LMFDB - Embedded newform 4022.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.a (trivial)

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:	yes
Analytic conductor:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.03510 q^{3} +1.00000 q^{4} -3.10204 q^{5} +2.03510 q^{6} -0.000158603 q^{7} -1.00000 q^{8} +1.14162 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.03510 q^{3} +1.00000 q^{4} -3.10204 q^{5} +2.03510 q^{6} -0.000158603 q^{7} -1.00000 q^{8} +1.14162 q^{9} +3.10204 q^{10} -1.15171 q^{11} -2.03510 q^{12} -1.92309 q^{13} +0.000158603 q^{14} +6.31296 q^{15} +1.00000 q^{16} -2.77861 q^{17} -1.14162 q^{18} +3.95267 q^{19} -3.10204 q^{20} +0.000322773 q^{21} +1.15171 q^{22} -1.25173 q^{23} +2.03510 q^{24} +4.62267 q^{25} +1.92309 q^{26} +3.78199 q^{27} -0.000158603 q^{28} -7.67891 q^{29} -6.31296 q^{30} -5.07874 q^{31} -1.00000 q^{32} +2.34385 q^{33} +2.77861 q^{34} +0.000491994 q^{35} +1.14162 q^{36} +1.88166 q^{37} -3.95267 q^{38} +3.91367 q^{39} +3.10204 q^{40} -9.13353 q^{41} -0.000322773 q^{42} -7.81296 q^{43} -1.15171 q^{44} -3.54135 q^{45} +1.25173 q^{46} -1.52621 q^{47} -2.03510 q^{48} -7.00000 q^{49} -4.62267 q^{50} +5.65475 q^{51} -1.92309 q^{52} -4.44905 q^{53} -3.78199 q^{54} +3.57266 q^{55} +0.000158603 q^{56} -8.04406 q^{57} +7.67891 q^{58} -2.90576 q^{59} +6.31296 q^{60} -3.21513 q^{61} +5.07874 q^{62} -0.000181064 q^{63} +1.00000 q^{64} +5.96550 q^{65} -2.34385 q^{66} -6.33413 q^{67} -2.77861 q^{68} +2.54738 q^{69} -0.000491994 q^{70} -12.2401 q^{71} -1.14162 q^{72} +12.2476 q^{73} -1.88166 q^{74} -9.40757 q^{75} +3.95267 q^{76} +0.000182665 q^{77} -3.91367 q^{78} +10.5905 q^{79} -3.10204 q^{80} -11.1216 q^{81} +9.13353 q^{82} +9.54759 q^{83} +0.000322773 q^{84} +8.61937 q^{85} +7.81296 q^{86} +15.6273 q^{87} +1.15171 q^{88} -7.82879 q^{89} +3.54135 q^{90} +0.000305008 q^{91} -1.25173 q^{92} +10.3357 q^{93} +1.52621 q^{94} -12.2613 q^{95} +2.03510 q^{96} -14.9054 q^{97} +7.00000 q^{98} -1.31482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.03510	−1.17496	−0.587482	−	0.809237i	$-0.699881\pi$
$3$	−2.03510	−1.17496	−0.587482	+	0.809237i	$0.699881\pi$
$4$	1.00000	0.500000
$5$	−3.10204	−1.38728	−0.693638	−	0.720324i	$-0.743993\pi$
$5$	−3.10204	−1.38728	−0.693638	+	0.720324i	$0.743993\pi$
$6$	2.03510	0.830825
$7$	−0.000158603 0	−5.99464e−5 0	−2.99732e−5	−	1.00000i	$-0.500010\pi$
$7$	−0.000158603 0	−5.99464e−5 0	−2.99732e−5		1.00000i	$0.500010\pi$
$8$	−1.00000	−0.353553
$9$	1.14162	0.380539
$10$	3.10204	0.980952
$11$	−1.15171	−0.347255	−0.173627	−	0.984811i	$-0.555549\pi$
$11$	−1.15171	−0.347255	−0.173627	+	0.984811i	$0.555549\pi$
$12$	−2.03510	−0.587482
$13$	−1.92309	−0.533369	−0.266684	−	0.963784i	$-0.585928\pi$
$13$	−1.92309	−0.533369	−0.266684	+	0.963784i	$0.585928\pi$
$14$	0.000158603 0	4.23885e−5 0
$15$	6.31296	1.63000
$16$	1.00000	0.250000
$17$	−2.77861	−0.673913	−0.336956	−	0.941520i	$-0.609397\pi$
$17$	−2.77861	−0.673913	−0.336956	+	0.941520i	$0.609397\pi$
$18$	−1.14162	−0.269082
$19$	3.95267	0.906804	0.453402	−	0.891306i	$-0.350210\pi$
$19$	3.95267	0.906804	0.453402	+	0.891306i	$0.350210\pi$
$20$	−3.10204	−0.693638
$21$	0.000322773 0	7.04348e−5 0
$22$	1.15171	0.245546
$23$	−1.25173	−0.261003	−0.130501	−	0.991448i	$-0.541659\pi$
$23$	−1.25173	−0.261003	−0.130501	+	0.991448i	$0.541659\pi$
$24$	2.03510	0.415412
$25$	4.62267	0.924533
$26$	1.92309	0.377149
$27$	3.78199	0.727844
$28$	−0.000158603 0	−2.99732e−5 0
$29$	−7.67891	−1.42594	−0.712969	−	0.701196i	$-0.752650\pi$
$29$	−7.67891	−1.42594	−0.712969	+	0.701196i	$0.752650\pi$
$30$	−6.31296	−1.15258
$31$	−5.07874	−0.912168	−0.456084	−	0.889937i	$-0.650748\pi$
$31$	−5.07874	−0.912168	−0.456084	+	0.889937i	$0.650748\pi$
$32$	−1.00000	−0.176777
$33$	2.34385	0.408011
$34$	2.77861	0.476528
$35$	0.000491994 0	8.31622e−5 0
$36$	1.14162	0.190270
$37$	1.88166	0.309342	0.154671	−	0.987966i	$-0.450568\pi$
$37$	1.88166	0.309342	0.154671	+	0.987966i	$0.450568\pi$
$38$	−3.95267	−0.641207
$39$	3.91367	0.626689
$40$	3.10204	0.490476
$41$	−9.13353	−1.42642	−0.713209	−	0.700952i	$-0.752759\pi$
$41$	−9.13353	−1.42642	−0.713209	+	0.700952i	$0.752759\pi$
$42$	−0.000322773 0	−4.98050e−5 0
$43$	−7.81296	−1.19147	−0.595733	−	0.803183i	$-0.703138\pi$
$43$	−7.81296	−1.19147	−0.595733	+	0.803183i	$0.703138\pi$
$44$	−1.15171	−0.173627
$45$	−3.54135	−0.527913
$46$	1.25173	0.184557
$47$	−1.52621	−0.222621	−0.111311	−	0.993786i	$-0.535505\pi$
$47$	−1.52621	−0.222621	−0.111311	+	0.993786i	$0.535505\pi$
$48$	−2.03510	−0.293741
$49$	−7.00000	−1.00000
$50$	−4.62267	−0.653744
$51$	5.65475	0.791823
$52$	−1.92309	−0.266684
$53$	−4.44905	−0.611124	−0.305562	−	0.952172i	$-0.598844\pi$
$53$	−4.44905	−0.611124	−0.305562	+	0.952172i	$0.598844\pi$
$54$	−3.78199	−0.514663
$55$	3.57266	0.481738
$56$	0.000158603 0	2.11943e−5 0
$57$	−8.04406	−1.06546
$58$	7.67891	1.00829
$59$	−2.90576	−0.378298	−0.189149	−	0.981948i	$-0.560573\pi$
$59$	−2.90576	−0.378298	−0.189149	+	0.981948i	$0.560573\pi$
$60$	6.31296	0.814999
$61$	−3.21513	−0.411655	−0.205827	−	0.978588i	$-0.565989\pi$
$61$	−3.21513	−0.411655	−0.205827	+	0.978588i	$0.565989\pi$
$62$	5.07874	0.645000
$63$	−0.000181064 0	−2.28120e−5 0
$64$	1.00000	0.125000
$65$	5.96550	0.739929
$66$	−2.34385	−0.288508
$67$	−6.33413	−0.773837	−0.386919	−	0.922114i	$-0.626461\pi$
$67$	−6.33413	−0.773837	−0.386919	+	0.922114i	$0.626461\pi$
$68$	−2.77861	−0.336956
$69$	2.54738	0.306669
$70$	−0.000491994 0	−5.88045e−5 0
$71$	−12.2401	−1.45264	−0.726318	−	0.687359i	$-0.758770\pi$
$71$	−12.2401	−1.45264	−0.726318	+	0.687359i	$0.758770\pi$
$72$	−1.14162	−0.134541
$73$	12.2476	1.43347	0.716737	−	0.697344i	$-0.245635\pi$
$73$	12.2476	1.43347	0.716737	+	0.697344i	$0.245635\pi$
$74$	−1.88166	−0.218738
$75$	−9.40757	−1.08629
$76$	3.95267	0.453402
$77$	0.000182665 0	2.08167e−5 0
$78$	−3.91367	−0.443136
$79$	10.5905	1.19152	0.595759	−	0.803163i	$-0.296851\pi$
$79$	10.5905	1.19152	0.595759	+	0.803163i	$0.296851\pi$
$80$	−3.10204	−0.346819
$81$	−11.1216	−1.23573
$82$	9.13353	1.00863
$83$	9.54759	1.04798	0.523992	−	0.851723i	$-0.324442\pi$
$83$	9.54759	1.04798	0.523992	+	0.851723i	$0.324442\pi$
$84$	0.000322773 0	3.52174e−5 0
$85$	8.61937	0.934902
$86$	7.81296	0.842494
$87$	15.6273	1.67542
$88$	1.15171	0.122773
$89$	−7.82879	−0.829850	−0.414925	−	0.909856i	$-0.636192\pi$
$89$	−7.82879	−0.829850	−0.414925	+	0.909856i	$0.636192\pi$
$90$	3.54135	0.373291
$91$	0.000305008 0	3.19735e−5 0
$92$	−1.25173	−0.130501
$93$	10.3357	1.07176
$94$	1.52621	0.157417
$95$	−12.2613	−1.25799
$96$	2.03510	0.207706
$97$	−14.9054	−1.51342	−0.756709	−	0.653752i	$-0.773194\pi$
$97$	−14.9054	−1.51342	−0.756709	+	0.653752i	$0.773194\pi$
$98$	7.00000	0.707107
$99$	−1.31482	−0.132144
$100$	4.62267	0.462267
$101$	10.2298	1.01790	0.508952	−	0.860795i	$-0.330033\pi$
$101$	10.2298	1.01790	0.508952	+	0.860795i	$0.330033\pi$
$102$	−5.65475	−0.559903
$103$	−15.8367	−1.56043	−0.780216	−	0.625510i	$-0.784891\pi$
$103$	−15.8367	−1.56043	−0.780216	+	0.625510i	$0.784891\pi$
$104$	1.92309	0.188574
$105$	−0.00100126	−9.77125e−5 0
$106$	4.44905	0.432130
$107$	−5.44497	−0.526385	−0.263192	−	0.964743i	$-0.584775\pi$
$107$	−5.44497	−0.526385	−0.263192	+	0.964743i	$0.584775\pi$
$108$	3.78199	0.363922
$109$	−11.1255	−1.06563	−0.532816	−	0.846231i	$-0.678866\pi$
$109$	−11.1255	−1.06563	−0.532816	+	0.846231i	$0.678866\pi$
$110$	−3.57266	−0.340640
$111$	−3.82935	−0.363466
$112$	−0.000158603 0	−1.49866e−5 0
$113$	−15.7860	−1.48503	−0.742513	−	0.669832i	$-0.766366\pi$
$113$	−15.7860	−1.48503	−0.742513	+	0.669832i	$0.766366\pi$
$114$	8.04406	0.753395
$115$	3.88291	0.362083
$116$	−7.67891	−0.712969
$117$	−2.19543	−0.202968
$118$	2.90576	0.267497
$119$	0.000440697 0	4.03986e−5 0
$120$	−6.31296	−0.576291
$121$	−9.67356	−0.879414
$122$	3.21513	0.291084
$123$	18.5876	1.67599
$124$	−5.07874	−0.456084
$125$	1.17050	0.104693
$126$	0.000181064 0	1.61305e−5 0
$127$	14.2876	1.26782	0.633912	−	0.773405i	$-0.281448\pi$
$127$	14.2876	1.26782	0.633912	+	0.773405i	$0.281448\pi$
$128$	−1.00000	−0.0883883
$129$	15.9001	1.39993
$130$	−5.96550	−0.523209
$131$	−18.2316	−1.59291	−0.796453	−	0.604701i	$-0.793293\pi$
$131$	−18.2316	−1.59291	−0.796453	+	0.604701i	$0.793293\pi$
$132$	2.34385	0.204006
$133$	−0.000626906 0	−5.43596e−5 0
$134$	6.33413	0.547185
$135$	−11.7319	−1.00972
$136$	2.77861	0.238264
$137$	9.22935	0.788517	0.394258	−	0.919000i	$-0.371002\pi$
$137$	9.22935	0.788517	0.394258	+	0.919000i	$0.371002\pi$
$138$	−2.54738	−0.216848
$139$	20.5444	1.74255	0.871275	−	0.490795i	$-0.163294\pi$
$139$	20.5444	1.74255	0.871275	+	0.490795i	$0.163294\pi$
$140$	0.000491994 0	4.15811e−5 0
$141$	3.10599	0.261572
$142$	12.2401	1.02717
$143$	2.21485	0.185215
$144$	1.14162	0.0951348
$145$	23.8203	1.97817
$146$	−12.2476	−1.01362
$147$	14.2457	1.17496
$148$	1.88166	0.154671
$149$	−18.7793	−1.53846	−0.769229	−	0.638973i	$-0.779359\pi$
$149$	−18.7793	−1.53846	−0.769229	+	0.638973i	$0.779359\pi$
$150$	9.40757	0.768125
$151$	−3.52460	−0.286828	−0.143414	−	0.989663i	$-0.545808\pi$
$151$	−3.52460	−0.286828	−0.143414	+	0.989663i	$0.545808\pi$
$152$	−3.95267	−0.320604
$153$	−3.17211	−0.256450
$154$	−0.000182665 0	−1.47196e−5 0
$155$	15.7545	1.26543
$156$	3.91367	0.313344
$157$	−5.95848	−0.475539	−0.237769	−	0.971322i	$-0.576416\pi$
$157$	−5.95848	−0.475539	−0.237769	+	0.971322i	$0.576416\pi$
$158$	−10.5905	−0.842531
$159$	9.05425	0.718049
$160$	3.10204	0.245238
$161$	0.000198528 0	1.56462e−5 0
$162$	11.1216	0.873792
$163$	7.92921	0.621064	0.310532	−	0.950563i	$-0.399493\pi$
$163$	7.92921	0.621064	0.310532	+	0.950563i	$0.399493\pi$
$164$	−9.13353	−0.713209
$165$	−7.27071	−0.566024
$166$	−9.54759	−0.741037
$167$	−10.8912	−0.842786	−0.421393	−	0.906878i	$-0.638459\pi$
$167$	−10.8912	−0.842786	−0.421393	+	0.906878i	$0.638459\pi$
$168$	−0.000322773 0	−2.49025e−5 0
$169$	−9.30173	−0.715518
$170$	−8.61937	−0.661076
$171$	4.51244	0.345075
$172$	−7.81296	−0.595733
$173$	21.6655	1.64720	0.823598	−	0.567175i	$-0.191964\pi$
$173$	21.6655	1.64720	0.823598	+	0.567175i	$0.191964\pi$
$174$	−15.6273	−1.18470
$175$	−0.000733170 0	−5.54225e−5 0
$176$	−1.15171	−0.0868136
$177$	5.91351	0.444486
$178$	7.82879	0.586792
$179$	−12.1106	−0.905192	−0.452596	−	0.891716i	$-0.649502\pi$
$179$	−12.1106	−0.905192	−0.452596	+	0.891716i	$0.649502\pi$
$180$	−3.54135	−0.263956
$181$	−10.7526	−0.799233	−0.399617	−	0.916682i	$-0.630857\pi$
$181$	−10.7526	−0.799233	−0.399617	+	0.916682i	$0.630857\pi$
$182$	−0.000305008 0	−2.26087e−5 0
$183$	6.54309	0.483679
$184$	1.25173	0.0922785
$185$	−5.83698	−0.429143
$186$	−10.3357	−0.757852
$187$	3.20016	0.234019
$188$	−1.52621	−0.111311
$189$	−0.000599835 0	−4.36316e−5 0
$190$	12.2613	0.889531
$191$	2.47475	0.179066	0.0895332	−	0.995984i	$-0.471462\pi$
$191$	2.47475	0.179066	0.0895332	+	0.995984i	$0.471462\pi$
$192$	−2.03510	−0.146870
$193$	24.6074	1.77128	0.885639	−	0.464374i	$-0.153721\pi$
$193$	24.6074	1.77128	0.885639	+	0.464374i	$0.153721\pi$
$194$	14.9054	1.07015
$195$	−12.1404	−0.869390
$196$	−7.00000	−0.500000
$197$	17.7085	1.26168	0.630841	−	0.775913i	$-0.282710\pi$
$197$	17.7085	1.26168	0.630841	+	0.775913i	$0.282710\pi$
$198$	1.31482	0.0934399
$199$	−16.7007	−1.18388	−0.591941	−	0.805982i	$-0.701638\pi$
$199$	−16.7007	−1.18388	−0.591941	+	0.805982i	$0.701638\pi$
$200$	−4.62267	−0.326872
$201$	12.8906	0.909230
$202$	−10.2298	−0.719767
$203$	0.00121790	8.54798e−5 0
$204$	5.65475	0.395911
$205$	28.3326	1.97883
$206$	15.8367	1.10339
$207$	−1.42899	−0.0993219
$208$	−1.92309	−0.133342
$209$	−4.55234	−0.314892
$210$	0.00100126	6.90932e−5 0
$211$	20.5561	1.41514	0.707570	−	0.706643i	$-0.249791\pi$
$211$	20.5561	1.41514	0.707570	+	0.706643i	$0.249791\pi$
$212$	−4.44905	−0.305562
$213$	24.9098	1.70679
$214$	5.44497	0.372210
$215$	24.2361	1.65289
$216$	−3.78199	−0.257332
$217$	0.000805504 0	5.46812e−5 0
$218$	11.1255	0.753516
$219$	−24.9251	−1.68428
$220$	3.57266	0.240869
$221$	5.34352	0.359444
$222$	3.82935	0.257009
$223$	−17.6403	−1.18128	−0.590642	−	0.806933i	$-0.701126\pi$
$223$	−17.6403	−1.18128	−0.590642	+	0.806933i	$0.701126\pi$
$224$	0.000158603 0	1.05971e−5 0
$225$	5.27732	0.351821
$226$	15.7860	1.05007
$227$	−28.3240	−1.87993	−0.939965	−	0.341270i	$-0.889143\pi$
$227$	−28.3240	−1.87993	−0.939965	+	0.341270i	$0.889143\pi$
$228$	−8.04406	−0.532731
$229$	−0.195020	−0.0128873	−0.00644363	−	0.999979i	$-0.502051\pi$
$229$	−0.195020	−0.0128873	−0.00644363	+	0.999979i	$0.502051\pi$
$230$	−3.88291	−0.256031
$231$	−0.000371742 0	−2.44588e−5 0
$232$	7.67891	0.504145
$233$	17.9514	1.17603	0.588017	−	0.808848i	$-0.299909\pi$
$233$	17.9514	1.17603	0.588017	+	0.808848i	$0.299909\pi$
$234$	2.19543	0.143520
$235$	4.73438	0.308837
$236$	−2.90576	−0.189149
$237$	−21.5526	−1.39999
$238$	−0.000440697 0	−2.85661e−5 0
$239$	24.6541	1.59474	0.797369	−	0.603492i	$-0.206225\pi$
$239$	24.6541	1.59474	0.797369	+	0.603492i	$0.206225\pi$
$240$	6.31296	0.407500
$241$	13.2194	0.851537	0.425768	−	0.904832i	$-0.360004\pi$
$241$	13.2194	0.851537	0.425768	+	0.904832i	$0.360004\pi$
$242$	9.67356	0.621840
$243$	11.2875	0.724093
$244$	−3.21513	−0.205827
$245$	21.7143	1.38728
$246$	−18.5876	−1.18510
$247$	−7.60133	−0.483661
$248$	5.07874	0.322500
$249$	−19.4303	−1.23134
$250$	−1.17050	−0.0740291
$251$	−3.80363	−0.240083	−0.120041	−	0.992769i	$-0.538303\pi$
$251$	−3.80363	−0.240083	−0.120041	+	0.992769i	$0.538303\pi$
$252$	−0.000181064 0	−1.14060e−5 0
$253$	1.44163	0.0906345
$254$	−14.2876	−0.896486
$255$	−17.5413	−1.09848
$256$	1.00000	0.0625000
$257$	−10.9260	−0.681546	−0.340773	−	0.940146i	$-0.610689\pi$
$257$	−10.9260	−0.681546	−0.340773	+	0.940146i	$0.610689\pi$
$258$	−15.9001	−0.989899
$259$	−0.000298437 0	−1.85440e−5 0
$260$	5.96550	0.369965
$261$	−8.76638	−0.542625
$262$	18.2316	1.12635
$263$	16.7915	1.03541	0.517705	−	0.855559i	$-0.326787\pi$
$263$	16.7915	1.03541	0.517705	+	0.855559i	$0.326787\pi$
$264$	−2.34385	−0.144254
$265$	13.8011	0.847798
$266$	0.000626906 0	3.84381e−5 0
$267$	15.9323	0.975043
$268$	−6.33413	−0.386919
$269$	19.6130	1.19583	0.597914	−	0.801560i	$-0.295996\pi$
$269$	19.6130	1.19583	0.597914	+	0.801560i	$0.295996\pi$
$270$	11.7319	0.713980
$271$	0.145480	0.00883731	0.00441865	−	0.999990i	$-0.498593\pi$
$271$	0.145480	0.00883731	0.00441865	+	0.999990i	$0.498593\pi$
$272$	−2.77861	−0.168478
$273$	−0.000620721 0	−3.75677e−5 0
$274$	−9.22935	−0.557565
$275$	−5.32399	−0.321048
$276$	2.54738	0.153334
$277$	24.0865	1.44722	0.723610	−	0.690209i	$-0.242482\pi$
$277$	24.0865	1.44722	0.723610	+	0.690209i	$0.242482\pi$
$278$	−20.5444	−1.23217
$279$	−5.79798	−0.347116
$280$	−0.000491994 0	−2.94023e−5 0
$281$	−13.4864	−0.804530	−0.402265	−	0.915523i	$-0.631777\pi$
$281$	−13.4864	−0.804530	−0.402265	+	0.915523i	$0.631777\pi$
$282$	−3.10599	−0.184959
$283$	26.4744	1.57374	0.786871	−	0.617118i	$-0.211700\pi$
$283$	26.4744	1.57374	0.786871	+	0.617118i	$0.211700\pi$
$284$	−12.2401	−0.726318
$285$	24.9530	1.47809
$286$	−2.21485	−0.130967
$287$	0.00144861	8.55086e−5 0
$288$	−1.14162	−0.0672705
$289$	−9.27931	−0.545842
$290$	−23.8203	−1.39878
$291$	30.3340	1.77821
$292$	12.2476	0.716737
$293$	0.387188	0.0226198	0.0113099	−	0.999936i	$-0.496400\pi$
$293$	0.387188	0.0226198	0.0113099	+	0.999936i	$0.496400\pi$
$294$	−14.2457	−0.830825
$295$	9.01380	0.524803
$296$	−1.88166	−0.109369
$297$	−4.35576	−0.252747
$298$	18.7793	1.08785
$299$	2.40718	0.139211
$300$	−9.40757	−0.543147
$301$	0.00123916	7.14241e−5 0
$302$	3.52460	0.202818
$303$	−20.8186	−1.19600
$304$	3.95267	0.226701
$305$	9.97346	0.571079
$306$	3.17211	0.181338
$307$	4.49916	0.256780	0.128390	−	0.991724i	$-0.459019\pi$
$307$	4.49916	0.256780	0.128390	+	0.991724i	$0.459019\pi$
$308$	0.000182665 0	1.04083e−5 0
$309$	32.2291	1.83345
$310$	−15.7545	−0.894793
$311$	2.53846	0.143943	0.0719715	−	0.997407i	$-0.477071\pi$
$311$	2.53846	0.143943	0.0719715	+	0.997407i	$0.477071\pi$
$312$	−3.91367	−0.221568
$313$	−20.0726	−1.13457	−0.567285	−	0.823521i	$-0.692006\pi$
$313$	−20.0726	−1.13457	−0.567285	+	0.823521i	$0.692006\pi$
$314$	5.95848	0.336256
$315$	0.000561669 0	3.16465e−5 0
$316$	10.5905	0.595759
$317$	33.2270	1.86622	0.933108	−	0.359596i	$-0.117086\pi$
$317$	33.2270	1.86622	0.933108	+	0.359596i	$0.117086\pi$
$318$	−9.05425	−0.507737
$319$	8.84390	0.495163
$320$	−3.10204	−0.173409
$321$	11.0810	0.618483
$322$	−0.000198528 0	−1.10635e−5 0
$323$	−10.9829	−0.611106
$324$	−11.1216	−0.617865
$325$	−8.88980	−0.493117
$326$	−7.92921	−0.439159
$327$	22.6415	1.25208
$328$	9.13353	0.504315
$329$	0.000242062 0	1.33453e−5 0
$330$	7.27071	0.400240
$331$	−3.73128	−0.205090	−0.102545	−	0.994728i	$-0.532699\pi$
$331$	−3.73128	−0.205090	−0.102545	+	0.994728i	$0.532699\pi$
$332$	9.54759	0.523992
$333$	2.14813	0.117717
$334$	10.8912	0.595940
$335$	19.6487	1.07353
$336$	0.000322773 0	1.76087e−5 0
$337$	−18.7528	−1.02153	−0.510765	−	0.859720i	$-0.670638\pi$
$337$	−18.7528	−1.02153	−0.510765	+	0.859720i	$0.670638\pi$
$338$	9.30173	0.505947
$339$	32.1261	1.74485
$340$	8.61937	0.467451
$341$	5.84925	0.316754
$342$	−4.51244	−0.244005
$343$	0.00222045	0.000119893 0
$344$	7.81296	0.421247
$345$	−7.90209	−0.425434
$346$	−21.6655	−1.16474
$347$	−9.58015	−0.514290	−0.257145	−	0.966373i	$-0.582782\pi$
$347$	−9.58015	−0.514290	−0.257145	+	0.966373i	$0.582782\pi$
$348$	15.6273	0.837712
$349$	8.53768	0.457012	0.228506	−	0.973543i	$-0.426616\pi$
$349$	8.53768	0.457012	0.228506	+	0.973543i	$0.426616\pi$
$350$	0.000733170 0	3.91896e−5 0
$351$	−7.27309	−0.388209
$352$	1.15171	0.0613865
$353$	−6.59829	−0.351192	−0.175596	−	0.984462i	$-0.556185\pi$
$353$	−6.59829	−0.351192	−0.175596	+	0.984462i	$0.556185\pi$
$354$	−5.91351	−0.314299
$355$	37.9694	2.01521
$356$	−7.82879	−0.414925
$357$	−0.000896861 0	−4.74669e−5 0
$358$	12.1106	0.640067
$359$	−17.8959	−0.944510	−0.472255	−	0.881462i	$-0.656560\pi$
$359$	−17.8959	−0.944510	−0.472255	+	0.881462i	$0.656560\pi$
$360$	3.54135	0.186645
$361$	−3.37643	−0.177707
$362$	10.7526	0.565143
$363$	19.6866	1.03328
$364$	0.000305008 0	1.59868e−5 0
$365$	−37.9926	−1.98862
$366$	−6.54309	−0.342013
$367$	17.9939	0.939276	0.469638	−	0.882859i	$-0.344385\pi$
$367$	17.9939	0.939276	0.469638	+	0.882859i	$0.344385\pi$
$368$	−1.25173	−0.0652507
$369$	−10.4270	−0.542808
$370$	5.83698	0.303450
$371$	0.000705634 0	3.66347e−5 0
$372$	10.3357	0.535882
$373$	16.8801	0.874021	0.437010	−	0.899456i	$-0.356037\pi$
$373$	16.8801	0.874021	0.437010	+	0.899456i	$0.356037\pi$
$374$	−3.20016	−0.165477
$375$	−2.38209	−0.123010
$376$	1.52621	0.0787084
$377$	14.7672	0.760550
$378$	0.000599835 0	3.08522e−5 0
$379$	−29.4961	−1.51511	−0.757555	−	0.652771i	$-0.773606\pi$
$379$	−29.4961	−1.51511	−0.757555	+	0.652771i	$0.773606\pi$
$380$	−12.2613	−0.628993
$381$	−29.0767	−1.48965
$382$	−2.47475	−0.126619
$383$	−33.7222	−1.72312	−0.861562	−	0.507653i	$-0.830513\pi$
$383$	−33.7222	−1.72312	−0.861562	+	0.507653i	$0.830513\pi$
$384$	2.03510	0.103853
$385$	−0.000566636 0	−2.88784e−5 0
$386$	−24.6074	−1.25248
$387$	−8.91942	−0.453400
$388$	−14.9054	−0.756709
$389$	28.3997	1.43992	0.719961	−	0.694014i	$-0.244160\pi$
$389$	28.3997	1.43992	0.719961	+	0.694014i	$0.244160\pi$
$390$	12.1404	0.614752
$391$	3.47806	0.175893
$392$	7.00000	0.353553
$393$	37.1031	1.87161
$394$	−17.7085	−0.892143
$395$	−32.8520	−1.65297
$396$	−1.31482	−0.0660720
$397$	19.2291	0.965078	0.482539	−	0.875874i	$-0.339715\pi$
$397$	19.2291	0.965078	0.482539	+	0.875874i	$0.339715\pi$
$398$	16.7007	0.837131
$399$	0.00127581	6.38706e−5 0
$400$	4.62267	0.231133
$401$	5.18462	0.258908	0.129454	−	0.991585i	$-0.458678\pi$
$401$	5.18462	0.258908	0.129454	+	0.991585i	$0.458678\pi$
$402$	−12.8906	−0.642923
$403$	9.76686	0.486522
$404$	10.2298	0.508952
$405$	34.4996	1.71430
$406$	−0.00121790	−6.04433e−5 0
$407$	−2.16713	−0.107421
$408$	−5.65475	−0.279952
$409$	8.68004	0.429200	0.214600	−	0.976702i	$-0.431155\pi$
$409$	8.68004	0.429200	0.214600	+	0.976702i	$0.431155\pi$
$410$	−28.3326	−1.39925
$411$	−18.7826	−0.926478
$412$	−15.8367	−0.780216
$413$	0.000460863 0	2.26776e−5 0
$414$	1.42899	0.0702312
$415$	−29.6170	−1.45384
$416$	1.92309	0.0942872
$417$	−41.8098	−2.04743
$418$	4.55234	0.222662
$419$	30.4671	1.48842	0.744209	−	0.667947i	$-0.232827\pi$
$419$	30.4671	1.48842	0.744209	+	0.667947i	$0.232827\pi$
$420$	−0.00100126	−4.88563e−5 0
$421$	−21.2489	−1.03561	−0.517804	−	0.855499i	$-0.673250\pi$
$421$	−21.2489	−1.03561	−0.517804	+	0.855499i	$0.673250\pi$
$422$	−20.5561	−1.00065
$423$	−1.74235	−0.0847161
$424$	4.44905	0.216065
$425$	−12.8446	−0.623055
$426$	−24.9098	−1.20689
$427$	0.000509930 0	2.46772e−5 0
$428$	−5.44497	−0.263192
$429$	−4.50743	−0.217621
$430$	−24.2361	−1.16877
$431$	−8.29753	−0.399678	−0.199839	−	0.979829i	$-0.564042\pi$
$431$	−8.29753	−0.399678	−0.199839	+	0.979829i	$0.564042\pi$
$432$	3.78199	0.181961
$433$	41.3422	1.98678	0.993390	−	0.114785i	$-0.0366179\pi$
$433$	41.3422	1.98678	0.993390	+	0.114785i	$0.0366179\pi$
$434$	−0.000805504 0	−3.86654e−5 0
$435$	−48.4766	−2.32427
$436$	−11.1255	−0.532816
$437$	−4.94766	−0.236678
$438$	24.9251	1.19097
$439$	28.3393	1.35256	0.676281	−	0.736644i	$-0.263591\pi$
$439$	28.3393	1.35256	0.676281	+	0.736644i	$0.263591\pi$
$440$	−3.57266	−0.170320
$441$	−7.99133	−0.380539
$442$	−5.34352	−0.254165
$443$	−22.9856	−1.09208	−0.546039	−	0.837760i	$-0.683865\pi$
$443$	−22.9856	−1.09208	−0.546039	+	0.837760i	$0.683865\pi$
$444$	−3.82935	−0.181733
$445$	24.2852	1.15123
$446$	17.6403	0.835294
$447$	38.2176	1.80763
$448$	−0.000158603 0	−7.49330e−6 0
$449$	4.32687	0.204198	0.102099	−	0.994774i	$-0.467444\pi$
$449$	4.32687	0.204198	0.102099	+	0.994774i	$0.467444\pi$
$450$	−5.27732	−0.248775
$451$	10.5192	0.495330
$452$	−15.7860	−0.742513
$453$	7.17290	0.337012
$454$	28.3240	1.32931
$455$	−0.000946148 0	−4.43561e−5 0
$456$	8.04406	0.376698
$457$	16.6142	0.777179	0.388590	−	0.921411i	$-0.372962\pi$
$457$	16.6142	0.777179	0.388590	+	0.921411i	$0.372962\pi$
$458$	0.195020	0.00911267
$459$	−10.5087	−0.490503
$460$	3.88291	0.181042
$461$	34.0721	1.58689	0.793447	−	0.608639i	$-0.208284\pi$
$461$	34.0721	1.58689	0.793447	+	0.608639i	$0.208284\pi$
$462$	0.000371742 0	1.72950e−5 0
$463$	−3.17379	−0.147499	−0.0737493	−	0.997277i	$-0.523496\pi$
$463$	−3.17379	−0.147499	−0.0737493	+	0.997277i	$0.523496\pi$
$464$	−7.67891	−0.356484
$465$	−32.0618	−1.48683
$466$	−17.9514	−0.831582
$467$	2.77806	0.128553	0.0642767	−	0.997932i	$-0.479526\pi$
$467$	2.77806	0.128553	0.0642767	+	0.997932i	$0.479526\pi$
$468$	−2.19543	−0.101484
$469$	0.00100461	4.63887e−5 0
$470$	−4.73438	−0.218381
$471$	12.1261	0.558740
$472$	2.90576	0.133749
$473$	8.99829	0.413742
$474$	21.5526	0.989943
$475$	18.2719	0.838370
$476$	0.000440697 0	2.01993e−5 0
$477$	−5.07912	−0.232557
$478$	−24.6541	−1.12765
$479$	−10.2999	−0.470613	−0.235307	−	0.971921i	$-0.575609\pi$
$479$	−10.2999	−0.470613	−0.235307	+	0.971921i	$0.575609\pi$
$480$	−6.31296	−0.288146
$481$	−3.61859	−0.164994
$482$	−13.2194	−0.602127
$483$	−0.000404023 0	−1.83837e−5 0
$484$	−9.67356	−0.439707
$485$	46.2373	2.09953
$486$	−11.2875	−0.512011
$487$	10.1376	0.459377	0.229688	−	0.973264i	$-0.426229\pi$
$487$	10.1376	0.459377	0.229688	+	0.973264i	$0.426229\pi$
$488$	3.21513	0.145542
$489$	−16.1367	−0.729728
$490$	−21.7143	−0.980952
$491$	12.0448	0.543575	0.271787	−	0.962357i	$-0.412385\pi$
$491$	12.0448	0.543575	0.271787	+	0.962357i	$0.412385\pi$
$492$	18.5876	0.837994
$493$	21.3367	0.960957
$494$	7.60133	0.342000
$495$	4.07862	0.183320
$496$	−5.07874	−0.228042
$497$	0.00194132	8.70803e−5 0
$498$	19.4303	0.870691
$499$	−33.0238	−1.47835	−0.739175	−	0.673513i	$-0.764784\pi$
$499$	−33.0238	−1.47835	−0.739175	+	0.673513i	$0.764784\pi$
$500$	1.17050	0.0523465
$501$	22.1646	0.990243
$502$	3.80363	0.169764
$503$	−32.1723	−1.43449	−0.717245	−	0.696821i	$-0.754597\pi$
$503$	−32.1723	−1.43449	−0.717245	+	0.696821i	$0.754597\pi$
$504$	0.000181064 0	8.06525e−6 0
$505$	−31.7333	−1.41211
$506$	−1.44163	−0.0640882
$507$	18.9299	0.840707
$508$	14.2876	0.633912
$509$	13.8556	0.614137	0.307069	−	0.951687i	$-0.400652\pi$
$509$	13.8556	0.614137	0.307069	+	0.951687i	$0.400652\pi$
$510$	17.5413	0.776740
$511$	−0.00194251	−8.59316e−5 0
$512$	−1.00000	−0.0441942
$513$	14.9489	0.660011
$514$	10.9260	0.481926
$515$	49.1260	2.16475
$516$	15.9001	0.699964
$517$	1.75776	0.0773062
$518$	0.000298437 0	1.31126e−5 0
$519$	−44.0913	−1.93539
$520$	−5.96550	−0.261605
$521$	−13.1038	−0.574087	−0.287044	−	0.957918i	$-0.592672\pi$
$521$	−13.1038	−0.574087	−0.287044	+	0.957918i	$0.592672\pi$
$522$	8.76638	0.383694
$523$	−28.1969	−1.23296	−0.616482	−	0.787369i	$-0.711443\pi$
$523$	−28.1969	−1.23296	−0.616482	+	0.787369i	$0.711443\pi$
$524$	−18.2316	−0.796453
$525$	0.00149207	6.51194e−5 0
$526$	−16.7915	−0.732145
$527$	14.1118	0.614721
$528$	2.34385	0.102003
$529$	−21.4332	−0.931877
$530$	−13.8011	−0.599484
$531$	−3.31727	−0.143957
$532$	−0.000626906 0	−2.71798e−5 0
$533$	17.5646	0.760807
$534$	−15.9323	−0.689460
$535$	16.8905	0.730241
$536$	6.33413	0.273593
$537$	24.6463	1.06357
$538$	−19.6130	−0.845578
$539$	8.06199	0.347255
$540$	−11.7319	−0.504860
$541$	−17.7508	−0.763165	−0.381582	−	0.924335i	$-0.624621\pi$
$541$	−17.7508	−0.763165	−0.381582	+	0.924335i	$0.624621\pi$
$542$	−0.145480	−0.00624892
$543$	21.8825	0.939070
$544$	2.77861	0.119132
$545$	34.5118	1.47833
$546$	0.000620721 0	2.65644e−5 0
$547$	−6.76497	−0.289249	−0.144625	−	0.989487i	$-0.546197\pi$
$547$	−6.76497	−0.289249	−0.144625	+	0.989487i	$0.546197\pi$
$548$	9.22935	0.394258
$549$	−3.67045	−0.156651
$550$	5.32399	0.227016
$551$	−30.3522	−1.29305
$552$	−2.54738	−0.108424
$553$	−0.00167968	−7.14273e−5 0
$554$	−24.0865	−1.02334
$555$	11.8788	0.504228
$556$	20.5444	0.871275
$557$	−31.8268	−1.34854	−0.674272	−	0.738483i	$-0.735543\pi$
$557$	−31.8268	−1.34854	−0.674272	+	0.738483i	$0.735543\pi$
$558$	5.79798	0.245448
$559$	15.0250	0.635491
$560$	0.000491994 0	2.07905e−5 0
$561$	−6.51264	−0.274964
$562$	13.4864	0.568889
$563$	1.94333	0.0819017	0.0409508	−	0.999161i	$-0.486961\pi$
$563$	1.94333	0.0819017	0.0409508	+	0.999161i	$0.486961\pi$
$564$	3.10599	0.130786
$565$	48.9690	2.06014
$566$	−26.4744	−1.11280
$567$	0.00176392	7.40775e−5 0
$568$	12.2401	0.513584
$569$	−23.9467	−1.00390	−0.501949	−	0.864897i	$-0.667384\pi$
$569$	−23.9467	−1.00390	−0.501949	+	0.864897i	$0.667384\pi$
$570$	−24.9530	−1.04517
$571$	−45.7973	−1.91656	−0.958279	−	0.285836i	$-0.907729\pi$
$571$	−45.7973	−1.91656	−0.958279	+	0.285836i	$0.907729\pi$
$572$	2.21485	0.0926074
$573$	−5.03635	−0.210396
$574$	−0.00144861	−6.04637e−5 0
$575$	−5.78631	−0.241306
$576$	1.14162	0.0475674
$577$	−36.0346	−1.50014	−0.750070	−	0.661359i	$-0.769980\pi$
$577$	−36.0346	−1.50014	−0.750070	+	0.661359i	$0.769980\pi$
$578$	9.27931	0.385968
$579$	−50.0784	−2.08119
$580$	23.8203	0.989084
$581$	−0.00151428	−6.28229e−5 0
$582$	−30.3340	−1.25738
$583$	5.12403	0.212216
$584$	−12.2476	−0.506809
$585$	6.81033	0.281572
$586$	−0.387188	−0.0159946
$587$	−21.6037	−0.891682	−0.445841	−	0.895112i	$-0.647095\pi$
$587$	−21.6037	−0.891682	−0.445841	+	0.895112i	$0.647095\pi$
$588$	14.2457	0.587482
$589$	−20.0745	−0.827157
$590$	−9.01380	−0.371092
$591$	−36.0386	−1.48243
$592$	1.88166	0.0773356
$593$	16.6679	0.684468	0.342234	−	0.939615i	$-0.388816\pi$
$593$	16.6679	0.684468	0.342234	+	0.939615i	$0.388816\pi$
$594$	4.35576	0.178719
$595$	−0.00136706	−5.60440e−5 0
$596$	−18.7793	−0.769229
$597$	33.9875	1.39102
$598$	−2.40718	−0.0984369
$599$	−12.9001	−0.527086	−0.263543	−	0.964648i	$-0.584891\pi$
$599$	−12.9001	−0.527086	−0.263543	+	0.964648i	$0.584891\pi$
$600$	9.40757	0.384063
$601$	37.6738	1.53674	0.768372	−	0.640003i	$-0.221067\pi$
$601$	37.6738	1.53674	0.768372	+	0.640003i	$0.221067\pi$
$602$	−0.00123916	−5.05045e−5 0
$603$	−7.23116	−0.294475
$604$	−3.52460	−0.143414
$605$	30.0078	1.21999
$606$	20.8186	0.845700
$607$	−12.6552	−0.513659	−0.256830	−	0.966457i	$-0.582678\pi$
$607$	−12.6552	−0.513659	−0.256830	+	0.966457i	$0.582678\pi$
$608$	−3.95267	−0.160302
$609$	−0.00247854	−0.000100436 0
$610$	−9.97346	−0.403814
$611$	2.93504	0.118739
$612$	−3.17211	−0.128225
$613$	7.06436	0.285327	0.142663	−	0.989771i	$-0.454433\pi$
$613$	7.06436	0.285327	0.142663	+	0.989771i	$0.454433\pi$
$614$	−4.49916	−0.181571
$615$	−57.6596	−2.32506
$616$	−0.000182665 0	−7.35980e−6 0
$617$	27.5301	1.10832	0.554161	−	0.832410i	$-0.313039\pi$
$617$	27.5301	1.10832	0.554161	+	0.832410i	$0.313039\pi$
$618$	−32.2291	−1.29645
$619$	25.0552	1.00705	0.503527	−	0.863980i	$-0.332036\pi$
$619$	25.0552	1.00705	0.503527	+	0.863980i	$0.332036\pi$
$620$	15.7545	0.632714
$621$	−4.73401	−0.189969
$622$	−2.53846	−0.101783
$623$	0.00124167	4.97465e−5 0
$624$	3.91367	0.156672
$625$	−26.7443	−1.06977
$626$	20.0726	0.802262
$627$	9.26445	0.369986
$628$	−5.95848	−0.237769
$629$	−5.22840	−0.208470
$630$	−0.000561669 0	−2.23774e−5 0
$631$	24.0838	0.958762	0.479381	−	0.877607i	$-0.340861\pi$
$631$	24.0838	0.958762	0.479381	+	0.877607i	$0.340861\pi$
$632$	−10.5905	−0.421266
$633$	−41.8336	−1.66274
$634$	−33.2270	−1.31961
$635$	−44.3209	−1.75882
$636$	9.05425	0.359024
$637$	13.4616	0.533369
$638$	−8.84390	−0.350133
$639$	−13.9736	−0.552785
$640$	3.10204	0.122619
$641$	−34.4280	−1.35983	−0.679913	−	0.733293i	$-0.737982\pi$
$641$	−34.4280	−1.35983	−0.679913	+	0.733293i	$0.737982\pi$
$642$	−11.0810	−0.437333
$643$	37.8433	1.49239	0.746196	−	0.665726i	$-0.231878\pi$
$643$	37.8433	1.49239	0.746196	+	0.665726i	$0.231878\pi$
$644$	0.000198528 0	7.82309e−6 0
$645$	−49.3229	−1.94209
$646$	10.9829	0.432118
$647$	23.1762	0.911149	0.455575	−	0.890198i	$-0.349434\pi$
$647$	23.1762	0.911149	0.455575	+	0.890198i	$0.349434\pi$
$648$	11.1216	0.436896
$649$	3.34660	0.131366
$650$	8.88980	0.348687
$651$	−0.00163928	−6.42484e−5 0
$652$	7.92921	0.310532
$653$	−50.8271	−1.98902	−0.994508	−	0.104658i	$-0.966625\pi$
$653$	−50.8271	−1.98902	−0.994508	+	0.104658i	$0.966625\pi$
$654$	−22.6415	−0.885353
$655$	56.5553	2.20980
$656$	−9.13353	−0.356604
$657$	13.9821	0.545493
$658$	−0.000242062 0	−9.43658e−6 0
$659$	−7.32525	−0.285351	−0.142676	−	0.989770i	$-0.545571\pi$
$659$	−7.32525	−0.285351	−0.142676	+	0.989770i	$0.545571\pi$
$660$	−7.27071	−0.283012
$661$	−6.40421	−0.249095	−0.124547	−	0.992214i	$-0.539748\pi$
$661$	−6.40421	−0.249095	−0.124547	+	0.992214i	$0.539748\pi$
$662$	3.73128	0.145020
$663$	−10.8746	−0.422334
$664$	−9.54759	−0.370518
$665$	0.00194469	7.54118e−5 0
$666$	−2.14813	−0.0832385
$667$	9.61189	0.372174
$668$	−10.8912	−0.421393
$669$	35.8998	1.38797
$670$	−19.6487	−0.759097
$671$	3.70290	0.142949
$672$	−0.000322773 0	−1.24512e−5 0
$673$	42.2006	1.62671	0.813356	−	0.581766i	$-0.197638\pi$
$673$	42.2006	1.62671	0.813356	+	0.581766i	$0.197638\pi$
$674$	18.7528	0.722331
$675$	17.4829	0.672916
$676$	−9.30173	−0.357759
$677$	−30.4881	−1.17175	−0.585877	−	0.810400i	$-0.699250\pi$
$677$	−30.4881	−1.17175	−0.585877	+	0.810400i	$0.699250\pi$
$678$	−32.1261	−1.23380
$679$	0.00236405	9.07239e−5 0
$680$	−8.61937	−0.330538
$681$	57.6421	2.20885
$682$	−5.84925	−0.223979
$683$	−6.79209	−0.259892	−0.129946	−	0.991521i	$-0.541480\pi$
$683$	−6.79209	−0.259892	−0.129946	+	0.991521i	$0.541480\pi$
$684$	4.51244	0.172537
$685$	−28.6298	−1.09389
$686$	−0.00222045	−8.47770e−5 0
$687$	0.396884	0.0151421
$688$	−7.81296	−0.297866
$689$	8.55592	0.325955
$690$	7.90209	0.300828
$691$	18.3970	0.699853	0.349927	−	0.936777i	$-0.386206\pi$
$691$	18.3970	0.699853	0.349927	+	0.936777i	$0.386206\pi$
$692$	21.6655	0.823598
$693$	0.000208534 0	7.92156e−6 0
$694$	9.58015	0.363658
$695$	−63.7295	−2.41740
$696$	−15.6273	−0.592352
$697$	25.3785	0.961281
$698$	−8.53768	−0.323156
$699$	−36.5328	−1.38180
$700$	−0.000733170 0	−2.77112e−5 0
$701$	46.7719	1.76655	0.883276	−	0.468853i	$-0.155333\pi$
$701$	46.7719	1.76655	0.883276	+	0.468853i	$0.155333\pi$
$702$	7.27309	0.274505
$703$	7.43756	0.280513
$704$	−1.15171	−0.0434068
$705$	−9.63492	−0.362872
$706$	6.59829	0.248330
$707$	−0.00162248	−6.10197e−5 0
$708$	5.91351	0.222243
$709$	−45.3755	−1.70411	−0.852056	−	0.523450i	$-0.824645\pi$
$709$	−45.3755	−1.70411	−0.852056	+	0.523450i	$0.824645\pi$
$710$	−37.9694	−1.42497
$711$	12.0903	0.453420
$712$	7.82879	0.293396
$713$	6.35719	0.238079
$714$	0.000896861 0	3.35642e−5 0
$715$	−6.87055	−0.256944
$716$	−12.1106	−0.452596
$717$	−50.1734	−1.87376
$718$	17.8959	0.667870
$719$	−0.736183	−0.0274550	−0.0137275	−	0.999906i	$-0.504370\pi$
$719$	−0.736183	−0.0274550	−0.0137275	+	0.999906i	$0.504370\pi$
$720$	−3.54135	−0.131978
$721$	0.00251174	9.35423e−5 0
$722$	3.37643	0.125658
$723$	−26.9028	−1.00052
$724$	−10.7526	−0.399617
$725$	−35.4970	−1.31833
$726$	−19.6866	−0.730639
$727$	27.4071	1.01647	0.508236	−	0.861218i	$-0.330298\pi$
$727$	27.4071	1.01647	0.508236	+	0.861218i	$0.330298\pi$
$728$	−0.000305008 0	−1.13044e−5 0
$729$	10.3935	0.384946
$730$	37.9926	1.40617
$731$	21.7092	0.802944
$732$	6.54309	0.241840
$733$	−3.36123	−0.124150	−0.0620750	−	0.998071i	$-0.519772\pi$
$733$	−3.36123	−0.124150	−0.0620750	+	0.998071i	$0.519772\pi$
$734$	−17.9939	−0.664168
$735$	−44.1907	−1.63000
$736$	1.25173	0.0461392
$737$	7.29510	0.268718
$738$	10.4270	0.383823
$739$	−29.4478	−1.08325	−0.541627	−	0.840619i	$-0.682191\pi$
$739$	−29.4478	−1.08325	−0.541627	+	0.840619i	$0.682191\pi$
$740$	−5.83698	−0.214572
$741$	15.4694	0.568284
$742$	−0.000705634 0	−2.59046e−5 0
$743$	0.316422	0.0116084	0.00580420	−	0.999983i	$-0.498152\pi$
$743$	0.316422	0.0116084	0.00580420	+	0.999983i	$0.498152\pi$
$744$	−10.3357	−0.378926
$745$	58.2541	2.13427
$746$	−16.8801	−0.618026
$747$	10.8997	0.398799
$748$	3.20016	0.117010
$749$	0.000863589 0	3.15549e−5 0
$750$	2.38209	0.0869815
$751$	−38.8221	−1.41664	−0.708320	−	0.705891i	$-0.750547\pi$
$751$	−38.8221	−1.41664	−0.708320	+	0.705891i	$0.750547\pi$
$752$	−1.52621	−0.0556553
$753$	7.74074	0.282088
$754$	−14.7672	−0.537790
$755$	10.9334	0.397909
$756$	−0.000599835 0	−2.18158e−5 0
$757$	40.8858	1.48602	0.743009	−	0.669281i	$-0.233398\pi$
$757$	40.8858	1.48602	0.743009	+	0.669281i	$0.233398\pi$
$758$	29.4961	1.07134
$759$	−2.93386	−0.106492
$760$	12.2613	0.444765
$761$	−8.77300	−0.318021	−0.159011	−	0.987277i	$-0.550830\pi$
$761$	−8.77300	−0.318021	−0.159011	+	0.987277i	$0.550830\pi$
$762$	29.0767	1.05334
$763$	0.00176454	6.38808e−5 0
$764$	2.47475	0.0895332
$765$	9.84003	0.355767
$766$	33.7222	1.21843
$767$	5.58804	0.201772
$768$	−2.03510	−0.0734352
$769$	−6.26651	−0.225976	−0.112988	−	0.993596i	$-0.536042\pi$
$769$	−6.26651	−0.225976	−0.112988	+	0.993596i	$0.536042\pi$
$770$	0.000566636 0	2.04201e−5 0
$771$	22.2355	0.800792
$772$	24.6074	0.885639
$773$	54.2091	1.94977	0.974883	−	0.222718i	$-0.0714928\pi$
$773$	54.2091	1.94977	0.974883	+	0.222718i	$0.0714928\pi$
$774$	8.91942	0.320602
$775$	−23.4773	−0.843330
$776$	14.9054	0.535074
$777$	0.000607348 0	2.17885e−5 0
$778$	−28.3997	−1.01818
$779$	−36.1018	−1.29348
$780$	−12.1404	−0.434695
$781$	14.0971	0.504434
$782$	−3.47806	−0.124375
$783$	−29.0415	−1.03786
$784$	−7.00000	−0.250000
$785$	18.4835	0.659703
$786$	−37.1031	−1.32343
$787$	31.0368	1.10634	0.553172	−	0.833067i	$-0.313417\pi$
$787$	31.0368	1.10634	0.553172	+	0.833067i	$0.313417\pi$
$788$	17.7085	0.630841
$789$	−34.1724	−1.21657
$790$	32.8520	1.16882
$791$	0.00250372	8.90220e−5 0
$792$	1.31482	0.0467200
$793$	6.18297	0.219564
$794$	−19.2291	−0.682414
$795$	−28.0867	−0.996131
$796$	−16.7007	−0.591941
$797$	2.42118	0.0857625	0.0428812	−	0.999080i	$-0.486346\pi$
$797$	2.42118	0.0857625	0.0428812	+	0.999080i	$0.486346\pi$
$798$	−0.00127581	−4.51633e−5 0
$799$	4.24076	0.150027
$800$	−4.62267	−0.163436
$801$	−8.93748	−0.315790
$802$	−5.18462	−0.183075
$803$	−14.1057	−0.497780
$804$	12.8906	0.454615
$805$	−0.000615842 0	−2.17056e−5 0
$806$	−9.76686	−0.344023
$807$	−39.9144	−1.40505
$808$	−10.2298	−0.359883
$809$	6.49837	0.228471	0.114235	−	0.993454i	$-0.463558\pi$
$809$	6.49837	0.228471	0.114235	+	0.993454i	$0.463558\pi$
$810$	−34.4996	−1.21219
$811$	13.2631	0.465729	0.232864	−	0.972509i	$-0.425190\pi$
$811$	13.2631	0.465729	0.232864	+	0.972509i	$0.425190\pi$
$812$	0.00121790	4.27399e−5 0
$813$	−0.296067	−0.0103835
$814$	2.16713	0.0759578
$815$	−24.5968	−0.861587
$816$	5.65475	0.197956
$817$	−30.8820	−1.08043
$818$	−8.68004	−0.303490
$819$	0.000348203 0	1.21672e−5 0
$820$	28.3326	0.989417
$821$	9.75584	0.340481	0.170241	−	0.985403i	$-0.445546\pi$
$821$	9.75584	0.340481	0.170241	+	0.985403i	$0.445546\pi$
$822$	18.7826	0.655119
$823$	−19.9137	−0.694148	−0.347074	−	0.937838i	$-0.612825\pi$
$823$	−19.9137	−0.694148	−0.347074	+	0.937838i	$0.612825\pi$
$824$	15.8367	0.551696
$825$	10.8348	0.377220
$826$	−0.000460863 0	−1.60355e−5 0
$827$	6.59077	0.229184	0.114592	−	0.993413i	$-0.463444\pi$
$827$	6.59077	0.229184	0.114592	+	0.993413i	$0.463444\pi$
$828$	−1.42899	−0.0496610
$829$	−24.0021	−0.833626	−0.416813	−	0.908992i	$-0.636853\pi$
$829$	−24.0021	−0.833626	−0.416813	+	0.908992i	$0.636853\pi$
$830$	29.6170	1.02802
$831$	−49.0184	−1.70043
$832$	−1.92309	−0.0666711
$833$	19.4503	0.673913
$834$	41.8098	1.44775
$835$	33.7849	1.16918
$836$	−4.55234	−0.157446
$837$	−19.2077	−0.663916
$838$	−30.4671	−1.05247
$839$	30.8132	1.06379	0.531895	−	0.846811i	$-0.321480\pi$
$839$	30.8132	1.06379	0.531895	+	0.846811i	$0.321480\pi$
$840$	0.00100126	3.45466e−5 0
$841$	29.9656	1.03330
$842$	21.2489	0.732285
$843$	27.4461	0.945293
$844$	20.5561	0.707570
$845$	28.8544	0.992620
$846$	1.74235	0.0599033
$847$	0.00153426	5.27177e−5 0
$848$	−4.44905	−0.152781
$849$	−53.8780	−1.84909
$850$	12.8446	0.440566
$851$	−2.35532	−0.0807393
$852$	24.9098	0.853397
$853$	25.9275	0.887739	0.443870	−	0.896091i	$-0.353605\pi$
$853$	25.9275	0.887739	0.443870	+	0.896091i	$0.353605\pi$
$854$	−0.000509930 0	−1.74494e−5 0
$855$	−13.9978	−0.478714
$856$	5.44497	0.186105
$857$	−10.6514	−0.363844	−0.181922	−	0.983313i	$-0.558232\pi$
$857$	−10.6514	−0.363844	−0.181922	+	0.983313i	$0.558232\pi$
$858$	4.50743	0.153881
$859$	54.1077	1.84613	0.923065	−	0.384645i	$-0.125676\pi$
$859$	54.1077	1.84613	0.923065	+	0.384645i	$0.125676\pi$
$860$	24.2361	0.826446
$861$	−0.00294806	−0.000100470 0
$862$	8.29753	0.282615
$863$	−38.5189	−1.31120	−0.655599	−	0.755109i	$-0.727584\pi$
$863$	−38.5189	−1.31120	−0.655599	+	0.755109i	$0.727584\pi$
$864$	−3.78199	−0.128666
$865$	−67.2072	−2.28511
$866$	−41.3422	−1.40487
$867$	18.8843	0.641344
$868$	0.000805504 0	2.73406e−5 0
$869$	−12.1972	−0.413760
$870$	48.4766	1.64351
$871$	12.1811	0.412741
$872$	11.1255	0.376758
$873$	−17.0163	−0.575915
$874$	4.94766	0.167357
$875$	−0.000185646 0	−6.27596e−6 0
$876$	−24.9251	−0.842139
$877$	−14.8641	−0.501926	−0.250963	−	0.967997i	$-0.580747\pi$
$877$	−14.8641	−0.501926	−0.250963	+	0.967997i	$0.580747\pi$
$878$	−28.3393	−0.956405
$879$	−0.787965	−0.0265774
$880$	3.57266	0.120434
$881$	−20.4905	−0.690341	−0.345171	−	0.938540i	$-0.612179\pi$
$881$	−20.4905	−0.690341	−0.345171	+	0.938540i	$0.612179\pi$
$882$	7.99133	0.269082
$883$	11.1634	0.375677	0.187839	−	0.982200i	$-0.439852\pi$
$883$	11.1634	0.375677	0.187839	+	0.982200i	$0.439852\pi$
$884$	5.34352	0.179722
$885$	−18.3439	−0.616625
$886$	22.9856	0.772215
$887$	−11.7200	−0.393519	−0.196760	−	0.980452i	$-0.563042\pi$
$887$	−11.7200	−0.393519	−0.196760	+	0.980452i	$0.563042\pi$
$888$	3.82935	0.128505
$889$	−0.00226607	−7.60014e−5 0
$890$	−24.2852	−0.814043
$891$	12.8088	0.429113
$892$	−17.6403	−0.590642
$893$	−6.03261	−0.201874
$894$	−38.2176	−1.27819
$895$	37.5677	1.25575
$896$	0.000158603 0	5.29856e−6 0
$897$	−4.89884	−0.163568
$898$	−4.32687	−0.144389
$899$	38.9991	1.30069
$900$	5.27732	0.175911
$901$	12.3622	0.411844
$902$	−10.5192	−0.350251
$903$	−0.00252181	−8.39207e−5 0
$904$	15.7860	0.525036
$905$	33.3550	1.10876
$906$	−7.17290	−0.238303
$907$	−58.5801	−1.94512	−0.972559	−	0.232654i	$-0.925259\pi$
$907$	−58.5801	−1.94512	−0.972559	+	0.232654i	$0.925259\pi$
$908$	−28.3240	−0.939965
$909$	11.6785	0.387352
$910$	0.000946148 0	3.13645e−5 0
$911$	8.47209	0.280693	0.140346	−	0.990102i	$-0.455178\pi$
$911$	8.47209	0.280693	0.140346	+	0.990102i	$0.455178\pi$
$912$	−8.04406	−0.266365
$913$	−10.9961	−0.363917
$914$	−16.6142	−0.549549
$915$	−20.2970	−0.670997
$916$	−0.195020	−0.00644363
$917$	0.00289160	9.54890e−5 0
$918$	10.5087	0.346838
$919$	−43.9485	−1.44973	−0.724864	−	0.688892i	$-0.758097\pi$
$919$	−43.9485	−1.44973	−0.724864	+	0.688892i	$0.758097\pi$
$920$	−3.88291	−0.128016
$921$	−9.15622	−0.301708
$922$	−34.0721	−1.12210
$923$	23.5388	0.774791
$924$	−0.000371742 0	−1.22294e−5 0
$925$	8.69827	0.285997
$926$	3.17379	0.104297
$927$	−18.0794	−0.593806
$928$	7.67891	0.252072
$929$	−14.9311	−0.489873	−0.244937	−	0.969539i	$-0.578767\pi$
$929$	−14.9311	−0.489873	−0.244937	+	0.969539i	$0.578767\pi$
$930$	32.0618	1.05135
$931$	−27.6687	−0.906804
$932$	17.9514	0.588017
$933$	−5.16602	−0.169128
$934$	−2.77806	−0.0909009
$935$	−9.92705	−0.324649
$936$	2.19543	0.0717600
$937$	−34.8636	−1.13894	−0.569471	−	0.822011i	$-0.692852\pi$
$937$	−34.8636	−1.13894	−0.569471	+	0.822011i	$0.692852\pi$
$938$	−0.00100461	−3.28018e−5 0
$939$	40.8497	1.33308
$940$	4.73438	0.154418
$941$	−13.1875	−0.429900	−0.214950	−	0.976625i	$-0.568959\pi$
$941$	−13.1875	−0.429900	−0.214950	+	0.976625i	$0.568959\pi$
$942$	−12.1261	−0.395089
$943$	11.4327	0.372299
$944$	−2.90576	−0.0945745
$945$	0.00186072	6.05291e−5 0
$946$	−8.99829	−0.292560
$947$	−49.1344	−1.59665	−0.798327	−	0.602224i	$-0.794281\pi$
$947$	−49.1344	−1.59665	−0.798327	+	0.602224i	$0.794281\pi$
$948$	−21.5526	−0.699996
$949$	−23.5532	−0.764570
$950$	−18.2719	−0.592817
$951$	−67.6202	−2.19274
$952$	−0.000440697 0	−1.42831e−5 0
$953$	−58.8700	−1.90699	−0.953493	−	0.301414i	$-0.902542\pi$
$953$	−58.8700	−1.90699	−0.953493	+	0.301414i	$0.902542\pi$
$954$	5.07912	0.164443
$955$	−7.67677	−0.248414
$956$	24.6541	0.797369
$957$	−17.9982	−0.581799
$958$	10.2999	0.332774
$959$	−0.00146381	−4.72687e−5 0
$960$	6.31296	0.203750
$961$	−5.20644	−0.167950
$962$	3.61859	0.116668
$963$	−6.21607	−0.200310
$964$	13.2194	0.425768
$965$	−76.3332	−2.45725
$966$	0.000404023 0	1.29992e−5 0
$967$	−8.61717	−0.277110	−0.138555	−	0.990355i	$-0.544246\pi$
$967$	−8.61717	−0.277110	−0.138555	+	0.990355i	$0.544246\pi$
$968$	9.67356	0.310920
$969$	22.3513	0.718028
$970$	−46.2373	−1.48459
$971$	−1.09313	−0.0350801	−0.0175401	−	0.999846i	$-0.505583\pi$
$971$	−1.09313	−0.0350801	−0.0175401	+	0.999846i	$0.505583\pi$
$972$	11.2875	0.362047
$973$	−0.00325840	−0.000104460 0
$974$	−10.1376	−0.324828
$975$	18.0916	0.579395
$976$	−3.21513	−0.102914
$977$	−60.3567	−1.93098	−0.965491	−	0.260437i	$-0.916133\pi$
$977$	−60.3567	−1.93098	−0.965491	+	0.260437i	$0.916133\pi$
$978$	16.1367	0.515995
$979$	9.01652	0.288169
$980$	21.7143	0.693638
$981$	−12.7011	−0.405515
$982$	−12.0448	−0.384365
$983$	17.1141	0.545855	0.272928	−	0.962035i	$-0.412008\pi$
$983$	17.1141	0.545855	0.272928	+	0.962035i	$0.412008\pi$
$984$	−18.5876	−0.592552
$985$	−54.9326	−1.75030
$986$	−21.3367	−0.679499
$987$	−0.000492620 0	−1.56803e−5 0
$988$	−7.60133	−0.241830
$989$	9.77969	0.310976
$990$	−4.07862	−0.129627
$991$	−41.0231	−1.30314	−0.651571	−	0.758588i	$-0.725890\pi$
$991$	−41.0231	−1.30314	−0.651571	+	0.758588i	$0.725890\pi$
$992$	5.07874	0.161250
$993$	7.59351	0.240973
$994$	−0.00194132	−6.15751e−5 0
$995$	51.8063	1.64237
$996$	−19.4303	−0.615672
$997$	−38.1481	−1.20816	−0.604081	−	0.796923i	$-0.706460\pi$
$997$	−38.1481	−1.20816	−0.604081	+	0.796923i	$0.706460\pi$
$998$	33.0238	1.04535
$999$	7.11640	0.225153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.10	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.10	✓	46	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.03510 q^{3} +1.00000 q^{4} -3.10204 q^{5} +2.03510 q^{6} -0.000158603 q^{7} -1.00000 q^{8} +1.14162 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.03510 q^{3} +1.00000 q^{4} -3.10204 q^{5} +2.03510 q^{6} -0.000158603 q^{7} -1.00000 q^{8} +1.14162 q^{9} +3.10204 q^{10} -1.15171 q^{11} -2.03510 q^{12} -1.92309 q^{13} +0.000158603 q^{14} +6.31296 q^{15} +1.00000 q^{16} -2.77861 q^{17} -1.14162 q^{18} +3.95267 q^{19} -3.10204 q^{20} +0.000322773 q^{21} +1.15171 q^{22} -1.25173 q^{23} +2.03510 q^{24} +4.62267 q^{25} +1.92309 q^{26} +3.78199 q^{27} -0.000158603 q^{28} -7.67891 q^{29} -6.31296 q^{30} -5.07874 q^{31} -1.00000 q^{32} +2.34385 q^{33} +2.77861 q^{34} +0.000491994 q^{35} +1.14162 q^{36} +1.88166 q^{37} -3.95267 q^{38} +3.91367 q^{39} +3.10204 q^{40} -9.13353 q^{41} -0.000322773 q^{42} -7.81296 q^{43} -1.15171 q^{44} -3.54135 q^{45} +1.25173 q^{46} -1.52621 q^{47} -2.03510 q^{48} -7.00000 q^{49} -4.62267 q^{50} +5.65475 q^{51} -1.92309 q^{52} -4.44905 q^{53} -3.78199 q^{54} +3.57266 q^{55} +0.000158603 q^{56} -8.04406 q^{57} +7.67891 q^{58} -2.90576 q^{59} +6.31296 q^{60} -3.21513 q^{61} +5.07874 q^{62} -0.000181064 q^{63} +1.00000 q^{64} +5.96550 q^{65} -2.34385 q^{66} -6.33413 q^{67} -2.77861 q^{68} +2.54738 q^{69} -0.000491994 q^{70} -12.2401 q^{71} -1.14162 q^{72} +12.2476 q^{73} -1.88166 q^{74} -9.40757 q^{75} +3.95267 q^{76} +0.000182665 q^{77} -3.91367 q^{78} +10.5905 q^{79} -3.10204 q^{80} -11.1216 q^{81} +9.13353 q^{82} +9.54759 q^{83} +0.000322773 q^{84} +8.61937 q^{85} +7.81296 q^{86} +15.6273 q^{87} +1.15171 q^{88} -7.82879 q^{89} +3.54135 q^{90} +0.000305008 q^{91} -1.25173 q^{92} +10.3357 q^{93} +1.52621 q^{94} -12.2613 q^{95} +2.03510 q^{96} -14.9054 q^{97} +7.00000 q^{98} -1.31482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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