LMFDB - Embedded newform 784.2.m.h.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.3
Root			$-1.40471 + 0.163666i$ of defining polynomial
Character	$\chi$	$=$	784.197
Dual form			784.2.m.h.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +O(q^{10})$	\(q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +(-4.27801 + 3.38515i) q^{10} +(0.919616 + 0.919616i) q^{11} +(-4.94480 + 3.05500i) q^{12} +(1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(3.57715 + 1.78996i) q^{16} +1.50885 q^{17} +(-7.65008 - 0.891330i) q^{18} +(-1.46271 + 1.46271i) q^{19} +(4.05500 + 6.56340i) q^{20} +(1.44230 - 1.14128i) q^{22} -4.77031i q^{23} +(3.48209 + 7.44602i) q^{24} +9.88030i q^{25} +(-1.39751 - 1.76611i) q^{26} +(-5.02656 - 5.02656i) q^{27} +(4.10069 - 4.10069i) q^{29} +(-1.83481 + 15.7478i) q^{30} -4.10999 q^{31} +(3.09984 - 4.73191i) q^{32} +3.77961 q^{33} +(0.246948 - 2.11950i) q^{34} +(-2.50412 + 10.6003i) q^{36} +(-1.65467 - 1.65467i) q^{37} +(1.81529 + 2.29409i) q^{38} -4.62815i q^{39} +(9.88334 - 4.62189i) q^{40} +7.45533i q^{41} +(5.68992 + 5.68992i) q^{43} +(-1.36712 - 2.21281i) q^{44} +(-14.8549 + 14.8549i) q^{45} +(-6.70090 - 0.780738i) q^{46} -3.59748 q^{47} +(11.0294 - 3.67267i) q^{48} +(13.8790 + 1.61707i) q^{50} +(3.10069 - 3.10069i) q^{51} +(-2.70960 + 1.67404i) q^{52} +(-0.675714 - 0.675714i) q^{53} +(-7.88355 + 6.23819i) q^{54} -5.01680i q^{55} +6.01174i q^{57} +(-5.08913 - 6.43142i) q^{58} +(-1.13843 - 1.13843i) q^{59} +(21.8208 + 5.15476i) q^{60} +(3.21881 - 3.21881i) q^{61} +(-0.672667 + 5.77335i) q^{62} +(-6.13963 - 5.12884i) q^{64} -6.14310 q^{65} +(0.618595 - 5.30926i) q^{66} +(-1.52640 + 1.52640i) q^{67} +(-2.93687 - 0.693782i) q^{68} +(-9.80296 - 9.80296i) q^{69} -13.8202i q^{71} +(14.4805 + 5.25248i) q^{72} -14.4749i q^{73} +(-2.59514 + 2.05351i) q^{74} +(20.3040 + 20.3040i) q^{75} +(3.51963 - 2.17450i) q^{76} +(-6.50122 - 0.757473i) q^{78} -1.77961 q^{79} +(-4.87485 - 14.6397i) q^{80} -4.32107 q^{81} +(10.4726 + 1.22019i) q^{82} +(7.16133 - 7.16133i) q^{83} +(-4.11564 - 4.11564i) q^{85} +(8.92394 - 7.06145i) q^{86} -16.8538i q^{87} +(-3.33211 + 1.55824i) q^{88} -8.45899i q^{89} +(18.4356 + 23.2981i) q^{90} +(-2.19342 + 9.28505i) q^{92} +(-8.44602 + 8.44602i) q^{93} +(-0.588786 + 5.05342i) q^{94} +7.97958 q^{95} +(-3.35389 - 16.0942i) q^{96} -16.2227 q^{97} +(5.00824 - 5.00824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * q^50 - 16 * q^51 + 16 * q^52 + 4 * q^53 - 64 * q^54 + 14 * q^58 + 16 * q^59 + 60 * q^60 + 20 * q^61 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	0.163666	−	1.40471i	0.115730	−	0.993281i
$2$	0.163666	−	1.40471i	0.115730	−	0.993281i
$3$	2.05500	−	2.05500i	1.18645	−	1.18645i	0.208411	−	0.978041i	$-0.433171\pi$
$3$	2.05500	−	2.05500i	1.18645	−	1.18645i	0.978041	−	0.208411i	$-0.0668293\pi$
$4$	−1.94643	−	0.459808i	−0.973213	−	0.229904i
$5$	−2.72766	−	2.72766i	−1.21985	−	1.21985i	−0.967685	−	0.252164i	$-0.918858\pi$
$5$	−2.72766	−	2.72766i	−1.21985	−	1.21985i	−0.252164	−	0.967685i	$-0.581142\pi$
$6$	−2.55034	−	3.22301i	−1.04117	−	1.31579i
$7$		0			0
$7$		0			0
$8$	−0.964462	+	2.65891i	−0.340989	+	0.940067i
$9$		−	5.44602i		−	1.81534i
$10$	−4.27801	+	3.38515i	−1.35282	+	1.07048i
$11$	0.919616	+	0.919616i	0.277275	+	0.277275i	0.832020	−	0.554746i	$-0.187184\pi$
$11$	0.919616	+	0.919616i	0.277275	+	0.277275i	−0.554746	+	0.832020i	$0.687184\pi$
$12$	−4.94480	+	3.05500i	−1.42744	+	0.881901i
$13$	1.12607	−	1.12607i	0.312316	−	0.312316i	−0.533490	−	0.845806i	$-0.679120\pi$
$13$	1.12607	−	1.12607i	0.312316	−	0.312316i	0.845806	+	0.533490i	$0.179120\pi$
$14$		0			0
$15$	−11.2107			−2.89458
$16$	3.57715	+	1.78996i	0.894288	+	0.447491i
$17$	1.50885			0.365950			0.182975	−	0.983118i	$-0.441427\pi$
$17$	1.50885			0.365950			0.182975	+	0.983118i	$0.441427\pi$
$18$	−7.65008	−	0.891330i	−1.80314	−	0.210088i
$19$	−1.46271	+	1.46271i	−0.335569	+	0.335569i	−0.854697	−	0.519127i	$-0.826257\pi$
$19$	−1.46271	+	1.46271i	−0.335569	+	0.335569i	0.519127	+	0.854697i	$0.326257\pi$
$20$	4.05500	+	6.56340i	0.906725	+	1.46762i
$21$		0			0
$22$	1.44230	−	1.14128i	0.307500	−	0.243323i
$23$		−	4.77031i		−	0.994677i	−0.867556	−	0.497339i	$-0.834311\pi$
$23$		−	4.77031i		−	0.994677i	0.867556	−	0.497339i	$-0.165689\pi$
$24$	3.48209	+	7.44602i	0.710779	+	1.51991i
$25$			9.88030i			1.97606i
$26$	−1.39751	−	1.76611i	−0.274074	−	0.346362i
$27$	−5.02656	−	5.02656i	−0.967362	−	0.967362i
$28$		0			0
$29$	4.10069	−	4.10069i	0.761478	−	0.761478i	−0.215111	−	0.976590i	$-0.569011\pi$
$29$	4.10069	−	4.10069i	0.761478	−	0.761478i	0.976590	+	0.215111i	$0.0690115\pi$
$30$	−1.83481	+	15.7478i	−0.334989	+	2.87514i
$31$	−4.10999			−0.738176			−0.369088	−	0.929394i	$-0.620330\pi$
$31$	−4.10999			−0.738176			−0.369088	+	0.929394i	$0.620330\pi$
$32$	3.09984	−	4.73191i	0.547980	−	0.836492i
$33$	3.77961			0.657946
$34$	0.246948	−	2.11950i	0.0423513	−	0.363491i
$35$		0			0
$36$	−2.50412	+	10.6003i	−0.417354	+	1.76671i
$37$	−1.65467	−	1.65467i	−0.272025	−	0.272025i	0.557890	−	0.829915i	$-0.311611\pi$
$37$	−1.65467	−	1.65467i	−0.272025	−	0.272025i	−0.829915	+	0.557890i	$0.811611\pi$
$38$	1.81529	+	2.29409i	0.294479	+	0.372150i
$39$		−	4.62815i		−	0.741097i
$40$	9.88334	−	4.62189i	1.56269	−	0.730785i
$41$			7.45533i			1.16433i	0.813072	+	0.582163i	$0.197794\pi$
$41$			7.45533i			1.16433i	−0.813072	+	0.582163i	$0.802206\pi$
$42$		0			0
$43$	5.68992	+	5.68992i	0.867705	+	0.867705i	0.992218	−	0.124513i	$-0.0397369\pi$
$43$	5.68992	+	5.68992i	0.867705	+	0.867705i	−0.124513	+	0.992218i	$0.539737\pi$
$44$	−1.36712	−	2.21281i	−0.206101	−	0.333594i
$45$	−14.8549	+	14.8549i	−2.21444	+	2.21444i
$46$	−6.70090	−	0.780738i	−0.987994	−	0.115114i
$47$	−3.59748			−0.524747			−0.262373	−	0.964966i	$-0.584505\pi$
$47$	−3.59748			−0.524747			−0.262373	+	0.964966i	$0.584505\pi$
$48$	11.0294	−	3.67267i	1.59196	−	0.530104i
$49$		0			0
$50$	13.8790	+	1.61707i	1.96278	+	0.228689i
$51$	3.10069	−	3.10069i	0.434183	−	0.434183i
$52$	−2.70960	+	1.67404i	−0.375753	+	0.232148i
$53$	−0.675714	−	0.675714i	−0.0928165	−	0.0928165i	0.659174	−	0.751990i	$-0.270906\pi$
$53$	−0.675714	−	0.675714i	−0.0928165	−	0.0928165i	−0.751990	+	0.659174i	$0.770906\pi$
$54$	−7.88355	+	6.23819i	−1.07281	+	0.848910i
$55$		−	5.01680i		−	0.676466i
$56$		0			0
$57$			6.01174i			0.796275i
$58$	−5.08913	−	6.43142i	−0.668236	−	0.844487i
$59$	−1.13843	−	1.13843i	−0.148211	−	0.148211i	0.629108	−	0.777318i	$-0.283420\pi$
$59$	−1.13843	−	1.13843i	−0.148211	−	0.148211i	−0.777318	+	0.629108i	$0.783420\pi$
$60$	21.8208	+	5.15476i	2.81705	+	0.665476i
$61$	3.21881	−	3.21881i	0.412127	−	0.412127i	−0.470352	−	0.882479i	$-0.655873\pi$
$61$	3.21881	−	3.21881i	0.412127	−	0.412127i	0.882479	+	0.470352i	$0.155873\pi$
$62$	−0.672667	+	5.77335i	−0.0854288	+	0.733216i
$63$		0			0
$64$	−6.13963	−	5.12884i	−0.767453	−	0.641105i
$65$	−6.14310			−0.761957
$66$	0.618595	−	5.30926i	0.0761438	−	0.653525i
$67$	−1.52640	+	1.52640i	−0.186480	+	0.186480i	−0.794172	−	0.607692i	$-0.792095\pi$
$67$	−1.52640	+	1.52640i	−0.186480	+	0.186480i	0.607692	+	0.794172i	$0.292095\pi$
$68$	−2.93687	−	0.693782i	−0.356148	−	0.0841334i
$69$	−9.80296	−	9.80296i	−1.18014	−	1.18014i
$70$		0			0
$71$		−	13.8202i		−	1.64016i	−0.572251	−	0.820079i	$-0.693930\pi$
$71$		−	13.8202i		−	1.64016i	0.572251	−	0.820079i	$-0.306070\pi$
$72$	14.4805	+	5.25248i	1.70654	+	0.619010i
$73$		−	14.4749i		−	1.69416i	−0.531468	−	0.847078i	$-0.678359\pi$
$73$		−	14.4749i		−	1.69416i	0.531468	−	0.847078i	$-0.321641\pi$
$74$	−2.59514	+	2.05351i	−0.301679	+	0.238716i
$75$	20.3040	+	20.3040i	2.34450	+	2.34450i
$76$	3.51963	−	2.17450i	0.403729	−	0.249432i
$77$		0			0
$78$	−6.50122	−	0.757473i	−0.736118	−	0.0857669i
$79$	−1.77961			−0.200222			−0.100111	−	0.994976i	$-0.531920\pi$
$79$	−1.77961			−0.200222			−0.100111	+	0.994976i	$0.531920\pi$
$80$	−4.87485	−	14.6397i	−0.545025	−	1.63677i
$81$	−4.32107			−0.480119
$82$	10.4726	+	1.22019i	1.15650	+	0.134747i
$83$	7.16133	−	7.16133i	0.786058	−	0.786058i	−0.194787	−	0.980845i	$-0.562402\pi$
$83$	7.16133	−	7.16133i	0.786058	−	0.786058i	0.980845	+	0.194787i	$0.0624017\pi$
$84$		0			0
$85$	−4.11564	−	4.11564i	−0.446404	−	0.446404i
$86$	8.92394	−	7.06145i	0.962294	−	0.761455i
$87$		−	16.8538i		−	1.80692i
$88$	−3.33211	+	1.55824i	−0.355204	+	0.166109i
$89$		−	8.45899i		−	0.896651i	−0.893870	−	0.448325i	$-0.852021\pi$
$89$		−	8.45899i		−	0.896651i	0.893870	−	0.448325i	$-0.147979\pi$
$90$	18.4356	+	23.2981i	1.94328	+	2.45584i
$91$		0			0
$92$	−2.19342	+	9.28505i	−0.228680	+	0.968033i
$93$	−8.44602	+	8.44602i	−0.875811	+	0.875811i
$94$	−0.588786	+	5.05342i	−0.0607287	+	0.521221i
$95$	7.97958			0.818688
$96$	−3.35389	−	16.0942i	−0.342305	−	1.64261i
$97$	−16.2227			−1.64717			−0.823585	−	0.567194i	$-0.808029\pi$
$97$	−16.2227			−1.64717			−0.823585	+	0.567194i	$0.808029\pi$
$98$		0			0
$99$	5.00824	−	5.00824i	0.503348	−	0.503348i
$100$	4.54304	−	19.2313i	0.454304	−	1.92313i
$101$	11.5664	+	11.5664i	1.15090	+	1.15090i	0.986372	+	0.164533i	$0.0526116\pi$
$101$	11.5664	+	11.5664i	1.15090	+	1.15090i	0.164533	+	0.986372i	$0.447388\pi$
$102$	−3.84809	−	4.86304i	−0.381018	−	0.481513i
$103$			17.1875i			1.69354i	0.531963	+	0.846768i	$0.321455\pi$
$103$			17.1875i			1.69354i	−0.531963	+	0.846768i	$0.678545\pi$
$104$	1.90808	+	4.08018i	0.187102	+	0.400095i
$105$		0			0
$106$	−1.05977	+	0.838591i	−0.102934	+	0.0814512i
$107$	4.10143	+	4.10143i	0.396501	+	0.396501i	0.876997	−	0.480496i	$-0.159543\pi$
$107$	4.10143	+	4.10143i	0.396501	+	0.396501i	−0.480496	+	0.876997i	$0.659543\pi$
$108$	7.47258	+	12.0951i	0.719049	+	1.16385i
$109$	−3.27351	+	3.27351i	−0.313545	+	0.313545i	−0.846281	−	0.532736i	$-0.821164\pi$
$109$	−3.27351	+	3.27351i	−0.313545	+	0.313545i	0.532736	+	0.846281i	$0.321164\pi$
$110$	−7.04716	−	0.821082i	−0.671920	−	0.0782871i
$111$	−6.80066			−0.645490
$112$		0			0
$113$	−9.17193			−0.862822			−0.431411	−	0.902155i	$-0.641984\pi$
$113$	−9.17193			−0.862822			−0.431411	+	0.902155i	$0.641984\pi$
$114$	8.44476	+	0.983920i	0.790924	+	0.0921525i
$115$	−13.0118	+	13.0118i	−1.21336	+	1.21336i
$116$	−9.86721	+	6.09616i	−0.916147	+	0.566014i
$117$	−6.13262	−	6.13262i	−0.566961	−	0.566961i
$118$	−1.78548	+	1.41284i	−0.164367	+	0.130062i
$119$		0			0
$120$	10.8123	−	29.8082i	0.987021	−	2.72110i
$121$		−	9.30861i		−	0.846238i
$122$	−3.99469	−	5.04831i	−0.361662	−	0.457053i
$123$	15.3207	+	15.3207i	1.38142	+	1.38142i
$124$	7.99980	+	1.88981i	0.718403	+	0.169710i
$125$	13.3118	−	13.3118i	1.19064	−	1.19064i
$126$		0			0
$127$	−12.9787			−1.15167			−0.575835	−	0.817566i	$-0.695323\pi$
$127$	−12.9787			−1.15167			−0.575835	+	0.817566i	$0.695323\pi$
$128$	−8.20939	+	7.78499i	−0.725614	+	0.688102i
$129$	23.3855			2.05898
$130$	−1.00542	+	8.62928i	−0.0881810	+	0.756838i
$131$	6.81965	−	6.81965i	0.595836	−	0.595836i	−0.343366	−	0.939202i	$-0.611567\pi$
$131$	6.81965	−	6.81965i	0.595836	−	0.595836i	0.939202	+	0.343366i	$0.111567\pi$
$132$	−7.35674	−	1.73790i	−0.640322	−	0.151264i
$133$		0			0
$134$	1.89434	+	2.39398i	0.163646	+	0.206808i
$135$			27.4215i			2.36007i
$136$	−1.45523	+	4.01190i	−0.124785	+	0.344018i
$137$		−	22.6543i		−	1.93548i	−0.251943	−	0.967742i	$-0.581069\pi$
$137$		−	22.6543i		−	1.93548i	0.251943	−	0.967742i	$-0.418931\pi$
$138$	−15.3747	+	12.1659i	−1.30878	+	1.03563i
$139$	6.64728	+	6.64728i	0.563815	+	0.563815i	0.930389	−	0.366574i	$-0.119469\pi$
$139$	6.64728	+	6.64728i	0.563815	+	0.563815i	−0.366574	+	0.930389i	$0.619469\pi$
$140$		0			0
$141$	−7.39281	+	7.39281i	−0.622587	+	0.622587i
$142$	−19.4134	−	2.26190i	−1.62914	−	0.189815i
$143$	2.07111			0.173195
$144$	9.74818	−	19.4812i	0.812348	−	1.62344i
$145$	−22.3706			−1.85778
$146$	−20.3330	−	2.36905i	−1.68277	−	0.196064i
$147$		0			0
$148$	2.45986	+	3.98151i	0.202199	+	0.327278i
$149$	7.77031	+	7.77031i	0.636568	+	0.636568i	0.949707	−	0.313139i	$-0.101381\pi$
$149$	7.77031	+	7.77031i	0.636568	+	0.636568i	−0.313139	+	0.949707i	$0.601381\pi$
$150$	31.8443	−	25.1981i	2.60008	−	2.05742i
$151$			5.46829i			0.445004i	0.974932	+	0.222502i	$0.0714223\pi$
$151$			5.46829i			0.445004i	−0.974932	+	0.222502i	$0.928578\pi$
$152$	−2.47850	−	5.29996i	−0.201033	−	0.429883i
$153$		−	8.21724i		−	0.664324i
$154$		0			0
$155$	11.2107	+	11.2107i	0.900463	+	0.900463i
$156$	−2.12806	+	9.00836i	−0.170381	+	0.721246i
$157$	5.61722	−	5.61722i	0.448303	−	0.448303i	−0.446487	−	0.894790i	$-0.647325\pi$
$157$	5.61722	−	5.61722i	0.448303	−	0.448303i	0.894790	+	0.446487i	$0.147325\pi$
$158$	−0.291263	+	2.49984i	−0.0231716	+	0.198877i
$159$	−2.77718			−0.220245
$160$	−21.3624	+	4.45173i	−1.68885	+	0.351940i
$161$		0			0
$162$	−0.707214	+	6.06986i	−0.0555640	+	0.476893i
$163$	−6.31758	+	6.31758i	−0.494831	+	0.494831i	−0.909824	−	0.414994i	$-0.863784\pi$
$163$	−6.31758	+	6.31758i	−0.494831	+	0.494831i	0.414994	+	0.909824i	$0.363784\pi$
$164$	3.42802	−	14.5112i	0.267683	−	1.13314i
$165$	−10.3095	−	10.3095i	−0.802595	−	0.802595i
$166$	−8.88753	−	11.2317i	−0.689806	−	0.871746i
$167$			11.8175i			0.914463i	0.889348	+	0.457231i	$0.151159\pi$
$167$			11.8175i			0.914463i	−0.889348	+	0.457231i	$0.848841\pi$
$168$		0			0
$169$			10.4639i			0.804917i
$170$	−6.45488	+	5.10769i	−0.495067	+	0.391742i
$171$	7.96597	+	7.96597i	0.609173	+	0.609173i
$172$	−8.45874	−	13.6913i	−0.644973	−	1.04395i
$173$	−5.63858	+	5.63858i	−0.428694	+	0.428694i	−0.888183	−	0.459490i	$-0.848032\pi$
$173$	−5.63858	+	5.63858i	−0.428694	+	0.428694i	0.459490	+	0.888183i	$0.348032\pi$
$174$	−23.6747	−	2.75840i	−1.79477	−	0.209114i
$175$		0			0
$176$	1.64353	+	4.93569i	0.123886	+	0.372041i
$177$	−4.67893			−0.351690
$178$	−11.8824	−	1.38445i	−0.890626	−	0.103769i
$179$	11.7278	−	11.7278i	0.876575	−	0.876575i	−0.116604	−	0.993179i	$-0.537201\pi$
$179$	11.7278	−	11.7278i	0.876575	−	0.876575i	0.993179	+	0.116604i	$0.0372007\pi$
$180$	35.7444	−	22.0836i	2.66423	−	1.64601i
$181$	4.18574	+	4.18574i	0.311124	+	0.311124i	0.845345	−	0.534221i	$-0.179395\pi$
$181$	4.18574	+	4.18574i	0.311124	+	0.311124i	−0.534221	+	0.845345i	$0.679395\pi$
$182$		0			0
$183$		−	13.2293i		−	0.977937i
$184$	12.6838	+	4.60078i	0.935064	+	0.339174i
$185$			9.02674i			0.663659i
$186$	10.4819	+	13.2465i	0.768569	+	0.971284i
$187$	1.38756	+	1.38756i	0.101469	+	0.101469i
$188$	7.00223	+	1.65415i	0.510690	+	0.120641i
$189$		0			0
$190$	1.30599	−	11.2090i	0.0947464	−	0.813187i
$191$	12.3676			0.894891			0.447445	−	0.894311i	$-0.352334\pi$
$191$	12.3676			0.894891			0.447445	+	0.894311i	$0.352334\pi$
$192$	−23.1567	+	2.07717i	−1.67119	+	0.149907i
$193$	23.6837			1.70479			0.852395	−	0.522898i	$-0.175149\pi$
$193$	23.6837			1.70479			0.852395	+	0.522898i	$0.175149\pi$
$194$	−2.65512	+	22.7883i	−0.190626	+	1.63610i
$195$	−12.6240	+	12.6240i	−0.904026	+	0.904026i
$196$		0			0
$197$	−11.4195	−	11.4195i	−0.813606	−	0.813606i	0.171566	−	0.985173i	$-0.445117\pi$
$197$	−11.4195	−	11.4195i	−0.813606	−	0.813606i	−0.985173	+	0.171566i	$0.945117\pi$
$198$	−6.21546	−	7.85482i	−0.441713	−	0.558218i
$199$		−	5.49683i		−	0.389660i	−0.980837	−	0.194830i	$-0.937585\pi$
$199$		−	5.49683i		−	0.389660i	0.980837	−	0.194830i	$-0.0624155\pi$
$200$	−26.2708	−	9.52917i	−1.85763	−	0.673814i
$201$			6.27351i			0.442499i
$202$	18.1406	−	14.3545i	1.27636	−	1.00998i
$203$		0			0
$204$	−7.46098	+	4.60954i	−0.522373	+	0.322732i
$205$	20.3356	−	20.3356i	1.42030	−	1.42030i
$206$	24.1435	+	2.81302i	1.68216	+	0.195992i
$207$	−25.9792			−1.80568
$208$	6.04377	−	2.01251i	0.419060	−	0.139542i
$209$	−2.69027			−0.186090
$210$		0			0
$211$	0.907874	−	0.907874i	0.0625007	−	0.0625007i	−0.675166	−	0.737666i	$-0.735928\pi$
$211$	0.907874	−	0.907874i	0.0625007	−	0.0625007i	0.737666	+	0.675166i	$0.235928\pi$
$212$	1.00453	+	1.62593i	0.0689914	+	0.111669i
$213$	−28.4005	−	28.4005i	−1.94597	−	1.94597i
$214$	6.43260	−	5.09006i	0.439723	−	0.347949i
$215$		−	31.0404i		−	2.11694i
$216$	18.2131	−	8.51726i	1.23925	−	0.579526i
$217$		0			0
$218$	4.06257	+	5.13410i	0.275152	+	0.347725i
$219$	−29.7458	−	29.7458i	−2.01004	−	2.01004i
$220$	−2.30677	+	9.76484i	−0.155522	+	0.658345i
$221$	1.69908	−	1.69908i	0.114292	−	0.114292i
$222$	−1.11304	+	9.55297i	−0.0747023	+	0.641153i
$223$	3.20318			0.214501			0.107250	−	0.994232i	$-0.465795\pi$
$223$	3.20318			0.214501			0.107250	+	0.994232i	$0.465795\pi$
$224$		0			0
$225$	53.8083			3.58722
$226$	−1.50114	+	12.8839i	−0.0998540	+	0.857025i
$227$	13.7931	−	13.7931i	0.915480	−	0.915480i	−0.0812167	−	0.996696i	$-0.525881\pi$
$227$	13.7931	−	13.7931i	0.915480	−	0.915480i	0.996696	+	0.0812167i	$0.0258806\pi$
$228$	2.76425	−	11.7014i	0.183067	−	0.774945i
$229$	−7.02177	−	7.02177i	−0.464012	−	0.464012i	0.435956	−	0.899968i	$-0.356410\pi$
$229$	−7.02177	−	7.02177i	−0.464012	−	0.464012i	−0.899968	+	0.435956i	$0.856410\pi$
$230$	16.1482	+	20.4074i	1.06478	+	1.34562i
$231$		0			0
$232$	6.94841	+	14.8583i	0.456185	+	0.975496i
$233$			2.93857i			0.192512i	0.995357	+	0.0962561i	$0.0306868\pi$
$233$			2.93857i			0.192512i	−0.995357	+	0.0962561i	$0.969313\pi$
$234$	−9.61826	+	7.61085i	−0.628765	+	0.497537i
$235$	9.81272	+	9.81272i	0.640111	+	0.640111i
$236$	1.69241	+	2.73932i	0.110166	+	0.178315i
$237$	−3.65710	+	3.65710i	−0.237554	+	0.237554i
$238$		0			0
$239$	16.2109			1.04859			0.524297	−	0.851536i	$-0.324328\pi$
$239$	16.2109			1.04859			0.524297	+	0.851536i	$0.324328\pi$
$240$	−40.1023	−	20.0667i	−2.58859	−	1.29530i
$241$	14.1166			0.909329			0.454665	−	0.890663i	$-0.349759\pi$
$241$	14.1166			0.909329			0.454665	+	0.890663i	$0.349759\pi$
$242$	−13.0759	−	1.52351i	−0.840552	−	0.0979347i
$243$	6.19990	−	6.19990i	0.397724	−	0.397724i
$244$	−7.74522	+	4.78515i	−0.495837	+	0.306338i
$245$		0			0
$246$	24.0286	−	19.0136i	1.53201	−	1.21227i
$247$			3.29424i			0.209608i
$248$	3.96393	−	10.9281i	0.251710	−	0.693936i
$249$		−	29.4330i		−	1.86524i
$250$	−16.5206	−	20.8779i	−1.04485	−	1.32044i
$251$	14.1967	+	14.1967i	0.896091	+	0.896091i	0.995088	−	0.0989969i	$-0.0315634\pi$
$251$	14.1967	+	14.1967i	0.896091	+	0.896091i	−0.0989969	+	0.995088i	$0.531563\pi$
$252$		0			0
$253$	4.38685	−	4.38685i	0.275799	−	0.275799i
$254$	−2.12417	+	18.2313i	−0.133282	+	1.14393i
$255$	−16.9153			−1.05927
$256$	9.59206	+	12.8060i	0.599503	+	0.800372i
$257$	3.23679			0.201905			0.100953	−	0.994891i	$-0.467811\pi$
$257$	3.23679			0.201905			0.100953	+	0.994891i	$0.467811\pi$
$258$	3.82742	−	32.8499i	0.238285	−	2.04515i
$259$		0			0
$260$	11.9571	+	2.82464i	0.741547	+	0.175177i
$261$	−22.3324	−	22.3324i	−1.38234	−	1.38234i
$262$	−8.46350	−	10.6958i	−0.522877	−	0.660788i
$263$			24.0161i			1.48090i	0.672114	+	0.740448i	$0.265386\pi$
$263$			24.0161i			1.48090i	−0.672114	+	0.740448i	$0.734614\pi$
$264$	−3.64529	+	10.0497i	−0.224352	+	0.618514i
$265$			3.68624i			0.226444i
$266$		0			0
$267$	−17.3832	−	17.3832i	−1.06383	−	1.06383i
$268$	3.67289	−	2.26918i	0.224357	−	0.138612i
$269$	0.0875040	−	0.0875040i	0.00533521	−	0.00533521i	−0.704434	−	0.709769i	$-0.748799\pi$
$269$	0.0875040	−	0.0875040i	0.00533521	−	0.00533521i	0.709769	+	0.704434i	$0.248799\pi$
$270$	38.5193	+	4.48798i	2.34421	+	0.273130i
$271$	10.1138			0.614372			0.307186	−	0.951650i	$-0.400613\pi$
$271$	10.1138			0.614372			0.307186	+	0.951650i	$0.400613\pi$
$272$	5.39739	+	2.70079i	0.327265	+	0.163760i
$273$		0			0
$274$	−31.8227	−	3.70774i	−1.92248	−	0.223993i
$275$	−9.08608	+	9.08608i	−0.547911	+	0.547911i
$276$	14.5733	+	23.5882i	0.877208	+	1.41984i
$277$	−11.0080	−	11.0080i	−0.661406	−	0.661406i	0.294305	−	0.955711i	$-0.404912\pi$
$277$	−11.0080	−	11.0080i	−0.661406	−	0.661406i	−0.955711	+	0.294305i	$0.904912\pi$
$278$	10.4254	−	8.24957i	0.625277	−	0.494776i
$279$			22.3831i			1.34004i
$280$		0			0
$281$		−	4.21999i		−	0.251743i	−0.992047	−	0.125872i	$-0.959827\pi$
$281$		−	4.21999i		−	0.251743i	0.992047	−	0.125872i	$-0.0401727\pi$
$282$	9.17481	+	11.5947i	0.546352	+	0.690455i
$283$	16.5834	+	16.5834i	0.985781	+	0.985781i	0.999900	−	0.0141195i	$-0.00449452\pi$
$283$	16.5834	+	16.5834i	0.985781	+	0.985781i	−0.0141195	+	0.999900i	$0.504495\pi$
$284$	−6.35464	+	26.9000i	−0.377079	+	1.59622i
$285$	16.3980	−	16.3980i	0.971334	−	0.971334i
$286$	0.338971	−	2.90931i	0.0200438	−	0.172031i
$287$		0			0
$288$	−25.7701	−	16.8818i	−1.51852	−	0.994770i
$289$	−14.7234			−0.866080
$290$	−3.66131	+	31.4242i	−0.215000	+	1.84529i
$291$	−33.3377	+	33.3377i	−1.95429	+	1.95429i
$292$	−6.65566	+	28.1743i	−0.389493	+	1.64878i
$293$	13.5242	+	13.5242i	0.790093	+	0.790093i	0.981509	−	0.191416i	$-0.0613079\pi$
$293$	13.5242	+	13.5242i	0.790093	+	0.790093i	−0.191416	+	0.981509i	$0.561308\pi$
$294$		0			0
$295$			6.21049i			0.361589i
$296$	5.99547	−	2.80375i	0.348480	−	0.162965i
$297$		−	9.24501i		−	0.536450i
$298$	12.1868	−	9.64330i	0.705961	−	0.558621i
$299$	−5.37171	−	5.37171i	−0.310654	−	0.310654i
$300$	−30.1843	−	48.8561i	−1.74269	−	2.82071i
$301$		0			0
$302$	7.68137	+	0.894976i	0.442013	+	0.0515001i
$303$	47.5380			2.73099
$304$	−7.85056	+	2.61415i	−0.450260	+	0.149932i
$305$	−17.5597			−1.00546
$306$	−11.5428	−	1.34488i	−0.659860	−	0.0768820i
$307$	8.93389	−	8.93389i	0.509884	−	0.509884i	−0.404607	−	0.914491i	$-0.632592\pi$
$307$	8.93389	−	8.93389i	0.509884	−	0.509884i	0.914491	+	0.404607i	$0.132592\pi$
$308$		0			0
$309$	35.3203	+	35.3203i	2.00930	+	2.00930i
$310$	17.5826	−	13.9130i	0.998623	−	0.790203i
$311$		−	19.7737i		−	1.12126i	−0.828066	−	0.560631i	$-0.810558\pi$
$311$		−	19.7737i		−	1.12126i	0.828066	−	0.560631i	$-0.189442\pi$
$312$	12.3058	+	4.46368i	0.696682	+	0.252706i
$313$		−	8.72743i		−	0.493303i	−0.969104	−	0.246652i	$-0.920670\pi$
$313$		−	8.72743i		−	0.493303i	0.969104	−	0.246652i	$-0.0793304\pi$
$314$	−6.97122	−	8.80992i	−0.393409	−	0.497173i
$315$		0			0
$316$	3.46389	+	0.818280i	0.194859	+	0.0460319i
$317$	19.0197	−	19.0197i	1.06825	−	1.06825i	0.0707615	−	0.997493i	$-0.477457\pi$
$317$	19.0197	−	19.0197i	1.06825	−	1.06825i	0.997493	−	0.0707615i	$-0.0225429\pi$
$318$	−0.454531	+	3.90114i	−0.0254888	+	0.218765i
$319$	7.54211			0.422277
$320$	2.75710	+	30.7366i	0.154126	+	1.71823i
$321$	16.8569			0.940858
$322$		0			0
$323$	−2.20702	+	2.20702i	−0.122802	+	0.122802i
$324$	8.41065	+	1.98686i	0.467258	+	0.110381i
$325$	11.1259	+	11.1259i	0.617156	+	0.617156i
$326$	7.84039	+	9.90834i	0.434239	+	0.548772i
$327$			13.4541i			0.744013i
$328$	−19.8231	−	7.19038i	−1.09455	−	0.397022i
$329$		0			0
$330$	−16.1692	+	12.7946i	−0.890086	+	0.704318i
$331$	22.3328	+	22.3328i	1.22752	+	1.22752i	0.964899	+	0.262620i	$0.0845866\pi$
$331$	22.3328	+	22.3328i	1.22752	+	1.22752i	0.262620	+	0.964899i	$0.415413\pi$
$332$	−17.2318	+	10.6462i	−0.945720	+	0.584284i
$333$	−9.01134	+	9.01134i	−0.493818	+	0.493818i
$334$	16.6001	+	1.93412i	0.908318	+	0.105830i
$335$	8.32703			0.454954
$336$		0			0
$337$	−23.4825			−1.27918			−0.639588	−	0.768718i	$-0.720895\pi$
$337$	−23.4825			−1.27918			−0.639588	+	0.768718i	$0.720895\pi$
$338$	14.6988	+	1.71259i	0.799508	+	0.0931527i
$339$	−18.8483	+	18.8483i	−1.02370	+	1.02370i
$340$	6.11839	+	9.90320i	0.331816	+	0.537076i
$341$	−3.77961	−	3.77961i	−0.204678	−	0.204678i
$342$	12.4936	−	9.88612i	0.675579	−	0.534580i
$343$		0			0
$344$	−20.6167	+	9.64129i	−1.11158	+	0.519824i
$345$			53.4784i			2.87918i
$346$	6.99774	+	8.84343i	0.376201	+	0.475426i
$347$	−6.29716	−	6.29716i	−0.338049	−	0.338049i	0.517584	−	0.855633i	$-0.326832\pi$
$347$	−6.29716	−	6.29716i	−0.338049	−	0.338049i	−0.855633	+	0.517584i	$0.826832\pi$
$348$	−7.74950	+	32.8047i	−0.415417	+	1.75851i
$349$	−6.94033	+	6.94033i	−0.371507	+	0.371507i	−0.868026	−	0.496519i	$-0.834611\pi$
$349$	−6.94033	+	6.94033i	−0.371507	+	0.371507i	0.496519	+	0.868026i	$0.334611\pi$
$350$		0			0
$351$	−11.3206			−0.604246
$352$	7.20220	−	1.50088i	0.383879	−	0.0799969i
$353$	−30.0934			−1.60171			−0.800856	−	0.598857i	$-0.795622\pi$
$353$	−30.0934			−1.60171			−0.800856	+	0.598857i	$0.795622\pi$
$354$	−0.765783	+	6.57254i	−0.0407009	+	0.349327i
$355$	−37.6969	+	37.6969i	−2.00074	+	2.00074i
$356$	−3.88951	+	16.4648i	−0.206144	+	0.872633i
$357$		0			0
$358$	−14.5547	−	18.3936i	−0.769239	−	0.972131i
$359$			10.3716i			0.547394i	0.961816	+	0.273697i	$0.0882465\pi$
$359$			10.3716i			0.547394i	−0.961816	+	0.273697i	$0.911754\pi$
$360$	−25.1709	−	53.8249i	−1.32662	−	2.83682i
$361$			14.7209i			0.774786i
$362$	6.56482	−	5.19469i	0.345039	−	0.273027i
$363$	−19.1292	−	19.1292i	−1.00402	−	1.00402i
$364$		0			0
$365$	−39.4826	+	39.4826i	−2.06661	+	2.06661i
$366$	−18.5833	−	2.16519i	−0.971366	−	0.113176i
$367$	8.12973			0.424368			0.212184	−	0.977230i	$-0.431942\pi$
$367$	8.12973			0.424368			0.212184	+	0.977230i	$0.431942\pi$
$368$	8.53868	−	17.0641i	0.445109	−	0.889529i
$369$	40.6019			2.11365
$370$	12.6800	+	1.47737i	0.659200	+	0.0768050i
$371$		0			0
$372$	20.3231	−	12.5560i	1.05370	−	0.650999i
$373$	−3.18688	−	3.18688i	−0.165010	−	0.165010i	0.619772	−	0.784782i	$-0.287225\pi$
$373$	−3.18688	−	3.18688i	−0.165010	−	0.165010i	−0.784782	+	0.619772i	$0.787225\pi$
$374$	2.17622	−	1.72203i	0.112530	−	0.0890440i
$375$		−	54.7115i		−	2.82529i
$376$	3.46963	−	9.56539i	0.178933	−	0.493297i
$377$		−	9.23534i		−	0.475644i
$378$		0			0
$379$	−0.839080	−	0.839080i	−0.0431006	−	0.0431006i	0.685228	−	0.728329i	$-0.259703\pi$
$379$	−0.839080	−	0.839080i	−0.0431006	−	0.0431006i	−0.728329	+	0.685228i	$0.759703\pi$
$380$	−15.5317	−	3.66907i	−0.796758	−	0.188219i
$381$	−26.6711	+	26.6711i	−1.36640	+	1.36640i
$382$	2.02417	−	17.3730i	0.103565	−	0.888878i
$383$	34.3749			1.75647			0.878237	−	0.478225i	$-0.158720\pi$
$383$	34.3749			1.75647			0.878237	+	0.478225i	$0.158720\pi$
$384$	−0.872140	+	32.8684i	−0.0445062	+	1.67731i
$385$		0			0
$386$	3.87623	−	33.2688i	0.197295	−	1.69334i
$387$	30.9874	−	30.9874i	1.57518	−	1.57518i
$388$	31.5764	+	7.45934i	1.60305	+	0.378691i
$389$	10.9633	+	10.9633i	0.555860	+	0.555860i	0.928126	−	0.372266i	$-0.121419\pi$
$389$	10.9633	+	10.9633i	0.555860	+	0.555860i	−0.372266	+	0.928126i	$0.621419\pi$
$390$	15.6670	+	19.7993i	0.793329	+	1.00257i
$391$		−	7.19768i		−	0.364003i
$392$		0			0
$393$		−	28.0287i		−	1.41386i
$394$	−17.9101	+	14.1721i	−0.902298	+	0.713981i
$395$	4.85419	+	4.85419i	0.244241	+	0.244241i
$396$	−12.0510	+	7.44535i	−0.605586	+	0.374143i
$397$	−26.4375	+	26.4375i	−1.32686	+	1.32686i	−0.418764	+	0.908095i	$0.637537\pi$
$397$	−26.4375	+	26.4375i	−1.32686	+	1.32686i	−0.908095	+	0.418764i	$0.862463\pi$
$398$	−7.72146	−	0.899646i	−0.387042	−	0.0450952i
$399$		0			0
$400$	−17.6854	+	35.3433i	−0.884269	+	1.76717i
$401$	4.97625			0.248502			0.124251	−	0.992251i	$-0.460347\pi$
$401$	4.97625			0.248502			0.124251	+	0.992251i	$0.460347\pi$
$402$	8.81247	+	1.02676i	0.439526	+	0.0512102i
$403$	−4.62815	+	4.62815i	−0.230545	+	0.230545i
$404$	−17.1949	−	27.8316i	−0.855478	−	1.38467i
$405$	11.7864	+	11.7864i	0.585672	+	0.585672i
$406$		0			0
$407$		−	3.04331i		−	0.150851i
$408$	5.25396	+	11.2349i	0.260110	+	0.556212i
$409$		−	4.06359i		−	0.200932i	−0.994941	−	0.100466i	$-0.967967\pi$
$409$		−	4.06359i		−	0.200932i	0.994941	−	0.100466i	$-0.0320333\pi$
$410$	−25.2374	−	31.8939i	−1.24639	−	1.57513i
$411$	−46.5544	−	46.5544i	−2.29636	−	2.29636i
$412$	7.90295	−	33.4542i	0.389350	−	1.64817i
$413$		0			0
$414$	−4.25192	+	36.4932i	−0.208970	+	1.79354i
$415$	−39.0674			−1.91774
$416$	−1.83783	−	8.81913i	−0.0901069	−	0.432393i
$417$	27.3203			1.33788
$418$	−0.440306	+	3.77905i	−0.0215361	+	0.184839i
$419$	−0.552238	+	0.552238i	−0.0269786	+	0.0269786i	−0.720467	−	0.693489i	$-0.756073\pi$
$419$	−0.552238	+	0.552238i	−0.0269786	+	0.0269786i	0.693489	+	0.720467i	$0.256073\pi$
$420$		0			0
$421$	−3.77763	−	3.77763i	−0.184110	−	0.184110i	0.609034	−	0.793144i	$-0.291557\pi$
$421$	−3.77763	−	3.77763i	−0.184110	−	0.184110i	−0.793144	+	0.609034i	$0.791557\pi$
$422$	−1.12671	−	1.42389i	−0.0548475	−	0.0693139i
$423$			19.5920i			0.952593i
$424$	2.44836	−	1.14496i	0.118903	−	0.0556044i
$425$			14.9079i			0.723140i
$426$	−44.5427	+	35.2463i	−2.15810	+	1.70769i
$427$		0			0
$428$	−6.09727	−	9.86901i	−0.294723	−	0.477037i
$429$	4.25612	−	4.25612i	0.205487	−	0.205487i
$430$	−43.6028	−	5.08027i	−2.10271	−	0.244992i
$431$	1.18186			0.0569283			0.0284641	−	0.999595i	$-0.490938\pi$
$431$	1.18186			0.0569283			0.0284641	+	0.999595i	$0.490938\pi$
$432$	−8.98342	−	26.9781i	−0.432215	−	1.29799i
$433$	15.2584			0.733273			0.366637	−	0.930364i	$-0.380509\pi$
$433$	15.2584			0.733273			0.366637	+	0.930364i	$0.380509\pi$
$434$		0			0
$435$	−45.9715	+	45.9715i	−2.20416	+	2.20416i
$436$	7.87683	−	4.86646i	0.377232	−	0.233061i
$437$	6.97759	+	6.97759i	0.333783	+	0.333783i
$438$	−46.6527	+	36.9159i	−2.22915	+	1.76391i
$439$		−	4.34502i		−	0.207376i	−0.994610	−	0.103688i	$-0.966936\pi$
$439$		−	4.34502i		−	0.207376i	0.994610	−	0.103688i	$-0.0330644\pi$
$440$	13.3392	+	4.83851i	0.635923	+	0.230667i
$441$		0			0
$442$	−2.10863	−	2.66479i	−0.100297	−	0.126751i
$443$	−4.31392	−	4.31392i	−0.204961	−	0.204961i	0.597161	−	0.802121i	$-0.296295\pi$
$443$	−4.31392	−	4.31392i	−0.204961	−	0.204961i	−0.802121	+	0.597161i	$0.796295\pi$
$444$	13.2370	+	3.12700i	0.628200	+	0.148401i
$445$	−23.0733	+	23.0733i	−1.09378	+	1.09378i
$446$	0.524253	−	4.49954i	0.0248241	−	0.213060i
$447$	31.9359			1.51052
$448$		0			0
$449$	3.72499			0.175793			0.0878967	−	0.996130i	$-0.471985\pi$
$449$	3.72499			0.175793			0.0878967	+	0.996130i	$0.471985\pi$
$450$	8.80661	−	75.5851i	0.415147	−	3.56312i
$451$	−6.85604	+	6.85604i	−0.322838	+	0.322838i
$452$	17.8525	+	4.21732i	0.839710	+	0.198366i
$453$	11.2373	+	11.2373i	0.527976	+	0.527976i
$454$	−17.1178	−	21.6328i	−0.803380	−	1.01528i
$455$		0			0
$456$	−15.9847	−	5.79809i	−0.748552	−	0.271521i
$457$			10.7451i			0.502636i	0.967905	+	0.251318i	$0.0808640\pi$
$457$			10.7451i			0.502636i	−0.967905	+	0.251318i	$0.919136\pi$
$458$	−11.0128	+	8.71433i	−0.514594	+	0.407194i
$459$	−7.58434	−	7.58434i	−0.354007	−	0.354007i
$460$	31.3094	−	19.3436i	1.45981	−	0.901899i
$461$	−7.88785	+	7.88785i	−0.367374	+	0.367374i	−0.866519	−	0.499145i	$-0.833648\pi$
$461$	−7.88785	+	7.88785i	−0.367374	+	0.367374i	0.499145	+	0.866519i	$0.333648\pi$
$462$		0			0
$463$	27.3485			1.27099			0.635496	−	0.772104i	$-0.280796\pi$
$463$	27.3485			1.27099			0.635496	+	0.772104i	$0.280796\pi$
$464$	22.0089	−	7.32870i	1.02174	−	0.340226i
$465$	46.0758			2.13671
$466$	4.12784	+	0.480945i	0.191219	+	0.0222794i
$467$	−11.3915	+	11.3915i	−0.527135	+	0.527135i	−0.919717	−	0.392582i	$-0.871582\pi$
$467$	−11.3915	+	11.3915i	−0.527135	+	0.527135i	0.392582	+	0.919717i	$0.371582\pi$
$468$	9.11686	+	14.7565i	0.421427	+	0.682120i
$469$		0			0
$470$	15.3900	−	12.1780i	0.709890	−	0.561730i
$471$		−	23.0867i		−	1.06378i
$472$	4.12495	−	1.92901i	0.189866	−	0.0887898i
$473$			10.4651i			0.481185i
$474$	4.53862	+	5.73571i	0.208466	+	0.263450i
$475$	−14.4520	−	14.4520i	−0.663105	−	0.663105i
$476$		0			0
$477$	−3.67995	+	3.67995i	−0.168493	+	0.168493i
$478$	2.65317	−	22.7716i	0.121353	−	1.04155i
$479$	−11.3880			−0.520330			−0.260165	−	0.965564i	$-0.583777\pi$
$479$	−11.3880			−0.520330			−0.260165	+	0.965564i	$0.583777\pi$
$480$	−34.7513	+	53.0479i	−1.58617	+	2.42130i
$481$	−3.72655			−0.169916
$482$	2.31041	−	19.8297i	0.105236	−	0.903219i
$483$		0			0
$484$	−4.28017	+	18.1185i	−0.194553	+	0.823570i
$485$	44.2502	+	44.2502i	2.00930	+	2.00930i
$486$	−7.69435	−	9.72378i	−0.349023	−	0.441080i
$487$		−	31.3531i		−	1.42075i	−0.703826	−	0.710373i	$-0.748526\pi$
$487$		−	31.3531i		−	1.42075i	0.703826	−	0.710373i	$-0.251474\pi$
$488$	5.45412	+	11.6630i	0.246896	+	0.527957i
$489$			25.9652i			1.17419i
$490$		0			0
$491$	20.2775	+	20.2775i	0.915112	+	0.915112i	0.996669	−	0.0815572i	$-0.0259893\pi$
$491$	20.2775	+	20.2775i	0.915112	+	0.915112i	−0.0815572	+	0.996669i	$0.525989\pi$
$492$	−22.7760	−	36.8651i	−1.02682	−	1.66201i
$493$	6.18733	−	6.18733i	0.278663	−	0.278663i
$494$	4.62746	+	0.539157i	0.208199	+	0.0242578i
$495$	−27.3216			−1.22802
$496$	−14.7021	−	7.35674i	−0.660143	−	0.330327i
$497$		0			0
$498$	−41.3449	−	4.81719i	−1.85271	−	0.215864i
$499$	−18.5167	+	18.5167i	−0.828921	+	0.828921i	−0.987368	−	0.158446i	$-0.949351\pi$
$499$	−18.5167	+	18.5167i	−0.828921	+	0.828921i	0.158446	+	0.987368i	$0.449351\pi$
$500$	−32.0313	+	19.7896i	−1.43249	+	0.885017i
$501$	24.2848	+	24.2848i	1.08497	+	1.08497i
$502$	22.2659	−	17.6188i	0.993774	−	0.786366i
$503$			31.9854i			1.42616i	0.701082	+	0.713080i	$0.252701\pi$
$503$			31.9854i			1.42616i	−0.701082	+	0.713080i	$0.747299\pi$
$504$		0			0
$505$		−	63.0987i		−	2.80786i
$506$	−5.44427	−	6.88023i	−0.242028	−	0.305864i
$507$	21.5033	+	21.5033i	0.954996	+	0.954996i
$508$	25.2620	+	5.96769i	1.12082	+	0.264774i
$509$	−12.1644	+	12.1644i	−0.539176	+	0.539176i	−0.923287	−	0.384111i	$-0.874508\pi$
$509$	−12.1644	+	12.1644i	−0.539176	+	0.539176i	0.384111	+	0.923287i	$0.374508\pi$
$510$	−2.76846	+	23.7610i	−0.122589	+	1.05216i
$511$		0			0
$512$	19.5586	−	11.3782i	0.864375	−	0.502849i
$513$	14.7048			0.649234
$514$	0.529753	−	4.54675i	0.0233664	−	0.200549i
$515$	46.8817	−	46.8817i	2.06586	−	2.06586i
$516$	−45.5182	−	10.7529i	−2.00383	−	0.473368i
$517$	−3.30830	−	3.30830i	−0.145499	−	0.145499i
$518$		0			0
$519$			23.1745i			1.01725i
$520$	5.92478	−	16.3340i	0.259819	−	0.716291i
$521$			34.4322i			1.50850i	0.656586	+	0.754251i	$0.272000\pi$
$521$			34.4322i			1.50850i	−0.656586	+	0.754251i	$0.728000\pi$
$522$	−35.0257	+	27.7155i	−1.53303	+	1.21308i
$523$	15.4031	+	15.4031i	0.673530	+	0.673530i	0.958528	−	0.284998i	$-0.0919929\pi$
$523$	15.4031	+	15.4031i	0.673530	+	0.673530i	−0.284998	+	0.958528i	$0.591993\pi$
$524$	−16.4097	+	10.1382i	−0.716861	+	0.442890i
$525$		0			0
$526$	33.7357	+	3.93062i	1.47094	+	0.171383i
$527$	−6.20137			−0.270136
$528$	13.5203	+	6.76537i	0.588394	+	0.294425i
$529$	0.244184			0.0106167
$530$	5.17810	+	0.603314i	0.224922	+	0.0262063i
$531$	−6.19990	+	6.19990i	−0.269053	+	0.269053i
$532$		0			0
$533$	8.39524	+	8.39524i	0.363638	+	0.363638i
$534$	−27.2634	+	21.5733i	−1.17980	+	0.933569i
$535$		−	22.3747i		−	0.967341i
$536$	−2.58642	−	5.53073i	−0.111716	−	0.238891i
$537$		−	48.2011i		−	2.08003i
$538$	−0.108596	−	0.137239i	−0.00468192	−	0.00591681i
$539$		0			0
$540$	12.6086	−	53.3740i	0.542589	−	2.29685i
$541$	−23.7164	+	23.7164i	−1.01965	+	1.01965i	−0.0198437	+	0.999803i	$0.506317\pi$
$541$	−23.7164	+	23.7164i	−1.01965	+	1.01965i	−0.999803	+	0.0198437i	$0.993683\pi$
$542$	1.65529	−	14.2070i	0.0711010	−	0.610244i
$543$	17.2034			0.738267
$544$	4.67720	−	7.13975i	0.200533	−	0.306114i
$545$	17.8581			0.764956
$546$		0			0
$547$	27.8819	−	27.8819i	1.19214	−	1.19214i	0.215680	−	0.976464i	$-0.430803\pi$
$547$	27.8819	−	27.8819i	1.19214	−	1.19214i	0.976464	−	0.215680i	$-0.0691967\pi$
$548$	−10.4166	+	44.0949i	−0.444975	+	1.88364i
$549$	−17.5297	−	17.5297i	−0.748150	−	0.748150i
$550$	11.2762	+	14.2504i	0.480820	+	0.607639i
$551$			11.9963i			0.511058i
$552$	35.5198	−	16.6106i	1.51182	−	0.706995i
$553$		0			0
$554$	−17.2647	+	13.6614i	−0.733506	+	0.580418i
$555$	18.5499	+	18.5499i	0.787400	+	0.787400i
$556$	−9.88197	−	15.9949i	−0.419089	−	0.678335i
$557$	0.275943	−	0.275943i	0.0116921	−	0.0116921i	−0.701237	−	0.712929i	$-0.747368\pi$
$557$	0.275943	−	0.275943i	0.0116921	−	0.0116921i	0.712929	+	0.701237i	$0.247368\pi$
$558$	31.4418	+	3.66336i	1.33104	+	0.155082i
$559$	12.8145			0.541997
$560$		0			0
$561$	5.70288			0.240776
$562$	−5.92786	−	0.690669i	−0.250052	−	0.0291341i
$563$	13.8911	−	13.8911i	0.585438	−	0.585438i	−0.350954	−	0.936393i	$-0.614143\pi$
$563$	13.8911	−	13.8911i	0.585438	−	0.585438i	0.936393	+	0.350954i	$0.114143\pi$
$564$	17.7888	−	10.9903i	0.749045	−	0.462775i
$565$	25.0179	+	25.0179i	1.05251	+	1.05251i
$566$	26.0090	−	20.5807i	1.09324	−	0.865073i
$567$		0			0
$568$	36.7467	+	13.3291i	1.54186	+	0.559275i
$569$		−	8.08076i		−	0.338763i	−0.985551	−	0.169381i	$-0.945823\pi$
$569$		−	8.08076i		−	0.338763i	0.985551	−	0.169381i	$-0.0541770\pi$
$570$	−20.3507	−	25.7183i	−0.852395	−	1.07722i
$571$	−7.55816	−	7.55816i	−0.316299	−	0.316299i	0.531045	−	0.847344i	$-0.321800\pi$
$571$	−7.55816	−	7.55816i	−0.316299	−	0.316299i	−0.847344	+	0.531045i	$0.821800\pi$
$572$	−4.03126	−	0.952312i	−0.168556	−	0.0398182i
$573$	25.4154	−	25.4154i	1.06175	−	1.06175i
$574$		0			0
$575$	47.1320			1.96554
$576$	−27.9317	+	33.4365i	−1.16382	+	1.39319i
$577$	−1.95969			−0.0815831			−0.0407915	−	0.999168i	$-0.512988\pi$
$577$	−1.95969			−0.0815831			−0.0407915	+	0.999168i	$0.512988\pi$
$578$	−2.40972	+	20.6821i	−0.100231	+	0.860261i
$579$	48.6699	−	48.6699i	2.02265	−	2.02265i
$580$	43.5427	+	10.2862i	1.80801	+	0.427110i
$581$		0			0
$582$	41.3735	+	52.2860i	1.71499	+	2.16733i
$583$		−	1.24279i		−	0.0514713i
$584$	38.4874	+	13.9605i	1.59262	+	0.577688i
$585$			33.4554i			1.38321i
$586$	21.2111	−	16.7842i	0.876221	−	0.693347i
$587$	−24.6131	−	24.6131i	−1.01589	−	1.01589i	−0.999872	−	0.0160192i	$-0.994901\pi$
$587$	−24.6131	−	24.6131i	−1.01589	−	1.01589i	−0.0160192	−	0.999872i	$-0.505099\pi$
$588$		0			0
$589$	6.01174	−	6.01174i	0.247709	−	0.247709i
$590$	8.72395	+	1.01645i	0.359159	+	0.0418465i
$591$	−46.9341			−1.93061
$592$	−2.95720	−	8.88078i	−0.121540	−	0.364998i
$593$	−16.5483			−0.679558			−0.339779	−	0.940505i	$-0.610352\pi$
$593$	−16.5483			−0.679558			−0.339779	+	0.940505i	$0.610352\pi$
$594$	−12.9866	−	1.51310i	−0.532845	−	0.0620831i
$595$		0			0
$596$	−11.5515	−	18.6972i	−0.473167	−	0.765866i
$597$	−11.2960	−	11.2960i	−0.462313	−	0.462313i
$598$	−8.42487	+	6.66654i	−0.344519	+	0.272615i
$599$			10.2649i			0.419412i	0.977764	+	0.209706i	$0.0672507\pi$
$599$			10.2649i			0.419412i	−0.977764	+	0.209706i	$0.932749\pi$
$600$	−73.5689	+	34.4041i	−3.00344	+	1.40454i
$601$		−	35.6586i		−	1.45455i	−0.686348	−	0.727273i	$-0.740787\pi$
$601$		−	35.6586i		−	1.45455i	0.686348	−	0.727273i	$-0.259213\pi$
$602$		0			0
$603$	8.31283	+	8.31283i	0.338524	+	0.338524i
$604$	2.51436	−	10.6436i	0.102308	−	0.433083i
$605$	−25.3908	+	25.3908i	−1.03228	+	1.03228i
$606$	7.78037	−	66.7772i	0.316056	−	2.71264i
$607$	−23.1111			−0.938052			−0.469026	−	0.883184i	$-0.655395\pi$
$607$	−23.1111			−0.938052			−0.469026	+	0.883184i	$0.655395\pi$
$608$	2.38725	+	11.4556i	0.0968157	+	0.464586i
$609$		0			0
$610$	−2.87393	+	24.6663i	−0.116362	+	0.998708i
$611$	−4.05103	+	4.05103i	−0.163887	+	0.163887i
$612$	−3.77835	+	15.9942i	−0.152731	+	0.646529i
$613$	−26.9200	−	26.9200i	−1.08729	−	1.08729i	−0.995807	−	0.0914813i	$-0.970840\pi$
$613$	−26.9200	−	26.9200i	−1.08729	−	1.08729i	−0.0914813	−	0.995807i	$-0.529160\pi$
$614$	−11.0874	−	14.0117i	−0.447449	−	0.565467i
$615$		−	83.5793i		−	3.37024i
$616$		0			0
$617$			47.9337i			1.92974i	0.262732	+	0.964869i	$0.415377\pi$
$617$			47.9337i			1.92974i	−0.262732	+	0.964869i	$0.584623\pi$
$618$	55.3955	−	43.8340i	2.22833	−	1.76326i
$619$	−4.05053	−	4.05053i	−0.162805	−	0.162805i	0.621003	−	0.783808i	$-0.286725\pi$
$619$	−4.05053	−	4.05053i	−0.162805	−	0.162805i	−0.783808	+	0.621003i	$0.786725\pi$
$620$	−16.6660	−	26.9755i	−0.669323	−	1.08336i
$621$	−23.9782	+	23.9782i	−0.962213	+	0.962213i
$622$	−27.7763	−	3.23629i	−1.11373	−	0.129763i
$623$		0			0
$624$	8.28423	−	16.5556i	0.331634	−	0.662755i
$625$	−23.2188			−0.928752
$626$	−12.2595	−	1.42839i	−0.489989	−	0.0570898i
$627$	−5.52849	+	5.52849i	−0.220787	+	0.220787i
$628$	−13.5164	+	8.35067i	−0.539361	+	0.333228i
$629$	−2.49664	−	2.49664i	−0.0995477	−	0.0995477i
$630$		0			0
$631$			2.35784i			0.0938640i	0.998898	+	0.0469320i	$0.0149444\pi$
$631$			2.35784i			0.0938640i	−0.998898	+	0.0469320i	$0.985056\pi$
$632$	1.71637	−	4.73184i	0.0682735	−	0.188222i
$633$		−	3.73136i		−	0.148308i
$634$	−23.6043	−	29.8301i	−0.937448	−	1.18471i
$635$	35.4014	+	35.4014i	1.40486	+	1.40486i
$636$	5.40558	+	1.27697i	0.214345	+	0.0506351i
$637$		0			0
$638$	1.23439	−	10.5945i	0.0488699	−	0.419440i
$639$	−75.2652			−2.97744
$640$	43.6273	+	1.15762i	1.72452	+	0.0457590i
$641$	−49.8415			−1.96862			−0.984311	−	0.176440i	$-0.943542\pi$
$641$	−49.8415			−1.96862			−0.984311	+	0.176440i	$0.943542\pi$
$642$	2.75890	−	23.6790i	0.108885	−	0.934536i
$643$	6.07975	−	6.07975i	0.239762	−	0.239762i	−0.576990	−	0.816751i	$-0.695773\pi$
$643$	6.07975	−	6.07975i	0.239762	−	0.239762i	0.816751	+	0.576990i	$0.195773\pi$
$644$		0			0
$645$	−63.7879	−	63.7879i	−2.51165	−	2.51165i
$646$	2.73901	+	3.46144i	0.107765	+	0.136188i
$647$			0.463264i			0.0182128i	0.999959	+	0.00910640i	$0.00289870\pi$
$647$			0.463264i			0.0182128i	−0.999959	+	0.00910640i	$0.997101\pi$
$648$	4.16751	−	11.4894i	0.163715	−	0.451344i
$649$		−	2.09383i		−	0.0821901i
$650$	17.4497	−	13.8078i	0.684432	−	0.541586i
$651$		0			0
$652$	15.2016	−	9.39183i	0.595339	−	0.367812i
$653$	6.63668	−	6.63668i	0.259713	−	0.259713i	−0.565224	−	0.824937i	$-0.691210\pi$
$653$	6.63668	−	6.63668i	0.259713	−	0.259713i	0.824937	+	0.565224i	$0.191210\pi$
$654$	18.8991	+	2.20198i	0.739014	+	0.0861044i
$655$	−37.2034			−1.45366
$656$	−13.3448	+	26.6689i	−0.521026	+	1.04124i
$657$	−78.8305			−3.07547
$658$		0			0
$659$	−4.62922	+	4.62922i	−0.180329	+	0.180329i	−0.791499	−	0.611170i	$-0.790699\pi$
$659$	−4.62922	+	4.62922i	−0.180329	+	0.180329i	0.611170	+	0.791499i	$0.290699\pi$
$660$	15.3263	+	24.8071i	0.596576	+	0.965615i
$661$	2.25711	+	2.25711i	0.0877916	+	0.0877916i	0.749639	−	0.661847i	$-0.230227\pi$
$661$	2.25711	+	2.25711i	0.0877916	+	0.0877916i	−0.661847	+	0.749639i	$0.730227\pi$
$662$	35.0262	−	27.7160i	1.36133	−	1.07721i
$663$		−	6.98320i		−	0.271205i
$664$	12.1345	+	25.9482i	0.470911	+	1.00698i
$665$		0			0
$666$	11.1835	+	14.1332i	0.433351	+	0.547650i
$667$	−19.5615	−	19.5615i	−0.757425	−	0.757425i
$668$	5.43376	−	23.0018i	0.210239	−	0.889968i
$669$	6.58253	−	6.58253i	0.254495	−	0.254495i
$670$	1.36286	−	11.6971i	0.0526517	−	0.451898i
$671$	5.92014			0.228544
$672$		0			0
$673$	6.82222			0.262977			0.131489	−	0.991318i	$-0.458024\pi$
$673$	6.82222			0.262977			0.131489	+	0.991318i	$0.458024\pi$
$674$	−3.84330	+	32.9862i	−0.148038	+	1.27058i
$675$	49.6639	−	49.6639i	1.91157	−	1.91157i
$676$	4.81139	−	20.3673i	0.185054	−	0.783356i
$677$	−4.77844	−	4.77844i	−0.183650	−	0.183650i	0.609294	−	0.792944i	$-0.291453\pi$
$677$	−4.77844	−	4.77844i	−0.183650	−	0.183650i	−0.792944	+	0.609294i	$0.791453\pi$
$678$	23.3916	+	29.5612i	0.898347	+	1.13529i
$679$		0			0
$680$	14.9125	−	6.97375i	0.571868	−	0.267431i
$681$		−	56.6895i		−	2.17235i
$682$	−5.92786	+	4.69067i	−0.226990	+	0.179615i
$683$	−29.2736	−	29.2736i	−1.12012	−	1.12012i	−0.991723	−	0.128400i	$-0.959016\pi$
$683$	−29.2736	−	29.2736i	−1.12012	−	1.12012i	−0.128400	−	0.991723i	$-0.540984\pi$
$684$	−11.8424	−	19.1680i	−0.452804	−	0.732906i
$685$	−61.7932	+	61.7932i	−2.36100	+	2.36100i
$686$		0			0
$687$	−28.8594			−1.10106
$688$	10.1690	+	30.5385i	0.387688	+	1.16427i
$689$	−1.52181			−0.0579762
$690$	75.1216	+	8.75261i	2.85983	+	0.333206i
$691$	4.65064	−	4.65064i	0.176919	−	0.176919i	−0.613092	−	0.790011i	$-0.710075\pi$
$691$	4.65064	−	4.65064i	0.176919	−	0.176919i	0.790011	+	0.613092i	$0.210075\pi$
$692$	13.5678	−	8.38243i	0.515769	−	0.318652i
$693$		0			0
$694$	−9.87632	+	7.81505i	−0.374900	+	0.296655i
$695$		−	36.2631i		−	1.37554i
$696$	44.8127	+	16.2548i	1.69862	+	0.616138i
$697$			11.2490i			0.426086i
$698$	8.61326	+	10.8851i	0.326017	+	0.412005i
$699$	6.03875	+	6.03875i	0.228407	+	0.228407i
$700$		0			0
$701$	−4.01206	+	4.01206i	−0.151533	+	0.151533i	−0.778802	−	0.627269i	$-0.784173\pi$
$701$	−4.01206	+	4.01206i	−0.151533	+	0.151533i	0.627269	+	0.778802i	$0.284173\pi$
$702$	−1.85279	+	15.9021i	−0.0699292	+	0.600186i
$703$	4.84060			0.182567
$704$	−0.929538	−	10.3627i	−0.0350333	−	0.390557i
$705$	40.3302			1.51892
$706$	−4.92528	+	42.2726i	−0.185365	+	1.59095i
$707$		0			0
$708$	9.10719	+	2.15141i	0.342269	+	0.0808549i
$709$	36.0117	+	36.0117i	1.35245	+	1.35245i	0.882915	+	0.469533i	$0.155578\pi$
$709$	36.0117	+	36.0117i	1.35245	+	1.35245i	0.469533	+	0.882915i	$0.344422\pi$
$710$	46.7835	+	59.1230i	1.75575	+	2.21885i
$711$			9.69181i			0.363471i
$712$	22.4917	+	8.15837i	0.842912	+	0.305748i
$713$			19.6059i			0.734248i
$714$		0			0
$715$	−5.64929	−	5.64929i	−0.211271	−	0.211271i
$716$	−28.2198	+	17.4347i	−1.05462	+	0.651566i
$717$	33.3133	−	33.3133i	1.24411	−	1.24411i
$718$	14.5691	+	1.69749i	0.543716	+	0.0633496i
$719$	−7.62249			−0.284271			−0.142135	−	0.989847i	$-0.545397\pi$
$719$	−7.62249			−0.284271			−0.142135	+	0.989847i	$0.545397\pi$
$720$	−79.7281	+	26.5485i	−2.97129	+	0.989406i
$721$		0			0
$722$	20.6787	+	2.40932i	0.769580	+	0.0896657i
$723$	29.0095	−	29.0095i	1.07888	−	1.07888i
$724$	−6.22260	−	10.0719i	−0.231261	−	0.374318i
$725$	40.5160	+	40.5160i	1.50473	+	1.50473i
$726$	−30.0018	+	23.7402i	−1.11347	+	0.881080i
$727$			25.4856i			0.945207i	0.881275	+	0.472604i	$0.156686\pi$
$727$			25.4856i			0.945207i	−0.881275	+	0.472604i	$0.843314\pi$
$728$		0			0
$729$		−	38.4448i		−	1.42388i
$730$	48.9997	+	61.9236i	1.81356	+	2.29190i
$731$	8.58525	+	8.58525i	0.317537	+	0.317537i
$732$	−6.08293	+	25.7498i	−0.224832	+	0.951742i
$733$	14.9748	−	14.9748i	0.553106	−	0.553106i	−0.374230	−	0.927336i	$-0.622093\pi$
$733$	14.9748	−	14.9748i	0.553106	−	0.553106i	0.927336	+	0.374230i	$0.122093\pi$
$734$	1.33056	−	11.4199i	0.0491120	−	0.421517i
$735$		0			0
$736$	−22.5727	−	14.7872i	−0.832039	−	0.545063i
$737$	−2.80741			−0.103412
$738$	6.64516	−	57.0339i	0.244612	−	2.09945i
$739$	−12.3417	+	12.3417i	−0.453996	+	0.453996i	−0.896679	−	0.442682i	$-0.854027\pi$
$739$	−12.3417	+	12.3417i	−0.453996	+	0.453996i	0.442682	+	0.896679i	$0.354027\pi$
$740$	4.15057	−	17.5699i	0.152578	−	0.645882i
$741$	6.76966	+	6.76966i	0.248690	+	0.248690i
$742$		0			0
$743$			10.6724i			0.391531i	0.980651	+	0.195766i	$0.0627192\pi$
$743$			10.6724i			0.391531i	−0.980651	+	0.195766i	$0.937281\pi$
$744$	−14.3114	−	30.6031i	−0.524680	−	1.12196i
$745$		−	42.3896i		−	1.55303i
$746$	−4.99823	+	3.95506i	−0.182998	+	0.144805i
$747$	−39.0007	−	39.0007i	−1.42696	−	1.42696i
$748$	−2.06278	−	3.33880i	−0.0754226	−	0.122079i
$749$		0			0
$750$	−76.8538	−	8.95442i	−2.80630	−	0.326969i
$751$	−2.82952			−0.103251			−0.0516254	−	0.998667i	$-0.516440\pi$
$751$	−2.82952			−0.103251			−0.0516254	+	0.998667i	$0.516440\pi$
$752$	−12.8687	−	6.43936i	−0.469275	−	0.234819i
$753$	58.3485			2.12634
$754$	−12.9730	−	1.51151i	−0.472448	−	0.0550461i
$755$	14.9157	−	14.9157i	0.542837	−	0.542837i
$756$		0			0
$757$	15.6590	+	15.6590i	0.569136	+	0.569136i	0.931886	−	0.362750i	$-0.118162\pi$
$757$	15.6590	+	15.6590i	0.569136	+	0.569136i	−0.362750	+	0.931886i	$0.618162\pi$
$758$	−1.31599	+	1.04134i	−0.0477990	+	0.0378230i
$759$		−	18.0299i		−	0.654444i
$760$	−7.69600	+	21.2170i	−0.279163	+	0.769622i
$761$		−	4.79367i		−	0.173770i	−0.996218	−	0.0868852i	$-0.972309\pi$
$761$		−	4.79367i		−	0.173770i	0.996218	−	0.0868852i	$-0.0276913\pi$
$762$	33.1001	+	41.8304i	1.19909	+	1.51535i
$763$		0			0
$764$	−24.0727	−	5.68674i	−0.870920	−	0.205739i
$765$	−22.4139	+	22.4139i	−0.810375	+	0.810375i
$766$	5.62601	−	48.2868i	0.203276	−	1.74467i
$767$	−2.56390			−0.0925772
$768$	46.0278	+	6.60455i	1.66089	+	0.238321i
$769$	−13.5489			−0.488585			−0.244293	−	0.969702i	$-0.578556\pi$
$769$	−13.5489			−0.488585			−0.244293	+	0.969702i	$0.578556\pi$
$770$		0			0
$771$	6.65159	−	6.65159i	0.239551	−	0.239551i
$772$	−46.0986	−	10.8900i	−1.65913	−	0.391938i
$773$	−18.7803	−	18.7803i	−0.675480	−	0.675480i	0.283494	−	0.958974i	$-0.408506\pi$
$773$	−18.7803	−	18.7803i	−0.675480	−	0.675480i	−0.958974	+	0.283494i	$0.908506\pi$
$774$	−38.4568	−	48.6000i	−1.38230	−	1.74689i
$775$		−	40.6080i		−	1.45868i
$776$	15.6462	−	43.1348i	0.561666	−	1.54845i
$777$		0			0
$778$	17.1945	−	13.6059i	0.616454	−	0.487795i
$779$	−10.9050	−	10.9050i	−0.390712	−	0.390712i
$780$	30.3764	−	18.7671i	1.08765	−	0.671971i
$781$	12.7093	−	12.7093i	0.454774	−	0.454774i
$782$	−10.1107	−	1.17802i	−0.361557	−	0.0421259i
$783$	−41.2247			−1.47325
$784$		0			0
$785$	−30.6438			−1.09372
$786$	−39.3723	−	4.58736i	−1.40436	−	0.163626i
$787$	−24.4838	+	24.4838i	−0.872752	+	0.872752i	−0.992772	−	0.120020i	$-0.961704\pi$
$787$	−24.4838	+	24.4838i	−0.872752	+	0.872752i	0.120020	+	0.992772i	$0.461704\pi$
$788$	16.9765	+	27.4780i	0.604761	+	0.978864i
$789$	49.3530	+	49.3530i	1.75701	+	1.75701i
$790$	7.61320	−	6.02426i	0.270865	−	0.214334i
$791$		0			0
$792$	8.48622	+	18.1467i	0.301545	+	0.644816i
$793$		−	7.24923i		−	0.257428i
$794$	32.8101	+	41.4640i	1.16439	+	1.47150i
$795$	7.57521	+	7.57521i	0.268665	+	0.268665i
$796$	−2.52748	+	10.6992i	−0.0895843	+	0.379222i
$797$	17.6690	−	17.6690i	0.625870	−	0.625870i	−0.321157	−	0.947026i	$-0.604072\pi$
$797$	17.6690	−	17.6690i	0.625870	−	0.625870i	0.947026	+	0.321157i	$0.104072\pi$
$798$		0			0
$799$	−5.42807			−0.192031
$800$	46.7527	+	30.6274i	1.65296	+	1.08284i
$801$	−46.0678			−1.62773
$802$	0.814444	−	6.99019i	0.0287590	−	0.246832i
$803$	13.3113	−	13.3113i	0.469746	−	0.469746i
$804$	2.88461	−	12.2109i	0.101732	−	0.430646i
$805$		0			0
$806$	5.74374	+	7.25869i	0.202315	+	0.255676i
$807$		−	0.359641i		−	0.0126600i
$808$	−41.9096	+	19.5988i	−1.47437	+	0.689482i
$809$		−	2.99378i		−	0.105256i	−0.998614	−	0.0526278i	$-0.983240\pi$
$809$		−	2.99378i		−	0.105256i	0.998614	−	0.0526278i	$-0.0167597\pi$
$810$	18.4856	−	14.6275i	0.649517	−	0.513958i
$811$	2.28628	+	2.28628i	0.0802820	+	0.0802820i	0.746108	−	0.665825i	$-0.231920\pi$
$811$	2.28628	+	2.28628i	0.0802820	+	0.0802820i	−0.665825	+	0.746108i	$0.731920\pi$
$812$		0			0
$813$	20.7839	−	20.7839i	0.728923	−	0.728923i
$814$	−4.27497	−	0.498088i	−0.149838	−	0.0174580i
$815$	34.4644			1.20724
$816$	16.6417	−	5.54151i	0.582577	−	0.193992i
$817$	−16.6454			−0.582351
$818$	−5.70817	−	0.665073i	−0.199582	−	0.0232537i
$819$		0			0
$820$	−48.9323	+	30.2313i	−1.70879	+	1.05572i
$821$	−28.6342	−	28.6342i	−0.999339	−	0.999339i	0.000660747	−	1.00000i	$-0.499790\pi$
$821$	−28.6342	−	28.6342i	−0.999339	−	0.999339i	−1.00000		0.000660747i	$0.999790\pi$
$822$	−73.0149	+	57.7761i	−2.54669	+	2.01517i
$823$			41.0492i			1.43088i	0.698672	+	0.715442i	$0.253775\pi$
$823$			41.0492i			1.43088i	−0.698672	+	0.715442i	$0.746225\pi$
$824$	−45.7001	−	16.5767i	−1.59204	−	0.577476i
$825$			37.3437i			1.30014i
$826$		0			0
$827$	−20.3987	−	20.3987i	−0.709331	−	0.709331i	0.257064	−	0.966394i	$-0.417245\pi$
$827$	−20.3987	−	20.3987i	−0.709331	−	0.709331i	−0.966394	+	0.257064i	$0.917245\pi$
$828$	50.5666	+	11.9454i	1.75731	+	0.415132i
$829$	18.4892	−	18.4892i	0.642155	−	0.642155i	−0.308930	−	0.951085i	$-0.599971\pi$
$829$	18.4892	−	18.4892i	0.642155	−	0.642155i	0.951085	+	0.308930i	$0.0999708\pi$
$830$	−6.39402	+	54.8784i	−0.221940	+	1.90486i
$831$	−45.2428			−1.56945
$832$	−12.6891	+	1.13822i	−0.439916	+	0.0394608i
$833$		0			0
$834$	4.47141	−	38.3771i	0.154832	−	1.32889i
$835$	32.2341	−	32.2341i	1.11551	−	1.11551i
$836$	5.23641	+	1.23701i	0.181105	+	0.0427828i
$837$	20.6591	+	20.6591i	0.714084	+	0.714084i
$838$	0.685352	+	0.866117i	0.0236751	+	0.0299195i
$839$			41.9862i			1.44953i	0.688999	+	0.724763i	$0.258051\pi$
$839$			41.9862i			1.44953i	−0.688999	+	0.724763i	$0.741949\pi$
$840$		0			0
$841$		−	4.63123i		−	0.159698i
$842$	−5.92474	+	4.68820i	−0.204180	+	0.161566i
$843$	−8.67205	−	8.67205i	−0.298681	−	0.298681i
$844$	−2.18456	+	1.34966i	−0.0751956	+	0.0464573i
$845$	28.5421	−	28.5421i	0.981876	−	0.981876i
$846$	27.5210	+	3.20654i	0.946193	+	0.110243i
$847$		0			0
$848$	−1.20763	−	3.62664i	−0.0414701	−	0.124539i
$849$	68.1577			2.33916
$850$	20.9413	+	2.43992i	0.718281	+	0.0836886i
$851$	−7.89326	+	7.89326i	−0.270577	+	0.270577i
$852$	42.2207	+	68.3382i	1.44646	+	2.34123i
$853$	−10.9845	−	10.9845i	−0.376104	−	0.376104i	0.493591	−	0.869694i	$-0.335684\pi$
$853$	−10.9845	−	10.9845i	−0.376104	−	0.376104i	−0.869694	+	0.493591i	$0.835684\pi$
$854$		0			0
$855$		−	43.4570i		−	1.48620i
$856$	−14.8610	+	6.94968i	−0.507939	+	0.237535i
$857$		−	47.3215i		−	1.61647i	−0.588858	−	0.808237i	$-0.700422\pi$
$857$		−	47.3215i		−	1.61647i	0.588858	−	0.808237i	$-0.299578\pi$
$858$	−5.28204	−	6.67520i	−0.180326	−	0.227888i
$859$	−5.11128	−	5.11128i	−0.174395	−	0.174395i	0.614512	−	0.788907i	$-0.289353\pi$
$859$	−5.11128	−	5.11128i	−0.174395	−	0.174395i	−0.788907	+	0.614512i	$0.789353\pi$
$860$	−14.2726	+	60.4178i	−0.486692	+	2.06023i
$861$		0			0
$862$	0.193431	−	1.66017i	0.00658828	−	0.0565458i
$863$	10.1105			0.344167			0.172084	−	0.985082i	$-0.444950\pi$
$863$	10.1105			0.344167			0.172084	+	0.985082i	$0.444950\pi$
$864$	−39.3668	+	8.20369i	−1.33929	+	0.279095i
$865$	30.7603			1.04588
$866$	2.49729	−	21.4337i	0.0848614	−	0.728346i
$867$	−30.2565	+	30.2565i	−1.02756	+	1.02756i
$868$		0			0
$869$	−1.63656	−	1.63656i	−0.0555165	−	0.0555165i
$870$	57.0526	+	72.1006i	1.93427	+	2.44444i
$871$			3.43769i			0.116482i
$872$	−5.54680	−	11.8611i	−0.187838	−	0.401669i
$873$			88.3493i			2.99017i
$874$	10.9435	−	8.65950i	0.370169	−	0.292912i
$875$		0			0
$876$	44.2207	+	71.5754i	1.49408	+	2.41831i
$877$	−38.0640	+	38.0640i	−1.28533	+	1.28533i	−0.347738	+	0.937592i	$0.613050\pi$
$877$	−38.0640	+	38.0640i	−1.28533	+	1.28533i	−0.937592	+	0.347738i	$0.886950\pi$
$878$	−6.10350	−	0.711133i	−0.205983	−	0.0239996i
$879$	55.5844			1.87482
$880$	8.97990	−	17.9459i	0.302712	−	0.604955i
$881$	21.5769			0.726946			0.363473	−	0.931605i	$-0.381591\pi$
$881$	21.5769			0.726946			0.363473	+	0.931605i	$0.381591\pi$
$882$		0			0
$883$	21.5700	−	21.5700i	0.725888	−	0.725888i	−0.243910	−	0.969798i	$-0.578430\pi$
$883$	21.5700	−	21.5700i	0.725888	−	0.725888i	0.969798	+	0.243910i	$0.0784300\pi$
$884$	−4.08838	+	2.52588i	−0.137507	+	0.0849546i
$885$	12.7625	+	12.7625i	0.429008	+	0.429008i
$886$	−6.76586	+	5.35377i	−0.227303	+	0.179863i
$887$		−	33.7110i		−	1.13191i	−0.824437	−	0.565953i	$-0.808508\pi$
$887$		−	33.7110i		−	1.13191i	0.824437	−	0.565953i	$-0.191492\pi$
$888$	6.55898	−	18.0824i	0.220105	−	0.606804i
$889$		0			0
$890$	28.6350	+	36.1876i	0.959846	+	1.21301i
$891$	−3.97372	−	3.97372i	−0.133125	−	0.133125i
$892$	−6.23476	−	1.47285i	−0.208755	−	0.0493146i
$893$	5.26208	−	5.26208i	0.176089	−	0.176089i
$894$	5.22683	−	44.8607i	0.174811	−	1.50037i
$895$	−63.9788			−2.13858
$896$		0			0
$897$	−22.0777			−0.737153
$898$	0.609656	−	5.23254i	0.0203445	−	0.174612i
$899$	−16.8538	+	16.8538i	−0.562105	+	0.562105i
$900$	−104.734	−	24.7415i	−3.49113	−	0.824716i
$901$	−1.01955	−	1.01955i	−0.0339662	−	0.0339662i
$902$	8.50865	+	10.7529i	0.283307	+	0.358031i
$903$		0			0
$904$	8.84597	−	24.3873i	0.294213	−	0.811111i
$905$		−	22.8346i		−	0.759047i
$906$	17.6244	−	13.9460i	0.585530	−	0.463326i
$907$	0.923962	+	0.923962i	0.0306797	+	0.0306797i	0.722280	−	0.691601i	$-0.243094\pi$
$907$	0.923962	+	0.923962i	0.0306797	+	0.0306797i	−0.691601	+	0.722280i	$0.743094\pi$
$908$	−33.1894	+	20.5051i	−1.10143	+	0.680485i
$909$	62.9911	−	62.9911i	2.08928	−	2.08928i
$910$		0			0
$911$	−29.9873			−0.993522			−0.496761	−	0.867887i	$-0.665477\pi$
$911$	−29.9873			−0.993522			−0.496761	+	0.867887i	$0.665477\pi$
$912$	−10.7608	+	21.5049i	−0.356326	+	0.712099i
$913$	13.1713			0.435908
$914$	15.0938	+	1.75862i	0.499259	+	0.0581699i
$915$	−36.0851	+	36.0851i	−1.19294	+	1.19294i
$916$	10.4387	+	16.8960i	0.344904	+	0.558261i
$917$		0			0
$918$	−11.8951	+	9.41250i	−0.392597	+	0.310659i
$919$			13.0725i			0.431220i	0.976480	+	0.215610i	$0.0691741\pi$
$919$			13.0725i			0.431220i	−0.976480	+	0.215610i	$0.930826\pi$
$920$	−22.0478	−	47.1466i	−0.726896	−	1.55438i
$921$		−	36.7182i		−	1.20991i
$922$	9.78917	+	12.3711i	0.322389	+	0.407421i
$923$	−15.5626	−	15.5626i	−0.512248	−	0.512248i
$924$		0			0
$925$	16.3486	−	16.3486i	0.537538	−	0.537538i
$926$	4.47603	−	38.4167i	0.147091	−	1.26245i
$927$	93.6035			3.07434
$928$	−6.69260	−	32.1156i	−0.219695	−	1.05424i
$929$	20.7057			0.679333			0.339667	−	0.940546i	$-0.389686\pi$
$929$	20.7057			0.679333			0.339667	+	0.940546i	$0.389686\pi$
$930$	7.54106	−	64.7232i	0.247281	−	2.12236i
$931$		0			0
$932$	1.35118	−	5.71971i	0.0442593	−	0.187355i
$933$	−40.6348	−	40.6348i	−1.33033	−	1.33033i
$934$	14.1373	+	17.8661i	0.462588	+	0.584598i
$935$		−	7.56961i		−	0.247553i
$936$	22.2208	−	10.3914i	0.726308	−	0.339654i
$937$		−	5.93799i		−	0.193986i	−0.995285	−	0.0969929i	$-0.969078\pi$
$937$		−	5.93799i		−	0.193986i	0.995285	−	0.0969929i	$-0.0309224\pi$
$938$		0			0
$939$	−17.9348	−	17.9348i	−0.585281	−	0.585281i
$940$	−14.5878	−	23.6117i	−0.475801	−	0.770129i
$941$	13.9955	−	13.9955i	0.456241	−	0.456241i	−0.441178	−	0.897419i	$-0.645439\pi$
$941$	13.9955	−	13.9955i	0.456241	−	0.456241i	0.897419	+	0.441178i	$0.145439\pi$
$942$	−32.4302	−	3.77852i	−1.05663	−	0.123111i
$943$	35.5642			1.15813
$944$	−2.03459	−	6.11007i	−0.0662201	−	0.198866i
$945$		0			0
$946$	14.7004	+	1.71278i	0.477952	+	0.0556873i
$947$	−30.2690	+	30.2690i	−0.983611	+	0.983611i	−0.999868	−	0.0162570i	$-0.994825\pi$
$947$	−30.2690	+	30.2690i	−0.983611	+	0.983611i	0.0162570	+	0.999868i	$0.494825\pi$
$948$	8.79984	−	5.43671i	0.285805	−	0.176576i
$949$	−16.2998	−	16.2998i	−0.529113	−	0.529113i
$950$	−22.6663	+	17.9356i	−0.735391	+	0.581909i
$951$		−	78.1710i		−	2.53487i
$952$		0			0
$953$		−	0.689500i		−	0.0223351i	−0.999938	−	0.0111675i	$-0.996445\pi$
$953$		−	0.689500i		−	0.0223351i	0.999938	−	0.0111675i	$-0.00355481\pi$
$954$	4.56699	+	5.77155i	0.147862	+	0.186861i
$955$	−33.7348	−	33.7348i	−1.09163	−	1.09163i
$956$	−31.5533	−	7.45388i	−1.02051	−	0.241076i
$957$	15.4990	−	15.4990i	0.501012	−	0.501012i
$958$	−1.86383	+	15.9968i	−0.0602176	+	0.516834i
$959$		0			0
$960$	68.8294	+	57.4977i	2.22146	+	1.85573i
$961$	−14.1080			−0.455096
$962$	−0.609910	+	5.23472i	−0.0196643	+	0.168774i
$963$	22.3365	−	22.3365i	0.719783	−	0.719783i
$964$	−27.4769	−	6.49092i	−0.884971	−	0.209058i
$965$	−64.6012	−	64.6012i	−2.07959	−	2.07959i
$966$		0			0
$967$			14.1022i			0.453497i	0.973953	+	0.226749i	$0.0728096\pi$
$967$			14.1022i			0.453497i	−0.973953	+	0.226749i	$0.927190\pi$
$968$	24.7508	+	8.97780i	0.795520	+	0.288557i
$969$			9.07083i			0.291397i
$970$	69.4010	−	54.9164i	2.22833	−	1.76326i
$971$	0.255230	+	0.255230i	0.00819071	+	0.00819071i	0.711190	−	0.703000i	$-0.248156\pi$
$971$	0.255230	+	0.255230i	0.00819071	+	0.00819071i	−0.703000	+	0.711190i	$0.748156\pi$
$972$	−14.9184	+	9.21689i	−0.478508	+	0.295632i
$973$		0			0
$974$	−44.0421	−	5.13145i	−1.41120	−	0.164422i
$975$	45.7275			1.46445
$976$	17.2757	−	5.75263i	0.552983	−	0.184137i
$977$	−9.83910			−0.314781			−0.157390	−	0.987536i	$-0.550308\pi$
$977$	−9.83910			−0.314781			−0.157390	+	0.987536i	$0.550308\pi$
$978$	36.4736	+	4.24963i	1.16630	+	0.135888i
$979$	7.77902	−	7.77902i	0.248618	−	0.248618i
$980$		0			0
$981$	17.8276	+	17.8276i	0.569191	+	0.569191i
$982$	31.8028	−	25.1653i	1.01487	−	0.803057i
$983$			26.6489i			0.849968i	0.905201	+	0.424984i	$0.139720\pi$
$983$			26.6489i			0.849968i	−0.905201	+	0.424984i	$0.860280\pi$
$984$	−55.5125	+	25.9601i	−1.76967	+	0.827578i
$985$			62.2971i			1.98495i
$986$	−7.67875	−	9.70406i	−0.244541	−	0.309040i
$987$		0			0
$988$	1.51472	−	6.41201i	0.0481896	−	0.203993i
$989$	27.1427	−	27.1427i	0.863086	−	0.863086i
$990$	−4.47163	+	38.3790i	−0.142118	+	1.21976i
$991$	16.8287			0.534583			0.267291	−	0.963616i	$-0.413871\pi$
$991$	16.8287			0.534583			0.267291	+	0.963616i	$0.413871\pi$
$992$	−12.7403	+	19.4481i	−0.404506	+	0.617478i
$993$	91.7875			2.91279
$994$		0			0
$995$	−14.9935	+	14.9935i	−0.475326	+	0.475326i
$996$	−13.5335	+	57.2892i	−0.428826	+	1.81528i
$997$	25.7816	+	25.7816i	0.816511	+	0.816511i	0.985601	−	0.169089i	$-0.0540827\pi$
$997$	25.7816	+	25.7816i	0.816511	+	0.816511i	−0.169089	+	0.985601i	$0.554083\pi$
$998$	22.9800	+	29.0412i	0.727421	+	0.919282i
$999$			16.6346i			0.526294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.h.197.3		12
7.2	even	3		784.2.x.m.165.2		24
7.3	odd	6		784.2.x.l.373.5		24
7.4	even	3		784.2.x.m.373.5		24
7.5	odd	6		784.2.x.l.165.2		24
7.6	odd	2		112.2.m.d.85.3	yes	12
16.13	even	4	inner	784.2.m.h.589.3		12
28.27	even	2		448.2.m.d.113.6		12
56.13	odd	2		896.2.m.g.225.6		12
56.27	even	2		896.2.m.h.225.1		12
112.13	odd	4		112.2.m.d.29.3	✓	12
112.27	even	4		896.2.m.h.673.1		12
112.45	odd	12		784.2.x.l.765.2		24
112.61	odd	12		784.2.x.l.557.5		24
112.69	odd	4		896.2.m.g.673.6		12
112.83	even	4		448.2.m.d.337.6		12
112.93	even	12		784.2.x.m.557.5		24
112.109	even	12		784.2.x.m.765.2		24
224.13	odd	8		7168.2.a.bj.1.11		12
224.83	even	8		7168.2.a.bi.1.2		12
224.125	odd	8		7168.2.a.bj.1.2		12
224.195	even	8		7168.2.a.bi.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.3	✓	12	112.13	odd	4
112.2.m.d.85.3	yes	12	7.6	odd	2
448.2.m.d.113.6		12	28.27	even	2
448.2.m.d.337.6		12	112.83	even	4
784.2.m.h.197.3		12	1.1	even	1	trivial
784.2.m.h.589.3		12	16.13	even	4	inner
784.2.x.l.165.2		24	7.5	odd	6
784.2.x.l.373.5		24	7.3	odd	6
784.2.x.l.557.5		24	112.61	odd	12
784.2.x.l.765.2		24	112.45	odd	12
784.2.x.m.165.2		24	7.2	even	3
784.2.x.m.373.5		24	7.4	even	3
784.2.x.m.557.5		24	112.93	even	12
784.2.x.m.765.2		24	112.109	even	12
896.2.m.g.225.6		12	56.13	odd	2
896.2.m.g.673.6		12	112.69	odd	4
896.2.m.h.225.1		12	56.27	even	2
896.2.m.h.673.1		12	112.27	even	4
7168.2.a.bi.1.2		12	224.83	even	8
7168.2.a.bi.1.11		12	224.195	even	8
7168.2.a.bj.1.2		12	224.125	odd	8
7168.2.a.bj.1.11		12	224.13	odd	8

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +O(q^{10})\)	\(q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +(-4.27801 + 3.38515i) q^{10} +(0.919616 + 0.919616i) q^{11} +(-4.94480 + 3.05500i) q^{12} +(1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(3.57715 + 1.78996i) q^{16} +1.50885 q^{17} +(-7.65008 - 0.891330i) q^{18} +(-1.46271 + 1.46271i) q^{19} +(4.05500 + 6.56340i) q^{20} +(1.44230 - 1.14128i) q^{22} -4.77031i q^{23} +(3.48209 + 7.44602i) q^{24} +9.88030i q^{25} +(-1.39751 - 1.76611i) q^{26} +(-5.02656 - 5.02656i) q^{27} +(4.10069 - 4.10069i) q^{29} +(-1.83481 + 15.7478i) q^{30} -4.10999 q^{31} +(3.09984 - 4.73191i) q^{32} +3.77961 q^{33} +(0.246948 - 2.11950i) q^{34} +(-2.50412 + 10.6003i) q^{36} +(-1.65467 - 1.65467i) q^{37} +(1.81529 + 2.29409i) q^{38} -4.62815i q^{39} +(9.88334 - 4.62189i) q^{40} +7.45533i q^{41} +(5.68992 + 5.68992i) q^{43} +(-1.36712 - 2.21281i) q^{44} +(-14.8549 + 14.8549i) q^{45} +(-6.70090 - 0.780738i) q^{46} -3.59748 q^{47} +(11.0294 - 3.67267i) q^{48} +(13.8790 + 1.61707i) q^{50} +(3.10069 - 3.10069i) q^{51} +(-2.70960 + 1.67404i) q^{52} +(-0.675714 - 0.675714i) q^{53} +(-7.88355 + 6.23819i) q^{54} -5.01680i q^{55} +6.01174i q^{57} +(-5.08913 - 6.43142i) q^{58} +(-1.13843 - 1.13843i) q^{59} +(21.8208 + 5.15476i) q^{60} +(3.21881 - 3.21881i) q^{61} +(-0.672667 + 5.77335i) q^{62} +(-6.13963 - 5.12884i) q^{64} -6.14310 q^{65} +(0.618595 - 5.30926i) q^{66} +(-1.52640 + 1.52640i) q^{67} +(-2.93687 - 0.693782i) q^{68} +(-9.80296 - 9.80296i) q^{69} -13.8202i q^{71} +(14.4805 + 5.25248i) q^{72} -14.4749i q^{73} +(-2.59514 + 2.05351i) q^{74} +(20.3040 + 20.3040i) q^{75} +(3.51963 - 2.17450i) q^{76} +(-6.50122 - 0.757473i) q^{78} -1.77961 q^{79} +(-4.87485 - 14.6397i) q^{80} -4.32107 q^{81} +(10.4726 + 1.22019i) q^{82} +(7.16133 - 7.16133i) q^{83} +(-4.11564 - 4.11564i) q^{85} +(8.92394 - 7.06145i) q^{86} -16.8538i q^{87} +(-3.33211 + 1.55824i) q^{88} -8.45899i q^{89} +(18.4356 + 23.2981i) q^{90} +(-2.19342 + 9.28505i) q^{92} +(-8.44602 + 8.44602i) q^{93} +(-0.588786 + 5.05342i) q^{94} +7.97958 q^{95} +(-3.35389 - 16.0942i) q^{96} -16.2227 q^{97} +(5.00824 - 5.00824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * q^50 - 16 * q^51 + 16 * q^52 + 4 * q^53 - 64 * q^54 + 14 * q^58 + 16 * q^59 + 60 * q^60 + 20 * q^61 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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