34	+	19681.6i	0.387671	+	1.27798i	0.906175	+	0.422904i	$0.138989\pi$
$619$	5970.34	+	19681.6i	0.387671	+	1.27798i	−0.518504	+	0.855075i	$0.673511\pi$
$620$	7006.40	−	4086.20i	0.453845	−	0.264687i
$621$	−15062.3	+	18353.5i	−0.973317	+	1.18599i
$622$	23526.1	−	2758.72i	1.51658	−	0.177837i
$623$	3017.37	−	1249.83i	0.194042	−	0.0803749i
$624$	−11203.3	+	19803.6i	−0.718734	+	1.27048i
$625$	−9691.87	−	4014.50i	−0.620280	−	0.256928i
$626$	135.137	+	38.2704i	0.00862807	+	0.00244344i
$627$	1341.64	+	13621.9i	0.0854542	+	0.867631i
$628$	−1037.51	−	3012.95i	−0.0659253	−	0.191449i
$629$	−4779.58	+	8941.96i	−0.302980	+	0.566835i
$630$	4475.75	−	3112.24i	0.283044	−	0.196817i
$631$	−10748.4	−	7181.85i	−0.678109	−	0.453098i	0.168226	−	0.985748i	$-0.446196\pi$
$631$	−10748.4	−	7181.85i	−0.678109	−	0.453098i	−0.846335	+	0.532650i	$0.821196\pi$
$632$	510.822	+	3294.31i	0.0321510	+	0.207343i
$633$	2164.33	+	3239.15i	0.135899	+	0.203388i
$634$	−22366.0	+	9754.31i	−1.40105	+	0.611030i
$635$	−5940.17	−	585.056i	−0.371226	−	0.0365626i
$636$	−18833.7	+	13621.4i	−1.17422	+	0.849249i
$637$	13101.5	+	3974.31i	0.814917	+	0.247202i
$638$	−19320.1	+	16464.9i	−1.19889	+	1.02171i
$639$	−16238.3			−1.00528
$640$	−13804.4	+	1803.04i	−0.852603	+	0.111361i
$641$	15551.2			0.958244			0.479122	−	0.877748i	$-0.340955\pi$
$641$	15551.2			0.958244			0.479122	+	0.877748i	$0.340955\pi$
$642$	32755.4	−	27914.6i	2.01364	−	1.71605i
$643$	5560.59	+	1686.79i	0.341039	+	0.103453i	0.456158	−	0.889899i	$-0.349225\pi$
$643$	5560.59	+	1686.79i	0.341039	+	0.103453i	−0.115119	+	0.993352i	$0.536725\pi$
$644$	4159.27	+	5750.85i	0.254500	+	0.351887i
$645$	8772.98	+	864.063i	0.535559	+	0.0527480i
$646$	5815.92	−	2536.45i	0.354217	−	0.154482i
$647$	−10926.0	−	16351.9i	−0.663904	−	0.993603i	−0.998683	−	0.0513059i	$-0.983662\pi$
$647$	−10926.0	−	16351.9i	−0.663904	−	0.993603i	0.334779	−	0.942297i	$-0.391338\pi$
$648$	−1538.72	−	1125.59i	−0.0932820	−	0.0682366i
$649$	13786.7	+	9211.96i	0.833859	+	0.557167i
$650$	−3232.34	+	2247.63i	−0.195051	+	0.135630i
$651$	−1962.96	+	3672.45i	−0.118179	+	0.221098i
$652$	−24757.6	+	8525.28i	−1.48709	+	0.512079i
$653$	−142.497	−	1446.79i	−0.00853955	−	0.0867035i	0.989970	−	0.141276i	$-0.0451204\pi$
$653$	−142.497	−	1446.79i	−0.00853955	−	0.0867035i	−0.998510	+	0.0545724i	$0.982620\pi$
$654$	29412.8	+	8329.59i	1.75861	+	0.498032i
$655$	17544.7	+	7267.26i	1.04661	+	0.433520i
$656$	−20386.4	−	2502.32i	−1.21335	−	0.148932i
$657$	−20551.8	+	8512.84i	−1.22040	+	0.505506i
$658$	−2592.60	+	304.013i	−0.153602	+	0.0180116i
$659$	−6891.25	+	8397.01i	−0.407352	+	0.496360i	−0.935763	−	0.352629i	$-0.885288\pi$
$659$	−6891.25	+	8397.01i	−0.407352	+	0.496360i	0.528411	+	0.848989i	$0.322788\pi$
$660$	−11766.8	−	20176.0i	−0.693974	−	1.18992i
$661$	5272.82	+	17382.1i	0.310270	+	1.02282i	0.963957	+	0.266059i	$0.0857216\pi$
$661$	5272.82	+	17382.1i	0.310270	+	1.02282i	−0.653686	+	0.756766i	$0.726778\pi$
$662$	5473.85	+	25077.9i	0.321371	+	1.47233i
$663$	3452.13	+	17355.0i	0.202217	+	1.01661i
$664$	28972.6	+	4103.19i	1.69331	+	0.239811i
$665$	2016.17	+	401.040i	0.117569	+	0.0233860i
$666$	−17532.8	−	16894.0i	−1.02010	−	0.982927i
$667$	−29173.1	−	35547.6i	−1.69354	−	2.06358i
$668$	21076.6	+	7827.36i	1.22077	+	0.453368i
$669$	27031.8	−	14448.8i	1.56220	−	0.835013i
$670$	−10917.2	+	3534.18i	−0.629507	+	0.203787i
$671$	−17074.7	−	17074.7i	−0.982357	−	0.982357i
$672$	5549.42	−	4504.32i	0.318562	−	0.258568i
$673$	8451.61	−	8451.61i	0.484080	−	0.484080i	−0.422352	−	0.906432i	$-0.638795\pi$
$673$	8451.61	−	8451.61i	0.484080	−	0.484080i	0.906432	+	0.422352i	$0.138795\pi$
$674$	12692.1	−	24843.2i	0.725342	−	1.41977i
$675$	1950.29	+	3648.74i	0.111210	+	0.208060i
$676$	110.428	+	2974.50i	0.00628291	+	0.169236i
$677$	1455.86	−	1194.79i	0.0826486	−	0.0678280i	−0.592162	−	0.805819i	$-0.701725\pi$
$677$	1455.86	−	1194.79i	0.0826486	−	0.0678280i	0.674810	+	0.737991i	$0.264225\pi$
$678$	−408.515	−	22015.0i	−0.0231400	−	1.24702i
$679$	1305.81	−	6564.75i	0.0738033	−	0.371034i
$680$	−7218.01	+	8069.85i	−0.407056	+	0.455095i
$681$	−25601.0	+	5092.35i	−1.44058	+	0.286548i
$682$	9161.83	+	5878.84i	0.514406	+	0.330077i
$683$	−4888.72	+	1482.98i	−0.273882	+	0.0830812i	−0.424238	−	0.905551i	$-0.639458\pi$
$683$	−4888.72	+	1482.98i	−0.273882	+	0.0830812i	0.150356	+	0.988632i	$0.451958\pi$
$684$	2054.95	+	15097.2i	0.114873	+	0.843942i
$685$	16590.9	+	13615.8i	0.925408	+	0.759463i
$686$	−6986.22	−	5519.74i	−0.388826	−	0.307208i
$687$	3230.96	+	7800.24i	0.179431	+	0.433184i
$688$	7050.01	+	168.941i	0.390668	+	0.00936165i
$689$	5707.38	−	13778.8i	0.315579	−	0.761875i
$690$	36939.9	−	20634.9i	2.03808	−	1.13849i
$691$	26481.3	−	2608.18i	1.45788	−	0.143589i	0.662210	−	0.749318i	$-0.269619\pi$
$691$	26481.3	−	2608.18i	1.45788	−	0.143589i	0.795671	+	0.605730i	$0.207119\pi$
$692$	−1136.00	+	1005.09i	−0.0624052	+	0.0552136i
$693$	6452.56	+	3448.97i	0.353698	+	0.189055i
$694$	14716.7	+	2644.49i	0.804956	+	0.144645i
$695$	10421.1	−	15596.3i	0.568770	−	0.851225i
$696$	−34108.4	+	31325.0i	−1.85758	+	1.70599i
$697$	−13281.6	+	8874.47i	−0.721773	+	0.482273i
$698$	4258.81	−	10846.6i	0.230943	−	0.588182i
$699$	−5450.63	+	55341.1i	−0.294938	+	2.99456i
$700$	1203.18	−	286.108i	0.0649655	−	0.0154484i
$701$	−9820.24	+	32373.0i	−0.529109	+	1.74424i	0.129327	+	0.991602i	$0.458718\pi$
$701$	−9820.24	+	32373.0i	−0.529109	+	1.74424i	−0.658436	+	0.752637i	$0.728782\pi$
$702$	−15293.5	−	1220.26i	−0.822247	−	0.0656066i
$703$		−	9181.15i		−	0.492566i
$704$	−10583.9	−	15397.7i	−0.566613	−	0.824323i
$705$			15562.4i			0.831367i
$706$	651.047	−	8159.56i	0.0347060	−	0.434970i
$707$	−2526.36	+	8328.28i	−0.134390	+	0.443023i
$708$	25758.2	+	15861.3i	1.36731	+	0.841957i
$709$	2042.91	−	20742.0i	0.108213	−	1.09871i	−0.775715	−	0.631083i	$-0.782611\pi$
$709$	2042.91	−	20742.0i	0.108213	−	1.09871i	0.883928	−	0.467622i	$-0.154889\pi$
$710$	9725.72	+	3818.70i	0.514084	+	0.201850i
$711$	−5176.53	+	3458.85i	−0.273045	+	0.182443i
$712$	−5343.75	−	14630.8i	−0.281272	−	0.770101i
$713$	−10956.2	+	16397.1i	−0.575472	+	0.861255i
$714$	983.086	−	5470.92i	0.0515281	−	0.286757i
$715$	13217.2	+	7064.72i	0.691320	+	0.369518i
$716$	1443.20	−	23603.8i	0.0753281	−	1.23200i
$717$	14346.8	−	1413.04i	0.747270	−	0.0735997i
$718$	13516.3	+	24196.4i	0.702539	+	1.25766i
$719$	−6254.29	+	15099.2i	−0.324403	+	0.783178i	0.674585	+	0.738197i	$0.264323\pi$
$719$	−6254.29	+	15099.2i	−0.324403	+	0.783178i	−0.998988	+	0.0449805i	$0.985677\pi$
$720$	−13922.3	−	21957.3i	−0.720631	−	1.13653i
$721$	581.324	+	1403.44i	0.0300272	+	0.0724921i
$722$	8465.15	−	10714.2i	0.436344	−	0.552271i
$723$	3403.43	+	2793.12i	0.175069	+	0.143675i
$724$	18175.1	−	23902.4i	0.932970	−	1.22697i
$725$	−7668.14	+	2326.10i	−0.392810	+	0.119158i
$726$	9.44748	−	14.7234i	0.000482960	−	0.000752665i
$727$	−4572.17	+	909.461i	−0.233250	+	0.0463962i	−0.310331	−	0.950629i	$-0.600440\pi$
$727$	−4572.17	+	909.461i	−0.233250	+	0.0463962i	0.0770814	+	0.997025i	$0.475440\pi$
$728$	−1516.60	+	4328.11i	−0.0772100	+	0.220344i
$729$	6260.69	−	31474.6i	0.318076	−	1.59908i
$730$	14311.2	−	265.561i	0.725591	−	0.0134642i
$731$	4239.50	−	3479.27i	0.214506	−	0.176040i
$732$	−32284.8	−	29973.5i	−1.63017	−	1.51346i
$733$	−12418.2	−	23232.8i	−0.625751	−	1.17070i	−0.972536	−	0.232753i	$-0.925226\pi$
$733$	−12418.2	−	23232.8i	−0.625751	−	1.17070i	0.346785	−	0.937945i	$-0.387274\pi$
$734$	−9421.23	−	4813.19i	−0.473765	−	0.242041i
$735$	−18130.4	+	18130.4i	−0.909865	+	0.909865i
$736$	28245.3	−	18652.9i	1.41459	−	0.934178i
$737$	−10890.0	−	10890.0i	−0.544287	−	0.544287i
$738$	−11813.9	−	36493.6i	−0.589262	−	1.82025i
$739$	8756.46	−	4680.42i	0.435875	−	0.232980i	−0.238839	−	0.971059i	$-0.576767\pi$
$739$	8756.46	−	4680.42i	0.435875	−	0.232980i	0.674714	+	0.738079i	$0.264267\pi$
$740$	6528.18	+	14241.6i	0.324298	+	0.707475i
$741$	−10164.9	−	12386.0i	−0.503938	−	0.614050i
$742$	−3250.74	+	3373.67i	−0.160834	+	0.166915i
$743$	−3956.92	−	787.081i	−0.195377	−	0.0388630i	0.0964315	−	0.995340i	$-0.469257\pi$
$743$	−3956.92	−	787.081i	−0.195377	−	0.0388630i	−0.291809	+	0.956477i	$0.594257\pi$
$744$	17101.0	+	10097.7i	0.842678	+	0.497580i
$745$	3267.17	+	16425.2i	0.160671	+	0.807747i
$746$	12304.8	−	2685.82i	0.603902	−	0.131816i
$747$	15863.3	+	52294.3i	0.776984	+	2.56137i
$748$	−14052.2	−	3699.34i	−0.686898	−	0.180830i
$749$	5503.08	−	6705.52i	0.268462	−	0.327122i
$750$	−4152.94	−	35415.9i	−0.202192	−	1.72427i
$751$	−10592.4	+	4387.51i	−0.514676	+	0.213186i	−0.624877	−	0.780724i	$-0.714851\pi$
$751$	−10592.4	+	4387.51i	−0.514676	+	0.213186i	0.110200	+	0.993909i	$0.464851\pi$
$752$	923.097	+	12415.1i	0.0447631	+	0.602038i
$753$	−39709.2	−	16448.1i	−1.92176	−	0.796018i
$754$	8096.79	−	28590.7i	0.391071	−	1.38092i
$755$	1294.83	+	13146.6i	0.0624155	+	0.633715i
$756$	4331.72	+	2112.61i	0.208390	+	0.101634i
$757$	1106.00	−	2069.18i	0.0531020	−	0.0993469i	−0.853970	−	0.520322i	$-0.825812\pi$
$757$	1106.00	−	2069.18i	0.0531020	−	0.0993469i	0.907072	+	0.420975i	$0.138312\pi$
$758$	6321.98	+	9091.71i	0.302935	+	0.435654i
$759$	47217.8	+	31549.9i	2.25810	+	1.50881i
$760$	2319.58	−	9525.55i	0.110710	−	0.454642i
$761$	−4196.92	−	6281.13i	−0.199919	−	0.299200i	0.717941	−	0.696104i	$-0.245085\pi$
$761$	−4196.92	−	6281.13i	−0.199919	−	0.299200i	−0.917860	+	0.396904i	$0.870085\pi$
$762$	−5842.46	−	13396.4i	−0.277756	−	0.636877i
$763$	6131.99	+	603.948i	0.290947	+	0.0286558i
$764$	−29962.3	−	4811.98i	−1.41885	−	0.227868i
$765$	−19349.0	−	5869.46i	−0.914464	−	0.277400i
$766$	−3311.22	−	3885.43i	−0.156187	−	0.183272i
$767$	−19410.0			−0.913763
$768$	−20337.8	−	27355.4i	−0.955571	−	1.28529i
$769$	−37476.8			−1.75741			−0.878704	−	0.477367i	$-0.841591\pi$
$769$	−37476.8			−1.75741			−0.878704	+	0.477367i	$0.841591\pi$
$770$	−3053.60	−	3583.15i	−0.142915	−	0.167698i
$771$	−29382.8	−	8913.17i	−1.37250	−	0.416342i
$772$	−20885.1	−	3354.17i	−0.973667	−	0.156372i
$773$	14191.7	+	1397.76i	0.660337	+	0.0650375i	0.422634	−	0.906300i	$-0.361106\pi$
$773$	14191.7	+	1397.76i	0.660337	+	0.0650375i	0.237703	+	0.971338i	$0.423606\pi$
$774$	5264.79	+	12071.8i	0.244495	+	0.560611i
$775$	1909.14	+	2857.24i	0.0884884	+	0.132432i
$776$	−31015.7	−	7552.68i	−1.43479	−	0.349388i
$777$	−6687.69	−	4468.57i	−0.308777	−	0.206318i
$778$	−17712.6	−	25472.7i	−0.816232	−	1.17383i
$779$	6818.43	−	12756.4i	0.313602	−	0.586707i
$780$	24574.6	+	11985.2i	1.12809	+	0.550179i
$781$	1374.51	+	13955.6i	0.0629755	+	0.639401i
$782$	7172.84	−	25328.1i	0.328005	−	1.15823i
$783$	−28849.7	−	11950.0i	−1.31674	−	0.545411i
$784$	−13388.4	+	15539.2i	−0.609893	+	0.707872i
$785$	−3537.74	+	1465.38i	−0.160850	+	0.0666262i
$786$	5415.34	+	46181.6i	0.245749	+	2.09573i
$787$	2003.22	−	2440.93i	0.0907332	−	0.110559i	−0.725665	−	0.688048i	$-0.758468\pi$
$787$	2003.22	−	2440.93i	0.0907332	−	0.110559i	0.816398	+	0.577490i	$0.195968\pi$
$788$	−4932.53	−	1298.52i	−0.222987	−	0.0587030i
$789$	−9188.47	−	30290.3i	−0.414598	−	1.36675i
$790$	3913.83	−	854.288i	0.176263	−	0.0384737i
$791$	−865.844	−	4352.89i	−0.0389202	−	0.195665i
$792$	17741.9	−	30046.8i	0.795998	−	1.34806i
$793$	27724.0	+	5514.64i	1.24150	+	0.246949i
$794$	15428.2	−	16011.6i	0.689581	−	0.715657i
$795$	17719.1	+	21590.7i	0.790479	+	0.963201i
$796$	−1809.60	−	3947.76i	−0.0805775	−	0.175785i
$797$	14098.8	−	7535.95i	0.626605	−	0.334927i	−0.127346	−	0.991858i	$-0.540646\pi$
$797$	14098.8	−	7535.95i	0.626605	−	0.334927i	0.753951	+	0.656931i	$0.228146\pi$
$798$	1550.21	+	4788.66i	0.0687680	+	0.212427i
$799$	6846.17	+	6846.17i	0.303129	+	0.303129i
$800$	−1119.40	−	5791.02i	−0.0494711	−	0.255929i
$801$	20569.0	−	20569.0i	0.907329	−	0.907329i
$802$	−21891.3	−	11184.0i	−0.963853	−	0.492421i
$803$	9055.81	+	16942.2i	0.397974	+	0.744556i
$804$	−20590.9	−	19116.7i	−0.903214	−	0.838550i
$805$	6592.72	−	5410.50i	0.288649	−	0.236888i
$806$	−12740.8	+	236.421i	−0.556795	+	0.0103320i
$807$	−5375.27	+	27023.3i	−0.234472	+	1.17877i
$808$	39171.4	+	13725.9i	1.70550	+	0.597619i
$809$	345.559	−	68.7360i	0.0150176	−	0.00298718i	−0.187576	−	0.982250i	$-0.560063\pi$
$809$	345.559	−	68.7360i	0.0150176	−	0.00298718i	0.202593	+	0.979263i	$0.435063\pi$
$810$	−1237.22	+	1928.14i	−0.0536685	+	0.0836393i
$811$	−3085.73	+	936.047i	−0.133606	+	0.0405291i	−0.356380	−	0.934341i	$-0.615989\pi$
$811$	−3085.73	+	936.047i	−0.133606	+	0.0405291i	0.222773	+	0.974870i	$0.428489\pi$
$812$	−5649.92	+	7430.33i	−0.244179	+	0.321125i
$813$	−10029.5	−	8231.01i	−0.432657	−	0.355073i
$814$	−13035.1	+	16498.2i	−0.561278	+	0.710397i
$815$	12041.1	+	29069.8i	0.517523	+	1.24941i
$816$	−25869.2	−	5793.22i	−1.10981	−	0.248533i
$817$	−1900.48	+	4588.17i	−0.0813824	+	0.196474i
$818$	−1761.72	−	3153.77i	−0.0753022	−	0.134803i
$819$	−8523.53	+	839.494i	−0.363658	+	0.0358172i
$820$	−1506.29	+	24635.6i	−0.0641486	+	1.04916i
$821$	−37482.1	−	20034.6i	−1.59334	−	0.851658i	−0.998869	−	0.0475415i	$-0.984861\pi$
$821$	−37482.1	−	20034.6i	−1.59334	−	0.851658i	−0.594471	−	0.804117i	$-0.702639\pi$
$822$	−9294.32	+	51723.3i	−0.394375	+	2.19472i
$823$	17466.9	−	26141.1i	0.739803	−	1.10719i	−0.250479	−	0.968122i	$-0.580588\pi$
$823$	17466.9	−	26141.1i	0.739803	−	1.10719i	0.990282	−	0.139072i	$-0.0444119\pi$
$824$	6805.09	−	2485.49i	0.287702	−	0.105080i
$825$	8227.84	−	5497.67i	0.347220	−	0.232005i
$826$	5675.47	+	2228.42i	0.239074	+	0.0938698i
$827$	897.862	−	9116.15i	0.0377530	−	0.383313i	−0.957679	−	0.287839i	$-0.907063\pi$
$827$	897.862	−	9116.15i	0.0377530	−	0.383313i	0.995432	−	0.0954740i	$-0.0304367\pi$
$828$	53826.8	+	33145.4i	2.25919	+	1.39116i
$829$	−8049.52	+	26535.7i	−0.337239	+	1.11173i	0.610321	+	0.792154i	$0.291040\pi$
$829$	−8049.52	+	26535.7i	−0.337239	+	1.11173i	−0.947561	+	0.319575i	$0.896460\pi$
$830$	2796.74	−	35051.5i	0.116959	−	1.46585i
$831$		−	7868.10i		−	0.328449i
$832$	20315.6	+	8103.71i	0.846536	+	0.337675i
$833$			15951.8i			0.663501i
$834$	45782.6	+	3652.97i	1.90086	+	0.151669i
$835$	7842.69	−	25853.9i	0.325039	−	1.07151i
$836$	12801.0	−	3044.00i	0.529585	−	0.125932i
$837$	−1312.57	+	13326.8i	−0.0542045	+	0.550348i
$838$	−9634.81	+	24538.6i	−0.397171	+	1.01154i
$839$	−3209.58	+	2144.57i	−0.132070	+	0.0882465i	−0.619850	−	0.784720i	$-0.712807\pi$
$839$	−3209.58	+	2144.57i	−0.132070	+	0.0882465i	0.487780	+	0.872966i	$0.337807\pi$
$840$	−5809.59	−	6325.81i	−0.238631	−	0.259835i
$841$	20051.6	−	30009.3i	0.822156	−	1.23044i
$842$	37784.7	+	6789.64i	1.54649	+	0.277893i
$843$	43594.9	+	23301.9i	1.78112	+	0.952031i
$844$	2804.72	−	2481.50i	0.114387	−	0.101205i
$845$	3559.60	−	350.590i	0.144916	−	0.0142730i
$846$	−20297.5	+	11338.3i	−0.824873	+	0.460781i
$847$	1.34938	−	3.25768i	5.47404e−5	−	0.000132155i
$848$	15416.3	+	16173.3i	0.624290	+	0.654945i
$849$	12100.9	+	29214.1i	0.489165	+	1.18095i
$850$	−3599.23	−	2843.72i	−0.145239	−	0.114752i
$851$	−29444.8	−	24164.7i	−1.18608	−	0.973392i
$852$	3450.45	+	25349.7i	0.138745	+	1.01933i
$853$	−20904.7	+	6341.38i	−0.839115	+	0.254543i	−0.680454	−	0.732791i	$-0.738217\pi$
$853$	−20904.7	+	6341.38i	−0.839115	+	0.254543i	−0.158660	+	0.987333i	$0.550717\pi$
$854$	−7473.33	−	4795.39i	−0.299452	−	0.192148i
$855$	17957.3	−	3571.94i	0.718279	−	0.142875i
$856$	−30835.7	−	27580.8i	−1.23124	−	1.10128i
$857$	798.459	−	4014.13i	0.0318260	−	0.160000i	−0.961604	−	0.274440i	$-0.911507\pi$
$857$	798.459	−	4014.13i	0.0318260	−	0.160000i	0.993430	+	0.114440i	$0.0365075\pi$
$858$	680.809	+	36689.1i	0.0270891	+	1.45984i
$859$	21839.2	−	17922.9i	0.867454	−	0.711901i	−0.0913961	−	0.995815i	$-0.529133\pi$
$859$	21839.2	−	17922.9i	0.867454	−	0.711901i	0.958850	+	0.283914i	$0.0916329\pi$
$860$	−314.390	−	8468.39i	−0.0124658	−	0.335779i
$861$	−5973.34	−	11175.3i	−0.236435	−	0.442339i
$862$	8536.73	−	16709.6i	0.337311	−	0.660245i
$863$	−6780.98	+	6780.98i	−0.267471	+	0.267471i	−0.828080	−	0.560610i	$-0.810567\pi$
$863$	−6780.98	+	6780.98i	−0.267471	+	0.267471i	0.560610	+	0.828080i	$0.310567\pi$
$864$	10944.4	−	20212.0i	0.430945	−	0.795864i
$865$	1288.85	+	1288.85i	0.0506614	+	0.0506614i
$866$	−24021.6	+	7776.41i	−0.942597	+	0.305142i
$867$	17876.2	−	9555.04i	0.700241	−	0.374286i
$868$	3752.55	+	1393.61i	0.146739	+	0.0544957i
$869$	3410.81	+	4156.08i	0.133146	+	0.162239i
$870$	40073.5	+	38613.4i	1.56163	+	1.50473i
$871$	17682.0	+	3517.17i	0.687866	+	0.136825i
$872$	4120.65	−	29095.9i	0.160026	−	1.12995i
$873$	−11630.4	−	58470.2i	−0.450894	−	2.26680i
$874$	5083.30	+	23288.6i	0.196733	+	0.901313i
$875$	−2086.40	−	6877.94i	−0.0806094	−	0.265734i
$876$	17656.5	+	30274.7i	0.681002	+	1.16768i
$877$	−15031.7	+	18316.2i	−0.578773	+	0.705237i	−0.977286	−	0.211926i	$-0.932026\pi$
$877$	−15031.7	+	18316.2i	−0.578773	+	0.705237i	0.398513	+	0.917163i	$0.369526\pi$
$878$	−28545.0	+	3347.24i	−1.09721	+	0.128660i
$879$	29247.5	−	12114.7i	1.12229	−	0.464868i
$880$	−17692.3	+	13823.9i	−0.677735	+	0.529548i
$881$	14016.2	+	5805.72i	0.536004	+	0.222020i	0.634230	−	0.773144i	$-0.281317\pi$
$881$	14016.2	+	5805.72i	0.536004	+	0.222020i	−0.0982267	+	0.995164i	$0.531317\pi$
$882$	−36856.3	−	10437.6i	−1.40705	−	0.398471i
$883$	−69.4518	−	705.156i	−0.00264693	−	0.0268747i	0.993771	−	0.111446i	$-0.0355481\pi$
$883$	−69.4518	−	705.156i	−0.00264693	−	0.0268747i	−0.996417	+	0.0845708i	$0.973048\pi$
$884$	16083.3	−	5538.28i	0.611923	−	0.210716i
$885$	17135.6	−	32058.4i	0.650854	−	1.21766i
$886$	2693.42	−	1872.89i	0.102130	−	0.0710168i
$887$	−41664.4	−	27839.2i	−1.57717	−	1.05383i	−0.964703	−	0.263339i	$-0.915176\pi$
$887$	−41664.4	−	27839.2i	−1.57717	−	1.05383i	−0.612470	−	0.790494i	$-0.709824\pi$
$888$	−22647.8	+	30960.5i	−0.855869	+	1.17001i
$889$	−1636.62	−	2449.37i	−0.0617440	−	0.0924064i
$890$	−17156.7	+	7482.42i	−0.646174	+	0.281810i
$891$	−3059.91	−	301.375i	−0.115051	−	0.0113316i
$892$	−17267.4	−	23874.8i	−0.648155	−	0.896176i
$893$	−8389.61	−	2544.96i	−0.314387	−	0.0953682i
$894$	−31209.4	+	26597.0i	−1.16756	+	0.995009i
$895$	−28416.9			−1.06131
$896$	−5009.90	−	4701.90i	−0.186796	−	0.175312i
$897$	−66477.2			−2.47448
$898$	−24407.0	+	20800.0i	−0.906986	+	0.772945i
$899$	−24819.8	−	7529.00i	−0.920785	−	0.279317i
$900$	8925.41	−	6455.26i	0.330571	−	0.239084i
$901$	17293.1	+	1703.22i	0.639418	+	0.0629772i
$902$	−30363.6	+	13242.2i	−1.12084	+	0.488823i
$903$	2417.10	+	3617.45i	0.0890766	+	0.133313i
$904$	−20916.6	+	3243.37i	−0.769554	+	0.119329i
$905$	−30002.1	−	20046.8i	−1.10199	−	0.736329i
$906$	−26556.3	+	18466.1i	−0.973812	+	0.677146i
$907$	9609.57	−	17978.2i	0.351798	−	0.658167i	−0.642324	−	0.766433i	$-0.722030\pi$
$907$	9609.57	−	17978.2i	0.351798	−	0.658167i	0.994122	+	0.108266i	$0.0345298\pi$
$908$	8169.70	+	23725.0i	0.298592	+	0.867117i
$909$	7597.81	+	77141.8i	0.277231	+	2.81478i
$910$	5302.49	+	1501.64i	0.193160	+	0.0547022i
$911$	−25857.3	−	10710.5i	−0.940387	−	0.389521i	−0.140777	−	0.990041i	$-0.544960\pi$
$911$	−25857.3	−	10710.5i	−0.940387	−	0.389521i	−0.799609	+	0.600520i	$0.794960\pi$
$912$	23131.7	−	6415.99i	0.839878	−	0.232955i
$913$	43600.4	−	18059.9i	1.58046	−	0.654649i
$914$	34039.1	−	3991.49i	1.23185	−	0.144449i
$915$	−33583.4	+	40921.5i	−1.21337	+	1.47850i
$916$	7010.92	−	4088.83i	0.252890	−	0.147488i
$917$	2720.62	+	8968.69i	0.0979747	+	0.322979i
$918$	−3812.00	−	17464.3i	−0.137053	−	0.627894i
$919$	1563.85	+	7862.02i	0.0561336	+	0.282203i	0.998649	−	0.0519596i	$-0.0165467\pi$
$919$	1563.85	+	7862.02i	0.0561336	+	0.282203i	−0.942516	+	0.334162i	$0.891547\pi$
$920$	−24444.2	−	32510.3i	−0.875981	−	1.16504i
$921$	42134.7	+	8381.11i	1.50748	+	0.299856i
$922$	−25920.5	−	24976.1i	−0.925865	−	0.892130i
$923$	−10414.0	−	12689.5i	−0.371377	−	0.452524i
$924$	4013.11	−	10806.0i	0.142881	−	0.384732i
$925$	−5853.74	+	3128.89i	−0.208076	+	0.111219i
$926$	9392.34	−	3040.54i	0.333317	−	0.107903i
$927$	9567.08	+	9567.08i	0.338969	+	0.338969i
$928$	34259.6	+	28427.4i	1.21188	+	1.00558i
$929$	−13650.8	+	13650.8i	−0.482097	+	0.482097i	−0.905801	−	0.423704i	$-0.860730\pi$
$929$	−13650.8	+	13650.8i	−0.482097	+	0.482097i	0.423704	+	0.905801i	$0.360730\pi$
$930$	10857.4	−	21252.0i	0.382825	−	0.749332i
$931$	−6809.11	−	12738.9i	−0.239699	−	0.448445i
$932$	53419.8	−	1983.21i	1.87749	−	0.0697021i
$933$	53875.3	−	44214.3i	1.89046	−	1.55146i
$934$	−577.723	−	31133.8i	−0.0202395	−	1.09071i
$935$	−3406.56	+	17125.9i	−0.119151	+	0.599014i
$936$	2272.47	+	40783.9i	0.0793568	+	1.42421i
$937$	33870.5	−	6737.26i	1.18090	−	0.234895i	0.434672	−	0.900589i	$-0.356864\pi$
$937$	33870.5	−	6737.26i	1.18090	−	0.234895i	0.746225	+	0.665694i	$0.231864\pi$
$938$	−4766.40	−	3058.44i	−0.165915	−	0.106462i
$939$	395.458	−	119.961i	0.0137437	−	0.00416909i
$940$	14823.4	−	2017.67i	0.514345	−	0.0700097i
$941$	8086.03	+	6636.03i	0.280124	+	0.229892i	0.763955	−	0.645269i	$-0.223255\pi$
$941$	8086.03	+	6636.03i	0.280124	+	0.229892i	−0.483831	+	0.875162i	$0.660755\pi$
$942$	−7356.78	−	5812.52i	−0.254455	−	0.201043i
$943$	−22964.9	−	55442.1i	−0.793043	−	1.91457i
$944$	11768.6	−	26591.4i	0.405756	−	0.916819i
$945$	2216.26	−	5350.52i	0.0762909	−	0.184183i
$946$	9929.24	−	5546.55i	0.341255	−	0.190628i
$947$	36081.1	−	3553.68i	1.23810	−	0.121942i	0.542302	−	0.840183i	$-0.317553\pi$
$947$	36081.1	−	3553.68i	1.23810	−	0.121942i	0.695794	+	0.718241i	$0.255053\pi$
$948$	6499.60	+	7346.16i	0.222676	+	0.251680i
$949$	−19832.8	−	10600.8i	−0.678398	−	0.362611i
$950$	4088.17	+	734.616i	0.139619	+	0.0250885i
$951$	−39886.6	+	59694.5i	−1.36005	+	2.03546i
$952$	−5338.58	−	227.094i	−0.181748	−	0.00773126i
$953$	−12920.1	+	8632.97i	−0.439165	+	0.293441i	−0.755429	−	0.655230i	$-0.772572\pi$
$953$	−12920.1	+	8632.97i	−0.439165	+	0.293441i	0.316264	+	0.948671i	$0.397572\pi$
$954$	−15250.4	+	38840.8i	−0.517559	+	1.31815i
$955$	−3574.31	+	36290.6i	−0.121112	+	1.22967i
$956$	−3206.01	−	13482.3i	−0.108462	−	0.456119i
$957$	−21680.9	+	71472.3i	−0.732334	+	2.41418i
$958$	43638.3	+	3481.87i	1.47170	+	0.117426i
$959$			10592.5i			0.356672i
$960$	−31319.4	+	26400.0i	−1.05295	+	0.887557i
$961$		−	18668.4i		−	0.626644i
$962$	1957.69	−	24535.7i	0.0656116	−	0.822310i
$963$	22427.8	−	73934.6i	0.750495	−	2.47405i
$964$	2219.22	−	3603.93i	0.0741457	−	0.120410i
$965$	−2491.46	+	25296.2i	−0.0831118	+	0.843848i
$966$	19437.9	+	7632.07i	0.647415	+	0.254201i
$967$	47746.0	−	31902.9i	1.58781	−	1.06094i	0.628796	−	0.777570i	$-0.283548\pi$
$967$	47746.0	−	31902.9i	1.58781	−	1.06094i	0.959011	−	0.283368i	$-0.0914519\pi$
$968$	−15.2490	−	7.08995i	−0.000506325	−	0.000235413i
$969$	10371.9	−	15522.6i	0.343851	−	0.514610i
$970$	−6784.32	+	37755.1i	−0.224569	+	1.24974i
$971$	40296.0	+	21538.7i	1.33178	+	0.711852i	0.974973	−	0.222325i	$-0.0713645\pi$
$971$	40296.0	+	21538.7i	1.33178	+	0.711852i	0.356810	+	0.934177i	$0.383865\pi$
$972$	−32974.4	−	2016.14i	−1.08812	−	0.0665307i
$973$	9212.80	−	907.382i	0.303545	−	0.0298965i
$974$	−257.082	−	460.219i	−0.00845732	−	0.0151400i
$975$	−4432.95	+	10702.1i	−0.145608	+	0.351529i
$976$	−24364.3	+	34637.7i	−0.799061	+	1.13599i
$977$	−13344.6	−	32216.8i	−0.436983	−	1.05497i	−0.976985	−	0.213307i	$-0.931577\pi$
$977$	−13344.6	−	32216.8i	−0.436983	−	1.05497i	0.540002	−	0.841664i	$-0.318423\pi$
$978$	−47761.9	+	60451.2i	−1.56161	+	1.97650i
$979$	−19418.7	−	15936.5i	−0.633937	−	0.520259i
$980$	19620.1	+	14918.8i	0.639530	+	0.486290i
$981$	52516.8	−	15930.8i	1.70921	−	0.518482i
$982$	−11677.1	+	18198.0i	−0.379460	+	0.591367i
$983$	−1758.06	+	349.699i	−0.0570430	+	0.0113466i	−0.223529	−	0.974697i	$-0.571758\pi$
$983$	−1758.06	+	349.699i	−0.0570430	+	0.0113466i	0.166486	+	0.986044i	$0.446758\pi$
$984$	−54460.1	+	26197.2i	−1.76435	+	0.848717i
$985$	−1195.75	+	6011.45i	−0.0386800	+	0.194458i
$986$	34615.8	−	642.336i	1.11804	−	0.0207466i
$987$	−5937.11	+	4872.46i	−0.191469	+	0.157135i
$988$	−10479.9	+	11288.1i	−0.337460	+	0.363483i
$989$	9712.63	+	18171.1i	0.312279	+	0.584233i
$990$	−37340.1	−	19076.6i	−1.19873	−	0.612419i
$991$	3149.49	−	3149.49i	0.100955	−	0.100955i	−0.654825	−	0.755780i	$-0.727258\pi$
$991$	3149.49	−	3149.49i	0.100955	−	0.100955i	0.755780	+	0.654825i	$0.227258\pi$
$992$	7401.03	−	17598.1i	0.236878	−	0.563245i
$993$	53403.7	+	53403.7i	1.70666	+	1.70666i
$994$	1588.19	+	4906.00i	0.0506785	+	0.156548i
$995$	−4602.35	+	2460.01i	−0.146637	+	0.0783793i
$996$	78266.2	−	35876.3i	2.48992	−	1.14135i
$997$	10600.2	+	12916.4i	0.336723	+	0.410298i	0.913653	−	0.406496i	$-0.133249\pi$
$997$	10600.2	+	12916.4i	0.336723	+	0.410298i	−0.576930	+	0.816794i	$0.695749\pi$
$998$	−22156.7	+	22994.5i	−0.702762	+	0.729336i
$999$	−25368.8	−	5046.16i	−0.803436	−	0.159813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.14	✓	752
128.77	even	32	inner	128.4.k.a.77.14	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.14	✓	752	1.1	even	1	trivial
128.4.k.a.77.14	yes	752	128.77	even	32	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83459 - 2.15274i) q^{2} +(-7.96376 - 2.41578i) q^{3} +(-1.26855 + 7.89878i) q^{4} +(9.56707 + 0.942274i) q^{5} +(9.40970 + 21.5759i) q^{6} +(2.63589 + 3.94489i) q^{7} +(19.3313 - 11.7602i) q^{8} +(35.1358 + 23.4770i) q^{9} +O(q^{10})\)	\(q+(-1.83459 - 2.15274i) q^{2} +(-7.96376 - 2.41578i) q^{3} +(-1.26855 + 7.89878i) q^{4} +(9.56707 + 0.942274i) q^{5} +(9.40970 + 21.5759i) q^{6} +(2.63589 + 3.94489i) q^{7} +(19.3313 - 11.7602i) q^{8} +(35.1358 + 23.4770i) q^{9} +(-15.5232 - 22.3241i) q^{10} +(17.2027 - 32.1840i) q^{11} +(29.1842 - 59.8395i) q^{12} +(4.18722 + 42.5135i) q^{13} +(3.65653 - 12.9116i) q^{14} +(-73.9135 - 30.6160i) q^{15} +(-60.7815 - 20.0401i) q^{16} +(-45.9844 + 19.0473i) q^{17} +(-13.9200 - 118.709i) q^{18} +(28.5922 - 34.8397i) q^{19} +(-19.5792 + 74.3729i) q^{20} +(-11.4616 - 37.7839i) q^{21} +(-100.844 + 22.0116i) q^{22} +(-36.4797 - 183.396i) q^{23} +(-182.360 + 46.9550i) q^{24} +(-31.9573 - 6.35670i) q^{25} +(83.8386 - 87.0089i) q^{26} +(-80.5520 - 98.1529i) q^{27} +(-34.5036 + 15.8160i) q^{28} +(216.890 - 115.930i) q^{29} +(69.6929 + 215.284i) q^{30} +(-74.5743 - 74.5743i) q^{31} +(68.3682 + 167.612i) q^{32} +(-214.748 + 214.748i) q^{33} +(125.366 + 64.0482i) q^{34} +(21.5006 + 40.2247i) q^{35} +(-230.012 + 247.749i) q^{36} +(157.468 - 129.231i) q^{37} +(-127.456 + 2.36509i) q^{38} +(69.3574 - 348.683i) q^{39} +(196.025 - 94.2949i) q^{40} +(314.762 - 62.6101i) q^{41} +(-60.3114 + 93.9918i) q^{42} +(-105.443 + 31.9859i) q^{43} +(232.392 + 176.708i) q^{44} +(314.025 + 257.714i) q^{45} +(-327.878 + 414.988i) q^{46} +(-74.4402 - 179.714i) q^{47} +(435.637 + 306.429i) q^{48} +(122.646 - 296.094i) q^{49} +(44.9442 + 80.4576i) q^{50} +(412.223 - 40.6004i) q^{51} +(-341.117 - 20.8568i) q^{52} +(-307.896 - 164.574i) q^{53} +(-63.5174 + 353.478i) q^{54} +(194.906 - 291.697i) q^{55} +(97.3477 + 45.2612i) q^{56} +(-311.867 + 208.383i) q^{57} +(-647.470 - 254.222i) q^{58} +(-44.5354 + 452.175i) q^{59} +(335.592 - 544.989i) q^{60} +(192.080 - 633.203i) q^{61} +(-23.7255 + 297.352i) q^{62} +200.490i q^{63} +(235.397 - 454.678i) q^{64} +410.675i q^{65} +(856.270 + 68.3213i) q^{66} +(122.506 - 403.849i) q^{67} +(-92.1172 - 387.383i) q^{68} +(-152.529 + 1548.65i) q^{69} +(47.1485 - 120.081i) q^{70} +(-319.508 + 213.489i) q^{71} +(955.315 + 40.6375i) q^{72} +(-292.462 + 437.700i) q^{73} +(-567.090 - 101.902i) q^{74} +(239.144 + 127.825i) q^{75} +(238.920 + 270.040i) q^{76} +(172.307 - 16.9707i) q^{77} +(-877.865 + 490.382i) q^{78} +(-56.3804 + 136.114i) q^{79} +(-562.618 - 248.998i) q^{80} +(-32.2429 - 77.8413i) q^{81} +(-712.243 - 562.736i) q^{82} +(999.656 + 820.396i) q^{83} +(312.986 - 42.6019i) q^{84} +(-457.883 + 138.897i) q^{85} +(262.303 + 168.311i) q^{86} +(-2007.32 + 399.281i) q^{87} +(-45.9389 - 824.465i) q^{88} +(134.295 - 675.147i) q^{89} +(-21.3176 - 1148.81i) q^{90} +(-156.674 + 128.579i) q^{91} +(1494.88 - 55.4976i) q^{92} +(413.737 + 774.047i) q^{93} +(-250.311 + 489.953i) q^{94} +(306.372 - 306.372i) q^{95} +(-139.554 - 1499.99i) q^{96} +(-997.565 - 997.565i) q^{97} +(-862.418 + 279.186i) q^{98} +(1360.02 - 726.944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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