LMFDB - Embedded newform 750.2.m.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	750.91
Dual form			750.2.m.b.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 + 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.14929 - 0.616880i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.0420378 - 0.129379i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(0.728969 + 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.14929 - 0.616880i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.0420378 - 0.129379i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-1.14448 - 1.92098i) q^{10} +(-2.93231 - 2.75362i) q^{11} +(-0.876307 - 0.481754i) q^{12} +(-0.623865 - 1.32578i) q^{13} +(0.0579218 - 0.123090i) q^{14} +(1.67250 - 1.48417i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.339594 - 5.39770i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.344343 + 0.542598i) q^{19} +(0.480707 - 2.18379i) q^{20} +(0.131763 + 0.0338310i) q^{21} +(-0.252578 - 4.01461i) q^{22} +(-0.423031 - 2.21761i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.23892 + 2.65171i) q^{25} +(0.452782 - 1.39352i) q^{26} +(0.992115 + 0.125333i) q^{27} +(0.126484 - 0.0500786i) q^{28} +(0.0190258 - 0.00753283i) q^{29} +(2.23518 + 0.0629919i) q^{30} +(0.0131033 - 0.208271i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(3.89617 - 1.00037i) q^{33} +(3.94253 - 3.70228i) q^{34} +(0.0105402 + 0.304005i) q^{35} +(0.876307 - 0.481754i) q^{36} +(-9.37078 + 1.18380i) q^{37} +(-0.120419 + 0.631256i) q^{38} +(1.45368 + 0.183642i) q^{39} +(1.84532 - 1.26284i) q^{40} +(0.931932 - 4.88536i) q^{41} +(0.0728923 + 0.114860i) q^{42} +(-2.57022 + 1.86737i) q^{43} +(2.56407 - 3.09943i) q^{44} +(0.356955 + 2.20739i) q^{45} +(1.20968 - 1.90615i) q^{46} +(-2.66005 - 3.21545i) q^{47} +(0.425779 - 0.904827i) q^{48} +(5.64815 - 4.10362i) q^{49} +(1.27482 + 4.83475i) q^{50} +(4.37546 + 3.17896i) q^{51} +(1.28399 - 0.705881i) q^{52} +(-4.37504 - 1.12332i) q^{53} +(0.637424 + 0.770513i) q^{54} +(4.60374 + 7.72723i) q^{55} +(0.126484 + 0.0500786i) q^{56} -0.642639 q^{57} +(0.0190258 + 0.00753283i) q^{58} +(-3.08030 - 1.69341i) q^{59} +(1.58626 + 1.57601i) q^{60} +(-0.313519 - 1.64353i) q^{61} +(0.152123 - 0.142853i) q^{62} +(-0.0991668 + 0.0931238i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(0.523022 + 3.23434i) q^{65} +(3.52499 + 1.93788i) q^{66} +(-11.0655 - 4.38112i) q^{67} +5.40837 q^{68} +(2.09906 + 0.831076i) q^{69} +(-0.200423 + 0.228826i) q^{70} +(-0.746910 - 0.902859i) q^{71} +(0.968583 + 0.248690i) q^{72} +(6.68934 - 3.67749i) q^{73} +(-7.64137 - 5.55178i) q^{74} +(-4.51024 + 2.15818i) q^{75} +(-0.519906 + 0.377734i) q^{76} +(-0.232993 + 0.495136i) q^{77} +(0.933974 + 1.12898i) q^{78} +(-1.68247 + 2.65115i) q^{79} +(2.20966 + 0.342638i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(4.02361 - 2.92332i) q^{82} +(6.85618 + 10.8036i) q^{83} +(-0.0254908 + 0.133627i) q^{84} +(-4.05962 + 11.3917i) q^{85} +(-3.15191 - 0.398179i) q^{86} +(-0.00383433 + 0.0201003i) q^{87} +(3.99083 - 0.504159i) q^{88} +(-1.88348 + 1.03545i) q^{89} +(-1.25086 + 1.85347i) q^{90} +(-0.145302 + 0.136448i) q^{91} +(2.18667 - 0.561441i) q^{92} +(0.168828 + 0.122660i) q^{93} +(0.262033 - 4.16489i) q^{94} +(-0.405377 - 1.37862i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-17.8809 + 7.07955i) q^{97} +(6.92644 + 0.875013i) q^{98} +(-1.24304 + 3.82567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) $ 120 * q + 20 * q^5 - 5 * q^7	$ 120 q + 20 q^{5} - 5 q^{7} - 20 q^{10} + 5 q^{11} - 10 q^{13} - 20 q^{14} + 20 q^{15} - 5 q^{17} - 30 q^{18} + 15 q^{19} + 5 q^{20} - 15 q^{23} + 30 q^{24} - 20 q^{25} + 10 q^{26} - 5 q^{29} + 5 q^{30} - 50 q^{31} - 30 q^{32} + 30 q^{34} - 10 q^{35} + 10 q^{37} + 35 q^{38} + 10 q^{39} - 5 q^{40} - 35 q^{41} + 5 q^{43} - 25 q^{44} - 10 q^{46} + 130 q^{47} - 15 q^{49} - 20 q^{50} - 5 q^{51} + 40 q^{52} + 15 q^{53} + 10 q^{55} - 20 q^{57} - 5 q^{58} - 55 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 40 q^{65} + 20 q^{66} + 85 q^{67} - 20 q^{68} + 10 q^{69} - 45 q^{70} - 30 q^{71} - 30 q^{74} + 45 q^{75} - 5 q^{76} - 35 q^{77} - 10 q^{78} + 70 q^{79} - 45 q^{82} - 35 q^{83} - 5 q^{84} + 100 q^{85} - 15 q^{86} - 15 q^{87} + 5 q^{88} + 70 q^{89} - 5 q^{90} - 105 q^{91} + 65 q^{92} - 20 q^{94} - 65 q^{95} - 5 q^{97} + 50 q^{98} - 10 q^{99}+O(q^{100}) $ 120 * q + 20 * q^5 - 5 * q^7 - 20 * q^10 + 5 * q^11 - 10 * q^13 - 20 * q^14 + 20 * q^15 - 5 * q^17 - 30 * q^18 + 15 * q^19 + 5 * q^20 - 15 * q^23 + 30 * q^24 - 20 * q^25 + 10 * q^26 - 5 * q^29 + 5 * q^30 - 50 * q^31 - 30 * q^32 + 30 * q^34 - 10 * q^35 + 10 * q^37 + 35 * q^38 + 10 * q^39 - 5 * q^40 - 35 * q^41 + 5 * q^43 - 25 * q^44 - 10 * q^46 + 130 * q^47 - 15 * q^49 - 20 * q^50 - 5 * q^51 + 40 * q^52 + 15 * q^53 + 10 * q^55 - 20 * q^57 - 5 * q^58 - 55 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 40 * q^65 + 20 * q^66 + 85 * q^67 - 20 * q^68 + 10 * q^69 - 45 * q^70 - 30 * q^71 - 30 * q^74 + 45 * q^75 - 5 * q^76 - 35 * q^77 - 10 * q^78 + 70 * q^79 - 45 * q^82 - 35 * q^83 - 5 * q^84 + 100 * q^85 - 15 * q^86 - 15 * q^87 + 5 * q^88 + 70 * q^89 - 5 * q^90 - 105 * q^91 + 65 * q^92 - 20 * q^94 - 65 * q^95 - 5 * q^97 + 50 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{6}{25}\right)$	$1$

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 $

$2$	0.728969	+	0.684547i	0.515459	+	0.484048i
$2$	0.728969	+	0.684547i	0.515459	+	0.484048i
$3$	−0.535827	+	0.844328i	−0.309360	+	0.487473i
$3$	−0.535827	+	0.844328i	−0.309360	+	0.487473i
$4$	0.0627905	+	0.998027i	0.0313953	+	0.499013i
$5$	−2.14929	−	0.616880i	−0.961193	−	0.275877i
$5$	−2.14929	−	0.616880i	−0.961193	−	0.275877i
$6$	−0.968583	+	0.248690i	−0.395422	+	0.101527i
$7$	−0.0420378	−	0.129379i	−0.0158888	−	0.0489006i	0.942798	−	0.333365i	$-0.108184\pi$
$7$	−0.0420378	−	0.129379i	−0.0158888	−	0.0489006i	−0.958687	+	0.284465i	$0.908184\pi$
$8$	−0.637424	+	0.770513i	−0.225363	+	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	−1.14448	−	1.92098i	−0.361918	−	0.607467i
$11$	−2.93231	−	2.75362i	−0.884125	−	0.830249i	0.102250	−	0.994759i	$-0.467396\pi$
$11$	−2.93231	−	2.75362i	−0.884125	−	0.830249i	−0.986375	+	0.164510i	$0.947396\pi$
$12$	−0.876307	−	0.481754i	−0.252968	−	0.139070i
$13$	−0.623865	−	1.32578i	−0.173029	−	0.367706i	0.799437	−	0.600750i	$-0.205131\pi$
$13$	−0.623865	−	1.32578i	−0.173029	−	0.367706i	−0.972466	+	0.233044i	$0.925131\pi$
$14$	0.0579218	−	0.123090i	0.0154802	−	0.0328972i
$15$	1.67250	−	1.48417i	0.431837	−	0.383210i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	0.339594	−	5.39770i	0.0823637	−	1.30913i	−0.712210	−	0.701966i	$-0.752306\pi$
$17$	0.339594	−	5.39770i	0.0823637	−	1.30913i	0.794574	−	0.607168i	$-0.207694\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	0.344343	+	0.542598i	0.0789977	+	0.124481i	0.881530	−	0.472129i	$-0.156514\pi$
$19$	0.344343	+	0.542598i	0.0789977	+	0.124481i	−0.802532	+	0.596609i	$0.796514\pi$
$20$	0.480707	−	2.18379i	0.107489	−	0.488309i
$21$	0.131763	+	0.0338310i	0.0287531	+	0.00738254i
$22$	−0.252578	−	4.01461i	−0.0538498	−	0.855918i
$23$	−0.423031	−	2.21761i	−0.0882081	−	0.462403i	−0.998795	−	0.0490845i	$-0.984370\pi$
$23$	−0.423031	−	2.21761i	−0.0882081	−	0.462403i	0.910587	−	0.413318i	$-0.135630\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	4.23892	+	2.65171i	0.847784	+	0.530342i
$26$	0.452782	−	1.39352i	0.0887978	−	0.273291i
$27$	0.992115	+	0.125333i	0.190933	+	0.0241204i
$28$	0.126484	−	0.0500786i	0.0239032	−	0.00946396i
$29$	0.0190258	−	0.00753283i	0.00353300	−	0.00139881i	−0.366357	−	0.930474i	$-0.619395\pi$
$29$	0.0190258	−	0.00753283i	0.00353300	−	0.00139881i	0.369890	+	0.929075i	$0.379395\pi$
$30$	2.23518	+	0.0629919i	0.408086	+	0.0115007i
$31$	0.0131033	−	0.208271i	0.00235342	−	0.0374065i	−0.996675	−	0.0814827i	$-0.974034\pi$
$31$	0.0131033	−	0.208271i	0.00235342	−	0.0374065i	0.999028	+	0.0440762i	$0.0140344\pi$
$32$	−0.809017	−	0.587785i	−0.143015	−	0.103907i
$33$	3.89617	−	1.00037i	0.678237	−	0.174142i
$34$	3.94253	−	3.70228i	0.676139	−	0.634936i
$35$	0.0105402	+	0.304005i	0.00178162	+	0.0513863i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	−9.37078	+	1.18380i	−1.54055	+	0.194616i	−0.849264	−	0.527969i	$-0.822954\pi$
$37$	−9.37078	+	1.18380i	−1.54055	+	0.194616i	−0.691282	+	0.722585i	$0.742954\pi$
$38$	−0.120419	+	0.631256i	−0.0195345	+	0.102403i
$39$	1.45368	+	0.183642i	0.232775	+	0.0294063i
$40$	1.84532	−	1.26284i	0.291771	−	0.199673i
$41$	0.931932	−	4.88536i	0.145543	−	0.762965i	−0.832413	−	0.554156i	$-0.813041\pi$
$41$	0.931932	−	4.88536i	0.145543	−	0.762965i	0.977956	−	0.208809i	$-0.0669587\pi$
$42$	0.0728923	+	0.114860i	0.0112475	+	0.0177233i
$43$	−2.57022	+	1.86737i	−0.391954	+	0.284772i	−0.766256	−	0.642536i	$-0.777883\pi$
$43$	−2.57022	+	1.86737i	−0.391954	+	0.284772i	0.374302	+	0.927307i	$0.377883\pi$
$44$	2.56407	−	3.09943i	0.386548	−	0.467256i
$45$	0.356955	+	2.20739i	0.0532117	+	0.329059i
$46$	1.20968	−	1.90615i	0.178358	−	0.281047i
$47$	−2.66005	−	3.21545i	−0.388008	−	0.469021i	0.539955	−	0.841694i	$-0.318441\pi$
$47$	−2.66005	−	3.21545i	−0.388008	−	0.469021i	−0.927963	+	0.372673i	$0.878441\pi$
$48$	0.425779	−	0.904827i	0.0614559	−	0.130601i
$49$	5.64815	−	4.10362i	0.806878	−	0.586231i
$50$	1.27482	+	4.83475i	0.180287	+	0.683737i
$51$	4.37546	+	3.17896i	0.612687	+	0.445143i
$52$	1.28399	−	0.705881i	0.178058	−	0.0978881i
$53$	−4.37504	−	1.12332i	−0.600958	−	0.154300i	−0.0640587	−	0.997946i	$-0.520404\pi$
$53$	−4.37504	−	1.12332i	−0.600958	−	0.154300i	−0.536899	+	0.843646i	$0.680404\pi$
$54$	0.637424	+	0.770513i	0.0867424	+	0.104854i
$55$	4.60374	+	7.72723i	0.620769	+	1.04194i
$56$	0.126484	+	0.0500786i	0.0169021	+	0.00669203i
$57$	−0.642639			−0.0851196
$58$	0.0190258	+	0.00753283i	0.00249821	+	0.000989109i
$59$	−3.08030	−	1.69341i	−0.401020	−	0.220463i	0.268463	−	0.963290i	$-0.413484\pi$
$59$	−3.08030	−	1.69341i	−0.401020	−	0.220463i	−0.669483	+	0.742827i	$0.733484\pi$
$60$	1.58626	+	1.57601i	0.204785	+	0.203461i
$61$	−0.313519	−	1.64353i	−0.0401420	−	0.210432i	0.956565	−	0.291519i	$-0.0941607\pi$
$61$	−0.313519	−	1.64353i	−0.0401420	−	0.210432i	−0.996707	+	0.0810874i	$0.974161\pi$
$62$	0.152123	−	0.142853i	0.0193196	−	0.0181423i
$63$	−0.0991668	+	0.0931238i	−0.0124938	+	0.0117325i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	0.523022	+	3.23434i	0.0648729	+	0.401171i
$66$	3.52499	+	1.93788i	0.433896	+	0.238536i
$67$	−11.0655	−	4.38112i	−1.35186	−	0.535239i	−0.423155	−	0.906057i	$-0.639077\pi$
$67$	−11.0655	−	4.38112i	−1.35186	−	0.535239i	−0.928706	+	0.370818i	$0.879077\pi$
$68$	5.40837			0.655861
$69$	2.09906	+	0.831076i	0.252697	+	0.100050i
$70$	−0.200423	+	0.228826i	−0.0239551	+	0.0273499i
$71$	−0.746910	−	0.902859i	−0.0886419	−	0.107150i	0.724327	−	0.689456i	$-0.242150\pi$
$71$	−0.746910	−	0.902859i	−0.0886419	−	0.107150i	−0.812969	+	0.582306i	$0.802150\pi$
$72$	0.968583	+	0.248690i	0.114149	+	0.0293084i
$73$	6.68934	−	3.67749i	0.782928	−	0.430418i	−0.0395484	−	0.999218i	$-0.512592\pi$
$73$	6.68934	−	3.67749i	0.782928	−	0.430418i	0.822476	+	0.568799i	$0.192592\pi$
$74$	−7.64137	−	5.55178i	−0.888291	−	0.645382i
$75$	−4.51024	+	2.15818i	−0.520798	+	0.249205i
$76$	−0.519906	+	0.377734i	−0.0596373	+	0.0433290i
$77$	−0.232993	+	0.495136i	−0.0265520	+	0.0564260i
$78$	0.933974	+	1.12898i	0.105752	+	0.127832i
$79$	−1.68247	+	2.65115i	−0.189293	+	0.298278i	−0.925698	−	0.378263i	$-0.876522\pi$
$79$	−1.68247	+	2.65115i	−0.189293	+	0.298278i	0.736405	+	0.676541i	$0.236522\pi$
$80$	2.20966	+	0.342638i	0.247048	+	0.0383080i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	4.02361	−	2.92332i	0.444333	−	0.322827i
$83$	6.85618	+	10.8036i	0.752563	+	1.18585i	0.977389	+	0.211451i	$0.0678189\pi$
$83$	6.85618	+	10.8036i	0.752563	+	1.18585i	−0.224825	+	0.974399i	$0.572181\pi$
$84$	−0.0254908	+	0.133627i	−0.00278128	+	0.0145800i
$85$	−4.05962	+	11.3917i	−0.440327	+	1.23561i
$86$	−3.15191	−	0.398179i	−0.339879	−	0.0429367i
$87$	−0.00383433	+	0.0201003i	−0.000411084	+	0.00215498i
$88$	3.99083	−	0.504159i	0.425424	−	0.0537435i
$89$	−1.88348	+	1.03545i	−0.199649	+	0.109758i	−0.578442	−	0.815724i	$-0.696339\pi$
$89$	−1.88348	+	1.03545i	−0.199649	+	0.109758i	0.378793	+	0.925481i	$0.376339\pi$
$90$	−1.25086	+	1.85347i	−0.131852	+	0.195373i
$91$	−0.145302	+	0.136448i	−0.0152318	+	0.0143036i
$92$	2.18667	−	0.561441i	0.227976	−	0.0585343i
$93$	0.168828	+	0.122660i	0.0175066	+	0.0127193i
$94$	0.262033	−	4.16489i	0.0270266	−	0.429576i
$95$	−0.405377	−	1.37862i	−0.0415908	−	0.141443i
$96$	0.929776	−	0.368125i	0.0948949	−	0.0375716i
$97$	−17.8809	+	7.07955i	−1.81553	+	0.718819i	−0.828138	+	0.560524i	$0.810600\pi$
$97$	−17.8809	+	7.07955i	−1.81553	+	0.718819i	−0.987392	+	0.158295i	$0.949400\pi$
$98$	6.92644	+	0.875013i	0.699676	+	0.0883897i
$99$	−1.24304	+	3.82567i	−0.124930	+	0.384494i
$100$	−2.38031	+	4.39706i	−0.238031	+	0.439706i
$101$	−0.0457104	−	0.140682i	−0.00454836	−	0.0139984i	0.948757	−	0.316008i	$-0.102343\pi$
$101$	−0.0457104	−	0.140682i	−0.00454836	−	0.0139984i	−0.953305	+	0.302009i	$0.902343\pi$
$102$	1.01343	+	5.31257i	0.100344	+	0.526023i
$103$	1.13771	+	18.0833i	0.112102	+	1.78180i	0.505885	+	0.862601i	$0.331166\pi$
$103$	1.13771	+	18.0833i	0.112102	+	1.78180i	−0.393784	+	0.919203i	$0.628834\pi$
$104$	1.41920	+	0.364388i	0.139164	+	0.0357312i
$105$	−0.262328	−	0.153995i	−0.0256006	−	0.0150284i
$106$	−2.42030	−	3.81379i	−0.235081	−	0.370428i
$107$	1.76906	−	5.44462i	0.171022	−	0.526351i	−0.828408	−	0.560126i	$-0.810753\pi$
$107$	1.76906	−	5.44462i	0.171022	−	0.526351i	0.999429	+	0.0337745i	$0.0107528\pi$
$108$	−0.0627905	+	0.998027i	−0.00604202	+	0.0960352i
$109$	13.1175	−	1.65712i	1.25643	−	0.158724i	0.531208	−	0.847241i	$-0.321738\pi$
$109$	13.1175	−	1.65712i	1.25643	−	0.158724i	0.725220	+	0.688517i	$0.241738\pi$
$110$	−1.93367	+	8.78439i	−0.184368	+	0.837558i
$111$	4.02159	−	8.54632i	0.381713	−	0.811181i
$112$	0.0579218	+	0.123090i	0.00547309	+	0.0116309i
$113$	−4.42853	−	2.43461i	−0.416601	−	0.229028i	0.259645	−	0.965704i	$-0.416394\pi$
$113$	−4.42853	−	2.43461i	−0.416601	−	0.229028i	−0.676246	+	0.736676i	$0.736394\pi$
$114$	−0.468464	−	0.439917i	−0.0438756	−	0.0412020i
$115$	−0.458779	+	5.02725i	−0.0427813	+	0.468793i
$116$	0.00871261	+	0.0185152i	0.000808945	+	0.00171910i
$117$	−0.933974	+	1.12898i	−0.0863459	+	0.104374i
$118$	−1.08622	−	3.34305i	−0.0999949	−	0.307753i
$119$	−0.712624	+	0.182971i	−0.0653262	+	0.0167729i
$120$	0.0774806	+	2.23473i	0.00707298	+	0.204002i
$121$	0.325312	+	5.17068i	0.0295738	+	0.470062i
$122$	0.896525	−	1.41270i	0.0811675	−	0.127900i
$123$	3.62549	+	3.40456i	0.326899	+	0.306979i
$124$	0.208682			0.0187402
$125$	−7.47489	−	8.31420i	−0.668575	−	0.743645i
$126$	−0.136037			−0.0121191
$127$	−0.376621	−	0.353671i	−0.0334197	−	0.0313832i	0.667657	−	0.744469i	$-0.267297\pi$
$127$	−0.376621	−	0.353671i	−0.0334197	−	0.0313832i	−0.701077	+	0.713085i	$0.747297\pi$
$128$	0.535827	−	0.844328i	0.0473608	−	0.0746288i
$129$	−0.199483	−	3.17069i	−0.0175635	−	0.279164i
$130$	−1.83279	+	2.71577i	−0.160747	+	0.238189i
$131$	−1.63440	+	0.419644i	−0.142799	+	0.0366644i	−0.319413	−	0.947616i	$-0.603486\pi$
$131$	−1.63440	+	0.419644i	−0.142799	+	0.0366644i	0.176614	+	0.984280i	$0.443486\pi$
$132$	1.24304	+	3.82567i	0.108192	+	0.332982i
$133$	0.0557253	−	0.0673604i	0.00483200	−	0.00584089i
$134$	−5.06728	−	10.7685i	−0.437747	−	0.930259i
$135$	−2.05503	−	0.881393i	−0.176869	−	0.0758582i
$136$	3.94253	+	3.70228i	0.338069	+	0.317468i
$137$	−16.1862	−	8.89841i	−1.38288	−	0.760243i	−0.395475	−	0.918477i	$-0.629420\pi$
$137$	−16.1862	−	8.89841i	−1.38288	−	0.760243i	−0.987402	+	0.158234i	$0.949420\pi$
$138$	0.961237	+	2.04273i	0.0818259	+	0.173889i
$139$	−6.85504	+	14.5677i	−0.581437	+	1.23562i	0.370360	+	0.928888i	$0.379234\pi$
$139$	−6.85504	+	14.5677i	−0.581437	+	1.23562i	−0.951797	+	0.306728i	$0.900766\pi$
$140$	−0.302744	+	0.0296081i	−0.0255865	+	0.00250234i
$141$	4.14022	−	0.523031i	0.348669	−	0.0440472i
$142$	0.0735756	−	1.16945i	0.00617433	−	0.0981382i
$143$	−1.82134	+	5.60550i	−0.152308	+	0.468755i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	−0.0455388	+	0.00445366i	−0.00378179	+	0.000369856i
$146$	7.39374	+	1.89839i	0.611910	+	0.157112i
$147$	0.438372	+	6.96772i	0.0361563	+	0.574688i
$148$	−1.76986	−	9.27795i	−0.145482	−	0.762643i
$149$	−4.51611	−	13.8992i	−0.369974	−	1.13866i	−0.946807	−	0.321801i	$-0.895712\pi$
$149$	−4.51611	−	13.8992i	−0.369974	−	1.13866i	0.576833	−	0.816862i	$-0.304288\pi$
$150$	−4.76520	−	1.51423i	−0.389077	−	0.123636i
$151$	0.858458	−	2.64206i	0.0698603	−	0.215008i	−0.910031	−	0.414540i	$-0.863942\pi$
$151$	0.858458	−	2.64206i	0.0698603	−	0.215008i	0.979891	+	0.199533i	$0.0639423\pi$
$152$	−0.637572	−	0.0805440i	−0.0517139	−	0.00653298i
$153$	−5.02857	+	1.99095i	−0.406536	+	0.160959i
$154$	−0.508788	+	0.201444i	−0.0409993	+	0.0162328i
$155$	−0.156641	+	0.439551i	−0.0125817	+	0.0353056i
$156$	−0.0920027	+	1.46234i	−0.00736611	+	0.117081i
$157$	−3.68049	−	2.67403i	−0.293735	−	0.213411i	0.431151	−	0.902280i	$-0.358108\pi$
$157$	−3.68049	−	2.67403i	−0.293735	−	0.213411i	−0.724886	+	0.688869i	$0.758108\pi$
$158$	−3.04131	+	0.780875i	−0.241954	+	0.0621231i
$159$	3.29271	−	3.09206i	0.261129	−	0.245217i
$160$	1.37622	+	1.76239i	0.108800	+	0.139329i
$161$	−0.269128	+	0.147955i	−0.0212103	+	0.0116605i
$162$	−0.992115	+	0.125333i	−0.0779479	+	0.00984711i
$163$	2.59319	−	13.5940i	0.203114	−	1.06476i	−0.723948	−	0.689855i	$-0.757674\pi$
$163$	2.59319	−	13.5940i	0.203114	−	1.06476i	0.927062	−	0.374908i	$-0.122326\pi$
$164$	4.93423	+	0.623339i	0.385299	+	0.0486746i
$165$	−8.99112	−	0.253388i	−0.699958	−	0.0197262i
$166$	−2.39764	+	12.5689i	−0.186093	+	0.975533i
$167$	3.99400	+	6.29354i	0.309065	+	0.487009i	0.962985	−	0.269555i	$-0.0868766\pi$
$167$	3.99400	+	6.29354i	0.309065	+	0.487009i	−0.653920	+	0.756564i	$0.726877\pi$
$168$	−0.110056	+	0.0799606i	−0.00849103	+	0.00616909i
$169$	6.91802	−	8.36245i	0.532156	−	0.643266i
$170$	−10.7575	+	5.52522i	−0.825064	+	0.423765i
$171$	0.344343	−	0.542598i	0.0263326	−	0.0414935i
$172$	−2.02507	−	2.44789i	−0.154410	−	0.186650i
$173$	−6.15068	+	13.0709i	−0.467628	+	0.993760i	0.522375	+	0.852716i	$0.325046\pi$
$173$	−6.15068	+	13.0709i	−0.467628	+	0.993760i	−0.990003	+	0.141044i	$0.954954\pi$
$174$	−0.0165547	+	0.0120277i	−0.00125501	+	0.000911817i
$175$	0.164881	−	0.659899i	0.0124638	−	0.0498837i
$176$	3.25431	+	2.36440i	0.245303	+	0.178223i
$177$	3.08030	−	1.69341i	0.231529	−	0.127284i
$178$	−2.08181	−	0.534519i	−0.156039	−	0.0400639i
$179$	5.19793	+	6.28322i	0.388512	+	0.469630i	0.928117	−	0.372288i	$-0.121427\pi$
$179$	5.19793	+	6.28322i	0.388512	+	0.469630i	−0.539606	+	0.841918i	$0.681427\pi$
$180$	−2.18062	+	0.494854i	−0.162534	+	0.0368842i
$181$	9.13336	+	3.61615i	0.678877	+	0.268786i	0.682154	−	0.731208i	$-0.261043\pi$
$181$	9.13336	+	3.61615i	0.678877	+	0.268786i	−0.00327728	+	0.999995i	$0.501043\pi$
$182$	−0.199326			−0.0147750
$183$	1.55567	+	0.615932i	0.114998	+	0.0455310i
$184$	1.97835	+	1.08760i	0.145846	+	0.0801793i
$185$	20.8708	+	3.23630i	1.53445	+	0.237937i
$186$	0.0391032	+	0.204986i	0.00286718	+	0.0150303i
$187$	−15.8590	+	14.8926i	−1.15973	+	1.08906i
$188$	3.04208	−	2.85670i	0.221866	−	0.208346i
$189$	−0.0254908	−	0.133627i	−0.00185418	−	0.00971997i
$190$	0.648224	−	1.28247i	0.0470271	−	0.0930402i
$191$	−1.42892	−	0.785556i	−0.103393	−	0.0568408i	0.429218	−	0.903201i	$-0.358789\pi$
$191$	−1.42892	−	0.785556i	−0.103393	−	0.0568408i	−0.532611	+	0.846360i	$0.678789\pi$
$192$	0.929776	+	0.368125i	0.0671008	+	0.0265671i
$193$	9.53116			0.686068			0.343034	−	0.939323i	$-0.388545\pi$
$193$	9.53116			0.686068			0.343034	+	0.939323i	$0.388545\pi$
$194$	−17.8809	−	7.07955i	−1.28377	−	0.508282i
$195$	−3.01110	−	1.29145i	−0.215629	−	0.0924823i
$196$	4.45017	+	5.37933i	0.317869	+	0.384238i
$197$	−14.8547	−	3.81404i	−1.05835	−	0.271739i	−0.320883	−	0.947119i	$-0.603980\pi$
$197$	−14.8547	−	3.81404i	−1.05835	−	0.271739i	−0.737470	+	0.675380i	$0.763980\pi$
$198$	−3.52499	+	1.93788i	−0.250510	+	0.137719i
$199$	5.19099	+	3.77148i	0.367980	+	0.267353i	0.756373	−	0.654141i	$-0.226970\pi$
$199$	5.19099	+	3.77148i	0.367980	+	0.267353i	−0.388393	+	0.921494i	$0.626970\pi$
$200$	−4.74517	+	1.57588i	−0.335534	+	0.111432i
$201$	9.62827	−	6.99535i	0.679126	−	0.493414i
$202$	0.0629822	−	0.133844i	0.00443141	−	0.00941723i
$203$	−0.00177439	−	0.00214487i	−0.000124538	−	0.000150540i
$204$	−2.89795	+	4.56644i	−0.202897	+	0.319715i
$205$	−5.01667	+	9.92517i	−0.350380	+	0.693204i
$206$	−11.5495	+	13.9610i	−0.804695	+	0.972709i
$207$	−1.82643	+	1.32698i	−0.126946	+	0.0922316i
$208$	0.785111	+	1.23714i	0.0544376	+	0.0857800i
$209$	0.484390	−	2.53926i	0.0335059	−	0.175644i
$210$	−0.0858122	−	0.291833i	−0.00592160	−	0.0201384i
$211$	13.0672	+	1.65077i	0.899584	+	0.113644i	0.561505	−	0.827474i	$-0.310223\pi$
$211$	13.0672	+	1.65077i	0.899584	+	0.113644i	0.338080	+	0.941118i	$0.390223\pi$
$212$	0.846392	−	4.43694i	0.0581304	−	0.304730i
$213$	1.16252	−	0.146861i	0.0796548	−	0.0100627i
$214$	5.01669	−	2.75795i	0.342934	−	0.188530i
$215$	6.67609	−	2.42801i	0.455306	−	0.165589i
$216$	−0.728969	+	0.684547i	−0.0496000	+	0.0465775i
$217$	−0.0274967	+	0.00705994i	−0.00186660	+	0.000479260i
$218$	10.6966	+	7.77155i	0.724467	+	0.526356i
$219$	−0.479315	+	7.61850i	−0.0323891	+	0.514810i
$220$	−7.42291	+	5.07986i	−0.500453	+	0.342484i
$221$	−7.36803	+	2.91721i	−0.495627	+	0.196233i
$222$	8.78198	−	3.47703i	0.589408	−	0.233363i
$223$	17.1594	+	2.16774i	1.14908	+	0.145162i	0.676718	−	0.736243i	$-0.263402\pi$
$223$	17.1594	+	2.16774i	1.14908	+	0.145162i	0.472361	+	0.881405i	$0.343402\pi$
$224$	−0.0420378	+	0.129379i	−0.00280877	+	0.00864449i
$225$	0.594495	−	4.96453i	0.0396330	−	0.330969i
$226$	−1.56166	−	4.80629i	−0.103880	−	0.319710i
$227$	1.09862	+	5.75918i	0.0729182	+	0.382250i	0.999973	+	0.00732503i	$0.00233165\pi$
$227$	1.09862	+	5.75918i	0.0729182	+	0.382250i	−0.927055	+	0.374925i	$0.877668\pi$
$228$	−0.0403516	−	0.641371i	−0.00267235	−	0.0424758i
$229$	27.9358	+	7.17270i	1.84605	+	0.473985i	0.998399	−	0.0565686i	$-0.0180159\pi$
$229$	27.9358	+	7.17270i	1.84605	+	0.473985i	0.847651	+	0.530554i	$0.178016\pi$
$230$	−3.77582	+	3.35065i	−0.248970	+	0.220935i
$231$	−0.293213	−	0.462030i	−0.0192920	−	0.0303993i
$232$	−0.00632333	+	0.0194612i	−0.000415147	+	0.00127769i
$233$	0.852800	−	13.5549i	0.0558688	−	0.888009i	−0.865887	−	0.500239i	$-0.833245\pi$
$233$	0.852800	−	13.5549i	0.0558688	−	0.888009i	0.921756	−	0.387770i	$-0.126755\pi$
$234$	−1.45368	+	0.183642i	−0.0950299	+	0.0120051i
$235$	3.73368	+	8.55187i	0.243559	+	0.557862i
$236$	1.49665	−	3.18055i	0.0974237	−	0.207036i
$237$	−1.33693	−	2.84112i	−0.0868428	−	0.184550i
$238$	−0.644733	−	0.354445i	−0.0417918	−	0.0229752i
$239$	−4.86085	−	4.56464i	−0.314422	−	0.295262i	0.511227	−	0.859446i	$-0.329191\pi$
$239$	−4.86085	−	4.56464i	−0.314422	−	0.295262i	−0.825650	+	0.564183i	$0.809191\pi$
$240$	−1.47329	+	1.68208i	−0.0951007	+	0.108578i
$241$	−13.0500	−	27.7326i	−0.840621	−	1.78641i	−0.564865	−	0.825184i	$-0.691072\pi$
$241$	−13.0500	−	27.7326i	−0.840621	−	1.78641i	−0.275757	−	0.961227i	$-0.588928\pi$
$242$	−3.30243	+	3.99196i	−0.212288	+	0.256613i
$243$	−0.309017	−	0.951057i	−0.0198234	−	0.0610103i
$244$	1.62060	−	0.416098i	0.103748	−	0.0266380i
$245$	−14.6710	+	5.33565i	−0.937293	+	0.340882i
$246$	0.312286	+	4.96364i	0.0199106	+	0.316470i
$247$	0.504543	−	0.795032i	0.0321033	−	0.0505867i
$248$	0.152123	+	0.142853i	0.00965982	+	0.00907117i
$249$	−12.7955			−0.810883
$250$	0.242502	−	11.1777i	0.0153372	−	0.706940i
$251$	26.3102			1.66068			0.830342	−	0.557255i	$-0.188145\pi$
$251$	26.3102			1.66068			0.830342	+	0.557255i	$0.188145\pi$
$252$	−0.0991668	−	0.0931238i	−0.00624692	−	0.00586625i
$253$	−4.86600	+	7.66758i	−0.305923	+	0.482057i
$254$	−0.0324407	−	0.515630i	−0.00203551	−	0.0323535i
$255$	−7.44312	−	9.53165i	−0.466106	−	0.596895i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	−1.07800	−	3.31776i	−0.0672440	−	0.206956i	0.911788	−	0.410660i	$-0.134702\pi$
$257$	−1.07800	−	3.31776i	−0.0672440	−	0.206956i	−0.979032	+	0.203705i	$0.934702\pi$
$258$	2.02507	−	2.44789i	0.126075	−	0.152399i
$259$	0.547086	+	1.16262i	0.0339943	+	0.0722415i
$260$	−3.19512	+	0.725076i	−0.198153	+	0.0449673i
$261$	−0.0149167	−	0.0140077i	−0.000923320	−	0.000867055i
$262$	−1.47870	−	0.812920i	−0.0913541	−	0.0502223i
$263$	9.44185	+	20.0650i	0.582210	+	1.23726i	0.951415	+	0.307911i	$0.0996298\pi$
$263$	9.44185	+	20.0650i	0.582210	+	1.23726i	−0.369206	+	0.929348i	$0.620370\pi$
$264$	−1.71272	+	3.63971i	−0.105411	+	0.224009i
$265$	8.71029	+	5.11322i	0.535069	+	0.314102i
$266$	0.0867334	−	0.0109570i	0.00531796	−	0.000671815i
$267$	0.134958	−	2.14510i	0.00825930	−	0.131278i
$268$	3.67767	−	11.3187i	0.224650	−	0.691400i
$269$	−12.6481	−	19.9303i	−0.771171	−	1.21517i	−0.971870	−	0.235518i	$-0.924321\pi$
$269$	−12.6481	−	19.9303i	−0.771171	−	1.21517i	0.200699	−	0.979653i	$-0.435679\pi$
$270$	−0.894697	−	2.04927i	−0.0544495	−	0.124715i
$271$	18.7960	+	4.82600i	1.14178	+	0.293159i	0.771790	−	0.635878i	$-0.219362\pi$
$271$	18.7960	+	4.82600i	1.14178	+	0.293159i	0.369988	+	0.929037i	$0.379362\pi$
$272$	0.339594	+	5.39770i	0.0205909	+	0.327283i
$273$	−0.0373499	−	0.195795i	−0.00226052	−	0.0118501i
$274$	−5.70781	−	17.5668i	−0.344822	−	1.06125i
$275$	−5.12802	−	19.4480i	−0.309231	−	1.17276i
$276$	−0.697635	+	2.14710i	−0.0419927	+	0.129240i
$277$	−7.81919	−	0.987794i	−0.469810	−	0.0593508i	−0.113135	−	0.993580i	$-0.536089\pi$
$277$	−7.81919	−	0.987794i	−0.469810	−	0.0593508i	−0.356674	+	0.934229i	$0.616089\pi$
$278$	−14.9694	+	5.92680i	−0.897804	+	0.355466i
$279$	−0.194028	+	0.0768211i	−0.0116162	+	0.00459916i
$280$	−0.240959	−	0.185659i	−0.0144000	−	0.0110952i
$281$	−0.367420	+	5.83997i	−0.0219184	+	0.348383i	0.971749	+	0.236018i	$0.0758426\pi$
$281$	−0.367420	+	5.83997i	−0.0219184	+	0.348383i	−0.993667	+	0.112365i	$0.964157\pi$
$282$	3.37613	+	2.45290i	0.201046	+	0.146068i
$283$	−13.1352	+	3.37255i	−0.780808	+	0.200477i	−0.617998	−	0.786180i	$-0.712056\pi$
$283$	−13.1352	+	3.37255i	−0.780808	+	0.200477i	−0.162810	+	0.986657i	$0.552056\pi$
$284$	0.854179	−	0.802127i	0.0506862	−	0.0475975i
$285$	1.38122	+	0.396431i	0.0818164	+	0.0234825i
$286$	−5.16492	+	2.83944i	−0.305408	+	0.167900i
$287$	−0.671239	+	0.0847972i	−0.0396220	+	0.00500542i
$288$	−0.187381	+	0.982287i	−0.0110415	+	0.0578818i
$289$	−12.1539	−	1.53539i	−0.714933	−	0.0903171i
$290$	−0.0362451	−	0.0279269i	−0.00212838	−	0.00163992i
$291$	3.60360	−	18.8908i	0.211247	−	1.10740i
$292$	4.09027	+	6.44523i	0.239365	+	0.377178i
$293$	−8.17360	+	5.93847i	−0.477507	+	0.346929i	−0.800360	−	0.599520i	$-0.795358\pi$
$293$	−8.17360	+	5.93847i	−0.477507	+	0.346929i	0.322853	+	0.946449i	$0.395358\pi$
$294$	−4.45017	+	5.37933i	−0.259539	+	0.313729i
$295$	5.57583	+	5.53980i	0.324637	+	0.322540i
$296$	5.06102	−	7.97489i	0.294166	−	0.463531i
$297$	−2.56407	−	3.09943i	−0.148782	−	0.179847i
$298$	6.22252	−	13.2235i	0.360461	−	0.766019i
$299$	−2.67615	+	1.94434i	−0.154766	+	0.112444i
$300$	−2.43712	−	4.36583i	−0.140707	−	0.252061i
$301$	0.349645	+	0.254032i	0.0201532	+	0.0146421i
$302$	2.43440	−	1.33833i	0.140084	−	0.0770120i
$303$	0.143275	+	0.0367867i	0.00823093	+	0.00211334i
$304$	−0.409634	−	0.495162i	−0.0234941	−	0.0283995i
$305$	−0.340013	+	3.72582i	−0.0194691	+	0.213340i
$306$	−5.02857	−	1.99095i	−0.287464	−	0.113815i
$307$	18.3080			1.04489			0.522446	−	0.852672i	$-0.325020\pi$
$307$	18.3080			1.04489			0.522446	+	0.852672i	$0.325020\pi$
$308$	−0.508788	−	0.201444i	−0.0289909	−	0.0114783i
$309$	−15.8779	−	8.72894i	−0.903261	−	0.496572i
$310$	−0.415080	+	0.213191i	−0.0235749	+	0.0121084i
$311$	−3.25588	−	17.0679i	−0.184624	−	0.967833i	−0.947130	−	0.320851i	$-0.896031\pi$
$311$	−3.25588	−	17.0679i	−0.184624	−	0.967833i	0.762506	−	0.646982i	$-0.223969\pi$
$312$	−1.06811	+	1.00302i	−0.0604697	+	0.0567848i
$313$	17.2437	−	16.1929i	0.974673	−	0.915279i	−0.0217519	−	0.999763i	$-0.506924\pi$
$313$	17.2437	−	16.1929i	0.974673	−	0.915279i	0.996425	+	0.0844847i	$0.0269244\pi$
$314$	−0.852461	−	4.46876i	−0.0481071	−	0.252186i
$315$	0.270585	−	0.138976i	0.0152457	−	0.00783043i
$316$	−2.75156	−	1.51269i	−0.154788	−	0.0850952i
$317$	8.90176	+	3.52446i	0.499973	+	0.197953i	0.604556	−	0.796563i	$-0.293351\pi$
$317$	8.90176	+	3.52446i	0.499973	+	0.197953i	−0.104583	+	0.994516i	$0.533351\pi$
$318$	4.51695			0.253298
$319$	−0.0765321	−	0.0303012i	−0.00428497	−	0.00169654i
$320$	−0.203216	+	2.22681i	−0.0113601	+	0.124483i
$321$	3.64913	+	4.41104i	0.203675	+	0.246200i
$322$	−0.297468	−	0.0763768i	−0.0165772	−	0.00425631i
$323$	3.04572	−	1.67440i	0.169468	−	0.0931659i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	0.871073	−	7.27419i	0.0483184	−	0.403500i
$326$	11.1961	−	8.13442i	0.620093	−	0.450524i
$327$	−5.62955	+	11.9634i	−0.311315	+	0.661577i
$328$	3.17020	+	3.83211i	0.175045	+	0.211593i
$329$	−0.304189	+	0.479325i	−0.0167705	+	0.0264260i
$330$	−6.38079	−	6.33956i	−0.351251	−	0.348981i
$331$	−6.02252	+	7.27998i	−0.331028	+	0.400144i	−0.909598	−	0.415489i	$-0.863611\pi$
$331$	−6.02252	+	7.27998i	−0.331028	+	0.400144i	0.578571	+	0.815632i	$0.303611\pi$
$332$	−10.3518	+	7.52101i	−0.568128	+	0.412769i
$333$	5.06102	+	7.97489i	0.277342	+	0.437021i
$334$	−1.39672	+	7.32188i	−0.0764253	+	0.400635i
$335$	21.0803	+	16.2424i	1.15174	+	0.887415i
$336$	−0.134964	−	0.0170500i	−0.00736291	−	0.000930152i
$337$	2.95369	−	15.4838i	0.160898	−	0.843457i	−0.806700	−	0.590961i	$-0.798749\pi$
$337$	2.95369	−	15.4838i	0.160898	−	0.843457i	0.967598	−	0.252496i	$-0.0812513\pi$
$338$	10.7675	−	1.36025i	0.585676	−	0.0739880i
$339$	4.42853	−	2.43461i	0.240525	−	0.132230i
$340$	−11.6242	−	3.33631i	−0.630409	−	0.180937i
$341$	−0.611922	+	0.574633i	−0.0331374	+	0.0311181i
$342$	0.622449	−	0.159818i	0.0336582	−	0.00864196i
$343$	−1.53875	−	1.11797i	−0.0830848	−	0.0603646i
$344$	0.199483	−	3.17069i	0.0107554	−	0.170952i
$345$	−3.99882	−	3.08109i	−0.215289	−	0.165880i
$346$	−13.4313	+	5.31782i	−0.722070	+	0.285888i
$347$	30.4611	−	12.0604i	1.63524	−	0.647436i	0.642340	−	0.766420i	$-0.277964\pi$
$347$	30.4611	−	12.0604i	1.63524	−	0.647436i	0.992896	+	0.118984i	$0.0379636\pi$
$348$	−0.0203014	−	0.00256466i	−0.00108827	−	0.000137480i
$349$	−1.59180	+	4.89904i	−0.0852068	+	0.262240i	−0.984578	−	0.174946i	$-0.944025\pi$
$349$	−1.59180	+	4.89904i	−0.0852068	+	0.262240i	0.899371	+	0.437186i	$0.144025\pi$
$350$	0.571925	−	0.368177i	0.0305707	−	0.0196799i
$351$	−0.452782	−	1.39352i	−0.0241677	−	0.0743805i
$352$	0.753751	+	3.95130i	0.0401750	+	0.210605i
$353$	0.635886	+	10.1071i	0.0338448	+	0.537948i	0.978021	+	0.208507i	$0.0668603\pi$
$353$	0.635886	+	10.1071i	0.0338448	+	0.537948i	−0.944176	+	0.329441i	$0.893140\pi$
$354$	3.40466	+	0.874167i	0.180955	+	0.0464615i
$355$	1.04837	+	2.40126i	0.0556419	+	0.127446i
$356$	−1.15167	−	1.81475i	−0.0610386	−	0.0961814i
$357$	0.227356	−	0.699729i	0.0120329	−	0.0370336i
$358$	−0.512031	+	8.13850i	−0.0270617	+	0.430133i
$359$	18.5598	−	2.34464i	0.979547	−	0.123746i	0.380777	−	0.924667i	$-0.375656\pi$
$359$	18.5598	−	2.34464i	0.979547	−	0.123746i	0.598770	+	0.800921i	$0.295656\pi$
$360$	−1.92836	−	1.13201i	−0.101633	−	0.0596620i
$361$	7.91397	−	16.8180i	0.416525	−	0.885160i
$362$	4.18250	+	8.88827i	0.219828	+	0.467157i
$363$	−4.54006	−	2.49592i	−0.238291	−	0.131002i
$364$	−0.145302	−	0.136448i	−0.00761591	−	0.00715182i
$365$	−16.6459	+	3.77750i	−0.871287	+	0.197723i
$366$	0.712398	+	1.51392i	0.0372376	+	0.0791340i
$367$	−6.88007	+	8.31658i	−0.359137	+	0.434122i	−0.918876	−	0.394547i	$-0.870901\pi$
$367$	−6.88007	+	8.31658i	−0.359137	+	0.434122i	0.559739	+	0.828669i	$0.310901\pi$
$368$	0.697635	+	2.14710i	0.0363667	+	0.111925i
$369$	−4.81720	+	1.23685i	−0.250773	+	0.0643877i
$370$	12.9988	+	16.6462i	0.675774	+	0.865395i
$371$	0.0385830	+	0.613260i	0.00200313	+	0.0318389i
$372$	−0.111818	+	0.176196i	−0.00579747	+	0.00913536i
$373$	−0.969393	−	0.910321i	−0.0501933	−	0.0471346i	0.659045	−	0.752104i	$-0.270961\pi$
$373$	−0.969393	−	0.910321i	−0.0501933	−	0.0471346i	−0.709238	+	0.704969i	$0.750961\pi$
$374$	−21.7554			−1.12495
$375$	11.0252	−	1.85629i	0.569337	−	0.0958582i
$376$	4.17312			0.215212
$377$	−0.0218564	−	0.0205245i	−0.00112566	−	0.00105707i
$378$	0.0728923	−	0.114860i	0.00374918	−	0.00590776i
$379$	−1.25187	−	19.8979i	−0.0643044	−	1.02209i	−0.889410	−	0.457110i	$-0.848884\pi$
$379$	−1.25187	−	19.8979i	−0.0643044	−	1.02209i	0.825106	−	0.564978i	$-0.191116\pi$
$380$	1.35045	−	0.491141i	0.0692764	−	0.0251950i
$381$	0.500418	−	0.128485i	0.0256372	−	0.00658251i
$382$	−0.503889	−	1.55081i	−0.0257812	−	0.0793463i
$383$	4.16366	−	5.03300i	0.212753	−	0.257174i	−0.653331	−	0.757072i	$-0.726629\pi$
$383$	4.16366	−	5.03300i	0.212753	−	0.257174i	0.866084	+	0.499898i	$0.166629\pi$
$384$	0.425779	+	0.904827i	0.0217280	+	0.0461743i
$385$	0.806210	−	0.920463i	0.0410883	−	0.0469111i
$386$	6.94792	+	6.52453i	0.353640	+	0.332090i
$387$	2.78399	+	1.53051i	0.141518	+	0.0778004i
$388$	−8.18833	−	17.4011i	−0.415699	−	0.883406i
$389$	−12.0786	+	25.6683i	−0.612408	+	1.30143i	0.322508	+	0.946567i	$0.395474\pi$
$389$	−12.0786	+	25.6683i	−0.612408	+	1.30143i	−0.934917	+	0.354867i	$0.884526\pi$
$390$	−1.31094	−	3.00266i	−0.0663820	−	0.152046i
$391$	−12.1136	+	1.53031i	−0.612613	+	0.0773910i
$392$	−0.438372	+	6.96772i	−0.0221411	+	0.351923i
$393$	0.521441	−	1.60483i	0.0263032	−	0.0809529i
$394$	−8.21772	−	12.9490i	−0.414003	−	0.652364i
$395$	5.25157	−	4.66022i	0.264235	−	0.234481i
$396$	−3.89617	−	1.00037i	−0.195790	−	0.0502704i
$397$	−2.01956	−	32.0999i	−0.101359	−	1.61105i	−0.639905	−	0.768454i	$-0.721026\pi$
$397$	−2.01956	−	32.0999i	−0.101359	−	1.61105i	0.538546	−	0.842596i	$-0.318974\pi$
$398$	1.20232	+	6.30277i	0.0602667	+	0.315929i
$399$	0.0270151	+	0.0831440i	0.00135245	+	0.00416240i
$400$	−4.53784	−	2.09952i	−0.226892	−	0.104976i
$401$	5.65002	−	17.3890i	0.282149	−	0.868364i	−0.705090	−	0.709118i	$-0.749094\pi$
$401$	5.65002	−	17.3890i	0.282149	−	0.868364i	0.987239	−	0.159247i	$-0.0509065\pi$
$402$	11.8074	+	1.49162i	0.588897	+	0.0743950i
$403$	−0.284296	+	0.112561i	−0.0141618	+	0.00560705i
$404$	0.137534	−	0.0544538i	0.00684260	−	0.00270918i
$405$	1.84532	−	1.26284i	0.0916949	−	0.0627513i
$406$	0.000174789	−	0.00277820i	8.67465e−6	−	0.000137880i
$407$	30.7378	+	22.3323i	1.52362	+	1.10697i
$408$	−5.23846	+	1.34501i	−0.259342	+	0.0665878i
$409$	22.0794	−	20.7339i	1.09176	−	1.02523i	0.0921901	−	0.995741i	$-0.470613\pi$
$409$	22.0794	−	20.7339i	1.09176	−	1.02523i	0.999565	−	0.0294851i	$-0.00938676\pi$
$410$	−10.4512	+	3.80099i	−0.516150	+	0.187718i
$411$	16.1862	−	8.89841i	0.798404	−	0.438926i
$412$	−17.9762	+	2.27092i	−0.885625	+	0.111880i
$413$	−0.0896025	+	0.469713i	−0.00440905	+	0.0231130i
$414$	−2.23979	−	0.282952i	−0.110080	−	0.0139063i
$415$	−8.07141	−	27.4496i	−0.396210	−	1.34745i
$416$	−0.274557	+	1.43928i	−0.0134613	+	0.0705664i
$417$	−8.62680	−	13.5937i	−0.422456	−	0.665685i
$418$	2.09135	−	1.51945i	0.102291	−	0.0743189i
$419$	0.174012	−	0.210344i	0.00850103	−	0.0102760i	−0.766246	−	0.642548i	$-0.777877\pi$
$419$	0.174012	−	0.210344i	0.00850103	−	0.0102760i	0.774747	+	0.632272i	$0.217877\pi$
$420$	0.137219	−	0.271480i	0.00669562	−	0.0132469i
$421$	−16.4659	+	25.9461i	−0.802498	+	1.26453i	0.158329	+	0.987386i	$0.449389\pi$
$421$	−16.4659	+	25.9461i	−0.802498	+	1.26453i	−0.960827	+	0.277148i	$0.910611\pi$
$422$	8.39556	+	10.1485i	0.408689	+	0.494021i
$423$	−1.77683	+	3.77596i	−0.0863924	+	0.183593i
$424$	3.65429	−	2.65500i	0.177468	−	0.128938i
$425$	15.7526	−	21.9799i	0.764115	−	1.06618i
$426$	0.947976	+	0.688745i	0.0459296	+	0.0333698i
$427$	−0.199458	+	0.109653i	−0.00965245	+	0.00530648i
$428$	5.54496	+	1.42370i	0.268026	+	0.0688173i
$429$	−3.75696	−	4.54138i	−0.181388	−	0.219260i
$430$	6.52875	+	2.80015i	0.314844	+	0.135035i
$431$	−8.59768	−	3.40406i	−0.414136	−	0.163968i	0.151811	−	0.988409i	$-0.451489\pi$
$431$	−8.59768	−	3.40406i	−0.414136	−	0.163968i	−0.565947	+	0.824442i	$0.691489\pi$
$432$	−1.00000			−0.0481125
$433$	1.19787	+	0.474270i	0.0575660	+	0.0227920i	0.396731	−	0.917935i	$-0.370145\pi$
$433$	1.19787	+	0.474270i	0.0575660	+	0.0227920i	−0.339165	+	0.940727i	$0.610145\pi$
$434$	−0.0248771	−	0.0136763i	−0.00119414	−	0.000656483i
$435$	0.0206406	−	0.0408361i	0.000989639	−	0.00195794i
$436$	2.47751	+	12.9876i	0.118651	+	0.621991i
$437$	1.05760	−	0.993154i	0.0505919	−	0.0475090i
$438$	−5.56462	+	5.22553i	−0.265888	+	0.249685i
$439$	1.63949	+	8.59449i	0.0782485	+	0.410193i	0.999761	+	0.0218451i	$0.00695406\pi$
$439$	1.63949	+	8.59449i	0.0782485	+	0.410193i	−0.921513	+	0.388348i	$0.873046\pi$
$440$	−8.88847	−	1.37828i	−0.423741	−	0.0657068i
$441$	−6.11793	−	3.36336i	−0.291330	−	0.160160i
$442$	−7.36803	−	2.91721i	−0.350461	−	0.138757i
$443$	−17.6748			−0.839753			−0.419876	−	0.907581i	$-0.637927\pi$
$443$	−17.6748			−0.839753			−0.419876	+	0.907581i	$0.637927\pi$
$444$	8.78198	+	3.47703i	0.416774	+	0.165013i
$445$	4.68690	−	1.06361i	0.222180	−	0.0504199i
$446$	11.0247	+	13.3266i	0.522037	+	0.631034i
$447$	14.1553	+	3.63446i	0.669523	+	0.171904i
$448$	−0.119210	+	0.0655364i	−0.00563215	+	0.00309630i
$449$	−1.60400	−	1.16538i	−0.0756976	−	0.0549975i	0.549293	−	0.835630i	$-0.314897\pi$
$449$	−1.60400	−	1.16538i	−0.0756976	−	0.0549975i	−0.624990	+	0.780632i	$0.714897\pi$
$450$	3.83182	−	3.21203i	0.180634	−	0.151416i
$451$	−16.1852	+	11.7592i	−0.762129	+	0.553719i
$452$	2.15173	−	4.57266i	0.101209	−	0.215080i
$453$	1.77078	+	2.14051i	0.0831986	+	0.100570i
$454$	−3.14157	+	4.95032i	−0.147441	+	0.232330i
$455$	0.396469	−	0.203633i	0.0185868	−	0.00954644i
$456$	0.409634	−	0.495162i	0.0191828	−	0.0231881i
$457$	−16.0356	+	11.6505i	−0.750112	+	0.544988i	−0.895862	−	0.444333i	$-0.853441\pi$
$457$	−16.0356	+	11.6505i	−0.750112	+	0.544988i	0.145750	+	0.989321i	$0.453441\pi$
$458$	15.4543	+	24.3520i	0.722131	+	1.13790i
$459$	1.01343	−	5.31257i	0.0473027	−	0.247970i
$460$	−5.04613	−	0.142210i	−0.235277	−	0.00663058i
$461$	−9.15208	−	1.15618i	−0.426255	−	0.0538485i	−0.0907202	−	0.995876i	$-0.528917\pi$
$461$	−9.15208	−	1.15618i	−0.426255	−	0.0538485i	−0.335534	+	0.942028i	$0.608917\pi$
$462$	0.102538	−	0.537523i	0.00477050	−	0.0250078i
$463$	−38.5041	+	4.86420i	−1.78944	+	0.226058i	−0.948874	−	0.315656i	$-0.897775\pi$
$463$	−38.5041	+	4.86420i	−1.78944	+	0.226058i	−0.840562	+	0.541715i	$0.817775\pi$
$464$	−0.0179316	+	0.00985799i	−0.000832455	+	0.000457646i
$465$	−0.287193	−	0.367780i	−0.0133183	−	0.0170554i
$466$	9.90061	−	9.29729i	0.458637	−	0.430689i
$467$	22.2038	−	5.70098i	1.02747	−	0.263810i	0.302909	−	0.953019i	$-0.402042\pi$
$467$	22.2038	−	5.70098i	1.02747	−	0.263810i	0.724562	+	0.689210i	$0.242042\pi$
$468$	−1.18540	−	0.861242i	−0.0547950	−	0.0398109i
$469$	−0.101658	+	1.61581i	−0.00469414	+	0.0746111i
$470$	−3.13242	+	8.78993i	−0.144488	+	0.405449i
$471$	4.22987	−	1.67472i	0.194902	−	0.0771671i
$472$	3.26825	−	1.29399i	0.150433	−	0.0595607i
$473$	12.6787	+	1.60169i	0.582968	+	0.0736460i
$474$	0.970300	−	2.98628i	0.0445673	−	0.137164i
$475$	0.0208302	+	3.21313i	0.000955757	+	0.147428i
$476$	−0.227356	−	0.699729i	−0.0104208	−	0.0320720i
$477$	0.846392	+	4.43694i	0.0387536	+	0.203154i
$478$	−0.418695	−	6.65496i	−0.0191507	−	0.304391i
$479$	28.3977	+	7.29128i	1.29752	+	0.333147i	0.833423	−	0.552636i	$-0.186378\pi$
$479$	28.3977	+	7.29128i	1.29752	+	0.333147i	0.464100	+	0.885783i	$0.346378\pi$
$480$	−2.22545	+	0.217647i	−0.101577	+	0.00993419i
$481$	7.41557	+	11.6851i	0.338121	+	0.532793i
$482$	9.47124	−	29.1495i	0.431403	−	1.32772i
$483$	0.0192840	−	0.306511i	0.000877453	−	0.0139467i
$484$	−5.14005	+	0.649340i	−0.233639	+	0.0295154i
$485$	42.7985	−	4.18566i	1.94338	−	0.190061i
$486$	0.425779	−	0.904827i	0.0193137	−	0.0410438i
$487$	−17.9275	−	38.0978i	−0.812371	−	1.72638i	−0.677513	−	0.735511i	$-0.736942\pi$
$487$	−17.9275	−	38.0978i	−0.812371	−	1.72638i	−0.134858	−	0.990865i	$-0.543058\pi$
$488$	1.46620	+	0.806052i	0.0663719	+	0.0364882i
$489$	10.0883	+	9.47352i	0.456207	+	0.428407i
$490$	−14.3472	−	6.15344i	−0.648139	−	0.277984i
$491$	−11.1738	−	23.7455i	−0.504266	−	1.07162i	−0.981256	−	0.192711i	$-0.938272\pi$
$491$	−11.1738	−	23.7455i	−0.504266	−	1.07162i	0.476990	−	0.878909i	$-0.341728\pi$
$492$	−3.17020	+	3.83211i	−0.142923	+	0.172765i
$493$	−0.0341989	−	0.105253i	−0.00154024	−	0.00474038i
$494$	0.912033	−	0.234170i	0.0410343	−	0.0105358i
$495$	5.03163	−	7.45569i	0.226155	−	0.335108i
$496$	0.0131033	+	0.208271i	0.000588355	+	0.00935163i
$497$	−0.0854125	+	0.134589i	−0.00383128	+	0.00603713i
$498$	−9.32753	−	8.75913i	−0.417976	−	0.392506i
$499$	−28.0255			−1.25459			−0.627297	−	0.778780i	$-0.715839\pi$
$499$	−28.0255			−1.25459			−0.627297	+	0.778780i	$0.715839\pi$
$500$	7.82845	−	7.98220i	0.350099	−	0.356975i
$501$	−7.45391			−0.333016
$502$	19.1793	+	18.0106i	0.856014	+	0.803850i
$503$	−16.2708	+	25.6387i	−0.725479	+	1.14317i	0.258694	+	0.965959i	$0.416708\pi$
$503$	−16.2708	+	25.6387i	−0.725479	+	1.14317i	−0.984173	+	0.177212i	$0.943292\pi$
$504$	−0.00854184	−	0.135769i	−0.000380484	−	0.00604762i
$505$	0.0114611	+	0.330565i	0.000510012	+	0.0147100i
$506$	−8.79598	+	2.25842i	−0.391029	+	0.100399i
$507$	3.35379	+	10.3219i	0.148947	+	0.458412i
$508$	0.329324	−	0.398085i	0.0146114	−	0.0176622i
$509$	0.365500	+	0.776727i	0.0162005	+	0.0344278i	0.912764	−	0.408488i	$-0.133944\pi$
$509$	0.365500	+	0.776727i	0.0162005	+	0.0344278i	−0.896563	+	0.442916i	$0.853944\pi$
$510$	1.09907	−	12.0434i	0.0486674	−	0.533292i
$511$	−0.756995	−	0.710866i	−0.0334875	−	0.0314469i
$512$	0.876307	+	0.481754i	0.0387276	+	0.0212907i
$513$	0.273622	+	0.581477i	0.0120807	+	0.0256728i
$514$	1.48533	−	3.15648i	0.0655150	−	0.139227i
$515$	8.70998	−	39.5682i	0.383807	−	1.74358i
$516$	3.15191	−	0.398179i	0.138755	−	0.0175289i
$517$	−1.05404	+	16.7535i	−0.0463566	+	0.736817i
$518$	−0.397057	+	1.22202i	−0.0174457	+	0.0536924i
$519$	−7.74040	−	12.1969i	−0.339766	−	0.535385i
$520$	−2.82549	−	1.65865i	−0.123906	−	0.0727367i
$521$	20.3329	+	5.22061i	0.890803	+	0.228719i	0.666237	−	0.745740i	$-0.267904\pi$
$521$	20.3329	+	5.22061i	0.890803	+	0.228719i	0.224565	+	0.974459i	$0.427904\pi$
$522$	−0.00128487	−	0.0204223i	−5.62370e−5	−	0.000893862i
$523$	−7.97657	−	41.8146i	−0.348791	−	1.82843i	−0.533704	−	0.845671i	$-0.679200\pi$
$523$	−7.97657	−	41.8146i	−0.348791	−	1.82843i	0.184913	−	0.982755i	$-0.440800\pi$
$524$	−0.521441	−	1.60483i	−0.0227792	−	0.0701073i
$525$	0.468824	+	0.492805i	0.0204611	+	0.0215078i
$526$	−6.85260	+	21.0901i	−0.298787	+	0.919573i
$527$	−1.11973	−	0.141455i	−0.0487763	−	0.00616188i
$528$	−3.74007	+	1.48080i	−0.162766	+	0.0644435i
$529$	16.6460	−	6.59063i	0.723741	−	0.286549i
$530$	2.84929	+	9.68998i	0.123765	+	0.420906i
$531$	−0.220714	+	3.50815i	−0.00957818	+	0.152241i
$532$	0.0707265	+	0.0513858i	0.00306638	+	0.00222786i
$533$	−7.05832	+	1.81227i	−0.305730	+	0.0784980i
$534$	1.56680	−	1.47132i	0.0678021	−	0.0636704i
$535$	−7.16091	+	10.6108i	−0.309593	+	0.458744i
$536$	10.4291	−	5.73345i	0.450468	−	0.247647i
$537$	−8.09029	+	1.02204i	−0.349122	+	0.0441043i
$538$	4.42312	−	23.1868i	0.190694	−	0.999654i
$539$	−27.8620	−	3.51978i	−1.20010	−	0.151608i
$540$	0.750618	−	2.10632i	0.0323014	−	0.0906415i
$541$	−0.261632	+	1.37152i	−0.0112484	+	0.0589664i	−0.987469	−	0.157814i	$-0.949555\pi$
$541$	−0.261632	+	1.37152i	−0.0112484	+	0.0589664i	0.976220	+	0.216780i	$0.0695555\pi$
$542$	10.3981	+	16.3848i	0.446636	+	0.703786i
$543$	−7.94712	+	5.77392i	−0.341043	+	0.247783i
$544$	−3.44742	+	4.16722i	−0.147807	+	0.178668i
$545$	−29.2156	−	4.53027i	−1.25146	−	0.194055i
$546$	0.106804	−	0.168296i	0.00457080	−	0.00720242i
$547$	−10.8600	−	13.1275i	−0.464341	−	0.561292i	0.485415	−	0.874284i	$-0.338669\pi$
$547$	−10.8600	−	13.1275i	−0.464341	−	0.561292i	−0.949756	+	0.312992i	$0.898669\pi$
$548$	7.86452	−	16.7129i	0.335956	−	0.713942i
$549$	−1.35362	+	0.983460i	−0.0577709	+	0.0419730i
$550$	9.57493	−	17.6874i	0.408276	−	0.754192i
$551$	0.0106387	+	0.00772946i	0.000453224	+	0.000329286i
$552$	−1.97835	+	1.08760i	−0.0842040	+	0.0462915i
$553$	0.413731	+	0.106228i	0.0175936	+	0.00451727i
$554$	−5.02376	−	6.07268i	−0.213439	−	0.258003i
$555$	−13.9156	+	15.8877i	−0.590686	+	0.674396i
$556$	−14.9694	−	5.92680i	−0.634843	−	0.251352i
$557$	27.6441			1.17132			0.585659	−	0.810557i	$-0.300836\pi$
$557$	27.6441			1.17132			0.585659	+	0.810557i	$0.300836\pi$
$558$	−0.194028	−	0.0768211i	−0.00821386	−	0.00325210i
$559$	4.07920	+	2.24256i	0.172532	+	0.0948501i
$560$	−0.0485591	−	0.300287i	−0.00205200	−	0.0126895i
$561$	−4.07656	−	21.3701i	−0.172113	−	0.902246i
$562$	−4.26557	+	4.00564i	−0.179932	+	0.168968i
$563$	−19.1418	+	17.9754i	−0.806731	+	0.757571i	−0.973564	−	0.228414i	$-0.926646\pi$
$563$	−19.1418	+	17.9754i	−0.806731	+	0.757571i	0.166833	+	0.985985i	$0.446646\pi$
$564$	0.781966	+	4.09921i	0.0329267	+	0.172608i
$565$	8.01635	+	7.96455i	0.337250	+	0.335071i
$566$	−11.8838	−	6.53319i	−0.499515	−	0.274611i
$567$	0.126484	+	0.0500786i	0.00531183	+	0.00210310i
$568$	1.17176			0.0491661
$569$	4.79850	+	1.89986i	0.201164	+	0.0796463i	0.466546	−	0.884497i	$-0.345498\pi$
$569$	4.79850	+	1.89986i	0.201164	+	0.0796463i	−0.265382	+	0.964143i	$0.585498\pi$
$570$	0.735490	+	1.23450i	0.0308063	+	0.0517073i
$571$	9.77124	+	11.8114i	0.408914	+	0.494292i	0.934258	−	0.356598i	$-0.116063\pi$
$571$	9.77124	+	11.8114i	0.408914	+	0.494292i	−0.525344	+	0.850890i	$0.676063\pi$
$572$	−5.70880	−	1.46577i	−0.238697	−	0.0612869i
$573$	1.42892	−	0.785556i	0.0596940	−	0.0328171i
$574$	−0.547360	−	0.397680i	−0.0228463	−	0.0165988i
$575$	4.08726	−	10.5220i	0.170450	−	0.438798i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	5.45363	−	11.5895i	0.227037	−	0.482479i	−0.758557	−	0.651607i	$-0.774095\pi$
$577$	5.45363	−	11.5895i	0.227037	−	0.482479i	0.985594	+	0.169128i	$0.0540951\pi$
$578$	−7.80874	−	9.43914i	−0.324801	−	0.392617i
$579$	−5.10705	+	8.04743i	−0.212242	+	0.334440i
$580$	−0.00730427	−	0.0451693i	−0.000303293	−	0.00187555i
$581$	1.10954	−	1.34120i	0.0460315	−	0.0556425i
$582$	15.5585	−	11.3039i	0.644922	−	0.468563i
$583$	9.73579	+	15.3411i	0.403215	+	0.635365i
$584$	−1.43039	+	7.49835i	−0.0591898	+	0.310284i
$585$	2.70383	−	1.85036i	0.111790	−	0.0765030i
$586$	−10.0235	−	1.26626i	−0.414065	−	0.0523086i
$587$	−1.97737	+	10.3657i	−0.0816146	+	0.427839i	0.917904	+	0.396803i	$0.129880\pi$
$587$	−1.97737	+	10.3657i	−0.0816146	+	0.427839i	−0.999518	+	0.0310355i	$0.990120\pi$
$588$	−6.92644	+	0.875013i	−0.285642	+	0.0360849i
$589$	0.117519	−	0.0646068i	0.00484230	−	0.00266208i
$590$	0.272351	+	7.85526i	0.0112125	+	0.323396i
$591$	11.1798	−	10.4986i	0.459877	−	0.431853i
$592$	9.14852	−	2.34894i	0.376002	−	0.0965408i
$593$	26.9142	+	19.5543i	1.10523	+	0.802998i	0.981906	−	0.189368i	$-0.0606439\pi$
$593$	26.9142	+	19.5543i	1.10523	+	0.802998i	0.123326	+	0.992366i	$0.460644\pi$
$594$	0.252578	−	4.01461i	0.0103634	−	0.164722i
$595$	1.64451	+	0.0463456i	0.0674183	+	0.00189998i
$596$	13.5882	−	5.37993i	0.556593	−	0.220371i
$597$	−5.96583	+	2.36204i	−0.244165	+	0.0966719i
$598$	−3.28182	−	0.414590i	−0.134203	−	0.0169538i
$599$	−5.32888	+	16.4006i	−0.217732	+	0.670110i	0.781216	+	0.624261i	$0.214600\pi$
$599$	−5.32888	+	16.4006i	−0.217732	+	0.670110i	−0.998948	+	0.0458500i	$0.985400\pi$
$600$	1.21203	−	4.85087i	0.0494808	−	0.198036i
$601$	−9.36628	−	28.8264i	−0.382058	−	1.17585i	−0.938592	−	0.345030i	$-0.887869\pi$
$601$	−9.36628	−	28.8264i	−0.382058	−	1.17585i	0.556533	−	0.830825i	$-0.312131\pi$
$602$	0.0809833	+	0.424530i	0.00330063	+	0.0173025i
$603$	0.747282	+	11.8777i	0.0304317	+	0.483698i
$604$	2.69075	+	0.690867i	0.109485	+	0.0281110i
$605$	2.49050	−	11.3140i	0.101253	−	0.459979i
$606$	0.0792606	+	0.124895i	0.00321974	+	0.00507350i
$607$	−2.83272	+	8.71821i	−0.114977	+	0.353861i	−0.991942	−	0.126692i	$-0.959564\pi$
$607$	−2.83272	+	8.71821i	−0.114977	+	0.353861i	0.876966	+	0.480553i	$0.159564\pi$
$608$	0.0403516	−	0.641371i	0.00163647	−	0.0260110i
$609$	0.00276174		0.000348889i	0.000111911		1.41377e-5i
$610$	−2.79836	+	2.48325i	−0.113302	+	0.100544i
$611$	−2.60347	+	5.53265i	−0.105325	+	0.223827i
$612$	−2.30277	−	4.89364i	−0.0930840	−	0.197814i
$613$	−32.0411	−	17.6148i	−1.29413	−	0.711454i	−0.322188	−	0.946676i	$-0.604418\pi$
$613$	−32.0411	−	17.6148i	−1.29413	−	0.711454i	−0.971942	+	0.235222i	$0.924418\pi$
$614$	13.3459	+	12.5327i	0.538599	+	0.505778i
$615$	−5.69203	−	9.55389i	−0.229525	−	0.385250i
$616$	−0.232993	−	0.495136i	−0.00938756	−	0.0199496i
$617$	7.38357	−	8.92520i	0.297251	−	0.359315i	−0.600650	−	0.799512i	$-0.705091\pi$
$617$	7.38357	−	8.92520i	0.297251	−	0.359315i	0.897901	+	0.440197i	$0.145091\pi$
$618$	−5.59911	−	17.2323i	−0.225229	−	0.693184i
$619$	23.6805	−	6.08012i	0.951800	−	0.244381i	0.259299	−	0.965797i	$-0.416509\pi$
$619$	23.6805	−	6.08012i	0.951800	−	0.244381i	0.692502	+	0.721416i	$0.256509\pi$
$620$	−0.448520	−	0.128732i	−0.0180130	−	0.00517000i
$621$	−0.141756	−	2.25314i	−0.00568845	−	0.0904154i
$622$	9.31036	−	14.6708i	0.373311	−	0.588245i
$623$	0.213143	+	0.200155i	0.00853940	+	0.00801903i
$624$	−1.46523			−0.0586562
$625$	10.9369	+	22.4808i	0.437475	+	0.899231i
$626$	23.6550			0.945442
$627$	1.88442	+	1.76959i	0.0752564	+	0.0706705i
$628$	2.43766	−	3.84113i	0.0972731	−	0.153278i
$629$	3.20756	+	50.9826i	0.127894	+	2.03281i
$630$	0.292384	+	0.0839185i	0.0116488	+	0.00334339i
$631$	−25.6878	+	6.59552i	−1.02262	+	0.262563i	−0.722524	−	0.691346i	$-0.757018\pi$
$631$	−25.6878	+	6.59552i	−1.02262	+	0.262563i	−0.300094	+	0.953910i	$0.597018\pi$
$632$	−0.970300	−	2.98628i	−0.0385965	−	0.118788i
$633$	−8.39556	+	10.1485i	−0.333693	+	0.403366i
$634$	4.07645	+	8.66289i	0.161896	+	0.344047i
$635$	0.591296	+	0.992471i	0.0234649	+	0.0393850i
$636$	3.29271	+	3.09206i	0.130565	+	0.122608i
$637$	−8.96419	−	4.92810i	−0.355174	−	0.195259i
$638$	−0.0350469	−	0.0744784i	−0.00138752	−	0.00294863i
$639$	−0.498913	+	1.06024i	−0.0197367	+	0.0419426i
$640$	−1.67250	+	1.48417i	−0.0661113	+	0.0586669i
$641$	−30.5715	+	3.86208i	−1.20750	+	0.152543i	−0.703205	−	0.710987i	$-0.748248\pi$
$641$	−30.5715	+	3.86208i	−1.20750	+	0.152543i	−0.504297	+	0.863530i	$0.668248\pi$
$642$	−0.359464	+	5.71351i	−0.0141869	+	0.225494i
$643$	−0.505217	+	1.55490i	−0.0199238	+	0.0613192i	−0.960524	−	0.278197i	$-0.910263\pi$
$643$	−0.505217	+	1.55490i	−0.0199238	+	0.0613192i	0.940600	+	0.339516i	$0.110263\pi$
$644$	−0.164561	−	0.259307i	−0.00648462	−	0.0102181i
$645$	−1.52719	+	6.93781i	−0.0601330	+	0.273176i
$646$	3.36644	+	0.864354i	0.132451	+	0.0340075i
$647$	−2.24414	−	35.6696i	−0.0882264	−	1.40232i	−0.754348	−	0.656475i	$-0.772047\pi$
$647$	−2.24414	−	35.6696i	−0.0882264	−	1.40232i	0.666121	−	0.745843i	$-0.267953\pi$
$648$	−0.187381	−	0.982287i	−0.00736103	−	0.0385879i
$649$	4.36938	+	13.4476i	0.171513	+	0.527864i
$650$	5.61451	−	4.70637i	0.220219	−	0.184599i
$651$	0.00877254	−	0.0269991i	0.000343823	−	0.00105818i
$652$	13.7300	+	1.73450i	0.537707	+	0.0679283i
$653$	−9.42520	+	3.73170i	−0.368836	+	0.146033i	−0.545229	−	0.838287i	$-0.683557\pi$
$653$	−9.42520	+	3.73170i	−0.368836	+	0.146033i	0.176392	+	0.984320i	$0.443557\pi$
$654$	−12.2933	+	4.86725i	−0.480705	+	0.190325i
$655$	3.77168	+	0.106294i	0.147372	+	0.00415323i
$656$	−0.312286	+	4.96364i	−0.0121927	+	0.193797i
$657$	−6.17568	−	4.48689i	−0.240936	−	0.175050i
$658$	−0.549864	+	0.141181i	−0.0214359	+	0.00550382i
$659$	−28.9982	+	27.2311i	−1.12961	+	1.06077i	−0.132030	+	0.991246i	$0.542149\pi$
$659$	−28.9982	+	27.2311i	−1.12961	+	1.06077i	−0.997580	+	0.0695286i	$0.977851\pi$
$660$	−0.311669	−	8.98929i	−0.0121317	−	0.349908i
$661$	−19.6686	+	10.8129i	−0.765022	+	0.420574i	−0.815946	−	0.578128i	$-0.803783\pi$
$661$	−19.6686	+	10.8129i	−0.765022	+	0.420574i	0.0509243	+	0.998703i	$0.483783\pi$
$662$	−9.37371	+	1.18418i	−0.364320	+	0.0460243i
$663$	1.48491	−	7.78415i	0.0576690	−	0.302311i
$664$	−12.6946	−	1.60370i	−0.492647	−	0.0622357i
$665$	−0.161323	+	0.110401i	−0.00625585	+	0.00428118i
$666$	−1.76986	+	9.27795i	−0.0685809	+	0.359513i
$667$	−0.0247534	−	0.0390050i	−0.000958454	−	0.00151028i
$668$	−6.03034	+	4.38130i	−0.233321	+	0.169517i
$669$	−11.0247	+	13.3266i	−0.426241	+	0.515237i
$670$	4.24819	+	26.2706i	0.164122	+	1.01492i
$671$	−3.60632	+	5.68264i	−0.139220	+	0.219376i
$672$	−0.0867133	−	0.104818i	−0.00334504	−	0.00404346i
$673$	−8.23960	+	17.5100i	−0.317613	+	0.674963i	−0.998341	−	0.0575738i	$-0.981664\pi$
$673$	−8.23960	+	17.5100i	−0.317613	+	0.674963i	0.680728	+	0.732536i	$0.261664\pi$
$674$	12.7525	−	9.26527i	0.491210	−	0.356885i
$675$	3.87315	+	3.16208i	0.149077	+	0.121708i
$676$	8.78034	+	6.37929i	0.337705	+	0.245357i
$677$	−27.9604	+	15.3714i	−1.07461	+	0.590770i	−0.917874	−	0.396872i	$-0.870096\pi$
$677$	−27.9604	+	15.3714i	−1.07461	+	0.590770i	−0.156732	+	0.987641i	$0.550096\pi$
$678$	4.89486	+	1.25679i	0.187986	+	0.0482666i
$679$	1.66762	+	2.01580i	0.0639973	+	0.0773594i
$680$	−6.18979	−	10.3894i	−0.237368	−	0.398414i
$681$	−5.45131	−	2.15833i	−0.208895	−	0.0827072i
$682$	−0.839435			−0.0321436
$683$	−3.97872	−	1.57529i	−0.152241	−	0.0602767i	0.290768	−	0.956794i	$-0.406089\pi$
$683$	−3.97872	−	1.57529i	−0.152241	−	0.0602767i	−0.443009	+	0.896517i	$0.646089\pi$
$684$	0.563149	+	0.309594i	0.0215325	+	0.0118376i
$685$	29.2995	+	29.1102i	1.11948	+	1.11224i
$686$	−0.356400	−	1.86831i	−0.0136074	−	0.0713325i
$687$	−21.0249	+	19.7437i	−0.802148	+	0.753268i
$688$	2.31591	−	2.17478i	0.0882931	−	0.0829127i
$689$	1.24016	+	6.50115i	0.0472463	+	0.247674i
$690$	−0.805860	−	4.98340i	−0.0306786	−	0.189715i
$691$	−2.11691	−	1.16378i	−0.0805310	−	0.0442723i	0.440979	−	0.897517i	$-0.354631\pi$
$691$	−2.11691	−	1.16378i	−0.0805310	−	0.0442723i	−0.521510	+	0.853245i	$0.674631\pi$
$692$	−13.4313	−	5.31782i	−0.510581	−	0.202153i
$693$	0.547216			0.0207870
$694$	30.4611	+	12.0604i	1.15629	+	0.457806i
$695$	23.7200	−	27.0815i	0.899751	−	1.02726i
$696$	−0.0130434	−	0.0157668i	−0.000494410	−	0.000597639i
$697$	−26.0532	−	6.68932i	−0.986835	−	0.253376i
$698$	−4.51399	+	2.48159i	−0.170857	+	0.0939295i
$699$	10.9878	+	7.98311i	0.415597	+	0.301949i
$700$	0.668950	+	0.123120i	0.0252839	+	0.00465350i
$701$	−14.9509	+	10.8624i	−0.564686	+	0.410269i	−0.833171	−	0.553015i	$-0.813477\pi$
$701$	−14.9509	+	10.8624i	−0.564686	+	0.410269i	0.268485	+	0.963284i	$0.413477\pi$
$702$	0.623865	−	1.32578i	0.0235463	−	0.0500384i
$703$	−3.86909	−	4.67693i	−0.145926	−	0.176394i
$704$	−2.15539	+	3.39635i	−0.0812343	+	0.128005i
$705$	−9.22119	−	1.42987i	−0.347290	−	0.0538520i
$706$	−6.45526	+	7.80307i	−0.242947	+	0.293672i
$707$	−0.0162798	+	0.0118279i	−0.000612263	+	0.000444835i
$708$	1.88348	+	2.96789i	0.0707855	+	0.111540i
$709$	6.09642	−	31.9586i	0.228956	−	1.20023i	−0.663179	−	0.748461i	$-0.730793\pi$
$709$	6.09642	−	31.9586i	0.228956	−	1.20023i	0.892135	−	0.451769i	$-0.149207\pi$
$710$	−0.879546	+	2.46811i	−0.0330088	+	0.0926264i
$711$	3.11520	+	0.393541i	0.116829	+	0.0147589i
$712$	0.402746	−	2.11127i	0.0150935	−	0.0791231i
$713$	−0.467405	+	0.0590470i	−0.0175045	+	0.00221133i
$714$	0.644733	−	0.354445i	0.0241285	−	0.0132648i
$715$	7.37250	−	10.9243i	0.275716	−	0.408546i
$716$	−5.94444	+	5.58220i	−0.222154	+	0.208617i
$717$	6.45863	−	1.65829i	0.241202	−	0.0619302i
$718$	15.1345	+	10.9959i	0.564815	+	0.410362i
$719$	−2.09081	+	33.2325i	−0.0779741	+	1.23936i	0.743351	+	0.668902i	$0.233235\pi$
$719$	−2.09081	+	33.2325i	−0.0779741	+	1.23936i	−0.821325	+	0.570461i	$0.806765\pi$
$720$	−0.630800	−	2.14525i	−0.0235085	−	0.0799487i
$721$	2.29178	−	0.907378i	0.0853502	−	0.0337925i
$722$	17.2818	−	6.84234i	0.643161	−	0.254645i
$723$	30.4079	+	3.84141i	1.13088	+	0.142864i
$724$	−3.03553	+	9.34239i	−0.112815	+	0.347207i
$725$	0.100624	+	0.0185197i	0.00373707	+	0.000687806i
$726$	−1.60099	−	4.92733i	−0.0594182	−	0.182870i
$727$	8.00923	+	41.9858i	0.297046	+	1.55717i	0.747434	+	0.664336i	$0.231286\pi$
$727$	8.00923	+	41.9858i	0.297046	+	1.55717i	−0.450388	+	0.892833i	$0.648714\pi$
$728$	−0.0125158	−	0.198933i	−0.000463866	−	0.00737293i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	−14.7202	−	8.64124i	−0.544820	−	0.319827i
$731$	9.20668	+	14.5074i	0.340521	+	0.536576i
$732$	−0.517035	+	1.59127i	−0.0191102	+	0.0588151i
$733$	1.32256	−	21.0214i	0.0488497	−	0.776444i	−0.894999	−	0.446067i	$-0.852824\pi$
$733$	1.32256	−	21.0214i	0.0488497	−	0.776444i	0.943849	−	0.330377i	$-0.107176\pi$
$734$	−10.7084	+	1.35279i	−0.395256	+	0.0499324i
$735$	3.35605	−	15.2461i	0.123790	−	0.562360i
$736$	−0.961237	+	2.04273i	−0.0354317	+	0.0752961i
$737$	20.3834	+	43.3169i	0.750832	+	1.59560i
$738$	−4.35827	−	2.39598i	−0.160430	−	0.0881972i
$739$	−2.21938	−	2.08414i	−0.0816414	−	0.0766664i	0.642652	−	0.766158i	$-0.277834\pi$
$739$	−2.21938	−	2.08414i	−0.0816414	−	0.0766664i	−0.724294	+	0.689492i	$0.757834\pi$
$740$	−1.91942	+	21.0328i	−0.0705594	+	0.773182i
$741$	0.400920	+	0.851999i	0.0147282	+	0.0312990i
$742$	−0.391680	+	0.473459i	−0.0143790	+	0.0173812i
$743$	11.9022	+	36.6311i	0.436649	+	1.34387i	0.891388	+	0.453242i	$0.149733\pi$
$743$	11.9022	+	36.6311i	0.436649	+	1.34387i	−0.454739	+	0.890625i	$0.650267\pi$
$744$	−0.202126	+	0.0518972i	−0.00741031	+	0.00190264i
$745$	1.13234	+	32.6592i	0.0414855	+	1.19654i
$746$	−0.0834997	−	1.32719i	−0.00305714	−	0.0485919i
$747$	6.85618	−	10.8036i	0.250854	−	0.395283i
$748$	−15.8590	−	14.8926i	−0.579864	−	0.544528i
$749$	−0.778787			−0.0284562
$750$	9.30771	+	6.19407i	0.339870	+	0.226175i
$751$	−23.5795			−0.860428			−0.430214	−	0.902727i	$-0.641562\pi$
$751$	−23.5795			−0.860428			−0.430214	+	0.902727i	$0.641562\pi$
$752$	3.04208	+	2.85670i	0.110933	+	0.104173i
$753$	−14.0977	+	22.2144i	−0.513749	+	0.809538i
$754$	−0.00188263	−	0.0299235i	−6.85612e−5	−	0.00108975i
$755$	−3.47491	+	5.14900i	−0.126465	+	0.187391i
$756$	0.131763	−	0.0338310i	0.00479218	−	0.00123042i
$757$	9.54400	+	29.3734i	0.346883	+	1.06759i	0.960568	+	0.278044i	$0.0896862\pi$
$757$	9.54400	+	29.3734i	0.346883	+	1.06759i	−0.613686	+	0.789550i	$0.710314\pi$
$758$	12.7085	−	15.3619i	0.461594	−	0.557971i
$759$	−3.86662	−	8.21699i	−0.140350	−	0.298258i
$760$	1.32064	+	0.566418i	0.0479047	+	0.0205461i
$761$	17.5879	+	16.5162i	0.637562	+	0.598711i	0.934404	−	0.356216i	$-0.115933\pi$
$761$	17.5879	+	16.5162i	0.637562	+	0.598711i	−0.296841	+	0.954927i	$0.595933\pi$
$762$	0.452743	+	0.248898i	0.0164011	+	0.00901661i
$763$	−0.765827	−	1.62747i	−0.0277248	−	0.0589182i
$764$	0.694283	−	1.47543i	0.0251183	−	0.0533791i
$765$	12.0361	−	1.17712i	0.435165	−	0.0425587i
$766$	6.48050	−	0.818678i	0.234150	−	0.0295800i
$767$	−0.323398	+	5.14026i	−0.0116772	+	0.185604i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	26.1088	+	41.1409i	0.941507	+	1.48358i	0.874038	+	0.485857i	$0.161492\pi$
$769$	26.1088	+	41.1409i	0.941507	+	1.48358i	0.0674690	+	0.997721i	$0.478508\pi$
$770$	1.21780	−	0.119100i	0.0438865	−	0.00429207i
$771$	3.37890	+	0.867553i	0.121688	+	0.0312442i
$772$	0.598467	+	9.51236i	0.0215393	+	0.342357i
$773$	−3.71687	−	19.4845i	−0.133687	−	0.700810i	−0.984506	−	0.175352i	$-0.943894\pi$
$773$	−3.71687	−	19.4845i	−0.133687	−	0.700810i	0.850819	−	0.525459i	$-0.176106\pi$
$774$	0.981735	+	3.02147i	0.0352877	+	0.108605i
$775$	0.607817	−	0.848096i	0.0218334	−	0.0304645i
$776$	5.94283	−	18.2901i	0.213335	−	0.656578i
$777$	−1.27477	−	0.161041i	−0.0457322	−	0.00577732i
$778$	−26.3761	+	10.4430i	−0.945628	+	0.374400i
$779$	2.97169	−	1.17658i	0.106472	−	0.0421552i
$780$	1.09983	−	3.08624i	0.0393802	−	0.110505i
$781$	−0.295962	+	4.70418i	−0.0105903	+	0.168329i
$782$	−9.87802	−	7.17680i	−0.353237	−	0.256642i
$783$	0.0198199	−	0.00508887i	0.000708304	−	0.000181862i
$784$	−5.08929	+	4.77916i	−0.181760	+	0.170684i
$785$	6.26090	+	8.01770i	0.223461	+	0.286164i
$786$	1.47870	−	0.812920i	0.0527433	−	0.0289959i
$787$	−30.6278	+	3.86919i	−1.09176	+	0.137922i	−0.650537	−	0.759475i	$-0.725456\pi$
$787$	−30.6278	+	3.86919i	−1.09176	+	0.137922i	−0.441226	+	0.897396i	$0.645456\pi$
$788$	2.87378	−	15.0649i	0.102374	−	0.536664i
$789$	−22.0006	−	2.77932i	−0.783242	−	0.0989465i
$790$	7.01837	+	0.197792i	0.249702	+	0.00703711i
$791$	−0.128821	+	0.675304i	−0.00458035	+	0.0240111i
$792$	−2.15539	−	3.39635i	−0.0765884	−	0.120684i
$793$	−1.98336	+	1.44100i	−0.0704312	+	0.0511713i
$794$	20.5017	−	24.7823i	0.727579	−	0.879492i
$795$	−8.98444	+	4.61454i	−0.318645	+	0.163661i
$796$	−3.43809	+	5.41756i	−0.121860	+	0.192020i
$797$	11.0484	+	13.3552i	0.391353	+	0.473064i	0.928986	−	0.370114i	$-0.120682\pi$
$797$	11.0484	+	13.3552i	0.391353	+	0.473064i	−0.537633	+	0.843179i	$0.680682\pi$
$798$	−0.0372228	+	0.0791025i	−0.00131767	+	0.00280020i
$799$	−18.2594	+	13.2662i	−0.645969	+	0.469324i
$800$	−1.87072	−	4.63685i	−0.0661400	−	0.163937i
$801$	1.73885	+	1.26335i	0.0614393	+	0.0446383i
$802$	16.0223	−	8.80831i	0.565766	−	0.311032i
$803$	−29.7417	−	7.63636i	−1.04956	−	0.269481i
$804$	7.58611	+	9.17003i	0.267541	+	0.323402i
$805$	0.669706	−	0.151978i	0.0236040	−	0.00535652i
$806$	−0.284296	−	0.112561i	−0.0100139	−	0.00396478i
$807$	23.6049			0.830932
$808$	0.137534	+	0.0544538i	0.00483845	+	0.00191568i
$809$	41.2569	+	22.6812i	1.45052	+	0.797428i	0.995654	−	0.0931340i	$-0.0296885\pi$
$809$	41.2569	+	22.6812i	1.45052	+	0.797428i	0.454862	+	0.890562i	$0.349688\pi$
$810$	2.20966	+	0.342638i	0.0776396	+	0.0120391i
$811$	−2.28881	−	11.9984i	−0.0803709	−	0.421319i	−0.999618	−	0.0276380i	$-0.991201\pi$
$811$	−2.28881	−	11.9984i	−0.0803709	−	0.421319i	0.919247	−	0.393681i	$-0.128799\pi$
$812$	0.00202922	−	0.00190557i	7.12118e−5	−	6.68723e-5i
$813$	−14.1461	+	13.2841i	−0.496127	+	0.465894i
$814$	7.11937	+	37.3210i	0.249534	+	1.30810i
$815$	−13.9594	+	27.6177i	−0.488975	+	0.967408i
$816$	−4.73939	−	2.60550i	−0.165912	−	0.0912108i
$817$	−1.89827	−	0.751578i	−0.0664120	−	0.0262944i
$818$	30.2885			1.05901
$819$	0.185329	+	0.0733768i	0.00647590	+	0.00256399i
$820$	−10.2206	−	4.38357i	−0.356918	−	0.153081i
$821$	−12.3070	−	14.8766i	−0.429516	−	0.519196i	0.510707	−	0.859755i	$-0.329384\pi$
$821$	−12.3070	−	14.8766i	−0.429516	−	0.519196i	−0.940223	+	0.340559i	$0.889384\pi$
$822$	17.8906	+	4.59352i	0.624006	+	0.160217i
$823$	38.1198	−	20.9566i	1.32877	−	0.730500i	0.350255	−	0.936654i	$-0.386095\pi$
$823$	38.1198	−	20.9566i	1.32877	−	0.730500i	0.978519	+	0.206155i	$0.0660950\pi$
$824$	−14.6587	−	10.6501i	−0.510658	−	0.371015i
$825$	19.1682	+	6.09105i	0.667353	+	0.212063i
$826$	−0.386858	+	0.281069i	−0.0134605	+	0.00977963i
$827$	−12.9902	+	27.6057i	−0.451715	+	0.959943i	0.541176	+	0.840910i	$0.317979\pi$
$827$	−12.9902	+	27.6057i	−0.451715	+	0.959943i	−0.992890	+	0.119033i	$0.962021\pi$
$828$	−1.43905	−	1.73951i	−0.0500103	−	0.0604520i
$829$	−4.36189	+	6.87324i	−0.151495	+	0.238718i	−0.911596	−	0.411087i	$-0.865149\pi$
$829$	−4.36189	+	6.87324i	−0.151495	+	0.238718i	0.760101	+	0.649805i	$0.225149\pi$
$830$	12.9067	−	25.5351i	0.447998	−	0.886337i
$831$	5.02376	−	6.07268i	0.174272	−	0.210659i
$832$	−1.18540	+	0.861242i	−0.0410963	+	0.0298582i
$833$	−20.2320	−	31.8806i	−0.700998	−	1.10460i
$834$	3.01684	−	15.8148i	0.104464	−	0.547622i
$835$	−4.70192	−	15.9905i	−0.162717	−	0.553373i
$836$	2.56466	+	0.323992i	0.0887007	+	0.0112055i
$837$	0.0391032	−	0.204986i	0.00135160	−	0.00708536i
$838$	0.270840	−	0.0342150i	0.00935600	−	0.00118194i
$839$	−8.78593	+	4.83011i	−0.303324	+	0.166754i	−0.626146	−	0.779706i	$-0.715369\pi$
$839$	−8.78593	+	4.83011i	−0.303324	+	0.166754i	0.322822	+	0.946460i	$0.395369\pi$
$840$	0.285869	−	0.103967i	0.00986343	−	0.00358721i
$841$	−21.1398	+	19.8516i	−0.728958	+	0.684537i
$842$	−29.7644	+	7.64221i	−1.02575	+	0.263368i
$843$	−4.73398	−	3.43944i	−0.163047	−	0.118460i
$844$	−0.827018	+	13.1451i	−0.0284671	+	0.452472i
$845$	−20.0275	+	13.7058i	−0.688966	+	0.471493i
$846$	−3.88007	+	1.53623i	−0.133400	+	0.0528167i
$847$	0.655302	−	0.259452i	0.0225164	−	0.00891489i
$848$	4.48133	+	0.566124i	0.153890	+	0.0194408i
$849$	4.19066	−	12.8975i	0.143823	−	0.442642i
$850$	26.5295	−	5.23923i	0.909953	−	0.179704i
$851$	6.58934	+	20.2799i	0.225880	+	0.695186i
$852$	0.219567	+	1.15101i	0.00752223	+	0.0394329i
$853$	−1.22496	−	19.4702i	−0.0419418	−	0.666646i	−0.961690	−	0.274138i	$-0.911608\pi$
$853$	−1.22496	−	19.4702i	−0.0419418	−	0.666646i	0.919749	−	0.392508i	$-0.128392\pi$
$854$	−0.220461	−	0.0566048i	−0.00754403	−	0.00193698i
$855$	−1.07481	+	0.953784i	−0.0367578	+	0.0326187i
$856$	3.06751	+	4.83362i	0.104845	+	0.165210i
$857$	15.3404	−	47.2129i	0.524018	−	1.61276i	−0.242231	−	0.970219i	$-0.577879\pi$
$857$	15.3404	−	47.2129i	0.524018	−	1.61276i	0.766249	−	0.642543i	$-0.222121\pi$
$858$	0.370085	−	5.88234i	0.0126345	−	0.200820i
$859$	−0.524899	+	0.0663102i	−0.0179093	+	0.00226248i	−0.134283	−	0.990943i	$-0.542873\pi$
$859$	−0.524899	+	0.0663102i	−0.0179093	+	0.00226248i	0.116373	+	0.993206i	$0.462873\pi$
$860$	2.84242	+	6.51046i	0.0969257	+	0.222005i
$861$	0.288071	−	0.612182i	0.00981744	−	0.0208631i
$862$	−3.93720	−	8.36698i	−0.134102	−	0.284980i
$863$	−40.1097	−	22.0505i	−1.36535	−	0.750608i	−0.380627	−	0.924729i	$-0.624292\pi$
$863$	−40.1097	−	22.0505i	−1.36535	−	0.750608i	−0.984724	+	0.174120i	$0.944292\pi$
$864$	−0.728969	−	0.684547i	−0.0248000	−	0.0232888i
$865$	21.2828	−	24.2989i	0.723636	−	0.826187i
$866$	0.548549	+	1.16573i	0.0186405	+	0.0396130i
$867$	7.80874	−	9.43914i	0.265199	−	0.320570i
$868$	−0.00877254	−	0.0269991i	−0.000297760	−	0.000916410i
$869$	12.2338	−	3.14111i	0.415004	−	0.106555i
$870$	0.0430005	−	0.0156388i	0.00145785	−	0.000530204i
$871$	1.09494	+	17.4036i	0.0371007	+	0.589699i
$872$	−7.08457	+	11.1635i	−0.239914	+	0.378044i
$873$	14.0191	+	13.1648i	0.474474	+	0.445561i
$874$	1.45082			0.0490747
$875$	−0.761455	+	1.31660i	−0.0257419	+	0.0445093i
$876$	−7.63356			−0.257914
$877$	2.24454	+	2.10776i	0.0757927	+	0.0711740i	0.721518	−	0.692396i	$-0.243445\pi$
$877$	2.24454	+	2.10776i	0.0757927	+	0.0711740i	−0.645725	+	0.763570i	$0.723445\pi$
$878$	−4.68820	+	7.38742i	−0.158219	+	0.249313i
$879$	−0.634381	−	10.0832i	−0.0213971	−	0.340098i
$880$	−5.53592	−	7.08930i	−0.186616	−	0.238980i
$881$	−18.2695	+	4.69081i	−0.615516	+	0.158038i	−0.543560	−	0.839370i	$-0.682924\pi$
$881$	−18.2695	+	4.69081i	−0.615516	+	0.158038i	−0.0719556	+	0.997408i	$0.522924\pi$
$882$	−2.15740	−	6.63980i	−0.0726434	−	0.223574i
$883$	16.4173	−	19.8451i	0.552487	−	0.667841i	−0.418154	−	0.908376i	$-0.637323\pi$
$883$	16.4173	−	19.8451i	0.552487	−	0.667841i	0.970641	+	0.240535i	$0.0773228\pi$
$884$	−3.37410	−	7.17032i	−0.113483	−	0.241164i
$885$	−7.66509	+	1.73946i	−0.257659	+	0.0584712i
$886$	−12.8843	−	12.0992i	−0.432858	−	0.406481i
$887$	35.8226	+	19.6936i	1.20281	+	0.661248i	0.951794	−	0.306736i	$-0.0992370\pi$
$887$	35.8226	+	19.6936i	1.20281	+	0.661248i	0.251011	+	0.967984i	$0.419237\pi$
$888$	4.02159	+	8.54632i	0.134956	+	0.286796i
$889$	−0.0299252	+	0.0635943i	−0.00100366	+	0.00213289i
$890$	4.14469	+	2.43307i	0.138930	+	0.0815566i
$891$	3.99083	−	0.504159i	0.133698	−	0.0168900i
$892$	−1.08601	+	17.2617i	−0.0363623	+	0.577963i
$893$	0.828726	−	2.55056i	0.0277322	−	0.0853511i
$894$	7.83081	+	12.3394i	0.261901	+	0.412690i
$895$	−7.29589	−	16.7110i	−0.243875	−	0.558586i
$896$	−0.131763	−	0.0338310i	−0.00440190	−	0.00113022i
$897$	−0.207705	−	3.30137i	−0.00693506	−	0.110230i
$898$	−0.371513	−	1.94754i	−0.0123975	−	0.0649902i
$899$	−0.00131957	−	0.00406121i	−4.40101e−5	−	0.000135449i
$900$	4.99206	+	0.281596i	0.166402	+	0.00938655i
$901$	−7.54908	+	23.2337i	−0.251496	+	0.774026i
$902$	−19.8482	−	2.50741i	−0.660873	−	0.0834876i
$903$	−0.401835	+	0.159098i	−0.0133722	+	0.00529444i
$904$	4.69875	−	1.86037i	0.156278	−	0.0618749i
$905$	−17.3995	−	13.4064i	−0.578380	−	0.445642i
$906$	−0.174434	+	2.77255i	−0.00579518	+	0.0921117i
$907$	−9.34100	−	6.78664i	−0.310163	−	0.225347i	0.421804	−	0.906687i	$-0.361397\pi$
$907$	−9.34100	−	6.78664i	−0.310163	−	0.225347i	−0.731966	+	0.681341i	$0.761397\pi$
$908$	−5.67883	+	1.45808i	−0.188459	+	0.0483880i
$909$	−0.107831	+	0.101260i	−0.00357651	+	0.00335857i
$910$	0.428410	+	0.122960i	0.0142016	+	0.00407609i
$911$	−28.2489	+	15.5300i	−0.935928	+	0.514531i	−0.875274	−	0.483628i	$-0.839319\pi$
$911$	−28.2489	+	15.5300i	−0.935928	+	0.514531i	−0.0606546	+	0.998159i	$0.519319\pi$
$912$	0.637572	−	0.0805440i	0.0211121	−	0.00266708i
$913$	9.64462	−	50.5589i	0.319190	−	1.67326i
$914$	−19.6647	−	2.48424i	−0.650452	−	0.0821712i
$915$	−2.96363	−	2.28348i	−0.0979745	−	0.0754894i
$916$	−5.40444	+	28.3311i	−0.178568	+	0.936085i
$917$	0.123000	+	0.193817i	0.00406181	+	0.00640039i
$918$	4.37546	−	3.17896i	0.144412	−	0.104921i
$919$	15.4716	−	18.7020i	0.510363	−	0.616922i	−0.450894	−	0.892577i	$-0.648895\pi$
$919$	15.4716	−	18.7020i	0.510363	−	0.616922i	0.961257	+	0.275655i	$0.0888948\pi$
$920$	−3.58112	−	3.55798i	−0.118066	−	0.117303i
$921$	−9.80991	+	15.4579i	−0.323247	+	0.509356i
$922$	−5.88012	−	7.10784i	−0.193651	−	0.234084i
$923$	−0.731023	+	1.55350i	−0.0240619	+	0.0511342i
$924$	0.442707	−	0.321645i	0.0145640	−	0.0105814i
$925$	−42.8611	−	19.8305i	−1.40926	−	0.652024i
$926$	−31.3980	−	22.8120i	−1.03180	−	0.749649i
$927$	15.8779	−	8.72894i	0.521498	−	0.286696i
$928$	−0.0198199	−	0.00508887i	−0.000650619	−	0.000167050i
$929$	33.0989	+	40.0097i	1.08594	+	1.31267i	0.946593	+	0.322431i	$0.104500\pi$
$929$	33.0989	+	40.0097i	1.08594	+	1.31267i	0.139346	+	0.990244i	$0.455500\pi$
$930$	0.0424075	−	0.464697i	0.00139060	−	0.0152380i
$931$	4.17152	+	1.65162i	0.136716	+	0.0541297i
$932$	13.5817			0.444882
$933$	16.1555	+	6.39642i	0.528908	+	0.209409i
$934$	20.0885	+	11.0437i	0.657315	+	0.361362i
$935$	43.2727	−	22.2255i	1.41517	−	0.726851i
$936$	−0.274557	−	1.43928i	−0.00897418	−	0.0470443i
$937$	18.9957	−	17.8381i	0.620561	−	0.582745i	−0.309160	−	0.951010i	$-0.600048\pi$
$937$	18.9957	−	17.8381i	0.620561	−	0.582745i	0.929721	+	0.368264i	$0.120048\pi$
$938$	−1.18020	+	1.10828i	−0.0385350	+	0.0361868i
$939$	4.43250	+	23.2360i	0.144649	+	0.758277i
$940$	−8.30055	+	4.26329i	−0.270734	+	0.139053i
$941$	−7.12735	−	3.91830i	−0.232345	−	0.127733i	0.361329	−	0.932438i	$-0.382323\pi$
$941$	−7.12735	−	3.91830i	−0.232345	−	0.127733i	−0.593674	+	0.804706i	$0.702323\pi$
$942$	4.22987	+	1.67472i	0.137816	+	0.0545654i
$943$	−11.2280			−0.365635
$944$	3.26825	+	1.29399i	0.106372	+	0.0421158i
$945$	−0.0276449	+	0.302929i	−0.000899288	+	0.00985429i
$946$	8.14595	+	9.84677i	0.264848	+	0.320146i
$947$	−23.5810	−	6.05457i	−0.766279	−	0.196747i	−0.154733	−	0.987956i	$-0.549452\pi$
$947$	−23.5810	−	6.05457i	−0.766279	−	0.196747i	−0.611545	+	0.791209i	$0.709452\pi$
$948$	2.75156	−	1.51269i	0.0893667	−	0.0491297i
$949$	−9.04880	−	6.57434i	−0.293737	−	0.213412i
$950$	−2.18435	+	2.35653i	−0.0708698	+	0.0764559i
$951$	−7.74560	+	5.62751i	−0.251168	+	0.182484i
$952$	0.313262	−	0.665716i	0.0101529	−	0.0215760i
$953$	−35.0666	−	42.3882i	−1.13592	−	1.37309i	−0.917740	−	0.397181i	$-0.869989\pi$
$953$	−35.0666	−	42.3882i	−1.13592	−	1.37309i	−0.218178	−	0.975909i	$-0.570011\pi$
$954$	−2.42030	+	3.81379i	−0.0783602	+	0.123476i
$955$	2.58658	+	2.56986i	0.0836996	+	0.0831588i
$956$	4.25042	−	5.13788i	0.137468	−	0.166171i
$957$	0.0665921	−	0.0483820i	0.00215262	−	0.00156397i
$958$	15.7098	+	24.7547i	0.507560	+	0.799787i
$959$	−0.470838	+	2.46822i	−0.0152041	+	0.0797029i
$960$	−1.77127	−	1.36477i	−0.0571676	−	0.0440477i
$961$	30.7124	+	3.87987i	0.990721	+	0.125157i
$962$	−2.59326	+	13.5944i	−0.0836101	+	0.438300i
$963$	−5.67967	+	0.717509i	−0.183025	+	0.0231214i
$964$	26.8584	−	14.7655i	0.865051	−	0.475566i
$965$	−20.4853	−	5.87958i	−0.659444	−	0.189270i
$966$	0.223878	−	0.210236i	0.00720317	−	0.00676423i
$967$	43.6775	−	11.2145i	1.40457	−	0.360633i	0.531018	−	0.847360i	$-0.321810\pi$
$967$	43.6775	−	11.2145i	1.40457	−	0.360633i	0.873554	+	0.486728i	$0.161810\pi$
$968$	−4.19144	−	3.04526i	−0.134718	−	0.0978783i
$969$	−0.218237	+	3.46877i	−0.00701077	+	0.111433i
$970$	34.0641	+	26.2464i	1.09373	+	0.842721i
$971$	−17.9455	+	7.10512i	−0.575898	+	0.228014i	−0.637975	−	0.770057i	$-0.720228\pi$
$971$	−17.9455	+	7.10512i	−0.575898	+	0.228014i	0.0620769	+	0.998071i	$0.480228\pi$
$972$	0.929776	−	0.368125i	0.0298226	−	0.0118076i
$973$	2.17292	+	0.274504i	0.0696608	+	0.00880020i
$974$	13.0112	−	40.0443i	0.416905	−	1.28310i
$975$	5.67506	+	4.63318i	0.181747	+	0.148380i
$976$	0.517035	+	1.59127i	0.0165499	+	0.0509353i
$977$	−1.89903	−	9.95505i	−0.0607553	−	0.318490i	0.938916	−	0.344148i	$-0.111832\pi$
$977$	−1.89903	−	9.95505i	−0.0607553	−	0.318490i	−0.999671	+	0.0256574i	$0.991832\pi$
$978$	0.868965	+	13.8118i	0.0277864	+	0.441653i
$979$	8.37420	+	2.15013i	0.267641	+	0.0687184i
$980$	−6.24632	−	14.3070i	−0.199531	−	0.457020i
$981$	−7.08457	−	11.1635i	−0.226193	−	0.356423i
$982$	8.10958	−	24.9587i	0.258787	−	0.796464i
$983$	0.588751	−	9.35793i	0.0187782	−	0.298471i	−0.977417	−	0.211320i	$-0.932224\pi$
$983$	0.588751	−	9.35793i	0.0187782	−	0.298471i	0.996195	−	0.0871512i	$-0.0277763\pi$
$984$	−4.93423	+	0.623339i	−0.157298	+	0.0198713i
$985$	29.5743	+	17.3610i	0.942315	+	0.553169i
$986$	0.0471210	−	0.100137i	0.00150064	−	0.00318902i
$987$	−0.241715	−	0.513670i	−0.00769387	−	0.0163503i
$988$	0.825144	+	0.453627i	0.0262513	+	0.0144318i
$989$	5.22838	+	4.90977i	0.166253	+	0.156122i
$990$	8.77167	−	1.99057i	0.278782	−	0.0632646i
$991$	−21.8991	−	46.5381i	−0.695649	−	1.47833i	−0.869693	−	0.493592i	$-0.835684\pi$
$991$	−21.8991	−	46.5381i	−0.695649	−	1.47833i	0.174044	−	0.984738i	$-0.444316\pi$
$992$	−0.133019	+	0.160793i	−0.00422336	+	0.00510517i
$993$	−2.91966	−	8.98579i	−0.0926526	−	0.285155i
$994$	−0.154395	+	0.0396420i	−0.00489712	+	0.00125737i
$995$	−8.83041	−	11.3082i	−0.279943	−	0.358495i
$996$	−0.803437	−	12.7703i	−0.0254579	−	0.404641i
$997$	25.0760	−	39.5134i	0.794164	−	1.25140i	−0.169829	−	0.985474i	$-0.554322\pi$
$997$	25.0760	−	39.5134i	0.794164	−	1.25140i	0.963993	−	0.265928i	$-0.0856785\pi$
$998$	−20.4297	−	19.1848i	−0.646691	−	0.607283i
$999$	−9.44526			−0.298835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.b.91.1	✓	120
125.11	even	25	inner	750.2.m.b.511.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.b.91.1	✓	120	1.1	even	1	trivial
750.2.m.b.511.1	yes	120	125.11	even	25	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.728969 + 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.14929 - 0.616880i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.0420378 - 0.129379i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(0.728969 + 0.684547i) q^{2} +(-0.535827 + 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-2.14929 - 0.616880i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-0.0420378 - 0.129379i) q^{7} +(-0.637424 + 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-1.14448 - 1.92098i) q^{10} +(-2.93231 - 2.75362i) q^{11} +(-0.876307 - 0.481754i) q^{12} +(-0.623865 - 1.32578i) q^{13} +(0.0579218 - 0.123090i) q^{14} +(1.67250 - 1.48417i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.339594 - 5.39770i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.344343 + 0.542598i) q^{19} +(0.480707 - 2.18379i) q^{20} +(0.131763 + 0.0338310i) q^{21} +(-0.252578 - 4.01461i) q^{22} +(-0.423031 - 2.21761i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(4.23892 + 2.65171i) q^{25} +(0.452782 - 1.39352i) q^{26} +(0.992115 + 0.125333i) q^{27} +(0.126484 - 0.0500786i) q^{28} +(0.0190258 - 0.00753283i) q^{29} +(2.23518 + 0.0629919i) q^{30} +(0.0131033 - 0.208271i) q^{31} +(-0.809017 - 0.587785i) q^{32} +(3.89617 - 1.00037i) q^{33} +(3.94253 - 3.70228i) q^{34} +(0.0105402 + 0.304005i) q^{35} +(0.876307 - 0.481754i) q^{36} +(-9.37078 + 1.18380i) q^{37} +(-0.120419 + 0.631256i) q^{38} +(1.45368 + 0.183642i) q^{39} +(1.84532 - 1.26284i) q^{40} +(0.931932 - 4.88536i) q^{41} +(0.0728923 + 0.114860i) q^{42} +(-2.57022 + 1.86737i) q^{43} +(2.56407 - 3.09943i) q^{44} +(0.356955 + 2.20739i) q^{45} +(1.20968 - 1.90615i) q^{46} +(-2.66005 - 3.21545i) q^{47} +(0.425779 - 0.904827i) q^{48} +(5.64815 - 4.10362i) q^{49} +(1.27482 + 4.83475i) q^{50} +(4.37546 + 3.17896i) q^{51} +(1.28399 - 0.705881i) q^{52} +(-4.37504 - 1.12332i) q^{53} +(0.637424 + 0.770513i) q^{54} +(4.60374 + 7.72723i) q^{55} +(0.126484 + 0.0500786i) q^{56} -0.642639 q^{57} +(0.0190258 + 0.00753283i) q^{58} +(-3.08030 - 1.69341i) q^{59} +(1.58626 + 1.57601i) q^{60} +(-0.313519 - 1.64353i) q^{61} +(0.152123 - 0.142853i) q^{62} +(-0.0991668 + 0.0931238i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(0.523022 + 3.23434i) q^{65} +(3.52499 + 1.93788i) q^{66} +(-11.0655 - 4.38112i) q^{67} +5.40837 q^{68} +(2.09906 + 0.831076i) q^{69} +(-0.200423 + 0.228826i) q^{70} +(-0.746910 - 0.902859i) q^{71} +(0.968583 + 0.248690i) q^{72} +(6.68934 - 3.67749i) q^{73} +(-7.64137 - 5.55178i) q^{74} +(-4.51024 + 2.15818i) q^{75} +(-0.519906 + 0.377734i) q^{76} +(-0.232993 + 0.495136i) q^{77} +(0.933974 + 1.12898i) q^{78} +(-1.68247 + 2.65115i) q^{79} +(2.20966 + 0.342638i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(4.02361 - 2.92332i) q^{82} +(6.85618 + 10.8036i) q^{83} +(-0.0254908 + 0.133627i) q^{84} +(-4.05962 + 11.3917i) q^{85} +(-3.15191 - 0.398179i) q^{86} +(-0.00383433 + 0.0201003i) q^{87} +(3.99083 - 0.504159i) q^{88} +(-1.88348 + 1.03545i) q^{89} +(-1.25086 + 1.85347i) q^{90} +(-0.145302 + 0.136448i) q^{91} +(2.18667 - 0.561441i) q^{92} +(0.168828 + 0.122660i) q^{93} +(0.262033 - 4.16489i) q^{94} +(-0.405377 - 1.37862i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-17.8809 + 7.07955i) q^{97} +(6.92644 + 0.875013i) q^{98} +(-1.24304 + 3.82567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) \) 120 * q + 20 * q^5 - 5 * q^7	\( 120 q + 20 q^{5} - 5 q^{7} - 20 q^{10} + 5 q^{11} - 10 q^{13} - 20 q^{14} + 20 q^{15} - 5 q^{17} - 30 q^{18} + 15 q^{19} + 5 q^{20} - 15 q^{23} + 30 q^{24} - 20 q^{25} + 10 q^{26} - 5 q^{29} + 5 q^{30} - 50 q^{31} - 30 q^{32} + 30 q^{34} - 10 q^{35} + 10 q^{37} + 35 q^{38} + 10 q^{39} - 5 q^{40} - 35 q^{41} + 5 q^{43} - 25 q^{44} - 10 q^{46} + 130 q^{47} - 15 q^{49} - 20 q^{50} - 5 q^{51} + 40 q^{52} + 15 q^{53} + 10 q^{55} - 20 q^{57} - 5 q^{58} - 55 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 40 q^{65} + 20 q^{66} + 85 q^{67} - 20 q^{68} + 10 q^{69} - 45 q^{70} - 30 q^{71} - 30 q^{74} + 45 q^{75} - 5 q^{76} - 35 q^{77} - 10 q^{78} + 70 q^{79} - 45 q^{82} - 35 q^{83} - 5 q^{84} + 100 q^{85} - 15 q^{86} - 15 q^{87} + 5 q^{88} + 70 q^{89} - 5 q^{90} - 105 q^{91} + 65 q^{92} - 20 q^{94} - 65 q^{95} - 5 q^{97} + 50 q^{98} - 10 q^{99}+O(q^{100}) \) 120 * q + 20 * q^5 - 5 * q^7 - 20 * q^10 + 5 * q^11 - 10 * q^13 - 20 * q^14 + 20 * q^15 - 5 * q^17 - 30 * q^18 + 15 * q^19 + 5 * q^20 - 15 * q^23 + 30 * q^24 - 20 * q^25 + 10 * q^26 - 5 * q^29 + 5 * q^30 - 50 * q^31 - 30 * q^32 + 30 * q^34 - 10 * q^35 + 10 * q^37 + 35 * q^38 + 10 * q^39 - 5 * q^40 - 35 * q^41 + 5 * q^43 - 25 * q^44 - 10 * q^46 + 130 * q^47 - 15 * q^49 - 20 * q^50 - 5 * q^51 + 40 * q^52 + 15 * q^53 + 10 * q^55 - 20 * q^57 - 5 * q^58 - 55 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 40 * q^65 + 20 * q^66 + 85 * q^67 - 20 * q^68 + 10 * q^69 - 45 * q^70 - 30 * q^71 - 30 * q^74 + 45 * q^75 - 5 * q^76 - 35 * q^77 - 10 * q^78 + 70 * q^79 - 45 * q^82 - 35 * q^83 - 5 * q^84 + 100 * q^85 - 15 * q^86 - 15 * q^87 + 5 * q^88 + 70 * q^89 - 5 * q^90 - 105 * q^91 + 65 * q^92 - 20 * q^94 - 65 * q^95 - 5 * q^97 + 50 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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