LMFDB - Embedded newform 961.2.d.o.531.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.2
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.o.628.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.571745 - 1.75965i) q^{2} +(0.154309 - 0.474914i) q^{3} +(-1.15144 + 0.836573i) q^{4} +1.20736 q^{5} -0.923909 q^{6} +(-3.02009 + 2.19423i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(2.22532 + 1.61679i) q^{9} +(-0.690303 - 2.12453i) q^{10} +(1.50195 - 1.09123i) q^{11} +(0.219622 + 0.675928i) q^{12} +(-1.60209 + 4.93072i) q^{13} +(5.58780 + 4.05977i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(4.58508 + 3.33126i) q^{17} +(1.57267 - 4.84017i) q^{18} +(-0.444517 - 1.36808i) q^{19} +(-1.39021 + 1.01005i) q^{20} +(0.576042 + 1.77288i) q^{21} +(-2.77891 - 2.01900i) q^{22} +(2.86762 + 2.08345i) q^{23} +(-0.431086 + 0.313203i) q^{24} -3.54228 q^{25} +9.59234 q^{26} +(2.32318 - 1.68789i) q^{27} +(1.64184 - 5.05306i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(3.24035 - 9.97278i) q^{34} +(-3.64635 + 2.64923i) q^{35} -3.91489 q^{36} +4.50281 q^{37} +(-2.15320 + 1.56439i) q^{38} +(2.09445 + 1.52171i) q^{39} +(-1.04230 - 0.757275i) q^{40} +(-1.45829 - 4.48814i) q^{41} +(2.79029 - 2.02727i) q^{42} +(2.02691 + 6.23819i) q^{43} +(-0.816516 + 2.51298i) q^{44} +(2.68676 + 1.95205i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(1.94756 + 1.41498i) q^{48} +(2.14322 - 6.59615i) q^{49} +(2.02528 + 6.23317i) q^{50} +(2.28958 - 1.66348i) q^{51} +(-2.28019 - 7.01772i) q^{52} +(10.4875 + 7.61964i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(1.81339 - 1.31751i) q^{55} +3.98346 q^{56} -0.718314 q^{57} +(2.05458 - 1.49274i) q^{58} +(-0.674139 + 2.07479i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(-1.93430 + 5.95317i) q^{65} +(-1.38766 + 1.00820i) q^{66} +2.88300 q^{67} -8.06631 q^{68} +(1.43196 - 1.04038i) q^{69} +(6.74649 + 4.90161i) q^{70} +(-7.28247 - 5.29103i) q^{71} +(-0.907016 - 2.79151i) q^{72} +(3.40115 - 2.47108i) q^{73} +(-2.57446 - 7.92338i) q^{74} +(-0.546605 + 1.68228i) q^{75} +(1.65634 + 1.20340i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(-9.08664 - 6.60183i) q^{79} +(-1.79864 + 5.53563i) q^{80} +(2.10687 + 6.48429i) q^{81} +(-7.06379 + 5.13215i) q^{82} +(-3.23771 - 9.96463i) q^{83} +(-2.14642 - 1.55947i) q^{84} +(5.53585 + 4.02203i) q^{85} +(9.81816 - 7.13331i) q^{86} +0.685415 q^{87} -1.98105 q^{88} +(2.18575 - 1.58804i) q^{89} +(1.89878 - 5.84384i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(1.04705 - 3.22248i) q^{96} +(6.70942 - 4.87468i) q^{97} -12.8323 q^{98} +5.10660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	−0.921491	−	0.388400i	$-0.873028\pi$
$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	0.517206	−	0.855861i	$-0.326972\pi$
$3$	0.154309	−	0.474914i	0.0890903	−	0.274192i	−0.896578	−	0.442885i	$-0.853955\pi$
$3$	0.154309	−	0.474914i	0.0890903	−	0.274192i	0.985669	+	0.168694i	$0.0539548\pi$
$4$	−1.15144	+	0.836573i	−0.575722	+	0.418287i
$5$	1.20736			0.539948			0.269974	−	0.962868i	$-0.412985\pi$
$5$	1.20736			0.539948			0.269974	+	0.962868i	$0.412985\pi$
$6$	−0.923909			−0.377184
$7$	−3.02009	+	2.19423i	−1.14149	+	0.829340i	−0.987326	−	0.158706i	$-0.949268\pi$
$7$	−3.02009	+	2.19423i	−1.14149	+	0.829340i	−0.154163	+	0.988046i	$0.549268\pi$
$8$	−0.863288	−	0.627215i	−0.305218	−	0.221754i
$9$	2.22532	+	1.61679i	0.741773	+	0.538930i
$10$	−0.690303	−	2.12453i	−0.218293	−	0.671837i
$11$	1.50195	−	1.09123i	0.452854	−	0.329018i	−0.337867	−	0.941194i	$-0.609706\pi$
$11$	1.50195	−	1.09123i	0.452854	−	0.329018i	0.790722	+	0.612176i	$0.209706\pi$
$12$	0.219622	+	0.675928i	0.0633995	+	0.195124i
$13$	−1.60209	+	4.93072i	−0.444340	+	1.36754i	0.438867	+	0.898552i	$0.355380\pi$
$13$	−1.60209	+	4.93072i	−0.444340	+	1.36754i	−0.883206	+	0.468985i	$0.844620\pi$
$14$	5.58780	+	4.05977i	1.49340	+	1.08502i
$15$	0.186307	−	0.573393i	0.0481042	−	0.148049i
$16$	−1.48972	+	4.58490i	−0.372431	+	1.14622i
$17$	4.58508	+	3.33126i	1.11205	+	0.807949i	0.982985	−	0.183688i	$-0.0588035\pi$
$17$	4.58508	+	3.33126i	1.11205	+	0.807949i	0.129062	+	0.991637i	$0.458804\pi$
$18$	1.57267	−	4.84017i	0.370681	−	1.14084i
$19$	−0.444517	−	1.36808i	−0.101979	−	0.313859i	0.887030	−	0.461711i	$-0.152764\pi$
$19$	−0.444517	−	1.36808i	−0.101979	−	0.313859i	−0.989010	+	0.147851i	$0.952764\pi$
$20$	−1.39021	+	1.01005i	−0.310860	+	0.225853i
$21$	0.576042	+	1.77288i	0.125703	+	0.386873i
$22$	−2.77891	−	2.01900i	−0.592466	−	0.430452i
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	0.845147	−	0.534534i	$-0.179513\pi$
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	−0.247207	+	0.968963i	$0.579513\pi$
$24$	−0.431086	+	0.313203i	−0.0879952	+	0.0639322i
$25$	−3.54228			−0.708456
$26$	9.59234			1.88121
$27$	2.32318	−	1.68789i	0.447096	−	0.324835i
$28$	1.64184	−	5.05306i	0.310278	−	0.954939i
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	0.982684	−	0.185292i	$-0.0593230\pi$
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	−0.903919	+	0.427703i	$0.859323\pi$
$30$	−1.11549			−0.203660
$31$		0			0
$31$		0			0
$32$	6.78540			1.19950
$33$	−0.286476	−	0.881683i	−0.0498691	−	0.153481i
$34$	3.24035	−	9.97278i	0.555716	−	1.71032i
$35$	−3.64635	+	2.64923i	−0.616345	+	0.447801i
$36$	−3.91489			−0.652482
$37$	4.50281			0.740258			0.370129	−	0.928980i	$-0.379313\pi$
$37$	4.50281			0.740258			0.370129	+	0.928980i	$0.379313\pi$
$38$	−2.15320	+	1.56439i	−0.349294	+	0.253777i
$39$	2.09445	+	1.52171i	0.335381	+	0.243669i
$40$	−1.04230	−	0.757275i	−0.164802	−	0.119736i
$41$	−1.45829	−	4.48814i	−0.227746	−	0.700930i	−0.998001	−	0.0631942i	$-0.979871\pi$
$41$	−1.45829	−	4.48814i	−0.227746	−	0.700930i	0.770255	−	0.637736i	$-0.220129\pi$
$42$	2.79029	−	2.02727i	0.430551	−	0.312814i
$43$	2.02691	+	6.23819i	0.309101	+	0.951315i	0.978115	+	0.208065i	$0.0667166\pi$
$43$	2.02691	+	6.23819i	0.309101	+	0.951315i	−0.669014	+	0.743250i	$0.733283\pi$
$44$	−0.816516	+	2.51298i	−0.123094	+	0.378846i
$45$	2.68676	+	1.95205i	0.400519	+	0.290994i
$46$	2.02659	−	6.23721i	0.298805	−	0.919627i
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	−1.00000		0.000618100i	$-0.999803\pi$
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	0.809380	+	0.587285i	$0.199803\pi$
$48$	1.94756	+	1.41498i	0.281106	+	0.204235i
$49$	2.14322	−	6.59615i	0.306174	−	0.942307i
$50$	2.02528	+	6.23317i	0.286418	+	0.881504i
$51$	2.28958	−	1.66348i	0.320606	−	0.232934i
$52$	−2.28019	−	7.01772i	−0.316206	−	0.973182i
$53$	10.4875	+	7.61964i	1.44057	+	1.04664i	0.987922	+	0.154950i	$0.0495217\pi$
$53$	10.4875	+	7.61964i	1.44057	+	1.04664i	0.452651	+	0.891688i	$0.350478\pi$
$54$	−4.29836	−	3.12294i	−0.584933	−	0.424979i
$55$	1.81339	−	1.31751i	0.244518	−	0.177653i
$56$	3.98346			0.532313
$57$	−0.718314			−0.0951431
$58$	2.05458	−	1.49274i	0.269779	−	0.196006i
$59$	−0.674139	+	2.07479i	−0.0877654	+	0.270114i	−0.985301	−	0.170828i	$-0.945356\pi$
$59$	−0.674139	+	2.07479i	−0.0877654	+	0.270114i	0.897535	+	0.440942i	$0.145356\pi$
$60$	0.265164	+	0.816089i	0.0342325	+	0.105357i
$61$	−2.68087			−0.343251			−0.171625	−	0.985162i	$-0.554902\pi$
$61$	−2.68087			−0.343251			−0.171625	+	0.985162i	$0.554902\pi$
$62$		0			0
$63$	−10.2683			−1.29368
$64$	−0.900071	−	2.77013i	−0.112509	−	0.346267i
$65$	−1.93430	+	5.95317i	−0.239921	+	0.738399i
$66$	−1.38766	+	1.00820i	−0.170809	+	0.124100i
$67$	2.88300			0.352214			0.176107	−	0.984371i	$-0.443649\pi$
$67$	2.88300			0.352214			0.176107	+	0.984371i	$0.443649\pi$
$68$	−8.06631			−0.978184
$69$	1.43196	−	1.04038i	0.172388	−	0.125247i
$70$	6.74649	+	4.90161i	0.806360	+	0.585855i
$71$	−7.28247	−	5.29103i	−0.864271	−	0.627929i	0.0647727	−	0.997900i	$-0.479368\pi$
$71$	−7.28247	−	5.29103i	−0.864271	−	0.627929i	−0.929043	+	0.369971i	$0.879368\pi$
$72$	−0.907016	−	2.79151i	−0.106893	−	0.328982i
$73$	3.40115	−	2.47108i	0.398074	−	0.289218i	−0.370682	−	0.928760i	$-0.620876\pi$
$73$	3.40115	−	2.47108i	0.398074	−	0.289218i	0.768756	+	0.639542i	$0.220876\pi$
$74$	−2.57446	−	7.92338i	−0.299275	−	0.921074i
$75$	−0.546605	+	1.68228i	−0.0631166	+	0.194253i
$76$	1.65634	+	1.20340i	0.189995	+	0.138039i
$77$	−2.14162	+	6.59123i	−0.244060	+	0.751140i
$78$	1.48018	−	4.55554i	0.167598	−	0.515813i
$79$	−9.08664	−	6.60183i	−1.02233	−	0.742764i	−0.0555681	−	0.998455i	$-0.517697\pi$
$79$	−9.08664	−	6.60183i	−1.02233	−	0.742764i	−0.966759	+	0.255691i	$0.917697\pi$
$80$	−1.79864	+	5.53563i	−0.201094	+	0.618902i
$81$	2.10687	+	6.48429i	0.234097	+	0.720476i
$82$	−7.06379	+	5.13215i	−0.780065	+	0.566751i
$83$	−3.23771	−	9.96463i	−0.355384	−	1.09376i	−0.955786	−	0.294062i	$-0.904993\pi$
$83$	−3.23771	−	9.96463i	−0.355384	−	1.09376i	0.600402	−	0.799698i	$-0.295007\pi$
$84$	−2.14642	−	1.55947i	−0.234194	−	0.170152i
$85$	5.53585	+	4.02203i	0.600448	+	0.436251i
$86$	9.81816	−	7.13331i	1.05872	−	0.769204i
$87$	0.685415			0.0734842
$88$	−1.98105			−0.211180
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	−0.465884	−	0.884846i	$-0.654263\pi$
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	0.697573	+	0.716514i	$0.254263\pi$
$90$	1.89878	−	5.84384i	0.200149	−	0.615995i
$91$	−5.98067	−	18.4066i	−0.626944	−	1.92954i
$92$	−5.04486			−0.525963
$93$		0			0
$94$	7.82446			0.807031
$95$	−0.536692	−	1.65177i	−0.0550635	−	0.169468i
$96$	1.04705	−	3.22248i	0.106864	−	0.328893i
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	−0.192530	−	0.981291i	$-0.561669\pi$
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	0.873768	+	0.486342i	$0.161669\pi$
$98$	−12.8323			−1.29626
$99$	5.10660			0.513233
$100$	4.07874	−	2.96337i	0.407874	−	0.296337i
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	0.521586	−	0.853199i	$-0.325341\pi$
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	−0.650261	+	0.759711i	$0.725341\pi$
$102$	−4.23620	−	3.07778i	−0.419446	−	0.304746i
$103$	5.65743	+	17.4118i	0.557444	+	1.71564i	0.689401	+	0.724380i	$0.257874\pi$
$103$	5.65743	+	17.4118i	0.557444	+	1.71564i	−0.131958	+	0.991255i	$0.542126\pi$
$104$	4.47569	−	3.25178i	0.438877	−	0.318863i
$105$	0.695491	+	2.14050i	0.0678730	+	0.208892i
$106$	7.41171	−	22.8109i	0.719889	−	2.21559i
$107$	−9.36460	−	6.80378i	−0.905310	−	0.657746i	0.0345146	−	0.999404i	$-0.489011\pi$
$107$	−9.36460	−	6.80378i	−0.905310	−	0.657746i	−0.939824	+	0.341658i	$0.889011\pi$
$108$	−1.26297	+	3.88702i	−0.121529	+	0.374029i
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	−0.928317	−	0.371789i	$-0.878744\pi$
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	0.969557	+	0.244867i	$0.0787444\pi$
$110$	−3.35515	−	2.43766i	−0.319901	−	0.232422i
$111$	0.694825	−	2.13845i	0.0659498	−	0.202973i
$112$	−5.56120	−	17.1156i	−0.525484	−	1.61727i
$113$	2.63381	−	1.91357i	0.247768	−	0.180014i	−0.456969	−	0.889483i	$-0.651065\pi$
$113$	2.63381	−	1.91357i	0.247768	−	0.180014i	0.704737	+	0.709469i	$0.251065\pi$
$114$	0.410693	+	1.26398i	0.0384649	+	0.118383i
$115$	3.46226	+	2.51548i	0.322857	+	0.234569i
$116$	−1.58047	−	1.14828i	−0.146743	−	0.106615i
$117$	−11.5371	+	8.38219i	−1.06661	+	0.774934i
$118$	4.03633			0.371575
$119$	−21.1569			−1.93945
$120$	−0.520477	+	0.378149i	−0.0475129	+	0.0345201i
$121$	−2.33412	+	7.18368i	−0.212193	+	0.653062i
$122$	1.53278	+	4.71740i	0.138771	+	0.427093i
$123$	−2.35651			−0.212479
$124$		0			0
$125$	−10.3136			−0.922478
$126$	5.87084	+	18.0686i	0.523016	+	1.60968i
$127$	2.96392	−	9.12200i	0.263005	−	0.809447i	−0.729141	−	0.684363i	$-0.760080\pi$
$127$	2.96392	−	9.12200i	0.263005	−	0.809447i	0.992146	−	0.125083i	$-0.0399198\pi$
$128$	6.61915	−	4.80909i	0.585056	−	0.425068i
$129$	3.27538			0.288381
$130$	11.5814			1.01576
$131$	9.29737	−	6.75493i	0.812315	−	0.590181i	−0.102186	−	0.994765i	$-0.532584\pi$
$131$	9.29737	−	6.75493i	0.812315	−	0.590181i	0.914501	+	0.404584i	$0.132584\pi$
$132$	1.06745	+	0.775550i	0.0929099	+	0.0675030i
$133$	4.34436	+	3.15636i	0.376704	+	0.273692i
$134$	−1.64834	−	5.07307i	−0.142395	−	0.438247i
$135$	2.80492	−	2.03789i	0.241409	−	0.175394i
$136$	−1.86883	−	5.75167i	−0.160251	−	0.493202i
$137$	−4.87868	+	15.0150i	−0.416814	+	1.28282i	0.493805	+	0.869573i	$0.335606\pi$
$137$	−4.87868	+	15.0150i	−0.416814	+	1.28282i	−0.910619	+	0.413248i	$0.864394\pi$
$138$	−2.64942	−	1.92492i	−0.225534	−	0.163860i
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	0.723521	+	0.690303i	$0.242523\pi$
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	−0.991090	+	0.133192i	$0.957477\pi$
$140$	1.98229	−	6.10087i	0.167534	−	0.515618i
$141$	1.70844	+	1.24126i	0.143877	+	0.104533i
$142$	−5.14664	+	15.8397i	−0.431896	+	1.32924i
$143$	2.97429	+	9.15394i	0.248723	+	0.765491i
$144$	−10.7279	+	7.79429i	−0.893994	+	0.649524i
$145$	0.512111	+	1.57612i	0.0425285	+	0.130889i
$146$	−6.29283	−	4.57201i	−0.520798	−	0.378382i
$147$	−2.80189	−	2.03569i	−0.231096	−	0.167901i
$148$	−5.18474	+	3.76693i	−0.426183	+	0.309640i
$149$	3.82067			0.313001			0.156501	−	0.987678i	$-0.449979\pi$
$149$	3.82067			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$150$	3.27274			0.267218
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	−0.256283	−	0.966602i	$-0.582498\pi$
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	0.840097	+	0.542436i	$0.182498\pi$
$152$	−0.474336	+	1.45986i	−0.0384737	+	0.118410i
$153$	4.81733	+	14.8262i	0.389458	+	1.19863i
$154$	12.8227			1.03328
$155$		0			0
$156$	−3.68467			−0.295010
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	0.866701	−	0.498829i	$-0.166236\pi$
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	−0.994380	+	0.105873i	$0.966236\pi$
$158$	−6.42167	+	19.7639i	−0.510881	+	1.57233i
$159$	5.23700	−	3.80490i	0.415321	−	0.301748i
$160$	8.19243			0.647668
$161$	−13.2320			−1.04283
$162$	10.2055	−	7.41472i	0.801819	−	0.582556i
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	0.570101	−	0.821574i	$-0.306904\pi$
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	−0.605193	+	0.796079i	$0.706904\pi$
$164$	5.43379	+	3.94788i	0.424308	+	0.308278i
$165$	−0.345880	−	1.06451i	−0.0269267	−	0.0828720i
$166$	−15.6831	+	11.3945i	−1.21725	+	0.884382i
$167$	0.617417	+	1.90022i	0.0477772	+	0.147043i	0.972099	−	0.234571i	$-0.0753684\pi$
$167$	0.617417	+	1.90022i	0.0477772	+	0.147043i	−0.924322	+	0.381614i	$0.875368\pi$
$168$	0.614684	−	1.89180i	0.0474239	−	0.145956i
$169$	−11.2281	−	8.15772i	−0.863703	−	0.627517i
$170$	3.91228	−	12.0407i	0.300058	−	0.923483i
$171$	1.22271	−	3.76311i	0.0935028	−	0.287772i
$172$	−7.55257	−	5.48727i	−0.575878	−	0.418400i
$173$	−1.25387	+	3.85900i	−0.0953296	+	0.293394i	−0.987339	−	0.158622i	$-0.949295\pi$
$173$	−1.25387	+	3.85900i	−0.0953296	+	0.293394i	0.892010	+	0.452016i	$0.149295\pi$
$174$	−0.391883	−	1.20609i	−0.0297086	−	0.0914335i
$175$	10.6980	−	7.77256i	0.808694	−	0.587551i
$176$	2.76569	+	8.51191i	0.208472	+	0.641609i
$177$	0.881320	+	0.640316i	0.0662440	+	0.0481291i
$178$	−4.04409	−	2.93820i	−0.303117	−	0.220227i
$179$	3.20683	−	2.32990i	0.239690	−	0.174145i	−0.461455	−	0.887164i	$-0.652673\pi$
$179$	3.20683	−	2.32990i	0.239690	−	0.174145i	0.701145	+	0.713019i	$0.252673\pi$
$180$	−4.72669			−0.352307
$181$	6.39742			0.475517			0.237758	−	0.971324i	$-0.423587\pi$
$181$	6.39742			0.475517			0.237758	+	0.971324i	$0.423587\pi$
$182$	−28.9698	+	21.0478i	−2.14738	+	1.56016i
$183$	−0.413683	+	1.27319i	−0.0305803	+	0.0941166i
$184$	−1.16881	−	3.59723i	−0.0861659	−	0.265191i
$185$	5.43652			0.399701
$186$		0			0
$187$	10.5217			0.769425
$188$	−1.85995	−	5.72434i	−0.135651	−	0.417491i
$189$	−3.31261	+	10.1952i	−0.240957	+	0.741590i
$190$	−2.59968	+	1.88878i	−0.188601	+	0.137027i
$191$	11.6256			0.841202			0.420601	−	0.907246i	$-0.361819\pi$
$191$	11.6256			0.841202			0.420601	+	0.907246i	$0.361819\pi$
$192$	−1.45447			−0.104967
$193$	−10.9569	+	7.96069i	−0.788698	+	0.573023i	−0.907577	−	0.419886i	$-0.862070\pi$
$193$	−10.9569	+	7.96069i	−0.788698	+	0.573023i	0.118879	+	0.992909i	$0.462070\pi$
$194$	−12.4138	−	9.01917i	−0.891260	−	0.647538i
$195$	2.52876	+	1.83725i	0.181089	+	0.131569i
$196$	3.05037	+	9.38806i	0.217883	+	0.670576i
$197$	−18.9345	+	13.7567i	−1.34903	+	0.980124i	−0.349966	+	0.936762i	$0.613807\pi$
$197$	−18.9345	+	13.7567i	−1.34903	+	0.980124i	−0.999059	+	0.0433620i	$0.986193\pi$
$198$	−2.91967	−	8.98583i	−0.207492	−	0.638595i
$199$	2.03888	−	6.27504i	0.144533	−	0.444826i	−0.852418	−	0.522861i	$-0.824865\pi$
$199$	2.03888	−	6.27504i	0.144533	−	0.444826i	0.996951	+	0.0780353i	$0.0248647\pi$
$200$	3.05800	+	2.22177i	0.216234	+	0.157103i
$201$	0.444873	−	1.36918i	0.0313789	−	0.0965744i
$202$	−0.913902	+	2.81270i	−0.0643019	+	0.197901i
$203$	−4.14539	−	3.01180i	−0.290949	−	0.211387i
$204$	−1.24470	+	3.83081i	−0.0871467	+	0.268210i
$205$	−1.76068	−	5.41881i	−0.122971	−	0.378466i
$206$	27.4041	−	19.9102i	1.90933	−	1.38721i
$207$	3.01287	+	9.27268i	0.209409	+	0.644495i
$208$	−20.2202	−	14.6908i	−1.40202	−	1.01863i
$209$	−2.16053	−	1.56972i	−0.149447	−	0.108580i
$210$	3.36889	−	2.44764i	0.232476	−	0.168903i
$211$	−19.3651			−1.33315			−0.666574	−	0.745439i	$-0.732240\pi$
$211$	−19.3651			−1.33315			−0.666574	+	0.745439i	$0.732240\pi$
$212$	−18.4502			−1.26716
$213$	−3.63654	+	2.64210i	−0.249171	+	0.181034i
$214$	−6.61811	+	20.3684i	−0.452405	+	1.39236i
$215$	2.44721	+	7.53175i	0.166899	+	0.513661i
$216$	−3.06424			−0.208495
$217$		0			0
$218$	−2.57788			−0.174596
$219$	−0.648723	−	1.99656i	−0.0438366	−	0.134915i
$220$	−0.985830	+	3.03407i	−0.0664647	+	0.204557i
$221$	−23.7712	+	17.2708i	−1.59903	+	1.16176i
$222$	−4.16019			−0.279214
$223$	7.05971			0.472753			0.236377	−	0.971662i	$-0.424040\pi$
$223$	7.05971			0.472753			0.236377	+	0.971662i	$0.424040\pi$
$224$	−20.4925	+	14.8887i	−1.36922	+	0.994794i
$225$	−7.88270	−	5.72712i	−0.525513	−	0.381808i
$226$	−4.87308	−	3.54050i	−0.324153	−	0.235511i
$227$	−2.78727	−	8.57835i	−0.184998	−	0.569365i	0.814950	−	0.579531i	$-0.196764\pi$
$227$	−2.78727	−	8.57835i	−0.184998	−	0.569365i	−0.999948	+	0.0101657i	$0.996764\pi$
$228$	0.827099	−	0.600922i	0.0547760	−	0.0397971i
$229$	5.54804	+	17.0751i	0.366625	+	1.12836i	0.948957	+	0.315404i	$0.102140\pi$
$229$	5.54804	+	17.0751i	0.366625	+	1.12836i	−0.582333	+	0.812951i	$0.697860\pi$
$230$	2.44683	−	7.53057i	0.161339	−	0.496551i
$231$	2.79980	+	2.03417i	0.184213	+	0.133839i
$232$	0.452611	−	1.39299i	0.0297154	−	0.0914545i
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	−0.712597	−	0.701574i	$-0.752481\pi$
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	0.988878	−	0.148731i	$-0.0475190\pi$
$234$	21.3460	+	15.5088i	1.39543	+	1.01384i
$235$	−1.57781	+	4.85599i	−0.102925	+	0.316770i
$236$	−0.959477	−	2.95297i	−0.0624566	−	0.192222i
$237$	−4.53745	+	3.29665i	−0.294739	+	0.214141i
$238$	12.0964	+	37.2288i	0.784091	+	2.41318i
$239$	7.96981	+	5.79041i	0.515524	+	0.374550i	0.814915	−	0.579580i	$-0.196783\pi$
$239$	7.96981	+	5.79041i	0.515524	+	0.374550i	−0.299391	+	0.954131i	$0.596783\pi$
$240$	2.35140	+	1.70840i	0.151783	+	0.110276i
$241$	5.39599	−	3.92042i	0.347586	−	0.252536i	−0.400269	−	0.916398i	$-0.631083\pi$
$241$	5.39599	−	3.92042i	0.347586	−	0.252536i	0.747856	+	0.663861i	$0.231083\pi$
$242$	13.9753			0.898366
$243$	12.0194			0.771046
$244$	3.08688	−	2.24275i	0.197617	−	0.143577i
$245$	2.58764	−	7.96394i	0.165318	−	0.508797i
$246$	1.34732	+	4.14663i	0.0859021	+	0.264380i
$247$	7.45779			0.474528
$248$		0			0
$249$	−5.23195			−0.331562
$250$	5.89676	+	18.1484i	0.372944	+	1.14780i
$251$	−9.05975	+	27.8830i	−0.571846	+	1.75996i	0.0748286	+	0.997196i	$0.476159\pi$
$251$	−9.05975	+	27.8830i	−0.571846	+	1.75996i	−0.646675	+	0.762766i	$0.723841\pi$
$252$	11.8233	−	8.59016i	0.744801	−	0.541129i
$253$	6.58054			0.413715
$254$	−17.7461			−1.11349
$255$	2.76435	−	2.00842i	0.173111	−	0.125772i
$256$	−16.9596	−	12.3219i	−1.05998	−	0.770118i
$257$	19.3747	+	14.0766i	1.20856	+	0.878073i	0.995100	−	0.0988784i	$-0.0315255\pi$
$257$	19.3747	+	14.0766i	1.20856	+	0.878073i	0.213464	+	0.976951i	$0.431525\pi$
$258$	−1.87268	−	5.76352i	−0.116588	−	0.358821i
$259$	−13.5989	+	9.88020i	−0.844996	+	0.613926i
$260$	−2.75302	−	8.47292i	−0.170735	−	0.525468i
$261$	−1.16671	+	3.59075i	−0.0722173	+	0.222262i
$262$	−17.2021	−	12.4980i	−1.06275	−	0.772130i
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	−0.906420	−	0.422378i	$-0.861196\pi$
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	0.981577	+	0.191070i	$0.0611956\pi$
$264$	−0.305694	+	0.940828i	−0.0188141	+	0.0579040i
$265$	12.6622	+	9.19966i	0.777835	+	0.565131i
$266$	3.07023	−	9.44920i	0.188248	−	0.579368i
$267$	−0.416902	−	1.28309i	−0.0255140	−	0.0785240i
$268$	−3.31961	+	2.41184i	−0.202778	+	0.147327i
$269$	3.94066	+	12.1281i	0.240266	+	0.739463i	0.996379	+	0.0850221i	$0.0270961\pi$
$269$	3.94066	+	12.1281i	0.240266	+	0.739463i	−0.756113	+	0.654441i	$0.772904\pi$
$270$	−5.18968	−	3.77052i	−0.315834	−	0.229467i
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	0.666428	−	0.745569i	$-0.267822\pi$
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	−0.503141	+	0.864204i	$0.667822\pi$
$272$	−22.1040	+	16.0595i	−1.34025	+	0.973750i
$273$	−9.66443			−0.584918
$274$	29.2106			1.76467
$275$	−5.32032	+	3.86544i	−0.320827	+	0.233095i
$276$	−0.778468	+	2.39588i	−0.0468583	+	0.144215i
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	0.932624	+	0.360849i	$0.117513\pi$
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	−0.542407	+	0.840116i	$0.682487\pi$
$278$	18.8878			1.13282
$279$		0			0
$280$	4.80948			0.287421
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	0.826847	−	0.562426i	$-0.190132\pi$
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	−0.999519	+	0.0309964i	$0.990132\pi$
$282$	1.20738	−	3.71595i	0.0718987	−	0.221281i
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	−0.316837	−	0.948480i	$-0.602621\pi$
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	0.804150	+	0.594426i	$0.202621\pi$
$284$	12.8117			0.760234
$285$	−0.867265			−0.0513723
$286$	14.4072	−	10.4674i	0.851915	−	0.618953i
$287$	14.2522	+	10.3548i	0.841278	+	0.611225i
$288$	15.0997	+	10.9706i	0.889757	+	0.646446i
$289$	4.67242	+	14.3802i	0.274848	+	0.845897i
$290$	2.48062	−	1.80227i	0.145667	−	0.105833i
$291$	−1.27973	−	3.93861i	−0.0750192	−	0.230885i
$292$	−1.84899	+	5.69062i	−0.108204	+	0.333018i
$293$	17.2079	+	12.5022i	1.00529	+	0.730389i	0.963217	−	0.268725i	$-0.0866024\pi$
$293$	17.2079	+	12.5022i	1.00529	+	0.730389i	0.0420775	+	0.999114i	$0.486602\pi$
$294$	−1.98014	+	6.09424i	−0.115484	+	0.355423i
$295$	−0.813929	+	2.50502i	−0.0473888	+	0.145848i
$296$	−3.88722	−	2.82423i	−0.225940	−	0.164155i
$297$	1.64742	−	5.07025i	0.0955932	−	0.294206i
$298$	−2.18445	−	6.72304i	−0.126542	−	0.389455i
$299$	−14.8671	+	10.8016i	−0.859786	+	0.624671i
$300$	−0.777963	−	2.39433i	−0.0449157	−	0.138236i
$301$	−19.8095	−	14.3924i	−1.14180	−	0.829565i
$302$	−13.2734	−	9.64371i	−0.763800	−	0.554933i
$303$	−0.645749	+	0.469164i	−0.0370973	+	0.0269528i
$304$	6.93472			0.397734
$305$	−3.23678			−0.185338
$306$	23.3347	−	16.9536i	1.33396	−	0.969175i
$307$	5.01882	−	15.4463i	0.286439	−	0.881568i	−0.699525	−	0.714608i	$-0.746605\pi$
$307$	5.01882	−	15.4463i	0.286439	−	0.881568i	0.985964	−	0.166960i	$-0.0533951\pi$
$308$	−3.04809	−	9.38105i	−0.173681	−	0.534535i
$309$	9.14210			0.520076
$310$		0			0
$311$	−10.3858			−0.588924			−0.294462	−	0.955663i	$-0.595141\pi$
$311$	−10.3858			−0.588924			−0.294462	+	0.955663i	$0.595141\pi$
$312$	−0.853677	−	2.62735i	−0.0483299	−	0.148744i
$313$	9.90204	−	30.4754i	0.559696	−	1.72257i	−0.123510	−	0.992343i	$-0.539415\pi$
$313$	9.90204	−	30.4754i	0.559696	−	1.72257i	0.683206	−	0.730225i	$-0.260585\pi$
$314$	−7.74935	+	5.63023i	−0.437321	+	0.317732i
$315$	−12.3975			−0.698521
$316$	15.9857			0.899264
$317$	−20.4800	+	14.8796i	−1.15027	+	0.835722i	−0.988517	−	0.151109i	$-0.951716\pi$
$317$	−20.4800	+	14.8796i	−1.15027	+	0.835722i	−0.161756	+	0.986831i	$0.551716\pi$
$318$	−9.68952	−	7.03985i	−0.543361	−	0.394775i
$319$	2.06158	+	1.49782i	0.115426	+	0.0838620i
$320$	−1.08671	−	3.34455i	−0.0607490	−	0.186966i
$321$	−4.67625	+	3.39750i	−0.261003	+	0.189630i
$322$	7.56536	+	23.2838i	0.421601	+	1.29755i
$323$	2.51929	−	7.75357i	0.140177	−	0.431420i
$324$	−7.85053	−	5.70374i	−0.436140	−	0.316875i
$325$	5.67505	−	17.4660i	0.314795	−	0.968839i
$326$	−0.316619	+	0.974453i	−0.0175359	+	0.0539700i
$327$	−0.562872	−	0.408950i	−0.0311269	−	0.0226150i
$328$	−1.55611	+	4.78922i	−0.0859218	+	0.264440i
$329$	−4.87842	−	15.0142i	−0.268956	−	0.827762i
$330$	−1.67541	+	1.21726i	−0.0922283	+	0.0670078i
$331$	−10.1714	−	31.3044i	−0.559071	−	1.72064i	−0.684942	−	0.728597i	$-0.740173\pi$
$331$	−10.1714	−	31.3044i	−0.559071	−	1.72064i	0.125871	−	0.992047i	$-0.459827\pi$
$332$	12.0642	+	8.76514i	0.662108	+	0.481050i
$333$	10.0202	+	7.28010i	0.549103	+	0.398947i
$334$	2.99071	−	2.17288i	0.163644	−	0.118895i
$335$	3.48082			0.190178
$336$	−8.98660			−0.490259
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	−0.671426	−	0.741072i	$-0.734318\pi$
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	0.497319	+	0.867568i	$0.334318\pi$
$338$	−7.93510	+	24.4217i	−0.431613	+	1.32837i
$339$	−0.502363	−	1.54611i	−0.0272846	−	0.0839734i
$340$	−9.73895			−0.528169
$341$		0			0
$342$	−7.32083			−0.395865
$343$	−0.0742848	−	0.228625i	−0.00401100	−	0.0123446i
$344$	2.16288	−	6.65666i	0.116615	−	0.358903i
$345$	1.72889	−	1.25611i	0.0930804	−	0.0676269i
$346$	7.50739			0.403600
$347$	−13.6844			−0.734619			−0.367310	−	0.930099i	$-0.619721\pi$
$347$	−13.6844			−0.734619			−0.367310	+	0.930099i	$0.619721\pi$
$348$	−0.789217	+	0.573400i	−0.0423065	+	0.0307375i
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	0.665110	−	0.746745i	$-0.268385\pi$
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	−0.504667	+	0.863314i	$0.668385\pi$
$350$	−19.7935	−	14.3808i	−1.05801	−	0.768689i
$351$	4.60058	+	14.1591i	0.245561	+	0.755758i
$352$	10.1913	−	7.40442i	0.543199	−	0.394657i
$353$	−4.78713	−	14.7333i	−0.254793	−	0.784173i	−0.993870	−	0.110552i	$-0.964738\pi$
$353$	−4.78713	−	14.7333i	−0.254793	−	0.784173i	0.739077	−	0.673621i	$-0.235262\pi$
$354$	0.622843	−	1.91691i	0.0331037	−	0.101883i
$355$	−8.79258	−	6.38818i	−0.466662	−	0.339050i
$356$	−1.18826	+	3.65708i	−0.0629775	+	0.193825i
$357$	−3.26470	+	10.0477i	−0.172786	+	0.531782i
$358$	−5.93330	−	4.31080i	−0.313585	−	0.227833i
$359$	−1.65923	+	5.10658i	−0.0875707	+	0.269515i	−0.985246	−	0.171142i	$-0.945254\pi$
$359$	−1.65923	+	5.10658i	−0.0875707	+	0.269515i	0.897676	+	0.440657i	$0.145254\pi$
$360$	−1.09510	−	3.37036i	−0.0577166	−	0.177633i
$361$	13.6973	−	9.95165i	0.720909	−	0.523771i
$362$	−3.65769	−	11.2572i	−0.192244	−	0.591667i
$363$	3.05146	+	2.21701i	0.160160	+	0.116363i
$364$	22.2849	+	16.1909i	1.16804	+	0.848634i
$365$	4.10642	−	2.98349i	0.214940	−	0.156163i
$366$	2.47688			0.129469
$367$	−14.7209			−0.768425			−0.384212	−	0.923245i	$-0.625527\pi$
$367$	−14.7209			−0.768425			−0.384212	+	0.923245i	$0.625527\pi$
$368$	−13.8244	+	10.0440i	−0.720645	+	0.523579i
$369$	4.01123	−	12.3453i	0.208816	−	0.642670i
$370$	−3.10831	−	9.56638i	−0.161593	−	0.497333i
$371$	−48.3926			−2.51242
$372$		0			0
$373$	23.8449			1.23464			0.617320	−	0.786712i	$-0.288218\pi$
$373$	23.8449			1.23464			0.617320	+	0.786712i	$0.288218\pi$
$374$	−6.01574	−	18.5146i	−0.311067	−	0.957365i
$375$	−1.59148	+	4.89808i	−0.0821839	+	0.252936i
$376$	3.65081	−	2.65247i	0.188276	−	0.136791i
$377$	−7.11622			−0.366504
$378$	19.8339			1.02015
$379$	17.9012	−	13.0060i	0.919522	−	0.668072i	−0.0238829	−	0.999715i	$-0.507603\pi$
$379$	17.9012	−	13.0060i	0.919522	−	0.668072i	0.943405	+	0.331643i	$0.107603\pi$
$380$	1.99980	+	1.45294i	0.102587	+	0.0745341i
$381$	−3.87481	−	2.81521i	−0.198512	−	0.144228i
$382$	−6.64690	−	20.4571i	−0.340085	−	1.04667i
$383$	19.2535	−	13.9885i	0.983806	−	0.714777i	0.0252501	−	0.999681i	$-0.491962\pi$
$383$	19.2535	−	13.9885i	0.983806	−	0.714777i	0.958556	+	0.284904i	$0.0919618\pi$
$384$	−1.26251	−	3.88562i	−0.0644273	−	0.198287i
$385$	−2.58571	+	7.95800i	−0.131780	+	0.405577i
$386$	20.2726	+	14.7289i	1.03185	+	0.749682i
$387$	−5.57531	+	17.1590i	−0.283409	+	0.872243i
$388$	−3.64750	+	11.2258i	−0.185174	+	0.569906i
$389$	−13.7973	−	10.0243i	−0.699551	−	0.508254i	0.180235	−	0.983624i	$-0.442314\pi$
$389$	−13.7973	−	10.0243i	−0.699551	−	0.508254i	−0.879786	+	0.475370i	$0.842314\pi$
$390$	1.78712	−	5.50018i	0.0904942	−	0.278513i
$391$	6.20778	+	19.1056i	0.313941	+	0.966211i
$392$	−5.98742	+	4.35012i	−0.302410	+	0.219714i
$393$	−1.77335	−	5.45780i	−0.0894535	−	0.275310i
$394$	35.0327	+	25.4527i	1.76492	+	1.28229i
$395$	−10.9709	−	7.97079i	−0.552004	−	0.401054i
$396$	−5.87996	+	4.27204i	−0.295479	+	0.214678i
$397$	−10.0215			−0.502965			−0.251482	−	0.967862i	$-0.580918\pi$
$397$	−10.0215			−0.502965			−0.251482	+	0.967862i	$0.580918\pi$
$398$	−12.2076			−0.611912
$399$	2.16938	−	1.57614i	0.108605	−	0.0789059i
$400$	5.27702	−	16.2410i	0.263851	−	0.812049i
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	−0.887213	−	0.461360i	$-0.847362\pi$
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	0.446590	−	0.894739i	$-0.352638\pi$
$402$	−2.66363			−0.132850
$403$		0			0
$404$	2.27501			0.113186
$405$	2.54376	+	7.82888i	0.126400	+	0.389020i
$406$	−2.92961	+	9.01642i	−0.145394	+	0.447477i
$407$	6.76299	−	4.91360i	0.335229	−	0.243558i
$408$	−3.01993			−0.149509
$409$	−23.0102			−1.13778			−0.568891	−	0.822413i	$-0.692628\pi$
$409$	−23.0102			−1.13778			−0.568891	+	0.822413i	$0.692628\pi$
$410$	−8.52855	+	6.19636i	−0.421195	+	0.306016i
$411$	6.37803	+	4.63391i	0.314605	+	0.228574i
$412$	−21.0805	−	15.3158i	−1.03856	−	0.754558i
$413$	−2.51659	−	7.74526i	−0.123833	−	0.381119i
$414$	14.5941	−	10.6032i	0.717260	−	0.521120i
$415$	−3.90908	−	12.0309i	−0.191889	−	0.590574i
$416$	−10.8708	+	33.4569i	−0.532986	+	1.64036i
$417$	4.12409	+	2.99633i	0.201958	+	0.146731i
$418$	−1.52688	+	4.69926i	−0.0746822	+	0.229848i
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	−0.292137	−	0.956377i	$-0.594366\pi$
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	0.798488	−	0.602011i	$-0.205634\pi$
$420$	−2.59150	−	1.88284i	−0.126452	−	0.0918731i
$421$	2.78958	−	8.58544i	0.135956	−	0.418429i	−0.859782	−	0.510662i	$-0.829400\pi$
$421$	2.78958	−	8.58544i	0.135956	−	0.418429i	0.995737	+	0.0922329i	$0.0294004\pi$
$422$	11.0719	+	34.0758i	0.538971	+	1.65878i
$423$	−9.41080	+	6.83735i	−0.457569	+	0.332443i
$424$	−4.27460	−	13.1559i	−0.207593	−	0.638906i
$425$	−16.2416	−	11.8002i	−0.787835	−	0.572396i
$426$	6.72834	+	4.88843i	0.325989	+	0.236845i
$427$	8.09649	−	5.88245i	0.391817	−	0.284672i
$428$	16.4747			0.796333
$429$	4.80630			0.232050
$430$	11.8541	−	8.61248i	0.571654	−	0.415331i
$431$	3.49398	−	10.7534i	0.168299	−	0.517972i	−0.830965	−	0.556325i	$-0.812211\pi$
$431$	3.49398	−	10.7534i	0.168299	−	0.517972i	0.999264	+	0.0383529i	$0.0122111\pi$
$432$	4.27791	+	13.1660i	0.205821	+	0.633452i
$433$	9.10433			0.437526			0.218763	−	0.975778i	$-0.429798\pi$
$433$	9.10433			0.437526			0.218763	+	0.975778i	$0.429798\pi$
$434$		0			0
$435$	0.827544			0.0396777
$436$	0.612788	+	1.88597i	0.0293472	+	0.0903215i
$437$	1.57562	−	4.84927i	0.0753722	−	0.231972i
$438$	−3.14235	+	2.28305i	−0.150147	+	0.109088i
$439$	−39.6053			−1.89026			−0.945128	−	0.326700i	$-0.894063\pi$
$439$	−39.6053			−1.89026			−0.945128	+	0.326700i	$0.894063\pi$
$440$	−2.39184			−0.114027
$441$	15.4339	−	11.2134i	0.734949	−	0.533972i
$442$	43.9817	+	31.9546i	2.09200	+	1.51992i
$443$	−20.4344	−	14.8465i	−0.970868	−	0.705377i	−0.0152186	−	0.999884i	$-0.504844\pi$
$443$	−20.4344	−	14.8465i	−0.970868	−	0.705377i	−0.955649	+	0.294507i	$0.904844\pi$
$444$	0.988918	+	3.04358i	0.0469320	+	0.144442i
$445$	2.63899	−	1.91734i	0.125100	−	0.0908905i
$446$	−4.03636	−	12.4226i	−0.191127	−	0.588228i
$447$	0.589563	−	1.81449i	0.0278854	−	0.0858224i
$448$	8.79660	+	6.39111i	0.415600	+	0.301951i
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	−0.936810	−	0.349839i	$-0.886236\pi$
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	0.963525	+	0.267617i	$0.0862363\pi$
$450$	−5.57083	+	17.1452i	−0.262611	+	0.808235i
$451$	−7.08786	−	5.14963i	−0.333754	−	0.242487i
$452$	−1.43184	+	4.40674i	−0.0673480	+	0.207276i
$453$	−1.36835	−	4.21134i	−0.0642906	−	0.197866i
$454$	−13.5013	+	9.80926i	−0.633647	+	0.460371i
$455$	−7.22083	−	22.2234i	−0.338518	−	1.04185i
$456$	0.620112	+	0.450538i	0.0290394	+	0.0210984i
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.998402	−	0.0565045i	$-0.982004\pi$
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.362262	−	0.932076i	$-0.617996\pi$
$458$	26.8742	−	19.5252i	1.25575	−	0.912354i
$459$	16.2748			0.759642
$460$	−6.09097			−0.283993
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	−0.562317	−	0.826922i	$-0.690090\pi$
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	0.612684	+	0.790328i	$0.290090\pi$
$462$	1.97866	−	6.08969i	0.0920557	−	0.283318i
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	0.830325	−	0.557280i	$-0.188155\pi$
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	−0.999308	+	0.0372039i	$0.988155\pi$
$464$	−6.61711			−0.307192
$465$		0			0
$466$	−25.2503			−1.16970
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	0.998385	−	0.0568157i	$-0.0180947\pi$
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	−0.841106	+	0.540871i	$0.818095\pi$
$468$	6.27201	−	19.3033i	0.289924	−	0.892293i
$469$	−8.70693	+	6.32596i	−0.402049	+	0.292106i
$470$	9.44695			0.435755
$471$	−2.58521			−0.119120
$472$	1.88331	−	1.36831i	0.0866865	−	0.0629814i
$473$	9.85161	+	7.15761i	0.452977	+	0.329107i
$474$	8.39522	+	6.09949i	0.385605	+	0.280159i
$475$	1.57460	+	4.84612i	0.0722477	+	0.222355i
$476$	24.3610	−	17.6993i	1.11659	−	0.811247i
$477$	11.0188	+	33.9123i	0.504514	+	1.55274i
$478$	5.63239	−	17.3347i	0.257620	−	0.792872i
$479$	0.543461	+	0.394848i	0.0248314	+	0.0180411i	0.600132	−	0.799901i	$-0.295115\pi$
$479$	0.543461	+	0.394848i	0.0248314	+	0.0180411i	−0.575300	+	0.817942i	$0.695115\pi$
$480$	1.26417	−	3.89070i	0.0577010	−	0.177585i
$481$	−7.21391	+	22.2021i	−0.328926	+	1.01233i
$482$	−9.98370	−	7.25358i	−0.454745	−	0.330392i
$483$	−2.04182	+	6.28409i	−0.0929062	+	0.285936i
$484$	−3.32207	−	10.2243i	−0.151003	−	0.464740i
$485$	8.10070	−	5.88550i	0.367834	−	0.267247i
$486$	−6.87205	−	21.1500i	−0.311722	−	0.959383i
$487$	19.8820	+	14.4451i	0.900939	+	0.654571i	0.938707	−	0.344716i	$-0.112025\pi$
$487$	19.8820	+	14.4451i	0.900939	+	0.654571i	−0.0377677	+	0.999287i	$0.512025\pi$
$488$	2.31437	+	1.68148i	0.104766	+	0.0761172i
$489$	−0.223718	+	0.162541i	−0.0101169	+	0.00735034i
$490$	−15.4932			−0.699912
$491$	8.63428			0.389660			0.194830	−	0.980837i	$-0.437585\pi$
$491$	8.63428			0.389660			0.194830	+	0.980837i	$0.437585\pi$
$492$	2.71339	−	1.97139i	0.122329	−	0.0888772i
$493$	−2.40390	+	7.39845i	−0.108266	+	0.333209i
$494$	−4.26395	−	13.1231i	−0.191844	−	0.590436i
$495$	6.16551			0.277119
$496$		0			0
$497$	33.6035			1.50732
$498$	2.99134	+	9.20641i	0.134045	+	0.412549i
$499$	9.60931	−	29.5744i	0.430172	−	1.32393i	−0.467782	−	0.883844i	$-0.654947\pi$
$499$	9.60931	−	29.5744i	0.430172	−	1.32393i	0.897954	−	0.440089i	$-0.145053\pi$
$500$	11.8756	−	8.62809i	0.531091	−	0.385860i
$501$	0.997713			0.0445745
$502$	54.2443			2.42104
$503$	13.3847	−	9.72453i	0.596793	−	0.433595i	−0.247946	−	0.968774i	$-0.579756\pi$
$503$	13.3847	−	9.72453i	0.596793	−	0.433595i	0.844739	+	0.535178i	$0.179756\pi$
$504$	8.86447	+	6.44042i	0.394855	+	0.286879i
$505$	−1.56132	−	1.13437i	−0.0694779	−	0.0504786i
$506$	−3.76239	−	11.5794i	−0.167259	−	0.514769i
$507$	−5.60682	+	4.07359i	−0.249008	+	0.180915i
$508$	4.21843	+	12.9830i	0.187163	+	0.576028i
$509$	9.54772	−	29.3849i	0.423195	−	1.30246i	−0.481516	−	0.876437i	$-0.659914\pi$
$509$	9.54772	−	29.3849i	0.423195	−	1.30246i	0.904712	−	0.426024i	$-0.140086\pi$
$510$	−5.11462	−	3.71599i	−0.226479	−	0.164547i
$511$	−4.84968	+	14.9258i	−0.214537	+	0.660278i
$512$	−6.92906	+	21.3254i	−0.306224	+	0.942460i
$513$	−3.34186	−	2.42801i	−0.147547	−	0.107199i
$514$	13.6924	−	42.1410i	0.603948	−	1.85876i
$515$	6.83057	+	21.0223i	0.300991	+	0.926355i
$516$	−3.77141	+	2.74009i	−0.166027	+	0.120626i
$517$	2.42613	+	7.46686i	0.106701	+	0.328392i
$518$	25.1608	+	18.2804i	1.10550	+	0.803195i
$519$	1.63921	+	1.19096i	0.0719534	+	0.0522772i
$520$	5.40377	−	3.92607i	0.236971	−	0.172170i
$521$	−14.7219			−0.644980			−0.322490	−	0.946573i	$-0.604520\pi$
$521$	−14.7219			−0.644980			−0.322490	+	0.946573i	$0.604520\pi$
$522$	6.98553			0.305748
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.0973541	−	0.995250i	$-0.468962\pi$
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.976623	+	0.214960i	$0.0689621\pi$
$524$	−5.05440	+	15.5559i	−0.220803	+	0.679561i
$525$	−2.04050	−	6.28002i	−0.0890548	−	0.274082i
$526$	−7.29764			−0.318192
$527$		0			0
$528$	4.46920			0.194497
$529$	−3.22490	−	9.92522i	−0.140213	−	0.431531i
$530$	8.94861	−	27.5410i	0.388703	−	1.19630i
$531$	−4.85466	+	3.52712i	−0.210674	+	0.153064i
$532$	−7.64282			−0.331358
$533$	24.4661			1.05974
$534$	−2.01943	+	1.46720i	−0.0873894	+	0.0634921i
$535$	−11.3065	−	8.21462i	−0.488821	−	0.355149i
$536$	−2.48886	−	1.80826i	−0.107502	−	0.0781050i
$537$	−0.611660	−	1.88250i	−0.0263951	−	0.0812357i
$538$	19.0882	−	13.8684i	0.822949	−	0.597908i
$539$	−3.97891	−	12.2458i	−0.171384	−	0.527465i
$540$	−1.52486	+	4.69304i	−0.0656196	+	0.201956i
$541$	21.9252	+	15.9296i	0.942636	+	0.684865i	0.949054	−	0.315114i	$-0.102043\pi$
$541$	21.9252	+	15.9296i	0.942636	+	0.684865i	−0.00641782	+	0.999979i	$0.502043\pi$
$542$	1.89969	−	5.84664i	0.0815986	−	0.251135i
$543$	0.987180	−	3.03823i	0.0423639	−	0.130383i
$544$	31.1116	+	22.6039i	1.33390	+	0.969135i
$545$	0.519831	−	1.59988i	0.0222671	−	0.0685312i
$546$	5.52559	+	17.0060i	0.236473	+	0.727790i
$547$	−26.5864	+	19.3161i	−1.13675	+	0.825899i	−0.986663	−	0.162774i	$-0.947956\pi$
$547$	−26.5864	+	19.3161i	−1.13675	+	0.825899i	−0.150089	+	0.988673i	$0.547956\pi$
$548$	−6.94364	−	21.3703i	−0.296618	−	0.912896i
$549$	−5.96580	−	4.33441i	−0.254614	−	0.184988i
$550$	9.84368	+	7.15186i	0.419736	+	0.304956i
$551$	1.59738	−	1.16056i	0.0680506	−	0.0494417i
$552$	−1.88873			−0.0803899
$553$	41.9284			1.78298
$554$	31.4588	−	22.8561i	1.33655	−	0.971064i
$555$	0.838905	−	2.58188i	0.0356095	−	0.109595i
$556$	−4.48982	−	13.8183i	−0.190411	−	0.586025i
$557$	−3.79343			−0.160733			−0.0803663	−	0.996765i	$-0.525609\pi$
$557$	−3.79343			−0.160733			−0.0803663	+	0.996765i	$0.525609\pi$
$558$		0			0
$559$	−34.0061			−1.43830
$560$	−6.71438	−	20.6647i	−0.283734	−	0.873245i
$561$	1.62360	−	4.99692i	0.0685483	−	0.210970i
$562$	−14.0207	+	10.1867i	−0.591429	+	0.429698i
$563$	−8.97818			−0.378385			−0.189193	−	0.981940i	$-0.560587\pi$
$563$	−8.97818			−0.378385			−0.189193	+	0.981940i	$0.560587\pi$
$564$	−3.00558			−0.126558
$565$	3.17996	−	2.31037i	0.133782	−	0.0971981i
$566$	−15.1678	−	11.0200i	−0.637549	−	0.463206i
$567$	−20.5910	−	14.9602i	−0.864739	−	0.628270i
$568$	2.96826	+	9.13536i	0.124545	+	0.383311i
$569$	−7.68209	+	5.58136i	−0.322050	+	0.233983i	−0.737050	−	0.675839i	$-0.763782\pi$
$569$	−7.68209	+	5.58136i	−0.322050	+	0.233983i	0.415000	+	0.909821i	$0.363782\pi$
$570$	0.495855	+	1.52608i	0.0207691	+	0.0639206i
$571$	1.98029	−	6.09472i	0.0828727	−	0.255056i	−0.901031	−	0.433754i	$-0.857189\pi$
$571$	1.98029	−	6.09472i	0.0828727	−	0.255056i	0.983904	+	0.178698i	$0.0571886\pi$
$572$	−11.0827	−	8.05203i	−0.463390	−	0.336672i
$573$	1.79394	−	5.52118i	0.0749429	−	0.230651i
$574$	10.0722	−	30.9991i	0.420407	−	1.29388i
$575$	−10.1579	−	7.38016i	−0.423614	−	0.307774i
$576$	2.47578	−	7.61966i	0.103157	−	0.317486i
$577$	2.43357	+	7.48975i	0.101311	+	0.311802i	0.988847	−	0.148936i	$-0.0475848\pi$
$577$	2.43357	+	7.48975i	0.101311	+	0.311802i	−0.887536	+	0.460738i	$0.847585\pi$
$578$	22.6328	−	16.4437i	0.941399	−	0.683966i
$579$	2.08989	+	6.43202i	0.0868528	+	0.267305i
$580$	−1.90820	−	1.38639i	−0.0792339	−	0.0575668i
$581$	31.6428	+	22.9899i	1.31277	+	0.953781i
$582$	−6.19889	+	4.50376i	−0.256952	+	0.186687i
$583$	24.0665			0.996733
$584$	−4.48607			−0.185635
$585$	−13.9294	+	10.1203i	−0.575912	+	0.418424i
$586$	12.1611	−	37.4279i	0.502369	−	1.54613i
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	0.588144	+	0.808756i	$0.299859\pi$
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	−0.000443412		1.00000i	$0.500141\pi$
$588$	4.92922			0.203278
$589$		0			0
$590$	4.87331			0.200631
$591$	3.61149	+	11.1150i	0.148557	+	0.457211i
$592$	−6.70795	+	20.6449i	−0.275695	+	0.848502i
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	−0.721298	−	0.692625i	$-0.756454\pi$
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	0.435832	+	0.900028i	$0.356454\pi$
$594$	−9.86377			−0.404715
$595$	−25.5441			−1.04720
$596$	−4.39928	+	3.19627i	−0.180202	+	0.130924i
$597$	−2.66549	−	1.93659i	−0.109091	−	0.0792594i
$598$	27.5072	+	19.9851i	1.12485	+	0.817254i
$599$	−7.85123	−	24.1636i	−0.320793	−	0.987298i	−0.973304	−	0.229519i	$-0.926285\pi$
$599$	−7.85123	−	24.1636i	−0.320793	−	0.987298i	0.652511	−	0.757779i	$-0.273715\pi$
$600$	1.52703	−	1.10945i	0.0623407	−	0.0452931i
$601$	−7.77657	−	23.9338i	−0.317213	−	0.976281i	−0.974834	−	0.222932i	$-0.928437\pi$
$601$	−7.77657	−	23.9338i	−0.317213	−	0.976281i	0.657621	−	0.753349i	$-0.271563\pi$
$602$	−13.9997	+	43.0865i	−0.570584	+	1.75608i
$603$	6.41559	+	4.66120i	0.261263	+	0.189819i
$604$	−3.90007	+	12.0032i	−0.158692	+	0.488403i
$605$	−2.81813	+	8.67330i	−0.114573	+	0.352620i
$606$	1.19477	+	0.868050i	0.0485342	+	0.0352621i
$607$	2.90074	−	8.92757i	0.117738	−	0.362359i	−0.874771	−	0.484537i	$-0.838988\pi$
$607$	2.90074	−	8.92757i	0.117738	−	0.362359i	0.992508	+	0.122178i	$0.0389880\pi$
$608$	−3.01622	−	9.28298i	−0.122324	−	0.376474i
$609$	−2.07002	+	1.50396i	−0.0838814	+	0.0609434i
$610$	1.85062	+	5.69561i	0.0749292	+	0.230608i
$611$	−17.7377	−	12.8872i	−0.717589	−	0.521359i
$612$	−17.9501	−	13.0415i	−0.725590	−	0.527172i
$613$	−9.29233	+	6.75128i	−0.375314	+	0.272681i	−0.759411	−	0.650611i	$-0.774513\pi$
$613$	−9.29233	+	6.75128i	−0.375314	+	0.272681i	0.384097	+	0.923293i	$0.374513\pi$
$614$	−30.0496			−1.21270
$615$	−2.84516			−0.114728
$616$	5.98295	−	4.34687i	0.241060	−	0.175140i
$617$	−0.696336	+	2.14310i	−0.0280334	+	0.0862780i	−0.964094	−	0.265560i	$-0.914443\pi$
$617$	−0.696336	+	2.14310i	−0.0280334	+	0.0862780i	0.936061	+	0.351838i	$0.114443\pi$
$618$	−5.22695	−	16.0869i	−0.210259	−	0.647110i
$619$	23.6684			0.951314			0.475657	−	0.879631i	$-0.342210\pi$
$619$	23.6684			0.951314			0.475657	+	0.879631i	$0.342210\pi$
$620$		0			0
$621$	10.1786			0.408455
$622$	5.93803	+	18.2754i	0.238093	+	0.732776i
$623$	−3.11665	+	9.59206i	−0.124866	+	0.384298i
$624$	−10.0970	+	7.33594i	−0.404205	+	0.293672i
$625$	5.25913			0.210365
$626$	−59.2874			−2.36960
$627$	−1.07887	+	0.783845i	−0.0430859	+	0.0313038i
$628$	5.96115	+	4.33103i	0.237876	+	0.172827i
$629$	20.6458	+	15.0000i	0.823201	+	0.598091i
$630$	7.08822	+	21.8153i	0.282402	+	0.869142i
$631$	28.0745	−	20.3973i	1.11763	−	0.812004i	0.133780	−	0.991011i	$-0.457289\pi$
$631$	28.0745	−	20.3973i	1.11763	−	0.812004i	0.983848	+	0.179007i	$0.0572885\pi$
$632$	3.70361	+	11.3986i	0.147322	+	0.453410i
$633$	−2.98821	+	9.19675i	−0.118771	+	0.365538i
$634$	37.8923	+	27.5303i	1.50489	+	1.09337i
$635$	3.57852	−	11.0136i	0.142009	−	0.437059i
$636$	−2.84703	+	8.76226i	−0.112892	+	0.347446i
$637$	29.0902	+	21.1353i	1.15259	+	0.837409i
$638$	1.45695	−	4.48403i	0.0576812	−	0.177524i
$639$	−7.65135	−	23.5484i	−0.302683	−	0.931562i
$640$	7.99171	−	5.80631i	0.315900	−	0.229515i
$641$	8.15581	+	25.1010i	0.322135	+	0.991430i	0.972717	+	0.231994i	$0.0745250\pi$
$641$	8.15581	+	25.1010i	0.322135	+	0.991430i	−0.650582	+	0.759436i	$0.725475\pi$
$642$	8.65203	+	6.28607i	0.341468	+	0.248091i
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	0.388383	−	0.921498i	$-0.373034\pi$
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	−0.756379	+	0.654133i	$0.773034\pi$
$644$	15.2360	−	11.0696i	0.600381	−	0.436202i
$645$	3.95456			0.155711
$646$	−15.0840			−0.593471
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.371332	+	0.928500i	$0.621099\pi$
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.997804	+	0.0662355i	$0.978901\pi$
$648$	2.24821	−	6.91927i	0.0883179	−	0.271815i
$649$	1.25154	+	3.85186i	0.0491274	+	0.151199i
$650$	−33.9787			−1.33276
$651$		0			0
$652$	0.788169			0.0308671
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	−0.627213	−	0.778848i	$-0.715805\pi$
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	0.0496311	−	0.998768i	$-0.484195\pi$
$654$	−0.397790	+	1.22427i	−0.0155548	+	0.0478729i
$655$	11.2253	−	8.15565i	0.438608	−	0.318668i
$656$	22.7501			0.888243
$657$	11.5639			0.451149
$658$	−23.6306	+	17.1686i	−0.921217	+	0.669303i
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	0.886578	−	0.462579i	$-0.153076\pi$
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	−0.165971	+	0.986131i	$0.553076\pi$
$660$	1.28880	+	0.936370i	0.0501666	+	0.0364481i
$661$	−6.15079	−	18.9302i	−0.239238	−	0.736299i	−0.996531	−	0.0832235i	$-0.973478\pi$
$661$	−6.15079	−	18.9302i	−0.239238	−	0.736299i	0.757293	−	0.653075i	$-0.226522\pi$
$662$	−49.2693	+	35.7962i	−1.91491	+	1.39126i
$663$	4.53404	+	13.9543i	0.176088	+	0.541942i
$664$	−3.45490	+	10.6331i	−0.134076	+	0.412644i
$665$	5.24522	+	3.81087i	0.203401	+	0.147779i
$666$	7.08143	−	21.7944i	0.274400	−	0.844516i
$667$	−1.50346	+	4.62717i	−0.0582141	+	0.179165i
$668$	−2.30059	−	1.67148i	−0.0890125	−	0.0646714i
$669$	1.08938	−	3.35276i	0.0421178	−	0.129625i
$670$	−1.99014	−	6.12503i	−0.0768860	−	0.236631i
$671$	−4.02653	+	2.92545i	−0.155443	+	0.112936i
$672$	3.90868	+	12.0297i	0.150780	+	0.464054i
$673$	−14.0988	−	10.2434i	−0.543467	−	0.394852i	0.281904	−	0.959443i	$-0.409034\pi$
$673$	−14.0988	−	10.2434i	−0.543467	−	0.394852i	−0.825371	+	0.564591i	$0.809034\pi$
$674$	5.91359	+	4.29648i	0.227783	+	0.165494i
$675$	−8.22936	+	5.97898i	−0.316748	+	0.230131i
$676$	19.7531			0.759734
$677$	31.8257			1.22316			0.611581	−	0.791182i	$-0.290534\pi$
$677$	31.8257			1.22316			0.611581	+	0.791182i	$0.290534\pi$
$678$	−2.43340	+	1.76797i	−0.0934540	+	0.0678983i
$679$	−9.56693	+	29.4440i	−0.367145	+	1.12996i
$680$	−2.25635	−	6.94434i	−0.0865272	−	0.266303i
$681$	−4.50408			−0.172597
$682$		0			0
$683$	19.9935			0.765031			0.382515	−	0.923949i	$-0.375058\pi$
$683$	19.9935			0.765031			0.382515	+	0.923949i	$0.375058\pi$
$684$	1.74023	+	5.35589i	0.0665395	+	0.204788i
$685$	−5.89033	+	18.1286i	−0.225058	+	0.692657i
$686$	−0.359828	+	0.261431i	−0.0137383	+	0.00998147i
$687$	8.96533			0.342049
$688$	−31.6210			−1.20554
$689$	−54.3723	+	39.5038i	−2.07142	+	1.50497i
$690$	−3.19881	−	2.32407i	−0.121777	−	0.0884758i
$691$	11.5362	+	8.38155i	0.438858	+	0.318849i	0.785181	−	0.619266i	$-0.212570\pi$
$691$	11.5362	+	8.38155i	0.438858	+	0.318849i	−0.346323	+	0.938115i	$0.612570\pi$
$692$	−1.78458	−	5.49237i	−0.0678396	−	0.208789i
$693$	−15.4224	+	11.2050i	−0.585849	+	0.425644i
$694$	7.82401	+	24.0798i	0.296995	+	0.914058i
$695$	−3.80874	+	11.7221i	−0.144474	+	0.444645i
$696$	−0.591710	−	0.429903i	−0.0224287	−	0.0162954i
$697$	8.26480	−	25.4364i	0.313052	−	0.963473i
$698$	2.11826	−	6.51934i	0.0801773	−	0.246760i
$699$	−5.51332	−	4.00566i	−0.208533	−	0.151508i
$700$	−5.81585	+	17.8993i	−0.219818	+	0.676532i
$701$	−14.3832	−	44.2670i	−0.543247	−	1.67194i	−0.725122	−	0.688621i	$-0.758217\pi$
$701$	−14.3832	−	44.2670i	−0.543247	−	1.67194i	0.181875	−	0.983322i	$-0.441783\pi$
$702$	22.2847	−	16.1908i	0.841084	−	0.611083i
$703$	−2.00158	−	6.16022i	−0.0754908	−	0.232337i
$704$	−4.37471	−	3.17841i	−0.164878	−	0.119791i
$705$	2.06271	+	1.49865i	0.0776861	+	0.0564423i
$706$	−23.1884	+	16.8474i	−0.872707	+	0.634058i
$707$	5.96706			0.224414
$708$	−1.55046			−0.0582699
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	−0.871798	−	0.489866i	$-0.837046\pi$
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	0.196489	+	0.980506i	$0.437046\pi$
$710$	−6.21386	+	19.1243i	−0.233202	+	0.717721i
$711$	−9.54690	−	29.3823i	−0.358037	−	1.10192i
$712$	−2.88297			−0.108044
$713$		0			0
$714$	19.5471			0.731531
$715$	3.59105	+	11.0521i	0.134298	+	0.413326i
$716$	−1.74336	+	5.36550i	−0.0651523	+	0.200518i
$717$	3.97976	−	2.89147i	0.148627	−	0.107984i
$718$	9.93445			0.370750
$719$	44.0914			1.64433			0.822165	−	0.569249i	$-0.192766\pi$
$719$	44.0914			1.64433			0.822165	+	0.569249i	$0.192766\pi$
$720$	−12.9525	+	9.41053i	−0.482710	+	0.350710i
$721$	−55.2914	−	40.1716i	−2.05916	−	1.49607i
$722$	−25.3428	−	18.4126i	−0.943160	−	0.685246i
$723$	−1.02921	−	3.16759i	−0.0382768	−	0.117804i
$724$	−7.36627	+	5.35191i	−0.273765	+	0.198902i
$725$	−1.50248	−	4.62417i	−0.0558008	−	0.171737i
$726$	2.15651	−	6.63707i	0.0800357	−	0.246325i
$727$	−31.5599	−	22.9296i	−1.17049	−	0.850413i	−0.179426	−	0.983772i	$-0.557424\pi$
$727$	−31.5599	−	22.9296i	−1.17049	−	0.850413i	−0.991068	+	0.133358i	$0.957424\pi$
$728$	−6.38186	+	19.6414i	−0.236528	+	0.727957i
$729$	−4.46591	+	13.7447i	−0.165404	+	0.509062i
$730$	−7.59772	−	5.52006i	−0.281204	−	0.204307i
$731$	−11.4875	+	35.3548i	−0.424879	+	1.30764i
$732$	−0.588780	−	1.81208i	−0.0217619	−	0.0669763i
$733$	−5.51028	+	4.00345i	−0.203527	+	0.147871i	−0.684880	−	0.728656i	$-0.740145\pi$
$733$	−5.51028	+	4.00345i	−0.203527	+	0.147871i	0.481353	+	0.876527i	$0.340145\pi$
$734$	8.41660	+	25.9036i	0.310663	+	0.956121i
$735$	−3.38289	−	2.45782i	−0.124780	−	0.0906579i
$736$	19.4580	+	14.1370i	0.717230	+	0.521098i
$737$	4.33012	−	3.14601i	0.159502	−	0.115885i
$738$	−24.0168			−0.884070
$739$	−33.2004			−1.22130			−0.610649	−	0.791902i	$-0.709091\pi$
$739$	−33.2004			−1.22130			−0.610649	+	0.791902i	$0.709091\pi$
$740$	−6.25985	+	4.54805i	−0.230117	+	0.167190i
$741$	1.15080	−	3.54181i	0.0422758	−	0.130112i
$742$	27.6682	+	85.1540i	1.01573	+	3.12610i
$743$	22.5011			0.825484			0.412742	−	0.910848i	$-0.364571\pi$
$743$	22.5011			0.825484			0.412742	+	0.910848i	$0.364571\pi$
$744$		0			0
$745$	4.61293			0.169005
$746$	−13.6332	−	41.9586i	−0.499146	−	1.53621i
$747$	8.90578	−	27.4092i	0.325845	−	1.00285i
$748$	−12.1152	+	8.80219i	−0.442975	+	0.321840i
$749$	43.2110			1.57890
$750$	9.52884			0.347944
$751$	−5.18946	+	3.77036i	−0.189366	+	0.137583i	−0.678429	−	0.734666i	$-0.737339\pi$
$751$	−5.18946	+	3.77036i	−0.189366	+	0.137583i	0.489063	+	0.872249i	$0.337339\pi$
$752$	−16.4936	−	11.9833i	−0.601460	−	0.436986i
$753$	11.8441	+	8.60521i	0.431621	+	0.313591i
$754$	4.06866	+	12.5221i	0.148172	+	0.456026i
$755$	8.66164	−	6.29305i	0.315229	−	0.229028i
$756$	−4.71472	−	14.5104i	−0.171473	−	0.527739i
$757$	−7.99547	+	24.6075i	−0.290600	+	0.894375i	0.694064	+	0.719914i	$0.255819\pi$
$757$	−7.99547	+	24.6075i	−0.290600	+	0.894375i	−0.984664	+	0.174462i	$0.944181\pi$
$758$	−33.1209	−	24.0637i	−1.20300	−	0.874034i
$759$	1.01544	−	3.12519i	0.0368580	−	0.113437i
$760$	−0.572695	+	1.76257i	−0.0207738	+	0.0639352i
$761$	36.1894	+	26.2932i	1.31187	+	0.953126i	0.999995	+	0.00300175i	$0.000955488\pi$
$761$	36.1894	+	26.2932i	1.31187	+	0.953126i	0.311870	+	0.950125i	$0.399045\pi$
$762$	−2.73839	+	8.42789i	−0.0992014	+	0.305310i
$763$	1.60727	+	4.94666i	0.0581870	+	0.179081i
$764$	−13.3863	+	9.72569i	−0.484298	+	0.351863i
$765$	5.81626	+	17.9006i	0.210287	+	0.647198i
$766$	−35.6229	−	25.8815i	−1.28711	−	0.935138i
$767$	−9.15016	−	6.64798i	−0.330393	−	0.240045i
$768$	−8.46886	+	6.15299i	−0.305594	+	0.222027i
$769$	12.6875			0.457524			0.228762	−	0.973482i	$-0.426532\pi$
$769$	12.6875			0.457524			0.228762	+	0.973482i	$0.426532\pi$
$770$	15.4817			0.557920
$771$	9.67486	−	7.02920i	0.348432	−	0.253150i
$772$	5.95661	−	18.3326i	0.214383	−	0.659804i
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	0.989097	−	0.147265i	$-0.0470471\pi$
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	−0.886757	+	0.462236i	$0.847047\pi$
$774$	33.3816			1.19988
$775$		0			0
$776$	−8.84964			−0.317683
$777$	2.59381	+	7.98293i	0.0930524	+	0.286386i
$778$	−9.75078	+	30.0098i	−0.349582	+	1.07590i
$779$	−5.49191	+	3.99011i	−0.196768	+	0.142960i
$780$	−4.44873			−0.159290
$781$	−16.7116			−0.597989
$782$	30.0699	−	21.8470i	1.07530	−	0.781249i
$783$	3.18880	+	2.31680i	0.113959	+	0.0827958i
$784$	27.0499	+	19.6529i	0.966067	+	0.701889i
$785$	−1.93156	−	5.94472i	−0.0689402	−	0.212176i
$786$	−8.58992	+	6.24094i	−0.306392	+	0.222607i
$787$	−14.4482	−	44.4670i	−0.515023	−	1.58508i	−0.783241	−	0.621718i	$-0.786435\pi$
$787$	−14.4482	−	44.4670i	−0.515023	−	1.58508i	0.268218	−	0.963358i	$-0.413565\pi$
$788$	10.2935	−	31.6801i	0.366691	−	1.12856i
$789$	−1.59342	−	1.15768i	−0.0567271	−	0.0412147i
$790$	−7.75328	+	23.8621i	−0.275849	+	0.848977i
$791$	−3.75553	+	11.5583i	−0.133531	+	0.410967i
$792$	−4.40846	−	3.20294i	−0.156648	−	0.113811i
$793$	4.29500	−	13.2186i	0.152520	−	0.469408i
$794$	5.72974	+	17.6343i	0.203341	+	0.625819i
$795$	6.32295	−	4.59389i	0.224252	−	0.162929i
$796$	2.90187	+	8.93103i	0.102854	+	0.316552i
$797$	0.291229	+	0.211590i	0.0103159	+	0.00749491i	0.592931	−	0.805253i	$-0.297971\pi$
$797$	0.291229	+	0.211590i	0.0103159	+	0.00749491i	−0.582615	+	0.812748i	$0.697971\pi$
$798$	−4.01380	−	2.91619i	−0.142087	−	0.103232i
$799$	−19.3902	+	14.0878i	−0.685975	+	0.498390i
$800$	−24.0358			−0.849793
$801$	7.43151			0.262580
$802$	−42.7400	+	31.0525i	−1.50920	+	1.09650i
$803$	2.41184	−	7.42286i	0.0851118	−	0.261947i
$804$	0.633171	+	1.94870i	0.0223302	+	0.0687254i
$805$	−15.9759			−0.563075
$806$		0			0
$807$	6.36789			0.224160
$808$	0.527081	+	1.62219i	0.0185426	+	0.0570684i
$809$	−8.87530	+	27.3154i	−0.312039	+	0.960357i	0.664917	+	0.746917i	$0.268467\pi$
$809$	−8.87530	+	27.3154i	−0.312039	+	0.960357i	−0.976956	+	0.213440i	$0.931533\pi$
$810$	12.3217	−	8.95225i	0.432941	−	0.314550i
$811$	−19.9135			−0.699258			−0.349629	−	0.936888i	$-0.613692\pi$
$811$	−19.9135			−0.699258			−0.349629	+	0.936888i	$0.613692\pi$
$812$	7.29278			0.255926
$813$	1.34229	−	0.975231i	0.0470762	−	0.0342028i
$814$	−12.5129	−	9.09117i	−0.438578	−	0.318646i
$815$	−0.540915	−	0.392998i	−0.0189474	−	0.0137661i
$816$	4.21604	+	12.9756i	0.147591	+	0.454238i
$817$	7.63335	−	5.54596i	0.267057	−	0.194028i
$818$	13.1560	+	40.4900i	0.459988	+	1.41570i
$819$	16.4507	−	50.6300i	0.574834	−	1.76916i
$820$	6.56055	+	4.76652i	0.229104	+	0.166454i
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	−0.318220	−	0.948017i	$-0.603085\pi$
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	0.814676	−	0.579917i	$-0.196915\pi$
$822$	4.50745	−	13.8725i	0.157216	−	0.483860i
$823$	10.7037	+	7.77667i	0.373106	+	0.271078i	0.758498	−	0.651676i	$-0.225934\pi$
$823$	10.7037	+	7.77667i	0.373106	+	0.271078i	−0.385392	+	0.922753i	$0.625934\pi$
$824$	6.03695	−	18.5798i	0.210307	−	0.647259i
$825$	1.01478	+	3.12317i	0.0353300	+	0.108735i
$826$	−12.1901	+	8.85663i	−0.424148	+	0.308162i
$827$	3.52516	+	10.8493i	0.122582	+	0.377268i	0.993453	−	0.114244i	$-0.0364444\pi$
$827$	3.52516	+	10.8493i	0.122582	+	0.377268i	−0.870871	+	0.491512i	$0.836444\pi$
$828$	−11.2264	−	8.15648i	−0.390145	−	0.283457i
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.214766	−	0.976666i	$-0.568899\pi$
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.995230	+	0.0975520i	$0.968899\pi$
$830$	−18.9352	+	13.7572i	−0.657251	+	0.477521i
$831$	10.4948			0.364059
$832$	15.1008			0.523525
$833$	31.8003	−	23.1043i	1.10182	−	0.800516i
$834$	2.91456	−	8.97010i	0.100923	−	0.310609i
$835$	0.745446	+	2.29425i	0.0257972	+	0.0793957i
$836$	3.80091			0.131457
$837$		0			0
$838$	−62.0578			−2.14375
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	0.861856	+	0.507153i	$0.169302\pi$
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	−0.399159	+	0.916882i	$0.630698\pi$
$840$	0.742146	−	2.28409i	0.0256065	−	0.0788086i
$841$	21.9373	−	15.9384i	0.756458	−	0.549599i
$842$	−16.7023			−0.575600
$843$	−4.67737			−0.161097
$844$	22.2978	−	16.2003i	0.767522	−	0.557637i
$845$	−13.5564	−	9.84931i	−0.466355	−	0.338827i
$846$	17.4119	+	12.6505i	0.598634	+	0.434933i
$847$	−8.71337	−	26.8170i	−0.299395	−	0.921443i
$848$	−50.5588	+	36.7331i	−1.73620	+	1.26142i
$849$	−1.56363	−	4.81237i	−0.0536638	−	0.165160i
$850$	−11.4782	+	35.3264i	−0.393700	+	1.21168i
$851$	12.9124	+	9.38138i	0.442630	+	0.321590i
$852$	1.97696	−	6.08446i	0.0677295	−	0.208450i
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	−0.908959	−	0.416885i	$-0.863122\pi$
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	0.980402	+	0.197005i	$0.0631217\pi$
$854$	−14.9802	−	10.8837i	−0.512611	−	0.372434i
$855$	1.47625	−	4.54343i	0.0504867	−	0.155382i
$856$	3.81691	+	11.7472i	0.130459	+	0.401512i
$857$	20.1009	−	14.6042i	0.686635	−	0.498870i	−0.188917	−	0.981993i	$-0.560498\pi$
$857$	20.1009	−	14.6042i	0.686635	−	0.498870i	0.875552	+	0.483123i	$0.160498\pi$
$858$	−2.74798	−	8.45740i	−0.0938144	−	0.288731i
$859$	−1.29270	−	0.939204i	−0.0441065	−	0.0320452i	0.565514	−	0.824739i	$-0.308678\pi$
$859$	−1.29270	−	0.939204i	−0.0441065	−	0.0320452i	−0.609620	+	0.792694i	$0.708678\pi$
$860$	−9.11869	−	6.62511i	−0.310945	−	0.225915i
$861$	7.11688	−	5.17072i	0.242543	−	0.176218i
$862$	−20.9198			−0.712533
$863$	−30.7713			−1.04747			−0.523734	−	0.851882i	$-0.675461\pi$
$863$	−30.7713			−1.04747			−0.523734	+	0.851882i	$0.675461\pi$
$864$	15.7637	−	11.4530i	0.536292	−	0.389639i
$865$	−1.51387	+	4.65921i	−0.0514731	+	0.158418i
$866$	−5.20536	−	16.0204i	−0.176885	−	0.544397i
$867$	7.55038			0.256424
$868$		0			0
$869$	−20.8518			−0.707348
$870$	−0.473144	−	1.45619i	−0.0160411	−	0.0493694i
$871$	−4.61882	+	14.2153i	−0.156503	+	0.481666i
$872$	−1.20281	+	0.873895i	−0.0407324	+	0.0295938i
$873$	22.8119			0.772067
$874$	−9.43387			−0.319105
$875$	31.1481	−	22.6304i	1.05300	−	0.765048i
$876$	2.41724	+	1.75623i	0.0816710	+	0.0593374i
$877$	−6.73981	−	4.89676i	−0.227587	−	0.165352i	0.468148	−	0.883650i	$-0.344921\pi$
$877$	−6.73981	−	4.89676i	−0.227587	−	0.165352i	−0.695735	+	0.718298i	$0.744921\pi$
$878$	22.6441	+	69.6914i	0.764202	+	2.35197i
$879$	8.59283	−	6.24305i	0.289829	−	0.210573i
$880$	3.33918	+	10.2770i	0.112564	+	0.346436i
$881$	6.75616	−	20.7933i	0.227621	−	0.700544i	−0.770394	−	0.637568i	$-0.779941\pi$
$881$	6.75616	−	20.7933i	0.227621	−	0.700544i	0.998015	−	0.0629767i	$-0.0200594\pi$
$882$	−28.5560	−	20.7471i	−0.961529	−	0.698592i
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	−0.994725	−	0.102576i	$-0.967292\pi$
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	0.865042	+	0.501699i	$0.167292\pi$
$884$	12.9229	−	39.7727i	0.434646	−	1.33770i
$885$	1.06407	+	0.773093i	0.0357684	+	0.0259872i
$886$	−14.4413	+	44.4458i	−0.485166	+	1.49319i
$887$	−7.64568	−	23.5310i	−0.256717	−	0.790093i	−0.993487	−	0.113949i	$-0.963650\pi$
$887$	−7.64568	−	23.5310i	−0.256717	−	0.790093i	0.736770	−	0.676144i	$-0.236350\pi$
$888$	−1.94110	+	1.41029i	−0.0651391	+	0.0473263i
$889$	11.0644	+	34.0528i	0.371089	+	1.14209i
$890$	−4.88267	−	3.54747i	−0.163668	−	0.118911i
$891$	10.2403	+	7.43998i	0.343062	+	0.249249i
$892$	−8.12886	+	5.90597i	−0.272174	+	0.197746i
$893$	6.08331			0.203570
$894$	−3.52995			−0.118059
$895$	3.87181	−	2.81303i	0.129420	−	0.0940293i
$896$	−9.43821	+	29.0478i	−0.315309	+	0.970420i
$897$	2.83570	+	8.72738i	0.0946812	+	0.291399i
$898$	−3.38940			−0.113106
$899$		0			0
$900$	13.8676			0.462255
$901$	22.7032	+	69.8734i	0.756354	+	2.32782i
$902$	−5.00910	+	15.4164i	−0.166785	+	0.513311i
$903$	−9.89194	+	7.18692i	−0.329183	+	0.239166i
$904$	−3.47395			−0.115542
$905$	7.72400			0.256754
$906$	−6.62814	+	4.81563i	−0.220205	+	0.159989i
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	0.923654	−	0.383227i	$-0.125187\pi$
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	−0.0790457	+	0.996871i	$0.525187\pi$
$908$	10.3858	+	7.54573i	0.344665	+	0.250414i
$909$	−1.35867	−	4.18156i	−0.0450643	−	0.138694i
$910$	−34.9770	+	25.4123i	−1.15948	+	0.842409i
$911$	2.59075	+	7.97351i	0.0858354	+	0.264174i	0.984757	−	0.173935i	$-0.0556483\pi$
$911$	2.59075	+	7.97351i	0.0858354	+	0.264174i	−0.898922	+	0.438109i	$0.855648\pi$
$912$	1.07009	−	3.29340i	0.0354342	−	0.109055i
$913$	−15.7366	−	11.4333i	−0.520804	−	0.378386i
$914$	−20.5567	+	63.2671i	−0.679956	+	2.09269i
$915$	−0.499465	+	1.53719i	−0.0165118	+	0.0508181i
$916$	−20.6728	−	15.0197i	−0.683050	−	0.496265i
$917$	−13.2571	+	40.8011i	−0.437787	+	1.34737i
$918$	−9.30503	−	28.6379i	−0.307112	−	0.945193i
$919$	32.4723	−	23.5925i	1.07116	−	0.778245i	0.0950416	−	0.995473i	$-0.469702\pi$
$919$	32.4723	−	23.5925i	1.07116	−	0.778245i	0.976121	+	0.217228i	$0.0697016\pi$
$920$	−1.41118	−	4.34316i	−0.0465251	−	0.143190i
$921$	−6.56123	−	4.76701i	−0.216200	−	0.157078i
$922$	−2.00088	−	1.45373i	−0.0658956	−	0.0478759i
$923$	37.7558	−	27.4312i	1.24275	−	0.902908i
$924$	−4.92554			−0.162039
$925$	−15.9502			−0.524440
$926$	−17.6128	+	12.7965i	−0.578793	+	0.420518i
$927$	−15.5616	+	47.8937i	−0.511110	+	1.57303i
$928$	2.87808	+	8.85781i	0.0944775	+	0.290772i
$929$	54.6187			1.79198			0.895991	−	0.444072i	$-0.146467\pi$
$929$	54.6187			1.79198			0.895991	+	0.444072i	$0.146467\pi$
$930$		0			0
$931$	−9.97677			−0.326975
$932$	6.00225	+	18.4730i	0.196610	+	0.605104i
$933$	−1.60262	+	4.93236i	−0.0524675	+	0.161478i
$934$	16.4636	−	11.9615i	0.538705	−	0.391392i
$935$	12.7035			0.415450
$936$	15.2173			0.497392
$937$	10.8326	−	7.87037i	0.353887	−	0.257114i	−0.396611	−	0.917987i	$-0.629814\pi$
$937$	10.8326	−	7.87037i	0.353887	−	0.257114i	0.750498	+	0.660873i	$0.229814\pi$
$938$	16.1096	+	11.7043i	0.525998	+	0.382160i
$939$	−12.9452	−	9.40524i	−0.422451	−	0.306928i
$940$	−2.24563	−	6.91135i	−0.0732445	−	0.225423i
$941$	31.0272	−	22.5426i	1.01146	−	0.734866i	0.0469426	−	0.998898i	$-0.485052\pi$
$941$	31.0272	−	22.5426i	1.01146	−	0.734866i	0.964514	+	0.264031i	$0.0850522\pi$
$942$	1.47808	+	4.54907i	0.0481586	+	0.148217i
$943$	5.16900	−	15.9086i	0.168326	−	0.518054i
$944$	−8.50840	−	6.18172i	−0.276925	−	0.201198i
$945$	−3.99952	+	12.3093i	−0.130104	+	0.400420i
$946$	6.96229	−	21.4277i	0.226363	−	0.696675i
$947$	−35.1821	−	25.5613i	−1.14327	−	0.830631i	−0.155695	−	0.987805i	$-0.549762\pi$
$947$	−35.1821	−	25.5613i	−1.14327	−	0.830631i	−0.987571	+	0.157174i	$0.949762\pi$
$948$	2.46673	−	7.59182i	0.0801157	−	0.246571i
$949$	6.73527	+	20.7290i	0.218636	+	0.672892i
$950$	7.62722	−	5.54150i	0.247460	−	0.179790i
$951$	3.90629	+	12.0223i	0.126670	+	0.389850i
$952$	18.2645	+	13.2699i	0.591956	+	0.430081i
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.972949	−	0.231018i	$-0.0742057\pi$
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.0809464	+	0.996718i	$0.474206\pi$
$954$	53.3738	−	38.7783i	1.72804	−	1.25549i
$955$	14.0363			0.454205
$956$	−14.0209			−0.453468
$957$	1.02946	−	0.747945i	0.0332776	−	0.0241776i
$958$	0.384073	−	1.18205i	0.0124088	−	0.0381904i
$959$	−18.2123	−	56.0517i	−0.588106	−	1.81001i
$960$	−1.75607			−0.0566768
$961$		0			0
$962$	43.1925			1.39258
$963$	−9.83894	−	30.2811i	−0.317055	−	0.975796i
$964$	−2.93347	+	9.02829i	−0.0944806	+	0.290781i
$965$	−13.2290	+	9.61143i	−0.425856	+	0.309403i
$966$	12.2252			0.393339
$967$	43.8720			1.41083			0.705414	−	0.708795i	$-0.250761\pi$
$967$	43.8720			1.41083			0.705414	+	0.708795i	$0.250761\pi$
$968$	6.52073	−	4.73759i	0.209584	−	0.152272i
$969$	−3.29353	−	2.39289i	−0.105803	−	0.0768707i
$970$	−14.9880	−	10.8894i	−0.481234	−	0.349637i
$971$	15.9201	+	48.9969i	0.510899	+	1.57239i	0.790621	+	0.612305i	$0.209758\pi$
$971$	15.9201	+	48.9969i	0.510899	+	1.57239i	−0.279722	+	0.960081i	$0.590242\pi$
$972$	−13.8397	+	10.0551i	−0.443908	+	0.322518i
$973$	−11.7762	−	36.2436i	−0.377529	−	1.16192i
$974$	14.0509	−	43.2443i	0.450221	−	1.38564i
$975$	−7.41914	−	5.39032i	−0.237603	−	0.172628i
$976$	3.99376	−	12.2915i	0.127837	−	0.393442i
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	−0.854510	−	0.519435i	$-0.826142\pi$
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	0.996629	+	0.0820365i	$0.0261424\pi$
$978$	0.413924	+	0.300734i	0.0132358	+	0.00961640i
$979$	1.54997	−	4.77031i	0.0495371	−	0.152460i
$980$	3.68289	+	11.3348i	0.117646	+	0.362076i
$981$	3.10052	−	2.25266i	0.0989921	−	0.0719220i
$982$	−4.93661	−	15.1933i	−0.157534	−	0.484838i
$983$	43.4233	+	31.5489i	1.38499	+	1.00625i	0.996394	+	0.0848433i	$0.0270390\pi$
$983$	43.4233	+	31.5489i	1.38499	+	1.00625i	0.388594	+	0.921409i	$0.372961\pi$
$984$	2.03434	+	1.47804i	0.0648525	+	0.0471181i
$985$	−22.8608	+	16.6093i	−0.728404	+	0.529217i
$986$	14.3931			0.458370
$987$	−7.88326			−0.250927
$988$	−8.58723	+	6.23898i	−0.273196	+	0.198489i
$989$	−7.18454	+	22.1117i	−0.228455	+	0.703112i
$990$	−3.52510	−	10.8491i	−0.112035	−	0.344808i
$991$	−35.5382			−1.12891			−0.564453	−	0.825465i	$-0.690913\pi$
$991$	−35.5382			−1.12891			−0.564453	+	0.825465i	$0.690913\pi$
$992$		0			0
$993$	−16.4364			−0.521594
$994$	−19.2126	−	59.1304i	−0.609388	−	1.87550i
$995$	2.46167	−	7.57624i	0.0780402	−	0.240183i
$996$	6.02430	−	4.37691i	0.190887	−	0.138688i
$997$	−30.5225			−0.966658			−0.483329	−	0.875439i	$-0.660573\pi$
$997$	−30.5225			−0.966658			−0.483329	+	0.875439i	$0.660573\pi$
$998$	−57.5347			−1.82123
$999$	10.4609	−	7.60025i	0.330967	−	0.240461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.o.531.2		16
31.2	even	5		961.2.d.p.388.3		16
31.3	odd	30		961.2.c.i.439.2		16
31.4	even	5		961.2.d.p.374.3		16
31.5	even	3		31.2.g.a.7.1	✓	16
31.6	odd	6		961.2.g.j.547.1		16
31.7	even	15		961.2.g.s.816.2		16
31.8	even	5	inner	961.2.d.o.628.2		16
31.9	even	15		961.2.g.k.448.1		16
31.10	even	15		961.2.g.s.338.2		16
31.11	odd	30		961.2.g.n.732.2		16
31.12	odd	30		961.2.g.n.235.2		16
31.13	odd	30		961.2.c.i.521.2		16
31.14	even	15		31.2.g.a.9.1	yes	16
31.15	odd	10		961.2.a.j.1.2		8
31.16	even	5		961.2.a.i.1.2		8
31.17	odd	30		961.2.g.l.846.1		16
31.18	even	15		961.2.c.j.521.2		16
31.19	even	15		961.2.g.t.235.2		16
31.20	even	15		961.2.g.t.732.2		16
31.21	odd	30		961.2.g.m.338.2		16
31.22	odd	30		961.2.g.j.448.1		16
31.23	odd	10		961.2.d.n.628.2		16
31.24	odd	30		961.2.g.m.816.2		16
31.25	even	3		961.2.g.k.547.1		16
31.26	odd	6		961.2.g.l.844.1		16
31.27	odd	10		961.2.d.q.374.3		16
31.28	even	15		961.2.c.j.439.2		16
31.29	odd	10		961.2.d.q.388.3		16
31.30	odd	2		961.2.d.n.531.2		16
93.5	odd	6		279.2.y.c.100.2		16
93.14	odd	30		279.2.y.c.226.2		16
93.47	odd	10		8649.2.a.bf.1.7		8
93.77	even	10		8649.2.a.be.1.7		8
124.67	odd	6		496.2.bg.c.193.1		16
124.107	odd	30		496.2.bg.c.257.1		16
155.14	even	30		775.2.bl.a.226.2		16
155.67	odd	12		775.2.ck.a.224.4		32
155.98	odd	12		775.2.ck.a.224.1		32
155.107	odd	60		775.2.ck.a.474.1		32
155.129	even	6		775.2.bl.a.751.2		16
155.138	odd	60		775.2.ck.a.474.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.1	✓	16	31.5	even	3
31.2.g.a.9.1	yes	16	31.14	even	15
279.2.y.c.100.2		16	93.5	odd	6
279.2.y.c.226.2		16	93.14	odd	30
496.2.bg.c.193.1		16	124.67	odd	6
496.2.bg.c.257.1		16	124.107	odd	30
775.2.bl.a.226.2		16	155.14	even	30
775.2.bl.a.751.2		16	155.129	even	6
775.2.ck.a.224.1		32	155.98	odd	12
775.2.ck.a.224.4		32	155.67	odd	12
775.2.ck.a.474.1		32	155.107	odd	60
775.2.ck.a.474.4		32	155.138	odd	60
961.2.a.i.1.2		8	31.16	even	5
961.2.a.j.1.2		8	31.15	odd	10
961.2.c.i.439.2		16	31.3	odd	30
961.2.c.i.521.2		16	31.13	odd	30
961.2.c.j.439.2		16	31.28	even	15
961.2.c.j.521.2		16	31.18	even	15
961.2.d.n.531.2		16	31.30	odd	2
961.2.d.n.628.2		16	31.23	odd	10
961.2.d.o.531.2		16	1.1	even	1	trivial
961.2.d.o.628.2		16	31.8	even	5	inner
961.2.d.p.374.3		16	31.4	even	5
961.2.d.p.388.3		16	31.2	even	5
961.2.d.q.374.3		16	31.27	odd	10
961.2.d.q.388.3		16	31.29	odd	10
961.2.g.j.448.1		16	31.22	odd	30
961.2.g.j.547.1		16	31.6	odd	6
961.2.g.k.448.1		16	31.9	even	15
961.2.g.k.547.1		16	31.25	even	3
961.2.g.l.844.1		16	31.26	odd	6
961.2.g.l.846.1		16	31.17	odd	30
961.2.g.m.338.2		16	31.21	odd	30
961.2.g.m.816.2		16	31.24	odd	30
961.2.g.n.235.2		16	31.12	odd	30
961.2.g.n.732.2		16	31.11	odd	30
961.2.g.s.338.2		16	31.10	even	15
961.2.g.s.816.2		16	31.7	even	15
961.2.g.t.235.2		16	31.19	even	15
961.2.g.t.732.2		16	31.20	even	15
8649.2.a.be.1.7		8	93.77	even	10
8649.2.a.bf.1.7		8	93.47	odd	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.571745 - 1.75965i) q^{2} +(0.154309 - 0.474914i) q^{3} +(-1.15144 + 0.836573i) q^{4} +1.20736 q^{5} -0.923909 q^{6} +(-3.02009 + 2.19423i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(2.22532 + 1.61679i) q^{9} +(-0.690303 - 2.12453i) q^{10} +(1.50195 - 1.09123i) q^{11} +(0.219622 + 0.675928i) q^{12} +(-1.60209 + 4.93072i) q^{13} +(5.58780 + 4.05977i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(4.58508 + 3.33126i) q^{17} +(1.57267 - 4.84017i) q^{18} +(-0.444517 - 1.36808i) q^{19} +(-1.39021 + 1.01005i) q^{20} +(0.576042 + 1.77288i) q^{21} +(-2.77891 - 2.01900i) q^{22} +(2.86762 + 2.08345i) q^{23} +(-0.431086 + 0.313203i) q^{24} -3.54228 q^{25} +9.59234 q^{26} +(2.32318 - 1.68789i) q^{27} +(1.64184 - 5.05306i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(3.24035 - 9.97278i) q^{34} +(-3.64635 + 2.64923i) q^{35} -3.91489 q^{36} +4.50281 q^{37} +(-2.15320 + 1.56439i) q^{38} +(2.09445 + 1.52171i) q^{39} +(-1.04230 - 0.757275i) q^{40} +(-1.45829 - 4.48814i) q^{41} +(2.79029 - 2.02727i) q^{42} +(2.02691 + 6.23819i) q^{43} +(-0.816516 + 2.51298i) q^{44} +(2.68676 + 1.95205i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(1.94756 + 1.41498i) q^{48} +(2.14322 - 6.59615i) q^{49} +(2.02528 + 6.23317i) q^{50} +(2.28958 - 1.66348i) q^{51} +(-2.28019 - 7.01772i) q^{52} +(10.4875 + 7.61964i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(1.81339 - 1.31751i) q^{55} +3.98346 q^{56} -0.718314 q^{57} +(2.05458 - 1.49274i) q^{58} +(-0.674139 + 2.07479i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(-1.93430 + 5.95317i) q^{65} +(-1.38766 + 1.00820i) q^{66} +2.88300 q^{67} -8.06631 q^{68} +(1.43196 - 1.04038i) q^{69} +(6.74649 + 4.90161i) q^{70} +(-7.28247 - 5.29103i) q^{71} +(-0.907016 - 2.79151i) q^{72} +(3.40115 - 2.47108i) q^{73} +(-2.57446 - 7.92338i) q^{74} +(-0.546605 + 1.68228i) q^{75} +(1.65634 + 1.20340i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(-9.08664 - 6.60183i) q^{79} +(-1.79864 + 5.53563i) q^{80} +(2.10687 + 6.48429i) q^{81} +(-7.06379 + 5.13215i) q^{82} +(-3.23771 - 9.96463i) q^{83} +(-2.14642 - 1.55947i) q^{84} +(5.53585 + 4.02203i) q^{85} +(9.81816 - 7.13331i) q^{86} +0.685415 q^{87} -1.98105 q^{88} +(2.18575 - 1.58804i) q^{89} +(1.89878 - 5.84384i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(1.04705 - 3.22248i) q^{96} +(6.70942 - 4.87468i) q^{97} -12.8323 q^{98} +5.10660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

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