LMFDB - Embedded newform 256.4.g.b.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("256.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.g (of order $8$, degree $4$, 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:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	256.97
Dual form			256.4.g.b.161.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.66269 - 1.10292i) q^{3} +(5.50788 - 13.2972i) q^{5} +(-6.48055 - 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +O(q^{10})$	\(q+(2.66269 - 1.10292i) q^{3} +(5.50788 - 13.2972i) q^{5} +(-6.48055 - 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +(-49.3605 - 20.4458i) q^{11} +(-21.4409 - 51.7628i) q^{13} -41.4811i q^{15} +3.73808i q^{17} +(36.7064 + 88.6171i) q^{19} +(-24.4033 - 10.1082i) q^{21} +(-45.4559 + 45.4559i) q^{23} +(-58.0905 - 58.0905i) q^{25} +(-50.3966 + 121.668i) q^{27} +(-51.9617 + 21.5233i) q^{29} -73.5204 q^{31} -153.982 q^{33} +(-121.867 + 50.4791i) q^{35} +(165.530 - 399.624i) q^{37} +(-114.181 - 114.181i) q^{39} +(334.781 - 334.781i) q^{41} +(-328.962 - 136.261i) q^{43} +(102.962 + 248.573i) q^{45} +185.755i q^{47} -259.005i q^{49} +(4.12282 + 9.95337i) q^{51} +(-412.832 - 171.001i) q^{53} +(-543.744 + 543.744i) q^{55} +(195.476 + 195.476i) q^{57} +(214.856 - 518.709i) q^{59} +(-85.1187 + 35.2573i) q^{61} +171.325 q^{63} -806.394 q^{65} +(252.042 - 104.399i) q^{67} +(-70.9008 + 171.170i) q^{69} +(430.147 + 430.147i) q^{71} +(41.8371 - 41.8371i) q^{73} +(-218.746 - 90.6077i) q^{75} +(187.383 + 452.383i) q^{77} -1211.19i q^{79} -125.180i q^{81} +(290.920 + 702.342i) q^{83} +(49.7061 + 20.5889i) q^{85} +(-114.620 + 114.620i) q^{87} +(365.332 + 365.332i) q^{89} +(-196.503 + 474.400i) q^{91} +(-195.762 + 81.0874i) q^{93} +1380.53 q^{95} +508.891 q^{97} +(922.727 - 382.206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.66269	−	1.10292i	0.512435	−	0.212258i	−0.111455	−	0.993769i	$-0.535551\pi$
$3$	2.66269	−	1.10292i	0.512435	−	0.212258i	0.623890	+	0.781512i	$0.285551\pi$
$4$		0			0
$5$	5.50788	−	13.2972i	0.492640	−	1.18934i	−0.460732	−	0.887539i	$-0.652413\pi$
$5$	5.50788	−	13.2972i	0.492640	−	1.18934i	0.953372	−	0.301798i	$-0.0975870\pi$
$6$		0			0
$7$	−6.48055	−	6.48055i	−0.349917	−	0.349917i	0.510162	−	0.860079i	$-0.329586\pi$
$7$	−6.48055	−	6.48055i	−0.349917	−	0.349917i	−0.860079	+	0.510162i	$0.829586\pi$
$8$		0			0
$9$	−13.2184	+	13.2184i	−0.489570	+	0.489570i
$10$		0			0
$11$	−49.3605	−	20.4458i	−1.35298	−	0.560422i	−0.415858	−	0.909430i	$-0.636519\pi$
$11$	−49.3605	−	20.4458i	−1.35298	−	0.560422i	−0.937120	+	0.349008i	$0.886519\pi$
$12$		0			0
$13$	−21.4409	−	51.7628i	−0.457433	−	1.10434i	−0.969433	−	0.245355i	$-0.921096\pi$
$13$	−21.4409	−	51.7628i	−0.457433	−	1.10434i	0.512001	−	0.858985i	$-0.328904\pi$
$14$		0			0
$15$		−	41.4811i		−	0.714025i
$16$		0			0
$17$			3.73808i			0.0533305i	0.999644	+	0.0266653i	$0.00848882\pi$
$17$			3.73808i			0.0533305i	−0.999644	+	0.0266653i	$0.991511\pi$
$18$		0			0
$19$	36.7064	+	88.6171i	0.443212	+	1.07001i	0.974815	+	0.223015i	$0.0715899\pi$
$19$	36.7064	+	88.6171i	0.443212	+	1.07001i	−0.531603	+	0.846994i	$0.678410\pi$
$20$		0			0
$21$	−24.4033	−	10.1082i	−0.253582	−	0.105037i
$22$		0			0
$23$	−45.4559	+	45.4559i	−0.412097	+	0.412097i	−0.882468	−	0.470372i	$-0.844120\pi$
$23$	−45.4559	+	45.4559i	−0.412097	+	0.412097i	0.470372	+	0.882468i	$0.344120\pi$
$24$		0			0
$25$	−58.0905	−	58.0905i	−0.464724	−	0.464724i
$26$		0			0
$27$	−50.3966	+	121.668i	−0.359216	+	0.867223i
$28$		0			0
$29$	−51.9617	+	21.5233i	−0.332726	+	0.137820i	−0.542791	−	0.839868i	$-0.682632\pi$
$29$	−51.9617	+	21.5233i	−0.332726	+	0.137820i	0.210065	+	0.977687i	$0.432632\pi$
$30$		0			0
$31$	−73.5204			−0.425957			−0.212978	−	0.977057i	$-0.568316\pi$
$31$	−73.5204			−0.425957			−0.212978	+	0.977057i	$0.568316\pi$
$32$		0			0
$33$	−153.982			−0.812267
$34$		0			0
$35$	−121.867	+	50.4791i	−0.588552	+	0.243786i
$36$		0			0
$37$	165.530	−	399.624i	0.735485	−	1.77562i	0.112109	−	0.993696i	$-0.464240\pi$
$37$	165.530	−	399.624i	0.735485	−	1.77562i	0.623376	−	0.781922i	$-0.285760\pi$
$38$		0			0
$39$	−114.181	−	114.181i	−0.468809	−	0.468809i
$40$		0			0
$41$	334.781	−	334.781i	1.27522	−	1.27522i	0.331906	−	0.943312i	$-0.392308\pi$
$41$	334.781	−	334.781i	1.27522	−	1.27522i	0.943312	−	0.331906i	$-0.107692\pi$
$42$		0			0
$43$	−328.962	−	136.261i	−1.16666	−	0.483245i	−0.286570	−	0.958059i	$-0.592515\pi$
$43$	−328.962	−	136.261i	−1.16666	−	0.483245i	−0.880086	+	0.474814i	$0.842515\pi$
$44$		0			0
$45$	102.962	+	248.573i	0.341083	+	0.823446i
$46$		0			0
$47$			185.755i			0.576492i	0.957556	+	0.288246i	$0.0930721\pi$
$47$			185.755i			0.576492i	−0.957556	+	0.288246i	$0.906928\pi$
$48$		0			0
$49$		−	259.005i		−	0.755116i
$50$		0			0
$51$	4.12282	+	9.95337i	0.0113198	+	0.0273284i
$52$		0			0
$53$	−412.832	−	171.001i	−1.06994	−	0.443184i	−0.222971	−	0.974825i	$-0.571576\pi$
$53$	−412.832	−	171.001i	−1.06994	−	0.443184i	−0.846970	+	0.531641i	$0.821576\pi$
$54$		0			0
$55$	−543.744	+	543.744i	−1.33306	+	1.33306i
$56$		0			0
$57$	195.476	+	195.476i	0.454235	+	0.454235i
$58$		0			0
$59$	214.856	−	518.709i	0.474100	−	1.14458i	−0.488235	−	0.872712i	$-0.662359\pi$
$59$	214.856	−	518.709i	0.474100	−	1.14458i	0.962335	−	0.271867i	$-0.0876410\pi$
$60$		0			0
$61$	−85.1187	+	35.2573i	−0.178661	+	0.0740038i	−0.470221	−	0.882549i	$-0.655826\pi$
$61$	−85.1187	+	35.2573i	−0.178661	+	0.0740038i	0.291560	+	0.956553i	$0.405826\pi$
$62$		0			0
$63$	171.325			0.342618
$64$		0			0
$65$	−806.394			−1.53878
$66$		0			0
$67$	252.042	−	104.399i	0.459579	−	0.190364i	−0.140868	−	0.990028i	$-0.544989\pi$
$67$	252.042	−	104.399i	0.459579	−	0.190364i	0.600447	+	0.799665i	$0.294989\pi$
$68$		0			0
$69$	−70.9008	+	171.170i	−0.123702	+	0.298643i
$70$		0			0
$71$	430.147	+	430.147i	0.719001	+	0.719001i	0.968401	−	0.249400i	$-0.0802333\pi$
$71$	430.147	+	430.147i	0.719001	+	0.719001i	−0.249400	+	0.968401i	$0.580233\pi$
$72$		0			0
$73$	41.8371	−	41.8371i	0.0670775	−	0.0670775i	−0.672772	−	0.739850i	$-0.734897\pi$
$73$	41.8371	−	41.8371i	0.0670775	−	0.0670775i	0.739850	+	0.672772i	$0.234897\pi$
$74$		0			0
$75$	−218.746	−	90.6077i	−0.336782	−	0.139500i
$76$		0			0
$77$	187.383	+	452.383i	0.277329	+	0.669531i
$78$		0			0
$79$		−	1211.19i		−	1.72493i	−0.506119	−	0.862464i	$-0.668920\pi$
$79$		−	1211.19i		−	1.72493i	0.506119	−	0.862464i	$-0.331080\pi$
$80$		0			0
$81$		−	125.180i		−	0.171715i
$82$		0			0
$83$	290.920	+	702.342i	0.384730	+	0.928820i	0.991037	+	0.133589i	$0.0426504\pi$
$83$	290.920	+	702.342i	0.384730	+	0.928820i	−0.606307	+	0.795231i	$0.707350\pi$
$84$		0			0
$85$	49.7061	+	20.5889i	0.0634280	+	0.0262727i
$86$		0			0
$87$	−114.620	+	114.620i	−0.141247	+	0.141247i
$88$		0			0
$89$	365.332	+	365.332i	0.435113	+	0.435113i	0.890363	−	0.455250i	$-0.150450\pi$
$89$	365.332	+	365.332i	0.435113	+	0.435113i	−0.455250	+	0.890363i	$0.650450\pi$
$90$		0			0
$91$	−196.503	+	474.400i	−0.226364	+	0.546491i
$92$		0			0
$93$	−195.762	+	81.0874i	−0.218275	+	0.0904126i
$94$		0			0
$95$	1380.53			1.49095
$96$		0			0
$97$	508.891			0.532681			0.266340	−	0.963879i	$-0.414185\pi$
$97$	508.891			0.532681			0.266340	+	0.963879i	$0.414185\pi$
$98$		0			0
$99$	922.727	−	382.206i	0.936743	−	0.388012i
$100$		0			0
$101$	184.802	−	446.152i	0.182065	−	0.439543i	−0.806327	−	0.591470i	$-0.798548\pi$
$101$	184.802	−	446.152i	0.182065	−	0.439543i	0.988392	+	0.151927i	$0.0485479\pi$
$102$		0			0
$103$	−610.875	−	610.875i	−0.584382	−	0.584382i	0.351722	−	0.936104i	$-0.385596\pi$
$103$	−610.875	−	610.875i	−0.584382	−	0.584382i	−0.936104	+	0.351722i	$0.885596\pi$
$104$		0			0
$105$	−268.821	+	268.821i	−0.249849	+	0.249849i
$106$		0			0
$107$	−603.347	−	249.914i	−0.545119	−	0.225796i	0.0930915	−	0.995658i	$-0.470325\pi$
$107$	−603.347	−	249.914i	−0.545119	−	0.225796i	−0.638211	+	0.769862i	$0.720325\pi$
$108$		0			0
$109$	271.916	+	656.462i	0.238943	+	0.576860i	0.997174	−	0.0751265i	$-0.0239361\pi$
$109$	271.916	+	656.462i	0.238943	+	0.576860i	−0.758231	+	0.651986i	$0.773936\pi$
$110$		0			0
$111$		−	1246.64i		−	1.06600i
$112$		0			0
$113$			1651.29i			1.37469i	0.726329	+	0.687347i	$0.241225\pi$
$113$			1651.29i			1.37469i	−0.726329	+	0.687347i	$0.758775\pi$
$114$		0			0
$115$	354.071	+	854.803i	0.287107	+	0.693137i
$116$		0			0
$117$	967.635	+	400.807i	0.764597	+	0.316707i
$118$		0			0
$119$	24.2248	−	24.2248i	0.0186612	−	0.0186612i
$120$		0			0
$121$	1077.27	+	1077.27i	0.809369	+	0.809369i
$122$		0			0
$123$	522.180	−	1260.66i	0.382792	−	0.924142i
$124$		0			0
$125$	569.754	−	236.000i	0.407683	−	0.168868i
$126$		0			0
$127$	313.499			0.219044			0.109522	−	0.993984i	$-0.465068\pi$
$127$	313.499			0.219044			0.109522	+	0.993984i	$0.465068\pi$
$128$		0			0
$129$	−1026.21			−0.700408
$130$		0			0
$131$	−516.522	+	213.951i	−0.344494	+	0.142694i	−0.548221	−	0.836334i	$-0.684695\pi$
$131$	−516.522	+	213.951i	−0.344494	+	0.142694i	0.203726	+	0.979028i	$0.434695\pi$
$132$		0			0
$133$	336.410	−	812.166i	0.219327	−	0.529501i
$134$		0			0
$135$	1340.27	+	1340.27i	0.854458	+	0.854458i
$136$		0			0
$137$	544.876	−	544.876i	0.339795	−	0.339795i	−0.516495	−	0.856290i	$-0.672764\pi$
$137$	544.876	−	544.876i	0.339795	−	0.339795i	0.856290	+	0.516495i	$0.172764\pi$
$138$		0			0
$139$	2149.49	+	890.348i	1.31164	+	0.543297i	0.925361	−	0.379086i	$-0.123762\pi$
$139$	2149.49	+	890.348i	1.31164	+	0.543297i	0.386275	+	0.922384i	$0.373762\pi$
$140$		0			0
$141$	204.873	+	494.608i	0.122365	+	0.295415i
$142$		0			0
$143$			2993.41i			1.75050i
$144$		0			0
$145$			809.493i			0.463619i
$146$		0			0
$147$	−285.662	−	689.650i	−0.160279	−	0.386948i
$148$		0			0
$149$	−1483.83	−	614.624i	−0.815841	−	0.337932i	−0.0645591	−	0.997914i	$-0.520564\pi$
$149$	−1483.83	−	614.624i	−0.815841	−	0.337932i	−0.751282	+	0.659982i	$0.770564\pi$
$150$		0			0
$151$	2047.66	−	2047.66i	1.10355	−	1.10355i	0.109572	−	0.993979i	$-0.465052\pi$
$151$	2047.66	−	2047.66i	1.10355	−	1.10355i	0.993979	−	0.109572i	$-0.0349481\pi$
$152$		0			0
$153$	−49.4115	−	49.4115i	−0.0261090	−	0.0261090i
$154$		0			0
$155$	−404.942	+	977.616i	−0.209843	+	0.506606i
$156$		0			0
$157$	−1545.54	+	640.184i	−0.785653	+	0.325428i	−0.739194	−	0.673492i	$-0.764794\pi$
$157$	−1545.54	+	640.184i	−0.785653	+	0.325428i	−0.0464585	+	0.998920i	$0.514794\pi$
$158$		0			0
$159$	−1287.85			−0.642345
$160$		0			0
$161$	589.159			0.288399
$162$		0			0
$163$	1275.93	−	528.509i	0.613121	−	0.253963i	−0.0544412	−	0.998517i	$-0.517338\pi$
$163$	1275.93	−	528.509i	0.613121	−	0.253963i	0.667562	+	0.744554i	$0.267338\pi$
$164$		0			0
$165$	−848.114	+	2047.53i	−0.400155	+	0.966060i
$166$		0			0
$167$	−1744.38	−	1744.38i	−0.808287	−	0.808287i	0.176088	−	0.984375i	$-0.443656\pi$
$167$	−1744.38	−	1744.38i	−0.808287	−	0.808287i	−0.984375	+	0.176088i	$0.943656\pi$
$168$		0			0
$169$	−666.164	+	666.164i	−0.303215	+	0.303215i
$170$		0			0
$171$	−1656.58	−	686.176i	−0.740828	−	0.306861i
$172$		0			0
$173$	286.418	+	691.473i	0.125872	+	0.303883i	0.974236	−	0.225531i	$-0.0724118\pi$
$173$	286.418	+	691.473i	0.125872	+	0.303883i	−0.848364	+	0.529414i	$0.822412\pi$
$174$		0			0
$175$			752.916i			0.325229i
$176$		0			0
$177$		−	1618.13i		−	0.687154i
$178$		0			0
$179$	−944.647	−	2280.58i	−0.394448	−	0.952282i	−0.988958	−	0.148194i	$-0.952654\pi$
$179$	−944.647	−	2280.58i	−0.394448	−	0.952282i	0.594510	−	0.804088i	$-0.297346\pi$
$180$		0			0
$181$	1523.13	+	630.902i	0.625489	+	0.259086i	0.672835	−	0.739793i	$-0.265076\pi$
$181$	1523.13	+	630.902i	0.625489	+	0.259086i	−0.0473461	+	0.998879i	$0.515076\pi$
$182$		0			0
$183$	−187.759	+	187.759i	−0.0758444	+	0.0758444i
$184$		0			0
$185$	−4402.17	−	4402.17i	−1.74948	−	1.74948i
$186$		0			0
$187$	76.4281	−	184.514i	0.0298876	−	0.0721550i
$188$		0			0
$189$	1115.07	−	461.879i	0.429152	−	0.177760i
$190$		0			0
$191$	−1792.15			−0.678931			−0.339465	−	0.940619i	$-0.610246\pi$
$191$	−1792.15			−0.678931			−0.339465	+	0.940619i	$0.610246\pi$
$192$		0			0
$193$	3221.65			1.20155			0.600776	−	0.799417i	$-0.294858\pi$
$193$	3221.65			1.20155			0.600776	+	0.799417i	$0.294858\pi$
$194$		0			0
$195$	−2147.18	+	889.391i	−0.788527	+	0.326618i
$196$		0			0
$197$	−365.826	+	883.183i	−0.132305	+	0.319412i	−0.976123	−	0.217216i	$-0.930302\pi$
$197$	−365.826	+	883.183i	−0.132305	+	0.319412i	0.843819	+	0.536628i	$0.180302\pi$
$198$		0			0
$199$	198.562	+	198.562i	0.0707321	+	0.0707321i	0.741588	−	0.670856i	$-0.234073\pi$
$199$	198.562	+	198.562i	0.0707321	+	0.0707321i	−0.670856	+	0.741588i	$0.734073\pi$
$200$		0			0
$201$	555.965	−	555.965i	0.195098	−	0.195098i
$202$		0			0
$203$	476.223	+	197.258i	0.164652	+	0.0682010i
$204$		0			0
$205$	−2607.71	−	6295.58i	−0.888442	−	2.14489i
$206$		0			0
$207$		−	1201.71i		−	0.403500i
$208$		0			0
$209$		−	5124.68i		−	1.69608i
$210$		0			0
$211$	−87.1014	−	210.281i	−0.0284185	−	0.0686084i	0.909033	−	0.416724i	$-0.136822\pi$
$211$	−87.1014	−	210.281i	−0.0284185	−	0.0686084i	−0.937452	+	0.348115i	$0.886822\pi$
$212$		0			0
$213$	1619.77	+	670.930i	0.521055	+	0.215828i
$214$		0			0
$215$	−3623.77	+	3623.77i	−1.14948	+	1.14948i
$216$		0			0
$217$	476.453	+	476.453i	0.149049	+	0.149049i
$218$		0			0
$219$	65.2562	−	157.542i	0.0201352	−	0.0486106i
$220$		0			0
$221$	193.494	−	80.1477i	0.0588950	−	0.0243951i
$222$		0			0
$223$	−2508.49			−0.753278			−0.376639	−	0.926360i	$-0.622920\pi$
$223$	−2508.49			−0.753278			−0.376639	+	0.926360i	$0.622920\pi$
$224$		0			0
$225$	1535.73			0.455030
$226$		0			0
$227$	−2537.71	+	1051.15i	−0.741998	+	0.307345i	−0.721472	−	0.692444i	$-0.756534\pi$
$227$	−2537.71	+	1051.15i	−0.741998	+	0.307345i	−0.0205258	+	0.999789i	$0.506534\pi$
$228$		0			0
$229$	−697.363	+	1683.58i	−0.201236	+	0.485826i	−0.991991	−	0.126306i	$-0.959688\pi$
$229$	−697.363	+	1683.58i	−0.201236	+	0.485826i	0.790755	+	0.612132i	$0.209688\pi$
$230$		0			0
$231$	997.888	+	997.888i	0.284226	+	0.284226i
$232$		0			0
$233$	−2051.84	+	2051.84i	−0.576911	+	0.576911i	−0.934051	−	0.357140i	$-0.883752\pi$
$233$	−2051.84	+	2051.84i	−0.576911	+	0.576911i	0.357140	+	0.934051i	$0.383752\pi$
$234$		0			0
$235$	2470.02	+	1023.12i	0.685644	+	0.284003i
$236$		0			0
$237$	−1335.85	−	3225.02i	−0.366129	−	0.883914i
$238$		0			0
$239$			2551.88i			0.690659i	0.938482	+	0.345329i	$0.112233\pi$
$239$			2551.88i			0.690659i	−0.938482	+	0.345329i	$0.887767\pi$
$240$		0			0
$241$			2268.42i			0.606314i	0.952941	+	0.303157i	$0.0980407\pi$
$241$			2268.42i			0.606314i	−0.952941	+	0.303157i	$0.901959\pi$
$242$		0			0
$243$	−1498.77	−	3618.35i	−0.395663	−	0.955216i
$244$		0			0
$245$	−3444.04	−	1426.57i	−0.898088	−	0.372000i
$246$		0			0
$247$	3800.05	−	3800.05i	0.978914	−	0.978914i
$248$		0			0
$249$	1549.26	+	1549.26i	0.394298	+	0.394298i
$250$		0			0
$251$	−2808.05	+	6779.23i	−0.706145	+	1.70479i	0.00326968	+	0.999995i	$0.498959\pi$
$251$	−2808.05	+	6779.23i	−0.706145	+	1.70479i	−0.709415	+	0.704791i	$0.751041\pi$
$252$		0			0
$253$	3173.11	−	1314.35i	0.788505	−	0.326610i
$254$		0			0
$255$	155.060			0.0380793
$256$		0			0
$257$	−2117.45			−0.513942			−0.256971	−	0.966419i	$-0.582724\pi$
$257$	−2117.45			−0.513942			−0.256971	+	0.966419i	$0.582724\pi$
$258$		0			0
$259$	−3662.51	+	1517.06i	−0.878677	+	0.363960i
$260$		0			0
$261$	402.348	−	971.354i	0.0954203	−	0.230365i
$262$		0			0
$263$	632.092	+	632.092i	0.148200	+	0.148200i	0.777313	−	0.629114i	$-0.216582\pi$
$263$	632.092	+	632.092i	0.148200	+	0.148200i	−0.629114	+	0.777313i	$0.716582\pi$
$264$		0			0
$265$	−4547.66	+	4547.66i	−1.05419	+	1.05419i
$266$		0			0
$267$	1375.70	+	569.833i	0.315323	+	0.130611i
$268$		0			0
$269$	−835.101	−	2016.11i	−0.189283	−	0.456968i	0.800539	−	0.599280i	$-0.204546\pi$
$269$	−835.101	−	2016.11i	−0.189283	−	0.456968i	−0.989822	+	0.142312i	$0.954546\pi$
$270$		0			0
$271$			2528.01i			0.566663i	0.959022	+	0.283331i	$0.0914396\pi$
$271$			2528.01i			0.566663i	−0.959022	+	0.283331i	$0.908560\pi$
$272$		0			0
$273$			1479.91i			0.328088i
$274$		0			0
$275$	1679.67	+	4055.08i	0.368320	+	0.889202i
$276$		0			0
$277$	1743.13	+	722.029i	0.378103	+	0.156616i	0.563637	−	0.826022i	$-0.309402\pi$
$277$	1743.13	+	722.029i	0.378103	+	0.156616i	−0.185534	+	0.982638i	$0.559402\pi$
$278$		0			0
$279$	971.822	−	971.822i	0.208536	−	0.208536i
$280$		0			0
$281$	−3983.45	−	3983.45i	−0.845667	−	0.845667i	0.143922	−	0.989589i	$-0.454029\pi$
$281$	−3983.45	−	3983.45i	−0.845667	−	0.845667i	−0.989589	+	0.143922i	$0.954029\pi$
$282$		0			0
$283$	580.183	−	1400.69i	0.121867	−	0.294213i	−0.851159	−	0.524907i	$-0.824100\pi$
$283$	580.183	−	1400.69i	0.121867	−	0.294213i	0.973026	+	0.230695i	$0.0740999\pi$
$284$		0			0
$285$	3675.94	−	1522.62i	0.764013	−	0.316465i
$286$		0			0
$287$	−4339.13			−0.892441
$288$		0			0
$289$	4899.03			0.997156
$290$		0			0
$291$	1355.02	−	561.267i	0.272964	−	0.113066i
$292$		0			0
$293$	797.079	−	1924.32i	0.158928	−	0.383686i	−0.824278	−	0.566185i	$-0.808419\pi$
$293$	797.079	−	1924.32i	0.158928	−	0.383686i	0.983206	+	0.182499i	$0.0584188\pi$
$294$		0			0
$295$	−5713.98	−	5713.98i	−1.12773	−	1.12773i
$296$		0			0
$297$	4975.20	−	4975.20i	0.972021	−	0.972021i
$298$		0			0
$299$	3327.54	+	1378.31i	0.643601	+	0.266588i
$300$		0			0
$301$	1248.81	+	3014.90i	0.239137	+	0.577328i
$302$		0			0
$303$		−	1391.79i		−	0.263882i
$304$		0			0
$305$			1326.03i			0.248946i
$306$		0			0
$307$	−2999.31	−	7240.97i	−0.557588	−	1.34614i	−0.911670	−	0.410923i	$-0.865206\pi$
$307$	−2999.31	−	7240.97i	−0.557588	−	1.34614i	0.354082	−	0.935215i	$-0.384794\pi$
$308$		0			0
$309$	−2300.32	−	952.824i	−0.423498	−	0.175418i
$310$		0			0
$311$	5951.01	−	5951.01i	1.08505	−	1.08505i	0.0890208	−	0.996030i	$-0.471626\pi$
$311$	5951.01	−	5951.01i	1.08505	−	1.08505i	0.996030	−	0.0890208i	$-0.0283738\pi$
$312$		0			0
$313$	2649.88	+	2649.88i	0.478531	+	0.478531i	0.904661	−	0.426131i	$-0.140124\pi$
$313$	2649.88	+	2649.88i	0.478531	+	0.478531i	−0.426131	+	0.904661i	$0.640124\pi$
$314$		0			0
$315$	943.638	−	2278.14i	0.168787	−	0.407488i
$316$		0			0
$317$	−5107.96	+	2115.79i	−0.905021	+	0.374872i	−0.786149	−	0.618038i	$-0.787928\pi$
$317$	−5107.96	+	2115.79i	−0.905021	+	0.374872i	−0.118873	+	0.992910i	$0.537928\pi$
$318$		0			0
$319$	3004.92			0.527408
$320$		0			0
$321$	−1882.16			−0.327265
$322$		0			0
$323$	−331.258	+	137.212i	−0.0570641	+	0.0236367i
$324$		0			0
$325$	−1761.42	+	4252.43i	−0.300633	+	0.725793i
$326$		0			0
$327$	1448.05	+	1448.05i	0.244886	+	0.244886i
$328$		0			0
$329$	1203.79	−	1203.79i	0.201724	−	0.201724i
$330$		0			0
$331$	−2534.49	−	1049.82i	−0.420870	−	0.174330i	0.162189	−	0.986760i	$-0.448145\pi$
$331$	−2534.49	−	1049.82i	−0.420870	−	0.174330i	−0.583059	+	0.812430i	$0.698145\pi$
$332$		0			0
$333$	3094.35	+	7470.43i	0.509218	+	1.22936i
$334$		0			0
$335$		−	3926.47i		−	0.640376i
$336$		0			0
$337$		−	3412.65i		−	0.551629i	−0.961211	−	0.275814i	$-0.911053\pi$
$337$		−	3412.65i		−	0.551629i	0.961211	−	0.275814i	$-0.0889475\pi$
$338$		0			0
$339$	1821.25	+	4396.88i	0.291789	+	0.704442i
$340$		0			0
$341$	3629.01	+	1503.18i	0.576310	+	0.238715i
$342$		0			0
$343$	−3901.32	+	3901.32i	−0.614145	+	0.614145i
$344$		0			0
$345$	1885.56	+	1885.56i	0.294247	+	0.294247i
$346$		0			0
$347$	1608.37	−	3882.95i	0.248824	−	0.600714i	−0.749281	−	0.662252i	$-0.769601\pi$
$347$	1608.37	−	3882.95i	0.248824	−	0.600714i	0.998105	+	0.0615384i	$0.0196007\pi$
$348$		0			0
$349$	−5617.33	+	2326.78i	−0.861573	+	0.356875i	−0.769323	−	0.638861i	$-0.779406\pi$
$349$	−5617.33	+	2326.78i	−0.861573	+	0.356875i	−0.0922505	+	0.995736i	$0.529406\pi$
$350$		0			0
$351$	7378.43			1.12203
$352$		0			0
$353$	−8007.64			−1.20738			−0.603688	−	0.797221i	$-0.706303\pi$
$353$	−8007.64			−1.20738			−0.603688	+	0.797221i	$0.706303\pi$
$354$		0			0
$355$	8088.95	−	3350.55i	1.20934	−	0.500927i
$356$		0			0
$357$	37.7852	−	91.2214i	0.00560169	−	0.0135237i
$358$		0			0
$359$	7420.49	+	7420.49i	1.09092	+	1.09092i	0.995431	+	0.0954845i	$0.0304400\pi$
$359$	7420.49	+	7420.49i	1.09092	+	1.09092i	0.0954845	+	0.995431i	$0.469560\pi$
$360$		0			0
$361$	−1655.59	+	1655.59i	−0.241375	+	0.241375i
$362$		0			0
$363$	4056.58	+	1680.29i	0.586544	+	0.242954i
$364$		0			0
$365$	−325.882	−	786.750i	−0.0467328	−	0.112823i
$366$		0			0
$367$			4739.58i			0.674126i	0.941482	+	0.337063i	$0.109434\pi$
$367$			4739.58i			0.674126i	−0.941482	+	0.337063i	$0.890566\pi$
$368$		0			0
$369$			8850.53i			1.24862i
$370$		0			0
$371$	1567.20	+	3783.56i	0.219313	+	0.529468i
$372$		0			0
$373$	6348.63	+	2629.69i	0.881285	+	0.365040i	0.776995	−	0.629507i	$-0.216743\pi$
$373$	6348.63	+	2629.69i	0.881285	+	0.365040i	0.104290	+	0.994547i	$0.466743\pi$
$374$		0			0
$375$	1256.79	−	1256.79i	0.173068	−	0.173068i
$376$		0			0
$377$	2228.21	+	2228.21i	0.304399	+	0.304399i
$378$		0			0
$379$	2437.33	−	5884.23i	0.330335	−	0.797500i	−0.668230	−	0.743955i	$-0.732948\pi$
$379$	2437.33	−	5884.23i	0.330335	−	0.797500i	0.998565	−	0.0535452i	$-0.0170521\pi$
$380$		0			0
$381$	834.752	−	345.765i	0.112246	−	0.0464937i
$382$		0			0
$383$	205.714			0.0274451			0.0137226	−	0.999906i	$-0.495632\pi$
$383$	205.714			0.0274451			0.0137226	+	0.999906i	$0.495632\pi$
$384$		0			0
$385$	7047.52			0.932921
$386$		0			0
$387$	6149.49	−	2547.20i	0.807743	−	0.334578i
$388$		0			0
$389$	−736.006	+	1776.88i	−0.0959305	+	0.231597i	−0.964559	−	0.263867i	$-0.915002\pi$
$389$	−736.006	+	1776.88i	−0.0959305	+	0.231597i	0.868629	+	0.495464i	$0.165002\pi$
$390$		0			0
$391$	−169.918	−	169.918i	−0.0219773	−	0.0219773i
$392$		0			0
$393$	−1139.37	+	1139.37i	−0.146243	+	0.146243i
$394$		0			0
$395$	−16105.4	−	6671.08i	−2.05152	−	0.849768i
$396$		0			0
$397$	1882.80	+	4545.49i	0.238023	+	0.574638i	0.997078	−	0.0763880i	$-0.0243388\pi$
$397$	1882.80	+	4545.49i	0.238023	+	0.574638i	−0.759055	+	0.651026i	$0.774339\pi$
$398$		0			0
$399$		−	2533.58i		−	0.317889i
$400$		0			0
$401$			6670.63i			0.830712i	0.909659	+	0.415356i	$0.136343\pi$
$401$			6670.63i			0.830712i	−0.909659	+	0.415356i	$0.863657\pi$
$402$		0			0
$403$	1576.34	+	3805.62i	0.194846	+	0.470401i
$404$		0			0
$405$	−1664.54	−	689.476i	−0.204227	−	0.0845935i
$406$		0			0
$407$	−16341.3	+	16341.3i	−1.99019	+	1.99019i
$408$		0			0
$409$	−2441.40	−	2441.40i	−0.295158	−	0.295158i	0.543956	−	0.839114i	$-0.316926\pi$
$409$	−2441.40	−	2441.40i	−0.295158	−	0.295158i	−0.839114	+	0.543956i	$0.816926\pi$
$410$		0			0
$411$	849.880	−	2051.79i	0.101999	−	0.246247i
$412$		0			0
$413$	−4753.91	+	1969.13i	−0.566403	+	0.234612i
$414$		0			0
$415$	10941.5			1.29421
$416$		0			0
$417$	6705.42			0.787448
$418$		0			0
$419$	15396.0	−	6377.25i	1.79510	−	0.743554i	0.806838	−	0.590772i	$-0.201177\pi$
$419$	15396.0	−	6377.25i	1.79510	−	0.743554i	0.988260	−	0.152782i	$-0.0488231\pi$
$420$		0			0
$421$	1566.59	−	3782.09i	0.181356	−	0.437833i	−0.806890	−	0.590702i	$-0.798851\pi$
$421$	1566.59	−	3782.09i	0.181356	−	0.437833i	0.988247	+	0.152868i	$0.0488511\pi$
$422$		0			0
$423$	−2455.38	−	2455.38i	−0.282233	−	0.282233i
$424$		0			0
$425$	217.147	−	217.147i	0.0247840	−	0.0247840i
$426$		0			0
$427$	780.103	+	323.129i	0.0884117	+	0.0366213i
$428$		0			0
$429$	3301.50	+	7970.54i	0.371557	+	0.897019i
$430$		0			0
$431$		−	8391.23i		−	0.937799i	−0.883252	−	0.468899i	$-0.844651\pi$
$431$		−	8391.23i		−	0.937799i	0.883252	−	0.468899i	$-0.155349\pi$
$432$		0			0
$433$		−	14275.6i		−	1.58439i	−0.610270	−	0.792193i	$-0.708939\pi$
$433$		−	14275.6i		−	1.58439i	0.610270	−	0.792193i	$-0.291061\pi$
$434$		0			0
$435$	892.809	+	2155.43i	0.0984067	+	0.237575i
$436$		0			0
$437$	−5696.70	−	2359.65i	−0.623593	−	0.258301i
$438$		0			0
$439$	11181.1	−	11181.1i	1.21559	−	1.21559i	0.246429	−	0.969161i	$-0.420743\pi$
$439$	11181.1	−	11181.1i	1.21559	−	1.21559i	0.969161	−	0.246429i	$-0.0792571\pi$
$440$		0			0
$441$	3423.63	+	3423.63i	0.369682	+	0.369682i
$442$		0			0
$443$	−4372.54	+	10556.2i	−0.468952	+	1.13215i	0.495670	+	0.868511i	$0.334923\pi$
$443$	−4372.54	+	10556.2i	−0.468952	+	1.13215i	−0.964622	+	0.263639i	$0.915077\pi$
$444$		0			0
$445$	6870.09	−	2845.68i	0.731850	−	0.303142i
$446$		0			0
$447$	−4628.87			−0.489794
$448$		0			0
$449$	−9965.25			−1.04741			−0.523707	−	0.851898i	$-0.675451\pi$
$449$	−9965.25			−1.04741			−0.523707	+	0.851898i	$0.675451\pi$
$450$		0			0
$451$	−23369.8	+	9680.09i	−2.44000	+	1.01068i
$452$		0			0
$453$	3193.88	−	7710.70i	0.331261	−	0.799736i
$454$		0			0
$455$	5225.88	+	5225.88i	0.538446	+	0.538446i
$456$		0			0
$457$	11250.2	−	11250.2i	1.15155	−	1.15155i	0.165312	−	0.986241i	$-0.447137\pi$
$457$	11250.2	−	11250.2i	1.15155	−	1.15155i	0.986241	−	0.165312i	$-0.0528632\pi$
$458$		0			0
$459$	−454.805	−	188.387i	−0.0462495	−	0.0191572i
$460$		0			0
$461$	−567.298	−	1369.58i	−0.0573139	−	0.138368i	0.892629	−	0.450793i	$-0.148859\pi$
$461$	−567.298	−	1369.58i	−0.0573139	−	0.138368i	−0.949942	+	0.312425i	$0.898859\pi$
$462$		0			0
$463$		−	1601.42i		−	0.160744i	−0.996765	−	0.0803720i	$-0.974389\pi$
$463$		−	1601.42i		−	0.160744i	0.996765	−	0.0803720i	$-0.0256108\pi$
$464$		0			0
$465$			3049.71i			0.304144i
$466$		0			0
$467$	4458.09	+	10762.8i	0.441747	+	1.06647i	0.975335	+	0.220728i	$0.0708433\pi$
$467$	4458.09	+	10762.8i	0.441747	+	1.06647i	−0.533588	+	0.845744i	$0.679157\pi$
$468$		0			0
$469$	−2309.93	−	956.805i	−0.227426	−	0.0942029i
$470$		0			0
$471$	−3409.22	+	3409.22i	−0.333522	+	0.333522i
$472$		0			0
$473$	13451.8	+	13451.8i	1.30764	+	1.30764i
$474$		0			0
$475$	3015.52	−	7280.10i	0.291287	−	0.703229i
$476$		0			0
$477$	7717.33	−	3196.62i	0.740781	−	0.306841i
$478$		0			0
$479$	−3203.43			−0.305571			−0.152785	−	0.988259i	$-0.548824\pi$
$479$	−3203.43			−0.305571			−0.152785	+	0.988259i	$0.548824\pi$
$480$		0			0
$481$	−24234.8			−2.29732
$482$		0			0
$483$	1568.75	−	649.797i	0.147786	−	0.0612149i
$484$		0			0
$485$	2802.91	−	6766.82i	0.262420	−	0.633537i
$486$		0			0
$487$	−12622.9	−	12622.9i	−1.17454	−	1.17454i	−0.981116	−	0.193422i	$-0.938041\pi$
$487$	−12622.9	−	12622.9i	−1.17454	−	1.17454i	−0.193422	−	0.981116i	$-0.561959\pi$
$488$		0			0
$489$	2814.51	−	2814.51i	0.260279	−	0.260279i
$490$		0			0
$491$	−2183.75	−	904.539i	−0.200716	−	0.0831391i	0.280061	−	0.959982i	$-0.409645\pi$
$491$	−2183.75	−	904.539i	−0.200716	−	0.0831391i	−0.480777	+	0.876843i	$0.659645\pi$
$492$		0			0
$493$	−80.4558	−	194.237i	−0.00734999	−	0.0177444i
$494$		0			0
$495$		−	14374.8i		−	1.30525i
$496$		0			0
$497$		−	5575.18i		−	0.503181i
$498$		0			0
$499$	−3796.86	−	9166.43i	−0.340623	−	0.822336i	−0.997653	−	0.0684718i	$-0.978188\pi$
$499$	−3796.86	−	9166.43i	−0.340623	−	0.822336i	0.657030	−	0.753864i	$-0.271812\pi$
$500$		0			0
$501$	−6568.65	−	2720.82i	−0.585760	−	0.242630i
$502$		0			0
$503$	−5777.19	+	5777.19i	−0.512112	+	0.512112i	−0.915173	−	0.403061i	$-0.867946\pi$
$503$	−5777.19	+	5777.19i	−0.512112	+	0.512112i	0.403061	+	0.915173i	$0.367946\pi$
$504$		0			0
$505$	−4914.71	−	4914.71i	−0.433073	−	0.433073i
$506$		0			0
$507$	−1039.06	+	2508.52i	−0.0910184	+	0.219738i
$508$		0			0
$509$	−10526.2	+	4360.11i	−0.916636	+	0.379683i	−0.790593	−	0.612342i	$-0.790228\pi$
$509$	−10526.2	+	4360.11i	−0.916636	+	0.379683i	−0.126043	+	0.992025i	$0.540228\pi$
$510$		0			0
$511$	−542.255			−0.0469431
$512$		0			0
$513$	−12631.8			−1.08715
$514$		0			0
$515$	−11487.6	+	4758.30i	−0.982917	+	0.407138i
$516$		0			0
$517$	3797.90	−	9168.95i	0.323079	−	0.779981i
$518$		0			0
$519$	1525.28	+	1525.28i	0.129003	+	0.129003i
$520$		0			0
$521$	−3790.76	+	3790.76i	−0.318764	+	0.318764i	−0.848292	−	0.529528i	$-0.822369\pi$
$521$	−3790.76	+	3790.76i	−0.318764	+	0.318764i	0.529528	+	0.848292i	$0.322369\pi$
$522$		0			0
$523$	10160.9	+	4208.78i	0.849531	+	0.351887i	0.764604	−	0.644500i	$-0.222934\pi$
$523$	10160.9	+	4208.78i	0.849531	+	0.351887i	0.0849264	+	0.996387i	$0.472934\pi$
$524$		0			0
$525$	830.409	+	2004.78i	0.0690324	+	0.166659i
$526$		0			0
$527$		−	274.826i		−	0.0227165i
$528$		0			0
$529$			8034.51i			0.660353i
$530$		0			0
$531$	4016.45	+	9696.56i	0.328247	+	0.792457i
$532$		0			0
$533$	−24507.2	−	10151.2i	−1.99160	−	0.824948i
$534$		0			0
$535$	−6646.33	+	6646.33i	−0.537095	+	0.537095i
$536$		0			0
$537$	−5030.61	−	5030.61i	−0.404258	−	0.404258i
$538$		0			0
$539$	−5295.56	+	12784.6i	−0.423184	+	1.02166i
$540$		0			0
$541$	−870.092	+	360.404i	−0.0691463	+	0.0286413i	−0.416989	−	0.908912i	$-0.636914\pi$
$541$	−870.092	+	360.404i	−0.0691463	+	0.0286413i	0.347842	+	0.937553i	$0.386914\pi$
$542$		0			0
$543$	4751.47			0.375516
$544$		0			0
$545$	10226.8			0.803794
$546$		0			0
$547$	−1669.92	+	691.704i	−0.130531	+	0.0540679i	−0.446993	−	0.894537i	$-0.647505\pi$
$547$	−1669.92	+	691.704i	−0.130531	+	0.0540679i	0.316462	+	0.948605i	$0.397505\pi$
$548$		0			0
$549$	659.087	−	1591.18i	0.0512371	−	0.123697i
$550$		0			0
$551$	−3814.66	−	3814.66i	−0.294936	−	0.294936i
$552$		0			0
$553$	−7849.17	+	7849.17i	−0.603581	+	0.603581i
$554$		0			0
$555$	−16576.9	−	6866.36i	−1.26784	−	0.525155i
$556$		0			0
$557$	−4440.93	−	10721.4i	−0.337825	−	0.815581i	−0.997924	−	0.0644026i	$-0.979486\pi$
$557$	−4440.93	−	10721.4i	−0.337825	−	0.815581i	0.660099	−	0.751178i	$-0.270514\pi$
$558$		0			0
$559$			19949.5i			1.50944i
$560$		0			0
$561$		−	575.598i		−	0.0433186i
$562$		0			0
$563$	−4527.75	−	10931.0i	−0.338938	−	0.818268i	−0.997818	−	0.0660203i	$-0.978970\pi$
$563$	−4527.75	−	10931.0i	−0.338938	−	0.818268i	0.658881	−	0.752247i	$-0.271030\pi$
$564$		0			0
$565$	21957.5	+	9095.11i	1.63498	+	0.677229i
$566$		0			0
$567$	−811.235	+	811.235i	−0.0600859	+	0.0600859i
$568$		0			0
$569$	−10557.5	−	10557.5i	−0.777844	−	0.777844i	0.201620	−	0.979464i	$-0.435379\pi$
$569$	−10557.5	−	10557.5i	−0.777844	−	0.777844i	−0.979464	+	0.201620i	$0.935379\pi$
$570$		0			0
$571$	4454.66	−	10754.5i	0.326483	−	0.788199i	−0.672366	−	0.740219i	$-0.734722\pi$
$571$	4454.66	−	10754.5i	0.326483	−	0.788199i	0.998848	−	0.0479798i	$-0.0152783\pi$
$572$		0			0
$573$	−4771.96	+	1976.61i	−0.347908	+	0.144108i
$574$		0			0
$575$	5281.11			0.383022
$576$		0			0
$577$	17387.0			1.25447			0.627234	−	0.778831i	$-0.284187\pi$
$577$	17387.0			1.25447			0.627234	+	0.778831i	$0.284187\pi$
$578$		0			0
$579$	8578.27	−	3553.24i	0.615718	−	0.255039i
$580$		0			0
$581$	2666.25	−	6436.89i	0.190386	−	0.459633i
$582$		0			0
$583$	16881.4	+	16881.4i	1.19924	+	1.19924i
$584$		0			0
$585$	10659.2	−	10659.2i	0.753342	−	0.753342i
$586$		0			0
$587$	−7009.84	−	2903.57i	−0.492891	−	0.204162i	0.122372	−	0.992484i	$-0.460950\pi$
$587$	−7009.84	−	2903.57i	−0.492891	−	0.204162i	−0.615263	+	0.788322i	$0.710950\pi$
$588$		0			0
$589$	−2698.67	−	6515.17i	−0.188789	−	0.455777i
$590$		0			0
$591$			2755.12i			0.191761i
$592$		0			0
$593$		−	10833.0i		−	0.750181i	−0.926988	−	0.375091i	$-0.877612\pi$
$593$		−	10833.0i		−	0.750181i	0.926988	−	0.375091i	$-0.122388\pi$
$594$		0			0
$595$	−188.695	−	455.550i	−0.0130013	−	0.0313878i
$596$		0			0
$597$	747.708	+	309.711i	0.0512590	+	0.0212322i
$598$		0			0
$599$	−3185.59	+	3185.59i	−0.217295	+	0.217295i	−0.807358	−	0.590063i	$-0.799103\pi$
$599$	−3185.59	+	3185.59i	−0.217295	+	0.217295i	0.590063	+	0.807358i	$0.299103\pi$
$600$		0			0
$601$	2409.29	+	2409.29i	0.163522	+	0.163522i	0.784125	−	0.620603i	$-0.213112\pi$
$601$	2409.29	+	2409.29i	0.163522	+	0.163522i	−0.620603	+	0.784125i	$0.713112\pi$
$602$		0			0
$603$	−1951.60	+	4711.57i	−0.131800	+	0.318193i
$604$		0			0
$605$	20258.2	−	8391.20i	1.36134	−	0.563886i
$606$		0			0
$607$	−28227.6			−1.88752			−0.943759	−	0.330636i	$-0.892737\pi$
$607$	−28227.6			−1.88752			−0.943759	+	0.330636i	$0.892737\pi$
$608$		0			0
$609$	1485.60			0.0988496
$610$		0			0
$611$	9615.19	−	3982.74i	0.636643	−	0.263706i
$612$		0			0
$613$	−9916.41	+	23940.3i	−0.653377	+	1.57739i	0.154470	+	0.987998i	$0.450633\pi$
$613$	−9916.41	+	23940.3i	−0.653377	+	1.57739i	−0.807846	+	0.589393i	$0.799367\pi$
$614$		0			0
$615$	−13887.1	−	13887.1i	−0.910538	−	0.910538i
$616$		0			0
$617$	10610.2	−	10610.2i	0.692304	−	0.692304i	−0.270435	−	0.962738i	$-0.587167\pi$
$617$	10610.2	−	10610.2i	0.692304	−	0.692304i	0.962738	+	0.270435i	$0.0871674\pi$
$618$		0			0
$619$	2228.33	+	923.005i	0.144692	+	0.0599333i	0.453854	−	0.891076i	$-0.350049\pi$
$619$	2228.33	+	923.005i	0.144692	+	0.0599333i	−0.309162	+	0.951009i	$0.600049\pi$
$620$		0			0
$621$	−3239.71	−	7821.36i	−0.209348	−	0.505411i
$622$		0			0
$623$		−	4735.10i		−	0.304507i
$624$		0			0
$625$		−	19145.0i		−	1.22528i
$626$		0			0
$627$	−5652.13	−	13645.4i	−0.360007	−	0.869133i
$628$		0			0
$629$	1493.83	+	618.765i	0.0946946	+	0.0392238i
$630$		0			0
$631$	4628.63	−	4628.63i	0.292017	−	0.292017i	−0.545860	−	0.837877i	$-0.683797\pi$
$631$	4628.63	−	4628.63i	0.292017	−	0.292017i	0.837877	+	0.545860i	$0.183797\pi$
$632$		0			0
$633$	−463.848	−	463.848i	−0.0291253	−	0.0291253i
$634$		0			0
$635$	1726.72	−	4168.66i	0.107910	−	0.260517i
$636$		0			0
$637$	−13406.8	+	5553.29i	−0.833905	+	0.345415i
$638$		0			0
$639$	−11371.7			−0.704003
$640$		0			0
$641$	6544.85			0.403286			0.201643	−	0.979459i	$-0.435372\pi$
$641$	6544.85			0.403286			0.201643	+	0.979459i	$0.435372\pi$
$642$		0			0
$643$	−12954.9	+	5366.09i	−0.794543	+	0.329110i	−0.742768	−	0.669548i	$-0.766488\pi$
$643$	−12954.9	+	5366.09i	−0.794543	+	0.329110i	−0.0517744	+	0.998659i	$0.516488\pi$
$644$		0			0
$645$	−5652.24	+	13645.7i	−0.345049	+	0.833022i
$646$		0			0
$647$	6054.03	+	6054.03i	0.367865	+	0.367865i	0.866698	−	0.498833i	$-0.166238\pi$
$647$	6054.03	+	6054.03i	0.367865	+	0.367865i	−0.498833	+	0.866698i	$0.666238\pi$
$648$		0			0
$649$	−21210.8	+	21210.8i	−1.28289	+	1.28289i
$650$		0			0
$651$	1794.14	+	743.156i	0.108015	+	0.0447413i
$652$		0			0
$653$	5840.08	+	14099.2i	0.349985	+	0.844937i	0.996621	+	0.0821390i	$0.0261751\pi$
$653$	5840.08	+	14099.2i	0.349985	+	0.844937i	−0.646636	+	0.762798i	$0.723825\pi$
$654$		0			0
$655$			8046.71i			0.480017i
$656$		0			0
$657$			1106.04i			0.0656783i
$658$		0			0
$659$	7839.56	+	18926.4i	0.463408	+	1.11877i	0.966989	+	0.254818i	$0.0820157\pi$
$659$	7839.56	+	18926.4i	0.463408	+	1.11877i	−0.503581	+	0.863948i	$0.667984\pi$
$660$		0			0
$661$	29468.7	+	12206.3i	1.73404	+	0.718262i	0.999199	+	0.0400217i	$0.0127427\pi$
$661$	29468.7	+	12206.3i	1.73404	+	0.718262i	0.734840	+	0.678241i	$0.237257\pi$
$662$		0			0
$663$	426.817	−	426.817i	0.0250018	−	0.0250018i
$664$		0			0
$665$	−8946.62	−	8946.62i	−0.521707	−	0.521707i
$666$		0			0
$667$	1383.61	−	3340.33i	0.0803202	−	0.193910i
$668$		0			0
$669$	−6679.34	+	2766.67i	−0.386006	+	0.159889i
$670$		0			0
$671$	4922.36			0.283198
$672$		0			0
$673$	17972.6			1.02941			0.514704	−	0.857368i	$-0.327902\pi$
$673$	17972.6			1.02941			0.514704	+	0.857368i	$0.327902\pi$
$674$		0			0
$675$	9995.31	−	4140.19i	0.569955	−	0.236083i
$676$		0			0
$677$	1779.19	−	4295.35i	0.101004	−	0.243846i	−0.865297	−	0.501259i	$-0.832870\pi$
$677$	1779.19	−	4295.35i	0.101004	−	0.243846i	0.966301	+	0.257414i	$0.0828703\pi$
$678$		0			0
$679$	−3297.89	−	3297.89i	−0.186394	−	0.186394i
$680$		0			0
$681$	−5597.79	+	5597.79i	−0.314989	+	0.314989i
$682$		0			0
$683$	7660.17	+	3172.95i	0.429149	+	0.177759i	0.586793	−	0.809737i	$-0.300390\pi$
$683$	7660.17	+	3172.95i	0.429149	+	0.177759i	−0.157645	+	0.987496i	$0.550390\pi$
$684$		0			0
$685$	−4244.21	−	10246.4i	−0.236734	−	0.571527i
$686$		0			0
$687$			5252.00i			0.291668i
$688$		0			0
$689$			25035.8i			1.38431i
$690$		0			0
$691$	−3344.80	−	8075.06i	−0.184142	−	0.444558i	0.804670	−	0.593722i	$-0.202342\pi$
$691$	−3344.80	−	8075.06i	−0.184142	−	0.444558i	−0.988813	+	0.149163i	$0.952342\pi$
$692$		0			0
$693$	−8456.69	−	3502.87i	−0.463554	−	0.192010i
$694$		0			0
$695$	23678.3	−	23678.3i	1.29233	−	1.29233i
$696$		0			0
$697$	1251.44	+	1251.44i	0.0680080	+	0.0680080i
$698$		0			0
$699$	−3200.39	+	7726.43i	−0.173176	+	0.418084i
$700$		0			0
$701$	11050.1	−	4577.09i	0.595371	−	0.246611i	−0.0645882	−	0.997912i	$-0.520573\pi$
$701$	11050.1	−	4577.09i	0.595371	−	0.246611i	0.659960	+	0.751301i	$0.270573\pi$
$702$		0			0
$703$	41489.6			2.22590
$704$		0			0
$705$	7705.32			0.411630
$706$		0			0
$707$	−4088.94	+	1693.69i	−0.217511	+	0.0900960i
$708$		0			0
$709$	−10279.5	+	24817.0i	−0.544508	+	1.31456i	0.377005	+	0.926211i	$0.376954\pi$
$709$	−10279.5	+	24817.0i	−0.544508	+	1.31456i	−0.921513	+	0.388347i	$0.873046\pi$
$710$		0			0
$711$	16010.0	+	16010.0i	0.844473	+	0.844473i
$712$		0			0
$713$	3341.94	−	3341.94i	0.175535	−	0.175535i
$714$		0			0
$715$	39804.0	+	16487.4i	2.08194	+	0.862367i
$716$		0			0
$717$	2814.53	+	6794.87i	0.146598	+	0.353918i
$718$		0			0
$719$			8782.64i			0.455546i	0.973714	+	0.227773i	$0.0731444\pi$
$719$			8782.64i			0.455546i	−0.973714	+	0.227773i	$0.926856\pi$
$720$		0			0
$721$			7917.62i			0.408970i
$722$		0			0
$723$	2501.89	+	6040.10i	0.128695	+	0.310697i
$724$		0			0
$725$	4268.78	+	1768.19i	0.218674	+	0.0905776i
$726$		0			0
$727$	19402.1	−	19402.1i	0.989798	−	0.989798i	−0.0101501	−	0.999948i	$-0.503231\pi$
$727$	19402.1	−	19402.1i	0.989798	−	0.989798i	0.999948	+	0.0101501i	$0.00323095\pi$
$728$		0			0
$729$	−5591.61	−	5591.61i	−0.284083	−	0.284083i
$730$		0			0
$731$	509.353	−	1229.69i	0.0257717	−	0.0622184i
$732$		0			0
$733$	−12567.1	+	5205.47i	−0.633256	+	0.262303i	−0.676136	−	0.736777i	$-0.736347\pi$
$733$	−12567.1	+	5205.47i	−0.633256	+	0.262303i	0.0428799	+	0.999080i	$0.486347\pi$
$734$		0			0
$735$	−10743.8			−0.539172
$736$		0			0
$737$	−14575.4			−0.728484
$738$		0			0
$739$	9220.93	−	3819.43i	0.458995	−	0.190122i	−0.141191	−	0.989982i	$-0.545093\pi$
$739$	9220.93	−	3819.43i	0.458995	−	0.190122i	0.600186	+	0.799860i	$0.295093\pi$
$740$		0			0
$741$	5927.21	−	14309.5i	0.293848	−	0.709412i
$742$		0			0
$743$	−22825.1	−	22825.1i	−1.12702	−	1.12702i	−0.990660	−	0.136355i	$-0.956461\pi$
$743$	−22825.1	−	22825.1i	−1.12702	−	1.12702i	−0.136355	−	0.990660i	$-0.543539\pi$
$744$		0			0
$745$	−16345.5	+	16345.5i	−0.803831	+	0.803831i
$746$		0			0
$747$	−13129.3	−	5438.35i	−0.643075	−	0.266370i
$748$		0			0
$749$	2290.44	+	5529.60i	0.111737	+	0.269756i
$750$		0			0
$751$			16863.5i			0.819384i	0.912224	+	0.409692i	$0.134364\pi$
$751$			16863.5i			0.819384i	−0.912224	+	0.409692i	$0.865636\pi$
$752$		0			0
$753$			21148.1i			1.02348i
$754$		0			0
$755$	−15949.9	−	38506.4i	−0.768842	−	1.85615i
$756$		0			0
$757$	−13042.4	−	5402.33i	−0.626200	−	0.259381i	0.0469375	−	0.998898i	$-0.485054\pi$
$757$	−13042.4	−	5402.33i	−0.626200	−	0.259381i	−0.673138	+	0.739517i	$0.735054\pi$
$758$		0			0
$759$	6999.40	−	6999.40i	0.334733	−	0.334733i
$760$		0			0
$761$	14227.7	+	14227.7i	0.677732	+	0.677732i	0.959487	−	0.281754i	$-0.0909163\pi$
$761$	14227.7	+	14227.7i	0.677732	+	0.677732i	−0.281754	+	0.959487i	$0.590916\pi$
$762$		0			0
$763$	2492.07	−	6016.40i	0.118243	−	0.285463i
$764$		0			0
$765$	−929.187	+	384.882i	−0.0439148	+	0.0181901i
$766$		0			0
$767$	−31456.5			−1.48087
$768$		0			0
$769$	22350.4			1.04808			0.524041	−	0.851693i	$-0.324424\pi$
$769$	22350.4			1.04808			0.524041	+	0.851693i	$0.324424\pi$
$770$		0			0
$771$	−5638.12	+	2335.39i	−0.263362	+	0.109088i
$772$		0			0
$773$	−4110.34	+	9923.25i	−0.191253	+	0.461726i	−0.990197	−	0.139680i	$-0.955393\pi$
$773$	−4110.34	+	9923.25i	−0.191253	+	0.461726i	0.798943	+	0.601406i	$0.205393\pi$
$774$		0			0
$775$	4270.84	+	4270.84i	0.197952	+	0.197952i
$776$		0			0
$777$	−8078.94	+	8078.94i	−0.373012	+	0.373012i
$778$		0			0
$779$	41955.9	+	17378.7i	1.92969	+	0.799302i
$780$		0			0
$781$	−12437.6	−	30027.0i	−0.569849	−	1.37574i
$782$		0			0
$783$		−	7406.78i		−	0.338055i
$784$		0			0
$785$			24077.4i			1.09473i
$786$		0			0
$787$	−8016.15	−	19352.7i	−0.363081	−	0.876555i	−0.994846	−	0.101395i	$-0.967669\pi$
$787$	−8016.15	−	19352.7i	−0.363081	−	0.876555i	0.631765	−	0.775160i	$-0.282331\pi$
$788$		0			0
$789$	2380.22	+	985.918i	0.107399	+	0.0444862i
$790$		0			0
$791$	10701.3	−	10701.3i	0.481029	−	0.481029i
$792$		0			0
$793$	3650.03	+	3650.03i	0.163451	+	0.163451i
$794$		0			0
$795$	−7093.30	+	17124.7i	−0.316445	+	0.763965i
$796$		0			0
$797$	29414.5	−	12183.9i	1.30730	−	0.541500i	0.383203	−	0.923664i	$-0.374821\pi$
$797$	29414.5	−	12183.9i	1.30730	−	0.541500i	0.924095	+	0.382164i	$0.124821\pi$
$798$		0			0
$799$	−694.367			−0.0307446
$800$		0			0
$801$	−9658.19			−0.426037
$802$		0			0
$803$	−2920.49	+	1209.71i	−0.128346	+	0.0531627i
$804$		0			0
$805$	3245.02	−	7834.17i	0.142077	−	0.343004i
$806$		0			0
$807$	−4447.23	−	4447.23i	−0.193990	−	0.193990i
$808$		0			0
$809$	12484.4	−	12484.4i	0.542558	−	0.542558i	−0.381720	−	0.924278i	$-0.624668\pi$
$809$	12484.4	−	12484.4i	0.542558	−	0.542558i	0.924278	+	0.381720i	$0.124668\pi$
$810$		0			0
$811$	9708.35	+	4021.33i	0.420353	+	0.174116i	0.582826	−	0.812597i	$-0.301947\pi$
$811$	9708.35	+	4021.33i	0.420353	+	0.174116i	−0.162473	+	0.986713i	$0.551947\pi$
$812$		0			0
$813$	2788.20	+	6731.31i	0.120279	+	0.290378i
$814$		0			0
$815$		−	19877.3i		−	0.854321i
$816$		0			0
$817$		−	34153.3i		−	1.46251i
$818$		0			0
$819$	−3673.35	−	8868.26i	−0.156725	−	0.378366i
$820$		0			0
$821$	11520.4	+	4771.89i	0.489724	+	0.202850i	0.613860	−	0.789415i	$-0.289616\pi$
$821$	11520.4	+	4771.89i	0.489724	+	0.202850i	−0.124136	+	0.992265i	$0.539616\pi$
$822$		0			0
$823$	6083.57	−	6083.57i	0.257667	−	0.257667i	−0.566438	−	0.824105i	$-0.691679\pi$
$823$	6083.57	−	6083.57i	0.257667	−	0.257667i	0.824105	+	0.566438i	$0.191679\pi$
$824$		0			0
$825$	8944.88	+	8944.88i	0.377480	+	0.377480i
$826$		0			0
$827$	12142.2	−	29314.0i	0.510553	−	1.23258i	−0.433010	−	0.901389i	$-0.642549\pi$
$827$	12142.2	−	29314.0i	0.510553	−	1.23258i	0.943563	−	0.331194i	$-0.107451\pi$
$828$		0			0
$829$	27644.8	−	11450.9i	1.15820	−	0.479740i	0.280922	−	0.959731i	$-0.409360\pi$
$829$	27644.8	−	11450.9i	1.15820	−	0.479740i	0.877274	+	0.479990i	$0.159360\pi$
$830$		0			0
$831$	5437.77			0.226996
$832$		0			0
$833$	968.182			0.0402707
$834$		0			0
$835$	−32803.1	+	13587.5i	−1.35952	+	0.563132i
$836$		0			0
$837$	3705.18	−	8945.09i	0.153010	−	0.369400i
$838$		0			0
$839$	23430.1	+	23430.1i	0.964119	+	0.964119i	0.999378	−	0.0352588i	$-0.0112255\pi$
$839$	23430.1	+	23430.1i	0.964119	+	0.964119i	−0.0352588	+	0.999378i	$0.511226\pi$
$840$		0			0
$841$	−15008.9	+	15008.9i	−0.615394	+	0.615394i
$842$		0			0
$843$	−15000.1	−	6213.26i	−0.612849	−	0.253850i
$844$		0			0
$845$	5188.96	+	12527.3i	0.211249	+	0.510001i
$846$		0			0
$847$		−	13962.6i		−	0.566424i
$848$		0			0
$849$		−	4369.49i		−	0.176632i
$850$		0			0
$851$	10641.0	+	25689.6i	0.428635	+	1.03482i
$852$		0			0
$853$	14855.1	+	6153.17i	0.596281	+	0.246988i	0.660350	−	0.750958i	$-0.270408\pi$
$853$	14855.1	+	6153.17i	0.596281	+	0.246988i	−0.0640694	+	0.997945i	$0.520408\pi$
$854$		0			0
$855$	−18248.4	+	18248.4i	−0.729922	+	0.729922i
$856$		0			0
$857$	−7730.96	−	7730.96i	−0.308150	−	0.308150i	0.536042	−	0.844192i	$-0.319919\pi$
$857$	−7730.96	−	7730.96i	−0.308150	−	0.308150i	−0.844192	+	0.536042i	$0.819919\pi$
$858$		0			0
$859$	−13473.0	+	32526.7i	−0.535149	+	1.29196i	0.392925	+	0.919570i	$0.371463\pi$
$859$	−13473.0	+	32526.7i	−0.535149	+	1.29196i	−0.928075	+	0.372394i	$0.878537\pi$
$860$		0			0
$861$	−11553.8	+	4785.72i	−0.457318	+	0.189427i
$862$		0			0
$863$	35318.4			1.39311			0.696555	−	0.717504i	$-0.254715\pi$
$863$	35318.4			1.39311			0.696555	+	0.717504i	$0.254715\pi$
$864$		0			0
$865$	10772.2			0.423429
$866$		0			0
$867$	13044.6	−	5403.25i	0.510978	−	0.211654i
$868$		0			0
$869$	−24763.7	+	59784.8i	−0.966687	+	2.33379i
$870$		0			0
$871$	−10808.0	−	10808.0i	−0.420453	−	0.420453i
$872$		0			0
$873$	−6726.72	+	6726.72i	−0.260785	+	0.260785i
$874$		0			0
$875$	−5221.73	−	2162.91i	−0.201745	−	0.0835654i
$876$		0			0
$877$	−15599.5	−	37660.6i	−0.600637	−	1.45007i	−0.872927	−	0.487850i	$-0.837781\pi$
$877$	−15599.5	−	37660.6i	−0.600637	−	1.45007i	0.272290	−	0.962215i	$-0.412219\pi$
$878$		0			0
$879$		−	6002.98i		−	0.230348i
$880$		0			0
$881$		−	4797.82i		−	0.183476i	−0.995783	−	0.0917382i	$-0.970758\pi$
$881$		−	4797.82i		−	0.183476i	0.995783	−	0.0917382i	$-0.0292423\pi$
$882$		0			0
$883$	17629.3	+	42560.9i	0.671884	+	1.62207i	0.778406	+	0.627761i	$0.216029\pi$
$883$	17629.3	+	42560.9i	0.671884	+	1.62207i	−0.106522	+	0.994310i	$0.533971\pi$
$884$		0			0
$885$	−21516.6	−	8912.48i	−0.817259	−	0.338520i
$886$		0			0
$887$	−15374.2	+	15374.2i	−0.581978	+	0.581978i	−0.935446	−	0.353469i	$-0.885002\pi$
$887$	−15374.2	+	15374.2i	−0.581978	+	0.581978i	0.353469	+	0.935446i	$0.385002\pi$
$888$		0			0
$889$	−2031.65	−	2031.65i	−0.0766471	−	0.0766471i
$890$		0			0
$891$	−2559.40	+	6178.95i	−0.0962326	+	0.232326i
$892$		0			0
$893$	−16461.1	+	6818.39i	−0.616851	+	0.255508i
$894$		0			0
$895$	−35528.3			−1.32691
$896$		0			0
$897$	10380.4			0.386389
$898$		0			0
$899$	3820.25	−	1582.40i	0.141727	−	0.0587052i
$900$		0			0
$901$	639.215	−	1543.20i	0.0236352	−	0.0570605i
$902$		0			0
$903$	6650.40	+	6650.40i	0.245085	+	0.245085i
$904$		0			0
$905$	16778.5	−	16778.5i	0.616282	−	0.616282i
$906$		0			0
$907$	−39565.2	−	16388.4i	−1.44844	−	0.599965i	−0.486616	−	0.873616i	$-0.661769\pi$
$907$	−39565.2	−	16388.4i	−1.44844	−	0.599965i	−0.961829	+	0.273651i	$0.911769\pi$
$908$		0			0
$909$	3454.63	+	8340.21i	0.126054	+	0.304320i
$910$		0			0
$911$			16563.3i			0.602379i	0.953564	+	0.301189i	$0.0973837\pi$
$911$			16563.3i			0.602379i	−0.953564	+	0.301189i	$0.902616\pi$
$912$		0			0
$913$		−	40616.1i		−	1.47228i
$914$		0			0
$915$	1462.51	+	3530.82i	0.0528406	+	0.127569i
$916$		0			0
$917$	4733.87	+	1960.83i	0.170476	+	0.0706133i
$918$		0			0
$919$	−21215.7	+	21215.7i	−0.761526	+	0.761526i	−0.976598	−	0.215072i	$-0.931001\pi$
$919$	−21215.7	+	21215.7i	−0.761526	+	0.761526i	0.215072	+	0.976598i	$0.431001\pi$
$920$		0			0
$921$	−15972.5	−	15972.5i	−0.571456	−	0.571456i
$922$		0			0
$923$	13042.9	−	31488.3i	0.465127	−	1.12292i
$924$		0			0
$925$	−32830.1	+	13598.7i	−1.16697	+	0.483374i
$926$		0			0
$927$	16149.6			0.572192
$928$		0			0
$929$	−2955.93			−0.104393			−0.0521963	−	0.998637i	$-0.516622\pi$
$929$	−2955.93			−0.104393			−0.0521963	+	0.998637i	$0.516622\pi$
$930$		0			0
$931$	22952.3	−	9507.14i	0.807981	−	0.334677i
$932$		0			0
$933$	9282.20	−	22409.2i	0.325708	−	0.786328i
$934$		0			0
$935$	−2032.56	−	2032.56i	−0.0710928	−	0.0710928i
$936$		0			0
$937$	8962.97	−	8962.97i	0.312495	−	0.312495i	−0.533381	−	0.845875i	$-0.679079\pi$
$937$	8962.97	−	8962.97i	0.312495	−	0.312495i	0.845875	+	0.533381i	$0.179079\pi$
$938$		0			0
$939$	9978.43	+	4133.20i	0.346788	+	0.143644i
$940$		0			0
$941$	19192.4	+	46334.5i	0.664882	+	1.60517i	0.790058	+	0.613033i	$0.210051\pi$
$941$	19192.4	+	46334.5i	0.664882	+	1.60517i	−0.125176	+	0.992135i	$0.539949\pi$
$942$		0			0
$943$			30435.5i			1.05103i
$944$		0			0
$945$		−	17371.3i		−	0.597978i
$946$		0			0
$947$	−6058.72	−	14627.0i	−0.207901	−	0.501916i	0.785192	−	0.619253i	$-0.212564\pi$
$947$	−6058.72	−	14627.0i	−0.207901	−	0.501916i	−0.993092	+	0.117336i	$0.962564\pi$
$948$		0			0
$949$	−3062.63	−	1268.58i	−0.104760	−	0.0433929i
$950$		0			0
$951$	−11267.4	+	11267.4i	−0.384195	+	0.384195i
$952$		0			0
$953$	−10134.7	−	10134.7i	−0.344487	−	0.344487i	0.513564	−	0.858051i	$-0.328325\pi$
$953$	−10134.7	−	10134.7i	−0.344487	−	0.344487i	−0.858051	+	0.513564i	$0.828325\pi$
$954$		0			0
$955$	−9870.97	+	23830.6i	−0.334468	+	0.807478i
$956$		0			0
$957$	8001.17	−	3314.19i	0.270262	−	0.111946i
$958$		0			0
$959$	−7062.19			−0.237800
$960$		0			0
$961$	−24385.7			−0.818561
$962$		0			0
$963$	11278.7	−	4671.81i	0.377417	−	0.156331i
$964$		0			0
$965$	17744.5	−	42839.0i	0.591933	−	1.42905i
$966$		0			0
$967$	−28442.7	−	28442.7i	−0.945869	−	0.945869i	0.0527388	−	0.998608i	$-0.483205\pi$
$967$	−28442.7	−	28442.7i	−0.945869	−	0.945869i	−0.998608	+	0.0527388i	$0.983205\pi$
$968$		0			0
$969$	−730.705	+	730.705i	−0.0242246	+	0.0242246i
$970$		0			0
$971$	−43067.2	−	17839.0i	−1.42337	−	0.589579i	−0.467664	−	0.883906i	$-0.654904\pi$
$971$	−43067.2	−	17839.0i	−1.42337	−	0.589579i	−0.955705	+	0.294328i	$0.904904\pi$
$972$		0			0
$973$	−8159.94	−	19699.8i	−0.268855	−	0.649072i
$974$		0			0
$975$			13265.6i			0.435733i
$976$		0			0
$977$		−	4088.33i		−	0.133877i	−0.997757	−	0.0669383i	$-0.978677\pi$
$977$		−	4088.33i		−	0.133877i	0.997757	−	0.0669383i	$-0.0213231\pi$
$978$		0			0
$979$	−10563.5	−	25502.4i	−0.344851	−	0.832545i
$980$		0			0
$981$	−12271.7	−	5083.09i	−0.399393	−	0.165434i
$982$		0			0
$983$	−19001.7	+	19001.7i	−0.616541	+	0.616541i	−0.944643	−	0.328101i	$-0.893591\pi$
$983$	−19001.7	+	19001.7i	−0.616541	+	0.616541i	0.328101	+	0.944643i	$0.393591\pi$
$984$		0			0
$985$	9728.93	+	9728.93i	0.314710	+	0.314710i
$986$		0			0
$987$	1877.64	−	4533.02i	0.0605531	−	0.146188i
$988$		0			0
$989$	21147.1	−	8759.43i	0.679919	−	0.281632i
$990$		0			0
$991$	−31837.0			−1.02052			−0.510261	−	0.860020i	$-0.670451\pi$
$991$	−31837.0			−1.02052			−0.510261	+	0.860020i	$0.670451\pi$
$992$		0			0
$993$	−7906.43			−0.252672
$994$		0			0
$995$	3733.97	−	1546.66i	0.118970	−	0.0492789i
$996$		0			0
$997$	12897.2	−	31136.5i	0.409686	−	0.989070i	−0.575534	−	0.817778i	$-0.695206\pi$
$997$	12897.2	−	31136.5i	0.409686	−	0.989070i	0.985220	−	0.171292i	$-0.0547943\pi$
$998$		0			0
$999$	40279.4	+	40279.4i	1.27566	+	1.27566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.b.97.8		44
4.3	odd	2		256.4.g.a.97.4		44
8.3	odd	2		128.4.g.a.49.8		44
8.5	even	2		32.4.g.a.21.6	✓	44
32.3	odd	8		256.4.g.a.161.4		44
32.13	even	8		32.4.g.a.29.6	yes	44
32.19	odd	8		128.4.g.a.81.8		44
32.29	even	8	inner	256.4.g.b.161.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.6	✓	44	8.5	even	2
32.4.g.a.29.6	yes	44	32.13	even	8
128.4.g.a.49.8		44	8.3	odd	2
128.4.g.a.81.8		44	32.19	odd	8
256.4.g.a.97.4		44	4.3	odd	2
256.4.g.a.161.4		44	32.3	odd	8
256.4.g.b.97.8		44	1.1	even	1	trivial
256.4.g.b.161.8		44	32.29	even	8	inner

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.66269 - 1.10292i) q^{3} +(5.50788 - 13.2972i) q^{5} +(-6.48055 - 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +O(q^{10})\)	\(q+(2.66269 - 1.10292i) q^{3} +(5.50788 - 13.2972i) q^{5} +(-6.48055 - 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +(-49.3605 - 20.4458i) q^{11} +(-21.4409 - 51.7628i) q^{13} -41.4811i q^{15} +3.73808i q^{17} +(36.7064 + 88.6171i) q^{19} +(-24.4033 - 10.1082i) q^{21} +(-45.4559 + 45.4559i) q^{23} +(-58.0905 - 58.0905i) q^{25} +(-50.3966 + 121.668i) q^{27} +(-51.9617 + 21.5233i) q^{29} -73.5204 q^{31} -153.982 q^{33} +(-121.867 + 50.4791i) q^{35} +(165.530 - 399.624i) q^{37} +(-114.181 - 114.181i) q^{39} +(334.781 - 334.781i) q^{41} +(-328.962 - 136.261i) q^{43} +(102.962 + 248.573i) q^{45} +185.755i q^{47} -259.005i q^{49} +(4.12282 + 9.95337i) q^{51} +(-412.832 - 171.001i) q^{53} +(-543.744 + 543.744i) q^{55} +(195.476 + 195.476i) q^{57} +(214.856 - 518.709i) q^{59} +(-85.1187 + 35.2573i) q^{61} +171.325 q^{63} -806.394 q^{65} +(252.042 - 104.399i) q^{67} +(-70.9008 + 171.170i) q^{69} +(430.147 + 430.147i) q^{71} +(41.8371 - 41.8371i) q^{73} +(-218.746 - 90.6077i) q^{75} +(187.383 + 452.383i) q^{77} -1211.19i q^{79} -125.180i q^{81} +(290.920 + 702.342i) q^{83} +(49.7061 + 20.5889i) q^{85} +(-114.620 + 114.620i) q^{87} +(365.332 + 365.332i) q^{89} +(-196.503 + 474.400i) q^{91} +(-195.762 + 81.0874i) q^{93} +1380.53 q^{95} +508.891 q^{97} +(922.727 - 382.206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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