LMFDB - Embedded newform 128.2.k.a.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	128.109
Dual form			128.2.k.a.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.957090 - 1.04114i) q^{2} +(-2.86311 - 1.53036i) q^{3} +(-0.167958 + 1.99294i) q^{4} +(-0.865631 + 1.05477i) q^{5} +(1.14693 + 4.44560i) q^{6} +(0.162245 + 0.108408i) q^{7} +(2.23568 - 1.73255i) q^{8} +(4.18867 + 6.26879i) q^{9} +(1.92666 - 0.108268i) q^{10} +(-0.144127 - 0.0437204i) q^{11} +(3.53080 - 5.44896i) q^{12} +(-3.75158 + 3.07884i) q^{13} +(-0.0424141 - 0.272677i) q^{14} +(4.09258 - 1.69520i) q^{15} +(-3.94358 - 0.669457i) q^{16} +(-0.223463 - 0.0925613i) q^{17} +(2.51777 - 10.3608i) q^{18} +(-0.742006 + 7.53372i) q^{19} +(-1.95671 - 1.90230i) q^{20} +(-0.298620 - 0.558679i) q^{21} +(0.0924232 + 0.191901i) q^{22} +(-6.74055 - 1.34078i) q^{23} +(-9.05243 + 1.53908i) q^{24} +(0.612220 + 3.07784i) q^{25} +(6.79611 + 0.959202i) q^{26} +(-1.44447 - 14.6660i) q^{27} +(-0.243301 + 0.305135i) q^{28} +(-1.92135 - 6.33383i) q^{29} +(-5.68192 - 2.63850i) q^{30} +(-2.37838 + 2.37838i) q^{31} +(3.07736 + 4.74656i) q^{32} +(0.345743 + 0.345743i) q^{33} +(0.117504 + 0.321246i) q^{34} +(-0.254791 + 0.0772899i) q^{35} +(-13.1968 + 7.29486i) q^{36} +(3.51713 - 0.346407i) q^{37} +(8.55384 - 6.43791i) q^{38} +(15.4529 - 3.07378i) q^{39} +(-0.107825 + 3.85789i) q^{40} +(0.456936 - 2.29717i) q^{41} +(-0.295858 + 0.845612i) q^{42} +(4.58870 - 2.45271i) q^{43} +(0.111339 - 0.279892i) q^{44} +(-10.2380 - 1.00836i) q^{45} +(5.05537 + 8.30112i) q^{46} +(-3.90401 + 9.42513i) q^{47} +(10.2664 + 7.95184i) q^{48} +(-2.66421 - 6.43198i) q^{49} +(2.61852 - 3.58317i) q^{50} +(0.498146 + 0.606993i) q^{51} +(-5.50582 - 7.99376i) q^{52} +(-0.703882 + 2.32039i) q^{53} +(-13.8869 + 15.5406i) q^{54} +(0.170876 - 0.114176i) q^{55} +(0.550551 - 0.0387305i) q^{56} +(13.6538 - 20.4343i) q^{57} +(-4.75552 + 8.06244i) q^{58} +(-1.33800 - 1.09807i) q^{59} +(2.69105 + 8.44098i) q^{60} +(-3.57815 + 6.69426i) q^{61} +(4.75256 + 0.199910i) q^{62} +1.47117i q^{63} +(1.99654 - 7.74686i) q^{64} -6.62221i q^{65} +(0.0290607 - 0.690875i) q^{66} +(1.30359 - 2.43884i) q^{67} +(0.222001 - 0.429801i) q^{68} +(17.2471 + 14.1543i) q^{69} +(0.324327 + 0.191300i) q^{70} +(-3.30056 + 4.93964i) q^{71} +(20.2255 + 6.75793i) q^{72} +(-8.33969 + 5.57240i) q^{73} +(-3.72687 - 3.33030i) q^{74} +(2.95736 - 9.74910i) q^{75} +(-14.8896 - 2.74411i) q^{76} +(-0.0186442 - 0.0227180i) q^{77} +(-17.9901 - 13.1468i) q^{78} +(-0.333360 - 0.804803i) q^{79} +(4.11981 - 3.58008i) q^{80} +(-9.65299 + 23.3044i) q^{81} +(-2.82902 + 1.72287i) q^{82} +(-1.71796 - 0.169204i) q^{83} +(1.16357 - 0.501296i) q^{84} +(0.291068 - 0.155579i) q^{85} +(-6.94543 - 2.43003i) q^{86} +(-4.19204 + 21.0748i) q^{87} +(-0.397970 + 0.151962i) q^{88} +(8.77606 - 1.74567i) q^{89} +(8.74885 + 11.6243i) q^{90} +(-0.942446 + 0.0928229i) q^{91} +(3.80421 - 13.2083i) q^{92} +(10.4494 - 3.16978i) q^{93} +(13.5494 - 4.95606i) q^{94} +(-7.30407 - 7.30407i) q^{95} +(-1.54686 - 18.2994i) q^{96} +(5.19447 - 5.19447i) q^{97} +(-4.14672 + 8.92981i) q^{98} +(-0.329626 - 1.08663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) $ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{23}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.957090	−	1.04114i	−0.676765	−	0.736199i
$2$	−0.957090	−	1.04114i	−0.676765	−	0.736199i
$3$	−2.86311	−	1.53036i	−1.65302	−	0.883556i	−0.990968	−	0.134095i	$-0.957187\pi$
$3$	−2.86311	−	1.53036i	−1.65302	−	0.883556i	−0.662049	−	0.749461i	$-0.730313\pi$
$4$	−0.167958	+	1.99294i	−0.0839788	+	0.996468i
$5$	−0.865631	+	1.05477i	−0.387122	+	0.471709i	−0.929712	−	0.368288i	$-0.879944\pi$
$5$	−0.865631	+	1.05477i	−0.387122	+	0.471709i	0.542590	+	0.839998i	$0.317444\pi$
$6$	1.14693	+	4.44560i	0.468231	+	1.81491i
$7$	0.162245	+	0.108408i	0.0613228	+	0.0409746i	0.585854	−	0.810417i	$-0.300759\pi$
$7$	0.162245	+	0.108408i	0.0613228	+	0.0409746i	−0.524531	+	0.851391i	$0.675759\pi$
$8$	2.23568	−	1.73255i	0.790433	−	0.612549i
$9$	4.18867	+	6.26879i	1.39622	+	2.08960i
$10$	1.92666	−	0.108268i	0.609263	−	0.0342375i
$11$	−0.144127	−	0.0437204i	−0.0434559	−	0.0131822i	0.268482	−	0.963285i	$-0.413478\pi$
$11$	−0.144127	−	0.0437204i	−0.0434559	−	0.0131822i	−0.311938	+	0.950103i	$0.600978\pi$
$12$	3.53080	−	5.44896i	1.01925	−	1.57298i
$13$	−3.75158	+	3.07884i	−1.04050	+	0.853917i	−0.989464	−	0.144780i	$-0.953752\pi$
$13$	−3.75158	+	3.07884i	−1.04050	+	0.853917i	−0.0510365	+	0.998697i	$0.516252\pi$
$14$	−0.0424141	−	0.272677i	−0.0113356	−	0.0728759i
$15$	4.09258	−	1.69520i	1.05670	−	0.437700i
$16$	−3.94358	−	0.669457i	−0.985895	−	0.167364i
$17$	−0.223463	−	0.0925613i	−0.0541977	−	0.0224494i	0.355420	−	0.934707i	$-0.384338\pi$
$17$	−0.223463	−	0.0925613i	−0.0541977	−	0.0224494i	−0.409618	+	0.912257i	$0.634338\pi$
$18$	2.51777	−	10.3608i	0.593445	−	2.44207i
$19$	−0.742006	+	7.53372i	−0.170228	+	1.72835i	0.408436	+	0.912787i	$0.366074\pi$
$19$	−0.742006	+	7.53372i	−0.170228	+	1.72835i	−0.578664	+	0.815566i	$0.696426\pi$
$20$	−1.95671	−	1.90230i	−0.437533	−	0.425368i
$21$	−0.298620	−	0.558679i	−0.0651643	−	0.121914i
$22$	0.0924232	+	0.191901i	0.0197047	+	0.0409135i
$23$	−6.74055	−	1.34078i	−1.40550	−	0.279572i	−0.566662	−	0.823950i	$-0.691766\pi$
$23$	−6.74055	−	1.34078i	−1.40550	−	0.279572i	−0.838840	+	0.544378i	$0.816766\pi$
$24$	−9.05243	+	1.53908i	−1.84782	+	0.314163i
$25$	0.612220	+	3.07784i	0.122444	+	0.615567i
$26$	6.79611	+	0.959202i	1.33283	+	0.188115i
$27$	−1.44447	−	14.6660i	−0.277989	−	2.82247i
$28$	−0.243301	+	0.305135i	−0.0459796	+	0.0576651i
$29$	−1.92135	−	6.33383i	−0.356785	−	1.17616i	−0.933307	−	0.359081i	$-0.883090\pi$
$29$	−1.92135	−	6.33383i	−0.356785	−	1.17616i	0.576522	−	0.817082i	$-0.304410\pi$
$30$	−5.68192	−	2.63850i	−1.03737	−	0.481723i
$31$	−2.37838	+	2.37838i	−0.427170	+	0.427170i	−0.887663	−	0.460493i	$-0.847673\pi$
$31$	−2.37838	+	2.37838i	−0.427170	+	0.427170i	0.460493	+	0.887663i	$0.347673\pi$
$32$	3.07736	+	4.74656i	0.544006	+	0.839082i
$33$	0.345743	+	0.345743i	0.0601861	+	0.0601861i
$34$	0.117504	+	0.321246i	0.0201518	+	0.0550933i
$35$	−0.254791	+	0.0772899i	−0.0430675	+	0.0130644i
$36$	−13.1968	+	7.29486i	−2.19947	+	1.21581i
$37$	3.51713	−	0.346407i	0.578213	−	0.0569490i	0.195317	−	0.980740i	$-0.437427\pi$
$37$	3.51713	−	0.346407i	0.578213	−	0.0569490i	0.382897	+	0.923791i	$0.374927\pi$
$38$	8.55384	−	6.43791i	1.38762	−	1.04437i
$39$	15.4529	−	3.07378i	2.47445	−	0.492198i
$40$	−0.107825	+	3.85789i	−0.0170486	+	0.609986i
$41$	0.456936	−	2.29717i	0.0713615	−	0.358758i	−0.928561	−	0.371179i	$-0.878954\pi$
$41$	0.456936	−	2.29717i	0.0713615	−	0.358758i	0.999923	+	0.0124205i	$0.00395366\pi$
$42$	−0.295858	+	0.845612i	−0.0456519	+	0.130481i
$43$	4.58870	−	2.45271i	0.699771	−	0.374035i	−0.0828263	−	0.996564i	$-0.526395\pi$
$43$	4.58870	−	2.45271i	0.699771	−	0.374035i	0.782597	+	0.622529i	$0.213895\pi$
$44$	0.111339	−	0.279892i	0.0167850	−	0.0421954i
$45$	−10.2380	−	1.00836i	−1.52619	−	0.150317i
$46$	5.05537	+	8.30112i	0.745374	+	1.22393i
$47$	−3.90401	+	9.42513i	−0.569459	+	1.37480i	0.332553	+	0.943085i	$0.392090\pi$
$47$	−3.90401	+	9.42513i	−0.569459	+	1.37480i	−0.902012	+	0.431711i	$0.857910\pi$
$48$	10.2664	+	7.95184i	1.48183	+	1.14775i
$49$	−2.66421	−	6.43198i	−0.380602	−	0.918854i
$50$	2.61852	−	3.58317i	0.370314	−	0.506737i
$51$	0.498146	+	0.606993i	0.0697544	+	0.0849960i
$52$	−5.50582	−	7.99376i	−0.763520	−	1.10854i
$53$	−0.703882	+	2.32039i	−0.0966856	+	0.318730i	−0.991920	−	0.126866i	$-0.959508\pi$
$53$	−0.703882	+	2.32039i	−0.0966856	+	0.318730i	0.895234	+	0.445596i	$0.147008\pi$
$54$	−13.8869	+	15.5406i	−1.88977	+	2.11480i
$55$	0.170876	−	0.114176i	0.0230409	−	0.0153954i
$56$	0.550551	−	0.0387305i	0.0735704	−	0.00517558i
$57$	13.6538	−	20.4343i	1.80849	−	2.70659i
$58$	−4.75552	+	8.06244i	−0.624430	+	1.05865i
$59$	−1.33800	−	1.09807i	−0.174193	−	0.142956i	0.543257	−	0.839566i	$-0.317191\pi$
$59$	−1.33800	−	1.09807i	−0.174193	−	0.142956i	−0.717450	+	0.696610i	$0.754691\pi$
$60$	2.69105	+	8.44098i	0.347413	+	1.08973i
$61$	−3.57815	+	6.69426i	−0.458136	+	0.857112i	0.541727	+	0.840554i	$0.317771\pi$
$61$	−3.57815	+	6.69426i	−0.458136	+	0.857112i	−0.999863	+	0.0165573i	$0.994729\pi$
$62$	4.75256	+	0.199910i	0.603576	+	0.0253886i
$63$			1.47117i			0.185350i
$64$	1.99654	−	7.74686i	0.249567	−	0.968357i
$65$		−	6.62221i		−	0.821384i
$66$	0.0290607	−	0.690875i	0.00357713	−	0.0850408i
$67$	1.30359	−	2.43884i	0.159259	−	0.297952i	−0.789618	−	0.613599i	$-0.789721\pi$
$67$	1.30359	−	2.43884i	0.159259	−	0.297952i	0.948877	+	0.315646i	$0.102221\pi$
$68$	0.222001	−	0.429801i	0.0269216	−	0.0521210i
$69$	17.2471	+	14.1543i	2.07630	+	1.70398i
$70$	0.324327	+	0.191300i	0.0387645	+	0.0228647i
$71$	−3.30056	+	4.93964i	−0.391704	+	0.586227i	−0.973944	−	0.226790i	$-0.927177\pi$
$71$	−3.30056	+	4.93964i	−0.391704	+	0.586227i	0.582239	+	0.813018i	$0.302177\pi$
$72$	20.2255	+	6.75793i	2.38360	+	0.796430i
$73$	−8.33969	+	5.57240i	−0.976086	+	0.652200i	−0.937840	−	0.347068i	$-0.887177\pi$
$73$	−8.33969	+	5.57240i	−0.976086	+	0.652200i	−0.0382465	+	0.999268i	$0.512177\pi$
$74$	−3.72687	−	3.33030i	−0.433240	−	0.387139i
$75$	2.95736	−	9.74910i	0.341486	−	1.12573i
$76$	−14.8896	−	2.74411i	−1.70795	−	0.314772i
$77$	−0.0186442	−	0.0227180i	−0.00212470	−	0.00258896i
$78$	−17.9901	−	13.1468i	−2.03698	−	1.48858i
$79$	−0.333360	−	0.804803i	−0.0375060	−	0.0905474i	0.904017	−	0.427497i	$-0.140605\pi$
$79$	−0.333360	−	0.804803i	−0.0375060	−	0.0905474i	−0.941523	+	0.336950i	$0.890605\pi$
$80$	4.11981	−	3.58008i	0.460609	−	0.400266i
$81$	−9.65299	+	23.3044i	−1.07255	+	2.58938i
$82$	−2.82902	+	1.72287i	−0.312413	+	0.190259i
$83$	−1.71796	−	0.169204i	−0.188571	−	0.0185726i	0.00329100	−	0.999995i	$-0.498952\pi$
$83$	−1.71796	−	0.169204i	−0.188571	−	0.0185726i	−0.191862	+	0.981422i	$0.561452\pi$
$84$	1.16357	−	0.501296i	0.126956	−	0.0546959i
$85$	0.291068	−	0.155579i	0.0315707	−	0.0168749i
$86$	−6.94543	−	2.43003i	−0.748945	−	0.262037i
$87$	−4.19204	+	21.0748i	−0.449434	+	2.25946i
$88$	−0.397970	+	0.151962i	−0.0424237	+	0.0161992i
$89$	8.77606	−	1.74567i	0.930260	−	0.185040i	0.293374	−	0.955998i	$-0.405222\pi$
$89$	8.77606	−	1.74567i	0.930260	−	0.185040i	0.636886	+	0.770958i	$0.280222\pi$
$90$	8.74885	+	11.6243i	0.922210	+	1.22531i
$91$	−0.942446	+	0.0928229i	−0.0987952	+	0.00973048i
$92$	3.80421	−	13.2083i	0.396616	−	1.37706i
$93$	10.4494	−	3.16978i	1.08355	−	0.328691i
$94$	13.5494	−	4.95606i	1.39751	−	0.511178i
$95$	−7.30407	−	7.30407i	−0.749381	−	0.749381i
$96$	−1.54686	−	18.2994i	−0.157875	−	1.86768i
$97$	5.19447	−	5.19447i	0.527418	−	0.527418i	−0.392383	−	0.919802i	$-0.628349\pi$
$97$	5.19447	−	5.19447i	0.527418	−	0.527418i	0.919802	+	0.392383i	$0.128349\pi$
$98$	−4.14672	+	8.92981i	−0.418882	+	0.902047i
$99$	−0.329626	−	1.08663i	−0.0331287	−	0.109211i
$100$	−6.23675	+	0.703168i	−0.623675	+	0.0703168i
$101$	−0.0387557	−	0.393493i	−0.00385634	−	0.0391540i	0.993064	−	0.117575i	$-0.0375121\pi$
$101$	−0.0387557	−	0.393493i	−0.00385634	−	0.0391540i	−0.996920	+	0.0784211i	$0.975012\pi$
$102$	0.155196	−	1.09959i	0.0153667	−	0.108875i
$103$	−1.46072	−	7.34354i	−0.143929	−	0.723580i	−0.983583	−	0.180458i	$-0.942242\pi$
$103$	−1.46072	−	7.34354i	−0.143929	−	0.723580i	0.839654	−	0.543122i	$-0.182758\pi$
$104$	−3.05308	+	13.3831i	−0.299380	+	1.31232i
$105$	0.847775	+	0.168633i	0.0827344	+	0.0164569i
$106$	3.08953	−	1.48798i	0.300082	−	0.144525i
$107$	7.44829	+	13.9348i	0.720053	+	1.34712i	0.929323	+	0.369267i	$0.120391\pi$
$107$	7.44829	+	13.9348i	0.720053	+	1.34712i	−0.209270	+	0.977858i	$0.567109\pi$
$108$	29.4710	−	0.415479i	2.83585	−	0.0399795i
$109$	1.12348	−	11.4069i	0.107610	−	1.09258i	−0.778036	−	0.628220i	$-0.783784\pi$
$109$	1.12348	−	11.4069i	0.107610	−	1.09258i	0.885645	−	0.464362i	$-0.153716\pi$
$110$	−0.282417	−	0.0686299i	−0.0269274	−	0.00654360i
$111$	−10.6001	−	4.39069i	−1.00611	−	0.416746i
$112$	−0.567251	−	0.536134i	−0.0536001	−	0.0506599i
$113$	2.62802	−	1.08856i	0.247224	−	0.102403i	−0.255631	−	0.966774i	$-0.582283\pi$
$113$	2.62802	−	1.08856i	0.247224	−	0.102403i	0.502854	+	0.864371i	$0.332283\pi$
$114$	−34.3429	+	5.34195i	−3.21651	+	0.500319i
$115$	7.24905	−	5.94914i	0.675977	−	0.554760i
$116$	12.9456	−	2.76530i	1.20197	−	0.256752i
$117$	−35.0147	−	10.6216i	−3.23711	−	0.981968i
$118$	0.137340	+	2.44400i	0.0126432	+	0.224988i
$119$	−0.0262212	−	0.0392429i	−0.00240370	−	0.00359739i
$120$	6.21269	−	10.8805i	0.567138	−	0.993253i
$121$	−9.12730	−	6.09867i	−0.829755	−	0.554425i
$122$	10.3943	−	2.68163i	0.941055	−	0.242784i
$123$	−4.82377	+	5.87778i	−0.434945	+	0.529982i
$124$	−4.34049	−	5.13943i	−0.389788	−	0.461534i
$125$	−9.79329	−	5.23463i	−0.875939	−	0.468199i
$126$	1.53169	−	1.40804i	0.136454	−	0.125438i
$127$	−1.79922			−0.159655			−0.0798275	−	0.996809i	$-0.525437\pi$
$127$	−1.79922			−0.159655			−0.0798275	+	0.996809i	$0.525437\pi$
$128$	−9.97646	+	5.33576i	−0.881802	+	0.471619i
$129$	−16.8915			−1.48721
$130$	−6.89466	+	6.33805i	−0.604702	+	0.555884i
$131$	−7.98472	−	4.26792i	−0.697628	−	0.372890i	0.0841445	−	0.996454i	$-0.473184\pi$
$131$	−7.98472	−	4.26792i	−0.697628	−	0.372890i	−0.781773	+	0.623564i	$0.785684\pi$
$132$	−0.747114	+	0.630973i	−0.0650279	+	0.0549192i
$133$	−0.937106	+	1.14187i	−0.0812574	+	0.0990124i
$134$	−3.78684	+	0.976970i	−0.327133	+	0.0843974i
$135$	16.7197	+	11.1717i	1.43900	+	0.961510i
$136$	−0.659959	+	0.180223i	−0.0565910	+	0.0154540i
$137$	−0.528159	−	0.790446i	−0.0451237	−	0.0675323i	0.808222	−	0.588878i	$-0.200430\pi$
$137$	−0.528159	−	0.790446i	−0.0451237	−	0.0675323i	−0.853346	+	0.521346i	$0.825430\pi$
$138$	−1.77034	−	31.5036i	−0.150701	−	2.68176i
$139$	15.2367	+	4.62199i	1.29236	+	0.392032i	0.860288	−	0.509809i	$-0.170284\pi$
$139$	15.2367	+	4.62199i	1.29236	+	0.392032i	0.432068	+	0.901841i	$0.357784\pi$
$140$	−0.111240	−	0.520763i	−0.00940147	−	0.0440125i
$141$	25.6015	−	21.0106i	2.15603	−	1.76941i
$142$	8.30180	−	1.29132i	0.696672	−	0.108365i
$143$	0.675311	−	0.279723i	0.0564724	−	0.0233916i
$144$	−12.3217	−	27.5256i	−1.02681	−	2.29380i
$145$	8.34394	+	3.45617i	0.692926	+	0.287019i
$146$	13.7835	+	3.34952i	1.14073	+	0.277208i
$147$	−2.21534	+	22.4927i	−0.182718	+	1.85516i
$148$	0.0996385	+	7.06760i	0.00819023	+	0.580953i
$149$	6.11873	+	11.4473i	0.501266	+	0.937803i	0.997571	+	0.0696548i	$0.0221898\pi$
$149$	6.11873	+	11.4473i	0.501266	+	0.937803i	−0.496305	+	0.868148i	$0.665310\pi$
$150$	−12.9807	+	6.25174i	−1.05987	+	0.510452i
$151$	6.96948	+	1.38632i	0.567169	+	0.112817i	0.470342	−	0.882484i	$-0.344131\pi$
$151$	6.96948	+	1.38632i	0.567169	+	0.112817i	0.0968269	+	0.995301i	$0.469131\pi$
$152$	11.3937	+	18.1286i	0.924147	+	1.47042i
$153$	−0.355765	−	1.78855i	−0.0287619	−	0.144596i
$154$	−0.00580853	+	0.0411544i	−0.000468064	+	0.00331632i
$155$	−0.449855	−	4.56746i	−0.0361332	−	0.366867i
$156$	3.53040	+	31.3129i	0.282659	+	2.50704i
$157$	4.80591	+	15.8430i	0.383553	+	1.26441i	0.910146	+	0.414288i	$0.135969\pi$
$157$	4.80591	+	15.8430i	0.383553	+	1.26441i	−0.526593	+	0.850118i	$0.676531\pi$
$158$	−0.518859	+	1.11734i	−0.0412782	+	0.0888912i
$159$	5.56633	−	5.56633i	0.441439	−	0.441439i
$160$	−7.67041	−	0.862849i	−0.606399	−	0.0682142i
$161$	−0.948267	−	0.948267i	−0.0747339	−	0.0747339i
$162$	33.5020	−	12.2543i	2.63216	−	0.962785i
$163$	6.28708	−	1.90716i	0.492442	−	0.149381i	−0.0342903	−	0.999412i	$-0.510917\pi$
$163$	6.28708	−	1.90716i	0.492442	−	0.149381i	0.526732	+	0.850031i	$0.323417\pi$
$164$	4.50137	+	1.29647i	0.351498	+	0.101237i
$165$	−0.663967	+	0.0653950i	−0.0516897	+	0.00509099i
$166$	1.46808	+	1.95058i	0.113945	+	0.151395i
$167$	3.04803	−	0.606292i	0.235864	−	0.0469163i	−0.0757428	−	0.997127i	$-0.524133\pi$
$167$	3.04803	−	0.606292i	0.235864	−	0.0469163i	0.311607	+	0.950211i	$0.399133\pi$
$168$	−1.63556	−	0.731654i	−0.126186	−	0.0564483i
$169$	2.05890	−	10.3508i	0.158377	−	0.796216i
$170$	−0.440558	−	0.154140i	−0.0337892	−	0.0118220i
$171$	−50.3353	+	26.9048i	−3.84924	+	2.05746i
$172$	4.11739	+	9.55694i	0.313948	+	0.728710i
$173$	−15.4705	−	1.52371i	−1.17620	−	0.115845i	−0.509027	−	0.860751i	$-0.669995\pi$
$173$	−15.4705	−	1.52371i	−1.17620	−	0.115845i	−0.667170	+	0.744905i	$0.732495\pi$
$174$	25.9540	−	15.8060i	1.96757	−	1.19825i
$175$	−0.234334	+	0.565733i	−0.0177140	+	0.0427654i
$176$	0.539107	+	0.268902i	0.0406367	+	0.0202692i
$177$	2.15039	+	5.19151i	0.161634	+	0.390218i
$178$	−10.2170	−	7.46637i	−0.765794	−	0.559628i
$179$	7.82280	+	9.53211i	0.584703	+	0.712463i	0.978387	−	0.206783i	$-0.0662994\pi$
$179$	7.82280	+	9.53211i	0.584703	+	0.712463i	−0.393683	+	0.919246i	$0.628799\pi$
$180$	3.72914	−	20.2343i	0.277953	−	1.50818i
$181$	−0.181651	+	0.598824i	−0.0135020	+	0.0445102i	−0.963433	−	0.267951i	$-0.913653\pi$
$181$	−0.181651	+	0.598824i	−0.0135020	+	0.0445102i	0.949930	+	0.312461i	$0.101153\pi$
$182$	0.998648	+	0.892382i	0.0740247	+	0.0661477i
$183$	20.4893	−	13.6905i	1.51461	−	1.01203i
$184$	−17.3927	+	8.68079i	−1.28221	+	0.639956i
$185$	−2.67916	+	4.00964i	−0.196976	+	0.294795i
$186$	−13.3012	−	7.84551i	−0.975289	−	0.575261i
$187$	0.0281602	+	0.0231105i	0.00205928	+	0.00169000i
$188$	−18.1280	−	9.36347i	−1.32212	−	0.682901i
$189$	1.35556	−	2.53607i	0.0986025	−	0.184472i
$190$	−0.613929	+	14.5952i	−0.0445391	+	1.05885i
$191$			23.7786i			1.72056i	0.509822	+	0.860280i	$0.329711\pi$
$191$			23.7786i			1.72056i	−0.509822	+	0.860280i	$0.670289\pi$
$192$	−17.5718	+	19.1247i	−1.26814	+	1.38020i
$193$			19.6161i			1.41200i	0.708214	+	0.705998i	$0.249501\pi$
$193$			19.6161i			1.41200i	−0.708214	+	0.705998i	$0.750499\pi$
$194$	−10.3798	−	0.436611i	−0.745223	−	0.0313468i
$195$	−10.1344	+	18.9601i	−0.725738	+	1.35776i
$196$	13.2660	−	4.22930i	0.947571	−	0.302093i
$197$	−6.21590	−	5.10126i	−0.442865	−	0.363450i	0.386376	−	0.922341i	$-0.373727\pi$
$197$	−6.21590	−	5.10126i	−0.442865	−	0.363450i	−0.829241	+	0.558892i	$0.811227\pi$
$198$	−0.815857	+	1.38319i	−0.0579805	+	0.0982992i
$199$	12.4091	−	18.5716i	0.879659	−	1.31650i	−0.0681530	−	0.997675i	$-0.521711\pi$
$199$	12.4091	−	18.5716i	0.879659	−	1.31650i	0.947812	−	0.318828i	$-0.103289\pi$
$200$	6.70123	+	5.82036i	0.473849	+	0.411561i
$201$	−7.46464	+	4.98771i	−0.526515	+	0.351806i
$202$	−0.372590	+	0.416959i	−0.0262153	+	0.0293371i
$203$	0.374913	−	1.23592i	0.0263137	−	0.0867446i
$204$	−1.29336	+	0.890824i	−0.0905536	+	0.0623701i
$205$	2.02746	+	2.47047i	0.141604	+	0.172545i
$206$	−6.24763	+	8.54925i	−0.435293	+	0.595654i
$207$	−19.8289	−	47.8712i	−1.37820	−	3.32728i
$208$	16.8558	−	9.63013i	1.16874	−	0.667730i
$209$	0.436320	−	1.05337i	0.0301809	−	0.0728632i
$210$	−0.635826	−	1.04405i	−0.0438762	−	0.0720464i
$211$	−1.26380	−	0.124474i	−0.0870038	−	0.00856913i	0.0544215	−	0.998518i	$-0.482669\pi$
$211$	−1.26380	−	0.124474i	−0.0870038	−	0.00856913i	−0.141425	+	0.989949i	$0.545169\pi$
$212$	−4.50616	−	1.79252i	−0.309484	−	0.123111i
$213$	17.0093	−	9.09167i	1.16546	−	0.622951i
$214$	7.37940	−	21.0916i	0.504446	−	1.44179i
$215$	−1.38506	+	6.96319i	−0.0944606	+	0.474886i
$216$	−28.6390	−	30.2859i	−1.94863	−	2.06069i
$217$	−0.643717	+	0.128043i	−0.0436983	+	0.00869214i
$218$	−12.9515	+	9.74772i	−0.877185	+	0.660199i
$219$	32.4052	−	3.19164i	2.18974	−	0.215671i
$220$	0.198845	+	0.359721i	0.0134061	+	0.0242524i
$221$	1.12332	−	0.340755i	0.0755627	−	0.0229217i
$222$	5.57388	+	15.2385i	0.374094	+	1.02274i
$223$	3.40850	+	3.40850i	0.228250	+	0.228250i	0.811961	−	0.583711i	$-0.198400\pi$
$223$	3.40850	+	3.40850i	0.228250	+	0.228250i	−0.583711	+	0.811961i	$0.698400\pi$
$224$	−0.0152819	+	1.10372i	−0.00102106	+	0.0737452i
$225$	−16.7299	+	16.7299i	−1.11533	+	1.11533i
$226$	−3.64860	−	1.69429i	−0.242701	−	0.112703i
$227$	−3.52798	−	11.6302i	−0.234160	−	0.771923i	−0.992733	−	0.120335i	$-0.961603\pi$
$227$	−3.52798	−	11.6302i	−0.234160	−	0.771923i	0.758573	−	0.651588i	$-0.225897\pi$
$228$	38.4310	+	30.6432i	2.54516	+	2.02939i
$229$	1.04627	+	10.6230i	0.0691394	+	0.701984i	0.965804	+	0.259274i	$0.0834832\pi$
$229$	1.04627	+	10.6230i	0.0691394	+	0.701984i	−0.896664	+	0.442711i	$0.854017\pi$
$230$	−13.1319	−	1.85343i	−0.865892	−	0.122212i
$231$	0.0186135	+	0.0935765i	0.00122468	+	0.00615688i
$232$	−15.2692	−	10.8316i	−1.00247	−	0.711129i
$233$	0.564171	+	0.112221i	0.0369600	+	0.00735181i	0.213536	−	0.976935i	$-0.431502\pi$
$233$	0.564171	+	0.112221i	0.0369600	+	0.00735181i	−0.176576	+	0.984287i	$0.556502\pi$
$234$	22.4536	+	46.6212i	1.46784	+	3.04772i
$235$	−6.56194	−	12.2765i	−0.428054	−	0.800833i
$236$	2.41310	−	2.48212i	0.157080	−	0.161572i
$237$	−0.277194	+	2.81440i	−0.0180057	+	0.182815i
$238$	−0.0157613	+	0.0648590i	−0.00102166	+	0.00420419i
$239$	−8.23481	−	3.41097i	−0.532665	−	0.220637i	0.100105	−	0.994977i	$-0.468082\pi$
$239$	−8.23481	−	3.41097i	−0.532665	−	0.220637i	−0.632770	+	0.774340i	$0.718082\pi$
$240$	−17.2743	+	3.94536i	−1.11505	+	0.254672i
$241$	13.1850	−	5.46139i	0.849319	−	0.351799i	0.0847977	−	0.996398i	$-0.472976\pi$
$241$	13.1850	−	5.46139i	0.849319	−	0.351799i	0.764521	+	0.644599i	$0.222976\pi$
$242$	2.38606	+	15.3398i	0.153382	+	0.986080i
$243$	29.1263	−	23.9034i	1.86845	−	1.53340i
$244$	−12.7402	−	8.25538i	−0.815610	−	0.528497i
$245$	9.09051	+	2.75758i	0.580771	+	0.176175i
$246$	10.7364	−	0.603331i	0.684528	−	0.0384670i
$247$	−20.4114	−	30.5478i	−1.29875	−	1.94371i
$248$	−1.19664	+	9.43797i	−0.0759865	+	0.599311i
$249$	4.65976	+	3.11355i	0.295300	+	0.197313i
$250$	3.92307	+	15.2062i	0.248117	+	0.961726i
$251$	10.0256	−	12.2162i	0.632811	−	0.771082i	−0.353597	−	0.935398i	$-0.615042\pi$
$251$	10.0256	−	12.2162i	0.632811	−	0.771082i	0.986408	+	0.164316i	$0.0525416\pi$
$252$	−2.93194	−	0.247093i	−0.184695	−	0.0155654i
$253$	0.912875	+	0.487942i	0.0573920	+	0.0306767i
$254$	1.72202	+	1.87325i	0.108049	+	0.117538i
$255$	−1.07145			−0.0670969
$256$	15.1037	+	5.28011i	0.943978	+	0.330007i
$257$	3.04880			0.190179			0.0950894	−	0.995469i	$-0.469686\pi$
$257$	3.04880			0.190179			0.0950894	+	0.995469i	$0.469686\pi$
$258$	16.1667	+	17.5865i	1.00649	+	1.09489i
$259$	0.608190	+	0.325084i	0.0377911	+	0.0201998i
$260$	13.1976	+	1.11225i	0.818482	+	0.0689788i
$261$	31.6576	−	38.5749i	1.95955	−	2.38772i
$262$	3.19858	+	12.3980i	0.197609	+	0.765952i
$263$	−18.0928	−	12.0892i	−1.11565	−	0.745454i	−0.145839	−	0.989308i	$-0.546588\pi$
$263$	−18.0928	−	12.0892i	−1.11565	−	0.745454i	−0.969812	+	0.243854i	$0.921588\pi$
$264$	1.37199	+	0.173954i	0.0844400	+	0.0107061i
$265$	−1.83818	−	2.75104i	−0.112919	−	0.168995i
$266$	2.08574	−	0.117208i	0.127885	−	0.00718648i
$267$	−27.7983	−	8.43253i	−1.70123	−	0.516062i
$268$	4.64151	+	3.00759i	0.283525	+	0.183718i
$269$	14.0961	−	11.5684i	0.859456	−	0.705338i	−0.0976042	−	0.995225i	$-0.531118\pi$
$269$	14.0961	−	11.5684i	0.859456	−	0.705338i	0.957061	+	0.289888i	$0.0936179\pi$
$270$	−4.37087	−	28.1000i	−0.266003	−	1.71011i
$271$	18.5319	−	7.67617i	1.12573	−	0.466294i	0.259405	−	0.965769i	$-0.416473\pi$
$271$	18.5319	−	7.67617i	1.12573	−	0.466294i	0.866329	+	0.499474i	$0.166473\pi$
$272$	0.819278	+	0.514622i	0.0496760	+	0.0312035i
$273$	2.84038	+	1.17652i	0.171908	+	0.0712065i
$274$	−0.317471	+	1.30642i	−0.0191791	+	0.0789235i
$275$	0.0463270	−	0.470366i	0.00279362	−	0.0283641i
$276$	−31.1054	+	31.9949i	−1.87232	+	1.92587i
$277$	10.3694	+	19.3997i	0.623035	+	1.16562i	0.973423	+	0.229012i	$0.0735497\pi$
$277$	10.3694	+	19.3997i	0.623035	+	1.16562i	−0.350388	+	0.936605i	$0.613950\pi$
$278$	−9.77070	−	20.2872i	−0.586008	−	1.21675i
$279$	−24.8718	−	4.94732i	−1.48904	−	0.296188i
$280$	−0.435722	+	0.614233i	−0.0260394	+	0.0367074i
$281$	3.85751	+	19.3930i	0.230120	+	1.15689i	0.907108	+	0.420897i	$0.138285\pi$
$281$	3.85751	+	19.3930i	0.230120	+	1.15689i	−0.676988	+	0.735994i	$0.736715\pi$
$282$	−46.3780	−	6.54578i	−2.76177	−	0.389795i
$283$	1.31008	+	13.3014i	0.0778760	+	0.790688i	0.952226	+	0.305393i	$0.0987878\pi$
$283$	1.31008	+	13.3014i	0.0778760	+	0.790688i	−0.874350	+	0.485295i	$0.838712\pi$
$284$	−9.29002	−	7.40745i	−0.551262	−	0.439551i
$285$	9.73446	+	32.0902i	0.576620	+	1.90086i
$286$	−0.937566	−	0.435376i	−0.0554394	−	0.0257443i
$287$	0.323169	−	0.323169i	0.0190761	−	0.0190761i
$288$	−16.8651	+	39.1731i	−0.993788	+	2.30830i
$289$	−11.9794	−	11.9794i	−0.704673	−	0.704673i
$290$	−4.38753	−	11.9951i	−0.257645	−	0.704376i
$291$	−22.8218	+	6.92290i	−1.33784	+	0.405828i
$292$	−9.70472	−	17.5564i	−0.567926	−	1.02741i
$293$	−16.6050	+	1.63545i	−0.970072	+	0.0955437i	−0.570623	−	0.821212i	$-0.693298\pi$
$293$	−16.6050	+	1.63545i	−0.970072	+	0.0955437i	−0.399448	+	0.916756i	$0.630798\pi$
$294$	25.5384	−	19.2210i	1.48943	−	1.12099i
$295$	2.31643	−	0.460766i	0.134867	−	0.0268268i
$296$	7.26302	−	6.86807i	0.422154	−	0.399198i
$297$	−0.433016	+	2.17692i	−0.0251261	+	0.126318i
$298$	6.06214	−	17.3266i	0.351171	−	1.00370i
$299$	29.4157	−	15.7230i	1.70116	−	0.909287i
$300$	18.9326	+	7.53126i	1.09308	+	0.434817i
$301$	1.01039	+	0.0995145i	0.0582378	+	0.00573592i
$302$	−5.22707	−	8.58306i	−0.300784	−	0.493900i
$303$	−0.491226	+	1.18592i	−0.0282202	+	0.0681296i
$304$	7.96966	−	29.2131i	0.457091	−	1.67548i
$305$	−3.96357	−	9.56890i	−0.226953	−	0.547914i
$306$	−1.52164	+	2.08221i	−0.0869863	+	0.119032i
$307$	−3.74974	−	4.56907i	−0.214009	−	0.260771i	0.654930	−	0.755689i	$-0.272698\pi$
$307$	−3.74974	−	4.56907i	−0.214009	−	0.260771i	−0.868939	+	0.494918i	$0.835198\pi$
$308$	0.0484069	−	0.0333410i	0.00275824	−	0.00189978i
$309$	−7.05608	+	23.2608i	−0.401407	+	1.32326i
$310$	−4.32482	+	4.83983i	−0.245633	+	0.274884i
$311$	−16.3214	+	10.9056i	−0.925499	+	0.618399i	−0.924327	−	0.381601i	$-0.875373\pi$
$311$	−16.3214	+	10.9056i	−0.925499	+	0.618399i	−0.00117166	+	0.999999i	$0.500373\pi$
$312$	29.2223	−	33.6450i	1.65439	−	1.90477i
$313$	−8.80698	+	13.1806i	−0.497800	+	0.745011i	−0.992258	−	0.124191i	$-0.960367\pi$
$313$	−8.80698	+	13.1806i	−0.497800	+	0.745011i	0.494458	+	0.869201i	$0.335367\pi$
$314$	11.8951	−	20.1668i	0.671279	−	1.13808i
$315$	−1.55175	−	1.27349i	−0.0874311	−	0.0717529i
$316$	1.65991	−	0.529193i	0.0933773	−	0.0297694i
$317$	−2.36221	+	4.41939i	−0.132675	+	0.248218i	−0.939483	−	0.342597i	$-0.888694\pi$
$317$	−2.36221	+	4.41939i	−0.132675	+	0.248218i	0.806807	+	0.590815i	$0.201194\pi$
$318$	−11.1228	−	0.467867i	−0.623737	−	0.0262367i
$319$			0.996877i			0.0558144i
$320$	6.44292	+	8.81182i	0.360170	+	0.492596i
$321$		−	51.2954i		−	2.86303i
$322$	−0.0797047	+	1.89486i	−0.00444177	+	0.105596i
$323$	0.863142	−	1.61482i	0.0480265	−	0.0898512i
$324$	−44.8228	−	23.1519i	−2.49016	−	1.28622i
$325$	−11.7730	−	9.66181i	−0.653046	−	0.535941i
$326$	−8.00293	−	4.72042i	−0.443241	−	0.261440i
$327$	−20.6733	+	30.9399i	−1.14324	+	1.71098i
$328$	−2.95841	−	5.92741i	−0.163351	−	0.327287i
$329$	−1.65517	+	1.10595i	−0.0912525	+	0.0609729i
$330$	0.703561	+	0.628695i	0.0387298	+	0.0346085i
$331$	−0.0486908	+	0.160512i	−0.00267629	+	0.00882254i	−0.958268	−	0.285870i	$-0.907717\pi$
$331$	−0.0486908	+	0.160512i	−0.00267629	+	0.00882254i	0.955592	+	0.294693i	$0.0952173\pi$
$332$	0.625757	−	3.39536i	0.0343429	−	0.186345i
$333$	16.9037	+	20.5972i	0.926316	+	1.12872i
$334$	−3.54848	−	2.59316i	−0.194164	−	0.141892i
$335$	1.44400	+	3.48613i	0.0788943	+	0.190468i
$336$	0.803621	+	2.40311i	0.0438411	+	0.131100i
$337$	−0.0500988	+	0.120949i	−0.00272906	+	0.00658852i	−0.925238	−	0.379387i	$-0.876135\pi$
$337$	−0.0500988	+	0.120949i	−0.00272906	+	0.00658852i	0.922509	+	0.385975i	$0.126135\pi$
$338$	−12.7472	+	7.76304i	−0.693358	+	0.422254i
$339$	−9.19021	−	0.905157i	−0.499144	−	0.0491614i
$340$	0.261172	+	0.606210i	0.0141640	+	0.0328763i
$341$	0.446773	−	0.238805i	0.0241941	−	0.0129320i
$342$	76.1872	+	26.6560i	4.11973	+	1.44139i
$343$	0.531503	−	2.67204i	0.0286984	−	0.144277i
$344$	6.00943	−	13.4336i	0.324007	−	0.724293i
$345$	−29.8592	+	5.93936i	−1.60756	+	0.319764i
$346$	13.2202	+	17.5653i	0.710723	+	0.944315i
$347$	11.1775	−	1.10089i	0.600041	−	0.0590989i	0.206564	−	0.978433i	$-0.433772\pi$
$347$	11.1775	−	1.10089i	0.600041	−	0.0590989i	0.393477	+	0.919334i	$0.371272\pi$
$348$	−41.2966	−	11.8941i	−2.21373	−	0.637593i
$349$	−30.0494	+	9.11537i	−1.60851	+	0.487935i	−0.961558	−	0.274601i	$-0.911454\pi$
$349$	−30.0494	+	9.11537i	−1.60851	+	0.487935i	−0.646947	+	0.762535i	$0.723954\pi$
$350$	0.813287	−	0.297482i	0.0434720	−	0.0159011i
$351$	50.5733	+	50.5733i	2.69940	+	2.69940i
$352$	−0.236009	−	0.818651i	−0.0125793	−	0.0436342i
$353$	4.28714	−	4.28714i	0.228182	−	0.228182i	−0.583751	−	0.811933i	$-0.698416\pi$
$353$	4.28714	−	4.28714i	0.228182	−	0.228182i	0.811933	+	0.583751i	$0.198416\pi$
$354$	3.34698	−	7.20761i	0.177890	−	0.383080i
$355$	−2.35314	−	7.75725i	−0.124891	−	0.411712i
$356$	2.00499	+	17.7833i	0.106264	+	0.942513i
$357$	0.0150184	+	0.152485i	0.000794860	+	0.00807034i
$358$	2.43717	−	17.2677i	0.128808	−	0.912628i
$359$	−3.28081	−	16.4938i	−0.173155	−	0.870507i	−0.965494	−	0.260426i	$-0.916137\pi$
$359$	−3.28081	−	16.4938i	−0.173155	−	0.870507i	0.792339	−	0.610081i	$-0.208863\pi$
$360$	−24.6359	+	15.4835i	−1.29843	+	0.816052i
$361$	−37.5714	−	7.47342i	−1.97744	−	0.393338i
$362$	0.797318	−	0.384003i	0.0419061	−	0.0201828i
$363$	16.7993	+	31.4293i	0.881734	+	1.64961i
$364$	−0.0266990	−	1.89382i	−0.00139941	−	0.0992634i
$365$	1.34147	−	13.6201i	0.0702155	−	0.712910i
$366$	−33.8639	−	8.22924i	−1.77009	−	0.430149i
$367$	20.2741	+	8.39780i	1.05830	+	0.438362i	0.842847	−	0.538153i	$-0.180878\pi$
$367$	20.2741	+	8.39780i	1.05830	+	0.438362i	0.215452	+	0.976515i	$0.430878\pi$
$368$	25.6843	+	9.79998i	1.33889	+	0.510859i
$369$	16.3145	−	6.75767i	0.849297	−	0.351790i
$370$	6.73881	−	1.04820i	0.350334	−	0.0544935i
$371$	−0.365751	+	0.300164i	−0.0189888	+	0.0155837i
$372$	4.56211	+	21.3573i	0.236535	+	1.10732i
$373$	2.60073	+	0.788923i	0.134661	+	0.0408489i	0.356896	−	0.934144i	$-0.383835\pi$
$373$	2.60073	+	0.788923i	0.134661	+	0.0408489i	−0.222235	+	0.974993i	$0.571335\pi$
$374$	−0.00289053	−	0.0514376i	−0.000149466	−	0.00265977i
$375$	20.0284	+	29.9746i	1.03426	+	1.54788i
$376$	7.60137	+	27.8355i	0.392011	+	1.43550i
$377$	26.7089	+	17.8463i	1.37558	+	0.919133i
$378$	−3.93781	+	1.01592i	−0.202539	+	0.0522533i
$379$	−4.18516	+	5.09963i	−0.214977	+	0.261950i	−0.869322	−	0.494246i	$-0.835444\pi$
$379$	−4.18516	+	5.09963i	−0.214977	+	0.261950i	0.654345	+	0.756196i	$0.272944\pi$
$380$	15.7833	−	13.3298i	0.809666	−	0.683802i
$381$	5.15137	+	2.75346i	0.263913	+	0.141064i
$382$	24.7569	−	22.7583i	1.26667	−	1.16441i
$383$	−13.8834			−0.709410			−0.354705	−	0.934978i	$-0.615419\pi$
$383$	−13.8834			−0.709410			−0.354705	+	0.934978i	$0.615419\pi$
$384$	36.7293	−	0.00925813i	1.87434	−	0.000472452i
$385$	0.0401013			0.00204375
$386$	20.4231	−	18.7743i	1.03951	−	0.955589i
$387$	34.5961	+	18.4920i	1.75862	+	0.940002i
$388$	9.47979	+	11.2247i	0.481263	+	0.569847i
$389$	−15.9507	+	19.4360i	−0.808733	+	0.985445i	0.191259	+	0.981540i	$0.438743\pi$
$389$	−15.9507	+	19.4360i	−0.808733	+	0.985445i	−0.999992	+	0.00390496i	$0.998757\pi$
$390$	29.4397	−	7.59518i	1.49074	−	0.384597i
$391$	1.38216	+	0.923529i	0.0698988	+	0.0467049i
$392$	−17.1001	−	9.76397i	−0.863683	−	0.493155i
$393$	16.3297	+	24.4391i	0.823722	+	1.23279i
$394$	0.638037	+	11.3540i	0.0321439	+	0.572007i
$395$	1.13745	+	0.345042i	0.0572315	+	0.0173610i
$396$	2.22095	−	0.474416i	0.111607	−	0.0238403i
$397$	−17.5168	+	14.3757i	−0.879145	+	0.721496i	−0.961411	−	0.275114i	$-0.911284\pi$
$397$	−17.5168	+	14.3757i	−0.879145	+	0.721496i	0.0822661	+	0.996610i	$0.473784\pi$
$398$	−31.2123	+	4.85499i	−1.56453	+	0.243359i
$399$	4.43051	−	1.83518i	0.221803	−	0.0918737i
$400$	−0.353859	−	12.5475i	−0.0176929	−	0.627377i
$401$	24.4143	+	10.1127i	1.21919	+	0.505005i	0.897152	−	0.441721i	$-0.145632\pi$
$401$	24.4143	+	10.1127i	1.21919	+	0.505005i	0.322038	+	0.946727i	$0.395632\pi$
$402$	12.3373	+	2.99807i	0.615326	+	0.149530i
$403$	1.60003	−	16.2453i	0.0797030	−	0.809238i
$404$	0.790716	−	0.0111474i	0.0393396	−	0.000554606i
$405$	−16.2249	−	30.3547i	−0.806224	−	1.50834i
$406$	−1.64560	+	0.792550i	−0.0816695	+	0.0393336i
$407$	−0.522059	−	0.103844i	−0.0258775	−	0.00514735i
$408$	2.16534	+	0.493979i	0.107200	+	0.0244556i
$409$	2.28299	+	11.4774i	0.112886	+	0.567519i	0.995283	+	0.0970124i	$0.0309287\pi$
$409$	2.28299	+	11.4774i	0.112886	+	0.567519i	−0.882397	+	0.470506i	$0.844071\pi$
$410$	0.631649	−	4.47534i	0.0311949	−	0.221021i
$411$	0.302507	+	3.07141i	0.0149216	+	0.151501i
$412$	14.8805	−	1.67772i	0.733111	−	0.0826553i
$413$	−0.0980435	−	0.323206i	−0.00482440	−	0.0159039i
$414$	−30.8627	+	66.4618i	−1.51682	+	3.26642i
$415$	1.66559	−	1.66559i	0.0817606	−	0.0817606i
$416$	−26.1589	−	8.33239i	−1.28254	−	0.408529i
$417$	−36.5509	−	36.5509i	−1.78990	−	1.78990i
$418$	−1.51431	+	0.553898i	−0.0740672	+	0.0270921i
$419$	−26.2140	+	7.95192i	−1.28064	+	0.388477i	−0.856041	−	0.516907i	$-0.827083\pi$
$419$	−26.2140	+	7.95192i	−1.28064	+	0.388477i	−0.424594	+	0.905384i	$0.639583\pi$
$420$	−0.478465	+	1.66124i	−0.0233467	+	0.0810601i
$421$	39.8566	−	3.92553i	1.94249	−	0.191319i	0.949876	−	0.312628i	$-0.101209\pi$
$421$	39.8566	−	3.92553i	1.94249	−	0.191319i	0.992615	+	0.121309i	$0.0387093\pi$
$422$	1.07998	+	1.43493i	0.0525725	+	0.0698514i
$423$	−75.4368	+	15.0053i	−3.66786	+	0.729583i
$424$	2.44653	+	6.40716i	0.118814	+	0.311159i
$425$	0.148080	−	0.744450i	0.00718295	−	0.0361111i
$426$	−25.7452	−	9.00758i	−1.24736	−	0.436419i
$427$	−1.30625	+	0.698206i	−0.0632139	+	0.0337885i
$428$	−29.0221	+	12.5035i	−1.40284	+	0.604380i
$429$	−2.36157	−	0.232594i	−0.114018	−	0.0112298i
$430$	8.57531	−	5.22235i	0.413538	−	0.251844i
$431$	−1.00757	+	2.43249i	−0.0485330	+	0.117169i	−0.946287	−	0.323329i	$-0.895198\pi$
$431$	−1.00757	+	2.43249i	−0.0485330	+	0.117169i	0.897754	+	0.440498i	$0.145198\pi$
$432$	−4.12185	+	58.8035i	−0.198313	+	2.82919i
$433$	−4.69123	−	11.3256i	−0.225446	−	0.544275i	0.770167	−	0.637842i	$-0.220173\pi$
$433$	−4.69123	−	11.3256i	−0.225446	−	0.544275i	−0.995613	+	0.0935676i	$0.970173\pi$
$434$	0.749406	+	0.547652i	0.0359726	+	0.0262881i
$435$	−18.6004	−	22.6647i	−0.891821	−	1.08669i
$436$	22.5445	+	4.15490i	1.07969	+	0.198984i
$437$	15.1026	−	49.7865i	0.722454	−	2.38161i
$438$	−34.3377	−	30.6838i	−1.64072	−	1.46613i
$439$	13.1415	−	8.78085i	0.627208	−	0.419087i	−0.200934	−	0.979605i	$-0.564398\pi$
$439$	13.1415	−	8.78085i	0.627208	−	0.419087i	0.828143	+	0.560518i	$0.189398\pi$
$440$	0.184209	−	0.551311i	0.00878182	−	0.0262827i
$441$	29.1612	−	43.6429i	1.38863	−	2.07823i
$442$	−1.42989	−	0.843403i	−0.0680131	−	0.0401166i
$443$	−1.62908	−	1.33695i	−0.0774001	−	0.0635206i	0.594898	−	0.803801i	$-0.297193\pi$
$443$	−1.62908	−	1.33695i	−0.0774001	−	0.0635206i	−0.672298	+	0.740281i	$0.734693\pi$
$444$	10.5307	−	20.3878i	0.499766	−	0.967562i
$445$	−5.75554	+	10.7679i	−0.272839	+	0.510446i
$446$	0.286494	−	6.81097i	0.0135659	−	0.322509i
$447$		−	42.1389i		−	1.99310i
$448$	1.16375	−	1.04045i	0.0549822	−	0.0491564i
$449$			36.1725i			1.70709i	0.521023	+	0.853543i	$0.325551\pi$
$449$			36.1725i			1.70709i	−0.521023	+	0.853543i	$0.674449\pi$
$450$	33.4303	+	1.40620i	1.57592	+	0.0662889i
$451$	−0.166290	+	0.311107i	−0.00783030	+	0.0146495i
$452$	1.72804	+	5.42031i	0.0812801	+	0.254950i
$453$	−17.8328	−	14.6350i	−0.837859	−	0.687613i
$454$	−8.73209	+	14.8043i	−0.409817	+	0.694799i
$455$	0.717903	−	1.07442i	0.0336558	−	0.0503695i
$456$	−4.87800	−	69.3405i	−0.228433	−	3.24716i
$457$	1.06878	−	0.714133i	0.0499952	−	0.0334057i	−0.530321	−	0.847797i	$-0.677929\pi$
$457$	1.06878	−	0.714133i	0.0499952	−	0.0334057i	0.580317	+	0.814391i	$0.302929\pi$
$458$	10.0586	−	11.2564i	0.470009	−	0.525979i
$459$	−1.03472	+	3.41101i	−0.0482965	+	0.159212i
$460$	10.6387	+	15.4461i	0.496033	+	0.720177i
$461$	−18.2743	−	22.2673i	−0.851117	−	1.03709i	−0.998844	−	0.0480615i	$-0.984696\pi$
$461$	−18.2743	−	22.2673i	−0.851117	−	1.03709i	0.147727	−	0.989028i	$-0.452804\pi$
$462$	0.0796117	−	0.108940i	0.00370387	−	0.00506837i
$463$	13.5855	+	32.7983i	0.631371	+	1.52426i	0.837900	+	0.545824i	$0.183783\pi$
$463$	13.5855	+	32.7983i	0.631371	+	1.52426i	−0.206529	+	0.978440i	$0.566217\pi$
$464$	3.33676	+	26.2642i	0.154905	+	1.21929i
$465$	−5.70188	+	13.7656i	−0.264419	+	0.638363i
$466$	−0.423124	−	0.694787i	−0.0196009	−	0.0321854i
$467$	27.8915	+	2.74707i	1.29066	+	0.127119i	0.719948	−	0.694028i	$-0.244166\pi$
$467$	27.8915	+	2.74707i	1.29066	+	0.127119i	0.570716	+	0.821148i	$0.306666\pi$
$468$	27.0492	−	67.9981i	1.25035	−	3.14321i
$469$	0.475892	−	0.254370i	0.0219746	−	0.0117457i
$470$	−6.50126	+	18.5817i	−0.299881	+	0.857108i
$471$	10.4856	−	52.7149i	0.483153	−	2.42897i
$472$	−4.89379	−	0.136778i	−0.225255	−	0.00629570i
$473$	−0.768589	+	0.152882i	−0.0353398	+	0.00702952i
$474$	3.19550	−	2.40504i	0.146774	−	0.110467i
$475$	−23.6418	+	2.32852i	−1.08476	+	0.106840i
$476$	0.0826125	−	0.0456661i	0.00378654	−	0.00209310i
$477$	−17.4944	+	5.30685i	−0.801011	+	0.242984i
$478$	4.33014	+	11.8382i	0.198056	+	0.541467i
$479$	12.6269	+	12.6269i	0.576937	+	0.576937i	0.934058	−	0.357121i	$-0.116242\pi$
$479$	12.6269	+	12.6269i	0.576937	+	0.576937i	−0.357121	+	0.934058i	$0.616242\pi$
$480$	20.6408	+	14.2090i	0.942117	+	0.648547i
$481$	−12.1283	+	12.1283i	−0.553001	+	0.553001i
$482$	−18.3053	−	8.50039i	−0.833783	−	0.387182i
$483$	1.26380	+	4.16619i	0.0575049	+	0.189568i
$484$	13.6873	−	17.1658i	0.622148	−	0.780264i
$485$	0.982499	+	9.97548i	0.0446130	+	0.452963i
$486$	−52.7633	−	7.44701i	−2.39339	−	0.337803i
$487$	−2.66111	−	13.3783i	−0.120586	−	0.606229i	−0.993064	−	0.117575i	$-0.962488\pi$
$487$	−2.66111	−	13.3783i	−0.120586	−	0.606229i	0.872478	−	0.488654i	$-0.162512\pi$
$488$	3.59852	+	21.1656i	0.162898	+	0.958120i
$489$	−20.9192	−	4.16110i	−0.946001	−	0.188171i
$490$	−5.82941	−	12.1038i	−0.263346	−	0.546793i
$491$	−4.76807	−	8.92043i	−0.215180	−	0.402573i	0.751054	−	0.660241i	$-0.229546\pi$
$491$	−4.76807	−	8.92043i	−0.215180	−	0.402573i	−0.966234	+	0.257668i	$0.917046\pi$
$492$	−10.9039	−	10.6007i	−0.491584	−	0.477916i
$493$	−0.156918	+	1.59322i	−0.00706724	+	0.0717549i
$494$	−12.2691	+	50.4882i	−0.552013	+	2.27157i
$495$	1.43149	+	0.592941i	0.0643405	+	0.0266507i
$496$	10.9716	−	7.78711i	0.492638	−	0.349652i
$497$	−1.07100	+	0.443622i	−0.0480408	+	0.0198992i
$498$	−1.21816	−	7.83143i	−0.0545869	−	0.350935i
$499$	−17.4315	+	14.3057i	−0.780342	+	0.640410i	−0.937824	−	0.347112i	$-0.887162\pi$
$499$	−17.4315	+	14.3057i	−0.780342	+	0.640410i	0.157482	+	0.987522i	$0.449662\pi$
$500$	12.0771	−	18.6382i	0.540105	−	0.833526i
$501$	−9.65471	−	2.92872i	−0.431340	−	0.130846i
$502$	−22.3143	+	1.25395i	−0.995934	+	0.0559664i
$503$	16.4770	+	24.6595i	0.734672	+	1.09951i	0.991122	+	0.132957i	$0.0424473\pi$
$503$	16.4770	+	24.6595i	0.734672	+	1.09951i	−0.256450	+	0.966558i	$0.582553\pi$
$504$	2.54887	+	3.28906i	0.113536	+	0.146506i
$505$	0.448595	+	0.299741i	0.0199622	+	0.0133383i
$506$	−0.365686	−	1.41744i	−0.0162567	−	0.0630128i
$507$	−21.7354	+	26.4846i	−0.965301	+	1.17622i
$508$	0.302193	−	3.58573i	0.0134076	−	0.159091i
$509$	−18.5335	−	9.90636i	−0.821483	−	0.439092i	0.00640920	−	0.999979i	$-0.497960\pi$
$509$	−18.5335	−	9.90636i	−0.821483	−	0.439092i	−0.827892	+	0.560888i	$0.810460\pi$
$510$	1.02547	+	1.11553i	0.0454088	+	0.0493967i
$511$	−1.95717			−0.0865799
$512$	−8.95820	−	20.7786i	−0.395900	−	0.918293i
$513$	111.561			4.92555
$514$	−2.91797	−	3.17423i	−0.128706	−	0.140009i
$515$	9.01022	+	4.81606i	0.397038	+	0.212221i
$516$	2.83706	−	33.6637i	0.124894	−	1.48196i
$517$	0.974744	−	1.18773i	0.0428692	−	0.0522363i
$518$	−0.243633	−	0.944348i	−0.0107046	−	0.0414923i
$519$	41.9618	+	28.0380i	1.84192	+	1.23073i
$520$	−11.4733	−	14.8051i	−0.503138	−	0.649248i
$521$	4.11838	+	6.16359i	0.180429	+	0.270032i	0.910649	−	0.413181i	$-0.135582\pi$
$521$	4.11838	+	6.16359i	0.180429	+	0.270032i	−0.730220	+	0.683213i	$0.760582\pi$
$522$	−70.4611	+	3.95955i	−3.08400	+	0.173305i
$523$	−22.7413	−	6.89849i	−0.994407	−	0.301650i	−0.249177	−	0.968458i	$-0.580160\pi$
$523$	−22.7413	−	6.89849i	−0.994407	−	0.301650i	−0.745230	+	0.666808i	$0.767660\pi$
$524$	9.84678	−	15.1962i	0.430159	−	0.663849i
$525$	1.53670	−	1.26114i	0.0670671	−	0.0550406i
$526$	4.72983	+	30.4077i	0.206231	+	1.32584i
$527$	0.751626	−	0.311334i	0.0327413	−	0.0135619i
$528$	−1.13201	−	1.59493i	−0.0492642	−	0.0694102i
$529$	22.3881	+	9.27346i	0.973396	+	0.403194i
$530$	−1.10491	+	4.54680i	−0.0479944	+	0.197500i
$531$	1.27912	−	12.9871i	0.0555089	−	0.563591i
$532$	−2.11827	−	2.05938i	−0.0918387	−	0.0892853i
$533$	5.35840	+	10.0249i	0.232098	+	0.434225i
$534$	17.8260	+	37.0127i	0.771407	+	1.60170i
$535$	−21.1455	−	4.20610i	−0.914200	−	0.181846i
$536$	−1.31101	−	7.71101i	−0.0566270	−	0.333065i
$537$	−7.80994	−	39.2632i	−0.337024	−	1.69433i
$538$	−25.5356	−	3.60409i	−1.10092	−	0.155383i
$539$	0.102776	+	1.04350i	0.00442687	+	0.0449468i
$540$	−25.0728	+	31.4449i	−1.07896	+	1.35317i
$541$	2.53495	+	8.35660i	0.108986	+	0.359278i	0.994421	−	0.105485i	$-0.0336395\pi$
$541$	2.53495	+	8.35660i	0.108986	+	0.359278i	−0.885435	+	0.464763i	$0.846139\pi$
$542$	−25.7287	−	11.9476i	−1.10514	−	0.513193i
$543$	1.43651	−	1.43651i	0.0616464	−	0.0616464i
$544$	−0.248328	−	1.34552i	−0.0106470	−	0.0576889i
$545$	11.0592	+	11.0592i	0.473723	+	0.473723i
$546$	−1.49357	−	4.08328i	−0.0639189	−	0.174748i
$547$	−16.0061	+	4.85540i	−0.684372	+	0.207602i	−0.613277	−	0.789868i	$-0.710149\pi$
$547$	−16.0061	+	4.85540i	−0.684372	+	0.207602i	−0.0710944	+	0.997470i	$0.522649\pi$
$548$	1.66401	−	0.919825i	0.0710832	−	0.0392930i
$549$	−56.9526	+	5.60934i	−2.43068	+	0.239401i
$550$	−0.534057	+	0.401949i	−0.0227723	+	0.0171392i
$551$	49.1429	−	9.77514i	2.09356	−	0.416435i
$552$	63.0819	+	1.76309i	2.68495	+	0.0750420i
$553$	0.0331615	−	0.166714i	0.00141017	−	0.00708941i
$554$	10.2735	−	29.3633i	0.436478	−	1.24753i
$555$	13.8069	−	7.37996i	0.586072	−	0.313262i
$556$	−11.7704	+	29.5894i	−0.499178	+	1.25487i
$557$	38.4640	+	3.78837i	1.62977	+	0.160518i	0.871151	−	0.491015i	$-0.163374\pi$
$557$	38.4640	+	3.78837i	1.62977	+	0.160518i	0.758620	+	0.651534i	$0.225874\pi$
$558$	18.6537	+	30.6302i	0.789675	+	1.29668i
$559$	−9.66336	+	23.3294i	−0.408717	+	0.986729i
$560$	1.05653	−	0.134228i	0.0446465	−	0.00567215i
$561$	−0.0452583	−	0.109263i	−0.00191081	−	0.00461309i
$562$	16.4989	−	22.5771i	0.695965	−	0.952357i
$563$	−7.38497	−	8.99862i	−0.311240	−	0.379246i	0.593772	−	0.804633i	$-0.297638\pi$
$563$	−7.38497	−	8.99862i	−0.311240	−	0.379246i	−0.905012	+	0.425387i	$0.860138\pi$
$564$	37.5728	+	54.5510i	1.58210	+	2.29701i
$565$	−1.12671	+	3.71426i	−0.0474010	+	0.156260i
$566$	12.5948	−	14.0946i	0.529400	−	0.592442i
$567$	−4.09254	+	2.73455i	−0.171871	+	0.114840i
$568$	1.17917	+	16.7618i	0.0494769	+	0.703311i
$569$	−18.0568	+	27.0239i	−0.756979	+	1.13290i	0.230179	+	0.973148i	$0.426069\pi$
$569$	−18.0568	+	27.0239i	−0.756979	+	1.13290i	−0.987157	+	0.159750i	$0.948931\pi$
$570$	24.0938	−	40.8482i	1.00918	−	1.71094i
$571$	−34.6976	−	28.4755i	−1.45205	−	1.19166i	−0.943828	−	0.330437i	$-0.892804\pi$
$571$	−34.6976	−	28.4755i	−1.45205	−	1.19166i	−0.508219	−	0.861228i	$-0.669696\pi$
$572$	0.444046	+	1.39283i	0.0185665	+	0.0582373i
$573$	36.3899	−	68.0808i	1.52021	−	2.84412i
$574$	−0.645767	−	0.0271633i	−0.0269538	−	0.00113377i
$575$		−	21.5672i		−	0.899413i
$576$	56.9263	−	19.9332i	2.37193	−	0.830549i
$577$		−	9.94863i		−	0.414167i	−0.978323	−	0.207083i	$-0.933603\pi$
$577$		−	9.94863i		−	0.414167i	0.978323	−	0.207083i	$-0.0663971\pi$
$578$	−1.00691	+	23.9377i	−0.0418819	+	0.995678i
$579$	30.0197	−	56.1630i	1.24758	−	2.33405i
$580$	−8.28935	+	16.0484i	−0.344197	+	0.666375i
$581$	−0.260387	−	0.213694i	−0.0108027	−	0.00886552i
$582$	29.0502	+	17.1349i	1.20417	+	0.710263i
$583$	0.202897	−	0.303656i	0.00840312	−	0.0125762i
$584$	−8.99041	+	26.9070i	−0.372026	+	1.11342i
$585$	41.5132	−	27.7383i	1.71636	−	1.14684i
$586$	17.5952	+	15.7229i	0.726850	+	0.649505i
$587$	−2.75765	+	9.09076i	−0.113820	+	0.375216i	−0.995280	−	0.0970434i	$-0.969061\pi$
$587$	−2.75765	+	9.09076i	−0.113820	+	0.375216i	0.881460	+	0.472259i	$0.156561\pi$
$588$	−44.4544	−	8.19283i	−1.83327	−	0.337867i
$589$	−16.1533	−	19.6828i	−0.665584	−	0.811017i
$590$	−2.69675	−	1.97074i	−0.111023	−	0.0811339i
$591$	9.99003	+	24.1181i	0.410935	+	0.992084i
$592$	−14.1020	−	0.988484i	−0.579589	−	0.0406264i
$593$	10.9497	−	26.4350i	0.449652	−	1.08556i	−0.522800	−	0.852455i	$-0.675113\pi$
$593$	10.9497	−	26.4350i	0.449652	−	1.08556i	0.972452	−	0.233101i	$-0.0748874\pi$
$594$	2.68092	−	1.63267i	0.109999	−	0.0669894i
$595$	0.0640903	+	0.00631234i	0.00262745	+	0.000258781i
$596$	−23.8415	+	10.2716i	−0.976586	+	0.420740i
$597$	−63.9499	+	34.1820i	−2.61730	+	1.39897i
$598$	−44.5234	−	15.5776i	−1.82070	−	0.637017i
$599$	−8.41706	+	42.3154i	−0.343912	+	1.72896i	0.291307	+	0.956630i	$0.405910\pi$
$599$	−8.41706	+	42.3154i	−0.343912	+	1.72896i	−0.635219	+	0.772332i	$0.719090\pi$
$600$	−10.2791	−	26.9197i	−0.419643	−	1.09899i
$601$	−18.4819	+	3.67629i	−0.753894	+	0.149959i	−0.557054	−	0.830477i	$-0.688068\pi$
$601$	−18.4819	+	3.67629i	−0.753894	+	0.149959i	−0.196841	+	0.980435i	$0.563068\pi$
$602$	−0.863423	−	1.14720i	−0.0351905	−	0.0467565i
$603$	20.7489	−	2.04359i	0.844961	−	0.0832214i
$604$	−3.93342	+	13.6569i	−0.160048	+	0.555691i
$605$	14.3336	−	4.34805i	0.582744	−	0.176773i
$606$	1.70487	−	0.623600i	0.0692554	−	0.0253320i
$607$	−15.4956	−	15.4956i	−0.628947	−	0.628947i	0.318856	−	0.947803i	$-0.396701\pi$
$607$	−15.4956	−	15.4956i	−0.628947	−	0.628947i	−0.947803	+	0.318856i	$0.896701\pi$
$608$	−38.0427	+	19.6620i	−1.54283	+	0.797399i
$609$	−2.96482	+	2.96482i	−0.120141	+	0.120141i
$610$	−6.16910	+	13.2849i	−0.249780	+	0.537891i
$611$	−14.3722	−	47.3789i	−0.581439	−	1.91675i
$612$	3.62422	−	0.408616i	0.146500	−	0.0165173i
$613$	−2.56143	−	26.0066i	−0.103455	−	1.05040i	−0.897044	−	0.441942i	$-0.854290\pi$
$613$	−2.56143	−	26.0066i	−0.103455	−	1.05040i	0.793589	−	0.608455i	$-0.208210\pi$
$614$	−1.16822	+	8.27703i	−0.0471455	+	0.334034i
$615$	−2.02413	−	10.1760i	−0.0816207	−	0.410335i
$616$	−0.0810425	−	0.0184882i	−0.00326530	−	0.000744911i
$617$	15.1008	+	3.00375i	0.607937	+	0.120926i	0.489453	−	0.872030i	$-0.337196\pi$
$617$	15.1008	+	3.00375i	0.607937	+	0.120926i	0.118484	+	0.992956i	$0.462196\pi$
$618$	30.9711	−	14.9163i	1.24584	−	0.600021i
$619$	13.8857	+	25.9783i	0.558112	+	1.04416i	0.989845	+	0.142153i	$0.0454026\pi$
$619$	13.8857	+	25.9783i	0.558112	+	1.04416i	−0.431732	+	0.902002i	$0.642097\pi$
$620$	9.17820	−	0.129394i	0.368605	−	0.00519657i
$621$	−9.92730	+	100.794i	−0.398369	+	4.04471i
$622$	26.9753	+	6.55524i	1.08161	+	0.262841i
$623$	1.61311	+	0.668174i	0.0646281	+	0.0267698i
$624$	−62.9976	+	1.77662i	−2.52192	+	0.0711219i
$625$	−0.497564	+	0.206098i	−0.0199026	+	0.00824392i
$626$	22.1519	−	3.44567i	0.885370	−	0.137717i
$627$	−2.86127	+	2.34819i	−0.114268	+	0.0937775i
$628$	−32.3812	+	6.91692i	−1.29215	+	0.276015i
$629$	−0.818013	−	0.248141i	−0.0326163	−	0.00989405i
$630$	0.159281	+	2.83443i	0.00634590	+	0.112927i
$631$	−0.870439	−	1.30270i	−0.0346516	−	0.0518598i	0.813739	−	0.581230i	$-0.197428\pi$
$631$	−0.870439	−	1.30270i	−0.0346516	−	0.0518598i	−0.848391	+	0.529370i	$0.822428\pi$
$632$	−2.13965	−	1.22172i	−0.0851107	−	0.0485974i
$633$	3.42792	+	2.29046i	0.136247	+	0.0910377i
$634$	6.86207	−	1.77035i	0.272528	−	0.0703097i
$635$	1.55746	−	1.89777i	0.0618060	−	0.0753108i
$636$	10.1584	+	12.0282i	0.402808	+	0.476951i
$637$	29.7980	+	15.9274i	1.18064	+	0.631066i
$638$	1.03789	−	0.954101i	0.0410905	−	0.0377732i
$639$	−44.7905			−1.77189
$640$	3.00791	−	15.1417i	0.118898	−	0.598529i
$641$	−0.546606			−0.0215897			−0.0107948	−	0.999942i	$-0.503436\pi$
$641$	−0.546606			−0.0215897			−0.0107948	+	0.999942i	$0.503436\pi$
$642$	−53.4058	+	49.0943i	−2.10776	+	1.93760i
$643$	24.9021	+	13.3105i	0.982043	+	0.524913i	0.882597	−	0.470130i	$-0.155793\pi$
$643$	24.9021	+	13.3105i	0.982043	+	0.524913i	0.0994462	+	0.995043i	$0.468293\pi$
$644$	2.04910	−	1.73057i	0.0807460	−	0.0681939i
$645$	14.6218	−	17.8167i	0.575733	−	0.701533i
$646$	−2.50737	+	0.646878i	−0.0986511	+	0.0254511i
$647$	16.1546	+	10.7942i	0.635104	+	0.424363i	0.831008	−	0.556260i	$-0.187764\pi$
$647$	16.1546	+	10.7942i	0.635104	+	0.424363i	−0.195904	+	0.980623i	$0.562764\pi$
$648$	18.7950	+	68.8255i	0.738338	+	2.70372i
$649$	0.144834	+	0.216759i	0.00568522	+	0.00850853i
$650$	1.20845	+	21.5046i	0.0473992	+	0.843478i
$651$	2.03898	+	0.618519i	0.0799141	+	0.0242417i
$652$	2.74489	+	12.8501i	0.107498	+	0.503247i
$653$	−15.9635	+	13.1009i	−0.624701	+	0.512679i	−0.892648	−	0.450755i	$-0.851155\pi$
$653$	−15.9635	+	13.1009i	−0.624701	+	0.512679i	0.267947	+	0.963434i	$0.413655\pi$
$654$	51.9991	−	8.08831i	2.03332	−	0.316278i
$655$	11.4135	−	4.72763i	0.445963	−	0.184724i
$656$	−3.33982	+	8.75319i	−0.130398	+	0.341755i
$657$	−69.8644	−	28.9388i	−2.72567	−	1.12901i
$658$	2.73560	+	0.664776i	0.106645	+	0.0259157i
$659$	−0.237451	+	2.41088i	−0.00924979	+	0.0939147i	−0.998701	−	0.0509506i	$-0.983775\pi$
$659$	−0.237451	+	2.41088i	−0.00924979	+	0.0939147i	0.989451	+	0.144865i	$0.0462749\pi$
$660$	−0.0188098	−	1.33423i	−0.000732171	−	0.0519347i
$661$	−19.0704	−	35.6782i	−0.741752	−	1.38772i	−0.915250	−	0.402886i	$-0.868007\pi$
$661$	−19.0704	−	35.6782i	−0.741752	−	1.38772i	0.173498	−	0.984834i	$-0.444493\pi$
$662$	0.213718	−	0.102930i	0.00830637	−	0.00400050i
$663$	−3.73767	−	0.743468i	−0.145159	−	0.0288739i
$664$	−4.13396	+	2.59816i	−0.160429	+	0.100828i
$665$	−0.393224	−	1.97687i	−0.0152486	−	0.0766597i
$666$	5.26628	−	37.3125i	0.204064	−	1.44583i
$667$	4.45867	+	45.2696i	0.172640	+	1.75285i
$668$	0.696360	+	6.17637i	0.0269430	+	0.238971i
$669$	−4.54266	−	14.9751i	−0.175629	−	0.578972i
$670$	2.24752	−	4.83995i	0.0868293	−	0.186984i
$671$	0.808384	−	0.808384i	0.0312073	−	0.0312073i
$672$	1.73284	−	3.13668i	0.0668458	−	0.121000i
$673$	2.88867	+	2.88867i	0.111350	+	0.111350i	0.760587	−	0.649237i	$-0.224911\pi$
$673$	2.88867	+	2.88867i	0.111350	+	0.111350i	−0.649237	+	0.760587i	$0.724911\pi$
$674$	0.173875	−	0.0635993i	0.00669740	−	0.00244975i
$675$	44.2552	−	13.4247i	1.70338	−	0.516716i
$676$	20.2827	+	5.84176i	0.780103	+	0.224683i
$677$	−19.5225	+	1.92280i	−0.750310	+	0.0738991i	−0.465941	−	0.884816i	$-0.654284\pi$
$677$	−19.5225	+	1.92280i	−0.750310	+	0.0738991i	−0.284369	+	0.958715i	$0.591784\pi$
$678$	7.85346	+	10.4346i	0.301610	+	0.400740i
$679$	1.40590	−	0.279651i	0.0539535	−	0.0107320i
$680$	0.381186	−	0.852114i	0.0146178	−	0.0326771i
$681$	−7.69743	+	38.6976i	−0.294966	+	1.48289i
$682$	−0.676232	−	0.236596i	−0.0258942	−	0.00905974i
$683$	23.2162	−	12.4093i	0.888345	−	0.474830i	0.0369267	−	0.999318i	$-0.488243\pi$
$683$	23.2162	−	12.4093i	0.888345	−	0.474830i	0.851418	+	0.524488i	$0.175743\pi$
$684$	−45.1653	−	104.834i	−1.72694	−	4.00842i
$685$	1.29093	+	0.127146i	0.0493240	+	0.00485799i
$686$	−3.29068	+	2.00402i	−0.125639	+	0.0765137i
$687$	13.2614	−	32.0159i	0.505954	−	1.22148i
$688$	−19.7379	+	6.60053i	−0.752501	+	0.251643i
$689$	−4.50343	−	10.8723i	−0.171567	−	0.414200i
$690$	34.7616	+	25.4032i	1.32335	+	0.967082i
$691$	30.1714	+	36.7639i	1.14777	+	1.39856i	0.903354	+	0.428895i	$0.141097\pi$
$691$	30.1714	+	36.7639i	1.14777	+	1.39856i	0.244418	+	0.969670i	$0.421403\pi$
$692$	5.63503	−	30.5757i	0.214212	−	1.16231i
$693$	0.0643200	−	0.212035i	0.00244332	−	0.00805453i
$694$	−11.8441	−	10.5838i	−0.449595	−	0.401754i
$695$	−18.0645	+	12.0703i	−0.685224	+	0.457852i
$696$	27.1411	+	54.3795i	1.02878	+	2.06125i
$697$	−0.314738	+	0.471038i	−0.0119215	+	0.0178419i
$698$	38.2503	+	22.5614i	1.44780	+	0.853963i
$699$	−1.44354	−	1.18469i	−0.0545999	−	0.0448089i
$700$	−1.08811	−	0.562032i	−0.0411267	−	0.0212428i
$701$	20.3759	−	38.1206i	0.769587	−	1.43980i	−0.124649	−	0.992201i	$-0.539781\pi$
$701$	20.3759	−	38.1206i	0.769587	−	1.43980i	0.894236	−	0.447595i	$-0.147719\pi$
$702$	4.25084	−	101.057i	0.160438	−	3.81416i
$703$			26.7541i			1.00905i
$704$	−0.626451	+	1.02924i	−0.0236103	+	0.0387910i
$705$			45.1912i			1.70200i
$706$	−8.56671	−	0.360347i	−0.322412	−	0.0135619i
$707$	0.0363701	−	0.0680437i	0.00136784	−	0.00255905i
$708$	−10.7075	+	3.41364i	−0.402413	+	0.128293i
$709$	−24.6436	−	20.2245i	−0.925510	−	0.759546i	0.0454055	−	0.998969i	$-0.485542\pi$
$709$	−24.6436	−	20.2245i	−0.925510	−	0.759546i	−0.970916	+	0.239422i	$0.923042\pi$
$710$	−5.82424	+	9.87434i	−0.218580	+	0.370577i
$711$	3.64881	−	5.46082i	0.136841	−	0.204797i
$712$	16.5960	−	19.1077i	0.621962	−	0.716092i
$713$	19.2205	−	12.8427i	0.719813	−	0.480964i
$714$	0.144384	−	0.161578i	0.00540345	−	0.00604690i
$715$	−0.289526	+	0.954438i	−0.0108276	+	0.0356940i
$716$	−20.3108	+	13.9893i	−0.759049	+	0.522806i
$717$	18.3571	+	22.3682i	0.685560	+	0.835357i
$718$	−14.0323	+	19.2018i	−0.523682	+	0.716605i
$719$	−7.12269	−	17.1957i	−0.265632	−	0.641291i	0.733637	−	0.679542i	$-0.237821\pi$
$719$	−7.12269	−	17.1957i	−0.265632	−	0.641291i	−0.999268	+	0.0382507i	$0.987821\pi$
$720$	39.6993	+	10.8304i	1.47951	+	0.403626i
$721$	0.559108	−	1.34981i	0.0208223	−	0.0502694i
$722$	28.1783	+	46.2699i	1.04869	+	1.72199i
$723$	−46.1079	−	4.54124i	−1.71477	−	0.168890i
$724$	−1.16291	−	0.462596i	−0.0432191	−	0.0171922i
$725$	18.3182	−	9.79128i	0.680321	−	0.363639i
$726$	16.6439	−	47.5711i	0.617714	−	1.76553i
$727$	−6.68420	+	33.6037i	−0.247903	+	1.24629i	0.633431	+	0.773799i	$0.281646\pi$
$727$	−6.68420	+	33.6037i	−0.247903	+	1.24629i	−0.881334	+	0.472494i	$0.843354\pi$
$728$	−1.94619	+	1.84036i	−0.0721306	+	0.0682082i
$729$	−45.7533	+	9.10089i	−1.69457	+	0.337070i
$730$	−15.4644	+	11.6390i	−0.572363	+	0.430780i
$731$	−1.25243	+	0.123354i	−0.0463228	+	0.00456240i
$732$	23.8430	+	43.1333i	0.881261	+	1.59425i
$733$	45.8766	−	13.9165i	1.69449	−	0.514018i	0.712295	−	0.701880i	$-0.247656\pi$
$733$	45.8766	−	13.9165i	1.69449	−	0.514018i	0.982195	+	0.187862i	$0.0601558\pi$
$734$	−10.6608	−	29.1457i	−0.393498	−	1.07579i
$735$	−21.8070	−	21.8070i	−0.804365	−	0.804365i
$736$	−14.3790	−	36.1205i	−0.530018	−	1.33142i
$737$	−0.294510	+	0.294510i	−0.0108484	+	0.0108484i
$738$	−22.6501	−	10.5180i	−0.833762	−	0.387173i
$739$	−11.5396	−	38.0411i	−0.424492	−	1.39936i	−0.865071	−	0.501649i	$-0.832727\pi$
$739$	−11.5396	−	38.0411i	−0.424492	−	1.39936i	0.440579	−	0.897714i	$-0.354773\pi$
$740$	−7.54097	−	6.01284i	−0.277212	−	0.221036i
$741$	11.6908	+	118.699i	0.429472	+	4.36051i
$742$	0.662570	+	0.0935150i	0.0243237	+	0.00343304i
$743$	2.46999	+	12.4175i	0.0906151	+	0.455553i	0.999277	+	0.0380201i	$0.0121051\pi$
$743$	2.46999	+	12.4175i	0.0906151	+	0.455553i	−0.908662	+	0.417533i	$0.862895\pi$
$744$	17.8696	−	25.1906i	0.655132	−	0.923534i
$745$	−17.3709	−	3.45529i	−0.636422	−	0.126592i
$746$	−1.66775	−	3.46280i	−0.0610607	−	0.126782i
$747$	−6.13526	−	11.4783i	−0.224478	−	0.419968i
$748$	−0.0507874	+	0.0522399i	−0.00185697	+	0.00191008i
$749$	−0.302201	+	3.06830i	−0.0110422	+	0.112113i
$750$	12.0389	−	49.5408i	0.439598	−	1.80898i
$751$	17.7882	+	7.36812i	0.649101	+	0.268867i	0.682844	−	0.730564i	$-0.260743\pi$
$751$	17.7882	+	7.36812i	0.649101	+	0.268867i	−0.0337429	+	0.999431i	$0.510743\pi$
$752$	21.7055	−	34.5552i	0.791519	−	1.26010i
$753$	−47.3997	+	19.6336i	−1.72734	+	0.715488i
$754$	−6.98226	−	44.8884i	−0.254279	−	1.63474i
$755$	−7.49525	+	6.15119i	−0.272780	+	0.223865i
$756$	4.82655	+	3.12750i	0.175540	+	0.113746i
$757$	33.7719	+	10.2446i	1.22746	+	0.372346i	0.836452	−	0.548041i	$-0.184626\pi$
$757$	33.7719	+	10.2446i	1.22746	+	0.372346i	0.391009	+	0.920387i	$0.372126\pi$
$758$	9.31502	−	0.523457i	0.338337	−	0.0190128i
$759$	−1.86693	−	2.79406i	−0.0677654	−	0.101418i
$760$	−28.9842	−	3.67490i	−1.05137	−	0.133303i
$761$	−18.9623	−	12.6702i	−0.687384	−	0.459295i	0.162194	−	0.986759i	$-0.448143\pi$
$761$	−18.9623	−	12.6702i	−0.687384	−	0.459295i	−0.849578	+	0.527464i	$0.823143\pi$
$762$	−2.06357	−	7.99862i	−0.0747554	−	0.289760i
$763$	1.41888	−	1.72891i	0.0513670	−	0.0625909i
$764$	−47.3892	−	3.99380i	−1.71448	−	0.144490i
$765$	2.19448	+	1.17297i	0.0793415	+	0.0424089i
$766$	13.2877	+	14.4546i	0.480104	+	0.522267i
$767$	8.40038			0.303320
$768$	−35.1629	−	38.2316i	−1.26883	−	1.37957i
$769$	34.0603			1.22825			0.614123	−	0.789210i	$-0.289510\pi$
$769$	34.0603			1.22825			0.614123	+	0.789210i	$0.289510\pi$
$770$	−0.0383806	−	0.0417512i	−0.00138314	−	0.00150461i
$771$	−8.72904	−	4.66577i	−0.314369	−	0.168034i
$772$	−39.0936	−	3.29467i	−1.40701	−	0.118578i
$773$	8.79030	−	10.7110i	0.316165	−	0.385249i	−0.590543	−	0.807006i	$-0.701087\pi$
$773$	8.79030	−	10.7110i	0.316165	−	0.385249i	0.906709	+	0.421757i	$0.138587\pi$
$774$	−13.8588	−	53.7180i	−0.498143	−	1.93085i
$775$	−8.77636	−	5.86418i	−0.315256	−	0.210647i
$776$	2.61350	−	20.6128i	0.0938190	−	0.739958i
$777$	−1.24382	−	1.86150i	−0.0446217	−	0.0667811i
$778$	35.5019	−	1.99503i	1.27281	−	0.0715252i
$779$	16.9672	+	5.14695i	0.607913	+	0.184409i
$780$	−36.0841	−	23.3817i	−1.29202	−	0.837198i
$781$	0.691663	−	0.567633i	0.0247496	−	0.0203115i
$782$	−0.361324	−	2.32292i	−0.0129209	−	0.0830676i
$783$	−90.1166	+	37.3275i	−3.22050	+	1.33398i
$784$	6.20061	+	27.1486i	0.221450	+	0.969593i
$785$	−20.8709	−	8.64500i	−0.744914	−	0.308553i
$786$	9.81560	−	40.3919i	0.350111	−	1.44073i
$787$	1.71371	−	17.3996i	0.0610872	−	0.620229i	−0.915089	−	0.403251i	$-0.867880\pi$
$787$	1.71371	−	17.3996i	0.0610872	−	0.620229i	0.976177	−	0.216978i	$-0.0696199\pi$
$788$	11.2105	−	11.5311i	0.399357	−	0.410778i
$789$	33.3008	+	62.3014i	1.18554	+	2.21799i
$790$	−0.729406	−	1.51449i	−0.0259511	−	0.0538830i
$791$	0.544392	+	0.108286i	0.0193564	+	0.00385022i
$792$	−2.61958	−	1.85827i	−0.0930829	−	0.0660307i
$793$	−7.18682	−	36.1306i	−0.255211	−	1.28303i
$794$	31.7324	+	4.47870i	1.12614	+	0.158943i
$795$	1.05283	+	10.6896i	0.0373402	+	0.379121i
$796$	34.9277	+	27.8498i	1.23798	+	0.987110i
$797$	7.77476	+	25.6299i	0.275396	+	0.907859i	0.980125	+	0.198382i	$0.0635687\pi$
$797$	7.77476	+	25.6299i	0.275396	+	0.907859i	−0.704729	+	0.709477i	$0.748931\pi$
$798$	−6.15108	−	2.85636i	−0.217746	−	0.101114i
$799$	1.74480	−	1.74480i	0.0617267	−	0.0617267i
$800$	−12.7251	+	12.3776i	−0.449901	+	0.437613i
$801$	47.7032	+	47.7032i	1.68551	+	1.68551i
$802$	−12.8379	−	35.0975i	−0.453321	−	1.23934i
$803$	1.44560	−	0.438518i	0.0510141	−	0.0154750i
$804$	−8.68644	−	15.7143i	−0.306347	−	0.554199i
$805$	1.82106	−	0.179359i	0.0641838	−	0.00632156i
$806$	−18.4451	+	13.8824i	−0.649700	+	0.488986i
$807$	−58.0626	+	11.5494i	−2.04390	+	0.406557i
$808$	−0.768392	−	0.812579i	−0.0270320	−	0.0285864i
$809$	5.04354	−	25.3556i	0.177322	−	0.891456i	−0.784990	−	0.619508i	$-0.787332\pi$
$809$	5.04354	−	25.3556i	0.177322	−	0.891456i	0.962312	−	0.271948i	$-0.0876678\pi$
$810$	−16.0749	+	45.9447i	−0.564814	+	1.61433i
$811$	−12.6496	+	6.76135i	−0.444187	+	0.237423i	−0.678298	−	0.734787i	$-0.737282\pi$
$811$	−12.6496	+	6.76135i	−0.444187	+	0.237423i	0.234111	+	0.972210i	$0.424782\pi$
$812$	2.40014	+	0.954759i	0.0842284	+	0.0335055i
$813$	−64.8063	−	6.38286i	−2.27286	−	0.223857i
$814$	0.391541	+	0.642926i	0.0137235	+	0.0225345i
$815$	−3.43066	+	8.28235i	−0.120171	+	0.290118i
$816$	−1.55812	−	2.72721i	−0.0545452	−	0.0954715i
$817$	15.0732	+	36.3899i	0.527344	+	1.27312i
$818$	9.76454	−	13.3618i	0.341409	−	0.467184i
$819$	−4.52949	−	5.51919i	−0.158273	−	0.192856i
$820$	−5.26401	+	3.62567i	−0.183827	+	0.126614i
$821$	0.620931	−	2.04693i	0.0216706	−	0.0714385i	−0.945438	−	0.325802i	$-0.894366\pi$
$821$	0.620931	−	2.04693i	0.0216706	−	0.0714385i	0.967109	+	0.254363i	$0.0818658\pi$
$822$	2.90825	−	3.25457i	0.101437	−	0.113516i
$823$	25.0522	−	16.7393i	0.873265	−	0.583497i	−0.0361688	−	0.999346i	$-0.511515\pi$
$823$	25.0522	−	16.7393i	0.873265	−	0.583497i	0.909434	+	0.415849i	$0.136515\pi$
$824$	−15.9888	−	13.8870i	−0.556995	−	0.483778i
$825$	−0.852470	+	1.27581i	−0.0296792	+	0.0444180i
$826$	−0.242667	+	0.411414i	−0.00844347	+	0.0143149i
$827$	−17.2781	−	14.1797i	−0.600817	−	0.493078i	0.284120	−	0.958789i	$-0.408299\pi$
$827$	−17.2781	−	14.1797i	−0.600817	−	0.493078i	−0.884937	+	0.465711i	$0.845799\pi$
$828$	98.7346	−	31.4774i	3.43126	−	1.09391i
$829$	−13.3858	+	25.0432i	−0.464910	+	0.869785i	0.534783	+	0.844989i	$0.320393\pi$
$829$	−13.3858	+	25.0432i	−0.464910	+	0.869785i	−0.999693	+	0.0247952i	$0.992107\pi$
$830$	−3.32824	−	0.139998i	−0.115525	−	0.00485940i
$831$		−	71.4125i		−	2.47727i
$832$	16.3612	+	35.2100i	0.567222	+	1.22069i
$833$			1.68391i			0.0583441i
$834$	−3.07221	+	73.0372i	−0.106382	+	2.52907i
$835$	−1.99897	+	3.73981i	−0.0691773	+	0.129422i
$836$	2.02602	+	1.04648i	0.0700712	+	0.0361933i
$837$	38.3168	+	31.4458i	1.32442	+	1.08693i
$838$	33.3682	+	19.6818i	1.15269	+	0.679896i
$839$	26.5008	−	39.6613i	0.914910	−	1.36926i	−0.0143760	−	0.999897i	$-0.504576\pi$
$839$	26.5008	−	39.6613i	0.914910	−	1.36926i	0.929285	−	0.369362i	$-0.120424\pi$
$840$	2.18752	−	1.09180i	0.0754766	−	0.0376708i
$841$	−12.3132	+	8.22742i	−0.424593	+	0.283704i
$842$	−42.2334	−	37.7393i	−1.45546	−	1.30058i
$843$	18.6339	−	61.4278i	0.641786	−	2.11569i
$844$	0.460333	−	2.49777i	0.0158453	−	0.0859768i
$845$	9.13551	+	11.1317i	0.314271	+	0.382941i
$846$	87.8225	+	64.1790i	3.01940	+	2.20652i
$847$	−0.819710	−	1.97895i	−0.0281656	−	0.0679977i
$848$	4.32921	−	8.67942i	0.148666	−	0.298052i
$849$	16.6051	−	40.0883i	0.569887	−	1.37583i
$850$	−0.916805	+	0.558333i	−0.0314461	+	0.0191507i
$851$	−24.1719	−	2.38072i	−0.828601	−	0.0816101i
$852$	15.2623	+	35.4255i	0.522876	+	1.21366i
$853$	18.9420	−	10.1247i	0.648562	−	0.346664i	−0.114092	−	0.993470i	$-0.536396\pi$
$853$	18.9420	−	10.1247i	0.648562	−	0.346664i	0.762654	+	0.646807i	$0.223896\pi$
$854$	1.97713	+	0.691748i	0.0676561	+	0.0236711i
$855$	15.1933	−	76.3820i	0.519601	−	2.61221i
$856$	40.7947	+	18.2492i	1.39433	+	0.623743i
$857$	44.3065	−	8.81310i	1.51348	−	0.301050i	0.632633	−	0.774451i	$-0.281974\pi$
$857$	44.3065	−	8.81310i	1.51348	−	0.301050i	0.880847	+	0.473401i	$0.156974\pi$
$858$	2.01807	+	2.68134i	0.0688958	+	0.0915396i
$859$	−25.1481	+	2.47687i	−0.858041	+	0.0845097i	−0.517462	−	0.855706i	$-0.673123\pi$
$859$	−25.1481	+	2.47687i	−0.858041	+	0.0845097i	−0.340579	+	0.940216i	$0.610623\pi$
$860$	−13.6446	−	3.92986i	−0.465275	−	0.134007i
$861$	−1.41983	+	0.430702i	−0.0483878	+	0.0146783i
$862$	3.49691	−	1.27909i	0.119105	−	0.0435659i
$863$	−4.10853	−	4.10853i	−0.139856	−	0.139856i	0.633713	−	0.773569i	$-0.281530\pi$
$863$	−4.10853	−	4.10853i	−0.139856	−	0.139856i	−0.773569	+	0.633713i	$0.781530\pi$
$864$	65.1679	−	51.9888i	2.21706	−	1.76870i
$865$	14.9989	−	14.9989i	0.509977	−	0.509977i
$866$	−7.30167	+	15.7239i	−0.248121	+	0.534319i
$867$	15.9656	+	52.6314i	0.542219	+	1.78746i
$868$	−0.147065	−	1.30439i	−0.00499170	−	0.0442739i
$869$	0.0128599	+	0.130568i	0.000436241	+	0.00442923i
$870$	−5.79489	+	41.0578i	−0.196465	+	1.39199i
$871$	2.61829	+	13.1631i	0.0887175	+	0.446013i
$872$	−17.2513	−	27.4487i	−0.584202	−	0.929529i
$873$	54.3210	+	10.8051i	1.83849	+	0.365698i
$874$	−66.2894	+	31.9262i	−2.24227	+	1.07992i
$875$	−1.02143	−	1.91097i	−0.0345307	−	0.0646025i
$876$	0.918023	+	65.1176i	0.0310171	+	2.20012i
$877$	4.15053	−	42.1410i	0.140153	−	1.42300i	−0.625739	−	0.780032i	$-0.715203\pi$
$877$	4.15053	−	42.1410i	0.140153	−	1.42300i	0.765893	−	0.642968i	$-0.222297\pi$
$878$	−21.7197	−	5.27809i	−0.733004	−	0.178127i
$879$	50.0446	+	20.7292i	1.68796	+	0.699177i
$880$	−0.750298	+	0.335867i	−0.0252926	+	0.0113221i
$881$	−47.0203	+	19.4765i	−1.58415	+	0.656178i	−0.989065	−	0.147481i	$-0.952884\pi$
$881$	−47.0203	+	19.4765i	−1.58415	+	0.656178i	−0.595090	+	0.803659i	$0.702884\pi$
$882$	−73.3484	+	11.4091i	−2.46977	+	0.384166i
$883$	−28.1130	+	23.0718i	−0.946079	+	0.776427i	−0.974782	−	0.223161i	$-0.928363\pi$
$883$	−28.1130	+	23.0718i	−0.946079	+	0.776427i	0.0287023	+	0.999588i	$0.490863\pi$
$884$	0.490433	+	2.29594i	0.0164951	+	0.0772207i
$885$	−7.33732	−	2.22575i	−0.246641	−	0.0748178i
$886$	0.167219	+	2.97569i	0.00561783	+	0.0999704i
$887$	−1.48282	−	2.21919i	−0.0497881	−	0.0745131i	0.805740	−	0.592269i	$-0.201768\pi$
$887$	−1.48282	−	2.21919i	−0.0497881	−	0.0745131i	−0.855529	+	0.517756i	$0.826768\pi$
$888$	−31.3055	+	8.54897i	−1.05054	+	0.286885i
$889$	−0.291914	−	0.195051i	−0.00979049	−	0.00654180i
$890$	16.7195	−	4.31347i	0.560437	−	0.144588i
$891$	2.41013	−	2.93676i	0.0807425	−	0.0983851i
$892$	−7.36539	+	6.22043i	−0.246612	+	0.208275i
$893$	−68.1094	−	36.4052i	−2.27919	−	1.21825i
$894$	−43.8726	+	40.3307i	−1.46732	+	1.34886i
$895$	−16.8259			−0.562427
$896$	−2.19707	−	0.215833i	−0.0733989	−	0.00721048i
$897$	−108.282			−3.61545
$898$	37.6607	−	34.6203i	1.25676	−	1.15530i
$899$	19.6340	+	10.4946i	0.654829	+	0.350013i
$900$	−30.5317	−	36.1516i	−1.01772	−	1.20505i
$901$	0.372070	−	0.453368i	0.0123954	−	0.0151039i
$902$	0.483062	−	0.124626i	0.0160842	−	0.00414958i
$903$	−2.74056	−	1.83118i	−0.0912001	−	0.0609379i
$904$	3.98943	−	6.98686i	0.132686	−	0.232380i
$905$	−0.474381	−	0.709961i	−0.0157690	−	0.0235999i
$906$	1.83047	+	32.5736i	0.0608133	+	1.08218i
$907$	−22.0926	−	6.70171i	−0.733572	−	0.222527i	−0.0986712	−	0.995120i	$-0.531459\pi$
$907$	−22.0926	−	6.70171i	−0.733572	−	0.222527i	−0.634901	+	0.772593i	$0.718959\pi$
$908$	23.7708	−	5.07765i	0.788860	−	0.168508i
$909$	2.30439	−	1.89117i	0.0764319	−	0.0627260i
$910$	−1.80572	+	0.280875i	−0.0598591	+	0.00931091i
$911$	4.55436	−	1.88648i	0.150893	−	0.0625019i	−0.305959	−	0.952045i	$-0.598977\pi$
$911$	4.55436	−	1.88648i	0.150893	−	0.0625019i	0.456852	+	0.889543i	$0.348977\pi$
$912$	−67.5247	+	71.4438i	−2.23596	+	2.36574i
$913$	0.240206	+	0.0994968i	0.00794967	+	0.00329286i
$914$	−1.76643	−	0.429259i	−0.0584283	−	0.0141986i
$915$	−3.29577	+	33.4625i	−0.108955	+	1.10624i
$916$	−21.3466	+	0.300942i	−0.705311	+	0.00994342i
$917$	−0.832800	−	1.55806i	−0.0275015	−	0.0514517i
$918$	4.54166	−	2.18735i	0.149897	−	0.0721933i
$919$	12.1036	+	2.40756i	0.399262	+	0.0794181i	0.390637	−	0.920545i	$-0.372255\pi$
$919$	12.1036	+	2.40756i	0.399262	+	0.0794181i	0.00862457	+	0.999963i	$0.497255\pi$
$920$	5.89937	−	25.8597i	0.194497	−	0.852570i
$921$	3.74358	+	18.8202i	0.123355	+	0.620148i
$922$	−5.69328	+	40.3379i	−0.187498	+	1.32846i
$923$	−2.82605	−	28.6933i	−0.0930205	−	0.944453i
$924$	−0.189618	+	0.0213787i	−0.00623798	+	0.000703306i
$925$	3.21944	+	10.6131i	0.105855	+	0.348956i
$926$	21.1451	−	45.5353i	0.694873	−	1.49638i
$927$	39.9166	−	39.9166i	1.31103	−	1.31103i
$928$	24.1512	−	28.6113i	0.792803	−	0.939211i
$929$	−10.7155	−	10.7155i	−0.351566	−	0.351566i	0.509126	−	0.860692i	$-0.329969\pi$
$929$	−10.7155	−	10.7155i	−0.351566	−	0.351566i	−0.860692	+	0.509126i	$0.829969\pi$
$930$	19.7891	−	7.23841i	0.648912	−	0.237357i
$931$	50.4336	−	15.2989i	1.65289	−	0.501400i
$932$	−0.318405	+	1.10551i	−0.0104297	+	0.0362121i
$933$	63.4193	−	6.24626i	2.07626	−	0.204493i
$934$	−23.8346	−	31.6682i	−0.779891	−	1.03622i
$935$	−0.0487527	+	0.00969751i	−0.00159438	+	0.000317142i
$936$	−96.6842	+	36.9183i	−3.16022	+	1.20671i
$937$	6.65123	−	33.4380i	0.217286	−	1.09237i	−0.705986	−	0.708226i	$-0.749496\pi$
$937$	6.65123	−	33.4380i	0.217286	−	1.09237i	0.923272	−	0.384146i	$-0.125504\pi$
$938$	−0.720306	−	0.252017i	−0.0235188	−	0.00822865i
$939$	45.3865	−	24.2596i	1.48113	−	0.791681i
$940$	25.5685	−	11.0156i	0.833951	−	0.359289i
$941$	24.6978	+	2.43252i	0.805124	+	0.0792978i	0.492202	−	0.870481i	$-0.336192\pi$
$941$	24.6978	+	2.43252i	0.805124	+	0.0792978i	0.312922	+	0.949779i	$0.398692\pi$
$942$	−64.9194	+	39.5358i	−2.11519	+	1.28815i
$943$	−6.16001	+	14.8716i	−0.200597	+	0.484285i
$944$	4.54140	+	5.22605i	0.147810	+	0.170093i
$945$	1.50157	+	3.62511i	0.0488461	+	0.117925i
$946$	0.894781	+	0.653890i	0.0290918	+	0.0212598i
$947$	13.6876	+	16.6784i	0.444787	+	0.541975i	0.946349	−	0.323147i	$-0.104741\pi$
$947$	13.6876	+	16.6784i	0.444787	+	0.541975i	−0.501562	+	0.865122i	$0.667241\pi$
$948$	−5.56236	−	1.02513i	−0.180657	−	0.0332947i
$949$	14.1304	−	46.5818i	0.458694	−	1.51211i
$950$	25.0517	+	22.3859i	0.812783	+	0.726295i
$951$	13.5266	−	9.03815i	0.438629	−	0.293082i
$952$	−0.126613	−	0.0423049i	−0.00410354	−	0.00137111i
$953$	−33.0015	+	49.3903i	−1.06902	+	1.59991i	−0.307764	+	0.951463i	$0.599581\pi$
$953$	−33.0015	+	49.3903i	−1.06902	+	1.59991i	−0.761261	+	0.648446i	$0.775419\pi$
$954$	22.2689	+	13.1350i	0.720981	+	0.425261i
$955$	−25.0811	−	20.5835i	−0.811604	−	0.666066i
$956$	8.18094	−	15.8385i	0.264590	−	0.512255i
$957$	1.52559	−	2.85417i	0.0493152	−	0.0922622i
$958$	1.06133	−	25.2315i	0.0342900	−	0.815192i
$959$		−	0.185503i		−	0.00599019i
$960$	−4.96151	−	35.0892i	−0.160132	−	1.13250i
$961$			19.6866i			0.635052i
$962$	24.2351	+	1.01942i	0.781371	+	0.0328673i
$963$	−56.1557	+	105.060i	−1.80959	+	3.38551i
$964$	8.66969	+	27.1941i	0.279232	+	0.875862i
$965$	−20.6905	−	16.9803i	−0.666052	−	0.546615i
$966$	3.12803	−	5.30321i	0.100643	−	0.170628i
$967$	−2.51428	+	3.76288i	−0.0808537	+	0.121006i	−0.869692	−	0.493594i	$-0.835683\pi$
$967$	−2.51428	+	3.76288i	−0.0808537	+	0.121006i	0.788839	+	0.614600i	$0.210683\pi$
$968$	−30.9720	+	2.17884i	−0.995478	+	0.0700304i
$969$	−4.94254	+	3.30250i	−0.158777	+	0.106092i
$970$	9.44556	−	10.5704i	0.303279	−	0.339394i
$971$	−4.47380	+	14.7482i	−0.143571	+	0.473291i	−0.999004	−	0.0446232i	$-0.985791\pi$
$971$	−4.47380	+	14.7482i	−0.143571	+	0.473291i	0.855433	+	0.517914i	$0.173291\pi$
$972$	42.7459	+	62.0616i	1.37107	+	1.99063i
$973$	1.97100	+	2.40168i	0.0631875	+	0.0769942i
$974$	−11.3818	+	15.5748i	−0.364697	+	0.499050i
$975$	18.9212	+	45.6797i	0.605962	+	1.46292i
$976$	18.5923	−	24.0039i	0.595124	−	0.768347i
$977$	−10.0872	+	24.3526i	−0.322717	+	0.779108i	0.676377	+	0.736555i	$0.263549\pi$
$977$	−10.0872	+	24.3526i	−0.322717	+	0.779108i	−0.999094	+	0.0425525i	$0.986451\pi$
$978$	15.6893	+	25.7625i	0.501689	+	0.823793i
$979$	−1.34119	−	0.132095i	−0.0428645	−	0.00422179i
$980$	−7.02249	+	17.6536i	−0.224325	+	0.563925i
$981$	76.2133	−	40.7369i	2.43330	−	1.30063i
$982$	−4.72397	+	13.5019i	−0.150748	+	0.430863i
$983$	−1.83343	+	9.21726i	−0.0584772	+	0.293985i	−0.998946	−	0.0458944i	$-0.985386\pi$
$983$	−1.83343	+	9.21726i	−0.0584772	+	0.293985i	0.940469	+	0.339879i	$0.110386\pi$
$984$	−0.600859	+	21.4983i	−0.0191547	+	0.685340i
$985$	10.7614	−	2.14057i	0.342885	−	0.0682041i
$986$	1.80895	−	1.36148i	0.0576088	−	0.0433583i
$987$	6.43144	−	0.633441i	0.204715	−	0.0201627i
$988$	64.3081	−	35.5479i	2.04591	−	1.13093i
$989$	−34.2189	+	10.3802i	−1.08810	+	0.330071i
$990$	−0.752725	−	2.05788i	−0.0239232	−	0.0654037i
$991$	−29.5439	−	29.5439i	−0.938492	−	0.938492i	0.0597231	−	0.998215i	$-0.480978\pi$
$991$	−29.5439	−	29.5439i	−0.938492	−	0.938492i	−0.998215	+	0.0597231i	$0.980978\pi$
$992$	−18.6083	−	3.97000i	−0.590813	−	0.126047i
$993$	0.385049	−	0.385049i	0.0122192	−	0.0122192i
$994$	1.48691	+	0.690476i	0.0471621	+	0.0219006i
$995$	8.84709	+	29.1649i	0.280472	+	0.924591i
$996$	−6.98775	+	8.76366i	−0.221415	+	0.277687i
$997$	−3.80500	−	38.6328i	−0.120506	−	1.22351i	−0.845203	−	0.534446i	$-0.820520\pi$
$997$	−3.80500	−	38.6328i	−0.120506	−	1.22351i	0.724697	−	0.689067i	$-0.241980\pi$
$998$	31.5778	+	4.45688i	0.999577	+	0.141080i
$999$	−10.1608	−	51.0819i	−0.321474	−	1.61616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.109.4	yes	240
4.3	odd	2		512.2.k.a.273.15		240
128.27	odd	32		512.2.k.a.497.15		240
128.101	even	32	inner	128.2.k.a.101.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.4	✓	240	128.101	even	32	inner
128.2.k.a.109.4	yes	240	1.1	even	1	trivial
512.2.k.a.273.15		240	4.3	odd	2
512.2.k.a.497.15		240	128.27	odd	32

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.957090 - 1.04114i) q^{2} +(-2.86311 - 1.53036i) q^{3} +(-0.167958 + 1.99294i) q^{4} +(-0.865631 + 1.05477i) q^{5} +(1.14693 + 4.44560i) q^{6} +(0.162245 + 0.108408i) q^{7} +(2.23568 - 1.73255i) q^{8} +(4.18867 + 6.26879i) q^{9} +(1.92666 - 0.108268i) q^{10} +(-0.144127 - 0.0437204i) q^{11} +(3.53080 - 5.44896i) q^{12} +(-3.75158 + 3.07884i) q^{13} +(-0.0424141 - 0.272677i) q^{14} +(4.09258 - 1.69520i) q^{15} +(-3.94358 - 0.669457i) q^{16} +(-0.223463 - 0.0925613i) q^{17} +(2.51777 - 10.3608i) q^{18} +(-0.742006 + 7.53372i) q^{19} +(-1.95671 - 1.90230i) q^{20} +(-0.298620 - 0.558679i) q^{21} +(0.0924232 + 0.191901i) q^{22} +(-6.74055 - 1.34078i) q^{23} +(-9.05243 + 1.53908i) q^{24} +(0.612220 + 3.07784i) q^{25} +(6.79611 + 0.959202i) q^{26} +(-1.44447 - 14.6660i) q^{27} +(-0.243301 + 0.305135i) q^{28} +(-1.92135 - 6.33383i) q^{29} +(-5.68192 - 2.63850i) q^{30} +(-2.37838 + 2.37838i) q^{31} +(3.07736 + 4.74656i) q^{32} +(0.345743 + 0.345743i) q^{33} +(0.117504 + 0.321246i) q^{34} +(-0.254791 + 0.0772899i) q^{35} +(-13.1968 + 7.29486i) q^{36} +(3.51713 - 0.346407i) q^{37} +(8.55384 - 6.43791i) q^{38} +(15.4529 - 3.07378i) q^{39} +(-0.107825 + 3.85789i) q^{40} +(0.456936 - 2.29717i) q^{41} +(-0.295858 + 0.845612i) q^{42} +(4.58870 - 2.45271i) q^{43} +(0.111339 - 0.279892i) q^{44} +(-10.2380 - 1.00836i) q^{45} +(5.05537 + 8.30112i) q^{46} +(-3.90401 + 9.42513i) q^{47} +(10.2664 + 7.95184i) q^{48} +(-2.66421 - 6.43198i) q^{49} +(2.61852 - 3.58317i) q^{50} +(0.498146 + 0.606993i) q^{51} +(-5.50582 - 7.99376i) q^{52} +(-0.703882 + 2.32039i) q^{53} +(-13.8869 + 15.5406i) q^{54} +(0.170876 - 0.114176i) q^{55} +(0.550551 - 0.0387305i) q^{56} +(13.6538 - 20.4343i) q^{57} +(-4.75552 + 8.06244i) q^{58} +(-1.33800 - 1.09807i) q^{59} +(2.69105 + 8.44098i) q^{60} +(-3.57815 + 6.69426i) q^{61} +(4.75256 + 0.199910i) q^{62} +1.47117i q^{63} +(1.99654 - 7.74686i) q^{64} -6.62221i q^{65} +(0.0290607 - 0.690875i) q^{66} +(1.30359 - 2.43884i) q^{67} +(0.222001 - 0.429801i) q^{68} +(17.2471 + 14.1543i) q^{69} +(0.324327 + 0.191300i) q^{70} +(-3.30056 + 4.93964i) q^{71} +(20.2255 + 6.75793i) q^{72} +(-8.33969 + 5.57240i) q^{73} +(-3.72687 - 3.33030i) q^{74} +(2.95736 - 9.74910i) q^{75} +(-14.8896 - 2.74411i) q^{76} +(-0.0186442 - 0.0227180i) q^{77} +(-17.9901 - 13.1468i) q^{78} +(-0.333360 - 0.804803i) q^{79} +(4.11981 - 3.58008i) q^{80} +(-9.65299 + 23.3044i) q^{81} +(-2.82902 + 1.72287i) q^{82} +(-1.71796 - 0.169204i) q^{83} +(1.16357 - 0.501296i) q^{84} +(0.291068 - 0.155579i) q^{85} +(-6.94543 - 2.43003i) q^{86} +(-4.19204 + 21.0748i) q^{87} +(-0.397970 + 0.151962i) q^{88} +(8.77606 - 1.74567i) q^{89} +(8.74885 + 11.6243i) q^{90} +(-0.942446 + 0.0928229i) q^{91} +(3.80421 - 13.2083i) q^{92} +(10.4494 - 3.16978i) q^{93} +(13.5494 - 4.95606i) q^{94} +(-7.30407 - 7.30407i) q^{95} +(-1.54686 - 18.2994i) q^{96} +(5.19447 - 5.19447i) q^{97} +(-4.14672 + 8.92981i) q^{98} +(-0.329626 - 1.08663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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