LMFDB - Embedded newform 930.2.bj.b.643.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(277,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("930.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bj (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			643.12
Character	$\chi$	$=$	930.643
Dual form			930.2.bj.b.337.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 + 0.891007i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.0743292 - 2.23483i) q^{5} -1.00000i q^{6} +(2.80479 - 0.444236i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(0.453990 + 0.891007i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.0743292 - 2.23483i) q^{5} -1.00000i q^{6} +(2.80479 - 0.444236i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.95751 - 1.08082i) q^{10} +(0.168794 - 0.232325i) q^{11} +(0.891007 - 0.453990i) q^{12} +(-2.26759 - 1.15539i) q^{13} +(1.66917 + 2.29741i) q^{14} +(-0.948365 + 2.02499i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.46808 + 0.549291i) q^{17} +(-0.453990 + 0.891007i) q^{18} +(-5.50346 - 1.78818i) q^{19} +(1.85171 + 1.25347i) q^{20} +(-2.70077 - 0.877533i) q^{21} +(0.283633 + 0.0449231i) q^{22} +(0.758554 - 4.78932i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.98895 + 0.332227i) q^{25} -2.54497i q^{26} +(-0.156434 - 0.987688i) q^{27} +(-1.28922 + 2.53024i) q^{28} +(1.12606 - 3.46564i) q^{29} +(-2.23483 + 0.0743292i) q^{30} +(4.58550 - 3.15804i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.255869 + 0.130372i) q^{33} +(1.08506 + 3.33946i) q^{34} +(-1.20127 - 6.23522i) q^{35} -1.00000 q^{36} +(-2.05138 - 2.05138i) q^{37} +(-0.905237 - 5.71544i) q^{38} +(1.49590 + 2.05893i) q^{39} +(-0.276191 + 2.21895i) q^{40} +(2.08375 - 6.41313i) q^{41} +(-0.444236 - 2.80479i) q^{42} +(0.0455218 + 0.0893415i) q^{43} +(0.0887401 + 0.273114i) q^{44} +(1.76433 - 1.37374i) q^{45} +(4.61169 - 1.49843i) q^{46} +(4.83486 + 2.46348i) q^{47} +(-0.156434 + 0.987688i) q^{48} +(1.01213 - 0.328861i) q^{49} +(-2.56095 - 4.29436i) q^{50} +(-2.84071 - 2.06390i) q^{51} +(2.26759 - 1.15539i) q^{52} +(-0.0146746 + 0.0926515i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.531753 - 0.359957i) q^{55} -2.83976 q^{56} +(4.09180 + 4.09180i) q^{57} +(3.59913 - 0.570046i) q^{58} +(12.6253 - 4.10220i) q^{59} +(-1.08082 - 1.95751i) q^{60} -8.78699i q^{61} +(4.89560 + 2.65199i) q^{62} +(2.00801 + 2.00801i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.41356 + 5.15356i) q^{65} +(-0.232325 - 0.168794i) q^{66} +(-1.63957 + 1.63957i) q^{67} +(-2.48287 + 2.48287i) q^{68} +(-2.85018 + 3.92294i) q^{69} +(5.01026 - 3.90107i) q^{70} +(-8.47158 + 6.15496i) q^{71} +(-0.453990 - 0.891007i) q^{72} +(-3.79785 + 0.601520i) q^{73} +(0.896484 - 2.75909i) q^{74} +(4.59602 + 1.96892i) q^{75} +(4.68153 - 3.40133i) q^{76} +(0.370225 - 0.726607i) q^{77} +(-1.15539 + 2.26759i) q^{78} +(11.1178 - 8.07757i) q^{79} +(-2.10248 + 0.761292i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(6.66015 - 1.05486i) q^{82} +(0.645189 + 1.26626i) q^{83} +(2.29741 - 1.66917i) q^{84} +(0.969792 - 7.79142i) q^{85} +(-0.0589374 + 0.0811204i) q^{86} +(-2.57669 + 2.57669i) q^{87} +(-0.203059 + 0.203059i) q^{88} +(7.19004 + 5.22387i) q^{89} +(2.02499 + 0.948365i) q^{90} +(-6.87339 - 2.23330i) q^{91} +(3.42878 + 3.42878i) q^{92} +(-5.51943 + 0.732059i) q^{93} +5.42629i q^{94} +(-3.58722 + 12.4322i) q^{95} +(-0.951057 + 0.309017i) q^{96} +(-15.0446 + 2.38283i) q^{97} +(0.752514 + 0.752514i) q^{98} +0.287169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{7}+O(q^{10}) $ 128 * q + 4 * q^7	$ 128 q + 4 q^{7} - 4 q^{10} - 4 q^{15} + 32 q^{16} + 12 q^{17} + 40 q^{19} + 40 q^{21} + 4 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{28} - 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} - 64 q^{37} - 16 q^{38} - 24 q^{41} + 16 q^{42} - 24 q^{43} + 8 q^{44} + 20 q^{46} - 12 q^{47} + 100 q^{49} - 24 q^{50} + 64 q^{53} + 32 q^{54} + 68 q^{55} - 16 q^{57} + 40 q^{58} + 8 q^{62} - 4 q^{63} + 84 q^{65} - 12 q^{66} - 32 q^{67} - 8 q^{68} + 88 q^{70} + 24 q^{71} + 20 q^{73} + 16 q^{74} - 24 q^{75} - 24 q^{76} + 60 q^{77} + 56 q^{79} + 32 q^{81} - 16 q^{82} + 8 q^{83} - 68 q^{85} - 20 q^{87} + 4 q^{88} - 136 q^{89} - 40 q^{91} + 48 q^{93} - 92 q^{95} + 64 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) $ 128 * q + 4 * q^7 - 4 * q^10 - 4 * q^15 + 32 * q^16 + 12 * q^17 + 40 * q^19 + 40 * q^21 + 4 * q^22 + 32 * q^24 - 8 * q^25 - 4 * q^28 - 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 - 64 * q^37 - 16 * q^38 - 24 * q^41 + 16 * q^42 - 24 * q^43 + 8 * q^44 + 20 * q^46 - 12 * q^47 + 100 * q^49 - 24 * q^50 + 64 * q^53 + 32 * q^54 + 68 * q^55 - 16 * q^57 + 40 * q^58 + 8 * q^62 - 4 * q^63 + 84 * q^65 - 12 * q^66 - 32 * q^67 - 8 * q^68 + 88 * q^70 + 24 * q^71 + 20 * q^73 + 16 * q^74 - 24 * q^75 - 24 * q^76 + 60 * q^77 + 56 * q^79 + 32 * q^81 - 16 * q^82 + 8 * q^83 - 68 * q^85 - 20 * q^87 + 4 * q^88 - 136 * q^89 - 40 * q^91 + 48 * q^93 - 92 * q^95 + 64 * q^97 - 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	−0.0743292	−	2.23483i	−0.0332410	−	0.999447i
$5$	−0.0743292	−	2.23483i	−0.0332410	−	0.999447i
$6$		−	1.00000i		−	0.408248i
$7$	2.80479	−	0.444236i	1.06011	−	0.167905i	0.398057	−	0.917360i	$-0.369684\pi$
$7$	2.80479	−	0.444236i	1.06011	−	0.167905i	0.662055	+	0.749455i	$0.269684\pi$
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	1.95751	−	1.08082i	0.619018	−	0.341785i
$11$	0.168794	−	0.232325i	0.0508932	−	0.0700485i	−0.782812	−	0.622258i	$-0.786215\pi$
$11$	0.168794	−	0.232325i	0.0508932	−	0.0700485i	0.833705	+	0.552210i	$0.186215\pi$
$12$	0.891007	−	0.453990i	0.257211	−	0.131056i
$13$	−2.26759	−	1.15539i	−0.628916	−	0.320449i	0.110319	−	0.993896i	$-0.464813\pi$
$13$	−2.26759	−	1.15539i	−0.628916	−	0.320449i	−0.739235	+	0.673448i	$0.764813\pi$
$14$	1.66917	+	2.29741i	0.446104	+	0.614009i
$15$	−0.948365	+	2.02499i	−0.244867	+	0.522851i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.46808	+	0.549291i	0.841134	+	0.133223i	0.562111	−	0.827062i	$-0.309989\pi$
$17$	3.46808	+	0.549291i	0.841134	+	0.133223i	0.279023	+	0.960284i	$0.409989\pi$
$18$	−0.453990	+	0.891007i	−0.107007	+	0.210012i
$19$	−5.50346	−	1.78818i	−1.26258	−	0.410238i	−0.400168	−	0.916442i	$-0.631048\pi$
$19$	−5.50346	−	1.78818i	−1.26258	−	0.410238i	−0.862414	+	0.506204i	$0.831048\pi$
$20$	1.85171	+	1.25347i	0.414054	+	0.280284i
$21$	−2.70077	−	0.877533i	−0.589356	−	0.191493i
$22$	0.283633	+	0.0449231i	0.0604709	+	0.00957764i
$23$	0.758554	−	4.78932i	0.158169	−	0.998643i	−0.773093	−	0.634293i	$-0.781291\pi$
$23$	0.758554	−	4.78932i	0.158169	−	0.998643i	0.931262	−	0.364350i	$-0.118709\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−4.98895	+	0.332227i	−0.997790	+	0.0664453i
$26$		−	2.54497i		−	0.499110i
$27$	−0.156434	−	0.987688i	−0.0301058	−	0.190081i
$28$	−1.28922	+	2.53024i	−0.243640	+	0.478171i
$29$	1.12606	−	3.46564i	0.209103	−	0.643554i	−0.790417	−	0.612570i	$-0.790136\pi$
$29$	1.12606	−	3.46564i	0.209103	−	0.643554i	0.999520	−	0.0309841i	$-0.00986413\pi$
$30$	−2.23483	+	0.0743292i	−0.408023	+	0.0135706i
$31$	4.58550	−	3.15804i	0.823580	−	0.567200i
$31$	4.58550	−	3.15804i	0.823580	−	0.567200i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.255869	+	0.130372i	−0.0445412	+	0.0226949i
$34$	1.08506	+	3.33946i	0.186086	+	0.572712i
$35$	−1.20127	−	6.23522i	−0.203052	−	1.05395i
$36$	−1.00000			−0.166667
$37$	−2.05138	−	2.05138i	−0.337244	−	0.337244i	0.518085	−	0.855329i	$-0.326645\pi$
$37$	−2.05138	−	2.05138i	−0.337244	−	0.337244i	−0.855329	+	0.518085i	$0.826645\pi$
$38$	−0.905237	−	5.71544i	−0.146849	−	0.927167i
$39$	1.49590	+	2.05893i	0.239535	+	0.329692i
$40$	−0.276191	+	2.21895i	−0.0436696	+	0.350846i
$41$	2.08375	−	6.41313i	0.325427	−	1.00156i	−0.645820	−	0.763490i	$-0.723484\pi$
$41$	2.08375	−	6.41313i	0.325427	−	1.00156i	0.971247	−	0.238073i	$-0.0765157\pi$
$42$	−0.444236	−	2.80479i	−0.0685471	−	0.432789i
$43$	0.0455218	+	0.0893415i	0.00694200	+	0.0136244i	0.894451	−	0.447165i	$-0.147566\pi$
$43$	0.0455218	+	0.0893415i	0.00694200	+	0.0136244i	−0.887509	+	0.460789i	$0.847566\pi$
$44$	0.0887401	+	0.273114i	0.0133781	+	0.0411735i
$45$	1.76433	−	1.37374i	0.263010	−	0.204784i
$46$	4.61169	−	1.49843i	0.679957	−	0.220932i
$47$	4.83486	+	2.46348i	0.705237	+	0.359336i	0.769544	−	0.638594i	$-0.220484\pi$
$47$	4.83486	+	2.46348i	0.705237	+	0.359336i	−0.0643071	+	0.997930i	$0.520484\pi$
$48$	−0.156434	+	0.987688i	−0.0225794	+	0.142561i
$49$	1.01213	−	0.328861i	0.144590	−	0.0469801i
$50$	−2.56095	−	4.29436i	−0.362173	−	0.607314i
$51$	−2.84071	−	2.06390i	−0.397779	−	0.289004i
$52$	2.26759	−	1.15539i	0.314458	−	0.160224i
$53$	−0.0146746	+	0.0926515i	−0.00201571	+	0.0127267i	−0.988676	−	0.150068i	$-0.952051\pi$
$53$	−0.0146746	+	0.0926515i	−0.00201571	+	0.0127267i	0.986660	+	0.162795i	$0.0520508\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−0.531753	−	0.359957i	−0.0717015	−	0.0485366i
$56$	−2.83976			−0.379478
$57$	4.09180	+	4.09180i	0.541973	+	0.541973i
$58$	3.59913	−	0.570046i	0.472589	−	0.0748507i
$59$	12.6253	−	4.10220i	1.64367	−	0.534060i	0.666315	−	0.745671i	$-0.267871\pi$
$59$	12.6253	−	4.10220i	1.64367	−	0.534060i	0.977354	+	0.211610i	$0.0678708\pi$
$60$	−1.08082	−	1.95751i	−0.139533	−	0.252713i
$61$		−	8.78699i		−	1.12506i	−0.826777	−	0.562530i	$-0.809828\pi$
$61$		−	8.78699i		−	1.12506i	0.826777	−	0.562530i	$-0.190172\pi$
$62$	4.89560	+	2.65199i	0.621742	+	0.336803i
$63$	2.00801	+	2.00801i	0.252986	+	0.252986i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−2.41356	+	5.15356i	−0.299366	+	0.639220i
$66$	−0.232325	−	0.168794i	−0.0285972	−	0.0207771i
$67$	−1.63957	+	1.63957i	−0.200306	+	0.200306i	−0.800131	−	0.599825i	$-0.795237\pi$
$67$	−1.63957	+	1.63957i	−0.200306	+	0.200306i	0.599825	+	0.800131i	$0.295237\pi$
$68$	−2.48287	+	2.48287i	−0.301093	+	0.301093i
$69$	−2.85018	+	3.92294i	−0.343122	+	0.472267i
$70$	5.01026	−	3.90107i	0.598841	−	0.466267i
$71$	−8.47158	+	6.15496i	−1.00539	+	0.730460i	−0.963238	−	0.268651i	$-0.913422\pi$
$71$	−8.47158	+	6.15496i	−1.00539	+	0.730460i	−0.0421543	+	0.999111i	$0.513422\pi$
$72$	−0.453990	−	0.891007i	−0.0535033	−	0.105006i
$73$	−3.79785	+	0.601520i	−0.444505	+	0.0704026i	−0.374675	−	0.927156i	$-0.622246\pi$
$73$	−3.79785	+	0.601520i	−0.444505	+	0.0704026i	−0.0698298	+	0.997559i	$0.522246\pi$
$74$	0.896484	−	2.75909i	0.104214	−	0.320738i
$75$	4.59602	+	1.96892i	0.530702	+	0.227351i
$76$	4.68153	−	3.40133i	0.537008	−	0.390159i
$77$	0.370225	−	0.726607i	0.0421910	−	0.0828045i
$78$	−1.15539	+	2.26759i	−0.130823	+	0.256754i
$79$	11.1178	−	8.07757i	1.25085	−	0.908798i	0.252582	−	0.967576i	$-0.418720\pi$
$79$	11.1178	−	8.07757i	1.25085	−	0.908798i	0.998271	+	0.0587780i	$0.0187204\pi$
$80$	−2.10248	+	0.761292i	−0.235065	+	0.0851151i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	6.66015	−	1.05486i	0.735490	−	0.116490i
$83$	0.645189	+	1.26626i	0.0708187	+	0.138990i	0.923702	−	0.383113i	$-0.125148\pi$
$83$	0.645189	+	1.26626i	0.0708187	+	0.138990i	−0.852883	+	0.522102i	$0.825148\pi$
$84$	2.29741	−	1.66917i	0.250668	−	0.182121i
$85$	0.969792	−	7.79142i	0.105189	−	0.845098i
$86$	−0.0589374	+	0.0811204i	−0.00635538	+	0.00874743i
$87$	−2.57669	+	2.57669i	−0.276250	+	0.276250i
$88$	−0.203059	+	0.203059i	−0.0216462	+	0.0216462i
$89$	7.19004	+	5.22387i	0.762143	+	0.553729i	0.899567	−	0.436783i	$-0.143882\pi$
$89$	7.19004	+	5.22387i	0.762143	+	0.553729i	−0.137424	+	0.990512i	$0.543882\pi$
$90$	2.02499	+	0.948365i	0.213453	+	0.0999664i
$91$	−6.87339	−	2.23330i	−0.720527	−	0.234113i
$92$	3.42878	+	3.42878i	0.357475	+	0.357475i
$93$	−5.51943	+	0.732059i	−0.572338	+	0.0759110i
$94$			5.42629i			0.559679i
$95$	−3.58722	+	12.4322i	−0.368041	+	1.27552i
$96$	−0.951057	+	0.309017i	−0.0970668	+	0.0315389i
$97$	−15.0446	+	2.38283i	−1.52755	+	0.241940i	−0.862961	−	0.505270i	$-0.831393\pi$
$97$	−15.0446	+	2.38283i	−1.52755	+	0.241940i	−0.664588	+	0.747210i	$0.731393\pi$
$98$	0.752514	+	0.752514i	0.0760154	+	0.0760154i
$99$	0.287169			0.0288616
$100$	2.66365	−	4.23142i	0.266365	−	0.423142i
$101$	4.88897	−	3.55205i	0.486471	−	0.353442i	−0.317354	−	0.948307i	$-0.602794\pi$
$101$	4.88897	−	3.55205i	0.486471	−	0.353442i	0.803826	+	0.594865i	$0.202794\pi$
$102$	0.549291	−	3.46808i	0.0543879	−	0.343392i
$103$	−0.799318	+	0.407273i	−0.0787591	+	0.0401298i	−0.492926	−	0.870071i	$-0.664073\pi$
$103$	−0.799318	+	0.407273i	−0.0787591	+	0.0401298i	0.414167	+	0.910201i	$0.364073\pi$
$104$	2.05893	+	1.49590i	0.201894	+	0.146685i
$105$	−1.76039	+	6.10099i	−0.171797	+	0.595396i
$106$	−0.0892152	+	0.0289878i	−0.00866535	+	0.00281554i
$107$	1.24914	−	7.88677i	0.120759	−	0.762443i	−0.850773	−	0.525534i	$-0.823866\pi$
$107$	1.24914	−	7.88677i	0.120759	−	0.762443i	0.971532	−	0.236909i	$-0.0761344\pi$
$108$	0.891007	+	0.453990i	0.0857371	+	0.0436853i
$109$	−5.38894	+	1.75097i	−0.516167	+	0.167713i	−0.555505	−	0.831513i	$-0.687475\pi$
$109$	−5.38894	+	1.75097i	−0.516167	+	0.167713i	0.0393384	+	0.999226i	$0.487475\pi$
$110$	0.0793134	−	0.637212i	0.00756224	−	0.0607558i
$111$	0.896484	+	2.75909i	0.0850905	+	0.261882i
$112$	−1.28922	−	2.53024i	−0.121820	−	0.239085i
$113$	1.46658	+	9.25964i	0.137965	+	0.871074i	0.955456	+	0.295133i	$0.0953641\pi$
$113$	1.46658	+	9.25964i	0.137965	+	0.871074i	−0.817492	+	0.575941i	$0.804636\pi$
$114$	−1.78818	+	5.50346i	−0.167479	+	0.515447i
$115$	−10.7597	−	1.33925i	−1.00335	−	0.124886i
$116$	2.14189	+	2.94805i	0.198869	+	0.273720i
$117$	−0.398122	−	2.51364i	−0.0368064	−	0.232386i
$118$	9.38683	+	9.38683i	0.864128	+	0.864128i
$119$	9.97128			0.914065
$120$	1.25347	−	1.85171i	0.114425	−	0.169037i
$121$	3.37370	+	10.3832i	0.306700	+	0.943927i
$122$	7.82927	−	3.98921i	0.708829	−	0.361166i
$123$	−4.76814	+	4.76814i	−0.429929	+	0.429929i
$124$	−0.140383	+	5.56599i	−0.0126068	+	0.499841i
$125$	1.11330	+	11.1248i	0.0995762	+	0.995030i
$126$	−0.877533	+	2.70077i	−0.0781768	+	0.240604i
$127$	0.877696	−	1.72257i	0.0778829	−	0.152854i	−0.848781	−	0.528744i	$-0.822663\pi$
$127$	0.877696	−	1.72257i	0.0778829	−	0.152854i	0.926664	+	0.375890i	$0.122663\pi$
$128$	0.156434	+	0.987688i	0.0138270	+	0.0873001i
$129$		−	0.100270i		−	0.00882831i
$130$	−5.68759	+	0.189166i	−0.498835	+	0.0165909i
$131$	−4.76199	−	3.45979i	−0.416057	−	0.302283i	0.359993	−	0.932955i	$-0.382779\pi$
$131$	−4.76199	−	3.45979i	−0.416057	−	0.302283i	−0.776049	+	0.630672i	$0.782779\pi$
$132$	0.0449231	−	0.283633i	0.00391006	−	0.0246871i
$133$	−16.2305	−	2.57065i	−1.40736	−	0.222904i
$134$	−2.20522	−	0.716519i	−0.190502	−	0.0618978i
$135$	−2.19569	+	0.423019i	−0.188975	+	0.0364077i
$136$	−3.33946	−	1.08506i	−0.286356	−	0.0930428i
$137$	−5.41202	+	10.6217i	−0.462380	+	0.907471i	0.535633	+	0.844451i	$0.320073\pi$
$137$	−5.41202	+	10.6217i	−0.462380	+	0.907471i	−0.998012	+	0.0630201i	$0.979927\pi$
$138$	−4.78932	−	0.758554i	−0.407694	−	0.0645724i
$139$	3.74642	+	11.5303i	0.317767	+	0.977986i	0.974601	+	0.223950i	$0.0718953\pi$
$139$	3.74642	+	11.5303i	0.317767	+	0.977986i	−0.656834	+	0.754035i	$0.728105\pi$
$140$	5.75049	+	2.69312i	0.486005	+	0.227611i
$141$	−3.18949	−	4.38996i	−0.268604	−	0.369701i
$142$	−9.33013	−	4.75394i	−0.782967	−	0.398942i
$143$	−0.651181	+	0.331793i	−0.0544545	+	0.0277460i
$144$	0.587785	−	0.809017i	0.0489821	−	0.0674181i
$145$	−7.82883	−	2.25895i	−0.650149	−	0.187595i
$146$	−2.26015	−	3.11082i	−0.187051	−	0.257454i
$147$	−1.05111	−	0.166480i	−0.0866944	−	0.0137310i
$148$	2.86537	−	0.453829i	0.235532	−	0.0373045i
$149$		−	8.57473i		−	0.702469i	−0.936288	−	0.351234i	$-0.885762\pi$
$149$		−	8.57473i		−	0.702469i	0.936288	−	0.351234i	$-0.114238\pi$
$150$	0.332227	+	4.98895i	0.0271262	+	0.407346i
$151$	0.0281251	−	0.0387108i	0.00228879	−	0.00315024i	−0.807871	−	0.589359i	$-0.799380\pi$
$151$	0.0281251	−	0.0387108i	0.00228879	−	0.00315024i	0.810160	+	0.586209i	$0.199380\pi$
$152$	5.15597	+	2.62710i	0.418205	+	0.213086i
$153$	1.59410	+	3.12860i	0.128876	+	0.252933i
$154$	0.815490			0.0657141
$155$	−7.39852	−	10.0131i	−0.594263	−	0.804270i
$156$	−2.54497			−0.203761
$157$	3.89855	+	7.65133i	0.311138	+	0.610642i	0.992630	−	0.121183i	$-0.0386687\pi$
$157$	3.89855	+	7.65133i	0.311138	+	0.610642i	−0.681492	+	0.731825i	$0.738669\pi$
$158$	12.2446	+	6.23891i	0.974124	+	0.496341i
$159$	0.0551380	−	0.0758910i	0.00437273	−	0.00601855i
$160$	−1.63282	−	1.52771i	−0.129086	−	0.120776i
$161$		−	13.7700i		−	1.08523i
$162$	−0.987688	+	0.156434i	−0.0776001	+	0.0122907i
$163$	−16.5672	−	2.62398i	−1.29764	−	0.205526i	−0.530873	−	0.847451i	$-0.678136\pi$
$163$	−16.5672	−	2.62398i	−1.29764	−	0.205526i	−0.766767	+	0.641926i	$0.778136\pi$
$164$	3.96353	+	5.45534i	0.309500	+	0.425990i
$165$	0.310378	+	0.562135i	0.0241629	+	0.0437621i
$166$	−0.835332	+	1.14974i	−0.0648343	+	0.0892368i
$167$	18.2888	−	9.31859i	1.41523	−	0.721094i	0.431727	−	0.902004i	$-0.357904\pi$
$167$	18.2888	−	9.31859i	1.41523	−	0.721094i	0.983500	+	0.180910i	$0.0579044\pi$
$168$	2.53024	+	1.28922i	0.195212	+	0.0994657i
$169$	−3.83419	−	5.27731i	−0.294937	−	0.405947i
$170$	7.38248	−	2.67314i	0.566210	−	0.205020i
$171$	−1.78818	−	5.50346i	−0.136746	−	0.420860i
$172$	−0.0990358	−	0.0156857i	−0.00755141	−	0.00119603i
$173$	−8.54430	+	16.7691i	−0.649611	+	1.27493i	0.297712	+	0.954656i	$0.403776\pi$
$173$	−8.54430	+	16.7691i	−0.649611	+	1.27493i	−0.947324	+	0.320278i	$0.896224\pi$
$174$	−3.46564	−	1.12606i	−0.262730	−	0.0853661i
$175$	−13.8454	+	3.14810i	−1.04661	+	0.237974i
$176$	−0.273114	−	0.0887401i	−0.0205867	−	0.00668904i
$177$	−13.1115	−	2.07666i	−0.985524	−	0.156092i
$178$	−1.39029	+	8.77796i	−0.104207	+	0.657936i
$179$	−14.1573	−	10.2859i	−1.05817	−	0.768803i	−0.0844179	−	0.996430i	$-0.526903\pi$
$179$	−14.1573	−	10.2859i	−1.05817	−	0.768803i	−0.973748	+	0.227628i	$0.926903\pi$
$180$	0.0743292	+	2.23483i	0.00554017	+	0.166575i
$181$			11.8968i			0.884280i	0.896946	+	0.442140i	$0.145781\pi$
$181$			11.8968i			0.884280i	−0.896946	+	0.442140i	$0.854219\pi$
$182$	−1.13057	−	7.13813i	−0.0838033	−	0.529113i
$183$	−3.98921	+	7.82927i	−0.294891	+	0.578756i
$184$	−1.49843	+	4.61169i	−0.110466	+	0.339979i
$185$	−4.43200	+	4.73696i	−0.325847	+	0.348268i
$186$	−3.15804	−	4.58550i	−0.231559	−	0.336225i
$187$	0.713005	−	0.713005i	0.0521401	−	0.0521401i
$188$	−4.83486	+	2.46348i	−0.352618	+	0.179668i
$189$	−0.877533	−	2.70077i	−0.0638311	−	0.196452i
$190$	−12.7058	+	2.44788i	−0.921773	+	0.177588i
$191$	19.8357			1.43526			0.717630	−	0.696424i	$-0.245227\pi$
$191$	19.8357			1.43526			0.717630	+	0.696424i	$0.245227\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	3.45946	+	21.8422i	0.249017	+	1.57223i	0.722463	+	0.691410i	$0.243010\pi$
$193$	3.45946	+	21.8422i	0.249017	+	1.57223i	−0.473446	+	0.880823i	$0.656990\pi$
$194$	−8.95323	−	12.3231i	−0.642805	−	0.884745i
$195$	4.49017	−	3.49612i	0.321548	−	0.250362i
$196$	−0.328861	+	1.01213i	−0.0234900	+	0.0722949i
$197$	2.36763	+	14.9486i	0.168686	+	1.06504i	0.916178	+	0.400772i	$0.131258\pi$
$197$	2.36763	+	14.9486i	0.168686	+	1.06504i	−0.747491	+	0.664271i	$0.768742\pi$
$198$	0.130372	+	0.255869i	0.00926514	+	0.0181839i
$199$	−4.62946	−	14.2480i	−0.328173	−	1.01001i	−0.969988	−	0.243154i	$-0.921818\pi$
$199$	−4.62946	−	14.2480i	−0.328173	−	1.01001i	0.641814	−	0.766860i	$-0.278182\pi$
$200$	4.97950	+	0.452307i	0.352104	+	0.0319830i
$201$	2.20522	−	0.716519i	0.155544	−	0.0505394i
$202$	5.38445	+	2.74351i	0.378848	+	0.193033i
$203$	1.61879	−	10.2207i	0.113617	−	0.717349i
$204$	3.33946	−	1.08506i	0.233809	−	0.0759691i
$205$	−14.4872	−	4.18015i	−1.01183	−	0.291955i
$206$	−0.725765	−	0.527299i	−0.0505665	−	0.0367387i
$207$	4.32051	−	2.20141i	0.300296	−	0.153009i
$208$	−0.398122	+	2.51364i	−0.0276048	+	0.174290i
$209$	−1.34439	+	0.976756i	−0.0929934	+	0.0675636i
$210$	−6.23522	+	1.20127i	−0.430271	+	0.0828955i
$211$	16.1214			1.10984			0.554920	−	0.831904i	$-0.312749\pi$
$211$	16.1214			1.10984			0.554920	+	0.831904i	$0.312749\pi$
$212$	−0.0663312	−	0.0663312i	−0.00455564	−	0.00455564i
$213$	10.3425	−	1.63810i	0.708659	−	0.112240i
$214$	7.59427	−	2.46753i	0.519133	−	0.168677i
$215$	0.196280	−	0.108374i	0.0133862	−	0.00739106i
$216$			1.00000i			0.0680414i
$217$	11.4585	−	10.8947i	0.777851	−	0.739580i
$218$	−4.00665	−	4.00665i	−0.271365	−	0.271365i
$219$	3.65699	+	1.18823i	0.247117	+	0.0802931i
$220$	0.603768	−	0.218620i	0.0407060	−	0.0147393i
$221$	−7.22954	−	5.25257i	−0.486311	−	0.353326i
$222$	−2.05138	+	2.05138i	−0.137679	+	0.137679i
$223$	−0.504855	+	0.504855i	−0.0338076	+	0.0338076i	−0.723808	−	0.690001i	$-0.757610\pi$
$223$	−0.504855	+	0.504855i	−0.0338076	+	0.0338076i	0.690001	+	0.723808i	$0.257610\pi$
$224$	1.66917	−	2.29741i	0.111526	−	0.153502i
$225$	−3.20121	−	3.84087i	−0.213414	−	0.256058i
$226$	−7.58459	+	5.51053i	−0.504519	+	0.366555i
$227$	5.81850	+	11.4194i	0.386187	+	0.757935i	0.999491	−	0.0319122i	$-0.0101597\pi$
$227$	5.81850	+	11.4194i	0.386187	+	0.757935i	−0.613303	+	0.789847i	$0.710160\pi$
$228$	−5.71544	+	0.905237i	−0.378514	+	0.0599508i
$229$	−4.19222	+	12.9023i	−0.277030	+	0.852610i	0.711645	+	0.702539i	$0.247950\pi$
$229$	−4.19222	+	12.9023i	−0.277030	+	0.852610i	−0.988675	+	0.150071i	$0.952050\pi$
$230$	−3.69152	−	10.1950i	−0.243412	−	0.672237i
$231$	−0.659745	+	0.479333i	−0.0434081	+	0.0315378i
$232$	−1.65434	+	3.24682i	−0.108613	+	0.213164i
$233$	−8.40150	+	16.4889i	−0.550401	+	1.08022i	0.433441	+	0.901182i	$0.357299\pi$
$233$	−8.40150	+	16.4889i	−0.550401	+	1.08022i	−0.983842	+	0.179040i	$0.942701\pi$
$234$	2.05893	−	1.49590i	0.134596	−	0.0977899i
$235$	5.14610	−	10.9882i	0.335695	−	0.716791i
$236$	−4.10220	+	12.6253i	−0.267030	+	0.821834i
$237$	−13.5732	+	2.14978i	−0.881673	+	0.139643i
$238$	4.52687	+	8.88447i	0.293433	+	0.575895i
$239$	19.8597	−	14.4289i	1.28461	−	0.933327i	0.284933	−	0.958547i	$-0.408029\pi$
$239$	19.8597	−	14.4289i	1.28461	−	0.933327i	0.999682	+	0.0252201i	$0.00802866\pi$
$240$	2.21895	+	0.276191i	0.143232	+	0.0178280i
$241$	1.00329	−	1.38090i	0.0646273	−	0.0889518i	−0.775480	−	0.631372i	$-0.782492\pi$
$241$	1.00329	−	1.38090i	0.0646273	−	0.0889518i	0.840107	+	0.542420i	$0.182492\pi$
$242$	−7.71986	+	7.71986i	−0.496252	+	0.496252i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	7.10883	+	5.16486i	0.455096	+	0.330647i
$245$	−0.810179	−	2.23749i	−0.0517604	−	0.142948i
$246$	−6.41313	−	2.08375i	−0.408886	−	0.132855i
$247$	10.4135	+	10.4135i	0.662597	+	0.662597i
$248$	−5.02307	+	2.40183i	−0.318965	+	0.152516i
$249$		−	1.42115i		−	0.0900618i
$250$	−9.40682	+	6.04249i	−0.594940	+	0.382161i
$251$	24.4643	−	7.94894i	1.54417	−	0.501733i	0.591650	−	0.806195i	$-0.298477\pi$
$251$	24.4643	−	7.94894i	1.54417	−	0.501733i	0.952524	+	0.304462i	$0.0984767\pi$
$252$	−2.80479	+	0.444236i	−0.176685	+	0.0279842i
$253$	−0.984638	−	0.984638i	−0.0619037	−	0.0619037i
$254$	1.93329			0.121305
$255$	−4.40132	+	6.50193i	−0.275621	+	0.407166i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.526858	+	3.32645i	−0.0328645	+	0.207498i	−0.998656	−	0.0518199i	$-0.983498\pi$
$257$	−0.526858	+	3.32645i	−0.0328645	+	0.207498i	0.965792	+	0.259318i	$0.0834978\pi$
$258$	0.0893415	−	0.0455218i	0.00556216	−	0.00283406i
$259$	−6.66498	−	4.84239i	−0.414142	−	0.300892i
$260$	−2.75066	−	4.98180i	−0.170589	−	0.308958i
$261$	3.46564	−	1.12606i	0.214518	−	0.0697011i
$262$	0.920795	−	5.81367i	0.0568869	−	0.359170i
$263$	6.47184	+	3.29757i	0.399071	+	0.203337i	0.641996	−	0.766708i	$-0.278107\pi$
$263$	6.47184	+	3.29757i	0.399071	+	0.203337i	−0.242925	+	0.970045i	$0.578107\pi$
$264$	0.273114	−	0.0887401i	0.0168090	−	0.00546158i
$265$	0.208151	+	0.0259085i	0.0127866	+	0.00159154i
$266$	−5.07801	−	15.6285i	−0.311353	−	0.958245i
$267$	−4.03478	−	7.91871i	−0.246925	−	0.484617i
$268$	−0.362725	−	2.29016i	−0.0221570	−	0.139894i
$269$	−1.94481	+	5.98550i	−0.118577	+	0.364942i	−0.992676	−	0.120805i	$-0.961452\pi$
$269$	−1.94481	+	5.98550i	−0.118577	+	0.364942i	0.874099	+	0.485747i	$0.161452\pi$
$270$	−1.37374	−	1.76433i	−0.0836029	−	0.107374i
$271$	19.2038	+	26.4317i	1.16655	+	1.60561i	0.683325	+	0.730114i	$0.260533\pi$
$271$	19.2038	+	26.4317i	1.16655	+	1.60561i	0.483221	+	0.875498i	$0.339467\pi$
$272$	−0.549291	−	3.46808i	−0.0333056	−	0.210284i
$273$	5.11033	+	5.11033i	0.309292	+	0.309292i
$274$	−11.9210			−0.720173
$275$	−0.764919	+	1.21513i	−0.0461264	+	0.0732753i
$276$	−1.49843	−	4.61169i	−0.0901949	−	0.277591i
$277$	−5.52150	+	2.81334i	−0.331755	+	0.169037i	−0.611931	−	0.790911i	$-0.709607\pi$
$277$	−5.52150	+	2.81334i	−0.331755	+	0.169037i	0.280177	+	0.959948i	$0.409607\pi$
$278$	−8.57272	+	8.57272i	−0.514157	+	0.514157i
$279$	5.25019	+	1.85350i	0.314321	+	0.110966i
$280$	0.211077	+	6.34638i	0.0126143	+	0.379269i
$281$	0.933304	−	2.87241i	0.0556763	−	0.171354i	−0.919351	−	0.393437i	$-0.871286\pi$
$281$	0.933304	−	2.87241i	0.0556763	−	0.171354i	0.975028	+	0.222084i	$0.0712858\pi$
$282$	2.46348	−	4.83486i	0.146698	−	0.287912i
$283$	−0.849055	−	5.36072i	−0.0504711	−	0.318662i	−0.999988	−	0.00494534i	$-0.998426\pi$
$283$	−0.849055	−	5.36072i	−0.0504711	−	0.318662i	0.949517	−	0.313717i	$-0.101574\pi$
$284$		−	10.4715i		−	0.621366i
$285$	8.84036	−	9.44864i	0.523657	−	0.559689i
$286$	−0.591260	−	0.429576i	−0.0349619	−	0.0254013i
$287$	2.99556	−	18.9132i	0.176822	−	1.11641i
$288$	0.987688	+	0.156434i	0.0582001	+	0.00921799i
$289$	−4.44207	−	1.44332i	−0.261298	−	0.0849010i
$290$	−1.54148	−	8.00108i	−0.0905187	−	0.469840i
$291$	14.4866	+	4.70699i	0.849221	+	0.275929i
$292$	1.74568	−	3.42609i	0.102158	−	0.200497i
$293$	20.5564	+	3.25581i	1.20092	+	0.190207i	0.724664	−	0.689102i	$-0.241995\pi$
$293$	20.5564	+	3.25581i	1.20092	+	0.190207i	0.476253	+	0.879309i	$0.341995\pi$
$294$	−0.328861	−	1.01213i	−0.0191795	−	0.0590286i
$295$	−10.1061	−	27.9104i	−0.588402	−	1.62501i
$296$	1.70521	+	2.34703i	0.0991135	+	0.136418i
$297$	−0.255869	−	0.130372i	−0.0148471	−	0.00756495i
$298$	7.64014	−	3.89284i	0.442581	−	0.225506i
$299$	−7.25364	+	9.98378i	−0.419489	+	0.577377i
$300$	−4.29436	+	2.56095i	−0.247935	+	0.147857i
$301$	0.167368	+	0.230362i	0.00964692	+	0.0132778i
$302$	0.0472601	+	0.00748527i	0.00271951	+	0.000430729i
$303$	−5.96870	+	0.945350i	−0.342893	+	0.0543089i
$304$			5.78669i			0.331889i
$305$	−19.6375	+	0.653130i	−1.12444	+	0.0373981i
$306$	−2.06390	+	2.84071i	−0.117985	+	0.162393i
$307$	10.0745	+	5.13323i	0.574984	+	0.292969i	0.717201	−	0.696867i	$-0.245423\pi$
$307$	10.0745	+	5.13323i	0.574984	+	0.292969i	−0.142217	+	0.989836i	$0.545423\pi$
$308$	0.370225	+	0.726607i	0.0210955	+	0.0414023i
$309$	0.897095			0.0510340
$310$	5.56287	−	11.1380i	0.315950	−	0.632595i
$311$	−23.5677			−1.33640			−0.668202	−	0.743980i	$-0.732936\pi$
$311$	−23.5677			−1.33640			−0.668202	+	0.743980i	$0.732936\pi$
$312$	−1.15539	−	2.26759i	−0.0654113	−	0.128377i
$313$	3.08768	+	1.57325i	0.174526	+	0.0889255i	0.539071	−	0.842260i	$-0.318775\pi$
$313$	3.08768	+	1.57325i	0.174526	+	0.0889255i	−0.364545	+	0.931186i	$0.618775\pi$
$314$	−5.04748	+	6.94726i	−0.284846	+	0.392057i
$315$	4.33831	−	4.63682i	0.244436	−	0.261255i
$316$			13.7424i			0.773069i
$317$	−29.4539	+	4.66504i	−1.65430	+	0.262015i	−0.912640	−	0.408765i	$-0.865960\pi$
$317$	−29.4539	+	4.66504i	−1.65430	+	0.262015i	−0.741657	+	0.670780i	$0.765960\pi$
$318$	0.0926515	+	0.0146746i	0.00519564	+	0.000822908i
$319$	−0.615083	−	0.846589i	−0.0344380	−	0.0473999i
$320$	0.619910	−	2.14842i	0.0346540	−	0.120100i
$321$	−4.69351	+	6.46007i	−0.261966	+	0.360566i
$322$	12.2692	−	6.25147i	0.683736	−	0.348381i
$323$	−18.1042	−	9.22457i	−1.00735	−	0.513269i
$324$	−0.587785	−	0.809017i	−0.0326547	−	0.0449454i
$325$	11.6967	+	5.01085i	0.648818	+	0.277952i
$326$	−5.18335	−	15.9527i	−0.287079	−	0.883539i
$327$	5.59650	+	0.886399i	0.309487	+	0.0490180i
$328$	−3.06133	+	6.00820i	−0.169034	+	0.331748i
$329$	14.6551	+	4.76175i	0.807965	+	0.262524i
$330$	−0.359957	+	0.531753i	−0.0198150	+	0.0292720i
$331$	−12.2810	−	3.99034i	−0.675025	−	0.219329i	−0.0486088	−	0.998818i	$-0.515479\pi$
$331$	−12.2810	−	3.99034i	−0.675025	−	0.219329i	−0.626416	+	0.779489i	$0.715479\pi$
$332$	−1.40366	−	0.222317i	−0.0770356	−	0.0122012i
$333$	0.453829	−	2.86537i	0.0248697	−	0.157021i
$334$	16.6058	+	12.0649i	0.908631	+	0.660159i
$335$	3.78604	+	3.54230i	0.206853	+	0.193537i
$336$			2.83976i			0.154921i
$337$	−0.372616	−	2.35260i	−0.0202977	−	0.128154i	0.975459	−	0.220182i	$-0.0706652\pi$
$337$	−0.372616	−	2.35260i	−0.0202977	−	0.128154i	−0.995756	+	0.0920277i	$0.970665\pi$
$338$	2.96143	−	5.81213i	0.161081	−	0.316138i
$339$	2.89705	−	8.91622i	0.157346	−	0.484262i
$340$	5.73336	+	5.36426i	0.310935	+	0.290918i
$341$	0.0403136	−	1.59838i	0.00218310	−	0.0865572i
$342$	4.09180	−	4.09180i	0.221259	−	0.221259i
$343$	−15.0190	+	7.65255i	−0.810948	+	0.413199i
$344$	−0.0309852	−	0.0953627i	−0.00167061	−	0.00514161i
$345$	8.97897	+	6.07809i	0.483411	+	0.327234i
$346$	−18.8204			−1.01179
$347$	−1.71635	−	1.71635i	−0.0921386	−	0.0921386i	0.659535	−	0.751674i	$-0.270753\pi$
$347$	−1.71635	−	1.71635i	−0.0921386	−	0.0921386i	−0.751674	+	0.659535i	$0.770753\pi$
$348$	−0.570046	−	3.59913i	−0.0305577	−	0.192934i
$349$	−4.28533	−	5.89825i	−0.229388	−	0.315726i	0.678772	−	0.734350i	$-0.262513\pi$
$349$	−4.28533	−	5.89825i	−0.229388	−	0.315726i	−0.908160	+	0.418624i	$0.862513\pi$
$350$	−9.09065	−	10.9071i	−0.485916	−	0.583011i
$351$	−0.786440	+	2.42041i	−0.0419771	+	0.129192i
$352$	−0.0449231	−	0.283633i	−0.00239441	−	0.0151177i
$353$	2.63428	+	5.17007i	0.140209	+	0.275175i	0.950424	−	0.310958i	$-0.100650\pi$
$353$	2.63428	+	5.17007i	0.140209	+	0.275175i	−0.810215	+	0.586133i	$0.800650\pi$
$354$	−4.10220	−	12.6253i	−0.218029	−	0.671025i
$355$	14.3850	+	18.4751i	0.763477	+	0.980555i
$356$	−8.45240	+	2.74635i	−0.447976	+	0.145556i
$357$	−8.88447	−	4.52687i	−0.470216	−	0.239587i
$358$	2.73751	−	17.2839i	0.144682	−	0.913484i
$359$	−9.61252	+	3.12330i	−0.507329	+	0.164841i	−0.551487	−	0.834183i	$-0.685939\pi$
$359$	−9.61252	+	3.12330i	−0.507329	+	0.164841i	0.0441580	+	0.999025i	$0.485939\pi$
$360$	−1.95751	+	1.08082i	−0.103170	+	0.0569642i
$361$	11.7192	+	8.51450i	0.616800	+	0.448131i
$362$	−10.6001	+	5.40102i	−0.557129	+	0.283871i
$363$	1.70788	−	10.7831i	0.0896404	−	0.565967i
$364$	5.84685	−	4.24799i	0.306458	−	0.222655i
$365$	1.62659	+	8.44284i	0.0851395	+	0.441919i
$366$	−8.78699			−0.459303
$367$	25.7207	+	25.7207i	1.34261	+	1.34261i	0.893454	+	0.449155i	$0.148275\pi$
$367$	25.7207	+	25.7207i	1.34261	+	1.34261i	0.449155	+	0.893454i	$0.351725\pi$
$368$	−4.78932	+	0.758554i	−0.249661	+	0.0395424i
$369$	6.41313	−	2.08375i	0.333854	−	0.108476i
$370$	−6.23275	−	1.79841i	−0.324025	−	0.0934949i
$371$			0.266387i			0.0138301i
$372$	2.65199	−	4.89560i	0.137499	−	0.253825i
$373$	−15.5610	−	15.5610i	−0.805720	−	0.805720i	0.178263	−	0.983983i	$-0.442952\pi$
$373$	−15.5610	−	15.5610i	−0.805720	−	0.805720i	−0.983983	+	0.178263i	$0.942952\pi$
$374$	0.958989	+	0.311594i	0.0495881	+	0.0161122i
$375$	4.05859	−	10.4177i	0.209585	−	0.537966i
$376$	−4.38996	−	3.18949i	−0.226395	−	0.164485i
$377$	−6.55761	+	6.55761i	−0.337734	+	0.337734i
$378$	2.00801	−	2.00801i	0.103281	−	0.103281i
$379$	−16.5151	+	22.7311i	−0.848324	+	1.16762i	0.135906	+	0.990722i	$0.456606\pi$
$379$	−16.5151	+	22.7311i	−0.848324	+	1.16762i	−0.984230	+	0.176896i	$0.943394\pi$
$380$	−7.94937	−	10.2096i	−0.407794	−	0.523742i
$381$	−1.56406	+	1.13636i	−0.0801295	+	0.0582175i
$382$	9.00522	+	17.6737i	0.460747	+	0.904267i
$383$	4.56616	−	0.723209i	0.233320	−	0.0369543i	−0.0386794	−	0.999252i	$-0.512315\pi$
$383$	4.56616	−	0.723209i	0.233320	−	0.0369543i	0.271999	+	0.962297i	$0.412315\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	−1.65136	−	0.773382i	−0.0841613	−	0.0394152i
$386$	−17.8909	+	12.9985i	−0.910625	+	0.661608i
$387$	−0.0455218	+	0.0893415i	−0.00231400	+	0.00454148i
$388$	6.91525	−	13.5719i	0.351069	−	0.689011i
$389$	14.0127	−	10.1808i	0.710473	−	0.516189i	−0.172853	−	0.984948i	$-0.555299\pi$
$389$	14.0127	−	10.1808i	0.710473	−	0.516189i	0.883326	+	0.468759i	$0.155299\pi$
$390$	5.15356	+	2.41356i	0.260961	+	0.122216i
$391$	5.26146	−	16.1931i	0.266083	−	0.818921i
$392$	−1.05111	+	0.166480i	−0.0530892	+	0.00840851i
$393$	2.67225	+	5.24459i	0.134797	+	0.264554i
$394$	−12.2444	+	8.89609i	−0.616865	+	0.448179i
$395$	−18.8784	−	24.2461i	−0.949875	−	1.21995i
$396$	−0.168794	+	0.232325i	−0.00848220	+	0.0116748i
$397$	10.9378	−	10.9378i	0.548953	−	0.548953i	−0.377185	−	0.926138i	$-0.623108\pi$
$397$	10.9378	−	10.9378i	0.548953	−	0.548953i	0.926138	+	0.377185i	$0.123108\pi$
$398$	10.5933	−	10.5933i	0.530996	−	0.530996i
$399$	13.2944	+	9.65894i	0.665552	+	0.483552i
$400$	1.85764	+	4.64211i	0.0928818	+	0.232106i
$401$	24.6450	+	8.00765i	1.23071	+	0.399883i	0.850972	−	0.525210i	$-0.176013\pi$
$401$	24.6450	+	8.00765i	1.23071	+	0.399883i	0.379740	+	0.925093i	$0.376013\pi$
$402$	1.63957	+	1.63957i	0.0817744	+	0.0817744i
$403$	−14.0468	+	1.86307i	−0.699721	+	0.0928061i
$404$			6.04311i			0.300656i
$405$	2.14842	+	0.619910i	0.106756	+	0.0308036i
$406$	9.84158	−	3.19772i	0.488430	−	0.158700i
$407$	−0.822844	+	0.130326i	−0.0407869	+	0.00646001i
$408$	2.48287	+	2.48287i	0.122921	+	0.122921i
$409$	26.7449			1.32245			0.661226	−	0.750187i	$-0.270037\pi$
$409$	26.7449			1.32245			0.661226	+	0.750187i	$0.270037\pi$
$410$	−2.85249	−	14.8059i	−0.140874	−	0.731211i
$411$	9.64428	−	7.00698i	0.475717	−	0.345629i
$412$	0.140337	−	0.886051i	0.00691389	−	0.0436526i
$413$	33.5889	−	17.1144i	1.65280	−	0.842145i
$414$	3.92294	+	2.85018i	0.192802	+	0.140079i
$415$	2.78191	−	1.53601i	0.136559	−	0.0753998i
$416$	−2.42041	+	0.786440i	−0.118671	+	0.0385584i
$417$	1.89656	−	11.9744i	0.0928748	−	0.586389i
$418$	−1.48064	−	0.754422i	−0.0724203	−	0.0369000i
$419$	15.3820	−	4.99792i	0.751461	−	0.244164i	0.0918510	−	0.995773i	$-0.470722\pi$
$419$	15.3820	−	4.99792i	0.751461	−	0.244164i	0.659610	+	0.751608i	$0.270722\pi$
$420$	−3.90107	−	5.01026i	−0.190353	−	0.244476i
$421$	5.02772	+	15.4737i	0.245036	+	0.754143i	0.995631	+	0.0933802i	$0.0297672\pi$
$421$	5.02772	+	15.4737i	0.245036	+	0.754143i	−0.750594	+	0.660763i	$0.770233\pi$
$422$	7.31894	+	14.3642i	0.356281	+	0.699240i
$423$	0.848858	+	5.35948i	0.0412729	+	0.260587i
$424$	0.0289878	−	0.0892152i	0.00140777	−	0.00433267i
$425$	−17.4846	−	1.58819i	−0.848127	−	0.0770387i
$426$	6.15496	+	8.47158i	0.298209	+	0.410450i
$427$	−3.90350	−	24.6457i	−0.188903	−	1.19269i
$428$	5.64631	+	5.64631i	0.272925	+	0.272925i
$429$	0.730838			0.0352852
$430$	0.185671	+	0.125686i	0.00895386	+	0.00606110i
$431$	4.27085	+	13.1443i	0.205720	+	0.633140i	0.999683	+	0.0251747i	$0.00801419\pi$
$431$	4.27085	+	13.1443i	0.205720	+	0.633140i	−0.793963	+	0.607966i	$0.791986\pi$
$432$	−0.891007	+	0.453990i	−0.0428686	+	0.0218426i
$433$	3.52190	−	3.52190i	0.169252	−	0.169252i	−0.617399	−	0.786650i	$-0.711813\pi$
$433$	3.52190	−	3.52190i	0.169252	−	0.169252i	0.786650	+	0.617399i	$0.211813\pi$
$434$	14.9093	+	5.26348i	0.715668	+	0.252655i
$435$	5.95000	+	5.56695i	0.285281	+	0.266915i
$436$	1.75097	−	5.38894i	0.0838563	−	0.258083i
$437$	−12.7389	+	25.0014i	−0.609383	+	1.19598i
$438$	0.601520	+	3.79785i	0.0287417	+	0.181468i
$439$		−	31.2520i		−	1.49158i	−0.666183	−	0.745789i	$-0.732073\pi$
$439$		−	31.2520i		−	1.49158i	0.666183	−	0.745789i	$-0.267927\pi$
$440$	0.468896	+	0.438710i	0.0223538	+	0.0209147i
$441$	0.860968	+	0.625530i	0.0409985	+	0.0297871i
$442$	1.39793	−	8.82618i	0.0664928	−	0.419819i
$443$	8.73609	+	1.38366i	0.415064	+	0.0657397i	0.360474	−	0.932769i	$-0.382615\pi$
$443$	8.73609	+	1.38366i	0.415064	+	0.0657397i	0.0545898	+	0.998509i	$0.482615\pi$
$444$	−2.75909	−	0.896484i	−0.130941	−	0.0425452i
$445$	11.1400	−	16.4568i	0.528089	−	0.780128i
$446$	−0.679028	−	0.220630i	−0.0321529	−	0.0104471i
$447$	−3.89284	+	7.64014i	−0.184125	+	0.361366i
$448$	2.80479	+	0.444236i	0.132514	+	0.0209882i
$449$	−7.53427	−	23.1881i	−0.355564	−	1.09431i	−0.955682	−	0.294402i	$-0.904879\pi$
$449$	−7.53427	−	23.1881i	−0.355564	−	1.09431i	0.600117	−	0.799912i	$-0.295121\pi$
$450$	1.96892	−	4.59602i	0.0928158	−	0.216658i
$451$	−1.13820	−	1.56660i	−0.0535959	−	0.0737685i
$452$	−8.35325	−	4.25619i	−0.392904	−	0.200194i
$453$	−0.0426340	+	0.0217231i	−0.00200312	+	0.00102064i
$454$	−7.53326	+	10.3686i	−0.353553	+	0.486624i
$455$	−4.48015	+	15.5269i	−0.210033	+	0.727911i
$456$	−3.40133	−	4.68153i	−0.159282	−	0.219233i
$457$	20.4000	+	3.23105i	0.954274	+	0.151142i	0.614107	−	0.789223i	$-0.289516\pi$
$457$	20.4000	+	3.23105i	0.954274	+	0.151142i	0.340167	+	0.940365i	$0.389516\pi$
$458$	−13.3993	+	2.12224i	−0.626108	+	0.0991657i
$459$		−	3.51131i		−	0.163894i
$460$	7.40788	−	7.91760i	0.345394	−	0.369160i
$461$	16.1820	−	22.2726i	0.753672	−	1.03734i	−0.244042	−	0.969765i	$-0.578473\pi$
$461$	16.1820	−	22.2726i	0.753672	−	1.03734i	0.997714	−	0.0675760i	$-0.0215265\pi$
$462$	−0.726607	−	0.370225i	−0.0338048	−	0.0172244i
$463$	−17.6188	−	34.5789i	−0.818816	−	1.60702i	−0.794463	−	0.607313i	$-0.792247\pi$
$463$	−17.6188	−	34.5789i	−0.818816	−	1.60702i	−0.0243533	−	0.999703i	$-0.507753\pi$
$464$	−3.64399			−0.169168
$465$	2.04628	+	12.2806i	0.0948941	+	0.569498i
$466$	−18.5059			−0.857269
$467$	9.23220	+	18.1192i	0.427215	+	0.838457i	0.999826	+	0.0186303i	$0.00593054\pi$
$467$	9.23220	+	18.1192i	0.427215	+	0.838457i	−0.572611	+	0.819827i	$0.694069\pi$
$468$	2.26759	+	1.15539i	0.104819	+	0.0534081i
$469$	−3.87031	+	5.32702i	−0.178714	+	0.245979i
$470$	12.1268	−	0.403332i	0.559370	−	0.0186043i
$471$		−	8.58728i		−	0.395681i
$472$	−13.1115	+	2.07666i	−0.603508	+	0.0955863i
$473$	0.0284400	+	0.00450446i	0.00130767	+	0.000207115i
$474$	−8.07757	−	11.1178i	−0.371015	−	0.510658i
$475$	28.0506	+	7.09276i	1.28705	+	0.325438i
$476$	−5.86097	+	8.06693i	−0.268637	+	0.369747i
$477$	−0.0835821	+	0.0425872i	−0.00382696	+	0.00194994i
$478$	21.8723	+	11.1445i	1.00042	+	0.509738i
$479$	8.28765	+	11.4070i	0.378672	+	0.521198i	0.955232	−	0.295857i	$-0.0956053\pi$
$479$	8.28765	+	11.4070i	0.378672	+	0.521198i	−0.576560	+	0.817055i	$0.695605\pi$
$480$	0.761292	+	2.10248i	0.0347481	+	0.0959648i
$481$	2.28153	+	7.02182i	0.104029	+	0.320167i
$482$	1.68588	+	0.267017i	0.0767896	+	0.0121623i
$483$	−6.25147	+	12.2692i	−0.284452	+	0.558268i
$484$	−10.3832	−	3.37370i	−0.471963	−	0.153350i
$485$	6.44349	+	33.4451i	0.292584	+	1.51866i
$486$	0.951057	+	0.309017i	0.0431408	+	0.0140173i
$487$	2.54199	+	0.402612i	0.115189	+	0.0182441i	0.213763	−	0.976886i	$-0.431428\pi$
$487$	2.54199	+	0.402612i	0.115189	+	0.0182441i	−0.0985740	+	0.995130i	$0.531428\pi$
$488$	−1.37459	+	8.67881i	−0.0622247	+	0.392871i
$489$	13.5702	+	9.85932i	0.613665	+	0.445854i
$490$	1.62581	−	1.73768i	0.0734465	−	0.0785002i
$491$		−	24.8099i		−	1.11966i	−0.828609	−	0.559828i	$-0.810867\pi$
$491$		−	24.8099i		−	1.11966i	0.828609	−	0.559828i	$-0.189133\pi$
$492$	−1.05486	−	6.66015i	−0.0475569	−	0.300263i
$493$	5.80890	−	11.4006i	0.261620	−	0.513458i
$494$	−4.55088	+	14.0062i	−0.204754	+	0.630168i
$495$	−0.0213450	−	0.641775i	−0.000959388	−	0.0288456i
$496$	−4.42047	−	3.38518i	−0.198485	−	0.151999i
$497$	−21.0268	+	21.0268i	−0.943180	+	0.943180i
$498$	1.26626	−	0.645189i	0.0567423	−	0.0289116i
$499$	8.18064	+	25.1774i	0.366216	+	1.12710i	0.949216	+	0.314624i	$0.101878\pi$
$499$	8.18064	+	25.1774i	0.366216	+	1.12710i	−0.583001	+	0.812472i	$0.698122\pi$
$500$	−9.65451	−	5.63830i	−0.431763	−	0.252153i
$501$	−20.5260			−0.917032
$502$	18.1891	+	18.1891i	0.811821	+	0.811821i
$503$	−0.355765	−	2.24621i	−0.0158628	−	0.100154i	0.978487	−	0.206310i	$-0.0661456\pi$
$503$	−0.355765	−	2.24621i	−0.0158628	−	0.100154i	−0.994349	+	0.106156i	$0.966146\pi$
$504$	−1.66917	−	2.29741i	−0.0743506	−	0.102335i
$505$	−8.30163	−	10.6620i	−0.369417	−	0.474454i
$506$	0.430303	−	1.32434i	0.0191293	−	0.0588739i
$507$	1.02044	+	6.44280i	0.0453193	+	0.286135i
$508$	0.877696	+	1.72257i	0.0389414	+	0.0764269i
$509$	−9.39001	−	28.8995i	−0.416205	−	1.28095i	−0.911169	−	0.412033i	$-0.864819\pi$
$509$	−9.39001	−	28.8995i	−0.416205	−	1.28095i	0.494964	−	0.868914i	$-0.335181\pi$
$510$	−7.79142	−	0.969792i	−0.345010	−	0.0429431i
$511$	−10.3850	+	3.37428i	−0.459404	+	0.149269i
$512$	−0.891007	−	0.453990i	−0.0393773	−	0.0200637i
$513$	−0.905237	+	5.71544i	−0.0399672	+	0.252343i
$514$	−3.20308	+	1.04074i	−0.141282	+	0.0459052i
$515$	0.969599	+	1.75607i	0.0427256	+	0.0773817i
$516$	0.0811204	+	0.0589374i	0.00357113	+	0.00259457i
$517$	1.38842	−	0.707436i	0.0610627	−	0.0311130i
$518$	1.28876	−	8.13694i	0.0566251	−	0.357517i
$519$	15.2261	−	11.0624i	0.668350	−	0.485584i
$520$	3.19004	−	4.71255i	0.139893	−	0.206659i
$521$	13.5090			0.591839			0.295920	−	0.955213i	$-0.404374\pi$
$521$	13.5090			0.591839			0.295920	+	0.955213i	$0.404374\pi$
$522$	2.57669	+	2.57669i	0.112779	+	0.112779i
$523$	−2.70179	+	0.427921i	−0.118141	+	0.0187117i	−0.215225	−	0.976564i	$-0.569048\pi$
$523$	−2.70179	+	0.427921i	−0.118141	+	0.0187117i	0.0970839	+	0.995276i	$0.469048\pi$
$524$	5.59805	−	1.81892i	0.244552	−	0.0794598i
$525$	13.7655	+	3.48070i	0.600777	+	0.151910i
$526$			7.26352i			0.316705i
$527$	17.6376	−	8.43357i	0.768305	−	0.367372i
$528$	0.203059	+	0.203059i	0.00883702	+	0.00883702i
$529$	−0.487910	−	0.158532i	−0.0212135	−	0.00689268i
$530$	0.0714141	+	0.197226i	0.00310203	+	0.00856697i
$531$	10.7397	+	7.80284i	0.466063	+	0.338614i
$532$	11.6197	−	11.6197i	0.503779	−	0.503779i
$533$	−12.1348	+	12.1348i	−0.525616	+	0.525616i
$534$	5.22387	−	7.19004i	0.226059	−	0.311143i
$535$	−17.7185	−	2.20541i	−0.766036	−	0.0953480i
$536$	1.87587	−	1.36290i	0.0810253	−	0.0588683i
$537$	7.94455	+	15.5921i	0.342833	+	0.672847i
$538$	−6.21604	+	0.984524i	−0.267992	+	0.0424458i
$539$	0.0944386	−	0.290652i	0.00406776	−	0.0125193i
$540$	0.948365	−	2.02499i	0.0408111	−	0.0871419i
$541$	20.6226	−	14.9832i	0.886635	−	0.644178i	−0.0483631	−	0.998830i	$-0.515400\pi$
$541$	20.6226	−	14.9832i	0.886635	−	0.644178i	0.934999	+	0.354651i	$0.115400\pi$
$542$	−14.8325	+	29.1104i	−0.637111	+	1.25040i
$543$	5.40102	−	10.6001i	0.231780	−	0.454894i
$544$	2.84071	−	2.06390i	0.121795	−	0.0884889i
$545$	4.31368	+	11.9132i	0.184778	+	0.510306i
$546$	−2.23330	+	6.87339i	−0.0955763	+	0.294154i
$547$	−9.62781	+	1.52490i	−0.411656	+	0.0651998i	−0.358828	−	0.933404i	$-0.616823\pi$
$547$	−9.62781	+	1.52490i	−0.411656	+	0.0651998i	−0.0528278	+	0.998604i	$0.516823\pi$
$548$	−5.41202	−	10.6217i	−0.231190	−	0.453736i
$549$	7.10883	−	5.16486i	0.303397	−	0.220431i
$550$	−1.42996	−	0.129889i	−0.0609736	−	0.00553847i
$551$	−12.3944	+	17.0595i	−0.528020	+	0.726757i
$552$	3.42878	−	3.42878i	0.145938	−	0.145938i
$553$	27.5949	−	27.5949i	1.17345	−	1.17345i
$554$	−5.01341	−	3.64246i	−0.213000	−	0.154753i
$555$	6.09948	−	2.20857i	0.258908	−	0.0937487i
$556$	−11.5303	−	3.74642i	−0.488993	−	0.158883i
$557$	−13.1052	−	13.1052i	−0.555285	−	0.555285i	0.372676	−	0.927961i	$-0.378440\pi$
$557$	−13.1052	−	13.1052i	−0.555285	−	0.555285i	−0.927961	+	0.372676i	$0.878440\pi$
$558$	0.732059	+	5.51943i	0.0309905	+	0.233656i
$559$		−	0.255185i		−	0.0107932i
$560$	−5.55884	+	3.06927i	−0.234904	+	0.129700i
$561$	−0.958989	+	0.311594i	−0.0404885	+	0.0131555i
$562$	2.98305	−	0.472469i	0.125832	−	0.0199299i
$563$	26.3086	+	26.3086i	1.10878	+	1.10878i	0.993312	+	0.115464i	$0.0368355\pi$
$563$	26.3086	+	26.3086i	1.10878	+	1.10878i	0.115464	+	0.993312i	$0.463165\pi$
$564$	5.42629			0.228488
$565$	20.5847	−	3.96583i	0.866007	−	0.166844i
$566$	4.39098	−	3.19023i	0.184566	−	0.134095i
$567$	−0.444236	+	2.80479i	−0.0186561	+	0.117790i
$568$	9.33013	−	4.75394i	0.391484	−	0.199471i
$569$	−31.9440	−	23.2087i	−1.33916	−	0.972960i	−0.999474	−	0.0324221i	$-0.989678\pi$
$569$	−31.9440	−	23.2087i	−1.33916	−	0.972960i	−0.339690	−	0.940538i	$-0.610322\pi$
$570$	12.4322	+	3.58722i	0.520729	+	0.150252i
$571$	−43.2200	+	14.0430i	−1.80870	+	0.587682i	−1.00000		0.000538509i	$-0.999829\pi$
$571$	−43.2200	+	14.0430i	−1.80870	+	0.587682i	−0.808700	+	0.588221i	$0.799829\pi$
$572$	0.114328	−	0.721840i	0.00478030	−	0.0301816i
$573$	−17.6737	−	9.00522i	−0.738331	−	0.376198i
$574$	18.2117	−	5.91735i	0.760143	−	0.246985i
$575$	−2.19325	+	24.1457i	−0.0914648	+	1.00695i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	10.6225	+	20.8478i	0.442220	+	0.867906i	0.999299	+	0.0374461i	$0.0119222\pi$
$577$	10.6225	+	20.8478i	0.442220	+	0.867906i	−0.557078	+	0.830460i	$0.688078\pi$
$578$	−0.730654	−	4.61317i	−0.0303912	−	0.191882i
$579$	6.83373	−	21.0321i	0.284000	−	0.874063i
$580$	6.42920	−	5.00588i	0.266958	−	0.207858i
$581$	2.37214	+	3.26497i	0.0984129	+	0.135454i
$582$	2.38283	+	15.0446i	0.0987716	+	0.623619i
$583$	0.0190483	+	0.0190483i	0.000788898	+	0.000788898i
$584$	3.84519			0.159115
$585$	−5.58797	+	1.07657i	−0.231034	+	0.0445108i
$586$	6.43146	+	19.7940i	0.265681	+	0.817682i
$587$	37.2273	−	18.9683i	1.53654	−	0.782905i	0.538329	−	0.842735i	$-0.319056\pi$
$587$	37.2273	−	18.9683i	1.53654	−	0.782905i	0.998209	+	0.0598303i	$0.0190560\pi$
$588$	0.752514	−	0.752514i	0.0310332	−	0.0310332i
$589$	−30.8833	+	9.18043i	−1.27252	+	0.378273i
$590$	20.2803	−	21.6757i	0.834926	−	0.892375i
$591$	4.67695	−	14.3942i	0.192384	−	0.592097i
$592$	−1.31706	+	2.58488i	−0.0541310	+	0.106238i
$593$	2.77382	+	17.5132i	0.113907	+	0.719182i	0.976857	+	0.213893i	$0.0686143\pi$
$593$	2.77382	+	17.5132i	0.113907	+	0.719182i	−0.862950	+	0.505290i	$0.831386\pi$
$594$		−	0.287169i		−	0.0117827i
$595$	−0.741157	−	22.2841i	−0.0303845	−	0.913560i
$596$	6.93710	+	5.04010i	0.284155	+	0.206450i
$597$	−2.34358	+	14.7968i	−0.0959164	+	0.605592i
$598$	−12.1887	−	1.93050i	−0.498433	−	0.0789440i
$599$	6.97806	+	2.26731i	0.285116	+	0.0926398i	0.448084	−	0.893992i	$-0.352107\pi$
$599$	6.97806	+	2.26731i	0.285116	+	0.0926398i	−0.162968	+	0.986631i	$0.552107\pi$
$600$	−4.23142	−	2.66365i	−0.172747	−	0.108743i
$601$	−23.0930	−	7.50337i	−0.941983	−	0.306069i	−0.202529	−	0.979276i	$-0.564916\pi$
$601$	−23.0930	−	7.50337i	−0.941983	−	0.306069i	−0.739454	+	0.673207i	$0.764916\pi$
$602$	−0.129271	+	0.253708i	−0.00526868	+	0.0103404i
$603$	−2.29016	−	0.362725i	−0.0932624	−	0.0147713i
$604$	0.0147862	+	0.0455073i	0.000601643	+	0.00185167i
$605$	22.9539	−	8.31144i	0.933210	−	0.337908i
$606$	−3.55205	−	4.88897i	−0.144292	−	0.198601i
$607$	8.15446	+	4.15491i	0.330979	+	0.168642i	0.611581	−	0.791182i	$-0.290534\pi$
$607$	8.15446	+	4.15491i	0.330979	+	0.168642i	−0.280601	+	0.959824i	$0.590534\pi$
$608$	−5.15597	+	2.62710i	−0.209102	+	0.106543i
$609$	−6.08243	+	8.37175i	−0.246473	+	0.339240i
$610$	−9.49716	−	17.2006i	−0.384529	−	0.696431i
$611$	−8.11717	−	11.1723i	−0.328386	−	0.451984i
$612$	−3.46808	−	0.549291i	−0.140189	−	0.0222038i
$613$	29.2803	−	4.63755i	1.18262	−	0.187309i	0.466009	−	0.884780i	$-0.345692\pi$
$613$	29.2803	−	4.63755i	1.18262	−	0.187309i	0.716613	+	0.697471i	$0.245692\pi$
$614$			11.3069i			0.456310i
$615$	11.0104	+	10.3016i	0.443982	+	0.415400i
$616$	−0.479333	+	0.659745i	−0.0193129	+	0.0265819i
$617$	−33.5640	−	17.1017i	−1.35123	−	0.688489i	−0.379639	−	0.925135i	$-0.623952\pi$
$617$	−33.5640	−	17.1017i	−1.35123	−	0.688489i	−0.971596	+	0.236646i	$0.923952\pi$
$618$	0.407273	+	0.799318i	0.0163829	+	0.0321533i
$619$	−13.2571			−0.532850			−0.266425	−	0.963856i	$-0.585842\pi$
$619$	−13.2571			−0.532850			−0.266425	+	0.963856i	$0.585842\pi$
$620$	12.4495	−	0.0999838i	0.499984	−	0.00401545i
$621$	−4.84902			−0.194585
$622$	−10.6995	−	20.9990i	−0.429012	−	0.841983i
$623$	22.4872	+	11.4578i	0.900931	+	0.459047i
$624$	1.49590	−	2.05893i	0.0598838	−	0.0824230i
$625$	24.7793	−	3.31492i	0.991170	−	0.132597i
$626$			3.46539i			0.138505i
$627$	1.64130	−	0.259956i	0.0655471	−	0.0103816i
$628$	−8.48156	−	1.34335i	−0.338451	−	0.0536054i
$629$	−5.98754	−	8.24114i	−0.238739	−	0.328596i
$630$	6.10099	+	1.76039i	0.243069	+	0.0701357i
$631$	18.5743	−	25.5653i	0.739430	−	1.01774i	−0.259222	−	0.965818i	$-0.583466\pi$
$631$	18.5743	−	25.5653i	0.739430	−	1.01774i	0.998651	−	0.0519197i	$-0.0165340\pi$
$632$	−12.2446	+	6.23891i	−0.487062	+	0.248171i
$633$	−14.3642	−	7.31894i	−0.570927	−	0.290902i
$634$	−17.5284	−	24.1257i	−0.696141	−	0.958156i
$635$	−3.91490	−	1.83346i	−0.155358	−	0.0727588i
$636$	0.0289878	+	0.0892152i	0.00114944	+	0.00353761i
$637$	−2.67506	−	0.423687i	−0.105990	−	0.0167871i
$638$	0.475075	−	0.932387i	0.0188084	−	0.0369135i
$639$	−9.95894	−	3.23586i	−0.393970	−	0.128009i
$640$	2.19569	−	0.423019i	0.0867923	−	0.0167213i
$641$	−37.6204	−	12.2236i	−1.48592	−	0.482804i	−0.550043	−	0.835137i	$-0.685389\pi$
$641$	−37.6204	−	12.2236i	−1.48592	−	0.482804i	−0.935875	+	0.352333i	$0.885389\pi$
$642$	−7.88677	−	1.24914i	−0.311266	−	0.0492997i
$643$	7.04307	−	44.4682i	0.277751	−	1.75365i	−0.315770	−	0.948836i	$-0.602263\pi$
$643$	7.04307	−	44.4682i	0.277751	−	1.75365i	0.593522	−	0.804818i	$-0.297737\pi$
$644$	11.1402	+	8.09383i	0.438985	+	0.318941i
$645$	−0.224087	+	0.00745301i	−0.00882343	+	0.000293462i
$646$		−	20.3189i		−	0.799435i
$647$	−1.94595	−	12.2863i	−0.0765033	−	0.483023i	−0.995958	−	0.0898256i	$-0.971369\pi$
$647$	−1.94595	−	12.2863i	−0.0765033	−	0.483023i	0.919454	−	0.393197i	$-0.128631\pi$
$648$	0.453990	−	0.891007i	0.0178344	−	0.0350020i
$649$	1.17802	−	3.62558i	0.0462415	−	0.142317i
$650$	0.845508	+	12.6967i	0.0331636	+	0.498007i
$651$	−15.1557	+	4.50520i	−0.593997	+	0.176573i
$652$	11.8608	−	11.8608i	0.464504	−	0.464504i
$653$	−2.74232	+	1.39728i	−0.107315	+	0.0546798i	−0.506824	−	0.862049i	$-0.669181\pi$
$653$	−2.74232	+	1.39728i	−0.107315	+	0.0546798i	0.399509	+	0.916729i	$0.369181\pi$
$654$	1.75097	+	5.38894i	0.0684684	+	0.210724i
$655$	−7.37809	+	10.8994i	−0.288286	+	0.425875i
$656$	−6.74317			−0.263276
$657$	−2.71896	−	2.71896i	−0.106077	−	0.106077i
$658$	2.41055	+	15.2196i	0.0939731	+	0.593323i
$659$	−14.4086	−	19.8317i	−0.561278	−	0.772533i	0.430210	−	0.902729i	$-0.358439\pi$
$659$	−14.4086	−	19.8317i	−0.561278	−	0.772533i	−0.991488	+	0.130196i	$0.958439\pi$
$660$	−0.637212	−	0.0793134i	−0.0248035	−	0.00308727i
$661$	−1.67659	+	5.16002i	−0.0652119	+	0.200702i	−0.978353	−	0.206941i	$-0.933649\pi$
$661$	−1.67659	+	5.16002i	−0.0652119	+	0.200702i	0.913141	+	0.407643i	$0.133649\pi$
$662$	−2.02004	−	12.7540i	−0.0785110	−	0.495699i
$663$	4.05695	+	7.96221i	0.157559	+	0.309227i
$664$	−0.439160	−	1.35160i	−0.0170427	−	0.0524521i
$665$	−4.53858	+	36.4634i	−0.175999	+	1.41399i
$666$	2.75909	−	0.896484i	0.106913	−	0.0347380i
$667$	−15.7439	−	8.02192i	−0.609607	−	0.310610i
$668$	−3.21097	+	20.2732i	−0.124236	+	0.784395i
$669$	0.679028	−	0.220630i	0.0262527	−	0.00853004i
$670$	−1.43739	+	4.98155i	−0.0555311	+	0.192454i
$671$	−2.04143	−	1.48319i	−0.0788087	−	0.0572579i
$672$	−2.53024	+	1.28922i	−0.0976062	+	0.0497328i
$673$	7.73920	−	48.8634i	0.298324	−	1.88355i	−0.148482	−	0.988915i	$-0.547439\pi$
$673$	7.73920	−	48.8634i	0.298324	−	1.88355i	0.446807	−	0.894631i	$-0.352561\pi$
$674$	1.92702	−	1.40006i	0.0742261	−	0.0539284i
$675$	1.10858	+	4.87556i	0.0426693	+	0.187660i
$676$	6.52311			0.250889
$677$	−6.61073	−	6.61073i	−0.254071	−	0.254071i	0.568566	−	0.822637i	$-0.307498\pi$
$677$	−6.61073	−	6.61073i	−0.254071	−	0.254071i	−0.822637	+	0.568566i	$0.807498\pi$
$678$	9.25964	−	1.46658i	0.355614	−	0.0563238i
$679$	−41.1385	+	13.3667i	−1.57875	+	0.512967i
$680$	−2.17670	+	7.54378i	−0.0834726	+	0.289291i
$681$		−	12.8163i		−	0.491123i
$682$	1.44247	−	0.689730i	0.0552350	−	0.0264111i
$683$	0.163054	+	0.163054i	0.00623910	+	0.00623910i	0.710219	−	0.703980i	$-0.248596\pi$
$683$	0.163054	+	0.163054i	0.00623910	+	0.00623910i	−0.703980	+	0.710219i	$0.748596\pi$
$684$	5.50346	+	1.78818i	0.210430	+	0.0683729i
$685$	24.1399	+	11.3054i	0.922340	+	0.431959i
$686$	−13.6369	−	9.90781i	−0.520661	−	0.378282i
$687$	9.59283	−	9.59283i	0.365989	−	0.365989i
$688$	0.0709018	−	0.0709018i	0.00270311	−	0.00270311i
$689$	0.140325	−	0.193141i	0.00534595	−	0.00735807i
$690$	−1.33925	+	10.7597i	−0.0509846	+	0.409615i
$691$	−22.2615	+	16.1739i	−0.846866	+	0.615284i	−0.924280	−	0.381715i	$-0.875334\pi$
$691$	−22.2615	+	16.1739i	−0.846866	+	0.615284i	0.0774143	+	0.996999i	$0.475334\pi$
$692$	−8.54430	−	16.7691i	−0.324806	−	0.637467i
$693$	0.805450	−	0.127571i	0.0305965	−	0.00484601i
$694$	0.750073	−	2.30849i	0.0284724	−	0.0876290i
$695$	25.4898	−	9.22965i	0.966882	−	0.350100i
$696$	2.94805	−	2.14189i	0.111746	−	0.0811880i
$697$	10.7493	−	21.0967i	0.407159	−	0.799094i
$698$	3.30988	−	6.49600i	0.125281	−	0.245877i
$699$	14.9716	−	10.8775i	0.566277	−	0.411425i
$700$	5.59125	−	13.0516i	0.211329	−	0.493303i
$701$	−7.40177	+	22.7803i	−0.279561	+	0.860400i	0.708416	+	0.705796i	$0.249410\pi$
$701$	−7.40177	+	22.7803i	−0.279561	+	0.860400i	−0.987976	+	0.154604i	$0.950590\pi$
$702$	−2.51364	+	0.398122i	−0.0948713	+	0.0150261i
$703$	7.62143	+	14.9579i	0.287448	+	0.564148i
$704$	0.232325	−	0.168794i	0.00875606	−	0.00636165i
$705$	−9.57375	+	7.45428i	−0.360568	+	0.280745i
$706$	−3.41063	+	4.69433i	−0.128361	+	0.176673i
$707$	12.1346	−	12.1346i	0.456369	−	0.456369i
$708$	9.38683	−	9.38683i	0.352779	−	0.352779i
$709$	12.9689	+	9.42246i	0.487058	+	0.353868i	0.804052	−	0.594559i	$-0.202674\pi$
$709$	12.9689	+	9.42246i	0.487058	+	0.353868i	−0.316994	+	0.948428i	$0.602674\pi$
$710$	−9.93076	+	21.2046i	−0.372695	+	0.795796i
$711$	13.0698	+	4.24663i	0.490155	+	0.159261i
$712$	−6.28432	−	6.28432i	−0.235515	−	0.235515i
$713$	−11.6465	−	24.3570i	−0.436165	−	0.912176i
$714$		−	9.97128i		−	0.373166i
$715$	0.789904	+	1.43062i	0.0295407	+	0.0535021i
$716$	16.6429	−	5.40761i	0.621974	−	0.202092i
$717$	−24.2457	+	3.84014i	−0.905471	+	0.143413i
$718$	−7.14687	−	7.14687i	−0.266719	−	0.266719i
$719$	−39.8959			−1.48787			−0.743933	−	0.668254i	$-0.767042\pi$
$719$	−39.8959			−1.48787			−0.743933	+	0.668254i	$0.767042\pi$
$720$	−1.85171	−	1.25347i	−0.0690090	−	0.0467140i
$721$	−2.06100	+	1.49740i	−0.0767555	+	0.0557662i
$722$	−2.26607	+	14.3074i	−0.0843343	+	0.532466i
$723$	−1.52085	+	0.774912i	−0.0565611	+	0.0288193i
$724$	−9.62469	−	6.99274i	−0.357699	−	0.259883i
$725$	−4.46646	+	17.6640i	−0.165880	+	0.656026i
$726$	10.3832	−	3.37370i	0.385356	−	0.125210i
$727$	1.56524	−	9.88252i	0.0580514	−	0.366522i	−0.941512	−	0.336979i	$-0.890595\pi$
$727$	1.56524	−	9.88252i	0.0580514	−	0.366522i	0.999564	−	0.0295431i	$-0.00940521\pi$
$728$	6.43940	+	3.28104i	0.238660	+	0.121603i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	−6.78417	+	5.28227i	−0.251094	+	0.195506i
$731$	0.108799	+	0.334848i	0.00402407	+	0.0123848i
$732$	−3.98921	−	7.82927i	−0.147445	−	0.289378i
$733$	1.96874	+	12.4302i	0.0727172	+	0.459118i	0.996999	+	0.0774086i	$0.0246646\pi$
$733$	1.96874	+	12.4302i	0.0727172	+	0.459118i	−0.924282	+	0.381710i	$0.875335\pi$
$734$	−11.2404	+	34.5942i	−0.414889	+	1.27690i
$735$	−0.293926	+	2.36144i	−0.0108416	+	0.0871029i
$736$	−2.85018	−	3.92294i	−0.105059	−	0.144602i
$737$	0.104163	+	0.657662i	0.00383691	+	0.0242253i
$738$	4.76814	+	4.76814i	0.175518	+	0.175518i
$739$	12.3886			0.455723			0.227861	−	0.973694i	$-0.426827\pi$
$739$	12.3886			0.455723			0.227861	+	0.973694i	$0.426827\pi$
$740$	−1.22721	−	6.36988i	−0.0451132	−	0.234161i
$741$	−4.55088	−	14.0062i	−0.167181	−	0.514530i
$742$	−0.237353	+	0.120937i	−0.00871350	+	0.00443975i
$743$	−7.27220	+	7.27220i	−0.266791	+	0.266791i	−0.827806	−	0.561015i	$-0.810411\pi$
$743$	−7.27220	+	7.27220i	−0.266791	+	0.266791i	0.561015	+	0.827806i	$0.310411\pi$
$744$	5.56599	+	0.140383i	0.204059	+	0.00514669i
$745$	−19.1631	+	0.637353i	−0.702081	+	0.0233508i
$746$	6.80042	−	20.9295i	0.248981	−	0.766285i
$747$	−0.645189	+	1.26626i	−0.0236062	+	0.0463299i
$748$	0.157739	+	0.995926i	0.00576752	+	0.0364147i
$749$		−	22.6757i		−	0.828552i
$750$	11.1248	−	1.11330i	0.406219	−	0.0406518i
$751$	40.2018	+	29.2083i	1.46698	+	1.06583i	0.981474	+	0.191594i	$0.0613658\pi$
$751$	40.2018	+	29.2083i	1.46698	+	1.06583i	0.485509	+	0.874232i	$0.338634\pi$
$752$	0.848858	−	5.35948i	0.0309547	−	0.195440i
$753$	−25.4066	−	4.02401i	−0.925869	−	0.146643i
$754$	−8.81997	−	2.86578i	−0.321204	−	0.104366i
$755$	−0.0886027	−	0.0599775i	−0.00322458	−	0.00218280i
$756$	2.70077	+	0.877533i	0.0982260	+	0.0319156i
$757$	12.7145	−	24.9537i	0.462118	−	0.906957i	−0.535915	−	0.844272i	$-0.680033\pi$
$757$	12.7145	−	24.9537i	0.462118	−	0.906957i	0.998033	−	0.0626857i	$-0.0199666\pi$
$758$	−27.7513	−	4.39537i	−1.00797	−	0.159647i
$759$	0.430303	+	1.32434i	0.0156190	+	0.0480703i
$760$	5.48789	−	11.7180i	0.199067	−	0.425057i
$761$	−12.8061	−	17.6260i	−0.464220	−	0.638943i	0.511158	−	0.859487i	$-0.329217\pi$
$761$	−12.8061	−	17.6260i	−0.464220	−	0.638943i	−0.975377	+	0.220544i	$0.929217\pi$
$762$	−1.72257	−	0.877696i	−0.0624023	−	0.0317956i
$763$	−14.3370	+	7.30507i	−0.519035	+	0.264461i
$764$	−11.6591	+	16.0474i	−0.421812	+	0.580575i
$765$	6.87342	−	3.79510i	0.248509	−	0.137212i
$766$	2.71738	+	3.74015i	0.0981829	+	0.135137i
$767$	−33.3685	−	5.28506i	−1.20487	−	0.190832i
$768$	0.987688	−	0.156434i	0.0356401	−	0.00564484i
$769$		−	15.3903i		−	0.554989i	−0.960727	−	0.277495i	$-0.910496\pi$
$769$		−	15.3903i		−	0.554989i	0.960727	−	0.277495i	$-0.0895040\pi$
$770$	−0.0606147	−	1.82248i	−0.00218440	−	0.0656777i
$771$	1.97961	−	2.72470i	0.0712940	−	0.0981277i
$772$	−19.7041	−	10.0397i	−0.709166	−	0.361338i
$773$	−10.3248	−	20.2635i	−0.371356	−	0.728827i	0.627400	−	0.778697i	$-0.284119\pi$
$773$	−10.3248	−	20.2635i	−0.371356	−	0.728827i	−0.998756	+	0.0498701i	$0.984119\pi$
$774$	−0.100270			−0.00360414
$775$	−21.8276	+	17.2787i	−0.784072	+	0.620670i
$776$	15.2321			0.546802
$777$	3.74014	+	7.34044i	0.134177	+	0.263337i
$778$	15.4328	+	7.86342i	0.553294	+	0.281917i
$779$	−22.9357	+	31.5683i	−0.821757	+	1.13105i
$780$	0.189166	+	5.68759i	0.00677322	+	0.203648i
$781$			3.00708i			0.107602i
$782$	16.8168	−	2.66352i	0.601368	−	0.0952474i
$783$	−3.59913	−	0.570046i	−0.128622	−	0.0203718i
$784$	−0.625530	−	0.860968i	−0.0223404	−	0.0307489i
$785$	16.8097	−	9.28131i	0.599962	−	0.331264i
$786$	−3.45979	+	4.76199i	−0.123406	+	0.169854i
$787$	−8.37192	+	4.26571i	−0.298427	+	0.152056i	−0.596793	−	0.802396i	$-0.703558\pi$
$787$	−8.37192	+	4.26571i	−0.298427	+	0.152056i	0.298366	+	0.954452i	$0.403558\pi$
$788$	−13.4853	−	6.87112i	−0.480395	−	0.244773i
$789$	−4.26939	−	5.87631i	−0.151994	−	0.209202i
$790$	13.0328	−	27.8283i	0.463686	−	0.990085i
$791$	8.22693	+	25.3199i	0.292516	+	0.900271i
$792$	−0.283633	−	0.0449231i	−0.0100785	−	0.00159627i
$793$	−10.1524	+	19.9253i	−0.360524	+	0.707567i
$794$	14.7113	+	4.78000i	0.522085	+	0.169636i
$795$	−0.173702	−	0.117583i	−0.00616058	−	0.00417025i
$796$	14.2480	+	4.62946i	0.505007	+	0.164087i
$797$	−24.2158	−	3.83541i	−0.857768	−	0.135857i	−0.287967	−	0.957640i	$-0.592980\pi$
$797$	−24.2158	−	3.83541i	−0.857768	−	0.135857i	−0.569800	+	0.821783i	$0.692980\pi$
$798$	−2.57065	+	16.2305i	−0.0910001	+	0.574552i
$799$	15.4145	+	11.1993i	0.545327	+	0.396203i
$800$	−3.29280	+	3.76264i	−0.116418	+	0.133029i
$801$			8.88738i			0.314020i
$802$	4.05373	+	25.5943i	0.143142	+	0.903765i
$803$	−0.501305	+	0.983867i	−0.0176907	+	0.0347199i
$804$	−0.716519	+	2.20522i	−0.0252697	+	0.0777721i
$805$	−30.7737	+	1.02352i	−1.08463	+	0.0360742i
$806$	−8.03712	−	11.6700i	−0.283096	−	0.411057i
$807$	4.45019	−	4.45019i	0.156654	−	0.156654i
$808$	−5.38445	+	2.74351i	−0.189424	+	0.0965164i
$809$	10.4714	+	32.2276i	0.368154	+	1.13306i	0.947982	+	0.318324i	$0.103120\pi$
$809$	10.4714	+	32.2276i	0.368154	+	1.13306i	−0.579828	+	0.814739i	$0.696880\pi$
$810$	0.423019	+	2.19569i	0.0148634	+	0.0771487i
$811$	42.6960			1.49926			0.749630	−	0.661857i	$-0.230231\pi$
$811$	42.6960			1.49926			0.749630	+	0.661857i	$0.230231\pi$
$812$	7.31718	+	7.31718i	0.256783	+	0.256783i
$813$	−5.11093	−	32.2692i	−0.179248	−	1.13173i
$814$	−0.489685	−	0.673993i	−0.0171634	−	0.0236234i
$815$	−4.63273	+	37.2199i	−0.162277	+	1.30375i
$816$	−1.08506	+	3.33946i	−0.0379846	+	0.116904i
$817$	−0.0907684	−	0.573089i	−0.00317558	−	0.0200498i
$818$	12.1419	+	23.8299i	0.424533	+	0.833193i
$819$	−2.23330	−	6.87339i	−0.0780378	−	0.240176i
$820$	11.8972	−	9.26332i	0.415467	−	0.323489i
$821$	−26.3761	+	8.57011i	−0.920532	+	0.299099i	−0.730685	−	0.682715i	$-0.760799\pi$
$821$	−26.3761	+	8.57011i	−0.920532	+	0.299099i	−0.189847	+	0.981814i	$0.560799\pi$
$822$	10.6217	+	5.41202i	0.370474	+	0.188766i
$823$	−2.69143	+	16.9930i	−0.0938174	+	0.592340i	0.895329	+	0.445406i	$0.146941\pi$
$823$	−2.69143	+	16.9930i	−0.0938174	+	0.592340i	−0.989146	+	0.146934i	$0.953059\pi$
$824$	0.853189	−	0.277218i	0.0297222	−	0.00965734i
$825$	1.23321	−	0.735426i	0.0429348	−	0.0256043i
$826$	30.4981	+	22.1582i	1.06116	+	0.770981i
$827$	−24.1864	+	12.3236i	−0.841044	+	0.428533i	−0.820768	−	0.571261i	$-0.806454\pi$
$827$	−24.1864	+	12.3236i	−0.841044	+	0.428533i	−0.0202758	+	0.999794i	$0.506454\pi$
$828$	−0.758554	+	4.78932i	−0.0263616	+	0.166440i
$829$	−42.3350	+	30.7582i	−1.47036	+	1.06828i	−0.489845	+	0.871809i	$0.662947\pi$
$829$	−42.3350	+	30.7582i	−1.47036	+	1.06828i	−0.980510	+	0.196467i	$0.937053\pi$
$830$	2.63156	+	1.78137i	0.0913427	+	0.0618322i
$831$	6.19692			0.214969
$832$	−1.79957	−	1.79957i	−0.0623888	−	0.0623888i
$833$	3.69079	−	0.584564i	0.127878	−	0.0202539i
$834$	11.5303	−	3.74642i	0.399261	−	0.129728i
$835$	−22.1849	−	40.1797i	−0.767739	−	1.39047i
$836$		−	1.66176i		−	0.0574731i
$837$	−3.83649	−	4.03502i	−0.132608	−	0.139471i
$838$	11.4365	+	11.4365i	0.395066	+	0.395066i
$839$	−26.6806	−	8.66905i	−0.921116	−	0.299289i	−0.190192	−	0.981747i	$-0.560911\pi$
$839$	−26.6806	−	8.66905i	−0.921116	−	0.299289i	−0.730925	+	0.682458i	$0.760911\pi$
$840$	2.69312	−	5.75049i	0.0929216	−	0.198411i
$841$	12.7188	+	9.24076i	0.438580	+	0.318647i
$842$	−11.5047	+	11.5047i	−0.396477	+	0.396477i
$843$	−2.13563	+	2.13563i	−0.0735550	+	0.0735550i
$844$	−9.47589	+	13.0424i	−0.326174	+	0.448940i
$845$	−11.5089	+	8.96102i	−0.395918	+	0.308269i
$846$	−4.38996	+	3.18949i	−0.150930	+	0.109657i
$847$	14.0751	+	27.6240i	0.483627	+	0.949172i
$848$	0.0926515	−	0.0146746i	0.00318167	−	0.000503926i
$849$	−1.67720	+	5.16190i	−0.0575615	+	0.177156i
$850$	−6.52275	−	16.2999i	−0.223728	−	0.559082i
$851$	−11.3808	+	8.26862i	−0.390128	+	0.283445i
$852$	−4.75394	+	9.33013i	−0.162867	+	0.319645i
$853$	−11.0955	+	21.7761i	−0.379903	+	0.745601i	−0.999218	−	0.0395413i	$-0.987410\pi$
$853$	−11.0955	+	21.7761i	−0.379903	+	0.745601i	0.619315	+	0.785142i	$0.287410\pi$
$854$	20.1873	−	14.6670i	0.690796	−	0.501893i
$855$	−12.1664	+	4.40536i	−0.416082	+	0.150660i
$856$	−2.46753	+	7.59427i	−0.0843383	+	0.259567i
$857$	−26.0205	+	4.12125i	−0.888844	+	0.140779i	−0.584126	−	0.811663i	$-0.698562\pi$
$857$	−26.0205	+	4.12125i	−0.888844	+	0.140779i	−0.304719	+	0.952442i	$0.598562\pi$
$858$	0.331793	+	0.651181i	0.0113272	+	0.0222310i
$859$	−12.6651	+	9.20172i	−0.432127	+	0.313959i	−0.782499	−	0.622652i	$-0.786055\pi$
$859$	−12.6651	+	9.20172i	−0.432127	+	0.313959i	0.350372	+	0.936611i	$0.386055\pi$
$860$	−0.0276937	+	0.222494i	−0.000944348	+	0.00758699i
$861$	−11.2555	+	15.4918i	−0.383585	+	0.527960i
$862$	−9.77276	+	9.77276i	−0.332862	+	0.332862i
$863$	−16.6311	+	16.6311i	−0.566130	+	0.566130i	−0.931042	−	0.364912i	$-0.881099\pi$
$863$	−16.6311	+	16.6311i	−0.566130	+	0.566130i	0.364912	+	0.931042i	$0.381099\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	38.1113	+	17.8486i	1.29582	+	0.606872i
$866$	4.73695	+	1.53913i	0.160968	+	0.0523017i
$867$	3.30266	+	3.30266i	0.112164	+	0.112164i
$868$	2.07887	+	15.6738i	0.0705614	+	0.532004i
$869$		−	3.94639i		−	0.133872i
$870$	−2.25895	+	7.82883i	−0.0765855	+	0.265422i
$871$	5.61223	−	1.82352i	0.190163	−	0.0617877i
$872$	5.59650	−	0.886399i	0.189521	−	0.0300173i
$873$	−10.7708	−	10.7708i	−0.364535	−	0.364535i
$874$	−28.0598			−0.949136
$875$	8.06459	+	30.7081i	0.272633	+	1.03812i
$876$	−3.11082	+	2.26015i	−0.105105	+	0.0763632i
$877$	5.14913	−	32.5104i	0.173874	−	1.09780i	−0.734184	−	0.678951i	$-0.762435\pi$
$877$	5.14913	−	32.5104i	0.173874	−	1.09780i	0.908057	−	0.418846i	$-0.137565\pi$
$878$	27.8457	−	14.1881i	0.939748	−	0.478826i
$879$	−16.8378	−	12.2334i	−0.567924	−	0.412621i
$880$	−0.178019	+	0.616960i	−0.00600102	+	0.0207977i
$881$	−0.563164	+	0.182983i	−0.0189735	+	0.00616486i	−0.318488	−	0.947927i	$-0.603175\pi$
$881$	−0.563164	+	0.182983i	−0.0189735	+	0.00616486i	0.299515	+	0.954092i	$0.403175\pi$
$882$	−0.166480	+	1.05111i	−0.00560567	+	0.0353928i
$883$	20.2581	+	10.3220i	0.681740	+	0.347364i	0.760324	−	0.649544i	$-0.225040\pi$
$883$	20.2581	+	10.3220i	0.681740	+	0.347364i	−0.0785844	+	0.996907i	$0.525040\pi$
$884$	8.49883	−	2.76144i	0.285847	−	0.0928772i
$885$	−3.66643	+	29.4565i	−0.123246	+	0.990168i
$886$	2.73325	+	8.41208i	0.0918253	+	0.282609i
$887$	7.17723	+	14.0861i	0.240988	+	0.472965i	0.979545	−	0.201226i	$-0.0644925\pi$
$887$	7.17723	+	14.0861i	0.240988	+	0.472965i	−0.738557	+	0.674191i	$0.764492\pi$
$888$	−0.453829	−	2.86537i	−0.0152295	−	0.0961554i
$889$	1.69653	−	5.22137i	0.0568997	−	0.175119i
$890$	19.7206	+	2.45461i	0.661036	+	0.0822787i
$891$	0.168794	+	0.232325i	0.00565480	+	0.00778317i
$892$	−0.111690	−	0.705182i	−0.00373966	−	0.0236113i
$893$	−22.2033	−	22.2033i	−0.743005	−	0.743005i
$894$	−8.57473			−0.286782
$895$	−21.9349	+	32.4037i	−0.733203	+	1.08314i
$896$	0.877533	+	2.70077i	0.0293163	+	0.0902263i
$897$	10.9956	−	5.60253i	0.367132	−	0.187063i
$898$	17.2403	−	17.2403i	0.575315	−	0.575315i
$899$	−5.78110	−	19.4478i	−0.192811	−	0.648621i
$900$	4.98895	−	0.332227i	0.166298	−	0.0110742i
$901$	−0.101785	+	0.313263i	−0.00339096	+	0.0104363i
$902$	0.879120	−	1.72537i	0.0292715	−	0.0574485i
$903$	−0.0445436	−	0.281238i	−0.00148232	−	0.00935900i
$904$		−	9.37507i		−	0.311810i
$905$	26.5873	−	0.884277i	0.883791	−	0.0293944i
$906$	−0.0387108	−	0.0281251i	−0.00128608	−	0.000934393i
$907$	−2.35589	+	14.8745i	−0.0782260	+	0.493899i	0.917205	+	0.398416i	$0.130440\pi$
$907$	−2.35589	+	14.8745i	−0.0782260	+	0.493899i	−0.995431	+	0.0954838i	$0.969560\pi$
$908$	−12.6586	−	2.00492i	−0.420089	−	0.0665355i
$909$	5.74733	+	1.86742i	0.190627	+	0.0619385i
$910$	−15.8685	+	3.05720i	−0.526035	+	0.101345i
$911$	21.6261	+	7.02676i	0.716506	+	0.232807i	0.644508	−	0.764598i	$-0.277062\pi$
$911$	21.6261	+	7.02676i	0.716506	+	0.232807i	0.0719984	+	0.997405i	$0.477062\pi$
$912$	2.62710	−	5.15597i	0.0869920	−	0.170731i
$913$	0.403086	+	0.0638426i	0.0133402	+	0.00211288i
$914$	6.38254	+	19.6434i	0.211116	+	0.649747i
$915$	17.7936	+	8.33327i	0.588239	+	0.275490i
$916$	−7.97408	−	10.9754i	−0.263471	−	0.362637i
$917$	−14.8934	−	7.58854i	−0.491822	−	0.250596i
$918$	3.12860	−	1.59410i	0.103259	−	0.0526133i
$919$	−32.8159	+	45.1672i	−1.08250	+	1.48993i	−0.225756	+	0.974184i	$0.572485\pi$
$919$	−32.8159	+	45.1672i	−1.08250	+	1.48993i	−0.856742	+	0.515746i	$0.827515\pi$
$920$	10.4177	+	3.00596i	0.343463	+	0.0991035i
$921$	−6.64604	−	9.14749i	−0.218994	−	0.301420i
$922$	27.1916	+	4.30672i	0.895506	+	0.141834i
$923$	26.3215	−	4.16891i	0.866382	−	0.137221i
$924$		−	0.815490i		−	0.0268277i
$925$	10.9157	+	9.55269i	0.358907	+	0.314090i
$926$	22.8112	−	31.3970i	0.749623	−	1.03177i
$927$	−0.799318	−	0.407273i	−0.0262530	−	0.0133766i
$928$	−1.65434	−	3.24682i	−0.0543063	−	0.106582i
$929$	−39.8763			−1.30830			−0.654150	−	0.756365i	$-0.726974\pi$
$929$	−39.8763			−1.30830			−0.654150	+	0.756365i	$0.726974\pi$
$930$	−10.0131	+	7.39852i	−0.328342	+	0.242607i
$931$	−6.15828			−0.201829
$932$	−8.40150	−	16.4889i	−0.275200	−	0.540111i
$933$	20.9990	+	10.6995i	0.687476	+	0.350287i
$934$	−11.9530	+	16.4519i	−0.391114	+	0.538323i
$935$	−1.64644	−	1.54045i	−0.0538444	−	0.0503781i
$936$			2.54497i			0.0831851i
$937$	33.1763	−	5.25460i	1.08382	−	0.171660i	0.411125	−	0.911579i	$-0.365136\pi$
$937$	33.1763	−	5.25460i	1.08382	−	0.171660i	0.672696	+	0.739919i	$0.265136\pi$
$938$	−6.50349	−	1.03005i	−0.212346	−	0.0336324i
$939$	−2.03690	−	2.80356i	−0.0664718	−	0.0914906i
$940$	5.86484	+	10.6220i	0.191290	+	0.346451i
$941$	−13.8777	+	19.1010i	−0.452400	+	0.622675i	−0.972911	−	0.231180i	$-0.925741\pi$
$941$	−13.8777	+	19.1010i	−0.452400	+	0.622675i	0.520511	+	0.853855i	$0.325741\pi$
$942$	7.65133	−	3.89855i	0.249294	−	0.127021i
$943$	−29.1339	−	14.8445i	−0.948731	−	0.483403i
$944$	−7.80284	−	10.7397i	−0.253961	−	0.349547i
$945$	−5.97054	+	2.16188i	−0.194222	+	0.0703261i
$946$	0.00889800	+	0.0273852i	0.000289299	+	0.000890370i
$947$	41.3159	+	6.54380i	1.34259	+	0.212645i	0.786043	−	0.618172i	$-0.212127\pi$
$947$	41.3159	+	6.54380i	1.34259	+	0.212645i	0.556545	+	0.830817i	$0.312127\pi$
$948$	6.23891	−	12.2446i	0.202630	−	0.397685i
$949$	9.30695	+	3.02401i	0.302116	+	0.0981635i
$950$	6.41500	+	28.2133i	0.208130	+	0.915361i
$951$	28.3615	+	9.21521i	0.919685	+	0.298824i
$952$	−9.84851	−	1.55985i	−0.319192	−	0.0505551i
$953$	5.85802	−	36.9861i	0.189760	−	1.19810i	−0.690403	−	0.723425i	$-0.742567\pi$
$953$	5.85802	−	36.9861i	0.189760	−	1.19810i	0.880163	−	0.474672i	$-0.157433\pi$
$954$	−0.0758910	−	0.0551380i	−0.00245706	−	0.00178516i
$955$	−1.47437	−	44.3294i	−0.0477095	−	1.43447i
$956$			24.5479i			0.793936i
$957$	0.163700	+	1.03356i	0.00529166	+	0.0334102i
$958$	−6.40117	+	12.5630i	−0.206812	+	0.405892i
$959$	−10.4611	+	32.1958i	−0.337805	+	1.03966i
$960$	−1.52771	+	1.63282i	−0.0493065	+	0.0526992i
$961$	11.0536	−	28.9624i	0.356568	−	0.934269i
$962$	−5.22070	+	5.22070i	−0.168322	+	0.168322i
$963$	7.11476	−	3.62515i	0.229270	−	0.116819i
$964$	0.527458	+	1.62335i	0.0169883	+	0.0522846i
$965$	48.5564	−	9.35482i	1.56309	−	0.301142i
$966$	−13.7700			−0.443044
$967$	16.9835	+	16.9835i	0.546151	+	0.546151i	0.925325	−	0.379174i	$-0.123792\pi$
$967$	16.9835	+	16.9835i	0.546151	+	0.546151i	−0.379174	+	0.925325i	$0.623792\pi$
$968$	−1.70788	−	10.7831i	−0.0548933	−	0.346583i
$969$	11.9431	+	16.4383i	0.383669	+	0.528075i
$970$	−26.8745	+	20.9249i	−0.862888	+	0.671859i
$971$	5.83115	−	17.9464i	0.187131	−	0.575928i	−0.812848	−	0.582476i	$-0.802084\pi$
$971$	5.83115	−	17.9464i	0.187131	−	0.575928i	0.999979	+	0.00654730i	$0.00208409\pi$
$972$	0.156434	+	0.987688i	0.00501764	+	0.0316801i
$973$	15.6301	+	30.6758i	0.501078	+	0.983420i
$974$	0.795310	+	2.44771i	0.0254834	+	0.0784297i
$975$	−8.14699	−	9.77491i	−0.260913	−	0.313048i
$976$	−8.35693	+	2.71533i	−0.267499	+	0.0869156i
$977$	36.1941	+	18.4418i	1.15795	+	0.590005i	0.924056	−	0.382257i	$-0.124853\pi$
$977$	36.1941	+	18.4418i	1.15795	+	0.590005i	0.233895	+	0.972262i	$0.424853\pi$
$978$	−2.62398	+	16.5672i	−0.0839056	+	0.529759i
$979$	2.42727	−	0.788667i	0.0775758	−	0.0252059i
$980$	2.28638	+	0.659718i	0.0730358	+	0.0210739i
$981$	−4.58410	−	3.33055i	−0.146359	−	0.106336i
$982$	22.1058	−	11.2635i	0.705424	−	0.359431i
$983$	−1.45710	+	9.19977i	−0.0464743	+	0.293427i	−0.999968	−	0.00798550i	$-0.997458\pi$
$983$	−1.45710	+	9.19977i	−0.0464743	+	0.293427i	0.953494	+	0.301412i	$0.0974581\pi$
$984$	5.45534	−	3.96353i	0.173910	−	0.126353i
$985$	33.2316	−	6.40236i	1.05885	−	0.203996i
$986$	12.7952			0.407482
$987$	−10.8960	−	10.8960i	−0.346825	−	0.346825i
$988$	−14.5456	+	2.30380i	−0.462759	+	0.0732938i
$989$	0.462416	−	0.150248i	0.0147040	−	0.00477761i
$990$	0.562135	−	0.310378i	0.0178658	−	0.00986447i
$991$			28.0982i			0.892569i	0.894891	+	0.446285i	$0.147253\pi$
$991$			28.0982i			0.892569i	−0.894891	+	0.446285i	$0.852747\pi$
$992$	1.00937	−	5.47551i	0.0320475	−	0.173848i
$993$	9.13087	+	9.13087i	0.289759	+	0.289759i
$994$	−28.2810	−	9.18904i	−0.897018	−	0.291459i
$995$	−31.4978	+	11.4051i	−0.998547	+	0.361566i
$996$	1.14974	+	0.835332i	0.0364308	+	0.0264685i
$997$	−24.7784	+	24.7784i	−0.784739	+	0.784739i	−0.980626	−	0.195887i	$-0.937241\pi$
$997$	−24.7784	+	24.7784i	−0.784739	+	0.784739i	0.195887	+	0.980626i	$0.437241\pi$
$998$	−18.7193	+	18.7193i	−0.592549	+	0.592549i
$999$	−1.70521	+	2.34703i	−0.0539506	+	0.0742566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bj.b.643.12	yes	128
5.2	odd	4		930.2.bj.a.457.4	✓	128
31.27	odd	10		930.2.bj.a.523.4	yes	128
155.27	even	20	inner	930.2.bj.b.337.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bj.a.457.4	✓	128	5.2	odd	4
930.2.bj.a.523.4	yes	128	31.27	odd	10
930.2.bj.b.337.12	yes	128	155.27	even	20	inner
930.2.bj.b.643.12	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.0743292 - 2.23483i) q^{5} -1.00000i q^{6} +(2.80479 - 0.444236i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.0743292 - 2.23483i) q^{5} -1.00000i q^{6} +(2.80479 - 0.444236i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.95751 - 1.08082i) q^{10} +(0.168794 - 0.232325i) q^{11} +(0.891007 - 0.453990i) q^{12} +(-2.26759 - 1.15539i) q^{13} +(1.66917 + 2.29741i) q^{14} +(-0.948365 + 2.02499i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.46808 + 0.549291i) q^{17} +(-0.453990 + 0.891007i) q^{18} +(-5.50346 - 1.78818i) q^{19} +(1.85171 + 1.25347i) q^{20} +(-2.70077 - 0.877533i) q^{21} +(0.283633 + 0.0449231i) q^{22} +(0.758554 - 4.78932i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.98895 + 0.332227i) q^{25} -2.54497i q^{26} +(-0.156434 - 0.987688i) q^{27} +(-1.28922 + 2.53024i) q^{28} +(1.12606 - 3.46564i) q^{29} +(-2.23483 + 0.0743292i) q^{30} +(4.58550 - 3.15804i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.255869 + 0.130372i) q^{33} +(1.08506 + 3.33946i) q^{34} +(-1.20127 - 6.23522i) q^{35} -1.00000 q^{36} +(-2.05138 - 2.05138i) q^{37} +(-0.905237 - 5.71544i) q^{38} +(1.49590 + 2.05893i) q^{39} +(-0.276191 + 2.21895i) q^{40} +(2.08375 - 6.41313i) q^{41} +(-0.444236 - 2.80479i) q^{42} +(0.0455218 + 0.0893415i) q^{43} +(0.0887401 + 0.273114i) q^{44} +(1.76433 - 1.37374i) q^{45} +(4.61169 - 1.49843i) q^{46} +(4.83486 + 2.46348i) q^{47} +(-0.156434 + 0.987688i) q^{48} +(1.01213 - 0.328861i) q^{49} +(-2.56095 - 4.29436i) q^{50} +(-2.84071 - 2.06390i) q^{51} +(2.26759 - 1.15539i) q^{52} +(-0.0146746 + 0.0926515i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.531753 - 0.359957i) q^{55} -2.83976 q^{56} +(4.09180 + 4.09180i) q^{57} +(3.59913 - 0.570046i) q^{58} +(12.6253 - 4.10220i) q^{59} +(-1.08082 - 1.95751i) q^{60} -8.78699i q^{61} +(4.89560 + 2.65199i) q^{62} +(2.00801 + 2.00801i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.41356 + 5.15356i) q^{65} +(-0.232325 - 0.168794i) q^{66} +(-1.63957 + 1.63957i) q^{67} +(-2.48287 + 2.48287i) q^{68} +(-2.85018 + 3.92294i) q^{69} +(5.01026 - 3.90107i) q^{70} +(-8.47158 + 6.15496i) q^{71} +(-0.453990 - 0.891007i) q^{72} +(-3.79785 + 0.601520i) q^{73} +(0.896484 - 2.75909i) q^{74} +(4.59602 + 1.96892i) q^{75} +(4.68153 - 3.40133i) q^{76} +(0.370225 - 0.726607i) q^{77} +(-1.15539 + 2.26759i) q^{78} +(11.1178 - 8.07757i) q^{79} +(-2.10248 + 0.761292i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(6.66015 - 1.05486i) q^{82} +(0.645189 + 1.26626i) q^{83} +(2.29741 - 1.66917i) q^{84} +(0.969792 - 7.79142i) q^{85} +(-0.0589374 + 0.0811204i) q^{86} +(-2.57669 + 2.57669i) q^{87} +(-0.203059 + 0.203059i) q^{88} +(7.19004 + 5.22387i) q^{89} +(2.02499 + 0.948365i) q^{90} +(-6.87339 - 2.23330i) q^{91} +(3.42878 + 3.42878i) q^{92} +(-5.51943 + 0.732059i) q^{93} +5.42629i q^{94} +(-3.58722 + 12.4322i) q^{95} +(-0.951057 + 0.309017i) q^{96} +(-15.0446 + 2.38283i) q^{97} +(0.752514 + 0.752514i) q^{98} +0.287169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{7}+O(q^{10}) \) 128 * q + 4 * q^7	\( 128 q + 4 q^{7} - 4 q^{10} - 4 q^{15} + 32 q^{16} + 12 q^{17} + 40 q^{19} + 40 q^{21} + 4 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{28} - 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} - 64 q^{37} - 16 q^{38} - 24 q^{41} + 16 q^{42} - 24 q^{43} + 8 q^{44} + 20 q^{46} - 12 q^{47} + 100 q^{49} - 24 q^{50} + 64 q^{53} + 32 q^{54} + 68 q^{55} - 16 q^{57} + 40 q^{58} + 8 q^{62} - 4 q^{63} + 84 q^{65} - 12 q^{66} - 32 q^{67} - 8 q^{68} + 88 q^{70} + 24 q^{71} + 20 q^{73} + 16 q^{74} - 24 q^{75} - 24 q^{76} + 60 q^{77} + 56 q^{79} + 32 q^{81} - 16 q^{82} + 8 q^{83} - 68 q^{85} - 20 q^{87} + 4 q^{88} - 136 q^{89} - 40 q^{91} + 48 q^{93} - 92 q^{95} + 64 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 128 * q + 4 * q^7 - 4 * q^10 - 4 * q^15 + 32 * q^16 + 12 * q^17 + 40 * q^19 + 40 * q^21 + 4 * q^22 + 32 * q^24 - 8 * q^25 - 4 * q^28 - 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 - 64 * q^37 - 16 * q^38 - 24 * q^41 + 16 * q^42 - 24 * q^43 + 8 * q^44 + 20 * q^46 - 12 * q^47 + 100 * q^49 - 24 * q^50 + 64 * q^53 + 32 * q^54 + 68 * q^55 - 16 * q^57 + 40 * q^58 + 8 * q^62 - 4 * q^63 + 84 * q^65 - 12 * q^66 - 32 * q^67 - 8 * q^68 + 88 * q^70 + 24 * q^71 + 20 * q^73 + 16 * q^74 - 24 * q^75 - 24 * q^76 + 60 * q^77 + 56 * q^79 + 32 * q^81 - 16 * q^82 + 8 * q^83 - 68 * q^85 - 20 * q^87 + 4 * q^88 - 136 * q^89 - 40 * q^91 + 48 * q^93 - 92 * q^95 + 64 * q^97 - 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more