LMFDB - Embedded newform 100.4.i.a.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(9,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

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("100.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	100.89
Dual form			100.4.i.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.71349 - 1.53150i) q^{3} +(3.20187 - 10.7121i) q^{5} +16.8592i q^{7} +(-1.97201 - 1.43275i) q^{9} +O(q^{10})$	\(q+(-4.71349 - 1.53150i) q^{3} +(3.20187 - 10.7121i) q^{5} +16.8592i q^{7} +(-1.97201 - 1.43275i) q^{9} +(-47.8389 + 34.7570i) q^{11} +(-3.71191 + 5.10901i) q^{13} +(-31.4975 + 45.5874i) q^{15} +(-125.140 + 40.6606i) q^{17} +(-25.3925 - 78.1500i) q^{19} +(25.8199 - 79.4654i) q^{21} +(93.7224 + 128.998i) q^{23} +(-104.496 - 68.5972i) q^{25} +(85.7543 + 118.031i) q^{27} +(15.4646 - 47.5950i) q^{29} +(-13.8066 - 42.4924i) q^{31} +(278.718 - 90.5611i) q^{33} +(180.596 + 53.9808i) q^{35} +(44.1117 - 60.7145i) q^{37} +(25.3205 - 18.3964i) q^{39} +(-286.091 - 207.857i) q^{41} -79.3703i q^{43} +(-21.6618 + 16.5368i) q^{45} +(-289.874 - 94.1857i) q^{47} +58.7686 q^{49} +652.120 q^{51} +(322.676 + 104.844i) q^{53} +(219.145 + 623.740i) q^{55} +407.248i q^{57} +(-636.533 - 462.468i) q^{59} +(675.055 - 490.456i) q^{61} +(24.1549 - 33.2464i) q^{63} +(42.8429 + 56.1206i) q^{65} +(-578.147 + 187.851i) q^{67} +(-244.198 - 751.566i) q^{69} +(-18.9894 + 58.4435i) q^{71} +(-23.2607 - 32.0156i) q^{73} +(387.484 + 483.368i) q^{75} +(-585.973 - 806.523i) q^{77} +(-178.592 + 549.648i) q^{79} +(-203.100 - 625.077i) q^{81} +(50.7554 - 16.4914i) q^{83} +(34.8749 + 1470.70i) q^{85} +(-145.784 + 200.654i) q^{87} +(-1170.83 + 850.656i) q^{89} +(-86.1336 - 62.5797i) q^{91} +221.432i q^{93} +(-918.450 + 21.7793i) q^{95} +(50.9127 + 16.5425i) q^{97} +144.136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) $ 32 * q + 6 * q^5 + 122 * q^9	$ 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) $ 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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			0
$2$		0			0
$3$	−4.71349	−	1.53150i	−0.907111	−	0.294738i	−0.181942	−	0.983309i	$-0.558238\pi$
$3$	−4.71349	−	1.53150i	−0.907111	−	0.294738i	−0.725169	+	0.688571i	$0.758238\pi$
$4$		0			0
$5$	3.20187	−	10.7121i	0.286384	−	0.958115i
$5$	3.20187	−	10.7121i	0.286384	−	0.958115i
$6$		0			0
$7$			16.8592i			0.910309i	0.890412	+	0.455155i	$0.150416\pi$
$7$			16.8592i			0.910309i	−0.890412	+	0.455155i	$0.849584\pi$
$8$		0			0
$9$	−1.97201	−	1.43275i	−0.0730373	−	0.0530647i
$10$		0			0
$11$	−47.8389	+	34.7570i	−1.31127	+	0.952693i	−0.311272	+	0.950321i	$0.600755\pi$
$11$	−47.8389	+	34.7570i	−1.31127	+	0.952693i	−0.999997	+	0.00237169i	$0.999245\pi$
$12$		0			0
$13$	−3.71191	+	5.10901i	−0.0791922	+	0.108999i	−0.846775	−	0.531951i	$-0.821459\pi$
$13$	−3.71191	+	5.10901i	−0.0791922	+	0.108999i	0.767583	+	0.640949i	$0.221459\pi$
$14$		0			0
$15$	−31.4975	+	45.5874i	−0.542175	+	0.784708i
$16$		0			0
$17$	−125.140	+	40.6606i	−1.78535	+	0.580097i	−0.999277	−	0.0380312i	$-0.987891\pi$
$17$	−125.140	+	40.6606i	−1.78535	+	0.580097i	−0.786078	+	0.618128i	$0.787891\pi$
$18$		0			0
$19$	−25.3925	−	78.1500i	−0.306602	−	0.943623i	−0.979075	−	0.203501i	$-0.934768\pi$
$19$	−25.3925	−	78.1500i	−0.306602	−	0.943623i	0.672473	−	0.740122i	$-0.265232\pi$
$20$		0			0
$21$	25.8199	−	79.4654i	0.268303	−	0.825752i
$22$		0			0
$23$	93.7224	+	128.998i	0.849672	+	1.16947i	0.983935	+	0.178528i	$0.0571335\pi$
$23$	93.7224	+	128.998i	0.849672	+	1.16947i	−0.134262	+	0.990946i	$0.542866\pi$
$24$		0			0
$25$	−104.496	−	68.5972i	−0.835968	−	0.548777i
$26$		0			0
$27$	85.7543	+	118.031i	0.611238	+	0.841297i
$28$		0			0
$29$	15.4646	−	47.5950i	0.0990240	−	0.304765i	−0.889257	−	0.457407i	$-0.848778\pi$
$29$	15.4646	−	47.5950i	0.0990240	−	0.304765i	0.988281	+	0.152642i	$0.0487783\pi$
$30$		0			0
$31$	−13.8066	−	42.4924i	−0.0799917	−	0.246189i	0.903061	−	0.429512i	$-0.141315\pi$
$31$	−13.8066	−	42.4924i	−0.0799917	−	0.246189i	−0.983053	+	0.183323i	$0.941315\pi$
$32$		0			0
$33$	278.718	−	90.5611i	1.47026	−	0.477717i
$34$		0			0
$35$	180.596	+	53.9808i	0.872181	+	0.260698i
$36$		0			0
$37$	44.1117	−	60.7145i	0.195998	−	0.269768i	−0.699695	−	0.714442i	$-0.746681\pi$
$37$	44.1117	−	60.7145i	0.195998	−	0.269768i	0.895692	+	0.444674i	$0.146681\pi$
$38$		0			0
$39$	25.3205	−	18.3964i	0.103962	−	0.0755330i
$40$		0			0
$41$	−286.091	−	207.857i	−1.08975	−	0.791752i	−0.110395	−	0.993888i	$-0.535212\pi$
$41$	−286.091	−	207.857i	−1.08975	−	0.791752i	−0.979357	+	0.202136i	$0.935212\pi$
$42$		0			0
$43$		−	79.3703i		−	0.281485i	−0.990046	−	0.140743i	$-0.955051\pi$
$43$		−	79.3703i		−	0.281485i	0.990046	−	0.140743i	$-0.0449490\pi$
$44$		0			0
$45$	−21.6618	+	16.5368i	−0.0717588	+	0.0547812i
$46$		0			0
$47$	−289.874	−	94.1857i	−0.899626	−	0.292306i	−0.177543	−	0.984113i	$-0.556815\pi$
$47$	−289.874	−	94.1857i	−0.899626	−	0.292306i	−0.722083	+	0.691807i	$0.756815\pi$
$48$		0			0
$49$	58.7686			0.171337
$50$		0			0
$51$	652.120			1.79049
$52$		0			0
$53$	322.676	+	104.844i	0.836282	+	0.271725i	0.695689	−	0.718343i	$-0.255099\pi$
$53$	322.676	+	104.844i	0.836282	+	0.271725i	0.140593	+	0.990067i	$0.455099\pi$
$54$		0			0
$55$	219.145	+	623.740i	0.537263	+	1.52918i
$56$		0			0
$57$			407.248i			0.946338i
$58$		0			0
$59$	−636.533	−	462.468i	−1.40457	−	1.02048i	−0.994084	−	0.108610i	$-0.965360\pi$
$59$	−636.533	−	462.468i	−1.40457	−	1.02048i	−0.410483	−	0.911868i	$-0.634640\pi$
$60$		0			0
$61$	675.055	−	490.456i	1.41692	−	1.02945i	0.424645	−	0.905360i	$-0.360399\pi$
$61$	675.055	−	490.456i	1.41692	−	1.02945i	0.992271	−	0.124090i	$-0.0396011\pi$
$62$		0			0
$63$	24.1549	−	33.2464i	0.0483053	−	0.0664865i
$64$		0			0
$65$	42.8429	+	56.1206i	0.0817540	+	0.107091i
$66$		0			0
$67$	−578.147	+	187.851i	−1.05421	+	0.342533i	−0.784318	−	0.620359i	$-0.786987\pi$
$67$	−578.147	+	187.851i	−1.05421	+	0.342533i	−0.269889	+	0.962891i	$0.586987\pi$
$68$		0			0
$69$	−244.198	−	751.566i	−0.426059	−	1.31127i
$70$		0			0
$71$	−18.9894	+	58.4435i	−0.0317413	+	0.0976897i	−0.965672	−	0.259764i	$-0.916355\pi$
$71$	−18.9894	+	58.4435i	−0.0317413	+	0.0976897i	0.933931	+	0.357454i	$0.116355\pi$
$72$		0			0
$73$	−23.2607	−	32.0156i	−0.0372940	−	0.0513307i	0.789963	−	0.613155i	$-0.210100\pi$
$73$	−23.2607	−	32.0156i	−0.0372940	−	0.0513307i	−0.827257	+	0.561824i	$0.810100\pi$
$74$		0			0
$75$	387.484	+	483.368i	0.596570	+	0.744194i
$76$		0			0
$77$	−585.973	−	806.523i	−0.867245	−	1.19366i
$78$		0			0
$79$	−178.592	+	549.648i	−0.254343	+	0.782788i	0.739615	+	0.673030i	$0.235008\pi$
$79$	−178.592	+	549.648i	−0.254343	+	0.782788i	−0.993958	+	0.109758i	$0.964992\pi$
$80$		0			0
$81$	−203.100	−	625.077i	−0.278601	−	0.857445i
$82$		0			0
$83$	50.7554	−	16.4914i	0.0671220	−	0.0218093i	−0.275264	−	0.961369i	$-0.588765\pi$
$83$	50.7554	−	16.4914i	0.0671220	−	0.0218093i	0.342386	+	0.939560i	$0.388765\pi$
$84$		0			0
$85$	34.8749	+	1470.70i	0.0445026	+	1.87670i
$86$		0			0
$87$	−145.784	+	200.654i	−0.179652	+	0.247269i
$88$		0			0
$89$	−1170.83	+	850.656i	−1.39447	+	1.01314i	−0.399107	+	0.916904i	$0.630680\pi$
$89$	−1170.83	+	850.656i	−1.39447	+	1.01314i	−0.995359	+	0.0962343i	$0.969320\pi$
$90$		0			0
$91$	−86.1336	−	62.5797i	−0.0992226	−	0.0720894i
$92$		0			0
$93$			221.432i			0.246898i
$94$		0			0
$95$	−918.450	+	21.7793i	−0.991905	+	0.0235212i
$96$		0			0
$97$	50.9127	+	16.5425i	0.0532928	+	0.0173159i	0.335542	−	0.942025i	$-0.391081\pi$
$97$	50.9127	+	16.5425i	0.0532928	+	0.0173159i	−0.282249	+	0.959341i	$0.591081\pi$
$98$		0			0
$99$	144.136			0.146326
$100$		0			0
$101$	−47.2102			−0.0465108			−0.0232554	−	0.999730i	$-0.507403\pi$
$101$	−47.2102			−0.0465108			−0.0232554	+	0.999730i	$0.507403\pi$
$102$		0			0
$103$	139.952	+	45.4731i	0.133882	+	0.0435009i	0.375192	−	0.926947i	$-0.377577\pi$
$103$	139.952	+	45.4731i	0.133882	+	0.0435009i	−0.241310	+	0.970448i	$0.577577\pi$
$104$		0			0
$105$	−768.566	−	531.022i	−0.714327	−	0.493547i
$106$		0			0
$107$			1350.74i			1.22038i	0.792254	+	0.610192i	$0.208908\pi$
$107$			1350.74i			1.22038i	−0.792254	+	0.610192i	$0.791092\pi$
$108$		0			0
$109$	220.694	+	160.344i	0.193933	+	0.140900i	0.680514	−	0.732735i	$-0.261756\pi$
$109$	220.694	+	160.344i	0.193933	+	0.140900i	−0.486582	+	0.873635i	$0.661756\pi$
$110$		0			0
$111$	−300.904	+	218.620i	−0.257302	+	0.186941i
$112$		0			0
$113$	371.744	−	511.662i	0.309476	−	0.425957i	−0.625742	−	0.780030i	$-0.715204\pi$
$113$	371.744	−	511.662i	0.309476	−	0.425957i	0.935218	+	0.354073i	$0.115204\pi$
$114$		0			0
$115$	1681.92	−	590.925i	1.36382	−	0.479165i
$116$		0			0
$117$	14.6398	−	4.75677i	0.0115680	−	0.00375866i
$118$		0			0
$119$	−685.504	−	2109.76i	−0.528067	−	1.62522i
$120$		0			0
$121$	669.208	−	2059.61i	0.502786	−	1.54742i
$122$		0			0
$123$	1030.15	+	1417.88i	0.755167	+	1.03940i
$124$		0			0
$125$	−1069.40	+	899.728i	−0.765200	+	0.643793i
$126$		0			0
$127$	−538.581	−	741.293i	−0.376310	−	0.517946i	0.578293	−	0.815829i	$-0.303719\pi$
$127$	−538.581	−	741.293i	−0.376310	−	0.517946i	−0.954602	+	0.297884i	$0.903719\pi$
$128$		0			0
$129$	−121.556	+	374.111i	−0.0829644	+	0.255338i
$130$		0			0
$131$	202.335	+	622.722i	0.134947	+	0.415324i	0.995582	−	0.0938986i	$-0.0299330\pi$
$131$	202.335	+	622.722i	0.134947	+	0.415324i	−0.860635	+	0.509223i	$0.829933\pi$
$132$		0			0
$133$	1317.54	−	428.096i	0.858989	−	0.279102i
$134$		0			0
$135$	1538.93	−	540.686i	0.981108	−	0.344702i
$136$		0			0
$137$	333.970	−	459.671i	0.208270	−	0.286659i	−0.692084	−	0.721817i	$-0.743307\pi$
$137$	333.970	−	459.671i	0.208270	−	0.286659i	0.900354	+	0.435158i	$0.143307\pi$
$138$		0			0
$139$	2079.69	−	1510.98i	1.26904	−	0.922014i	0.269879	−	0.962894i	$-0.413016\pi$
$139$	2079.69	−	1510.98i	1.26904	−	0.922014i	0.999164	+	0.0408805i	$0.0130163\pi$
$140$		0			0
$141$	1222.07	+	887.886i	0.729907	+	0.530308i
$142$		0			0
$143$		−	373.424i		−	0.218373i
$144$		0			0
$145$	−460.325	−	318.050i	−0.263641	−	0.182156i
$146$		0			0
$147$	−277.005	−	90.0044i	−0.155422	−	0.0504996i
$148$		0			0
$149$	3146.97			1.73027			0.865134	−	0.501541i	$-0.167233\pi$
$149$	3146.97			1.73027			0.865134	+	0.501541i	$0.167233\pi$
$150$		0			0
$151$	−1560.39			−0.840946			−0.420473	−	0.907305i	$-0.638136\pi$
$151$	−1560.39			−0.840946			−0.420473	+	0.907305i	$0.638136\pi$
$152$		0			0
$153$	305.034	+	99.1116i	0.161180	+	0.0523706i
$154$		0			0
$155$	−499.388	+	11.8421i	−0.258786	+	0.00613663i
$156$		0			0
$157$			2777.66i			1.41198i	0.708219	+	0.705992i	$0.249499\pi$
$157$			2777.66i			1.41198i	−0.708219	+	0.705992i	$0.750501\pi$
$158$		0			0
$159$	−1360.36	−	988.360i	−0.678513	−	0.492969i
$160$		0			0
$161$	−2174.79	+	1580.08i	−1.06458	+	0.773465i
$162$		0			0
$163$	−319.367	+	439.571i	−0.153465	+	0.211226i	−0.878826	−	0.477142i	$-0.841673\pi$
$163$	−319.367	+	439.571i	−0.153465	+	0.211226i	0.725361	+	0.688368i	$0.241673\pi$
$164$		0			0
$165$	−77.6750	−	3275.61i	−0.0366484	−	1.54549i
$166$		0			0
$167$	458.479	−	148.969i	0.212444	−	0.0690273i	−0.200862	−	0.979620i	$-0.564374\pi$
$167$	458.479	−	148.969i	0.212444	−	0.0690273i	0.413306	+	0.910592i	$0.364374\pi$
$168$		0			0
$169$	666.587	+	2051.54i	0.303408	+	0.933793i
$170$		0			0
$171$	−61.8950	+	190.493i	−0.0276797	+	0.0851893i
$172$		0			0
$173$	−2069.40	−	2848.28i	−0.909442	−	1.25174i	−0.967357	−	0.253418i	$-0.918445\pi$
$173$	−2069.40	−	2848.28i	−0.909442	−	1.25174i	0.0579150	−	0.998322i	$-0.481555\pi$
$174$		0			0
$175$	1156.49	−	1761.72i	0.499557	−	0.760990i
$176$		0			0
$177$	2292.02	+	3154.69i	0.973325	+	1.33967i
$178$		0			0
$179$	−468.991	+	1443.41i	−0.195833	+	0.602711i	0.804133	+	0.594449i	$0.202630\pi$
$179$	−468.991	+	1443.41i	−0.195833	+	0.602711i	−0.999966	+	0.00826192i	$0.997370\pi$
$180$		0			0
$181$	1017.44	+	3131.37i	0.417823	+	1.28593i	0.909702	+	0.415262i	$0.136310\pi$
$181$	1017.44	+	3131.37i	0.417823	+	1.28593i	−0.491879	+	0.870664i	$0.663690\pi$
$182$		0			0
$183$	−3933.00	+	1277.91i	−1.58872	+	0.516206i
$184$		0			0
$185$	−509.137	−	666.926i	−0.202338	−	0.265045i
$186$		0			0
$187$	4573.34	−	6294.66i	1.78843	−	2.46156i
$188$		0			0
$189$	−1989.90	+	1445.75i	−0.765841	+	0.556416i
$190$		0			0
$191$	−3404.02	−	2473.17i	−1.28956	−	0.936922i	−0.289765	−	0.957098i	$-0.593577\pi$
$191$	−3404.02	−	2473.17i	−1.28956	−	0.936922i	−0.999796	+	0.0201762i	$0.993577\pi$
$192$		0			0
$193$			1843.42i			0.687524i	0.939057	+	0.343762i	$0.111701\pi$
$193$			1843.42i			0.687524i	−0.939057	+	0.343762i	$0.888299\pi$
$194$		0			0
$195$	−115.991	−	330.138i	−0.0425962	−	0.121239i
$196$		0			0
$197$	−3542.01	−	1150.87i	−1.28101	−	0.416224i	−0.412071	−	0.911152i	$-0.635195\pi$
$197$	−3542.01	−	1150.87i	−1.28101	−	0.416224i	−0.868934	+	0.494928i	$0.835195\pi$
$198$		0			0
$199$	324.095			0.115450			0.0577248	−	0.998333i	$-0.481615\pi$
$199$	324.095			0.115450			0.0577248	+	0.998333i	$0.481615\pi$
$200$		0			0
$201$	3012.78			1.05724
$202$		0			0
$203$	802.412	+	260.720i	0.277430	+	0.0901425i
$204$		0			0
$205$	−3142.60	+	2399.09i	−1.07068	+	0.817363i
$206$		0			0
$207$		−	388.665i		−	0.130503i
$208$		0			0
$209$	3931.00	+	2856.04i	1.30102	+	0.945246i
$210$		0			0
$211$	−3043.05	+	2210.91i	−0.992855	+	0.721352i	−0.960545	−	0.278126i	$-0.910287\pi$
$211$	−3043.05	+	2210.91i	−0.992855	+	0.721352i	−0.0323107	+	0.999478i	$0.510287\pi$
$212$		0			0
$213$	179.013	−	246.390i	0.0575858	−	0.0792600i
$214$		0			0
$215$	−850.219	−	254.133i	−0.269695	−	0.0806128i
$216$		0			0
$217$	716.387	−	232.768i	0.224108	−	0.0728172i
$218$		0			0
$219$	60.6070	+	186.529i	0.0187006	+	0.0575546i
$220$		0			0
$221$	256.775	−	790.272i	0.0781564	−	0.240541i
$222$		0			0
$223$	−1628.08	−	2240.86i	−0.488898	−	0.672911i	0.491286	−	0.870998i	$-0.336527\pi$
$223$	−1628.08	−	2240.86i	−0.488898	−	0.672911i	−0.980184	+	0.198088i	$0.936527\pi$
$224$		0			0
$225$	107.785	+	284.990i	0.0319362	+	0.0844416i
$226$		0			0
$227$	−1038.20	−	1428.96i	−0.303559	−	0.417813i	0.629800	−	0.776757i	$-0.283137\pi$
$227$	−1038.20	−	1428.96i	−0.303559	−	0.417813i	−0.933359	+	0.358945i	$0.883137\pi$
$228$		0			0
$229$	−332.536	+	1023.44i	−0.0959588	+	0.295331i	−0.987502	−	0.157604i	$-0.949623\pi$
$229$	−332.536	+	1023.44i	−0.0959588	+	0.295331i	0.891544	+	0.452935i	$0.149623\pi$
$230$		0			0
$231$	1526.78	+	4698.96i	0.434870	+	1.33839i
$232$		0			0
$233$	−3225.67	+	1048.08i	−0.906955	+	0.294688i	−0.725105	−	0.688639i	$-0.758209\pi$
$233$	−3225.67	+	1048.08i	−0.906955	+	0.294688i	−0.181850	+	0.983326i	$0.558209\pi$
$234$		0			0
$235$	−1937.06	+	2803.57i	−0.537702	+	0.778234i
$236$		0			0
$237$	1683.58	−	2317.25i	0.461435	−	0.635111i
$238$		0			0
$239$	−3460.57	+	2514.25i	−0.936594	+	0.680475i	−0.947598	−	0.319464i	$-0.896497\pi$
$239$	−3460.57	+	2514.25i	−0.936594	+	0.680475i	0.0110046	+	0.999939i	$0.496497\pi$
$240$		0			0
$241$	−1761.89	−	1280.09i	−0.470927	−	0.342149i	0.326875	−	0.945067i	$-0.394004\pi$
$241$	−1761.89	−	1280.09i	−0.470927	−	0.342149i	−0.797803	+	0.602919i	$0.794004\pi$
$242$		0			0
$243$		−	681.796i		−	0.179989i
$244$		0			0
$245$	188.169	−	629.532i	0.0490682	−	0.164161i
$246$		0			0
$247$	493.523	+	160.355i	0.127134	+	0.0413084i
$248$		0			0
$249$	−264.492			−0.0673152
$250$		0			0
$251$	3829.18			0.962931			0.481465	−	0.876465i	$-0.340105\pi$
$251$	3829.18			0.962931			0.481465	+	0.876465i	$0.340105\pi$
$252$		0			0
$253$	−8967.14	−	2913.60i	−2.22830	−	0.724018i
$254$		0			0
$255$	2088.00	−	6985.54i	0.512768	−	1.71550i
$256$		0			0
$257$			1052.72i			0.255513i	0.991806	+	0.127757i	$0.0407776\pi$
$257$			1052.72i			0.255513i	−0.991806	+	0.127757i	$0.959222\pi$
$258$		0			0
$259$	1023.60	+	743.686i	0.245572	+	0.178419i
$260$		0			0
$261$	−98.6878	+	71.7009i	−0.0234047	+	0.0170045i
$262$		0			0
$263$	−2377.23	+	3271.97i	−0.557361	+	0.767142i	−0.990988	−	0.133951i	$-0.957234\pi$
$263$	−2377.23	+	3271.97i	−0.557361	+	0.767142i	0.433627	+	0.901093i	$0.357234\pi$
$264$		0			0
$265$	2156.26	−	3120.83i	0.499841	−	0.723437i
$266$		0			0
$267$	6821.46	−	2216.43i	1.56355	−	0.508027i
$268$		0			0
$269$	1125.70	+	3464.56i	0.255150	+	0.785272i	0.993800	+	0.111182i	$0.0354638\pi$
$269$	1125.70	+	3464.56i	0.255150	+	0.785272i	−0.738650	+	0.674090i	$0.764536\pi$
$270$		0			0
$271$	−893.315	+	2749.34i	−0.200240	+	0.616275i	0.799635	+	0.600486i	$0.205026\pi$
$271$	−893.315	+	2749.34i	−0.200240	+	0.616275i	−0.999875	+	0.0157892i	$0.994974\pi$
$272$		0			0
$273$	310.148	+	426.883i	0.0687584	+	0.0946378i
$274$		0			0
$275$	7383.20	−	350.355i	1.61900	−	0.0768262i
$276$		0			0
$277$	2661.63	+	3663.41i	0.577334	+	0.794633i	0.993400	−	0.114702i	$-0.0365913\pi$
$277$	2661.63	+	3663.41i	0.577334	+	0.794633i	−0.416066	+	0.909335i	$0.636591\pi$
$278$		0			0
$279$	−33.6541	+	103.577i	−0.00722158	+	0.0222257i
$280$		0			0
$281$	934.864	+	2877.21i	0.198467	+	0.610819i	0.999919	+	0.0127594i	$0.00406156\pi$
$281$	934.864	+	2877.21i	0.198467	+	0.610819i	−0.801451	+	0.598060i	$0.795938\pi$
$282$		0			0
$283$	5425.06	−	1762.71i	1.13953	−	0.370255i	0.322338	−	0.946625i	$-0.395531\pi$
$283$	5425.06	−	1762.71i	1.13953	−	0.370255i	0.817189	+	0.576370i	$0.195531\pi$
$284$		0			0
$285$	4362.46	+	1303.95i	0.906700	+	0.271016i
$286$		0			0
$287$	3504.30	−	4823.25i	0.720739	−	0.992012i
$288$		0			0
$289$	10032.2	−	7288.78i	2.04196	−	1.48357i
$290$		0			0
$291$	−214.641	−	155.946i	−0.0432388	−	0.0314148i
$292$		0			0
$293$		−	6874.37i		−	1.37067i	−0.728230	−	0.685333i	$-0.759657\pi$
$293$		−	6874.37i		−	1.37067i	0.728230	−	0.685333i	$-0.240343\pi$
$294$		0			0
$295$	−6992.08	+	5337.81i	−1.37998	+	1.05349i
$296$		0			0
$297$	−8204.78	−	2665.89i	−1.60300	−	0.520845i
$298$		0			0
$299$	−1006.94			−0.194759
$300$		0			0
$301$	1338.12			0.256238
$302$		0			0
$303$	222.524	+	72.3026i	0.0421904	+	0.0137085i
$304$		0			0
$305$	−3092.35	−	8801.59i	−0.580549	−	1.65239i
$306$		0			0
$307$			4653.22i			0.865060i	0.901620	+	0.432530i	$0.142379\pi$
$307$			4653.22i			0.865060i	−0.901620	+	0.432530i	$0.857621\pi$
$308$		0			0
$309$	−590.018	−	428.674i	−0.108625	−	0.0789203i
$310$		0			0
$311$	−4202.31	+	3053.16i	−0.766210	+	0.556684i	−0.900809	−	0.434216i	$-0.857025\pi$
$311$	−4202.31	+	3053.16i	−0.766210	+	0.556684i	0.134599	+	0.990900i	$0.457025\pi$
$312$		0			0
$313$	2799.64	−	3853.37i	0.505574	−	0.695863i	−0.477591	−	0.878582i	$-0.658490\pi$
$313$	2799.64	−	3853.37i	0.505574	−	0.695863i	0.983165	+	0.182719i	$0.0584899\pi$
$314$		0			0
$315$	−278.796	−	365.199i	−0.0498679	−	0.0653227i
$316$		0			0
$317$	5960.65	−	1936.73i	1.05610	−	0.343148i	0.271040	−	0.962568i	$-0.412632\pi$
$317$	5960.65	−	1936.73i	1.05610	−	0.343148i	0.785060	+	0.619420i	$0.212632\pi$
$318$		0			0
$319$	914.452	+	2814.39i	0.160500	+	0.493968i
$320$		0			0
$321$	2068.67	−	6366.70i	0.359694	−	1.10702i
$322$		0			0
$323$	6355.25	+	8747.25i	1.09478	+	1.50684i
$324$		0			0
$325$	738.344	−	279.245i	0.126018	−	0.0476606i
$326$		0			0
$327$	−794.671	−	1093.77i	−0.134390	−	0.184971i
$328$		0			0
$329$	1587.89	−	4887.03i	0.266089	−	0.818938i
$330$		0			0
$331$	−2918.94	−	8983.56i	−0.484711	−	1.49179i	−0.832399	−	0.554176i	$-0.813033\pi$
$331$	−2918.94	−	8983.56i	−0.484711	−	1.49179i	0.347688	−	0.937610i	$-0.386967\pi$
$332$		0			0
$333$	−173.977	+	56.5285i	−0.0286303	+	0.00930254i
$334$		0			0
$335$	161.122	+	6794.61i	0.0262777	+	1.10815i
$336$		0			0
$337$	−6480.14	+	8919.14i	−1.04746	+	1.44171i	−0.156478	+	0.987681i	$0.550014\pi$
$337$	−6480.14	+	8919.14i	−1.04746	+	1.44171i	−0.890987	+	0.454030i	$0.849986\pi$
$338$		0			0
$339$	−2535.83	+	1842.39i	−0.406275	+	0.295176i
$340$		0			0
$341$	2137.40	+	1552.91i	0.339433	+	0.246613i
$342$		0			0
$343$			6773.48i			1.06628i
$344$		0			0
$345$	−8832.70	+	209.451i	−1.37837	+	0.0326854i
$346$		0			0
$347$	−9594.55	−	3117.46i	−1.48433	−	0.482288i	−0.548927	−	0.835870i	$-0.684964\pi$
$347$	−9594.55	−	3117.46i	−1.48433	−	0.482288i	−0.935404	+	0.353582i	$0.884964\pi$
$348$		0			0
$349$	−7071.09			−1.08455			−0.542273	−	0.840202i	$-0.682436\pi$
$349$	−7071.09			−1.08455			−0.542273	+	0.840202i	$0.682436\pi$
$350$		0			0
$351$	−921.332			−0.140106
$352$		0			0
$353$	9680.64	+	3145.43i	1.45963	+	0.474262i	0.927956	−	0.372689i	$-0.121564\pi$
$353$	9680.64	+	3145.43i	1.45963	+	0.474262i	0.531671	+	0.846951i	$0.321564\pi$
$354$		0			0
$355$	565.248	+	390.544i	0.0845078	+	0.0583886i
$356$		0			0
$357$			10994.2i			1.62990i
$358$		0			0
$359$	−2756.36	−	2002.61i	−0.405223	−	0.294412i	0.366442	−	0.930441i	$-0.380576\pi$
$359$	−2756.36	−	2002.61i	−0.405223	−	0.294412i	−0.771665	+	0.636029i	$0.780576\pi$
$360$		0			0
$361$	86.4079	−	62.7790i	0.0125977	−	0.00915280i
$362$		0			0
$363$	−6308.61	+	8683.05i	−0.912165	+	1.25549i
$364$		0			0
$365$	−417.431	+	146.660i	−0.0598611	+	0.0210316i
$366$		0			0
$367$	6336.96	−	2059.00i	0.901326	−	0.292859i	0.178542	−	0.983932i	$-0.442862\pi$
$367$	6336.96	−	2059.00i	0.901326	−	0.292859i	0.722784	+	0.691074i	$0.242862\pi$
$368$		0			0
$369$	266.366	+	819.791i	0.0375785	+	0.115655i
$370$		0			0
$371$	−1767.58	+	5440.05i	−0.247353	+	0.761275i
$372$		0			0
$373$	−3602.45	−	4958.34i	−0.500074	−	0.688293i	0.482132	−	0.876099i	$-0.339863\pi$
$373$	−3602.45	−	4958.34i	−0.500074	−	0.688293i	−0.982206	+	0.187805i	$0.939863\pi$
$374$		0			0
$375$	6418.54	−	2603.07i	0.883872	−	0.358458i
$376$		0			0
$377$	185.760	+	255.677i	0.0253770	+	0.0349285i
$378$		0			0
$379$	3610.91	−	11113.2i	0.489393	−	1.50620i	−0.336124	−	0.941818i	$-0.609116\pi$
$379$	3610.91	−	11113.2i	0.489393	−	1.50620i	0.825517	−	0.564378i	$-0.190884\pi$
$380$		0			0
$381$	1403.30	+	4318.91i	0.188696	+	0.580747i
$382$		0			0
$383$	9743.83	−	3165.96i	1.29996	−	0.422384i	0.424395	−	0.905477i	$-0.360487\pi$
$383$	9743.83	−	3165.96i	1.29996	−	0.422384i	0.875569	+	0.483093i	$0.160487\pi$
$384$		0			0
$385$	−10515.7	+	3694.59i	−1.39203	+	0.489075i
$386$		0			0
$387$	−113.718	+	156.519i	−0.0149369	+	0.0205589i
$388$		0			0
$389$	−3651.69	+	2653.11i	−0.475960	+	0.345805i	−0.799759	−	0.600321i	$-0.795040\pi$
$389$	−3651.69	+	2653.11i	−0.475960	+	0.345805i	0.323800	+	0.946126i	$0.395040\pi$
$390$		0			0
$391$	−16973.6	−	12332.0i	−2.19537	−	1.59503i
$392$		0			0
$393$		−	3245.07i		−	0.416519i
$394$		0			0
$395$	5316.03	+	3672.98i	0.677161	+	0.467868i
$396$		0			0
$397$	−11189.7	−	3635.76i	−1.41460	−	0.459631i	−0.500716	−	0.865612i	$-0.666930\pi$
$397$	−11189.7	−	3635.76i	−1.41460	−	0.459631i	−0.913881	+	0.405981i	$0.866930\pi$
$398$		0			0
$399$	−6865.85			−0.861460
$400$		0			0
$401$	6156.96			0.766743			0.383371	−	0.923594i	$-0.374763\pi$
$401$	6156.96			0.766743			0.383371	+	0.923594i	$0.374763\pi$
$402$		0			0
$403$	268.343	+	87.1900i	0.0331690	+	0.0107773i
$404$		0			0
$405$	−7346.16	+	174.201i	−0.901317	+	0.0213731i
$406$		0			0
$407$			4437.70i			0.540463i
$408$		0			0
$409$	4636.63	+	3368.71i	0.560554	+	0.407266i	0.831662	−	0.555283i	$-0.187390\pi$
$409$	4636.63	+	3368.71i	0.560554	+	0.407266i	−0.271108	+	0.962549i	$0.587390\pi$
$410$		0			0
$411$	−2278.15	+	1655.17i	−0.273413	+	0.198647i
$412$		0			0
$413$	7796.82	−	10731.4i	0.928951	−	1.27859i
$414$		0			0
$415$	−14.1448	−	596.498i	−0.00167312	−	0.0705564i
$416$		0			0
$417$	−12116.7	+	3936.94i	−1.42292	+	0.462333i
$418$		0			0
$419$	−484.018	−	1489.65i	−0.0564339	−	0.173686i	0.918866	−	0.394569i	$-0.129106\pi$
$419$	−484.018	−	1489.65i	−0.0564339	−	0.173686i	−0.975300	+	0.220883i	$0.929106\pi$
$420$		0			0
$421$	4904.78	−	15095.4i	0.567801	−	1.74751i	−0.0916782	−	0.995789i	$-0.529223\pi$
$421$	4904.78	−	15095.4i	0.567801	−	1.74751i	0.659479	−	0.751723i	$-0.270777\pi$
$422$		0			0
$423$	436.689	+	601.050i	0.0501951	+	0.0690876i
$424$		0			0
$425$	15865.9	+	4335.41i	1.81084	+	0.494820i
$426$		0			0
$427$	8268.68	+	11380.9i	0.937118	+	1.28983i
$428$		0			0
$429$	−571.900	+	1760.13i	−0.0643627	+	0.198088i
$430$		0			0
$431$	3851.68	+	11854.2i	0.430461	+	1.32482i	0.897667	+	0.440674i	$0.145261\pi$
$431$	3851.68	+	11854.2i	0.430461	+	1.32482i	−0.467206	+	0.884149i	$0.654739\pi$
$432$		0			0
$433$	−13943.4	+	4530.50i	−1.54753	+	0.502822i	−0.953441	−	0.301579i	$-0.902486\pi$
$433$	−13943.4	+	4530.50i	−1.54753	+	0.502822i	−0.594086	+	0.804401i	$0.702486\pi$
$434$		0			0
$435$	1682.64	+	2204.12i	0.185463	+	0.242941i
$436$		0			0
$437$	7701.33	−	10600.0i	0.843031	−	1.16033i
$438$		0			0
$439$	3142.95	−	2283.49i	0.341697	−	0.248257i	−0.403681	−	0.914900i	$-0.632269\pi$
$439$	3142.95	−	2283.49i	0.341697	−	0.248257i	0.745377	+	0.666643i	$0.232269\pi$
$440$		0			0
$441$	−115.892	−	84.2005i	−0.0125140	−	0.00909194i
$442$		0			0
$443$			4840.23i			0.519111i	0.965728	+	0.259556i	$0.0835761\pi$
$443$			4840.23i			0.519111i	−0.965728	+	0.259556i	$0.916424\pi$
$444$		0			0
$445$	5363.43	+	15265.7i	0.571351	+	1.62621i
$446$		0			0
$447$	−14833.2	−	4819.60i	−1.56955	−	0.509976i
$448$		0			0
$449$	−9780.24			−1.02797			−0.513985	−	0.857799i	$-0.671831\pi$
$449$	−9780.24			−1.02797			−0.513985	+	0.857799i	$0.671831\pi$
$450$		0			0
$451$	20910.7			2.18325
$452$		0			0
$453$	7354.88	+	2389.75i	0.762831	+	0.247859i
$454$		0			0
$455$	−946.146	+	722.295i	−0.0974857	+	0.0744214i
$456$		0			0
$457$			3537.61i			0.362106i	0.983473	+	0.181053i	$0.0579505\pi$
$457$			3537.61i			0.362106i	−0.983473	+	0.181053i	$0.942050\pi$
$458$		0			0
$459$	−15530.5	−	11283.6i	−1.57931	−	1.14744i
$460$		0			0
$461$	9138.35	−	6639.40i	0.923243	−	0.670776i	−0.0210859	−	0.999778i	$-0.506712\pi$
$461$	9138.35	−	6639.40i	0.923243	−	0.670776i	0.944329	+	0.329002i	$0.106712\pi$
$462$		0			0
$463$	1174.11	−	1616.02i	0.117852	−	0.162209i	−0.746015	−	0.665929i	$-0.768035\pi$
$463$	1174.11	−	1616.02i	0.117852	−	0.162209i	0.863867	+	0.503719i	$0.168035\pi$
$464$		0			0
$465$	2372.00	+	708.998i	0.236556	+	0.0707075i
$466$		0			0
$467$	−10886.4	+	3537.19i	−1.07872	+	0.350496i	−0.793877	−	0.608079i	$-0.791941\pi$
$467$	−10886.4	+	3537.19i	−1.07872	+	0.350496i	−0.284840	+	0.958575i	$0.591941\pi$
$468$		0			0
$469$	−3167.02	−	9747.07i	−0.311811	−	0.959655i
$470$		0			0
$471$	4254.00	−	13092.5i	0.416166	−	1.28083i
$472$		0			0
$473$	2758.67	+	3796.98i	0.268169	+	0.369103i
$474$		0			0
$475$	−2707.46	+	9908.21i	−0.261530	+	0.957095i
$476$		0			0
$477$	−486.105	−	669.065i	−0.0466608	−	0.0642231i
$478$		0			0
$479$	1357.34	−	4177.45i	0.129474	−	0.398481i	−0.865215	−	0.501401i	$-0.832818\pi$
$479$	1357.34	−	4177.45i	0.129474	−	0.398481i	0.994690	+	0.102919i	$0.0328183\pi$
$480$		0			0
$481$	146.452	+	450.734i	0.0138828	+	0.0427270i
$482$		0			0
$483$	12670.8	−	4116.98i	1.19366	−	0.387845i
$484$		0			0
$485$	340.220	−	492.412i	0.0318528	−	0.0461016i
$486$		0			0
$487$	4407.69	−	6066.67i	0.410127	−	0.564491i	−0.553123	−	0.833100i	$-0.686564\pi$
$487$	4407.69	−	6066.67i	0.410127	−	0.564491i	0.963249	+	0.268609i	$0.0865640\pi$
$488$		0			0
$489$	2178.54	−	1582.80i	0.201466	−	0.146374i
$490$		0			0
$491$	−348.167	−	252.958i	−0.0320011	−	0.0232502i	0.571670	−	0.820484i	$-0.306296\pi$
$491$	−348.167	−	252.958i	−0.0320011	−	0.0232502i	−0.603671	+	0.797234i	$0.706296\pi$
$492$		0			0
$493$			6584.86i			0.601556i
$494$		0			0
$495$	461.506	−	1544.00i	0.0419054	−	0.140197i
$496$		0			0
$497$	−985.309	−	320.146i	−0.0889278	−	0.0288944i
$498$		0			0
$499$	1063.14			0.0953765			0.0476883	−	0.998862i	$-0.484815\pi$
$499$	1063.14			0.0953765			0.0476883	+	0.998862i	$0.484815\pi$
$500$		0			0
$501$	−2389.18			−0.213055
$502$		0			0
$503$	2601.15	+	845.164i	0.230575	+	0.0749185i	0.422026	−	0.906584i	$-0.361319\pi$
$503$	2601.15	+	845.164i	0.230575	+	0.0749185i	−0.191450	+	0.981502i	$0.561319\pi$
$504$		0			0
$505$	−151.161	+	505.718i	−0.0133199	+	0.0445626i
$506$		0			0
$507$		−	10690.8i		−	0.936480i
$508$		0			0
$509$	7550.83	+	5486.00i	0.657533	+	0.477726i	0.865829	−	0.500340i	$-0.166792\pi$
$509$	7550.83	+	5486.00i	0.657533	+	0.477726i	−0.208296	+	0.978066i	$0.566792\pi$
$510$		0			0
$511$	539.757	−	392.156i	0.0467269	−	0.0339490i
$512$		0			0
$513$	7046.58	−	9698.79i	0.606460	−	0.834721i
$514$		0			0
$515$	935.217	−	1353.57i	0.0800206	−	0.115816i
$516$		0			0
$517$	17140.8	−	5569.40i	1.45813	−	0.473775i
$518$		0			0
$519$	5391.92	+	16594.6i	0.456029	+	1.40351i
$520$		0			0
$521$	6778.80	−	20863.0i	0.570028	−	1.75437i	−0.0824889	−	0.996592i	$-0.526287\pi$
$521$	6778.80	−	20863.0i	0.570028	−	1.75437i	0.652517	−	0.757774i	$-0.273713\pi$
$522$		0			0
$523$	−5930.64	−	8162.82i	−0.495848	−	0.682477i	0.485605	−	0.874178i	$-0.338599\pi$
$523$	−5930.64	−	8162.82i	−0.495848	−	0.682477i	−0.981453	+	0.191702i	$0.938599\pi$
$524$		0			0
$525$	−8149.18	+	6532.65i	−0.677447	+	0.543064i
$526$		0			0
$527$	3455.54	+	4756.14i	0.285627	+	0.393132i
$528$		0			0
$529$	−4096.74	+	12608.5i	−0.336709	+	1.03628i
$530$		0			0
$531$	592.647	+	1823.98i	0.0484344	+	0.149066i
$532$		0			0
$533$	2123.89	−	690.093i	0.172600	−	0.0560811i
$534$		0			0
$535$	14469.2	+	4324.90i	1.16927	+	0.349498i
$536$		0			0
$537$	4421.17	−	6085.22i	0.355284	−	0.489007i
$538$		0			0
$539$	−2811.42	+	2042.62i	−0.224669	+	0.163232i
$540$		0			0
$541$	3988.34	+	2897.70i	0.316954	+	0.230281i	0.734875	−	0.678203i	$-0.237241\pi$
$541$	3988.34	+	2897.70i	0.316954	+	0.230281i	−0.417920	+	0.908484i	$0.637241\pi$
$542$		0			0
$543$		−	16317.9i		−	1.28963i
$544$		0			0
$545$	2424.24	−	1850.69i	0.190538	−	0.145458i
$546$		0			0
$547$	−15836.7	−	5145.67i	−1.23790	−	0.402217i	−0.384328	−	0.923196i	$-0.625567\pi$
$547$	−15836.7	−	5145.67i	−1.23790	−	0.402217i	−0.853569	+	0.520979i	$0.825567\pi$
$548$		0			0
$549$	−2033.91			−0.158115
$550$		0			0
$551$	−4112.23			−0.317944
$552$		0			0
$553$	−9266.61	−	3010.90i	−0.712579	−	0.231531i
$554$		0			0
$555$	1378.41	+	3923.29i	0.105424	+	0.300062i
$556$		0			0
$557$			13982.7i			1.06367i	0.846847	+	0.531836i	$0.178498\pi$
$557$			13982.7i			1.06367i	−0.846847	+	0.531836i	$0.821502\pi$
$558$		0			0
$559$	405.504	+	294.616i	0.0306815	+	0.0222914i
$560$		0			0
$561$	−31196.7	+	22665.7i	−2.34782	+	1.70579i
$562$		0			0
$563$	−5828.84	+	8022.71i	−0.436334	+	0.600563i	−0.969393	−	0.245516i	$-0.921043\pi$
$563$	−5828.84	+	8022.71i	−0.436334	+	0.600563i	0.533058	+	0.846079i	$0.321043\pi$
$564$		0			0
$565$	−4290.68	−	5620.42i	−0.319487	−	0.418501i
$566$		0			0
$567$	10538.3	−	3424.09i	0.780540	−	0.253613i
$568$		0			0
$569$	−2562.12	−	7885.39i	−0.188769	−	0.580972i	0.811224	−	0.584736i	$-0.198802\pi$
$569$	−2562.12	−	7885.39i	−0.188769	−	0.580972i	−0.999993	+	0.00376415i	$0.998802\pi$
$570$		0			0
$571$	1824.42	−	5614.99i	0.133712	−	0.411524i	−0.861675	−	0.507460i	$-0.830585\pi$
$571$	1824.42	−	5614.99i	0.133712	−	0.411524i	0.995387	+	0.0959364i	$0.0305845\pi$
$572$		0			0
$573$	12257.1	+	16870.5i	0.893629	+	1.22997i
$574$		0			0
$575$	−944.734	−	19908.9i	−0.0685185	−	1.44392i
$576$		0			0
$577$	3535.47	+	4866.15i	0.255084	+	0.351093i	0.917284	−	0.398234i	$-0.130377\pi$
$577$	3535.47	+	4866.15i	0.255084	+	0.351093i	−0.662200	+	0.749327i	$0.730377\pi$
$578$		0			0
$579$	2823.20	−	8688.92i	0.202639	−	0.623660i
$580$		0			0
$581$	278.032	+	855.694i	0.0198532	+	0.0611018i
$582$		0			0
$583$	−19080.5	+	6199.63i	−1.35546	+	0.440416i
$584$		0			0
$585$	−4.07992	−	172.053i	−0.000288349	−	0.0121599i
$586$		0			0
$587$	−5035.76	+	6931.13i	−0.354085	+	0.487357i	−0.948489	−	0.316810i	$-0.897388\pi$
$587$	−5035.76	+	6931.13i	−0.354085	+	0.487357i	0.594404	+	0.804167i	$0.297388\pi$
$588$		0			0
$589$	−2970.20	+	2157.97i	−0.207784	+	0.150964i
$590$		0			0
$591$	14932.7	+	10849.2i	1.03934	+	0.755123i
$592$		0			0
$593$			19704.6i			1.36453i	0.731103	+	0.682267i	$0.239006\pi$
$593$			19704.6i			1.36453i	−0.731103	+	0.682267i	$0.760994\pi$
$594$		0			0
$595$	−24794.8	+	587.962i	−1.70838	+	0.0405111i
$596$		0			0
$597$	−1527.62	−	496.353i	−0.104726	−	0.0340274i
$598$		0			0
$599$	2540.05			0.173262			0.0866308	−	0.996240i	$-0.472390\pi$
$599$	2540.05			0.173262			0.0866308	+	0.996240i	$0.472390\pi$
$600$		0			0
$601$	−18593.4			−1.26197			−0.630983	−	0.775797i	$-0.717348\pi$
$601$	−18593.4			−1.26197			−0.630983	+	0.775797i	$0.717348\pi$
$602$		0			0
$603$	1409.25	+	457.894i	0.0951728	+	0.0309235i
$604$		0			0
$605$	−19919.9	−	13763.2i	−1.33861	−	0.924882i
$606$		0			0
$607$			22878.6i			1.52984i	0.644123	+	0.764922i	$0.277222\pi$
$607$			22878.6i			1.52984i	−0.644123	+	0.764922i	$0.722778\pi$
$608$		0			0
$609$	−3382.87	−	2457.80i	−0.225091	−	0.163538i
$610$		0			0
$611$	1557.18	−	1131.36i	0.103104	−	0.0749098i
$612$		0			0
$613$	−8498.54	+	11697.2i	−0.559956	+	0.770713i	−0.991321	−	0.131464i	$-0.958032\pi$
$613$	−8498.54	+	11697.2i	−0.559956	+	0.770713i	0.431365	+	0.902178i	$0.358032\pi$
$614$		0			0
$615$	18486.8	−	6495.16i	1.21213	−	0.425870i
$616$		0			0
$617$	−18583.9	+	6038.28i	−1.21258	+	0.393990i	−0.844373	−	0.535755i	$-0.820027\pi$
$617$	−18583.9	+	6038.28i	−1.21258	+	0.393990i	−0.368203	+	0.929745i	$0.620027\pi$
$618$		0			0
$619$	−5737.53	−	17658.3i	−0.372553	−	1.14660i	−0.945114	−	0.326740i	$-0.894050\pi$
$619$	−5737.53	−	17658.3i	−0.372553	−	1.14660i	0.572561	−	0.819862i	$-0.305950\pi$
$620$		0			0
$621$	−7188.60	+	22124.2i	−0.464523	+	1.42965i
$622$		0			0
$623$	−14341.3	−	19739.2i	−0.922270	−	1.26940i
$624$		0			0
$625$	6213.85	+	14336.3i	0.397687	+	0.917521i
$626$		0			0
$627$	−14154.7	−	19482.3i	−0.901569	−	1.24090i
$628$		0			0
$629$	−3051.47	+	9391.45i	−0.193434	+	0.595328i
$630$		0			0
$631$	−1938.92	−	5967.39i	−0.122325	−	0.376479i	0.871079	−	0.491143i	$-0.163421\pi$
$631$	−1938.92	−	5967.39i	−0.122325	−	0.376479i	−0.993404	+	0.114664i	$0.963421\pi$
$632$		0			0
$633$	17729.4	−	5760.63i	1.11324	−	0.361714i
$634$		0			0
$635$	−9665.23	+	3395.78i	−0.604021	+	0.212217i
$636$		0			0
$637$	−218.144	+	300.249i	−0.0135686	+	0.0186755i
$638$		0			0
$639$	121.182	−	88.0439i	0.00750217	−	0.00545065i
$640$		0			0
$641$	−5365.30	−	3898.12i	−0.330603	−	0.240197i	0.410083	−	0.912048i	$-0.365500\pi$
$641$	−5365.30	−	3898.12i	−0.330603	−	0.240197i	−0.740687	+	0.671851i	$0.765500\pi$
$642$		0			0
$643$		−	12509.7i		−	0.767240i	−0.923491	−	0.383620i	$-0.874677\pi$
$643$		−	12509.7i		−	0.767240i	0.923491	−	0.383620i	$-0.125323\pi$
$644$		0			0
$645$	3618.29	+	2499.97i	0.220884	+	0.152614i
$646$		0			0
$647$	24076.1	+	7822.81i	1.46295	+	0.475342i	0.928970	−	0.370154i	$-0.120695\pi$
$647$	24076.1	+	7822.81i	1.46295	+	0.475342i	0.533982	+	0.845496i	$0.320695\pi$
$648$		0			0
$649$	46525.0			2.81397
$650$		0			0
$651$	−3733.17			−0.224753
$652$		0			0
$653$	−862.934	−	280.384i	−0.0517140	−	0.0168029i	0.283046	−	0.959106i	$-0.408655\pi$
$653$	−862.934	−	280.384i	−0.0517140	−	0.0168029i	−0.334760	+	0.942304i	$0.608655\pi$
$654$		0			0
$655$	7318.48	−	173.544i	0.436575	−	0.0103526i
$656$		0			0
$657$			96.4617i			0.00572805i
$658$		0			0
$659$	9417.94	+	6842.54i	0.556709	+	0.404473i	0.830253	−	0.557387i	$-0.188196\pi$
$659$	9417.94	+	6842.54i	0.556709	+	0.404473i	−0.273544	+	0.961859i	$0.588196\pi$
$660$		0			0
$661$	16022.0	−	11640.7i	0.942791	−	0.684977i	−0.00630023	−	0.999980i	$-0.502005\pi$
$661$	16022.0	−	11640.7i	0.942791	−	0.684977i	0.949091	+	0.315003i	$0.102005\pi$
$662$		0			0
$663$	−2420.61	+	3331.69i	−0.141793	+	0.195161i
$664$		0			0
$665$	−367.181	−	15484.3i	−0.0214116	−	0.902940i
$666$		0			0
$667$	7589.03	−	2465.82i	0.440552	−	0.143144i
$668$		0			0
$669$	4242.05	+	13055.7i	0.245152	+	0.754502i
$670$		0			0
$671$	−15247.1	+	46925.7i	−0.877209	+	2.69977i
$672$		0			0
$673$	−2320.74	−	3194.22i	−0.132924	−	0.182954i	0.737367	−	0.675493i	$-0.236069\pi$
$673$	−2320.74	−	3194.22i	−0.132924	−	0.182954i	−0.870291	+	0.492538i	$0.836069\pi$
$674$		0			0
$675$	−864.415	−	18216.3i	−0.0492909	−	1.03873i
$676$		0			0
$677$	−14742.6	−	20291.5i	−0.836935	−	1.15194i	−0.986592	−	0.163204i	$-0.947817\pi$
$677$	−14742.6	−	20291.5i	−0.836935	−	1.15194i	0.149657	−	0.988738i	$-0.452183\pi$
$678$		0			0
$679$	−278.893	+	858.345i	−0.0157628	+	0.0485129i
$680$		0			0
$681$	2705.09	+	8325.40i	0.152216	+	0.468473i
$682$		0			0
$683$	−7011.29	+	2278.10i	−0.392796	+	0.127627i	−0.498754	−	0.866744i	$-0.666209\pi$
$683$	−7011.29	+	2278.10i	−0.392796	+	0.127627i	0.105959	+	0.994371i	$0.466209\pi$
$684$		0			0
$685$	−3854.69	−	5049.31i	−0.215007	−	0.281641i
$686$		0			0
$687$	3134.80	−	4314.69i	0.174091	−	0.239615i
$688$		0			0
$689$	−1733.39	+	1259.38i	−0.0958447	+	0.0696353i
$690$		0			0
$691$	−24373.2	−	17708.2i	−1.34183	−	0.974894i	−0.999375	−	0.0353584i	$-0.988743\pi$
$691$	−24373.2	−	17708.2i	−1.34183	−	0.974894i	−0.342452	−	0.939535i	$-0.611257\pi$
$692$		0			0
$693$			2430.02i			0.133202i
$694$		0			0
$695$	−9526.83	−	27115.7i	−0.519962	−	1.47994i
$696$		0			0
$697$	44253.1	+	14378.7i	2.40489	+	0.781395i
$698$		0			0
$699$	16809.3			0.909564
$700$		0			0
$701$	275.799			0.0148599			0.00742994	−	0.999972i	$-0.497635\pi$
$701$	275.799			0.0148599			0.00742994	+	0.999972i	$0.497635\pi$
$702$		0			0
$703$	−5864.94	−	1905.63i	−0.314652	−	0.102237i
$704$		0			0
$705$	13424.0	−	10248.0i	0.717130	−	0.547463i
$706$		0			0
$707$		−	795.924i		−	0.0423392i
$708$		0			0
$709$	−3614.00	−	2625.72i	−0.191434	−	0.139085i	0.487940	−	0.872877i	$-0.337748\pi$
$709$	−3614.00	−	2625.72i	−0.191434	−	0.139085i	−0.679374	+	0.733792i	$0.737748\pi$
$710$		0			0
$711$	1139.69	−	828.033i	0.0601149	−	0.0436760i
$712$		0			0
$713$	4187.44	−	5763.52i	0.219945	−	0.302728i
$714$		0			0
$715$	−4000.14	−	1195.65i	−0.209226	−	0.0625384i
$716$		0			0
$717$	20162.0	−	6551.02i	1.05016	−	0.341217i
$718$		0			0
$719$	−1471.37	−	4528.41i	−0.0763183	−	0.234883i	0.905618	−	0.424094i	$-0.139407\pi$
$719$	−1471.37	−	4528.41i	−0.0763183	−	0.234883i	−0.981937	+	0.189210i	$0.939407\pi$
$720$		0			0
$721$	−766.638	+	2359.47i	−0.0395993	+	0.121874i
$722$		0			0
$723$	6344.19	+	8732.03i	0.326339	+	0.449167i
$724$		0			0
$725$	−4880.87	+	3912.67i	−0.250029	+	0.200431i
$726$		0			0
$727$	11696.4	+	16098.8i	0.596694	+	0.821279i	0.995401	−	0.0957995i	$-0.0305408\pi$
$727$	11696.4	+	16098.8i	0.596694	+	0.821279i	−0.398707	+	0.917079i	$0.630541\pi$
$728$		0			0
$729$	−6527.87	+	20090.7i	−0.331650	+	1.02071i
$730$		0			0
$731$	3227.24	+	9932.44i	0.163289	+	0.502551i
$732$		0			0
$733$	−21893.7	+	7113.68i	−1.10322	+	0.358458i	−0.803341	−	0.595519i	$-0.796946\pi$
$733$	−21893.7	+	7113.68i	−1.10322	+	0.358458i	−0.299879	+	0.953977i	$0.596946\pi$
$734$		0			0
$735$	−1851.07	+	2679.11i	−0.0928947	+	0.134450i
$736$		0			0
$737$	21128.7	−	29081.2i	1.05602	−	1.45349i
$738$		0			0
$739$	−3899.72	+	2833.31i	−0.194119	+	0.141035i	−0.680599	−	0.732656i	$-0.738280\pi$
$739$	−3899.72	+	2833.31i	−0.194119	+	0.141035i	0.486481	+	0.873691i	$0.338280\pi$
$740$		0			0
$741$	−2080.63	−	1511.67i	−0.103150	−	0.0749426i
$742$		0			0
$743$		−	11267.6i		−	0.556348i	−0.960531	−	0.278174i	$-0.910271\pi$
$743$		−	11267.6i		−	0.556348i	0.960531	−	0.278174i	$-0.0897291\pi$
$744$		0			0
$745$	10076.2	−	33710.5i	0.495521	−	1.65780i
$746$		0			0
$747$	−123.718	−	40.1984i	−0.00605971	−	0.00196892i
$748$		0			0
$749$	−22772.4			−1.11093
$750$		0			0
$751$	21124.7			1.02643			0.513216	−	0.858259i	$-0.328454\pi$
$751$	21124.7			1.02643			0.513216	+	0.858259i	$0.328454\pi$
$752$		0			0
$753$	−18048.8	−	5864.41i	−0.873485	−	0.283813i
$754$		0			0
$755$	−4996.17	+	16715.0i	−0.240833	+	0.805723i
$756$		0			0
$757$		−	25198.7i		−	1.20986i	−0.796279	−	0.604929i	$-0.793201\pi$
$757$		−	25198.7i		−	1.20986i	0.796279	−	0.604929i	$-0.206799\pi$
$758$		0			0
$759$	37804.3	+	27466.4i	1.80792	+	1.31353i
$760$		0			0
$761$	−7499.45	+	5448.67i	−0.357234	+	0.259546i	−0.751897	−	0.659280i	$-0.770861\pi$
$761$	−7499.45	+	5448.67i	−0.357234	+	0.259546i	0.394664	+	0.918826i	$0.370861\pi$
$762$		0			0
$763$	−2703.26	+	3720.72i	−0.128263	+	0.176539i
$764$		0			0
$765$	2038.37	−	2950.20i	0.0963364	−	0.139431i
$766$		0			0
$767$	4725.51	−	1535.41i	0.222462	−	0.0722822i
$768$		0			0
$769$	2189.37	+	6738.20i	0.102667	+	0.315976i	0.989176	−	0.146735i	$-0.0468766\pi$
$769$	2189.37	+	6738.20i	0.102667	+	0.315976i	−0.886509	+	0.462712i	$0.846877\pi$
$770$		0			0
$771$	1612.25	−	4961.98i	0.0753095	−	0.231779i
$772$		0			0
$773$	−7895.59	−	10867.3i	−0.367380	−	0.505655i	0.584806	−	0.811173i	$-0.301170\pi$
$773$	−7895.59	−	10867.3i	−0.367380	−	0.505655i	−0.952186	+	0.305518i	$0.901170\pi$
$774$		0			0
$775$	−1472.12	+	5387.39i	−0.0682325	+	0.249704i
$776$		0			0
$777$	−3685.75	−	5073.00i	−0.170174	−	0.234225i
$778$		0			0
$779$	−8979.47	+	27636.0i	−0.412995	+	1.27107i
$780$		0			0
$781$	−1122.89	−	3455.89i	−0.0514469	−	0.158337i
$782$		0			0
$783$	6943.83	−	2256.19i	0.316925	−	0.102975i
$784$		0			0
$785$	29754.5	+	8893.71i	1.35284	+	0.404370i
$786$		0			0
$787$	−7420.09	+	10212.9i	−0.336084	+	0.462579i	−0.943292	−	0.331963i	$-0.892289\pi$
$787$	−7420.09	+	10212.9i	−0.336084	+	0.462579i	0.607209	+	0.794542i	$0.292289\pi$
$788$		0			0
$789$	16216.1	−	11781.7i	0.731695	−	0.531607i
$790$		0			0
$791$	8626.20	+	6267.30i	0.387753	+	0.281719i
$792$		0			0
$793$			5269.39i			0.235967i
$794$		0			0
$795$	−14943.1	+	11407.7i	−0.666636	+	0.508915i
$796$		0			0
$797$	−19301.2	−	6271.34i	−0.857822	−	0.278723i	−0.153103	−	0.988210i	$-0.548927\pi$
$797$	−19301.2	−	6271.34i	−0.857822	−	0.278723i	−0.704718	+	0.709487i	$0.748927\pi$
$798$		0			0
$799$	40104.6			1.77572
$800$		0			0
$801$	3527.65			0.155610
$802$		0			0
$803$	2225.53	+	723.119i	0.0978048	+	0.0317787i
$804$		0			0
$805$	9962.50	+	28355.7i	0.436189	+	1.24150i
$806$		0			0
$807$		−	18054.2i		−	0.787531i
$808$		0			0
$809$	−34293.3	−	24915.5i	−1.49034	−	1.08280i	−0.974036	−	0.226395i	$-0.927306\pi$
$809$	−34293.3	−	24915.5i	−1.49034	−	1.08280i	−0.516308	−	0.856403i	$-0.672694\pi$
$810$		0			0
$811$	18821.8	−	13674.9i	0.814949	−	0.592095i	−0.100312	−	0.994956i	$-0.531984\pi$
$811$	18821.8	−	13674.9i	0.814949	−	0.592095i	0.915261	+	0.402861i	$0.131984\pi$
$812$		0			0
$813$	8421.25	−	11590.9i	0.363280	−	0.500011i
$814$		0			0
$815$	3686.14	+	4828.53i	0.158429	+	0.207529i
$816$		0			0
$817$	−6202.79	+	2015.41i	−0.265616	+	0.0863038i
$818$		0			0
$819$	80.1951	+	246.815i	0.00342154	+	0.0105304i
$820$		0			0
$821$	−6419.92	+	19758.5i	−0.272907	+	0.839921i	0.716859	+	0.697219i	$0.245579\pi$
$821$	−6419.92	+	19758.5i	−0.272907	+	0.839921i	−0.989766	+	0.142703i	$0.954421\pi$
$822$		0			0
$823$	1454.67	+	2002.18i	0.0616120	+	0.0848017i	0.838711	−	0.544577i	$-0.183310\pi$
$823$	1454.67	+	2002.18i	0.0616120	+	0.0848017i	−0.777099	+	0.629378i	$0.783310\pi$
$824$		0			0
$825$	−35337.2	−	9656.02i	−1.49125	−	0.407490i
$826$		0			0
$827$	−6256.34	−	8611.12i	−0.263064	−	0.362077i	0.656969	−	0.753918i	$-0.271838\pi$
$827$	−6256.34	−	8611.12i	−0.263064	−	0.362077i	−0.920033	+	0.391841i	$0.871838\pi$
$828$		0			0
$829$	6995.29	−	21529.3i	0.293072	−	0.901982i	−0.690791	−	0.723055i	$-0.742737\pi$
$829$	6995.29	−	21529.3i	0.293072	−	0.901982i	0.983862	−	0.178927i	$-0.0572626\pi$
$830$		0			0
$831$	−6935.00	−	21343.8i	−0.289498	−	0.890983i
$832$		0			0
$833$	−7354.33	+	2389.57i	−0.305897	+	0.0993920i
$834$		0			0
$835$	−127.772	−	5388.23i	−0.00529548	−	0.223314i
$836$		0			0
$837$	3831.43	−	5273.52i	0.158224	−	0.217777i
$838$		0			0
$839$	−27328.7	+	19855.5i	−1.12454	+	0.817029i	−0.984892	−	0.173171i	$-0.944599\pi$
$839$	−27328.7	+	19855.5i	−1.12454	+	0.817029i	−0.139653	+	0.990201i	$0.544599\pi$
$840$		0			0
$841$	17705.0	+	12863.4i	0.725941	+	0.527427i
$842$		0			0
$843$		−	14993.5i		−	0.612577i
$844$		0			0
$845$	24110.6	−	571.737i	0.981572	−	0.0232762i
$846$		0			0
$847$	34723.3	+	11282.3i	1.40863	+	0.457691i
$848$		0			0
$849$	−28270.5			−1.14281
$850$		0			0
$851$	11966.3			0.482020
$852$		0			0
$853$	−35704.6	−	11601.1i	−1.43318	−	0.465669i	−0.513416	−	0.858140i	$-0.671620\pi$
$853$	−35704.6	−	11601.1i	−1.43318	−	0.465669i	−0.919764	+	0.392471i	$0.871620\pi$
$854$		0			0
$855$	1842.39	+	1272.96i	0.0736942	+	0.0509172i
$856$		0			0
$857$		−	24120.1i		−	0.961408i	−0.876883	−	0.480704i	$-0.840381\pi$
$857$		−	24120.1i		−	0.961408i	0.876883	−	0.480704i	$-0.159619\pi$
$858$		0			0
$859$	−5422.85	−	3939.93i	−0.215396	−	0.156494i	0.474856	−	0.880064i	$-0.342500\pi$
$859$	−5422.85	−	3939.93i	−0.215396	−	0.156494i	−0.690252	+	0.723569i	$0.742500\pi$
$860$		0			0
$861$	−23904.3	+	17367.5i	−0.946174	+	0.687436i
$862$		0			0
$863$	−18359.9	+	25270.2i	−0.724193	+	0.996766i	0.275181	+	0.961392i	$0.411262\pi$
$863$	−18359.9	+	25270.2i	−0.724193	+	0.996766i	−0.999374	+	0.0353735i	$0.988738\pi$
$864$		0			0
$865$	−37136.9	+	13047.7i	−1.45976	+	0.512872i
$866$		0			0
$867$	−58449.2	+	18991.3i	−2.28955	+	0.743920i
$868$		0			0
$869$	−10560.5	−	32501.8i	−0.412244	−	1.26876i
$870$		0			0
$871$	1186.30	−	3651.04i	0.0461494	−	0.142033i
$872$		0			0
$873$	−76.6988	−	105.567i	−0.00297350	−	0.00409267i
$874$		0			0
$875$	−15168.7	−	18029.2i	−0.586051	−	0.696569i
$876$		0			0
$877$	14264.4	+	19633.2i	0.549228	+	0.755948i	0.989907	−	0.141717i	$-0.0452623\pi$
$877$	14264.4	+	19633.2i	0.549228	+	0.755948i	−0.440679	+	0.897665i	$0.645262\pi$
$878$		0			0
$879$	−10528.1	+	32402.3i	−0.403988	+	1.24335i
$880$		0			0
$881$	1004.56	+	3091.71i	0.0384159	+	0.118232i	0.968425	−	0.249304i	$-0.0802017\pi$
$881$	1004.56	+	3091.71i	0.0384159	+	0.118232i	−0.930010	+	0.367535i	$0.880202\pi$
$882$		0			0
$883$	−11569.0	+	3759.01i	−0.440916	+	0.143262i	−0.521058	−	0.853521i	$-0.674463\pi$
$883$	−11569.0	+	3759.01i	−0.440916	+	0.143262i	0.0801422	+	0.996783i	$0.474463\pi$
$884$		0			0
$885$	41131.9	−	14451.3i	1.56230	−	0.548898i
$886$		0			0
$887$	−7631.43	+	10503.8i	−0.288882	+	0.397612i	−0.928651	−	0.370956i	$-0.879030\pi$
$887$	−7631.43	+	10503.8i	−0.288882	+	0.397612i	0.639768	+	0.768568i	$0.279030\pi$
$888$		0			0
$889$	12497.6	−	9080.02i	0.471491	−	0.342558i
$890$		0			0
$891$	31441.9	+	22843.8i	1.18220	+	0.858920i
$892$		0			0
$893$			25045.2i			0.938529i
$894$		0			0
$895$	13960.2	+	9645.46i	0.521383	+	0.360237i
$896$		0			0
$897$	4746.20	+	1542.13i	0.176668	+	0.0574028i
$898$		0			0
$899$	−2235.94			−0.0829509
$900$		0			0
$901$	−44642.8			−1.65069
$902$		0			0
$903$	−6307.20	−	2049.33i	−0.232437	−	0.0755233i
$904$		0			0
$905$	36801.1	−	872.669i	1.35172	−	0.0320536i
$906$		0			0
$907$			34569.1i			1.26554i	0.774339	+	0.632771i	$0.218083\pi$
$907$			34569.1i			1.26554i	−0.774339	+	0.632771i	$0.781917\pi$
$908$		0			0
$909$	93.0987	+	67.6402i	0.00339702	+	0.00246808i
$910$		0			0
$911$	−7607.64	+	5527.27i	−0.276676	+	0.201017i	−0.717466	−	0.696593i	$-0.754698\pi$
$911$	−7607.64	+	5527.27i	−0.276676	+	0.201017i	0.440790	+	0.897610i	$0.354698\pi$
$912$		0			0
$913$	−1854.89	+	2553.03i	−0.0672375	+	0.0925445i
$914$		0			0
$915$	1096.07	+	46222.2i	0.0396011	+	1.67001i
$916$		0			0
$917$	−10498.6	+	3411.19i	−0.378073	+	0.122843i
$918$		0			0
$919$	12428.8	+	38251.9i	0.446124	+	1.37303i	0.881246	+	0.472658i	$0.156705\pi$
$919$	12428.8	+	38251.9i	0.446124	+	1.37303i	−0.435121	+	0.900372i	$0.643295\pi$
$920$		0			0
$921$	7126.43	−	21932.9i	0.254966	−	0.784705i
$922$		0			0
$923$	−228.101	−	313.954i	−0.00813439	−	0.0111960i
$924$		0			0
$925$	−8774.34	+	3318.49i	−0.311890	+	0.117958i
$926$		0			0
$927$	−210.834	−	290.189i	−0.00747002	−	0.0102816i
$928$		0			0
$929$	−4084.78	+	12571.7i	−0.144260	+	0.443986i	−0.996915	−	0.0784880i	$-0.974991\pi$
$929$	−4084.78	+	12571.7i	−0.144260	+	0.443986i	0.852655	+	0.522474i	$0.174991\pi$
$930$		0			0
$931$	−1492.28	−	4592.76i	−0.0525322	−	0.161677i
$932$		0			0
$933$	24483.5	−	7955.16i	0.859114	−	0.279143i
$934$		0			0
$935$	−52785.5	−	69144.5i	−1.84628	−	2.41847i
$936$		0			0
$937$	−3967.34	+	5460.58i	−0.138322	+	0.190384i	−0.872558	−	0.488510i	$-0.837540\pi$
$937$	−3967.34	+	5460.58i	−0.138322	+	0.190384i	0.734236	+	0.678894i	$0.237540\pi$
$938$		0			0
$939$	−19097.5	+	13875.1i	−0.663709	+	0.482213i
$940$		0			0
$941$	−19548.5	−	14202.8i	−0.677219	−	0.492028i	0.195215	−	0.980760i	$-0.437460\pi$
$941$	−19548.5	−	14202.8i	−0.677219	−	0.492028i	−0.872434	+	0.488732i	$0.837460\pi$
$942$		0			0
$943$		−	56385.9i		−	1.94717i
$944$		0			0
$945$	9115.51	+	25945.0i	0.313786	+	0.893112i
$946$		0			0
$947$	−2569.36	−	834.834i	−0.0881656	−	0.0286467i	0.264602	−	0.964358i	$-0.414759\pi$
$947$	−2569.36	−	834.834i	−0.0881656	−	0.0286467i	−0.352768	+	0.935711i	$0.614759\pi$
$948$		0			0
$949$	249.910			0.00854838
$950$		0			0
$951$	−31061.6			−1.05914
$952$		0			0
$953$	33842.8	+	10996.2i	1.15034	+	0.373768i	0.821272	−	0.570537i	$-0.193265\pi$
$953$	33842.8	+	10996.2i	1.15034	+	0.373768i	0.329069	+	0.944306i	$0.393265\pi$
$954$		0			0
$955$	−37391.9	+	28545.3i	−1.26699	+	0.967229i
$956$		0			0
$957$		−	14666.1i		−	0.495389i
$958$		0			0
$959$	7749.66	+	5630.46i	0.260948	+	0.189590i
$960$		0			0
$961$	22486.4	−	16337.4i	0.754807	−	0.548399i
$962$		0			0
$963$	1935.27	−	2663.67i	0.0647593	−	0.0891335i
$964$		0			0
$965$	19746.8	+	5902.38i	0.658727	+	0.196896i
$966$		0			0
$967$	−5597.59	+	1818.77i	−0.186149	+	0.0604836i	−0.400608	−	0.916249i	$-0.631201\pi$
$967$	−5597.59	+	1818.77i	−0.186149	+	0.0604836i	0.214459	+	0.976733i	$0.431201\pi$
$968$		0			0
$969$	−16558.9	−	50963.1i	−0.548967	−	1.68955i
$970$		0			0
$971$	12777.2	−	39324.0i	0.422285	−	1.29966i	−0.483286	−	0.875463i	$-0.660557\pi$
$971$	12777.2	−	39324.0i	0.422285	−	1.29966i	0.905570	−	0.424196i	$-0.139443\pi$
$972$		0			0
$973$	25473.9	+	35061.8i	0.839318	+	1.15522i
$974$		0			0
$975$	−3907.84	+	185.439i	−0.128360	+	0.00609106i
$976$		0			0
$977$	−16220.0	−	22324.9i	−0.531141	−	0.731052i	0.456163	−	0.889896i	$-0.349223\pi$
$977$	−16220.0	−	22324.9i	−0.531141	−	0.731052i	−0.987304	+	0.158844i	$0.949223\pi$
$978$		0			0
$979$	26444.8	−	81388.8i	0.863310	−	2.65699i
$980$		0			0
$981$	−205.478	−	632.397i	−0.00668748	−	0.0205819i
$982$		0			0
$983$	53965.8	−	17534.5i	1.75101	−	0.568937i	0.754801	−	0.655954i	$-0.227733\pi$
$983$	53965.8	−	17534.5i	1.75101	−	0.568937i	0.996207	+	0.0870170i	$0.0277335\pi$
$984$		0			0
$985$	−23669.3	+	34257.3i	−0.765650	+	1.10815i
$986$		0			0
$987$	−14969.0	+	20603.1i	−0.482745	+	0.664441i
$988$		0			0
$989$	10238.6	−	7438.77i	0.329189	−	0.239170i
$990$		0			0
$991$	−14200.8	−	10317.5i	−0.455200	−	0.330722i	0.336445	−	0.941703i	$-0.390775\pi$
$991$	−14200.8	−	10317.5i	−0.455200	−	0.330722i	−0.791646	+	0.610981i	$0.790775\pi$
$992$		0			0
$993$			46814.3i			1.49608i
$994$		0			0
$995$	1037.71	−	3471.72i	0.0330629	−	0.110614i
$996$		0			0
$997$	20217.4	+	6569.04i	0.642219	+	0.208669i	0.611980	−	0.790873i	$-0.290373\pi$
$997$	20217.4	+	6569.04i	0.642219	+	0.208669i	0.0302386	+	0.999543i	$0.490373\pi$
$998$		0			0
$999$	10948.9			0.346756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.89.3	yes	32
5.2	odd	4		500.4.g.b.301.5		64
5.3	odd	4		500.4.g.b.301.12		64
5.4	even	2		500.4.i.a.449.6		32
25.3	odd	20		2500.4.a.g.1.24		32
25.9	even	10	inner	100.4.i.a.9.3	✓	32
25.12	odd	20		500.4.g.b.201.5		64
25.13	odd	20		500.4.g.b.201.12		64
25.16	even	5		500.4.i.a.49.6		32
25.22	odd	20		2500.4.a.g.1.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.9.3	✓	32	25.9	even	10	inner
100.4.i.a.89.3	yes	32	1.1	even	1	trivial
500.4.g.b.201.5		64	25.12	odd	20
500.4.g.b.201.12		64	25.13	odd	20
500.4.g.b.301.5		64	5.2	odd	4
500.4.g.b.301.12		64	5.3	odd	4
500.4.i.a.49.6		32	25.16	even	5
500.4.i.a.449.6		32	5.4	even	2
2500.4.a.g.1.9		32	25.22	odd	20
2500.4.a.g.1.24		32	25.3	odd	20

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.71349 - 1.53150i) q^{3} +(3.20187 - 10.7121i) q^{5} +16.8592i q^{7} +(-1.97201 - 1.43275i) q^{9} +O(q^{10})\)	\(q+(-4.71349 - 1.53150i) q^{3} +(3.20187 - 10.7121i) q^{5} +16.8592i q^{7} +(-1.97201 - 1.43275i) q^{9} +(-47.8389 + 34.7570i) q^{11} +(-3.71191 + 5.10901i) q^{13} +(-31.4975 + 45.5874i) q^{15} +(-125.140 + 40.6606i) q^{17} +(-25.3925 - 78.1500i) q^{19} +(25.8199 - 79.4654i) q^{21} +(93.7224 + 128.998i) q^{23} +(-104.496 - 68.5972i) q^{25} +(85.7543 + 118.031i) q^{27} +(15.4646 - 47.5950i) q^{29} +(-13.8066 - 42.4924i) q^{31} +(278.718 - 90.5611i) q^{33} +(180.596 + 53.9808i) q^{35} +(44.1117 - 60.7145i) q^{37} +(25.3205 - 18.3964i) q^{39} +(-286.091 - 207.857i) q^{41} -79.3703i q^{43} +(-21.6618 + 16.5368i) q^{45} +(-289.874 - 94.1857i) q^{47} +58.7686 q^{49} +652.120 q^{51} +(322.676 + 104.844i) q^{53} +(219.145 + 623.740i) q^{55} +407.248i q^{57} +(-636.533 - 462.468i) q^{59} +(675.055 - 490.456i) q^{61} +(24.1549 - 33.2464i) q^{63} +(42.8429 + 56.1206i) q^{65} +(-578.147 + 187.851i) q^{67} +(-244.198 - 751.566i) q^{69} +(-18.9894 + 58.4435i) q^{71} +(-23.2607 - 32.0156i) q^{73} +(387.484 + 483.368i) q^{75} +(-585.973 - 806.523i) q^{77} +(-178.592 + 549.648i) q^{79} +(-203.100 - 625.077i) q^{81} +(50.7554 - 16.4914i) q^{83} +(34.8749 + 1470.70i) q^{85} +(-145.784 + 200.654i) q^{87} +(-1170.83 + 850.656i) q^{89} +(-86.1336 - 62.5797i) q^{91} +221.432i q^{93} +(-918.450 + 21.7793i) q^{95} +(50.9127 + 16.5425i) q^{97} +144.136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 32 * q + 6 * q^5 + 122 * q^9	\( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more