LMFDB - Embedded newform 430.2.q.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	430.101
Dual form			430.2.q.b.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 - 0.781831i) q^{2} +(-0.320555 + 0.816762i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.438707 + 0.759863i) q^{6} +(-0.337906 + 0.585270i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(1.63481 + 1.51688i) q^{9} +O(q^{10})$	\(q+(0.623490 - 0.781831i) q^{2} +(-0.320555 + 0.816762i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.438707 + 0.759863i) q^{6} +(-0.337906 + 0.585270i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(1.63481 + 1.51688i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(0.565020 - 2.47551i) q^{11} +(0.867614 + 0.130772i) q^{12} +(5.72492 - 3.90318i) q^{13} +(0.246902 + 0.629095i) q^{14} +(0.838433 + 0.258622i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.113754 - 1.51794i) q^{17} +(2.20524 - 0.332386i) q^{18} +(4.25751 - 3.95039i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.369709 - 0.463600i) q^{21} +(-1.58315 - 1.98521i) q^{22} +(-3.51210 + 1.08334i) q^{23} +(0.643190 - 0.596793i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.517797 - 6.90952i) q^{26} +(-4.13455 + 1.99109i) q^{27} +(0.645787 + 0.199199i) q^{28} +(3.42131 + 8.71735i) q^{29} +(0.724954 - 0.494265i) q^{30} +(-2.39674 - 0.361250i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(1.84079 + 1.25503i) q^{33} +(-1.11585 - 1.03536i) q^{34} +(0.608885 + 0.293224i) q^{35} +(1.11507 - 1.93136i) q^{36} +(-2.87930 - 4.98709i) q^{37} +(-0.434027 - 5.79169i) q^{38} +(1.35282 + 5.92708i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(0.555795 - 0.696944i) q^{41} -0.592966 q^{42} +(-1.56088 - 6.36896i) q^{43} -2.53918 q^{44} +(1.39047 - 1.74360i) q^{45} +(-1.34277 + 3.42132i) q^{46} +(1.08469 + 4.75234i) q^{47} +(-0.0655692 - 0.874961i) q^{48} +(3.27164 + 5.66665i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.20333 + 0.579495i) q^{51} +(-5.07924 - 4.71284i) q^{52} +(4.53199 + 3.08986i) q^{53} +(-1.02115 + 4.47395i) q^{54} +(-2.51082 - 0.378445i) q^{55} +(0.558382 - 0.380698i) q^{56} +(1.86176 + 4.74369i) q^{57} +(8.94865 + 2.76029i) q^{58} +(-0.575346 + 0.277072i) q^{59} +(0.0655692 - 0.874961i) q^{60} +(-2.58224 + 0.389210i) q^{61} +(-1.77678 + 1.64861i) q^{62} +(-1.44020 + 0.444242i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-4.32009 - 5.41723i) q^{65} +(2.12893 - 0.656688i) q^{66} +(-10.0882 + 9.36045i) q^{67} +(-1.50520 + 0.226872i) q^{68} +(0.240993 - 3.21582i) q^{69} +(0.608885 - 0.293224i) q^{70} +(-1.25318 - 0.386554i) q^{71} +(-0.814763 - 2.07598i) q^{72} +(-8.20684 + 5.59533i) q^{73} +(-5.69428 - 0.858275i) q^{74} +(0.195243 - 0.855416i) q^{75} +(-4.79874 - 3.27172i) q^{76} +(1.25792 + 1.16718i) q^{77} +(5.47745 + 2.63780i) q^{78} +(4.60048 - 7.96826i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.199079 + 2.65653i) q^{81} +(-0.198361 - 0.869075i) q^{82} +(-4.43273 + 11.2944i) q^{83} +(-0.369709 + 0.463600i) q^{84} -1.52220 q^{85} +(-5.95265 - 2.75063i) q^{86} -8.21672 q^{87} +(-1.58315 + 1.98521i) q^{88} +(-3.56653 + 9.08737i) q^{89} +(-0.496254 - 2.17423i) q^{90} +(0.349933 + 4.66953i) q^{91} +(1.83770 + 3.18298i) q^{92} +(1.06334 - 1.84176i) q^{93} +(4.39182 + 2.11499i) q^{94} +(-4.25751 - 3.95039i) q^{95} +(-0.724954 - 0.494265i) q^{96} +(3.49292 - 15.3035i) q^{97} +(6.47020 + 0.975225i) q^{98} +(4.67877 - 3.18993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$3$	−0.320555	+	0.816762i	−0.185073	+	0.471558i	−0.993055	−	0.117649i	$-0.962464\pi$
$3$	−0.320555	+	0.816762i	−0.185073	+	0.471558i	0.807983	+	0.589206i	$0.200560\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$5$	−0.0747301	−	0.997204i	−0.0334203	−	0.445963i
$6$	0.438707	+	0.759863i	0.179101	+	0.310213i
$7$	−0.337906	+	0.585270i	−0.127716	+	0.221211i	−0.922791	−	0.385300i	$-0.874098\pi$
$7$	−0.337906	+	0.585270i	−0.127716	+	0.221211i	0.795075	+	0.606511i	$0.207431\pi$
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	1.63481	+	1.51688i	0.544937	+	0.505628i
$10$	−0.826239	−	0.563320i	−0.261280	−	0.178137i
$11$	0.565020	−	2.47551i	0.170360	−	0.746396i	−0.815491	−	0.578770i	$-0.803533\pi$
$11$	0.565020	−	2.47551i	0.170360	−	0.746396i	0.985851	−	0.167626i	$-0.0536100\pi$
$12$	0.867614	+	0.130772i	0.250459	+	0.0377506i
$13$	5.72492	−	3.90318i	1.58781	−	1.08255i	0.637853	−	0.770158i	$-0.279823\pi$
$13$	5.72492	−	3.90318i	1.58781	−	1.08255i	0.949954	−	0.312390i	$-0.101130\pi$
$14$	0.246902	+	0.629095i	0.0659872	+	0.168133i
$15$	0.838433	+	0.258622i	0.216482	+	0.0667760i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.113754	−	1.51794i	0.0275894	−	0.368155i	−0.966272	−	0.257524i	$-0.917094\pi$
$17$	0.113754	−	1.51794i	0.0275894	−	0.368155i	0.993861	−	0.110632i	$-0.0352874\pi$
$18$	2.20524	−	0.332386i	0.519779	−	0.0783441i
$19$	4.25751	−	3.95039i	0.976740	−	0.906283i	−0.0188753	−	0.999822i	$-0.506009\pi$
$19$	4.25751	−	3.95039i	0.976740	−	0.906283i	0.995616	+	0.0935393i	$0.0298181\pi$
$20$	−0.955573	+	0.294755i	−0.213673	+	0.0659093i
$21$	−0.369709	−	0.463600i	−0.0806770	−	0.101166i
$22$	−1.58315	−	1.98521i	−0.337529	−	0.423248i
$23$	−3.51210	+	1.08334i	−0.732324	+	0.225892i	−0.638419	−	0.769689i	$-0.720411\pi$
$23$	−3.51210	+	1.08334i	−0.732324	+	0.225892i	−0.0939052	+	0.995581i	$0.529935\pi$
$24$	0.643190	−	0.596793i	0.131291	−	0.121820i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	0.517797	−	6.90952i	0.101548	−	1.35507i
$27$	−4.13455	+	1.99109i	−0.795694	+	0.383186i
$28$	0.645787	+	0.199199i	0.122042	+	0.0376451i
$29$	3.42131	+	8.71735i	0.635321	+	1.61877i	0.777466	+	0.628925i	$0.216505\pi$
$29$	3.42131	+	8.71735i	0.635321	+	1.61877i	−0.142145	+	0.989846i	$0.545400\pi$
$30$	0.724954	−	0.494265i	0.132358	−	0.0902400i
$31$	−2.39674	−	0.361250i	−0.430467	−	0.0648825i	−0.0697648	−	0.997563i	$-0.522225\pi$
$31$	−2.39674	−	0.361250i	−0.430467	−	0.0648825i	−0.360702	+	0.932681i	$0.617463\pi$
$32$	−0.222521	+	0.974928i	−0.0393365	+	0.172345i
$33$	1.84079	+	1.25503i	0.320440	+	0.218472i
$34$	−1.11585	−	1.03536i	−0.191367	−	0.177563i
$35$	0.608885	+	0.293224i	0.102920	+	0.0495638i
$36$	1.11507	−	1.93136i	0.185845	−	0.321894i
$37$	−2.87930	−	4.98709i	−0.473354	−	0.819873i	0.526181	−	0.850373i	$-0.323623\pi$
$37$	−2.87930	−	4.98709i	−0.473354	−	0.819873i	−0.999535	+	0.0304997i	$0.990290\pi$
$38$	−0.434027	−	5.79169i	−0.0704085	−	0.939536i
$39$	1.35282	+	5.92708i	0.216624	+	0.949093i
$40$	−0.365341	+	0.930874i	−0.0577655	+	0.147184i
$41$	0.555795	−	0.696944i	0.0868005	−	0.108844i	−0.736535	−	0.676400i	$-0.763539\pi$
$41$	0.555795	−	0.696944i	0.0868005	−	0.108844i	0.823335	+	0.567555i	$0.192111\pi$
$42$	−0.592966			−0.0914967
$43$	−1.56088	−	6.36896i	−0.238032	−	0.971257i
$43$	−1.56088	−	6.36896i	−0.238032	−	0.971257i
$44$	−2.53918			−0.382795
$45$	1.39047	−	1.74360i	0.207279	−	0.259920i
$46$	−1.34277	+	3.42132i	−0.197981	+	0.504447i
$47$	1.08469	+	4.75234i	0.158218	+	0.693200i	0.990346	+	0.138616i	$0.0442654\pi$
$47$	1.08469	+	4.75234i	0.158218	+	0.693200i	−0.832128	+	0.554584i	$0.812877\pi$
$48$	−0.0655692	−	0.874961i	−0.00946410	−	0.126290i
$49$	3.27164	+	5.66665i	0.467377	+	0.809521i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	1.20333	+	0.579495i	0.168500	+	0.0811455i
$52$	−5.07924	−	4.71284i	−0.704363	−	0.653554i
$53$	4.53199	+	3.08986i	0.622517	+	0.424425i	0.833078	−	0.553156i	$-0.186577\pi$
$53$	4.53199	+	3.08986i	0.622517	+	0.424425i	−0.210561	+	0.977581i	$0.567529\pi$
$54$	−1.02115	+	4.47395i	−0.138961	+	0.608827i
$55$	−2.51082	−	0.378445i	−0.338558	−	0.0510295i
$56$	0.558382	−	0.380698i	0.0746169	−	0.0508729i
$57$	1.86176	+	4.74369i	0.246596	+	0.628318i
$58$	8.94865	+	2.76029i	1.17502	+	0.362444i
$59$	−0.575346	+	0.277072i	−0.0749036	+	0.0360717i	−0.470961	−	0.882154i	$-0.656093\pi$
$59$	−0.575346	+	0.277072i	−0.0749036	+	0.0360717i	0.396057	+	0.918226i	$0.370378\pi$
$60$	0.0655692	−	0.874961i	0.00846495	−	0.112957i
$61$	−2.58224	+	0.389210i	−0.330622	+	0.0498332i	−0.312256	−	0.949998i	$-0.601085\pi$
$61$	−2.58224	+	0.389210i	−0.330622	+	0.0498332i	−0.0183661	+	0.999831i	$0.505846\pi$
$62$	−1.77678	+	1.64861i	−0.225651	+	0.209374i
$63$	−1.44020	+	0.444242i	−0.181448	+	0.0559693i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−4.32009	−	5.41723i	−0.535842	−	0.671924i
$66$	2.12893	−	0.656688i	0.262053	−	0.0808327i
$67$	−10.0882	+	9.36045i	−1.23247	+	1.14356i	−0.247855	+	0.968797i	$0.579726\pi$
$67$	−10.0882	+	9.36045i	−1.23247	+	1.14356i	−0.984610	+	0.174764i	$0.944084\pi$
$68$	−1.50520	+	0.226872i	−0.182532	+	0.0275123i
$69$	0.240993	−	3.21582i	0.0290121	−	0.387140i
$70$	0.608885	−	0.293224i	0.0727757	−	0.0350469i
$71$	−1.25318	−	0.386554i	−0.148725	−	0.0458755i	0.219499	−	0.975613i	$-0.429558\pi$
$71$	−1.25318	−	0.386554i	−0.148725	−	0.0458755i	−0.368224	+	0.929737i	$0.620034\pi$
$72$	−0.814763	−	2.07598i	−0.0960208	−	0.244657i
$73$	−8.20684	+	5.59533i	−0.960538	+	0.654884i	−0.938648	−	0.344877i	$-0.887921\pi$
$73$	−8.20684	+	5.59533i	−0.960538	+	0.654884i	−0.0218899	+	0.999760i	$0.506968\pi$
$74$	−5.69428	−	0.858275i	−0.661947	−	0.0997724i
$75$	0.195243	−	0.855416i	0.0225447	−	0.0987749i
$76$	−4.79874	−	3.27172i	−0.550453	−	0.375292i
$77$	1.25792	+	1.16718i	0.143353	+	0.133012i
$78$	5.47745	+	2.63780i	0.620199	+	0.298672i
$79$	4.60048	−	7.96826i	0.517594	−	0.896500i	−0.482197	−	0.876063i	$-0.660161\pi$
$79$	4.60048	−	7.96826i	0.517594	−	0.896500i	0.999791	−	0.0204368i	$-0.00650568\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	0.199079	+	2.65653i	0.0221199	+	0.295170i
$82$	−0.198361	−	0.869075i	−0.0219053	−	0.0959733i
$83$	−4.43273	+	11.2944i	−0.486555	+	1.23972i	0.451199	+	0.892423i	$0.350996\pi$
$83$	−4.43273	+	11.2944i	−0.486555	+	1.23972i	−0.937754	+	0.347299i	$0.887099\pi$
$84$	−0.369709	+	0.463600i	−0.0403385	+	0.0505829i
$85$	−1.52220			−0.165106
$86$	−5.95265	−	2.75063i	−0.641891	−	0.296608i
$87$	−8.21672			−0.880925
$88$	−1.58315	+	1.98521i	−0.168764	+	0.211624i
$89$	−3.56653	+	9.08737i	−0.378051	+	0.963259i	0.607566	+	0.794269i	$0.292146\pi$
$89$	−3.56653	+	9.08737i	−0.378051	+	0.963259i	−0.985618	+	0.168990i	$0.945949\pi$
$90$	−0.496254	−	2.17423i	−0.0523097	−	0.229184i
$91$	0.349933	+	4.66953i	0.0366829	+	0.489500i
$92$	1.83770	+	3.18298i	0.191593	+	0.331849i
$93$	1.06334	−	1.84176i	0.110264	−	0.190982i
$94$	4.39182	+	2.11499i	0.452982	+	0.218145i
$95$	−4.25751	−	3.95039i	−0.436812	−	0.405302i
$96$	−0.724954	−	0.494265i	−0.0739903	−	0.0504457i
$97$	3.49292	−	15.3035i	0.354653	−	1.55383i	−0.411642	−	0.911346i	$-0.635045\pi$
$97$	3.49292	−	15.3035i	0.354653	−	1.55383i	0.766295	−	0.642489i	$-0.222098\pi$
$98$	6.47020	+	0.975225i	0.653588	+	0.0985126i
$99$	4.67877	−	3.18993i	0.470234	−	0.320600i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	5.07947	+	1.56681i	0.505426	+	0.155903i	0.536974	−	0.843599i	$-0.319567\pi$
$101$	5.07947	+	1.56681i	0.505426	+	0.155903i	−0.0315475	+	0.999502i	$0.510044\pi$
$102$	1.20333	−	0.579495i	0.119148	−	0.0573785i
$103$	−0.894037	+	11.9301i	−0.0880921	+	1.17551i	0.761535	+	0.648124i	$0.224446\pi$
$103$	−0.894037	+	11.9301i	−0.0880921	+	1.17551i	−0.849627	+	0.527384i	$0.823173\pi$
$104$	−6.85150	+	1.03270i	−0.671845	+	0.101264i
$105$	−0.434675	+	0.403320i	−0.0424200	+	0.0393600i
$106$	5.24140	−	1.61676i	0.509090	−	0.157033i
$107$	−9.21909	−	11.5604i	−0.891243	−	1.11758i	−0.992442	−	0.122718i	$-0.960839\pi$
$107$	−9.21909	−	11.5604i	−0.891243	−	1.11758i	0.101198	−	0.994866i	$-0.467732\pi$
$108$	2.86120	+	3.58783i	0.275319	+	0.345239i
$109$	3.22697	−	0.995390i	0.309088	−	0.0953410i	−0.136331	−	0.990663i	$-0.543531\pi$
$109$	3.22697	−	0.995390i	0.309088	−	0.0953410i	0.445419	+	0.895322i	$0.353055\pi$
$110$	−1.86135	+	1.72708i	−0.177473	+	0.164671i
$111$	4.99624	−	0.753062i	0.474222	−	0.0714775i
$112$	0.0505034	−	0.673922i	0.00477213	−	0.0636796i
$113$	−11.5506	+	5.56249i	−1.08659	+	0.523275i	−0.889419	−	0.457094i	$-0.848890\pi$
$113$	−11.5506	+	5.56249i	−1.08659	+	0.523275i	−0.197173	+	0.980369i	$0.563176\pi$
$114$	4.86956	+	1.50206i	0.456076	+	0.140681i
$115$	1.34277	+	3.42132i	0.125214	+	0.319040i
$116$	7.73748	−	5.27532i	0.718407	−	0.489801i
$117$	15.2798	+	2.30306i	1.41262	+	0.212918i
$118$	−0.142099	+	0.622575i	−0.0130812	+	0.0573126i
$119$	0.849968	+	0.579499i	0.0779165	+	0.0531225i
$120$	−0.643190	−	0.596793i	−0.0587150	−	0.0544795i
$121$	4.10173	+	1.97529i	0.372885	+	0.179572i
$122$	−1.30570	+	2.26154i	−0.118213	+	0.204751i
$123$	0.391075	+	0.677361i	0.0352620	+	0.0610756i
$124$	0.181132	+	2.41703i	0.0162661	+	0.217056i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	−0.550626	+	1.40297i	−0.0490537	+	0.124987i
$127$	3.29454	−	4.13122i	0.292343	−	0.366587i	−0.613871	−	0.789407i	$-0.710388\pi$
$127$	3.29454	−	4.13122i	0.292343	−	0.366587i	0.906214	+	0.422820i	$0.138960\pi$
$128$	1.00000			0.0883883
$129$	5.70227	+	0.766734i	0.502057	+	0.0675072i
$130$	−6.92889			−0.607704
$131$	−6.22858	+	7.81040i	−0.544194	+	0.682398i	−0.975548	−	0.219785i	$-0.929464\pi$
$131$	−6.22858	+	7.81040i	−0.544194	+	0.682398i	0.431354	+	0.902183i	$0.358036\pi$
$132$	0.813947	−	2.07390i	0.0708450	−	0.180510i
$133$	0.873409	+	3.82665i	0.0757342	+	0.331813i
$134$	1.02843	+	13.7234i	0.0888425	+	1.18552i
$135$	2.29450	+	3.97419i	0.197479	+	0.342044i
$136$	−0.761100	+	1.31826i	−0.0652638	+	0.113040i
$137$	−15.9377	−	7.67519i	−1.36165	−	0.655736i	−0.396645	−	0.917972i	$-0.629826\pi$
$137$	−15.9377	−	7.67519i	−1.36165	−	0.655736i	−0.965004	+	0.262236i	$0.915540\pi$
$138$	−2.36397	−	2.19345i	−0.201235	−	0.186719i
$139$	10.7829	+	7.35166i	0.914594	+	0.623560i	0.926470	−	0.376370i	$-0.122828\pi$
$139$	10.7829	+	7.35166i	0.914594	+	0.623560i	−0.0118754	+	0.999929i	$0.503780\pi$
$140$	0.150382	−	0.658867i	0.0127096	−	0.0556845i
$141$	−4.22923	−	0.637454i	−0.356166	−	0.0536833i
$142$	−1.08356	+	0.738761i	−0.0909306	+	0.0619954i
$143$	−6.42769	−	16.3775i	−0.537511	−	1.36956i
$144$	−2.13107	−	0.657347i	−0.177589	−	0.0547789i
$145$	8.43730	−	4.06319i	0.700680	−	0.337430i
$146$	−0.742277	+	9.90499i	−0.0614313	+	0.819743i
$147$	−5.67704	+	0.855676i	−0.468234	+	0.0705750i
$148$	−4.22135	+	3.91684i	−0.346993	+	0.321962i
$149$	21.6833	−	6.68840i	1.77636	−	0.547935i	0.779451	−	0.626464i	$-0.215498\pi$
$149$	21.6833	−	6.68840i	1.77636	−	0.547935i	0.996912	+	0.0785282i	$0.0250221\pi$
$150$	−0.547059	−	0.685990i	−0.0446672	−	0.0560108i
$151$	−2.74419	−	3.44111i	−0.223319	−	0.280033i	0.657532	−	0.753426i	$-0.271600\pi$
$151$	−2.74419	−	3.44111i	−0.223319	−	0.280033i	−0.880851	+	0.473393i	$0.843029\pi$
$152$	−5.54990	+	1.71192i	−0.450156	+	0.138855i
$153$	2.48851	−	2.30900i	0.201184	−	0.186672i
$154$	1.69684	−	0.255757i	0.136735	−	0.0206095i
$155$	−0.181132	+	2.41703i	−0.0145488	+	0.194141i
$156$	5.47745	−	2.63780i	0.438547	−	0.211193i
$157$	0.176897	+	0.0545656i	0.0141179	+	0.00435481i	0.301806	−	0.953369i	$-0.402410\pi$
$157$	0.176897	+	0.0545656i	0.0141179	+	0.00435481i	−0.287688	+	0.957724i	$0.592887\pi$
$158$	−3.36149	−	8.56493i	−0.267426	−	0.681389i
$159$	−3.97643	+	2.71109i	−0.315352	+	0.215003i
$160$	0.988831	+	0.149042i	0.0781739	+	0.0117828i
$161$	0.552713	−	2.42160i	0.0435599	−	0.190848i
$162$	2.20108	+	1.50067i	0.172933	+	0.117904i
$163$	−2.90672	−	2.69704i	−0.227672	−	0.211248i	0.558086	−	0.829783i	$-0.311536\pi$
$163$	−2.90672	−	2.69704i	−0.227672	−	0.211248i	−0.785757	+	0.618535i	$0.787727\pi$
$164$	−0.803146	−	0.386775i	−0.0627152	−	0.0302020i
$165$	1.11395	−	1.92943i	0.0867213	−	0.150206i
$166$	6.06656	+	10.5076i	0.470857	+	0.815548i
$167$	0.129308	+	1.72549i	0.0100061	+	0.133522i	0.999970	−	0.00780125i	$-0.00248324\pi$
$167$	0.129308	+	1.72549i	0.0100061	+	0.133522i	−0.989963	+	0.141324i	$0.954864\pi$
$168$	0.131947	+	0.578100i	0.0101800	+	0.0446014i
$169$	12.7904	−	32.5895i	0.983878	−	2.50688i
$170$	−0.949076	+	1.19010i	−0.0727908	+	0.0912768i
$171$	12.9525			0.990504
$172$	−5.86195	+	2.93898i	−0.446969	+	0.224095i
$173$	20.5080			1.55919			0.779596	−	0.626283i	$-0.215425\pi$
$173$	20.5080			1.55919			0.779596	+	0.626283i	$0.215425\pi$
$174$	−5.12304	+	6.42409i	−0.388377	+	0.487009i
$175$	0.246902	−	0.629095i	0.0186640	−	0.0475551i
$176$	0.565020	+	2.47551i	0.0425900	+	0.186599i
$177$	−0.0418716	−	0.558737i	−0.00314726	−	0.0419973i
$178$	4.88110	+	8.45431i	0.365854	+	0.633677i
$179$	−4.91241	+	8.50854i	−0.367170	+	0.635958i	−0.989122	−	0.147098i	$-0.953007\pi$
$179$	−4.91241	+	8.50854i	−0.367170	+	0.635958i	0.621952	+	0.783056i	$0.286340\pi$
$180$	−2.00929	−	0.967623i	−0.149764	−	0.0721224i
$181$	−8.25162	−	7.65639i	−0.613338	−	0.569095i	0.311123	−	0.950369i	$-0.399295\pi$
$181$	−8.25162	−	7.65639i	−0.613338	−	0.569095i	−0.924462	+	0.381275i	$0.875485\pi$
$182$	3.86897	+	2.63782i	0.286787	+	0.195528i
$183$	0.509859	−	2.23384i	0.0376898	−	0.165130i
$184$	3.63434	+	0.547789i	0.267927	+	0.0403835i
$185$	−4.75798	+	3.24393i	−0.349813	+	0.238499i
$186$	−0.776966	−	1.97968i	−0.0569699	−	0.145157i
$187$	−3.69342	−	1.13927i	−0.270089	−	0.0833116i
$188$	4.39182	−	2.11499i	0.320306	−	0.154251i
$189$	0.231760	−	3.09263i	0.0168581	−	0.224956i
$190$	−5.74306	+	0.865627i	−0.416645	+	0.0627992i
$191$	−18.1540	+	16.8444i	−1.31357	+	1.21882i	−0.354702	+	0.934979i	$0.615418\pi$
$191$	−18.1540	+	16.8444i	−1.31357	+	1.21882i	−0.958872	+	0.283839i	$0.908392\pi$
$192$	−0.838433	+	0.258622i	−0.0605087	+	0.0186645i
$193$	−8.59093	−	10.7727i	−0.618388	−	0.775435i	0.369728	−	0.929140i	$-0.379451\pi$
$193$	−8.59093	−	10.7727i	−0.618388	−	0.775435i	−0.988117	+	0.153705i	$0.950879\pi$
$194$	−9.78695	−	12.2725i	−0.702662	−	0.881111i
$195$	5.80941	−	1.79197i	0.416021	−	0.128325i
$196$	4.79656	−	4.45056i	0.342612	−	0.317897i
$197$	−11.3467	+	1.71024i	−0.808419	+	0.121850i	−0.540231	−	0.841517i	$-0.681663\pi$
$197$	−11.3467	+	1.71024i	−0.808419	+	0.121850i	−0.268188	+	0.963367i	$0.586425\pi$
$198$	0.423176	−	5.64690i	0.0300738	−	0.401308i
$199$	−8.57729	+	4.13060i	−0.608028	+	0.292811i	−0.712451	−	0.701722i	$-0.752415\pi$
$199$	−8.57729	+	4.13060i	−0.608028	+	0.292811i	0.104423	+	0.994533i	$0.466700\pi$
$200$	0.955573	+	0.294755i	0.0675692	+	0.0208423i
$201$	−4.41144	−	11.2402i	−0.311159	−	0.792821i
$202$	4.39198	−	2.99440i	0.309019	−	0.210685i
$203$	−6.25808	−	0.943254i	−0.439231	−	0.0662035i
$204$	0.297199	−	1.30211i	0.0208081	−	0.0911662i
$205$	−0.736530	−	0.502158i	−0.0514415	−	0.0350722i
$206$	8.76990	+	8.13728i	0.611028	+	0.566951i
$207$	−7.38493	−	3.55639i	−0.513288	−	0.247186i
$208$	−3.46445	+	6.00060i	−0.240216	+	0.416066i
$209$	−7.37368	−	12.7716i	−0.510048	−	0.883429i
$210$	0.0443124	+	0.591308i	0.00305785	+	0.0408042i
$211$	−0.121298	−	0.531441i	−0.00835050	−	0.0365859i	0.970581	−	0.240775i	$-0.0774015\pi$
$211$	−0.121298	−	0.531441i	−0.00835050	−	0.0365859i	−0.978932	+	0.204189i	$0.934544\pi$
$212$	2.00393	−	5.10592i	0.137630	−	0.350676i
$213$	0.717435	−	0.899635i	0.0491578	−	0.0616420i
$214$	−14.7863			−1.01077
$215$	−6.23451	+	2.03247i	−0.425190	+	0.138613i
$216$	4.58900			0.312242
$217$	1.02130	−	1.28067i	0.0693304	−	0.0869376i
$218$	1.23376	−	3.14357i	0.0835607	−	0.212909i
$219$	−1.93930	−	8.49664i	−0.131046	−	0.574150i
$220$	0.189753	+	2.53208i	0.0127931	+	0.170713i
$221$	−5.27358	−	9.13411i	−0.354739	−	0.614426i
$222$	2.52634	−	4.37575i	0.169557	−	0.293681i
$223$	23.8973	+	11.5083i	1.60028	+	0.770656i	0.999585	−	0.0288199i	$-0.00917492\pi$
$223$	23.8973	+	11.5083i	1.60028	+	0.770656i	0.600699	+	0.799476i	$0.294889\pi$
$224$	−0.495405	−	0.459668i	−0.0331006	−	0.0307129i
$225$	−1.84263	−	1.25629i	−0.122842	−	0.0837523i
$226$	−2.85277	+	12.4988i	−0.189763	+	0.831408i
$227$	−4.94195	−	0.744878i	−0.328008	−	0.0494393i	−0.0170262	−	0.999855i	$-0.505420\pi$
$227$	−4.94195	−	0.744878i	−0.328008	−	0.0494393i	−0.310982	+	0.950416i	$0.600658\pi$
$228$	4.21048	−	2.87066i	0.278846	−	0.190114i
$229$	−0.0357737	−	0.0911498i	−0.00236399	−	0.00602335i	0.929687	−	0.368351i	$-0.120077\pi$
$229$	−0.0357737	−	0.0911498i	−0.00236399	−	0.00602335i	−0.932051	+	0.362327i	$0.881982\pi$
$230$	3.51210	+	1.08334i	0.231581	+	0.0714334i
$231$	−1.35654	+	0.653276i	−0.0892538	+	0.0429824i
$232$	0.699825	−	9.33851i	0.0459457	−	0.613103i
$233$	−3.07980	+	0.464205i	−0.201764	+	0.0304111i	−0.249147	−	0.968466i	$-0.580150\pi$
$233$	−3.07980	+	0.464205i	−0.201764	+	0.0304111i	0.0473825	+	0.998877i	$0.484912\pi$
$234$	11.3274	−	10.5103i	0.740497	−	0.687081i
$235$	4.65799	−	1.43680i	0.303854	−	0.0937265i
$236$	0.398151	+	0.499266i	0.0259175	+	0.0324995i
$237$	5.03346	+	6.31177i	0.326959	+	0.409993i
$238$	0.983017	−	0.303221i	0.0637195	−	0.0196549i
$239$	19.8761	−	18.4423i	1.28568	−	1.19293i	0.315939	−	0.948780i	$-0.397681\pi$
$239$	19.8761	−	18.4423i	1.28568	−	1.19293i	0.969737	−	0.244153i	$-0.0785098\pi$
$240$	−0.867614	+	0.130772i	−0.0560043	+	0.00844128i
$241$	1.15483	−	15.4102i	0.0743894	−	0.992658i	−0.827717	−	0.561145i	$-0.810361\pi$
$241$	1.15483	−	15.4102i	0.0743894	−	0.992658i	0.902107	−	0.431513i	$-0.142020\pi$
$242$	4.10173	−	1.97529i	0.263669	−	0.126976i
$243$	−15.3889	−	4.74686i	−0.987201	−	0.304511i
$244$	0.954053	+	2.43089i	0.0610770	+	0.155622i
$245$	5.40631	−	3.68596i	0.345397	−	0.235487i
$246$	0.773413	+	0.116573i	0.0493110	+	0.00743244i
$247$	8.95480	−	39.2335i	0.569780	−	2.49637i
$248$	2.00265	+	1.36538i	0.127168	+	0.0867018i
$249$	−7.80391	−	7.24097i	−0.494553	−	0.458878i
$250$	0.900969	+	0.433884i	0.0569823	+	0.0274412i
$251$	−10.1840	+	17.6392i	−0.642807	+	1.11338i	0.341996	+	0.939701i	$0.388897\pi$
$251$	−10.1840	+	17.6392i	−0.642807	+	1.11338i	−0.984803	+	0.173674i	$0.944436\pi$
$252$	0.753578	+	1.30524i	0.0474710	+	0.0822222i
$253$	0.697416	+	9.30637i	0.0438462	+	0.585087i
$254$	−1.17581	−	5.15155i	−0.0737767	−	0.323237i
$255$	0.487949	−	1.24327i	0.0305566	−	0.0778569i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	13.7765			0.859354			0.429677	−	0.902983i	$-0.358627\pi$
$257$	13.7765			0.859354			0.429677	+	0.902983i	$0.358627\pi$
$258$	4.15477	−	3.98017i	0.258664	−	0.247794i
$259$	3.89173			0.241820
$260$	−4.32009	+	5.41723i	−0.267921	+	0.335962i
$261$	−7.63001	+	19.4410i	−0.472286	+	1.20336i
$262$	2.22296	+	9.73941i	0.137335	+	0.601703i
$263$	0.156049	+	2.08233i	0.00962240	+	0.128402i	0.999946	−	0.0103741i	$-0.00330223\pi$
$263$	0.156049	+	2.08233i	0.00962240	+	0.128402i	−0.990324	+	0.138776i	$0.955683\pi$
$264$	−1.11395	−	1.92943i	−0.0685592	−	0.118748i
$265$	2.74254	−	4.75022i	0.168473	−	0.291804i
$266$	3.53636	+	1.70302i	0.216828	+	0.104419i
$267$	−6.27895	−	5.82601i	−0.384265	−	0.356546i
$268$	11.3706	+	7.75234i	0.694569	+	0.473549i
$269$	−6.23402	+	27.3130i	−0.380095	+	1.66531i	0.317075	+	0.948400i	$0.397299\pi$
$269$	−6.23402	+	27.3130i	−0.380095	+	1.66531i	−0.697170	+	0.716905i	$0.745558\pi$
$270$	4.53775	+	0.683955i	0.276159	+	0.0416242i
$271$	23.2739	−	15.8679i	1.41379	−	0.963905i	0.415259	−	0.909703i	$-0.363691\pi$
$271$	23.2739	−	15.8679i	1.41379	−	0.963905i	0.998530	−	0.0542017i	$-0.0172614\pi$
$272$	0.556122	+	1.41698i	0.0337198	+	0.0859168i
$273$	−3.92607	−	1.21103i	−0.237616	−	0.0732949i
$274$	−15.9377	+	7.67519i	−0.962831	+	0.463675i
$275$	−0.189753	+	2.53208i	−0.0114425	+	0.152690i
$276$	−3.18882	+	0.480637i	−0.191944	+	0.0289310i
$277$	−6.73800	+	6.25195i	−0.404847	+	0.375643i	−0.856150	−	0.516728i	$-0.827150\pi$
$277$	−6.73800	+	6.25195i	−0.404847	+	0.375643i	0.451303	+	0.892371i	$0.350960\pi$
$278$	12.4708	−	3.84673i	0.747948	−	0.230712i
$279$	−3.37024	−	4.22615i	−0.201771	−	0.253013i
$280$	−0.421362	−	0.528371i	−0.0251812	−	0.0315762i
$281$	−2.27758	+	0.702541i	−0.135869	+	0.0419101i	−0.361944	−	0.932200i	$-0.617887\pi$
$281$	−2.27758	+	0.702541i	−0.135869	+	0.0419101i	0.226075	+	0.974110i	$0.427411\pi$
$282$	−3.13526	+	2.90910i	−0.186702	+	0.173234i
$283$	4.28155	−	0.645339i	0.254512	−	0.0383614i	−0.0205471	−	0.999789i	$-0.506541\pi$
$283$	4.28155	−	0.645339i	0.254512	−	0.0383614i	0.275059	+	0.961427i	$0.411303\pi$
$284$	−0.0980040	+	1.30777i	−0.00581547	+	0.0776021i
$285$	4.59130	−	2.21105i	0.271965	−	0.130971i
$286$	−16.8120	−	5.18583i	−0.994117	−	0.306644i
$287$	0.220094	+	0.560791i	0.0129918	+	0.0331025i
$288$	−1.84263	+	1.25629i	−0.108578	+	0.0740273i
$289$	14.5189	+	2.18837i	0.854054	+	0.128728i
$290$	2.08384	−	9.12990i	0.122367	−	0.536126i
$291$	11.3796	+	7.75850i	0.667086	+	0.454812i
$292$	7.28123	+	6.75600i	0.426102	+	0.395365i
$293$	−2.30440	−	1.10974i	−0.134624	−	0.0648317i	0.365359	−	0.930867i	$-0.380946\pi$
$293$	−2.30440	−	1.10974i	−0.134624	−	0.0648317i	−0.499983	+	0.866035i	$0.666661\pi$
$294$	−2.87058	+	4.97200i	−0.167416	+	0.289973i
$295$	0.319293	+	0.553031i	0.0185899	+	0.0321987i
$296$	0.430341	+	5.74250i	0.0250130	+	0.333776i
$297$	2.59288	+	11.3601i	0.150454	+	0.659182i
$298$	8.29009	−	21.1228i	0.480232	−	1.22361i
$299$	−15.8780	+	19.9104i	−0.918250	+	1.15145i
$300$	−0.877414			−0.0506575
$301$	4.25499	+	1.23857i	0.245254	+	0.0713900i
$302$	−4.40134			−0.253269
$303$	−2.90796	+	3.64647i	−0.167058	+	0.209484i
$304$	−2.12187	+	5.40645i	−0.121698	+	0.310081i
$305$	0.581092	+	2.54593i	0.0332732	+	0.145780i
$306$	−0.253688	−	3.38523i	−0.0145024	−	0.193521i
$307$	12.3227	+	21.3436i	0.703294	+	1.21814i	0.967304	+	0.253621i	$0.0816216\pi$
$307$	12.3227	+	21.3436i	0.703294	+	1.21814i	−0.264010	+	0.964520i	$0.585045\pi$
$308$	0.858002	−	1.48610i	0.0488892	−	0.0846786i
$309$	−9.45746	−	4.55447i	−0.538016	−	0.259095i
$310$	1.77678	+	1.64861i	0.100914	+	0.0936348i
$311$	5.37045	+	3.66151i	0.304530	+	0.207625i	0.705937	−	0.708275i	$-0.250526\pi$
$311$	5.37045	+	3.66151i	0.304530	+	0.207625i	−0.401407	+	0.915900i	$0.631479\pi$
$312$	1.35282	−	5.92708i	0.0765882	−	0.335555i
$313$	2.46482	+	0.371511i	0.139320	+	0.0209991i	0.218332	−	0.975875i	$-0.429938\pi$
$313$	2.46482	+	0.371511i	0.139320	+	0.0209991i	−0.0790121	+	0.996874i	$0.525177\pi$
$314$	0.152955	−	0.104283i	0.00863173	−	0.00588502i
$315$	0.550626	+	1.40297i	0.0310243	+	0.0790486i
$316$	−8.79219	−	2.71203i	−0.494599	−	0.152564i
$317$	21.9173	−	10.5548i	1.23100	−	0.592818i	0.298646	−	0.954364i	$-0.403465\pi$
$317$	21.9173	−	10.5548i	1.23100	−	0.592818i	0.932354	+	0.361546i	$0.117751\pi$
$318$	−0.359653	+	4.79923i	−0.0201683	+	0.269128i
$319$	23.5130	−	3.54402i	1.31648	−	0.198427i
$320$	0.733052	−	0.680173i	0.0409788	−	0.0380228i
$321$	12.3973	−	3.82406i	0.691950	−	0.213438i
$322$	−1.54867	−	1.94197i	−0.0863039	−	0.108222i
$323$	−5.51216	−	6.91204i	−0.306705	−	0.384596i
$324$	2.54562	−	0.785221i	0.141424	−	0.0436234i
$325$	−5.07924	+	4.71284i	−0.281745	+	0.261421i
$326$	−3.92094	+	0.590986i	−0.217161	+	0.0327317i
$327$	−0.221428	+	2.95475i	−0.0122450	+	0.163398i
$328$	−0.803146	+	0.386775i	−0.0443463	+	0.0213561i
$329$	−3.14792	−	0.971006i	−0.173551	−	0.0535333i
$330$	−0.813947	−	2.07390i	−0.0448063	−	0.114165i
$331$	−1.30146	+	0.887318i	−0.0715345	+	0.0487714i	−0.598559	−	0.801079i	$-0.704260\pi$
$331$	−1.30146	+	0.887318i	−0.0715345	+	0.0487714i	0.527025	+	0.849850i	$0.323308\pi$
$332$	11.9976	+	1.80835i	0.658455	+	0.0992461i
$333$	2.85773	−	12.5205i	0.156602	−	0.686120i
$334$	1.42966	+	0.974728i	0.0782277	+	0.0533348i
$335$	10.0882	+	9.36045i	0.551175	+	0.511416i
$336$	0.534244	+	0.257279i	0.0291454	+	0.0140357i
$337$	−9.49751	+	16.4502i	−0.517362	+	0.896098i	0.482434	+	0.875932i	$0.339753\pi$
$337$	−9.49751	+	16.4502i	−0.517362	+	0.896098i	−0.999797	+	0.0201658i	$0.993581\pi$
$338$	−17.5048	−	30.3191i	−0.952134	−	1.64914i
$339$	−0.840613	−	11.2172i	−0.0456558	−	0.609234i
$340$	0.338721	+	1.48403i	0.0183697	+	0.0804831i
$341$	−2.24849	+	5.72905i	−0.121762	+	0.310245i
$342$	8.07576	−	10.1267i	0.436687	−	0.547588i
$343$	−9.15270			−0.494199
$344$	−1.35708	+	6.41548i	−0.0731689	+	0.345899i
$345$	−3.22484			−0.173620
$346$	12.7865	−	16.0338i	0.687407	−	0.861981i
$347$	5.64227	−	14.3763i	0.302893	−	0.771759i	−0.695680	−	0.718352i	$-0.744897\pi$
$347$	5.64227	−	14.3763i	0.302893	−	0.771759i	0.998573	−	0.0534067i	$-0.0170080\pi$
$348$	1.82839	+	8.01071i	0.0980121	+	0.429419i
$349$	1.30333	+	17.3917i	0.0697654	+	0.930955i	0.916782	+	0.399388i	$0.130777\pi$
$349$	1.30333	+	17.3917i	0.0697654	+	0.930955i	−0.847016	+	0.531567i	$0.821604\pi$
$350$	−0.337906	−	0.585270i	−0.0180618	−	0.0312840i
$351$	−15.8984	+	27.5368i	−0.848591	+	1.46980i
$352$	2.28772	+	1.10171i	0.121936	+	0.0587212i
$353$	−23.9994	−	22.2682i	−1.27736	−	1.18521i	−0.972522	−	0.232809i	$-0.925208\pi$
$353$	−23.9994	−	22.2682i	−1.27736	−	1.18521i	−0.304835	−	0.952405i	$-0.598601\pi$
$354$	−0.462945	−	0.315630i	−0.0246052	−	0.0167756i
$355$	−0.291823	+	1.27856i	−0.0154883	+	0.0678589i
$356$	9.65316	+	1.45498i	0.511616	+	0.0771138i
$357$	−0.745774	+	0.508460i	−0.0394706	+	0.0269106i
$358$	3.58941	+	9.14566i	0.189706	+	0.483363i
$359$	−24.8833	−	7.67547i	−1.31329	−	0.405096i	−0.442507	−	0.896765i	$-0.645911\pi$
$359$	−24.8833	−	7.67547i	−1.31329	−	0.405096i	−0.870782	+	0.491669i	$0.836387\pi$
$360$	−2.00929	+	0.967623i	−0.105899	+	0.0509982i
$361$	1.10093	−	14.6908i	0.0579435	−	0.773202i
$362$	−11.1308	+	1.67770i	−0.585022	+	0.0881779i
$363$	−2.92817	+	2.71695i	−0.153689	+	0.142603i
$364$	4.47459	−	1.38023i	0.234532	−	0.0723436i
$365$	6.19298	+	7.76575i	0.324155	+	0.406478i
$366$	−1.42859	−	1.79140i	−0.0746737	−	0.0936379i
$367$	−6.92344	+	2.13560i	−0.361400	+	0.111477i	−0.470137	−	0.882593i	$-0.655796\pi$
$367$	−6.92344	+	2.13560i	−0.361400	+	0.111477i	0.108737	+	0.994071i	$0.465319\pi$
$368$	2.69425	−	2.49990i	0.140448	−	0.130316i
$369$	1.96580	−	0.296297i	0.102336	−	0.0154246i
$370$	−0.430341	+	5.74250i	−0.0223723	+	0.298538i
$371$	−3.33979	+	1.60836i	−0.173393	+	0.0835017i
$372$	−2.03220	−	0.626852i	−0.105365	−	0.0325008i
$373$	7.88624	+	20.0938i	0.408334	+	1.04042i	0.976118	+	0.217241i	$0.0697057\pi$
$373$	7.88624	+	20.0938i	0.408334	+	1.04042i	−0.567784	+	0.823178i	$0.692199\pi$
$374$	−3.19352	+	2.17731i	−0.165133	+	0.112586i
$375$	−0.867614	−	0.130772i	−0.0448034	−	0.00675303i
$376$	1.08469	−	4.75234i	0.0559386	−	0.245083i
$377$	53.6121	+	36.5521i	2.76117	+	1.88253i
$378$	−2.27341	−	2.10942i	−0.116932	−	0.108497i
$379$	−11.3662	−	5.47370i	−0.583845	−	0.281165i	0.118555	−	0.992948i	$-0.462174\pi$
$379$	−11.3662	−	5.47370i	−0.583845	−	0.281165i	−0.702400	+	0.711783i	$0.747888\pi$
$380$	−2.90396	+	5.02981i	−0.148970	+	0.258024i
$381$	2.31814	+	4.01514i	0.118762	+	0.205702i
$382$	1.85068	+	24.6956i	0.0946892	+	1.26354i
$383$	0.103377	+	0.452926i	0.00528234	+	0.0231434i	0.977500	−	0.210934i	$-0.0676504\pi$
$383$	0.103377	+	0.452926i	0.00528234	+	0.0231434i	−0.972218	+	0.234077i	$0.924793\pi$
$384$	−0.320555	+	0.816762i	−0.0163583	+	0.0416802i
$385$	1.06991	−	1.34163i	0.0545277	−	0.0683756i
$386$	−13.7788			−0.701321
$387$	7.10922	−	12.7797i	0.361382	−	0.649630i
$388$	−15.6971			−0.796897
$389$	−10.7036	+	13.4219i	−0.542693	+	0.680515i	−0.975254	−	0.221089i	$-0.929039\pi$
$389$	−10.7036	+	13.4219i	−0.542693	+	0.680515i	0.432561	+	0.901605i	$0.357610\pi$
$390$	2.22109	−	5.65925i	0.112469	−	0.286567i
$391$	1.24493	+	5.45441i	0.0629590	+	0.275841i
$392$	−0.488980	−	6.52498i	−0.0246972	−	0.329561i
$393$	−4.38263	−	7.59093i	−0.221074	−	0.382912i
$394$	−5.73743	+	9.93752i	−0.289048	+	0.500645i
$395$	−8.28978	−	3.99215i	−0.417104	−	0.200867i
$396$	−4.15108	−	3.85164i	−0.208599	−	0.193552i
$397$	−9.56697	−	6.52265i	−0.480152	−	0.327362i	0.298940	−	0.954272i	$-0.403367\pi$
$397$	−9.56697	−	6.52265i	−0.480152	−	0.327362i	−0.779092	+	0.626910i	$0.784319\pi$
$398$	−2.11842	+	9.28138i	−0.106187	+	0.465234i
$399$	−3.40544	−	0.513288i	−0.170485	−	0.0256965i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	−8.57684	−	21.8534i	−0.428307	−	1.09131i	−0.968334	−	0.249660i	$-0.919681\pi$
$401$	−8.57684	−	21.8534i	−0.428307	−	1.09131i	0.540027	−	0.841648i	$-0.318414\pi$
$402$	−11.5384	−	3.55913i	−0.575484	−	0.177513i
$403$	−15.1312	+	7.28679i	−0.753737	+	0.362981i
$404$	0.397238	−	5.30077i	0.0197633	−	0.263723i
$405$	2.63422	−	0.397045i	0.130896	−	0.0197293i
$406$	−4.63932	+	4.30466i	−0.230245	+	0.213636i
$407$	−13.9725	+	4.30994i	−0.692590	+	0.213636i
$408$	−0.832733	−	1.04421i	−0.0412264	−	0.0516963i
$409$	−1.09913	−	1.37827i	−0.0543485	−	0.0681509i	0.753914	−	0.656973i	$-0.228163\pi$
$409$	−1.09913	−	1.37827i	−0.0543485	−	0.0681509i	−0.808263	+	0.588822i	$0.799592\pi$
$410$	−0.851822	+	0.262752i	−0.0420685	+	0.0129764i
$411$	11.3777	−	10.5570i	0.561221	−	0.520737i
$412$	11.8299	−	1.78307i	0.582819	−	0.0878458i
$413$	0.0322508	−	0.430357i	0.00158696	−	0.0211765i
$414$	−7.38493	+	3.55639i	−0.362949	+	0.174787i
$415$	11.5941	+	3.57630i	0.569131	+	0.175554i
$416$	2.53141	+	6.44992i	0.124112	+	0.316233i
$417$	−9.46107	+	6.45045i	−0.463311	+	0.315880i
$418$	−14.5826	−	2.19798i	−0.713260	−	0.107507i
$419$	−1.31699	+	5.77013i	−0.0643393	+	0.281889i	−0.996856	−	0.0792387i	$-0.974751\pi$
$419$	−1.31699	+	5.77013i	−0.0643393	+	0.281889i	0.932516	+	0.361128i	$0.117608\pi$
$420$	0.489932	+	0.334030i	0.0239062	+	0.0162990i
$421$	3.52683	+	3.27242i	0.171887	+	0.159488i	0.761426	−	0.648252i	$-0.224500\pi$
$421$	3.52683	+	3.27242i	0.171887	+	0.159488i	−0.589538	+	0.807740i	$0.700690\pi$
$422$	−0.491125	−	0.236514i	−0.0239076	−	0.0115133i
$423$	−5.43548	+	9.41453i	−0.264282	+	0.457750i
$424$	−2.74254	−	4.75022i	−0.133190	−	0.230691i
$425$	0.113754	+	1.51794i	0.00551789	+	0.0736311i
$426$	−0.256050	−	1.12183i	−0.0124056	−	0.0543527i
$427$	0.644760	−	1.64282i	0.0312021	−	0.0795017i
$428$	−9.21909	+	11.5604i	−0.445622	+	0.558792i
$429$	15.4369			0.745303
$430$	−2.29810	+	6.14156i	−0.110824	+	0.296172i
$431$	−17.8505			−0.859828			−0.429914	−	0.902870i	$-0.641456\pi$
$431$	−17.8505			−0.859828			−0.429914	+	0.902870i	$0.641456\pi$
$432$	2.86120	−	3.58783i	0.137659	−	0.172619i
$433$	−11.6542	+	29.6943i	−0.560064	+	1.42702i	0.317823	+	0.948150i	$0.397048\pi$
$433$	−11.6542	+	29.6943i	−0.560064	+	1.42702i	−0.877887	+	0.478869i	$0.841047\pi$
$434$	−0.364498	−	1.59697i	−0.0174965	−	0.0766570i
$435$	0.614036	+	8.19374i	0.0294408	+	0.392860i
$436$	−1.68850	−	2.92457i	−0.0808646	−	0.140062i
$437$	−10.6732	+	18.4865i	−0.510569	+	0.884331i
$438$	−7.85208	−	3.78136i	−0.375187	−	0.180681i
$439$	−6.06640	−	5.62880i	−0.289533	−	0.268648i	0.522011	−	0.852939i	$-0.325182\pi$
$439$	−6.06640	−	5.62880i	−0.289533	−	0.268648i	−0.811544	+	0.584291i	$0.801373\pi$
$440$	2.09797	+	1.43037i	0.100017	+	0.0681902i
$441$	−3.24713	+	14.2266i	−0.154625	+	0.677457i
$442$	−10.4294	−	1.57197i	−0.496074	−	0.0747711i
$443$	20.5512	−	14.0115i	0.976415	−	0.665708i	0.0337435	−	0.999431i	$-0.489257\pi$
$443$	20.5512	−	14.0115i	0.976415	−	0.665708i	0.942672	+	0.333722i	$0.108305\pi$
$444$	−1.84595	−	4.70340i	−0.0876049	−	0.223214i
$445$	9.32849	+	2.87746i	0.442213	+	0.136405i
$446$	23.8973	−	11.5083i	1.13157	−	0.544936i
$447$	−1.48786	+	19.8541i	−0.0703732	+	0.939065i
$448$	−0.668263	+	0.100724i	−0.0315725	+	0.00475878i
$449$	−24.8800	+	23.0852i	−1.17416	+	1.08946i	−0.179765	+	0.983710i	$0.557534\pi$
$449$	−24.8800	+	23.0852i	−1.17416	+	1.08946i	−0.994393	+	0.105750i	$0.966276\pi$
$450$	−2.13107	+	0.657347i	−0.100459	+	0.0309876i
$451$	−1.41126	−	1.76966i	−0.0664537	−	0.0833303i
$452$	7.99328	+	10.0233i	0.375972	+	0.471454i
$453$	3.69023	−	1.13828i	0.173382	−	0.0534813i
$454$	−3.66362	+	3.39934i	−0.171942	+	0.159539i
$455$	4.63032	−	0.697909i	0.217073	−	0.0327185i
$456$	0.380821	−	5.08171i	0.0178336	−	0.237973i
$457$	9.59764	−	4.62198i	0.448959	−	0.216207i	−0.195721	−	0.980660i	$-0.562705\pi$
$457$	9.59764	−	4.62198i	0.448959	−	0.216207i	0.644680	+	0.764452i	$0.276991\pi$
$458$	−0.0935683	−	0.0288620i	−0.00437216	−	0.00134863i
$459$	2.55205	+	6.50251i	0.119119	+	0.303511i
$460$	3.03675	−	2.07042i	0.141589	−	0.0965339i
$461$	−0.314891	−	0.0474621i	−0.0146659	−	0.00221053i	0.141705	−	0.989909i	$-0.454741\pi$
$461$	−0.314891	−	0.0474621i	−0.0146659	−	0.00221053i	−0.156371	+	0.987698i	$0.549980\pi$
$462$	−0.335038	+	1.46790i	−0.0155874	+	0.0682928i
$463$	21.4038	+	14.5929i	0.994720	+	0.678189i	0.947187	−	0.320681i	$-0.103912\pi$
$463$	21.4038	+	14.5929i	0.994720	+	0.678189i	0.0475331	+	0.998870i	$0.484864\pi$
$464$	−6.86481	−	6.36961i	−0.318691	−	0.295702i
$465$	−1.91608	−	0.922735i	−0.0888560	−	0.0427908i
$466$	−1.55729	+	2.69731i	−0.0721402	+	0.124950i
$467$	1.01558	+	1.75904i	0.0469957	+	0.0813989i	0.888566	−	0.458748i	$-0.151702\pi$
$467$	1.01558	+	1.75904i	0.0469957	+	0.0813989i	−0.841571	+	0.540147i	$0.818369\pi$
$468$	−1.15476	−	15.4092i	−0.0533789	−	0.712291i
$469$	−2.06954	−	9.06725i	−0.0955625	−	0.418687i
$470$	1.78087	−	4.53759i	0.0821456	−	0.209304i
$471$	−0.101272	+	0.126992i	−0.00466639	+	0.00585146i
$472$	0.638585			0.0293933
$473$	−16.6484	+	0.265400i	−0.765493	+	0.0122031i
$474$	8.07305			0.370808
$475$	−3.62118	+	4.54082i	−0.166151	+	0.208347i
$476$	0.375834	−	0.957608i	0.0172263	−	0.0438919i
$477$	2.72199	+	11.9258i	0.124632	+	0.546047i
$478$	−2.02624	−	27.0383i	−0.0926781	−	1.23670i
$479$	−7.95009	−	13.7700i	−0.363249	−	0.629166i	0.625245	−	0.780429i	$-0.284999\pi$
$479$	−7.95009	−	13.7700i	−0.363249	−	0.629166i	−0.988494	+	0.151263i	$0.951666\pi$
$480$	−0.438707	+	0.759863i	−0.0200241	+	0.0346828i
$481$	−35.9493	−	17.3123i	−1.63915	−	0.789371i
$482$	−11.3281	−	10.5110i	−0.515983	−	0.478762i
$483$	1.80069	+	1.22769i	0.0819343	+	0.0558619i
$484$	1.01304	−	4.43844i	0.0460475	−	0.201747i
$485$	−15.5217	−	2.33952i	−0.704805	−	0.106232i
$486$	−13.3061	+	9.07194i	−0.603577	+	0.411512i
$487$	3.75008	+	9.55506i	0.169933	+	0.432981i	0.990316	−	0.138833i	$-0.0443351\pi$
$487$	3.75008	+	9.55506i	0.169933	+	0.432981i	−0.820383	+	0.571814i	$0.806240\pi$
$488$	2.49539	+	0.769725i	0.112961	+	0.0348438i
$489$	3.13460	−	1.50954i	0.141752	−	0.0682640i
$490$	0.488980	−	6.52498i	0.0220899	−	0.294769i
$491$	−26.1620	+	3.94329i	−1.18068	+	0.177958i	−0.709905	−	0.704298i	$-0.751262\pi$
$491$	−26.1620	+	3.94329i	−1.18068	+	0.177958i	−0.470770	+	0.882256i	$0.656024\pi$
$492$	0.573356	−	0.531996i	0.0258489	−	0.0239843i
$493$	13.6216	−	4.20172i	0.613487	−	0.189236i
$494$	−25.0908	−	31.4629i	−1.12889	−	1.41558i
$495$	−3.53066	−	4.42730i	−0.158691	−	0.198992i
$496$	2.31613	−	0.714431i	0.103997	−	0.0320789i
$497$	0.649694	−	0.602828i	0.0291427	−	0.0270405i
$498$	−10.5269	+	1.58667i	−0.471721	+	0.0711004i
$499$	2.50061	−	33.3683i	0.111943	−	1.49377i	−0.604770	−	0.796400i	$-0.706735\pi$
$499$	2.50061	−	33.3683i	0.111943	−	1.49377i	0.716712	−	0.697369i	$-0.245646\pi$
$500$	0.900969	−	0.433884i	0.0402926	−	0.0194039i
$501$	−1.45076	−	0.447501i	−0.0648154	−	0.0199929i
$502$	7.44125	+	18.9600i	0.332119	+	0.846227i
$503$	26.1452	−	17.8255i	1.16576	−	0.794798i	0.183624	−	0.982997i	$-0.441217\pi$
$503$	26.1452	−	17.8255i	1.16576	−	0.794798i	0.982131	+	0.188198i	$0.0602647\pi$
$504$	1.49032	+	0.224630i	0.0663843	+	0.0100058i
$505$	1.18284	−	5.18236i	0.0526357	−	0.230612i
$506$	7.71085	+	5.25717i	0.342789	+	0.233710i
$507$	22.5178	+	20.8935i	1.00005	+	0.927911i
$508$	−4.76075	−	2.29265i	−0.211224	−	0.101720i
$509$	−3.39264	+	5.87623i	−0.150376	+	0.260459i	−0.931366	−	0.364085i	$-0.881382\pi$
$509$	−3.39264	+	5.87623i	−0.150376	+	0.260459i	0.780990	+	0.624544i	$0.214715\pi$
$510$	−0.667800	−	1.15666i	−0.0295707	−	0.0512179i
$511$	−0.501639	−	6.69391i	−0.0221912	−	0.296121i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	−9.73729	+	24.8102i	−0.429912	+	1.09540i
$514$	8.58950	−	10.7709i	0.378867	−	0.475084i
$515$	11.9635			0.527177
$516$	−0.521364	−	5.72992i	−0.0229518	−	0.252246i
$517$	12.3774			0.544355
$518$	2.42645	−	3.04267i	0.106612	−	0.133687i
$519$	−6.57394	+	16.7501i	−0.288564	+	0.735249i
$520$	1.54182	+	6.75517i	0.0676134	+	0.296234i
$521$	−2.03098	−	27.1015i	−0.0889787	−	1.18734i	−0.845721	−	0.533625i	$-0.820829\pi$
$521$	−2.03098	−	27.1015i	−0.0889787	−	1.18734i	0.756742	−	0.653713i	$-0.226790\pi$
$522$	10.4423	+	18.0866i	0.457048	+	0.791630i
$523$	−18.3825	+	31.8394i	−0.803809	+	1.39224i	0.113283	+	0.993563i	$0.463863\pi$
$523$	−18.3825	+	31.8394i	−0.803809	+	1.39224i	−0.917092	+	0.398675i	$0.869470\pi$
$524$	9.00057	+	4.33444i	0.393192	+	0.189351i
$525$	0.434675	+	0.403320i	0.0189708	+	0.0176023i
$526$	1.72533	+	1.17631i	0.0752278	+	0.0512894i
$527$	−0.820997	+	3.59702i	−0.0357632	+	0.156689i
$528$	−2.20303	−	0.332053i	−0.0958744	−	0.0144507i
$529$	−7.84225	+	5.34675i	−0.340967	+	0.232468i
$530$	−2.00393	−	5.10592i	−0.0870450	−	0.221787i
$531$	−1.36087	−	0.419772i	−0.0590566	−	0.0182165i
$532$	3.53636	−	1.70302i	0.153321	−	0.0738353i
$533$	0.461577	−	6.15932i	0.0199931	−	0.266790i
$534$	−8.46982	+	1.27662i	−0.366525	+	0.0552447i
$535$	−10.8391	+	10.0572i	−0.468616	+	0.434812i
$536$	13.1505	−	4.05638i	0.568014	−	0.175209i
$537$	−5.37475	−	6.73972i	−0.231938	−	0.290840i
$538$	17.4673	+	21.9034i	0.753071	+	0.944321i
$539$	15.8764	−	4.89722i	0.683845	−	0.210938i
$540$	3.36398	−	3.12131i	0.144763	−	0.134320i
$541$	−11.7282	+	1.76774i	−0.504233	+	0.0760010i	−0.396233	−	0.918150i	$-0.629683\pi$
$541$	−11.7282	+	1.76774i	−0.504233	+	0.0760010i	−0.108000	+	0.994151i	$0.534445\pi$
$542$	2.10503	−	28.0897i	0.0904190	−	1.20656i
$543$	8.89855	−	4.28531i	0.381873	−	0.183900i
$544$	1.45457	+	0.448676i	0.0623643	+	0.0192368i
$545$	−1.23376	−	3.14357i	−0.0528484	−	0.134656i
$546$	−3.39468	+	2.31446i	−0.145279	+	0.0990496i
$547$	16.6506	+	2.50968i	0.711929	+	0.107306i	0.495015	−	0.868885i	$-0.335163\pi$
$547$	16.6506	+	2.50968i	0.711929	+	0.107306i	0.216914	+	0.976191i	$0.430401\pi$
$548$	−3.93629	+	17.2460i	−0.168150	+	0.736712i
$549$	−4.81186	−	3.28067i	−0.205365	−	0.140016i
$550$	1.86135	+	1.72708i	0.0793682	+	0.0736429i
$551$	49.0032	+	23.5987i	2.08761	+	1.00534i
$552$	−1.61242	+	2.79279i	−0.0686292	+	0.118869i
$553$	3.10906	+	5.38504i	0.132211	+	0.228995i
$554$	0.686898	+	9.16601i	0.0291835	+	0.389426i
$555$	−1.12433	−	4.92599i	−0.0477250	−	0.209097i
$556$	4.76792	−	12.1485i	0.202205	−	0.515209i
$557$	6.24083	−	7.82576i	0.264433	−	0.331588i	−0.631834	−	0.775104i	$-0.717698\pi$
$557$	6.24083	−	7.82576i	0.264433	−	0.331588i	0.896267	+	0.443516i	$0.146269\pi$
$558$	−5.40545			−0.228831
$559$	−33.7951	−	30.3694i	−1.42938	−	1.28449i
$560$	−0.675811			−0.0285582
$561$	2.11446	−	2.65144i	0.0892724	−	0.111944i
$562$	−0.870780	+	2.21871i	−0.0367316	+	0.0935907i
$563$	−4.19496	−	18.3793i	−0.176796	−	0.774596i	−0.983096	−	0.183089i	$-0.941390\pi$
$563$	−4.19496	−	18.3793i	−0.176796	−	0.774596i	0.806300	−	0.591507i	$-0.201467\pi$
$564$	0.319621	+	4.26504i	0.0134585	+	0.179591i
$565$	6.41011	+	11.1026i	0.269676	+	0.467092i
$566$	2.16495	−	3.74981i	0.0909998	−	0.157616i
$567$	−1.62206	−	0.781141i	−0.0681199	−	0.0328048i
$568$	0.961354	+	0.892006i	0.0403375	+	0.0374277i
$569$	14.7355	+	10.0465i	0.617745	+	0.421171i	0.831350	−	0.555749i	$-0.187568\pi$
$569$	14.7355	+	10.0465i	0.617745	+	0.421171i	−0.213606	+	0.976920i	$0.568521\pi$
$570$	1.13396	−	4.96819i	0.0474962	−	0.208095i
$571$	40.2473	+	6.06630i	1.68430	+	0.253867i	0.920260	−	0.391308i	$-0.127977\pi$
$571$	40.2473	+	6.06630i	1.68430	+	0.253867i	0.764035	+	0.645174i	$0.223215\pi$
$572$	−14.5366	+	9.91087i	−0.607805	+	0.414394i
$573$	−7.93852	−	20.2270i	−0.331636	−	0.844996i
$574$	0.575671	+	0.177571i	0.0240280	+	0.00741167i
$575$	3.31141	−	1.59469i	0.138095	−	0.0665033i
$576$	−0.166659	+	2.22391i	−0.00694412	+	0.0926629i
$577$	−12.3532	+	1.86194i	−0.514270	+	0.0775137i	−0.401050	−	0.916056i	$-0.631355\pi$
$577$	−12.3532	+	1.86194i	−0.514270	+	0.0775137i	−0.113220	+	0.993570i	$0.536116\pi$
$578$	10.7633	−	9.98691i	0.447696	−	0.415401i
$579$	11.5526	−	3.56350i	0.480109	−	0.148094i
$580$	−5.83879	−	7.32161i	−0.242443	−	0.304014i
$581$	−5.11243	−	6.41079i	−0.212099	−	0.265964i
$582$	13.1609	−	4.05961i	0.545538	−	0.168276i
$583$	10.2097	−	9.47317i	0.422841	−	0.392339i
$584$	9.82183	−	1.48040i	0.406430	−	0.0612595i
$585$	1.15476	−	15.4092i	0.0477435	−	0.637093i
$586$	−2.30440	+	1.10974i	−0.0951939	+	0.0458429i
$587$	31.6151	+	9.75196i	1.30489	+	0.402507i	0.867802	−	0.496910i	$-0.165532\pi$
$587$	31.6151	+	9.75196i	1.30489	+	0.402507i	0.437092	+	0.899417i	$0.356008\pi$
$588$	2.09748	+	5.34430i	0.0864988	+	0.220395i
$589$	−11.6312	+	7.93004i	−0.479256	+	0.326752i
$590$	0.631453	+	0.0951762i	0.0259965	+	0.00391834i
$591$	2.24039	−	9.81578i	0.0921572	−	0.403767i
$592$	4.75798	+	3.24393i	0.195552	+	0.133325i
$593$	6.05555	+	5.61873i	0.248672	+	0.230733i	0.794653	−	0.607064i	$-0.207653\pi$
$593$	6.05555	+	5.61873i	0.248672	+	0.230733i	−0.545982	+	0.837797i	$0.683843\pi$
$594$	10.4984	+	5.05574i	0.430753	+	0.207439i
$595$	0.514360	−	0.890898i	0.0210867	−	0.0365232i
$596$	−11.3457	−	19.6513i	−0.464738	−	0.804949i
$597$	−0.624224	−	8.32969i	−0.0255478	−	0.340911i
$598$	5.66680	+	24.8279i	0.231733	+	1.01529i
$599$	2.02601	−	5.16219i	0.0827806	−	0.210921i	−0.883490	−	0.468450i	$-0.844813\pi$
$599$	2.02601	−	5.16219i	0.0827806	−	0.210921i	0.966271	+	0.257528i	$0.0829080\pi$
$600$	−0.547059	+	0.685990i	−0.0223336	+	0.0280054i
$601$	−9.82118			−0.400614			−0.200307	−	0.979733i	$-0.564194\pi$
$601$	−9.82118			−0.400614			−0.200307	+	0.979733i	$0.564194\pi$
$602$	3.62130	−	2.55445i	0.147593	−	0.104112i
$603$	−30.6910			−1.24983
$604$	−2.74419	+	3.44111i	−0.111660	+	0.140017i
$605$	1.66324	−	4.23788i	0.0676205	−	0.172294i
$606$	1.03784	+	4.54707i	0.0421594	+	0.184712i
$607$	−1.03962	−	13.8728i	−0.0421970	−	0.563080i	−0.977734	−	0.209850i	$-0.932702\pi$
$607$	−1.03962	−	13.8728i	−0.0421970	−	0.563080i	0.935537	−	0.353230i	$-0.114917\pi$
$608$	2.90396	+	5.02981i	0.117771	+	0.203986i
$609$	2.77648	−	4.80900i	0.112508	−	0.194870i
$610$	2.35279	+	1.13305i	0.0952619	+	0.0458757i
$611$	24.7590	+	22.9730i	1.00164	+	0.929388i
$612$	−2.80485	−	1.91232i	−0.113379	−	0.0773008i
$613$	2.65786	−	11.6448i	0.107350	−	0.470331i	−0.892465	−	0.451116i	$-0.851026\pi$
$613$	2.65786	−	11.6448i	0.107350	−	0.470331i	0.999815	−	0.0192151i	$-0.00611674\pi$
$614$	24.3701	+	3.67321i	0.983499	+	0.148239i
$615$	0.646242	−	0.440600i	0.0260590	−	0.0177667i
$616$	−0.626927	−	1.59738i	−0.0252596	−	0.0643604i
$617$	7.12195	+	2.19683i	0.286719	+	0.0884411i	0.434779	−	0.900537i	$-0.356827\pi$
$617$	7.12195	+	2.19683i	0.286719	+	0.0884411i	−0.148060	+	0.988978i	$0.547303\pi$
$618$	−9.45746	+	4.55447i	−0.380435	+	0.183208i
$619$	−3.06870	+	40.9489i	−0.123341	+	1.64587i	0.501525	+	0.865143i	$0.332773\pi$
$619$	−3.06870	+	40.9489i	−0.123341	+	1.64587i	−0.624866	+	0.780732i	$0.714847\pi$
$620$	2.39674	−	0.361250i	0.0962554	−	0.0145082i
$621$	12.3639	−	11.4721i	0.496147	−	0.460358i
$622$	6.21110	−	1.91587i	0.249043	−	0.0768194i
$623$	−4.11341	−	5.15806i	−0.164800	−	0.206653i
$624$	−3.79051	−	4.75315i	−0.151742	−	0.190278i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	1.82725	−	1.69544i	0.0730315	−	0.0677633i
$627$	12.7950	−	1.92854i	0.510984	−	0.0770184i
$628$	0.0138342	−	0.184604i	0.000552043	−	0.00736650i
$629$	−7.89766	+	3.80331i	−0.314900	+	0.151648i
$630$	1.44020	+	0.444242i	0.0573789	+	0.0176990i
$631$	−9.31103	−	23.7241i	−0.370666	−	0.944443i	−0.987538	−	0.157379i	$-0.949696\pi$
$631$	−9.31103	−	23.7241i	−0.370666	−	0.944443i	0.616872	−	0.787064i	$-0.288400\pi$
$632$	−7.60219	+	5.18308i	−0.302399	+	0.206172i
$633$	0.472944	+	0.0712848i	0.0187978	+	0.00283332i
$634$	5.41313	−	23.7165i	0.214983	−	0.941902i
$635$	−4.36587	−	2.97660i	−0.173254	−	0.118123i
$636$	3.52795	+	3.27346i	0.139892	+	0.129801i
$637$	40.8478	+	19.6713i	1.61845	+	0.779404i
$638$	11.8893	−	20.5929i	0.470702	−	0.815280i
$639$	−1.46235	−	2.53287i	−0.0578497	−	0.100199i
$640$	−0.0747301	−	0.997204i	−0.00295397	−	0.0394179i
$641$	−7.84138	−	34.3553i	−0.309716	−	1.35695i	−0.854968	−	0.518681i	$-0.826423\pi$
$641$	−7.84138	−	34.3553i	−0.309716	−	1.35695i	0.545252	−	0.838272i	$-0.316434\pi$
$642$	4.73982	−	12.0769i	0.187066	−	0.476636i
$643$	26.2774	−	32.9509i	1.03628	−	1.29946i	0.0832674	−	0.996527i	$-0.473464\pi$
$643$	26.2774	−	32.9509i	1.03628	−	1.29946i	0.953013	−	0.302928i	$-0.0979641\pi$
$644$	−2.48387			−0.0978782
$645$	0.338459	−	5.74363i	0.0133268	−	0.226155i
$646$	−8.84083			−0.347838
$647$	−5.44607	+	6.82915i	−0.214107	+	0.268482i	−0.877274	−	0.479990i	$-0.840640\pi$
$647$	−5.44607	+	6.82915i	−0.214107	+	0.268482i	0.663167	+	0.748471i	$0.269212\pi$
$648$	0.973260	−	2.47983i	0.0382333	−	0.0974168i
$649$	0.360814	+	1.58083i	0.0141632	+	0.0620529i
$650$	0.517797	+	6.90952i	0.0203097	+	0.271014i
$651$	0.718619	+	1.24469i	0.0281649	+	0.0487831i
$652$	−1.98261	+	3.43399i	−0.0776451	+	0.134485i
$653$	3.39131	+	1.63317i	0.132712	+	0.0639107i	0.499061	−	0.866567i	$-0.333678\pi$
$653$	3.39131	+	1.63317i	0.132712	+	0.0639107i	−0.366349	+	0.930477i	$0.619392\pi$
$654$	2.17206	+	2.01537i	0.0849341	+	0.0788073i
$655$	8.25402	+	5.62750i	0.322511	+	0.219884i
$656$	−0.198361	+	0.869075i	−0.00774469	+	0.0339317i
$657$	−21.9041	−	3.30151i	−0.854560	−	0.128804i
$658$	−2.72186	+	1.85573i	−0.106109	+	0.0723440i
$659$	−12.6674	−	32.2760i	−0.493452	−	1.25730i	−0.933259	−	0.359203i	$-0.883049\pi$
$659$	−12.6674	−	32.2760i	−0.493452	−	1.25730i	0.439807	−	0.898092i	$-0.355047\pi$
$660$	−2.12893	−	0.656688i	−0.0828685	−	0.0255615i
$661$	−22.7327	+	10.9475i	−0.884201	+	0.425809i	−0.820157	−	0.572138i	$-0.806114\pi$
$661$	−22.7327	+	10.9475i	−0.884201	+	0.425809i	−0.0640440	+	0.997947i	$0.520400\pi$
$662$	−0.117712	+	1.57075i	−0.00457499	+	0.0610490i
$663$	9.15086	−	1.37927i	0.355390	−	0.0535664i
$664$	8.89421	−	8.25262i	0.345162	−	0.320264i
$665$	3.75068	−	1.15693i	0.145445	−	0.0448639i
$666$	−8.00717	−	10.0407i	−0.310272	−	0.389068i
$667$	−21.4598	−	26.9098i	−0.830929	−	1.04195i
$668$	1.65345	−	0.510023i	0.0639741	−	0.0197334i
$669$	−17.0600	+	15.8294i	−0.659577	+	0.611998i
$670$	13.6082	−	2.05110i	0.525729	−	0.0792409i
$671$	−0.495522	+	6.61228i	−0.0191294	+	0.255264i
$672$	0.534244	−	0.257279i	0.0206089	−	0.00992473i
$673$	3.32621	+	1.02600i	0.128216	+	0.0395493i	0.358199	−	0.933645i	$-0.383391\pi$
$673$	3.32621	+	1.02600i	0.128216	+	0.0395493i	−0.229983	+	0.973195i	$0.573867\pi$
$674$	6.93966	+	17.6820i	0.267306	+	0.681084i
$675$	3.79161	−	2.58508i	0.145939	−	0.0994997i
$676$	−34.6185	−	5.21790i	−1.33148	−	0.200688i
$677$	−1.04315	+	4.57032i	−0.0400913	+	0.175652i	−0.991010	−	0.133790i	$-0.957285\pi$
$677$	−1.04315	+	4.57032i	−0.0400913	+	0.175652i	0.950918	+	0.309442i	$0.100142\pi$
$678$	−9.29407	−	6.33659i	−0.356937	−	0.243355i
$679$	7.77640	+	7.21544i	0.298431	+	0.276903i
$680$	1.37145	+	0.660458i	0.0525929	+	0.0253274i
$681$	2.19256	−	3.79762i	0.0840189	−	0.145525i
$682$	3.07724	+	5.32994i	0.117834	+	0.204094i
$683$	−2.47916	−	33.0821i	−0.0948626	−	1.26585i	−0.818028	−	0.575178i	$-0.804933\pi$
$683$	−2.47916	−	33.0821i	−0.0948626	−	1.26585i	0.723165	−	0.690675i	$-0.242686\pi$
$684$	−2.88221	−	12.6278i	−0.110204	−	0.482835i
$685$	−6.46270	+	16.4667i	−0.246927	+	0.629160i
$686$	−5.70662	+	7.15587i	−0.217880	+	0.273212i
$687$	0.0859152			0.00327787
$688$	4.16970	+	5.06099i	0.158968	+	0.192949i
$689$	38.0056			1.44790
$690$	−2.01065	+	2.52128i	−0.0765443	+	0.0959835i
$691$	13.4254	−	34.2075i	0.510728	−	1.30131i	−0.410347	−	0.911929i	$-0.634592\pi$
$691$	13.4254	−	34.2075i	0.510728	−	1.30131i	0.921075	−	0.389385i	$-0.127312\pi$
$692$	−4.56345	−	19.9938i	−0.173476	−	0.760050i
$693$	0.285987	+	3.81624i	0.0108638	+	0.144967i
$694$	−7.72192	−	13.3748i	−0.293120	−	0.507699i
$695$	6.52530	−	11.3021i	0.247519	−	0.428715i
$696$	7.40301	+	3.56510i	0.280610	+	0.135135i
$697$	−0.994698	−	0.922945i	−0.0376769	−	0.0349590i
$698$	14.4100	+	9.82455i	0.545425	+	0.371865i
$699$	0.608101	−	2.66426i	0.0230005	−	0.100772i
$700$	−0.668263	−	0.100724i	−0.0252580	−	0.00380703i
$701$	22.2499	−	15.1697i	0.840367	−	0.572952i	−0.0648535	−	0.997895i	$-0.520658\pi$
$701$	22.2499	−	15.1697i	0.840367	−	0.572952i	0.905220	+	0.424942i	$0.139706\pi$
$702$	11.6166	+	29.5987i	0.438442	+	1.11713i
$703$	−31.9596	−	9.85824i	−1.20538	−	0.371811i
$704$	2.28772	−	1.10171i	0.0862217	−	0.0415222i
$705$	−0.319621	+	4.26504i	−0.0120376	+	0.160631i
$706$	−32.3733	+	4.87949i	−1.21839	+	0.183642i
$707$	−2.63339	+	2.44343i	−0.0990388	+	0.0918946i
$708$	−0.535411	+	0.165152i	−0.0201220	+	0.00620681i
$709$	7.73877	+	9.70411i	0.290636	+	0.364446i	0.905617	−	0.424096i	$-0.139408\pi$
$709$	7.73877	+	9.70411i	0.290636	+	0.364446i	−0.614982	+	0.788541i	$0.710837\pi$
$710$	0.817670	+	1.02533i	0.0306866	+	0.0384798i
$711$	19.6078	−	6.04822i	0.735352	−	0.226826i
$712$	7.15619	−	6.63998i	0.268190	−	0.248844i
$713$	8.80895	−	1.32774i	0.329898	−	0.0497241i
$714$	−0.0674524	+	0.900090i	−0.00252434	+	0.0336850i
$715$	−15.8514	+	7.63361i	−0.592807	+	0.285481i
$716$	9.38832	+	2.89591i	0.350858	+	0.108225i
$717$	8.69158	+	22.1458i	0.324593	+	0.827049i
$718$	−21.5154	+	14.6689i	−0.802948	+	0.547440i
$719$	2.35938	+	0.355619i	0.0879900	+	0.0132624i	0.192890	−	0.981220i	$-0.438214\pi$
$719$	2.35938	+	0.355619i	0.0879900	+	0.0132624i	−0.104900	+	0.994483i	$0.533452\pi$
$720$	−0.496254	+	2.17423i	−0.0184943	+	0.0810288i
$721$	−6.68022	−	4.55450i	−0.248785	−	0.169618i
$722$	−10.7993	−	10.0203i	−0.401910	−	0.372918i
$723$	12.2163	+	5.88304i	0.454328	+	0.218793i
$724$	−5.62827	+	9.74844i	−0.209173	+	0.362298i
$725$	−4.68235	−	8.11007i	−0.173898	−	0.301200i
$726$	0.298509	+	3.98333i	0.0110787	+	0.147835i
$727$	−5.76946	−	25.2777i	−0.213978	−	0.937497i	−0.961833	−	0.273636i	$-0.911774\pi$
$727$	−5.76946	−	25.2777i	−0.213978	−	0.937497i	0.747856	−	0.663861i	$-0.231083\pi$
$728$	1.71075	−	4.35893i	0.0634048	−	0.161553i
$729$	3.82718	−	4.79913i	0.141747	−	0.177745i
$730$	9.93277			0.367628
$731$	−9.84528	+	1.64484i	−0.364141	+	0.0608365i
$732$	−2.29128			−0.0846883
$733$	−24.7301	+	31.0106i	−0.913427	+	1.14540i	0.0755221	+	0.997144i	$0.475938\pi$
$733$	−24.7301	+	31.0106i	−0.913427	+	1.14540i	−0.988949	+	0.148257i	$0.952634\pi$
$734$	−2.64701	+	6.74448i	−0.0977031	+	0.248943i
$735$	1.27753	+	5.59722i	0.0471224	+	0.206457i
$736$	−0.274662	−	3.66511i	−0.0101242	−	0.135098i
$737$	17.4719	+	30.2622i	0.643586	+	1.11472i
$738$	0.994003	−	1.72166i	0.0365898	−	0.0633753i
$739$	−45.2022	−	21.7683i	−1.66279	−	0.800758i	−0.998583	−	0.0532103i	$-0.983055\pi$
$739$	−45.2022	−	21.7683i	−1.66279	−	0.800758i	−0.664208	−	0.747548i	$-0.731231\pi$
$740$	4.22135	+	3.91684i	0.155180	+	0.143986i
$741$	29.1739	+	19.8905i	1.07173	+	0.730694i
$742$	−0.824859	+	3.61394i	−0.0302815	+	0.132672i
$743$	14.3157	+	2.15774i	0.525191	+	0.0791598i	0.406286	−	0.913746i	$-0.366824\pi$
$743$	14.3157	+	2.15774i	0.525191	+	0.0791598i	0.118905	+	0.992906i	$0.462062\pi$
$744$	−1.75715	+	1.19801i	−0.0644203	+	0.0439210i
$745$	−8.29009	−	21.1228i	−0.303726	−	0.773880i
$746$	20.6270	+	6.36258i	0.755207	+	0.232951i
$747$	−24.3790	+	11.7403i	−0.891980	+	0.429555i
$748$	−0.288842	+	3.85433i	−0.0105611	+	0.140928i
$749$	9.88113	−	1.48934i	0.361048	−	0.0544193i
$750$	−0.643190	+	0.596793i	−0.0234860	+	0.0217918i
$751$	36.6676	−	11.3105i	1.33802	−	0.412725i	0.458546	−	0.888671i	$-0.348371\pi$
$751$	36.6676	−	11.3105i	1.33802	−	0.412725i	0.879474	+	0.475946i	$0.157894\pi$
$752$	−3.03923	−	3.81108i	−0.110829	−	0.138976i
$753$	−11.1425	−	13.9722i	−0.406054	−	0.509176i
$754$	62.0042	−	19.1258i	2.25806	−	0.696519i
$755$	−3.22641	+	2.99367i	−0.117421	+	0.108951i
$756$	−3.06666	+	0.462225i	−0.111533	+	0.0168110i
$757$	0.948896	−	12.6621i	0.0344882	−	0.460213i	−0.953048	−	0.302820i	$-0.902072\pi$
$757$	0.948896	−	12.6621i	0.0344882	−	0.460213i	0.987536	−	0.157393i	$-0.0503090\pi$
$758$	−11.3662	+	5.47370i	−0.412841	+	0.198814i
$759$	−7.82465	−	2.41358i	−0.284017	−	0.0876076i
$760$	2.12187	+	5.40645i	0.0769685	+	0.196112i
$761$	−0.811827	+	0.553494i	−0.0294287	+	0.0200642i	−0.577945	−	0.816076i	$-0.696145\pi$
$761$	−0.811827	+	0.553494i	−0.0294287	+	0.0200642i	0.548516	+	0.836140i	$0.315193\pi$
$762$	4.58450	+	0.691002i	0.166079	+	0.0250324i
$763$	−0.507841	+	2.22500i	−0.0183851	+	0.0805504i
$764$	20.4617	+	13.9506i	0.740279	+	0.504714i
$765$	−2.48851	−	2.30900i	−0.0899723	−	0.0834821i
$766$	0.418567	+	0.201571i	0.0151234	+	0.00728306i
$767$	−2.21234	+	3.83189i	−0.0798831	+	0.138362i
$768$	0.438707	+	0.759863i	0.0158305	+	0.0274192i
$769$	−2.54200	−	33.9206i	−0.0916667	−	1.22321i	−0.833460	−	0.552579i	$-0.813644\pi$
$769$	−2.54200	−	33.9206i	−0.0916667	−	1.22321i	0.741794	−	0.670628i	$-0.233975\pi$
$770$	−0.381847	−	1.67298i	−0.0137608	−	0.0602900i
$771$	−4.41613	+	11.2521i	−0.159043	+	0.405235i
$772$	−8.59093	+	10.7727i	−0.309194	+	0.387717i
$773$	−8.33075			−0.299636			−0.149818	−	0.988714i	$-0.547869\pi$
$773$	−8.33075			−0.299636			−0.149818	+	0.988714i	$0.547869\pi$
$774$	−5.55907	−	13.5262i	−0.199817	−	0.486191i
$775$	2.42381			0.0870659
$776$	−9.78695	+	12.2725i	−0.351331	+	0.440555i
$777$	−1.24751	+	3.17861i	−0.0447543	+	0.114032i
$778$	3.82006	+	16.7368i	0.136956	+	0.600043i
$779$	−0.386903	−	5.16286i	−0.0138622	−	0.184979i
$780$	−3.03975	−	5.26501i	−0.108841	−	0.188518i
$781$	−1.66499	+	2.88385i	−0.0595780	+	0.103192i
$782$	5.04063	+	2.42744i	0.180253	+	0.0868051i
$783$	−31.5026	−	29.2302i	−1.12581	−	1.04460i
$784$	−5.40631	−	3.68596i	−0.193083	−	0.131641i
$785$	0.0411934	−	0.180480i	0.00147026	−	0.00644162i
$786$	−8.66736	−	1.30639i	−0.309154	−	0.0465975i
$787$	14.1317	−	9.63483i	0.503741	−	0.343445i	−0.284638	−	0.958635i	$-0.591873\pi$
$787$	14.1317	−	9.63483i	0.503741	−	0.343445i	0.788379	+	0.615190i	$0.210921\pi$
$788$	4.19224	+	10.6816i	0.149342	+	0.380518i
$789$	−1.75079	−	0.540047i	−0.0623298	−	0.0192262i
$790$	−8.28978	+	3.99215i	−0.294937	+	0.142034i
$791$	0.647466	−	8.63983i	0.0230212	−	0.307197i
$792$	−5.59948	+	0.843986i	−0.198969	+	0.0299897i
$793$	−13.2639	+	12.3071i	−0.471016	+	0.437039i
$794$	−11.0645	+	3.41295i	−0.392665	+	0.121121i
$795$	3.00066	+	3.76271i	0.106423	+	0.133450i
$796$	5.93567	+	7.44309i	0.210384	+	0.263813i
$797$	11.0649	−	3.41307i	0.391938	−	0.120897i	−0.0925210	−	0.995711i	$-0.529493\pi$
$797$	11.0649	−	3.41307i	0.391938	−	0.120897i	0.484459	+	0.874814i	$0.339016\pi$
$798$	−2.52456	+	2.34245i	−0.0893685	+	0.0829219i
$799$	7.33717	−	1.10590i	0.259570	−	0.0391239i
$800$	0.0747301	−	0.997204i	0.00264211	−	0.0352565i
$801$	−19.6151	+	9.44613i	−0.693065	+	0.333762i
$802$	−22.4333	−	6.91975i	−0.792146	−	0.244345i
$803$	9.21429	+	23.4776i	0.325165	+	0.828507i
$804$	−9.97672	+	6.80201i	−0.351852	+	0.239888i
$805$	−2.45613	−	0.370202i	−0.0865671	−	0.0130479i
$806$	−3.73709	+	16.3733i	−0.131633	+	0.576723i
$807$	−20.3099	−	13.8471i	−0.714942	−	0.487440i
$808$	−3.89663	−	3.61555i	−0.137083	−	0.127195i
$809$	−39.1170	−	18.8377i	−1.37528	−	0.662300i	−0.407292	−	0.913298i	$-0.633527\pi$
$809$	−39.1170	−	18.8377i	−1.37528	−	0.662300i	−0.967987	+	0.250999i	$0.919241\pi$
$810$	1.33199	−	2.30707i	0.0468013	−	0.0810622i
$811$	−7.88492	−	13.6571i	−0.276877	−	0.479565i	0.693730	−	0.720235i	$-0.255966\pi$
$811$	−7.88492	−	13.6571i	−0.276877	−	0.479565i	−0.970607	+	0.240670i	$0.922633\pi$
$812$	0.472949	+	6.31107i	0.0165973	+	0.221475i
$813$	5.49970	+	24.0958i	0.192883	+	0.845076i
$814$	−5.34205	+	13.6113i	−0.187239	+	0.477077i
$815$	−2.47228	+	3.10014i	−0.0866001	+	0.108593i
$816$	−1.33560			−0.0467553
$817$	−31.8054	−	20.9498i	−1.11273	−	0.732941i
$818$	−1.76287			−0.0616373
$819$	−6.51106	+	8.16461i	−0.227515	+	0.285295i
$820$	−0.325674	+	0.829804i	−0.0113730	+	0.0289780i
$821$	3.87013	+	16.9562i	0.135069	+	0.591774i	0.996477	+	0.0838617i	$0.0267254\pi$
$821$	3.87013	+	16.9562i	0.135069	+	0.591774i	−0.861409	+	0.507912i	$0.830417\pi$
$822$	−1.15989	−	15.4776i	−0.0404557	−	0.539844i
$823$	18.6539	+	32.3095i	0.650234	+	1.12624i	0.983066	+	0.183253i	$0.0586627\pi$
$823$	18.6539	+	32.3095i	0.650234	+	1.12624i	−0.332831	+	0.942986i	$0.608004\pi$
$824$	5.98177	−	10.3607i	0.208385	−	0.360933i
$825$	−2.00728	−	0.966654i	−0.0698844	−	0.0336546i
$826$	−0.316358	−	0.293538i	−0.0110075	−	0.0102135i
$827$	−6.68038	−	4.55460i	−0.232299	−	0.158379i	0.441576	−	0.897224i	$-0.354419\pi$
$827$	−6.68038	−	4.55460i	−0.232299	−	0.158379i	−0.673876	+	0.738845i	$0.735372\pi$
$828$	−1.82393	+	7.99115i	−0.0633858	+	0.277711i
$829$	−30.4704	−	4.59267i	−1.05828	−	0.159510i	−0.403232	−	0.915098i	$-0.632113\pi$
$829$	−30.4704	−	4.59267i	−1.05828	−	0.159510i	−0.655048	+	0.755588i	$0.727351\pi$
$830$	10.0249	−	6.83484i	0.347968	−	0.237241i
$831$	−2.94645	−	7.50744i	−0.102211	−	0.260430i
$832$	6.62106	+	2.04233i	0.229544	+	0.0708049i
$833$	8.97381	−	4.32156i	0.310924	−	0.149733i
$834$	−0.855718	+	11.4188i	−0.0296311	+	0.395399i
$835$	1.71100	−	0.257892i	0.0592116	−	0.00892472i
$836$	−10.8106	+	10.0307i	−0.373892	+	0.346921i
$837$	10.6287	−	3.27853i	0.367382	−	0.113322i
$838$	3.69013	+	4.62728i	0.127474	+	0.159847i
$839$	26.4789	+	33.2035i	0.914152	+	1.14631i	0.988822	+	0.149102i	$0.0476384\pi$
$839$	26.4789	+	33.2035i	0.914152	+	1.14631i	−0.0746694	+	0.997208i	$0.523790\pi$
$840$	0.566623	−	0.174780i	0.0195503	−	0.00603048i
$841$	−43.0283	+	39.9245i	−1.48374	+	1.37671i
$842$	4.75743	−	0.717067i	0.163952	−	0.0247118i
$843$	0.156282	−	2.08544i	0.00538265	−	0.0718265i
$844$	−0.491125	+	0.236514i	−0.0169052	+	0.00814113i
$845$	−33.4542	−	10.3192i	−1.15086	−	0.354993i
$846$	3.97161	+	10.1195i	0.136547	+	0.347915i
$847$	−2.54208	+	1.73316i	−0.0873468	+	0.0595520i
$848$	−5.42382	−	0.817509i	−0.186255	−	0.0280734i
$849$	−0.845384	+	3.70387i	−0.0290135	+	0.127117i
$850$	1.25770	+	0.857486i	0.0431388	+	0.0294115i
$851$	15.5151	+	14.3959i	0.531851	+	0.493486i
$852$	−1.03672	−	0.499260i	−0.0355176	−	0.0171044i
$853$	22.0898	−	38.2607i	0.756342	−	1.31002i	−0.188363	−	0.982100i	$-0.560318\pi$
$853$	22.0898	−	38.2607i	0.756342	−	1.31002i	0.944704	−	0.327923i	$-0.106349\pi$
$854$	−0.882409	−	1.52838i	−0.0301954	−	0.0523000i
$855$	−0.967943	−	12.9163i	−0.0331029	−	0.441728i
$856$	3.29026	+	14.4156i	0.112459	+	0.492714i
$857$	1.00946	−	2.57205i	0.0344823	−	0.0878596i	−0.912595	−	0.408864i	$-0.865925\pi$
$857$	1.00946	−	2.57205i	0.0344823	−	0.0878596i	0.947078	+	0.321004i	$0.104020\pi$
$858$	9.62478	−	12.0691i	0.328585	−	0.412032i
$859$	27.1790			0.927336			0.463668	−	0.886009i	$-0.346533\pi$
$859$	27.1790			0.927336			0.463668	+	0.886009i	$0.346533\pi$
$860$	3.36882	+	5.62593i	0.114876	+	0.191842i
$861$	−0.528585			−0.0180141
$862$	−11.1296	+	13.9561i	−0.379076	+	0.475346i
$863$	15.0437	−	38.3307i	0.512093	−	1.30479i	−0.407960	−	0.913000i	$-0.633760\pi$
$863$	15.0437	−	38.3307i	0.512093	−	1.30479i	0.920053	−	0.391793i	$-0.128145\pi$
$864$	−1.02115	−	4.47395i	−0.0347402	−	0.152207i
$865$	−1.53256	−	20.4506i	−0.0521087	−	0.695342i
$866$	15.9497	+	27.6257i	0.541993	+	0.938760i
$867$	−6.44150	+	11.1570i	−0.218765	+	0.378912i
$868$	−1.47582	−	0.710719i	−0.0500927	−	0.0241234i
$869$	−17.1262	−	15.8908i	−0.580966	−	0.539058i
$870$	6.78897	+	4.62864i	0.230168	+	0.156926i
$871$	−21.2184	+	92.9638i	−0.718957	+	3.14996i
$872$	−3.33929	−	0.503317i	−0.113083	−	0.0170444i
$873$	28.9239	−	19.7200i	0.978925	−	0.667420i
$874$	7.79872	+	19.8708i	0.263796	+	0.672140i
$875$	−0.645787	−	0.199199i	−0.0218316	−	0.00673415i
$876$	−7.85208	+	3.78136i	−0.265297	+	0.127760i
$877$	−1.58876	+	21.2005i	−0.0536485	+	0.715889i	0.903923	+	0.427695i	$0.140674\pi$
$877$	−1.58876	+	21.2005i	−0.0536485	+	0.715889i	−0.957572	+	0.288195i	$0.906945\pi$
$878$	−8.18311	+	1.23341i	−0.276167	+	0.0416254i
$879$	1.64508	−	1.52641i	0.0554872	−	0.0514846i
$880$	2.42637	−	0.748436i	0.0817929	−	0.0252298i
$881$	−2.91871	−	3.65994i	−0.0983337	−	0.123307i	0.730230	−	0.683201i	$-0.239413\pi$
$881$	−2.91871	−	3.65994i	−0.0983337	−	0.123307i	−0.828564	+	0.559895i	$0.810842\pi$
$882$	9.09825	+	11.4088i	0.306354	+	0.384156i
$883$	23.4687	−	7.23914i	0.789785	−	0.243617i	0.126484	−	0.991969i	$-0.459631\pi$
$883$	23.4687	−	7.23914i	0.789785	−	0.243617i	0.663302	+	0.748352i	$0.269155\pi$
$884$	−7.73161	+	7.17389i	−0.260042	+	0.241284i
$885$	−0.554046	+	0.0835090i	−0.0186240	+	0.00280712i
$886$	1.85877	−	24.8036i	0.0624467	−	0.833293i
$887$	−12.2652	+	5.90659i	−0.411824	+	0.198324i	−0.628312	−	0.777961i	$-0.716254\pi$
$887$	−12.2652	+	5.90659i	−0.411824	+	0.198324i	0.216489	+	0.976285i	$0.430540\pi$
$888$	−4.82820	−	1.48930i	−0.162024	−	0.0499777i
$889$	1.30464	+	3.32416i	0.0437561	+	0.111489i
$890$	8.06590	−	5.49924i	0.270370	−	0.184335i
$891$	6.68876	+	1.00817i	0.224082	+	0.0337749i
$892$	5.90215	−	25.8590i	0.197619	−	0.865824i
$893$	23.3917	+	15.9482i	0.782773	+	0.533686i
$894$	14.5949	+	13.5421i	0.488126	+	0.452914i
$895$	8.85185	+	4.26283i	0.295885	+	0.142491i
$896$	−0.337906	+	0.585270i	−0.0112886	+	0.0195525i
$897$	−11.1723	−	19.3510i	−0.373032	−	0.646110i
$898$	2.53636	+	33.8453i	0.0846393	+	1.12943i
$899$	−5.05084	−	22.1292i	−0.168455	−	0.738049i
$900$	−0.814763	+	2.07598i	−0.0271588	+	0.0691994i
$901$	5.20576	−	6.52782i	0.173429	−	0.217473i
$902$	−2.26349			−0.0753659
$903$	−2.37558	+	3.07828i	−0.0790542	+	0.102439i
$904$	12.8202			0.426394
$905$	−7.01833	+	8.80071i	−0.233297	+	0.292546i
$906$	1.41087	−	3.59485i	0.0468731	−	0.119431i
$907$	−12.7538	−	55.8778i	−0.423481	−	1.85539i	−0.511513	−	0.859275i	$-0.670915\pi$
$907$	−12.7538	−	55.8778i	−0.423481	−	1.85539i	0.0880321	−	0.996118i	$-0.471942\pi$
$908$	0.373484	+	4.98379i	0.0123945	+	0.165393i
$909$	5.92731	+	10.2664i	0.196597	+	0.340515i
$910$	2.34131	−	4.05527i	0.0776137	−	0.134431i
$911$	−39.1188	−	18.8386i	−1.29606	−	0.624151i	−0.346594	−	0.938015i	$-0.612662\pi$
$911$	−39.1188	−	18.8386i	−1.29606	−	0.624151i	−0.949468	+	0.313865i	$0.898376\pi$
$912$	−3.73560	−	3.46613i	−0.123698	−	0.114775i
$913$	25.4549	+	17.3549i	0.842434	+	0.574362i
$914$	2.37042	−	10.3855i	0.0784066	−	0.343522i
$915$	−2.26569	−	0.341498i	−0.0749015	−	0.0112896i
$916$	−0.0809041	+	0.0551595i	−0.00267315	+	0.00182252i
$917$	−2.46652	−	6.28458i	−0.0814515	−	0.207535i
$918$	6.67504	+	2.05898i	0.220309	+	0.0679563i
$919$	−7.47804	+	3.60124i	−0.246678	+	0.118794i	−0.553138	−	0.833090i	$-0.686570\pi$
$919$	−7.47804	+	3.60124i	−0.246678	+	0.118794i	0.306460	+	0.951884i	$0.400855\pi$
$920$	0.274662	−	3.66511i	0.00905535	−	0.120835i
$921$	−21.3827	+	3.22292i	−0.704584	+	0.106199i
$922$	−0.233439	+	0.216599i	−0.00768789	+	0.00713332i
$923$	−8.68312	+	2.67839i	−0.285808	+	0.0881602i
$924$	0.938755	+	1.17716i	0.0308828	+	0.0387258i
$925$	3.59043	+	4.50225i	0.118053	+	0.148033i
$926$	24.7542	−	7.63567i	0.813475	−	0.250924i
$927$	−19.5581	+	18.1473i	−0.642374	+	0.596036i
$928$	−9.26010	+	1.39574i	−0.303978	+	0.0458173i
$929$	−3.29479	+	43.9660i	−0.108099	+	1.44248i	0.634595	+	0.772845i	$0.281167\pi$
$929$	−3.29479	+	43.9660i	−0.108099	+	1.44248i	−0.742694	+	0.669631i	$0.766452\pi$
$930$	−1.91608	+	0.922735i	−0.0628307	+	0.0302577i
$931$	36.3145	+	11.2015i	1.19016	+	0.367116i
$932$	1.13789	+	2.89928i	0.0372727	+	0.0949692i
$933$	−4.71211	+	3.21266i	−0.154267	+	0.105178i
$934$	2.00848	+	0.302730i	0.0657196	+	0.00990563i
$935$	−0.860073	+	3.76823i	−0.0281274	+	0.123234i
$936$	−12.7674	−	8.70466i	−0.417315	−	0.284521i
$937$	−31.8945	−	29.5938i	−1.04195	−	0.966787i	−0.0424712	−	0.999098i	$-0.513523\pi$
$937$	−31.8945	−	29.5938i	−1.04195	−	0.966787i	−0.999478	+	0.0323102i	$0.989714\pi$
$938$	−8.37940	−	4.03531i	−0.273597	−	0.131757i
$939$	−1.09355	+	1.89408i	−0.0356866	+	0.0618109i
$940$	−2.43728	−	4.22149i	−0.0794952	−	0.137690i
$941$	−0.186208	−	2.48478i	−0.00607022	−	0.0810014i	0.993346	−	0.115169i	$-0.0367410\pi$
$941$	−0.186208	−	2.48478i	−0.00607022	−	0.0810014i	−0.999416	+	0.0341677i	$0.989122\pi$
$942$	0.0361437	+	0.158356i	0.00117763	+	0.00515952i
$943$	−1.19698	+	3.04986i	−0.0389790	+	0.0993169i
$944$	0.398151	−	0.499266i	0.0129587	−	0.0162497i
$945$	−3.10130			−0.100885
$946$	−10.1726	+	13.1817i	−0.330740	+	0.428574i
$947$	44.1564			1.43489			0.717445	−	0.696615i	$-0.245311\pi$
$947$	44.1564			1.43489			0.717445	+	0.696615i	$0.245311\pi$
$948$	5.03346	−	6.31177i	0.163479	−	0.204997i
$949$	−25.1439	+	64.0656i	−0.816205	+	2.07966i
$950$	1.29239	+	5.66231i	0.0419305	+	0.183710i
$951$	1.59506	+	21.2846i	0.0517235	+	0.690202i
$952$	−0.514360	−	0.890898i	−0.0166705	−	0.0288742i
$953$	−1.08441	+	1.87825i	−0.0351275	+	0.0608426i	−0.883055	−	0.469270i	$-0.844517\pi$
$953$	−1.08441	+	1.87825i	−0.0351275	+	0.0608426i	0.847927	+	0.530113i	$0.177850\pi$
$954$	11.0211	+	5.30750i	0.356822	+	0.171837i
$955$	18.1540	+	16.8444i	0.587448	+	0.545072i
$956$	−22.4027	−	15.2739i	−0.724556	−	0.493994i
$957$	−4.64261	+	20.3406i	−0.150074	+	0.657518i
$958$	−15.7226	−	2.36980i	−0.507974	−	0.0765647i
$959$	9.87749	−	6.73436i	0.318961	−	0.217464i
$960$	0.320555	+	0.816762i	0.0103459	+	0.0263609i
$961$	−24.0089	−	7.40576i	−0.774481	−	0.238896i
$962$	−35.9493	+	17.3123i	−1.15905	+	0.558170i
$963$	2.46427	−	32.8833i	0.0794098	−	1.05965i
$964$	−15.2808	+	2.30321i	−0.492161	+	0.0741814i
$965$	−10.1006	+	9.37195i	−0.325148	+	0.301694i
$966$	2.08256	−	0.642385i	0.0670053	−	0.0206684i
$967$	−17.5386	−	21.9927i	−0.564002	−	0.707236i	0.415290	−	0.909689i	$-0.363680\pi$
$967$	−17.5386	−	21.9927i	−0.564002	−	0.707236i	−0.979292	+	0.202453i	$0.935109\pi$
$968$	−2.83849	−	3.55935i	−0.0912324	−	0.114402i
$969$	7.41244	−	2.28644i	0.238122	−	0.0734509i
$970$	−11.5068	+	10.6767i	−0.369460	+	0.342808i
$971$	−7.81066	+	1.17727i	−0.250656	+	0.0377803i	−0.273168	−	0.961966i	$-0.588072\pi$
$971$	−7.81066	+	1.17727i	−0.250656	+	0.0377803i	0.0225123	+	0.999747i	$0.492834\pi$
$972$	−1.20348	+	16.0594i	−0.0386018	+	0.515105i
$973$	−7.94631	+	3.82674i	−0.254747	+	0.122680i
$974$	9.80858	+	3.02555i	0.314287	+	0.0969448i
$975$	−2.22109	−	5.65925i	−0.0711319	−	0.181241i
$976$	2.15764	−	1.47106i	0.0690645	−	0.0470874i
$977$	−13.5596	−	2.04378i	−0.433810	−	0.0653863i	−0.0714926	−	0.997441i	$-0.522776\pi$
$977$	−13.5596	−	2.04378i	−0.433810	−	0.0653863i	−0.362317	+	0.932055i	$0.618014\pi$
$978$	0.774183	−	3.39192i	0.0247556	−	0.108462i
$979$	20.4808	+	13.9635i	0.654568	+	0.446277i
$980$	−4.79656	−	4.45056i	−0.153221	−	0.142168i
$981$	6.78539	+	3.26767i	0.216641	+	0.104329i
$982$	−13.2288	+	22.9129i	−0.422147	+	0.731180i
$983$	15.3047	+	26.5086i	0.488145	+	0.845493i	0.999907	−	0.0136348i	$-0.00434022\pi$
$983$	15.3047	+	26.5086i	0.488145	+	0.845493i	−0.511762	+	0.859128i	$0.671007\pi$
$984$	−0.0584501	−	0.779962i	−0.00186332	−	0.0248643i
$985$	2.55340	+	11.1872i	0.0813580	+	0.356453i
$986$	5.20791	−	13.2695i	0.165854	−	0.422588i
$987$	1.80216	−	2.25984i	0.0573635	−	0.0719316i
$988$	−40.2425			−1.28028
$989$	12.3817	+	20.6775i	0.393716	+	0.657506i
$990$	−5.66273			−0.179973
$991$	13.3471	−	16.7367i	0.423984	−	0.531659i	−0.523260	−	0.852173i	$-0.675284\pi$
$991$	13.3471	−	16.7367i	0.423984	−	0.531659i	0.947244	+	0.320514i	$0.103856\pi$
$992$	0.885518	−	2.25626i	0.0281152	−	0.0716364i
$993$	−0.307538	−	1.34741i	−0.00975944	−	0.0427589i
$994$	−0.0662322	−	0.883808i	−0.00210076	−	0.0280327i
$995$	4.76004	+	8.24462i	0.150903	+	0.261372i
$996$	−5.32289	+	9.21952i	−0.168662	+	0.292132i
$997$	−6.76241	−	3.25661i	−0.214168	−	0.103138i	0.323724	−	0.946151i	$-0.395065\pi$
$997$	−6.76241	−	3.25661i	−0.214168	−	0.103138i	−0.537892	+	0.843014i	$0.680779\pi$
$998$	−24.5293	−	22.7598i	−0.776460	−	0.720450i
$999$	21.8344	+	14.8864i	0.690809	+	0.470986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.101.2	✓	48
43.23	even	21	inner	430.2.q.b.281.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.101.2	✓	48	1.1	even	1	trivial
430.2.q.b.281.2	yes	48	43.23	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.320555 + 0.816762i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.438707 + 0.759863i) q^{6} +(-0.337906 + 0.585270i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(1.63481 + 1.51688i) q^{9} +O(q^{10})\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.320555 + 0.816762i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.438707 + 0.759863i) q^{6} +(-0.337906 + 0.585270i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(1.63481 + 1.51688i) q^{9} +(-0.826239 - 0.563320i) q^{10} +(0.565020 - 2.47551i) q^{11} +(0.867614 + 0.130772i) q^{12} +(5.72492 - 3.90318i) q^{13} +(0.246902 + 0.629095i) q^{14} +(0.838433 + 0.258622i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.113754 - 1.51794i) q^{17} +(2.20524 - 0.332386i) q^{18} +(4.25751 - 3.95039i) q^{19} +(-0.955573 + 0.294755i) q^{20} +(-0.369709 - 0.463600i) q^{21} +(-1.58315 - 1.98521i) q^{22} +(-3.51210 + 1.08334i) q^{23} +(0.643190 - 0.596793i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.517797 - 6.90952i) q^{26} +(-4.13455 + 1.99109i) q^{27} +(0.645787 + 0.199199i) q^{28} +(3.42131 + 8.71735i) q^{29} +(0.724954 - 0.494265i) q^{30} +(-2.39674 - 0.361250i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(1.84079 + 1.25503i) q^{33} +(-1.11585 - 1.03536i) q^{34} +(0.608885 + 0.293224i) q^{35} +(1.11507 - 1.93136i) q^{36} +(-2.87930 - 4.98709i) q^{37} +(-0.434027 - 5.79169i) q^{38} +(1.35282 + 5.92708i) q^{39} +(-0.365341 + 0.930874i) q^{40} +(0.555795 - 0.696944i) q^{41} -0.592966 q^{42} +(-1.56088 - 6.36896i) q^{43} -2.53918 q^{44} +(1.39047 - 1.74360i) q^{45} +(-1.34277 + 3.42132i) q^{46} +(1.08469 + 4.75234i) q^{47} +(-0.0655692 - 0.874961i) q^{48} +(3.27164 + 5.66665i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.20333 + 0.579495i) q^{51} +(-5.07924 - 4.71284i) q^{52} +(4.53199 + 3.08986i) q^{53} +(-1.02115 + 4.47395i) q^{54} +(-2.51082 - 0.378445i) q^{55} +(0.558382 - 0.380698i) q^{56} +(1.86176 + 4.74369i) q^{57} +(8.94865 + 2.76029i) q^{58} +(-0.575346 + 0.277072i) q^{59} +(0.0655692 - 0.874961i) q^{60} +(-2.58224 + 0.389210i) q^{61} +(-1.77678 + 1.64861i) q^{62} +(-1.44020 + 0.444242i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-4.32009 - 5.41723i) q^{65} +(2.12893 - 0.656688i) q^{66} +(-10.0882 + 9.36045i) q^{67} +(-1.50520 + 0.226872i) q^{68} +(0.240993 - 3.21582i) q^{69} +(0.608885 - 0.293224i) q^{70} +(-1.25318 - 0.386554i) q^{71} +(-0.814763 - 2.07598i) q^{72} +(-8.20684 + 5.59533i) q^{73} +(-5.69428 - 0.858275i) q^{74} +(0.195243 - 0.855416i) q^{75} +(-4.79874 - 3.27172i) q^{76} +(1.25792 + 1.16718i) q^{77} +(5.47745 + 2.63780i) q^{78} +(4.60048 - 7.96826i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.199079 + 2.65653i) q^{81} +(-0.198361 - 0.869075i) q^{82} +(-4.43273 + 11.2944i) q^{83} +(-0.369709 + 0.463600i) q^{84} -1.52220 q^{85} +(-5.95265 - 2.75063i) q^{86} -8.21672 q^{87} +(-1.58315 + 1.98521i) q^{88} +(-3.56653 + 9.08737i) q^{89} +(-0.496254 - 2.17423i) q^{90} +(0.349933 + 4.66953i) q^{91} +(1.83770 + 3.18298i) q^{92} +(1.06334 - 1.84176i) q^{93} +(4.39182 + 2.11499i) q^{94} +(-4.25751 - 3.95039i) q^{95} +(-0.724954 - 0.494265i) q^{96} +(3.49292 - 15.3035i) q^{97} +(6.47020 + 0.975225i) q^{98} +(4.67877 - 3.18993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

L-functions

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