LMFDB - Embedded newform 875.2.bb.b.143.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([27, 50]))

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

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

chi := DirichletCharacter("875.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			143.10
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.b.257.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.00196093 + 0.0374168i) q^{2} +(0.0849253 + 0.0687711i) q^{3} +(1.98765 - 0.208910i) q^{4} +(-0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.0234370 + 0.147975i) q^{8} +(-0.621252 - 2.92276i) q^{9} +(-1.34592 - 0.286085i) q^{11} +(0.183169 + 0.118951i) q^{12} +(0.730661 + 1.43400i) q^{13} +(-0.0795726 + 0.0591203i) q^{14} +(3.90435 - 0.829896i) q^{16} +(4.07660 + 1.56486i) q^{17} +(0.108142 - 0.0289766i) q^{18} +(0.00716074 - 0.0681299i) q^{19} +(-0.0271520 + 0.287846i) q^{21} +(0.00806510 - 0.0509210i) q^{22} +(5.63942 - 0.295550i) q^{23} +(-0.00818604 + 0.0141786i) q^{24} +(-0.0522229 + 0.0301509i) q^{26} +(0.297076 - 0.583044i) q^{27} +(3.37137 + 4.07364i) q^{28} +(-3.88840 - 5.35192i) q^{29} +(1.42674 + 3.20452i) q^{31} +(0.116261 + 0.433891i) q^{32} +(-0.0946285 - 0.116856i) q^{33} +(-0.0505580 + 0.155602i) q^{34} +(-1.84543 - 5.67963i) q^{36} +(-4.21599 + 6.49205i) q^{37} +(0.00256324 + 0.000134334i) q^{38} +(-0.0365664 + 0.172031i) q^{39} +(9.12263 + 2.96412i) q^{41} +(-0.0108235 - 0.000451493i) q^{42} +(-3.38639 - 3.38639i) q^{43} +(-2.73499 - 0.287459i) q^{44} +(0.0221170 + 0.210429i) q^{46} +(-2.55469 - 6.65520i) q^{47} +(0.388651 + 0.198028i) q^{48} +(-2.71005 + 6.45412i) q^{49} +(0.238589 + 0.413248i) q^{51} +(1.75187 + 2.69765i) q^{52} +(-1.86647 + 2.30489i) q^{53} +(0.0223982 + 0.00997230i) q^{54} +(-0.291725 + 0.268362i) q^{56} +(0.00529350 - 0.00529350i) q^{57} +(0.192627 - 0.155986i) q^{58} +(-6.88713 - 7.64893i) q^{59} +(5.62046 + 5.06069i) q^{61} +(-0.117105 + 0.0596680i) q^{62} +(5.53018 - 5.64947i) q^{63} +(7.57643 - 2.46173i) q^{64} +(0.00418683 - 0.00376984i) q^{66} +(-3.18113 + 8.28713i) q^{67} +(8.42975 + 2.25874i) q^{68} +(0.499255 + 0.362730i) q^{69} +(5.52909 - 4.01712i) q^{71} +(0.417936 - 0.160431i) q^{72} +(0.359648 - 0.233558i) q^{73} +(-0.251179 - 0.145018i) q^{74} -0.136914i q^{76} +(-1.34084 - 3.38461i) q^{77} +(-0.00650856 - 0.00103085i) q^{78} +(3.70296 - 8.31698i) q^{79} +(-8.12386 + 3.61697i) q^{81} +(-0.0930190 + 0.347152i) q^{82} +(-4.19080 + 0.663758i) q^{83} +(0.00616537 + 0.577808i) q^{84} +(0.120067 - 0.133348i) q^{86} +(0.0378344 - 0.721923i) q^{87} +(0.0107891 - 0.205868i) q^{88} +(5.38706 - 5.98294i) q^{89} +(-2.08959 + 3.71015i) q^{91} +(11.1474 - 1.76558i) q^{92} +(-0.0992118 + 0.370263i) q^{93} +(0.244007 - 0.108639i) q^{94} +(-0.0199657 + 0.0448436i) q^{96} +(16.3848 + 2.59509i) q^{97} +(-0.246806 - 0.0887454i) q^{98} +4.11154i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.00196093	+	0.0374168i	0.00138659	+	0.0264576i	0.999235	−	0.0391025i	$-0.0124499\pi$
$2$	0.00196093	+	0.0374168i	0.00138659	+	0.0264576i	−0.997849	+	0.0655602i	$0.979117\pi$
$3$	0.0849253	+	0.0687711i	0.0490316	+	0.0397050i	0.653523	−	0.756907i	$-0.273290\pi$
$3$	0.0849253	+	0.0687711i	0.0490316	+	0.0397050i	−0.604491	+	0.796612i	$0.706624\pi$
$4$	1.98765	−	0.208910i	0.993824	−	0.104455i
$5$		0			0
$5$		0			0
$6$	−0.00240666	+	0.00331248i	−0.000982515	+	0.00135232i
$7$	1.46457	+	2.20341i	0.553556	+	0.832812i
$7$	1.46457	+	2.20341i	0.553556	+	0.832812i
$8$	0.0234370	+	0.147975i	0.00828623	+	0.0523172i
$9$	−0.621252	−	2.92276i	−0.207084	−	0.974254i
$10$		0			0
$11$	−1.34592	−	0.286085i	−0.405811	−	0.0862578i	0.000483800	−	1.00000i	$-0.499846\pi$
$11$	−1.34592	−	0.286085i	−0.405811	−	0.0862578i	−0.406295	+	0.913742i	$0.633179\pi$
$12$	0.183169	+	0.118951i	0.0528762	+	0.0343382i
$13$	0.730661	+	1.43400i	0.202649	+	0.397721i	0.969856	−	0.243679i	$-0.0783542\pi$
$13$	0.730661	+	1.43400i	0.202649	+	0.397721i	−0.767207	+	0.641399i	$0.778354\pi$
$14$	−0.0795726	+	0.0591203i	−0.0212667	+	0.0158006i
$15$		0			0
$16$	3.90435	−	0.829896i	0.976088	−	0.207474i
$17$	4.07660	+	1.56486i	0.988720	+	0.379534i	0.798360	−	0.602180i	$-0.205701\pi$
$17$	4.07660	+	1.56486i	0.988720	+	0.379534i	0.190360	+	0.981714i	$0.439035\pi$
$18$	0.108142	−	0.0289766i	0.0254893	−	0.00682984i
$19$	0.00716074	−	0.0681299i	0.00164279	−	0.0156301i	−0.993670	−	0.112340i	$-0.964165\pi$
$19$	0.00716074	−	0.0681299i	0.00164279	−	0.0156301i	0.995313	+	0.0967102i	$0.0308320\pi$
$20$		0			0
$21$	−0.0271520	+	0.287846i	−0.00592504	+	0.0628131i
$22$	0.00806510	−	0.0509210i	0.00171949	−	0.0108564i
$23$	5.63942	−	0.295550i	1.17590	−	0.0616263i	0.545647	−	0.838015i	$-0.316284\pi$
$23$	5.63942	−	0.295550i	1.17590	−	0.0616263i	0.630254	+	0.776389i	$0.282951\pi$
$24$	−0.00818604	+	0.0141786i	−0.00167097	+	0.00289420i
$25$		0			0
$26$	−0.0522229	+	0.0301509i	−0.0102418	+	0.00591308i
$27$	0.297076	−	0.583044i	0.0571722	−	0.112207i
$28$	3.37137	+	4.07364i	0.637129	+	0.769846i
$29$	−3.88840	−	5.35192i	−0.722058	−	0.993827i	−0.999453	−	0.0330712i	$-0.989471\pi$
$29$	−3.88840	−	5.35192i	−0.722058	−	0.993827i	0.277395	−	0.960756i	$-0.410529\pi$
$30$		0			0
$31$	1.42674	+	3.20452i	0.256251	+	0.575549i	0.995161	−	0.0982550i	$-0.0313261\pi$
$31$	1.42674	+	3.20452i	0.256251	+	0.575549i	−0.738911	+	0.673804i	$0.764659\pi$
$32$	0.116261	+	0.433891i	0.0205522	+	0.0767017i
$33$	−0.0946285	−	0.116856i	−0.0164727	−	0.0203421i
$34$	−0.0505580	+	0.155602i	−0.00867063	+	0.0266855i
$35$		0			0
$36$	−1.84543	−	5.67963i	−0.307571	−	0.946606i
$37$	−4.21599	+	6.49205i	−0.693104	+	1.06729i	0.300436	+	0.953802i	$0.402868\pi$
$37$	−4.21599	+	6.49205i	−0.693104	+	1.06729i	−0.993540	+	0.113485i	$0.963799\pi$
$38$	0.00256324		0.000134334i	0.000415813		2.17918e-5i
$39$	−0.0365664	+	0.172031i	−0.00585531	+	0.0275471i
$40$		0			0
$41$	9.12263	+	2.96412i	1.42472	+	0.462918i	0.917097	−	0.398664i	$-0.130526\pi$
$41$	9.12263	+	2.96412i	1.42472	+	0.462918i	0.507618	+	0.861582i	$0.330526\pi$
$42$	−0.0108235		0.000451493i	−0.00167010		6.96669e-5i
$43$	−3.38639	−	3.38639i	−0.516420	−	0.516420i	0.400067	−	0.916486i	$-0.368987\pi$
$43$	−3.38639	−	3.38639i	−0.516420	−	0.516420i	−0.916486	+	0.400067i	$0.868987\pi$
$44$	−2.73499	−	0.287459i	−0.412315	−	0.0433360i
$45$		0			0
$46$	0.0221170	+	0.210429i	0.00326098	+	0.0310261i
$47$	−2.55469	−	6.65520i	−0.372640	−	0.970761i	−0.983803	−	0.179256i	$-0.942631\pi$
$47$	−2.55469	−	6.65520i	−0.372640	−	0.970761i	0.611162	−	0.791505i	$-0.290702\pi$
$48$	0.388651	+	0.198028i	0.0560970	+	0.0285828i
$49$	−2.71005	+	6.45412i	−0.387151	+	0.922016i
$50$		0			0
$51$	0.238589	+	0.413248i	0.0334091	+	0.0578663i
$52$	1.75187	+	2.69765i	0.242941	+	0.374097i
$53$	−1.86647	+	2.30489i	−0.256379	+	0.316601i	−0.889042	−	0.457826i	$-0.848628\pi$
$53$	−1.86647	+	2.30489i	−0.256379	+	0.316601i	0.632663	+	0.774427i	$0.281962\pi$
$54$	0.0223982	+	0.00997230i	0.00304800	+	0.00135706i
$55$		0			0
$56$	−0.291725	+	0.268362i	−0.0389835	+	0.0358614i
$57$	0.00529350	−	0.00529350i	0.000701141	−	0.000701141i
$58$	0.192627	−	0.155986i	0.0252931	−	0.0204820i
$59$	−6.88713	−	7.64893i	−0.896627	−	0.995806i	−0.999999	−	0.00116291i	$-0.999630\pi$
$59$	−6.88713	−	7.64893i	−0.896627	−	0.995806i	0.103372	−	0.994643i	$-0.467037\pi$
$60$		0			0
$61$	5.62046	+	5.06069i	0.719626	+	0.647954i	0.945283	−	0.326253i	$-0.105786\pi$
$61$	5.62046	+	5.06069i	0.719626	+	0.647954i	−0.225656	+	0.974207i	$0.572453\pi$
$62$	−0.117105	+	0.0596680i	−0.0148723	+	0.00757784i
$63$	5.53018	−	5.64947i	0.696737	−	0.711767i
$64$	7.57643	−	2.46173i	0.947053	−	0.307716i
$65$		0			0
$66$	0.00418683	−	0.00376984i	0.000515363	−	0.000464035i
$67$	−3.18113	+	8.28713i	−0.388637	+	1.01243i	0.590103	+	0.807328i	$0.299087\pi$
$67$	−3.18113	+	8.28713i	−0.388637	+	1.01243i	−0.978740	+	0.205106i	$0.934246\pi$
$68$	8.42975	+	2.25874i	1.02226	+	0.273913i
$69$	0.499255	+	0.362730i	0.0601032	+	0.0436675i
$70$		0			0
$71$	5.52909	−	4.01712i	0.656182	−	0.476744i	−0.209189	−	0.977875i	$-0.567082\pi$
$71$	5.52909	−	4.01712i	0.656182	−	0.476744i	0.865372	+	0.501131i	$0.167082\pi$
$72$	0.417936	−	0.160431i	0.0492543	−	0.0189069i
$73$	0.359648	−	0.233558i	0.0420936	−	0.0273359i	−0.523421	−	0.852074i	$-0.675344\pi$
$73$	0.359648	−	0.233558i	0.0420936	−	0.0273359i	0.565514	+	0.824738i	$0.308678\pi$
$74$	−0.251179	−	0.145018i	−0.0291989	−	0.0168580i
$75$		0			0
$76$		−	0.136914i		−	0.0157051i
$77$	−1.34084	−	3.38461i	−0.152803	−	0.385713i
$78$	−0.00650856	−	0.00103085i	−0.000736949	−	0.000116721i
$79$	3.70296	−	8.31698i	0.416616	−	0.935734i	−0.576336	−	0.817213i	$-0.695518\pi$
$79$	3.70296	−	8.31698i	0.416616	−	0.935734i	0.992952	−	0.118521i	$-0.0378153\pi$
$80$		0			0
$81$	−8.12386	+	3.61697i	−0.902651	+	0.401886i
$82$	−0.0930190	+	0.347152i	−0.0102722	+	0.0383365i
$83$	−4.19080	+	0.663758i	−0.460000	+	0.0728569i	−0.382134	−	0.924107i	$-0.624811\pi$
$83$	−4.19080	+	0.663758i	−0.460000	+	0.0728569i	−0.0778662	+	0.996964i	$0.524811\pi$
$84$	0.00616537	+	0.577808i	0.000672697	+	0.0630440i
$85$		0			0
$86$	0.120067	−	0.133348i	0.0129472	−	0.0143793i
$87$	0.0378344	−	0.721923i	0.00405627	−	0.0773983i
$88$	0.0107891	−	0.205868i	0.00115012	−	0.0219456i
$89$	5.38706	−	5.98294i	0.571027	−	0.634190i	−0.386584	−	0.922254i	$-0.626345\pi$
$89$	5.38706	−	5.98294i	0.571027	−	0.634190i	0.957611	+	0.288064i	$0.0930116\pi$
$90$		0			0
$91$	−2.08959	+	3.71015i	−0.219049	+	0.388929i
$92$	11.1474	−	1.76558i	1.16220	−	0.184075i
$93$	−0.0992118	+	0.370263i	−0.0102878	+	0.0383945i
$94$	0.244007	−	0.108639i	0.0251674	−	0.0112052i
$95$		0			0
$96$	−0.0199657	+	0.0448436i	−0.00203774	+	0.00457684i
$97$	16.3848	+	2.59509i	1.66362	+	0.263492i	0.916159	−	0.400814i	$-0.131273\pi$
$97$	16.3848	+	2.59509i	1.66362	+	0.263492i	0.747461	+	0.664306i	$0.231273\pi$
$98$	−0.246806	−	0.0887454i	−0.0249312	−	0.00896464i
$99$			4.11154i			0.413225i
$100$		0			0
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	0.320366	−	0.947294i	$-0.396194\pi$
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	−0.660197	+	0.751092i	$0.729527\pi$
$102$	−0.0149945	+	0.00973757i	−0.00148468	+	0.000964164i
$103$	−7.16976	+	2.75221i	−0.706457	+	0.271184i	−0.684955	−	0.728585i	$-0.740178\pi$
$103$	−7.16976	+	2.75221i	−0.706457	+	0.271184i	−0.0215022	+	0.999769i	$0.506845\pi$
$104$	−0.195072	+	0.141728i	−0.0191284	+	0.0138976i
$105$		0			0
$106$	−0.0899016	−	0.0653174i	−0.00873202	−	0.00634418i
$107$	−10.4235	−	2.79297i	−1.00768	−	0.270006i	−0.283019	−	0.959114i	$-0.591336\pi$
$107$	−10.4235	−	2.79297i	−1.00768	−	0.270006i	−0.724659	+	0.689108i	$0.758003\pi$
$108$	0.468678	−	1.22095i	0.0450986	−	0.117486i
$109$	−2.14125	+	1.92799i	−0.205094	+	0.184668i	−0.765277	−	0.643702i	$-0.777398\pi$
$109$	−2.14125	+	1.92799i	−0.205094	+	0.184668i	0.560182	+	0.828369i	$0.310731\pi$
$110$		0			0
$111$	−0.804510	+	0.261401i	−0.0763607	+	0.0248111i
$112$	7.54681	+	7.38746i	0.713107	+	0.698049i
$113$	−9.05056	+	4.61149i	−0.851405	+	0.433812i	−0.824524	−	0.565826i	$-0.808557\pi$
$113$	−9.05056	+	4.61149i	−0.851405	+	0.433812i	−0.0268803	+	0.999639i	$0.508557\pi$
$114$	0.000208446	0	0.000187685i	1.95227e−5	0	1.75783e-5i
$115$		0			0
$116$	−8.84684	−	9.82541i	−0.821408	−	0.912266i
$117$	3.73732	−	3.02642i	0.345516	−	0.279793i
$118$	0.272693	−	0.272693i	0.0251034	−	0.0251034i
$119$	2.52244	+	11.2743i	0.231232	+	1.03351i
$120$		0			0
$121$	−8.31934	−	3.70401i	−0.756303	−	0.336728i
$122$	−0.178333	+	0.220223i	−0.0161455	+	0.0199381i
$123$	0.570896	+	0.879102i	0.0514759	+	0.0792660i
$124$	3.50532	+	6.07139i	0.314787	+	0.545227i
$125$		0			0
$126$	0.222229	+	0.195843i	0.0197978	+	0.0174471i
$127$	−18.8553	−	9.60727i	−1.67314	−	0.852507i	−0.992824	−	0.119588i	$-0.961843\pi$
$127$	−18.8553	−	9.60727i	−1.67314	−	0.852507i	−0.680316	−	0.732919i	$-0.738157\pi$
$128$	0.428922	+	1.11738i	0.0379117	+	0.0987634i
$129$	−0.0547042	−	0.520476i	−0.00481644	−	0.0458253i
$130$		0			0
$131$	−1.73179	−	0.182019i	−0.151307	−	0.0159030i	0.0285719	−	0.999592i	$-0.490904\pi$
$131$	−1.73179	−	0.182019i	−0.151307	−	0.0159030i	−0.179879	+	0.983689i	$0.557571\pi$
$132$	−0.212501	−	0.212501i	−0.0184958	−	0.0184958i
$133$	0.160606	−	0.0840031i	0.0139263	−	0.00728400i
$134$	−0.316315	−	0.102777i	−0.0273255	−	0.00887859i
$135$		0			0
$136$	−0.136017	+	0.639911i	−0.0116634	+	0.0548719i
$137$	6.36074	+	0.333352i	0.543435	+	0.0284802i	0.322079	−	0.946713i	$-0.395618\pi$
$137$	6.36074	+	0.333352i	0.543435	+	0.0284802i	0.221356	+	0.975193i	$0.428952\pi$
$138$	−0.0125932	+	0.0193918i	−0.00107200	+	0.00165074i
$139$	6.65731	+	20.4891i	0.564665	+	1.73786i	0.668944	+	0.743313i	$0.266747\pi$
$139$	6.65731	+	20.4891i	0.564665	+	1.73786i	−0.104278	+	0.994548i	$0.533253\pi$
$140$		0			0
$141$	0.240728	−	0.740884i	0.0202729	−	0.0623937i
$142$	0.161150	+	0.199003i	0.0135234	+	0.0167000i
$143$	−0.573166	−	2.13909i	−0.0479306	−	0.178879i
$144$	−4.85118	−	10.8959i	−0.404265	−	0.907993i
$145$		0			0
$146$	0.00944423	+	0.0129989i	0.000781610	+	0.00107579i
$147$	−0.674009	+	0.361744i	−0.0555913	+	0.0298361i
$148$	−7.02364	+	13.7847i	−0.577340	+	1.13309i
$149$	−16.9996	+	9.81475i	−1.39266	+	0.804055i	−0.993610	−	0.112871i	$-0.963995\pi$
$149$	−16.9996	+	9.81475i	−1.39266	+	0.804055i	−0.399055	+	0.916927i	$0.630662\pi$
$150$		0			0
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	−0.618467	−	0.785811i	$-0.712246\pi$
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	0.989766	+	0.142703i	$0.0455793\pi$
$152$	0.0102494		0.000537147i	0.000831334		4.35684e-5i
$153$	2.04111	−	12.8871i	0.165014	−	1.04186i
$154$	0.124012	−	0.0568068i	0.00999317	−	0.00457762i
$155$		0			0
$156$	−0.0367420	+	0.349577i	−0.00294171	+	0.0279885i
$157$	−17.8330	+	4.77834i	−1.42323	+	0.381353i	−0.886628	−	0.462483i	$-0.846959\pi$
$157$	−17.8330	+	4.77834i	−1.42323	+	0.381353i	−0.536601	+	0.843836i	$0.680292\pi$
$158$	0.318456	+	0.122244i	0.0253350	+	0.00972519i
$159$	−0.317020	+	0.0673847i	−0.0251413	+	0.00534396i
$160$		0			0
$161$	8.91056	+	11.9931i	0.702250	+	0.945190i
$162$	−0.151266	−	0.296876i	−0.0118846	−	0.0233248i
$163$	2.89908	+	1.88268i	0.227073	+	0.147463i	0.653162	−	0.757218i	$-0.273442\pi$
$163$	2.89908	+	1.88268i	0.227073	+	0.147463i	−0.426088	+	0.904682i	$0.640109\pi$
$164$	18.7518	+	3.98582i	1.46427	+	0.311240i
$165$		0			0
$166$	−0.0330535	−	0.155505i	−0.00256545	−	0.0120695i
$167$	−2.07246	−	13.0850i	−0.160372	−	1.01255i	−0.928251	−	0.371954i	$-0.878688\pi$
$167$	−2.07246	−	13.0850i	−0.160372	−	1.01255i	0.767879	−	0.640595i	$-0.221312\pi$
$168$	−0.0432304	+	0.00272842i	−0.00333530	+	0.000210502i
$169$	6.11871	−	8.42168i	0.470670	−	0.647822i
$170$		0			0
$171$	−0.203576	+	0.0213967i	−0.0155679	+	0.00163625i
$172$	−7.43840	−	6.02350i	−0.567173	−	0.459287i
$173$	−0.531152	−	10.1350i	−0.0403828	−	0.770549i	−0.941508	−	0.336990i	$-0.890591\pi$
$173$	−0.531152	−	10.1350i	−0.0403828	−	0.770549i	0.901125	−	0.433559i	$-0.142742\pi$
$174$	0.0270862			0.00205340
$175$		0			0
$176$	−5.49238			−0.414003
$177$	−0.0588656	−	1.12322i	−0.00442461	−	0.0844266i
$178$	0.234426	+	0.189834i	0.0175710	+	0.0142287i
$179$	−8.97496	+	0.943306i	−0.670820	+	0.0705060i	−0.433814	−	0.901002i	$-0.642833\pi$
$179$	−8.97496	+	0.943306i	−0.670820	+	0.0705060i	−0.237006	+	0.971508i	$0.576166\pi$
$180$		0			0
$181$	9.31589	−	12.8222i	0.692445	−	0.953069i	−0.307554	−	0.951531i	$-0.599510\pi$
$181$	9.31589	−	12.8222i	0.692445	−	0.953069i	0.999999	−	0.00153805i	$-0.000489576\pi$
$182$	−0.142919	−	0.0709105i	−0.0105939	−	0.00525623i
$183$	0.129290	+	0.816306i	0.00955740	+	0.0603430i
$184$	0.175905	+	0.827568i	0.0129679	+	0.0610091i
$185$		0			0
$186$	−0.0140486	−	0.00298612i	−0.00103009	−	0.000218953i
$187$	−5.03910	−	3.27243i	−0.368495	−	0.239304i
$188$	−6.46817	−	12.6945i	−0.471740	−	0.925841i
$189$	1.71978	−	0.199330i	0.125095	−	0.0144991i
$190$		0			0
$191$	−21.8970	+	4.65434i	−1.58441	+	0.336776i	−0.914158	−	0.405358i	$-0.867147\pi$
$191$	−21.8970	+	4.65434i	−1.58441	+	0.336776i	−0.670251	+	0.742135i	$0.733813\pi$
$192$	0.812726	+	0.311976i	0.0586535	+	0.0225150i
$193$	−11.7643	+	3.15224i	−0.846814	+	0.226903i	−0.656036	−	0.754730i	$-0.727768\pi$
$193$	−11.7643	+	3.15224i	−0.846814	+	0.226903i	−0.190779	+	0.981633i	$0.561101\pi$
$194$	−0.0649705	+	0.618153i	−0.00466461	+	0.0443808i
$195$		0			0
$196$	−4.03830	+	13.3947i	−0.288450	+	0.956762i
$197$	2.08757	−	13.1804i	0.148734	−	0.939067i	−0.794579	−	0.607161i	$-0.792308\pi$
$197$	2.08757	−	13.1804i	0.148734	−	0.939067i	0.943313	−	0.331906i	$-0.107692\pi$
$198$	−0.153841	+	0.00806244i	−0.0109330	+	0.000572973i
$199$	−9.16969	+	15.8824i	−0.650022	+	1.12587i	0.333095	+	0.942893i	$0.391907\pi$
$199$	−9.16969	+	15.8824i	−0.650022	+	1.12587i	−0.983117	+	0.182978i	$0.941426\pi$
$200$		0			0
$201$	−0.840074	+	0.485017i	−0.0592542	+	0.0342104i
$202$	0.0670813	−	0.131654i	0.00471982	−	0.00926318i
$203$	6.09765	−	16.4060i	0.427971	−	1.15148i
$204$	0.560562	+	0.771548i	0.0392472	+	0.0540192i
$205$		0			0
$206$	−0.117038	−	0.262872i	−0.00815444	−	0.0183152i
$207$	−4.36732	−	16.2991i	−0.303550	−	1.13286i
$208$	4.04283	+	4.99248i	0.280320	+	0.346166i
$209$	−0.0291287	+	0.0896490i	−0.00201488	+	0.00620115i
$210$		0			0
$211$	−2.94624	−	9.06760i	−0.202828	−	0.624239i	−0.999796	−	0.0202178i	$-0.993564\pi$
$211$	−2.94624	−	9.06760i	−0.202828	−	0.624239i	0.796968	−	0.604022i	$-0.206436\pi$
$212$	−3.22836	+	4.97124i	−0.221725	+	0.341426i
$213$	0.745822	+	0.0390869i	0.0511029	+	0.00267819i
$214$	0.0840641	−	0.395490i	0.00574650	−	0.0270352i
$215$		0			0
$216$	0.0932387	+	0.0302951i	0.00634409	+	0.00206132i
$217$	−4.97131	+	7.83695i	−0.337474	+	0.532007i
$218$	−0.0763379	−	0.0763379i	−0.00517026	−	0.00517026i
$219$	0.0466053	+	0.00489841i	0.00314929	+	0.000331004i
$220$		0			0
$221$	0.734597	+	6.98923i	0.0494144	+	0.470146i
$222$	−0.0113584	−	0.0295896i	−0.000762324	−	0.00198592i
$223$	−22.3918	−	11.4092i	−1.49946	−	0.764015i	−0.504421	−	0.863458i	$-0.668294\pi$
$223$	−22.3918	−	11.4092i	−1.49946	−	0.764015i	−0.995043	+	0.0994426i	$0.968294\pi$
$224$	−0.785768	+	0.891634i	−0.0525013	+	0.0595748i
$225$		0			0
$226$	−0.190294	−	0.329600i	−0.0126582	−	0.0219246i
$227$	−6.73926	−	10.3775i	−0.447300	−	0.688782i	0.541048	−	0.840992i	$-0.318028\pi$
$227$	−6.73926	−	10.3775i	−0.447300	−	0.688782i	−0.988348	+	0.152210i	$0.951361\pi$
$228$	0.00941575	−	0.0116275i	0.000623573	−	0.000770048i
$229$	−13.4922	−	6.00710i	−0.891587	−	0.396960i	−0.0907719	−	0.995872i	$-0.528933\pi$
$229$	−13.4922	−	6.00710i	−0.891587	−	0.396960i	−0.800815	+	0.598912i	$0.795600\pi$
$230$		0			0
$231$	0.118893	−	0.379650i	0.00782256	−	0.0249791i
$232$	0.700820	−	0.700820i	0.0460111	−	0.0460111i
$233$	0.943130	−	0.763731i	0.0617865	−	0.0500337i	−0.597930	−	0.801549i	$-0.704010\pi$
$233$	0.943130	−	0.763731i	0.0617865	−	0.0500337i	0.659716	+	0.751515i	$0.270676\pi$
$234$	0.120568	+	0.133904i	0.00788175	+	0.00875357i
$235$		0			0
$236$	−15.2871	−	13.7646i	−0.995107	−	0.895998i
$237$	0.886443	−	0.451665i	0.0575807	−	0.0293388i
$238$	−0.416900	+	0.116490i	−0.0270236	+	0.00755090i
$239$	24.4748	−	7.95235i	1.58314	−	0.514395i	0.620280	−	0.784380i	$-0.287019\pi$
$239$	24.4748	−	7.95235i	1.58314	−	0.514395i	0.962864	+	0.269986i	$0.0870189\pi$
$240$		0			0
$241$	−10.1804	+	9.16652i	−0.655780	+	0.590467i	−0.928367	−	0.371664i	$-0.878787\pi$
$241$	−10.1804	+	9.16652i	−0.655780	+	0.590467i	0.272587	+	0.962131i	$0.412121\pi$
$242$	0.122278	−	0.318546i	0.00786035	−	0.0204769i
$243$	−2.83487	−	0.759601i	−0.181857	−	0.0487284i
$244$	12.2287	+	8.88469i	0.782864	+	0.568784i
$245$		0			0
$246$	−0.0317737	+	0.0230849i	−0.00202582	+	0.00147184i
$247$	0.102931	−	0.0395113i	0.00654931	−	0.00251405i
$248$	−0.440751	+	0.286227i	−0.0279877	+	0.0181754i
$249$	−0.401552	−	0.231836i	−0.0254473	−	0.0146920i
$250$		0			0
$251$			24.5816i			1.55158i	0.630992	+	0.775789i	$0.282648\pi$
$251$			24.5816i			1.55158i	−0.630992	+	0.775789i	$0.717352\pi$
$252$	9.81182	−	12.3845i	0.618087	−	0.780148i
$253$	−7.67477	−	1.21556i	−0.482509	−	0.0764219i
$254$	0.322499	−	0.724344i	0.0202354	−	0.0454494i
$255$		0			0
$256$	14.5142	−	6.46215i	0.907140	−	0.403885i
$257$	−5.30267	+	19.7898i	−0.330772	+	1.23446i	0.577610	+	0.816313i	$0.303986\pi$
$257$	−5.30267	+	19.7898i	−0.330772	+	1.23446i	−0.908381	+	0.418143i	$0.862681\pi$
$258$	0.0193672	−	0.00306747i	0.00120575	−	0.000190972i
$259$	−20.4793	+	0.218520i	−1.27252	+	0.0135782i
$260$		0			0
$261$	−13.2267	+	14.6898i	−0.818713	+	0.909273i
$262$	0.00341463	−	0.0651550i	0.000210956	−	0.00402529i
$263$	−0.666689	+	12.7212i	−0.0411098	+	0.784422i	0.897830	+	0.440341i	$0.145143\pi$
$263$	−0.666689	+	12.7212i	−0.0411098	+	0.784422i	−0.938940	+	0.344080i	$0.888191\pi$
$264$	0.0150741	−	0.0167414i	0.000927744	−	0.00103036i
$265$		0			0
$266$	0.00345806	+	0.00584462i	0.000212027	+	0.000358357i
$267$	0.868951	−	0.137628i	0.0531790	−	0.00842272i
$268$	−4.59170	+	17.1365i	−0.280483	+	1.04678i
$269$	−18.1556	+	8.08338i	−1.10696	+	0.492852i	−0.877070	−	0.480363i	$-0.840505\pi$
$269$	−18.1556	+	8.08338i	−1.10696	+	0.492852i	−0.229895	+	0.973215i	$0.573838\pi$
$270$		0			0
$271$	3.28374	−	7.37540i	0.199473	−	0.448024i	−0.785918	−	0.618331i	$-0.787809\pi$
$271$	3.28374	−	7.37540i	0.199473	−	0.448024i	0.985391	+	0.170307i	$0.0544760\pi$
$272$	17.2151	+	2.72661i	1.04382	+	0.165325i
$273$	−0.432610	+	0.171382i	−0.0261828	+	0.0103725i
$274$			0.238652i			0.0144175i
$275$		0			0
$276$	1.06812	+	0.616679i	0.0642933	+	0.0371197i
$277$	3.39560	−	2.20513i	0.204022	−	0.132493i	−0.438584	−	0.898690i	$-0.644520\pi$
$277$	3.39560	−	2.20513i	0.204022	−	0.132493i	0.642606	+	0.766197i	$0.277853\pi$
$278$	−0.753580	+	0.289272i	−0.0451968	+	0.0173494i
$279$	8.47968	−	6.16085i	0.507665	−	0.368840i
$280$		0			0
$281$	1.03849	+	0.754506i	0.0619510	+	0.0450100i	0.618330	−	0.785919i	$-0.287810\pi$
$281$	1.03849	+	0.754506i	0.0619510	+	0.0450100i	−0.556379	+	0.830929i	$0.687810\pi$
$282$	0.0281935	+	0.00755443i	0.00167890	+	0.000449860i
$283$	0.112220	−	0.292342i	0.00667076	−	0.0173779i	−0.930205	−	0.367041i	$-0.880371\pi$
$283$	0.112220	−	0.292342i	0.00667076	−	0.0173779i	0.936875	+	0.349663i	$0.113704\pi$
$284$	10.1507	−	9.13970i	0.602331	−	0.542342i
$285$		0			0
$286$	0.0789137	−	0.0256406i	0.00466627	−	0.00151616i
$287$	6.82957	+	24.4421i	0.403137	+	1.44277i
$288$	1.19593	−	0.609358i	0.0704709	−	0.0359067i
$289$	1.53639	+	1.38337i	0.0903759	+	0.0813748i
$290$		0			0
$291$	1.21301	+	1.34719i	0.0711081	+	0.0789735i
$292$	0.666061	−	0.539365i	0.0389783	−	0.0315640i
$293$	13.9434	−	13.9434i	0.814584	−	0.814584i	−0.170733	−	0.985317i	$-0.554614\pi$
$293$	13.9434	−	13.9434i	0.814584	−	0.814584i	0.985317	+	0.170733i	$0.0546137\pi$
$294$	−0.0148570	−	0.0245099i	−0.000866476	−	0.00142944i
$295$		0			0
$296$	−1.05947	−	0.471708i	−0.0615806	−	0.0274175i
$297$	−0.566641	+	0.699743i	−0.0328798	+	0.0406032i
$298$	−0.400571	−	0.616825i	−0.0232045	−	0.0357317i
$299$	4.54432	+	7.87099i	0.262805	+	0.455191i
$300$		0			0
$301$	2.50200	−	12.4212i	0.144213	−	0.715948i
$302$	0.304638	+	0.155221i	0.0175300	+	0.00893196i
$303$	−0.154439	−	0.402327i	−0.00887228	−	0.0231131i
$304$	−0.0285827	−	0.271946i	−0.00163933	−	0.0155972i
$305$		0			0
$306$	0.486196	+	0.0511012i	0.0277940	+	0.00292126i
$307$	14.7442	+	14.7442i	0.841499	+	0.841499i	0.989054	−	0.147555i	$-0.0471404\pi$
$307$	14.7442	+	14.7442i	0.841499	+	0.841499i	−0.147555	+	0.989054i	$0.547140\pi$
$308$	−3.37219	−	6.44730i	−0.192149	−	0.367369i
$309$	−0.798166	−	0.259340i	−0.0454061	−	0.0147533i
$310$		0			0
$311$	1.78340	−	8.39025i	0.101128	−	0.475768i	−0.898217	−	0.439553i	$-0.855137\pi$
$311$	1.78340	−	8.39025i	0.101128	−	0.475768i	0.999344	−	0.0362144i	$-0.0115299\pi$
$312$	−0.0263134	−	0.00137903i	−0.00148970	−	7.80720e-5i
$313$	−13.2447	+	20.3951i	−0.748636	+	1.15280i	0.234888	+	0.972022i	$0.424528\pi$
$313$	−13.2447	+	20.3951i	−0.748636	+	1.15280i	−0.983524	+	0.180776i	$0.942139\pi$
$314$	−0.213759	−	0.657884i	−0.0120631	−	0.0371265i
$315$		0			0
$316$	5.62268	−	17.3048i	0.316300	−	0.973472i
$317$	2.87966	+	3.55609i	0.161738	+	0.199730i	0.851572	−	0.524238i	$-0.175650\pi$
$317$	2.87966	+	3.55609i	0.161738	+	0.199730i	−0.689834	+	0.723968i	$0.742316\pi$
$318$	−0.00314297	−	0.0117297i	−0.000176249	−	0.000657771i
$319$	3.70238	+	8.31568i	0.207293	+	0.465589i
$320$		0			0
$321$	−0.693143	−	0.954029i	−0.0386875	−	0.0532487i
$322$	−0.431271	+	0.356922i	−0.0240338	+	0.0198905i
$323$	0.135805	−	0.266533i	0.00755640	−	0.0148303i
$324$	−15.3917	+	8.88642i	−0.855097	+	0.493690i
$325$		0			0
$326$	−0.0647591	+	0.112166i	−0.00358667	+	0.00621230i
$327$	−0.314436	+	0.0164789i	−0.0173884	+	0.000911285i
$328$	−0.224810	+	1.41939i	−0.0124130	+	0.0783729i
$329$	10.9226	−	15.3761i	0.602184	−	0.847710i
$330$		0			0
$331$	−0.248393	+	2.36330i	−0.0136529	+	0.129899i	−0.999225	−	0.0393560i	$-0.987469\pi$
$331$	−0.248393	+	2.36330i	−0.0136529	+	0.129899i	0.985572	+	0.169255i	$0.0541360\pi$
$332$	−8.19117	+	2.19482i	−0.449549	+	0.120456i
$333$	21.5939	+	8.28913i	1.18334	+	0.454241i
$334$	0.485535	−	0.103204i	0.0265673	−	0.00564705i
$335$		0			0
$336$	0.132871	+	1.14638i	0.00724872	+	0.0625404i
$337$	−9.69727	−	19.0320i	−0.528244	−	1.03674i	−0.988820	−	0.149117i	$-0.952357\pi$
$337$	−9.69727	−	19.0320i	−0.528244	−	1.03674i	0.460575	−	0.887621i	$-0.347643\pi$
$338$	0.327110	+	0.212428i	0.0177925	+	0.0115546i
$339$	−1.08576	−	0.230785i	−0.0589703	−	0.0125345i
$340$		0			0
$341$	−1.00352	−	4.72120i	−0.0543438	−	0.255667i
$342$	−0.00119979	−	0.00757520i	−6.48774e−5	−	0.000409620i
$343$	−18.1902	+	3.48115i	−0.982176	+	0.187964i
$344$	0.421735	−	0.580469i	0.0227384	−	0.0312968i
$345$		0			0
$346$	0.378177	−	0.0397480i	0.0203309	−	0.00213686i
$347$	−20.3955	−	16.5160i	−1.09489	−	0.886624i	−0.100770	−	0.994910i	$-0.532130\pi$
$347$	−20.3955	−	16.5160i	−1.09489	−	0.886624i	−0.994120	+	0.108286i	$0.965464\pi$
$348$	−0.0756157	−	1.44283i	−0.00405342	−	0.0773439i
$349$	16.7152			0.894745			0.447373	−	0.894348i	$-0.352360\pi$
$349$	16.7152			0.894745			0.447373	+	0.894348i	$0.352360\pi$
$350$		0			0
$351$	1.05315			0.0562129
$352$	−0.0323484	−	0.617243i	−0.00172417	−	0.0328992i
$353$	22.3839	+	18.1261i	1.19138	+	0.964758i	0.999860	−	0.0167319i	$-0.00532618\pi$
$353$	22.3839	+	18.1261i	1.19138	+	0.964758i	0.191516	+	0.981489i	$0.438660\pi$
$354$	0.0419119	−	0.00440512i	0.00222759	−	0.000234130i
$355$		0			0
$356$	9.45769	−	13.0174i	0.501256	−	0.689920i
$357$	−0.561125	+	1.13094i	−0.0296979	+	0.0598558i
$358$	−0.0528947	−	0.333964i	−0.00279557	−	0.0176505i
$359$	−0.933188	−	4.39030i	−0.0492518	−	0.231711i	0.946636	−	0.322304i	$-0.104457\pi$
$359$	−0.933188	−	4.39030i	−0.0492518	−	0.231711i	−0.995888	+	0.0905925i	$0.971124\pi$
$360$		0			0
$361$	18.5802	+	3.94935i	0.977906	+	0.207860i
$362$	0.498034	+	0.323427i	0.0261761	+	0.0169989i
$363$	−0.451793	−	0.886694i	−0.0237130	−	0.0465394i
$364$	−3.37829	+	7.81100i	−0.177070	+	0.409408i
$365$		0			0
$366$	−0.0302900	+	0.00643833i	−0.00158328	+	0.000336537i
$367$	30.6289	+	11.7573i	1.59882	+	0.613728i	0.984508	−	0.175339i	$-0.0561023\pi$
$367$	30.6289	+	11.7573i	1.59882	+	0.613728i	0.614307	+	0.789067i	$0.289436\pi$
$368$	21.7730	−	5.83406i	1.13500	−	0.304121i
$369$	2.99597	−	28.5047i	0.155964	−	1.48390i
$370$		0			0
$371$	−7.81221	−	0.736911i	−0.405590	−	0.0382585i
$372$	−0.119846	+	0.756679i	−0.00621374	+	0.0392320i
$373$	37.6781	−	1.97463i	1.95090	−	0.102242i	0.964239	−	0.265033i	$-0.0853830\pi$
$373$	37.6781	−	1.97463i	1.95090	−	0.102242i	0.986661	+	0.162791i	$0.0520496\pi$
$374$	0.112562	−	0.194964i	0.00582046	−	0.0100813i
$375$		0			0
$376$	0.924931	−	0.534009i	0.0476997	−	0.0275394i
$377$	4.83357	−	9.48641i	0.248941	−	0.488575i
$378$	0.0108306	+	0.0639575i	0.000557067	+	0.00328962i
$379$	2.24596	+	3.09129i	0.115367	+	0.158789i	0.862795	−	0.505553i	$-0.168712\pi$
$379$	2.24596	+	3.09129i	0.115367	+	0.158789i	−0.747428	+	0.664343i	$0.768712\pi$
$380$		0			0
$381$	−0.940591	−	2.11260i	−0.0481879	−	0.108232i
$382$	−0.217089	−	0.810186i	−0.0111072	−	0.0414527i
$383$	−10.1248	−	12.5030i	−0.517351	−	0.638876i	0.449784	−	0.893137i	$-0.351501\pi$
$383$	−10.1248	−	12.5030i	−0.517351	−	0.638876i	−0.967135	+	0.254262i	$0.918168\pi$
$384$	−0.0404172	+	0.124391i	−0.00206253	+	0.00634782i
$385$		0			0
$386$	−0.141016	−	0.434001i	−0.00717751	−	0.0220901i
$387$	−7.79381	+	12.0014i	−0.396182	+	0.610066i
$388$	33.1093	+	1.73518i	1.68087	+	0.0880906i
$389$	3.20212	−	15.0648i	0.162354	−	0.763815i	−0.819334	−	0.573317i	$-0.805656\pi$
$389$	3.20212	−	15.0648i	0.162354	−	0.763815i	0.981688	−	0.190498i	$-0.0610103\pi$
$390$		0			0
$391$	23.4521	+	7.62006i	1.18603	+	0.385363i
$392$	−1.01857	−	0.249756i	−0.0514453	−	0.0126146i
$393$	−0.134555	−	0.134555i	−0.00678742	−	0.00678742i
$394$	0.497262	+	0.0522644i	0.0250517	+	0.00263304i
$395$		0			0
$396$	0.858943	+	8.17229i	0.0431635	+	0.410673i
$397$	4.19748	+	10.9348i	0.210665	+	0.548802i	0.997676	−	0.0681376i	$-0.0217057\pi$
$397$	4.19748	+	10.9348i	0.210665	+	0.548802i	−0.787011	+	0.616939i	$0.788372\pi$
$398$	−0.612248	−	0.311956i	−0.0306892	−	0.0156369i
$399$	0.0194165	+	0.00391105i	0.000972040	+	0.000195797i
$400$		0			0
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	0.980129	−	0.198363i	$-0.0635626\pi$
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	−0.661852	+	0.749635i	$0.730229\pi$
$402$	−0.0197951	−	0.0304818i	−0.000987289	−	0.00152029i
$403$	−3.55282	+	4.38737i	−0.176979	+	0.218550i
$404$	−7.20026	−	3.20576i	−0.358226	−	0.159493i
$405$		0			0
$406$	0.625817	+	0.195983i	0.0310588	+	0.00972649i
$407$	7.53167	−	7.53167i	0.373331	−	0.373331i
$408$	−0.0555587	+	0.0449906i	−0.00275057	+	0.00222736i
$409$	−6.77254	−	7.52166i	−0.334880	−	0.371922i	0.552061	−	0.833803i	$-0.313841\pi$
$409$	−6.77254	−	7.52166i	−0.334880	−	0.371922i	−0.886942	+	0.461881i	$0.847175\pi$
$410$		0			0
$411$	0.517262	+	0.465745i	0.0255147	+	0.0229735i
$412$	−13.6760	+	6.96826i	−0.673768	+	0.343302i
$413$	6.76705	−	26.3776i	0.332985	−	1.29796i
$414$	0.601294	−	0.195372i	0.0295520	−	0.00960203i
$415$		0			0
$416$	−0.537253	+	0.483745i	−0.0263410	+	0.0237175i
$417$	−0.843684	+	2.19787i	−0.0413154	+	0.107630i
$418$	−0.00341149		0.000914107i	−0.000166862		4.47104e-5i
$419$	2.20460	+	1.60174i	0.107702	+	0.0782499i	0.640333	−	0.768098i	$-0.278797\pi$
$419$	2.20460	+	1.60174i	0.107702	+	0.0782499i	−0.532631	+	0.846348i	$0.678797\pi$
$420$		0			0
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.318286	−	0.947995i	$-0.396893\pi$
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.999952	−	0.00976112i	$-0.00310711\pi$
$422$	0.333503	−	0.128020i	0.0162347	−	0.00623190i
$423$	−17.8645	+	11.6013i	−0.868600	+	0.564075i
$424$	−0.384812	−	0.222171i	−0.0186881	−	0.0107896i
$425$		0			0
$426$			0.0279829i			0.00135577i
$427$	−2.91921	+	19.7959i	−0.141270	+	0.957993i
$428$	−21.3017	−	3.37386i	−1.02966	−	0.163082i
$429$	0.0984310	−	0.221080i	0.00475230	−	0.0106738i
$430$		0			0
$431$	−28.4527	+	12.6680i	−1.37052	+	0.610194i	−0.954240	−	0.299043i	$-0.903332\pi$
$431$	−28.4527	+	12.6680i	−1.37052	+	0.610194i	−0.416278	+	0.909237i	$0.636666\pi$
$432$	0.676023	−	2.52295i	0.0325252	−	0.121386i
$433$	5.27787	−	0.835932i	0.253638	−	0.0401723i	−0.0283205	−	0.999599i	$-0.509016\pi$
$433$	5.27787	−	0.835932i	0.253638	−	0.0401723i	0.281959	+	0.959427i	$0.409016\pi$
$434$	−0.302982	−	0.170642i	−0.0145436	−	0.00819110i
$435$		0			0
$436$	−3.85327	+	4.27949i	−0.184538	+	0.204950i
$437$	0.0202467	−	0.386330i	0.000968530	−	0.0184807i
$438$	−9.18930e−5		0.00175342i	−4.39082e−6		8.37818e-5i
$439$	−17.8883	+	19.8670i	−0.853763	+	0.948200i	−0.999152	−	0.0411749i	$-0.986890\pi$
$439$	−17.8883	+	19.8670i	−0.853763	+	0.948200i	0.145389	+	0.989375i	$0.453557\pi$
$440$		0			0
$441$	20.5475	+	3.91121i	0.978451	+	0.186248i
$442$	−0.260074	+	0.0411916i	−0.0123704	+	0.00195929i
$443$	−7.64058	+	28.5150i	−0.363015	+	1.35479i	0.507077	+	0.861901i	$0.330726\pi$
$443$	−7.64058	+	28.5150i	−0.363015	+	1.35479i	−0.870092	+	0.492889i	$0.835941\pi$
$444$	−1.54447	+	0.687643i	−0.0732974	+	0.0326341i
$445$		0			0
$446$	0.382986	−	0.860200i	0.0181349	−	0.0407317i
$447$	−2.11867	−	0.335564i	−0.100210	−	0.0158717i
$448$	16.5204	+	13.0886i	0.780517	+	0.618379i
$449$		−	16.6858i		−	0.787450i	−0.919228	−	0.393725i	$-0.871186\pi$
$449$		−	16.6858i		−	0.787450i	0.919228	−	0.393725i	$-0.128814\pi$
$450$		0			0
$451$	−11.4304	−	6.59932i	−0.538235	−	0.310750i
$452$	−17.0259	+	11.0568i	−0.800832	+	0.520067i
$453$	0.930953	−	0.357359i	0.0437400	−	0.0167902i
$454$	0.375079	−	0.272511i	0.0176033	−	0.0127896i
$455$		0			0
$456$	0.000907371	0	0.000659243i	4.24915e−5	0	3.08719e-5i
$457$	10.2464	+	2.74552i	0.479308	+	0.128430i	0.490380	−	0.871509i	$-0.336858\pi$
$457$	10.2464	+	2.74552i	0.479308	+	0.128430i	−0.0110724	+	0.999939i	$0.503525\pi$
$458$	0.198309	−	0.516612i	0.00926637	−	0.0241397i
$459$	2.12344	−	1.91195i	0.0991136	−	0.0892423i
$460$		0			0
$461$	19.5350	−	6.34729i	0.909833	−	0.295623i	0.183544	−	0.983012i	$-0.441243\pi$
$461$	19.5350	−	6.34729i	0.909833	−	0.295623i	0.726290	+	0.687389i	$0.241243\pi$
$462$	0.0144384	+	0.00370411i	0.000671736	+	0.000172331i
$463$	2.59137	−	1.32037i	0.120431	−	0.0613628i	−0.392737	−	0.919651i	$-0.628472\pi$
$463$	2.59137	−	1.32037i	0.120431	−	0.0613628i	0.513168	+	0.858288i	$0.328472\pi$
$464$	−19.6232	−	17.6688i	−0.910985	−	0.820255i
$465$		0			0
$466$	0.0304258	+	0.0337912i	0.00140945	+	0.00156535i
$467$	5.69972	−	4.61554i	0.263752	−	0.213582i	−0.488318	−	0.872666i	$-0.662389\pi$
$467$	5.69972	−	4.61554i	0.263752	−	0.213582i	0.752069	+	0.659084i	$0.229056\pi$
$468$	6.79623	−	6.79623i	0.314156	−	0.314156i
$469$	−22.9190	+	5.12776i	−1.05830	+	0.236778i
$470$		0			0
$471$	−1.84309	−	0.820595i	−0.0849249	−	0.0378110i
$472$	0.970439	−	1.19839i	0.0446681	−	0.0551605i
$473$	3.58902	+	5.52661i	0.165023	+	0.254114i
$474$	0.0186381	+	0.0322821i	0.000856077	+	0.00148277i
$475$		0			0
$476$	7.36903	+	21.8823i	0.337759	+	1.00297i
$477$	7.89620	+	4.02332i	0.361542	+	0.184215i
$478$	0.345545	+	0.900174i	0.0158048	+	0.0411730i
$479$	−0.617027	−	5.87062i	−0.0281927	−	0.268235i	−0.999533	−	0.0305441i	$-0.990276\pi$
$479$	−0.617027	−	5.87062i	−0.0281927	−	0.268235i	0.971341	−	0.237691i	$-0.0763907\pi$
$480$		0			0
$481$	−12.3901	−	1.30225i	−0.564939	−	0.0593774i
$482$	−0.362945	−	0.362945i	−0.0165317	−	0.0165317i
$483$	−0.0680487	+	1.63131i	−0.00309632	+	0.0742271i
$484$	−17.3097	−	5.62427i	−0.786805	−	0.255649i
$485$		0			0
$486$	0.0228628	−	0.107561i	0.00103708	−	0.00487907i
$487$	17.3674	+	0.910186i	0.786991	+	0.0412444i	0.441597	−	0.897213i	$-0.354412\pi$
$487$	17.3674	+	0.910186i	0.786991	+	0.0412444i	0.345394	+	0.938458i	$0.387745\pi$
$488$	−0.617130	+	0.950297i	−0.0279362	+	0.0430179i
$489$	0.116731	+	0.359261i	0.00527875	+	0.0162463i
$490$		0			0
$491$	−1.67096	+	5.14268i	−0.0754092	+	0.232086i	−0.981655	−	0.190665i	$-0.938936\pi$
$491$	−1.67096	+	5.14268i	−0.0754092	+	0.232086i	0.906246	+	0.422751i	$0.138936\pi$
$492$	1.31839	+	1.62808i	0.0594377	+	0.0733995i
$493$	−7.47643	−	27.9024i	−0.336721	−	1.25666i
$494$	0.00168022	+	0.00377385i	7.55969e−5	+	0.000169793i
$495$		0			0
$496$	8.22993	+	11.3275i	0.369535	+	0.508621i
$497$	16.9491	+	6.29951i	0.760272	+	0.282572i
$498$	0.00788715	−	0.0154794i	0.000353432	−	0.000693648i
$499$	2.08554	−	1.20409i	0.0933616	−	0.0539023i	−0.452592	−	0.891718i	$-0.649501\pi$
$499$	2.08554	−	1.20409i	0.0933616	−	0.0539023i	0.545954	+	0.837815i	$0.316167\pi$
$500$		0			0
$501$	0.723867	−	1.25377i	0.0323400	−	0.0560145i
$502$	−0.919765	+	0.0482028i	−0.0410511	+	0.00215140i
$503$	−3.80370	+	24.0156i	−0.169599	+	1.07080i	0.745184	+	0.666859i	$0.232362\pi$
$503$	−3.80370	+	24.0156i	−0.169599	+	1.07080i	−0.914783	+	0.403946i	$0.867638\pi$
$504$	0.965593	+	0.685924i	0.0430109	+	0.0305535i
$505$		0			0
$506$	0.0304328	−	0.289549i	0.00135290	−	0.0128720i
$507$	1.09880	−	0.294423i	0.0487995	−	0.0130758i
$508$	−39.4848	−	15.1568i	−1.75185	−	0.672474i
$509$	17.7343	−	3.76954i	0.786058	−	0.167082i	0.202639	−	0.979253i	$-0.435048\pi$
$509$	17.7343	−	3.76954i	0.786058	−	0.167082i	0.583419	+	0.812172i	$0.301715\pi$
$510$		0			0
$511$	1.04136	+	0.450390i	0.0460668	+	0.0199241i
$512$	1.35700	+	2.66325i	0.0599713	+	0.117700i
$513$	−0.0375954	−	0.0244148i	−0.00165988	−	0.00107794i
$514$	−0.750870	−	0.159602i	−0.0331194	−	0.00703976i
$515$		0			0
$516$	−0.217465	−	1.02309i	−0.00957338	−	0.0450392i
$517$	1.53447	+	9.68824i	0.0674858	+	0.426088i
$518$	−0.0483347	−	0.765840i	−0.00212371	−	0.0336491i
$519$	0.651886	−	0.897245i	0.0286146	−	0.0393847i
$520$		0			0
$521$	15.4005	−	1.61866i	0.674708	−	0.0709147i	0.239023	−	0.971014i	$-0.423173\pi$
$521$	15.4005	−	1.61866i	0.674708	−	0.0709147i	0.435685	+	0.900099i	$0.356506\pi$
$522$	−0.575580	−	0.466095i	−0.0251924	−	0.0204004i
$523$	−1.03294	−	19.7096i	−0.0451673	−	0.861843i	−0.923454	−	0.383709i	$-0.874647\pi$
$523$	−1.03294	−	19.7096i	−0.0451673	−	0.861843i	0.878287	−	0.478134i	$-0.158687\pi$
$524$	−3.48022			−0.152034
$525$		0			0
$526$	−0.477293			−0.0208110
$527$	0.801639	+	15.2962i	0.0349199	+	0.666312i
$528$	−0.466442	−	0.377717i	−0.0202993	−	0.0164380i
$529$	8.84171	−	0.929301i	0.384422	−	0.0404044i
$530$		0			0
$531$	−18.0774	+	24.8813i	−0.784490	+	1.07976i
$532$	0.301679	−	0.200521i	0.0130794	−	0.00869368i
$533$	2.41499	+	15.2476i	0.104605	+	0.660448i
$534$	0.00685356	+	0.0322435i	0.000296582	+	0.00139531i
$535$		0			0
$536$	−1.30085	−	0.276503i	−0.0561880	−	0.0119431i
$537$	−0.827073	−	0.537107i	−0.0356908	−	0.0231779i
$538$	−0.338056	−	0.663472i	−0.0145746	−	0.0286043i
$539$	5.49395	−	7.91143i	0.236641	−	0.340770i
$540$		0			0
$541$	26.7198	−	5.67947i	1.14877	−	0.244179i	0.406098	−	0.913830i	$-0.366889\pi$
$541$	26.7198	−	5.67947i	1.14877	−	0.244179i	0.742677	+	0.669650i	$0.233556\pi$
$542$	0.282403	+	0.108404i	0.0121302	+	0.00465636i
$543$	1.67295	−	0.448267i	0.0717933	−	0.0192370i
$544$	−0.205030	+	1.95073i	−0.00879058	+	0.0836368i
$545$		0			0
$546$	−0.00726086	−	0.0158508i	−0.000310736	−	0.000678352i
$547$	1.58597	−	10.0134i	0.0678111	−	0.428143i	−0.930305	−	0.366787i	$-0.880458\pi$
$547$	1.58597	−	10.0134i	0.0678111	−	0.428143i	0.998116	−	0.0613554i	$-0.0195423\pi$
$548$	12.7125	−	0.666236i	0.543053	−	0.0284602i
$549$	11.2995	−	19.5712i	0.482249	−	0.835280i
$550$		0			0
$551$	−0.392470	+	0.226593i	−0.0167198	+	0.00965317i
$552$	−0.0419740	+	0.0823786i	−0.00178653	+	0.00350627i
$553$	23.7490	−	4.02168i	1.00991	−	0.171019i
$554$	0.0891673	+	0.122728i	0.00378836	+	0.00521423i
$555$		0			0
$556$	17.5128	+	39.3343i	0.742706	+	1.66815i
$557$	0.0898136	+	0.335189i	0.00380552	+	0.0142024i	0.967802	−	0.251711i	$-0.0809932\pi$
$557$	0.0898136	+	0.335189i	0.00380552	+	0.0142024i	−0.963997	+	0.265913i	$0.914327\pi$
$558$	0.247147	+	0.305201i	0.0104626	+	0.0129202i
$559$	2.38179	−	7.33039i	0.100739	−	0.310042i
$560$		0			0
$561$	−0.202898	−	0.624456i	−0.00856637	−	0.0263646i
$562$	−0.0261948	+	0.0403364i	−0.00110496	+	0.00170149i
$563$	−15.1129	−	0.792034i	−0.636933	−	0.0333803i	−0.268863	−	0.963178i	$-0.586648\pi$
$563$	−15.1129	−	0.792034i	−0.636933	−	0.0333803i	−0.368070	+	0.929798i	$0.619981\pi$
$564$	0.323704	−	1.52291i	0.0136304	−	0.0641259i
$565$		0			0
$566$	0.0111585	+	0.00362563i	0.000469029	+	0.000152397i
$567$	−19.8677	−	12.6029i	−0.834363	−	0.529271i
$568$	0.724020	+	0.724020i	0.0303792	+	0.0303792i
$569$	8.99190	+	0.945086i	0.376960	+	0.0396201i	0.291114	−	0.956688i	$-0.405974\pi$
$569$	8.99190	+	0.945086i	0.376960	+	0.0396201i	0.0858458	+	0.996308i	$0.472641\pi$
$570$		0			0
$571$	−1.93251	−	18.3867i	−0.0808732	−	0.769457i	−0.957529	−	0.288338i	$-0.906897\pi$
$571$	−1.93251	−	18.3867i	−0.0808732	−	0.769457i	0.876655	−	0.481119i	$-0.159769\pi$
$572$	−1.58613	−	4.13201i	−0.0663194	−	0.172768i
$573$	−2.17969	−	1.11061i	−0.0910579	−	0.0463963i
$574$	−0.901151	+	0.303469i	−0.0376133	+	0.0126666i
$575$		0			0
$576$	−11.9019	−	20.6147i	−0.495914	−	0.858947i
$577$	14.4031	+	22.1789i	0.599610	+	0.923318i	0.999976	+	0.00696286i	$0.00221637\pi$
$577$	14.4031	+	22.1789i	0.599610	+	0.923318i	−0.400366	+	0.916355i	$0.631117\pi$
$578$	−0.0487485	+	0.0601994i	−0.00202767	+	0.00250397i
$579$	−1.21587	−	0.541341i	−0.0505299	−	0.0224974i
$580$		0			0
$581$	−7.60026	−	8.26194i	−0.315312	−	0.342763i
$582$	−0.0480288	+	0.0480288i	−0.00199086	+	0.00199086i
$583$	3.17151	−	2.56824i	0.131351	−	0.106366i
$584$	0.0429899	+	0.0477451i	0.00177893	+	0.00197571i
$585$		0			0
$586$	0.549060	+	0.494376i	0.0226815	+	0.0204225i
$587$	17.2602	−	8.79450i	0.712404	−	0.362988i	−0.0599321	−	0.998202i	$-0.519088\pi$
$587$	17.2602	−	8.79450i	0.712404	−	0.362988i	0.772336	+	0.635215i	$0.219088\pi$
$588$	−1.26412	+	0.859827i	−0.0521314	+	0.0354587i
$589$	0.228540	−	0.0742572i	0.00941683	−	0.00305971i
$590$		0			0
$591$	1.08372	−	0.975787i	0.0445783	−	0.0401385i
$592$	−11.0730	+	28.8461i	−0.455097	+	1.18557i
$593$	39.8994	+	10.6910i	1.63847	+	0.439027i	0.956353	−	0.292215i	$-0.0943924\pi$
$593$	39.8994	+	10.6910i	1.63847	+	0.439027i	0.682118	+	0.731242i	$0.261059\pi$
$594$	−0.0272933	−	0.0198297i	−0.00111986	−	0.000813623i
$595$		0			0
$596$	−31.7389	+	23.0597i	−1.30008	+	0.944560i
$597$	−1.87099	+	0.718205i	−0.0765744	+	0.0293942i
$598$	−0.285596	+	0.185468i	−0.0116789	+	0.00758436i
$599$	2.44181	+	1.40978i	0.0997698	+	0.0576021i	0.549055	−	0.835786i	$-0.314988\pi$
$599$	2.44181	+	1.40978i	0.0997698	+	0.0576021i	−0.449285	+	0.893389i	$0.648321\pi$
$600$		0			0
$601$		−	33.6982i		−	1.37458i	−0.726384	−	0.687289i	$-0.758801\pi$
$601$		−	33.6982i		−	1.37458i	0.726384	−	0.687289i	$-0.241199\pi$
$602$	0.469668	+	0.0692596i	0.0191422	+	0.00282281i
$603$	26.1976	+	4.14929i	1.06685	+	0.168972i
$604$	7.41788	−	16.6608i	0.301829	−	0.677920i
$605$		0			0
$606$	0.0147509	−	0.00656754i	0.000599215	−	0.000266788i
$607$	8.74821	−	32.6488i	0.355079	−	1.32517i	−0.525306	−	0.850913i	$-0.676049\pi$
$607$	8.74821	−	32.6488i	0.355079	−	1.32517i	0.880385	−	0.474259i	$-0.157284\pi$
$608$	0.0303934	−	0.00481385i	0.00123262	−	0.000195227i
$609$	1.64611	−	0.973944i	0.0667036	−	0.0394662i
$610$		0			0
$611$	7.67696	−	8.52613i	0.310577	−	0.344930i
$612$	1.36477	−	26.0414i	0.0551676	−	1.05266i
$613$	−0.309370	+	5.90313i	−0.0124953	+	0.238425i	0.985241	+	0.171174i	$0.0547561\pi$
$613$	−0.309370	+	5.90313i	−0.0124953	+	0.238425i	−0.997736	+	0.0672508i	$0.978577\pi$
$614$	−0.522769	+	0.580594i	−0.0210973	+	0.0234309i
$615$		0			0
$616$	0.469414	−	0.277736i	0.0189132	−	0.0111903i
$617$	−4.67312	+	0.740149i	−0.188133	+	0.0297973i	−0.249790	−	0.968300i	$-0.580361\pi$
$617$	−4.67312	+	0.740149i	−0.188133	+	0.0297973i	0.0616571	+	0.998097i	$0.480361\pi$
$618$	0.00813851	−	0.0303733i	0.000327379	−	0.00122180i
$619$	0.987941	−	0.439860i	0.0397087	−	0.0176795i	−0.386786	−	0.922169i	$-0.626415\pi$
$619$	0.987941	−	0.439860i	0.0397087	−	0.0176795i	0.426495	+	0.904490i	$0.359748\pi$
$620$		0			0
$621$	1.50302	−	3.37583i	0.0603140	−	0.135467i
$622$	0.317433	+	0.0502765i	0.0127279	+	0.00201590i
$623$	21.0726	+	3.10747i	0.844257	+	0.124498i
$624$			0.702018i			0.0281032i
$625$		0			0
$626$	−0.789090	−	0.455581i	−0.0315384	−	0.0182087i
$627$	−0.00863903	+	0.00561025i	−0.000345010	+	0.000224052i
$628$	−34.4475	+	13.2232i	−1.37460	+	0.527661i
$629$	−27.3460	+	19.8680i	−1.09036	+	0.792191i
$630$		0			0
$631$	−17.6839	−	12.8481i	−0.703983	−	0.511474i	0.177244	−	0.984167i	$-0.443282\pi$
$631$	−17.6839	−	12.8481i	−0.703983	−	0.511474i	−0.881227	+	0.472693i	$0.843282\pi$
$632$	1.31749	+	0.353022i	0.0524071	+	0.0140424i
$633$	0.373379	−	0.972685i	0.0148405	−	0.0386608i
$634$	−0.127410	+	0.114721i	−0.00506012	+	0.00455615i
$635$		0			0
$636$	−0.616047	+	0.200166i	−0.0244279	+	0.00793709i
$637$	−11.2353	+	0.829543i	−0.445161	+	0.0328677i
$638$	−0.303886	+	0.154838i	−0.0120310	+	0.00613008i
$639$	−15.1760	−	13.6646i	−0.600355	−	0.540562i
$640$		0			0
$641$	−14.7391	−	16.3694i	−0.582159	−	0.646553i	0.378066	−	0.925779i	$-0.376589\pi$
$641$	−14.7391	−	16.3694i	−0.582159	−	0.646553i	−0.960226	+	0.279225i	$0.909922\pi$
$642$	0.0343375	−	0.0278059i	0.00135519	−	0.00109741i
$643$	−7.57933	+	7.57933i	−0.298899	+	0.298899i	−0.840583	−	0.541683i	$-0.817787\pi$
$643$	−7.57933	+	7.57933i	−0.298899	+	0.298899i	0.541683	+	0.840583i	$0.317787\pi$
$644$	20.2165	+	21.9766i	0.796643	+	0.865999i
$645$		0			0
$646$	0.0102391	+	0.00455874i	0.000402852	+	0.000179361i
$647$	−21.8601	+	26.9950i	−0.859410	+	1.06128i	0.138077	+	0.990422i	$0.455908\pi$
$647$	−21.8601	+	26.9950i	−0.859410	+	1.06128i	−0.997486	+	0.0708609i	$0.977425\pi$
$648$	−0.725621	−	1.11736i	−0.0285051	−	0.0438940i
$649$	7.08130	+	12.2652i	0.277965	+	0.481450i
$650$		0			0
$651$	−0.961146	+	0.323673i	−0.0376703	+	0.0126857i
$652$	6.15566	+	3.13647i	0.241074	+	0.122834i
$653$	−5.94863	−	15.4967i	−0.232788	−	0.606433i	0.766574	−	0.642156i	$-0.221960\pi$
$653$	−5.94863	−	15.4967i	−0.232788	−	0.606433i	−0.999362	+	0.0357231i	$0.988627\pi$
$654$	−0.00123317	−	0.0117329i	−4.82209e−5	−	0.000458791i
$655$		0			0
$656$	38.0779	+	4.00215i	1.48669	+	0.156258i
$657$	−0.906067	−	0.906067i	−0.0353490	−	0.0353490i
$658$	0.596741	+	0.378538i	0.0232634	+	0.0147569i
$659$	23.7349	+	7.71192i	0.924579	+	0.300414i	0.732344	−	0.680935i	$-0.238426\pi$
$659$	23.7349	+	7.71192i	0.924579	+	0.300414i	0.192235	+	0.981349i	$0.438426\pi$
$660$		0			0
$661$	−0.637712	+	3.00020i	−0.0248041	+	0.116694i	−0.988808	−	0.149194i	$-0.952332\pi$
$661$	−0.637712	+	3.00020i	−0.0248041	+	0.116694i	0.964004	+	0.265889i	$0.0856653\pi$
$662$	−0.0889140	−	0.00465979i	−0.00345574	−	0.000181108i
$663$	−0.418271	+	0.644081i	−0.0162443	+	0.0250140i
$664$	−0.196439	−	0.604578i	−0.00762333	−	0.0234622i
$665$		0			0
$666$	−0.267808	+	0.824229i	−0.0103774	+	0.0319382i
$667$	−23.5101	−	29.0325i	−0.910314	−	1.12414i
$668$	−6.85292	−	25.5754i	−0.265147	−	0.989543i
$669$	−1.11701	−	2.50884i	−0.0431859	−	0.0969972i
$670$		0			0
$671$	−6.11692	−	8.41922i	−0.236141	−	0.325020i
$672$	−0.128050	+	0.0216841i	−0.00493965	+	0.000836484i
$673$	−4.32228	+	8.48294i	−0.166611	+	0.326993i	−0.959183	−	0.282785i	$-0.908742\pi$
$673$	−4.32228	+	8.48294i	−0.166611	+	0.326993i	0.792572	+	0.609779i	$0.208742\pi$
$674$	0.693099	−	0.400161i	0.0266972	−	0.0154136i
$675$		0			0
$676$	10.4025	−	18.0176i	0.400095	−	0.692985i
$677$	−10.4146	+	0.545808i	−0.400267	+	0.0209771i	−0.251408	−	0.967881i	$-0.580893\pi$
$677$	−10.4146	+	0.545808i	−0.400267	+	0.0209771i	−0.148859	+	0.988858i	$0.547560\pi$
$678$	0.00650613	−	0.0410781i	0.000249867	−	0.00157760i
$679$	18.2786	+	39.9031i	0.701469	+	1.53134i
$680$		0			0
$681$	0.141342	−	1.34478i	0.00541625	−	0.0515322i
$682$	0.174684	−	0.0468065i	0.00668901	−	0.00179231i
$683$	8.91768	+	3.42318i	0.341226	+	0.130984i	0.522946	−	0.852366i	$-0.324833\pi$
$683$	8.91768	+	3.42318i	0.341226	+	0.130984i	−0.181720	+	0.983350i	$0.558166\pi$
$684$	−0.400168	+	0.0850583i	−0.0153008	+	0.00325228i
$685$		0			0
$686$	−0.165923	−	0.673790i	−0.00633497	−	0.0257254i
$687$	−0.732711	−	1.43803i	−0.0279546	−	0.0548641i
$688$	−16.0320	−	10.4113i	−0.611215	−	0.396927i
$689$	−4.66898	−	0.992421i	−0.177874	−	0.0378082i
$690$		0			0
$691$	4.86605	+	22.8929i	0.185113	+	0.870889i	0.968434	+	0.249271i	$0.0801910\pi$
$691$	4.86605	+	22.8929i	0.185113	+	0.870889i	−0.783321	+	0.621618i	$0.786476\pi$
$692$	−3.17305	−	20.0338i	−0.120621	−	0.761572i
$693$	−9.05942	+	6.02165i	−0.344139	+	0.228744i
$694$	0.577980	−	0.795521i	0.0219398	−	0.0301976i
$695$		0			0
$696$	0.107713	−	0.0113211i	0.00408287	−	0.000429127i
$697$	32.5508	+	26.3592i	1.23295	+	0.998424i
$698$	0.0327774	+	0.625429i	0.00124064	+	0.0236728i
$699$	0.132618			0.00501608
$700$		0			0
$701$	24.9909			0.943892			0.471946	−	0.881628i	$-0.343552\pi$
$701$	24.9909			0.943892			0.471946	+	0.881628i	$0.343552\pi$
$702$	0.00206515	+	0.0394054i	7.79440e−5	+	0.00148726i
$703$	0.412113	+	0.333723i	0.0155431	+	0.0125866i
$704$	−10.9015	+	1.14580i	−0.410867	+	0.0431839i
$705$		0			0
$706$	−0.634328	+	0.873078i	−0.0238733	+	0.0328587i
$707$	−0.657204	−	10.4131i	−0.0247167	−	0.391624i
$708$	−0.351657	−	2.22027i	−0.0132161	−	0.0834430i
$709$	10.0976	+	47.5054i	0.379223	+	1.78410i	0.590881	+	0.806759i	$0.298780\pi$
$709$	10.0976	+	47.5054i	0.379223	+	1.78410i	−0.211658	+	0.977344i	$0.567886\pi$
$710$		0			0
$711$	−26.6090	−	5.65593i	−0.997917	−	0.212114i
$712$	1.01158	+	0.656930i	0.0379107	+	0.0246195i
$713$	8.99310	+	17.6500i	0.336794	+	0.660996i
$714$	−0.0434165	−	0.0187778i	−0.00162482	−	0.000702741i
$715$		0			0
$716$	−17.6420	+	3.74992i	−0.659312	+	0.140141i
$717$	2.62542	+	1.00781i	0.0980482	+	0.0376372i
$718$	0.162441	−	0.0435259i	0.00606224	−	0.00162437i
$719$	0.622106	−	5.91894i	0.0232006	−	0.220739i	−0.976778	−	0.214252i	$-0.931269\pi$
$719$	0.622106	−	5.91894i	0.0232006	−	0.220739i	0.999979	−	0.00648680i	$-0.00206483\pi$
$720$		0			0
$721$	−16.5649	−	11.7671i	−0.616909	−	0.438231i
$722$	−0.111337	+	0.702956i	−0.00414354	+	0.0261613i
$723$	−1.49497	+	0.0783480i	−0.0555985	+	0.00291379i
$724$	15.8380	−	27.4323i	0.588615	−	1.01951i
$725$		0			0
$726$	0.0322913	−	0.0186434i	0.00119844	−	0.000691921i
$727$	4.72308	−	9.26956i	0.175169	−	0.343789i	−0.786684	−	0.617356i	$-0.788204\pi$
$727$	4.72308	−	9.26956i	0.175169	−	0.343789i	0.961853	+	0.273567i	$0.0882037\pi$
$728$	−0.597984	−	0.222253i	−0.0221628	−	0.00823726i
$729$	15.4924	+	21.3235i	0.573793	+	0.789759i
$730$		0			0
$731$	−8.50572	−	19.1042i	−0.314595	−	0.706593i
$732$	0.427518	+	1.59552i	0.0158015	+	0.0589720i
$733$	24.1284	+	29.7961i	0.891202	+	1.10054i	0.994379	+	0.105880i	$0.0337660\pi$
$733$	24.1284	+	29.7961i	0.891202	+	1.10054i	−0.103177	+	0.994663i	$0.532901\pi$
$734$	−0.379860	+	1.16909i	−0.0140209	+	0.0431519i
$735$		0			0
$736$	0.783879	+	2.41253i	0.0288942	+	0.0889271i
$737$	6.65238	−	10.2438i	0.245043	−	0.377334i
$738$	1.07243	+	0.0562037i	0.0394767	+	0.00206889i
$739$	−6.02962	+	28.3671i	−0.221803	+	1.04350i	0.716473	+	0.697615i	$0.245755\pi$
$739$	−6.02962	+	28.3671i	−0.221803	+	1.04350i	−0.938276	+	0.345887i	$0.887578\pi$
$740$		0			0
$741$	0.0114586	+	0.00372314i	0.000420944	+	0.000136773i
$742$	0.0122536	−	0.293752i	0.000449845	−	0.0107840i
$743$	−26.0302	−	26.0302i	−0.954956	−	0.954956i	0.0440723	−	0.999028i	$-0.485967\pi$
$743$	−26.0302	−	26.0302i	−0.954956	−	0.954956i	−0.999028	+	0.0440723i	$0.985967\pi$
$744$	−0.0571151	−	0.00600303i	−0.00209394	−	0.000220082i
$745$		0			0
$746$	0.147768	+	1.40592i	0.00541018	+	0.0514744i
$747$	4.54355	+	11.8364i	0.166240	+	0.433069i
$748$	−10.6996	−	5.45172i	−0.391216	−	0.199335i
$749$	−9.11191	−	27.0578i	−0.332942	−	0.988669i
$750$		0			0
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	0.924648	−	0.380822i	$-0.124359\pi$
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	−0.792126	+	0.610358i	$0.791026\pi$
$752$	−15.4975	−	23.8641i	−0.565137	−	0.870235i
$753$	−1.69051	+	2.08760i	−0.0616055	+	0.0760764i
$754$	0.364429	+	0.162254i	0.0132717	+	0.00590895i
$755$		0			0
$756$	3.37667	−	0.755476i	0.122808	−	0.0274764i
$757$	−19.0809	+	19.0809i	−0.693507	+	0.693507i	−0.963002	−	0.269495i	$-0.913143\pi$
$757$	−19.0809	+	19.0809i	−0.693507	+	0.693507i	0.269495	+	0.963002i	$0.413143\pi$
$758$	−0.111262	+	0.0900982i	−0.00404122	+	0.00327252i
$759$	−0.568187	−	0.631035i	−0.0206239	−	0.0229051i
$760$		0			0
$761$	4.12455	+	3.71376i	0.149515	+	0.134624i	0.740494	−	0.672063i	$-0.234592\pi$
$761$	4.12455	+	3.71376i	0.149515	+	0.134624i	−0.590979	+	0.806687i	$0.701258\pi$
$762$	0.0772023	−	0.0393365i	0.00279674	−	0.00142501i
$763$	−7.38417	−	1.89438i	−0.267325	−	0.0685810i
$764$	−42.5511	+	13.8257i	−1.53944	+	0.500196i
$765$		0			0
$766$	0.447969	−	0.403353i	0.0161858	−	0.0145738i
$767$	5.93643	−	15.4649i	0.214352	−	0.558406i
$768$	1.67704	+	0.449360i	0.0605148	+	0.0162149i
$769$	−19.1561	−	13.9177i	−0.690787	−	0.501886i	0.186131	−	0.982525i	$-0.440405\pi$
$769$	−19.1561	−	13.9177i	−0.690787	−	0.501886i	−0.876919	+	0.480638i	$0.840405\pi$
$770$		0			0
$771$	−1.81130	+	1.31599i	−0.0652324	+	0.0473941i
$772$	−22.7248	+	8.72323i	−0.817883	+	0.313956i
$773$	−37.2561	+	24.1944i	−1.34001	+	0.870213i	−0.997593	−	0.0693350i	$-0.977912\pi$
$773$	−37.2561	+	24.1944i	−1.34001	+	0.870213i	−0.342417	+	0.939548i	$0.611246\pi$
$774$	−0.464337	−	0.268085i	−0.0166902	−	0.00963612i
$775$		0			0
$776$			2.48536i			0.0892193i
$777$	−1.75424	−	1.38983i	−0.0629329	−	0.0498597i
$778$	0.569955	+	0.0902720i	0.0204339	+	0.00323641i
$779$	0.267270	−	0.600299i	0.00957595	−	0.0215079i
$780$		0			0
$781$	−8.59096	+	3.82494i	−0.307409	+	0.136867i
$782$	−0.239130	+	0.892445i	−0.00855127	+	0.0319138i
$783$	−4.27555	+	0.677181i	−0.152796	+	0.0242005i
$784$	−5.22477	+	27.4482i	−0.186599	+	0.980293i
$785$		0			0
$786$	0.00477077	−	0.00529848i	0.000170168	−	0.000188990i
$787$	0.236701	−	4.51652i	0.00843747	−	0.160996i	−0.991161	−	0.132664i	$-0.957647\pi$
$787$	0.236701	−	4.51652i	0.00843747	−	0.160996i	0.999599	−	0.0283326i	$-0.00901975\pi$
$788$	1.39584	−	26.6342i	0.0497246	−	0.948803i
$789$	−0.931469	+	1.03450i	−0.0331612	+	0.0368292i
$790$		0			0
$791$	−23.4162	−	13.1883i	−0.832585	−	0.468920i
$792$	−0.608406	+	0.0963621i	−0.0216188	+	0.00342408i
$793$	−3.15038	+	11.7574i	−0.111873	+	0.417517i
$794$	−0.400914	+	0.178498i	−0.0142279	+	0.00633467i
$795$		0			0
$796$	−14.9081	+	33.4842i	−0.528405	+	1.18682i
$797$	−43.4081	−	6.87517i	−1.53759	−	0.243531i	−0.670588	−	0.741830i	$-0.733958\pi$
$797$	−43.4081	−	6.87517i	−1.53759	−	0.243531i	−0.867005	+	0.498299i	$0.833958\pi$
$798$	−0.000108264	0	0.000734171i	−3.83252e−6	0	2.59894e-5i
$799$		−	31.1283i		−	1.10124i
$800$		0			0
$801$	−20.8334	−	12.0282i	−0.736113	−	0.424995i
$802$	−0.400553	+	0.260122i	−0.0141440	+	0.00918524i
$803$	−0.550876	+	0.211461i	−0.0194400	+	0.00746231i
$804$	−1.56845	+	1.13954i	−0.0553148	+	0.0401886i
$805$		0			0
$806$	−0.171128	−	0.124332i	−0.00602772	−	0.00437940i
$807$	−2.09777	−	0.562096i	−0.0738450	−	0.0197867i
$808$	0.211734	−	0.551587i	0.00744879	−	0.0194048i
$809$	−13.6744	+	12.3125i	−0.480768	+	0.432885i	−0.873541	−	0.486750i	$-0.838182\pi$
$809$	−13.6744	+	12.3125i	−0.480768	+	0.432885i	0.392774	+	0.919635i	$0.371516\pi$
$810$		0			0
$811$	−29.0804	+	9.44881i	−1.02115	+	0.331793i	−0.771287	−	0.636488i	$-0.780387\pi$
$811$	−29.0804	+	9.44881i	−1.02115	+	0.331793i	−0.249866	+	0.968280i	$0.580387\pi$
$812$	8.69260	−	33.8833i	0.305050	−	1.18907i
$813$	0.786087	−	0.400531i	0.0275693	−	0.0140472i
$814$	0.296580	+	0.267042i	0.0103951	+	0.00935980i
$815$		0			0
$816$	1.27449	+	1.41546i	0.0446160	+	0.0495511i
$817$	−0.254963	+	0.206465i	−0.00892004	+	0.00722331i
$818$	0.268156	−	0.268156i	0.00937585	−	0.00937585i
$819$	12.1420	+	3.80245i	0.424277	+	0.132868i
$820$		0			0
$821$	5.77197	+	2.56985i	0.201443	+	0.0896883i	0.504979	−	0.863132i	$-0.331500\pi$
$821$	5.77197	+	2.56985i	0.201443	+	0.0896883i	−0.303535	+	0.952820i	$0.598167\pi$
$822$	−0.0164124	+	0.0202676i	−0.000572447	+	0.000706913i
$823$	−19.1851	−	29.5425i	−0.668752	−	1.02979i	−0.996382	−	0.0849819i	$-0.972917\pi$
$823$	−19.1851	−	29.5425i	−0.668752	−	1.02979i	0.327630	−	0.944806i	$-0.393750\pi$
$824$	−0.575297	−	0.996444i	−0.0200414	−	0.0347128i
$825$		0			0
$826$	1.00023	+	0.201477i	0.0348026	+	0.00701026i
$827$	27.3997	+	13.9609i	0.952782	+	0.485466i	0.860042	−	0.510224i	$-0.170437\pi$
$827$	27.3997	+	13.9609i	0.952782	+	0.485466i	0.0927399	+	0.995690i	$0.470437\pi$
$828$	−12.0857	−	31.4844i	−0.420009	−	1.09416i
$829$	5.00644	+	47.6331i	0.173881	+	1.65437i	0.639066	+	0.769152i	$0.279321\pi$
$829$	5.00644	+	47.6331i	0.173881	+	1.65437i	−0.465185	+	0.885213i	$0.654012\pi$
$830$		0			0
$831$	0.440022	+	0.0462481i	0.0152642	+	0.00160433i
$832$	9.06592	+	9.06592i	0.314304	+	0.314304i
$833$	−21.1476	+	22.0700i	−0.732720	+	0.764679i
$834$	−0.0838916	−	0.0272580i	−0.00290493	−	0.000943869i
$835$		0			0
$836$	−0.0391690	+	0.184276i	−0.00135469	+	0.00637331i
$837$	2.29223	+	0.120130i	0.0792309	+	0.00415232i
$838$	−0.0556087	+	0.0856299i	−0.00192097	+	0.00295803i
$839$	4.53318	+	13.9517i	0.156503	+	0.481666i	0.998310	−	0.0581120i	$-0.0185080\pi$
$839$	4.53318	+	13.9517i	0.156503	+	0.481666i	−0.841807	+	0.539778i	$0.818508\pi$
$840$		0			0
$841$	−4.56193	+	14.0402i	−0.157308	+	0.484144i
$842$	0.788335	+	0.973513i	0.0271678	+	0.0335495i
$843$	0.0363057	+	0.135495i	0.00125043	+	0.00466668i
$844$	−7.75041	−	17.4077i	−0.266780	−	0.599198i
$845$		0			0
$846$	−0.469115	−	0.645681i	−0.0161285	−	0.0221990i
$847$	−4.02282	−	23.7557i	−0.138226	−	0.816256i
$848$	−5.37452	+	10.5481i	−0.184562	+	0.362223i
$849$	0.0296350	−	0.0171098i	0.00101707	−	0.000587205i
$850$		0			0
$851$	−21.8570	+	37.8574i	−0.749249	+	1.29774i
$852$	1.49060	−	0.0781188i	0.0510670	−	0.00267631i
$853$	3.66049	−	23.1114i	0.125333	−	0.791320i	−0.842310	−	0.538994i	$-0.818805\pi$
$853$	3.66049	−	23.1114i	0.125333	−	0.791320i	0.967642	−	0.252326i	$-0.0811954\pi$
$854$	−0.746424	−	0.0704088i	−0.0255421	−	0.00240934i
$855$		0			0
$856$	0.168995	−	1.60788i	0.00577613	−	0.0549562i
$857$	40.5488	−	10.8650i	1.38512	−	0.371142i	0.512143	−	0.858900i	$-0.328852\pi$
$857$	40.5488	−	10.8650i	1.38512	−	0.371142i	0.872979	+	0.487758i	$0.162185\pi$
$858$	0.00846510	+	0.00324945i	0.000288994	+	0.000110934i
$859$	45.8315	−	9.74179i	1.56375	−	0.332386i	0.656947	−	0.753937i	$-0.271848\pi$
$859$	45.8315	−	9.74179i	1.56375	−	0.332386i	0.906805	+	0.421551i	$0.138514\pi$
$860$		0			0
$861$	−1.10091	+	2.54543i	−0.0375188	+	0.0867480i
$862$	−0.529787	−	1.03977i	−0.0180446	−	0.0354146i
$863$	−36.4708	−	23.6844i	−1.24148	−	0.806226i	−0.254500	−	0.967073i	$-0.581911\pi$
$863$	−36.4708	−	23.6844i	−1.24148	−	0.806226i	−0.986979	+	0.160847i	$0.948577\pi$
$864$	0.287515	+	0.0611133i	0.00978147	+	0.00207912i
$865$		0			0
$866$	0.0416274	+	0.195842i	0.00141456	+	0.00665497i
$867$	0.0353423	+	0.223142i	0.00120029	+	0.00757832i
$868$	−8.24399	+	16.6157i	−0.279819	+	0.563972i
$869$	−7.36326	+	10.1347i	−0.249781	+	0.343795i
$870$		0			0
$871$	−14.2081	+	1.49333i	−0.481423	+	0.0505996i
$872$	−0.335479	−	0.271666i	−0.0113608	−	0.00919976i
$873$	−2.59424	−	49.5010i	−0.0878016	−	1.67535i
$874$	0.0144949			0.000490297
$875$		0			0
$876$	0.0936581			0.00316442
$877$	−1.52164	−	29.0345i	−0.0513820	−	0.980427i	−0.895721	−	0.444617i	$-0.853340\pi$
$877$	−1.52164	−	29.0345i	−0.0513820	−	0.980427i	0.844339	−	0.535810i	$-0.179994\pi$
$878$	−0.778436	−	0.630365i	−0.0262709	−	0.0212738i
$879$	2.14306	−	0.225244i	0.0722835	−	0.00759730i
$880$		0			0
$881$	3.61462	−	4.97510i	0.121780	−	0.167616i	−0.743774	−	0.668431i	$-0.766966\pi$
$881$	3.61462	−	4.97510i	0.121780	−	0.167616i	0.865554	+	0.500815i	$0.166966\pi$
$882$	−0.106053	+	0.776489i	−0.00357098	+	0.0261458i
$883$	−4.04343	−	25.5292i	−0.136072	−	0.859126i	−0.957420	−	0.288698i	$-0.906777\pi$
$883$	−4.04343	−	25.5292i	−0.136072	−	0.859126i	0.821348	−	0.570428i	$-0.193223\pi$
$884$	2.92024	+	13.7387i	0.0982184	+	0.462081i
$885$		0			0
$886$	−1.08192	−	0.229970i	−0.0363479	−	0.00772598i
$887$	−29.9286	−	19.4358i	−1.00490	−	0.652591i	−0.0663746	−	0.997795i	$-0.521143\pi$
$887$	−29.9286	−	19.4358i	−1.00490	−	0.652591i	−0.938528	+	0.345204i	$0.887810\pi$
$888$	−0.0575362	−	0.112921i	−0.00193079	−	0.00378938i
$889$	−6.44621	−	55.6166i	−0.216199	−	1.86532i
$890$		0			0
$891$	11.9688	−	2.54406i	0.400971	−	0.0852290i
$892$	−46.8905	−	17.9996i	−1.57001	−	0.602670i
$893$	−0.471712	+	0.126395i	−0.0157852	+	0.00422964i
$894$	0.00840117	−	0.0799318i	0.000280977	−	0.00267332i
$895$		0			0
$896$	−1.83386	+	2.58158i	−0.0612650	+	0.0862444i
$897$	−0.155370	+	0.980964i	−0.00518764	+	0.0327534i
$898$	0.624327	−	0.0327196i	0.0208341	−	0.00109187i
$899$	11.6026	−	20.0963i	0.386968	−	0.670248i
$900$		0			0
$901$	−11.2157	+	6.47536i	−0.373648	+	0.215726i
$902$	0.224511	−	0.440628i	0.00747540	−	0.0146713i
$903$	1.06670	−	0.882811i	0.0354977	−	0.0293781i
$904$	−0.894504	−	1.23118i	−0.0297508	−	0.0409484i
$905$		0			0
$906$	0.0151968	+	0.0341325i	0.000504879	+	0.00113398i
$907$	0.544417	+	2.03179i	0.0180771	+	0.0674645i	0.974375	−	0.224929i	$-0.0722150\pi$
$907$	0.544417	+	2.03179i	0.0180771	+	0.0674645i	−0.956298	+	0.292393i	$0.905548\pi$
$908$	−15.5632	−	19.2190i	−0.516484	−	0.637805i
$909$	−3.64137	+	11.2070i	−0.120777	+	0.371712i
$910$		0			0
$911$	7.06918	+	21.7567i	0.234212	+	0.720831i	0.997225	+	0.0744476i	$0.0237194\pi$
$911$	7.06918	+	21.7567i	0.234212	+	0.720831i	−0.763013	+	0.646383i	$0.776281\pi$
$912$	0.0162746	−	0.0250607i	0.000538907	−	0.000829844i
$913$	5.83038	+	0.305557i	0.192957	+	0.0101125i
$914$	−0.0826361	+	0.388772i	−0.00273336	+	0.0128594i
$915$		0			0
$916$	−28.0726	−	9.12134i	−0.927545	−	0.301378i
$917$	−2.13527	−	4.08243i	−0.0705129	−	0.134814i
$918$	0.0757030	+	0.0757030i	0.00249857	+	0.00249857i
$919$	54.4417	+	5.72206i	1.79587	+	0.188753i	0.942870	−	0.333162i	$-0.108116\pi$
$919$	54.4417	+	5.72206i	1.79587	+	0.188753i	0.852997	+	0.521915i	$0.174782\pi$
$920$		0			0
$921$	0.238181	+	2.26614i	0.00784832	+	0.0746718i
$922$	0.275802	+	0.718488i	0.00908305	+	0.0236621i
$923$	9.80045	+	4.99358i	0.322586	+	0.164366i
$924$	0.157004	−	0.779449i	0.00516505	−	0.0256420i
$925$		0			0
$926$	0.0544855	+	0.0943716i	0.00179050	+	0.00310124i
$927$	12.4983	+	19.2457i	0.410498	+	0.632111i
$928$	1.87008	−	2.30936i	0.0613884	−	0.0758084i
$929$	−7.03630	−	3.13276i	−0.230854	−	0.102783i	0.288050	−	0.957615i	$-0.406993\pi$
$929$	−7.03630	−	3.13276i	−0.230854	−	0.102783i	−0.518904	+	0.854833i	$0.673660\pi$
$930$		0			0
$931$	0.420312	+	0.230852i	0.0137752	+	0.00756587i
$932$	1.71506	−	1.71506i	0.0561786	−	0.0561786i
$933$	0.728463	−	0.589898i	0.0238488	−	0.0193124i
$934$	0.183875	+	0.204214i	0.00601659	+	0.00668210i
$935$		0			0
$936$	0.535428	+	0.482101i	0.0175010	+	0.0157580i
$937$	−11.7089	+	5.96599i	−0.382514	+	0.194901i	−0.634665	−	0.772787i	$-0.718862\pi$
$937$	−11.7089	+	5.96599i	−0.382514	+	0.194901i	0.252151	+	0.967688i	$0.418862\pi$
$938$	−0.236807	−	0.847498i	−0.00773201	−	0.0276718i
$939$	−2.52741	+	0.821204i	−0.0824788	+	0.0267990i
$940$		0			0
$941$	−14.0897	+	12.6864i	−0.459309	+	0.413564i	−0.866033	−	0.499987i	$-0.833338\pi$
$941$	−14.0897	+	12.6864i	−0.459309	+	0.413564i	0.406723	+	0.913551i	$0.366671\pi$
$942$	0.0270898	−	0.0705714i	0.000882634	−	0.00229934i
$943$	52.3224	+	14.0197i	1.70385	+	0.456546i
$944$	−33.2376	−	24.1485i	−1.08179	−	0.785967i
$945$		0			0
$946$	−0.199750	+	0.145127i	−0.00649443	+	0.00471848i
$947$	2.53480	−	0.973020i	0.0823700	−	0.0316189i	−0.316834	−	0.948481i	$-0.602620\pi$
$947$	2.53480	−	0.973020i	0.0823700	−	0.0316189i	0.399204	+	0.916862i	$0.369286\pi$
$948$	1.66758	−	1.08294i	0.0541605	−	0.0351722i
$949$	0.597703	+	0.345084i	0.0194023	+	0.0112019i
$950$		0			0
$951$			0.500039i			0.0162149i
$952$	−1.60920	+	0.637494i	−0.0521543	+	0.0206613i
$953$	29.7958	+	4.71919i	0.965180	+	0.152870i	0.619080	−	0.785328i	$-0.287506\pi$
$953$	29.7958	+	4.71919i	0.965180	+	0.152870i	0.346100	+	0.938197i	$0.387506\pi$
$954$	−0.135056	+	0.303340i	−0.00437258	+	0.00982098i
$955$		0			0
$956$	46.9860	−	20.9195i	1.51964	−	0.676585i
$957$	−0.257453	+	0.960828i	−0.00832228	+	0.0310592i
$958$	0.218450	−	0.0345990i	0.00705779	−	0.00111784i
$959$	8.58125	+	14.5036i	0.277103	+	0.468344i
$960$		0			0
$961$	12.5097	−	13.8934i	0.403539	−	0.448175i
$962$	0.0244299	−	0.466150i	0.000787651	−	0.0150293i
$963$	−1.68756	+	32.2005i	−0.0543808	+	1.03765i
$964$	−18.3202	+	20.3466i	−0.590053	+	0.655320i
$965$		0			0
$966$	−0.0611717		0.000652719i	−0.00196817		2.10009e-5i
$967$	−47.1384	+	7.46599i	−1.51587	+	0.240090i	−0.858239	−	0.513250i	$-0.828441\pi$
$967$	−47.1384	+	7.46599i	−1.51587	+	0.240090i	−0.657631	+	0.753341i	$0.728441\pi$
$968$	0.353121	−	1.31787i	0.0113498	−	0.0423579i
$969$	0.0298630	−	0.0132959i	0.000959339	−	0.000427125i
$970$		0			0
$971$	21.4242	−	48.1195i	0.687535	−	1.54423i	−0.144499	−	0.989505i	$-0.546157\pi$
$971$	21.4242	−	48.1195i	0.687535	−	1.54423i	0.832034	−	0.554724i	$-0.187176\pi$
$972$	−5.79341	−	0.917586i	−0.185824	−	0.0294316i
$973$	−35.3958	+	44.6765i	−1.13474	+	1.43226i
$974$			0.651616i			0.0208791i
$975$		0			0
$976$	26.1441	+	15.0943i	0.836853	+	0.483157i
$977$	35.6446	−	23.1478i	1.14037	−	0.740565i	0.170783	−	0.985309i	$-0.445370\pi$
$977$	35.6446	−	23.1478i	1.14037	−	0.740565i	0.969588	+	0.244744i	$0.0787038\pi$
$978$	−0.0132135	+	0.00507217i	−0.000422520	+	0.000162190i
$979$	−8.96219	+	6.51142i	−0.286433	+	0.208106i
$980$		0			0
$981$	6.96531	+	5.06059i	0.222385	+	0.161572i
$982$	−0.195699	−	0.0524374i	−0.00624500	−	0.00167334i
$983$	−6.71323	+	17.4886i	−0.214119	+	0.557799i	−0.998007	−	0.0631034i	$-0.979900\pi$
$983$	−6.71323	+	17.4886i	−0.214119	+	0.557799i	0.783888	+	0.620902i	$0.213234\pi$
$984$	−0.116705	+	0.105082i	−0.00372043	+	0.00334989i
$985$		0			0
$986$	1.02936	−	0.334458i	0.0327814	−	0.0106513i
$987$	1.98504	−	0.554656i	0.0631844	−	0.0176549i
$988$	0.196335	−	0.100038i	0.00624626	−	0.00318263i
$989$	−20.0981	−	18.0964i	−0.639083	−	0.575433i
$990$		0			0
$991$	14.7280	+	16.3571i	0.467849	+	0.519599i	0.930178	−	0.367109i	$-0.119653\pi$
$991$	14.7280	+	16.3571i	0.467849	+	0.519599i	−0.462328	+	0.886709i	$0.652986\pi$
$992$	−1.22454	+	0.991610i	−0.0388791	+	0.0314836i
$993$	−0.183622	+	0.183622i	−0.00582705	+	0.00582705i
$994$	−0.202471	+	0.646534i	−0.00642199	+	0.0205068i
$995$		0			0
$996$	−0.846577	−	0.376921i	−0.0268248	−	0.0119432i
$997$	−10.4518	+	12.9069i	−0.331013	+	0.408767i	−0.915295	−	0.402784i	$-0.868043\pi$
$997$	−10.4518	+	12.9069i	−0.331013	+	0.408767i	0.584282	+	0.811550i	$0.301376\pi$
$998$	0.0491426	+	0.0756730i	0.00155558	+	0.00239539i
$999$	2.53268	+	4.38674i	0.0801306	+	0.138790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.143.10		288
5.2	odd	4		175.2.x.a.17.9	yes	288
5.3	odd	4		875.2.bb.c.857.10		288
5.4	even	2		875.2.bb.a.143.9		288
7.5	odd	6	inner	875.2.bb.b.768.10		288
25.3	odd	20		875.2.bb.a.507.9		288
25.4	even	10		875.2.bb.c.493.9		288
25.21	even	5		175.2.x.a.3.10	✓	288
25.22	odd	20	inner	875.2.bb.b.507.10		288
35.12	even	12		175.2.x.a.117.10	yes	288
35.19	odd	6		875.2.bb.a.768.9		288
35.33	even	12		875.2.bb.c.607.9		288
175.47	even	60	inner	875.2.bb.b.257.10		288
175.54	odd	30		875.2.bb.c.243.10		288
175.96	odd	30		175.2.x.a.103.9	yes	288
175.103	even	60		875.2.bb.a.257.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.10	✓	288	25.21	even	5
175.2.x.a.17.9	yes	288	5.2	odd	4
175.2.x.a.103.9	yes	288	175.96	odd	30
175.2.x.a.117.10	yes	288	35.12	even	12
875.2.bb.a.143.9		288	5.4	even	2
875.2.bb.a.257.9		288	175.103	even	60
875.2.bb.a.507.9		288	25.3	odd	20
875.2.bb.a.768.9		288	35.19	odd	6
875.2.bb.b.143.10		288	1.1	even	1	trivial
875.2.bb.b.257.10		288	175.47	even	60	inner
875.2.bb.b.507.10		288	25.22	odd	20	inner
875.2.bb.b.768.10		288	7.5	odd	6	inner
875.2.bb.c.243.10		288	175.54	odd	30
875.2.bb.c.493.9		288	25.4	even	10
875.2.bb.c.607.9		288	35.33	even	12
875.2.bb.c.857.10		288	5.3	odd	4

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.00196093 + 0.0374168i) q^{2} +(0.0849253 + 0.0687711i) q^{3} +(1.98765 - 0.208910i) q^{4} +(-0.00240666 + 0.00331248i) q^{6} +(1.46457 + 2.20341i) q^{7} +(0.0234370 + 0.147975i) q^{8} +(-0.621252 - 2.92276i) q^{9} +(-1.34592 - 0.286085i) q^{11} +(0.183169 + 0.118951i) q^{12} +(0.730661 + 1.43400i) q^{13} +(-0.0795726 + 0.0591203i) q^{14} +(3.90435 - 0.829896i) q^{16} +(4.07660 + 1.56486i) q^{17} +(0.108142 - 0.0289766i) q^{18} +(0.00716074 - 0.0681299i) q^{19} +(-0.0271520 + 0.287846i) q^{21} +(0.00806510 - 0.0509210i) q^{22} +(5.63942 - 0.295550i) q^{23} +(-0.00818604 + 0.0141786i) q^{24} +(-0.0522229 + 0.0301509i) q^{26} +(0.297076 - 0.583044i) q^{27} +(3.37137 + 4.07364i) q^{28} +(-3.88840 - 5.35192i) q^{29} +(1.42674 + 3.20452i) q^{31} +(0.116261 + 0.433891i) q^{32} +(-0.0946285 - 0.116856i) q^{33} +(-0.0505580 + 0.155602i) q^{34} +(-1.84543 - 5.67963i) q^{36} +(-4.21599 + 6.49205i) q^{37} +(0.00256324 + 0.000134334i) q^{38} +(-0.0365664 + 0.172031i) q^{39} +(9.12263 + 2.96412i) q^{41} +(-0.0108235 - 0.000451493i) q^{42} +(-3.38639 - 3.38639i) q^{43} +(-2.73499 - 0.287459i) q^{44} +(0.0221170 + 0.210429i) q^{46} +(-2.55469 - 6.65520i) q^{47} +(0.388651 + 0.198028i) q^{48} +(-2.71005 + 6.45412i) q^{49} +(0.238589 + 0.413248i) q^{51} +(1.75187 + 2.69765i) q^{52} +(-1.86647 + 2.30489i) q^{53} +(0.0223982 + 0.00997230i) q^{54} +(-0.291725 + 0.268362i) q^{56} +(0.00529350 - 0.00529350i) q^{57} +(0.192627 - 0.155986i) q^{58} +(-6.88713 - 7.64893i) q^{59} +(5.62046 + 5.06069i) q^{61} +(-0.117105 + 0.0596680i) q^{62} +(5.53018 - 5.64947i) q^{63} +(7.57643 - 2.46173i) q^{64} +(0.00418683 - 0.00376984i) q^{66} +(-3.18113 + 8.28713i) q^{67} +(8.42975 + 2.25874i) q^{68} +(0.499255 + 0.362730i) q^{69} +(5.52909 - 4.01712i) q^{71} +(0.417936 - 0.160431i) q^{72} +(0.359648 - 0.233558i) q^{73} +(-0.251179 - 0.145018i) q^{74} -0.136914i q^{76} +(-1.34084 - 3.38461i) q^{77} +(-0.00650856 - 0.00103085i) q^{78} +(3.70296 - 8.31698i) q^{79} +(-8.12386 + 3.61697i) q^{81} +(-0.0930190 + 0.347152i) q^{82} +(-4.19080 + 0.663758i) q^{83} +(0.00616537 + 0.577808i) q^{84} +(0.120067 - 0.133348i) q^{86} +(0.0378344 - 0.721923i) q^{87} +(0.0107891 - 0.205868i) q^{88} +(5.38706 - 5.98294i) q^{89} +(-2.08959 + 3.71015i) q^{91} +(11.1474 - 1.76558i) q^{92} +(-0.0992118 + 0.370263i) q^{93} +(0.244007 - 0.108639i) q^{94} +(-0.0199657 + 0.0448436i) q^{96} +(16.3848 + 2.59509i) q^{97} +(-0.246806 - 0.0887454i) q^{98} +4.11154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

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