LMFDB - Embedded newform 128.4.k.a.5.5

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			5.5
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.71781 + 0.783272i) q^{2} +(-1.31785 - 0.399764i) q^{3} +(6.77297 - 4.25757i) q^{4} +(-18.9129 - 1.86275i) q^{5} +(3.89478 + 0.0542507i) q^{6} +(16.8694 + 25.2468i) q^{7} +(-15.0728 + 16.8763i) q^{8} +(-20.8728 - 13.9467i) q^{9} +O(q^{10})$	\(q+(-2.71781 + 0.783272i) q^{2} +(-1.31785 - 0.399764i) q^{3} +(6.77297 - 4.25757i) q^{4} +(-18.9129 - 1.86275i) q^{5} +(3.89478 + 0.0542507i) q^{6} +(16.8694 + 25.2468i) q^{7} +(-15.0728 + 16.8763i) q^{8} +(-20.8728 - 13.9467i) q^{9} +(52.8606 - 9.75131i) q^{10} +(16.6257 - 31.1045i) q^{11} +(-10.6278 + 2.90323i) q^{12} +(1.83665 + 18.6478i) q^{13} +(-65.6228 - 55.4026i) q^{14} +(24.1796 + 10.0155i) q^{15} +(27.7462 - 57.6728i) q^{16} +(20.4704 - 8.47913i) q^{17} +(67.6523 + 21.5555i) q^{18} +(84.7406 - 103.257i) q^{19} +(-136.027 + 67.9064i) q^{20} +(-12.1385 - 40.0151i) q^{21} +(-20.8222 + 97.5585i) q^{22} +(9.68094 + 48.6694i) q^{23} +(26.6102 - 16.2148i) q^{24} +(231.628 + 46.0737i) q^{25} +(-19.5980 - 49.2427i) q^{26} +(45.5203 + 55.4666i) q^{27} +(221.746 + 99.1733i) q^{28} +(264.413 - 141.332i) q^{29} +(-73.5603 - 8.28105i) q^{30} +(12.7089 + 12.7089i) q^{31} +(-30.2355 + 178.476i) q^{32} +(-34.3445 + 34.3445i) q^{33} +(-48.9933 + 39.0786i) q^{34} +(-272.019 - 508.913i) q^{35} +(-200.750 - 5.59361i) q^{36} +(240.443 - 197.326i) q^{37} +(-149.431 + 347.007i) q^{38} +(5.03431 - 25.3092i) q^{39} +(316.506 - 291.103i) q^{40} +(-40.7045 + 8.09662i) q^{41} +(64.3328 + 99.2458i) q^{42} +(-269.365 + 81.7110i) q^{43} +(-19.8241 - 281.455i) q^{44} +(368.785 + 302.654i) q^{45} +(-64.4323 - 124.691i) q^{46} +(-20.4409 - 49.3487i) q^{47} +(-59.6208 + 64.9118i) q^{48} +(-221.565 + 534.904i) q^{49} +(-665.610 + 56.2084i) q^{50} +(-30.3665 + 2.99084i) q^{51} +(91.8340 + 118.482i) q^{52} +(-244.259 - 130.559i) q^{53} +(-167.161 - 115.093i) q^{54} +(-372.379 + 557.305i) q^{55} +(-680.342 - 95.8468i) q^{56} +(-152.953 + 102.200i) q^{57} +(-607.924 + 591.221i) q^{58} +(1.10923 - 11.2622i) q^{59} +(206.409 - 35.1114i) q^{60} +(-119.720 + 394.663i) q^{61} +(-44.4949 - 24.5858i) q^{62} -762.243i q^{63} +(-57.6212 - 508.747i) q^{64} -356.105i q^{65} +(66.4408 - 120.243i) q^{66} +(125.405 - 413.405i) q^{67} +(102.545 - 144.583i) q^{68} +(6.69829 - 68.0088i) q^{69} +(1137.91 + 1170.06i) q^{70} +(286.683 - 191.556i) q^{71} +(549.981 - 142.039i) q^{72} +(-47.0648 + 70.4374i) q^{73} +(-498.917 + 724.627i) q^{74} +(-286.832 - 153.315i) q^{75} +(134.323 - 1060.14i) q^{76} +(1065.75 - 104.968i) q^{77} +(6.14169 + 72.7288i) q^{78} +(381.993 - 922.212i) q^{79} +(-632.191 + 1039.07i) q^{80} +(221.565 + 534.906i) q^{81} +(104.285 - 53.8877i) q^{82} +(734.428 + 602.729i) q^{83} +(-252.581 - 219.341i) q^{84} +(-402.949 + 122.233i) q^{85} +(668.081 - 433.061i) q^{86} +(-404.955 + 80.5506i) q^{87} +(274.334 + 749.412i) q^{88} +(132.952 - 668.394i) q^{89} +(-1239.35 - 533.696i) q^{90} +(-439.815 + 360.947i) q^{91} +(272.782 + 288.419i) q^{92} +(-11.6678 - 21.8289i) q^{93} +(94.2080 + 118.110i) q^{94} +(-1795.03 + 1795.03i) q^{95} +(111.194 - 223.117i) q^{96} +(-801.443 - 801.443i) q^{97} +(183.195 - 1627.31i) q^{98} +(-780.830 + 417.363i) 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 $

$2$	−2.71781	+	0.783272i	−0.960891	+	0.276929i
$2$	−2.71781	+	0.783272i	−0.960891	+	0.276929i
$3$	−1.31785	−	0.399764i	−0.253620	−	0.0769346i	0.160915	−	0.986968i	$-0.448556\pi$
$3$	−1.31785	−	0.399764i	−0.253620	−	0.0769346i	−0.414534	+	0.910034i	$0.636056\pi$
$4$	6.77297	−	4.25757i	0.846621	−	0.532196i
$5$	−18.9129	−	1.86275i	−1.69162	−	0.166610i	−0.794160	−	0.607709i	$-0.792089\pi$
$5$	−18.9129	−	1.86275i	−1.69162	−	0.166610i	−0.897458	+	0.441099i	$0.854589\pi$
$6$	3.89478	+	0.0542507i	0.265006	+	0.00369129i
$7$	16.8694	+	25.2468i	0.910860	+	1.36320i	0.931628	+	0.363414i	$0.118389\pi$
$7$	16.8694	+	25.2468i	0.910860	+	1.36320i	−0.0207675	+	0.999784i	$0.506611\pi$
$8$	−15.0728	+	16.8763i	−0.666130	+	0.745836i
$9$	−20.8728	−	13.9467i	−0.773066	−	0.516546i
$10$	52.8606	−	9.75131i	1.67160	−	0.308363i
$11$	16.6257	−	31.1045i	0.455712	−	0.852577i	−0.544195	−	0.838959i	$-0.683165\pi$
$11$	16.6257	−	31.1045i	0.455712	−	0.852577i	0.999907	−	0.0136188i	$-0.00433513\pi$
$12$	−10.6278	+	2.90323i	−0.255664	+	0.0698408i
$13$	1.83665	+	18.6478i	0.0391843	+	0.397845i	0.994693	+	0.102883i	$0.0328068\pi$
$13$	1.83665	+	18.6478i	0.0391843	+	0.397845i	−0.955509	+	0.294961i	$0.904693\pi$
$14$	−65.6228	−	55.4026i	−1.25275	−	1.05764i
$15$	24.1796	+	10.0155i	0.416209	+	0.172400i
$16$	27.7462	−	57.6728i	0.433535	−	0.901137i
$17$	20.4704	−	8.47913i	0.292048	−	0.120970i	−0.231849	−	0.972752i	$-0.574478\pi$
$17$	20.4704	−	8.47913i	0.292048	−	0.120970i	0.523897	+	0.851782i	$0.324478\pi$
$18$	67.6523	+	21.5555i	0.885878	+	0.282260i
$19$	84.7406	−	103.257i	1.02320	−	1.24677i	0.0545080	−	0.998513i	$-0.482641\pi$
$19$	84.7406	−	103.257i	1.02320	−	1.24677i	0.968693	−	0.248261i	$-0.0798590\pi$
$20$	−136.027	+	67.9064i	−1.52083	+	0.759217i
$21$	−12.1385	−	40.0151i	−0.126135	−	0.415810i
$22$	−20.8222	+	97.5585i	−0.201786	+	0.945433i
$23$	9.68094	+	48.6694i	0.0877659	+	0.441229i	0.999534	+	0.0305237i	$0.00971751\pi$
$23$	9.68094	+	48.6694i	0.0877659	+	0.441229i	−0.911768	+	0.410705i	$0.865282\pi$
$24$	26.6102	−	16.2148i	0.226324	−	0.137910i
$25$	231.628	+	46.0737i	1.85303	+	0.368590i
$26$	−19.5980	−	49.2427i	−0.147826	−	0.371434i
$27$	45.5203	+	55.4666i	0.324459	+	0.395354i
$28$	221.746	+	99.1733i	1.49664	+	0.669357i
$29$	264.413	−	141.332i	1.69311	−	0.904989i	0.714407	−	0.699730i	$-0.246696\pi$
$29$	264.413	−	141.332i	1.69311	−	0.904989i	0.978708	−	0.205259i	$-0.0658036\pi$
$30$	−73.5603	−	8.28105i	−0.447674	−	0.0503969i
$31$	12.7089	+	12.7089i	0.0736318	+	0.0736318i	0.742964	−	0.669332i	$-0.233420\pi$
$31$	12.7089	+	12.7089i	0.0736318	+	0.0736318i	−0.669332	+	0.742964i	$0.733420\pi$
$32$	−30.2355	+	178.476i	−0.167029	+	0.985952i
$33$	−34.3445	+	34.3445i	−0.181170	+	0.181170i
$34$	−48.9933	+	39.0786i	−0.247126	+	0.197115i
$35$	−272.019	−	508.913i	−1.31371	−	2.45777i
$36$	−200.750	−	5.59361i	−0.929397	−	0.0258963i
$37$	240.443	−	197.326i	1.06834	−	0.876763i	0.0756098	−	0.997137i	$-0.475910\pi$
$37$	240.443	−	197.326i	1.06834	−	0.876763i	0.992729	+	0.120375i	$0.0384097\pi$
$38$	−149.431	+	347.007i	−0.637917	+	1.48137i
$39$	5.03431	−	25.3092i	0.0206701	−	0.103916i
$40$	316.506	−	291.103i	1.25110	−	1.15068i
$41$	−40.7045	+	8.09662i	−0.155048	+	0.0308410i	−0.272004	−	0.962296i	$-0.587686\pi$
$41$	−40.7045	+	8.09662i	−0.155048	+	0.0308410i	0.116956	+	0.993137i	$0.462686\pi$
$42$	64.3328	+	99.2458i	0.236351	+	0.364618i
$43$	−269.365	+	81.7110i	−0.955297	+	0.289786i	−0.729186	−	0.684315i	$-0.760101\pi$
$43$	−269.365	+	81.7110i	−0.955297	+	0.289786i	−0.226111	+	0.974102i	$0.572601\pi$
$44$	−19.8241	−	281.455i	−0.0679227	−	0.964338i
$45$	368.785	+	302.654i	1.22167	+	1.00260i
$46$	−64.4323	−	124.691i	−0.206522	−	0.399668i
$47$	−20.4409	−	49.3487i	−0.0634386	−	0.153154i	0.888981	−	0.457944i	$-0.151414\pi$
$47$	−20.4409	−	49.3487i	−0.0634386	−	0.153154i	−0.952420	+	0.304789i	$0.901414\pi$
$48$	−59.6208	+	64.9118i	−0.179282	+	0.195192i
$49$	−221.565	+	534.904i	−0.645961	+	1.55949i
$50$	−665.610	+	56.2084i	−1.88263	+	0.158981i
$51$	−30.3665	+	2.99084i	−0.0833758	+	0.00821180i
$52$	91.8340	+	118.482i	0.244906	+	0.315970i
$53$	−244.259	−	130.559i	−0.633049	−	0.338372i	0.123465	−	0.992349i	$-0.460599\pi$
$53$	−244.259	−	130.559i	−0.633049	−	0.338372i	−0.756514	+	0.653977i	$0.773099\pi$
$54$	−167.161	−	115.093i	−0.421254	−	0.290040i
$55$	−372.379	+	557.305i	−0.912939	+	1.36631i
$56$	−680.342	−	95.8468i	−1.62347	−	0.228716i
$57$	−152.953	+	102.200i	−0.355424	+	0.237487i
$58$	−607.924	+	591.221i	−1.37628	+	1.33847i
$59$	1.10923	−	11.2622i	0.00244762	−	0.0248511i	−0.993883	−	0.110435i	$-0.964776\pi$
$59$	1.10923	−	11.2622i	0.00244762	−	0.0248511i	0.996331	+	0.0855840i	$0.0272756\pi$
$60$	206.409	−	35.1114i	0.444122	−	0.0755478i
$61$	−119.720	+	394.663i	−0.251287	+	0.828384i	0.737015	+	0.675876i	$0.236235\pi$
$61$	−119.720	+	394.663i	−0.251287	+	0.828384i	−0.988302	+	0.152507i	$0.951265\pi$
$62$	−44.4949	−	24.5858i	−0.0911428	−	0.0503613i
$63$		−	762.243i		−	1.52434i
$64$	−57.6212	−	508.747i	−0.112541	−	0.993647i
$65$		−	356.105i		−	0.679530i
$66$	66.4408	−	120.243i	0.123914	−	0.224256i
$67$	125.405	−	413.405i	0.228667	−	0.753813i	−0.765255	−	0.643727i	$-0.777387\pi$
$67$	125.405	−	413.405i	0.228667	−	0.753813i	0.993922	−	0.110086i	$-0.0351127\pi$
$68$	102.545	−	144.583i	0.182874	−	0.257842i
$69$	6.69829	−	68.0088i	0.0116866	−	0.118657i
$70$	1137.91	+	1170.06i	1.94295	+	1.99784i
$71$	286.683	−	191.556i	0.479198	−	0.320190i	−0.292405	−	0.956295i	$-0.594455\pi$
$71$	286.683	−	191.556i	0.479198	−	0.320190i	0.771603	+	0.636105i	$0.219455\pi$
$72$	549.981	−	142.039i	0.900221	−	0.232493i
$73$	−47.0648	+	70.4374i	−0.0754591	+	0.112933i	−0.867280	−	0.497821i	$-0.834134\pi$
$73$	−47.0648	+	70.4374i	−0.0754591	+	0.112933i	0.791821	+	0.610754i	$0.209134\pi$
$74$	−498.917	+	724.627i	−0.783756	+	1.13833i
$75$	−286.832	−	153.315i	−0.441606	−	0.236044i
$76$	134.323	−	1060.14i	0.202736	−	1.60009i
$77$	1065.75	−	104.968i	1.57732	−	0.155353i
$78$	6.14169	+	72.7288i	0.00891551	+	0.105576i
$79$	381.993	−	922.212i	0.544019	−	1.31338i	−0.377846	−	0.925868i	$-0.623335\pi$
$79$	381.993	−	922.212i	0.544019	−	1.31338i	0.921865	−	0.387510i	$-0.126665\pi$
$80$	−632.191	+	1039.07i	−0.883514	+	1.45215i
$81$	221.565	+	534.906i	0.303930	+	0.733753i
$82$	104.285	−	53.8877i	0.140443	−	0.0725720i
$83$	734.428	+	602.729i	0.971252	+	0.797086i	0.979203	−	0.202882i	$-0.0650309\pi$
$83$	734.428	+	602.729i	0.971252	+	0.797086i	−0.00795093	+	0.999968i	$0.502531\pi$
$84$	−252.581	−	219.341i	−0.328081	−	0.284906i
$85$	−402.949	+	122.233i	−0.514188	+	0.155977i
$86$	668.081	−	433.061i	0.837686	−	0.543002i
$87$	−404.955	+	80.5506i	−0.499032	+	0.0992636i
$88$	274.334	+	749.412i	0.332319	+	0.907814i
$89$	132.952	−	668.394i	0.158347	−	0.796063i	−0.817214	−	0.576334i	$-0.804483\pi$
$89$	132.952	−	668.394i	0.158347	−	0.796063i	0.975561	−	0.219729i	$-0.0705174\pi$
$90$	−1239.35	−	533.696i	−1.45154	−	0.625072i
$91$	−439.815	+	360.947i	−0.506650	+	0.415797i
$92$	272.782	+	288.419i	0.309125	+	0.326845i
$93$	−11.6678	−	21.8289i	−0.0130096	−	0.0243393i
$94$	94.2080	+	118.110i	0.103370	+	0.129597i
$95$	−1795.03	+	1795.03i	−1.93859	+	1.93859i
$96$	111.194	−	223.117i	0.118216	−	0.237206i
$97$	−801.443	−	801.443i	−0.838910	−	0.838910i	0.149806	−	0.988715i	$-0.452135\pi$
$97$	−801.443	−	801.443i	−0.838910	−	0.838910i	−0.988715	+	0.149806i	$0.952135\pi$
$98$	183.195	−	1627.31i	0.188831	−	1.67738i
$99$	−780.830	+	417.363i	−0.792691	+	0.423702i
$100$	1764.97	−	674.117i	1.76497	−	0.674117i
$101$	239.638	+	291.999i	0.236087	+	0.287673i	0.877554	−	0.479477i	$-0.159174\pi$
$101$	239.638	+	291.999i	0.236087	+	0.287673i	−0.641467	+	0.767151i	$0.721674\pi$
$102$	80.1878	−	31.9138i	0.0778409	−	0.0309798i
$103$	1557.18	+	309.743i	1.48965	+	0.296309i	0.871751	−	0.489949i	$-0.162985\pi$
$103$	1557.18	+	309.743i	1.48965	+	0.296309i	0.617897	+	0.786259i	$0.287985\pi$
$104$	−342.391	−	250.079i	−0.322829	−	0.235791i
$105$	155.035	+	779.412i	0.144094	+	0.724408i
$106$	766.113	+	163.514i	0.701995	+	0.149829i
$107$	−190.074	−	626.592i	−0.171731	−	0.566121i	−0.999983	−	0.00576562i	$-0.998165\pi$
$107$	−190.074	−	626.592i	−0.171731	−	0.566121i	0.828253	−	0.560355i	$-0.189335\pi$
$108$	544.460	+	181.868i	0.485099	+	0.162039i
$109$	−972.293	+	1184.74i	−0.854392	+	1.04108i	0.144279	+	0.989537i	$0.453914\pi$
$109$	−972.293	+	1184.74i	−0.854392	+	1.04108i	−0.998671	+	0.0515427i	$0.983586\pi$
$110$	575.534	−	1806.32i	0.498864	−	1.56569i
$111$	−395.750	+	163.925i	−0.338405	+	0.140172i
$112$	1924.11	−	272.399i	1.62332	−	0.229815i
$113$	1797.29	+	744.461i	1.49624	+	0.619761i	0.972663	−	0.232220i	$-0.0745989\pi$
$113$	1797.29	+	744.461i	1.49624	+	0.619761i	0.523573	+	0.851981i	$0.324599\pi$
$114$	335.647	−	397.565i	0.275757	−	0.326626i
$115$	−92.4352	−	938.511i	−0.0749533	−	0.761014i
$116$	1189.13	−	2082.99i	0.951796	−	1.66725i
$117$	221.741	−	414.848i	0.175213	−	0.327801i
$118$	5.80670	+	31.4774i	0.00453008	+	0.0245570i
$119$	559.394	+	373.775i	0.430921	+	0.287932i
$120$	−533.479	+	257.101i	−0.405831	+	0.195583i
$121$	48.3891	+	72.4194i	0.0363554	+	0.0544098i
$122$	16.2468	−	1166.39i	0.0120567	−	0.865575i
$123$	56.8789	+	5.60209i	0.0416959	+	0.00410669i
$124$	140.186	+	31.9680i	0.101525	+	0.0231517i
$125$	−2021.67	−	613.268i	−1.44659	−	0.438819i
$126$	597.044	+	2071.63i	0.422134	+	1.46473i
$127$	−989.978			−0.691703			−0.345852	−	0.938289i	$-0.612410\pi$
$127$	−989.978			−0.691703			−0.345852	+	0.938289i	$0.612410\pi$
$128$	555.091	+	1337.54i	0.383309	+	0.923620i
$129$	387.647			0.264577
$130$	278.927	+	967.826i	0.188181	+	0.652954i
$131$	−1177.74	−	357.265i	−0.785497	−	0.238278i	−0.128039	−	0.991769i	$-0.540868\pi$
$131$	−1177.74	−	357.265i	−0.785497	−	0.238278i	−0.657458	+	0.753491i	$0.728368\pi$
$132$	−86.3903	+	378.839i	−0.0569645	+	0.249801i
$133$	4036.42	+	397.553i	2.63159	+	0.259189i
$134$	−17.0183	+	1221.78i	−0.0109713	+	0.787656i
$135$	−757.598	−	1133.83i	−0.482990	−	0.722846i
$136$	−165.450	+	473.270i	−0.104318	+	0.298401i
$137$	200.286	+	133.827i	0.124902	+	0.0834569i	0.616452	−	0.787393i	$-0.288569\pi$
$137$	200.286	+	133.827i	0.124902	+	0.0834569i	−0.491550	+	0.870849i	$0.663569\pi$
$138$	35.0648	+	190.082i	0.0216298	+	0.117252i
$139$	1019.13	−	1906.65i	0.621880	−	1.16346i	−0.351916	−	0.936032i	$-0.614470\pi$
$139$	1019.13	−	1906.65i	0.621880	−	1.16346i	0.973796	−	0.227424i	$-0.0730303\pi$
$140$	−4009.11	−	2288.71i	−2.42023	−	1.38165i
$141$	7.21012	+	73.2056i	0.00430639	+	0.0437236i
$142$	−629.110	+	745.163i	−0.371787	+	0.440371i
$143$	610.567	+	252.905i	0.357050	+	0.147895i
$144$	−1383.49	+	816.821i	−0.800630	+	0.472697i
$145$	−5264.08	+	2180.45i	−3.01488	+	1.24881i
$146$	72.7414	−	228.300i	0.0412337	−	0.129413i
$147$	505.823	−	616.347i	0.283807	−	0.345820i
$148$	788.381	−	2360.18i	0.437868	−	1.31085i
$149$	−357.799	−	1179.51i	−0.196725	−	0.648517i	−0.998691	−	0.0511466i	$-0.983712\pi$
$149$	−357.799	−	1179.51i	−0.196725	−	0.648517i	0.801966	−	0.597370i	$-0.203788\pi$
$150$	899.641	+	192.013i	0.489703	+	0.104519i
$151$	171.388	+	861.626i	0.0923667	+	0.464359i	0.999091	+	0.0426342i	$0.0135750\pi$
$151$	171.388	+	861.626i	0.0923667	+	0.464359i	−0.906724	+	0.421724i	$0.861425\pi$
$152$	465.316	+	2986.48i	0.248304	+	1.59365i
$153$	−545.531	−	108.513i	−0.288259	−	0.0573382i
$154$	−2814.29	+	1120.06i	−1.47261	+	0.586083i
$155$	−216.688	−	264.035i	−0.112289	−	0.136825i
$156$	−73.6584	−	192.852i	−0.0378038	−	0.0989779i
$157$	2490.54	−	1331.22i	1.26603	−	0.676707i	0.304790	−	0.952420i	$-0.401414\pi$
$157$	2490.54	−	1331.22i	1.26603	−	0.676707i	0.961240	+	0.275713i	$0.0889138\pi$
$158$	−315.840	+	2805.60i	−0.159031	+	1.41267i
$159$	269.703	+	269.703i	0.134521	+	0.134521i
$160$	904.298	−	3319.18i	0.446819	−	1.64003i
$161$	−1065.43	+	1065.43i	−0.521540	+	0.521540i
$162$	−1021.15	−	1280.23i	−0.495241	−	0.620889i
$163$	−1649.53	−	3086.06i	−0.792648	−	1.48294i	−0.873826	−	0.486240i	$-0.838368\pi$
$163$	−1649.53	−	3086.06i	−0.792648	−	1.48294i	0.0811780	−	0.996700i	$-0.474132\pi$
$164$	−241.218	+	228.140i	−0.114854	+	0.108627i
$165$	713.529	−	585.578i	0.336656	−	0.276286i
$166$	−2468.14	−	1062.85i	−1.15400	−	0.496945i
$167$	−343.226	+	1725.52i	−0.159040	+	0.799547i	0.816092	+	0.577922i	$0.196136\pi$
$167$	−343.226	+	1725.52i	−0.159040	+	0.799547i	−0.975132	+	0.221625i	$0.928864\pi$
$168$	858.269	+	398.288i	0.394148	+	0.182908i
$169$	1810.42	−	360.114i	0.824040	−	0.163912i
$170$	999.397	−	647.825i	0.450884	−	0.292270i
$171$	−3208.87	+	973.399i	−1.43502	+	0.435308i
$172$	−1476.51	+	1700.27i	−0.654552	+	0.753745i
$173$	−1862.18	−	1528.25i	−0.818376	−	0.671624i	0.129036	−	0.991640i	$-0.458812\pi$
$173$	−1862.18	−	1528.25i	−0.818376	−	0.671624i	−0.947412	+	0.320016i	$0.896312\pi$
$174$	1037.50	−	536.112i	0.452026	−	0.233578i
$175$	2744.21	+	6625.11i	1.18539	+	2.86178i
$176$	−1332.58	−	1821.88i	−0.570722	−	0.780281i
$177$	−5.96402	+	14.3984i	−0.00253267	+	0.00611441i
$178$	162.197	+	1920.71i	0.0682987	+	0.808781i
$179$	−1167.47	+	114.986i	−0.487492	+	0.0480137i	−0.338778	−	0.940866i	$-0.610013\pi$
$179$	−1167.47	+	114.986i	−0.487492	+	0.0480137i	−0.148714	+	0.988880i	$0.547513\pi$
$180$	3786.33	+	479.739i	1.56787	+	0.198653i
$181$	3760.34	+	2009.95i	1.54422	+	0.825404i	0.999909	−	0.0134792i	$-0.00429068\pi$
$181$	3760.34	+	2009.95i	1.54422	+	0.825404i	0.544312	+	0.838883i	$0.316791\pi$
$182$	912.614	−	1325.48i	0.371689	−	0.539841i
$183$	315.544	−	472.245i	0.127463	−	0.190762i
$184$	−967.280	−	570.205i	−0.387548	−	0.228457i
$185$	−4915.03	+	3284.12i	−1.95330	+	1.30515i
$186$	48.8088	+	50.1878i	0.0192411	+	0.0197847i
$187$	76.5961	−	777.694i	0.0299533	−	0.304121i
$188$	−348.551	−	247.209i	−0.135217	−	0.0959019i
$189$	−632.456	+	2084.93i	−0.243410	+	0.802414i
$190$	3472.55	−	6284.54i	1.32592	−	2.39962i
$191$			406.312i			0.153925i	0.997034	+	0.0769625i	$0.0245222\pi$
$191$			406.312i			0.153925i	−0.997034	+	0.0769625i	$0.975478\pi$
$192$	−127.443	+	693.485i	−0.0479032	+	0.260667i
$193$		−	4154.44i		−	1.54945i	−0.632301	−	0.774723i	$-0.717889\pi$
$193$		−	4154.44i		−	1.54945i	0.632301	−	0.774723i	$-0.282111\pi$
$194$	2805.92	+	1550.42i	1.03842	+	0.573782i
$195$	−142.358	+	469.292i	−0.0522794	+	0.172342i
$196$	776.741	+	4566.22i	0.283069	+	1.66407i
$197$	312.472	−	3172.59i	0.113009	−	1.14740i	−0.756676	−	0.653790i	$-0.773178\pi$
$197$	312.472	−	3172.59i	0.113009	−	1.14740i	0.869685	−	0.493608i	$-0.164322\pi$
$198$	1795.24	−	1745.91i	0.644354	−	0.626650i
$199$	3484.38	−	2328.19i	1.24121	−	0.829352i	0.250874	−	0.968020i	$-0.419282\pi$
$199$	3484.38	−	2328.19i	1.24121	−	0.829352i	0.990339	+	0.138668i	$0.0442821\pi$
$200$	−4268.84	+	3214.58i	−1.50926	+	1.13652i
$201$	−330.529	+	494.672i	−0.115989	+	0.173589i
$202$	−880.004	−	605.897i	−0.306519	−	0.211043i
$203$	8028.66	+	4291.41i	2.77587	+	1.48373i
$204$	−192.938	+	149.544i	−0.0662174	+	0.0513245i
$205$	784.920	−	77.3079i	0.267420	−	0.0263386i
$206$	−4474.74	+	377.876i	−1.51345	+	0.127805i
$207$	476.711	−	1150.88i	0.160066	−	0.386434i
$208$	1126.43	+	411.483i	0.375500	+	0.137169i
$209$	−1802.87	−	4352.53i	−0.596686	−	1.44053i
$210$	−1031.85	−	1996.86i	−0.339067	−	0.656173i
$211$	−2558.55	−	2099.74i	−0.834775	−	0.685082i	0.116579	−	0.993181i	$-0.462807\pi$
$211$	−2558.55	−	2099.74i	−0.834775	−	0.685082i	−0.951354	+	0.308099i	$0.900307\pi$
$212$	−2210.23	+	155.676i	−0.716032	+	0.0504334i
$213$	−454.381	+	137.835i	−0.146168	+	0.0443395i
$214$	1007.38	+	1554.08i	0.321789	+	0.496423i
$215$	5246.67	−	1043.63i	1.66428	−	0.331046i
$216$	−1622.19	−	67.8220i	−0.511001	−	0.0213644i
$217$	−106.468	+	535.250i	−0.0333065	+	0.167443i
$218$	1714.53	−	3981.47i	0.532673	−	1.23697i
$219$	90.1824	−	74.0108i	0.0278263	−	0.0228365i
$220$	−149.350	+	5360.04i	−0.0457690	+	1.64261i
$221$	195.715	+	366.156i	0.0595710	+	0.111449i
$222$	947.175	−	755.497i	0.286352	−	0.228404i
$223$	−1945.77	+	1945.77i	−0.584298	+	0.584298i	−0.936081	−	0.351783i	$-0.885575\pi$
$223$	−1945.77	+	1945.77i	−0.584298	+	0.584298i	0.351783	+	0.936081i	$0.385575\pi$
$224$	−5016.01	+	2247.43i	−1.49619	+	0.670371i
$225$	−4192.15	−	4192.15i	−1.24212	−	1.24212i
$226$	−5467.80	−	615.537i	−1.60935	−	0.181172i
$227$	−2599.95	+	1389.70i	−0.760196	+	0.406333i	−0.805466	−	0.592641i	$-0.798085\pi$
$227$	−2599.95	+	1389.70i	−0.760196	+	0.406333i	0.0452701	+	0.998975i	$0.485585\pi$
$228$	−600.824	+	1343.41i	−0.174520	+	0.390216i
$229$	−1956.94	−	2384.54i	−0.564709	−	0.688100i	0.409870	−	0.912144i	$-0.365574\pi$
$229$	−1956.94	−	2384.54i	−0.564709	−	0.688100i	−0.974579	+	0.224044i	$0.928074\pi$
$230$	986.330	+	2478.29i	0.282768	+	0.710494i
$231$	−1446.46	−	287.719i	−0.411992	−	0.0819503i
$232$	−1600.29	+	6592.60i	−0.452862	+	1.86563i
$233$	241.317	+	1213.18i	0.0678506	+	0.341108i	0.999767	−	0.0215640i	$-0.00686457\pi$
$233$	241.317	+	1213.18i	0.0678506	+	0.341108i	−0.931917	+	0.362672i	$0.881865\pi$
$234$	−277.710	+	1301.16i	−0.0775832	+	0.363502i
$235$	294.672	+	971.402i	0.0817969	+	0.269648i
$236$	−40.4368	−	81.0012i	−0.0111534	−	0.0223421i
$237$	−872.074	+	1062.63i	−0.239018	+	0.291245i
$238$	−1813.09	−	577.692i	−0.493804	−	0.157337i
$239$	897.658	−	371.822i	0.242948	−	0.100632i	−0.257887	−	0.966175i	$-0.583026\pi$
$239$	897.658	−	371.822i	0.242948	−	0.100632i	0.500835	+	0.865543i	$0.333026\pi$
$240$	1248.51	−	1116.61i	0.335797	−	0.300320i
$241$	−451.933	−	187.197i	−0.120795	−	0.0500349i	0.321467	−	0.946921i	$-0.395824\pi$
$241$	−451.933	−	187.197i	−0.120795	−	0.0500349i	−0.442262	+	0.896886i	$0.645824\pi$
$242$	−188.236	−	158.920i	−0.0500012	−	0.0422140i
$243$	−268.047	−	2721.53i	−0.0707622	−	0.718461i
$244$	869.446	+	3182.75i	0.228117	+	0.835061i
$245$	5186.81	−	9703.85i	1.35254	−	2.53043i
$246$	−158.974	+	29.3263i	−0.0412025	+	0.00760071i
$247$	2081.15	+	1390.58i	0.536116	+	0.358221i
$248$	−406.038	+	22.9209i	−0.103966	+	0.00586886i
$249$	−726.913	−	1087.90i	−0.185005	−	0.276880i
$250$	5974.88	+	83.2246i	1.51154	+	0.0210544i
$251$	4010.87	+	395.036i	1.00862	+	0.0993405i	0.588810	−	0.808271i	$-0.299597\pi$
$251$	4010.87	+	395.036i	1.00862	+	0.0993405i	0.419811	+	0.907612i	$0.362097\pi$
$252$	−3245.30	−	5162.65i	−0.811249	−	1.29054i
$253$	1674.79	+	508.041i	0.416178	+	0.126246i
$254$	2690.57	−	775.422i	0.664651	−	0.191552i
$255$	579.889			0.142408
$256$	−2556.29	−	3200.40i	−0.624095	−	0.781349i
$257$	2533.26			0.614865			0.307433	−	0.951570i	$-0.400530\pi$
$257$	2533.26			0.614865			0.307433	+	0.951570i	$0.400530\pi$
$258$	−1053.55	+	303.633i	−0.254229	+	0.0732688i
$259$	9037.97	+	2741.64i	2.16831	+	0.657749i
$260$	−1516.14	−	2411.89i	−0.361643	−	0.575304i
$261$	−7490.16	−	737.716i	−1.77636	−	0.174956i
$262$	3480.72	+	48.4833i	0.820762	+	0.0114325i
$263$	−370.729	−	554.836i	−0.0869207	−	0.130086i	0.785461	−	0.618911i	$-0.212426\pi$
$263$	−370.729	−	554.836i	−0.0869207	−	0.130086i	−0.872382	+	0.488825i	$0.837426\pi$
$264$	−61.9414	−	1097.28i	−0.0144403	−	0.255806i
$265$	4376.44	+	2924.24i	1.01450	+	0.677868i
$266$	−11281.6	+	2081.14i	−2.60045	+	0.479711i
$267$	−442.410	+	827.691i	−0.101405	+	0.189715i
$268$	−910.735	−	3333.90i	−0.207582	−	0.759889i
$269$	639.921	+	6497.23i	0.145043	+	1.47265i	0.742013	+	0.670386i	$0.233871\pi$
$269$	639.921	+	6497.23i	0.145043	+	1.47265i	−0.596969	+	0.802264i	$0.703629\pi$
$270$	2947.10	+	2488.12i	0.664277	+	0.560822i
$271$	−3756.43	−	1555.96i	−0.842018	−	0.348775i	−0.0803692	−	0.996765i	$-0.525610\pi$
$271$	−3756.43	−	1555.96i	−0.842018	−	0.348775i	−0.761649	+	0.647990i	$0.775610\pi$
$272$	78.9626	−	1415.85i	0.0176023	−	0.315620i
$273$	723.902	−	299.850i	0.160485	−	0.0664753i
$274$	−649.162	−	206.837i	−0.143129	−	0.0456040i
$275$	5284.08	−	6438.67i	1.15870	−	1.41188i
$276$	−244.185	−	489.140i	−0.0532544	−	0.106677i
$277$	580.827	+	1914.73i	0.125987	+	0.415325i	0.997130	−	0.0757047i	$-0.0241206\pi$
$277$	580.827	+	1914.73i	0.125987	+	0.415325i	−0.871143	+	0.491030i	$0.836621\pi$
$278$	−1276.37	+	5980.18i	−0.275365	+	1.29017i
$279$	−88.0222	−	442.518i	−0.0188880	−	0.0949564i
$280$	12688.7	+	3080.05i	2.70819	+	0.657386i
$281$	6609.55	+	1314.72i	1.40318	+	0.279109i	0.837915	−	0.545801i	$-0.183775\pi$
$281$	6609.55	+	1314.72i	1.40318	+	0.279109i	0.565263	+	0.824911i	$0.308775\pi$
$282$	−76.9356	−	193.311i	−0.0162463	−	0.0408210i
$283$	328.974	+	400.856i	0.0691006	+	0.0841993i	0.806413	−	0.591352i	$-0.201406\pi$
$283$	328.974	+	400.856i	0.0691006	+	0.0841993i	−0.737313	+	0.675551i	$0.763906\pi$
$284$	1126.14	−	2517.97i	0.235295	−	0.526107i
$285$	3083.16	−	1647.98i	0.640809	−	0.342520i
$286$	−1857.50	−	209.108i	−0.384043	−	0.0432336i
$287$	−891.072	−	891.072i	−0.183269	−	0.183269i
$288$	3120.26	−	3303.61i	0.638414	−	0.675927i
$289$	−3126.87	+	3126.87i	−0.636449	+	0.636449i
$290$	12598.9	−	10049.3i	2.55114	−	2.03487i
$291$	735.790	+	1376.57i	0.148223	+	0.277305i
$292$	−18.8762	+	677.452i	−0.00378304	+	0.135770i
$293$	−4823.51	+	3958.55i	−0.961749	+	0.789287i	−0.977575	−	0.210588i	$-0.932462\pi$
$293$	−4823.51	+	3958.55i	−0.961749	+	0.789287i	0.0158260	+	0.999875i	$0.494962\pi$
$294$	−891.963	+	2071.31i	−0.176940	+	0.410889i
$295$	−41.9574	+	210.934i	−0.00828087	+	0.0416307i
$296$	−294.002	+	7032.05i	−0.0577315	+	1.38084i
$297$	2482.07	−	493.714i	0.484930	−	0.0964585i
$298$	1896.31	+	2925.42i	0.368624	+	0.568675i
$299$	−889.799	+	269.917i	−0.172102	+	0.0522065i
$300$	−2595.45	+	182.809i	−0.499495	+	0.0351817i
$301$	−6606.96	−	5422.19i	−1.26518	−	1.03831i
$302$	−1140.69	−	2207.49i	−0.217348	−	0.420619i
$303$	−199.075	−	480.608i	−0.0377443	−	0.0911229i
$304$	−3603.87	−	7752.21i	−0.679921	−	1.46256i
$305$	2999.40	−	7241.20i	0.563099	−	1.35944i
$306$	1567.64	−	132.382i	0.292864	−	0.0247313i
$307$	−4337.94	+	427.250i	−0.806448	+	0.0794282i	−0.492835	−	0.870123i	$-0.664039\pi$
$307$	−4337.94	+	427.250i	−0.806448	+	0.0794282i	−0.313613	+	0.949551i	$0.601539\pi$
$308$	6771.41	−	5248.46i	1.25272	−	0.970970i
$309$	−1928.30	−	1030.70i	−0.355007	−	0.189755i
$310$	795.728	+	547.871i	0.145788	+	0.100377i
$311$	−2457.45	+	3677.83i	−0.448068	+	0.670581i	−0.984903	−	0.173106i	$-0.944620\pi$
$311$	−2457.45	+	3677.83i	−0.448068	+	0.670581i	0.536835	+	0.843687i	$0.319620\pi$
$312$	351.245	+	466.441i	0.0637351	+	0.0846380i
$313$	26.3001	−	17.5731i	0.00474942	−	0.00317346i	−0.553193	−	0.833053i	$-0.686591\pi$
$313$	26.3001	−	17.5731i	0.00474942	−	0.00317346i	0.557943	+	0.829879i	$0.311591\pi$
$314$	−5726.10	+	5568.77i	−1.02912	+	1.00084i
$315$	−1419.87	+	14416.2i	−0.253971	+	2.57861i
$316$	−1339.15	−	7872.47i	−0.238397	−	1.40146i
$317$	−702.297	+	2315.16i	−0.124432	+	0.410197i	−0.996919	−	0.0784404i	$-0.975006\pi$
$317$	−702.297	+	2315.16i	−0.124432	+	0.410197i	0.872487	+	0.488638i	$0.162506\pi$
$318$	−944.252	−	521.750i	−0.166513	−	0.0920073i
$319$		−	10574.2i		−	1.85593i
$320$	142.111	+	9729.20i	0.0248259	+	1.69962i
$321$			901.736i			0.156791i
$322$	2061.12	−	3730.17i	0.356714	−	0.645573i
$323$	859.149	−	2832.24i	0.148001	−	0.487894i
$324$	3778.05	+	2679.57i	0.647814	+	0.459460i
$325$	−433.755	+	4403.99i	−0.0740320	+	0.751660i
$326$	6900.35	+	7095.29i	1.17232	+	1.20544i
$327$	1754.95	−	1172.62i	0.296786	−	0.198306i
$328$	476.889	−	808.981i	0.0802799	−	0.136184i
$329$	901.072	−	1348.55i	0.150996	−	0.225982i
$330$	−1480.57	+	2150.38i	−0.246978	+	0.358710i
$331$	−10025.8	−	5358.91i	−1.66486	−	0.889886i	−0.988124	−	0.153661i	$-0.950893\pi$
$331$	−10025.8	−	5358.91i	−1.66486	−	0.889886i	−0.676737	−	0.736225i	$-0.736607\pi$
$332$	7540.42	+	955.391i	1.24649	+	0.157933i
$333$	−7770.76	+	765.353i	−1.27878	+	0.125949i
$334$	−418.725	−	4958.46i	−0.0685976	−	0.812320i
$335$	−3141.84	+	7585.07i	−0.512409	+	1.23707i
$336$	−2644.58	−	410.211i	−0.429386	−	0.0666037i
$337$	2557.86	+	6175.21i	0.413458	+	0.998176i	0.984202	+	0.177048i	$0.0566548\pi$
$337$	2557.86	+	6175.21i	0.413458	+	0.998176i	−0.570744	+	0.821128i	$0.693345\pi$
$338$	−4638.30	+	2396.77i	−0.746421	+	0.385702i
$339$	−2070.94	−	1699.58i	−0.331794	−	0.272296i
$340$	−2208.75	+	2543.47i	−0.352312	+	0.405702i
$341$	606.598	−	184.009i	0.0963317	−	0.0292219i
$342$	7958.65	−	5158.93i	1.25835	−	0.815681i
$343$	−7027.51	+	1397.86i	−1.10627	+	0.220050i
$344$	2681.10	−	5777.51i	0.420219	−	0.905530i
$345$	−253.367	+	1273.76i	−0.0395387	+	0.198774i
$346$	6258.09	+	2694.91i	0.972362	+	0.418725i
$347$	4588.94	−	3766.05i	0.709935	−	0.582629i	−0.208584	−	0.978004i	$-0.566886\pi$
$347$	4588.94	−	3766.05i	0.709935	−	0.582629i	0.918519	+	0.395376i	$0.129386\pi$
$348$	−2399.80	+	2269.69i	−0.369663	+	0.349622i
$349$	3571.68	+	6682.15i	0.547816	+	1.02489i	0.991671	+	0.128794i	$0.0411104\pi$
$349$	3571.68	+	6682.15i	0.547816	+	1.02489i	−0.443855	+	0.896099i	$0.646390\pi$
$350$	−12647.5	−	15856.3i	−1.93153	−	2.42159i
$351$	−950.728	+	950.728i	−0.144576	+	0.144576i
$352$	5048.73	+	3907.75i	0.764483	+	0.591716i
$353$	5201.85	+	5201.85i	0.784325	+	0.784325i	0.980557	−	0.196233i	$-0.0628707\pi$
$353$	5201.85	+	5201.85i	0.784325	+	0.784325i	−0.196233	+	0.980557i	$0.562871\pi$
$354$	4.93119	−	43.8036i	0.000740366	−	0.00657665i
$355$	−5778.82	+	3088.85i	−0.863967	+	0.461800i
$356$	−1945.25	−	5093.07i	−0.289602	−	0.758236i
$357$	−587.773	−	716.204i	−0.0871380	−	0.106178i
$358$	3082.90	−	1226.96i	0.455130	−	0.181136i
$359$	10106.0	+	2010.20i	1.48572	+	0.295528i	0.870241	−	0.492626i	$-0.163963\pi$
$359$	10106.0	+	2010.20i	1.48572	+	0.295528i	0.615478	+	0.788154i	$0.288963\pi$
$360$	−10666.3	+	1661.89i	−1.56156	+	0.243304i
$361$	−2142.85	−	10772.9i	−0.312415	−	1.57062i
$362$	−11794.2	−	2517.27i	−1.71241	−	0.365484i
$363$	−34.8187	−	114.782i	−0.00503445	−	0.0165964i
$364$	−1442.10	+	4317.22i	−0.207655	+	0.621660i
$365$	1021.34	−	1244.50i	0.146464	−	0.178466i
$366$	−487.692	+	1530.63i	−0.0696505	+	0.218599i
$367$	−10539.1	+	4365.46i	−1.49902	+	0.620913i	−0.973257	−	0.229720i	$-0.926219\pi$
$367$	−10539.1	+	4365.46i	−1.49902	+	0.620913i	−0.525760	+	0.850633i	$0.676219\pi$
$368$	3075.51	+	792.066i	0.435657	+	0.112199i
$369$	962.537	+	398.696i	0.135793	+	0.0562473i
$370$	10785.7	−	12775.4i	1.51547	−	1.79503i
$371$	−824.296	−	8369.21i	−0.115351	−	1.17118i
$372$	−171.964	−	98.1702i	−0.0239675	−	0.0136825i
$373$	292.111	−	546.501i	0.0405494	−	0.0758626i	−0.860830	−	0.508892i	$-0.830055\pi$
$373$	292.111	−	546.501i	0.0405494	−	0.0758626i	0.901380	+	0.433029i	$0.142555\pi$
$374$	400.972	+	2173.62i	0.0554379	+	0.300522i
$375$	2419.09	+	1616.39i	0.333124	+	0.222586i
$376$	1140.93	+	398.856i	0.156486	+	0.0547059i
$377$	3121.17	+	4671.16i	0.426389	+	0.638136i
$378$	85.8285	−	6161.82i	0.0116787	−	0.838439i
$379$	−317.249	−	31.2463i	−0.0429974	−	0.00423487i	0.0764956	−	0.997070i	$-0.475627\pi$
$379$	−317.249	−	31.2463i	−0.0429974	−	0.00423487i	−0.119493	+	0.992835i	$0.538127\pi$
$380$	−4515.22	+	19800.1i	−0.609542	+	2.67296i
$381$	1304.64	+	395.758i	0.175429	+	0.0532159i
$382$	−318.253	−	1104.28i	−0.0426262	−	0.147905i
$383$	2594.71			0.346171			0.173085	−	0.984907i	$-0.444626\pi$
$383$	2594.71			0.346171			0.173085	+	0.984907i	$0.444626\pi$
$384$	−196.822	−	1984.58i	−0.0261563	−	0.263738i
$385$	−20352.0			−2.69411
$386$	3254.06	+	11291.0i	0.429086	+	1.48885i
$387$	6762.00	+	2051.23i	0.888196	+	0.269431i
$388$	−8840.35	−	2015.95i	−1.15670	−	0.263774i
$389$	−144.751	−	14.2567i	−0.0188667	−	0.00185821i	0.0885794	−	0.996069i	$-0.471767\pi$
$389$	−144.751	−	14.2567i	−0.0188667	−	0.00185821i	−0.107446	+	0.994211i	$0.534267\pi$
$390$	19.3190	−	1386.95i	0.00250834	−	0.180079i
$391$	610.847	+	914.198i	0.0790074	+	0.118243i
$392$	−5687.62	−	11801.7i	−0.732827	−	1.52060i
$393$	1409.26	+	941.640i	0.180885	+	0.120864i
$394$	1635.76	+	8867.23i	0.209158	+	1.13382i
$395$	−8942.43	+	16730.1i	−1.13909	+	2.13110i
$396$	−3511.59	+	6151.22i	−0.445616	+	0.780582i
$397$	564.148	+	5727.89i	0.0713193	+	0.724117i	0.962647	+	0.270758i	$0.0872744\pi$
$397$	564.148	+	5727.89i	0.0713193	+	0.724117i	−0.891328	+	0.453359i	$0.850226\pi$
$398$	−7646.28	+	9056.80i	−0.962998	+	1.14064i
$399$	−5160.45	−	2137.53i	−0.647483	−	0.268196i
$400$	9084.01	−	12080.3i	1.13550	−	1.51003i
$401$	−3735.06	+	1547.11i	−0.465137	+	0.192666i	−0.602929	−	0.797795i	$-0.706000\pi$
$401$	−3735.06	+	1547.11i	−0.465137	+	0.192666i	0.137791	+	0.990461i	$0.456000\pi$
$402$	510.852	−	1603.32i	0.0633806	−	0.198921i
$403$	−213.652	+	260.335i	−0.0264088	+	0.0321792i
$404$	2866.26	+	957.429i	0.352975	+	0.117906i
$405$	−3194.04	−	10529.3i	−0.391884	−	1.29187i
$406$	−25181.7	−	5374.60i	−3.07820	−	0.656988i
$407$	−2140.20	−	10759.5i	−0.260653	−	1.31039i
$408$	407.234	−	557.556i	0.0494145	−	0.0676547i
$409$	3286.85	+	653.795i	0.397370	+	0.0790417i	0.389730	−	0.920929i	$-0.372568\pi$
$409$	3286.85	+	653.795i	0.397370	+	0.0790417i	0.00763945	+	0.999971i	$0.497568\pi$
$410$	−2072.71	+	824.914i	−0.249668	+	0.0993649i
$411$	−210.447	−	256.430i	−0.0252569	−	0.0307756i
$412$	11865.5	−	4531.93i	1.41886	−	0.541923i
$413$	303.047	−	161.982i	0.0361064	−	0.0192993i
$414$	−394.156	+	3501.27i	−0.0467915	+	0.415648i
$415$	−12767.4	−	12767.4i	−1.51019	−	1.51019i
$416$	−3383.73	−	236.028i	−0.398801	−	0.0278178i
$417$	−2105.27	+	2105.27i	−0.247231	+	0.247231i
$418$	8309.08	+	10417.2i	0.972274	+	1.21895i
$419$	5743.91	+	10746.1i	0.669710	+	1.25294i	0.955597	+	0.294676i	$0.0952118\pi$
$419$	5743.91	+	10746.1i	0.669710	+	1.25294i	−0.285887	+	0.958263i	$0.592288\pi$
$420$	4368.44	+	4618.86i	0.507520	+	0.536613i
$421$	−674.540	+	553.581i	−0.0780880	+	0.0640852i	−0.672628	−	0.739981i	$-0.734834\pi$
$421$	−674.540	+	553.581i	−0.0780880	+	0.0640852i	0.594540	+	0.804066i	$0.297334\pi$
$422$	8598.31	+	3702.67i	0.991847	+	0.427116i
$423$	−261.595	+	1315.13i	−0.0300690	+	0.151167i
$424$	5885.03	−	2154.31i	0.674062	−	0.246751i
$425$	5132.20	−	1020.86i	0.585760	−	0.116515i
$426$	1126.96	−	730.514i	0.128172	−	0.0830834i
$427$	−11983.6	+	3635.17i	−1.35814	+	0.411987i
$428$	−3955.13	−	3434.63i	−0.446678	−	0.387895i
$429$	−703.531	−	577.373i	−0.0791766	−	0.0649786i
$430$	−13442.0	+	6945.95i	−1.50751	+	0.778985i
$431$	−127.817	−	308.579i	−0.0142848	−	0.0344866i	0.916576	−	0.399860i	$-0.130941\pi$
$431$	−127.817	−	308.579i	−0.0142848	−	0.0344866i	−0.930861	+	0.365373i	$0.880941\pi$
$432$	4461.93	−	1086.29i	0.496932	−	0.120982i
$433$	−3689.45	+	8907.12i	−0.409477	+	0.988566i	0.575798	+	0.817592i	$0.304691\pi$
$433$	−3689.45	+	8907.12i	−0.409477	+	0.988566i	−0.985276	+	0.170974i	$0.945309\pi$
$434$	−129.887	−	1538.10i	−0.0143659	−	0.170118i
$435$	7808.91	−	769.111i	0.860710	−	0.0847725i
$436$	−1541.19	+	12163.8i	−0.169288	+	1.33610i
$437$	5845.81	+	3124.65i	0.639915	+	0.342042i
$438$	−187.128	+	271.785i	−0.0204140	+	0.0296492i
$439$	7287.53	−	10906.6i	0.792289	−	1.18574i	−0.186818	−	0.982395i	$-0.559817\pi$
$439$	7287.53	−	10906.6i	0.792289	−	1.18574i	0.979106	−	0.203349i	$-0.0651826\pi$
$440$	−3792.47	−	14684.5i	−0.410906	−	1.59104i
$441$	12084.8	−	8074.83i	1.30492	−	0.871918i
$442$	−818.715	−	841.845i	−0.0881047	−	0.0905938i
$443$	−5.90579	+	59.9625i	−0.000633391	+	0.00643093i	−0.995496	−	0.0948012i	$-0.969778\pi$
$443$	−5.90579	+	59.9625i	−0.000633391	+	0.00643093i	0.994863	+	0.101232i	$0.0322785\pi$
$444$	−1982.48	+	2795.19i	−0.211902	+	0.298770i
$445$	−3759.56	+	12393.6i	−0.400494	+	1.32025i
$446$	3764.17	−	6812.30i	0.399638	−	0.723255i
$447$			1697.44i			0.179611i
$448$	11872.2	−	10037.0i	1.25203	−	1.05849i
$449$		−	15184.0i		−	1.59594i	−0.602697	−	0.797970i	$-0.705907\pi$
$449$		−	15184.0i		−	1.59594i	0.602697	−	0.797970i	$-0.294093\pi$
$450$	14677.0	+	8109.86i	1.53752	+	0.849561i
$451$	−424.899	+	1400.70i	−0.0443630	+	0.146245i
$452$	15342.6	−	2609.86i	1.59658	−	0.271588i
$453$	118.584	−	1204.01i	0.0122993	−	0.124877i
$454$	5977.65	−	5813.41i	0.617940	−	0.600962i
$455$	8990.52	−	6007.27i	0.926334	−	0.618957i
$456$	580.672	−	4121.73i	0.0596325	−	0.423285i
$457$	98.6762	−	147.679i	0.0101004	−	0.0151163i	−0.826385	−	0.563105i	$-0.809606\pi$
$457$	98.6762	−	147.679i	0.0101004	−	0.0151163i	0.836485	+	0.547989i	$0.184606\pi$
$458$	7186.33	+	4947.91i	0.733178	+	0.504804i
$459$	1402.13	+	749.453i	0.142583	+	0.0762124i
$460$	−4621.83	−	5962.95i	−0.468465	−	0.604400i
$461$	−8421.79	+	829.474i	−0.850850	+	0.0838014i	−0.514035	−	0.857769i	$-0.671850\pi$
$461$	−8421.79	+	829.474i	−0.850850	+	0.0838014i	−0.336815	+	0.941571i	$0.609350\pi$
$462$	4156.56	−	351.007i	0.418573	−	0.0353470i
$463$	476.932	−	1151.42i	0.0478724	−	0.115574i	−0.898134	−	0.439721i	$-0.855077\pi$
$463$	476.932	−	1151.42i	0.0478724	−	0.115574i	0.946007	+	0.324147i	$0.105077\pi$
$464$	−814.524	−	19170.9i	−0.0814942	−	1.91807i
$465$	180.010	+	434.582i	0.0179521	+	0.0433403i
$466$	−1606.10	−	3108.18i	−0.159659	−	0.308978i
$467$	−10889.4	−	8936.67i	−1.07901	−	0.885524i	−0.0851763	−	0.996366i	$-0.527145\pi$
$467$	−10889.4	−	8936.67i	−1.07901	−	0.885524i	−0.993838	+	0.110842i	$0.964645\pi$
$468$	−264.399	−	3753.83i	−0.0261151	−	0.370771i
$469$	12552.7	−	3807.81i	1.23588	−	0.374900i
$470$	−1561.73	−	2409.28i	−0.153271	−	0.236450i
$471$	−3814.32	+	758.716i	−0.373152	+	0.0742246i
$472$	173.346	+	188.473i	0.0169044	+	0.0183796i
$473$	−1936.80	+	9736.96i	−0.188275	+	0.946524i
$474$	1537.81	−	3571.08i	0.149016	−	0.346045i
$475$	24385.7	−	20012.9i	2.35557	−	1.93316i
$476$	5380.13	+	149.910i	0.518063	+	0.0144351i
$477$	3277.49	+	6131.75i	0.314604	+	0.588582i
$478$	−2148.42	+	1713.65i	−0.205579	+	0.163976i
$479$	−5338.17	+	5338.17i	−0.509201	+	0.509201i	−0.914281	−	0.405080i	$-0.867244\pi$
$479$	−5338.17	+	5338.17i	−0.509201	+	0.509201i	0.405080	+	0.914281i	$0.367244\pi$
$480$	−2518.61	+	4012.66i	−0.239497	+	0.381567i
$481$	4121.32	+	4121.32i	0.390677	+	0.390677i
$482$	1374.89	+	154.779i	0.129927	+	0.0146265i
$483$	1830.00	−	978.156i	0.172397	−	0.0921483i
$484$	636.068	+	284.474i	0.0597359	+	0.0267162i
$485$	13664.7	+	16650.5i	1.27934	+	1.55889i
$486$	2860.20	+	7186.64i	0.266957	+	0.670766i
$487$	−336.548	−	66.9435i	−0.0313150	−	0.00622895i	0.179408	−	0.983775i	$-0.442582\pi$
$487$	−336.548	−	66.9435i	−0.0313150	−	0.00622895i	−0.210723	+	0.977546i	$0.567582\pi$
$488$	−4855.95	−	7969.10i	−0.450448	−	0.739230i
$489$	940.135	+	4726.38i	0.0869415	+	0.437084i
$490$	−6496.02	+	30435.9i	−0.598898	+	2.80603i
$491$	148.066	+	488.109i	0.0136092	+	0.0448637i	0.963482	−	0.267773i	$-0.0862878\pi$
$491$	148.066	+	488.109i	0.0136092	+	0.0448637i	−0.949873	+	0.312637i	$0.898788\pi$
$492$	409.091	−	204.223i	0.0374862	−	0.0187136i
$493$	4214.29	−	5135.12i	0.384994	−	0.469116i
$494$	−6745.38	−	2149.23i	−0.614350	−	0.195746i
$495$	15545.2	−	6439.02i	1.41152	−	0.584672i
$496$	1085.58	−	380.333i	0.0982742	−	0.0344303i
$497$	9672.33	+	4006.41i	0.872965	+	0.361594i
$498$	2827.73	+	2387.34i	0.254445	+	0.214818i
$499$	1038.56	+	10544.6i	0.0931706	+	0.945977i	0.922185	+	0.386749i	$0.126402\pi$
$499$	1038.56	+	10544.6i	0.0931706	+	0.945977i	−0.829014	+	0.559227i	$0.811098\pi$
$500$	−16303.8	+	4453.77i	−1.45825	+	0.398357i
$501$	1142.12	−	2136.75i	0.101849	−	0.190545i
$502$	−11210.2	+	2067.97i	−0.996684	+	0.183861i
$503$	−12854.6	−	8589.14i	−1.13948	−	0.761373i	−0.165095	−	0.986278i	$-0.552793\pi$
$503$	−12854.6	−	8589.14i	−1.13948	−	0.761373i	−0.974381	+	0.224905i	$0.927793\pi$
$504$	12863.9	+	11489.1i	1.13691	+	1.01541i
$505$	−3988.31	−	5968.93i	−0.351440	−	0.525968i
$506$	−4949.69	−	68.9446i	−0.434863	−	0.00605724i
$507$	−2529.81	−	249.165i	−0.221603	−	0.0218260i
$508$	−6705.09	+	4214.90i	−0.585611	+	0.368122i
$509$	12688.0	+	3848.86i	1.10488	+	0.335163i	0.789469	−	0.613791i	$-0.210356\pi$
$509$	12688.0	+	3848.86i	1.10488	+	0.335163i	0.315415	+	0.948954i	$0.397856\pi$
$510$	−1576.03	+	454.211i	−0.136839	+	0.0394369i
$511$	−2572.27			−0.222682
$512$	9454.30	+	6695.81i	0.816065	+	0.577961i
$513$	9584.72			0.824904
$514$	−6884.92	+	1984.23i	−0.590818	+	0.170274i
$515$	−28873.8	−	8758.77i	−2.47055	−	0.749432i
$516$	2625.52	−	1650.43i	0.223996	−	0.140807i
$517$	−1874.81	−	184.653i	−0.159486	−	0.0157080i
$518$	−26710.9	−	372.059i	−2.26566	−	0.0315585i
$519$	1843.13	+	2758.44i	0.155885	+	0.233298i
$520$	6009.75	+	5367.51i	0.506817	+	0.452655i
$521$	107.384	+	71.7520i	0.00902994	+	0.00603361i	0.560077	−	0.828441i	$-0.310772\pi$
$521$	107.384	+	71.7520i	0.00902994	+	0.00603361i	−0.551047	+	0.834474i	$0.685772\pi$
$522$	20934.7	−	3861.86i	1.75534	−	0.323811i
$523$	13.4287	−	25.1233i	0.00112274	−	0.00210051i	−0.881359	−	0.472447i	$-0.843371\pi$
$523$	13.4287	−	25.1233i	0.00112274	−	0.00210051i	0.882482	+	0.470346i	$0.155871\pi$
$524$	−9497.91	+	2594.58i	−0.791828	+	0.216307i
$525$	−967.964	−	9827.91i	−0.0804675	−	0.817000i
$526$	1442.16	+	1217.56i	0.119546	+	0.100928i
$527$	367.917	+	152.396i	0.0304112	+	0.0125967i
$528$	1027.81	+	2933.68i	0.0847155	+	0.241803i
$529$	8965.85	−	3713.78i	0.736899	−	0.305234i
$530$	−14184.8	−	4519.59i	−1.16254	−	0.370412i
$531$	−180.224	+	219.603i	−0.0147289	+	0.0179472i
$532$	29031.2	−	14492.7i	2.36590	−	1.18109i
$533$	−225.744	−	744.180i	−0.0183454	−	0.0604766i
$534$	554.079	−	2596.03i	0.0449014	−	0.210377i
$535$	2427.67	+	12204.7i	0.196182	+	0.986272i
$536$	5086.56	+	8347.55i	0.409899	+	0.672685i
$537$	1584.52	+	315.180i	0.127331	+	0.0253278i
$538$	−6828.28	−	17157.0i	−0.547190	−	1.37489i
$539$	12954.2	+	15784.8i	1.03521	+	1.26141i
$540$	−9958.53	−	4453.84i	−0.793605	−	0.354931i
$541$	−16663.4	+	8906.77i	−1.32424	+	0.707822i	−0.973508	−	0.228653i	$-0.926568\pi$
$541$	−16663.4	+	8906.77i	−1.32424	+	0.707822i	−0.350734	+	0.936475i	$0.614068\pi$
$542$	11428.0	+	1286.51i	0.905673	+	0.101956i
$543$	−4152.05	−	4152.05i	−0.328143	−	0.328143i
$544$	894.391	+	3909.86i	0.0704902	+	0.308150i
$545$	20595.7	−	20595.7i	1.61876	−	1.61876i
$546$	−1732.56	+	1381.95i	−0.135800	+	0.108318i
$547$	1382.08	+	2585.69i	0.108032	+	0.202114i	0.930128	−	0.367235i	$-0.119695\pi$
$547$	1382.08	+	2585.69i	0.108032	+	0.202114i	−0.822096	+	0.569349i	$0.807195\pi$
$548$	1926.31	+	53.6738i	0.150160	+	0.00418400i
$549$	8003.14	−	6568.01i	0.622160	−	0.510593i
$550$	−9317.89	+	21637.9i	−0.722393	+	1.67754i
$551$	7813.08	−	39279.0i	0.604081	−	3.03692i
$552$	1046.78	+	1138.13i	0.0807134	+	0.0877570i
$553$	29726.9	−	5913.04i	2.28592	−	0.454698i
$554$	−3078.33	−	4748.93i	−0.236075	−	0.364192i
$555$	7790.12	−	2363.11i	0.595806	−	0.180736i
$556$	−1215.19	−	17252.7i	−0.0926896	−	1.31597i
$557$	−15123.9	−	12411.9i	−1.15049	−	0.944180i	−0.151467	−	0.988462i	$-0.548400\pi$
$557$	−15123.9	−	12411.9i	−1.15049	−	0.944180i	−0.999019	+	0.0442825i	$0.985900\pi$
$558$	585.839	+	1133.73i	0.0444454	+	0.0860121i
$559$	−2018.46	−	4873.00i	−0.152723	−	0.368705i
$560$	−36897.9	+	1567.70i	−2.78432	+	0.118299i
$561$	−411.836	+	994.260i	−0.0309942	+	0.0748265i
$562$	−18993.3	+	1603.92i	−1.42559	+	0.120386i
$563$	16610.7	−	1636.01i	1.24344	−	0.122468i	0.545185	−	0.838316i	$-0.316459\pi$
$563$	16610.7	−	1636.01i	1.24344	−	0.122468i	0.698257	+	0.715847i	$0.253959\pi$
$564$	360.512	+	465.122i	0.0269154	+	0.0347254i
$565$	−32605.1	−	17427.8i	−2.42780	−	1.29769i
$566$	−1208.07	−	831.773i	−0.0897153	−	0.0617704i
$567$	−9766.99	+	14617.3i	−0.723413	+	1.08266i
$568$	−1088.36	+	7725.44i	−0.0803992	+	0.570691i
$569$	−2471.65	+	1651.50i	−0.182104	+	0.121678i	−0.643281	−	0.765630i	$-0.722427\pi$
$569$	−2471.65	+	1651.50i	−0.182104	+	0.121678i	0.461177	+	0.887308i	$0.347427\pi$
$570$	−7088.62	+	6893.85i	−0.520894	+	0.506582i
$571$	79.5639	−	807.826i	0.00583126	−	0.0592057i	−0.991829	−	0.127577i	$-0.959280\pi$
$571$	79.5639	−	807.826i	0.00583126	−	0.0592057i	0.997660	+	0.0683709i	$0.0217801\pi$
$572$	5212.11	−	886.612i	0.380995	−	0.0648096i
$573$	162.429	−	535.456i	0.0118422	−	0.0390384i
$574$	3119.72	+	1723.81i	0.226854	+	0.125349i
$575$			11719.2i			0.849959i
$576$	−5892.65	+	11422.6i	−0.426262	+	0.826287i
$577$		−	6879.38i		−	0.496347i	−0.968716	−	0.248174i	$-0.920170\pi$
$577$		−	6879.38i		−	0.496347i	0.968716	−	0.248174i	$-0.0798303\pi$
$578$	6049.05	−	10947.4i	0.435307	−	0.787808i
$579$	−1660.80	+	5474.91i	−0.119206	+	0.392970i
$580$	−26370.0	+	37180.3i	−1.88785	+	2.66177i
$581$	−2827.65	+	28709.6i	−0.201912	+	2.05004i
$582$	−3077.96	−	3164.92i	−0.219219	−	0.225413i
$583$	−8121.96	+	5426.92i	−0.576976	+	0.385523i
$584$	−479.327	−	1855.97i	−0.0339635	−	0.131508i
$585$	−4966.51	+	7432.91i	−0.351008	+	0.525321i
$586$	10008.8	−	14536.7i	0.705559	−	1.02475i
$587$	−4017.81	−	2147.56i	−0.282509	−	0.151004i	0.324057	−	0.946038i	$-0.394953\pi$
$587$	−4017.81	−	2147.56i	−0.282509	−	0.151004i	−0.606565	+	0.795034i	$0.707453\pi$
$588$	801.785	−	6328.08i	0.0562331	−	0.443819i
$589$	2389.24	−	235.319i	0.167142	−	0.0164621i
$590$	−51.1867	−	606.143i	−0.00357173	−	0.0422958i
$591$	−1680.08	+	4056.06i	−0.116936	+	0.282308i
$592$	−4708.96	−	19342.0i	−0.326921	−	1.34283i
$593$	−1948.96	−	4705.21i	−0.134965	−	0.325834i	0.841919	−	0.539604i	$-0.181426\pi$
$593$	−1948.96	−	4705.21i	−0.134965	−	0.325834i	−0.976884	+	0.213769i	$0.931426\pi$
$594$	−6359.07	+	3285.95i	−0.439252	+	0.226977i
$595$	−9883.49	−	8111.17i	−0.680981	−	0.558867i
$596$	−7445.20	−	6465.41i	−0.511690	−	0.444351i
$597$	−5522.61	+	1675.26i	−0.378602	+	0.114848i
$598$	2206.88	−	1430.54i	0.150913	−	0.0978245i
$599$	−7853.57	+	1562.17i	−0.535706	+	0.106559i	−0.455527	−	0.890222i	$-0.650549\pi$
$599$	−7853.57	+	1562.17i	−0.535706	+	0.106559i	−0.0801790	+	0.996780i	$0.525549\pi$
$600$	6910.75	−	2529.79i	0.470217	−	0.172130i
$601$	−4593.22	+	23091.7i	−0.311749	+	1.56727i	0.433919	+	0.900952i	$0.357130\pi$
$601$	−4593.22	+	23091.7i	−0.311749	+	1.56727i	−0.745669	+	0.666317i	$0.767870\pi$
$602$	22203.5	+	9561.43i	1.50323	+	0.647334i
$603$	−8383.20	+	6879.92i	−0.566153	+	0.464630i
$604$	4829.24	+	5106.07i	0.325329	+	0.343979i
$605$	−780.277	−	1459.79i	−0.0524343	−	0.0980977i
$606$	917.494	+	1150.27i	0.0615027	+	0.0771066i
$607$	4702.06	−	4702.06i	0.314417	−	0.314417i	−0.532201	−	0.846618i	$-0.678635\pi$
$607$	4702.06	−	4702.06i	0.314417	−	0.314417i	0.846618	+	0.532201i	$0.178635\pi$
$608$	15866.7	+	18246.2i	1.05836	+	1.21707i
$609$	−8864.99	−	8864.99i	−0.589864	−	0.589864i
$610$	−2479.97	+	22029.5i	−0.164608	+	1.46221i
$611$	882.705	−	471.816i	0.0584458	−	0.0312400i
$612$	−4156.87	+	1587.68i	−0.274561	+	0.104866i
$613$	−7202.96	−	8776.83i	−0.474592	−	0.578291i	0.479600	−	0.877487i	$-0.340782\pi$
$613$	−7202.96	−	8776.83i	−0.474592	−	0.578291i	−0.954192	+	0.299196i	$0.903282\pi$
$614$	11455.0	−	4558.97i	0.752912	−	0.299650i
$615$	−1065.31	−	211.903i	−0.0698494	−	0.0138939i
$616$	−14292.4	+	19568.2i	−0.934834	+	1.27991i
$617$	−1246.83	−	6268.21i	−0.0813538	−	0.408993i	−0.999906	−	0.0136940i	$-0.995641\pi$
$617$	−1246.83	−	6268.21i	−0.0813538	−	0.408993i	0.918552	−	0.395299i	$-0.129359\pi$
$618$	6048.07	+	1290.86i	0.393672	+	0.0840225i
$619$	406.174	+	1338.98i	0.0263740	+	0.0869434i	0.969139	−	0.246513i	$-0.0792849\pi$
$619$	406.174	+	1338.98i	0.0263740	+	0.0869434i	−0.942765	+	0.333457i	$0.891785\pi$
$620$	−2591.77	−	865.738i	−0.167884	−	0.0560788i
$621$	−2258.85	+	2752.41i	−0.145965	+	0.177859i
$622$	3798.13	−	11920.5i	0.244841	−	0.768437i
$623$	19117.6	−	7918.78i	1.22942	−	0.509244i
$624$	−1319.97	−	992.578i	−0.0846811	−	0.0636778i
$625$	9819.64	+	4067.43i	0.628457	+	0.260315i
$626$	−57.7140	+	68.3606i	−0.00368485	+	0.00436460i
$627$	635.928	+	6456.68i	0.0405048	+	0.411252i
$628$	11200.6	−	19620.0i	0.711707	−	1.24669i
$629$	3248.81	−	6078.10i	0.205944	−	0.385293i
$630$	−7432.87	−	40292.6i	−0.470052	−	2.54809i
$631$	−7024.19	−	4693.41i	−0.443151	−	0.296104i	0.313904	−	0.949455i	$-0.398363\pi$
$631$	−7024.19	−	4693.41i	−0.443151	−	0.296104i	−0.757056	+	0.653350i	$0.773363\pi$
$632$	9805.85	+	20346.9i	0.617177	+	1.28063i
$633$	2532.37	+	3789.95i	0.159009	+	0.237973i
$634$	95.3065	−	6842.26i	0.00597019	−	0.428613i
$635$	18723.3	+	1844.09i	1.17010	+	0.115245i
$636$	2974.97	+	678.412i	0.185480	+	0.0422968i
$637$	−10381.7	−	3149.27i	−0.645745	−	0.195885i
$638$	8282.46	+	28738.6i	0.513959	+	1.78334i
$639$	−8655.45			−0.535844
$640$	−8006.84	−	26330.8i	−0.494529	−	1.62628i
$641$	−12531.3			−0.772164			−0.386082	−	0.922465i	$-0.626172\pi$
$641$	−12531.3			−0.772164			−0.386082	+	0.922465i	$0.626172\pi$
$642$	−706.305	−	2450.75i	−0.0434200	−	0.150659i
$643$	8672.87	+	2630.89i	0.531920	+	0.161356i	0.544808	−	0.838561i	$-0.316602\pi$
$643$	8672.87	+	2630.89i	0.531920	+	0.161356i	−0.0128879	+	0.999917i	$0.504102\pi$
$644$	−2680.00	+	11752.3i	−0.163985	+	0.719109i
$645$	−7331.51	−	722.091i	−0.447563	−	0.0440811i
$646$	−116.592	+	8370.42i	−0.00710103	+	0.509799i
$647$	10736.6	+	16068.4i	0.652393	+	0.976375i	0.999260	+	0.0384611i	$0.0122456\pi$
$647$	10736.6	+	16068.4i	0.652393	+	0.976375i	−0.346867	+	0.937914i	$0.612754\pi$
$648$	−12366.9	−	4323.32i	−0.749716	−	0.262093i
$649$	−331.863	−	221.744i	−0.0200721	−	0.0134117i
$650$	−2270.66	−	12309.0i	−0.137019	−	0.742764i
$651$	354.282	−	662.815i	0.0213293	−	0.0399044i
$652$	−24311.4	−	13878.8i	−1.46029	−	0.833644i
$653$	1574.16	+	15982.8i	0.0943366	+	0.957815i	0.919544	+	0.392986i	$0.128558\pi$
$653$	1574.16	+	15982.8i	0.0943366	+	0.957815i	−0.825208	+	0.564829i	$0.808942\pi$
$654$	−3851.14	+	4561.56i	−0.230262	+	0.272739i
$655$	21609.0	+	8950.75i	1.28906	+	0.533946i
$656$	−662.441	+	2572.19i	−0.0394268	+	0.153090i
$657$	1964.74	−	813.824i	0.116670	−	0.0483262i
$658$	−1392.66	+	4370.88i	−0.0825100	+	0.258959i
$659$	−8525.26	+	10388.1i	−0.503941	+	0.614054i	−0.961392	−	0.275181i	$-0.911262\pi$
$659$	−8525.26	+	10388.1i	−0.503941	+	0.614054i	0.457452	+	0.889234i	$0.348762\pi$
$660$	2339.57	−	7004.00i	0.137981	−	0.413076i
$661$	7030.72	+	23177.2i	0.413711	+	1.36382i	0.878221	+	0.478256i	$0.158731\pi$
$661$	7030.72	+	23177.2i	0.413711	+	1.36382i	−0.464509	+	0.885568i	$0.653769\pi$
$662$	31445.7	+	6711.55i	1.84618	+	0.394036i
$663$	−111.546	−	560.777i	−0.00653404	−	0.0328488i
$664$	−21241.7	+	3309.63i	−1.24148	+	0.193431i
$665$	−75599.7	−	15037.7i	−4.40847	−	0.876899i
$666$	20520.0	−	8166.70i	1.19389	−	0.475155i
$667$	9438.31	+	11500.6i	0.547905	+	0.667624i
$668$	5021.84	+	13148.2i	0.290869	+	0.761554i
$669$	3342.08	−	1786.38i	0.193142	−	0.103237i
$670$	2597.75	−	23075.7i	0.149791	−	1.33059i
$671$	10285.4	+	10285.4i	0.591746	+	0.591746i
$672$	7508.77	−	956.550i	0.431037	−	0.0549103i
$673$	13555.9	−	13555.9i	0.776438	−	0.776438i	−0.202785	−	0.979223i	$-0.564999\pi$
$673$	13555.9	−	13555.9i	0.776438	−	0.776438i	0.979223	+	0.202785i	$0.0649993\pi$
$674$	−11788.6	−	14779.6i	−0.673711	−	0.844640i
$675$	7988.23	+	14944.9i	0.455507	+	0.852194i
$676$	10728.7	−	10147.0i	0.610417	−	0.577322i
$677$	−6590.57	+	5408.74i	−0.374145	+	0.307053i	−0.802608	−	0.596506i	$-0.796555\pi$
$677$	−6590.57	+	5408.74i	−0.374145	+	0.307053i	0.428463	+	0.903559i	$0.359055\pi$
$678$	6959.65	+	2997.01i	0.394224	+	0.169763i
$679$	6714.03	−	33753.7i	0.379471	−	1.90773i
$680$	4010.72	−	8642.70i	0.226183	−	0.487401i
$681$	3981.88	−	792.046i	0.224062	−	0.0445687i
$682$	−1504.49	+	975.233i	−0.0844718	+	0.0547560i
$683$	19089.6	−	5790.76i	1.06946	−	0.324418i	0.293996	−	0.955807i	$-0.405015\pi$
$683$	19089.6	−	5790.76i	1.06946	−	0.324418i	0.775466	+	0.631389i	$0.217515\pi$
$684$	−17589.2	+	20254.8i	−0.983248	+	1.13225i
$685$	−3538.70	−	2904.13i	−0.197382	−	0.161987i
$686$	18004.5	−	9303.57i	1.00206	−	0.517802i
$687$	1625.69	+	3924.77i	0.0902825	+	0.217961i
$688$	−2761.37	+	17802.2i	−0.153018	+	0.986486i
$689$	1986.03	−	4794.70i	0.109814	−	0.265114i
$690$	−309.100	−	3660.30i	−0.0170539	−	0.201950i
$691$	8544.16	−	841.526i	0.470384	−	0.0463287i	0.139951	−	0.990158i	$-0.455305\pi$
$691$	8544.16	−	841.526i	0.470384	−	0.0463287i	0.330432	+	0.943830i	$0.392805\pi$
$692$	−19119.1	−	2422.45i	−1.05029	−	0.133075i
$693$	−23709.2	−	12672.8i	−1.29962	−	0.694662i
$694$	−9522.03	+	13829.8i	−0.520823	+	0.756444i
$695$	−22826.3	+	34161.9i	−1.24583	+	1.86451i
$696$	4744.41	−	8048.29i	0.258386	−	0.438318i
$697$	−764.586	+	510.880i	−0.0415506	+	0.0277632i
$698$	−14941.1	−	15363.2i	−0.810213	−	0.833103i
$699$	166.968	−	1695.26i	0.00903478	−	0.0917317i
$700$	46793.3	+	33188.0i	2.52660	+	1.79198i
$701$	9648.64	−	31807.3i	0.519863	−	1.71376i	−0.166088	−	0.986111i	$-0.553113\pi$
$701$	9648.64	−	31807.3i	0.519863	−	1.71376i	0.685951	−	0.727648i	$-0.259387\pi$
$702$	1839.22	−	3328.58i	0.0988844	−	0.178959i
$703$		−	41548.8i		−	2.22908i
$704$	−16782.3	−	6666.00i	−0.898448	−	0.356867i
$705$		−	1397.96i		−	0.0746810i
$706$	−18212.1	−	10063.2i	−0.970852	−	0.536448i
$707$	−3329.51	+	10975.9i	−0.177113	+	0.583864i
$708$	20.9081	+	122.912i	0.00110985	+	0.00652447i
$709$	−1445.33	+	14674.7i	−0.0765592	+	0.777318i	0.877874	+	0.478892i	$0.158962\pi$
$709$	−1445.33	+	14674.7i	−0.0765592	+	0.777318i	−0.954433	+	0.298426i	$0.903538\pi$
$710$	13286.3	−	12921.3i	0.702292	−	0.682996i
$711$	−20835.1	+	13921.6i	−1.09898	+	0.734317i
$712$	9276.09	+	12318.3i	0.488253	+	0.648383i
$713$	−495.500	+	741.568i	−0.0260261	+	0.0389508i
$714$	2158.44	+	1486.12i	0.113134	+	0.0778944i
$715$	−11076.5	−	5920.50i	−0.579352	−	0.309670i
$716$	−7417.70	+	5749.39i	−0.387168	+	0.300091i
$717$	−1331.62	+	131.153i	−0.0693586	+	0.00683122i
$718$	−29040.6	+	2452.38i	−1.50945	+	0.127468i
$719$	−933.739	+	2254.25i	−0.0484320	+	0.116925i	−0.946244	−	0.323454i	$-0.895156\pi$
$719$	−933.739	+	2254.25i	−0.0484320	+	0.116925i	0.897812	+	0.440379i	$0.145156\pi$
$720$	27687.3	−	12871.3i	1.43312	−	0.666230i
$721$	18448.7	+	44539.0i	0.952933	+	2.30058i
$722$	14262.0	+	27600.1i	0.735145	+	1.42267i
$723$	520.743	+	427.363i	0.0267865	+	0.0219831i
$724$	34026.2	−	2396.62i	1.74665	−	0.123024i
$725$	67757.3	−	20554.0i	3.47096	−	1.05290i
$726$	184.536	+	284.682i	0.00943357	+	0.0145531i
$727$	13635.8	−	2712.34i	0.695633	−	0.138370i	0.165406	−	0.986226i	$-0.447107\pi$
$727$	13635.8	−	2712.34i	0.695633	−	0.138370i	0.530227	+	0.847856i	$0.322107\pi$
$728$	537.786	−	12862.9i	0.0273787	−	0.654852i
$729$	2315.01	−	11638.3i	0.117615	−	0.591288i
$730$	−1801.01	+	4182.30i	−0.0913131	+	0.212047i
$731$	−4821.18	+	3956.64i	−0.243937	+	0.200194i
$732$	126.555	−	4541.95i	0.00639018	−	0.229338i
$733$	551.646	+	1032.06i	0.0277974	+	0.0520053i	0.895437	−	0.445189i	$-0.146864\pi$
$733$	551.646	+	1032.06i	0.0277974	+	0.0520053i	−0.867639	+	0.497194i	$0.834364\pi$
$734$	25224.0	−	20119.5i	1.26844	−	1.01175i
$735$	−10714.7	+	10714.7i	−0.537710	+	0.537710i
$736$	−8979.04	+	256.276i	−0.449690	+	0.0128349i
$737$	−10773.8	−	10773.8i	−0.538478	−	0.538478i
$738$	−2928.28	−	329.651i	−0.146059	−	0.0164426i
$739$	−1161.97	+	621.087i	−0.0578401	+	0.0309162i	−0.500063	−	0.865989i	$-0.666690\pi$
$739$	−1161.97	+	621.087i	−0.0578401	+	0.0309162i	0.442223	+	0.896905i	$0.354190\pi$
$740$	−19307.0	+	43169.3i	−0.959107	+	2.14451i
$741$	−2186.73	−	2664.54i	−0.108410	−	0.132098i
$742$	8795.65	+	22100.3i	0.435173	+	1.09343i
$743$	−16871.6	−	3355.98i	−0.833056	−	0.165705i	−0.239905	−	0.970796i	$-0.577116\pi$
$743$	−16871.6	−	3355.98i	−0.833056	−	0.165705i	−0.593151	+	0.805091i	$0.702116\pi$
$744$	544.259	+	132.113i	0.0268192	+	0.00651009i
$745$	4569.88	+	22974.3i	0.224735	+	1.12982i
$746$	−365.842	+	1714.09i	−0.0179550	+	0.0841249i
$747$	−6923.44	−	22823.5i	−0.339110	−	1.11790i
$748$	−2792.30	−	5593.41i	−0.136493	−	0.273416i
$749$	12613.0	−	15369.0i	0.615312	−	0.749760i
$750$	−7840.70	−	2498.22i	−0.381736	−	0.121629i
$751$	1660.45	−	687.783i	0.0806802	−	0.0334188i	−0.341978	−	0.939708i	$-0.611097\pi$
$751$	1660.45	−	687.783i	0.0806802	−	0.0334188i	0.422659	+	0.906289i	$0.361097\pi$
$752$	−3413.24	−	190.358i	−0.165516	−	0.00923089i
$753$	−5127.79	−	2124.00i	−0.248163	−	0.102793i
$754$	−12141.5	−	10250.6i	−0.586431	−	0.495099i
$755$	−1636.44	−	16615.1i	−0.0788824	−	0.800906i
$756$	4593.12	+	16813.9i	0.220966	+	0.808882i
$757$	−14486.4	+	27102.2i	−0.695533	+	1.30125i	0.247608	+	0.968860i	$0.420355\pi$
$757$	−14486.4	+	27102.2i	−0.695533	+	1.30125i	−0.943142	+	0.332391i	$0.892145\pi$
$758$	886.698	−	163.571i	0.0424885	−	0.00783795i
$759$	−2004.02	−	1339.04i	−0.0958381	−	0.0640370i
$760$	−3237.39	−	57349.6i	−0.154516	−	2.73722i
$761$	−11729.2	−	17553.9i	−0.558715	−	0.836176i	0.439352	−	0.898315i	$-0.355208\pi$
$761$	−11729.2	−	17553.9i	−0.558715	−	0.836176i	−0.998068	+	0.0621385i	$0.980208\pi$
$762$	−3855.74	−	53.7070i	−0.183306	−	0.00255328i
$763$	−46312.9	−	4561.42i	−2.19743	−	0.216428i
$764$	1729.90	+	2751.94i	0.0819183	+	0.130316i
$765$	10115.4	+	3068.48i	0.478070	+	0.145021i
$766$	−7051.92	+	2032.36i	−0.332632	+	0.0958645i
$767$	212.053			0.00998278
$768$	2089.39	+	5239.55i	0.0981699	+	0.246180i
$769$	−12173.1			−0.570836			−0.285418	−	0.958403i	$-0.592132\pi$
$769$	−12173.1			−0.570836			−0.285418	+	0.958403i	$0.592132\pi$
$770$	55312.8	−	15941.1i	2.58874	−	0.746076i
$771$	−3338.45	−	1012.71i	−0.155942	−	0.0473044i
$772$	−17687.8	−	28137.9i	−0.824609	−	1.31179i
$773$	−3261.92	−	321.271i	−0.151776	−	0.0149487i	0.0218436	−	0.999761i	$-0.493046\pi$
$773$	−3261.92	−	321.271i	−0.151776	−	0.0149487i	−0.173620	+	0.984813i	$0.555546\pi$
$774$	−19984.5	−	278.366i	−0.928072	−	0.0129272i
$775$	2358.19	+	3529.29i	0.109302	+	0.163582i
$776$	25605.4	−	1445.43i	1.18451	−	0.0668658i
$777$	−10814.6	−	7226.11i	−0.499322	−	0.333636i
$778$	404.572	−	74.6323i	0.0186435	−	0.00343920i
$779$	−2613.29	+	4889.12i	−0.120194	+	0.224866i
$780$	1033.85	+	3784.60i	0.0474589	+	0.173731i
$781$	−1191.93	−	12101.9i	−0.0546103	−	0.554468i
$782$	−2376.23	−	2006.15i	−0.108662	−	0.0917391i
$783$	19875.4	+	8232.65i	0.907137	+	0.375748i
$784$	24701.8	+	27619.8i	1.12526	+	1.25819i
$785$	−49583.0	+	20537.9i	−2.25438	+	0.933797i
$786$	−4567.67	−	1455.36i	−0.207282	−	0.0660445i
$787$	−7375.01	+	8986.47i	−0.334041	+	0.407031i	−0.912760	−	0.408497i	$-0.866053\pi$
$787$	−7375.01	+	8986.47i	−0.334041	+	0.407031i	0.578718	+	0.815528i	$0.303553\pi$
$788$	−11391.1	−	22818.2i	−0.514965	−	1.03155i
$789$	266.761	+	879.392i	0.0120367	+	0.0396796i
$790$	11199.6	−	52473.6i	0.504384	−	2.36320i
$791$	11523.9	+	57934.3i	0.518004	+	2.60418i
$792$	4725.75	−	19468.4i	0.212023	−	0.873458i
$793$	−7579.49	−	1507.66i	−0.339415	−	0.0675138i
$794$	−6019.74	−	15125.4i	−0.269059	−	0.676047i
$795$	−4598.47	−	5603.25i	−0.205146	−	0.249971i
$796$	13687.2	−	30603.8i	0.609459	−	1.36272i
$797$	37448.6	−	20016.7i	1.66437	−	0.889622i	0.676111	−	0.736799i	$-0.263664\pi$
$797$	37448.6	−	20016.7i	1.66437	−	0.889622i	0.988254	−	0.152822i	$-0.0488362\pi$
$798$	15699.4	+	1767.36i	0.696431	+	0.0784007i
$799$	−836.869	−	836.869i	−0.0370542	−	0.0370542i
$800$	−15226.5	+	39947.1i	−0.672921	+	1.76543i
$801$	−12097.0	+	12097.0i	−0.533616	+	0.533616i
$802$	8939.37	−	7130.32i	0.393591	−	0.313941i
$803$	1408.43	+	2634.99i	0.0618961	+	0.115799i
$804$	−132.565	+	4757.65i	−0.00581494	+	0.208693i
$805$	22135.1	−	18165.8i	0.969141	−	0.795353i
$806$	376.751	−	874.889i	0.0164646	−	0.0382341i
$807$	1754.04	−	8818.16i	0.0765120	−	0.384652i
$808$	−8539.89	−	357.043i	−0.371822	−	0.0155455i
$809$	16397.3	−	3261.63i	0.712606	−	0.141746i	0.174542	−	0.984650i	$-0.444156\pi$
$809$	16397.3	−	3261.63i	0.712606	−	0.141746i	0.538065	+	0.842904i	$0.319156\pi$
$810$	16928.1	+	26114.9i	0.734312	+	1.13282i
$811$	−15892.3	+	4820.87i	−0.688105	+	0.208734i	−0.614927	−	0.788584i	$-0.710814\pi$
$811$	−15892.3	+	4820.87i	−0.688105	+	0.208734i	−0.0731787	+	0.997319i	$0.523314\pi$
$812$	72648.9	−	5116.99i	3.13975	−	0.221147i
$813$	4328.38	+	3552.21i	0.186719	+	0.153237i
$814$	14244.3	+	27566.0i	0.613344	+	1.18696i
$815$	25448.9	+	61439.0i	1.09378	+	2.64063i
$816$	−670.067	+	1834.31i	−0.0287464	+	0.0786931i
$817$	−14388.9	+	34738.0i	−0.616163	+	1.48755i
$818$	−9445.12	+	797.607i	−0.403718	+	0.0340925i
$819$	14214.2	−	1399.98i	0.606452	−	0.0597303i
$820$	4987.10	−	3865.45i	0.212387	−	0.164619i
$821$	9633.92	+	5149.44i	0.409532	+	0.218900i	0.663281	−	0.748371i	$-0.269164\pi$
$821$	9633.92	+	5149.44i	0.409532	+	0.218900i	−0.253748	+	0.967270i	$0.581664\pi$
$822$	772.809	+	532.091i	0.0327917	+	0.0225776i
$823$	−17545.2	+	26258.3i	−0.743120	+	1.11216i	0.246597	+	0.969118i	$0.420688\pi$
$823$	−17545.2	+	26258.3i	−0.743120	+	1.11216i	−0.989717	+	0.143039i	$0.954312\pi$
$824$	−28698.4	+	21610.8i	−1.21330	+	0.913652i
$825$	−9537.55	+	6372.79i	−0.402491	+	0.268936i
$826$	−696.747	+	677.603i	−0.0293498	+	0.0285434i
$827$	1970.96	−	20011.5i	0.0828743	−	0.841437i	−0.860443	−	0.509546i	$-0.829813\pi$
$827$	1970.96	−	20011.5i	0.0828743	−	0.841437i	0.943318	−	0.331891i	$-0.107687\pi$
$828$	−1671.21	−	9824.52i	−0.0701432	−	0.412350i
$829$	360.102	−	1187.10i	0.0150867	−	0.0497341i	−0.949074	−	0.315054i	$-0.897977\pi$
$829$	360.102	−	1187.10i	0.0150867	−	0.0497341i	0.964161	+	0.265320i	$0.0854775\pi$
$830$	44699.7	+	24699.0i	1.86934	+	1.03291i
$831$		−	2755.51i		−	0.115027i
$832$	9381.21	−	2008.90i	0.390907	−	0.0837094i
$833$			12828.4i			0.533586i
$834$	4072.71	−	7370.71i	0.169097	−	0.306027i
$835$	9705.61	−	31995.1i	0.402247	−	1.32603i
$836$	−30742.0	−	21803.7i	−1.27181	−	0.902028i
$837$	−126.407	+	1283.43i	−0.00522015	+	0.0530011i
$838$	−24028.0	−	24706.8i	−0.990493	−	1.01848i
$839$	9355.74	−	6251.31i	0.384977	−	0.257234i	−0.347989	−	0.937499i	$-0.613135\pi$
$839$	9355.74	−	6251.31i	0.384977	−	0.257234i	0.732966	+	0.680265i	$0.238135\pi$
$840$	−15490.4	−	9131.50i	−0.636274	−	0.375080i
$841$	36389.9	−	54461.4i	1.49206	−	2.23303i
$842$	1399.67	−	2032.87i	0.0572870	−	0.0832037i
$843$	−8184.79	−	4374.86i	−0.334400	−	0.178741i
$844$	−26268.8	−	3328.32i	−1.07134	−	0.135741i
$845$	−34911.0	+	3438.43i	−1.42127	+	0.139983i
$846$	−319.138	−	3779.17i	−0.0129695	−	0.153582i
$847$	−1012.06	+	2443.34i	−0.0410566	+	0.0991194i
$848$	−14307.0	+	10464.6i	−0.579368	+	0.423768i
$849$	−273.289	−	659.778i	−0.0110474	−	0.0266708i
$850$	−13148.7	+	6794.40i	−0.530585	+	0.274172i
$851$	11931.5	+	9791.89i	0.480617	+	0.394432i
$852$	−2490.67	+	2868.11i	−0.100151	+	0.115329i
$853$	−46280.3	+	14039.0i	−1.85769	+	0.563523i	−0.859018	+	0.511946i	$0.828925\pi$
$853$	−46280.3	+	14039.0i	−1.85769	+	0.563523i	−0.998669	+	0.0515775i	$0.983575\pi$
$854$	29721.7	−	19266.1i	1.19093	−	0.771982i
$855$	62502.0	−	12432.4i	2.50003	−	0.497287i
$856$	13439.5	+	6236.73i	0.536628	+	0.249027i
$857$	−2204.63	+	11083.4i	−0.0878749	+	0.441777i	0.911650	+	0.410967i	$0.134809\pi$
$857$	−2204.63	+	11083.4i	−0.0878749	+	0.441777i	−0.999525	+	0.0308104i	$0.990191\pi$
$858$	2364.30	+	1018.13i	0.0940745	+	0.0405110i
$859$	8286.34	−	6800.42i	0.329134	−	0.270114i	−0.455283	−	0.890347i	$-0.650462\pi$
$859$	8286.34	−	6800.42i	0.329134	−	0.270114i	0.784418	+	0.620233i	$0.212962\pi$
$860$	31092.2	−	29406.5i	1.23283	−	1.16599i
$861$	818.077	+	1530.51i	0.0323809	+	0.0605805i
$862$	589.084	+	738.542i	0.0232764	+	0.0291819i
$863$	−6316.49	+	6316.49i	−0.249149	+	0.249149i	−0.820621	−	0.571472i	$-0.806373\pi$
$863$	−6316.49	+	6316.49i	−0.249149	+	0.249149i	0.571472	+	0.820621i	$0.306373\pi$
$864$	−11275.8	+	6447.23i	−0.443994	+	0.253865i
$865$	32372.4	+	32372.4i	1.27248	+	1.27248i
$866$	3050.52	−	27097.7i	0.119701	−	1.06330i
$867$	5370.75	−	2870.72i	0.210381	−	0.112451i
$868$	1557.76	+	4078.52i	0.0609145	+	0.159486i
$869$	−22334.0	−	27214.1i	−0.871841	−	1.06234i
$870$	−20620.7	+	8206.80i	−0.803572	+	0.319812i
$871$	7939.44	+	1579.25i	0.308861	+	0.0614362i
$872$	−5338.93	−	34266.1i	−0.207338	−	1.33073i
$873$	5550.82	+	27905.9i	0.215197	+	1.08187i
$874$	−18335.2	−	3913.34i	−0.709610	−	0.151454i
$875$	−18621.3	−	61386.2i	−0.719446	−	2.37170i
$876$	295.697	−	885.231i	0.0114049	−	0.0341429i
$877$	−13941.9	+	16988.2i	−0.536811	+	0.654106i	−0.968821	−	0.247763i	$-0.920305\pi$
$877$	−13941.9	+	16988.2i	−0.536811	+	0.654106i	0.432009	+	0.901869i	$0.357805\pi$
$878$	−11263.3	+	35350.0i	−0.432936	+	1.35878i
$879$	7939.13	−	3288.49i	0.304642	−	0.126187i
$880$	21809.2	+	36939.3i	0.835441	+	1.41503i
$881$	−17972.9	−	7444.63i	−0.687313	−	0.284695i	0.0115670	−	0.999933i	$-0.496318\pi$
$881$	−17972.9	−	7444.63i	−0.687313	−	0.284695i	−0.698880	+	0.715239i	$0.746318\pi$
$882$	−26519.5	+	31411.6i	−1.01242	+	1.19919i
$883$	−2372.59	−	24089.3i	−0.0904236	−	0.918086i	−0.928202	−	0.372076i	$-0.878646\pi$
$883$	−2372.59	−	24089.3i	−0.0904236	−	0.918086i	0.837779	−	0.546010i	$-0.183854\pi$
$884$	2884.50	+	1646.70i	0.109747	+	0.0626521i
$885$	139.617	−	261.206i	0.00530304	−	0.00992128i
$886$	−30.9161	−	167.592i	−0.00117229	−	0.00635482i
$887$	26575.4	+	17757.1i	1.00599	+	0.672181i	0.945377	−	0.325980i	$-0.105694\pi$
$887$	26575.4	+	17757.1i	1.00599	+	0.672181i	0.0606133	+	0.998161i	$0.480694\pi$
$888$	3198.61	−	9149.62i	0.120876	−	0.345767i
$889$	−16700.3	−	24993.8i	−0.630045	−	0.942929i
$890$	510.197	−	36628.2i	0.0192156	−	1.37953i
$891$	20321.6	+	2001.51i	0.764086	+	0.0752559i
$892$	−4894.40	+	21462.9i	−0.183718	+	0.805640i
$893$	−6827.76	−	2071.18i	−0.255859	−	0.0776141i
$894$	−1329.56	−	4613.33i	−0.0497395	−	0.172587i
$895$	22294.4			0.832649
$896$	−24404.7	+	36577.8i	−0.909936	+	1.36382i
$897$	1280.52			0.0476648
$898$	11893.2	+	41267.2i	0.441962	+	1.53352i
$899$	5156.57	+	1564.23i	0.191303	+	0.0580311i
$900$	−46241.6	−	10544.9i	−1.71265	−	0.390553i
$901$	−6107.12	−	601.499i	−0.225813	−	0.0222407i
$902$	57.6616	−	4139.65i	0.00212852	−	0.152811i
$903$	6539.35	+	9786.84i	0.240992	+	0.360671i
$904$	−39653.9	+	19110.5i	−1.45893	+	0.703104i
$905$	−67374.8	−	45018.4i	−2.47471	−	1.65355i
$906$	620.775	+	3365.14i	0.0227636	+	0.123399i
$907$	7739.08	−	14478.8i	0.283321	−	0.530056i	−0.699497	−	0.714636i	$-0.746592\pi$
$907$	7739.08	−	14478.8i	0.283321	−	0.530056i	0.982818	+	0.184580i	$0.0590924\pi$
$908$	−11692.6	+	20481.9i	−0.427349	+	0.748584i
$909$	−929.463	−	9437.00i	−0.0339146	−	0.344340i
$910$	−19729.2	+	23368.6i	−0.718699	+	0.851278i
$911$	−43788.1	−	18137.6i	−1.59250	−	0.659634i	−0.602169	−	0.798369i	$-0.705697\pi$
$911$	−43788.1	−	18137.6i	−1.59250	−	0.659634i	−0.990330	+	0.138734i	$0.955697\pi$
$912$	1650.28	+	11656.9i	0.0599193	+	0.423244i
$913$	30958.0	−	12823.2i	1.12219	−	0.464826i
$914$	−152.510	+	478.655i	−0.00551923	+	0.0173222i
$915$	−6847.52	+	8343.73i	−0.247401	+	0.301459i
$916$	−23406.6	−	7818.60i	−0.844298	−	0.282024i
$917$	−10848.0	−	35761.1i	−0.390658	−	1.28783i
$918$	−4397.74	−	938.623i	−0.158112	−	0.0337464i
$919$	−2182.53	−	10972.3i	−0.0783405	−	0.393844i	−0.999983	−	0.00580460i	$-0.998152\pi$
$919$	−2182.53	−	10972.3i	−0.0783405	−	0.393844i	0.921643	−	0.388040i	$-0.126848\pi$
$920$	17231.9	+	12586.0i	0.617520	+	0.451031i
$921$	5887.54	+	1171.10i	0.210642	+	0.0418992i
$922$	22239.1	−	8850.91i	0.794367	−	0.316149i
$923$	4098.64	+	4994.21i	0.146163	+	0.178100i
$924$	−11021.8	+	4209.69i	−0.392415	+	0.149880i
$925$	64784.9	−	34628.2i	2.30283	−	1.23089i
$926$	−394.338	+	3502.89i	−0.0139943	+	0.124311i
$927$	−28182.8	−	28182.8i	−0.998538	−	0.998538i
$928$	17229.7	+	51464.8i	0.609476	+	1.82049i
$929$	−12886.1	+	12886.1i	−0.455090	+	0.455090i	−0.897040	−	0.441950i	$-0.854287\pi$
$929$	−12886.1	+	12886.1i	−0.455090	+	0.455090i	0.441950	+	0.897040i	$0.354287\pi$
$930$	−829.627	−	1040.11i	−0.0292522	−	0.0366738i
$931$	36456.9	+	68206.1i	1.28338	+	2.40104i
$932$	6799.63	+	7189.42i	0.238980	+	0.252679i
$933$	4708.80	−	3864.41i	0.165230	−	0.135600i
$934$	36595.1	+	15758.8i	1.28204	+	0.552082i
$935$	−2897.30	+	14565.7i	−0.101339	+	0.509466i
$936$	3658.85	+	9995.08i	0.127771	+	0.349038i
$937$	−871.484	+	173.349i	−0.0303843	+	0.00604382i	−0.210259	−	0.977646i	$-0.567431\pi$
$937$	−871.484	+	173.349i	−0.0303843	+	0.00604382i	0.179875	+	0.983690i	$0.442431\pi$
$938$	−31133.2	+	20181.0i	−1.08372	+	0.702488i
$939$	−41.6845	+	12.6449i	−0.00144869	+	0.000439457i
$940$	6131.61	+	5324.69i	0.212757	+	0.184758i
$941$	16353.9	+	13421.3i	0.566548	+	0.464954i	0.873536	−	0.486760i	$-0.161821\pi$
$941$	16353.9	+	13421.3i	0.566548	+	0.464954i	−0.306988	+	0.951713i	$0.599321\pi$
$942$	9772.31	−	5049.70i	0.338003	−	0.174658i
$943$	−788.115	−	1902.68i	−0.0272159	−	0.0657049i
$944$	−618.745	−	376.456i	−0.0213331	−	0.0129795i
$945$	15845.3	−	38253.8i	0.545446	−	1.31682i
$946$	−2362.83	−	27980.2i	−0.0812075	−	0.961645i
$947$	46625.4	−	4592.20i	1.59992	−	0.157578i	0.741653	−	0.670784i	$-0.234042\pi$
$947$	46625.4	−	4592.20i	1.59992	−	0.157578i	0.858266	+	0.513206i	$0.171542\pi$
$948$	−1382.33	+	10910.0i	−0.0473587	+	0.373778i
$949$	−1399.95	−	748.287i	−0.0478864	−	0.0255958i
$950$	−50600.3	+	73491.8i	−1.72809	+	2.50988i
$951$	1851.04	−	2770.27i	0.0631168	−	0.0944609i
$952$	−14739.6	+	3806.68i	−0.501799	+	0.129596i
$953$	5981.96	−	3997.02i	0.203331	−	0.135862i	−0.449736	−	0.893162i	$-0.648482\pi$
$953$	5981.96	−	3997.02i	0.203331	−	0.135862i	0.653067	+	0.757300i	$0.273482\pi$
$954$	−13710.4	−	14097.8i	−0.465295	−	0.478440i
$955$	756.859	−	7684.52i	0.0256454	−	0.260382i
$956$	4496.75	−	6340.18i	0.152129	−	0.214494i
$957$	−4227.18	+	13935.1i	−0.142785	+	0.470699i
$958$	10326.9	−	18689.4i	0.348274	−	0.630299i
$959$			7314.15i			0.246284i
$960$	3702.10	−	12878.4i	0.124463	−	0.432967i
$961$		−	29468.0i		−	0.989157i
$962$	−14429.1	−	7972.84i	−0.483588	−	0.267209i
$963$	−4771.53	+	15729.6i	−0.159668	+	0.526355i
$964$	−3857.93	+	656.257i	−0.128896	+	0.0219260i
$965$	−7738.70	+	78572.3i	−0.258153	+	2.62107i
$966$	−4207.43	+	4091.83i	−0.140136	+	0.136286i
$967$	−18824.9	+	12578.4i	−0.626028	+	0.418299i	−0.827713	−	0.561152i	$-0.810358\pi$
$967$	−18824.9	+	12578.4i	−0.626028	+	0.418299i	0.201685	+	0.979451i	$0.435358\pi$
$968$	−1951.53	−	274.933i	−0.0647982	−	0.00912879i
$969$	−2264.45	+	3388.99i	−0.0750719	+	0.112353i
$970$	−50179.9	−	34549.6i	−1.66101	−	1.14363i
$971$	−18197.7	−	9726.89i	−0.601435	−	0.321474i	0.142429	−	0.989805i	$-0.454509\pi$
$971$	−18197.7	−	9726.89i	−0.601435	−	0.321474i	−0.743864	+	0.668332i	$0.767009\pi$
$972$	−13402.6	−	17291.6i	−0.442271	−	0.570605i
$973$	65329.0	−	6434.34i	2.15247	−	0.211999i
$974$	967.107	−	81.6688i	0.0318153	−	0.00268669i
$975$	2332.18	−	5630.38i	0.0766046	−	0.184940i
$976$	19439.5	+	17855.0i	0.637545	+	0.585578i
$977$	13696.9	+	33067.2i	0.448518	+	1.08282i	0.972878	+	0.231321i	$0.0743047\pi$
$977$	13696.9	+	33067.2i	0.448518	+	1.08282i	−0.524360	+	0.851497i	$0.675695\pi$
$978$	−6257.15	−	12109.0i	−0.204582	−	0.395914i
$979$	−18579.6	−	15247.9i	−0.606545	−	0.497779i
$980$	−6184.65	−	87807.1i	−0.201593	−	2.86214i
$981$	36817.7	−	11168.5i	1.19827	−	0.363490i
$982$	−784.738	−	1210.61i	−0.0255010	−	0.0393403i
$983$	−26008.3	+	5173.37i	−0.843881	+	0.167858i	−0.598054	−	0.801456i	$-0.704059\pi$
$983$	−26008.3	+	5173.37i	−0.843881	+	0.167858i	−0.245826	+	0.969314i	$0.579059\pi$
$984$	−951.868	+	875.469i	−0.0308378	+	0.0283627i
$985$	−11819.5	+	59420.6i	−0.382335	+	1.92213i
$986$	−7431.42	+	17257.2i	−0.240025	+	0.557385i
$987$	−1726.58	+	1416.96i	−0.0556814	+	0.0456965i
$988$	20016.1	+	557.720i	0.644531	+	0.0179589i
$989$	−6584.53	−	12318.8i	−0.211705	−	0.396072i
$990$	−37205.3	+	29676.1i	−1.19441	+	0.952697i
$991$	30175.2	−	30175.2i	0.967253	−	0.967253i	−0.0322279	−	0.999481i	$-0.510260\pi$
$991$	30175.2	−	30175.2i	0.967253	−	0.967253i	0.999481	+	0.0322279i	$0.0102602\pi$
$992$	−2652.50	+	1883.98i	−0.0848960	+	0.0602987i
$993$	11070.2	+	11070.2i	0.353778	+	0.353778i
$994$	−29425.7	−	3312.59i	−0.938959	−	0.105703i
$995$	−70236.5	+	37542.2i	−2.23784	+	1.19615i
$996$	−9555.18	−	4273.45i	−0.303983	−	0.135953i
$997$	−11885.4	−	14482.4i	−0.377546	−	0.460041i	0.549221	−	0.835677i	$-0.314924\pi$
$997$	−11885.4	−	14482.4i	−0.377546	−	0.460041i	−0.926767	+	0.375636i	$0.877424\pi$
$998$	−11081.9	−	27844.8i	−0.351495	−	0.883179i
$999$	21890.0	+	4354.20i	0.693263	+	0.137899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.5	✓	752
128.77	even	32	inner	128.4.k.a.77.5	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.5	✓	752	1.1	even	1	trivial
128.4.k.a.77.5	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)

\(f(q)\)	\(=\)	\(q+(-2.71781 + 0.783272i) q^{2} +(-1.31785 - 0.399764i) q^{3} +(6.77297 - 4.25757i) q^{4} +(-18.9129 - 1.86275i) q^{5} +(3.89478 + 0.0542507i) q^{6} +(16.8694 + 25.2468i) q^{7} +(-15.0728 + 16.8763i) q^{8} +(-20.8728 - 13.9467i) q^{9} +O(q^{10})\)	\(q+(-2.71781 + 0.783272i) q^{2} +(-1.31785 - 0.399764i) q^{3} +(6.77297 - 4.25757i) q^{4} +(-18.9129 - 1.86275i) q^{5} +(3.89478 + 0.0542507i) q^{6} +(16.8694 + 25.2468i) q^{7} +(-15.0728 + 16.8763i) q^{8} +(-20.8728 - 13.9467i) q^{9} +(52.8606 - 9.75131i) q^{10} +(16.6257 - 31.1045i) q^{11} +(-10.6278 + 2.90323i) q^{12} +(1.83665 + 18.6478i) q^{13} +(-65.6228 - 55.4026i) q^{14} +(24.1796 + 10.0155i) q^{15} +(27.7462 - 57.6728i) q^{16} +(20.4704 - 8.47913i) q^{17} +(67.6523 + 21.5555i) q^{18} +(84.7406 - 103.257i) q^{19} +(-136.027 + 67.9064i) q^{20} +(-12.1385 - 40.0151i) q^{21} +(-20.8222 + 97.5585i) q^{22} +(9.68094 + 48.6694i) q^{23} +(26.6102 - 16.2148i) q^{24} +(231.628 + 46.0737i) q^{25} +(-19.5980 - 49.2427i) q^{26} +(45.5203 + 55.4666i) q^{27} +(221.746 + 99.1733i) q^{28} +(264.413 - 141.332i) q^{29} +(-73.5603 - 8.28105i) q^{30} +(12.7089 + 12.7089i) q^{31} +(-30.2355 + 178.476i) q^{32} +(-34.3445 + 34.3445i) q^{33} +(-48.9933 + 39.0786i) q^{34} +(-272.019 - 508.913i) q^{35} +(-200.750 - 5.59361i) q^{36} +(240.443 - 197.326i) q^{37} +(-149.431 + 347.007i) q^{38} +(5.03431 - 25.3092i) q^{39} +(316.506 - 291.103i) q^{40} +(-40.7045 + 8.09662i) q^{41} +(64.3328 + 99.2458i) q^{42} +(-269.365 + 81.7110i) q^{43} +(-19.8241 - 281.455i) q^{44} +(368.785 + 302.654i) q^{45} +(-64.4323 - 124.691i) q^{46} +(-20.4409 - 49.3487i) q^{47} +(-59.6208 + 64.9118i) q^{48} +(-221.565 + 534.904i) q^{49} +(-665.610 + 56.2084i) q^{50} +(-30.3665 + 2.99084i) q^{51} +(91.8340 + 118.482i) q^{52} +(-244.259 - 130.559i) q^{53} +(-167.161 - 115.093i) q^{54} +(-372.379 + 557.305i) q^{55} +(-680.342 - 95.8468i) q^{56} +(-152.953 + 102.200i) q^{57} +(-607.924 + 591.221i) q^{58} +(1.10923 - 11.2622i) q^{59} +(206.409 - 35.1114i) q^{60} +(-119.720 + 394.663i) q^{61} +(-44.4949 - 24.5858i) q^{62} -762.243i q^{63} +(-57.6212 - 508.747i) q^{64} -356.105i q^{65} +(66.4408 - 120.243i) q^{66} +(125.405 - 413.405i) q^{67} +(102.545 - 144.583i) q^{68} +(6.69829 - 68.0088i) q^{69} +(1137.91 + 1170.06i) q^{70} +(286.683 - 191.556i) q^{71} +(549.981 - 142.039i) q^{72} +(-47.0648 + 70.4374i) q^{73} +(-498.917 + 724.627i) q^{74} +(-286.832 - 153.315i) q^{75} +(134.323 - 1060.14i) q^{76} +(1065.75 - 104.968i) q^{77} +(6.14169 + 72.7288i) q^{78} +(381.993 - 922.212i) q^{79} +(-632.191 + 1039.07i) q^{80} +(221.565 + 534.906i) q^{81} +(104.285 - 53.8877i) q^{82} +(734.428 + 602.729i) q^{83} +(-252.581 - 219.341i) q^{84} +(-402.949 + 122.233i) q^{85} +(668.081 - 433.061i) q^{86} +(-404.955 + 80.5506i) q^{87} +(274.334 + 749.412i) q^{88} +(132.952 - 668.394i) q^{89} +(-1239.35 - 533.696i) q^{90} +(-439.815 + 360.947i) q^{91} +(272.782 + 288.419i) q^{92} +(-11.6678 - 21.8289i) q^{93} +(94.2080 + 118.110i) q^{94} +(-1795.03 + 1795.03i) q^{95} +(111.194 - 223.117i) q^{96} +(-801.443 - 801.443i) q^{97} +(183.195 - 1627.31i) q^{98} +(-780.830 + 417.363i) 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

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