LMFDB - Embedded newform 378.2.u.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.2
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	378.43
Dual form			378.2.u.b.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.23102 + 1.21844i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.667901 + 0.243096i) q^{5} +(0.159815 + 1.72466i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.0308031 + 2.99984i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.23102 + 1.21844i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.667901 + 0.243096i) q^{5} +(0.159815 + 1.72466i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.0308031 + 2.99984i) q^{9} +(0.355383 + 0.615541i) q^{10} +(0.297791 - 0.108387i) q^{11} +(-0.986166 + 1.42389i) q^{12} +(-0.797414 + 0.669110i) q^{13} +(0.766044 - 0.642788i) q^{14} +(0.525999 + 1.11305i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.219898 + 0.380875i) q^{17} +(-1.90466 + 2.31781i) q^{18} +(2.10431 - 3.64477i) q^{19} +(-0.123423 + 0.699967i) q^{20} +(1.41369 - 1.00073i) q^{21} +(0.297791 + 0.108387i) q^{22} +(-0.0614472 - 0.348484i) q^{23} +(-1.67071 + 0.456871i) q^{24} +(-3.44323 - 2.88921i) q^{25} -1.04095 q^{26} +(-3.61721 + 3.73039i) q^{27} +1.00000 q^{28} +(0.815550 + 0.684328i) q^{29} +(-0.312518 + 1.19075i) q^{30} +(0.00644467 + 0.0365495i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.498648 + 0.229414i) q^{33} +(-0.0763698 + 0.433115i) q^{34} +(0.355383 - 0.615541i) q^{35} +(-2.94892 + 0.551252i) q^{36} +(-3.45851 - 5.99032i) q^{37} +(3.95481 - 1.43943i) q^{38} +(-1.79690 - 0.147917i) q^{39} +(-0.544478 + 0.456871i) q^{40} +(1.76082 - 1.47750i) q^{41} +(1.72621 + 0.142098i) q^{42} +(2.77470 - 1.00991i) q^{43} +(0.158451 + 0.274445i) q^{44} +(-0.708676 + 2.01108i) q^{45} +(0.176930 - 0.306452i) q^{46} +(-0.124417 + 0.705603i) q^{47} +(-1.57351 - 0.723928i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.780516 - 4.42653i) q^{50} +(-0.193375 + 0.736796i) q^{51} +(-0.797414 - 0.669110i) q^{52} -2.66131 q^{53} +(-5.16879 + 0.532543i) q^{54} +0.225243 q^{55} +(0.766044 + 0.642788i) q^{56} +(7.03138 - 1.92280i) q^{57} +(0.184870 + 1.04845i) q^{58} +(11.9263 + 4.34081i) q^{59} +(-1.00480 + 0.711287i) q^{60} +(2.13004 - 12.0800i) q^{61} +(-0.0185567 + 0.0321411i) q^{62} +(2.95962 + 0.490582i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.695251 + 0.253051i) q^{65} +(0.234522 + 0.496266i) q^{66} +(-7.32181 + 6.14373i) q^{67} +(-0.336904 + 0.282696i) q^{68} +(0.348965 - 0.503859i) q^{69} +(0.667901 - 0.243096i) q^{70} +(3.46684 + 6.00474i) q^{71} +(-2.61334 - 1.47324i) q^{72} +(5.26678 - 9.12233i) q^{73} +(1.20113 - 6.81194i) q^{74} +(-0.718336 - 7.75203i) q^{75} +(3.95481 + 1.43943i) q^{76} +(-0.0550295 - 0.312088i) q^{77} +(-1.28143 - 1.26834i) q^{78} +(-8.98910 - 7.54275i) q^{79} -0.710765 q^{80} +(-8.99810 + 0.184809i) q^{81} +2.29858 q^{82} +(3.97128 + 3.33230i) q^{83} +(1.23102 + 1.21844i) q^{84} +(0.0542810 + 0.307843i) q^{85} +(2.77470 + 1.00991i) q^{86} +(0.170143 + 1.83612i) q^{87} +(-0.0550295 + 0.312088i) q^{88} +(-5.34183 + 9.25232i) q^{89} +(-1.83558 + 1.08505i) q^{90} +(0.520475 + 0.901489i) q^{91} +(0.332520 - 0.121027i) q^{92} +(-0.0365999 + 0.0528455i) q^{93} +(-0.548862 + 0.460550i) q^{94} +(2.29150 - 1.92280i) q^{95} +(-0.740046 - 1.56599i) q^{96} +(3.98948 - 1.45205i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.334316 + 0.889986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	$ 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	1.23102	+	1.21844i	0.710728	+	0.703467i
$3$	1.23102	+	1.21844i	0.710728	+	0.703467i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.667901	+	0.243096i	0.298694	+	0.108716i	0.487020	−	0.873391i	$-0.338084\pi$
$5$	0.667901	+	0.243096i	0.298694	+	0.108716i	−0.188326	+	0.982107i	$0.560306\pi$
$6$	0.159815	+	1.72466i	0.0652440	+	0.704090i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.0308031	+	2.99984i	0.0102677	+	0.999947i
$10$	0.355383	+	0.615541i	0.112382	+	0.194651i
$11$	0.297791	−	0.108387i	0.0897872	−	0.0326799i	−0.296736	−	0.954960i	$-0.595898\pi$
$11$	0.297791	−	0.108387i	0.0897872	−	0.0326799i	0.386523	+	0.922280i	$0.373676\pi$
$12$	−0.986166	+	1.42389i	−0.284682	+	0.411043i
$13$	−0.797414	+	0.669110i	−0.221163	+	0.185578i	−0.746637	−	0.665232i	$-0.768333\pi$
$13$	−0.797414	+	0.669110i	−0.221163	+	0.185578i	0.525474	+	0.850810i	$0.323888\pi$
$14$	0.766044	−	0.642788i	0.204734	−	0.171792i
$15$	0.525999	+	1.11305i	0.135812	+	0.287389i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.219898	+	0.380875i	0.0533331	+	0.0923757i	0.891459	−	0.453101i	$-0.149682\pi$
$17$	0.219898	+	0.380875i	0.0533331	+	0.0923757i	−0.838126	+	0.545476i	$0.816349\pi$
$18$	−1.90466	+	2.31781i	−0.448934	+	0.546314i
$19$	2.10431	−	3.64477i	0.482762	−	0.836169i	−0.517042	−	0.855960i	$-0.672967\pi$
$19$	2.10431	−	3.64477i	0.482762	−	0.836169i	0.999804	+	0.0197914i	$0.00630022\pi$
$20$	−0.123423	+	0.699967i	−0.0275982	+	0.156517i
$21$	1.41369	−	1.00073i	0.308493	−	0.218378i
$22$	0.297791	+	0.108387i	0.0634892	+	0.0231082i
$23$	−0.0614472	−	0.348484i	−0.0128126	−	0.0726640i	0.977731	−	0.209862i	$-0.0673015\pi$
$23$	−0.0614472	−	0.348484i	−0.0128126	−	0.0726640i	−0.990544	+	0.137198i	$0.956190\pi$
$24$	−1.67071	+	0.456871i	−0.341032	+	0.0932584i
$25$	−3.44323	−	2.88921i	−0.688645	−	0.577842i
$26$	−1.04095			−0.204147
$27$	−3.61721	+	3.73039i	−0.696133	+	0.717913i
$28$	1.00000			0.188982
$29$	0.815550	+	0.684328i	0.151444	+	0.127077i	0.715362	−	0.698755i	$-0.246262\pi$
$29$	0.815550	+	0.684328i	0.151444	+	0.127077i	−0.563918	+	0.825831i	$0.690706\pi$
$30$	−0.312518	+	1.19075i	−0.0570578	+	0.217401i
$31$	0.00644467	+	0.0365495i	0.00115750	+	0.00656449i	0.985381	−	0.170365i	$-0.0544947\pi$
$31$	0.00644467	+	0.0365495i	0.00115750	+	0.00656449i	−0.984224	+	0.176929i	$0.943384\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.498648	+	0.229414i	0.0868035	+	0.0399359i
$34$	−0.0763698	+	0.433115i	−0.0130973	+	0.0742786i
$35$	0.355383	−	0.615541i	0.0600706	−	0.104045i
$36$	−2.94892	+	0.551252i	−0.491486	+	0.0918754i
$37$	−3.45851	−	5.99032i	−0.568576	−	0.984803i	−0.996707	−	0.0810862i	$-0.974161\pi$
$37$	−3.45851	−	5.99032i	−0.568576	−	0.984803i	0.428131	−	0.903717i	$-0.359172\pi$
$38$	3.95481	−	1.43943i	0.641555	−	0.233507i
$39$	−1.79690	−	0.147917i	−0.287734	−	0.0236856i
$40$	−0.544478	+	0.456871i	−0.0860895	+	0.0722377i
$41$	1.76082	−	1.47750i	0.274993	−	0.230747i	−0.494852	−	0.868977i	$-0.664778\pi$
$41$	1.76082	−	1.47750i	0.274993	−	0.230747i	0.769845	+	0.638230i	$0.220333\pi$
$42$	1.72621	+	0.142098i	0.266360	+	0.0219262i
$43$	2.77470	−	1.00991i	0.423138	−	0.154010i	−0.121669	−	0.992571i	$-0.538825\pi$
$43$	2.77470	−	1.00991i	0.423138	−	0.154010i	0.544808	+	0.838561i	$0.316603\pi$
$44$	0.158451	+	0.274445i	0.0238874	+	0.0413742i
$45$	−0.708676	+	2.01108i	−0.105643	+	0.299795i
$46$	0.176930	−	0.306452i	0.0260869	−	0.0451839i
$47$	−0.124417	+	0.705603i	−0.0181481	+	0.102923i	−0.992536	−	0.121950i	$-0.961085\pi$
$47$	−0.124417	+	0.705603i	−0.0181481	+	0.102923i	0.974388	+	0.224872i	$0.0721965\pi$
$48$	−1.57351	−	0.723928i	−0.227116	−	0.104490i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	−0.780516	−	4.42653i	−0.110382	−	0.626005i
$51$	−0.193375	+	0.736796i	−0.0270779	+	0.103172i
$52$	−0.797414	−	0.669110i	−0.110581	−	0.0927888i
$53$	−2.66131			−0.365559			−0.182779	−	0.983154i	$-0.558509\pi$
$53$	−2.66131			−0.365559			−0.182779	+	0.983154i	$0.558509\pi$
$54$	−5.16879	+	0.532543i	−0.703383	+	0.0724700i
$55$	0.225243			0.0303718
$56$	0.766044	+	0.642788i	0.102367	+	0.0858961i
$57$	7.03138	−	1.92280i	0.931330	−	0.254681i
$58$	0.184870	+	1.04845i	0.0242747	+	0.137668i
$59$	11.9263	+	4.34081i	1.55267	+	0.565125i	0.969042	−	0.246896i	$-0.0794107\pi$
$59$	11.9263	+	4.34081i	1.55267	+	0.565125i	0.583627	+	0.812022i	$0.301633\pi$
$60$	−1.00480	+	0.711287i	−0.129720	+	0.0918268i
$61$	2.13004	−	12.0800i	0.272723	−	1.54669i	−0.473378	−	0.880859i	$-0.656966\pi$
$61$	2.13004	−	12.0800i	0.272723	−	1.54669i	0.746102	−	0.665832i	$-0.231923\pi$
$62$	−0.0185567	+	0.0321411i	−0.00235670	+	0.00408193i
$63$	2.95962	+	0.490582i	0.372877	+	0.0618075i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.695251	+	0.253051i	−0.0862353	+	0.0313871i
$66$	0.234522	+	0.496266i	0.0288677	+	0.0610862i
$67$	−7.32181	+	6.14373i	−0.894502	+	0.750576i	−0.969108	−	0.246637i	$-0.920674\pi$
$67$	−7.32181	+	6.14373i	−0.894502	+	0.750576i	0.0746063	+	0.997213i	$0.476230\pi$
$68$	−0.336904	+	0.282696i	−0.0408556	+	0.0342819i
$69$	0.348965	−	0.503859i	0.0420104	−	0.0606575i
$70$	0.667901	−	0.243096i	0.0798294	−	0.0290555i
$71$	3.46684	+	6.00474i	0.411438	+	0.712631i	0.995047	−	0.0994032i	$-0.0316934\pi$
$71$	3.46684	+	6.00474i	0.411438	+	0.712631i	−0.583609	+	0.812035i	$0.698360\pi$
$72$	−2.61334	−	1.47324i	−0.307985	−	0.173624i
$73$	5.26678	−	9.12233i	0.616430	−	1.06769i	−0.373702	−	0.927549i	$-0.621912\pi$
$73$	5.26678	−	9.12233i	0.616430	−	1.06769i	0.990132	−	0.140139i	$-0.0447549\pi$
$74$	1.20113	−	6.81194i	0.139628	−	0.791872i
$75$	−0.718336	−	7.75203i	−0.0829464	−	0.895128i
$76$	3.95481	+	1.43943i	0.453648	+	0.165114i
$77$	−0.0550295	−	0.312088i	−0.00627119	−	0.0355657i
$78$	−1.28143	−	1.26834i	−0.145093	−	0.143611i
$79$	−8.98910	−	7.54275i	−1.01135	−	0.848626i	−0.0228366	−	0.999739i	$-0.507270\pi$
$79$	−8.98910	−	7.54275i	−1.01135	−	0.848626i	−0.988516	+	0.151113i	$0.951714\pi$
$80$	−0.710765			−0.0794660
$81$	−8.99810	+	0.184809i	−0.999789	+	0.0205343i
$82$	2.29858			0.253836
$83$	3.97128	+	3.33230i	0.435905	+	0.365767i	0.834174	−	0.551501i	$-0.185945\pi$
$83$	3.97128	+	3.33230i	0.435905	+	0.365767i	−0.398270	+	0.917268i	$0.630389\pi$
$84$	1.23102	+	1.21844i	0.134315	+	0.132943i
$85$	0.0542810	+	0.307843i	0.00588760	+	0.0333903i
$86$	2.77470	+	1.00991i	0.299204	+	0.108901i
$87$	0.170143	+	1.83612i	0.0182412	+	0.196853i
$88$	−0.0550295	+	0.312088i	−0.00586616	+	0.0332687i
$89$	−5.34183	+	9.25232i	−0.566233	+	0.980744i	0.430701	+	0.902495i	$0.358266\pi$
$89$	−5.34183	+	9.25232i	−0.566233	+	0.980744i	−0.996934	+	0.0782490i	$0.975067\pi$
$90$	−1.83558	+	1.08505i	−0.193487	+	0.114375i
$91$	0.520475	+	0.901489i	0.0545606	+	0.0945017i
$92$	0.332520	−	0.121027i	0.0346676	−	0.0126180i
$93$	−0.0365999	+	0.0528455i	−0.00379524	+	0.00547982i
$94$	−0.548862	+	0.460550i	−0.0566108	+	0.0475021i
$95$	2.29150	−	1.92280i	0.235103	−	0.197275i
$96$	−0.740046	−	1.56599i	−0.0755306	−	0.159828i
$97$	3.98948	−	1.45205i	0.405070	−	0.147434i	−0.131446	−	0.991323i	$-0.541962\pi$
$97$	3.98948	−	1.45205i	0.405070	−	0.147434i	0.536517	+	0.843890i	$0.319740\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	0.334316	+	0.889986i	0.0336001	+	0.0894470i
$100$	2.24741	−	3.89262i	0.224741	−	0.389262i
$101$	1.70023	−	9.64249i	0.169179	−	0.959463i	−0.775471	−	0.631383i	$-0.782487\pi$
$101$	1.70023	−	9.64249i	0.169179	−	0.959463i	0.944650	−	0.328080i	$-0.106401\pi$
$102$	−0.621738	+	0.440119i	−0.0615612	+	0.0435783i
$103$	2.61040	+	0.950109i	0.257211	+	0.0936170i	0.467407	−	0.884042i	$-0.345188\pi$
$103$	2.61040	+	0.950109i	0.257211	+	0.0936170i	−0.210197	+	0.977659i	$0.567410\pi$
$104$	−0.180759	−	1.02514i	−0.0177249	−	0.100523i
$105$	1.18748	−	0.324728i	0.115886	−	0.0316902i
$106$	−2.03868	−	1.71066i	−0.198014	−	0.166154i
$107$	−5.03129			−0.486393			−0.243197	−	0.969977i	$-0.578196\pi$
$107$	−5.03129			−0.486393			−0.243197	+	0.969977i	$0.578196\pi$
$108$	−4.30184	−	2.91448i	−0.413944	−	0.280446i
$109$	−16.3742			−1.56836			−0.784182	−	0.620531i	$-0.786917\pi$
$109$	−16.3742			−1.56836			−0.784182	+	0.620531i	$0.786917\pi$
$110$	0.172546	+	0.144783i	0.0164516	+	0.0138046i
$111$	3.04137	−	11.5882i	0.288674	−	1.09990i
$112$	0.173648	+	0.984808i	0.0164082	+	0.0930556i
$113$	10.9473	+	3.98450i	1.02984	+	0.374831i	0.801019	−	0.598638i	$-0.204291\pi$
$113$	10.9473	+	3.98450i	1.02984	+	0.374831i	0.228819	+	0.973469i	$0.426514\pi$
$114$	6.62230	+	3.04674i	0.620236	+	0.285353i
$115$	0.0436745	−	0.247690i	0.00407267	−	0.0230972i
$116$	−0.532313	+	0.921992i	−0.0494240	+	0.0856049i
$117$	−2.03179	−	2.37151i	−0.187839	−	0.219246i
$118$	6.34584	+	10.9913i	0.584182	+	1.01183i
$119$	0.413273	−	0.150419i	0.0378847	−	0.0137889i
$120$	−1.22693	−	0.100998i	−0.112003	−	0.00921983i
$121$	−8.34956	+	7.00611i	−0.759051	+	0.636919i
$122$	9.39661	−	7.88469i	0.850729	−	0.713846i
$123$	3.96784	+	0.326623i	0.357768	+	0.0294506i
$124$	−0.0348752	+	0.0126935i	−0.00313188	+	0.00113991i
$125$	−3.37429	−	5.84444i	−0.301806	−	0.522743i
$126$	1.95186	+	2.27821i	0.173885	+	0.202959i
$127$	2.65330	−	4.59565i	0.235442	−	0.407798i	−0.723959	−	0.689843i	$-0.757680\pi$
$127$	2.65330	−	4.59565i	0.235442	−	0.407798i	0.959401	+	0.282045i	$0.0910128\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	4.64622	+	2.13760i	0.409077	+	0.188205i
$130$	−0.695251	−	0.253051i	−0.0609776	−	0.0221940i
$131$	1.26878	+	7.19563i	0.110854	+	0.628685i	0.988720	+	0.149778i	$0.0478558\pi$
$131$	1.26878	+	7.19563i	0.110854	+	0.628685i	−0.877866	+	0.478907i	$0.841033\pi$
$132$	−0.139340	+	0.530910i	−0.0121279	+	0.0462098i
$133$	−3.22399	−	2.70525i	−0.279556	−	0.234575i
$134$	−9.55795			−0.825681
$135$	−3.32278	+	1.61220i	−0.285979	+	0.138756i
$136$	−0.439796			−0.0377122
$137$	−11.7981	−	9.89976i	−1.00798	−	0.845794i	−0.0199083	−	0.999802i	$-0.506337\pi$
$137$	−11.7981	−	9.89976i	−1.00798	−	0.845794i	−0.988070	+	0.154008i	$0.950782\pi$
$138$	0.591197	−	0.161668i	0.0503260	−	0.0137621i
$139$	2.71705	+	15.4092i	0.230458	+	1.30699i	0.851972	+	0.523587i	$0.175407\pi$
$139$	2.71705	+	15.4092i	0.230458	+	1.30699i	−0.621515	+	0.783403i	$0.713482\pi$
$140$	0.667901	+	0.243096i	0.0564479	+	0.0205454i
$141$	−1.01289	+	0.717014i	−0.0853011	+	0.0603835i
$142$	−1.20402	+	6.82834i	−0.101039	+	0.573021i
$143$	−0.164940	+	0.285684i	−0.0137929	+	0.0238901i
$144$	−1.05495	−	2.80839i	−0.0879126	−	0.234033i
$145$	0.378349	+	0.655320i	0.0314202	+	0.0544214i
$146$	9.89831	−	3.60269i	0.819190	−	0.298161i
$147$	−0.740046	−	1.56599i	−0.0610379	−	0.129161i
$148$	5.29875	−	4.44618i	0.435555	−	0.365474i
$149$	−7.58908	+	6.36799i	−0.621721	+	0.521686i	−0.898344	−	0.439292i	$-0.855229\pi$
$149$	−7.58908	+	6.36799i	−0.621721	+	0.521686i	0.276623	+	0.960979i	$0.410785\pi$
$150$	4.43263	−	6.40014i	0.361923	−	0.522569i
$151$	−2.50954	+	0.913399i	−0.204224	+	0.0743313i	−0.442107	−	0.896962i	$-0.645769\pi$
$151$	−2.50954	+	0.913399i	−0.204224	+	0.0743313i	0.237883	+	0.971294i	$0.423547\pi$
$152$	2.10431	+	3.64477i	0.170682	+	0.295630i
$153$	−1.13579	+	0.671392i	−0.0918232	+	0.0542788i
$154$	0.158451	−	0.274445i	0.0127683	−	0.0221154i
$155$	−0.00458065	+	0.0259781i	−0.000367926	+	0.00208661i
$156$	−0.166359	−	1.79529i	−0.0133194	−	0.143738i
$157$	−2.43198	−	0.885168i	−0.194093	−	0.0706441i	0.243145	−	0.969990i	$-0.421821\pi$
$157$	−2.43198	−	0.885168i	−0.194093	−	0.0706441i	−0.437238	+	0.899346i	$0.644043\pi$
$158$	−2.03766	−	11.5562i	−0.162108	−	0.919359i
$159$	−3.27611	−	3.24265i	−0.259813	−	0.257159i
$160$	−0.544478	−	0.456871i	−0.0430447	−	0.0361188i
$161$	−0.353860			−0.0278881
$162$	−7.01174	−	5.64230i	−0.550894	−	0.443301i
$163$	−11.0196			−0.863123			−0.431561	−	0.902084i	$-0.642037\pi$
$163$	−11.0196			−0.863123			−0.431561	+	0.902084i	$0.642037\pi$
$164$	1.76082	+	1.47750i	0.137497	+	0.115373i
$165$	0.277278	+	0.274445i	0.0215860	+	0.0213655i
$166$	0.900216	+	5.10538i	0.0698703	+	0.396254i
$167$	14.7404	+	5.36507i	1.14065	+	0.415161i	0.842147	−	0.539248i	$-0.181292\pi$
$167$	14.7404	+	5.36507i	1.14065	+	0.415161i	0.298500	+	0.954410i	$0.403514\pi$
$168$	0.159815	+	1.72466i	0.0123300	+	0.133061i
$169$	−2.06927	+	11.7354i	−0.159174	+	0.902722i
$170$	−0.156296	+	0.270713i	−0.0119874	+	0.0207627i
$171$	10.9986	+	6.20033i	0.841081	+	0.474151i
$172$	1.47639	+	2.55718i	0.112574	+	0.194983i
$173$	−19.8102	+	7.21033i	−1.50614	+	0.548191i	−0.957643	−	0.287960i	$-0.907023\pi$
$173$	−19.8102	+	7.21033i	−1.50614	+	0.548191i	−0.548500	+	0.836151i	$0.684801\pi$
$174$	−1.04990	+	1.51591i	−0.0795925	+	0.114921i
$175$	−3.44323	+	2.88921i	−0.260283	+	0.218404i
$176$	−0.242761	+	0.203701i	−0.0182988	+	0.0153545i
$177$	9.39242	+	19.8751i	0.705978	+	1.49390i
$178$	−10.0394	+	3.65402i	−0.752481	+	0.273881i
$179$	4.53265	+	7.85078i	0.338786	+	0.586795i	0.984205	−	0.177034i	$-0.0566503\pi$
$179$	4.53265	+	7.85078i	0.338786	+	0.586795i	−0.645418	+	0.763829i	$0.723317\pi$
$180$	−2.10359	−	0.348689i	−0.156793	−	0.0259897i
$181$	8.95886	−	15.5172i	0.665907	−	1.15338i	−0.313132	−	0.949710i	$-0.601378\pi$
$181$	8.95886	−	15.5172i	0.665907	−	1.15338i	0.979039	−	0.203675i	$-0.0652885\pi$
$182$	−0.180759	+	1.02514i	−0.0133988	+	0.0759881i
$183$	17.3409	−	12.2754i	1.28188	−	0.907424i
$184$	0.332520	+	0.121027i	0.0245137	+	0.00892225i
$185$	−0.853721	−	4.84169i	−0.0627668	−	0.355968i
$186$	−0.0620056	+	0.0169560i	−0.00454647	+	0.00124328i
$187$	0.106765	+	0.0895869i	0.00780746	+	0.00655124i
$188$	−0.716488			−0.0522553
$189$	3.04559	+	4.21003i	0.221534	+	0.306235i
$190$	2.99134			0.217015
$191$	−1.59185	−	1.33572i	−0.115182	−	0.0966491i	0.583378	−	0.812201i	$-0.301731\pi$
$191$	−1.59185	−	1.33572i	−0.115182	−	0.0966491i	−0.698559	+	0.715552i	$0.746175\pi$
$192$	0.439693	−	1.67531i	0.0317321	−	0.120905i
$193$	3.01918	+	17.1226i	0.217326	+	1.23251i	0.876825	+	0.480809i	$0.159657\pi$
$193$	3.01918	+	17.1226i	0.217326	+	1.23251i	−0.659500	+	0.751705i	$0.729232\pi$
$194$	3.98948	+	1.45205i	0.286428	+	0.104251i
$195$	−1.16419	−	0.535613i	−0.0833696	−	0.0383560i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	−13.8089	+	23.9177i	−0.983843	+	1.70407i	−0.336874	+	0.941550i	$0.609370\pi$
$197$	−13.8089	+	23.9177i	−0.983843	+	1.70407i	−0.646969	+	0.762517i	$0.723964\pi$
$198$	−0.315971	+	0.896663i	−0.0224551	+	0.0637231i
$199$	7.04613	+	12.2043i	0.499487	+	0.865137i	1.00000		0.000592426i	$-0.000188575\pi$
$199$	7.04613	+	12.2043i	0.499487	+	0.865137i	−0.500513	+	0.865729i	$0.666855\pi$
$200$	4.22374	−	1.53732i	0.298664	−	0.108705i
$201$	−16.4990	−	1.35816i	−1.16375	−	0.0957974i
$202$	7.50052	−	6.29369i	0.527735	−	0.442822i
$203$	0.815550	−	0.684328i	0.0572404	−	0.0480304i
$204$	−0.759182	−	0.0624941i	−0.0531534	−	0.00437546i
$205$	1.53522	−	0.558776i	0.107225	−	0.0390266i
$206$	1.38897	+	2.40576i	0.0967738	+	0.167617i
$207$	1.04350	−	0.195066i	0.0725286	−	0.0135580i
$208$	0.520475	−	0.901489i	0.0360885	−	0.0625070i
$209$	0.231598	−	1.31346i	0.0160200	−	0.0908539i
$210$	1.11839	+	0.514543i	0.0771766	+	0.0355068i
$211$	12.1954	+	4.43878i	0.839569	+	0.305578i	0.725780	−	0.687927i	$-0.241479\pi$
$211$	12.1954	+	4.43878i	0.839569	+	0.305578i	0.113789	+	0.993505i	$0.463701\pi$
$212$	−0.462131	−	2.62088i	−0.0317393	−	0.180003i
$213$	−3.04869	+	11.6161i	−0.208892	+	0.795920i
$214$	−3.85419	−	3.23405i	−0.263467	−	0.221075i
$215$	2.09873			0.143132
$216$	−1.42200	−	4.99779i	−0.0967551	−	0.340057i
$217$	0.0371134			0.00251942
$218$	−12.5434	−	10.5251i	−0.849544	−	0.712852i
$219$	17.5985	−	4.81248i	1.18920	−	0.325197i
$220$	0.0391130	+	0.221821i	0.00263700	+	0.0149552i
$221$	−0.430197	−	0.156579i	−0.0289382	−	0.0105326i
$222$	9.77856	−	6.92211i	0.656294	−	0.464582i
$223$	−1.50759	+	8.54997i	−0.100956	+	0.572548i	0.891803	+	0.452424i	$0.149441\pi$
$223$	−1.50759	+	8.54997i	−0.100956	+	0.572548i	−0.992759	+	0.120125i	$0.961671\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	8.56111	−	10.4181i	0.570741	−	0.694542i
$226$	5.82496	+	10.0891i	0.387470	+	0.671118i
$227$	−18.4781	+	6.72548i	−1.22643	+	0.446386i	−0.872375	−	0.488837i	$-0.837421\pi$
$227$	−18.4781	+	6.72548i	−1.22643	+	0.446386i	−0.354059	+	0.935223i	$0.615199\pi$
$228$	3.11457	+	6.59067i	0.206268	+	0.436478i
$229$	−7.17308	+	6.01893i	−0.474011	+	0.397742i	−0.848255	−	0.529588i	$-0.822347\pi$
$229$	−7.17308	+	6.01893i	−0.474011	+	0.397742i	0.374244	+	0.927330i	$0.377902\pi$
$230$	0.192669	−	0.161668i	0.0127042	−	0.0106601i
$231$	0.312518	−	0.451235i	0.0205622	−	0.0296891i
$232$	−1.00042	+	0.364123i	−0.0656808	+	0.0239059i
$233$	−7.43410	−	12.8762i	−0.487024	−	0.843551i	0.512864	−	0.858470i	$-0.328584\pi$
$233$	−7.43410	−	12.8762i	−0.487024	−	0.843551i	−0.999889	+	0.0149188i	$0.995251\pi$
$234$	−0.0320645	−	3.12269i	−0.00209612	−	0.204136i
$235$	−0.254627	+	0.441027i	−0.0166101	+	0.0287695i
$236$	−2.20389	+	12.4989i	−0.143461	+	0.813607i
$237$	−1.87533	−	20.2379i	−0.121816	−	1.31460i
$238$	0.413273	+	0.150419i	0.0267885	+	0.00975023i
$239$	2.58855	+	14.6804i	0.167440	+	0.949597i	0.946513	+	0.322665i	$0.104579\pi$
$239$	2.58855	+	14.6804i	0.167440	+	0.949597i	−0.779074	+	0.626932i	$0.784310\pi$
$240$	−0.874964	−	0.866025i	−0.0564787	−	0.0559017i
$241$	11.5894	+	9.72466i	0.746539	+	0.626420i	0.934585	−	0.355740i	$-0.115771\pi$
$241$	11.5894	+	9.72466i	0.746539	+	0.626420i	−0.188046	+	0.982160i	$0.560215\pi$
$242$	−10.8996			−0.700651
$243$	−11.3020	−	10.7362i	−0.725023	−	0.688725i
$244$	12.2664			0.785276
$245$	−0.544478	−	0.456871i	−0.0347854	−	0.0291884i
$246$	2.82959	+	2.80069i	0.180408	+	0.178565i
$247$	0.760747	+	4.31441i	0.0484052	+	0.274519i
$248$	−0.0348752	−	0.0126935i	−0.00221457	−	0.000806039i
$249$	0.828501	+	8.94089i	0.0525041	+	0.566606i
$250$	1.17188	−	6.64606i	0.0741161	−	0.420333i
$251$	4.88176	−	8.45545i	0.308134	−	0.533704i	−0.669820	−	0.742523i	$-0.733629\pi$
$251$	4.88176	−	8.45545i	0.308134	−	0.533704i	0.977954	+	0.208820i	$0.0669622\pi$
$252$	0.0308031	+	2.99984i	0.00194041	+	0.188972i
$253$	−0.0560695	−	0.0971152i	−0.00352506	−	0.00610558i
$254$	4.98657	−	1.81496i	0.312885	−	0.113881i
$255$	−0.308268	+	0.445098i	−0.0193045	+	0.0278731i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.8048	+	19.9746i	−1.48490	+	1.24598i	−0.584156	+	0.811641i	$0.698574\pi$
$257$	−23.8048	+	19.9746i	−1.48490	+	1.24598i	−0.900748	+	0.434342i	$0.856981\pi$
$258$	2.18519	+	4.62403i	0.136044	+	0.287879i
$259$	−6.49988	+	2.36576i	−0.403883	+	0.147001i
$260$	−0.369936	−	0.640747i	−0.0229424	−	0.0397374i
$261$	−2.02775	+	2.46760i	−0.125515	+	0.152741i
$262$	−3.65332	+	6.32773i	−0.225703	+	0.390928i
$263$	4.73969	−	26.8801i	0.292262	−	1.65750i	−0.385867	−	0.922554i	$-0.626098\pi$
$263$	4.73969	−	26.8801i	0.292262	−	1.65750i	0.678129	−	0.734943i	$-0.262791\pi$
$264$	−0.448003	+	0.317135i	−0.0275727	+	0.0195183i
$265$	−1.77749	−	0.646954i	−0.109190	−	0.0397420i
$266$	−0.730820	−	4.14468i	−0.0448094	−	0.254127i
$267$	−17.8493	+	4.88105i	−1.09236	+	0.298716i
$268$	−7.32181	−	6.14373i	−0.447251	−	0.375288i
$269$	−3.42609			−0.208892			−0.104446	−	0.994531i	$-0.533307\pi$
$269$	−3.42609			−0.208892			−0.104446	+	0.994531i	$0.533307\pi$
$270$	−3.58170	−	0.900826i	−0.217975	−	0.0548225i
$271$	17.6653			1.07309			0.536547	−	0.843871i	$-0.319729\pi$
$271$	17.6653			1.07309			0.536547	+	0.843871i	$0.319729\pi$
$272$	−0.336904	−	0.282696i	−0.0204278	−	0.0171409i
$273$	−0.457698	+	1.74392i	−0.0277011	+	0.105547i
$274$	−2.67441	−	15.1673i	−0.161567	−	0.916291i
$275$	−1.33851	−	0.487179i	−0.0807154	−	0.0293780i
$276$	0.556802	+	0.256169i	0.0335155	+	0.0154196i
$277$	−0.491127	+	2.78532i	−0.0295090	+	0.167354i	−0.996001	−	0.0893433i	$-0.971523\pi$
$277$	−0.491127	+	2.78532i	−0.0295090	+	0.167354i	0.966492	+	0.256697i	$0.0826343\pi$
$278$	−7.82345	+	13.5506i	−0.469219	+	0.812711i
$279$	−0.109444	+	0.0204588i	−0.00655226	+	0.00122484i
$280$	0.355383	+	0.615541i	0.0212382	+	0.0367856i
$281$	−4.47035	+	1.62708i	−0.266679	+	0.0970632i	−0.471899	−	0.881653i	$-0.656431\pi$
$281$	−4.47035	+	1.62708i	−0.266679	+	0.0970632i	0.205220	+	0.978716i	$0.434209\pi$
$282$	−1.23681	−	0.101811i	−0.0736510	−	0.00606278i
$283$	3.13851	−	2.63352i	0.186565	−	0.156547i	−0.544722	−	0.838617i	$-0.683365\pi$
$283$	3.13851	−	2.63352i	0.186565	−	0.156547i	0.731287	+	0.682070i	$0.238920\pi$
$284$	−5.31150	+	4.45688i	−0.315180	+	0.264467i
$285$	5.16369	+	0.425063i	0.305871	+	0.0251786i
$286$	−0.309985	+	0.112825i	−0.0183298	+	0.00667150i
$287$	−1.14929	−	1.99063i	−0.0678405	−	0.117503i
$288$	0.997061	−	2.82946i	0.0587524	−	0.166728i
$289$	8.40329	−	14.5549i	0.494311	−	0.856172i
$290$	−0.131399	+	0.745203i	−0.00771603	+	0.0437598i
$291$	6.68036	+	3.07345i	0.391609	+	0.180169i
$292$	9.89831	+	3.60269i	0.579255	+	0.210831i
$293$	−2.73342	−	15.5020i	−0.159688	−	0.905635i	−0.954374	−	0.298614i	$-0.903476\pi$
$293$	−2.73342	−	15.5020i	−0.159688	−	0.905635i	0.794686	−	0.607021i	$-0.207635\pi$
$294$	0.439693	−	1.67531i	0.0256434	−	0.0977062i
$295$	6.91034	+	5.79846i	0.402335	+	0.337599i
$296$	6.91703			0.402044
$297$	−0.672846	+	1.50293i	−0.0390425	+	0.0872090i
$298$	−9.90684			−0.573888
$299$	0.282173	+	0.236771i	0.0163185	+	0.0136928i
$300$	7.50952	−	2.05355i	0.433563	−	0.118562i
$301$	−0.512745	−	2.90792i	−0.0295541	−	0.167610i
$302$	−2.50954	−	0.913399i	−0.144408	−	0.0525602i
$303$	13.8418	−	9.79843i	0.795191	−	0.562905i
$304$	−0.730820	+	4.14468i	−0.0419154	+	0.237714i
$305$	4.35926	−	7.55047i	0.249611	−	0.432338i
$306$	−1.30163	−	0.215756i	−0.0744092	−	0.0123340i
$307$	9.73348	+	16.8589i	0.555519	+	0.962188i	0.997863	+	0.0653419i	$0.0208138\pi$
$307$	9.73348	+	16.8589i	0.555519	+	0.962188i	−0.442344	+	0.896846i	$0.645853\pi$
$308$	0.297791	−	0.108387i	0.0169682	−	0.00617592i
$309$	2.05580	+	4.35022i	0.116950	+	0.247475i
$310$	−0.0202074	+	0.0169560i	−0.00114770	+	0.000963037i
$311$	7.98632	−	6.70132i	0.452862	−	0.379997i	−0.387634	−	0.921813i	$-0.626708\pi$
$311$	7.98632	−	6.70132i	0.452862	−	0.379997i	0.840497	+	0.541816i	$0.182263\pi$
$312$	1.02655	−	1.48220i	0.0581169	−	0.0839132i
$313$	16.8397	−	6.12915i	0.951836	−	0.346440i	0.181007	−	0.983482i	$-0.442064\pi$
$313$	16.8397	−	6.12915i	0.951836	−	0.346440i	0.770829	+	0.637042i	$0.219842\pi$
$314$	−1.29403	−	2.24132i	−0.0730262	−	0.126485i
$315$	1.85747	+	1.04713i	0.104657	+	0.0589991i
$316$	5.86722	−	10.1623i	0.330057	−	0.571675i
$317$	1.81529	−	10.2950i	0.101957	−	0.578225i	−0.890436	−	0.455109i	$-0.849600\pi$
$317$	1.81529	−	10.2950i	0.101957	−	0.578225i	0.992392	−	0.123116i	$-0.0392886\pi$
$318$	−0.425316	−	4.58986i	−0.0238505	−	0.257386i
$319$	0.317035	+	0.115391i	0.0177506	+	0.00646068i
$320$	−0.123423	−	0.699967i	−0.00689956	−	0.0391293i
$321$	−6.19360	−	6.13033i	−0.345693	−	0.342162i
$322$	−0.271073	−	0.227457i	−0.0151063	−	0.0126757i
$323$	1.85094			0.102989
$324$	−1.74451	−	8.82931i	−0.0969170	−	0.490517i
$325$	4.67888			0.259537
$326$	−8.44151	−	7.08327i	−0.467532	−	0.392306i
$327$	−20.1569	−	19.9510i	−1.11468	−	1.10329i
$328$	0.399145	+	2.26366i	0.0220391	+	0.124990i
$329$	0.673278	+	0.245053i	0.0371190	+	0.0135102i
$330$	0.0359971	+	0.388468i	0.00198158	+	0.0213845i
$331$	2.39460	−	13.5804i	0.131619	−	0.746448i	−0.845536	−	0.533919i	$-0.820719\pi$
$331$	2.39460	−	13.5804i	0.131619	−	0.746448i	0.977155	−	0.212529i	$-0.0681701\pi$
$332$	−2.59207	+	4.48959i	−0.142258	+	0.246399i
$333$	17.8635	−	10.5595i	0.978913	−	0.578658i
$334$	7.84321	+	13.5848i	0.429161	+	0.743329i
$335$	−6.38376	+	2.32350i	−0.348782	+	0.126946i
$336$	−0.986166	+	1.42389i	−0.0537998	+	0.0776798i
$337$	14.6298	−	12.2759i	0.796937	−	0.668709i	−0.150515	−	0.988608i	$-0.548093\pi$
$337$	14.6298	−	12.2759i	0.796937	−	0.668709i	0.947452	+	0.319898i	$0.103649\pi$
$338$	−9.12851	+	7.65973i	−0.496525	+	0.416634i
$339$	8.62147	+	18.2437i	0.468254	+	0.990860i
$340$	−0.293740	+	0.106913i	−0.0159303	+	0.00579816i
$341$	0.00588065	+	0.0101856i	0.000318455	+	0.000551580i
$342$	4.43989	+	11.8195i	0.240082	+	0.639124i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−0.512745	+	2.90792i	−0.0276453	+	0.156784i
$345$	0.355560	−	0.251696i	0.0191427	−	0.0135509i
$346$	−19.8102	−	7.21033i	−1.06500	−	0.387630i
$347$	1.78057	+	10.0981i	0.0955860	+	0.542095i	0.994566	+	0.104106i	$0.0331981\pi$
$347$	1.78057	+	10.0981i	0.0955860	+	0.542095i	−0.898980	+	0.437989i	$0.855691\pi$
$348$	−1.77868	+	0.486396i	−0.0953472	+	0.0260736i
$349$	−9.49751	−	7.96936i	−0.508390	−	0.426590i	0.352172	−	0.935935i	$-0.385443\pi$
$349$	−9.49751	−	7.96936i	−0.508390	−	0.426590i	−0.860562	+	0.509345i	$0.829888\pi$
$350$	−4.49481			−0.240258
$351$	0.388377	−	5.39497i	0.0207300	−	0.287962i
$352$	−0.316902			−0.0168909
$353$	−22.9363	−	19.2458i	−1.22078	−	1.02435i	−0.998784	−	0.0493035i	$-0.984300\pi$
$353$	−22.9363	−	19.2458i	−1.22078	−	1.02435i	−0.221991	−	0.975049i	$-0.571256\pi$
$354$	−5.58044	+	21.2625i	−0.296597	+	1.13009i
$355$	0.855775	+	4.85334i	0.0454198	+	0.257589i
$356$	−10.0394	−	3.65402i	−0.532085	−	0.193663i
$357$	0.692023	+	0.318381i	0.0366258	+	0.0168505i
$358$	−1.57417	+	8.92758i	−0.0831976	+	0.471837i
$359$	17.4399	−	30.2068i	0.920442	−	1.59425i	0.121710	−	0.992566i	$-0.461162\pi$
$359$	17.4399	−	30.2068i	0.920442	−	1.59425i	0.798732	−	0.601687i	$-0.205505\pi$
$360$	−1.38731	−	1.61927i	−0.0731178	−	0.0853432i
$361$	0.643746	+	1.11500i	0.0338814	+	0.0586842i
$362$	16.8371	−	6.12822i	0.884941	−	0.322092i
$363$	−18.8150	−	1.54881i	−0.987530	−	0.0812912i
$364$	−0.797414	+	0.669110i	−0.0417959	+	0.0350709i
$365$	5.73529	−	4.81248i	0.300199	−	0.251897i
$366$	21.1744	+	1.74303i	1.10680	+	0.0911095i
$367$	−20.0830	+	7.30961i	−1.04832	+	0.381558i	−0.808030	−	0.589142i	$-0.799466\pi$
$367$	−20.0830	+	7.30961i	−1.04832	+	0.381558i	−0.240293	+	0.970700i	$0.577244\pi$
$368$	0.176930	+	0.306452i	0.00922312	+	0.0159749i
$369$	4.48651	+	5.23666i	0.233558	+	0.272610i
$370$	2.45819	−	4.25771i	0.127795	−	0.221348i
$371$	−0.462131	+	2.62088i	−0.0239927	+	0.136069i
$372$	−0.0583982	−	0.0268674i	−0.00302780	−	0.00139301i
$373$	3.12351	+	1.13687i	0.161729	+	0.0588647i	0.421616	−	0.906774i	$-0.361463\pi$
$373$	3.12351	+	1.13687i	0.161729	+	0.0588647i	−0.259887	+	0.965639i	$0.583685\pi$
$374$	0.0242018	+	0.137255i	0.00125144	+	0.00709729i
$375$	2.96730	−	11.3060i	0.153231	−	0.583838i
$376$	−0.548862	−	0.460550i	−0.0283054	−	0.0237510i
$377$	−1.10822			−0.0570763
$378$	−0.373098	+	5.18274i	−0.0191901	+	0.266571i
$379$	−30.3916			−1.56111			−0.780555	−	0.625087i	$-0.785064\pi$
$379$	−30.3916			−1.56111			−0.780555	+	0.625087i	$0.785064\pi$
$380$	2.29150	+	1.92280i	0.117552	+	0.0986375i
$381$	8.86578	−	2.42443i	0.454208	−	0.124207i
$382$	−0.360842	−	2.04644i	−0.0184623	−	0.104705i
$383$	−16.2552	−	5.91640i	−0.830600	−	0.302314i	−0.108495	−	0.994097i	$-0.534603\pi$
$383$	−16.2552	−	5.91640i	−0.830600	−	0.302314i	−0.722105	+	0.691783i	$0.756825\pi$
$384$	1.41369	−	1.00073i	0.0721423	−	0.0510685i
$385$	0.0391130	−	0.221821i	0.00199338	−	0.0113050i
$386$	−8.69339	+	15.0574i	−0.442482	+	0.766401i
$387$	3.11504	+	8.29256i	0.158346	+	0.421535i
$388$	2.12276	+	3.67673i	0.107767	+	0.186657i
$389$	12.5305	−	4.56071i	0.635319	−	0.231237i	−0.00422549	−	0.999991i	$-0.501345\pi$
$389$	12.5305	−	4.56071i	0.635319	−	0.231237i	0.639545	+	0.768754i	$0.279123\pi$
$390$	−0.547538	−	1.15863i	−0.0277257	−	0.0586696i
$391$	0.119217	−	0.100035i	0.00602905	−	0.00505897i
$392$	0.766044	−	0.642788i	0.0386911	−	0.0324657i
$393$	−7.20555	+	10.4039i	−0.363472	+	0.524806i
$394$	−25.9522	+	9.44584i	−1.30745	+	0.475875i
$395$	−4.17022	−	7.22303i	−0.209826	−	0.363430i
$396$	−0.818412	+	0.483782i	−0.0411267	+	0.0243110i
$397$	13.0425	−	22.5902i	0.654583	−	1.13377i	−0.327416	−	0.944880i	$-0.606178\pi$
$397$	13.0425	−	22.5902i	0.654583	−	1.13377i	0.981998	−	0.188890i	$-0.0604889\pi$
$398$	−2.44709	+	13.8782i	−0.122662	+	0.695650i
$399$	−0.672599	−	7.25845i	−0.0336721	−	0.363377i
$400$	4.22374	+	1.53732i	0.211187	+	0.0768658i
$401$	−3.07414	−	17.4343i	−0.153515	−	0.870629i	−0.960131	−	0.279552i	$-0.909814\pi$
$401$	−3.07414	−	17.4343i	−0.153515	−	0.870629i	0.806615	−	0.591077i	$-0.201297\pi$
$402$	−11.7660	−	11.6458i	−0.586834	−	0.580839i
$403$	−0.0295947	−	0.0248329i	−0.00147422	−	0.00123702i
$404$	9.79124			0.487132
$405$	−6.05477	−	2.06397i	−0.300864	−	0.102559i
$406$	1.06463			0.0528365
$407$	−1.67919	−	1.40900i	−0.0832341	−	0.0698417i
$408$	−0.541397	−	0.535866i	−0.0268031	−	0.0265293i
$409$	−2.11240	−	11.9800i	−0.104452	−	0.592374i	−0.991438	−	0.130579i	$-0.958317\pi$
$409$	−2.11240	−	11.9800i	−0.104452	−	0.592374i	0.886986	−	0.461796i	$-0.152795\pi$
$410$	1.53522	+	0.558776i	0.0758193	+	0.0275960i
$411$	−2.46135	−	26.5620i	−0.121410	−	1.31021i
$412$	−0.482383	+	2.73573i	−0.0237653	+	0.134780i
$413$	6.34584	−	10.9913i	0.312258	−	0.540847i
$414$	0.924757	+	0.521322i	0.0454493	+	0.0256216i
$415$	1.84235	+	3.19105i	0.0904375	+	0.156642i
$416$	0.978173	−	0.356026i	0.0479589	−	0.0174556i
$417$	−15.4304	+	22.2795i	−0.755632	+	1.09103i
$418$	1.02169	−	0.857300i	0.0499725	−	0.0419319i
$419$	−15.6759	+	13.1537i	−0.765819	+	0.642599i	−0.939635	−	0.342180i	$-0.888835\pi$
$419$	−15.6759	+	13.1537i	−0.765819	+	0.642599i	0.173815	+	0.984778i	$0.444390\pi$
$420$	0.525999	+	1.11305i	0.0256661	+	0.0543114i
$421$	14.9735	−	5.44991i	0.729764	−	0.265612i	0.0496991	−	0.998764i	$-0.484174\pi$
$421$	14.9735	−	5.44991i	0.729764	−	0.265612i	0.680065	+	0.733152i	$0.261952\pi$
$422$	6.48906	+	11.2394i	0.315883	+	0.547125i
$423$	−2.12053	−	0.351496i	−0.103104	−	0.0170903i
$424$	1.33065	−	2.30476i	0.0646223	−	0.111929i
$425$	0.343268	−	1.94677i	0.0166510	−	0.0944322i
$426$	−9.80209	+	6.93877i	−0.474913	+	0.336184i
$427$	−11.5266	−	4.19535i	−0.557813	−	0.203027i
$428$	−0.873674	−	4.95485i	−0.0422306	−	0.239502i
$429$	−0.551132	+	0.150712i	−0.0266089	+	0.00727646i
$430$	1.60772	+	1.34904i	0.0775312	+	0.0650564i
$431$	41.0697			1.97826			0.989128	−	0.147057i	$-0.0469800\pi$
$431$	41.0697			1.97826			0.989128	+	0.147057i	$0.0469800\pi$
$432$	2.12320	−	4.74258i	0.102152	−	0.228177i
$433$	−1.11049			−0.0533668			−0.0266834	−	0.999644i	$-0.508495\pi$
$433$	−1.11049			−0.0533668			−0.0266834	+	0.999644i	$0.508495\pi$
$434$	0.0284305	+	0.0238560i	0.00136471	+	0.00114513i
$435$	−0.332715	+	1.26771i	−0.0159525	+	0.0607819i
$436$	−2.84335	−	16.1254i	−0.136172	−	0.772268i
$437$	−1.39945	−	0.509358i	−0.0669448	−	0.0243659i
$438$	16.5746	+	7.62553i	0.791967	+	0.364362i
$439$	3.87182	−	21.9582i	0.184792	−	1.04801i	−0.741431	−	0.671030i	$-0.765852\pi$
$439$	3.87182	−	21.9582i	0.184792	−	1.04801i	0.926222	−	0.376977i	$-0.123037\pi$
$440$	−0.112621	+	0.195066i	−0.00536902	+	0.00929941i
$441$	0.997061	−	2.82946i	0.0474791	−	0.134736i
$442$	−0.228903	−	0.396472i	−0.0108878	−	0.0188582i
$443$	3.98956	−	1.45208i	0.189550	−	0.0689905i	−0.245501	−	0.969396i	$-0.578953\pi$
$443$	3.98956	−	1.45208i	0.189550	−	0.0689905i	0.435051	+	0.900406i	$0.356730\pi$
$444$	11.9403	+	0.982895i	0.566660	+	0.0466461i
$445$	−5.81701	+	4.88105i	−0.275753	+	0.231384i
$446$	−6.65070	+	5.58060i	−0.314920	+	0.264249i
$447$	−17.1013	−	1.40774i	−0.808864	−	0.0665838i
$448$	−0.939693	+	0.342020i	−0.0443963	+	0.0161589i
$449$	0.145051	+	0.251236i	0.00684540	+	0.0118566i	0.869428	−	0.494060i	$-0.164488\pi$
$449$	0.145051	+	0.251236i	0.00684540	+	0.0118566i	−0.862582	+	0.505917i	$0.831154\pi$
$450$	13.2548	−	2.47778i	0.624839	−	0.116803i
$451$	0.364213	−	0.630835i	0.0171501	−	0.0297049i
$452$	−2.02299	+	11.4729i	−0.0951533	+	0.539641i
$453$	−4.20221	−	1.93332i	−0.197437	−	0.0908353i
$454$	−18.4781	−	6.72548i	−0.867220	−	0.315642i
$455$	0.128477	+	0.728631i	0.00602311	+	0.0341587i
$456$	−1.85050	+	7.05076i	−0.0866576	+	0.330182i
$457$	24.1057	+	20.2270i	1.12761	+	0.946181i	0.998964	−	0.0455088i	$-0.0144909\pi$
$457$	24.1057	+	20.2270i	1.12761	+	0.946181i	0.128651	+	0.991690i	$0.458935\pi$
$458$	−9.36379			−0.437541
$459$	−2.21623	−	0.557400i	−0.103445	−	0.0260172i
$460$	0.251511			0.0117268
$461$	16.7730	+	14.0742i	0.781196	+	0.655502i	0.943550	−	0.331231i	$-0.107464\pi$
$461$	16.7730	+	14.0742i	0.781196	+	0.655502i	−0.162353	+	0.986733i	$0.551908\pi$
$462$	0.529451	−	0.144783i	0.0246323	−	0.00673593i
$463$	−3.07505	−	17.4395i	−0.142910	−	0.810482i	−0.969022	−	0.246976i	$-0.920563\pi$
$463$	−3.07505	−	17.4395i	−0.142910	−	0.810482i	0.826112	−	0.563506i	$-0.190548\pi$
$464$	−1.00042	−	0.364123i	−0.0464434	−	0.0169040i
$465$	−0.0372917	+	0.0263983i	−0.00172936	+	0.00122419i
$466$	2.58184	−	14.6423i	0.119601	−	0.678293i
$467$	7.37387	−	12.7719i	0.341222	−	0.591014i	−0.643438	−	0.765498i	$-0.722493\pi$
$467$	7.37387	−	12.7719i	0.341222	−	0.591014i	0.984660	+	0.174485i	$0.0558259\pi$
$468$	1.98266	−	2.41273i	0.0916485	−	0.111528i
$469$	4.77897	+	8.27742i	0.220672	+	0.382216i
$470$	−0.478543	+	0.174175i	−0.0220735	+	0.00803411i
$471$	−1.91528	−	4.05288i	−0.0882515	−	0.186747i
$472$	−9.72239	+	8.15805i	−0.447509	+	0.375505i
$473$	0.716820	−	0.601483i	0.0329594	−	0.0276562i
$474$	11.5721	−	16.7086i	0.531525	−	0.767452i
$475$	−17.7761	+	6.46999i	−0.815625	+	0.296863i
$476$	0.219898	+	0.380875i	0.0100790	+	0.0174574i
$477$	−0.0819765	−	7.98351i	−0.00375345	−	0.365540i
$478$	−7.45344	+	12.9097i	−0.340913	+	0.590478i
$479$	1.55557	−	8.82208i	0.0710758	−	0.403091i	−0.928426	−	0.371518i	$-0.878837\pi$
$479$	1.55557	−	8.82208i	0.0710758	−	0.403091i	0.999501	−	0.0315727i	$-0.0100516\pi$
$480$	−0.113591	−	1.22583i	−0.00518468	−	0.0559512i
$481$	6.76605	+	2.46264i	0.308505	+	0.112287i
$482$	2.62710	+	14.8990i	0.119661	+	0.678633i
$483$	−0.435608	−	0.431158i	−0.0198208	−	0.0196184i
$484$	−8.34956	−	7.00611i	−0.379525	−	0.318460i
$485$	3.01757			0.137021
$486$	−1.75676	−	15.4892i	−0.0796883	−	0.702602i
$487$	−24.5700			−1.11337			−0.556686	−	0.830723i	$-0.687927\pi$
$487$	−24.5700			−1.11337			−0.556686	+	0.830723i	$0.687927\pi$
$488$	9.39661	+	7.88469i	0.425364	+	0.356923i
$489$	−13.5653	−	13.4267i	−0.613445	−	0.607178i
$490$	−0.123423	−	0.699967i	−0.00557569	−	0.0316213i
$491$	38.2597	+	13.9254i	1.72664	+	0.628444i	0.998382	−	0.0568622i	$-0.0181096\pi$
$491$	38.2597	+	13.9254i	1.72664	+	0.628444i	0.728255	+	0.685307i	$0.240332\pi$
$492$	0.367347	+	3.96428i	0.0165613	+	0.178723i
$493$	−0.0813053	+	0.461105i	−0.00366180	+	0.0207671i
$494$	−2.19048	+	3.79403i	−0.0985545	+	0.170701i
$495$	0.00693818	+	0.675693i	0.000311848	+	0.0303702i
$496$	−0.0185567	−	0.0321411i	−0.000833220	−	0.00144318i
$497$	6.51552	−	2.37146i	0.292261	−	0.106374i
$498$	−5.11242	+	7.38167i	−0.229093	+	0.330780i
$499$	−5.70104	+	4.78374i	−0.255214	+	0.214150i	−0.761414	−	0.648266i	$-0.775494\pi$
$499$	−5.70104	+	4.78374i	−0.255214	+	0.214150i	0.506200	+	0.862416i	$0.331050\pi$
$500$	5.16971	−	4.33791i	0.231197	−	0.193997i
$501$	11.6087	+	24.5648i	0.518637	+	1.09747i
$502$	9.17471	−	3.33932i	0.409487	−	0.149041i
$503$	−4.58930	−	7.94889i	−0.204627	−	0.354424i	0.745387	−	0.666632i	$-0.232265\pi$
$503$	−4.58930	−	7.94889i	−0.204627	−	0.354424i	−0.950014	+	0.312208i	$0.898931\pi$
$504$	−1.90466	+	2.31781i	−0.0848405	+	0.103244i
$505$	3.47963	−	6.02690i	0.154842	−	0.268194i
$506$	0.0194727	−	0.110435i	0.000865669	−	0.00490945i
$507$	−16.8462	+	11.9252i	−0.748165	+	0.529616i
$508$	4.98657	+	1.81496i	0.221243	+	0.0805260i
$509$	5.97540	+	33.8882i	0.264855	+	1.50207i	0.769447	+	0.638710i	$0.220532\pi$
$509$	5.97540	+	33.8882i	0.264855	+	1.50207i	−0.504592	+	0.863358i	$0.668357\pi$
$510$	−0.522250	+	0.142814i	−0.0231256	+	0.00632392i
$511$	−8.06917	−	6.77084i	−0.356959	−	0.299524i
$512$	1.00000			0.0441942
$513$	5.98468	+	21.0338i	0.264230	+	0.928666i
$514$	−31.0750			−1.37066
$515$	1.51252	+	1.26916i	0.0666497	+	0.0559257i
$516$	−1.29831	+	4.94682i	−0.0571551	+	0.217772i
$517$	0.0394280	+	0.223607i	0.00173404	+	0.00983423i
$518$	−6.49988	−	2.36576i	−0.285588	−	0.103946i
$519$	−33.1721	−	15.2615i	−1.45609	−	0.669907i
$520$	0.128477	−	0.728631i	0.00563410	−	0.0319526i
$521$	5.05150	−	8.74945i	0.221310	−	0.383320i	−0.733896	−	0.679262i	$-0.762300\pi$
$521$	5.05150	−	8.74945i	0.221310	−	0.383320i	0.955206	+	0.295942i	$0.0956334\pi$
$522$	−3.13949	+	0.586877i	−0.137412	+	0.0256869i
$523$	17.9183	+	31.0354i	0.783511	+	1.35708i	0.929884	+	0.367852i	$0.119907\pi$
$523$	17.9183	+	31.0354i	0.783511	+	1.35708i	−0.146373	+	0.989229i	$0.546760\pi$
$524$	−6.86599	+	2.49902i	−0.299942	+	0.109170i
$525$	−7.75900	−	0.638703i	−0.338631	−	0.0278753i
$526$	20.9090	−	17.5447i	0.911676	−	0.764987i
$527$	−0.0125036	+	0.0104918i	−0.000544666	+	0.000457029i
$528$	−0.547040	−	0.0450311i	−0.0238069	−	0.00195973i
$529$	21.4953	−	7.82364i	0.934577	−	0.340158i
$530$	−0.945783	−	1.63814i	−0.0410822	−	0.0711564i
$531$	−12.6544	+	35.9107i	−0.549153	+	1.55839i
$532$	2.10431	−	3.64477i	0.0912335	−	0.158021i
$533$	−0.415490	+	2.35636i	−0.0179969	+	0.102065i
$534$	−16.8108	−	7.73419i	−0.727475	−	0.334691i
$535$	−3.36040	−	1.22309i	−0.145283	−	0.0528786i
$536$	−1.65972	−	9.41274i	−0.0716890	−	0.406568i
$537$	−3.98595	+	15.1872i	−0.172006	+	0.655377i
$538$	−2.62454	−	2.20225i	−0.113152	−	0.0949457i
$539$	−0.316902			−0.0136499
$540$	−2.16470	−	2.99234i	−0.0931539	−	0.128770i
$541$	−23.0842			−0.992466			−0.496233	−	0.868189i	$-0.665284\pi$
$541$	−23.0842			−0.992466			−0.496233	+	0.868189i	$0.665284\pi$
$542$	13.5324	+	11.3551i	0.581268	+	0.487742i
$543$	29.9353	−	8.18609i	1.28465	−	0.351299i
$544$	−0.0763698	−	0.433115i	−0.00327433	−	0.0185696i
$545$	−10.9363	−	3.98050i	−0.468461	−	0.170506i
$546$	−1.47158	+	1.04171i	−0.0629780	+	0.0445813i
$547$	−6.76293	+	38.3545i	−0.289162	+	1.63992i	0.400865	+	0.916137i	$0.368710\pi$
$547$	−6.76293	+	38.3545i	−0.289162	+	1.63992i	−0.690027	+	0.723783i	$0.742402\pi$
$548$	7.70065	−	13.3379i	0.328955	−	0.569768i
$549$	36.3038	+	6.01767i	1.54941	+	0.256828i
$550$	−0.712208	−	1.23358i	−0.0303686	−	0.0526000i
$551$	4.21039	−	1.53246i	0.179369	−	0.0652849i
$552$	0.261873	+	0.554142i	0.0111460	+	0.0235859i
$553$	−8.98910	+	7.54275i	−0.382256	+	0.320750i
$554$	−2.16660	+	1.81799i	−0.0920498	+	0.0772390i
$555$	4.84837	−	7.00041i	0.205802	−	0.297151i
$556$	−14.7033	+	5.35155i	−0.623558	+	0.226956i
$557$	19.3192	+	33.4619i	0.818582	+	1.41783i	0.906727	+	0.421718i	$0.138573\pi$
$557$	19.3192	+	33.4619i	0.818582	+	1.41783i	−0.0881449	+	0.996108i	$0.528094\pi$
$558$	−0.0969899	−	0.0546771i	−0.00410591	−	0.00231466i
$559$	−1.53685	+	2.66190i	−0.0650017	+	0.112586i
$560$	−0.123423	+	0.699967i	−0.00521558	+	0.0295790i
$561$	0.0222737	+	0.240370i	0.000940398	+	0.0101484i
$562$	−4.47035	−	1.62708i	−0.188570	−	0.0686340i
$563$	−0.537965	−	3.05095i	−0.0226725	−	0.128582i	0.971371	−	0.237569i	$-0.0763505\pi$
$563$	−0.537965	−	3.05095i	−0.0226725	−	0.128582i	−0.994043	+	0.108987i	$0.965239\pi$
$564$	−0.882008	−	0.872998i	−0.0371393	−	0.0367599i
$565$	6.34312	+	5.32251i	0.266857	+	0.223920i
$566$	4.09703			0.172211
$567$	−1.38050	+	8.89349i	−0.0579757	+	0.373492i
$568$	−6.93367			−0.290931
$569$	24.0602	+	20.1889i	1.00865	+	0.846362i	0.988160	−	0.153428i	$-0.0490313\pi$
$569$	24.0602	+	20.1889i	1.00865	+	0.846362i	0.0204950	+	0.999790i	$0.493476\pi$
$570$	3.68239	+	3.64477i	0.154238	+	0.152663i
$571$	−0.974927	−	5.52909i	−0.0407994	−	0.231385i	0.957589	−	0.288138i	$-0.0930363\pi$
$571$	−0.974927	−	5.52909i	−0.0407994	−	0.231385i	−0.998388	+	0.0567532i	$0.981925\pi$
$572$	−0.309985	−	0.112825i	−0.0129611	−	0.00471746i
$573$	−0.332096	−	3.58386i	−0.0138735	−	0.149718i
$574$	0.399145	−	2.26366i	0.0166600	−	0.0944834i
$575$	−0.795267	+	1.37744i	−0.0331649	+	0.0574434i
$576$	2.58254	−	1.52660i	0.107606	−	0.0636082i
$577$	−2.23897	−	3.87800i	−0.0932094	−	0.161443i	0.815650	−	0.578545i	$-0.196379\pi$
$577$	−2.23897	−	3.87800i	−0.0932094	−	0.161443i	−0.908860	+	0.417102i	$0.863046\pi$
$578$	15.7930	−	5.74819i	0.656903	−	0.239093i
$579$	−17.1463	+	24.7569i	−0.712574	+	1.02886i
$580$	−0.579665	+	0.486396i	−0.0240693	+	0.0201965i
$581$	3.97128	−	3.33230i	0.164756	−	0.138247i
$582$	3.14188	+	6.64845i	0.130235	+	0.275587i
$583$	−0.792513	+	0.288451i	−0.0328225	+	0.0119464i
$584$	5.26678	+	9.12233i	0.217941	+	0.377485i
$585$	−0.780528	−	2.07785i	−0.0322709	−	0.0859085i
$586$	7.87056	−	13.6322i	0.325130	−	0.563141i
$587$	−7.07940	+	40.1493i	−0.292198	+	1.65714i	0.386178	+	0.922424i	$0.373795\pi$
$587$	−7.07940	+	40.1493i	−0.292198	+	1.65714i	−0.678376	+	0.734715i	$0.737316\pi$
$588$	1.41369	−	1.00073i	0.0582998	−	0.0412696i
$589$	0.146776	+	0.0534222i	0.00604781	+	0.00220122i
$590$	1.56645	+	8.88376i	0.0644896	+	0.365739i
$591$	−46.1413	+	12.6178i	−1.89800	+	0.519026i
$592$	5.29875	+	4.44618i	0.217777	+	0.182737i
$593$	37.6571			1.54639			0.773196	−	0.634167i	$-0.218657\pi$
$593$	37.6571			1.54639			0.773196	+	0.634167i	$0.218657\pi$
$594$	−1.48150	+	0.718816i	−0.0607865	+	0.0294934i
$595$	0.312592			0.0128150
$596$	−7.58908	−	6.36799i	−0.310861	−	0.260843i
$597$	−6.19626	+	23.6089i	−0.253596	+	0.966249i
$598$	0.0639634	+	0.362755i	0.00261566	+	0.0148341i
$599$	13.8231	+	5.03121i	0.564798	+	0.205570i	0.608609	−	0.793470i	$-0.291728\pi$
$599$	13.8231	+	5.03121i	0.564798	+	0.205570i	−0.0438113	+	0.999040i	$0.513950\pi$
$600$	7.07263	+	3.25392i	0.288739	+	0.132841i
$601$	3.21107	−	18.2109i	0.130982	−	0.742837i	−0.846591	−	0.532243i	$-0.821349\pi$
$601$	3.21107	−	18.2109i	0.130982	−	0.742837i	0.977574	−	0.210594i	$-0.0675398\pi$
$602$	1.47639	−	2.55718i	0.0601731	−	0.104223i
$603$	−18.6557	−	21.7750i	−0.759721	−	0.886748i
$604$	−1.33530	−	2.31281i	−0.0543326	−	0.0941068i
$605$	−7.27983	+	2.64964i	−0.295967	+	0.107723i
$606$	16.9018	+	1.39131i	0.686587	+	0.0565182i
$607$	5.65601	−	4.74595i	0.229570	−	0.192632i	−0.520745	−	0.853712i	$-0.674346\pi$
$607$	5.65601	−	4.74595i	0.229570	−	0.192632i	0.750316	+	0.661080i	$0.229901\pi$
$608$	−3.22399	+	2.70525i	−0.130750	+	0.109712i
$609$	1.83777	+	0.151281i	0.0744702	+	0.00613021i
$610$	8.19274	−	2.98191i	0.331714	−	0.120734i
$611$	−0.372914	−	0.645906i	−0.0150865	−	0.0261306i
$612$	−0.858420	−	1.00195i	−0.0346996	−	0.0405014i
$613$	−9.97458	+	17.2765i	−0.402869	+	0.697790i	−0.994071	−	0.108734i	$-0.965320\pi$
$613$	−9.97458	+	17.2765i	−0.402869	+	0.697790i	0.591202	+	0.806524i	$0.298654\pi$
$614$	−3.38040	+	19.1712i	−0.136422	+	0.773687i
$615$	2.57072	+	1.18272i	0.103662	+	0.0476918i
$616$	0.297791	+	0.108387i	0.0119983	+	0.00436703i
$617$	−1.96967	−	11.1705i	−0.0792959	−	0.449709i	−0.998442	−	0.0557934i	$-0.982231\pi$
$617$	−1.96967	−	11.1705i	−0.0792959	−	0.449709i	0.919146	−	0.393916i	$-0.128880\pi$
$618$	−1.22144	+	4.65390i	−0.0491334	+	0.187207i
$619$	16.8949	+	14.1765i	0.679063	+	0.569802i	0.915732	−	0.401789i	$-0.131611\pi$
$619$	16.8949	+	14.1765i	0.679063	+	0.569802i	−0.236669	+	0.971590i	$0.576056\pi$
$620$	−0.0263789			−0.00105940
$621$	1.52225	+	1.03132i	0.0610857	+	0.0413854i
$622$	10.4254			0.418020
$623$	8.18415	+	6.86732i	0.327891	+	0.275133i
$624$	1.73912	−	0.475580i	0.0696207	−	0.0190384i
$625$	3.06965	+	17.4088i	0.122786	+	0.696354i
$626$	16.8397	+	6.12915i	0.673050	+	0.244970i
$627$	1.88547	−	1.33470i	0.0752986	−	0.0533028i
$628$	0.449411	−	2.54874i	0.0179335	−	0.101706i
$629$	1.52104	−	2.63452i	0.0606479	−	0.105045i
$630$	0.749823	+	1.99611i	0.0298737	+	0.0795269i
$631$	0.263910	+	0.457106i	0.0105061	+	0.0181971i	0.871231	−	0.490874i	$-0.163322\pi$
$631$	0.263910	+	0.457106i	0.0105061	+	0.0181971i	−0.860725	+	0.509071i	$0.829989\pi$
$632$	11.0268	−	4.01341i	0.438621	−	0.159645i
$633$	9.60441	+	20.3236i	0.381741	+	0.807792i
$634$	8.00809	−	6.71958i	0.318042	−	0.266869i
$635$	2.88932	−	2.42443i	0.114659	−	0.0962106i
$636$	2.62449	−	3.78942i	0.104068	−	0.150260i
$637$	0.978173	−	0.356026i	0.0387566	−	0.0141063i
$638$	0.168691	+	0.292181i	0.00667854	+	0.0115676i
$639$	−17.9065	+	10.5849i	−0.708369	+	0.418733i
$640$	0.355383	−	0.615541i	0.0140477	−	0.0243314i
$641$	3.30794	−	18.7602i	0.130656	−	0.740985i	−0.847131	−	0.531384i	$-0.821672\pi$
$641$	3.30794	−	18.7602i	0.130656	−	0.740985i	0.977787	−	0.209601i	$-0.0672166\pi$
$642$	−0.804073	−	8.67727i	−0.0317342	−	0.342465i
$643$	−28.0855	−	10.2223i	−1.10759	−	0.403128i	−0.277478	−	0.960732i	$-0.589499\pi$
$643$	−28.0855	−	10.2223i	−1.10759	−	0.403128i	−0.830107	+	0.557604i	$0.811721\pi$
$644$	−0.0614472	−	0.348484i	−0.00242136	−	0.0137322i
$645$	2.58357	+	2.55718i	0.101728	+	0.100689i
$646$	1.41790	+	1.18976i	0.0557865	+	0.0468105i
$647$	−25.2248			−0.991688			−0.495844	−	0.868412i	$-0.665141\pi$
$647$	−25.2248			−0.991688			−0.495844	+	0.868412i	$0.665141\pi$
$648$	4.33900	−	7.88499i	0.170452	−	0.309752i
$649$	4.02202			0.157878
$650$	3.58423	+	3.00752i	0.140585	+	0.117965i
$651$	0.0456872	+	0.0452204i	0.00179062	+	0.00177233i
$652$	−1.91354	−	10.8522i	−0.0749398	−	0.425005i
$653$	−23.2190	−	8.45103i	−0.908631	−	0.330714i	−0.154925	−	0.987926i	$-0.549513\pi$
$653$	−23.2190	−	8.45103i	−0.908631	−	0.330714i	−0.753706	+	0.657212i	$0.771736\pi$
$654$	−2.61684	−	28.2400i	−0.102326	−	1.10427i
$655$	−0.901807	+	5.11440i	−0.0352365	+	0.199836i
$656$	−1.14929	+	1.99063i	−0.0448723	+	0.0777211i
$657$	27.5278	+	15.5185i	1.07396	+	0.605435i
$658$	0.358244	+	0.620497i	0.0139658	+	0.0241895i
$659$	−24.0047	+	8.73701i	−0.935092	+	0.340346i	−0.764226	−	0.644949i	$-0.776879\pi$
$659$	−24.0047	+	8.73701i	−0.935092	+	0.340346i	−0.170866	+	0.985294i	$0.554657\pi$
$660$	−0.222127	+	0.320722i	−0.00864628	+	0.0124841i
$661$	32.2958	−	27.0994i	1.25616	−	1.05404i	0.260081	−	0.965587i	$-0.416251\pi$
$661$	32.2958	−	27.0994i	1.25616	−	1.05404i	0.996080	−	0.0884570i	$-0.0281936\pi$
$662$	10.5637	−	8.86400i	0.410570	−	0.344509i
$663$	−0.338797	−	0.716921i	−0.0131578	−	0.0278429i
$664$	−4.87150	+	1.77308i	−0.189051	+	0.0688088i
$665$	−1.49567	−	2.59058i	−0.0579996	−	0.100458i
$666$	20.4718	+	3.39337i	0.793264	+	0.131490i
$667$	0.188364	−	0.326256i	0.00729349	−	0.0126327i
$668$	−2.72392	+	15.4481i	−0.105392	+	0.597705i
$669$	−12.2735	+	8.68824i	−0.474521	+	0.335907i
$670$	−6.38376	−	2.32350i	−0.246626	−	0.0897646i
$671$	−0.675013	−	3.82819i	−0.0260586	−	0.147786i
$672$	−1.67071	+	0.456871i	−0.0644490	+	0.0176242i
$673$	17.0651	+	14.3193i	0.657810	+	0.551968i	0.909430	−	0.415858i	$-0.136519\pi$
$673$	17.0651	+	14.3193i	0.657810	+	0.551968i	−0.251620	+	0.967826i	$0.580963\pi$
$674$	19.0979			0.735622
$675$	23.2327	−	2.39368i	0.894229	−	0.0921329i
$676$	−11.9164			−0.458324
$677$	27.2843	+	22.8943i	1.04862	+	0.879898i	0.992948	−	0.118551i	$-0.0378249\pi$
$677$	27.2843	+	22.8943i	1.04862	+	0.879898i	0.0556736	+	0.998449i	$0.482269\pi$
$678$	−5.12238	+	19.5172i	−0.196724	+	0.749555i
$679$	−0.737226	−	4.18102i	−0.0282921	−	0.160453i
$680$	−0.293740	−	0.106913i	−0.0112644	−	0.00409992i
$681$	−30.9414	−	14.2353i	−1.18568	−	0.545498i
$682$	−0.00204233	+	0.0115826i	−7.82048e−5	+	0.000443521i
$683$	15.6269	−	27.0666i	0.597947	−	1.03568i	−0.395176	−	0.918605i	$-0.629316\pi$
$683$	15.6269	−	27.0666i	0.597947	−	1.03568i	0.993124	−	0.117070i	$-0.0373502\pi$
$684$	−4.19625	+	11.9081i	−0.160448	+	0.455319i
$685$	−5.47335	−	9.48013i	−0.209126	−	0.362217i
$686$	−0.939693	+	0.342020i	−0.0358776	+	0.0130584i
$687$	−16.1639	−	1.33057i	−0.616691	−	0.0507646i
$688$	−2.26196	+	1.89801i	−0.0862364	+	0.0723609i
$689$	2.12216	−	1.78071i	0.0808480	−	0.0678396i
$690$	0.434162	+	0.0357392i	0.0165283	+	0.00136057i
$691$	9.75707	−	3.55128i	0.371177	−	0.135097i	−0.149695	−	0.988732i	$-0.547829\pi$
$691$	9.75707	−	3.55128i	0.371177	−	0.135097i	0.520872	+	0.853635i	$0.325607\pi$
$692$	−10.5408	−	18.2572i	−0.400701	−	0.694034i
$693$	0.934519	−	0.174693i	0.0354994	−	0.00663604i
$694$	−5.12695	+	8.88013i	−0.194616	+	0.337085i
$695$	−1.93119	+	10.9523i	−0.0732541	+	0.415445i
$696$	−1.67520	−	0.770712i	−0.0634982	−	0.0292137i
$697$	0.949943	+	0.345751i	0.0359817	+	0.0130963i
$698$	−2.15291	−	12.2098i	−0.0814889	−	0.462146i
$699$	6.53744	−	24.9089i	0.247269	−	0.942141i
$700$	−3.44323	−	2.88921i	−0.130142	−	0.109202i
$701$	−3.43141			−0.129603			−0.0648013	−	0.997898i	$-0.520641\pi$
$701$	−3.43141			−0.129603			−0.0648013	+	0.997898i	$0.520641\pi$
$702$	3.76534	−	3.88315i	0.142113	−	0.146560i
$703$	−29.1112			−1.09795
$704$	−0.242761	−	0.203701i	−0.00914940	−	0.00767726i
$705$	−0.850816	+	0.232664i	−0.0320436	+	0.00876262i
$706$	−5.19923	−	29.4863i	−0.195676	−	1.10973i
$707$	−9.20075	−	3.34880i	−0.346030	−	0.125945i
$708$	−17.9422	+	12.7010i	−0.674307	+	0.477333i
$709$	4.51366	−	25.5982i	0.169514	−	0.961362i	−0.774773	−	0.632240i	$-0.782136\pi$
$709$	4.51366	−	25.5982i	0.169514	−	0.961362i	0.944287	−	0.329123i	$-0.106753\pi$
$710$	−2.46411	+	4.26796i	−0.0924763	+	0.160174i
$711$	22.3502	−	27.1982i	0.838197	−	1.02001i
$712$	−5.34183	−	9.25232i	−0.200193	−	0.346745i
$713$	0.0123409	−	0.00449173i	0.000462171	−	0.000168217i
$714$	0.325469	+	0.688718i	0.0121804	+	0.0257746i
$715$	−0.179612	+	0.150712i	−0.00671710	+	0.00563632i
$716$	−6.94442	+	5.82706i	−0.259525	+	0.217768i
$717$	−14.7007	+	21.2258i	−0.549007	+	0.792693i
$718$	32.7763	−	11.9296i	1.22320	−	0.445208i
$719$	−10.3356	−	17.9018i	−0.385453	−	0.667624i	0.606379	−	0.795176i	$-0.292621\pi$
$719$	−10.3356	−	17.9018i	−0.385453	−	0.667624i	−0.991832	+	0.127552i	$0.959288\pi$
$720$	−0.0218938	−	2.13218i	−0.000815932	−	0.0794618i
$721$	1.38897	−	2.40576i	0.0517278	−	0.0895952i
$722$	−0.223571	+	1.26793i	−0.00832044	+	0.0471875i
$723$	2.41782	+	26.0922i	0.0899195	+	0.970380i
$724$	16.8371	+	6.12822i	0.625748	+	0.227754i
$725$	−0.830957	−	4.71259i	−0.0308610	−	0.175021i
$726$	−13.4176	−	13.2805i	−0.497972	−	0.492885i
$727$	−9.51131	−	7.98094i	−0.352755	−	0.295997i	0.449140	−	0.893461i	$-0.351730\pi$
$727$	−9.51131	−	7.98094i	−0.352755	−	0.295997i	−0.801895	+	0.597465i	$0.796175\pi$
$728$	−1.04095			−0.0385802
$729$	−0.831566	−	26.9872i	−0.0307988	−	0.999526i
$730$	7.48689			0.277102
$731$	0.994802	+	0.834738i	0.0367941	+	0.0308739i
$732$	15.1001	+	14.9459i	0.558117	+	0.552416i
$733$	0.239065	+	1.35580i	0.00883006	+	0.0500778i	0.988904	−	0.148553i	$-0.0474616\pi$
$733$	0.239065	+	1.35580i	0.00883006	+	0.0500778i	−0.980074	+	0.198631i	$0.936350\pi$
$734$	−20.0830	−	7.30961i	−0.741276	−	0.269803i
$735$	−0.113591	−	1.22583i	−0.00418985	−	0.0452154i
$736$	−0.0614472	+	0.348484i	−0.00226497	+	0.0128453i
$737$	−1.51447	+	2.62313i	−0.0557861	+	0.0966243i
$738$	0.0708034	+	6.89538i	0.00260631	+	0.253823i
$739$	−12.8366	−	22.2337i	−0.472202	−	0.817878i	0.527292	−	0.849684i	$-0.323207\pi$
$739$	−12.8366	−	22.2337i	−0.472202	−	0.817878i	−0.999494	+	0.0318059i	$0.989874\pi$
$740$	4.61989	−	1.68150i	0.169830	−	0.0618132i
$741$	−4.32036	+	6.23803i	−0.158712	+	0.229160i
$742$	−2.03868	+	1.71066i	−0.0748423	+	0.0628002i
$743$	30.2494	−	25.3823i	1.10974	−	0.931184i	0.111701	−	0.993742i	$-0.464370\pi$
$743$	30.2494	−	25.3823i	1.10974	−	0.931184i	0.998041	+	0.0625574i	$0.0199257\pi$
$744$	−0.0274656	−	0.0581192i	−0.00100694	−	0.00213075i
$745$	−6.61678	+	2.40831i	−0.242420	+	0.0882337i
$746$	1.66199	+	2.87865i	0.0608497	+	0.105395i
$747$	−9.87404	+	12.0159i	−0.361272	+	0.439637i
$748$	−0.0696862	+	0.120700i	−0.00254798	+	0.00441323i
$749$	−0.873674	+	4.95485i	−0.0319234	+	0.181046i
$750$	9.54043	−	6.75354i	0.348367	−	0.246604i
$751$	4.43165	+	1.61299i	0.161713	+	0.0588587i	0.421608	−	0.906778i	$-0.361466\pi$
$751$	4.43165	+	1.61299i	0.161713	+	0.0588587i	−0.259895	+	0.965637i	$0.583688\pi$
$752$	−0.124417	−	0.705603i	−0.00453701	−	0.0257307i
$753$	16.3120	−	4.46067i	0.594442	−	0.162556i
$754$	−0.848947	−	0.712351i	−0.0309168	−	0.0259423i
$755$	−1.89817			−0.0690814
$756$	−3.61721	+	3.73039i	−0.131557	+	0.135673i
$757$	−50.3789			−1.83105			−0.915527	−	0.402257i	$-0.868226\pi$
$757$	−50.3789			−1.83105			−0.915527	+	0.402257i	$0.868226\pi$
$758$	−23.2813	−	19.5353i	−0.845615	−	0.709555i
$759$	0.0493067	−	0.187868i	0.00178972	−	0.00681917i
$760$	0.519441	+	2.94590i	0.0188421	+	0.106859i
$761$	−42.0690	−	15.3118i	−1.52500	−	0.555054i	−0.562608	−	0.826724i	$-0.690202\pi$
$761$	−42.0690	−	15.3118i	−1.52500	−	0.555054i	−0.962391	+	0.271670i	$0.912424\pi$
$762$	8.34997	+	3.84159i	0.302488	+	0.139166i
$763$	−2.84335	+	16.1254i	−0.102936	+	0.583780i
$764$	1.03900	−	1.79961i	0.0375898	−	0.0651075i
$765$	−0.921808	+	0.172317i	−0.0333280	+	0.00623013i
$766$	−8.64919	−	14.9808i	−0.312508	−	0.541280i
$767$	−12.4147	+	4.51857i	−0.448267	+	0.163156i
$768$	1.72621	+	0.142098i	0.0622893	+	0.00512751i
$769$	−4.46582	+	3.74727i	−0.161042	+	0.135130i	−0.719748	−	0.694236i	$-0.755742\pi$
$769$	−4.46582	+	3.74727i	−0.161042	+	0.135130i	0.558706	+	0.829366i	$0.311298\pi$
$770$	0.172546	−	0.144783i	0.00621813	−	0.00521763i
$771$	−53.6420	−	4.41569i	−1.93187	−	0.159027i
$772$	−16.3382	+	5.94663i	−0.588026	+	0.214024i
$773$	−3.09411	−	5.35916i	−0.111288	−	0.192756i	0.805002	−	0.593272i	$-0.202164\pi$
$773$	−3.09411	−	5.35916i	−0.111288	−	0.192756i	−0.916290	+	0.400516i	$0.868831\pi$
$774$	−2.94410	+	8.35478i	−0.105823	+	0.300306i
$775$	0.0834088	−	0.144468i	0.00299613	−	0.00518945i
$776$	−0.737226	+	4.18102i	−0.0264649	+	0.150090i
$777$	−10.8840	−	5.00743i	−0.390461	−	0.179640i
$778$	12.5305	+	4.56071i	0.449239	+	0.163510i
$779$	−1.67985	−	9.52690i	−0.0601868	−	0.341337i
$780$	0.325316	−	1.23951i	0.0116482	−	0.0443818i
$781$	1.68323	+	1.41239i	0.0602306	+	0.0505395i
$782$	0.155626			0.00556519
$783$	−5.50282	+	0.566959i	−0.196655	+	0.0202615i
$784$	1.00000			0.0357143
$785$	−1.40914	−	1.18241i	−0.0502943	−	0.0422020i
$786$	−12.2073	+	3.33819i	−0.435418	+	0.119069i
$787$	−6.44408	−	36.5462i	−0.229707	−	1.30273i	−0.853480	−	0.521126i	$-0.825512\pi$
$787$	−6.44408	−	36.5462i	−0.229707	−	1.30273i	0.623773	−	0.781606i	$-0.285599\pi$
$788$	−25.9522	−	9.44584i	−0.924510	−	0.336494i
$789$	38.5864	−	27.3148i	1.37371	−	0.972433i
$790$	1.44830	−	8.21372i	0.0515282	−	0.292231i
$791$	5.82496	−	10.0891i	0.207112	−	0.358728i
$792$	−0.937909	−	0.155466i	−0.0333271	−	0.00552426i
$793$	6.38435	+	11.0580i	0.226715	+	0.392682i
$794$	24.5118	−	8.92157i	0.869892	−	0.316615i
$795$	−1.39985	−	2.96218i	−0.0496474	−	0.105058i
$796$	−10.7953	+	9.05833i	−0.382629	+	0.321064i
$797$	−13.3318	+	11.1867i	−0.472237	+	0.396254i	−0.847610	−	0.530620i	$-0.821959\pi$
$797$	−13.3318	+	11.1867i	−0.472237	+	0.396254i	0.375373	+	0.926874i	$0.377515\pi$
$798$	4.15040	−	5.99264i	0.146923	−	0.212137i
$799$	−0.296105	+	0.107774i	−0.0104755	+	0.00381275i
$800$	2.24741	+	3.89262i	0.0794578	+	0.137625i
$801$	−27.9200	−	15.7396i	−0.986506	−	0.556133i
$802$	8.85164	−	15.3315i	0.312562	−	0.541374i
$803$	0.579656	−	3.28739i	0.0204556	−	0.116010i
$804$	−1.52750	−	16.4842i	−0.0538707	−	0.581354i
$805$	−0.236343	−	0.0860220i	−0.00833001	−	0.00303188i
$806$	−0.00670858	−	0.0380462i	−0.000236300	−	0.00134012i
$807$	−4.21757	−	4.17449i	−0.148466	−	0.146949i
$808$	7.50052	+	6.29369i	0.263867	+	0.221411i
$809$	−8.42701			−0.296278			−0.148139	−	0.988967i	$-0.547328\pi$
$809$	−8.42701			−0.296278			−0.148139	+	0.988967i	$0.547328\pi$
$810$	−3.31153	−	5.47302i	−0.116355	−	0.192302i
$811$	3.40177			0.119452			0.0597261	−	0.998215i	$-0.480977\pi$
$811$	3.40177			0.119452			0.0597261	+	0.998215i	$0.480977\pi$
$812$	0.815550	+	0.684328i	0.0286202	+	0.0240152i
$813$	21.7463	+	21.5242i	0.762677	+	0.754886i
$814$	−0.380640	−	2.15872i	−0.0133414	−	0.0756631i
$815$	−7.36001	−	2.67882i	−0.257810	−	0.0938351i
$816$	−0.0702859	−	0.758500i	−0.00246050	−	0.0265528i
$817$	2.15795	−	12.2383i	0.0754971	−	0.428165i
$818$	6.08242	−	10.5351i	0.212667	−	0.368350i
$819$	−2.68829	+	1.58911i	−0.0939366	+	0.0555280i
$820$	0.816876	+	1.41487i	0.0285265	+	0.0494094i
$821$	−7.08018	+	2.57697i	−0.247100	+	0.0899370i	−0.462601	−	0.886567i	$-0.653084\pi$
$821$	−7.08018	+	2.57697i	−0.247100	+	0.0899370i	0.215501	+	0.976504i	$0.430862\pi$
$822$	15.1882	−	21.9298i	0.529751	−	0.764891i
$823$	28.0453	−	23.5328i	0.977599	−	0.820303i	−0.00612677	−	0.999981i	$-0.501950\pi$
$823$	28.0453	−	23.5328i	0.977599	−	0.820303i	0.983725	+	0.179679i	$0.0575058\pi$
$824$	−2.12802	+	1.78562i	−0.0741331	+	0.0622050i
$825$	−1.05413	−	2.23062i	−0.0367002	−	0.0776604i
$826$	11.9263	−	4.34081i	0.414968	−	0.151036i
$827$	−2.03273	−	3.52078i	−0.0706848	−	0.122430i	0.828517	−	0.559964i	$-0.189185\pi$
$827$	−2.03273	−	3.52078i	−0.0706848	−	0.122430i	−0.899202	+	0.437535i	$0.855852\pi$
$828$	0.373305	+	0.993778i	0.0129733	+	0.0345362i
$829$	7.59414	−	13.1534i	0.263755	−	0.456838i	−0.703481	−	0.710714i	$-0.748372\pi$
$829$	7.59414	−	13.1534i	0.263755	−	0.456838i	0.967237	+	0.253876i	$0.0817055\pi$
$830$	−0.639842	+	3.62873i	−0.0222092	+	0.125955i
$831$	−3.99834	+	2.83037i	−0.138701	+	0.0981844i
$832$	0.978173	+	0.356026i	0.0339121	+	0.0123430i
$833$	−0.0763698	−	0.433115i	−0.00264606	−	0.0150065i
$834$	−26.1414	+	7.14861i	−0.905203	+	0.247536i
$835$	8.54090	+	7.16667i	0.295570	+	0.248013i
$836$	1.33372			0.0461277
$837$	−0.159656	−	0.108166i	−0.00551850	−	0.00373877i
$838$	−20.4635			−0.706899
$839$	20.0595	+	16.8320i	0.692532	+	0.581104i	0.919638	−	0.392766i	$-0.128482\pi$
$839$	20.0595	+	16.8320i	0.692532	+	0.581104i	−0.227106	+	0.973870i	$0.572926\pi$
$840$	−0.312518	+	1.19075i	−0.0107829	+	0.0410849i
$841$	−4.83898	−	27.4432i	−0.166861	−	0.946318i
$842$	14.9735	+	5.44991i	0.516021	+	0.187816i
$843$	−7.48557	−	3.44390i	−0.257817	−	0.118614i
$844$	−2.25363	+	12.7810i	−0.0775731	+	0.439939i
$845$	−4.23489	+	7.33504i	−0.145685	+	0.252333i
$846$	−1.39848	−	1.63231i	−0.0480808	−	0.0561200i
$847$	5.44979	+	9.43931i	0.187257	+	0.324338i
$848$	2.50081	−	0.910221i	0.0858782	−	0.0312571i
$849$	7.07235	+	0.582180i	0.242722	+	0.0199804i
$850$	1.51432	−	1.27066i	0.0519407	−	0.0435834i
$851$	−1.87502	+	1.57333i	−0.0642747	+	0.0539329i
$852$	−11.9690	−	0.985260i	−0.410051	−	0.0337545i
$853$	31.9105	−	11.6145i	1.09260	−	0.397672i	0.268014	−	0.963415i	$-0.413633\pi$
$853$	31.9105	−	11.6145i	1.09260	−	0.397672i	0.824582	+	0.565743i	$0.191410\pi$
$854$	−6.13320	−	10.6230i	−0.209874	−	0.363512i
$855$	5.83868	+	6.81491i	0.199678	+	0.233065i
$856$	2.51564	−	4.35722i	0.0859830	−	0.148927i
$857$	4.74187	−	26.8925i	0.161979	−	0.918629i	−0.790146	−	0.612919i	$-0.789995\pi$
$857$	4.74187	−	26.8925i	0.161979	−	0.918629i	0.952125	−	0.305710i	$-0.0988938\pi$
$858$	−0.519068	−	0.238809i	−0.0177207	−	0.00815279i
$859$	24.9042	+	9.06438i	0.849720	+	0.309273i	0.729926	−	0.683526i	$-0.239554\pi$
$859$	24.9042	+	9.06438i	0.849720	+	0.309273i	0.119794	+	0.992799i	$0.461777\pi$
$860$	0.364441	+	2.06685i	0.0124273	+	0.0704789i
$861$	1.01067	−	3.85084i	0.0344435	−	0.131236i
$862$	31.4612	+	26.3991i	1.07157	+	0.899156i
$863$	−47.1126			−1.60373			−0.801866	−	0.597504i	$-0.796159\pi$
$863$	−47.1126			−1.60373			−0.801866	+	0.597504i	$0.796159\pi$
$864$	4.67493	−	2.26826i	0.159044	−	0.0771677i
$865$	−14.9841			−0.509473
$866$	−0.850685	−	0.713809i	−0.0289074	−	0.0242562i
$867$	28.0789	−	7.67844i	0.953610	−	0.260773i
$868$	0.00644467	+	0.0365495i	0.000218746	+	0.00124057i
$869$	−3.49441	−	1.27186i	−0.118540	−	0.0431449i
$870$	−1.06974	+	0.757254i	−0.0362676	+	0.0256733i
$871$	1.72769	−	9.79819i	0.0585404	−	0.331999i
$872$	8.18710	−	14.1805i	0.277250	−	0.480211i
$873$	4.47882	+	11.9231i	0.151585	+	0.403535i
$874$	−0.744632	−	1.28974i	−0.0251875	−	0.0436261i
$875$	−6.34159	+	2.30815i	−0.214385	+	0.0780297i
$876$	7.79531	+	16.4955i	0.263379	+	0.557330i
$877$	−31.9226	+	26.7862i	−1.07795	+	0.904507i	−0.995749	−	0.0921090i	$-0.970639\pi$
$877$	−31.9226	+	26.7862i	−1.07795	+	0.904507i	−0.0822003	+	0.996616i	$0.526195\pi$
$878$	17.0804	−	14.3322i	0.576437	−	0.483688i
$879$	15.5234	−	22.4137i	0.523590	−	0.755995i
$880$	−0.211659	+	0.0770376i	−0.00713503	+	0.00259694i
$881$	0.0390675	+	0.0676669i	0.00131622	+	0.00227976i	0.866683	−	0.498860i	$-0.166248\pi$
$881$	0.0390675	+	0.0676669i	0.00131622	+	0.00227976i	−0.865367	+	0.501139i	$0.832914\pi$
$882$	2.58254	−	1.52660i	0.0869586	−	0.0514032i
$883$	−17.7901	+	30.8133i	−0.598684	+	1.03695i	0.394331	+	0.918968i	$0.370976\pi$
$883$	−17.7901	+	30.8133i	−0.598684	+	1.03695i	−0.993016	+	0.117983i	$0.962357\pi$
$884$	0.0794972	−	0.450851i	0.00267378	−	0.0151638i
$885$	1.44166	+	15.5578i	0.0484607	+	0.522971i
$886$	3.98956	+	1.45208i	0.134032	+	0.0487836i
$887$	−2.45959	−	13.9490i	−0.0825850	−	0.468363i	−0.997852	−	0.0655143i	$-0.979131\pi$
$887$	−2.45959	−	13.9490i	−0.0825850	−	0.468363i	0.915267	−	0.402849i	$-0.131980\pi$
$888$	8.51498	+	8.42799i	0.285744	+	0.282825i
$889$	−4.06509	−	3.41101i	−0.136339	−	0.114402i
$890$	−7.59357			−0.254537
$891$	−2.65952	+	1.03031i	−0.0890972	+	0.0345167i
$892$	−8.68187			−0.290690
$893$	2.30995	+	1.93828i	0.0772996	+	0.0648621i
$894$	−12.1955	−	12.0709i	−0.407878	−	0.403711i
$895$	1.11887	+	6.34541i	0.0373996	+	0.212104i
$896$	−0.939693	−	0.342020i	−0.0313929	−	0.0114261i
$897$	0.0588678	+	0.635280i	0.00196554	+	0.0212114i
$898$	−0.0503758	+	0.285696i	−0.00168106	+	0.00953379i
$899$	−0.0197559	+	0.0342182i	−0.000658896	+	0.00114124i
$900$	11.7465	+	6.62196i	0.391549	+	0.220732i
$901$	−0.585217	−	1.01363i	−0.0194964	−	0.0337688i
$902$	0.684496	−	0.249136i	0.0227912	−	0.00829533i
$903$	2.91193	−	4.20445i	0.0969030	−	0.139915i
$904$	−8.92435	+	7.48842i	−0.296819	+	0.249061i
$905$	9.75580	−	8.18609i	0.324294	−	0.272115i
$906$	−1.97637	−	4.18214i	−0.0656603	−	0.138942i
$907$	10.4686	−	3.81026i	0.347604	−	0.126518i	−0.162317	−	0.986739i	$-0.551897\pi$
$907$	10.4686	−	3.81026i	0.347604	−	0.126518i	0.509921	+	0.860221i	$0.329674\pi$
$908$	−9.83199	−	17.0295i	−0.326286	−	0.565144i
$909$	28.9783	+	4.80340i	0.961150	+	0.159319i
$910$	−0.369936	+	0.640747i	−0.0122632	+	0.0212406i
$911$	3.47926	−	19.7319i	0.115273	−	0.653746i	−0.871342	−	0.490677i	$-0.836750\pi$
$911$	3.47926	−	19.7319i	0.115273	−	0.653746i	0.986615	−	0.163069i	$-0.0521393\pi$
$912$	−5.94970	+	4.21171i	−0.197014	+	0.139464i
$913$	1.54379	+	0.561893i	0.0510919	+	0.0185959i
$914$	5.46431	+	30.9896i	0.180743	+	1.02505i
$915$	14.5661	−	3.98324i	0.481541	−	0.131682i
$916$	−7.17308	−	6.01893i	−0.237005	−	0.198871i
$917$	7.30663			0.241286
$918$	−1.33944	−	1.85156i	−0.0442081	−	0.0611105i
$919$	0.210234			0.00693498			0.00346749	−	0.999994i	$-0.498896\pi$
$919$	0.210234			0.00693498			0.00346749	+	0.999994i	$0.498896\pi$
$920$	0.192669	+	0.161668i	0.00635211	+	0.00533005i
$921$	−8.55948	+	32.6132i	−0.282045	+	1.07464i
$922$	3.80213	+	21.5629i	0.125216	+	0.710138i
$923$	−6.78233	−	2.46857i	−0.223243	−	0.0812539i
$924$	0.498648	+	0.229414i	0.0164043	+	0.00754717i
$925$	−5.39885	+	30.6184i	−0.177513	+	1.00673i
$926$	8.85426	−	15.3360i	0.290969	−	0.503973i
$927$	−2.76977	+	7.86006i	−0.0909711	+	0.258158i
$928$	−0.532313	−	0.921992i	−0.0174740	−	0.0302659i
$929$	12.0356	−	4.38059i	0.394874	−	0.143722i	−0.136949	−	0.990578i	$-0.543730\pi$
$929$	12.0356	−	4.38059i	0.394874	−	0.143722i	0.531823	+	0.846856i	$0.321507\pi$
$930$	−0.0455355	−	0.00374838i	−0.00149317	−	0.000122914i
$931$	−3.22399	+	2.70525i	−0.105662	+	0.0886610i
$932$	11.3897	−	9.55710i	0.373082	−	0.313053i
$933$	17.9964	+	1.48143i	0.589177	+	0.0484997i
$934$	13.8583	−	5.04402i	0.453459	−	0.165045i
$935$	0.0495305	+	0.0857894i	0.00161982	+	0.00280561i
$936$	3.06968	−	0.573826i	0.100336	−	0.0187561i
$937$	5.55809	−	9.62689i	0.181575	−	0.314497i	−0.760842	−	0.648937i	$-0.775214\pi$
$937$	5.55809	−	9.62689i	0.181575	−	0.314497i	0.942417	+	0.334440i	$0.108547\pi$
$938$	−1.65972	+	9.41274i	−0.0541918	+	0.307337i
$939$	28.1980	+	12.9731i	0.920205	+	0.423361i
$940$	−0.478543	−	0.174175i	−0.0156083	−	0.00568097i
$941$	−2.25652	−	12.7973i	−0.0735603	−	0.417181i	−0.999244	−	0.0388823i	$-0.987620\pi$
$941$	−2.25652	−	12.7973i	−0.0735603	−	0.417181i	0.925683	−	0.378299i	$-0.123491\pi$
$942$	1.13795	−	4.33580i	0.0370764	−	0.141268i
$943$	−0.623082	−	0.522828i	−0.0202904	−	0.0170256i
$944$	−12.6917			−0.413079
$945$	1.01071	+	3.55226i	0.0328784	+	0.115555i
$946$	0.935742			0.0304236
$947$	31.5951	+	26.5114i	1.02670	+	0.861505i	0.990455	−	0.137838i	$-0.0440152\pi$
$947$	31.5951	+	26.5114i	1.02670	+	0.861505i	0.0362472	+	0.999343i	$0.488460\pi$
$948$	19.6048	−	5.36113i	0.636735	−	0.174121i
$949$	1.90404	+	10.7983i	0.0618076	+	0.350529i
$950$	−17.7761	−	6.46999i	−0.576734	−	0.209914i
$951$	14.7785	−	10.4615i	0.479226	−	0.339237i
$952$	−0.0763698	+	0.433115i	−0.00247516	+	0.0140373i
$953$	−25.2680	+	43.7655i	−0.818511	+	1.41770i	0.0882674	+	0.996097i	$0.471867\pi$
$953$	−25.2680	+	43.7655i	−0.818511	+	1.41770i	−0.906779	+	0.421607i	$0.861466\pi$
$954$	5.06890	−	6.16841i	0.164112	−	0.199710i
$955$	−0.738487	−	1.27910i	−0.0238969	−	0.0413906i
$956$	−14.0079	+	5.09846i	−0.453048	+	0.164896i
$957$	0.249678	+	0.528338i	0.00807095	+	0.0170787i
$958$	6.86236	−	5.75820i	0.221713	−	0.186039i
$959$	−11.7981	+	9.89976i	−0.380980	+	0.319680i
$960$	0.700933	−	1.01205i	0.0226225	−	0.0326639i
$961$	29.1292	−	10.6022i	0.939651	−	0.342005i
$962$	3.60014	+	6.23563i	0.116073	+	0.201045i
$963$	−0.154979	−	15.0931i	−0.00499414	−	0.486367i
$964$	−7.56444	+	13.1020i	−0.243634	+	0.421987i
$965$	−2.14593	+	12.1702i	−0.0690799	+	0.391772i
$966$	−0.0565520	−	0.610289i	−0.00181953	−	0.0196357i
$967$	12.4640	+	4.53654i	0.400817	+	0.145885i	0.534560	−	0.845131i	$-0.320477\pi$
$967$	12.4640	+	4.53654i	0.400817	+	0.145885i	−0.133743	+	0.991016i	$0.542700\pi$
$968$	−1.89269	−	10.7340i	−0.0608334	−	0.345003i
$969$	2.27853	+	2.25526i	0.0731971	+	0.0724493i
$970$	2.31159	+	1.93965i	0.0742207	+	0.0622785i
$971$	42.0612			1.34981			0.674905	−	0.737905i	$-0.264185\pi$
$971$	42.0612			1.34981			0.674905	+	0.737905i	$0.264185\pi$
$972$	8.61048	−	12.9946i	0.276181	−	0.416802i
$973$	15.6469			0.501616
$974$	−18.8217	−	15.7933i	−0.603086	−	0.506050i
$975$	5.75977	+	5.70093i	0.184460	+	0.182576i
$976$	2.13004	+	12.0800i	0.0681808	+	0.386673i
$977$	−23.1574	−	8.42860i	−0.740870	−	0.269655i	−0.0561116	−	0.998425i	$-0.517870\pi$
$977$	−23.1574	−	8.42860i	−0.740870	−	0.269655i	−0.684759	+	0.728770i	$0.740092\pi$
$978$	−1.76109	−	19.0051i	−0.0563136	−	0.607716i
$979$	−0.587916	+	3.33424i	−0.0187899	+	0.106563i
$980$	0.355383	−	0.615541i	0.0113523	−	0.0196627i
$981$	−0.504376	−	49.1200i	−0.0161035	−	1.56828i
$982$	20.3576	+	35.2603i	0.649636	+	1.12520i
$983$	−48.0261	+	17.4801i	−1.53179	+	0.557528i	−0.964060	−	0.265684i	$-0.914402\pi$
$983$	−48.0261	+	17.4801i	−1.53179	+	0.557528i	−0.567734	+	0.823212i	$0.692180\pi$
$984$	−2.26678	+	3.27294i	−0.0722624	+	0.104337i
$985$	−15.0373	+	12.6178i	−0.479127	+	0.402036i
$986$	−0.358676	+	0.300965i	−0.0114226	+	0.00958468i
$987$	0.530234	+	1.12201i	0.0168775	+	0.0357141i
$988$	−4.11676	+	1.49838i	−0.130972	+	0.0476698i
$989$	−0.522435	−	0.904884i	−0.0166125	−	0.0287736i
$990$	−0.429012	+	0.522071i	−0.0136349	+	0.0165925i
$991$	−0.341921	+	0.592225i	−0.0108615	+	0.0188127i	−0.871405	−	0.490564i	$-0.836791\pi$
$991$	−0.341921	+	0.592225i	−0.0108615	+	0.0188127i	0.860544	+	0.509377i	$0.170124\pi$
$992$	0.00644467	−	0.0365495i	0.000204618	−	0.00116045i
$993$	19.4947	−	13.8001i	0.618647	−	0.437932i
$994$	6.51552	+	2.37146i	0.206660	+	0.0752180i
$995$	1.73931	+	9.86412i	0.0551398	+	0.312714i
$996$	−8.66119	+	2.36848i	−0.274440	+	0.0750482i
$997$	24.9330	+	20.9212i	0.789635	+	0.662582i	0.945655	−	0.325171i	$-0.105422\pi$
$997$	24.9330	+	20.9212i	0.789635	+	0.662582i	−0.156020	+	0.987754i	$0.549866\pi$
$998$	−7.44218			−0.235578
$999$	34.8564	+	8.76667i	1.10281	+	0.277365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.b.43.2	✓	12
27.22	even	9	inner	378.2.u.b.211.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.b.43.2	✓	12	1.1	even	1	trivial
378.2.u.b.211.2	yes	12	27.22	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.23102 + 1.21844i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.667901 + 0.243096i) q^{5} +(0.159815 + 1.72466i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.0308031 + 2.99984i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.23102 + 1.21844i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.667901 + 0.243096i) q^{5} +(0.159815 + 1.72466i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.0308031 + 2.99984i) q^{9} +(0.355383 + 0.615541i) q^{10} +(0.297791 - 0.108387i) q^{11} +(-0.986166 + 1.42389i) q^{12} +(-0.797414 + 0.669110i) q^{13} +(0.766044 - 0.642788i) q^{14} +(0.525999 + 1.11305i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.219898 + 0.380875i) q^{17} +(-1.90466 + 2.31781i) q^{18} +(2.10431 - 3.64477i) q^{19} +(-0.123423 + 0.699967i) q^{20} +(1.41369 - 1.00073i) q^{21} +(0.297791 + 0.108387i) q^{22} +(-0.0614472 - 0.348484i) q^{23} +(-1.67071 + 0.456871i) q^{24} +(-3.44323 - 2.88921i) q^{25} -1.04095 q^{26} +(-3.61721 + 3.73039i) q^{27} +1.00000 q^{28} +(0.815550 + 0.684328i) q^{29} +(-0.312518 + 1.19075i) q^{30} +(0.00644467 + 0.0365495i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.498648 + 0.229414i) q^{33} +(-0.0763698 + 0.433115i) q^{34} +(0.355383 - 0.615541i) q^{35} +(-2.94892 + 0.551252i) q^{36} +(-3.45851 - 5.99032i) q^{37} +(3.95481 - 1.43943i) q^{38} +(-1.79690 - 0.147917i) q^{39} +(-0.544478 + 0.456871i) q^{40} +(1.76082 - 1.47750i) q^{41} +(1.72621 + 0.142098i) q^{42} +(2.77470 - 1.00991i) q^{43} +(0.158451 + 0.274445i) q^{44} +(-0.708676 + 2.01108i) q^{45} +(0.176930 - 0.306452i) q^{46} +(-0.124417 + 0.705603i) q^{47} +(-1.57351 - 0.723928i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.780516 - 4.42653i) q^{50} +(-0.193375 + 0.736796i) q^{51} +(-0.797414 - 0.669110i) q^{52} -2.66131 q^{53} +(-5.16879 + 0.532543i) q^{54} +0.225243 q^{55} +(0.766044 + 0.642788i) q^{56} +(7.03138 - 1.92280i) q^{57} +(0.184870 + 1.04845i) q^{58} +(11.9263 + 4.34081i) q^{59} +(-1.00480 + 0.711287i) q^{60} +(2.13004 - 12.0800i) q^{61} +(-0.0185567 + 0.0321411i) q^{62} +(2.95962 + 0.490582i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.695251 + 0.253051i) q^{65} +(0.234522 + 0.496266i) q^{66} +(-7.32181 + 6.14373i) q^{67} +(-0.336904 + 0.282696i) q^{68} +(0.348965 - 0.503859i) q^{69} +(0.667901 - 0.243096i) q^{70} +(3.46684 + 6.00474i) q^{71} +(-2.61334 - 1.47324i) q^{72} +(5.26678 - 9.12233i) q^{73} +(1.20113 - 6.81194i) q^{74} +(-0.718336 - 7.75203i) q^{75} +(3.95481 + 1.43943i) q^{76} +(-0.0550295 - 0.312088i) q^{77} +(-1.28143 - 1.26834i) q^{78} +(-8.98910 - 7.54275i) q^{79} -0.710765 q^{80} +(-8.99810 + 0.184809i) q^{81} +2.29858 q^{82} +(3.97128 + 3.33230i) q^{83} +(1.23102 + 1.21844i) q^{84} +(0.0542810 + 0.307843i) q^{85} +(2.77470 + 1.00991i) q^{86} +(0.170143 + 1.83612i) q^{87} +(-0.0550295 + 0.312088i) q^{88} +(-5.34183 + 9.25232i) q^{89} +(-1.83558 + 1.08505i) q^{90} +(0.520475 + 0.901489i) q^{91} +(0.332520 - 0.121027i) q^{92} +(-0.0365999 + 0.0528455i) q^{93} +(-0.548862 + 0.460550i) q^{94} +(2.29150 - 1.92280i) q^{95} +(-0.740046 - 1.56599i) q^{96} +(3.98948 - 1.45205i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.334316 + 0.889986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9	\( 12 q + 3 q^{3} - 6 q^{6} - 6 q^{8} + 9 q^{9} + 3 q^{11} - 6 q^{12} + 12 q^{13} + 9 q^{15} - 9 q^{18} + 12 q^{19} - 9 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} - 24 q^{25} - 18 q^{26} + 18 q^{27} + 12 q^{28} - 3 q^{29} + 21 q^{31} - 27 q^{33} + 9 q^{34} + 15 q^{37} + 15 q^{38} - 48 q^{39} + 9 q^{40} + 12 q^{41} + 3 q^{42} + 21 q^{43} + 12 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{47} + 3 q^{48} + 21 q^{50} - 9 q^{51} + 12 q^{52} - 42 q^{53} - 27 q^{54} - 12 q^{55} + 33 q^{57} - 3 q^{58} + 18 q^{59} - 18 q^{60} + 9 q^{62} + 9 q^{63} - 6 q^{64} - 36 q^{65} - 9 q^{66} - 33 q^{67} - 18 q^{68} + 9 q^{69} + 24 q^{71} - 18 q^{72} + 9 q^{73} - 36 q^{74} - 33 q^{75} + 15 q^{76} + 3 q^{77} - 21 q^{78} + 9 q^{81} - 24 q^{82} + 15 q^{83} + 3 q^{84} - 24 q^{85} + 21 q^{86} + 3 q^{88} - 51 q^{89} + 9 q^{91} - 6 q^{92} - 30 q^{93} - 15 q^{94} - 45 q^{95} + 3 q^{96} + 48 q^{97} - 6 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^6 - 6 * q^8 + 9 * q^9 + 3 * q^11 - 6 * q^12 + 12 * q^13 + 9 * q^15 - 9 * q^18 + 12 * q^19 - 9 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 - 24 * q^25 - 18 * q^26 + 18 * q^27 + 12 * q^28 - 3 * q^29 + 21 * q^31 - 27 * q^33 + 9 * q^34 + 15 * q^37 + 15 * q^38 - 48 * q^39 + 9 * q^40 + 12 * q^41 + 3 * q^42 + 21 * q^43 + 12 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^47 + 3 * q^48 + 21 * q^50 - 9 * q^51 + 12 * q^52 - 42 * q^53 - 27 * q^54 - 12 * q^55 + 33 * q^57 - 3 * q^58 + 18 * q^59 - 18 * q^60 + 9 * q^62 + 9 * q^63 - 6 * q^64 - 36 * q^65 - 9 * q^66 - 33 * q^67 - 18 * q^68 + 9 * q^69 + 24 * q^71 - 18 * q^72 + 9 * q^73 - 36 * q^74 - 33 * q^75 + 15 * q^76 + 3 * q^77 - 21 * q^78 + 9 * q^81 - 24 * q^82 + 15 * q^83 + 3 * q^84 - 24 * q^85 + 21 * q^86 + 3 * q^88 - 51 * q^89 + 9 * q^91 - 6 * q^92 - 30 * q^93 - 15 * q^94 - 45 * q^95 + 3 * q^96 + 48 * q^97 - 6 * q^98 + 36 * q^99

Introduction

L-functions

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