LMFDB - Embedded newform 850.2.v.a.607.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			607.3
Character	$\chi$	$=$	850.607
Dual form			850.2.v.a.843.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(0.437319 - 2.19855i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.86384 + 1.24538i) q^{6} +(1.94597 + 1.30026i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-1.87075 - 0.774889i) q^{9} +(2.08242 - 3.11656i) q^{11} +(-1.86384 + 1.24538i) q^{12} +1.83794 q^{13} +(-1.94597 + 1.30026i) q^{14} +1.00000i q^{16} +(-2.84065 + 2.98843i) q^{17} +(1.43181 - 1.43181i) q^{18} +(6.19346 - 2.56542i) q^{19} +(3.70970 - 3.70970i) q^{21} +(2.08242 + 3.11656i) q^{22} +(-5.00678 + 0.995910i) q^{23} +(-0.437319 - 2.19855i) q^{24} +(-0.703348 + 1.69803i) q^{26} +(1.21439 - 1.81746i) q^{27} +(-0.456590 - 2.29543i) q^{28} +(0.598780 + 0.119105i) q^{29} +(2.46039 + 3.68223i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-5.94124 - 5.94124i) q^{33} +(-1.67388 - 3.76804i) q^{34} +(0.774889 + 1.87075i) q^{36} +(-1.64915 - 0.328036i) q^{37} +6.70375i q^{38} +(0.803765 - 4.04080i) q^{39} +(3.38971 - 0.674255i) q^{41} +(2.00768 + 4.84696i) q^{42} +(0.926479 + 2.23672i) q^{43} +(-3.67624 + 0.731249i) q^{44} +(0.995910 - 5.00678i) q^{46} -10.6121i q^{47} +(2.19855 + 0.437319i) q^{48} +(-0.582639 - 1.40662i) q^{49} +(5.32794 + 7.55222i) q^{51} +(-1.29962 - 1.29962i) q^{52} +(1.76897 + 0.732730i) q^{53} +(1.21439 + 1.81746i) q^{54} +(2.29543 + 0.456590i) q^{56} +(-2.93168 - 14.7386i) q^{57} +(-0.339182 + 0.507621i) q^{58} +(4.86169 - 11.7372i) q^{59} +(-1.29314 - 6.50106i) q^{61} +(-4.34349 + 0.863974i) q^{62} +(-2.63287 - 3.94037i) q^{63} +(0.707107 - 0.707107i) q^{64} +(7.76261 - 3.21538i) q^{66} +(0.983164 - 0.983164i) q^{67} +(4.12178 - 0.104492i) q^{68} +11.4432i q^{69} +(7.07898 - 4.73002i) q^{71} -2.02488 q^{72} +(-3.82200 + 2.55378i) q^{73} +(0.934169 - 1.39808i) q^{74} +(-6.19346 - 2.56542i) q^{76} +(8.10467 - 3.35707i) q^{77} +(3.42563 + 2.28893i) q^{78} +(-4.28663 - 2.86424i) q^{79} +(-7.76014 - 7.76014i) q^{81} +(-0.674255 + 3.38971i) q^{82} +(-5.34887 + 12.9133i) q^{83} -5.24631 q^{84} -2.42101 q^{86} +(0.523716 - 1.26436i) q^{87} +(0.731249 - 3.67624i) q^{88} +(-11.0963 - 11.0963i) q^{89} +(3.57658 + 2.38979i) q^{91} +(4.24454 + 2.83611i) q^{92} +(9.17156 - 3.79898i) q^{93} +(9.80427 + 4.06106i) q^{94} +(-1.24538 + 1.86384i) q^{96} +(9.35564 - 6.25124i) q^{97} +1.52251 q^{98} +(-6.31067 + 4.21666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	0.437319	−	2.19855i	0.252486	−	1.26934i	−0.621511	−	0.783405i	$-0.713481\pi$
$3$	0.437319	−	2.19855i	0.252486	−	1.26934i	0.873998	−	0.485930i	$-0.161519\pi$
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	1.86384	+	1.24538i	0.760911	+	0.508424i
$7$	1.94597	+	1.30026i	0.735509	+	0.491452i	0.866029	−	0.499994i	$-0.166665\pi$
$7$	1.94597	+	1.30026i	0.735509	+	0.491452i	−0.130519	+	0.991446i	$0.541665\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−1.87075	−	0.774889i	−0.623583	−	0.258296i
$10$		0			0
$11$	2.08242	−	3.11656i	0.627873	−	0.939679i	−0.372061	−	0.928208i	$-0.621349\pi$
$11$	2.08242	−	3.11656i	0.627873	−	0.939679i	0.999934	−	0.0114704i	$-0.00365123\pi$
$12$	−1.86384	+	1.24538i	−0.538045	+	0.359510i
$13$	1.83794			0.509752			0.254876	−	0.966974i	$-0.417965\pi$
$13$	1.83794			0.509752			0.254876	+	0.966974i	$0.417965\pi$
$14$	−1.94597	+	1.30026i	−0.520084	+	0.347509i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	−2.84065	+	2.98843i	−0.688960	+	0.724800i
$17$	−2.84065	+	2.98843i	−0.688960	+	0.724800i
$18$	1.43181	−	1.43181i	0.337481	−	0.337481i
$19$	6.19346	−	2.56542i	1.42088	−	0.588547i	0.465797	−	0.884892i	$-0.345768\pi$
$19$	6.19346	−	2.56542i	1.42088	−	0.588547i	0.955081	+	0.296345i	$0.0957678\pi$
$20$		0			0
$21$	3.70970	−	3.70970i	0.809523	−	0.809523i
$22$	2.08242	+	3.11656i	0.443973	+	0.664453i
$23$	−5.00678	+	0.995910i	−1.04398	+	0.207661i	−0.687157	−	0.726509i	$-0.741142\pi$
$23$	−5.00678	+	0.995910i	−1.04398	+	0.207661i	−0.356828	+	0.934170i	$0.616142\pi$
$24$	−0.437319	−	2.19855i	−0.0892674	−	0.448778i
$25$		0			0
$26$	−0.703348	+	1.69803i	−0.137938	+	0.333011i
$27$	1.21439	−	1.81746i	0.233710	−	0.349771i
$28$	−0.456590	−	2.29543i	−0.0862874	−	0.433796i
$29$	0.598780	+	0.119105i	0.111191	+	0.0221172i	0.250372	−	0.968150i	$-0.419447\pi$
$29$	0.598780	+	0.119105i	0.111191	+	0.0221172i	−0.139181	+	0.990267i	$0.544447\pi$
$30$		0			0
$31$	2.46039	+	3.68223i	0.441899	+	0.661349i	0.983836	−	0.179070i	$-0.0573090\pi$
$31$	2.46039	+	3.68223i	0.441899	+	0.661349i	−0.541937	+	0.840419i	$0.682309\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	−5.94124	−	5.94124i	−1.03424	−	1.03424i
$34$	−1.67388	−	3.76804i	−0.287067	−	0.646214i
$35$		0			0
$36$	0.774889	+	1.87075i	0.129148	+	0.311791i
$37$	−1.64915	−	0.328036i	−0.271119	−	0.0539289i	0.0576586	−	0.998336i	$-0.481637\pi$
$37$	−1.64915	−	0.328036i	−0.271119	−	0.0539289i	−0.328777	+	0.944408i	$0.606637\pi$
$38$			6.70375i			1.08749i
$39$	0.803765	−	4.04080i	0.128705	−	0.647046i
$40$		0			0
$41$	3.38971	−	0.674255i	0.529384	−	0.105301i	0.0768405	−	0.997043i	$-0.475517\pi$
$41$	3.38971	−	0.674255i	0.529384	−	0.105301i	0.452543	+	0.891742i	$0.350517\pi$
$42$	2.00768	+	4.84696i	0.309791	+	0.747902i
$43$	0.926479	+	2.23672i	0.141287	+	0.341096i	0.978645	−	0.205558i	$-0.0659010\pi$
$43$	0.926479	+	2.23672i	0.141287	+	0.341096i	−0.837358	+	0.546655i	$0.815901\pi$
$44$	−3.67624	+	0.731249i	−0.554213	+	0.110240i
$45$		0			0
$46$	0.995910	−	5.00678i	0.146839	−	0.738209i
$47$		−	10.6121i		−	1.54793i	−0.633229	−	0.773965i	$-0.718271\pi$
$47$		−	10.6121i		−	1.54793i	0.633229	−	0.773965i	$-0.281729\pi$
$48$	2.19855	+	0.437319i	0.317334	+	0.0631216i
$49$	−0.582639	−	1.40662i	−0.0832342	−	0.200945i
$50$		0			0
$51$	5.32794	+	7.55222i	0.746061	+	1.05752i
$52$	−1.29962	−	1.29962i	−0.180224	−	0.180224i
$53$	1.76897	+	0.732730i	0.242986	+	0.100648i	0.500853	−	0.865532i	$-0.333020\pi$
$53$	1.76897	+	0.732730i	0.242986	+	0.100648i	−0.257867	+	0.966180i	$0.583020\pi$
$54$	1.21439	+	1.81746i	0.165258	+	0.247326i
$55$		0			0
$56$	2.29543	+	0.456590i	0.306740	+	0.0610144i
$57$	−2.93168	−	14.7386i	−0.388311	−	1.95217i
$58$	−0.339182	+	0.507621i	−0.0445367	+	0.0666539i
$59$	4.86169	−	11.7372i	0.632938	−	1.52805i	−0.202973	−	0.979184i	$-0.565061\pi$
$59$	4.86169	−	11.7372i	0.632938	−	1.52805i	0.835912	−	0.548864i	$-0.184939\pi$
$60$		0			0
$61$	−1.29314	−	6.50106i	−0.165570	−	0.832375i	−0.970888	−	0.239533i	$-0.923006\pi$
$61$	−1.29314	−	6.50106i	−0.165570	−	0.832375i	0.805318	−	0.592842i	$-0.201994\pi$
$62$	−4.34349	+	0.863974i	−0.551624	+	0.109725i
$63$	−2.63287	−	3.94037i	−0.331711	−	0.496440i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$		0			0
$66$	7.76261	−	3.21538i	0.955511	−	0.395786i
$67$	0.983164	−	0.983164i	0.120113	−	0.120113i	−0.644495	−	0.764608i	$-0.722933\pi$
$67$	0.983164	−	0.983164i	0.120113	−	0.120113i	0.764608	+	0.644495i	$0.222933\pi$
$68$	4.12178	−	0.104492i	0.499839	−	0.0126715i
$69$			11.4432i			1.37760i
$70$		0			0
$71$	7.07898	−	4.73002i	0.840120	−	0.561350i	−0.0593975	−	0.998234i	$-0.518918\pi$
$71$	7.07898	−	4.73002i	0.840120	−	0.561350i	0.899518	+	0.436884i	$0.143918\pi$
$72$	−2.02488			−0.238635
$73$	−3.82200	+	2.55378i	−0.447331	+	0.298897i	−0.758758	−	0.651373i	$-0.774193\pi$
$73$	−3.82200	+	2.55378i	−0.447331	+	0.298897i	0.311426	+	0.950270i	$0.399193\pi$
$74$	0.934169	−	1.39808i	0.108595	−	0.162524i
$75$		0			0
$76$	−6.19346	−	2.56542i	−0.710439	−	0.294273i
$77$	8.10467	−	3.35707i	0.923613	−	0.382573i
$78$	3.42563	+	2.28893i	0.387876	+	0.259170i
$79$	−4.28663	−	2.86424i	−0.482284	−	0.322252i	0.290551	−	0.956860i	$-0.406162\pi$
$79$	−4.28663	−	2.86424i	−0.482284	−	0.322252i	−0.772834	+	0.634608i	$0.781162\pi$
$80$		0			0
$81$	−7.76014	−	7.76014i	−0.862238	−	0.862238i
$82$	−0.674255	+	3.38971i	−0.0744590	+	0.374331i
$83$	−5.34887	+	12.9133i	−0.587114	+	1.41742i	0.299135	+	0.954211i	$0.403302\pi$
$83$	−5.34887	+	12.9133i	−0.587114	+	1.41742i	−0.886249	+	0.463208i	$0.846698\pi$
$84$	−5.24631			−0.572419
$85$		0			0
$86$	−2.42101			−0.261064
$87$	0.523716	−	1.26436i	0.0561483	−	0.135554i
$88$	0.731249	−	3.67624i	0.0779514	−	0.391888i
$89$	−11.0963	−	11.0963i	−1.17620	−	1.17620i	−0.980704	−	0.195500i	$-0.937367\pi$
$89$	−11.0963	−	11.0963i	−1.17620	−	1.17620i	−0.195500	−	0.980704i	$-0.562633\pi$
$90$		0			0
$91$	3.57658	+	2.38979i	0.374927	+	0.250518i
$92$	4.24454	+	2.83611i	0.442524	+	0.295685i
$93$	9.17156	−	3.79898i	0.951046	−	0.393936i
$94$	9.80427	+	4.06106i	1.01123	+	0.418867i
$95$		0			0
$96$	−1.24538	+	1.86384i	−0.127106	+	0.190228i
$97$	9.35564	−	6.25124i	0.949921	−	0.634717i	0.0189540	−	0.999820i	$-0.493966\pi$
$97$	9.35564	−	6.25124i	0.949921	−	0.634717i	0.930967	+	0.365103i	$0.118966\pi$
$98$	1.52251			0.153797
$99$	−6.31067	+	4.21666i	−0.634247	+	0.423790i
$100$		0			0
$101$			16.4108i			1.63294i	0.577389	+	0.816469i	$0.304072\pi$
$101$			16.4108i			1.63294i	−0.577389	+	0.816469i	$0.695928\pi$
$102$	−9.01626	+	2.03227i	−0.892743	+	0.201224i
$103$	−11.2381	+	11.2381i	−1.10733	+	1.10733i	−0.113825	+	0.993501i	$0.536310\pi$
$103$	−11.2381	+	11.2381i	−1.10733	+	1.10733i	−0.993501	+	0.113825i	$0.963690\pi$
$104$	1.69803	−	0.703348i	0.166506	−	0.0689689i
$105$		0			0
$106$	−1.35391	+	1.35391i	−0.131503	+	0.131503i
$107$	−0.445180	−	0.666259i	−0.0430372	−	0.0644097i	0.809327	−	0.587358i	$-0.199832\pi$
$107$	−0.445180	−	0.666259i	−0.0430372	−	0.0644097i	−0.852364	+	0.522948i	$0.824832\pi$
$108$	−2.14385	+	0.426437i	−0.206292	+	0.0410340i
$109$	2.71439	+	13.6462i	0.259991	+	1.30707i	0.861320	+	0.508063i	$0.169638\pi$
$109$	2.71439	+	13.6462i	0.259991	+	1.30707i	−0.601328	+	0.799002i	$0.705362\pi$
$110$		0			0
$111$	−1.44241	+	3.48229i	−0.136908	+	0.330524i
$112$	−1.30026	+	1.94597i	−0.122863	+	0.183877i
$113$	0.0285995	+	0.143780i	0.00269042	+	0.0135256i	0.982107	−	0.188323i	$-0.0603051\pi$
$113$	0.0285995	+	0.143780i	0.00269042	+	0.0135256i	−0.979417	+	0.201849i	$0.935305\pi$
$114$	14.7386	+	2.93168i	1.38039	+	0.274577i
$115$		0			0
$116$	−0.339182	−	0.507621i	−0.0314922	−	0.0471314i
$117$	−3.43832	−	1.42420i	−0.317872	−	0.131667i
$118$	8.98323	+	8.98323i	0.826974	+	0.826974i
$119$	−9.41357	+	2.12182i	−0.862940	+	0.194507i
$120$		0			0
$121$	−1.16697	−	2.81731i	−0.106088	−	0.256119i
$122$	6.50106	+	1.29314i	0.588578	+	0.117075i
$123$		−	7.74732i		−	0.698552i
$124$	0.863974	−	4.34349i	0.0775871	−	0.390057i
$125$		0			0
$126$	4.64799	−	0.924542i	0.414075	−	0.0823647i
$127$	8.16676	+	19.7163i	0.724683	+	1.74954i	0.659547	+	0.751664i	$0.270748\pi$
$127$	8.16676	+	19.7163i	0.724683	+	1.74954i	0.0651365	+	0.997876i	$0.479252\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	5.32271	−	1.05875i	0.468639	−	0.0932180i
$130$		0			0
$131$	−2.51893	+	12.6635i	−0.220080	+	1.10642i	0.699837	+	0.714302i	$0.253256\pi$
$131$	−2.51893	+	12.6635i	−0.220080	+	1.10642i	−0.919917	+	0.392113i	$0.871744\pi$
$132$			8.40219i			0.731317i
$133$	15.3880	+	3.06087i	1.33431	+	0.265411i
$134$	0.532085	+	1.28457i	0.0459651	+	0.110970i
$135$		0			0
$136$	−1.48080	+	3.84802i	−0.126978	+	0.329965i
$137$	1.52157	+	1.52157i	0.129997	+	0.129997i	0.769111	−	0.639115i	$-0.220699\pi$
$137$	1.52157	+	1.52157i	0.129997	+	0.129997i	−0.639115	+	0.769111i	$0.720699\pi$
$138$	−10.5721	−	4.37912i	−0.899959	−	0.372775i
$139$	10.8206	+	16.1941i	0.917788	+	1.37357i	0.927584	+	0.373614i	$0.121882\pi$
$139$	10.8206	+	16.1941i	0.917788	+	1.37357i	−0.00979673	+	0.999952i	$0.503118\pi$
$140$		0			0
$141$	−23.3312	−	4.64086i	−1.96484	−	0.390831i
$142$	1.66096	+	8.35023i	0.139385	+	0.700735i
$143$	3.82736	−	5.72804i	0.320060	−	0.479003i
$144$	0.774889	−	1.87075i	0.0645741	−	0.155896i
$145$		0			0
$146$	−0.896768	−	4.50836i	−0.0742170	−	0.373114i
$147$	−3.34732	+	0.665823i	−0.276082	+	0.0549161i
$148$	0.934169	+	1.39808i	0.0767882	+	0.114922i
$149$	−13.4649	+	13.4649i	−1.10308	+	1.10308i	−0.109047	+	0.994037i	$0.534780\pi$
$149$	−13.4649	+	13.4649i	−1.10308	+	1.10308i	−0.994037	+	0.109047i	$0.965220\pi$
$150$		0			0
$151$	−5.17302	+	2.14274i	−0.420975	+	0.174373i	−0.583107	−	0.812396i	$-0.698163\pi$
$151$	−5.17302	+	2.14274i	−0.420975	+	0.174373i	0.162132	+	0.986769i	$0.448163\pi$
$152$	4.74027	−	4.74027i	0.384487	−	0.384487i
$153$	7.62985	−	3.38940i	0.616836	−	0.274017i
$154$			8.77244i			0.706903i
$155$		0			0
$156$	−3.42563	+	2.28893i	−0.274270	+	0.183261i
$157$	2.43885			0.194642			0.0973209	−	0.995253i	$-0.468973\pi$
$157$	2.43885			0.194642			0.0973209	+	0.995253i	$0.468973\pi$
$158$	4.28663	−	2.86424i	0.341026	−	0.227866i
$159$	2.38455	−	3.56873i	0.189107	−	0.283019i
$160$		0			0
$161$	−11.0380	−	4.57209i	−0.869916	−	0.360331i
$162$	10.1391	−	4.19976i	0.796604	−	0.329964i
$163$	−5.99898	−	4.00839i	−0.469876	−	0.313961i	0.297993	−	0.954568i	$-0.403683\pi$
$163$	−5.99898	−	4.00839i	−0.469876	−	0.313961i	−0.767869	+	0.640607i	$0.778683\pi$
$164$	−2.87366	−	1.92012i	−0.224395	−	0.149936i
$165$		0			0
$166$	−9.88341	−	9.88341i	−0.767102	−	0.767102i
$167$	−3.00246	+	15.0944i	−0.232337	+	1.16804i	0.671779	+	0.740752i	$0.265531\pi$
$167$	−3.00246	+	15.0944i	−0.232337	+	1.16804i	−0.904116	+	0.427287i	$0.859469\pi$
$168$	2.00768	−	4.84696i	0.154896	−	0.373951i
$169$	−9.62199			−0.740153
$170$		0			0
$171$	−13.5743			−1.03805
$172$	0.926479	−	2.23672i	0.0706434	−	0.170548i
$173$	0.592427	−	2.97833i	0.0450414	−	0.226438i	−0.951708	−	0.307005i	$-0.900673\pi$
$173$	0.592427	−	2.97833i	0.0450414	−	0.226438i	0.996749	+	0.0805670i	$0.0256731\pi$
$174$	0.967701	+	0.967701i	0.0733612	+	0.0733612i
$175$		0			0
$176$	3.11656	+	2.08242i	0.234920	+	0.156968i
$177$	−23.6787	−	15.8216i	−1.77980	−	1.18922i
$178$	14.4980	−	6.00527i	1.08667	−	0.450114i
$179$	−12.6642	−	5.24569i	−0.946568	−	0.392081i	−0.144628	−	0.989486i	$-0.546199\pi$
$179$	−12.6642	−	5.24569i	−0.946568	−	0.392081i	−0.801940	+	0.597405i	$0.796199\pi$
$180$		0			0
$181$	5.41668	−	8.10663i	0.402618	−	0.602561i	−0.573656	−	0.819096i	$-0.694476\pi$
$181$	5.41668	−	8.10663i	0.402618	−	0.602561i	0.976275	+	0.216535i	$0.0694755\pi$
$182$	−3.57658	+	2.38979i	−0.265114	+	0.177143i
$183$	−14.8584			−1.09837
$184$	−4.24454	+	2.83611i	−0.312912	+	0.209081i
$185$		0			0
$186$			9.92722i			0.727899i
$187$	3.39818	+	15.0762i	0.248500	+	1.10248i
$188$	−7.50387	+	7.50387i	−0.547276	+	0.547276i
$189$	4.72635	−	1.95772i	0.343791	−	0.142403i
$190$		0			0
$191$	−13.0447	+	13.0447i	−0.943881	+	0.943881i	−0.998507	−	0.0546255i	$-0.982603\pi$
$191$	−13.0447	+	13.0447i	−0.943881	+	0.943881i	0.0546255	+	0.998507i	$0.482603\pi$
$192$	−1.24538	−	1.86384i	−0.0898776	−	0.134511i
$193$	20.4235	−	4.06249i	1.47012	−	0.292424i	0.605899	−	0.795542i	$-0.292814\pi$
$193$	20.4235	−	4.06249i	1.47012	−	0.292424i	0.864218	+	0.503117i	$0.167814\pi$
$194$	2.19514	+	11.0357i	0.157602	+	0.792319i
$195$		0			0
$196$	−0.582639	+	1.40662i	−0.0416171	+	0.100473i
$197$	2.35217	−	3.52027i	0.167585	−	0.250809i	−0.738166	−	0.674619i	$-0.764308\pi$
$197$	2.35217	−	3.52027i	0.167585	−	0.250809i	0.905751	+	0.423811i	$0.139308\pi$
$198$	−1.48069	−	7.44395i	−0.105228	−	0.529018i
$199$	25.8402	+	5.13993i	1.83176	+	0.364360i	0.985671	−	0.168681i	$-0.0539508\pi$
$199$	25.8402	+	5.13993i	1.83176	+	0.364360i	0.846089	+	0.533041i	$0.178951\pi$
$200$		0			0
$201$	−1.73158	−	2.59150i	−0.122136	−	0.182790i
$202$	−15.1616	−	6.28015i	−1.06677	−	0.441870i
$203$	1.01034	+	1.01034i	0.0709122	+	0.0709122i
$204$	1.57280	−	9.10765i	0.110118	−	0.637663i
$205$		0			0
$206$	−6.08203	−	14.6833i	−0.423755	−	1.02304i
$207$	10.1381	+	2.01660i	0.704649	+	0.140163i
$208$			1.83794i			0.127438i
$209$	4.90211	−	24.6446i	0.339086	−	1.70470i
$210$		0			0
$211$	21.7949	−	4.33527i	1.50042	−	0.298452i	0.624545	−	0.780989i	$-0.285284\pi$
$211$	21.7949	−	4.33527i	1.50042	−	0.298452i	0.875876	+	0.482536i	$0.160284\pi$
$212$	−0.732730	−	1.76897i	−0.0503241	−	0.121493i
$213$	−7.30343	−	17.6320i	−0.500423	−	1.20813i
$214$	0.785906	−	0.156326i	0.0537234	−	0.0106863i
$215$		0			0
$216$	0.426437	−	2.14385i	0.0290154	−	0.145870i
$217$			10.3647i			0.703600i
$218$	−13.6462	−	2.71439i	−0.924235	−	0.183842i
$219$	3.94318	+	9.51969i	0.266456	+	0.643281i
$220$		0			0
$221$	−5.22094	+	5.49254i	−0.351198	+	0.369468i
$222$	−2.66523	−	2.66523i	−0.178878	−	0.178878i
$223$	−11.8905	−	4.92520i	−0.796246	−	0.329816i	−0.0527941	−	0.998605i	$-0.516813\pi$
$223$	−11.8905	−	4.92520i	−0.796246	−	0.329816i	−0.743452	+	0.668790i	$0.766813\pi$
$224$	−1.30026	−	1.94597i	−0.0868772	−	0.130021i
$225$		0			0
$226$	−0.143780	−	0.0285995i	−0.00956408	−	0.00190241i
$227$	−4.99137	−	25.0933i	−0.331289	−	1.66550i	−0.683780	−	0.729688i	$-0.739665\pi$
$227$	−4.99137	−	25.0933i	−0.331289	−	1.66550i	0.352491	−	0.935815i	$-0.385335\pi$
$228$	−8.34872	+	12.4947i	−0.552908	+	0.827485i
$229$	4.78226	−	11.5454i	0.316021	−	0.762942i	−0.683437	−	0.730010i	$-0.739515\pi$
$229$	4.78226	−	11.5454i	0.316021	−	0.762942i	0.999458	−	0.0329322i	$-0.0104845\pi$
$230$		0			0
$231$	−3.83636	−	19.2867i	−0.252414	−	1.26897i
$232$	0.598780	−	0.119105i	0.0393118	−	0.00781961i
$233$	−3.93433	−	5.88814i	−0.257747	−	0.385745i	0.679917	−	0.733289i	$-0.262016\pi$
$233$	−3.93433	−	5.88814i	−0.257747	−	0.385745i	−0.937664	+	0.347544i	$0.887016\pi$
$234$	2.63157	−	2.63157i	0.172031	−	0.172031i
$235$		0			0
$236$	−11.7372	+	4.86169i	−0.764024	+	0.316469i
$237$	−8.17180	+	8.17180i	−0.530815	+	0.530815i
$238$	1.64211	−	9.50899i	0.106442	−	0.616376i
$239$			19.6102i			1.26848i	0.773137	+	0.634239i	$0.218687\pi$
$239$			19.6102i			1.26848i	−0.773137	+	0.634239i	$0.781313\pi$
$240$		0			0
$241$	−3.93961	+	2.63236i	−0.253772	+	0.169565i	−0.675949	−	0.736948i	$-0.736266\pi$
$241$	−3.93961	+	2.63236i	−0.253772	+	0.169565i	0.422177	+	0.906513i	$0.361266\pi$
$242$	3.04943			0.196025
$243$	−15.0023	+	10.0242i	−0.962401	+	0.643056i
$244$	−3.68255	+	5.51133i	−0.235751	+	0.352827i
$245$		0			0
$246$	7.15759	+	2.96477i	0.456351	+	0.189027i
$247$	11.3832	−	4.71507i	0.724295	−	0.300013i
$248$	3.68223	+	2.46039i	0.233822	+	0.156235i
$249$	26.0514	+	17.4070i	1.65094	+	1.10312i
$250$		0			0
$251$	1.58594	+	1.58594i	0.100104	+	0.100104i	0.755385	−	0.655281i	$-0.227450\pi$
$251$	1.58594	+	1.58594i	0.100104	+	0.100104i	−0.655281	+	0.755385i	$0.727450\pi$
$252$	−0.924542	+	4.64799i	−0.0582407	+	0.292796i
$253$	−7.32240	+	17.6778i	−0.460355	+	1.11140i
$254$	−21.3408			−1.33904
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	2.51235	−	6.06534i	0.156716	−	0.378345i	−0.825947	−	0.563748i	$-0.809359\pi$
$257$	2.51235	−	6.06534i	0.156716	−	0.378345i	0.982663	+	0.185403i	$0.0593589\pi$
$258$	−1.05875	+	5.32271i	−0.0659151	+	0.331378i
$259$	−2.78267	−	2.78267i	−0.172907	−	0.172907i
$260$		0			0
$261$	−1.02787	−	0.686803i	−0.0636238	−	0.0425120i
$262$	−10.7356	−	7.17330i	−0.663248	−	0.443168i
$263$	−4.74347	+	1.96481i	−0.292495	+	0.121155i	−0.524106	−	0.851653i	$-0.675600\pi$
$263$	−4.74347	+	1.96481i	−0.292495	+	0.121155i	0.231611	+	0.972808i	$0.425600\pi$
$264$	−7.76261	−	3.21538i	−0.477756	−	0.197893i
$265$		0			0
$266$	−8.71662	+	13.0453i	−0.534450	+	0.799861i
$267$	−29.2484	+	19.5432i	−1.78997	+	1.19602i
$268$	−1.39040			−0.0849325
$269$	−22.7608	+	15.2083i	−1.38775	+	0.927266i	−0.387767	+	0.921757i	$0.626754\pi$
$269$	−22.7608	+	15.2083i	−1.38775	+	0.927266i	−0.999985	+	0.00550888i	$0.998246\pi$
$270$		0			0
$271$			17.4427i			1.05957i	0.848132	+	0.529785i	$0.177727\pi$
$271$			17.4427i			1.05957i	−0.848132	+	0.529785i	$0.822273\pi$
$272$	−2.98843	−	2.84065i	−0.181200	−	0.172240i
$273$	6.81819	−	6.81819i	0.412656	−	0.412656i
$274$	−1.98803	+	0.823469i	−0.120101	+	0.0497476i
$275$		0			0
$276$	8.09156	−	8.09156i	0.487055	−	0.487055i
$277$	−12.6377	−	18.9137i	−0.759327	−	1.13641i	−0.986692	−	0.162603i	$-0.948011\pi$
$277$	−12.6377	−	18.9137i	−0.759327	−	1.13641i	0.227365	−	0.973810i	$-0.426989\pi$
$278$	−19.1022	+	3.79967i	−1.14568	+	0.227889i
$279$	−1.74945	−	8.79506i	−0.104737	−	0.526546i
$280$		0			0
$281$	−3.35617	+	8.10250i	−0.200212	+	0.483355i	−0.991815	−	0.127681i	$-0.959247\pi$
$281$	−3.35617	+	8.10250i	−0.200212	+	0.483355i	0.791603	+	0.611035i	$0.209247\pi$
$282$	13.2161	−	19.7792i	0.787005	−	1.17784i
$283$	4.18603	+	21.0446i	0.248834	+	1.25097i	0.879869	+	0.475216i	$0.157630\pi$
$283$	4.18603	+	21.0446i	0.248834	+	1.25097i	−0.631035	+	0.775754i	$0.717370\pi$
$284$	−8.35023	−	1.66096i	−0.495495	−	0.0985600i
$285$		0			0
$286$	3.82736	+	5.72804i	0.226316	+	0.338706i
$287$	7.47300	+	3.09542i	0.441117	+	0.182717i
$288$	1.43181	+	1.43181i	0.0843701	+	0.0843701i
$289$	−0.861383	−	16.9782i	−0.0506696	−	0.998715i
$290$		0			0
$291$	−9.65227	−	23.3026i	−0.565826	−	1.36603i
$292$	4.50836	+	0.896768i	0.263832	+	0.0524794i
$293$		−	30.1287i		−	1.76014i	−0.474847	−	0.880068i	$-0.657497\pi$
$293$		−	30.1287i		−	1.76014i	0.474847	−	0.880068i	$-0.342503\pi$
$294$	0.665823	−	3.34732i	0.0388316	−	0.195219i
$295$		0			0
$296$	−1.64915	+	0.328036i	−0.0958549	+	0.0190667i
$297$	−3.13537	−	7.56945i	−0.181933	−	0.439224i
$298$	−7.28713	−	17.5927i	−0.422132	−	1.01912i
$299$	−9.20213	+	1.83042i	−0.532173	+	0.105856i
$300$		0			0
$301$	−1.10541	+	5.55726i	−0.0637146	+	0.320315i
$302$		−	5.59924i		−	0.322200i
$303$	36.0801	+	7.17677i	2.07275	+	0.412295i
$304$	2.56542	+	6.19346i	0.147137	+	0.355219i
$305$		0			0
$306$	0.211583	+	8.34613i	0.0120954	+	0.477116i
$307$	3.26677	+	3.26677i	0.186445	+	0.186445i	0.794157	−	0.607713i	$-0.207913\pi$
$307$	3.26677	+	3.26677i	0.186445	+	0.186445i	−0.607713	+	0.794157i	$0.707913\pi$
$308$	−8.10467	−	3.35707i	−0.461807	−	0.191287i
$309$	19.7930	+	29.6223i	1.12598	+	1.68515i
$310$		0			0
$311$	21.3083	+	4.23849i	1.20828	+	0.240343i	0.757827	−	0.652455i	$-0.226261\pi$
$311$	21.3083	+	4.23849i	1.20828	+	0.240343i	0.450457	+	0.892798i	$0.351261\pi$
$312$	−0.803765	−	4.04080i	−0.0455042	−	0.228765i
$313$	−11.6411	+	17.4221i	−0.657993	+	0.984757i	0.341007	+	0.940061i	$0.389232\pi$
$313$	−11.6411	+	17.4221i	−0.657993	+	0.984757i	−0.999001	+	0.0446961i	$0.985768\pi$
$314$	−0.933309	+	2.25321i	−0.0526697	+	0.127156i
$315$		0			0
$316$	1.00579	+	5.05643i	0.0565799	+	0.284446i
$317$	5.61256	−	1.11641i	0.315233	−	0.0627037i	−0.0349384	−	0.999389i	$-0.511123\pi$
$317$	5.61256	−	1.11641i	0.315233	−	0.0627037i	0.350171	+	0.936686i	$0.386123\pi$
$318$	2.38455	+	3.56873i	0.133719	+	0.200124i
$319$	1.61811	−	1.61811i	0.0905967	−	0.0905967i
$320$		0			0
$321$	−1.65949	+	0.687384i	−0.0926238	+	0.0383660i
$322$	8.44812	−	8.44812i	0.470795	−	0.470795i
$323$	−9.92692	+	25.7962i	−0.552349	+	1.43534i
$324$			10.9745i			0.609694i
$325$		0			0
$326$	5.99898	−	4.00839i	0.332253	−	0.222004i
$327$	31.1889			1.72475
$328$	2.87366	−	1.92012i	0.158671	−	0.106021i
$329$	13.7984	−	20.6508i	0.760732	−	1.13852i
$330$		0			0
$331$	−27.3797	−	11.3411i	−1.50493	−	0.623361i	−0.530423	−	0.847733i	$-0.677967\pi$
$331$	−27.3797	−	11.3411i	−1.50493	−	0.623361i	−0.974503	+	0.224372i	$0.927967\pi$
$332$	12.9133	−	5.34887i	0.708710	−	0.293557i
$333$	2.83095	+	1.89158i	0.155135	+	0.103658i
$334$	−12.7964	−	8.55028i	−0.700188	−	0.467851i
$335$		0			0
$336$	3.70970	+	3.70970i	0.202381	+	0.202381i
$337$	−6.41803	+	32.2656i	−0.349612	+	1.75762i	0.260662	+	0.965430i	$0.416059\pi$
$337$	−6.41803	+	32.2656i	−0.349612	+	1.75762i	−0.610275	+	0.792190i	$0.708941\pi$
$338$	3.68218	−	8.88956i	0.200284	−	0.483528i
$339$	0.328614			0.0178479
$340$		0			0
$341$	16.5995			0.898912
$342$	5.19467	−	12.5410i	0.280895	−	0.678142i
$343$	3.89129	−	19.5629i	0.210110	−	1.05629i
$344$	1.71191	+	1.71191i	0.0923000	+	0.0923000i
$345$		0			0
$346$	2.52491	+	1.68709i	0.135740	+	0.0906985i
$347$	−16.3048	−	10.8945i	−0.875290	−	0.584850i	0.0347382	−	0.999396i	$-0.488940\pi$
$347$	−16.3048	−	10.8945i	−0.875290	−	0.584850i	−0.910028	+	0.414546i	$0.863940\pi$
$348$	−1.26436	+	0.523716i	−0.0677770	+	0.0280741i
$349$	8.38547	+	3.47337i	0.448864	+	0.185925i	0.595652	−	0.803242i	$-0.296894\pi$
$349$	8.38547	+	3.47337i	0.448864	+	0.185925i	−0.146788	+	0.989168i	$0.546894\pi$
$350$		0			0
$351$	2.23197	−	3.34038i	0.119134	−	0.178297i
$352$	−3.11656	+	2.08242i	−0.166113	+	0.110993i
$353$	30.7498			1.63665			0.818323	−	0.574759i	$-0.194904\pi$
$353$	30.7498			1.63665			0.818323	+	0.574759i	$0.194904\pi$
$354$	23.6787	−	15.8216i	1.25851	−	0.840907i
$355$		0			0
$356$			15.6925i			0.831702i
$357$	0.548195	+	21.6241i	0.0290136	+	1.14447i
$358$	9.69278	−	9.69278i	0.512279	−	0.512279i
$359$	−14.0992	+	5.84010i	−0.744129	+	0.308228i	−0.722344	−	0.691534i	$-0.756935\pi$
$359$	−14.0992	+	5.84010i	−0.744129	+	0.308228i	−0.0217856	+	0.999763i	$0.506935\pi$
$360$		0			0
$361$	18.3426	−	18.3426i	0.965399	−	0.965399i
$362$	5.41668	+	8.10663i	0.284694	+	0.426075i
$363$	−6.70433	+	1.33357i	−0.351886	+	0.0699945i
$364$	−0.839184	−	4.21886i	−0.0439852	−	0.221128i
$365$		0			0
$366$	5.68608	−	13.7274i	0.297216	−	0.717543i
$367$	−18.3527	+	27.4667i	−0.958003	+	1.43375i	−0.0577767	+	0.998330i	$0.518401\pi$
$367$	−18.3527	+	27.4667i	−0.958003	+	1.43375i	−0.900226	+	0.435423i	$0.856599\pi$
$368$	−0.995910	−	5.00678i	−0.0519154	−	0.260996i
$369$	−6.86377	−	1.36529i	−0.357313	−	0.0710741i
$370$		0			0
$371$	2.48963	+	3.72599i	0.129255	+	0.193444i
$372$	−9.17156	−	3.79898i	−0.475523	−	0.196968i
$373$	−2.61742	−	2.61742i	−0.135525	−	0.135525i	0.636090	−	0.771615i	$-0.280551\pi$
$373$	−2.61742	−	2.61742i	−0.135525	−	0.135525i	−0.771615	+	0.636090i	$0.780551\pi$
$374$	−15.2290	−	2.62991i	−0.787475	−	0.135989i
$375$		0			0
$376$	−4.06106	−	9.80427i	−0.209433	−	0.505617i
$377$	1.10052	+	0.218907i	0.0566796	+	0.0112743i
$378$			5.11576i			0.263126i
$379$	1.01649	−	5.11024i	0.0522136	−	0.262495i	−0.945857	−	0.324583i	$-0.894776\pi$
$379$	1.01649	−	5.11024i	0.0522136	−	0.262495i	0.998071	+	0.0620880i	$0.0197759\pi$
$380$		0			0
$381$	46.9188	−	9.33274i	2.40373	−	0.478131i
$382$	−7.05974	−	17.0437i	−0.361208	−	0.872033i
$383$	−0.781961	−	1.88782i	−0.0399564	−	0.0964632i	0.902642	−	0.430393i	$-0.141625\pi$
$383$	−0.781961	−	1.88782i	−0.0399564	−	0.0964632i	−0.942598	+	0.333930i	$0.891625\pi$
$384$	2.19855	−	0.437319i	0.112194	−	0.0223169i
$385$		0			0
$386$	−4.06249	+	20.4235i	−0.206775	+	1.03953i
$387$		−	4.90226i		−	0.249196i
$388$	−11.0357	−	2.19514i	−0.560254	−	0.111441i
$389$	−1.19281	−	2.87969i	−0.0604777	−	0.146006i	0.890752	−	0.454490i	$-0.150178\pi$
$389$	−1.19281	−	2.87969i	−0.0604777	−	0.146006i	−0.951230	+	0.308484i	$0.900178\pi$
$390$		0			0
$391$	11.2463	−	17.7914i	0.568750	−	0.899750i
$392$	−1.07658	−	1.07658i	−0.0543753	−	0.0543753i
$393$	26.7398	+	11.0760i	1.34885	+	0.558710i
$394$	2.35217	+	3.52027i	0.118500	+	0.177348i
$395$		0			0
$396$	7.44395	+	1.48069i	0.374072	+	0.0744076i
$397$	1.62321	+	8.16045i	0.0814668	+	0.409561i	0.999902	+	0.0139900i	$0.00445331\pi$
$397$	1.62321	+	8.16045i	0.0814668	+	0.409561i	−0.918435	+	0.395571i	$0.870547\pi$
$398$	−14.6373	+	21.9062i	−0.733700	+	1.09806i
$399$	13.4590	−	32.4928i	0.673791	−	1.62668i
$400$		0			0
$401$	3.90028	+	19.6080i	0.194771	+	0.979178i	0.947234	+	0.320544i	$0.103866\pi$
$401$	3.90028	+	19.6080i	0.194771	+	0.979178i	−0.752463	+	0.658635i	$0.771134\pi$
$402$	3.05688	−	0.608051i	0.152463	−	0.0303268i
$403$	4.52204	+	6.76771i	0.225259	+	0.337124i
$404$	11.6042	−	11.6042i	0.577331	−	0.577331i
$405$		0			0
$406$	−1.32008	+	0.546794i	−0.0655144	+	0.0271369i
$407$	−4.45657	+	4.45657i	−0.220904	+	0.220904i
$408$	7.81249	+	4.93843i	0.386776	+	0.244489i
$409$		−	30.7813i		−	1.52203i	−0.648731	−	0.761017i	$-0.724700\pi$
$409$		−	30.7813i		−	1.52203i	0.648731	−	0.761017i	$-0.275300\pi$
$410$		0			0
$411$	4.01067	−	2.67985i	0.197832	−	0.132187i
$412$	15.8931			0.782997
$413$	24.7221	−	16.5188i	1.21649	−	0.812835i
$414$	−5.74279	+	8.59470i	−0.282243	+	0.422406i
$415$		0			0
$416$	−1.69803	−	0.703348i	−0.0832529	−	0.0344845i
$417$	40.3356	−	16.7076i	1.97524	−	0.818173i
$418$	20.8927	+	13.9600i	1.02189	+	0.682808i
$419$	−12.4734	−	8.33444i	−0.609364	−	0.407164i	0.212244	−	0.977217i	$-0.431923\pi$
$419$	−12.4734	−	8.33444i	−0.609364	−	0.407164i	−0.821608	+	0.570053i	$0.806923\pi$
$420$		0			0
$421$	9.43644	+	9.43644i	0.459904	+	0.459904i	0.898624	−	0.438720i	$-0.144568\pi$
$421$	9.43644	+	9.43644i	0.459904	+	0.459904i	−0.438720	+	0.898624i	$0.644568\pi$
$422$	−4.33527	+	21.7949i	−0.211038	+	1.06096i
$423$	−8.22318	+	19.8525i	−0.399825	+	0.965262i
$424$	1.91472			0.0929868
$425$		0			0
$426$	19.0848			0.924661
$427$	5.93664	−	14.3323i	0.287294	−	0.693589i
$428$	−0.156326	+	0.785906i	−0.00755632	+	0.0379882i
$429$	−10.9196	−	10.9196i	−0.527205	−	0.527205i
$430$		0			0
$431$	−0.709006	−	0.473743i	−0.0341516	−	0.0228194i	0.538377	−	0.842704i	$-0.319038\pi$
$431$	−0.709006	−	0.473743i	−0.0341516	−	0.0228194i	−0.572529	+	0.819885i	$0.694038\pi$
$432$	1.81746	+	1.21439i	0.0874428	+	0.0584274i
$433$	8.69207	−	3.60038i	0.417714	−	0.173023i	−0.163919	−	0.986474i	$-0.552414\pi$
$433$	8.69207	−	3.60038i	0.417714	−	0.173023i	0.581634	+	0.813451i	$0.302414\pi$
$434$	−9.57571	−	3.96639i	−0.459649	−	0.190393i
$435$		0			0
$436$	7.72993	−	11.5687i	0.370197	−	0.554038i
$437$	−28.4544	+	19.0126i	−1.36116	+	0.909496i
$438$	−10.3040			−0.492346
$439$	−21.0410	+	14.0592i	−1.00423	+	0.671007i	−0.944944	−	0.327233i	$-0.893884\pi$
$439$	−21.0410	+	14.0592i	−1.00423	+	0.671007i	−0.0592901	+	0.998241i	$0.518884\pi$
$440$		0			0
$441$			3.08290i			0.146805i
$442$	−3.07648	−	6.92542i	−0.146333	−	0.329409i
$443$	15.8653	−	15.8653i	0.753785	−	0.753785i	−0.221398	−	0.975184i	$-0.571062\pi$
$443$	15.8653	−	15.8653i	0.753785	−	0.753785i	0.975184	+	0.221398i	$0.0710620\pi$
$444$	3.48229	−	1.44241i	0.165262	−	0.0684538i
$445$		0			0
$446$	9.10058	−	9.10058i	0.430925	−	0.430925i
$447$	23.7147	+	35.4916i	1.12167	+	1.67870i
$448$	2.29543	−	0.456590i	0.108449	−	0.0215719i
$449$	−4.30949	−	21.6653i	−0.203378	−	1.02245i	−0.938701	−	0.344732i	$-0.887970\pi$
$449$	−4.30949	−	21.6653i	−0.203378	−	1.02245i	0.735324	−	0.677716i	$-0.237030\pi$
$450$		0			0
$451$	4.95744	−	11.9683i	0.233437	−	0.563566i
$452$	0.0814446	−	0.121890i	0.00383083	−	0.00573325i
$453$	2.44866	+	12.3102i	0.115048	+	0.578385i
$454$	25.0933	+	4.99137i	1.17769	+	0.234257i
$455$		0			0
$456$	−8.34872	−	12.4947i	−0.390965	−	0.585120i
$457$	−12.0290	−	4.98260i	−0.562695	−	0.233076i	0.0831596	−	0.996536i	$-0.473499\pi$
$457$	−12.0290	−	4.98260i	−0.562695	−	0.233076i	−0.645855	+	0.763460i	$0.723499\pi$
$458$	8.83647	+	8.83647i	0.412901	+	0.412901i
$459$	1.98170	+	8.79191i	0.0924976	+	0.410371i
$460$		0			0
$461$	−1.87457	−	4.52561i	−0.0873073	−	0.210779i	0.874195	−	0.485575i	$-0.161390\pi$
$461$	−1.87457	−	4.52561i	−0.0873073	−	0.210779i	−0.961503	+	0.274796i	$0.911390\pi$
$462$	19.2867	+	3.83636i	0.897297	+	0.178483i
$463$		−	5.65812i		−	0.262955i	−0.991319	−	0.131478i	$-0.958028\pi$
$463$		−	5.65812i		−	0.262955i	0.991319	−	0.131478i	$-0.0419722\pi$
$464$	−0.119105	+	0.598780i	−0.00552930	+	0.0277977i
$465$		0			0
$466$	6.94554	−	1.38155i	0.321746	−	0.0639992i
$467$	10.5662	+	25.5090i	0.488944	+	1.18042i	0.955252	+	0.295793i	$0.0955839\pi$
$467$	10.5662	+	25.5090i	0.488944	+	1.18042i	−0.466308	+	0.884622i	$0.654416\pi$
$468$	1.42420	+	3.43832i	0.0658335	+	0.158936i
$469$	3.19158	−	0.634845i	0.147373	−	0.0293144i
$470$		0			0
$471$	1.06656	−	5.36195i	0.0491444	−	0.247066i
$472$		−	12.7042i		−	0.584759i
$473$	8.90019	+	1.77036i	0.409231	+	0.0814011i
$474$	−4.42255	−	10.6770i	−0.203134	−	0.490409i
$475$		0			0
$476$	8.15675	+	5.15604i	0.373864	+	0.236327i
$477$	−2.74151	−	2.74151i	−0.125525	−	0.125525i
$478$	−18.1175	−	7.50450i	−0.828673	−	0.343248i
$479$	1.20322	+	1.80075i	0.0549767	+	0.0822784i	0.857940	−	0.513751i	$-0.171744\pi$
$479$	1.20322	+	1.80075i	0.0549767	+	0.0822784i	−0.802963	+	0.596029i	$0.796744\pi$
$480$		0			0
$481$	−3.03103	−	0.602910i	−0.138203	−	0.0274903i
$482$	−0.924362	−	4.64708i	−0.0421035	−	0.211669i
$483$	−14.8791	+	22.2682i	−0.677023	+	1.01324i
$484$	−1.16697	+	2.81731i	−0.0530439	+	0.128059i
$485$		0			0
$486$	−3.52005	−	17.6965i	−0.159673	−	0.802728i
$487$	34.1092	−	6.78474i	1.54564	−	0.307446i	0.652695	−	0.757620i	$-0.273638\pi$
$487$	34.1092	−	6.78474i	1.54564	−	0.307446i	0.892941	+	0.450174i	$0.148638\pi$
$488$	−3.68255	−	5.51133i	−0.166701	−	0.249486i
$489$	−11.4361	+	11.4361i	−0.517159	+	0.517159i
$490$		0			0
$491$	1.19271	−	0.494037i	0.0538263	−	0.0222956i	−0.355608	−	0.934635i	$-0.615726\pi$
$491$	1.19271	−	0.494037i	0.0538263	−	0.0222956i	0.409434	+	0.912340i	$0.365726\pi$
$492$	−5.47818	+	5.47818i	−0.246976	+	0.246976i
$493$	−2.05686	+	1.45107i	−0.0926364	+	0.0653531i
$494$			12.3211i			0.554351i
$495$		0			0
$496$	−3.68223	+	2.46039i	−0.165337	+	0.110475i
$497$	19.9258			0.893793
$498$	−26.0514	+	17.4070i	−1.16739	+	0.780026i
$499$	6.25854	−	9.36656i	0.280171	−	0.419305i	−0.664519	−	0.747272i	$-0.731363\pi$
$499$	6.25854	−	9.36656i	0.280171	−	0.419305i	0.944689	+	0.327967i	$0.106363\pi$
$500$		0			0
$501$	31.8728	+	13.2021i	1.42397	+	0.589828i
$502$	−2.07213	+	0.858306i	−0.0924839	+	0.0383081i
$503$	−2.04917	−	1.36921i	−0.0913680	−	0.0610501i	0.509047	−	0.860739i	$-0.329998\pi$
$503$	−2.04917	−	1.36921i	−0.0913680	−	0.0610501i	−0.600415	+	0.799689i	$0.704998\pi$
$504$	−3.94037	−	2.63287i	−0.175518	−	0.117277i
$505$		0			0
$506$	−13.5300	−	13.5300i	−0.601483	−	0.601483i
$507$	−4.20788	+	21.1545i	−0.186879	+	0.939502i
$508$	8.16676	−	19.7163i	0.362342	−	0.874770i
$509$	0.909764			0.0403246			0.0201623	−	0.999797i	$-0.493582\pi$
$509$	0.909764			0.0403246			0.0201623	+	0.999797i	$0.493582\pi$
$510$		0			0
$511$	−10.7581			−0.475910
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	2.85873	−	14.3718i	0.126216	−	0.634531i
$514$	4.64221	+	4.64221i	0.204759	+	0.204759i
$515$		0			0
$516$	−4.51238	−	3.01507i	−0.198646	−	0.132731i
$517$	−33.0732	−	22.0988i	−1.45456	−	0.971904i
$518$	3.63574	−	1.50597i	0.159745	−	0.0661686i
$519$	−6.28894	−	2.60496i	−0.276054	−	0.114345i
$520$		0			0
$521$	−11.4721	+	17.1692i	−0.502603	+	0.752198i	−0.992848	−	0.119386i	$-0.961907\pi$
$521$	−11.4721	+	17.1692i	−0.502603	+	0.752198i	0.490245	+	0.871585i	$0.336907\pi$
$522$	1.02787	−	0.686803i	0.0449888	−	0.0300606i
$523$	−36.0415			−1.57599			−0.787993	−	0.615684i	$-0.788880\pi$
$523$	−36.0415			−1.57599			−0.787993	+	0.615684i	$0.788880\pi$
$524$	10.7356	−	7.17330i	0.468987	−	0.313367i
$525$		0			0
$526$		−	5.13429i		−	0.223866i
$527$	−17.9932	−	3.10725i	−0.783796	−	0.135354i
$528$	5.94124	−	5.94124i	0.258559	−	0.258559i
$529$	2.82674	−	1.17087i	0.122902	−	0.0509075i
$530$		0			0
$531$	−18.1900	+	18.1900i	−0.789379	+	0.789379i
$532$	−8.71662	−	13.0453i	−0.377913	−	0.565587i
$533$	6.23007	−	1.23924i	0.269854	−	0.0536774i
$534$	−6.86264	−	34.5008i	−0.296976	−	1.49300i
$535$		0			0
$536$	0.532085	−	1.28457i	0.0229826	−	0.0554848i
$537$	−17.0712	+	25.5489i	−0.736678	+	1.10252i
$538$	−5.34044	−	26.8482i	−0.230243	−	1.15751i
$539$	−5.59710	−	1.11333i	−0.241084	−	0.0479546i
$540$		0			0
$541$	23.7268	+	35.5096i	1.02009	+	1.52668i	0.839677	+	0.543086i	$0.182744\pi$
$541$	23.7268	+	35.5096i	1.02009	+	1.52668i	0.180416	+	0.983590i	$0.442256\pi$
$542$	−16.1150	−	6.67504i	−0.692197	−	0.286717i
$543$	−15.4540	−	15.4540i	−0.663196	−	0.663196i
$544$	3.76804	−	1.67388i	0.161553	−	0.0717668i
$545$		0			0
$546$	3.68998	+	8.90840i	0.157917	+	0.381244i
$547$	16.4468	+	3.27148i	0.703216	+	0.139878i	0.533731	−	0.845655i	$-0.320790\pi$
$547$	16.4468	+	3.27148i	0.703216	+	0.139878i	0.169485	+	0.985533i	$0.445790\pi$
$548$		−	2.15183i		−	0.0919216i
$549$	−2.61846	+	13.1639i	−0.111753	+	0.561821i
$550$		0			0
$551$	4.01407	−	0.798449i	0.171005	−	0.0340151i
$552$	4.37912	+	10.5721i	0.186388	+	0.449980i
$553$	−4.61743	−	11.1475i	−0.196353	−	0.474038i
$554$	22.3102	−	4.43778i	0.947870	−	0.188543i
$555$		0			0
$556$	3.79967	−	19.1022i	0.161142	−	0.810116i
$557$		−	27.0952i		−	1.14806i	−0.818835	−	0.574029i	$-0.805379\pi$
$557$		−	27.0952i		−	1.14806i	0.818835	−	0.574029i	$-0.194621\pi$
$558$	8.79506	+	1.74945i	0.372325	+	0.0740600i
$559$	1.70281	+	4.11095i	0.0720212	+	0.173874i
$560$		0			0
$561$	34.6320	−	0.877958i	1.46216	−	0.0370674i
$562$	−6.20139	−	6.20139i	−0.261590	−	0.261590i
$563$	−14.8543	−	6.15287i	−0.626036	−	0.259313i	0.0470317	−	0.998893i	$-0.485024\pi$
$563$	−14.8543	−	6.15287i	−0.626036	−	0.259313i	−0.673068	+	0.739581i	$0.735024\pi$
$564$	13.2161	+	19.7792i	0.556497	+	0.832856i
$565$		0			0
$566$	−21.0446	−	4.18603i	−0.884570	−	0.175952i
$567$	−5.01085	−	25.1912i	−0.210436	−	1.05793i
$568$	4.73002	−	7.07898i	0.198467	−	0.297027i
$569$	−8.22349	+	19.8533i	−0.344747	+	0.832292i	0.652476	+	0.757810i	$0.273730\pi$
$569$	−8.22349	+	19.8533i	−0.344747	+	0.832292i	−0.997222	+	0.0744822i	$0.976270\pi$
$570$		0			0
$571$	0.517900	+	2.60366i	0.0216735	+	0.108960i	0.990108	−	0.140309i	$-0.0448097\pi$
$571$	0.517900	+	2.60366i	0.0216735	+	0.108960i	−0.968434	+	0.249269i	$0.919810\pi$
$572$	−6.75669	+	1.34399i	−0.282511	+	0.0561950i
$573$	22.9748	+	34.3842i	0.959785	+	1.43642i
$574$	−5.71958	+	5.71958i	−0.238731	+	0.238731i
$575$		0			0
$576$	−1.87075	+	0.774889i	−0.0779478	+	0.0322871i
$577$	−13.7472	+	13.7472i	−0.572302	+	0.572302i	−0.932771	−	0.360469i	$-0.882617\pi$
$577$	−13.7472	+	13.7472i	−0.572302	+	0.572302i	0.360469	+	0.932771i	$0.382617\pi$
$578$	16.0154	+	5.70145i	0.666153	+	0.237149i
$579$		−	46.6788i		−	1.93990i
$580$		0			0
$581$	−27.1994	+	18.1741i	−1.12842	+	0.753987i
$582$	25.2226			1.04551
$583$	5.96733	−	3.98724i	0.247141	−	0.165135i
$584$	−2.55378	+	3.82200i	−0.105676	+	0.158155i
$585$		0			0
$586$	27.8353	+	11.5297i	1.14986	+	0.476289i
$587$	−34.6515	+	14.3531i	−1.43022	+	0.592416i	−0.957406	−	0.288746i	$-0.906762\pi$
$587$	−34.6515	+	14.3531i	−1.43022	+	0.592416i	−0.472814	+	0.881162i	$0.656762\pi$
$588$	2.83772	+	1.89610i	0.117026	+	0.0781940i
$589$	24.6848	+	16.4938i	1.01712	+	0.679617i
$590$		0			0
$591$	−6.71084	−	6.71084i	−0.276047	−	0.276047i
$592$	0.328036	−	1.64915i	0.0134822	−	0.0677797i
$593$	−12.9310	+	31.2183i	−0.531014	+	1.28198i	0.399838	+	0.916586i	$0.369066\pi$
$593$	−12.9310	+	31.2183i	−0.531014	+	1.28198i	−0.930852	+	0.365396i	$0.880934\pi$
$594$	8.19311			0.336168
$595$		0			0
$596$	19.0422			0.779998
$597$	22.6008	−	54.5632i	0.924989	−	2.23312i
$598$	1.83042	−	9.20213i	0.0748514	−	0.376303i
$599$	−9.94392	−	9.94392i	−0.406297	−	0.406297i	0.474148	−	0.880445i	$-0.342756\pi$
$599$	−9.94392	−	9.94392i	−0.406297	−	0.406297i	−0.880445	+	0.474148i	$0.842756\pi$
$600$		0			0
$601$	−11.0793	−	7.40292i	−0.451932	−	0.301972i	0.308694	−	0.951161i	$-0.400108\pi$
$601$	−11.0793	−	7.40292i	−0.451932	−	0.301972i	−0.760626	+	0.649190i	$0.775108\pi$
$602$	−4.71122	−	3.14793i	−0.192015	−	0.128300i
$603$	−2.60110	+	1.07741i	−0.105925	+	0.0438755i
$604$	5.17302	+	2.14274i	0.210487	+	0.0871867i
$605$		0			0
$606$	−20.4377	+	30.5872i	−0.830226	+	1.24252i
$607$	30.4622	−	20.3542i	1.23642	−	0.826152i	0.246693	−	0.969094i	$-0.420656\pi$
$607$	30.4622	−	20.3542i	1.23642	−	0.826152i	0.989731	+	0.142942i	$0.0456561\pi$
$608$	−6.70375			−0.271873
$609$	2.66314	−	1.77945i	0.107916	−	0.0721070i
$610$		0			0
$611$		−	19.5043i		−	0.789060i
$612$	−7.79178	−	2.99845i	−0.314964	−	0.121205i
$613$	−14.5991	+	14.5991i	−0.589652	+	0.589652i	−0.937537	−	0.347885i	$-0.886900\pi$
$613$	−14.5991	+	14.5991i	−0.589652	+	0.589652i	0.347885	+	0.937537i	$0.386900\pi$
$614$	−4.26824	+	1.76796i	−0.172252	+	0.0713493i
$615$		0			0
$616$	6.20305	−	6.20305i	0.249928	−	0.249928i
$617$	−12.4489	−	18.6311i	−0.501174	−	0.750060i	0.491501	−	0.870877i	$-0.336449\pi$
$617$	−12.4489	−	18.6311i	−0.501174	−	0.750060i	−0.992675	+	0.120817i	$0.961449\pi$
$618$	−34.9418	+	6.95036i	−1.40557	+	0.279585i
$619$	6.26244	+	31.4834i	0.251709	+	1.26543i	0.875264	+	0.483646i	$0.160688\pi$
$619$	6.26244	+	31.4834i	0.251709	+	1.26543i	−0.623555	+	0.781780i	$0.714312\pi$
$620$		0			0
$621$	−4.27015	+	10.3091i	−0.171355	+	0.413688i
$622$	−12.0702	+	18.0643i	−0.483971	+	0.724314i
$623$	−7.16505	−	36.0211i	−0.287062	−	1.44316i
$624$	4.04080	+	0.803765i	0.161761	+	0.0321764i
$625$		0			0
$626$	−11.6411	−	17.4221i	−0.465272	−	0.696328i
$627$	−52.0386	−	21.5551i	−2.07822	−	0.860828i
$628$	−1.72453	−	1.72453i	−0.0688163	−	0.0688163i
$629$	5.66498	−	3.99653i	0.225877	−	0.159352i
$630$		0			0
$631$	−10.6606	−	25.7369i	−0.424390	−	1.02457i	−0.981037	−	0.193819i	$-0.937912\pi$
$631$	−10.6606	−	25.7369i	−0.424390	−	1.02457i	0.556647	−	0.830749i	$-0.312088\pi$
$632$	−5.05643	−	1.00579i	−0.201134	−	0.0400080i
$633$		−	49.8131i		−	1.97989i
$634$	−1.11641	+	5.61256i	−0.0443382	+	0.222903i
$635$		0			0
$636$	−4.20960	+	0.837342i	−0.166922	+	0.0332028i
$637$	−1.07085	−	2.58527i	−0.0424288	−	0.102432i
$638$	0.875714	+	2.11416i	0.0346699	+	0.0837004i
$639$	−16.9082	+	3.36326i	−0.668879	+	0.133048i
$640$		0			0
$641$	−3.83093	+	19.2594i	−0.151313	+	0.760700i	0.828376	+	0.560173i	$0.189265\pi$
$641$	−3.83093	+	19.2594i	−0.151313	+	0.760700i	−0.979688	+	0.200527i	$0.935735\pi$
$642$		−	1.79622i		−	0.0708912i
$643$	9.58258	+	1.90609i	0.377900	+	0.0751690i	0.380386	−	0.924828i	$-0.375791\pi$
$643$	9.58258	+	1.90609i	0.377900	+	0.0751690i	−0.00248571	+	0.999997i	$0.500791\pi$
$644$	4.57209	+	11.0380i	0.180166	+	0.434958i
$645$		0			0
$646$	−20.0337	−	19.0430i	−0.788214	−	0.749238i
$647$	3.93429	+	3.93429i	0.154673	+	0.154673i	0.780201	−	0.625528i	$-0.215117\pi$
$647$	3.93429	+	3.93429i	0.154673	+	0.154673i	−0.625528	+	0.780201i	$0.715117\pi$
$648$	−10.1391	−	4.19976i	−0.398302	−	0.164982i
$649$	−26.4555	−	39.5935i	−1.03847	−	1.55418i
$650$		0			0
$651$	22.7873	+	4.53267i	0.893104	+	0.177649i
$652$	1.40756	+	7.07627i	0.0551242	+	0.277128i
$653$	1.42563	−	2.13360i	0.0557891	−	0.0834942i	−0.802526	−	0.596617i	$-0.796511\pi$
$653$	1.42563	−	2.13360i	0.0557891	−	0.0834942i	0.858315	+	0.513122i	$0.171511\pi$
$654$	−11.9355	+	28.8148i	−0.466714	+	1.12675i
$655$		0			0
$656$	0.674255	+	3.38971i	0.0263252	+	0.132346i
$657$	9.12889	−	1.81585i	0.356152	−	0.0708431i
$658$	13.7984	+	20.6508i	0.537919	+	0.805053i
$659$	−20.6837	+	20.6837i	−0.805724	+	0.805724i	−0.983984	−	0.178259i	$-0.942953\pi$
$659$	−20.6837	+	20.6837i	−0.805724	+	0.805724i	0.178259	+	0.983984i	$0.442953\pi$
$660$		0			0
$661$	20.8000	−	8.61565i	0.809027	−	0.335110i	0.0604611	−	0.998171i	$-0.480743\pi$
$661$	20.8000	−	8.61565i	0.809027	−	0.335110i	0.748566	+	0.663061i	$0.230743\pi$
$662$	20.9555	−	20.9555i	0.814460	−	0.814460i
$663$	9.79242	+	13.8805i	0.380306	+	0.539074i
$664$			13.9773i			0.542423i
$665$		0			0
$666$	−2.83095	+	1.89158i	−0.109697	+	0.0732973i
$667$	−3.11657			−0.120674
$668$	12.7964	−	8.55028i	0.495108	−	0.330820i
$669$	−16.0283	+	23.9880i	−0.619688	+	0.927429i
$670$		0			0
$671$	−22.9538	−	9.50778i	−0.886122	−	0.367044i
$672$	−4.84696	+	2.00768i	−0.186975	+	0.0774478i
$673$	−24.0812	−	16.0905i	−0.928260	−	0.620244i	−0.00317165	−	0.999995i	$-0.501010\pi$
$673$	−24.0812	−	16.0905i	−0.928260	−	0.620244i	−0.925089	+	0.379751i	$0.876010\pi$
$674$	−27.3535	−	18.2770i	−1.05362	−	0.704004i
$675$		0			0
$676$	6.80377	+	6.80377i	0.261684	+	0.261684i
$677$	−2.97809	+	14.9719i	−0.114457	+	0.575416i	0.880409	+	0.474216i	$0.157268\pi$
$677$	−2.97809	+	14.9719i	−0.114457	+	0.575416i	−0.994866	+	0.101200i	$0.967732\pi$
$678$	−0.125755	+	0.303600i	−0.00482960	+	0.0116597i
$679$	26.3341			1.01061
$680$		0			0
$681$	−57.3518			−2.19773
$682$	−6.35234	+	15.3359i	−0.243244	+	0.587242i
$683$	2.38725	−	12.0015i	0.0913457	−	0.459226i	−0.907856	−	0.419282i	$-0.862282\pi$
$683$	2.38725	−	12.0015i	0.0913457	−	0.459226i	0.999202	−	0.0399442i	$-0.0127180\pi$
$684$	9.59849	+	9.59849i	0.367008	+	0.367008i
$685$		0			0
$686$	16.5846	+	11.0815i	0.633203	+	0.423092i
$687$	−23.2918	−	15.5631i	−0.888638	−	0.593769i
$688$	−2.23672	+	0.926479i	−0.0852741	+	0.0353217i
$689$	3.25125	+	1.34671i	0.123863	+	0.0513056i
$690$		0			0
$691$	2.95856	−	4.42779i	0.112549	−	0.168441i	−0.770919	−	0.636933i	$-0.780203\pi$
$691$	2.95856	−	4.42779i	0.112549	−	0.168441i	0.883468	+	0.468492i	$0.155203\pi$
$692$	−2.52491	+	1.68709i	−0.0959826	+	0.0641335i
$693$	−17.7632			−0.674767
$694$	16.3048	−	10.8945i	0.618923	−	0.413551i
$695$		0			0
$696$		−	1.36854i		−	0.0518742i
$697$	−7.61403	+	12.0452i	−0.288402	+	0.456245i
$698$	−6.41796	+	6.41796i	−0.242923	+	0.242923i
$699$	−14.6659	+	6.07483i	−0.554717	+	0.229771i
$700$		0			0
$701$	20.0755	−	20.0755i	0.758242	−	0.758242i	−0.217760	−	0.976002i	$-0.569875\pi$
$701$	20.0755	−	20.0755i	0.758242	−	0.758242i	0.976002	+	0.217760i	$0.0698750\pi$
$702$	2.23197	+	3.34038i	0.0842404	+	0.126075i
$703$	−11.0555	+	2.19908i	−0.416966	+	0.0829397i
$704$	−0.731249	−	3.67624i	−0.0275600	−	0.138553i
$705$		0			0
$706$	−11.7674	+	28.4091i	−0.442873	+	1.06919i
$707$	−21.3383	+	31.9351i	−0.802510	+	1.20104i
$708$	5.55580	+	27.9309i	0.208800	+	1.04971i
$709$	4.13454	+	0.822411i	0.155276	+	0.0308863i	0.272116	−	0.962264i	$-0.412277\pi$
$709$	4.13454	+	0.822411i	0.155276	+	0.0308863i	−0.116840	+	0.993151i	$0.537277\pi$
$710$		0			0
$711$	5.79974	+	8.67993i	0.217507	+	0.325523i
$712$	−14.4980	−	6.00527i	−0.543335	−	0.225057i
$713$	−15.9858	−	15.9858i	−0.598672	−	0.598672i
$714$	−20.1879	−	7.76873i	−0.755512	−	0.290738i
$715$		0			0
$716$	5.24569	+	12.6642i	0.196041	+	0.473284i
$717$	43.1141	+	8.57592i	1.61012	+	0.320274i
$718$		−	15.2609i		−	0.569532i
$719$	−4.31495	+	21.6927i	−0.160921	+	0.809003i	0.813026	+	0.582227i	$0.197818\pi$
$719$	−4.31495	+	21.6927i	−0.160921	+	0.809003i	−0.973947	+	0.226776i	$0.927182\pi$
$720$		0			0
$721$	−36.4816	+	7.25664i	−1.35865	+	0.270251i
$722$	9.92693	+	23.9657i	0.369442	+	0.891913i
$723$	4.06452	+	9.81262i	0.151161	+	0.364935i
$724$	−9.56242	+	1.90208i	−0.355385	+	0.0706904i
$725$		0			0
$726$	1.33357	−	6.70433i	0.0494936	−	0.248821i
$727$		−	13.9898i		−	0.518853i	−0.965763	−	0.259427i	$-0.916466\pi$
$727$		−	13.9898i		−	0.518853i	0.965763	−	0.259427i	$-0.0835335\pi$
$728$	4.21886	+	0.839184i	0.156361	+	0.0311022i
$729$	2.87875	+	6.94991i	0.106620	+	0.257404i
$730$		0			0
$731$	−9.31607	−	3.58503i	−0.344567	−	0.132597i
$732$	10.5065	+	10.5065i	0.388332	+	0.388332i
$733$	−33.9907	−	14.0794i	−1.25548	−	0.520035i	−0.346958	−	0.937881i	$-0.612785\pi$
$733$	−33.9907	−	14.0794i	−1.25548	−	0.520035i	−0.908518	+	0.417845i	$0.862785\pi$
$734$	−18.3527	−	27.4667i	−0.677410	−	1.01382i
$735$		0			0
$736$	5.00678	+	0.995910i	0.184552	+	0.0367097i
$737$	−1.01673	−	5.11145i	−0.0374518	−	0.188283i
$738$	3.88801	−	5.81882i	0.143120	−	0.214194i
$739$	−9.20457	+	22.2218i	−0.338596	+	0.817442i	0.659255	+	0.751919i	$0.270872\pi$
$739$	−9.20457	+	22.2218i	−0.338596	+	0.817442i	−0.997851	+	0.0655233i	$0.979128\pi$
$740$		0			0
$741$	−5.38824	−	27.0885i	−0.197942	−	0.995122i
$742$	−4.39510	+	0.874240i	−0.161349	+	0.0320944i
$743$	3.30617	+	4.94803i	0.121292	+	0.181526i	0.887147	−	0.461487i	$-0.152684\pi$
$743$	3.30617	+	4.94803i	0.121292	+	0.181526i	−0.765855	+	0.643013i	$0.777684\pi$
$744$	7.01961	−	7.01961i	0.257351	−	0.257351i
$745$		0			0
$746$	3.41982	−	1.41654i	0.125209	−	0.0518631i
$747$	20.0128	−	20.0128i	0.732229	−	0.732229i
$748$	8.25763	−	13.0634i	0.301929	−	0.477645i
$749$		−	1.87537i		−	0.0685246i
$750$		0			0
$751$	−11.7286	+	7.83680i	−0.427983	+	0.285969i	−0.750847	−	0.660476i	$-0.770354\pi$
$751$	−11.7286	+	7.83680i	−0.427983	+	0.285969i	0.322864	+	0.946445i	$0.395354\pi$
$752$	10.6121			0.386982
$753$	4.18034	−	2.79322i	0.152340	−	0.101790i
$754$	−0.623394	+	0.932975i	−0.0227027	+	0.0339770i
$755$		0			0
$756$	−4.72635	−	1.95772i	−0.171896	−	0.0712015i
$757$	29.1438	−	12.0718i	1.05925	−	0.438755i	0.216064	−	0.976379i	$-0.430678\pi$
$757$	29.1438	−	12.0718i	1.05925	−	0.438755i	0.843185	+	0.537624i	$0.180678\pi$
$758$	4.33225	+	2.89472i	0.157354	+	0.105141i
$759$	35.6634	+	23.8295i	1.29450	+	0.864957i
$760$		0			0
$761$	−8.41792	−	8.41792i	−0.305149	−	0.305149i	0.537875	−	0.843024i	$-0.319227\pi$
$761$	−8.41792	−	8.41792i	−0.305149	−	0.305149i	−0.843024	+	0.537875i	$0.819227\pi$
$762$	−9.33274	+	46.9188i	−0.338089	+	1.69969i
$763$	−12.4614	+	30.0845i	−0.451133	+	1.08913i
$764$	18.4480			0.667425
$765$		0			0
$766$	2.04336			0.0738297
$767$	8.93548	−	21.5722i	0.322641	−	0.778925i
$768$	−0.437319	+	2.19855i	−0.0157804	+	0.0793334i
$769$	−7.10275	−	7.10275i	−0.256132	−	0.256132i	0.567347	−	0.823479i	$-0.307970\pi$
$769$	−7.10275	−	7.10275i	−0.256132	−	0.256132i	−0.823479	+	0.567347i	$0.807970\pi$
$770$		0			0
$771$	−12.2363	−	8.17601i	−0.440678	−	0.294452i
$772$	−17.3142	−	11.5690i	−0.623152	−	0.416377i
$773$	−1.12415	+	0.465637i	−0.0404328	+	0.0167478i	−0.402808	−	0.915284i	$-0.631966\pi$
$773$	−1.12415	+	0.465637i	−0.0404328	+	0.0167478i	0.362375	+	0.932032i	$0.381966\pi$
$774$	4.52909	+	1.87601i	0.162795	+	0.0674319i
$775$		0			0
$776$	6.25124	−	9.35564i	0.224406	−	0.335848i
$777$	−7.33477	+	4.90094i	−0.263133	+	0.175820i
$778$	3.11695			0.111748
$779$	19.2643	−	12.8720i	0.690215	−	0.461187i
$780$		0			0
$781$		−	31.9120i		−	1.14190i
$782$	12.1333	+	17.1987i	0.433888	+	0.615025i
$783$	0.943622	−	0.943622i	0.0337223	−	0.0337223i
$784$	1.40662	−	0.582639i	0.0502363	−	0.0208085i
$785$		0			0
$786$	−20.4658	+	20.4658i	−0.729990	+	0.729990i
$787$	3.54648	+	5.30768i	0.126418	+	0.189198i	0.889280	−	0.457364i	$-0.151206\pi$
$787$	3.54648	+	5.30768i	0.126418	+	0.189198i	−0.762862	+	0.646562i	$0.776206\pi$
$788$	−4.15244	+	0.825971i	−0.147924	+	0.0294240i
$789$	2.24532	+	11.2880i	0.0799357	+	0.401864i
$790$		0			0
$791$	−0.131297	+	0.316978i	−0.00466837	+	0.0112705i
$792$	−4.21666	+	6.31067i	−0.149832	+	0.224240i
$793$	−2.37671	−	11.9485i	−0.0843995	−	0.424305i
$794$	−8.16045	−	1.62321i	−0.289603	−	0.0576057i
$795$		0			0
$796$	−14.6373	−	21.9062i	−0.518804	−	0.776446i
$797$	3.16463	+	1.31083i	0.112097	+	0.0464320i	0.438027	−	0.898962i	$-0.355677\pi$
$797$	3.16463	+	1.31083i	0.112097	+	0.0464320i	−0.325930	+	0.945394i	$0.605677\pi$
$798$	24.8689	+	24.8689i	0.880350	+	0.880350i
$799$	31.7134	+	30.1452i	1.12194	+	1.06646i
$800$		0			0
$801$	12.1600	+	29.3568i	0.429651	+	1.03727i
$802$	−19.6080	−	3.90028i	−0.692384	−	0.137724i
$803$			17.2295i			0.608017i
$804$	−0.608051	+	3.05688i	−0.0214443	+	0.107808i
$805$		0			0
$806$	−7.98306	+	1.58793i	−0.281191	+	0.0559324i
$807$	23.4825	+	56.6918i	0.826623	+	1.99564i
$808$	6.28015	+	15.1616i	0.220935	+	0.533384i
$809$	27.1193	−	5.39436i	0.953464	−	0.189656i	0.306239	−	0.951955i	$-0.400929\pi$
$809$	27.1193	−	5.39436i	0.953464	−	0.189656i	0.647225	+	0.762299i	$0.275929\pi$
$810$		0			0
$811$	−7.20886	+	36.2414i	−0.253137	+	1.27261i	0.619794	+	0.784764i	$0.287216\pi$
$811$	−7.20886	+	36.2414i	−0.253137	+	1.27261i	−0.872932	+	0.487843i	$0.837784\pi$
$812$		−	1.42884i		−	0.0501425i
$813$	38.3487	+	7.62804i	1.34495	+	0.267527i
$814$	−2.41188	−	5.82279i	−0.0845363	−	0.204089i
$815$		0			0
$816$	−7.55222	+	5.32794i	−0.264381	+	0.186515i
$817$	11.4762	+	11.4762i	0.401502	+	0.401502i
$818$	28.4382	+	11.7795i	0.994317	+	0.411860i
$819$	−4.83905	−	7.24215i	−0.169090	−	0.253061i
$820$		0			0
$821$	−14.0812	−	2.80092i	−0.491436	−	0.0977528i	−0.0568496	−	0.998383i	$-0.518106\pi$
$821$	−14.0812	−	2.80092i	−0.491436	−	0.0977528i	−0.434587	+	0.900630i	$0.643106\pi$
$822$	0.941037	+	4.73091i	0.0328224	+	0.165009i
$823$	26.8104	−	40.1247i	0.934553	−	1.39866i	0.0175205	−	0.999847i	$-0.494423\pi$
$823$	26.8104	−	40.1247i	0.934553	−	1.39866i	0.917033	−	0.398812i	$-0.130577\pi$
$824$	−6.08203	+	14.6833i	−0.211878	+	0.511518i
$825$		0			0
$826$	5.80062	+	29.1617i	0.201829	+	1.01466i
$827$	23.6452	−	4.70333i	0.822225	−	0.163551i	0.233988	−	0.972239i	$-0.424822\pi$
$827$	23.6452	−	4.70333i	0.822225	−	0.163551i	0.588237	+	0.808689i	$0.299822\pi$
$828$	−5.74279	−	8.59470i	−0.199576	−	0.298686i
$829$	16.0770	−	16.0770i	0.558377	−	0.558377i	−0.370468	−	0.928845i	$-0.620803\pi$
$829$	16.0770	−	16.0770i	0.558377	−	0.558377i	0.928845	+	0.370468i	$0.120803\pi$
$830$		0			0
$831$	−47.1094	+	19.5134i	−1.63421	+	0.676911i
$832$	1.29962	−	1.29962i	0.0450561	−	0.0450561i
$833$	5.85864	+	2.25453i	0.202990	+	0.0781149i
$834$			43.6590i			1.51179i
$835$		0			0
$836$	−20.8927	+	13.9600i	−0.722588	+	0.482818i
$837$	9.68020			0.334597
$838$	12.4734	−	8.33444i	0.430885	−	0.287908i
$839$	12.5864	−	18.8368i	0.434530	−	0.650320i	−0.547988	−	0.836486i	$-0.684606\pi$
$839$	12.5864	−	18.8368i	0.434530	−	0.650320i	0.982518	+	0.186166i	$0.0596062\pi$
$840$		0			0
$841$	−26.4482	−	10.9552i	−0.912005	−	0.377765i
$842$	−12.3293	+	5.10697i	−0.424896	+	0.175998i
$843$	16.3461	+	10.9221i	0.562988	+	0.376177i
$844$	−18.4768	−	12.3458i	−0.635998	−	0.424960i
$845$		0			0
$846$	−15.1945	−	15.1945i	−0.522396	−	0.522396i
$847$	1.39234	−	6.99977i	0.0478414	−	0.240515i
$848$	−0.732730	+	1.76897i	−0.0251620	+	0.0607465i
$849$	48.0983			1.65073
$850$		0			0
$851$	8.58362			0.294243
$852$	−7.30343	+	17.6320i	−0.250211	+	0.604064i
$853$	−7.76738	+	39.0492i	−0.265950	+	1.33702i	0.584684	+	0.811261i	$0.301219\pi$
$853$	−7.76738	+	39.0492i	−0.265950	+	1.33702i	−0.850634	+	0.525759i	$0.823781\pi$
$854$	10.9695	+	10.9695i	0.375368	+	0.375368i
$855$		0			0
$856$	−0.666259	−	0.445180i	−0.0227723	−	0.0152159i
$857$	−10.1407	−	6.77577i	−0.346398	−	0.231456i	0.370184	−	0.928958i	$-0.379295\pi$
$857$	−10.1407	−	6.77577i	−0.346398	−	0.231456i	−0.716582	+	0.697502i	$0.754295\pi$
$858$	14.2672	−	5.90966i	0.487074	−	0.201752i
$859$	28.2759	+	11.7123i	0.964762	+	0.399617i	0.808760	−	0.588139i	$-0.200139\pi$
$859$	28.2759	+	11.7123i	0.964762	+	0.399617i	0.156002	+	0.987757i	$0.450139\pi$
$860$		0			0
$861$	10.0735	−	15.0761i	0.343305	−	0.513792i
$862$	0.709006	−	0.473743i	0.0241488	−	0.0161357i
$863$	32.7720			1.11557			0.557785	−	0.829985i	$-0.311651\pi$
$863$	32.7720			1.11557			0.557785	+	0.829985i	$0.311651\pi$
$864$	−1.81746	+	1.21439i	−0.0618314	+	0.0413144i
$865$		0			0
$866$			9.40823i			0.319705i
$867$	−37.7041	−	5.53108i	−1.28050	−	0.187845i
$868$	7.32893	−	7.32893i	0.248760	−	0.248760i
$869$	−17.8531	+	7.39501i	−0.605626	+	0.250859i
$870$		0			0
$871$	1.80699	−	1.80699i	0.0612276	−	0.0612276i
$872$	7.72993	+	11.5687i	0.261768	+	0.391764i
$873$	−22.3461	+	4.44491i	−0.756299	+	0.150437i
$874$	−6.67633	−	33.5642i	−0.225830	−	1.13533i
$875$		0			0
$876$	3.94318	−	9.51969i	0.133228	−	0.321640i
$877$	24.0243	−	35.9550i	0.811244	−	1.21411i	−0.162554	−	0.986700i	$-0.551973\pi$
$877$	24.0243	−	35.9550i	0.811244	−	1.21411i	0.973798	−	0.227413i	$-0.0730267\pi$
$878$	−4.93692	−	24.8196i	−0.166613	−	0.837621i
$879$	−66.2395	−	13.1759i	−2.23420	−	0.444411i
$880$		0			0
$881$	−15.1740	−	22.7095i	−0.511225	−	0.765103i	0.482626	−	0.875827i	$-0.339683\pi$
$881$	−15.1740	−	22.7095i	−0.511225	−	0.765103i	−0.993851	+	0.110724i	$0.964683\pi$
$882$	−2.84823	−	1.17978i	−0.0959049	−	0.0397251i
$883$	−4.46322	−	4.46322i	−0.150199	−	0.150199i	0.628008	−	0.778207i	$-0.283871\pi$
$883$	−4.46322	−	4.46322i	−0.150199	−	0.150199i	−0.778207	+	0.628008i	$0.783871\pi$
$884$	7.57557	−	0.192049i	0.254794	−	0.00645930i
$885$		0			0
$886$	8.58626	+	20.7291i	0.288461	+	0.696407i
$887$	32.0754	+	6.38020i	1.07699	+	0.214226i	0.701549	−	0.712621i	$-0.252492\pi$
$887$	32.0754	+	6.38020i	1.07699	+	0.214226i	0.375439	+	0.926847i	$0.377492\pi$
$888$			3.76920i			0.126486i
$889$	−9.74399	+	48.9864i	−0.326803	+	1.64295i
$890$		0			0
$891$	−40.3448	+	8.02509i	−1.35160	+	0.268851i
$892$	4.92520	+	11.8905i	0.164908	+	0.398123i
$893$	−27.2244	−	65.7255i	−0.911029	−	2.19942i
$894$	−41.8652	+	8.32751i	−1.40018	+	0.278514i
$895$		0			0
$896$	−0.456590	+	2.29543i	−0.0152536	+	0.0766851i
$897$			21.0319i			0.702233i
$898$	21.6653	+	4.30949i	0.722980	+	0.143810i
$899$	1.03466	+	2.49789i	0.0345079	+	0.0833093i
$900$		0			0
$901$	−7.21473	+	3.20499i	−0.240357	+	0.106774i
$902$	9.16016	+	9.16016i	0.305000	+	0.305000i
$903$	11.7345	+	4.86059i	0.390500	+	0.161750i
$904$	0.0814446	+	0.121890i	0.00270881	+	0.00405402i
$905$		0			0
$906$	−12.3102	−	2.44866i	−0.408980	−	0.0813511i
$907$	−9.55754	−	48.0490i	−0.317353	−	1.59544i	−0.729274	−	0.684221i	$-0.760142\pi$
$907$	−9.55754	−	48.0490i	−0.317353	−	1.59544i	0.411922	−	0.911219i	$-0.364858\pi$
$908$	−14.2142	+	21.2731i	−0.471716	+	0.705973i
$909$	12.7166	−	30.7005i	0.421782	−	1.01827i
$910$		0			0
$911$	3.36353	+	16.9096i	0.111439	+	0.560241i	0.995651	+	0.0931564i	$0.0296957\pi$
$911$	3.36353	+	16.9096i	0.111439	+	0.560241i	−0.884213	+	0.467085i	$0.845304\pi$
$912$	14.7386	−	2.93168i	0.488042	−	0.0970777i
$913$	29.1065	+	43.5610i	0.963285	+	1.44166i
$914$	9.20664	−	9.20664i	0.304528	−	0.304528i
$915$		0			0
$916$	−11.5454	+	4.78226i	−0.381471	+	0.158010i
$917$	−21.3676	+	21.3676i	−0.705620	+	0.705620i
$918$	−8.88102	−	1.53367i	−0.293117	−	0.0506186i
$919$		−	34.3332i		−	1.13255i	−0.824217	−	0.566274i	$-0.808385\pi$
$919$		−	34.3332i		−	1.13255i	0.824217	−	0.566274i	$-0.191615\pi$
$920$		0			0
$921$	8.61080	−	5.75355i	0.283735	−	0.189586i
$922$	4.89848			0.161323
$923$	13.0107	−	8.69348i	0.428253	−	0.286149i
$924$	−10.9250	+	16.3504i	−0.359407	+	0.537890i
$925$		0			0
$926$	5.22742	+	2.16527i	0.171784	+	0.0711552i
$927$	29.7320	−	12.3154i	0.976527	−	0.404491i
$928$	−0.507621	−	0.339182i	−0.0166635	−	0.0111342i
$929$	9.78051	+	6.53513i	0.320888	+	0.214411i	0.705573	−	0.708637i	$-0.250690\pi$
$929$	9.78051	+	6.53513i	0.320888	+	0.214411i	−0.384685	+	0.923048i	$0.625690\pi$
$930$		0			0
$931$	−7.21711	−	7.21711i	−0.236531	−	0.236531i
$932$	−1.38155	+	6.94554i	−0.0452543	+	0.227509i
$933$	18.6371	−	44.9939i	0.610151	−	1.47303i
$934$	−27.6107			−0.903451
$935$		0			0
$936$	−3.72161			−0.121645
$937$	8.46339	−	20.4324i	0.276487	−	0.667498i	−0.723246	−	0.690590i	$-0.757351\pi$
$937$	8.46339	−	20.4324i	0.276487	−	0.667498i	0.999733	+	0.0230916i	$0.00735093\pi$
$938$	−0.634845	+	3.19158i	−0.0207284	+	0.104209i
$939$	33.2126	+	33.2126i	1.08385	+	1.08385i
$940$		0			0
$941$	−6.14772	−	4.10778i	−0.200410	−	0.133910i	0.451316	−	0.892364i	$-0.350955\pi$
$941$	−6.14772	−	4.10778i	−0.200410	−	0.133910i	−0.651726	+	0.758455i	$0.725955\pi$
$942$	4.54564	+	3.03730i	0.148105	+	0.0989606i
$943$	−16.3000	+	6.75169i	−0.530802	+	0.219865i
$944$	11.7372	+	4.86169i	0.382012	+	0.158235i
$945$		0			0
$946$	−5.04155	+	7.54522i	−0.163915	+	0.245316i
$947$	−6.90636	+	4.61468i	−0.224427	+	0.149957i	−0.662701	−	0.748884i	$-0.730590\pi$
$947$	−6.90636	+	4.61468i	−0.224427	+	0.149957i	0.438274	+	0.898841i	$0.355590\pi$
$948$	11.5567			0.375343
$949$	−7.02459	+	4.69368i	−0.228028	+	0.152363i
$950$		0			0
$951$		−	12.8277i		−	0.415968i
$952$	−7.88502	+	5.56272i	−0.255555	+	0.180289i
$953$	−18.9533	+	18.9533i	−0.613958	+	0.613958i	−0.943975	−	0.330017i	$-0.892946\pi$
$953$	−18.9533	+	18.9533i	−0.613958	+	0.613958i	0.330017	+	0.943975i	$0.392946\pi$
$954$	3.58195	−	1.48369i	0.115970	−	0.0480363i
$955$		0			0
$956$	13.8665	−	13.8665i	0.448475	−	0.448475i
$957$	−2.84987	−	4.26513i	−0.0921231	−	0.137872i
$958$	−2.12413	+	0.422516i	−0.0686275	+	0.0136509i
$959$	0.982504	+	4.93938i	0.0317267	+	0.159501i
$960$		0			0
$961$	4.35786	−	10.5208i	0.140576	−	0.339381i
$962$	1.71694	−	2.56959i	0.0553564	−	0.0828468i
$963$	0.316543	+	1.59137i	0.0102004	+	0.0512811i
$964$	4.64708	+	0.924362i	0.149672	+	0.0297717i
$965$		0			0
$966$	−14.8791	−	22.2682i	−0.478728	−	0.716466i
$967$	−2.71453	−	1.12440i	−0.0872936	−	0.0361582i	0.338609	−	0.940927i	$-0.390043\pi$
$967$	−2.71453	−	1.12440i	−0.0872936	−	0.0361582i	−0.425903	+	0.904769i	$0.640043\pi$
$968$	−2.15627	−	2.15627i	−0.0693052	−	0.0693052i
$969$	52.3730	+	33.1060i	1.68246	+	1.06352i
$970$		0			0
$971$	21.5927	+	52.1293i	0.692941	+	1.67291i	0.738769	+	0.673959i	$0.235408\pi$
$971$	21.5927	+	52.1293i	0.692941	+	1.67291i	−0.0458273	+	0.998949i	$0.514592\pi$
$972$	17.6965	+	3.52005i	0.567615	+	0.112906i
$973$			45.5828i			1.46132i
$974$	−6.78474	+	34.1092i	−0.217397	+	1.09293i
$975$		0			0
$976$	6.50106	−	1.29314i	0.208094	−	0.0413924i
$977$	−0.198220	−	0.478546i	−0.00634163	−	0.0153100i	0.920677	−	0.390325i	$-0.127637\pi$
$977$	−0.198220	−	0.478546i	−0.00634163	−	0.0153100i	−0.927019	+	0.375015i	$0.877637\pi$
$978$	−6.18918	−	14.9420i	−0.197908	−	0.477793i
$979$	−57.6894	+	11.4751i	−1.84376	+	0.366747i
$980$		0			0
$981$	5.49632	−	27.6319i	0.175484	−	0.882218i
$982$			1.29098i			0.0411969i
$983$	18.9985	+	3.77904i	0.605958	+	0.120533i	0.488527	−	0.872549i	$-0.337534\pi$
$983$	18.9985	+	3.77904i	0.605958	+	0.120533i	0.117431	+	0.993081i	$0.462534\pi$
$984$	−2.96477	−	7.15759i	−0.0945135	−	0.228176i
$985$		0			0
$986$	−0.553491	−	2.45559i	−0.0176268	−	0.0782021i
$987$	−39.3676	−	39.3676i	−1.25308	−	1.25308i
$988$	−11.3832	−	4.71507i	−0.362147	−	0.150006i
$989$	−6.86624	−	10.2761i	−0.218334	−	0.326760i
$990$		0			0
$991$	17.3723	+	3.45556i	0.551848	+	0.109769i	0.463135	−	0.886288i	$-0.346725\pi$
$991$	17.3723	+	3.45556i	0.551848	+	0.109769i	0.0887133	+	0.996057i	$0.471725\pi$
$992$	−0.863974	−	4.34349i	−0.0274312	−	0.137906i
$993$	−36.9076	+	55.2361i	−1.17123	+	1.75287i
$994$	−7.62526	+	18.4090i	−0.241859	+	0.583898i
$995$		0			0
$996$	−6.11253	−	30.7297i	−0.193683	−	0.973709i
$997$	−39.3912	+	7.83540i	−1.24753	+	0.248150i	−0.774317	−	0.632798i	$-0.781907\pi$
$997$	−39.3912	+	7.83540i	−1.24753	+	0.248150i	−0.473215	+	0.880947i	$0.656907\pi$
$998$	6.25854	+	9.36656i	0.198110	+	0.296493i
$999$	−2.59891	+	2.59891i	−0.0822258	+	0.0822258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.a.607.3	yes	24
5.2	odd	4		850.2.s.a.743.1	yes	24
5.3	odd	4		850.2.s.b.743.3	yes	24
5.4	even	2		850.2.v.b.607.1	yes	24
17.10	odd	16		850.2.s.b.707.3	yes	24
85.27	even	16		850.2.v.b.843.1	yes	24
85.44	odd	16		850.2.s.a.707.1	✓	24
85.78	even	16	inner	850.2.v.a.843.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.s.a.707.1	✓	24	85.44	odd	16
850.2.s.a.743.1	yes	24	5.2	odd	4
850.2.s.b.707.3	yes	24	17.10	odd	16
850.2.s.b.743.3	yes	24	5.3	odd	4
850.2.v.a.607.3	yes	24	1.1	even	1	trivial
850.2.v.a.843.3	yes	24	85.78	even	16	inner
850.2.v.b.607.1	yes	24	5.4	even	2
850.2.v.b.843.1	yes	24	85.27	even	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(0.437319 - 2.19855i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.86384 + 1.24538i) q^{6} +(1.94597 + 1.30026i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-1.87075 - 0.774889i) q^{9} +(2.08242 - 3.11656i) q^{11} +(-1.86384 + 1.24538i) q^{12} +1.83794 q^{13} +(-1.94597 + 1.30026i) q^{14} +1.00000i q^{16} +(-2.84065 + 2.98843i) q^{17} +(1.43181 - 1.43181i) q^{18} +(6.19346 - 2.56542i) q^{19} +(3.70970 - 3.70970i) q^{21} +(2.08242 + 3.11656i) q^{22} +(-5.00678 + 0.995910i) q^{23} +(-0.437319 - 2.19855i) q^{24} +(-0.703348 + 1.69803i) q^{26} +(1.21439 - 1.81746i) q^{27} +(-0.456590 - 2.29543i) q^{28} +(0.598780 + 0.119105i) q^{29} +(2.46039 + 3.68223i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-5.94124 - 5.94124i) q^{33} +(-1.67388 - 3.76804i) q^{34} +(0.774889 + 1.87075i) q^{36} +(-1.64915 - 0.328036i) q^{37} +6.70375i q^{38} +(0.803765 - 4.04080i) q^{39} +(3.38971 - 0.674255i) q^{41} +(2.00768 + 4.84696i) q^{42} +(0.926479 + 2.23672i) q^{43} +(-3.67624 + 0.731249i) q^{44} +(0.995910 - 5.00678i) q^{46} -10.6121i q^{47} +(2.19855 + 0.437319i) q^{48} +(-0.582639 - 1.40662i) q^{49} +(5.32794 + 7.55222i) q^{51} +(-1.29962 - 1.29962i) q^{52} +(1.76897 + 0.732730i) q^{53} +(1.21439 + 1.81746i) q^{54} +(2.29543 + 0.456590i) q^{56} +(-2.93168 - 14.7386i) q^{57} +(-0.339182 + 0.507621i) q^{58} +(4.86169 - 11.7372i) q^{59} +(-1.29314 - 6.50106i) q^{61} +(-4.34349 + 0.863974i) q^{62} +(-2.63287 - 3.94037i) q^{63} +(0.707107 - 0.707107i) q^{64} +(7.76261 - 3.21538i) q^{66} +(0.983164 - 0.983164i) q^{67} +(4.12178 - 0.104492i) q^{68} +11.4432i q^{69} +(7.07898 - 4.73002i) q^{71} -2.02488 q^{72} +(-3.82200 + 2.55378i) q^{73} +(0.934169 - 1.39808i) q^{74} +(-6.19346 - 2.56542i) q^{76} +(8.10467 - 3.35707i) q^{77} +(3.42563 + 2.28893i) q^{78} +(-4.28663 - 2.86424i) q^{79} +(-7.76014 - 7.76014i) q^{81} +(-0.674255 + 3.38971i) q^{82} +(-5.34887 + 12.9133i) q^{83} -5.24631 q^{84} -2.42101 q^{86} +(0.523716 - 1.26436i) q^{87} +(0.731249 - 3.67624i) q^{88} +(-11.0963 - 11.0963i) q^{89} +(3.57658 + 2.38979i) q^{91} +(4.24454 + 2.83611i) q^{92} +(9.17156 - 3.79898i) q^{93} +(9.80427 + 4.06106i) q^{94} +(-1.24538 + 1.86384i) q^{96} +(9.35564 - 6.25124i) q^{97} +1.52251 q^{98} +(-6.31067 + 4.21666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Introduction

L-functions

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