LMFDB - Embedded newform 672.2.ch.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(11,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))

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

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

chi := DirichletCharacter("672.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.ch (of order $24$, degree $8$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$124$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35950 - 0.389562i) q^{2} +(-0.721966 - 1.57441i) q^{3} +(1.69648 + 1.05922i) q^{4} +(0.456804 + 3.46977i) q^{5} +(0.368183 + 2.42166i) q^{6} +(2.57029 + 0.627378i) q^{7} +(-1.89374 - 2.10089i) q^{8} +(-1.95753 + 2.27334i) q^{9} +O(q^{10})$	\(q+(-1.35950 - 0.389562i) q^{2} +(-0.721966 - 1.57441i) q^{3} +(1.69648 + 1.05922i) q^{4} +(0.456804 + 3.46977i) q^{5} +(0.368183 + 2.42166i) q^{6} +(2.57029 + 0.627378i) q^{7} +(-1.89374 - 2.10089i) q^{8} +(-1.95753 + 2.27334i) q^{9} +(0.730665 - 4.89511i) q^{10} +(0.116570 - 0.0894476i) q^{11} +(0.442842 - 3.43568i) q^{12} +(0.737702 + 1.78097i) q^{13} +(-3.24991 - 1.85421i) q^{14} +(5.13305 - 3.22425i) q^{15} +(1.75611 + 3.59389i) q^{16} +(-3.06574 + 5.31002i) q^{17} +(3.54687 - 2.32803i) q^{18} +(-0.543482 - 0.417028i) q^{19} +(-2.90029 + 6.37027i) q^{20} +(-0.867911 - 4.49964i) q^{21} +(-0.193323 + 0.0761927i) q^{22} +(-8.89102 - 2.38234i) q^{23} +(-1.94045 + 4.49829i) q^{24} +(-7.00102 + 1.87592i) q^{25} +(-0.309108 - 2.70861i) q^{26} +(4.99244 + 1.44068i) q^{27} +(3.69593 + 3.78684i) q^{28} +(-0.662412 - 1.59920i) q^{29} +(-8.23443 + 2.38374i) q^{30} +(-3.37506 - 1.94859i) q^{31} +(-0.987391 - 5.57001i) q^{32} +(-0.224987 - 0.118952i) q^{33} +(6.23646 - 6.02468i) q^{34} +(-1.00274 + 9.20492i) q^{35} +(-5.72888 + 1.78323i) q^{36} +(-7.20918 + 0.949106i) q^{37} +(0.576406 + 0.778670i) q^{38} +(2.27138 - 2.44724i) q^{39} +(6.42455 - 7.53054i) q^{40} +(-2.11769 - 2.11769i) q^{41} +(-0.572960 + 6.45536i) q^{42} +(-3.18822 + 7.69705i) q^{43} +(0.292504 - 0.0282728i) q^{44} +(-8.78218 - 5.75372i) q^{45} +(11.1593 + 6.70239i) q^{46} +(3.12385 - 1.80355i) q^{47} +(4.39041 - 5.35951i) q^{48} +(6.21279 + 3.22509i) q^{49} +(10.2487 + 0.177018i) q^{50} +(10.5735 + 0.993081i) q^{51} +(-0.634938 + 3.80277i) q^{52} +(3.45179 + 4.49846i) q^{53} +(-6.22599 - 3.90347i) q^{54} +(0.363613 + 0.363613i) q^{55} +(-3.54941 - 6.58800i) q^{56} +(-0.264198 + 1.15674i) q^{57} +(0.277561 + 2.43217i) q^{58} +(8.61821 + 11.2315i) q^{59} +(12.1233 - 0.0328728i) q^{60} +(2.95623 + 2.26840i) q^{61} +(3.82930 + 3.96391i) q^{62} +(-6.45767 + 4.61503i) q^{63} +(-0.827506 + 7.95709i) q^{64} +(-5.84258 + 3.37321i) q^{65} +(0.259531 + 0.249361i) q^{66} +(11.1503 + 1.46796i) q^{67} +(-10.8254 + 5.76107i) q^{68} +(2.66823 + 15.7181i) q^{69} +(4.94911 - 12.1235i) q^{70} +(6.24534 + 6.24534i) q^{71} +(8.48310 - 0.192546i) q^{72} +(-1.43800 - 5.36669i) q^{73} +(10.1706 + 1.51811i) q^{74} +(8.00796 + 9.66813i) q^{75} +(-0.480284 - 1.28315i) q^{76} +(0.355737 - 0.156773i) q^{77} +(-4.04130 + 2.44219i) q^{78} +(-3.60767 - 6.24866i) q^{79} +(-11.6678 + 7.73501i) q^{80} +(-1.33614 - 8.90027i) q^{81} +(2.05403 + 3.70397i) q^{82} +(-5.23636 - 12.6417i) q^{83} +(3.29370 - 8.55287i) q^{84} +(-19.8250 - 8.21178i) q^{85} +(7.33287 - 9.22214i) q^{86} +(-2.03956 + 2.19748i) q^{87} +(-0.408674 - 0.0755116i) q^{88} +(9.52725 + 2.55282i) q^{89} +(9.69795 + 11.2434i) q^{90} +(0.778767 + 5.04043i) q^{91} +(-12.5600 - 13.4591i) q^{92} +(-0.631205 + 6.72055i) q^{93} +(-4.94947 + 1.23500i) q^{94} +(1.19873 - 2.07626i) q^{95} +(-8.05662 + 5.57592i) q^{96} -2.90486 q^{97} +(-7.18992 - 6.80478i) q^{98} +(-0.0248455 + 0.440101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.35950	−	0.389562i	−0.961312	−	0.275462i
$2$	−1.35950	−	0.389562i	−0.961312	−	0.275462i
$3$	−0.721966	−	1.57441i	−0.416827	−	0.908986i
$3$	−0.721966	−	1.57441i	−0.416827	−	0.908986i
$4$	1.69648	+	1.05922i	0.848242	+	0.529609i
$5$	0.456804	+	3.46977i	0.204289	+	1.55173i	0.719394	+	0.694602i	$0.244420\pi$
$5$	0.456804	+	3.46977i	0.204289	+	1.55173i	−0.515105	+	0.857127i	$0.672247\pi$
$6$	0.368183	+	2.42166i	0.150310	+	0.988639i
$7$	2.57029	+	0.627378i	0.971479	+	0.237127i
$7$	2.57029	+	0.627378i	0.971479	+	0.237127i
$8$	−1.89374	−	2.10089i	−0.669538	−	0.742778i
$9$	−1.95753	+	2.27334i	−0.652511	+	0.757780i
$10$	0.730665	−	4.89511i	0.231057	−	1.54797i
$11$	0.116570	−	0.0894476i	0.0351473	−	0.0269695i	−0.591038	−	0.806643i	$-0.701282\pi$
$11$	0.116570	−	0.0894476i	0.0351473	−	0.0269695i	0.626186	+	0.779674i	$0.284615\pi$
$12$	0.442842	−	3.43568i	0.127837	−	0.991795i
$13$	0.737702	+	1.78097i	0.204602	+	0.493952i	0.992557	−	0.121780i	$-0.0388603\pi$
$13$	0.737702	+	1.78097i	0.204602	+	0.493952i	−0.787955	+	0.615732i	$0.788860\pi$
$14$	−3.24991	−	1.85421i	−0.868575	−	0.495558i
$15$	5.13305	−	3.22425i	1.32535	−	0.832499i
$16$	1.75611	+	3.59389i	0.439028	+	0.898473i
$17$	−3.06574	+	5.31002i	−0.743551	+	1.28787i	0.207317	+	0.978274i	$0.433527\pi$
$17$	−3.06574	+	5.31002i	−0.743551	+	1.28787i	−0.950869	+	0.309595i	$0.899807\pi$
$18$	3.54687	−	2.32803i	0.836006	−	0.548721i
$19$	−0.543482	−	0.417028i	−0.124683	−	0.0956729i	0.544537	−	0.838737i	$-0.316705\pi$
$19$	−0.543482	−	0.417028i	−0.124683	−	0.0956729i	−0.669221	+	0.743064i	$0.733372\pi$
$20$	−2.90029	+	6.37027i	−0.648524	+	1.42444i
$21$	−0.867911	−	4.49964i	−0.189394	−	0.981901i
$22$	−0.193323	+	0.0761927i	−0.0412166	+	0.0162443i
$23$	−8.89102	−	2.38234i	−1.85391	−	0.496752i	−0.854175	−	0.519986i	$-0.825937\pi$
$23$	−8.89102	−	2.38234i	−1.85391	−	0.496752i	−0.999730	+	0.0232331i	$0.992604\pi$
$24$	−1.94045	+	4.49829i	−0.396093	+	0.918210i
$25$	−7.00102	+	1.87592i	−1.40020	+	0.375184i
$26$	−0.309108	−	2.70861i	−0.0606212	−	0.531202i
$27$	4.99244	+	1.44068i	0.960795	+	0.277260i
$28$	3.69593	+	3.78684i	0.698464	+	0.715645i
$29$	−0.662412	−	1.59920i	−0.123007	−	0.296965i	0.850366	−	0.526191i	$-0.176380\pi$
$29$	−0.662412	−	1.59920i	−0.123007	−	0.296965i	−0.973373	+	0.229226i	$0.926380\pi$
$30$	−8.23443	+	2.38374i	−1.50339	+	0.435209i
$31$	−3.37506	−	1.94859i	−0.606179	−	0.349978i	0.165289	−	0.986245i	$-0.447144\pi$
$31$	−3.37506	−	1.94859i	−0.606179	−	0.349978i	−0.771469	+	0.636267i	$0.780477\pi$
$32$	−0.987391	−	5.57001i	−0.174548	−	0.984649i
$33$	−0.224987	−	0.118952i	−0.0391652	−	0.0207068i
$34$	6.23646	−	6.02468i	1.06954	−	1.03322i
$35$	−1.00274	+	9.20492i	−0.169494	+	1.55591i
$36$	−5.72888	+	1.78323i	−0.954814	+	0.297205i
$37$	−7.20918	+	0.949106i	−1.18518	+	0.156032i	−0.697236	−	0.716842i	$-0.745587\pi$
$37$	−7.20918	+	0.949106i	−1.18518	+	0.156032i	−0.487946	+	0.872874i	$0.662254\pi$
$38$	0.576406	+	0.778670i	0.0935053	+	0.126317i
$39$	2.27138	−	2.44724i	0.363712	−	0.391873i
$40$	6.42455	−	7.53054i	1.01581	−	1.19068i
$41$	−2.11769	−	2.11769i	−0.330728	−	0.330728i	0.522135	−	0.852863i	$-0.325136\pi$
$41$	−2.11769	−	2.11769i	−0.330728	−	0.330728i	−0.852863	+	0.522135i	$0.825136\pi$
$42$	−0.572960	+	6.45536i	−0.0884097	+	0.996084i
$43$	−3.18822	+	7.69705i	−0.486200	+	1.17379i	0.470418	+	0.882444i	$0.344103\pi$
$43$	−3.18822	+	7.69705i	−0.486200	+	1.17379i	−0.956618	+	0.291346i	$0.905897\pi$
$44$	0.292504	−	0.0282728i	0.0440967	−	0.00426229i
$45$	−8.78218	−	5.75372i	−1.30917	−	0.857714i
$46$	11.1593	+	6.70239i	1.64535	+	0.988214i
$47$	3.12385	−	1.80355i	0.455660	−	0.263075i	−0.254558	−	0.967058i	$-0.581930\pi$
$47$	3.12385	−	1.80355i	0.455660	−	0.263075i	0.710218	+	0.703982i	$0.248597\pi$
$48$	4.39041	−	5.35951i	0.633701	−	0.773578i
$49$	6.21279	+	3.22509i	0.887542	+	0.460727i
$50$	10.2487	+	0.177018i	1.44938	+	0.0250342i
$51$	10.5735	+	0.993081i	1.48059	+	0.139059i
$52$	−0.634938	+	3.80277i	−0.0880500	+	0.527350i
$53$	3.45179	+	4.49846i	0.474140	+	0.617911i	0.967793	−	0.251748i	$-0.0810054\pi$
$53$	3.45179	+	4.49846i	0.474140	+	0.617911i	−0.493653	+	0.869659i	$0.664339\pi$
$54$	−6.22599	−	3.90347i	−0.847249	−	0.531195i
$55$	0.363613	+	0.363613i	0.0490295	+	0.0490295i
$56$	−3.54941	−	6.58800i	−0.474309	−	0.880358i
$57$	−0.264198	+	1.15674i	−0.0349939	+	0.153214i
$58$	0.277561	+	2.43217i	0.0364455	+	0.319359i
$59$	8.61821	+	11.2315i	1.12199	+	1.46221i	0.869045	+	0.494733i	$0.164734\pi$
$59$	8.61821	+	11.2315i	1.12199	+	1.46221i	0.252950	+	0.967479i	$0.418599\pi$
$60$	12.1233	−	0.0328728i	1.56511	−	0.00424387i
$61$	2.95623	+	2.26840i	0.378507	+	0.290439i	0.780440	−	0.625230i	$-0.214995\pi$
$61$	2.95623	+	2.26840i	0.378507	+	0.290439i	−0.401933	+	0.915669i	$0.631662\pi$
$62$	3.82930	+	3.96391i	0.486322	+	0.503417i
$63$	−6.45767	+	4.61503i	−0.813590	+	0.581439i
$64$	−0.827506	+	7.95709i	−0.103438	+	0.994636i
$65$	−5.84258	+	3.37321i	−0.724682	+	0.418396i
$66$	0.259531	+	0.249361i	0.0319461	+	0.0306942i
$67$	11.1503	+	1.46796i	1.36223	+	0.179340i	0.775962	−	0.630780i	$-0.217265\pi$
$67$	11.1503	+	1.46796i	1.36223	+	0.179340i	0.586264	+	0.810120i	$0.300598\pi$
$68$	−10.8254	+	5.76107i	−1.31278	+	0.698632i
$69$	2.66823	+	15.7181i	0.321217	+	1.89223i
$70$	4.94911	−	12.1235i	0.591532	−	1.44903i
$71$	6.24534	+	6.24534i	0.741186	+	0.741186i	0.972806	−	0.231621i	$-0.0744028\pi$
$71$	6.24534	+	6.24534i	0.741186	+	0.741186i	−0.231621	+	0.972806i	$0.574403\pi$
$72$	8.48310	−	0.192546i	0.999743	−	0.0226917i
$73$	−1.43800	−	5.36669i	−0.168305	−	0.628124i	−0.997595	−	0.0693057i	$-0.977922\pi$
$73$	−1.43800	−	5.36669i	−0.168305	−	0.628124i	0.829290	−	0.558818i	$-0.188745\pi$
$74$	10.1706	+	1.51811i	1.18231	+	0.176477i
$75$	8.00796	+	9.66813i	0.924680	+	1.11638i
$76$	−0.480284	−	1.28315i	−0.0550923	−	0.147187i
$77$	0.355737	−	0.156773i	0.0405400	−	0.0178659i
$78$	−4.04130	+	2.44219i	−0.457587	+	0.276523i
$79$	−3.60767	−	6.24866i	−0.405894	−	0.703029i	0.588531	−	0.808475i	$-0.299707\pi$
$79$	−3.60767	−	6.24866i	−0.405894	−	0.703029i	−0.994425	+	0.105445i	$0.966373\pi$
$80$	−11.6678	+	7.73501i	−1.30450	+	0.864801i
$81$	−1.33614	−	8.90027i	−0.148460	−	0.988918i
$82$	2.05403	+	3.70397i	0.226830	+	0.409035i
$83$	−5.23636	−	12.6417i	−0.574766	−	1.38761i	−0.897457	−	0.441103i	$-0.854587\pi$
$83$	−5.23636	−	12.6417i	−0.574766	−	1.38761i	0.322691	−	0.946504i	$-0.395413\pi$
$84$	3.29370	−	8.55287i	0.359372	−	0.933194i
$85$	−19.8250	−	8.21178i	−2.15032	−	0.890693i
$86$	7.33287	−	9.22214i	0.790724	−	0.994449i
$87$	−2.03956	+	2.19748i	−0.218664	+	0.235594i
$88$	−0.408674	−	0.0755116i	−0.0435648	−	0.00804956i
$89$	9.52725	+	2.55282i	1.00989	+	0.270598i	0.725582	−	0.688136i	$-0.241571\pi$
$89$	9.52725	+	2.55282i	1.00989	+	0.270598i	0.284304	+	0.958734i	$0.408237\pi$
$90$	9.69795	+	11.2434i	1.02225	+	1.18516i
$91$	0.778767	+	5.04043i	0.0816370	+	0.528381i
$92$	−12.5600	−	13.4591i	−1.30947	−	1.40321i
$93$	−0.631205	+	6.72055i	−0.0654529	+	0.696888i
$94$	−4.94947	+	1.23500i	−0.510499	+	0.127381i
$95$	1.19873	−	2.07626i	0.122987	−	0.213020i
$96$	−8.05662	+	5.57592i	−0.822276	+	0.569090i
$97$	−2.90486			−0.294944			−0.147472	−	0.989066i	$-0.547114\pi$
$97$	−2.90486			−0.294944			−0.147472	+	0.989066i	$0.547114\pi$
$98$	−7.18992	−	6.80478i	−0.726292	−	0.687386i
$99$	−0.0248455	+	0.440101i	−0.00249707	+	0.0442318i
$100$	−13.8641	−	4.23315i	−1.38641	−	0.423315i
$101$	7.14251	−	5.48064i	0.710706	−	0.545344i	−0.188927	−	0.981991i	$-0.560501\pi$
$101$	7.14251	−	5.48064i	0.710706	−	0.545344i	0.899633	+	0.436647i	$0.143834\pi$
$102$	−13.9878	−	5.46913i	−1.38500	−	0.541524i
$103$	−7.99451	−	2.14212i	−0.787722	−	0.211070i	−0.157536	−	0.987513i	$-0.550355\pi$
$103$	−7.99451	−	2.14212i	−0.787722	−	0.211070i	−0.630187	+	0.776444i	$0.717022\pi$
$104$	2.34461	−	4.92253i	0.229908	−	0.482693i
$105$	15.2163	−	5.06691i	1.48495	−	0.494480i
$106$	−2.94028	−	7.46035i	−0.285586	−	0.724613i
$107$	2.29060	+	17.3988i	0.221440	+	1.68201i	0.635770	+	0.771879i	$0.280683\pi$
$107$	2.29060	+	17.3988i	0.221440	+	1.68201i	−0.414330	+	0.910127i	$0.635984\pi$
$108$	6.94359	+	7.73218i	0.668147	+	0.744029i
$109$	−1.26382	−	0.166385i	−0.121052	−	0.0159368i	0.0697567	−	0.997564i	$-0.477778\pi$
$109$	−1.26382	−	0.166385i	−0.121052	−	0.0159368i	−0.190809	+	0.981627i	$0.561111\pi$
$110$	−0.352682	−	0.635982i	−0.0336269	−	0.0606385i
$111$	6.69906	+	10.6650i	0.635847	+	1.01227i
$112$	2.25899	+	10.3391i	0.213454	+	0.976953i
$113$	−8.42499			−0.792556			−0.396278	−	0.918131i	$-0.629698\pi$
$113$	−8.42499			−0.792556			−0.396278	+	0.918131i	$0.629698\pi$
$114$	0.809800	−	1.46967i	0.0758448	−	0.137647i
$115$	4.20473	−	31.9381i	0.392093	−	2.97824i
$116$	0.570136	−	3.41466i	0.0529358	−	0.317043i
$117$	−5.49282	−	1.80926i	−0.507812	−	0.167266i
$118$	−7.34111	−	18.6265i	−0.675804	−	1.71471i
$119$	−11.2112	+	11.7249i	−1.02773	+	1.07482i
$120$	−16.4945	−	4.67809i	−1.50573	−	0.427049i
$121$	−2.84142	+	10.6043i	−0.258311	+	0.964030i
$122$	−3.13532	−	4.23552i	−0.283859	−	0.383466i
$123$	−1.80521	+	4.86301i	−0.162770	+	0.438483i
$124$	−3.66175	−	6.88068i	−0.328835	−	0.617904i
$125$	−3.01070	−	7.26847i	−0.269285	−	0.650111i
$126$	10.5770	−	3.75848i	0.942278	−	0.334832i
$127$			3.16701i			0.281027i	0.990079	+	0.140514i	$0.0448753\pi$
$127$			3.16701i			0.281027i	−0.990079	+	0.140514i	$0.955125\pi$
$128$	4.22477	−	10.4953i	0.373421	−	0.927662i
$129$	14.4201	−	0.537437i	1.26962	−	0.0473187i
$130$	9.25706	−	2.30984i	0.811898	−	0.202586i
$131$	3.39226	+	2.60297i	0.296383	+	0.227423i	0.746239	−	0.665679i	$-0.231858\pi$
$131$	3.39226	+	2.60297i	0.296383	+	0.227423i	−0.449855	+	0.893101i	$0.648524\pi$
$132$	−0.255691	−	0.440110i	−0.0222551	−	0.0383066i
$133$	−1.13527	−	1.41285i	−0.0984406	−	0.122510i
$134$	−14.5870	−	6.33943i	−1.26012	−	0.547643i
$135$	−2.71828	+	17.9807i	−0.233952	+	1.54754i
$136$	16.9615	−	3.61499i	1.45444	−	0.309983i
$137$	−9.33481	+	2.50126i	−0.797527	+	0.213697i	−0.634498	−	0.772925i	$-0.718793\pi$
$137$	−9.33481	+	2.50126i	−0.797527	+	0.213697i	−0.163029	+	0.986621i	$0.552126\pi$
$138$	2.49570	−	22.4082i	0.212448	−	1.90751i
$139$	−2.91434	+	7.03585i	−0.247191	+	0.596773i	−0.997963	−	0.0637886i	$-0.979682\pi$
$139$	−2.91434	+	7.03585i	−0.247191	+	0.596773i	0.750772	+	0.660561i	$0.229682\pi$
$140$	−11.4512	+	14.5539i	−0.967799	+	1.23003i
$141$	−5.09484	−	3.61611i	−0.429063	−	0.304532i
$142$	−6.05760	−	10.9235i	−0.508342	−	0.916679i
$143$	0.245298	+	0.141623i	0.0205128	+	0.0118431i
$144$	−11.6078	−	3.04292i	−0.967315	−	0.253577i
$145$	5.24628	−	3.02894i	0.435680	−	0.251540i
$146$	−0.135695	+	7.85621i	−0.0112302	+	0.650185i
$147$	0.592189	−	12.1099i	0.0488430	−	0.998806i
$148$	−13.2356	−	6.02595i	−1.08796	−	0.495330i
$149$	11.5702	−	1.52325i	0.947871	−	0.124790i	0.359288	−	0.933227i	$-0.383020\pi$
$149$	11.5702	−	1.52325i	0.947871	−	0.124790i	0.588583	+	0.808437i	$0.299686\pi$
$150$	−7.12050	−	16.2634i	−0.581386	−	1.32790i
$151$	1.75387	−	0.469949i	0.142728	−	0.0382439i	−0.186748	−	0.982408i	$-0.559795\pi$
$151$	1.75387	−	0.469949i	0.142728	−	0.0382439i	0.329476	+	0.944164i	$0.393128\pi$
$152$	0.153081	+	1.93154i	0.0124165	+	0.156669i
$153$	−6.07019	−	17.3640i	−0.490746	−	1.40380i
$154$	−0.544698	+	0.0745509i	−0.0438930	+	0.00600748i
$155$	5.21943	−	12.6008i	0.419235	−	1.01212i
$156$	6.44553	−	1.74582i	0.516055	−	0.139777i
$157$	0.798174	−	6.06273i	0.0637012	−	0.483859i	−0.929624	−	0.368510i	$-0.879868\pi$
$157$	0.798174	−	6.06273i	0.0637012	−	0.483859i	0.993325	−	0.115349i	$-0.0367986\pi$
$158$	2.47039	+	9.90047i	0.196533	+	0.787639i
$159$	4.59035	−	8.68227i	0.364038	−	0.688549i
$160$	18.8756	−	5.97043i	1.49225	−	0.472004i
$161$	−21.3579	−	11.7013i	−1.68324	−	0.922195i
$162$	−1.65072	+	12.6204i	−0.129693	+	0.991554i
$163$	−4.52206	+	5.89327i	−0.354195	+	0.461596i	−0.936138	−	0.351634i	$-0.885626\pi$
$163$	−4.52206	+	5.89327i	−0.354195	+	0.461596i	0.581942	+	0.813230i	$0.302293\pi$
$164$	−1.34953	−	5.83572i	−0.105380	−	0.455693i
$165$	0.309960	−	0.834992i	0.0241303	−	0.0650040i
$166$	2.19412	+	19.2263i	0.170296	+	1.49225i
$167$	−7.33465	−	7.33465i	−0.567572	−	0.567572i	0.363876	−	0.931448i	$-0.381453\pi$
$167$	−7.33465	−	7.33465i	−0.567572	−	0.567572i	−0.931448	+	0.363876i	$0.881453\pi$
$168$	−7.80966	+	10.3445i	−0.602528	+	0.798098i
$169$	6.56474	−	6.56474i	0.504980	−	0.504980i
$170$	23.7531	+	18.8870i	1.82178	+	1.44857i
$171$	2.01193	−	0.419172i	0.153856	−	0.0320549i
$172$	−13.5616	+	9.68090i	−1.03406	+	0.738162i
$173$	15.1981	+	11.6619i	1.15549	+	0.886639i	0.994948	−	0.100389i	$-0.0320089\pi$
$173$	15.1981	+	11.6619i	1.15549	+	0.886639i	0.160543	+	0.987029i	$0.448676\pi$
$174$	3.62884	−	2.19294i	0.275102	−	0.166246i
$175$	−19.1716	+	0.429367i	−1.44924	+	0.0324571i
$176$	0.526176	+	0.261862i	0.0396620	+	0.0197386i
$177$	11.4609	−	21.6773i	0.861452	−	1.62937i
$178$	−11.9578	−	7.18201i	−0.896276	−	0.538314i
$179$	12.2975	+	1.61899i	0.919156	+	0.121009i	0.575234	−	0.817989i	$-0.304911\pi$
$179$	12.2975	+	1.61899i	0.919156	+	0.121009i	0.343922	+	0.938998i	$0.388244\pi$
$180$	−8.80437	−	19.0633i	−0.656239	−	1.42090i
$181$	7.79552	+	3.22901i	0.579437	+	0.240010i	0.653099	−	0.757273i	$-0.273469\pi$
$181$	7.79552	+	3.22901i	0.579437	+	0.240010i	−0.0736622	+	0.997283i	$0.523469\pi$
$182$	0.904825	−	7.15585i	0.0670701	−	0.530427i
$183$	1.43709	−	6.29203i	0.106233	−	0.465120i
$184$	11.8322	+	23.1906i	0.872283	+	1.70963i
$185$	−6.58636	−	24.5806i	−0.484239	−	1.80721i
$186$	3.47619	−	8.89069i	0.254887	−	0.651897i
$187$	0.117594	+	0.893214i	0.00859932	+	0.0653183i
$188$	7.20991	+	0.249138i	0.525837	+	0.0181703i
$189$	11.9282	+	6.83512i	0.867646	+	0.497182i
$190$	−2.43850	+	2.35570i	−0.176908	+	0.170900i
$191$	−6.95285	−	12.0427i	−0.503091	−	0.871379i	−0.999994	−	0.00357278i	$-0.998863\pi$
$191$	−6.95285	−	12.0427i	−0.503091	−	0.871379i	0.496903	−	0.867806i	$-0.334471\pi$
$192$	13.1251	−	4.44191i	0.947226	−	0.320567i
$193$	−11.3712	+	19.6954i	−0.818514	+	1.41771i	0.0882636	+	0.996097i	$0.471868\pi$
$193$	−11.3712	+	19.6954i	−0.818514	+	1.41771i	−0.906777	+	0.421610i	$0.861465\pi$
$194$	3.94915	+	1.13162i	0.283533	+	0.0812457i
$195$	9.52896	+	6.76327i	0.682383	+	0.484327i
$196$	7.12382	+	12.0520i	0.508845	+	0.860858i
$197$	11.7174	+	4.85352i	0.834832	+	0.345799i	0.758814	−	0.651308i	$-0.225779\pi$
$197$	11.7174	+	4.85352i	0.834832	+	0.345799i	0.0760183	+	0.997106i	$0.475779\pi$
$198$	0.205224	−	0.588638i	0.0145846	−	0.0418327i
$199$	6.04582	+	22.5633i	0.428577	+	1.59947i	0.755986	+	0.654588i	$0.227158\pi$
$199$	6.04582	+	22.5633i	0.428577	+	1.59947i	−0.327409	+	0.944883i	$0.606176\pi$
$200$	17.1992	+	11.1559i	1.21617	+	0.788842i
$201$	−5.73895	−	18.6150i	−0.404795	−	1.31300i
$202$	−11.8453	+	4.66848i	−0.833432	+	0.328473i
$203$	−0.699286	−	4.52600i	−0.0490802	−	0.317663i
$204$	16.8859	+	12.8844i	1.18225	+	0.902088i
$205$	6.38053	−	8.31527i	0.445636	−	0.580764i
$206$	10.0340	+	6.02657i	0.699105	+	0.419891i
$207$	22.8203	−	15.5488i	1.58612	−	1.08072i
$208$	−5.10513	+	5.77880i	−0.353977	+	0.400688i
$209$	−0.100656			−0.00696253
$210$	−22.6604	+	0.960795i	−1.56371	+	0.0663012i
$211$	0.727152	−	0.301196i	0.0500592	−	0.0207352i	−0.357513	−	0.933908i	$-0.616375\pi$
$211$	0.727152	−	0.301196i	0.0500592	−	0.0207352i	0.407573	+	0.913173i	$0.366375\pi$
$212$	1.09105	+	11.2878i	0.0749337	+	0.775247i
$213$	5.32380	−	14.3416i	0.364781	−	0.982673i
$214$	3.66384	−	24.5460i	0.250455	−	1.67793i
$215$	−28.1634	−	7.54637i	−1.92073	−	0.514658i
$216$	−6.42765	−	13.2169i	−0.437346	−	0.899293i
$217$	−7.45239	−	7.12589i	−0.505901	−	0.483737i
$218$	1.65335	+	0.718537i	0.111979	+	0.0486654i
$219$	−7.41119	+	6.13857i	−0.500802	+	0.414806i
$220$	0.231718	+	1.00201i	0.0156224	+	0.0675554i
$221$	−11.7186	−	1.54278i	−0.788278	−	0.103779i
$222$	−4.95271	−	17.1087i	−0.332404	−	1.14826i
$223$		−	14.0062i		−	0.937925i	−0.883218	−	0.468962i	$-0.844628\pi$
$223$		−	14.0062i		−	0.937925i	0.883218	−	0.468962i	$-0.155372\pi$
$224$	0.956624	−	14.9360i	0.0639171	−	0.997955i
$225$	9.44013	−	19.5879i	0.629342	−	1.30586i
$226$	11.4538	+	3.28205i	0.761894	+	0.218319i
$227$	3.89844	−	29.6116i	0.258748	−	1.96539i	−0.00205613	−	0.999998i	$-0.500654\pi$
$227$	3.89844	−	29.6116i	0.258748	−	1.96539i	0.260805	−	0.965392i	$-0.416012\pi$
$228$	−1.67345	+	1.68255i	−0.110827	+	0.111430i
$229$	−12.9114	+	1.69982i	−0.853211	+	0.112327i	−0.544431	−	0.838806i	$-0.683254\pi$
$229$	−12.9114	+	1.69982i	−0.853211	+	0.112327i	−0.308781	+	0.951133i	$0.599921\pi$
$230$	−18.1582	+	41.7818i	−1.19731	+	2.75501i
$231$	−0.503655	−	0.446892i	−0.0331380	−	0.0294033i
$232$	−2.10532	+	4.42013i	−0.138221	+	0.290196i
$233$	−0.880699	+	3.28681i	−0.0576965	+	0.215326i	−0.988755	−	0.149543i	$-0.952220\pi$
$233$	−0.880699	+	3.28681i	−0.0576965	+	0.215326i	0.931059	+	0.364869i	$0.118886\pi$
$234$	6.76268	+	4.59948i	0.442090	+	0.300678i
$235$	7.68491	+	10.0152i	0.501308	+	0.653318i
$236$	2.72407	+	28.1826i	0.177322	+	1.83453i
$237$	−7.23334	+	10.1913i	−0.469856	+	0.661994i
$238$	19.8093	−	11.5726i	1.28404	−	0.750138i
$239$		−	14.3870i		−	0.930617i	−0.885149	−	0.465308i	$-0.845943\pi$
$239$		−	14.3870i		−	0.930617i	0.885149	−	0.465308i	$-0.154057\pi$
$240$	20.6018	+	12.7855i	1.32984	+	0.825299i
$241$	19.6220	+	11.3287i	1.26396	+	0.729748i	0.973838	−	0.227241i	$-0.0729706\pi$
$241$	19.6220	+	11.3287i	1.26396	+	0.729748i	0.290122	+	0.956990i	$0.406304\pi$
$242$	7.99396	−	13.3097i	0.513871	−	0.855579i
$243$	−13.0480	+	8.52932i	−0.837031	+	0.547156i
$244$	2.61247	+	6.97960i	0.167246	+	0.446823i
$245$	−8.35230	+	23.0302i	−0.533609	+	1.47135i
$246$	4.34863	−	5.90802i	0.277258	−	0.376682i
$247$	0.341787	−	1.27557i	0.0217474	−	0.0811624i
$248$	2.29770	+	10.7808i	0.145904	+	0.684580i
$249$	−16.1227	+	17.3711i	−1.02174	+	1.10085i
$250$	1.26153	+	11.0543i	0.0797861	+	0.699138i
$251$	4.64050	−	11.2032i	0.292906	−	0.707137i	−0.707094	−	0.707119i	$-0.749994\pi$
$251$	4.64050	−	11.2032i	0.292906	−	0.707137i	1.00000		1.76054e-5i	$-5.60398e-6\pi$
$252$	−15.8437	+	0.989238i	−0.998056	+	0.0623161i
$253$	−1.24952	+	0.517570i	−0.0785569	+	0.0325393i
$254$	1.23375	−	4.30556i	0.0774122	−	0.270155i
$255$	1.38426	+	37.1413i	0.0866854	+	2.32588i
$256$	−9.83215	+	12.6226i	−0.614509	+	0.788910i
$257$	19.0821	−	11.0170i	1.19031	−	0.687224i	0.231931	−	0.972732i	$-0.425496\pi$
$257$	19.0821	−	11.0170i	1.19031	−	0.687224i	0.958376	+	0.285508i	$0.0921624\pi$
$258$	−19.8135	−	4.88688i	−1.23353	−	0.304244i
$259$	−19.1251	−	2.08340i	−1.18838	−	0.129456i
$260$	−13.4848	−	0.465967i	−0.836292	−	0.0288980i
$261$	4.93222	+	1.62461i	0.305297	+	0.100561i
$262$	−3.59776	−	4.86024i	−0.222270	−	0.300267i
$263$	19.1400	−	5.12854i	1.18022	−	0.316239i	0.385207	−	0.922830i	$-0.374130\pi$
$263$	19.1400	−	5.12854i	1.18022	−	0.316239i	0.795014	+	0.606591i	$0.207463\pi$
$264$	0.176162	+	0.697937i	0.0108420	+	0.0429550i
$265$	−14.0318	+	14.0318i	−0.861969	+	0.861969i
$266$	0.993010	+	2.36303i	0.0608853	+	0.144887i
$267$	−2.85916	−	16.8428i	−0.174978	−	1.03076i
$268$	17.3614	+	14.3010i	1.06052	+	0.873572i
$269$	1.14129	−	8.66899i	0.0695859	−	0.528557i	−0.920780	−	0.390082i	$-0.872447\pi$
$269$	1.14129	−	8.66899i	0.0695859	−	0.528557i	0.990366	−	0.138475i	$-0.0442201\pi$
$270$	10.7001	−	23.3859i	0.651188	−	1.42322i
$271$	1.99427	+	3.45418i	0.121143	+	0.209826i	0.920219	−	0.391404i	$-0.128011\pi$
$271$	1.99427	+	3.45418i	0.121143	+	0.209826i	−0.799076	+	0.601231i	$0.794677\pi$
$272$	−24.4674	−	1.69296i	−1.48356	−	0.102651i
$273$	7.37346	−	4.86512i	0.446262	−	0.294450i
$274$	13.6651	+	0.236028i	0.825538	+	0.0142589i
$275$	−0.648316	+	0.844902i	−0.0390949	+	0.0509495i
$276$	−12.1223	+	29.4917i	−0.729675	+	1.77519i
$277$	−3.32439	+	2.55090i	−0.199743	+	0.153268i	−0.703790	−	0.710408i	$-0.748511\pi$
$277$	−3.32439	+	2.55090i	−0.199743	+	0.153268i	0.504047	+	0.863676i	$0.331844\pi$
$278$	6.70295	−	8.42992i	0.402016	−	0.505593i
$279$	11.0366	−	3.85823i	0.660744	−	0.230986i
$280$	21.2375	−	15.3251i	1.26918	−	0.915847i
$281$	−15.5759	+	15.5759i	−0.929181	+	0.929181i	−0.997653	−	0.0684719i	$-0.978188\pi$
$281$	−15.5759	+	15.5759i	−0.929181	+	0.929181i	0.0684719	+	0.997653i	$0.478188\pi$
$282$	5.51774	+	6.90086i	0.328577	+	0.410940i
$283$	4.86747	−	3.73494i	0.289341	−	0.222019i	−0.453884	−	0.891061i	$-0.649962\pi$
$283$	4.86747	−	3.73494i	0.289341	−	0.222019i	0.743225	+	0.669042i	$0.233295\pi$
$284$	3.97993	+	17.2103i	0.236166	+	1.02124i
$285$	−4.13432	−	0.388303i	−0.244896	−	0.0230011i
$286$	−0.278312	−	0.288095i	−0.0164569	−	0.0170354i
$287$	−4.11449	−	6.77167i	−0.242870	−	0.399719i
$288$	14.5954	+	8.65880i	0.860041	+	0.510225i
$289$	−10.2975	−	17.8359i	−0.605737	−	1.04917i
$290$	−8.31228	+	2.07410i	−0.488114	+	0.121795i
$291$	2.09721	+	4.57344i	0.122940	+	0.268100i
$292$	3.24496	−	10.6277i	0.189897	−	0.621937i
$293$	2.47789	+	1.02638i	0.144760	+	0.0599615i	0.453887	−	0.891059i	$-0.350037\pi$
$293$	2.47789	+	1.02638i	0.144760	+	0.0599615i	−0.309127	+	0.951021i	$0.600037\pi$
$294$	−5.52263	+	16.2327i	−0.322086	+	0.946710i
$295$	−35.0338	+	35.0338i	−2.03975	+	2.03975i
$296$	15.6463	+	13.3484i	0.909421	+	0.775857i
$297$	0.710836	−	0.278621i	0.0412469	−	0.0161672i
$298$	−16.3231	−	2.43646i	−0.945574	−	0.141140i
$299$	−2.31604	−	17.5921i	−0.133940	−	1.01738i
$300$	3.34471	+	24.8840i	0.193107	+	1.43668i
$301$	−13.0236	+	17.7834i	−0.750669	+	1.02502i
$302$	−2.56747	−	0.0443461i	−0.147741	−	0.00255183i
$303$	−13.7854	−	7.28840i	−0.791951	−	0.418708i
$304$	0.544341	−	2.68556i	0.0312201	−	0.154028i
$305$	−6.52040	+	11.2937i	−0.373357	+	0.646674i
$306$	1.48808	+	25.9711i	0.0850677	+	1.48467i
$307$	19.1991	−	7.95254i	1.09575	−	0.453875i	0.239743	−	0.970836i	$-0.422937\pi$
$307$	19.1991	−	7.95254i	1.09575	−	0.453875i	0.856009	+	0.516961i	$0.172937\pi$
$308$	0.769559	+	0.110841i	0.0438497	+	0.00631578i
$309$	2.39918	+	14.1332i	0.136485	+	0.804008i
$310$	−12.0046	+	15.0975i	−0.681817	+	0.857482i
$311$	−1.76618	−	6.59148i	−0.100151	−	0.373768i	0.897599	−	0.440813i	$-0.145310\pi$
$311$	−1.76618	−	6.59148i	−0.100151	−	0.373768i	−0.997750	+	0.0670444i	$0.978643\pi$
$312$	−9.44280	−	0.137488i	−0.534593	−	0.00778373i
$313$	−1.45532	+	5.43133i	−0.0822596	+	0.306997i	−0.994781	−	0.102032i	$-0.967466\pi$
$313$	−1.45532	+	5.43133i	−0.0822596	+	0.306997i	0.912522	+	0.409029i	$0.134132\pi$
$314$	−3.44693	+	7.93135i	−0.194521	+	0.447592i
$315$	−18.9630	−	20.2985i	−1.06844	−	1.14369i
$316$	0.498353	−	14.4221i	0.0280346	−	0.811304i
$317$	−19.4599	+	25.3606i	−1.09298	+	1.42439i	−0.196938	+	0.980416i	$0.563100\pi$
$317$	−19.4599	+	25.3606i	−1.09298	+	1.42439i	−0.896038	+	0.443977i	$0.853567\pi$
$318$	−9.62286	+	10.0153i	−0.539623	+	0.561631i
$319$	−0.220263	−	0.127169i	−0.0123323	−	0.00712008i
$320$	−27.9873	+	0.763574i	−1.56454	+	0.0426851i
$321$	25.7391	−	16.1677i	1.43662	−	0.902391i
$322$	24.4776	+	24.2282i	1.36409	+	1.35018i
$323$	3.88060	−	1.60740i	0.215923	−	0.0894380i
$324$	7.16059	−	16.5144i	0.397810	−	0.917468i
$325$	−8.50562	−	11.0847i	−0.471807	−	0.614871i
$326$	8.44354	−	6.25028i	0.467644	−	0.346171i
$327$	0.650476	+	2.10990i	0.0359714	+	0.116677i
$328$	−0.438689	+	8.45939i	−0.0242225	+	0.467092i
$329$	9.16071	−	2.67583i	0.505046	−	0.147523i
$330$	−0.746671	+	1.01442i	−0.0411029	+	0.0558421i
$331$	26.3351	−	3.46708i	1.44751	−	0.190568i	0.634545	−	0.772886i	$-0.281188\pi$
$331$	26.3351	−	3.46708i	1.44751	−	0.190568i	0.812961	+	0.582318i	$0.197854\pi$
$332$	4.50692	−	26.9929i	0.247349	−	1.48143i
$333$	11.9545	−	18.2468i	0.655105	−	0.999919i
$334$	7.11416	+	12.8288i	0.389269	+	0.701958i
$335$			39.3596i			2.15044i
$336$	14.6471	−	11.0210i	0.799063	−	0.601247i
$337$		−	6.67166i		−	0.363428i	−0.983351	−	0.181714i	$-0.941835\pi$
$337$		−	6.67166i		−	0.363428i	0.983351	−	0.181714i	$-0.0581646\pi$
$338$	−11.4821	+	6.36739i	−0.624546	+	0.346341i
$339$	6.08255	+	13.2644i	0.330359	+	0.720422i
$340$	−24.9347	−	34.9302i	−1.35227	−	1.89435i
$341$	−0.567730	+	0.0747430i	−0.0307443	+	0.00404756i
$342$	−2.89851	−	0.213906i	−0.156734	−	0.0115667i
$343$	13.9453	+	12.1872i	0.752977	+	0.658046i
$344$	22.2084	−	7.87809i	1.19739	−	0.424758i
$345$	−53.3193	+	16.4382i	−2.87061	+	0.885004i
$346$	−16.1188	−	21.7750i	−0.866552	−	1.17063i
$347$	0.950982	+	1.23934i	0.0510514	+	0.0665315i	0.818181	−	0.574960i	$-0.194983\pi$
$347$	0.950982	+	1.23934i	0.0510514	+	0.0665315i	−0.767130	+	0.641492i	$0.778316\pi$
$348$	−5.78769	+	1.56764i	−0.310253	+	0.0840344i
$349$	−7.66208	+	3.17374i	−0.410142	+	0.169886i	−0.578208	−	0.815890i	$-0.696248\pi$
$349$	−7.66208	+	3.17374i	−0.410142	+	0.169886i	0.168066	+	0.985776i	$0.446248\pi$
$350$	26.2310	+	6.88479i	1.40211	+	0.368007i
$351$	1.11712	+	9.95418i	0.0596272	+	0.531315i
$352$	−0.613325	−	0.560979i	−0.0326903	−	0.0299003i
$353$	17.1365	+	9.89375i	0.912083	+	0.526591i	0.881101	−	0.472929i	$-0.156803\pi$
$353$	17.1365	+	9.89375i	0.912083	+	0.526591i	0.0309821	+	0.999520i	$0.490137\pi$
$354$	−24.0257	+	25.0056i	−1.27695	+	1.32903i
$355$	−18.8170	+	24.5228i	−0.998703	+	1.30154i
$356$	13.4588	+	14.4223i	0.713316	+	0.764378i
$357$	26.5539	+	9.18609i	1.40538	+	0.486180i
$358$	−16.0877	−	6.99165i	−0.850263	−	0.369520i
$359$	4.22211	−	15.7571i	0.222834	−	0.831629i	−0.760426	−	0.649424i	$-0.775010\pi$
$359$	4.22211	−	15.7571i	0.222834	−	0.831629i	0.983261	−	0.182205i	$-0.0583234\pi$
$360$	4.54320	+	29.3465i	0.239448	+	1.54669i
$361$	−4.79610	−	17.8993i	−0.252426	−	0.942068i
$362$	−9.34012	−	7.42668i	−0.490906	−	0.390338i
$363$	18.7470	−	3.18240i	0.983961	−	0.167033i
$364$	−4.01775	+	9.37589i	−0.210587	+	0.491430i
$365$	17.9643	−	7.44107i	0.940296	−	0.389483i
$366$	−4.40486	+	7.99418i	−0.230245	+	0.417862i
$367$	9.02083	−	15.6245i	0.470884	−	0.815594i	−0.528562	−	0.848895i	$-0.677269\pi$
$367$	9.02083	−	15.6245i	0.470884	−	0.815594i	0.999445	+	0.0333006i	$0.0106019\pi$
$368$	−7.05174	−	36.1370i	−0.367597	−	1.88377i
$369$	8.95967	−	0.668782i	0.466422	−	0.0348154i
$370$	−0.621513	+	35.9832i	−0.0323109	+	1.87068i
$371$	6.04987	+	13.7279i	0.314094	+	0.712719i
$372$	−8.18936	+	10.7327i	−0.424598	+	0.556465i
$373$	−4.25064	−	32.2869i	−0.220090	−	1.67175i	−0.643220	−	0.765681i	$-0.722402\pi$
$373$	−4.25064	−	32.2869i	−0.220090	−	1.67175i	0.423130	−	0.906069i	$-0.360931\pi$
$374$	0.188093	−	1.26014i	0.00972607	−	0.0651601i
$375$	−9.26992	+	9.98765i	−0.478697	+	0.515760i
$376$	−9.70483	−	3.14741i	−0.500488	−	0.162315i
$377$	2.35947	−	2.35947i	0.121519	−	0.121519i
$378$	−13.5536	−	13.9391i	−0.697124	−	0.716950i
$379$	7.54895	+	3.12688i	0.387763	+	0.160617i	0.568044	−	0.822998i	$-0.307700\pi$
$379$	7.54895	+	3.12688i	0.387763	+	0.160617i	−0.180280	+	0.983615i	$0.557700\pi$
$380$	4.23284	−	2.25262i	0.217140	−	0.115557i
$381$	4.98618	−	2.28647i	0.255450	−	0.117140i
$382$	4.76104	+	19.0806i	0.243596	+	0.976249i
$383$	7.09794	+	12.2940i	0.362688	+	0.628193i	0.988402	−	0.151859i	$-0.0485259\pi$
$383$	7.09794	+	12.2940i	0.362688	+	0.628193i	−0.625715	+	0.780052i	$0.715193\pi$
$384$	−19.5740	+	0.925724i	−0.998884	+	0.0472406i
$385$	0.706468	+	1.16271i	0.0360049	+	0.0592574i
$386$	23.1317	−	22.3462i	1.17737	−	1.13739i
$387$	−11.2570	−	22.3151i	−0.572224	−	1.13434i
$388$	−4.92804	−	3.07688i	−0.250183	−	0.156205i
$389$	−27.5515	+	21.1410i	−1.39691	+	1.07189i	−0.409748	+	0.912199i	$0.634383\pi$
$389$	−27.5515	+	21.1410i	−1.39691	+	1.07189i	−0.987167	+	0.159692i	$0.948950\pi$
$390$	−10.3199	−	12.9068i	−0.522569	−	0.653560i
$391$	39.9078	−	39.9078i	2.01823	−	2.01823i
$392$	−4.98984	−	19.1599i	−0.252025	−	0.967721i
$393$	1.64905	−	7.22007i	0.0831836	−	0.364204i
$394$	−14.0391	−	11.1630i	−0.707280	−	0.562385i
$395$	20.0334	−	15.3722i	1.00799	−	0.773459i
$396$	−0.508313	+	0.720307i	−0.0255437	+	0.0361968i
$397$	−7.35157	+	9.58075i	−0.368964	+	0.480844i	−0.940529	−	0.339713i	$-0.889670\pi$
$397$	−7.35157	+	9.58075i	−0.368964	+	0.480844i	0.571565	+	0.820557i	$0.306337\pi$
$398$	0.570505	−	33.0300i	0.0285968	−	1.65565i
$399$	−1.40478	+	2.80741i	−0.0703271	+	0.140547i
$400$	−19.0364	−	21.8666i	−0.951822	−	1.09333i
$401$	−1.82511	−	3.16118i	−0.0911417	−	0.157862i	0.816850	−	0.576850i	$-0.195718\pi$
$401$	−1.82511	−	3.16118i	−0.0911417	−	0.157862i	−0.907992	+	0.418988i	$0.862385\pi$
$402$	0.550436	+	27.5427i	0.0274532	+	1.37371i
$403$	0.980596	−	7.44837i	0.0488470	−	0.371030i
$404$	17.9223	−	1.73233i	0.891670	−	0.0861869i
$405$	30.2715	−	8.70178i	1.50421	−	0.432395i
$406$	−0.812478	+	6.42552i	−0.0403226	+	0.318893i
$407$	−0.755481	+	0.755481i	−0.0374478	+	0.0374478i
$408$	−17.9371	−	24.0944i	−0.888019	−	1.19285i
$409$	24.3261	−	6.51816i	1.20285	−	0.322302i	0.398896	−	0.916996i	$-0.369393\pi$
$409$	24.3261	−	6.51816i	1.20285	−	0.322302i	0.803952	+	0.594694i	$0.202727\pi$
$410$	−11.9136	+	8.81900i	−0.588373	+	0.435540i
$411$	10.6774	+	12.8910i	0.526678	+	0.635866i
$412$	−11.2936	−	12.1020i	−0.556394	−	0.596223i
$413$	15.1049	+	34.2750i	0.743265	+	1.68656i
$414$	−37.0814	+	12.2487i	−1.82245	+	0.601989i
$415$	41.4718	−	23.9438i	2.03577	−	1.17535i
$416$	9.19163	−	5.86752i	0.450657	−	0.287679i
$417$	13.1814	−	0.491269i	0.645494	−	0.0240575i
$418$	0.136842	+	0.0392118i	0.00669316	+	0.00191791i
$419$	−7.69862	+	3.18887i	−0.376102	+	0.155787i	−0.562723	−	0.826645i	$-0.690246\pi$
$419$	−7.69862	+	3.18887i	−0.376102	+	0.155787i	0.186621	+	0.982432i	$0.440246\pi$
$420$	31.1811	+	7.52141i	1.52148	+	0.367007i
$421$	5.49180	−	13.2584i	0.267654	−	0.646173i	−0.731718	−	0.681607i	$-0.761281\pi$
$421$	5.49180	−	13.2584i	0.267654	−	0.646173i	0.999372	+	0.0354338i	$0.0112813\pi$
$422$	−1.10590	+	0.126206i	−0.0538343	+	0.00614360i
$423$	−2.01494	+	10.6321i	−0.0979697	+	0.516949i
$424$	2.91400	−	15.7708i	0.141516	−	0.765896i
$425$	11.5022	−	42.9266i	0.557937	−	2.08225i
$426$	−12.8247	+	17.4235i	−0.621357	+	0.844172i
$427$	6.17524	+	7.68512i	0.298841	+	0.371909i
$428$	−14.5432	+	31.9430i	−0.702971	+	1.54402i
$429$	0.0458757	−	0.488446i	0.00221490	−	0.0235824i
$430$	35.3484	+	21.2307i	1.70465	+	1.02383i
$431$	−12.4129	−	7.16661i	−0.597910	−	0.345204i	0.170309	−	0.985391i	$-0.445523\pi$
$431$	−12.4129	−	7.16661i	−0.597910	−	0.345204i	−0.768219	+	0.640187i	$0.778857\pi$
$432$	3.58961	+	20.4723i	0.172705	+	0.984974i
$433$			4.50912i			0.216694i	0.994113	+	0.108347i	$0.0345558\pi$
$433$			4.50912i			0.216694i	−0.994113	+	0.108347i	$0.965444\pi$
$434$	7.35555	+	12.5908i	0.353078	+	0.604379i
$435$	−8.55643	−	6.07300i	−0.410249	−	0.291178i
$436$	−1.96781	−	1.62093i	−0.0942411	−	0.0776285i
$437$	3.83860	+	5.00256i	0.183625	+	0.239305i
$438$	12.4669	−	5.45828i	0.595690	−	0.260806i
$439$	−4.01037	+	14.9669i	−0.191405	+	0.714332i	0.801764	+	0.597641i	$0.203895\pi$
$439$	−4.01037	+	14.9669i	−0.191405	+	0.714332i	−0.993168	+	0.116691i	$0.962771\pi$
$440$	0.0753240	−	1.45250i	0.00359093	−	0.0692452i
$441$	−19.4935	+	7.81057i	−0.928260	+	0.371932i
$442$	15.3304	+	6.66253i	0.729194	+	0.316904i
$443$	−6.66050	+	0.876871i	−0.316450	+	0.0416614i	−0.287078	−	0.957907i	$-0.592684\pi$
$443$	−6.66050	+	0.876871i	−0.316450	+	0.0416614i	−0.0293716	+	0.999569i	$0.509351\pi$
$444$	0.0683002	+	25.1887i	0.00324138	+	1.19540i
$445$	−4.50561	+	34.2235i	−0.213586	+	1.62235i
$446$	−5.45628	+	19.0414i	−0.258362	+	0.901638i
$447$	−10.7515	−	17.1166i	−0.508530	−	0.809585i
$448$	−7.11903	+	19.9329i	−0.336343	+	0.941740i
$449$			30.5942i			1.44383i	0.691983	+	0.721914i	$0.256737\pi$
$449$			30.5942i			1.44383i	−0.691983	+	0.721914i	$0.743263\pi$
$450$	−20.4645	+	22.9522i	−0.964708	+	1.08198i
$451$	−0.436282	−	0.0574377i	−0.0205437	−	0.00270463i
$452$	−14.2928	−	8.92390i	−0.672279	−	0.419745i
$453$	−2.00613	−	2.42203i	−0.0942562	−	0.113797i
$454$	−16.8355	+	38.7383i	−0.790128	+	1.81808i
$455$	−17.1334	+	5.00463i	−0.803226	+	0.234621i
$456$	2.93052	−	1.63552i	0.137234	−	0.0765901i
$457$	3.32987	+	0.892236i	0.155765	+	0.0417370i	0.335859	−	0.941912i	$-0.390974\pi$
$457$	3.32987	+	0.892236i	0.155765	+	0.0417370i	−0.180094	+	0.983649i	$0.557640\pi$
$458$	18.2153	+	2.71889i	0.851144	+	0.127045i
$459$	−22.9556	+	22.0932i	−1.07147	+	1.03122i
$460$	40.9627	−	49.7287i	1.90989	−	2.31861i
$461$	12.3334	−	5.10866i	0.574423	−	0.237934i	−0.0765101	−	0.997069i	$-0.524378\pi$
$461$	12.3334	−	5.10866i	0.574423	−	0.237934i	0.650933	+	0.759135i	$0.274378\pi$
$462$	0.510627	+	0.803754i	0.0237565	+	0.0373940i
$463$	−34.0946			−1.58451			−0.792256	−	0.610188i	$-0.791094\pi$
$463$	−34.0946			−1.58451			−0.792256	+	0.610188i	$0.791094\pi$
$464$	4.58410	−	5.18902i	0.212811	−	0.240894i
$465$	−23.6071	+	0.879836i	−1.09475	+	0.0408014i
$466$	2.47773	−	4.12534i	0.114778	−	0.191102i
$467$	3.31573	−	4.32114i	0.153434	−	0.199959i	−0.710312	−	0.703887i	$-0.751446\pi$
$467$	3.31573	−	4.32114i	0.153434	−	0.199959i	0.863745	+	0.503929i	$0.168113\pi$
$468$	−7.40208	−	8.88748i	−0.342161	−	0.410824i
$469$	27.7385	+	10.7686i	1.28085	+	0.497246i
$470$	−6.54611	−	16.6094i	−0.301950	−	0.766133i
$471$	−10.1215	+	3.12043i	−0.466373	+	0.143782i
$472$	7.27548	−	39.3754i	0.334881	−	1.81240i
$473$	0.316831	+	1.18243i	0.0145679	+	0.0543681i
$474$	13.8039	−	11.0372i	0.634032	−	0.506955i
$475$	4.58724	+	1.90010i	0.210477	+	0.0871824i
$476$	−31.4389	+	8.01597i	−1.44100	+	0.367411i
$477$	−16.9835	−	0.958789i	−0.777622	−	0.0438999i
$478$	−5.60462	+	19.5591i	−0.256349	+	0.894613i
$479$	−5.93534	+	10.2803i	−0.271192	+	0.469719i	−0.969167	−	0.246403i	$-0.920751\pi$
$479$	−5.93534	+	10.2803i	−0.271192	+	0.469719i	0.697975	+	0.716122i	$0.254085\pi$
$480$	−23.0275	−	25.4075i	−1.05105	−	1.15969i
$481$	−7.00855	−	12.1392i	−0.319563	−	0.553499i
$482$	−22.2628	−	23.0454i	−1.01404	−	1.04969i
$483$	−3.00305	+	42.0740i	−0.136644	+	1.91443i
$484$	−16.0527	+	14.9804i	−0.729670	+	0.680926i
$485$	−1.32695	−	10.0792i	−0.0602537	−	0.457673i
$486$	21.0615	−	6.51260i	0.955368	−	0.295418i
$487$	−6.73430	−	25.1327i	−0.305160	−	1.13887i	−0.932807	−	0.360375i	$-0.882649\pi$
$487$	−6.73430	−	25.1327i	−0.305160	−	1.13887i	0.627647	−	0.778498i	$-0.284018\pi$
$488$	−0.832673	−	10.5065i	−0.0376933	−	0.475606i
$489$	12.5432	+	2.86484i	0.567223	+	0.129553i
$490$	20.3266	−	28.0559i	0.918264	−	1.26743i
$491$	−33.1553	−	13.7334i	−1.49628	−	0.619778i	−0.523604	−	0.851962i	$-0.675413\pi$
$491$	−33.1553	−	13.7334i	−1.49628	−	0.619778i	−0.972672	+	0.232184i	$0.925413\pi$
$492$	−8.21350	+	6.33790i	−0.370293	+	0.285735i
$493$	10.5226	+	1.38532i	0.473913	+	0.0623919i
$494$	−0.961572	+	1.60099i	−0.0432632	+	0.0720318i
$495$	−1.53840	+	0.114832i	−0.0691459	+	0.00516130i
$496$	1.07605	−	15.5516i	0.0483161	−	0.698286i
$497$	12.1342	+	19.9705i	0.544291	+	0.895801i
$498$	28.6860	−	17.3352i	1.28545	−	0.776807i
$499$	12.6602	+	9.71452i	0.566749	+	0.434882i	0.851978	−	0.523578i	$-0.175403\pi$
$499$	12.6602	+	9.71452i	0.566749	+	0.434882i	−0.285229	+	0.958459i	$0.592070\pi$
$500$	2.59130	−	15.5198i	0.115886	−	0.694067i
$501$	−6.25237	+	16.8431i	−0.279336	+	0.752494i
$502$	−10.6731	+	13.4229i	−0.476363	+	0.599095i
$503$	22.7143	−	22.7143i	1.01278	−	1.01278i	0.0128652	−	0.999917i	$-0.495905\pi$
$503$	22.7143	−	22.7143i	1.01278	−	1.01278i	0.999917	−	0.0128652i	$-0.00409523\pi$
$504$	21.9248	+	4.82721i	0.976609	+	0.215021i
$505$	22.2793	+	22.2793i	0.991416	+	0.991416i
$506$	1.90035	−	0.216870i	0.0844811	−	0.00964104i
$507$	−15.0751	−	5.59607i	−0.669509	−	0.248530i
$508$	−3.35456	+	5.37279i	−0.148835	+	0.238379i
$509$	−12.1741	+	15.8656i	−0.539607	+	0.703230i	−0.980983	−	0.194092i	$-0.937824\pi$
$509$	−12.1741	+	15.8656i	−0.539607	+	0.703230i	0.441376	+	0.897322i	$0.354491\pi$
$510$	12.5869	−	51.0329i	0.557359	−	2.25977i
$511$	−0.329135	−	14.6961i	−0.0145601	−	0.650119i
$512$	18.2841	−	13.3301i	0.808049	−	0.589115i
$513$	−2.11249	−	2.86497i	−0.0932688	−	0.126492i
$514$	−30.2339	+	7.54403i	−1.33356	+	0.332753i
$515$	3.78075	−	28.7177i	0.166600	−	1.26545i
$516$	25.0327	+	14.3623i	1.10200	+	0.632265i
$517$	0.202825	−	0.489662i	0.00892022	−	0.0215353i
$518$	25.1890	+	10.2828i	1.10674	+	0.451800i
$519$	7.38813	−	32.3476i	0.324303	−	1.41990i
$520$	18.1511	+	5.88665i	0.795977	+	0.258146i
$521$	7.40662	−	1.98460i	0.324490	−	0.0869468i	−0.0928970	−	0.995676i	$-0.529613\pi$
$521$	7.40662	−	1.98460i	0.324490	−	0.0869468i	0.417387	+	0.908729i	$0.362946\pi$
$522$	−6.07248	−	4.13006i	−0.265785	−	0.180768i
$523$	22.4458	−	2.95505i	0.981487	−	0.129215i	0.377329	−	0.926079i	$-0.376843\pi$
$523$	22.4458	−	2.95505i	0.981487	−	0.129215i	0.604158	+	0.796864i	$0.293509\pi$
$524$	2.99780	+	8.00905i	0.130959	+	0.349877i
$525$	14.5172	+	29.8739i	0.633583	+	1.30381i
$526$	−28.0187	−	0.483948i	−1.22167	−	0.0211011i
$527$	20.6941	−	11.9478i	0.901451	−	0.520453i
$528$	0.0323967	−	1.01747i	0.00140989	−	0.0442798i
$529$	53.4560	+	30.8629i	2.32418	+	1.34186i
$530$	24.5426	−	13.6100i	1.06606	−	0.591182i
$531$	−42.4033	−	2.39384i	−1.84015	−	0.103884i
$532$	−0.429450	−	3.59938i	−0.0186190	−	0.156053i
$533$	2.20932	−	5.33377i	0.0956962	−	0.231031i
$534$	−2.67429	+	24.0117i	−0.115728	+	1.03909i
$535$	−59.3235	+	15.8957i	−2.56478	+	0.687231i
$536$	−18.0317	−	26.2055i	−0.778852	−	1.13191i
$537$	−6.32939	−	20.5301i	−0.273133	−	0.885940i
$538$	−4.92869	+	11.3409i	−0.212491	+	0.488940i
$539$	1.01270	−	0.179770i	0.0436203	−	0.00774322i
$540$	−23.6570	+	27.6248i	−1.01804	+	1.18878i
$541$	4.74945	+	3.64438i	0.204195	+	0.156684i	0.705797	−	0.708414i	$-0.250589\pi$
$541$	4.74945	+	3.64438i	0.204195	+	0.156684i	−0.501602	+	0.865099i	$0.667256\pi$
$542$	−1.36560	−	5.47284i	−0.0586573	−	0.235079i
$543$	−0.544312	−	14.6046i	−0.0233587	−	0.626742i
$544$	32.6040	+	11.8332i	1.39788	+	0.507342i
$545$		−	4.46117i		−	0.191096i
$546$	−11.9195	+	3.74171i	−0.510107	+	0.160130i
$547$	6.57199	+	15.8662i	0.280998	+	0.678389i	0.999859	−	0.0167644i	$-0.00533653\pi$
$547$	6.57199	+	15.8662i	0.280998	+	0.678389i	−0.718862	+	0.695153i	$0.755337\pi$
$548$	−18.4857	−	5.64427i	−0.789671	−	0.241111i
$549$	−10.9438	+	2.28006i	−0.467068	+	0.0973106i
$550$	1.21053	−	0.896085i	0.0516171	−	0.0382092i
$551$	−0.306904	+	1.14538i	−0.0130746	+	0.0487949i
$552$	27.9691	−	35.3716i	1.19044	−	1.50551i
$553$	−5.35248	−	18.3243i	−0.227611	−	0.779226i
$554$	5.51324	−	2.17289i	0.234235	−	0.0923172i
$555$	−33.9449	+	28.1160i	−1.44088	+	1.19346i
$556$	−12.3966	+	8.84927i	−0.525734	+	0.375293i
$557$	−2.93360	+	22.2829i	−0.124301	+	0.944156i	0.809690	+	0.586858i	$0.199635\pi$
$557$	−2.93360	+	22.2829i	−0.124301	+	0.944156i	−0.933990	+	0.357298i	$0.883698\pi$
$558$	−16.5073	+	0.945825i	−0.698809	+	0.0400400i
$559$	−16.0602			−0.679273
$560$	−34.8424	+	12.5611i	−1.47236	+	0.530804i
$561$	1.32139	−	0.830011i	0.0557890	−	0.0350431i
$562$	27.2432	−	15.1077i	1.14919	−	0.637279i
$563$	−5.36061	−	0.705738i	−0.225923	−	0.0297433i	0.0167147	−	0.999860i	$-0.494679\pi$
$563$	−5.36061	−	0.705738i	−0.225923	−	0.0297433i	−0.242638	+	0.970117i	$0.578013\pi$
$564$	−4.81306	−	11.5312i	−0.202667	−	0.485552i
$565$	−3.84857	−	29.2328i	−0.161911	−	1.22983i
$566$	−8.07231	+	3.18147i	−0.339305	+	0.133727i
$567$	2.14956	−	23.7145i	0.0902731	−	0.995917i
$568$	1.29375	−	24.9478i	0.0542846	−	1.04679i
$569$	10.7026	+	2.86776i	0.448678	+	0.120223i	0.476081	−	0.879402i	$-0.342057\pi$
$569$	10.7026	+	2.86776i	0.448678	+	0.120223i	−0.0274029	+	0.999624i	$0.508724\pi$
$570$	5.46935	+	2.13847i	0.229086	+	0.0895707i
$571$	3.57410	−	2.74250i	0.149571	−	0.114770i	−0.531265	−	0.847206i	$-0.678283\pi$
$571$	3.57410	−	2.74250i	0.149571	−	0.114770i	0.680836	+	0.732436i	$0.261616\pi$
$572$	0.266134	+	0.500085i	0.0111276	+	0.0209096i
$573$	−13.9404	+	19.6411i	−0.582369	+	0.820517i
$574$	2.95566	+	10.8089i	0.123367	+	0.451156i
$575$	66.7153			2.78222
$576$	−16.4693	−	17.4575i	−0.686220	−	0.727394i
$577$	4.13941	−	7.16967i	0.172326	−	0.298477i	−0.766907	−	0.641759i	$-0.778205\pi$
$577$	4.13941	−	7.16967i	0.172326	−	0.298477i	0.939233	+	0.343281i	$0.111538\pi$
$578$	7.05134	+	28.2594i	0.293297	+	1.17543i
$579$	39.2182	+	3.68344i	1.62985	+	0.153079i
$580$	12.1085	+	0.418410i	0.502780	+	0.0173735i
$581$	−5.52785	−	35.7780i	−0.229334	−	1.48432i
$582$	−1.06952	−	7.03458i	−0.0443330	−	0.291593i
$583$	0.804753	+	0.215633i	0.0333295	+	0.00893061i
$584$	−8.55165	+	13.1842i	−0.353870	+	0.545566i
$585$	3.76857	−	19.8853i	0.155811	−	0.822157i
$586$	−2.96886	−	2.36065i	−0.122642	−	0.0975176i
$587$	0.361985	+	0.149939i	0.0149407	+	0.00618865i	0.390141	−	0.920755i	$-0.372426\pi$
$587$	0.361985	+	0.149939i	0.0149407	+	0.00618865i	−0.375201	+	0.926944i	$0.622426\pi$
$588$	13.8317	−	19.9170i	0.570408	−	0.821362i
$589$	1.02167	+	2.46652i	0.0420970	+	0.101631i
$590$	61.2763	−	33.9806i	2.52271	−	1.39896i
$591$	−0.818154	−	21.9521i	−0.0336544	−	0.902989i
$592$	−16.0711	−	24.2423i	−0.660518	−	0.996351i
$593$	11.0828	+	19.1959i	0.455114	+	0.788281i	0.998695	−	0.0510763i	$-0.0162652\pi$
$593$	11.0828	+	19.1959i	0.455114	+	0.788281i	−0.543581	+	0.839357i	$0.682932\pi$
$594$	−1.07492	+	0.101870i	−0.0441046	+	0.00417978i
$595$	−45.8041	−	33.5445i	−1.87779	−	1.37519i
$596$	21.2422	+	9.67124i	0.870113	+	0.396150i
$597$	31.1590	−	25.8085i	1.27525	−	1.05627i
$598$	−3.70454	+	24.8187i	−0.151490	+	1.01491i
$599$	6.05169	+	22.5852i	0.247265	+	0.922807i	0.972231	+	0.234022i	$0.0751888\pi$
$599$	6.05169	+	22.5852i	0.247265	+	0.922807i	−0.724966	+	0.688785i	$0.758145\pi$
$600$	5.14672	−	35.1328i	0.210114	−	1.43429i
$601$	−7.02646	−	7.02646i	−0.286615	−	0.286615i	0.549125	−	0.835740i	$-0.314961\pi$
$601$	−7.02646	−	7.02646i	−0.286615	−	0.286615i	−0.835740	+	0.549125i	$0.814961\pi$
$602$	24.6334	−	19.1031i	1.00398	−	0.778584i
$603$	−25.1642	+	22.4748i	−1.02477	+	0.915246i
$604$	3.47320	+	1.06048i	0.141322	+	0.0431501i
$605$	−38.0926	−	5.01498i	−1.54868	−	0.203888i
$606$	15.9020	+	15.2789i	0.645975	+	0.620661i
$607$	−35.1905	+	20.3172i	−1.42834	+	0.824651i	−0.996990	−	0.0775347i	$-0.975295\pi$
$607$	−35.1905	+	20.3172i	−1.42834	+	0.824651i	−0.431348	+	0.902186i	$0.641962\pi$
$608$	−1.78622	+	3.43897i	−0.0724410	+	0.139469i
$609$	−6.62092	+	4.36858i	−0.268293	+	0.177024i
$610$	13.2641	−	12.8137i	0.537047	−	0.518810i
$611$	5.51655	+	4.23299i	0.223176	+	0.171249i
$612$	8.09430	−	35.8874i	0.327193	−	1.45066i
$613$	−25.3291	−	33.0096i	−1.02303	−	1.33324i	−0.941662	−	0.336560i	$-0.890737\pi$
$613$	−25.3291	−	33.0096i	−1.02303	−	1.33324i	−0.0813717	−	0.996684i	$-0.525930\pi$
$614$	−29.1992	+	3.33223i	−1.17838	+	0.134478i
$615$	−17.6982	−	4.04223i	−0.713659	−	0.162999i
$616$	−1.00304	−	0.450480i	−0.0404135	−	0.0181504i
$617$	−28.6583	−	28.6583i	−1.15374	−	1.15374i	−0.985796	−	0.167945i	$-0.946287\pi$
$617$	−28.6583	−	28.6583i	−1.15374	−	1.15374i	−0.167945	−	0.985796i	$-0.553713\pi$
$618$	2.24405	−	20.1487i	0.0902690	−	0.810499i
$619$	15.7675	+	20.5486i	0.633748	+	0.825917i	0.994277	−	0.106831i	$-0.0340705\pi$
$619$	15.7675	+	20.5486i	0.633748	+	0.825917i	−0.360529	+	0.932748i	$0.617404\pi$
$620$	22.2017	−	15.8486i	0.891642	−	0.636494i
$621$	−40.9556	−	24.7028i	−1.64349	−	0.991291i
$622$	−0.166663	+	9.64915i	−0.00668259	+	0.386896i
$623$	22.8862	+	12.5387i	0.916917	+	0.502351i
$624$	12.7839	+	3.86547i	0.511767	+	0.154743i
$625$	−7.54010	+	4.35328i	−0.301604	+	0.174131i
$626$	4.09435	−	6.81696i	0.163643	−	0.272461i
$627$	0.0726702	+	0.158474i	0.00290217	+	0.00632884i
$628$	7.77585	−	9.43989i	0.310290	−	0.376693i
$629$	17.0617	−	41.1906i	0.680294	−	1.64238i
$630$	17.8727	+	34.9831i	0.712065	+	1.39376i
$631$	−27.2039	−	27.2039i	−1.08297	−	1.08297i	−0.996231	−	0.0867372i	$-0.972356\pi$
$631$	−27.2039	−	27.2039i	−1.08297	−	1.08297i	−0.0867372	−	0.996231i	$-0.527644\pi$
$632$	−6.29579	+	19.4127i	−0.250433	+	0.772194i
$633$	−0.999185	−	0.927382i	−0.0397140	−	0.0368601i
$634$	36.3352	−	26.8969i	1.44306	−	1.06821i
$635$	−10.9888	+	1.44671i	−0.436078	+	0.0574107i
$636$	16.9839	−	9.86714i	0.673454	−	0.391258i
$637$	−1.16060	+	13.4440i	−0.0459846	+	0.532669i
$638$	0.249907	+	0.258692i	0.00989392	+	0.0102417i
$639$	−26.4232	+	1.97233i	−1.04529	+	0.0780240i
$640$	38.3462	+	9.86470i	1.51577	+	0.389936i
$641$	14.2351	+	8.21862i	0.562251	+	0.324616i	0.754049	−	0.656819i	$-0.228098\pi$
$641$	14.2351	+	8.21862i	0.562251	+	0.324616i	−0.191797	+	0.981435i	$0.561432\pi$
$642$	−41.2906	+	11.9530i	−1.62961	+	0.471747i
$643$	−7.65685	−	18.4853i	−0.301957	−	0.728988i	−0.999917	−	0.0128516i	$-0.995909\pi$
$643$	−7.65685	−	18.4853i	−0.301957	−	0.728988i	0.697961	−	0.716136i	$-0.254091\pi$
$644$	−23.8390	−	42.4738i	−0.939388	−	1.67370i
$645$	8.45195	+	49.7890i	0.332795	+	1.96044i
$646$	−5.90186	+	0.673525i	−0.232206	+	0.0264995i
$647$	−28.2892	+	7.58006i	−1.11216	+	0.298003i	−0.767708	−	0.640800i	$-0.778603\pi$
$647$	−28.2892	+	7.58006i	−1.11216	+	0.298003i	−0.344454	+	0.938803i	$0.611936\pi$
$648$	−16.1682	+	19.6619i	−0.635147	+	0.772391i
$649$	2.00926	+	0.538379i	0.0788702	+	0.0211332i
$650$	7.24521	+	18.3832i	0.284180	+	0.721048i
$651$	−5.83871	+	16.8778i	−0.228837	+	0.661492i
$652$	−13.9139	+	5.20797i	−0.544909	+	0.203960i
$653$	−11.5164	−	8.83682i	−0.450670	−	0.345811i	0.358355	−	0.933585i	$-0.383338\pi$
$653$	−11.5164	−	8.83682i	−0.450670	−	0.345811i	−0.809025	+	0.587774i	$0.800004\pi$
$654$	−0.0623886	−	3.12180i	−0.00243959	−	0.122072i
$655$	−7.48213	+	12.9594i	−0.292351	+	0.506367i
$656$	3.89185	−	11.3297i	0.151951	−	0.442349i
$657$	15.0152	+	7.23641i	0.585801	+	0.282319i
$658$	−13.4964	+	0.0691248i	−0.526144	+	0.00269476i
$659$	0.230126	+	0.555573i	0.00896444	+	0.0216421i	0.928298	−	0.371836i	$-0.121272\pi$
$659$	0.230126	+	0.555573i	0.00896444	+	0.0216421i	−0.919334	+	0.393478i	$0.871272\pi$
$660$	1.41028	−	1.08823i	0.0548951	−	0.0423595i
$661$	−21.8746	+	16.7850i	−0.850825	+	0.652861i	−0.939254	−	0.343222i	$-0.888482\pi$
$661$	−21.8746	+	16.7850i	−0.850825	+	0.652861i	0.0884297	+	0.996082i	$0.471815\pi$
$662$	−37.1532	−	5.54564i	−1.44400	−	0.215537i
$663$	6.03145	+	19.5637i	0.234242	+	0.759791i
$664$	−16.6426	+	34.9411i	−0.645857	+	1.35598i
$665$	4.38368	−	4.58453i	0.169992	−	0.177781i
$666$	−23.3605	+	20.1495i	−0.905200	+	0.780778i
$667$	2.07967	+	15.7966i	0.0805250	+	0.611648i
$668$	−4.67411	−	20.2121i	−0.180847	−	0.782029i
$669$	−22.0515	+	10.1120i	−0.852560	+	0.390952i
$670$	15.3330	−	53.5094i	0.592365	−	2.06725i
$671$	0.547512			0.0211365
$672$	−24.2061	+	9.27718i	−0.933770	+	0.357875i
$673$	42.2846			1.62995			0.814975	−	0.579495i	$-0.196750\pi$
$673$	42.2846			1.62995			0.814975	+	0.579495i	$0.196750\pi$
$674$	−2.59902	+	9.07012i	−0.100111	+	0.349368i
$675$	−37.6548	−	0.720857i	−1.44933	−	0.0277458i
$676$	18.0905	−	4.18347i	0.695787	−	0.160903i
$677$	−3.23241	−	24.5526i	−0.124232	−	0.943634i	−0.934097	−	0.357018i	$-0.883793\pi$
$677$	−3.23241	−	24.5526i	−0.124232	−	0.943634i	0.809866	−	0.586615i	$-0.199540\pi$
$678$	−3.10194	−	20.4025i	−0.119129	−	0.783552i
$679$	−7.46633	−	1.82244i	−0.286531	−	0.0699390i
$680$	20.2913	+	57.2012i	0.778136	+	2.19357i
$681$	−49.4353	+	15.2408i	−1.89436	+	0.584029i
$682$	0.800946	+	0.119553i	0.0306698	+	0.00457790i
$683$	−19.3640	+	14.8585i	−0.740941	+	0.568544i	−0.908783	−	0.417270i	$-0.862987\pi$
$683$	−19.3640	+	14.8585i	−0.740941	+	0.568544i	0.167841	+	0.985814i	$0.446320\pi$
$684$	3.85720	+	1.41995i	0.147484	+	0.0542933i
$685$	−12.9430	−	31.2471i	−0.494526	−	1.19389i
$686$	−14.2110	−	22.0011i	−0.542580	−	0.840004i
$687$	11.9978	+	19.1007i	0.457745	+	0.728736i
$688$	−33.2613	+	2.05875i	−1.26807	+	0.0784889i
$689$	−5.46523	+	9.46606i	−0.208209	+	0.360628i
$690$	78.8913	−	1.57663i	3.00334	−	0.0600211i
$691$	12.4424	+	9.54740i	0.473332	+	0.363200i	0.817710	−	0.575631i	$-0.195243\pi$
$691$	12.4424	+	9.54740i	0.473332	+	0.363200i	−0.344378	+	0.938831i	$0.611910\pi$
$692$	13.4308	+	35.8824i	0.510563	+	1.36404i
$693$	−0.339970	+	1.11560i	−0.0129144	+	0.0423781i
$694$	−0.810060	−	2.05535i	−0.0307494	−	0.0780202i
$695$	−25.7441	−	6.89810i	−0.976528	−	0.261660i
$696$	8.47907	+	0.123456i	0.321398	+	0.00467959i
$697$	17.7373	−	4.75268i	0.671847	−	0.180021i
$698$	11.6530	−	1.32984i	0.441071	−	0.0503353i
$699$	5.81062	−	0.986384i	0.219778	−	0.0373085i
$700$	−32.9791	−	19.5785i	−1.24649	−	0.739997i
$701$	5.88198	+	14.2004i	0.222159	+	0.536340i	0.995183	−	0.0980373i	$-0.0312565\pi$
$701$	5.88198	+	14.2004i	0.222159	+	0.536340i	−0.773023	+	0.634378i	$0.781256\pi$
$702$	2.35905	−	13.9679i	0.0890365	−	0.527184i
$703$	4.31386	+	2.49061i	0.162700	+	0.0939351i
$704$	0.615280	+	1.00158i	0.0231892	+	0.0377484i
$705$	10.2197	−	19.3298i	0.384898	−	0.728003i
$706$	−19.4428	−	20.1263i	−0.731740	−	0.757462i
$707$	21.7968	−	9.60578i	0.819751	−	0.361263i
$708$	42.4042	−	24.6356i	1.59365	−	0.925864i
$709$	−2.70559	+	0.356197i	−0.101610	+	0.0133773i	−0.181160	−	0.983454i	$-0.557985\pi$
$709$	−2.70559	+	0.356197i	−0.101610	+	0.0133773i	0.0795495	+	0.996831i	$0.474652\pi$
$710$	35.1349	−	26.0084i	1.31859	−	0.976077i
$711$	21.2674	+	4.03050i	0.797592	+	0.151156i
$712$	−12.6789	−	24.8501i	−0.475163	−	0.931297i
$713$	25.3655	+	25.3655i	0.949946	+	0.949946i
$714$	−32.5216	−	22.8329i	−1.21709	−	0.854500i
$715$	−0.379346	+	0.915822i	−0.0141867	+	0.0342498i
$716$	19.1476	+	15.7723i	0.715579	+	0.589439i
$717$	−22.6510	+	10.3869i	−0.845917	+	0.387906i
$718$	−11.8783	+	19.7770i	−0.443295	+	0.738073i
$719$	32.4657	−	18.7441i	1.21077	−	0.699036i	0.247840	−	0.968801i	$-0.420279\pi$
$719$	32.4657	−	18.7441i	1.21077	−	0.699036i	0.962926	+	0.269765i	$0.0869461\pi$
$720$	5.25577	−	41.6664i	0.195871	−	1.55281i
$721$	−19.2043	−	10.5215i	−0.715205	−	0.391840i
$722$	−0.452578	+	26.2025i	−0.0168432	+	0.975155i
$723$	3.66970	−	39.0719i	0.136478	−	1.45310i
$724$	9.80474	+	13.7351i	0.364390	+	0.510462i
$725$	7.63754	+	9.95343i	0.283651	+	0.369661i
$726$	−26.7263	−	2.97663i	−0.991904	−	0.110473i
$727$	−3.55047	−	3.55047i	−0.131680	−	0.131680i	0.638195	−	0.769875i	$-0.279681\pi$
$727$	−3.55047	−	3.55047i	−0.131680	−	0.131680i	−0.769875	+	0.638195i	$0.779681\pi$
$728$	9.11463	−	11.1814i	0.337810	−	0.414409i
$729$	22.8489	+	14.3850i	0.846254	+	0.532780i
$730$	−27.3213	+	3.11792i	−1.01121	+	0.115399i
$731$	−31.0972	−	40.5267i	−1.15017	−	1.49893i
$732$	9.10263	−	9.15213i	0.336443	−	0.338272i
$733$	28.2469	+	21.6746i	1.04332	+	0.800569i	0.980314	−	0.197444i	$-0.0632642\pi$
$733$	28.2469	+	21.6746i	1.04332	+	0.800569i	0.0630073	+	0.998013i	$0.479931\pi$
$734$	−18.3505	+	17.7274i	−0.677331	+	0.654330i
$735$	42.2891	−	3.47708i	1.55986	−	0.128254i
$736$	−4.49076	+	51.8754i	−0.165532	+	1.91215i
$737$	1.43110	−	0.826247i	0.0527153	−	0.0304352i
$738$	−12.4412	−	2.58113i	−0.457967	−	0.0950129i
$739$	−3.83043	−	0.504285i	−0.140904	−	0.0185504i	0.0597440	−	0.998214i	$-0.480972\pi$
$739$	−3.83043	−	0.504285i	−0.140904	−	0.0185504i	−0.200648	+	0.979663i	$0.564305\pi$
$740$	14.8626	−	48.6771i	0.546361	−	1.78940i
$741$	−2.25502	+	0.382803i	−0.0828404	+	0.0140626i
$742$	−2.87692	−	21.0199i	−0.105615	−	0.771666i
$743$	11.8473	+	11.8473i	0.434636	+	0.434636i	0.890202	−	0.455566i	$-0.150563\pi$
$743$	11.8473	+	11.8473i	0.434636	+	0.434636i	−0.455566	+	0.890202i	$0.650563\pi$
$744$	15.3145	−	11.4009i	0.561456	−	0.417976i
$745$	10.5707	+	39.4503i	0.387279	+	1.44535i
$746$	−6.79897	+	45.5499i	−0.248928	+	1.66770i
$747$	38.9892	+	12.8425i	1.42654	+	0.469882i
$748$	−0.746613	+	1.63988i	−0.0272989	+	0.0599600i
$749$	−5.02813	+	46.1571i	−0.183724	+	1.68654i
$750$	16.4933	−	9.96701i	0.602249	−	0.363944i
$751$	−17.6522	−	30.5745i	−0.644138	−	1.11568i	−0.984500	−	0.175385i	$-0.943883\pi$
$751$	−17.6522	−	30.5745i	−0.644138	−	1.11568i	0.340362	−	0.940294i	$-0.389450\pi$
$752$	11.9676	+	8.05954i	0.436414	+	0.293901i
$753$	−20.9886	+	0.782246i	−0.764868	+	0.0285066i
$754$	−4.12686	+	2.28854i	−0.150291	+	0.0833438i
$755$	2.43179	+	5.87087i	0.0885020	+	0.213663i
$756$	12.9960	+	24.2302i	0.472661	+	0.881244i
$757$	17.7965	+	7.37154i	0.646824	+	0.267923i	0.681882	−	0.731462i	$-0.261162\pi$
$757$	17.7965	+	7.37154i	0.646824	+	0.267923i	−0.0350583	+	0.999385i	$0.511162\pi$
$758$	−9.04469	−	7.19177i	−0.328518	−	0.261217i
$759$	1.71698	+	1.59360i	0.0623225	+	0.0578439i
$760$	−6.63208	+	1.41349i	−0.240571	+	0.0512727i
$761$	30.5121	+	8.17570i	1.10606	+	0.296369i	0.765232	−	0.643755i	$-0.222624\pi$
$761$	30.5121	+	8.17570i	1.10606	+	0.296369i	0.340833	+	0.940124i	$0.389291\pi$
$762$	−7.66943	+	1.16604i	−0.277834	+	0.0422412i
$763$	−3.14400	−	1.22055i	−0.113820	−	0.0441869i
$764$	0.960449	−	27.7948i	0.0347478	−	1.00558i
$765$	57.4762	−	28.9941i	2.07806	−	1.04828i
$766$	−4.86038	−	19.4788i	−0.175613	−	0.703796i
$767$	−13.6452	+	23.6342i	−0.492701	+	0.853383i
$768$	26.9715	+	6.36677i	0.973252	+	0.229741i
$769$	23.1059			0.833219			0.416610	−	0.909085i	$-0.363218\pi$
$769$	23.1059			0.833219			0.416610	+	0.909085i	$0.363218\pi$
$770$	−0.507495	−	1.85592i	−0.0182889	−	0.0668828i
$771$	−31.1219	−	22.0891i	−1.12083	−	0.795519i
$772$	−40.1527	+	21.3684i	−1.44513	+	0.769066i
$773$	−26.8527	+	20.6048i	−0.965826	+	0.741105i	−0.965905	−	0.258895i	$-0.916641\pi$
$773$	−26.8527	+	20.6048i	−0.965826	+	0.741105i	7.91263e−5		1.00000i	$0.499975\pi$
$774$	6.61072	+	34.7227i	0.237618	+	1.24808i
$775$	27.2843	+	7.31080i	0.980081	+	0.262612i
$776$	5.50104	+	6.10280i	0.197476	+	0.219078i
$777$	10.5276	+	31.6149i	0.377674	+	1.13418i
$778$	45.6919	−	18.0082i	1.63814	−	0.645625i
$779$	0.267789	+	2.03406i	0.00959455	+	0.0728778i
$780$	9.00194	+	21.5670i	0.322321	+	0.772223i
$781$	1.28665	+	0.169391i	0.0460401	+	0.00606129i
$782$	−69.8013	+	38.7082i	−2.49609	+	1.38420i
$783$	−1.00310	−	8.93825i	−0.0358480	−	0.319427i
$784$	−0.680273	+	27.9917i	−0.0242954	+	0.999705i
$785$	21.4009			0.763832
$786$	−5.05455	+	9.17328i	−0.180290	+	0.327200i
$787$	−1.72268	+	13.0851i	−0.0614069	+	0.466432i	0.932922	+	0.360080i	$0.117250\pi$
$787$	−1.72268	+	13.0851i	−0.0614069	+	0.466432i	−0.994329	+	0.106352i	$0.966083\pi$
$788$	14.7375	+	20.6452i	0.525001	+	0.735456i
$789$	−21.8928	−	26.4315i	−0.779406	−	0.940988i
$790$	−33.2239	+	13.0943i	−1.18205	+	0.465873i
$791$	−21.6547	−	5.28565i	−0.769951	−	0.187936i
$792$	0.971655	−	0.781238i	0.0345263	−	0.0277601i
$793$	−1.85913	+	6.93837i	−0.0660196	+	0.246389i
$794$	13.7267	−	10.1611i	0.487144	−	0.360605i
$795$	32.2224	+	11.9614i	1.14281	+	0.424226i
$796$	−13.6428	+	44.6821i	−0.483558	+	1.58372i
$797$	12.3506	+	29.8170i	0.437481	+	1.05617i	0.976816	+	0.214082i	$0.0686760\pi$
$797$	12.3506	+	29.8170i	0.437481	+	1.05617i	−0.539334	+	0.842092i	$0.681324\pi$
$798$	3.00346	−	3.26943i	0.106321	−	0.115737i
$799$			22.1169i			0.782440i
$800$	17.3616	+	37.1435i	0.613827	+	1.31322i
$801$	−24.4533	+	16.6614i	−0.864015	+	0.588703i
$802$	1.24976	+	5.00863i	0.0441307	+	0.176861i
$803$	−0.647666	−	0.496972i	−0.0228557	−	0.0175378i
$804$	9.98127	−	37.6588i	0.352012	−	1.32812i
$805$	30.8446	−	79.4522i	1.08713	−	2.80032i
$806$	−4.23472	+	9.74406i	−0.149162	+	0.343220i
$807$	−14.4725	+	4.46185i	−0.509457	+	0.157064i
$808$	−25.0403	−	4.62675i	−0.880914	−	0.162768i
$809$	−8.77086	+	2.35014i	−0.308367	+	0.0826267i	−0.409684	−	0.912228i	$-0.634361\pi$
$809$	−8.77086	+	2.35014i	−0.308367	+	0.0826267i	0.101317	+	0.994854i	$0.467694\pi$
$810$	−44.5441	+	0.0374449i	−1.56512	+	0.00131568i
$811$	14.8726	−	35.9057i	0.522248	−	1.26082i	−0.414256	−	0.910160i	$-0.635958\pi$
$811$	14.8726	−	35.9057i	0.522248	−	1.26082i	0.936504	−	0.350658i	$-0.114042\pi$
$812$	3.60770	−	8.41898i	0.126605	−	0.295448i
$813$	3.99849	−	5.63359i	0.140233	−	0.197579i
$814$	1.32138	−	0.732771i	0.0463145	−	0.0256836i
$815$	−22.5140	−	12.9985i	−0.788631	−	0.455316i
$816$	14.9992	+	39.7440i	0.525078	+	1.39132i
$817$	4.94263	−	2.85363i	0.172921	−	0.0998359i
$818$	−35.6106	−	0.615077i	−1.24509	−	0.0215057i
$819$	−12.9831	−	8.09640i	−0.453665	−	0.282911i
$820$	19.6322	−	7.34834i	0.685585	−	0.256615i
$821$	−6.40595	+	0.843359i	−0.223569	+	0.0294334i	−0.241478	−	0.970406i	$-0.577632\pi$
$821$	−6.40595	+	0.843359i	−0.223569	+	0.0294334i	0.0179094	+	0.999840i	$0.494299\pi$
$822$	−9.49411	−	21.6848i	−0.331145	−	0.756345i
$823$	−6.88857	+	1.84579i	−0.240120	+	0.0643401i	−0.376872	−	0.926265i	$-0.623000\pi$
$823$	−6.88857	+	1.84579i	−0.240120	+	0.0643401i	0.136752	+	0.990605i	$0.456334\pi$
$824$	10.6391	+	20.8522i	0.370632	+	0.726422i
$825$	1.79828	+	0.410725i	0.0626082	+	0.0142996i
$826$	−7.18292	−	52.4812i	−0.249926	−	1.82605i
$827$	6.77143	−	16.3477i	0.235466	−	0.568464i	−0.761338	−	0.648355i	$-0.775457\pi$
$827$	6.77143	−	16.3477i	0.235466	−	0.568464i	0.996804	+	0.0798909i	$0.0254572\pi$
$828$	55.1838	−	2.20656i	1.91777	−	0.0766831i
$829$	5.59411	−	42.4915i	0.194291	−	1.47579i	−0.565028	−	0.825071i	$-0.691135\pi$
$829$	5.59411	−	42.4915i	0.194291	−	1.47579i	0.759320	−	0.650718i	$-0.225532\pi$
$830$	−65.7086	+	16.3957i	−2.28078	+	0.569104i
$831$	6.41625	+	3.39230i	0.222577	+	0.117677i
$832$	−14.7818	+	4.39620i	−0.512466	+	0.152411i
$833$	−36.1721	+	23.1028i	−1.25329	+	0.800463i
$834$	−18.1114	−	4.46707i	−0.627148	−	0.154682i
$835$	22.0991	−	28.8000i	0.764769	−	0.996667i
$836$	−0.170761	−	0.106617i	−0.00590591	−	0.00368742i
$837$	−14.0425	−	14.5906i	−0.485379	−	0.504326i
$838$	11.7085	−	1.33619i	0.404465	−	0.0461578i
$839$	12.1806	+	12.1806i	0.420521	+	0.420521i	0.885383	−	0.464862i	$-0.153896\pi$
$839$	12.1806	+	12.1806i	0.420521	+	0.420521i	−0.464862	+	0.885383i	$0.653896\pi$
$840$	−39.4606	−	22.3723i	−1.36152	−	0.771918i
$841$	18.3874	−	18.3874i	0.634049	−	0.634049i
$842$	−12.6311	+	15.8854i	−0.435295	+	0.547446i
$843$	35.7681	+	13.2776i	1.23192	+	0.457305i
$844$	1.55263	+	0.259239i	0.0534439	+	0.00892336i
$845$	25.7769	+	19.7793i	0.886754	+	0.680430i
$846$	6.88116	−	13.6694i	0.236579	−	0.469963i
$847$	−13.9562	+	25.4736i	−0.479541	+	0.875282i
$848$	−10.1053	+	20.3052i	−0.347016	+	0.697282i
$849$	−9.39447	−	4.96689i	−0.322417	−	0.170463i
$850$	−32.3598	+	53.8780i	−1.10993	+	1.84800i
$851$	66.3580	+	8.73620i	2.27472	+	0.299473i
$852$	24.2227	−	18.6913i	0.829855	−	0.640353i
$853$	37.2672	+	15.4366i	1.27600	+	0.528538i	0.914784	−	0.403943i	$-0.132361\pi$
$853$	37.2672	+	15.4366i	1.27600	+	0.528538i	0.361219	+	0.932481i	$0.382361\pi$
$854$	−5.40141	−	12.8536i	−0.184832	−	0.439840i
$855$	2.37349	+	6.78946i	0.0811717	+	0.232195i
$856$	32.2152	−	37.7611i	1.10109	−	1.29065i
$857$	2.69890	+	10.0724i	0.0921928	+	0.344068i	0.996579	−	0.0826469i	$-0.0263374\pi$
$857$	2.69890	+	10.0724i	0.0921928	+	0.344068i	−0.904386	+	0.426715i	$0.859671\pi$
$858$	−0.252648	+	0.646171i	−0.00862526	+	0.0220599i
$859$	0.458887	+	3.48559i	0.0156570	+	0.118927i	0.997489	−	0.0708278i	$-0.0225641\pi$
$859$	0.458887	+	3.48559i	0.0156570	+	0.118927i	−0.981832	+	0.189755i	$0.939231\pi$
$860$	−39.7855	−	42.6335i	−1.35668	−	1.45379i
$861$	−7.69087	+	11.3668i	−0.262104	+	0.387380i
$862$	14.0836	+	14.5786i	0.479688	+	0.496550i
$863$	6.41418	+	11.1097i	0.218341	+	0.378178i	0.954301	−	0.298847i	$-0.0966021\pi$
$863$	6.41418	+	11.1097i	0.218341	+	0.378178i	−0.735960	+	0.677025i	$0.763269\pi$
$864$	3.09514	−	29.2305i	0.105299	−	0.994441i
$865$	−33.5217	+	58.0612i	−1.13977	+	1.97414i
$866$	1.75658	−	6.13014i	0.0596910	−	0.208311i
$867$	−20.6465	+	29.0894i	−0.701191	+	0.987928i
$868$	−5.09497	−	19.9827i	−0.172935	−	0.678256i
$869$	−0.979475	−	0.405712i	−0.0332264	−	0.0137628i
$870$	9.26666	+	11.5895i	0.314169	+	0.392921i
$871$	5.61120	+	20.9413i	0.190128	+	0.709568i
$872$	2.04379	+	2.97024i	0.0692114	+	0.100585i
$873$	5.68635	−	6.60373i	0.192454	−	0.223502i
$874$	−3.26977	−	8.29636i	−0.110602	−	0.280629i
$875$	−3.17829	−	20.5709i	−0.107446	−	0.695424i
$876$	−19.0750	+	2.56391i	−0.644486	+	0.0866267i
$877$	−14.3600	+	18.7144i	−0.484904	+	0.631939i	−0.970169	−	0.242428i	$-0.922056\pi$
$877$	−14.3600	+	18.7144i	−0.484904	+	0.631939i	0.485266	+	0.874367i	$0.338723\pi$
$878$	11.2826	−	18.7852i	0.380771	−	0.633971i
$879$	−0.173016	−	4.64222i	−0.00583567	−	0.156578i
$880$	−0.668241	+	1.94533i	−0.0225264	+	0.0655771i
$881$	−46.7340			−1.57451			−0.787255	−	0.616628i	$-0.788498\pi$
$881$	−46.7340			−1.57451			−0.787255	+	0.616628i	$0.788498\pi$
$882$	29.5441	−	3.02457i	0.994801	−	0.101843i
$883$	−32.6054	+	13.5056i	−1.09726	+	0.454499i	−0.856532	−	0.516094i	$-0.827386\pi$
$883$	−32.6054	+	13.5056i	−1.09726	+	0.454499i	−0.240726	+	0.970593i	$0.577386\pi$
$884$	−18.2462	−	15.0299i	−0.613688	−	0.505509i
$885$	80.4507	+	29.8644i	2.70432	+	1.00388i
$886$	9.39655	+	1.40257i	0.315683	+	0.0471202i
$887$	−20.5027	−	5.49368i	−0.688413	−	0.184460i	−0.102378	−	0.994746i	$-0.532645\pi$
$887$	−20.5027	−	5.49368i	−0.688413	−	0.184460i	−0.586035	+	0.810286i	$0.699312\pi$
$888$	9.71971	−	34.2707i	0.326172	−	1.15005i
$889$	−1.98692	+	8.14015i	−0.0666390	+	0.273012i
$890$	19.4576	−	44.7717i	0.652219	−	1.50075i
$891$	−0.951862	−	0.917993i	−0.0318886	−	0.0307539i
$892$	14.8356	−	23.7613i	0.496734	−	0.795587i
$893$	−2.44989	−	0.322534i	−0.0819824	−	0.0107932i
$894$	7.94876	+	27.4584i	0.265846	+	0.918345i
$895$			43.4090i			1.45100i
$896$	17.4434	−	24.3254i	0.582744	−	0.812656i
$897$	−26.0251	+	16.3473i	−0.868951	+	0.545820i
$898$	11.9183	−	41.5928i	0.397719	−	1.38797i
$899$	−0.880516	+	6.68818i	−0.0293669	+	0.223063i
$900$	36.7629	−	23.2313i	1.22543	−	0.774378i
$901$	−34.4692	+	4.53796i	−1.14834	+	0.151181i
$902$	0.570751	+	0.248045i	0.0190039	+	0.00825901i
$903$	37.4010	+	7.66549i	1.24463	+	0.255092i
$904$	15.9547	+	17.7000i	0.530646	+	0.588693i
$905$	−7.64291	+	28.5237i	−0.254059	+	0.948160i
$906$	1.78380	+	4.07426i	0.0592629	+	0.135358i
$907$	−28.2511	−	36.8176i	−0.938063	−	1.22251i	−0.974777	−	0.223181i	$-0.928356\pi$
$907$	−28.2511	−	36.8176i	−0.938063	−	1.22251i	0.0367142	−	0.999326i	$-0.488311\pi$
$908$	37.9788	−	46.1063i	1.26037	−	1.53009i
$909$	−1.52233	+	26.9659i	−0.0504926	+	0.894401i
$910$	25.2425	−	0.129285i	0.836780	−	0.00428576i
$911$		−	46.6318i		−	1.54498i	−0.635027	−	0.772490i	$-0.719011\pi$
$911$		−	46.6318i		−	1.54498i	0.635027	−	0.772490i	$-0.280989\pi$
$912$	−4.62117	+	1.08187i	−0.153022	+	0.0358243i
$913$	−1.74118	−	1.00527i	−0.0576245	−	0.0332695i
$914$	−4.17938	−	2.51018i	−0.138242	−	0.0830295i
$915$	22.4884	+	2.11215i	0.743443	+	0.0698254i
$916$	−23.7045	−	10.7923i	−0.783219	−	0.356588i
$917$	7.08605	+	8.81863i	0.234002	+	0.291217i
$918$	39.8148	−	21.0931i	1.31408	−	0.696175i
$919$	−7.72343	+	28.8242i	−0.254772	+	0.950824i	0.713444	+	0.700712i	$0.247134\pi$
$919$	−7.72343	+	28.8242i	−0.254772	+	0.950824i	−0.968217	+	0.250112i	$0.919533\pi$
$920$	−75.0611	+	51.6487i	−2.47469	+	1.70281i
$921$	−26.3817	−	24.4858i	−0.869305	−	0.806835i
$922$	−18.7574	+	2.14061i	−0.617742	+	0.0704971i
$923$	−6.51557	+	15.7300i	−0.214462	+	0.517758i
$924$	−0.381085	−	1.29163i	−0.0125368	−	0.0424914i
$925$	48.6912	−	20.1685i	1.60096	−	0.663138i
$926$	46.3517	+	13.2820i	1.52321	+	0.436473i
$927$	20.5193	−	13.9810i	0.673941	−	0.459195i
$928$	−8.25353	+	5.26868i	−0.270935	+	0.172953i
$929$	−33.7416	+	19.4808i	−1.10703	+	0.639143i	−0.938058	−	0.346479i	$-0.887377\pi$
$929$	−33.7416	+	19.4808i	−1.10703	+	0.639143i	−0.168970	+	0.985621i	$0.554044\pi$
$930$	32.4366	+	8.00029i	1.06364	+	0.262340i
$931$	−2.03159	−	4.34369i	−0.0665826	−	0.142359i
$932$	−4.97554	+	4.64317i	−0.162979	+	0.152092i
$933$	−9.10256	+	7.53951i	−0.298005	+	0.246833i
$934$	−6.19109	+	4.58292i	−0.202579	+	0.149958i
$935$	−3.04553	+	0.816048i	−0.0995996	+	0.0266876i
$936$	6.60092	+	14.9661i	0.215758	+	0.489182i
$937$	−34.5351	+	34.5351i	−1.12821	+	1.12821i	−0.137746	+	0.990468i	$0.543986\pi$
$937$	−34.5351	+	34.5351i	−1.12821	+	1.12821i	−0.990468	+	0.137746i	$0.956014\pi$
$938$	−33.5156	−	25.4457i	−1.09432	−	0.830832i
$939$	9.60183	−	1.62996i	0.313344	−	0.0531918i
$940$	2.42907	+	25.1306i	0.0792274	+	0.819669i
$941$	7.68607	−	58.3815i	0.250559	−	1.90318i	−0.152997	−	0.988227i	$-0.548893\pi$
$941$	7.68607	−	58.3815i	0.250559	−	1.90318i	0.403556	−	0.914955i	$-0.367774\pi$
$942$	14.9758	−	0.299287i	0.487937	−	0.00975131i
$943$	13.7834	+	23.8735i	0.448848	+	0.777427i
$944$	−25.2302	+	50.6966i	−0.821172	+	1.65003i
$945$	−18.2675	+	44.5103i	−0.594242	+	1.44792i
$946$	0.0298973	−	1.73094i	0.000972045	−	0.0562776i
$947$	−34.5683	+	45.0503i	−1.12332	+	1.46394i	−0.255670	+	0.966764i	$0.582296\pi$
$947$	−34.5683	+	45.0503i	−1.12332	+	1.46394i	−0.867650	+	0.497175i	$0.834371\pi$
$948$	−23.0660	+	9.62762i	−0.749150	+	0.312690i
$949$	8.49710	−	6.52006i	0.275828	−	0.211650i
$950$	−5.49615	−	4.37020i	−0.178319	−	0.141788i
$951$	53.9773	+	12.3283i	1.75034	+	0.399774i
$952$	45.8640	+	1.34968i	1.48646	+	0.0437435i
$953$	39.2829	−	39.2829i	1.27250	−	1.27250i	0.327723	−	0.944774i	$-0.393719\pi$
$953$	39.2829	−	39.2829i	1.27250	−	1.27250i	0.944774	−	0.327723i	$-0.106281\pi$
$954$	22.7156	+	7.91960i	0.735444	+	0.256407i
$955$	38.6093	−	29.6260i	1.24937	−	0.958674i
$956$	15.2390	−	24.4073i	0.492863	−	0.789388i
$957$	−0.0411936	+	0.438595i	−0.00133160	+	0.0141778i
$958$	12.0739	−	11.6639i	0.390090	−	0.376843i
$959$	−25.5624	+	0.572497i	−0.825454	+	0.0184869i
$960$	21.4080	+	43.5122i	0.690941	+	1.40435i
$961$	−7.90597	−	13.6935i	−0.255031	−	0.441727i
$962$	4.79918	+	19.2335i	0.154732	+	0.620112i
$963$	−44.0373	−	28.8514i	−1.41908	−	0.929723i
$964$	21.2887	+	40.0030i	0.685663	+	1.28841i
$965$	−73.5330	−	30.4584i	−2.36711	−	0.980490i
$966$	20.4731	−	56.0298i	0.658710	−	1.80273i
$967$	4.42429	−	4.42429i	0.142276	−	0.142276i	−0.632381	−	0.774657i	$-0.717922\pi$
$967$	4.42429	−	4.42429i	0.142276	−	0.142276i	0.774657	+	0.632381i	$0.217922\pi$
$968$	27.6595	−	14.1123i	0.889009	−	0.453587i
$969$	−5.33236	−	4.94917i	−0.171300	−	0.158990i
$970$	−2.12248	+	14.2196i	−0.0681486	+	0.456564i
$971$	3.63864	+	27.6382i	0.116769	+	0.886952i	0.945116	+	0.326736i	$0.105949\pi$
$971$	3.63864	+	27.6382i	0.116769	+	0.886952i	−0.828346	+	0.560216i	$0.810718\pi$
$972$	−31.1702	+	0.649142i	−0.999783	+	0.0208213i
$973$	−11.9048	+	16.2558i	−0.381652	+	0.521136i
$974$	−0.635473	+	36.7914i	−0.0203619	+	1.17887i
$975$	−11.3112	+	21.3941i	−0.362247	+	0.685161i
$976$	−2.96091	+	14.6079i	−0.0947763	+	0.467589i
$977$	8.92653	−	15.4612i	0.285585	−	0.494648i	−0.687166	−	0.726501i	$-0.741145\pi$
$977$	8.92653	−	15.4612i	0.285585	−	0.494648i	0.972751	+	0.231853i	$0.0744788\pi$
$978$	−15.9364	−	8.78110i	−0.509591	−	0.280789i
$979$	1.33894	−	0.554607i	0.0427927	−	0.0177253i
$980$	−38.5636	+	30.2235i	−1.23187	+	0.965453i
$981$	2.85222	−	2.54739i	0.0910643	−	0.0813318i
$982$	39.7246	+	31.5865i	1.26766	+	1.00797i
$983$	2.47518	+	9.23749i	0.0789459	+	0.294630i	0.994099	−	0.108476i	$-0.0345971\pi$
$983$	2.47518	+	9.23749i	0.0789459	+	0.294630i	−0.915153	+	0.403106i	$0.867930\pi$
$984$	13.6353	−	5.41671i	0.434676	−	0.172678i
$985$	−11.4880	+	42.8739i	−0.366039	+	1.36608i
$986$	−13.7658	−	5.98255i	−0.438392	−	0.190523i
$987$	−10.8266	−	12.4909i	−0.344613	−	0.397588i
$988$	1.93094	−	1.80195i	0.0614314	−	0.0573277i
$989$	46.6836	−	60.8392i	1.48445	−	1.93457i
$990$	2.13619	+	0.443188i	0.0678925	+	0.0140854i
$991$	14.2258	+	8.21327i	0.451898	+	0.260903i	0.708631	−	0.705579i	$-0.249313\pi$
$991$	14.2258	+	8.21327i	0.451898	+	0.260903i	−0.256734	+	0.966482i	$0.582646\pi$
$992$	−7.52119	+	20.7232i	−0.238798	+	0.657961i
$993$	−24.4716	−	38.9591i	−0.776583	−	1.23633i
$994$	−8.71663	−	31.8770i	−0.276475	−	1.01108i
$995$	−75.5278	+	31.2846i	−2.39439	+	0.991789i
$996$	−45.7517	+	12.3922i	−1.44970	+	0.392662i
$997$	25.9406	+	33.8065i	0.821547	+	1.07066i	0.996291	+	0.0860475i	$0.0274237\pi$
$997$	25.9406	+	33.8065i	0.821547	+	1.07066i	−0.174744	+	0.984614i	$0.555910\pi$
$998$	−13.4272	−	18.1388i	−0.425029	−	0.574175i
$999$	−37.3587	−	5.64779i	−1.18198	−	0.178688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.10	✓	992
3.2	odd	2	inner	672.2.ch.a.11.115	yes	992
7.2	even	3	inner	672.2.ch.a.107.73	yes	992
21.2	odd	6	inner	672.2.ch.a.107.52	yes	992
32.3	odd	8	inner	672.2.ch.a.515.52	yes	992
96.35	even	8	inner	672.2.ch.a.515.73	yes	992
224.163	odd	24	inner	672.2.ch.a.611.115	yes	992
672.611	even	24	inner	672.2.ch.a.611.10	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.10	✓	992	1.1	even	1	trivial
672.2.ch.a.11.115	yes	992	3.2	odd	2	inner
672.2.ch.a.107.52	yes	992	21.2	odd	6	inner
672.2.ch.a.107.73	yes	992	7.2	even	3	inner
672.2.ch.a.515.52	yes	992	32.3	odd	8	inner
672.2.ch.a.515.73	yes	992	96.35	even	8	inner
672.2.ch.a.611.10	yes	992	672.611	even	24	inner
672.2.ch.a.611.115	yes	992	224.163	odd	24	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35950 - 0.389562i) q^{2} +(-0.721966 - 1.57441i) q^{3} +(1.69648 + 1.05922i) q^{4} +(0.456804 + 3.46977i) q^{5} +(0.368183 + 2.42166i) q^{6} +(2.57029 + 0.627378i) q^{7} +(-1.89374 - 2.10089i) q^{8} +(-1.95753 + 2.27334i) q^{9} +O(q^{10})\)	\(q+(-1.35950 - 0.389562i) q^{2} +(-0.721966 - 1.57441i) q^{3} +(1.69648 + 1.05922i) q^{4} +(0.456804 + 3.46977i) q^{5} +(0.368183 + 2.42166i) q^{6} +(2.57029 + 0.627378i) q^{7} +(-1.89374 - 2.10089i) q^{8} +(-1.95753 + 2.27334i) q^{9} +(0.730665 - 4.89511i) q^{10} +(0.116570 - 0.0894476i) q^{11} +(0.442842 - 3.43568i) q^{12} +(0.737702 + 1.78097i) q^{13} +(-3.24991 - 1.85421i) q^{14} +(5.13305 - 3.22425i) q^{15} +(1.75611 + 3.59389i) q^{16} +(-3.06574 + 5.31002i) q^{17} +(3.54687 - 2.32803i) q^{18} +(-0.543482 - 0.417028i) q^{19} +(-2.90029 + 6.37027i) q^{20} +(-0.867911 - 4.49964i) q^{21} +(-0.193323 + 0.0761927i) q^{22} +(-8.89102 - 2.38234i) q^{23} +(-1.94045 + 4.49829i) q^{24} +(-7.00102 + 1.87592i) q^{25} +(-0.309108 - 2.70861i) q^{26} +(4.99244 + 1.44068i) q^{27} +(3.69593 + 3.78684i) q^{28} +(-0.662412 - 1.59920i) q^{29} +(-8.23443 + 2.38374i) q^{30} +(-3.37506 - 1.94859i) q^{31} +(-0.987391 - 5.57001i) q^{32} +(-0.224987 - 0.118952i) q^{33} +(6.23646 - 6.02468i) q^{34} +(-1.00274 + 9.20492i) q^{35} +(-5.72888 + 1.78323i) q^{36} +(-7.20918 + 0.949106i) q^{37} +(0.576406 + 0.778670i) q^{38} +(2.27138 - 2.44724i) q^{39} +(6.42455 - 7.53054i) q^{40} +(-2.11769 - 2.11769i) q^{41} +(-0.572960 + 6.45536i) q^{42} +(-3.18822 + 7.69705i) q^{43} +(0.292504 - 0.0282728i) q^{44} +(-8.78218 - 5.75372i) q^{45} +(11.1593 + 6.70239i) q^{46} +(3.12385 - 1.80355i) q^{47} +(4.39041 - 5.35951i) q^{48} +(6.21279 + 3.22509i) q^{49} +(10.2487 + 0.177018i) q^{50} +(10.5735 + 0.993081i) q^{51} +(-0.634938 + 3.80277i) q^{52} +(3.45179 + 4.49846i) q^{53} +(-6.22599 - 3.90347i) q^{54} +(0.363613 + 0.363613i) q^{55} +(-3.54941 - 6.58800i) q^{56} +(-0.264198 + 1.15674i) q^{57} +(0.277561 + 2.43217i) q^{58} +(8.61821 + 11.2315i) q^{59} +(12.1233 - 0.0328728i) q^{60} +(2.95623 + 2.26840i) q^{61} +(3.82930 + 3.96391i) q^{62} +(-6.45767 + 4.61503i) q^{63} +(-0.827506 + 7.95709i) q^{64} +(-5.84258 + 3.37321i) q^{65} +(0.259531 + 0.249361i) q^{66} +(11.1503 + 1.46796i) q^{67} +(-10.8254 + 5.76107i) q^{68} +(2.66823 + 15.7181i) q^{69} +(4.94911 - 12.1235i) q^{70} +(6.24534 + 6.24534i) q^{71} +(8.48310 - 0.192546i) q^{72} +(-1.43800 - 5.36669i) q^{73} +(10.1706 + 1.51811i) q^{74} +(8.00796 + 9.66813i) q^{75} +(-0.480284 - 1.28315i) q^{76} +(0.355737 - 0.156773i) q^{77} +(-4.04130 + 2.44219i) q^{78} +(-3.60767 - 6.24866i) q^{79} +(-11.6678 + 7.73501i) q^{80} +(-1.33614 - 8.90027i) q^{81} +(2.05403 + 3.70397i) q^{82} +(-5.23636 - 12.6417i) q^{83} +(3.29370 - 8.55287i) q^{84} +(-19.8250 - 8.21178i) q^{85} +(7.33287 - 9.22214i) q^{86} +(-2.03956 + 2.19748i) q^{87} +(-0.408674 - 0.0755116i) q^{88} +(9.52725 + 2.55282i) q^{89} +(9.69795 + 11.2434i) q^{90} +(0.778767 + 5.04043i) q^{91} +(-12.5600 - 13.4591i) q^{92} +(-0.631205 + 6.72055i) q^{93} +(-4.94947 + 1.23500i) q^{94} +(1.19873 - 2.07626i) q^{95} +(-8.05662 + 5.57592i) q^{96} -2.90486 q^{97} +(-7.18992 - 6.80478i) q^{98} +(-0.0248455 + 0.440101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Introduction

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