LMFDB - Embedded newform 750.2.m.d.91.4

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:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	750.91
Dual form			750.2.m.d.511.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.13246 - 1.92809i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-1.48776 - 4.57885i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})$	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.13246 - 1.92809i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-1.48776 - 4.57885i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-0.494339 + 2.18074i) q^{10} +(-1.04060 - 0.977187i) q^{11} +(0.876307 + 0.481754i) q^{12} +(0.655738 + 1.39351i) q^{13} +(-2.04991 + 4.35628i) q^{14} +(-2.23474 - 0.0769525i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.202923 - 3.22537i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.94495 + 3.06476i) q^{19} +(1.85318 - 1.25129i) q^{20} +(-4.66323 - 1.19731i) q^{21} +(0.0896331 + 1.42468i) q^{22} +(0.446225 + 2.33919i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(-2.43506 + 4.36698i) q^{25} +(0.475913 - 1.46471i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(4.47639 - 1.77233i) q^{28} +(-2.84216 + 1.12529i) q^{29} +(1.57638 + 1.58588i) q^{30} +(-0.474555 + 7.54283i) q^{31} +(0.809017 + 0.587785i) q^{32} +(-1.38265 + 0.355003i) q^{33} +(-2.35584 + 2.21228i) q^{34} +(-7.14360 + 8.05390i) q^{35} +(0.876307 - 0.481754i) q^{36} +(-0.180338 + 0.0227820i) q^{37} +(0.680160 - 3.56553i) q^{38} +(1.52794 + 0.193024i) q^{39} +(-2.20748 - 0.356433i) q^{40} +(1.50131 - 7.87012i) q^{41} +(2.57973 + 4.06500i) q^{42} +(7.96085 - 5.78390i) q^{43} +(0.909919 - 1.09990i) q^{44} +(-1.26241 + 1.84562i) q^{45} +(1.27600 - 2.01066i) q^{46} +(-4.06660 - 4.91568i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(-13.0893 + 9.50993i) q^{49} +(4.76448 - 1.51648i) q^{50} +(-2.61454 - 1.89957i) q^{51} +(-1.34959 + 0.741943i) q^{52} +(-9.50471 - 2.44039i) q^{53} +(0.637424 + 0.770513i) q^{54} +(-0.705665 + 3.11299i) q^{55} +(-4.47639 - 1.77233i) q^{56} +3.62982 q^{57} +(2.84216 + 1.12529i) q^{58} +(-10.9356 - 6.01191i) q^{59} +(-0.0635200 - 2.23517i) q^{60} +(-1.82715 - 9.57824i) q^{61} +(5.50936 - 5.17363i) q^{62} +(-3.50961 + 3.29574i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(1.94422 - 2.84242i) q^{65} +(1.25092 + 0.687700i) q^{66} +(13.5094 + 5.34873i) q^{67} +3.23175 q^{68} +(2.21414 + 0.876641i) q^{69} +(10.7207 - 0.980912i) q^{70} +(5.57607 + 6.74031i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(1.41440 - 0.777573i) q^{73} +(0.147056 + 0.106843i) q^{74} +(2.38239 + 4.39593i) q^{75} +(-2.93659 + 2.13355i) q^{76} +(-2.92623 + 6.21856i) q^{77} +(-0.981689 - 1.18666i) q^{78} +(-5.49069 + 8.65194i) q^{79} +(1.36519 + 1.77095i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-6.48187 + 4.70935i) q^{82} +(-3.35959 - 5.29386i) q^{83} +(0.902144 - 4.72921i) q^{84} +(-6.44860 + 3.26135i) q^{85} +(-9.76256 - 1.23330i) q^{86} +(-0.572792 + 3.00268i) q^{87} +(-1.41624 + 0.178912i) q^{88} +(9.59159 - 5.27302i) q^{89} +(2.18367 - 0.481223i) q^{90} +(5.40511 - 5.07573i) q^{91} +(-2.30656 + 0.592223i) q^{92} +(6.11435 + 4.44233i) q^{93} +(-0.400588 + 6.36716i) q^{94} +(3.70654 - 7.22077i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-5.72717 + 2.26755i) q^{97} +(16.0517 + 2.02780i) q^{98} +(-0.441120 + 1.35763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) $ 140 * q - 20 * q^5 + 5 * q^7	$ 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) $ 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * 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
$5$	−1.13246	−	1.92809i	−0.506453	−	0.862268i
$5$	−1.13246	−	1.92809i	−0.506453	−	0.862268i
$6$	−0.968583	+	0.248690i	−0.395422	+	0.101527i
$7$	−1.48776	−	4.57885i	−0.562319	−	1.73064i	−0.675784	−	0.737099i	$-0.736195\pi$
$7$	−1.48776	−	4.57885i	−0.562319	−	1.73064i	0.113465	−	0.993542i	$-0.463805\pi$
$8$	0.637424	−	0.770513i	0.225363	−	0.272418i
$9$	−0.425779	−	0.904827i	−0.141926	−	0.301609i
$10$	−0.494339	+	2.18074i	−0.156324	+	0.689611i
$11$	−1.04060	−	0.977187i	−0.313752	−	0.294633i	0.511632	−	0.859205i	$-0.329041\pi$
$11$	−1.04060	−	0.977187i	−0.313752	−	0.294633i	−0.825384	+	0.564572i	$0.809041\pi$
$12$	0.876307	+	0.481754i	0.252968	+	0.139070i
$13$	0.655738	+	1.39351i	0.181869	+	0.386491i	0.974885	−	0.222710i	$-0.0714903\pi$
$13$	0.655738	+	1.39351i	0.181869	+	0.386491i	−0.793016	+	0.609201i	$0.791490\pi$
$14$	−2.04991	+	4.35628i	−0.547861	+	1.16426i
$15$	−2.23474	−	0.0769525i	−0.577008	−	0.0198691i
$16$	−0.992115	+	0.125333i	−0.248029	+	0.0313333i
$17$	0.202923	−	3.22537i	0.0492161	−	0.782267i	−0.893581	−	0.448901i	$-0.851816\pi$
$17$	0.202923	−	3.22537i	0.0492161	−	0.782267i	0.942798	−	0.333366i	$-0.108184\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	1.94495	+	3.06476i	0.446203	+	0.703104i	0.990761	−	0.135620i	$-0.0433025\pi$
$19$	1.94495	+	3.06476i	0.446203	+	0.703104i	−0.544558	+	0.838723i	$0.683302\pi$
$20$	1.85318	−	1.25129i	0.414383	−	0.279798i
$21$	−4.66323	−	1.19731i	−1.01760	−	0.261275i
$22$	0.0896331	+	1.42468i	0.0191098	+	0.303742i
$23$	0.446225	+	2.33919i	0.0930443	+	0.487755i	0.998054	+	0.0623632i	$0.0198637\pi$
$23$	0.446225	+	2.33919i	0.0930443	+	0.487755i	−0.905009	+	0.425392i	$0.860136\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	−2.43506	+	4.36698i	−0.487012	+	0.873395i
$26$	0.475913	−	1.46471i	0.0933343	−	0.287253i
$27$	−0.992115	−	0.125333i	−0.190933	−	0.0241204i
$28$	4.47639	−	1.77233i	0.845959	−	0.334939i
$29$	−2.84216	+	1.12529i	−0.527777	+	0.208962i	−0.616875	−	0.787061i	$-0.711602\pi$
$29$	−2.84216	+	1.12529i	−0.527777	+	0.208962i	0.0890981	+	0.996023i	$0.471602\pi$
$30$	1.57638	+	1.58588i	0.287806	+	0.289541i
$31$	−0.474555	+	7.54283i	−0.0852326	+	1.35473i	0.690345	+	0.723481i	$0.257459\pi$
$31$	−0.474555	+	7.54283i	−0.0852326	+	1.35473i	−0.775577	+	0.631253i	$0.782541\pi$
$32$	0.809017	+	0.587785i	0.143015	+	0.103907i
$33$	−1.38265	+	0.355003i	−0.240688	+	0.0617981i
$34$	−2.35584	+	2.21228i	−0.404023	+	0.379403i
$35$	−7.14360	+	8.05390i	−1.20749	+	1.36136i
$36$	0.876307	−	0.481754i	0.146051	−	0.0802923i
$37$	−0.180338	+	0.0227820i	−0.0296475	+	0.00374535i	−0.140143	−	0.990131i	$-0.544756\pi$
$37$	−0.180338	+	0.0227820i	−0.0296475	+	0.00374535i	0.110496	+	0.993877i	$0.464756\pi$
$38$	0.680160	−	3.56553i	0.110337	−	0.578405i
$39$	1.52794	+	0.193024i	0.244667	+	0.0309086i
$40$	−2.20748	−	0.356433i	−0.349033	−	0.0563571i
$41$	1.50131	−	7.87012i	0.234464	−	1.22911i	−0.649066	−	0.760732i	$-0.724840\pi$
$41$	1.50131	−	7.87012i	0.234464	−	1.22911i	0.883530	−	0.468374i	$-0.155160\pi$
$42$	2.57973	+	4.06500i	0.398061	+	0.627244i
$43$	7.96085	−	5.78390i	1.21402	−	0.882036i	0.218429	−	0.975853i	$-0.429907\pi$
$43$	7.96085	−	5.78390i	1.21402	−	0.882036i	0.995589	+	0.0938168i	$0.0299068\pi$
$44$	0.909919	−	1.09990i	0.137175	−	0.165817i
$45$	−1.26241	+	1.84562i	−0.188189	+	0.275129i
$46$	1.27600	−	2.01066i	0.188136	−	0.296455i
$47$	−4.06660	−	4.91568i	−0.593175	−	0.717026i	0.385438	−	0.922734i	$-0.374050\pi$
$47$	−4.06660	−	4.91568i	−0.593175	−	0.717026i	−0.978613	+	0.205708i	$0.934050\pi$
$48$	−0.425779	+	0.904827i	−0.0614559	+	0.130601i
$49$	−13.0893	+	9.50993i	−1.86990	+	1.35856i
$50$	4.76448	−	1.51648i	0.673800	−	0.214462i
$51$	−2.61454	−	1.89957i	−0.366108	−	0.265993i
$52$	−1.34959	+	0.741943i	−0.187154	+	0.102889i
$53$	−9.50471	−	2.44039i	−1.30557	−	0.335214i	−0.469062	−	0.883165i	$-0.655408\pi$
$53$	−9.50471	−	2.44039i	−1.30557	−	0.335214i	−0.836510	+	0.547951i	$0.815408\pi$
$54$	0.637424	+	0.770513i	0.0867424	+	0.104854i
$55$	−0.705665	+	3.11299i	−0.0951519	+	0.419756i
$56$	−4.47639	−	1.77233i	−0.598183	−	0.236838i
$57$	3.62982			0.480781
$58$	2.84216	+	1.12529i	0.373195	+	0.147758i
$59$	−10.9356	−	6.01191i	−1.42370	−	0.782684i	−0.430890	−	0.902405i	$-0.641800\pi$
$59$	−10.9356	−	6.01191i	−1.42370	−	0.782684i	−0.992808	+	0.119721i	$0.961800\pi$
$60$	−0.0635200	−	2.23517i	−0.00820040	−	0.288559i
$61$	−1.82715	−	9.57824i	−0.233942	−	1.22637i	−0.884365	−	0.466796i	$-0.845408\pi$
$61$	−1.82715	−	9.57824i	−0.233942	−	1.22637i	0.650423	−	0.759572i	$-0.274592\pi$
$62$	5.50936	−	5.17363i	0.699690	−	0.657052i
$63$	−3.50961	+	3.29574i	−0.442169	+	0.415224i
$64$	−0.187381	−	0.982287i	−0.0234227	−	0.122786i
$65$	1.94422	−	2.84242i	0.241151	−	0.352559i
$66$	1.25092	+	0.687700i	0.153978	+	0.0846500i
$67$	13.5094	+	5.34873i	1.65043	+	0.653452i	0.994820	−	0.101648i	$-0.0324114\pi$
$67$	13.5094	+	5.34873i	1.65043	+	0.653452i	0.655610	+	0.755099i	$0.272411\pi$
$68$	3.23175			0.391907
$69$	2.21414	+	0.876641i	0.266552	+	0.105535i
$70$	10.7207	−	0.980912i	1.28137	−	0.117241i
$71$	5.57607	+	6.74031i	0.661758	+	0.799928i	0.989453	−	0.144856i	$-0.0462718\pi$
$71$	5.57607	+	6.74031i	0.661758	+	0.799928i	−0.327695	+	0.944784i	$0.606272\pi$
$72$	−0.968583	−	0.248690i	−0.114149	−	0.0293084i
$73$	1.41440	−	0.777573i	0.165543	−	0.0910080i	−0.396828	−	0.917893i	$-0.629889\pi$
$73$	1.41440	−	0.777573i	0.165543	−	0.0910080i	0.562371	+	0.826885i	$0.309889\pi$
$74$	0.147056	+	0.106843i	0.0170950	+	0.0124202i
$75$	2.38239	+	4.39593i	0.275095	+	0.507598i
$76$	−2.93659	+	2.13355i	−0.336850	+	0.244735i
$77$	−2.92623	+	6.21856i	−0.333475	+	0.708670i
$78$	−0.981689	−	1.18666i	−0.111154	−	0.134363i
$79$	−5.49069	+	8.65194i	−0.617750	+	0.973419i	0.381055	+	0.924552i	$0.375561\pi$
$79$	−5.49069	+	8.65194i	−0.617750	+	0.973419i	−0.998805	+	0.0488664i	$0.984439\pi$
$80$	1.36519	+	1.77095i	0.152632	+	0.197998i
$81$	−0.637424	+	0.770513i	−0.0708249	+	0.0856126i
$82$	−6.48187	+	4.70935i	−0.715803	+	0.520061i
$83$	−3.35959	−	5.29386i	−0.368763	−	0.581077i	0.608384	−	0.793643i	$-0.291818\pi$
$83$	−3.35959	−	5.29386i	−0.368763	−	0.581077i	−0.977147	+	0.212566i	$0.931818\pi$
$84$	0.902144	−	4.72921i	0.0984320	−	0.515999i
$85$	−6.44860	+	3.26135i	−0.699449	+	0.353744i
$86$	−9.76256	−	1.23330i	−1.05272	−	0.132990i
$87$	−0.572792	+	3.00268i	−0.0614098	+	0.321921i
$88$	−1.41624	+	0.178912i	−0.150971	+	0.0190721i
$89$	9.59159	−	5.27302i	1.01671	−	0.558939i	0.115946	−	0.993256i	$-0.463010\pi$
$89$	9.59159	−	5.27302i	1.01671	−	0.558939i	0.900760	+	0.434316i	$0.143010\pi$
$90$	2.18367	−	0.481223i	0.230179	−	0.0507254i
$91$	5.40511	−	5.07573i	0.566609	−	0.532081i
$92$	−2.30656	+	0.592223i	−0.240475	+	0.0617435i
$93$	6.11435	+	4.44233i	0.634028	+	0.460648i
$94$	−0.400588	+	6.36716i	−0.0413175	+	0.656722i
$95$	3.70654	−	7.22077i	0.380283	−	0.740835i
$96$	0.929776	−	0.368125i	0.0948949	−	0.0375716i
$97$	−5.72717	+	2.26755i	−0.581506	+	0.230235i	−0.640415	−	0.768029i	$-0.721238\pi$
$97$	−5.72717	+	2.26755i	−0.581506	+	0.230235i	0.0589092	+	0.998263i	$0.481238\pi$
$98$	16.0517	+	2.02780i	1.62146	+	0.204839i
$99$	−0.441120	+	1.35763i	−0.0443342	+	0.136447i
$100$	−4.51126	−	2.15605i	−0.451126	−	0.215605i
$101$	0.296737	+	0.913264i	0.0295265	+	0.0908732i	0.964734	−	0.263228i	$-0.0847870\pi$
$101$	0.296737	+	0.913264i	0.0295265	+	0.0908732i	−0.935207	+	0.354101i	$0.884787\pi$
$102$	0.605569	+	3.17450i	0.0599603	+	0.314323i
$103$	0.422667	+	6.71810i	0.0416466	+	0.661954i	0.962371	+	0.271740i	$0.0875990\pi$
$103$	0.422667	+	6.71810i	0.0416466	+	0.661954i	−0.920724	+	0.390214i	$0.872401\pi$
$104$	1.49170	+	0.383004i	0.146274	+	0.0375567i
$105$	2.97240	+	10.3470i	0.290077	+	1.00977i
$106$	5.25807	+	8.28539i	0.510709	+	0.804748i
$107$	0.624824	−	1.92301i	0.0604040	−	0.185904i	−0.916301	−	0.400490i	$-0.868840\pi$
$107$	0.624824	−	1.92301i	0.0604040	−	0.185904i	0.976705	+	0.214585i	$0.0688400\pi$
$108$	0.0627905	−	0.998027i	0.00604202	−	0.0960352i
$109$	−0.648718	+	0.0819522i	−0.0621360	+	0.00784960i	−0.156340	−	0.987703i	$-0.549969\pi$
$109$	−0.648718	+	0.0819522i	−0.0621360	+	0.00784960i	0.0942038	+	0.995553i	$0.469969\pi$
$110$	2.64540	−	1.78621i	0.252229	−	0.170309i
$111$	−0.0773947	+	0.164472i	−0.00734598	+	0.0156110i
$112$	2.04991	+	4.35628i	0.193698	+	0.411629i
$113$	0.738769	+	0.406142i	0.0694976	+	0.0382066i	0.516124	−	0.856514i	$-0.327375\pi$
$113$	0.738769	+	0.406142i	0.0694976	+	0.0382066i	−0.446626	+	0.894721i	$0.647375\pi$
$114$	−2.64602	−	2.48478i	−0.247823	−	0.232721i
$115$	4.00484	−	3.50941i	0.373453	−	0.327254i
$116$	−1.30153	−	2.76590i	−0.120844	−	0.256807i
$117$	0.981689	−	1.18666i	0.0907572	−	0.109707i
$118$	3.85629	+	11.8684i	0.355000	+	1.09258i
$119$	−15.0704	+	3.86941i	−1.38150	+	0.354709i
$120$	−1.48377	+	1.67285i	−0.135449	+	0.152709i
$121$	−0.562745	−	8.94458i	−0.0511586	−	0.813143i
$122$	−5.22482	+	8.23301i	−0.473033	+	0.745381i
$123$	−5.84052	−	5.48461i	−0.526622	−	0.494531i
$124$	−7.55775			−0.678706
$125$	11.1775	−	0.250426i	0.999749	−	0.0223988i
$126$	4.81448			0.428908
$127$	−13.4866	−	12.6648i	−1.19675	−	1.12382i	−0.989349	−	0.145561i	$-0.953501\pi$
$127$	−13.4866	−	12.6648i	−1.19675	−	1.12382i	−0.207396	−	0.978257i	$-0.566499\pi$
$128$	−0.535827	+	0.844328i	−0.0473608	+	0.0746288i
$129$	−0.617868	−	9.82074i	−0.0544003	−	0.864668i
$130$	−3.36305	+	0.741126i	−0.294959	+	0.0650011i
$131$	3.09497	−	0.794654i	0.270409	−	0.0694293i	−0.111051	−	0.993815i	$-0.535422\pi$
$131$	3.09497	−	0.794654i	0.270409	−	0.0694293i	0.381460	+	0.924386i	$0.375422\pi$
$132$	−0.441120	−	1.35763i	−0.0383945	−	0.118166i
$133$	11.1394	−	13.4653i	0.965912	−	1.16759i
$134$	−6.18644	−	13.1469i	−0.534427	−	1.13571i
$135$	0.881879	+	2.05482i	0.0759000	+	0.176851i
$136$	−2.35584	−	2.21228i	−0.202012	−	0.189702i
$137$	12.2023	+	6.70829i	1.04252	+	0.573128i	0.908514	−	0.417854i	$-0.137217\pi$
$137$	12.2023	+	6.70829i	1.04252	+	0.573128i	0.134001	+	0.990981i	$0.457217\pi$
$138$	−1.01394	−	2.15473i	−0.0863122	−	0.183423i
$139$	−4.43789	+	9.43100i	−0.376417	+	0.799927i	0.623420	+	0.781887i	$0.285743\pi$
$139$	−4.43789	+	9.43100i	−0.376417	+	0.799927i	−0.999837	+	0.0180398i	$0.994257\pi$
$140$	−8.48656	−	6.62379i	−0.717245	−	0.559813i
$141$	−6.32944	+	0.799594i	−0.533035	+	0.0673380i
$142$	0.549280	−	8.73056i	0.0460946	−	0.732652i
$143$	0.679363	−	2.09087i	0.0568112	−	0.174847i
$144$	0.535827	+	0.844328i	0.0446522	+	0.0703607i
$145$	5.38831	+	4.20560i	0.447475	+	0.349256i
$146$	−1.56334	−	0.401397i	−0.129383	−	0.0332198i
$147$	1.01590	+	16.1473i	0.0837904	+	1.33181i
$148$	−0.0340606	−	0.178552i	−0.00279977	−	0.0146769i
$149$	−1.40469	−	4.32318i	−0.115076	−	0.354169i	0.876887	−	0.480697i	$-0.159616\pi$
$149$	−1.40469	−	4.32318i	−0.115076	−	0.354169i	−0.991963	+	0.126529i	$0.959616\pi$
$150$	1.27253	−	4.83536i	0.103902	−	0.394805i
$151$	5.94929	−	18.3100i	0.484146	−	1.49005i	−0.349067	−	0.937098i	$-0.613502\pi$
$151$	5.94929	−	18.3100i	0.484146	−	1.49005i	0.833214	−	0.552951i	$-0.186498\pi$
$152$	3.60120	+	0.454937i	0.292096	+	0.0369003i
$153$	−3.00480	+	1.18969i	−0.242924	+	0.0961803i
$154$	6.39002	−	2.52999i	0.514923	−	0.203872i
$155$	15.0807	−	7.62699i	1.21131	−	0.612615i
$156$	−0.0967029	+	1.53705i	−0.00774243	+	0.123062i
$157$	−3.00273	−	2.18161i	−0.239644	−	0.174112i	0.461481	−	0.887150i	$-0.347318\pi$
$157$	−3.00273	−	2.18161i	−0.239644	−	0.174112i	−0.701125	+	0.713039i	$0.747318\pi$
$158$	9.92520	−	2.54836i	0.789606	−	0.202736i
$159$	−7.15337	+	6.71746i	−0.567299	+	0.532729i
$160$	0.217121	−	2.22550i	0.0171650	−	0.175941i
$161$	10.0469	−	5.52334i	0.791809	−	0.435300i
$162$	0.992115	−	0.125333i	0.0779479	−	0.00984711i
$163$	4.35551	−	22.8324i	0.341150	−	1.78837i	−0.236021	−	0.971748i	$-0.575843\pi$
$163$	4.35551	−	22.8324i	0.341150	−	1.78837i	0.577171	−	0.816623i	$-0.304157\pi$
$164$	7.94885	+	1.00417i	0.620701	+	0.0784128i
$165$	2.25027	+	2.26384i	0.175183	+	0.176240i
$166$	−1.17486	+	6.15885i	−0.0911872	+	0.478020i
$167$	5.48017	+	8.63536i	0.424068	+	0.668224i	0.987443	−	0.157977i	$-0.0504973\pi$
$167$	5.48017	+	8.63536i	0.424068	+	0.668224i	−0.563375	+	0.826201i	$0.690497\pi$
$168$	−3.89500	+	2.82988i	−0.300506	+	0.218330i
$169$	6.77462	−	8.18911i	0.521125	−	0.629932i
$170$	6.93338	+	2.03695i	0.531766	+	0.156227i
$171$	1.94495	−	3.06476i	0.148734	−	0.234368i
$172$	6.27235	+	7.58197i	0.478262	+	0.578120i
$173$	4.84995	−	10.3067i	0.368735	−	0.783602i	−0.631233	−	0.775593i	$-0.717451\pi$
$173$	4.84995	−	10.3067i	0.368735	−	0.783602i	0.999968	−	0.00800866i	$-0.00254926\pi$
$174$	2.47302	−	1.79676i	0.187479	−	0.136212i
$175$	23.6185	+	4.65276i	1.78539	+	0.351715i
$176$	1.15487	+	0.839060i	0.0870513	+	0.0632465i
$177$	−10.9356	+	6.01191i	−0.821972	+	0.451883i
$178$	−10.6016	−	2.72203i	−0.794623	−	0.204025i
$179$	−7.08363	−	8.56263i	−0.529455	−	0.640001i	0.436193	−	0.899853i	$-0.356326\pi$
$179$	−7.08363	−	8.56263i	−0.529455	−	0.640001i	−0.965649	+	0.259852i	$0.916326\pi$
$180$	−1.92125	−	1.14403i	−0.143201	−	0.0852710i
$181$	−20.5743	−	8.14596i	−1.52928	−	0.605484i	−0.555205	−	0.831713i	$-0.687360\pi$
$181$	−20.5743	−	8.14596i	−1.52928	−	0.605484i	−0.974074	+	0.226229i	$0.927360\pi$
$182$	−7.41473			−0.549616
$183$	−9.06621	−	3.58957i	−0.670194	−	0.265348i
$184$	2.08681	+	1.14723i	0.153842	+	0.0845753i
$185$	0.248152	+	0.321909i	0.0182445	+	0.0236672i
$186$	−1.41618	−	7.42388i	−0.103839	−	0.544345i
$187$	−3.36295	+	3.15802i	−0.245923	+	0.230937i
$188$	4.65064	−	4.36724i	0.339182	−	0.318514i
$189$	0.902144	+	4.72921i	0.0656214	+	0.343999i
$190$	−7.64491	+	2.72641i	−0.554620	+	0.197795i
$191$	−1.85599	−	1.02034i	−0.134295	−	0.0738293i	0.413190	−	0.910645i	$-0.364415\pi$
$191$	−1.85599	−	1.02034i	−0.134295	−	0.0738293i	−0.547485	+	0.836816i	$0.684415\pi$
$192$	−0.929776	−	0.368125i	−0.0671008	−	0.0265671i
$193$	3.47469			0.250114			0.125057	−	0.992150i	$-0.460089\pi$
$193$	3.47469			0.250114			0.125057	+	0.992150i	$0.460089\pi$
$194$	5.72717	+	2.26755i	0.411187	+	0.162800i
$195$	−1.35817	−	3.16461i	−0.0972606	−	0.226622i
$196$	−10.3130	−	12.4663i	−0.736646	−	0.890452i
$197$	−2.55881	−	0.656992i	−0.182308	−	0.0468087i	0.156432	−	0.987689i	$-0.450001\pi$
$197$	−2.55881	−	0.656992i	−0.182308	−	0.0468087i	−0.338740	+	0.940880i	$0.610001\pi$
$198$	1.25092	−	0.687700i	0.0888992	−	0.0488727i
$199$	13.2045	+	9.59363i	0.936042	+	0.680074i	0.947465	−	0.319860i	$-0.103636\pi$
$199$	13.2045	+	9.59363i	0.936042	+	0.680074i	−0.0114225	+	0.999935i	$0.503636\pi$
$200$	1.81265	+	4.65986i	0.128174	+	0.329502i
$201$	11.7548	−	8.54033i	0.829117	−	0.602389i
$202$	0.408860	−	0.868872i	0.0287673	−	0.0611336i
$203$	9.38100	+	11.3397i	0.658417	+	0.795889i
$204$	1.73166	−	2.72865i	0.121240	−	0.191044i
$205$	−16.8745	+	6.01796i	−1.17856	+	0.420313i
$206$	4.29074	−	5.18662i	0.298950	−	0.361369i
$207$	1.92657	−	1.39974i	0.133906	−	0.0972883i
$208$	−0.825220	−	1.30034i	−0.0572187	−	0.0901623i
$209$	0.970925	−	5.08976i	0.0671603	−	0.352066i
$210$	4.91624	−	9.57741i	0.339253	−	0.660904i
$211$	13.9914	+	1.76752i	0.963205	+	0.121681i	0.591178	−	0.806541i	$-0.298663\pi$
$211$	13.9914	+	1.76752i	0.963205	+	0.121681i	0.372027	+	0.928222i	$0.378663\pi$
$212$	1.83877	−	9.63919i	0.126287	−	0.662022i
$213$	8.67884	−	1.09639i	0.594664	−	0.0751236i
$214$	−1.77187	+	0.974092i	−0.121122	+	0.0665876i
$215$	−20.1672	−	8.79919i	−1.37539	−	0.600100i
$216$	−0.728969	+	0.684547i	−0.0496000	+	0.0465775i
$217$	35.2435	−	9.04899i	2.39249	−	0.614286i
$218$	0.528995	+	0.384338i	0.0358281	+	0.0260306i
$219$	0.101347	−	1.61086i	0.00684838	−	0.108852i
$220$	−3.15116	−	0.508806i	−0.212451	−	0.0343037i
$221$	4.62766	−	1.83222i	0.311290	−	0.123248i
$222$	0.169007	−	0.0669147i	0.0113430	−	0.00449102i
$223$	−5.84452	−	0.738334i	−0.391378	−	0.0494425i	−0.0728179	−	0.997345i	$-0.523199\pi$
$223$	−5.84452	−	0.738334i	−0.391378	−	0.0494425i	−0.318560	+	0.947903i	$0.603199\pi$
$224$	1.48776	−	4.57885i	0.0994050	−	0.305937i
$225$	4.98816	+	0.343938i	0.332544	+	0.0229292i
$226$	−0.260516	−	0.801787i	−0.0173293	−	0.0533341i
$227$	4.84690	+	25.4084i	0.321700	+	1.68641i	0.664727	+	0.747086i	$0.268548\pi$
$227$	4.84690	+	25.4084i	0.321700	+	1.68641i	−0.343027	+	0.939326i	$0.611452\pi$
$228$	0.227918	+	3.62266i	0.0150943	+	0.239916i
$229$	−7.49269	−	1.92380i	−0.495131	−	0.127128i	−0.00713615	−	0.999975i	$-0.502272\pi$
$229$	−7.49269	−	1.92380i	−0.495131	−	0.127128i	−0.487995	+	0.872846i	$0.662272\pi$
$230$	−5.32176	−	0.183253i	−0.350906	−	0.0120833i
$231$	3.68255	+	5.80277i	0.242294	+	0.381794i
$232$	−0.944611	+	2.90721i	−0.0620168	+	0.190868i
$233$	1.09942	−	17.4748i	0.0720254	−	1.14481i	−0.781550	−	0.623842i	$-0.785571\pi$
$233$	1.09942	−	17.4748i	0.0720254	−	1.14481i	0.853576	−	0.520969i	$-0.174429\pi$
$234$	−1.52794	+	0.193024i	−0.0998848	+	0.0126184i
$235$	−4.87260	+	13.4076i	−0.317853	+	0.874615i
$236$	5.31339	−	11.2915i	0.345873	−	0.735016i
$237$	4.36301	+	9.27188i	0.283408	+	0.602273i
$238$	13.6346	+	7.49570i	0.883801	+	0.485874i
$239$	6.12066	+	5.74768i	0.395912	+	0.371787i	0.856780	−	0.515683i	$-0.172462\pi$
$239$	6.12066	+	5.74768i	0.395912	+	0.371787i	−0.460867	+	0.887469i	$0.652462\pi$
$240$	2.22677	−	0.203742i	0.143737	−	0.0131515i
$241$	−7.85810	−	16.6993i	−0.506185	−	1.07570i	−0.980712	−	0.195457i	$-0.937381\pi$
$241$	−7.85810	−	16.6993i	−0.506185	−	1.07570i	0.474527	−	0.880241i	$-0.342619\pi$
$242$	−5.71276	+	6.90554i	−0.367230	+	0.443905i
$243$	0.309017	+	0.951057i	0.0198234	+	0.0610103i
$244$	9.44461	−	2.42496i	0.604629	−	0.155242i
$245$	33.1591	+	14.4677i	2.11846	+	0.924307i
$246$	0.503080	+	7.99622i	0.0320752	+	0.509820i
$247$	−2.99540	+	4.72000i	−0.190593	+	0.300326i
$248$	5.50936	+	5.17363i	0.349845	+	0.328526i
$249$	−6.26991			−0.397340
$250$	−8.31950	−	7.46900i	−0.526171	−	0.472381i
$251$	−17.5020			−1.10472			−0.552358	−	0.833607i	$-0.686272\pi$
$251$	−17.5020			−1.10472			−0.552358	+	0.833607i	$0.686272\pi$
$252$	−3.50961	−	3.29574i	−0.221085	−	0.207612i
$253$	1.82149	−	2.87020i	0.114516	−	0.180448i
$254$	1.16169	+	18.4645i	0.0728907	+	1.15856i
$255$	−0.701681	+	7.19226i	−0.0439410	+	0.450397i
$256$	0.968583	−	0.248690i	0.0605364	−	0.0155431i
$257$	−8.67398	−	26.6958i	−0.541068	−	1.66524i	−0.730159	−	0.683277i	$-0.760554\pi$
$257$	−8.67398	−	26.6958i	−0.541068	−	1.66524i	0.189091	−	0.981960i	$-0.439446\pi$
$258$	−6.27235	+	7.58197i	−0.390499	+	0.472033i
$259$	0.372615	+	0.791848i	0.0231532	+	0.0492030i
$260$	2.95889	+	1.76191i	0.183503	+	0.109269i
$261$	2.22833	+	2.09254i	0.137930	+	0.129525i
$262$	−2.80012	−	1.53938i	−0.172992	−	0.0951030i
$263$	2.25969	+	4.80209i	0.139339	+	0.296110i	0.962301	−	0.271986i	$-0.0876804\pi$
$263$	2.25969	+	4.80209i	0.139339	+	0.296110i	−0.822963	+	0.568096i	$0.807680\pi$
$264$	−0.607797	+	1.29163i	−0.0374073	+	0.0794946i
$265$	6.05842	+	21.0896i	0.372166	+	1.29552i
$266$	−17.3379	+	2.19029i	−1.06306	+	0.134295i
$267$	0.687272	−	10.9239i	0.0420604	−	0.668530i
$268$	−4.48992	+	13.8186i	−0.274265	+	0.844102i
$269$	−5.68963	−	8.96542i	−0.346903	−	0.546631i	0.625416	−	0.780292i	$-0.284929\pi$
$269$	−5.68963	−	8.96542i	−0.346903	−	0.546631i	−0.972318	+	0.233661i	$0.924929\pi$
$270$	0.763760	−	2.10159i	0.0464809	−	0.127899i
$271$	4.97125	+	1.27640i	0.301982	+	0.0775358i	0.396641	−	0.917974i	$-0.370176\pi$
$271$	4.97125	+	1.27640i	0.301982	+	0.0775358i	−0.0946586	+	0.995510i	$0.530176\pi$
$272$	0.202923	+	3.22537i	0.0123040	+	0.195567i
$273$	−1.38938	−	7.28339i	−0.0840892	−	0.440811i
$274$	−4.30298	−	13.2432i	−0.259952	−	0.800051i
$275$	6.80127	−	2.16476i	0.410132	−	0.130540i
$276$	−0.735884	+	2.26482i	−0.0442950	+	0.136326i
$277$	25.2018	+	3.18373i	1.51423	+	0.191292i	0.838112	−	0.545499i	$-0.183660\pi$
$277$	25.2018	+	3.18373i	1.51423	+	0.191292i	0.676121	+	0.736791i	$0.263660\pi$
$278$	9.69104	−	3.83696i	0.581230	−	0.230125i
$279$	7.02702	−	2.78219i	0.420696	−	0.166566i
$280$	1.65214	+	10.6380i	0.0987341	+	0.635741i
$281$	0.348869	−	5.54511i	0.0208118	−	0.330794i	−0.973820	−	0.227319i	$-0.927004\pi$
$281$	0.348869	−	5.54511i	0.0208118	−	0.330794i	0.994632	−	0.103475i	$-0.0329960\pi$
$282$	5.16132	+	3.74992i	0.307352	+	0.223305i
$283$	−19.1713	+	4.92234i	−1.13961	+	0.292603i	−0.770910	−	0.636944i	$-0.780198\pi$
$283$	−19.1713	+	4.92234i	−1.13961	+	0.292603i	−0.368703	+	0.929547i	$0.620198\pi$
$284$	−6.37689	+	5.98830i	−0.378399	+	0.355340i
$285$	−4.11063	−	6.99862i	−0.243493	−	0.414562i
$286$	−1.92653	+	1.05912i	−0.113918	+	0.0626270i
$287$	−38.2696	+	4.83458i	−2.25899	+	0.285376i
$288$	0.187381	−	0.982287i	0.0110415	−	0.0578818i
$289$	6.50412	+	0.821662i	0.382595	+	0.0483330i
$290$	−1.04898	−	6.75430i	−0.0615982	−	0.396626i
$291$	−1.15422	+	6.05062i	−0.0676615	+	0.354694i
$292$	0.864849	+	1.36278i	0.0506115	+	0.0797509i
$293$	−9.72535	+	7.06588i	−0.568161	+	0.412793i	−0.834437	−	0.551104i	$-0.814207\pi$
$293$	−9.72535	+	7.06588i	−0.568161	+	0.412793i	0.266276	+	0.963897i	$0.414207\pi$
$294$	10.3130	−	12.4663i	0.601469	−	0.727051i
$295$	0.792680	+	27.8931i	0.0461516	+	1.62400i
$296$	−0.0973982	+	0.153475i	−0.00566115	+	0.00892055i
$297$	0.909919	+	1.09990i	0.0527988	+	0.0638228i
$298$	−1.93545	+	4.11304i	−0.112117	+	0.238262i
$299$	−2.96709	+	2.15572i	−0.171591	+	0.124668i
$300$	−4.23767	+	2.65371i	−0.244662	+	0.153212i
$301$	−38.3274	−	27.8465i	−2.20915	−	1.60504i
$302$	−16.8709	+	9.27487i	−0.970812	+	0.533709i
$303$	0.930094	+	0.238808i	0.0534325	+	0.0137191i
$304$	−2.31373	−	2.79682i	−0.132702	−	0.160409i
$305$	−16.3985	+	14.3699i	−0.938977	+	0.822818i
$306$	3.00480	+	1.18969i	0.171773	+	0.0680098i
$307$	22.2930			1.27233			0.636163	−	0.771555i	$-0.280521\pi$
$307$	22.2930			1.27233			0.636163	+	0.771555i	$0.280521\pi$
$308$	−6.39002	−	2.52999i	−0.364105	−	0.144160i
$309$	5.89875	+	3.24287i	0.335568	+	0.184480i
$310$	−16.2144	−	4.76360i	−0.920915	−	0.270554i
$311$	6.58303	+	34.5095i	0.373290	+	1.95685i	0.273654	+	0.961828i	$0.411768\pi$
$311$	6.58303	+	34.5095i	0.373290	+	1.95685i	0.0996357	+	0.995024i	$0.468232\pi$
$312$	1.12268	−	1.05426i	0.0635590	−	0.0596859i
$313$	10.1425	−	9.52446i	0.573289	−	0.538354i	−0.342759	−	0.939424i	$-0.611361\pi$
$313$	10.1425	−	9.52446i	0.573289	−	0.538354i	0.916048	+	0.401069i	$0.131361\pi$
$314$	0.695481	+	3.64584i	0.0392483	+	0.205747i
$315$	10.3290	+	3.03454i	0.581972	+	0.170977i
$316$	−8.97963	−	4.93659i	−0.505143	−	0.277705i
$317$	−7.59965	−	3.00891i	−0.426839	−	0.168997i	0.144876	−	0.989450i	$-0.453722\pi$
$317$	−7.59965	−	3.00891i	−0.426839	−	0.168997i	−0.571715	+	0.820452i	$0.693722\pi$
$318$	9.81300			0.550286
$319$	4.05717	+	1.60635i	0.227158	+	0.0899382i
$320$	−1.68174	+	1.47369i	−0.0940119	+	0.0823818i
$321$	−1.28885	−	1.55796i	−0.0719368	−	0.0869566i
$322$	−11.1049	−	2.85125i	−0.618851	−	0.158894i
$323$	10.2797	−	5.65129i	0.571975	−	0.314446i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−7.68220	−	0.529695i	−0.426132	−	0.0293822i
$326$	−18.8049	+	13.6625i	−1.04151	+	0.756699i
$327$	−0.278406	+	0.591643i	−0.0153959	+	0.0327179i
$328$	−5.10706	−	6.17338i	−0.281990	−	0.340868i
$329$	−16.4580	+	25.9337i	−0.907360	+	1.42977i
$330$	−0.0906744	−	3.19068i	−0.00499146	−	0.175641i
$331$	−7.25547	+	8.77036i	−0.398797	+	0.482063i	−0.931242	−	0.364402i	$-0.881273\pi$
$331$	−7.25547	+	8.77036i	−0.398797	+	0.482063i	0.532445	+	0.846465i	$0.321273\pi$
$332$	5.07247	−	3.68536i	0.278388	−	0.202261i
$333$	0.0973982	+	0.153475i	0.00533739	+	0.00841038i
$334$	1.91644	−	10.0463i	0.104863	−	0.549711i
$335$	−4.98600	−	32.1045i	−0.272414	−	1.75406i
$336$	4.77652	+	0.603415i	0.260581	+	0.0329190i
$337$	1.65897	−	8.69664i	0.0903701	−	0.473736i	−0.908115	−	0.418720i	$-0.862479\pi$
$337$	1.65897	−	8.69664i	0.0903701	−	0.473736i	0.998485	−	0.0550164i	$-0.0175211\pi$
$338$	−10.5443	+	1.33206i	−0.573536	+	0.0724544i
$339$	0.738769	−	0.406142i	0.0401244	−	0.0220586i
$340$	−3.65983	−	6.23110i	−0.198482	−	0.337929i
$341$	7.86458	−	7.38533i	0.425891	−	0.399938i
$342$	−3.51578	+	0.902699i	−0.190112	+	0.0488124i
$343$	35.7532	+	25.9762i	1.93049	+	1.40258i
$344$	0.617868	−	9.82074i	0.0333132	−	0.529499i
$345$	−0.817191	−	5.26183i	−0.0439961	−	0.283287i
$346$	−10.5909	+	4.19322i	−0.569369	+	0.225429i
$347$	−14.2534	+	5.64333i	−0.765164	+	0.302950i	−0.718098	−	0.695942i	$-0.754987\pi$
$347$	−14.2534	+	5.64333i	−0.765164	+	0.302950i	−0.0470661	+	0.998892i	$0.514987\pi$
$348$	−3.03272	−	0.383122i	−0.162571	−	0.0205375i
$349$	−1.57259	+	4.83993i	−0.0841787	+	0.259075i	−0.984283	−	0.176600i	$-0.943490\pi$
$349$	−1.57259	+	4.83993i	−0.0841787	+	0.259075i	0.900104	+	0.435675i	$0.143490\pi$
$350$	−14.0321	−	19.5597i	−0.750048	−	1.04551i
$351$	−0.475913	−	1.46471i	−0.0254024	−	0.0781805i
$352$	−0.267486	−	1.40221i	−0.0142570	−	0.0747380i
$353$	−0.451756	−	7.18046i	−0.0240446	−	0.382177i	−0.991585	−	0.129460i	$-0.958676\pi$
$353$	−0.451756	−	7.18046i	−0.0240446	−	0.382177i	0.967540	−	0.252717i	$-0.0813243\pi$
$354$	12.0872	+	3.10346i	0.642426	+	0.164947i
$355$	6.68123	−	18.3843i	0.354603	−	0.975738i
$356$	5.86488	+	9.24157i	0.310838	+	0.489802i
$357$	−4.80805	+	14.7977i	−0.254469	+	0.783176i
$358$	−0.697785	+	11.0910i	−0.0368791	+	0.586176i
$359$	−25.2764	+	3.19315i	−1.33404	+	0.168528i	−0.759798	−	0.650159i	$-0.774702\pi$
$359$	−25.2764	+	3.19315i	−1.33404	+	0.168528i	−0.574240	+	0.818687i	$0.694702\pi$
$360$	0.617388	+	2.14915i	0.0325392	+	0.113270i
$361$	2.47991	−	5.27008i	0.130522	−	0.277373i
$362$	9.42176	+	20.0223i	0.495197	+	1.05235i
$363$	−7.85369	−	4.31760i	−0.412212	−	0.226615i
$364$	5.40511	+	5.07573i	0.283305	+	0.266041i
$365$	−3.10098	−	1.84652i	−0.162313	−	0.0966511i
$366$	4.15176	+	8.82293i	0.217016	+	0.461182i
$367$	12.4537	−	15.0539i	0.650077	−	0.785808i	−0.337771	−	0.941228i	$-0.609673\pi$
$367$	12.4537	−	15.0539i	0.650077	−	0.785808i	0.987849	+	0.155420i	$0.0496730\pi$
$368$	−0.735884	−	2.26482i	−0.0383606	−	0.118062i
$369$	−7.76032	+	1.99251i	−0.403986	+	0.103726i
$370$	0.0394665	−	0.404533i	0.00205177	−	0.0210307i
$371$	2.96651	+	47.1513i	0.154013	+	2.44797i
$372$	−4.04964	+	6.38122i	−0.209964	+	0.330851i
$373$	−19.6009	−	18.4064i	−1.01489	−	0.953050i	−0.0159917	−	0.999872i	$-0.505091\pi$
$373$	−19.6009	−	18.4064i	−1.01489	−	0.953050i	−0.998903	+	0.0468223i	$0.985091\pi$
$374$	4.61330			0.238548
$375$	5.77778	−	9.57169i	0.298363	−	0.494280i
$376$	−6.37975			−0.329010
$377$	−3.43182	−	3.22270i	−0.176748	−	0.165977i
$378$	2.57973	−	4.06500i	0.132687	−	0.209081i
$379$	1.91144	+	30.3815i	0.0981843	+	1.56059i	0.671341	+	0.741149i	$0.265719\pi$
$379$	1.91144	+	30.3815i	0.0981843	+	1.56059i	−0.573156	+	0.819446i	$0.694281\pi$
$380$	7.43926	+	3.24583i	0.381626	+	0.166508i
$381$	−17.9197	+	4.60101i	−0.918056	+	0.235717i
$382$	0.654490	+	2.01431i	0.0334866	+	0.103061i
$383$	16.4019	−	19.8265i	0.838099	−	1.01309i	−0.161557	−	0.986863i	$-0.551652\pi$
$383$	16.4019	−	19.8265i	0.838099	−	1.01309i	0.999656	−	0.0262245i	$-0.00834847\pi$
$384$	0.425779	+	0.904827i	0.0217280	+	0.0461743i
$385$	15.3038	−	1.40025i	0.779953	−	0.0713631i
$386$	−2.53294	−	2.37859i	−0.128923	−	0.121067i
$387$	−8.62299	−	4.74053i	−0.438331	−	0.240975i
$388$	−2.62268	−	5.57349i	−0.133147	−	0.282951i
$389$	−15.0546	+	31.9927i	−0.763300	+	1.62209i	0.0194919	+	0.999810i	$0.493795\pi$
$389$	−15.0546	+	31.9927i	−0.763300	+	1.62209i	−0.782791	+	0.622284i	$0.786205\pi$
$390$	−1.17626	+	3.23663i	−0.0595621	+	0.163893i
$391$	7.63530	−	0.964563i	0.386134	−	0.0487801i
$392$	−1.01590	+	16.1473i	−0.0513109	+	0.815564i
$393$	0.987421	−	3.03897i	0.0498088	−	0.153296i
$394$	1.41555	+	2.23055i	0.0713145	+	0.112374i
$395$	22.8997	+	0.788542i	1.15221	+	0.0396759i
$396$	−1.38265	−	0.355003i	−0.0694806	−	0.0178396i
$397$	−0.864197	−	13.7360i	−0.0433728	−	0.689391i	−0.958299	−	0.285769i	$-0.907751\pi$
$397$	−0.864197	−	13.7360i	−0.0433728	−	0.689391i	0.914926	−	0.403622i	$-0.132249\pi$
$398$	−3.05837	−	16.0326i	−0.153302	−	0.803640i
$399$	−5.40029	−	16.6204i	−0.270353	−	0.832060i
$400$	1.86853	−	4.63774i	0.0934265	−	0.231887i
$401$	1.15180	−	3.54488i	0.0575182	−	0.177023i	−0.918170	−	0.396187i	$-0.870333\pi$
$401$	1.15180	−	3.54488i	0.0575182	−	0.177023i	0.975688	+	0.219164i	$0.0703331\pi$
$402$	−14.4151	−	1.82105i	−0.718960	−	0.0908258i
$403$	−10.8222	+	4.28482i	−0.539093	+	0.213442i
$404$	−0.892830	+	0.353496i	−0.0444199	+	0.0175871i
$405$	2.20748	+	0.356433i	0.109690	+	0.0177113i
$406$	0.924091	−	14.6880i	0.0458618	−	0.728953i
$407$	0.209922	+	0.152517i	0.0104055	+	0.00756000i
$408$	−3.13021	+	0.803703i	−0.154969	+	0.0397892i
$409$	−12.8083	+	12.0278i	−0.633328	+	0.594734i	−0.933249	−	0.359230i	$-0.883040\pi$
$409$	−12.8083	+	12.0278i	−0.633328	+	0.594734i	0.299922	+	0.953964i	$0.403040\pi$
$410$	16.4205	+	7.16446i	0.810952	+	0.353827i
$411$	12.2023	−	6.70829i	0.601896	−	0.330895i
$412$	−6.67830	+	0.843666i	−0.329016	+	0.0415644i
$413$	−11.2581	+	59.0168i	−0.553973	+	2.90403i
$414$	−2.36259	−	0.298465i	−0.116115	−	0.0146688i
$415$	−6.40243	+	12.4727i	−0.314283	+	0.612260i
$416$	−0.288584	+	1.51281i	−0.0141490	+	0.0741716i
$417$	5.58491	+	8.80042i	0.273494	+	0.430958i
$418$	−4.19196	+	3.04564i	−0.205035	+	0.148967i
$419$	13.1227	−	15.8627i	0.641088	−	0.774942i	−0.345457	−	0.938435i	$-0.612276\pi$
$419$	13.1227	−	15.8627i	0.641088	−	0.774942i	0.986545	+	0.163493i	$0.0522760\pi$
$420$	−10.1400	+	3.61623i	−0.494780	+	0.176454i
$421$	2.40032	−	3.78230i	0.116984	−	0.184338i	−0.780790	−	0.624794i	$-0.785183\pi$
$421$	2.40032	−	3.78230i	0.116984	−	0.184338i	0.897774	+	0.440456i	$0.145183\pi$
$422$	−8.98931	−	10.8662i	−0.437593	−	0.528959i
$423$	−2.71636	+	5.77257i	−0.132074	+	0.280672i
$424$	−7.93888	+	5.76794i	−0.385546	+	0.280116i
$425$	13.5910	+	8.74012i	0.659260	+	0.423958i
$426$	−7.07714	−	5.14184i	−0.342888	−	0.249123i
$427$	−41.1390	+	22.6163i	−1.99085	+	1.09448i
$428$	1.95845	+	0.502844i	0.0946652	+	0.0243059i
$429$	−1.40135	−	1.69395i	−0.0676580	−	0.0817845i
$430$	8.67782	+	20.2198i	0.418482	+	0.975083i
$431$	37.2393	+	14.7441i	1.79375	+	0.710197i	0.993937	+	0.109954i	$0.0350703\pi$
$431$	37.2393	+	14.7441i	1.79375	+	0.710197i	0.799817	+	0.600243i	$0.204930\pi$
$432$	1.00000			0.0481125
$433$	15.0144	+	5.94464i	0.721548	+	0.285681i	0.700056	−	0.714088i	$-0.253158\pi$
$433$	15.0144	+	5.94464i	0.721548	+	0.285681i	0.0214920	+	0.999769i	$0.493158\pi$
$434$	−31.8859	−	17.5294i	−1.53057	−	0.841438i
$435$	6.43810	−	2.29603i	0.308683	−	0.110086i
$436$	−0.122524	−	0.642292i	−0.00586783	−	0.0307602i
$437$	−6.30117	+	5.91719i	−0.301426	+	0.283058i
$438$	−1.17659	+	1.10489i	−0.0562196	+	0.0527937i
$439$	−6.36775	−	33.3809i	−0.303916	−	1.59318i	−0.726702	−	0.686953i	$-0.758948\pi$
$439$	−6.36775	−	33.3809i	−0.303916	−	1.59318i	0.422786	−	0.906230i	$-0.361052\pi$
$440$	1.94879	+	2.52802i	0.0929051	+	0.120519i
$441$	14.1780	+	7.79442i	0.675143	+	0.371163i
$442$	−4.62766	−	1.83222i	−0.220115	−	0.0871498i
$443$	−32.1300			−1.52654			−0.763272	−	0.646077i	$-0.776408\pi$
$443$	−32.1300			−1.52654			−0.763272	+	0.646077i	$0.776408\pi$
$444$	−0.169007	−	0.0669147i	−0.00802072	−	0.00317563i
$445$	−21.0290	−	12.5219i	−0.996869	−	0.593597i
$446$	3.75504	+	4.53907i	0.177807	+	0.214931i
$447$	−4.40285	−	1.13046i	−0.208248	−	0.0534689i
$448$	−4.21896	+	2.31940i	−0.199327	+	0.109581i
$449$	21.3527	+	15.5136i	1.00769	+	0.732133i	0.963724	−	0.266900i	$-0.0859994\pi$
$449$	21.3527	+	15.5136i	1.00769	+	0.732133i	0.0439701	+	0.999033i	$0.485999\pi$
$450$	−3.40077	−	3.66535i	−0.160314	−	0.172786i
$451$	−9.25283	+	6.72257i	−0.435699	+	0.316554i
$452$	−0.358953	+	0.762814i	−0.0168837	+	0.0358797i
$453$	−12.2719	−	14.8342i	−0.576583	−	0.696969i
$454$	13.8600	−	21.8398i	0.650481	−	1.02499i
$455$	−15.9075	−	4.67345i	−0.745757	−	0.219095i
$456$	2.31373	−	2.79682i	0.108351	−	0.130973i
$457$	−1.38813	+	1.00854i	−0.0649340	+	0.0471773i	−0.619779	−	0.784777i	$-0.712778\pi$
$457$	−1.38813	+	1.00854i	−0.0649340	+	0.0471773i	0.554845	+	0.831954i	$0.312778\pi$
$458$	4.14501	+	6.53149i	0.193684	+	0.305196i
$459$	−0.605569	+	3.17450i	−0.0282655	+	0.148173i
$460$	3.75395	+	3.77658i	0.175029	+	0.176084i
$461$	32.2852	+	4.07856i	1.50367	+	0.189958i	0.833612	−	0.552351i	$-0.186269\pi$
$461$	32.2852	+	4.07856i	1.50367	+	0.189958i	0.670058	+	0.742309i	$0.266269\pi$
$462$	1.28781	−	6.75091i	0.0599141	−	0.314081i
$463$	−31.7149	+	4.00653i	−1.47392	+	0.186199i	−0.820869	−	0.571116i	$-0.806511\pi$
$463$	−31.7149	+	4.00653i	−1.47392	+	0.186199i	−0.653049	+	0.757316i	$0.726511\pi$
$464$	2.67872	−	1.47264i	0.124356	−	0.0683655i
$465$	1.64095	−	16.8198i	0.0760972	−	0.779999i
$466$	−12.7638	+	11.9860i	−0.591270	+	0.555239i
$467$	−7.48723	+	1.92239i	−0.346468	+	0.0889578i	−0.417914	−	0.908487i	$-0.637239\pi$
$467$	−7.48723	+	1.92239i	−0.346468	+	0.0889578i	0.0714461	+	0.997444i	$0.477239\pi$
$468$	1.24596	+	0.905241i	0.0575944	+	0.0418448i
$469$	4.39238	−	69.8149i	0.202821	−	3.22375i
$470$	12.7301	−	6.43820i	0.587196	−	0.296972i
$471$	−3.45094	+	1.36633i	−0.159011	+	0.0629569i
$472$	−11.6029	+	4.59391i	−0.534066	+	0.211452i
$473$	−13.9360	−	1.76053i	−0.640778	−	0.0809490i
$474$	3.16654	−	9.74560i	0.145444	−	0.447630i
$475$	−18.1198	+	1.03071i	−0.831394	+	0.0472921i
$476$	−4.80805	−	14.7977i	−0.220377	−	0.678250i
$477$	1.83877	+	9.63919i	0.0841916	+	0.441348i
$478$	−0.527210	−	8.37976i	−0.0241140	−	0.383281i
$479$	8.12364	+	2.08580i	0.371178	+	0.0953024i	0.429671	−	0.902985i	$-0.358629\pi$
$479$	8.12364	+	2.08580i	0.371178	+	0.0953024i	−0.0584928	+	0.998288i	$0.518629\pi$
$480$	−1.76271	−	1.37581i	−0.0804565	−	0.0627966i
$481$	−0.150002	−	0.236365i	−0.00683949	−	0.0107773i
$482$	−5.70316	+	17.5525i	−0.259772	+	0.799496i
$483$	0.719898	−	11.4425i	0.0327565	−	0.520650i
$484$	8.89159	−	1.12327i	0.404163	−	0.0510577i
$485$	10.8578	+	8.47459i	0.493029	+	0.384811i
$486$	0.425779	−	0.904827i	0.0193137	−	0.0410438i
$487$	−2.99963	−	6.37454i	−0.135926	−	0.288858i	0.825263	−	0.564749i	$-0.191027\pi$
$487$	−2.99963	−	6.37454i	−0.135926	−	0.288858i	−0.961189	+	0.275891i	$0.911027\pi$
$488$	−8.54483	−	4.69756i	−0.386806	−	0.212649i
$489$	−16.9442	−	15.9117i	−0.766245	−	0.719552i
$490$	−14.2681	−	33.2455i	−0.644569	−	1.50188i
$491$	13.1385	+	27.9207i	0.592931	+	1.26004i	0.945915	+	0.324413i	$0.105167\pi$
$491$	13.1385	+	27.9207i	0.592931	+	1.26004i	−0.352984	+	0.935629i	$0.614833\pi$
$492$	5.10706	−	6.17338i	0.230244	−	0.278317i
$493$	3.05274	+	9.39538i	0.137489	+	0.423147i
$494$	5.41461	−	1.39024i	0.243615	−	0.0625497i
$495$	3.11718	−	0.686943i	0.140107	−	0.0308758i
$496$	−0.474555	−	7.54283i	−0.0213081	−	0.338683i
$497$	22.5670	−	35.5599i	1.01227	−	1.59508i
$498$	4.57057	+	4.29205i	0.204812	+	0.192331i
$499$	−7.64895			−0.342414			−0.171207	−	0.985235i	$-0.554767\pi$
$499$	−7.64895			−0.342414			−0.171207	+	0.985235i	$0.554767\pi$
$500$	0.951775	+	11.1398i	0.0425647	+	0.498185i
$501$	10.2275			0.456931
$502$	12.7584	+	11.9809i	0.569435	+	0.534735i
$503$	−20.7415	+	32.6834i	−0.924817	+	1.45728i	−0.0358240	+	0.999358i	$0.511406\pi$
$503$	−20.7415	+	32.6834i	−0.924817	+	1.45728i	−0.888993	+	0.457921i	$0.848594\pi$
$504$	0.302304	+	4.80498i	0.0134657	+	0.214031i
$505$	1.42481	−	1.60637i	0.0634032	−	0.0714827i
$506$	−3.29259	+	0.845395i	−0.146374	+	0.0375824i
$507$	−3.28427	−	10.1080i	−0.145860	−	0.448910i
$508$	11.7930	−	14.2552i	0.523228	−	0.632474i
$509$	−10.6927	−	22.7232i	−0.473947	−	1.00719i	−0.988708	−	0.149856i	$-0.952119\pi$
$509$	−10.6927	−	22.7232i	−0.473947	−	1.00719i	0.514760	−	0.857334i	$-0.327881\pi$
$510$	5.43494	−	4.76260i	0.240663	−	0.210891i
$511$	−5.66467	−	5.31948i	−0.250590	−	0.235320i
$512$	−0.876307	−	0.481754i	−0.0387276	−	0.0212907i
$513$	−1.54550	−	3.28436i	−0.0682356	−	0.145008i
$514$	−11.9515	+	25.3981i	−0.527156	+	1.12026i
$515$	12.4744	−	8.42293i	0.549690	−	0.371159i
$516$	9.76256	−	1.23330i	0.429773	−	0.0542929i
$517$	−0.571836	+	9.08908i	−0.0251493	+	0.399737i
$518$	0.270432	−	0.832305i	0.0118821	−	0.0365694i
$519$	−6.10348	−	9.61754i	−0.267913	−	0.422163i
$520$	−0.950831	−	3.30988i	−0.0416967	−	0.145148i
$521$	30.8890	+	7.93095i	1.35327	+	0.347461i	0.854581	−	0.519318i	$-0.173814\pi$
$521$	30.8890	+	7.93095i	1.35327	+	0.347461i	0.498691	+	0.866780i	$0.333814\pi$
$522$	−0.191940	−	3.05079i	−0.00840097	−	0.133530i
$523$	−4.42403	−	23.1916i	−0.193449	−	1.01410i	−0.938027	−	0.346562i	$-0.887349\pi$
$523$	−4.42403	−	23.1916i	−0.193449	−	1.01410i	0.744578	−	0.667536i	$-0.232651\pi$
$524$	0.987421	+	3.03897i	0.0431357	+	0.132758i
$525$	16.5839	−	17.4487i	0.723780	−	0.761523i
$526$	1.64001	−	5.04744i	0.0715080	−	0.220079i
$527$	24.2321	+	3.06123i	1.05557	+	0.133349i
$528$	1.32725	−	0.525495i	0.0577611	−	0.0228693i
$529$	16.1122	−	6.37926i	0.700529	−	0.277359i
$530$	10.0204	−	19.5209i	0.435259	−	0.847935i
$531$	−0.783577	+	12.4546i	−0.0340043	+	0.540483i
$532$	14.1381	+	10.2720i	0.612966	+	0.445346i
$533$	11.9516	−	3.06864i	0.517680	−	0.132918i
$534$	−7.97891	+	7.49269i	−0.345281	+	0.324240i
$535$	−4.41532	+	0.973020i	−0.190891	+	0.0420673i
$536$	12.7325	−	6.99973i	0.549958	−	0.302342i
$537$	−11.0253	+	1.39282i	−0.475775	+	0.0601044i
$538$	−1.98969	+	10.4303i	−0.0857817	+	0.449683i
$539$	22.9137	+	2.89467i	0.986962	+	0.124682i
$540$	−1.99539	+	1.00916i	−0.0858680	+	0.0434274i
$541$	−6.02055	+	31.5608i	−0.258843	+	1.35691i	0.580924	+	0.813958i	$0.302692\pi$
$541$	−6.02055	+	31.5608i	−0.258843	+	1.35691i	−0.839767	+	0.542947i	$0.817308\pi$
$542$	−2.75013	−	4.33351i	−0.118128	−	0.186140i
$543$	−17.9021	+	13.0067i	−0.768255	+	0.558170i
$544$	2.05999	−	2.49010i	0.0883215	−	0.106762i
$545$	0.892660	+	1.15798i	0.0382374	+	0.0496024i
$546$	−3.97301	+	6.26046i	−0.170029	+	0.267923i
$547$	10.9175	+	13.1970i	0.466800	+	0.564264i	0.950402	−	0.311024i	$-0.100672\pi$
$547$	10.9175	+	13.1970i	0.466800	+	0.564264i	−0.483602	+	0.875288i	$0.660672\pi$
$548$	−5.92886	+	12.5995i	−0.253268	+	0.538223i
$549$	−7.88869	+	5.73147i	−0.336681	+	0.244613i
$550$	−6.43979	−	3.07775i	−0.274594	−	0.131236i
$551$	−8.97663	−	6.52191i	−0.382417	−	0.277842i
$552$	2.08681	−	1.14723i	0.0888206	−	0.0488296i
$553$	47.7847	+	12.2690i	2.03201	+	0.521732i
$554$	−16.1919	−	19.5727i	−0.687930	−	0.831564i
$555$	0.404763	−	0.0370345i	0.0171812	−	0.00157203i
$556$	−9.69104	−	3.83696i	−0.410992	−	0.162723i
$557$	−20.9445			−0.887445			−0.443723	−	0.896164i	$-0.646342\pi$
$557$	−20.9445			−0.887445			−0.443723	+	0.896164i	$0.646342\pi$
$558$	−7.02702	−	2.78219i	−0.297477	−	0.117780i
$559$	13.2802	+	7.30083i	0.561691	+	0.308792i
$560$	6.07785	−	8.88572i	0.256836	−	0.375490i
$561$	0.864446	+	4.53158i	0.0364969	+	0.191324i
$562$	−4.05021	+	3.80340i	−0.170848	+	0.160437i
$563$	−2.28233	+	2.14325i	−0.0961889	+	0.0903274i	−0.731150	−	0.682217i	$-0.761016\pi$
$563$	−2.28233	+	2.14325i	−0.0961889	+	0.0903274i	0.634961	+	0.772544i	$0.281016\pi$
$564$	−1.19545	−	6.26674i	−0.0503373	−	0.263878i
$565$	−0.0535505	−	1.88435i	−0.00225289	−	0.0792754i
$566$	17.3448	+	9.53540i	0.729057	+	0.400803i
$567$	4.47639	+	1.77233i	0.187991	+	0.0744309i
$568$	8.74782			0.367050
$569$	27.5234	+	10.8973i	1.15384	+	0.456839i	0.865608	−	0.500721i	$-0.166932\pi$
$569$	27.5234	+	10.8973i	1.15384	+	0.456839i	0.288234	+	0.957560i	$0.406932\pi$
$570$	−1.79436	+	7.91570i	−0.0751575	+	0.331552i
$571$	7.28985	+	8.81192i	0.305071	+	0.368767i	0.900662	−	0.434520i	$-0.143082\pi$
$571$	7.28985	+	8.81192i	0.305071	+	0.368767i	−0.595591	+	0.803288i	$0.703082\pi$
$572$	2.12940	+	0.546736i	0.0890346	+	0.0228602i
$573$	−1.85599	+	1.02034i	−0.0775353	+	0.0426254i
$574$	31.2069	+	22.6731i	1.30255	+	0.946357i
$575$	−11.3018	−	3.74741i	−0.471317	−	0.156278i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	11.5506	−	24.5463i	0.480858	−	1.02187i	−0.506334	−	0.862337i	$-0.669000\pi$
$577$	11.5506	−	24.5463i	0.480858	−	1.02187i	0.987192	−	0.159537i	$-0.0510001\pi$
$578$	−4.17883	−	5.05134i	−0.173817	−	0.210108i
$579$	1.86183	−	2.93378i	0.0773752	−	0.121924i
$580$	−3.85896	+	5.64175i	−0.160235	+	0.234261i
$581$	−19.2415	+	23.2590i	−0.798273	+	0.964947i
$582$	4.98333	−	3.62060i	0.206565	−	0.150079i
$583$	7.50586	+	11.8273i	0.310861	+	0.489838i
$584$	0.302442	−	1.58546i	0.0125151	−	0.0656067i
$585$	−3.39971	−	0.548939i	−0.140561	−	0.0226958i
$586$	11.9264	+	1.50666i	0.492675	+	0.0622394i
$587$	−1.79423	+	9.40570i	−0.0740559	+	0.388215i	0.925890	+	0.377794i	$0.123317\pi$
$587$	−1.79423	+	9.40570i	−0.0740559	+	0.388215i	−0.999946	+	0.0104211i	$0.996683\pi$
$588$	−16.0517	+	2.02780i	−0.661960	+	0.0836250i
$589$	−24.0400	+	13.2161i	−0.990549	+	0.544559i
$590$	18.5163	−	20.8758i	0.762305	−	0.859445i
$591$	−1.92580	+	1.80844i	−0.0792167	+	0.0743894i
$592$	0.176061	−	0.0452048i	0.00723607	−	0.00185791i
$593$	−15.9443	−	11.5842i	−0.654756	−	0.475708i	0.210132	−	0.977673i	$-0.432611\pi$
$593$	−15.9443	−	11.5842i	−0.654756	−	0.475708i	−0.864888	+	0.501965i	$0.832611\pi$
$594$	0.0896331	−	1.42468i	0.00367769	−	0.0584552i
$595$	24.5272	+	24.6751i	1.00552	+	1.01158i
$596$	4.22645	−	1.67337i	0.173122	−	0.0685439i
$597$	15.1755	−	6.00840i	0.621092	−	0.245908i
$598$	3.63860	+	0.459662i	0.148794	+	0.0187970i
$599$	7.11232	−	21.8895i	0.290602	−	0.894380i	−0.694062	−	0.719915i	$-0.744181\pi$
$599$	7.11232	−	21.8895i	0.290602	−	0.894380i	0.984663	−	0.174465i	$-0.0558194\pi$
$600$	4.90572	+	0.966408i	0.200275	+	0.0394534i
$601$	4.02000	+	12.3723i	0.163979	+	0.504677i	0.998960	−	0.0456033i	$-0.0145210\pi$
$601$	4.02000	+	12.3723i	0.163979	+	0.504677i	−0.834980	+	0.550280i	$0.814521\pi$
$602$	8.87724	+	46.5361i	0.361809	+	1.89667i
$603$	−0.912326	−	14.5010i	−0.0371528	−	0.590527i
$604$	18.6475	+	4.78785i	0.758754	+	0.194815i
$605$	−16.6087	+	11.2144i	−0.675238	+	0.455931i
$606$	−0.514534	−	0.810776i	−0.0209015	−	0.0329355i
$607$	14.9533	−	46.0214i	0.606934	−	1.86795i	0.124030	−	0.992279i	$-0.460418\pi$
$607$	14.9533	−	46.0214i	0.606934	−	1.86795i	0.482905	−	0.875673i	$-0.339582\pi$
$608$	−0.227918	+	3.62266i	−0.00924331	+	0.146918i
$609$	14.6010	−	1.84453i	0.591662	−	0.0747443i
$610$	21.7909	+	0.750361i	0.882287	+	0.0303812i
$611$	4.18344	−	8.89026i	0.169244	−	0.359662i
$612$	−1.37601	−	2.92417i	−0.0556219	−	0.118203i
$613$	6.66838	+	3.66597i	0.269333	+	0.148067i	0.610698	−	0.791864i	$-0.290889\pi$
$613$	6.66838	+	3.66597i	0.269333	+	0.148067i	−0.341365	+	0.939931i	$0.610889\pi$
$614$	−16.2509	−	15.2606i	−0.655831	−	0.615867i
$615$	−3.96066	+	17.4722i	−0.159709	+	0.704546i
$616$	2.92623	+	6.21856i	0.117901	+	0.250553i
$617$	1.93037	−	2.33341i	0.0777136	−	0.0939396i	−0.730223	−	0.683208i	$-0.760584\pi$
$617$	1.93037	−	2.33341i	0.0777136	−	0.0939396i	0.807937	+	0.589269i	$0.200584\pi$
$618$	−2.08011	−	6.40192i	−0.0836743	−	0.257523i
$619$	−10.9029	+	2.79939i	−0.438225	+	0.112517i	−0.461355	−	0.887215i	$-0.652637\pi$
$619$	−10.9029	+	2.79939i	−0.438225	+	0.112517i	0.0231304	+	0.999732i	$0.492637\pi$
$620$	8.55886	+	14.5720i	0.343732	+	0.585226i
$621$	−0.149528	−	2.37667i	−0.00600034	−	0.0953726i
$622$	18.8245	−	29.6627i	0.754795	−	1.18937i
$623$	−38.4143	−	36.0734i	−1.53904	−	1.44525i
$624$	−1.54009			−0.0616529
$625$	−13.1410	−	21.2677i	−0.525639	−	0.850708i
$626$	−13.9135			−0.556096
$627$	−3.77718	−	3.54701i	−0.150846	−	0.141654i
$628$	1.98877	−	3.13379i	0.0793604	−	0.125052i
$629$	0.0368857	+	0.586281i	0.00147073	+	0.0233766i
$630$	−5.45222	−	9.28276i	−0.217222	−	0.369834i
$631$	35.1177	−	9.01670i	1.39802	−	0.358949i	0.526858	−	0.849953i	$-0.323370\pi$
$631$	35.1177	−	9.01670i	1.39802	−	0.358949i	0.871157	+	0.491004i	$0.163370\pi$
$632$	3.16654	+	9.74560i	0.125958	+	0.387659i
$633$	8.98931	−	10.8662i	0.357293	−	0.431893i
$634$	3.48016	+	7.39572i	0.138215	+	0.293722i
$635$	−9.14575	+	40.3458i	−0.362938	+	1.60108i
$636$	−7.15337	−	6.71746i	−0.283650	−	0.266365i
$637$	−21.8354	−	12.0041i	−0.865148	−	0.475619i
$638$	−1.85793	−	3.94830i	−0.0735562	−	0.156315i
$639$	3.72464	−	7.91526i	0.147345	−	0.313123i
$640$	2.23474	+	0.0769525i	0.0883360	+	0.00304182i
$641$	−11.2613	+	1.42264i	−0.444796	+	0.0561909i	−0.344542	−	0.938771i	$-0.611966\pi$
$641$	−11.2613	+	1.42264i	−0.444796	+	0.0561909i	−0.100255	+	0.994962i	$0.531966\pi$
$642$	−0.126961	+	2.01798i	−0.00501074	+	0.0796434i
$643$	−2.10287	+	6.47196i	−0.0829290	+	0.255229i	−0.983920	−	0.178608i	$-0.942841\pi$
$643$	−2.10287	+	6.47196i	−0.0829290	+	0.255229i	0.900991	+	0.433837i	$0.142841\pi$
$644$	6.14330	+	9.68029i	0.242080	+	0.381457i
$645$	−18.2355	+	12.3129i	−0.718024	+	0.484821i
$646$	−11.3621	−	2.91730i	−0.447036	−	0.114779i
$647$	−2.65574	−	42.2118i	−0.104408	−	1.65952i	−0.606784	−	0.794867i	$-0.707541\pi$
$647$	−2.65574	−	42.2118i	−0.104408	−	1.65952i	0.502376	−	0.864649i	$-0.332459\pi$
$648$	0.187381	+	0.982287i	0.00736103	+	0.0385879i
$649$	5.50483	+	16.9421i	0.216084	+	0.665037i
$650$	5.23748	+	5.64496i	0.205431	+	0.221414i
$651$	11.2441	−	34.6058i	0.440691	−	1.35631i
$652$	23.0608	+	2.91326i	0.903132	+	0.114092i
$653$	−20.6338	+	8.16948i	−0.807461	+	0.319697i	−0.735339	−	0.677699i	$-0.762977\pi$
$653$	−20.6338	+	8.16948i	−0.807461	+	0.319697i	−0.0721222	+	0.997396i	$0.522977\pi$
$654$	0.607957	−	0.240707i	0.0237730	−	0.00941240i
$655$	−5.03711	−	5.06747i	−0.196816	−	0.198002i
$656$	−0.503080	+	7.99622i	−0.0196420	+	0.312200i
$657$	−1.30579	−	0.948712i	−0.0509437	−	0.0370128i
$658$	29.7502	−	7.63856i	1.15978	−	0.297782i
$659$	−9.19770	+	8.63722i	−0.358292	+	0.336458i	−0.842700	−	0.538384i	$-0.819035\pi$
$659$	−9.19770	+	8.63722i	−0.358292	+	0.336458i	0.484408	+	0.874842i	$0.339035\pi$
$660$	−2.11807	+	2.38798i	−0.0824460	+	0.0929520i
$661$	31.6266	−	17.3869i	1.23013	−	0.676270i	0.271916	−	0.962321i	$-0.412343\pi$
$661$	31.6266	−	17.3869i	1.23013	−	0.676270i	0.958214	+	0.286051i	$0.0923426\pi$
$662$	11.2927	−	1.42660i	0.438905	−	0.0554466i
$663$	0.932629	−	4.88901i	0.0362203	−	0.189874i
$664$	−6.22047	−	0.785828i	−0.241401	−	0.0304961i
$665$	−38.5772	−	6.22893i	−1.49596	−	0.241547i
$666$	0.0340606	−	0.178552i	0.00131982	−	0.00691875i
$667$	−3.90052	−	6.14623i	−0.151029	−	0.237983i
$668$	−8.27422	+	6.01157i	−0.320139	+	0.232595i
$669$	−3.75504	+	4.53907i	−0.145178	+	0.175491i
$670$	−18.3424	+	26.8163i	−0.708629	+	1.03600i
$671$	−7.45840	+	11.7526i	−0.287928	+	0.453703i
$672$	−3.06887	−	3.70962i	−0.118384	−	0.143102i
$673$	−3.27537	+	6.96051i	−0.126256	+	0.268308i	−0.957955	−	0.286919i	$-0.907369\pi$
$673$	−3.27537	+	6.96051i	−0.126256	+	0.268308i	0.831699	+	0.555228i	$0.187369\pi$
$674$	−7.16260	+	5.20394i	−0.275893	+	0.200448i
$675$	2.96318	−	4.02735i	0.114053	−	0.155013i
$676$	8.59834	+	6.24706i	0.330705	+	0.240271i
$677$	41.4602	−	22.7930i	1.59345	−	0.876005i	0.596123	−	0.802893i	$-0.296707\pi$
$677$	41.4602	−	22.7930i	1.59345	−	0.876005i	0.997324	−	0.0731116i	$-0.0232929\pi$
$678$	−0.816563	−	0.209658i	−0.0313599	−	0.00805186i
$679$	18.9034	+	22.8503i	0.725446	+	0.876913i
$680$	−1.59758	+	7.04760i	−0.0612643	+	0.270263i
$681$	24.0501	+	9.52210i	0.921601	+	0.364888i
$682$	−10.7886			−0.413118
$683$	35.4365	+	14.0303i	1.35594	+	0.536854i	0.929887	−	0.367844i	$-0.119904\pi$
$683$	35.4365	+	14.0303i	1.35594	+	0.536854i	0.426052	+	0.904699i	$0.359904\pi$
$684$	3.18084	+	1.74868i	0.121622	+	0.0668624i
$685$	−0.884499	−	31.1241i	−0.0337950	−	1.18919i
$686$	−8.28102	−	43.4106i	−0.316171	−	1.65743i
$687$	−5.63910	+	5.29547i	−0.215145	+	0.202035i
$688$	−7.17316	+	6.73605i	−0.273474	+	0.256809i
$689$	−2.83187	−	14.8452i	−0.107886	−	0.565557i
$690$	−3.00626	+	4.39511i	−0.114447	+	0.167319i
$691$	−8.29613	−	4.56083i	−0.315600	−	0.173502i	0.316079	−	0.948733i	$-0.397634\pi$
$691$	−8.29613	−	4.56083i	−0.315600	−	0.173502i	−0.631678	+	0.775231i	$0.717634\pi$
$692$	10.5909	+	4.19322i	0.402604	+	0.159402i
$693$	6.87265			0.261070
$694$	14.2534	+	5.64333i	0.541053	+	0.214218i
$695$	23.2095	−	2.12360i	0.880388	−	0.0805527i
$696$	1.94849	+	2.35532i	0.0738575	+	0.0892784i
$697$	−25.0794	−	6.43929i	−0.949949	−	0.243906i
$698$	4.45952	−	2.45164i	0.168796	−	0.0927961i
$699$	−14.1654	−	10.2917i	−0.535783	−	0.389269i
$700$	−3.16056	+	23.8640i	−0.119458	+	0.901976i
$701$	−12.1828	+	8.85129i	−0.460136	+	0.334309i	−0.793585	−	0.608460i	$-0.791788\pi$
$701$	−12.1828	+	8.85129i	−0.460136	+	0.334309i	0.333448	+	0.942768i	$0.391788\pi$
$702$	−0.655738	+	1.39351i	−0.0247492	+	0.0525948i
$703$	−0.420572	−	0.508384i	−0.0158622	−	0.0191741i
$704$	−0.764889	+	1.20527i	−0.0288278	+	0.0454254i
$705$	8.70954	+	11.2982i	0.328020	+	0.425516i
$706$	−4.58605	+	5.54358i	−0.172598	+	0.208635i
$707$	3.74022	−	2.71743i	0.140666	−	0.102199i
$708$	−6.68670	−	10.5366i	−0.251302	−	0.395988i
$709$	−8.13093	+	42.6238i	−0.305364	+	1.60077i	0.416766	+	0.909014i	$0.363164\pi$
$709$	−8.13093	+	42.6238i	−0.305364	+	1.60077i	−0.722129	+	0.691758i	$0.756836\pi$
$710$	−17.4553	+	8.82797i	−0.655087	+	0.331308i
$711$	10.1663	+	1.28431i	0.381267	+	0.0481652i
$712$	2.05098	−	10.7516i	0.0768636	−	0.402933i
$713$	−17.8559	+	2.25572i	−0.668708	+	0.0844775i
$714$	13.6346	−	7.49570i	0.510263	−	0.280519i
$715$	−4.80073	+	1.05795i	−0.179537	+	0.0395652i
$716$	8.10095	−	7.60730i	0.302747	−	0.284298i
$717$	8.13254	−	2.08808i	0.303715	−	0.0779808i
$718$	20.6116	+	14.9752i	0.769217	+	0.558869i
$719$	2.24926	−	35.7510i	0.0838834	−	1.33329i	−0.700785	−	0.713372i	$-0.747167\pi$
$719$	2.24926	−	35.7510i	0.0838834	−	1.33329i	0.784669	−	0.619916i	$-0.212833\pi$
$720$	1.02114	−	1.98929i	0.0380555	−	0.0741365i
$721$	30.1323	−	11.9302i	1.12219	−	0.444305i
$722$	−5.41540	+	2.14411i	−0.201540	+	0.0797954i
$723$	−18.3103	−	2.31313i	−0.680967	−	0.0860261i
$724$	6.83801	−	21.0452i	0.254133	−	0.782140i
$725$	2.00671	−	15.1518i	0.0745273	−	0.562725i
$726$	2.76949	+	8.52362i	0.102785	+	0.316341i
$727$	0.526878	+	2.76199i	0.0195408	+	0.102437i	0.990721	−	0.135908i	$-0.0433952\pi$
$727$	0.526878	+	2.76199i	0.0195408	+	0.102437i	−0.971181	+	0.238345i	$0.923395\pi$
$728$	−0.465575	−	7.40010i	−0.0172553	−	0.274266i
$729$	0.968583	+	0.248690i	0.0358735	+	0.00921074i
$730$	0.996492	+	3.46882i	0.0368818	+	0.128387i
$731$	−17.0398	−	26.8504i	−0.630238	−	0.993097i
$732$	3.01321	−	9.27371i	0.111372	−	0.342766i
$733$	1.59271	−	25.3154i	0.0588280	−	0.935044i	−0.852334	−	0.522997i	$-0.824814\pi$
$733$	1.59271	−	25.3154i	0.0588280	−	0.935044i	0.911162	−	0.412047i	$-0.135186\pi$
$734$	−19.3835	+	2.44870i	−0.715457	+	0.0903832i
$735$	29.9830	−	20.2450i	1.10594	−	0.746748i
$736$	−1.01394	+	2.15473i	−0.0373743	+	0.0794244i
$737$	−8.83110	−	18.7670i	−0.325298	−	0.691293i
$738$	7.02100	+	3.85983i	0.258446	+	0.142082i
$739$	14.1347	+	13.2734i	0.519954	+	0.488270i	0.899511	−	0.436899i	$-0.143923\pi$
$739$	14.1347	+	13.2734i	0.519954	+	0.488270i	−0.379556	+	0.925169i	$0.623923\pi$
$740$	−0.305692	+	0.267875i	−0.0112375	+	0.00984730i
$741$	2.38021	+	5.05820i	0.0874392	+	0.185818i
$742$	30.1148	−	36.4025i	1.10555	−	1.33638i
$743$	2.04684	+	6.29952i	0.0750912	+	0.231107i	0.981556	−	0.191174i	$-0.0612295\pi$
$743$	2.04684	+	6.29952i	0.0750912	+	0.231107i	−0.906465	+	0.422281i	$0.861230\pi$
$744$	7.32031	−	1.87954i	0.268375	−	0.0689071i
$745$	−6.74472	+	7.60420i	−0.247107	+	0.278596i
$746$	1.68834	+	26.8354i	0.0618146	+	0.982516i
$747$	−3.35959	+	5.29386i	−0.122921	+	0.193692i
$748$	−3.36295	−	3.15802i	−0.122962	−	0.115469i
$749$	−9.73475			−0.355700
$750$	−10.7641	+	3.02230i	−0.393049	+	0.110359i
$751$	−33.6328			−1.22728			−0.613638	−	0.789587i	$-0.710295\pi$
$751$	−33.6328			−1.22728			−0.613638	+	0.789587i	$0.710295\pi$
$752$	4.65064	+	4.36724i	0.169591	+	0.159257i
$753$	−9.37803	+	14.7774i	−0.341754	+	0.538519i
$754$	0.295604	+	4.69849i	0.0107653	+	0.171109i
$755$	−42.0407	+	9.26465i	−1.53002	+	0.337175i
$756$	−4.66323	+	1.19731i	−0.169600	+	0.0435459i
$757$	−8.80285	−	27.0924i	−0.319945	−	0.984689i	−0.973671	−	0.227958i	$-0.926795\pi$
$757$	−8.80285	−	27.0924i	−0.319945	−	0.984689i	0.653726	−	0.756731i	$-0.273205\pi$
$758$	19.4042	−	23.4557i	0.704793	−	0.851948i
$759$	−1.44739	−	3.07586i	−0.0525370	−	0.111647i
$760$	−3.20106	−	7.45863i	−0.116115	−	0.270553i
$761$	6.81011	+	6.39512i	0.246866	+	0.231823i	0.798095	−	0.602531i	$-0.205841\pi$
$761$	6.81011	+	6.39512i	0.246866	+	0.231823i	−0.551229	+	0.834354i	$0.685841\pi$
$762$	16.2125	+	8.91291i	0.587318	+	0.322881i
$763$	1.34038	+	2.84846i	0.0485251	+	0.103121i
$764$	0.901789	−	1.91640i	0.0326256	−	0.0693329i
$765$	5.69664	+	4.44625i	0.205963	+	0.160755i
$766$	−25.5287	+	3.22502i	−0.922389	+	0.116525i
$767$	1.20678	−	19.1812i	0.0435742	−	0.692592i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	10.7969	+	17.0131i	0.389345	+	0.613509i	0.981305	−	0.192458i	$-0.0616459\pi$
$769$	10.7969	+	17.0131i	0.389345	+	0.613509i	−0.591961	+	0.805967i	$0.701646\pi$
$770$	−12.1145	−	9.45542i	−0.436577	−	0.340750i
$771$	−27.1877	−	6.98063i	−0.979143	−	0.251401i
$772$	0.218178	+	3.46784i	0.00785239	+	0.124810i
$773$	−0.0714530	−	0.374570i	−0.00256999	−	0.0134723i	0.980979	−	0.194113i	$-0.0621829\pi$
$773$	−0.0714530	−	0.374570i	−0.00256999	−	0.0134723i	−0.983549	+	0.180641i	$0.942183\pi$
$774$	3.04077	+	9.35854i	0.109298	+	0.336386i
$775$	−31.7838	−	20.4396i	−1.14171	−	0.734213i
$776$	−1.90346	+	5.85825i	−0.0683303	+	0.210299i
$777$	0.868237	+	0.109684i	0.0311478	+	0.00393488i
$778$	32.8749	−	13.0161i	1.17862	−	0.466649i
$779$	27.0400	−	10.7059i	0.968808	−	0.383578i
$780$	3.07308	−	1.55420i	0.110034	−	0.0556492i
$781$	0.784094	−	12.4628i	0.0280571	−	0.445955i
$782$	−6.22619	−	4.52359i	−0.222648	−	0.161763i
$783$	2.96079	−	0.760202i	0.105810	−	0.0271674i
$784$	11.7942	−	11.0755i	0.421220	−	0.395552i
$785$	−0.805864	+	8.26014i	−0.0287625	+	0.294817i
$786$	−2.80012	+	1.53938i	−0.0998769	+	0.0549078i
$787$	18.0125	−	2.27551i	0.642077	−	0.0811132i	0.202448	−	0.979293i	$-0.435110\pi$
$787$	18.0125	−	2.27551i	0.642077	−	0.0811132i	0.439628	+	0.898180i	$0.355110\pi$
$788$	0.495026	−	2.59502i	0.0176346	−	0.0924437i
$789$	5.26535	+	0.665168i	0.187451	+	0.0236806i
$790$	−16.1534	−	16.2507i	−0.574711	−	0.578176i
$791$	0.760552	−	3.98695i	0.0270421	−	0.141760i
$792$	0.764889	+	1.20527i	0.0271792	+	0.0428275i
$793$	12.1493	−	8.82697i	0.431434	−	0.313455i
$794$	−8.77298	+	10.6047i	−0.311341	+	0.376347i
$795$	21.0528	+	6.18507i	0.746665	+	0.219362i
$796$	−8.74558	+	13.7808i	−0.309979	+	0.488449i
$797$	−5.42215	−	6.55426i	−0.192062	−	0.232164i	0.665688	−	0.746230i	$-0.268138\pi$
$797$	−5.42215	−	6.55426i	−0.192062	−	0.232164i	−0.857750	+	0.514067i	$0.828138\pi$
$798$	−7.44080	+	15.8125i	−0.263401	+	0.559756i
$799$	−16.6801	+	12.1188i	−0.590099	+	0.428732i
$800$	−4.53685	+	2.10167i	−0.160402	+	0.0743052i
$801$	−8.85507	−	6.43359i	−0.312879	−	0.227320i
$802$	−3.26626	+	1.79564i	−0.115336	+	0.0634063i
$803$	−2.23165	−	0.572991i	−0.0787534	−	0.0202204i
$804$	9.26157	+	11.1953i	0.326630	+	0.394828i
$805$	−22.0273	−	13.1164i	−0.776359	−	0.462292i
$806$	10.8222	+	4.28482i	0.381197	+	0.150926i
$807$	−10.6184			−0.373786
$808$	0.892830	+	0.353496i	0.0314096	+	0.0124360i
$809$	33.2220	+	18.2639i	1.16802	+	0.642125i	0.943184	−	0.332271i	$-0.107815\pi$
$809$	33.2220	+	18.2639i	1.16802	+	0.642125i	0.224838	+	0.974396i	$0.427815\pi$
$810$	−1.36519	−	1.77095i	−0.0479678	−	0.0622249i
$811$	3.93858	+	20.6468i	0.138302	+	0.725006i	0.982102	+	0.188348i	$0.0603133\pi$
$811$	3.93858	+	20.6468i	0.138302	+	0.725006i	−0.843800	+	0.536658i	$0.819687\pi$
$812$	−10.7283	+	10.0745i	−0.376488	+	0.353546i
$813$	3.74143	−	3.51344i	0.131218	−	0.123222i
$814$	−0.0486213	−	0.254882i	−0.00170418	−	0.00893361i
$815$	−48.9554	+	17.4590i	−1.71483	+	0.611562i
$816$	2.83200	+	1.55691i	0.0991399	+	0.0545026i
$817$	33.2097	+	13.1487i	1.16186	+	0.460014i
$818$	17.5704			0.614334
$819$	−6.89404	−	2.72954i	−0.240897	−	0.0953780i
$820$	−7.06564	−	16.4633i	−0.246743	−	0.574923i
$821$	−13.3316	−	16.1152i	−0.465278	−	0.562424i	0.484725	−	0.874667i	$-0.338920\pi$
$821$	−13.3316	−	16.1152i	−0.465278	−	0.562424i	−0.950002	+	0.312243i	$0.898920\pi$
$822$	−13.4873	−	3.46294i	−0.470422	−	0.120784i
$823$	−20.1369	+	11.0703i	−0.701927	+	0.385888i	−0.792392	−	0.610012i	$-0.791165\pi$
$823$	−20.1369	+	11.0703i	−0.701927	+	0.385888i	0.0904652	+	0.995900i	$0.471165\pi$
$824$	5.44580	+	3.95661i	0.189713	+	0.137835i
$825$	1.81653	−	6.90244i	0.0632436	−	0.240312i
$826$	48.6066	−	35.3147i	1.69124	−	1.22876i
$827$	16.4917	−	35.0466i	0.573472	−	1.21869i	−0.382151	−	0.924100i	$-0.624817\pi$
$827$	16.4917	−	35.0466i	0.573472	−	1.21869i	0.955624	−	0.294591i	$-0.0951833\pi$
$828$	1.51794	+	1.83488i	0.0527522	+	0.0637664i
$829$	−11.9440	+	18.8208i	−0.414833	+	0.653673i	−0.985920	−	0.167217i	$-0.946522\pi$
$829$	−11.9440	+	18.8208i	−0.414833	+	0.653673i	0.571087	+	0.820890i	$0.306522\pi$
$830$	13.2053	−	4.70943i	0.458363	−	0.163467i
$831$	16.1919	−	19.5727i	0.561692	−	0.678969i
$832$	1.24596	−	0.905241i	0.0431958	−	0.0313836i
$833$	28.0169	+	44.1476i	0.970729	+	1.52962i
$834$	1.95307	−	10.2384i	0.0676294	−	0.354526i
$835$	10.4437	−	20.3455i	0.361418	−	0.704084i
$836$	5.14069	+	0.649420i	0.177794	+	0.0224606i
$837$	1.41618	−	7.42388i	0.0489504	−	0.256607i
$838$	−20.4248	+	2.58025i	−0.705563	+	0.0891334i
$839$	32.8465	−	18.0575i	1.13399	−	0.623414i	0.199671	−	0.979863i	$-0.436013\pi$
$839$	32.8465	−	18.0575i	1.13399	−	0.623414i	0.934315	+	0.356449i	$0.116013\pi$
$840$	9.86721	+	4.30517i	0.340451	+	0.148543i
$841$	−14.3285	+	13.4553i	−0.494085	+	0.463977i
$842$	−4.33892	+	1.11405i	−0.149529	+	0.0383925i
$843$	−4.49496	−	3.26578i	−0.154815	−	0.112479i
$844$	−0.885507	+	14.0747i	−0.0304804	+	0.484472i
$845$	−23.4614	−	3.78822i	−0.807095	−	0.130319i
$846$	5.93174	−	2.34854i	0.203937	−	0.0807445i
$847$	−40.1186	+	15.8841i	−1.37849	+	0.545784i
$848$	9.73562	+	1.22990i	0.334323	+	0.0422348i
$849$	−6.11640	+	18.8244i	−0.209914	+	0.646050i
$850$	−3.92438	−	15.6749i	−0.134605	−	0.537646i
$851$	−0.133763	−	0.411680i	−0.00458534	−	0.0141122i
$852$	1.63918	+	8.59287i	0.0561573	+	0.294387i
$853$	−0.739088	−	11.7475i	−0.0253059	−	0.402226i	−0.990207	−	0.139610i	$-0.955415\pi$
$853$	−0.739088	−	11.7475i	−0.0253059	−	0.402226i	0.964901	−	0.262615i	$-0.0845850\pi$
$854$	45.4709	+	11.6750i	1.55598	+	0.399509i
$855$	−8.11172	−	0.279324i	−0.277415	−	0.00955267i
$856$	−1.08343	−	1.70721i	−0.0370308	−	0.0583511i
$857$	1.39143	−	4.28238i	0.0475303	−	0.146283i	−0.924475	−	0.381243i	$-0.875496\pi$
$857$	1.39143	−	4.28238i	0.0475303	−	0.146283i	0.972005	+	0.234960i	$0.0754960\pi$
$858$	−0.138043	+	2.19413i	−0.00471270	+	0.0749063i
$859$	−11.4563	+	1.44726i	−0.390883	+	0.0493800i	−0.318319	−	0.947984i	$-0.603118\pi$
$859$	−11.4563	+	1.44726i	−0.390883	+	0.0493800i	−0.0725643	+	0.997364i	$0.523118\pi$
$860$	7.51552	−	20.6799i	0.256277	−	0.705180i
$861$	−16.4239	+	34.9026i	−0.559726	+	1.18948i
$862$	−17.0533	−	36.2400i	−0.580836	−	1.23434i
$863$	−11.1219	−	6.11431i	−0.378593	−	0.208133i	0.281083	−	0.959684i	$-0.409306\pi$
$863$	−11.1219	−	6.11431i	−0.378593	−	0.208133i	−0.659676	+	0.751550i	$0.729306\pi$
$864$	−0.728969	−	0.684547i	−0.0248000	−	0.0232888i
$865$	−25.3646	+	2.32078i	−0.862422	+	0.0789088i
$866$	−6.87567	−	14.6115i	−0.233645	−	0.496521i
$867$	4.17883	−	5.05134i	0.141921	−	0.171553i
$868$	11.2441	+	34.6058i	0.381650	+	1.17460i
$869$	14.1682	−	3.63776i	0.480622	−	0.123403i
$870$	−6.26492	−	2.73345i	−0.212401	−	0.0926727i
$871$	1.40506	+	22.3328i	0.0476087	+	0.756719i
$872$	−0.350363	+	0.552084i	−0.0118648	+	0.0186959i
$873$	4.49025	+	4.21662i	0.151972	+	0.142711i
$874$	8.64395			0.292386
$875$	−17.7761	−	50.8076i	−0.600943	−	1.71761i
$876$	1.61405			0.0545336
$877$	−10.7175	−	10.0644i	−0.361905	−	0.339851i	0.482169	−	0.876078i	$-0.339849\pi$
$877$	−10.7175	−	10.0644i	−0.361905	−	0.339851i	−0.844074	+	0.536227i	$0.819849\pi$
$878$	−18.2089	+	28.6926i	−0.614521	+	0.968330i
$879$	0.754817	+	11.9975i	0.0254593	+	0.404665i
$880$	0.309939	−	3.17689i	0.0104481	−	0.107093i
$881$	−23.0970	+	5.93030i	−0.778158	+	0.199797i	−0.616822	−	0.787103i	$-0.711580\pi$
$881$	−23.0970	+	5.93030i	−0.778158	+	0.199797i	−0.161336	+	0.986900i	$0.551580\pi$
$882$	−4.99967	−	15.3874i	−0.168348	−	0.518120i
$883$	−8.60633	+	10.4033i	−0.289626	+	0.350098i	−0.895179	−	0.445707i	$-0.852952\pi$
$883$	−8.60633	+	10.4033i	−0.289626	+	0.350098i	0.605553	+	0.795805i	$0.292952\pi$
$884$	2.11918	+	4.50348i	0.0712757	+	0.151468i
$885$	23.9757	+	14.2766i	0.805934	+	0.479903i
$886$	23.4218	+	21.9945i	0.786870	+	0.738920i
$887$	7.87579	+	4.32975i	0.264443	+	0.145379i	0.608460	−	0.793585i	$-0.291788\pi$
$887$	7.87579	+	4.32975i	0.264443	+	0.145379i	−0.344017	+	0.938964i	$0.611788\pi$
$888$	0.0773947	+	0.164472i	0.00259719	+	0.00551932i
$889$	−37.9253	+	80.5954i	−1.27197	+	2.70308i
$890$	6.75760	+	23.5234i	0.226515	+	0.788507i
$891$	1.41624	−	0.178912i	0.0474457	−	0.00599379i
$892$	0.369897	−	5.87934i	0.0123851	−	0.196855i
$893$	7.15601	−	22.0239i	0.239467	−	0.737003i
$894$	2.43569	+	3.83803i	0.0814615	+	0.128363i
$895$	−8.48759	+	23.3547i	−0.283709	+	0.780662i
$896$	4.66323	+	1.19731i	0.155788	+	0.0399994i
$897$	0.230286	+	3.66029i	0.00768901	+	0.122213i
$898$	−4.94562	−	25.9258i	−0.165037	−	0.865156i
$899$	−7.13913	−	21.9720i	−0.238103	−	0.732807i
$900$	−0.0300507	+	4.99991i	−0.00100169	+	0.166664i
$901$	−9.79990	+	30.1610i	−0.326482	+	1.00481i
$902$	11.3469	+	1.43345i	0.377812	+	0.0477287i
$903$	−44.0484	+	17.4400i	−1.46584	+	0.580367i
$904$	0.783847	−	0.310347i	0.0260704	−	0.0103220i
$905$	7.59353	+	48.8942i	0.252418	+	1.62530i
$906$	−1.20886	+	19.2143i	−0.0401617	+	0.638353i
$907$	42.2938	+	30.7282i	1.40434	+	1.02031i	0.994115	+	0.108331i	$0.0345506\pi$
$907$	42.2938	+	30.7282i	1.40434	+	1.02031i	0.410227	+	0.911983i	$0.365449\pi$
$908$	−25.0539	+	6.43274i	−0.831442	+	0.213478i
$909$	0.700001	−	0.657345i	0.0232176	−	0.0218028i
$910$	8.39690	+	14.2963i	0.278355	+	0.473917i
$911$	24.2572	−	13.3355i	0.803676	−	0.441824i	−0.0262795	−	0.999655i	$-0.508366\pi$
$911$	24.2572	−	13.3355i	0.803676	−	0.441824i	0.829955	+	0.557830i	$0.188366\pi$
$912$	−3.60120	+	0.454937i	−0.119248	+	0.0150645i
$913$	−1.67711	+	8.79172i	−0.0555043	+	0.290964i
$914$	1.70229	+	0.215050i	0.0563069	+	0.00711322i
$915$	3.34614	+	21.5455i	0.110620	+	0.712273i
$916$	1.44953	−	7.59870i	0.0478938	−	0.251068i
$917$	−8.24317	−	12.9892i	−0.272213	−	0.428940i
$918$	2.61454	−	1.89957i	0.0862926	−	0.0626952i
$919$	28.6328	−	34.6112i	0.944510	−	1.14172i	−0.0452497	−	0.998976i	$-0.514408\pi$
$919$	28.6328	−	34.6112i	0.944510	−	1.14172i	0.989760	−	0.142741i	$-0.0455917\pi$
$920$	−0.151265	−	5.32276i	−0.00498705	−	0.175486i
$921$	11.9452	−	18.8226i	0.393606	−	0.620224i
$922$	−20.7429	−	25.0739i	−0.683131	−	0.825763i
$923$	−5.73627	+	12.1902i	−0.188812	+	0.401245i
$924$	−5.56009	+	4.03964i	−0.182913	+	0.132894i
$925$	0.339646	−	0.843010i	0.0111675	−	0.0277180i
$926$	25.8619	+	18.7897i	0.849873	+	0.617469i
$927$	5.89875	−	3.24287i	0.193741	−	0.106510i
$928$	−2.96079	−	0.760202i	−0.0971927	−	0.0249548i
$929$	31.1533	+	37.6578i	1.02211	+	1.23551i	0.971560	+	0.236792i	$0.0760960\pi$
$929$	31.1533	+	37.6578i	1.02211	+	1.23551i	0.0505456	+	0.998722i	$0.483904\pi$
$930$	−12.7101	+	11.1378i	−0.416782	+	0.365222i
$931$	−54.6037	−	21.6191i	−1.78956	−	0.708539i
$932$	17.5093			0.573538
$933$	32.6647	+	12.9329i	1.06939	+	0.423403i
$934$	6.77392	+	3.72400i	0.221650	+	0.121853i
$935$	9.89736	+	2.90773i	0.323678	+	0.0950929i
$936$	−0.288584	−	1.51281i	−0.00943265	−	0.0494477i
$937$	4.34955	−	4.08450i	0.142094	−	0.133435i	−0.610241	−	0.792216i	$-0.708928\pi$
$937$	4.34955	−	4.08450i	0.142094	−	0.133435i	0.752335	+	0.658781i	$0.228928\pi$
$938$	−50.9935	+	47.8861i	−1.66500	+	1.56354i
$939$	−2.60713	−	13.6671i	−0.0850806	−	0.446008i
$940$	−13.6871	−	4.02111i	−0.446424	−	0.131154i
$941$	−0.666546	−	0.366437i	−0.0217288	−	0.0119455i	0.470852	−	0.882212i	$-0.343946\pi$
$941$	−0.666546	−	0.366437i	−0.0217288	−	0.0119455i	−0.492581	+	0.870267i	$0.663946\pi$
$942$	3.45094	+	1.36633i	0.112438	+	0.0445173i
$943$	19.0796			0.621318
$944$	11.6029	+	4.59391i	0.377642	+	0.149519i
$945$	8.09669	−	7.09506i	0.263385	−	0.230802i
$946$	8.95374	+	10.8232i	0.291111	+	0.351893i
$947$	43.7080	+	11.2223i	1.42032	+	0.364676i	0.879274	−	0.476317i	$-0.158028\pi$
$947$	43.7080	+	11.2223i	1.42032	+	0.364676i	0.541046	+	0.840993i	$0.318028\pi$
$948$	−8.97963	+	4.93659i	−0.291645	+	0.160333i
$949$	2.01103	+	1.46110i	0.0652809	+	0.0474293i
$950$	13.9143	+	11.6525i	0.451441	+	0.378057i
$951$	−6.61260	+	4.80434i	−0.214428	+	0.155791i
$952$	−6.62478	+	14.0784i	−0.214710	+	0.456283i
$953$	1.70975	+	2.06673i	0.0553841	+	0.0669479i	0.797478	−	0.603348i	$-0.206167\pi$
$953$	1.70975	+	2.06673i	0.0553841	+	0.0669479i	−0.742094	+	0.670296i	$0.766167\pi$
$954$	5.25807	−	8.28539i	0.170236	−	0.268249i
$955$	0.134534	+	4.73402i	0.00435341	+	0.153189i
$956$	−5.35202	+	6.46948i	−0.173097	+	0.209238i
$957$	3.53023	−	2.56486i	0.114116	−	0.0829101i
$958$	−4.49405	−	7.08149i	−0.145196	−	0.228793i
$959$	12.5621	−	65.8529i	0.405652	−	2.12650i
$960$	0.343160	+	2.20958i	0.0110754	+	0.0713139i
$961$	−25.9136	−	3.27365i	−0.835922	−	0.105602i
$962$	−0.0524564	+	0.274986i	−0.00169126	+	0.00886590i
$963$	−2.00603	+	0.253420i	−0.0646433	+	0.00816635i
$964$	16.1730	−	8.89116i	0.520896	−	0.286365i
$965$	−3.93496	−	6.69952i	−0.126671	−	0.215665i
$966$	−8.35768	+	7.84839i	−0.268904	+	0.252518i
$967$	43.3215	−	11.1231i	1.39313	−	0.357694i	0.523762	−	0.851865i	$-0.324528\pi$
$967$	43.3215	−	11.1231i	1.39313	−	0.357694i	0.869365	+	0.494171i	$0.164528\pi$
$968$	−7.25062	−	5.26789i	−0.233044	−	0.169316i
$969$	0.736574	−	11.7075i	0.0236622	−	0.376099i
$970$	−2.11377	−	13.6104i	−0.0678691	−	0.437004i
$971$	−4.28996	+	1.69852i	−0.137671	+	0.0545080i	−0.435950	−	0.899971i	$-0.643588\pi$
$971$	−4.28996	+	1.69852i	−0.137671	+	0.0545080i	0.298279	+	0.954479i	$0.403588\pi$
$972$	−0.929776	+	0.368125i	−0.0298226	+	0.0118076i
$973$	49.7856	+	6.28938i	1.59605	+	0.201628i
$974$	−2.17704	+	6.70023i	−0.0697567	+	0.214689i
$975$	−4.56357	+	6.20247i	−0.146151	+	0.198638i
$976$	3.01321	+	9.27371i	0.0964506	+	0.296844i
$977$	9.91485	+	51.9755i	0.317204	+	1.66284i	0.681695	+	0.731636i	$0.261243\pi$
$977$	9.91485	+	51.9755i	0.317204	+	1.66284i	−0.364491	+	0.931207i	$0.618757\pi$
$978$	1.45951	+	23.1982i	0.0466700	+	0.741798i
$979$	−15.1337	−	3.88568i	−0.483676	−	0.124187i
$980$	−12.3571	+	34.0021i	−0.394732	+	1.08616i
$981$	0.350363	+	0.552084i	0.0111862	+	0.0176267i
$982$	9.53549	−	29.3472i	0.304290	−	0.936507i
$983$	0.0706548	−	1.12303i	0.00225354	−	0.0358189i	−0.996739	−	0.0806899i	$-0.974288\pi$
$983$	0.0706548	−	1.12303i	0.00225354	−	0.0358189i	0.998993	+	0.0448709i	$0.0142877\pi$
$984$	−7.94885	+	1.00417i	−0.253400	+	0.0320119i
$985$	1.63102	+	5.67764i	0.0519687	+	0.180905i
$986$	4.20622	−	8.93868i	0.133953	−	0.284666i
$987$	13.0779	+	27.7919i	0.416274	+	0.884627i
$988$	−4.89877	−	2.69312i	−0.155851	−	0.0856795i
$989$	17.0820	+	16.0410i	0.543175	+	0.510075i
$990$	−2.74257	−	1.63310i	−0.0871646	−	0.0519032i
$991$	15.8990	+	33.7871i	0.505049	+	1.07328i	0.981035	+	0.193831i	$0.0620913\pi$
$991$	15.8990	+	33.7871i	0.505049	+	1.07328i	−0.475986	+	0.879453i	$0.657909\pi$
$992$	−4.81749	+	5.82334i	−0.152955	+	0.184891i
$993$	3.51738	+	10.8254i	0.111621	+	0.343533i
$994$	−40.7931	+	10.4739i	−1.29388	+	0.332211i
$995$	3.54378	−	36.3239i	0.112345	−	1.15154i
$996$	−0.393691	−	6.25754i	−0.0124746	−	0.198278i
$997$	1.45985	−	2.30036i	0.0462341	−	0.0728532i	−0.820425	−	0.571755i	$-0.806263\pi$
$997$	1.45985	−	2.30036i	0.0462341	−	0.0728532i	0.866659	+	0.498901i	$0.166263\pi$
$998$	5.57584	+	5.23606i	0.176500	+	0.165745i
$999$	0.181772			0.00575100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.d.91.4	✓	140
125.11	even	25	inner	750.2.m.d.511.4	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.d.91.4	✓	140	1.1	even	1	trivial
750.2.m.d.511.4	yes	140	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)

\(f(q)\)	\(=\)	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.13246 - 1.92809i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-1.48776 - 4.57885i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +O(q^{10})\)	\(q+(-0.728969 - 0.684547i) q^{2} +(0.535827 - 0.844328i) q^{3} +(0.0627905 + 0.998027i) q^{4} +(-1.13246 - 1.92809i) q^{5} +(-0.968583 + 0.248690i) q^{6} +(-1.48776 - 4.57885i) q^{7} +(0.637424 - 0.770513i) q^{8} +(-0.425779 - 0.904827i) q^{9} +(-0.494339 + 2.18074i) q^{10} +(-1.04060 - 0.977187i) q^{11} +(0.876307 + 0.481754i) q^{12} +(0.655738 + 1.39351i) q^{13} +(-2.04991 + 4.35628i) q^{14} +(-2.23474 - 0.0769525i) q^{15} +(-0.992115 + 0.125333i) q^{16} +(0.202923 - 3.22537i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.94495 + 3.06476i) q^{19} +(1.85318 - 1.25129i) q^{20} +(-4.66323 - 1.19731i) q^{21} +(0.0896331 + 1.42468i) q^{22} +(0.446225 + 2.33919i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(-2.43506 + 4.36698i) q^{25} +(0.475913 - 1.46471i) q^{26} +(-0.992115 - 0.125333i) q^{27} +(4.47639 - 1.77233i) q^{28} +(-2.84216 + 1.12529i) q^{29} +(1.57638 + 1.58588i) q^{30} +(-0.474555 + 7.54283i) q^{31} +(0.809017 + 0.587785i) q^{32} +(-1.38265 + 0.355003i) q^{33} +(-2.35584 + 2.21228i) q^{34} +(-7.14360 + 8.05390i) q^{35} +(0.876307 - 0.481754i) q^{36} +(-0.180338 + 0.0227820i) q^{37} +(0.680160 - 3.56553i) q^{38} +(1.52794 + 0.193024i) q^{39} +(-2.20748 - 0.356433i) q^{40} +(1.50131 - 7.87012i) q^{41} +(2.57973 + 4.06500i) q^{42} +(7.96085 - 5.78390i) q^{43} +(0.909919 - 1.09990i) q^{44} +(-1.26241 + 1.84562i) q^{45} +(1.27600 - 2.01066i) q^{46} +(-4.06660 - 4.91568i) q^{47} +(-0.425779 + 0.904827i) q^{48} +(-13.0893 + 9.50993i) q^{49} +(4.76448 - 1.51648i) q^{50} +(-2.61454 - 1.89957i) q^{51} +(-1.34959 + 0.741943i) q^{52} +(-9.50471 - 2.44039i) q^{53} +(0.637424 + 0.770513i) q^{54} +(-0.705665 + 3.11299i) q^{55} +(-4.47639 - 1.77233i) q^{56} +3.62982 q^{57} +(2.84216 + 1.12529i) q^{58} +(-10.9356 - 6.01191i) q^{59} +(-0.0635200 - 2.23517i) q^{60} +(-1.82715 - 9.57824i) q^{61} +(5.50936 - 5.17363i) q^{62} +(-3.50961 + 3.29574i) q^{63} +(-0.187381 - 0.982287i) q^{64} +(1.94422 - 2.84242i) q^{65} +(1.25092 + 0.687700i) q^{66} +(13.5094 + 5.34873i) q^{67} +3.23175 q^{68} +(2.21414 + 0.876641i) q^{69} +(10.7207 - 0.980912i) q^{70} +(5.57607 + 6.74031i) q^{71} +(-0.968583 - 0.248690i) q^{72} +(1.41440 - 0.777573i) q^{73} +(0.147056 + 0.106843i) q^{74} +(2.38239 + 4.39593i) q^{75} +(-2.93659 + 2.13355i) q^{76} +(-2.92623 + 6.21856i) q^{77} +(-0.981689 - 1.18666i) q^{78} +(-5.49069 + 8.65194i) q^{79} +(1.36519 + 1.77095i) q^{80} +(-0.637424 + 0.770513i) q^{81} +(-6.48187 + 4.70935i) q^{82} +(-3.35959 - 5.29386i) q^{83} +(0.902144 - 4.72921i) q^{84} +(-6.44860 + 3.26135i) q^{85} +(-9.76256 - 1.23330i) q^{86} +(-0.572792 + 3.00268i) q^{87} +(-1.41624 + 0.178912i) q^{88} +(9.59159 - 5.27302i) q^{89} +(2.18367 - 0.481223i) q^{90} +(5.40511 - 5.07573i) q^{91} +(-2.30656 + 0.592223i) q^{92} +(6.11435 + 4.44233i) q^{93} +(-0.400588 + 6.36716i) q^{94} +(3.70654 - 7.22077i) q^{95} +(0.929776 - 0.368125i) q^{96} +(-5.72717 + 2.26755i) q^{97} +(16.0517 + 2.02780i) q^{98} +(-0.441120 + 1.35763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{5} + 5 q^{7}+O(q^{10}) \) 140 * q - 20 * q^5 + 5 * q^7	\( 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32} - 15 q^{34} - 25 q^{37} + 35 q^{38} - 10 q^{39} + 5 q^{40} + 55 q^{41} + 35 q^{43} + 25 q^{44} + 20 q^{46} + 10 q^{47} - 60 q^{49} - 5 q^{51} + 40 q^{52} + 40 q^{55} + 20 q^{57} - 25 q^{58} + 75 q^{59} + 50 q^{61} + 5 q^{62} + 5 q^{63} - 35 q^{65} + 20 q^{66} - 95 q^{67} + 20 q^{68} - 20 q^{69} + 65 q^{70} - 50 q^{71} + 20 q^{73} + 30 q^{74} + 35 q^{75} - 5 q^{76} + 15 q^{77} + 5 q^{78} + 70 q^{79} - 15 q^{82} + 25 q^{83} + 5 q^{84} - 95 q^{85} - 5 q^{86} - 5 q^{88} - 105 q^{89} - 5 q^{90} - 65 q^{91} + 55 q^{92} - 30 q^{93} - 10 q^{94} + 125 q^{95} - 5 q^{97} + 70 q^{98} - 10 q^{99}+O(q^{100}) \) 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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