LMFDB - Embedded newform 148.2.l.b.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [148,2,Mod(23,148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(148, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("148.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 148 = 2^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	148.l (of order $12$, degree $4$, 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:	$1.18178594991$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	148.103
Dual form			148.2.l.b.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27876 + 0.603964i) q^{2} +(-1.67719 + 2.90497i) q^{3} +(1.27045 - 1.54465i) q^{4} +(0.880766 + 3.28706i) q^{5} +(0.390219 - 4.72772i) q^{6} +(1.73451 + 1.00142i) q^{7} +(-0.691691 + 2.74255i) q^{8} +(-4.12591 - 7.14629i) q^{9} +O(q^{10})$	\(q+(-1.27876 + 0.603964i) q^{2} +(-1.67719 + 2.90497i) q^{3} +(1.27045 - 1.54465i) q^{4} +(0.880766 + 3.28706i) q^{5} +(0.390219 - 4.72772i) q^{6} +(1.73451 + 1.00142i) q^{7} +(-0.691691 + 2.74255i) q^{8} +(-4.12591 - 7.14629i) q^{9} +(-3.11156 - 3.67141i) q^{10} -1.10438 q^{11} +(2.35638 + 6.28130i) q^{12} +(-0.297754 - 1.11123i) q^{13} +(-2.82285 - 0.232994i) q^{14} +(-11.0260 - 2.95442i) q^{15} +(-0.771894 - 3.92482i) q^{16} +(0.152704 + 0.0409170i) q^{17} +(9.59215 + 6.64648i) q^{18} +(4.03499 - 1.08117i) q^{19} +(6.19634 + 2.81559i) q^{20} +(-5.81820 + 3.35914i) q^{21} +(1.41224 - 0.667007i) q^{22} +(-0.236543 - 0.236543i) q^{23} +(-6.80693 - 6.60911i) q^{24} +(-5.69891 + 3.29027i) q^{25} +(1.05190 + 1.24117i) q^{26} +17.6166 q^{27} +(3.75046 - 1.40696i) q^{28} +(2.64791 + 2.64791i) q^{29} +(15.8840 - 2.88134i) q^{30} +(-2.34186 + 2.34186i) q^{31} +(3.35752 + 4.55270i) q^{32} +(1.85225 - 3.20820i) q^{33} +(-0.219985 + 0.0399050i) q^{34} +(-1.76404 + 6.58347i) q^{35} +(-16.2803 - 2.70594i) q^{36} +(0.739562 + 6.03764i) q^{37} +(-4.50680 + 3.81955i) q^{38} +(3.72749 + 0.998778i) q^{39} +(-9.62414 + 0.141909i) q^{40} +(2.96460 + 1.71161i) q^{41} +(5.41128 - 7.80952i) q^{42} +(-3.84821 - 3.84821i) q^{43} +(-1.40307 + 1.70588i) q^{44} +(19.8563 - 19.8563i) q^{45} +(0.445345 + 0.159618i) q^{46} -3.15854i q^{47} +(12.6961 + 4.34032i) q^{48} +(-1.49431 - 2.58822i) q^{49} +(5.30033 - 7.64940i) q^{50} +(-0.374976 + 0.374976i) q^{51} +(-2.09475 - 0.951845i) q^{52} +(-1.49203 - 2.58428i) q^{53} +(-22.5274 + 10.6398i) q^{54} +(-0.972702 - 3.63017i) q^{55} +(-3.94619 + 4.06431i) q^{56} +(-3.62666 + 13.5349i) q^{57} +(-4.98529 - 1.78680i) q^{58} +(-2.80065 + 10.4522i) q^{59} +(-18.5716 + 13.2779i) q^{60} +(5.69761 - 1.52667i) q^{61} +(1.58028 - 4.40908i) q^{62} -16.5271i q^{63} +(-7.04313 - 3.79399i) q^{64} +(3.39044 - 1.95747i) q^{65} +(-0.430951 + 5.22121i) q^{66} +(-3.95553 + 6.85118i) q^{67} +(0.257206 - 0.183892i) q^{68} +(1.08388 - 0.290424i) q^{69} +(-1.72040 - 9.48409i) q^{70} +(0.339798 + 0.196183i) q^{71} +(22.4529 - 6.37248i) q^{72} +14.7805i q^{73} +(-4.59224 - 7.27402i) q^{74} -22.0736i q^{75} +(3.45624 - 7.60624i) q^{76} +(-1.91556 - 1.10595i) q^{77} +(-5.36979 + 0.974075i) q^{78} +(8.07109 - 2.16264i) q^{79} +(12.2213 - 5.99411i) q^{80} +(-17.1685 + 29.7368i) q^{81} +(-4.82476 - 0.398228i) q^{82} +(-2.06154 + 1.19023i) q^{83} +(-2.20306 + 13.2547i) q^{84} +0.537987i q^{85} +(7.24512 + 2.59676i) q^{86} +(-12.1332 + 3.25107i) q^{87} +(0.763891 - 3.02882i) q^{88} +(3.99470 - 14.9084i) q^{89} +(-13.3990 + 37.3840i) q^{90} +(0.596354 - 2.22563i) q^{91} +(-0.665893 + 0.0648594i) q^{92} +(-2.87530 - 10.7308i) q^{93} +(1.90764 + 4.03901i) q^{94} +(7.10777 + 12.3110i) q^{95} +(-18.8567 + 2.11776i) q^{96} +(3.66478 - 3.66478i) q^{97} +(3.47406 + 2.40720i) q^{98} +(4.55658 + 7.89223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{2} - 4 q^{5} + 8 q^{8} - 36 q^{9}+O(q^{10}) $ 64 * q - 4 * q^2 - 4 * q^5 + 8 * q^8 - 36 * q^9	$ 64 q - 4 q^{2} - 4 q^{5} + 8 q^{8} - 36 q^{9} + 4 q^{10} + 10 q^{12} - 28 q^{13} + 4 q^{14} - 20 q^{16} - 36 q^{17} + 44 q^{18} - 26 q^{20} - 12 q^{21} - 4 q^{22} - 22 q^{24} - 24 q^{25} + 32 q^{26} - 6 q^{28} + 4 q^{29} + 54 q^{30} + 16 q^{32} - 16 q^{33} + 8 q^{34} + 20 q^{37} - 112 q^{38} - 18 q^{40} + 12 q^{41} - 44 q^{42} - 32 q^{44} + 20 q^{45} + 46 q^{46} + 44 q^{49} - 72 q^{50} - 52 q^{52} + 4 q^{53} - 44 q^{54} - 46 q^{56} + 28 q^{57} + 30 q^{58} + 8 q^{60} + 24 q^{61} + 24 q^{62} + 72 q^{65} + 8 q^{66} + 64 q^{68} + 28 q^{69} + 50 q^{70} + 128 q^{72} - 8 q^{74} + 52 q^{76} - 144 q^{77} + 36 q^{78} + 40 q^{80} - 24 q^{82} + 104 q^{84} - 6 q^{86} - 44 q^{88} + 4 q^{89} + 62 q^{90} - 142 q^{92} + 92 q^{93} + 28 q^{94} + 70 q^{96} - 12 q^{97} + 24 q^{98}+O(q^{100}) $ 64 * q - 4 * q^2 - 4 * q^5 + 8 * q^8 - 36 * q^9 + 4 * q^10 + 10 * q^12 - 28 * q^13 + 4 * q^14 - 20 * q^16 - 36 * q^17 + 44 * q^18 - 26 * q^20 - 12 * q^21 - 4 * q^22 - 22 * q^24 - 24 * q^25 + 32 * q^26 - 6 * q^28 + 4 * q^29 + 54 * q^30 + 16 * q^32 - 16 * q^33 + 8 * q^34 + 20 * q^37 - 112 * q^38 - 18 * q^40 + 12 * q^41 - 44 * q^42 - 32 * q^44 + 20 * q^45 + 46 * q^46 + 44 * q^49 - 72 * q^50 - 52 * q^52 + 4 * q^53 - 44 * q^54 - 46 * q^56 + 28 * q^57 + 30 * q^58 + 8 * q^60 + 24 * q^61 + 24 * q^62 + 72 * q^65 + 8 * q^66 + 64 * q^68 + 28 * q^69 + 50 * q^70 + 128 * q^72 - 8 * q^74 + 52 * q^76 - 144 * q^77 + 36 * q^78 + 40 * q^80 - 24 * q^82 + 104 * q^84 - 6 * q^86 - 44 * q^88 + 4 * q^89 + 62 * q^90 - 142 * q^92 + 92 * q^93 + 28 * q^94 + 70 * q^96 - 12 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/148\mathbb{Z}\right)^\times$.

$n$	$75$	$113$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−1.27876	+	0.603964i	−0.904220	+	0.427067i
$2$	−1.27876	+	0.603964i	−0.904220	+	0.427067i
$3$	−1.67719	+	2.90497i	−0.968324	+	1.67719i	−0.267919	+	0.963441i	$0.586336\pi$
$3$	−1.67719	+	2.90497i	−0.968324	+	1.67719i	−0.700405	+	0.713745i	$0.746997\pi$
$4$	1.27045	−	1.54465i	0.635227	−	0.772326i
$5$	0.880766	+	3.28706i	0.393891	+	1.47002i	0.823662	+	0.567082i	$0.191928\pi$
$5$	0.880766	+	3.28706i	0.393891	+	1.47002i	−0.429771	+	0.902938i	$0.641406\pi$
$6$	0.390219	−	4.72772i	0.159306	−	1.93009i
$7$	1.73451	+	1.00142i	0.655584	+	0.378502i	0.790592	−	0.612343i	$-0.209773\pi$
$7$	1.73451	+	1.00142i	0.655584	+	0.378502i	−0.135008	+	0.990844i	$0.543106\pi$
$8$	−0.691691	+	2.74255i	−0.244550	+	0.969637i
$9$	−4.12591	−	7.14629i	−1.37530	−	2.38210i
$10$	−3.11156	−	3.67141i	−0.983961	−	1.16100i
$11$	−1.10438			−0.332984			−0.166492	−	0.986043i	$-0.553244\pi$
$11$	−1.10438			−0.332984			−0.166492	+	0.986043i	$0.553244\pi$
$12$	2.35638	+	6.28130i	0.680228	+	1.81326i
$13$	−0.297754	−	1.11123i	−0.0825821	−	0.308201i	0.912263	−	0.409604i	$-0.134333\pi$
$13$	−0.297754	−	1.11123i	−0.0825821	−	0.308201i	−0.994845	+	0.101404i	$0.967667\pi$
$14$	−2.82285	−	0.232994i	−0.754438	−	0.0622701i
$15$	−11.0260	−	2.95442i	−2.84691	−	0.762827i
$16$	−0.771894	−	3.92482i	−0.192973	−	0.981204i
$17$	0.152704	+	0.0409170i	0.0370362	+	0.00992383i	0.277290	−	0.960786i	$-0.410564\pi$
$17$	0.152704	+	0.0409170i	0.0370362	+	0.00992383i	−0.240253	+	0.970710i	$0.577231\pi$
$18$	9.59215	+	6.64648i	2.26089	+	1.56659i
$19$	4.03499	−	1.08117i	0.925691	−	0.248038i	0.235675	−	0.971832i	$-0.424270\pi$
$19$	4.03499	−	1.08117i	0.925691	−	0.248038i	0.690016	+	0.723794i	$0.257603\pi$
$20$	6.19634	+	2.81559i	1.38554	+	0.629584i
$21$	−5.81820	+	3.35914i	−1.26964	+	0.733025i
$22$	1.41224	−	0.667007i	0.301090	−	0.142206i
$23$	−0.236543	−	0.236543i	−0.0493226	−	0.0493226i	0.682015	−	0.731338i	$-0.261104\pi$
$23$	−0.236543	−	0.236543i	−0.0493226	−	0.0493226i	−0.731338	+	0.682015i	$0.761104\pi$
$24$	−6.80693	−	6.60911i	−1.38946	−	1.34908i
$25$	−5.69891	+	3.29027i	−1.13978	+	0.658053i
$26$	1.05190	+	1.24117i	0.206295	+	0.243413i
$27$	17.6166			3.39031
$28$	3.75046	−	1.40696i	0.708771	−	0.265890i
$29$	2.64791	+	2.64791i	0.491705	+	0.491705i	0.908843	−	0.417138i	$-0.136967\pi$
$29$	2.64791	+	2.64791i	0.491705	+	0.491705i	−0.417138	+	0.908843i	$0.636967\pi$
$30$	15.8840	−	2.88134i	2.90001	−	0.526059i
$31$	−2.34186	+	2.34186i	−0.420611	+	0.420611i	−0.885414	−	0.464803i	$-0.846125\pi$
$31$	−2.34186	+	2.34186i	−0.420611	+	0.420611i	0.464803	+	0.885414i	$0.346125\pi$
$32$	3.35752	+	4.55270i	0.593531	+	0.804811i
$33$	1.85225	−	3.20820i	0.322436	−	0.558476i
$34$	−0.219985	+	0.0399050i	−0.0377270	+	0.00684364i
$35$	−1.76404	+	6.58347i	−0.298176	+	1.11281i
$36$	−16.2803	−	2.70594i	−2.71338	−	0.450989i
$37$	0.739562	+	6.03764i	0.121583	+	0.992581i
$37$	0.739562	+	6.03764i	0.121583	+	0.992581i
$38$	−4.50680	+	3.81955i	−0.731099	+	0.619613i
$39$	3.72749	+	0.998778i	0.596876	+	0.159933i
$40$	−9.62414	+	0.141909i	−1.52171	+	0.0224378i
$41$	2.96460	+	1.71161i	0.462992	+	0.267309i	0.713302	−	0.700857i	$-0.247199\pi$
$41$	2.96460	+	1.71161i	0.462992	+	0.267309i	−0.250309	+	0.968166i	$0.580532\pi$
$42$	5.41128	−	7.80952i	0.834979	−	1.20504i
$43$	−3.84821	−	3.84821i	−0.586847	−	0.586847i	0.349929	−	0.936776i	$-0.386206\pi$
$43$	−3.84821	−	3.84821i	−0.586847	−	0.586847i	−0.936776	+	0.349929i	$0.886206\pi$
$44$	−1.40307	+	1.70588i	−0.211520	+	0.257172i
$45$	19.8563	−	19.8563i	2.96001	−	2.96001i
$46$	0.445345	+	0.159618i	0.0656625	+	0.0235344i
$47$		−	3.15854i		−	0.460720i	−0.973105	−	0.230360i	$-0.926010\pi$
$47$		−	3.15854i		−	0.460720i	0.973105	−	0.230360i	$-0.0739904\pi$
$48$	12.6961	+	4.34032i	1.83252	+	0.626471i
$49$	−1.49431	−	2.58822i	−0.213473	−	0.369746i
$50$	5.30033	−	7.64940i	0.749580	−	1.08179i
$51$	−0.374976	+	0.374976i	−0.0525072	+	0.0525072i
$52$	−2.09475	−	0.951845i	−0.290490	−	0.131997i
$53$	−1.49203	−	2.58428i	−0.204946	−	0.354977i	0.745169	−	0.666875i	$-0.232369\pi$
$53$	−1.49203	−	2.58428i	−0.204946	−	0.354977i	−0.950116	+	0.311898i	$0.899035\pi$
$54$	−22.5274	+	10.6398i	−3.06559	+	1.44789i
$55$	−0.972702	−	3.63017i	−0.131159	−	0.489492i
$56$	−3.94619	+	4.06431i	−0.527332	+	0.543116i
$57$	−3.62666	+	13.5349i	−0.480363	+	1.79274i
$58$	−4.98529	−	1.78680i	−0.654601	−	0.234618i
$59$	−2.80065	+	10.4522i	−0.364614	+	1.36076i	0.503330	+	0.864094i	$0.332108\pi$
$59$	−2.80065	+	10.4522i	−0.364614	+	1.36076i	−0.867944	+	0.496662i	$0.834559\pi$
$60$	−18.5716	+	13.2779i	−2.39759	+	1.71417i
$61$	5.69761	−	1.52667i	0.729504	−	0.195470i	0.125096	−	0.992145i	$-0.460076\pi$
$61$	5.69761	−	1.52667i	0.729504	−	0.195470i	0.604408	+	0.796675i	$0.293410\pi$
$62$	1.58028	−	4.40908i	0.200695	−	0.559953i
$63$		−	16.5271i		−	2.08222i
$64$	−7.04313	−	3.79399i	−0.880391	−	0.474249i
$65$	3.39044	−	1.95747i	0.420533	−	0.242795i
$66$	−0.430951	+	5.22121i	−0.0530464	+	0.642687i
$67$	−3.95553	+	6.85118i	−0.483245	+	0.837005i	−0.999815	−	0.0192401i	$-0.993875\pi$
$67$	−3.95553	+	6.85118i	−0.483245	+	0.837005i	0.516570	+	0.856245i	$0.327209\pi$
$68$	0.257206	−	0.183892i	0.0311908	−	0.0223001i
$69$	1.08388	−	0.290424i	0.130483	−	0.0349629i
$70$	−1.72040	−	9.48409i	−0.205628	−	1.13357i
$71$	0.339798	+	0.196183i	0.0403266	+	0.0232826i	0.520028	−	0.854149i	$-0.325922\pi$
$71$	0.339798	+	0.196183i	0.0403266	+	0.0232826i	−0.479701	+	0.877432i	$0.659255\pi$
$72$	22.4529	−	6.37248i	2.64610	−	0.751004i
$73$			14.7805i			1.72993i	0.501834	+	0.864964i	$0.332659\pi$
$73$			14.7805i			1.72993i	−0.501834	+	0.864964i	$0.667341\pi$
$74$	−4.59224	−	7.27402i	−0.533837	−	0.845587i
$75$		−	22.0736i		−	2.54884i
$76$	3.45624	−	7.60624i	0.396458	−	0.872495i
$77$	−1.91556	−	1.10595i	−0.218299	−	0.126035i
$78$	−5.36979	+	0.974075i	−0.608009	+	0.110292i
$79$	8.07109	−	2.16264i	0.908069	−	0.243316i	0.225591	−	0.974222i	$-0.427569\pi$
$79$	8.07109	−	2.16264i	0.908069	−	0.243316i	0.682478	+	0.730906i	$0.260902\pi$
$80$	12.2213	−	5.99411i	1.36638	−	0.670162i
$81$	−17.1685	+	29.7368i	−1.90762	+	3.30409i
$82$	−4.82476	−	0.398228i	−0.532806	−	0.0439770i
$83$	−2.06154	+	1.19023i	−0.226283	+	0.130645i	−0.608856	−	0.793281i	$-0.708371\pi$
$83$	−2.06154	+	1.19023i	−0.226283	+	0.130645i	0.382573	+	0.923925i	$0.375038\pi$
$84$	−2.20306	+	13.2547i	−0.240373	+	1.44621i
$85$			0.537987i			0.0583529i
$86$	7.24512	+	2.59676i	0.781262	+	0.280015i
$87$	−12.1332	+	3.25107i	−1.30081	+	0.348551i
$88$	0.763891	−	3.02882i	0.0814311	−	0.322873i
$89$	3.99470	−	14.9084i	0.423437	−	1.58029i	−0.343876	−	0.939015i	$-0.611740\pi$
$89$	3.99470	−	14.9084i	0.423437	−	1.58029i	0.767313	−	0.641273i	$-0.221593\pi$
$90$	−13.3990	+	37.3840i	−1.41238	+	3.94062i
$91$	0.596354	−	2.22563i	0.0625149	−	0.233309i
$92$	−0.665893	+	0.0648594i	−0.0694241	+	0.00676206i
$93$	−2.87530	−	10.7308i	−0.298155	−	1.11273i
$94$	1.90764	+	4.03901i	0.196759	+	0.416592i
$95$	7.10777	+	12.3110i	0.729242	+	1.26308i
$96$	−18.8567	+	2.11776i	−1.92455	+	0.216143i
$97$	3.66478	−	3.66478i	0.372102	−	0.372102i	−0.496140	−	0.868242i	$-0.665250\pi$
$97$	3.66478	−	3.66478i	0.372102	−	0.372102i	0.868242	+	0.496140i	$0.165250\pi$
$98$	3.47406	+	2.40720i	0.350933	+	0.243164i
$99$	4.55658	+	7.89223i	0.457953	+	0.793199i
$100$	−2.15789	+	12.9830i	−0.215789	+	1.29830i
$101$		−	5.67393i		−	0.564578i	−0.959329	−	0.282289i	$-0.908906\pi$
$101$		−	5.67393i		−	0.564578i	0.959329	−	0.282289i	$-0.0910936\pi$
$102$	0.253032	−	0.705977i	0.0250539	−	0.0699022i
$103$	11.4925	−	11.4925i	1.13239	−	1.13239i	0.142609	−	0.989779i	$-0.454451\pi$
$103$	11.4925	−	11.4925i	1.13239	−	1.13239i	0.989779	−	0.142609i	$-0.0455492\pi$
$104$	3.25356	−	0.0479741i	0.319038	−	0.00470424i
$105$	−16.1662	−	16.1662i	−1.57766	−	1.57766i
$106$	3.46876	+	2.40353i	0.336916	+	0.233452i
$107$	−7.42823	−	4.28869i	−0.718114	−	0.414603i	0.0959442	−	0.995387i	$-0.469413\pi$
$107$	−7.42823	−	4.28869i	−0.718114	−	0.414603i	−0.814058	+	0.580783i	$0.802746\pi$
$108$	22.3810	−	27.2115i	2.15362	−	2.61842i
$109$	13.7744	+	3.69083i	1.31934	+	0.353517i	0.848732	−	0.528823i	$-0.177367\pi$
$109$	13.7744	+	3.69083i	1.31934	+	0.353517i	0.470612	+	0.882340i	$0.344033\pi$
$110$	3.43635	+	4.05464i	0.327643	+	0.386595i
$111$	−18.7796	−	7.97784i	−1.78248	−	0.757223i
$112$	2.59154	−	7.58063i	0.244877	−	0.716303i
$113$	−0.308304	+	1.15061i	−0.0290028	+	0.108240i	−0.978910	−	0.204293i	$-0.934511\pi$
$113$	−0.308304	+	1.15061i	−0.0290028	+	0.108240i	0.949907	+	0.312532i	$0.101177\pi$
$114$	−3.53696	−	19.4982i	−0.331266	−	1.82618i
$115$	0.569192	−	0.985870i	0.0530775	−	0.0919329i
$116$	7.45416	−	0.726050i	0.692101	−	0.0674121i
$117$	−6.71269	+	6.71269i	−0.620588	+	0.620588i
$118$	−2.73138	−	15.0573i	−0.251444	−	1.38614i
$119$	0.223892	+	0.223892i	0.0205242	+	0.0205242i
$120$	15.7292	−	28.1959i	1.43588	−	2.57392i
$121$	−9.78034			−0.889122
$122$	−6.36382	+	5.39340i	−0.576153	+	0.488295i
$123$	−9.94437	+	5.74138i	−0.896654	+	0.517683i
$124$	0.642131	+	6.59258i	0.0576651	+	0.592031i
$125$	−3.80324	−	3.80324i	−0.340172	−	0.340172i
$126$	9.98178	+	21.1342i	0.889248	+	1.88278i
$127$	12.9754	−	7.49136i	1.15138	−	0.664751i	0.202158	−	0.979353i	$-0.435204\pi$
$127$	12.9754	−	7.49136i	1.15138	−	0.664751i	0.949224	+	0.314602i	$0.101871\pi$
$128$	11.2979	+	0.597807i	0.998603	+	0.0528391i
$129$	17.6331	−	4.72478i	1.55251	−	0.415994i
$130$	−3.15332	+	4.55084i	−0.276564	+	0.399135i
$131$	1.53576	+	0.411506i	0.134180	+	0.0359535i	0.325284	−	0.945616i	$-0.394540\pi$
$131$	1.53576	+	0.411506i	0.134180	+	0.0359535i	−0.191104	+	0.981570i	$0.561207\pi$
$132$	−2.60234	−	6.93695i	−0.226505	−	0.603784i
$133$	8.08146	+	2.16542i	0.700751	+	0.187766i
$134$	0.920305	−	11.1500i	0.0795023	−	0.963215i
$135$	15.5161	+	57.9068i	1.33541	+	4.98382i
$136$	−0.217841	+	0.390497i	−0.0186797	+	0.0334848i
$137$	10.4009			0.888610			0.444305	−	0.895876i	$-0.353451\pi$
$137$	10.4009			0.888610			0.444305	+	0.895876i	$0.353451\pi$
$138$	−1.21061	+	1.02601i	−0.103054	+	0.0873394i
$139$	−2.41354	−	4.18038i	−0.204714	−	0.354575i	0.745327	−	0.666699i	$-0.232293\pi$
$139$	−2.41354	−	4.18038i	−0.204714	−	0.354575i	−0.950042	+	0.312123i	$0.898960\pi$
$140$	7.92804	+	11.0888i	0.670042	+	0.937176i
$141$	9.17547	+	5.29746i	0.772714	+	0.446127i
$142$	−0.553008	−	0.0456444i	−0.0464074	−	0.00383039i
$143$	0.328834	+	1.22723i	0.0274985	+	0.102626i
$144$	−24.8631	+	21.7096i	−2.07192	+	1.80913i
$145$	−6.37167	+	11.0361i	−0.529138	+	0.916494i
$146$	−8.92690	−	18.9007i	−0.738796	−	1.56424i
$147$	10.0250			0.826844
$148$	10.2656	+	6.52817i	0.843829	+	0.536613i
$149$	−16.0873			−1.31792			−0.658961	−	0.752177i	$-0.729004\pi$
$149$	−16.0873			−1.31792			−0.658961	+	0.752177i	$0.729004\pi$
$150$	13.3317	+	28.2268i	1.08852	+	2.30471i
$151$	−6.71118	+	11.6241i	−0.546148	+	0.945957i	0.452385	+	0.891823i	$0.350573\pi$
$151$	−6.71118	+	11.6241i	−0.546148	+	0.945957i	−0.998534	+	0.0541340i	$0.982760\pi$
$152$	0.174198	+	11.8140i	0.0141294	+	0.958242i
$153$	−0.337640	−	1.26009i	−0.0272966	−	0.101872i
$154$	3.11750	+	0.257314i	0.251215	+	0.0207349i
$155$	−9.76048	−	5.63521i	−0.783980	−	0.452631i
$156$	6.27837	−	4.48877i	0.502672	−	0.359389i
$157$	−4.30001	−	7.44784i	−0.343178	−	0.594402i	0.641843	−	0.766836i	$-0.278170\pi$
$157$	−4.30001	−	7.44784i	−0.343178	−	0.594402i	−0.985021	+	0.172434i	$0.944837\pi$
$158$	−9.01483	+	7.64015i	−0.717181	+	0.607818i
$159$	10.0097			0.793818
$160$	−12.0078	+	15.0462i	−0.949302	+	1.18951i
$161$	−0.173407	−	0.647166i	−0.0136664	−	0.0510038i
$162$	3.99448	−	48.3954i	0.313836	−	3.80230i
$163$	20.1985	+	5.41218i	1.58207	+	0.423914i	0.939566	−	0.342368i	$-0.111229\pi$
$163$	20.1985	+	5.41218i	1.58207	+	0.423914i	0.642504	+	0.766282i	$0.277896\pi$
$164$	6.41023	−	2.40475i	0.500555	−	0.187779i
$165$	12.1770	+	3.26280i	0.947974	+	0.254009i
$166$	1.91735	−	2.76711i	0.148816	−	0.214769i
$167$	−1.77269	+	0.474991i	−0.137175	+	0.0367559i	−0.326753	−	0.945110i	$-0.605955\pi$
$167$	−1.77269	+	0.474991i	−0.137175	+	0.0367559i	0.189578	+	0.981866i	$0.439288\pi$
$168$	−5.18820	−	18.2802i	−0.400278	−	1.41035i
$169$	10.1121	−	5.83825i	0.777858	−	0.449096i
$170$	−0.324925	−	0.687956i	−0.0249206	−	0.0527638i
$171$	−24.3744	−	24.3744i	−1.86396	−	1.86396i
$172$	−10.8331	+	1.05517i	−0.826018	+	0.0804558i
$173$	−15.3242	+	8.84743i	−1.16508	+	0.672657i	−0.952515	−	0.304490i	$-0.901514\pi$
$173$	−15.3242	+	8.84743i	−1.16508	+	0.672657i	−0.212561	+	0.977148i	$0.568181\pi$
$174$	13.5519	−	11.4853i	1.02736	−	0.870701i
$175$	−13.1798			−0.996297
$176$	0.852465	+	4.33449i	0.0642570	+	0.326725i
$177$	−25.6661	−	25.6661i	−1.92918	−	1.92918i
$178$	3.89589	+	21.4769i	0.292009	+	1.60976i
$179$	10.3799	−	10.3799i	0.775827	−	0.775827i	−0.203291	−	0.979118i	$-0.565164\pi$
$179$	10.3799	−	10.3799i	0.775827	−	0.775827i	0.979118	+	0.203291i	$0.0651637\pi$
$180$	−5.44455	−	55.8977i	−0.405813	−	4.16637i
$181$	5.18661	−	8.98347i	0.385518	−	0.667736i	−0.606323	−	0.795218i	$-0.707356\pi$
$181$	5.18661	−	8.98347i	0.385518	−	0.667736i	0.991841	+	0.127482i	$0.0406895\pi$
$182$	0.581604	+	3.20622i	0.0431114	+	0.237661i
$183$	−5.12102	+	19.1119i	−0.378557	+	1.41279i
$184$	0.812344	−	0.485115i	0.0598868	−	0.0357632i
$185$	−19.1947	+	7.74873i	−1.41122	+	0.569698i
$186$	10.1578	+	11.9855i	0.744808	+	0.878820i
$187$	−0.168644	−	0.0451880i	−0.0123325	−	0.00330447i
$188$	−4.87884	−	4.01278i	−0.355826	−	0.292662i
$189$	30.5562	+	17.6416i	2.22263	+	1.28324i
$190$	−16.5245	−	11.4500i	−1.19882	−	0.830670i
$191$	−3.79606	−	3.79606i	−0.274673	−	0.274673i	0.556305	−	0.830978i	$-0.312219\pi$
$191$	−3.79606	−	3.79606i	−0.274673	−	0.274673i	−0.830978	+	0.556305i	$0.812219\pi$
$192$	22.8341	−	14.0969i	1.64791	−	1.01735i
$193$	−13.6935	+	13.6935i	−0.985682	+	0.985682i	−0.999899	−	0.0142168i	$-0.995474\pi$
$193$	−13.6935	+	13.6935i	−0.985682	+	0.985682i	0.0142168	+	0.999899i	$0.495474\pi$
$194$	−2.47298	+	6.89977i	−0.177549	+	0.495375i
$195$			13.1322i			0.940416i
$196$	−5.89635	−	0.980028i	−0.421168	−	0.0700020i
$197$	−12.8171	−	22.1998i	−0.913178	−	1.58167i	−0.809547	−	0.587055i	$-0.800287\pi$
$197$	−12.8171	−	22.1998i	−0.913178	−	1.58167i	−0.103631	−	0.994616i	$-0.533046\pi$
$198$	−10.5934	−	7.34025i	−0.752840	−	0.521649i
$199$	12.5546	−	12.5546i	0.889969	−	0.889969i	−0.104551	−	0.994520i	$-0.533340\pi$
$199$	12.5546	−	12.5546i	0.889969	−	0.889969i	0.994520	+	0.104551i	$0.0333404\pi$
$200$	−5.08183	−	17.9054i	−0.359339	−	1.26610i
$201$	−13.2683	−	22.9814i	−0.935876	−	1.62098i
$202$	3.42685	+	7.25560i	0.241113	+	0.510502i
$203$	1.94116	+	7.24452i	0.136243	+	0.508465i
$204$	0.102817	+	1.05560i	0.00719866	+	0.0739067i
$205$	−3.01506	+	11.2524i	−0.210581	+	0.785898i
$206$	−7.75508	+	21.6372i	−0.540322	+	1.50753i
$207$	−0.714448	+	2.66636i	−0.0496576	+	0.185325i
$208$	−4.13155	+	2.02638i	−0.286472	+	0.140504i
$209$	−4.45617	+	1.19403i	−0.308240	+	0.0825926i
$210$	30.4365	+	10.9089i	2.10032	+	0.752783i
$211$			18.9327i			1.30338i	0.758484	+	0.651692i	$0.225940\pi$
$211$			18.9327i			1.30338i	−0.758484	+	0.651692i	$0.774060\pi$
$212$	−5.88736	−	0.978534i	−0.404346	−	0.0672060i
$213$	−1.13981	+	0.658070i	−0.0780985	+	0.0450902i
$214$	12.0891	+	0.997819i	0.826396	+	0.0682095i
$215$	9.25994	−	16.0387i	0.631523	−	1.09383i
$216$	−12.1852	+	48.3143i	−0.829100	+	3.28737i
$217$	−6.40718	+	1.71680i	−0.434947	+	0.116544i
$218$	−19.8432	+	3.59954i	−1.34395	+	0.243791i
$219$	−42.9370	−	24.7897i	−2.90141	−	1.67513i
$220$	−6.84312	−	3.10948i	−0.461363	−	0.209641i
$221$		−	0.181873i		−	0.0122341i
$222$	28.8329	−	1.14044i	1.93514	−	0.0765415i
$223$			12.1769i			0.815427i	0.913110	+	0.407713i	$0.133674\pi$
$223$			12.1769i			0.815427i	−0.913110	+	0.407713i	$0.866326\pi$
$224$	1.26448	+	11.2590i	0.0844867	+	0.752274i
$225$	47.0264	+	27.1507i	3.13509	+	1.81005i
$226$	−0.300678	−	1.65755i	−0.0200008	−	0.110259i
$227$	−15.9194	+	4.26558i	−1.05660	+	0.283116i	−0.744978	−	0.667089i	$-0.767540\pi$
$227$	−15.9194	+	4.26558i	−1.05660	+	0.283116i	−0.311626	+	0.950205i	$0.600874\pi$
$228$	16.2992	+	22.7974i	1.07944	+	1.50979i
$229$	4.75748	−	8.24019i	0.314383	−	0.544527i	−0.664923	−	0.746912i	$-0.731536\pi$
$229$	4.75748	−	8.24019i	0.314383	−	0.544527i	0.979306	+	0.202385i	$0.0648691\pi$
$230$	−0.132430	+	1.60446i	−0.00873217	+	0.105795i
$231$	6.42552	−	3.70977i	0.422768	−	0.244085i
$232$	−9.09357	+	5.43049i	−0.597022	+	0.356529i
$233$			8.77283i			0.574727i	0.957822	+	0.287364i	$0.0927788\pi$
$233$			8.77283i			0.574727i	−0.957822	+	0.287364i	$0.907221\pi$
$234$	4.52969	−	12.6381i	0.296115	−	0.826181i
$235$	10.3823	−	2.78193i	0.677268	−	0.181473i
$236$	12.5869	+	17.6050i	0.819335	+	1.14599i
$237$	−7.25431	+	27.0735i	−0.471218	+	1.75861i
$238$	−0.421528	−	0.151082i	−0.0273236	−	0.00979317i
$239$	5.68943	−	21.2332i	0.368019	−	1.37346i	−0.495264	−	0.868743i	$-0.664929\pi$
$239$	5.68943	−	21.2332i	0.368019	−	1.37346i	0.863282	−	0.504721i	$-0.168405\pi$
$240$	−3.08462	+	45.5557i	−0.199111	+	2.94061i
$241$	0.698878	+	2.60825i	0.0450187	+	0.168012i	0.984775	−	0.173832i	$-0.0556151\pi$
$241$	0.698878	+	2.60825i	0.0450187	+	0.168012i	−0.939757	+	0.341844i	$0.888948\pi$
$242$	12.5067	−	5.90698i	0.803962	−	0.379715i
$243$	−31.1649	−	53.9791i	−1.99923	−	3.46276i
$244$	4.88038	−	10.7404i	0.312434	−	0.687582i
$245$	7.19151	−	7.19151i	0.459449	−	0.459449i
$246$	9.24887	−	13.3479i	0.589686	−	0.851031i
$247$	−2.40287	−	4.16189i	−0.152891	−	0.264815i
$248$	−4.80282	−	8.04251i	−0.304979	−	0.510700i
$249$		−	7.98494i		−	0.506025i
$250$	7.16045	+	2.56641i	0.452866	+	0.162314i
$251$	−2.79672	+	2.79672i	−0.176528	+	0.176528i	−0.789840	−	0.613313i	$-0.789837\pi$
$251$	−2.79672	+	2.79672i	−0.176528	+	0.176528i	0.613313	+	0.789840i	$0.289837\pi$
$252$	−25.5286	−	20.9969i	−1.60815	−	1.32268i
$253$	0.261234	+	0.261234i	0.0164236	+	0.0164236i
$254$	−12.0679	+	17.4163i	−0.757209	+	1.09280i
$255$	−1.56284	−	0.902305i	−0.0978687	−	0.0565045i
$256$	−14.8084	+	6.05908i	−0.925523	+	0.378693i
$257$	19.3409	+	5.18238i	1.20645	+	0.323268i	0.805369	−	0.592774i	$-0.201967\pi$
$257$	19.3409	+	5.18238i	1.20645	+	0.323268i	0.401083	+	0.916042i	$0.368634\pi$
$258$	−19.6949	+	16.6916i	−1.22615	+	1.03918i
$259$	−4.76344	+	11.2130i	−0.295986	+	0.696740i
$260$	1.28379	−	7.72393i	0.0796172	−	0.479018i
$261$	7.99770	−	29.8478i	0.495045	−	1.84753i
$262$	−2.21241	+	0.401328i	−0.136683	+	0.0247941i
$263$	8.38229	−	14.5185i	0.516874	−	0.895252i	−0.482934	−	0.875657i	$-0.660429\pi$
$263$	8.38229	−	14.5185i	0.516874	−	0.895252i	0.999808	−	0.0195951i	$-0.00623771\pi$
$264$	7.51744	+	7.29898i	0.462667	+	0.449221i
$265$	7.18055	−	7.18055i	0.441097	−	0.441097i
$266$	−11.6421	+	2.11186i	−0.713822	+	0.129486i
$267$	36.6087	+	36.6087i	2.24041	+	2.24041i
$268$	5.55736	+	14.8140i	0.339470	+	0.904911i
$269$	25.7116			1.56766			0.783831	−	0.620975i	$-0.213263\pi$
$269$	25.7116			1.56766			0.783831	+	0.620975i	$0.213263\pi$
$270$	−54.8150	−	64.6777i	−3.33593	−	3.93616i
$271$	12.8021	−	7.39128i	0.777670	−	0.448988i	−0.0579338	−	0.998320i	$-0.518451\pi$
$271$	12.8021	−	7.39128i	0.777670	−	0.448988i	0.835604	+	0.549332i	$0.185118\pi$
$272$	0.0427202	−	0.630920i	0.00259029	−	0.0382551i
$273$	5.46518	+	5.46518i	0.330768	+	0.330768i
$274$	−13.3003	+	6.28178i	−0.803499	+	0.379496i
$275$	6.29377	−	3.63371i	0.379529	−	0.219121i
$276$	0.928412	−	2.04318i	0.0558838	−	0.122985i
$277$	−15.1432	+	4.05760i	−0.909864	+	0.243797i	−0.683248	−	0.730187i	$-0.739433\pi$
$277$	−15.1432	+	4.05760i	−0.909864	+	0.243797i	−0.226616	+	0.973984i	$0.572766\pi$
$278$	5.61114	+	3.88801i	0.336534	+	0.233187i
$279$	26.3979	+	7.07330i	1.58040	+	0.423467i
$280$	−16.8353	−	9.39168i	−1.00610	−	0.561260i
$281$	12.0950	+	3.24084i	0.721526	+	0.193332i	0.600852	−	0.799360i	$-0.294828\pi$
$281$	12.0950	+	3.24084i	0.721526	+	0.193332i	0.120674	+	0.992692i	$0.461495\pi$
$282$	−14.9327	−	1.23252i	−0.889229	−	0.0733956i
$283$	2.96007	+	11.0471i	0.175958	+	0.656684i	0.996387	+	0.0849347i	$0.0270682\pi$
$283$	2.96007	+	11.0471i	0.175958	+	0.656684i	−0.820429	+	0.571749i	$0.806265\pi$
$284$	0.734732	−	0.275629i	0.0435983	−	0.0163556i
$285$	−47.6842			−2.82457
$286$	−1.16170	−	1.37072i	−0.0686928	−	0.0810525i
$287$	3.42809	+	5.93762i	0.202354	+	0.350487i
$288$	18.6821	−	42.7778i	1.10085	−	2.52071i
$289$	−14.7008	−	8.48750i	−0.864752	−	0.499265i
$290$	1.48245	−	17.9607i	0.0870525	−	1.05469i
$291$	4.49957	+	16.7926i	0.263769	+	0.984400i
$292$	22.8307	+	18.7780i	1.33607	+	1.09890i
$293$	1.50687	−	2.60998i	0.0880323	−	0.152476i	−0.818647	−	0.574297i	$-0.805275\pi$
$293$	1.50687	−	2.60998i	0.0880323	−	0.152476i	0.906679	+	0.421821i	$0.138609\pi$
$294$	−12.8195	+	6.05472i	−0.747649	+	0.353118i
$295$	−36.8237			−2.14396
$296$	−17.0700	−	2.14790i	−0.992176	−	0.124844i
$297$	−19.4554			−1.12892
$298$	20.5718	−	9.71615i	1.19169	−	0.562842i
$299$	−0.192423	+	0.333286i	−0.0111281	+	0.0192744i
$300$	−34.0960	−	28.0435i	−1.96853	−	1.61909i
$301$	−2.82109	−	10.5285i	−0.162605	−	0.606850i
$302$	1.56144	−	18.9178i	0.0898509	−	1.08859i
$303$	16.4826	+	9.51625i	0.946902	+	0.546694i
$304$	−7.35799	−	15.0021i	−0.422010	−	0.860427i
$305$	10.0365	+	17.3838i	0.574689	+	0.995391i
$306$	1.19281	+	1.40743i	0.0681884	+	0.0804574i
$307$	12.3728			0.706156			0.353078	−	0.935594i	$-0.385135\pi$
$307$	12.3728			0.706156			0.353078	+	0.935594i	$0.385135\pi$
$308$	−4.14194	+	1.55382i	−0.236009	+	0.0885369i
$309$	14.1103	+	52.6604i	0.802708	+	2.99575i
$310$	15.8848	+	1.31110i	0.902194	+	0.0744657i
$311$	−8.24023	−	2.20796i	−0.467261	−	0.125202i	0.0175038	−	0.999847i	$-0.494428\pi$
$311$	−8.24023	−	2.20796i	−0.467261	−	0.125202i	−0.484765	+	0.874645i	$0.661095\pi$
$312$	−5.31747	+	9.53197i	−0.301042	+	0.539642i
$313$	6.36553	+	1.70564i	0.359801	+	0.0964084i	0.434191	−	0.900821i	$-0.357034\pi$
$313$	6.36553	+	1.70564i	0.359801	+	0.0964084i	−0.0743899	+	0.997229i	$0.523701\pi$
$314$	9.99691	+	6.92695i	0.564159	+	0.390910i
$315$	54.3256	−	14.5565i	3.06090	−	0.820166i
$316$	6.91342	−	15.2146i	0.388910	−	0.855886i
$317$	8.65593	−	4.99751i	0.486166	−	0.280688i	−0.236817	−	0.971554i	$-0.576104\pi$
$317$	8.65593	−	4.99751i	0.486166	−	0.280688i	0.722982	+	0.690866i	$0.242771\pi$
$318$	−12.8000	+	6.04548i	−0.717786	+	0.339014i
$319$	−2.92431	−	2.92431i	−0.163730	−	0.163730i
$320$	6.26774	−	26.4928i	0.350378	−	1.48099i
$321$	24.9170	−	14.3859i	1.39073	−	0.802941i
$322$	0.612612	+	0.722837i	0.0341395	+	0.0402822i
$323$	0.660399			0.0367456
$324$	24.1211	+	64.2987i	1.34006	+	3.57215i
$325$	5.35313	+	5.35313i	0.296938	+	0.296938i
$326$	−29.0978	+	5.27831i	−1.61158	+	0.292339i
$327$	−33.8239	+	33.8239i	−1.87047	+	1.87047i
$328$	−6.74476	+	6.94664i	−0.372417	+	0.383564i
$329$	3.16303	−	5.47852i	0.174383	−	0.302041i
$330$	−17.5420	+	3.18210i	−0.965656	+	0.175169i
$331$	−1.20131	+	4.48334i	−0.0660298	+	0.246427i	−0.991050	−	0.133491i	$-0.957381\pi$
$331$	−1.20131	+	4.48334i	−0.0660298	+	0.246427i	0.925020	+	0.379918i	$0.124048\pi$
$332$	−0.780599	+	4.69648i	−0.0428409	+	0.257753i
$333$	40.0953	−	30.1959i	2.19721	−	1.65472i
$334$	1.97997	−	1.67804i	0.108339	−	0.0918184i
$335$	−26.0042	−	6.96779i	−1.42076	−	0.380691i
$336$	17.6750	+	20.2425i	0.964253	+	1.10432i
$337$	−28.3991	−	16.3962i	−1.54700	−	0.893160i	−0.998369	−	0.0570949i	$-0.981816\pi$
$337$	−28.3991	−	16.3962i	−1.54700	−	0.893160i	−0.548630	−	0.836065i	$-0.684850\pi$
$338$	−9.40491	+	13.5731i	−0.511560	+	0.738279i
$339$	−2.82540	−	2.82540i	−0.153454	−	0.153454i
$340$	0.831002	+	0.683488i	0.0450674	+	0.0370673i
$341$	2.58631	−	2.58631i	0.140056	−	0.140056i
$342$	45.8903	+	16.4477i	2.48146	+	0.889392i
$343$		−	20.0056i		−	1.08020i
$344$	13.2157	−	7.89213i	0.712541	−	0.425515i
$345$	1.90928	+	3.30698i	0.102792	+	0.178042i
$346$	14.2524	−	20.5690i	0.766215	−	1.10580i
$347$	13.1802	−	13.1802i	0.707552	−	0.707552i	−0.258468	−	0.966020i	$-0.583218\pi$
$347$	13.1802	−	13.1802i	0.707552	−	0.707552i	0.966020	+	0.258468i	$0.0832176\pi$
$348$	−10.3929	+	22.8718i	−0.557115	+	1.22606i
$349$	9.27473	+	16.0643i	0.496465	+	0.859902i	0.999992	−	0.00407718i	$-0.00129781\pi$
$349$	9.27473	+	16.0643i	0.496465	+	0.859902i	−0.503527	+	0.863980i	$0.667964\pi$
$350$	16.8538	−	7.96012i	0.900872	−	0.425486i
$351$	−5.24541	−	19.5761i	−0.279979	−	1.04490i
$352$	−3.70798	−	5.02792i	−0.197636	−	0.267989i
$353$	3.61789	−	13.5021i	0.192561	−	0.718647i	−0.800324	−	0.599568i	$-0.795339\pi$
$353$	3.61789	−	13.5021i	0.192561	−	0.718647i	0.992885	−	0.119079i	$-0.0379942\pi$
$354$	48.3221	+	17.3193i	2.56829	+	0.920512i
$355$	−0.345582	+	1.28973i	−0.0183416	+	0.0684517i
$356$	−17.9532	−	25.1109i	−0.951518	−	1.33087i
$357$	−1.02591	+	0.274892i	−0.0542970	+	0.0145488i
$358$	−7.00428	+	19.5424i	−0.370188	+	1.03285i
$359$		−	28.3582i		−	1.49669i	−0.663311	−	0.748344i	$-0.730849\pi$
$359$		−	28.3582i		−	1.49669i	0.663311	−	0.748344i	$-0.269151\pi$
$360$	40.7225	+	68.1914i	2.14626	+	3.59400i
$361$	−1.34225	+	0.774946i	−0.0706446	+	0.0407867i
$362$	−1.20673	+	14.6202i	−0.0634244	+	0.768422i
$363$	16.4035	−	28.4116i	0.860958	−	1.49122i
$364$	−2.68017	−	3.74871i	−0.140479	−	0.196486i
$365$	−48.5845	+	13.0182i	−2.54303	+	0.681402i
$366$	−4.99436	−	27.5325i	−0.261059	−	1.43914i
$367$	9.94334	+	5.74079i	0.519038	+	0.299667i	0.736541	−	0.676393i	$-0.236458\pi$
$367$	9.94334	+	5.74079i	0.519038	+	0.299667i	−0.217503	+	0.976060i	$0.569791\pi$
$368$	−0.745801	+	1.11097i	−0.0388776	+	0.0579135i
$369$		−	28.2478i		−	1.47052i
$370$	19.8655	−	21.5017i	1.03276	−	1.11782i
$371$		−	5.97661i		−	0.310290i
$372$	−20.2282	−	9.19162i	−1.04879	−	0.476563i
$373$	5.37230	+	3.10170i	0.278167	+	0.160600i	0.632593	−	0.774484i	$-0.281990\pi$
$373$	5.37230	+	3.10170i	0.278167	+	0.160600i	−0.354426	+	0.935084i	$0.615324\pi$
$374$	0.242947	−	0.0440703i	0.0125625	−	0.00227882i
$375$	17.4270	−	4.66956i	0.899928	−	0.241135i
$376$	8.66244	+	2.18473i	0.446731	+	0.112669i
$377$	2.15402	−	3.73088i	0.110938	−	0.192150i
$378$	−49.7289	−	4.10455i	−2.55778	−	0.211115i
$379$	−6.73653	+	3.88933i	−0.346032	+	0.199782i	−0.662936	−	0.748676i	$-0.730690\pi$
$379$	−6.73653	+	3.88933i	−0.346032	+	0.199782i	0.316904	+	0.948458i	$0.397357\pi$
$380$	28.0463	+	4.66156i	1.43875	+	0.239133i
$381$			50.2576i			2.57478i
$382$	7.14694	+	2.56157i	0.365669	+	0.131061i
$383$	−18.6072	+	4.98577i	−0.950781	+	0.254761i	−0.700694	−	0.713462i	$-0.747126\pi$
$383$	−18.6072	+	4.98577i	−0.950781	+	0.254761i	−0.250087	+	0.968223i	$0.580459\pi$
$384$	−20.6853	+	31.8175i	−1.05559	+	1.62368i
$385$	1.94817	−	7.27066i	0.0992878	−	0.370547i
$386$	9.24033	−	25.7811i	0.470321	−	1.31223i
$387$	−11.6230	+	43.3778i	−0.590833	+	2.20502i
$388$	−1.00487	−	10.3167i	−0.0510147	−	0.523753i
$389$	2.33012	+	8.69611i	0.118142	+	0.440910i	0.999503	−	0.0315329i	$-0.0100389\pi$
$389$	2.33012	+	8.69611i	0.118142	+	0.440910i	−0.881361	+	0.472443i	$0.843372\pi$
$390$	−7.93138	−	16.7929i	−0.401621	−	0.850342i
$391$	−0.0264425	−	0.0457997i	−0.00133725	−	0.00231619i
$392$	8.13192	−	2.30797i	0.410724	−	0.116570i
$393$	−3.77117	+	3.77117i	−0.190231	+	0.190231i
$394$	29.7978	+	20.6472i	1.50119	+	1.04019i
$395$	14.2175	+	24.6254i	0.715360	+	1.23904i
$396$	17.9797	+	2.98839i	0.903512	+	0.150172i
$397$		−	26.3117i		−	1.32055i	−0.751026	−	0.660273i	$-0.770441\pi$
$397$		−	26.3117i		−	1.32055i	0.751026	−	0.660273i	$-0.229559\pi$
$398$	−8.47176	+	23.6368i	−0.424651	+	1.18480i
$399$	−19.8446	+	19.8446i	−0.993472	+	0.993472i
$400$	17.3126	+	19.8274i	0.865632	+	0.991372i
$401$	19.3469	+	19.3469i	0.966136	+	0.966136i	0.999445	−	0.0333087i	$-0.0106044\pi$
$401$	19.3469	+	19.3469i	0.966136	+	0.966136i	−0.0333087	+	0.999445i	$0.510604\pi$
$402$	30.8470	+	21.3741i	1.53851	+	1.06604i
$403$	3.29965	+	1.90505i	0.164367	+	0.0948975i
$404$	−8.76425	−	7.20847i	−0.436038	−	0.358635i
$405$	−112.868	−	30.2429i	−5.60847	−	1.50278i
$406$	−6.85771	−	8.09160i	−0.340343	−	0.401580i
$407$	−0.816758	−	6.66785i	−0.0404852	−	0.330513i
$408$	−0.769023	−	1.28776i	−0.0380723	−	0.0637535i
$409$	−1.57937	+	5.89430i	−0.0780950	+	0.291454i	−0.993917	−	0.110129i	$-0.964873\pi$
$409$	−1.57937	+	5.89430i	−0.0780950	+	0.291454i	0.915822	+	0.401584i	$0.131540\pi$
$410$	−2.94048	−	16.2100i	−0.145220	−	0.800557i
$411$	−17.4443	+	30.2144i	−0.860463	+	1.49036i
$412$	−3.15121	−	32.3526i	−0.155249	−	1.59390i
$413$	−15.3248	+	15.3248i	−0.754083	+	0.754083i
$414$	−0.696777	−	3.84113i	−0.0342447	−	0.188781i
$415$	−5.72809	−	5.72809i	−0.281181	−	0.281181i
$416$	4.05940	−	5.08657i	0.199028	−	0.249390i
$417$	16.1919			0.792919
$418$	4.97722	−	4.21824i	0.243444	−	0.206321i
$419$	−14.2497	+	8.22705i	−0.696142	+	0.401918i	−0.805909	−	0.592039i	$-0.798323\pi$
$419$	−14.2497	+	8.22705i	−0.696142	+	0.401918i	0.109767	+	0.993957i	$0.464990\pi$
$420$	−45.5095	+	4.43272i	−2.22064	+	0.216295i
$421$	−8.14474	−	8.14474i	−0.396950	−	0.396950i	0.480206	−	0.877156i	$-0.340562\pi$
$421$	−8.14474	−	8.14474i	−0.396950	−	0.396950i	−0.877156	+	0.480206i	$0.840562\pi$
$422$	−11.4347	−	24.2104i	−0.556633	−	1.17855i
$423$	−22.5718	+	13.0318i	−1.09748	+	0.633630i
$424$	8.11952	−	2.30445i	0.394319	−	0.111914i
$425$	−1.00488	+	0.269256i	−0.0487437	+	0.0130608i
$426$	1.06009	−	1.52992i	0.0513617	−	0.0741248i
$427$	11.4114	+	3.05768i	0.552237	+	0.147971i
$428$	−16.0617	+	6.02544i	−0.776374	+	0.291251i
$429$	−4.11657	−	1.10303i	−0.198750	−	0.0532549i
$430$	−2.15444	+	26.1023i	−0.103897	+	1.25877i
$431$	−1.02498	−	3.82527i	−0.0493714	−	0.184257i	0.936837	−	0.349767i	$-0.113739\pi$
$431$	−1.02498	−	3.82527i	−0.0493714	−	0.184257i	−0.986208	+	0.165511i	$0.947073\pi$
$432$	−13.5981	−	69.1418i	−0.654240	−	3.32659i
$433$	5.92338			0.284659			0.142330	−	0.989819i	$-0.454541\pi$
$433$	5.92338			0.284659			0.142330	+	0.989819i	$0.454541\pi$
$434$	7.15635	−	6.06508i	0.343516	−	0.291133i
$435$	−21.3730	−	37.0190i	−1.02475	−	1.77493i
$436$	23.2007	−	16.5875i	1.11111	−	0.794399i
$437$	−1.21019	−	0.698705i	−0.0578914	−	0.0334236i
$438$	69.8782	+	5.76764i	3.33891	+	0.275588i
$439$	2.10879	+	7.87010i	0.100647	+	0.375619i	0.997815	−	0.0660698i	$-0.0210460\pi$
$439$	2.10879	+	7.87010i	0.100647	+	0.375619i	−0.897168	+	0.441689i	$0.854379\pi$
$440$	10.6287	−	0.156721i	0.506705	−	0.00747140i
$441$	−12.3308	+	21.3575i	−0.587180	+	1.01703i
$442$	0.109845	+	0.232572i	0.00522480	+	0.0110623i
$443$	−23.9181			−1.13638			−0.568191	−	0.822897i	$-0.692356\pi$
$443$	−23.9181			−1.13638			−0.568191	+	0.822897i	$0.692356\pi$
$444$	−36.1815	+	18.8724i	−1.71710	+	0.895643i
$445$	52.5233			2.48984
$446$	−7.35442	−	15.5714i	−0.348242	−	0.737325i
$447$	26.9814	−	46.7331i	1.27618	−	2.21040i
$448$	−8.41701	−	13.6339i	−0.397666	−	0.644139i
$449$	−7.35658	−	27.4551i	−0.347179	−	1.29569i	−0.890046	−	0.455870i	$-0.849328\pi$
$449$	−7.35658	−	27.4551i	−0.347179	−	1.29569i	0.542868	−	0.839818i	$-0.317338\pi$
$450$	−76.5335	−	6.31696i	−3.60782	−	0.297784i
$451$	−3.27405	−	1.89027i	−0.154169	−	0.0890094i
$452$	1.38560	+	1.93801i	0.0651731	+	0.0911565i
$453$	−22.5118	−	38.9916i	−1.05770	−	1.83199i
$454$	17.7808	−	15.0694i	0.834493	−	0.707241i
$455$	7.84102			0.367593
$456$	−34.6115	−	19.3082i	−1.62083	−	0.904191i
$457$	−1.16678	−	4.35447i	−0.0545795	−	0.203693i	0.933252	−	0.359223i	$-0.116958\pi$
$457$	−1.16678	−	4.35447i	−0.0545795	−	0.203693i	−0.987831	+	0.155530i	$0.950292\pi$
$458$	−1.10689	+	13.4106i	−0.0517215	+	0.626635i
$459$	2.69013	+	0.720817i	0.125564	+	0.0336449i
$460$	−0.799693	−	2.13171i	−0.0372859	−	0.0993913i
$461$	10.9930	+	2.94557i	0.511996	+	0.137189i	0.505562	−	0.862790i	$-0.331285\pi$
$461$	10.9930	+	2.94557i	0.511996	+	0.137189i	0.00643405	+	0.999979i	$0.497952\pi$
$462$	−5.97612	+	8.62469i	−0.278034	+	0.401257i
$463$	−10.1806	+	2.72790i	−0.473135	+	0.126776i	−0.487504	−	0.873121i	$-0.662093\pi$
$463$	−10.1806	+	2.72790i	−0.473135	+	0.126776i	0.0143693	+	0.999897i	$0.495426\pi$
$464$	8.34867	−	12.4365i	0.387577	−	0.577349i
$465$	32.7403	−	18.9026i	1.51829	−	0.876588i
$466$	−5.29848	−	11.2183i	−0.245447	−	0.519680i
$467$	16.9863	+	16.9863i	0.786031	+	0.786031i	0.980841	−	0.194810i	$-0.0624091\pi$
$467$	16.9863	+	16.9863i	0.786031	+	0.786031i	−0.194810	+	0.980841i	$0.562409\pi$
$468$	1.84060	+	18.8969i	0.0850817	+	0.873510i
$469$	−13.7218	+	7.92231i	−0.633616	+	0.365818i
$470$	−11.5963	+	9.82797i	−0.534897	+	0.453331i
$471$	28.8477			1.32923
$472$	−26.7284	−	14.9106i	−1.23027	−	0.686315i
$473$	4.24989	+	4.24989i	0.195410	+	0.195410i
$474$	−7.07488	−	39.0018i	−0.324960	−	1.79141i
$475$	−19.4377	+	19.4377i	−0.891864	+	0.891864i
$476$	0.630281	−	0.0613907i	0.0288889	−	0.00281384i
$477$	−12.3120	+	21.3250i	−0.563727	+	0.976404i
$478$	5.54871	+	30.5884i	0.253792	+	1.39908i
$479$	−6.94618	+	25.9235i	−0.317379	+	1.18447i	0.604375	+	0.796700i	$0.293423\pi$
$479$	−6.94618	+	25.9235i	−0.317379	+	1.18447i	−0.921754	+	0.387775i	$0.873244\pi$
$480$	−23.5695	−	60.1178i	−1.07580	−	2.74399i
$481$	6.48901	−	2.61956i	0.295874	−	0.119441i
$482$	−2.46899	−	2.91323i	−0.112459	−	0.132694i
$483$	2.17084	+	0.581673i	0.0987764	+	0.0264671i
$484$	−12.4255	+	15.1072i	−0.564794	+	0.686692i
$485$	15.2742	+	8.81855i	0.693565	+	0.400430i
$486$	72.4539	+	50.2039i	3.28657	+	2.27729i
$487$	−28.4111	−	28.4111i	−1.28743	−	1.28743i	−0.936342	−	0.351090i	$-0.885811\pi$
$487$	−28.4111	−	28.4111i	−1.28743	−	1.28743i	−0.351090	−	0.936342i	$-0.614189\pi$
$488$	0.245977	+	16.6819i	0.0111348	+	0.755156i
$489$	−49.5989	+	49.5989i	−2.24294	+	2.24294i
$490$	−4.85280	+	13.5396i	−0.219227	+	0.611658i
$491$			31.7161i			1.43133i	0.698445	+	0.715664i	$0.253876\pi$
$491$			31.7161i			1.43133i	−0.698445	+	0.715664i	$0.746124\pi$
$492$	−3.76543	+	22.6547i	−0.169759	+	1.02135i
$493$	0.296003	+	0.512693i	0.0133313	+	0.0230905i
$494$	5.58633	+	3.87082i	0.251341	+	0.174156i
$495$	−21.9290	+	21.9290i	−0.985634	+	0.985634i
$496$	10.9990	+	7.38370i	0.493871	+	0.331538i
$497$	0.392923	+	0.680562i	0.0176250	+	0.0305274i
$498$	4.82262	+	10.2108i	0.216107	+	0.457558i
$499$	−4.82467	−	18.0059i	−0.215982	−	0.806056i	−0.985819	−	0.167815i	$-0.946329\pi$
$499$	−4.82467	−	18.0059i	−0.215982	−	0.806056i	0.769836	−	0.638241i	$-0.220338\pi$
$500$	−10.7065	+	1.04284i	−0.478810	+	0.0466371i
$501$	1.59330	−	5.94627i	0.0711833	−	0.265660i
$502$	1.88722	−	5.26546i	0.0842306	−	0.235009i
$503$	−7.62680	+	28.4636i	−0.340062	+	1.26913i	0.558214	+	0.829697i	$0.311487\pi$
$503$	−7.62680	+	28.4636i	−0.340062	+	1.26913i	−0.898276	+	0.439432i	$0.855180\pi$
$504$	45.3263	+	11.4317i	2.01900	+	0.509206i
$505$	18.6506	−	4.99741i	0.829940	−	0.222382i
$506$	−0.491831	−	0.176279i	−0.0218645	−	0.00783657i
$507$			39.1674i			1.73948i
$508$	4.91313	−	29.5599i	0.217985	−	1.31151i
$509$	−16.7005	+	9.64203i	−0.740236	+	0.427375i	−0.822155	−	0.569264i	$-0.807228\pi$
$509$	−16.7005	+	9.64203i	−0.740236	+	0.427375i	0.0819192	+	0.996639i	$0.473895\pi$
$510$	2.54345	+	0.209933i	0.112626	+	0.00929598i
$511$	−14.8015	+	25.6370i	−0.654781	+	1.13411i
$512$	15.2769	−	16.6918i	0.675149	−	0.737682i
$513$	71.0828	−	19.0466i	3.13838	−	0.840926i
$514$	−27.8623	+	5.05420i	−1.22896	+	0.222931i
$515$	47.8987	+	27.6543i	2.11067	+	1.21860i
$516$	15.1039	−	33.2396i	0.664913	−	1.46329i
$517$			3.48823i			0.153412i
$518$	−0.680940	−	17.2156i	−0.0299188	−	0.756412i
$519$		−	59.3551i		−	2.60540i
$520$	3.02332	+	10.6524i	0.132581	+	0.467139i
$521$	−13.9579	−	8.05862i	−0.611509	−	0.353055i	0.162047	−	0.986783i	$-0.448190\pi$
$521$	−13.9579	−	8.05862i	−0.611509	−	0.353055i	−0.773556	+	0.633728i	$0.781524\pi$
$522$	7.79988	+	42.9985i	0.341392	+	1.88199i
$523$	−24.3849	+	6.53392i	−1.06628	+	0.285708i	−0.748963	−	0.662612i	$-0.769448\pi$
$523$	−24.3849	+	6.53392i	−1.06628	+	0.285708i	−0.317315	+	0.948320i	$0.602781\pi$
$524$	2.58675	−	1.84942i	0.113003	−	0.0807921i
$525$	22.1049	−	38.2869i	0.964739	−	1.67098i
$526$	−1.95025	+	23.6283i	−0.0850348	+	1.03024i
$527$	−0.453434	+	0.261790i	−0.0197519	+	0.0114038i
$528$	−14.0213	−	4.79337i	−0.610200	−	0.208605i
$529$		−	22.8881i		−	0.995135i
$530$	−4.84540	+	13.5190i	−0.210471	+	0.587227i
$531$	86.2494	−	23.1105i	3.74291	−	1.00291i
$532$	13.6119	−	9.73196i	0.590152	−	0.421934i
$533$	1.01928	−	3.80400i	0.0441499	−	0.164769i
$534$	−68.9240	−	24.7034i	−2.98263	−	1.06902i
$535$	7.55466	−	28.1944i	0.326617	−	1.21895i
$536$	−16.0537	−	15.5871i	−0.693413	−	0.673262i
$537$	12.7442	+	47.5622i	0.549955	+	2.05246i
$538$	−32.8789	+	15.5289i	−1.41751	+	0.669497i
$539$	1.65029	+	2.85838i	0.0710830	+	0.123119i
$540$	109.158	+	49.6010i	4.69742	+	2.13449i
$541$	14.7179	−	14.7179i	0.632774	−	0.632774i	−0.315989	−	0.948763i	$-0.602336\pi$
$541$	14.7179	−	14.7179i	0.632774	−	0.632774i	0.948763	+	0.315989i	$0.102336\pi$
$542$	−11.9067	+	17.1837i	−0.511437	+	0.738102i
$543$	17.3978	+	30.1339i	0.746612	+	1.29317i
$544$	0.326424	+	0.832597i	0.0139953	+	0.0356973i
$545$			48.5279i			2.07871i
$546$	−10.2894	−	3.68788i	−0.440347	−	0.157827i
$547$	0.543587	−	0.543587i	0.0232421	−	0.0232421i	−0.695390	−	0.718632i	$-0.744768\pi$
$547$	0.543587	−	0.543587i	0.0232421	−	0.0232421i	0.718632	+	0.695390i	$0.244768\pi$
$548$	13.2139	−	16.0658i	0.564469	−	0.686296i
$549$	−34.4178	−	34.4178i	−1.46892	−	1.46892i
$550$	−5.85359	+	8.44786i	−0.249598	+	0.360218i
$551$	13.5472	+	7.82146i	0.577129	+	0.333205i
$552$	0.0467930	+	3.17347i	0.00199164	+	0.135072i
$553$	16.1651	+	4.33143i	0.687411	+	0.184191i
$554$	16.9138	−	14.3346i	0.718599	−	0.609020i
$555$	9.68327	−	68.7562i	0.411032	−	2.91854i
$556$	−9.52353	−	1.58290i	−0.403887	−	0.0671298i
$557$	4.92734	−	18.3891i	0.208778	−	0.779170i	−0.779487	−	0.626419i	$-0.784520\pi$
$557$	4.92734	−	18.3891i	0.208778	−	0.779170i	0.988265	−	0.152751i	$-0.0488133\pi$
$558$	−38.0286	+	6.89835i	−1.60988	+	0.292030i
$559$	−3.13044	+	5.42208i	−0.132404	+	0.229330i
$560$	27.2006	+	1.84178i	1.14943	+	0.0778293i
$561$	0.414117	−	0.414117i	0.0174840	−	0.0174840i
$562$	−17.4239	+	3.16068i	−0.734984	+	0.133325i
$563$	−21.3753	−	21.3753i	−0.900863	−	0.900863i	0.0946475	−	0.995511i	$-0.469828\pi$
$563$	−21.3753	−	21.3753i	−0.900863	−	0.900863i	−0.995511	+	0.0946475i	$0.969828\pi$
$564$	19.8397	−	7.44272i	0.835404	−	0.313395i
$565$	−4.05366			−0.170539
$566$	−10.4573	−	12.3388i	−0.439553	−	0.518640i
$567$	−59.5581	+	34.3859i	−2.50121	+	1.44407i
$568$	−0.773075	+	0.796215i	−0.0324375	+	0.0334084i
$569$	3.50783	+	3.50783i	0.147056	+	0.147056i	0.776801	−	0.629746i	$-0.216841\pi$
$569$	3.50783	+	3.50783i	0.147056	+	0.147056i	−0.629746	+	0.776801i	$0.716841\pi$
$570$	60.9767	−	28.7996i	2.55403	−	1.20628i
$571$	−31.4895	+	18.1805i	−1.31780	+	0.760830i	−0.983374	−	0.181593i	$-0.941875\pi$
$571$	−31.4895	+	18.1805i	−1.31780	+	0.760830i	−0.334422	+	0.942423i	$0.608541\pi$
$572$	2.31340	+	1.05120i	0.0967283	+	0.0439529i
$573$	17.3942	−	4.66075i	0.726652	−	0.194706i
$574$	−7.96982	−	5.52235i	−0.332654	−	0.230498i
$575$	2.12633	+	0.569747i	0.0886739	+	0.0237601i
$576$	1.94636	+	65.9859i	0.0810982	+	2.74941i
$577$	−13.0313	−	3.49172i	−0.542500	−	0.145362i	−0.0228455	−	0.999739i	$-0.507273\pi$
$577$	−13.0313	−	3.49172i	−0.542500	−	0.145362i	−0.519654	+	0.854377i	$0.673939\pi$
$578$	23.9249	+	1.97473i	0.995146	+	0.0821378i
$579$	−16.8127	−	62.7460i	−0.698713	−	2.60763i
$580$	8.95194	+	23.8628i	0.371709	+	0.990849i
$581$	−4.76768			−0.197797
$582$	−15.8960	−	18.7561i	−0.658910	−	0.777467i
$583$	1.64777	+	2.85403i	0.0682438	+	0.118202i
$584$	−40.5362	−	10.2236i	−1.67740	−	0.423054i
$585$	−27.9773	−	16.1527i	−1.15672	−	0.667833i
$586$	−0.350593	+	4.24763i	−0.0144829	+	0.175468i
$587$	−7.63437	−	28.4919i	−0.315104	−	1.17598i	−0.923893	−	0.382652i	$-0.875011\pi$
$587$	−7.63437	−	28.4919i	−0.315104	−	1.17598i	0.608788	−	0.793333i	$-0.291656\pi$
$588$	12.7362	−	15.4851i	0.525234	−	0.638593i
$589$	−6.91743	+	11.9813i	−0.285028	+	0.493683i
$590$	47.0886	−	22.2402i	1.93861	−	0.915614i
$591$	85.9865			3.53701
$592$	23.1257	−	7.56306i	0.950462	−	0.310840i
$593$	23.9691			0.984294			0.492147	−	0.870512i	$-0.336212\pi$
$593$	23.9691			0.984294			0.492147	+	0.870512i	$0.336212\pi$
$594$	24.8788	−	11.7504i	1.02079	−	0.482124i
$595$	−0.538752	+	0.933145i	−0.0220867	+	0.0382552i
$596$	−20.4382	+	24.8493i	−0.837180	+	1.01787i
$597$	15.4143	+	57.5270i	0.630866	+	2.35442i
$598$	0.0447696	−	0.542409i	0.00183077	−	0.0221808i
$599$	9.91694	+	5.72555i	0.405195	+	0.233940i	0.688723	−	0.725024i	$-0.258172\pi$
$599$	9.91694	+	5.72555i	0.405195	+	0.233940i	−0.283528	+	0.958964i	$0.591505\pi$
$600$	60.5378	+	15.2681i	2.47145	+	0.623317i
$601$	−0.125000	−	0.216506i	−0.00509884	−	0.00883145i	0.863465	−	0.504409i	$-0.168290\pi$
$601$	−0.125000	−	0.216506i	−0.00509884	−	0.00883145i	−0.868564	+	0.495578i	$0.834956\pi$
$602$	9.96631	+	11.7595i	0.406196	+	0.479282i
$603$	65.2807			2.65843
$604$	9.42894	+	25.1343i	0.383658	+	1.02270i
$605$	−8.61419	−	32.1486i	−0.350217	−	1.30703i
$606$	−26.8248	−	2.21408i	−1.08968	−	0.0899407i
$607$	−12.2215	−	3.27475i	−0.496057	−	0.132918i	0.00211252	−	0.999998i	$-0.499328\pi$
$607$	−12.2215	−	3.27475i	−0.496057	−	0.132918i	−0.498169	+	0.867080i	$0.665994\pi$
$608$	18.4698	+	14.7401i	0.749050	+	0.597788i
$609$	−24.3008	−	6.51138i	−0.984719	−	0.263855i
$610$	−23.3335	−	16.1680i	−0.944745	−	0.654621i
$611$	−3.50987	+	0.940468i	−0.141994	+	0.0380472i
$612$	−2.37535	−	1.07935i	−0.0960180	−	0.0436301i
$613$	−16.4303	+	9.48604i	−0.663614	+	0.383138i	−0.793653	−	0.608371i	$-0.791823\pi$
$613$	−16.4303	+	9.48604i	−0.663614	+	0.383138i	0.130039	+	0.991509i	$0.458490\pi$
$614$	−15.8219	+	7.47276i	−0.638520	+	0.301576i
$615$	−27.6310	−	27.6310i	−1.11419	−	1.11419i
$616$	4.35810	−	4.48855i	0.175593	−	0.180849i
$617$	−26.1929	+	15.1225i	−1.05449	+	0.608808i	−0.923902	−	0.382630i	$-0.875019\pi$
$617$	−26.1929	+	15.1225i	−1.05449	+	0.608808i	−0.130584	+	0.991437i	$0.541685\pi$
$618$	−49.8487	−	58.8179i	−2.00521	−	2.36600i
$619$	−47.0542			−1.89127			−0.945634	−	0.325233i	$-0.894557\pi$
$619$	−47.0542			−1.89127			−0.945634	+	0.325233i	$0.894557\pi$
$620$	−21.1047	+	7.91725i	−0.847584	+	0.317964i
$621$	−4.16707	−	4.16707i	−0.167219	−	0.167219i
$622$	11.8708	−	2.15335i	0.475976	−	0.0863416i
$623$	21.8584	−	21.8584i	0.875740	−	0.875740i
$624$	1.04279	−	15.4007i	0.0417452	−	0.616520i
$625$	−7.29962	+	12.6433i	−0.291985	+	0.505732i
$626$	−9.17013	+	1.66345i	−0.366512	+	0.0664849i
$627$	4.00521	−	14.9477i	0.159953	−	0.596952i
$628$	−16.9673	−	2.82012i	−0.677068	−	0.112535i
$629$	−0.134108	+	0.952234i	−0.00534723	+	0.0379681i
$630$	−60.6778	+	51.4250i	−2.41746	+	2.04882i
$631$	43.7903	+	11.7336i	1.74326	+	0.467106i	0.983168	−	0.182706i	$-0.0584856\pi$
$631$	43.7903	+	11.7336i	1.74326	+	0.467106i	0.760095	+	0.649812i	$0.225152\pi$
$632$	0.348445	+	23.6312i	0.0138604	+	0.940000i
$633$	−54.9991	−	31.7537i	−2.18602	−	1.26210i
$634$	−8.05055	+	11.6185i	−0.319728	+	0.461429i
$635$	36.0529	+	36.0529i	1.43071	+	1.43071i
$636$	12.7168	−	15.4614i	0.504255	−	0.613086i
$637$	−2.43118	+	2.43118i	−0.0963269	+	0.0963269i
$638$	5.50566	+	1.97331i	0.217971	+	0.0781241i
$639$		−	3.23773i		−	0.128083i
$640$	7.98578	+	37.6635i	0.315666	+	1.48878i
$641$	8.67859	+	15.0318i	0.342784	+	0.593719i	0.984949	−	0.172848i	$-0.0552969\pi$
$641$	8.67859	+	15.0318i	0.342784	+	0.593719i	−0.642165	+	0.766567i	$0.721964\pi$
$642$	−23.1744	+	33.4451i	−0.914620	+	1.31997i
$643$	10.7463	−	10.7463i	0.423792	−	0.423792i	−0.462715	−	0.886507i	$-0.653125\pi$
$643$	10.7463	−	10.7463i	0.423792	−	0.423792i	0.886507	+	0.462715i	$0.153125\pi$
$644$	−1.21995	−	0.554340i	−0.0480728	−	0.0218441i
$645$	31.0613	+	53.7998i	1.22304	+	2.11836i
$646$	−0.844492	+	0.398858i	−0.0332261	+	0.0156928i
$647$	−0.961514	−	3.58842i	−0.0378010	−	0.141075i	0.944446	−	0.328666i	$-0.106599\pi$
$647$	−0.961514	−	3.58842i	−0.0378010	−	0.141075i	−0.982247	+	0.187590i	$0.939932\pi$
$648$	−69.6792	−	67.6542i	−2.73726	−	2.65771i
$649$	3.09299	−	11.5432i	0.121410	−	0.453109i
$650$	−10.0785	−	3.61227i	−0.395310	−	0.141685i
$651$	5.75878	−	21.4921i	0.225704	−	0.842340i
$652$	34.0212	−	24.3237i	1.33237	−	0.952591i
$653$	−17.2724	+	4.62813i	−0.675922	+	0.181113i	−0.580421	−	0.814317i	$-0.697112\pi$
$653$	−17.2724	+	4.62813i	−0.675922	+	0.181113i	−0.0955011	+	0.995429i	$0.530445\pi$
$654$	22.8242	−	63.6811i	0.892498	−	2.49013i
$655$			5.41059i			0.211409i
$656$	4.42941	−	12.9567i	0.172939	−	0.505874i
$657$	105.626	−	60.9831i	4.12085	−	2.37918i
$658$	−0.735919	+	8.91607i	−0.0286891	+	0.347585i
$659$	13.5239	−	23.4241i	0.526818	−	0.912475i	−0.472694	−	0.881227i	$-0.656718\pi$
$659$	13.5239	−	23.4241i	0.526818	−	0.912475i	0.999512	−	0.0312484i	$-0.00994829\pi$
$660$	20.5102	−	14.6639i	0.798357	−	0.570791i
$661$	−10.2748	+	2.75313i	−0.399645	+	0.107085i	−0.453043	−	0.891489i	$-0.649661\pi$
$661$	−10.2748	+	2.75313i	−0.399645	+	0.107085i	0.0533979	+	0.998573i	$0.482995\pi$
$662$	−1.17159	−	6.45866i	−0.0455353	−	0.251023i
$663$	0.528337	+	0.305036i	0.0205189	+	0.0118466i
$664$	−1.83831	−	6.47713i	−0.0713403	−	0.251361i
$665$			28.4715i			1.10408i
$666$	−33.0351	+	62.8294i	−1.28008	+	2.43459i
$667$		−	1.25269i		−	0.0485044i
$668$	−1.51843	+	3.34164i	−0.0587497	+	0.129292i
$669$	−35.3736	−	20.4230i	−1.36762	−	0.789597i
$670$	37.4614	−	6.79545i	1.44726	−	0.262531i
$671$	−6.29233	+	1.68603i	−0.242913	+	0.0650883i
$672$	−34.8279	−	15.2102i	−1.34351	−	0.586745i
$673$	−10.1321	+	17.5493i	−0.390564	+	0.676477i	−0.992524	−	0.122050i	$-0.961053\pi$
$673$	−10.1321	+	17.5493i	−0.390564	+	0.676477i	0.601960	+	0.798526i	$0.294387\pi$
$674$	46.2184	+	3.81480i	1.78027	+	0.146940i
$675$	−100.395	+	57.9632i	−3.86422	+	2.23101i
$676$	3.82896	−	23.0370i	0.147268	−	0.886037i
$677$			1.04996i			0.0403534i	0.999796	+	0.0201767i	$0.00642287\pi$
$677$			1.04996i			0.0403534i	−0.999796	+	0.0201767i	$0.993577\pi$
$678$	5.31944	+	1.90656i	0.204292	+	0.0732212i
$679$	10.0266	−	2.68662i	0.384785	−	0.103103i
$680$	−1.47545	−	0.372121i	−0.0565811	−	0.0142702i
$681$	14.3083	−	53.3995i	0.548297	−	2.04627i
$682$	−1.74523	+	4.86930i	−0.0668283	+	0.186455i
$683$	−1.30273	+	4.86187i	−0.0498478	+	0.186034i	−0.986361	−	0.164599i	$-0.947367\pi$
$683$	−1.30273	+	4.86187i	−0.0498478	+	0.186034i	0.936513	+	0.350633i	$0.114034\pi$
$684$	−68.6165	+	6.68339i	−2.62362	+	0.255546i
$685$	9.16077	+	34.1885i	0.350015	+	1.30627i
$686$	12.0827	+	25.5824i	0.461319	+	0.976741i
$687$	15.9583	+	27.6407i	0.608849	+	1.05456i
$688$	−12.1331	+	18.0739i	−0.462571	+	0.689062i
$689$	−2.42747	+	2.42747i	−0.0924794	+	0.0924794i
$690$	−4.43881	−	3.07569i	−0.168983	−	0.117090i
$691$	−19.6181	−	33.9796i	−0.746310	−	1.29265i	−0.949580	−	0.313524i	$-0.898491\pi$
$691$	−19.6181	−	33.9796i	−0.746310	−	1.29265i	0.203271	−	0.979123i	$-0.434843\pi$
$692$	−5.80249	+	34.9108i	−0.220578	+	1.32711i
$693$			18.2522i			0.693345i
$694$	−8.89396	+	24.8148i	−0.337610	+	0.941955i
$695$	11.6154	−	11.6154i	0.440598	−	0.440598i
$696$	−0.523812	−	35.5245i	−0.0198550	−	1.34655i
$697$	0.382673	+	0.382673i	0.0144948	+	0.0144948i
$698$	−21.5624	−	14.9408i	−0.816150	−	0.565517i
$699$	−25.4848	−	14.7137i	−0.963925	−	0.556522i
$700$	−16.7443	+	20.3582i	−0.632875	+	0.769466i
$701$	8.34536	+	2.23613i	0.315200	+	0.0844575i	0.412951	−	0.910753i	$-0.364498\pi$
$701$	8.34536	+	2.23613i	0.315200	+	0.0844575i	−0.0977509	+	0.995211i	$0.531165\pi$
$702$	18.5309	+	21.8651i	0.699404	+	0.825246i
$703$	9.51186	+	23.5622i	0.358746	+	0.888666i
$704$	7.77830	+	4.19001i	0.293156	+	0.157917i
$705$	−9.33164	+	34.8262i	−0.351450	+	1.31163i
$706$	3.52841	+	19.4511i	0.132793	+	0.732051i
$707$	5.68200	−	9.84151i	0.213694	−	0.370128i
$708$	−72.2526	+	7.03756i	−2.71542	+	0.264488i
$709$	−5.69370	+	5.69370i	−0.213831	+	0.213831i	−0.805893	−	0.592061i	$-0.798314\pi$
$709$	−5.69370	+	5.69370i	−0.213831	+	0.213831i	0.592061	+	0.805893i	$0.298314\pi$
$710$	−0.337034	−	1.85797i	−0.0126487	−	0.0697285i
$711$	−48.7555	−	48.7555i	−1.82847	−	1.82847i
$712$	38.1239	+	21.2677i	1.42875	+	0.797039i
$713$	1.10790			0.0414912
$714$	1.14587	−	0.971135i	0.0428831	−	0.0363438i
$715$	−3.74434	+	2.16180i	−0.140030	+	0.0808466i
$716$	−2.84613	−	29.2204i	−0.106365	−	1.09202i
$717$	52.1397	+	52.1397i	1.94719	+	1.94719i
$718$	17.1273	+	36.2633i	0.639186	+	1.35333i
$719$	12.0634	−	6.96481i	0.449889	−	0.259743i	−0.257894	−	0.966173i	$-0.583029\pi$
$719$	12.0634	−	6.96481i	0.449889	−	0.259743i	0.707783	+	0.706430i	$0.249695\pi$
$720$	−93.2595	−	62.6055i	−3.47557	−	2.33317i
$721$	31.4427	−	8.42504i	1.17099	−	0.313765i
$722$	1.24837	−	1.80164i	0.0464596	−	0.0670501i
$723$	−8.74904	−	2.34430i	−0.325380	−	0.0871854i
$724$	−7.28698	−	19.4246i	−0.270819	−	0.721909i
$725$	−23.8026	−	6.37788i	−0.884005	−	0.236868i
$726$	−3.81648	+	46.2388i	−0.141643	+	1.71608i
$727$	0.572082	+	2.13504i	0.0212174	+	0.0791842i	0.975723	−	0.219009i	$-0.0702825\pi$
$727$	0.572082	+	2.13504i	0.0212174	+	0.0791842i	−0.954505	+	0.298194i	$0.903616\pi$
$728$	5.69139	+	3.17498i	0.210937	+	0.117672i
$729$	106.066			3.92837
$730$	54.2654	−	45.9904i	2.00845	−	1.70218i
$731$	−0.430181	−	0.745096i	−0.0159108	−	0.0275584i
$732$	23.0152	+	32.1910i	0.850666	+	1.18981i
$733$	8.18819	+	4.72746i	0.302438	+	0.174613i	0.643538	−	0.765415i	$-0.277466\pi$
$733$	8.18819	+	4.72746i	0.302438	+	0.174613i	−0.341100	+	0.940027i	$0.610799\pi$
$734$	−16.1824	−	1.33567i	−0.597302	−	0.0493004i
$735$	8.82964	+	32.9527i	0.325686	+	1.21548i
$736$	0.282713	−	1.87111i	0.0104209	−	0.0689699i
$737$	4.36842	−	7.56632i	0.160913	−	0.278709i
$738$	17.0607	+	36.1222i	0.628012	+	1.32968i
$739$	−6.32774			−0.232770			−0.116385	−	0.993204i	$-0.537131\pi$
$739$	−6.32774			−0.232770			−0.116385	+	0.993204i	$0.537131\pi$
$740$	−12.4169	+	39.4935i	−0.456455	+	1.45181i
$741$	16.1203			0.592192
$742$	3.60966	+	7.64265i	0.132515	+	0.280571i
$743$	9.20465	−	15.9429i	0.337686	−	0.584889i	−0.646311	−	0.763074i	$-0.723689\pi$
$743$	9.20465	−	15.9429i	0.337686	−	0.584889i	0.983997	+	0.178185i	$0.0570226\pi$
$744$	31.4185	−	0.463268i	1.15186	−	0.0169842i
$745$	−14.1691	−	52.8800i	−0.519117	−	1.93737i
$746$	−8.74320	−	0.721650i	−0.320111	−	0.0264215i
$747$	17.0114	+	9.82155i	0.622416	+	0.359352i
$748$	−0.284054	+	0.203087i	−0.0103860	+	0.00742558i
$749$	−8.58957	−	14.8776i	−0.313856	−	0.543615i
$750$	−19.4647	+	16.4966i	−0.710752	+	0.602369i
$751$	−20.1185			−0.734133			−0.367067	−	0.930195i	$-0.619638\pi$
$751$	−20.1185			−0.734133			−0.367067	+	0.930195i	$0.619638\pi$
$752$	−12.3967	+	2.43806i	−0.452060	+	0.0889067i
$753$	−3.43378	−	12.8150i	−0.125134	−	0.467006i
$754$	−0.501161	+	6.07185i	−0.0182512	+	0.221124i
$755$	−44.1202	−	11.8220i	−1.60570	−	0.430245i
$756$	66.0703	−	24.7858i	2.40295	−	0.901449i
$757$	−43.1838	−	11.5711i	−1.56954	−	0.420557i	−0.633873	−	0.773437i	$-0.718536\pi$
$757$	−43.1838	−	11.5711i	−1.56954	−	0.420557i	−0.935669	+	0.352880i	$0.885203\pi$
$758$	6.26538	−	9.04215i	0.227569	−	0.328426i
$759$	−1.19701	+	0.320739i	−0.0434488	+	0.0116421i
$760$	−38.6799	+	10.9780i	−1.40307	+	0.398213i
$761$	34.0972	−	19.6860i	1.23602	−	0.713618i	0.267744	−	0.963490i	$-0.413722\pi$
$761$	34.0972	−	19.6860i	1.23602	−	0.713618i	0.968279	+	0.249872i	$0.0803886\pi$
$762$	−30.3538	−	64.2674i	−1.09960	−	2.32816i
$763$	20.1957	+	20.1957i	0.731134	+	0.731134i
$764$	−10.6863	+	1.04087i	−0.386617	+	0.0376573i
$765$	3.84461	−	2.21969i	0.139002	−	0.0802530i
$766$	20.7829	−	17.6137i	0.750915	−	0.636407i
$767$	12.4487			0.449497
$768$	7.23492	−	53.1801i	0.261068	−	1.91897i
$769$	−0.0258775	−	0.0258775i	−0.000933166	−	0.000933166i	0.706640	−	0.707573i	$-0.250210\pi$
$769$	−0.0258775	−	0.0258775i	−0.000933166	−	0.000933166i	−0.707573	+	0.706640i	$0.750210\pi$
$770$	1.89998	+	10.4741i	0.0684706	+	0.377459i
$771$	−47.4930	+	47.4930i	−1.71042	+	1.71042i
$772$	3.75473	+	38.5487i	0.135136	+	1.38740i
$773$	10.7841	−	18.6785i	0.387875	−	0.671820i	−0.604288	−	0.796766i	$-0.706542\pi$
$773$	10.7841	−	18.6785i	0.387875	−	0.671820i	0.992164	+	0.124946i	$0.0398758\pi$
$774$	−11.3356	−	62.4897i	−0.407448	−	2.24615i
$775$	5.64071	−	21.0514i	0.202620	−	0.756189i
$776$	7.51593	+	12.5857i	0.269806	+	0.451801i
$777$	−24.5842	−	32.6439i	−0.881953	−	1.17109i
$778$	−8.23180	−	9.71293i	−0.295124	−	0.348225i
$779$	13.8127	+	3.70110i	0.494891	+	0.132606i
$780$	20.2847	+	16.6838i	0.726307	+	0.597377i
$781$	−0.375267	−	0.216660i	−0.0134281	−	0.00775272i
$782$	0.0614750	+	0.0425966i	0.00219834	+	0.00152325i
$783$	46.6472	+	46.6472i	1.66703	+	1.66703i
$784$	−9.00485	+	7.86273i	−0.321602	+	0.280812i
$785$	20.6942	−	20.6942i	0.738608	−	0.738608i
$786$	2.54477	−	7.10008i	0.0907690	−	0.253251i
$787$		−	43.4054i		−	1.54723i	−0.633653	−	0.773617i	$-0.718445\pi$
$787$		−	43.4054i		−	1.54723i	0.633653	−	0.773617i	$-0.281555\pi$
$788$	−50.5745	−	8.40594i	−1.80164	−	0.299449i
$789$	28.1173	+	48.7006i	1.00100	+	1.73379i
$790$	−33.0536	−	22.9031i	−1.17600	−	0.814857i
$791$	−1.68700	+	1.68700i	−0.0599828	+	0.0599828i
$792$	−24.7965	+	7.03765i	−0.881107	+	0.250072i
$793$	−3.39297	−	5.87680i	−0.120488	−	0.208691i
$794$	15.8913	+	33.6463i	0.563962	+	1.19406i
$795$	8.81617	+	32.9024i	0.312677	+	1.16693i
$796$	−3.44242	−	35.3424i	−0.122013	−	1.25268i
$797$	10.3840	−	38.7538i	0.367822	−	1.37273i	−0.495733	−	0.868475i	$-0.665101\pi$
$797$	10.3840	−	38.7538i	0.367822	−	1.37273i	0.863555	−	0.504255i	$-0.168233\pi$
$798$	13.3910	−	37.3619i	0.474038	−	1.32260i
$799$	0.129238	−	0.482323i	0.00457211	−	0.0170633i
$800$	−34.1138	−	14.8983i	−1.20610	−	0.526735i
$801$	−123.022	+	32.9635i	−4.34675	+	1.16471i
$802$	−36.4248	−	13.0552i	−1.28621	−	0.460994i
$803$		−	16.3233i		−	0.576038i
$804$	−52.3551	−	8.70190i	−1.84642	−	0.306892i
$805$	1.97454	−	1.14000i	0.0695935	−	0.0401798i
$806$	−5.37005	−	0.443235i	−0.189152	−	0.0156123i
$807$	−43.1231	+	74.6914i	−1.51800	+	2.62926i
$808$	15.5610	+	3.92461i	0.547435	+	0.138067i
$809$	−38.9534	+	10.4375i	−1.36953	+	0.366964i	−0.867306	−	0.497775i	$-0.834151\pi$
$809$	−38.9534	+	10.4375i	−1.36953	+	0.366964i	−0.502222	+	0.864739i	$0.667484\pi$
$810$	162.597	−	29.4949i	5.71308	−	1.03635i
$811$	−7.33179	−	4.23301i	−0.257454	−	0.148641i	0.365719	−	0.930725i	$-0.380823\pi$
$811$	−7.33179	−	4.23301i	−0.257454	−	0.148641i	−0.623173	+	0.782084i	$0.714157\pi$
$812$	13.6564	+	6.20541i	0.479246	+	0.217767i
$813$			49.5862i			1.73906i
$814$	5.07158	+	8.03329i	0.177759	+	0.281567i
$815$			71.1607i			2.49265i
$816$	1.76116	+	1.18227i	0.0616528	+	0.0413878i
$817$	−19.6881	−	11.3669i	−0.688799	−	0.397678i
$818$	−1.54031	−	8.49128i	−0.0538556	−	0.296891i
$819$	−18.3655	+	4.92101i	−0.641741	+	0.171954i
$820$	13.5505	+	18.9528i	0.473203	+	0.661861i
$821$	3.57600	−	6.19381i	0.124803	−	0.216166i	−0.796853	−	0.604174i	$-0.793503\pi$
$821$	3.57600	−	6.19381i	0.124803	−	0.216166i	0.921656	+	0.388008i	$0.126837\pi$
$822$	4.05863	−	49.1726i	0.141561	−	1.71509i
$823$	13.4998	−	7.79412i	0.470574	−	0.271686i	−0.245906	−	0.969294i	$-0.579085\pi$
$823$	13.4998	−	7.79412i	0.470574	−	0.271686i	0.716480	+	0.697608i	$0.245752\pi$
$824$	23.5694	+	39.4679i	0.821080	+	1.37493i
$825$			24.3776i			0.848721i
$826$	10.3411	−	28.8524i	0.359813	−	1.00390i
$827$	−18.3469	+	4.91603i	−0.637983	+	0.170947i	−0.563290	−	0.826260i	$-0.690464\pi$
$827$	−18.3469	+	4.91603i	−0.637983	+	0.170947i	−0.0746933	+	0.997207i	$0.523798\pi$
$828$	3.21092	+	4.49106i	0.111587	+	0.156075i
$829$	1.70498	−	6.36307i	0.0592164	−	0.220998i	−0.929976	−	0.367619i	$-0.880173\pi$
$829$	1.70498	−	6.36307i	0.0592164	−	0.220998i	0.989193	+	0.146621i	$0.0468397\pi$
$830$	10.7844	+	3.86529i	0.374332	+	0.134166i
$831$	13.6107	−	50.7958i	0.472150	−	1.76209i
$832$	−2.11889	+	8.95623i	−0.0734593	+	0.310501i
$833$	−0.122285	−	0.456375i	−0.00423694	−	0.0158125i
$834$	−20.7055	+	9.77930i	−0.716973	+	0.338630i
$835$	−3.12265	−	5.40859i	−0.108064	−	0.187172i
$836$	−3.81700	+	8.40019i	−0.132014	+	0.290527i
$837$	−41.2556	+	41.2556i	−1.42600	+	1.42600i
$838$	13.2531	−	19.1267i	0.457820	−	0.660722i
$839$	16.3793	+	28.3698i	0.565476	+	0.979433i	0.997005	+	0.0773338i	$0.0246407\pi$
$839$	16.3793	+	28.3698i	0.565476	+	0.979433i	−0.431530	+	0.902099i	$0.642026\pi$
$840$	55.5185	−	33.1545i	1.91557	−	1.14394i
$841$		−	14.9771i		−	0.516452i
$842$	15.3343	+	5.49603i	0.528455	+	0.189406i
$843$	−29.7001	+	29.7001i	−1.02293	+	1.02293i
$844$	29.2445	+	24.0532i	1.00664	+	0.827945i
$845$	28.0971	+	28.0971i	0.966571	+	0.966571i
$846$	20.9932	−	30.2972i	0.721760	−	1.04164i
$847$	−16.9641	−	9.79424i	−0.582894	−	0.336534i
$848$	−8.99111	+	7.85074i	−0.308756	+	0.269595i
$849$	−37.0562	−	9.92918i	−1.27177	−	0.340768i
$850$	1.12237	−	0.951223i	0.0384971	−	0.0326267i
$851$	1.25322	−	1.60310i	0.0429599	−	0.0549535i
$852$	−0.431588	+	2.59666i	−0.0147860	+	0.0889600i
$853$	−9.37033	+	34.9706i	−0.320834	+	1.19737i	0.597600	+	0.801795i	$0.296121\pi$
$853$	−9.37033	+	34.9706i	−0.320834	+	1.19737i	−0.918434	+	0.395575i	$0.870546\pi$
$854$	−16.4392	+	2.98205i	−0.562537	+	0.102044i
$855$	58.6521	−	101.588i	2.00586	−	3.47425i
$856$	16.9000	−	17.4058i	0.577629	−	0.594918i
$857$	−0.656096	+	0.656096i	−0.0224118	+	0.0224118i	−0.718224	−	0.695812i	$-0.755045\pi$
$857$	−0.656096	+	0.656096i	−0.0224118	+	0.0224118i	0.695812	+	0.718224i	$0.255045\pi$
$858$	5.93030	−	1.07575i	0.202457	−	0.0367255i
$859$	21.0542	+	21.0542i	0.718360	+	0.718360i	0.968269	−	0.249910i	$-0.0804009\pi$
$859$	21.0542	+	21.0542i	0.718360	+	0.718360i	−0.249910	+	0.968269i	$0.580401\pi$
$860$	−13.0098	−	34.6798i	−0.443632	−	1.18257i
$861$	−22.9982			−0.783776
$862$	3.62102	+	4.27255i	0.123333	+	0.145524i
$863$	2.46738	−	1.42454i	0.0839907	−	0.0484920i	−0.457416	−	0.889253i	$-0.651225\pi$
$863$	2.46738	−	1.42454i	0.0839907	−	0.0484920i	0.541407	+	0.840761i	$0.317892\pi$
$864$	59.1479	+	80.2030i	2.01225	+	2.72856i
$865$	−42.5791	−	42.5791i	−1.44773	−	1.44773i
$866$	−7.57458	+	3.57751i	−0.257395	+	0.121569i
$867$	49.3119	−	28.4703i	1.67472	−	0.966901i
$868$	−5.48817	+	12.0780i	−0.186281	+	0.409953i
$869$	−8.91357	+	2.38838i	−0.302372	+	0.0810203i
$870$	49.6891	+	34.4300i	1.68462	+	1.16729i
$871$	8.79104	+	2.35555i	0.297873	+	0.0798148i
$872$	−19.6499	+	35.2239i	−0.665428	+	1.19283i
$873$	−41.3101	−	11.0690i	−1.39814	−	0.374629i
$874$	1.96954	+	0.162563i	0.0666206	+	0.00549877i
$875$	−2.78812	−	10.4054i	−0.0942557	−	0.351767i
$876$	−92.8409	+	34.8285i	−3.13680	+	1.17675i
$877$	−27.1359			−0.916315			−0.458158	−	0.888871i	$-0.651490\pi$
$877$	−27.1359			−0.916315			−0.458158	+	0.888871i	$0.651490\pi$
$878$	−7.44989	−	8.79034i	−0.251422	−	0.296660i
$879$	5.05461	+	8.75484i	0.170488	+	0.295293i
$880$	−13.4969	+	6.61978i	−0.454982	+	0.223153i
$881$	15.4899	+	8.94309i	0.521868	+	0.301300i	0.737698	−	0.675130i	$-0.235913\pi$
$881$	15.4899	+	8.94309i	0.521868	+	0.301300i	−0.215831	+	0.976431i	$0.569246\pi$
$882$	2.86892	−	34.7585i	0.0966014	−	1.17038i
$883$	−4.68442	−	17.4825i	−0.157643	−	0.588333i	−0.998864	−	0.0476415i	$-0.984829\pi$
$883$	−4.68442	−	17.4825i	−0.157643	−	0.588333i	0.841221	−	0.540691i	$-0.181837\pi$
$884$	−0.280931	−	0.231062i	−0.00944873	−	0.00777145i
$885$	61.7602	−	106.972i	2.07604	−	3.59582i
$886$	30.5855	−	14.4457i	1.02754	−	0.485311i
$887$	19.3816			0.650771			0.325386	−	0.945581i	$-0.394506\pi$
$887$	19.3816			0.650771			0.325386	+	0.945581i	$0.394506\pi$
$888$	34.8692	−	45.9856i	1.17014	−	1.54318i
$889$	30.0080			1.00644
$890$	−67.1647	+	31.7222i	−2.25136	+	1.06333i
$891$	18.9606	−	32.8408i	0.635205	−	1.10021i
$892$	18.8091	+	15.4702i	0.629775	+	0.517981i
$893$	−3.41493	−	12.7447i	−0.114276	−	0.426485i
$894$	−6.27757	+	76.0563i	−0.209953	+	2.54370i
$895$	43.2615	+	24.9770i	1.44607	+	0.834890i
$896$	18.9977	+	12.3509i	0.634669	+	0.412613i
$897$	−0.645458	−	1.11797i	−0.0215512	−	0.0373278i
$898$	25.9892	+	30.6654i	0.867272	+	1.02332i
$899$	−12.4021			−0.413633
$900$	101.683	−	38.1457i	3.38944	−	1.27152i
$901$	−0.122099	−	0.455680i	−0.00406771	−	0.0151809i
$902$	5.32838	+	0.439796i	0.177416	+	0.0146436i
$903$	35.3164	+	9.46299i	1.17525	+	0.314909i
$904$	−2.94234	−	1.64140i	−0.0978608	−	0.0545922i
$905$	34.0974	+	9.13638i	1.13344	+	0.303704i
$906$	52.3367	+	36.2646i	1.73877	+	1.20481i
$907$	25.9841	−	6.96241i	0.862787	−	0.231183i	0.199821	−	0.979832i	$-0.435964\pi$
$907$	25.9841	−	6.96241i	0.862787	−	0.231183i	0.662966	+	0.748649i	$0.269297\pi$
$908$	−13.6360	+	30.0091i	−0.452526	+	0.995886i
$909$	−40.5476	+	23.4101i	−1.34488	+	0.776466i
$910$	−10.0268	+	4.73570i	−0.332385	+	0.156987i
$911$	−32.7481	−	32.7481i	−1.08499	−	1.08499i	−0.996035	−	0.0889581i	$-0.971646\pi$
$911$	−32.7481	−	32.7481i	−1.08499	−	1.08499i	−0.0889581	−	0.996035i	$-0.528354\pi$
$912$	55.9213	+	3.78648i	1.85174	+	0.125383i
$913$	2.27672	−	1.31447i	0.0753485	−	0.0435025i
$914$	4.12197	+	4.86363i	0.136343	+	0.160875i
$915$	−67.3325			−2.22594
$916$	−6.68406	−	17.8174i	−0.220848	−	0.588704i
$917$	2.25171	+	2.25171i	0.0743579	+	0.0743579i
$918$	−3.87537	+	0.702989i	−0.127906	+	0.0232021i
$919$	−22.0309	+	22.0309i	−0.726733	+	0.726733i	−0.969967	−	0.243235i	$-0.921791\pi$
$919$	−22.0309	+	22.0309i	−0.726733	+	0.726733i	0.243235	+	0.969967i	$0.421791\pi$
$920$	2.31009	+	2.24295i	0.0761614	+	0.0739480i
$921$	−20.7516	+	35.9428i	−0.683788	+	1.18435i
$922$	−15.8364	+	2.87271i	−0.521546	+	0.0946078i
$923$	0.116828	−	0.436009i	0.00384545	−	0.0143514i
$924$	2.43302	−	14.6383i	0.0800404	−	0.481564i
$925$	−24.0801	−	31.9746i	−0.791750	−	1.05132i
$926$	11.3711	−	9.63707i	0.373676	−	0.316694i
$927$	−129.546	−	34.7116i	−4.25484	−	1.14008i
$928$	−3.16475	+	20.9456i	−0.103888	+	0.687572i
$929$	41.0038	+	23.6735i	1.34529	+	0.776703i	0.987578	−	0.157129i	$-0.0502238\pi$
$929$	41.0038	+	23.6735i	1.34529	+	0.776703i	0.357712	+	0.933832i	$0.383557\pi$
$930$	−30.4505	+	43.9459i	−0.998510	+	1.44104i
$931$	−8.82785	−	8.82785i	−0.289321	−	0.289321i
$932$	13.5510	+	11.1455i	0.443876	+	0.365082i
$933$	20.2345	−	20.2345i	0.662447	−	0.662447i
$934$	−31.9805	−	11.4623i	−1.04643	−	0.375057i
$935$		−	0.594143i		−	0.0194306i
$936$	−13.7667	−	23.0530i	−0.449980	−	0.753510i
$937$	8.37452	+	14.5051i	0.273584	+	0.473861i	0.969777	−	0.243994i	$-0.0784577\pi$
$937$	8.37452	+	14.5051i	0.273584	+	0.473861i	−0.696193	+	0.717854i	$0.745124\pi$
$938$	12.7621	−	18.4182i	0.416699	−	0.601376i
$939$	−15.6310	+	15.6310i	−0.510099	+	0.510099i
$940$	8.89314	−	19.5714i	0.290062	−	0.638348i
$941$	−9.18712	−	15.9126i	−0.299491	−	0.518734i	0.676528	−	0.736417i	$-0.263484\pi$
$941$	−9.18712	−	15.9126i	−0.299491	−	0.518734i	−0.976020	+	0.217682i	$0.930150\pi$
$942$	−36.8893	+	17.4230i	−1.20192	+	0.567671i
$943$	−0.296385	−	1.10612i	−0.00965162	−	0.0360204i
$944$	43.1846	+	2.92407i	1.40554	+	0.0951705i
$945$	−31.0763	+	115.978i	−1.01091	+	3.77277i
$946$	−8.00138	−	2.86781i	−0.260147	−	0.0932405i
$947$	−2.31388	+	8.63551i	−0.0751909	+	0.280616i	−0.993277	−	0.115766i	$-0.963068\pi$
$947$	−2.31388	+	8.63551i	−0.0751909	+	0.280616i	0.918086	+	0.396382i	$0.129734\pi$
$948$	32.6028	+	45.6010i	1.05889	+	1.48105i
$949$	16.4246	−	4.40096i	0.533165	−	0.142861i
$950$	13.1165	−	36.5959i	0.425555	−	1.18733i
$951$			33.5270i			1.08719i
$952$	−0.768900	+	0.459171i	−0.0249202	+	0.0148818i
$953$	3.78957	−	2.18791i	0.122756	−	0.0708733i	−0.437365	−	0.899284i	$-0.644088\pi$
$953$	3.78957	−	2.18791i	0.122756	−	0.0708733i	0.560121	+	0.828411i	$0.310755\pi$
$954$	2.86454	−	34.7055i	0.0927429	−	1.12363i
$955$	9.13446	−	15.8213i	0.295584	−	0.511967i
$956$	−25.5698	−	35.7640i	−0.826986	−	1.15669i
$957$	13.3996	−	3.59042i	0.433149	−	0.116062i
$958$	−6.77437	−	37.3452i	−0.218870	−	1.20657i
$959$	18.0405	+	10.4157i	0.582559	+	0.336340i
$960$	66.4487	+	62.6410i	2.14462	+	2.02173i
$961$			20.0314i			0.646174i
$962$	−6.71577	+	7.26892i	−0.216525	+	0.234359i
$963$			70.7790i			2.28082i
$964$	4.91673	+	2.23414i	0.158357	+	0.0719567i
$965$	−57.0723	−	32.9507i	−1.83722	−	1.06072i
$966$	−3.12729	+	0.567286i	−0.100619	+	0.0182521i
$967$	39.1992	−	10.5034i	1.26056	−	0.337766i	0.434154	−	0.900839i	$-0.357047\pi$
$967$	39.1992	−	10.5034i	1.26056	−	0.337766i	0.826408	+	0.563072i	$0.190381\pi$
$968$	6.76498	−	26.8230i	0.217435	−	0.862125i
$969$	−1.10761	+	1.91844i	−0.0355817	+	0.0616292i
$970$	−24.8581	−	2.05175i	−0.798145	−	0.0658777i
$971$	50.6569	−	29.2468i	1.62566	−	0.938573i	0.640288	−	0.768135i	$-0.278815\pi$
$971$	50.6569	−	29.2468i	1.62566	−	0.938573i	0.985368	−	0.170438i	$-0.0545182\pi$
$972$	−122.972	−	20.4392i	−3.94434	−	0.655586i
$973$		−	9.66790i		−	0.309939i
$974$	53.4903	+	19.1717i	1.71394	+	0.614301i
$975$	−24.5289	+	6.57250i	−0.785553	+	0.210488i
$976$	−10.3898	−	21.1836i	−0.332571	−	0.678072i
$977$	−11.2616	+	42.0290i	−0.360291	+	1.34463i	0.513402	+	0.858148i	$0.328385\pi$
$977$	−11.2616	+	42.0290i	−0.360291	+	1.34463i	−0.873693	+	0.486477i	$0.838282\pi$
$978$	33.4691	−	93.3811i	1.07022	−	2.98600i
$979$	−4.41167	+	16.4646i	−0.140998	+	0.526210i
$980$	−1.97189	−	20.2449i	−0.0629898	−	0.646698i
$981$	−30.4560	−	113.664i	−0.972387	−	3.62900i
$982$	−19.1554	−	40.5573i	−0.611274	−	1.29424i
$983$	−24.7895	−	42.9367i	−0.790663	−	1.36947i	−0.925557	−	0.378608i	$-0.876403\pi$
$983$	−24.7895	−	42.9367i	−0.790663	−	1.36947i	0.134894	−	0.990860i	$-0.456931\pi$
$984$	−8.86758	−	31.2442i	−0.282688	−	0.996028i
$985$	61.6833	−	61.6833i	1.96539	−	1.96539i
$986$	−0.688165	−	0.476835i	−0.0219156	−	0.0151855i
$987$	10.6100	+	18.3770i	0.337719	+	0.584947i
$988$	−9.48141	−	1.57590i	−0.301644	−	0.0501360i
$989$			1.82053i			0.0578896i
$990$	14.7976	−	41.2862i	0.470298	−	1.31216i
$991$	−32.5336	+	32.5336i	−1.03346	+	1.03346i	−0.0340431	+	0.999420i	$0.510838\pi$
$991$	−32.5336	+	32.5336i	−1.03346	+	1.03346i	−0.999420	+	0.0340431i	$0.989162\pi$
$992$	−18.5246	−	2.79896i	−0.588157	−	0.0888670i
$993$	−11.0092	−	11.0092i	−0.349365	−	0.349365i
$994$	−0.913489	−	0.632964i	−0.0289741	−	0.0200764i
$995$	52.3253	+	30.2100i	1.65882	+	0.957721i
$996$	−12.3339	−	10.1445i	−0.390816	−	0.321441i
$997$	9.37631	+	2.51238i	0.296951	+	0.0795677i	0.404219	−	0.914662i	$-0.367544\pi$
$997$	9.37631	+	2.51238i	0.296951	+	0.0795677i	−0.107268	+	0.994230i	$0.534210\pi$
$998$	17.0445	+	20.1113i	0.539535	+	0.636613i
$999$	13.0285	+	106.362i	0.412205	+	3.36516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	148.2.l.b.103.3	yes	64
4.3	odd	2	inner	148.2.l.b.103.11	yes	64
37.23	odd	12	inner	148.2.l.b.23.11	yes	64
148.23	even	12	inner	148.2.l.b.23.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.l.b.23.3	✓	64	148.23	even	12	inner
148.2.l.b.23.11	yes	64	37.23	odd	12	inner
148.2.l.b.103.3	yes	64	1.1	even	1	trivial
148.2.l.b.103.11	yes	64	4.3	odd	2	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:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	148.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27876 + 0.603964i) q^{2} +(-1.67719 + 2.90497i) q^{3} +(1.27045 - 1.54465i) q^{4} +(0.880766 + 3.28706i) q^{5} +(0.390219 - 4.72772i) q^{6} +(1.73451 + 1.00142i) q^{7} +(-0.691691 + 2.74255i) q^{8} +(-4.12591 - 7.14629i) q^{9} +O(q^{10})\)	\(q+(-1.27876 + 0.603964i) q^{2} +(-1.67719 + 2.90497i) q^{3} +(1.27045 - 1.54465i) q^{4} +(0.880766 + 3.28706i) q^{5} +(0.390219 - 4.72772i) q^{6} +(1.73451 + 1.00142i) q^{7} +(-0.691691 + 2.74255i) q^{8} +(-4.12591 - 7.14629i) q^{9} +(-3.11156 - 3.67141i) q^{10} -1.10438 q^{11} +(2.35638 + 6.28130i) q^{12} +(-0.297754 - 1.11123i) q^{13} +(-2.82285 - 0.232994i) q^{14} +(-11.0260 - 2.95442i) q^{15} +(-0.771894 - 3.92482i) q^{16} +(0.152704 + 0.0409170i) q^{17} +(9.59215 + 6.64648i) q^{18} +(4.03499 - 1.08117i) q^{19} +(6.19634 + 2.81559i) q^{20} +(-5.81820 + 3.35914i) q^{21} +(1.41224 - 0.667007i) q^{22} +(-0.236543 - 0.236543i) q^{23} +(-6.80693 - 6.60911i) q^{24} +(-5.69891 + 3.29027i) q^{25} +(1.05190 + 1.24117i) q^{26} +17.6166 q^{27} +(3.75046 - 1.40696i) q^{28} +(2.64791 + 2.64791i) q^{29} +(15.8840 - 2.88134i) q^{30} +(-2.34186 + 2.34186i) q^{31} +(3.35752 + 4.55270i) q^{32} +(1.85225 - 3.20820i) q^{33} +(-0.219985 + 0.0399050i) q^{34} +(-1.76404 + 6.58347i) q^{35} +(-16.2803 - 2.70594i) q^{36} +(0.739562 + 6.03764i) q^{37} +(-4.50680 + 3.81955i) q^{38} +(3.72749 + 0.998778i) q^{39} +(-9.62414 + 0.141909i) q^{40} +(2.96460 + 1.71161i) q^{41} +(5.41128 - 7.80952i) q^{42} +(-3.84821 - 3.84821i) q^{43} +(-1.40307 + 1.70588i) q^{44} +(19.8563 - 19.8563i) q^{45} +(0.445345 + 0.159618i) q^{46} -3.15854i q^{47} +(12.6961 + 4.34032i) q^{48} +(-1.49431 - 2.58822i) q^{49} +(5.30033 - 7.64940i) q^{50} +(-0.374976 + 0.374976i) q^{51} +(-2.09475 - 0.951845i) q^{52} +(-1.49203 - 2.58428i) q^{53} +(-22.5274 + 10.6398i) q^{54} +(-0.972702 - 3.63017i) q^{55} +(-3.94619 + 4.06431i) q^{56} +(-3.62666 + 13.5349i) q^{57} +(-4.98529 - 1.78680i) q^{58} +(-2.80065 + 10.4522i) q^{59} +(-18.5716 + 13.2779i) q^{60} +(5.69761 - 1.52667i) q^{61} +(1.58028 - 4.40908i) q^{62} -16.5271i q^{63} +(-7.04313 - 3.79399i) q^{64} +(3.39044 - 1.95747i) q^{65} +(-0.430951 + 5.22121i) q^{66} +(-3.95553 + 6.85118i) q^{67} +(0.257206 - 0.183892i) q^{68} +(1.08388 - 0.290424i) q^{69} +(-1.72040 - 9.48409i) q^{70} +(0.339798 + 0.196183i) q^{71} +(22.4529 - 6.37248i) q^{72} +14.7805i q^{73} +(-4.59224 - 7.27402i) q^{74} -22.0736i q^{75} +(3.45624 - 7.60624i) q^{76} +(-1.91556 - 1.10595i) q^{77} +(-5.36979 + 0.974075i) q^{78} +(8.07109 - 2.16264i) q^{79} +(12.2213 - 5.99411i) q^{80} +(-17.1685 + 29.7368i) q^{81} +(-4.82476 - 0.398228i) q^{82} +(-2.06154 + 1.19023i) q^{83} +(-2.20306 + 13.2547i) q^{84} +0.537987i q^{85} +(7.24512 + 2.59676i) q^{86} +(-12.1332 + 3.25107i) q^{87} +(0.763891 - 3.02882i) q^{88} +(3.99470 - 14.9084i) q^{89} +(-13.3990 + 37.3840i) q^{90} +(0.596354 - 2.22563i) q^{91} +(-0.665893 + 0.0648594i) q^{92} +(-2.87530 - 10.7308i) q^{93} +(1.90764 + 4.03901i) q^{94} +(7.10777 + 12.3110i) q^{95} +(-18.8567 + 2.11776i) q^{96} +(3.66478 - 3.66478i) q^{97} +(3.47406 + 2.40720i) q^{98} +(4.55658 + 7.89223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{2} - 4 q^{5} + 8 q^{8} - 36 q^{9}+O(q^{10}) \) 64 * q - 4 * q^2 - 4 * q^5 + 8 * q^8 - 36 * q^9	\( 64 q - 4 q^{2} - 4 q^{5} + 8 q^{8} - 36 q^{9} + 4 q^{10} + 10 q^{12} - 28 q^{13} + 4 q^{14} - 20 q^{16} - 36 q^{17} + 44 q^{18} - 26 q^{20} - 12 q^{21} - 4 q^{22} - 22 q^{24} - 24 q^{25} + 32 q^{26} - 6 q^{28} + 4 q^{29} + 54 q^{30} + 16 q^{32} - 16 q^{33} + 8 q^{34} + 20 q^{37} - 112 q^{38} - 18 q^{40} + 12 q^{41} - 44 q^{42} - 32 q^{44} + 20 q^{45} + 46 q^{46} + 44 q^{49} - 72 q^{50} - 52 q^{52} + 4 q^{53} - 44 q^{54} - 46 q^{56} + 28 q^{57} + 30 q^{58} + 8 q^{60} + 24 q^{61} + 24 q^{62} + 72 q^{65} + 8 q^{66} + 64 q^{68} + 28 q^{69} + 50 q^{70} + 128 q^{72} - 8 q^{74} + 52 q^{76} - 144 q^{77} + 36 q^{78} + 40 q^{80} - 24 q^{82} + 104 q^{84} - 6 q^{86} - 44 q^{88} + 4 q^{89} + 62 q^{90} - 142 q^{92} + 92 q^{93} + 28 q^{94} + 70 q^{96} - 12 q^{97} + 24 q^{98}+O(q^{100}) \) 64 * q - 4 * q^2 - 4 * q^5 + 8 * q^8 - 36 * q^9 + 4 * q^10 + 10 * q^12 - 28 * q^13 + 4 * q^14 - 20 * q^16 - 36 * q^17 + 44 * q^18 - 26 * q^20 - 12 * q^21 - 4 * q^22 - 22 * q^24 - 24 * q^25 + 32 * q^26 - 6 * q^28 + 4 * q^29 + 54 * q^30 + 16 * q^32 - 16 * q^33 + 8 * q^34 + 20 * q^37 - 112 * q^38 - 18 * q^40 + 12 * q^41 - 44 * q^42 - 32 * q^44 + 20 * q^45 + 46 * q^46 + 44 * q^49 - 72 * q^50 - 52 * q^52 + 4 * q^53 - 44 * q^54 - 46 * q^56 + 28 * q^57 + 30 * q^58 + 8 * q^60 + 24 * q^61 + 24 * q^62 + 72 * q^65 + 8 * q^66 + 64 * q^68 + 28 * q^69 + 50 * q^70 + 128 * q^72 - 8 * q^74 + 52 * q^76 - 144 * q^77 + 36 * q^78 + 40 * q^80 - 24 * q^82 + 104 * q^84 - 6 * q^86 - 44 * q^88 + 4 * q^89 + 62 * q^90 - 142 * q^92 + 92 * q^93 + 28 * q^94 + 70 * q^96 - 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more