LMFDB - Embedded newform 605.2.j.j.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.4
Root			$-0.833856 - 1.51812i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.j.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40079 - 0.780063i) q^{2} +(-0.465695 + 0.640974i) q^{3} +(3.53725 - 2.56996i) q^{4} +(2.23606 + 0.00508966i) q^{5} +(-0.618034 + 1.90211i) q^{6} +(-2.03615 - 2.80252i) q^{7} +(3.51992 - 4.84475i) q^{8} +(0.733075 + 2.25617i) q^{9} +O(q^{10})$	\(q+(2.40079 - 0.780063i) q^{2} +(-0.465695 + 0.640974i) q^{3} +(3.53725 - 2.56996i) q^{4} +(2.23606 + 0.00508966i) q^{5} +(-0.618034 + 1.90211i) q^{6} +(-2.03615 - 2.80252i) q^{7} +(3.51992 - 4.84475i) q^{8} +(0.733075 + 2.25617i) q^{9} +(5.37228 - 1.73205i) q^{10} +3.46410i q^{12} +(-7.07450 - 5.13992i) q^{14} +(-1.04458 + 1.43089i) q^{15} +(1.96914 - 6.06040i) q^{16} +(1.50702 + 0.489660i) q^{17} +(3.51992 + 4.84475i) q^{18} +(-3.23607 - 2.35114i) q^{19} +(7.92259 - 5.72859i) q^{20} +2.74456 q^{21} +0.792287i q^{23} +(1.46615 + 4.51235i) q^{24} +(4.99995 + 0.0227616i) q^{25} +(-4.04807 - 1.31530i) q^{27} +(-14.4047 - 4.68038i) q^{28} +(-7.07450 + 5.13992i) q^{29} +(-1.39164 + 4.25010i) q^{30} +(1.04209 + 3.20723i) q^{31} -4.10891i q^{32} +4.00000 q^{34} +(-4.53869 - 6.27697i) q^{35} +(8.39135 + 6.09667i) q^{36} +(-0.639064 - 0.879596i) q^{37} +(-9.60315 - 3.12025i) q^{38} +(7.89541 - 10.8152i) q^{40} +(7.07450 + 5.13992i) q^{41} +(6.58911 - 2.14093i) q^{42} -3.46410i q^{43} +(1.62772 + 5.04868i) q^{45} +(0.618034 + 1.90211i) q^{46} +(3.89893 - 5.36641i) q^{47} +(2.96754 + 4.08446i) q^{48} +(-1.54508 + 4.75528i) q^{49} +(12.0216 - 3.84563i) q^{50} +(-1.01567 + 0.737928i) q^{51} +(-9.60315 + 3.12025i) q^{53} -10.7446 q^{54} -20.7446 q^{56} +(3.01404 - 0.979321i) q^{57} +(-12.9749 + 17.8584i) q^{58} +(-5.96430 + 4.33332i) q^{59} +(-0.0176311 + 7.74595i) q^{60} +(0.230083 - 0.708121i) q^{61} +(5.00368 + 6.88698i) q^{62} +(4.83032 - 6.64836i) q^{63} +(0.733075 + 2.25617i) q^{64} -9.30506i q^{67} +(6.58911 - 2.14093i) q^{68} +(-0.507835 - 0.368964i) q^{69} +(-15.7929 - 11.5292i) q^{70} +(-3.12628 + 9.62169i) q^{71} +(13.5110 + 4.38998i) q^{72} +(-4.07230 - 5.60503i) q^{73} +(-2.22040 - 1.61321i) q^{74} +(-2.34304 + 3.19424i) q^{75} -17.4891 q^{76} +(0.387951 + 1.19399i) q^{79} +(4.43397 - 13.5414i) q^{80} +(-3.02941 + 2.20100i) q^{81} +(20.9938 + 6.82131i) q^{82} +(-6.30860 - 2.04979i) q^{83} +(9.70820 - 7.05342i) q^{84} +(3.36730 + 1.10258i) q^{85} +(-2.70222 - 8.31657i) q^{86} -6.92820i q^{87} -1.37228 q^{89} +(7.84609 + 10.8511i) q^{90} +(2.03615 + 2.80252i) q^{92} +(-2.54105 - 0.825636i) q^{93} +(5.17435 - 15.9250i) q^{94} +(-7.22408 - 5.27377i) q^{95} +(2.63370 + 1.91350i) q^{96} +(5.55509 - 1.80496i) q^{97} +12.6217i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9	$ 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35} + 30 q^{36} + 28 q^{40} + 12 q^{41} + 72 q^{45} - 8 q^{46} + 20 q^{49} - 18 q^{50} - 28 q^{51} - 80 q^{54} - 240 q^{56} - 18 q^{59} + 18 q^{60} + 20 q^{61} + 2 q^{64} - 14 q^{69} - 24 q^{70} + 6 q^{71} + 12 q^{74} - 15 q^{75} - 96 q^{76} - 28 q^{79} - 6 q^{80} + 8 q^{81} + 48 q^{84} + 2 q^{85} + 12 q^{86} + 24 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.40079	−	0.780063i	1.69761	−	0.551588i	0.709418	−	0.704788i	$-0.248958\pi$
$2$	2.40079	−	0.780063i	1.69761	−	0.551588i	0.988195	+	0.153200i	$0.0489578\pi$
$3$	−0.465695	+	0.640974i	−0.268869	+	0.370066i	−0.922007	−	0.387172i	$-0.873452\pi$
$3$	−0.465695	+	0.640974i	−0.268869	+	0.370066i	0.653139	+	0.757238i	$0.273452\pi$
$4$	3.53725	−	2.56996i	1.76862	−	1.28498i
$5$	2.23606	+	0.00508966i	0.999997	+	0.00227617i
$5$	2.23606	+	0.00508966i	0.999997	+	0.00227617i
$6$	−0.618034	+	1.90211i	−0.252311	+	0.776534i
$7$	−2.03615	−	2.80252i	−0.769592	−	1.05925i	−0.996355	−	0.0853021i	$-0.972814\pi$
$7$	−2.03615	−	2.80252i	−0.769592	−	1.05925i	0.226764	−	0.973950i	$-0.427186\pi$
$8$	3.51992	−	4.84475i	1.24448	−	1.71288i
$9$	0.733075	+	2.25617i	0.244358	+	0.752058i
$10$	5.37228	−	1.73205i	1.69886	−	0.547723i
$11$		0			0
$11$		0			0
$12$			3.46410i			1.00000i
$13$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$13$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$14$	−7.07450	−	5.13992i	−1.89074	−	1.37370i
$15$	−1.04458	+	1.43089i	−0.269711	+	0.369453i
$16$	1.96914	−	6.06040i	0.492286	−	1.51510i
$17$	1.50702	+	0.489660i	0.365506	+	0.118760i	0.486011	−	0.873953i	$-0.338451\pi$
$17$	1.50702	+	0.489660i	0.365506	+	0.118760i	−0.120505	+	0.992713i	$0.538451\pi$
$18$	3.51992	+	4.84475i	0.829652	+	1.14192i
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	0.151058	−	0.988525i	$-0.451732\pi$
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	−0.893463	+	0.449136i	$0.851732\pi$
$20$	7.92259	−	5.72859i	1.77155	−	1.28095i
$21$	2.74456			0.598913
$22$		0			0
$23$			0.792287i			0.165203i	0.996583	+	0.0826016i	$0.0263229\pi$
$23$			0.792287i			0.165203i	−0.996583	+	0.0826016i	$0.973677\pi$
$24$	1.46615	+	4.51235i	0.299277	+	0.921079i
$25$	4.99995	+	0.0227616i	0.999990	+	0.00455232i
$26$		0			0
$27$	−4.04807	−	1.31530i	−0.779051	−	0.253129i
$28$	−14.4047	−	4.68038i	−2.72224	−	0.884509i
$29$	−7.07450	+	5.13992i	−1.31370	+	0.954460i	−0.313714	+	0.949518i	$0.601573\pi$
$29$	−7.07450	+	5.13992i	−1.31370	+	0.954460i	−0.999988	+	0.00494253i	$0.998427\pi$
$30$	−1.39164	+	4.25010i	−0.254078	+	0.775958i
$31$	1.04209	+	3.20723i	0.187165	+	0.576036i	0.999979	−	0.00648824i	$-0.00206529\pi$
$31$	1.04209	+	3.20723i	0.187165	+	0.576036i	−0.812814	+	0.582524i	$0.802065\pi$
$32$		−	4.10891i		−	0.726360i
$33$		0			0
$34$	4.00000			0.685994
$35$	−4.53869	−	6.27697i	−0.767179	−	1.06100i
$36$	8.39135	+	6.09667i	1.39856	+	1.01611i
$37$	−0.639064	−	0.879596i	−0.105061	−	0.144605i	0.753249	−	0.657736i	$-0.228486\pi$
$37$	−0.639064	−	0.879596i	−0.105061	−	0.144605i	−0.858310	+	0.513131i	$0.828486\pi$
$38$	−9.60315	−	3.12025i	−1.55784	−	0.506172i
$39$		0			0
$40$	7.89541	−	10.8152i	1.24837	−	1.71004i
$41$	7.07450	+	5.13992i	1.10485	+	0.802721i	0.981845	−	0.189684i	$-0.0607465\pi$
$41$	7.07450	+	5.13992i	1.10485	+	0.802721i	0.123006	+	0.992406i	$0.460747\pi$
$42$	6.58911	−	2.14093i	1.01672	−	0.330353i
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$		0			0
$45$	1.62772	+	5.04868i	0.242646	+	0.752612i
$46$	0.618034	+	1.90211i	0.0911241	+	0.280451i
$47$	3.89893	−	5.36641i	0.568717	−	0.782772i	−0.423685	−	0.905810i	$-0.639264\pi$
$47$	3.89893	−	5.36641i	0.568717	−	0.782772i	0.992402	+	0.123038i	$0.0392637\pi$
$48$	2.96754	+	4.08446i	0.428327	+	0.589542i
$49$	−1.54508	+	4.75528i	−0.220726	+	0.679326i
$50$	12.0216	−	3.84563i	1.70011	−	0.543854i
$51$	−1.01567	+	0.737928i	−0.142222	+	0.103331i
$52$		0			0
$53$	−9.60315	+	3.12025i	−1.31909	+	0.428600i	−0.882184	−	0.470905i	$-0.843927\pi$
$53$	−9.60315	+	3.12025i	−1.31909	+	0.428600i	−0.436911	+	0.899505i	$0.643927\pi$
$54$	−10.7446			−1.46215
$55$		0			0
$56$	−20.7446			−2.77211
$57$	3.01404	−	0.979321i	0.399219	−	0.129714i
$58$	−12.9749	+	17.8584i	−1.70369	+	2.34493i
$59$	−5.96430	+	4.33332i	−0.776486	+	0.564150i	−0.903922	−	0.427697i	$-0.859325\pi$
$59$	−5.96430	+	4.33332i	−0.776486	+	0.564150i	0.127436	+	0.991847i	$0.459325\pi$
$60$	−0.0176311	+	7.74595i	−0.00227617	+	0.999997i
$61$	0.230083	−	0.708121i	0.0294590	−	0.0906656i	−0.935246	−	0.353999i	$-0.884822\pi$
$61$	0.230083	−	0.708121i	0.0294590	−	0.0906656i	0.964705	+	0.263333i	$0.0848218\pi$
$62$	5.00368	+	6.88698i	0.635469	+	0.874648i
$63$	4.83032	−	6.64836i	0.608563	−	0.837614i
$64$	0.733075	+	2.25617i	0.0916344	+	0.282022i
$65$		0			0
$66$		0			0
$67$		−	9.30506i		−	1.13679i	−0.822754	−	0.568397i	$-0.807564\pi$
$67$		−	9.30506i		−	1.13679i	0.822754	−	0.568397i	$-0.192436\pi$
$68$	6.58911	−	2.14093i	0.799047	−	0.259626i
$69$	−0.507835	−	0.368964i	−0.0611362	−	0.0444180i
$70$	−15.7929	−	11.5292i	−1.88761	−	1.37800i
$71$	−3.12628	+	9.62169i	−0.371021	+	1.14188i	0.575103	+	0.818081i	$0.304962\pi$
$71$	−3.12628	+	9.62169i	−0.371021	+	1.14188i	−0.946124	+	0.323804i	$0.895038\pi$
$72$	13.5110	+	4.38998i	1.59228	+	0.517364i
$73$	−4.07230	−	5.60503i	−0.476626	−	0.656020i	0.501226	−	0.865316i	$-0.332883\pi$
$73$	−4.07230	−	5.60503i	−0.476626	−	0.656020i	−0.977852	+	0.209297i	$0.932883\pi$
$74$	−2.22040	−	1.61321i	−0.258116	−	0.187532i
$75$	−2.34304	+	3.19424i	−0.270551	+	0.368838i
$76$	−17.4891			−2.00614
$77$		0			0
$78$		0			0
$79$	0.387951	+	1.19399i	0.0436480	+	0.134335i	0.970506	−	0.241078i	$-0.0775010\pi$
$79$	0.387951	+	1.19399i	0.0436480	+	0.134335i	−0.926858	+	0.375413i	$0.877501\pi$
$80$	4.43397	−	13.5414i	0.495733	−	1.51398i
$81$	−3.02941	+	2.20100i	−0.336602	+	0.244555i
$82$	20.9938	+	6.82131i	2.31838	+	0.753288i
$83$	−6.30860	−	2.04979i	−0.692458	−	0.224993i	−0.0584167	−	0.998292i	$-0.518605\pi$
$83$	−6.30860	−	2.04979i	−0.692458	−	0.224993i	−0.634042	+	0.773299i	$0.718605\pi$
$84$	9.70820	−	7.05342i	1.05925	−	0.769592i
$85$	3.36730	+	1.10258i	0.365235	+	0.119592i
$86$	−2.70222	−	8.31657i	−0.291388	−	0.896799i
$87$		−	6.92820i		−	0.742781i
$88$		0			0
$89$	−1.37228			−0.145462			−0.0727308	−	0.997352i	$-0.523171\pi$
$89$	−1.37228			−0.145462			−0.0727308	+	0.997352i	$0.523171\pi$
$90$	7.84609	+	10.8511i	0.827051	+	1.14380i
$91$		0			0
$92$	2.03615	+	2.80252i	0.212283	+	0.292183i
$93$	−2.54105	−	0.825636i	−0.263494	−	0.0856145i
$94$	5.17435	−	15.9250i	0.533694	−	1.64254i
$95$	−7.22408	−	5.27377i	−0.741175	−	0.541077i
$96$	2.63370	+	1.91350i	0.268801	+	0.195296i
$97$	5.55509	−	1.80496i	0.564033	−	0.183266i	−0.0131018	−	0.999914i	$-0.504171\pi$
$97$	5.55509	−	1.80496i	0.564033	−	0.183266i	0.577135	+	0.816649i	$0.304171\pi$
$98$			12.6217i			1.27498i
$99$		0			0
$100$	17.7446	−	12.7692i	1.77446	−	1.27692i
$101$	−1.85410	−	5.70634i	−0.184490	−	0.567802i	0.815449	−	0.578829i	$-0.196490\pi$
$101$	−1.85410	−	5.70634i	−0.184490	−	0.567802i	−0.999939	+	0.0110267i	$0.996490\pi$
$102$	−1.86278	+	2.56389i	−0.184443	+	0.253863i
$103$	6.10844	+	8.40755i	0.601883	+	0.828421i	0.995879	−	0.0906914i	$-0.0289077\pi$
$103$	6.10844	+	8.40755i	0.601883	+	0.828421i	−0.393996	+	0.919112i	$0.628908\pi$
$104$		0			0
$105$	6.13701	+	0.0139689i	0.598911	+	0.00136322i
$106$	−20.6211	+	14.9821i	−2.00290	+	1.45519i
$107$	−3.89893	+	5.36641i	−0.376923	+	0.518791i	−0.954766	−	0.297358i	$-0.903895\pi$
$107$	−3.89893	+	5.36641i	−0.376923	+	0.518791i	0.577843	+	0.816148i	$0.303895\pi$
$108$	−17.6993	+	5.75085i	−1.70311	+	0.553375i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	0.861407			0.0817611
$112$	−20.9938	+	6.82131i	−1.98373	+	0.644553i
$113$	−0.292325	+	0.402351i	−0.0274996	+	0.0378500i	−0.822545	−	0.568699i	$-0.807447\pi$
$113$	−0.292325	+	0.402351i	−0.0274996	+	0.0378500i	0.795046	+	0.606549i	$0.207447\pi$
$114$	6.47214	−	4.70228i	0.606171	−	0.440409i
$115$	−0.00403247	+	1.77160i	−0.000376030	+	0.165203i
$116$	−11.8149	+	36.3624i	−1.09698	+	3.37616i
$117$		0			0
$118$	−10.9388	+	15.0559i	−1.00699	+	1.38601i
$119$	−1.69623	−	5.22047i	−0.155493	−	0.478560i
$120$	3.25544	+	10.0974i	0.297179	+	0.921758i
$121$		0			0
$122$		−	1.87953i		−	0.170164i
$123$	−6.58911	+	2.14093i	−0.594120	+	0.193041i
$124$	11.9286	+	8.66664i	1.07122	+	0.778287i
$125$	11.1801	+	0.0763444i	0.999977	+	0.00682845i
$126$	6.41042	−	19.7293i	0.571086	−	1.75762i
$127$	−7.81561	−	2.53945i	−0.693524	−	0.225339i	−0.0590171	−	0.998257i	$-0.518797\pi$
$127$	−7.81561	−	2.53945i	−0.693524	−	0.225339i	−0.634507	+	0.772917i	$0.718797\pi$
$128$	8.35023	+	11.4931i	0.738063	+	1.01586i
$129$	2.22040	+	1.61321i	0.195495	+	0.142036i
$130$		0			0
$131$	2.74456			0.239794			0.119897	−	0.992786i	$-0.461744\pi$
$131$	2.74456			0.239794			0.119897	+	0.992786i	$0.461744\pi$
$132$		0			0
$133$			13.8564i			1.20150i
$134$	−7.25854	−	22.3395i	−0.627042	−	1.92984i
$135$	−9.04503	−	2.96169i	−0.778473	−	0.254902i
$136$	7.67686	−	5.57757i	0.658286	−	0.478273i
$137$	−13.6512	−	4.43555i	−1.16630	−	0.378955i	−0.339041	−	0.940772i	$-0.610102\pi$
$137$	−13.6512	−	4.43555i	−1.16630	−	0.378955i	−0.827261	+	0.561817i	$0.810102\pi$
$138$	−1.50702	−	0.489660i	−0.128286	−	0.0416827i
$139$	13.1333	−	9.54192i	1.11395	−	0.809335i	0.130673	−	0.991426i	$-0.458286\pi$
$139$	13.1333	−	9.54192i	1.11395	−	0.809335i	0.983282	+	0.182090i	$0.0582863\pi$
$140$	−32.1860	−	10.5389i	−2.72022	−	0.890703i
$141$	1.62402	+	4.99822i	0.136767	+	0.420926i
$142$			25.5383i			2.14313i
$143$		0			0
$144$	15.1168			1.25974
$145$	−15.8452	+	11.4572i	−1.31587	+	0.951467i
$146$	−14.1490	−	10.2798i	−1.17098	−	0.850766i
$147$	−2.32847	−	3.20487i	−0.192049	−	0.264333i
$148$	−4.52106	−	1.46898i	−0.371629	−	0.120749i
$149$	−3.55033	+	10.9268i	−0.290855	+	0.895159i	0.693728	+	0.720237i	$0.255967\pi$
$149$	−3.55033	+	10.9268i	−0.290855	+	0.895159i	−0.984582	+	0.174921i	$0.944033\pi$
$150$	−3.13343	+	9.49640i	−0.255844	+	0.775378i
$151$	−9.89726	−	7.19078i	−0.805428	−	0.585177i	0.107074	−	0.994251i	$-0.465852\pi$
$151$	−9.89726	−	7.19078i	−0.805428	−	0.585177i	−0.912501	+	0.409074i	$0.865852\pi$
$152$	−22.7814	+	7.40212i	−1.84781	+	0.600391i
$153$			3.75906i			0.303902i
$154$		0			0
$155$	2.31386	+	7.17687i	0.185854	+	0.576460i
$156$		0			0
$157$	14.3720	−	19.7813i	1.14701	−	1.57872i	0.396258	−	0.918139i	$-0.370309\pi$
$157$	14.3720	−	19.7813i	1.14701	−	1.57872i	0.750752	−	0.660584i	$-0.229691\pi$
$158$	1.86278	+	2.56389i	0.148195	+	0.203972i
$159$	2.47214	−	7.60845i	0.196053	−	0.603390i
$160$	0.0209130	−	9.18778i	0.00165331	−	0.726358i
$161$	2.22040	−	1.61321i	0.174992	−	0.127139i
$162$	−5.55606	+	7.64727i	−0.436526	+	0.600826i
$163$	3.29456	−	1.07047i	0.258050	−	0.0838454i	−0.177135	−	0.984187i	$-0.556683\pi$
$163$	3.29456	−	1.07047i	0.258050	−	0.0838454i	0.435185	+	0.900341i	$0.356683\pi$
$164$	38.2337			2.98555
$165$		0			0
$166$	−16.7446			−1.29963
$167$	14.9658	−	4.86267i	1.15809	−	0.376285i	0.333902	−	0.942608i	$-0.391635\pi$
$167$	14.9658	−	4.86267i	1.15809	−	0.376285i	0.824183	+	0.566323i	$0.191635\pi$
$168$	9.66063	−	13.2967i	0.745334	−	1.02586i
$169$	−10.5172	+	7.64121i	−0.809017	+	0.587785i
$170$	8.94425	+	0.0203586i	0.685993	+	0.00156144i
$171$	2.93230	−	9.02469i	0.224239	−	0.690136i
$172$	−8.90261	−	12.2534i	−0.678818	−	0.934312i
$173$	5.00368	−	6.88698i	0.380423	−	0.523608i	−0.575273	−	0.817961i	$-0.695104\pi$
$173$	5.00368	−	6.88698i	0.380423	−	0.523608i	0.955697	+	0.294354i	$0.0951044\pi$
$174$	−5.40444	−	16.6331i	−0.409709	−	1.26096i
$175$	−10.1168	−	14.0588i	−0.764762	−	1.06274i
$176$		0			0
$177$		−	5.84096i		−	0.439034i
$178$	−3.29456	+	1.07047i	−0.246937	+	0.0802348i
$179$	10.4051	+	7.55975i	0.777713	+	0.565042i	0.904292	−	0.426915i	$-0.140400\pi$
$179$	10.4051	+	7.55975i	0.777713	+	0.565042i	−0.126578	+	0.991957i	$0.540400\pi$
$180$	18.7326	+	13.6753i	1.39624	+	1.01929i
$181$	7.45251	−	22.9365i	0.553941	−	1.70486i	−0.144783	−	0.989464i	$-0.546248\pi$
$181$	7.45251	−	22.9365i	0.553941	−	1.70486i	0.698724	−	0.715392i	$-0.253752\pi$
$182$		0			0
$183$	0.346739	+	0.477245i	0.0256317	+	0.0352790i
$184$	3.83843	+	2.78878i	0.282973	+	0.205592i
$185$	−1.42451	−	1.97008i	−0.104732	−	0.144843i
$186$	−6.74456			−0.494535
$187$		0			0
$188$		−	29.0024i		−	2.11522i
$189$	4.55632	+	14.0229i	0.331424	+	1.02002i
$190$	−21.4574	−	7.02596i	−1.55668	−	0.509716i
$191$	15.6725	−	11.3867i	1.13402	−	0.823916i	0.147747	−	0.989025i	$-0.452798\pi$
$191$	15.6725	−	11.3867i	1.13402	−	0.823916i	0.986275	+	0.165109i	$0.0527977\pi$
$192$	−1.78754	−	0.580806i	−0.129004	−	0.0419161i
$193$	15.6312	+	5.07889i	1.12516	+	0.365587i	0.811735	−	0.584026i	$-0.198523\pi$
$193$	15.6312	+	5.07889i	1.12516	+	0.365587i	0.313426	+	0.949613i	$0.398523\pi$
$194$	11.9286	−	8.66664i	0.856424	−	0.622228i
$195$		0			0
$196$	6.75555	+	20.7914i	0.482539	+	1.48510i
$197$			8.51278i			0.606510i	0.952909	+	0.303255i	$0.0980734\pi$
$197$			8.51278i			0.606510i	−0.952909	+	0.303255i	$0.901927\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	17.7097	−	24.1434i	1.25226	−	1.70719i
$201$	5.96430	+	4.33332i	0.420689	+	0.305649i
$202$	−8.90261	−	12.2534i	−0.626386	−	0.862146i
$203$	28.8095	+	9.36076i	2.02203	+	0.656997i
$204$	−1.69623	+	5.22047i	−0.118760	+	0.365506i
$205$	15.7929	+	11.5292i	1.10302	+	0.805234i
$206$	21.2235	+	15.4198i	1.47871	+	1.07435i
$207$	−1.78754	+	0.580806i	−0.124242	+	0.0403688i
$208$		0			0
$209$		0			0
$210$	14.7446	−	4.75372i	1.01747	−	0.328038i
$211$	−0.460165	−	1.41624i	−0.0316791	−	0.0974981i	0.933967	−	0.357360i	$-0.116323\pi$
$211$	−0.460165	−	1.41624i	−0.0316791	−	0.0974981i	−0.965646	+	0.259862i	$0.916323\pi$
$212$	−25.9498	+	35.7169i	−1.78224	+	2.45304i
$213$	−4.71136	−	6.48463i	−0.322817	−	0.444320i
$214$	−5.17435	+	15.9250i	−0.353712	+	1.08861i
$215$	0.0176311	−	7.74595i	0.00120243	−	0.528269i
$216$	−20.6211	+	14.9821i	−1.40309	+	1.01940i
$217$	6.86646	−	9.45088i	0.466126	−	0.641567i
$218$	24.0079	−	7.80063i	1.62602	−	0.528326i
$219$	5.48913			0.370921
$220$		0			0
$221$		0			0
$222$	2.06805	−	0.671952i	0.138799	−	0.0450984i
$223$	−1.39708	+	1.92292i	−0.0935557	+	0.128768i	−0.853229	−	0.521537i	$-0.825359\pi$
$223$	−1.39708	+	1.92292i	−0.0935557	+	0.128768i	0.759673	+	0.650305i	$0.225359\pi$
$224$	−11.5153	+	8.36635i	−0.769398	+	0.559000i
$225$	3.61398	+	11.2974i	0.240932	+	0.753162i
$226$	−0.387951	+	1.19399i	−0.0258061	+	0.0794232i
$227$	−9.83400	−	13.5353i	−0.652706	−	0.898372i	0.346507	−	0.938047i	$-0.387368\pi$
$227$	−9.83400	−	13.5353i	−0.652706	−	0.898372i	−0.999213	+	0.0396753i	$0.987368\pi$
$228$	8.14459	−	11.2101i	0.539389	−	0.742405i
$229$	−4.52021	−	13.9118i	−0.298704	−	0.919317i	−0.981952	−	0.189130i	$-0.939433\pi$
$229$	−4.52021	−	13.9118i	−0.298704	−	0.919317i	0.683248	−	0.730187i	$-0.260567\pi$
$230$	1.37228	+	4.25639i	0.0904856	+	0.280658i
$231$		0			0
$232$			52.3663i			3.43801i
$233$	−3.57507	+	1.16161i	−0.234211	+	0.0760997i	−0.423771	−	0.905769i	$-0.639294\pi$
$233$	−3.57507	+	1.16161i	−0.234211	+	0.0760997i	0.189560	+	0.981869i	$0.439294\pi$
$234$		0			0
$235$	8.74555	−	11.9798i	0.570497	−	0.781475i
$236$	−9.96076	+	30.6561i	−0.648390	+	1.99554i
$237$	−0.945984	−	0.307369i	−0.0614483	−	0.0199658i
$238$	−8.14459	−	11.2101i	−0.527935	−	0.726641i
$239$	11.9286	+	8.66664i	0.771597	+	0.560598i	0.902445	−	0.430804i	$-0.141770\pi$
$239$	11.9286	+	8.66664i	0.771597	+	0.560598i	−0.130848	+	0.991402i	$0.541770\pi$
$240$	6.61481	+	9.14822i	0.426984	+	0.590515i
$241$	−16.7446			−1.07861			−0.539306	−	0.842110i	$-0.681313\pi$
$241$	−16.7446			−1.07861			−0.539306	+	0.842110i	$0.681313\pi$
$242$		0			0
$243$		−	15.7359i		−	1.00946i
$244$	−1.00599	−	3.09610i	−0.0644016	−	0.198208i
$245$	−3.47911	+	10.6252i	−0.222272	+	0.678822i
$246$	−14.1490	+	10.2798i	−0.902107	+	0.655419i
$247$		0			0
$248$	19.2063	+	6.24051i	1.21960	+	0.396273i
$249$	4.25174	−	3.08907i	0.269443	−	0.195762i
$250$	26.9006	−	8.53788i	1.70134	−	0.539983i
$251$	−6.83448	−	21.0344i	−0.431389	−	1.32768i	−0.896742	−	0.442553i	$-0.854073\pi$
$251$	−6.83448	−	21.0344i	−0.431389	−	1.32768i	0.465354	−	0.885125i	$-0.345927\pi$
$252$		−	35.9306i		−	2.26342i
$253$		0			0
$254$	−20.7446			−1.30163
$255$	−2.27486	+	1.64488i	−0.142457	+	0.103007i
$256$	25.1741	+	18.2900i	1.57338	+	1.14313i
$257$	6.28181	+	8.64617i	0.391849	+	0.539334i	0.958675	−	0.284504i	$-0.0918289\pi$
$257$	6.28181	+	8.64617i	0.391849	+	0.539334i	−0.566826	+	0.823837i	$0.691829\pi$
$258$	6.58911	+	2.14093i	0.410220	+	0.133289i
$259$	−1.16385	+	3.58198i	−0.0723184	+	0.222573i
$260$		0			0
$261$	−16.7827	−	12.1933i	−1.03882	−	0.754749i
$262$	6.58911	−	2.14093i	0.407077	−	0.132267i
$263$		−	27.4179i		−	1.69066i	−0.534246	−	0.845329i	$-0.679405\pi$
$263$		−	27.4179i		−	1.69066i	0.534246	−	0.845329i	$-0.320595\pi$
$264$		0			0
$265$	−21.4891	+	6.92820i	−1.32007	+	0.425596i
$266$	10.8089	+	33.2663i	0.662735	+	2.03969i
$267$	0.639064	−	0.879596i	0.0391101	−	0.0538304i
$268$	−23.9137	−	32.9143i	−1.46076	−	2.01056i
$269$	3.55033	−	10.9268i	0.216468	−	0.666219i	−0.782578	−	0.622552i	$-0.786096\pi$
$269$	3.55033	−	10.9268i	0.216468	−	0.666219i	0.999046	−	0.0436672i	$-0.0139041\pi$
$270$	−24.0255	−	0.0546862i	−1.46215	−	0.00332809i
$271$	10.9129	−	7.92871i	0.662913	−	0.481635i	−0.204732	−	0.978818i	$-0.565632\pi$
$271$	10.9129	−	7.92871i	0.662913	−	0.481635i	0.867646	+	0.497183i	$0.165632\pi$
$272$	5.93507	−	8.16893i	0.359867	−	0.495314i
$273$		0			0
$274$	−36.2337			−2.18896
$275$		0			0
$276$	−2.74456			−0.165203
$277$	11.1102	−	3.60991i	0.667545	−	0.216899i	0.0444110	−	0.999013i	$-0.485859\pi$
$277$	11.1102	−	3.60991i	0.667545	−	0.216899i	0.623135	+	0.782115i	$0.285859\pi$
$278$	24.0870	−	33.1530i	1.44464	−	1.98838i
$279$	−6.47214	+	4.70228i	−0.387477	+	0.281518i
$280$	−46.3861	−	0.105583i	−2.77210	−	0.00630978i
$281$	0.157869	−	0.485871i	0.00941767	−	0.0289846i	−0.946237	−	0.323473i	$-0.895149\pi$
$281$	0.157869	−	0.485871i	0.00941767	−	0.0289846i	0.955655	+	0.294489i	$0.0951494\pi$
$282$	7.79785	+	10.7328i	0.464355	+	0.639130i
$283$	−8.90261	+	12.2534i	−0.529205	+	0.728389i	−0.987009	−	0.160665i	$-0.948636\pi$
$283$	−8.90261	+	12.2534i	−0.529205	+	0.728389i	0.457804	+	0.889053i	$0.348636\pi$
$284$	13.6690	+	42.0687i	0.811104	+	2.49632i
$285$	6.74456	−	2.17448i	0.399513	−	0.128805i
$286$		0			0
$287$		−	30.2921i		−	1.78808i
$288$	9.27042	−	3.01214i	0.546265	−	0.177492i
$289$	−11.7219	−	8.51649i	−0.689526	−	0.500970i
$290$	−29.1036	+	39.8665i	−1.70902	+	2.34104i
$291$	−1.43004	+	4.40122i	−0.0838306	+	0.258004i
$292$	−28.8095	−	9.36076i	−1.68595	−	0.547797i
$293$	1.86278	+	2.56389i	0.108825	+	0.149784i	0.859955	−	0.510369i	$-0.170491\pi$
$293$	1.86278	+	2.56389i	0.108825	+	0.149784i	−0.751131	+	0.660153i	$0.770491\pi$
$294$	−8.09017	−	5.87785i	−0.471828	−	0.342803i
$295$	−13.3586	+	9.65921i	−0.777768	+	0.562381i
$296$	−6.51087			−0.378437
$297$		0			0
$298$			29.0024i			1.68007i
$299$		0			0
$300$	−0.0788485	+	17.3203i	−0.00455232	+	0.999990i
$301$	−9.70820	+	7.05342i	−0.559572	+	0.406553i
$302$	−29.3705	−	9.54305i	−1.69008	−	0.549141i
$303$	4.52106	+	1.46898i	0.259728	+	0.0843907i
$304$	−20.6211	+	14.9821i	−1.18270	+	0.859284i
$305$	0.518083	−	1.58223i	0.0296653	−	0.0905983i
$306$	2.93230	+	9.02469i	0.167628	+	0.515907i
$307$			31.5817i			1.80246i	0.433340	+	0.901231i	$0.357335\pi$
$307$			31.5817i			1.80246i	−0.433340	+	0.901231i	$0.642665\pi$
$308$		0			0
$309$	−8.23369			−0.468398
$310$	11.1535	+	15.4252i	0.633476	+	0.876092i
$311$	−4.44080	−	3.22643i	−0.251814	−	0.182954i	0.454716	−	0.890636i	$-0.349741\pi$
$311$	−4.44080	−	3.22643i	−0.251814	−	0.182954i	−0.706531	+	0.707683i	$0.749741\pi$
$312$		0			0
$313$	−20.8014	−	6.75877i	−1.17576	−	0.382028i	−0.344972	−	0.938613i	$-0.612112\pi$
$313$	−20.8014	−	6.75877i	−1.17576	−	0.382028i	−0.830791	+	0.556585i	$0.812112\pi$
$314$	19.0734	−	58.7019i	1.07637	−	3.31274i
$315$	10.8347	−	14.8416i	0.610468	−	0.836227i
$316$	4.44080	+	3.22643i	0.249814	+	0.181501i
$317$	31.3505	−	10.1864i	1.76082	−	0.572125i	0.763535	−	0.645767i	$-0.223462\pi$
$317$	31.3505	−	10.1864i	1.76082	−	0.572125i	0.997285	+	0.0736417i	$0.0234621\pi$
$318$		−	20.1947i		−	1.13246i
$319$		0			0
$320$	1.62772	+	5.04868i	0.0909922	+	0.282230i
$321$	−1.62402	−	4.99822i	−0.0906439	−	0.278973i
$322$	4.07230	−	5.60503i	0.226940	−	0.312356i
$323$	−3.72556	−	5.12779i	−0.207296	−	0.285318i
$324$	−5.05931	+	15.5710i	−0.281073	+	0.865054i
$325$		0			0
$326$	7.07450	−	5.13992i	0.391820	−	0.284674i
$327$	−4.65695	+	6.40974i	−0.257530	+	0.354459i
$328$	49.8033	−	16.1821i	2.74993	−	0.893505i
$329$	−22.9783			−1.26683
$330$		0			0
$331$	−14.1168			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$331$	−14.1168			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$332$	−27.5830	+	8.96224i	−1.51381	+	0.491867i
$333$	1.51604	−	2.08665i	0.0830785	−	0.114348i
$334$	32.1364	−	23.3485i	1.75843	−	1.27757i
$335$	0.0473596	−	20.8067i	0.00258753	−	1.13679i
$336$	5.40444	−	16.6331i	0.294836	−	0.907413i
$337$	19.0834	+	26.2660i	1.03954	+	1.43080i	0.897541	+	0.440932i	$0.145352\pi$
$337$	19.0834	+	26.2660i	1.03954	+	1.43080i	0.141996	+	0.989867i	$0.454648\pi$
$338$	−19.2890	+	26.5490i	−1.04918	+	1.44408i
$339$	−0.121762	−	0.374746i	−0.00661321	−	0.0203534i
$340$	14.7446	−	4.75372i	0.799636	−	0.257807i
$341$		0			0
$342$		−	23.9538i		−	1.29527i
$343$	−6.58911	+	2.14093i	−0.355779	+	0.115599i
$344$	−16.7827	−	12.1933i	−0.904863	−	0.657421i
$345$	−1.13367	−	0.827611i	−0.0610349	−	0.0445571i
$346$	6.64050	−	20.4374i	0.356996	−	1.09872i
$347$	−21.5549	−	7.00360i	−1.15713	−	0.375973i	−0.333303	−	0.942820i	$-0.608163\pi$
$347$	−21.5549	−	7.00360i	−1.15713	−	0.375973i	−0.823823	+	0.566847i	$0.808163\pi$
$348$	−17.8052	−	24.5068i	−0.954460	−	1.31370i
$349$	−12.5310	−	9.10428i	−0.670767	−	0.487341i	0.199515	−	0.979895i	$-0.436063\pi$
$349$	−12.5310	−	9.10428i	−0.670767	−	0.487341i	−0.870282	+	0.492554i	$0.836063\pi$
$350$	−35.2551	−	25.8604i	−1.88447	−	1.38230i
$351$		0			0
$352$		0			0
$353$			25.0410i			1.33280i	0.745595	+	0.666399i	$0.232165\pi$
$353$			25.0410i			1.33280i	−0.745595	+	0.666399i	$0.767835\pi$
$354$	−4.55632	−	14.0229i	−0.242166	−	0.745309i
$355$	−7.03952	+	21.4988i	−0.373619	+	1.14104i
$356$	−4.85410	+	3.52671i	−0.257267	+	0.186915i
$357$	4.13611	+	1.34390i	0.218906	+	0.0711269i
$358$	30.8775	+	10.0327i	1.63193	+	0.530245i
$359$	−23.8572	+	17.3333i	−1.25914	+	0.914815i	−0.998715	−	0.0506802i	$-0.983861\pi$
$359$	−23.8572	+	17.3333i	−1.25914	+	0.914815i	−0.260420	+	0.965495i	$0.583861\pi$
$360$	30.1890	+	9.88503i	1.59110	+	0.520987i
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$		−	60.8791i		−	3.19973i
$363$		0			0
$364$		0			0
$365$	−9.07738	−	12.5539i	−0.475132	−	0.657103i
$366$	1.20473	+	0.875286i	0.0629721	+	0.0457519i
$367$	15.1300	+	20.8247i	0.789780	+	1.08704i	0.994135	+	0.108142i	$0.0344902\pi$
$367$	15.1300	+	20.8247i	0.789780	+	1.08704i	−0.204355	+	0.978897i	$0.565510\pi$
$368$	4.80158	+	1.56013i	0.250299	+	0.0813272i
$369$	−6.41042	+	19.7293i	−0.333713	+	1.02706i
$370$	−4.95674	−	3.61855i	−0.257688	−	0.188119i
$371$	28.2980	+	20.5597i	1.46916	+	1.06741i
$372$	−11.1102	+	3.60991i	−0.576036	+	0.187165i
$373$			11.6819i			0.604867i	0.953170	+	0.302434i	$0.0977990\pi$
$373$			11.6819i			0.604867i	−0.953170	+	0.302434i	$0.902201\pi$
$374$		0			0
$375$	−5.25544	+	7.13058i	−0.271390	+	0.368222i
$376$	−12.2750	−	37.7786i	−0.633036	−	1.94828i
$377$		0			0
$378$	21.8775	+	30.1118i	1.12526	+	1.54878i
$379$	0.193976	−	0.596996i	0.00996386	−	0.0306656i	−0.945951	−	0.324310i	$-0.894868\pi$
$379$	0.193976	−	0.596996i	0.00996386	−	0.0306656i	0.955915	+	0.293644i	$0.0948680\pi$
$380$	−39.1068	−	0.0890137i	−2.00614	−	0.00456631i
$381$	5.26741	−	3.82700i	0.269858	−	0.196063i
$382$	28.7440	−	39.5627i	1.47067	−	2.02420i
$383$	10.3567	−	3.36508i	0.529201	−	0.171948i	−0.0322161	−	0.999481i	$-0.510256\pi$
$383$	10.3567	−	3.36508i	0.529201	−	0.171948i	0.561417	+	0.827533i	$0.310256\pi$
$384$	−11.2554			−0.574377
$385$		0			0
$386$	41.4891			2.11174
$387$	7.81561	−	2.53945i	0.397290	−	0.129087i
$388$	15.0111	−	20.6609i	0.762071	−	1.04890i
$389$	15.2592	−	11.0865i	0.773672	−	0.562106i	−0.129401	−	0.991592i	$-0.541305\pi$
$389$	15.2592	−	11.0865i	0.773672	−	0.562106i	0.903073	+	0.429487i	$0.141305\pi$
$390$		0			0
$391$	−0.387951	+	1.19399i	−0.0196195	+	0.0603828i
$392$	17.5996	+	24.2237i	0.888913	+	1.22348i
$393$	−1.27813	+	1.75919i	−0.0644730	+	0.0887395i
$394$	6.64050	+	20.4374i	0.334544	+	1.02962i
$395$	0.861407	+	2.67181i	0.0433421	+	0.134434i
$396$		0			0
$397$			16.4356i			0.824881i	0.910984	+	0.412441i	$0.135324\pi$
$397$			16.4356i			0.824881i	−0.910984	+	0.412441i	$0.864676\pi$
$398$	19.2063	−	6.24051i	0.962725	−	0.312808i
$399$	−8.88159	−	6.45285i	−0.444636	−	0.323047i
$400$	9.98356	−	30.2569i	0.499178	−	1.51284i
$401$	−3.55033	+	10.9268i	−0.177295	+	0.545659i	−0.999731	−	0.0231995i	$-0.992615\pi$
$401$	−3.55033	+	10.9268i	−0.177295	+	0.545659i	0.822436	+	0.568858i	$0.192615\pi$
$402$	17.6993	+	5.75085i	0.882760	+	0.286826i
$403$		0			0
$404$	−21.2235	−	15.4198i	−1.05591	−	0.767162i
$405$	−6.78516	+	4.90615i	−0.337157	+	0.243789i
$406$	76.4674			3.79501
$407$		0			0
$408$			7.51811i			0.372202i
$409$	8.49461	+	26.1437i	0.420031	+	1.29272i	0.907672	+	0.419679i	$0.137857\pi$
$409$	8.49461	+	26.1437i	0.420031	+	1.29272i	−0.487641	+	0.873044i	$0.662143\pi$
$410$	46.9088	+	15.3597i	2.31666	+	0.758563i
$411$	9.20037	−	6.68446i	0.453821	−	0.329720i
$412$	43.2142	+	14.0411i	2.12901	+	0.691757i
$413$	24.2884	+	7.89178i	1.19515	+	0.388329i
$414$	−3.83843	+	2.78878i	−0.188649	+	0.137061i
$415$	−14.0960	−	4.61556i	−0.691944	−	0.226569i
$416$		0			0
$417$			12.8617i			0.629842i
$418$		0			0
$419$	22.9783			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$419$	22.9783			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$420$	21.7440	−	15.7225i	1.06100	−	0.767179i
$421$	−6.88544	−	5.00257i	−0.335576	−	0.243810i	0.407217	−	0.913331i	$-0.366499\pi$
$421$	−6.88544	−	5.00257i	−0.335576	−	0.243810i	−0.742793	+	0.669521i	$0.766499\pi$
$422$	−2.20952	−	3.04114i	−0.107558	−	0.148040i
$423$	14.9658	+	4.86267i	0.727660	+	0.236431i
$424$	−18.6854	+	57.5079i	−0.907446	+	2.79283i
$425$	7.52387	+	2.48258i	0.364961	+	0.120423i
$426$	−16.3694	−	11.8931i	−0.793100	−	0.576221i
$427$	−2.45300	+	0.797029i	−0.118709	+	0.0385709i
$428$			29.0024i			1.40189i
$429$		0			0
$430$	−6.00000	−	18.6101i	−0.289346	−	0.897460i
$431$	7.94879	+	24.4638i	0.382880	+	1.17838i	0.938007	+	0.346617i	$0.112670\pi$
$431$	7.94879	+	24.4638i	0.382880	+	1.17838i	−0.555127	+	0.831765i	$0.687330\pi$
$432$	−15.9424	+	21.9429i	−0.767031	+	1.05573i
$433$	−17.1662	−	23.6272i	−0.824953	−	1.13545i	−0.988842	−	0.148971i	$-0.952404\pi$
$433$	−17.1662	−	23.6272i	−0.824953	−	1.13545i	0.163889	−	0.986479i	$-0.447596\pi$
$434$	9.11264	−	28.0458i	0.437421	−	1.34624i
$435$	0.0352622	−	15.4919i	0.00169069	−	0.742779i
$436$	35.3725	−	25.6996i	1.69404	−	1.23079i
$437$	1.86278	−	2.56389i	0.0891088	−	0.122648i
$438$	13.1782	−	4.28187i	0.629680	−	0.204595i
$439$	21.4891			1.02562			0.512810	−	0.858502i	$-0.328605\pi$
$439$	21.4891			1.02562			0.512810	+	0.858502i	$0.328605\pi$
$440$		0			0
$441$	−11.8614			−0.564829
$442$		0			0
$443$	−18.6177	+	25.6250i	−0.884552	+	1.21748i	0.0905879	+	0.995888i	$0.471125\pi$
$443$	−18.6177	+	25.6250i	−0.884552	+	1.21748i	−0.975139	+	0.221592i	$0.928875\pi$
$444$	3.04701	−	2.21378i	0.144605	−	0.105061i
$445$	−3.06851	−	0.00698444i	−0.145461	−	0.000331094i
$446$	−1.85410	+	5.70634i	−0.0877943	+	0.270203i
$447$	−5.35042	−	7.36423i	−0.253066	−	0.348316i
$448$	4.83032	−	6.64836i	0.228211	−	0.314105i
$449$	−2.12029	−	6.52559i	−0.100063	−	0.307961i	0.888477	−	0.458921i	$-0.151764\pi$
$449$	−2.12029	−	6.52559i	−0.100063	−	0.307961i	−0.988540	+	0.150959i	$0.951764\pi$
$450$	17.4891	+	24.3036i	0.824445	+	1.14568i
$451$		0			0
$452$			2.17448i			0.102279i
$453$	9.21820	−	2.99518i	0.433109	−	0.140726i
$454$	−34.1678	−	24.8243i	−1.60357	−	1.16506i
$455$		0			0
$456$	5.86460	−	18.0494i	0.274635	−	0.845240i
$457$	−19.7673	−	6.42280i	−0.924677	−	0.300446i	−0.192293	−	0.981338i	$-0.561592\pi$
$457$	−19.7673	−	6.42280i	−0.924677	−	0.300446i	−0.732384	+	0.680892i	$0.761592\pi$
$458$	−21.7041	−	29.8732i	−1.01417	−	1.39588i
$459$	−5.45647	−	3.96435i	−0.254686	−	0.185040i
$460$	4.53869	+	6.27697i	0.211617	+	0.292665i
$461$	−2.23369			−0.104033			−0.0520166	−	0.998646i	$-0.516565\pi$
$461$	−2.23369			−0.104033			−0.0520166	+	0.998646i	$0.516565\pi$
$462$		0			0
$463$		−	30.0897i		−	1.39839i	−0.714933	−	0.699193i	$-0.753543\pi$
$463$		−	30.0897i		−	1.39839i	0.714933	−	0.699193i	$-0.246457\pi$
$464$	17.2193	+	52.9955i	0.799386	+	2.46026i
$465$	−5.67774	−	1.85911i	−0.263299	−	0.0862140i
$466$	−7.67686	+	5.57757i	−0.355624	+	0.258376i
$467$	7.34262	+	2.38576i	0.339776	+	0.110400i	0.473935	−	0.880560i	$-0.342833\pi$
$467$	7.34262	+	2.38576i	0.339776	+	0.110400i	−0.134159	+	0.990960i	$0.542833\pi$
$468$		0			0
$469$	−26.0776	+	18.9465i	−1.20415	+	0.874867i
$470$	11.6512	−	35.5830i	0.537431	−	1.64132i
$471$	5.98636	+	18.4241i	0.275837	+	0.848939i
$472$			44.1485i			2.03210i
$473$		0			0
$474$	−2.51087			−0.115328
$475$	−16.1267	−	11.8292i	−0.739942	−	0.542763i
$476$	−19.4164	−	14.1068i	−0.889950	−	0.646586i
$477$	−14.0797	−	19.3790i	−0.644664	−	0.887303i
$478$	35.3986	+	11.5017i	1.61909	+	0.526075i
$479$	−1.69623	+	5.22047i	−0.0775029	+	0.238529i	−0.982300	−	0.187313i	$-0.940022\pi$
$479$	−1.69623	+	5.22047i	−0.0775029	+	0.238529i	0.904797	+	0.425842i	$0.140022\pi$
$480$	5.87939	+	4.29211i	0.268356	+	0.195907i
$481$		0			0
$482$	−40.2001	+	13.0618i	−1.83107	+	0.594950i
$483$			2.17448i			0.0989423i
$484$		0			0
$485$	12.4307	−	4.00772i	0.564449	−	0.181981i
$486$	−12.2750	−	37.7786i	−0.556806	−	1.71367i
$487$	4.19125	−	5.76876i	0.189924	−	0.261408i	−0.703427	−	0.710767i	$-0.748348\pi$
$487$	4.19125	−	5.76876i	0.189924	−	0.261408i	0.893351	+	0.449360i	$0.148348\pi$
$488$	−2.62080	−	3.60722i	−0.118638	−	0.163291i
$489$	−0.848116	+	2.61023i	−0.0383532	+	0.118039i
$490$	−0.0642401	+	28.2229i	−0.00290207	+	1.27498i
$491$	5.26741	−	3.82700i	0.237715	−	0.172710i	−0.462550	−	0.886593i	$-0.653065\pi$
$491$	5.26741	−	3.82700i	0.237715	−	0.172710i	0.700265	+	0.713883i	$0.253065\pi$
$492$	−17.8052	+	24.5068i	−0.802721	+	1.10485i
$493$	−13.1782	+	4.28187i	−0.593517	+	0.192846i
$494$		0			0
$495$		0			0
$496$	21.4891			0.964890
$497$	33.3305	−	10.8297i	1.49508	−	0.485780i
$498$	7.79785	−	10.7328i	0.349430	−	0.480949i
$499$	−16.1803	+	11.7557i	−0.724331	+	0.526258i	−0.887765	−	0.460297i	$-0.847743\pi$
$499$	−16.1803	+	11.7557i	−0.724331	+	0.526258i	0.163434	+	0.986554i	$0.447743\pi$
$500$	39.7429	−	28.4623i	1.77736	−	1.27287i
$501$	−3.85263	+	11.8572i	−0.172123	+	0.529740i
$502$	−32.8163	−	45.1677i	−1.46466	−	2.01593i
$503$	−7.97122	+	10.9714i	−0.355419	+	0.489193i	−0.948865	−	0.315681i	$-0.897767\pi$
$503$	−7.97122	+	10.9714i	−0.355419	+	0.489193i	0.593446	+	0.804874i	$0.297767\pi$
$504$	−15.2073	−	46.8033i	−0.677388	−	2.08479i
$505$	−4.11684	−	12.7692i	−0.183197	−	0.568220i
$506$		0			0
$507$		−	10.2997i		−	0.457427i
$508$	−34.1721	+	11.1032i	−1.51614	+	0.492624i
$509$	18.3062	+	13.3002i	0.811408	+	0.589523i	0.914239	−	0.405176i	$-0.132790\pi$
$509$	18.3062	+	13.3002i	0.811408	+	0.589523i	−0.102830	+	0.994699i	$0.532790\pi$
$510$	−4.17834	+	5.72355i	−0.185020	+	0.253443i
$511$	−7.41641	+	22.8254i	−0.328083	+	1.00973i
$512$	47.6830	+	15.4932i	2.10731	+	0.684707i
$513$	10.0074	+	13.7740i	0.441836	+	0.608135i
$514$	21.8259	+	15.8574i	0.962698	+	0.699441i
$515$	13.6161	+	18.8309i	0.599996	+	0.829788i
$516$	12.0000			0.528271
$517$		0			0
$518$			9.50744i			0.417733i
$519$	2.08418	+	6.41446i	0.0914855	+	0.281564i
$520$		0			0
$521$	17.4796	−	12.6997i	0.765795	−	0.556383i	−0.134887	−	0.990861i	$-0.543067\pi$
$521$	17.4796	−	12.6997i	0.765795	−	0.556383i	0.900682	+	0.434478i	$0.143067\pi$
$522$	−49.8033	−	16.1821i	−2.17983	−	0.708270i
$523$	−27.5830	−	8.96224i	−1.20612	−	0.391892i	−0.364110	−	0.931356i	$-0.618627\pi$
$523$	−27.5830	−	8.96224i	−1.20612	−	0.391892i	−0.842008	+	0.539464i	$0.818627\pi$
$524$	9.70820	−	7.05342i	0.424105	−	0.308130i
$525$	13.7227	+	0.0624706i	0.598906	+	0.00272644i
$526$	−21.3877	−	65.8245i	−0.932547	−	2.87008i
$527$			5.34363i			0.232772i
$528$		0			0
$529$	22.3723			0.972708
$530$	−46.1864	+	33.3960i	−2.00621	+	1.45063i
$531$	−14.1490	−	10.2798i	−0.614014	−	0.446107i
$532$	35.6104	+	49.0136i	1.54391	+	2.12501i
$533$		0			0
$534$	0.848116	−	2.61023i	0.0367016	−	0.112956i
$535$	−8.74555	+	11.9798i	−0.378103	+	0.517931i
$536$	−45.0807	−	32.7530i	−1.94719	−	1.41472i
$537$	−9.69119	+	3.14886i	−0.418206	+	0.135883i
$538$		−	29.0024i		−	1.25038i
$539$		0			0
$540$	−39.6060	+	12.7692i	−1.70437	+	0.549497i
$541$	−10.5788	−	32.5582i	−0.454818	−	1.39979i	−0.871349	−	0.490664i	$-0.836754\pi$
$541$	−10.5788	−	32.5582i	−0.454818	−	1.39979i	0.416531	−	0.909121i	$-0.363246\pi$
$542$	20.0147	−	27.5479i	0.859707	−	1.18328i
$543$	11.2311	+	15.4583i	0.481972	+	0.663377i
$544$	2.01197	−	6.19221i	0.0862625	−	0.265489i
$545$	22.3606	+	0.0508966i	0.957824	+	0.00218017i
$546$		0			0
$547$	−17.0472	+	23.4635i	−0.728886	+	1.00323i	0.270296	+	0.962777i	$0.412878\pi$
$547$	−17.0472	+	23.4635i	−0.728886	+	1.00323i	−0.999182	+	0.0404479i	$0.987122\pi$
$548$	−59.6870	+	19.3935i	−2.54970	+	0.828448i
$549$	1.76631			0.0753844
$550$		0			0
$551$	34.9783			1.49012
$552$	−3.57507	+	1.16161i	−0.152165	+	0.0494415i
$553$	2.55626	−	3.51838i	0.108703	−	0.149617i
$554$	23.8572	−	17.3333i	1.01360	−	0.736420i
$555$	1.92616	+	0.00438427i	0.0817609	+	0.000186102i
$556$	21.9335	−	67.5043i	0.930187	−	2.86282i
$557$	0.584650	+	0.804702i	0.0247724	+	0.0340963i	0.821224	−	0.570607i	$-0.193292\pi$
$557$	0.584650	+	0.804702i	0.0247724	+	0.0340963i	−0.796451	+	0.604703i	$0.793292\pi$
$558$	−11.8701	+	16.3379i	−0.502503	+	0.691637i
$559$		0			0
$560$	−46.9783	+	15.1460i	−1.98519	+	0.640036i
$561$		0			0
$562$		−	1.28962i		−	0.0543994i
$563$	−17.9798	+	5.84199i	−0.757758	+	0.246211i	−0.662316	−	0.749224i	$-0.730426\pi$
$563$	−17.9798	+	5.84199i	−0.757758	+	0.246211i	−0.0954420	+	0.995435i	$0.530426\pi$
$564$	18.5898	+	13.5063i	0.782772	+	0.568717i
$565$	−0.655705	+	0.898194i	−0.0275857	+	0.0377873i
$566$	−11.8149	+	36.3624i	−0.496616	+	1.52843i
$567$	12.3367	+	4.00843i	0.518092	+	0.168338i
$568$	35.6104	+	49.0136i	1.49418	+	2.05656i
$569$	22.0501	+	16.0203i	0.924389	+	0.671608i	0.944613	−	0.328188i	$-0.106438\pi$
$569$	22.0501	+	16.0203i	0.924389	+	0.671608i	−0.0202237	+	0.999795i	$0.506438\pi$
$570$	14.4960	−	10.4817i	0.607172	−	0.439028i
$571$	−1.48913			−0.0623180			−0.0311590	−	0.999514i	$-0.509920\pi$
$571$	−1.48913			−0.0623180			−0.0311590	+	0.999514i	$0.509920\pi$
$572$		0			0
$573$			15.3484i			0.641189i
$574$	−23.6297	−	72.7248i	−0.986285	−	3.03547i
$575$	−0.0180337	+	3.96139i	−0.000752058	+	0.165202i
$576$	−4.55292	+	3.30789i	−0.189705	+	0.137829i
$577$	−20.8014	−	6.75877i	−0.865972	−	0.281371i	−0.157852	−	0.987463i	$-0.550457\pi$
$577$	−20.8014	−	6.75877i	−0.865972	−	0.281371i	−0.708121	+	0.706091i	$0.750457\pi$
$578$	−34.7853	−	11.3024i	−1.44688	−	0.470119i
$579$	−10.5348	+	7.65399i	−0.437812	+	0.318089i
$580$	−26.6038	+	81.2484i	−1.10466	+	3.37366i
$581$	7.10067	+	21.8536i	0.294585	+	0.906641i
$582$			11.6819i			0.484231i
$583$		0			0
$584$	−41.4891			−1.71683
$585$		0			0
$586$	6.47214	+	4.70228i	0.267361	+	0.194249i
$587$	−24.2604	−	33.3916i	−1.00133	−	1.37822i	−0.924503	−	0.381174i	$-0.875520\pi$
$587$	−24.2604	−	33.3916i	−1.00133	−	1.37822i	−0.0768307	−	0.997044i	$-0.524480\pi$
$588$	−16.4728	−	5.35233i	−0.679326	−	0.220726i
$589$	4.16837	−	12.8289i	0.171755	−	0.528606i
$590$	−24.5364	+	33.6103i	−1.01015	+	1.38371i
$591$	−5.45647	−	3.96435i	−0.224449	−	0.163072i
$592$	−6.58911	+	2.14093i	−0.270811	+	0.0879918i
$593$			22.7739i			0.935214i	0.883937	+	0.467607i	$0.154884\pi$
$593$			22.7739i			0.935214i	−0.883937	+	0.467607i	$0.845116\pi$
$594$		0			0
$595$	−3.76631	−	11.6819i	−0.154404	−	0.478912i
$596$	15.5231	+	47.7751i	0.635849	+	1.95694i
$597$	−3.72556	+	5.12779i	−0.152477	+	0.209866i
$598$		0			0
$599$	−3.39247	+	10.4409i	−0.138612	+	0.426605i	−0.996134	−	0.0878422i	$-0.972003\pi$
$599$	−3.39247	+	10.4409i	−0.138612	+	0.426605i	0.857522	+	0.514447i	$0.172003\pi$
$600$	7.22797	+	22.5949i	0.295081	+	0.922432i
$601$	−31.1208	+	22.6106i	−1.26944	+	0.922304i	−0.999180	−	0.0404830i	$-0.987110\pi$
$601$	−31.1208	+	22.6106i	−1.26944	+	0.922304i	−0.270262	+	0.962787i	$0.587110\pi$
$602$	−17.8052	+	24.5068i	−0.725687	+	0.998822i
$603$	20.9938	−	6.82131i	0.854935	−	0.277785i
$604$	−53.4891			−2.17644
$605$		0			0
$606$	12.0000			0.487467
$607$	−3.29456	+	1.07047i	−0.133722	+	0.0434489i	−0.375113	−	0.926979i	$-0.622396\pi$
$607$	−3.29456	+	1.07047i	−0.133722	+	0.0434489i	0.241391	+	0.970428i	$0.422396\pi$
$608$	−9.66063	+	13.2967i	−0.391790	+	0.539253i
$609$	−19.4164	+	14.1068i	−0.786793	+	0.571638i
$610$	0.00956616	−	4.20274i	0.000387322	−	0.170164i
$611$		0			0
$612$	9.66063	+	13.2967i	0.390508	+	0.537488i
$613$	2.55626	−	3.51838i	0.103246	−	0.142106i	−0.754268	−	0.656567i	$-0.772008\pi$
$613$	2.55626	−	3.51838i	0.103246	−	0.142106i	0.857514	+	0.514461i	$0.172008\pi$
$614$	24.6357	+	75.8209i	0.994216	+	3.05988i
$615$	−14.7446	+	4.75372i	−0.594558	+	0.191689i
$616$		0			0
$617$			17.0256i			0.685423i	0.939441	+	0.342712i	$0.111345\pi$
$617$			17.0256i			0.685423i	−0.939441	+	0.342712i	$0.888655\pi$
$618$	−19.7673	+	6.42280i	−0.795159	+	0.258363i
$619$	11.4208	+	8.29767i	0.459039	+	0.333512i	0.793154	−	0.609021i	$-0.208437\pi$
$619$	11.4208	+	8.29767i	0.459039	+	0.333512i	−0.334115	+	0.942532i	$0.608437\pi$
$620$	26.6290	+	19.4399i	1.06945	+	0.780723i
$621$	1.04209	−	3.20723i	0.0418177	−	0.128702i
$622$	−13.1782	−	4.28187i	−0.528399	−	0.171687i
$623$	2.79417	+	3.84584i	0.111946	+	0.154080i
$624$		0			0
$625$	24.9990	+	0.227614i	0.999959	+	0.00910454i
$626$	−55.2119			−2.20671
$627$		0			0
$628$		−	106.907i		−	4.26606i
$629$	−0.532379	−	1.63849i	−0.0212273	−	0.0653310i
$630$	14.4345	−	44.0832i	0.575085	−	1.75632i
$631$	−19.0976	+	13.8752i	−0.760265	+	0.552365i	−0.898991	−	0.437966i	$-0.855699\pi$
$631$	−19.0976	+	13.8752i	−0.760265	+	0.552365i	0.138727	+	0.990331i	$0.455699\pi$
$632$	7.15015	+	2.32322i	0.284418	+	0.0924129i
$633$	1.12207	+	0.364583i	0.0445983	+	0.0144909i
$634$	67.3199	−	48.9108i	2.67361	−	1.94249i
$635$	−17.4633	−	5.71814i	−0.693009	−	0.226917i
$636$	−10.8089	−	33.2663i	−0.428600	−	1.31909i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	18.6131	+	25.7418i	0.735749	+	1.01753i
$641$	20.5266	+	14.9135i	0.810752	+	0.589046i	0.914049	−	0.405605i	$-0.132939\pi$
$641$	20.5266	+	14.9135i	0.810752	+	0.589046i	−0.103296	+	0.994651i	$0.532939\pi$
$642$	−7.79785	−	10.7328i	−0.307757	−	0.423591i
$643$	−29.0019	−	9.42330i	−1.14372	−	0.371619i	−0.324948	−	0.945732i	$-0.605347\pi$
$643$	−29.0019	−	9.42330i	−1.14372	−	0.371619i	−0.818776	+	0.574113i	$0.805347\pi$
$644$	3.70820	−	11.4127i	0.146124	−	0.449723i
$645$	4.95674	+	3.61855i	0.195171	+	0.142480i
$646$	−12.9443	−	9.40456i	−0.509286	−	0.370018i
$647$	−20.9058	+	6.79271i	−0.821892	+	0.267049i	−0.689626	−	0.724166i	$-0.742225\pi$
$647$	−20.9058	+	6.79271i	−0.821892	+	0.267049i	−0.132265	+	0.991214i	$0.542225\pi$
$648$			22.4241i			0.880901i
$649$		0			0
$650$		0			0
$651$	2.86009	+	8.80244i	0.112096	+	0.344995i
$652$	8.90261	−	12.2534i	0.348653	−	0.479880i
$653$	18.0975	+	24.9091i	0.708212	+	0.974770i	0.999834	+	0.0182362i	$0.00580509\pi$
$653$	18.0975	+	24.9091i	0.708212	+	0.974770i	−0.291622	+	0.956534i	$0.594195\pi$
$654$	−6.18034	+	19.0211i	−0.241670	+	0.743785i
$655$	6.13701	+	0.0139689i	0.239793	+	0.000545810i
$656$	45.0807	−	32.7530i	1.76011	−	1.27879i
$657$	9.66063	−	13.2967i	0.376897	−	0.518754i
$658$	−55.1659	+	17.9245i	−2.15059	+	0.698769i
$659$	21.2554			0.827994			0.413997	−	0.910278i	$-0.364132\pi$
$659$	21.2554			0.827994			0.413997	+	0.910278i	$0.364132\pi$
$660$		0			0
$661$	−16.3505			−0.635962			−0.317981	−	0.948097i	$-0.603005\pi$
$661$	−16.3505			−0.635962			−0.317981	+	0.948097i	$0.603005\pi$
$662$	−33.8915	+	11.0120i	−1.31723	+	0.427995i
$663$		0			0
$664$	−32.1364	+	23.3485i	−1.24714	+	0.906097i
$665$	−0.0705244	+	30.9838i	−0.00273482	+	1.20150i
$666$	2.01197	−	6.19221i	0.0779623	−	0.239943i
$667$	−4.07230	−	5.60503i	−0.157680	−	0.217028i
$668$	40.4408	−	55.6619i	1.56470	−	2.15362i
$669$	−0.581927	−	1.79099i	−0.0224986	−	0.0692436i
$670$	−16.1168	−	49.9894i	−0.622648	−	1.93126i
$671$		0			0
$672$		−	11.2772i		−	0.435026i
$673$	17.6993	−	5.75085i	0.682257	−	0.221679i	0.0526739	−	0.998612i	$-0.483226\pi$
$673$	17.6993	−	5.75085i	0.682257	−	0.221679i	0.629583	+	0.776933i	$0.283226\pi$
$674$	66.3042	+	48.1728i	2.55394	+	1.85555i
$675$	−20.2102	−	6.66855i	−0.777890	−	0.256673i
$676$	−17.5644	+	54.0577i	−0.675555	+	2.07914i
$677$	47.6308	+	15.4762i	1.83060	+	0.594798i	0.999236	+	0.0390703i	$0.0124396\pi$
$677$	47.6308	+	15.4762i	1.83060	+	0.594798i	0.831364	+	0.555728i	$0.187560\pi$
$678$	−0.584650	−	0.804702i	−0.0224534	−	0.0309044i
$679$	−16.3694	−	11.8931i	−0.628200	−	0.456414i
$680$	17.1943	−	12.4327i	0.659373	−	0.476773i
$681$	13.2554			0.507949
$682$		0			0
$683$			17.9104i			0.685323i	0.939459	+	0.342661i	$0.111328\pi$
$683$			17.9104i			0.685323i	−0.939459	+	0.342661i	$0.888672\pi$
$684$	−12.8208	−	39.4585i	−0.490217	−	1.50873i
$685$	−30.5024	−	9.98764i	−1.16544	−	0.381608i
$686$	−14.1490	+	10.2798i	−0.540211	+	0.392486i
$687$	11.0221	+	3.58131i	0.420520	+	0.136635i
$688$	−20.9938	−	6.82131i	−0.800383	−	0.260060i
$689$		0			0
$690$	−3.36730	−	1.10258i	−0.128191	−	0.0419745i
$691$	13.8629	+	42.6657i	0.527371	+	1.62308i	0.759579	+	0.650415i	$0.225405\pi$
$691$	13.8629	+	42.6657i	0.527371	+	1.62308i	−0.232208	+	0.972666i	$0.574595\pi$
$692$		−	37.2203i		−	1.41490i
$693$		0			0
$694$	−57.2119			−2.17174
$695$	29.4155	−	21.2695i	1.11579	−	0.806798i
$696$	−33.5654	−	24.3867i	−1.27229	−	0.924375i
$697$	8.14459	+	11.2101i	0.308498	+	0.424612i
$698$	−37.1861	−	12.0825i	−1.40751	−	0.457329i
$699$	0.920330	−	2.83248i	0.0348101	−	0.107134i
$700$	−71.9164	−	23.7295i	−2.71818	−	0.896892i
$701$	−10.1215	−	7.35371i	−0.382284	−	0.277746i	0.380002	−	0.924986i	$-0.375923\pi$
$701$	−10.1215	−	7.35371i	−0.382284	−	0.277746i	−0.762286	+	0.647240i	$0.775923\pi$
$702$		0			0
$703$			4.34896i			0.164024i
$704$		0			0
$705$	3.60597	+	11.1846i	0.135809	+	0.421236i
$706$	19.5336	+	60.1181i	0.735155	+	2.26258i
$707$	−12.2169	+	16.8151i	−0.459463	+	0.632397i
$708$	−15.0111	−	20.6609i	−0.564150	−	0.776486i
$709$	−7.38030	+	22.7142i	−0.277173	+	0.853051i	0.711463	+	0.702723i	$0.248033\pi$
$709$	−7.38030	+	22.7142i	−0.277173	+	0.853051i	−0.988636	+	0.150328i	$0.951967\pi$
$710$	−0.129981	+	57.1053i	−0.00487812	+	2.14312i
$711$	−2.40946	+	1.75057i	−0.0903616	+	0.0656516i
$712$	−4.83032	+	6.64836i	−0.181024	+	0.249158i
$713$	−2.54105	+	0.825636i	−0.0951629	+	0.0309203i
$714$	10.9783			0.410851
$715$		0			0
$716$	56.2337			2.10155
$717$	−11.1102	+	3.60991i	−0.414917	+	0.134815i
$718$	−43.7550	+	60.2236i	−1.63292	+	2.24753i
$719$	−24.5541	+	17.8396i	−0.915713	+	0.665305i	−0.942453	−	0.334338i	$-0.891487\pi$
$719$	−24.5541	+	17.8396i	−0.915713	+	0.665305i	0.0267400	+	0.999642i	$0.491487\pi$
$720$	33.8022	+	0.0769396i	1.25973	+	0.00286737i
$721$	11.1246	−	34.2380i	0.414302	−	1.27509i
$722$	−4.45131	−	6.12670i	−0.165660	−	0.228012i
$723$	7.79785	−	10.7328i	0.290005	−	0.399158i
$724$	−32.5845	−	100.285i	−1.21099	−	3.72705i
$725$	−35.4891	+	25.5383i	−1.31803	+	0.948470i
$726$		0			0
$727$		−	14.0588i		−	0.521412i	−0.965418	−	0.260706i	$-0.916045\pi$
$727$		−	14.0588i		−	0.521412i	0.965418	−	0.260706i	$-0.0839552\pi$
$728$		0			0
$729$	0.998075	+	0.725144i	0.0369657	+	0.0268572i
$730$	−31.5857	−	23.0584i	−1.16904	−	0.853430i
$731$	1.69623	−	5.22047i	0.0627374	−	0.193086i
$732$	2.45300	+	0.797029i	0.0906656	+	0.0294590i
$733$	−5.58834	−	7.69168i	−0.206410	−	0.284099i	0.693244	−	0.720703i	$-0.256181\pi$
$733$	−5.58834	−	7.69168i	−0.206410	−	0.284099i	−0.899654	+	0.436604i	$0.856181\pi$
$734$	52.5685	+	38.1933i	1.94034	+	1.40974i
$735$	−5.19030	−	7.17814i	−0.191447	−	0.264770i
$736$	3.25544			0.119997
$737$		0			0
$738$			52.3663i			1.92763i
$739$	−3.32025	−	10.2187i	−0.122137	−	0.375900i	0.871231	−	0.490873i	$-0.163322\pi$
$739$	−3.32025	−	10.2187i	−0.122137	−	0.375900i	−0.993369	+	0.114972i	$0.963322\pi$
$740$	−10.1019	−	3.30774i	−0.371353	−	0.121595i
$741$		0			0
$742$	83.9754	+	27.2852i	3.08283	+	1.00167i
$743$	−10.8297	−	3.51877i	−0.397301	−	0.129091i	0.103550	−	0.994624i	$-0.466980\pi$
$743$	−10.8297	−	3.51877i	−0.397301	−	0.129091i	−0.500852	+	0.865533i	$0.666980\pi$
$744$	−12.9443	+	9.40456i	−0.474560	+	0.344788i
$745$	−7.99438	+	24.4150i	−0.292892	+	0.894495i
$746$	9.11264	+	28.0458i	0.333637	+	1.02683i
$747$		−	15.7359i		−	0.575748i
$748$		0			0
$749$	22.9783			0.839607
$750$	−7.05488	+	21.2186i	−0.257608	+	0.774793i
$751$	−22.1446	−	16.0890i	−0.808069	−	0.587097i	0.105201	−	0.994451i	$-0.466451\pi$
$751$	−22.1446	−	16.0890i	−0.808069	−	0.587097i	−0.913270	+	0.407354i	$0.866451\pi$
$752$	−24.8451	−	34.1963i	−0.906006	−	1.24701i
$753$	16.6653	+	5.41487i	0.607316	+	0.197329i
$754$		0			0
$755$	−22.0943	−	16.1294i	−0.804094	−	0.587009i
$756$	52.1552	+	37.8930i	1.89687	+	1.37815i
$757$	37.8516	−	12.2987i	1.37574	−	0.447005i	0.474473	−	0.880270i	$-0.342639\pi$
$757$	37.8516	−	12.2987i	1.37574	−	0.447005i	0.901266	+	0.433266i	$0.142639\pi$
$758$		−	1.58457i		−	0.0575543i
$759$		0			0
$760$	−50.9783	+	16.4356i	−1.84918	+	0.596184i
$761$	−10.1186	−	31.1419i	−0.366800	−	1.12889i	−0.948846	−	0.315738i	$-0.897748\pi$
$761$	−10.1186	−	31.1419i	−0.366800	−	1.12889i	0.582046	−	0.813156i	$-0.302252\pi$
$762$	9.66063	−	13.2967i	0.349968	−	0.481689i
$763$	−20.3615	−	28.0252i	−0.737135	−	1.01458i
$764$	26.1741	−	80.5555i	0.946945	−	2.91440i
$765$	−0.0191323	+	8.40548i	−0.000691730	+	0.303901i
$766$	22.2392	−	16.1577i	0.803534	−	0.583802i
$767$		0			0
$768$	−23.4468	+	7.61834i	−0.846065	+	0.274903i
$769$	29.2119			1.05341			0.526705	−	0.850048i	$-0.323427\pi$
$769$	29.2119			1.05341			0.526705	+	0.850048i	$0.323427\pi$
$770$		0			0
$771$	−8.46738			−0.304945
$772$	68.3441	−	22.2064i	2.45976	−	0.799224i
$773$	−10.3541	+	14.2512i	−0.372411	+	0.512580i	−0.953554	−	0.301221i	$-0.902606\pi$
$773$	−10.3541	+	14.2512i	−0.372411	+	0.512580i	0.581143	+	0.813802i	$0.302606\pi$
$774$	16.7827	−	12.1933i	0.603242	−	0.438281i
$775$	5.13741	+	16.0597i	0.184541	+	0.576882i
$776$	10.8089	−	33.2663i	0.388016	−	1.19419i
$777$	−1.75395	−	2.41411i	−0.0629226	−	0.0866056i
$778$	27.9860	−	38.5194i	1.00335	−	1.38099i
$779$	−10.8089	−	33.2663i	−0.387268	−	1.19189i
$780$		0			0
$781$		0			0
$782$			3.16915i			0.113328i
$783$	35.3986	−	11.5017i	1.26504	−	0.411037i
$784$	25.7764	+	18.7277i	0.920586	+	0.668845i
$785$	32.2373	−	44.1592i	1.15060	−	1.57611i
$786$	−1.69623	+	5.22047i	−0.0605026	+	0.186208i
$787$	−14.4047	−	4.68038i	−0.513473	−	0.166838i	0.0408081	−	0.999167i	$-0.487007\pi$
$787$	−14.4047	−	4.68038i	−0.513473	−	0.166838i	−0.554281	+	0.832329i	$0.687007\pi$
$788$	21.8775	+	30.1118i	0.779354	+	1.07269i
$789$	17.5741	+	12.7683i	0.625655	+	0.454565i
$790$	4.15224	+	5.74251i	0.147730	+	0.204309i
$791$	1.72281			0.0612562
$792$		0			0
$793$		0			0
$794$	12.8208	+	39.4585i	0.454995	+	1.40033i
$795$	5.56657	−	17.0004i	0.197426	−	0.602942i
$796$	28.2980	−	20.5597i	1.00300	−	0.728719i
$797$	−4.99405	−	1.62267i	−0.176898	−	0.0574778i	0.219229	−	0.975674i	$-0.429646\pi$
$797$	−4.99405	−	1.62267i	−0.176898	−	0.0574778i	−0.396127	+	0.918196i	$0.629646\pi$
$798$	−26.3565	−	8.56373i	−0.933008	−	0.303153i
$799$	8.50348	−	6.17814i	0.300831	−	0.218567i
$800$	0.0935254	−	20.5443i	0.00330662	−	0.726352i
$801$	−1.00599	−	3.09610i	−0.0355447	−	0.109395i
$802$			29.0024i			1.02411i
$803$		0			0
$804$	32.2337			1.13679
$805$	4.97316	−	3.59594i	0.175281	−	0.126740i
$806$		0			0
$807$	5.35042	+	7.36423i	0.188344	+	0.259233i
$808$	−34.1721	−	11.1032i	−1.20217	−	0.390608i
$809$	−10.1186	+	31.1419i	−0.355752	+	1.09489i	0.599820	+	0.800135i	$0.295239\pi$
$809$	−10.1186	+	31.1419i	−0.355752	+	1.09489i	−0.955572	+	0.294757i	$0.904761\pi$
$810$	−12.4626	+	17.0715i	−0.437892	+	0.599831i
$811$	−0.189058	−	0.137358i	−0.00663871	−	0.00482330i	0.584461	−	0.811422i	$-0.301306\pi$
$811$	−0.189058	−	0.137358i	−0.00663871	−	0.00482330i	−0.591100	+	0.806599i	$0.701306\pi$
$812$	125.963	−	40.9279i	4.42044	−	1.43629i
$813$			10.6873i			0.374819i
$814$		0			0
$815$	7.37228	−	2.37686i	0.258240	−	0.0832578i
$816$	2.47214	+	7.60845i	0.0865421	+	0.266349i
$817$	−8.14459	+	11.2101i	−0.284943	+	0.392191i
$818$	40.7875	+	56.1392i	1.42610	+	1.96286i
$819$		0			0
$820$	85.4929	+	0.194596i	2.98554	+	0.00679560i
$821$	−14.5623	+	10.5801i	−0.508228	+	0.369249i	−0.812151	−	0.583447i	$-0.801703\pi$
$821$	−14.5623	+	10.5801i	−0.508228	+	0.369249i	0.303923	+	0.952697i	$0.401703\pi$
$822$	16.8738	−	23.2248i	0.588543	−	0.810059i
$823$	−53.2903	+	17.3151i	−1.85758	+	0.603566i	−0.862319	+	0.506365i	$0.830989\pi$
$823$	−53.2903	+	17.3151i	−1.85758	+	0.603566i	−0.995265	+	0.0972005i	$0.969011\pi$
$824$	62.2337			2.16801
$825$		0			0
$826$	64.4674			2.24311
$827$	−27.0219	+	8.77995i	−0.939644	+	0.305309i	−0.738501	−	0.674253i	$-0.764466\pi$
$827$	−27.0219	+	8.77995i	−0.939644	+	0.305309i	−0.201144	+	0.979562i	$0.564466\pi$
$828$	−4.83032	+	6.64836i	−0.167865	+	0.231046i
$829$	−16.4639	+	11.9617i	−0.571816	+	0.415448i	−0.835764	−	0.549088i	$-0.814975\pi$
$829$	−16.4639	+	11.9617i	−0.571816	+	0.415448i	0.263949	+	0.964537i	$0.414975\pi$
$830$	−37.4419	−	0.0852241i	−1.29963	−	0.00295817i
$831$	−2.86009	+	8.80244i	−0.0992153	+	0.305353i
$832$		0			0
$833$	−4.65695	+	6.40974i	−0.161354	+	0.222084i
$834$	10.0330	+	30.8783i	0.347413	+	1.06923i
$835$	33.4891	−	10.7971i	1.15894	−	0.373648i
$836$		0			0
$837$		−	14.3537i		−	0.496138i
$838$	55.1659	−	17.9245i	1.90567	−	0.619191i
$839$	−8.18470	−	5.94653i	−0.282567	−	0.205297i	0.437469	−	0.899233i	$-0.355875\pi$
$839$	−8.18470	−	5.94653i	−0.282567	−	0.205297i	−0.720036	+	0.693936i	$0.755875\pi$
$840$	21.6694	−	29.6831i	0.747667	−	1.02416i
$841$	14.6682	−	45.1442i	0.505801	−	1.55670i
$842$	−20.4328	−	6.63902i	−0.704161	−	0.228796i
$843$	0.237912	+	0.327457i	0.00819411	+	0.0112782i
$844$	−5.26741	−	3.82700i	−0.181312	−	0.131731i
$845$	−23.5561	+	17.0327i	−0.810353	+	0.585942i
$846$	39.7228			1.36570
$847$		0			0
$848$			64.3432i			2.20955i
$849$	−3.70820	−	11.4127i	−0.127265	−	0.391682i
$850$	19.9998	+	0.0910464i	0.685987	+	0.00312286i
$851$	0.696893	−	0.506322i	0.0238892	−	0.0173565i
$852$	−33.3305	−	10.8297i	−1.14188	−	0.371021i
$853$	−33.3305	−	10.8297i	−1.14122	−	0.370803i	−0.323387	−	0.946267i	$-0.604822\pi$
$853$	−33.3305	−	10.8297i	−1.14122	−	0.370803i	−0.817828	+	0.575463i	$0.804822\pi$
$854$	−5.26741	+	3.82700i	−0.180247	+	0.130957i
$855$	6.60274	−	20.1649i	0.225809	−	0.689623i
$856$	12.2750	+	37.7786i	0.419552	+	1.29125i
$857$		−	23.9538i		−	0.818245i	−0.912480	−	0.409122i	$-0.865835\pi$
$857$		−	23.9538i		−	0.818245i	0.912480	−	0.409122i	$-0.134165\pi$
$858$		0			0
$859$	6.11684			0.208704			0.104352	−	0.994540i	$-0.466723\pi$
$859$	6.11684			0.208704			0.104352	+	0.994540i	$0.466723\pi$
$860$	−19.8444	−	27.4447i	−0.676689	−	0.935855i
$861$	19.4164	+	14.1068i	0.661709	+	0.480760i
$862$	38.1667	+	52.5320i	1.29996	+	1.78925i
$863$	−2.73352	−	0.888175i	−0.0930501	−	0.0302338i	0.262122	−	0.965035i	$-0.415578\pi$
$863$	−2.73352	−	0.888175i	−0.0930501	−	0.0302338i	−0.355172	+	0.934801i	$0.615578\pi$
$864$	−5.40444	+	16.6331i	−0.183863	+	0.565871i
$865$	11.2236	−	15.3743i	0.381614	−	0.522740i
$866$	−59.6430	−	43.3332i	−2.02675	−	1.47252i
$867$	10.9177	−	3.54737i	0.370784	−	0.120475i
$868$		−	51.0767i		−	1.73365i
$869$		0			0
$870$	−12.0000	−	37.2203i	−0.406838	−	1.26188i
$871$		0			0
$872$	35.1992	−	48.4475i	1.19199	−	1.64064i
$873$	8.14459	+	11.2101i	0.275653	+	0.379403i
$874$	2.47214	−	7.60845i	0.0836212	−	0.257360i
$875$	−22.5503	−	31.4878i	−0.762341	−	1.06448i
$876$	19.4164	−	14.1068i	0.656020	−	0.476626i
$877$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$877$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$878$	51.5908	−	16.7629i	1.74111	−	0.565720i
$879$	−2.51087			−0.0846897
$880$		0			0
$881$	−6.86141			−0.231167			−0.115583	−	0.993298i	$-0.536874\pi$
$881$	−6.86141			−0.231167			−0.115583	+	0.993298i	$0.536874\pi$
$882$	−28.4767	+	9.25265i	−0.958861	+	0.311553i
$883$	14.2530	−	19.6176i	0.479653	−	0.660185i	−0.498785	−	0.866726i	$-0.666220\pi$
$883$	14.2530	−	19.6176i	0.479653	−	0.660185i	0.978438	+	0.206540i	$0.0662204\pi$
$884$		0			0
$885$	0.0297285	−	13.0608i	0.000999313	−	0.439032i
$886$	−24.7079	+	76.0432i	−0.830079	+	2.55472i
$887$	16.1158	+	22.1815i	0.541116	+	0.744782i	0.988773	−	0.149423i	$-0.0477416\pi$
$887$	16.1158	+	22.1815i	0.541116	+	0.744782i	−0.447657	+	0.894205i	$0.647742\pi$
$888$	3.03208	−	4.17330i	0.101750	−	0.140047i
$889$	8.79690	+	27.0741i	0.295039	+	0.908036i
$890$	−7.37228	+	2.37686i	−0.247119	+	0.0796726i
$891$		0			0
$892$			10.3923i			0.347960i
$893$	−25.2344	+	8.19915i	−0.844436	+	0.274374i
$894$	−18.5898	−	13.5063i	−0.621736	−	0.451717i
$895$	23.2280	+	16.9570i	0.776425	+	0.566811i
$896$	15.2073	−	46.8033i	0.508041	−	1.56359i
$897$		0			0
$898$	−10.1807	−	14.0126i	−0.339736	−	0.467606i
$899$	−23.8572	−	17.3333i	−0.795682	−	0.578097i
$900$	41.8176	+	30.6741i	1.39392	+	1.02247i
$901$	−16.0000			−0.533037
$902$		0			0
$903$		−	9.50744i		−	0.316388i
$904$	0.920330	+	2.83248i	0.0306097	+	0.0942070i
$905$	16.7810	−	51.2495i	0.557820	−	1.70359i
$906$	19.7945	−	14.3816i	0.657629	−	0.477795i
$907$	18.9258	+	6.14936i	0.628420	+	0.204186i	0.605875	−	0.795560i	$-0.292823\pi$
$907$	18.9258	+	6.14936i	0.628420	+	0.204186i	0.0225451	+	0.999746i	$0.492823\pi$
$908$	−69.5706	−	22.6049i	−2.30878	−	0.750169i
$909$	11.5153	−	8.36635i	0.381938	−	0.277494i
$910$		0			0
$911$	−16.5290	−	50.8712i	−0.547632	−	1.68544i	−0.714649	−	0.699483i	$-0.753413\pi$
$911$	−16.5290	−	50.8712i	−0.547632	−	1.68544i	0.167017	−	0.985954i	$-0.446587\pi$
$912$		−	20.1947i		−	0.668713i
$913$		0			0
$914$	−52.4674			−1.73547
$915$	0.772901	+	1.06891i	0.0255513	+	0.0353372i
$916$	−51.7419	−	37.5927i	−1.70960	−	1.24210i
$917$	−5.58834	−	7.69168i	−0.184543	−	0.254002i
$918$	−16.1923	−	5.26119i	−0.534424	−	0.173645i
$919$	−8.72469	+	26.8518i	−0.287801	+	0.885760i	0.697744	+	0.716347i	$0.254187\pi$
$919$	−8.72469	+	26.8518i	−0.287801	+	0.885760i	−0.985545	+	0.169413i	$0.945813\pi$
$920$	8.56878	+	6.25543i	0.282504	+	0.206235i
$921$	−20.2430	−	14.7074i	−0.667030	−	0.484626i
$922$	−5.36261	+	1.74242i	−0.176608	+	0.0573835i
$923$		0			0
$924$		0			0
$925$	−3.17527	−	4.41248i	−0.104402	−	0.145081i
$926$	−23.4718	−	72.2389i	−0.771333	−	2.37392i
$927$	−14.4909	+	19.9451i	−0.475945	+	0.655082i
$928$	21.1195	+	29.0685i	0.693281	+	0.954220i
$929$	2.16984	−	6.67808i	0.0711901	−	0.219101i	−0.909131	−	0.416510i	$-0.863253\pi$
$929$	2.16984	−	6.67808i	0.0711901	−	0.219101i	0.980321	+	0.197410i	$0.0632529\pi$
$930$	−15.0813	−	0.0343275i	−0.494534	−	0.00112564i
$931$	16.1803	−	11.7557i	0.530289	−	0.385278i
$932$	−9.66063	+	13.2967i	−0.316444	+	0.435548i
$933$	4.13611	−	1.34390i	0.135410	−	0.0439974i
$934$	19.4891			0.637704
$935$		0			0
$936$		0			0
$937$	−51.0298	+	16.5806i	−1.66707	+	0.541664i	−0.982336	−	0.187128i	$-0.940082\pi$
$937$	−51.0298	+	16.5806i	−1.66707	+	0.541664i	−0.684735	+	0.728792i	$0.740082\pi$
$938$	−47.8273	+	65.8287i	−1.56162	+	2.14938i
$939$	14.0193	−	10.1856i	0.457502	−	0.332395i
$940$	0.147613	−	64.8512i	0.00481459	−	2.11521i
$941$	18.0674	−	55.6058i	0.588981	−	1.81270i	0.00632159	−	0.999980i	$-0.497988\pi$
$941$	18.0674	−	55.6058i	0.588981	−	1.81270i	0.582659	−	0.812717i	$-0.302012\pi$
$942$	28.7440	+	39.5627i	0.936530	+	1.28902i
$943$	−4.07230	+	5.60503i	−0.132612	+	0.182525i
$944$	14.5171	+	44.6790i	0.472491	+	1.45418i
$945$	10.1168	+	31.3793i	0.329101	+	1.02077i
$946$		0			0
$947$			26.7354i			0.868783i	0.900724	+	0.434392i	$0.143037\pi$
$947$			26.7354i			0.868783i	−0.900724	+	0.434392i	$0.856963\pi$
$948$	−4.13611	+	1.34390i	−0.134335	+	0.0436480i
$949$		0			0
$950$	−47.9442	−	15.8197i	−1.55552	−	0.513258i
$951$	−8.07055	+	24.8386i	−0.261705	+	0.805447i
$952$	−31.2625	−	10.1578i	−1.01322	−	0.329216i
$953$	18.3899	+	25.3115i	0.595706	+	0.819920i	0.995307	−	0.0967699i	$-0.0308511\pi$
$953$	18.3899	+	25.3115i	0.595706	+	0.819920i	−0.399600	+	0.916689i	$0.630851\pi$
$954$	−48.9191	−	35.5418i	−1.58382	−	1.15071i
$955$	35.1026	−	25.3817i	1.13590	−	0.821332i
$956$	64.4674			2.08502
$957$		0			0
$958$			13.8564i			0.447680i
$959$	15.3652	+	47.2892i	0.496168	+	1.52705i
$960$	−3.99409	−	1.30782i	−0.128909	−	0.0422096i
$961$	15.8792	−	11.5369i	0.512231	−	0.372158i
$962$		0			0
$963$	−14.9658	−	4.86267i	−0.482265	−	0.156697i
$964$	−59.2297	+	43.0329i	−1.90766	+	1.38600i
$965$	34.9266	+	11.4363i	1.12433	+	0.368147i
$966$	1.69623	+	5.22047i	0.0545754	+	0.167966i
$967$		−	26.4232i		−	0.849713i	−0.905261	−	0.424856i	$-0.860325\pi$
$967$		−	26.4232i		−	0.849713i	0.905261	−	0.424856i	$-0.139675\pi$
$968$		0			0
$969$	5.02175			0.161322
$970$	26.7172	−	19.3184i	0.857838	−	0.620277i
$971$	7.35809	+	5.34596i	0.236132	+	0.171560i	0.699558	−	0.714575i	$-0.253380\pi$
$971$	7.35809	+	5.34596i	0.236132	+	0.171560i	−0.463426	+	0.886136i	$0.653380\pi$
$972$	−40.4408	−	55.6619i	−1.29714	−	1.78536i
$973$	−53.4828	−	17.3776i	−1.71458	−	0.557101i
$974$	5.56231	−	17.1190i	0.178228	−	0.548529i
$975$		0			0
$976$	−3.83843	−	2.78878i	−0.122865	−	0.0892668i
$977$	−48.1038	+	15.6299i	−1.53898	+	0.500044i	−0.951094	−	0.308902i	$-0.900038\pi$
$977$	−48.1038	+	15.6299i	−1.53898	+	0.500044i	−0.587883	+	0.808946i	$0.700038\pi$
$978$			6.92820i			0.221540i
$979$		0			0
$980$	15.0000	+	46.5253i	0.479157	+	1.48620i
$981$	7.33075	+	22.5617i	0.234053	+	0.720341i
$982$	9.66063	−	13.2967i	0.308283	−	0.424315i
$983$	14.5454	+	20.0200i	0.463925	+	0.638538i	0.975317	−	0.220810i	$-0.0708700\pi$
$983$	14.5454	+	20.0200i	0.463925	+	0.638538i	−0.511392	+	0.859348i	$0.670870\pi$
$984$	−12.8208	+	39.4585i	−0.408714	+	1.25789i
$985$	−0.0433271	+	19.0351i	−0.00138052	+	0.606509i
$986$	−28.2980	+	20.5597i	−0.901192	+	0.654754i
$987$	10.7008	−	14.7285i	0.340612	−	0.468812i
$988$		0			0
$989$	2.74456			0.0872720
$990$		0			0
$991$	18.9783			0.602864			0.301432	−	0.953488i	$-0.402535\pi$
$991$	18.9783			0.602864			0.301432	+	0.953488i	$0.402535\pi$
$992$	13.1782	−	4.28187i	0.418409	−	0.135949i
$993$	6.57414	−	9.04852i	0.208624	−	0.287146i
$994$	71.5716	−	51.9998i	2.27011	−	1.64933i
$995$	17.8885	+	0.0407173i	0.567103	+	0.00129082i
$996$	7.10067	−	21.8536i	0.224993	−	0.692458i
$997$	−1.27813	−	1.75919i	−0.0404787	−	0.0557142i	0.788298	−	0.615294i	$-0.210963\pi$
$997$	−1.27813	−	1.75919i	−0.0404787	−	0.0557142i	−0.828777	+	0.559580i	$0.810963\pi$
$998$	−29.6754	+	40.8446i	−0.939357	+	1.29291i
$999$	1.43004	+	4.40122i	0.0452446	+	0.139249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.j.269.4		16
5.4	even	2	inner	605.2.j.j.269.1		16
11.2	odd	10		605.2.j.i.9.4		16
11.3	even	5		605.2.b.c.364.1		4
11.4	even	5	inner	605.2.j.j.124.4		16
11.5	even	5	inner	605.2.j.j.444.1		16
11.6	odd	10		605.2.j.i.444.4		16
11.7	odd	10		605.2.j.i.124.1		16
11.8	odd	10		55.2.b.a.34.4	yes	4
11.9	even	5	inner	605.2.j.j.9.1		16
11.10	odd	2		605.2.j.i.269.1		16
33.8	even	10		495.2.c.a.199.1		4
44.19	even	10		880.2.b.h.529.3		4
55.3	odd	20		3025.2.a.ba.1.1		4
55.4	even	10	inner	605.2.j.j.124.1		16
55.8	even	20		275.2.a.h.1.4		4
55.9	even	10	inner	605.2.j.j.9.4		16
55.14	even	10		605.2.b.c.364.4		4
55.19	odd	10		55.2.b.a.34.1	✓	4
55.24	odd	10		605.2.j.i.9.1		16
55.29	odd	10		605.2.j.i.124.4		16
55.39	odd	10		605.2.j.i.444.1		16
55.47	odd	20		3025.2.a.ba.1.4		4
55.49	even	10	inner	605.2.j.j.444.4		16
55.52	even	20		275.2.a.h.1.1		4
55.54	odd	2		605.2.j.i.269.4		16
165.8	odd	20		2475.2.a.bi.1.1		4
165.74	even	10		495.2.c.a.199.4		4
165.107	odd	20		2475.2.a.bi.1.4		4
220.19	even	10		880.2.b.h.529.2		4
220.63	odd	20		4400.2.a.cc.1.2		4
220.107	odd	20		4400.2.a.cc.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.1	✓	4	55.19	odd	10
55.2.b.a.34.4	yes	4	11.8	odd	10
275.2.a.h.1.1		4	55.52	even	20
275.2.a.h.1.4		4	55.8	even	20
495.2.c.a.199.1		4	33.8	even	10
495.2.c.a.199.4		4	165.74	even	10
605.2.b.c.364.1		4	11.3	even	5
605.2.b.c.364.4		4	55.14	even	10
605.2.j.i.9.1		16	55.24	odd	10
605.2.j.i.9.4		16	11.2	odd	10
605.2.j.i.124.1		16	11.7	odd	10
605.2.j.i.124.4		16	55.29	odd	10
605.2.j.i.269.1		16	11.10	odd	2
605.2.j.i.269.4		16	55.54	odd	2
605.2.j.i.444.1		16	55.39	odd	10
605.2.j.i.444.4		16	11.6	odd	10
605.2.j.j.9.1		16	11.9	even	5	inner
605.2.j.j.9.4		16	55.9	even	10	inner
605.2.j.j.124.1		16	55.4	even	10	inner
605.2.j.j.124.4		16	11.4	even	5	inner
605.2.j.j.269.1		16	5.4	even	2	inner
605.2.j.j.269.4		16	1.1	even	1	trivial
605.2.j.j.444.1		16	11.5	even	5	inner
605.2.j.j.444.4		16	55.49	even	10	inner
880.2.b.h.529.2		4	220.19	even	10
880.2.b.h.529.3		4	44.19	even	10
2475.2.a.bi.1.1		4	165.8	odd	20
2475.2.a.bi.1.4		4	165.107	odd	20
3025.2.a.ba.1.1		4	55.3	odd	20
3025.2.a.ba.1.4		4	55.47	odd	20
4400.2.a.cc.1.2		4	220.63	odd	20
4400.2.a.cc.1.3		4	220.107	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.40079 - 0.780063i) q^{2} +(-0.465695 + 0.640974i) q^{3} +(3.53725 - 2.56996i) q^{4} +(2.23606 + 0.00508966i) q^{5} +(-0.618034 + 1.90211i) q^{6} +(-2.03615 - 2.80252i) q^{7} +(3.51992 - 4.84475i) q^{8} +(0.733075 + 2.25617i) q^{9} +O(q^{10})\)	\(q+(2.40079 - 0.780063i) q^{2} +(-0.465695 + 0.640974i) q^{3} +(3.53725 - 2.56996i) q^{4} +(2.23606 + 0.00508966i) q^{5} +(-0.618034 + 1.90211i) q^{6} +(-2.03615 - 2.80252i) q^{7} +(3.51992 - 4.84475i) q^{8} +(0.733075 + 2.25617i) q^{9} +(5.37228 - 1.73205i) q^{10} +3.46410i q^{12} +(-7.07450 - 5.13992i) q^{14} +(-1.04458 + 1.43089i) q^{15} +(1.96914 - 6.06040i) q^{16} +(1.50702 + 0.489660i) q^{17} +(3.51992 + 4.84475i) q^{18} +(-3.23607 - 2.35114i) q^{19} +(7.92259 - 5.72859i) q^{20} +2.74456 q^{21} +0.792287i q^{23} +(1.46615 + 4.51235i) q^{24} +(4.99995 + 0.0227616i) q^{25} +(-4.04807 - 1.31530i) q^{27} +(-14.4047 - 4.68038i) q^{28} +(-7.07450 + 5.13992i) q^{29} +(-1.39164 + 4.25010i) q^{30} +(1.04209 + 3.20723i) q^{31} -4.10891i q^{32} +4.00000 q^{34} +(-4.53869 - 6.27697i) q^{35} +(8.39135 + 6.09667i) q^{36} +(-0.639064 - 0.879596i) q^{37} +(-9.60315 - 3.12025i) q^{38} +(7.89541 - 10.8152i) q^{40} +(7.07450 + 5.13992i) q^{41} +(6.58911 - 2.14093i) q^{42} -3.46410i q^{43} +(1.62772 + 5.04868i) q^{45} +(0.618034 + 1.90211i) q^{46} +(3.89893 - 5.36641i) q^{47} +(2.96754 + 4.08446i) q^{48} +(-1.54508 + 4.75528i) q^{49} +(12.0216 - 3.84563i) q^{50} +(-1.01567 + 0.737928i) q^{51} +(-9.60315 + 3.12025i) q^{53} -10.7446 q^{54} -20.7446 q^{56} +(3.01404 - 0.979321i) q^{57} +(-12.9749 + 17.8584i) q^{58} +(-5.96430 + 4.33332i) q^{59} +(-0.0176311 + 7.74595i) q^{60} +(0.230083 - 0.708121i) q^{61} +(5.00368 + 6.88698i) q^{62} +(4.83032 - 6.64836i) q^{63} +(0.733075 + 2.25617i) q^{64} -9.30506i q^{67} +(6.58911 - 2.14093i) q^{68} +(-0.507835 - 0.368964i) q^{69} +(-15.7929 - 11.5292i) q^{70} +(-3.12628 + 9.62169i) q^{71} +(13.5110 + 4.38998i) q^{72} +(-4.07230 - 5.60503i) q^{73} +(-2.22040 - 1.61321i) q^{74} +(-2.34304 + 3.19424i) q^{75} -17.4891 q^{76} +(0.387951 + 1.19399i) q^{79} +(4.43397 - 13.5414i) q^{80} +(-3.02941 + 2.20100i) q^{81} +(20.9938 + 6.82131i) q^{82} +(-6.30860 - 2.04979i) q^{83} +(9.70820 - 7.05342i) q^{84} +(3.36730 + 1.10258i) q^{85} +(-2.70222 - 8.31657i) q^{86} -6.92820i q^{87} -1.37228 q^{89} +(7.84609 + 10.8511i) q^{90} +(2.03615 + 2.80252i) q^{92} +(-2.54105 - 0.825636i) q^{93} +(5.17435 - 15.9250i) q^{94} +(-7.22408 - 5.27377i) q^{95} +(2.63370 + 1.91350i) q^{96} +(5.55509 - 1.80496i) q^{97} +12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9	\( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35} + 30 q^{36} + 28 q^{40} + 12 q^{41} + 72 q^{45} - 8 q^{46} + 20 q^{49} - 18 q^{50} - 28 q^{51} - 80 q^{54} - 240 q^{56} - 18 q^{59} + 18 q^{60} + 20 q^{61} + 2 q^{64} - 14 q^{69} - 24 q^{70} + 6 q^{71} + 12 q^{74} - 15 q^{75} - 96 q^{76} - 28 q^{79} - 6 q^{80} + 8 q^{81} + 48 q^{84} + 2 q^{85} + 12 q^{86} + 24 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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