LMFDB - Embedded newform 725.2.r.d.574.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(24,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 4]))

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

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

chi := DirichletCharacter("725.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.r (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			574.1
Character	$\chi$	$=$	725.574
Dual form			725.2.r.d.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18993 - 1.74641i) q^{2} +(-0.690597 - 0.157624i) q^{3} +(1.30080 + 5.69919i) q^{4} +(1.23708 + 1.55125i) q^{6} +(-1.77264 - 0.404594i) q^{7} +(4.67383 - 9.70531i) q^{8} +(-2.25083 - 1.08394i) q^{9} +O(q^{10})$	\(q+(-2.18993 - 1.74641i) q^{2} +(-0.690597 - 0.157624i) q^{3} +(1.30080 + 5.69919i) q^{4} +(1.23708 + 1.55125i) q^{6} +(-1.77264 - 0.404594i) q^{7} +(4.67383 - 9.70531i) q^{8} +(-2.25083 - 1.08394i) q^{9} +(3.09974 - 1.49276i) q^{11} -4.14088i q^{12} +(0.547090 + 1.13604i) q^{13} +(3.17538 + 3.98180i) q^{14} +(-16.6512 + 8.01877i) q^{16} +6.04532i q^{17} +(3.03615 + 6.30463i) q^{18} +(0.717470 + 3.14344i) q^{19} +(1.16041 + 0.558823i) q^{21} +(-9.39519 - 2.14439i) q^{22} +(0.539083 - 0.429904i) q^{23} +(-4.75752 + 5.96575i) q^{24} +(0.785912 - 3.44330i) q^{26} +(3.04501 + 2.42831i) q^{27} -10.6289i q^{28} +(0.718081 - 5.33707i) q^{29} +(0.304181 - 0.381431i) q^{31} +(29.4650 + 6.72519i) q^{32} +(-2.37597 + 0.542299i) q^{33} +(10.5576 - 13.2388i) q^{34} +(3.24971 - 14.2379i) q^{36} +(2.34141 - 4.86199i) q^{37} +(3.91853 - 8.13692i) q^{38} +(-0.198751 - 0.870783i) q^{39} +3.37890 q^{41} +(-1.56528 - 3.25033i) q^{42} +(-2.28412 + 1.82152i) q^{43} +(12.5397 + 15.7242i) q^{44} -1.93134 q^{46} +(-3.79352 - 7.87732i) q^{47} +(12.7632 - 2.91311i) q^{48} +(-3.32822 - 1.60279i) q^{49} +(0.952888 - 4.17488i) q^{51} +(-5.76288 + 4.59574i) q^{52} +(4.30737 + 3.43501i) q^{53} +(-2.42752 - 10.6357i) q^{54} +(-12.2117 + 15.3130i) q^{56} -2.28394i q^{57} +(-10.8933 + 10.4338i) q^{58} +11.4694 q^{59} +(1.82638 - 8.00189i) q^{61} +(-1.33227 + 0.304082i) q^{62} +(3.55136 + 2.83211i) q^{63} +(-29.7354 - 37.2870i) q^{64} +(6.15028 + 2.96182i) q^{66} +(6.25922 - 12.9974i) q^{67} +(-34.4534 + 7.86377i) q^{68} +(-0.440052 + 0.211918i) q^{69} +(3.47791 - 1.67487i) q^{71} +(-21.0400 + 16.7788i) q^{72} +(1.92414 - 1.53445i) q^{73} +(-13.6186 + 6.55835i) q^{74} +(-16.9818 + 8.17800i) q^{76} +(-6.09869 + 1.39199i) q^{77} +(-1.08550 + 2.25406i) q^{78} +(0.240998 + 0.116059i) q^{79} +(2.95275 + 3.70264i) q^{81} +(-7.39955 - 5.90095i) q^{82} +(5.40078 - 1.23269i) q^{83} +(-1.67538 + 7.34030i) q^{84} +8.18319 q^{86} +(-1.33716 + 3.57258i) q^{87} -37.0608i q^{88} +(0.696833 - 0.873801i) q^{89} +(-0.510158 - 2.23515i) q^{91} +(3.15135 + 2.51312i) q^{92} +(-0.270189 + 0.215468i) q^{93} +(-5.44950 + 23.8758i) q^{94} +(-19.2884 - 9.28879i) q^{96} +(1.10746 - 0.252772i) q^{97} +(4.48945 + 9.32243i) q^{98} -8.59505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 20 q^{4} + 4 q^{6} + 36 q^{9}+O(q^{10}) $ 72 * q + 20 * q^4 + 4 * q^6 + 36 * q^9	$ 72 q + 20 q^{4} + 4 q^{6} + 36 q^{9} + 8 q^{11} - 32 q^{14} - 40 q^{16} + 12 q^{19} + 62 q^{21} - 32 q^{24} - 64 q^{26} + 42 q^{29} - 14 q^{31} + 96 q^{34} - 24 q^{36} - 38 q^{39} - 56 q^{41} + 62 q^{44} + 152 q^{46} - 100 q^{49} - 28 q^{51} - 86 q^{54} + 12 q^{56} - 4 q^{59} - 8 q^{61} - 174 q^{64} + 132 q^{66} + 96 q^{69} + 54 q^{71} + 46 q^{74} - 80 q^{76} - 164 q^{79} - 98 q^{81} + 68 q^{84} - 252 q^{86} - 72 q^{89} - 90 q^{91} - 178 q^{96} + 16 q^{99}+O(q^{100}) $ 72 * q + 20 * q^4 + 4 * q^6 + 36 * q^9 + 8 * q^11 - 32 * q^14 - 40 * q^16 + 12 * q^19 + 62 * q^21 - 32 * q^24 - 64 * q^26 + 42 * q^29 - 14 * q^31 + 96 * q^34 - 24 * q^36 - 38 * q^39 - 56 * q^41 + 62 * q^44 + 152 * q^46 - 100 * q^49 - 28 * q^51 - 86 * q^54 + 12 * q^56 - 4 * q^59 - 8 * q^61 - 174 * q^64 + 132 * q^66 + 96 * q^69 + 54 * q^71 + 46 * q^74 - 80 * q^76 - 164 * q^79 - 98 * q^81 + 68 * q^84 - 252 * q^86 - 72 * q^89 - 90 * q^91 - 178 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$-1$

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 $

$2$	−2.18993	−	1.74641i	−1.54852	−	1.23490i	−0.860831	−	0.508891i	$-0.830056\pi$
$2$	−2.18993	−	1.74641i	−1.54852	−	1.23490i	−0.687685	−	0.726009i	$-0.741373\pi$
$3$	−0.690597	−	0.157624i	−0.398716	−	0.0910044i	0.0184609	−	0.999830i	$-0.494123\pi$
$3$	−0.690597	−	0.157624i	−0.398716	−	0.0910044i	−0.417177	+	0.908825i	$0.636981\pi$
$4$	1.30080	+	5.69919i	0.650402	+	2.84960i
$5$		0			0
$5$		0			0
$6$	1.23708	+	1.55125i	0.505037	+	0.633297i
$7$	−1.77264	−	0.404594i	−0.669996	−	0.152922i	−0.126026	−	0.992027i	$-0.540222\pi$
$7$	−1.77264	−	0.404594i	−0.669996	−	0.152922i	−0.543970	+	0.839105i	$0.683079\pi$
$8$	4.67383	−	9.70531i	1.65245	−	3.43135i
$9$	−2.25083	−	1.08394i	−0.750276	−	0.361314i
$10$		0			0
$11$	3.09974	−	1.49276i	0.934607	−	0.450083i	0.0963435	−	0.995348i	$-0.469285\pi$
$11$	3.09974	−	1.49276i	0.934607	−	0.450083i	0.838264	+	0.545265i	$0.183571\pi$
$12$		−	4.14088i		−	1.19537i
$13$	0.547090	+	1.13604i	0.151735	+	0.315082i	0.962956	−	0.269658i	$-0.0869107\pi$
$13$	0.547090	+	1.13604i	0.151735	+	0.315082i	−0.811221	+	0.584740i	$0.801196\pi$
$14$	3.17538	+	3.98180i	0.848655	+	1.06418i
$15$		0			0
$16$	−16.6512	+	8.01877i	−4.16279	+	2.00469i
$17$			6.04532i			1.46620i	0.680118	+	0.733102i	$0.261928\pi$
$17$			6.04532i			1.46620i	−0.680118	+	0.733102i	$0.738072\pi$
$18$	3.03615	+	6.30463i	0.715628	+	1.48602i
$19$	0.717470	+	3.14344i	0.164599	+	0.721154i	0.988097	+	0.153835i	$0.0491624\pi$
$19$	0.717470	+	3.14344i	0.164599	+	0.721154i	−0.823498	+	0.567320i	$0.807980\pi$
$20$		0			0
$21$	1.16041	+	0.558823i	0.253222	+	0.121945i
$22$	−9.39519	−	2.14439i	−2.00306	−	0.457186i
$23$	0.539083	−	0.429904i	0.112407	−	0.0896412i	−0.565673	−	0.824629i	$-0.691384\pi$
$23$	0.539083	−	0.429904i	0.112407	−	0.0896412i	0.678080	+	0.734988i	$0.262812\pi$
$24$	−4.75752	+	5.96575i	−0.971126	+	1.21775i
$25$		0			0
$26$	0.785912	−	3.44330i	0.154130	−	0.675288i
$27$	3.04501	+	2.42831i	0.586012	+	0.467329i
$28$		−	10.6289i		−	2.00868i
$29$	0.718081	−	5.33707i	0.133344	−	0.991070i
$29$	0.718081	−	5.33707i	0.133344	−	0.991070i
$30$		0			0
$31$	0.304181	−	0.381431i	0.0546325	−	0.0685070i	−0.753765	−	0.657145i	$-0.771764\pi$
$31$	0.304181	−	0.381431i	0.0546325	−	0.0685070i	0.808397	+	0.588638i	$0.200336\pi$
$32$	29.4650	+	6.72519i	5.20872	+	1.18886i
$33$	−2.37597	+	0.542299i	−0.413603	+	0.0944021i
$34$	10.5576	−	13.2388i	1.81062	−	2.27044i
$35$		0			0
$36$	3.24971	−	14.2379i	0.541618	−	2.37298i
$37$	2.34141	−	4.86199i	0.384925	−	0.799306i	−0.615017	−	0.788514i	$-0.710851\pi$
$37$	2.34141	−	4.86199i	0.384925	−	0.799306i	0.999942	−	0.0107913i	$-0.00343505\pi$
$38$	3.91853	−	8.13692i	0.635670	−	1.31998i
$39$	−0.198751	−	0.870783i	−0.0318256	−	0.139437i
$40$		0			0
$41$	3.37890			0.527695			0.263848	−	0.964564i	$-0.415008\pi$
$41$	3.37890			0.527695			0.263848	+	0.964564i	$0.415008\pi$
$42$	−1.56528	−	3.25033i	−0.241528	−	0.501537i
$43$	−2.28412	+	1.82152i	−0.348324	+	0.277779i	−0.781986	−	0.623297i	$-0.785793\pi$
$43$	−2.28412	+	1.82152i	−0.348324	+	0.277779i	0.433661	+	0.901076i	$0.357222\pi$
$44$	12.5397	+	15.7242i	1.89043	+	2.37052i
$45$		0			0
$46$	−1.93134			−0.284761
$47$	−3.79352	−	7.87732i	−0.553341	−	1.14902i	−0.970703	−	0.240284i	$-0.922759\pi$
$47$	−3.79352	−	7.87732i	−0.553341	−	1.14902i	0.417362	−	0.908741i	$-0.362955\pi$
$48$	12.7632	−	2.91311i	1.84221	−	0.420472i
$49$	−3.32822	−	1.60279i	−0.475460	−	0.228969i
$50$		0			0
$51$	0.952888	−	4.17488i	0.133431	−	0.584600i
$52$	−5.76288	+	4.59574i	−0.799168	+	0.637315i
$53$	4.30737	+	3.43501i	0.591663	+	0.471835i	0.872964	−	0.487784i	$-0.162195\pi$
$53$	4.30737	+	3.43501i	0.591663	+	0.471835i	−0.281302	+	0.959619i	$0.590766\pi$
$54$	−2.42752	−	10.6357i	−0.330344	−	1.44733i
$55$		0			0
$56$	−12.2117	+	15.3130i	−1.63186	+	2.04629i
$57$		−	2.28394i		−	0.302515i
$58$	−10.8933	+	10.4338i	−1.43036	+	1.37002i
$59$	11.4694			1.49318			0.746591	−	0.665283i	$-0.231689\pi$
$59$	11.4694			1.49318			0.746591	+	0.665283i	$0.231689\pi$
$60$		0			0
$61$	1.82638	−	8.00189i	0.233844	−	1.02454i	−0.712575	−	0.701596i	$-0.752471\pi$
$61$	1.82638	−	8.00189i	0.233844	−	1.02454i	0.946419	−	0.322941i	$-0.104672\pi$
$62$	−1.33227	+	0.304082i	−0.169198	+	0.0386185i
$63$	3.55136	+	2.83211i	0.447429	+	0.356813i
$64$	−29.7354	−	37.2870i	−3.71693	−	4.66088i
$65$		0			0
$66$	6.15028	+	2.96182i	0.757047	+	0.364575i
$67$	6.25922	−	12.9974i	0.764686	−	1.58789i	−0.0435665	−	0.999051i	$-0.513872\pi$
$67$	6.25922	−	12.9974i	0.764686	−	1.58789i	0.808252	−	0.588836i	$-0.200414\pi$
$68$	−34.4534	+	7.86377i	−4.17809	+	0.953622i
$69$	−0.440052	+	0.211918i	−0.0529761	+	0.0255119i
$70$		0			0
$71$	3.47791	−	1.67487i	0.412752	−	0.198771i	−0.215972	−	0.976400i	$-0.569292\pi$
$71$	3.47791	−	1.67487i	0.412752	−	0.198771i	0.628724	+	0.777629i	$0.283578\pi$
$72$	−21.0400	+	16.7788i	−2.47959	+	1.97740i
$73$	1.92414	−	1.53445i	0.225204	−	0.179594i	−0.504387	−	0.863477i	$-0.668282\pi$
$73$	1.92414	−	1.53445i	0.225204	−	0.179594i	0.729591	+	0.683883i	$0.239710\pi$
$74$	−13.6186	+	6.55835i	−1.58313	+	0.762393i
$75$		0			0
$76$	−16.9818	+	8.17800i	−1.94794	+	0.938080i
$77$	−6.09869	+	1.39199i	−0.695010	+	0.158632i
$78$	−1.08550	+	2.25406i	−0.122908	+	0.255222i
$79$	0.240998	+	0.116059i	0.0271144	+	0.0130576i	0.447392	−	0.894338i	$-0.352353\pi$
$79$	0.240998	+	0.116059i	0.0271144	+	0.0130576i	−0.420277	+	0.907396i	$0.638067\pi$
$80$		0			0
$81$	2.95275	+	3.70264i	0.328084	+	0.411404i
$82$	−7.39955	−	5.90095i	−0.817144	−	0.651651i
$83$	5.40078	−	1.23269i	0.592813	−	0.135306i	0.0844191	−	0.996430i	$-0.473097\pi$
$83$	5.40078	−	1.23269i	0.592813	−	0.135306i	0.508394	+	0.861125i	$0.330239\pi$
$84$	−1.67538	+	7.34030i	−0.182799	+	0.800893i
$85$		0			0
$86$	8.18319			0.882416
$87$	−1.33716	+	3.57258i	−0.143358	+	0.383021i
$88$		−	37.0608i		−	3.95070i
$89$	0.696833	−	0.873801i	0.0738641	−	0.0926227i	−0.743527	−	0.668706i	$-0.766848\pi$
$89$	0.696833	−	0.873801i	0.0738641	−	0.0926227i	0.817391	+	0.576084i	$0.195420\pi$
$90$		0			0
$91$	−0.510158	−	2.23515i	−0.0534791	−	0.234307i
$92$	3.15135	+	2.51312i	0.328551	+	0.262010i
$93$	−0.270189	+	0.215468i	−0.0280173	+	0.0223430i
$94$	−5.44950	+	23.8758i	−0.562073	+	2.46260i
$95$		0			0
$96$	−19.2884	−	9.28879i	−1.96861	−	0.948033i
$97$	1.10746	−	0.252772i	0.112446	−	0.0256651i	−0.165928	−	0.986138i	$-0.553062\pi$
$97$	1.10746	−	0.252772i	0.112446	−	0.0256651i	0.278374	+	0.960473i	$0.410205\pi$
$98$	4.48945	+	9.32243i	0.453503	+	0.941708i
$99$	−8.59505			−0.863835
$100$		0			0
$101$	−5.98735	−	7.50790i	−0.595763	−	0.747064i	0.388948	−	0.921260i	$-0.372839\pi$
$101$	−5.98735	−	7.50790i	−0.595763	−	0.747064i	−0.984711	+	0.174196i	$0.944267\pi$
$102$	−9.37782	+	7.47856i	−0.928542	+	0.740488i
$103$	2.12634	+	4.41538i	0.209514	+	0.435060i	0.979071	−	0.203517i	$-0.0652373\pi$
$103$	2.12634	+	4.41538i	0.209514	+	0.435060i	−0.769557	+	0.638578i	$0.779523\pi$
$104$	13.5827			1.33189
$105$		0			0
$106$	−3.43390	−	15.0449i	−0.333530	−	1.46129i
$107$	5.15423	−	10.7029i	0.498278	−	1.03469i	−0.488493	−	0.872568i	$-0.662453\pi$
$107$	5.15423	−	10.7029i	0.498278	−	1.03469i	0.986771	−	0.162118i	$-0.0518324\pi$
$108$	−9.87846	+	20.5128i	−0.950555	+	1.97385i
$109$	3.12370	−	13.6858i	0.299196	−	1.31086i	−0.572132	−	0.820162i	$-0.693883\pi$
$109$	3.12370	−	13.6858i	0.299196	−	1.31086i	0.871328	−	0.490701i	$-0.163259\pi$
$110$		0			0
$111$	−2.38334	+	2.98861i	−0.226216	+	0.283666i
$112$	32.7609	−	7.47746i	3.09561	−	0.706553i
$113$	−4.06166	−	0.927048i	−0.382089	−	0.0872093i	0.0271623	−	0.999631i	$-0.491353\pi$
$113$	−4.06166	−	0.927048i	−0.382089	−	0.0872093i	−0.409251	+	0.912422i	$0.634210\pi$
$114$	−3.98870	+	5.00167i	−0.373576	+	0.468450i
$115$		0			0
$116$	31.3511	−	2.85000i	2.91088	−	0.264616i
$117$		−	3.15005i		−	0.291223i
$118$	−25.1171	−	20.0302i	−2.31222	−	1.84393i
$119$	2.44590	−	10.7162i	0.224215	−	0.982351i
$120$		0			0
$121$	0.521685	−	0.654173i	0.0474259	−	0.0594703i
$122$	−17.9743	+	14.3340i	−1.62731	+	1.29774i
$123$	−2.33346	−	0.532596i	−0.210401	−	0.0480226i
$124$	2.56953	+	1.23742i	0.230750	+	0.111123i
$125$		0			0
$126$	−2.83119	−	12.4043i	−0.252223	−	1.10506i
$127$	1.94287	+	4.03441i	0.172402	+	0.357996i	0.969210	−	0.246236i	$-0.0791940\pi$
$127$	1.94287	+	4.03441i	0.172402	+	0.357996i	−0.796808	+	0.604233i	$0.793480\pi$
$128$			73.1410i			6.46481i
$129$	1.86452	−	0.897905i	0.164162	−	0.0790561i
$130$		0			0
$131$	12.2530	+	15.3647i	1.07055	+	1.34242i	0.936192	+	0.351490i	$0.114325\pi$
$131$	12.2530	+	15.3647i	1.07055	+	1.34242i	0.134355	+	0.990933i	$0.457104\pi$
$132$	−6.18133	−	12.8357i	−0.538016	−	1.11720i
$133$		−	5.86248i		−	0.508341i
$134$	−36.4061	+	17.5323i	−3.14501	+	1.51456i
$135$		0			0
$136$	58.6717	+	28.2548i	5.03105	+	2.42283i
$137$	−2.08578	+	4.33116i	−0.178200	+	0.370036i	−0.970867	−	0.239619i	$-0.922978\pi$
$137$	−2.08578	+	4.33116i	−0.178200	+	0.370036i	0.792667	+	0.609655i	$0.208692\pi$
$138$	1.33378	+	0.304427i	0.113539	+	0.0259145i
$139$	3.12690	+	3.92101i	0.265220	+	0.332576i	0.896553	−	0.442936i	$-0.146063\pi$
$139$	3.12690	+	3.92101i	0.265220	+	0.332576i	−0.631333	+	0.775512i	$0.717492\pi$
$140$		0			0
$141$	1.37813	+	6.03800i	0.116060	+	0.508491i
$142$	−10.5414	−	2.40601i	−0.884616	−	0.201908i
$143$	3.39167	+	2.70477i	0.283626	+	0.226184i
$144$	46.1708			3.84756
$145$		0			0
$146$	−6.89353			−0.570513
$147$	2.04582	+	1.63149i	0.168736	+	0.134563i
$148$	30.7551	+	7.01965i	2.52805	+	0.577012i
$149$	−2.56850	−	11.2533i	−0.210420	−	0.921909i	−0.964282	−	0.264877i	$-0.914669\pi$
$149$	−2.56850	−	11.2533i	−0.210420	−	0.921909i	0.753863	−	0.657032i	$-0.228188\pi$
$150$		0			0
$151$	−3.37357	−	4.23032i	−0.274537	−	0.344258i	0.625380	−	0.780321i	$-0.284944\pi$
$151$	−3.37357	−	4.23032i	−0.274537	−	0.344258i	−0.899916	+	0.436062i	$0.856373\pi$
$152$	33.8614	+	7.72864i	2.74652	+	0.626875i
$153$	6.55277	−	13.6070i	0.529760	−	1.10006i
$154$	15.7867	+	7.60248i	1.27213	+	0.612625i
$155$		0			0
$156$	4.70423	−	2.26544i	0.376640	−	0.181380i
$157$			3.21678i			0.256727i	0.991727	+	0.128364i	$0.0409725\pi$
$157$			3.21678i			0.256727i	−0.991727	+	0.128364i	$0.959028\pi$
$158$	−0.325084	−	0.675043i	−0.0258623	−	0.0537035i
$159$	−2.43321	−	3.05115i	−0.192966	−	0.241972i
$160$		0			0
$161$	−1.12954	+	0.543957i	−0.0890200	+	0.0428698i
$162$		−	13.2652i		−	1.04222i
$163$	5.15261	+	10.6995i	0.403584	+	0.838050i	0.999390	+	0.0349221i	$0.0111183\pi$
$163$	5.15261	+	10.6995i	0.403584	+	0.838050i	−0.595806	+	0.803128i	$0.703167\pi$
$164$	4.39528	+	19.2570i	0.343214	+	1.50372i
$165$		0			0
$166$	−13.9801	−	6.73248i	−1.08507	−	0.522542i
$167$	15.0098	+	3.42589i	1.16149	+	0.265103i	0.759480	−	0.650531i	$-0.225454\pi$
$167$	15.0098	+	3.42589i	1.16149	+	0.265103i	0.402013	+	0.915634i	$0.368311\pi$
$168$	10.8471	−	8.65027i	0.836871	−	0.667383i
$169$	7.11408	−	8.92077i	0.547237	−	0.686213i
$170$		0			0
$171$	1.79240	−	7.85304i	0.137069	−	0.600537i
$172$	−13.3524	−	10.6482i	−1.01811	−	0.811916i
$173$		−	24.9271i		−	1.89517i	−0.319499	−	0.947587i	$-0.603515\pi$
$173$		−	24.9271i		−	1.89517i	0.319499	−	0.947587i	$-0.396485\pi$
$174$	9.16748	−	5.48848i	0.694985	−	0.416081i
$175$		0			0
$176$	−39.6442	+	49.7122i	−2.98829	+	3.74720i
$177$	−7.92070	−	1.80785i	−0.595356	−	0.135886i
$178$	−3.05203	+	0.696607i	−0.228760	+	0.0522129i
$179$	−4.11700	+	5.16255i	−0.307719	+	0.385867i	−0.911512	−	0.411274i	$-0.865084\pi$
$179$	−4.11700	+	5.16255i	−0.307719	+	0.385867i	0.603793	+	0.797141i	$0.293655\pi$
$180$		0			0
$181$	−2.06054	+	9.02783i	−0.153159	+	0.671033i	0.838796	+	0.544445i	$0.183260\pi$
$181$	−2.06054	+	9.02783i	−0.153159	+	0.671033i	−0.991955	+	0.126588i	$0.959597\pi$
$182$	−2.78628	+	5.78577i	−0.206533	+	0.428870i
$183$	−2.52258	+	5.23820i	−0.186475	+	0.387219i
$184$	−1.65277	−	7.24126i	−0.121844	−	0.533833i
$185$		0			0
$186$	0.967992			0.0709766
$187$	9.02419	+	18.7389i	0.659914	+	1.37033i
$188$	39.9597	−	31.8668i	2.91436	−	2.32413i
$189$	−4.41523	−	5.53652i	−0.321160	−	0.402722i
$190$		0			0
$191$	−2.58646			−0.187149			−0.0935747	−	0.995612i	$-0.529829\pi$
$191$	−2.58646			−0.187149			−0.0935747	+	0.995612i	$0.529829\pi$
$192$	14.6578	+	30.4373i	1.05784	+	2.19663i
$193$	7.08788	−	1.61776i	0.510197	−	0.116449i	0.0403299	−	0.999186i	$-0.487159\pi$
$193$	7.08788	−	1.61776i	0.510197	−	0.116449i	0.469867	+	0.882737i	$0.344302\pi$
$194$	−2.86672	−	1.38054i	−0.205818	−	0.0991168i
$195$		0			0
$196$	4.80523	−	21.0531i	0.343230	−	1.50379i
$197$	16.0126	−	12.7696i	1.14085	−	0.909799i	0.144039	−	0.989572i	$-0.453991\pi$
$197$	16.0126	−	12.7696i	1.14085	−	0.909799i	0.996813	+	0.0797725i	$0.0254194\pi$
$198$	18.8226	+	15.0105i	1.33766	+	1.06675i
$199$	2.41093	+	10.5630i	0.170907	+	0.748791i	0.985627	+	0.168937i	$0.0540333\pi$
$199$	2.41093	+	10.5630i	0.170907	+	0.748791i	−0.814720	+	0.579854i	$0.803110\pi$
$200$		0			0
$201$	−6.37131	+	7.98937i	−0.449397	+	0.563526i
$202$			26.8982i			1.89255i
$203$	−3.43225	+	9.17019i	−0.240897	+	0.643621i
$204$	25.0329			1.75266
$205$		0			0
$206$	3.05455	−	13.3828i	0.212820	−	0.932427i
$207$	−1.67937	+	0.383306i	−0.116725	+	0.0266416i
$208$	−18.2194	−	14.5295i	−1.26329	−	1.00744i
$209$	6.91636	+	8.67284i	0.478415	+	0.599913i
$210$		0			0
$211$	−12.6081	−	6.07175i	−0.867978	−	0.417996i	−0.0537590	−	0.998554i	$-0.517120\pi$
$211$	−12.6081	−	6.07175i	−0.867978	−	0.417996i	−0.814219	+	0.580558i	$0.802835\pi$
$212$	−13.9738	+	29.0168i	−0.959722	+	1.99288i
$213$	−2.66584	+	0.608460i	−0.182660	+	0.0416910i
$214$	−29.9790	+	14.4371i	−2.04933	+	0.986903i
$215$		0			0
$216$	37.7994	−	18.2032i	2.57192	−	1.23857i
$217$	−0.693528	+	0.553070i	−0.0470798	+	0.0375448i
$218$	−30.7418	+	24.5157i	−2.08209	+	1.66042i
$219$	−1.57067	+	0.756397i	−0.106136	+	0.0511126i
$220$		0			0
$221$	−6.86775	+	3.30733i	−0.461975	+	0.222475i
$222$	10.4387	−	2.38256i	0.700599	−	0.159907i
$223$	−7.29137	+	15.1407i	−0.488266	+	1.01390i	0.500682	+	0.865632i	$0.333083\pi$
$223$	−7.29137	+	15.1407i	−0.488266	+	1.01390i	−0.988948	+	0.148264i	$0.952632\pi$
$224$	−49.5099	−	23.8427i	−3.30802	−	1.59306i
$225$		0			0
$226$	7.27575	+	9.12351i	0.483976	+	0.606887i
$227$	4.84963	+	3.86745i	0.321881	+	0.256692i	0.771077	−	0.636741i	$-0.219718\pi$
$227$	4.84963	+	3.86745i	0.321881	+	0.256692i	−0.449196	+	0.893433i	$0.648290\pi$
$228$	13.0166	−	2.97096i	0.862046	−	0.196756i
$229$	−5.63524	+	24.6896i	−0.372387	+	1.63153i	0.347668	+	0.937618i	$0.386974\pi$
$229$	−5.63524	+	24.6896i	−0.372387	+	1.63153i	−0.720055	+	0.693917i	$0.755884\pi$
$230$		0			0
$231$	4.43115			0.291548
$232$	−48.4418	−	31.9138i	−3.18036	−	2.09524i
$233$		−	14.6568i		−	0.960201i	−0.877213	−	0.480101i	$-0.840600\pi$
$233$		−	14.6568i		−	0.960201i	0.877213	−	0.480101i	$-0.159400\pi$
$234$	−5.50129	+	6.89840i	−0.359631	+	0.450963i
$235$		0			0
$236$	14.9194	+	65.3661i	0.971169	+	4.25497i
$237$	−0.148139	−	0.118137i	−0.00962266	−	0.00767382i
$238$	−24.0712	+	19.1962i	−1.56031	+	1.24430i
$239$	2.83553	−	12.4233i	0.183415	−	0.803594i	−0.796574	−	0.604542i	$-0.793356\pi$
$239$	2.83553	−	12.4233i	0.183415	−	0.803594i	0.979989	−	0.199053i	$-0.0637865\pi$
$240$		0			0
$241$	−15.2323	−	7.33551i	−0.981201	−	0.472521i	−0.126683	−	0.991943i	$-0.540433\pi$
$241$	−15.2323	−	7.33551i	−0.981201	−	0.472521i	−0.854518	+	0.519422i	$0.826147\pi$
$242$	−2.28491	+	0.521516i	−0.146880	+	0.0335243i
$243$	−6.52509	−	13.5495i	−0.418585	−	0.869200i
$244$	47.9801			3.07161
$245$		0			0
$246$	4.17998	+	5.24153i	0.266506	+	0.334187i
$247$	−3.17857	+	2.53482i	−0.202247	+	0.161287i
$248$	−2.28021	−	4.73491i	−0.144794	−	0.300667i
$249$	−3.92407			−0.248678
$250$		0			0
$251$	−0.953932	−	4.17945i	−0.0602116	−	0.263804i	0.935858	−	0.352377i	$-0.114627\pi$
$251$	−0.953932	−	4.17945i	−0.0602116	−	0.263804i	−0.996070	+	0.0885727i	$0.971769\pi$
$252$	−11.5211	+	23.9239i	−0.725763	+	1.50706i
$253$	1.02927	−	2.13731i	0.0647099	−	0.134372i
$254$	2.79100	−	12.2281i	0.175123	−	0.767262i
$255$		0			0
$256$	68.2635	−	85.5997i	4.26647	−	5.34998i
$257$	−8.26148	+	1.88563i	−0.515337	+	0.117622i	−0.472277	−	0.881450i	$-0.656568\pi$
$257$	−8.26148	+	1.88563i	−0.515337	+	0.117622i	−0.0430598	+	0.999072i	$0.513711\pi$
$258$	−5.65128	−	1.28987i	−0.351834	−	0.0803037i
$259$	−6.11761	+	7.67124i	−0.380130	+	0.476668i
$260$		0			0
$261$	−7.40135	+	11.2345i	−0.458132	+	0.695397i
$262$		−	55.0465i		−	3.40078i
$263$	5.52154	+	4.40328i	0.340473	+	0.271518i	0.778767	−	0.627314i	$-0.215846\pi$
$263$	5.52154	+	4.40328i	0.340473	+	0.271518i	−0.438294	+	0.898832i	$0.644417\pi$
$264$	−5.84169	+	25.5941i	−0.359531	+	1.57521i
$265$		0			0
$266$	−10.2383	+	12.8384i	−0.627751	+	0.787174i
$267$	−0.618963	+	0.493606i	−0.0378799	+	0.0302082i
$268$	82.2168	+	18.7654i	5.02219	+	1.14628i
$269$	21.1126	+	10.1673i	1.28726	+	0.619912i	0.947246	−	0.320508i	$-0.103854\pi$
$269$	21.1126	+	10.1673i	1.28726	+	0.619912i	0.340015	+	0.940420i	$0.389568\pi$
$270$		0			0
$271$	3.34691	+	14.6638i	0.203311	+	0.890762i	0.968904	+	0.247437i	$0.0795883\pi$
$271$	3.34691	+	14.6638i	0.203311	+	0.890762i	−0.765594	+	0.643325i	$0.777555\pi$
$272$	−48.4760	−	100.661i	−2.93929	−	6.10350i
$273$			1.62400i			0.0982889i
$274$	12.1317	−	5.84232i	0.732903	−	0.352948i
$275$		0			0
$276$	−1.78018	−	2.23228i	−0.107154	−	0.134367i
$277$	−1.19861	−	2.48894i	−0.0720174	−	0.149546i	0.861852	−	0.507160i	$-0.169305\pi$
$277$	−1.19861	−	2.48894i	−0.0720174	−	0.149546i	−0.933869	+	0.357614i	$0.883590\pi$
$278$		−	14.0476i		−	0.842519i
$279$	−1.09811	+	0.528820i	−0.0657419	+	0.0316597i
$280$		0			0
$281$	−26.7047	−	12.8603i	−1.59307	−	0.767181i	−0.593770	−	0.804635i	$-0.702361\pi$
$281$	−26.7047	−	12.8603i	−1.59307	−	0.767181i	−0.999298	+	0.0374541i	$0.988075\pi$
$282$	7.52682	−	15.6296i	0.448215	−	0.930729i
$283$	−3.17889	−	0.725560i	−0.188965	−	0.0431301i	0.126991	−	0.991904i	$-0.459468\pi$
$283$	−3.17889	−	0.725560i	−0.188965	−	0.0431301i	−0.315956	+	0.948774i	$0.602325\pi$
$284$	14.0695	+	17.6426i	0.834872	+	1.04690i
$285$		0			0
$286$	−2.70389	−	11.8465i	−0.159885	−	0.700500i
$287$	−5.98957	−	1.36708i	−0.353553	−	0.0806963i
$288$	−59.0309	−	47.0756i	−3.47843	−	2.77395i
$289$	−19.5458			−1.14976
$290$		0			0
$291$	−0.804655			−0.0471697
$292$	11.2481	+	8.97005i	0.658244	+	0.524932i
$293$	9.93245	+	2.26702i	0.580260	+	0.132441i	0.502569	−	0.864537i	$-0.332388\pi$
$293$	9.93245	+	2.26702i	0.580260	+	0.132441i	0.0776908	+	0.996978i	$0.475245\pi$
$294$	−1.63096	−	7.14569i	−0.0951193	−	0.416745i
$295$		0			0
$296$	−36.2437	−	45.4482i	−2.10662	−	2.64162i
$297$	13.0636	+	2.98168i	0.758028	+	0.173015i
$298$	−14.0281	+	29.1297i	−0.812627	+	1.68744i
$299$	0.783317	+	0.377226i	0.0453004	+	0.0218155i
$300$		0			0
$301$	4.78590	−	2.30477i	0.275855	−	0.132845i
$302$			15.1557i			0.872115i
$303$	2.95142	+	6.12868i	0.169554	+	0.352083i
$304$	−37.1532	−	46.5887i	−2.13088	−	2.67204i
$305$		0			0
$306$	−38.1135	+	18.3545i	−2.17880	+	1.04926i
$307$			30.1707i			1.72193i	0.508663	+	0.860966i	$0.330140\pi$
$307$			30.1707i			1.72193i	−0.508663	+	0.860966i	$0.669860\pi$
$308$	−15.8664	−	32.9469i	−0.904072	−	1.87733i
$309$	−0.772469	−	3.38441i	−0.0439443	−	0.192532i
$310$		0			0
$311$	26.9819	+	12.9938i	1.53000	+	0.736811i	0.994202	−	0.107532i	$-0.0342948\pi$
$311$	26.9819	+	12.9938i	1.53000	+	0.736811i	0.535803	+	0.844343i	$0.320009\pi$
$312$	−9.38015	−	2.14096i	−0.531046	−	0.121208i
$313$	−13.1084	+	10.4536i	−0.740928	+	0.590871i	−0.919516	−	0.393054i	$-0.871419\pi$
$313$	−13.1084	+	10.4536i	−0.740928	+	0.590871i	0.178587	+	0.983924i	$0.442847\pi$
$314$	5.61783	−	7.04454i	0.317033	−	0.397546i
$315$		0			0
$316$	−0.347949	+	1.52447i	−0.0195737	+	0.0857579i
$317$	9.99301	+	7.96916i	0.561263	+	0.447593i	0.862572	−	0.505934i	$-0.168852\pi$
$317$	9.99301	+	7.96916i	0.561263	+	0.447593i	−0.301309	+	0.953527i	$0.597424\pi$
$318$			10.9312i			0.612992i
$319$	−5.74109	−	17.6155i	−0.321439	−	0.986277i
$320$		0			0
$321$	−5.24653	+	6.57894i	−0.292833	+	0.367200i
$322$	3.42358	+	0.781410i	0.190789	+	0.0435463i
$323$	−19.0031	+	4.33733i	−1.05736	+	0.241335i
$324$	−17.2611	+	21.6447i	−0.958949	+	1.20248i
$325$		0			0
$326$	7.40189	−	32.4298i	0.409953	−	1.79612i
$327$	−4.31443	+	8.95901i	−0.238589	+	0.495434i
$328$	15.7924	−	32.7932i	0.871989	−	1.81070i
$329$	3.53743	+	15.4985i	0.195025	+	0.854460i
$330$		0			0
$331$	13.2637			0.729037			0.364518	−	0.931196i	$-0.381234\pi$
$331$	13.2637			0.729037			0.364518	+	0.931196i	$0.381234\pi$
$332$	14.0507	+	29.1766i	0.771134	+	1.60128i
$333$	−10.5402	+	8.40554i	−0.577600	+	0.460621i
$334$	−26.8874	−	33.7157i	−1.47121	−	1.84484i
$335$		0			0
$336$	−23.8032			−1.29857
$337$	−1.95093	−	4.05115i	−0.106274	−	0.220680i	0.841050	−	0.540958i	$-0.181938\pi$
$337$	−1.95093	−	4.05115i	−0.106274	−	0.220680i	−0.947324	+	0.320277i	$0.896224\pi$
$338$	−31.1587	+	7.11177i	−1.69481	+	0.386829i
$339$	2.65884	+	1.28043i	0.144409	+	0.0695435i
$340$		0			0
$341$	0.373499	−	1.63640i	0.0202261	−	0.0886162i
$342$	−17.6399	+	14.0673i	−0.953856	+	0.760675i
$343$	15.2021	+	12.1233i	0.820836	+	0.654595i
$344$	7.00286	+	30.6815i	0.377569	+	1.65424i
$345$		0			0
$346$	−43.5330	+	54.5887i	−2.34035	+	2.93471i
$347$			8.91901i			0.478798i	0.970921	+	0.239399i	$0.0769503\pi$
$347$			8.91901i			0.478798i	−0.970921	+	0.239399i	$0.923050\pi$
$348$	−22.1002	−	2.97349i	−1.18470	−	0.159396i
$349$	−16.4945			−0.882933			−0.441466	−	0.897278i	$-0.645542\pi$
$349$	−16.4945			−0.882933			−0.441466	+	0.897278i	$0.645542\pi$
$350$		0			0
$351$	−1.09278	+	4.78777i	−0.0583281	+	0.255552i
$352$	101.373	−	23.1377i	5.40319	−	1.23324i
$353$	−17.7796	−	14.1787i	−0.946311	−	0.754658i	0.0231933	−	0.999731i	$-0.492617\pi$
$353$	−17.7796	−	14.1787i	−0.946311	−	0.754658i	−0.969505	+	0.245073i	$0.921188\pi$
$354$	14.1885	+	17.7919i	0.754113	+	0.945628i
$355$		0			0
$356$	5.88640	+	2.83474i	0.311979	+	0.150241i
$357$	−3.37826	+	7.01503i	−0.178796	+	0.371275i
$358$	18.0319	−	4.11566i	0.953014	−	0.217519i
$359$	13.6918	−	6.59362i	0.722625	−	0.347998i	−0.0361538	−	0.999346i	$-0.511511\pi$
$359$	13.6918	−	6.59362i	0.722625	−	0.347998i	0.758779	+	0.651348i	$0.225796\pi$
$360$		0			0
$361$	7.75196	−	3.73315i	0.407998	−	0.196481i
$362$	20.2788	−	16.1718i	1.06583	−	0.849969i
$363$	−0.463388	+	0.369539i	−0.0243216	+	0.0193958i
$364$	12.0749	−	5.81498i	0.632898	−	0.304788i
$365$		0			0
$366$	14.6723	−	7.06583i	0.766936	−	0.369337i
$367$	25.5363	−	5.82850i	1.33299	−	0.304245i	0.504091	−	0.863650i	$-0.331828\pi$
$367$	25.5363	−	5.82850i	1.33299	−	0.304245i	0.828894	+	0.559405i	$0.188970\pi$
$368$	−5.52905	+	11.4812i	−0.288221	+	0.598498i
$369$	−7.60532	−	3.66253i	−0.395917	−	0.190664i
$370$		0			0
$371$	−6.24564	−	7.83178i	−0.324257	−	0.406606i
$372$	−1.57946	−	1.25958i	−0.0818912	−	0.0653060i
$373$	17.6582	−	4.03038i	0.914309	−	0.208685i	0.260614	−	0.965443i	$-0.416075\pi$
$373$	17.6582	−	4.03038i	0.914309	−	0.208685i	0.653695	+	0.756758i	$0.273218\pi$
$374$	12.9635	−	56.7969i	0.670328	−	2.93690i
$375$		0			0
$376$	−94.1820			−4.85707
$377$	6.45601	−	2.10409i	0.332501	−	0.108366i
$378$			19.8354i			1.02022i
$379$	−3.11944	+	3.91166i	−0.160235	+	0.200928i	−0.855467	−	0.517857i	$-0.826730\pi$
$379$	−3.11944	+	3.91166i	−0.160235	+	0.200928i	0.695232	+	0.718785i	$0.255301\pi$
$380$		0			0
$381$	−0.705820	−	3.09240i	−0.0361602	−	0.158428i
$382$	5.66416	+	4.51702i	0.289804	+	0.231111i
$383$	17.9465	−	14.3119i	0.917025	−	0.731303i	−0.0465008	−	0.998918i	$-0.514807\pi$
$383$	17.9465	−	14.3119i	0.917025	−	0.731303i	0.963526	+	0.267615i	$0.0862356\pi$
$384$	11.5288	−	50.5109i	0.588326	−	2.57763i
$385$		0			0
$386$	−18.3473	−	8.83557i	−0.933851	−	0.449719i
$387$	7.11558	−	1.62408i	0.361705	−	0.0825568i
$388$	2.88119	+	5.98285i	0.146270	+	0.303733i
$389$	−8.54415			−0.433205			−0.216603	−	0.976260i	$-0.569498\pi$
$389$	−8.54415			−0.433205			−0.216603	+	0.976260i	$0.569498\pi$
$390$		0			0
$391$	2.59891	+	3.25893i	0.131432	+	0.164811i
$392$	−31.1111	+	24.8102i	−1.57135	+	1.25311i
$393$	−6.04001	−	12.5422i	−0.304678	−	0.632670i
$394$	−57.3676			−2.89014
$395$		0			0
$396$	−11.1805	−	48.9848i	−0.561840	−	2.46158i
$397$	0.883346	−	1.83429i	0.0443339	−	0.0920602i	−0.877625	−	0.479347i	$-0.840873\pi$
$397$	0.883346	−	1.83429i	0.0443339	−	0.0920602i	0.921959	+	0.387287i	$0.126588\pi$
$398$	13.1676	−	27.3427i	0.660030	−	1.37057i
$399$	−0.924068	+	4.04861i	−0.0462613	+	0.202684i
$400$		0			0
$401$	−15.3418	+	19.2380i	−0.766132	+	0.960699i	−0.999933	−	0.0115852i	$-0.996312\pi$
$401$	−15.3418	+	19.2380i	−0.766132	+	0.960699i	0.233801	+	0.972285i	$0.424884\pi$
$402$	27.9055	−	6.36924i	1.39180	−	0.317669i
$403$	0.599736	+	0.136886i	0.0298750	+	0.00681877i
$404$	35.0006	−	43.8894i	1.74134	−	2.18358i
$405$		0			0
$406$	23.5313	−	14.0880i	1.16784	−	0.699174i
$407$		−	18.5661i		−	0.920285i
$408$	−36.0648	−	28.7607i	−1.78547	−	1.42387i
$409$	1.96847	−	8.62445i	0.0973348	−	0.426452i	−0.902658	−	0.430360i	$-0.858387\pi$
$409$	1.96847	−	8.62445i	0.0973348	−	0.426452i	0.999992	+	0.00390791i	$0.00124393\pi$
$410$		0			0
$411$	2.12313	−	2.66232i	0.104726	−	0.131322i
$412$	−22.3982	+	17.8619i	−1.10348	+	0.879995i
$413$	−20.3311	−	4.64043i	−1.00043	−	0.228341i
$414$	4.34712	+	2.09346i	0.213650	+	0.102888i
$415$		0			0
$416$	8.47988	+	37.1528i	0.415760	+	1.82157i
$417$	−1.54138	−	3.20071i	−0.0754817	−	0.156739i
$418$		−	31.0718i		−	1.51977i
$419$	5.04772	−	2.43086i	0.246597	−	0.118755i	−0.306503	−	0.951870i	$-0.599159\pi$
$419$	5.04772	−	2.43086i	0.246597	−	0.118755i	0.553100	+	0.833115i	$0.313445\pi$
$420$		0			0
$421$	−11.5526	−	14.4865i	−0.563040	−	0.706030i	0.416076	−	0.909330i	$-0.363405\pi$
$421$	−11.5526	−	14.4865i	−0.563040	−	0.706030i	−0.979117	+	0.203299i	$0.934834\pi$
$422$	17.0071	+	35.3157i	0.827894	+	1.71914i
$423$			21.8424i			1.06202i
$424$	53.4698	−	25.7497i	2.59672	−	1.25051i
$425$		0			0
$426$	6.90062	+	3.32317i	0.334336	+	0.161008i
$427$	−6.47503	+	13.4455i	−0.313349	+	0.650676i
$428$	67.7024	+	15.4526i	3.27252	+	0.746931i
$429$	−1.91594	−	2.40252i	−0.0925026	−	0.115995i
$430$		0			0
$431$	5.61452	+	24.5988i	0.270442	+	1.18488i	0.909493	+	0.415719i	$0.136470\pi$
$431$	5.61452	+	24.5988i	0.270442	+	1.18488i	−0.639051	+	0.769164i	$0.720673\pi$
$432$	−70.1749	−	16.0170i	−3.37629	−	0.770617i
$433$	−4.69878	−	3.74715i	−0.225809	−	0.180076i	0.504050	−	0.863674i	$-0.331843\pi$
$433$	−4.69878	−	3.74715i	−0.225809	−	0.180076i	−0.729859	+	0.683598i	$0.760414\pi$
$434$	2.48467			0.119268
$435$		0			0
$436$	82.0614			3.93003
$437$	1.73815	+	1.38613i	0.0831471	+	0.0663076i
$438$	4.76065	+	1.08659i	0.227473	+	0.0519192i
$439$	−0.359081	−	1.57324i	−0.0171380	−	0.0750864i	0.965636	−	0.259899i	$-0.0836893\pi$
$439$	−0.359081	−	1.57324i	−0.0171380	−	0.0750864i	−0.982774	+	0.184813i	$0.940832\pi$
$440$		0			0
$441$	5.75392	+	7.21519i	0.273996	+	0.343580i
$442$	20.8159	+	4.75108i	0.990110	+	0.225986i
$443$	8.38304	−	17.4076i	0.398290	−	0.827059i	−0.601316	−	0.799011i	$-0.705357\pi$
$443$	8.38304	−	17.4076i	0.398290	−	0.827059i	0.999607	−	0.0280475i	$-0.00892895\pi$
$444$	−20.1329	−	9.69550i	−0.955466	−	0.460128i
$445$		0			0
$446$	42.4095	−	20.4233i	2.00815	−	0.967073i
$447$			8.17637i			0.386729i
$448$	37.6242	+	78.1274i	1.77757	+	3.69117i
$449$	21.7030	+	27.2147i	1.02423	+	1.28434i	0.958071	+	0.286530i	$0.0925018\pi$
$449$	21.7030	+	27.2147i	1.02423	+	1.28434i	0.0661551	+	0.997809i	$0.478927\pi$
$450$		0			0
$451$	10.4737	−	5.04387i	0.493188	−	0.237507i
$452$		−	24.3541i		−	1.14552i
$453$	1.66297	+	3.45320i	0.0781333	+	0.162245i
$454$	−3.86620	−	16.9389i	−0.181450	−	0.794983i
$455$		0			0
$456$	−22.1663	−	10.6747i	−1.03803	−	0.499891i
$457$	−6.73762	−	1.53782i	−0.315173	−	0.0719361i	0.0620084	−	0.998076i	$-0.480249\pi$
$457$	−6.73762	−	1.53782i	−0.315173	−	0.0719361i	−0.377181	+	0.926140i	$0.623107\pi$
$458$	55.4590	−	44.2271i	2.59143	−	2.06660i
$459$	−14.6799	+	18.4080i	−0.685199	+	0.859213i
$460$		0			0
$461$	−2.98798	+	13.0912i	−0.139164	+	0.609718i	0.856455	+	0.516221i	$0.172662\pi$
$461$	−2.98798	+	13.0912i	−0.139164	+	0.609718i	−0.995620	+	0.0934970i	$0.970195\pi$
$462$	−9.70391	−	7.73861i	−0.451467	−	0.360033i
$463$			11.0362i			0.512896i	0.966558	+	0.256448i	$0.0825523\pi$
$463$			11.0362i			0.512896i	−0.966558	+	0.256448i	$0.917448\pi$
$464$	30.8399	+	94.6266i	1.43171	+	4.39293i
$465$		0			0
$466$	−25.5969	+	32.0975i	−1.18575	+	1.48689i
$467$	−11.6557	−	2.66034i	−0.539361	−	0.123106i	−0.0558422	−	0.998440i	$-0.517784\pi$
$467$	−11.6557	−	2.66034i	−0.539361	−	0.123106i	−0.483519	+	0.875334i	$0.660642\pi$
$468$	17.9528	−	4.09760i	0.829867	−	0.189412i
$469$	−16.3540	+	20.5073i	−0.755159	+	0.946940i
$470$		0			0
$471$	0.507043	−	2.22150i	0.0233633	−	0.102361i
$472$	53.6058	−	111.314i	2.46741	−	5.12363i
$473$	−4.36108	+	9.05588i	−0.200523	+	0.416390i
$474$	0.118099	+	0.517424i	0.00542445	+	0.0237660i
$475$		0			0
$476$	64.2552			2.94513
$477$	−5.97179	−	12.4006i	−0.273430	−	0.567782i
$478$	−27.9058	+	22.2541i	−1.27638	+	1.01788i
$479$	−22.0796	−	27.6869i	−1.00884	−	1.26505i	−0.963958	−	0.266054i	$-0.914280\pi$
$479$	−22.0796	−	27.6869i	−1.00884	−	1.26505i	−0.0448823	−	0.998992i	$-0.514291\pi$
$480$		0			0
$481$	6.80439			0.310254
$482$	20.5470	+	42.6662i	0.935888	+	1.94339i
$483$	0.865796	−	0.197612i	0.0393951	−	0.00899167i
$484$	4.40687	+	2.12224i	0.200312	+	0.0964653i
$485$		0			0
$486$	−9.37349	+	41.0680i	−0.425190	+	1.86288i
$487$	−11.5147	+	9.18266i	−0.521780	+	0.416106i	−0.848643	−	0.528966i	$-0.822580\pi$
$487$	−11.5147	+	9.18266i	−0.521780	+	0.416106i	0.326863	+	0.945072i	$0.394009\pi$
$488$	−69.1246	−	55.1251i	−3.12913	−	2.49539i
$489$	−1.87188	−	8.20122i	−0.0846492	−	0.370872i
$490$		0			0
$491$	11.6547	−	14.6146i	0.525970	−	0.659546i	−0.445895	−	0.895085i	$-0.647114\pi$
$491$	11.6547	−	14.6146i	0.525970	−	0.659546i	0.971865	+	0.235540i	$0.0756858\pi$
$492$		−	13.9916i		−	0.630791i
$493$	32.2643	+	4.34103i	1.45311	+	0.195510i
$494$	11.3877			0.512356
$495$		0			0
$496$	−2.00635	+	8.79041i	−0.0900880	+	0.394701i
$497$	−6.84274	+	1.56181i	−0.306939	+	0.0700568i
$498$	8.59344	+	6.85304i	0.385081	+	0.307092i
$499$	−4.50786	−	5.65268i	−0.201800	−	0.253049i	0.670626	−	0.741796i	$-0.266026\pi$
$499$	−4.50786	−	5.65268i	−0.201800	−	0.253049i	−0.872426	+	0.488747i	$0.837454\pi$
$500$		0			0
$501$	−9.82571	−	4.73181i	−0.438980	−	0.211402i
$502$	−5.21000	+	10.8187i	−0.232533	+	0.482861i
$503$	−5.65385	+	1.29045i	−0.252093	+	0.0575385i	−0.346700	−	0.937976i	$-0.612698\pi$
$503$	−5.65385	+	1.29045i	−0.252093	+	0.0575385i	0.0946070	+	0.995515i	$0.469841\pi$
$504$	44.0850	−	21.2302i	1.96370	−	0.945668i
$505$		0			0
$506$	−5.98667	+	2.88303i	−0.266140	+	0.128166i
$507$	−6.31909	+	5.03931i	−0.280641	+	0.223803i
$508$	−20.4656	+	16.3208i	−0.908015	+	0.724118i
$509$	32.2732	−	15.5420i	1.43048	−	0.688885i	0.451397	−	0.892323i	$-0.350926\pi$
$509$	32.2732	−	15.5420i	1.43048	−	0.688885i	0.979088	+	0.203438i	$0.0652116\pi$
$510$		0			0
$511$	−4.03165	+	1.94154i	−0.178350	+	0.0858887i
$512$	−156.370	+	35.6905i	−6.91066	+	1.57731i
$513$	−5.44855	+	11.3140i	−0.240559	+	0.499527i
$514$	21.3852	+	10.2985i	0.943259	+	0.454250i
$515$		0			0
$516$	7.54271	+	9.45826i	0.332049	+	0.416377i
$517$	−23.5178	−	18.7548i	−1.03431	−	0.824837i
$518$	26.7943	−	6.11562i	1.17727	−	0.268705i
$519$	−3.92912	+	17.2146i	−0.172469	+	0.755636i
$520$		0			0
$521$	−10.6623			−0.467125			−0.233562	−	0.972342i	$-0.575038\pi$
$521$	−10.6623			−0.467125			−0.233562	+	0.972342i	$0.575038\pi$
$522$	35.8285	−	11.6769i	1.56817	−	0.511085i
$523$			7.23345i			0.316297i	0.987415	+	0.158148i	$0.0505524\pi$
$523$			7.23345i			0.316297i	−0.987415	+	0.158148i	$0.949448\pi$
$524$	−71.6279	+	89.8185i	−3.12908	+	3.92374i
$525$		0			0
$526$	−4.40185	−	19.2858i	−0.191930	−	0.840899i
$527$	2.30587	+	1.83887i	0.100445	+	0.0801024i
$528$	35.2140	−	28.0822i	1.53249	−	1.22212i
$529$	−5.01219	+	21.9598i	−0.217921	+	0.954775i
$530$		0			0
$531$	−25.8155	−	12.4321i	−1.12030	−	0.539508i
$532$	33.4114	−	7.62593i	1.44857	−	0.330626i
$533$	1.84856	+	3.83858i	0.0800701	+	0.166267i
$534$	2.21753			0.0959617
$535$		0			0
$536$	−96.8894	−	121.495i	−4.18498	−	5.24780i
$537$	3.65693	−	2.91630i	0.157808	−	0.125848i
$538$	−28.4789	−	59.1371i	−1.22781	−	2.54958i
$539$	−12.7092			−0.547423
$540$		0			0
$541$	0.153391	+	0.672049i	0.00659479	+	0.0288937i	0.978118	−	0.208050i	$-0.0667116\pi$
$541$	0.153391	+	0.672049i	0.00659479	+	0.0288937i	−0.971523	+	0.236943i	$0.923854\pi$
$542$	18.2795	−	37.9578i	0.785172	−	1.63043i
$543$	2.84601	−	5.90980i	0.122134	−	0.253614i
$544$	−40.6559	+	178.125i	−1.74311	+	7.63705i
$545$		0			0
$546$	2.83617	−	3.55645i	0.121377	−	0.152202i
$547$	−26.9245	+	6.14533i	−1.15121	+	0.262756i	−0.755202	−	0.655493i	$-0.772461\pi$
$547$	−26.9245	+	6.14533i	−1.15121	+	0.262756i	−0.396006	+	0.918248i	$0.629604\pi$
$548$	−27.3973	−	6.25326i	−1.17036	−	0.267126i
$549$	−12.7845	+	16.0312i	−0.545627	+	0.684195i
$550$		0			0
$551$	17.2920	−	1.57194i	0.736663	−	0.0669670i
$552$			5.26131i			0.223936i
$553$	−0.380247	−	0.303237i	−0.0161697	−	0.0128949i
$554$	−1.72184	+	7.54386i	−0.0731539	+	0.320508i
$555$		0			0
$556$	−18.2791	+	22.9213i	−0.775207	+	0.972078i
$557$	−0.0644581	+	0.0514036i	−0.00273118	+	0.00217804i	−0.624854	−	0.780741i	$-0.714842\pi$
$557$	−0.0644581	+	0.0514036i	−0.00273118	+	0.00217804i	0.622123	+	0.782919i	$0.286270\pi$
$558$	3.32832	+	0.759667i	0.140899	+	0.0321593i
$559$	−3.31895	−	1.59832i	−0.140376	−	0.0676017i
$560$		0			0
$561$	−3.27837	−	14.3635i	−0.138413	−	0.606426i
$562$	36.0221	+	74.8006i	1.51950	+	3.15527i
$563$		−	11.1085i		−	0.468167i	−0.972217	−	0.234083i	$-0.924791\pi$
$563$		−	11.1085i		−	0.468167i	0.972217	−	0.234083i	$-0.0752088\pi$
$564$	−32.6190	+	15.7085i	−1.37351	+	0.661447i
$565$		0			0
$566$	5.69442	+	7.14057i	0.239354	+	0.300141i
$567$	−3.73611	−	7.75811i	−0.156902	−	0.325810i
$568$		−	41.5823i		−	1.74475i
$569$	25.8173	−	12.4330i	1.08232	−	0.521217i	0.194262	−	0.980950i	$-0.437769\pi$
$569$	25.8173	−	12.4330i	1.08232	−	0.521217i	0.888058	+	0.459732i	$0.152055\pi$
$570$		0			0
$571$	18.3904	+	8.85636i	0.769616	+	0.370627i	0.777126	−	0.629344i	$-0.216677\pi$
$571$	18.3904	+	8.85636i	0.769616	+	0.370627i	−0.00751092	+	0.999972i	$0.502391\pi$
$572$	−11.0031	+	22.8482i	−0.460063	+	0.955331i
$573$	1.78620	+	0.407688i	0.0746195	+	0.0170314i
$574$	10.7293	+	13.4541i	0.447831	+	0.561563i
$575$		0			0
$576$	26.5123	+	116.158i	1.10468	+	4.83992i
$577$	10.8343	+	2.47287i	0.451039	+	0.102947i	0.442005	−	0.897012i	$-0.354267\pi$
$577$	10.8343	+	2.47287i	0.451039	+	0.102947i	0.00903403	+	0.999959i	$0.497124\pi$
$578$	42.8041	+	34.1351i	1.78041	+	1.41983i
$579$	−5.14986			−0.214021
$580$		0			0
$581$	−10.0724			−0.417873
$582$	1.76214	+	1.40526i	0.0730430	+	0.0582499i
$583$	18.4794	+	4.21779i	0.765337	+	0.174683i
$584$	−5.89922	−	25.8462i	−0.244112	−	1.06952i
$585$		0			0
$586$	−17.7922	−	22.3108i	−0.734991	−	0.921650i
$587$	−36.2404	−	8.27164i	−1.49580	−	0.341407i	−0.605157	−	0.796106i	$-0.706890\pi$
$587$	−36.2404	−	8.27164i	−1.49580	−	0.341407i	−0.890645	+	0.454699i	$0.849747\pi$
$588$	−6.63695	+	13.7818i	−0.273703	+	0.568350i
$589$	1.41724	+	0.682509i	0.0583965	+	0.0281223i
$590$		0			0
$591$	−13.0711	+	6.29470i	−0.537672	+	0.258929i
$592$			99.7329i			4.09900i
$593$	−16.7495	−	34.7808i	−0.687821	−	1.42828i	−0.893230	−	0.449600i	$-0.851567\pi$
$593$	−16.7495	−	34.7808i	−0.687821	−	1.42828i	0.205409	−	0.978676i	$-0.434148\pi$
$594$	−23.4012	−	29.3441i	−0.960162	−	1.20400i
$595$		0			0
$596$	60.7938	−	29.2767i	2.49021	−	1.19922i
$597$		−	7.67479i		−	0.314108i
$598$	−1.05662	−	2.19409i	−0.0432084	−	0.0897231i
$599$	−3.04410	−	13.3371i	−0.124379	−	0.544938i	−0.998269	−	0.0588148i	$-0.981268\pi$
$599$	−3.04410	−	13.3371i	−0.124379	−	0.544938i	0.873890	−	0.486123i	$-0.161589\pi$
$600$		0			0
$601$	3.45201	+	1.66240i	0.140811	+	0.0678108i	0.502962	−	0.864308i	$-0.332243\pi$
$601$	3.45201	+	1.66240i	0.140811	+	0.0678108i	−0.362152	+	0.932119i	$0.617958\pi$
$602$	−14.5059	−	3.31087i	−0.591215	−	0.134941i
$603$	−28.1769	+	22.4703i	−1.14745	+	0.915062i
$604$	19.7211	−	24.7294i	0.802438	−	1.00623i
$605$		0			0
$606$	4.23980	−	18.5758i	0.172230	−	0.754590i
$607$	−22.2336	−	17.7307i	−0.902432	−	0.719665i	0.0579597	−	0.998319i	$-0.481540\pi$
$607$	−22.2336	−	17.7307i	−0.902432	−	0.719665i	−0.960392	+	0.278653i	$0.910112\pi$
$608$			97.4465i			3.95198i
$609$	3.81574	−	5.79190i	0.154622	−	0.234700i
$610$		0			0
$611$	6.87358	−	8.61920i	0.278075	−	0.348696i
$612$	86.0726	+	19.6455i	3.47928	+	0.794123i
$613$	−46.3083	+	10.5696i	−1.87038	+	0.426901i	−0.998072	−	0.0620623i	$-0.980232\pi$
$613$	−46.3083	+	10.5696i	−1.87038	+	0.426901i	−0.872304	+	0.488964i	$0.837375\pi$
$614$	52.6904	−	66.0717i	2.12641	−	2.66644i
$615$		0			0
$616$	−14.9946	+	65.6956i	−0.604149	+	2.64695i
$617$	9.69761	−	20.1373i	0.390411	−	0.810697i	−0.609429	−	0.792840i	$-0.708601\pi$
$617$	9.69761	−	20.1373i	0.390411	−	0.810697i	0.999841	−	0.0178568i	$-0.00568430\pi$
$618$	−4.21892	+	8.76068i	−0.169710	+	0.352406i
$619$	6.41964	+	28.1263i	0.258027	+	1.13049i	0.923357	+	0.383941i	$0.125434\pi$
$619$	6.41964	+	28.1263i	0.258027	+	1.13049i	−0.665330	+	0.746549i	$0.731709\pi$
$620$		0			0
$621$	2.68545			0.107763
$622$	−36.3960	−	75.5771i	−1.45935	−	3.03037i
$623$	−1.58877	+	1.26700i	−0.0636527	+	0.0507613i
$624$	10.2920	+	12.9058i	0.412011	+	0.516646i
$625$		0			0
$626$	46.9627			1.87701
$627$	−3.40937	−	7.07962i	−0.136157	−	0.282733i
$628$	−18.3331	+	4.18440i	−0.731569	+	0.166976i
$629$	29.3922	+	14.1546i	1.17195	+	0.564379i
$630$		0			0
$631$	−5.51970	+	24.1834i	−0.219736	+	0.962726i	0.737938	+	0.674869i	$0.235800\pi$
$631$	−5.51970	+	24.1834i	−0.219736	+	0.962726i	−0.957673	+	0.287857i	$0.907057\pi$
$632$	2.25277	−	1.79652i	0.0896104	−	0.0714619i
$633$	7.75007	+	6.18047i	0.308037	+	0.245652i
$634$	−7.96657	−	34.9038i	−0.316393	−	1.38621i
$635$		0			0
$636$	14.2240	−	17.8363i	0.564018	−	0.707256i
$637$		−	4.65787i		−	0.184552i
$638$	−18.1913	+	48.6030i	−0.720200	+	1.92421i
$639$	−9.64365			−0.381497
$640$		0			0
$641$	−2.82243	+	12.3659i	−0.111479	+	0.488423i	0.888106	+	0.459638i	$0.152021\pi$
$641$	−2.82243	+	12.3659i	−0.111479	+	0.488423i	−0.999586	+	0.0287849i	$0.990836\pi$
$642$	22.9791	−	5.24482i	0.906912	−	0.206997i
$643$	1.28982	+	1.02859i	0.0508654	+	0.0405638i	0.648593	−	0.761136i	$-0.275358\pi$
$643$	1.28982	+	1.02859i	0.0508654	+	0.0405638i	−0.597727	+	0.801700i	$0.703929\pi$
$644$	−4.56942	−	5.72987i	−0.180060	−	0.225789i
$645$		0			0
$646$	49.1902	+	23.6888i	1.93536	+	0.932022i
$647$	9.67703	−	20.0945i	0.380443	−	0.789998i	−0.619544	−	0.784962i	$-0.712683\pi$
$647$	9.67703	−	20.0945i	0.380443	−	0.789998i	0.999987	−	0.00503650i	$-0.00160318\pi$
$648$	49.7359	−	11.3519i	1.95381	−	0.445944i
$649$	35.5520	−	17.1210i	1.39554	−	0.672056i
$650$		0			0
$651$	0.566126	−	0.272632i	0.0221882	−	0.0106853i
$652$	−54.2760	+	43.2837i	−2.12561	+	1.69512i
$653$	−19.2909	+	15.3840i	−0.754911	+	0.602021i	−0.923470	−	0.383670i	$-0.874660\pi$
$653$	−19.2909	+	15.3840i	−0.754911	+	0.602021i	0.168559	+	0.985692i	$0.446089\pi$
$654$	25.0944	−	12.0848i	0.981270	−	0.472555i
$655$		0			0
$656$	−56.2625	+	27.0946i	−2.19668	+	1.05787i
$657$	−5.99417	+	1.36813i	−0.233855	+	0.0533759i
$658$	19.3200	−	40.1185i	0.753173	−	1.56398i
$659$	24.5652	+	11.8300i	0.956924	+	0.460830i	0.846109	−	0.533011i	$-0.178939\pi$
$659$	24.5652	+	11.8300i	0.956924	+	0.460830i	0.110816	+	0.993841i	$0.464654\pi$
$660$		0			0
$661$	−2.56656	−	3.21837i	−0.0998278	−	0.125180i	0.729408	−	0.684079i	$-0.239796\pi$
$661$	−2.56656	−	3.21837i	−0.0998278	−	0.125180i	−0.829236	+	0.558899i	$0.811224\pi$
$662$	−29.0465	−	23.1638i	−1.12893	−	0.900288i
$663$	5.26416	−	1.20151i	0.204443	−	0.0466628i
$664$	13.2787	−	58.1777i	0.515313	−	2.25773i
$665$		0			0
$666$	37.7619			1.46324
$667$	−1.90733	−	3.18583i	−0.0738519	−	0.123356i
$668$			90.0001i			3.48221i
$669$	7.42194	−	9.30681i	0.286949	−	0.359822i
$670$		0			0
$671$	−6.28357	−	27.5301i	−0.242575	−	1.06279i
$672$	30.4332	+	24.2696i	1.17399	+	0.936222i
$673$	22.4143	−	17.8748i	0.864008	−	0.689023i	−0.0876605	−	0.996150i	$-0.527939\pi$
$673$	22.4143	−	17.8748i	0.864008	−	0.689023i	0.951669	+	0.307127i	$0.0993676\pi$
$674$	−2.80258	+	12.2789i	−0.107951	+	0.472965i
$675$		0			0
$676$	60.0952	+	28.9403i	2.31136	+	1.11309i
$677$	−25.5179	+	5.82430i	−0.980734	+	0.223846i	−0.682692	−	0.730706i	$-0.739191\pi$
$677$	−25.5179	+	5.82430i	−0.980734	+	0.223846i	−0.298042	+	0.954553i	$0.596334\pi$
$678$	−3.58653	−	7.44750i	−0.137740	−	0.286020i
$679$	−2.06541			−0.0792631
$680$		0			0
$681$	−2.73954	−	3.43527i	−0.104979	−	0.131640i
$682$	−3.67577	+	2.93133i	−0.140753	+	0.112246i
$683$	8.95404	+	18.5933i	0.342617	+	0.711451i	0.999079	−	0.0429078i	$-0.0136622\pi$
$683$	8.95404	+	18.5933i	0.342617	+	0.711451i	−0.656462	+	0.754359i	$0.727948\pi$
$684$	47.0875			1.80044
$685$		0			0
$686$	−12.1193	−	53.0983i	−0.462718	−	2.02730i
$687$	7.78336	−	16.1623i	0.296954	−	0.616630i
$688$	23.4268	−	48.6462i	0.893138	−	1.85462i
$689$	−1.54581	+	6.77262i	−0.0588905	+	0.258016i
$690$		0			0
$691$	31.6231	−	39.6541i	1.20300	−	1.50851i	0.395689	−	0.918385i	$-0.370506\pi$
$691$	31.6231	−	39.6541i	1.20300	−	1.50851i	0.807310	−	0.590128i	$-0.200923\pi$
$692$	142.064	−	32.4253i	5.40048	−	1.23262i
$693$	15.2359	+	3.47750i	0.578765	+	0.132099i
$694$	15.5763	−	19.5320i	0.591267	−	0.741426i
$695$		0			0
$696$	28.4233	+	29.6752i	1.07738	+	1.12483i
$697$			20.4265i			0.773709i
$698$	36.1219	+	28.8063i	1.36724	+	1.09033i
$699$	−2.31027	+	10.1220i	−0.0873825	+	0.382848i
$700$		0			0
$701$	13.8465	−	17.3630i	0.522976	−	0.655792i	−0.448262	−	0.893902i	$-0.647957\pi$
$701$	13.8465	−	17.3630i	0.522976	−	0.655792i	0.971238	+	0.238111i	$0.0765281\pi$
$702$	10.7545	−	8.57644i	0.405903	−	0.323697i
$703$	16.9632	+	3.87175i	0.639781	+	0.146026i
$704$	−147.833	−	71.1924i	−5.57165	−	2.68317i
$705$		0			0
$706$	14.1741	+	62.1009i	0.533451	+	2.33720i
$707$	7.57577	+	15.7313i	0.284916	+	0.591635i
$708$		−	47.4933i		−	1.78491i
$709$	12.0714	−	5.81327i	0.453350	−	0.218322i	−0.193252	−	0.981149i	$-0.561904\pi$
$709$	12.0714	−	5.81327i	0.453350	−	0.218322i	0.646602	+	0.762827i	$0.276189\pi$
$710$		0			0
$711$	−0.416645	−	0.522456i	−0.0156254	−	0.0195936i
$712$	−5.22363	−	10.8470i	−0.195764	−	0.406508i
$713$		−	0.336391i		−	0.0125979i
$714$	19.6493	−	9.46260i	0.735356	−	0.354129i
$715$		0			0
$716$	−34.7778	−	16.7481i	−1.29971	−	0.625906i
$717$	−3.91642	+	8.13252i	−0.146261	+	0.303715i
$718$	−41.4993	−	9.47194i	−1.54874	−	0.353490i
$719$	−20.1882	−	25.3152i	−0.752892	−	0.944097i	0.246796	−	0.969067i	$-0.420622\pi$
$719$	−20.1882	−	25.3152i	−0.752892	−	0.944097i	−0.999688	+	0.0249704i	$0.992051\pi$
$720$		0			0
$721$	−1.98279	−	8.68719i	−0.0738431	−	0.323528i
$722$	−23.4959	−	5.36278i	−0.874426	−	0.199582i
$723$	9.36315	+	7.46686i	0.348219	+	0.277696i
$724$	−54.1317			−2.01179
$725$		0			0
$726$	1.66016			0.0616142
$727$	16.0746	+	12.8191i	0.596175	+	0.475434i	0.874482	−	0.485058i	$-0.161202\pi$
$727$	16.0746	+	12.8191i	0.596175	+	0.475434i	−0.278306	+	0.960492i	$0.589773\pi$
$728$	−24.0772	−	5.49546i	−0.892361	−	0.203675i
$729$	−0.790997	−	3.46559i	−0.0292962	−	0.128355i
$730$		0			0
$731$	−11.0117	−	13.8082i	−0.407282	−	0.510715i
$732$	−33.1349	−	7.56283i	−1.22470	−	0.279530i
$733$	18.5398	−	38.4982i	0.684782	−	1.42197i	−0.211006	−	0.977485i	$-0.567674\pi$
$733$	18.5398	−	38.4982i	0.684782	−	1.42197i	0.895789	−	0.444480i	$-0.146612\pi$
$734$	−66.1018	−	31.8329i	−2.43986	−	1.17498i
$735$		0			0
$736$	18.7752	−	9.04168i	0.692065	−	0.333281i
$737$		−	49.6321i		−	1.82822i
$738$	10.2588	+	21.3027i	0.377633	+	0.784163i
$739$	22.1975	+	27.8348i	0.816549	+	1.02392i	0.999170	+	0.0407362i	$0.0129703\pi$
$739$	22.1975	+	27.8348i	0.816549	+	1.02392i	−0.182621	+	0.983183i	$0.558458\pi$
$740$		0			0
$741$	2.59466	−	1.24952i	0.0953171	−	0.0459023i
$742$			28.0585i			1.03006i
$743$	−16.3036	−	33.8547i	−0.598120	−	1.24201i	−0.951822	−	0.306650i	$-0.900792\pi$
$743$	−16.3036	−	33.8547i	−0.598120	−	1.24201i	0.353703	−	0.935358i	$-0.384922\pi$
$744$	0.828371	+	3.62933i	0.0303696	+	0.133058i
$745$		0			0
$746$	−45.7091	−	22.0123i	−1.67353	−	0.805928i
$747$	−13.4924	−	3.07955i	−0.493661	−	0.112675i
$748$	−95.0580	+	75.8062i	−3.47567	+	2.77175i
$749$	−13.4669	+	16.8870i	−0.492071	+	0.617037i
$750$		0			0
$751$	6.15586	−	26.9706i	0.224631	−	0.984171i	−0.729312	−	0.684181i	$-0.760160\pi$
$751$	6.15586	−	26.9706i	0.224631	−	0.984171i	0.953942	−	0.299990i	$-0.0969832\pi$
$752$	126.333	+	100.747i	4.60688	+	3.67387i
$753$			3.03668i			0.110663i
$754$	−17.8128	−	6.66704i	−0.648705	−	0.242799i
$755$		0			0
$756$	25.8103	−	32.3652i	0.938713	−	1.17711i
$757$	3.56312	+	0.813259i	0.129504	+	0.0295584i	0.286781	−	0.957996i	$-0.407415\pi$
$757$	3.56312	+	0.813259i	0.129504	+	0.0295584i	−0.157278	+	0.987554i	$0.550272\pi$
$758$	13.6627	−	3.11843i	0.496253	−	0.113267i
$759$	−1.04771	+	1.31378i	−0.0380293	+	0.0476873i
$760$		0			0
$761$	−2.91296	+	12.7625i	−0.105595	+	0.462640i	0.894291	+	0.447487i	$0.147681\pi$
$761$	−2.91296	+	12.7625i	−0.105595	+	0.462640i	−0.999885	+	0.0151534i	$0.995176\pi$
$762$	−3.85491	+	8.00479i	−0.139648	+	0.289983i
$763$	−11.0744	+	22.9962i	−0.400920	+	0.832519i
$764$	−3.36447	−	14.7407i	−0.121722	−	0.533300i
$765$		0			0
$766$	−64.2961			−2.32311
$767$	6.27477	+	13.0297i	0.226569	+	0.470475i
$768$	−60.6351	+	48.3549i	−2.18798	+	1.74486i
$769$	−17.1156	−	21.4623i	−0.617204	−	0.773949i	0.370744	−	0.928735i	$-0.379103\pi$
$769$	−17.1156	−	21.4623i	−0.617204	−	0.773949i	−0.987948	+	0.154786i	$0.950531\pi$
$770$		0			0
$771$	6.00257			0.216177
$772$	18.4399	+	38.2908i	0.663666	+	1.37812i
$773$	−45.3087	+	10.3414i	−1.62964	+	0.371955i	−0.937000	−	0.349329i	$-0.886410\pi$
$773$	−45.3087	+	10.3414i	−1.62964	+	0.371955i	−0.692640	+	0.721283i	$0.743553\pi$
$774$	−18.4189	−	8.87010i	−0.662055	−	0.318829i
$775$		0			0
$776$	2.72288	−	11.9297i	0.0977456	−	0.428251i
$777$	5.43398	−	4.33345i	0.194943	−	0.155462i
$778$	18.7111	+	14.9216i	0.670825	+	0.534965i
$779$	2.42426	+	10.6214i	0.0868580	+	0.380550i
$780$		0			0
$781$	8.28045	−	10.3834i	0.296298	−	0.371546i
$782$		−	11.6756i		−	0.417518i
$783$	15.1466	−	14.5077i	0.541297	−	0.518463i
$784$	68.2710			2.43825
$785$		0			0
$786$	−8.67666	+	38.0149i	−0.309486	+	1.35595i
$787$	−9.31321	+	2.12568i	−0.331980	+	0.0757722i	−0.385262	−	0.922807i	$-0.625889\pi$
$787$	−9.31321	+	2.12568i	−0.331980	+	0.0757722i	0.0532820	+	0.998580i	$0.483032\pi$
$788$	93.6060	+	74.6483i	3.33457	+	2.65923i
$789$	−3.11909	−	3.91122i	−0.111043	−	0.139243i
$790$		0			0
$791$	6.82479	+	3.28665i	0.242662	+	0.116860i
$792$	−40.1718	+	83.4176i	−1.42744	+	2.96411i
$793$	10.0897	−	2.30291i	0.358296	−	0.0817786i
$794$	−5.13789	+	2.47428i	−0.182337	+	0.0878088i
$795$		0			0
$796$	−57.0644	+	27.4808i	−2.02259	+	0.974030i
$797$	−19.7530	+	15.7525i	−0.699688	+	0.557982i	−0.907431	−	0.420201i	$-0.861960\pi$
$797$	−19.7530	+	15.7525i	−0.699688	+	0.557982i	0.207743	+	0.978183i	$0.433388\pi$
$798$	9.09419	−	7.25237i	0.321931	−	0.256731i
$799$	47.6209	−	22.9330i	1.68471	−	0.811311i
$800$		0			0
$801$	−2.51560	+	1.21145i	−0.0888843	+	0.0428044i
$802$	67.1949	−	15.3368i	2.37274	−	0.541561i
$803$	3.67378	−	7.62869i	0.129645	−	0.269211i
$804$	−53.8208	−	25.9187i	−1.89811	−	0.914083i
$805$		0			0
$806$	−1.07432	−	1.34716i	−0.0378414	−	0.0474516i
$807$	−12.9777	−	10.3494i	−0.456837	−	0.364315i
$808$	−100.850	+	23.0184i	−3.54790	+	0.809785i
$809$	0.146459	−	0.641681i	0.00514924	−	0.0225603i	−0.972288	−	0.233786i	$-0.924888\pi$
$809$	0.146459	−	0.641681i	0.00514924	−	0.0225603i	0.977437	+	0.211226i	$0.0677456\pi$
$810$		0			0
$811$	16.0989			0.565311			0.282655	−	0.959222i	$-0.408785\pi$
$811$	16.0989			0.565311			0.282655	+	0.959222i	$0.408785\pi$
$812$	−56.7274	−	7.63243i	−1.99074	−	0.267846i
$813$		−	10.6543i		−	0.373663i
$814$	−32.4240	+	40.6584i	−1.13646	+	1.42508i
$815$		0			0
$816$	17.6107	+	77.1575i	0.616498	+	2.70105i
$817$	−7.36463	−	5.87309i	−0.257656	−	0.205474i
$818$	−19.3727	+	15.4492i	−0.677350	+	0.540168i
$819$	−1.27449	+	5.58392i	−0.0445344	+	0.195118i
$820$		0			0
$821$	5.26138	+	2.53375i	0.183624	+	0.0884284i	0.523437	−	0.852064i	$-0.324650\pi$
$821$	5.26138	+	2.53375i	0.183624	+	0.0884284i	−0.339813	+	0.940493i	$0.610364\pi$
$822$	−9.29901	+	2.12244i	−0.324340	+	0.0740286i
$823$	10.2952	+	21.3783i	0.358869	+	0.745199i	0.999748	−	0.0224426i	$-0.00714431\pi$
$823$	10.2952	+	21.3783i	0.358869	+	0.745199i	−0.640879	+	0.767642i	$0.721430\pi$
$824$	52.7908			1.83905
$825$		0			0
$826$	36.4195	+	45.6687i	1.26720	+	1.58902i
$827$	−33.6848	+	26.8628i	−1.17134	+	0.934110i	−0.998705	−	0.0508766i	$-0.983798\pi$
$827$	−33.6848	+	26.8628i	−1.17134	+	0.934110i	−0.172632	+	0.984986i	$0.555227\pi$
$828$	−4.36907	−	9.07247i	−0.151836	−	0.315290i
$829$	−37.8281			−1.31382			−0.656912	−	0.753967i	$-0.728138\pi$
$829$	−37.8281			−1.31382			−0.656912	+	0.753967i	$0.728138\pi$
$830$		0			0
$831$	0.435438	+	1.90778i	0.0151052	+	0.0661802i
$832$	26.0918	−	54.1801i	0.904569	−	1.87836i
$833$	9.68935	−	20.1201i	0.335716	−	0.697121i
$834$	−2.21424	+	9.70123i	−0.0766729	+	0.335926i
$835$		0			0
$836$	−40.4314	+	50.6993i	−1.39835	+	1.75347i
$837$	1.85246	−	0.422813i	0.0640305	−	0.0146146i
$838$	−15.2994	−	3.49200i	−0.528511	−	0.120629i
$839$	−14.1276	+	17.7155i	−0.487740	+	0.611607i	−0.963415	−	0.268014i	$-0.913633\pi$
$839$	−14.1276	+	17.7155i	−0.487740	+	0.611607i	0.475675	+	0.879621i	$0.342204\pi$
$840$		0			0
$841$	−27.9687	−	7.66490i	−0.964439	−	0.264307i
$842$			51.9002i			1.78860i
$843$	16.4151	+	13.0906i	0.565365	+	0.450864i
$844$	18.2034	−	79.7542i	0.626586	−	2.74525i
$845$		0			0
$846$	38.1459	−	47.8334i	1.31148	−	1.64455i
$847$	−1.18944	+	0.948543i	−0.0408695	+	0.0325923i
$848$	−99.2672	−	22.6571i	−3.40885	−	0.778048i
$849$	2.08096	+	1.00214i	0.0714185	+	0.0343933i
$850$		0			0
$851$	−0.827975	−	3.62759i	−0.0283826	−	0.124352i
$852$	−6.93546	−	14.4016i	−0.237605	−	0.493392i
$853$		−	1.64615i		−	0.0563630i	−0.999603	−	0.0281815i	$-0.991028\pi$
$853$		−	1.64615i		−	0.0563630i	0.999603	−	0.0281815i	$-0.00897165\pi$
$854$	37.6614	−	18.1368i	1.28875	−	0.620627i
$855$		0			0
$856$	−79.7847	−	100.047i	−2.72698	−	3.41953i
$857$	4.36555	+	9.06517i	0.149124	+	0.309660i	0.962128	−	0.272599i	$-0.0878832\pi$
$857$	4.36555	+	9.06517i	0.149124	+	0.309660i	−0.813003	+	0.582259i	$0.802169\pi$
$858$			8.60737i			0.293851i
$859$	−35.0681	+	16.8879i	−1.19651	+	0.576208i	−0.922678	−	0.385570i	$-0.874005\pi$
$859$	−35.0681	+	16.8879i	−1.19651	+	0.576208i	−0.273830	+	0.961778i	$0.588290\pi$
$860$		0			0
$861$	3.92090	+	1.88820i	0.133624	+	0.0643498i
$862$	30.6643	−	63.6750i	1.04443	−	2.16878i
$863$	−23.5821	−	5.38247i	−0.802745	−	0.183221i	−0.198585	−	0.980084i	$-0.563634\pi$
$863$	−23.5821	−	5.38247i	−0.802745	−	0.183221i	−0.604161	+	0.796862i	$0.706492\pi$
$864$	73.3902	+	92.0284i	2.49678	+	3.13087i
$865$		0			0
$866$	3.74593	+	16.4120i	0.127292	+	0.557703i
$867$	13.4983	+	3.08090i	0.458426	+	0.104633i
$868$	−4.05420	−	3.23312i	−0.137608	−	0.109739i
$869$	0.920280			0.0312183
$870$		0			0
$871$	18.1900			0.616344
$872$	−118.225	−	94.2816i	−4.00362	−	3.19278i
$873$	−2.76670	−	0.631482i	−0.0936387	−	0.0213724i
$874$	−1.38568	−	6.07106i	−0.0468714	−	0.205357i
$875$		0			0
$876$	−6.35399	−	7.96766i	−0.214682	−	0.269202i
$877$	2.18453	+	0.498604i	0.0737663	+	0.0168367i	0.259245	−	0.965812i	$-0.416526\pi$
$877$	2.18453	+	0.498604i	0.0737663	+	0.0168367i	−0.185478	+	0.982648i	$0.559384\pi$
$878$	−1.96116	+	4.07238i	−0.0661858	+	0.137436i
$879$	−6.50198	−	3.13119i	−0.219306	−	0.105612i
$880$		0			0
$881$	50.6838	−	24.4081i	1.70758	−	0.822328i	0.715230	−	0.698889i	$-0.246322\pi$
$881$	50.6838	−	24.4081i	1.70758	−	0.822328i	0.992352	−	0.123439i	$-0.0393923\pi$
$882$		−	25.8495i		−	0.870398i
$883$	−25.1648	−	52.2552i	−0.846862	−	1.75853i	−0.620005	−	0.784598i	$-0.712869\pi$
$883$	−25.1648	−	52.2552i	−0.846862	−	1.75853i	−0.226857	−	0.973928i	$-0.572845\pi$
$884$	−27.7827	−	34.8384i	−0.934434	−	1.17174i
$885$		0			0
$886$	−48.7591	+	23.4811i	−1.63809	+	0.788864i
$887$		−	4.31316i		−	0.144822i	−0.997375	−	0.0724108i	$-0.976931\pi$
$887$		−	4.31316i		−	0.144822i	0.997375	−	0.0724108i	$-0.0230693\pi$
$888$	17.8661	+	37.0993i	0.599546	+	1.24497i
$889$	−1.81172	−	7.93765i	−0.0607630	−	0.266220i
$890$		0			0
$891$	14.6799	+	7.06947i	0.491795	+	0.236836i
$892$	−95.7744	−	21.8599i	−3.20676	−	0.731923i
$893$	22.0401	−	17.5764i	0.737545	−	0.588172i
$894$	14.2793	−	17.9057i	0.477572	−	0.598856i
$895$		0			0
$896$	29.5924	−	129.653i	0.988613	−	4.33140i
$897$	−0.481496	−	0.383980i	−0.0160767	−	0.0128207i
$898$		−	97.5006i		−	3.25364i
$899$	−1.81730	−	1.89733i	−0.0606102	−	0.0632796i
$900$		0			0
$901$	−20.7657	+	26.0394i	−0.691807	+	0.867498i
$902$	−31.7454	−	7.24568i	−1.05701	−	0.241255i
$903$	−3.66841	+	0.837291i	−0.122077	+	0.0278633i
$904$	−27.9808	+	35.0868i	−0.930628	+	1.16697i
$905$		0			0
$906$	2.38891	−	10.4665i	0.0793663	−	0.347726i
$907$	−5.64261	+	11.7170i	−0.187360	+	0.389057i	−0.973398	−	0.229121i	$-0.926415\pi$
$907$	−5.64261	+	11.7170i	−0.187360	+	0.389057i	0.786038	+	0.618178i	$0.212129\pi$
$908$	−15.7329	+	32.6698i	−0.522116	+	1.08418i
$909$	5.33837	+	23.3889i	0.177062	+	0.775761i
$910$		0			0
$911$	15.9042			0.526928			0.263464	−	0.964669i	$-0.415135\pi$
$911$	15.9042			0.526928			0.263464	+	0.964669i	$0.415135\pi$
$912$	18.3144	+	38.0302i	0.606450	+	1.25931i
$913$	14.9009	−	11.8831i	0.493149	−	0.393273i
$914$	12.0693	+	15.1344i	0.399216	+	0.500601i
$915$		0			0
$916$	−148.041			−4.89142
$917$	−15.5036	−	32.1937i	−0.511975	−	1.06313i
$918$	64.2960	−	14.6751i	2.12208	−	0.484352i
$919$	6.11088	+	2.94284i	0.201579	+	0.0970755i	0.531950	−	0.846776i	$-0.321459\pi$
$919$	6.11088	+	2.94284i	0.201579	+	0.0970755i	−0.330371	+	0.943851i	$0.607174\pi$
$920$		0			0
$921$	4.75563	−	20.8358i	0.156703	−	0.686562i
$922$	29.4061	−	23.4506i	0.968439	−	0.772304i
$923$	3.80546	+	3.03476i	0.125258	+	0.0998902i
$924$	5.76405	+	25.2540i	0.189623	+	0.830795i
$925$		0			0
$926$	19.2738	−	24.1686i	0.633376	−	0.794228i
$927$		−	12.2431i		−	0.402116i
$928$	57.0511	−	152.428i	1.87279	−	5.00368i
$929$	1.28775			0.0422498			0.0211249	−	0.999777i	$-0.493275\pi$
$929$	1.28775			0.0422498			0.0211249	+	0.999777i	$0.493275\pi$
$930$		0			0
$931$	2.65036	−	11.6120i	0.0868622	−	0.380568i
$932$	83.5321	−	19.0657i	2.73619	−	0.624517i
$933$	−16.5855	−	13.2265i	−0.542985	−	0.433016i
$934$	20.8791	+	26.1816i	0.683186	+	0.856688i
$935$		0			0
$936$	−30.5722	−	14.7228i	−0.999285	−	0.481230i
$937$	13.2400	−	27.4931i	0.432531	−	0.898159i	−0.564806	−	0.825224i	$-0.691049\pi$
$937$	13.2400	−	27.4931i	0.432531	−	0.898159i	0.997337	−	0.0729354i	$-0.0232367\pi$
$938$	71.6285	−	16.3487i	2.33875	−	0.533805i
$939$	10.7003	−	5.15301i	0.349192	−	0.168162i
$940$		0			0
$941$	49.7489	−	23.9578i	1.62177	−	0.781003i	0.621771	−	0.783199i	$-0.286413\pi$
$941$	49.7489	−	23.9578i	1.62177	−	0.781003i	0.999998	+	0.00219594i	$0.000698991\pi$
$942$	−4.99005	+	3.97943i	−0.162584	+	0.129657i
$943$	1.82151	−	1.45260i	0.0593164	−	0.0473032i
$944$	−190.978	+	91.9702i	−6.21580	+	2.99337i
$945$		0			0
$946$	25.3658	−	12.2155i	0.824712	−	0.397160i
$947$	−35.3376	+	8.06558i	−1.14832	+	0.262096i	−0.753998	−	0.656877i	$-0.771877\pi$
$947$	−35.3376	+	8.06558i	−1.14832	+	0.262096i	−0.394320	+	0.918973i	$0.629020\pi$
$948$	0.480585	−	0.997946i	0.0156087	−	0.0324118i
$949$	2.79589	+	1.34643i	0.0907583	+	0.0437069i
$950$		0			0
$951$	−5.64501	−	7.07862i	−0.183052	−	0.229540i
$952$	−92.5721	−	73.8238i	−3.00028	−	2.39264i
$953$	−47.3095	+	10.7981i	−1.53250	+	0.349784i	−0.903833	−	0.427886i	$-0.859258\pi$
$953$	−47.3095	+	10.7981i	−1.53250	+	0.349784i	−0.628672	+	0.777670i	$0.716401\pi$
$954$	−8.57867	+	37.5856i	−0.277745	+	1.21688i
$955$		0			0
$956$	74.4911			2.40921
$957$	1.18815	+	13.0701i	0.0384075	+	0.422497i
$958$			99.1924i			3.20476i
$959$	5.44970	−	6.83371i	0.175980	−	0.220672i
$960$		0			0
$961$	6.84519	+	29.9907i	0.220812	+	0.967443i
$962$	−14.9012	−	11.8833i	−0.480433	−	0.383132i
$963$	−23.2026	+	18.5034i	−0.747692	+	0.596265i
$964$	21.9922	−	96.3541i	0.708321	−	3.10336i
$965$		0			0
$966$	−2.24115	−	1.07928i	−0.0721077	−	0.0347252i
$967$	32.3141	−	7.37547i	1.03915	−	0.237179i	0.331288	−	0.943530i	$-0.392517\pi$
$967$	32.3141	−	7.37547i	1.03915	−	0.237179i	0.707862	+	0.706351i	$0.249660\pi$
$968$	−3.91068	−	8.12061i	−0.125694	−	0.261006i
$969$	13.8071			0.443549
$970$		0			0
$971$	31.9199	+	40.0262i	1.02436	+	1.28450i	0.958019	+	0.286706i	$0.0925604\pi$
$971$	31.9199	+	40.0262i	1.02436	+	1.28450i	0.0663388	+	0.997797i	$0.478868\pi$
$972$	68.7333	−	54.8130i	2.20462	−	1.75813i
$973$	−3.95646	−	8.21567i	−0.126838	−	0.263382i
$974$	41.2531			1.32183
$975$		0			0
$976$	33.7540	+	147.886i	1.08044	+	4.73372i
$977$	−20.2855	+	42.1234i	−0.648992	+	1.34765i	0.273591	+	0.961846i	$0.411789\pi$
$977$	−20.2855	+	42.1234i	−0.648992	+	1.34765i	−0.922583	+	0.385799i	$0.873926\pi$
$978$	−10.2234	+	21.2292i	−0.326910	+	0.678835i
$979$	0.855629	−	3.74876i	0.0273460	−	0.119811i
$980$		0			0
$981$	−21.8655	+	27.4185i	−0.698113	+	0.875406i
$982$	−51.0461	+	11.6509i	−1.62895	+	0.371796i
$983$	25.8090	+	5.89073i	0.823178	+	0.187885i	0.613308	−	0.789844i	$-0.289839\pi$
$983$	25.8090	+	5.89073i	0.823178	+	0.187885i	0.209870	+	0.977729i	$0.432696\pi$
$984$	−16.0752	+	20.1576i	−0.512458	+	0.642602i
$985$		0			0
$986$	−63.0754	−	65.8533i	−2.00873	−	2.09720i
$987$		−	11.2608i		−	0.358435i
$988$	−18.5811	−	14.8180i	−0.591144	−	0.471422i
$989$	−0.448248	+	1.96390i	−0.0142535	+	0.0624485i
$990$		0			0
$991$	14.3938	−	18.0493i	0.457235	−	0.573354i	−0.498759	−	0.866741i	$-0.666211\pi$
$991$	14.3938	−	18.0493i	0.457235	−	0.573354i	0.955994	+	0.293386i	$0.0947822\pi$
$992$	11.5279	−	9.19317i	0.366010	−	0.291883i
$993$	−9.15984	−	2.09067i	−0.290679	−	0.0663456i
$994$	17.7127	+	8.52999i	0.561813	+	0.270555i
$995$		0			0
$996$	−5.10444	−	22.3640i	−0.161740	−	0.708631i
$997$	−20.6327	−	42.8441i	−0.653443	−	1.35689i	−0.919561	−	0.392947i	$-0.871455\pi$
$997$	−20.6327	−	42.8441i	−0.653443	−	1.35689i	0.266118	−	0.963940i	$-0.414259\pi$
$998$			20.2516i			0.641052i
$999$	18.9360	−	9.11911i	0.599109	−	0.288516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.r.d.574.1		72
5.2	odd	4		725.2.l.e.226.6		36
5.3	odd	4		145.2.k.b.81.1	✓	36
5.4	even	2	inner	725.2.r.d.574.12		72
29.24	even	7	inner	725.2.r.d.24.12		72
145.13	odd	28		4205.2.a.t.1.18		18
145.24	even	14	inner	725.2.r.d.24.1		72
145.53	odd	28		145.2.k.b.111.1	yes	36
145.82	odd	28		725.2.l.e.401.6		36
145.103	odd	28		4205.2.a.s.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.k.b.81.1	✓	36	5.3	odd	4
145.2.k.b.111.1	yes	36	145.53	odd	28
725.2.l.e.226.6		36	5.2	odd	4
725.2.l.e.401.6		36	145.82	odd	28
725.2.r.d.24.1		72	145.24	even	14	inner
725.2.r.d.24.12		72	29.24	even	7	inner
725.2.r.d.574.1		72	1.1	even	1	trivial
725.2.r.d.574.12		72	5.4	even	2	inner
4205.2.a.s.1.1		18	145.103	odd	28
4205.2.a.t.1.18		18	145.13	odd	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.r (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18993 - 1.74641i) q^{2} +(-0.690597 - 0.157624i) q^{3} +(1.30080 + 5.69919i) q^{4} +(1.23708 + 1.55125i) q^{6} +(-1.77264 - 0.404594i) q^{7} +(4.67383 - 9.70531i) q^{8} +(-2.25083 - 1.08394i) q^{9} +O(q^{10})\)	\(q+(-2.18993 - 1.74641i) q^{2} +(-0.690597 - 0.157624i) q^{3} +(1.30080 + 5.69919i) q^{4} +(1.23708 + 1.55125i) q^{6} +(-1.77264 - 0.404594i) q^{7} +(4.67383 - 9.70531i) q^{8} +(-2.25083 - 1.08394i) q^{9} +(3.09974 - 1.49276i) q^{11} -4.14088i q^{12} +(0.547090 + 1.13604i) q^{13} +(3.17538 + 3.98180i) q^{14} +(-16.6512 + 8.01877i) q^{16} +6.04532i q^{17} +(3.03615 + 6.30463i) q^{18} +(0.717470 + 3.14344i) q^{19} +(1.16041 + 0.558823i) q^{21} +(-9.39519 - 2.14439i) q^{22} +(0.539083 - 0.429904i) q^{23} +(-4.75752 + 5.96575i) q^{24} +(0.785912 - 3.44330i) q^{26} +(3.04501 + 2.42831i) q^{27} -10.6289i q^{28} +(0.718081 - 5.33707i) q^{29} +(0.304181 - 0.381431i) q^{31} +(29.4650 + 6.72519i) q^{32} +(-2.37597 + 0.542299i) q^{33} +(10.5576 - 13.2388i) q^{34} +(3.24971 - 14.2379i) q^{36} +(2.34141 - 4.86199i) q^{37} +(3.91853 - 8.13692i) q^{38} +(-0.198751 - 0.870783i) q^{39} +3.37890 q^{41} +(-1.56528 - 3.25033i) q^{42} +(-2.28412 + 1.82152i) q^{43} +(12.5397 + 15.7242i) q^{44} -1.93134 q^{46} +(-3.79352 - 7.87732i) q^{47} +(12.7632 - 2.91311i) q^{48} +(-3.32822 - 1.60279i) q^{49} +(0.952888 - 4.17488i) q^{51} +(-5.76288 + 4.59574i) q^{52} +(4.30737 + 3.43501i) q^{53} +(-2.42752 - 10.6357i) q^{54} +(-12.2117 + 15.3130i) q^{56} -2.28394i q^{57} +(-10.8933 + 10.4338i) q^{58} +11.4694 q^{59} +(1.82638 - 8.00189i) q^{61} +(-1.33227 + 0.304082i) q^{62} +(3.55136 + 2.83211i) q^{63} +(-29.7354 - 37.2870i) q^{64} +(6.15028 + 2.96182i) q^{66} +(6.25922 - 12.9974i) q^{67} +(-34.4534 + 7.86377i) q^{68} +(-0.440052 + 0.211918i) q^{69} +(3.47791 - 1.67487i) q^{71} +(-21.0400 + 16.7788i) q^{72} +(1.92414 - 1.53445i) q^{73} +(-13.6186 + 6.55835i) q^{74} +(-16.9818 + 8.17800i) q^{76} +(-6.09869 + 1.39199i) q^{77} +(-1.08550 + 2.25406i) q^{78} +(0.240998 + 0.116059i) q^{79} +(2.95275 + 3.70264i) q^{81} +(-7.39955 - 5.90095i) q^{82} +(5.40078 - 1.23269i) q^{83} +(-1.67538 + 7.34030i) q^{84} +8.18319 q^{86} +(-1.33716 + 3.57258i) q^{87} -37.0608i q^{88} +(0.696833 - 0.873801i) q^{89} +(-0.510158 - 2.23515i) q^{91} +(3.15135 + 2.51312i) q^{92} +(-0.270189 + 0.215468i) q^{93} +(-5.44950 + 23.8758i) q^{94} +(-19.2884 - 9.28879i) q^{96} +(1.10746 - 0.252772i) q^{97} +(4.48945 + 9.32243i) q^{98} -8.59505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 20 q^{4} + 4 q^{6} + 36 q^{9}+O(q^{10}) \) 72 * q + 20 * q^4 + 4 * q^6 + 36 * q^9	\( 72 q + 20 q^{4} + 4 q^{6} + 36 q^{9} + 8 q^{11} - 32 q^{14} - 40 q^{16} + 12 q^{19} + 62 q^{21} - 32 q^{24} - 64 q^{26} + 42 q^{29} - 14 q^{31} + 96 q^{34} - 24 q^{36} - 38 q^{39} - 56 q^{41} + 62 q^{44} + 152 q^{46} - 100 q^{49} - 28 q^{51} - 86 q^{54} + 12 q^{56} - 4 q^{59} - 8 q^{61} - 174 q^{64} + 132 q^{66} + 96 q^{69} + 54 q^{71} + 46 q^{74} - 80 q^{76} - 164 q^{79} - 98 q^{81} + 68 q^{84} - 252 q^{86} - 72 q^{89} - 90 q^{91} - 178 q^{96} + 16 q^{99}+O(q^{100}) \) 72 * q + 20 * q^4 + 4 * q^6 + 36 * q^9 + 8 * q^11 - 32 * q^14 - 40 * q^16 + 12 * q^19 + 62 * q^21 - 32 * q^24 - 64 * q^26 + 42 * q^29 - 14 * q^31 + 96 * q^34 - 24 * q^36 - 38 * q^39 - 56 * q^41 + 62 * q^44 + 152 * q^46 - 100 * q^49 - 28 * q^51 - 86 * q^54 + 12 * q^56 - 4 * q^59 - 8 * q^61 - 174 * q^64 + 132 * q^66 + 96 * q^69 + 54 * q^71 + 46 * q^74 - 80 * q^76 - 164 * q^79 - 98 * q^81 + 68 * q^84 - 252 * q^86 - 72 * q^89 - 90 * q^91 - 178 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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