LMFDB - Embedded newform 735.2.u.b.211.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(106,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("735.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.u (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			211.7
Character	$\chi$	$=$	735.211
Dual form			735.2.u.b.526.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.414664 - 1.81676i) q^{2} +(0.623490 - 0.781831i) q^{3} +(-1.32673 - 0.638921i) q^{4} +(0.623490 - 0.781831i) q^{5} +(-1.16186 - 1.45693i) q^{6} +(-1.39768 - 2.24644i) q^{7} +(0.612808 - 0.768437i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-1.16186 - 1.45693i) q^{10} +(0.588199 - 2.57707i) q^{11} +(-1.32673 + 0.638921i) q^{12} +(-1.09145 + 4.78194i) q^{13} +(-4.66081 + 1.60773i) q^{14} +(-0.222521 - 0.974928i) q^{15} +(-2.97821 - 3.73456i) q^{16} +(-0.367983 + 0.177211i) q^{17} -1.86348 q^{18} +2.86965 q^{19} +(-1.32673 + 0.638921i) q^{20} +(-2.62778 - 0.307883i) q^{21} +(-4.43801 - 2.13723i) q^{22} +(3.19557 + 1.53891i) q^{23} +(-0.218709 - 0.958226i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(8.23505 + 3.96579i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(0.419050 + 3.87343i) q^{28} +(0.312801 - 0.150637i) q^{29} -1.86348 q^{30} +0.169086 q^{31} +(-6.24869 + 3.00921i) q^{32} +(-1.64810 - 2.06665i) q^{33} +(0.169361 + 0.742021i) q^{34} +(-2.62778 - 0.307883i) q^{35} +(-0.327676 + 1.43564i) q^{36} +(-5.12827 + 2.46965i) q^{37} +(1.18994 - 5.21347i) q^{38} +(3.05816 + 3.83481i) q^{39} +(-0.218709 - 0.958226i) q^{40} +(-1.35858 + 1.70360i) q^{41} +(-1.64899 + 4.64637i) q^{42} +(-5.16523 - 6.47699i) q^{43} +(-2.42693 + 3.04327i) q^{44} +(-0.900969 - 0.433884i) q^{45} +(4.12092 - 5.16746i) q^{46} +(1.06876 - 4.68256i) q^{47} -4.77668 q^{48} +(-3.09299 + 6.27961i) q^{49} -1.86348 q^{50} +(-0.0908844 + 0.398190i) q^{51} +(4.50334 - 5.64701i) q^{52} +(1.37791 + 0.663564i) q^{53} +(-1.16186 + 1.45693i) q^{54} +(-1.64810 - 2.06665i) q^{55} +(-2.58276 - 0.302608i) q^{56} +(1.78920 - 2.24359i) q^{57} +(-0.143964 - 0.630749i) q^{58} +(4.42037 + 5.54297i) q^{59} +(-0.327676 + 1.43564i) q^{60} +(9.04769 - 4.35714i) q^{61} +(0.0701138 - 0.307189i) q^{62} +(-1.87910 + 1.86252i) q^{63} +(0.750086 + 3.28634i) q^{64} +(3.05816 + 3.83481i) q^{65} +(-4.43801 + 2.13723i) q^{66} +6.15332 q^{67} +0.601440 q^{68} +(3.19557 - 1.53891i) q^{69} +(-1.64899 + 4.64637i) q^{70} +(7.02539 + 3.38325i) q^{71} +(-0.885534 - 0.426451i) q^{72} +(-1.42656 - 6.25017i) q^{73} +(2.36025 + 10.3409i) q^{74} +(-0.900969 - 0.433884i) q^{75} +(-3.80727 - 1.83348i) q^{76} +(-6.61134 + 2.28056i) q^{77} +(8.23505 - 3.96579i) q^{78} +8.15231 q^{79} -4.77668 q^{80} +(-0.900969 + 0.433884i) q^{81} +(2.53168 + 3.17463i) q^{82} +(2.94782 + 12.9152i) q^{83} +(3.28965 + 2.08742i) q^{84} +(-0.0908844 + 0.398190i) q^{85} +(-13.9090 + 6.69821i) q^{86} +(0.0772556 - 0.338479i) q^{87} +(-1.61986 - 2.03124i) q^{88} +(3.84634 + 16.8519i) q^{89} +(-1.16186 + 1.45693i) q^{90} +(12.2678 - 4.23175i) q^{91} +(-3.25644 - 4.08344i) q^{92} +(0.105423 - 0.132197i) q^{93} +(-8.06391 - 3.88337i) q^{94} +(1.78920 - 2.24359i) q^{95} +(-1.54330 + 6.76164i) q^{96} -14.0274 q^{97} +(10.1260 + 8.22314i) q^{98} -2.64334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.414664	−	1.81676i	0.293211	−	1.28464i	−0.586816	−	0.809720i	$-0.699619\pi$
$2$	0.414664	−	1.81676i	0.293211	−	1.28464i	0.880027	−	0.474923i	$-0.157524\pi$
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$4$	−1.32673	−	0.638921i	−0.663367	−	0.319461i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$6$	−1.16186	−	1.45693i	−0.474328	−	0.594789i
$7$	−1.39768	−	2.24644i	−0.528273	−	0.849075i
$7$	−1.39768	−	2.24644i	−0.528273	−	0.849075i
$8$	0.612808	−	0.768437i	0.216660	−	0.271684i
$9$	−0.222521	−	0.974928i	−0.0741736	−	0.324976i
$10$	−1.16186	−	1.45693i	−0.367413	−	0.460721i
$11$	0.588199	−	2.57707i	0.177349	−	0.777015i	−0.805499	−	0.592597i	$-0.798103\pi$
$11$	0.588199	−	2.57707i	0.177349	−	0.777015i	0.982848	−	0.184418i	$-0.0590402\pi$
$12$	−1.32673	+	0.638921i	−0.382995	+	0.184441i
$13$	−1.09145	+	4.78194i	−0.302713	+	1.32627i	0.563302	+	0.826251i	$0.309531\pi$
$13$	−1.09145	+	4.78194i	−0.302713	+	1.32627i	−0.866014	+	0.500019i	$0.833326\pi$
$14$	−4.66081	+	1.60773i	−1.24565	+	0.429684i
$15$	−0.222521	−	0.974928i	−0.0574547	−	0.251725i
$16$	−2.97821	−	3.73456i	−0.744553	−	0.933640i
$17$	−0.367983	+	0.177211i	−0.0892491	+	0.0429801i	−0.477976	−	0.878373i	$-0.658629\pi$
$17$	−0.367983	+	0.177211i	−0.0892491	+	0.0429801i	0.388727	+	0.921353i	$0.372915\pi$
$18$	−1.86348			−0.439227
$19$	2.86965			0.658344			0.329172	−	0.944270i	$-0.393230\pi$
$19$	2.86965			0.658344			0.329172	+	0.944270i	$0.393230\pi$
$20$	−1.32673	+	0.638921i	−0.296667	+	0.142867i
$21$	−2.62778	−	0.307883i	−0.573428	−	0.0671855i
$22$	−4.43801	−	2.13723i	−0.946187	−	0.455660i
$23$	3.19557	+	1.53891i	0.666323	+	0.320884i	0.736291	−	0.676665i	$-0.236575\pi$
$23$	3.19557	+	1.53891i	0.666323	+	0.320884i	−0.0699678	+	0.997549i	$0.522290\pi$
$24$	−0.218709	−	0.958226i	−0.0446437	−	0.195597i
$25$	−0.222521	−	0.974928i	−0.0445042	−	0.194986i
$26$	8.23505	+	3.96579i	1.61503	+	0.777755i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	0.419050	+	3.87343i	0.0791930	+	0.732010i
$29$	0.312801	−	0.150637i	0.0580858	−	0.0279726i	−0.404615	−	0.914487i	$-0.632595\pi$
$29$	0.312801	−	0.150637i	0.0580858	−	0.0279726i	0.462701	+	0.886514i	$0.346880\pi$
$30$	−1.86348			−0.340224
$31$	0.169086			0.0303687			0.0151844	−	0.999885i	$-0.495166\pi$
$31$	0.169086			0.0303687			0.0151844	+	0.999885i	$0.495166\pi$
$32$	−6.24869	+	3.00921i	−1.10462	+	0.531958i
$33$	−1.64810	−	2.06665i	−0.286897	−	0.359757i
$34$	0.169361	+	0.742021i	0.0290452	+	0.127255i
$35$	−2.62778	−	0.307883i	−0.444175	−	0.0520417i
$36$	−0.327676	+	1.43564i	−0.0546127	+	0.239274i
$37$	−5.12827	+	2.46965i	−0.843083	+	0.406007i	−0.805005	−	0.593268i	$-0.797838\pi$
$37$	−5.12827	+	2.46965i	−0.843083	+	0.406007i	−0.0380773	+	0.999275i	$0.512123\pi$
$38$	1.18994	−	5.21347i	0.193034	−	0.845737i
$39$	3.05816	+	3.83481i	0.489698	+	0.614062i
$40$	−0.218709	−	0.958226i	−0.0345809	−	0.151509i
$41$	−1.35858	+	1.70360i	−0.212174	+	0.266058i	−0.876518	−	0.481369i	$-0.840140\pi$
$41$	−1.35858	+	1.70360i	−0.212174	+	0.266058i	0.664344	+	0.747427i	$0.268711\pi$
$42$	−1.64899	+	4.64637i	−0.254445	+	0.716951i
$43$	−5.16523	−	6.47699i	−0.787690	−	0.987732i	−0.999945	−	0.0105178i	$-0.996652\pi$
$43$	−5.16523	−	6.47699i	−0.787690	−	0.987732i	0.212254	−	0.977214i	$-0.431919\pi$
$44$	−2.42693	+	3.04327i	−0.365873	+	0.458790i
$45$	−0.900969	−	0.433884i	−0.134309	−	0.0646796i
$46$	4.12092	−	5.16746i	0.607596	−	0.761901i
$47$	1.06876	−	4.68256i	0.155895	−	0.683021i	−0.835209	−	0.549933i	$-0.814653\pi$
$47$	1.06876	−	4.68256i	0.155895	−	0.683021i	0.991104	−	0.133089i	$-0.0424895\pi$
$48$	−4.77668			−0.689455
$49$	−3.09299	+	6.27961i	−0.441855	+	0.897086i
$50$	−1.86348			−0.263536
$51$	−0.0908844	+	0.398190i	−0.0127264	+	0.0557578i
$52$	4.50334	−	5.64701i	0.624501	−	0.783099i
$53$	1.37791	+	0.663564i	0.189270	+	0.0911476i	0.526119	−	0.850411i	$-0.323647\pi$
$53$	1.37791	+	0.663564i	0.189270	+	0.0911476i	−0.336849	+	0.941559i	$0.609361\pi$
$54$	−1.16186	+	1.45693i	−0.158109	+	0.198263i
$55$	−1.64810	−	2.06665i	−0.222229	−	0.278667i
$56$	−2.58276	−	0.302608i	−0.345136	−	0.0404377i
$57$	1.78920	−	2.24359i	0.236985	−	0.297170i
$58$	−0.143964	−	0.630749i	−0.0189034	−	0.0828214i
$59$	4.42037	+	5.54297i	0.575484	+	0.721634i	0.981335	−	0.192305i	$-0.0615964\pi$
$59$	4.42037	+	5.54297i	0.575484	+	0.721634i	−0.405852	+	0.913939i	$0.633025\pi$
$60$	−0.327676	+	1.43564i	−0.0423028	+	0.185341i
$61$	9.04769	−	4.35714i	1.15844	−	0.557875i	0.246881	−	0.969046i	$-0.420594\pi$
$61$	9.04769	−	4.35714i	1.15844	−	0.557875i	0.911558	+	0.411171i	$0.134880\pi$
$62$	0.0701138	−	0.307189i	0.00890446	−	0.0390130i
$63$	−1.87910	+	1.86252i	−0.236745	+	0.234655i
$64$	0.750086	+	3.28634i	0.0937607	+	0.410793i
$65$	3.05816	+	3.83481i	0.379318	+	0.475650i
$66$	−4.43801	+	2.13723i	−0.546281	+	0.263075i
$67$	6.15332			0.751748			0.375874	−	0.926671i	$-0.377343\pi$
$67$	6.15332			0.751748			0.375874	+	0.926671i	$0.377343\pi$
$68$	0.601440			0.0729353
$69$	3.19557	−	1.53891i	0.384702	−	0.185263i
$70$	−1.64899	+	4.64637i	−0.197092	+	0.555348i
$71$	7.02539	+	3.38325i	0.833760	+	0.401518i	0.801524	−	0.597963i	$-0.204023\pi$
$71$	7.02539	+	3.38325i	0.833760	+	0.401518i	0.0322361	+	0.999480i	$0.489737\pi$
$72$	−0.885534	−	0.426451i	−0.104361	−	0.0502577i
$73$	−1.42656	−	6.25017i	−0.166966	−	0.731527i	−0.987199	−	0.159496i	$-0.949013\pi$
$73$	−1.42656	−	6.25017i	−0.166966	−	0.731527i	0.820232	−	0.572031i	$-0.193844\pi$
$74$	2.36025	+	10.3409i	0.274373	+	1.20211i
$75$	−0.900969	−	0.433884i	−0.104035	−	0.0501006i
$76$	−3.80727	−	1.83348i	−0.436723	−	0.210315i
$77$	−6.61134	+	2.28056i	−0.753432	+	0.259894i
$78$	8.23505	−	3.96579i	0.932436	−	0.449037i
$79$	8.15231			0.917206			0.458603	−	0.888641i	$-0.348350\pi$
$79$	8.15231			0.917206			0.458603	+	0.888641i	$0.348350\pi$
$80$	−4.77668			−0.534049
$81$	−0.900969	+	0.433884i	−0.100108	+	0.0482093i
$82$	2.53168	+	3.17463i	0.279577	+	0.350579i
$83$	2.94782	+	12.9152i	0.323565	+	1.41763i	0.831159	+	0.556035i	$0.187678\pi$
$83$	2.94782	+	12.9152i	0.323565	+	1.41763i	−0.507594	+	0.861597i	$0.669465\pi$
$84$	3.28965	+	2.08742i	0.358930	+	0.227756i
$85$	−0.0908844	+	0.398190i	−0.00985779	+	0.0431898i
$86$	−13.9090	+	6.69821i	−1.49984	+	0.722287i
$87$	0.0772556	−	0.338479i	0.00828267	−	0.0362887i
$88$	−1.61986	−	2.03124i	−0.172678	−	0.216531i
$89$	3.84634	+	16.8519i	0.407711	+	1.78630i	0.594711	+	0.803939i	$0.297266\pi$
$89$	3.84634	+	16.8519i	0.407711	+	1.78630i	−0.187000	+	0.982360i	$0.559877\pi$
$90$	−1.16186	+	1.45693i	−0.122471	+	0.153574i
$91$	12.2678	−	4.23175i	1.28602	−	0.443607i
$92$	−3.25644	−	4.08344i	−0.339507	−	0.425728i
$93$	0.105423	−	0.132197i	0.0109319	−	0.0137082i
$94$	−8.06391	−	3.88337i	−0.831729	−	0.400539i
$95$	1.78920	−	2.24359i	0.183568	−	0.230187i
$96$	−1.54330	+	6.76164i	−0.157512	+	0.690107i
$97$	−14.0274			−1.42427			−0.712134	−	0.702044i	$-0.752271\pi$
$97$	−14.0274			−1.42427			−0.712134	+	0.702044i	$0.752271\pi$
$98$	10.1260	+	8.22314i	1.02288	+	0.830662i
$99$	−2.64334			−0.265666
$100$	−0.327676	+	1.43564i	−0.0327676	+	0.143564i
$101$	12.3369	−	15.4699i	1.22756	−	1.53932i	0.476352	−	0.879254i	$-0.341959\pi$
$101$	12.3369	−	15.4699i	1.22756	−	1.53932i	0.751211	−	0.660062i	$-0.229470\pi$
$102$	0.685730	+	0.330230i	0.0678974	+	0.0326977i
$103$	9.40291	−	11.7909i	0.926497	−	1.16179i	−0.0600312	−	0.998197i	$-0.519120\pi$
$103$	9.40291	−	11.7909i	0.926497	−	1.16179i	0.986528	−	0.163594i	$-0.0523086\pi$
$104$	3.00577	+	3.76912i	0.294740	+	0.369592i
$105$	−1.87910	+	1.86252i	−0.183382	+	0.181763i
$106$	1.77690	−	2.22817i	0.172588	−	0.216419i
$107$	0.793229	+	3.47536i	0.0766843	+	0.335976i	0.998688	−	0.0512047i	$-0.0163061\pi$
$107$	0.793229	+	3.47536i	0.0766843	+	0.335976i	−0.922004	+	0.387181i	$0.873449\pi$
$108$	0.918128	+	1.15130i	0.0883469	+	0.110784i
$109$	2.31026	−	10.1219i	0.221282	−	0.969501i	−0.735232	−	0.677816i	$-0.762927\pi$
$109$	2.31026	−	10.1219i	0.221282	−	0.969501i	0.956514	−	0.291686i	$-0.0942161\pi$
$110$	−4.43801	+	2.13723i	−0.423148	+	0.203777i
$111$	−1.26658	+	5.54924i	−0.120218	+	0.526711i
$112$	−4.22688	+	11.9101i	−0.399403	+	1.12540i
$113$	−0.459199	−	2.01188i	−0.0431978	−	0.189262i	0.948725	−	0.316101i	$-0.102374\pi$
$113$	−0.459199	−	2.01188i	−0.0431978	−	0.189262i	−0.991923	+	0.126839i	$0.959517\pi$
$114$	−3.33414	−	4.18088i	−0.312271	−	0.391575i
$115$	3.19557	−	1.53891i	0.297989	−	0.143504i
$116$	−0.511249			−0.0474683
$117$	4.90491			0.453459
$118$	11.9032	−	5.73229i	1.09578	−	0.527700i
$119$	0.912417	+	0.578968i	0.0836412	+	0.0530739i
$120$	−0.885534	−	0.426451i	−0.0808378	−	0.0389294i
$121$	3.61535	+	1.74106i	0.328669	+	0.158278i
$122$	−4.16413	−	18.2442i	−0.377002	−	1.65176i
$123$	0.484870	+	2.12435i	0.0437193	+	0.191547i
$124$	−0.224332	−	0.108033i	−0.0201456	−	0.00970162i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	2.60455	+	4.18620i	0.232032	+	0.372936i
$127$	−7.92496	+	3.81646i	−0.703227	+	0.338656i	−0.751092	−	0.660198i	$-0.770472\pi$
$127$	−7.92496	+	3.81646i	−0.703227	+	0.338656i	0.0478652	+	0.998854i	$0.484758\pi$
$128$	−7.58952			−0.670825
$129$	−8.28439			−0.729399
$130$	8.23505	−	3.96579i	0.722261	−	0.347823i
$131$	3.89885	+	4.88901i	0.340644	+	0.427155i	0.922416	−	0.386198i	$-0.126212\pi$
$131$	3.89885	+	4.88901i	0.340644	+	0.427155i	−0.581772	+	0.813352i	$0.697640\pi$
$132$	0.866160	+	3.79490i	0.0753896	+	0.330303i
$133$	−4.01086	−	6.44651i	−0.347785	−	0.558983i
$134$	2.55156	−	11.1791i	0.220421	−	0.965728i
$135$	−0.900969	+	0.433884i	−0.0775431	+	0.0373428i
$136$	−0.0893274	+	0.391369i	−0.00765976	+	0.0335596i
$137$	−5.14224	−	6.44816i	−0.439331	−	0.550904i	0.512036	−	0.858964i	$-0.328892\pi$
$137$	−5.14224	−	6.44816i	−0.439331	−	0.550904i	−0.951367	+	0.308060i	$0.900320\pi$
$138$	−1.47074	−	6.44372i	−0.125197	−	0.548526i
$139$	−4.01035	+	5.02882i	−0.340153	+	0.426539i	−0.922258	−	0.386575i	$-0.873658\pi$
$139$	−4.01035	+	5.02882i	−0.340153	+	0.426539i	0.582105	+	0.813114i	$0.302229\pi$
$140$	3.28965	+	2.08742i	0.278026	+	0.176419i
$141$	−2.99461	−	3.75512i	−0.252192	−	0.316238i
$142$	9.05972	−	11.3605i	0.760275	−	0.953355i
$143$	11.6814	+	5.62546i	0.976847	+	0.470425i
$144$	−2.97821	+	3.73456i	−0.248184	+	0.311213i
$145$	0.0772556	−	0.338479i	0.00641573	−	0.0281091i
$146$	−11.9466			−0.988707
$147$	2.98115	+	6.33346i	0.245881	+	0.522375i
$148$	8.38176			0.688976
$149$	0.694858	−	3.04437i	0.0569250	−	0.249405i	−0.938457	−	0.345395i	$-0.887745\pi$
$149$	0.694858	−	3.04437i	0.0569250	−	0.249405i	0.995382	+	0.0959908i	$0.0306019\pi$
$150$	−1.16186	+	1.45693i	−0.0948656	+	0.118958i
$151$	8.74294	+	4.21038i	0.711490	+	0.342636i	0.754374	−	0.656444i	$-0.227940\pi$
$151$	8.74294	+	4.21038i	0.711490	+	0.342636i	−0.0428840	+	0.999080i	$0.513655\pi$
$152$	1.75855	−	2.20515i	0.142637	−	0.178861i
$153$	0.254652	+	0.319324i	0.0205874	+	0.0258158i
$154$	1.40175	+	12.9569i	0.112956	+	1.04410i
$155$	0.105423	−	0.132197i	0.00846781	−	0.0106183i
$156$	−1.60722	−	7.04170i	−0.128681	−	0.563787i
$157$	9.74878	+	12.2246i	0.778038	+	0.975628i	1.00000		0.000573155i	$0.000182441\pi$
$157$	9.74878	+	12.2246i	0.778038	+	0.975628i	−0.221962	+	0.975055i	$0.571246\pi$
$158$	3.38047	−	14.8108i	0.268935	−	1.17828i
$159$	1.37791	−	0.663564i	0.109275	−	0.0526241i
$160$	−1.54330	+	6.76164i	−0.122009	+	0.534554i
$161$	−1.00932	−	9.32957i	−0.0795459	−	0.735273i
$162$	0.414664	+	1.81676i	0.0325791	+	0.142738i
$163$	−12.4910	−	15.6632i	−0.978369	−	1.22684i	−0.973931	−	0.226845i	$-0.927159\pi$
$163$	−12.4910	−	15.6632i	−0.978369	−	1.22684i	−0.00443782	−	0.999990i	$-0.501413\pi$
$164$	2.89093	−	1.39220i	0.225744	−	0.108713i
$165$	−2.64334			−0.205784
$166$	24.6862			1.91602
$167$	12.3545	−	5.94962i	0.956021	−	0.460396i	0.110228	−	0.993906i	$-0.464842\pi$
$167$	12.3545	−	5.94962i	0.956021	−	0.460396i	0.845793	+	0.533511i	$0.179128\pi$
$168$	−1.84691	+	1.83061i	−0.142492	+	0.141235i
$169$	−9.96306	−	4.79796i	−0.766389	−	0.369074i
$170$	0.685730	+	0.330230i	0.0525931	+	0.0253275i
$171$	−0.638558	−	2.79771i	−0.0488318	−	0.213946i
$172$	2.71460	+	11.8934i	0.206986	+	0.906865i
$173$	13.2462	+	6.37905i	1.00709	+	0.484990i	0.863340	−	0.504623i	$-0.168369\pi$
$173$	13.2462	+	6.37905i	1.00709	+	0.484990i	0.143753	+	0.989614i	$0.454083\pi$
$174$	−0.582900	−	0.280710i	−0.0441895	−	0.0212805i
$175$	−1.87910	+	1.86252i	−0.142047	+	0.140793i
$176$	−11.3760	+	5.47839i	−0.857499	+	0.412950i
$177$	7.08973			0.532897
$178$	32.2108			2.41430
$179$	−12.3532	+	5.94900i	−0.923323	+	0.444649i	−0.834256	−	0.551377i	$-0.814103\pi$
$179$	−12.3532	+	5.94900i	−0.923323	+	0.444649i	−0.0890665	+	0.996026i	$0.528388\pi$
$180$	0.918128	+	1.15130i	0.0684332	+	0.0858126i
$181$	−3.14196	−	13.7658i	−0.233540	−	1.02320i	−0.946678	−	0.322181i	$-0.895584\pi$
$181$	−3.14196	−	13.7658i	−0.233540	−	1.02320i	0.713138	−	0.701023i	$-0.247273\pi$
$182$	−2.60105	−	24.0424i	−0.192802	−	1.78214i
$183$	2.23460	−	9.79041i	0.165186	−	0.723728i
$184$	3.14083	−	1.51254i	0.231545	−	0.111506i
$185$	−1.26658	+	5.54924i	−0.0931207	+	0.407988i
$186$	−0.196455	−	0.246346i	−0.0144047	−	0.0180630i
$187$	0.240239	+	1.05255i	0.0175680	+	0.0769704i
$188$	−4.40975	+	5.52965i	−0.321614	+	0.403291i
$189$	0.284572	+	2.63040i	0.0206995	+	0.191334i
$190$	−3.33414	−	4.18088i	−0.241884	−	0.303313i
$191$	−4.26861	+	5.35267i	−0.308866	+	0.387306i	−0.911902	−	0.410408i	$-0.865386\pi$
$191$	−4.26861	+	5.35267i	−0.308866	+	0.387306i	0.603036	+	0.797714i	$0.293958\pi$
$192$	3.03704	+	1.46256i	0.219179	+	0.105551i
$193$	−4.92498	+	6.17573i	−0.354508	+	0.444539i	−0.926825	−	0.375494i	$-0.877473\pi$
$193$	−4.92498	+	6.17573i	−0.354508	+	0.444539i	0.572317	+	0.820032i	$0.306045\pi$
$194$	−5.81665	+	25.4844i	−0.417611	+	1.82968i
$195$	4.90491			0.351248
$196$	8.11574	−	6.35519i	0.579696	−	0.453942i
$197$	−18.7891			−1.33867			−0.669333	−	0.742962i	$-0.733420\pi$
$197$	−18.7891			−1.33867			−0.669333	+	0.742962i	$0.733420\pi$
$198$	−1.09610	+	4.80232i	−0.0778963	+	0.341286i
$199$	−4.78330	+	5.99806i	−0.339079	+	0.425191i	−0.921911	−	0.387401i	$-0.873373\pi$
$199$	−4.78330	+	5.99806i	−0.339079	+	0.425191i	0.582833	+	0.812592i	$0.301944\pi$
$200$	−0.885534	−	0.426451i	−0.0626167	−	0.0301546i
$201$	3.83653	−	4.81086i	0.270608	−	0.339332i
$202$	−22.9895	−	28.8279i	−1.61754	−	2.02833i
$203$	−0.775593	−	0.492147i	−0.0544360	−	0.0345419i
$204$	0.374992	−	0.470225i	0.0262547	−	0.0329223i
$205$	0.484870	+	2.12435i	0.0338648	+	0.148371i
$206$	−17.5222	−	21.9721i	−1.22083	−	1.53087i
$207$	0.789242	−	3.45789i	0.0548561	−	0.240340i
$208$	21.1090	−	10.1656i	1.46365	−	0.704854i
$209$	1.68793	−	7.39529i	0.116756	−	0.511543i
$210$	2.60455	+	4.18620i	0.179731	+	0.288875i
$211$	1.38057	+	6.04868i	0.0950424	+	0.416408i	0.999958	−	0.00918336i	$-0.00292319\pi$
$211$	1.38057	+	6.04868i	0.0950424	+	0.416408i	−0.904915	+	0.425592i	$0.860066\pi$
$212$	−1.40415	−	1.76075i	−0.0964373	−	0.120929i
$213$	7.02539	−	3.38325i	0.481372	−	0.231816i
$214$	6.64282			0.454094
$215$	−8.28439			−0.564990
$216$	−0.885534	+	0.426451i	−0.0602529	+	0.0290163i
$217$	−0.236328	−	0.379842i	−0.0160430	−	0.0257853i
$218$	−17.4311	−	8.39436i	−1.18058	−	0.568538i
$219$	−5.77602	−	2.78159i	−0.390307	−	0.187962i
$220$	0.866160	+	3.79490i	0.0583965	+	0.255852i
$221$	−0.445780	−	1.95309i	−0.0299864	−	0.131379i
$222$	9.55644	+	4.60214i	0.641386	+	0.308875i
$223$	−11.7102	−	5.63935i	−0.784176	−	0.377639i	−0.00144437	−	0.999999i	$-0.500460\pi$
$223$	−11.7102	−	5.63935i	−0.784176	−	0.377639i	−0.782731	+	0.622360i	$0.786174\pi$
$224$	15.4937	+	9.83140i	1.03522	+	0.656888i
$225$	−0.900969	+	0.433884i	−0.0600646	+	0.0289256i
$226$	−3.84552			−0.255800
$227$	16.4173			1.08966			0.544828	−	0.838548i	$-0.316595\pi$
$227$	16.4173			1.08966			0.544828	+	0.838548i	$0.316595\pi$
$228$	−3.80727	+	1.83348i	−0.252142	+	0.121425i
$229$	4.64119	+	5.81986i	0.306698	+	0.384587i	0.911164	−	0.412044i	$-0.135185\pi$
$229$	4.64119	+	5.81986i	0.306698	+	0.384587i	−0.604466	+	0.796631i	$0.706613\pi$
$230$	−1.47074	−	6.44372i	−0.0969776	−	0.424886i
$231$	−2.33909	+	6.59086i	−0.153901	+	0.433647i
$232$	0.0759320	−	0.332680i	0.00498518	−	0.0218415i
$233$	20.0143	−	9.63839i	1.31118	−	0.631432i	0.357969	−	0.933733i	$-0.383469\pi$
$233$	20.0143	−	9.63839i	1.31118	−	0.631432i	0.953212	+	0.302302i	$0.0977550\pi$
$234$	2.03389	−	8.91105i	0.132959	−	0.582533i
$235$	−2.99461	−	3.75512i	−0.195347	−	0.244957i
$236$	−2.32314	−	10.1783i	−0.151223	−	0.662552i
$237$	5.08288	−	6.37373i	0.330169	−	0.414018i
$238$	1.43019	−	1.41757i	0.0927056	−	0.0918872i
$239$	−14.5725	−	18.2733i	−0.942614	−	1.18200i	−0.983146	−	0.182822i	$-0.941477\pi$
$239$	−14.5725	−	18.2733i	−0.942614	−	1.18200i	0.0405318	−	0.999178i	$-0.487095\pi$
$240$	−2.97821	+	3.73456i	−0.192243	+	0.241065i
$241$	5.29722	+	2.55101i	0.341224	+	0.164325i	0.596645	−	0.802505i	$-0.296500\pi$
$241$	5.29722	+	2.55101i	0.341224	+	0.164325i	−0.255421	+	0.966830i	$0.582214\pi$
$242$	4.66225	−	5.84628i	0.299701	−	0.375813i
$243$	−0.222521	+	0.974928i	−0.0142747	+	0.0625417i
$244$	−14.7878			−0.946689
$245$	2.98115	+	6.33346i	0.190459	+	0.404630i
$246$	4.06050			0.258888
$247$	−3.13207	+	13.7225i	−0.199289	+	0.873142i
$248$	0.103617	−	0.129932i	0.00657971	−	0.00825069i
$249$	11.9355	+	5.74782i	0.756380	+	0.364253i
$250$	−1.16186	+	1.45693i	−0.0734826	+	0.0921443i
$251$	18.9938	+	23.8174i	1.19888	+	1.50334i	0.814497	+	0.580167i	$0.197013\pi$
$251$	18.9938	+	23.8174i	1.19888	+	1.50334i	0.384378	+	0.923176i	$0.374416\pi$
$252$	3.68307	−	1.27046i	0.232012	−	0.0800317i
$253$	5.84550	−	7.33003i	0.367504	−	0.460835i
$254$	3.64740	+	15.9803i	0.228858	+	1.00269i
$255$	0.254652	+	0.319324i	0.0159469	+	0.0199968i
$256$	−4.64727	+	20.3610i	−0.290454	+	1.27256i
$257$	11.8511	−	5.70718i	0.739250	−	0.356004i	−0.0260646	−	0.999660i	$-0.508298\pi$
$257$	11.8511	−	5.70718i	0.739250	−	0.356004i	0.765315	+	0.643656i	$0.222583\pi$
$258$	−3.43523	+	15.0507i	−0.213868	+	0.937018i
$259$	12.7156	+	8.06858i	0.790108	+	0.501357i
$260$	−1.60722	−	7.04170i	−0.0996757	−	0.436708i
$261$	−0.216465	−	0.271439i	−0.0133989	−	0.0168016i
$262$	10.4989	−	5.05599i	0.648622	−	0.312360i
$263$	−27.3095			−1.68398			−0.841989	−	0.539495i	$-0.818615\pi$
$263$	−27.3095			−1.68398			−0.841989	+	0.539495i	$0.818615\pi$
$264$	−2.59806			−0.159899
$265$	1.37791	−	0.663564i	0.0846441	−	0.0407624i
$266$	−13.3749	+	4.61363i	−0.820068	+	0.282880i
$267$	15.5735	+	7.49981i	0.953083	+	0.458981i
$268$	−8.16382	−	3.93149i	−0.498685	−	0.240154i
$269$	−1.84349	−	8.07686i	−0.112400	−	0.492455i	−0.999522	−	0.0309202i	$-0.990156\pi$
$269$	−1.84349	−	8.07686i	−0.112400	−	0.492455i	0.887122	−	0.461534i	$-0.152701\pi$
$270$	0.414664	+	1.81676i	0.0252356	+	0.110565i
$271$	2.21476	+	1.06657i	0.134537	+	0.0647896i	0.499941	−	0.866059i	$-0.333355\pi$
$271$	2.21476	+	1.06657i	0.134537	+	0.0647896i	−0.365404	+	0.930849i	$0.619069\pi$
$272$	1.75774	+	0.846483i	0.106579	+	0.0513256i
$273$	4.34035	−	12.2298i	0.262690	−	0.740182i
$274$	−13.8471	+	6.66840i	−0.836532	+	0.402853i
$275$	−2.64334			−0.159400
$276$	−5.22292			−0.314383
$277$	−10.9509	+	5.27365i	−0.657973	+	0.316863i	−0.732911	−	0.680325i	$-0.761839\pi$
$277$	−10.9509	+	5.27365i	−0.657973	+	0.316863i	0.0749373	+	0.997188i	$0.476124\pi$
$278$	7.47321	+	9.37111i	0.448213	+	0.562042i
$279$	−0.0376252	−	0.164847i	−0.00225256	−	0.00986911i
$280$	−1.84691	+	1.83061i	−0.110374	+	0.109400i
$281$	−3.07935	+	13.4915i	−0.183699	+	0.804837i	0.796150	+	0.605099i	$0.206866\pi$
$281$	−3.07935	+	13.4915i	−0.183699	+	0.804837i	−0.979849	+	0.199738i	$0.935991\pi$
$282$	−8.06391	+	3.88337i	−0.480199	+	0.231252i
$283$	−7.02749	+	30.7895i	−0.417741	+	1.83024i	0.127338	+	0.991859i	$0.459357\pi$
$283$	−7.02749	+	30.7895i	−0.417741	+	1.83024i	−0.545079	+	0.838384i	$0.683500\pi$
$284$	−7.15919	−	8.97734i	−0.424820	−	0.532707i
$285$	−0.638558	−	2.79771i	−0.0378249	−	0.165722i
$286$	15.0640	−	18.8896i	0.890751	−	1.11697i
$287$	5.72589	+	0.670872i	0.337989	+	0.0396003i
$288$	4.32423	+	5.42241i	0.254808	+	0.319519i
$289$	−10.4953	+	13.1607i	−0.617372	+	0.774160i
$290$	−0.582900	−	0.280710i	−0.0342290	−	0.0164838i
$291$	−8.74594	+	10.9671i	−0.512696	+	0.642901i
$292$	−2.10070	+	9.20377i	−0.122934	+	0.538610i
$293$	−1.80445			−0.105417			−0.0527085	−	0.998610i	$-0.516785\pi$
$293$	−1.80445			−0.105417			−0.0527085	+	0.998610i	$0.516785\pi$
$294$	12.7426	−	2.78977i	0.743161	−	0.162703i
$295$	7.08973			0.412780
$296$	−1.24488	+	5.45417i	−0.0723572	+	0.317017i
$297$	−1.64810	+	2.06665i	−0.0956323	+	0.119919i
$298$	−5.24276	−	2.52478i	−0.303705	−	0.146257i
$299$	−10.8468	+	13.6014i	−0.627284	+	0.786589i
$300$	0.918128	+	1.15130i	0.0530082	+	0.0664701i
$301$	−7.33084	+	20.6561i	−0.422543	+	1.19060i
$302$	11.2746	−	14.1379i	0.648782	−	0.813547i
$303$	−4.40298	−	19.2907i	−0.252944	−	1.10822i
$304$	−8.54644	−	10.7169i	−0.490172	−	0.614656i
$305$	2.23460	−	9.79041i	0.127953	−	0.560597i
$306$	0.685730	−	0.330230i	0.0392006	−	0.0188780i
$307$	−2.69911	+	11.8256i	−0.154047	+	0.674922i	0.837638	+	0.546227i	$0.183936\pi$
$307$	−2.69911	+	11.8256i	−0.154047	+	0.674922i	−0.991684	+	0.128696i	$0.958921\pi$
$308$	10.2286	+	1.19843i	0.582828	+	0.0682869i
$309$	−3.35586	−	14.7030i	−0.190908	−	0.836424i
$310$	−0.196455	−	0.246346i	−0.0111579	−	0.0139915i
$311$	−3.74894	+	1.80540i	−0.212583	+	0.102375i	−0.537145	−	0.843490i	$-0.680497\pi$
$311$	−3.74894	+	1.80540i	−0.212583	+	0.102375i	0.324562	+	0.945864i	$0.394783\pi$
$312$	4.82088			0.272929
$313$	−18.3995			−1.04000			−0.520001	−	0.854166i	$-0.674068\pi$
$313$	−18.3995			−1.04000			−0.520001	+	0.854166i	$0.674068\pi$
$314$	26.2516	−	12.6421i	1.48146	−	0.713436i
$315$	0.284572	+	2.63040i	0.0160338	+	0.148206i
$316$	−10.8159	−	5.20868i	−0.608444	−	0.293011i
$317$	11.8859	+	5.72394i	0.667577	+	0.321488i	0.736798	−	0.676113i	$-0.236337\pi$
$317$	11.8859	+	5.72394i	0.667577	+	0.321488i	−0.0692206	+	0.997601i	$0.522051\pi$
$318$	−0.634170	−	2.77848i	−0.0355625	−	0.155809i
$319$	−0.204213	−	0.894715i	−0.0114337	−	0.0500944i
$320$	3.03704	+	1.46256i	0.169775	+	0.0817596i
$321$	3.21172	+	1.54668i	0.179261	+	0.0863274i
$322$	−17.3681	−	2.03493i	−0.967887	−	0.113402i
$323$	−1.05598	+	0.508535i	−0.0587566	+	0.0282957i
$324$	1.47256			0.0818091
$325$	4.90491			0.272076
$326$	−33.6358	+	16.1982i	−1.86291	+	0.897133i
$327$	−6.47319	−	8.11713i	−0.357968	−	0.448878i
$328$	0.476563	+	2.08796i	0.0263138	+	0.115288i
$329$	−12.0129	+	4.14380i	−0.662291	+	0.228455i
$330$	−1.09610	+	4.80232i	−0.0603382	+	0.264359i
$331$	15.3943	−	7.41350i	0.846146	−	0.407483i	0.0400005	−	0.999200i	$-0.487264\pi$
$331$	15.3943	−	7.41350i	0.846146	−	0.407483i	0.806146	+	0.591717i	$0.201550\pi$
$332$	4.34085	−	19.0185i	0.238235	−	1.04378i
$333$	3.54887	+	4.45015i	0.194477	+	0.243867i
$334$	−5.68607	−	24.9123i	−0.311128	−	1.36314i
$335$	3.83653	−	4.81086i	0.209612	−	0.262845i
$336$	6.67627	+	10.7305i	0.364221	+	0.585399i
$337$	10.5966	+	13.2877i	0.577233	+	0.723827i	0.981638	−	0.190753i	$-0.0610929\pi$
$337$	10.5966	+	13.2877i	0.577233	+	0.723827i	−0.404405	+	0.914580i	$0.632521\pi$
$338$	−12.8481	+	16.1110i	−0.698842	+	0.876320i
$339$	−1.85926	−	0.895372i	−0.100981	−	0.0486299i
$340$	0.374992	−	0.470225i	0.0203368	−	0.0255015i
$341$	0.0994562	−	0.435746i	0.00538586	−	0.0235970i
$342$	−5.34755			−0.289162
$343$	18.4298	−	1.82867i	0.995113	−	0.0987388i
$344$	−8.14246			−0.439012
$345$	0.789242	−	3.45789i	0.0424914	−	0.186167i
$346$	17.0819	−	21.4201i	0.918331	−	1.15155i
$347$	2.37941	+	1.14586i	0.127734	+	0.0615132i	0.496659	−	0.867946i	$-0.334560\pi$
$347$	2.37941	+	1.14586i	0.127734	+	0.0615132i	−0.368925	+	0.929459i	$0.620274\pi$
$348$	−0.318759	+	0.399711i	−0.0170873	+	0.0214268i
$349$	−14.2564	−	17.8769i	−0.763126	−	0.956930i	0.236766	−	0.971567i	$-0.423912\pi$
$349$	−14.2564	−	17.8769i	−0.763126	−	0.956930i	−0.999893	+	0.0146363i	$0.995341\pi$
$350$	2.60455	+	4.18620i	0.139219	+	0.223762i
$351$	3.05816	−	3.83481i	0.163233	−	0.204687i
$352$	4.07947	+	17.8733i	0.217436	+	0.952651i
$353$	−1.00698	−	1.26271i	−0.0535962	−	0.0672075i	0.754311	−	0.656517i	$-0.227971\pi$
$353$	−1.00698	−	1.26271i	−0.0535962	−	0.0672075i	−0.807907	+	0.589310i	$0.799400\pi$
$354$	2.93985	−	12.8803i	0.156251	−	0.684582i
$355$	7.02539	−	3.38325i	0.372869	−	0.179564i
$356$	5.66398	−	24.8155i	0.300190	−	1.31522i
$357$	1.02154	−	0.352376i	0.0540655	−	0.0186497i
$358$	5.68547	+	24.9097i	0.300486	+	1.31652i
$359$	7.93076	+	9.94485i	0.418569	+	0.524869i	0.945755	−	0.324881i	$-0.105324\pi$
$359$	7.93076	+	9.94485i	0.418569	+	0.524869i	−0.527186	+	0.849750i	$0.676753\pi$
$360$	−0.885534	+	0.426451i	−0.0466717	+	0.0224759i
$361$	−10.7651			−0.566583
$362$	−26.3120			−1.38293
$363$	3.61535	−	1.74106i	0.189757	−	0.0913821i
$364$	−18.9799	−	2.22377i	−0.994816	−	0.116557i
$365$	−5.77602	−	2.78159i	−0.302331	−	0.145595i
$366$	−16.8602	−	8.11945i	−0.881297	−	0.424410i
$367$	4.44585	+	19.4786i	0.232072	+	1.01677i	0.947918	+	0.318514i	$0.103184\pi$
$367$	4.44585	+	19.4786i	0.232072	+	1.01677i	−0.715846	+	0.698258i	$0.753959\pi$
$368$	−3.76996	−	16.5173i	−0.196523	−	0.861022i
$369$	1.96320	+	0.945427i	0.102200	+	0.0492170i
$370$	9.55644	+	4.60214i	0.496816	+	0.239254i
$371$	−0.435213	−	4.02283i	−0.0225951	−	0.208855i
$372$	−0.224332	+	0.108033i	−0.0116311	+	0.00560123i
$373$	−21.1072			−1.09289			−0.546446	−	0.837494i	$-0.684020\pi$
$373$	−21.1072			−1.09289			−0.546446	+	0.837494i	$0.684020\pi$
$374$	2.01186			0.104031
$375$	−0.900969	+	0.433884i	−0.0465258	+	0.0224057i
$376$	−2.94331	−	3.69079i	−0.151789	−	0.190338i
$377$	0.378932	+	1.66021i	0.0195160	+	0.0855051i
$378$	4.89681	+	0.573734i	0.251865	+	0.0295097i
$379$	4.55837	−	19.9715i	0.234148	−	1.02587i	−0.712011	−	0.702168i	$-0.752216\pi$
$379$	4.55837	−	19.9715i	0.234148	−	1.02587i	0.946159	−	0.323701i	$-0.104927\pi$
$380$	−3.80727	+	1.83348i	−0.195309	+	0.0940557i
$381$	−1.95730	+	8.57551i	−0.100276	+	0.439337i
$382$	7.95448	+	9.97460i	0.406986	+	0.510345i
$383$	−3.46342	−	15.1742i	−0.176972	−	0.775367i	−0.983017	−	0.183512i	$-0.941253\pi$
$383$	−3.46342	−	15.1742i	−0.176972	−	0.775367i	0.806045	−	0.591854i	$-0.201604\pi$
$384$	−4.73199	+	5.93373i	−0.241478	+	0.302804i
$385$	−2.33909	+	6.59086i	−0.119211	+	0.335901i
$386$	9.17761	+	11.5084i	0.467128	+	0.585760i
$387$	−5.16523	+	6.47699i	−0.262563	+	0.329244i
$388$	18.6106	+	8.96241i	0.944812	+	0.454997i
$389$	−20.5143	+	25.7241i	−1.04012	+	1.30427i	−0.0888005	+	0.996049i	$0.528303\pi$
$389$	−20.5143	+	25.7241i	−1.04012	+	1.30427i	−0.951316	+	0.308216i	$0.900268\pi$
$390$	2.03389	−	8.91105i	0.102990	−	0.451229i
$391$	−1.44863			−0.0732604
$392$	2.93008	+	6.22496i	0.147991	+	0.314408i
$393$	6.25328			0.315436
$394$	−7.79115	+	34.1353i	−0.392513	+	1.71971i
$395$	5.08288	−	6.37373i	0.255748	−	0.320697i
$396$	3.50701	+	1.68889i	0.176234	+	0.0848698i
$397$	−19.6087	+	24.5885i	−0.984132	+	1.23406i	−0.0119280	+	0.999929i	$0.503797\pi$
$397$	−19.6087	+	24.5885i	−0.984132	+	1.23406i	−0.972204	+	0.234134i	$0.924775\pi$
$398$	8.91358	+	11.1773i	0.446798	+	0.560266i
$399$	−7.54081	−	0.883517i	−0.377513	−	0.0442312i
$400$	−2.97821	+	3.73456i	−0.148911	+	0.186728i
$401$	0.893892	+	3.91640i	0.0446388	+	0.195576i	0.992331	−	0.123611i	$-0.0394475\pi$
$401$	0.893892	+	3.91640i	0.0446388	+	0.195576i	−0.947692	+	0.319187i	$0.896590\pi$
$402$	−7.14931	−	8.96495i	−0.356575	−	0.447131i
$403$	−0.184548	+	0.808558i	−0.00919300	+	0.0402772i
$404$	−26.2518	+	12.6422i	−1.30608	+	0.628973i
$405$	−0.222521	+	0.974928i	−0.0110572	+	0.0484446i
$406$	−1.21572	+	1.20499i	−0.0603353	+	0.0598027i
$407$	3.34800	+	14.6685i	0.165954	+	0.727093i
$408$	0.250290	+	0.313853i	0.0123912	+	0.0155381i
$409$	−32.9852	+	15.8848i	−1.63101	+	0.785455i	−0.631061	+	0.775733i	$0.717380\pi$
$409$	−32.9852	+	15.8848i	−1.63101	+	0.785455i	−0.999953	+	0.00972136i	$0.996906\pi$
$410$	4.06050			0.200534
$411$	−8.24751			−0.406820
$412$	−20.0086	+	9.63564i	−0.985753	+	0.474714i
$413$	6.27369	−	17.6774i	0.308708	−	0.869848i
$414$	−5.95489	−	2.86773i	−0.292667	−	0.140941i
$415$	11.9355	+	5.74782i	0.585889	+	0.282149i
$416$	−7.56975	−	33.1652i	−0.371137	−	1.62606i
$417$	1.43128	+	6.27083i	0.0700899	+	0.307084i
$418$	−12.7356	−	6.13312i	−0.622916	−	0.299981i
$419$	−16.5754	−	7.98231i	−0.809763	−	0.389961i	−0.0172766	−	0.999851i	$-0.505500\pi$
$419$	−16.5754	−	7.98231i	−0.809763	−	0.389961i	−0.792487	+	0.609889i	$0.791214\pi$
$420$	3.68307	−	1.27046i	0.179716	−	0.0619923i
$421$	9.44251	−	4.54727i	0.460200	−	0.221620i	−0.189395	−	0.981901i	$-0.560653\pi$
$421$	9.44251	−	4.54727i	0.460200	−	0.221620i	0.649595	+	0.760280i	$0.274939\pi$
$422$	11.5615			0.562804
$423$	−4.80298			−0.233529
$424$	1.35430	−	0.652196i	0.0657706	−	0.0316735i
$425$	0.254652	+	0.319324i	0.0123525	+	0.0154895i
$426$	−3.23338	−	14.1664i	−0.156658	−	0.686362i
$427$	−22.4338	−	14.2352i	−1.08565	−	0.688891i
$428$	1.16808	−	5.11769i	0.0564613	−	0.247373i
$429$	11.6814	−	5.62546i	0.563983	−	0.271600i
$430$	−3.43523	+	15.0507i	−0.165662	+	0.725811i
$431$	−5.63734	−	7.06900i	−0.271541	−	0.340502i	0.627299	−	0.778779i	$-0.284160\pi$
$431$	−5.63734	−	7.06900i	−0.271541	−	0.340502i	−0.898840	+	0.438277i	$0.855589\pi$
$432$	1.06291	+	4.65692i	0.0511394	+	0.224056i
$433$	−21.2397	+	26.6338i	−1.02072	+	1.27994i	−0.0612475	+	0.998123i	$0.519508\pi$
$433$	−21.2397	+	26.6338i	−1.02072	+	1.27994i	−0.959469	+	0.281815i	$0.909064\pi$
$434$	−0.788078	+	0.271845i	−0.0378289	+	0.0130490i
$435$	−0.216465	−	0.271439i	−0.0103787	−	0.0130145i
$436$	−9.53219	+	11.9530i	−0.456509	+	0.572444i
$437$	9.17019	+	4.41613i	0.438670	+	0.211252i
$438$	−7.44858	+	9.34023i	−0.355907	+	0.446293i
$439$	−3.03334	+	13.2899i	−0.144774	+	0.634294i	0.849515	+	0.527565i	$0.176895\pi$
$439$	−3.03334	+	13.2899i	−0.144774	+	0.634294i	−0.994288	+	0.106729i	$0.965962\pi$
$440$	−2.59806			−0.123858
$441$	6.81042	+	1.61809i	0.324306	+	0.0770521i
$442$	−3.73314			−0.177568
$443$	−1.39942	+	6.13126i	−0.0664885	+	0.291305i	−0.997231	−	0.0743710i	$-0.976305\pi$
$443$	−1.39942	+	6.13126i	−0.0664885	+	0.291305i	0.930742	+	0.365676i	$0.119162\pi$
$444$	5.22594	−	6.55312i	0.248012	−	0.310997i
$445$	15.5735	+	7.49981i	0.738255	+	0.355525i
$446$	−15.1012	+	18.9363i	−0.715061	+	0.896658i
$447$	−1.94695	−	2.44140i	−0.0920875	−	0.115474i
$448$	6.33419	−	6.27827i	0.299262	−	0.296621i
$449$	20.7553	−	26.0263i	0.979503	−	1.22826i	0.00590696	−	0.999983i	$-0.498120\pi$
$449$	20.7553	−	26.0263i	0.979503	−	1.22826i	0.973596	−	0.228276i	$-0.0733088\pi$
$450$	0.414664	+	1.81676i	0.0195474	+	0.0856429i
$451$	3.59118	+	4.50320i	0.169102	+	0.212047i
$452$	−0.676200	+	2.96263i	−0.0318058	+	0.139350i
$453$	8.74294	−	4.21038i	0.410779	−	0.197821i
$454$	6.80767	−	29.8263i	0.319500	−	1.39982i
$455$	4.34035	−	12.2298i	0.203479	−	0.573343i
$456$	−0.627619	−	2.74978i	−0.0293909	−	0.128770i
$457$	7.10615	+	8.91083i	0.332412	+	0.416831i	0.919746	−	0.392513i	$-0.128394\pi$
$457$	7.10615	+	8.91083i	0.332412	+	0.416831i	−0.587335	+	0.809344i	$0.699823\pi$
$458$	12.4978	−	6.01864i	0.583985	−	0.281232i
$459$	0.408431			0.0190639
$460$	−5.22292			−0.243520
$461$	−15.2781	+	7.35755i	−0.711573	+	0.342675i	−0.754407	−	0.656407i	$-0.772076\pi$
$461$	−15.2781	+	7.35755i	−0.711573	+	0.342675i	0.0428344	+	0.999082i	$0.486361\pi$
$462$	11.0041	+	6.98256i	0.511956	+	0.324858i
$463$	−19.8435	−	9.55615i	−0.922208	−	0.444112i	−0.0883488	−	0.996090i	$-0.528159\pi$
$463$	−19.8435	−	9.55615i	−0.922208	−	0.444112i	−0.833859	+	0.551978i	$0.813873\pi$
$464$	−1.49415	−	0.719546i	−0.0693643	−	0.0334041i
$465$	−0.0376252	−	0.164847i	−0.00174483	−	0.00764458i
$466$	−9.21143	−	40.3579i	−0.426711	−	1.86954i
$467$	24.3550	+	11.7287i	1.12701	+	0.542741i	0.902052	−	0.431627i	$-0.142060\pi$
$467$	24.3550	+	11.7287i	1.12701	+	0.542741i	0.224961	+	0.974368i	$0.427774\pi$
$468$	−6.50751	−	3.13385i	−0.300810	−	0.144862i
$469$	−8.60037	−	13.8231i	−0.397128	−	0.638290i
$470$	−8.06391	+	3.88337i	−0.371960	+	0.179127i
$471$	15.6358			0.720461
$472$	6.96827			0.320741
$473$	−19.7298	+	9.50139i	−0.907179	+	0.436874i
$474$	−9.47186	−	11.8773i	−0.435057	−	0.545544i
$475$	−0.638558	−	2.79771i	−0.0292991	−	0.128368i
$476$	−0.840620	−	1.35110i	−0.0385298	−	0.0619275i
$477$	0.340315	−	1.49102i	0.0155819	−	0.0682689i
$478$	−39.2408	+	18.8974i	−1.79483	+	0.864347i
$479$	−0.917635	+	4.02042i	−0.0419278	+	0.183698i	−0.991556	−	0.129682i	$-0.958604\pi$
$479$	−0.917635	+	4.02042i	−0.0419278	+	0.183698i	0.949628	+	0.313380i	$0.101461\pi$
$480$	4.32423	+	5.42241i	0.197373	+	0.247498i
$481$	−6.21246	−	27.2185i	−0.283264	−	1.24106i
$482$	6.83113	−	8.56597i	0.311150	−	0.390169i
$483$	−7.92345	−	5.02777i	−0.360530	−	0.228771i
$484$	−3.68421	−	4.61985i	−0.167464	−	0.209993i
$485$	−8.74594	+	10.9671i	−0.397133	+	0.497989i
$486$	1.67894	+	0.808534i	0.0761582	+	0.0366759i
$487$	2.35220	−	2.94956i	0.106588	−	0.133657i	−0.725676	−	0.688037i	$-0.758473\pi$
$487$	2.35220	−	2.94956i	0.106588	−	0.133657i	0.832264	+	0.554379i	$0.187044\pi$
$488$	2.19631	−	9.62268i	0.0994225	−	0.435598i
$489$	−20.0340			−0.905967
$490$	12.7426	−	2.78977i	0.575650	−	0.126029i
$491$	20.8982			0.943121			0.471560	−	0.881834i	$-0.343691\pi$
$491$	20.8982			0.943121			0.471560	+	0.881834i	$0.343691\pi$
$492$	0.714002	−	3.12825i	0.0321897	−	0.141032i
$493$	−0.0884110	+	0.110864i	−0.00398183	+	0.00499306i
$494$	23.6317	+	11.3804i	1.06324	+	0.512030i
$495$	−1.64810	+	2.06665i	−0.0740765	+	0.0928889i
$496$	−0.503574	−	0.631462i	−0.0226112	−	0.0283535i
$497$	−2.21897	−	20.5108i	−0.0995346	−	0.920036i
$498$	15.3916	−	19.3005i	0.689715	−	0.864875i
$499$	6.52040	+	28.5678i	0.291893	+	1.27887i	0.881887	+	0.471461i	$0.156273\pi$
$499$	6.52040	+	28.5678i	0.291893	+	1.27887i	−0.589994	+	0.807408i	$0.700870\pi$
$500$	0.918128	+	1.15130i	0.0410599	+	0.0514875i
$501$	3.05131	−	13.3687i	0.136323	−	0.597268i
$502$	51.1466	−	24.6309i	2.28278	−	1.09933i
$503$	−5.22856	+	22.9078i	−0.233130	+	1.02141i	0.713896	+	0.700252i	$0.246929\pi$
$503$	−5.22856	+	22.9078i	−0.233130	+	1.02141i	−0.947026	+	0.321157i	$0.895928\pi$
$504$	0.279697	+	2.58534i	0.0124587	+	0.115160i
$505$	−4.40298	−	19.2907i	−0.195930	−	0.858425i
$506$	−10.8930	−	13.6594i	−0.484252	−	0.607233i
$507$	−9.96306	+	4.79796i	−0.442475	+	0.213085i
$508$	12.9527			0.574685
$509$	−24.5710			−1.08909			−0.544545	−	0.838732i	$-0.683298\pi$
$509$	−24.5710			−1.08909			−0.544545	+	0.838732i	$0.683298\pi$
$510$	0.685730	−	0.330230i	0.0303646	−	0.0146228i
$511$	−12.0468	+	11.9404i	−0.532917	+	0.528213i
$512$	21.3882	+	10.3000i	0.945234	+	0.455201i
$513$	−2.58547	−	1.24510i	−0.114151	−	0.0549723i
$514$	−5.45437	−	23.8971i	−0.240582	−	1.05406i
$515$	−3.35586	−	14.7030i	−0.147877	−	0.647891i
$516$	10.9912	+	5.29307i	0.483859	+	0.233014i
$517$	−11.4386	−	5.50855i	−0.503070	−	0.242266i
$518$	19.9314	−	19.7554i	0.875734	−	0.868004i
$519$	13.2462	−	6.37905i	0.581445	−	0.280009i
$520$	4.82088			0.211410
$521$	22.7426			0.996372			0.498186	−	0.867070i	$-0.334000\pi$
$521$	22.7426			0.996372			0.498186	+	0.867070i	$0.334000\pi$
$522$	−0.582900	+	0.280710i	−0.0255128	+	0.0122863i
$523$	−18.2089	−	22.8332i	−0.796219	−	0.998427i	−0.999812	−	0.0193717i	$-0.993833\pi$
$523$	−18.2089	−	22.8332i	−0.796219	−	0.998427i	0.203593	−	0.979056i	$-0.434738\pi$
$524$	−2.04905	−	8.97747i	−0.0895131	−	0.392183i
$525$	0.284572	+	2.63040i	0.0124197	+	0.114800i
$526$	−11.3243	+	49.6149i	−0.493761	+	2.16331i
$527$	−0.0622208	+	0.0299640i	−0.00271038	+	0.00130525i
$528$	−2.80964	+	12.3098i	−0.122274	+	0.535717i
$529$	−6.49680	−	8.14673i	−0.282470	−	0.354206i
$530$	−0.634170	−	2.77848i	−0.0275466	−	0.120689i
$531$	4.42037	−	5.54297i	0.191828	−	0.240545i
$532$	1.20253	+	11.1154i	0.0521362	+	0.481914i
$533$	−6.66369	−	8.35601i	−0.288637	−	0.361939i
$534$	20.0831	−	25.1834i	0.869081	−	1.08979i
$535$	3.21172	+	1.54668i	0.138855	+	0.0668689i
$536$	3.77081	−	4.72844i	0.162874	−	0.204238i
$537$	−3.05099	+	13.3673i	−0.131660	+	0.576840i
$538$	−15.4381			−0.665586
$539$	14.3637	+	11.6645i	0.618688	+	0.502425i
$540$	1.47256			0.0633690
$541$	5.27660	−	23.1183i	0.226859	−	0.993934i	−0.725325	−	0.688407i	$-0.758310\pi$
$541$	5.27660	−	23.1183i	0.226859	−	0.993934i	0.952183	−	0.305527i	$-0.0988326\pi$
$542$	2.85608	−	3.58141i	0.122679	−	0.153835i
$543$	−12.7215	−	6.12636i	−0.545933	−	0.262907i
$544$	1.76615	−	2.21468i	0.0757230	−	0.0949536i
$545$	−6.47319	−	8.11713i	−0.277281	−	0.347700i
$546$	−20.4189	−	12.9566i	−0.873847	−	0.554493i
$547$	17.9112	−	22.4600i	0.765828	−	0.960318i	−0.234101	−	0.972212i	$-0.575215\pi$
$547$	17.9112	−	22.4600i	0.765828	−	0.960318i	0.999929	+	0.0118939i	$0.00378605\pi$
$548$	2.70251	+	11.8405i	0.115446	+	0.505800i
$549$	−6.26120	−	7.85130i	−0.267221	−	0.335085i
$550$	−1.09610	+	4.80232i	−0.0467378	+	0.204772i
$551$	0.897632	−	0.432277i	0.0382404	−	0.0184156i
$552$	0.775721	−	3.39866i	0.0330169	−	0.144656i
$553$	−11.3943	−	18.3137i	−0.484536	−	0.778777i
$554$	5.04004	+	22.0819i	0.214131	+	0.938169i
$555$	3.54887	+	4.45015i	0.150641	+	0.188898i
$556$	8.53369	−	4.10961i	0.361909	−	0.174286i
$557$	−38.9214			−1.64915			−0.824576	−	0.565751i	$-0.808586\pi$
$557$	−38.9214			−1.64915			−0.824576	+	0.565751i	$0.808586\pi$
$558$	−0.315089			−0.0133388
$559$	36.6101	−	17.6305i	1.54844	−	0.745691i
$560$	6.67627	+	10.7305i	0.282124	+	0.453448i
$561$	0.972706	+	0.468430i	0.0410677	+	0.0197772i
$562$	23.2340	+	11.1889i	0.980066	+	0.471975i
$563$	4.80605	+	21.0567i	0.202551	+	0.887433i	0.969377	+	0.245578i	$0.0789778\pi$
$563$	4.80605	+	21.0567i	0.202551	+	0.887433i	−0.766826	+	0.641855i	$0.778165\pi$
$564$	1.57382	+	6.89537i	0.0662699	+	0.290347i
$565$	−1.85926	−	0.895372i	−0.0782196	−	0.0376686i
$566$	53.0230	+	25.5345i	2.22872	+	1.07330i
$567$	2.23396	+	1.41754i	0.0938175	+	0.0595312i
$568$	6.90503	−	3.32529i	0.289729	−	0.139526i
$569$	46.9279			1.96732			0.983661	−	0.180032i	$-0.0576201\pi$
$569$	46.9279			1.96732			0.983661	+	0.180032i	$0.0576201\pi$
$570$	−5.34755			−0.223984
$571$	−38.7435	+	18.6579i	−1.62136	+	0.780808i	−0.999996	−	0.00271062i	$-0.999137\pi$
$571$	−38.7435	+	18.6579i	−1.62136	+	0.780808i	−0.621368	+	0.783519i	$0.713423\pi$
$572$	−11.9039	−	14.9270i	−0.497726	−	0.624128i
$573$	1.52345	+	6.67467i	0.0636430	+	0.278838i
$574$	3.59313	−	10.1244i	0.149974	−	0.422583i
$575$	0.789242	−	3.45789i	0.0329137	−	0.144204i
$576$	3.03704	−	1.46256i	0.126543	−	0.0609400i
$577$	−3.43373	+	15.0442i	−0.142948	+	0.626297i	0.851793	+	0.523878i	$0.175515\pi$
$577$	−3.43373	+	15.0442i	−0.142948	+	0.626297i	−0.994741	+	0.102419i	$0.967342\pi$
$578$	19.5578	+	24.5247i	0.813499	+	1.02009i
$579$	1.75770	+	7.70101i	0.0730477	+	0.320043i
$580$	−0.318759	+	0.399711i	−0.0132357	+	0.0165971i
$581$	24.8932	−	24.6735i	1.03274	−	1.02363i
$582$	16.2979	+	20.4369i	0.675570	+	0.847138i
$583$	2.52053	−	3.16065i	0.104390	−	0.130901i
$584$	−5.67707	−	2.73393i	−0.234919	−	0.113131i
$585$	3.05816	−	3.83481i	0.126439	−	0.158550i
$586$	−0.748239	+	3.27825i	−0.0309095	+	0.135423i
$587$	19.3038			0.796751			0.398376	−	0.917222i	$-0.369574\pi$
$587$	19.3038			0.796751			0.398376	+	0.917222i	$0.369574\pi$
$588$	0.0913944	−	10.3075i	0.00376904	−	0.425076i
$589$	0.485218			0.0199931
$590$	2.93985	−	12.8803i	0.121032	−	0.530275i
$591$	−11.7148	+	14.6899i	−0.481883	+	0.604262i
$592$	24.4961	+	11.7967i	1.00678	+	0.484842i
$593$	3.73578	−	4.68452i	0.153410	−	0.192370i	−0.699187	−	0.714939i	$-0.746455\pi$
$593$	3.73578	−	4.68452i	0.153410	−	0.192370i	0.852597	+	0.522568i	$0.175026\pi$
$594$	3.07120	+	3.85116i	0.126013	+	0.158015i
$595$	1.02154	−	0.352376i	0.0418790	−	0.0144460i
$596$	−2.86701	+	3.59511i	−0.117437	+	0.147261i
$597$	1.70714	+	7.47946i	0.0698685	+	0.306114i
$598$	20.2127	+	25.3460i	0.826560	+	1.03647i
$599$	6.31099	−	27.6502i	0.257860	−	1.12976i	−0.665674	−	0.746242i	$-0.731856\pi$
$599$	6.31099	−	27.6502i	0.257860	−	1.12976i	0.923534	−	0.383516i	$-0.125287\pi$
$600$	−0.885534	+	0.426451i	−0.0361518	+	0.0174098i
$601$	2.62428	−	11.4977i	0.107047	−	0.469002i	−0.892782	−	0.450489i	$-0.851250\pi$
$601$	2.62428	−	11.4977i	0.107047	−	0.469002i	0.999829	−	0.0185130i	$-0.00589321\pi$
$602$	34.4874	+	21.8837i	1.40560	+	0.891914i
$603$	−1.36924	−	5.99905i	−0.0557599	−	0.244300i
$604$	−8.90945	−	11.1721i	−0.362521	−	0.454586i
$605$	3.61535	−	1.74106i	0.146985	−	0.0707843i
$606$	−36.8723			−1.49784
$607$	−32.9876			−1.33892			−0.669462	−	0.742846i	$-0.733475\pi$
$607$	−32.9876			−1.33892			−0.669462	+	0.742846i	$0.733475\pi$
$608$	−17.9316	+	8.63540i	−0.727222	+	0.350212i
$609$	−0.868351	+	0.299535i	−0.0351873	+	0.0121378i
$610$	−16.8602	−	8.11945i	−0.682650	−	0.328747i
$611$	21.2252	+	10.2215i	0.858680	+	0.413518i
$612$	−0.133833	−	0.586361i	−0.00540988	−	0.0237022i
$613$	−7.63275	−	33.4413i	−0.308284	−	1.35068i	−0.857278	−	0.514854i	$-0.827846\pi$
$613$	−7.63275	−	33.4413i	−0.308284	−	1.35068i	0.548994	−	0.835826i	$-0.315011\pi$
$614$	20.3650	+	9.80729i	0.821866	+	0.395790i
$615$	1.96320	+	0.945427i	0.0791638	+	0.0381233i
$616$	−2.29902	+	6.47795i	−0.0926301	+	0.261004i
$617$	12.9535	−	6.23806i	0.521487	−	0.251135i	−0.154573	−	0.987981i	$-0.549400\pi$
$617$	12.9535	−	6.23806i	0.521487	−	0.251135i	0.676060	+	0.736847i	$0.263686\pi$
$618$	−28.1034			−1.13048
$619$	−37.3422			−1.50091			−0.750455	−	0.660921i	$-0.770166\pi$
$619$	−37.3422			−1.50091			−0.750455	+	0.660921i	$0.770166\pi$
$620$	−0.224332	+	0.108033i	−0.00900939	+	0.00433870i
$621$	−2.21141	−	2.77302i	−0.0887407	−	0.111277i
$622$	1.72542	+	7.55957i	0.0691831	+	0.303111i
$623$	32.4809	−	32.1941i	1.30132	−	1.28983i
$624$	5.21349	−	22.8418i	0.208707	−	0.914404i
$625$	−0.900969	+	0.433884i	−0.0360388	+	0.0173553i
$626$	−7.62961	+	33.4275i	−0.304941	+	1.33603i
$627$	−4.72947	−	5.93057i	−0.188877	−	0.236844i
$628$	−5.12349	−	22.4475i	−0.204450	−	0.895752i
$629$	1.44947	−	1.81758i	0.0577941	−	0.0724715i
$630$	4.89681	+	0.573734i	0.195094	+	0.0228581i
$631$	13.9889	+	17.5416i	0.556891	+	0.698319i	0.977980	−	0.208700i	$-0.0669233\pi$
$631$	13.9889	+	17.5416i	0.556891	+	0.698319i	−0.421089	+	0.907020i	$0.638352\pi$
$632$	4.99580	−	6.26454i	0.198722	−	0.249190i
$633$	5.58982	+	2.69191i	0.222175	+	0.106994i
$634$	15.3277	−	19.2203i	0.608739	−	0.763335i
$635$	−1.95730	+	8.57551i	−0.0776732	+	0.340309i
$636$	−2.25208			−0.0893008
$637$	−26.6528	−	21.6443i	−1.05602	−	0.857579i
$638$	−1.71016			−0.0677060
$639$	1.73513	−	7.60209i	0.0686406	−	0.300734i
$640$	−4.73199	+	5.93373i	−0.187048	+	0.234551i
$641$	−4.41481	−	2.12606i	−0.174375	−	0.0839743i	0.344660	−	0.938728i	$-0.387994\pi$
$641$	−4.41481	−	2.12606i	−0.174375	−	0.0839743i	−0.519035	+	0.854753i	$0.673708\pi$
$642$	4.14173	−	5.19357i	0.163461	−	0.204974i
$643$	−3.70100	−	4.64091i	−0.145953	−	0.183020i	0.703481	−	0.710714i	$-0.251628\pi$
$643$	−3.70100	−	4.64091i	−0.145953	−	0.183020i	−0.849434	+	0.527694i	$0.823057\pi$
$644$	−4.62175	+	13.0227i	−0.182123	+	0.513167i
$645$	−5.16523	+	6.47699i	−0.203381	+	0.255031i
$646$	0.486008	+	2.12934i	0.0191217	+	0.0837778i
$647$	6.65924	+	8.35042i	0.261802	+	0.328289i	0.895307	−	0.445449i	$-0.146956\pi$
$647$	6.65924	+	8.35042i	0.261802	+	0.328289i	−0.633506	+	0.773738i	$0.718385\pi$
$648$	−0.218709	+	0.958226i	−0.00859169	+	0.0376427i
$649$	16.8847	−	8.13123i	0.662782	−	0.319179i
$650$	2.03389	−	8.91105i	0.0797757	−	0.349520i
$651$	−0.444320	−	0.0520587i	−0.0174143	−	0.00204034i
$652$	6.56465	+	28.7616i	0.257092	+	1.12639i
$653$	−13.8732	−	17.3965i	−0.542901	−	0.680776i	0.432394	−	0.901685i	$-0.357669\pi$
$653$	−13.8732	−	17.3965i	−0.542901	−	0.680776i	−0.975294	+	0.220909i	$0.929098\pi$
$654$	−17.4311	+	8.39436i	−0.681609	+	0.328245i
$655$	6.25328			0.244336
$656$	10.4083			0.406377
$657$	−5.77602	+	2.78159i	−0.225344	+	0.108520i
$658$	2.54699	+	23.5428i	0.0992921	+	0.917794i
$659$	9.80152	+	4.72016i	0.381813	+	0.183871i	0.614938	−	0.788575i	$-0.289181\pi$
$659$	9.80152	+	4.72016i	0.381813	+	0.183871i	−0.233125	+	0.972447i	$0.574895\pi$
$660$	3.50701	+	1.68889i	0.136510	+	0.0657399i
$661$	2.10649	+	9.22915i	0.0819330	+	0.358972i	0.999230	−	0.0392313i	$-0.0124909\pi$
$661$	2.10649	+	9.22915i	0.0819330	+	0.358972i	−0.917297	+	0.398203i	$0.869634\pi$
$662$	−7.08509	−	31.0418i	−0.275370	−	1.20647i
$663$	−1.80493	−	0.869206i	−0.0700975	−	0.0337572i
$664$	11.7310	+	5.64935i	0.455251	+	0.219237i
$665$	−7.54081	−	0.883517i	−0.292420	−	0.0342613i
$666$	9.55644	−	4.60214i	0.370304	−	0.178329i
$667$	1.23140			0.0476799
$668$	−20.1925			−0.781271
$669$	−11.7102	+	5.63935i	−0.452744	+	0.218030i
$670$	−7.14931	−	8.96495i	−0.276202	−	0.346346i
$671$	−5.90680	−	25.8794i	−0.228030	−	0.999063i
$672$	17.3466	−	5.98367i	0.669162	−	0.230825i
$673$	−3.57330	+	15.6557i	−0.137741	+	0.603481i	0.858188	+	0.513336i	$0.171590\pi$
$673$	−3.57330	+	15.6557i	−0.137741	+	0.603481i	−0.995929	+	0.0901456i	$0.971267\pi$
$674$	28.5346	−	13.7415i	1.09911	−	0.529304i
$675$	−0.222521	+	0.974928i	−0.00856483	+	0.0375250i
$676$	10.1528	+	12.7312i	0.390493	+	0.489662i
$677$	−4.79996	−	21.0300i	−0.184478	−	0.808249i	−0.979464	−	0.201621i	$-0.935379\pi$
$677$	−4.79996	−	21.0300i	−0.184478	−	0.808249i	0.794986	−	0.606628i	$-0.207478\pi$
$678$	−2.39764	+	3.00655i	−0.0920810	+	0.115466i
$679$	19.6058	+	31.5117i	0.752402	+	1.20931i
$680$	0.250290	+	0.313853i	0.00959817	+	0.0120357i
$681$	10.2360	−	12.8356i	0.392246	−	0.491860i
$682$	−0.750405	−	0.361376i	−0.0287345	−	0.0138378i
$683$	−19.5000	+	24.4522i	−0.746147	+	0.935638i	−0.999496	−	0.0317365i	$-0.989896\pi$
$683$	−19.5000	+	24.4522i	−0.746147	+	0.935638i	0.253350	+	0.967375i	$0.418468\pi$
$684$	−0.940317	+	4.11980i	−0.0359539	+	0.157524i
$685$	−8.24751			−0.315121
$686$	4.31990	−	34.2407i	0.164935	−	1.30732i
$687$	7.44389			0.284002
$688$	−8.80557	+	38.5797i	−0.335709	+	1.47084i
$689$	−4.67703	+	5.86481i	−0.178181	+	0.223432i
$690$	−5.95489	−	2.86773i	−0.226699	−	0.109172i
$691$	21.6047	−	27.0914i	0.821880	−	1.03060i	−0.177043	−	0.984203i	$-0.556653\pi$
$691$	21.6047	−	27.0914i	0.821880	−	1.03060i	0.998923	−	0.0464015i	$-0.0147754\pi$
$692$	−13.4985	−	16.9266i	−0.513137	−	0.643453i
$693$	3.69455	+	5.93811i	0.140344	+	0.225570i
$694$	3.06842	−	3.84767i	0.116476	−	0.146056i
$695$	1.43128	+	6.27083i	0.0542914	+	0.237866i
$696$	−0.212757	−	0.266789i	−0.00806453	−	0.0101126i
$697$	0.198036	−	0.867652i	0.00750114	−	0.0328646i
$698$	−38.3897	+	18.4875i	−1.45307	+	0.699762i
$699$	4.94313	−	21.6573i	0.186966	−	0.819153i
$700$	3.68307	−	1.27046i	0.139207	−	0.0480190i
$701$	9.13309	+	40.0147i	0.344952	+	1.51133i	0.788473	+	0.615070i	$0.210872\pi$
$701$	9.13309	+	40.0147i	0.344952	+	1.51133i	−0.443521	+	0.896264i	$0.646271\pi$
$702$	−5.69883	−	7.14611i	−0.215088	−	0.269712i
$703$	−14.7164	+	7.08703i	−0.555038	+	0.267292i
$704$	8.91033			0.335821
$705$	−4.80298			−0.180891
$706$	−2.71161	+	1.30584i	−0.102053	+	0.0491460i
$707$	−51.9953	−	6.09201i	−1.95548	−	0.229114i
$708$	−9.40618	−	4.52978i	−0.353506	−	0.170239i
$709$	−7.29981	−	3.51540i	−0.274150	−	0.132024i	0.291758	−	0.956492i	$-0.405760\pi$
$709$	−7.29981	−	3.51540i	−0.274150	−	0.132024i	−0.565908	+	0.824469i	$0.691474\pi$
$710$	−3.23338	−	14.1664i	−0.121347	−	0.531654i
$711$	−1.81406	−	7.94791i	−0.0680325	−	0.298070i
$712$	15.3067	+	7.37132i	0.573643	+	0.276252i
$713$	0.540327	+	0.260208i	0.0202354	+	0.00974486i
$714$	−0.216588	−	2.00201i	−0.00810562	−	0.0749232i
$715$	11.6814	−	5.62546i	0.436859	−	0.210380i
$716$	20.1904			0.754550
$717$	−23.3724			−0.872859
$718$	21.3560	−	10.2845i	0.796999	−	0.383815i
$719$	12.7873	+	16.0347i	0.476885	+	0.597995i	0.960842	−	0.277097i	$-0.0893722\pi$
$719$	12.7873	+	16.0347i	0.476885	+	0.597995i	−0.483957	+	0.875092i	$0.660801\pi$
$720$	1.06291	+	4.65692i	0.0396124	+	0.173553i
$721$	−39.6298	−	4.64321i	−1.47589	−	0.172922i
$722$	−4.46389	+	19.5576i	−0.166129	+	0.727858i
$723$	5.29722	−	2.55101i	0.197006	−	0.0948730i
$724$	−4.62673	+	20.2710i	−0.171951	+	0.753367i
$725$	−0.216465	−	0.271439i	−0.00803932	−	0.0100810i
$726$	−1.66394	−	7.29019i	−0.0617545	−	0.270564i
$727$	−10.3355	+	12.9603i	−0.383323	+	0.480672i	−0.935637	−	0.352965i	$-0.885174\pi$
$727$	−10.3355	+	12.9603i	−0.383323	+	0.480672i	0.552314	+	0.833636i	$0.313745\pi$
$728$	4.26599	−	12.0203i	0.158108	−	0.445502i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−7.44858	+	9.34023i	−0.275684	+	0.345697i
$731$	3.04852	+	1.46809i	0.112753	+	0.0542992i
$732$	−9.22001	+	11.5615i	−0.340781	+	0.427326i
$733$	7.68641	−	33.6764i	0.283904	−	1.24387i	−0.608837	−	0.793295i	$-0.708364\pi$
$733$	7.68641	−	33.6764i	0.283904	−	1.24387i	0.892741	−	0.450570i	$-0.148779\pi$
$734$	37.2314			1.37424
$735$	6.81042	+	1.61809i	0.251206	+	0.0596843i
$736$	−24.5991			−0.906734
$737$	3.61938	−	15.8575i	0.133322	−	0.584120i
$738$	2.53168	−	3.17463i	0.0931925	−	0.116860i
$739$	43.1207	+	20.7658i	1.58622	+	0.763883i	0.998964	−	0.0455181i	$-0.0144939\pi$
$739$	43.1207	+	20.7658i	1.58622	+	0.763883i	0.587256	+	0.809401i	$0.300208\pi$
$740$	5.22594	−	6.55312i	0.192109	−	0.240898i
$741$	8.77587	+	11.0046i	0.322390	+	0.404264i
$742$	−7.48899	−	0.877446i	−0.274929	−	0.0322120i
$743$	0.268631	−	0.336852i	0.00985510	−	0.0123579i	−0.776880	−	0.629649i	$-0.783199\pi$
$743$	0.268631	−	0.336852i	0.00985510	−	0.0123579i	0.786735	+	0.617291i	$0.211770\pi$
$744$	−0.0369806	−	0.162023i	−0.00135577	−	0.00594004i
$745$	−1.94695	−	2.44140i	−0.0713307	−	0.0894458i
$746$	−8.75241	+	38.3468i	−0.320448	+	1.40398i
$747$	11.9355	−	5.74782i	0.436696	−	0.210302i
$748$	0.353766	−	1.54995i	0.0129350	−	0.0566719i
$749$	6.69852	−	6.63938i	0.244758	−	0.242598i
$750$	0.414664	+	1.81676i	0.0151414	+	0.0663387i
$751$	31.1582	+	39.0711i	1.13698	+	1.42573i	0.889561	+	0.456817i	$0.151011\pi$
$751$	31.1582	+	39.0711i	1.13698	+	1.42573i	0.247418	+	0.968909i	$0.420418\pi$
$752$	−20.6703	+	9.95430i	−0.753769	+	0.362996i
$753$	30.4636			1.11016
$754$	3.17333			0.115566
$755$	8.74294	−	4.21038i	0.318188	−	0.153231i
$756$	1.30307	−	3.67166i	0.0473922	−	0.133537i
$757$	−16.1763	−	7.79011i	−0.587939	−	0.283136i	0.116169	−	0.993229i	$-0.462939\pi$
$757$	−16.1763	−	7.79011i	−0.587939	−	0.283136i	−0.704108	+	0.710093i	$0.748653\pi$
$758$	−34.3933	−	16.5629i	−1.24922	−	0.601593i
$759$	−2.08624	−	9.14040i	−0.0757256	−	0.331775i
$760$	−0.627619	−	2.74978i	−0.0227661	−	0.0997449i
$761$	31.1085	+	14.9811i	1.12768	+	0.543063i	0.902258	−	0.431197i	$-0.141909\pi$
$761$	31.1085	+	14.9811i	1.12768	+	0.543063i	0.225425	+	0.974260i	$0.427623\pi$
$762$	14.7680	+	7.11190i	0.534989	+	0.257637i
$763$	−25.9672	+	8.95731i	−0.940076	+	0.324276i
$764$	9.08324	−	4.37426i	0.328620	−	0.158255i
$765$	0.408431			0.0147668
$766$	−29.0041			−1.04796
$767$	−31.3307	+	15.0881i	−1.13129	+	0.544799i
$768$	13.0214	+	16.3283i	0.469868	+	0.589196i
$769$	−5.95438	−	26.0878i	−0.214720	−	0.940751i	−0.961311	−	0.275467i	$-0.911168\pi$
$769$	−5.95438	−	26.0878i	−0.214720	−	0.940751i	0.746590	−	0.665284i	$-0.231690\pi$
$770$	11.0041	+	6.98256i	0.396560	+	0.251634i
$771$	2.92698	−	12.8239i	0.105412	−	0.461842i
$772$	10.4799	−	5.04687i	0.377181	−	0.181641i
$773$	−9.92406	+	43.4801i	−0.356944	+	1.56387i	0.403817	+	0.914840i	$0.367683\pi$
$773$	−9.92406	+	43.4801i	−0.356944	+	1.56387i	−0.760761	+	0.649032i	$0.775174\pi$
$774$	9.62531	+	12.0698i	0.345975	+	0.433838i
$775$	−0.0376252	−	0.164847i	−0.00135154	−	0.00592147i
$776$	−8.59611	+	10.7792i	−0.308582	+	0.386950i
$777$	14.2363	−	4.91077i	0.510725	−	0.176173i
$778$	38.2280	+	47.9364i	1.37054	+	1.71860i
$779$	−3.89864	+	4.88874i	−0.139683	+	0.175157i
$780$	−6.50751	−	3.13385i	−0.233006	−	0.112210i
$781$	12.8512	−	16.1149i	0.459852	−	0.576636i
$782$	−0.600694	+	2.63181i	−0.0214808	+	0.0941135i
$783$	−0.347183			−0.0124073
$784$	32.6631	−	7.15106i	1.16654	−	0.255395i
$785$	15.6358			0.558067
$786$	2.59301	−	11.3607i	0.0924895	−	0.405223i
$787$	20.7897	−	26.0695i	0.741074	−	0.929277i	−0.258249	−	0.966078i	$-0.583145\pi$
$787$	20.7897	−	26.0695i	0.741074	−	0.929277i	0.999323	+	0.0368011i	$0.0117168\pi$
$788$	24.9281	+	12.0047i	0.888027	+	0.427651i
$789$	−17.0272	+	21.3514i	−0.606185	+	0.760132i
$790$	−9.47186	−	11.8773i	−0.336994	−	0.422577i
$791$	−3.87776	+	3.84353i	−0.137877	+	0.136660i
$792$	−1.61986	+	2.03124i	−0.0575593	+	0.0721771i
$793$	10.9605	+	48.0211i	0.389219	+	1.70528i
$794$	36.5404	+	45.8203i	1.29677	+	1.62610i
$795$	0.340315	−	1.49102i	0.0120697	−	0.0528809i
$796$	10.1785	−	4.90168i	0.360766	−	0.173736i
$797$	3.16491	−	13.8664i	0.112107	−	0.491172i	−0.887436	−	0.460931i	$-0.847515\pi$
$797$	3.16491	−	13.8664i	0.112107	−	0.491172i	0.999543	−	0.0302409i	$-0.00962745\pi$
$798$	−4.73204	+	13.3335i	−0.167512	+	0.472000i
$799$	0.436516	+	1.91250i	0.0154428	+	0.0676594i
$800$	4.32423	+	5.42241i	0.152885	+	0.191711i
$801$	15.5735	−	7.49981i	0.550263	−	0.264993i
$802$	7.48582			0.264333
$803$	−16.9462			−0.598019
$804$	−8.16382	+	3.93149i	−0.287916	+	0.138653i
$805$	−7.92345	−	5.02777i	−0.279265	−	0.177206i
$806$	1.39243	+	0.670560i	0.0490463	+	0.0236195i
$807$	−7.46414	−	3.59454i	−0.262750	−	0.126534i
$808$	−4.32755	−	18.9602i	−0.152243	−	0.667018i
$809$	−9.99894	−	43.8082i	−0.351544	−	1.54021i	−0.773617	−	0.633653i	$-0.781555\pi$
$809$	−9.99894	−	43.8082i	−0.351544	−	1.54021i	0.422073	−	0.906562i	$-0.361302\pi$
$810$	1.67894	+	0.808534i	0.0589919	+	0.0284090i
$811$	5.58379	+	2.68901i	0.196073	+	0.0944240i	0.529344	−	0.848407i	$-0.322438\pi$
$811$	5.58379	+	2.68901i	0.196073	+	0.0944240i	−0.333271	+	0.942831i	$0.608152\pi$
$812$	0.714563	+	1.14849i	0.0250762	+	0.0403041i
$813$	2.21476	−	1.06657i	0.0776749	−	0.0374063i
$814$	28.0375			0.982715
$815$	−20.0340			−0.701759
$816$	1.75774	−	0.846483i	0.0615332	−	0.0296328i
$817$	−14.8224	−	18.5867i	−0.518571	−	0.650267i
$818$	15.1812	+	66.5131i	0.530797	+	2.32558i
$819$	−6.85549	−	11.0186i	−0.239550	−	0.385021i
$820$	0.714002	−	3.12825i	0.0249340	−	0.109243i
$821$	36.1400	−	17.4041i	1.26129	−	0.607408i	0.320778	−	0.947154i	$-0.396056\pi$
$821$	36.1400	−	17.4041i	1.26129	−	0.607408i	0.940517	+	0.339747i	$0.110341\pi$
$822$	−3.41994	+	14.9837i	−0.119284	+	0.522618i
$823$	7.42081	+	9.30540i	0.258673	+	0.324366i	0.894161	−	0.447745i	$-0.147773\pi$
$823$	7.42081	+	9.30540i	0.258673	+	0.324366i	−0.635488	+	0.772110i	$0.719201\pi$
$824$	−3.29837	−	14.4511i	−0.114904	−	0.503428i
$825$	−1.64810	+	2.06665i	−0.0573794	+	0.0719515i
$826$	−29.5141	−	18.7280i	−1.02693	−	0.651629i
$827$	−34.2727	−	42.9766i	−1.19178	−	1.49444i	−0.825934	−	0.563767i	$-0.809352\pi$
$827$	−34.2727	−	42.9766i	−1.19178	−	1.49444i	−0.365845	−	0.930676i	$-0.619220\pi$
$828$	−3.25644	+	4.08344i	−0.113169	+	0.141909i
$829$	−27.7436	−	13.3606i	−0.963574	−	0.464033i	−0.115149	−	0.993348i	$-0.536734\pi$
$829$	−27.7436	−	13.3606i	−0.963574	−	0.464033i	−0.848425	+	0.529316i	$0.822449\pi$
$830$	15.3916	−	19.3005i	0.534251	−	0.669930i
$831$	−2.70464	+	11.8498i	−0.0938229	+	0.411065i
$832$	−16.5338			−0.573205
$833$	0.0253492	−	2.85890i	0.000878297	−	0.0990551i
$834$	11.9861			0.415045
$835$	3.05131	−	13.3687i	0.105595	−	0.462642i
$836$	−6.96444	+	8.73313i	−0.240870	+	0.302042i
$837$	−0.152341	−	0.0733637i	−0.00526568	−	0.00253582i
$838$	−21.3752	+	26.8036i	−0.738393	+	0.925916i
$839$	9.89703	+	12.4105i	0.341683	+	0.428457i	0.922750	−	0.385398i	$-0.125936\pi$
$839$	9.89703	+	12.4105i	0.341683	+	0.428457i	−0.581067	+	0.813856i	$0.697365\pi$
$840$	0.279697	+	2.58534i	0.00965045	+	0.0892027i
$841$	−18.0061	+	22.5789i	−0.620898	+	0.778582i
$842$	−4.34584	−	19.0404i	−0.149767	−	0.656174i
$843$	8.62816	+	10.8194i	0.297169	+	0.372639i
$844$	2.03298	−	8.90706i	0.0699780	−	0.306594i
$845$	−9.96306	+	4.79796i	−0.342740	+	0.165055i
$846$	−1.99162	+	8.72586i	−0.0684734	+	0.300001i
$847$	−1.14191	−	10.5551i	−0.0392366	−	0.362678i
$848$	−1.62558	−	7.12211i	−0.0558225	−	0.244574i
$849$	19.6906	+	24.6912i	0.675780	+	0.847401i
$850$	0.685730	−	0.330230i	0.0235203	−	0.0113268i
$851$	−20.1883			−0.692047
$852$	−11.4824			−0.393382
$853$	25.7503	−	12.4007i	0.881675	−	0.424592i	0.0624391	−	0.998049i	$-0.480112\pi$
$853$	25.7503	−	12.4007i	0.881675	−	0.424592i	0.819236	+	0.573456i	$0.194398\pi$
$854$	−35.1645	+	34.8541i	−1.20330	+	1.19268i
$855$	−2.58547	−	1.24510i	−0.0884212	−	0.0425814i
$856$	3.15670	+	1.52019i	0.107894	+	0.0519589i
$857$	−3.49775	−	15.3247i	−0.119481	−	0.523480i	−0.998877	−	0.0473885i	$-0.984910\pi$
$857$	−3.49775	−	15.3247i	−0.119481	−	0.523480i	0.879396	−	0.476092i	$-0.157947\pi$
$858$	−5.37626	−	23.5550i	−0.183543	−	0.804153i
$859$	−18.8605	−	9.08276i	−0.643513	−	0.309900i	0.0835156	−	0.996506i	$-0.473385\pi$
$859$	−18.8605	−	9.08276i	−0.643513	−	0.309900i	−0.727029	+	0.686607i	$0.759099\pi$
$860$	10.9912	+	5.29307i	0.374796	+	0.180492i
$861$	4.09454	−	4.05840i	0.139542	−	0.138310i
$862$	−15.1803	+	7.31044i	−0.517043	+	0.248995i
$863$	−5.32973			−0.181426			−0.0907130	−	0.995877i	$-0.528915\pi$
$863$	−5.32973			−0.181426			−0.0907130	+	0.995877i	$0.528915\pi$
$864$	6.93553			0.235951
$865$	13.2462	−	6.37905i	0.450386	−	0.216894i
$866$	39.5798	+	49.6316i	1.34498	+	1.68655i
$867$	3.74574	+	16.4111i	0.127212	+	0.557352i
$868$	0.0708555	+	0.654944i	0.00240499	+	0.0222302i
$869$	4.79518	−	21.0091i	0.162665	−	0.712684i
$870$	−0.582900	+	0.280710i	−0.0197621	+	0.00951695i
$871$	−6.71602	+	29.4248i	−0.227564	+	0.997021i
$872$	−6.36230	−	7.97807i	−0.215455	−	0.270171i
$873$	3.12139	+	13.6757i	0.105643	+	0.462853i
$874$	11.8256	−	14.8288i	0.400007	−	0.501593i
$875$	0.284572	+	2.63040i	0.00962028	+	0.0889238i
$876$	5.88603	+	7.38085i	0.198871	+	0.249376i
$877$	24.2674	−	30.4304i	0.819452	−	1.02756i	−0.179587	−	0.983742i	$-0.557476\pi$
$877$	24.2674	−	30.4304i	0.819452	−	1.02756i	0.999040	−	0.0438186i	$-0.0139524\pi$
$878$	22.8868	+	11.0217i	0.772393	+	0.371965i
$879$	−1.12506	+	1.41077i	−0.0379472	+	0.0475842i
$880$	−2.80964	+	12.3098i	−0.0947130	+	0.414965i
$881$	−53.0122			−1.78603			−0.893013	−	0.450032i	$-0.851413\pi$
$881$	−53.0122			−1.78603			−0.893013	+	0.450032i	$0.851413\pi$
$882$	5.76372	−	11.7019i	0.194075	−	0.394024i
$883$	35.7667			1.20364			0.601822	−	0.798630i	$-0.294442\pi$
$883$	35.7667			1.20364			0.601822	+	0.798630i	$0.294442\pi$
$884$	−0.656439	+	2.87605i	−0.0220784	+	0.0967319i
$885$	4.42037	−	5.54297i	0.148589	−	0.186325i
$886$	10.5587	+	5.08483i	0.354728	+	0.170828i
$887$	18.4242	−	23.1032i	0.618623	−	0.775728i	−0.369527	−	0.929220i	$-0.620480\pi$
$887$	18.4242	−	23.1032i	0.618623	−	0.775728i	0.988150	+	0.153492i	$0.0490518\pi$
$888$	3.48808	+	4.37391i	0.117052	+	0.146779i
$889$	19.6500	+	12.4688i	0.659040	+	0.418189i
$890$	20.0831	−	25.1834i	0.673188	−	0.844151i
$891$	0.588199	+	2.57707i	0.0197054	+	0.0863350i
$892$	11.9333	+	14.9638i	0.399555	+	0.501026i
$893$	3.06698	−	13.4373i	0.102633	−	0.449663i
$894$	−5.24276	+	2.52478i	−0.175344	+	0.0844413i
$895$	−3.05099	+	13.3673i	−0.101983	+	0.446819i
$896$	10.6077	+	17.0494i	0.354379	+	0.569581i
$897$	3.87116	+	16.9607i	0.129254	+	0.566300i
$898$	−38.6771	−	48.4996i	−1.29067	−	1.61845i
$899$	0.0528903	−	0.0254706i	0.00176399	−	0.000849493i
$900$	1.47256			0.0490854
$901$	−0.624637			−0.0208097
$902$	9.67036	−	4.65700i	0.321988	−	0.155061i
$903$	11.5789	+	18.6104i	0.385322	+	0.619315i
$904$	−1.82741	−	0.880033i	−0.0607787	−	0.0292695i
$905$	−12.7215	−	6.12636i	−0.422878	−	0.203647i
$906$	−4.02387	−	17.6297i	−0.133684	−	0.585708i
$907$	12.6348	+	55.3567i	0.419532	+	1.83809i	0.535099	+	0.844789i	$0.320274\pi$
$907$	12.6348	+	55.3567i	0.419532	+	1.83809i	−0.115568	+	0.993300i	$0.536869\pi$
$908$	−21.7814	−	10.4894i	−0.722841	−	0.348102i
$909$	−17.8273	−	8.58517i	−0.591294	−	0.284752i
$910$	−20.4189	−	12.9566i	−0.676879	−	0.429508i
$911$	0.349588	−	0.168353i	0.0115824	−	0.00557777i	−0.428084	−	0.903739i	$-0.640811\pi$
$911$	0.349588	−	0.168353i	0.0115824	−	0.00557777i	0.439666	+	0.898161i	$0.355097\pi$
$912$	−13.7074			−0.453898
$913$	35.0174			1.15891
$914$	19.1355	−	9.21518i	0.632947	−	0.304811i
$915$	−6.26120	−	7.85130i	−0.206989	−	0.259556i
$916$	−2.43918	−	10.6868i	−0.0805929	−	0.353101i
$917$	5.53352	−	15.5918i	0.182733	−	0.514887i
$918$	0.169361	−	0.742021i	0.00558976	−	0.0244903i
$919$	43.0864	−	20.7493i	1.42129	−	0.684457i	0.443933	−	0.896060i	$-0.353583\pi$
$919$	43.0864	−	20.7493i	1.42129	−	0.684457i	0.977356	+	0.211603i	$0.0678684\pi$
$920$	0.775721	−	3.39866i	0.0255748	−	0.112050i
$921$	7.56275	+	9.48339i	0.249201	+	0.312488i
$922$	7.03163	+	30.8076i	0.231574	+	1.01459i
$923$	−23.8463	+	29.9023i	−0.784911	+	0.984247i
$924$	7.31439	−	7.24983i	0.240626	−	0.238502i
$925$	3.54887	+	4.45015i	0.116686	+	0.146320i
$926$	−25.5896	+	32.0884i	−0.840927	+	1.05449i
$927$	−13.5876	−	6.54345i	−0.446275	−	0.214915i
$928$	−1.50130	+	1.88257i	−0.0492826	+	0.0617984i
$929$	−1.82438	+	7.99314i	−0.0598560	+	0.262246i	−0.995998	−	0.0893760i	$-0.971513\pi$
$929$	−1.82438	+	7.99314i	−0.0598560	+	0.262246i	0.936142	+	0.351622i	$0.114370\pi$
$930$	−0.315089			−0.0103322
$931$	−8.87580	+	18.0203i	−0.290893	+	0.590591i
$932$	−32.7118			−1.07151
$933$	−0.925913	+	4.05669i	−0.0303130	+	0.132810i
$934$	31.4074	−	39.3837i	1.02768	−	1.28867i
$935$	0.972706	+	0.468430i	0.0318109	+	0.0153193i
$936$	3.00577	−	3.76912i	0.0982467	−	0.123197i
$937$	4.58116	+	5.74460i	0.149660	+	0.187668i	0.851010	−	0.525149i	$-0.175990\pi$
$937$	4.58116	+	5.74460i	0.149660	+	0.187668i	−0.701350	+	0.712817i	$0.747419\pi$
$938$	−28.6795	+	9.89289i	−0.936418	+	0.323014i
$939$	−11.4719	+	14.3853i	−0.374372	+	0.469447i
$940$	1.57382	+	6.89537i	0.0513324	+	0.224902i
$941$	−26.6177	−	33.3776i	−0.867713	−	1.08808i	−0.995356	−	0.0962572i	$-0.969313\pi$
$941$	−26.6177	−	33.3776i	−0.867713	−	1.08808i	0.127644	−	0.991820i	$-0.459259\pi$
$942$	6.48361	−	28.4066i	0.211248	−	0.925536i
$943$	−6.96311	+	3.35326i	−0.226750	+	0.109197i
$944$	7.53576	−	33.0163i	0.245268	−	1.07459i
$945$	2.23396	+	1.41754i	0.0726707	+	0.0461127i
$946$	9.08050	+	39.7843i	0.295232	+	1.29350i
$947$	−27.7826	−	34.8383i	−0.902814	−	1.13209i	−0.990714	−	0.135964i	$-0.956587\pi$
$947$	−27.7826	−	34.8383i	−0.902814	−	1.13209i	0.0878994	−	0.996129i	$-0.471985\pi$
$948$	−10.8159	+	5.20868i	−0.351286	+	0.169170i
$949$	31.4449			1.02074
$950$	−5.34755			−0.173497
$951$	11.8859	−	5.72394i	0.385426	−	0.185611i
$952$	1.00404	−	0.346339i	0.0325410	−	0.0112249i
$953$	26.1337	+	12.5853i	0.846555	+	0.407679i	0.806298	−	0.591510i	$-0.201468\pi$
$953$	26.1337	+	12.5853i	0.846555	+	0.407679i	0.0402571	+	0.999189i	$0.487182\pi$
$954$	−2.56770	−	1.23654i	−0.0831324	−	0.0400345i
$955$	1.52345	+	6.67467i	0.0492977	+	0.215987i
$956$	7.65858	+	33.5544i	0.247696	+	1.08523i
$957$	−0.826841	−	0.398186i	−0.0267280	−	0.0128715i
$958$	6.92364	+	3.33425i	0.223692	+	0.107725i
$959$	−7.29821	+	20.5642i	−0.235672	+	0.664053i
$960$	3.03704	−	1.46256i	0.0980199	−	0.0472039i
$961$	−30.9714			−0.999078
$962$	−52.0256			−1.67737
$963$	3.21172	−	1.54668i	0.103496	−	0.0498411i
$964$	−5.39811	−	6.76901i	−0.173861	−	0.218015i
$965$	1.75770	+	7.70101i	0.0565825	+	0.247904i
$966$	−12.4198	+	12.3102i	−0.399601	+	0.396074i
$967$	7.45369	−	32.6568i	0.239695	−	1.05017i	−0.701596	−	0.712575i	$-0.747529\pi$
$967$	7.45369	−	32.6568i	0.239695	−	1.05017i	0.941291	−	0.337596i	$-0.109614\pi$
$968$	3.55342	−	1.71124i	0.114211	−	0.0550012i
$969$	−0.260807	+	1.14267i	−0.00837832	+	0.0367078i
$970$	16.2979	+	20.4369i	0.523294	+	0.656190i
$971$	−5.41275	−	23.7148i	−0.173703	−	0.761044i	−0.984453	−	0.175650i	$-0.943797\pi$
$971$	−5.41275	−	23.7148i	−0.173703	−	0.761044i	0.810749	−	0.585394i	$-0.199060\pi$
$972$	0.918128	−	1.15130i	0.0294490	−	0.0369278i
$973$	16.9021	+	1.98033i	0.541857	+	0.0634866i
$974$	−4.38328	−	5.49646i	−0.140449	−	0.176118i
$975$	3.05816	−	3.83481i	0.0979396	−	0.122812i
$976$	−43.2180	−	20.8127i	−1.38337	−	0.666198i
$977$	−20.7406	+	26.0078i	−0.663549	+	0.832065i	−0.993725	−	0.111855i	$-0.964321\pi$
$977$	−20.7406	+	26.0078i	−0.663549	+	0.832065i	0.330175	+	0.943920i	$0.392892\pi$
$978$	−8.30736	+	36.3969i	−0.265640	+	1.16384i
$979$	45.6909			1.46029
$980$	0.0913944	−	10.3075i	0.00291949	−	0.329262i
$981$	−10.3822			−0.331478
$982$	8.66571	−	37.9669i	0.276534	−	1.21157i
$983$	19.2652	−	24.1578i	0.614463	−	0.770513i	−0.373090	−	0.927795i	$-0.621702\pi$
$983$	19.2652	−	24.1578i	0.614463	−	0.770513i	0.987554	+	0.157282i	$0.0502733\pi$
$984$	1.92957	+	0.929230i	0.0615123	+	0.0296228i
$985$	−11.7148	+	14.6899i	−0.373265	+	0.468059i
$986$	0.164752	+	0.206593i	0.00524678	+	0.00657926i
$987$	−4.25015	+	11.9757i	−0.135284	+	0.381190i
$988$	12.9230	−	16.2050i	0.411136	−	0.515548i
$989$	−6.53838	−	28.6465i	−0.207909	−	0.910907i
$990$	3.07120	+	3.85116i	0.0976091	+	0.122398i
$991$	−6.26467	+	27.4473i	−0.199004	+	0.871893i	0.772527	+	0.634981i	$0.218992\pi$
$991$	−6.26467	+	27.4473i	−0.199004	+	0.871893i	−0.971531	+	0.236911i	$0.923865\pi$
$992$	−1.05657	+	0.508816i	−0.0335460	+	0.0161549i
$993$	3.80207	−	16.6580i	0.120655	−	0.528625i
$994$	−38.1833	−	4.47374i	−1.21110	−	0.141898i
$995$	1.70714	+	7.47946i	0.0541199	+	0.237115i
$996$	−12.1628	−	15.2517i	−0.385393	−	0.483267i
$997$	11.5734	−	5.57346i	0.366534	−	0.176513i	−0.241546	−	0.970389i	$-0.577654\pi$
$997$	11.5734	−	5.57346i	0.366534	−	0.176513i	0.608080	+	0.793876i	$0.291940\pi$
$998$	54.6045			1.72848
$999$	5.69195			0.180085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.u.b.211.7	✓	48
49.36	even	7	inner	735.2.u.b.526.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.u.b.211.7	✓	48	1.1	even	1	trivial
735.2.u.b.526.7	yes	48	49.36	even	7	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.414664 - 1.81676i) q^{2} +(0.623490 - 0.781831i) q^{3} +(-1.32673 - 0.638921i) q^{4} +(0.623490 - 0.781831i) q^{5} +(-1.16186 - 1.45693i) q^{6} +(-1.39768 - 2.24644i) q^{7} +(0.612808 - 0.768437i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-1.16186 - 1.45693i) q^{10} +(0.588199 - 2.57707i) q^{11} +(-1.32673 + 0.638921i) q^{12} +(-1.09145 + 4.78194i) q^{13} +(-4.66081 + 1.60773i) q^{14} +(-0.222521 - 0.974928i) q^{15} +(-2.97821 - 3.73456i) q^{16} +(-0.367983 + 0.177211i) q^{17} -1.86348 q^{18} +2.86965 q^{19} +(-1.32673 + 0.638921i) q^{20} +(-2.62778 - 0.307883i) q^{21} +(-4.43801 - 2.13723i) q^{22} +(3.19557 + 1.53891i) q^{23} +(-0.218709 - 0.958226i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(8.23505 + 3.96579i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(0.419050 + 3.87343i) q^{28} +(0.312801 - 0.150637i) q^{29} -1.86348 q^{30} +0.169086 q^{31} +(-6.24869 + 3.00921i) q^{32} +(-1.64810 - 2.06665i) q^{33} +(0.169361 + 0.742021i) q^{34} +(-2.62778 - 0.307883i) q^{35} +(-0.327676 + 1.43564i) q^{36} +(-5.12827 + 2.46965i) q^{37} +(1.18994 - 5.21347i) q^{38} +(3.05816 + 3.83481i) q^{39} +(-0.218709 - 0.958226i) q^{40} +(-1.35858 + 1.70360i) q^{41} +(-1.64899 + 4.64637i) q^{42} +(-5.16523 - 6.47699i) q^{43} +(-2.42693 + 3.04327i) q^{44} +(-0.900969 - 0.433884i) q^{45} +(4.12092 - 5.16746i) q^{46} +(1.06876 - 4.68256i) q^{47} -4.77668 q^{48} +(-3.09299 + 6.27961i) q^{49} -1.86348 q^{50} +(-0.0908844 + 0.398190i) q^{51} +(4.50334 - 5.64701i) q^{52} +(1.37791 + 0.663564i) q^{53} +(-1.16186 + 1.45693i) q^{54} +(-1.64810 - 2.06665i) q^{55} +(-2.58276 - 0.302608i) q^{56} +(1.78920 - 2.24359i) q^{57} +(-0.143964 - 0.630749i) q^{58} +(4.42037 + 5.54297i) q^{59} +(-0.327676 + 1.43564i) q^{60} +(9.04769 - 4.35714i) q^{61} +(0.0701138 - 0.307189i) q^{62} +(-1.87910 + 1.86252i) q^{63} +(0.750086 + 3.28634i) q^{64} +(3.05816 + 3.83481i) q^{65} +(-4.43801 + 2.13723i) q^{66} +6.15332 q^{67} +0.601440 q^{68} +(3.19557 - 1.53891i) q^{69} +(-1.64899 + 4.64637i) q^{70} +(7.02539 + 3.38325i) q^{71} +(-0.885534 - 0.426451i) q^{72} +(-1.42656 - 6.25017i) q^{73} +(2.36025 + 10.3409i) q^{74} +(-0.900969 - 0.433884i) q^{75} +(-3.80727 - 1.83348i) q^{76} +(-6.61134 + 2.28056i) q^{77} +(8.23505 - 3.96579i) q^{78} +8.15231 q^{79} -4.77668 q^{80} +(-0.900969 + 0.433884i) q^{81} +(2.53168 + 3.17463i) q^{82} +(2.94782 + 12.9152i) q^{83} +(3.28965 + 2.08742i) q^{84} +(-0.0908844 + 0.398190i) q^{85} +(-13.9090 + 6.69821i) q^{86} +(0.0772556 - 0.338479i) q^{87} +(-1.61986 - 2.03124i) q^{88} +(3.84634 + 16.8519i) q^{89} +(-1.16186 + 1.45693i) q^{90} +(12.2678 - 4.23175i) q^{91} +(-3.25644 - 4.08344i) q^{92} +(0.105423 - 0.132197i) q^{93} +(-8.06391 - 3.88337i) q^{94} +(1.78920 - 2.24359i) q^{95} +(-1.54330 + 6.76164i) q^{96} -14.0274 q^{97} +(10.1260 + 8.22314i) q^{98} -2.64334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

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