LMFDB - Embedded newform 804.2.bd.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	804.23
Dual form			804.2.bd.a.35.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30733 + 0.539338i) q^{2} +(1.73118 - 0.0550183i) q^{3} +(1.41823 - 1.41019i) q^{4} +(2.63175 - 1.20188i) q^{5} +(-2.23355 + 1.00562i) q^{6} +(0.694593 + 0.728468i) q^{7} +(-1.09353 + 2.60848i) q^{8} +(2.99395 - 0.190493i) q^{9} +O(q^{10})$	\(q+(-1.30733 + 0.539338i) q^{2} +(1.73118 - 0.0550183i) q^{3} +(1.41823 - 1.41019i) q^{4} +(2.63175 - 1.20188i) q^{5} +(-2.23355 + 1.00562i) q^{6} +(0.694593 + 0.728468i) q^{7} +(-1.09353 + 2.60848i) q^{8} +(2.99395 - 0.190493i) q^{9} +(-2.79235 + 2.99066i) q^{10} +(-1.29365 - 0.123529i) q^{11} +(2.37762 - 2.51931i) q^{12} +(5.25385 + 1.01260i) q^{13} +(-1.30095 - 0.577729i) q^{14} +(4.48990 - 2.22546i) q^{15} +(0.0227512 - 3.99994i) q^{16} +(-2.41551 + 4.68544i) q^{17} +(-3.81134 + 1.86379i) q^{18} +(-3.97078 + 4.16444i) q^{19} +(2.03755 - 5.41580i) q^{20} +(1.24254 + 1.22289i) q^{21} +(1.75785 - 0.536221i) q^{22} +(2.60993 - 1.04486i) q^{23} +(-1.74958 + 4.57591i) q^{24} +(2.20729 - 2.54735i) q^{25} +(-7.41465 + 1.50980i) q^{26} +(5.17257 - 0.494499i) q^{27} +(2.01237 + 0.0536299i) q^{28} +(-0.207920 - 0.120043i) q^{29} +(-4.66951 + 5.33099i) q^{30} +(0.254944 + 1.32277i) q^{31} +(2.12757 + 5.24151i) q^{32} +(-2.24633 - 0.142675i) q^{33} +(0.630840 - 7.42819i) q^{34} +(2.70353 + 1.08233i) q^{35} +(3.97747 - 4.49218i) q^{36} +(-1.30376 - 2.25817i) q^{37} +(2.94509 - 7.58589i) q^{38} +(9.15105 + 1.46392i) q^{39} +(0.257189 + 8.17917i) q^{40} +(-2.96058 + 0.141030i) q^{41} +(-2.28397 - 0.928575i) q^{42} +(-6.47484 - 10.0750i) q^{43} +(-2.00889 + 1.64910i) q^{44} +(7.65037 - 4.09969i) q^{45} +(-2.84851 + 2.77361i) q^{46} +(-7.55715 - 5.94301i) q^{47} +(-0.180683 - 6.92585i) q^{48} +(0.284867 - 5.98009i) q^{49} +(-1.51178 + 4.52070i) q^{50} +(-3.92389 + 8.24421i) q^{51} +(8.87911 - 5.97281i) q^{52} +(5.23723 - 8.14929i) q^{53} +(-6.49556 + 3.43623i) q^{54} +(-3.55303 + 1.22972i) q^{55} +(-2.65976 + 1.01523i) q^{56} +(-6.64501 + 7.42784i) q^{57} +(0.336564 + 0.0447964i) q^{58} +(6.62268 + 7.64298i) q^{59} +(3.22939 - 9.48781i) q^{60} +(-4.91037 + 0.468883i) q^{61} +(-1.04672 - 1.59180i) q^{62} +(2.21834 + 2.04868i) q^{63} +(-5.60839 - 5.70491i) q^{64} +(15.0438 - 3.64959i) q^{65} +(3.01365 - 1.02501i) q^{66} +(-7.61507 - 3.00180i) q^{67} +(3.18159 + 10.0513i) q^{68} +(4.46076 - 1.95243i) q^{69} +(-4.11814 + 0.0431516i) q^{70} +(0.00404944 - 0.00208763i) q^{71} +(-2.77707 + 8.01797i) q^{72} +(7.73998 - 0.739078i) q^{73} +(2.92236 + 2.24901i) q^{74} +(3.68106 - 4.53135i) q^{75} +(0.241148 + 11.5057i) q^{76} +(-0.808573 - 1.02818i) q^{77} +(-12.7530 + 3.02167i) q^{78} +(-13.1272 + 4.54337i) q^{79} +(-4.74757 - 10.5542i) q^{80} +(8.92742 - 1.14065i) q^{81} +(3.79440 - 1.78113i) q^{82} +(0.00396083 - 0.00556221i) q^{83} +(3.48671 - 0.0178742i) q^{84} +(-0.725687 + 15.2340i) q^{85} +(13.8986 + 9.67930i) q^{86} +(-0.366551 - 0.196376i) q^{87} +(1.73687 - 3.23938i) q^{88} +(11.8014 - 1.69678i) q^{89} +(-7.79045 + 9.48579i) q^{90} +(2.91164 + 4.53060i) q^{91} +(2.22804 - 5.16234i) q^{92} +(0.514130 + 2.27593i) q^{93} +(13.0850 + 3.69363i) q^{94} +(-5.44496 + 15.7322i) q^{95} +(3.97158 + 8.95693i) q^{96} +(-2.92429 - 5.06502i) q^{97} +(2.85287 + 7.97160i) q^{98} +(-3.89665 - 0.123407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{14}{33}\right)$	$-1$

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 $

$2$	−1.30733	+	0.539338i	−0.924423	+	0.381369i
$2$	−1.30733	+	0.539338i	−0.924423	+	0.381369i
$3$	1.73118	−	0.0550183i	0.999495	−	0.0317648i
$3$	1.73118	−	0.0550183i	0.999495	−	0.0317648i
$4$	1.41823	−	1.41019i	0.709115	−	0.705093i
$5$	2.63175	−	1.20188i	1.17695	−	0.537497i	0.271706	−	0.962380i	$-0.412412\pi$
$5$	2.63175	−	1.20188i	1.17695	−	0.537497i	0.905248	+	0.424883i	$0.139685\pi$
$6$	−2.23355	+	1.00562i	−0.911842	+	0.410541i
$7$	0.694593	+	0.728468i	0.262531	+	0.275335i	0.841786	−	0.539812i	$-0.181505\pi$
$7$	0.694593	+	0.728468i	0.262531	+	0.275335i	−0.579254	+	0.815147i	$0.696656\pi$
$8$	−1.09353	+	2.60848i	−0.386621	+	0.922239i
$9$	2.99395	−	0.190493i	0.997982	−	0.0634976i
$10$	−2.79235	+	2.99066i	−0.883019	+	0.945729i
$11$	−1.29365	−	0.123529i	−0.390050	−	0.0372453i	−0.101811	−	0.994804i	$-0.532464\pi$
$11$	−1.29365	−	0.123529i	−0.390050	−	0.0372453i	−0.288239	+	0.957558i	$0.593070\pi$
$12$	2.37762	−	2.51931i	0.686360	−	0.727262i
$13$	5.25385	+	1.01260i	1.45716	+	0.280844i	0.855454	−	0.517878i	$-0.173278\pi$
$13$	5.25385	+	1.01260i	1.45716	+	0.280844i	0.601701	+	0.798722i	$0.294490\pi$
$14$	−1.30095	−	0.577729i	−0.347694	−	0.154405i
$15$	4.48990	−	2.22546i	1.15929	−	0.574612i
$16$	0.0227512	−	3.99994i	0.00568781	−	0.999984i
$17$	−2.41551	+	4.68544i	−0.585847	+	1.13639i	0.390586	+	0.920566i	$0.372272\pi$
$17$	−2.41551	+	4.68544i	−0.585847	+	1.13639i	−0.976433	+	0.215819i	$0.930758\pi$
$18$	−3.81134	+	1.86379i	−0.898341	+	0.439298i
$19$	−3.97078	+	4.16444i	−0.910960	+	0.955388i	−0.999171	−	0.0407142i	$-0.987037\pi$
$19$	−3.97078	+	4.16444i	−0.910960	+	0.955388i	0.0882106	+	0.996102i	$0.471885\pi$
$20$	2.03755	−	5.41580i	0.455610	−	1.21101i
$21$	1.24254	+	1.22289i	0.271145	+	0.266857i
$22$	1.75785	−	0.536221i	0.374775	−	0.114323i
$23$	2.60993	−	1.04486i	0.544208	−	0.217868i	−0.0832358	−	0.996530i	$-0.526525\pi$
$23$	2.60993	−	1.04486i	0.544208	−	0.217868i	0.627444	+	0.778662i	$0.284101\pi$
$24$	−1.74958	+	4.57591i	−0.357131	+	0.934054i
$25$	2.20729	−	2.54735i	0.441458	−	0.509470i
$26$	−7.41465	+	1.50980i	−1.45413	+	0.296096i
$27$	5.17257	−	0.494499i	0.995461	−	0.0951663i
$28$	2.01237	+	0.0536299i	0.380302	+	0.0101351i
$29$	−0.207920	−	0.120043i	−0.0386098	−	0.0222913i	0.480571	−	0.876956i	$-0.340429\pi$
$29$	−0.207920	−	0.120043i	−0.0386098	−	0.0222913i	−0.519181	+	0.854665i	$0.673763\pi$
$30$	−4.66951	+	5.33099i	−0.852532	+	0.973301i
$31$	0.254944	+	1.32277i	0.0457893	+	0.237577i	0.997612	−	0.0690727i	$-0.0220040\pi$
$31$	0.254944	+	1.32277i	0.0457893	+	0.237577i	−0.951822	+	0.306650i	$0.900792\pi$
$32$	2.12757	+	5.24151i	0.376105	+	0.926577i
$33$	−2.24633	−	0.142675i	−0.391036	−	0.0248366i
$34$	0.630840	−	7.42819i	0.108188	−	1.27392i
$35$	2.70353	+	1.08233i	0.456979	+	0.182947i
$36$	3.97747	−	4.49218i	0.662912	−	0.748697i
$37$	−1.30376	−	2.25817i	−0.214336	−	0.371241i	0.738731	−	0.674001i	$-0.235425\pi$
$37$	−1.30376	−	2.25817i	−0.214336	−	0.371241i	−0.953067	+	0.302759i	$0.902092\pi$
$38$	2.94509	−	7.58589i	0.477757	−	1.23059i
$39$	9.15105	+	1.46392i	1.46534	+	0.234416i
$40$	0.257189	+	8.17917i	0.0406652	+	1.29324i
$41$	−2.96058	+	0.141030i	−0.462366	+	0.0220252i	−0.277473	−	0.960734i	$-0.589497\pi$
$41$	−2.96058	+	0.141030i	−0.462366	+	0.0220252i	−0.184893	+	0.982759i	$0.559194\pi$
$42$	−2.28397	−	0.928575i	−0.352424	−	0.143282i
$43$	−6.47484	−	10.0750i	−0.987404	−	1.53643i	−0.836562	−	0.547872i	$-0.815438\pi$
$43$	−6.47484	−	10.0750i	−0.987404	−	1.53643i	−0.150842	−	0.988558i	$-0.548198\pi$
$44$	−2.00889	+	1.64910i	−0.302852	+	0.248610i
$45$	7.65037	−	4.09969i	1.14045	−	0.611146i
$46$	−2.84851	+	2.77361i	−0.419990	+	0.408946i
$47$	−7.55715	−	5.94301i	−1.10232	−	0.866877i	−0.110423	−	0.993885i	$-0.535220\pi$
$47$	−7.55715	−	5.94301i	−1.10232	−	0.866877i	−0.991902	+	0.127007i	$0.959463\pi$
$48$	−0.180683	−	6.92585i	−0.0260794	−	0.999660i
$49$	0.284867	−	5.98009i	0.0406953	−	0.854299i
$50$	−1.51178	+	4.52070i	−0.213798	+	0.639324i
$51$	−3.92389	+	8.24421i	−0.549454	+	1.15442i
$52$	8.87911	−	5.97281i	1.23131	−	0.828279i
$53$	5.23723	−	8.14929i	0.719389	−	1.11939i	−0.268357	−	0.963320i	$-0.586481\pi$
$53$	5.23723	−	8.14929i	0.719389	−	1.11939i	0.987746	−	0.156072i	$-0.0498830\pi$
$54$	−6.49556	+	3.43623i	−0.883934	+	0.467612i
$55$	−3.55303	+	1.22972i	−0.479090	+	0.165815i
$56$	−2.65976	+	1.01523i	−0.355425	+	0.135666i
$57$	−6.64501	+	7.42784i	−0.880153	+	0.983842i
$58$	0.336564	+	0.0447964i	0.0441930	+	0.00588206i
$59$	6.62268	+	7.64298i	0.862199	+	0.995031i	0.999990	+	0.00456934i	$0.00145447\pi$
$59$	6.62268	+	7.64298i	0.862199	+	0.995031i	−0.137791	+	0.990461i	$0.544000\pi$
$60$	3.22939	−	9.48781i	0.416913	−	1.22487i
$61$	−4.91037	+	0.468883i	−0.628708	+	0.0600343i	−0.404546	−	0.914518i	$-0.632571\pi$
$61$	−4.91037	+	0.468883i	−0.628708	+	0.0600343i	−0.224162	+	0.974552i	$0.571964\pi$
$62$	−1.04672	−	1.59180i	−0.132933	−	0.202159i
$63$	2.21834	+	2.04868i	0.279485	+	0.258109i
$64$	−5.60839	−	5.70491i	−0.701048	−	0.713114i
$65$	15.0438	−	3.64959i	1.86596	−	0.452676i
$66$	3.01365	−	1.02501i	0.370955	−	0.126170i
$67$	−7.61507	−	3.00180i	−0.930328	−	0.366728i
$67$	−7.61507	−	3.00180i	−0.930328	−	0.366728i
$68$	3.18159	+	10.0513i	0.385824	+	1.21890i
$69$	4.46076	−	1.95243i	0.537013	−	0.235045i
$70$	−4.11814	+	0.0431516i	−0.492212	+	0.00515760i
$71$	0.00404944	−	0.00208763i	0.000480580	−	0.000247756i	−0.457986	−	0.888959i	$-0.651429\pi$
$71$	0.00404944	−	0.00208763i	0.000480580	−	0.000247756i	0.458467	+	0.888712i	$0.348399\pi$
$72$	−2.77707	+	8.01797i	−0.327281	+	0.944927i
$73$	7.73998	−	0.739078i	0.905896	−	0.0865026i	0.368302	−	0.929706i	$-0.379939\pi$
$73$	7.73998	−	0.739078i	0.905896	−	0.0865026i	0.537594	+	0.843204i	$0.319333\pi$
$74$	2.92236	+	2.24901i	0.339717	+	0.261443i
$75$	3.68106	−	4.53135i	0.425052	−	0.523235i
$76$	0.241148	+	11.5057i	0.0276616	+	1.31979i
$77$	−0.808573	−	1.02818i	−0.0921455	−	0.117173i
$78$	−12.7530	+	3.02167i	−1.44399	+	0.342137i
$79$	−13.1272	+	4.54337i	−1.47693	+	0.511169i	−0.942547	−	0.334075i	$-0.891576\pi$
$79$	−13.1272	+	4.54337i	−1.47693	+	0.511169i	−0.534381	+	0.845244i	$0.679455\pi$
$80$	−4.74757	−	10.5542i	−0.530794	−	1.17999i
$81$	8.92742	−	1.14065i	0.991936	−	0.126739i
$82$	3.79440	−	1.78113i	0.419022	−	0.196693i
$83$	0.00396083	−	0.00556221i	0.000434758	−	0.000610532i	−0.814359	−	0.580362i	$-0.802911\pi$
$83$	0.00396083	−	0.00556221i	0.000434758	−	0.000610532i	0.814793	+	0.579752i	$0.196850\pi$
$84$	3.48671	−	0.0178742i	0.380432	−	0.00195023i
$85$	−0.725687	+	15.2340i	−0.0787118	+	1.65236i
$86$	13.8986	+	9.67930i	1.49873	+	1.04375i
$87$	−0.366551	−	0.196376i	−0.0392983	−	0.0210537i
$88$	1.73687	−	3.23938i	0.185151	−	0.345320i
$89$	11.8014	−	1.69678i	1.25094	−	0.179859i	0.515171	−	0.857087i	$-0.327728\pi$
$89$	11.8014	−	1.69678i	1.25094	−	0.179859i	0.735772	+	0.677229i	$0.236819\pi$
$90$	−7.79045	+	9.48579i	−0.821185	+	0.999890i
$91$	2.91164	+	4.53060i	0.305223	+	0.474936i
$92$	2.22804	−	5.16234i	0.232289	−	0.538211i
$93$	0.514130	+	2.27593i	0.0533127	+	0.236003i
$94$	13.0850	+	3.69363i	1.34961	+	0.380969i
$95$	−5.44496	+	15.7322i	−0.558641	+	1.61409i
$96$	3.97158	+	8.95693i	0.405348	+	0.914162i
$97$	−2.92429	−	5.06502i	−0.296917	−	0.514275i	0.678512	−	0.734589i	$-0.262625\pi$
$97$	−2.92429	−	5.06502i	−0.296917	−	0.514275i	−0.975429	+	0.220314i	$0.929292\pi$
$98$	2.85287	+	7.97160i	0.288184	+	0.805253i
$99$	−3.89665	−	0.123407i	−0.391628	−	0.0124029i
$100$	−0.461791	−	6.72541i	−0.0461791	−	0.672541i
$101$	14.5279	+	3.52443i	1.44558	+	0.350693i	0.880383	−	0.474264i	$-0.157286\pi$
$101$	14.5279	+	3.52443i	1.44558	+	0.350693i	0.565195	+	0.824957i	$0.308801\pi$
$102$	0.683408	−	12.8942i	0.0676675	−	1.27672i
$103$	1.03275	+	5.35843i	0.101760	+	0.527982i	0.996656	+	0.0817074i	$0.0260373\pi$
$103$	1.03275	+	5.35843i	0.101760	+	0.527982i	−0.894896	+	0.446274i	$0.852751\pi$
$104$	−8.38658	+	12.5973i	−0.822372	+	1.23526i
$105$	4.73983	+	1.72496i	0.462560	+	0.168339i
$106$	−2.45158	+	13.4785i	−0.238118	+	1.30914i
$107$	−3.10491	+	6.79881i	−0.300163	+	0.657266i	−0.998274	−	0.0587237i	$-0.981297\pi$
$107$	−3.10491	+	6.79881i	−0.300163	+	0.657266i	0.698111	+	0.715990i	$0.254024\pi$
$108$	6.63856	−	7.99560i	0.638795	−	0.769377i
$109$	−2.57335	+	2.96981i	−0.246482	+	0.284456i	−0.865487	−	0.500932i	$-0.832991\pi$
$109$	−2.57335	+	2.96981i	−0.246482	+	0.284456i	0.619004	+	0.785387i	$0.287536\pi$
$110$	3.98176	−	3.52393i	0.379645	−	0.335993i
$111$	−2.38127	−	3.83757i	−0.226021	−	0.364246i
$112$	2.92963	−	2.76175i	0.276824	−	0.260961i
$113$	−4.57675	+	3.25909i	−0.430545	+	0.306590i	−0.774707	−	0.632321i	$-0.782102\pi$
$113$	−4.57675	+	3.25909i	−0.430545	+	0.306590i	0.344162	+	0.938910i	$0.388163\pi$
$114$	4.68111	−	13.2946i	0.438426	−	1.24515i
$115$	5.61289	−	5.88663i	0.523405	−	0.548931i
$116$	−0.464161	+	0.122958i	−0.0430962	+	0.0114163i
$117$	15.9226	+	2.03084i	1.47205	+	0.187751i
$118$	−12.7802	−	6.42004i	−1.17651	−	0.591013i
$119$	−5.09099	+	1.49485i	−0.466690	+	0.137033i
$120$	0.895244	+	14.1454i	0.0817242	+	1.29130i
$121$	−9.14294	−	1.76216i	−0.831177	−	0.160196i
$122$	6.16659	−	3.26133i	0.558297	−	0.295267i
$123$	−5.11754	+	0.407034i	−0.461433	+	0.0367010i
$124$	2.22693	+	1.51648i	0.199984	+	0.136184i
$125$	−1.32812	+	4.52316i	−0.118791	+	0.404564i
$126$	−4.00504	−	1.48187i	−0.356797	−	0.132015i
$127$	−4.32114	−	4.53188i	−0.383439	−	0.402139i	0.503523	−	0.863982i	$-0.332037\pi$
$127$	−4.32114	−	4.53188i	−0.383439	−	0.402139i	−0.886962	+	0.461843i	$0.847188\pi$
$128$	10.4089	+	4.43339i	0.920025	+	0.391860i
$129$	−11.7634	−	17.0855i	−1.03571	−	1.50429i
$130$	−17.6989	+	12.8849i	−1.55230	+	1.13008i
$131$	2.05198	−	14.2718i	0.179282	−	1.24693i	−0.679147	−	0.734002i	$-0.737650\pi$
$131$	2.05198	−	14.2718i	0.179282	−	1.24693i	0.858429	−	0.512932i	$-0.171441\pi$
$132$	−3.38702	+	2.96540i	−0.294802	+	0.258105i
$133$	−5.79174			−0.502207
$134$	11.5744	−	0.182752i	0.999875	−	0.0157873i
$135$	13.0186	−	7.51820i	1.12046	−	0.647064i
$136$	−9.58046	−	11.4245i	−0.821517	−	0.979641i
$137$	−17.3512	−	2.49472i	−1.48241	−	0.213139i	−0.646884	−	0.762588i	$-0.723928\pi$
$137$	−17.3512	−	2.49472i	−1.48241	−	0.213139i	−0.835527	+	0.549450i	$0.814837\pi$
$138$	−4.77868	+	4.95833i	−0.406788	+	0.422081i
$139$	13.2334	−	6.04351i	1.12245	−	0.512604i	0.234299	−	0.972164i	$-0.424720\pi$
$139$	13.2334	−	6.04351i	1.12245	−	0.512604i	0.888146	+	0.459561i	$0.151993\pi$
$140$	5.36051	−	2.27748i	0.453045	−	0.192483i
$141$	−13.4097	−	9.87262i	−1.12930	−	0.831425i
$142$	−0.00416802	+	0.00491324i	−0.000349772	+	0.000412310i
$143$	−6.67156	−	1.95895i	−0.557903	−	0.163815i
$144$	−0.693843	−	11.9799i	−0.0578203	−	0.998327i
$145$	−0.691470	−	0.0660274i	−0.0574235	−	0.00548328i
$146$	−9.72010	+	5.14068i	−0.804442	+	0.425446i
$147$	0.164140	−	10.3683i	0.0135381	−	0.855161i
$148$	−5.03347	−	1.36407i	−0.413749	−	0.112126i
$149$	−2.83682	−	9.66132i	−0.232401	−	0.791486i	−0.990280	−	0.139090i	$-0.955582\pi$
$149$	−2.83682	−	9.66132i	−0.232401	−	0.791486i	0.757878	−	0.652396i	$-0.226236\pi$
$150$	−2.36843	+	7.90931i	−0.193382	+	0.645792i
$151$	−2.53711	+	4.92130i	−0.206467	+	0.400490i	−0.969219	−	0.246202i	$-0.920817\pi$
$151$	−2.53711	+	4.92130i	−0.206467	+	0.400490i	0.762752	+	0.646691i	$0.223848\pi$
$152$	−6.52070	−	14.9117i	−0.528899	−	1.20950i
$153$	−6.33936	+	14.4881i	−0.512507	+	1.17129i
$154$	1.61161	+	0.908084i	0.129867	+	0.0731755i
$155$	2.26076	+	3.17480i	0.181589	+	0.255006i
$156$	15.0427	−	10.8285i	1.20438	−	0.866974i
$157$	−0.822903	+	0.329441i	−0.0656748	+	0.0262922i	−0.404267	−	0.914641i	$-0.632473\pi$
$157$	−0.822903	+	0.329441i	−0.0656748	+	0.0262922i	0.338592	+	0.940933i	$0.390049\pi$
$158$	14.7112	−	13.0197i	1.17036	−	1.03579i
$159$	8.61821	−	14.3960i	0.683469	−	1.14168i
$160$	11.8989	+	11.2373i	0.940691	+	0.888383i
$161$	2.57398	+	1.17550i	0.202858	+	0.0926423i
$162$	−11.0559	+	6.30610i	−0.868634	+	0.495454i
$163$	21.8744	+	12.6292i	1.71333	+	0.989193i	0.929975	+	0.367623i	$0.119828\pi$
$163$	21.8744	+	12.6292i	1.71333	+	0.989193i	0.783358	+	0.621571i	$0.213505\pi$
$164$	−3.99991	+	4.37499i	−0.312341	+	0.341629i
$165$	−6.08327	+	2.32434i	−0.473582	+	0.180949i
$166$	−0.00217821	+	0.00940788i	−0.000169062	+	0.000730193i
$167$	−4.55036	+	18.7568i	−0.352117	+	1.45145i	0.470272	+	0.882521i	$0.344156\pi$
$167$	−4.55036	+	18.7568i	−0.352117	+	1.45145i	−0.822389	+	0.568925i	$0.807359\pi$
$168$	−4.54865	+	1.90388i	−0.350936	+	0.146888i
$169$	14.5088	+	5.80844i	1.11606	+	0.446803i
$170$	−7.26758	−	20.3073i	−0.557398	−	1.55750i
$171$	−11.0950	+	13.2245i	−0.848457	+	1.01130i
$172$	−23.3905	−	5.15800i	−1.78351	−	0.393294i
$173$	0.576793	+	0.199630i	0.0438528	+	0.0151776i	0.348906	−	0.937158i	$-0.386553\pi$
$173$	0.576793	+	0.199630i	0.0438528	+	0.0151776i	−0.305054	+	0.952335i	$0.598674\pi$
$174$	0.585116	+	0.0590333i	0.0443575	+	0.00447531i
$175$	3.38883	−	0.161430i	0.256171	−	0.0122029i
$176$	−0.523539	+	5.17171i	−0.0394632	+	0.389832i
$177$	11.8855	+	12.8670i	0.893371	+	0.967141i
$178$	−14.5132	+	8.58318i	−1.08781	+	0.643337i
$179$	−2.00232	−	13.9264i	−0.149660	−	1.04091i	−0.916776	−	0.399401i	$-0.869218\pi$
$179$	−2.00232	−	13.9264i	−0.149660	−	1.04091i	0.767116	−	0.641508i	$-0.221691\pi$
$180$	5.06865	−	16.6027i	0.377795	−	1.23750i
$181$	2.28581	+	1.79758i	0.169903	+	0.133613i	0.699490	−	0.714643i	$-0.253411\pi$
$181$	2.28581	+	1.79758i	0.169903	+	0.133613i	−0.529587	+	0.848256i	$0.677653\pi$
$182$	−6.25000	−	4.35264i	−0.463281	−	0.322639i
$183$	−8.47492	+	1.08188i	−0.626484	+	0.0799749i
$184$	−0.128539	+	7.95055i	−0.00947599	+	0.586122i
$185$	−6.14521	−	4.37599i	−0.451805	−	0.321729i
$186$	−1.89963	−	2.69810i	−0.139288	−	0.197835i
$187$	3.70361	−	5.76293i	0.270835	−	0.421427i
$188$	−19.0985	+	2.22844i	−1.39290	+	0.162525i
$189$	3.95306	+	3.42458i	0.287543	+	0.249101i
$190$	−1.36659	−	23.5038i	−0.0991428	−	1.70515i
$191$	−19.9525	+	15.6908i	−1.44371	+	1.13535i	−0.477178	+	0.878807i	$0.658340\pi$
$191$	−19.9525	+	15.6908i	−1.44371	+	1.13535i	−0.966533	+	0.256541i	$0.917417\pi$
$192$	−10.0230	−	9.56764i	−0.723346	−	0.690485i
$193$	−8.15387	−	9.41007i	−0.586929	−	0.677352i	0.382151	−	0.924100i	$-0.375183\pi$
$193$	−8.15387	−	9.41007i	−0.586929	−	0.677352i	−0.969080	+	0.246748i	$0.920638\pi$
$194$	6.55477	+	5.04448i	0.470605	+	0.362172i
$195$	25.8427	−	7.14578i	1.85064	−	0.511720i
$196$	−8.02904	−	8.88286i	−0.573503	−	0.634490i
$197$	−8.21813	−	15.9409i	−0.585517	−	1.13575i	−0.976534	−	0.215362i	$-0.930907\pi$
$197$	−8.21813	−	15.9409i	−0.585517	−	1.13575i	0.391017	−	0.920384i	$-0.372123\pi$
$198$	5.16077	−	1.94028i	0.366760	−	0.137889i
$199$	13.9703	−	3.38917i	0.990331	−	0.240252i	0.292306	−	0.956325i	$-0.405577\pi$
$199$	13.9703	−	3.38917i	0.990331	−	0.240252i	0.698025	+	0.716073i	$0.254062\pi$
$200$	4.23098	+	8.54328i	0.299176	+	0.604101i
$201$	−13.3482	−	4.77767i	−0.941508	−	0.336991i
$202$	−20.8936	+	3.22784i	−1.47007	+	0.227110i
$203$	−0.0569725	−	0.234844i	−0.00399868	−	0.0164828i
$204$	6.06090	+	17.2256i	0.424348	+	1.20603i
$205$	−7.62202	+	3.92942i	−0.532345	+	0.274443i
$206$	−4.24015	−	6.44824i	−0.295425	−	0.449270i
$207$	7.61495	−	3.62542i	0.529276	−	0.251984i
$208$	4.16985	−	20.9920i	0.289127	−	1.45553i
$209$	5.65123	−	4.89682i	0.390904	−	0.338720i
$210$	−7.12686	+	0.301276i	−0.491800	+	0.0207900i
$211$	−11.9712	−	15.2226i	−0.824128	−	1.04796i	−0.998001	−	0.0631959i	$-0.979871\pi$
$211$	−11.9712	−	15.2226i	−0.824128	−	1.04796i	0.173873	−	0.984768i	$-0.444372\pi$
$212$	−4.06442	−	18.9430i	−0.279145	−	1.30101i
$213$	0.00689544	−	0.00383685i	0.000472467	−	0.000262897i
$214$	0.392295	−	10.5629i	0.0268167	−	0.722065i
$215$	−29.1492	−	18.7330i	−1.98796	−	1.27758i
$216$	−4.36647	+	14.0333i	−0.297100	+	0.954846i
$217$	−0.786516	+	1.10451i	−0.0533922	+	0.0749789i
$218$	1.76250	−	5.27043i	0.119371	−	0.356958i
$219$	13.3586	−	1.70532i	0.902691	−	0.115235i
$220$	−3.30489	+	6.75445i	−0.222815	+	0.455385i
$221$	−17.4352	+	22.1706i	−1.17282	+	1.49136i
$222$	5.18286	+	3.73266i	0.347851	+	0.250520i
$223$	−12.6630	+	1.82066i	−0.847976	+	0.121921i	−0.552586	−	0.833456i	$-0.686359\pi$
$223$	−12.6630	+	1.82066i	−0.847976	+	0.121921i	−0.295390	+	0.955377i	$0.595450\pi$
$224$	−2.34048	+	5.19058i	−0.156380	+	0.346811i
$225$	6.12325	−	8.04710i	0.408217	−	0.536473i
$226$	4.22558	−	6.72913i	0.281082	−	0.447615i
$227$	0.536922	+	11.2714i	0.0356367	+	0.748107i	0.944004	+	0.329934i	$0.107027\pi$
$227$	0.536922	+	11.2714i	0.0356367	+	0.748107i	−0.908367	+	0.418173i	$0.862670\pi$
$228$	1.05049	+	19.9051i	0.0695706	+	1.31825i
$229$	−7.01219	+	20.2604i	−0.463379	+	1.33885i	0.435319	+	0.900276i	$0.356636\pi$
$229$	−7.01219	+	20.2604i	−0.463379	+	1.33885i	−0.898698	+	0.438569i	$0.855486\pi$
$230$	−4.16302	+	10.7230i	−0.274502	+	0.707055i
$231$	−1.45635	−	1.73548i	−0.0958210	−	0.114186i
$232$	0.540496	−	0.411086i	0.0354853	−	0.0269891i
$233$	1.64739	−	4.11498i	0.107924	−	0.269581i	−0.864569	−	0.502515i	$-0.832408\pi$
$233$	1.64739	−	4.11498i	0.107924	−	0.269581i	0.972493	+	0.232934i	$0.0748325\pi$
$234$	−21.9115	+	5.93270i	−1.43240	+	0.387832i
$235$	−27.0313	−	6.55773i	−1.76333	−	0.427779i
$236$	20.1705	+	1.50029i	1.31299	+	0.0976606i
$237$	−22.4756	+	8.58762i	−1.45994	+	0.557826i
$238$	5.84938	−	4.70002i	0.379159	−	0.304657i
$239$	7.59649	−	13.1575i	0.491376	−	0.851089i	−0.508574	−	0.861018i	$-0.669827\pi$
$239$	7.59649	−	13.1575i	0.491376	−	0.851089i	0.999951	+	0.00992922i	$0.00316062\pi$
$240$	−8.79955	−	18.0099i	−0.568009	−	1.16254i
$241$	7.19799	−	15.7614i	0.463664	−	1.01528i	−0.522974	−	0.852349i	$-0.675177\pi$
$241$	7.19799	−	15.7614i	0.463664	−	1.01528i	0.986637	−	0.162933i	$-0.0520954\pi$
$242$	12.9033	−	2.62741i	0.829453	−	0.168896i
$243$	15.3922	−	2.46584i	0.987410	−	0.158184i
$244$	−6.30282	+	7.58951i	−0.403496	+	0.485869i
$245$	−6.43766	−	16.0805i	−0.411287	−	1.02734i
$246$	6.47078	−	3.29221i	0.412562	−	0.209904i
$247$	−25.0788	+	17.8585i	−1.59572	+	1.13631i
$248$	−3.72922	−	0.781475i	−0.236806	−	0.0496237i
$249$	0.00655088	−	0.00984709i	0.000415145	−	0.000624034i
$250$	−0.703218	−	6.62957i	−0.0444754	−	0.419291i
$251$	−12.6229	−	6.50754i	−0.796748	−	0.410752i	0.0112502	−	0.999937i	$-0.496419\pi$
$251$	−12.6229	−	6.50754i	−0.796748	−	0.410752i	−0.807999	+	0.589184i	$0.799449\pi$
$252$	6.03514	−	0.222777i	0.380178	−	0.0140336i
$253$	−3.50541	+	1.02928i	−0.220383	+	0.0647103i
$254$	8.09337	+	3.59411i	0.507823	+	0.225515i
$255$	−0.418141	+	26.4128i	−0.0261850	+	1.65403i
$256$	−15.9990	−	0.182007i	−0.999935	−	0.0113754i
$257$	−0.547378	+	5.73240i	−0.0341445	+	0.357577i	0.962213	+	0.272299i	$0.0877840\pi$
$257$	−0.547378	+	5.73240i	−0.0341445	+	0.357577i	−0.996357	+	0.0852783i	$0.972822\pi$
$258$	24.5935	+	15.9919i	1.53112	+	0.995612i
$259$	0.739427	−	2.51826i	0.0459457	−	0.156477i
$260$	16.1890	−	26.3906i	1.00400	−	1.63667i
$261$	−0.645368	−	0.319794i	−0.0399473	−	0.0197947i
$262$	5.01471	+	19.7647i	0.309810	+	1.22107i
$263$	−2.28425	−	5.00182i	−0.140853	−	0.308425i	0.826038	−	0.563614i	$-0.190590\pi$
$263$	−2.28425	−	5.00182i	−0.140853	−	0.308425i	−0.966891	+	0.255189i	$0.917862\pi$
$264$	2.82860	−	5.70351i	0.174088	−	0.351027i
$265$	3.98861	−	27.7414i	0.245019	−	1.70414i
$266$	7.57172	−	3.12370i	0.464252	−	0.191527i
$267$	20.3369	−	3.58672i	1.24460	−	0.219504i
$268$	−15.0330	+	6.48142i	−0.918287	+	0.395916i
$269$			12.7577i			0.777849i	0.921270	+	0.388924i	$0.127153\pi$
$269$			12.7577i			0.777849i	−0.921270	+	0.388924i	$0.872847\pi$
$270$	−12.9647	+	16.8502i	−0.789009	+	1.02547i
$271$	13.9760	+	2.00944i	0.848980	+	0.122065i	0.553054	−	0.833146i	$-0.313462\pi$
$271$	13.9760	+	2.00944i	0.848980	+	0.122065i	0.295927	+	0.955211i	$0.404372\pi$
$272$	18.6865	+	9.76848i	1.13303	+	0.592301i
$273$	5.28983	+	7.68308i	0.320155	+	0.465001i
$274$	24.0292	−	6.09672i	1.45166	−	0.368316i
$275$	−3.17013	+	3.02271i	−0.191166	+	0.182276i
$276$	3.57310	−	9.05950i	0.215075	−	0.545318i
$277$	−14.5200	−	4.26345i	−0.872421	−	0.256166i	−0.185276	−	0.982686i	$-0.559318\pi$
$277$	−14.5200	−	4.26345i	−0.872421	−	0.256166i	−0.687145	+	0.726521i	$0.741136\pi$
$278$	−14.0410	+	15.0382i	−0.842123	+	0.901929i
$279$	1.01527	+	3.91175i	0.0607824	+	0.234190i
$280$	−5.77962	+	5.86855i	−0.345399	+	0.350713i
$281$	0.291942	−	1.51474i	0.0174158	−	0.0903618i	−0.972181	−	0.234232i	$-0.924743\pi$
$281$	0.291942	−	1.51474i	0.0174158	−	0.0903618i	0.989597	+	0.143870i	$0.0459547\pi$
$282$	22.8557	+	5.67441i	1.36103	+	0.337906i
$283$	−1.28290	−	4.36916i	−0.0762606	−	0.259720i	0.912534	−	0.409000i	$-0.134122\pi$
$283$	−1.28290	−	4.36916i	−0.0762606	−	0.259720i	−0.988795	+	0.149280i	$0.952304\pi$
$284$	0.00279909	−	0.00867120i	0.000166095	−	0.000514541i
$285$	−8.56062	+	27.5347i	−0.507088	+	1.63102i
$286$	9.77847	−	1.03723i	0.578213	−	0.0613327i
$287$	−2.15914	−	2.05873i	−0.127450	−	0.121523i
$288$	7.36831	+	15.2875i	0.434182	+	0.900825i
$289$	−6.25765	−	8.78764i	−0.368097	−	0.516920i
$290$	0.939591	−	0.286616i	0.0551747	−	0.0168307i
$291$	−5.34113	−	8.60755i	−0.313103	−	0.504584i
$292$	9.93483	−	11.9630i	0.581392	−	0.700081i
$293$	3.59633	+	3.11623i	0.210100	+	0.182052i	0.753553	−	0.657387i	$-0.228338\pi$
$293$	3.59633	+	3.11623i	0.210100	+	0.182052i	−0.543454	+	0.839439i	$0.682884\pi$
$294$	5.37741	+	13.6433i	0.313617	+	0.795693i
$295$	26.6152	+	12.1547i	1.54960	+	0.707676i
$296$	7.31610	−	0.931451i	0.425240	−	0.0541395i
$297$	−6.75258		0.000748072i	−0.391824		4.34075e-5i
$298$	8.91938	+	11.1005i	0.516686	+	0.643037i
$299$	14.7702	−	2.84672i	0.854182	−	0.164630i
$300$	−1.16946	−	11.6175i	−0.0675189	−	0.670735i
$301$	2.84197	−	11.7148i	0.163809	−	0.675228i
$302$	0.662596	−	7.80213i	0.0381281	−	0.448962i
$303$	25.3442	+	5.30210i	1.45599	+	0.304598i
$304$	16.5671	+	15.9776i	0.950191	+	0.916380i
$305$	−12.3593	+	7.13566i	−0.707692	+	0.408586i
$306$	0.473682	−	22.3598i	0.0270786	−	1.27822i
$307$	4.17534	+	1.44510i	0.238300	+	0.0824763i	0.443608	−	0.896221i	$-0.353698\pi$
$307$	4.17534	+	1.44510i	0.238300	+	0.0824763i	−0.205308	+	0.978697i	$0.565820\pi$
$308$	−2.59667	−	0.317963i	−0.147959	−	0.0181176i
$309$	2.08269	+	9.21957i	0.118480	+	0.524483i
$310$	−4.66786	−	2.93120i	−0.265116	−	0.166481i
$311$	17.1982	−	11.0526i	0.975219	−	0.626735i	0.0470494	−	0.998893i	$-0.485018\pi$
$311$	17.1982	−	11.0526i	0.975219	−	0.626735i	0.928170	+	0.372157i	$0.121382\pi$
$312$	−13.8256	+	22.2695i	−0.782719	+	1.26076i
$313$	4.20846	+	29.2705i	0.237876	+	1.65446i	0.662476	+	0.749083i	$0.269506\pi$
$313$	4.20846	+	29.2705i	0.237876	+	1.65446i	−0.424600	+	0.905381i	$0.639585\pi$
$314$	0.898127	−	0.874511i	0.0506843	−	0.0493515i
$315$	8.30039	+	2.72543i	0.467674	+	0.153561i
$316$	−12.2104	+	24.9554i	−0.686889	+	1.40385i
$317$	−2.38069	−	0.113406i	−0.133713	−	0.00636953i	−0.0193812	−	0.999812i	$-0.506170\pi$
$317$	−2.38069	−	0.113406i	−0.133713	−	0.00636953i	−0.114332	+	0.993443i	$0.536473\pi$
$318$	−3.50255	+	23.4685i	−0.196413	+	1.31605i
$319$	0.254147	+	0.180977i	0.0142295	+	0.0101328i
$320$	−21.6165	−	8.27329i	−1.20840	−	0.462491i
$321$	−5.00109	+	11.9408i	−0.279134	+	0.666469i
$322$	−3.99904	−	0.148520i	−0.222858	−	0.00827670i
$323$	−9.92074	−	28.6641i	−0.552005	−	1.59491i
$324$	11.0526	−	14.2070i	0.614034	−	0.789280i
$325$	14.1762	−	11.1483i	0.786354	−	0.618396i
$326$	−35.4084	−	4.71284i	−1.96109	−	0.261020i
$327$	−4.29153	+	5.28284i	−0.237322	+	0.292142i
$328$	2.86961	−	7.87686i	0.158448	−	0.434927i
$329$	−0.919851	−	9.63312i	−0.0507131	−	0.531091i
$330$	6.69924	−	6.31961i	0.368781	−	0.347883i
$331$	5.33440	+	10.3473i	0.293205	+	0.568739i	0.988720	−	0.149773i	$-0.0478542\pi$
$331$	5.33440	+	10.3473i	0.293205	+	0.568739i	−0.695515	+	0.718511i	$0.744824\pi$
$332$	−0.00222638	−	0.0134740i	−0.000122189	−	0.000739482i
$333$	−4.33354	−	6.51249i	−0.237477	−	0.356882i
$334$	−4.16744	−	26.9756i	−0.228032	−	1.47604i
$335$	−23.6487	+	1.25242i	−1.29207	+	0.0684271i
$336$	4.91976	−	4.94227i	0.268395	−	0.269623i
$337$	3.46237	+	14.2721i	0.188607	+	0.777449i	0.984984	+	0.172648i	$0.0552323\pi$
$337$	3.46237	+	14.2721i	0.188607	+	0.777449i	−0.796377	+	0.604801i	$0.793253\pi$
$338$	−22.1005	+	0.231578i	−1.20211	+	0.0125962i
$339$	−7.74386	+	5.89387i	−0.420589	+	0.320111i
$340$	20.4537	+	22.6287i	1.10925	+	1.22722i
$341$	−0.166408	−	1.74270i	−0.00901148	−	0.0943725i
$342$	7.37238	−	23.2728i	0.398653	−	1.25845i
$343$	9.87903	−	8.56022i	0.533417	−	0.462209i
$344$	33.3610	−	5.87216i	1.79871	−	0.316606i
$345$	9.39303	−	10.4996i	0.505704	−	0.565280i
$346$	−0.861728	+	0.0501037i	−0.0463268	+	0.00269359i
$347$	3.55954	+	10.2846i	0.191086	+	0.552107i	0.999325	−	0.0367482i	$-0.0116999\pi$
$347$	3.55954	+	10.2846i	0.191086	+	0.552107i	−0.808238	+	0.588855i	$0.799579\pi$
$348$	−0.796779	+	0.238399i	−0.0427118	+	0.0127795i
$349$	7.36480	+	4.73307i	0.394228	+	0.253355i	0.722705	−	0.691157i	$-0.242899\pi$
$349$	7.36480	+	4.73307i	0.394228	+	0.253355i	−0.328476	+	0.944512i	$0.606535\pi$
$350$	−4.34326	+	2.03877i	−0.232157	+	0.108977i
$351$	27.6766	+	2.63970i	1.47727	+	0.140897i
$352$	−2.10486	−	7.04350i	−0.112189	−	0.375420i
$353$	−26.2268	−	1.24933i	−1.39591	−	0.0664954i	−0.663916	−	0.747807i	$-0.731107\pi$
$353$	−26.2268	−	1.24933i	−1.39591	−	0.0664954i	−0.731993	+	0.681312i	$0.761410\pi$
$354$	−22.4780	−	10.4111i	−1.19469	−	0.553343i
$355$	0.00814803	−	0.0103611i	0.000432452	−	0.000549908i
$356$	14.3443	−	19.0486i	0.760246	−	1.00957i
$357$	−8.73115	+	2.86794i	−0.462102	+	0.151788i
$358$	10.1287	+	17.1265i	0.535320	+	0.905164i
$359$	−6.44684	+	4.14313i	−0.340251	+	0.218666i	−0.699596	−	0.714539i	$-0.746637\pi$
$359$	−6.44684	+	4.14313i	−0.340251	+	0.218666i	0.359345	+	0.933205i	$0.383000\pi$
$360$	2.32808	+	24.4390i	0.122701	+	1.28805i
$361$	−0.671365	−	14.0937i	−0.0353350	−	0.741773i
$362$	−3.95781	−	1.11721i	−0.208018	−	0.0587192i
$363$	−15.9250	−	2.54758i	−0.835846	−	0.133713i
$364$	10.5184	+	2.31948i	0.551312	+	0.121574i
$365$	19.4814	−	11.2476i	1.01970	−	0.588726i
$366$	10.4960	−	5.98522i	0.548636	−	0.312852i
$367$	9.79947	−	24.4779i	0.511528	−	1.27774i	−0.417819	−	0.908530i	$-0.637205\pi$
$367$	9.79947	−	24.4779i	0.511528	−	1.27774i	0.929348	−	0.369206i	$-0.120370\pi$
$368$	−4.11999	−	10.4633i	−0.214769	−	0.545438i
$369$	−8.83696	+	0.986206i	−0.460034	+	0.0513399i
$370$	10.3940	+	2.40652i	0.540356	+	0.125109i
$371$	9.57424	−	1.84528i	0.497070	−	0.0958024i
$372$	3.93864	+	2.50277i	0.204209	+	0.129763i
$373$	−13.5683	+	23.5009i	−0.702539	+	1.21683i	0.265034	+	0.964239i	$0.414617\pi$
$373$	−13.5683	+	23.5009i	−0.702539	+	1.21683i	−0.967573	+	0.252593i	$0.918717\pi$
$374$	−1.73368	+	9.53155i	−0.0896464	+	0.492865i
$375$	−2.05035	+	7.90346i	−0.105880	+	0.408133i
$376$	23.7662	−	13.2139i	1.22565	−	0.681453i
$377$	−0.970825	−	0.841224i	−0.0500000	−	0.0433253i
$378$	−7.01496	−	2.34502i	−0.360810	−	0.120615i
$379$	3.41562	+	8.53181i	0.175449	+	0.438250i	0.989861	−	0.142036i	$-0.0453650\pi$
$379$	3.41562	+	8.53181i	0.175449	+	0.438250i	−0.814413	+	0.580286i	$0.802941\pi$
$380$	14.4631	+	29.9902i	0.741940	+	1.53847i
$381$	−7.72999	−	7.60774i	−0.396019	−	0.389756i
$382$	17.6219	−	31.2742i	0.901613	−	1.60013i
$383$	20.0163	+	19.0855i	1.02278	+	0.975223i	0.999700	−	0.0245105i	$-0.00780271\pi$
$383$	20.0163	+	19.0855i	1.02278	+	0.975223i	0.0230849	+	0.999734i	$0.492651\pi$
$384$	18.2635	+	7.10231i	0.932008	+	0.362438i
$385$	−3.36372	−	1.73412i	−0.171431	−	0.0883788i
$386$	15.7350	+	7.90439i	0.800891	+	0.402323i
$387$	−21.3045	−	28.9307i	−1.08297	−	1.47063i
$388$	−11.2899	−	3.05957i	−0.573159	−	0.155326i
$389$	−0.958839	+	4.97493i	−0.0486151	+	0.252239i	−0.998103	−	0.0615643i	$-0.980391\pi$
$389$	−0.958839	+	4.97493i	−0.0486151	+	0.252239i	0.949488	+	0.313803i	$0.101603\pi$
$390$	−29.9310	+	23.2799i	−1.51562	+	1.17882i
$391$	−1.40870	+	14.7525i	−0.0712408	+	0.746067i
$392$	15.2875	+	7.28248i	0.772134	+	0.367821i
$393$	2.76712	−	24.8199i	0.139583	−	1.25200i
$394$	19.3414	+	16.4078i	0.974404	+	0.826611i
$395$	−29.0870	+	27.7344i	−1.46352	+	1.39547i
$396$	−5.70037	+	5.31998i	−0.286454	+	0.267339i
$397$	2.92001	+	6.39392i	0.146551	+	0.320902i	0.968645	−	0.248450i	$-0.0799213\pi$
$397$	2.92001	+	6.39392i	0.146551	+	0.320902i	−0.822094	+	0.569352i	$0.807194\pi$
$398$	−16.4360	+	11.9655i	−0.823860	+	0.599776i
$399$	−10.0265	+	0.318652i	−0.501954	+	0.0159525i
$400$	−10.1390	−	8.88697i	−0.506950	−	0.444349i
$401$			36.5727i			1.82635i	0.407564	+	0.913177i	$0.366378\pi$
$401$			36.5727i			1.82635i	−0.407564	+	0.913177i	$0.633622\pi$
$402$	20.0273	−	0.953179i	0.998869	−	0.0475402i
$403$			7.20781i			0.359046i
$404$	25.5740	−	15.4886i	1.27235	−	0.770585i
$405$	22.1238	−	13.7316i	1.09934	−	0.682329i
$406$	0.201142	+	0.276291i	0.00998251	+	0.0137121i
$407$	1.40766	+	3.08234i	0.0697749	+	0.152786i
$408$	−17.2140	−	19.2507i	−0.852221	−	0.953052i
$409$	12.1379	−	11.5735i	0.600180	−	0.572271i	−0.327871	−	0.944722i	$-0.606331\pi$
$409$	12.1379	−	11.5735i	0.600180	−	0.572271i	0.928052	+	0.372452i	$0.121483\pi$
$410$	7.84521	−	9.24790i	0.387448	−	0.456721i
$411$	−30.1752	−	3.36417i	−1.48843	−	0.165942i
$412$	9.02106	+	6.14311i	0.444436	+	0.302649i
$413$	−0.967600	+	10.1332i	−0.0476125	+	0.498620i
$414$	−7.99994	+	8.84666i	−0.393175	+	0.434789i
$415$	0.00373881	−	0.0193988i	0.000183531	−	0.000952249i
$416$	5.87041	+	29.6925i	0.287820	+	1.45579i
$417$	22.5769	−	11.1905i	1.10560	−	0.547999i
$418$	−4.74699	+	9.44969i	−0.232183	+	0.462199i
$419$	10.0967	+	5.20521i	0.493256	+	0.254291i	0.686861	−	0.726788i	$-0.258988\pi$
$419$	10.0967	+	5.20521i	0.493256	+	0.254291i	−0.193606	+	0.981079i	$0.562018\pi$
$420$	9.15468	−	4.23765i	0.446703	−	0.206776i
$421$	9.96887	+	9.50529i	0.485853	+	0.463260i	0.892970	−	0.450116i	$-0.148617\pi$
$421$	9.96887	+	9.50529i	0.485853	+	0.463260i	−0.407117	+	0.913376i	$0.633466\pi$
$422$	23.8604	+	13.4444i	1.16150	+	0.654465i
$423$	−23.7578	−	16.3535i	−1.15514	−	0.795133i
$424$	15.5302	+	22.5727i	0.754215	+	1.09623i
$425$	6.60371	+	16.4953i	0.320327	+	0.800138i
$426$	−0.00694526	+	0.00873500i	−0.000336499	+	0.000423212i
$427$	−3.75227	−	3.25136i	−0.181585	−	0.157344i
$428$	5.18411	+	14.0208i	0.250583	+	0.677720i
$429$	−11.6574	−	3.02422i	−0.562825	−	0.146011i
$430$	48.2110	+	8.76903i	2.32494	+	0.422880i
$431$	0.818229	−	1.41721i	0.0394127	−	0.0682648i	−0.845646	−	0.533744i	$-0.820785\pi$
$431$	0.818229	−	1.41721i	0.0394127	−	0.0682648i	0.885059	+	0.465479i	$0.154118\pi$
$432$	−1.86028	−	20.7012i	−0.0895028	−	0.995987i
$433$	−6.22065	+	1.19893i	−0.298946	+	0.0576170i	−0.336519	−	0.941677i	$-0.609249\pi$
$433$	−6.22065	+	1.19893i	−0.298946	+	0.0576170i	0.0375729	+	0.999294i	$0.488037\pi$
$434$	0.432535	−	1.86816i	0.0207623	−	0.0896743i
$435$	−1.20069	−	0.0762615i	−0.0575687	−	0.00365646i
$436$	0.538375	+	7.84077i	0.0257835	+	0.375505i
$437$	−6.01222	+	15.0178i	−0.287603	+	0.718399i
$438$	−16.5444	+	9.43421i	−0.790521	+	0.450784i
$439$	1.77590	−	1.02532i	0.0847592	−	0.0489357i	−0.457021	−	0.889456i	$-0.651084\pi$
$439$	1.77590	−	1.02532i	0.0847592	−	0.0489357i	0.541781	+	0.840520i	$0.317750\pi$
$440$	0.677649	−	10.6128i	0.0323056	−	0.505943i
$441$	−0.286289	−	17.9583i	−0.0136328	−	0.855159i
$442$	10.8361	−	38.3878i	0.515420	−	1.82592i
$443$	−1.63584	−	34.3406i	−0.0777213	−	1.63157i	−0.615255	−	0.788328i	$-0.710947\pi$
$443$	−1.63584	−	34.3406i	−0.0777213	−	1.63157i	0.537534	−	0.843242i	$-0.319356\pi$
$444$	−8.78887	−	2.08451i	−0.417101	−	0.0989265i
$445$	29.0189	−	18.6493i	1.37563	−	0.884064i
$446$	15.5728	−	9.20983i	0.737391	−	0.436098i
$447$	−5.44259	−	16.5694i	−0.257426	−	0.783705i
$448$	0.260300	−	8.04812i	0.0122980	−	0.380238i
$449$	4.13689	−	5.26048i	0.195232	−	0.248257i	−0.678575	−	0.734532i	$-0.737402\pi$
$449$	4.13689	−	5.26048i	0.195232	−	0.248257i	0.873806	+	0.486274i	$0.161644\pi$
$450$	−3.66502	+	13.8227i	−0.172771	+	0.651609i
$451$	3.84738	+	0.183273i	0.181166	+	0.00863000i
$452$	−1.89496	+	11.0762i	−0.0891316	+	0.520981i
$453$	−4.12142	+	8.65923i	−0.193641	+	0.406846i
$454$	−6.78101	−	14.4458i	−0.318249	−	0.677977i
$455$	13.1080	+	8.42397i	0.614510	+	0.394922i
$456$	−12.1089	−	25.4560i	−0.567051	−	1.19209i
$457$	−0.536866	−	1.55117i	−0.0251135	−	0.0725608i	0.931747	−	0.363107i	$-0.118284\pi$
$457$	−0.536866	−	1.55117i	−0.0251135	−	0.0725608i	−0.956861	+	0.290546i	$0.906163\pi$
$458$	−1.75994	−	30.2690i	−0.0822366	−	1.41438i
$459$	−10.1775	+	25.4302i	−0.475043	+	1.18698i
$460$	−0.340875	−	16.2638i	−0.0158934	−	0.758304i
$461$	−18.8190	+	16.3067i	−0.876487	+	0.759481i	−0.971760	−	0.235971i	$-0.924173\pi$
$461$	−18.8190	+	16.3067i	−0.876487	+	0.759481i	0.0952728	+	0.995451i	$0.469628\pi$
$462$	2.83995	+	1.48339i	0.132126	+	0.0690133i
$463$	−3.72874	−	39.0491i	−0.173289	−	1.81477i	−0.496060	−	0.868288i	$-0.665220\pi$
$463$	−3.72874	−	39.0491i	−0.173289	−	1.81477i	0.322771	−	0.946477i	$-0.395386\pi$
$464$	−0.484893	+	0.828935i	−0.0225106	+	0.0384823i
$465$	4.08845	+	5.37175i	0.189598	+	0.249109i
$466$	0.0656800	+	6.26814i	0.00304257	+	0.290366i
$467$	8.27046	+	34.0913i	0.382711	+	1.57756i	0.759023	+	0.651064i	$0.225677\pi$
$467$	8.27046	+	34.0913i	0.382711	+	1.57756i	−0.376311	+	0.926493i	$0.622808\pi$
$468$	25.4458	−	19.5737i	1.17623	−	0.904793i
$469$	−3.10266	−	7.63236i	−0.143267	−	0.352430i
$470$	38.8757	−	6.00589i	1.79320	−	0.277031i
$471$	−1.40647	+	0.615595i	−0.0648065	+	0.0283651i
$472$	−27.1787	+	8.91733i	−1.25100	+	0.410453i
$473$	7.13162	+	13.8334i	0.327912	+	0.636061i
$474$	24.7514	−	23.3488i	1.13687	−	1.07245i
$475$	1.84360	+	19.3071i	0.0845903	+	0.885870i
$476$	−5.11217	+	9.29928i	−0.234316	+	0.426232i
$477$	14.1276	−	25.3962i	0.646859	−	1.16281i
$478$	−2.83479	+	21.2983i	−0.129660	+	0.974162i
$479$	−17.7398	+	13.9507i	−0.810550	+	0.637424i	−0.934938	−	0.354810i	$-0.884546\pi$
$479$	−17.7398	+	13.9507i	−0.810550	+	0.637424i	0.124388	+	0.992234i	$0.460303\pi$
$480$	21.2174	+	18.7990i	0.968436	+	0.858054i
$481$	−4.56312	−	13.1843i	−0.208060	−	0.601151i
$482$	−0.909441	+	24.4875i	−0.0414239	+	1.11538i
$483$	4.52070	+	1.89338i	0.205699	+	0.0861518i
$484$	−15.4518	+	10.3941i	−0.702353	+	0.472459i
$485$	−13.7835	−	9.81521i	−0.625878	−	0.445686i
$486$	−18.7928	+	11.5253i	−0.852458	+	0.522796i
$487$	16.3986	+	0.781159i	0.743089	+	0.0353977i	0.415712	−	0.909496i	$-0.363532\pi$
$487$	16.3986	+	0.781159i	0.743089	+	0.0353977i	0.327377	+	0.944894i	$0.393835\pi$
$488$	4.14656	−	13.3214i	0.187706	−	0.603029i
$489$	38.5632	+	20.6598i	1.74389	+	0.934270i
$490$	17.0890	+	17.5505i	0.772001	+	0.792849i
$491$	−2.36174	−	16.4263i	−0.106584	−	0.741308i	−0.971095	−	0.238694i	$-0.923281\pi$
$491$	−2.36174	−	16.4263i	−0.106584	−	0.741308i	0.864511	−	0.502614i	$-0.167628\pi$
$492$	−6.68385	+	7.79394i	−0.301331	+	0.351378i
$493$	1.06468	−	0.684231i	0.0479510	−	0.0308162i
$494$	23.1545	−	36.8729i	1.04177	−	1.65899i
$495$	−10.4033	+	4.35853i	−0.467595	+	0.195901i
$496$	5.29681	−	0.989664i	0.237834	−	0.0444372i
$497$	0.00433348	+	0.00149983i	0.000194383	+	6.72767e-5i
$498$	−0.00325326	+	0.0164065i	−0.000145782	+	0.000735195i
$499$	−18.7413	+	10.8203i	−0.838975	+	0.484382i	−0.856916	−	0.515457i	$-0.827622\pi$
$499$	−18.7413	+	10.8203i	−0.838975	+	0.484382i	0.0179408	+	0.999839i	$0.494289\pi$
$500$	4.49492	+	8.28777i	0.201019	+	0.370641i
$501$	−6.84550	+	32.7217i	−0.305834	+	1.46190i
$502$	20.0120	+	1.69952i	0.893181	+	0.0758534i
$503$	−2.30018	+	9.48146i	−0.102560	+	0.422757i	−0.999824	−	0.0187357i	$-0.994036\pi$
$503$	−2.30018	+	9.48146i	−0.102560	+	0.422757i	0.897265	+	0.441493i	$0.145551\pi$
$504$	−7.76977	+	3.54622i	−0.346093	+	0.157961i
$505$	42.4697	−	8.18536i	1.88988	−	0.364244i
$506$	4.02760	−	3.23621i	0.179049	−	0.143867i
$507$	25.4368	+	9.25719i	1.12969	+	0.411126i
$508$	−12.5192	−	0.333638i	−0.555448	−	0.0148028i
$509$	−18.4023	−	8.40404i	−0.815667	−	0.372503i	−0.0365114	−	0.999333i	$-0.511625\pi$
$509$	−18.4023	−	8.40404i	−0.815667	−	0.372503i	−0.779156	+	0.626831i	$0.784352\pi$
$510$	−13.6987	−	34.7557i	−0.606591	−	1.53901i
$511$	5.91453	+	5.12497i	0.261643	+	0.226715i
$512$	21.0141	−	8.39090i	0.928701	−	0.370829i
$513$	−18.4798	+	23.5044i	−0.815905	+	1.03774i
$514$	−2.37610	−	7.78937i	−0.104805	−	0.343574i
$515$	9.15813	+	12.8608i	0.403556	+	0.566715i
$516$	−40.7769	−	7.64251i	−1.79510	−	0.336443i
$517$	9.04218	+	8.62170i	0.397675	+	0.379182i
$518$	0.391515	+	3.69099i	0.0172022	+	0.162173i
$519$	1.00951	+	0.313861i	0.0443128	+	0.0137770i
$520$	−6.93097	+	43.2325i	−0.303943	+	1.89587i
$521$	−10.3531	−	35.2595i	−0.453579	−	1.54475i	−0.796057	−	0.605222i	$-0.793084\pi$
$521$	−10.3531	−	35.2595i	−0.453579	−	1.54475i	0.342477	−	0.939526i	$-0.388734\pi$
$522$	1.01619	+	0.0700051i	0.0444773	+	0.00306404i
$523$	−1.82994	+	9.49464i	−0.0800177	+	0.415171i	0.919727	+	0.392560i	$0.128410\pi$
$523$	−1.82994	+	9.49464i	−0.0800177	+	0.415171i	−0.999744	+	0.0226119i	$0.992802\pi$
$524$	−17.2157	−	23.1344i	−0.752073	−	1.01063i
$525$	5.85778	−	0.465911i	0.255655	−	0.0203340i
$526$	5.68395	+	5.30705i	0.247832	+	0.231398i
$527$	−6.81359	−	2.00065i	−0.296805	−	0.0871497i
$528$	−0.621799	+	8.98194i	−0.0270603	+	0.390889i
$529$	−10.9259	+	10.4178i	−0.475038	+	0.452948i
$530$	9.74755	+	38.4184i	0.423407	+	1.66879i
$531$	21.2839	+	21.6211i	0.923641	+	0.938275i
$532$	−8.21402	+	8.16743i	−0.356123	+	0.354103i
$533$	−15.6973	−	2.25693i	−0.679924	−	0.0977583i
$534$	−24.6526	+	15.6575i	−1.06682	+	0.677566i
$535$			21.6245i			0.934909i
$536$	16.1574	−	16.5812i	0.697895	−	0.716200i
$537$	−4.23257	−	23.9989i	−0.182649	−	1.03563i
$538$	−6.88069	−	16.6785i	−0.296648	−	0.719061i
$539$	−1.10723	+	7.70096i	−0.0476918	+	0.331704i
$540$	7.86127	−	29.0212i	0.338295	−	1.24887i
$541$	16.5447	+	36.2278i	0.711312	+	1.55756i	0.825694	+	0.564119i	$0.190784\pi$
$541$	16.5447	+	36.2278i	0.711312	+	1.55756i	−0.114382	+	0.993437i	$0.536489\pi$
$542$	−19.3550	+	4.91077i	−0.831369	+	0.210935i
$543$	4.05603	+	2.98616i	0.174061	+	0.128149i
$544$	−29.6979	−	2.69232i	−1.27329	−	0.115432i
$545$	−3.20307	+	10.9087i	−0.137204	+	0.467275i
$546$	−11.0593	−	7.19132i	−0.473296	−	0.307760i
$547$	2.88352	−	30.1976i	0.123291	−	1.29116i	−0.696110	−	0.717935i	$-0.745087\pi$
$547$	2.88352	−	30.1976i	0.123291	−	1.29116i	0.819400	−	0.573222i	$-0.194307\pi$
$548$	−28.1260	+	20.9303i	−1.20148	+	0.894098i
$549$	−14.6121	+	2.33920i	−0.623627	+	0.0998347i
$550$	2.51415	−	5.66146i	0.107204	−	0.241405i
$551$	1.32551	−	0.389206i	0.0564688	−	0.0165807i
$552$	0.214903	+	13.7709i	0.00914687	+	0.586127i
$553$	−12.4278	−	6.40696i	−0.528483	−	0.272452i
$554$	21.2819	−	2.25743i	0.904180	−	0.0959090i
$555$	−10.8792	−	7.23751i	−0.461797	−	0.307215i
$556$	10.2456	−	27.2327i	0.434510	−	1.15492i
$557$	22.1315	−	15.7598i	0.937743	−	0.667764i	−0.00545863	−	0.999985i	$-0.501738\pi$
$557$	22.1315	−	15.7598i	0.937743	−	0.667764i	0.943201	+	0.332221i	$0.107798\pi$
$558$	−3.43704	−	4.56638i	−0.145502	−	0.193310i
$559$	−23.8159	−	59.4892i	−1.00730	−	2.51612i
$560$	4.39075	−	10.7893i	0.185543	−	0.455931i
$561$	6.09454	−	10.1804i	0.257312	−	0.429817i
$562$	0.435291	+	2.13772i	0.0183616	+	0.0901744i
$563$	0.589874	−	1.29164i	0.0248602	−	0.0544363i	−0.896795	−	0.442447i	$-0.854110\pi$
$563$	0.589874	−	1.29164i	0.0248602	−	0.0544363i	0.921655	+	0.388011i	$0.126838\pi$
$564$	−32.9403	+	4.90859i	−1.38704	+	0.206689i
$565$	−8.12783	+	14.0778i	−0.341941	+	0.592258i
$566$	4.03363	+	5.02003i	0.169546	+	0.211007i
$567$	7.03185	+	5.71106i	0.295310	+	0.239842i
$568$	0.00101737	+	0.0128458i	4.26880e−5	+	0.000538997i
$569$	37.6172	+	9.12583i	1.57699	+	0.382575i	0.926307	−	0.376771i	$-0.122966\pi$
$569$	37.6172	+	9.12583i	1.57699	+	0.382575i	0.650688	+	0.759345i	$0.274481\pi$
$570$	−3.65895	−	40.6141i	−0.153257	−	1.70114i
$571$	−11.1163	+	27.7671i	−0.465201	+	1.16202i	0.491483	+	0.870887i	$0.336455\pi$
$571$	−11.1163	+	27.7671i	−0.465201	+	1.16202i	−0.956684	+	0.291129i	$0.905969\pi$
$572$	−12.2243	+	6.62990i	−0.511123	+	0.277210i
$573$	−33.6780	+	28.2613i	−1.40692	+	1.18063i
$574$	3.93306	+	1.52694i	0.164163	+	0.0637333i
$575$	3.09925	−	8.95470i	0.129248	−	0.373437i
$576$	−17.8779	−	16.0118i	−0.744915	−	0.667160i
$577$	−0.235240	−	4.93829i	−0.00979316	−	0.205584i	−0.998461	−	0.0554625i	$-0.982337\pi$
$577$	−0.235240	−	4.93829i	−0.00979316	−	0.205584i	0.988668	−	0.150121i	$-0.0479664\pi$
$578$	12.9203	+	8.11337i	0.537415	+	0.337472i
$579$	−14.6335	−	15.8419i	−0.608148	−	0.658366i
$580$	−1.07377	+	0.881459i	−0.0445860	+	0.0366006i
$581$	0.00680306		0.000978132i	0.000282238		4.05798e-5i
$582$	11.6250	+	8.37225i	0.481872	+	0.347041i
$583$	−7.78181	+	9.89538i	−0.322290	+	0.409825i
$584$	−6.53602	+	20.9978i	−0.270463	+	0.868896i
$585$	44.3452	−	13.7924i	1.83345	−	0.570247i
$586$	−6.38229	−	2.13432i	−0.263650	−	0.0881678i
$587$	3.45236	−	4.84815i	0.142494	−	0.200105i	−0.737161	−	0.675717i	$-0.763834\pi$
$587$	3.45236	−	4.84815i	0.142494	−	0.200105i	0.879655	+	0.475612i	$0.157773\pi$
$588$	−14.3884	−	14.9361i	−0.593368	−	0.615953i
$589$	−6.52094	−	4.19075i	−0.268691	−	0.172677i
$590$	−41.3504	−	1.53571i	−1.70237	−	0.0632241i
$591$	−15.1041	−	27.1445i	−0.621299	−	1.11657i
$592$	−9.06221	+	5.16357i	−0.372454	+	0.212221i
$593$	−17.6777	−	22.4791i	−0.725938	−	0.923105i	0.273308	−	0.961926i	$-0.411882\pi$
$593$	−17.6777	−	22.4791i	−0.725938	−	0.923105i	−0.999246	+	0.0388216i	$0.987640\pi$
$594$	8.82745	−	3.64290i	0.362195	−	0.149470i
$595$	−11.6016	+	10.0528i	−0.475618	+	0.412126i
$596$	−17.6475	−	9.70153i	−0.722871	−	0.397390i
$597$	23.9987	−	6.63587i	0.982200	−	0.271588i
$598$	−17.7742	+	11.6877i	−0.726841	+	0.477947i
$599$	26.0372	−	13.4231i	1.06385	−	0.548453i	0.164813	−	0.986325i	$-0.447298\pi$
$599$	26.0372	−	13.4231i	1.06385	−	0.548453i	0.899038	+	0.437871i	$0.144267\pi$
$600$	7.79462	+	14.5572i	0.318214	+	0.594293i
$601$	−8.22781	−	33.9155i	−0.335619	−	1.38344i	−0.850407	−	0.526125i	$-0.823644\pi$
$601$	−8.22781	−	33.9155i	−0.335619	−	1.38344i	0.514788	−	0.857318i	$-0.327871\pi$
$602$	2.60282	+	16.8479i	0.106083	+	0.686668i
$603$	−23.3709	−	7.53660i	−0.951737	−	0.306914i
$604$	3.34175	+	10.5573i	0.135974	+	0.429572i
$605$	−26.1798	+	6.35116i	−1.06436	+	0.258211i
$606$	−35.9929	+	6.73750i	−1.46211	+	0.273692i
$607$	6.03189	+	11.7002i	0.244827	+	0.474898i	0.978945	−	0.204124i	$-0.0654345\pi$
$607$	6.03189	+	11.7002i	0.244827	+	0.474898i	−0.734118	+	0.679022i	$0.762404\pi$
$608$	−30.2761	−	11.9528i	−1.22786	−	0.484749i
$609$	−0.111550	−	0.403421i	−0.00452024	−	0.0163475i
$610$	12.3092	−	15.9945i	0.498385	−	0.647599i
$611$	−33.6863	−	38.8760i	−1.36280	−	1.57276i
$612$	11.4402	+	29.4871i	0.462443	+	1.19195i
$613$	−30.6279	+	24.0861i	−1.23705	+	0.972828i	−0.237052	+	0.971497i	$0.576181\pi$
$613$	−30.6279	+	24.0861i	−1.23705	+	0.972828i	−0.999999	+	0.00133076i	$0.999576\pi$
$614$	−6.23796	+	0.362695i	−0.251743	+	0.0146372i
$615$	−12.9789	+	7.22188i	−0.523358	+	0.291214i
$616$	3.56620	−	0.984801i	0.143686	−	0.0396788i
$617$	26.0634	−	40.5554i	1.04927	−	1.63270i	0.321463	−	0.946922i	$-0.395825\pi$
$617$	26.0634	−	40.5554i	1.04927	−	1.63270i	0.727810	−	0.685779i	$-0.240538\pi$
$618$	−7.69522	−	10.9298i	−0.309547	−	0.439659i
$619$	21.8493	+	15.5588i	0.878199	+	0.625363i	0.927665	−	0.373413i	$-0.121813\pi$
$619$	21.8493	+	15.5588i	0.878199	+	0.625363i	−0.0494661	+	0.998776i	$0.515752\pi$
$620$	7.68334	+	1.31450i	0.308570	+	0.0527914i
$621$	12.9834	−	6.69521i	0.521004	−	0.268669i
$622$	−16.5226	+	23.7250i	−0.662497	+	0.951287i
$623$	9.43320	+	7.41835i	0.377933	+	0.297210i
$624$	6.06380	−	36.5703i	0.242746	−	1.46398i
$625$	4.33947	+	30.1816i	0.173579	+	1.20727i
$626$	−21.2885	−	35.9964i	−0.850860	−	1.43871i
$627$	9.51387	−	8.78818i	0.379947	−	0.350966i
$628$	−0.702493	+	1.62767i	−0.0280325	+	0.0649511i
$629$	13.7298	−	0.654029i	0.547441	−	0.0260778i
$630$	−12.3213	+	0.913671i	−0.490892	+	0.0364015i
$631$	16.7654	+	5.80255i	0.667418	+	0.230996i	0.639705	−	0.768620i	$-0.279056\pi$
$631$	16.7654	+	5.80255i	0.667418	+	0.230996i	0.0277130	+	0.999616i	$0.491178\pi$
$632$	2.50368	−	39.2105i	0.0995910	−	1.55971i
$633$	−21.5617	−	25.6943i	−0.857001	−	1.02126i
$634$	3.17351	−	1.13574i	0.126036	−	0.0451058i
$635$	−16.8189	−	6.73328i	−0.667439	−	0.267202i
$636$	−8.07844	−	32.5701i	−0.320331	−	1.29149i
$637$	7.55207	−	31.1300i	0.299224	−	1.23342i
$638$	−0.429862	−	0.0995261i	−0.0170184	−	0.00394028i
$639$	0.0117261	−	0.00702164i	0.000463878	−	0.000277772i
$640$	32.7220	−	0.842653i	1.29345	−	0.0333088i
$641$	−1.91883	−	1.10784i	−0.0757894	−	0.0437570i	0.461626	−	0.887074i	$-0.347266\pi$
$641$	−1.91883	−	1.10784i	−0.0757894	−	0.0437570i	−0.537416	+	0.843317i	$0.680599\pi$
$642$	0.0979787	−	18.3078i	0.00386691	−	0.722552i
$643$	0.0925111	+	0.0422484i	0.00364828	+	0.00166611i	0.417238	−	0.908797i	$-0.362998\pi$
$643$	0.0925111	+	0.0422484i	0.00364828	+	0.00166611i	−0.413590	+	0.910463i	$0.635725\pi$
$644$	5.30817	−	1.96267i	0.209171	−	0.0773400i
$645$	−51.4930	−	30.8264i	−2.02754	−	1.21379i
$646$	28.4293	+	32.1228i	1.11854	+	1.26386i
$647$	−44.2628	+	17.7202i	−1.74015	+	0.696652i	−0.740453	+	0.672108i	$0.765389\pi$
$647$	−44.2628	+	17.7202i	−1.74015	+	0.696652i	−0.999699	+	0.0245437i	$0.992187\pi$
$648$	−6.78703	+	24.5344i	−0.266620	+	0.963802i
$649$	−7.62330	−	10.7054i	−0.299241	−	0.420225i
$650$	−12.5203	+	22.2203i	−0.491086	+	0.871550i
$651$	−1.30083	+	1.95537i	−0.0509836	+	0.0766370i
$652$	48.8324	−	12.9359i	1.91242	−	0.506607i
$653$	−8.88634	+	17.2371i	−0.347749	+	0.674539i	−0.996236	−	0.0866869i	$-0.972372\pi$
$653$	−8.88634	+	17.2371i	−0.347749	+	0.674539i	0.648486	+	0.761226i	$0.275402\pi$
$654$	2.76122	−	9.22101i	0.107972	−	0.360570i
$655$	−11.7527	−	40.0261i	−0.459217	−	1.56395i
$656$	0.496754	+	11.8454i	0.0193950	+	0.462483i
$657$	23.0323	−	3.68717i	0.898575	−	0.143850i
$658$	6.39806	+	12.0976i	0.249422	+	0.471612i
$659$	14.8088	+	1.41407i	0.576870	+	0.0550844i	0.379414	−	0.925227i	$-0.376126\pi$
$659$	14.8088	+	1.41407i	0.576870	+	0.0550844i	0.197457	+	0.980312i	$0.436732\pi$
$660$	−5.34972	+	11.8750i	−0.208238	+	0.462233i
$661$	16.0791	+	4.72126i	0.625405	+	0.183636i	0.579053	−	0.815290i	$-0.303422\pi$
$661$	16.0791	+	4.72126i	0.625405	+	0.183636i	0.0463519	+	0.998925i	$0.485240\pi$
$662$	−12.5545	−	10.6503i	−0.487945	−	0.413935i
$663$	−28.9636	+	39.3405i	−1.12485	+	1.52786i
$664$	0.0101777	+	0.0164142i	0.000394970	+	0.000636995i
$665$	−15.2424	+	6.96097i	−0.591075	+	0.269935i
$666$	9.17781	+	6.17674i	0.355633	+	0.239344i
$667$	−0.668084	−	0.0960559i	−0.0258683	−	0.00371930i
$668$	19.9972	+	33.0183i	0.773713	+	1.27752i
$669$	−21.8217	+	3.84858i	−0.843675	+	0.148795i
$670$	30.2413	−	14.3920i	1.16832	−	0.556011i
$671$	6.41022			0.247464
$672$	−3.76620	+	9.11459i	−0.145284	+	0.351603i
$673$	−4.08726	+	28.4275i	−0.157552	+	1.09580i	0.745573	+	0.666424i	$0.232176\pi$
$673$	−4.08726	+	28.4275i	−0.157552	+	1.09580i	−0.903125	+	0.429377i	$0.858733\pi$
$674$	−12.2239	−	16.7909i	−0.470848	−	0.646763i
$675$	10.1577	−	14.2678i	0.390970	−	0.549169i
$676$	28.7678	−	12.2224i	1.10645	−	0.470091i
$677$	8.60559	+	9.02528i	0.330740	+	0.346870i	0.868016	−	0.496537i	$-0.165395\pi$
$677$	8.60559	+	9.02528i	0.330740	+	0.346870i	−0.537276	+	0.843406i	$0.680547\pi$
$678$	6.94500	−	11.8818i	0.266721	−	0.456318i
$679$	1.65851	−	5.64838i	0.0636479	−	0.216765i
$680$	−38.9442	−	18.5518i	−1.49344	−	0.711430i
$681$	1.54964	+	19.4832i	0.0593823	+	0.746598i
$682$	1.15745	+	2.18854i	0.0443212	+	0.0838033i
$683$	20.0702	+	3.86821i	0.767964	+	0.148013i	0.558163	−	0.829731i	$-0.311506\pi$
$683$	20.0702	+	3.86821i	0.767964	+	0.148013i	0.209801	+	0.977744i	$0.432718\pi$
$684$	2.91373	+	34.4014i	0.111409	+	1.31537i
$685$	−48.6623	+	14.2885i	−1.85929	+	0.545937i
$686$	−8.29831	+	16.5192i	−0.316831	+	0.630705i
$687$	−11.0247	+	35.4601i	−0.420617	+	1.35289i
$688$	−40.4468	+	25.6697i	−1.54202	+	0.978649i
$689$	35.7676	−	37.5119i	1.36264	−	1.42909i
$690$	−6.61697	+	18.7925i	−0.251904	+	0.715417i
$691$	14.6673	−	10.4446i	0.557971	−	0.397329i	−0.265990	−	0.963976i	$-0.585699\pi$
$691$	14.6673	−	10.4446i	0.557971	−	0.397329i	0.823961	+	0.566646i	$0.191759\pi$
$692$	1.09954	−	0.530265i	0.0417983	−	0.0201576i
$693$	−2.61669	−	2.92430i	−0.0993997	−	0.111085i
$694$	−10.2004	−	11.5256i	−0.387201	−	0.437506i
$695$	27.5635	−	31.8100i	1.04554	−	1.20662i
$696$	0.913077	−	0.741399i	0.0346101	−	0.0281027i
$697$	6.49053	−	14.2123i	0.245846	−	0.538329i
$698$	−12.1809	−	2.21557i	−0.461056	−	0.0838607i
$699$	2.62552	−	7.21439i	0.0993063	−	0.272873i
$700$	4.57849	−	5.00782i	0.173051	−	0.189278i
$701$	5.46761	+	28.3687i	0.206509	+	1.07147i	0.926159	+	0.377133i	$0.123090\pi$
$701$	5.46761	+	28.3687i	0.206509	+	1.07147i	−0.719650	+	0.694337i	$0.755698\pi$
$702$	−37.6062	+	11.4761i	−1.41935	+	0.433137i
$703$	14.5810	+	3.53730i	0.549931	+	0.133412i
$704$	6.55057	+	8.07295i	0.246884	+	0.304261i
$705$	−47.1568	−	9.86537i	−1.77603	−	0.371551i
$706$	34.9609	−	12.5118i	1.31577	−	0.470887i
$707$	7.52353	+	13.0311i	0.282952	+	0.490086i
$708$	35.0012	+	1.48752i	1.31543	+	0.0559045i
$709$	−2.54014	+	7.33925i	−0.0953969	+	0.275631i	−0.982596	−	0.185756i	$-0.940527\pi$
$709$	−2.54014	+	7.33925i	−0.0953969	+	0.275631i	0.887199	+	0.461387i	$0.152648\pi$
$710$	−0.00506406	+	0.0179399i	−0.000190051	+	0.000673272i
$711$	−38.4367	+	16.1033i	−1.44149	+	0.603919i
$712$	−8.47913	+	32.6392i	−0.317769	+	1.22321i
$713$	2.04750	+	3.18597i	0.0766793	+	0.119315i
$714$	9.86772	−	8.45839i	0.369290	−	0.316547i
$715$	−19.9123	+	2.86295i	−0.744677	+	0.107068i
$716$	−22.4786	−	16.9272i	−0.840064	−	0.632600i
$717$	12.4270	−	23.1959i	0.464094	−	0.866268i
$718$	6.19361	−	8.89347i	0.231143	−	0.331901i
$719$	1.88108	−	39.4888i	0.0701526	−	1.47268i	−0.639858	−	0.768493i	$-0.721007\pi$
$719$	1.88108	−	39.4888i	0.0701526	−	1.47268i	0.710011	−	0.704191i	$-0.248690\pi$
$720$	−16.2245	−	30.6943i	−0.604650	−	1.14391i
$721$	−3.18610	+	4.47425i	−0.118657	+	0.166630i
$722$	8.47895	+	18.0630i	0.315554	+	0.672236i
$723$	11.5938	−	27.6818i	0.431179	−	1.02950i
$724$	5.77672	−	0.674033i	0.214690	−	0.0250503i
$725$	−0.764730	+	0.264676i	−0.0284013	+	0.00982980i
$726$	22.1933	−	5.25843i	0.823669	−	0.195159i
$727$	26.4253	+	33.6025i	0.980059	+	1.24625i	0.969192	+	0.246306i	$0.0792167\pi$
$727$	26.4253	+	33.6025i	0.980059	+	1.24625i	0.0108671	+	0.999941i	$0.496541\pi$
$728$	−15.0020	+	2.64062i	−0.556010	+	0.0978680i
$729$	26.5109	−	5.11566i	0.981887	−	0.189469i
$730$	−19.4024	+	25.2114i	−0.718115	+	0.933115i
$731$	62.8460	−	6.00107i	2.32444	−	0.221958i
$732$	−10.4937	+	13.4856i	−0.387859	+	0.498441i
$733$	−23.6543	+	12.1947i	−0.873693	+	0.450420i	−0.835910	−	0.548866i	$-0.815060\pi$
$733$	−23.6543	+	12.1947i	−0.873693	+	0.450420i	−0.0377827	+	0.999286i	$0.512029\pi$
$734$	0.390697	+	37.2859i	0.0144209	+	1.37625i
$735$	−12.0294	−	27.4840i	−0.443713	−	1.01376i
$736$	11.0295	+	11.4570i	0.406551	+	0.422309i
$737$	9.48042	+	4.82395i	0.349216	+	0.177693i
$738$	11.0209	−	6.05541i	0.405686	−	0.222903i
$739$	−15.1767	+	3.68182i	−0.558283	+	0.135438i	−0.504965	−	0.863140i	$-0.668495\pi$
$739$	−15.1767	+	3.68182i	−0.558283	+	0.135438i	−0.0533176	+	0.998578i	$0.516980\pi$
$740$	−14.8863	+	2.45974i	−0.547231	+	0.0904218i
$741$	−42.4333	+	32.2961i	−1.55882	+	1.18643i
$742$	−11.5215	+	7.57615i	−0.422967	+	0.278129i
$743$	0.967274	−	0.0923635i	0.0354858	−	0.00338849i	−0.0772980	−	0.997008i	$-0.524629\pi$
$743$	0.967274	−	0.0923635i	0.0354858	−	0.00338849i	0.112784	+	0.993620i	$0.464023\pi$
$744$	−6.49894	−	1.14770i	−0.238263	−	0.0420766i
$745$	−19.0776	−	22.0167i	−0.698948	−	0.806628i
$746$	5.06329	−	38.0414i	0.185380	−	1.39279i
$747$	0.0107990	−	0.0174075i	0.000395113	−	0.000636906i
$748$	−2.87423	−	13.3959i	−0.105092	−	0.489804i
$749$	−7.10937	+	2.46058i	−0.259771	+	0.0899075i
$750$	−1.58214	−	11.4383i	−0.0577717	−	0.417667i
$751$	24.2918	−	37.7988i	0.886420	−	1.37930i	−0.0385493	−	0.999257i	$-0.512274\pi$
$751$	24.2918	−	37.7988i	0.886420	−	1.37930i	0.924970	−	0.380041i	$-0.124090\pi$
$752$	−23.9436	+	30.0929i	−0.873133	+	1.09738i
$753$	−22.2105	−	10.5712i	−0.809394	−	0.385236i
$754$	1.72289	+	0.576156i	0.0627441	+	0.0209824i
$755$	−0.762218	+	16.0009i	−0.0277400	+	0.582334i
$756$	10.4356	−	0.717709i	0.379540	−	0.0261028i
$757$	−39.9831	−	31.4430i	−1.45321	−	1.14282i	−0.962429	−	0.271534i	$-0.912469\pi$
$757$	−39.9831	−	31.4430i	−1.45321	−	1.14282i	−0.490781	−	0.871283i	$-0.663288\pi$
$758$	−9.06688	−	9.31173i	−0.329324	−	0.338217i
$759$	−6.01185	+	1.97473i	−0.218216	+	0.0716780i
$760$	−35.0829	−	31.4067i	−1.27259	−	1.13924i
$761$	26.5174	+	41.2618i	0.961253	+	1.49574i	0.865852	+	0.500301i	$0.166777\pi$
$761$	26.5174	+	41.2618i	0.961253	+	1.49574i	0.0954017	+	0.995439i	$0.469586\pi$
$762$	14.2088	+	5.77676i	0.514730	+	0.209270i
$763$	−3.95084	+	0.188202i	−0.143030	+	0.00681336i
$764$	−6.17025	+	50.3899i	−0.223232	+	1.82304i
$765$	0.729310	+	45.7482i	0.0263682	+	1.65403i
$766$	−36.4614	−	14.1555i	−1.31741	−	0.511460i
$767$	27.0553	+	46.8611i	0.976910	+	1.69206i
$768$	−27.7070	+	0.565150i	−0.999792	+	0.0203931i
$769$	8.41734	+	3.36979i	0.303537	+	0.121518i	0.518431	−	0.855120i	$-0.326516\pi$
$769$	8.41734	+	3.36979i	0.303537	+	0.121518i	−0.214894	+	0.976637i	$0.568941\pi$
$770$	5.33277	+	0.452886i	0.192180	+	0.0163209i
$771$	−0.632221	+	9.95391i	−0.0227689	+	0.358481i
$772$	−24.8340	−	1.84717i	−0.893796	−	0.0664809i
$773$	−4.19546	−	21.7681i	−0.150900	−	0.782945i	−0.975968	−	0.217912i	$-0.930075\pi$
$773$	−4.19546	−	21.7681i	−0.150900	−	0.782945i	0.825068	−	0.565033i	$-0.191137\pi$
$774$	43.4555	+	26.3317i	1.56198	+	0.946474i
$775$	3.93230	+	2.27031i	0.141252	+	0.0815521i
$776$	16.4098	−	2.08922i	0.589078	−	0.0749985i
$777$	1.14153	−	4.40023i	0.0409521	−	0.157857i
$778$	−1.42965	−	7.02102i	−0.0512553	−	0.251716i
$779$	11.1685	−	12.8892i	0.400154	−	0.461802i
$780$	26.5741	−	46.5774i	0.951504	−	1.66774i
$781$	−0.00549644	+	0.00220044i	−0.000196678	+	7.87380e-5i
$782$	−6.11496	−	20.0462i	−0.218671	−	0.716851i
$783$	−1.13484	−	0.518112i	−0.0405559	−	0.0185158i
$784$	−23.9135	−	1.27550i	−0.854054	−	0.0455537i
$785$	−1.76973	+	1.85604i	−0.0631643	+	0.0662448i
$786$	9.76877	+	33.9403i	0.348441	+	1.21061i
$787$	9.61824	−	18.6568i	0.342853	−	0.665042i	−0.652866	−	0.757474i	$-0.726433\pi$
$787$	9.61824	−	18.6568i	0.342853	−	0.665042i	0.995719	+	0.0924311i	$0.0294638\pi$
$788$	−34.1349	−	11.0188i	−1.21601	−	0.392530i
$789$	−4.22964	−	8.53336i	−0.150579	−	0.303796i
$790$	23.0681	−	51.9457i	0.820726	−	1.84814i
$791$	−5.55312	−	1.07028i	−0.197446	−	0.0380547i
$792$	4.58301	−	10.0294i	0.162850	−	0.356379i
$793$	−26.2731	−	2.50878i	−0.932985	−	0.0890893i
$794$	−7.26590	−	6.78411i	−0.257857	−	0.240759i
$795$	5.37871	−	48.2447i	0.190763	−	1.71106i
$796$	15.0338	−	24.5074i	0.532859	−	0.868642i
$797$	−21.8191	−	22.8832i	−0.772871	−	0.810564i	0.213179	−	0.977013i	$-0.431618\pi$
$797$	−21.8191	−	22.8832i	−0.772871	−	0.810564i	−0.986050	+	0.166449i	$0.946770\pi$
$798$	12.9361	−	5.82427i	0.457934	−	0.206177i
$799$	46.1000	−	21.0532i	1.63090	−	0.744807i
$800$	18.0481	+	6.14987i	0.638097	+	0.217431i
$801$	35.0095	−	7.32815i	1.23700	−	0.258928i
$802$	−19.7250	−	47.8126i	−0.696515	−	1.68832i
$803$	−10.1041			−0.356567
$804$	−25.6682	+	12.0476i	−0.905247	+	0.424885i
$805$	8.18689			0.288550
$806$	−3.88744	−	9.42299i	−0.136929	−	0.331911i
$807$	0.701905	+	22.0858i	0.0247082	+	0.777456i
$808$	−25.0801	+	34.0417i	−0.882314	+	1.19758i
$809$	38.6650	−	17.6577i	1.35939	−	0.620813i	0.403620	−	0.914927i	$-0.367752\pi$
$809$	38.6650	−	17.6577i	1.35939	−	0.620813i	0.955770	+	0.294114i	$0.0950245\pi$
$810$	−21.5172	+	29.8840i	−0.756037	+	1.05002i
$811$	30.1218	+	31.5908i	1.05772	+	1.10930i	0.993781	+	0.111351i	$0.0355177\pi$
$811$	30.1218	+	31.5908i	1.05772	+	1.10930i	0.0639386	+	0.997954i	$0.479634\pi$
$812$	−0.411973	−	0.252721i	−0.0144574	−	0.00886875i
$813$	24.3054	+	2.70977i	0.852429	+	0.0950356i
$814$	−3.50269	−	3.27043i	−0.122769	−	0.114629i
$815$	72.7466	+	6.94646i	2.54820	+	0.243324i
$816$	32.8871	+	15.8829i	1.15128	+	0.556012i
$817$	67.6671	+	13.0418i	2.36737	+	0.456274i
$818$	−9.62624	+	21.6768i	−0.336574	+	0.757910i
$819$	9.58034	+	13.0097i	0.334764	+	0.454597i
$820$	−5.26855	+	16.3213i	−0.183986	+	0.569964i
$821$	2.22822	−	4.32214i	0.0777653	−	0.150844i	−0.846747	−	0.531996i	$-0.821442\pi$
$821$	2.22822	−	4.32214i	0.0777653	−	0.150844i	0.924512	+	0.381152i	$0.124473\pi$
$822$	41.2634	−	11.8765i	1.43923	−	0.414242i
$823$	8.91773	−	9.35264i	0.310852	−	0.326013i	−0.549712	−	0.835354i	$-0.685263\pi$
$823$	8.91773	−	9.35264i	0.310852	−	0.326013i	0.860564	+	0.509342i	$0.170111\pi$
$824$	−15.1067	−	3.16568i	−0.526268	−	0.110282i
$825$	−5.32175	+	5.40727i	−0.185280	+	0.188257i
$826$	−4.20022	−	13.7693i	−0.146144	−	0.479094i
$827$	−8.56652	+	3.42952i	−0.297887	+	0.119256i	−0.515792	−	0.856714i	$-0.672502\pi$
$827$	−8.56652	+	3.42952i	−0.297887	+	0.119256i	0.217904	+	0.975970i	$0.430078\pi$
$828$	5.68723	−	15.8802i	0.197645	−	0.551874i
$829$	−20.1290	+	23.2301i	−0.699109	+	0.806815i	−0.988632	−	0.150356i	$-0.951958\pi$
$829$	−20.1290	+	23.2301i	−0.699109	+	0.806815i	0.289523	+	0.957171i	$0.406503\pi$
$830$	0.00557464	+	0.0273771i	0.000193498	+	0.000950274i
$831$	−25.3712	−	6.58192i	−0.880118	−	0.228324i
$832$	−23.6888	−	35.6518i	−0.821263	−	1.23600i
$833$	27.3312	+	15.7797i	0.946972	+	0.546734i
$834$	−23.4801	+	26.8062i	−0.813048	+	0.928224i
$835$	10.5680	+	54.8322i	0.365722	+	1.89755i
$836$	1.10932	−	14.9141i	0.0383666	−	0.515815i
$837$	1.97282	+	6.71607i	0.0681908	+	0.232141i
$838$	−16.0071	−	1.35940i	−0.552956	−	0.0469598i
$839$	34.3213	+	13.7402i	1.18490	+	0.474364i	0.878595	−	0.477568i	$-0.158482\pi$
$839$	34.3213	+	13.7402i	1.18490	+	0.474364i	0.306309	+	0.951932i	$0.400906\pi$
$840$	−9.68267	+	10.4775i	−0.334084	+	0.361507i
$841$	−14.4712	−	25.0648i	−0.499006	−	0.864304i
$842$	−18.1592	−	7.04998i	−0.625806	−	0.242958i
$843$	0.422065	−	2.63834i	0.0145367	−	0.0908694i
$844$	−38.4445	−	4.70753i	−1.32331	−	0.162040i
$845$	45.1645	−	2.15145i	1.55371	−	0.0740122i
$846$	39.8794	+	8.56592i	1.37108	+	0.294502i
$847$	−5.06695	−	7.88433i	−0.174102	−	0.270909i
$848$	−32.4775	−	21.1340i	−1.11528	−	0.725744i
$849$	−2.46131	−	7.49321i	−0.0844721	−	0.257166i
$850$	−17.5297	−	18.0031i	−0.601265	−	0.617503i
$851$	−5.76218	−	4.53143i	−0.197525	−	0.155335i
$852$	0.00436864	−	0.0151654i	0.000149667	−	0.000519557i
$853$	−2.25152	+	47.2652i	−0.0770905	+	1.61833i	0.547107	+	0.837062i	$0.315729\pi$
$853$	−2.25152	+	47.2652i	−0.0770905	+	1.61833i	−0.624198	+	0.781266i	$0.714574\pi$
$854$	6.65905	+	2.22687i	0.227868	+	0.0762018i
$855$	−13.3050	+	48.1385i	−0.455023	+	1.64630i
$856$	−14.3393	−	15.5338i	−0.490107	−	0.530935i
$857$	19.7976	−	30.8057i	0.676275	−	1.05230i	−0.318271	−	0.948000i	$-0.603102\pi$
$857$	19.7976	−	30.8057i	0.676275	−	1.05230i	0.994545	−	0.104304i	$-0.0332615\pi$
$858$	16.8712	−	2.33362i	0.575973	−	0.0796686i
$859$	12.0544	−	4.17205i	0.411289	−	0.142349i	−0.113585	−	0.993528i	$-0.536234\pi$
$859$	12.0544	−	4.17205i	0.411289	−	0.142349i	0.524874	+	0.851180i	$0.324112\pi$
$860$	−67.7573	+	14.5380i	−2.31050	+	0.495742i
$861$	−3.85112	−	3.44524i	−0.131246	−	0.117413i
$862$	−0.305339	+	2.29407i	−0.0103999	+	0.0781363i
$863$	−25.3043	−	29.2027i	−0.861367	−	0.994071i	−0.999993	−	0.00372620i	$-0.998814\pi$
$863$	−25.3043	−	29.2027i	−0.861367	−	0.994071i	0.138626	−	0.990345i	$-0.455732\pi$
$864$	13.5969	+	26.0600i	0.462577	+	0.886579i
$865$	1.75791	−	0.167860i	0.0597707	−	0.00570741i
$866$	7.48583	−	4.92244i	0.254379	−	0.167271i
$867$	−11.3166	−	14.8687i	−0.384331	−	0.504967i
$868$	0.442100	+	2.67558i	0.0150059	+	0.0908151i
$869$	17.5433	−	4.25595i	0.595114	−	0.144373i
$870$	1.61083	−	0.547878i	0.0546122	−	0.0185748i
$871$	−36.9688	−	23.4820i	−1.25264	−	0.795656i
$872$	−4.93266	−	9.96012i	−0.167041	−	0.337292i
$873$	−9.72001	−	14.6073i	−0.328973	−	0.494383i
$874$	−0.239702	−	22.8759i	−0.00810805	−	0.773787i
$875$	−4.21748	+	2.17426i	−0.142577	+	0.0735035i
$876$	16.5408	−	21.2567i	0.558861	−	0.718196i
$877$	−15.7344	+	1.50246i	−0.531314	+	0.0507343i	−0.357266	−	0.934003i	$-0.616291\pi$
$877$	−15.7344	+	1.50246i	−0.531314	+	0.0507343i	−0.174048	+	0.984737i	$0.555685\pi$
$878$	−1.76870	+	2.29824i	−0.0596907	+	0.0775619i
$879$	6.39733	+	5.19689i	0.215776	+	0.175287i
$880$	4.83795	+	14.2399i	0.163087	+	0.480026i
$881$	−0.380456	−	0.483790i	−0.0128179	−	0.0162993i	0.779602	−	0.626275i	$-0.215421\pi$
$881$	−0.380456	−	0.483790i	−0.0128179	−	0.0162993i	−0.792420	+	0.609976i	$0.791179\pi$
$882$	10.0599	+	23.3231i	0.338734	+	0.785329i
$883$	−32.7912	+	11.3491i	−1.10351	+	0.381929i	−0.817285	−	0.576233i	$-0.804522\pi$
$883$	−32.7912	+	11.3491i	−1.10351	+	0.381929i	−0.286226	+	0.958162i	$0.592401\pi$
$884$	6.53762	+	56.0299i	0.219884	+	1.88449i
$885$	46.7443	+	19.5777i	1.57129	+	0.658097i
$886$	20.6598	+	44.0122i	0.694078	+	1.47862i
$887$	11.9411	−	16.7689i	0.400942	−	0.563044i	−0.563911	−	0.825836i	$-0.690704\pi$
$887$	11.9411	−	16.7689i	0.400942	−	0.563044i	0.964853	+	0.262792i	$0.0846432\pi$
$888$	12.6142	−	2.01503i	0.423306	−	0.0676198i
$889$	0.299897	−	6.29562i	0.0100582	−	0.211148i
$890$	−27.8791	+	40.0319i	−0.934509	+	1.34187i
$891$	−11.6899	+	0.372811i	−0.391625	+	0.0124896i
$892$	−15.3915	+	20.4393i	−0.515347	+	0.684357i
$893$	54.7571	−	7.87289i	1.83238	−	0.263456i
$894$	16.0518	+	18.7263i	0.536851	+	0.626300i
$895$	−22.0075	−	34.2443i	−0.735628	−	1.14466i
$896$	4.00036	+	10.6619i	0.133643	+	0.356191i
$897$	25.4132	−	5.74081i	0.848522	−	0.191680i
$898$	−2.57111	+	9.10837i	−0.0857989	+	0.303950i
$899$	0.105781	−	0.305635i	0.00352800	−	0.0101935i
$900$	−2.66372	−	20.0476i	−0.0887906	−	0.668252i
$901$	25.5324	+	44.2234i	0.850607	+	1.47330i
$902$	−5.12865	+	1.83544i	−0.170765	+	0.0611134i
$903$	4.27543	−	20.4367i	0.142277	−	0.680091i
$904$	−3.49647	−	15.5023i	−0.116291	−	0.515599i
$905$	8.17615	+	1.98351i	0.271784	+	0.0659341i
$906$	0.717811	−	13.5433i	0.0238477	−	0.449947i
$907$	3.40551	+	17.6695i	0.113078	+	0.586705i	0.993624	+	0.112744i	$0.0359640\pi$
$907$	3.40551	+	17.6695i	0.113078	+	0.586705i	−0.880546	+	0.473961i	$0.842824\pi$
$908$	16.6562	+	15.2282i	0.552756	+	0.505367i
$909$	44.1671	+	7.78448i	1.46493	+	0.258195i
$910$	−21.6798	−	3.94331i	−0.718678	−	0.130719i
$911$	−11.9787	+	26.2297i	−0.396872	+	0.869029i	0.600705	+	0.799470i	$0.294886\pi$
$911$	−11.9787	+	26.2297i	−0.396872	+	0.869029i	−0.997578	+	0.0695588i	$0.977841\pi$
$912$	29.5597	+	26.7486i	0.978820	+	0.885734i
$913$	−0.00581102	+	0.00670628i	−0.000192317	+	0.000221945i
$914$	1.53847	+	1.73834i	0.0508880	+	0.0574993i
$915$	−21.0036	+	13.0331i	−0.694357	+	0.430860i
$916$	18.6260	+	38.6224i	0.615422	+	1.27612i
$917$	11.8218	−	8.41830i	0.390392	−	0.277997i
$918$	−0.410170	−	38.7348i	−0.0135376	−	1.27844i
$919$	16.0440	−	16.8264i	0.529241	−	0.555052i	−0.403788	−	0.914853i	$-0.632307\pi$
$919$	16.0440	−	16.8264i	0.529241	−	0.555052i	0.933029	+	0.359800i	$0.117155\pi$
$920$	9.21732	+	21.0783i	0.303886	+	0.694932i
$921$	7.30777	+	2.27200i	0.240799	+	0.0748651i
$922$	15.8078	−	31.4681i	0.520602	−	1.03635i
$923$	0.0233891	−	0.00686765i	0.000769860	−	0.000226051i
$924$	−4.51280	−	0.407586i	−0.148460	−	0.0134086i
$925$	−8.63012	−	1.66332i	−0.283757	−	0.0546896i
$926$	25.9353	+	49.0390i	0.852288	+	1.61152i
$927$	4.11275	+	15.8461i	0.135080	+	0.520455i
$928$	0.186840	−	1.34521i	0.00613332	−	0.0441588i
$929$	−3.65690	+	12.4543i	−0.119979	+	0.408611i	−0.997479	−	0.0709663i	$-0.977392\pi$
$929$	−3.65690	+	12.4543i	−0.119979	+	0.408611i	0.877500	+	0.479577i	$0.159210\pi$
$930$	−8.24215	−	4.81760i	−0.270271	−	0.157975i
$931$	23.7726	+	24.9320i	0.779115	+	0.817112i
$932$	−3.46651	−	8.15911i	−0.113549	−	0.267260i
$933$	29.1650	−	20.0802i	0.954819	−	0.657397i
$934$	−29.1990	−	40.1081i	−0.955419	−	1.31238i
$935$	2.82063	−	19.6179i	0.0922443	−	0.641573i
$936$	−22.7093	+	39.3132i	−0.742276	+	1.28499i
$937$	54.0298			1.76508			0.882539	−	0.470240i	$-0.155833\pi$
$937$	54.0298			1.76508			0.882539	+	0.470240i	$0.155833\pi$
$938$	8.17262	+	8.30464i	0.266846	+	0.271156i
$939$	8.89600	+	50.4408i	0.290310	+	1.64607i
$940$	−47.5843	+	28.8188i	−1.55203	+	0.939967i
$941$	−2.41852	−	0.347731i	−0.0788416	−	0.0113357i	0.102781	−	0.994704i	$-0.467226\pi$
$941$	−2.41852	−	0.347731i	−0.0788416	−	0.0113357i	−0.181623	+	0.983368i	$0.558135\pi$
$942$	1.50670	−	1.56335i	0.0490910	−	0.0509366i
$943$	−7.57956	+	3.46147i	−0.246824	+	0.112721i
$944$	30.7221	−	26.3164i	0.999919	−	0.856526i
$945$	14.5194	+	4.26153i	0.472316	+	0.138628i
$946$	−16.7843	−	14.2385i	−0.545704	−	0.462934i
$947$	17.0091	+	4.99433i	0.552722	+	0.162294i	0.546154	−	0.837685i	$-0.316091\pi$
$947$	17.0091	+	4.99433i	0.552722	+	0.162294i	0.00656780	+	0.999978i	$0.497909\pi$
$948$	−19.7654	+	43.8739i	−0.641949	+	1.42496i
$949$	41.4131	+	3.95447i	1.34432	+	0.128367i
$950$	−12.8232	−	24.2464i	−0.416041	−	0.786658i
$951$	−4.12763	−	0.0653447i	−0.133848	−	0.00211895i
$952$	1.66785	−	14.9144i	0.0540555	−	0.483379i
$953$	15.7640	+	53.6873i	0.510646	+	1.73910i	0.660920	+	0.750456i	$0.270166\pi$
$953$	15.7640	+	53.6873i	0.510646	+	1.73910i	−0.150274	+	0.988644i	$0.548016\pi$
$954$	−4.77234	+	40.8208i	−0.154510	+	1.32162i
$955$	−33.6515	+	65.2748i	−1.08894	+	2.11224i
$956$	−7.78097	−	29.3728i	−0.251654	−	0.949986i
$957$	0.449930	+	0.299321i	0.0145442	+	0.00967566i
$958$	15.6676	−	27.8059i	0.506197	−	0.898368i
$959$	−10.2347	−	14.3726i	−0.330495	−	0.464115i
$960$	−37.8771	−	13.1332i	−1.22248	−	0.423873i
$961$	27.0947	−	10.8471i	0.874022	−	0.349905i
$962$	13.0763	+	14.7751i	0.421596	+	0.476370i
$963$	−8.00082	+	20.9467i	−0.257823	+	0.674999i
$964$	−12.0181	−	32.5038i	−0.387077	−	1.04688i
$965$	−32.7687	−	14.9650i	−1.05486	−	0.481740i
$966$	−6.93122	−	0.0370941i	−0.223008	−	0.00119348i
$967$	−34.1129	−	19.6951i	−1.09700	−	0.633351i	−0.161566	−	0.986862i	$-0.551654\pi$
$967$	−34.1129	−	19.6951i	−1.09700	−	0.633351i	−0.935430	+	0.353511i	$0.884988\pi$
$968$	14.5946	−	21.9223i	0.469090	−	0.704608i
$969$	−18.7516	−	49.0768i	−0.602388	−	1.57657i
$970$	23.3134	+	5.39775i	0.748547	+	0.173311i
$971$	−5.16846	+	21.3047i	−0.165864	+	0.683700i	0.826769	+	0.562541i	$0.190176\pi$
$971$	−5.16846	+	21.3047i	−0.165864	+	0.683700i	−0.992633	+	0.121159i	$0.961339\pi$
$972$	18.3524	−	25.2030i	0.588653	−	0.808386i
$973$	13.5944	+	5.44236i	0.435815	+	0.174474i
$974$	−21.8596	+	7.82312i	−0.700428	+	0.250669i
$975$	23.9281	−	20.0796i	0.766314	−	0.643062i
$976$	1.76379	+	19.6518i	0.0564574	+	0.629039i
$977$	−32.3629	−	11.2009i	−1.03538	−	0.358349i	−0.244067	−	0.969758i	$-0.578482\pi$
$977$	−32.3629	−	11.2009i	−1.03538	−	0.358349i	−0.791314	+	0.611410i	$0.790603\pi$
$978$	−61.5576	−	6.21065i	−1.96839	−	0.198595i
$979$	−15.4765	+	0.737234i	−0.494630	+	0.0235621i
$980$	−31.8066	−	13.7275i	−1.01602	−	0.438510i
$981$	−7.13875	+	9.38165i	−0.227923	+	0.299533i
$982$	11.9469	+	20.2008i	0.381241	+	0.644634i
$983$	0.638917	+	4.44377i	0.0203783	+	0.141734i	0.997470	−	0.0710825i	$-0.0226454\pi$
$983$	0.638917	+	4.44377i	0.0203783	+	0.141734i	−0.977092	+	0.212817i	$0.931736\pi$
$984$	4.53443	−	13.7941i	0.144552	−	0.439740i
$985$	−40.7872	−	32.0754i	−1.29959	−	1.02201i
$986$	−1.02286	+	1.46874i	−0.0325746	+	0.0467742i
$987$	−2.12242	−	16.6260i	−0.0675575	−	0.529212i
$988$	−10.3836	+	60.6932i	−0.330348	+	1.93091i
$989$	−27.4259	−	19.5299i	−0.872092	−	0.621014i
$990$	11.2499	−	11.3089i	0.357545	−	0.359422i
$991$	30.0257	−	46.7209i	0.953798	−	1.48414i	0.0806146	−	0.996745i	$-0.474312\pi$
$991$	30.0257	−	46.7209i	0.953798	−	1.48414i	0.873183	−	0.487393i	$-0.162052\pi$
$992$	−6.39092	+	4.15059i	−0.202912	+	0.131781i
$993$	9.80408	+	17.6195i	0.311123	+	0.559138i
$994$	−0.00647422		0.000376432i	−0.000205350		1.19397e-5i
$995$	32.6931	−	25.7101i	1.03644	−	0.815066i
$996$	−0.00459558	−	0.0232034i	−0.000145616	−	0.000735228i
$997$	−20.2677	−	23.3902i	−0.641885	−	0.740774i	0.337822	−	0.941210i	$-0.390310\pi$
$997$	−20.2677	−	23.3902i	−0.641885	−	0.740774i	−0.979707	+	0.200436i	$0.935764\pi$
$998$	18.6653	−	24.2536i	0.590839	−	0.767733i
$999$	−7.86043	−	11.0358i	−0.248693	−	0.349159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.23.16	yes	2640
3.2	odd	2	inner	804.2.bd.a.23.117	yes	2640
4.3	odd	2	inner	804.2.bd.a.23.4	✓	2640
12.11	even	2	inner	804.2.bd.a.23.129	yes	2640
67.35	even	33	inner	804.2.bd.a.35.129	yes	2640
201.35	odd	66	inner	804.2.bd.a.35.4	yes	2640
268.35	odd	66	inner	804.2.bd.a.35.117	yes	2640
804.35	even	66	inner	804.2.bd.a.35.16	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.4	✓	2640	4.3	odd	2	inner
804.2.bd.a.23.16	yes	2640	1.1	even	1	trivial
804.2.bd.a.23.117	yes	2640	3.2	odd	2	inner
804.2.bd.a.23.129	yes	2640	12.11	even	2	inner
804.2.bd.a.35.4	yes	2640	201.35	odd	66	inner
804.2.bd.a.35.16	yes	2640	804.35	even	66	inner
804.2.bd.a.35.117	yes	2640	268.35	odd	66	inner
804.2.bd.a.35.129	yes	2640	67.35	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30733 + 0.539338i) q^{2} +(1.73118 - 0.0550183i) q^{3} +(1.41823 - 1.41019i) q^{4} +(2.63175 - 1.20188i) q^{5} +(-2.23355 + 1.00562i) q^{6} +(0.694593 + 0.728468i) q^{7} +(-1.09353 + 2.60848i) q^{8} +(2.99395 - 0.190493i) q^{9} +O(q^{10})\)	\(q+(-1.30733 + 0.539338i) q^{2} +(1.73118 - 0.0550183i) q^{3} +(1.41823 - 1.41019i) q^{4} +(2.63175 - 1.20188i) q^{5} +(-2.23355 + 1.00562i) q^{6} +(0.694593 + 0.728468i) q^{7} +(-1.09353 + 2.60848i) q^{8} +(2.99395 - 0.190493i) q^{9} +(-2.79235 + 2.99066i) q^{10} +(-1.29365 - 0.123529i) q^{11} +(2.37762 - 2.51931i) q^{12} +(5.25385 + 1.01260i) q^{13} +(-1.30095 - 0.577729i) q^{14} +(4.48990 - 2.22546i) q^{15} +(0.0227512 - 3.99994i) q^{16} +(-2.41551 + 4.68544i) q^{17} +(-3.81134 + 1.86379i) q^{18} +(-3.97078 + 4.16444i) q^{19} +(2.03755 - 5.41580i) q^{20} +(1.24254 + 1.22289i) q^{21} +(1.75785 - 0.536221i) q^{22} +(2.60993 - 1.04486i) q^{23} +(-1.74958 + 4.57591i) q^{24} +(2.20729 - 2.54735i) q^{25} +(-7.41465 + 1.50980i) q^{26} +(5.17257 - 0.494499i) q^{27} +(2.01237 + 0.0536299i) q^{28} +(-0.207920 - 0.120043i) q^{29} +(-4.66951 + 5.33099i) q^{30} +(0.254944 + 1.32277i) q^{31} +(2.12757 + 5.24151i) q^{32} +(-2.24633 - 0.142675i) q^{33} +(0.630840 - 7.42819i) q^{34} +(2.70353 + 1.08233i) q^{35} +(3.97747 - 4.49218i) q^{36} +(-1.30376 - 2.25817i) q^{37} +(2.94509 - 7.58589i) q^{38} +(9.15105 + 1.46392i) q^{39} +(0.257189 + 8.17917i) q^{40} +(-2.96058 + 0.141030i) q^{41} +(-2.28397 - 0.928575i) q^{42} +(-6.47484 - 10.0750i) q^{43} +(-2.00889 + 1.64910i) q^{44} +(7.65037 - 4.09969i) q^{45} +(-2.84851 + 2.77361i) q^{46} +(-7.55715 - 5.94301i) q^{47} +(-0.180683 - 6.92585i) q^{48} +(0.284867 - 5.98009i) q^{49} +(-1.51178 + 4.52070i) q^{50} +(-3.92389 + 8.24421i) q^{51} +(8.87911 - 5.97281i) q^{52} +(5.23723 - 8.14929i) q^{53} +(-6.49556 + 3.43623i) q^{54} +(-3.55303 + 1.22972i) q^{55} +(-2.65976 + 1.01523i) q^{56} +(-6.64501 + 7.42784i) q^{57} +(0.336564 + 0.0447964i) q^{58} +(6.62268 + 7.64298i) q^{59} +(3.22939 - 9.48781i) q^{60} +(-4.91037 + 0.468883i) q^{61} +(-1.04672 - 1.59180i) q^{62} +(2.21834 + 2.04868i) q^{63} +(-5.60839 - 5.70491i) q^{64} +(15.0438 - 3.64959i) q^{65} +(3.01365 - 1.02501i) q^{66} +(-7.61507 - 3.00180i) q^{67} +(3.18159 + 10.0513i) q^{68} +(4.46076 - 1.95243i) q^{69} +(-4.11814 + 0.0431516i) q^{70} +(0.00404944 - 0.00208763i) q^{71} +(-2.77707 + 8.01797i) q^{72} +(7.73998 - 0.739078i) q^{73} +(2.92236 + 2.24901i) q^{74} +(3.68106 - 4.53135i) q^{75} +(0.241148 + 11.5057i) q^{76} +(-0.808573 - 1.02818i) q^{77} +(-12.7530 + 3.02167i) q^{78} +(-13.1272 + 4.54337i) q^{79} +(-4.74757 - 10.5542i) q^{80} +(8.92742 - 1.14065i) q^{81} +(3.79440 - 1.78113i) q^{82} +(0.00396083 - 0.00556221i) q^{83} +(3.48671 - 0.0178742i) q^{84} +(-0.725687 + 15.2340i) q^{85} +(13.8986 + 9.67930i) q^{86} +(-0.366551 - 0.196376i) q^{87} +(1.73687 - 3.23938i) q^{88} +(11.8014 - 1.69678i) q^{89} +(-7.79045 + 9.48579i) q^{90} +(2.91164 + 4.53060i) q^{91} +(2.22804 - 5.16234i) q^{92} +(0.514130 + 2.27593i) q^{93} +(13.0850 + 3.69363i) q^{94} +(-5.44496 + 15.7322i) q^{95} +(3.97158 + 8.95693i) q^{96} +(-2.92429 - 5.06502i) q^{97} +(2.85287 + 7.97160i) q^{98} +(-3.89665 - 0.123407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

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