LMFDB - Embedded newform 1183.2.e.i.508.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 $ x^16 + 11x^14 + 85x^12 + 334x^10 + 952x^8 + 1050x^6 + 853x^4 + 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.8
Root			$1.14241 - 1.97871i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.i.170.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14241 + 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(1.06250 + 1.84030i) q^{5} -7.19813 q^{6} +(-0.331665 + 2.62488i) q^{7} -2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +O(q^{10})$	\(q+(1.14241 + 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(1.06250 + 1.84030i) q^{5} -7.19813 q^{6} +(-0.331665 + 2.62488i) q^{7} -2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +(-2.42760 + 4.20473i) q^{10} +(0.154233 - 0.267139i) q^{11} +(-5.07276 - 8.78629i) q^{12} +(-5.57276 + 2.34241i) q^{14} -6.69462 q^{15} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(7.91135 - 13.7029i) q^{18} +(0.890653 + 1.54266i) q^{19} -6.84326 q^{20} +(-6.63914 - 5.03964i) q^{21} +0.704786 q^{22} +(-0.575211 - 0.996294i) q^{23} +(4.39219 - 7.60750i) q^{24} +(0.242207 - 0.419515i) q^{25} +12.3659 q^{27} +(-6.78655 - 5.15153i) q^{28} +2.01052 q^{29} +(-7.64798 - 13.2467i) q^{30} +(-2.30242 + 3.98791i) q^{31} +(-2.86823 + 4.96792i) q^{32} +(0.485898 + 0.841600i) q^{33} +4.05494 q^{34} +(-5.18295 + 2.17856i) q^{35} +22.3016 q^{36} +(-2.77071 - 4.79901i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(-2.96258 - 5.13134i) q^{40} +6.72984 q^{41} +(2.38737 - 18.8942i) q^{42} +1.52611 q^{43} +(0.496686 + 0.860286i) q^{44} +(7.35795 - 12.7443i) q^{45} +(1.31425 - 2.27635i) q^{46} +(4.75908 + 8.24297i) q^{47} -0.220372 q^{48} +(-6.78000 - 1.74116i) q^{49} +1.10680 q^{50} +(2.79558 + 4.84209i) q^{51} +(-3.72037 + 6.44387i) q^{53} +(14.1269 + 24.4685i) q^{54} +0.655486 q^{55} +(0.924789 - 7.31901i) q^{56} -5.61186 q^{57} +(2.29683 + 3.97823i) q^{58} +(-4.06053 + 7.03304i) q^{59} +(10.7796 - 18.6708i) q^{60} +(1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +(16.8908 - 7.09974i) q^{63} -12.9669 q^{64} +(-1.11019 + 1.92290i) q^{66} +(6.30747 - 10.9249i) q^{67} +(2.85765 + 4.94960i) q^{68} +3.62431 q^{69} +(-10.2318 - 7.76673i) q^{70} +1.35070 q^{71} +(9.65478 + 16.7226i) q^{72} +(5.94059 - 10.2894i) q^{73} +(6.33056 - 10.9648i) q^{74} +(0.763054 + 1.32165i) q^{75} -5.73646 q^{76} +(0.650054 + 0.493443i) q^{77} +(3.96258 + 6.86339i) q^{79} +(-0.0743214 + 0.128728i) q^{80} +(-9.09116 + 15.7464i) q^{81} +(7.68821 + 13.3164i) q^{82} +11.2290 q^{83} +(24.7454 - 10.4013i) q^{84} +3.77130 q^{85} +(1.74344 + 3.01972i) q^{86} +(-3.16700 + 5.48540i) q^{87} +(-0.430050 + 0.744869i) q^{88} +(-0.829583 - 1.43688i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(-7.25360 - 12.5636i) q^{93} +(-10.8736 + 18.8336i) q^{94} +(-1.89263 + 3.27813i) q^{95} +(-9.03614 - 15.6511i) q^{96} +7.66641 q^{97} +(-4.30026 - 15.4047i) q^{98} -2.13617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	$ 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.14241	+	1.97871i	0.807803	+	1.39916i	0.914382	+	0.404852i	$0.132677\pi$
$2$	1.14241	+	1.97871i	0.807803	+	1.39916i	−0.106579	+	0.994304i	$0.533990\pi$
$3$	−1.57521	+	2.72835i	−0.909448	+	1.57521i	−0.0946163	+	0.995514i	$0.530162\pi$
$3$	−1.57521	+	2.72835i	−0.909448	+	1.57521i	−0.814832	+	0.579697i	$0.803171\pi$
$4$	−1.61019	+	2.78892i	−0.805093	+	1.39446i
$5$	1.06250	+	1.84030i	0.475162	+	0.823005i	0.999595	−	0.0284464i	$-0.00905598\pi$
$5$	1.06250	+	1.84030i	0.475162	+	0.823005i	−0.524433	+	0.851452i	$0.675723\pi$
$6$	−7.19813			−2.93862
$7$	−0.331665	+	2.62488i	−0.125358	+	0.992112i
$7$	−0.331665	+	2.62488i	−0.125358	+	0.992112i
$8$	−2.78832			−0.985820
$9$	−3.46258	−	5.99736i	−1.15419	−	1.99912i
$10$	−2.42760	+	4.20473i	−0.767676	+	1.32965i
$11$	0.154233	−	0.267139i	0.0465029	−	0.0805454i	−0.841837	−	0.539732i	$-0.818526\pi$
$11$	0.154233	−	0.267139i	0.0465029	−	0.0805454i	0.888340	+	0.459186i	$0.151859\pi$
$12$	−5.07276	−	8.78629i	−1.46438	−	2.53638i
$13$		0			0
$13$		0			0
$14$	−5.57276	+	2.34241i	−1.48938	+	0.626036i
$15$	−6.69462			−1.72854
$16$	0.0349749	+	0.0605784i	0.00874373	+	0.0151446i
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	−0.738122	−	0.674667i	$-0.764287\pi$
$17$	0.887368	−	1.53697i	0.215218	−	0.372769i	0.953340	+	0.301898i	$0.0976204\pi$
$18$	7.91135	−	13.7029i	1.86472	−	3.22979i
$19$	0.890653	+	1.54266i	0.204330	+	0.353909i	0.949919	−	0.312496i	$-0.101165\pi$
$19$	0.890653	+	1.54266i	0.204330	+	0.353909i	−0.745589	+	0.666406i	$0.767832\pi$
$20$	−6.84326			−1.53020
$21$	−6.63914	−	5.03964i	−1.44878	−	1.09974i
$22$	0.704786			0.150261
$23$	−0.575211	−	0.996294i	−0.119940	−	0.207742i	0.799804	−	0.600261i	$-0.204937\pi$
$23$	−0.575211	−	0.996294i	−0.119940	−	0.207742i	−0.919744	+	0.392520i	$0.871603\pi$
$24$	4.39219	−	7.60750i	0.896553	−	1.55288i
$25$	0.242207	−	0.419515i	0.0484414	−	0.0839029i
$26$		0			0
$27$	12.3659			2.37982
$28$	−6.78655	−	5.15153i	−1.28254	−	0.973548i
$29$	2.01052			0.373345			0.186672	−	0.982422i	$-0.440230\pi$
$29$	2.01052			0.373345			0.186672	+	0.982422i	$0.440230\pi$
$30$	−7.64798	−	13.2467i	−1.39632	−	2.41850i
$31$	−2.30242	+	3.98791i	−0.413527	+	0.716251i	−0.995273	−	0.0971205i	$-0.969037\pi$
$31$	−2.30242	+	3.98791i	−0.413527	+	0.716251i	0.581745	+	0.813371i	$0.302370\pi$
$32$	−2.86823	+	4.96792i	−0.507037	+	0.878213i
$33$	0.485898	+	0.841600i	0.0845840	+	0.146504i
$34$	4.05494			0.695416
$35$	−5.18295	+	2.17856i	−0.876078	+	0.368244i
$36$	22.3016			3.71693
$37$	−2.77071	−	4.79901i	−0.455502	−	0.788953i	0.543215	−	0.839594i	$-0.317207\pi$
$37$	−2.77071	−	4.79901i	−0.455502	−	0.788953i	−0.998717	+	0.0506410i	$0.983874\pi$
$38$	−2.03497	+	3.52468i	−0.330117	+	0.571779i
$39$		0			0
$40$	−2.96258	−	5.13134i	−0.468425	−	0.811336i
$41$	6.72984			1.05102			0.525512	−	0.850786i	$-0.323874\pi$
$41$	6.72984			1.05102			0.525512	+	0.850786i	$0.323874\pi$
$42$	2.38737	−	18.8942i	0.368379	−	2.91544i
$43$	1.52611			0.232729			0.116365	−	0.993207i	$-0.462876\pi$
$43$	1.52611			0.232729			0.116365	+	0.993207i	$0.462876\pi$
$44$	0.496686	+	0.860286i	0.0748783	+	0.129693i
$45$	7.35795	−	12.7443i	1.09686	−	1.89981i
$46$	1.31425	−	2.27635i	0.193776	−	0.335629i
$47$	4.75908	+	8.24297i	0.694183	+	1.20236i	0.970455	+	0.241281i	$0.0775675\pi$
$47$	4.75908	+	8.24297i	0.694183	+	1.20236i	−0.276272	+	0.961079i	$0.589099\pi$
$48$	−0.220372			−0.0318079
$49$	−6.78000	−	1.74116i	−0.968571	−	0.248738i
$50$	1.10680			0.156524
$51$	2.79558	+	4.84209i	0.391460	+	0.678028i
$52$		0			0
$53$	−3.72037	+	6.44387i	−0.511032	+	0.885134i	0.488886	+	0.872348i	$0.337403\pi$
$53$	−3.72037	+	6.44387i	−0.511032	+	0.885134i	−0.999918	+	0.0127862i	$0.995930\pi$
$54$	14.1269	+	24.4685i	1.92243	+	3.32974i
$55$	0.655486			0.0883857
$56$	0.924789	−	7.31901i	0.123580	−	0.978044i
$57$	−5.61186			−0.743309
$58$	2.29683	+	3.97823i	0.301589	+	0.522368i
$59$	−4.06053	+	7.03304i	−0.528636	+	0.915624i	0.470807	+	0.882236i	$0.343963\pi$
$59$	−4.06053	+	7.03304i	−0.528636	+	0.915624i	−0.999442	+	0.0333877i	$0.989370\pi$
$60$	10.7796	−	18.6708i	1.39164	−	2.41039i
$61$	1.72037	+	2.97977i	0.220271	+	0.381521i	0.954890	−	0.296959i	$-0.0959725\pi$
$61$	1.72037	+	2.97977i	0.220271	+	0.381521i	−0.734619	+	0.678480i	$0.762639\pi$
$62$	−10.5212			−1.33620
$63$	16.8908	−	7.09974i	2.12804	−	0.894483i
$64$	−12.9669			−1.62086
$65$		0			0
$66$	−1.11019	+	1.92290i	−0.136654	+	0.236692i
$67$	6.30747	−	10.9249i	0.770580	−	1.33468i	−0.166665	−	0.986014i	$-0.553300\pi$
$67$	6.30747	−	10.9249i	0.770580	−	1.33468i	0.937245	−	0.348671i	$-0.113367\pi$
$68$	2.85765	+	4.94960i	0.346541	+	0.600227i
$69$	3.62431			0.436316
$70$	−10.2318	−	7.76673i	−1.22293	−	0.928302i
$71$	1.35070			0.160299			0.0801494	−	0.996783i	$-0.474460\pi$
$71$	1.35070			0.160299			0.0801494	+	0.996783i	$0.474460\pi$
$72$	9.65478	+	16.7226i	1.13783	+	1.97077i
$73$	5.94059	−	10.2894i	0.695293	−	1.20428i	−0.274789	−	0.961505i	$-0.588608\pi$
$73$	5.94059	−	10.2894i	0.695293	−	1.20428i	0.970082	−	0.242778i	$-0.0780588\pi$
$74$	6.33056	−	10.9648i	0.735912	−	1.27464i
$75$	0.763054	+	1.32165i	0.0881099	+	0.152611i
$76$	−5.73646			−0.658018
$77$	0.650054	+	0.493443i	0.0740805	+	0.0562330i
$78$		0			0
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	0.998109	−	0.0614644i	$-0.0195771\pi$
$79$	3.96258	+	6.86339i	0.445825	+	0.772191i	−0.552284	+	0.833656i	$0.686244\pi$
$80$	−0.0743214	+	0.128728i	−0.00830939	+	0.0143923i
$81$	−9.09116	+	15.7464i	−1.01013	+	1.74960i
$82$	7.68821	+	13.3164i	0.849021	+	1.47055i
$83$	11.2290			1.23255			0.616273	−	0.787533i	$-0.288642\pi$
$83$	11.2290			1.23255			0.616273	+	0.787533i	$0.288642\pi$
$84$	24.7454	−	10.4013i	2.69995	−	1.13487i
$85$	3.77130			0.409055
$86$	1.74344	+	3.01972i	0.188000	+	0.325625i
$87$	−3.16700	+	5.48540i	−0.339538	+	0.588096i
$88$	−0.430050	+	0.744869i	−0.0458435	+	0.0794033i
$89$	−0.829583	−	1.43688i	−0.0879357	−	0.152309i	0.818703	−	0.574218i	$-0.194694\pi$
$89$	−0.829583	−	1.43688i	−0.0879357	−	0.152309i	−0.906638	+	0.421909i	$0.861360\pi$
$90$	33.6231			3.54418
$91$		0			0
$92$	3.70479			0.386251
$93$	−7.25360	−	12.5636i	−0.752164	−	1.30279i
$94$	−10.8736	+	18.8336i	−1.12153	+	1.94254i
$95$	−1.89263	+	3.27813i	−0.194180	+	0.336329i
$96$	−9.03614	−	15.6511i	−0.922247	−	1.59738i
$97$	7.66641			0.778406			0.389203	−	0.921152i	$-0.372750\pi$
$97$	7.66641			0.778406			0.389203	+	0.921152i	$0.372750\pi$
$98$	−4.30026	−	15.4047i	−0.434392	−	1.55611i
$99$	−2.13617			−0.214693
$100$	0.779996	+	1.35099i	0.0779996	+	0.135099i
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	−0.998607	−	0.0527721i	$-0.983194\pi$
$101$	−4.55864	+	7.89579i	−0.453601	+	0.785660i	0.545005	+	0.838433i	$0.316528\pi$
$102$	−6.38738	+	11.0633i	−0.632445	+	1.09543i
$103$	−3.02085	−	5.23226i	−0.297653	−	0.515550i	0.677946	−	0.735112i	$-0.262870\pi$
$103$	−3.02085	−	5.23226i	−0.297653	−	0.515550i	−0.975599	+	0.219562i	$0.929537\pi$
$104$		0			0
$105$	2.22037	−	17.5726i	0.216686	−	1.71491i
$106$	−17.0007			−1.65125
$107$	−6.04305	−	10.4669i	−0.584204	−	1.01187i	−0.994974	−	0.100132i	$-0.968074\pi$
$107$	−6.04305	−	10.4669i	−0.584204	−	1.01187i	0.410770	−	0.911739i	$-0.365260\pi$
$108$	−19.9114	+	34.4876i	−1.91598	+	3.31857i
$109$	0.680941	−	1.17942i	0.0652223	−	0.112968i	−0.831570	−	0.555420i	$-0.812558\pi$
$109$	0.680941	−	1.17942i	0.0652223	−	0.112968i	0.896793	+	0.442451i	$0.145891\pi$
$110$	0.748831	+	1.29701i	0.0713983	+	0.123665i
$111$	17.4578			1.65702
$112$	−0.170611	+	0.0717133i	−0.0161212	+	0.00677627i
$113$	−9.42009			−0.886168			−0.443084	−	0.896480i	$-0.646116\pi$
$113$	−9.42009			−0.886168			−0.443084	+	0.896480i	$0.646116\pi$
$114$	−6.41103	−	11.1042i	−0.600448	−	1.04001i
$115$	1.22232	−	2.11712i	0.113982	−	0.197422i
$116$	−3.23731	+	5.60719i	−0.300577	+	0.520615i
$117$		0			0
$118$	−18.5551			−1.70814
$119$	3.74004	+	2.83899i	0.342849	+	0.260250i
$120$	18.6667			1.70403
$121$	5.45242	+	9.44388i	0.495675	+	0.858534i
$122$	−3.93073	+	6.80822i	−0.355871	+	0.616387i
$123$	−10.6009	+	18.3613i	−0.955852	+	1.65558i
$124$	−7.41466	−	12.8426i	−0.665856	−	1.15330i
$125$	11.6543			1.04239
$126$	33.3444	+	25.3111i	2.97056	+	2.25489i
$127$	−13.3998			−1.18904			−0.594519	−	0.804081i	$-0.702658\pi$
$127$	−13.3998			−1.18904			−0.594519	+	0.804081i	$0.702658\pi$
$128$	−9.07695	−	15.7217i	−0.802297	−	1.38962i
$129$	−2.40394	+	4.16375i	−0.211655	+	0.366598i
$130$		0			0
$131$	−6.69854	−	11.6022i	−0.585254	−	1.01369i	−0.994844	−	0.101420i	$-0.967662\pi$
$131$	−6.69854	−	11.6022i	−0.585254	−	1.01369i	0.409590	−	0.912270i	$-0.365672\pi$
$132$	−3.12954			−0.272392
$133$	−4.34469	+	1.82621i	−0.376732	+	0.158353i
$134$	28.8228			2.48991
$135$	13.1387	+	22.7569i	1.13080	+	1.95860i
$136$	−2.47427	+	4.28555i	−0.212167	+	0.367483i
$137$	0.250522	−	0.433917i	0.0214036	−	0.0370720i	−0.855125	−	0.518421i	$-0.826520\pi$
$137$	0.250522	−	0.433917i	0.0214036	−	0.0370720i	0.876529	+	0.481349i	$0.159853\pi$
$138$	4.14044	+	7.17145i	0.352458	+	0.610475i
$139$	1.41936			0.120388			0.0601941	−	0.998187i	$-0.480828\pi$
$139$	1.41936			0.120388			0.0601941	+	0.998187i	$0.480828\pi$
$140$	2.26967	−	17.9627i	0.191822	−	1.51813i
$141$	−29.9862			−2.52529
$142$	1.54305	+	2.67264i	0.129490	+	0.224283i
$143$		0			0
$144$	0.242207	−	0.419515i	0.0201839	−	0.0349596i
$145$	2.13617	+	3.69996i	0.177399	+	0.307265i
$146$	27.1463			2.24664
$147$	15.4304	−	15.7555i	1.27268	−	1.29949i
$148$	17.8454			1.46689
$149$	−10.5454	−	18.2652i	−0.863916	−	1.49635i	−0.868120	−	0.496355i	$-0.834672\pi$
$149$	−10.5454	−	18.2652i	−0.863916	−	1.49635i	0.00420426	−	0.999991i	$-0.498662\pi$
$150$	−1.74344	+	3.01972i	−0.142351	+	0.246559i
$151$	−8.75211	+	15.1591i	−0.712236	+	1.23363i	0.251779	+	0.967785i	$0.418984\pi$
$151$	−8.75211	+	15.1591i	−0.712236	+	1.23363i	−0.964016	+	0.265845i	$0.914349\pi$
$152$	−2.48343	−	4.30142i	−0.201432	−	0.348891i
$153$	−12.2903			−0.993614
$154$	−0.233753	+	1.84998i	−0.0188363	+	0.149075i
$155$	−9.78526			−0.785971
$156$		0			0
$157$	−0.0377894	+	0.0654532i	−0.00301593	+	0.00522374i	−0.867529	−	0.497386i	$-0.834293\pi$
$157$	−0.0377894	+	0.0654532i	−0.00301593	+	0.00522374i	0.864514	+	0.502610i	$0.167627\pi$
$158$	−9.05375	+	15.6816i	−0.720278	+	1.24756i
$159$	−11.7207	−	20.3009i	−0.929515	−	1.60997i
$160$	−12.1899			−0.963699
$161$	2.80593	−	1.17942i	0.221138	−	0.0929516i
$162$	−41.5432			−3.26394
$163$	−5.04086	−	8.73102i	−0.394830	−	0.683866i	0.598249	−	0.801310i	$-0.295863\pi$
$163$	−5.04086	−	8.73102i	−0.394830	−	0.683866i	−0.993080	+	0.117444i	$0.962530\pi$
$164$	−10.8363	+	18.7690i	−0.846172	+	1.46561i
$165$	−1.03253	+	1.78839i	−0.0803822	+	0.139226i
$166$	12.8281	+	22.2189i	0.995655	+	1.72452i
$167$	5.84989			0.452678			0.226339	−	0.974049i	$-0.427324\pi$
$167$	5.84989			0.452678			0.226339	+	0.974049i	$0.427324\pi$
$168$	18.5120	+	14.0521i	1.42824	+	1.08415i
$169$		0			0
$170$	4.30835	+	7.46229i	0.330436	+	0.572331i
$171$	6.16791	−	10.6831i	0.471672	−	0.816960i
$172$	−2.45732	+	4.25620i	−0.187369	+	0.324532i
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	−0.984100	−	0.177617i	$-0.943161\pi$
$173$	−8.49511	−	14.7140i	−0.645871	−	1.11868i	0.338229	−	0.941064i	$-0.390172\pi$
$174$	−14.4720			−1.09712
$175$	1.02084	+	0.774903i	0.0771686	+	0.0585771i
$176$	0.0215771			0.00162644
$177$	−12.7924	−	22.1570i	−0.961534	−	1.66543i
$178$	1.89544	−	3.28300i	0.142069	−	0.246072i
$179$	7.65079	−	13.2516i	0.571847	−	0.990468i	−0.424529	−	0.905414i	$-0.639560\pi$
$179$	7.65079	−	13.2516i	0.571847	−	0.990468i	0.996376	−	0.0850537i	$-0.0271062\pi$
$180$	23.6953	+	41.0415i	1.76615	+	3.05905i
$181$	5.84958			0.434796			0.217398	−	0.976083i	$-0.430243\pi$
$181$	5.84958			0.434796			0.217398	+	0.976083i	$0.430243\pi$
$182$		0			0
$183$	−10.8398			−0.801301
$184$	1.60387	+	2.77799i	0.118239	+	0.204796i
$185$	5.88774	−	10.1979i	0.432875	−	0.749761i
$186$	16.5731	−	28.7055i	1.21520	−	2.10479i
$187$	−0.273722	−	0.474101i	−0.0200165	−	0.0346697i
$188$	−30.6520			−2.23553
$189$	−4.10134	+	32.4590i	−0.298329	+	2.36105i
$190$	−8.64861			−0.627436
$191$	13.4090	+	23.2250i	0.970238	+	1.68050i	0.694831	+	0.719173i	$0.255479\pi$
$191$	13.4090	+	23.2250i	0.970238	+	1.68050i	0.275407	+	0.961328i	$0.411188\pi$
$192$	20.4255	−	35.3780i	1.47409	−	2.55319i
$193$	−0.106992	+	0.185315i	−0.00770145	+	0.0133393i	−0.869850	−	0.493316i	$-0.835785\pi$
$193$	−0.106992	+	0.185315i	−0.00770145	+	0.0133393i	0.862149	+	0.506655i	$0.169118\pi$
$194$	8.75816	+	15.1696i	0.628799	+	1.08911i
$195$		0			0
$196$	15.7730	−	16.1053i	1.12664	−	1.15038i
$197$	−11.2290			−0.800035			−0.400017	−	0.916508i	$-0.630996\pi$
$197$	−11.2290			−0.800035			−0.400017	+	0.916508i	$0.630996\pi$
$198$	−2.44038	−	4.22685i	−0.173430	−	0.300389i
$199$	−10.2100	+	17.6843i	−0.723771	+	1.25361i	0.235707	+	0.971824i	$0.424259\pi$
$199$	−10.2100	+	17.6843i	−0.723771	+	1.25361i	−0.959478	+	0.281784i	$0.909074\pi$
$200$	−0.675351	+	1.16974i	−0.0477545	+	0.0827132i
$201$	19.8712	+	34.4179i	1.40161	+	2.42765i
$202$	−20.8313			−1.46568
$203$	−0.666820	+	5.27738i	−0.0468016	+	0.370399i
$204$	−18.0056			−1.26065
$205$	7.15042	+	12.3849i	0.499407	+	0.864999i
$206$	6.90207	−	11.9547i	0.480890	−	0.832926i
$207$	−3.98343	+	6.89950i	−0.276867	+	0.479548i
$208$		0			0
$209$	0.549471			0.0380077
$210$	37.3075	−	15.6816i	2.57446	−	1.08213i
$211$	8.41738			0.579476			0.289738	−	0.957106i	$-0.406432\pi$
$211$	8.41738			0.579476			0.289738	+	0.957106i	$0.406432\pi$
$212$	−11.9810	−	20.7517i	−0.822857	−	1.42523i
$213$	−2.12764	+	3.68518i	−0.145783	+	0.252504i
$214$	13.8072	−	23.9148i	0.943844	−	1.63479i
$215$	1.62148	+	2.80849i	0.110584	+	0.191537i
$216$	−34.4801			−2.34607
$217$	−9.70417	−	7.36624i	−0.658762	−	0.500053i
$218$	3.11164			0.210747
$219$	18.7154	+	32.4159i	1.26467	+	2.19047i
$220$	−1.05545	+	1.82810i	−0.0711587	+	0.123250i
$221$		0			0
$222$	19.9439	+	34.5439i	1.33855	+	2.31843i
$223$	−13.6091			−0.911333			−0.455666	−	0.890151i	$-0.650599\pi$
$223$	−13.6091			−0.911333			−0.455666	+	0.890151i	$0.650599\pi$
$224$	−12.0889	−	9.17646i	−0.807725	−	0.613128i
$225$	−3.35464			−0.223643
$226$	−10.7616	−	18.6396i	−0.715849	−	1.23989i
$227$	−1.80138	+	3.12008i	−0.119562	+	0.207087i	−0.919594	−	0.392870i	$-0.871482\pi$
$227$	−1.80138	+	3.12008i	−0.119562	+	0.207087i	0.800032	+	0.599957i	$0.204816\pi$
$228$	9.03614	−	15.6511i	0.598433	−	1.03652i
$229$	−9.19208	−	15.9212i	−0.607430	−	1.05210i	−0.991662	−	0.128863i	$-0.958867\pi$
$229$	−9.19208	−	15.9212i	−0.607430	−	1.05210i	0.384232	−	0.923236i	$-0.374466\pi$
$230$	5.58554			0.368299
$231$	−2.37025	+	0.996294i	−0.155951	+	0.0655514i
$232$	−5.60598			−0.368051
$233$	−10.1348	−	17.5541i	−0.663955	−	1.15000i	−0.979567	−	0.201116i	$-0.935543\pi$
$233$	−10.1348	−	17.5541i	−0.663955	−	1.15000i	0.315612	−	0.948888i	$-0.397790\pi$
$234$		0			0
$235$	−10.1130	+	17.5162i	−0.659699	+	1.14263i
$236$	−13.0764	−	22.6490i	−0.851202	−	1.47432i
$237$	−24.9676			−1.62182
$238$	−1.34488	+	10.6437i	−0.0871758	+	0.689931i
$239$	20.8097			1.34607			0.673033	−	0.739612i	$-0.264991\pi$
$239$	20.8097			1.34607			0.673033	+	0.739612i	$0.264991\pi$
$240$	−0.234144	−	0.405549i	−0.0151139	−	0.0261781i
$241$	6.35736	−	11.0113i	0.409514	−	0.709299i	−0.585322	−	0.810801i	$-0.699032\pi$
$241$	6.35736	−	11.0113i	0.409514	−	0.709299i	0.994835	+	0.101503i	$0.0323651\pi$
$242$	−12.4578	+	21.5775i	−0.800816	+	1.38705i
$243$	−10.0922	−	17.4801i	−0.647412	−	1.12135i
$244$	−11.0805			−0.709355
$245$	−3.99946	−	14.3272i	−0.255516	−	0.915330i
$246$	−48.4422			−3.08856
$247$		0			0
$248$	6.41990	−	11.1196i	0.407664	−	0.706094i
$249$	−17.6881	+	30.6367i	−1.12094	+	1.94152i
$250$	13.3140	+	23.0605i	0.842050	+	1.45847i
$251$	13.7436			0.867486			0.433743	−	0.901037i	$-0.357193\pi$
$251$	13.7436			0.867486			0.433743	+	0.901037i	$0.357193\pi$
$252$	−7.39666	+	58.5390i	−0.465946	+	3.68761i
$253$	−0.354865			−0.0223102
$254$	−15.3080	−	26.5142i	−0.960510	−	1.66365i
$255$	−5.94059	+	10.2894i	−0.372014	+	0.644347i
$256$	7.77229	−	13.4620i	0.485768	−	0.841375i
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	0.957442	−	0.288626i	$-0.0931983\pi$
$257$	3.66736	+	6.35206i	0.228764	+	0.396231i	−0.728678	+	0.684856i	$0.759865\pi$
$258$	−10.9851			−0.683904
$259$	13.5158	−	5.68112i	0.839830	−	0.353008i
$260$		0			0
$261$	−6.96159	−	12.0578i	−0.430912	−	0.746361i
$262$	15.3049	−	26.5089i	0.945540	−	1.63772i
$263$	3.33942	−	5.78405i	0.205918	−	0.356660i	−0.744507	−	0.667615i	$-0.767315\pi$
$263$	3.33942	−	5.78405i	0.205918	−	0.356660i	0.950425	+	0.310955i	$0.100649\pi$
$264$	−1.35484	−	2.34665i	−0.0833846	−	0.144426i
$265$	−15.8115			−0.971293
$266$	−8.57693	−	6.51058i	−0.525886	−	0.399189i
$267$	5.22708			0.319892
$268$	20.3124	+	35.1821i	1.24078	+	2.14909i
$269$	−8.11263	+	14.0515i	−0.494636	+	0.856735i	−0.999981	−	0.00618287i	$-0.998032\pi$
$269$	−8.11263	+	14.0515i	−0.494636	+	0.856735i	0.505345	+	0.862917i	$0.331365\pi$
$270$	−30.0195	+	51.9953i	−1.82693	+	3.16433i
$271$	9.36904	+	16.2277i	0.569129	+	0.985760i	0.996652	+	0.0817555i	$0.0260527\pi$
$271$	9.36904	+	16.2277i	0.569129	+	0.985760i	−0.427524	+	0.904004i	$0.640614\pi$
$272$	0.124143			0.00752725
$273$		0			0
$274$	1.14479			0.0691595
$275$	−0.0747124	−	0.129406i	−0.00450533	−	0.00780346i
$276$	−5.83582	+	10.1079i	−0.351275	+	0.608426i
$277$	−15.0163	+	26.0090i	−0.902243	+	1.56273i	−0.0776679	+	0.996979i	$0.524747\pi$
$277$	−15.0163	+	26.0090i	−0.902243	+	1.56273i	−0.824575	+	0.565752i	$0.808586\pi$
$278$	1.62148	+	2.80849i	0.0972501	+	0.168442i
$279$	31.8893			1.90916
$280$	14.4517	−	6.07453i	0.863656	−	0.363023i
$281$	2.23065			0.133070			0.0665348	−	0.997784i	$-0.478806\pi$
$281$	2.23065			0.133070			0.0665348	+	0.997784i	$0.478806\pi$
$282$	−34.2565	−	59.3339i	−2.03994	−	3.53328i
$283$	−6.88774	+	11.9299i	−0.409433	+	0.709159i	−0.994826	−	0.101590i	$-0.967607\pi$
$283$	−6.88774	+	11.9299i	−0.409433	+	0.709159i	0.585393	+	0.810750i	$0.300940\pi$
$284$	−2.17488	+	3.76700i	−0.129055	+	0.223531i
$285$	−5.96258	−	10.3275i	−0.353193	−	0.611748i
$286$		0			0
$287$	−2.23205	+	17.6650i	−0.131754	+	1.04273i
$288$	39.7259			2.34087
$289$	6.92516	+	11.9947i	0.407362	+	0.705572i
$290$	−4.88075	+	8.45371i	−0.286608	+	0.496419i
$291$	−12.0762	+	20.9166i	−0.707920	+	1.22615i
$292$	19.1309	+	33.1357i	1.11955	+	1.93912i
$293$	−1.01231			−0.0591400			−0.0295700	−	0.999563i	$-0.509414\pi$
$293$	−1.01231			−0.0591400			−0.0295700	+	0.999563i	$0.509414\pi$
$294$	48.8033	+	12.5331i	2.84626	+	0.730946i
$295$	−17.2572			−1.00475
$296$	7.72563	+	13.3812i	0.449043	+	0.777766i
$297$	1.90723	−	3.30341i	0.110668	−	0.191683i
$298$	24.0943	−	41.7326i	1.39575	−	2.41751i
$299$		0			0
$300$	−4.91464			−0.283747
$301$	−0.506157	+	4.00585i	−0.0291744	+	0.230893i
$302$	−39.9939			−2.30139
$303$	−14.3616	−	24.8751i	−0.825054	−	1.42904i
$304$	−0.0623010	+	0.107909i	−0.00357321	+	0.00618898i
$305$	−3.65577	+	6.33199i	−0.209329	+	0.362568i
$306$	−14.0405	−	24.3189i	−0.802645	−	1.39022i
$307$	24.0527			1.37276			0.686379	−	0.727244i	$-0.259199\pi$
$307$	24.0527			1.37276			0.686379	+	0.727244i	$0.259199\pi$
$308$	−2.42288	+	1.01842i	−0.138057	+	0.0580296i
$309$	19.0339			1.08280
$310$	−11.1787	−	19.3622i	−0.634910	−	1.09970i
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	−0.709957	−	0.704245i	$-0.751286\pi$
$311$	4.49548	−	7.78639i	0.254915	−	0.441526i	0.964872	+	0.262719i	$0.0846192\pi$
$312$		0			0
$313$	7.61806	+	13.1949i	0.430598	+	0.745818i	0.996925	−	0.0783626i	$-0.0249692\pi$
$313$	7.61806	+	13.1949i	0.430598	+	0.745818i	−0.566326	+	0.824181i	$0.691636\pi$
$314$	−0.172684			−0.00974510
$315$	31.0120	+	23.5406i	1.74733	+	1.32636i
$316$	−25.5220			−1.43572
$317$	−3.41775	−	5.91972i	−0.191960	−	0.332484i	0.753940	−	0.656944i	$-0.228151\pi$
$317$	−3.41775	−	5.91972i	−0.191960	−	0.332484i	−0.945900	+	0.324459i	$0.894818\pi$
$318$	26.7797	−	46.3838i	1.50173	−	2.60107i
$319$	0.310088	−	0.537088i	0.0173616	−	0.0300712i
$320$	−13.7772	−	23.8628i	−0.770170	−	1.33397i
$321$	38.0763			2.12521
$322$	5.53925	+	4.20473i	0.308690	+	0.234321i
$323$	3.16135			0.175902
$324$	−29.2769	−	50.7091i	−1.62650	−	2.81717i
$325$		0			0
$326$	11.5174	−	19.9487i	0.637890	−	1.10486i
$327$	2.14525	+	3.71568i	0.118633	+	0.205478i
$328$	−18.7649			−1.03612
$329$	−23.2152	+	9.75811i	−1.27990	+	0.537982i
$330$	−4.71827			−0.259732
$331$	−6.90727	−	11.9637i	−0.379658	−	0.657587i	0.611354	−	0.791357i	$-0.290625\pi$
$331$	−6.90727	−	11.9637i	−0.379658	−	0.657587i	−0.991012	+	0.133770i	$0.957292\pi$
$332$	−18.0808	+	31.3169i	−0.992314	+	1.71874i
$333$	−19.1876	+	33.2339i	−1.05147	+	1.82121i
$334$	6.68295	+	11.5752i	0.365675	+	0.633367i
$335$	26.8066			1.46460
$336$	0.0730896	−	0.578449i	0.00398736	−	0.0315570i
$337$	27.0432			1.47314			0.736568	−	0.676364i	$-0.236445\pi$
$337$	27.0432			1.47314			0.736568	+	0.676364i	$0.236445\pi$
$338$		0			0
$339$	14.8386	−	25.7013i	0.805924	−	1.39590i
$340$	−6.07249	+	10.5179i	−0.329327	+	0.570411i
$341$	0.710218	+	1.23013i	0.0384604	+	0.0666154i
$342$	28.1850			1.52407
$343$	6.81903	−	17.2192i	0.368193	−	0.929749i
$344$	−4.25528			−0.229429
$345$	3.85082	+	6.66981i	0.207321	+	0.359091i
$346$	19.4097	−	33.6186i	1.04347	−	1.80735i
$347$	9.65568	−	16.7241i	0.518344	−	0.897799i	−0.481429	−	0.876485i	$-0.659882\pi$
$347$	9.65568	−	16.7241i	0.518344	−	0.897799i	0.999773	−	0.0213132i	$-0.00678472\pi$
$348$	−10.1989	−	17.6650i	−0.546719	−	0.946944i
$349$	−14.1573			−0.757821			−0.378911	−	0.925433i	$-0.623701\pi$
$349$	−14.1573			−0.757821			−0.378911	+	0.925433i	$0.623701\pi$
$350$	−0.367085	+	2.90521i	−0.0196215	+	0.155290i
$351$		0			0
$352$	0.884750	+	1.53243i	0.0471573	+	0.0816789i
$353$	8.48235	−	14.6919i	0.451470	−	0.781969i	−0.547008	−	0.837128i	$-0.684233\pi$
$353$	8.48235	−	14.6919i	0.451470	−	0.781969i	0.998478	+	0.0551585i	$0.0175664\pi$
$354$	29.2282	−	50.6247i	1.55346	−	2.69067i
$355$	1.43511	+	2.48569i	0.0761680	+	0.131927i
$356$	5.34313			0.283186
$357$	−13.6371	+	5.73212i	−0.721752	+	0.303376i
$358$	34.9613			1.84776
$359$	−11.3816	−	19.7136i	−0.600700	−	1.04044i	−0.992715	−	0.120484i	$-0.961555\pi$
$359$	−11.3816	−	19.7136i	−0.600700	−	1.04044i	0.392016	−	0.919959i	$-0.371778\pi$
$360$	−20.5163	+	35.5353i	−1.08131	+	1.87288i
$361$	7.91348	−	13.7065i	0.416499	−	0.721397i
$362$	6.68260	+	11.5746i	0.351229	+	0.608347i
$363$	−34.3549			−1.80316
$364$		0			0
$365$	25.2474			1.32151
$366$	−12.3835	−	21.4488i	−0.647293	−	1.12114i
$367$	−8.29168	+	14.3616i	−0.432822	+	0.749670i	−0.997115	−	0.0759048i	$-0.975815\pi$
$367$	−8.29168	+	14.3616i	−0.432822	+	0.749670i	0.564293	+	0.825575i	$0.309149\pi$
$368$	0.0402359	−	0.0696907i	0.00209744	−	0.00363288i
$369$	−23.3026	−	40.3613i	−1.21308	−	2.10112i
$370$	26.9048			1.39871
$371$	−15.6805	−	11.9027i	−0.814090	−	0.617959i
$372$	46.7186			2.42225
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	−0.962677	−	0.270652i	$-0.912761\pi$
$373$	−13.8230	−	23.9422i	−0.715730	−	1.23968i	0.246947	−	0.969029i	$-0.420573\pi$
$374$	0.625404	−	1.08323i	0.0323389	−	0.0560126i
$375$	−18.3580	+	31.7970i	−0.948004	+	1.64199i
$376$	−13.2698	−	22.9840i	−0.684340	−	1.18531i
$377$		0			0
$378$	−68.9122	+	28.9660i	−3.54446	+	1.48985i
$379$	9.24228			0.474744			0.237372	−	0.971419i	$-0.423714\pi$
$379$	9.24228			0.474744			0.237372	+	0.971419i	$0.423714\pi$
$380$	−6.09497	−	10.5568i	−0.312665	−	0.541552i
$381$	21.1075	−	36.5592i	1.08137	−	1.87299i
$382$	−30.6369	+	53.0648i	−1.56752	+	2.71503i
$383$	3.82413	+	6.62358i	0.195404	+	0.338449i	0.947033	−	0.321137i	$-0.104065\pi$
$383$	3.82413	+	6.62358i	0.195404	+	0.338449i	−0.751629	+	0.659586i	$0.770732\pi$
$384$	57.1925			2.91859
$385$	−0.217402	+	1.72057i	−0.0110798	+	0.0876885i
$386$	−0.488913			−0.0248850
$387$	−5.28427	−	9.15262i	−0.268614	−	0.465254i
$388$	−12.3443	+	21.3810i	−0.626689	+	1.08546i
$389$	−3.26868	+	5.66153i	−0.165729	+	0.287051i	−0.936914	−	0.349560i	$-0.886331\pi$
$389$	−3.26868	+	5.66153i	−0.165729	+	0.287051i	0.771185	+	0.636611i	$0.219664\pi$
$390$		0			0
$391$	−2.04169			−0.103253
$392$	18.9048	+	4.85492i	0.954837	+	0.245211i
$393$	42.2064			2.12903
$394$	−12.8281	−	22.2189i	−0.646271	−	1.11937i
$395$	−8.42044	+	14.5846i	−0.423678	+	0.733833i
$396$	3.43963	−	5.95762i	0.172848	−	0.299381i
$397$	14.4654	+	25.0548i	0.725996	+	1.25746i	0.958563	+	0.284882i	$0.0919544\pi$
$397$	14.4654	+	25.0548i	0.725996	+	1.25746i	−0.232566	+	0.972581i	$0.574712\pi$
$398$	−46.6561			−2.33866
$399$	1.86126	−	14.7305i	0.0931795	−	0.737446i
$400$	0.0338847			0.00169423
$401$	13.3716	+	23.1603i	0.667747	+	1.15657i	0.978533	+	0.206092i	$0.0660746\pi$
$401$	13.3716	+	23.1603i	0.667747	+	1.15657i	−0.310786	+	0.950480i	$0.600592\pi$
$402$	−45.4020	+	78.6385i	−2.26444	+	3.92213i
$403$		0			0
$404$	−14.6805	−	25.4274i	−0.730382	−	1.26506i
$405$	−38.6373			−1.91990
$406$	−11.2042	+	4.70947i	−0.556053	+	0.233727i
$407$	−1.70934			−0.0847287
$408$	−7.79498	−	13.5013i	−0.385909	−	0.668414i
$409$	−17.3862	+	30.1138i	−0.859694	+	1.48903i	0.0125273	+	0.999922i	$0.496012\pi$
$409$	−17.3862	+	30.1138i	−0.859694	+	1.48903i	−0.872221	+	0.489112i	$0.837321\pi$
$410$	−16.3374	+	28.2972i	−0.806846	+	1.39750i
$411$	0.789250	+	1.36702i	0.0389309	+	0.0674302i
$412$	19.4565			0.958553
$413$	−17.1142	−	12.9910i	−0.842133	−	0.639246i
$414$	−18.2028			−0.894617
$415$	11.9308	+	20.6647i	0.585659	+	1.01439i
$416$		0			0
$417$	−2.23579	+	3.87250i	−0.109487	+	0.189637i
$418$	0.627719	+	1.08724i	0.0307027	+	0.0531787i
$419$	−4.19246			−0.204815			−0.102407	−	0.994743i	$-0.532655\pi$
$419$	−4.19246			−0.204815			−0.102407	+	0.994743i	$0.532655\pi$
$420$	45.4333	+	34.4876i	2.21692	+	1.68282i
$421$	20.9526			1.02117			0.510584	−	0.859828i	$-0.329429\pi$
$421$	20.9526			1.02117			0.510584	+	0.859828i	$0.329429\pi$
$422$	9.61607	+	16.6555i	0.468103	+	0.810778i
$423$	32.9574	−	57.0838i	1.60244	−	2.77551i
$424$	10.3736	−	17.9676i	0.503786	−	0.872583i
$425$	−0.429853	−	0.744528i	−0.0208509	−	0.0361149i
$426$	−9.72252			−0.471058
$427$	−8.39213	+	3.52748i	−0.406124	+	0.170707i
$428$	38.9217			1.88135
$429$		0			0
$430$	−3.70479	+	6.41688i	−0.178661	+	0.309449i
$431$	8.44713	−	14.6309i	0.406884	−	0.704744i	−0.587655	−	0.809112i	$-0.699949\pi$
$431$	8.44713	−	14.6309i	0.406884	−	0.704744i	0.994539	+	0.104368i	$0.0332820\pi$
$432$	0.432497	+	0.749106i	0.0208085	+	0.0360414i
$433$	−3.42241			−0.164471			−0.0822353	−	0.996613i	$-0.526206\pi$
$433$	−3.42241			−0.164471			−0.0822353	+	0.996613i	$0.526206\pi$
$434$	3.48952	−	27.6169i	0.167502	−	1.32566i
$435$	−13.4597			−0.645342
$436$	2.19288	+	3.79818i	0.105020	+	0.181900i
$437$	1.02463	−	1.77470i	0.0490145	−	0.0848956i
$438$	−42.7611	+	74.0644i	−2.04320	+	3.53893i
$439$	−9.03253	−	15.6448i	−0.431099	−	0.746685i	0.565869	−	0.824495i	$-0.308541\pi$
$439$	−9.03253	−	15.6448i	−0.431099	−	0.746685i	−0.996968	+	0.0778096i	$0.975207\pi$
$440$	−1.82771			−0.0871324
$441$	13.0339	+	46.6910i	0.620661	+	2.22338i
$442$		0			0
$443$	−3.22173	−	5.58020i	−0.153069	−	0.265123i	0.779285	−	0.626669i	$-0.215582\pi$
$443$	−3.22173	−	5.58020i	−0.153069	−	0.265123i	−0.932354	+	0.361546i	$0.882249\pi$
$444$	−28.1103	+	48.6885i	−1.33406	+	2.31065i
$445$	1.76286	−	3.05336i	0.0835674	−	0.144743i
$446$	−15.5471	−	26.9284i	−0.736178	−	1.27510i
$447$	66.4451			3.14275
$448$	4.30065	−	34.0364i	0.203187	−	1.60807i
$449$	−1.75306			−0.0827322			−0.0413661	−	0.999144i	$-0.513171\pi$
$449$	−1.75306			−0.0827322			−0.0413661	+	0.999144i	$0.513171\pi$
$450$	−3.83237	−	6.63785i	−0.180659	−	0.312911i
$451$	1.03796	−	1.79780i	0.0488757	−	0.0846551i
$452$	15.1681	−	26.2719i	0.713447	−	1.23573i
$453$	−27.5728	−	47.7575i	−1.29548	−	2.24385i
$454$	−8.23163			−0.386330
$455$		0			0
$456$	15.6477			0.732770
$457$	16.3550	+	28.3277i	0.765054	+	1.32511i	0.940218	+	0.340573i	$0.110621\pi$
$457$	16.3550	+	28.3277i	0.765054	+	1.32511i	−0.175164	+	0.984539i	$0.556046\pi$
$458$	21.0022	−	36.3769i	0.981368	−	1.69978i
$459$	10.9731	−	19.0060i	0.512180	−	0.887123i
$460$	3.93632	+	6.81790i	0.183532	+	0.317886i
$461$	−7.66641			−0.357060			−0.178530	−	0.983934i	$-0.557134\pi$
$461$	−7.66641			−0.357060			−0.178530	+	0.983934i	$0.557134\pi$
$462$	−4.67917	−	3.55186i	−0.217695	−	0.165248i
$463$	14.4720			0.672570			0.336285	−	0.941760i	$-0.390829\pi$
$463$	14.4720			0.672570			0.336285	+	0.941760i	$0.390829\pi$
$464$	0.0703179	+	0.121794i	0.00326443	+	0.00565415i
$465$	15.4138	−	26.6976i	0.714800	−	1.23807i
$466$	23.1562	−	40.1077i	1.07269	−	1.85795i
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	0.902435	−	0.430825i	$-0.141777\pi$
$467$	1.68801	+	2.92373i	0.0781120	+	0.135294i	−0.824323	+	0.566119i	$0.808444\pi$
$468$		0			0
$469$	26.5845	+	20.1798i	1.22756	+	0.931815i
$470$	−46.2126			−2.13163
$471$	−0.119053	−	0.206205i	−0.00548566	−	0.00950144i
$472$	11.3221	−	19.6104i	0.521140	−	0.902641i
$473$	0.235376	−	0.407683i	0.0108226	−	0.0187453i
$474$	−28.5231	−	49.4035i	−1.31011	−	2.26918i
$475$	0.862889			0.0395921
$476$	−13.9399	+	5.85939i	−0.638934	+	0.268565i
$477$	51.5283			2.35932
$478$	23.7731	+	41.1763i	1.08736	+	1.88336i
$479$	0.0726124	−	0.125768i	0.00331775	−	0.00574651i	−0.864362	−	0.502871i	$-0.832277\pi$
$479$	0.0726124	−	0.125768i	0.00331775	−	0.00574651i	0.867680	+	0.497124i	$0.165611\pi$
$480$	19.2017	−	33.2584i	0.876435	−	1.51803i
$481$		0			0
$482$	29.0508			1.32323
$483$	−1.20206	+	9.51339i	−0.0546956	+	0.432874i
$484$	−35.1177			−1.59626
$485$	8.14553	+	14.1085i	0.369869	+	0.640633i
$486$	23.0587	−	39.9388i	1.04596	−	1.81166i
$487$	−8.21073	+	14.2214i	−0.372064	+	0.644433i	−0.989883	−	0.141887i	$-0.954683\pi$
$487$	−8.21073	+	14.2214i	−0.372064	+	0.644433i	0.617819	+	0.786320i	$0.288016\pi$
$488$	−4.79695	−	8.30856i	−0.217148	−	0.376111i
$489$	31.7616			1.43631
$490$	23.7803	−	24.2812i	1.07428	−	1.09691i
$491$	18.2077			0.821701			0.410850	−	0.911703i	$-0.365232\pi$
$491$	18.2077			0.821701			0.410850	+	0.911703i	$0.365232\pi$
$492$	−34.1389	−	59.1303i	−1.53910	−	2.66580i
$493$	1.78407	−	3.09010i	0.0803506	−	0.139171i
$494$		0			0
$495$	−2.26967	−	3.93119i	−0.102014	−	0.176694i
$496$	−0.322108			−0.0144631
$497$	−0.447981	+	3.54543i	−0.0200947	+	0.159034i
$498$	−80.8279			−3.62199
$499$	18.7860	+	32.5383i	0.840976	+	1.45661i	0.889070	+	0.457770i	$0.151352\pi$
$499$	18.7860	+	32.5383i	0.840976	+	1.45661i	−0.0480945	+	0.998843i	$0.515315\pi$
$500$	−18.7656	+	32.5030i	−0.839225	+	1.45358i
$501$	−9.21481	+	15.9605i	−0.411687	+	0.713063i
$502$	15.7007	+	27.1945i	0.700758	+	1.21375i
$503$	−4.20535			−0.187507			−0.0937537	−	0.995595i	$-0.529887\pi$
$503$	−4.20535			−0.187507			−0.0937537	+	0.995595i	$0.529887\pi$
$504$	−47.0969	+	19.7964i	−2.09786	+	0.881800i
$505$	−19.3741			−0.862137
$506$	−0.405400	−	0.702174i	−0.0180222	−	0.0312154i
$507$		0			0
$508$	21.5761	−	37.3710i	0.957287	−	1.65807i
$509$	−4.21873	−	7.30705i	−0.186992	−	0.323879i	0.757254	−	0.653120i	$-0.226540\pi$
$509$	−4.21873	−	7.30705i	−0.186992	−	0.323879i	−0.944246	+	0.329241i	$0.893207\pi$
$510$	−27.1463			−1.20206
$511$	25.0382	+	19.0060i	1.10762	+	0.840775i
$512$	−0.791350			−0.0349731
$513$	11.0137	+	19.0763i	0.486268	+	0.842240i
$514$	−8.37924	+	14.5133i	−0.369593	+	0.640153i
$515$	6.41927	−	11.1185i	0.282867	−	0.489940i
$516$	−7.74159	−	13.4088i	−0.340804	−	0.590290i
$517$	2.93602			0.129126
$518$	26.6818	+	20.2536i	1.17233	+	0.889893i
$519$	53.5263			2.34955
$520$		0			0
$521$	−12.9140	+	22.3677i	−0.565773	+	0.979948i	0.431204	+	0.902254i	$0.358089\pi$
$521$	−12.9140	+	22.3677i	−0.565773	+	0.979948i	−0.996977	+	0.0776936i	$0.975244\pi$
$522$	15.9059	−	27.5499i	0.696184	−	1.20583i
$523$	0.378202	+	0.655065i	0.0165376	+	0.0286440i	0.874176	−	0.485610i	$-0.161402\pi$
$523$	0.378202	+	0.655065i	0.0165376	+	0.0286440i	−0.857638	+	0.514254i	$0.828069\pi$
$524$	43.1436			1.88473
$525$	−3.72225	+	1.56458i	−0.162452	+	0.0682839i
$526$	15.2599			0.665364
$527$	4.08619	+	7.07749i	0.177997	+	0.308300i
$528$	−0.0339885	+	0.0588698i	−0.00147916	+	0.00256198i
$529$	10.8383	−	18.7724i	0.471229	−	0.816192i
$530$	−18.0632	−	31.2863i	−0.784614	−	1.35899i
$531$	56.2396			2.44059
$532$	1.90259	−	15.0575i	0.0824876	−	0.652827i
$533$		0			0
$534$	5.97145	+	10.3428i	0.258410	+	0.447579i
$535$	12.8414	−	22.2420i	0.555183	−	0.961606i
$536$	−17.5873	+	30.4620i	−0.759654	+	1.31576i
$537$	24.1032	+	41.7480i	1.04013	+	1.80156i
$538$	−37.0717			−1.59827
$539$	−1.51083	+	1.54266i	−0.0650760	+	0.0664469i
$540$	−84.6231			−3.64160
$541$	11.2063	+	19.4099i	0.481797	+	0.834496i	0.999782	−	0.0208936i	$-0.00665111\pi$
$541$	11.2063	+	19.4099i	0.481797	+	0.834496i	−0.517985	+	0.855390i	$0.673318\pi$
$542$	−21.4065	+	37.0772i	−0.919488	+	1.59260i
$543$	−9.21432	+	15.9597i	−0.395424	+	0.684895i
$544$	5.09035	+	8.81675i	0.218247	+	0.378015i
$545$	2.89398			0.123965
$546$		0			0
$547$	−11.8059			−0.504784			−0.252392	−	0.967625i	$-0.581217\pi$
$547$	−11.8059			−0.504784			−0.252392	+	0.967625i	$0.581217\pi$
$548$	0.806774	+	1.39737i	0.0344637	+	0.0596929i
$549$	11.9138	−	20.6354i	0.508470	−	0.880697i
$550$	0.170704	−	0.295668i	0.00727884	−	0.0126073i
$551$	1.79068	+	3.10154i	0.0762854	+	0.132130i
$552$	−10.1058			−0.430129
$553$	−19.3298	+	8.12495i	−0.821988	+	0.345508i
$554$	−68.6190			−2.91534
$555$	18.5489	+	32.1276i	0.787355	+	1.36374i
$556$	−2.28543	+	3.95848i	−0.0969238	+	0.167877i
$557$	4.38366	−	7.59273i	0.185742	−	0.321714i	−0.758084	−	0.652156i	$-0.773865\pi$
$557$	4.38366	−	7.59273i	0.185742	−	0.321714i	0.943826	+	0.330442i	$0.107198\pi$
$558$	36.4305	+	63.0995i	1.54223	+	2.67122i
$559$		0			0
$560$	−0.313247	−	0.237780i	−0.0132371	−	0.0100480i
$561$	1.72468			0.0728161
$562$	2.54831	+	4.41380i	0.107494	+	0.186185i
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	0.159860	+	0.987140i	$0.448896\pi$
$563$	−18.3879	+	31.8488i	−0.774958	+	1.34227i	−0.934818	+	0.355127i	$0.884438\pi$
$564$	48.2834	−	83.6293i	2.03310	−	3.52143i
$565$	−10.0088	−	17.3358i	−0.421074	−	0.729321i
$566$	−31.4744			−1.32297
$567$	−38.3171	−	29.0857i	−1.60917	−	1.22149i
$568$	−3.76619			−0.158026
$569$	17.8918	+	30.9896i	0.750065	+	1.29915i	0.947791	+	0.318893i	$0.103311\pi$
$569$	17.8918	+	30.9896i	0.750065	+	1.29915i	−0.197726	+	0.980257i	$0.563356\pi$
$570$	13.6234	−	23.5964i	0.570621	−	0.988344i
$571$	−7.46920	+	12.9370i	−0.312576	+	0.541398i	−0.978919	−	0.204248i	$-0.934525\pi$
$571$	−7.46920	+	12.9370i	−0.312576	+	0.541398i	0.666343	+	0.745645i	$0.267859\pi$
$572$		0			0
$573$	−84.4877			−3.52952
$574$	−37.5038	+	15.7641i	−1.56538	+	0.657979i
$575$	−0.557280			−0.0232402
$576$	44.8987	+	77.7669i	1.87078	+	3.24029i
$577$	8.42309	−	14.5892i	0.350658	−	0.607357i	−0.635707	−	0.771930i	$-0.719291\pi$
$577$	8.42309	−	14.5892i	0.350658	−	0.607357i	0.986365	+	0.164573i	$0.0526247\pi$
$578$	−15.8227	+	27.4057i	−0.658137	+	1.13993i
$579$	−0.337070	−	0.583822i	−0.0140081	−	0.0242628i
$580$	−13.7585			−0.571292
$581$	−3.72428	+	29.4748i	−0.154509	+	1.22282i
$582$	−55.1838			−2.28744
$583$	1.14761	+	1.98771i	0.0475290	+	0.0823226i
$584$	−16.5643	+	28.6901i	−0.685434	+	1.18721i
$585$		0			0
$586$	−1.15647	−	2.00307i	−0.0477735	−	0.0827461i
$587$	36.8833			1.52234			0.761168	−	0.648555i	$-0.224626\pi$
$587$	36.8833			1.52234			0.761168	+	0.648555i	$0.224626\pi$
$588$	19.0950	+	68.4035i	0.787463	+	2.82091i
$589$	−8.20264			−0.337984
$590$	−19.7147	−	34.1469i	−0.811642	−	1.40580i
$591$	17.6881	−	30.6367i	0.727590	−	1.26022i
$592$	0.193811	−	0.335690i	0.00796558	−	0.0137968i
$593$	−8.07676	−	13.9894i	−0.331673	−	0.574474i	0.651167	−	0.758934i	$-0.274280\pi$
$593$	−8.07676	−	13.9894i	−0.331673	−	0.574474i	−0.982840	+	0.184460i	$0.940946\pi$
$594$	8.71531			0.357593
$595$	−1.25081	+	9.89920i	−0.0512781	+	0.405828i
$596$	67.9204			2.78213
$597$	−32.1660	−	55.7131i	−1.31646	−	2.28018i
$598$		0			0
$599$	1.24238	−	2.15186i	0.0507622	−	0.0879227i	−0.839528	−	0.543317i	$-0.817168\pi$
$599$	1.24238	−	2.15186i	0.0507622	−	0.0879227i	0.890290	+	0.455394i	$0.150502\pi$
$600$	−2.12764	−	3.68518i	−0.0868605	−	0.150447i
$601$	9.55999			0.389960			0.194980	−	0.980807i	$-0.437536\pi$
$601$	9.55999			0.389960			0.194980	+	0.980807i	$0.437536\pi$
$602$	−8.50464	+	3.57478i	−0.346623	+	0.145697i
$603$	−87.3605			−3.55759
$604$	−28.1850	−	48.8179i	−1.14683	−	1.98637i
$605$	−11.5864	+	20.0682i	−0.471052	+	0.815886i
$606$	32.8136	−	56.8349i	1.33296	−	2.30876i
$607$	9.74294	+	16.8753i	0.395454	+	0.684946i	0.993159	−	0.116770i	$-0.0372540\pi$
$607$	9.74294	+	16.8753i	0.395454	+	0.684946i	−0.597705	+	0.801716i	$0.703921\pi$
$608$	−10.2184			−0.414411
$609$	−13.3481	−	10.1323i	−0.540894	−	0.410582i
$610$	−16.7055			−0.676387
$611$		0			0
$612$	19.7897	−	34.2768i	0.799951	−	1.38556i
$613$	7.38409	−	12.7896i	0.298241	−	0.516568i	−0.677493	−	0.735529i	$-0.736934\pi$
$613$	7.38409	−	12.7896i	0.298241	−	0.516568i	0.975733	+	0.218962i	$0.0702669\pi$
$614$	27.4779	+	47.5931i	1.10892	+	1.92070i
$615$	−45.0537			−1.81674
$616$	−1.81256	−	1.37588i	−0.0730301	−	0.0554357i
$617$	30.9478			1.24591			0.622955	−	0.782257i	$-0.285932\pi$
$617$	30.9478			1.24591			0.622955	+	0.782257i	$0.285932\pi$
$618$	21.7444	+	37.6625i	0.874689	+	1.51501i
$619$	−6.54123	+	11.3297i	−0.262914	+	0.455380i	−0.967015	−	0.254719i	$-0.918017\pi$
$619$	−6.54123	+	11.3297i	−0.262914	+	0.455380i	0.704101	+	0.710100i	$0.251350\pi$
$620$	15.7561	−	27.2903i	0.632780	−	1.09601i
$621$	−7.11300	−	12.3201i	−0.285435	−	0.494388i
$622$	20.5426			0.823685
$623$	4.04678	−	1.70099i	0.162131	−	0.0681489i
$624$		0			0
$625$	11.1716	+	19.3498i	0.446865	+	0.773994i
$626$	−17.4059	+	30.1478i	−0.695678	+	1.20495i
$627$	−0.865532	+	1.49915i	−0.0345660	+	0.0598701i
$628$	−0.121696	−	0.210784i	−0.00485620	−	0.00841119i
$629$	−9.83456			−0.392130
$630$	−11.1516	+	88.2566i	−0.444291	+	3.51623i
$631$	35.3591			1.40762			0.703812	−	0.710387i	$-0.251480\pi$
$631$	35.3591			1.40762			0.703812	+	0.710387i	$0.251480\pi$
$632$	−11.0489	−	19.1373i	−0.439503	−	0.761242i
$633$	−13.2591	+	22.9655i	−0.527004	+	0.912797i
$634$	7.80892	−	13.5254i	0.310132	−	0.537164i
$635$	−14.2372	−	24.6596i	−0.564986	−	0.978585i
$636$	75.4903			2.99338
$637$		0			0
$638$	1.41699			0.0560990
$639$	−4.67691	−	8.10065i	−0.185016	−	0.320457i
$640$	19.2884	−	33.4086i	0.762443	−	1.32059i
$641$	10.6188	−	18.3923i	0.419417	−	0.726452i	−0.576464	−	0.817123i	$-0.695568\pi$
$641$	10.6188	−	18.3923i	0.419417	−	0.726452i	0.995881	+	0.0906706i	$0.0289010\pi$
$642$	43.4986	+	75.3418i	1.71675	+	2.97351i
$643$	−25.4808			−1.00486			−0.502432	−	0.864617i	$-0.667561\pi$
$643$	−25.4808			−1.00486			−0.502432	+	0.864617i	$0.667561\pi$
$644$	−1.22875	+	9.72462i	−0.0484195	+	0.383204i
$645$	−10.2167			−0.402283
$646$	3.61154	+	6.25537i	0.142094	+	0.246114i
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	−0.998249	−	0.0591522i	$-0.981160\pi$
$647$	−11.3928	+	19.7329i	−0.447897	+	0.775781i	0.550352	+	0.834933i	$0.314494\pi$
$648$	25.3491	−	43.9059i	0.995806	−	1.72479i
$649$	1.25253	+	2.16945i	0.0491662	+	0.0851583i
$650$		0			0
$651$	35.3837	−	14.8729i	1.38680	−	0.582916i
$652$	32.4669			1.27150
$653$	−8.13928	−	14.0976i	−0.318515	−	0.551684i	0.661664	−	0.749801i	$-0.269851\pi$
$653$	−8.13928	−	14.0976i	−0.318515	−	0.551684i	−0.980178	+	0.198117i	$0.936517\pi$
$654$	−4.90150	+	8.48964i	−0.191664	+	0.331971i
$655$	14.2343	−	24.6546i	0.556181	−	0.963334i
$656$	0.235376	+	0.407683i	0.00918988	+	0.0159173i
$657$	−82.2790			−3.21001
$658$	−45.8297	−	34.7884i	−1.78663	−	1.35619i
$659$	20.5596			0.800888			0.400444	−	0.916321i	$-0.368856\pi$
$659$	20.5596			0.800888			0.400444	+	0.916321i	$0.368856\pi$
$660$	−3.32513	−	5.75929i	−0.129430	−	0.224180i
$661$	−13.8863	+	24.0518i	−0.540115	+	0.935507i	0.458782	+	0.888549i	$0.348286\pi$
$661$	−13.8863	+	24.0518i	−0.540115	+	0.935507i	−0.998897	+	0.0469576i	$0.985047\pi$
$662$	15.7818	−	27.3349i	0.613378	−	1.06240i
$663$		0			0
$664$	−31.3101			−1.21507
$665$	−7.97698	−	6.05517i	−0.309334	−	0.234809i
$666$	−87.6802			−3.39754
$667$	−1.15647	−	2.00307i	−0.0447789	−	0.0775593i
$668$	−9.41941	+	16.3149i	−0.364448	+	0.631242i
$669$	21.4372	−	37.1303i	0.828810	−	1.43554i
$670$	30.6241	+	53.0425i	1.18311	+	2.04921i
$671$	1.06135			0.0409730
$672$	44.0791	−	18.5279i	1.70039	−	0.714729i
$673$	−5.20337			−0.200575			−0.100288	−	0.994958i	$-0.531976\pi$
$673$	−5.20337			−0.200575			−0.100288	+	0.994958i	$0.531976\pi$
$674$	30.8943	+	53.5105i	1.19000	+	2.06115i
$675$	2.99511	−	5.18768i	0.115282	−	0.199674i
$676$		0			0
$677$	−22.4239	−	38.8394i	−0.861821	−	1.49272i	−0.870169	−	0.492753i	$-0.835991\pi$
$677$	−22.4239	−	38.8394i	−0.861821	−	1.49272i	0.00834820	−	0.999965i	$-0.497343\pi$
$678$	67.8070			2.60411
$679$	−2.54268	+	20.1234i	−0.0975792	+	0.772266i
$680$	−10.5156			−0.403254
$681$	−5.67510	−	9.82957i	−0.217470	−	0.376670i
$682$	−1.62271	+	2.81062i	−0.0621370	+	0.107624i
$683$	9.48691	−	16.4318i	0.363006	−	0.628745i	−0.625448	−	0.780266i	$-0.715084\pi$
$683$	9.48691	−	16.4318i	0.363006	−	0.628745i	0.988454	+	0.151521i	$0.0484170\pi$
$684$	19.8630	+	34.4037i	0.759479	+	1.31546i
$685$	1.06471			0.0406807
$686$	41.8618	−	6.17846i	1.59829	−	0.235895i
$687$	57.9179			2.20970
$688$	0.0533755	+	0.0924491i	0.00203492	+	0.00352459i
$689$		0			0
$690$	−8.79840	+	15.2393i	−0.334949	+	0.580149i
$691$	18.7111	+	32.4085i	0.711803	+	1.23288i	0.964180	+	0.265250i	$0.0854545\pi$
$691$	18.7111	+	32.4085i	0.711803	+	1.23288i	−0.252376	+	0.967629i	$0.581212\pi$
$692$	54.7148			2.07994
$693$	0.708493	−	5.60719i	0.0269134	−	0.213000i
$694$	44.1229			1.67488
$695$	1.50806	+	2.61204i	0.0572040	+	0.0990802i
$696$	8.83060	−	15.2951i	0.334723	−	0.579757i
$697$	5.97184	−	10.3435i	0.226200	−	0.391789i
$698$	−16.1734	−	28.0131i	−0.612171	−	1.06031i
$699$	63.8580			2.41533
$700$	−3.80489	+	1.59932i	−0.143811	+	0.0604486i
$701$	−42.5513			−1.60714			−0.803570	−	0.595210i	$-0.797069\pi$
$701$	−42.5513			−1.60714			−0.803570	+	0.595210i	$0.797069\pi$
$702$		0			0
$703$	4.93548	−	8.54851i	0.186145	−	0.322413i
$704$	−1.99991	+	3.46395i	−0.0753745	+	0.130552i
$705$	−31.8602	−	55.1835i	−1.19993	−	2.07833i
$706$	38.7612			1.45880
$707$	−19.2136	−	14.5846i	−0.722600	−	0.548512i
$708$	82.3924			3.09650
$709$	−25.1661	−	43.5889i	−0.945131	−	1.63702i	−0.755488	−	0.655163i	$-0.772600\pi$
$709$	−25.1661	−	43.5889i	−0.945131	−	1.63702i	−0.189644	−	0.981853i	$-0.560733\pi$
$710$	−3.27897	+	5.67934i	−0.123057	+	0.213142i
$711$	27.4415	−	47.5300i	1.02914	−	1.78252i
$712$	2.31315	+	4.00648i	0.0866888	+	0.150149i
$713$	5.29752			0.198394
$714$	−26.9213	−	20.4354i	−1.00750	−	0.764776i
$715$		0			0
$716$	24.6384	+	42.6749i	0.920780	+	1.59484i
$717$	−32.7796	+	56.7760i	−1.22418	+	2.12034i
$718$	26.0049	−	45.0418i	0.970495	−	1.68095i
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	−0.998940	−	0.0460219i	$-0.985346\pi$
$719$	−14.4616	−	25.0482i	−0.539326	−	0.934141i	0.459614	−	0.888119i	$-0.347988\pi$
$720$	1.02938			0.0383625
$721$	14.7360	−	6.19400i	0.548796	−	0.230677i
$722$	36.1616			1.34580
$723$	20.0284	+	34.6902i	0.744863	+	1.29014i
$724$	−9.41891	+	16.3140i	−0.350051	+	0.606306i
$725$	0.486962	−	0.843444i	0.0180853	−	0.0313247i
$726$	−39.2472	−	67.9782i	−1.45660	−	2.52291i
$727$	−19.8593			−0.736539			−0.368269	−	0.929719i	$-0.620050\pi$
$727$	−19.8593			−0.736539			−0.368269	+	0.929719i	$0.620050\pi$
$728$		0			0
$729$	9.04209			0.334892
$730$	28.8428	+	49.9572i	1.06752	+	1.84900i
$731$	1.35422	−	2.34558i	0.0500876	−	0.0867543i
$732$	17.4541	−	30.2314i	0.645121	−	1.11738i
$733$	10.1751	+	17.6237i	0.375824	+	0.650947i	0.990450	−	0.137872i	$-0.0440263\pi$
$733$	10.1751	+	17.6237i	0.375824	+	0.650947i	−0.614626	+	0.788819i	$0.710693\pi$
$734$	−37.8899			−1.39854
$735$	45.3895	+	11.6564i	1.67422	+	0.429954i
$736$	6.59935			0.243255
$737$	−1.94564	−	3.36994i	−0.0716684	−	0.124133i
$738$	53.2421	−	92.2180i	1.95987	−	3.39459i
$739$	9.50055	−	16.4554i	0.349483	−	0.605323i	−0.636674	−	0.771133i	$-0.719690\pi$
$739$	9.50055	−	16.4554i	0.349483	−	0.605323i	0.986158	+	0.165810i	$0.0530238\pi$
$740$	18.9607	+	32.8409i	0.697009	+	1.20726i
$741$		0			0
$742$	5.63854	−	44.6248i	0.206997	−	1.63823i
$743$	−8.15098			−0.299030			−0.149515	−	0.988759i	$-0.547771\pi$
$743$	−8.15098			−0.299030			−0.149515	+	0.988759i	$0.547771\pi$
$744$	20.2254	+	35.0314i	0.741498	+	1.28431i
$745$	22.4090	−	38.8134i	0.821000	−	1.42201i
$746$	31.5831	−	54.7035i	1.15634	−	2.00284i
$747$	−38.8814	−	67.3445i	−1.42260	−	2.46401i
$748$	1.76297			0.0644607
$749$	29.4786	−	12.3908i	1.07712	−	0.452750i
$750$	−83.8893			−3.06320
$751$	−18.3713	−	31.8201i	−0.670379	−	1.16113i	−0.977797	−	0.209556i	$-0.932798\pi$
$751$	−18.3713	−	31.8201i	−0.670379	−	1.16113i	0.307417	−	0.951575i	$-0.400535\pi$
$752$	−0.332897	+	0.576595i	−0.0121395	+	0.0210262i
$753$	−21.6490	+	37.4972i	−0.788934	+	1.36647i
$754$		0			0
$755$	−37.1963			−1.35371
$756$	−83.9218	−	63.7034i	−3.05221	−	2.31687i
$757$	38.3971			1.39557			0.697783	−	0.716310i	$-0.254170\pi$
$757$	38.3971			1.39557			0.697783	+	0.716310i	$0.254170\pi$
$758$	10.5584	+	18.2878i	0.383500	+	0.664241i
$759$	0.558987	−	0.968195i	0.0202900	−	0.0351432i
$760$	5.27726	−	9.14048i	0.191426	−	0.331560i
$761$	6.23089	+	10.7922i	0.225870	+	0.391218i	0.956580	−	0.291470i	$-0.0941443\pi$
$761$	6.23089	+	10.7922i	0.225870	+	0.391218i	−0.730710	+	0.682688i	$0.760811\pi$
$762$	96.4533			3.49414
$763$	2.87000	+	2.17856i	0.103901	+	0.0788692i
$764$	−86.3636			−3.12453
$765$	−13.0584	−	22.6178i	−0.472128	−	0.817749i
$766$	−8.73742	+	15.1336i	−0.315696	+	0.546801i
$767$		0			0
$768$	24.4860	+	42.4110i	0.883562	+	1.53037i
$769$	−4.81390			−0.173594			−0.0867969	−	0.996226i	$-0.527663\pi$
$769$	−4.81390			−0.173594			−0.0867969	+	0.996226i	$0.527663\pi$
$770$	−3.65287	+	1.53542i	−0.131640	+	0.0553326i
$771$	−23.1075			−0.832196
$772$	−0.344554	−	0.596785i	−0.0124008	−	0.0214787i
$773$	14.1372	−	24.4863i	0.508480	−	0.880713i	−0.491472	−	0.870893i	$-0.663541\pi$
$773$	14.1372	−	24.4863i	0.508480	−	0.880713i	0.999952	−	0.00981931i	$-0.00312563\pi$
$774$	12.0736	−	20.9120i	0.433975	−	0.751668i
$775$	1.11533	+	1.93180i	0.0400637	+	0.0693923i
$776$	−21.3764			−0.767369
$777$	−5.79015	+	45.8247i	−0.207720	+	1.64395i
$778$	−14.9367			−0.535505
$779$	5.99395	+	10.3818i	0.214755	+	0.371967i
$780$		0			0
$781$	0.208322	−	0.360825i	0.00745436	−	0.0129113i
$782$	−2.33244	−	4.03991i	−0.0834081	−	0.144467i
$783$	24.8619			0.888492
$784$	−0.131653	−	0.471618i	−0.00470190	−	0.0168435i
$785$	−0.160604			−0.00573222
$786$	48.2169	+	83.5141i	1.71984	+	2.97885i
$787$	−24.8291	+	43.0053i	−0.885062	+	1.53297i	−0.0394193	+	0.999223i	$0.512551\pi$
$787$	−24.8291	+	43.0053i	−0.885062	+	1.53297i	−0.845643	+	0.533749i	$0.820783\pi$
$788$	18.0808	−	31.3169i	0.644102	−	1.11562i
$789$	10.5206	+	18.2222i	0.374543	+	0.648728i
$790$	−38.4783			−1.36900
$791$	3.12432	−	24.7266i	0.111088	−	0.879177i
$792$	5.95633			0.211649
$793$		0			0
$794$	−33.0507	+	57.2455i	−1.17292	+	2.03157i
$795$	24.9065	−	43.1393i	0.883341	−	1.52999i
$796$	−32.8801	−	56.9501i	−1.16541	−	2.01854i
$797$	5.37263			0.190308			0.0951542	−	0.995463i	$-0.469666\pi$
$797$	5.37263			0.190308			0.0951542	+	0.995463i	$0.469666\pi$
$798$	31.2736	−	13.1453i	1.10707	−	0.465339i
$799$	16.8922			0.597604
$800$	1.38941	+	2.40653i	0.0491231	+	0.0850837i
$801$	−5.74500	+	9.95062i	−0.202989	+	0.351588i
$802$	−30.5517	+	52.9170i	−1.07882	+	1.86857i
$803$	−1.83246	−	3.17392i	−0.0646663	−	0.112005i
$804$	−127.985			−4.51369
$805$	5.15178	+	3.91061i	0.181576	+	0.137831i
$806$		0			0
$807$	−25.5582	−	44.2681i	−0.899692	−	1.55831i
$808$	12.7109	−	22.0160i	0.447169	−	0.774520i
$809$	−20.6184	+	35.7122i	−0.724905	+	1.25557i	0.234107	+	0.972211i	$0.424783\pi$
$809$	−20.6184	+	35.7122i	−0.724905	+	1.25557i	−0.959013	+	0.283362i	$0.908550\pi$
$810$	−44.1395	−	76.4518i	−1.55090	−	2.68624i
$811$	−19.4366			−0.682512			−0.341256	−	0.939970i	$-0.610852\pi$
$811$	−19.4366			−0.682512			−0.341256	+	0.939970i	$0.610852\pi$
$812$	−13.6445	−	10.3573i	−0.478828	−	0.363469i
$813$	−59.0328			−2.07037
$814$	−1.95276	−	3.38227i	−0.0684441	−	0.118549i
$815$	10.7118	−	18.5533i	0.375217	−	0.649895i
$816$	−0.195551	+	0.338704i	−0.00684564	+	0.0118570i
$817$	1.35923	+	2.35426i	0.0475535	+	0.0823651i
$818$	−79.4486			−2.77785
$819$		0			0
$820$	−46.0540			−1.60828
$821$	−10.0953	−	17.4856i	−0.352329	−	0.610251i	0.634328	−	0.773064i	$-0.281277\pi$
$821$	−10.0953	−	17.4856i	−0.352329	−	0.610251i	−0.986657	+	0.162813i	$0.947943\pi$
$822$	−1.80329	+	3.12339i	−0.0628970	+	0.108941i
$823$	21.4049	−	37.0743i	0.746127	−	1.29233i	−0.203539	−	0.979067i	$-0.565244\pi$
$823$	21.4049	−	37.0743i	0.746127	−	1.29233i	0.949666	−	0.313263i	$-0.101422\pi$
$824$	8.42309	+	14.5892i	0.293432	+	0.508240i
$825$	0.470751			0.0163895
$826$	6.15408	−	48.7049i	0.214128	−	1.69466i
$827$	−33.5376			−1.16622			−0.583109	−	0.812394i	$-0.698164\pi$
$827$	−33.5376			−1.16622			−0.583109	+	0.812394i	$0.698164\pi$
$828$	−12.8281	−	22.2189i	−0.445808	−	0.772162i
$829$	19.8949	−	34.4590i	0.690978	−	1.19681i	−0.280540	−	0.959842i	$-0.590513\pi$
$829$	19.8949	−	34.4590i	0.690978	−	1.19681i	0.971518	−	0.236967i	$-0.0761533\pi$
$830$	−27.2596	+	47.2150i	−0.946195	+	1.63886i
$831$	−47.3077	−	81.9394i	−1.64109	−	2.84245i
$832$		0			0
$833$	−8.69246	+	8.87557i	−0.301176	+	0.307520i
$834$	−10.2167			−0.353776
$835$	6.21548	+	10.7655i	0.215096	+	0.372556i
$836$	−0.884750	+	1.53243i	−0.0305997	+	0.0530003i
$837$	−28.4715	+	49.3142i	−0.984120	+	1.70455i
$838$	−4.78949	−	8.29564i	−0.165450	−	0.286568i
$839$	36.7098			1.26736			0.633682	−	0.773594i	$-0.281543\pi$
$839$	36.7098			1.26736			0.633682	+	0.773594i	$0.281543\pi$
$840$	−6.19111	+	48.9980i	−0.213614	+	1.69059i
$841$	−24.9578			−0.860614
$842$	23.9364	+	41.4591i	0.824903	+	1.42877i
$843$	−3.51375	+	6.08599i	−0.121020	+	0.209613i
$844$	−13.5535	+	23.4754i	−0.466532	+	0.808058i
$845$		0			0
$846$	150.603			5.17783
$847$	−26.5974	+	11.1798i	−0.913898	+	0.384141i
$848$	−0.520479			−0.0178733
$849$	−21.6993	−	37.5842i	−0.744717	−	1.28989i
$850$	0.982134	−	1.70111i	0.0336869	−	0.0583475i
$851$	−3.18749	+	5.52089i	−0.109266	+	0.189254i
$852$	−6.85179	−	11.8676i	−0.234738	−	0.406579i
$853$	−11.7156			−0.401136			−0.200568	−	0.979680i	$-0.564279\pi$
$853$	−11.7156			−0.401136			−0.200568	+	0.979680i	$0.564279\pi$
$854$	−16.5671	−	12.5757i	−0.566914	−	0.430333i
$855$	26.2135			0.896483
$856$	16.8500	+	29.1850i	0.575920	+	0.997523i
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	−0.526576	−	0.850128i	$-0.676524\pi$
$857$	13.8453	−	23.9807i	0.472945	−	0.819164i	0.999521	+	0.0309639i	$0.00985769\pi$
$858$		0			0
$859$	19.2819	+	33.3972i	0.657890	+	1.13950i	0.981161	+	0.193192i	$0.0618840\pi$
$859$	19.2819	+	33.3972i	0.657890	+	1.13950i	−0.323271	+	0.946306i	$0.604783\pi$
$860$	−10.4436			−0.356122
$861$	−44.6803	−	33.9159i	−1.52270	−	1.15585i
$862$	38.6002			1.31473
$863$	−8.92660	−	15.4613i	−0.303865	−	0.526310i	0.673143	−	0.739512i	$-0.264944\pi$
$863$	−8.92660	−	15.4613i	−0.303865	−	0.526310i	−0.977008	+	0.213203i	$0.931611\pi$
$864$	−35.4683	+	61.4329i	−1.20666	+	2.08999i
$865$	18.0520	−	31.2670i	0.613787	−	1.06311i
$866$	−3.90979	−	6.77195i	−0.132860	−	0.230120i
$867$	−43.6343			−1.48190
$868$	36.1694	−	15.2032i	1.22767	−	0.516029i
$869$	2.44464			0.0829286
$870$	−15.3764	−	26.6327i	−0.521310	−	0.902935i
$871$		0			0
$872$	−1.89868	+	3.28861i	−0.0642975	+	0.111366i
$873$	−26.5456	−	45.9783i	−0.898431	−	1.55613i
$874$	4.68216			0.158376
$875$	−3.86534	+	30.5912i	−0.130672	+	1.03417i
$876$	−120.541			−4.07270
$877$	4.46017	+	7.72524i	0.150609	+	0.260863i	0.931452	−	0.363865i	$-0.118543\pi$
$877$	4.46017	+	7.72524i	0.150609	+	0.260863i	−0.780842	+	0.624728i	$0.785210\pi$
$878$	20.6376	−	35.7454i	0.696487	−	1.20635i
$879$	1.59461	−	2.76194i	0.0537848	−	0.0931580i
$880$	0.0229256	+	0.0397083i	0.000772821	+	0.00133857i
$881$	−54.6144			−1.84001			−0.920003	−	0.391911i	$-0.871814\pi$
$881$	−54.6144			−1.84001			−0.920003	+	0.391911i	$0.871814\pi$
$882$	−77.4978	+	79.1303i	−2.60949	+	2.66446i
$883$	7.51632			0.252944			0.126472	−	0.991970i	$-0.459635\pi$
$883$	7.51632			0.252944			0.126472	+	0.991970i	$0.459635\pi$
$884$		0			0
$885$	27.1837	−	47.0835i	0.913770	−	1.58270i
$886$	7.36105	−	12.7497i	0.247299	−	0.428335i
$887$	−22.5391	−	39.0389i	−0.756790	−	1.31080i	−0.944479	−	0.328571i	$-0.893433\pi$
$887$	−22.5391	−	39.0389i	−0.756790	−	1.31080i	0.187689	−	0.982229i	$-0.439900\pi$
$888$	−48.6780			−1.63353
$889$	4.44424	−	35.1728i	0.149055	−	1.17966i
$890$	8.05560			0.270024
$891$	2.80431	+	4.85720i	0.0939479	+	0.162722i
$892$	21.9132	−	37.9547i	0.733708	−	1.27082i
$893$	−8.47737	+	14.6832i	−0.283684	+	0.491356i
$894$	75.9074	+	131.475i	2.53872	+	4.39720i
$895$	32.5157			1.08688
$896$	44.2782	−	18.6116i	1.47923	−	0.621769i
$897$		0			0
$898$	−2.00271	−	3.46880i	−0.0668314	−	0.115755i
$899$	−4.62907	+	8.01779i	−0.154388	+	0.267408i
$900$	5.40160	−	9.35584i	0.180053	−	0.311861i
$901$	6.60268	+	11.4362i	0.219967	+	0.380994i
$902$	4.74309			0.157928
$903$	−10.1320	−	7.69103i	−0.337173	−	0.255942i
$904$	26.2662			0.873602
$905$	6.21515	+	10.7650i	0.206599	+	0.357839i
$906$	62.9988	−	109.117i	2.09299	−	3.62517i
$907$	−3.18295	+	5.51303i	−0.105688	+	0.183057i	−0.914019	−	0.405671i	$-0.867038\pi$
$907$	−3.18295	+	5.51303i	−0.105688	+	0.183057i	0.808331	+	0.588728i	$0.200371\pi$
$908$	−5.80111	−	10.0478i	−0.192517	−	0.333449i
$909$	63.1385			2.09417
$910$		0			0
$911$	20.9161			0.692982			0.346491	−	0.938053i	$-0.387373\pi$
$911$	20.9161			0.692982			0.346491	+	0.938053i	$0.387373\pi$
$912$	−0.196275	−	0.339958i	−0.00649930	−	0.0112571i
$913$	1.73188	−	2.99971i	0.0573169	−	0.0992758i
$914$	−37.3681	+	64.7234i	−1.23603	+	2.14086i
$915$	−11.5172	−	19.9484i	−0.380748	−	0.659475i
$916$	59.2038			1.95615
$917$	32.6761	−	13.7348i	1.07906	−	0.453563i
$918$	50.1430			1.65496
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	0.822910	−	0.568171i	$-0.192349\pi$
$919$	−2.44326	−	4.23185i	−0.0805957	−	0.139596i	−0.903506	+	0.428576i	$0.859016\pi$
$920$	−3.40821	+	5.90320i	−0.112366	+	0.194623i
$921$	−37.8880	+	65.6239i	−1.24845	+	2.16238i
$922$	−8.75816	−	15.1696i	−0.288435	−	0.499584i
$923$		0			0
$924$	1.03796	−	8.21468i	0.0341464	−	0.270243i
$925$	−2.68434			−0.0882606
$926$	16.5329	+	28.6358i	0.543305	+	0.941031i
$927$	−20.9198	+	36.2342i	−0.687098	+	1.19009i
$928$	−5.76664	+	9.98812i	−0.189299	+	0.327876i
$929$	−25.7675	−	44.6306i	−0.845404	−	1.46428i	−0.885270	−	0.465077i	$-0.846027\pi$
$929$	−25.7675	−	44.6306i	−0.845404	−	1.46428i	0.0398663	−	0.999205i	$-0.487307\pi$
$930$	70.4355			2.30967
$931$	−3.35261	−	12.0100i	−0.109877	−	0.393611i
$932$	65.2759			2.13818
$933$	14.1626	+	24.5304i	0.463664	+	0.803090i
$934$	−3.85680	+	6.68017i	−0.126198	+	0.218582i
$935$	0.581657	−	1.00746i	0.0190222	−	0.0329474i
$936$		0			0
$937$	20.3565			0.665016			0.332508	−	0.943100i	$-0.392105\pi$
$937$	20.3565			0.665016			0.332508	+	0.943100i	$0.392105\pi$
$938$	−9.55952	+	75.6564i	−0.312129	+	2.47027i
$939$	−48.0002			−1.56643
$940$	−32.5676	−	56.4088i	−1.06224	−	1.83985i
$941$	−17.1317	+	29.6730i	−0.558479	+	0.967314i	0.439145	+	0.898416i	$0.355281\pi$
$941$	−17.1317	+	29.6730i	−0.558479	+	0.967314i	−0.997624	+	0.0688974i	$0.978052\pi$
$942$	0.272013	−	0.471141i	0.00886267	−	0.0153506i
$943$	−3.87108	−	6.70490i	−0.126060	−	0.218342i
$944$	−0.568067			−0.0184890
$945$	−64.0918	+	26.9399i	−2.08491	+	0.876354i
$946$	1.07558			0.0349701
$947$	−27.6578	−	47.9046i	−0.898756	−	1.55669i	−0.829086	−	0.559122i	$-0.811138\pi$
$947$	−27.6578	−	47.9046i	−0.898756	−	1.55669i	−0.0696707	−	0.997570i	$-0.522195\pi$
$948$	40.2025	−	69.6327i	1.30572	−	2.26156i
$949$		0			0
$950$	0.985770	+	1.70740i	0.0319826	+	0.0553955i
$951$	21.5347			0.698311
$952$	−10.4284	−	7.91602i	−0.337988	−	0.256560i
$953$	14.8378			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$953$	14.8378			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$954$	58.8663	+	101.959i	1.90587	+	3.30106i
$955$	−28.4939	+	49.3529i	−0.922041	+	1.59702i
$956$	−33.5075	+	58.0366i	−1.08371	+	1.87704i
$957$	0.976908	+	1.69205i	0.0315790	+	0.0546964i
$958$	0.331812			0.0107203
$959$	1.05589	+	0.801506i	0.0340965	+	0.0258820i
$960$	86.8081			2.80172
$961$	4.89769	+	8.48305i	0.157990	+	0.273647i
$962$		0			0
$963$	−41.8491	+	72.4847i	−1.34857	+	2.33579i
$964$	20.4731	+	35.4604i	0.659393	+	1.14210i
$965$	−0.454714			−0.0146378
$966$	−20.1974	+	8.48964i	−0.649842	+	0.273150i
$967$	3.09473			0.0995199			0.0497600	−	0.998761i	$-0.484154\pi$
$967$	3.09473			0.0995199			0.0497600	+	0.998761i	$0.484154\pi$
$968$	−15.2031	−	26.3326i	−0.488647	−	0.846361i
$969$	−4.97979	+	8.62524i	−0.159974	+	0.277083i
$970$	−18.6110	+	32.2352i	−0.597564	+	1.03501i
$971$	−27.4506	−	47.5459i	−0.880933	−	1.52582i	−0.850305	−	0.526290i	$-0.823583\pi$
$971$	−27.4506	−	47.5459i	−0.880933	−	1.52582i	−0.0306280	−	0.999531i	$-0.509751\pi$
$972$	65.0010			2.08491
$973$	−0.470751	+	3.72564i	−0.0150916	+	0.119439i
$974$	−37.5200			−1.20222
$975$		0			0
$976$	−0.120340	+	0.208435i	−0.00385198	+	0.00667183i
$977$	21.6042	−	37.4196i	0.691181	−	1.19716i	−0.280270	−	0.959921i	$-0.590424\pi$
$977$	21.6042	−	37.4196i	0.691181	−	1.19716i	0.971451	−	0.237239i	$-0.0762425\pi$
$978$	36.2847	+	62.8470i	1.16026	+	2.00962i
$979$	−0.511795			−0.0163570
$980$	46.3973	+	11.9152i	1.48211	+	0.380618i
$981$	−9.43124			−0.301116
$982$	20.8006	+	36.0276i	0.663773	+	1.14969i
$983$	−12.4418	+	21.5498i	−0.396831	+	0.687332i	−0.993333	−	0.115280i	$-0.963224\pi$
$983$	−12.4418	+	21.5498i	−0.396831	+	0.687332i	0.596502	+	0.802612i	$0.296557\pi$
$984$	29.5588	−	51.1973i	0.942299	−	1.63211i
$985$	−11.9308	−	20.6647i	−0.380146	−	0.658433i
$986$	8.15254			0.259630
$987$	9.94538	−	78.7102i	0.316565	−	2.50537i
$988$		0			0
$989$	−0.877834	−	1.52045i	−0.0279135	−	0.0483476i
$990$	5.18578	−	8.98203i	0.164815	−	0.285468i
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	−0.901509	−	0.432760i	$-0.857540\pi$
$991$	−2.39164	+	4.14244i	−0.0759730	+	0.131589i	0.825536	+	0.564349i	$0.190873\pi$
$992$	−13.2078	−	22.8765i	−0.419347	−	0.726331i
$993$	43.5216			1.38112
$994$	−7.52714	+	3.16390i	−0.238746	+	0.100353i
$995$	−43.3925			−1.37564
$996$	−56.9622	−	98.6614i	−1.80492	−	3.12621i
$997$	−1.72037	+	2.97977i	−0.0544847	+	0.0943703i	−0.891981	−	0.452072i	$-0.850685\pi$
$997$	−1.72037	+	2.97977i	−0.0544847	+	0.0943703i	0.837497	+	0.546442i	$0.184018\pi$
$998$	−42.9225	+	74.3439i	−1.35869	+	2.35331i
$999$	−34.2623	−	59.3441i	−1.08401	−	1.87756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.i.508.8		16
7.2	even	3	inner	1183.2.e.i.170.8		16
7.3	odd	6		8281.2.a.cj.1.1		8
7.4	even	3		8281.2.a.ck.1.1		8
13.5	odd	4		91.2.r.a.25.8	yes	16
13.8	odd	4		91.2.r.a.25.1	✓	16
13.12	even	2	inner	1183.2.e.i.508.1		16
39.5	even	4		819.2.dl.e.298.1		16
39.8	even	4		819.2.dl.e.298.8		16
91.5	even	12		637.2.r.f.324.1		16
91.18	odd	12		637.2.c.f.246.8		8
91.25	even	6		8281.2.a.ck.1.8		8
91.31	even	12		637.2.c.e.246.8		8
91.34	even	4		637.2.r.f.116.1		16
91.38	odd	6		8281.2.a.cj.1.8		8
91.44	odd	12		91.2.r.a.51.1	yes	16
91.47	even	12		637.2.r.f.324.8		16
91.51	even	6	inner	1183.2.e.i.170.1		16
91.60	odd	12		637.2.c.f.246.1		8
91.73	even	12		637.2.c.e.246.1		8
91.83	even	4		637.2.r.f.116.8		16
91.86	odd	12		91.2.r.a.51.8	yes	16
273.44	even	12		819.2.dl.e.415.8		16
273.86	even	12		819.2.dl.e.415.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.1	✓	16	13.8	odd	4
91.2.r.a.25.8	yes	16	13.5	odd	4
91.2.r.a.51.1	yes	16	91.44	odd	12
91.2.r.a.51.8	yes	16	91.86	odd	12
637.2.c.e.246.1		8	91.73	even	12
637.2.c.e.246.8		8	91.31	even	12
637.2.c.f.246.1		8	91.60	odd	12
637.2.c.f.246.8		8	91.18	odd	12
637.2.r.f.116.1		16	91.34	even	4
637.2.r.f.116.8		16	91.83	even	4
637.2.r.f.324.1		16	91.5	even	12
637.2.r.f.324.8		16	91.47	even	12
819.2.dl.e.298.1		16	39.5	even	4
819.2.dl.e.298.8		16	39.8	even	4
819.2.dl.e.415.1		16	273.86	even	12
819.2.dl.e.415.8		16	273.44	even	12
1183.2.e.i.170.1		16	91.51	even	6	inner
1183.2.e.i.170.8		16	7.2	even	3	inner
1183.2.e.i.508.1		16	13.12	even	2	inner
1183.2.e.i.508.8		16	1.1	even	1	trivial
8281.2.a.cj.1.1		8	7.3	odd	6
8281.2.a.cj.1.8		8	91.38	odd	6
8281.2.a.ck.1.1		8	7.4	even	3
8281.2.a.ck.1.8		8	91.25	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14241 + 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(1.06250 + 1.84030i) q^{5} -7.19813 q^{6} +(-0.331665 + 2.62488i) q^{7} -2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +O(q^{10})\)	\(q+(1.14241 + 1.97871i) q^{2} +(-1.57521 + 2.72835i) q^{3} +(-1.61019 + 2.78892i) q^{4} +(1.06250 + 1.84030i) q^{5} -7.19813 q^{6} +(-0.331665 + 2.62488i) q^{7} -2.78832 q^{8} +(-3.46258 - 5.99736i) q^{9} +(-2.42760 + 4.20473i) q^{10} +(0.154233 - 0.267139i) q^{11} +(-5.07276 - 8.78629i) q^{12} +(-5.57276 + 2.34241i) q^{14} -6.69462 q^{15} +(0.0349749 + 0.0605784i) q^{16} +(0.887368 - 1.53697i) q^{17} +(7.91135 - 13.7029i) q^{18} +(0.890653 + 1.54266i) q^{19} -6.84326 q^{20} +(-6.63914 - 5.03964i) q^{21} +0.704786 q^{22} +(-0.575211 - 0.996294i) q^{23} +(4.39219 - 7.60750i) q^{24} +(0.242207 - 0.419515i) q^{25} +12.3659 q^{27} +(-6.78655 - 5.15153i) q^{28} +2.01052 q^{29} +(-7.64798 - 13.2467i) q^{30} +(-2.30242 + 3.98791i) q^{31} +(-2.86823 + 4.96792i) q^{32} +(0.485898 + 0.841600i) q^{33} +4.05494 q^{34} +(-5.18295 + 2.17856i) q^{35} +22.3016 q^{36} +(-2.77071 - 4.79901i) q^{37} +(-2.03497 + 3.52468i) q^{38} +(-2.96258 - 5.13134i) q^{40} +6.72984 q^{41} +(2.38737 - 18.8942i) q^{42} +1.52611 q^{43} +(0.496686 + 0.860286i) q^{44} +(7.35795 - 12.7443i) q^{45} +(1.31425 - 2.27635i) q^{46} +(4.75908 + 8.24297i) q^{47} -0.220372 q^{48} +(-6.78000 - 1.74116i) q^{49} +1.10680 q^{50} +(2.79558 + 4.84209i) q^{51} +(-3.72037 + 6.44387i) q^{53} +(14.1269 + 24.4685i) q^{54} +0.655486 q^{55} +(0.924789 - 7.31901i) q^{56} -5.61186 q^{57} +(2.29683 + 3.97823i) q^{58} +(-4.06053 + 7.03304i) q^{59} +(10.7796 - 18.6708i) q^{60} +(1.72037 + 2.97977i) q^{61} -10.5212 q^{62} +(16.8908 - 7.09974i) q^{63} -12.9669 q^{64} +(-1.11019 + 1.92290i) q^{66} +(6.30747 - 10.9249i) q^{67} +(2.85765 + 4.94960i) q^{68} +3.62431 q^{69} +(-10.2318 - 7.76673i) q^{70} +1.35070 q^{71} +(9.65478 + 16.7226i) q^{72} +(5.94059 - 10.2894i) q^{73} +(6.33056 - 10.9648i) q^{74} +(0.763054 + 1.32165i) q^{75} -5.73646 q^{76} +(0.650054 + 0.493443i) q^{77} +(3.96258 + 6.86339i) q^{79} +(-0.0743214 + 0.128728i) q^{80} +(-9.09116 + 15.7464i) q^{81} +(7.68821 + 13.3164i) q^{82} +11.2290 q^{83} +(24.7454 - 10.4013i) q^{84} +3.77130 q^{85} +(1.74344 + 3.01972i) q^{86} +(-3.16700 + 5.48540i) q^{87} +(-0.430050 + 0.744869i) q^{88} +(-0.829583 - 1.43688i) q^{89} +33.6231 q^{90} +3.70479 q^{92} +(-7.25360 - 12.5636i) q^{93} +(-10.8736 + 18.8336i) q^{94} +(-1.89263 + 3.27813i) q^{95} +(-9.03614 - 15.6511i) q^{96} +7.66641 q^{97} +(-4.30026 - 15.4047i) q^{98} -2.13617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9	\( 16 q - 4 q^{3} - 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} - 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 32 q^{27} - 16 q^{29} - 38 q^{30} + 56 q^{36} - 34 q^{38} - 4 q^{40} + 16 q^{42} - 16 q^{43} + 36 q^{48} - 40 q^{49} - 16 q^{51} - 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} - 88 q^{64} + 2 q^{66} - 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 76 q^{77} + 20 q^{79} - 24 q^{81} + 16 q^{82} - 68 q^{87} - 4 q^{88} + 216 q^{90} + 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q - 4 * q^3 - 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 - 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 32 * q^27 - 16 * q^29 - 38 * q^30 + 56 * q^36 - 34 * q^38 - 4 * q^40 + 16 * q^42 - 16 * q^43 + 36 * q^48 - 40 * q^49 - 16 * q^51 - 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 - 88 * q^64 + 2 * q^66 - 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 76 * q^77 + 20 * q^79 - 24 * q^81 + 16 * q^82 - 68 * q^87 - 4 * q^88 + 216 * q^90 + 12 * q^92 - 26 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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