LMFDB - Embedded newform 841.6.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,6,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	841.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:	$134.882792463$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.76979 q^{2} +21.5399 q^{3} -17.7887 q^{4} -23.8546 q^{5} -81.2008 q^{6} +230.214 q^{7} +187.693 q^{8} +220.966 q^{9} +O(q^{10})$	\(q-3.76979 q^{2} +21.5399 q^{3} -17.7887 q^{4} -23.8546 q^{5} -81.2008 q^{6} +230.214 q^{7} +187.693 q^{8} +220.966 q^{9} +89.9267 q^{10} +264.364 q^{11} -383.166 q^{12} -540.469 q^{13} -867.859 q^{14} -513.825 q^{15} -138.324 q^{16} -517.199 q^{17} -832.996 q^{18} -398.498 q^{19} +424.342 q^{20} +4958.79 q^{21} -996.597 q^{22} -1475.46 q^{23} +4042.88 q^{24} -2555.96 q^{25} +2037.45 q^{26} -474.605 q^{27} -4095.21 q^{28} +1937.01 q^{30} +7071.64 q^{31} -5484.72 q^{32} +5694.37 q^{33} +1949.73 q^{34} -5491.67 q^{35} -3930.70 q^{36} -13735.7 q^{37} +1502.25 q^{38} -11641.6 q^{39} -4477.34 q^{40} -12761.2 q^{41} -18693.6 q^{42} -17011.0 q^{43} -4702.69 q^{44} -5271.06 q^{45} +5562.16 q^{46} -21638.7 q^{47} -2979.48 q^{48} +36191.6 q^{49} +9635.42 q^{50} -11140.4 q^{51} +9614.23 q^{52} -566.892 q^{53} +1789.16 q^{54} -6306.30 q^{55} +43209.6 q^{56} -8583.59 q^{57} +24444.5 q^{59} +9140.28 q^{60} +16818.3 q^{61} -26658.6 q^{62} +50869.6 q^{63} +25102.6 q^{64} +12892.7 q^{65} -21466.6 q^{66} -48612.3 q^{67} +9200.30 q^{68} -31781.2 q^{69} +20702.4 q^{70} +22342.9 q^{71} +41473.8 q^{72} +29434.4 q^{73} +51780.6 q^{74} -55055.0 q^{75} +7088.75 q^{76} +60860.4 q^{77} +43886.5 q^{78} -17558.6 q^{79} +3299.66 q^{80} -63917.7 q^{81} +48106.9 q^{82} -45445.5 q^{83} -88210.4 q^{84} +12337.6 q^{85} +64127.9 q^{86} +49619.2 q^{88} +74852.9 q^{89} +19870.8 q^{90} -124424. q^{91} +26246.5 q^{92} +152322. q^{93} +81573.2 q^{94} +9506.00 q^{95} -118140. q^{96} +172532. q^{97} -136435. q^{98} +58415.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 12 q^{2} - q^{3} + 422 q^{4} - 157 q^{5} - 166 q^{6} - 331 q^{7} - 453 q^{8} + 1622 q^{9}+O(q^{10}) $ 33 * q - 12 * q^2 - q^3 + 422 * q^4 - 157 * q^5 - 166 * q^6 - 331 * q^7 - 453 * q^8 + 1622 * q^9	\( 33 q - 12 q^{2} - q^{3} + 422 q^{4} - 157 q^{5} - 166 q^{6} - 331 q^{7} - 453 q^{8} + 1622 q^{9} + 291 q^{10} + 491 q^{11} + 124 q^{12} - 1157 q^{13} - 620 q^{14} + 3960 q^{15} + 4566 q^{16} - 338 q^{17} - 6865 q^{18} + 451 q^{19} - 6636 q^{20} + 97 q^{21} - 11899 q^{22} - 8247 q^{23} - 13519 q^{24} + 7262 q^{25} + 11758 q^{26} - 9886 q^{27} + 3754 q^{28} - 20009 q^{30} + 11231 q^{31} - 17863 q^{32} - 22142 q^{33} + 7463 q^{34} - 26372 q^{35} - 516 q^{36} - 7149 q^{37} - 13318 q^{38} - 25700 q^{39} + 18611 q^{40} + 9360 q^{41} + 41603 q^{42} + 55165 q^{43} + 84442 q^{44} + 10619 q^{45} - 7924 q^{46} - 46957 q^{47} + 69535 q^{48} - 16038 q^{49} - 42663 q^{50} - 125432 q^{51} + 7049 q^{52} - 54523 q^{53} - 15016 q^{54} - 118472 q^{55} - 50285 q^{56} - 20081 q^{57} - 166756 q^{59} + 165453 q^{60} - 87433 q^{61} - 103656 q^{62} - 67869 q^{63} - 31945 q^{64} - 27116 q^{65} + 62548 q^{66} - 100267 q^{67} - 92443 q^{68} + 208538 q^{69} + 255839 q^{70} - 117725 q^{71} + 29044 q^{72} + 96829 q^{73} - 147314 q^{74} - 269104 q^{75} + 85334 q^{76} + 237412 q^{77} - 168156 q^{78} - 364713 q^{79} - 629809 q^{80} + 93985 q^{81} - 238717 q^{82} - 203241 q^{83} - 552428 q^{84} + 19206 q^{85} - 174200 q^{86} - 492819 q^{88} + 309027 q^{89} - 252630 q^{90} - 369702 q^{91} - 194235 q^{92} + 86514 q^{93} - 632929 q^{94} + 272214 q^{95} - 361521 q^{96} - 186709 q^{97} - 651857 q^{98} - 219304 q^{99}+O(q^{100}) \) 33 * q - 12 * q^2 - q^3 + 422 * q^4 - 157 * q^5 - 166 * q^6 - 331 * q^7 - 453 * q^8 + 1622 * q^9 + 291 * q^10 + 491 * q^11 + 124 * q^12 - 1157 * q^13 - 620 * q^14 + 3960 * q^15 + 4566 * q^16 - 338 * q^17 - 6865 * q^18 + 451 * q^19 - 6636 * q^20 + 97 * q^21 - 11899 * q^22 - 8247 * q^23 - 13519 * q^24 + 7262 * q^25 + 11758 * q^26 - 9886 * q^27 + 3754 * q^28 - 20009 * q^30 + 11231 * q^31 - 17863 * q^32 - 22142 * q^33 + 7463 * q^34 - 26372 * q^35 - 516 * q^36 - 7149 * q^37 - 13318 * q^38 - 25700 * q^39 + 18611 * q^40 + 9360 * q^41 + 41603 * q^42 + 55165 * q^43 + 84442 * q^44 + 10619 * q^45 - 7924 * q^46 - 46957 * q^47 + 69535 * q^48 - 16038 * q^49 - 42663 * q^50 - 125432 * q^51 + 7049 * q^52 - 54523 * q^53 - 15016 * q^54 - 118472 * q^55 - 50285 * q^56 - 20081 * q^57 - 166756 * q^59 + 165453 * q^60 - 87433 * q^61 - 103656 * q^62 - 67869 * q^63 - 31945 * q^64 - 27116 * q^65 + 62548 * q^66 - 100267 * q^67 - 92443 * q^68 + 208538 * q^69 + 255839 * q^70 - 117725 * q^71 + 29044 * q^72 + 96829 * q^73 - 147314 * q^74 - 269104 * q^75 + 85334 * q^76 + 237412 * q^77 - 168156 * q^78 - 364713 * q^79 - 629809 * q^80 + 93985 * q^81 - 238717 * q^82 - 203241 * q^83 - 552428 * q^84 + 19206 * q^85 - 174200 * q^86 - 492819 * q^88 + 309027 * q^89 - 252630 * q^90 - 369702 * q^91 - 194235 * q^92 + 86514 * q^93 - 632929 * q^94 + 272214 * q^95 - 361521 * q^96 - 186709 * q^97 - 651857 * q^98 - 219304 * 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 $

$2$	−3.76979	−0.666411	−0.333205	−	0.942854i	$-0.608130\pi$
$2$	−3.76979	−0.666411	−0.333205	+	0.942854i	$0.608130\pi$
$3$	21.5399	1.38178	0.690892	−	0.722958i	$-0.257218\pi$
$3$	21.5399	1.38178	0.690892	+	0.722958i	$0.257218\pi$
$4$	−17.7887	−0.555897
$5$	−23.8546	−0.426724	−0.213362	−	0.976973i	$-0.568441\pi$
$5$	−23.8546	−0.426724	−0.213362	+	0.976973i	$0.568441\pi$
$6$	−81.2008	−0.920835
$7$	230.214	1.77577	0.887886	−	0.460064i	$-0.152173\pi$
$7$	230.214	1.77577	0.887886	+	0.460064i	$0.152173\pi$
$8$	187.693	1.03687
$9$	220.966	0.909326
$10$	89.9267	0.284373
$11$	264.364	0.658750	0.329375	−	0.944199i	$-0.393162\pi$
$11$	264.364	0.658750	0.329375	+	0.944199i	$0.393162\pi$
$12$	−383.166	−0.768129
$13$	−540.469	−0.886976	−0.443488	−	0.896280i	$-0.646259\pi$
$13$	−540.469	−0.886976	−0.443488	+	0.896280i	$0.646259\pi$
$14$	−867.859	−1.18339
$15$	−513.825	−0.589640
$16$	−138.324	−0.135082
$17$	−517.199	−0.434046	−0.217023	−	0.976167i	$-0.569635\pi$
$17$	−517.199	−0.434046	−0.217023	+	0.976167i	$0.569635\pi$
$18$	−832.996	−0.605985
$19$	−398.498	−0.253245	−0.126623	−	0.991951i	$-0.540414\pi$
$19$	−398.498	−0.253245	−0.126623	+	0.991951i	$0.540414\pi$
$20$	424.342	0.237214
$21$	4958.79	2.45373
$22$	−996.597	−0.438998
$23$	−1475.46	−0.581577	−0.290789	−	0.956787i	$-0.593918\pi$
$23$	−1475.46	−0.581577	−0.290789	+	0.956787i	$0.593918\pi$
$24$	4042.88	1.43272
$25$	−2555.96	−0.817907
$26$	2037.45	0.591090
$27$	−474.605	−0.125292
$28$	−4095.21	−0.987146
$29$	0	0
$29$	0	0
$30$	1937.01	0.392942
$31$	7071.64	1.32165	0.660824	−	0.750541i	$-0.270207\pi$
$31$	7071.64	1.32165	0.660824	+	0.750541i	$0.270207\pi$
$32$	−5484.72	−0.946846
$33$	5694.37	0.910250
$34$	1949.73	0.289253
$35$	−5491.67	−0.757764
$36$	−3930.70	−0.505491
$37$	−13735.7	−1.64948	−0.824738	−	0.565515i	$-0.808678\pi$
$37$	−13735.7	−1.64948	−0.824738	+	0.565515i	$0.808678\pi$
$38$	1502.25	0.168765
$39$	−11641.6	−1.22561
$40$	−4477.34	−0.442456
$41$	−12761.2	−1.18558	−0.592789	−	0.805358i	$-0.701973\pi$
$41$	−12761.2	−1.18558	−0.592789	+	0.805358i	$0.701973\pi$
$42$	−18693.6	−1.63519
$43$	−17011.0	−1.40300	−0.701502	−	0.712668i	$-0.747487\pi$
$43$	−17011.0	−1.40300	−0.701502	+	0.712668i	$0.747487\pi$
$44$	−4702.69	−0.366197
$45$	−5271.06	−0.388031
$46$	5562.16	0.387569
$47$	−21638.7	−1.42885	−0.714424	−	0.699713i	$-0.753311\pi$
$47$	−21638.7	−1.42885	−0.714424	+	0.699713i	$0.753311\pi$
$48$	−2979.48	−0.186654
$49$	36191.6	2.15337
$50$	9635.42	0.545062
$51$	−11140.4	−0.599757
$52$	9614.23	0.493067
$53$	−566.892	−0.0277211	−0.0138606	−	0.999904i	$-0.504412\pi$
$53$	−566.892	−0.0277211	−0.0138606	+	0.999904i	$0.504412\pi$
$54$	1789.16	0.0834959
$55$	−6306.30	−0.281104
$56$	43209.6	1.84124
$57$	−8583.59	−0.349930
$58$	0	0
$59$	24444.5	0.914219	0.457110	−	0.889410i	$-0.348885\pi$
$59$	24444.5	0.914219	0.457110	+	0.889410i	$0.348885\pi$
$60$	9140.28	0.327779
$61$	16818.3	0.578706	0.289353	−	0.957223i	$-0.406560\pi$
$61$	16818.3	0.578706	0.289353	+	0.957223i	$0.406560\pi$
$62$	−26658.6	−0.880760
$63$	50869.6	1.61476
$64$	25102.6	0.766070
$65$	12892.7	0.378494
$66$	−21466.6	−0.606600
$67$	−48612.3	−1.32300	−0.661499	−	0.749946i	$-0.730080\pi$
$67$	−48612.3	−1.32300	−0.661499	+	0.749946i	$0.730080\pi$
$68$	9200.30	0.241285
$69$	−31781.2	−0.803614
$70$	20702.4	0.504982
$71$	22342.9	0.526010	0.263005	−	0.964794i	$-0.415286\pi$
$71$	22342.9	0.526010	0.263005	+	0.964794i	$0.415286\pi$
$72$	41473.8	0.942849
$73$	29434.4	0.646469	0.323235	−	0.946319i	$-0.395230\pi$
$73$	29434.4	0.646469	0.323235	+	0.946319i	$0.395230\pi$
$74$	51780.6	1.09923
$75$	−55055.0	−1.13017
$76$	7088.75	0.140778
$77$	60860.4	1.16979
$78$	43886.5	0.816759
$79$	−17558.6	−0.316536	−0.158268	−	0.987396i	$-0.550591\pi$
$79$	−17558.6	−0.316536	−0.158268	+	0.987396i	$0.550591\pi$
$80$	3299.66	0.0576427
$81$	−63917.7	−1.08245
$82$	48106.9	0.790082
$83$	−45445.5	−0.724096	−0.362048	−	0.932159i	$-0.617922\pi$
$83$	−45445.5	−0.724096	−0.362048	+	0.932159i	$0.617922\pi$
$84$	−88210.4	−1.36402
$85$	12337.6	0.185218
$86$	64127.9	0.934977
$87$	0	0
$88$	49619.2	0.683036
$89$	74852.9	1.00169	0.500845	−	0.865537i	$-0.333023\pi$
$89$	74852.9	1.00169	0.500845	+	0.865537i	$0.333023\pi$
$90$	19870.8	0.258588
$91$	−124424.	−1.57507
$92$	26246.5	0.323297
$93$	152322.	1.82623
$94$	81573.2	0.952200
$95$	9506.00	0.108066
$96$	−118140.	−1.30834
$97$	172532.	1.86183	0.930915	−	0.365237i	$-0.119012\pi$
$97$	172532.	1.86183	0.930915	+	0.365237i	$0.119012\pi$
$98$	−136435.	−1.43503
$99$	58415.5	0.599019
$100$	45467.2	0.454672
$101$	−187907.	−1.83290	−0.916451	−	0.400146i	$-0.868959\pi$
$101$	−187907.	−1.83290	−0.916451	+	0.400146i	$0.868959\pi$
$102$	41997.0	0.399685
$103$	9498.79	0.0882216	0.0441108	−	0.999027i	$-0.485955\pi$
$103$	9498.79	0.0882216	0.0441108	+	0.999027i	$0.485955\pi$
$104$	−101442.	−0.919676
$105$	−118290.	−1.04707
$106$	2137.06	0.0184737
$107$	99758.9	0.842349	0.421175	−	0.906980i	$-0.361618\pi$
$107$	99758.9	0.842349	0.421175	+	0.906980i	$0.361618\pi$
$108$	8442.61	0.0696494
$109$	−149771.	−1.20743	−0.603716	−	0.797200i	$-0.706314\pi$
$109$	−149771.	−1.20743	−0.603716	+	0.797200i	$0.706314\pi$
$110$	23773.4	0.187331
$111$	−295865.	−2.27922
$112$	−31844.1	−0.239875
$113$	−148892.	−1.09692	−0.548461	−	0.836176i	$-0.684786\pi$
$113$	−148892.	−1.09692	−0.548461	+	0.836176i	$0.684786\pi$
$114$	32358.3	0.233197
$115$	35196.4	0.248173
$116$	0	0
$117$	−119425.	−0.806551
$118$	−92150.4	−0.609245
$119$	−119067.	−0.770766
$120$	−96441.3	−0.611378
$121$	−91162.6	−0.566048
$122$	−63401.5	−0.385656
$123$	−274874.	−1.63821
$124$	−125795.	−0.734700
$125$	135517.	0.775744
$126$	−191768.	−1.07609
$127$	−76911.3	−0.423137	−0.211569	−	0.977363i	$-0.567857\pi$
$127$	−76911.3	−0.423137	−0.211569	+	0.977363i	$0.567857\pi$
$128$	80879.5	0.436329
$129$	−366415.	−1.93865
$130$	−48602.6	−0.252232
$131$	146855.	0.747672	0.373836	−	0.927495i	$-0.378042\pi$
$131$	146855.	0.747672	0.373836	+	0.927495i	$0.378042\pi$
$132$	−101295.	−0.506005
$133$	−91739.8	−0.449706
$134$	183258.	0.881661
$135$	11321.5	0.0534650
$136$	−97074.6	−0.450047
$137$	379959.	1.72956	0.864780	−	0.502150i	$-0.167458\pi$
$137$	379959.	1.72956	0.864780	+	0.502150i	$0.167458\pi$
$138$	119808.	0.535537
$139$	47358.6	0.207903	0.103952	−	0.994582i	$-0.466851\pi$
$139$	47358.6	0.207903	0.103952	+	0.994582i	$0.466851\pi$
$140$	97689.6	0.421239
$141$	−466095.	−1.97436
$142$	−84228.1	−0.350539
$143$	−142880.	−0.584296
$144$	−30564.9	−0.122834
$145$	0	0
$146$	−110961.	−0.430814
$147$	779563.	2.97549
$148$	244340.	0.916939
$149$	183962.	0.678832	0.339416	−	0.940636i	$-0.389771\pi$
$149$	183962.	0.678832	0.339416	+	0.940636i	$0.389771\pi$
$150$	207546.	0.753157
$151$	−162503.	−0.579988	−0.289994	−	0.957028i	$-0.593653\pi$
$151$	−162503.	−0.579988	−0.289994	+	0.957028i	$0.593653\pi$
$152$	−74795.1	−0.262582
$153$	−114284.	−0.394689
$154$	−229431.	−0.779561
$155$	−168691.	−0.563979
$156$	207089.	0.681312
$157$	−208213.	−0.674153	−0.337076	−	0.941477i	$-0.609438\pi$
$157$	−208213.	−0.674153	−0.337076	+	0.941477i	$0.609438\pi$
$158$	66192.4	0.210943
$159$	−12210.8	−0.0383046
$160$	130836.	0.404042
$161$	−339672.	−1.03275
$162$	240956.	0.721358
$163$	−93048.5	−0.274309	−0.137155	−	0.990550i	$-0.543796\pi$
$163$	−93048.5	−0.274309	−0.137155	+	0.990550i	$0.543796\pi$
$164$	227004.	0.659059
$165$	−135837.	−0.388425
$166$	171320.	0.482545
$167$	−317880.	−0.882007	−0.441003	−	0.897505i	$-0.645377\pi$
$167$	−317880.	−0.882007	−0.441003	+	0.897505i	$0.645377\pi$
$168$	930729.	2.54419
$169$	−79186.8	−0.213273
$170$	−46510.0	−0.123431
$171$	−88054.5	−0.230283
$172$	302604.	0.779925
$173$	−325635.	−0.827210	−0.413605	−	0.910456i	$-0.635731\pi$
$173$	−325635.	−0.827210	−0.413605	+	0.910456i	$0.635731\pi$
$174$	0	0
$175$	−588418.	−1.45242
$176$	−36567.9	−0.0889853
$177$	526531.	1.26325
$178$	−282179.	−0.667537
$179$	−509642.	−1.18887	−0.594433	−	0.804145i	$-0.702623\pi$
$179$	−509642.	−1.18887	−0.594433	+	0.804145i	$0.702623\pi$
$180$	93765.3	0.215705
$181$	603815.	1.36996	0.684979	−	0.728563i	$-0.259811\pi$
$181$	603815.	1.36996	0.684979	+	0.728563i	$0.259811\pi$
$182$	469051.	1.04964
$183$	362264.	0.799646
$184$	−276933.	−0.603018
$185$	327659.	0.703871
$186$	−574222.	−1.21702
$187$	−136729.	−0.285928
$188$	384924.	0.794292
$189$	−109261.	−0.222490
$190$	−35835.6	−0.0720163
$191$	−429708.	−0.852296	−0.426148	−	0.904653i	$-0.640130\pi$
$191$	−429708.	−0.852296	−0.426148	+	0.904653i	$0.640130\pi$
$192$	540707.	1.05854
$193$	−81608.7	−0.157704	−0.0788521	−	0.996886i	$-0.525125\pi$
$193$	−81608.7	−0.157704	−0.0788521	+	0.996886i	$0.525125\pi$
$194$	−650408.	−1.24074
$195$	277706.	0.522997
$196$	−643802.	−1.19705
$197$	701558.	1.28795	0.643974	−	0.765048i	$-0.277285\pi$
$197$	701558.	1.28795	0.643974	+	0.765048i	$0.277285\pi$
$198$	−220214.	−0.399192
$199$	624986.	1.11876	0.559381	−	0.828911i	$-0.311039\pi$
$199$	624986.	1.11876	0.559381	+	0.828911i	$0.311039\pi$
$200$	−479735.	−0.848060
$201$	−1.04710e6	−1.82810
$202$	708369.	1.22147
$203$	0	0
$204$	198173.	0.333403
$205$	304412.	0.505915
$206$	−35808.4	−0.0587918
$207$	−326026.	−0.528843
$208$	74759.7	0.119814
$209$	−105348.	−0.166825
$210$	445928.	0.697776
$211$	−45421.8	−0.0702358	−0.0351179	−	0.999383i	$-0.511181\pi$
$211$	−45421.8	−0.0702358	−0.0351179	+	0.999383i	$0.511181\pi$
$212$	10084.3	0.0154101
$213$	481264.	0.726832
$214$	−376070.	−0.561351
$215$	405791.	0.598695
$216$	−89080.0	−0.129911
$217$	1.62799e6	2.34694
$218$	564606.	0.804645
$219$	634013.	0.893281
$220$	112181.	0.156265
$221$	279530.	0.384988
$222$	1.11535e6	1.51890
$223$	27409.9	0.0369101	0.0184550	−	0.999830i	$-0.494125\pi$
$223$	27409.9	0.0369101	0.0184550	+	0.999830i	$0.494125\pi$
$224$	−1.26266e6	−1.68138
$225$	−564780.	−0.743744
$226$	561292.	0.731001
$227$	−1.02476e6	−1.31994	−0.659972	−	0.751290i	$-0.729432\pi$
$227$	−1.02476e6	−1.31994	−0.659972	+	0.751290i	$0.729432\pi$
$228$	152691.	0.194525
$229$	469810.	0.592016	0.296008	−	0.955185i	$-0.404344\pi$
$229$	469810.	0.592016	0.296008	+	0.955185i	$0.404344\pi$
$230$	−132683.	−0.165385
$231$	1.31093e6	1.61640
$232$	0	0
$233$	−1.13204e6	−1.36606	−0.683031	−	0.730389i	$-0.739339\pi$
$233$	−1.13204e6	−1.36606	−0.683031	+	0.730389i	$0.739339\pi$
$234$	450208.	0.537494
$235$	516182.	0.609724
$236$	−434835.	−0.508212
$237$	−378211.	−0.437384
$238$	448856.	0.513647
$239$	−1.38684e6	−1.57048	−0.785238	−	0.619194i	$-0.787459\pi$
$239$	−1.38684e6	−1.57048	−0.785238	+	0.619194i	$0.787459\pi$
$240$	71074.3	0.0796497
$241$	−63121.1	−0.0700054	−0.0350027	−	0.999387i	$-0.511144\pi$
$241$	−63121.1	−0.0700054	−0.0350027	+	0.999387i	$0.511144\pi$
$242$	343664.	0.377221
$243$	−1.26145e6	−1.37042
$244$	−299176.	−0.321701
$245$	−863336.	−0.918893
$246$	1.03622e6	1.09172
$247$	215375.	0.224623
$248$	1.32730e6	1.37037
$249$	−978891.	−1.00054
$250$	−510870.	−0.516964
$251$	200745.	0.201123	0.100561	−	0.994931i	$-0.467936\pi$
$251$	200745.	0.201123	0.100561	+	0.994931i	$0.467936\pi$
$252$	−904904.	−0.897637
$253$	−390058.	−0.383114
$254$	289939.	0.281983
$255$	265750.	0.255931
$256$	−1.10818e6	−1.05684
$257$	−1.14860e6	−1.08476	−0.542382	−	0.840132i	$-0.682478\pi$
$257$	−1.14860e6	−1.08476	−0.542382	+	0.840132i	$0.682478\pi$
$258$	1.38131e6	1.29194
$259$	−3.16215e6	−2.92909
$260$	−229344.	−0.210404
$261$	0	0
$262$	−553613.	−0.498257
$263$	4002.54	0.00356818	0.00178409	−	0.999998i	$-0.499432\pi$
$263$	4002.54	0.00356818	0.00178409	+	0.999998i	$0.499432\pi$
$264$	1.06879e6	0.943808
$265$	13523.0	0.0118293
$266$	345840.	0.299689
$267$	1.61232e6	1.38412
$268$	864750.	0.735451
$269$	1.81724e6	1.53120	0.765601	−	0.643316i	$-0.222442\pi$
$269$	1.81724e6	1.53120	0.765601	+	0.643316i	$0.222442\pi$
$270$	−42679.7	−0.0356297
$271$	−145985.	−0.120749	−0.0603746	−	0.998176i	$-0.519230\pi$
$271$	−145985.	−0.120749	−0.0603746	+	0.998176i	$0.519230\pi$
$272$	71541.0	0.0586317
$273$	−2.68007e6	−2.17640
$274$	−1.43237e6	−1.15260
$275$	−675704.	−0.538796
$276$	565346.	0.446726
$277$	−1.67598e6	−1.31241	−0.656206	−	0.754582i	$-0.727840\pi$
$277$	−1.67598e6	−1.31241	−0.656206	+	0.754582i	$0.727840\pi$
$278$	−178532.	−0.138549
$279$	1.56259e6	1.20181
$280$	−1.03075e6	−0.785700
$281$	−941146.	−0.711035	−0.355518	−	0.934670i	$-0.615695\pi$
$281$	−941146.	−0.711035	−0.355518	+	0.934670i	$0.615695\pi$
$282$	1.75708e6	1.31573
$283$	1.26549e6	0.939276	0.469638	−	0.882859i	$-0.344384\pi$
$283$	1.26549e6	0.939276	0.469638	+	0.882859i	$0.344384\pi$
$284$	−397451.	−0.292407
$285$	204758.	0.149324
$286$	538629.	0.389381
$287$	−2.93780e6	−2.10532
$288$	−1.21194e6	−0.860992
$289$	−1.15236e6	−0.811604
$290$	0	0
$291$	3.71631e6	2.57265
$292$	−523599.	−0.359370
$293$	1.01181e6	0.688538	0.344269	−	0.938871i	$-0.388127\pi$
$293$	1.01181e6	0.688538	0.344269	+	0.938871i	$0.388127\pi$
$294$	−2.93879e6	−1.98290
$295$	−583112.	−0.390119
$296$	−2.57809e6	−1.71029
$297$	−125469.	−0.0825361
$298$	−693498.	−0.452381
$299$	797439.	0.515845
$300$	979357.	0.628258
$301$	−3.91618e6	−2.49141
$302$	612602.	0.386511
$303$	−4.04749e6	−2.53268
$304$	55121.7	0.0342089
$305$	−401194.	−0.246948
$306$	430825.	0.263025
$307$	−605807.	−0.366850	−0.183425	−	0.983034i	$-0.558718\pi$
$307$	−605807.	−0.366850	−0.183425	+	0.983034i	$0.558718\pi$
$308$	−1.08263e6	−0.650283
$309$	204603.	0.121903
$310$	635929.	0.375841
$311$	343883.	0.201609	0.100805	−	0.994906i	$-0.467858\pi$
$311$	343883.	0.201609	0.100805	+	0.994906i	$0.467858\pi$
$312$	−2.18505e6	−1.27079
$313$	97174.8	0.0560651	0.0280326	−	0.999607i	$-0.491076\pi$
$313$	97174.8	0.0560651	0.0280326	+	0.999607i	$0.491076\pi$
$314$	784918.	0.449262
$315$	−1.21347e6	−0.689055
$316$	312345.	0.175961
$317$	1.81185e6	1.01268	0.506342	−	0.862333i	$-0.330997\pi$
$317$	1.81185e6	1.01268	0.506342	+	0.862333i	$0.330997\pi$
$318$	46032.1	0.0255266
$319$	0	0
$320$	−598812.	−0.326901
$321$	2.14879e6	1.16394
$322$	1.28049e6	0.688234
$323$	206103.	0.109920
$324$	1.13701e6	0.601732
$325$	1.38142e6	0.725464
$326$	350773.	0.182803
$327$	−3.22606e6	−1.66841
$328$	−2.39518e6	−1.22929
$329$	−4.98153e6	−2.53731
$330$	512076.	0.258851
$331$	95287.0	0.0478039	0.0239020	−	0.999714i	$-0.492391\pi$
$331$	95287.0	0.0478039	0.0239020	+	0.999714i	$0.492391\pi$
$332$	808417.	0.402523
$333$	−3.03512e6	−1.49991
$334$	1.19834e6	0.587779
$335$	1.15963e6	0.564555
$336$	−685919.	−0.331455
$337$	387494.	0.185862	0.0929310	−	0.995673i	$-0.470376\pi$
$337$	387494.	0.185862	0.0929310	+	0.995673i	$0.470376\pi$
$338$	298517.	0.142127
$339$	−3.20712e6	−1.51571
$340$	−219469.	−0.102962
$341$	1.86949e6	0.870636
$342$	331947.	0.153463
$343$	4.46262e6	2.04812
$344$	−3.19284e6	−1.45473
$345$	758127.	0.342921
$346$	1.22758e6	0.551262
$347$	−735013.	−0.327696	−0.163848	−	0.986486i	$-0.552391\pi$
$347$	−735013.	−0.327696	−0.163848	+	0.986486i	$0.552391\pi$
$348$	0	0
$349$	2.51402e6	1.10486	0.552428	−	0.833561i	$-0.313701\pi$
$349$	2.51402e6	1.10486	0.552428	+	0.833561i	$0.313701\pi$
$350$	2.21821e6	0.967905
$351$	256509.	0.111131
$352$	−1.44996e6	−0.623735
$353$	−2.67931e6	−1.14442	−0.572210	−	0.820107i	$-0.693914\pi$
$353$	−2.67931e6	−1.14442	−0.572210	+	0.820107i	$0.693914\pi$
$354$	−1.98491e6	−0.841845
$355$	−532981.	−0.224461
$356$	−1.33153e6	−0.556836
$357$	−2.56468e6	−1.06503
$358$	1.92124e6	0.792273
$359$	−1.69851e6	−0.695555	−0.347777	−	0.937577i	$-0.613064\pi$
$359$	−1.69851e6	−0.695555	−0.347777	+	0.937577i	$0.613064\pi$
$360$	−989340.	−0.402336
$361$	−2.31730e6	−0.935867
$362$	−2.27625e6	−0.912955
$363$	−1.96363e6	−0.782156
$364$	2.21333e6	0.875575
$365$	−702145.	−0.275864
$366$	−1.36566e6	−0.532893
$367$	2.68784e6	1.04169	0.520844	−	0.853652i	$-0.325617\pi$
$367$	2.68784e6	1.04169	0.520844	+	0.853652i	$0.325617\pi$
$368$	204091.	0.0785606
$369$	−2.81978e6	−1.07808
$370$	−1.23521e6	−0.469067
$371$	−130507.	−0.0492264
$372$	−2.70961e6	−1.01520
$373$	−327159.	−0.121755	−0.0608775	−	0.998145i	$-0.519390\pi$
$373$	−327159.	−0.121755	−0.0608775	+	0.998145i	$0.519390\pi$
$374$	515439.	0.190545
$375$	2.91902e6	1.07191
$376$	−4.06143e6	−1.48152
$377$	0	0
$378$	411890.	0.148270
$379$	−2.15254e6	−0.769757	−0.384878	−	0.922967i	$-0.625757\pi$
$379$	−2.15254e6	−0.769757	−0.384878	+	0.922967i	$0.625757\pi$
$380$	−169099.	−0.0600735
$381$	−1.65666e6	−0.584684
$382$	1.61991e6	0.567979
$383$	−1.55877e6	−0.542982	−0.271491	−	0.962441i	$-0.587517\pi$
$383$	−1.55877e6	−0.542982	−0.271491	+	0.962441i	$0.587517\pi$
$384$	1.74214e6	0.602912
$385$	−1.45180e6	−0.499177
$386$	307648.	0.105096
$387$	−3.75886e6	−1.27579
$388$	−3.06912e6	−1.03498
$389$	−1.61032e6	−0.539560	−0.269780	−	0.962922i	$-0.586951\pi$
$389$	−1.61032e6	−0.539560	−0.269780	+	0.962922i	$0.586951\pi$
$390$	−1.04689e6	−0.348531
$391$	763105.	0.252431
$392$	6.79291e6	2.23275
$393$	3.16324e6	1.03312
$394$	−2.64472e6	−0.858302
$395$	418854.	0.135073
$396$	−1.03914e6	−0.332993
$397$	5.54259e6	1.76497	0.882483	−	0.470344i	$-0.155870\pi$
$397$	5.54259e6	1.76497	0.882483	+	0.470344i	$0.155870\pi$
$398$	−2.35606e6	−0.745555
$399$	−1.97606e6	−0.621397
$400$	353550.	0.110484
$401$	−2.91262e6	−0.904529	−0.452265	−	0.891884i	$-0.649384\pi$
$401$	−2.91262e6	−0.904529	−0.452265	+	0.891884i	$0.649384\pi$
$402$	3.94736e6	1.21826
$403$	−3.82200e6	−1.17227
$404$	3.34262e6	1.01890
$405$	1.52473e6	0.461908
$406$	0	0
$407$	−3.63122e6	−1.08659
$408$	−2.09097e6	−0.621868
$409$	−1.59508e6	−0.471492	−0.235746	−	0.971815i	$-0.575753\pi$
$409$	−1.59508e6	−0.471492	−0.235746	+	0.971815i	$0.575753\pi$
$410$	−1.14757e6	−0.337147
$411$	8.18428e6	2.38988
$412$	−168971.	−0.0490421
$413$	5.62746e6	1.62344
$414$	1.22905e6	0.352427
$415$	1.08408e6	0.308989
$416$	2.96432e6	0.839830
$417$	1.02010e6	0.287277
$418$	397141.	0.111174
$419$	4.70300e6	1.30870	0.654349	−	0.756193i	$-0.272943\pi$
$419$	4.70300e6	1.30870	0.654349	+	0.756193i	$0.272943\pi$
$420$	2.10422e6	0.582061
$421$	−4.54103e6	−1.24867	−0.624337	−	0.781155i	$-0.714631\pi$
$421$	−4.54103e6	−1.24867	−0.624337	+	0.781155i	$0.714631\pi$
$422$	171231.	0.0468059
$423$	−4.78142e6	−1.29929
$424$	−106402.	−0.0287431
$425$	1.32194e6	0.355009
$426$	−1.81426e6	−0.484369
$427$	3.87181e6	1.02765
$428$	−1.77458e6	−0.468259
$429$	−3.07763e6	−0.807370
$430$	−1.52974e6	−0.398977
$431$	−6.10526e6	−1.58311	−0.791555	−	0.611098i	$-0.790728\pi$
$431$	−6.10526e6	−1.58311	−0.791555	+	0.611098i	$0.790728\pi$
$432$	65649.2	0.0169247
$433$	−4.08602e6	−1.04732	−0.523661	−	0.851926i	$-0.675434\pi$
$433$	−4.08602e6	−1.04732	−0.523661	+	0.851926i	$0.675434\pi$
$434$	−6.13718e6	−1.56403
$435$	0	0
$436$	2.66424e6	0.671207
$437$	587966.	0.147282
$438$	−2.39009e6	−0.595292
$439$	2.15506e6	0.533702	0.266851	−	0.963738i	$-0.414017\pi$
$439$	2.15506e6	0.533702	0.266851	+	0.963738i	$0.414017\pi$
$440$	−1.18365e6	−0.291468
$441$	7.99713e6	1.95811
$442$	−1.05377e6	−0.256560
$443$	6.58501e6	1.59422	0.797108	−	0.603837i	$-0.206362\pi$
$443$	6.58501e6	1.59422	0.797108	+	0.603837i	$0.206362\pi$
$444$	5.26305e6	1.26701
$445$	−1.78558e6	−0.427445
$446$	−103329.	−0.0245973
$447$	3.96252e6	0.937999
$448$	5.77898e6	1.36037
$449$	−176799.	−0.0413869	−0.0206935	−	0.999786i	$-0.506587\pi$
$449$	−176799.	−0.0413869	−0.0206935	+	0.999786i	$0.506587\pi$
$450$	2.12910e6	0.495639
$451$	−3.37359e6	−0.781000
$452$	2.64860e6	0.609776
$453$	−3.50030e6	−0.801419
$454$	3.86311e6	0.879625
$455$	2.96807e6	0.672119
$456$	−1.61108e6	−0.362831
$457$	1.55338e6	0.347925	0.173963	−	0.984752i	$-0.444343\pi$
$457$	1.55338e6	0.347925	0.173963	+	0.984752i	$0.444343\pi$
$458$	−1.77108e6	−0.394526
$459$	245465.	0.0543824
$460$	−626099.	−0.137958
$461$	3.31005e6	0.725407	0.362704	−	0.931905i	$-0.381854\pi$
$461$	3.31005e6	0.725407	0.362704	+	0.931905i	$0.381854\pi$
$462$	−4.94191e6	−1.07718
$463$	8.25802e6	1.79029	0.895145	−	0.445776i	$-0.147072\pi$
$463$	8.25802e6	1.79029	0.895145	+	0.445776i	$0.147072\pi$
$464$	0	0
$465$	−3.63358e6	−0.779296
$466$	4.26754e6	0.910359
$467$	2.37513e6	0.503959	0.251979	−	0.967733i	$-0.418918\pi$
$467$	2.37513e6	0.503959	0.251979	+	0.967733i	$0.418918\pi$
$468$	2.12442e6	0.448359
$469$	−1.11913e7	−2.34934
$470$	−1.94590e6	−0.406326
$471$	−4.48488e6	−0.931533
$472$	4.58805e6	0.947923
$473$	−4.49710e6	−0.924229
$474$	1.42578e6	0.291478
$475$	1.01854e6	0.207131
$476$	2.11804e6	0.428466
$477$	−125264.	−0.0252075
$478$	5.22809e6	1.04658
$479$	−633442.	−0.126144	−0.0630722	−	0.998009i	$-0.520090\pi$
$479$	−633442.	−0.126144	−0.0630722	+	0.998009i	$0.520090\pi$
$480$	2.81819e6	0.558298
$481$	7.42371e6	1.46305
$482$	237953.	0.0466524
$483$	−7.31648e6	−1.42703
$484$	1.62166e6	0.314664
$485$	−4.11568e6	−0.794487
$486$	4.75540e6	0.913264
$487$	−3.50793e6	−0.670238	−0.335119	−	0.942176i	$-0.608776\pi$
$487$	−3.50793e6	−0.670238	−0.335119	+	0.942176i	$0.608776\pi$
$488$	3.15668e6	0.600040
$489$	−2.00425e6	−0.379036
$490$	3.25459e6	0.612360
$491$	−2.41098e6	−0.451325	−0.225662	−	0.974206i	$-0.572455\pi$
$491$	−2.41098e6	−0.451325	−0.225662	+	0.974206i	$0.572455\pi$
$492$	4.88965e6	0.910678
$493$	0	0
$494$	−811920.	−0.149691
$495$	−1.39348e6	−0.255616
$496$	−978176.	−0.178531
$497$	5.14366e6	0.934074
$498$	3.69021e6	0.666773
$499$	2.18082e6	0.392074	0.196037	−	0.980597i	$-0.437193\pi$
$499$	2.18082e6	0.392074	0.196037	+	0.980597i	$0.437193\pi$
$500$	−2.41067e6	−0.431234
$501$	−6.84709e6	−1.21874
$502$	−756767.	−0.134030
$503$	7.73485e6	1.36311	0.681557	−	0.731765i	$-0.261303\pi$
$503$	7.73485e6	1.36311	0.681557	+	0.731765i	$0.261303\pi$
$504$	9.54786e6	1.67429
$505$	4.48244e6	0.782143
$506$	1.47044e6	0.255311
$507$	−1.70567e6	−0.294697
$508$	1.36815e6	0.235221
$509$	−5.69608e6	−0.974500	−0.487250	−	0.873263i	$-0.662000\pi$
$509$	−5.69608e6	−0.974500	−0.487250	+	0.873263i	$0.662000\pi$
$510$	−1.00182e6	−0.170555
$511$	6.77622e6	1.14798
$512$	1.58946e6	0.267964
$513$	189129.	0.0317296
$514$	4.32997e6	0.722899
$515$	−226590.	−0.0376463
$516$	6.51804e6	1.07769
$517$	−5.72049e6	−0.941254
$518$	1.19206e7	1.95198
$519$	−7.01414e6	−1.14303
$520$	2.41986e6	0.392448
$521$	4.28414e6	0.691463	0.345732	−	0.938333i	$-0.387631\pi$
$521$	4.28414e6	0.691463	0.345732	+	0.938333i	$0.387631\pi$
$522$	0	0
$523$	2.08888e6	0.333932	0.166966	−	0.985963i	$-0.446603\pi$
$523$	2.08888e6	0.333932	0.166966	+	0.985963i	$0.446603\pi$
$524$	−2.61236e6	−0.415628
$525$	−1.26745e7	−2.00692
$526$	−15088.7	−0.00237787
$527$	−3.65744e6	−0.573655
$528$	−787667.	−0.122958
$529$	−4.25937e6	−0.661768
$530$	−50978.8	−0.00788315
$531$	5.40140e6	0.831323
$532$	1.63193e6	0.249990
$533$	6.89700e6	1.05158
$534$	−6.07811e6	−0.922392
$535$	−2.37971e6	−0.359451
$536$	−9.12419e6	−1.37177
$537$	−1.09776e7	−1.64276
$538$	−6.85062e6	−1.02041
$539$	9.56777e6	1.41853
$540$	−201395.	−0.0297210
$541$	−6.16535e6	−0.905659	−0.452830	−	0.891597i	$-0.649585\pi$
$541$	−6.16535e6	−0.905659	−0.452830	+	0.891597i	$0.649585\pi$
$542$	550331.	0.0804685
$543$	1.30061e7	1.89299
$544$	2.83669e6	0.410974
$545$	3.57273e6	0.515240
$546$	1.01033e7	1.45038
$547$	9.32846e6	1.33304	0.666518	−	0.745489i	$-0.267784\pi$
$547$	9.32846e6	1.33304	0.666518	+	0.745489i	$0.267784\pi$
$548$	−6.75898e6	−0.961457
$549$	3.71628e6	0.526232
$550$	2.54726e6	0.359060
$551$	0	0
$552$	−5.96510e6	−0.833240
$553$	−4.04225e6	−0.562096
$554$	6.31810e6	0.874605
$555$	7.05774e6	0.972598
$556$	−842447.	−0.115573
$557$	−9.45200e6	−1.29088	−0.645440	−	0.763811i	$-0.723326\pi$
$557$	−9.45200e6	−1.29088	−0.645440	+	0.763811i	$0.723326\pi$
$558$	−5.89064e6	−0.800898
$559$	9.19391e6	1.24443
$560$	759629.	0.102360
$561$	−2.94512e6	−0.395090
$562$	3.54792e6	0.473842
$563$	2.61829e6	0.348134	0.174067	−	0.984734i	$-0.444309\pi$
$563$	2.61829e6	0.348134	0.174067	+	0.984734i	$0.444309\pi$
$564$	8.29121e6	1.09754
$565$	3.55176e6	0.468083
$566$	−4.77064e6	−0.625944
$567$	−1.47148e7	−1.92219
$568$	4.19361e6	0.545402
$569$	715636.	0.0926642	0.0463321	−	0.998926i	$-0.485247\pi$
$569$	715636.	0.0926642	0.0463321	+	0.998926i	$0.485247\pi$
$570$	−771894.	−0.0995109
$571$	−6.43378e6	−0.825802	−0.412901	−	0.910776i	$-0.635484\pi$
$571$	−6.43378e6	−0.825802	−0.412901	+	0.910776i	$0.635484\pi$
$572$	2.54166e6	0.324808
$573$	−9.25587e6	−1.17769
$574$	1.10749e7	1.40301
$575$	3.77121e6	0.475676
$576$	5.54683e6	0.696608
$577$	1.01122e7	1.26446	0.632231	−	0.774780i	$-0.282139\pi$
$577$	1.01122e7	1.26446	0.632231	+	0.774780i	$0.282139\pi$
$578$	4.34416e6	0.540862
$579$	−1.75784e6	−0.217913
$580$	0	0
$581$	−1.04622e7	−1.28583
$582$	−1.40097e7	−1.71444
$583$	−149866.	−0.0182613
$584$	5.52462e6	0.670302
$585$	2.84884e6	0.344174
$586$	−3.81429e6	−0.458849
$587$	−8.87663e6	−1.06329	−0.531646	−	0.846966i	$-0.678426\pi$
$587$	−8.87663e6	−1.06329	−0.531646	+	0.846966i	$0.678426\pi$
$588$	−1.38674e7	−1.65406
$589$	−2.81803e6	−0.334701
$590$	2.19821e6	0.259980
$591$	1.51115e7	1.77966
$592$	1.89997e6	0.222815
$593$	−3.87759e6	−0.452819	−0.226410	−	0.974032i	$-0.572699\pi$
$593$	−3.87759e6	−0.452819	−0.226410	+	0.974032i	$0.572699\pi$
$594$	472990.	0.0550029
$595$	2.84029e6	0.328904
$596$	−3.27244e6	−0.377361
$597$	1.34621e7	1.54589
$598$	−3.00617e6	−0.343765
$599$	−1.19417e7	−1.35988	−0.679940	−	0.733267i	$-0.737994\pi$
$599$	−1.19417e7	−1.35988	−0.679940	+	0.733267i	$0.737994\pi$
$600$	−1.03334e7	−1.17184
$601$	−1.01408e7	−1.14521	−0.572607	−	0.819830i	$-0.694068\pi$
$601$	−1.01408e7	−1.14521	−0.572607	+	0.819830i	$0.694068\pi$
$602$	1.47632e7	1.66031
$603$	−1.07417e7	−1.20304
$604$	2.89072e6	0.322414
$605$	2.17465e6	0.241546
$606$	1.52582e7	1.68780
$607$	1.19519e7	1.31664	0.658319	−	0.752739i	$-0.271268\pi$
$607$	1.19519e7	1.31664	0.658319	+	0.752739i	$0.271268\pi$
$608$	2.18565e6	0.239785
$609$	0	0
$610$	1.51242e6	0.164568
$611$	1.16950e7	1.26735
$612$	2.03295e6	0.219406
$613$	1.12257e7	1.20659	0.603297	−	0.797516i	$-0.293853\pi$
$613$	1.12257e7	1.20659	0.603297	+	0.797516i	$0.293853\pi$
$614$	2.28376e6	0.244473
$615$	6.55700e6	0.699065
$616$	1.14231e7	1.21292
$617$	−3.62773e6	−0.383638	−0.191819	−	0.981430i	$-0.561439\pi$
$617$	−3.62773e6	−0.383638	−0.191819	+	0.981430i	$0.561439\pi$
$618$	−771309.	−0.0812376
$619$	1.01259e7	1.06220	0.531101	−	0.847309i	$-0.321778\pi$
$619$	1.01259e7	1.06220	0.531101	+	0.847309i	$0.321778\pi$
$620$	3.00079e6	0.313514
$621$	700260.	0.0728669
$622$	−1.29637e6	−0.134355
$623$	1.72322e7	1.77877
$624$	1.61032e6	0.165558
$625$	4.75467e6	0.486878
$626$	−366329.	−0.0373624
$627$	−2.26919e6	−0.230517
$628$	3.70383e6	0.374759
$629$	7.10409e6	0.715948
$630$	4.57454e6	0.459193
$631$	−2.77951e6	−0.277904	−0.138952	−	0.990299i	$-0.544373\pi$
$631$	−2.77951e6	−0.277904	−0.138952	+	0.990299i	$0.544373\pi$
$632$	−3.29563e6	−0.328206
$633$	−978380.	−0.0970506
$634$	−6.83029e6	−0.674863
$635$	1.83469e6	0.180563
$636$	217214.	0.0212934
$637$	−1.95604e7	−1.90998
$638$	0	0
$639$	4.93703e6	0.478315
$640$	−1.92935e6	−0.186192
$641$	2.90009e6	0.278783	0.139391	−	0.990237i	$-0.455485\pi$
$641$	2.90009e6	0.278783	0.139391	+	0.990237i	$0.455485\pi$
$642$	−8.10050e6	−0.775665
$643$	1.61149e7	1.53709	0.768547	−	0.639794i	$-0.220980\pi$
$643$	1.61149e7	1.53709	0.768547	+	0.639794i	$0.220980\pi$
$644$	6.04231e6	0.574101
$645$	8.74068e6	0.827267
$646$	−776963.	−0.0732519
$647$	1.59971e7	1.50238	0.751191	−	0.660085i	$-0.229480\pi$
$647$	1.59971e7	1.50238	0.751191	+	0.660085i	$0.229480\pi$
$648$	−1.19969e7	−1.12236
$649$	6.46224e6	0.602242
$650$	−5.20764e6	−0.483457
$651$	3.50667e7	3.24297
$652$	1.65521e6	0.152488
$653$	−1.00594e7	−0.923189	−0.461595	−	0.887091i	$-0.652723\pi$
$653$	−1.00594e7	−0.923189	−0.461595	+	0.887091i	$0.652723\pi$
$654$	1.21615e7	1.11185
$655$	−3.50317e6	−0.319049
$656$	1.76517e6	0.160150
$657$	6.50400e6	0.587851
$658$	1.87793e7	1.69089
$659$	4.34282e6	0.389546	0.194773	−	0.980848i	$-0.437603\pi$
$659$	4.34282e6	0.389546	0.194773	+	0.980848i	$0.437603\pi$
$660$	2.41636e6	0.215924
$661$	−1.26341e7	−1.12471	−0.562354	−	0.826896i	$-0.690104\pi$
$661$	−1.26341e7	−1.12471	−0.562354	+	0.826896i	$0.690104\pi$
$662$	−359212.	−0.0318571
$663$	6.02104e6	0.531970
$664$	−8.52980e6	−0.750791
$665$	2.18842e6	0.191900
$666$	1.14418e7	0.999557
$667$	0	0
$668$	5.65467e6	0.490305
$669$	590405.	0.0510017
$670$	−4.37155e6	−0.376226
$671$	4.44616e6	0.381222
$672$	−2.71976e7	−2.32331
$673$	−8.48417e6	−0.722057	−0.361029	−	0.932555i	$-0.617574\pi$
$673$	−8.48417e6	−0.722057	−0.361029	+	0.932555i	$0.617574\pi$
$674$	−1.46077e6	−0.123860
$675$	1.21307e6	0.102477
$676$	1.40863e6	0.118558
$677$	8.74051e6	0.732935	0.366467	−	0.930431i	$-0.380567\pi$
$677$	8.74051e6	0.732935	0.366467	+	0.930431i	$0.380567\pi$
$678$	1.20902e7	1.01008
$679$	3.97193e7	3.30618
$680$	2.31567e6	0.192046
$681$	−2.20731e7	−1.82388
$682$	−7.04757e6	−0.580201
$683$	−1.60843e7	−1.31932	−0.659659	−	0.751565i	$-0.729299\pi$
$683$	−1.60843e7	−1.31932	−0.659659	+	0.751565i	$0.729299\pi$
$684$	1.56637e6	0.128013
$685$	−9.06378e6	−0.738045
$686$	−1.68231e7	−1.36489
$687$	1.01197e7	0.818038
$688$	2.35303e6	0.189520
$689$	306387.	0.0245880
$690$	−2.85798e6	−0.228526
$691$	−2.14539e7	−1.70928	−0.854638	−	0.519225i	$-0.826221\pi$
$691$	−2.14539e7	−1.70928	−0.854638	+	0.519225i	$0.826221\pi$
$692$	5.79263e6	0.459844
$693$	1.34481e7	1.06372
$694$	2.77084e6	0.218380
$695$	−1.12972e6	−0.0887173
$696$	0	0
$697$	6.60006e6	0.514595
$698$	−9.47733e6	−0.736288
$699$	−2.43839e7	−1.88760
$700$	1.04672e7	0.807393
$701$	1.83343e7	1.40919	0.704595	−	0.709609i	$-0.251129\pi$
$701$	1.83343e7	1.40919	0.704595	+	0.709609i	$0.251129\pi$
$702$	−966985.	−0.0740588
$703$	5.47364e6	0.417722
$704$	6.63622e6	0.504649
$705$	1.11185e7	0.842506
$706$	1.01004e7	0.762654
$707$	−4.32589e7	−3.25482
$708$	−9.36629e6	−0.702238
$709$	6.96887e6	0.520651	0.260326	−	0.965521i	$-0.416170\pi$
$709$	6.96887e6	0.520651	0.260326	+	0.965521i	$0.416170\pi$
$710$	2.00923e6	0.149583
$711$	−3.87987e6	−0.287834
$712$	1.40493e7	1.03862
$713$	−1.04339e7	−0.768640
$714$	9.66830e6	0.709749
$715$	3.40835e6	0.249333
$716$	9.06587e6	0.660887
$717$	−2.98723e7	−2.17006
$718$	6.40301e6	0.463525
$719$	−3.34584e6	−0.241370	−0.120685	−	0.992691i	$-0.538509\pi$
$719$	−3.34584e6	−0.241370	−0.120685	+	0.992691i	$0.538509\pi$
$720$	729113.	0.0524160
$721$	2.18676e6	0.156662
$722$	8.73573e6	0.623672
$723$	−1.35962e6	−0.0967324
$724$	−1.07411e7	−0.761555
$725$	0	0
$726$	7.40248e6	0.521237
$727$	−2.32206e7	−1.62943	−0.814717	−	0.579859i	$-0.803108\pi$
$727$	−2.32206e7	−1.62943	−0.814717	+	0.579859i	$0.803108\pi$
$728$	−2.33534e7	−1.63313
$729$	−1.16395e7	−0.811176
$730$	2.64694e6	0.183839
$731$	8.79808e6	0.608968
$732$	−6.44421e6	−0.444521
$733$	1.61090e7	1.10741	0.553704	−	0.832713i	$-0.313214\pi$
$733$	1.61090e7	1.10741	0.553704	+	0.832713i	$0.313214\pi$
$734$	−1.01326e7	−0.694192
$735$	−1.85962e7	−1.26971
$736$	8.09247e6	0.550664
$737$	−1.28514e7	−0.871526
$738$	1.06300e7	0.718442
$739$	−4.09261e6	−0.275670	−0.137835	−	0.990455i	$-0.544014\pi$
$739$	−4.09261e6	−0.275670	−0.137835	+	0.990455i	$0.544014\pi$
$740$	−5.82863e6	−0.391280
$741$	4.63916e6	0.310380
$742$	491983.	0.0328050
$743$	−2.07746e7	−1.38058	−0.690288	−	0.723535i	$-0.742516\pi$
$743$	−2.07746e7	−1.38058	−0.690288	+	0.723535i	$0.742516\pi$
$744$	2.85898e7	1.89356
$745$	−4.38834e6	−0.289674
$746$	1.23332e6	0.0811388
$747$	−1.00419e7	−0.658439
$748$	2.43223e6	0.158946
$749$	2.29659e7	1.49582
$750$	−1.10041e7	−0.714333
$751$	−1.04942e7	−0.678966	−0.339483	−	0.940612i	$-0.610252\pi$
$751$	−1.04942e7	−0.678966	−0.339483	+	0.940612i	$0.610252\pi$
$752$	2.99315e6	0.193012
$753$	4.32403e6	0.277908
$754$	0	0
$755$	3.87645e6	0.247495
$756$	1.94361e6	0.123681
$757$	1.63513e7	1.03708	0.518541	−	0.855053i	$-0.326475\pi$
$757$	1.63513e7	1.03708	0.518541	+	0.855053i	$0.326475\pi$
$758$	8.11462e6	0.512974
$759$	−8.40180e6	−0.529381
$760$	1.78421e6	0.112050
$761$	1.24346e7	0.778342	0.389171	−	0.921166i	$-0.372762\pi$
$761$	1.24346e7	0.778342	0.389171	+	0.921166i	$0.372762\pi$
$762$	6.24526e6	0.389640
$763$	−3.44795e7	−2.14412
$764$	7.64395e6	0.473789
$765$	2.72619e6	0.168423
$766$	5.87624e6	0.361849
$767$	−1.32115e7	−0.810891
$768$	−2.38701e7	−1.46033
$769$	1.06031e7	0.646570	0.323285	−	0.946302i	$-0.395213\pi$
$769$	1.06031e7	0.646570	0.323285	+	0.946302i	$0.395213\pi$
$770$	5.47298e6	0.332657
$771$	−2.47407e7	−1.49891
$772$	1.45171e6	0.0876673
$773$	−9.62548e6	−0.579394	−0.289697	−	0.957118i	$-0.593555\pi$
$773$	−9.62548e6	−0.579394	−0.289697	+	0.957118i	$0.593555\pi$
$774$	1.41701e7	0.850199
$775$	−1.80748e7	−1.08098
$776$	3.23830e7	1.93047
$777$	−6.81124e7	−4.04737
$778$	6.07058e6	0.359568
$779$	5.08529e6	0.300242
$780$	−4.94003e6	−0.290732
$781$	5.90666e6	0.346509
$782$	−2.87675e6	−0.168223
$783$	0	0
$784$	−5.00617e6	−0.290881
$785$	4.96683e6	0.287677
$786$	−1.19248e7	−0.688483
$787$	6.21042e6	0.357424	0.178712	−	0.983901i	$-0.442807\pi$
$787$	6.21042e6	0.357424	0.178712	+	0.983901i	$0.442807\pi$
$788$	−1.24798e7	−0.715966
$789$	86214.3	0.00493045
$790$	−1.57899e6	−0.0900144
$791$	−3.42771e7	−1.94788
$792$	1.09642e7	0.621102
$793$	−9.08977e6	−0.513298
$794$	−2.08944e7	−1.17619
$795$	291283.	0.0163455
$796$	−1.11177e7	−0.621916
$797$	7.22420e6	0.402850	0.201425	−	0.979504i	$-0.435443\pi$
$797$	7.22420e6	0.402850	0.201425	+	0.979504i	$0.435443\pi$
$798$	7.44935e6	0.414105
$799$	1.11915e7	0.620185
$800$	1.40187e7	0.774432
$801$	1.65400e7	0.910863
$802$	1.09800e7	0.602788
$803$	7.78139e6	0.425862
$804$	1.86266e7	1.01623
$805$	8.10272e6	0.440698
$806$	1.44081e7	0.781213
$807$	3.91432e7	2.11579
$808$	−3.52688e7	−1.90048
$809$	−3.50070e6	−0.188054	−0.0940271	−	0.995570i	$-0.529974\pi$
$809$	−3.50070e6	−0.188054	−0.0940271	+	0.995570i	$0.529974\pi$
$810$	−5.74791e6	−0.307821
$811$	−4.29926e6	−0.229531	−0.114766	−	0.993393i	$-0.536612\pi$
$811$	−4.29926e6	−0.229531	−0.114766	+	0.993393i	$0.536612\pi$
$812$	0	0
$813$	−3.14449e6	−0.166849
$814$	1.36889e7	0.724117
$815$	2.21963e6	0.117054
$816$	1.54098e6	0.0810164
$817$	6.77884e6	0.355304
$818$	6.01312e6	0.314207
$819$	−2.74934e7	−1.43225
$820$	−5.41510e6	−0.281236
$821$	−1.42947e7	−0.740146	−0.370073	−	0.929003i	$-0.620667\pi$
$821$	−1.42947e7	−0.740146	−0.370073	+	0.929003i	$0.620667\pi$
$822$	−3.08530e7	−1.59264
$823$	2.93264e7	1.50924	0.754621	−	0.656161i	$-0.227821\pi$
$823$	2.93264e7	1.50924	0.754621	+	0.656161i	$0.227821\pi$
$824$	1.78285e6	0.0914740
$825$	−1.45546e7	−0.744500
$826$	−2.12143e7	−1.08188
$827$	8.26399e6	0.420171	0.210086	−	0.977683i	$-0.432626\pi$
$827$	8.26399e6	0.420171	0.210086	+	0.977683i	$0.432626\pi$
$828$	5.79958e6	0.293982
$829$	9.03225e6	0.456467	0.228234	−	0.973606i	$-0.426705\pi$
$829$	9.03225e6	0.456467	0.228234	+	0.973606i	$0.426705\pi$
$830$	−4.08677e6	−0.205914
$831$	−3.61005e7	−1.81347
$832$	−1.35672e7	−0.679486
$833$	−1.87183e7	−0.934659
$834$	−3.84555e6	−0.191445
$835$	7.58289e6	0.376373
$836$	1.87401e6	0.0927378
$837$	−3.35623e6	−0.165592
$838$	−1.77293e7	−0.872130
$839$	3.52034e7	1.72655	0.863277	−	0.504731i	$-0.168408\pi$
$839$	3.52034e7	1.72655	0.863277	+	0.504731i	$0.168408\pi$
$840$	−2.22022e7	−1.08567
$841$	0	0
$842$	1.71187e7	0.832129
$843$	−2.02722e7	−0.982497
$844$	807995.	0.0390438
$845$	1.88897e6	0.0910087
$846$	1.80249e7	0.865860
$847$	−2.09869e7	−1.00517
$848$	78414.7	0.00374462
$849$	2.72585e7	1.29788
$850$	−4.98343e6	−0.236582
$851$	2.02664e7	0.959298
$852$	−8.56105e6	−0.404044
$853$	−1.15136e7	−0.541801	−0.270901	−	0.962607i	$-0.587322\pi$
$853$	−1.15136e7	−0.541801	−0.270901	+	0.962607i	$0.587322\pi$
$854$	−1.45959e7	−0.684836
$855$	2.10050e6	0.0982671
$856$	1.87240e7	0.873404
$857$	1.76618e7	0.821451	0.410726	−	0.911759i	$-0.365275\pi$
$857$	1.76618e7	0.821451	0.410726	+	0.911759i	$0.365275\pi$
$858$	1.16020e7	0.538040
$859$	−1.61212e6	−0.0745445	−0.0372722	−	0.999305i	$-0.511867\pi$
$859$	−1.61212e6	−0.0745445	−0.0372722	+	0.999305i	$0.511867\pi$
$860$	−7.21849e6	−0.332813
$861$	−6.32799e7	−2.90909
$862$	2.30155e7	1.05500
$863$	−2.79231e7	−1.27625	−0.638127	−	0.769931i	$-0.720290\pi$
$863$	−2.79231e7	−1.27625	−0.638127	+	0.769931i	$0.720290\pi$
$864$	2.60308e6	0.118632
$865$	7.76789e6	0.352990
$866$	1.54034e7	0.697947
$867$	−2.48217e7	−1.12146
$868$	−2.89599e7	−1.30466
$869$	−4.64187e6	−0.208518
$870$	0	0
$871$	2.62734e7	1.17347
$872$	−2.81110e7	−1.25195
$873$	3.81237e7	1.69301
$874$	−2.21651e6	−0.0981501
$875$	3.11979e7	1.37754
$876$	−1.12783e7	−0.496572
$877$	8.50763e6	0.373516	0.186758	−	0.982406i	$-0.440202\pi$
$877$	8.50763e6	0.373516	0.186758	+	0.982406i	$0.440202\pi$
$878$	−8.12413e6	−0.355665
$879$	2.17942e7	0.951411
$880$	872312.	0.0379721
$881$	−3.84090e6	−0.166722	−0.0833611	−	0.996519i	$-0.526565\pi$
$881$	−3.84090e6	−0.166722	−0.0833611	+	0.996519i	$0.526565\pi$
$882$	−3.01475e7	−1.30491
$883$	4.28487e6	0.184942	0.0924712	−	0.995715i	$-0.470523\pi$
$883$	4.28487e6	0.184942	0.0924712	+	0.995715i	$0.470523\pi$
$884$	−4.97247e6	−0.214014
$885$	−1.25602e7	−0.539060
$886$	−2.48241e7	−1.06240
$887$	4.72746e6	0.201752	0.100876	−	0.994899i	$-0.467835\pi$
$887$	4.72746e6	0.201752	0.100876	+	0.994899i	$0.467835\pi$
$888$	−5.55318e7	−2.36325
$889$	−1.77061e7	−0.751395
$890$	6.73127e6	0.284854
$891$	−1.68976e7	−0.713066
$892$	−487586.	−0.0205182
$893$	8.62296e6	0.361849
$894$	−1.49379e7	−0.625093
$895$	1.21573e7	0.507317
$896$	1.86196e7	0.774820
$897$	1.71767e7	0.712786
$898$	666494.	0.0275807
$899$	0	0
$900$	1.00467e7	0.413445
$901$	293196.	0.0120322
$902$	1.27177e7	0.520467
$903$	−8.43540e7	−3.44260
$904$	−2.79460e7	−1.13736
$905$	−1.44038e7	−0.584594
$906$	1.31954e7	0.534074
$907$	7.58482e6	0.306145	0.153073	−	0.988215i	$-0.451083\pi$
$907$	7.58482e6	0.306145	0.153073	+	0.988215i	$0.451083\pi$
$908$	1.82291e7	0.733753
$909$	−4.15211e7	−1.66671
$910$	−1.11890e7	−0.447907
$911$	1.54862e7	0.618228	0.309114	−	0.951025i	$-0.399968\pi$
$911$	1.54862e7	0.618228	0.309114	+	0.951025i	$0.399968\pi$
$912$	1.18732e6	0.0472693
$913$	−1.20142e7	−0.476998
$914$	−5.85590e6	−0.231861
$915$	−8.64167e6	−0.341228
$916$	−8.35731e6	−0.329100
$917$	3.38082e7	1.32769
$918$	−925352.	−0.0362410
$919$	1.08832e7	0.425076	0.212538	−	0.977153i	$-0.431827\pi$
$919$	1.08832e7	0.425076	0.212538	+	0.977153i	$0.431827\pi$
$920$	6.60612e6	0.257322
$921$	−1.30490e7	−0.506907
$922$	−1.24782e7	−0.483419
$923$	−1.20756e7	−0.466558
$924$	−2.33197e7	−0.898550
$925$	3.51079e7	1.34912
$926$	−3.11310e7	−1.19307
$927$	2.09891e6	0.0802222
$928$	0	0
$929$	1.60849e7	0.611475	0.305737	−	0.952116i	$-0.401097\pi$
$929$	1.60849e7	0.611475	0.305737	+	0.952116i	$0.401097\pi$
$930$	1.36978e7	0.519331
$931$	−1.44223e7	−0.545330
$932$	2.01375e7	0.759390
$933$	7.40721e6	0.278580
$934$	−8.95374e6	−0.335844
$935$	3.26161e6	0.122012
$936$	−2.24153e7	−0.836285
$937$	−3.97188e7	−1.47791	−0.738954	−	0.673756i	$-0.764680\pi$
$937$	−3.97188e7	−1.47791	−0.738954	+	0.673756i	$0.764680\pi$
$938$	4.21887e7	1.56563
$939$	2.09313e6	0.0774699
$940$	−9.18220e6	−0.338943
$941$	−4.35478e7	−1.60322	−0.801608	−	0.597850i	$-0.796022\pi$
$941$	−4.35478e7	−1.60322	−0.801608	+	0.597850i	$0.796022\pi$
$942$	1.69070e7	0.620783
$943$	1.88285e7	0.689505
$944$	−3.38125e6	−0.123495
$945$	2.60637e6	0.0949417
$946$	1.69531e7	0.615916
$947$	4.36347e7	1.58109	0.790546	−	0.612402i	$-0.209797\pi$
$947$	4.36347e7	1.58109	0.790546	+	0.612402i	$0.209797\pi$
$948$	6.72788e6	0.243141
$949$	−1.59084e7	−0.573403
$950$	−3.83969e6	−0.138034
$951$	3.90270e7	1.39931
$952$	−2.23480e7	−0.799181
$953$	1.86470e7	0.665084	0.332542	−	0.943088i	$-0.392094\pi$
$953$	1.86470e7	0.665084	0.332542	+	0.943088i	$0.392094\pi$
$954$	472219.	0.0167986
$955$	1.02505e7	0.363695
$956$	2.46701e7	0.873023
$957$	0	0
$958$	2.38794e6	0.0840639
$959$	8.74721e7	3.07131
$960$	−1.28983e7	−0.451706
$961$	2.13789e7	0.746752
$962$	−2.79858e7	−0.974990
$963$	2.20433e7	0.765970
$964$	1.12284e6	0.0389158
$965$	1.94674e6	0.0672962
$966$	2.75816e7	0.950991
$967$	−8.44182e6	−0.290315	−0.145158	−	0.989409i	$-0.546369\pi$
$967$	−8.44182e6	−0.290315	−0.145158	+	0.989409i	$0.546369\pi$
$968$	−1.71106e7	−0.586916
$969$	4.43942e6	0.151886
$970$	1.55152e7	0.529455
$971$	2.98967e7	1.01759	0.508797	−	0.860886i	$-0.330090\pi$
$971$	2.98967e7	1.01759	0.508797	+	0.860886i	$0.330090\pi$
$972$	2.24396e7	0.761814
$973$	1.09026e7	0.369189
$974$	1.32242e7	0.446654
$975$	2.97555e7	1.00243
$976$	−2.32637e6	−0.0781727
$977$	−1.02652e7	−0.344057	−0.172029	−	0.985092i	$-0.555032\pi$
$977$	−1.02652e7	−0.344057	−0.172029	+	0.985092i	$0.555032\pi$
$978$	7.55561e6	0.252594
$979$	1.97884e7	0.659864
$980$	1.53576e7	0.510810
$981$	−3.30944e7	−1.09795
$982$	9.08887e6	0.300768
$983$	3.58497e7	1.18332	0.591660	−	0.806188i	$-0.298473\pi$
$983$	3.58497e7	1.18332	0.591660	+	0.806188i	$0.298473\pi$
$984$	−5.15918e7	−1.69861
$985$	−1.67354e7	−0.549598
$986$	0	0
$987$	−1.07302e8	−3.50601
$988$	−3.83125e6	−0.124867
$989$	2.50990e7	0.815955
$990$	5.25312e6	0.170345
$991$	−7.48026e6	−0.241954	−0.120977	−	0.992655i	$-0.538603\pi$
$991$	−7.48026e6	−0.241954	−0.120977	+	0.992655i	$0.538603\pi$
$992$	−3.87859e7	−1.25140
$993$	2.05247e6	0.0660547
$994$	−1.93905e7	−0.622477
$995$	−1.49088e7	−0.477402
$996$	1.74132e7	0.556199
$997$	−3.21460e7	−1.02421	−0.512105	−	0.858923i	$-0.671134\pi$
$997$	−3.21460e7	−1.02421	−0.512105	+	0.858923i	$0.671134\pi$
$998$	−8.22122e6	−0.261282
$999$	6.51903e6	0.206666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.6.a.h.1.12		33
29.4	even	14		29.6.d.a.16.4	✓	66
29.22	even	14		29.6.d.a.20.4	yes	66
29.28	even	2		841.6.a.i.1.22		33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.d.a.16.4	✓	66	29.4	even	14
29.6.d.a.20.4	yes	66	29.22	even	14
841.6.a.h.1.12		33	1.1	even	1	trivial
841.6.a.i.1.22		33	29.28	even	2

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-3.76979 q^{2} +21.5399 q^{3} -17.7887 q^{4} -23.8546 q^{5} -81.2008 q^{6} +230.214 q^{7} +187.693 q^{8} +220.966 q^{9} +O(q^{10})\)	\(q-3.76979 q^{2} +21.5399 q^{3} -17.7887 q^{4} -23.8546 q^{5} -81.2008 q^{6} +230.214 q^{7} +187.693 q^{8} +220.966 q^{9} +89.9267 q^{10} +264.364 q^{11} -383.166 q^{12} -540.469 q^{13} -867.859 q^{14} -513.825 q^{15} -138.324 q^{16} -517.199 q^{17} -832.996 q^{18} -398.498 q^{19} +424.342 q^{20} +4958.79 q^{21} -996.597 q^{22} -1475.46 q^{23} +4042.88 q^{24} -2555.96 q^{25} +2037.45 q^{26} -474.605 q^{27} -4095.21 q^{28} +1937.01 q^{30} +7071.64 q^{31} -5484.72 q^{32} +5694.37 q^{33} +1949.73 q^{34} -5491.67 q^{35} -3930.70 q^{36} -13735.7 q^{37} +1502.25 q^{38} -11641.6 q^{39} -4477.34 q^{40} -12761.2 q^{41} -18693.6 q^{42} -17011.0 q^{43} -4702.69 q^{44} -5271.06 q^{45} +5562.16 q^{46} -21638.7 q^{47} -2979.48 q^{48} +36191.6 q^{49} +9635.42 q^{50} -11140.4 q^{51} +9614.23 q^{52} -566.892 q^{53} +1789.16 q^{54} -6306.30 q^{55} +43209.6 q^{56} -8583.59 q^{57} +24444.5 q^{59} +9140.28 q^{60} +16818.3 q^{61} -26658.6 q^{62} +50869.6 q^{63} +25102.6 q^{64} +12892.7 q^{65} -21466.6 q^{66} -48612.3 q^{67} +9200.30 q^{68} -31781.2 q^{69} +20702.4 q^{70} +22342.9 q^{71} +41473.8 q^{72} +29434.4 q^{73} +51780.6 q^{74} -55055.0 q^{75} +7088.75 q^{76} +60860.4 q^{77} +43886.5 q^{78} -17558.6 q^{79} +3299.66 q^{80} -63917.7 q^{81} +48106.9 q^{82} -45445.5 q^{83} -88210.4 q^{84} +12337.6 q^{85} +64127.9 q^{86} +49619.2 q^{88} +74852.9 q^{89} +19870.8 q^{90} -124424. q^{91} +26246.5 q^{92} +152322. q^{93} +81573.2 q^{94} +9506.00 q^{95} -118140. q^{96} +172532. q^{97} -136435. q^{98} +58415.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 12 q^{2} - q^{3} + 422 q^{4} - 157 q^{5} - 166 q^{6} - 331 q^{7} - 453 q^{8} + 1622 q^{9}+O(q^{10}) \) 33 * q - 12 * q^2 - q^3 + 422 * q^4 - 157 * q^5 - 166 * q^6 - 331 * q^7 - 453 * q^8 + 1622 * q^9	\( 33 q - 12 q^{2} - q^{3} + 422 q^{4} - 157 q^{5} - 166 q^{6} - 331 q^{7} - 453 q^{8} + 1622 q^{9} + 291 q^{10} + 491 q^{11} + 124 q^{12} - 1157 q^{13} - 620 q^{14} + 3960 q^{15} + 4566 q^{16} - 338 q^{17} - 6865 q^{18} + 451 q^{19} - 6636 q^{20} + 97 q^{21} - 11899 q^{22} - 8247 q^{23} - 13519 q^{24} + 7262 q^{25} + 11758 q^{26} - 9886 q^{27} + 3754 q^{28} - 20009 q^{30} + 11231 q^{31} - 17863 q^{32} - 22142 q^{33} + 7463 q^{34} - 26372 q^{35} - 516 q^{36} - 7149 q^{37} - 13318 q^{38} - 25700 q^{39} + 18611 q^{40} + 9360 q^{41} + 41603 q^{42} + 55165 q^{43} + 84442 q^{44} + 10619 q^{45} - 7924 q^{46} - 46957 q^{47} + 69535 q^{48} - 16038 q^{49} - 42663 q^{50} - 125432 q^{51} + 7049 q^{52} - 54523 q^{53} - 15016 q^{54} - 118472 q^{55} - 50285 q^{56} - 20081 q^{57} - 166756 q^{59} + 165453 q^{60} - 87433 q^{61} - 103656 q^{62} - 67869 q^{63} - 31945 q^{64} - 27116 q^{65} + 62548 q^{66} - 100267 q^{67} - 92443 q^{68} + 208538 q^{69} + 255839 q^{70} - 117725 q^{71} + 29044 q^{72} + 96829 q^{73} - 147314 q^{74} - 269104 q^{75} + 85334 q^{76} + 237412 q^{77} - 168156 q^{78} - 364713 q^{79} - 629809 q^{80} + 93985 q^{81} - 238717 q^{82} - 203241 q^{83} - 552428 q^{84} + 19206 q^{85} - 174200 q^{86} - 492819 q^{88} + 309027 q^{89} - 252630 q^{90} - 369702 q^{91} - 194235 q^{92} + 86514 q^{93} - 632929 q^{94} + 272214 q^{95} - 361521 q^{96} - 186709 q^{97} - 651857 q^{98} - 219304 q^{99}+O(q^{100}) \) 33 * q - 12 * q^2 - q^3 + 422 * q^4 - 157 * q^5 - 166 * q^6 - 331 * q^7 - 453 * q^8 + 1622 * q^9 + 291 * q^10 + 491 * q^11 + 124 * q^12 - 1157 * q^13 - 620 * q^14 + 3960 * q^15 + 4566 * q^16 - 338 * q^17 - 6865 * q^18 + 451 * q^19 - 6636 * q^20 + 97 * q^21 - 11899 * q^22 - 8247 * q^23 - 13519 * q^24 + 7262 * q^25 + 11758 * q^26 - 9886 * q^27 + 3754 * q^28 - 20009 * q^30 + 11231 * q^31 - 17863 * q^32 - 22142 * q^33 + 7463 * q^34 - 26372 * q^35 - 516 * q^36 - 7149 * q^37 - 13318 * q^38 - 25700 * q^39 + 18611 * q^40 + 9360 * q^41 + 41603 * q^42 + 55165 * q^43 + 84442 * q^44 + 10619 * q^45 - 7924 * q^46 - 46957 * q^47 + 69535 * q^48 - 16038 * q^49 - 42663 * q^50 - 125432 * q^51 + 7049 * q^52 - 54523 * q^53 - 15016 * q^54 - 118472 * q^55 - 50285 * q^56 - 20081 * q^57 - 166756 * q^59 + 165453 * q^60 - 87433 * q^61 - 103656 * q^62 - 67869 * q^63 - 31945 * q^64 - 27116 * q^65 + 62548 * q^66 - 100267 * q^67 - 92443 * q^68 + 208538 * q^69 + 255839 * q^70 - 117725 * q^71 + 29044 * q^72 + 96829 * q^73 - 147314 * q^74 - 269104 * q^75 + 85334 * q^76 + 237412 * q^77 - 168156 * q^78 - 364713 * q^79 - 629809 * q^80 + 93985 * q^81 - 238717 * q^82 - 203241 * q^83 - 552428 * q^84 + 19206 * q^85 - 174200 * q^86 - 492819 * q^88 + 309027 * q^89 - 252630 * q^90 - 369702 * q^91 - 194235 * q^92 + 86514 * q^93 - 632929 * q^94 + 272214 * q^95 - 361521 * q^96 - 186709 * q^97 - 651857 * q^98 - 219304 * q^99

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