LMFDB - Embedded newform 425.2.r.a.69.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.10
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50815 + 0.490028i) q^{2} +(0.441680 + 0.607920i) q^{3} +(0.416355 - 0.302500i) q^{4} +(1.21824 - 1.87507i) q^{5} +(-0.964016 - 0.700399i) q^{6} +4.59462i q^{7} +(1.38448 - 1.90558i) q^{8} +(0.752565 - 2.31616i) q^{9} +(-0.918447 + 3.42486i) q^{10} +(-0.580604 - 1.78691i) q^{11} +(0.367791 + 0.119503i) q^{12} +(2.66748 + 0.866716i) q^{13} +(-2.25149 - 6.92938i) q^{14} +(1.67796 - 0.0875909i) q^{15} +(-1.47229 + 4.53124i) q^{16} +(0.587785 - 0.809017i) q^{17} +3.86189i q^{18} +(1.61833 + 1.17579i) q^{19} +(-0.0599897 - 1.14921i) q^{20} +(-2.79316 + 2.02935i) q^{21} +(1.75128 + 2.41042i) q^{22} +(3.36088 - 1.09202i) q^{23} +1.76994 q^{24} +(-2.03180 - 4.56857i) q^{25} -4.44767 q^{26} +(3.88439 - 1.26211i) q^{27} +(1.38987 + 1.91299i) q^{28} +(-1.22150 + 0.887469i) q^{29} +(-2.48770 + 0.954349i) q^{30} +(4.57408 + 3.32326i) q^{31} -2.84441i q^{32} +(0.829860 - 1.14220i) q^{33} +(-0.490028 + 1.50815i) q^{34} +(8.61525 + 5.59734i) q^{35} +(-0.387303 - 1.19199i) q^{36} +(4.18554 + 1.35996i) q^{37} +(-3.01685 - 0.980236i) q^{38} +(0.651277 + 2.00442i) q^{39} +(-1.88647 - 4.91745i) q^{40} +(-3.39507 + 10.4489i) q^{41} +(3.21807 - 4.42929i) q^{42} +2.95472i q^{43} +(-0.782278 - 0.568359i) q^{44} +(-3.42616 - 4.23274i) q^{45} +(-4.53360 + 3.29385i) q^{46} +(4.76272 + 6.55533i) q^{47} +(-3.40491 + 1.10632i) q^{48} -14.1105 q^{49} +(5.30298 + 5.89445i) q^{50} +0.751430 q^{51} +(1.37280 - 0.446049i) q^{52} +(1.87755 + 2.58422i) q^{53} +(-5.23977 + 3.80692i) q^{54} +(-4.05791 - 1.08821i) q^{55} +(8.75541 + 6.36117i) q^{56} +1.50314i q^{57} +(1.40731 - 1.93700i) q^{58} +(2.34877 - 7.22878i) q^{59} +(0.672133 - 0.544052i) q^{60} +(0.213499 + 0.657082i) q^{61} +(-8.52689 - 2.77055i) q^{62} +(10.6419 + 3.45775i) q^{63} +(-1.55074 - 4.77269i) q^{64} +(4.87478 - 3.94585i) q^{65} +(-0.691842 + 2.12927i) q^{66} +(1.75144 - 2.41065i) q^{67} -0.514643i q^{68} +(2.14829 + 1.56083i) q^{69} +(-15.7359 - 4.21991i) q^{70} +(9.86671 - 7.16859i) q^{71} +(-3.37170 - 4.64075i) q^{72} +(2.16099 - 0.702147i) q^{73} -6.97884 q^{74} +(1.87992 - 3.25301i) q^{75} +1.02948 q^{76} +(8.21020 - 2.66765i) q^{77} +(-1.96445 - 2.70383i) q^{78} +(-7.09941 + 5.15802i) q^{79} +(6.70281 + 8.28078i) q^{80} +(-3.42781 - 2.49045i) q^{81} -17.4222i q^{82} +(-3.88373 + 5.34549i) q^{83} +(-0.549069 + 1.68986i) q^{84} +(-0.800904 - 2.08771i) q^{85} +(-1.44789 - 4.45616i) q^{86} +(-1.07902 - 0.350595i) q^{87} +(-4.20894 - 1.36757i) q^{88} +(-5.53854 - 17.0459i) q^{89} +(7.24133 + 4.70470i) q^{90} +(-3.98223 + 12.2560i) q^{91} +(1.06899 - 1.47133i) q^{92} +4.24849i q^{93} +(-10.3952 - 7.55255i) q^{94} +(4.17620 - 1.60210i) q^{95} +(1.72917 - 1.25632i) q^{96} +(-1.47298 - 2.02738i) q^{97} +(21.2808 - 6.91455i) q^{98} -4.57572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.50815	+	0.490028i	−1.06642	+	0.346502i	−0.789094	−	0.614273i	$-0.789449\pi$
$2$	−1.50815	+	0.490028i	−1.06642	+	0.346502i	−0.277329	+	0.960775i	$0.589449\pi$
$3$	0.441680	+	0.607920i	0.255004	+	0.350983i	0.917256	−	0.398299i	$-0.130399\pi$
$3$	0.441680	+	0.607920i	0.255004	+	0.350983i	−0.662252	+	0.749281i	$0.730399\pi$
$4$	0.416355	−	0.302500i	0.208178	−	0.151250i
$5$	1.21824	−	1.87507i	0.544812	−	0.838558i
$5$	1.21824	−	1.87507i	0.544812	−	0.838558i
$6$	−0.964016	−	0.700399i	−0.393558	−	0.285937i
$7$			4.59462i			1.73660i	0.496037	+	0.868302i	$0.334788\pi$
$7$			4.59462i			1.73660i	−0.496037	+	0.868302i	$0.665212\pi$
$8$	1.38448	−	1.90558i	0.489489	−	0.673723i
$9$	0.752565	−	2.31616i	0.250855	−	0.772053i
$10$	−0.918447	+	3.42486i	−0.290438	+	1.08304i
$11$	−0.580604	−	1.78691i	−0.175059	−	0.538775i	0.824577	−	0.565749i	$-0.191413\pi$
$11$	−0.580604	−	1.78691i	−0.175059	−	0.538775i	−0.999636	+	0.0269739i	$0.991413\pi$
$12$	0.367791	+	0.119503i	0.106172	+	0.0344974i
$13$	2.66748	+	0.866716i	0.739825	+	0.240384i	0.654597	−	0.755978i	$-0.272838\pi$
$13$	2.66748	+	0.866716i	0.739825	+	0.240384i	0.0852279	+	0.996361i	$0.472838\pi$
$14$	−2.25149	−	6.92938i	−0.601736	−	1.85195i
$15$	1.67796	−	0.0875909i	0.433249	−	0.0226159i
$16$	−1.47229	+	4.53124i	−0.368072	+	1.13281i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$			3.86189i			0.910257i
$19$	1.61833	+	1.17579i	0.371271	+	0.269744i	0.757738	−	0.652559i	$-0.226305\pi$
$19$	1.61833	+	1.17579i	0.371271	+	0.269744i	−0.386467	+	0.922303i	$0.626305\pi$
$20$	−0.0599897	−	1.14921i	−0.0134141	−	0.256972i
$21$	−2.79316	+	2.02935i	−0.609518	+	0.442840i
$22$	1.75128	+	2.41042i	0.373373	+	0.513904i
$23$	3.36088	−	1.09202i	0.700793	−	0.227701i	0.0631168	−	0.998006i	$-0.479896\pi$
$23$	3.36088	−	1.09202i	0.700793	−	0.227701i	0.637676	+	0.770305i	$0.279896\pi$
$24$	1.76994			0.361287
$25$	−2.03180	−	4.56857i	−0.406359	−	0.913713i
$26$	−4.44767			−0.872260
$27$	3.88439	−	1.26211i	0.747551	−	0.242894i
$28$	1.38987	+	1.91299i	0.262661	+	0.361522i
$29$	−1.22150	+	0.887469i	−0.226826	+	0.164799i	−0.695394	−	0.718629i	$-0.744770\pi$
$29$	−1.22150	+	0.887469i	−0.226826	+	0.164799i	0.468568	+	0.883427i	$0.344770\pi$
$30$	−2.48770	+	0.954349i	−0.454190	+	0.174240i
$31$	4.57408	+	3.32326i	0.821529	+	0.596876i	0.917150	−	0.398542i	$-0.130484\pi$
$31$	4.57408	+	3.32326i	0.821529	+	0.596876i	−0.0956212	+	0.995418i	$0.530484\pi$
$32$		−	2.84441i		−	0.502825i
$33$	0.829860	−	1.14220i	0.144460	−	0.198832i
$34$	−0.490028	+	1.50815i	−0.0840390	+	0.258646i
$35$	8.61525	+	5.59734i	1.45624	+	0.946123i
$36$	−0.387303	−	1.19199i	−0.0645504	−	0.198666i
$37$	4.18554	+	1.35996i	0.688099	+	0.223577i	0.632138	−	0.774856i	$-0.282178\pi$
$37$	4.18554	+	1.35996i	0.688099	+	0.223577i	0.0559612	+	0.998433i	$0.482178\pi$
$38$	−3.01685	−	0.980236i	−0.489399	−	0.159015i
$39$	0.651277	+	2.00442i	0.104288	+	0.320965i
$40$	−1.88647	−	4.91745i	−0.298277	−	0.777517i
$41$	−3.39507	+	10.4489i	−0.530220	+	1.63185i	0.223535	+	0.974696i	$0.428240\pi$
$41$	−3.39507	+	10.4489i	−0.530220	+	1.63185i	−0.753756	+	0.657155i	$0.771760\pi$
$42$	3.21807	−	4.42929i	0.496559	−	0.683454i
$43$			2.95472i			0.450590i	0.974291	+	0.225295i	$0.0723346\pi$
$43$			2.95472i			0.450590i	−0.974291	+	0.225295i	$0.927665\pi$
$44$	−0.782278	−	0.568359i	−0.117933	−	0.0856833i
$45$	−3.42616	−	4.23274i	−0.510742	−	0.630980i
$46$	−4.53360	+	3.29385i	−0.668443	+	0.485652i
$47$	4.76272	+	6.55533i	0.694715	+	0.956193i	0.999992	+	0.00392940i	$0.00125077\pi$
$47$	4.76272	+	6.55533i	0.694715	+	0.956193i	−0.305278	+	0.952263i	$0.598749\pi$
$48$	−3.40491	+	1.10632i	−0.491457	+	0.159684i
$49$	−14.1105			−2.01579
$50$	5.30298	+	5.89445i	0.749954	+	0.833601i
$51$	0.751430			0.105221
$52$	1.37280	−	0.446049i	0.190373	−	0.0618559i
$53$	1.87755	+	2.58422i	0.257901	+	0.354971i	0.918259	−	0.395981i	$-0.129595\pi$
$53$	1.87755	+	2.58422i	0.257901	+	0.354971i	−0.660358	+	0.750951i	$0.729595\pi$
$54$	−5.23977	+	3.80692i	−0.713042	+	0.518056i
$55$	−4.05791	−	1.08821i	−0.547168	−	0.146734i
$56$	8.75541	+	6.36117i	1.16999	+	0.850048i
$57$			1.50314i			0.199095i
$58$	1.40731	−	1.93700i	0.184789	−	0.254341i
$59$	2.34877	−	7.22878i	0.305784	−	0.941107i	−0.673599	−	0.739097i	$-0.735253\pi$
$59$	2.34877	−	7.22878i	0.305784	−	0.941107i	0.979383	−	0.202010i	$-0.0647475\pi$
$60$	0.672133	−	0.544052i	0.0867719	−	0.0702369i
$61$	0.213499	+	0.657082i	0.0273357	+	0.0841307i	0.963794	−	0.266649i	$-0.0859165\pi$
$61$	0.213499	+	0.657082i	0.0273357	+	0.0841307i	−0.936458	+	0.350780i	$0.885917\pi$
$62$	−8.52689	−	2.77055i	−1.08292	−	0.351861i
$63$	10.6419	+	3.45775i	1.34075	+	0.435636i
$64$	−1.55074	−	4.77269i	−0.193843	−	0.596586i
$65$	4.87478	−	3.94585i	0.604642	−	0.489422i
$66$	−0.691842	+	2.12927i	−0.0851598	+	0.262095i
$67$	1.75144	−	2.41065i	0.213972	−	0.294507i	−0.688517	−	0.725220i	$-0.741738\pi$
$67$	1.75144	−	2.41065i	0.213972	−	0.294507i	0.902489	+	0.430713i	$0.141738\pi$
$68$		−	0.514643i		−	0.0624096i
$69$	2.14829	+	1.56083i	0.258624	+	0.187901i
$70$	−15.7359	−	4.21991i	−1.88080	−	0.504376i
$71$	9.86671	−	7.16859i	1.17096	−	0.850755i	0.179840	−	0.983696i	$-0.442442\pi$
$71$	9.86671	−	7.16859i	1.17096	−	0.850755i	0.991124	+	0.132941i	$0.0424421\pi$
$72$	−3.37170	−	4.64075i	−0.397359	−	0.546918i
$73$	2.16099	−	0.702147i	0.252924	−	0.0821800i	−0.179811	−	0.983701i	$-0.557549\pi$
$73$	2.16099	−	0.702147i	0.252924	−	0.0821800i	0.432735	+	0.901521i	$0.357549\pi$
$74$	−6.97884			−0.811274
$75$	1.87992	−	3.25301i	0.217074	−	0.375625i
$76$	1.02948			0.118089
$77$	8.21020	−	2.66765i	0.935639	−	0.304007i
$78$	−1.96445	−	2.70383i	−0.222430	−	0.306148i
$79$	−7.09941	+	5.15802i	−0.798746	+	0.580323i	−0.910546	−	0.413408i	$-0.864338\pi$
$79$	−7.09941	+	5.15802i	−0.798746	+	0.580323i	0.111800	+	0.993731i	$0.464338\pi$
$80$	6.70281	+	8.28078i	0.749397	+	0.925819i
$81$	−3.42781	−	2.49045i	−0.380867	−	0.276716i
$82$		−	17.4222i		−	1.92397i
$83$	−3.88373	+	5.34549i	−0.426294	+	0.586744i	−0.967098	−	0.254405i	$-0.918120\pi$
$83$	−3.88373	+	5.34549i	−0.426294	+	0.586744i	0.540803	+	0.841149i	$0.318120\pi$
$84$	−0.549069	+	1.68986i	−0.0599083	+	0.184379i
$85$	−0.800904	−	2.08771i	−0.0868702	−	0.226444i
$86$	−1.44789	−	4.45616i	−0.156130	−	0.480520i
$87$	−1.07902	−	0.350595i	−0.115683	−	0.0375877i
$88$	−4.20894	−	1.36757i	−0.448675	−	0.145783i
$89$	−5.53854	−	17.0459i	−0.587084	−	1.80686i	−0.590736	−	0.806865i	$-0.701163\pi$
$89$	−5.53854	−	17.0459i	−0.587084	−	1.80686i	0.00365251	−	0.999993i	$-0.498837\pi$
$90$	7.24133	+	4.70470i	0.763303	+	0.495919i
$91$	−3.98223	+	12.2560i	−0.417451	+	1.28478i
$92$	1.06899	−	1.47133i	0.111449	−	0.153397i
$93$			4.24849i			0.440548i
$94$	−10.3952	−	7.55255i	−1.07218	−	0.778986i
$95$	4.17620	−	1.60210i	0.428469	−	0.164372i
$96$	1.72917	−	1.25632i	0.176483	−	0.128222i
$97$	−1.47298	−	2.02738i	−0.149558	−	0.205849i	0.727664	−	0.685934i	$-0.240606\pi$
$97$	−1.47298	−	2.02738i	−0.149558	−	0.205849i	−0.877222	+	0.480084i	$0.840606\pi$
$98$	21.2808	−	6.91455i	2.14969	−	0.698475i
$99$	−4.57572			−0.459877
$100$	−2.22794	−	1.28753i	−0.222794	−	0.128753i
$101$	−18.3740			−1.82828			−0.914142	−	0.405393i	$-0.867135\pi$
$101$	−18.3740			−1.82828			−0.914142	+	0.405393i	$0.867135\pi$
$102$	−1.13327	+	0.368222i	−0.112210	+	0.0364594i
$103$	−6.96865	−	9.59152i	−0.686641	−	0.945080i	0.313348	−	0.949638i	$-0.398549\pi$
$103$	−6.96865	−	9.59152i	−0.686641	−	0.945080i	−0.999990	+	0.00455778i	$0.998549\pi$
$104$	5.34467	−	3.88313i	0.524088	−	0.380772i
$105$	0.402447	+	7.70961i	0.0392748	+	0.752381i
$106$	−4.09797	−	2.97735i	−0.398030	−	0.289185i
$107$			0.449814i			0.0434852i	0.999764	+	0.0217426i	$0.00692143\pi$
$107$			0.449814i			0.0434852i	−0.999764	+	0.0217426i	$0.993079\pi$
$108$	1.23550	−	1.70051i	0.118886	−	0.163632i
$109$	5.10054	−	15.6979i	0.488543	−	1.50358i	−0.338240	−	0.941060i	$-0.609831\pi$
$109$	5.10054	−	15.6979i	0.488543	−	1.50358i	0.826783	−	0.562521i	$-0.190169\pi$
$110$	6.65319	−	0.347301i	0.634357	−	0.0331139i
$111$	1.02192	+	3.14514i	0.0969962	+	0.298524i
$112$	−20.8193	−	6.76461i	−1.96724	−	0.639196i
$113$	−9.45011	−	3.07053i	−0.888992	−	0.288851i	−0.171306	−	0.985218i	$-0.554799\pi$
$113$	−9.45011	−	3.07053i	−0.888992	−	0.288851i	−0.717686	+	0.696367i	$0.754799\pi$
$114$	−0.736579	−	2.26696i	−0.0689869	−	0.212320i
$115$	2.04674	−	7.63224i	0.190860	−	0.711710i
$116$	−0.240117	+	0.739004i	−0.0222943	+	0.0686148i
$117$	4.01490	−	5.52604i	0.371178	−	0.510883i
$118$			12.0531i			1.10957i
$119$	3.71713	+	2.70065i	0.340748	+	0.247568i
$120$	2.15620	−	3.31876i	0.196833	−	0.302960i
$121$	6.04322	−	4.39066i	0.549384	−	0.399151i
$122$	−0.643976	−	0.886358i	−0.0583029	−	0.0802470i
$123$	−7.85165	+	2.55116i	−0.707959	+	0.230030i
$124$	2.90973			0.261301
$125$	−11.0416	−	1.75583i	−0.987591	−	0.157046i
$126$	−17.7439			−1.58075
$127$	8.96561	−	2.91310i	0.795569	−	0.258496i	0.117095	−	0.993121i	$-0.462642\pi$
$127$	8.96561	−	2.91310i	0.795569	−	0.258496i	0.678474	+	0.734625i	$0.262642\pi$
$128$	8.02130	+	11.0404i	0.708990	+	0.975840i
$129$	−1.79623	+	1.30504i	−0.158149	+	0.114902i
$130$	−5.41832	+	8.33971i	−0.475218	+	0.731441i
$131$	−5.98766	−	4.35029i	−0.523144	−	0.380086i	0.294643	−	0.955607i	$-0.404799\pi$
$131$	−5.98766	−	4.35029i	−0.523144	−	0.380086i	−0.817787	+	0.575521i	$0.804799\pi$
$132$		−	0.726595i		−	0.0632420i
$133$	−5.40229	+	7.43562i	−0.468438	+	0.644750i
$134$	−1.46015	+	4.49387i	−0.126137	+	0.388211i
$135$	2.36555	−	8.82107i	0.203594	−	0.759196i
$136$	−0.727866	−	2.24014i	−0.0624140	−	0.192090i
$137$	−0.881187	−	0.286315i	−0.0752849	−	0.0244615i	0.271132	−	0.962542i	$-0.412602\pi$
$137$	−0.881187	−	0.286315i	−0.0752849	−	0.0244615i	−0.346417	+	0.938081i	$0.612602\pi$
$138$	−4.00479	−	1.30124i	−0.340911	−	0.110769i
$139$	3.69292	+	11.3656i	0.313230	+	0.964021i	0.976477	+	0.215621i	$0.0691776\pi$
$139$	3.69292	+	11.3656i	0.313230	+	0.964021i	−0.663248	+	0.748400i	$0.730822\pi$
$140$	5.28019	−	0.275630i	0.446258	−	0.0232950i
$141$	−1.88152	+	5.79071i	−0.158452	+	0.487666i
$142$	−11.3677	+	15.6463i	−0.953954	+	1.31301i
$143$		−	5.26978i		−	0.440681i
$144$	9.38708	+	6.82011i	0.782256	+	0.568343i
$145$	0.175997	+	3.37154i	0.0146157	+	0.279991i
$146$	−2.91502	+	2.11788i	−0.241249	+	0.175277i
$147$	−6.23234	−	8.57807i	−0.514034	−	0.707508i
$148$	2.15406	−	0.699897i	0.177063	−	0.0575311i
$149$	24.2546			1.98701			0.993506	−	0.113781i	$-0.0362962\pi$
$149$	24.2546			1.98701			0.993506	+	0.113781i	$0.0362962\pi$
$150$	−1.24113	+	5.82724i	−0.101338	+	0.475792i
$151$	−22.7880			−1.85446			−0.927229	−	0.374494i	$-0.877817\pi$
$151$	−22.7880			−1.85446			−0.927229	+	0.374494i	$0.877817\pi$
$152$	4.48111	−	1.45600i	0.363466	−	0.118097i
$153$	−1.43146	−	1.97024i	−0.115727	−	0.159285i
$154$	−11.0750	+	8.04645i	−0.892447	+	0.648401i
$155$	11.8037	−	4.52821i	0.948094	−	0.363714i
$156$	0.877500	+	0.637541i	0.0702562	+	0.0510441i
$157$			17.0163i			1.35805i	0.734115	+	0.679025i	$0.237597\pi$
$157$			17.0163i			1.35805i	−0.734115	+	0.679025i	$0.762403\pi$
$158$	8.17940	−	11.2580i	0.650718	−	0.895637i
$159$	−0.741726	+	2.28280i	−0.0588227	+	0.181038i
$160$	−5.33347	−	3.46516i	−0.421648	−	0.273945i
$161$	5.01741	+	15.4420i	0.395427	+	1.21700i
$162$	6.39003	+	2.07625i	0.502048	+	0.163125i
$163$	0.582616	+	0.189304i	0.0456340	+	0.0148274i	0.331745	−	0.943369i	$-0.392363\pi$
$163$	0.582616	+	0.189304i	0.0456340	+	0.0148274i	−0.286111	+	0.958196i	$0.592363\pi$
$164$	1.74725	+	5.37748i	0.136437	+	0.419910i
$165$	−1.13075	−	2.94752i	−0.0880288	−	0.229464i
$166$	3.23780	−	9.96493i	0.251302	−	0.773429i
$167$	−4.97479	+	6.84721i	−0.384961	+	0.529853i	−0.956890	−	0.290450i	$-0.906195\pi$
$167$	−4.97479	+	6.84721i	−0.384961	+	0.529853i	0.571929	+	0.820303i	$0.306195\pi$
$168$			8.13218i			0.627412i
$169$	−4.15298	−	3.01732i	−0.319460	−	0.232101i
$170$	2.23092	+	2.75612i	0.171104	+	0.211385i
$171$	3.94121	−	2.86346i	0.301392	−	0.218974i
$172$	0.893801	+	1.23021i	0.0681517	+	0.0938027i
$173$	1.88671	−	0.613030i	0.143444	−	0.0466078i	−0.236415	−	0.971652i	$-0.575972\pi$
$173$	1.88671	−	0.613030i	0.143444	−	0.0466078i	0.379859	+	0.925044i	$0.375972\pi$
$174$	1.79912			0.136391
$175$	20.9908	−	9.33533i	1.58676	−	0.705685i
$176$	8.95176			0.674764
$177$	5.43193	−	1.76494i	0.408289	−	0.132661i
$178$	16.7059	+	22.9937i	1.25216	+	1.72345i
$179$	−2.18729	+	1.58916i	−0.163486	+	0.118779i	−0.666520	−	0.745487i	$-0.732217\pi$
$179$	−2.18729	+	1.58916i	−0.163486	+	0.118779i	0.503034	+	0.864266i	$0.332217\pi$
$180$	−2.70690	−	0.725912i	−0.201761	−	0.0541063i
$181$	7.05980	+	5.12925i	0.524751	+	0.381254i	0.818391	−	0.574662i	$-0.194867\pi$
$181$	7.05980	+	5.12925i	0.524751	+	0.381254i	−0.293640	+	0.955916i	$0.594867\pi$
$182$		−	20.4354i		−	1.51477i
$183$	−0.305155	+	0.420010i	−0.0225577	+	0.0310480i
$184$	2.57216	−	7.91630i	0.189622	−	0.583598i
$185$	7.64902	−	6.19144i	0.562367	−	0.455203i
$186$	−2.08188	−	6.40736i	−0.152651	−	0.469810i
$187$	−1.78691	−	0.580604i	−0.130672	−	0.0424580i
$188$	3.96597	+	1.28862i	0.289248	+	0.0939824i
$189$	5.79894	+	17.8473i	0.421811	+	1.29820i
$190$	−5.51326	+	4.46266i	−0.399974	+	0.323756i
$191$	2.95140	−	9.08347i	0.213556	−	0.657257i	−0.785697	−	0.618611i	$-0.787696\pi$
$191$	2.95140	−	9.08347i	0.213556	−	0.657257i	0.999253	−	0.0386458i	$-0.0123044\pi$
$192$	2.21648	−	3.05073i	0.159961	−	0.220167i
$193$		−	10.0817i		−	0.725697i	−0.931848	−	0.362849i	$-0.881804\pi$
$193$		−	10.0817i		−	0.725697i	0.931848	−	0.362849i	$-0.118196\pi$
$194$	3.21494	+	2.33579i	0.230820	+	0.167700i
$195$	4.55185	+	1.22067i	0.325965	+	0.0874141i
$196$	−5.87499	+	4.26843i	−0.419642	+	0.304888i
$197$	−8.18822	−	11.2701i	−0.583386	−	0.802963i	0.410675	−	0.911782i	$-0.365293\pi$
$197$	−8.18822	−	11.2701i	−0.583386	−	0.802963i	−0.994062	+	0.108819i	$0.965293\pi$
$198$	6.90087	−	2.24223i	0.490424	−	0.159348i
$199$	−2.42587			−0.171965			−0.0859827	−	0.996297i	$-0.527403\pi$
$199$	−2.42587			−0.171965			−0.0859827	+	0.996297i	$0.527403\pi$
$200$	−11.5187	−	2.45336i	−0.814498	−	0.173479i
$201$	2.23905			0.157931
$202$	27.7108	−	9.00378i	1.94973	−	0.633504i
$203$	−4.07758	−	5.61231i	−0.286190	−	0.393907i
$204$	0.312862	−	0.227307i	0.0219047	−	0.0159147i
$205$	15.4565	+	19.0953i	1.07953	+	1.33367i
$206$	15.2099	+	11.0506i	1.05972	+	0.769933i
$207$		−	8.60615i		−	0.598169i
$208$	−7.85460	+	10.8109i	−0.544618	+	0.749603i
$209$	1.16142	−	3.57449i	0.0803372	−	0.247252i
$210$	−4.38487	−	11.4300i	−0.302585	−	0.788747i
$211$	−1.36939	−	4.21455i	−0.0942728	−	0.290142i	0.892791	−	0.450472i	$-0.148744\pi$
$211$	−1.36939	−	4.21455i	−0.0942728	−	0.290142i	−0.987063	+	0.160330i	$0.948744\pi$
$212$	1.56345	+	0.507997i	0.107378	+	0.0348894i
$213$	8.71585	+	2.83195i	0.597200	+	0.194042i
$214$	−0.220422	−	0.678388i	−0.0150677	−	0.0463736i
$215$	5.54031	+	3.59955i	0.377846	+	0.245487i
$216$	2.97281	−	9.14938i	0.202274	−	0.622536i
$217$	−15.2691	+	21.0162i	−1.03654	+	1.42667i
$218$			26.1741i			1.77273i
$219$	1.38131	+	1.00358i	0.0933404	+	0.0678158i
$220$	−2.01871	+	0.774434i	−0.136102	+	0.0522123i
$221$	2.26909	−	1.64859i	0.152636	−	0.110896i
$222$	−3.08241	−	4.24258i	−0.206878	−	0.284743i
$223$	−22.6433	+	7.35727i	−1.51631	+	0.492679i	−0.944725	−	0.327863i	$-0.893671\pi$
$223$	−22.6433	+	7.35727i	−1.51631	+	0.492679i	−0.571586	+	0.820542i	$0.693671\pi$
$224$	13.0690			0.873207
$225$	−12.1106	+	1.26782i	−0.807372	+	0.0845211i
$226$	15.7568			1.04813
$227$	−21.5778	+	7.01104i	−1.43217	+	0.465339i	−0.919446	−	0.393217i	$-0.871362\pi$
$227$	−21.5778	+	7.01104i	−1.43217	+	0.465339i	−0.512720	+	0.858556i	$0.671362\pi$
$228$	0.454698	+	0.625839i	0.0301131	+	0.0414472i
$229$	−9.08698	+	6.60208i	−0.600485	+	0.436278i	−0.846051	−	0.533102i	$-0.821026\pi$
$229$	−9.08698	+	6.60208i	−0.600485	+	0.436278i	0.245566	+	0.969380i	$0.421026\pi$
$230$	0.653215	+	12.5135i	0.0430717	+	0.825117i
$231$	5.24800	+	3.81289i	0.345293	+	0.250870i
$232$			3.55634i			0.233485i
$233$	−10.5994	+	14.5888i	−0.694389	+	0.955744i	0.305605	+	0.952158i	$0.401141\pi$
$233$	−10.5994	+	14.5888i	−0.694389	+	0.955744i	−0.999994	+	0.00358567i	$0.998859\pi$
$234$	−3.34716	+	10.3015i	−0.218811	+	0.673431i
$235$	18.0938	−	0.944512i	1.18031	−	0.0616131i
$236$	−1.20878	−	3.72024i	−0.0786849	−	0.242167i
$237$	−6.27133	−	2.03768i	−0.407367	−	0.132361i
$238$	−6.92938	−	2.25149i	−0.449165	−	0.145942i
$239$	1.96817	+	6.05741i	0.127311	+	0.391821i	0.994315	−	0.106479i	$-0.0339577\pi$
$239$	1.96817	+	6.05741i	0.127311	+	0.391821i	−0.867004	+	0.498300i	$0.833958\pi$
$240$	−2.07355	+	7.73222i	−0.133847	+	0.499113i
$241$	−1.30832	+	4.02660i	−0.0842764	+	0.259376i	−0.984311	−	0.176442i	$-0.943541\pi$
$241$	−1.30832	+	4.02660i	−0.0842764	+	0.259376i	0.900035	+	0.435819i	$0.143541\pi$
$242$	−6.96254	+	9.58312i	−0.447569	+	0.616026i
$243$		−	15.4367i		−	0.990263i
$244$	0.287658	+	0.208996i	0.0184154	+	0.0133796i
$245$	−17.1900	+	26.4583i	−1.09823	+	1.69036i
$246$	10.5913	−	7.69505i	0.675278	−	0.490618i
$247$	3.29779	+	4.53902i	0.209833	+	0.288811i
$248$	12.6655	−	4.11526i	0.804258	−	0.261319i
$249$	−4.96499			−0.314644
$250$	17.5128	−	2.76264i	1.10761	−	0.174724i
$251$	24.0766			1.51970			0.759850	−	0.650099i	$-0.225272\pi$
$251$	24.0766			1.51970			0.759850	+	0.650099i	$0.225272\pi$
$252$	5.47676	−	1.77951i	0.345004	−	0.112098i
$253$	−3.90268	−	5.37158i	−0.245360	−	0.337709i
$254$	−12.0940	+	8.78679i	−0.758844	+	0.551332i
$255$	0.915420	−	1.40899i	0.0573258	−	0.0882341i
$256$	−9.38762	−	6.82051i	−0.586727	−	0.426282i
$257$			24.3374i			1.51812i	0.651018	+	0.759062i	$0.274342\pi$
$257$			24.3374i			1.51812i	−0.651018	+	0.759062i	$0.725658\pi$
$258$	2.06948	−	2.84840i	0.128840	−	0.177333i
$259$	−6.24852	+	19.2310i	−0.388264	+	1.19495i
$260$	0.836020	−	3.11749i	0.0518477	−	0.193339i
$261$	1.13626	+	3.49706i	0.0703329	+	0.216462i
$262$	11.1620	+	3.62677i	0.689593	+	0.224062i
$263$	0.541278	+	0.175872i	0.0333766	+	0.0108447i	0.325658	−	0.945488i	$-0.394414\pi$
$263$	0.541278	+	0.175872i	0.0333766	+	0.0108447i	−0.292281	+	0.956332i	$0.594414\pi$
$264$	−1.02763	−	3.16273i	−0.0632464	−	0.194652i
$265$	7.13291	−	0.372343i	0.438171	−	0.0228728i
$266$	4.50381	−	13.8613i	0.276146	−	0.849891i
$267$	7.91626	−	10.8958i	0.484467	−	0.666812i
$268$		−	1.53349i		−	0.0936731i
$269$	0.109923	+	0.0798641i	0.00670215	+	0.00486940i	0.591131	−	0.806575i	$-0.298682\pi$
$269$	0.109923	+	0.0798641i	0.00670215	+	0.00486940i	−0.584429	+	0.811445i	$0.698682\pi$
$270$	0.754962	+	14.4627i	0.0459455	+	0.880170i
$271$	−0.907743	+	0.659514i	−0.0551414	+	0.0400626i	−0.615015	−	0.788516i	$-0.710850\pi$
$271$	−0.907743	+	0.659514i	−0.0551414	+	0.0400626i	0.559873	+	0.828578i	$0.310850\pi$
$272$	2.80046	+	3.85450i	0.169803	+	0.233714i
$273$	−9.20956	+	2.99237i	−0.557388	+	0.181106i
$274$	1.46926			0.0887615
$275$	−6.98397	+	6.28318i	−0.421149	+	0.378890i
$276$	1.36660			0.0822598
$277$	25.7459	−	8.36533i	1.54692	−	0.502624i	0.593643	−	0.804728i	$-0.297689\pi$
$277$	25.7459	−	8.36533i	1.54692	−	0.502624i	0.953275	+	0.302104i	$0.0976890\pi$
$278$	−11.1390	−	15.3315i	−0.668070	−	0.919520i
$279$	11.1395	−	8.09332i	0.666904	−	0.484534i
$280$	22.5938	−	8.66760i	1.35024	−	0.517988i
$281$	−18.8113	−	13.6672i	−1.12219	−	0.815319i	−0.137650	−	0.990481i	$-0.543955\pi$
$281$	−18.8113	−	13.6672i	−1.12219	−	0.815319i	−0.984540	+	0.175162i	$0.943955\pi$
$282$		−	9.65525i		−	0.574962i
$283$	5.37099	−	7.39253i	0.319272	−	0.439440i	−0.618973	−	0.785413i	$-0.712451\pi$
$283$	5.37099	−	7.39253i	0.319272	−	0.439440i	0.938245	+	0.345972i	$0.112451\pi$
$284$	1.93956	−	5.96936i	0.115092	−	0.354216i
$285$	2.81849	+	1.83118i	0.166953	+	0.108470i
$286$	2.58234	+	7.94761i	0.152697	+	0.469952i
$287$	−48.0089	−	15.5990i	−2.83388	−	0.920782i
$288$	−6.58809	−	2.14060i	−0.388207	−	0.126136i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−1.91758	−	4.99854i	−0.112604	−	0.293525i
$291$	0.581900	−	1.79090i	0.0341116	−	0.104985i
$292$	0.687338	−	0.946039i	0.0402234	−	0.0553628i
$293$			0.964935i			0.0563721i	0.999603	+	0.0281860i	$0.00897309\pi$
$293$			0.964935i			0.0563721i	−0.999603	+	0.0281860i	$0.991027\pi$
$294$	13.6028	+	9.88300i	0.793331	+	0.576389i
$295$	−10.6931	−	13.2105i	−0.622578	−	0.769145i
$296$	8.38633	−	6.09303i	0.487446	−	0.354150i
$297$	−4.51058	−	6.20828i	−0.261731	−	0.360241i
$298$	−36.5795	+	11.8854i	−2.11900	+	0.688503i
$299$	9.91155			0.573200
$300$	−0.201321	−	1.92308i	−0.0116233	−	0.111029i
$301$	−13.5758			−0.782496
$302$	34.3677	−	11.1667i	1.97764	−	0.642573i
$303$	−8.11544	−	11.1699i	−0.466220	−	0.641696i
$304$	−7.71043	+	5.60195i	−0.442223	+	0.321294i
$305$	1.49217	+	0.400156i	0.0854413	+	0.0229128i
$306$	3.12434	+	2.26996i	0.178606	+	0.129765i
$307$			4.22166i			0.240943i	0.992717	+	0.120472i	$0.0384406\pi$
$307$			4.22166i			0.240943i	−0.992717	+	0.120472i	$0.961559\pi$
$308$	2.61139	−	3.59427i	0.148798	−	0.204803i
$309$	2.75297	−	8.47276i	0.156611	−	0.481998i
$310$	−15.5828	+	12.6133i	−0.885041	+	0.716390i
$311$	−7.25060	−	22.3151i	−0.411144	−	1.26537i	−0.915655	−	0.401966i	$-0.868327\pi$
$311$	−7.25060	−	22.3151i	−0.411144	−	1.26537i	0.504511	−	0.863405i	$-0.331673\pi$
$312$	4.72127	+	1.53403i	0.267289	+	0.0868475i
$313$	−9.79474	−	3.18251i	−0.553632	−	0.179886i	0.0188221	−	0.999823i	$-0.494008\pi$
$313$	−9.79474	−	3.18251i	−0.553632	−	0.179886i	−0.572454	+	0.819937i	$0.694008\pi$
$314$	−8.33846	−	25.6631i	−0.470567	−	1.44825i
$315$	19.4479	−	15.7419i	1.09576	−	0.886956i
$316$	−1.39557	+	4.29514i	−0.0785072	+	0.241620i
$317$	−7.77892	+	10.7068i	−0.436908	+	0.601352i	−0.969521	−	0.245006i	$-0.921210\pi$
$317$	−7.77892	+	10.7068i	−0.436908	+	0.601352i	0.532614	+	0.846359i	$0.321210\pi$
$318$		−	3.80627i		−	0.213445i
$319$	2.29504	+	1.66744i	0.128497	+	0.0933588i
$320$	−10.8383	−	2.90652i	−0.605880	−	0.162479i
$321$	−0.273451	+	0.198674i	−0.0152626	+	0.0110889i
$322$	−15.1340	−	20.8302i	−0.843385	−	1.16082i
$323$	1.90246	−	0.618148i	0.105856	−	0.0343947i
$324$	−2.18054			−0.121141
$325$	−1.46012	−	13.9475i	−0.0809930	−	0.773670i
$326$	−0.971437			−0.0538029
$327$	11.7958	−	3.83270i	0.652311	−	0.211949i
$328$	15.2109	+	20.9359i	0.839879	+	1.15599i
$329$	−30.1192	+	21.8829i	−1.66053	+	1.20644i
$330$	3.14971	+	3.89121i	0.173386	+	0.214204i
$331$	23.5092	+	17.0804i	1.29218	+	0.938825i	0.999847	−	0.0174914i	$-0.00556797\pi$
$331$	23.5092	+	17.0804i	1.29218	+	0.938825i	0.292334	+	0.956316i	$0.405568\pi$
$332$			3.40045i			0.186624i
$333$	6.29979	−	8.67091i	0.345226	−	0.475163i
$334$	4.14741	−	12.7644i	0.226936	−	0.698437i
$335$	−2.38647	−	6.22081i	−0.130387	−	0.339879i
$336$	−5.08313	−	15.6443i	−0.277308	−	0.853465i
$337$	32.4530	+	10.5446i	1.76783	+	0.574402i	0.997963	−	0.0638028i	$-0.0203229\pi$
$337$	32.4530	+	10.5446i	1.76783	+	0.574402i	0.769866	+	0.638205i	$0.220323\pi$
$338$	7.74188	+	2.51549i	0.421103	+	0.136825i
$339$	−2.30729	−	7.10110i	−0.125315	−	0.385679i
$340$	−0.964993	−	0.626957i	−0.0523341	−	0.0340015i
$341$	3.28266	−	10.1030i	0.177766	−	0.547108i
$342$	−4.54076	+	6.24982i	−0.245536	+	0.337952i
$343$		−	32.6702i		−	1.76403i
$344$	5.63044	+	4.09076i	0.303573	+	0.220559i
$345$	5.54379	−	2.12675i	0.298468	−	0.114500i
$346$	−2.54504	+	1.84908i	−0.136822	+	0.0994073i
$347$	−10.3168	−	14.1999i	−0.553835	−	0.762289i	0.436691	−	0.899611i	$-0.356150\pi$
$347$	−10.3168	−	14.1999i	−0.553835	−	0.762289i	−0.990526	+	0.137323i	$0.956150\pi$
$348$	−0.555310	+	0.180431i	−0.0297677	+	0.00967212i
$349$	−16.4871			−0.882532			−0.441266	−	0.897376i	$-0.645470\pi$
$349$	−16.4871			−0.882532			−0.441266	+	0.897376i	$0.645470\pi$
$350$	−27.0827	+	24.3652i	−1.44763	+	1.30237i
$351$	11.4554			0.611445
$352$	−5.08271	+	1.65147i	−0.270909	+	0.0880238i
$353$	−19.5231	−	26.8712i	−1.03911	−	1.43021i	−0.897884	−	0.440233i	$-0.854896\pi$
$353$	−19.5231	−	26.8712i	−1.03911	−	1.43021i	−0.141225	−	0.989977i	$-0.545104\pi$
$354$	−7.32729	+	5.32359i	−0.389441	+	0.282945i
$355$	−1.42163	−	27.2338i	−0.0754521	−	1.44542i
$356$	−7.46237	−	5.42173i	−0.395505	−	0.287351i
$357$			3.45254i			0.182728i
$358$	2.52003	−	3.46853i	0.133188	−	0.183317i
$359$	−0.419191	+	1.29014i	−0.0221241	+	0.0680909i	−0.961509	−	0.274773i	$-0.911397\pi$
$359$	−0.419191	+	1.29014i	−0.0221241	+	0.0680909i	0.939385	+	0.342864i	$0.111397\pi$
$360$	−12.8093	+	0.668654i	−0.675109	+	0.0352412i
$361$	−4.63480	−	14.2644i	−0.243937	−	0.750760i
$362$	−13.1607	−	4.27618i	−0.691712	−	0.224751i
$363$	5.33834	+	1.73453i	0.280190	+	0.0910392i
$364$	2.04943	+	6.30749i	0.107419	+	0.330602i
$365$	1.31602	−	4.90739i	0.0688834	−	0.256864i
$366$	0.254403	−	0.782972i	0.0132979	−	0.0409266i
$367$	−17.4069	+	23.9585i	−0.908631	+	1.25062i	0.0590015	+	0.998258i	$0.481208\pi$
$367$	−17.4069	+	23.9585i	−0.908631	+	1.25062i	−0.967632	+	0.252365i	$0.918792\pi$
$368$			16.8367i			0.877676i
$369$	21.6464	+	15.7270i	1.12687	+	0.818716i
$370$	−8.50189	+	13.0858i	−0.441992	+	0.680301i
$371$	−11.8735	+	8.62662i	−0.616443	+	0.447872i
$372$	1.28517	+	1.76888i	0.0666328	+	0.0917122i
$373$	−19.1244	+	6.21388i	−0.990221	+	0.321742i	−0.758951	−	0.651147i	$-0.774288\pi$
$373$	−19.1244	+	6.21388i	−0.990221	+	0.321742i	−0.231270	+	0.972890i	$0.574288\pi$
$374$	2.97945			0.154064
$375$	−3.80945	−	7.48792i	−0.196719	−	0.386675i
$376$	19.0856			0.984265
$377$	−4.02750	+	1.30861i	−0.207427	+	0.0673970i
$378$	−17.4913	−	24.0748i	−0.899657	−	1.23827i
$379$	−17.1091	+	12.4305i	−0.878834	+	0.638510i	−0.932943	−	0.360025i	$-0.882768\pi$
$379$	−17.1091	+	12.4305i	−0.878834	+	0.638510i	0.0541090	+	0.998535i	$0.482768\pi$
$380$	1.25415	−	1.93034i	0.0643363	−	0.0990245i
$381$	5.73086	+	4.16371i	0.293601	+	0.213313i
$382$			15.1455i			0.774912i
$383$	6.29814	−	8.66865i	0.321820	−	0.442947i	−0.617202	−	0.786805i	$-0.711734\pi$
$383$	6.29814	−	8.66865i	0.321820	−	0.442947i	0.939022	+	0.343858i	$0.111734\pi$
$384$	−3.16882	+	9.75261i	−0.161708	+	0.497686i
$385$	4.99992	−	18.6446i	0.254819	−	0.950214i
$386$	4.94032	+	15.2047i	0.251455	+	0.773900i
$387$	6.84359	+	2.22362i	0.347879	+	0.113033i
$388$	−1.22656	−	0.398535i	−0.0622693	−	0.0202325i
$389$	−10.4417	−	32.1363i	−0.529416	−	1.62937i	−0.755415	−	0.655247i	$-0.772565\pi$
$389$	−10.4417	−	32.1363i	−0.529416	−	1.62937i	0.225999	−	0.974128i	$-0.427435\pi$
$390$	−7.46303	+	0.389576i	−0.377905	+	0.0197269i
$391$	1.09202	−	3.36088i	0.0552257	−	0.169967i
$392$	−19.5358	+	26.8887i	−0.986707	+	1.35809i
$393$		−	5.56145i		−	0.280538i
$394$	17.8717	+	12.9846i	0.900365	+	0.654153i
$395$	1.02290	+	19.5956i	0.0514679	+	0.985962i
$396$	−1.90512	+	1.38415i	−0.0957361	+	0.0695563i
$397$	−9.96439	−	13.7148i	−0.500098	−	0.688326i	0.482112	−	0.876109i	$-0.339870\pi$
$397$	−9.96439	−	13.7148i	−0.500098	−	0.688326i	−0.982210	+	0.187783i	$0.939870\pi$
$398$	3.65857	−	1.18874i	0.183388	−	0.0595863i
$399$	−6.90634			−0.345750
$400$	23.6927	−	2.48031i	1.18463	−	0.124015i
$401$	−8.32422			−0.415691			−0.207846	−	0.978162i	$-0.566645\pi$
$401$	−8.32422			−0.415691			−0.207846	+	0.978162i	$0.566645\pi$
$402$	−3.37683	+	1.09720i	−0.168421	+	0.0547233i
$403$	9.32093	+	12.8292i	0.464309	+	0.639066i
$404$	−7.65012	+	5.55814i	−0.380608	+	0.276528i
$405$	−8.84565	+	3.39343i	−0.439544	+	0.168621i
$406$	8.89979	+	6.46608i	0.441689	+	0.320906i
$407$		−	8.26881i		−	0.409870i
$408$	1.04034	−	1.43191i	0.0515046	−	0.0708900i
$409$	9.79663	−	30.1509i	0.484412	−	1.49087i	−0.348418	−	0.937339i	$-0.613281\pi$
$409$	9.79663	−	30.1509i	0.484412	−	1.49087i	0.832830	−	0.553529i	$-0.186719\pi$
$410$	−32.6680	−	21.2244i	−1.61336	−	1.04820i
$411$	−0.215146	−	0.662150i	−0.0106124	−	0.0326615i
$412$	−5.80286	−	1.88546i	−0.285886	−	0.0928901i
$413$	33.2135	+	10.7917i	1.63433	+	0.531026i
$414$	4.21725	+	12.9794i	0.207267	+	0.637901i
$415$	5.29188	+	13.7943i	0.259768	+	0.677138i
$416$	2.46529	−	7.58739i	0.120871	−	0.372002i
$417$	−5.27831	+	7.26497i	−0.258480	+	0.355767i
$418$			5.95999i			0.291513i
$419$	19.1921	+	13.9439i	0.937597	+	0.681204i	0.947841	−	0.318744i	$-0.103261\pi$
$419$	19.1921	+	13.9439i	0.937597	+	0.681204i	−0.0102444	+	0.999948i	$0.503261\pi$
$420$	2.49971	+	3.08819i	0.121974	+	0.150688i
$421$	−6.78616	+	4.93043i	−0.330737	+	0.240295i	−0.740743	−	0.671788i	$-0.765527\pi$
$421$	−6.78616	+	4.93043i	−0.330737	+	0.240295i	0.410006	+	0.912083i	$0.365527\pi$
$422$	4.13050	+	5.68514i	0.201069	+	0.276748i
$423$	18.7674	−	6.09791i	0.912504	−	0.296491i
$424$	7.52387			0.365392
$425$	−4.89031	−	1.04158i	−0.237215	−	0.0505240i
$426$	−14.5325			−0.704104
$427$	−3.01904	+	0.980946i	−0.146102	+	0.0474713i
$428$	0.136069	+	0.187283i	0.00657713	+	0.00905264i
$429$	3.20360	−	2.32755i	0.154671	−	0.112375i
$430$	−10.1195	−	2.71375i	−0.488005	−	0.130869i
$431$	−10.9491	−	7.95501i	−0.527401	−	0.383179i	0.291984	−	0.956423i	$-0.405685\pi$
$431$	−10.9491	−	7.95501i	−0.527401	−	0.383179i	−0.819385	+	0.573244i	$0.805685\pi$
$432$			19.4593i			0.936236i
$433$	−7.47855	+	10.2933i	−0.359396	+	0.494666i	−0.949980	−	0.312310i	$-0.898897\pi$
$433$	−7.47855	+	10.2933i	−0.359396	+	0.494666i	0.590584	+	0.806976i	$0.298897\pi$
$434$	12.7296	−	39.1778i	0.611042	−	1.88059i
$435$	−1.97189	+	1.59613i	−0.0945450	+	0.0765287i
$436$	−2.62496	−	8.07879i	−0.125713	−	0.386904i
$437$	6.72300	+	2.18444i	0.321605	+	0.104496i
$438$	−2.57501	−	0.836671i	−0.123039	−	0.0399777i
$439$	−6.37502	−	19.6203i	−0.304263	−	0.936425i	−0.979951	−	0.199238i	$-0.936153\pi$
$439$	−6.37502	−	19.6203i	−0.304263	−	0.936425i	0.675688	−	0.737188i	$-0.263847\pi$
$440$	−7.69178	+	6.22605i	−0.366691	+	0.296815i
$441$	−10.6191	+	32.6822i	−0.505672	+	1.55630i
$442$	−2.61428	+	3.59824i	−0.124348	+	0.171151i
$443$		−	2.50586i		−	0.119057i	−0.998227	−	0.0595284i	$-0.981040\pi$
$443$		−	2.50586i		−	0.119057i	0.998227	−	0.0595284i	$-0.0189597\pi$
$444$	1.37689	+	1.00037i	0.0653441	+	0.0474753i
$445$	−38.7095	−	10.3807i	−1.83501	−	0.492094i
$446$	30.5443	−	22.1917i	1.44631	−	1.05081i
$447$	10.7127	+	14.7448i	0.506696	+	0.697407i
$448$	21.9287	−	7.12507i	1.03603	−	0.336628i
$449$	30.7912			1.45313			0.726563	−	0.687100i	$-0.241117\pi$
$449$	30.7912			1.45313			0.726563	+	0.687100i	$0.241117\pi$
$450$	17.6433	−	7.84658i	0.831714	−	0.369891i
$451$	20.6426			0.972020
$452$	−4.86344	+	1.58023i	−0.228757	+	0.0743276i
$453$	−10.0650	−	13.8533i	−0.472894	−	0.650883i
$454$	29.1069	−	21.1474i	1.36605	−	0.992496i
$455$	18.1297	+	22.3977i	0.849933	+	1.05002i
$456$	2.86434	+	2.08107i	0.134135	+	0.0974549i
$457$			31.5511i			1.47590i	0.674856	+	0.737950i	$0.264206\pi$
$457$			31.5511i			1.47590i	−0.674856	+	0.737950i	$0.735794\pi$
$458$	10.4693	−	14.4098i	0.489200	−	0.673325i
$459$	1.26211	−	3.88439i	0.0589105	−	0.181308i
$460$	−1.45658	−	3.79686i	−0.0679133	−	0.177029i
$461$	−11.9021	−	36.6310i	−0.554337	−	1.70608i	−0.697687	−	0.716403i	$-0.745787\pi$
$461$	−11.9021	−	36.6310i	−0.554337	−	1.70608i	0.143349	−	0.989672i	$-0.454213\pi$
$462$	−9.78319	−	3.17875i	−0.455155	−	0.147889i
$463$	−16.9212	−	5.49805i	−0.786397	−	0.255516i	−0.111828	−	0.993728i	$-0.535671\pi$
$463$	−16.9212	−	5.49805i	−0.786397	−	0.255516i	−0.674569	+	0.738212i	$0.735671\pi$
$464$	−2.22294	−	6.84150i	−0.103197	−	0.317609i
$465$	7.96623	+	5.17567i	0.369425	+	0.240016i
$466$	8.83654	−	27.1961i	0.409345	−	1.25983i
$467$	−8.30844	+	11.4356i	−0.384469	+	0.529176i	−0.956762	−	0.290873i	$-0.906054\pi$
$467$	−8.30844	+	11.4356i	−0.384469	+	0.529176i	0.572293	+	0.820049i	$0.306054\pi$
$468$		−	3.51530i		−	0.162495i
$469$	11.0760	+	8.04719i	0.511443	+	0.371585i
$470$	−26.8254	+	10.2909i	−1.23736	+	0.474686i
$471$	−10.3445	+	7.51576i	−0.476652	+	0.346308i
$472$	−10.5232	−	14.4839i	−0.484368	−	0.666676i
$473$	5.27983	−	1.71552i	0.242767	−	0.0788797i
$474$	10.4566			0.480288
$475$	2.08354	−	9.78242i	0.0955994	−	0.448848i
$476$	2.36459			0.108381
$477$	7.39845	−	2.40390i	0.338752	−	0.110067i
$478$	−5.93660	−	8.17103i	−0.271534	−	0.373734i
$479$	22.0012	−	15.9848i	1.00526	−	0.730365i	0.0420510	−	0.999115i	$-0.486611\pi$
$479$	22.0012	−	15.9848i	1.00526	−	0.730365i	0.963210	+	0.268751i	$0.0866108\pi$
$480$	−0.249144	−	4.77281i	−0.0113718	−	0.217848i
$481$	9.98614	+	7.25535i	0.455329	+	0.330816i
$482$		−	6.71383i		−	0.305807i
$483$	−7.17140	+	9.87059i	−0.326310	+	0.449127i
$484$	1.18795	−	3.65615i	0.0539979	−	0.166188i
$485$	−5.59592	+	0.292111i	−0.254098	+	0.0132641i
$486$	7.56440	+	23.2808i	0.343128	+	1.05604i
$487$	31.7281	+	10.3091i	1.43774	+	0.467150i	0.921192	−	0.389109i	$-0.127217\pi$
$487$	31.7281	+	10.3091i	1.43774	+	0.467150i	0.516547	+	0.856259i	$0.327217\pi$
$488$	1.54771	+	0.502880i	0.0700614	+	0.0227643i
$489$	0.142248	+	0.437796i	0.00643270	+	0.0197978i
$490$	12.9598	−	48.3266i	0.585463	−	2.18317i
$491$	−12.1047	+	37.2543i	−0.546276	+	1.68127i	0.171660	+	0.985156i	$0.445087\pi$
$491$	−12.1047	+	37.2543i	−0.546276	+	1.68127i	−0.717936	+	0.696109i	$0.754913\pi$
$492$	−2.49735	+	3.43731i	−0.112589	+	0.154966i
$493$			1.50985i			0.0680003i
$494$	−7.19781	−	5.22951i	−0.323845	−	0.235287i
$495$	−5.57431	+	8.57981i	−0.250547	+	0.385634i
$496$	−21.7929	+	15.8334i	−0.978529	+	0.710943i
$497$	32.9369	+	45.3338i	1.47742	+	2.03350i
$498$	7.48795	−	2.43298i	0.335543	−	0.109025i
$499$	−18.9647			−0.848979			−0.424489	−	0.905433i	$-0.639546\pi$
$499$	−18.9647			−0.848979			−0.424489	+	0.905433i	$0.639546\pi$
$500$	−5.12837	+	2.60903i	−0.229348	+	0.116679i
$501$	−6.35982			−0.284136
$502$	−36.3111	+	11.7982i	−1.62064	+	0.526579i
$503$	25.8722	+	35.6101i	1.15359	+	1.58778i	0.732520	+	0.680745i	$0.238344\pi$
$503$	25.8722	+	35.6101i	1.15359	+	1.58778i	0.421066	+	0.907030i	$0.361656\pi$
$504$	21.3225	−	15.4917i	0.949780	−	0.690055i
$505$	−22.3839	+	34.4527i	−0.996072	+	1.53312i
$506$	8.51806	+	6.18873i	0.378674	+	0.275123i
$507$		−	3.85736i		−	0.171312i
$508$	2.85166	−	3.92498i	0.126522	−	0.174143i
$509$	−11.9047	+	36.6388i	−0.527664	+	1.62398i	0.231322	+	0.972877i	$0.425695\pi$
$509$	−11.9047	+	36.6388i	−0.527664	+	1.62398i	−0.758986	+	0.651107i	$0.774305\pi$
$510$	−0.690149	+	2.57354i	−0.0305603	+	0.113958i
$511$	3.22610	+	9.92891i	0.142714	+	0.439229i
$512$	−8.45729	−	2.74794i	−0.373763	−	0.121443i
$513$	7.77021	+	2.52469i	0.343063	+	0.111468i
$514$	−11.9260	−	36.7044i	−0.526033	−	1.61896i
$515$	−26.4743	+	1.38198i	−1.16660	+	0.0608971i
$516$	−0.353096	+	1.08672i	−0.0155442	+	0.0478401i
$517$	8.94856	−	12.3166i	0.393557	−	0.541685i
$518$		−	32.0651i		−	1.40886i
$519$	1.20600	+	0.876207i	0.0529373	+	0.0384612i
$520$	−0.770077	−	14.7522i	−0.0337701	−	0.646928i
$521$	−6.67196	+	4.84746i	−0.292304	+	0.212371i	−0.724266	−	0.689520i	$-0.757821\pi$
$521$	−6.67196	+	4.84746i	−0.292304	+	0.212371i	0.431962	+	0.901892i	$0.357821\pi$
$522$	−3.42731	−	4.71728i	−0.150009	−	0.206470i
$523$	−17.1836	+	5.58329i	−0.751387	+	0.244140i	−0.659578	−	0.751636i	$-0.729265\pi$
$523$	−17.1836	+	5.58329i	−0.751387	+	0.244140i	−0.0918091	+	0.995777i	$0.529265\pi$
$524$	−3.80895			−0.166395
$525$	14.9464	+	8.63751i	0.652312	+	0.376972i
$526$	−0.902511			−0.0393513
$527$	5.37715	−	1.74714i	0.234232	−	0.0761067i
$528$	3.95381	+	5.44195i	0.172067	+	0.236831i
$529$	−8.50435	+	6.17877i	−0.369754	+	0.268642i
$530$	−10.5750	+	4.05687i	−0.459350	+	0.176219i
$531$	−14.9754	−	10.8803i	−0.649877	−	0.472163i
$532$			4.73005i			0.205074i
$533$	−18.1125	+	24.9298i	−0.784541	+	1.07983i
$534$	−6.59966	+	20.3117i	−0.285595	+	0.878972i
$535$	0.843435	+	0.547981i	0.0364649	+	0.0236913i
$536$	−2.16884	−	6.67500i	−0.0936796	−	0.288316i
$537$	−1.93216	−	0.627798i	−0.0833790	−	0.0270915i
$538$	−0.204917	−	0.0665815i	−0.00883459	−	0.00287053i
$539$	8.19263	+	25.2143i	0.352882	+	1.08606i
$540$	−1.68346	−	4.38827i	−0.0724446	−	0.188841i
$541$	2.90063	−	8.92722i	0.124708	−	0.383811i	−0.869140	−	0.494566i	$-0.835327\pi$
$541$	2.90063	−	8.92722i	0.124708	−	0.383811i	0.993848	+	0.110755i	$0.0353269\pi$
$542$	1.04583	−	1.43946i	0.0449223	−	0.0618303i
$543$			6.55728i			0.281400i
$544$	−2.30117	−	1.67190i	−0.0986620	−	0.0716821i
$545$	−23.2209	−	28.6876i	−0.994676	−	1.22884i
$546$	12.4231	−	9.02588i	0.531658	−	0.386272i
$547$	24.8430	+	34.1935i	1.06221	+	1.46201i	0.877720	+	0.479173i	$0.159063\pi$
$547$	24.8430	+	34.1935i	1.06221	+	1.46201i	0.184490	+	0.982834i	$0.440937\pi$
$548$	−0.453497	+	0.147350i	−0.0193724	+	0.00629448i
$549$	1.68258			0.0718106
$550$	7.45395	−	12.8983i	0.317837	−	0.549986i
$551$	−3.02026			−0.128667
$552$	5.94855	−	1.93280i	0.253187	−	0.0822655i
$553$	−23.6992	−	32.6191i	−1.00779	−	1.38710i
$554$	−34.7294	+	25.2324i	−1.47551	+	1.07202i
$555$	7.14231	+	1.91536i	0.303174	+	0.0813024i
$556$	4.97567	+	3.61504i	0.211015	+	0.153312i
$557$		−	11.7511i		−	0.497912i	−0.968515	−	0.248956i	$-0.919913\pi$
$557$		−	11.7511i		−	0.497912i	0.968515	−	0.248956i	$-0.0800874\pi$
$558$	−12.8341	+	17.6646i	−0.543310	+	0.747802i
$559$	−2.56090	+	7.88164i	−0.108315	+	0.333358i
$560$	−38.0470	+	30.7969i	−1.60778	+	1.30141i
$561$	−0.436283	−	1.34274i	−0.0184199	−	0.0566906i
$562$	35.0676	+	11.3942i	1.47924	+	0.480634i
$563$	−31.5454	−	10.2497i	−1.32948	−	0.431974i	−0.443740	−	0.896156i	$-0.646348\pi$
$563$	−31.5454	−	10.2497i	−1.32948	−	0.431974i	−0.885740	+	0.464182i	$0.846348\pi$
$564$	0.968309	+	2.98015i	0.0407732	+	0.125487i
$565$	−17.2699	+	13.9790i	−0.726552	+	0.588102i
$566$	−4.47771	+	13.7810i	−0.188212	+	0.579258i
$567$	11.4427	−	15.7495i	0.480546	−	0.661415i
$568$		−	28.7266i		−	1.20534i
$569$	−22.6675	−	16.4689i	−0.950271	−	0.690412i	0.000600242	−	1.00000i	$-0.499809\pi$
$569$	−22.6675	−	16.4689i	−0.950271	−	0.690412i	−0.950871	+	0.309588i	$0.899809\pi$
$570$	−5.14803	−	1.38055i	−0.215627	−	0.0578249i
$571$	−0.399662	+	0.290372i	−0.0167253	+	0.0121517i	−0.596117	−	0.802898i	$-0.703290\pi$
$571$	−0.399662	+	0.290372i	−0.0167253	+	0.0121517i	0.579391	+	0.815050i	$0.303290\pi$
$572$	−1.59411	−	2.19410i	−0.0666529	−	0.0917398i
$573$	6.82560	−	2.21777i	0.285143	−	0.0926487i
$574$	80.0486			3.34116
$575$	−11.8176	−	13.1357i	−0.492827	−	0.547795i
$576$	−12.2213			−0.509223
$577$	25.4822	−	8.27966i	1.06084	−	0.344687i	0.273924	−	0.961751i	$-0.411678\pi$
$577$	25.4822	−	8.27966i	1.06084	−	0.344687i	0.786912	+	0.617065i	$0.211678\pi$
$578$	0.932088	+	1.28291i	0.0387697	+	0.0533620i
$579$	6.12887	−	4.45288i	0.254707	−	0.185056i
$580$	1.09317	+	1.35052i	0.0453913	+	0.0560772i
$581$	−24.5605	−	17.8442i	−1.01894	−	0.740304i
$582$			2.98610i			0.123778i
$583$	3.52768	−	4.85543i	0.146101	−	0.201091i
$584$	1.65385	−	5.09003i	0.0684369	−	0.210627i
$585$	−5.47062	−	14.2603i	−0.226182	−	0.589589i
$586$	−0.472845	−	1.45527i	−0.0195330	−	0.0601165i
$587$	34.2984	+	11.1442i	1.41564	+	0.459971i	0.914216	−	0.405228i	$-0.132808\pi$
$587$	34.2984	+	11.1442i	1.41564	+	0.459971i	0.501429	+	0.865199i	$0.332808\pi$
$588$	−5.18973	−	1.68624i	−0.214021	−	0.0695396i
$589$	3.49493	+	10.7563i	0.144006	+	0.443205i
$590$	22.6004	+	14.6835i	0.930442	+	0.604509i
$591$	3.23476	−	9.95556i	0.133060	−	0.409517i
$592$	−12.3247	+	16.9634i	−0.506540	+	0.697193i
$593$			19.5964i			0.804727i	0.915480	+	0.402363i	$0.131811\pi$
$593$			19.5964i			0.804727i	−0.915480	+	0.402363i	$0.868189\pi$
$594$	9.84486	+	7.15271i	0.403940	+	0.293479i
$595$	9.59226	−	3.67985i	0.393244	−	0.150859i
$596$	10.0985	−	7.33700i	0.413651	−	0.300535i
$597$	−1.07146	−	1.47473i	−0.0438518	−	0.0603568i
$598$	−14.9481	+	4.85693i	−0.611274	+	0.198615i
$599$	15.8685			0.648371			0.324186	−	0.945993i	$-0.394910\pi$
$599$	15.8685			0.648371			0.324186	+	0.945993i	$0.394910\pi$
$600$	−3.59615	−	8.08607i	−0.146812	−	0.330112i
$601$	45.8423			1.86995			0.934974	−	0.354717i	$-0.115423\pi$
$601$	45.8423			1.86995			0.934974	+	0.354717i	$0.115423\pi$
$602$	20.4743	−	6.65252i	0.834472	−	0.271136i
$603$	−4.26537	−	5.87078i	−0.173699	−	0.239077i
$604$	−9.48789	+	6.89335i	−0.386057	+	0.280487i
$605$	−0.870726	−	16.6803i	−0.0354000	−	0.678152i
$606$	17.7129	+	12.8692i	0.719536	+	0.522774i
$607$		−	43.1793i		−	1.75259i	−0.481773	−	0.876296i	$-0.660007\pi$
$607$		−	43.1793i		−	1.75259i	0.481773	−	0.876296i	$-0.339993\pi$
$608$	3.34442	−	4.60319i	0.135634	−	0.186684i
$609$	1.61085	−	4.95768i	0.0652749	−	0.200895i
$610$	−2.44650	+	0.127709i	−0.0990559	+	0.00517079i
$611$	7.02285	+	21.6141i	0.284114	+	0.874414i
$612$	−1.19199	−	0.387303i	−0.0481835	−	0.0156558i
$613$	−12.5761	−	4.08621i	−0.507942	−	0.165040i	0.0438240	−	0.999039i	$-0.486046\pi$
$613$	−12.5761	−	4.08621i	−0.507942	−	0.165040i	−0.551766	+	0.833999i	$0.686046\pi$
$614$	−2.06873	−	6.36690i	−0.0834872	−	0.256947i
$615$	−4.78157	+	17.8303i	−0.192811	+	0.718988i
$616$	6.28346	−	19.3385i	0.253168	−	0.779170i
$617$	16.7299	−	23.0267i	0.673520	−	0.927021i	−0.326314	−	0.945262i	$-0.605807\pi$
$617$	16.7299	−	23.0267i	0.673520	−	0.927021i	0.999834	+	0.0182409i	$0.00580658\pi$
$618$			14.1272i			0.568280i
$619$	17.4189	+	12.6556i	0.700124	+	0.508670i	0.879973	−	0.475024i	$-0.157561\pi$
$619$	17.4189	+	12.6556i	0.700124	+	0.508670i	−0.179848	+	0.983694i	$0.557561\pi$
$620$	3.54474	−	5.45595i	0.142360	−	0.219116i
$621$	11.6767	−	8.48364i	0.468571	−	0.340437i
$622$	21.8700	+	30.1015i	0.876907	+	1.20696i
$623$	78.3193	−	25.4475i	3.13780	−	1.01953i
$624$	−10.0414			−0.401977
$625$	−16.7436	+	18.5648i	−0.669744	+	0.742592i
$626$	16.3315			0.652736
$627$	2.68598	−	0.872727i	0.107268	−	0.0348534i
$628$	5.14743	+	7.08483i	0.205405	+	0.282715i
$629$	3.56043	−	2.58681i	0.141964	−	0.103143i
$630$	−21.6163	+	33.2712i	−0.861214	+	1.32555i
$631$	−3.47599	−	2.52546i	−0.138377	−	0.100537i	0.516443	−	0.856321i	$-0.327256\pi$
$631$	−3.47599	−	2.52546i	−0.138377	−	0.100537i	−0.654820	+	0.755785i	$0.727256\pi$
$632$			20.6697i			0.822195i
$633$	1.95728	−	2.69396i	0.0777948	−	0.107075i
$634$	6.48517	−	19.9593i	0.257559	−	0.792685i
$635$	5.45996	−	20.3600i	0.216672	−	0.807963i
$636$	0.381724	+	1.17483i	0.0151363	+	0.0465849i
$637$	−37.6395	−	12.2298i	−1.49133	−	0.484564i
$638$	−4.27835	−	1.39012i	−0.169382	−	0.0550354i
$639$	−9.17824	−	28.2477i	−0.363085	−	1.11746i
$640$	30.4734	−	1.59073i	1.20456	−	0.0628792i
$641$	4.77677	−	14.7014i	0.188671	−	0.580669i	−0.811321	−	0.584600i	$-0.801251\pi$
$641$	4.77677	−	14.7014i	0.188671	−	0.580669i	0.999992	+	0.00393103i	$0.00125129\pi$
$642$	0.315050	−	0.433629i	0.0124340	−	0.0171140i
$643$		−	29.8903i		−	1.17876i	−0.807857	−	0.589379i	$-0.799373\pi$
$643$		−	29.8903i		−	1.17876i	0.807857	−	0.589379i	$-0.200627\pi$
$644$	6.76022	+	4.91158i	0.266390	+	0.193544i
$645$	0.258806	+	4.95791i	0.0101905	+	0.195218i
$646$	−2.56629	+	1.86452i	−0.100969	+	0.0733585i
$647$	7.91559	+	10.8949i	0.311194	+	0.428322i	0.935753	−	0.352656i	$-0.114721\pi$
$647$	7.91559	+	10.8949i	0.311194	+	0.428322i	−0.624559	+	0.780977i	$0.714721\pi$
$648$	−9.49148	+	3.08397i	−0.372861	+	0.121150i
$649$	−14.2809			−0.560575
$650$	9.03676	+	20.3195i	0.354451	+	0.796996i
$651$	−19.5202			−0.765057
$652$	0.299840	−	0.0974238i	0.0117426	−	0.00381541i
$653$	2.85741	+	3.93289i	0.111819	+	0.153906i	0.861258	−	0.508167i	$-0.169677\pi$
$653$	2.85741	+	3.93289i	0.111819	+	0.153906i	−0.749439	+	0.662073i	$0.769677\pi$
$654$	−15.9118	+	11.5606i	−0.622199	+	0.452054i
$655$	−15.4515	+	5.92761i	−0.603740	+	0.231611i
$656$	−42.3482	−	30.7677i	−1.65342	−	1.20128i
$657$		−	5.53359i		−	0.215886i
$658$	34.7011	−	47.7620i	1.35279	−	1.86196i
$659$	−12.6808	+	39.0274i	−0.493972	+	1.52029i	0.324580	+	0.945858i	$0.394777\pi$
$659$	−12.6808	+	39.0274i	−0.493972	+	1.52029i	−0.818552	+	0.574432i	$0.805223\pi$
$660$	−1.36242	−	0.885165i	−0.0530321	−	0.0344550i
$661$	−2.32047	−	7.14168i	−0.0902559	−	0.277779i	0.895732	−	0.444594i	$-0.146652\pi$
$661$	−2.32047	−	7.14168i	−0.0902559	−	0.277779i	−0.985988	+	0.166814i	$0.946652\pi$
$662$	−43.8252	−	14.2397i	−1.70332	−	0.553441i
$663$	2.00442	+	0.651277i	0.0778454	+	0.0252935i
$664$	4.80929	+	14.8015i	0.186637	+	0.574409i
$665$	7.36105	+	19.1880i	0.285449	+	0.744080i
$666$	−5.25204	+	16.1641i	−0.203512	+	0.626346i
$667$	−3.13617	+	4.31657i	−0.121433	+	0.167138i
$668$			4.35574i			0.168529i
$669$	−14.4737	−	10.5158i	−0.559587	−	0.406564i
$670$	6.64753	+	8.21248i	0.256816	+	0.317276i
$671$	1.05019	−	0.763008i	0.0405422	−	0.0294556i
$672$	5.77230	+	7.94488i	0.222671	+	0.306480i
$673$	−12.9168	+	4.19691i	−0.497904	+	0.161779i	−0.547194	−	0.837006i	$-0.684304\pi$
$673$	−12.9168	+	4.19691i	−0.497904	+	0.161779i	0.0492901	+	0.998785i	$0.484304\pi$
$674$	−54.1112			−2.08428
$675$	−13.6583	−	15.1817i	−0.525710	−	0.584345i
$676$	−2.64185			−0.101610
$677$	20.9922	−	6.82079i	0.806797	−	0.262144i	0.123556	−	0.992338i	$-0.460570\pi$
$677$	20.9922	−	6.82079i	0.806797	−	0.262144i	0.683240	+	0.730193i	$0.260570\pi$
$678$	6.95947	+	9.57889i	0.267277	+	0.367875i
$679$	9.31504	−	6.76777i	0.357479	−	0.259723i
$680$	−5.08714	−	1.36422i	−0.195083	−	0.0523155i
$681$	−13.7926	−	10.0209i	−0.528534	−	0.384002i
$682$			16.8454i			0.645044i
$683$	−5.74233	+	7.90364i	−0.219724	+	0.302424i	−0.904622	−	0.426215i	$-0.859847\pi$
$683$	−5.74233	+	7.90364i	−0.219724	+	0.302424i	0.684898	+	0.728639i	$0.259847\pi$
$684$	0.774748	−	2.38443i	0.0296232	−	0.0911709i
$685$	−1.61036	+	1.30349i	−0.0615285	+	0.0498038i
$686$	16.0093	+	49.2716i	0.611238	+	1.88120i
$687$	−8.02707	−	2.60815i	−0.306252	−	0.0995072i
$688$	−13.3885	−	4.35020i	−0.510433	−	0.165850i
$689$	2.76853	+	8.52066i	0.105473	+	0.324611i
$690$	−7.31870	+	5.92407i	−0.278618	+	0.225525i
$691$	−14.6520	+	45.0941i	−0.557387	+	1.71546i	0.132168	+	0.991227i	$0.457806\pi$
$691$	−14.6520	+	45.0941i	−0.557387	+	1.71546i	−0.689555	+	0.724233i	$0.742194\pi$
$692$	0.600101	−	0.825968i	0.0228124	−	0.0313986i
$693$		−	21.0237i		−	0.798624i
$694$	22.5176	+	16.3600i	0.854757	+	0.621017i
$695$	25.8103	+	6.92155i	0.979039	+	0.262549i
$696$	−2.16197	+	1.57076i	−0.0819492	+	0.0595396i
$697$	6.45780	+	8.88840i	0.244607	+	0.336672i
$698$	24.8649	−	8.07911i	0.941152	−	0.305799i
$699$	−13.5504			−0.512521
$700$	5.91570	−	10.2365i	0.223593	−	0.386905i
$701$	3.09708			0.116975			0.0584875	−	0.998288i	$-0.481372\pi$
$701$	3.09708			0.116975			0.0584875	+	0.998288i	$0.481372\pi$
$702$	−17.2765	+	5.61347i	−0.652059	+	0.211867i
$703$	5.17457	+	7.12218i	0.195162	+	0.268618i
$704$	−7.62803	+	5.54209i	−0.287492	+	0.208875i
$705$	8.56587	+	10.5824i	0.322609	+	0.398558i
$706$	42.6114	+	30.9590i	1.60370	+	1.16516i
$707$		−	84.4217i		−	3.17501i
$708$	1.72772	−	2.37800i	0.0649315	−	0.0893706i
$709$	−11.0684	+	34.0650i	−0.415682	+	1.27934i	0.495957	+	0.868347i	$0.334817\pi$
$709$	−11.0684	+	34.0650i	−0.415682	+	1.27934i	−0.911639	+	0.410991i	$0.865183\pi$
$710$	15.4894	+	40.3761i	0.581305	+	1.51529i
$711$	6.60403	+	20.3251i	0.247670	+	0.762251i
$712$	−40.1502	−	13.0456i	−1.50469	−	0.488905i
$713$	19.0020	+	6.17413i	0.711631	+	0.231223i
$714$	−1.69184	−	5.20694i	−0.0633154	−	0.194865i
$715$	−9.88121	−	6.41984i	−0.369536	−	0.240088i
$716$	−0.429969	+	1.32331i	−0.0160687	+	0.0494544i
$717$	−2.81312	+	3.87193i	−0.105058	+	0.144600i
$718$		−	2.15114i		−	0.0802797i
$719$	−21.1887	−	15.3945i	−0.790204	−	0.574117i	0.117820	−	0.993035i	$-0.462409\pi$
$719$	−21.1887	−	15.3945i	−0.790204	−	0.574117i	−0.908024	+	0.418918i	$0.862409\pi$
$720$	24.2239	−	9.29294i	0.902771	−	0.346327i
$721$	44.0694	−	32.0183i	1.64123	−	1.19242i
$722$	13.9799	+	19.2417i	0.520280	+	0.716104i
$723$	−3.02571	+	0.983113i	−0.112527	+	0.0365624i
$724$	4.49098			0.166906
$725$	6.53629	+	3.77733i	0.242752	+	0.140286i
$726$	−8.90098			−0.330346
$727$	−27.1668	+	8.82704i	−1.00756	+	0.327377i	−0.765884	−	0.642979i	$-0.777698\pi$
$727$	−27.1668	+	8.82704i	−1.00756	+	0.327377i	−0.241679	+	0.970356i	$0.577698\pi$
$728$	17.8415	+	24.5567i	0.661251	+	0.910134i
$729$	−0.899160	+	0.653278i	−0.0333022	+	0.0241955i
$730$	0.420005	+	8.04596i	0.0155451	+	0.297794i
$731$	2.39042	+	1.73674i	0.0884127	+	0.0642356i
$732$			0.267182i			0.00987535i
$733$	4.10090	−	5.64441i	0.151470	−	0.208481i	−0.726538	−	0.687126i	$-0.758872\pi$
$733$	4.10090	−	5.64441i	0.151470	−	0.208481i	0.878008	+	0.478645i	$0.158872\pi$
$734$	14.5118	−	44.6628i	0.535642	−	1.64854i
$735$	−23.6770	+	1.23596i	−0.873338	+	0.0455889i
$736$	−3.10614	−	9.55972i	−0.114494	−	0.352376i
$737$	−5.32451	−	1.73004i	−0.196131	−	0.0637268i
$738$	−40.3527	−	13.1114i	−1.48540	−	0.482637i
$739$	−6.18294	−	19.0291i	−0.227443	−	0.699998i	−0.998034	−	0.0626683i	$-0.980039\pi$
$739$	−6.18294	−	19.0291i	−0.227443	−	0.699998i	0.770591	−	0.637330i	$-0.219961\pi$
$740$	1.31180	−	4.89166i	0.0482227	−	0.179821i
$741$	−1.30279	+	4.00958i	−0.0478593	+	0.147296i
$742$	13.6798	−	18.8286i	0.502200	−	0.691220i
$743$		−	25.3990i		−	0.931798i	−0.884838	−	0.465899i	$-0.845731\pi$
$743$		−	25.3990i		−	0.931798i	0.884838	−	0.465899i	$-0.154269\pi$
$744$	8.09583	+	5.88196i	0.296807	+	0.215643i
$745$	29.5478	−	45.4791i	1.08255	−	1.66622i
$746$	25.7974	−	18.7429i	0.944510	−	0.686227i
$747$	9.45824	+	13.0182i	0.346059	+	0.476309i
$748$	−0.919623	+	0.298804i	−0.0336248	+	0.0109253i
$749$	−2.06673			−0.0755166
$750$	9.41451	+	9.42618i	0.343769	+	0.344195i
$751$	3.47977			0.126979			0.0634893	−	0.997983i	$-0.479777\pi$
$751$	3.47977			0.126979			0.0634893	+	0.997983i	$0.479777\pi$
$752$	−36.7159	+	11.9297i	−1.33889	+	0.435032i
$753$	10.6341	+	14.6366i	0.387529	+	0.533388i
$754$	5.43281	−	3.94717i	0.197851	−	0.143747i
$755$	−27.7612	+	42.7291i	−1.01033	+	1.55507i
$756$	7.81322	+	5.67663i	0.284164	+	0.206457i
$757$			10.9069i			0.396419i	0.980160	+	0.198209i	$0.0635126\pi$
$757$			10.9069i			0.396419i	−0.980160	+	0.198209i	$0.936487\pi$
$758$	19.7118	−	27.1309i	0.715963	−	0.985439i
$759$	1.54176	−	4.74504i	0.0559622	−	0.172234i
$760$	2.72894	−	10.1762i	0.0989892	−	0.369128i
$761$	−7.56524	−	23.2834i	−0.274240	−	0.844024i	−0.989420	−	0.145083i	$-0.953655\pi$
$761$	−7.56524	−	23.2834i	−0.274240	−	0.844024i	0.715180	−	0.698941i	$-0.246345\pi$
$762$	−10.6833	−	3.47122i	−0.387016	−	0.125749i
$763$	72.1257	+	23.4350i	2.61112	+	0.848406i
$764$	−1.51892	−	4.67475i	−0.0549525	−	0.169126i
$765$	−5.43821	+	0.283878i	−0.196619	+	0.0102636i
$766$	−5.25066	+	16.1599i	−0.189714	+	0.583880i
$767$	12.5306	−	17.2469i	0.452454	−	0.622749i
$768$		−	8.71940i		−	0.314634i
$769$	10.3345	+	7.50845i	0.372671	+	0.270762i	0.758318	−	0.651885i	$-0.226022\pi$
$769$	10.3345	+	7.50845i	0.372671	+	0.270762i	−0.385646	+	0.922647i	$0.626022\pi$
$770$	1.59572	+	30.5689i	0.0575057	+	1.10163i
$771$	−14.7952	+	10.7493i	−0.532835	+	0.387127i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50815 + 0.490028i) q^{2} +(0.441680 + 0.607920i) q^{3} +(0.416355 - 0.302500i) q^{4} +(1.21824 - 1.87507i) q^{5} +(-0.964016 - 0.700399i) q^{6} +4.59462i q^{7} +(1.38448 - 1.90558i) q^{8} +(0.752565 - 2.31616i) q^{9} +(-0.918447 + 3.42486i) q^{10} +(-0.580604 - 1.78691i) q^{11} +(0.367791 + 0.119503i) q^{12} +(2.66748 + 0.866716i) q^{13} +(-2.25149 - 6.92938i) q^{14} +(1.67796 - 0.0875909i) q^{15} +(-1.47229 + 4.53124i) q^{16} +(0.587785 - 0.809017i) q^{17} +3.86189i q^{18} +(1.61833 + 1.17579i) q^{19} +(-0.0599897 - 1.14921i) q^{20} +(-2.79316 + 2.02935i) q^{21} +(1.75128 + 2.41042i) q^{22} +(3.36088 - 1.09202i) q^{23} +1.76994 q^{24} +(-2.03180 - 4.56857i) q^{25} -4.44767 q^{26} +(3.88439 - 1.26211i) q^{27} +(1.38987 + 1.91299i) q^{28} +(-1.22150 + 0.887469i) q^{29} +(-2.48770 + 0.954349i) q^{30} +(4.57408 + 3.32326i) q^{31} -2.84441i q^{32} +(0.829860 - 1.14220i) q^{33} +(-0.490028 + 1.50815i) q^{34} +(8.61525 + 5.59734i) q^{35} +(-0.387303 - 1.19199i) q^{36} +(4.18554 + 1.35996i) q^{37} +(-3.01685 - 0.980236i) q^{38} +(0.651277 + 2.00442i) q^{39} +(-1.88647 - 4.91745i) q^{40} +(-3.39507 + 10.4489i) q^{41} +(3.21807 - 4.42929i) q^{42} +2.95472i q^{43} +(-0.782278 - 0.568359i) q^{44} +(-3.42616 - 4.23274i) q^{45} +(-4.53360 + 3.29385i) q^{46} +(4.76272 + 6.55533i) q^{47} +(-3.40491 + 1.10632i) q^{48} -14.1105 q^{49} +(5.30298 + 5.89445i) q^{50} +0.751430 q^{51} +(1.37280 - 0.446049i) q^{52} +(1.87755 + 2.58422i) q^{53} +(-5.23977 + 3.80692i) q^{54} +(-4.05791 - 1.08821i) q^{55} +(8.75541 + 6.36117i) q^{56} +1.50314i q^{57} +(1.40731 - 1.93700i) q^{58} +(2.34877 - 7.22878i) q^{59} +(0.672133 - 0.544052i) q^{60} +(0.213499 + 0.657082i) q^{61} +(-8.52689 - 2.77055i) q^{62} +(10.6419 + 3.45775i) q^{63} +(-1.55074 - 4.77269i) q^{64} +(4.87478 - 3.94585i) q^{65} +(-0.691842 + 2.12927i) q^{66} +(1.75144 - 2.41065i) q^{67} -0.514643i q^{68} +(2.14829 + 1.56083i) q^{69} +(-15.7359 - 4.21991i) q^{70} +(9.86671 - 7.16859i) q^{71} +(-3.37170 - 4.64075i) q^{72} +(2.16099 - 0.702147i) q^{73} -6.97884 q^{74} +(1.87992 - 3.25301i) q^{75} +1.02948 q^{76} +(8.21020 - 2.66765i) q^{77} +(-1.96445 - 2.70383i) q^{78} +(-7.09941 + 5.15802i) q^{79} +(6.70281 + 8.28078i) q^{80} +(-3.42781 - 2.49045i) q^{81} -17.4222i q^{82} +(-3.88373 + 5.34549i) q^{83} +(-0.549069 + 1.68986i) q^{84} +(-0.800904 - 2.08771i) q^{85} +(-1.44789 - 4.45616i) q^{86} +(-1.07902 - 0.350595i) q^{87} +(-4.20894 - 1.36757i) q^{88} +(-5.53854 - 17.0459i) q^{89} +(7.24133 + 4.70470i) q^{90} +(-3.98223 + 12.2560i) q^{91} +(1.06899 - 1.47133i) q^{92} +4.24849i q^{93} +(-10.3952 - 7.55255i) q^{94} +(4.17620 - 1.60210i) q^{95} +(1.72917 - 1.25632i) q^{96} +(-1.47298 - 2.02738i) q^{97} +(21.2808 - 6.91455i) q^{98} -4.57572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

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Varieties

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Groups

Database

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