LMFDB - Embedded newform 690.2.x.a.77.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.5
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-1.39273 - 1.02971i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(0.737339 - 2.11100i) q^{5} +(0.0103038 + 1.73202i) q^{6} +(0.427775 + 1.96645i) q^{7} +(0.936950 - 0.349464i) q^{8} +(0.879385 + 2.86822i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.39273 - 1.02971i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(0.737339 - 2.11100i) q^{5} +(0.0103038 + 1.73202i) q^{6} +(0.427775 + 1.96645i) q^{7} +(0.936950 - 0.349464i) q^{8} +(0.879385 + 2.86822i) q^{9} +(-2.13182 + 0.674807i) q^{10} +(2.75644 - 0.396317i) q^{11} +(1.38038 - 1.04621i) q^{12} +(-0.708524 + 3.25703i) q^{13} +(1.31787 - 1.52090i) q^{14} +(-3.20064 + 2.18081i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-3.68689 + 6.75203i) q^{17} +(1.76913 - 2.42284i) q^{18} +(-0.595863 + 2.02932i) q^{19} +(1.81776 + 1.30221i) q^{20} +(1.42910 - 3.17922i) q^{21} +(-1.96914 - 1.96914i) q^{22} +(2.24140 + 4.23982i) q^{23} +(-1.66476 - 0.478080i) q^{24} +(-3.91266 - 3.11305i) q^{25} +(3.03199 - 1.38466i) q^{26} +(1.72870 - 4.90016i) q^{27} +(-2.00731 - 0.143566i) q^{28} +(8.71801 - 2.55984i) q^{29} +(3.66390 + 1.25533i) q^{30} +(-3.74038 + 8.19029i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.24707 - 2.28638i) q^{33} +(7.61474 - 1.09483i) q^{34} +(4.46660 + 0.546905i) q^{35} +(-2.99979 + 0.0356929i) q^{36} +(6.14840 - 0.439743i) q^{37} +(1.98164 - 0.739115i) q^{38} +(4.34059 - 3.80658i) q^{39} +(-0.0468706 - 2.23558i) q^{40} +(4.27571 - 3.70492i) q^{41} +(-3.40152 + 0.761177i) q^{42} +(-7.26097 - 2.70820i) q^{43} +(-0.396317 + 2.75644i) q^{44} +(6.70322 + 0.258465i) q^{45} +(2.05093 - 4.33517i) q^{46} +(-3.06623 + 3.06623i) q^{47} +(0.614933 + 1.61921i) q^{48} +(2.68349 - 1.22551i) q^{49} +(-0.147351 + 4.99783i) q^{50} +(12.0875 - 5.60731i) q^{51} +(-2.92548 - 1.59744i) q^{52} +(0.216673 + 0.996029i) q^{53} +(-4.95875 + 1.55267i) q^{54} +(1.19581 - 6.11108i) q^{55} +(1.08801 + 1.69297i) q^{56} +(2.91949 - 2.21273i) q^{57} +(-7.27377 - 5.44507i) q^{58} +(2.17379 - 1.39701i) q^{59} +(-1.19074 - 3.68539i) q^{60} +(3.11627 - 6.82367i) q^{61} +(8.79819 - 1.91393i) q^{62} +(-5.26403 + 2.95622i) q^{63} +(0.755750 - 0.654861i) q^{64} +(6.35318 + 3.89723i) q^{65} +(0.714830 + 4.77013i) q^{66} +(-6.59725 + 4.93864i) q^{67} +(-5.43981 - 5.43981i) q^{68} +(1.24413 - 8.21292i) q^{69} +(-2.23891 - 3.90344i) q^{70} +(-3.37763 - 0.485631i) q^{71} +(1.82628 + 2.38006i) q^{72} +(8.39682 - 4.58501i) q^{73} +(-4.03663 - 4.65852i) q^{74} +(2.24373 + 8.36455i) q^{75} +(-1.77925 - 1.14345i) q^{76} +(1.95847 + 5.25087i) q^{77} +(-5.64854 - 1.19362i) q^{78} +(6.84595 + 10.6525i) q^{79} +(-1.76158 + 1.37725i) q^{80} +(-7.45336 + 5.04454i) q^{81} +(-5.52828 - 1.20260i) q^{82} +(4.95429 - 0.354338i) q^{83} +(2.64781 + 2.26690i) q^{84} +(11.5351 + 12.7616i) q^{85} +(2.18331 + 7.43567i) q^{86} +(-14.7777 - 5.41188i) q^{87} +(2.44415 - 1.33461i) q^{88} +(-0.267827 - 0.586459i) q^{89} +(-3.81018 - 5.52110i) q^{90} -6.70788 q^{91} +(-4.69956 + 0.956114i) q^{92} +(13.6430 - 7.55534i) q^{93} +(4.29217 + 0.617121i) q^{94} +(3.84455 + 2.75416i) q^{95} +(0.927733 - 1.46264i) q^{96} +(-1.12817 + 15.7739i) q^{97} +(-2.58922 - 1.41382i) q^{98} +(3.56070 + 7.55757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−1.39273	−	1.02971i	−0.804092	−	0.594505i
$3$	−1.39273	−	1.02971i	−0.804092	−	0.594505i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	0.737339	−	2.11100i	0.329748	−	0.944069i
$5$	0.737339	−	2.11100i	0.329748	−	0.944069i
$6$	0.0103038	+	1.73202i	0.00420652	+	0.707094i
$7$	0.427775	+	1.96645i	0.161684	+	0.743248i	0.984563	+	0.175032i	$0.0560028\pi$
$7$	0.427775	+	1.96645i	0.161684	+	0.743248i	−0.822879	+	0.568217i	$0.807634\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	0.879385	+	2.86822i	0.293128	+	0.956073i
$10$	−2.13182	+	0.674807i	−0.674139	+	0.213393i
$11$	2.75644	−	0.396317i	0.831099	−	0.119494i	0.286384	−	0.958115i	$-0.407547\pi$
$11$	2.75644	−	0.396317i	0.831099	−	0.119494i	0.544715	+	0.838621i	$0.316638\pi$
$12$	1.38038	−	1.04621i	0.398481	−	0.302015i
$13$	−0.708524	+	3.25703i	−0.196509	+	0.903338i	0.768239	+	0.640163i	$0.221133\pi$
$13$	−0.708524	+	3.25703i	−0.196509	+	0.903338i	−0.964748	+	0.263175i	$0.915230\pi$
$14$	1.31787	−	1.52090i	0.352215	−	0.406478i
$15$	−3.20064	+	2.18081i	−0.826401	+	0.563082i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−3.68689	+	6.75203i	−0.894201	+	1.63761i	−0.131060	+	0.991374i	$0.541838\pi$
$17$	−3.68689	+	6.75203i	−0.894201	+	1.63761i	−0.763141	+	0.646232i	$0.776344\pi$
$18$	1.76913	−	2.42284i	0.416988	−	0.571070i
$19$	−0.595863	+	2.02932i	−0.136700	+	0.465558i	−0.999178	−	0.0405366i	$-0.987093\pi$
$19$	−0.595863	+	2.02932i	−0.136700	+	0.465558i	0.862478	+	0.506095i	$0.168911\pi$
$20$	1.81776	+	1.30221i	0.406463	+	0.291183i
$21$	1.42910	−	3.17922i	0.311856	−	0.693762i
$22$	−1.96914	−	1.96914i	−0.419823	−	0.419823i
$23$	2.24140	+	4.23982i	0.467365	+	0.884065i
$23$	2.24140	+	4.23982i	0.467365	+	0.884065i
$24$	−1.66476	−	0.478080i	−0.339819	−	0.0975877i
$25$	−3.91266	−	3.11305i	−0.782533	−	0.622609i
$26$	3.03199	−	1.38466i	0.594622	−	0.271555i
$27$	1.72870	−	4.90016i	0.332688	−	0.943037i
$28$	−2.00731	−	0.143566i	−0.379347	−	0.0271314i
$29$	8.71801	−	2.55984i	1.61889	−	0.475350i	0.658173	−	0.752867i	$-0.271329\pi$
$29$	8.71801	−	2.55984i	1.61889	−	0.475350i	0.960721	+	0.277516i	$0.0895113\pi$
$30$	3.66390	+	1.25533i	0.668933	+	0.229192i
$31$	−3.74038	+	8.19029i	−0.671792	+	1.47102i	0.199319	+	0.979935i	$0.436127\pi$
$31$	−3.74038	+	8.19029i	−0.671792	+	1.47102i	−0.871112	+	0.491085i	$0.836600\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−4.24707	−	2.28638i	−0.739320	−	0.398008i
$34$	7.61474	−	1.09483i	1.30592	−	0.187763i
$35$	4.46660	+	0.546905i	0.754993	+	0.0924439i
$36$	−2.99979	+	0.0356929i	−0.499965	+	0.00594882i
$37$	6.14840	−	0.439743i	1.01079	−	0.0722932i	0.443892	−	0.896080i	$-0.353597\pi$
$37$	6.14840	−	0.439743i	1.01079	−	0.0722932i	0.566899	+	0.823787i	$0.308143\pi$
$38$	1.98164	−	0.739115i	0.321465	−	0.119900i
$39$	4.34059	−	3.80658i	0.695050	−	0.609541i
$40$	−0.0468706	−	2.23558i	−0.00741089	−	0.353476i
$41$	4.27571	−	3.70492i	0.667753	−	0.578611i	−0.253614	−	0.967306i	$-0.581619\pi$
$41$	4.27571	−	3.70492i	0.667753	−	0.578611i	0.921367	+	0.388694i	$0.127074\pi$
$42$	−3.40152	+	0.761177i	−0.524867	+	0.117452i
$43$	−7.26097	−	2.70820i	−1.10729	−	0.412997i	−0.271715	−	0.962378i	$-0.587591\pi$
$43$	−7.26097	−	2.70820i	−1.10729	−	0.412997i	−0.835572	+	0.549381i	$0.814864\pi$
$44$	−0.396317	+	2.75644i	−0.0597470	+	0.415549i
$45$	6.70322	+	0.258465i	0.999257	+	0.0385297i
$46$	2.05093	−	4.33517i	0.302393	−	0.639186i
$47$	−3.06623	+	3.06623i	−0.447256	+	0.447256i	−0.894441	−	0.447185i	$-0.852426\pi$
$47$	−3.06623	+	3.06623i	−0.447256	+	0.447256i	0.447185	+	0.894441i	$0.352426\pi$
$48$	0.614933	+	1.61921i	0.0887580	+	0.233714i
$49$	2.68349	−	1.22551i	0.383355	−	0.175073i
$50$	−0.147351	+	4.99783i	−0.0208386	+	0.706800i
$51$	12.0875	−	5.60731i	1.69258	−	0.785180i
$52$	−2.92548	−	1.59744i	−0.405692	−	0.221524i
$53$	0.216673	+	0.996029i	0.0297623	+	0.136815i	0.989631	−	0.143636i	$-0.0458795\pi$
$53$	0.216673	+	0.996029i	0.0297623	+	0.136815i	−0.959868	+	0.280451i	$0.909516\pi$
$54$	−4.95875	+	1.55267i	−0.674801	+	0.211291i
$55$	1.19581	−	6.11108i	0.161242	−	0.824018i
$56$	1.08801	+	1.69297i	0.145391	+	0.226233i
$57$	2.91949	−	2.21273i	0.386696	−	0.293083i
$58$	−7.27377	−	5.44507i	−0.955092	−	0.714973i
$59$	2.17379	−	1.39701i	0.283003	−	0.181875i	−0.391437	−	0.920205i	$-0.628022\pi$
$59$	2.17379	−	1.39701i	0.283003	−	0.181875i	0.674439	+	0.738330i	$0.264385\pi$
$60$	−1.19074	−	3.68539i	−0.153724	−	0.475782i
$61$	3.11627	−	6.82367i	0.398997	−	0.873681i	−0.598374	−	0.801217i	$-0.704186\pi$
$61$	3.11627	−	6.82367i	0.398997	−	0.873681i	0.997371	−	0.0724645i	$-0.0230864\pi$
$62$	8.79819	−	1.91393i	1.11737	−	0.243069i
$63$	−5.26403	+	2.95622i	−0.663206	+	0.372449i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	6.35318	+	3.89723i	0.788015	+	0.483392i
$66$	0.714830	+	4.77013i	0.0879895	+	0.587163i
$67$	−6.59725	+	4.93864i	−0.805982	+	0.603351i	−0.920800	−	0.390036i	$-0.872463\pi$
$67$	−6.59725	+	4.93864i	−0.805982	+	0.603351i	0.114818	+	0.993387i	$0.463372\pi$
$68$	−5.43981	−	5.43981i	−0.659673	−	0.659673i
$69$	1.24413	−	8.21292i	0.149776	−	0.988720i
$70$	−2.23891	−	3.90344i	−0.267601	−	0.466551i
$71$	−3.37763	−	0.485631i	−0.400851	−	0.0576337i	−0.0610589	−	0.998134i	$-0.519448\pi$
$71$	−3.37763	−	0.485631i	−0.400851	−	0.0576337i	−0.339793	+	0.940500i	$0.610357\pi$
$72$	1.82628	+	2.38006i	0.215229	+	0.280493i
$73$	8.39682	−	4.58501i	0.982774	−	0.536635i	0.0942907	−	0.995545i	$-0.469942\pi$
$73$	8.39682	−	4.58501i	0.982774	−	0.536635i	0.888483	+	0.458910i	$0.151760\pi$
$74$	−4.03663	−	4.65852i	−0.469249	−	0.541542i
$75$	2.24373	+	8.36455i	0.259084	+	0.965855i
$76$	−1.77925	−	1.14345i	−0.204094	−	0.131163i
$77$	1.95847	+	5.25087i	0.223189	+	0.598393i
$78$	−5.64854	−	1.19362i	−0.639572	−	0.135151i
$79$	6.84595	+	10.6525i	0.770230	+	1.19850i	0.975544	+	0.219805i	$0.0705420\pi$
$79$	6.84595	+	10.6525i	0.770230	+	1.19850i	−0.205314	+	0.978696i	$0.565822\pi$
$80$	−1.76158	+	1.37725i	−0.196951	+	0.153982i
$81$	−7.45336	+	5.04454i	−0.828152	+	0.560504i
$82$	−5.52828	−	1.20260i	−0.610496	−	0.132805i
$83$	4.95429	−	0.354338i	0.543804	−	0.0388937i	0.203265	−	0.979124i	$-0.434845\pi$
$83$	4.95429	−	0.354338i	0.543804	−	0.0388937i	0.340540	+	0.940230i	$0.389390\pi$
$84$	2.64781	+	2.26690i	0.288900	+	0.247340i
$85$	11.5351	+	12.7616i	1.25115	+	1.38418i
$86$	2.18331	+	7.43567i	0.235432	+	0.801809i
$87$	−14.7777	−	5.41188i	−1.58434	−	0.580215i
$88$	2.44415	−	1.33461i	0.260547	−	0.142270i
$89$	−0.267827	−	0.586459i	−0.0283896	−	0.0621645i	0.894906	−	0.446255i	$-0.147242\pi$
$89$	−0.267827	−	0.586459i	−0.0283896	−	0.0621645i	−0.923296	+	0.384090i	$0.874515\pi$
$90$	−3.81018	−	5.52110i	−0.401628	−	0.581975i
$91$	−6.70788			−0.703177
$92$	−4.69956	+	0.956114i	−0.489963	+	0.0996818i
$93$	13.6430	−	7.55534i	1.41471	−	0.783452i
$94$	4.29217	+	0.617121i	0.442704	+	0.0636512i
$95$	3.84455	+	2.75416i	0.394443	+	0.282571i
$96$	0.927733	−	1.46264i	0.0946863	−	0.149280i
$97$	−1.12817	+	15.7739i	−0.114548	+	1.60159i	0.537398	+	0.843329i	$0.319407\pi$
$97$	−1.12817	+	15.7739i	−0.114548	+	1.60159i	−0.651946	+	0.758265i	$0.726047\pi$
$98$	−2.58922	−	1.41382i	−0.261551	−	0.142818i
$99$	3.56070	+	7.55757i	0.357864	+	0.759564i
$100$	4.08927	−	2.87713i	0.408927	−	0.287713i
$101$	−3.34035	−	2.89443i	−0.332377	−	0.288006i	0.472643	−	0.881254i	$-0.343300\pi$
$101$	−3.34035	−	2.89443i	−0.332377	−	0.288006i	−0.805020	+	0.593248i	$0.797845\pi$
$102$	−11.7326	−	6.31619i	−1.16170	−	0.625396i
$103$	−7.14457	−	5.34836i	−0.703976	−	0.526990i	0.186254	−	0.982502i	$-0.440365\pi$
$103$	−7.14457	−	5.34836i	−0.703976	−	0.526990i	−0.890230	+	0.455512i	$0.849456\pi$
$104$	0.474365	+	3.29928i	0.0465153	+	0.323521i
$105$	−5.65760	−	5.36100i	−0.552125	−	0.523180i
$106$	0.667515	−	0.770353i	0.0648348	−	0.0748233i
$107$	−5.39238	−	14.4575i	−0.521301	−	1.39766i	−0.884758	−	0.466051i	$-0.845676\pi$
$107$	−5.39238	−	14.4575i	−0.521301	−	1.39766i	0.363457	−	0.931611i	$-0.381596\pi$
$108$	4.21464	+	3.03921i	0.405554	+	0.292448i
$109$	2.58060	+	8.78872i	0.247177	+	0.841807i	0.985834	+	0.167725i	$0.0536422\pi$
$109$	2.58060	+	8.78872i	0.247177	+	0.841807i	−0.738657	+	0.674082i	$0.764540\pi$
$110$	−5.60879	+	2.70494i	−0.534777	+	0.257906i
$111$	−9.01587	−	5.71865i	−0.855748	−	0.542790i
$112$	0.703276	−	1.88556i	0.0664533	−	0.178168i
$113$	12.8688	−	9.63349i	1.21060	−	0.906242i	0.213106	−	0.977029i	$-0.431642\pi$
$113$	12.8688	−	9.63349i	1.21060	−	0.906242i	0.997491	+	0.0707869i	$0.0225510\pi$
$114$	−3.52097	−	1.01114i	−0.329769	−	0.0947016i
$115$	10.6030	−	1.60542i	0.988731	−	0.149706i
$116$			9.08606i			0.843620i
$117$	−9.96494	+	0.831983i	−0.921259	+	0.0769168i
$118$	−2.42106	−	0.903010i	−0.222877	−	0.0831288i
$119$	−14.8547	−	4.36173i	−1.36173	−	0.399839i
$120$	−2.23672	+	3.16181i	−0.204184	+	0.288633i
$121$	−3.11351	+	0.914210i	−0.283047	+	0.0831100i
$122$	−7.33014	+	1.59457i	−0.663639	+	0.144366i
$123$	−9.76990	+	0.757201i	−0.880922	+	0.0682745i
$124$	−6.80474	−	5.89634i	−0.611084	−	0.529507i
$125$	−9.45661	+	5.96427i	−0.845825	+	0.533461i
$126$	5.52119	+	2.44248i	0.491867	+	0.217593i
$127$	1.25633	−	1.67827i	0.111482	−	0.148922i	−0.741330	−	0.671141i	$-0.765805\pi$
$127$	1.25633	−	1.67827i	0.111482	−	0.148922i	0.852812	+	0.522219i	$0.174896\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	7.32389	+	11.2485i	0.644833	+	0.990375i
$130$	−0.687425	−	7.42150i	−0.0602911	−	0.650909i
$131$	−7.50989	+	11.6856i	−0.656142	+	1.02098i	0.340591	+	0.940212i	$0.389373\pi$
$131$	−7.50989	+	11.6856i	−0.656142	+	1.02098i	−0.996733	+	0.0807654i	$0.974264\pi$
$132$	3.39030	−	3.43088i	0.295088	−	0.298620i
$133$	−4.24546	−	0.303641i	−0.368128	−	0.0263290i
$134$	7.90716	+	2.32175i	0.683075	+	0.200569i
$135$	−9.06962	−	7.26236i	−0.780589	−	0.625045i
$136$	−1.09483	+	7.61474i	−0.0938813	+	0.652959i
$137$	−1.46084	+	1.46084i	−0.124808	+	0.124808i	−0.766752	−	0.641944i	$-0.778128\pi$
$137$	−1.46084	+	1.46084i	−0.124808	+	0.124808i	0.641944	+	0.766752i	$0.278128\pi$
$138$	−7.32037	+	3.92584i	−0.623151	+	0.334190i
$139$			6.55363i			0.555872i	0.960600	+	0.277936i	$0.0896503\pi$
$139$			6.55363i			0.555872i	−0.960600	+	0.277936i	$0.910350\pi$
$140$	−1.78314	+	4.13159i	−0.150703	+	0.349183i
$141$	7.42777	−	1.11309i	0.625531	−	0.0937393i
$142$	1.63537	+	2.99496i	0.137238	+	0.251332i
$143$	−0.662190	+	9.25862i	−0.0553751	+	0.774245i
$144$	0.810891	−	2.88833i	0.0675742	−	0.240694i
$145$	1.02430	−	20.2912i	0.0850634	−	1.68509i
$146$	−8.70252	−	3.97431i	−0.720226	−	0.328916i
$147$	−4.99929	−	1.05642i	−0.412334	−	0.0871321i
$148$	−1.31028	+	6.02324i	−0.107704	+	0.495107i
$149$	−3.01405	−	20.9631i	−0.246920	−	1.71737i	−0.615810	−	0.787895i	$-0.711171\pi$
$149$	−3.01405	−	20.9631i	−0.246920	−	1.71737i	0.368890	−	0.929473i	$-0.379738\pi$
$150$	5.35155	−	6.80889i	0.436952	−	0.555943i
$151$	−13.0659	+	8.39694i	−1.06329	+	0.683333i	−0.950638	−	0.310302i	$-0.899570\pi$
$151$	−13.0659	+	8.39694i	−1.06329	+	0.683333i	−0.112649	+	0.993635i	$0.535934\pi$
$152$	0.150882	+	2.10960i	0.0122381	+	0.171112i
$153$	−22.6085	−	4.63717i	−1.82779	−	0.374893i
$154$	3.02987	−	4.71457i	0.244154	−	0.379911i
$155$	14.5318	+	13.9350i	1.16722	+	1.11928i
$156$	2.42951	+	5.23720i	0.194516	+	0.419312i
$157$	−1.98945	−	3.64341i	−0.158776	−	0.290776i	0.786166	−	0.618016i	$-0.212063\pi$
$157$	−1.98945	−	3.64341i	−0.158776	−	0.290776i	−0.944941	+	0.327240i	$0.893881\pi$
$158$	4.42515	−	11.8643i	0.352046	−	0.943871i
$159$	0.723857	−	1.61031i	0.0574056	−	0.127706i
$160$	2.15823	+	0.584863i	0.170623	+	0.0462375i
$161$	−7.37859	+	6.22130i	−0.581514	+	0.490307i
$162$	8.50500	+	2.94365i	0.668216	+	0.231275i
$163$	10.4884	+	14.0109i	0.821516	+	1.09742i	0.993669	+	0.112347i	$0.0358367\pi$
$163$	10.4884	+	14.0109i	0.821516	+	1.09742i	−0.172153	+	0.985070i	$0.555072\pi$
$164$	2.35024	+	5.14631i	0.183523	+	0.401859i
$165$	−7.95809	+	7.27973i	−0.619536	+	0.566727i
$166$	−3.25266	−	3.75377i	−0.252455	−	0.291349i
$167$	−2.32039	+	4.24947i	−0.179557	+	0.328834i	−0.951920	−	0.306348i	$-0.900893\pi$
$167$	−2.32039	+	4.24947i	−0.179557	+	0.328834i	0.772363	+	0.635182i	$0.219075\pi$
$168$	0.227976	−	3.47819i	0.0175887	−	0.268348i
$169$	1.71897	+	0.785028i	0.132229	+	0.0603867i
$170$	3.30344	−	16.8820i	0.253363	−	1.29479i
$171$	−6.34453	+	0.0754902i	−0.485178	+	0.00577288i
$172$	4.64415	−	6.20386i	0.354113	−	0.473040i
$173$	−7.66531	+	10.2396i	−0.582782	+	0.778506i	−0.990926	−	0.134412i	$-0.957086\pi$
$173$	−7.66531	+	10.2396i	−0.582782	+	0.778506i	0.408143	+	0.912918i	$0.366176\pi$
$174$	4.52352	+	15.0734i	0.342927	+	1.14271i
$175$	4.44791	−	9.02574i	0.336231	−	0.682282i
$176$	−2.53313	−	1.15684i	−0.190942	−	0.0872003i
$177$	−4.46601	−	0.292722i	−0.335686	−	0.0220024i
$178$	−0.308982	+	0.565858i	−0.0231592	+	0.0424128i
$179$	12.4657	+	14.3862i	0.931734	+	1.07528i	0.996999	+	0.0774100i	$0.0246650\pi$
$179$	12.4657	+	14.3862i	0.931734	+	1.07528i	−0.0652658	+	0.997868i	$0.520790\pi$
$180$	−2.13651	+	6.35888i	−0.159246	+	0.473963i
$181$	8.95286	+	19.6040i	0.665461	+	1.45716i	0.877345	+	0.479861i	$0.159313\pi$
$181$	8.95286	+	19.6040i	0.665461	+	1.45716i	−0.211884	+	0.977295i	$0.567960\pi$
$182$	4.01988	+	5.36993i	0.297974	+	0.398046i
$183$	−11.3665	+	6.29466i	−0.840238	+	0.465315i
$184$	3.58175	+	3.18921i	0.264050	+	0.235112i
$185$	3.60516	−	13.3035i	0.265056	−	0.978095i
$186$	−14.2243	−	6.39402i	−1.04298	−	0.468833i
$187$	−7.48675	+	20.0727i	−0.547485	+	1.46786i
$188$	−2.07817	−	3.80589i	−0.151566	−	0.277573i
$189$	10.3754	+	1.30323i	0.754701	+	0.0947959i
$190$	−0.0991310	−	4.72823i	−0.00719172	−	0.343022i
$191$	7.75031	−	12.0597i	0.560793	−	0.872611i	−0.438871	−	0.898550i	$-0.644621\pi$
$191$	7.75031	−	12.0597i	0.560793	−	0.872611i	0.999664	+	0.0259395i	$0.00825773\pi$
$192$	−1.72687	+	0.133838i	−0.124626	+	0.00965896i
$193$	−1.10494	−	15.4491i	−0.0795355	−	1.11205i	−0.867866	−	0.496799i	$-0.834509\pi$
$193$	−1.10494	−	15.4491i	−0.0795355	−	1.11205i	0.788330	−	0.615252i	$-0.210946\pi$
$194$	13.3037	−	8.54978i	0.955152	−	0.613839i
$195$	−4.83523	−	11.9697i	−0.346258	−	0.857170i
$196$	0.419840	+	2.92005i	0.0299886	+	0.208575i
$197$	0.208160	−	0.956894i	0.0148308	−	0.0681759i	−0.969137	−	0.246524i	$-0.920712\pi$
$197$	0.208160	−	0.956894i	0.0148308	−	0.0681759i	0.983967	+	0.178348i	$0.0570753\pi$
$198$	3.91630	−	7.37957i	0.278319	−	0.524443i
$199$	3.08656	+	1.40958i	0.218800	+	0.0999228i	0.521800	−	0.853068i	$-0.325261\pi$
$199$	3.08656	+	1.40958i	0.218800	+	0.0999228i	−0.302999	+	0.952991i	$0.597988\pi$
$200$	−4.75387	−	1.54943i	−0.336149	−	0.109561i
$201$	14.2735	−	0.0849137i	1.00678	−	0.00598935i
$202$	−0.315313	+	4.40865i	−0.0221853	+	0.310191i
$203$	8.76315	+	16.0485i	0.615052	+	1.12638i
$204$	1.97474	+	13.1776i	0.138259	+	0.922617i
$205$	−4.66845	−	11.7578i	−0.326059	−	0.821201i
$206$			8.92468i			0.621812i
$207$	−10.1897	+	10.1573i	−0.708232	+	0.705979i
$208$	2.35693	−	2.35693i	0.163424	−	0.163424i
$209$	−0.838207	+	5.82986i	−0.0579800	+	0.403260i
$210$	−0.901228	+	7.74187i	−0.0621907	+	0.534240i
$211$	−24.9532	−	7.32692i	−1.71785	−	0.504406i	−0.733358	−	0.679843i	$-0.762048\pi$
$211$	−24.9532	−	7.32692i	−1.71785	−	0.504406i	−0.984491	+	0.175437i	$0.943866\pi$
$212$	−1.01673	−	0.0727177i	−0.0698290	−	0.00499427i
$213$	4.20407	+	4.15434i	0.288058	+	0.284651i
$214$	−8.34232	+	12.9809i	−0.570269	+	0.887356i
$215$	−11.0708	+	13.3311i	−0.755023	+	0.909171i
$216$	−0.0927301	−	5.19532i	−0.00630949	−	0.353497i
$217$	−17.7058	−	3.85167i	−1.20195	−	0.261468i
$218$	5.48924	−	7.33276i	0.371778	−	0.496637i
$219$	−16.4157	−	2.26064i	−1.10927	−	0.152760i
$220$	5.52664	+	2.86906i	0.372606	+	0.193432i
$221$	−19.3793	−	16.7923i	−1.30359	−	1.12957i
$222$	0.824995	+	10.6446i	0.0553700	+	0.714421i
$223$	17.9235	−	3.89901i	1.20024	−	0.261097i	0.432369	−	0.901697i	$-0.357678\pi$
$223$	17.9235	−	3.89901i	1.20024	−	0.261097i	0.767875	+	0.640600i	$0.221314\pi$
$224$	−1.93092	+	0.566970i	−0.129015	+	0.0378823i
$225$	5.48817	−	13.9599i	0.365878	−	0.930663i
$226$	−15.4240	−	4.52890i	−1.02599	−	0.301258i
$227$	−4.57783	−	1.70744i	−0.303841	−	0.113327i	0.192919	−	0.981215i	$-0.438204\pi$
$227$	−4.57783	−	1.70744i	−0.303841	−	0.113327i	−0.496760	+	0.867888i	$0.665477\pi$
$228$	1.30058	+	3.42463i	0.0861330	+	0.226802i
$229$		−	12.2131i		−	0.807067i	−0.914965	−	0.403533i	$-0.867782\pi$
$229$		−	12.2131i		−	0.807067i	0.914965	−	0.403533i	$-0.132218\pi$
$230$	−7.63932	−	7.52601i	−0.503722	−	0.496250i
$231$	2.67927	−	9.32971i	0.176283	−	0.613850i
$232$	7.27377	−	5.44507i	0.477546	−	0.357487i
$233$	3.84517	−	10.3093i	0.251905	−	0.675384i	−0.748026	−	0.663669i	$-0.768998\pi$
$233$	3.84517	−	10.3093i	0.251905	−	0.675384i	0.999931	−	0.0117147i	$-0.00372900\pi$
$234$	6.63781	+	7.47876i	0.433927	+	0.488902i
$235$	4.21198	+	8.73368i	0.274759	+	0.569723i
$236$	0.727992	+	2.47931i	0.0473883	+	0.161390i
$237$	1.43447	−	21.8854i	0.0931787	−	1.42161i
$238$	5.41034	+	14.5057i	0.350700	+	0.940263i
$239$	11.1926	−	12.9170i	0.723990	−	0.835529i	−0.267791	−	0.963477i	$-0.586294\pi$
$239$	11.1926	−	12.9170i	0.723990	−	0.835529i	0.991781	+	0.127948i	$0.0408391\pi$
$240$	3.87158	−	0.104216i	0.249909	−	0.00672710i
$241$	3.06772	+	21.3365i	0.197609	+	1.37440i	0.811195	+	0.584776i	$0.198817\pi$
$241$	3.06772	+	21.3365i	0.197609	+	1.37440i	−0.613586	+	0.789628i	$0.710273\pi$
$242$	2.59772	+	1.94463i	0.166988	+	0.125006i
$243$	15.5749	+	0.649150i	0.999133	+	0.0416430i
$244$	5.66931	+	4.91248i	0.362940	+	0.314490i
$245$	−0.608411	−	6.56846i	−0.0388700	−	0.419644i
$246$	6.46105	+	7.36743i	0.411942	+	0.469730i
$247$	−6.18738	−	3.37857i	−0.393694	−	0.214973i
$248$	−0.642335	+	8.98102i	−0.0407883	+	0.570295i
$249$	−7.26485	−	4.60800i	−0.460391	−	0.292020i
$250$	10.4418	+	3.99615i	0.660396	+	0.252739i
$251$	17.6095	+	2.53187i	1.11150	+	0.159810i	0.673517	−	0.739172i	$-0.264783\pi$
$251$	17.6095	+	2.53187i	1.11150	+	0.159810i	0.437986	+	0.898982i	$0.355692\pi$
$252$	−1.35342	−	5.88367i	−0.0852576	−	0.370636i
$253$	7.85861	+	10.7985i	0.494067	+	0.678898i
$254$	−2.09642			−0.131541
$255$	−2.92448	−	29.6512i	−0.183138	−	1.85683i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	3.34401	−	1.82597i	0.208593	−	0.113901i	−0.371557	−	0.928410i	$-0.621176\pi$
$257$	3.34401	−	1.82597i	0.208593	−	0.113901i	0.580150	+	0.814510i	$0.302994\pi$
$258$	4.61584	−	12.6041i	0.287370	−	0.784694i
$259$	3.49487	+	11.9024i	0.217160	+	0.739580i
$260$	−5.52926	+	4.99785i	−0.342910	+	0.309954i
$261$	15.0087	+	22.7541i	0.929013	+	1.40844i
$262$	13.8553	−	0.990952i	0.855985	−	0.0612212i
$263$	9.20469	+	2.00236i	0.567586	+	0.123471i	0.487196	−	0.873293i	$-0.338020\pi$
$263$	9.20469	+	2.00236i	0.567586	+	0.123471i	0.0803898	+	0.996763i	$0.474383\pi$
$264$	−4.77830	−	0.658026i	−0.294084	−	0.0404987i
$265$	2.26238	+	0.277014i	0.138977	+	0.0170168i
$266$	2.30113	+	3.58063i	0.141091	+	0.219542i
$267$	−0.230874	+	1.09256i	−0.0141293	+	0.0668637i
$268$	−2.87993	−	7.72139i	−0.175920	−	0.471659i
$269$	−3.25027	−	2.08882i	−0.198172	−	0.127358i	0.437791	−	0.899077i	$-0.355761\pi$
$269$	−3.25027	−	2.08882i	−0.198172	−	0.127358i	−0.635964	+	0.771719i	$0.719397\pi$
$270$	−0.378598	+	11.6128i	−0.0230407	+	0.706731i
$271$	−13.0266	−	15.0335i	−0.791311	−	0.913221i	0.206561	−	0.978434i	$-0.433773\pi$
$271$	−13.0266	−	15.0335i	−0.791311	−	0.913221i	−0.997871	+	0.0652126i	$0.979227\pi$
$272$	6.75203	−	3.68689i	0.409402	−	0.223550i
$273$	9.34225	+	6.90719i	0.565419	+	0.418042i
$274$	2.04492	+	0.294015i	0.123538	+	0.0177621i
$275$	−12.0188	−	7.03028i	−0.724760	−	0.423942i
$276$	7.52973	+	3.50759i	0.453237	+	0.211132i
$277$	10.8416	+	10.8416i	0.651407	+	0.651407i	0.953332	−	0.301924i	$-0.0976290\pi$
$277$	10.8416	+	10.8416i	0.651407	+	0.651407i	−0.301924	+	0.953332i	$0.597629\pi$
$278$	5.24645	−	3.92744i	0.314661	−	0.235552i
$279$	−26.7808	−	3.52581i	−1.60332	−	0.211085i
$280$	4.37610	−	1.04849i	0.261522	−	0.0626594i
$281$	5.66743	−	4.91086i	0.338091	−	0.292957i	−0.469223	−	0.883080i	$-0.655466\pi$
$281$	5.66743	−	4.91086i	0.338091	−	0.292957i	0.807314	+	0.590122i	$0.200921\pi$
$282$	−5.34237	−	5.27919i	−0.318134	−	0.314371i
$283$	6.14385	−	1.33651i	0.365214	−	0.0794475i	−0.0262135	−	0.999656i	$-0.508345\pi$
$283$	6.14385	−	1.33651i	0.365214	−	0.0794475i	0.391428	+	0.920209i	$0.371981\pi$
$284$	1.41755	−	3.10400i	0.0841160	−	0.184188i
$285$	−2.51842	−	7.79458i	−0.149178	−	0.461711i
$286$	7.80874	−	5.01837i	0.461741	−	0.296743i
$287$	9.11458	+	6.82309i	0.538017	+	0.402754i
$288$	−2.79818	+	1.08176i	−0.164884	+	0.0637434i
$289$	−22.8058	−	35.4866i	−1.34152	−	2.08745i
$290$	−16.8578	+	11.3401i	−0.989924	+	0.665912i
$291$	17.8138	−	20.8070i	1.04426	−	1.21973i
$292$	2.03363	+	9.34844i	0.119009	+	0.547076i
$293$	−10.6293	−	5.80401i	−0.620968	−	0.339074i	0.137776	−	0.990463i	$-0.456005\pi$
$293$	−10.6293	−	5.80401i	−0.620968	−	0.339074i	−0.758744	+	0.651389i	$0.774187\pi$
$294$	2.15025	+	4.63523i	0.125405	+	0.270332i
$295$	−1.34627	−	5.61893i	−0.0783828	−	0.327147i
$296$	5.60707	−	2.56066i	0.325904	−	0.148836i
$297$	2.82304	−	14.1921i	0.163809	−	0.823511i
$298$	−14.9756	+	14.9756i	−0.867514	+	0.867514i
$299$	−15.3973	+	4.29630i	−0.890450	+	0.248462i
$300$	−8.65786	−	0.203718i	−0.499862	−	0.0117617i
$301$	2.21948	−	15.4368i	0.127929	−	0.889765i
$302$	14.5522	+	5.42769i	0.837384	+	0.312328i
$303$	1.67177	+	7.47074i	0.0960406	+	0.429183i
$304$	1.59841	−	1.38503i	0.0916748	−	0.0794367i
$305$	−12.1070	−	11.6098i	−0.693247	−	0.664775i
$306$	9.83652	+	20.8780i	0.562316	+	1.19351i
$307$	1.81315	−	0.676268i	0.103482	−	0.0385967i	−0.297190	−	0.954818i	$-0.596049\pi$
$307$	1.81315	−	0.676268i	0.103482	−	0.0385967i	0.400672	+	0.916222i	$0.368777\pi$
$308$	−5.58994	+	0.399801i	−0.318517	+	0.0227808i
$309$	4.44318	+	14.8057i	0.252764	+	0.842265i
$310$	2.44694	−	19.9842i	0.138977	−	1.13503i
$311$	4.48545	−	0.644910i	0.254346	−	0.0365695i	−0.0139621	−	0.999903i	$-0.504444\pi$
$311$	4.48545	−	0.644910i	0.254346	−	0.0365695i	0.268309	+	0.963333i	$0.413535\pi$
$312$	2.73665	−	5.08346i	0.154932	−	0.287794i
$313$	−1.67477	−	23.4163i	−0.0946634	−	1.32357i	−0.793625	−	0.608407i	$-0.791809\pi$
$313$	−1.67477	−	23.4163i	−0.0946634	−	1.32357i	0.698962	−	0.715159i	$-0.253646\pi$
$314$	−1.72447	+	3.77606i	−0.0973173	+	0.213095i
$315$	2.35921	+	13.2921i	0.132927	+	0.748926i
$316$	−12.1497	+	3.56748i	−0.683476	+	0.200687i
$317$	15.5887	+	1.11492i	0.875546	+	0.0626203i	0.501874	−	0.864941i	$-0.332644\pi$
$317$	15.5887	+	1.11492i	0.875546	+	0.0626203i	0.373672	+	0.927561i	$0.378099\pi$
$318$	−1.72291	+	0.385544i	−0.0966159	+	0.0216203i
$319$	23.0162	−	10.5111i	1.28866	−	0.588511i
$320$	−0.825169	−	2.07824i	−0.0461284	−	0.116177i
$321$	−7.37698	+	25.6880i	−0.411743	+	1.43377i
$322$	9.40223	+	2.17858i	0.523966	+	0.121407i
$323$	−11.5052	−	11.5052i	−0.640164	−	0.640164i
$324$	−2.74034	−	8.57266i	−0.152241	−	0.476259i
$325$	12.9115	−	10.5380i	0.716202	−	0.584543i
$326$	4.93081	−	16.7928i	0.273093	−	0.930068i
$327$	5.45578	−	14.8976i	0.301705	−	0.823838i
$328$	2.71138	−	4.96553i	0.149711	−	0.274176i
$329$	−7.34126	−	4.71794i	−0.404737	−	0.260108i
$330$	10.5968	+	2.00819i	0.583336	+	0.110547i
$331$	15.9573	−	18.4157i	0.877091	−	1.01222i	−0.122714	−	0.992442i	$-0.539160\pi$
$331$	15.9573	−	18.4157i	0.877091	−	1.01222i	0.999804	−	0.0197746i	$-0.00629486\pi$
$332$	−1.05580	+	4.85344i	−0.0579446	+	0.266367i
$333$	6.66809	+	17.2483i	0.365409	+	0.945199i
$334$	4.79243	−	0.689048i	0.262230	−	0.0377030i
$335$	5.56107	+	17.5683i	0.303834	+	0.959856i
$336$	−2.92105	+	1.90190i	−0.159357	+	0.103757i
$337$	−11.0876	+	4.13548i	−0.603982	+	0.225274i	−0.632806	−	0.774311i	$-0.718097\pi$
$337$	−11.0876	+	4.13548i	−0.603982	+	0.225274i	0.0288231	+	0.999585i	$0.490824\pi$
$338$	−0.401694	−	1.84656i	−0.0218493	−	0.100439i
$339$	−27.8425	+	0.165636i	−1.51220	+	0.00899610i
$340$	−15.4944	+	7.47247i	−0.840303	+	0.405251i
$341$	−7.06420	+	24.0584i	−0.382548	+	1.30284i
$342$	3.86257	+	5.03382i	0.208864	+	0.272198i
$343$	11.9999	+	16.0300i	0.647934	+	0.865539i
$344$	−7.74958			−0.417830
$345$	−16.4202	−	8.68208i	−0.884032	−	0.467427i
$346$	12.7909			0.687643
$347$	−12.7487	−	17.0303i	−0.684387	−	0.914234i	0.315005	−	0.949090i	$-0.397994\pi$
$347$	−12.7487	−	17.0303i	−0.684387	−	0.914234i	−0.999392	+	0.0348559i	$0.988903\pi$
$348$	9.35603	−	12.6544i	0.501536	−	0.678348i
$349$	−0.576243	+	1.96250i	−0.0308456	+	0.105050i	−0.973477	−	0.228785i	$-0.926525\pi$
$349$	−0.576243	+	1.96250i	−0.0308456	+	0.105050i	0.942631	+	0.333835i	$0.108343\pi$
$350$	−9.89102	+	1.84819i	−0.528697	+	0.0987898i
$351$	14.7352	+	9.10230i	0.786505	+	0.485845i
$352$	0.591949	+	2.72115i	0.0315510	+	0.145038i
$353$	−7.16188	+	2.67124i	−0.381188	+	0.142176i	−0.532752	−	0.846272i	$-0.678842\pi$
$353$	−7.16188	+	2.67124i	−0.381188	+	0.142176i	0.151563	+	0.988448i	$0.451569\pi$
$354$	2.44204	+	3.75065i	0.129793	+	0.199345i
$355$	−3.51563	+	6.77212i	−0.186590	+	0.359427i
$356$	0.638159	−	0.0917533i	0.0338223	−	0.00486292i
$357$	16.1972	+	21.3708i	0.857247	+	1.13106i
$358$	4.04633	−	18.6007i	0.213855	−	0.983077i
$359$	−6.82390	+	7.87520i	−0.360151	+	0.415637i	−0.906690	−	0.421797i	$-0.861400\pi$
$359$	−6.82390	+	7.87520i	−0.360151	+	0.415637i	0.546539	+	0.837434i	$0.315945\pi$
$360$	6.37091	−	2.10037i	0.335776	−	0.110699i
$361$	12.2207	+	7.85378i	0.643196	+	0.413357i
$362$	10.3286	−	18.9154i	0.542858	−	0.994171i
$363$	5.27765	+	1.93278i	0.277005	+	0.101444i
$364$	1.88983	−	6.43616i	0.0990539	−	0.337347i
$365$	−3.48767	−	21.1064i	−0.182553	−	1.10476i
$366$	11.8508	+	5.32712i	0.619453	+	0.278453i
$367$	7.12141	+	7.12141i	0.371734	+	0.371734i	0.868109	−	0.496374i	$-0.165336\pi$
$367$	7.12141	+	7.12141i	0.371734	+	0.371734i	−0.496374	+	0.868109i	$0.665336\pi$
$368$	0.406634	−	4.77856i	0.0211973	−	0.249100i
$369$	14.3865	+	9.00561i	0.748932	+	0.468813i
$370$	−12.8105	+	5.08643i	−0.665987	+	0.264431i
$371$	−1.86595	+	0.852152i	−0.0968755	+	0.0442416i
$372$	3.40562	+	15.2189i	0.176573	+	0.789065i
$373$	−0.343455	−	0.0245644i	−0.0177834	−	0.00127190i	0.0624446	−	0.998048i	$-0.480110\pi$
$373$	−0.343455	−	0.0245644i	−0.0177834	−	0.00127190i	−0.0802281	+	0.996777i	$0.525565\pi$
$374$	20.5557	−	6.03570i	1.06291	−	0.312099i
$375$	19.3120	+	1.43097i	0.997266	+	0.0738952i
$376$	−1.80137	+	3.94445i	−0.0928985	+	0.203419i
$377$	2.16056	+	30.2085i	0.111274	+	1.55582i
$378$	−5.17447	−	9.08695i	−0.266146	−	0.467382i
$379$	−12.2399	+	1.75983i	−0.628722	+	0.0903965i	−0.449308	−	0.893377i	$-0.648329\pi$
$379$	−12.2399	+	1.75983i	−0.628722	+	0.0903965i	−0.179414	+	0.983774i	$0.557420\pi$
$380$	−3.72574	+	2.91288i	−0.191126	+	0.149428i
$381$	−3.47787	+	1.04371i	−0.178176	+	0.0534707i
$382$	−14.2989	+	1.02268i	−0.731595	+	0.0523247i
$383$	−17.6486	+	6.58260i	−0.901803	+	0.336355i	−0.757237	−	0.653140i	$-0.773451\pi$
$383$	−17.6486	+	6.58260i	−0.901803	+	0.336355i	−0.144566	+	0.989495i	$0.546179\pi$
$384$	1.14202	+	1.30223i	0.0582784	+	0.0664539i
$385$	12.5287	−	0.262673i	0.638520	−	0.0133871i
$386$	−11.7055	+	10.1429i	−0.595793	+	0.516258i
$387$	1.38253	−	23.2076i	0.0702779	−	1.17971i
$388$	−14.8171	−	5.52648i	−0.752223	−	0.280565i
$389$	−0.720974	+	5.01449i	−0.0365549	+	0.254245i	−0.999902	−	0.0140140i	$-0.995539\pi$
$389$	−0.720974	+	5.01449i	−0.0365549	+	0.254245i	0.963347	+	0.268259i	$0.0864482\pi$
$390$	−6.68462	+	11.0440i	−0.338489	+	0.559234i
$391$	−36.8912	−	0.497733i	−1.86567	−	0.0251714i
$392$	2.08602	−	2.08602i	0.105360	−	0.105360i
$393$	22.4921	−	8.54186i	1.13457	−	0.430880i
$394$	−0.890779	+	0.406805i	−0.0448768	+	0.0204945i
$395$	27.5353	−	6.59731i	1.38545	−	0.331947i
$396$	−8.25460	+	1.28725i	−0.414809	+	0.0646868i
$397$	20.8094	+	11.3628i	1.04439	+	0.570283i	0.907391	−	0.420288i	$-0.138071\pi$
$397$	20.8094	+	11.3628i	1.04439	+	0.570283i	0.137004	+	0.990571i	$0.456253\pi$
$398$	−0.721276	−	3.31565i	−0.0361543	−	0.166199i
$399$	5.60010	+	4.79449i	0.280356	+	0.240025i
$400$	1.60850	+	4.73421i	0.0804251	+	0.236710i
$401$	1.79656	+	2.79551i	0.0897161	+	0.139601i	0.883211	−	0.468976i	$-0.155377\pi$
$401$	1.79656	+	2.79551i	0.0897161	+	0.139601i	−0.793495	+	0.608577i	$0.791741\pi$
$402$	−8.62180	−	11.3757i	−0.430016	−	0.567367i
$403$	−24.0259	−	17.9856i	−1.19681	−	0.895924i
$404$	3.71827	−	2.38958i	0.184991	−	0.118886i
$405$	5.15338	+	19.4536i	0.256073	+	0.966657i
$406$	7.59593	−	16.6328i	0.376980	−	0.825471i
$407$	16.7734	−	3.64884i	0.831429	−	0.180866i
$408$	9.36580	−	9.47790i	0.463676	−	0.469226i
$409$	−7.80851	+	6.76611i	−0.386106	+	0.334563i	−0.826188	−	0.563395i	$-0.809495\pi$
$409$	−7.80851	+	6.76611i	−0.386106	+	0.334563i	0.440082	+	0.897958i	$0.354949\pi$
$410$	−6.61491	+	10.7835i	−0.326687	+	0.532558i
$411$	3.53881	−	0.530310i	0.174557	−	0.0261583i
$412$	7.14457	−	5.34836i	0.351988	−	0.263495i
$413$	3.67704	+	3.67704i	0.180935	+	0.180935i
$414$	14.2378	+	2.07024i	0.699748	+	0.101747i
$415$	2.90498	−	10.7198i	0.142600	−	0.526214i
$416$	−3.29928	−	0.474365i	−0.161760	−	0.0232576i
$417$	6.74835	−	9.12743i	0.330468	−	0.446972i
$418$	5.16936	−	2.82268i	0.252842	−	0.138062i
$419$	−9.14937	−	10.5589i	−0.446976	−	0.515838i	0.486889	−	0.873464i	$-0.338132\pi$
$419$	−9.14937	−	10.5589i	−0.446976	−	0.515838i	−0.933865	+	0.357626i	$0.883586\pi$
$420$	6.73777	−	3.91806i	0.328770	−	0.191182i
$421$	0.534769	+	0.343675i	0.0260631	+	0.0167497i	0.553607	−	0.832778i	$-0.313251\pi$
$421$	0.534769	+	0.343675i	0.0260631	+	0.0167497i	−0.527544	+	0.849527i	$0.676887\pi$
$422$	9.08839	+	24.3669i	0.442416	+	1.18616i
$423$	−11.4910	−	6.09823i	−0.558713	−	0.296506i
$424$	0.551088	+	0.857509i	0.0267632	+	0.0416443i
$425$	35.4449	−	14.9410i	1.71933	−	0.724743i
$426$	0.806319	−	5.85513i	0.0390663	−	0.283682i
$427$	14.7515	+	3.20899i	0.713874	+	0.155294i
$428$	15.3911	−	1.10079i	0.743957	−	0.0532089i
$429$	10.4560	−	12.2129i	0.504819	−	0.589643i
$430$	17.3066	+	0.873634i	0.834596	+	0.0421304i
$431$	−7.10617	−	24.2014i	−0.342292	−	1.16574i	−0.933307	−	0.359080i	$-0.883091\pi$
$431$	−7.10617	−	24.2014i	−0.342292	−	1.16574i	0.591015	−	0.806661i	$-0.298728\pi$
$432$	−4.10350	+	3.18768i	−0.197430	+	0.153367i
$433$	−22.5656	+	12.3217i	−1.08443	+	0.592145i	−0.919073	−	0.394088i	$-0.871060\pi$
$433$	−22.5656	+	12.3217i	−1.08443	+	0.592145i	−0.165360	+	0.986233i	$0.552879\pi$
$434$	7.52730	+	16.4825i	0.361322	+	0.791184i
$435$	−22.3207	+	27.2054i	−1.07019	+	1.30440i
$436$	−9.15976			−0.438673
$437$	−9.93954	+	2.02218i	−0.475472	+	0.0967338i
$438$	8.02785	+	14.4962i	0.383586	+	0.692656i
$439$	21.6025	+	3.10597i	1.03103	+	0.148240i	0.637005	−	0.770860i	$-0.280173\pi$
$439$	21.6025	+	3.10597i	1.03103	+	0.148240i	0.394025	+	0.919100i	$0.371082\pi$
$440$	−1.01519	−	6.14366i	−0.0483974	−	0.292888i
$441$	5.87484	+	6.61914i	0.279754	+	0.315197i
$442$	−1.82932	+	25.5772i	−0.0870117	+	1.21658i
$443$	10.4763	+	5.72048i	0.497743	+	0.271788i	0.708450	−	0.705761i	$-0.249395\pi$
$443$	10.4763	+	5.72048i	0.497743	+	0.271788i	−0.210707	+	0.977549i	$0.567577\pi$
$444$	8.02706	−	7.03953i	0.380948	−	0.334081i
$445$	−1.43549	+	0.132964i	−0.0680490	+	0.00630311i
$446$	−13.8624	−	12.0119i	−0.656406	−	0.568779i
$447$	−17.3883	+	32.2996i	−0.822437	+	1.52772i
$448$	1.61104	+	1.20601i	0.0761146	+	0.0569787i
$449$	2.94442	+	20.4789i	0.138956	+	0.966458i	0.933327	+	0.359026i	$0.116891\pi$
$449$	2.94442	+	20.4789i	0.138956	+	0.966458i	−0.794372	+	0.607432i	$0.792200\pi$
$450$	−14.4644	+	3.97238i	−0.681861	+	0.187260i
$451$	10.3174	−	11.9069i	0.485828	−	0.560676i
$452$	5.61769	+	15.0616i	0.264234	+	0.708439i
$453$	26.8437	+	1.75945i	1.26123	+	0.0826664i
$454$	1.37651	+	4.68797i	0.0646030	+	0.220017i
$455$	−4.94598	+	14.1604i	−0.231871	+	0.663847i
$456$	1.96215	−	3.09347i	0.0918860	−	0.144865i
$457$	−0.555920	+	1.49048i	−0.0260048	+	0.0697217i	−0.949303	−	0.314361i	$-0.898210\pi$
$457$	−0.555920	+	1.49048i	−0.0260048	+	0.0697217i	0.923299	+	0.384083i	$0.125482\pi$
$458$	−9.77712	+	7.31906i	−0.456855	+	0.341997i
$459$	26.7125	+	29.7385i	1.24683	+	1.38808i
$460$	−1.44681	+	10.6258i	−0.0674577	+	0.495429i
$461$			1.91124i			0.0890152i	0.999009	+	0.0445076i	$0.0141719\pi$
$461$			1.91124i			0.0890152i	−0.999009	+	0.0445076i	$0.985828\pi$
$462$	−9.07444	+	3.44622i	−0.422181	+	0.160333i
$463$	−7.13529	−	2.66133i	−0.331605	−	0.123682i	0.178146	−	0.984004i	$-0.442990\pi$
$463$	−7.13529	−	2.66133i	−0.331605	−	0.123682i	−0.509752	+	0.860322i	$0.670263\pi$
$464$	−8.71801	−	2.55984i	−0.404724	−	0.118838i
$465$	−5.88984	−	34.3712i	−0.273135	−	1.59393i
$466$	−10.5573	+	3.09991i	−0.489059	+	0.143601i
$467$	14.2734	−	3.10498i	0.660493	−	0.143681i	0.130189	−	0.991489i	$-0.458442\pi$
$467$	14.2734	−	3.10498i	0.660493	−	0.143681i	0.530304	+	0.847808i	$0.322078\pi$
$468$	2.00917	−	9.79569i	0.0928738	−	0.452806i
$469$	−12.5337	−	10.8605i	−0.578754	−	0.501493i
$470$	4.46753	−	8.60576i	0.206072	−	0.396954i
$471$	−0.980899	+	7.12285i	−0.0451974	+	0.328204i
$472$	1.54852	−	2.06859i	0.0712766	−	0.0952144i
$473$	−21.0878	−	4.58736i	−0.969616	−	0.210927i
$474$	−18.3798	+	11.9671i	−0.844213	+	0.549666i
$475$	8.64878	−	6.08510i	0.396833	−	0.279204i
$476$	8.37010	−	13.0241i	0.383643	−	0.596960i
$477$	−2.66629	+	1.49736i	−0.122081	+	0.0685593i
$478$	−17.0480	−	1.21930i	−0.779759	−	0.0557695i
$479$	−20.4870	−	6.01552i	−0.936074	−	0.274856i	−0.222097	−	0.975025i	$-0.571290\pi$
$479$	−20.4870	−	6.01552i	−0.936074	−	0.274856i	−0.713978	+	0.700169i	$0.753108\pi$
$480$	−2.40358	−	3.03691i	−0.109708	−	0.138615i
$481$	−2.92404	+	20.3371i	−0.133325	+	0.927292i
$482$	15.2423	−	15.2423i	0.694269	−	0.694269i
$483$	16.6825	−	1.06676i	0.759081	−	0.0485392i
$484$		−	3.24496i		−	0.147498i
$485$	32.4668	+	14.0123i	1.47424	+	0.636264i
$486$	−8.81404	−	12.8574i	−0.399813	−	0.583223i
$487$	−11.1941	−	20.5004i	−0.507252	−	0.928963i	−0.998326	−	0.0578448i	$-0.981577\pi$
$487$	−11.1941	−	20.5004i	−0.507252	−	0.928963i	0.491073	−	0.871118i	$-0.336605\pi$
$488$	0.535156	−	7.48246i	0.0242254	−	0.338715i
$489$	−0.180335	−	30.3134i	−0.00815504	−	1.37082i
$490$	−4.89372	+	4.42339i	−0.221076	+	0.199828i
$491$	−14.3408	−	6.54924i	−0.647193	−	0.295563i	0.0646437	−	0.997908i	$-0.479409\pi$
$491$	−14.3408	−	6.54924i	−0.647193	−	0.295563i	−0.711836	+	0.702345i	$0.752136\pi$
$492$	2.02597	−	9.58748i	0.0913378	−	0.432237i
$493$	−14.8582	+	68.3021i	−0.669180	+	3.07617i
$494$	1.00328	+	6.97795i	0.0451396	+	0.313953i
$495$	18.5795	−	1.94415i	0.835086	−	0.0873833i
$496$	7.57461	−	4.86791i	0.340110	−	0.218576i
$497$	−0.489900	−	6.84969i	−0.0219750	−	0.307251i
$498$	0.664769	+	8.57729i	0.0297890	+	0.384357i
$499$	11.0997	−	17.2714i	0.496890	−	0.773176i	−0.498721	−	0.866762i	$-0.666197\pi$
$499$	11.0997	−	17.2714i	0.496890	−	0.773176i	0.995611	+	0.0935866i	$0.0298332\pi$
$500$	−3.05844	−	10.7539i	−0.136778	−	0.480928i
$501$	7.60740	−	3.52903i	0.339874	−	0.157665i
$502$	−8.52612	−	15.6144i	−0.380539	−	0.696906i
$503$	6.05949	−	16.2461i	0.270179	−	0.724379i	−0.729025	−	0.684487i	$-0.760026\pi$
$503$	6.05949	−	16.2461i	0.270179	−	0.724379i	0.999204	−	0.0398914i	$-0.0127012\pi$
$504$	−3.89904	+	4.60942i	−0.173677	+	0.205320i
$505$	−8.57311	+	4.91731i	−0.381498	+	0.218817i
$506$	3.93518	−	12.7625i	0.174940	−	0.567361i
$507$	−1.58571	−	2.86338i	−0.0704237	−	0.127167i
$508$	1.25633	+	1.67827i	0.0557408	+	0.0744611i
$509$	−9.34613	−	20.4652i	−0.414260	−	0.907103i	−0.995623	−	0.0934586i	$-0.970208\pi$
$509$	−9.34613	−	20.4652i	−0.414260	−	0.907103i	0.581363	−	0.813644i	$-0.302520\pi$
$510$	−21.9844	+	20.1105i	−0.973486	+	0.890506i
$511$	12.6081	+	14.5506i	0.557752	+	0.643680i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	8.91394	+	6.42791i	0.393560	+	0.283799i
$514$	−3.46575	−	1.58275i	−0.152868	−	0.0698123i
$515$	−16.5584	+	11.1387i	−0.729649	+	0.490828i
$516$	−12.8562	+	3.85815i	−0.565964	+	0.169846i
$517$	−7.23670	+	9.66710i	−0.318270	+	0.425159i
$518$	7.43398	−	9.93064i	0.326631	−	0.436327i
$519$	21.2196	−	6.36799i	0.931436	−	0.279524i
$520$	7.31455	+	1.43130i	0.320764	+	0.0627667i
$521$	−19.8812	−	9.07945i	−0.871012	−	0.397778i	−0.0707970	−	0.997491i	$-0.522554\pi$
$521$	−19.8812	−	9.07945i	−0.871012	−	0.397778i	−0.800215	+	0.599713i	$0.795282\pi$
$522$	9.22122	−	25.6511i	0.403602	−	1.12272i
$523$	−4.65373	+	8.52268i	−0.203494	+	0.372671i	−0.959418	−	0.281988i	$-0.909006\pi$
$523$	−4.65373	+	8.52268i	−0.203494	+	0.372671i	0.755924	+	0.654659i	$0.227188\pi$
$524$	−9.09649	−	10.4979i	−0.397382	−	0.458603i
$525$	−15.4887	+	7.99034i	−0.675980	+	0.348727i
$526$	−3.91320	−	8.56870i	−0.170623	−	0.373613i
$527$	−41.5107	−	55.4518i	−1.80823	−	2.41552i
$528$	2.33675	+	4.21957i	0.101694	+	0.183633i
$529$	−12.9522	+	19.0063i	−0.563140	+	0.826361i
$530$	−1.13403	−	1.97714i	−0.0492592	−	0.0858813i
$531$	5.91852	+	5.00639i	0.256842	+	0.217259i
$532$	1.48742	−	3.98794i	0.0644880	−	0.172899i
$533$	9.03760	+	16.5511i	0.391462	+	0.716909i
$534$	1.01300	−	0.469924i	0.0438367	−	0.0203356i
$535$	−34.4959	+	0.723233i	−1.49139	+	0.0312681i
$536$	−4.45541	+	6.93276i	−0.192444	+	0.299449i
$537$	−2.54771	−	32.8723i	−0.109942	−	1.41854i
$538$	0.275626	+	3.85376i	0.0118831	+	0.166147i
$539$	6.91119	−	4.44155i	0.297686	−	0.191311i
$540$	9.52339	−	6.65620i	0.409822	−	0.286437i
$541$	−5.91612	−	41.1475i	−0.254354	−	1.76907i	−0.571411	−	0.820664i	$-0.693604\pi$
$541$	−5.91612	−	41.1475i	−0.254354	−	1.76907i	0.317057	−	0.948406i	$-0.397305\pi$
$542$	−4.22839	+	19.4376i	−0.181625	+	0.834916i
$543$	7.71761	−	36.5220i	0.331194	−	1.56731i
$544$	−6.99784	−	3.19581i	−0.300030	−	0.137019i
$545$	20.4558	+	1.03261i	0.876230	+	0.0442320i
$546$	−0.0691169	−	11.6182i	−0.00295793	−	0.497212i
$547$	0.293219	−	4.09974i	0.0125372	−	0.175292i	−0.987325	−	0.158709i	$-0.949267\pi$
$547$	0.293219	−	4.09974i	0.0125372	−	0.175292i	0.999862	−	0.0165830i	$-0.00527876\pi$
$548$	−0.990102	−	1.81324i	−0.0422951	−	0.0774577i
$549$	22.3122	+	2.93750i	0.952261	+	0.125369i
$550$	1.57456	+	13.8346i	0.0671394	+	0.589910i
$551$			19.2170i			0.818670i
$552$	−1.70443	−	8.12988i	−0.0725455	−	0.346031i
$553$	−18.0191	+	18.0191i	−0.766250	+	0.766250i
$554$	2.18202	−	15.1763i	0.0927050	−	0.644777i
$555$	−18.7198	+	14.8159i	−0.794612	+	0.628901i
$556$	−6.28816	−	1.84637i	−0.266677	−	0.0783036i
$557$	4.31409	+	0.308550i	0.182794	+	0.0130737i	0.162436	−	0.986719i	$-0.448065\pi$
$557$	4.31409	+	0.308550i	0.182794	+	0.0130737i	0.0203578	+	0.999793i	$0.493519\pi$
$558$	13.2266	+	23.5521i	0.559925	+	0.997038i
$559$	13.9653	−	21.7304i	0.590668	−	0.919097i
$560$	−3.46186	−	2.87491i	−0.146290	−	0.121487i
$561$	31.0962	−	20.2467i	1.31288	−	0.854816i
$562$	−7.32771	−	1.59405i	−0.309101	−	0.0672408i
$563$	−22.6745	+	30.2895i	−0.955614	+	1.27655i	0.00538075	+	0.999986i	$0.498287\pi$
$563$	−22.6745	+	30.2895i	−0.955614	+	1.27655i	−0.960995	+	0.276566i	$0.910804\pi$
$564$	−1.02464	+	7.44049i	−0.0431452	+	0.313301i
$565$	−10.8476	−	34.2693i	−0.456363	−	1.44172i
$566$	−4.75181	−	4.11747i	−0.199733	−	0.173070i
$567$	−13.1082	−	12.4987i	−0.550493	−	0.524898i
$568$	−3.33438	+	0.725351i	−0.139908	+	0.0304350i
$569$	1.38723	−	0.407328i	0.0581558	−	0.0170761i	−0.252525	−	0.967590i	$-0.581261\pi$
$569$	1.38723	−	0.407328i	0.0581558	−	0.0170761i	0.310681	+	0.950514i	$0.399443\pi$
$570$	−4.73065	+	6.68722i	−0.198145	+	0.280097i
$571$	27.0165	+	7.93276i	1.13061	+	0.331976i	0.792946	−	0.609293i	$-0.208546\pi$
$571$	27.0165	+	7.93276i	1.13061	+	0.331976i	0.337660	+	0.941268i	$0.390365\pi$
$572$	−8.69702	−	3.24382i	−0.363641	−	0.135631i
$573$	−23.2121	+	8.81532i	−0.969700	+	0.368265i
$574$		−	11.3855i		−	0.475223i
$575$	4.42892	−	23.5666i	0.184699	−	0.982795i
$576$	2.54288	+	1.59178i	0.105953	+	0.0663242i
$577$	6.97383	−	5.22054i	0.290324	−	0.217334i	−0.444181	−	0.895937i	$-0.646505\pi$
$577$	6.97383	−	5.22054i	0.290324	−	0.217334i	0.734505	+	0.678603i	$0.237414\pi$
$578$	−14.7414	+	39.5233i	−0.613163	+	1.64395i
$579$	−14.3693	+	22.6542i	−0.597166	+	0.941476i
$580$	19.1807	+	6.69950i	0.796435	+	0.278182i
$581$	2.81611	+	9.59080i	0.116832	+	0.397893i
$582$	−27.3323	−	1.79148i	−1.13296	−	0.0742593i
$583$	0.991989	+	2.65962i	0.0410840	+	0.110150i
$584$	6.26510	−	7.23031i	0.259252	−	0.299193i
$585$	−5.59122	+	21.6495i	−0.231169	+	0.895096i
$586$	1.72352	+	11.9874i	0.0711981	+	0.495194i
$587$	−12.1544	−	9.09869i	−0.501667	−	0.375543i	0.318267	−	0.948001i	$-0.396899\pi$
$587$	−12.1544	−	9.09869i	−0.501667	−	0.375543i	−0.819934	+	0.572458i	$0.805990\pi$
$588$	2.42209	−	4.49916i	0.0998854	−	0.185542i
$589$	−14.3920	−	12.4707i	−0.593011	−	0.513847i
$590$	−3.69140	+	4.44505i	−0.151972	+	0.183000i
$591$	−1.27524	+	1.11835i	−0.0524562	+	0.0460028i
$592$	−5.41011	−	2.95414i	−0.222354	−	0.121415i
$593$	−1.88871	+	26.4076i	−0.0775601	+	1.08443i	0.798425	+	0.602094i	$0.205667\pi$
$593$	−1.88871	+	26.4076i	−0.0775601	+	1.08443i	−0.875985	+	0.482338i	$0.839788\pi$
$594$	−13.0532	+	6.24507i	−0.535578	+	0.256238i
$595$	−20.1606	+	28.1422i	−0.826502	+	1.15372i
$596$	20.9631	+	3.01405i	0.858684	+	0.123460i
$597$	−2.84727	−	5.14144i	−0.116531	−	0.210425i
$598$	12.6666	+	9.75152i	0.517978	+	0.398769i
$599$	−27.1223			−1.10819			−0.554093	−	0.832455i	$-0.686935\pi$
$599$	−27.1223			−1.10819			−0.554093	+	0.832455i	$0.686935\pi$
$600$	5.02538	+	7.05306i	0.205160	+	0.287940i
$601$	0.106158	+	0.232454i	0.00433029	+	0.00948201i	0.911785	−	0.410668i	$-0.134705\pi$
$601$	0.106158	+	0.232454i	0.00433029	+	0.00948201i	−0.907454	+	0.420150i	$0.861977\pi$
$602$	−13.6879	+	7.47417i	−0.557878	+	0.304624i
$603$	−19.9666	−	14.5794i	−0.813103	−	0.593719i
$604$	−4.37572	−	14.9023i	−0.178045	−	0.606367i
$605$	−0.365814	+	7.24671i	−0.0148724	+	0.294621i
$606$	4.97879	−	5.81537i	0.202249	−	0.236233i
$607$	19.2085	−	1.37382i	0.779648	−	0.0557616i	0.324159	−	0.946003i	$-0.394919\pi$
$607$	19.2085	−	1.37382i	0.779648	−	0.0557616i	0.455490	+	0.890241i	$0.349464\pi$
$608$	−2.06666	−	0.449574i	−0.0838141	−	0.0182326i
$609$	4.32066	−	31.3747i	0.175082	−	1.27137i
$610$	−2.03864	+	16.6497i	−0.0825423	+	0.674126i
$611$	−7.81432	−	12.1593i	−0.316134	−	0.491913i
$612$	10.8189	−	20.3862i	0.437327	−	0.824065i
$613$	−11.8053	−	31.6511i	−0.476810	−	1.27838i	−0.923469	−	0.383673i	$-0.874659\pi$
$613$	−11.8053	−	31.6511i	−0.476810	−	1.27838i	0.446659	−	0.894704i	$-0.352614\pi$
$614$	−1.62796	−	1.04623i	−0.0656991	−	0.0422222i
$615$	−5.60527	+	21.1826i	−0.226026	+	0.854165i
$616$	3.66998	+	4.23539i	0.147868	+	0.170649i
$617$	15.6120	−	8.52482i	0.628517	−	0.343196i	−0.133216	−	0.991087i	$-0.542530\pi$
$617$	15.6120	−	8.52482i	0.628517	−	0.343196i	0.761733	+	0.647891i	$0.224349\pi$
$618$	9.18985	−	12.4297i	0.369670	−	0.499994i
$619$	15.6295	+	2.24718i	0.628201	+	0.0903217i	0.449060	−	0.893502i	$-0.351759\pi$
$619$	15.6295	+	2.24718i	0.628201	+	0.0903217i	0.179141	+	0.983823i	$0.442668\pi$
$620$	−17.4646	+	10.0172i	−0.701395	+	0.402301i
$621$	24.6505	−	3.65387i	0.989192	−	0.146625i
$622$	−3.20431	−	3.20431i	−0.128481	−	0.128481i
$623$	1.03867	−	0.777540i	0.0416135	−	0.0311515i
$624$	−5.70953	+	0.855604i	−0.228564	+	0.0342516i
$625$	5.61787	+	24.3606i	0.224715	+	0.974425i
$626$	−17.7421	+	15.3736i	−0.709115	+	0.614452i
$627$	7.17047	−	7.25630i	0.286361	−	0.289789i
$628$	4.05632	−	0.882399i	0.161865	−	0.0352116i
$629$	−19.6993	+	43.1355i	−0.785463	+	1.71992i
$630$	9.22707	−	9.85432i	0.367615	−	0.392605i
$631$	13.3709	−	8.59297i	0.532288	−	0.342081i	−0.246728	−	0.969085i	$-0.579355\pi$
$631$	13.3709	−	8.59297i	0.532288	−	0.342081i	0.779016	+	0.627004i	$0.215719\pi$
$632$	10.1370	+	7.58845i	0.403227	+	0.301852i
$633$	27.2084	+	35.8990i	1.08144	+	1.42686i
$634$	−8.44939	−	13.1475i	−0.335568	−	0.522154i
$635$	−2.61648	−	3.88958i	−0.103832	−	0.154353i
$636$	1.34115	+	1.14821i	0.0531799	+	0.0455295i
$637$	2.09020	+	9.60850i	0.0828168	+	0.380703i
$638$	−22.2077	−	12.1263i	−0.879211	−	0.480086i
$639$	−1.57735	−	10.1149i	−0.0623988	−	0.400137i
$640$	−1.16921	+	1.90603i	−0.0462172	+	0.0753423i
$641$	−33.9249	+	15.4930i	−1.33995	+	0.611935i	−0.950962	−	0.309307i	$-0.899903\pi$
$641$	−33.9249	+	15.4930i	−1.33995	+	0.611935i	−0.388989	+	0.921242i	$0.627176\pi$
$642$	24.9852	−	9.48868i	0.986086	−	0.374488i
$643$	−21.3268	+	21.3268i	−0.841048	+	0.841048i	−0.988995	−	0.147947i	$-0.952733\pi$
$643$	−21.3268	+	21.3268i	−0.841048	+	0.841048i	0.147947	+	0.988995i	$0.452733\pi$
$644$	−3.89051	−	8.83245i	−0.153307	−	0.348047i
$645$	29.1458	−	7.16680i	1.14761	−	0.282192i
$646$	−2.31557	+	16.1051i	−0.0911048	+	0.633648i
$647$	−26.2369	−	9.78586i	−1.03148	−	0.384722i	−0.223982	−	0.974593i	$-0.571906\pi$
$647$	−26.2369	−	9.78586i	−1.03148	−	0.384722i	−0.807497	+	0.589872i	$0.799178\pi$
$648$	−5.22054	+	7.33116i	−0.205082	+	0.287995i
$649$	5.43826	−	4.71228i	0.213470	−	0.184973i
$650$	−16.1737	−	4.02101i	−0.634384	−	0.157717i
$651$	20.6933	+	23.5963i	0.811035	+	0.924810i
$652$	−16.3983	+	6.11624i	−0.642206	+	0.239530i
$653$	47.0657	−	3.36620i	1.84182	−	0.131730i	0.893504	−	0.449054i	$-0.148239\pi$
$653$	47.0657	−	3.36620i	1.84182	−	0.131730i	0.948317	+	0.317325i	$0.102785\pi$
$654$	−15.1957	+	4.56021i	−0.594197	+	0.178318i
$655$	19.1310	+	24.4696i	0.747511	+	0.956108i
$656$	−5.59998	+	0.805156i	−0.218643	+	0.0314361i
$657$	20.5349	+	20.0519i	0.801141	+	0.782301i
$658$	0.622546	+	8.70433i	0.0242694	+	0.339330i
$659$	−12.4938	+	27.3576i	−0.486688	+	1.06570i	0.493882	+	0.869529i	$0.335578\pi$
$659$	−12.4938	+	27.3576i	−0.486688	+	1.06570i	−0.980570	+	0.196170i	$0.937150\pi$
$660$	−4.74280	−	9.68667i	−0.184613	−	0.377053i
$661$	−36.9318	+	10.8442i	−1.43648	+	0.421789i	−0.905048	−	0.425310i	$-0.860165\pi$
$661$	−36.9318	+	10.8442i	−1.43648	+	0.421789i	−0.531434	+	0.847099i	$0.678347\pi$
$662$	−24.3053	−	1.73835i	−0.944654	−	0.0675630i
$663$	9.69891	+	43.3422i	0.376675	+	1.68327i
$664$	4.51810	−	2.06335i	0.175336	−	0.0800733i
$665$	−3.77133	+	8.73828i	−0.146246	+	0.338856i
$666$	9.81191	−	15.6746i	0.380204	−	0.607378i
$667$	30.3938	+	31.2252i	1.17685	+	1.20904i
$668$	−3.42361	−	3.42361i	−0.132463	−	0.132463i
$669$	−28.9774	−	13.0257i	−1.12033	−	0.503604i
$670$	10.7315	−	14.9801i	0.414593	−	0.578733i
$671$	5.88547	−	20.0441i	0.227206	−	0.773793i
$672$	3.27307	+	1.19866i	0.126261	+	0.0462393i
$673$	17.1512	−	31.4101i	0.661131	−	1.21077i	−0.304909	−	0.952381i	$-0.598626\pi$
$673$	17.1512	−	31.4101i	0.661131	−	1.21077i	0.966041	−	0.258390i	$-0.0831921\pi$
$674$	9.95520	+	6.39782i	0.383460	+	0.246435i
$675$	−22.0183	+	13.7912i	−0.847483	+	0.530823i
$676$	−1.23752	+	1.42817i	−0.0475969	+	0.0549297i
$677$	−2.46405	+	11.3271i	−0.0947013	+	0.435335i	0.905244	+	0.424892i	$0.139688\pi$
$677$	−2.46405	+	11.3271i	−0.0947013	+	0.435335i	−0.999945	+	0.0104431i	$0.996676\pi$
$678$	16.8180	+	22.1898i	0.645891	+	0.852195i
$679$	−31.5011	+	4.52918i	−1.20890	+	0.173814i
$680$	15.2675	+	7.92584i	0.585481	+	0.303942i
$681$	4.61750	+	7.09185i	0.176943	+	0.271760i
$682$	23.4932	−	8.76251i	0.899601	−	0.335534i
$683$	−9.94315	−	45.7079i	−0.380464	−	1.74896i	−0.626232	−	0.779636i	$-0.715404\pi$
$683$	−9.94315	−	45.7079i	−0.380464	−	1.74896i	0.245768	−	0.969329i	$-0.420960\pi$
$684$	1.71503	−	6.10880i	0.0655758	−	0.233576i
$685$	2.00671	+	4.16098i	0.0766724	+	0.158983i
$686$	5.64140	−	19.2128i	0.215390	−	0.733550i
$687$	−12.5760	+	17.0096i	−0.479805	+	0.648956i
$688$	4.64415	+	6.20386i	0.177057	+	0.236520i
$689$	−3.39761			−0.129439
$690$	2.88987	+	18.3480i	0.110016	+	0.698496i
$691$	12.2988			0.467868			0.233934	−	0.972252i	$-0.424840\pi$
$691$	12.2988			0.467868			0.233934	+	0.972252i	$0.424840\pi$
$692$	−7.66531	−	10.2396i	−0.291391	−	0.389253i
$693$	−13.3384	+	10.2349i	−0.506684	+	0.388791i
$694$	−5.99343	+	20.4117i	−0.227507	+	0.774819i
$695$	13.8347	+	4.83224i	0.524781	+	0.183297i
$696$	−15.7372	+	0.0936213i	−0.596519	+	0.00354870i
$697$	9.25168	+	42.5293i	0.350432	+	1.61091i
$698$	1.91640	−	0.714779i	0.0725366	−	0.0270548i
$699$	−15.9709	+	10.3986i	−0.604074	+	0.393312i
$700$	7.40702	+	6.81059i	0.279959	+	0.257416i
$701$	−19.6404	+	2.82386i	−0.741808	+	0.106656i	−0.502849	−	0.864374i	$-0.667715\pi$
$701$	−19.6404	+	2.82386i	−0.741808	+	0.106656i	−0.238958	+	0.971030i	$0.576806\pi$
$702$	−1.54369	−	17.2509i	−0.0582627	−	0.651094i
$703$	−2.77122	+	12.7391i	−0.104519	+	0.480465i
$704$	1.82365	−	2.10460i	0.0687313	−	0.0793202i
$705$	3.12704	−	16.5008i	0.117771	−	0.621455i
$706$	6.43039	+	4.13256i	0.242011	+	0.155531i
$707$	4.26283	−	7.80679i	0.160320	−	0.293604i
$708$	1.53908	−	4.20263i	0.0578424	−	0.157945i
$709$	−6.94926	+	23.6670i	−0.260985	+	0.888832i	0.719873	+	0.694106i	$0.244200\pi$
$709$	−6.94926	+	23.6670i	−0.260985	+	0.888832i	−0.980858	+	0.194726i	$0.937618\pi$
$710$	7.52820	−	1.24398i	0.282528	−	0.0466856i
$711$	−24.5335	+	29.0033i	−0.920078	+	1.08771i
$712$	−0.455886	−	0.455886i	−0.0170851	−	0.0170851i
$713$	−43.1091	+	2.49919i	−1.61445	+	0.0935953i
$714$	7.40154	−	25.7736i	0.276996	−	0.964551i
$715$	19.0567	+	8.22462i	0.712681	+	0.307583i
$716$	−17.3155	+	7.90772i	−0.647111	+	0.295526i
$717$	−28.8890	+	6.46465i	−1.07888	+	0.241427i
$718$	10.3938	+	0.743381i	0.387894	+	0.0277427i
$719$	2.55655	−	0.750671i	0.0953432	−	0.0279953i	−0.233713	−	0.972306i	$-0.575088\pi$
$719$	2.55655	−	0.750671i	0.0953432	−	0.0279953i	0.329056	+	0.944310i	$0.393269\pi$
$720$	−5.49937	−	3.84147i	−0.204950	−	0.143163i
$721$	7.46102	−	16.3373i	0.277863	−	0.608435i
$722$	−1.03633	−	14.4898i	−0.0385682	−	0.539254i
$723$	17.6979	−	32.8748i	0.658193	−	1.22263i
$724$	−21.3322	+	3.06711i	−0.792806	+	0.113988i
$725$	−42.0795	−	17.1238i	−1.56280	−	0.635962i
$726$	−1.61551	−	5.38325i	−0.0599572	−	0.199791i
$727$	31.6026	−	2.26026i	1.17208	−	0.0838285i	0.528310	−	0.849051i	$-0.322826\pi$
$727$	31.6026	−	2.26026i	1.17208	−	0.0838285i	0.643766	+	0.765223i	$0.277371\pi$
$728$	−6.28495	+	2.34416i	−0.232936	+	0.0868805i
$729$	−21.0232	−	16.9418i	−0.778638	−	0.627474i
$730$	−14.8065	+	15.4406i	−0.548012	+	0.571483i
$731$	45.0562	−	39.0414i	1.66646	−	1.44400i
$732$	−2.83736	−	12.6795i	−0.104872	−	0.468648i
$733$	−21.2077	−	7.91005i	−0.783323	−	0.292164i	−0.0741948	−	0.997244i	$-0.523639\pi$
$733$	−21.2077	−	7.91005i	−0.783323	−	0.292164i	−0.709128	+	0.705079i	$0.750911\pi$
$734$	1.43328	−	9.96868i	0.0529033	−	0.367951i
$735$	−5.91628	+	9.77457i	−0.218225	+	0.360541i
$736$	−4.06912	+	2.53816i	−0.149990	+	0.0935577i
$737$	−16.2277	+	16.2277i	−0.597754	+	0.597754i
$738$	−1.41215	−	16.9139i	−0.0519821	−	0.622608i
$739$	−30.3153	+	13.8445i	−1.11517	+	0.509280i	−0.885803	−	0.464061i	$-0.846392\pi$
$739$	−30.3153	+	13.8445i	−1.11517	+	0.509280i	−0.229364	+	0.973341i	$0.573665\pi$
$740$	11.7490	+	7.20716i	0.431900	+	0.264941i
$741$	5.13839	+	11.0766i	0.188763	+	0.406911i
$742$	1.80041	+	0.983097i	0.0660950	+	0.0360906i
$743$	−7.01464	−	32.2458i	−0.257342	−	1.18298i	−0.906459	−	0.422294i	$-0.861225\pi$
$743$	−7.01464	−	32.2458i	−0.257342	−	1.18298i	0.649117	−	0.760689i	$-0.275139\pi$
$744$	10.1425	−	11.8467i	0.371841	−	0.434321i
$745$	−46.4756	−	9.09428i	−1.70274	−	0.333189i
$746$	0.186160	+	0.289671i	0.00681581	+	0.0106056i
$747$	5.37305	+	13.8984i	0.196590	+	0.508516i
$748$	−17.1504	−	12.8386i	−0.627081	−	0.469427i
$749$	26.1233	−	16.7884i	0.954524	−	0.613436i
$750$	−10.4277	−	16.3176i	−0.380765	−	0.595834i
$751$	9.72507	−	21.2949i	0.354873	−	0.777063i	−0.645044	−	0.764146i	$-0.723161\pi$
$751$	9.72507	−	21.2949i	0.354873	−	0.777063i	0.999917	−	0.0129176i	$-0.00411192\pi$
$752$	4.23721	−	0.921749i	0.154515	−	0.0336127i
$753$	−21.9182	−	21.6589i	−0.798743	−	0.789295i
$754$	22.8884	−	19.8329i	0.833547	−	0.722272i
$755$	8.09197	+	33.7735i	0.294497	+	1.22914i
$756$	−4.17353	+	9.58798i	−0.151790	+	0.348712i
$757$	6.97672	−	5.22271i	0.253573	−	0.189823i	−0.464927	−	0.885349i	$-0.653920\pi$
$757$	6.97672	−	5.22271i	0.253573	−	0.189823i	0.718501	+	0.695526i	$0.244829\pi$
$758$	8.74392	+	8.74392i	0.317593	+	0.317593i
$759$	0.174464	−	23.1315i	0.00633266	−	0.839621i
$760$	4.56463	+	1.23698i	0.165577	+	0.0448700i
$761$	−13.8902	−	1.99711i	−0.503520	−	0.0723952i	−0.114125	−	0.993466i	$-0.536407\pi$
$761$	−13.8902	−	1.99711i	−0.503520	−	0.0723952i	−0.389394	+	0.921071i	$0.627316\pi$
$762$	2.91974	+	2.15870i	0.105771	+	0.0782016i
$763$	−16.1787	+	8.83422i	−0.585707	+	0.319820i
$764$	9.38770	+	10.8340i	0.339635	+	0.391960i
$765$	−26.4592	+	44.3074i	−0.956633	+	1.60194i
$766$	15.8461	+	10.1837i	0.572542	+	0.367950i
$767$	3.00992	+	8.06990i	0.108682	+	0.291387i
$768$	0.358099	−	1.69463i	0.0129218	−	0.0611496i
$769$	2.52332	+	3.92636i	0.0909931	+	0.141588i	0.883766	−	0.467929i	$-0.155000\pi$
$769$	2.52332	+	3.92636i	0.0909931	+	0.141588i	−0.792773	+	0.609517i	$0.791363\pi$
$770$	−7.71843	−	9.87230i	−0.278153	−	0.355773i
$771$	−6.53751	−	0.900290i	−0.235443	−	0.0324232i
$772$	15.1346	+	3.29233i	0.544706	+	0.118494i
$773$	26.3469	−	1.88437i	0.947634	−	0.0677761i	0.411041	−	0.911617i	$-0.365165\pi$
$773$	26.3469	−	1.88437i	0.947634	−	0.0677761i	0.536593	+	0.843841i	$0.319711\pi$
$774$	−19.4072	+	12.8010i	−0.697576	+	0.460123i
$775$	40.1316	−	20.4019i	1.44157	−	0.732857i
$776$	4.45537	+	15.1736i	0.159938	+	0.544700i
$777$	7.38867	−	20.1755i	0.265067	−	0.723794i
$778$	4.44637	−	2.42790i	0.159410	−	0.0870444i
$779$	4.97074	+	10.8844i	0.178095	+	0.389974i
$780$	12.8471	−	1.26710i	0.460000	−	0.0453696i
$781$	−9.50272			−0.340034
$782$	21.7096	+	29.8312i	0.776334	+	1.06676i
$783$	2.52716	−	47.1449i	0.0903135	−	1.68482i
$784$	−2.92005	−	0.419840i	−0.104288	−	0.0149943i
$785$	−9.15816	+	1.51331i	−0.326869	+	0.0540125i
$786$	−20.3171	−	12.8869i	−0.724687	−	0.459660i
$787$	2.61653	−	36.5838i	0.0932691	−	1.30407i	−0.708189	−	0.706023i	$-0.750488\pi$
$787$	2.61653	−	36.5838i	0.0932691	−	1.30407i	0.801458	−	0.598050i	$-0.204058\pi$
$788$	0.859488	+	0.469316i	0.0306180	+	0.0167187i
$789$	−10.7578	−	12.2669i	−0.382987	−	0.436714i
$790$	−21.7827	−	18.0895i	−0.774993	−	0.643595i
$791$	24.4487	+	21.1850i	0.869297	+	0.753250i
$792$	5.97729	+	5.83672i	0.212394	+	0.207399i
$793$	20.0170	+	14.9845i	0.710823	+	0.532115i
$794$	−3.37423	−	23.4683i	−0.119747	−	0.832858i
$795$	−2.86564	−	2.71541i	−0.101634	−	0.0963055i
$796$	−2.22207	+	2.56441i	−0.0787592	+	0.0908930i
$797$	−17.2727	−	46.3098i	−0.611830	−	1.64038i	−0.758865	−	0.651247i	$-0.774246\pi$
$797$	−17.2727	−	46.3098i	−0.611830	−	1.64038i	0.147036	−	0.989131i	$-0.453027\pi$
$798$	0.482168	−	7.35634i	0.0170686	−	0.260412i
$799$	−9.39844	−	32.0081i	−0.332493	−	1.13237i
$800$	2.82599	−	4.12478i	0.0999138	−	0.145833i
$801$	1.44657	−	1.28391i	0.0511120	−	0.0453647i
$802$	1.16128	−	3.11351i	0.0410062	−	0.109942i
$803$	21.3282	−	15.9661i	0.752657	−	0.563432i
$804$	−3.93985	+	13.7193i	−0.138948	+	0.483842i
$805$	7.69266	+	20.1634i	0.271131	+	0.710667i
$806$			30.0121i			1.05713i
$807$	2.37586	+	6.25600i	0.0836341	+	0.220222i
$808$	−4.14123	−	1.54460i	−0.145688	−	0.0543389i
$809$	27.8276	+	8.17091i	0.978365	+	0.287274i	0.731549	−	0.681789i	$-0.238798\pi$
$809$	27.8276	+	8.17091i	0.978365	+	0.287274i	0.246816	+	0.969062i	$0.420616\pi$
$810$	12.4851	−	15.7836i	0.438682	−	0.554579i
$811$	−25.4909	+	7.48482i	−0.895108	+	0.262827i	−0.696760	−	0.717304i	$-0.745376\pi$
$811$	−25.4909	+	7.48482i	−0.895108	+	0.262827i	−0.198348	+	0.980132i	$0.563558\pi$
$812$	−17.8673	+	3.88679i	−0.627019	+	0.136400i
$813$	2.66234	+	34.3513i	0.0933724	+	1.20475i
$814$	−12.9730	−	11.2412i	−0.454703	−	0.394003i
$815$	37.3105	−	11.8103i	1.30693	−	0.413697i
$816$	−13.2002	−	1.81781i	−0.462098	−	0.0636362i
$817$	9.82235	−	13.1211i	0.343641	−	0.459050i
$818$	10.0960	+	2.19625i	0.352999	+	0.0767902i
$819$	−5.89881	−	19.2397i	−0.206121	−	0.672288i
$820$	12.5968	−	1.16679i	0.439899	−	0.0407461i
$821$	16.4739	−	25.6339i	0.574942	−	0.894628i	−0.425002	−	0.905192i	$-0.639727\pi$
$821$	16.4739	−	25.6339i	0.574942	−	0.894628i	0.999944	+	0.0105648i	$0.00336293\pi$
$822$	−2.54526	−	2.51516i	−0.0887763	−	0.0877263i
$823$	17.3990	+	1.24440i	0.606492	+	0.0433772i	0.371208	−	0.928550i	$-0.378944\pi$
$823$	17.3990	+	1.24440i	0.606492	+	0.0433772i	0.235284	+	0.971927i	$0.424398\pi$
$824$	−8.56317	−	2.51437i	−0.298312	−	0.0875923i
$825$	9.49974	+	22.1672i	0.330738	+	0.771762i
$826$	0.740054	−	5.14719i	0.0257498	−	0.179093i
$827$	−6.26893	+	6.26893i	−0.217992	+	0.217992i	−0.807652	−	0.589660i	$-0.799262\pi$
$827$	−6.26893	+	6.26893i	−0.217992	+	0.217992i	0.589660	+	0.807652i	$0.299262\pi$
$828$	−6.87507	−	12.6386i	−0.238925	−	0.439221i
$829$		−	41.7090i		−	1.44862i	−0.689477	−	0.724308i	$-0.742160\pi$
$829$		−	41.7090i		−	1.44862i	0.689477	−	0.724308i	$-0.257840\pi$
$830$	−10.3225	+	4.09857i	−0.358300	+	0.142264i
$831$	−3.93567	−	26.2631i	−0.136527	−	0.911056i
$832$	1.59744	+	2.92548i	0.0553811	+	0.101423i
$833$	−1.61905	+	22.6373i	−0.0560968	+	0.784335i
$834$	−11.3510	+	0.0675275i	−0.393054	+	0.00233829i
$835$	7.25973	+	8.03164i	0.251233	+	0.277946i
$836$	−5.35756	−	2.44672i	−0.185295	−	0.0846214i
$837$	33.6678	+	32.4870i	1.16373	+	1.12292i
$838$	−2.96985	+	13.6522i	−0.102592	+	0.471607i
$839$	0.999183	+	6.94947i	0.0344956	+	0.239922i	0.999773	−	0.0213046i	$-0.00678199\pi$
$839$	0.999183	+	6.94947i	0.0344956	+	0.239922i	−0.965277	+	0.261227i	$0.915873\pi$
$840$	−7.17437	−	3.04586i	−0.247539	−	0.105092i
$841$	45.0546	−	28.9548i	1.55361	−	0.998443i
$842$	−0.0453490	−	0.634062i	−0.00156283	−	0.0218512i
$843$	−12.9500	+	1.00367i	−0.446021	+	0.0345681i
$844$	14.0603	−	21.8782i	0.483974	−	0.753078i
$845$	2.92466	−	3.04992i	0.100611	−	0.104920i
$846$	2.00443	+	12.8536i	0.0689138	+	0.441915i
$847$	−3.12963	−	5.73149i	−0.107535	−	0.196936i
$848$	0.356217	−	0.955055i	0.0122325	−	0.0327967i
$849$	−9.93294	−	4.46500i	−0.340898	−	0.153238i
$850$	−33.2022	−	19.4213i	−1.13883	−	0.666146i
$851$	15.6455	+	25.0825i	0.536320	+	0.859817i
$852$	−5.17049	+	2.86336i	−0.177138	+	0.0980971i
$853$	−14.9271	−	19.9402i	−0.511094	−	0.682741i	0.468561	−	0.883431i	$-0.344773\pi$
$853$	−14.9271	−	19.9402i	−0.511094	−	0.682741i	−0.979655	+	0.200690i	$0.935682\pi$
$854$	−6.27130	−	13.7322i	−0.214600	−	0.469907i
$855$	−4.51871	+	13.4490i	−0.154537	+	0.459946i
$856$	−10.1048	−	11.6615i	−0.345374	−	0.398583i
$857$	21.6500	−	39.6491i	0.739551	−	1.35439i	−0.188552	−	0.982063i	$-0.560379\pi$
$857$	21.6500	−	39.6491i	0.739551	−	1.35439i	0.928103	−	0.372323i	$-0.121439\pi$
$858$	−16.0429	−	1.05153i	−0.547697	−	0.0358985i
$859$	−2.39169	−	1.09225i	−0.0816033	−	0.0372670i	0.374195	−	0.927350i	$-0.377919\pi$
$859$	−2.39169	−	1.09225i	−0.0816033	−	0.0372670i	−0.455799	+	0.890083i	$0.650646\pi$
$860$	−9.67205	−	14.3782i	−0.329814	−	0.490291i
$861$	−5.66832	−	18.8881i	−0.193176	−	0.643705i
$862$	−15.1156	+	20.1921i	−0.514841	+	0.687747i
$863$	−3.38433	+	4.52093i	−0.115204	+	0.153894i	−0.854437	−	0.519556i	$-0.826097\pi$
$863$	−3.38433	+	4.52093i	−0.115204	+	0.153894i	0.739233	+	0.673450i	$0.235188\pi$
$864$	5.01100	+	1.37472i	0.170478	+	0.0467689i
$865$	15.9640	+	23.7316i	0.542792	+	0.806898i
$866$	23.3871	+	10.6805i	0.794727	+	0.362939i
$867$	−4.77863	+	72.9066i	−0.162291	+	2.47604i
$868$	8.68396	−	15.9035i	0.294753	−	0.539800i
$869$	23.0922	+	26.6499i	0.783350	+	0.904035i
$870$	35.1553	+	1.56503i	1.19188	+	0.0530595i
$871$	−11.4110	−	24.9866i	−0.386647	−	0.846638i
$872$	5.48924	+	7.33276i	0.185889	+	0.248319i
$873$	−46.2350	+	10.6355i	−1.56482	+	0.359956i
$874$	7.57538	+	6.74516i	0.256241	+	0.228159i
$875$	−15.7738	−	16.0446i	−0.533250	−	0.542406i
$876$	6.79391	−	15.1139i	0.229545	−	0.510651i
$877$	11.2033	−	30.0372i	0.378308	−	1.01428i	−0.598680	−	0.800988i	$-0.704308\pi$
$877$	11.2033	−	30.0372i	0.378308	−	1.01428i	0.976988	−	0.213295i	$-0.0684194\pi$
$878$	−10.4594	−	19.1550i	−0.352988	−	0.646450i
$879$	8.82721	+	19.0285i	0.297734	+	0.641815i
$880$	−4.30987	+	4.49446i	−0.145286	+	0.151508i
$881$	9.21949	−	14.3458i	0.310613	−	0.483323i	−0.650490	−	0.759515i	$-0.725436\pi$
$881$	9.21949	−	14.3458i	0.310613	−	0.483323i	0.961102	+	0.276192i	$0.0890727\pi$
$882$	1.77823	−	8.66976i	0.0598761	−	0.291926i
$883$	0.738398	+	10.3242i	0.0248491	+	0.347435i	0.994633	+	0.103469i	$0.0329942\pi$
$883$	0.738398	+	10.3242i	0.0248491	+	0.347435i	−0.969784	+	0.243967i	$0.921551\pi$
$884$	21.5718	−	13.8634i	0.725540	−	0.466276i
$885$	−3.91090	+	9.21192i	−0.131463	+	0.309655i
$886$	−1.69872	−	11.8149i	−0.0570696	−	0.396928i
$887$	1.14417	−	5.25968i	0.0384175	−	0.176603i	−0.953940	−	0.299997i	$-0.903014\pi$
$887$	1.14417	−	5.25968i	0.0384175	−	0.176603i	0.992358	+	0.123394i	$0.0393780\pi$
$888$	−10.4459	−	2.20736i	−0.350541	−	0.0740742i
$889$	3.83766	+	1.75260i	0.128711	+	0.0587803i
$890$	0.966703	+	1.06949i	0.0324040	+	0.0358494i
$891$	−18.5455	+	16.8589i	−0.621299	+	0.564793i
$892$	−1.30855	+	18.2959i	−0.0438135	+	0.612592i
$893$	−4.39532	−	8.04943i	−0.147084	−	0.269364i
$894$	36.2775	−	5.43639i	1.21330	−	0.181820i
$895$	39.5609	−	15.7077i	1.32237	−	0.525050i
$896$		−	2.01244i		−	0.0672309i
$897$	25.8683	+	9.87123i	0.863716	+	0.329591i
$898$	14.6297	−	14.6297i	0.488198	−	0.488198i
$899$	−11.6429	+	80.9778i	−0.388311	+	2.70076i
$900$	11.8483	+	9.19883i	0.394942	+	0.306628i
$901$	−7.52406	−	2.20926i	−0.250663	−	0.0736012i
$902$	−15.7150	−	1.12396i	−0.523252	−	0.0374237i
$903$	−18.9866	+	19.2139i	−0.631836	+	0.639398i
$904$	8.69089	−	13.5233i	0.289055	−	0.449778i
$905$	47.9854	−	4.44470i	1.59509	−	0.147747i
$906$	−14.6783	−	22.5439i	−0.487654	−	0.748970i
$907$	18.0533	+	3.92725i	0.599448	+	0.130402i	0.502043	−	0.864843i	$-0.332582\pi$
$907$	18.0533	+	3.92725i	0.599448	+	0.130402i	0.0974056	+	0.995245i	$0.468946\pi$
$908$	2.92800	−	3.91135i	0.0971692	−	0.129803i
$909$	5.36440	−	12.1262i	0.177926	−	0.402199i
$910$	14.3000	−	4.52652i	0.474039	−	0.150053i
$911$	15.4834	+	13.4164i	0.512987	+	0.444506i	0.872486	−	0.488640i	$-0.162507\pi$
$911$	15.4834	+	13.4164i	0.512987	+	0.444506i	−0.359498	+	0.933146i	$0.617052\pi$
$912$	−3.65232	+	0.283068i	−0.120941	+	0.00937330i
$913$	13.5158	−	2.94018i	0.447308	−	0.0973058i
$914$	1.52634	−	0.448174i	0.0504868	−	0.0148243i
$915$	4.90707	+	28.6361i	0.162223	+	0.946679i
$916$	11.7184	+	3.44084i	0.387187	+	0.113688i
$917$	−26.1917	−	9.76901i	−0.864927	−	0.322601i
$918$	7.79871	−	39.2061i	0.257396	−	1.29400i
$919$		−	20.7301i		−	0.683822i	−0.939732	−	0.341911i	$-0.888926\pi$
$919$		−	20.7301i		−	0.683822i	0.939732	−	0.341911i	$-0.111074\pi$
$920$	9.37340	−	5.20955i	0.309032	−	0.171754i
$921$	−3.22158	−	0.925160i	−0.106155	−	0.0304851i
$922$	1.53002	−	1.14536i	0.0503887	−	0.0377205i
$923$	3.97485	−	10.6570i	0.130834	−	0.350779i
$924$	8.19695	+	5.19922i	0.269660	+	0.171042i
$925$	−25.4256	−	17.4197i	−0.835988	−	0.572756i
$926$	2.14552	+	7.30697i	0.0705061	+	0.240122i
$927$	9.05744	−	25.1955i	0.297485	−	0.827528i
$928$	3.17525	+	8.51318i	0.104233	+	0.279459i
$929$	21.8499	−	25.2162i	0.716873	−	0.827315i	−0.274054	−	0.961714i	$-0.588365\pi$
$929$	21.8499	−	25.2162i	0.716873	−	0.827315i	0.990927	+	0.134399i	$0.0429103\pi$
$930$	−23.9859	+	25.3130i	−0.786529	+	0.830044i
$931$	0.887959	+	6.17589i	0.0291017	+	0.202407i
$932$	8.80838	+	6.59387i	0.288528	+	0.215989i
$933$	−6.91108	−	3.72054i	−0.226259	−	0.121805i
$934$	−11.0394	−	9.56567i	−0.361219	−	0.312998i
$935$	36.8534	+	30.6050i	1.20523	+	1.00089i
$936$	−9.04590	+	4.26192i	−0.295675	+	0.139305i
$937$	13.0817	+	7.14317i	0.427362	+	0.233357i	0.678510	−	0.734592i	$-0.262626\pi$
$937$	13.0817	+	7.14317i	0.427362	+	0.233357i	−0.251148	+	0.967949i	$0.580808\pi$
$938$	−1.18312	+	16.5422i	−0.0386304	+	0.540123i
$939$	−21.7795	+	34.3371i	−0.710749	+	1.12055i
$940$	−9.56656	+	1.58080i	−0.312027	+	0.0515600i
$941$	14.8985	+	2.14207i	0.485676	+	0.0698296i	0.380803	−	0.924656i	$-0.375648\pi$
$941$	14.8985	+	2.14207i	0.485676	+	0.0698296i	0.104872	+	0.994486i	$0.466557\pi$
$942$	6.28997	−	3.48332i	0.204938	−	0.113493i
$943$	25.2918	+	9.82402i	0.823614	+	0.319914i
$944$	−2.58398			−0.0841015
$945$	10.4013	−	20.9416i	0.338355	−	0.681231i
$946$	8.96505	+	19.6307i	0.291479	+	0.638250i
$947$	−14.1330	+	7.71722i	−0.459262	+	0.250776i	−0.692186	−	0.721719i	$-0.743352\pi$
$947$	−14.1330	+	7.71722i	−0.459262	+	0.250776i	0.232925	+	0.972495i	$0.425170\pi$
$948$	20.5948	+	7.54219i	0.668887	+	0.244959i
$949$	8.98418	+	30.5973i	0.291639	+	0.993230i
$950$	−10.0544	−	3.27704i	−0.326208	−	0.106321i
$951$	−20.5627	−	17.6046i	−0.666792	−	0.570869i
$952$	−15.4424	+	1.10446i	−0.500490	+	0.0357957i
$953$	12.9986	+	2.82768i	0.421067	+	0.0915975i	0.418106	−	0.908398i	$-0.362694\pi$
$953$	12.9986	+	2.82768i	0.421067	+	0.0915975i	0.00296065	+	0.999996i	$0.499058\pi$
$954$	2.79654	+	1.23714i	0.0905415	+	0.0400539i
$955$	−19.7435	−	25.2530i	−0.638885	−	0.817169i
$956$	9.24041	+	14.3784i	0.298856	+	0.465029i
$957$	−42.8788	−	9.06089i	−1.38607	−	0.292897i
$958$	7.46172	+	20.0056i	0.241077	+	0.646353i
$959$	−3.49759	−	2.24777i	−0.112943	−	0.0725841i
$960$	−0.990756	+	3.74412i	−0.0319765	+	0.120841i
$961$	−32.7897	−	37.8414i	−1.05773	−	1.22069i
$962$	18.0330	−	9.84677i	0.581407	−	0.317472i
$963$	36.7254	−	28.1803i	1.18346	−	0.908096i
$964$	−21.3365	−	3.06772i	−0.687202	−	0.0988047i
$965$	−33.4278	−	9.05869i	−1.07608	−	0.291609i
$966$	−10.8514	−	12.7158i	−0.349140	−	0.409123i
$967$	−12.8893	−	12.8893i	−0.414492	−	0.414492i	0.468808	−	0.883300i	$-0.344684\pi$
$967$	−12.8893	−	12.8893i	−0.414492	−	0.414492i	−0.883300	+	0.468808i	$0.844684\pi$
$968$	−2.59772	+	1.94463i	−0.0834939	+	0.0625028i
$969$	4.17656	+	27.8706i	0.134170	+	0.895331i
$970$	−8.23927	−	34.3883i	−0.264547	−	1.10414i
$971$	6.62457	−	5.74023i	0.212593	−	0.184213i	−0.542055	−	0.840343i	$-0.682353\pi$
$971$	6.62457	−	5.74023i	0.212593	−	0.184213i	0.754647	+	0.656131i	$0.227808\pi$
$972$	−5.01082	+	14.7612i	−0.160722	+	0.473464i
$973$	−12.8874	+	2.80348i	−0.413151	+	0.0898755i
$974$	−9.70308	+	21.2468i	−0.310907	+	0.680790i
$975$	−28.8333	+	1.38143i	−0.923406	+	0.0442413i
$976$	−6.31072	+	4.05566i	−0.202001	+	0.129818i
$977$	4.98686	+	3.73312i	0.159544	+	0.119433i	0.676067	−	0.736840i	$-0.263683\pi$
$977$	4.98686	+	3.73312i	0.159544	+	0.119433i	−0.516523	+	0.856273i	$0.672774\pi$
$978$	−24.1591	+	18.3105i	−0.772521	+	0.585505i
$979$	−0.970672	−	1.51040i	−0.0310228	−	0.0482725i
$980$	6.47380	+	1.26678i	0.206798	+	0.0404659i
$981$	−22.9386	+	15.1304i	−0.732374	+	0.483077i
$982$	3.35120	+	15.4052i	0.106941	+	0.491601i
$983$	28.1891	+	15.3924i	0.899092	+	0.490941i	0.861157	−	0.508339i	$-0.169740\pi$
$983$	28.1891	+	15.3924i	0.899092	+	0.490941i	0.0379348	+	0.999280i	$0.487922\pi$
$984$	−8.88929	+	4.12369i	−0.283380	+	0.131458i
$985$	−1.86652	−	1.14498i	−0.0594724	−	0.0364821i
$986$	63.5828	−	29.0373i	2.02489	−	0.924736i
$987$	5.36626	+	14.1302i	0.170810	+	0.449769i
$988$	4.98490	−	4.98490i	0.158591	−	0.158591i
$989$	−4.79246	−	36.8554i	−0.152391	−	1.17193i
$990$	−12.6906	−	13.7086i	−0.403335	−	0.435686i
$991$	−6.27023	+	43.6104i	−0.199180	+	1.38533i	0.607490	+	0.794327i	$0.292177\pi$
$991$	−6.27023	+	43.6104i	−0.199180	+	1.38533i	−0.806670	+	0.591002i	$0.798733\pi$
$992$	−8.43626	−	3.14656i	−0.267852	−	0.0999034i
$993$	−41.1870	+	9.21663i	−1.30703	+	0.292481i
$994$	−5.18988	+	4.49705i	−0.164613	+	0.142638i
$995$	5.25147	−	5.47639i	0.166483	−	0.173613i
$996$	6.46809	−	5.67235i	0.204949	−	0.179735i
$997$	33.4963	−	12.4935i	1.06084	−	0.395672i	0.242346	−	0.970190i	$-0.422083\pi$
$997$	33.4963	−	12.4935i	1.06084	−	0.395672i	0.818492	+	0.574517i	$0.194810\pi$
$998$	−20.4783	+	1.46464i	−0.648229	+	0.0463622i
$999$	8.47391	−	30.8884i	0.268103	−	0.977265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.5	✓	960
3.2	odd	2	inner	690.2.x.a.77.26	yes	960
5.3	odd	4	inner	690.2.x.a.353.16	yes	960
15.8	even	4	inner	690.2.x.a.353.37	yes	960
23.3	even	11	inner	690.2.x.a.647.37	yes	960
69.26	odd	22	inner	690.2.x.a.647.16	yes	960
115.3	odd	44	inner	690.2.x.a.233.26	yes	960
345.233	even	44	inner	690.2.x.a.233.5	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.5	✓	960	1.1	even	1	trivial
690.2.x.a.77.26	yes	960	3.2	odd	2	inner
690.2.x.a.233.5	yes	960	345.233	even	44	inner
690.2.x.a.233.26	yes	960	115.3	odd	44	inner
690.2.x.a.353.16	yes	960	5.3	odd	4	inner
690.2.x.a.353.37	yes	960	15.8	even	4	inner
690.2.x.a.647.16	yes	960	69.26	odd	22	inner
690.2.x.a.647.37	yes	960	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.39273 - 1.02971i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(0.737339 - 2.11100i) q^{5} +(0.0103038 + 1.73202i) q^{6} +(0.427775 + 1.96645i) q^{7} +(0.936950 - 0.349464i) q^{8} +(0.879385 + 2.86822i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.39273 - 1.02971i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(0.737339 - 2.11100i) q^{5} +(0.0103038 + 1.73202i) q^{6} +(0.427775 + 1.96645i) q^{7} +(0.936950 - 0.349464i) q^{8} +(0.879385 + 2.86822i) q^{9} +(-2.13182 + 0.674807i) q^{10} +(2.75644 - 0.396317i) q^{11} +(1.38038 - 1.04621i) q^{12} +(-0.708524 + 3.25703i) q^{13} +(1.31787 - 1.52090i) q^{14} +(-3.20064 + 2.18081i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-3.68689 + 6.75203i) q^{17} +(1.76913 - 2.42284i) q^{18} +(-0.595863 + 2.02932i) q^{19} +(1.81776 + 1.30221i) q^{20} +(1.42910 - 3.17922i) q^{21} +(-1.96914 - 1.96914i) q^{22} +(2.24140 + 4.23982i) q^{23} +(-1.66476 - 0.478080i) q^{24} +(-3.91266 - 3.11305i) q^{25} +(3.03199 - 1.38466i) q^{26} +(1.72870 - 4.90016i) q^{27} +(-2.00731 - 0.143566i) q^{28} +(8.71801 - 2.55984i) q^{29} +(3.66390 + 1.25533i) q^{30} +(-3.74038 + 8.19029i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.24707 - 2.28638i) q^{33} +(7.61474 - 1.09483i) q^{34} +(4.46660 + 0.546905i) q^{35} +(-2.99979 + 0.0356929i) q^{36} +(6.14840 - 0.439743i) q^{37} +(1.98164 - 0.739115i) q^{38} +(4.34059 - 3.80658i) q^{39} +(-0.0468706 - 2.23558i) q^{40} +(4.27571 - 3.70492i) q^{41} +(-3.40152 + 0.761177i) q^{42} +(-7.26097 - 2.70820i) q^{43} +(-0.396317 + 2.75644i) q^{44} +(6.70322 + 0.258465i) q^{45} +(2.05093 - 4.33517i) q^{46} +(-3.06623 + 3.06623i) q^{47} +(0.614933 + 1.61921i) q^{48} +(2.68349 - 1.22551i) q^{49} +(-0.147351 + 4.99783i) q^{50} +(12.0875 - 5.60731i) q^{51} +(-2.92548 - 1.59744i) q^{52} +(0.216673 + 0.996029i) q^{53} +(-4.95875 + 1.55267i) q^{54} +(1.19581 - 6.11108i) q^{55} +(1.08801 + 1.69297i) q^{56} +(2.91949 - 2.21273i) q^{57} +(-7.27377 - 5.44507i) q^{58} +(2.17379 - 1.39701i) q^{59} +(-1.19074 - 3.68539i) q^{60} +(3.11627 - 6.82367i) q^{61} +(8.79819 - 1.91393i) q^{62} +(-5.26403 + 2.95622i) q^{63} +(0.755750 - 0.654861i) q^{64} +(6.35318 + 3.89723i) q^{65} +(0.714830 + 4.77013i) q^{66} +(-6.59725 + 4.93864i) q^{67} +(-5.43981 - 5.43981i) q^{68} +(1.24413 - 8.21292i) q^{69} +(-2.23891 - 3.90344i) q^{70} +(-3.37763 - 0.485631i) q^{71} +(1.82628 + 2.38006i) q^{72} +(8.39682 - 4.58501i) q^{73} +(-4.03663 - 4.65852i) q^{74} +(2.24373 + 8.36455i) q^{75} +(-1.77925 - 1.14345i) q^{76} +(1.95847 + 5.25087i) q^{77} +(-5.64854 - 1.19362i) q^{78} +(6.84595 + 10.6525i) q^{79} +(-1.76158 + 1.37725i) q^{80} +(-7.45336 + 5.04454i) q^{81} +(-5.52828 - 1.20260i) q^{82} +(4.95429 - 0.354338i) q^{83} +(2.64781 + 2.26690i) q^{84} +(11.5351 + 12.7616i) q^{85} +(2.18331 + 7.43567i) q^{86} +(-14.7777 - 5.41188i) q^{87} +(2.44415 - 1.33461i) q^{88} +(-0.267827 - 0.586459i) q^{89} +(-3.81018 - 5.52110i) q^{90} -6.70788 q^{91} +(-4.69956 + 0.956114i) q^{92} +(13.6430 - 7.55534i) q^{93} +(4.29217 + 0.617121i) q^{94} +(3.84455 + 2.75416i) q^{95} +(0.927733 - 1.46264i) q^{96} +(-1.12817 + 15.7739i) q^{97} +(-2.58922 - 1.41382i) q^{98} +(3.56070 + 7.55757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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