LMFDB - Embedded newform 833.2.e.h.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(18,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("833.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.e (of order $3$, degree $2$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 10x^{7} + 44x^{6} - 49x^{5} + 99x^{4} - 20x^{3} + 31x^{2} - 3x + 9 $ x^10 - 2x^9 + 9x^8 - 10x^7 + 44x^6 - 49x^5 + 99x^4 - 20x^3 + 31x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.3
Root			$1.16091 + 2.01076i$ of defining polynomial
Character	$\chi$	$=$	833.18
Dual form			833.2.e.h.324.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438917 - 0.760227i) q^{2} +(0.453789 - 0.785986i) q^{3} +(0.614704 - 1.06470i) q^{4} +(1.51909 + 2.63114i) q^{5} -0.796703 q^{6} -2.83488 q^{8} +(1.08815 + 1.88473i) q^{9} +O(q^{10})$	\(q+(-0.438917 - 0.760227i) q^{2} +(0.453789 - 0.785986i) q^{3} +(0.614704 - 1.06470i) q^{4} +(1.51909 + 2.63114i) q^{5} -0.796703 q^{6} -2.83488 q^{8} +(1.08815 + 1.88473i) q^{9} +(1.33351 - 2.30971i) q^{10} +(-2.39089 + 4.14114i) q^{11} +(-0.557892 - 0.966297i) q^{12} +4.39933 q^{13} +2.75739 q^{15} +(0.0148720 + 0.0257591i) q^{16} +(0.500000 - 0.866025i) q^{17} +(0.955216 - 1.65448i) q^{18} +(-1.32183 - 2.28947i) q^{19} +3.73516 q^{20} +4.19761 q^{22} +(4.22941 + 7.32555i) q^{23} +(-1.28644 + 2.22818i) q^{24} +(-2.11527 + 3.66376i) q^{25} +(-1.93094 - 3.34449i) q^{26} +4.69790 q^{27} +7.04298 q^{29} +(-1.21026 - 2.09624i) q^{30} +(-1.71032 + 2.96236i) q^{31} +(-2.82183 + 4.88755i) q^{32} +(2.16992 + 3.75841i) q^{33} -0.877834 q^{34} +2.67556 q^{36} +(-4.83488 - 8.37426i) q^{37} +(-1.16035 + 2.00978i) q^{38} +(1.99637 - 3.45781i) q^{39} +(-4.30645 - 7.45898i) q^{40} -1.33675 q^{41} +2.52513 q^{43} +(2.93938 + 5.09115i) q^{44} +(-3.30600 + 5.72616i) q^{45} +(3.71272 - 6.43062i) q^{46} +(-2.78541 - 4.82448i) q^{47} +0.0269950 q^{48} +3.71372 q^{50} +(-0.453789 - 0.785986i) q^{51} +(2.70428 - 4.68395i) q^{52} +(-2.58815 + 4.48281i) q^{53} +(-2.06199 - 3.57147i) q^{54} -14.5279 q^{55} -2.39933 q^{57} +(-3.09129 - 5.35426i) q^{58} +(4.64366 - 8.04305i) q^{59} +(1.69498 - 2.93578i) q^{60} +(3.33162 + 5.77054i) q^{61} +3.00275 q^{62} +5.01368 q^{64} +(6.68297 + 11.5753i) q^{65} +(1.90483 - 3.29926i) q^{66} +(-2.64126 + 4.57479i) q^{67} +(-0.614704 - 1.06470i) q^{68} +7.67704 q^{69} -11.9310 q^{71} +(-3.08478 - 5.34300i) q^{72} +(6.35773 - 11.0119i) q^{73} +(-4.24423 + 7.35122i) q^{74} +(1.91977 + 3.32515i) q^{75} -3.25013 q^{76} -3.50496 q^{78} +(-0.970256 - 1.68053i) q^{79} +(-0.0451838 + 0.0782607i) q^{80} +(-1.13260 + 1.96172i) q^{81} +(0.586724 + 1.01624i) q^{82} +4.58417 q^{83} +3.03818 q^{85} +(-1.10832 - 1.91967i) q^{86} +(3.19603 - 5.53569i) q^{87} +(6.77789 - 11.7397i) q^{88} +(-6.69779 - 11.6009i) q^{89} +5.80424 q^{90} +10.3993 q^{92} +(1.55225 + 2.68857i) q^{93} +(-2.44513 + 4.23509i) q^{94} +(4.01596 - 6.95584i) q^{95} +(2.56103 + 4.43583i) q^{96} +15.1668 q^{97} -10.4066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9	$ 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9} + 4 q^{10} + 2 q^{11} - 22 q^{12} - 4 q^{13} + 16 q^{15} - 4 q^{16} + 5 q^{17} + 18 q^{18} + 6 q^{19} + 38 q^{20} + 12 q^{22} + 10 q^{23} + 2 q^{24} - 21 q^{25} - 26 q^{26} + 52 q^{27} - 16 q^{29} + 51 q^{30} - 9 q^{32} + 6 q^{33} - 4 q^{34} + 78 q^{36} - 8 q^{37} + 14 q^{38} - 14 q^{39} + 5 q^{40} - 36 q^{41} + 16 q^{43} + 14 q^{44} - 8 q^{46} - 10 q^{47} + 54 q^{48} + 54 q^{50} + 2 q^{51} + 4 q^{52} - 4 q^{53} + 5 q^{54} + 48 q^{55} + 24 q^{57} - 12 q^{58} + 8 q^{59} + 7 q^{60} + 22 q^{61} - 32 q^{62} - 32 q^{64} + 30 q^{65} + 68 q^{66} - 16 q^{67} + 10 q^{68} + 64 q^{69} - 4 q^{71} - 9 q^{72} + 10 q^{73} + 40 q^{74} - 14 q^{75} - 48 q^{76} + 60 q^{78} - 18 q^{79} - 4 q^{80} - 25 q^{81} - 31 q^{82} + 24 q^{83} - 23 q^{86} - 26 q^{87} + 46 q^{88} + 20 q^{89} - 194 q^{90} + 56 q^{92} + 28 q^{93} - 42 q^{94} + 22 q^{95} - 18 q^{96} - 24 q^{97} - 124 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9 + 4 * q^10 + 2 * q^11 - 22 * q^12 - 4 * q^13 + 16 * q^15 - 4 * q^16 + 5 * q^17 + 18 * q^18 + 6 * q^19 + 38 * q^20 + 12 * q^22 + 10 * q^23 + 2 * q^24 - 21 * q^25 - 26 * q^26 + 52 * q^27 - 16 * q^29 + 51 * q^30 - 9 * q^32 + 6 * q^33 - 4 * q^34 + 78 * q^36 - 8 * q^37 + 14 * q^38 - 14 * q^39 + 5 * q^40 - 36 * q^41 + 16 * q^43 + 14 * q^44 - 8 * q^46 - 10 * q^47 + 54 * q^48 + 54 * q^50 + 2 * q^51 + 4 * q^52 - 4 * q^53 + 5 * q^54 + 48 * q^55 + 24 * q^57 - 12 * q^58 + 8 * q^59 + 7 * q^60 + 22 * q^61 - 32 * q^62 - 32 * q^64 + 30 * q^65 + 68 * q^66 - 16 * q^67 + 10 * q^68 + 64 * q^69 - 4 * q^71 - 9 * q^72 + 10 * q^73 + 40 * q^74 - 14 * q^75 - 48 * q^76 + 60 * q^78 - 18 * q^79 - 4 * q^80 - 25 * q^81 - 31 * q^82 + 24 * q^83 - 23 * q^86 - 26 * q^87 + 46 * q^88 + 20 * q^89 - 194 * q^90 + 56 * q^92 + 28 * q^93 - 42 * q^94 + 22 * q^95 - 18 * q^96 - 24 * q^97 - 124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.438917	−	0.760227i	−0.310361	−	0.537561i	0.668079	−	0.744090i	$-0.267117\pi$
$2$	−0.438917	−	0.760227i	−0.310361	−	0.537561i	−0.978441	+	0.206529i	$0.933783\pi$
$3$	0.453789	−	0.785986i	0.261995	−	0.453789i	−0.704777	−	0.709429i	$-0.748953\pi$
$3$	0.453789	−	0.785986i	0.261995	−	0.453789i	0.966772	+	0.255640i	$0.0822862\pi$
$4$	0.614704	−	1.06470i	0.307352	−	0.532349i
$5$	1.51909	+	2.63114i	0.679358	+	1.17668i	0.975175	+	0.221438i	$0.0710749\pi$
$5$	1.51909	+	2.63114i	0.679358	+	1.17668i	−0.295817	+	0.955245i	$0.595592\pi$
$6$	−0.796703			−0.325253
$7$		0			0
$7$		0			0
$8$	−2.83488			−1.00228
$9$	1.08815	+	1.88473i	0.362717	+	0.628244i
$10$	1.33351	−	2.30971i	0.421693	−	0.730393i
$11$	−2.39089	+	4.14114i	−0.720880	+	1.24860i	0.239767	+	0.970830i	$0.422929\pi$
$11$	−2.39089	+	4.14114i	−0.720880	+	1.24860i	−0.960647	+	0.277771i	$0.910404\pi$
$12$	−0.557892	−	0.966297i	−0.161049	−	0.278946i
$13$	4.39933			1.22015			0.610077	−	0.792342i	$-0.291139\pi$
$13$	4.39933			1.22015			0.610077	+	0.792342i	$0.291139\pi$
$14$		0			0
$15$	2.75739			0.711954
$16$	0.0148720	+	0.0257591i	0.00371800	+	0.00643977i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	0.955216	−	1.65448i	0.225147	−	0.389965i
$19$	−1.32183	−	2.28947i	−0.303248	−	0.525242i	0.673621	−	0.739077i	$-0.264738\pi$
$19$	−1.32183	−	2.28947i	−0.303248	−	0.525242i	−0.976870	+	0.213835i	$0.931405\pi$
$20$	3.73516			0.835207
$21$		0			0
$22$	4.19761			0.894933
$23$	4.22941	+	7.32555i	0.881892	+	1.52748i	0.849235	+	0.528016i	$0.177064\pi$
$23$	4.22941	+	7.32555i	0.881892	+	1.52748i	0.0326578	+	0.999467i	$0.489603\pi$
$24$	−1.28644	+	2.22818i	−0.262593	+	0.454825i
$25$	−2.11527	+	3.66376i	−0.423054	+	0.732751i
$26$	−1.93094	−	3.34449i	−0.378688	−	0.655908i
$27$	4.69790			0.904111
$28$		0			0
$29$	7.04298			1.30785			0.653925	−	0.756560i	$-0.273121\pi$
$29$	7.04298			1.30785			0.653925	+	0.756560i	$0.273121\pi$
$30$	−1.21026	−	2.09624i	−0.220963	−	0.382719i
$31$	−1.71032	+	2.96236i	−0.307182	+	0.532055i	−0.977745	−	0.209798i	$-0.932719\pi$
$31$	−1.71032	+	2.96236i	−0.307182	+	0.532055i	0.670563	+	0.741853i	$0.266053\pi$
$32$	−2.82183	+	4.88755i	−0.498834	+	0.864005i
$33$	2.16992	+	3.75841i	0.377734	+	0.654255i
$34$	−0.877834			−0.150547
$35$		0			0
$36$	2.67556			0.445927
$37$	−4.83488	−	8.37426i	−0.794850	−	1.37672i	−0.922934	−	0.384957i	$-0.874216\pi$
$37$	−4.83488	−	8.37426i	−0.794850	−	1.37672i	0.128084	−	0.991763i	$-0.459117\pi$
$38$	−1.16035	+	2.00978i	−0.188233	+	0.326029i
$39$	1.99637	−	3.45781i	0.319674	−	0.553692i
$40$	−4.30645	−	7.45898i	−0.680909	−	1.17937i
$41$	−1.33675			−0.208766			−0.104383	−	0.994537i	$-0.533287\pi$
$41$	−1.33675			−0.208766			−0.104383	+	0.994537i	$0.533287\pi$
$42$		0			0
$43$	2.52513			0.385078			0.192539	−	0.981289i	$-0.438328\pi$
$43$	2.52513			0.385078			0.192539	+	0.981289i	$0.438328\pi$
$44$	2.93938	+	5.09115i	0.443128	+	0.767520i
$45$	−3.30600	+	5.72616i	−0.492829	+	0.853605i
$46$	3.71272	−	6.43062i	0.547410	−	0.948143i
$47$	−2.78541	−	4.82448i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$47$	−2.78541	−	4.82448i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$48$	0.0269950			0.00389639
$49$		0			0
$50$	3.71372			0.525199
$51$	−0.453789	−	0.785986i	−0.0635432	−	0.110060i
$52$	2.70428	−	4.68395i	0.375016	−	0.649547i
$53$	−2.58815	+	4.48281i	−0.355510	+	0.615761i	−0.987205	−	0.159456i	$-0.949026\pi$
$53$	−2.58815	+	4.48281i	−0.355510	+	0.615761i	0.631695	+	0.775217i	$0.282359\pi$
$54$	−2.06199	−	3.57147i	−0.280601	−	0.486015i
$55$	−14.5279			−1.95894
$56$		0			0
$57$	−2.39933			−0.317799
$58$	−3.09129	−	5.35426i	−0.405906	−	0.703049i
$59$	4.64366	−	8.04305i	0.604553	−	1.04712i	−0.387569	−	0.921841i	$-0.626685\pi$
$59$	4.64366	−	8.04305i	0.604553	−	1.04712i	0.992122	−	0.125275i	$-0.0399815\pi$
$60$	1.69498	−	2.93578i	0.218820	−	0.379008i
$61$	3.33162	+	5.77054i	0.426571	+	0.738842i	0.996566	−	0.0828061i	$-0.0263882\pi$
$61$	3.33162	+	5.77054i	0.426571	+	0.738842i	−0.569995	+	0.821648i	$0.693055\pi$
$62$	3.00275			0.381350
$63$		0			0
$64$	5.01368			0.626710
$65$	6.68297	+	11.5753i	0.828921	+	1.43573i
$66$	1.90483	−	3.29926i	0.234468	−	0.406111i
$67$	−2.64126	+	4.57479i	−0.322681	+	0.558900i	−0.981040	−	0.193804i	$-0.937917\pi$
$67$	−2.64126	+	4.57479i	−0.322681	+	0.558900i	0.658359	+	0.752704i	$0.271251\pi$
$68$	−0.614704	−	1.06470i	−0.0745438	−	0.129114i
$69$	7.67704			0.924206
$70$		0			0
$71$	−11.9310			−1.41595			−0.707973	−	0.706239i	$-0.750390\pi$
$71$	−11.9310			−1.41595			−0.707973	+	0.706239i	$0.750390\pi$
$72$	−3.08478	−	5.34300i	−0.363545	−	0.629678i
$73$	6.35773	−	11.0119i	0.744116	−	1.28885i	−0.206490	−	0.978449i	$-0.566204\pi$
$73$	6.35773	−	11.0119i	0.744116	−	1.28885i	0.950606	−	0.310399i	$-0.100463\pi$
$74$	−4.24423	+	7.35122i	−0.493381	+	0.854562i
$75$	1.91977	+	3.32515i	0.221676	+	0.383955i
$76$	−3.25013			−0.372816
$77$		0			0
$78$	−3.50496			−0.396858
$79$	−0.970256	−	1.68053i	−0.109162	−	0.189075i	0.806269	−	0.591549i	$-0.201483\pi$
$79$	−0.970256	−	1.68053i	−0.109162	−	0.189075i	−0.915431	+	0.402475i	$0.868150\pi$
$80$	−0.0451838	+	0.0782607i	−0.00505171	+	0.00874981i
$81$	−1.13260	+	1.96172i	−0.125844	+	0.217968i
$82$	0.586724	+	1.01624i	0.0647928	+	0.112224i
$83$	4.58417			0.503178			0.251589	−	0.967834i	$-0.419047\pi$
$83$	4.58417			0.503178			0.251589	+	0.967834i	$0.419047\pi$
$84$		0			0
$85$	3.03818			0.329537
$86$	−1.10832	−	1.91967i	−0.119513	−	0.207003i
$87$	3.19603	−	5.53569i	0.342650	−	0.593488i
$88$	6.77789	−	11.7397i	0.722526	−	1.25145i
$89$	−6.69779	−	11.6009i	−0.709965	−	1.22969i	−0.964870	−	0.262729i	$-0.915378\pi$
$89$	−6.69779	−	11.6009i	−0.709965	−	1.22969i	0.254905	−	0.966966i	$-0.417956\pi$
$90$	5.80424			0.611820
$91$		0			0
$92$	10.3993			1.08420
$93$	1.55225	+	2.68857i	0.160960	+	0.278792i
$94$	−2.44513	+	4.23509i	−0.252196	+	0.436816i
$95$	4.01596	−	6.95584i	0.412028	−	0.713654i
$96$	2.56103	+	4.43583i	0.261384	+	0.452730i
$97$	15.1668			1.53995			0.769976	−	0.638073i	$-0.220268\pi$
$97$	15.1668			1.53995			0.769976	+	0.638073i	$0.220268\pi$
$98$		0			0
$99$	−10.4066			−1.04590
$100$	2.60053	+	4.50425i	0.260053	+	0.450425i
$101$	1.62393	−	2.81273i	0.161587	−	0.279877i	−0.773851	−	0.633368i	$-0.781672\pi$
$101$	1.62393	−	2.81273i	0.161587	−	0.279877i	0.935438	+	0.353491i	$0.115005\pi$
$102$	−0.398352	+	0.689965i	−0.0394427	+	0.0683167i
$103$	−6.35157	−	11.0012i	−0.625839	−	1.08399i	−0.988378	−	0.152016i	$-0.951423\pi$
$103$	−6.35157	−	11.0012i	−0.625839	−	1.08399i	0.362539	−	0.931969i	$-0.381910\pi$
$104$	−12.4716			−1.22294
$105$		0			0
$106$	4.54393			0.441346
$107$	−1.95705	−	3.38971i	−0.189195	−	0.327696i	0.755787	−	0.654818i	$-0.227255\pi$
$107$	−1.95705	−	3.38971i	−0.189195	−	0.327696i	−0.944982	+	0.327122i	$0.893921\pi$
$108$	2.88782	−	5.00184i	0.277880	−	0.481303i
$109$	1.78178	−	3.08613i	0.170663	−	0.295598i	−0.767989	−	0.640464i	$-0.778742\pi$
$109$	1.78178	−	3.08613i	0.170663	−	0.295598i	0.938652	+	0.344866i	$0.112076\pi$
$110$	6.37655	+	11.0445i	0.607980	+	1.05305i
$111$	−8.77607			−0.832988
$112$		0			0
$113$	0.966622			0.0909322			0.0454661	−	0.998966i	$-0.485523\pi$
$113$	0.966622			0.0909322			0.0454661	+	0.998966i	$0.485523\pi$
$114$	1.05311	+	1.82403i	0.0986323	+	0.170836i
$115$	−12.8497	+	22.2563i	−1.19824	+	2.07541i
$116$	4.32935	−	7.49865i	0.401970	−	0.696232i
$117$	4.78713	+	8.29155i	0.442570	+	0.766554i
$118$	−8.15272			−0.750519
$119$		0			0
$120$	−7.81687			−0.713579
$121$	−5.93270	−	10.2757i	−0.539337	−	0.934159i
$122$	2.92461	−	5.06558i	0.264782	−	0.458616i
$123$	−0.606604	+	1.05067i	−0.0546957	+	0.0947356i
$124$	2.10268	+	3.64194i	0.188826	+	0.327056i
$125$	2.33775			0.209095
$126$		0			0
$127$	−5.55875			−0.493260			−0.246630	−	0.969110i	$-0.579323\pi$
$127$	−5.55875			−0.493260			−0.246630	+	0.969110i	$0.579323\pi$
$128$	3.44307	+	5.96357i	0.304327	+	0.527110i
$129$	1.14587	−	1.98471i	0.100889	−	0.174744i
$130$	5.86654	−	10.1612i	0.514530	−	0.891192i
$131$	−1.75567	−	3.04091i	−0.153393	−	0.265685i	0.779079	−	0.626925i	$-0.215687\pi$
$131$	−1.75567	−	3.04091i	−0.153393	−	0.265685i	−0.932473	+	0.361240i	$0.882354\pi$
$132$	5.33543			0.464389
$133$		0			0
$134$	4.63717			0.400590
$135$	7.13653	+	12.3608i	0.614215	+	1.06385i
$136$	−1.41744	+	2.45508i	−0.121545	+	0.210522i
$137$	0.968898	−	1.67818i	0.0827786	−	0.143377i	−0.821664	−	0.569972i	$-0.806954\pi$
$137$	0.968898	−	1.67818i	0.0827786	−	0.143377i	0.904442	+	0.426596i	$0.140287\pi$
$138$	−3.36958	−	5.83629i	−0.286838	−	0.496818i
$139$	−4.69834			−0.398508			−0.199254	−	0.979948i	$-0.563852\pi$
$139$	−4.69834			−0.398508			−0.199254	+	0.979948i	$0.563852\pi$
$140$		0			0
$141$	−5.05596			−0.425789
$142$	5.23671	+	9.07024i	0.439455	+	0.761158i
$143$	−10.5183	+	18.2182i	−0.879585	+	1.52349i
$144$	−0.0323660	+	0.0560595i	−0.00269716	+	0.00467162i
$145$	10.6989	+	18.5311i	0.888498	+	1.53892i
$146$	−11.1621			−0.923780
$147$		0			0
$148$	−11.8881			−0.977194
$149$	−2.12081	−	3.67335i	−0.173743	−	0.300932i	0.765982	−	0.642862i	$-0.222253\pi$
$149$	−2.12081	−	3.67335i	−0.173743	−	0.300932i	−0.939726	+	0.341929i	$0.888920\pi$
$150$	1.68524	−	2.91893i	0.137600	−	0.238329i
$151$	−6.22919	+	10.7893i	−0.506924	+	0.878018i	0.493044	+	0.870004i	$0.335884\pi$
$151$	−6.22919	+	10.7893i	−0.506924	+	0.878018i	−0.999968	+	0.00801357i	$0.997449\pi$
$152$	3.74723	+	6.49040i	0.303941	+	0.526441i
$153$	2.17630			0.175944
$154$		0			0
$155$	−10.3925			−0.834746
$156$	−2.45435	−	4.25105i	−0.196505	−	0.340357i
$157$	−8.82359	+	15.2829i	−0.704199	+	1.21971i	0.262780	+	0.964856i	$0.415361\pi$
$157$	−8.82359	+	15.2829i	−0.704199	+	1.21971i	−0.966980	+	0.254853i	$0.917973\pi$
$158$	−0.851724	+	1.47523i	−0.0677595	+	0.117363i
$159$	2.34895	+	4.06850i	0.186284	+	0.322653i
$160$	−17.1465			−1.35555
$161$		0			0
$162$	1.98847			0.156229
$163$	1.33778	+	2.31711i	0.104783	+	0.181490i	0.913650	−	0.406503i	$-0.133252\pi$
$163$	1.33778	+	2.31711i	0.104783	+	0.181490i	−0.808866	+	0.587993i	$0.799918\pi$
$164$	−0.821707	+	1.42324i	−0.0641645	+	0.111136i
$165$	−6.59261	+	11.4187i	−0.513234	+	0.888947i
$166$	−2.01207	−	3.48501i	−0.156167	−	0.270489i
$167$	1.95783			0.151501			0.0757507	−	0.997127i	$-0.475865\pi$
$167$	1.95783			0.151501			0.0757507	+	0.997127i	$0.475865\pi$
$168$		0			0
$169$	6.35407			0.488775
$170$	−1.33351	−	2.30971i	−0.102276	−	0.177146i
$171$	2.87670	−	4.98259i	0.219987	−	0.381028i
$172$	1.55220	−	2.68850i	0.118354	−	0.204996i
$173$	3.00866	+	5.21115i	0.228744	+	0.396196i	0.957436	−	0.288645i	$-0.0932048\pi$
$173$	3.00866	+	5.21115i	0.228744	+	0.396196i	−0.728692	+	0.684841i	$0.759871\pi$
$174$	−5.61117			−0.425382
$175$		0			0
$176$	−0.142229			−0.0107209
$177$	−4.21448	−	7.29970i	−0.316780	−	0.548679i
$178$	−5.87955	+	10.1837i	−0.440691	+	0.763299i
$179$	−0.875558	+	1.51651i	−0.0654423	+	0.113349i	−0.896890	−	0.442253i	$-0.854179\pi$
$179$	−0.875558	+	1.51651i	−0.0654423	+	0.113349i	0.831448	+	0.555603i	$0.187512\pi$
$180$	4.06442	+	7.03978i	0.302944	+	0.524714i
$181$	−2.76491			−0.205514			−0.102757	−	0.994707i	$-0.532766\pi$
$181$	−2.76491			−0.205514			−0.102757	+	0.994707i	$0.532766\pi$
$182$		0			0
$183$	6.04742			0.447038
$184$	−11.9899	−	20.7671i	−0.883906	−	1.53097i
$185$	14.6893	−	25.4425i	1.07998	−	1.87057i
$186$	1.36261	−	2.36012i	0.0999118	−	0.173052i
$187$	2.39089	+	4.14114i	0.174839	+	0.302830i
$188$	−6.84881			−0.499501
$189$		0			0
$190$	−7.05069			−0.511511
$191$	−9.42303	−	16.3212i	−0.681827	−	1.18096i	−0.974423	−	0.224723i	$-0.927852\pi$
$191$	−9.42303	−	16.3212i	−0.681827	−	1.18096i	0.292596	−	0.956236i	$-0.405481\pi$
$192$	2.27516	−	3.94068i	0.164195	−	0.284394i
$193$	−5.95533	+	10.3149i	−0.428674	+	0.742485i	−0.996756	−	0.0804869i	$-0.974352\pi$
$193$	−5.95533	+	10.3149i	−0.428674	+	0.742485i	0.568082	+	0.822972i	$0.307686\pi$
$194$	−6.65695	−	11.5302i	−0.477941	−	0.827819i
$195$	12.1306			0.868693
$196$		0			0
$197$	−17.2682			−1.23031			−0.615153	−	0.788408i	$-0.710906\pi$
$197$	−17.2682			−1.23031			−0.615153	+	0.788408i	$0.710906\pi$
$198$	4.56763	+	7.91137i	0.324607	+	0.562237i
$199$	−7.62257	+	13.2027i	−0.540350	+	0.935913i	0.458534	+	0.888677i	$0.348375\pi$
$199$	−7.62257	+	13.2027i	−0.540350	+	0.935913i	−0.998884	+	0.0472365i	$0.984959\pi$
$200$	5.99655	−	10.3863i	0.424020	−	0.734424i
$201$	2.39715	+	4.15198i	0.169082	+	0.292858i
$202$	−2.85108			−0.200601
$203$		0			0
$204$	−1.11578			−0.0781204
$205$	−2.03065	−	3.51719i	−0.141827	−	0.245651i
$206$	−5.57563	+	9.65727i	−0.388472	+	0.672854i
$207$	−9.20447	+	15.9426i	−0.639755	+	1.10809i
$208$	0.0654268	+	0.113323i	0.00453653	+	0.00785750i
$209$	12.6414			0.874423
$210$		0			0
$211$	8.51331			0.586080			0.293040	−	0.956100i	$-0.405333\pi$
$211$	8.51331			0.586080			0.293040	+	0.956100i	$0.405333\pi$
$212$	3.18189	+	5.51120i	0.218533	+	0.378511i
$213$	−5.41415	+	9.37758i	−0.370971	+	0.642541i
$214$	−1.71797	+	2.97560i	−0.117438	+	0.203408i
$215$	3.83589	+	6.64396i	0.261606	+	0.453115i
$216$	−13.3180			−0.906175
$217$		0			0
$218$	−3.12821			−0.211869
$219$	−5.77014	−	9.99418i	−0.389910	−	0.675344i
$220$	−8.93036	+	15.4678i	−0.602085	+	1.04284i
$221$	2.19966	−	3.80993i	0.147965	−	0.256284i
$222$	3.85197	+	6.67180i	0.258527	+	0.447782i
$223$	2.49093			0.166805			0.0834027	−	0.996516i	$-0.473421\pi$
$223$	2.49093			0.166805			0.0834027	+	0.996516i	$0.473421\pi$
$224$		0			0
$225$	−9.20694			−0.613796
$226$	−0.424267	−	0.734852i	−0.0282218	−	0.0488816i
$227$	−8.49210	+	14.7087i	−0.563640	+	0.976253i	0.433535	+	0.901137i	$0.357266\pi$
$227$	−8.49210	+	14.7087i	−0.563640	+	0.976253i	−0.997175	+	0.0751165i	$0.976067\pi$
$228$	−1.47487	+	2.55456i	−0.0976759	+	0.169180i
$229$	−8.16515	−	14.1425i	−0.539568	−	0.934560i	−0.998927	−	0.0463089i	$-0.985254\pi$
$229$	−8.16515	−	14.1425i	−0.539568	−	0.934560i	0.459359	−	0.888251i	$-0.348079\pi$
$230$	22.5598			1.48755
$231$		0			0
$232$	−19.9660			−1.31083
$233$	2.88912	+	5.00411i	0.189273	+	0.327830i	0.945008	−	0.327047i	$-0.106054\pi$
$233$	2.88912	+	5.00411i	0.189273	+	0.327830i	−0.755735	+	0.654877i	$0.772720\pi$
$234$	4.20231	−	7.27861i	0.274713	−	0.475818i
$235$	8.46259	−	14.6576i	0.552038	−	0.956158i
$236$	−5.70895	−	9.88818i	−0.371621	−	0.643666i
$237$	−1.76117			−0.114400
$238$		0			0
$239$	7.44275			0.481432			0.240716	−	0.970596i	$-0.422618\pi$
$239$	7.44275			0.481432			0.240716	+	0.970596i	$0.422618\pi$
$240$	0.0410079	+	0.0710277i	0.00264705	+	0.00458482i
$241$	10.9518	−	18.9691i	0.705467	−	1.22190i	−0.261056	−	0.965324i	$-0.584071\pi$
$241$	10.9518	−	18.9691i	0.705467	−	1.22190i	0.966523	−	0.256581i	$-0.0825961\pi$
$242$	−5.20793	+	9.02040i	−0.334778	+	0.579853i
$243$	8.07477	+	13.9859i	0.517997	+	0.897197i
$244$	8.19184			0.524429
$245$		0			0
$246$	1.06500			0.0679016
$247$	−5.81516	−	10.0721i	−0.370010	−	0.640875i
$248$	4.84855	−	8.39793i	0.307883	−	0.533269i
$249$	2.08025	−	3.60309i	0.131830	−	0.228337i
$250$	−1.02608	−	1.77722i	−0.0648949	−	0.112401i
$251$	−16.5769			−1.04632			−0.523162	−	0.852233i	$-0.675248\pi$
$251$	−16.5769			−1.04632			−0.523162	+	0.852233i	$0.675248\pi$
$252$		0			0
$253$	−40.4482			−2.54296
$254$	2.43983	+	4.22591i	0.153089	+	0.265157i
$255$	1.37869	−	2.38797i	0.0863371	−	0.149540i
$256$	8.03613	−	13.9190i	0.502258	−	0.869936i
$257$	6.05791	+	10.4926i	0.377882	+	0.654511i	0.990754	−	0.135672i	$-0.0433192\pi$
$257$	6.05791	+	10.4926i	0.377882	+	0.654511i	−0.612872	+	0.790182i	$0.709986\pi$
$258$	−2.01178			−0.125248
$259$		0			0
$260$	16.4322			1.01908
$261$	7.66383	+	13.2741i	0.474379	+	0.821649i
$262$	−1.54119	+	2.66941i	−0.0952148	+	0.164917i
$263$	−1.60067	+	2.77245i	−0.0987018	+	0.170956i	−0.911148	−	0.412080i	$-0.864802\pi$
$263$	−1.60067	+	2.77245i	−0.0987018	+	0.170956i	0.812446	+	0.583037i	$0.198136\pi$
$264$	−6.15147	−	10.6547i	−0.378597	−	0.655749i
$265$	−15.7265			−0.966074
$266$		0			0
$267$	−12.1575			−0.744030
$268$	3.24718	+	5.62428i	0.198353	+	0.343558i
$269$	7.72002	−	13.3715i	0.470698	−	0.815273i	−0.528740	−	0.848784i	$-0.677336\pi$
$269$	7.72002	−	13.3715i	0.470698	−	0.815273i	0.999438	+	0.0335109i	$0.0106688\pi$
$270$	6.26469	−	10.8508i	0.381257	−	0.660357i
$271$	−12.4439	−	21.5534i	−0.755912	−	1.30928i	−0.944919	−	0.327303i	$-0.893860\pi$
$271$	−12.4439	−	21.5534i	−0.755912	−	1.30928i	0.189007	−	0.981976i	$-0.439473\pi$
$272$	0.0297440			0.00180349
$273$		0			0
$274$	−1.70106			−0.102765
$275$	−10.1148	−	17.5193i	−0.609943	−	1.05645i
$276$	4.71910	−	8.17372i	0.284056	−	0.492000i
$277$	5.64352	−	9.77486i	0.339086	−	0.587315i	−0.645175	−	0.764035i	$-0.723216\pi$
$277$	5.64352	−	9.77486i	0.339086	−	0.587315i	0.984261	+	0.176720i	$0.0565488\pi$
$278$	2.06218	+	3.57181i	0.123682	+	0.214223i
$279$	−7.44433			−0.445680
$280$		0			0
$281$	13.0332			0.777495			0.388747	−	0.921344i	$-0.372908\pi$
$281$	13.0332			0.777495			0.388747	+	0.921344i	$0.372908\pi$
$282$	2.21915	+	3.84368i	0.132148	+	0.228888i
$283$	10.8595	−	18.8092i	0.645531	−	1.11809i	−0.338648	−	0.940913i	$-0.609969\pi$
$283$	10.8595	−	18.8092i	0.645531	−	1.11809i	0.984179	−	0.177179i	$-0.0566972\pi$
$284$	−7.33401	+	12.7029i	−0.435194	+	0.753777i
$285$	−3.64479	−	6.31297i	−0.215899	−	0.373948i
$286$	18.4667			1.09196
$287$		0			0
$288$	−12.2823			−0.723742
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	9.39189	−	16.2672i	0.551511	−	0.955244i
$291$	6.88251	−	11.9209i	0.403460	−	0.698813i
$292$	−7.81624	−	13.5381i	−0.457411	−	0.792259i
$293$	28.9400			1.69069			0.845346	−	0.534219i	$-0.179394\pi$
$293$	28.9400			1.69069			0.845346	+	0.534219i	$0.179394\pi$
$294$		0			0
$295$	28.2165			1.64283
$296$	13.7063	+	23.7401i	0.796665	+	1.37986i
$297$	−11.2322	+	19.4547i	−0.651756	+	1.12887i
$298$	−1.86172	+	3.22459i	−0.107846	+	0.186795i
$299$	18.6065	+	32.2275i	1.07604	+	1.86376i
$300$	4.72037			0.272531
$301$		0			0
$302$	10.9364			0.629318
$303$	−1.47384	−	2.55277i	−0.0846701	−	0.146653i
$304$	0.0393165	−	0.0680981i	0.00225495	−	0.00390570i
$305$	−10.1221	+	17.5319i	−0.579588	+	1.00388i
$306$	−0.955216	−	1.65448i	−0.0546061	−	0.0945805i
$307$	11.5836			0.661110			0.330555	−	0.943787i	$-0.392764\pi$
$307$	11.5836			0.661110			0.330555	+	0.943787i	$0.392764\pi$
$308$		0			0
$309$	−11.5291			−0.655867
$310$	4.56145	+	7.90066i	0.259073	+	0.448727i
$311$	−7.89996	+	13.6831i	−0.447966	+	0.775900i	−0.998254	−	0.0590756i	$-0.981185\pi$
$311$	−7.89996	+	13.6831i	−0.447966	+	0.775900i	0.550288	+	0.834975i	$0.314518\pi$
$312$	−5.65947	+	9.80248i	−0.320404	+	0.554956i
$313$	10.1329	+	17.5507i	0.572745	+	0.992024i	0.996283	+	0.0861453i	$0.0274549\pi$
$313$	10.1329	+	17.5507i	0.572745	+	0.992024i	−0.423537	+	0.905879i	$0.639212\pi$
$314$	15.4913			0.874225
$315$		0			0
$316$	−2.38568			−0.134205
$317$	−3.18268	−	5.51257i	−0.178757	−	0.309617i	0.762698	−	0.646755i	$-0.223874\pi$
$317$	−3.18268	−	5.51257i	−0.178757	−	0.309617i	−0.941455	+	0.337138i	$0.890541\pi$
$318$	2.06199	−	3.57147i	0.115631	−	0.200278i
$319$	−16.8390	+	29.1660i	−0.942803	+	1.63298i
$320$	7.61624	+	13.1917i	0.425761	+	0.737439i
$321$	−3.55235			−0.198273
$322$		0			0
$323$	−2.64366			−0.147097
$324$	1.39242	+	2.41175i	0.0773569	+	0.133986i
$325$	−9.30577	+	16.1181i	−0.516191	+	0.894069i
$326$	1.17435	−	2.03404i	0.0650414	−	0.112655i
$327$	−1.61710	−	2.80091i	−0.0894260	−	0.154890i
$328$	3.78954			0.209242
$329$		0			0
$330$	11.5744			0.637151
$331$	−12.2955	−	21.2965i	−0.675823	−	1.17056i	−0.976228	−	0.216748i	$-0.930455\pi$
$331$	−12.2955	−	21.2965i	−0.675823	−	1.17056i	0.300405	−	0.953812i	$-0.402878\pi$
$332$	2.81791	−	4.88076i	0.154653	−	0.267866i
$333$	10.5222	−	18.2249i	0.576611	−	0.998720i
$334$	−0.859325	−	1.48839i	−0.0470202	−	0.0814413i
$335$	−16.0492			−0.876863
$336$		0			0
$337$	7.11956			0.387827			0.193913	−	0.981019i	$-0.437882\pi$
$337$	7.11956			0.387827			0.193913	+	0.981019i	$0.437882\pi$
$338$	−2.78891	−	4.83053i	−0.151697	−	0.262746i
$339$	0.438643	−	0.759751i	0.0238238	−	0.0412640i
$340$	1.86758	−	3.23474i	0.101284	−	0.175429i
$341$	−8.17836	−	14.1653i	−0.442883	−	0.767096i
$342$	−5.05053			−0.273101
$343$		0			0
$344$	−7.15844			−0.385957
$345$	11.6621	+	20.1994i	0.627867	+	1.08750i
$346$	2.64110	−	4.57453i	0.141987	−	0.245928i
$347$	−0.757387	+	1.31183i	−0.0406586	+	0.0704228i	−0.885639	−	0.464375i	$-0.846279\pi$
$347$	−0.757387	+	1.31183i	−0.0406586	+	0.0704228i	0.844980	+	0.534798i	$0.179612\pi$
$348$	−3.92922	−	6.80561i	−0.210628	−	0.364819i
$349$	−24.7937			−1.32717			−0.663587	−	0.748099i	$-0.730967\pi$
$349$	−24.7937			−1.32717			−0.663587	+	0.748099i	$0.730967\pi$
$350$		0			0
$351$	20.6676			1.10315
$352$	−13.4934	−	23.3712i	−0.719199	−	1.24569i
$353$	−5.92082	+	10.2552i	−0.315133	+	0.545827i	−0.979466	−	0.201610i	$-0.935383\pi$
$353$	−5.92082	+	10.2552i	−0.315133	+	0.545827i	0.664332	+	0.747437i	$0.268716\pi$
$354$	−3.69962	+	6.40792i	−0.196632	+	0.340577i
$355$	−18.1242	−	31.3921i	−0.961934	−	1.66612i
$356$	−16.4686			−0.872836
$357$		0			0
$358$	1.53719			0.0812430
$359$	13.3371	+	23.1006i	0.703907	+	1.21920i	0.967085	+	0.254455i	$0.0818962\pi$
$359$	13.3371	+	23.1006i	0.703907	+	1.21920i	−0.263177	+	0.964747i	$0.584770\pi$
$360$	9.37212	−	16.2330i	0.493954	−	0.855554i
$361$	6.00554	−	10.4019i	0.316081	−	0.547468i
$362$	1.21356	+	2.10195i	0.0637835	+	0.110476i
$363$	−10.7688			−0.565215
$364$		0			0
$365$	38.6319			2.02209
$366$	−2.65431	−	4.59741i	−0.138743	−	0.240310i
$367$	−14.3449	+	24.8460i	−0.748796	+	1.29695i	0.199604	+	0.979877i	$0.436034\pi$
$367$	−14.3449	+	24.8460i	−0.748796	+	1.29695i	−0.948400	+	0.317076i	$0.897299\pi$
$368$	−0.125799	+	0.217891i	−0.00655775	+	0.0113584i
$369$	−1.45459	−	2.51942i	−0.0757229	−	0.131156i
$370$	−25.7895			−1.34073
$371$		0			0
$372$	3.81668			0.197886
$373$	13.4473	+	23.2914i	0.696275	+	1.20598i	0.969749	+	0.244104i	$0.0784939\pi$
$373$	13.4473	+	23.2914i	0.696275	+	1.20598i	−0.273474	+	0.961879i	$0.588173\pi$
$374$	2.09880	−	3.63524i	0.108527	−	0.187974i
$375$	1.06085	−	1.83744i	0.0547818	−	0.0948849i
$376$	7.89632	+	13.6768i	0.407222	+	0.705329i
$377$	30.9844			1.59578
$378$		0			0
$379$	0.960453			0.0493351			0.0246676	−	0.999696i	$-0.492147\pi$
$379$	0.960453			0.0493351			0.0246676	+	0.999696i	$0.492147\pi$
$380$	−4.93724	−	8.55156i	−0.253275	−	0.438686i
$381$	−2.52250	+	4.36910i	−0.129232	+	0.223836i
$382$	−8.27186	+	14.3273i	−0.423225	+	0.733048i
$383$	−5.49563	−	9.51871i	−0.280814	−	0.486384i	0.690772	−	0.723073i	$-0.257271\pi$
$383$	−5.49563	−	9.51871i	−0.280814	−	0.486384i	−0.971585	+	0.236689i	$0.923938\pi$
$384$	6.24970			0.318929
$385$		0			0
$386$	10.4556			0.532175
$387$	2.74772	+	4.75919i	0.139674	+	0.241923i
$388$	9.32306	−	16.1480i	0.473307	−	0.819791i
$389$	12.7119	−	22.0177i	0.644520	−	1.11634i	−0.339892	−	0.940465i	$-0.610390\pi$
$389$	12.7119	−	22.0177i	0.644520	−	1.11634i	0.984412	−	0.175878i	$-0.0562763\pi$
$390$	−5.32435	−	9.22204i	−0.269609	−	0.466976i
$391$	8.45881			0.427781
$392$		0			0
$393$	−3.18681			−0.160753
$394$	7.57930	+	13.1277i	0.381839	+	0.661365i
$395$	2.94781	−	5.10576i	0.148321	−	0.256899i
$396$	−6.39697	+	11.0799i	−0.321460	+	0.556785i
$397$	−7.50702	−	13.0025i	−0.376767	−	0.652579i	0.613823	−	0.789444i	$-0.289631\pi$
$397$	−7.50702	−	13.0025i	−0.376767	−	0.652579i	−0.990590	+	0.136865i	$0.956297\pi$
$398$	13.3827			0.670815
$399$		0			0
$400$	−0.125833			−0.00629166
$401$	5.53278	+	9.58306i	0.276294	+	0.478555i	0.970461	−	0.241259i	$-0.0775603\pi$
$401$	5.53278	+	9.58306i	0.276294	+	0.478555i	−0.694167	+	0.719814i	$0.744227\pi$
$402$	2.10430	−	3.64475i	0.104953	−	0.181784i
$403$	−7.52424	+	13.0324i	−0.374809	+	0.649188i
$404$	−1.99647	−	3.45799i	−0.0993282	−	0.172041i
$405$	−6.88207			−0.341973
$406$		0			0
$407$	46.2387			2.29197
$408$	1.28644	+	2.22818i	0.0636882	+	0.110311i
$409$	14.2825	−	24.7380i	0.706225	−	1.22322i	−0.260023	−	0.965602i	$-0.583730\pi$
$409$	14.2825	−	24.7380i	0.706225	−	1.22322i	0.966248	−	0.257615i	$-0.0829365\pi$
$410$	−1.78257	+	3.08751i	−0.0880350	+	0.152481i
$411$	−0.879351	−	1.52308i	−0.0433752	−	0.0751280i
$412$	−15.6173			−0.769411
$413$		0			0
$414$	16.1600			0.794220
$415$	6.96377	+	12.0616i	0.341838	+	0.592081i
$416$	−12.4141	+	21.5019i	−0.608654	+	1.05422i
$417$	−2.13206	+	3.69283i	−0.104407	+	0.180839i
$418$	−5.54852	−	9.61032i	−0.271387	−	0.470056i
$419$	1.98566			0.0970057			0.0485029	−	0.998823i	$-0.484555\pi$
$419$	1.98566			0.0970057			0.0485029	+	0.998823i	$0.484555\pi$
$420$		0			0
$421$	25.1984			1.22810			0.614048	−	0.789269i	$-0.289540\pi$
$421$	25.1984			1.22810			0.614048	+	0.789269i	$0.289540\pi$
$422$	−3.73664	−	6.47204i	−0.181897	−	0.315054i
$423$	6.06190	−	10.4995i	0.294740	−	0.510504i
$424$	7.33711	−	12.7082i	0.356321	−	0.617167i
$425$	2.11527	+	3.66376i	0.102606	+	0.177718i
$426$	9.50544			0.460540
$427$		0			0
$428$	−4.81202			−0.232598
$429$	9.54618	+	16.5345i	0.460894	+	0.798292i
$430$	3.36728	−	5.83230i	0.162385	−	0.281258i
$431$	13.7492	−	23.8143i	0.662275	−	1.14709i	−0.317742	−	0.948177i	$-0.602925\pi$
$431$	13.7492	−	23.8143i	0.662275	−	1.14709i	0.980017	−	0.198916i	$-0.0637422\pi$
$432$	0.0698672	+	0.121013i	0.00336148	+	0.00582226i
$433$	−28.1977			−1.35509			−0.677547	−	0.735480i	$-0.736957\pi$
$433$	−28.1977			−1.35509			−0.677547	+	0.735480i	$0.736957\pi$
$434$		0			0
$435$	19.4202			0.931129
$436$	−2.19053	−	3.79411i	−0.104907	−	0.181705i
$437$	11.1811	−	19.3662i	0.534865	−	0.926413i
$438$	−5.06523	+	8.77323i	−0.242026	+	0.419201i
$439$	3.15649	+	5.46720i	0.150651	+	0.260935i	0.931467	−	0.363826i	$-0.118530\pi$
$439$	3.15649	+	5.46720i	0.150651	+	0.260935i	−0.780816	+	0.624761i	$0.785196\pi$
$440$	41.1849			1.96341
$441$		0			0
$442$	−3.86188			−0.183691
$443$	−13.2278	−	22.9113i	−0.628473	−	1.08855i	−0.987858	−	0.155358i	$-0.950347\pi$
$443$	−13.2278	−	22.9113i	−0.628473	−	1.08855i	0.359385	−	0.933189i	$-0.382986\pi$
$444$	−5.39468	+	9.34386i	−0.256020	+	0.443440i
$445$	20.3491	−	35.2457i	0.964640	−	1.67081i
$446$	−1.09331	−	1.89367i	−0.0517699	−	0.0896681i
$447$	−3.84960			−0.182080
$448$		0			0
$449$	−34.5555			−1.63077			−0.815387	−	0.578916i	$-0.803476\pi$
$449$	−34.5555			−1.63077			−0.815387	+	0.578916i	$0.803476\pi$
$450$	4.04108	+	6.99936i	0.190498	+	0.329953i
$451$	3.19603	−	5.53569i	0.150495	−	0.260665i
$452$	0.594186	−	1.02916i	0.0279482	−	0.0484076i
$453$	5.65347	+	9.79210i	0.265623	+	0.460073i
$454$	14.9093			0.699728
$455$		0			0
$456$	6.80181			0.318524
$457$	−13.2961	−	23.0295i	−0.621965	−	1.07728i	−0.989119	−	0.147115i	$-0.953001\pi$
$457$	−13.2961	−	23.0295i	−0.621965	−	1.07728i	0.367154	−	0.930160i	$-0.380332\pi$
$458$	−7.16765	+	12.4147i	−0.334922	+	0.580102i
$459$	2.34895	−	4.06850i	0.109640	−	0.189901i
$460$	15.7975	+	27.3621i	0.736563	+	1.27576i
$461$	0.310199			0.0144474			0.00722371	−	0.999974i	$-0.497701\pi$
$461$	0.310199			0.0144474			0.00722371	+	0.999974i	$0.497701\pi$
$462$		0			0
$463$	22.4654			1.04406			0.522028	−	0.852928i	$-0.325175\pi$
$463$	22.4654			1.04406			0.522028	+	0.852928i	$0.325175\pi$
$464$	0.104743	+	0.181421i	0.00486258	+	0.00842224i
$465$	−4.71600	+	8.16836i	−0.218699	+	0.378799i
$466$	2.53617	−	4.39278i	0.117486	−	0.203492i
$467$	−5.80628	−	10.0568i	−0.268682	−	0.465372i	0.699839	−	0.714300i	$-0.253255\pi$
$467$	−5.80628	−	10.0568i	−0.268682	−	0.465372i	−0.968522	+	0.248929i	$0.919922\pi$
$468$	11.7707			0.544099
$469$		0			0
$470$	−14.8575			−0.685325
$471$	8.00810	+	13.8704i	0.368994	+	0.639116i
$472$	−13.1642	+	22.8011i	−0.605933	+	1.04951i
$473$	−6.03730	+	10.4569i	−0.277595	+	0.480809i
$474$	0.773006	+	1.33889i	0.0355053	+	0.0614971i
$475$	11.1841			0.513162
$476$		0			0
$477$	−11.2652			−0.515798
$478$	−3.26675	−	5.65818i	−0.149418	−	0.258799i
$479$	15.8988	−	27.5376i	0.726435	−	1.25822i	−0.231945	−	0.972729i	$-0.574509\pi$
$479$	15.8988	−	27.5376i	0.726435	−	1.25822i	0.958380	−	0.285494i	$-0.0921577\pi$
$480$	−7.78087	+	13.4769i	−0.355147	+	0.615132i
$481$	−21.2702	−	36.8411i	−0.969839	−	1.67981i
$482$	−19.2277			−0.875799
$483$		0			0
$484$	−14.5874			−0.663064
$485$	23.0397	+	39.9059i	1.04618	+	1.81203i
$486$	7.08831	−	12.2773i	0.321532	−	0.556910i
$487$	11.5083	−	19.9329i	0.521490	−	0.903248i	−0.478197	−	0.878252i	$-0.658710\pi$
$487$	11.5083	−	19.9329i	0.521490	−	0.903248i	0.999688	−	0.0249951i	$-0.00795703\pi$
$488$	−9.44477	−	16.3588i	−0.427544	−	0.740529i
$489$	2.42829			0.109811
$490$		0			0
$491$	−33.3176			−1.50360			−0.751802	−	0.659389i	$-0.770815\pi$
$491$	−33.3176			−1.50360			−0.751802	+	0.659389i	$0.770815\pi$
$492$	0.745763	+	1.29170i	0.0336216	+	0.0582343i
$493$	3.52149	−	6.09940i	0.158600	−	0.274703i
$494$	−5.10474	+	8.84167i	−0.229673	+	0.397806i
$495$	−15.8086	−	27.3812i	−0.710542	−	1.23069i
$496$	−0.101743			−0.00456841
$497$		0			0
$498$	−3.65222			−0.163660
$499$	−18.5118	−	32.0634i	−0.828703	−	1.43536i	−0.899056	−	0.437833i	$-0.855746\pi$
$499$	−18.5118	−	32.0634i	−0.828703	−	1.43536i	0.0703537	−	0.997522i	$-0.477587\pi$
$500$	1.43702	−	2.48900i	0.0642656	−	0.111311i
$501$	0.888442	−	1.53883i	0.0396926	−	0.0687497i
$502$	7.27589	+	12.6022i	0.324739	+	0.562464i
$503$	12.4172			0.553654			0.276827	−	0.960920i	$-0.410717\pi$
$503$	12.4172			0.553654			0.276827	+	0.960920i	$0.410717\pi$
$504$		0			0
$505$	9.86759			0.439102
$506$	17.7534	+	30.7498i	0.789235	+	1.36699i
$507$	2.88341	−	4.99421i	0.128057	−	0.221801i
$508$	−3.41699	+	5.91839i	−0.151604	+	0.262586i
$509$	5.96285	+	10.3280i	0.264299	+	0.457779i	0.967380	−	0.253331i	$-0.0815262\pi$
$509$	5.96285	+	10.3280i	0.264299	+	0.457779i	−0.703081	+	0.711110i	$0.748193\pi$
$510$	−2.42053			−0.107183
$511$		0			0
$512$	−0.336507			−0.0148716
$513$	−6.20982	−	10.7557i	−0.274170	−	0.474877i
$514$	5.31784	−	9.21077i	0.234560	−	0.406270i
$515$	19.2972	−	33.4238i	0.850337	−	1.47283i
$516$	−1.40875	−	2.44002i	−0.0620166	−	0.107416i
$517$	26.6385			1.17156
$518$		0			0
$519$	5.46119			0.239719
$520$	−18.9455	−	32.8145i	−0.830813	−	1.43901i
$521$	13.1990	−	22.8613i	0.578259	−	1.00157i	−0.417420	−	0.908713i	$-0.637066\pi$
$521$	13.1990	−	22.8613i	0.578259	−	1.00157i	0.995679	−	0.0928600i	$-0.0296009\pi$
$522$	6.72757	−	11.6525i	0.294458	−	0.510016i
$523$	6.81358	+	11.8015i	0.297937	+	0.516042i	0.975664	−	0.219272i	$-0.0703682\pi$
$523$	6.81358	+	11.8015i	0.297937	+	0.516042i	−0.677727	+	0.735314i	$0.737035\pi$
$524$	−4.31686			−0.188583
$525$		0			0
$526$	2.81025			0.122533
$527$	1.71032	+	2.96236i	0.0745026	+	0.129042i
$528$	−0.0645421	+	0.111790i	−0.00280883	+	0.00486504i
$529$	−24.2758	+	42.0469i	−1.05547	+	1.82812i
$530$	6.90265	+	11.9557i	0.299832	+	0.519324i
$531$	20.2120			0.877126
$532$		0			0
$533$	−5.88081			−0.254726
$534$	5.33615	+	9.24249i	0.230918	+	0.399962i
$535$	5.94587	−	10.2986i	0.257062	−	0.445245i
$536$	7.48766	−	12.9690i	0.323417	−	0.560175i
$537$	0.794637	+	1.37635i	0.0342911	+	0.0593940i
$538$	−13.5538			−0.584346
$539$		0			0
$540$	17.5474			0.755120
$541$	−13.1679	−	22.8075i	−0.566132	−	0.980570i	−0.996943	−	0.0781276i	$-0.975106\pi$
$541$	−13.1679	−	22.8075i	−0.566132	−	0.980570i	0.430811	−	0.902442i	$-0.358227\pi$
$542$	−10.9237	+	18.9204i	−0.469212	+	0.812699i
$543$	−1.25468	+	2.17318i	−0.0538436	+	0.0932599i
$544$	2.82183	+	4.88755i	0.120985	+	0.209552i
$545$	10.8267			0.463766
$546$		0			0
$547$	−2.25139			−0.0962624			−0.0481312	−	0.998841i	$-0.515327\pi$
$547$	−2.25139			−0.0962624			−0.0481312	+	0.998841i	$0.515327\pi$
$548$	−1.19117	−	2.06317i	−0.0508843	−	0.0881342i
$549$	−7.25062	+	12.5584i	−0.309449	+	0.535981i
$550$	−8.87908	+	15.3790i	−0.378605	+	0.655764i
$551$	−9.30962	−	16.1247i	−0.396603	−	0.686937i
$552$	−21.7635			−0.926316
$553$		0			0
$554$	−9.90815			−0.420957
$555$	−13.3316	−	23.0911i	−0.565897	−	0.980162i
$556$	−2.88809	+	5.00231i	−0.122482	+	0.212145i
$557$	−15.1678	+	26.2713i	−0.642679	+	1.11315i	0.342154	+	0.939644i	$0.388844\pi$
$557$	−15.1678	+	26.2713i	−0.642679	+	1.11315i	−0.984832	+	0.173508i	$0.944490\pi$
$558$	3.26744	+	5.65938i	0.138322	+	0.239581i
$559$	11.1089			0.469854
$560$		0			0
$561$	4.33984			0.183228
$562$	−5.72049	−	9.90818i	−0.241304	−	0.417951i
$563$	5.49336	−	9.51478i	0.231518	−	0.401000i	−0.726737	−	0.686915i	$-0.758964\pi$
$563$	5.49336	−	9.51478i	0.231518	−	0.401000i	0.958255	+	0.285915i	$0.0922976\pi$
$564$	−3.10792	+	5.38307i	−0.130867	+	0.226668i
$565$	1.46839	+	2.54332i	0.0617755	+	0.106998i
$566$	−19.0657			−0.801391
$567$		0			0
$568$	33.8229			1.41918
$569$	14.4240	+	24.9831i	0.604684	+	1.04734i	0.992101	+	0.125440i	$0.0400341\pi$
$569$	14.4240	+	24.9831i	0.604684	+	1.04734i	−0.387417	+	0.921905i	$0.626633\pi$
$570$	−3.19952	+	5.54174i	−0.134013	+	0.232118i
$571$	5.25823	−	9.10753i	0.220050	−	0.381138i	−0.734773	−	0.678313i	$-0.762711\pi$
$571$	5.25823	−	9.10753i	0.220050	−	0.381138i	0.954823	+	0.297175i	$0.0960446\pi$
$572$	12.9313	+	22.3976i	0.540684	+	0.936492i
$573$	−17.1043			−0.714542
$574$		0			0
$575$	−35.7854			−1.49235
$576$	5.45564	+	9.44945i	0.227319	+	0.393727i
$577$	−18.4144	+	31.8947i	−0.766601	+	1.32779i	0.172794	+	0.984958i	$0.444720\pi$
$577$	−18.4144	+	31.8947i	−0.766601	+	1.32779i	−0.939396	+	0.342835i	$0.888613\pi$
$578$	−0.438917	+	0.760227i	−0.0182565	+	0.0316213i
$579$	5.40493	+	9.36161i	0.224621	+	0.389055i
$580$	26.3067			1.09233
$581$		0			0
$582$	−12.0834			−0.500873
$583$	−12.3760	−	21.4358i	−0.512560	−	0.887780i
$584$	−18.0234	+	31.2175i	−0.745815	+	1.29179i
$585$	−14.5442	+	25.1912i	−0.601327	+	1.04153i
$586$	−12.7023	−	22.0010i	−0.524726	−	0.908851i
$587$	−30.1420			−1.24409			−0.622047	−	0.782980i	$-0.713699\pi$
$587$	−30.1420			−1.24409			−0.622047	+	0.782980i	$0.713699\pi$
$588$		0			0
$589$	9.04298			0.372610
$590$	−12.3847	−	21.4510i	−0.509871	−	0.883122i
$591$	−7.83611	+	13.5725i	−0.322334	+	0.558300i
$592$	0.143809	−	0.249084i	0.00591051	−	0.0102373i
$593$	−3.94462	−	6.83229i	−0.161986	−	0.280568i	0.773595	−	0.633681i	$-0.218457\pi$
$593$	−3.94462	−	6.83229i	−0.161986	−	0.280568i	−0.935581	+	0.353112i	$0.885123\pi$
$594$	19.7199			0.809119
$595$		0			0
$596$	−5.21467			−0.213601
$597$	6.91808	+	11.9825i	0.283138	+	0.490410i
$598$	16.3335	−	28.2904i	0.667925	−	1.15688i
$599$	−14.9029	+	25.8126i	−0.608917	+	1.05468i	0.382502	+	0.923955i	$0.375062\pi$
$599$	−14.9029	+	25.8126i	−0.608917	+	1.05468i	−0.991419	+	0.130721i	$0.958271\pi$
$600$	−5.44234	−	9.42640i	−0.222182	−	0.384831i
$601$	−11.9432			−0.487175			−0.243587	−	0.969879i	$-0.578324\pi$
$601$	−11.9432			−0.487175			−0.243587	+	0.969879i	$0.578324\pi$
$602$		0			0
$603$	−11.4963			−0.468167
$604$	7.65820	+	13.2644i	0.311608	+	0.539721i
$605$	18.0246	−	31.2196i	0.732805	−	1.26926i
$606$	−1.29379	+	2.24091i	−0.0525566	+	0.0910308i
$607$	−2.33641	−	4.04677i	−0.0948318	−	0.164253i	0.814707	−	0.579873i	$-0.196898\pi$
$607$	−2.33641	−	4.04677i	−0.0948318	−	0.164253i	−0.909538	+	0.415620i	$0.863565\pi$
$608$	14.9199			0.605082
$609$		0			0
$610$	17.7710			0.719527
$611$	−12.2539	−	21.2244i	−0.495741	−	0.858649i
$612$	1.33778	−	2.31710i	0.0540766	−	0.0936634i
$613$	−21.1947	+	36.7103i	−0.856046	+	1.48271i	0.0196261	+	0.999807i	$0.493752\pi$
$613$	−21.1947	+	36.7103i	−0.856046	+	1.48271i	−0.875672	+	0.482907i	$0.839581\pi$
$614$	−5.08424	−	8.80615i	−0.205183	−	0.355387i
$615$	−3.68595			−0.148632
$616$		0			0
$617$	−23.2809			−0.937255			−0.468628	−	0.883396i	$-0.655251\pi$
$617$	−23.2809			−0.937255			−0.468628	+	0.883396i	$0.655251\pi$
$618$	5.06032	+	8.76473i	0.203556	+	0.352569i
$619$	−21.6101	+	37.4297i	−0.868582	+	1.50443i	−0.00513615	+	0.999987i	$0.501635\pi$
$619$	−21.6101	+	37.4297i	−0.868582	+	1.50443i	−0.863446	+	0.504441i	$0.831698\pi$
$620$	−6.38831	+	11.0649i	−0.256561	+	0.444376i
$621$	19.8693	+	34.4147i	0.797329	+	1.38101i
$622$	13.8697			0.556125
$623$		0			0
$624$	0.118760			0.00475420
$625$	14.1276	+	24.4697i	0.565104	+	0.978790i
$626$	8.89501	−	15.4066i	0.355516	−	0.615772i
$627$	5.73652	−	9.93595i	0.229095	−	0.396804i
$628$	10.8478	+	18.7889i	0.432874	+	0.749760i
$629$	−9.66977			−0.385559
$630$		0			0
$631$	30.6825			1.22145			0.610725	−	0.791843i	$-0.290878\pi$
$631$	30.6825			1.22145			0.610725	+	0.791843i	$0.290878\pi$
$632$	2.75056	+	4.76412i	0.109412	+	0.189506i
$633$	3.86325	−	6.69134i	0.153550	−	0.265957i
$634$	−2.79387	+	4.83912i	−0.110959	+	0.192186i
$635$	−8.44425	−	14.6259i	−0.335100	−	0.580410i
$636$	5.77563			0.229019
$637$		0			0
$638$	29.5637			1.17044
$639$	−12.9827	−	22.4867i	−0.513588	−	0.889560i
$640$	−10.4607	+	18.1184i	−0.413494	+	0.716192i
$641$	10.6781	−	18.4950i	0.421758	−	0.730507i	−0.574353	−	0.818608i	$-0.694746\pi$
$641$	10.6781	−	18.4950i	0.421758	−	0.730507i	0.996112	+	0.0881008i	$0.0280798\pi$
$642$	1.55919	+	2.70059i	0.0615362	+	0.106584i
$643$	−22.7013			−0.895253			−0.447626	−	0.894221i	$-0.647731\pi$
$643$	−22.7013			−0.895253			−0.447626	+	0.894221i	$0.647731\pi$
$644$		0			0
$645$	6.96275			0.274158
$646$	1.16035	+	2.00978i	0.0456532	+	0.0790737i
$647$	17.6315	−	30.5386i	0.693165	−	1.20060i	−0.277630	−	0.960688i	$-0.589549\pi$
$647$	17.6315	−	30.5386i	0.693165	−	1.20060i	0.970795	−	0.239909i	$-0.0771177\pi$
$648$	3.21078	−	5.56124i	0.126131	−	0.218466i
$649$	22.2049	+	38.4601i	0.871620	+	1.50969i
$650$	16.3378			0.640823
$651$		0			0
$652$	3.28936			0.128821
$653$	15.0296	+	26.0321i	0.588155	+	1.01871i	0.994474	+	0.104983i	$0.0334789\pi$
$653$	15.0296	+	26.0321i	0.588155	+	1.01871i	−0.406319	+	0.913731i	$0.633188\pi$
$654$	−1.41955	+	2.45873i	−0.0555088	+	0.0961440i
$655$	5.33404	−	9.23883i	0.208418	−	0.360991i
$656$	−0.0198802	−	0.0344335i	−0.000776191	−	0.00134440i
$657$	27.6727			1.07961
$658$		0			0
$659$	−18.9747			−0.739148			−0.369574	−	0.929201i	$-0.620496\pi$
$659$	−18.9747			−0.739148			−0.369574	+	0.929201i	$0.620496\pi$
$660$	8.10500	+	14.0383i	0.315487	+	0.546439i
$661$	12.9019	−	22.3467i	0.501825	−	0.869187i	−0.498172	−	0.867078i	$-0.665995\pi$
$661$	12.9019	−	22.3467i	0.501825	−	0.869187i	0.999998	−	0.00210905i	$-0.000671331\pi$
$662$	−10.7934	+	18.6948i	−0.419498	+	0.726593i
$663$	−1.99637	−	3.45781i	−0.0775324	−	0.134290i
$664$	−12.9956			−0.504327
$665$		0			0
$666$	−18.4734			−0.715831
$667$	29.7876	+	51.5937i	1.15338	+	1.99772i
$668$	1.20348	−	2.08450i	0.0465642	−	0.0806516i
$669$	1.13036	−	1.95784i	0.0437022	−	0.0756944i
$670$	7.04428	+	12.2011i	0.272144	+	0.471368i
$671$	−31.8622			−1.23003
$672$		0			0
$673$	4.38401			0.168991			0.0844956	−	0.996424i	$-0.473072\pi$
$673$	4.38401			0.168991			0.0844956	+	0.996424i	$0.473072\pi$
$674$	−3.12489	−	5.41248i	−0.120366	−	0.208481i
$675$	−9.93733	+	17.2120i	−0.382488	+	0.662489i
$676$	3.90587	−	6.76517i	0.150226	−	0.260199i
$677$	−16.0557	−	27.8094i	−0.617073	−	1.06880i	−0.990017	−	0.140947i	$-0.954985\pi$
$677$	−16.0557	−	27.8094i	−0.617073	−	1.06880i	0.372945	−	0.927854i	$-0.378348\pi$
$678$	−0.770111			−0.0295759
$679$		0			0
$680$	−8.61289			−0.330289
$681$	7.70724	+	13.3493i	0.295342	+	0.511548i
$682$	−7.17924	+	12.4348i	−0.274907	+	0.476153i
$683$	9.35466	−	16.2027i	0.357946	−	0.619981i	−0.629672	−	0.776861i	$-0.716811\pi$
$683$	9.35466	−	16.2027i	0.357946	−	0.619981i	0.987618	+	0.156881i	$0.0501438\pi$
$684$	−3.53663	−	6.12563i	−0.135227	−	0.234219i
$685$	5.88738			0.224945
$686$		0			0
$687$	−14.8210			−0.565457
$688$	0.0375537	+	0.0650449i	0.00143172	+	0.00247981i
$689$	−11.3861	+	19.7213i	−0.433777	+	0.751323i
$690$	10.2374	−	17.7317i	0.389731	−	0.675034i
$691$	−20.4566	−	35.4318i	−0.778205	−	1.34789i	−0.932976	−	0.359940i	$-0.882797\pi$
$691$	−20.4566	−	35.4318i	−0.778205	−	1.34789i	0.154771	−	0.987950i	$-0.450536\pi$
$692$	7.39773			0.281220
$693$		0			0
$694$	1.32972			0.0504755
$695$	−7.13721	−	12.3620i	−0.270730	−	0.468918i
$696$	−9.06037	+	15.6930i	−0.343433	+	0.594843i
$697$	−0.668377	+	1.15766i	−0.0253166	+	0.0438496i
$698$	10.8824	+	18.8488i	0.411903	+	0.713438i
$699$	5.24421			0.198354
$700$		0			0
$701$	−17.6240			−0.665649			−0.332825	−	0.942989i	$-0.608002\pi$
$701$	−17.6240			−0.665649			−0.332825	+	0.942989i	$0.608002\pi$
$702$	−9.07136	−	15.7121i	−0.342376	−	0.593013i
$703$	−12.7818	+	22.1387i	−0.482074	+	0.834977i
$704$	−11.9872	+	20.7624i	−0.451783	+	0.782511i
$705$	−7.68046	−	13.3029i	−0.289263	−	0.501018i
$706$	10.3950			0.391221
$707$		0			0
$708$	−10.3626			−0.389451
$709$	4.09345	+	7.09007i	0.153733	+	0.266273i	0.932597	−	0.360920i	$-0.117537\pi$
$709$	4.09345	+	7.09007i	0.153733	+	0.266273i	−0.778864	+	0.627193i	$0.784204\pi$
$710$	−15.9101	+	27.5570i	−0.597094	+	1.03420i
$711$	2.11157	−	3.65735i	0.0791901	−	0.137161i
$712$	18.9875	+	32.8873i	0.711585	+	1.23250i
$713$	−28.9345			−1.08361
$714$		0			0
$715$	−63.9130			−2.39021
$716$	1.07642	+	1.86441i	0.0402276	+	0.0696763i
$717$	3.37744	−	5.84990i	0.126133	−	0.218468i
$718$	11.7078	−	20.2785i	0.436931	−	0.756787i
$719$	21.3047	+	36.9008i	0.794530	+	1.37617i	0.923137	+	0.384470i	$0.125616\pi$
$719$	21.3047	+	36.9008i	0.794530	+	1.37617i	−0.128607	+	0.991696i	$0.541051\pi$
$720$	−0.196667			−0.00732936
$721$		0			0
$722$	−10.5437			−0.392397
$723$	−9.93961	−	17.2159i	−0.369658	−	0.640267i
$724$	−1.69960	+	2.94379i	−0.0631650	+	0.109405i
$725$	−14.8978	+	25.8038i	−0.553291	+	0.958329i
$726$	4.72660	+	8.18672i	0.175421	+	0.303838i
$727$	10.5470			0.391166			0.195583	−	0.980687i	$-0.437340\pi$
$727$	10.5470			0.391166			0.195583	+	0.980687i	$0.437340\pi$
$728$		0			0
$729$	7.86138			0.291162
$730$	−16.9562	−	29.3690i	−0.627577	−	1.08700i
$731$	1.26256	−	2.18682i	0.0466976	−	0.0808826i
$732$	3.71737	−	6.43867i	0.137398	−	0.237980i
$733$	3.30745	+	5.72868i	0.122164	+	0.211594i	0.920621	−	0.390458i	$-0.127683\pi$
$733$	3.30745	+	5.72868i	0.122164	+	0.211594i	−0.798457	+	0.602052i	$0.794350\pi$
$734$	25.1848			0.929589
$735$		0			0
$736$	−47.7387			−1.75967
$737$	−12.6299	−	21.8756i	−0.465228	−	0.805799i
$738$	−1.27689	+	2.21164i	−0.0470029	+	0.0814114i
$739$	0.417188	−	0.722591i	0.0153465	−	0.0265809i	−0.858250	−	0.513232i	$-0.828448\pi$
$739$	0.417188	−	0.722591i	0.0153465	−	0.0265809i	0.873597	+	0.486651i	$0.161782\pi$
$740$	−18.0591	−	31.2792i	−0.663865	−	1.14985i
$741$	−10.5554			−0.387763
$742$		0			0
$743$	52.9082			1.94101			0.970506	−	0.241077i	$-0.0775006\pi$
$743$	52.9082			1.94101			0.970506	+	0.241077i	$0.0775006\pi$
$744$	−4.40044	−	7.62178i	−0.161328	−	0.279428i
$745$	6.44340	−	11.1603i	0.236068	−	0.408882i
$746$	11.8045	−	20.4460i	0.432193	−	0.748581i
$747$	4.98827	+	8.63993i	0.182511	+	0.316119i
$748$	5.87875			0.214948
$749$		0			0
$750$	−1.86249			−0.0680086
$751$	−17.6840	−	30.6297i	−0.645300	−	1.11769i	−0.984232	−	0.176881i	$-0.943399\pi$
$751$	−17.6840	−	30.6297i	−0.645300	−	1.11769i	0.338932	−	0.940811i	$-0.389934\pi$
$752$	0.0828493	−	0.143499i	0.00302120	−	0.00523288i
$753$	−7.52242	+	13.0292i	−0.274132	+	0.474811i
$754$	−13.5996	−	23.5552i	−0.495267	−	0.857828i
$755$	−37.8508			−1.37753
$756$		0			0
$757$	−19.6550			−0.714372			−0.357186	−	0.934033i	$-0.616264\pi$
$757$	−19.6550			−0.714372			−0.357186	+	0.934033i	$0.616264\pi$
$758$	−0.421559	−	0.730162i	−0.0153117	−	0.0265207i
$759$	−18.3549	+	31.7917i	−0.666242	+	1.15397i
$760$	−11.3848	+	19.7190i	−0.412969	+	0.715283i
$761$	−3.40388	−	5.89569i	−0.123390	−	0.213719i	0.797712	−	0.603038i	$-0.206043\pi$
$761$	−3.40388	−	5.89569i	−0.123390	−	0.213719i	−0.921103	+	0.389320i	$0.872710\pi$
$762$	4.42868			0.160434
$763$		0			0
$764$	−23.1695			−0.838243
$765$	3.30600	+	5.72616i	0.119529	+	0.207030i
$766$	−4.82425	+	8.35585i	−0.174307	+	0.301909i
$767$	20.4290	−	35.3840i	0.737647	−	1.27764i
$768$	−7.29341	−	12.6326i	−0.263178	−	0.455838i
$769$	−44.3645			−1.59983			−0.799913	−	0.600116i	$-0.795121\pi$
$769$	−44.3645			−1.59983			−0.799913	+	0.600116i	$0.795121\pi$
$770$		0			0
$771$	10.9961			0.396013
$772$	7.32153	+	12.6813i	0.263508	+	0.456408i
$773$	−12.8487	+	22.2546i	−0.462135	+	0.800441i	−0.999067	−	0.0431843i	$-0.986250\pi$
$773$	−12.8487	+	22.2546i	−0.462135	+	0.800441i	0.536932	+	0.843625i	$0.319583\pi$
$774$	2.41204	−	4.17778i	0.0866990	−	0.150167i
$775$	−7.23557	−	12.5324i	−0.259909	−	0.450176i
$776$	−42.9960			−1.54347
$777$		0			0
$778$	−22.3179			−0.800137
$779$	1.76696	+	3.06046i	0.0633079	+	0.109652i
$780$	7.45675	−	12.9155i	0.266994	−	0.462448i
$781$	28.5256	−	49.4079i	1.02073	−	1.76795i
$782$	−3.71272	−	6.43062i	−0.132767	−	0.229958i
$783$	33.0872			1.18244
$784$		0			0
$785$	−53.6153			−1.91361
$786$	1.39875	+	2.42270i	0.0498916	+	0.0864149i
$787$	12.8283	−	22.2193i	0.457279	−	0.792031i	−0.541537	−	0.840677i	$-0.682157\pi$
$787$	12.8283	−	22.2193i	0.457279	−	0.792031i	0.998816	+	0.0486462i	$0.0154907\pi$
$788$	−10.6148	+	18.3854i	−0.378137	+	0.654952i
$789$	1.45274	+	2.51621i	0.0517188	+	0.0895796i
$790$	−5.17538			−0.184132
$791$		0			0
$792$	29.5015			1.04829
$793$	14.6569	+	25.3865i	0.520482	+	0.901501i
$794$	−6.58992	+	11.4141i	−0.233867	+	0.405070i
$795$	−7.13653	+	12.3608i	−0.253107	+	0.438394i
$796$	9.37124	+	16.2315i	0.332155	+	0.575309i
$797$	−20.3683			−0.721483			−0.360741	−	0.932666i	$-0.617476\pi$
$797$	−20.3683			−0.721483			−0.360741	+	0.932666i	$0.617476\pi$
$798$		0			0
$799$	−5.57082			−0.197082
$800$	−11.9379	−	20.6770i	−0.422067	−	0.731042i
$801$	14.5764	−	25.2471i	0.515032	−	0.892062i
$802$	4.85687	−	8.41234i	0.171502	−	0.297050i
$803$	30.4013	+	52.6566i	1.07284	+	1.85821i
$804$	5.89414			0.207870
$805$		0			0
$806$	13.2101			0.465305
$807$	−7.00652	−	12.1357i	−0.246641	−	0.427195i
$808$	−4.60365	+	7.97376i	−0.161956	+	0.280516i
$809$	18.2740	−	31.6515i	0.642480	−	1.11281i	−0.342398	−	0.939555i	$-0.611239\pi$
$809$	18.2740	−	31.6515i	0.642480	−	1.11281i	0.984877	−	0.173252i	$-0.0554277\pi$
$810$	3.02066	+	5.23193i	0.106135	+	0.183831i
$811$	−7.33037			−0.257404			−0.128702	−	0.991683i	$-0.541081\pi$
$811$	−7.33037			−0.257404			−0.128702	+	0.991683i	$0.541081\pi$
$812$		0			0
$813$	−22.5876			−0.792182
$814$	−20.2950	−	35.1519i	−0.711338	−	1.23207i
$815$	−4.06443	+	7.03980i	−0.142371	+	0.246593i
$816$	0.0134975	−	0.0233784i	0.000472507	−	0.000818406i
$817$	−3.33778	−	5.78121i	−0.116774	−	0.202259i
$818$	−25.0754			−0.876739
$819$		0			0
$820$	−4.99299			−0.174363
$821$	−0.881607	−	1.52699i	−0.0307683	−	0.0532922i	0.850231	−	0.526409i	$-0.176462\pi$
$821$	−0.881607	−	1.52699i	−0.0307683	−	0.0532922i	−0.881000	+	0.473117i	$0.843129\pi$
$822$	−0.771924	+	1.33701i	−0.0269240	+	0.0466337i
$823$	−0.318161	+	0.551072i	−0.0110904	+	0.0192092i	−0.871517	−	0.490365i	$-0.836864\pi$
$823$	−0.318161	+	0.551072i	−0.0110904	+	0.0192092i	0.860427	+	0.509574i	$0.170197\pi$
$824$	18.0060	+	31.1873i	0.627268	+	1.08646i
$825$	−18.3599			−0.639209
$826$		0			0
$827$	−6.81869			−0.237109			−0.118554	−	0.992948i	$-0.537826\pi$
$827$	−6.81869			−0.237109			−0.118554	+	0.992948i	$0.537826\pi$
$828$	11.3160	+	19.5999i	0.393259	+	0.681145i
$829$	25.4740	−	44.1223i	0.884749	−	1.53243i	0.0387473	−	0.999249i	$-0.487663\pi$
$829$	25.4740	−	44.1223i	0.884749	−	1.53243i	0.846001	−	0.533181i	$-0.179003\pi$
$830$	6.11303	−	10.5881i	0.212187	−	0.367518i
$831$	−5.12193	−	8.87145i	−0.177678	−	0.307747i
$832$	22.0568			0.764683
$833$		0			0
$834$	3.74318			0.129616
$835$	2.97412	+	5.15133i	0.102924	+	0.178269i
$836$	7.77071	−	13.4593i	0.268755	−	0.465498i
$837$	−8.03489	+	13.9168i	−0.277727	+	0.481037i
$838$	−0.871539	−	1.50955i	−0.0301068	−	0.0521466i
$839$	−2.95064			−0.101867			−0.0509336	−	0.998702i	$-0.516220\pi$
$839$	−2.95064			−0.101867			−0.0509336	+	0.998702i	$0.516220\pi$
$840$		0			0
$841$	20.6036			0.710470
$842$	−11.0600	−	19.1565i	−0.381153	−	0.660177i
$843$	5.91432	−	10.2439i	0.203700	−	0.352819i
$844$	5.23316	−	9.06410i	0.180133	−	0.311999i
$845$	9.65241	+	16.7185i	0.332053	+	0.575133i
$846$	−10.6427			−0.365903
$847$		0			0
$848$	−0.153964			−0.00528714
$849$	−9.85586	−	17.0708i	−0.338252	−	0.585870i
$850$	1.85686	−	3.21617i	0.0636897	−	0.110314i
$851$	40.8974	−	70.8363i	1.40194	−	2.42824i
$852$	6.65619	+	11.5289i	0.228037	+	0.394972i
$853$	28.8764			0.988709			0.494355	−	0.869260i	$-0.335404\pi$
$853$	28.8764			0.988709			0.494355	+	0.869260i	$0.335404\pi$
$854$		0			0
$855$	17.4799			0.597799
$856$	5.54801	+	9.60943i	0.189627	+	0.328444i
$857$	−4.91988	+	8.52149i	−0.168060	+	0.291089i	−0.937738	−	0.347344i	$-0.887084\pi$
$857$	−4.91988	+	8.52149i	−0.168060	+	0.291089i	0.769678	+	0.638433i	$0.220417\pi$
$858$	8.37997	−	14.5145i	0.286087	−	0.495518i
$859$	−5.56719	−	9.64266i	−0.189950	−	0.329003i	0.755283	−	0.655398i	$-0.227499\pi$
$859$	−5.56719	−	9.64266i	−0.189950	−	0.329003i	−0.945233	+	0.326395i	$0.894166\pi$
$860$	9.43175			0.321620
$861$		0			0
$862$	−24.1390			−0.822178
$863$	−11.3515	−	19.6613i	−0.386409	−	0.669280i	0.605555	−	0.795804i	$-0.292951\pi$
$863$	−11.3515	−	19.6613i	−0.386409	−	0.669280i	−0.991964	+	0.126524i	$0.959618\pi$
$864$	−13.2567	+	22.9612i	−0.451001	+	0.781157i
$865$	−9.14085	+	15.8324i	−0.310798	+	0.538318i
$866$	12.3764	+	21.4366i	0.420569	+	0.728446i
$867$	−0.907578			−0.0308230
$868$		0			0
$869$	9.27910			0.314772
$870$	−8.52387	−	14.7638i	−0.288986	−	0.500539i
$871$	−11.6197	+	20.1260i	−0.393720	+	0.681943i
$872$	−5.05114	+	8.74882i	−0.171053	+	0.296273i
$873$	16.5037	+	28.5853i	0.558567	+	0.967466i
$874$	−19.6303			−0.664005
$875$		0			0
$876$	−14.1877			−0.479358
$877$	−0.778586	−	1.34855i	−0.0262910	−	0.0455373i	0.852581	−	0.522596i	$-0.175036\pi$
$877$	−0.778586	−	1.34855i	−0.0262910	−	0.0455373i	−0.878872	+	0.477059i	$0.841703\pi$
$878$	2.77088	−	4.79930i	0.0935125	−	0.161968i
$879$	13.1327	−	22.7464i	0.442954	−	0.767218i
$880$	−0.216059	−	0.374225i	−0.00728335	−	0.0126151i
$881$	10.3326			0.348113			0.174056	−	0.984736i	$-0.444313\pi$
$881$	10.3326			0.348113			0.174056	+	0.984736i	$0.444313\pi$
$882$		0			0
$883$	23.6160			0.794743			0.397371	−	0.917658i	$-0.369922\pi$
$883$	23.6160			0.794743			0.397371	+	0.917658i	$0.369922\pi$
$884$	−2.70428	−	4.68395i	−0.0909548	−	0.157538i
$885$	12.8044	−	22.1778i	0.430414	−	0.745499i
$886$	−11.6118	+	20.1123i	−0.390107	+	0.675686i
$887$	6.96298	+	12.0602i	0.233794	+	0.404943i	0.958922	−	0.283672i	$-0.0915525\pi$
$887$	6.96298	+	12.0602i	0.233794	+	0.404943i	−0.725128	+	0.688615i	$0.758219\pi$
$888$	24.8791			0.834889
$889$		0			0
$890$	−35.7263			−1.19755
$891$	−5.41583	−	9.38049i	−0.181437	−	0.314258i
$892$	1.53119	−	2.65209i	0.0512679	−	0.0887986i
$893$	−7.36368	+	12.7543i	−0.246416	+	0.426805i
$894$	1.68965	+	2.92657i	0.0565105	+	0.0978791i
$895$	−5.32021			−0.177835
$896$		0			0
$897$	33.7738			1.12767
$898$	15.1670	+	26.2700i	0.506129	+	0.876641i
$899$	−12.0457	+	20.8638i	−0.401748	+	0.695847i
$900$	−5.65954	+	9.80261i	−0.188651	+	0.326754i
$901$	2.58815	+	4.48281i	0.0862238	+	0.149344i
$902$	−5.61117			−0.186831
$903$		0			0
$904$	−2.74026			−0.0911398
$905$	−4.20014	−	7.27486i	−0.139617	−	0.241824i
$906$	4.96281	−	8.59584i	0.164878	−	0.285578i
$907$	−5.68139	+	9.84046i	−0.188648	+	0.326747i	−0.944800	−	0.327649i	$-0.893744\pi$
$907$	−5.68139	+	9.84046i	−0.188648	+	0.326747i	0.756152	+	0.654396i	$0.227077\pi$
$908$	10.4402	+	18.0830i	0.346472	+	0.600106i
$909$	7.06832			0.234442
$910$		0			0
$911$	4.75507			0.157543			0.0787713	−	0.996893i	$-0.474900\pi$
$911$	4.75507			0.157543			0.0787713	+	0.996893i	$0.474900\pi$
$912$	−0.0356828	−	0.0618044i	−0.00118157	−	0.00204655i
$913$	−10.9602	+	18.9837i	−0.362731	+	0.628269i
$914$	−11.6718	+	20.2161i	−0.386068	+	0.668689i
$915$	9.18657	+	15.9116i	0.303699	+	0.526022i
$916$	−20.0766			−0.663349
$917$		0			0
$918$	−4.12398			−0.136111
$919$	16.3152	+	28.2587i	0.538187	+	0.932168i	0.999002	+	0.0446712i	$0.0142240\pi$
$919$	16.3152	+	28.2587i	0.538187	+	0.932168i	−0.460815	+	0.887496i	$0.652443\pi$
$920$	36.4274	−	63.0941i	1.20098	−	2.08015i
$921$	5.25651	−	9.10454i	0.173208	−	0.300005i
$922$	−0.136152	−	0.235822i	−0.00448392	−	0.00776637i
$923$	−52.4882			−1.72767
$924$		0			0
$925$	40.9084			1.34506
$926$	−9.86046	−	17.0788i	−0.324035	−	0.561245i
$927$	13.8229	−	23.9420i	0.454005	−	0.786360i
$928$	−19.8741	+	34.4229i	−0.652399	+	1.12999i
$929$	−23.6773	−	41.0103i	−0.776827	−	1.34550i	−0.933762	−	0.357895i	$-0.883494\pi$
$929$	−23.6773	−	41.0103i	−0.776827	−	1.34550i	0.156934	−	0.987609i	$-0.449839\pi$
$930$	8.27974			0.271503
$931$		0			0
$932$	7.10382			0.232693
$933$	7.16983	+	12.4185i	0.234730	+	0.406564i
$934$	−5.09695	+	8.82817i	−0.166777	+	0.288867i
$935$	−7.26395	+	12.5815i	−0.237557	+	0.411460i
$936$	−13.5710	−	23.5056i	−0.443581	−	0.768304i
$937$	51.6525			1.68741			0.843707	−	0.536803i	$-0.180368\pi$
$937$	51.6525			1.68741			0.843707	+	0.536803i	$0.180368\pi$
$938$		0			0
$939$	18.3928			0.600226
$940$	−10.4040	−	18.0202i	−0.339340	−	0.587754i
$941$	−27.3620	+	47.3923i	−0.891975	+	1.54495i	−0.0544710	+	0.998515i	$0.517347\pi$
$941$	−27.3620	+	47.3923i	−0.891975	+	1.54495i	−0.837504	+	0.546431i	$0.815986\pi$
$942$	7.02979	−	12.1759i	0.229043	−	0.396714i
$943$	−5.65367	−	9.79245i	−0.184109	−	0.318886i
$944$	0.276242			0.00899091
$945$		0			0
$946$	10.5995			0.344619
$947$	18.4864	+	32.0194i	0.600727	+	1.04049i	0.992711	+	0.120518i	$0.0384555\pi$
$947$	18.4864	+	32.0194i	0.600727	+	1.04049i	−0.391984	+	0.919972i	$0.628211\pi$
$948$	−1.08260	+	1.87511i	−0.0351611	+	0.0609007i
$949$	27.9697	−	48.4450i	0.907936	−	1.57259i
$950$	−4.90890	−	8.50246i	−0.159266	−	0.275856i
$951$	−5.77707			−0.187334
$952$		0			0
$953$	−7.91313			−0.256331			−0.128166	−	0.991753i	$-0.540909\pi$
$953$	−7.91313			−0.256331			−0.128166	+	0.991753i	$0.540909\pi$
$954$	4.94449	+	8.56410i	0.160084	+	0.277273i
$955$	28.6289	−	49.5867i	0.926409	−	1.60459i
$956$	4.57509	−	7.92428i	0.147969	−	0.256290i
$957$	15.2827	+	26.4704i	0.494020	+	0.855667i
$958$	−27.9130			−0.901830
$959$		0			0
$960$	13.8247			0.446189
$961$	9.64963	+	16.7137i	0.311279	+	0.539150i
$962$	−18.6717	+	32.3404i	−0.602001	+	1.04270i
$963$	4.25913	−	7.37703i	0.137249	−	0.237722i
$964$	−13.4642	−	23.3207i	−0.433653	−	0.751109i
$965$	−36.1867			−1.16489
$966$		0			0
$967$	8.05906			0.259162			0.129581	−	0.991569i	$-0.458637\pi$
$967$	8.05906			0.259162			0.129581	+	0.991569i	$0.458637\pi$
$968$	16.8185	+	29.1305i	0.540568	+	0.936291i
$969$	−1.19966	+	2.07788i	−0.0385387	+	0.0667510i
$970$	20.2250	−	35.0308i	0.649386	−	1.12477i
$971$	−0.905965	−	1.56918i	−0.0290738	−	0.0503573i	0.851122	−	0.524967i	$-0.175922\pi$
$971$	−0.905965	−	1.56918i	−0.0290738	−	0.0503573i	−0.880196	+	0.474610i	$0.842589\pi$
$972$	19.8544			0.636829
$973$		0			0
$974$	−20.2047			−0.647401
$975$	8.44571	+	14.6284i	0.270479	+	0.468484i
$976$	−0.0990958	+	0.171639i	−0.00317198	+	0.00549403i
$977$	−7.59669	+	13.1579i	−0.243040	+	0.420957i	−0.961579	−	0.274530i	$-0.911478\pi$
$977$	−7.59669	+	13.1579i	−0.243040	+	0.420957i	0.718539	+	0.695487i	$0.244811\pi$
$978$	−1.06582	−	1.84605i	−0.0340811	−	0.0590301i
$979$	64.0547			2.04720
$980$		0			0
$981$	7.75538			0.247610
$982$	14.6237	+	25.3290i	0.466661	+	0.808280i
$983$	5.82360	−	10.0868i	0.185744	−	0.321718i	−0.758083	−	0.652158i	$-0.773864\pi$
$983$	5.82360	−	10.0868i	0.185744	−	0.321718i	0.943827	+	0.330440i	$0.107197\pi$
$984$	1.71965	−	2.97853i	0.0548205	−	0.0949519i
$985$	−26.2319	−	45.4350i	−0.835818	−	1.44768i
$986$	−6.18257			−0.196893
$987$		0			0
$988$	−14.2984			−0.454892
$989$	10.6798	+	18.4979i	0.339597	+	0.588200i
$990$	−13.8773	+	24.0362i	−0.441049	+	0.763920i
$991$	23.5879	−	40.8555i	0.749296	−	1.29782i	−0.198865	−	0.980027i	$-0.563725\pi$
$991$	23.5879	−	40.8555i	0.749296	−	1.29782i	0.948161	−	0.317792i	$-0.102941\pi$
$992$	−9.65244	−	16.7185i	−0.306465	−	0.530814i
$993$	−22.3183			−0.708249
$994$		0			0
$995$	−46.3175			−1.46836
$996$	−2.55747	−	4.42967i	−0.0810365	−	0.140359i
$997$	19.8787	−	34.4309i	0.629564	−	1.09044i	−0.358075	−	0.933693i	$-0.616567\pi$
$997$	19.8787	−	34.4309i	0.629564	−	1.09044i	0.987639	−	0.156744i	$-0.0500998\pi$
$998$	−16.2503	+	28.1464i	−0.514394	+	0.890957i
$999$	−22.7138	−	39.3414i	−0.718633	−	1.24471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.e.h.18.3		10
7.2	even	3	inner	833.2.e.h.324.3		10
7.3	odd	6		119.2.a.b.1.3	✓	5
7.4	even	3		833.2.a.g.1.3		5
7.5	odd	6		833.2.e.i.324.3		10
7.6	odd	2		833.2.e.i.18.3		10
21.11	odd	6		7497.2.a.br.1.3		5
21.17	even	6		1071.2.a.m.1.3		5
28.3	even	6		1904.2.a.t.1.2		5
35.24	odd	6		2975.2.a.m.1.3		5
56.3	even	6		7616.2.a.bq.1.4		5
56.45	odd	6		7616.2.a.bt.1.2		5
119.101	odd	6		2023.2.a.j.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.3	✓	5	7.3	odd	6
833.2.a.g.1.3		5	7.4	even	3
833.2.e.h.18.3		10	1.1	even	1	trivial
833.2.e.h.324.3		10	7.2	even	3	inner
833.2.e.i.18.3		10	7.6	odd	2
833.2.e.i.324.3		10	7.5	odd	6
1071.2.a.m.1.3		5	21.17	even	6
1904.2.a.t.1.2		5	28.3	even	6
2023.2.a.j.1.3		5	119.101	odd	6
2975.2.a.m.1.3		5	35.24	odd	6
7497.2.a.br.1.3		5	21.11	odd	6
7616.2.a.bq.1.4		5	56.3	even	6
7616.2.a.bt.1.2		5	56.45	odd	6

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.438917 - 0.760227i) q^{2} +(0.453789 - 0.785986i) q^{3} +(0.614704 - 1.06470i) q^{4} +(1.51909 + 2.63114i) q^{5} -0.796703 q^{6} -2.83488 q^{8} +(1.08815 + 1.88473i) q^{9} +O(q^{10})\)	\(q+(-0.438917 - 0.760227i) q^{2} +(0.453789 - 0.785986i) q^{3} +(0.614704 - 1.06470i) q^{4} +(1.51909 + 2.63114i) q^{5} -0.796703 q^{6} -2.83488 q^{8} +(1.08815 + 1.88473i) q^{9} +(1.33351 - 2.30971i) q^{10} +(-2.39089 + 4.14114i) q^{11} +(-0.557892 - 0.966297i) q^{12} +4.39933 q^{13} +2.75739 q^{15} +(0.0148720 + 0.0257591i) q^{16} +(0.500000 - 0.866025i) q^{17} +(0.955216 - 1.65448i) q^{18} +(-1.32183 - 2.28947i) q^{19} +3.73516 q^{20} +4.19761 q^{22} +(4.22941 + 7.32555i) q^{23} +(-1.28644 + 2.22818i) q^{24} +(-2.11527 + 3.66376i) q^{25} +(-1.93094 - 3.34449i) q^{26} +4.69790 q^{27} +7.04298 q^{29} +(-1.21026 - 2.09624i) q^{30} +(-1.71032 + 2.96236i) q^{31} +(-2.82183 + 4.88755i) q^{32} +(2.16992 + 3.75841i) q^{33} -0.877834 q^{34} +2.67556 q^{36} +(-4.83488 - 8.37426i) q^{37} +(-1.16035 + 2.00978i) q^{38} +(1.99637 - 3.45781i) q^{39} +(-4.30645 - 7.45898i) q^{40} -1.33675 q^{41} +2.52513 q^{43} +(2.93938 + 5.09115i) q^{44} +(-3.30600 + 5.72616i) q^{45} +(3.71272 - 6.43062i) q^{46} +(-2.78541 - 4.82448i) q^{47} +0.0269950 q^{48} +3.71372 q^{50} +(-0.453789 - 0.785986i) q^{51} +(2.70428 - 4.68395i) q^{52} +(-2.58815 + 4.48281i) q^{53} +(-2.06199 - 3.57147i) q^{54} -14.5279 q^{55} -2.39933 q^{57} +(-3.09129 - 5.35426i) q^{58} +(4.64366 - 8.04305i) q^{59} +(1.69498 - 2.93578i) q^{60} +(3.33162 + 5.77054i) q^{61} +3.00275 q^{62} +5.01368 q^{64} +(6.68297 + 11.5753i) q^{65} +(1.90483 - 3.29926i) q^{66} +(-2.64126 + 4.57479i) q^{67} +(-0.614704 - 1.06470i) q^{68} +7.67704 q^{69} -11.9310 q^{71} +(-3.08478 - 5.34300i) q^{72} +(6.35773 - 11.0119i) q^{73} +(-4.24423 + 7.35122i) q^{74} +(1.91977 + 3.32515i) q^{75} -3.25013 q^{76} -3.50496 q^{78} +(-0.970256 - 1.68053i) q^{79} +(-0.0451838 + 0.0782607i) q^{80} +(-1.13260 + 1.96172i) q^{81} +(0.586724 + 1.01624i) q^{82} +4.58417 q^{83} +3.03818 q^{85} +(-1.10832 - 1.91967i) q^{86} +(3.19603 - 5.53569i) q^{87} +(6.77789 - 11.7397i) q^{88} +(-6.69779 - 11.6009i) q^{89} +5.80424 q^{90} +10.3993 q^{92} +(1.55225 + 2.68857i) q^{93} +(-2.44513 + 4.23509i) q^{94} +(4.01596 - 6.95584i) q^{95} +(2.56103 + 4.43583i) q^{96} +15.1668 q^{97} -10.4066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9	\( 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9} + 4 q^{10} + 2 q^{11} - 22 q^{12} - 4 q^{13} + 16 q^{15} - 4 q^{16} + 5 q^{17} + 18 q^{18} + 6 q^{19} + 38 q^{20} + 12 q^{22} + 10 q^{23} + 2 q^{24} - 21 q^{25} - 26 q^{26} + 52 q^{27} - 16 q^{29} + 51 q^{30} - 9 q^{32} + 6 q^{33} - 4 q^{34} + 78 q^{36} - 8 q^{37} + 14 q^{38} - 14 q^{39} + 5 q^{40} - 36 q^{41} + 16 q^{43} + 14 q^{44} - 8 q^{46} - 10 q^{47} + 54 q^{48} + 54 q^{50} + 2 q^{51} + 4 q^{52} - 4 q^{53} + 5 q^{54} + 48 q^{55} + 24 q^{57} - 12 q^{58} + 8 q^{59} + 7 q^{60} + 22 q^{61} - 32 q^{62} - 32 q^{64} + 30 q^{65} + 68 q^{66} - 16 q^{67} + 10 q^{68} + 64 q^{69} - 4 q^{71} - 9 q^{72} + 10 q^{73} + 40 q^{74} - 14 q^{75} - 48 q^{76} + 60 q^{78} - 18 q^{79} - 4 q^{80} - 25 q^{81} - 31 q^{82} + 24 q^{83} - 23 q^{86} - 26 q^{87} + 46 q^{88} + 20 q^{89} - 194 q^{90} + 56 q^{92} + 28 q^{93} - 42 q^{94} + 22 q^{95} - 18 q^{96} - 24 q^{97} - 124 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9 + 4 * q^10 + 2 * q^11 - 22 * q^12 - 4 * q^13 + 16 * q^15 - 4 * q^16 + 5 * q^17 + 18 * q^18 + 6 * q^19 + 38 * q^20 + 12 * q^22 + 10 * q^23 + 2 * q^24 - 21 * q^25 - 26 * q^26 + 52 * q^27 - 16 * q^29 + 51 * q^30 - 9 * q^32 + 6 * q^33 - 4 * q^34 + 78 * q^36 - 8 * q^37 + 14 * q^38 - 14 * q^39 + 5 * q^40 - 36 * q^41 + 16 * q^43 + 14 * q^44 - 8 * q^46 - 10 * q^47 + 54 * q^48 + 54 * q^50 + 2 * q^51 + 4 * q^52 - 4 * q^53 + 5 * q^54 + 48 * q^55 + 24 * q^57 - 12 * q^58 + 8 * q^59 + 7 * q^60 + 22 * q^61 - 32 * q^62 - 32 * q^64 + 30 * q^65 + 68 * q^66 - 16 * q^67 + 10 * q^68 + 64 * q^69 - 4 * q^71 - 9 * q^72 + 10 * q^73 + 40 * q^74 - 14 * q^75 - 48 * q^76 + 60 * q^78 - 18 * q^79 - 4 * q^80 - 25 * q^81 - 31 * q^82 + 24 * q^83 - 23 * q^86 - 26 * q^87 + 46 * q^88 + 20 * q^89 - 194 * q^90 + 56 * q^92 + 28 * q^93 - 42 * q^94 + 22 * q^95 - 18 * q^96 - 24 * q^97 - 124 * q^99

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