LMFDB - Embedded newform 1183.2.e.j.170.11

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.11
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.j.508.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15163 - 1.99469i) q^{2} +(0.736680 + 1.27597i) q^{3} +(-1.65252 - 2.86225i) q^{4} +(0.423646 - 0.733776i) q^{5} +3.39354 q^{6} +(1.00088 + 2.44913i) q^{7} -3.00585 q^{8} +(0.414604 - 0.718115i) q^{9} +O(q^{10})$	\(q+(1.15163 - 1.99469i) q^{2} +(0.736680 + 1.27597i) q^{3} +(-1.65252 - 2.86225i) q^{4} +(0.423646 - 0.733776i) q^{5} +3.39354 q^{6} +(1.00088 + 2.44913i) q^{7} -3.00585 q^{8} +(0.414604 - 0.718115i) q^{9} +(-0.975769 - 1.69008i) q^{10} +(-0.751701 - 1.30198i) q^{11} +(2.43476 - 4.21712i) q^{12} +(6.03790 + 0.824057i) q^{14} +1.24837 q^{15} +(-0.156597 + 0.271234i) q^{16} +(-1.03570 - 1.79389i) q^{17} +(-0.954943 - 1.65401i) q^{18} +(-0.0237136 + 0.0410731i) q^{19} -2.80033 q^{20} +(-2.38768 + 3.08132i) q^{21} -3.46274 q^{22} +(3.90935 - 6.77119i) q^{23} +(-2.21435 - 3.83536i) q^{24} +(2.14105 + 3.70840i) q^{25} +5.64180 q^{27} +(5.35604 - 6.91200i) q^{28} +1.35971 q^{29} +(1.43766 - 2.49010i) q^{30} +(3.93052 + 6.80787i) q^{31} +(-2.64516 - 4.58156i) q^{32} +(1.10753 - 1.91829i) q^{33} -4.77099 q^{34} +(2.22113 + 0.303142i) q^{35} -2.74056 q^{36} +(3.35110 - 5.80427i) q^{37} +(0.0546187 + 0.0946024i) q^{38} +(-1.27341 + 2.20562i) q^{40} -10.0184 q^{41} +(3.39653 + 8.31123i) q^{42} +9.26566 q^{43} +(-2.48440 + 4.30311i) q^{44} +(-0.351290 - 0.608453i) q^{45} +(-9.00428 - 15.5959i) q^{46} +(0.180007 - 0.311781i) q^{47} -0.461448 q^{48} +(-4.99648 + 4.90257i) q^{49} +9.86281 q^{50} +(1.52596 - 2.64304i) q^{51} +(-1.35591 - 2.34850i) q^{53} +(6.49729 - 11.2536i) q^{54} -1.27382 q^{55} +(-3.00849 - 7.36171i) q^{56} -0.0698773 q^{57} +(1.56588 - 2.71219i) q^{58} +(0.820598 + 1.42132i) q^{59} +(-2.06295 - 3.57313i) q^{60} +(-2.26097 + 3.91612i) q^{61} +18.1061 q^{62} +(2.17373 + 0.296672i) q^{63} -12.8114 q^{64} +(-2.55093 - 4.41834i) q^{66} +(-1.02133 - 1.76900i) q^{67} +(-3.42303 + 5.92886i) q^{68} +11.5198 q^{69} +(3.16260 - 4.08136i) q^{70} -14.2139 q^{71} +(-1.24624 + 2.15854i) q^{72} +(3.38075 + 5.85563i) q^{73} +(-7.71847 - 13.3688i) q^{74} +(-3.15454 + 5.46382i) q^{75} +0.156749 q^{76} +(2.43637 - 3.14414i) q^{77} +(-5.82952 + 10.0970i) q^{79} +(0.132683 + 0.229814i) q^{80} +(2.91240 + 5.04442i) q^{81} +(-11.5376 + 19.9837i) q^{82} -11.5362 q^{83} +(12.7652 + 1.74220i) q^{84} -1.75508 q^{85} +(10.6706 - 18.4821i) q^{86} +(1.00167 + 1.73494i) q^{87} +(2.25950 + 3.91357i) q^{88} +(-8.75561 + 15.1652i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(-5.79108 + 10.0304i) q^{93} +(-0.414604 - 0.718115i) q^{94} +(0.0200923 + 0.0348009i) q^{95} +(3.89728 - 6.75029i) q^{96} -0.426229 q^{97} +(4.02499 + 15.6124i) q^{98} -1.24663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.15163	−	1.99469i	0.814328	−	1.41046i	−0.0954820	−	0.995431i	$-0.530439\pi$
$2$	1.15163	−	1.99469i	0.814328	−	1.41046i	0.909810	−	0.415026i	$-0.136227\pi$
$3$	0.736680	+	1.27597i	0.425323	+	0.736680i	0.996451	−	0.0841807i	$-0.0268273\pi$
$3$	0.736680	+	1.27597i	0.425323	+	0.736680i	−0.571128	+	0.820861i	$0.693494\pi$
$4$	−1.65252	−	2.86225i	−0.826259	−	1.43112i
$5$	0.423646	−	0.733776i	0.189460	−	0.328155i	−0.755610	−	0.655022i	$-0.772660\pi$
$5$	0.423646	−	0.733776i	0.189460	−	0.328155i	0.945070	+	0.326867i	$0.105993\pi$
$6$	3.39354			1.38541
$7$	1.00088	+	2.44913i	0.378297	+	0.925684i
$7$	1.00088	+	2.44913i	0.378297	+	0.925684i
$8$	−3.00585			−1.06273
$9$	0.414604	−	0.718115i	0.138201	−	0.239372i
$10$	−0.975769	−	1.69008i	−0.308565	−	0.534451i
$11$	−0.751701	−	1.30198i	−0.226646	−	0.392563i	0.730166	−	0.683270i	$-0.239443\pi$
$11$	−0.751701	−	1.30198i	−0.226646	−	0.392563i	−0.956812	+	0.290707i	$0.906110\pi$
$12$	2.43476	−	4.21712i	0.702853	−	1.21738i
$13$		0			0
$13$		0			0
$14$	6.03790	+	0.824057i	1.61370	+	0.220238i
$15$	1.24837			0.322327
$16$	−0.156597	+	0.271234i	−0.0391492	+	0.0678085i
$17$	−1.03570	−	1.79389i	−0.251194	−	0.435081i	0.712661	−	0.701509i	$-0.247490\pi$
$17$	−1.03570	−	1.79389i	−0.251194	−	0.435081i	−0.963855	+	0.266428i	$0.914157\pi$
$18$	−0.954943	−	1.65401i	−0.225082	−	0.389854i
$19$	−0.0237136	+	0.0410731i	−0.00544027	+	0.00942282i	−0.868733	−	0.495281i	$-0.835065\pi$
$19$	−0.0237136	+	0.0410731i	−0.00544027	+	0.00942282i	0.863292	+	0.504704i	$0.168398\pi$
$20$	−2.80033			−0.626173
$21$	−2.38768	+	3.08132i	−0.521035	+	0.672399i
$22$	−3.46274			−0.738258
$23$	3.90935	−	6.77119i	0.815156	−	1.41189i	−0.0940598	−	0.995567i	$-0.529984\pi$
$23$	3.90935	−	6.77119i	0.815156	−	1.41189i	0.909216	−	0.416325i	$-0.136682\pi$
$24$	−2.21435	−	3.83536i	−0.452002	−	0.782891i
$25$	2.14105	+	3.70840i	0.428210	+	0.741681i
$26$		0			0
$27$	5.64180			1.08577
$28$	5.35604	−	6.91200i	1.01220	−	1.30624i
$29$	1.35971			0.252491			0.126246	−	0.991999i	$-0.459707\pi$
$29$	1.35971			0.252491			0.126246	+	0.991999i	$0.459707\pi$
$30$	1.43766	−	2.49010i	0.262480	−	0.454628i
$31$	3.93052	+	6.80787i	0.705943	+	1.22273i	0.966350	+	0.257230i	$0.0828099\pi$
$31$	3.93052	+	6.80787i	0.705943	+	1.22273i	−0.260407	+	0.965499i	$0.583857\pi$
$32$	−2.64516	−	4.58156i	−0.467603	−	0.809912i
$33$	1.10753	−	1.91829i	0.192796	−	0.333932i
$34$	−4.77099			−0.818218
$35$	2.22113	+	0.303142i	0.375440	+	0.0512403i
$36$	−2.74056			−0.456760
$37$	3.35110	−	5.80427i	0.550917	−	0.954216i	−0.447292	−	0.894388i	$-0.647612\pi$
$37$	3.35110	−	5.80427i	0.550917	−	0.954216i	0.998209	−	0.0598278i	$-0.0190551\pi$
$38$	0.0546187	+	0.0946024i	0.00886032	+	0.0153465i
$39$		0			0
$40$	−1.27341	+	2.20562i	−0.201345	+	0.348739i
$41$	−10.0184			−1.56462			−0.782309	−	0.622891i	$-0.785958\pi$
$41$	−10.0184			−1.56462			−0.782309	+	0.622891i	$0.785958\pi$
$42$	3.39653	+	8.31123i	0.524096	+	1.28245i
$43$	9.26566			1.41300			0.706500	−	0.707713i	$-0.250273\pi$
$43$	9.26566			1.41300			0.706500	+	0.707713i	$0.250273\pi$
$44$	−2.48440	+	4.30311i	−0.374537	+	0.648718i
$45$	−0.351290	−	0.608453i	−0.0523673	−	0.0907028i
$46$	−9.00428	−	15.5959i	−1.32761	−	2.29948i
$47$	0.180007	−	0.311781i	0.0262567	−	0.0454779i	−0.852598	−	0.522567i	$-0.824975\pi$
$47$	0.180007	−	0.311781i	0.0262567	−	0.0454779i	0.878855	+	0.477089i	$0.158308\pi$
$48$	−0.461448			−0.0666042
$49$	−4.99648	+	4.90257i	−0.713782	+	0.700367i
$50$	9.86281			1.39481
$51$	1.52596	−	2.64304i	0.213677	−	0.370100i
$52$		0			0
$53$	−1.35591	−	2.34850i	−0.186248	−	0.322591i	0.757748	−	0.652547i	$-0.226299\pi$
$53$	−1.35591	−	2.34850i	−0.186248	−	0.322591i	−0.943996	+	0.329956i	$0.892966\pi$
$54$	6.49729	−	11.2536i	0.884169	−	1.53143i
$55$	−1.27382			−0.171762
$56$	−3.00849	−	7.36171i	−0.402027	−	0.983750i
$57$	−0.0698773			−0.00925548
$58$	1.56588	−	2.71219i	0.205611	−	0.356128i
$59$	0.820598	+	1.42132i	0.106833	+	0.185040i	0.914486	−	0.404619i	$-0.132596\pi$
$59$	0.820598	+	1.42132i	0.106833	+	0.185040i	−0.807653	+	0.589658i	$0.799262\pi$
$60$	−2.06295	−	3.57313i	−0.266325	−	0.461289i
$61$	−2.26097	+	3.91612i	−0.289488	+	0.501407i	−0.973688	−	0.227887i	$-0.926818\pi$
$61$	−2.26097	+	3.91612i	−0.289488	+	0.501407i	0.684200	+	0.729295i	$0.260152\pi$
$62$	18.1061			2.29948
$63$	2.17373	+	0.296672i	0.273864	+	0.0373771i
$64$	−12.8114			−1.60143
$65$		0			0
$66$	−2.55093	−	4.41834i	−0.313998	−	0.543860i
$67$	−1.02133	−	1.76900i	−0.124775	−	0.216117i	0.796870	−	0.604151i	$-0.206488\pi$
$67$	−1.02133	−	1.76900i	−0.124775	−	0.216117i	−0.921645	+	0.388034i	$0.873154\pi$
$68$	−3.42303	+	5.92886i	−0.415103	+	0.718980i
$69$	11.5198			1.38682
$70$	3.16260	−	4.08136i	0.378003	−	0.487815i
$71$	−14.2139			−1.68688			−0.843442	−	0.537220i	$-0.819474\pi$
$71$	−14.2139			−1.68688			−0.843442	+	0.537220i	$0.819474\pi$
$72$	−1.24624	+	2.15854i	−0.146870	+	0.254387i
$73$	3.38075	+	5.85563i	0.395687	+	0.685349i	0.993189	−	0.116518i	$-0.0371733\pi$
$73$	3.38075	+	5.85563i	0.395687	+	0.685349i	−0.597502	+	0.801867i	$0.703840\pi$
$74$	−7.71847	−	13.3688i	−0.897253	−	1.55409i
$75$	−3.15454	+	5.46382i	−0.364255	+	0.630907i
$76$	0.156749			0.0179803
$77$	2.43637	−	3.14414i	0.277650	−	0.358308i
$78$		0			0
$79$	−5.82952	+	10.0970i	−0.655873	+	1.13600i	0.325801	+	0.945438i	$0.394366\pi$
$79$	−5.82952	+	10.0970i	−0.655873	+	1.13600i	−0.981674	+	0.190567i	$0.938967\pi$
$80$	0.132683	+	0.229814i	0.0148344	+	0.0256940i
$81$	2.91240	+	5.04442i	0.323600	+	0.560491i
$82$	−11.5376	+	19.9837i	−1.27411	+	2.20683i
$83$	−11.5362			−1.26627			−0.633133	−	0.774043i	$-0.718232\pi$
$83$	−11.5362			−1.26627			−0.633133	+	0.774043i	$0.718232\pi$
$84$	12.7652	+	1.74220i	1.39280	+	0.190090i
$85$	−1.75508			−0.190365
$86$	10.6706	−	18.4821i	1.15065	−	1.99298i
$87$	1.00167	+	1.73494i	0.107390	+	0.186006i
$88$	2.25950	+	3.91357i	0.240863	+	0.417188i
$89$	−8.75561	+	15.1652i	−0.928093	+	1.60750i	−0.141582	+	0.989927i	$0.545219\pi$
$89$	−8.75561	+	15.1652i	−0.928093	+	1.60750i	−0.786510	+	0.617577i	$0.788114\pi$
$90$	−1.61823			−0.170576
$91$		0			0
$92$	−25.8411			−2.69412
$93$	−5.79108	+	10.0304i	−0.600507	+	1.04011i
$94$	−0.414604	−	0.718115i	−0.0427631	−	0.0740679i
$95$	0.0200923	+	0.0348009i	0.00206143	+	0.00357050i
$96$	3.89728	−	6.75029i	0.397764	−	0.688948i
$97$	−0.426229			−0.0432770			−0.0216385	−	0.999766i	$-0.506888\pi$
$97$	−0.426229			−0.0432770			−0.0216385	+	0.999766i	$0.506888\pi$
$98$	4.02499	+	15.6124i	0.406585	+	1.57709i
$99$	−1.24663			−0.125291
$100$	7.07624	−	12.2564i	0.707624	−	1.22564i
$101$	−4.83499	−	8.37444i	−0.481099	−	0.833288i	0.518666	−	0.854977i	$-0.326429\pi$
$101$	−4.83499	−	8.37444i	−0.481099	−	0.833288i	−0.999765	+	0.0216891i	$0.993096\pi$
$102$	−3.51469	−	6.08763i	−0.348007	−	0.602765i
$103$	4.98912	−	8.64140i	0.491592	−	0.851463i	−0.508361	−	0.861144i	$-0.669748\pi$
$103$	4.98912	−	8.64140i	0.491592	−	0.851463i	0.999953	+	0.00968129i	$0.00308170\pi$
$104$		0			0
$105$	1.24947	+	3.05741i	0.121935	+	0.298373i
$106$	−6.24603			−0.606668
$107$	−4.93111	+	8.54094i	−0.476709	+	0.825684i	−0.999644	−	0.0266888i	$-0.991504\pi$
$107$	−4.93111	+	8.54094i	−0.476709	+	0.825684i	0.522935	+	0.852373i	$0.324837\pi$
$108$	−9.32319	−	16.1482i	−0.897124	−	1.55386i
$109$	5.80275	+	10.0507i	0.555803	+	0.962679i	0.997841	+	0.0656822i	$0.0209224\pi$
$109$	5.80275	+	10.0507i	0.555803	+	0.962679i	−0.442038	+	0.896996i	$0.645744\pi$
$110$	−1.46697	+	2.54087i	−0.139870	+	0.242263i
$111$	9.87475			0.937269
$112$	−0.821022	−	0.112054i	−0.0775793	−	0.0105881i
$113$	−3.47758			−0.327143			−0.163572	−	0.986531i	$-0.552301\pi$
$113$	−3.47758			−0.327143			−0.163572	+	0.986531i	$0.552301\pi$
$114$	−0.0804731	+	0.139383i	−0.00753699	+	0.0130545i
$115$	−3.31236	−	5.73718i	−0.308879	−	0.534994i
$116$	−2.24694	−	3.89182i	−0.208623	−	0.361346i
$117$		0			0
$118$	3.78011			0.347987
$119$	3.35685	−	4.33203i	0.307722	−	0.397117i
$120$	−3.75240			−0.342546
$121$	4.36989	−	7.56887i	0.397263	−	0.688079i
$122$	5.20762	+	9.01986i	0.471476	+	0.816620i
$123$	−7.38039	−	12.7832i	−0.665467	−	1.15262i
$124$	12.9905	−	22.5003i	1.16658	−	2.02058i
$125$	7.86464			0.703435
$126$	3.09510	−	3.99425i	0.275734	−	0.355836i
$127$	−15.6998			−1.39313			−0.696567	−	0.717491i	$-0.745290\pi$
$127$	−15.6998			−1.39313			−0.696567	+	0.717491i	$0.745290\pi$
$128$	−9.46373	+	16.3917i	−0.836483	+	1.44883i
$129$	6.82583	+	11.8227i	0.600981	+	1.04093i
$130$		0			0
$131$	1.27259	−	2.20418i	0.111186	−	0.192580i	−0.805063	−	0.593190i	$-0.797868\pi$
$131$	1.27259	−	2.20418i	0.111186	−	0.192580i	0.916249	+	0.400610i	$0.131202\pi$
$132$	−7.32083			−0.637197
$133$	−0.124328	−	0.0169684i	−0.0107806	−	0.00147134i
$134$	−4.70479			−0.406432
$135$	2.39013	−	4.13982i	0.205709	−	0.356299i
$136$	3.11316	+	5.39215i	0.266951	+	0.462373i
$137$	−0.932362	−	1.61490i	−0.0796571	−	0.137970i	0.823445	−	0.567396i	$-0.192049\pi$
$137$	−0.932362	−	1.61490i	−0.0796571	−	0.137970i	−0.903102	+	0.429426i	$0.858716\pi$
$138$	13.2665	−	22.9783i	1.12932	−	1.95605i
$139$	15.6092			1.32396			0.661979	−	0.749522i	$-0.269717\pi$
$139$	15.6092			1.32396			0.661979	+	0.749522i	$0.269717\pi$
$140$	−2.80280	−	6.85837i	−0.236879	−	0.579638i
$141$	0.530430			0.0446703
$142$	−16.3692	+	28.3524i	−1.37368	+	2.37928i
$143$		0			0
$144$	0.129851	+	0.224909i	0.0108209	+	0.0187424i
$145$	0.576035	−	0.997721i	0.0478371	−	0.0828562i
$146$	15.5735			1.28887
$147$	−9.93633	−	2.76372i	−0.819535	−	0.227947i
$148$	−22.1510			−1.82080
$149$	−3.18181	+	5.51106i	−0.260664	+	0.451484i	−0.966419	−	0.256973i	$-0.917275\pi$
$149$	−3.18181	+	5.51106i	−0.260664	+	0.451484i	0.705754	+	0.708457i	$0.250608\pi$
$150$	7.26574	+	12.5846i	0.593245	+	1.02753i
$151$	0.332047	+	0.575122i	0.0270216	+	0.0468028i	0.879220	−	0.476416i	$-0.158064\pi$
$151$	0.332047	+	0.575122i	0.0270216	+	0.0468028i	−0.852198	+	0.523219i	$0.824731\pi$
$152$	0.0712794	−	0.123460i	0.00578152	−	0.0100139i
$153$	−1.71762			−0.138861
$154$	−3.46578	−	8.48069i	−0.279281	−	0.683393i
$155$	6.66060			0.534992
$156$		0			0
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	0.980234	+	0.197842i	$0.0633933\pi$
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	−0.318781	+	0.947828i	$0.603273\pi$
$158$	13.4269	+	23.2562i	1.06819	+	1.85016i
$159$	1.99774	−	3.46019i	0.158431	−	0.274411i
$160$	−4.48245			−0.354369
$161$	20.4963	+	2.79735i	1.61534	+	0.220462i
$162$	13.4160			1.05406
$163$	4.52563	−	7.83863i	0.354475	−	0.613969i	−0.632553	−	0.774517i	$-0.717993\pi$
$163$	4.52563	−	7.83863i	0.354475	−	0.613969i	0.987028	+	0.160548i	$0.0513263\pi$
$164$	16.5557	+	28.6752i	1.29278	+	2.23916i
$165$	−0.938398	−	1.62535i	−0.0730542	−	0.126534i
$166$	−13.2855	+	23.0112i	−1.03116	+	1.78601i
$167$	2.65761			0.205652			0.102826	−	0.994699i	$-0.467212\pi$
$167$	2.65761			0.205652			0.102826	+	0.994699i	$0.467212\pi$
$168$	7.17701	−	9.26197i	0.553718	−	0.714576i
$169$		0			0
$170$	−2.02121	+	3.50084i	−0.155020	+	0.268502i
$171$	0.0196635	+	0.0340582i	0.00150370	+	0.00260449i
$172$	−15.3117	−	26.5206i	−1.16750	−	2.02218i
$173$	−9.79352	+	16.9629i	−0.744588	+	1.28966i	0.205799	+	0.978594i	$0.434021\pi$
$173$	−9.79352	+	16.9629i	−0.744588	+	1.28966i	−0.950387	+	0.311070i	$0.899313\pi$
$174$	4.61423			0.349804
$175$	−6.93943	+	8.95538i	−0.524572	+	0.676963i
$176$	0.470856			0.0354921
$177$	−1.20904	+	2.09411i	−0.0908768	+	0.157403i
$178$	20.1665	+	34.9294i	1.51154	+	2.61807i
$179$	1.44666	+	2.50569i	0.108129	+	0.187284i	0.915012	−	0.403426i	$-0.132181\pi$
$179$	1.44666	+	2.50569i	0.108129	+	0.187284i	−0.806884	+	0.590711i	$0.798848\pi$
$180$	−1.16103	+	2.01096i	−0.0865379	+	0.149888i
$181$	1.36804			0.101686			0.0508429	−	0.998707i	$-0.483809\pi$
$181$	1.36804			0.101686			0.0508429	+	0.998707i	$0.483809\pi$
$182$		0			0
$183$	−6.66245			−0.492503
$184$	−11.7509	+	20.3532i	−0.866289	+	1.50046i
$185$	−2.83936	−	4.91791i	−0.208754	−	0.361572i
$186$	13.3384	+	23.1028i	0.978019	+	1.69398i
$187$	−1.55707	+	2.69693i	−0.113865	+	0.197219i
$188$	−1.18986			−0.0867794
$189$	5.64677	+	13.8175i	0.410742	+	1.00508i
$190$	0.0925559			0.00671471
$191$	0.756625	−	1.31051i	0.0547475	−	0.0948254i	−0.837353	−	0.546663i	$-0.815898\pi$
$191$	0.756625	−	1.31051i	0.0547475	−	0.0948254i	0.892100	+	0.451837i	$0.149231\pi$
$192$	−9.43792	−	16.3470i	−0.681123	−	1.17974i
$193$	3.47697	+	6.02229i	0.250278	+	0.433494i	0.963602	−	0.267340i	$-0.0861447\pi$
$193$	3.47697	+	6.02229i	0.250278	+	0.433494i	−0.713324	+	0.700834i	$0.752811\pi$
$194$	−0.490860	+	0.850194i	−0.0352417	+	0.0610404i
$195$		0			0
$196$	22.2891	+	6.19955i	1.59208	+	0.442825i
$197$	−15.4772			−1.10271			−0.551353	−	0.834272i	$-0.685888\pi$
$197$	−15.4772			−1.10271			−0.551353	+	0.834272i	$0.685888\pi$
$198$	−1.43566	+	2.48664i	−0.102028	+	0.176718i
$199$	−3.30764	−	5.72901i	−0.234473	−	0.406118i	0.724647	−	0.689121i	$-0.242003\pi$
$199$	−3.30764	−	5.72901i	−0.234473	−	0.406118i	−0.959119	+	0.283002i	$0.908670\pi$
$200$	−6.43566	−	11.1469i	−0.455070	−	0.788205i
$201$	1.50479	−	2.60637i	0.106140	−	0.183839i
$202$	−22.2725			−1.56709
$203$	1.36090	+	3.33010i	0.0955168	+	0.233727i
$204$	−10.0867			−0.706211
$205$	−4.24427	+	7.35129i	−0.296433	+	0.513436i
$206$	−11.4913	−	19.9035i	−0.800634	−	1.38674i
$207$	−3.24166	−	5.61473i	−0.225311	−	0.390250i
$208$		0			0
$209$	0.0713021			0.00493207
$210$	7.53751	+	1.02872i	0.520137	+	0.0709887i
$211$	−8.09428			−0.557234			−0.278617	−	0.960402i	$-0.589876\pi$
$211$	−8.09428			−0.557234			−0.278617	+	0.960402i	$0.589876\pi$
$212$	−4.48132	+	7.76187i	−0.307778	+	0.533088i
$213$	−10.4711	−	18.1365i	−0.717470	−	1.24269i
$214$	11.3577	+	19.6721i	0.776394	+	1.34475i
$215$	3.92536	−	6.79892i	0.267707	−	0.463683i
$216$	−16.9584			−1.15387
$217$	−12.7394	+	16.4402i	−0.864805	+	1.11604i
$218$	26.7306			1.81042
$219$	−4.98106	+	8.62745i	−0.336589	+	0.582989i
$220$	2.10501	+	3.64599i	0.141920	+	0.245812i
$221$		0			0
$222$	11.3721	−	19.6970i	0.763244	−	1.32198i
$223$	16.0581			1.07533			0.537664	−	0.843159i	$-0.319307\pi$
$223$	16.0581			1.07533			0.537664	+	0.843159i	$0.319307\pi$
$224$	8.57334	−	11.0639i	0.572830	−	0.739240i
$225$	3.55075			0.236716
$226$	−4.00490	+	6.93668i	−0.266402	+	0.461421i
$227$	0.647903	+	1.12220i	0.0430029	+	0.0744831i	0.886726	−	0.462296i	$-0.152974\pi$
$227$	0.647903	+	1.12220i	0.0430029	+	0.0744831i	−0.843723	+	0.536779i	$0.819641\pi$
$228$	0.115474	+	0.200006i	0.00764742	+	0.0132457i
$229$	−10.4088	+	18.0285i	−0.687831	+	1.19136i	0.284707	+	0.958614i	$0.408104\pi$
$229$	−10.4088	+	18.0285i	−0.687831	+	1.19136i	−0.972538	+	0.232743i	$0.925230\pi$
$230$	−15.2585			−1.00612
$231$	5.80665	+	0.792496i	0.382050	+	0.0521424i
$232$	−4.08707			−0.268330
$233$	6.65213	−	11.5218i	0.435796	−	0.754820i	−0.561565	−	0.827433i	$-0.689800\pi$
$233$	6.65213	−	11.5218i	0.435796	−	0.754820i	0.997360	+	0.0726127i	$0.0231337\pi$
$234$		0			0
$235$	−0.152518	−	0.264169i	−0.00994920	−	0.0172325i
$236$	2.71211	−	4.69751i	0.176543	−	0.305782i
$237$	−17.1780			−1.11583
$238$	−4.77519	−	11.6848i	−0.309530	−	0.757411i
$239$	−13.3652			−0.864525			−0.432263	−	0.901748i	$-0.642285\pi$
$239$	−13.3652			−0.864525			−0.432263	+	0.901748i	$0.642285\pi$
$240$	−0.195490	+	0.338599i	−0.0126188	+	0.0218565i
$241$	−0.417076	−	0.722398i	−0.0268663	−	0.0465337i	0.852280	−	0.523086i	$-0.175219\pi$
$241$	−0.417076	−	0.722398i	−0.0268663	−	0.0465337i	−0.879146	+	0.476553i	$0.841886\pi$
$242$	−10.0650	−	17.4331i	−0.647004	−	1.12064i
$243$	4.17170	−	7.22559i	0.267614	−	0.463522i
$244$	14.9452			0.956767
$245$	1.48065	+	5.74325i	0.0945955	+	0.366923i
$246$	−33.9980			−2.16763
$247$		0			0
$248$	−11.8146	−	20.4634i	−0.750225	−	1.29943i
$249$	−8.49852	−	14.7199i	−0.538572	−	0.932834i
$250$	9.05718	−	15.6875i	0.572827	−	0.992165i
$251$	27.2721			1.72140			0.860699	−	0.509114i	$-0.170027\pi$
$251$	27.2721			1.72140			0.860699	+	0.509114i	$0.170027\pi$
$252$	−2.74297	−	6.71199i	−0.172791	−	0.422816i
$253$	−11.7547			−0.739009
$254$	−18.0804	+	31.3163i	−1.13447	+	1.96496i
$255$	−1.29293	−	2.23943i	−0.0809667	−	0.140238i
$256$	8.98607	+	15.5643i	0.561630	+	0.972771i
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	−0.949925	−	0.312479i	$-0.898841\pi$
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	0.745577	+	0.666419i	$0.232174\pi$
$258$	31.4434			1.95758
$259$	17.5695	+	2.39789i	1.09171	+	0.148998i
$260$		0			0
$261$	0.563740	−	0.976426i	0.0348946	−	0.0604393i
$262$	−2.93110	−	5.07682i	−0.181084	−	0.313647i
$263$	11.2945	+	19.5627i	0.696450	+	1.20629i	0.969689	+	0.244341i	$0.0785717\pi$
$263$	11.2945	+	19.5627i	0.696450	+	1.20629i	−0.273239	+	0.961946i	$0.588095\pi$
$264$	−3.32906	+	5.76610i	−0.204889	+	0.354879i
$265$	−2.29770			−0.141146
$266$	−0.177027	+	0.228454i	−0.0108542	+	0.0140074i
$267$	−25.8003			−1.57896
$268$	−3.37553	+	5.84660i	−0.206194	+	0.357138i
$269$	−8.00065	−	13.8575i	−0.487808	−	0.844909i	0.512093	−	0.858930i	$-0.328870\pi$
$269$	−8.00065	−	13.8575i	−0.487808	−	0.844909i	−0.999902	+	0.0140210i	$0.995537\pi$
$270$	−5.50510	−	9.53511i	−0.335030	−	0.580288i
$271$	4.37967	−	7.58582i	0.266046	−	0.460806i	−0.701791	−	0.712383i	$-0.747616\pi$
$271$	4.37967	−	7.58582i	0.266046	−	0.460806i	0.967837	+	0.251577i	$0.0809493\pi$
$272$	0.648750			0.0393363
$273$		0			0
$274$	−4.29496			−0.259468
$275$	3.21886	−	5.57522i	0.194104	−	0.336199i
$276$	−19.0366	−	32.9724i	−1.14587	−	1.98471i
$277$	9.95914	+	17.2497i	0.598387	+	1.03644i	0.993059	+	0.117614i	$0.0375246\pi$
$277$	9.95914	+	17.2497i	0.598387	+	1.03644i	−0.394673	+	0.918822i	$0.629142\pi$
$278$	17.9761	−	31.1355i	1.07814	−	1.86739i
$279$	6.51844			0.390249
$280$	−6.67638	−	0.911198i	−0.398990	−	0.0544545i
$281$	−14.0234			−0.836566			−0.418283	−	0.908317i	$-0.637368\pi$
$281$	−14.0234			−0.836566			−0.418283	+	0.908317i	$0.637368\pi$
$282$	0.610861	−	1.05804i	0.0363762	−	0.0630055i
$283$	−0.506295	−	0.876929i	−0.0300961	−	0.0521280i	0.850585	−	0.525838i	$-0.176248\pi$
$283$	−0.506295	−	0.876929i	−0.0300961	−	0.0521280i	−0.880681	+	0.473710i	$0.842915\pi$
$284$	23.4888	+	40.6838i	1.39380	+	2.41414i
$285$	−0.0296032	+	0.0512743i	−0.00175354	+	0.00303723i
$286$		0			0
$287$	−10.0273	−	24.5365i	−0.591890	−	1.44834i
$288$	−4.38678			−0.258493
$289$	6.35465	−	11.0066i	0.373803	−	0.647446i
$290$	−1.32676	−	2.29802i	−0.0779101	−	0.134944i
$291$	−0.313995	−	0.543855i	−0.0184067	−	0.0318813i
$292$	11.1735	−	19.3531i	0.653879	−	1.13255i
$293$	−0.199235			−0.0116394			−0.00581972	−	0.999983i	$-0.501852\pi$
$293$	−0.199235			−0.0116394			−0.00581972	+	0.999983i	$0.501852\pi$
$294$	−16.9558	+	16.6371i	−0.988880	+	0.970295i
$295$	1.39057			0.0809622
$296$	−10.0729	+	17.4467i	−0.585474	+	1.01407i
$297$	−4.24095	−	7.34554i	−0.246085	−	0.426232i
$298$	7.32857	+	12.6935i	0.424532	+	0.735312i
$299$		0			0
$300$	20.8517			1.20387
$301$	9.27382	+	22.6928i	0.534534	+	1.30799i
$302$	1.52958			0.0880177
$303$	7.12368	−	12.3386i	0.409245	−	0.708833i
$304$	−0.00742695	−	0.0128639i	−0.000425965	−	0.000737793i
$305$	1.91570	+	3.31809i	0.109693	+	0.189993i
$306$	−1.97807	+	3.42612i	−0.113079	+	0.195858i
$307$	−27.2004			−1.55241			−0.776204	−	0.630482i	$-0.782857\pi$
$307$	−27.2004			−1.55241			−0.776204	+	0.630482i	$0.782857\pi$
$308$	−13.0255	−	1.77772i	−0.742194	−	0.101295i
$309$	14.7015			0.836341
$310$	7.67057	−	13.2858i	0.435659	−	0.754584i
$311$	−13.5505	−	23.4701i	−0.768376	−	1.33087i	−0.938443	−	0.345434i	$-0.887732\pi$
$311$	−13.5505	−	23.4701i	−0.768376	−	1.33087i	0.170067	−	0.985432i	$-0.445602\pi$
$312$		0			0
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	−0.364763	−	0.931100i	$-0.618850\pi$
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	0.988738	−	0.149656i	$-0.0478165\pi$
$314$	38.1789			2.15456
$315$	1.13858	−	1.46934i	0.0641517	−	0.0827882i
$316$	38.5336			2.16768
$317$	−3.53411	+	6.12126i	−0.198496	+	0.343804i	−0.948041	−	0.318149i	$-0.896939\pi$
$317$	−3.53411	+	6.12126i	−0.198496	+	0.343804i	0.749545	+	0.661953i	$0.230272\pi$
$318$	−4.60133	−	7.96973i	−0.258030	−	0.446920i
$319$	−1.02209	−	1.77032i	−0.0572263	−	0.0991188i
$320$	−5.42750	+	9.40071i	−0.303407	+	0.525516i
$321$	−14.5306			−0.811020
$322$	29.1841	−	37.6622i	1.62637	−	2.09883i
$323$	0.0982407			0.00546626
$324$	9.62558	−	16.6720i	0.534754	−	0.926221i
$325$		0			0
$326$	−10.4237	−	18.0544i	−0.577318	−	0.999943i
$327$	−8.54955	+	14.8082i	−0.472791	+	0.818898i
$328$	30.1139			1.66276
$329$	0.943758	+	0.128805i	0.0520310	+	0.00710124i
$330$	−4.32276			−0.237960
$331$	−3.29429	+	5.70588i	−0.181071	+	0.313623i	−0.942245	−	0.334923i	$-0.891290\pi$
$331$	−3.29429	+	5.70588i	−0.181071	+	0.313623i	0.761175	+	0.648547i	$0.224623\pi$
$332$	19.0638	+	33.0195i	1.04626	+	1.81218i
$333$	−2.77875	−	4.81294i	−0.152275	−	0.263748i
$334$	3.06059	−	5.30110i	0.167468	−	0.290063i
$335$	−1.73073			−0.0945599
$336$	−0.461854	−	1.13015i	−0.0251962	−	0.0616545i
$337$	4.22290			0.230036			0.115018	−	0.993363i	$-0.463307\pi$
$337$	4.22290			0.230036			0.115018	+	0.993363i	$0.463307\pi$
$338$		0			0
$339$	−2.56187	−	4.43728i	−0.139141	−	0.241000i
$340$	2.90030	+	5.02347i	0.157291	+	0.272436i
$341$	5.90916	−	10.2350i	0.319999	−	0.554254i
$342$	0.0905805			0.00489803
$343$	−17.0079	−	7.33014i	−0.918341	−	0.395790i
$344$	−27.8512			−1.50163
$345$	4.88030	−	8.45293i	0.262747	−	0.455091i
$346$	22.5571	+	39.0700i	1.21268	+	2.10042i
$347$	4.54739	+	7.87631i	0.244117	+	0.422822i	0.961883	−	0.273462i	$-0.0881687\pi$
$347$	4.54739	+	7.87631i	0.244117	+	0.422822i	−0.717766	+	0.696284i	$0.754835\pi$
$348$	3.31056	−	5.73405i	0.177464	−	0.307378i
$349$	−9.22053			−0.493564			−0.246782	−	0.969071i	$-0.579373\pi$
$349$	−9.22053			−0.493564			−0.246782	+	0.969071i	$0.579373\pi$
$350$	9.87149	+	24.1553i	0.527653	+	1.29116i
$351$		0			0
$352$	−3.97674	+	6.88792i	−0.211961	+	0.367127i
$353$	1.07724	+	1.86584i	0.0573359	+	0.0993087i	0.893269	−	0.449523i	$-0.148406\pi$
$353$	1.07724	+	1.86584i	0.0573359	+	0.0993087i	−0.835933	+	0.548832i	$0.815073\pi$
$354$	2.78473	+	4.82330i	0.148007	+	0.256356i
$355$	−6.02167	+	10.4298i	−0.319597	+	0.553559i
$356$	57.8752			3.06738
$357$	8.00046	+	1.09191i	0.423429	+	0.0577899i
$358$	6.66410			0.352208
$359$	4.27878	−	7.41107i	0.225825	−	0.391141i	−0.730741	−	0.682654i	$-0.760825\pi$
$359$	4.27878	−	7.41107i	0.225825	−	0.391141i	0.956567	+	0.291513i	$0.0941588\pi$
$360$	1.05593	+	1.82892i	0.0556521	+	0.0963923i
$361$	9.49888	+	16.4525i	0.499941	+	0.865923i
$362$	1.57548	−	2.72881i	0.0828055	−	0.143423i
$363$	12.8769			0.675860
$364$		0			0
$365$	5.72896			0.299867
$366$	−7.67270	+	13.2895i	−0.401059	+	0.694654i
$367$	−1.14912	−	1.99033i	−0.0599833	−	0.103894i	0.834474	−	0.551047i	$-0.185771\pi$
$367$	−1.14912	−	1.99033i	−0.0599833	−	0.103894i	−0.894458	+	0.447153i	$0.852438\pi$
$368$	1.22438	+	2.12070i	0.0638255	+	0.110549i
$369$	−4.15368	+	7.19439i	−0.216232	+	0.374525i
$370$	−13.0796			−0.679975
$371$	4.39468	−	5.67136i	0.228160	−	0.294442i
$372$	38.2795			1.98470
$373$	−5.88418	+	10.1917i	−0.304672	+	0.527707i	−0.977188	−	0.212375i	$-0.931880\pi$
$373$	−5.88418	+	10.1917i	−0.304672	+	0.527707i	0.672517	+	0.740082i	$0.265213\pi$
$374$	3.58636	+	6.21175i	0.185446	+	0.321202i
$375$	5.79373	+	10.0350i	0.299187	+	0.518207i
$376$	−0.541073	+	0.937166i	−0.0279037	+	0.0483307i
$377$		0			0
$378$	34.0646	+	4.64917i	1.75210	+	0.239127i
$379$	−7.99093			−0.410466			−0.205233	−	0.978713i	$-0.565795\pi$
$379$	−7.99093			−0.410466			−0.205233	+	0.978713i	$0.565795\pi$
$380$	0.0664059	−	0.115018i	0.00340655	−	0.00590032i
$381$	−11.5658	−	20.0325i	−0.592532	−	1.02630i
$382$	−1.74271	−	3.01846i	−0.0891647	−	0.154438i
$383$	14.1223	−	24.4605i	0.721616	−	1.24988i	−0.238736	−	0.971084i	$-0.576733\pi$
$383$	14.1223	−	24.4605i	0.721616	−	1.24988i	0.960352	−	0.278791i	$-0.0899335\pi$
$384$	−27.8870			−1.42310
$385$	−1.27494	−	3.11975i	−0.0649770	−	0.158997i
$386$	16.0168			0.815233
$387$	3.84158	−	6.65381i	0.195278	−	0.338232i
$388$	0.704352	+	1.21997i	0.0357580	+	0.0619347i
$389$	−3.84043	−	6.65182i	−0.194717	−	0.337261i	0.752090	−	0.659060i	$-0.229046\pi$
$389$	−3.84043	−	6.65182i	−0.194717	−	0.337261i	−0.946808	+	0.321799i	$0.895712\pi$
$390$		0			0
$391$	−16.1957			−0.819050
$392$	15.0186	−	14.7364i	0.758556	−	0.744300i
$393$	3.74996			0.189160
$394$	−17.8241	+	30.8722i	−0.897964	+	1.55532i
$395$	4.93931	+	8.55513i	0.248524	+	0.430455i
$396$	2.06008	+	3.56817i	0.103523	+	0.179307i
$397$	3.72641	−	6.45433i	0.187023	−	0.323933i	−0.757233	−	0.653144i	$-0.773449\pi$
$397$	3.72641	−	6.45433i	0.187023	−	0.323933i	0.944256	+	0.329211i	$0.106783\pi$
$398$	−15.2368			−0.763750
$399$	−0.0699389	−	0.171139i	−0.00350132	−	0.00856765i
$400$	−1.34113			−0.0670563
$401$	9.09912	−	15.7601i	0.454389	−	0.787024i	−0.544264	−	0.838914i	$-0.683191\pi$
$401$	9.09912	−	15.7601i	0.454389	−	0.787024i	0.998653	+	0.0518898i	$0.0165244\pi$
$402$	−3.46593	−	6.00316i	−0.172865	−	0.299411i
$403$		0			0
$404$	−15.9798	+	27.6778i	−0.795025	+	1.37702i
$405$	4.93530			0.245237
$406$	8.20978	+	1.12048i	0.407444	+	0.0556083i
$407$	−10.0761			−0.499453
$408$	−4.58681	+	7.94458i	−0.227081	+	0.393315i
$409$	14.6413	+	25.3594i	0.723964	+	1.25394i	0.959399	+	0.282053i	$0.0910152\pi$
$409$	14.6413	+	25.3594i	0.723964	+	1.25394i	−0.235435	+	0.971890i	$0.575651\pi$
$410$	9.77568	+	16.9320i	0.482787	+	0.836211i
$411$	1.37371	−	2.37933i	0.0677599	−	0.117364i
$412$	−32.9784			−1.62473
$413$	−2.65967	+	3.43232i	−0.130874	+	0.168893i
$414$	−14.9328			−0.733909
$415$	−4.88728	+	8.46502i	−0.239907	+	0.415531i
$416$		0			0
$417$	11.4990	+	19.9169i	0.563109	+	0.975334i
$418$	0.0821139	−	0.142225i	0.00401632	−	0.00695647i
$419$	−20.7393			−1.01318			−0.506591	−	0.862187i	$-0.669095\pi$
$419$	−20.7393			−1.01318			−0.506591	+	0.862187i	$0.669095\pi$
$420$	6.68630	−	8.62871i	0.326258	−	0.421038i
$421$	24.8696			1.21207			0.606036	−	0.795437i	$-0.292759\pi$
$421$	24.8696			1.21207			0.606036	+	0.795437i	$0.292759\pi$
$422$	−9.32165	+	16.1456i	−0.453771	+	0.785954i
$423$	−0.149263	−	0.258531i	−0.00725742	−	0.0125702i
$424$	4.07565	+	7.05923i	0.197931	+	0.342826i
$425$	4.43497	−	7.68159i	0.215128	−	0.372612i
$426$	−48.2356			−2.33702
$427$	−11.8540	−	1.61785i	−0.573657	−	0.0782932i
$428$	32.5950			1.57554
$429$		0			0
$430$	−9.04115	−	15.6597i	−0.436003	−	0.755179i
$431$	−10.5844	−	18.3327i	−0.509832	−	0.883055i	−0.999935	−	0.0113906i	$-0.996374\pi$
$431$	−10.5844	−	18.3327i	−0.509832	−	0.883055i	0.490103	−	0.871665i	$-0.336959\pi$
$432$	−0.883489	+	1.53025i	−0.0425069	+	0.0736241i
$433$	−23.4296			−1.12595			−0.562977	−	0.826472i	$-0.690344\pi$
$433$	−23.4296			−1.12595			−0.562977	+	0.826472i	$0.690344\pi$
$434$	18.1220	+	44.3442i	0.869885	+	2.12859i
$435$	1.69741			0.0813848
$436$	19.1783	−	33.2178i	0.918474	−	1.59084i
$437$	0.185409	+	0.321139i	0.00886934	+	0.0153621i
$438$	11.4727	+	19.8713i	0.548187	+	0.949488i
$439$	6.01919	−	10.4256i	0.287280	−	0.497584i	−0.685879	−	0.727715i	$-0.740582\pi$
$439$	6.01919	−	10.4256i	0.287280	−	0.497584i	0.973160	+	0.230131i	$0.0739155\pi$
$440$	3.82891			0.182536
$441$	1.44905	+	5.62067i	0.0690025	+	0.267651i
$442$		0			0
$443$	−7.86656	+	13.6253i	−0.373752	+	0.647357i	−0.990139	−	0.140086i	$-0.955262\pi$
$443$	−7.86656	+	13.6253i	−0.373752	+	0.647357i	0.616388	+	0.787443i	$0.288595\pi$
$444$	−16.3182	−	28.2640i	−0.774427	−	1.34135i
$445$	7.41855	+	12.8493i	0.351673	+	0.609116i
$446$	18.4930	−	32.0308i	0.875669	−	1.51670i
$447$	−9.37592			−0.443466
$448$	−12.8227	−	31.3768i	−0.605815	−	1.48242i
$449$	26.0012			1.22707			0.613536	−	0.789667i	$-0.289747\pi$
$449$	26.0012			1.22707			0.613536	+	0.789667i	$0.289747\pi$
$450$	4.08916	−	7.08263i	0.192765	−	0.333878i
$451$	7.53087	+	13.0438i	0.354615	+	0.614211i
$452$	5.74676	+	9.95369i	0.270305	+	0.468182i
$453$	−0.489225	+	0.847362i	−0.0229858	+	0.0398125i
$454$	2.98459			0.140074
$455$		0			0
$456$	0.210041			0.00983605
$457$	15.3979	−	26.6700i	0.720284	−	1.24757i	−0.240602	−	0.970624i	$-0.577345\pi$
$457$	15.3979	−	26.6700i	0.720284	−	1.24757i	0.960886	−	0.276945i	$-0.0893219\pi$
$458$	23.9742	+	41.5245i	1.12024	+	1.94031i
$459$	−5.84322	−	10.1208i	−0.272738	−	0.472396i
$460$	−10.9475	+	18.9616i	−0.510429	+	0.884088i
$461$	34.0958			1.58800			0.794000	−	0.607918i	$-0.207995\pi$
$461$	34.0958			1.58800			0.794000	+	0.607918i	$0.207995\pi$
$462$	8.26791	−	10.6698i	0.384658	−	0.496403i
$463$	1.69184			0.0786263			0.0393131	−	0.999227i	$-0.487483\pi$
$463$	1.69184			0.0786263			0.0393131	+	0.999227i	$0.487483\pi$
$464$	−0.212926	+	0.368799i	−0.00988485	+	0.0171211i
$465$	4.90674	+	8.49871i	0.227544	+	0.394118i
$466$	−15.3216	−	26.5378i	−0.709761	−	1.22934i
$467$	−14.1762	+	24.5539i	−0.655996	+	1.13622i	0.325647	+	0.945491i	$0.394418\pi$
$467$	−14.1762	+	24.5539i	−0.655996	+	1.13622i	−0.981643	+	0.190727i	$0.938916\pi$
$468$		0			0
$469$	3.31027	−	4.27192i	0.152854	−	0.197259i
$470$	−0.702581			−0.0324076
$471$	−12.2112	+	21.1504i	−0.562662	+	0.974559i
$472$	−2.46659	−	4.27226i	−0.113534	−	0.196647i
$473$	−6.96501	−	12.0637i	−0.320251	−	0.554692i
$474$	−19.7827	+	34.2647i	−0.908651	+	1.57383i
$475$	−0.203088			−0.00931830
$476$	−17.9466	−	2.44936i	−0.822581	−	0.112266i
$477$	−2.24866			−0.102959
$478$	−15.3918	+	26.6595i	−0.704007	+	1.21938i
$479$	−3.14123	−	5.44077i	−0.143526	−	0.248595i	0.785296	−	0.619121i	$-0.212511\pi$
$479$	−3.14123	−	5.44077i	−0.143526	−	0.248595i	−0.928822	+	0.370526i	$0.879178\pi$
$480$	−3.30213	−	5.71946i	−0.150721	−	0.261056i
$481$		0			0
$482$	−1.92128			−0.0875117
$483$	11.5299	+	28.2134i	0.524629	+	1.28375i
$484$	−28.8853			−1.31297
$485$	−0.180570	+	0.312757i	−0.00819927	+	0.0142016i
$486$	−9.60853	−	16.6425i	−0.435852	−	0.754917i
$487$	6.50879	+	11.2736i	0.294942	+	0.510854i	0.974971	−	0.222331i	$-0.0713665\pi$
$487$	6.50879	+	11.2736i	0.294942	+	0.510854i	−0.680030	+	0.733185i	$0.738033\pi$
$488$	6.79613	−	11.7712i	0.307647	−	0.532859i
$489$	13.3358			0.603065
$490$	13.1612	+	3.66068i	0.594560	+	0.165373i
$491$	−12.3523			−0.557453			−0.278726	−	0.960371i	$-0.589912\pi$
$491$	−12.3523			−0.557453			−0.278726	+	0.960371i	$0.589912\pi$
$492$	−24.3925	+	42.2490i	−1.09970	+	1.90473i
$493$	−1.40825	−	2.43916i	−0.0634244	−	0.109854i
$494$		0			0
$495$	−0.528131	+	0.914749i	−0.0237377	+	0.0411149i
$496$	−2.46203			−0.110549
$497$	−14.2264	−	34.8118i	−0.638143	−	1.56152i
$498$	−39.1487			−1.75430
$499$	4.57670	−	7.92708i	0.204881	−	0.354865i	−0.745214	−	0.666826i	$-0.767652\pi$
$499$	4.57670	−	7.92708i	0.204881	−	0.354865i	0.950095	+	0.311961i	$0.100986\pi$
$500$	−12.9965	−	22.5105i	−0.581220	−	1.00670i
$501$	1.95781	+	3.39102i	0.0874684	+	0.151500i
$502$	31.4074	−	54.3993i	1.40178	−	2.42796i
$503$	22.5037			1.00339			0.501696	−	0.865044i	$-0.332710\pi$
$503$	22.5037			1.00339			0.501696	+	0.865044i	$0.332710\pi$
$504$	−6.53389	−	0.891750i	−0.291042	−	0.0397217i
$505$	−8.19329			−0.364596
$506$	−13.5370	+	23.4469i	−0.601795	+	1.04234i
$507$		0			0
$508$	25.9443	+	44.9368i	1.15109	+	1.99375i
$509$	−19.3303	+	33.4811i	−0.856800	+	1.48402i	0.0181646	+	0.999835i	$0.494218\pi$
$509$	−19.3303	+	33.4811i	−0.856800	+	1.48402i	−0.874965	+	0.484187i	$0.839116\pi$
$510$	−5.95594			−0.263734
$511$	−10.9575	+	14.1407i	−0.484730	+	0.625546i
$512$	3.53972			0.156435
$513$	−0.133787	+	0.231727i	−0.00590686	+	0.0102310i
$514$	7.54536	+	13.0690i	0.332812	+	0.576447i
$515$	−4.22724	−	7.32179i	−0.186274	−	0.322637i
$516$	22.5596	−	39.0744i	0.993132	−	1.72016i
$517$	−0.541245			−0.0238039
$518$	25.0166	−	32.2841i	1.09917	−	1.41848i
$519$	−28.8588			−1.26676
$520$		0			0
$521$	−20.1176	−	34.8446i	−0.881366	−	1.52657i	−0.849823	−	0.527068i	$-0.823291\pi$
$521$	−20.1176	−	34.8446i	−0.881366	−	1.52657i	−0.0315430	−	0.999502i	$-0.510042\pi$
$522$	−1.29844	−	2.24897i	−0.0568313	−	0.0984348i
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	−0.857911	−	0.513799i	$-0.828238\pi$
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	0.873918	+	0.486073i	$0.161571\pi$
$524$	−8.41189			−0.367475
$525$	−16.5389	−	2.25724i	−0.721818	−	0.0985142i
$526$	52.0286			2.26856
$527$	8.14169	−	14.1018i	0.354658	−	0.614285i
$528$	0.346871	+	0.600798i	0.0150956	+	0.0261464i
$529$	−19.0660	−	33.0234i	−0.828959	−	1.43580i
$530$	−2.64610	+	4.58319i	−0.114939	+	0.199081i
$531$	1.36089			0.0590577
$532$	0.156887	+	0.383898i	0.00680189	+	0.0166441i
$533$		0			0
$534$	−29.7125	+	51.4636i	−1.28579	+	2.22705i
$535$	4.17809	+	7.23667i	0.180635	+	0.312868i
$536$	3.06996	+	5.31733i	0.132602	+	0.229674i
$537$	−2.13146	+	3.69179i	−0.0919791	+	0.159312i
$538$	−36.8553			−1.58894
$539$	10.1389	+	2.82007i	0.436715	+	0.121469i
$540$	−15.7989			−0.679877
$541$	11.8268	−	20.4847i	0.508476	−	0.880705i	−0.491476	−	0.870891i	$-0.663543\pi$
$541$	11.8268	−	20.4847i	0.508476	−	0.880705i	0.999952	−	0.00981448i	$-0.00312409\pi$
$542$	−10.0876	−	17.4722i	−0.433298	−	0.750494i
$543$	1.00781	+	1.74558i	0.0432492	+	0.0749099i
$544$	−5.47919	+	9.49024i	−0.234918	+	0.406891i
$545$	9.83325			0.421210
$546$		0			0
$547$	−12.9472			−0.553582			−0.276791	−	0.960930i	$-0.589271\pi$
$547$	−12.9472			−0.553582			−0.276791	+	0.960930i	$0.589271\pi$
$548$	−3.08149	+	5.33730i	−0.131635	+	0.227998i
$549$	1.87481	+	3.24727i	0.0800151	+	0.138590i
$550$	−7.41388	−	12.8412i	−0.316129	−	0.547552i
$551$	−0.0322436	+	0.0558475i	−0.00137362	+	0.00237918i
$552$	−34.6267			−1.47381
$553$	−30.5636	−	4.17134i	−1.29970	−	0.177384i
$554$	45.8771			1.94913
$555$	4.18340	−	7.24585i	0.177575	−	0.307569i
$556$	−25.7946	−	44.6775i	−1.09393	−	1.89475i
$557$	−3.20340	−	5.54845i	−0.135732	−	0.235096i	0.790145	−	0.612921i	$-0.210005\pi$
$557$	−3.20340	−	5.54845i	−0.135732	−	0.235096i	−0.925877	+	0.377825i	$0.876672\pi$
$558$	7.50685	−	13.0023i	0.317790	−	0.550429i
$559$		0			0
$560$	−0.430045	+	0.554975i	−0.0181727	+	0.0234520i
$561$	−4.58827			−0.193717
$562$	−16.1498	+	27.9723i	−0.681239	+	1.17994i
$563$	−3.66042	−	6.34004i	−0.154268	−	0.267201i	0.778524	−	0.627615i	$-0.215969\pi$
$563$	−3.66042	−	6.34004i	−0.154268	−	0.267201i	−0.932792	+	0.360414i	$0.882635\pi$
$564$	−0.876546	−	1.51822i	−0.0369092	−	0.0639287i
$565$	−1.47326	+	2.55176i	−0.0619806	+	0.107354i
$566$	−2.33226			−0.0980324
$567$	−9.43948	+	12.1817i	−0.396421	+	0.511583i
$568$	42.7249			1.79270
$569$	2.15872	−	3.73901i	0.0904981	−	0.156747i	−0.817223	−	0.576322i	$-0.804487\pi$
$569$	2.15872	−	3.73901i	0.0904981	−	0.156747i	0.907721	+	0.419575i	$0.137821\pi$
$570$	0.0681842	+	0.118098i	0.00285592	+	0.00494660i
$571$	−17.0847	−	29.5916i	−0.714974	−	1.23837i	−0.962970	−	0.269610i	$-0.913105\pi$
$571$	−17.0847	−	29.5916i	−0.714974	−	1.23837i	0.247996	−	0.968761i	$-0.420228\pi$
$572$		0			0
$573$	2.22956			0.0931413
$574$	−60.4903	−	8.25576i	−2.52482	−	0.344589i
$575$	33.4804			1.39623
$576$	−5.31166	+	9.20007i	−0.221319	+	0.383336i
$577$	3.17828	+	5.50494i	0.132314	+	0.229174i	0.924568	−	0.381017i	$-0.124426\pi$
$577$	3.17828	+	5.50494i	0.132314	+	0.229174i	−0.792254	+	0.610191i	$0.791093\pi$
$578$	−14.6364	−	25.3511i	−0.608796	−	1.05447i
$579$	−5.12283	+	8.87301i	−0.212898	+	0.368750i
$580$	−3.80763			−0.158103
$581$	−11.5464	−	28.2537i	−0.479025	−	1.17216i
$582$	−1.44643			−0.0599563
$583$	−2.03847	+	3.53074i	−0.0844249	+	0.146228i
$584$	−10.1620	−	17.6011i	−0.420507	−	0.728339i
$585$		0			0
$586$	−0.229446	+	0.397412i	−0.00947832	+	0.0164169i
$587$	31.4120			1.29651			0.648256	−	0.761422i	$-0.275499\pi$
$587$	31.4120			1.29651			0.648256	+	0.761422i	$0.275499\pi$
$588$	8.50954	+	33.0073i	0.350927	+	1.36120i
$589$	−0.372827			−0.0153621
$590$	1.60143	−	2.77376i	0.0659298	−	0.114194i
$591$	−11.4018	−	19.7484i	−0.469006	−	0.812342i
$592$	1.04954	+	1.81786i	0.0431359	+	0.0747136i
$593$	−0.236506	+	0.409641i	−0.00971215	+	0.0168219i	−0.870841	−	0.491565i	$-0.836425\pi$
$593$	−0.236506	+	0.409641i	−0.00971215	+	0.0168219i	0.861128	+	0.508387i	$0.169758\pi$
$594$	−19.5361			−0.801575
$595$	−1.75663	−	4.29842i	−0.0720146	−	0.176218i
$596$	21.0320			0.861505
$597$	4.87335	−	8.44089i	0.199453	−	0.345463i
$598$		0			0
$599$	4.81348	+	8.33719i	0.196673	+	0.340648i	0.947448	−	0.319910i	$-0.103653\pi$
$599$	4.81348	+	8.33719i	0.196673	+	0.340648i	−0.750774	+	0.660559i	$0.770320\pi$
$600$	9.48206	−	16.4234i	0.387103	−	0.670483i
$601$	−41.0799			−1.67568			−0.837842	−	0.545914i	$-0.816183\pi$
$601$	−41.0799			−1.67568			−0.837842	+	0.545914i	$0.816183\pi$
$602$	55.9451	+	7.63543i	2.28015	+	0.311197i
$603$	−1.69379			−0.0689765
$604$	1.09743	−	1.90080i	0.0446537	−	0.0773424i
$605$	−3.70257	−	6.41304i	−0.150531	−	0.260727i
$606$	−16.4077	−	28.4190i	−0.666518	−	1.15444i
$607$	−9.54289	+	16.5288i	−0.387334	+	0.670882i	−0.992090	−	0.125529i	$-0.959937\pi$
$607$	−9.54289	+	16.5288i	−0.387334	+	0.670882i	0.604756	+	0.796411i	$0.293271\pi$
$608$	0.250905			0.0101755
$609$	−3.24655	+	4.18969i	−0.131557	+	0.169775i
$610$	8.82474			0.357303
$611$		0			0
$612$	2.83840	+	4.91626i	0.114736	+	0.198728i
$613$	−19.0024	−	32.9131i	−0.767500	−	1.32935i	−0.938915	−	0.344149i	$-0.888167\pi$
$613$	−19.0024	−	32.9131i	−0.767500	−	1.32935i	0.171415	−	0.985199i	$-0.445166\pi$
$614$	−31.3249	+	54.2563i	−1.26417	+	2.18961i
$615$	−12.5067			−0.504318
$616$	−7.32335	+	9.45082i	−0.295066	+	0.380784i
$617$	−8.31519			−0.334757			−0.167378	−	0.985893i	$-0.553530\pi$
$617$	−8.31519			−0.334757			−0.167378	+	0.985893i	$0.553530\pi$
$618$	16.9308	−	29.3250i	0.681056	−	1.17962i
$619$	−22.2364	−	38.5146i	−0.893756	−	1.54803i	−0.835336	−	0.549739i	$-0.814727\pi$
$619$	−22.2364	−	38.5146i	−0.893756	−	1.54803i	−0.0584199	−	0.998292i	$-0.518606\pi$
$620$	−11.0068	−	19.0643i	−0.442042	−	0.765640i
$621$	22.0558	−	38.2018i	0.885069	−	1.53298i
$622$	−62.4206			−2.50284
$623$	−45.9048	−	6.26512i	−1.83914	−	0.251007i
$624$		0			0
$625$	−7.37342	+	12.7711i	−0.294937	+	0.510845i
$626$	−25.4263	−	44.0397i	−1.01624	−	1.76018i
$627$	0.0525269	+	0.0909792i	0.00209772	+	0.00363336i
$628$	27.3921	−	47.4445i	1.09306	−	1.89324i
$629$	−13.8829			−0.553549
$630$	−1.61966	−	3.96326i	−0.0645286	−	0.157900i
$631$	−11.7524			−0.467858			−0.233929	−	0.972254i	$-0.575158\pi$
$631$	−11.7524			−0.467858			−0.233929	+	0.972254i	$0.575158\pi$
$632$	17.5227	−	30.3501i	0.697014	−	1.20726i
$633$	−5.96290	−	10.3280i	−0.237004	−	0.410503i
$634$	8.14001	+	14.0989i	0.323281	+	0.559939i
$635$	−6.65117	+	11.5202i	−0.263944	+	0.457164i
$636$	−13.2052			−0.523620
$637$		0			0
$638$	−4.70831			−0.186404
$639$	−5.89315	+	10.2072i	−0.233129	+	0.403792i
$640$	8.01854	+	13.8885i	0.316961	+	0.548992i
$641$	−5.24342	−	9.08186i	−0.207102	−	0.358712i	0.743698	−	0.668516i	$-0.233070\pi$
$641$	−5.24342	−	9.08186i	−0.207102	−	0.358712i	−0.950801	+	0.309804i	$0.899737\pi$
$642$	−16.7339	+	28.9840i	−0.660436	+	1.14391i
$643$	−31.2822			−1.23365			−0.616825	−	0.787101i	$-0.711581\pi$
$643$	−31.2822			−1.23365			−0.616825	+	0.787101i	$0.711581\pi$
$644$	−25.8638	−	63.2882i	−1.01918	−	2.49390i
$645$	11.5669			0.455448
$646$	0.113137	−	0.195959i	0.00445133	−	0.00770992i
$647$	13.4337	+	23.2679i	0.528135	+	0.914757i	0.999462	+	0.0327983i	$0.0104419\pi$
$647$	13.4337	+	23.2679i	0.528135	+	0.914757i	−0.471327	+	0.881959i	$0.656225\pi$
$648$	−8.75422	−	15.1627i	−0.343898	−	0.595649i
$649$	1.23369	−	2.13681i	0.0484265	−	0.0838772i
$650$		0			0
$651$	−30.3621	−	4.14384i	−1.18998	−	0.162410i
$652$	−29.9148			−1.17155
$653$	2.07081	−	3.58674i	0.0810369	−	0.140360i	−0.822659	−	0.568536i	$-0.807510\pi$
$653$	2.07081	−	3.58674i	0.0810369	−	0.140360i	0.903696	+	0.428176i	$0.140844\pi$
$654$	19.6919	+	34.1073i	0.770014	+	1.33370i
$655$	−1.07825	−	1.86759i	−0.0421308	−	0.0729726i
$656$	1.56886	−	2.71734i	0.0612536	−	0.106094i
$657$	5.60668			0.218738
$658$	1.34379	−	1.73417i	0.0523863	−	0.0676048i
$659$	21.4551			0.835773			0.417887	−	0.908499i	$-0.362771\pi$
$659$	21.4551			0.835773			0.417887	+	0.908499i	$0.362771\pi$
$660$	−3.10144	+	5.37185i	−0.120723	+	0.209099i
$661$	21.1936	+	36.7084i	0.824335	+	1.42779i	0.902426	+	0.430844i	$0.141784\pi$
$661$	21.1936	+	36.7084i	0.824335	+	1.42779i	−0.0780909	+	0.996946i	$0.524882\pi$
$662$	7.58763	+	13.1422i	0.294902	+	0.510785i
$663$		0			0
$664$	34.6762			1.34570
$665$	−0.0651220	+	0.0840403i	−0.00252532	+	0.00325894i
$666$	−12.8004			−0.496006
$667$	5.31558	−	9.20685i	0.205820	−	0.356491i
$668$	−4.39175	−	7.60673i	−0.169922	−	0.294313i
$669$	11.8297	+	20.4896i	0.457361	+	0.792173i
$670$	−1.99317	+	3.45226i	−0.0770027	+	0.133373i
$671$	6.79830			0.262445
$672$	20.4330	+	2.78872i	0.788222	+	0.107577i
$673$	−29.5856			−1.14044			−0.570220	−	0.821492i	$-0.693142\pi$
$673$	−29.5856			−1.14044			−0.570220	+	0.821492i	$0.693142\pi$
$674$	4.86323	−	8.42336i	0.187324	−	0.324456i
$675$	12.0794	+	20.9221i	0.464935	+	0.805292i
$676$		0			0
$677$	−16.0830	+	27.8565i	−0.618118	+	1.07061i	0.371711	+	0.928349i	$0.378771\pi$
$677$	−16.0830	+	27.8565i	−0.618118	+	1.07061i	−0.989829	+	0.142263i	$0.954562\pi$
$678$	−11.8013			−0.453227
$679$	−0.426604	−	1.04389i	−0.0163716	−	0.0400609i
$680$	5.27551			0.202306
$681$	−0.954596	+	1.65341i	−0.0365802	+	0.0633587i
$682$	−13.6104	−	23.5738i	−0.521168	−	0.902689i
$683$	−4.30118	−	7.44986i	−0.164580	−	0.285061i	0.771926	−	0.635712i	$-0.219294\pi$
$683$	−4.30118	−	7.44986i	−0.164580	−	0.285061i	−0.936506	+	0.350651i	$0.885960\pi$
$684$	0.0649885	−	0.112563i	0.00248490	−	0.00430397i
$685$	−1.57997			−0.0603674
$686$	−34.2082	+	25.4838i	−1.30608	+	0.972978i
$687$	−30.6717			−1.17020
$688$	−1.45097	+	2.51316i	−0.0553179	+	0.0958134i
$689$		0			0
$690$	−11.2406	−	19.4694i	−0.427924	−	0.741186i
$691$	10.2210	−	17.7033i	0.388826	−	0.673466i	−0.603466	−	0.797388i	$-0.706214\pi$
$691$	10.2210	−	17.7033i	0.388826	−	0.673466i	0.992292	+	0.123923i	$0.0395476\pi$
$692$	64.7359			2.46089
$693$	−1.24773	−	3.05316i	−0.0473973	−	0.115980i
$694$	20.9477			0.795164
$695$	6.61279	−	11.4537i	0.250837	−	0.434463i
$696$	−3.01087	−	5.21498i	−0.114127	−	0.197673i
$697$	10.3761	+	17.9719i	0.393023	+	0.680736i
$698$	−10.6187	+	18.3921i	−0.401922	+	0.696150i
$699$	19.6020			0.741415
$700$	37.1000	+	5.06344i	1.40225	+	0.191380i
$701$	25.1373			0.949422			0.474711	−	0.880142i	$-0.342553\pi$
$701$	25.1373			0.949422			0.474711	+	0.880142i	$0.342553\pi$
$702$		0			0
$703$	0.158933	+	0.275280i	0.00599427	+	0.0103824i
$704$	9.63036	+	16.6803i	0.362958	+	0.628661i
$705$	0.224715	−	0.389217i	0.00846324	−	0.0146588i
$706$	4.96236			0.186761
$707$	15.6709	−	20.2233i	0.589363	−	0.760576i
$708$	7.99182			0.300351
$709$	−14.7464	+	25.5416i	−0.553814	+	0.959234i	0.444181	+	0.895937i	$0.353495\pi$
$709$	−14.7464	+	25.5416i	−0.553814	+	0.959234i	−0.997995	+	0.0632970i	$0.979838\pi$
$710$	13.8695	+	24.0227i	0.520514	+	0.901556i
$711$	4.83389	+	8.37254i	0.181285	+	0.313995i
$712$	26.3180	−	45.5841i	0.986309	−	1.70834i
$713$	61.4632			2.30182
$714$	11.3916	−	14.7009i	0.426320	−	0.550169i
$715$		0			0
$716$	4.78127	−	8.28140i	0.178684	−	0.309491i
$717$	−9.84591	−	17.0536i	−0.367702	−	0.636879i
$718$	−9.85518	−	17.0697i	−0.367792	−	0.637034i
$719$	4.16576	−	7.21531i	0.155357	−	0.269086i	−0.777832	−	0.628472i	$-0.783681\pi$
$719$	4.16576	−	7.21531i	0.155357	−	0.269086i	0.933189	+	0.359386i	$0.117014\pi$
$720$	0.220044			0.00820055
$721$	26.1574	+	3.56999i	0.974154	+	0.132953i
$722$	43.7569			1.62846
$723$	0.614504	−	1.06435i	0.0228537	−	0.0395837i
$724$	−2.26071	−	3.91567i	−0.0840188	−	0.145525i
$725$	2.91120	+	5.04235i	0.108119	+	0.187268i
$726$	14.8294	−	25.6853i	0.550371	−	0.953271i
$727$	−9.66141			−0.358322			−0.179161	−	0.983820i	$-0.557338\pi$
$727$	−9.66141			−0.358322			−0.179161	+	0.983820i	$0.557338\pi$
$728$		0			0
$729$	29.7672			1.10249
$730$	6.59766	−	11.4275i	0.244190	−	0.422950i
$731$	−9.59645	−	16.6215i	−0.354938	−	0.614770i
$732$	11.0098	+	19.0696i	0.406935	+	0.704832i
$733$	−7.00894	+	12.1398i	−0.258881	+	0.448395i	−0.965942	−	0.258757i	$-0.916687\pi$
$733$	−7.00894	+	12.1398i	−0.258881	+	0.448395i	0.707061	+	0.707152i	$0.250020\pi$
$734$	−5.29344			−0.195384
$735$	−6.23743	+	6.12021i	−0.230071	+	0.225747i
$736$	−41.3635			−1.52468
$737$	−1.53547	+	2.65951i	−0.0565598	+	0.0979644i
$738$	9.56704	+	16.5706i	0.352168	+	0.609972i
$739$	−19.4073	−	33.6145i	−0.713910	−	1.23653i	−0.963378	−	0.268146i	$-0.913589\pi$
$739$	−19.4073	−	33.6145i	−0.713910	−	1.23653i	0.249468	−	0.968383i	$-0.419744\pi$
$740$	−9.38417	+	16.2539i	−0.344969	+	0.597504i
$741$		0			0
$742$	−6.25153	−	15.2973i	−0.229501	−	0.561583i
$743$	34.3942			1.26180			0.630901	−	0.775863i	$-0.282685\pi$
$743$	34.3942			1.26180			0.630901	+	0.775863i	$0.282685\pi$
$744$	17.4071	−	30.1500i	0.638175	−	1.10535i
$745$	2.69592	+	4.66948i	0.0987710	+	0.171076i
$746$	13.5528	+	23.4742i	0.496205	+	0.859452i
$747$	−4.78297	+	8.28434i	−0.175000	+	0.303108i
$748$	10.2924			0.376327
$749$	−25.8533	−	3.52848i	−0.944660	−	0.128928i
$750$	26.6890			0.974545
$751$	−24.0735	+	41.6965i	−0.878454	+	1.52153i	−0.0254165	+	0.999677i	$0.508091\pi$
$751$	−24.0735	+	41.6965i	−0.878454	+	1.52153i	−0.853037	+	0.521850i	$0.825242\pi$
$752$	0.0563770	+	0.0976479i	0.00205586	+	0.00356085i
$753$	20.0908	+	34.7983i	0.732150	+	1.26812i
$754$		0			0
$755$	0.562681			0.0204781
$756$	30.2177	−	38.9961i	1.09901	−	1.41828i
$757$	−6.90638			−0.251016			−0.125508	−	0.992093i	$-0.540056\pi$
$757$	−6.90638			−0.251016			−0.125508	+	0.992093i	$0.540056\pi$
$758$	−9.20262	+	15.9394i	−0.334254	+	0.578945i
$759$	−8.65942	−	14.9986i	−0.314317	−	0.544413i
$760$	−0.0603945	−	0.104606i	−0.00219074	−	0.00379447i
$761$	−15.9865	+	27.6895i	−0.579511	+	1.00374i	0.416025	+	0.909353i	$0.363423\pi$
$761$	−15.9865	+	27.6895i	−0.579511	+	1.00374i	−0.995535	+	0.0943888i	$0.969910\pi$
$762$	−53.2781			−1.93006
$763$	−18.8075	+	24.2712i	−0.680878	+	0.878676i
$764$	−5.00135			−0.180942
$765$	−0.727663	+	1.26035i	−0.0263087	+	0.0455680i
$766$	−32.5274	−	56.3391i	−1.17526	−	2.03562i
$767$		0			0
$768$	−13.2397	+	22.9319i	−0.477748	+	0.827483i
$769$	14.3950			0.519099			0.259549	−	0.965730i	$-0.416426\pi$
$769$	14.3950			0.519099			0.259549	+	0.965730i	$0.416426\pi$
$770$	−7.69119	−	1.04970i	−0.277171	−	0.0378285i
$771$	−9.65328			−0.347654
$772$	11.4915	−	19.9039i	0.413589	−	0.716357i
$773$	18.6385	+	32.2829i	0.670382	+	1.16114i	0.977796	+	0.209560i	$0.0672030\pi$
$773$	18.6385	+	32.2829i	0.670382	+	1.16114i	−0.307414	+	0.951576i	$0.599464\pi$
$774$	−8.84818	−	15.3255i	−0.318041	−	0.550864i
$775$	−16.8309	+	29.1520i	−0.604583	+	1.04717i
$776$	1.28118			0.0459917
$777$	9.88344	+	24.1845i	0.354566	+	0.867616i
$778$	−17.6911			−0.634255
$779$	0.237573	−	0.411489i	0.00851194	−	0.0147431i
$780$		0			0
$781$	10.6846	+	18.5063i	0.382326	+	0.662208i
$782$	−18.6515	+	32.3053i	−0.666975	+	1.15524i
$783$	7.67121			0.274147
$784$	−0.547311	−	2.12294i	−0.0195468	−	0.0758193i
$785$	14.0447			0.501276
$786$	4.31857	−	7.47999i	0.154038	−	0.266802i
$787$	−7.17430	−	12.4263i	−0.255736	−	0.442948i	0.709359	−	0.704847i	$-0.248985\pi$
$787$	−7.17430	−	12.4263i	−0.255736	−	0.442948i	−0.965095	+	0.261899i	$0.915651\pi$
$788$	25.5764	+	44.2996i	0.911120	+	1.57811i
$789$	−16.6409	+	28.8229i	−0.592432	+	1.02612i
$790$	22.7531			0.809518
$791$	−3.48064	−	8.51705i	−0.123757	−	0.302831i
$792$	3.74719			0.133150
$793$		0			0
$794$	−8.58291	−	14.8660i	−0.304596	−	0.527576i
$795$	−1.69267	−	2.93179i	−0.0600328	−	0.103980i
$796$	−10.9319	+	18.9346i	−0.387470	+	0.671118i
$797$	11.0844			0.392629			0.196314	−	0.980541i	$-0.437103\pi$
$797$	11.0844			0.392629			0.196314	+	0.980541i	$0.437103\pi$
$798$	−0.421912	−	0.0575829i	−0.0149355	−	0.00203841i
$799$	−0.745733			−0.0263821
$800$	11.3268	−	19.6187i	0.400464	−	0.693625i
$801$	7.26022	+	12.5751i	0.256527	+	0.444318i
$802$	−20.9577	−	36.2998i	−0.740042	−	1.28179i
$803$	5.08262	−	8.80336i	0.179362	−	0.310664i
$804$	−9.94676			−0.350795
$805$	10.7358	−	13.8546i	0.378388	−	0.488312i
$806$		0			0
$807$	11.7878	−	20.4171i	0.414952	−	0.718718i
$808$	14.5332	+	25.1723i	0.511277	+	0.885558i
$809$	21.2768	+	36.8525i	0.748052	+	1.29566i	0.948755	+	0.316013i	$0.102344\pi$
$809$	21.2768	+	36.8525i	0.748052	+	1.29566i	−0.200703	+	0.979652i	$0.564323\pi$
$810$	5.68365	−	9.84438i	0.199703	−	0.345896i
$811$	16.3622			0.574554			0.287277	−	0.957848i	$-0.407250\pi$
$811$	16.3622			0.574554			0.287277	+	0.957848i	$0.407250\pi$
$812$	7.28265	−	9.39830i	0.255571	−	0.329816i
$813$	12.9057			0.452622
$814$	−11.6040	+	20.0986i	−0.406719	+	0.704457i
$815$	−3.83453	−	6.64160i	−0.134318	−	0.232645i
$816$	0.477922	+	0.827785i	0.0167306	+	0.0289783i
$817$	−0.219722	+	0.380570i	−0.00768710	+	0.0133145i
$818$	67.4455			2.35818
$819$		0			0
$820$	28.0549			0.979721
$821$	1.55275	−	2.68944i	0.0541913	−	0.0938621i	−0.837657	−	0.546196i	$-0.816075\pi$
$821$	1.55275	−	2.68944i	0.0541913	−	0.0938621i	0.891848	+	0.452334i	$0.149409\pi$
$822$	−3.16401	−	5.48023i	−0.110358	−	0.191145i
$823$	−24.5082	−	42.4494i	−0.854301	−	1.47969i	−0.877292	−	0.479958i	$-0.840652\pi$
$823$	−24.5082	−	42.4494i	−0.854301	−	1.47969i	0.0229903	−	0.999736i	$-0.492681\pi$
$824$	−14.9965	+	25.9747i	−0.522429	+	0.904873i
$825$	9.48507			0.330228
$826$	3.78344	+	9.25799i	0.131643	+	0.322127i
$827$	13.0887			0.455140			0.227570	−	0.973762i	$-0.426922\pi$
$827$	13.0887			0.455140			0.227570	+	0.973762i	$0.426922\pi$
$828$	−10.7138	+	18.5569i	−0.372331	+	0.644896i
$829$	−24.6282	−	42.6574i	−0.855374	−	1.48155i	−0.876297	−	0.481771i	$-0.839994\pi$
$829$	−24.6282	−	42.6574i	−0.855374	−	1.48155i	0.0209227	−	0.999781i	$-0.493340\pi$
$830$	11.2567	+	19.4972i	0.390726	+	0.676757i
$831$	−14.6734	+	25.4151i	−0.509015	+	0.881639i
$832$		0			0
$833$	13.9695	+	3.88551i	0.484015	+	0.134625i
$834$	52.9706			1.83422
$835$	1.12588	−	1.95009i	0.0389629	−	0.0674856i
$836$	−0.117828	−	0.204084i	−0.00407517	−	0.00705840i
$837$	22.1753	+	38.4087i	0.766489	+	1.32760i
$838$	−23.8841	+	41.3684i	−0.825062	+	1.42905i
$839$	17.2636			0.596007			0.298004	−	0.954565i	$-0.403679\pi$
$839$	17.2636			0.596007			0.298004	+	0.954565i	$0.403679\pi$
$840$	−3.75570	−	9.19011i	−0.129584	−	0.317089i
$841$	−27.1512			−0.936248
$842$	28.6407	−	49.6071i	0.987024	−	1.70957i
$843$	−10.3308	−	17.8934i	−0.355810	−	0.616282i
$844$	13.3760	+	23.1678i	0.460419	+	0.797470i
$845$		0			0
$846$	−0.687585			−0.0236397
$847$	22.9109	+	3.12690i	0.787228	+	0.107441i
$848$	0.849323			0.0291659
$849$	0.745955	−	1.29203i	0.0256011	−	0.0443424i
$850$	−10.2149	−	17.6928i	−0.350369	−	0.606857i
$851$	−26.2012	−	45.3818i	−0.898166	−	1.55567i
$852$	−34.6075	+	59.9419i	−1.18563	+	2.05358i
$853$	52.4163			1.79470			0.897350	−	0.441319i	$-0.145489\pi$
$853$	52.4163			1.79470			0.897350	+	0.441319i	$0.145489\pi$
$854$	−16.8786	+	21.7819i	−0.577574	+	0.745363i
$855$	0.0333214			0.00113957
$856$	14.8222	−	25.6728i	0.506611	−	0.877477i
$857$	−5.06355	−	8.77032i	−0.172967	−	0.299588i	0.766489	−	0.642258i	$-0.222002\pi$
$857$	−5.06355	−	8.77032i	−0.172967	−	0.299588i	−0.939456	+	0.342670i	$0.888669\pi$
$858$		0			0
$859$	0.255118	−	0.441878i	0.00870452	−	0.0150767i	−0.861640	−	0.507519i	$-0.830563\pi$
$859$	0.255118	−	0.441878i	0.00870452	−	0.0150767i	0.870345	+	0.492443i	$0.163896\pi$
$860$	−25.9469			−0.884782
$861$	23.9209	−	30.8700i	0.815220	−	1.05205i
$862$	−48.7573			−1.66068
$863$	−10.2495	+	17.7527i	−0.348898	+	0.604310i	−0.986054	−	0.166426i	$-0.946777\pi$
$863$	−10.2495	+	17.7527i	−0.348898	+	0.604310i	0.637156	+	0.770735i	$0.280111\pi$
$864$	−14.9235	−	25.8482i	−0.507707	−	0.879375i
$865$	8.29797	+	14.3725i	0.282139	+	0.488680i
$866$	−26.9823	+	46.7347i	−0.916896	+	1.58811i
$867$	18.7254			0.635947
$868$	68.1080	+	9.29543i	2.31174	+	0.315508i
$869$	17.5282			0.594605
$870$	1.95480	−	3.38581i	0.0662739	−	0.114790i
$871$		0			0
$872$	−17.4422	−	30.2107i	−0.590667	−	1.02306i
$873$	−0.176716	+	0.306082i	−0.00598094	+	0.0103593i
$874$	0.854095			0.0288902
$875$	7.87157	+	19.2615i	0.266108	+	0.651159i
$876$	32.9252			1.11244
$877$	5.64530	−	9.77794i	0.190628	−	0.330178i	−0.754830	−	0.655920i	$-0.772281\pi$
$877$	5.64530	−	9.77794i	0.190628	−	0.330178i	0.945459	+	0.325742i	$0.105614\pi$
$878$	−13.8638	−	24.0128i	−0.467881	−	0.810394i
$879$	−0.146773	−	0.254218i	−0.00495052	−	0.00857455i
$880$	0.199476	−	0.345503i	0.00672435	−	0.0116469i
$881$	22.5268			0.758947			0.379474	−	0.925203i	$-0.376105\pi$
$881$	22.5268			0.758947			0.379474	+	0.925203i	$0.376105\pi$
$882$	12.8803	+	3.58255i	0.433701	+	0.120631i
$883$	28.0268			0.943178			0.471589	−	0.881819i	$-0.343681\pi$
$883$	28.0268			0.943178			0.471589	+	0.881819i	$0.343681\pi$
$884$		0			0
$885$	1.02441	+	1.77432i	0.0344351	+	0.0596433i
$886$	18.1188	+	31.3827i	0.608713	+	1.05432i
$887$	10.3118	−	17.8605i	0.346235	−	0.599696i	−0.639342	−	0.768922i	$-0.720793\pi$
$887$	10.3118	−	17.8605i	0.346235	−	0.599696i	0.985577	+	0.169226i	$0.0541267\pi$
$888$	−29.6820			−0.996062
$889$	−15.7137	−	38.4509i	−0.527019	−	1.28960i
$890$	34.1738			1.14551
$891$	4.37850	−	7.58379i	0.146685	−	0.254066i
$892$	−26.5362	−	45.9621i	−0.888499	−	1.53893i
$893$	0.00853722	+	0.0147869i	0.000285687	+	0.000494824i
$894$	−10.7976	+	18.7020i	−0.361127	+	0.625490i
$895$	2.45149			0.0819443
$896$	−49.6174	−	6.77181i	−1.65760	−	0.226230i
$897$		0			0
$898$	29.9438	−	51.8642i	0.999238	−	1.73073i
$899$	5.34437	+	9.25671i	0.178245	+	0.308729i
$900$	−5.86767	−	10.1631i	−0.195589	−	0.338770i
$901$	−2.80863	+	4.86468i	−0.0935689	+	0.162066i
$902$	34.6912			1.15509
$903$	−22.1235	+	28.5504i	−0.736223	+	0.950099i
$904$	10.4531			0.347664
$905$	0.579565	−	1.00384i	0.0192654	−	0.0333686i
$906$	1.12681	+	1.95170i	0.0374359	+	0.0648409i
$907$	−20.7315	−	35.9081i	−0.688379	−	1.19231i	−0.972362	−	0.233479i	$-0.924989\pi$
$907$	−20.7315	−	35.9081i	−0.688379	−	1.19231i	0.283982	−	0.958829i	$-0.408344\pi$
$908$	2.14134	−	3.70892i	0.0710630	−	0.123085i
$909$	−8.01841			−0.265954
$910$		0			0
$911$	40.8187			1.35239			0.676193	−	0.736725i	$-0.263629\pi$
$911$	40.8187			1.35239			0.676193	+	0.736725i	$0.263629\pi$
$912$	0.0109426	−	0.0189531i	0.000362345	−	0.000627600i
$913$	8.67180	+	15.0200i	0.286995	+	0.497090i
$914$	−35.4655	−	61.4280i	−1.17309	−	2.03186i
$915$	−2.82252	+	4.88875i	−0.0933096	+	0.161617i
$916$	68.8027			2.27331
$917$	6.67204	+	0.910605i	0.220330	+	0.0300708i
$918$	−26.9170			−0.888393
$919$	24.3839	−	42.2341i	0.804350	−	1.39318i	−0.112379	−	0.993665i	$-0.535847\pi$
$919$	24.3839	−	42.2341i	0.804350	−	1.39318i	0.916729	−	0.399510i	$-0.130820\pi$
$920$	9.95645	+	17.2451i	0.328254	+	0.568553i
$921$	−20.0380	−	34.7068i	−0.660274	−	1.14363i
$922$	39.2659	−	68.0105i	1.29315	−	2.23981i
$923$		0			0
$924$	−7.32728	−	17.9297i	−0.241050	−	0.589843i
$925$	28.6994			0.943631
$926$	1.94837	−	3.37468i	0.0640275	−	0.110899i
$927$	−4.13701	−	7.16552i	−0.135877	−	0.235346i
$928$	−3.59665	−	6.22958i	−0.118066	−	0.204496i
$929$	14.6915	−	25.4464i	0.482012	−	0.834868i	−0.517775	−	0.855517i	$-0.673240\pi$
$929$	14.6915	−	25.4464i	0.482012	−	0.834868i	0.999787	+	0.0206482i	$0.00657301\pi$
$930$	22.6030			0.741183
$931$	−0.0828796	−	0.321479i	−0.00271627	−	0.0105360i
$932$	−43.9711			−1.44032
$933$	19.9647	−	34.5799i	0.653615	−	1.13210i
$934$	32.6515	+	56.5541i	1.06839	+	1.85051i
$935$	1.31930	+	2.28509i	0.0431456	+	0.0747304i
$936$		0			0
$937$	−21.0196			−0.686681			−0.343340	−	0.939211i	$-0.611558\pi$
$937$	−21.0196			−0.686681			−0.343340	+	0.939211i	$0.611558\pi$
$938$	−4.70893	−	11.5226i	−0.153752	−	0.376228i
$939$	32.5296			1.06156
$940$	−0.504079	+	0.873090i	−0.0164412	+	0.0284770i
$941$	12.0516	+	20.8740i	0.392872	+	0.680474i	0.992827	−	0.119560i	$-0.0381482\pi$
$941$	12.0516	+	20.8740i	0.392872	+	0.680474i	−0.599955	+	0.800034i	$0.704815\pi$
$942$	28.1256	+	48.7150i	0.916383	+	1.58722i
$943$	−39.1656	+	67.8368i	−1.27541	+	2.20907i
$944$	−0.514013			−0.0167297
$945$	12.5312	+	1.71027i	0.407640	+	0.0556350i
$946$	−32.0845			−1.04316
$947$	1.67023	−	2.89292i	0.0542751	−	0.0940072i	−0.837611	−	0.546267i	$-0.816049\pi$
$947$	1.67023	−	2.89292i	0.0542751	−	0.0940072i	0.891886	+	0.452259i	$0.149382\pi$
$948$	28.3869	+	49.1676i	0.921965	+	1.59689i
$949$		0			0
$950$	−0.233883	+	0.405097i	−0.00758815	+	0.0131431i
$951$	−10.4141			−0.337699
$952$	−10.0902	+	13.0214i	−0.327024	+	0.422027i
$953$	−4.97124			−0.161034			−0.0805171	−	0.996753i	$-0.525657\pi$
$953$	−4.97124			−0.161034			−0.0805171	+	0.996753i	$0.525657\pi$
$954$	−2.58963	+	4.48537i	−0.0838423	+	0.145219i
$955$	−0.641082	−	1.11039i	−0.0207449	−	0.0359313i
$956$	22.0863	+	38.2546i	0.714322	+	1.23724i
$957$	1.50591	−	2.60832i	0.0486793	−	0.0843150i
$958$	−14.4702			−0.467510
$959$	3.02191	−	3.89980i	0.0975827	−	0.125931i
$960$	−15.9933			−0.516183
$961$	−15.3981	+	26.6702i	−0.496711	+	0.860329i
$962$		0			0
$963$	4.08892	+	7.08221i	0.131763	+	0.228221i
$964$	−1.37845	+	2.38755i	−0.0443970	+	0.0768978i
$965$	5.89202			0.189671
$966$	69.5552	+	9.49294i	2.23790	+	0.305430i
$967$	47.4943			1.52731			0.763657	−	0.645623i	$-0.223402\pi$
$967$	47.4943			1.52731			0.763657	+	0.645623i	$0.223402\pi$
$968$	−13.1352	+	22.7509i	−0.422182	+	0.731241i
$969$	0.0723720	+	0.125352i	0.00232492	+	0.00402689i
$970$	0.415901	+	0.720362i	0.0133538	+	0.0231294i
$971$	−17.2357	+	29.8532i	−0.553121	+	0.958033i	0.444926	+	0.895567i	$0.353230\pi$
$971$	−17.2357	+	29.8532i	−0.553121	+	0.958033i	−0.998047	+	0.0624662i	$0.980103\pi$
$972$	−27.5752			−0.884476
$973$	15.6230	+	38.2291i	0.500850	+	1.22557i
$974$	29.9830			0.960717
$975$		0			0
$976$	−0.708122	−	1.22650i	−0.0226664	−	0.0392594i
$977$	6.67406	+	11.5598i	0.213522	+	0.369831i	0.952814	−	0.303553i	$-0.0981731\pi$
$977$	6.67406	+	11.5598i	0.213522	+	0.369831i	−0.739292	+	0.673385i	$0.764840\pi$
$978$	15.3579	−	26.6007i	0.491093	−	0.850597i
$979$	26.3264			0.841395
$980$	13.9918	−	13.7288i	0.446951	−	0.438551i
$981$	9.62337			0.307251
$982$	−14.2253	+	24.6390i	−0.453949	+	0.786263i
$983$	−6.26720	−	10.8551i	−0.199893	−	0.346224i	0.748601	−	0.663021i	$-0.230726\pi$
$983$	−6.26720	−	10.8551i	−0.199893	−	0.346224i	−0.948493	+	0.316797i	$0.897393\pi$
$984$	22.1843	+	38.4244i	0.707210	+	1.22492i
$985$	−6.55685	+	11.3568i	−0.208919	+	0.361858i
$986$	−6.48715			−0.206593
$987$	0.530897	+	1.29909i	0.0168986	+	0.0413506i
$988$		0			0
$989$	36.2227	−	62.7396i	1.15182	−	1.99500i
$990$	1.21643	+	2.10691i	0.0386605	+	0.0669620i
$991$	5.20596	+	9.01698i	0.165373	+	0.286434i	0.936788	−	0.349899i	$-0.113784\pi$
$991$	5.20596	+	9.01698i	0.165373	+	0.286434i	−0.771415	+	0.636332i	$0.780451\pi$
$992$	20.7938	−	36.0158i	0.660202	−	1.14350i
$993$	−9.70736			−0.308054
$994$	−85.8223	−	11.7131i	−2.72212	−	0.371517i
$995$	−5.60508			−0.177693
$996$	−28.0879	+	48.6497i	−0.890000	+	1.54153i
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	0.816877	−	0.576812i	$-0.195703\pi$
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	−0.907972	+	0.419031i	$0.862370\pi$
$998$	−10.5414	−	18.2582i	−0.333681	−	0.577953i
$999$	18.9062	−	32.7465i	0.598167	−	1.03605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.170.11		24
7.2	even	3		8281.2.a.cp.1.2		12
7.4	even	3	inner	1183.2.e.j.508.11		24
7.5	odd	6		8281.2.a.co.1.2		12
13.2	odd	12		91.2.u.b.30.6	yes	12
13.7	odd	12		91.2.k.b.23.1	yes	12
13.12	even	2	inner	1183.2.e.j.170.2		24
39.2	even	12		819.2.do.e.667.1		12
39.20	even	12		819.2.bm.f.478.6		12
91.2	odd	12		637.2.q.g.589.1		12
91.12	odd	6		8281.2.a.co.1.11		12
91.20	even	12		637.2.k.i.569.1		12
91.25	even	6	inner	1183.2.e.j.508.2		24
91.33	even	12		637.2.q.i.491.1		12
91.41	even	12		637.2.u.g.30.6		12
91.46	odd	12		91.2.u.b.88.6	yes	12
91.51	even	6		8281.2.a.cp.1.11		12
91.54	even	12		637.2.q.i.589.1		12
91.59	even	12		637.2.u.g.361.6		12
91.67	odd	12		91.2.k.b.4.6	✓	12
91.72	odd	12		637.2.q.g.491.1		12
91.80	even	12		637.2.k.i.459.6		12
273.137	even	12		819.2.do.e.361.1		12
273.158	even	12		819.2.bm.f.550.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.6	✓	12	91.67	odd	12
91.2.k.b.23.1	yes	12	13.7	odd	12
91.2.u.b.30.6	yes	12	13.2	odd	12
91.2.u.b.88.6	yes	12	91.46	odd	12
637.2.k.i.459.6		12	91.80	even	12
637.2.k.i.569.1		12	91.20	even	12
637.2.q.g.491.1		12	91.72	odd	12
637.2.q.g.589.1		12	91.2	odd	12
637.2.q.i.491.1		12	91.33	even	12
637.2.q.i.589.1		12	91.54	even	12
637.2.u.g.30.6		12	91.41	even	12
637.2.u.g.361.6		12	91.59	even	12
819.2.bm.f.478.6		12	39.20	even	12
819.2.bm.f.550.1		12	273.158	even	12
819.2.do.e.361.1		12	273.137	even	12
819.2.do.e.667.1		12	39.2	even	12
1183.2.e.j.170.2		24	13.12	even	2	inner
1183.2.e.j.170.11		24	1.1	even	1	trivial
1183.2.e.j.508.2		24	91.25	even	6	inner
1183.2.e.j.508.11		24	7.4	even	3	inner
8281.2.a.co.1.2		12	7.5	odd	6
8281.2.a.co.1.11		12	91.12	odd	6
8281.2.a.cp.1.2		12	7.2	even	3
8281.2.a.cp.1.11		12	91.51	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)

\(f(q)\)	\(=\)	\(q+(1.15163 - 1.99469i) q^{2} +(0.736680 + 1.27597i) q^{3} +(-1.65252 - 2.86225i) q^{4} +(0.423646 - 0.733776i) q^{5} +3.39354 q^{6} +(1.00088 + 2.44913i) q^{7} -3.00585 q^{8} +(0.414604 - 0.718115i) q^{9} +O(q^{10})\)	\(q+(1.15163 - 1.99469i) q^{2} +(0.736680 + 1.27597i) q^{3} +(-1.65252 - 2.86225i) q^{4} +(0.423646 - 0.733776i) q^{5} +3.39354 q^{6} +(1.00088 + 2.44913i) q^{7} -3.00585 q^{8} +(0.414604 - 0.718115i) q^{9} +(-0.975769 - 1.69008i) q^{10} +(-0.751701 - 1.30198i) q^{11} +(2.43476 - 4.21712i) q^{12} +(6.03790 + 0.824057i) q^{14} +1.24837 q^{15} +(-0.156597 + 0.271234i) q^{16} +(-1.03570 - 1.79389i) q^{17} +(-0.954943 - 1.65401i) q^{18} +(-0.0237136 + 0.0410731i) q^{19} -2.80033 q^{20} +(-2.38768 + 3.08132i) q^{21} -3.46274 q^{22} +(3.90935 - 6.77119i) q^{23} +(-2.21435 - 3.83536i) q^{24} +(2.14105 + 3.70840i) q^{25} +5.64180 q^{27} +(5.35604 - 6.91200i) q^{28} +1.35971 q^{29} +(1.43766 - 2.49010i) q^{30} +(3.93052 + 6.80787i) q^{31} +(-2.64516 - 4.58156i) q^{32} +(1.10753 - 1.91829i) q^{33} -4.77099 q^{34} +(2.22113 + 0.303142i) q^{35} -2.74056 q^{36} +(3.35110 - 5.80427i) q^{37} +(0.0546187 + 0.0946024i) q^{38} +(-1.27341 + 2.20562i) q^{40} -10.0184 q^{41} +(3.39653 + 8.31123i) q^{42} +9.26566 q^{43} +(-2.48440 + 4.30311i) q^{44} +(-0.351290 - 0.608453i) q^{45} +(-9.00428 - 15.5959i) q^{46} +(0.180007 - 0.311781i) q^{47} -0.461448 q^{48} +(-4.99648 + 4.90257i) q^{49} +9.86281 q^{50} +(1.52596 - 2.64304i) q^{51} +(-1.35591 - 2.34850i) q^{53} +(6.49729 - 11.2536i) q^{54} -1.27382 q^{55} +(-3.00849 - 7.36171i) q^{56} -0.0698773 q^{57} +(1.56588 - 2.71219i) q^{58} +(0.820598 + 1.42132i) q^{59} +(-2.06295 - 3.57313i) q^{60} +(-2.26097 + 3.91612i) q^{61} +18.1061 q^{62} +(2.17373 + 0.296672i) q^{63} -12.8114 q^{64} +(-2.55093 - 4.41834i) q^{66} +(-1.02133 - 1.76900i) q^{67} +(-3.42303 + 5.92886i) q^{68} +11.5198 q^{69} +(3.16260 - 4.08136i) q^{70} -14.2139 q^{71} +(-1.24624 + 2.15854i) q^{72} +(3.38075 + 5.85563i) q^{73} +(-7.71847 - 13.3688i) q^{74} +(-3.15454 + 5.46382i) q^{75} +0.156749 q^{76} +(2.43637 - 3.14414i) q^{77} +(-5.82952 + 10.0970i) q^{79} +(0.132683 + 0.229814i) q^{80} +(2.91240 + 5.04442i) q^{81} +(-11.5376 + 19.9837i) q^{82} -11.5362 q^{83} +(12.7652 + 1.74220i) q^{84} -1.75508 q^{85} +(10.6706 - 18.4821i) q^{86} +(1.00167 + 1.73494i) q^{87} +(2.25950 + 3.91357i) q^{88} +(-8.75561 + 15.1652i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(-5.79108 + 10.0304i) q^{93} +(-0.414604 - 0.718115i) q^{94} +(0.0200923 + 0.0348009i) q^{95} +(3.89728 - 6.75029i) q^{96} -0.426229 q^{97} +(4.02499 + 15.6124i) q^{98} -1.24663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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