LMFDB - Embedded newform 690.2.w.a.7.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.9
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.32705 - 1.79970i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.34666 - 2.46622i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.32705 - 1.79970i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.34666 - 2.46622i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-1.45206 - 1.70045i) q^{10} +(2.90083 - 2.51359i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-4.18159 + 2.28332i) q^{13} +(1.16729 - 2.55600i) q^{14} +(2.04066 - 0.914169i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.22491 - 2.97213i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-1.08787 - 7.56633i) q^{19} +(-1.56967 - 1.59253i) q^{20} +(2.12360 + 1.84011i) q^{21} +(2.71413 - 2.71413i) q^{22} +(3.76822 + 2.96656i) q^{23} +1.00000i q^{24} +(-1.47787 + 4.77660i) q^{25} +(-4.00804 + 2.57581i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.981970 - 2.63276i) q^{28} +(9.50124 + 1.36607i) q^{29} +(1.97025 - 1.05742i) q^{30} +(-1.98920 - 1.27838i) q^{31} +(0.936950 - 0.349464i) q^{32} +(1.83953 + 3.36884i) q^{33} +(-2.43127 - 2.80583i) q^{34} +(-6.22555 + 0.849212i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.81388 - 10.2254i) q^{37} +(-1.62488 - 7.46944i) q^{38} +(-1.34228 - 4.57138i) q^{39} +(-1.67928 - 1.47649i) q^{40} +(0.540507 + 1.18355i) q^{41} +(2.24947 + 1.68393i) q^{42} +(6.89999 + 1.50100i) q^{43} +(2.51359 - 2.90083i) q^{44} +(0.459504 + 2.18835i) q^{45} +(3.97025 + 2.69018i) q^{46} +(4.20381 + 4.20381i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(-0.484261 - 0.753524i) q^{49} +(-1.13335 + 4.86986i) q^{50} +(3.37714 - 1.54229i) q^{51} +(-3.81408 + 2.85518i) q^{52} +(4.12654 + 2.25326i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-8.37327 - 1.88499i) q^{55} +(0.791649 - 2.69611i) q^{56} +(7.62466 + 0.545326i) q^{57} +(9.57449 + 0.684781i) q^{58} +(-2.89397 + 9.85594i) q^{59} +(1.88979 - 1.19528i) q^{60} +(-3.27367 + 5.09393i) q^{61} +(-2.07533 - 1.13322i) q^{62} +(-2.24947 + 1.68393i) q^{63} +(0.909632 - 0.415415i) q^{64} +(9.65848 + 4.49554i) q^{65} +(2.07517 + 3.22903i) q^{66} +(0.349266 + 4.88337i) q^{67} +(-2.62524 - 2.62524i) q^{68} +(-3.69976 + 3.05152i) q^{69} +(-6.14910 + 1.29117i) q^{70} +(1.96697 - 2.27000i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(1.14966 + 0.860625i) q^{73} +(-4.53363 - 9.92727i) q^{74} +(-4.35329 - 2.45944i) q^{75} +(-2.15360 - 7.33449i) q^{76} +(-2.29262 - 10.5390i) q^{77} +(-1.66498 - 4.46398i) q^{78} +(-6.34227 - 1.86226i) q^{79} +(-1.78033 - 1.35293i) q^{80} +(0.654861 + 0.755750i) q^{81} +(0.623563 + 1.14197i) q^{82} +(-15.6190 + 5.82559i) q^{83} +(2.36386 + 1.51916i) q^{84} +(-2.39639 + 7.94834i) q^{85} +(6.98948 + 1.00494i) q^{86} +(-3.35449 + 8.99373i) q^{87} +(2.30024 - 3.07276i) q^{88} +(6.94947 - 4.46615i) q^{89} +(0.614448 + 2.14999i) q^{90} +13.3876i q^{91} +(4.15205 + 2.40010i) q^{92} +(1.67200 - 1.67200i) q^{93} +(4.49299 + 3.89320i) q^{94} +(-12.1735 + 11.9988i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-2.33879 - 0.872323i) q^{97} +(-0.536783 - 0.717058i) q^{98} +(-3.68287 + 1.08139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−1.32705	−	1.79970i	−0.593475	−	0.804852i
$5$	−1.32705	−	1.79970i	−0.593475	−	0.804852i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	1.34666	−	2.46622i	0.508988	−	0.932143i	−0.489211	−	0.872165i	$-0.662715\pi$
$7$	1.34666	−	2.46622i	0.508988	−	0.932143i	0.998200	−	0.0599775i	$-0.0191029\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	−1.45206	−	1.70045i	−0.459181	−	0.537729i
$11$	2.90083	−	2.51359i	0.874634	−	0.757875i	−0.0967700	−	0.995307i	$-0.530851\pi$
$11$	2.90083	−	2.51359i	0.874634	−	0.757875i	0.971404	+	0.237432i	$0.0763057\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	−4.18159	+	2.28332i	−1.15976	+	0.633279i	−0.939630	−	0.342191i	$-0.888831\pi$
$13$	−4.18159	+	2.28332i	−1.15976	+	0.633279i	−0.220133	+	0.975470i	$0.570649\pi$
$14$	1.16729	−	2.55600i	0.311971	−	0.683121i
$15$	2.04066	−	0.914169i	0.526896	−	0.236037i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−2.22491	−	2.97213i	−0.539619	−	0.720847i	0.445006	−	0.895528i	$-0.353201\pi$
$17$	−2.22491	−	2.97213i	−0.539619	−	0.720847i	−0.984625	+	0.174681i	$0.944111\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	−1.08787	−	7.56633i	−0.249575	−	1.73584i	−0.600672	−	0.799496i	$-0.705100\pi$
$19$	−1.08787	−	7.56633i	−0.249575	−	1.73584i	0.351096	−	0.936339i	$-0.385809\pi$
$20$	−1.56967	−	1.59253i	−0.350988	−	0.356100i
$21$	2.12360	+	1.84011i	0.463409	+	0.401546i
$22$	2.71413	−	2.71413i	0.578653	−	0.578653i
$23$	3.76822	+	2.96656i	0.785729	+	0.618571i
$23$	3.76822	+	2.96656i	0.785729	+	0.618571i
$24$			1.00000i			0.204124i
$25$	−1.47787	+	4.77660i	−0.295575	+	0.955320i
$26$	−4.00804	+	2.57581i	−0.786042	+	0.505159i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	0.981970	−	2.63276i	0.185575	−	0.497546i
$29$	9.50124	+	1.36607i	1.76434	+	0.253673i	0.946712	−	0.322080i	$-0.104382\pi$
$29$	9.50124	+	1.36607i	1.76434	+	0.253673i	0.817623	+	0.575753i	$0.195291\pi$
$30$	1.97025	−	1.05742i	0.359716	−	0.193057i
$31$	−1.98920	−	1.27838i	−0.357271	−	0.229604i	0.349676	−	0.936871i	$-0.386292\pi$
$31$	−1.98920	−	1.27838i	−0.357271	−	0.229604i	−0.706947	+	0.707266i	$0.749928\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	1.83953	+	3.36884i	0.320220	+	0.586440i
$34$	−2.43127	−	2.80583i	−0.416959	−	0.481196i
$35$	−6.22555	+	0.849212i	−1.05231	+	0.143543i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−3.81388	−	10.2254i	−0.626998	−	1.68105i	−0.727499	−	0.686109i	$-0.759317\pi$
$37$	−3.81388	−	10.2254i	−0.626998	−	1.68105i	0.100501	−	0.994937i	$-0.467955\pi$
$38$	−1.62488	−	7.46944i	−0.263590	−	1.21170i
$39$	−1.34228	−	4.57138i	−0.214937	−	0.732007i
$40$	−1.67928	−	1.47649i	−0.265517	−	0.233454i
$41$	0.540507	+	1.18355i	0.0844130	+	0.184839i	0.947131	−	0.320846i	$-0.103967\pi$
$41$	0.540507	+	1.18355i	0.0844130	+	0.184839i	−0.862718	+	0.505685i	$0.831240\pi$
$42$	2.24947	+	1.68393i	0.347100	+	0.259836i
$43$	6.89999	+	1.50100i	1.05224	+	0.228900i	0.705242	−	0.708966i	$-0.250838\pi$
$43$	6.89999	+	1.50100i	1.05224	+	0.228900i	0.346996	+	0.937867i	$0.387202\pi$
$44$	2.51359	−	2.90083i	0.378937	−	0.437317i
$45$	0.459504	+	2.18835i	0.0684987	+	0.326219i
$46$	3.97025	+	2.69018i	0.585382	+	0.396646i
$47$	4.20381	+	4.20381i	0.613188	+	0.613188i	0.943775	−	0.330587i	$-0.107247\pi$
$47$	4.20381	+	4.20381i	0.613188	+	0.613188i	−0.330587	+	0.943775i	$0.607247\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	−0.484261	−	0.753524i	−0.0691801	−	0.107646i
$50$	−1.13335	+	4.86986i	−0.160280	+	0.688702i
$51$	3.37714	−	1.54229i	0.472894	−	0.215964i
$52$	−3.81408	+	2.85518i	−0.528917	+	0.395942i
$53$	4.12654	+	2.25326i	0.566824	+	0.309509i	0.736987	−	0.675906i	$-0.236248\pi$
$53$	4.12654	+	2.25326i	0.566824	+	0.309509i	−0.170163	+	0.985416i	$0.554430\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	−8.37327	−	1.88499i	−1.12905	−	0.254171i
$56$	0.791649	−	2.69611i	0.105789	−	0.360283i
$57$	7.62466	+	0.545326i	1.00991	+	0.0722303i
$58$	9.57449	+	0.684781i	1.25719	+	0.0899161i
$59$	−2.89397	+	9.85594i	−0.376762	+	1.28313i	0.525074	+	0.851057i	$0.324038\pi$
$59$	−2.89397	+	9.85594i	−0.376762	+	1.28313i	−0.901836	+	0.432078i	$0.857780\pi$
$60$	1.88979	−	1.19528i	0.243971	−	0.154310i
$61$	−3.27367	+	5.09393i	−0.419150	+	0.652210i	−0.985051	−	0.172263i	$-0.944892\pi$
$61$	−3.27367	+	5.09393i	−0.419150	+	0.652210i	0.565901	+	0.824473i	$0.308528\pi$
$62$	−2.07533	−	1.13322i	−0.263568	−	0.143919i
$63$	−2.24947	+	1.68393i	−0.283406	+	0.212155i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	9.65848	+	4.49554i	1.19799	+	0.557603i
$66$	2.07517	+	3.22903i	0.255436	+	0.397466i
$67$	0.349266	+	4.88337i	0.0426696	+	0.596599i	0.973137	+	0.230225i	$0.0739463\pi$
$67$	0.349266	+	4.88337i	0.0426696	+	0.596599i	−0.930468	+	0.366374i	$0.880599\pi$
$68$	−2.62524	−	2.62524i	−0.318357	−	0.318357i
$69$	−3.69976	+	3.05152i	−0.445399	+	0.367360i
$70$	−6.14910	+	1.29117i	−0.734958	+	0.154325i
$71$	1.96697	−	2.27000i	0.233436	−	0.269400i	−0.626931	−	0.779075i	$-0.715689\pi$
$71$	1.96697	−	2.27000i	0.233436	−	0.269400i	0.860367	+	0.509675i	$0.170234\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	1.14966	+	0.860625i	0.134558	+	0.100729i	0.664436	−	0.747345i	$-0.268672\pi$
$73$	1.14966	+	0.860625i	0.134558	+	0.100729i	−0.529879	+	0.848073i	$0.677763\pi$
$74$	−4.53363	−	9.92727i	−0.527024	−	1.15402i
$75$	−4.35329	−	2.45944i	−0.502675	−	0.283991i
$76$	−2.15360	−	7.33449i	−0.247035	−	0.841324i
$77$	−2.29262	−	10.5390i	−0.261269	−	1.20103i
$78$	−1.66498	−	4.46398i	−0.188522	−	0.505446i
$79$	−6.34227	−	1.86226i	−0.713561	−	0.209520i	−0.0952495	−	0.995453i	$-0.530365\pi$
$79$	−6.34227	−	1.86226i	−0.713561	−	0.209520i	−0.618312	+	0.785933i	$0.712183\pi$
$80$	−1.78033	−	1.35293i	−0.199047	−	0.151262i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	0.623563	+	1.14197i	0.0688610	+	0.126110i
$83$	−15.6190	+	5.82559i	−1.71441	+	0.639442i	−0.998286	−	0.0585307i	$-0.981358\pi$
$83$	−15.6190	+	5.82559i	−1.71441	+	0.639442i	−0.716124	+	0.697973i	$0.754086\pi$
$84$	2.36386	+	1.51916i	0.257919	+	0.165754i
$85$	−2.39639	+	7.94834i	−0.259925	+	0.862118i
$86$	6.98948	+	1.00494i	0.753696	+	0.108365i
$87$	−3.35449	+	8.99373i	−0.359639	+	0.964229i
$88$	2.30024	−	3.07276i	0.245206	−	0.327557i
$89$	6.94947	−	4.46615i	0.736642	−	0.473411i	−0.117748	−	0.993044i	$-0.537567\pi$
$89$	6.94947	−	4.46615i	0.736642	−	0.473411i	0.854390	+	0.519632i	$0.173931\pi$
$90$	0.614448	+	2.14999i	0.0647685	+	0.226629i
$91$			13.3876i			1.40340i
$92$	4.15205	+	2.40010i	0.432881	+	0.250227i
$93$	1.67200	−	1.67200i	0.173379	−	0.173379i
$94$	4.49299	+	3.89320i	0.463417	+	0.401553i
$95$	−12.1735	+	11.9988i	−1.24897	+	1.23105i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	−2.33879	−	0.872323i	−0.237468	−	0.0885710i	0.227913	−	0.973682i	$-0.426810\pi$
$97$	−2.33879	−	0.872323i	−0.237468	−	0.0885710i	−0.465381	+	0.885111i	$0.654083\pi$
$98$	−0.536783	−	0.717058i	−0.0542232	−	0.0724338i
$99$	−3.68287	+	1.08139i	−0.370143	+	0.108684i
$100$	−0.783049	+	4.93830i	−0.0783049	+	0.493830i
$101$	2.25893	−	4.94637i	0.224772	−	0.492183i	−0.763325	−	0.646015i	$-0.776434\pi$
$101$	2.25893	−	4.94637i	0.224772	−	0.492183i	0.988097	+	0.153832i	$0.0491616\pi$
$102$	3.25851	−	1.77928i	0.322641	−	0.176175i
$103$	−0.678777	+	9.49054i	−0.0668818	+	0.935130i	0.847634	+	0.530581i	$0.178026\pi$
$103$	−0.678777	+	9.49054i	−0.0668818	+	0.935130i	−0.914516	+	0.404549i	$0.867428\pi$
$104$	−3.60067	+	3.12000i	−0.353075	+	0.305941i
$105$	0.493530	−	6.26379i	0.0481636	−	0.611283i
$106$	4.27677	+	1.95314i	0.415397	+	0.189705i
$107$	−5.71002	+	1.24214i	−0.552008	+	0.120082i	−0.479914	−	0.877316i	$-0.659332\pi$
$107$	−5.71002	+	1.24214i	−0.552008	+	0.120082i	−0.0720946	+	0.997398i	$0.522968\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	2.22156	−	15.4513i	0.212787	−	1.47996i	−0.551005	−	0.834502i	$-0.685755\pi$
$109$	2.22156	−	15.4513i	0.212787	−	1.47996i	0.763792	−	0.645463i	$-0.223335\pi$
$110$	−8.48640	−	1.28284i	−0.809147	−	0.122314i
$111$	10.8024	−	1.55315i	1.02532	−	0.147419i
$112$	0.597294	−	2.74572i	0.0564390	−	0.259446i
$113$	−15.1284	+	1.08201i	−1.42316	+	0.101787i	−0.761573	−	0.648080i	$-0.775572\pi$
$113$	−15.1284	+	1.08201i	−1.42316	+	0.101787i	−0.661589	+	0.749866i	$0.730118\pi$
$114$	7.64414			0.715939
$115$	0.338318	−	10.7185i	0.0315484	−	0.999502i
$116$	9.59894			0.891239
$117$	4.75223	−	0.339886i	0.439344	−	0.0314225i
$118$	−2.18348	+	10.0373i	−0.201005	+	0.924007i
$119$	−10.3261	+	1.48467i	−0.946592	+	0.136099i
$120$	1.79970	−	1.32705i	0.164290	−	0.121143i
$121$	0.531254	−	3.69495i	0.0482958	−	0.335905i
$122$	−2.90193	+	5.31449i	−0.262728	+	0.481151i
$123$	−1.27139	+	0.276574i	−0.114637	+	0.0249378i
$124$	−2.15089	−	0.982278i	−0.193156	−	0.0882112i
$125$	10.5577	−	3.67905i	0.944307	−	0.329065i
$126$	−2.12360	+	1.84011i	−0.189186	+	0.163930i
$127$	−1.04779	+	14.6501i	−0.0929767	+	1.29998i	0.710097	+	0.704104i	$0.248651\pi$
$127$	−1.04779	+	14.6501i	−0.0929767	+	1.29998i	−0.803074	+	0.595880i	$0.796804\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	−2.93339	+	6.42324i	−0.258271	+	0.565535i
$130$	9.95458	+	3.79506i	0.873074	+	0.332849i
$131$	15.1210	−	4.43992i	1.32113	−	0.387918i	0.456227	−	0.889863i	$-0.349200\pi$
$131$	15.1210	−	4.43992i	1.32113	−	0.387918i	0.864899	+	0.501946i	$0.167382\pi$
$132$	2.30024	+	3.07276i	0.200210	+	0.267449i
$133$	−20.1252	−	7.50632i	−1.74508	−	0.650880i
$134$	0.696752	+	4.84601i	0.0601902	+	0.418632i
$135$	−2.23601	−	0.0161639i	−0.192445	−	0.00139117i
$136$	−2.80583	−	2.43127i	−0.240598	−	0.208479i
$137$	−7.12955	+	7.12955i	−0.609119	+	0.609119i	−0.942716	−	0.333597i	$-0.891738\pi$
$137$	−7.12955	+	7.12955i	−0.609119	+	0.609119i	0.333597	+	0.942716i	$0.391738\pi$
$138$	−3.47264	+	3.30768i	−0.295611	+	0.281568i
$139$		−	12.3937i		−	1.05122i	−0.850725	−	0.525612i	$-0.823836\pi$
$139$		−	12.3937i		−	1.05122i	0.850725	−	0.525612i	$-0.176164\pi$
$140$	−6.04132	+	1.72656i	−0.510585	+	0.145921i
$141$	−5.00132	+	3.21415i	−0.421187	+	0.270681i
$142$	1.80002	−	2.40454i	0.151054	−	0.201785i
$143$	−6.39077	+	17.1343i	−0.534423	+	1.43284i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−10.1501	−	18.9123i	−0.842920	−	1.57058i
$146$	1.20813	+	0.776417i	0.0999854	+	0.0642567i
$147$	0.839241	−	0.313021i	0.0692194	−	0.0258175i
$148$	−5.23028	−	9.57855i	−0.429927	−	0.787352i
$149$	6.34716	+	7.32501i	0.519979	+	0.600088i	0.953626	−	0.300995i	$-0.0973188\pi$
$149$	6.34716	+	7.32501i	0.519979	+	0.600088i	−0.433646	+	0.901083i	$0.642773\pi$
$150$	−4.51766	−	2.14261i	−0.368865	−	0.174943i
$151$	−11.7041	−	3.43664i	−0.952468	−	0.279670i	−0.231654	−	0.972798i	$-0.574414\pi$
$151$	−11.7041	−	3.43664i	−0.952468	−	0.279670i	−0.720814	+	0.693129i	$0.756232\pi$
$152$	−2.67135	−	7.16217i	−0.216675	−	0.580929i
$153$	0.789180	+	3.62780i	0.0638014	+	0.293290i
$154$	−3.03863	−	10.3486i	−0.244860	−	0.833916i
$155$	0.339061	+	5.27646i	0.0272341	+	0.423815i
$156$	−1.97919	−	4.33382i	−0.158462	−	0.346984i
$157$	15.0934	+	11.2988i	1.20458	+	0.901739i	0.997070	−	0.0764933i	$-0.0243724\pi$
$157$	15.0934	+	11.2988i	1.20458	+	0.901739i	0.207512	+	0.978232i	$0.433463\pi$
$158$	−6.45896	−	1.40506i	−0.513848	−	0.111781i
$159$	−3.07893	+	3.55327i	−0.244175	+	0.281793i
$160$	−1.87231	−	1.22248i	−0.148019	−	0.0966452i
$161$	12.3907	−	5.29831i	0.976524	−	0.417565i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−0.845418	−	11.8205i	−0.0662182	−	0.925852i	−0.916631	−	0.399735i	$-0.869102\pi$
$163$	−0.845418	−	11.8205i	−0.0662182	−	0.925852i	0.850412	−	0.526117i	$-0.176352\pi$
$164$	0.703441	+	1.09458i	0.0549296	+	0.0854721i
$165$	3.62177	−	7.78123i	0.281955	−	0.605768i
$166$	−15.1636	+	6.92500i	−1.17693	+	0.537484i
$167$	5.02179	−	3.75927i	0.388598	−	0.290901i	−0.387060	−	0.922055i	$-0.626509\pi$
$167$	5.02179	−	3.75927i	0.388598	−	0.290901i	0.775658	+	0.631154i	$0.217418\pi$
$168$	2.46622	+	1.34666i	0.190273	+	0.103897i
$169$	5.24380	−	8.15951i	0.403369	−	0.627655i
$170$	−1.82325	+	8.09904i	−0.139837	+	0.621168i
$171$	−2.15360	+	7.33449i	−0.164690	+	0.560883i
$172$	7.04337	+	0.503752i	0.537052	+	0.0384107i
$173$	22.8203	+	1.63214i	1.73499	+	0.124089i	0.902707	−	0.430256i	$-0.141577\pi$
$173$	22.8203	+	1.63214i	1.73499	+	0.124089i	0.832287	+	0.554345i	$0.187031\pi$
$174$	−2.70433	+	9.21012i	−0.205015	+	0.698217i
$175$	9.78995	+	10.0772i	0.740050	+	0.761764i
$176$	2.07517	−	3.22903i	0.156422	−	0.243397i
$177$	−9.01555	−	4.92286i	−0.677650	−	0.370025i
$178$	6.61315	−	4.95054i	0.495676	−	0.371059i
$179$	11.3875	−	5.20051i	0.851144	−	0.388704i	0.0584252	−	0.998292i	$-0.481392\pi$
$179$	11.3875	−	5.20051i	0.851144	−	0.388704i	0.792719	+	0.609587i	$0.208665\pi$
$180$	0.766260	+	2.10068i	0.0571137	+	0.156575i
$181$	−4.66370	−	7.25685i	−0.346650	−	0.539398i	0.623525	−	0.781803i	$-0.285700\pi$
$181$	−4.66370	−	7.25685i	−0.346650	−	0.539398i	−0.970175	+	0.242406i	$0.922064\pi$
$182$	0.955057	+	13.3534i	0.0707936	+	0.989823i
$183$	−4.28165	−	4.28165i	−0.316508	−	0.316508i
$184$	4.31269	+	2.09778i	0.317936	+	0.154650i
$185$	−13.3415	+	20.4335i	−0.980886	+	1.50230i
$186$	1.54846	−	1.78702i	0.113539	−	0.131031i
$187$	−13.9248	−	3.02915i	−1.01828	−	0.221513i
$188$	4.75928	+	3.56275i	0.347106	+	0.259841i
$189$	−1.16729	−	2.55600i	−0.0849077	−	0.185922i
$190$	−11.2865	+	12.8366i	−0.818808	+	0.931267i
$191$	5.07914	+	17.2980i	0.367514	+	1.25164i	0.911066	+	0.412261i	$0.135261\pi$
$191$	5.07914	+	17.2980i	0.367514	+	1.25164i	−0.543552	+	0.839375i	$0.682921\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	4.20115	+	11.2637i	0.302405	+	0.810780i	0.995912	+	0.0903299i	$0.0287922\pi$
$193$	4.20115	+	11.2637i	0.302405	+	0.810780i	−0.693506	+	0.720450i	$0.743935\pi$
$194$	−2.39506	−	0.703253i	−0.171955	−	0.0504906i
$195$	−6.44586	+	8.48216i	−0.461598	+	0.607420i
$196$	−0.586569	−	0.676937i	−0.0418978	−	0.0483527i
$197$	11.6297	+	21.2981i	0.828578	+	1.51743i	0.855507	+	0.517791i	$0.173245\pi$
$197$	11.6297	+	21.2981i	0.828578	+	1.51743i	−0.0269288	+	0.999637i	$0.508573\pi$
$198$	−3.59634	+	1.34137i	−0.255581	+	0.0953268i
$199$	16.9912	+	10.9196i	1.20448	+	0.774070i	0.979725	−	0.200346i	$-0.0642065\pi$
$199$	16.9912	+	10.9196i	1.20448	+	0.774070i	0.224752	+	0.974416i	$0.427843\pi$
$200$	−0.428760	+	4.98158i	−0.0303179	+	0.352251i
$201$	−4.84601	−	0.696752i	−0.341812	−	0.0491451i
$202$	1.90031	−	5.09492i	0.133705	−	0.358477i
$203$	16.1639	−	21.5925i	1.13449	−	1.51550i
$204$	3.12328	−	2.00721i	0.218673	−	0.140533i
$205$	1.41275	−	2.54338i	0.0986709	−	0.177637i
$206$			9.51478i			0.662926i
$207$	−2.19534	−	4.26386i	−0.152587	−	0.296359i
$208$	−3.36892	+	3.36892i	−0.233592	+	0.233592i
$209$	−22.1744	−	19.2142i	−1.53383	−	1.32907i
$210$	0.0454195	−	6.28303i	0.00313424	−	0.433571i
$211$	0.161994	+	1.12669i	0.0111521	+	0.0775647i	0.994637	−	0.103423i	$-0.0329796\pi$
$211$	0.161994	+	1.12669i	0.0111521	+	0.0775647i	−0.983485	+	0.180988i	$0.942071\pi$
$212$	4.40521	+	1.64306i	0.302551	+	0.112846i
$213$	1.80002	+	2.40454i	0.123335	+	0.164756i
$214$	−5.60685	+	1.64632i	−0.383277	+	0.112540i
$215$	−6.45527	−	14.4098i	−0.440246	−	0.982743i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−5.83155	+	3.18427i	−0.395871	+	0.216162i
$218$	1.11362	−	15.5704i	0.0754237	−	1.05456i
$219$	−1.08534	+	0.940448i	−0.0733402	+	0.0635496i
$220$	−8.55630	−	0.674160i	−0.576866	−	0.0454519i
$221$	16.0900	+	7.34804i	1.08233	+	0.494282i
$222$	10.6641	−	2.31983i	0.715727	−	0.155697i
$223$	−11.0213	+	20.1841i	−0.738044	+	1.35163i	0.190976	+	0.981595i	$0.438835\pi$
$223$	−11.0213	+	20.1841i	−0.738044	+	1.35163i	−0.929019	+	0.370031i	$0.879347\pi$
$224$	0.399895	−	2.78133i	0.0267191	−	0.185835i
$225$	3.32859	−	3.73102i	0.221906	−	0.248734i
$226$	−15.0127	+	2.15850i	−0.998629	+	0.143581i
$227$	3.75079	−	17.2421i	0.248949	−	1.14440i	−0.667614	−	0.744507i	$-0.732684\pi$
$227$	3.75079	−	17.2421i	0.248949	−	1.14440i	0.916563	−	0.399891i	$-0.130952\pi$
$228$	7.62466	−	0.545326i	0.504955	−	0.0361151i
$229$	−10.0942			−0.667042			−0.333521	−	0.942743i	$-0.608237\pi$
$229$	−10.0942			−0.667042			−0.333521	+	0.942743i	$0.608237\pi$
$230$	−0.427190	−	10.7153i	−0.0281681	−	0.706546i
$231$	10.7855			0.709634
$232$	9.57449	−	0.684781i	0.628596	−	0.0449581i
$233$	2.68731	−	12.3534i	0.176052	−	0.809297i	−0.801398	−	0.598131i	$-0.795910\pi$
$233$	2.68731	−	12.3534i	0.176052	−	0.809297i	0.977450	−	0.211166i	$-0.0677261\pi$
$234$	4.71588	−	0.678041i	0.308286	−	0.0443249i
$235$	1.98695	−	13.1443i	0.129614	−	0.857438i
$236$	−1.46186	+	10.1675i	−0.0951592	+	0.661847i
$237$	3.16785	−	5.80148i	0.205774	−	0.376847i
$238$	−10.1939	+	2.21754i	−0.660771	+	0.143742i
$239$	9.51936	+	4.34734i	0.615756	+	0.281206i	0.698775	−	0.715342i	$-0.253729\pi$
$239$	9.51936	+	4.34734i	0.615756	+	0.281206i	−0.0830189	+	0.996548i	$0.526456\pi$
$240$	1.70045	−	1.45206i	0.109763	−	0.0937300i
$241$	5.79809	−	5.02407i	0.373488	−	0.323629i	−0.447810	−	0.894129i	$-0.647796\pi$
$241$	5.79809	−	5.02407i	0.373488	−	0.323629i	0.821298	+	0.570500i	$0.193250\pi$
$242$	0.266306	−	3.72344i	0.0171188	−	0.239352i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	−2.51541	+	5.50797i	−0.161032	+	0.352612i
$245$	−0.713483	+	1.87149i	−0.0455827	+	0.119565i
$246$	−1.24842	+	0.366569i	−0.0795964	+	0.0233716i
$247$	21.8254	+	29.1553i	1.38872	+	1.85511i
$248$	−2.21548	−	0.826333i	−0.140683	−	0.0524722i
$249$	−2.37240	−	16.5004i	−0.150345	−	1.04567i
$250$	10.2683	−	4.42286i	0.649425	−	0.279726i
$251$	14.1856	+	12.2919i	0.895388	+	0.775858i	0.975286	−	0.220945i	$-0.0709142\pi$
$251$	14.1856	+	12.2919i	0.895388	+	0.775858i	−0.0798986	+	0.996803i	$0.525460\pi$
$252$	−1.98692	+	1.98692i	−0.125164	+	0.125164i
$253$	18.3877	−	0.866241i	1.15602	−	0.0544601i
$254$			14.6875i			0.921575i
$255$	−7.25730	−	4.03116i	−0.454470	−	0.252441i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	5.65544	−	7.55479i	0.352777	−	0.471255i	−0.588691	−	0.808358i	$-0.700356\pi$
$257$	5.65544	−	7.55479i	0.352777	−	0.471255i	0.941468	+	0.337104i	$0.109447\pi$
$258$	−2.46769	+	6.61614i	−0.153632	+	0.411903i
$259$	−30.3541	−	4.36425i	−1.88611	−	0.271182i
$260$	10.2000	+	3.07524i	0.632574	+	0.190718i
$261$	−8.07514	−	5.18958i	−0.499839	−	0.321227i
$262$	14.7657	−	5.50733i	0.912229	−	0.340244i
$263$	2.46279	+	4.51027i	0.151862	+	0.278115i	0.942524	−	0.334138i	$-0.108445\pi$
$263$	2.46279	+	4.51027i	0.151862	+	0.278115i	−0.790662	+	0.612253i	$0.790263\pi$
$264$	2.51359	+	2.90083i	0.154701	+	0.178534i
$265$	−1.42092	−	10.4167i	−0.0872867	−	0.639896i
$266$	−20.6094	−	6.05147i	−1.26365	−	0.371040i
$267$	2.88687	+	7.74000i	0.176674	+	0.473680i
$268$	1.04069	+	4.78396i	0.0635701	+	0.292227i
$269$	−0.728660	−	2.48159i	−0.0444272	−	0.151305i	0.934292	−	0.356508i	$-0.116033\pi$
$269$	−0.728660	−	2.48159i	−0.0444272	−	0.151305i	−0.978719	+	0.205203i	$0.934215\pi$
$270$	−2.23147	+	0.143392i	−0.135803	+	0.00872658i
$271$	−7.46460	−	16.3452i	−0.453442	−	0.992900i	−0.988934	−	0.148359i	$-0.952601\pi$
$271$	−7.46460	−	16.3452i	−0.453442	−	0.992900i	0.535491	−	0.844541i	$-0.320127\pi$
$272$	−2.97213	−	2.22491i	−0.180212	−	0.134905i
$273$	−13.0816	−	2.84573i	−0.791735	−	0.172231i
$274$	−6.60277	+	7.62000i	−0.398888	+	0.460341i
$275$	7.71933	+	17.5709i	0.465493	+	1.05956i
$276$	−3.22783	+	3.54699i	−0.194292	+	0.213504i
$277$	6.03634	+	6.03634i	0.362688	+	0.362688i	0.864802	−	0.502113i	$-0.167444\pi$
$277$	6.03634	+	6.03634i	0.362688	+	0.362688i	−0.502113	+	0.864802i	$0.667444\pi$
$278$	−0.884159	−	12.3622i	−0.0530284	−	0.741433i
$279$	1.27838	+	1.98920i	0.0765348	+	0.119090i
$280$	−5.90276	+	2.15314i	−0.352757	+	0.128675i
$281$	2.70369	−	1.23473i	0.161289	−	0.0736580i	−0.333135	−	0.942879i	$-0.608106\pi$
$281$	2.70369	−	1.23473i	0.161289	−	0.0736580i	0.494424	+	0.869221i	$0.335379\pi$
$282$	−4.75928	+	3.56275i	−0.283411	+	0.212159i
$283$	4.07297	+	2.22401i	0.242113	+	0.132204i	0.595725	−	0.803188i	$-0.296865\pi$
$283$	4.07297	+	2.22401i	0.242113	+	0.132204i	−0.353612	+	0.935392i	$0.615047\pi$
$284$	1.62389	−	2.52683i	0.0963603	−	0.149940i
$285$	−9.13688	−	14.4458i	−0.541222	−	0.855696i
$286$	−5.15214	+	17.5466i	−0.304652	+	1.03755i
$287$	3.64676	+	0.260821i	0.215261	+	0.0153958i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	0.906124	−	3.08598i	0.0533014	−	0.181528i
$290$	−11.4734	−	18.1400i	−0.673743	−	1.06522i
$291$	1.34953	−	2.09991i	0.0791110	−	0.123099i
$292$	1.26044	+	0.688252i	0.0737616	+	0.0402769i
$293$	1.96707	−	1.47253i	0.114917	−	0.0860261i	−0.540273	−	0.841490i	$-0.681679\pi$
$293$	1.96707	−	1.47253i	0.114917	−	0.0860261i	0.655191	+	0.755463i	$0.272588\pi$
$294$	0.814772	−	0.372094i	0.0475185	−	0.0217010i
$295$	21.5782	−	7.87105i	1.25633	−	0.458270i
$296$	−5.90028	−	9.18102i	−0.342947	−	0.533636i
$297$	−0.273825	−	3.82857i	−0.0158889	−	0.222156i
$298$	6.85354	+	6.85354i	0.397015	+	0.397015i
$299$	−22.5308	−	3.80090i	−1.30299	−	0.219811i
$300$	−4.65900	−	1.81487i	−0.268987	−	0.104781i
$301$	12.9937	−	14.9955i	0.748945	−	0.864328i
$302$	−11.9195	−	2.59292i	−0.685888	−	0.149206i
$303$	4.35316	+	3.25874i	0.250083	+	0.187210i
$304$	−3.17549	−	6.95335i	−0.182127	−	0.398802i
$305$	13.5119	−	0.868264i	0.773688	−	0.0497166i
$306$	1.04597	+	3.56226i	0.0597943	+	0.203641i
$307$	−1.01147	−	4.64967i	−0.0577278	−	0.265371i	0.939232	−	0.343282i	$-0.111539\pi$
$307$	−1.01147	−	4.64967i	−0.0577278	−	0.265371i	−0.996960	+	0.0779112i	$0.975175\pi$
$308$	−3.76915	−	10.1055i	−0.214767	−	0.575813i
$309$	−9.12936	−	2.68062i	−0.519351	−	0.152495i
$310$	0.714616	+	5.23883i	0.0405874	+	0.297545i
$311$	−4.10135	−	4.73321i	−0.232566	−	0.268396i	0.627456	−	0.778652i	$-0.284096\pi$
$311$	−4.10135	−	4.73321i	−0.232566	−	0.268396i	−0.860023	+	0.510256i	$0.829551\pi$
$312$	−2.28332	−	4.18159i	−0.129268	−	0.236736i
$313$	−0.480478	+	0.179209i	−0.0271582	+	0.0101295i	−0.363007	−	0.931787i	$-0.618250\pi$
$313$	−0.480478	+	0.179209i	−0.0271582	+	0.0101295i	0.335848	+	0.941916i	$0.390977\pi$
$314$	15.8610	+	10.1932i	0.895086	+	0.575237i
$315$	6.01573	+	1.81371i	0.338948	+	0.102191i
$316$	−6.54274	−	0.940704i	−0.368058	−	0.0529188i
$317$	3.01551	−	8.08490i	0.169368	−	0.454093i	−0.824340	−	0.566095i	$-0.808454\pi$
$317$	3.01551	−	8.08490i	0.169368	−	0.454093i	0.993708	+	0.112002i	$0.0357262\pi$
$318$	−2.81760	+	3.76387i	−0.158003	+	0.211067i
$319$	30.9953	−	19.9194i	1.73540	−	1.11527i
$320$	−1.95475	−	1.08579i	−0.109274	−	0.0606976i
$321$		−	5.84356i		−	0.326156i
$322$	11.9811	−	6.16875i	0.667683	−	0.343771i
$323$	−20.0677	+	20.0677i	−1.11660	+	1.11660i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−4.72665	−	23.3482i	−0.262187	−	1.29513i
$326$	−1.68653	−	11.7301i	−0.0934081	−	0.649668i
$327$	14.6259	+	5.45520i	0.808817	+	0.301673i
$328$	0.779735	+	1.04160i	0.0430537	+	0.0575130i
$329$	16.0286	−	4.70642i	0.883685	−	0.259473i
$330$	3.05744	−	8.01978i	0.168307	−	0.441474i
$331$	3.70220	−	8.10669i	0.203491	−	0.445584i	−0.780181	−	0.625554i	$-0.784873\pi$
$331$	3.70220	−	8.10669i	0.203491	−	0.445584i	0.983672	+	0.179970i	$0.0576001\pi$
$332$	−14.6310	+	7.98911i	−0.802979	+	0.438460i
$333$	−0.778560	+	10.8857i	−0.0426648	+	0.596532i
$334$	4.74081	−	4.10794i	0.259406	−	0.224776i
$335$	8.32514	−	7.10906i	0.454851	−	0.388409i
$336$	2.55600	+	1.16729i	0.139441	+	0.0636808i
$337$	−29.4282	+	6.40171i	−1.60306	+	0.348723i	−0.923109	−	0.384538i	$-0.874361\pi$
$337$	−29.4282	+	6.40171i	−1.60306	+	0.348723i	−0.679947	+	0.733261i	$0.737997\pi$
$338$	4.64834	−	8.51281i	0.252837	−	0.463036i
$339$	2.15850	−	15.0127i	0.117234	−	0.815377i
$340$	−1.24083	+	8.20847i	−0.0672934	+	0.445167i
$341$	−8.98367	+	1.29166i	−0.486493	+	0.0699472i
$342$	−1.62488	+	7.46944i	−0.0878633	+	0.403901i
$343$	17.1089	−	1.22365i	0.923795	−	0.0660711i
$344$	7.06136			0.380723
$345$	10.4016	+	2.60896i	0.560003	+	0.140462i
$346$	22.8786			1.22996
$347$	−18.6784	+	1.33591i	−1.00271	+	0.0717153i	−0.563028	−	0.826438i	$-0.690364\pi$
$347$	−18.6784	+	1.33591i	−1.00271	+	0.0717153i	−0.439683	+	0.898153i	$0.644909\pi$
$348$	−2.04040	+	9.37958i	−0.109377	+	0.502798i
$349$	8.80266	−	1.26563i	0.471196	−	0.0677477i	0.0973731	−	0.995248i	$-0.468956\pi$
$349$	8.80266	−	1.26563i	0.471196	−	0.0677477i	0.373823	+	0.927500i	$0.378047\pi$
$350$	10.4839	+	9.35311i	0.560388	+	0.499945i
$351$	−0.678041	+	4.71588i	−0.0361911	+	0.251715i
$352$	1.83953	−	3.36884i	0.0980471	−	0.179560i
$353$	−10.0755	+	2.19179i	−0.536264	+	0.116657i	−0.472538	−	0.881310i	$-0.656662\pi$
$353$	−10.0755	+	2.19179i	−0.536264	+	0.116657i	−0.0637261	+	0.997967i	$0.520298\pi$
$354$	−9.34377	−	4.26716i	−0.496616	−	0.226797i
$355$	−6.69560	−	0.527553i	−0.355366	−	0.0279996i
$356$	6.24313	−	5.40970i	0.330885	−	0.286714i
$357$	0.744231	−	10.4057i	0.0393889	−	0.550728i
$358$	10.9875	−	5.99964i	0.580708	−	0.317091i
$359$	−6.95696	+	15.2336i	−0.367174	+	0.803999i	0.632395	+	0.774646i	$0.282072\pi$
$359$	−6.95696	+	15.2336i	−0.367174	+	0.803999i	−0.999569	+	0.0293531i	$0.990655\pi$
$360$	0.914169	+	2.04066i	0.0481809	+	0.107552i
$361$	−37.8355	+	11.1095i	−1.99134	+	0.584711i
$362$	−5.16951	−	6.90566i	−0.271704	−	0.362953i
$363$	3.49759	+	1.30453i	0.183576	+	0.0684702i
$364$	1.90525	+	13.2513i	0.0998621	+	0.694556i
$365$	0.0232131	−	3.21114i	0.00121503	−	0.168079i
$366$	−4.57619	−	3.96529i	−0.239201	−	0.207269i
$367$	−24.1597	+	24.1597i	−1.26113	+	1.26113i	−0.310579	+	0.950548i	$0.600523\pi$
$367$	−24.1597	+	24.1597i	−1.26113	+	1.26113i	−0.950548	+	0.310579i	$0.899477\pi$
$368$	4.45136	+	1.78477i	0.232043	+	0.0930374i
$369$		−	1.30113i		−	0.0677339i
$370$	−11.8498	+	21.3332i	−0.616041	+	1.10906i
$371$	11.1141	−	7.14258i	0.577014	−	0.370824i
$372$	1.41703	−	1.89294i	0.0734698	−	0.0981442i
$373$	6.31128	−	16.9212i	0.326786	−	0.876146i	−0.664838	−	0.746987i	$-0.731499\pi$
$373$	6.31128	−	16.9212i	0.326786	−	0.876146i	0.991624	−	0.129159i	$-0.0412278\pi$
$374$	−14.1054	−	2.02805i	−0.729373	−	0.104868i
$375$	1.35078	+	11.0984i	0.0697540	+	0.573121i
$376$	5.00132	+	3.21415i	0.257923	+	0.165757i
$377$	−42.8494	+	15.9820i	−2.20686	+	0.823116i
$378$	−1.34666	−	2.46622i	−0.0692646	−	0.126849i
$379$	−17.5995	−	20.3109i	−0.904025	−	1.04330i	−0.998857	−	0.0478075i	$-0.984777\pi$
$379$	−17.5995	−	20.3109i	−0.904025	−	1.04330i	0.0948312	−	0.995493i	$-0.469769\pi$
$380$	−10.3420	+	13.6091i	−0.530533	+	0.698132i
$381$	−14.0925	−	4.13794i	−0.721983	−	0.211993i
$382$	6.30022	+	16.8915i	0.322347	+	0.864247i
$383$	−2.93943	−	13.5123i	−0.150198	−	0.690448i	−0.989230	−	0.146367i	$-0.953242\pi$
$383$	−2.93943	−	13.5123i	−0.150198	−	0.690448i	0.839033	−	0.544081i	$-0.183122\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	−15.9247	+	18.1119i	−0.811598	+	0.923066i
$386$	4.99399	+	10.9353i	0.254187	+	0.556593i
$387$	−5.65291	−	4.23171i	−0.287354	−	0.215110i
$388$	−2.43913	−	0.530600i	−0.123828	−	0.0269371i
$389$	−7.85980	+	9.07069i	−0.398508	+	0.459902i	−0.919170	−	0.393860i	$-0.871139\pi$
$389$	−7.85980	+	9.07069i	−0.398508	+	0.459902i	0.520663	+	0.853762i	$0.325685\pi$
$390$	−5.82433	+	8.92039i	−0.294926	+	0.451701i
$391$	0.433066	−	17.8000i	0.0219011	−	0.900183i
$392$	−0.633367	−	0.633367i	−0.0319899	−	0.0319899i
$393$	1.12426	+	15.7192i	0.0567114	+	0.792928i
$394$	13.1194	+	20.4142i	0.660946	+	1.02845i
$395$	5.06500	+	13.8855i	0.254848	+	0.698657i
$396$	−3.49149	+	1.59451i	−0.175454	+	0.0801271i
$397$	12.3536	−	9.24777i	0.620008	−	0.464132i	−0.242517	−	0.970147i	$-0.577973\pi$
$397$	12.3536	−	9.24777i	0.620008	−	0.464132i	0.862525	+	0.506015i	$0.168882\pi$
$398$	17.7269	+	9.67964i	0.888571	+	0.485197i
$399$	11.6127	−	18.0697i	0.581362	−	0.904617i
$400$	−0.0722853	+	4.99948i	−0.00361427	+	0.249974i
$401$	7.43880	−	25.3342i	0.371476	−	1.26513i	−0.535710	−	0.844402i	$-0.679956\pi$
$401$	7.43880	−	25.3342i	0.371476	−	1.26513i	0.907186	−	0.420730i	$-0.138226\pi$
$402$	−4.88337	−	0.349266i	−0.243561	−	0.0174198i
$403$	11.2370	+	0.803685i	0.559754	+	0.0400344i
$404$	1.53200	−	5.21751i	0.0762197	−	0.259581i
$405$	0.491093	−	2.18147i	0.0244026	−	0.108398i
$406$	14.5824	−	22.6906i	0.723711	−	1.12612i
$407$	−36.7659	−	20.0757i	−1.82242	−	0.995114i
$408$	2.97213	−	2.22491i	0.147142	−	0.110149i
$409$	13.8901	−	6.34338i	0.686819	−	0.313660i	−0.0412644	−	0.999148i	$-0.513139\pi$
$409$	13.8901	−	6.34338i	0.686819	−	0.313660i	0.728083	+	0.685489i	$0.240411\pi$
$410$	1.22771	−	2.63768i	0.0606323	−	0.130266i
$411$	−5.45112	−	8.48212i	−0.268884	−	0.418392i
$412$	0.678777	+	9.49054i	0.0334409	+	0.467565i
$413$	20.4097	+	20.4097i	1.00430	+	1.00430i
$414$	−2.49393	−	4.09638i	−0.122570	−	0.201326i
$415$	31.2116	+	20.3788i	1.53212	+	1.00035i
$416$	−3.12000	+	3.60067i	−0.152971	+	0.176537i
$417$	12.1105	+	2.63448i	0.593054	+	0.129011i
$418$	−23.4886	−	17.5833i	−1.14886	−	0.860029i
$419$	−3.48692	−	7.63530i	−0.170347	−	0.373009i	0.805133	−	0.593094i	$-0.202094\pi$
$419$	−3.48692	−	7.63530i	−0.170347	−	0.373009i	−0.975481	+	0.220085i	$0.929366\pi$
$420$	−0.402923	−	6.27027i	−0.0196606	−	0.305958i
$421$	7.54928	+	25.7105i	0.367929	+	1.25305i	0.910664	+	0.413148i	$0.135571\pi$
$421$	7.54928	+	25.7105i	0.367929	+	1.25305i	−0.542735	+	0.839904i	$0.682611\pi$
$422$	0.241958	+	1.11226i	0.0117784	+	0.0541442i
$423$	−2.07759	−	5.57024i	−0.101016	−	0.270834i
$424$	4.51120	+	1.32461i	0.219083	+	0.0643287i
$425$	17.4848	−	6.23506i	0.848137	−	0.302445i
$426$	1.96697	+	2.27000i	0.0952999	+	0.109982i
$427$	8.15423	+	14.9333i	0.394611	+	0.722675i
$428$	−5.47512	+	2.04211i	−0.264650	+	0.0987093i
$429$	−15.3843	−	9.88688i	−0.742760	−	0.477343i
$430$	−7.46681	−	13.9126i	−0.360082	−	0.670926i
$431$	−13.5063	−	1.94191i	−0.650574	−	0.0935384i	−0.190876	−	0.981614i	$-0.561133\pi$
$431$	−13.5063	−	1.94191i	−0.650574	−	0.0935384i	−0.459697	+	0.888076i	$0.652042\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	−7.80684	+	10.4287i	−0.375173	+	0.501172i	−0.947897	−	0.318576i	$-0.896795\pi$
$433$	−7.80684	+	10.4287i	−0.375173	+	0.501172i	0.572725	+	0.819748i	$0.305886\pi$
$434$	−5.58953	+	3.59217i	−0.268306	+	0.172430i
$435$	20.6376	−	5.89805i	0.989498	−	0.282790i
$436$		−	15.6102i		−	0.747592i
$437$	18.3467	−	31.7389i	0.877640	−	1.51828i
$438$	−1.01548	+	1.01548i	−0.0485215	+	0.0485215i
$439$	22.1173	+	19.1648i	1.05560	+	0.914684i	0.996502	−	0.0835679i	$-0.0266315\pi$
$439$	22.1173	+	19.1648i	1.05560	+	0.914684i	0.0590998	+	0.998252i	$0.481177\pi$
$440$	−8.58259	−	0.0620428i	−0.409159	−	0.00295777i
$441$	0.127474	+	0.886599i	0.00607018	+	0.0422190i
$442$	16.5732	+	6.18147i	0.788305	+	0.294023i
$443$	−18.8942	−	25.2396i	−0.897688	−	1.19917i	−0.979281	−	0.202505i	$-0.935092\pi$
$443$	−18.8942	−	25.2396i	−0.897688	−	1.19917i	0.0815929	−	0.996666i	$-0.473999\pi$
$444$	10.4714	−	3.07469i	0.496952	−	0.145918i
$445$	−17.2600	−	6.58018i	−0.818205	−	0.311930i
$446$	−9.55334	+	20.9189i	−0.452364	+	0.990539i
$447$	−8.50679	+	4.64506i	−0.402358	+	0.219704i
$448$	0.200458	−	2.80277i	0.00947076	−	0.132419i
$449$	20.8632	−	18.0780i	0.984593	−	0.853155i	−0.00456769	−	0.999990i	$-0.501454\pi$
$449$	20.8632	−	18.0780i	0.984593	−	0.853155i	0.989161	+	0.146835i	$0.0469085\pi$
$450$	3.05394	−	3.95897i	0.143964	−	0.186628i
$451$	4.54286	+	2.07466i	0.213915	+	0.0976918i
$452$	−14.8204	+	3.22399i	−0.697095	+	0.151644i
$453$	5.84599	−	10.7061i	0.274669	−	0.503018i
$454$	2.51120	−	17.4657i	0.117856	−	0.819708i
$455$	24.0936	−	17.7660i	1.12953	−	0.832881i
$456$	7.56633	−	1.08787i	0.354326	−	0.0509444i
$457$	8.38648	−	38.5520i	0.392303	−	1.80339i	−0.180364	−	0.983600i	$-0.557728\pi$
$457$	8.38648	−	38.5520i	0.392303	−	1.80339i	0.572667	−	0.819788i	$-0.305909\pi$
$458$	−10.0685	+	0.720110i	−0.470468	+	0.0336485i
$459$	−3.71265			−0.173291
$460$	−1.19052	−	10.6575i	−0.0555084	−	0.496909i
$461$	2.84528			0.132518			0.0662589	−	0.997802i	$-0.478894\pi$
$461$	2.84528			0.132518			0.0662589	+	0.997802i	$0.478894\pi$
$462$	10.7580	−	0.769429i	0.500509	−	0.0357971i
$463$	−4.33207	+	19.9142i	−0.201328	+	0.925491i	0.759965	+	0.649964i	$0.225216\pi$
$463$	−4.33207	+	19.9142i	−0.201328	+	0.925491i	−0.961293	+	0.275527i	$0.911148\pi$
$464$	9.50124	−	1.36607i	0.441084	−	0.0634183i
$465$	−5.22795	−	0.790279i	−0.242440	−	0.0366483i
$466$	1.79919	−	12.5136i	0.0833457	−	0.579682i
$467$	−6.51489	+	11.9311i	−0.301473	+	0.552106i	−0.983872	−	0.178873i	$-0.942755\pi$
$467$	−6.51489	+	11.9311i	−0.301473	+	0.552106i	0.682399	+	0.730980i	$0.260937\pi$
$468$	4.65549	−	1.01274i	0.215200	−	0.0468139i
$469$	12.5138	+	5.71486i	0.577834	+	0.263888i
$470$	1.04418	−	13.2525i	0.0481645	−	0.611294i
$471$	−14.2489	+	12.3467i	−0.656553	+	0.568907i
$472$	−0.732799	+	10.2459i	−0.0337298	+	0.471604i
$473$	23.7886	−	12.9896i	1.09380	−	0.597261i
$474$	2.74590	−	6.01269i	0.126124	−	0.276172i
$475$	37.7491	+	5.98574i	1.73205	+	0.274644i
$476$	−10.0097	+	2.93911i	−0.458794	+	0.134714i
$477$	−2.81760	−	3.76387i	−0.129009	−	0.172336i
$478$	9.80524	+	3.65717i	0.448481	+	0.167275i
$479$	1.97714	+	13.7513i	0.0903377	+	0.628313i	0.983813	+	0.179200i	$0.0573509\pi$
$479$	1.97714	+	13.7513i	0.0903377	+	0.628313i	−0.893475	+	0.449113i	$0.851740\pi$
$480$	1.59253	−	1.56967i	0.0726886	−	0.0716452i
$481$	39.2959	+	34.0501i	1.79174	+	1.55255i
$482$	5.42490	−	5.42490i	0.247098	−	0.247098i
$483$	2.54340	+	13.2338i	0.115729	+	0.602157i
$484$		−	3.73295i		−	0.169680i
$485$	1.53377	+	5.36675i	0.0696448	+	0.243691i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−1.91599	+	2.55947i	−0.0868219	+	0.115980i	−0.841849	−	0.539713i	$-0.818533\pi$
$487$	−1.91599	+	2.55947i	−0.0868219	+	0.115980i	0.755027	+	0.655694i	$0.227624\pi$
$488$	−2.11606	+	5.67338i	−0.0957896	+	0.256822i
$489$	11.7301	+	1.68653i	0.530452	+	0.0762674i
$490$	−0.578154	+	1.91762i	−0.0261183	+	0.0866294i
$491$	−19.5412	−	12.5584i	−0.881882	−	0.566751i	0.0194838	−	0.999810i	$-0.493798\pi$
$491$	−19.5412	−	12.5584i	−0.881882	−	0.566751i	−0.901365	+	0.433059i	$0.857434\pi$
$492$	−1.21909	+	0.454697i	−0.0549608	+	0.0204993i
$493$	−17.0792	−	31.2783i	−0.769210	−	1.40870i
$494$	23.8497	+	27.5240i	1.07305	+	1.23836i
$495$	6.83354	+	5.19302i	0.307145	+	0.233409i
$496$	−2.26879	−	0.666177i	−0.101872	−	0.0299122i
$497$	−2.94949	−	7.90789i	−0.132303	−	0.354717i
$498$	−3.54348	−	16.2891i	−0.158787	−	0.729932i
$499$	2.52913	+	8.61341i	0.113219	+	0.385589i	0.996534	−	0.0831920i	$-0.0265115\pi$
$499$	2.52913	+	8.61341i	0.113219	+	0.385589i	−0.883314	+	0.468781i	$0.844693\pi$
$500$	9.92663	−	5.14412i	0.443932	−	0.230052i
$501$	2.60590	+	5.70612i	0.116423	+	0.254930i
$502$	15.0264	+	11.2486i	0.670659	+	0.502049i
$503$	−22.5109	−	4.89695i	−1.00371	−	0.218344i	−0.319468	−	0.947597i	$-0.603504\pi$
$503$	−22.5109	−	4.89695i	−1.00371	−	0.218344i	−0.684245	+	0.729253i	$0.739868\pi$
$504$	−1.84011	+	2.12360i	−0.0819652	+	0.0945929i
$505$	−11.8997	+	2.49868i	−0.529531	+	0.111190i
$506$	18.2791	−	2.17580i	0.812603	−	0.0967260i
$507$	6.85839	+	6.85839i	0.304592	+	0.304592i
$508$	1.04779	+	14.6501i	0.0464883	+	0.649992i
$509$	−12.8554	−	20.0033i	−0.569803	−	0.886631i	0.430066	−	0.902798i	$-0.358490\pi$
$509$	−12.8554	−	20.0033i	−0.569803	−	0.886631i	−0.999869	+	0.0161661i	$0.994854\pi$
$510$	−7.52639	−	3.50316i	−0.333274	−	0.155123i
$511$	3.67069	−	1.67635i	0.162382	−	0.0741572i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	−6.70910	−	3.66344i	−0.296214	−	0.161745i
$514$	5.10208	−	7.93899i	0.225043	−	0.350174i
$515$	17.9809	−	11.3728i	0.792335	−	0.501147i
$516$	−1.98941	+	6.77532i	−0.0875791	+	0.298267i
$517$	22.7612	+	1.62791i	1.00104	+	0.0715955i
$518$	−30.5881	−	2.18770i	−1.34396	−	0.0961221i
$519$	−6.44564	+	21.9518i	−0.282932	+	0.963578i
$520$	10.3933	+	2.33975i	0.455779	+	0.102605i
$521$	13.3238	−	20.7322i	0.583725	−	0.908294i	−0.416275	−	0.909239i	$-0.636665\pi$
$521$	13.3238	−	20.7322i	0.583725	−	0.908294i	1.00000		0.000945368i	$0.000300920\pi$
$522$	−8.42479	−	4.60028i	−0.368743	−	0.201349i
$523$	5.85720	−	4.38464i	0.256117	−	0.191727i	−0.463502	−	0.886096i	$-0.653407\pi$
$523$	5.85720	−	4.38464i	0.256117	−	0.191727i	0.719619	+	0.694369i	$0.244316\pi$
$524$	14.3352	−	6.54667i	0.626236	−	0.285993i
$525$	−11.9279	+	7.42415i	−0.520576	+	0.324017i
$526$	2.77828	+	4.32308i	0.121139	+	0.188495i
$527$	0.626273	+	8.75645i	0.0272809	+	0.381437i
$528$	2.71413	+	2.71413i	0.118117	+	0.118117i
$529$	5.39899	+	22.3573i	0.234739	+	0.972059i
$530$	−2.16043	−	10.2888i	−0.0938429	−	0.446919i
$531$	6.72675	−	7.76309i	0.291916	−	0.336889i
$532$	−20.9886	−	4.56580i	−0.909972	−	0.197952i
$533$	−4.96259	−	3.71495i	−0.214954	−	0.160912i
$534$	3.43168	+	7.51433i	0.148503	+	0.325177i
$535$	9.81296	+	8.62796i	0.424251	+	0.373019i
$536$	1.37932	+	4.69753i	0.0595775	+	0.202902i
$537$	2.66107	+	12.2327i	0.114834	+	0.527882i
$538$	−0.903838	−	2.42328i	−0.0389672	−	0.104475i
$539$	−3.29881	−	0.968618i	−0.142090	−	0.0417213i
$540$	−2.21555	+	0.302218i	−0.0953421	+	0.0130054i
$541$	5.17348	+	5.97052i	0.222425	+	0.256693i	0.855984	−	0.517002i	$-0.172952\pi$
$541$	5.17348	+	5.97052i	0.222425	+	0.256693i	−0.633559	+	0.773695i	$0.718407\pi$
$542$	−8.61164	−	15.7710i	−0.369901	−	0.677424i
$543$	8.08235	−	3.01456i	0.346847	−	0.129367i
$544$	−3.12328	−	2.00721i	−0.133909	−	0.0860583i
$545$	−30.7559	+	16.5065i	−1.31744	+	0.707060i
$546$	−13.2513	−	1.90525i	−0.567103	−	0.0815371i
$547$	7.78962	−	20.8848i	0.333060	−	0.892969i	−0.657197	−	0.753719i	$-0.728258\pi$
$547$	7.78962	−	20.8848i	0.333060	−	0.892969i	0.990257	−	0.139250i	$-0.0444692\pi$
$548$	−6.04234	+	8.07162i	−0.258116	+	0.344803i
$549$	5.09393	−	3.27367i	0.217403	−	0.139717i
$550$	8.95315	+	16.9754i	0.381764	+	0.723834i
$551$		−	73.3756i		−	3.12591i
$552$	−2.96656	+	3.76822i	−0.126265	+	0.160386i
$553$	−13.1336	+	13.1336i	−0.558497	+	0.558497i
$554$	6.45159	+	5.59033i	0.274102	+	0.237510i
$555$	−17.1306	−	17.3800i	−0.727152	−	0.737742i
$556$	−1.76381	−	12.2676i	−0.0748024	−	0.520262i
$557$	−39.9998	−	14.9192i	−1.69485	−	0.632145i	−0.698348	−	0.715758i	$-0.746081\pi$
$557$	−39.9998	−	14.9192i	−1.69485	−	0.632145i	−0.996498	+	0.0836129i	$0.973354\pi$
$558$	1.41703	+	1.89294i	0.0599878	+	0.0801344i
$559$	−32.2802	+	9.47831i	−1.36531	+	0.400890i
$560$	−5.73412	+	2.56875i	−0.242311	+	0.108550i
$561$	5.91985	−	12.9627i	0.249936	−	0.547284i
$562$	2.60872	−	1.42447i	0.110042	−	0.0600875i
$563$	−1.21461	+	16.9824i	−0.0511896	+	0.715725i	0.905450	+	0.424452i	$0.139533\pi$
$563$	−1.21461	+	16.9824i	−0.0511896	+	0.715725i	−0.956640	+	0.291273i	$0.905921\pi$
$564$	−4.49299	+	3.89320i	−0.189189	+	0.163933i
$565$	22.0235	+	25.7908i	0.926534	+	1.08503i
$566$	4.22125	+	1.92778i	0.177433	+	0.0810307i
$567$	2.74572	−	0.597294i	0.115309	−	0.0250840i
$568$	1.43949	−	2.63623i	0.0603998	−	0.110614i
$569$	−2.16262	+	15.0413i	−0.0906617	+	0.630566i	0.892935	+	0.450185i	$0.148642\pi$
$569$	−2.16262	+	15.0413i	−0.0906617	+	0.630566i	−0.983597	+	0.180381i	$0.942267\pi$
$570$	−10.1442	−	13.7572i	−0.424892	−	0.576225i
$571$	−29.7648	+	4.27954i	−1.24562	+	0.179093i	−0.733422	−	0.679774i	$-0.762078\pi$
$571$	−29.7648	+	4.27954i	−1.24562	+	0.179093i	−0.512198	+	0.858867i	$0.671169\pi$
$572$	−3.88725	+	17.8694i	−0.162534	+	0.747158i
$573$	−17.9823	+	1.28612i	−0.751221	+	0.0537284i
$574$	3.65607			0.152602
$575$	−19.7390	+	13.6151i	−0.823175	+	0.567788i
$576$	−1.00000			−0.0416667
$577$	−6.77042	+	0.484230i	−0.281856	+	0.0201588i	−0.211552	−	0.977367i	$-0.567852\pi$
$577$	−6.77042	+	0.484230i	−0.281856	+	0.0201588i	−0.0703046	+	0.997526i	$0.522397\pi$
$578$	0.683665	−	3.14276i	0.0284367	−	0.130721i
$579$	−11.8993	+	1.71087i	−0.494519	+	0.0711011i
$580$	−12.7383	−	17.2753i	−0.528928	−	0.717316i
$581$	−6.66628	+	46.3650i	−0.276564	+	1.92354i
$582$	1.19629	−	2.19084i	0.0495878	−	0.0908132i
$583$	17.6342	−	3.83608i	0.730333	−	0.158874i
$584$	1.30633	+	0.596579i	0.0540562	+	0.0246866i
$585$	−6.91815	−	8.10157i	−0.286030	−	0.334959i
$586$	1.85701	−	1.60911i	0.0767123	−	0.0664716i
$587$	−1.17103	+	16.3732i	−0.0483337	+	0.675794i	0.914309	+	0.405018i	$0.132735\pi$
$587$	−1.17103	+	16.3732i	−0.0483337	+	0.675794i	−0.962642	+	0.270776i	$0.912720\pi$
$588$	0.786151	−	0.429271i	0.0324203	−	0.0177028i
$589$	−7.50867	+	16.4417i	−0.309389	+	0.677468i
$590$	20.9617	−	9.39037i	0.862981	−	0.386596i
$591$	−23.2835	+	6.83664i	−0.957753	+	0.281222i
$592$	−6.54022	−	8.73671i	−0.268801	−	0.359076i
$593$	23.2373	+	8.66706i	0.954241	+	0.355913i	0.777880	−	0.628412i	$-0.216295\pi$
$593$	23.2373	+	8.66706i	0.954241	+	0.355913i	0.176360	+	0.984326i	$0.443568\pi$
$594$	−0.546255	−	3.79928i	−0.0224131	−	0.155886i
$595$	16.3752	+	16.6137i	0.671319	+	0.681095i
$596$	7.32501	+	6.34716i	0.300044	+	0.259990i
$597$	−14.2818	+	14.2818i	−0.584515	+	0.584515i
$598$	−22.7445	−	2.18388i	−0.930092	−	0.0893057i
$599$		−	0.187872i		−	0.00767623i	−0.999993	−	0.00383812i	$-0.998778\pi$
$599$		−	0.187872i		−	0.00767623i	0.999993	−	0.00383812i	$-0.00122171\pi$
$600$	−4.77660	−	1.47787i	−0.195004	−	0.0603339i
$601$	−18.6693	+	11.9980i	−0.761538	+	0.489410i	−0.862860	−	0.505443i	$-0.831329\pi$
$601$	−18.6693	+	11.9980i	−0.761538	+	0.489410i	0.101322	+	0.994854i	$0.467693\pi$
$602$	11.8908	−	15.8843i	0.484634	−	0.647395i
$603$	1.71092	−	4.58716i	0.0696742	−	0.186804i
$604$	−12.0741	−	1.73599i	−0.491287	−	0.0706364i
$605$	−7.35483	+	3.94729i	−0.299016	+	0.160480i
$606$	4.57455	+	2.93988i	0.185828	+	0.119425i
$607$	−8.97667	+	3.34813i	−0.364352	+	0.135896i	−0.524971	−	0.851120i	$-0.675924\pi$
$607$	−8.97667	+	3.34813i	−0.364352	+	0.135896i	0.160619	+	0.987017i	$0.448651\pi$
$608$	−3.66344	−	6.70910i	−0.148572	−	0.272090i
$609$	17.6631	+	20.3844i	0.715747	+	0.826016i
$610$	13.4155	−	1.82998i	0.543178	−	0.0740937i
$611$	−27.1772	−	7.97995i	−1.09947	−	0.322834i
$612$	1.29744	+	3.47856i	0.0524458	+	0.140613i
$613$	−7.52706	−	34.6014i	−0.304015	−	1.39754i	−0.835045	−	0.550182i	$-0.814558\pi$
$613$	−7.52706	−	34.6014i	−0.304015	−	1.39754i	0.531029	−	0.847353i	$-0.321805\pi$
$614$	−1.34060	−	4.56566i	−0.0541022	−	0.184255i
$615$	2.18495	+	1.92110i	0.0881057	+	0.0774662i
$616$	−4.48046	−	9.81084i	−0.180523	−	0.395290i
$617$	15.9931	+	11.9723i	0.643858	+	0.481986i	0.870615	−	0.491965i	$-0.163721\pi$
$617$	15.9931	+	11.9723i	0.643858	+	0.481986i	−0.226757	+	0.973951i	$0.572812\pi$
$618$	−9.29734	−	2.02251i	−0.373994	−	0.0813574i
$619$	−20.7914	+	23.9946i	−0.835678	+	0.964424i	−0.999757	−	0.0220229i	$-0.992989\pi$
$619$	−20.7914	+	23.9946i	−0.835678	+	0.964424i	0.164079	+	0.986447i	$0.447535\pi$
$620$	1.08653	+	5.17450i	0.0436360	+	0.207813i
$621$	4.63307	−	1.23882i	0.185919	−	0.0497122i
$622$	−4.42857	−	4.42857i	−0.177569	−	0.177569i
$623$	−1.65595	−	23.1533i	−0.0663444	−	0.927616i
$624$	−2.57581	−	4.00804i	−0.103115	−	0.160450i
$625$	−20.6318	−	14.1184i	−0.825271	−	0.564736i
$626$	−0.466469	+	0.213029i	−0.0186439	+	0.00851436i
$627$	23.4886	−	17.5833i	0.938044	−	0.702211i
$628$	16.5477	+	9.03574i	0.660326	+	0.360565i
$629$	−21.9057	+	34.0859i	−0.873436	+	1.35909i
$630$	6.12979	+	1.37994i	0.244217	+	0.0549780i
$631$	−7.54527	+	25.6968i	−0.300372	+	1.02297i	0.661606	+	0.749851i	$0.269875\pi$
$631$	−7.54527	+	25.6968i	−0.300372	+	1.02297i	−0.961979	+	0.273124i	$0.911943\pi$
$632$	−6.59318	−	0.471554i	−0.262263	−	0.0187574i
$633$	−1.13538	−	0.0812038i	−0.0451272	−	0.00322756i
$634$	2.43106	−	8.27943i	0.0965497	−	0.328818i
$635$	27.7563	−	17.5557i	1.10147	−	0.696675i
$636$	−2.54191	+	3.95528i	−0.100793	+	0.156837i
$637$	3.74552	+	2.04521i	0.148403	+	0.0810340i
$638$	29.4952	−	22.0799i	1.16773	−	0.874150i
$639$	−2.73221	+	1.24776i	−0.108085	+	0.0493606i
$640$	−2.02723	−	0.943575i	−0.0801333	−	0.0372981i
$641$	−10.5053	−	16.3465i	−0.414934	−	0.645649i	0.569381	−	0.822074i	$-0.307183\pi$
$641$	−10.5053	−	16.3465i	−0.414934	−	0.645649i	−0.984314	+	0.176425i	$0.943547\pi$
$642$	−0.416875	−	5.82867i	−0.0164527	−	0.230039i
$643$	5.07198	+	5.07198i	0.200019	+	0.200019i	0.800008	−	0.599989i	$-0.204828\pi$
$643$	5.07198	+	5.07198i	0.200019	+	0.200019i	−0.599989	+	0.800008i	$0.704828\pi$
$644$	11.5105	−	7.00776i	0.453579	−	0.276145i
$645$	15.4527	−	3.24472i	0.608449	−	0.127761i
$646$	−18.5849	+	21.4482i	−0.731214	+	0.843866i
$647$	8.06398	+	1.75421i	0.317028	+	0.0689652i	0.368264	−	0.929721i	$-0.379952\pi$
$647$	8.06398	+	1.75421i	0.317028	+	0.0689652i	−0.0512358	+	0.998687i	$0.516316\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	16.3789	+	35.8647i	0.642926	+	1.40781i
$650$	−6.38025	−	22.9515i	−0.250254	−	0.900233i
$651$	−1.87191	−	6.37514i	−0.0733660	−	0.249862i
$652$	−2.51904	−	11.5799i	−0.0986533	−	0.453502i
$653$	12.4823	+	33.4664i	0.488470	+	1.30964i	0.914374	+	0.404871i	$0.132684\pi$
$653$	12.4823	+	33.4664i	0.488470	+	1.30964i	−0.425903	+	0.904769i	$0.640044\pi$
$654$	14.9779	+	4.39789i	0.585680	+	0.171971i
$655$	−28.0569	−	21.3213i	−1.09627	−	0.833092i
$656$	0.852056	+	0.983325i	0.0332672	+	0.0383924i
$657$	−0.688252	−	1.26044i	−0.0268512	−	0.0491744i
$658$	15.6520	−	5.83789i	0.610178	−	0.227585i
$659$	7.03618	+	4.52188i	0.274091	+	0.176147i	0.670464	−	0.741942i	$-0.266095\pi$
$659$	7.03618	+	4.52188i	0.274091	+	0.176147i	−0.396373	+	0.918089i	$0.629731\pi$
$660$	2.47753	−	8.21746i	0.0964375	−	0.319864i
$661$	−27.6533	−	3.97594i	−1.07559	−	0.154646i	−0.418317	−	0.908301i	$-0.637380\pi$
$661$	−27.6533	−	3.97594i	−1.07559	−	0.154646i	−0.657270	+	0.753655i	$0.728289\pi$
$662$	3.11444	−	8.35015i	0.121046	−	0.324538i
$663$	−10.6003	+	14.1603i	−0.411681	+	0.549941i
$664$	−14.0238	+	9.01252i	−0.544227	+	0.349754i
$665$	13.1980	+	46.1807i	0.511798	+	1.79081i
$666$			10.9135i			0.422890i
$667$	31.7502	+	33.3337i	1.22937	+	1.29069i
$668$	4.43568	−	4.43568i	0.171621	−	0.171621i
$669$	−17.3801	−	15.0599i	−0.671952	−	0.582250i
$670$	7.79677	−	7.68485i	0.301215	−	0.296892i
$671$	3.30766	+	23.0053i	0.127691	+	0.888109i
$672$	2.63276	+	0.981970i	0.101561	+	0.0378803i
$673$	15.9653	+	21.3272i	0.615418	+	0.822102i	0.994661	−	0.103195i	$-0.0329066\pi$
$673$	15.9653	+	21.3272i	0.615418	+	0.822102i	−0.379244	+	0.925297i	$0.623816\pi$
$674$	−28.8965	+	8.48478i	−1.11305	+	0.326822i
$675$	2.93821	+	4.04561i	0.113092	+	0.155715i
$676$	4.02920	−	8.82273i	0.154969	−	0.339336i
$677$	−11.0420	+	6.02941i	−0.424380	+	0.231729i	−0.677222	−	0.735779i	$-0.736816\pi$
$677$	−11.0420	+	6.02941i	−0.424380	+	0.231729i	0.252842	+	0.967507i	$0.418635\pi$
$678$	1.08201	−	15.1284i	0.0415542	−	0.581003i
$679$	−5.30089	+	4.59324i	−0.203429	+	0.176272i
$680$	−0.652081	+	8.27608i	−0.0250062	+	0.317373i
$681$	16.0508	+	7.33014i	0.615067	+	0.280892i
$682$	−8.86864	+	1.92925i	−0.339598	+	0.0738750i
$683$	9.79901	−	17.9456i	0.374949	−	0.686668i	−0.620265	−	0.784393i	$-0.712975\pi$
$683$	9.79901	−	17.9456i	0.374949	−	0.686668i	0.995213	+	0.0977251i	$0.0311566\pi$
$684$	−1.08787	+	7.56633i	−0.0415959	+	0.289306i
$685$	22.2924	+	3.36981i	0.851747	+	0.128754i
$686$	16.9780	−	2.44107i	0.648224	−	0.0932006i
$687$	2.14567	−	9.86349i	0.0818624	−	0.376316i
$688$	7.04337	−	0.503752i	0.268526	−	0.0192053i
$689$	−22.4004			−0.853388
$690$	10.5612	+	1.86027i	0.402059	+	0.0708193i
$691$	3.91440			0.148911			0.0744553	−	0.997224i	$-0.476278\pi$
$691$	3.91440			0.148911			0.0744553	+	0.997224i	$0.476278\pi$
$692$	22.8203	−	1.63214i	0.867497	−	0.0620446i
$693$	−2.29262	+	10.5390i	−0.0870896	+	0.400344i
$694$	−18.5355	+	2.66501i	−0.703600	+	0.101162i
$695$	−22.3051	+	16.4471i	−0.846080	+	0.623875i
$696$	−1.36607	+	9.50124i	−0.0517808	+	0.360144i
$697$	2.31507	−	4.23973i	0.0876895	−	0.160591i
$698$	8.68994	−	1.89038i	0.328919	−	0.0715520i
$699$	11.4998	+	5.25180i	0.434964	+	0.198641i
$700$	11.1244	+	8.58137i	0.420464	+	0.324345i
$701$	5.65559	−	4.90059i	0.213609	−	0.185093i	−0.541484	−	0.840711i	$-0.682137\pi$
$701$	5.65559	−	4.90059i	0.213609	−	0.185093i	0.755093	+	0.655618i	$0.227592\pi$
$702$	−0.339886	+	4.75223i	−0.0128282	+	0.179361i
$703$	−73.2198	+	39.9810i	−2.76154	+	1.50791i
$704$	1.59451	−	3.49149i	0.0600953	−	0.131590i
$705$	12.4215	+	4.73555i	0.467822	+	0.178351i
$706$	−9.89345	+	2.90498i	−0.372345	+	0.109330i
$707$	−9.15683	−	12.2321i	−0.344378	−	0.460035i
$708$	−9.62438	−	3.58971i	−0.361706	−	0.134909i
$709$	3.69532	+	25.7015i	0.138781	+	0.965241i	0.933580	+	0.358369i	$0.116667\pi$
$709$	3.69532	+	25.7015i	0.138781	+	0.965241i	−0.794799	+	0.606872i	$0.792424\pi$
$710$	−6.71618	−	0.0485506i	−0.252054	−	0.00182207i
$711$	4.99552	+	4.32864i	0.187347	+	0.162337i
$712$	5.84130	−	5.84130i	0.218912	−	0.218912i
$713$	−3.70335	−	10.7183i	−0.138692	−	0.401405i
$714$		−	10.4323i		−	0.390418i
$715$	39.3176	−	11.2366i	1.47039	−	0.420225i
$716$	10.5315	−	6.76819i	0.393581	−	0.252939i
$717$	−6.27148	+	8.37772i	−0.234213	+	0.312872i
$718$	−5.85248	+	15.6911i	−0.218413	+	0.585587i
$719$	2.91764	+	0.419494i	0.108810	+	0.0156445i	0.196505	−	0.980503i	$-0.437041\pi$
$719$	2.91764	+	0.419494i	0.108810	+	0.0156445i	−0.0876948	+	0.996147i	$0.527950\pi$
$720$	1.05742	+	1.97025i	0.0394077	+	0.0734267i
$721$	22.4917	+	14.4545i	0.837633	+	0.538314i
$722$	−36.9466	+	13.7804i	−1.37501	+	0.512852i
$723$	3.67679	+	6.73353i	0.136741	+	0.250423i
$724$	−5.64899	−	6.51928i	−0.209943	−	0.242287i
$725$	−20.5668	+	43.3647i	−0.763832	+	1.61053i
$726$	3.58174	+	1.05169i	0.132931	+	0.0390320i
$727$	1.48862	+	3.99115i	0.0552099	+	0.148024i	0.961627	−	0.274360i	$-0.0884661\pi$
$727$	1.48862	+	3.99115i	0.0552099	+	0.148024i	−0.906417	+	0.422384i	$0.861193\pi$
$728$	2.84573	+	13.0816i	0.105470	+	0.484837i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−0.205926	−	3.20462i	−0.00762168	−	0.118608i
$731$	−10.8907	−	23.8472i	−0.402805	−	0.882021i
$732$	−4.84741	−	3.62872i	−0.179165	−	0.134121i
$733$	22.9854	+	5.00016i	0.848984	+	0.184685i	0.615952	−	0.787784i	$-0.288772\pi$
$733$	22.9854	+	5.00016i	0.848984	+	0.184685i	0.233032	+	0.972469i	$0.425135\pi$
$734$	−22.3746	+	25.8217i	−0.825862	+	0.953096i
$735$	−1.67706	−	1.09499i	−0.0618593	−	0.0403894i
$736$	4.56734	+	1.46266i	0.168354	+	0.0539145i
$737$	13.2879	+	13.2879i	0.489468	+	0.489468i
$738$	−0.0928212	−	1.29781i	−0.00341680	−	0.0477731i
$739$	−8.79084	−	13.6788i	−0.323376	−	0.503183i	0.641063	−	0.767488i	$-0.278494\pi$
$739$	−8.79084	−	13.6788i	−0.323376	−	0.503183i	−0.964439	+	0.264305i	$0.914857\pi$
$740$	−10.2977	+	22.1242i	−0.378551	+	0.813301i
$741$	−33.1283	+	15.1292i	−1.21700	+	0.555785i
$742$	10.5762	−	7.91725i	0.388265	−	0.290651i
$743$	4.78443	+	2.61250i	0.175524	+	0.0958432i	0.564609	−	0.825359i	$-0.309027\pi$
$743$	4.78443	+	2.61250i	0.175524	+	0.0958432i	−0.389085	+	0.921202i	$0.627209\pi$
$744$	1.27838	−	1.98920i	0.0468678	−	0.0729277i
$745$	4.75985	−	21.1437i	0.174388	−	0.774644i
$746$	5.08806	−	17.3283i	0.186287	−	0.634435i
$747$	16.6276	+	1.18923i	0.608372	+	0.0435116i
$748$	−14.2141	−	1.01662i	−0.519720	−	0.0371711i
$749$	−4.62605	+	15.7549i	−0.169032	+	0.575671i
$750$	2.13909	+	10.9738i	0.0781086	+	0.400707i
$751$	−23.6575	+	36.8118i	−0.863275	+	1.34328i	0.0749248	+	0.997189i	$0.476128\pi$
$751$	−23.6575	+	36.8118i	−0.863275	+	1.34328i	−0.938200	+	0.346093i	$0.887508\pi$
$752$	5.21787	+	2.84917i	0.190276	+	0.103899i
$753$	−15.0264	+	11.2486i	−0.547591	+	0.409921i
$754$	−41.6001	+	18.9981i	−1.51499	+	0.691872i
$755$	9.34702	+	25.6246i	0.340173	+	0.932573i
$756$	−1.51916	−	2.36386i	−0.0552515	−	0.0859729i
$757$	−1.21048	−	16.9247i	−0.0439956	−	0.615138i	−0.970845	−	0.239706i	$-0.922949\pi$
$757$	−1.21048	−	16.9247i	−0.0439956	−	0.615138i	0.926850	−	0.375432i	$-0.122506\pi$
$758$	−19.0036	−	19.0036i	−0.690242	−	0.690242i
$759$	−3.06214	+	18.1516i	−0.111149	+	0.658862i
$760$	−9.34477	+	14.3122i	−0.338971	+	0.519158i
$761$	−29.0493	+	33.5247i	−1.05304	+	1.21527i	−0.0771453	+	0.997020i	$0.524581\pi$
$761$	−29.0493	+	33.5247i	−1.05304	+	1.21527i	−0.975893	+	0.218251i	$0.929965\pi$
$762$	−14.3518	−	3.12205i	−0.519912	−	0.113100i
$763$	−35.1146	−	26.2864i	−1.27123	−	0.951633i
$764$	7.48920	+	16.3991i	0.270950	+	0.593297i
$765$	5.48169	−	6.23457i	0.198191	−	0.225411i
$766$	−3.89590	−	13.2682i	−0.140764	−	0.479400i
$767$	−10.4029	−	47.8214i	−0.375627	−	1.72673i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	−0.0784133	−	0.0230242i	−0.00282766	−	0.000830275i	0.280318	−	0.959907i	$-0.409560\pi$
$769$	−0.0784133	−	0.0230242i	−0.00282766	−	0.000830275i	−0.283146	+	0.959077i	$0.591378\pi$
$770$	−14.5920	+	19.2018i	−0.525861	+	0.691984i
$771$	6.17999	+	7.13208i	0.222567	+	0.256856i
$772$	5.76138	+	10.5512i	0.207357	+	0.379745i
$773$	0.0803889	−	0.0299835i	0.00289139	−	0.00107843i	−0.348018	−	0.937488i	$-0.613145\pi$
$773$	0.0803889	−	0.0299835i	0.00289139	−	0.00107843i	0.350909	+	0.936409i	$0.385872\pi$
$774$	−5.94039	−	3.81766i	−0.213523	−	0.137223i
$775$	9.04611	−	7.61234i	0.324946	−	0.273443i
$776$	−2.47077	−	0.355242i	−0.0886953	−	0.0127525i
$777$	10.7167	−	28.7327i	0.384461	−	1.03078i
$778$	−7.19268	+	9.60830i	−0.257870	+	0.344474i
$779$	8.36709	−	5.37720i	0.299782	−	0.192658i
$780$	−5.17312	+	9.31316i	−0.185227	+	0.333465i
$781$		−	11.5290i		−	0.412542i
$782$	−0.837872	−	17.7855i	−0.0299622	−	0.636008i
$783$	6.78748	−	6.78748i	0.242565	−	0.242565i
$784$	−0.676937	−	0.586569i	−0.0241763	−	0.0209489i
$785$	0.304754	−	42.1576i	0.0108771	−	1.50467i
$786$	2.24279	+	15.5989i	0.0799976	+	0.556396i
$787$	−16.0473	−	5.98532i	−0.572023	−	0.213354i	0.0467726	−	0.998906i	$-0.485106\pi$
$787$	−16.0473	−	5.98532i	−0.572023	−	0.213354i	−0.618796	+	0.785552i	$0.712379\pi$
$788$	14.5423	+	19.4263i	0.518049	+	0.692032i
$789$	−4.93070	+	1.44778i	−0.175537	+	0.0515424i
$790$	6.04268	+	13.4888i	0.214989	+	0.479910i
$791$	−17.7043	+	38.7671i	−0.629493	+	1.37840i
$792$	−3.36884	+	1.83953i	−0.119707	+	0.0653647i
$793$	2.05807	−	28.7755i	0.0730841	−	1.02185i
$794$	11.6624	−	10.1055i	0.413882	−	0.358631i
$795$	10.4807	+	0.825788i	0.371713	+	0.0292877i
$796$	18.3723	+	8.39035i	0.651189	+	0.297388i
$797$	11.7102	−	2.54739i	0.414796	−	0.0902333i	−0.000324153	−	1.00000i	$-0.500103\pi$
$797$	11.7102	−	2.54739i	0.414796	−	0.0902333i	0.415120	+	0.909767i	$0.363740\pi$
$798$	10.2940	−	18.8521i	0.364405	−	0.667357i
$799$	3.14117	−	21.8473i	0.111127	−	0.772903i
$800$	0.284557	+	4.99190i	0.0100606	+	0.176490i
$801$	−8.17676	+	1.17564i	−0.288912	+	0.0415392i
$802$	5.61253	−	25.8004i	0.198185	−	0.911043i
$803$	5.49823	−	0.393241i	0.194028	−	0.0138772i
$804$	−4.89585			−0.172663
$805$	−25.9785	−	15.2685i	−0.915621	−	0.538143i
$806$	11.2657			0.396817
$807$	2.57976	−	0.184508i	0.0908119	−	0.00649500i
$808$	1.15588	−	5.31350i	0.0406638	−	0.186928i
$809$	25.6686	−	3.69059i	0.902460	−	0.129754i	0.324563	−	0.945864i	$-0.394783\pi$
$809$	25.6686	−	3.69059i	0.902460	−	0.129754i	0.577897	+	0.816110i	$0.303874\pi$
$810$	0.334217	−	2.21095i	0.0117432	−	0.0776849i
$811$	2.40682	−	16.7398i	0.0845149	−	0.587814i	−0.902922	−	0.429803i	$-0.858583\pi$
$811$	2.40682	−	16.7398i	0.0845149	−	0.587814i	0.987437	−	0.158011i	$-0.0505081\pi$
$812$	12.9265	−	23.6731i	0.453631	−	0.830762i
$813$	17.5584	−	3.81959i	0.615799	−	0.133959i
$814$	−38.1044	−	17.4017i	−1.33556	−	0.609929i
$815$	−20.1515	+	17.2079i	−0.705875	+	0.602766i
$816$	2.80583	−	2.43127i	0.0982237	−	0.0851113i
$817$	3.85075	−	53.8405i	0.134721	−	1.88364i
$818$	13.4021	−	7.31812i	0.468595	−	0.255872i
$819$	5.56139	−	12.1777i	0.194331	−	0.425525i
$820$	1.03641	−	2.71855i	0.0361931	−	0.0949357i
$821$	50.1718	−	14.7318i	1.75101	−	0.514142i	0.760231	−	0.649653i	$-0.225086\pi$
$821$	50.1718	−	14.7318i	1.75101	−	0.514142i	0.990776	+	0.135511i	$0.0432677\pi$
$822$	−6.04234	−	8.07162i	−0.210751	−	0.281530i
$823$	53.4219	+	19.9253i	1.86217	+	0.694553i	0.970125	+	0.242604i	$0.0780016\pi$
$823$	53.4219	+	19.9253i	1.86217	+	0.694553i	0.892044	+	0.451949i	$0.149271\pi$
$824$	1.35409	+	9.41793i	0.0471721	+	0.328089i
$825$	−18.8102	+	3.80796i	−0.654887	+	0.132576i
$826$	21.8137	+	18.9017i	0.758997	+	0.657675i
$827$	−12.5835	+	12.5835i	−0.437572	+	0.437572i	−0.891194	−	0.453622i	$-0.850132\pi$
$827$	−12.5835	+	12.5835i	−0.437572	+	0.437572i	0.453622	+	0.891194i	$0.350132\pi$
$828$	−2.77980	−	3.90803i	−0.0966049	−	0.135813i
$829$		−	6.79586i		−	0.236030i	−0.993012	−	0.118015i	$-0.962347\pi$
$829$		−	6.79586i		−	0.236030i	0.993012	−	0.118015i	$-0.0376531\pi$
$830$	32.5859	+	18.1002i	1.13107	+	0.628268i
$831$	−7.18151	+	4.61527i	−0.249124	+	0.160102i
$832$	−2.85518	+	3.81408i	−0.0989856	+	0.132229i
$833$	−1.16214	+	3.11581i	−0.0402656	+	0.107956i
$834$	12.2676	+	1.76381i	0.424792	+	0.0610759i
$835$	−13.4297	−	4.04900i	−0.464755	−	0.140122i
$836$	−24.6831	−	15.8629i	−0.853684	−	0.548629i
$837$	−2.21548	+	0.826333i	−0.0765783	+	0.0285622i
$838$	−4.02274	−	7.36709i	−0.138963	−	0.254492i
$839$	13.4788	+	15.5554i	0.465340	+	0.537031i	0.939109	−	0.343618i	$-0.111653\pi$
$839$	13.4788	+	15.5554i	0.465340	+	0.537031i	−0.473770	+	0.880649i	$0.657107\pi$
$840$	−0.849212	−	6.22555i	−0.0293006	−	0.214802i
$841$	60.5821	+	17.7885i	2.08904	+	0.613397i
$842$	9.36421	+	25.1064i	0.322712	+	0.865224i
$843$	0.631806	+	2.90436i	0.0217605	+	0.100032i
$844$	0.320690	+	1.09217i	0.0110386	+	0.0375940i
$845$	−21.6435	+	1.39080i	−0.744559	+	0.0478448i
$846$	−2.46968	−	5.40784i	−0.0849092	−	0.185925i
$847$	−8.39715	−	6.28602i	−0.288529	−	0.215990i
$848$	4.59421	+	0.999408i	0.157766	+	0.0343198i
$849$	−3.03896	+	3.50714i	−0.104297	+	0.120365i
$850$	16.9954	−	7.46652i	0.582938	−	0.256100i
$851$	15.9628	−	49.8457i	0.547197	−	1.70869i
$852$	2.12390	+	2.12390i	0.0727635	+	0.0727635i
$853$	1.85748	+	25.9710i	0.0635991	+	0.889231i	0.924676	+	0.380756i	$0.124336\pi$
$853$	1.85748	+	25.9710i	0.0635991	+	0.889231i	−0.861077	+	0.508475i	$0.830209\pi$
$854$	9.19878	+	14.3136i	0.314776	+	0.489801i
$855$	16.0579	−	5.85740i	0.549167	−	0.200319i
$856$	−5.31549	+	2.42750i	−0.181680	+	0.0829703i
$857$	−26.4117	+	19.7716i	−0.902207	+	0.675384i	−0.946177	−	0.323649i	$-0.895090\pi$
$857$	−26.4117	+	19.7716i	−0.902207	+	0.675384i	0.0439702	+	0.999033i	$0.485999\pi$
$858$	−16.0504	−	8.76419i	−0.547952	−	0.299204i
$859$	−5.64415	+	8.78247i	−0.192576	+	0.299654i	−0.924092	−	0.382170i	$-0.875177\pi$
$859$	−5.64415	+	8.78247i	−0.192576	+	0.299654i	0.731516	+	0.681824i	$0.238813\pi$
$860$	−8.44030	−	13.3445i	−0.287812	−	0.455043i
$861$	−1.03003	+	3.50798i	−0.0351035	+	0.119552i
$862$	−13.6104	−	0.973434i	−0.463571	−	0.0331553i
$863$	10.1736	+	0.727629i	0.346313	+	0.0247688i	0.243412	−	0.969923i	$-0.421733\pi$
$863$	10.1736	+	0.727629i	0.346313	+	0.0247688i	0.102900	+	0.994692i	$0.467188\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	−27.3463	−	43.2357i	−0.929802	−	1.47006i
$866$	−7.04297	+	10.9591i	−0.239330	+	0.372405i
$867$	2.82284	+	1.54139i	0.0958687	+	0.0523483i
$868$	−5.31902	+	3.98177i	−0.180539	+	0.135150i
$869$	−23.0788	+	10.5397i	−0.782895	+	0.357536i
$870$	20.1643	−	7.35529i	0.683633	−	0.249368i
$871$	−12.6108	−	19.6228i	−0.427300	−	0.664892i
$872$	−1.11362	−	15.5704i	−0.0377118	−	0.527280i
$873$	1.76506	+	1.76506i	0.0597383	+	0.0597383i
$874$	16.0357	−	32.9668i	0.542415	−	1.11512i
$875$	5.14422	−	30.9920i	0.173906	−	1.04772i
$876$	−0.940448	+	1.08534i	−0.0317748	+	0.0366701i
$877$	−53.5674	−	11.6529i	−1.80884	−	0.393490i	−0.823952	−	0.566660i	$-0.808235\pi$
$877$	−53.5674	−	11.6529i	−1.80884	−	0.393490i	−0.984892	+	0.173170i	$0.944599\pi$
$878$	23.4282	+	17.5381i	0.790662	+	0.591882i
$879$	1.02075	+	2.23513i	0.0344290	+	0.0753889i
$880$	−8.56515	+	0.550390i	−0.288731	+	0.0185537i
$881$	5.23088	+	17.8147i	0.176233	+	0.600194i	0.999472	+	0.0324987i	$0.0103465\pi$
$881$	5.23088	+	17.8147i	0.176233	+	0.600194i	−0.823239	+	0.567695i	$0.807835\pi$
$882$	0.190398	+	0.875246i	0.00641104	+	0.0294711i
$883$	−14.3823	−	38.5604i	−0.484002	−	1.29766i	−0.917941	−	0.396717i	$-0.870149\pi$
$883$	−14.3823	−	38.5604i	−0.484002	−	1.29766i	0.433939	−	0.900942i	$-0.357123\pi$
$884$	16.9719	+	4.98340i	0.570827	+	0.167610i
$885$	3.10439	+	22.7582i	0.104353	+	0.765009i
$886$	−20.6466	−	23.8274i	−0.693636	−	0.800498i
$887$	4.70665	+	8.61959i	0.158034	+	0.289417i	0.944684	−	0.327981i	$-0.106368\pi$
$887$	4.70665	+	8.61959i	0.158034	+	0.289417i	−0.786650	+	0.617399i	$0.788187\pi$
$888$	10.2254	−	3.81388i	0.343142	−	0.127985i
$889$	34.7192	+	22.3127i	1.16445	+	0.748344i
$890$	−17.6855	−	5.33210i	−0.592819	−	0.178732i
$891$	3.79928	+	0.546255i	0.127281	+	0.0183002i
$892$	−8.03667	+	21.5471i	−0.269087	+	0.721451i
$893$	27.2342	−	36.3806i	0.911357	−	1.21743i
$894$	−8.15374	+	5.24009i	−0.272702	+	0.175255i
$895$	−24.4712	−	13.5929i	−0.817983	−	0.454359i
$896$		−	2.80993i		−	0.0938732i
$897$	8.50329	−	21.2079i	0.283917	−	0.708112i
$898$	19.5203	−	19.5203i	0.651402	−	0.651402i
$899$	−17.1535	−	14.8636i	−0.572102	−	0.495730i
$900$	2.76373	−	4.16675i	0.0921244	−	0.138892i
$901$	−2.48419	−	17.2779i	−0.0827603	−	0.575610i
$902$	4.67929	+	1.74529i	0.155803	+	0.0581117i
$903$	11.8908	+	15.8843i	0.395702	+	0.528596i
$904$	−14.5527	+	4.27306i	−0.484015	+	0.142120i
$905$	−6.87123	+	18.0235i	−0.228407	+	0.599121i
$906$	5.06733	−	11.0959i	0.168351	−	0.368637i
$907$	−4.83062	+	2.63772i	−0.160398	+	0.0875840i	−0.557443	−	0.830215i	$-0.688218\pi$
$907$	−4.83062	+	2.63772i	−0.160398	+	0.0875840i	0.397045	+	0.917799i	$0.370036\pi$
$908$	1.25880	−	17.6004i	0.0417749	−	0.584090i
$909$	−4.10960	+	3.56098i	−0.136307	+	0.118110i
$910$	22.7648	−	19.4395i	0.754647	−	0.644414i
$911$	−22.9647	−	10.4876i	−0.760854	−	0.347470i	−0.00308671	−	0.999995i	$-0.500983\pi$
$911$	−22.9647	−	10.4876i	−0.760854	−	0.347470i	−0.757767	+	0.652525i	$0.773710\pi$
$912$	7.46944	−	1.62488i	0.247338	−	0.0538051i
$913$	−30.6650	+	56.1588i	−1.01486	+	1.85859i
$914$	5.61484	−	39.0521i	0.185722	−	1.29173i
$915$	−2.02374	+	13.3877i	−0.0669027	+	0.442582i
$916$	−9.99143	+	1.43655i	−0.330126	+	0.0474650i
$917$	9.41296	−	43.2707i	0.310843	−	1.42892i
$918$	−3.70319	+	0.264857i	−0.122223	+	0.00874159i
$919$	29.5647			0.975249			0.487624	−	0.873053i	$-0.337864\pi$
$919$	29.5647			0.975249			0.487624	+	0.873053i	$0.337864\pi$
$920$	−1.94779	−	10.5454i	−0.0642166	−	0.347673i
$921$	4.75841			0.156795
$922$	2.83803	−	0.202980i	0.0934655	−	0.00668479i
$923$	−3.04191	+	13.9834i	−0.100126	+	0.460270i
$924$	10.6757	−	1.53494i	0.351206	−	0.0504957i
$925$	54.4791	−	3.10552i	1.79126	−	0.102109i
$926$	−2.90037	+	20.1725i	−0.0953119	+	0.662909i
$927$	4.55995	−	8.35092i	0.149768	−	0.274280i
$928$	9.37958	−	2.04040i	0.307900	−	0.0669795i
$929$	−39.5009	−	18.0395i	−1.29598	−	0.591856i	−0.356451	−	0.934314i	$-0.616013\pi$
$929$	−39.5009	−	18.0395i	−1.29598	−	0.591856i	−0.939533	+	0.342458i	$0.888741\pi$
$930$	−5.27100	−	0.415308i	−0.172843	−	0.0136185i
$931$	−5.17460	+	4.48382i	−0.169591	+	0.146951i
$932$	0.901891	−	12.6101i	0.0295424	−	0.413057i
$933$	5.49685	−	3.00151i	0.179959	−	0.0982649i
$934$	−5.64713	+	12.3655i	−0.184780	+	0.404611i
$935$	13.0273	+	29.0803i	0.426039	+	0.951028i
$936$	4.57138	−	1.34228i	0.149420	−	0.0438737i
$937$	−17.1570	−	22.9190i	−0.560494	−	0.748733i	0.427366	−	0.904079i	$-0.359442\pi$
$937$	−17.1570	−	22.9190i	−0.560494	−	0.748733i	−0.987860	+	0.155346i	$0.950351\pi$
$938$	12.8896	+	4.80758i	0.420861	+	0.156973i
$939$	−0.0729806	−	0.507591i	−0.00238163	−	0.0165646i
$940$	0.0960958	−	13.2933i	0.00313430	−	0.433578i
$941$	4.09084	+	3.54473i	0.133357	+	0.115555i	0.718986	−	0.695025i	$-0.244607\pi$
$941$	4.09084	+	3.54473i	0.133357	+	0.115555i	−0.585628	+	0.810580i	$0.699152\pi$
$942$	−13.3318	+	13.3318i	−0.434372	+	0.434372i
$943$	−1.47431	+	6.06331i	−0.0480102	+	0.197449i
$944$			10.2720i			0.334326i
$945$	−3.05100	+	5.49272i	−0.0992491	+	0.178678i
$946$	22.8013	−	14.6535i	0.741335	−	0.476427i
$947$	−24.2405	+	32.3816i	−0.787711	+	1.05226i	0.209513	+	0.977806i	$0.432812\pi$
$947$	−24.2405	+	32.3816i	−0.787711	+	1.05226i	−0.997224	+	0.0744533i	$0.976279\pi$
$948$	2.30997	−	6.19326i	0.0750242	−	0.201148i
$949$	−6.77249	−	0.973737i	−0.219844	−	0.0316088i
$950$	38.0799	+	3.27750i	1.23547	+	0.106336i
$951$	7.25914	+	4.66517i	0.235394	+	0.151278i
$952$	−9.77452	+	3.64571i	−0.316794	+	0.118158i
$953$	15.9655	+	29.2386i	0.517173	+	0.947131i	0.997542	+	0.0700652i	$0.0223207\pi$
$953$	15.9655	+	29.2386i	0.517173	+	0.947131i	−0.480370	+	0.877066i	$0.659497\pi$
$954$	−3.07893	−	3.55327i	−0.0996840	−	0.115041i
$955$	24.3909	−	32.0962i	0.789272	−	1.03861i
$956$	10.0412	+	2.94835i	0.324754	+	0.0953564i
$957$	12.8757	+	34.5211i	0.416212	+	1.11591i
$958$	2.95311	+	13.5752i	0.0954106	+	0.438595i
$959$	7.98197	+	27.1841i	0.257751	+	0.877820i
$960$	1.47649	−	1.67928i	0.0476535	−	0.0541985i
$961$	−10.5552	−	23.1127i	−0.340490	−	0.745570i
$962$	41.6249	+	31.1600i	1.34204	+	1.00464i
$963$	5.71002	+	1.24214i	0.184003	+	0.0400273i
$964$	5.02407	−	5.79809i	0.161815	−	0.186744i
$965$	14.6962	−	22.5084i	0.473088	−	0.724570i
$966$	3.48100	+	13.0186i	0.111999	+	0.418867i
$967$	15.9211	+	15.9211i	0.511989	+	0.511989i	0.915135	−	0.403147i	$-0.132084\pi$
$967$	15.9211	+	15.9211i	0.511989	+	0.511989i	−0.403147	+	0.915135i	$0.632084\pi$
$968$	−0.266306	−	3.72344i	−0.00855939	−	0.119676i
$969$	−15.3434	−	23.8748i	−0.492900	−	0.766968i
$970$	1.91272	+	5.24365i	0.0614137	+	0.168364i
$971$	−20.3578	+	9.29712i	−0.653314	+	0.298359i	−0.714362	−	0.699776i	$-0.753283\pi$
$971$	−20.3578	+	9.29712i	−0.653314	+	0.298359i	0.0610478	+	0.998135i	$0.480556\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	−30.5657	−	16.6901i	−0.979890	−	0.535061i
$974$	−1.72852	+	2.68963i	−0.0553853	+	0.0861813i
$975$	23.8194	+	0.344394i	0.762830	+	0.0110294i
$976$	−1.70594	+	5.80989i	−0.0546057	+	0.185970i
$977$	−23.7687	−	1.69997i	−0.760428	−	0.0543869i	−0.314261	−	0.949337i	$-0.601757\pi$
$977$	−23.7687	−	1.69997i	−0.760428	−	0.0543869i	−0.446167	+	0.894950i	$0.647211\pi$
$978$	11.8205	+	0.845418i	0.377977	+	0.0270335i
$979$	8.93319	−	30.4236i	0.285506	−	0.972344i
$980$	−0.439880	+	1.95398i	−0.0140514	+	0.0624177i
$981$	−8.43950	+	13.1321i	−0.269452	+	0.419276i
$982$	−20.3873	−	11.1323i	−0.650585	−	0.355246i
$983$	−9.67888	+	7.24552i	−0.308708	+	0.231096i	−0.742387	−	0.669972i	$-0.766306\pi$
$983$	−9.67888	+	7.24552i	−0.308708	+	0.231096i	0.433678	+	0.901068i	$0.357215\pi$
$984$	−1.18355	+	0.540507i	−0.0377300	+	0.0172307i
$985$	22.8972	−	49.1936i	0.729565	−	1.56744i
$986$	−19.2671	−	29.9802i	−0.613589	−	0.954763i
$987$	1.19174	+	16.6627i	0.0379335	+	0.530380i
$988$	25.7525	+	25.7525i	0.819295	+	0.819295i
$989$	21.5479	+	26.1254i	0.685182	+	0.830738i
$990$	7.18659	+	4.69229i	0.228405	+	0.149131i
$991$	−34.6487	+	39.9867i	−1.10065	+	1.27022i	−0.140701	+	0.990052i	$0.544936\pi$
$991$	−34.6487	+	39.9867i	−1.10065	+	1.27022i	−0.959951	+	0.280168i	$0.909610\pi$
$992$	−2.31053	−	0.502626i	−0.0733595	−	0.0159584i
$993$	7.13447	+	5.34080i	0.226406	+	0.169485i
$994$	−3.50612	−	7.67732i	−0.111207	−	0.243510i
$995$	−2.89617	−	45.0701i	−0.0918148	−	1.42882i
$996$	−4.69650	−	15.9948i	−0.148814	−	0.506815i
$997$	−9.23301	−	42.4435i	−0.292412	−	1.34420i	−0.855501	−	0.517801i	$-0.826751\pi$
$997$	−9.23301	−	42.4435i	−0.292412	−	1.34420i	0.563089	−	0.826397i	$-0.309613\pi$
$998$	3.13716	+	8.41104i	0.0993049	+	0.266247i
$999$	−10.4714	−	3.07469i	−0.331301	−	0.0972788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.9	✓	240
5.3	odd	4	inner	690.2.w.a.283.5	yes	240
23.10	odd	22	inner	690.2.w.a.217.5	yes	240
115.33	even	44	inner	690.2.w.a.493.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.9	✓	240	1.1	even	1	trivial
690.2.w.a.217.5	yes	240	23.10	odd	22	inner
690.2.w.a.283.5	yes	240	5.3	odd	4	inner
690.2.w.a.493.9	yes	240	115.33	even	44	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.32705 - 1.79970i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.34666 - 2.46622i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.32705 - 1.79970i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(1.34666 - 2.46622i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-1.45206 - 1.70045i) q^{10} +(2.90083 - 2.51359i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-4.18159 + 2.28332i) q^{13} +(1.16729 - 2.55600i) q^{14} +(2.04066 - 0.914169i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.22491 - 2.97213i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-1.08787 - 7.56633i) q^{19} +(-1.56967 - 1.59253i) q^{20} +(2.12360 + 1.84011i) q^{21} +(2.71413 - 2.71413i) q^{22} +(3.76822 + 2.96656i) q^{23} +1.00000i q^{24} +(-1.47787 + 4.77660i) q^{25} +(-4.00804 + 2.57581i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.981970 - 2.63276i) q^{28} +(9.50124 + 1.36607i) q^{29} +(1.97025 - 1.05742i) q^{30} +(-1.98920 - 1.27838i) q^{31} +(0.936950 - 0.349464i) q^{32} +(1.83953 + 3.36884i) q^{33} +(-2.43127 - 2.80583i) q^{34} +(-6.22555 + 0.849212i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.81388 - 10.2254i) q^{37} +(-1.62488 - 7.46944i) q^{38} +(-1.34228 - 4.57138i) q^{39} +(-1.67928 - 1.47649i) q^{40} +(0.540507 + 1.18355i) q^{41} +(2.24947 + 1.68393i) q^{42} +(6.89999 + 1.50100i) q^{43} +(2.51359 - 2.90083i) q^{44} +(0.459504 + 2.18835i) q^{45} +(3.97025 + 2.69018i) q^{46} +(4.20381 + 4.20381i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(-0.484261 - 0.753524i) q^{49} +(-1.13335 + 4.86986i) q^{50} +(3.37714 - 1.54229i) q^{51} +(-3.81408 + 2.85518i) q^{52} +(4.12654 + 2.25326i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-8.37327 - 1.88499i) q^{55} +(0.791649 - 2.69611i) q^{56} +(7.62466 + 0.545326i) q^{57} +(9.57449 + 0.684781i) q^{58} +(-2.89397 + 9.85594i) q^{59} +(1.88979 - 1.19528i) q^{60} +(-3.27367 + 5.09393i) q^{61} +(-2.07533 - 1.13322i) q^{62} +(-2.24947 + 1.68393i) q^{63} +(0.909632 - 0.415415i) q^{64} +(9.65848 + 4.49554i) q^{65} +(2.07517 + 3.22903i) q^{66} +(0.349266 + 4.88337i) q^{67} +(-2.62524 - 2.62524i) q^{68} +(-3.69976 + 3.05152i) q^{69} +(-6.14910 + 1.29117i) q^{70} +(1.96697 - 2.27000i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(1.14966 + 0.860625i) q^{73} +(-4.53363 - 9.92727i) q^{74} +(-4.35329 - 2.45944i) q^{75} +(-2.15360 - 7.33449i) q^{76} +(-2.29262 - 10.5390i) q^{77} +(-1.66498 - 4.46398i) q^{78} +(-6.34227 - 1.86226i) q^{79} +(-1.78033 - 1.35293i) q^{80} +(0.654861 + 0.755750i) q^{81} +(0.623563 + 1.14197i) q^{82} +(-15.6190 + 5.82559i) q^{83} +(2.36386 + 1.51916i) q^{84} +(-2.39639 + 7.94834i) q^{85} +(6.98948 + 1.00494i) q^{86} +(-3.35449 + 8.99373i) q^{87} +(2.30024 - 3.07276i) q^{88} +(6.94947 - 4.46615i) q^{89} +(0.614448 + 2.14999i) q^{90} +13.3876i q^{91} +(4.15205 + 2.40010i) q^{92} +(1.67200 - 1.67200i) q^{93} +(4.49299 + 3.89320i) q^{94} +(-12.1735 + 11.9988i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-2.33879 - 0.872323i) q^{97} +(-0.536783 - 0.717058i) q^{98} +(-3.68287 + 1.08139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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