LMFDB - Embedded newform 841.6.a.h.1.30

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			1.30
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)

$f(q)$	$=$	$q+9.00678 q^{2} -23.2316 q^{3} +49.1221 q^{4} +27.9935 q^{5} -209.242 q^{6} -76.9940 q^{7} +154.215 q^{8} +296.706 q^{9} +O(q^{10})$	\(q+9.00678 q^{2} -23.2316 q^{3} +49.1221 q^{4} +27.9935 q^{5} -209.242 q^{6} -76.9940 q^{7} +154.215 q^{8} +296.706 q^{9} +252.131 q^{10} -288.965 q^{11} -1141.18 q^{12} +1051.30 q^{13} -693.468 q^{14} -650.332 q^{15} -182.925 q^{16} -971.108 q^{17} +2672.37 q^{18} +2853.15 q^{19} +1375.10 q^{20} +1788.69 q^{21} -2602.64 q^{22} -2669.40 q^{23} -3582.66 q^{24} -2341.37 q^{25} +9468.82 q^{26} -1247.68 q^{27} -3782.11 q^{28} -5857.40 q^{30} +4958.17 q^{31} -6582.45 q^{32} +6713.11 q^{33} -8746.56 q^{34} -2155.33 q^{35} +14574.8 q^{36} +478.647 q^{37} +25697.7 q^{38} -24423.3 q^{39} +4317.02 q^{40} +8379.08 q^{41} +16110.4 q^{42} +14036.6 q^{43} -14194.6 q^{44} +8305.84 q^{45} -24042.7 q^{46} -8185.22 q^{47} +4249.65 q^{48} -10878.9 q^{49} -21088.2 q^{50} +22560.4 q^{51} +51642.0 q^{52} -23863.2 q^{53} -11237.6 q^{54} -8089.13 q^{55} -11873.6 q^{56} -66283.2 q^{57} -34925.4 q^{59} -31945.7 q^{60} +8657.33 q^{61} +44657.1 q^{62} -22844.6 q^{63} -53433.1 q^{64} +29429.5 q^{65} +60463.5 q^{66} -24221.5 q^{67} -47702.9 q^{68} +62014.3 q^{69} -19412.6 q^{70} +15650.2 q^{71} +45756.6 q^{72} +22731.6 q^{73} +4311.07 q^{74} +54393.6 q^{75} +140153. q^{76} +22248.6 q^{77} -219976. q^{78} -97698.9 q^{79} -5120.72 q^{80} -43114.0 q^{81} +75468.6 q^{82} +37201.8 q^{83} +87864.3 q^{84} -27184.7 q^{85} +126425. q^{86} -44562.8 q^{88} -45954.5 q^{89} +74808.9 q^{90} -80943.7 q^{91} -131126. q^{92} -115186. q^{93} -73722.5 q^{94} +79869.6 q^{95} +152921. q^{96} +109146. q^{97} -97984.1 q^{98} -85737.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.00678	1.59219	0.796095	−	0.605172i	$-0.206896\pi$
$2$	9.00678	1.59219	0.796095	+	0.605172i	$0.206896\pi$
$3$	−23.2316	−1.49031	−0.745153	−	0.666893i	$-0.767624\pi$
$3$	−23.2316	−1.49031	−0.745153	+	0.666893i	$0.767624\pi$
$4$	49.1221	1.53507
$5$	27.9935	0.500762	0.250381	−	0.968147i	$-0.419444\pi$
$5$	27.9935	0.500762	0.250381	+	0.968147i	$0.419444\pi$
$6$	−209.242	−2.37285
$7$	−76.9940	−0.593898	−0.296949	−	0.954893i	$-0.595969\pi$
$7$	−76.9940	−0.593898	−0.296949	+	0.954893i	$0.595969\pi$
$8$	154.215	0.851926
$9$	296.706	1.22101
$10$	252.131	0.797308
$11$	−288.965	−0.720051	−0.360026	−	0.932942i	$-0.617232\pi$
$11$	−288.965	−0.720051	−0.360026	+	0.932942i	$0.617232\pi$
$12$	−1141.18	−2.28772
$13$	1051.30	1.72531	0.862656	−	0.505790i	$-0.168799\pi$
$13$	1051.30	1.72531	0.862656	+	0.505790i	$0.168799\pi$
$14$	−693.468	−0.945598
$15$	−650.332	−0.746289
$16$	−182.925	−0.178638
$17$	−971.108	−0.814977	−0.407488	−	0.913210i	$-0.633595\pi$
$17$	−971.108	−0.814977	−0.407488	+	0.913210i	$0.633595\pi$
$18$	2672.37	1.94408
$19$	2853.15	1.81318	0.906590	−	0.422013i	$-0.138676\pi$
$19$	2853.15	1.81318	0.906590	+	0.422013i	$0.138676\pi$
$20$	1375.10	0.768703
$21$	1788.69	0.885090
$22$	−2602.64	−1.14646
$23$	−2669.40	−1.05219	−0.526094	−	0.850426i	$-0.676344\pi$
$23$	−2669.40	−1.05219	−0.526094	+	0.850426i	$0.676344\pi$
$24$	−3582.66	−1.26963
$25$	−2341.37	−0.749237
$26$	9468.82	2.74702
$27$	−1247.68	−0.329378
$28$	−3782.11	−0.911672
$29$	0	0
$29$	0	0
$30$	−5857.40	−1.18823
$31$	4958.17	0.926653	0.463326	−	0.886188i	$-0.346656\pi$
$31$	4958.17	0.926653	0.463326	+	0.886188i	$0.346656\pi$
$32$	−6582.45	−1.13635
$33$	6713.11	1.07310
$34$	−8746.56	−1.29760
$35$	−2155.33	−0.297402
$36$	14574.8	1.87434
$37$	478.647	0.0574793	0.0287396	−	0.999587i	$-0.490851\pi$
$37$	478.647	0.0574793	0.0287396	+	0.999587i	$0.490851\pi$
$38$	25697.7	2.88692
$39$	−24423.3	−2.57124
$40$	4317.02	0.426613
$41$	8379.08	0.778461	0.389230	−	0.921140i	$-0.372741\pi$
$41$	8379.08	0.778461	0.389230	+	0.921140i	$0.372741\pi$
$42$	16110.4	1.40923
$43$	14036.6	1.15769	0.578845	−	0.815438i	$-0.303504\pi$
$43$	14036.6	1.15769	0.578845	+	0.815438i	$0.303504\pi$
$44$	−14194.6	−1.10533
$45$	8305.84	0.611438
$46$	−24042.7	−1.67528
$47$	−8185.22	−0.540487	−0.270244	−	0.962792i	$-0.587104\pi$
$47$	−8185.22	−0.540487	−0.270244	+	0.962792i	$0.587104\pi$
$48$	4249.65	0.266226
$49$	−10878.9	−0.647285
$50$	−21088.2	−1.19293
$51$	22560.4	1.21457
$52$	51642.0	2.64847
$53$	−23863.2	−1.16692	−0.583458	−	0.812143i	$-0.698301\pi$
$53$	−23863.2	−1.16692	−0.583458	+	0.812143i	$0.698301\pi$
$54$	−11237.6	−0.524432
$55$	−8089.13	−0.360575
$56$	−11873.6	−0.505957
$57$	−66283.2	−2.70219
$58$	0	0
$59$	−34925.4	−1.30621	−0.653103	−	0.757269i	$-0.726533\pi$
$59$	−34925.4	−1.30621	−0.653103	+	0.757269i	$0.726533\pi$
$60$	−31945.7	−1.14560
$61$	8657.33	0.297893	0.148946	−	0.988845i	$-0.452412\pi$
$61$	8657.33	0.297893	0.148946	+	0.988845i	$0.452412\pi$
$62$	44657.1	1.47541
$63$	−22844.6	−0.725157
$64$	−53433.1	−1.63065
$65$	29429.5	0.863972
$66$	60463.5	1.70857
$67$	−24221.5	−0.659195	−0.329597	−	0.944122i	$-0.606913\pi$
$67$	−24221.5	−0.659195	−0.329597	+	0.944122i	$0.606913\pi$
$68$	−47702.9	−1.25104
$69$	62014.3	1.56808
$70$	−19412.6	−0.473520
$71$	15650.2	0.368447	0.184224	−	0.982884i	$-0.441023\pi$
$71$	15650.2	0.368447	0.184224	+	0.982884i	$0.441023\pi$
$72$	45756.6	1.04021
$73$	22731.6	0.499255	0.249627	−	0.968342i	$-0.419692\pi$
$73$	22731.6	0.499255	0.249627	+	0.968342i	$0.419692\pi$
$74$	4311.07	0.0915178
$75$	54393.6	1.11659
$76$	140153.	2.78335
$77$	22248.6	0.427637
$78$	−219976.	−4.09391
$79$	−97698.9	−1.76125	−0.880627	−	0.473811i	$-0.842878\pi$
$79$	−97698.9	−1.76125	−0.880627	+	0.473811i	$0.842878\pi$
$80$	−5120.72	−0.0894553
$81$	−43114.0	−0.730139
$82$	75468.6	1.23946
$83$	37201.8	0.592746	0.296373	−	0.955072i	$-0.404223\pi$
$83$	37201.8	0.592746	0.296373	+	0.955072i	$0.404223\pi$
$84$	87864.3	1.35867
$85$	−27184.7	−0.408110
$86$	126425.	1.84326
$87$	0	0
$88$	−44562.8	−0.613431
$89$	−45954.5	−0.614969	−0.307484	−	0.951553i	$-0.599487\pi$
$89$	−45954.5	−0.614969	−0.307484	+	0.951553i	$0.599487\pi$
$90$	74808.9	0.973524
$91$	−80943.7	−1.02466
$92$	−131126.	−1.61518
$93$	−115186.	−1.38100
$94$	−73722.5	−0.860558
$95$	79869.6	0.907972
$96$	152921.	1.69351
$97$	109146.	1.17782	0.588909	−	0.808199i	$-0.299558\pi$
$97$	109146.	1.17782	0.588909	+	0.808199i	$0.299558\pi$
$98$	−97984.1	−1.03060
$99$	−85737.7	−0.879193
$100$	−115013.	−1.15013
$101$	−41877.3	−0.408485	−0.204242	−	0.978920i	$-0.565473\pi$
$101$	−41877.3	−0.408485	−0.204242	+	0.978920i	$0.565473\pi$
$102$	203196.	1.93382
$103$	15214.7	0.141309	0.0706544	−	0.997501i	$-0.477491\pi$
$103$	15214.7	0.141309	0.0706544	+	0.997501i	$0.477491\pi$
$104$	162126.	1.46984
$105$	50071.7	0.443220
$106$	−214931.	−1.85795
$107$	−217741.	−1.83857	−0.919287	−	0.393588i	$-0.871234\pi$
$107$	−217741.	−1.83857	−0.919287	+	0.393588i	$0.871234\pi$
$108$	−61288.8	−0.505617
$109$	−57118.1	−0.460476	−0.230238	−	0.973134i	$-0.573951\pi$
$109$	−57118.1	−0.460476	−0.230238	+	0.973134i	$0.573951\pi$
$110$	−72857.0	−0.574103
$111$	−11119.7	−0.0856617
$112$	14084.2	0.106093
$113$	16040.7	0.118176	0.0590879	−	0.998253i	$-0.481181\pi$
$113$	16040.7	0.118176	0.0590879	+	0.998253i	$0.481181\pi$
$114$	−596998.	−4.30240
$115$	−74725.7	−0.526897
$116$	0	0
$117$	311927.	2.10663
$118$	−314566.	−2.07973
$119$	74769.5	0.484013
$120$	−100291.	−0.635784
$121$	−77550.3	−0.481526
$122$	77974.7	0.474301
$123$	−194659.	−1.16015
$124$	243556.	1.42247
$125$	−153023.	−0.875952
$126$	−205756.	−1.15459
$127$	67072.8	0.369009	0.184504	−	0.982832i	$-0.440932\pi$
$127$	67072.8	0.369009	0.184504	+	0.982832i	$0.440932\pi$
$128$	−270622.	−1.45995
$129$	−326093.	−1.72531
$130$	265065.	1.37561
$131$	−311705.	−1.58696	−0.793479	−	0.608597i	$-0.791733\pi$
$131$	−311705.	−1.58696	−0.793479	+	0.608597i	$0.791733\pi$
$132$	329762.	1.64728
$133$	−219676.	−1.07684
$134$	−218158.	−1.04956
$135$	−34927.0	−0.164940
$136$	−149760.	−0.694300
$137$	−330315.	−1.50358	−0.751790	−	0.659403i	$-0.770809\pi$
$137$	−330315.	−1.50358	−0.751790	+	0.659403i	$0.770809\pi$
$138$	558549.	2.49669
$139$	−65043.4	−0.285540	−0.142770	−	0.989756i	$-0.545601\pi$
$139$	−65043.4	−0.285540	−0.142770	+	0.989756i	$0.545601\pi$
$140$	−105874.	−0.456531
$141$	190156.	0.805492
$142$	140958.	0.586637
$143$	−303789.	−1.24231
$144$	−54275.1	−0.218120
$145$	0	0
$146$	204738.	0.794908
$147$	252735.	0.964654
$148$	23512.2	0.0882345
$149$	92058.0	0.339700	0.169850	−	0.985470i	$-0.445672\pi$
$149$	92058.0	0.339700	0.169850	+	0.985470i	$0.445672\pi$
$150$	489912.	1.77783
$151$	−58268.0	−0.207964	−0.103982	−	0.994579i	$-0.533158\pi$
$151$	−58268.0	−0.207964	−0.103982	+	0.994579i	$0.533158\pi$
$152$	439999.	1.54470
$153$	−288134.	−0.995098
$154$	200388.	0.680879
$155$	138796.	0.464033
$156$	−1.19973e6	−3.94703
$157$	−127312.	−0.412213	−0.206107	−	0.978530i	$-0.566079\pi$
$157$	−127312.	−0.412213	−0.206107	+	0.978530i	$0.566079\pi$
$158$	−879952.	−2.80425
$159$	554381.	1.73906
$160$	−184266.	−0.569042
$161$	205528.	0.624893
$162$	−388318.	−1.16252
$163$	−271289.	−0.799767	−0.399883	−	0.916566i	$-0.630949\pi$
$163$	−271289.	−0.799767	−0.399883	+	0.916566i	$0.630949\pi$
$164$	411598.	1.19499
$165$	187923.	0.537367
$166$	335068.	0.943763
$167$	−368302.	−1.02191	−0.510955	−	0.859607i	$-0.670708\pi$
$167$	−368302.	−1.02191	−0.510955	+	0.859607i	$0.670708\pi$
$168$	275843.	0.754031
$169$	733936.	1.97670
$170$	−244846.	−0.649788
$171$	846548.	2.21392
$172$	689509.	1.77713
$173$	−298436.	−0.758117	−0.379059	−	0.925373i	$-0.623752\pi$
$173$	−298436.	−0.758117	−0.379059	+	0.925373i	$0.623752\pi$
$174$	0	0
$175$	180271.	0.444970
$176$	52859.1	0.128629
$177$	811373.	1.94665
$178$	−413902.	−0.979147
$179$	−347027.	−0.809525	−0.404762	−	0.914422i	$-0.632646\pi$
$179$	−347027.	−0.809525	−0.404762	+	0.914422i	$0.632646\pi$
$180$	408000.	0.938597
$181$	759672.	1.72357	0.861787	−	0.507270i	$-0.169345\pi$
$181$	759672.	1.72357	0.861787	+	0.507270i	$0.169345\pi$
$182$	−729042.	−1.63145
$183$	−201124.	−0.443951
$184$	−411662.	−0.896387
$185$	13399.0	0.0287834
$186$	−1.03746e6	−2.19881
$187$	280616.	0.586825
$188$	−402075.	−0.829684
$189$	96064.1	0.195617
$190$	719368.	1.44566
$191$	−569227.	−1.12902	−0.564511	−	0.825426i	$-0.690935\pi$
$191$	−569227.	−1.12902	−0.564511	+	0.825426i	$0.690935\pi$
$192$	1.24134e6	2.43017
$193$	807006.	1.55949	0.779747	−	0.626095i	$-0.215348\pi$
$193$	807006.	1.55949	0.779747	+	0.626095i	$0.215348\pi$
$194$	983054.	1.87531
$195$	−683694.	−1.28758
$196$	−534396.	−0.993626
$197$	22665.8	0.0416107	0.0208054	−	0.999784i	$-0.493377\pi$
$197$	22665.8	0.0416107	0.0208054	+	0.999784i	$0.493377\pi$
$198$	−772221.	−1.39984
$199$	798271.	1.42895	0.714476	−	0.699660i	$-0.246665\pi$
$199$	798271.	1.42895	0.714476	+	0.699660i	$0.246665\pi$
$200$	−361074.	−0.638295
$201$	562703.	0.982402
$202$	−377180.	−0.650385
$203$	0	0
$204$	1.10821e6	1.86444
$205$	234560.	0.389824
$206$	137035.	0.224990
$207$	−792027.	−1.28474
$208$	−192309.	−0.308207
$209$	−824461.	−1.30558
$210$	450985.	0.705689
$211$	−453190.	−0.700767	−0.350384	−	0.936606i	$-0.613949\pi$
$211$	−453190.	−0.700767	−0.350384	+	0.936606i	$0.613949\pi$
$212$	−1.17221e6	−1.79129
$213$	−363580.	−0.549099
$214$	−1.96115e6	−2.92736
$215$	392934.	0.579727
$216$	−192412.	−0.280606
$217$	−381749.	−0.550337
$218$	−514450.	−0.733166
$219$	−528090.	−0.744043
$220$	−397355.	−0.553506
$221$	−1.02092e6	−1.40609
$222$	−100153.	−0.136390
$223$	−939845.	−1.26559	−0.632796	−	0.774318i	$-0.718093\pi$
$223$	−939845.	−1.26559	−0.632796	+	0.774318i	$0.718093\pi$
$224$	506809.	0.674877
$225$	−694698.	−0.914829
$226$	144475.	0.188158
$227$	−345794.	−0.445402	−0.222701	−	0.974887i	$-0.571487\pi$
$227$	−345794.	−0.445402	−0.222701	+	0.974887i	$0.571487\pi$
$228$	−3.25597e6	−4.14805
$229$	−1.12968e6	−1.42353	−0.711766	−	0.702416i	$-0.752105\pi$
$229$	−1.12968e6	−1.42353	−0.711766	+	0.702416i	$0.752105\pi$
$230$	−673038.	−0.838919
$231$	−516869.	−0.637310
$232$	0	0
$233$	−109838.	−0.132545	−0.0662724	−	0.997802i	$-0.521111\pi$
$233$	−109838.	−0.132545	−0.0662724	+	0.997802i	$0.521111\pi$
$234$	2.80946e6	3.35415
$235$	−229133.	−0.270656
$236$	−1.71561e6	−2.00511
$237$	2.26970e6	2.62481
$238$	673432.	0.770640
$239$	−1.10007e6	−1.24574	−0.622870	−	0.782326i	$-0.714033\pi$
$239$	−1.10007e6	−1.24574	−0.622870	+	0.782326i	$0.714033\pi$
$240$	118962.	0.133316
$241$	925989.	1.02698	0.513492	−	0.858095i	$-0.328352\pi$
$241$	925989.	1.02698	0.513492	+	0.858095i	$0.328352\pi$
$242$	−698478.	−0.766681
$243$	1.30479e6	1.41751
$244$	425267.	0.457285
$245$	−304539.	−0.324136
$246$	−1.75325e6	−1.84717
$247$	2.99952e6	3.12830
$248$	764625.	0.789440
$249$	−864256.	−0.883373
$250$	−1.37824e6	−1.39468
$251$	43155.1	0.0432362	0.0216181	−	0.999766i	$-0.493118\pi$
$251$	43155.1	0.0432362	0.0216181	+	0.999766i	$0.493118\pi$
$252$	−1.12218e6	−1.11316
$253$	771362.	0.757630
$254$	604110.	0.587532
$255$	631543.	0.608208
$256$	−727572.	−0.693867
$257$	182465.	0.172324	0.0861622	−	0.996281i	$-0.472540\pi$
$257$	182465.	0.172324	0.0861622	+	0.996281i	$0.472540\pi$
$258$	−2.93705e6	−2.74702
$259$	−36852.9	−0.0341368
$260$	1.44564e6	1.32625
$261$	0	0
$262$	−2.80746e6	−2.52674
$263$	−1.83476e6	−1.63565	−0.817824	−	0.575468i	$-0.804820\pi$
$263$	−1.83476e6	−1.63565	−0.817824	+	0.575468i	$0.804820\pi$
$264$	1.03526e6	0.914200
$265$	−668015.	−0.584348
$266$	−1.97857e6	−1.71454
$267$	1.06760e6	0.916492
$268$	−1.18981e6	−1.01191
$269$	1.31829e6	1.11078	0.555392	−	0.831589i	$-0.312568\pi$
$269$	1.31829e6	1.11078	0.555392	+	0.831589i	$0.312568\pi$
$270$	−314579.	−0.262616
$271$	342413.	0.283222	0.141611	−	0.989922i	$-0.454772\pi$
$271$	342413.	0.283222	0.141611	+	0.989922i	$0.454772\pi$
$272$	177640.	0.145586
$273$	1.88045e6	1.52706
$274$	−2.97507e6	−2.39398
$275$	676573.	0.539489
$276$	3.04627e6	2.40711
$277$	−532943.	−0.417332	−0.208666	−	0.977987i	$-0.566912\pi$
$277$	−532943.	−0.417332	−0.208666	+	0.977987i	$0.566912\pi$
$278$	−585832.	−0.454633
$279$	1.47112e6	1.13146
$280$	−332384.	−0.253364
$281$	−205685.	−0.155395	−0.0776975	−	0.996977i	$-0.524757\pi$
$281$	−205685.	−0.155395	−0.0776975	+	0.996977i	$0.524757\pi$
$282$	1.71269e6	1.28250
$283$	−944659.	−0.701147	−0.350574	−	0.936535i	$-0.614013\pi$
$283$	−944659.	−0.701147	−0.350574	+	0.936535i	$0.614013\pi$
$284$	768773.	0.565591
$285$	−1.85550e6	−1.35316
$286$	−2.73616e6	−1.97800
$287$	−645139.	−0.462326
$288$	−1.95306e6	−1.38750
$289$	−476807.	−0.335813
$290$	0	0
$291$	−2.53563e6	−1.75531
$292$	1.11662e6	0.766389
$293$	−1.15053e6	−0.782940	−0.391470	−	0.920191i	$-0.628033\pi$
$293$	−1.15053e6	−0.782940	−0.391470	+	0.920191i	$0.628033\pi$
$294$	2.27633e6	1.53591
$295$	−977684.	−0.654099
$296$	73814.6	0.0489681
$297$	360537.	0.237169
$298$	829146.	0.540867
$299$	−2.80633e6	−1.81535
$300$	2.67193e6	1.71404
$301$	−1.08074e6	−0.687549
$302$	−524808.	−0.331118
$303$	972877.	0.608767
$304$	−521914.	−0.323903
$305$	242349.	0.149173
$306$	−2.59516e6	−1.58438
$307$	1.20869e6	0.731930	0.365965	−	0.930629i	$-0.380739\pi$
$307$	1.20869e6	0.731930	0.365965	+	0.930629i	$0.380739\pi$
$308$	1.09290e6	0.656451
$309$	−353461.	−0.210593
$310$	1.25011e6	0.738828
$311$	953208.	0.558839	0.279419	−	0.960169i	$-0.409858\pi$
$311$	953208.	0.558839	0.279419	+	0.960169i	$0.409858\pi$
$312$	−3.76645e6	−2.19051
$313$	536330.	0.309436	0.154718	−	0.987959i	$-0.450553\pi$
$313$	536330.	0.309436	0.154718	+	0.987959i	$0.450553\pi$
$314$	−1.14668e6	−0.656321
$315$	−639500.	−0.363131
$316$	−4.79917e6	−2.70364
$317$	1.01839e6	0.569202	0.284601	−	0.958646i	$-0.408139\pi$
$317$	1.01839e6	0.569202	0.284601	+	0.958646i	$0.408139\pi$
$318$	4.99319e6	2.76892
$319$	0	0
$320$	−1.49578e6	−0.816568
$321$	5.05847e6	2.74004
$322$	1.85114e6	0.994947
$323$	−2.77072e6	−1.47770
$324$	−2.11785e6	−1.12081
$325$	−2.46148e6	−1.29267
$326$	−2.44344e6	−1.27338
$327$	1.32694e6	0.686251
$328$	1.29218e6	0.663191
$329$	630213.	0.320994
$330$	1.69258e6	0.855589
$331$	−2.56162e6	−1.28512	−0.642562	−	0.766234i	$-0.722128\pi$
$331$	−2.56162e6	−1.28512	−0.642562	+	0.766234i	$0.722128\pi$
$332$	1.82743e6	0.909904
$333$	142018.	0.0701829
$334$	−3.31721e6	−1.62707
$335$	−678043.	−0.330100
$336$	−327197.	−0.158111
$337$	3.41187e6	1.63651	0.818254	−	0.574857i	$-0.194942\pi$
$337$	3.41187e6	1.63651	0.818254	+	0.574857i	$0.194942\pi$
$338$	6.61041e6	3.14729
$339$	−372652.	−0.176118
$340$	−1.33537e6	−0.626475
$341$	−1.43274e6	−0.667238
$342$	7.62467e6	3.52497
$343$	2.13165e6	0.978319
$344$	2.16466e6	0.986266
$345$	1.73600e6	0.785237
$346$	−2.68795e6	−1.20707
$347$	2.16244e6	0.964098	0.482049	−	0.876144i	$-0.339893\pi$
$347$	2.16244e6	0.964098	0.482049	+	0.876144i	$0.339893\pi$
$348$	0	0
$349$	−1.18480e6	−0.520692	−0.260346	−	0.965515i	$-0.583837\pi$
$349$	−1.18480e6	−0.520692	−0.260346	+	0.965515i	$0.583837\pi$
$350$	1.62366e6	0.708477
$351$	−1.31169e6	−0.568280
$352$	1.90210e6	0.818232
$353$	4.57931e6	1.95597	0.977987	−	0.208668i	$-0.0669127\pi$
$353$	4.57931e6	1.95597	0.977987	+	0.208668i	$0.0669127\pi$
$354$	7.30786e6	3.09943
$355$	438104.	0.184504
$356$	−2.25738e6	−0.944018
$357$	−1.73701e6	−0.721328
$358$	−3.12559e6	−1.28892
$359$	280516.	0.114874	0.0574369	−	0.998349i	$-0.481707\pi$
$359$	280516.	0.114874	0.0574369	+	0.998349i	$0.481707\pi$
$360$	1.28089e6	0.520900
$361$	5.66437e6	2.28762
$362$	6.84220e6	2.74426
$363$	1.80161e6	0.717621
$364$	−3.97613e6	−1.57292
$365$	636335.	0.250008
$366$	−1.81148e6	−0.706854
$367$	−532629.	−0.206424	−0.103212	−	0.994659i	$-0.532912\pi$
$367$	−532629.	−0.206424	−0.103212	+	0.994659i	$0.532912\pi$
$368$	488301.	0.187961
$369$	2.48613e6	0.950511
$370$	120682.	0.0458287
$371$	1.83733e6	0.693029
$372$	−5.65818e6	−2.11992
$373$	3.25674e6	1.21202	0.606012	−	0.795455i	$-0.292768\pi$
$373$	3.25674e6	1.21202	0.606012	+	0.795455i	$0.292768\pi$
$374$	2.52745e6	0.934336
$375$	3.55495e6	1.30544
$376$	−1.26228e6	−0.460455
$377$	0	0
$378$	865228.	0.311459
$379$	347302.	0.124196	0.0620982	−	0.998070i	$-0.480221\pi$
$379$	347302.	0.124196	0.0620982	+	0.998070i	$0.480221\pi$
$380$	3.92336e6	1.39380
$381$	−1.55821e6	−0.549937
$382$	−5.12691e6	−1.79762
$383$	−1.99125e6	−0.693633	−0.346817	−	0.937933i	$-0.612737\pi$
$383$	−1.99125e6	−0.693633	−0.346817	+	0.937933i	$0.612737\pi$
$384$	6.28697e6	2.17577
$385$	622814.	0.214144
$386$	7.26853e6	2.48301
$387$	4.16476e6	1.41355
$388$	5.36148e6	1.80803
$389$	2.55832e6	0.857196	0.428598	−	0.903495i	$-0.359008\pi$
$389$	2.55832e6	0.857196	0.428598	+	0.903495i	$0.359008\pi$
$390$	−6.15788e6	−2.05007
$391$	2.59227e6	0.857509
$392$	−1.67770e6	−0.551440
$393$	7.24140e6	2.36506
$394$	204146.	0.0662522
$395$	−2.73493e6	−0.881969
$396$	−4.21162e6	−1.34962
$397$	5.59519e6	1.78172	0.890858	−	0.454282i	$-0.150104\pi$
$397$	5.59519e6	1.78172	0.890858	+	0.454282i	$0.150104\pi$
$398$	7.18986e6	2.27516
$399$	5.10341e6	1.60483
$400$	428296.	0.133842
$401$	−1.19182e6	−0.370125	−0.185063	−	0.982727i	$-0.559249\pi$
$401$	−1.19182e6	−0.370125	−0.185063	+	0.982727i	$0.559249\pi$
$402$	5.06815e6	1.56417
$403$	5.21252e6	1.59877
$404$	−2.05710e6	−0.627051
$405$	−1.20691e6	−0.365626
$406$	0	0
$407$	−138312.	−0.0413880
$408$	3.47915e6	1.03472
$409$	3.72938e6	1.10237	0.551186	−	0.834383i	$-0.314176\pi$
$409$	3.72938e6	1.10237	0.551186	+	0.834383i	$0.314176\pi$
$410$	2.11263e6	0.620673
$411$	7.67373e6	2.24080
$412$	747376.	0.216918
$413$	2.68905e6	0.775753
$414$	−7.13362e6	−2.04554
$415$	1.04141e6	0.296825
$416$	−6.92013e6	−1.96056
$417$	1.51106e6	0.425542
$418$	−7.42574e6	−2.07873
$419$	−5.64925e6	−1.57201	−0.786006	−	0.618219i	$-0.787854\pi$
$419$	−5.64925e6	−1.57201	−0.786006	+	0.618219i	$0.787854\pi$
$420$	2.45963e6	0.680371
$421$	−3.69284e6	−1.01544	−0.507721	−	0.861522i	$-0.669512\pi$
$421$	−3.69284e6	−1.01544	−0.507721	+	0.861522i	$0.669512\pi$
$422$	−4.08178e6	−1.11575
$423$	−2.42861e6	−0.659942
$424$	−3.68007e6	−0.994127
$425$	2.27372e6	0.610611
$426$	−3.27468e6	−0.874270
$427$	−666563.	−0.176918
$428$	−1.06959e7	−2.82233
$429$	7.05749e6	1.85143
$430$	3.53907e6	0.923035
$431$	−2.80600e6	−0.727604	−0.363802	−	0.931476i	$-0.618522\pi$
$431$	−2.80600e6	−0.727604	−0.363802	+	0.931476i	$0.618522\pi$
$432$	228233.	0.0588395
$433$	1.55047e6	0.397413	0.198707	−	0.980059i	$-0.436326\pi$
$433$	1.55047e6	0.397413	0.198707	+	0.980059i	$0.436326\pi$
$434$	−3.43833e6	−0.876241
$435$	0	0
$436$	−2.80576e6	−0.706862
$437$	−7.61620e6	−1.90781
$438$	−4.75639e6	−1.18466
$439$	−6.27273e6	−1.55344	−0.776721	−	0.629845i	$-0.783119\pi$
$439$	−6.27273e6	−1.55344	−0.776721	+	0.629845i	$0.783119\pi$
$440$	−1.24747e6	−0.307183
$441$	−3.22785e6	−0.790344
$442$	−9.19525e6	−2.23876
$443$	3.83052e6	0.927359	0.463679	−	0.886003i	$-0.346529\pi$
$443$	3.83052e6	0.927359	0.463679	+	0.886003i	$0.346529\pi$
$444$	−546225.	−0.131496
$445$	−1.28643e6	−0.307953
$446$	−8.46498e6	−2.01506
$447$	−2.13865e6	−0.506258
$448$	4.11403e6	0.968439
$449$	4.76764e6	1.11606	0.558030	−	0.829821i	$-0.311557\pi$
$449$	4.76764e6	1.11606	0.558030	+	0.829821i	$0.311557\pi$
$450$	−6.25699e6	−1.45658
$451$	−2.42126e6	−0.560532
$452$	787955.	0.181408
$453$	1.35366e6	0.309930
$454$	−3.11449e6	−0.709164
$455$	−2.26589e6	−0.513111
$456$	−1.02219e7	−2.30207
$457$	5.30388e6	1.18796	0.593982	−	0.804478i	$-0.297555\pi$
$457$	5.30388e6	1.18796	0.593982	+	0.804478i	$0.297555\pi$
$458$	−1.01748e7	−2.26653
$459$	1.21163e6	0.268435
$460$	−3.67068e6	−0.808821
$461$	4.04038e6	0.885461	0.442731	−	0.896655i	$-0.354010\pi$
$461$	4.04038e6	0.885461	0.442731	+	0.896655i	$0.354010\pi$
$462$	−4.65533e6	−1.01472
$463$	4.21068e6	0.912851	0.456425	−	0.889762i	$-0.349130\pi$
$463$	4.21068e6	0.912851	0.456425	+	0.889762i	$0.349130\pi$
$464$	0	0
$465$	−3.22446e6	−0.691551
$466$	−989286.	−0.211036
$467$	254531.	0.0540069	0.0270034	−	0.999635i	$-0.491403\pi$
$467$	254531.	0.0540069	0.0270034	+	0.999635i	$0.491403\pi$
$468$	1.53225e7	3.23382
$469$	1.86491e6	0.391494
$470$	−2.06375e6	−0.430935
$471$	2.95767e6	0.614324
$472$	−5.38603e6	−1.11279
$473$	−4.05610e6	−0.833596
$474$	2.04427e7	4.17919
$475$	−6.68027e6	−1.35850
$476$	3.67283e6	0.742992
$477$	−7.08037e6	−1.42482
$478$	−9.90813e6	−1.98345
$479$	3.26357e6	0.649911	0.324956	−	0.945729i	$-0.394651\pi$
$479$	3.26357e6	0.649911	0.324956	+	0.945729i	$0.394651\pi$
$480$	4.28078e6	0.848048
$481$	503201.	0.0991697
$482$	8.34018e6	1.63515
$483$	−4.77473e6	−0.931282
$484$	−3.80943e6	−0.739174
$485$	3.05537e6	0.589807
$486$	1.17520e7	2.25694
$487$	−9.31574e6	−1.77990	−0.889949	−	0.456061i	$-0.849260\pi$
$487$	−9.31574e6	−1.77990	−0.889949	+	0.456061i	$0.849260\pi$
$488$	1.33509e6	0.253783
$489$	6.30247e6	1.19190
$490$	−2.74291e6	−0.516086
$491$	−1.00843e6	−0.188774	−0.0943872	−	0.995536i	$-0.530089\pi$
$491$	−1.00843e6	−0.188774	−0.0943872	+	0.995536i	$0.530089\pi$
$492$	−9.56208e6	−1.78090
$493$	0	0
$494$	2.70160e7	4.98085
$495$	−2.40010e6	−0.440266
$496$	−906975.	−0.165536
$497$	−1.20497e6	−0.218820
$498$	−7.78416e6	−1.40650
$499$	−1.78365e6	−0.320670	−0.160335	−	0.987063i	$-0.551258\pi$
$499$	−1.78365e6	−0.320670	−0.160335	+	0.987063i	$0.551258\pi$
$500$	−7.51679e6	−1.34464
$501$	8.55624e6	1.52296
$502$	388688.	0.0688402
$503$	−4.16202e6	−0.733473	−0.366736	−	0.930325i	$-0.619525\pi$
$503$	−4.16202e6	−0.733473	−0.366736	+	0.930325i	$0.619525\pi$
$504$	−3.52298e6	−0.617781
$505$	−1.17229e6	−0.204554
$506$	6.94749e6	1.20629
$507$	−1.70505e7	−2.94590
$508$	3.29476e6	0.566453
$509$	−2.16616e6	−0.370591	−0.185296	−	0.982683i	$-0.559324\pi$
$509$	−2.16616e6	−0.370591	−0.185296	+	0.982683i	$0.559324\pi$
$510$	5.68817e6	0.968383
$511$	−1.75019e6	−0.296506
$512$	2.10681e6	0.355182
$513$	−3.55983e6	−0.597222
$514$	1.64342e6	0.274373
$515$	425911.	0.0707621
$516$	−1.60184e7	−2.64847
$517$	2.36524e6	0.389179
$518$	−331926.	−0.0543522
$519$	6.93315e6	1.12983
$520$	4.53847e6	0.736040
$521$	6.23753e6	1.00674	0.503371	−	0.864070i	$-0.332093\pi$
$521$	6.23753e6	1.00674	0.503371	+	0.864070i	$0.332093\pi$
$522$	0	0
$523$	−3.64004e6	−0.581905	−0.290953	−	0.956737i	$-0.593972\pi$
$523$	−3.64004e6	−0.581905	−0.290953	+	0.956737i	$0.593972\pi$
$524$	−1.53116e7	−2.43609
$525$	−4.18798e6	−0.663142
$526$	−1.65253e7	−2.60426
$527$	−4.81492e6	−0.755200
$528$	−1.22800e6	−0.191696
$529$	689341.	0.107101
$530$	−6.01666e6	−0.930392
$531$	−1.03626e7	−1.59490
$532$	−1.07909e7	−1.65303
$533$	8.80892e6	1.34309
$534$	9.61560e6	1.45923
$535$	−6.09533e6	−0.920689
$536$	−3.73532e6	−0.561585
$537$	8.06198e6	1.20644
$538$	1.18735e7	1.76858
$539$	3.14363e6	0.466079
$540$	−1.71569e6	−0.253194
$541$	2.07032e6	0.304119	0.152059	−	0.988371i	$-0.451409\pi$
$541$	2.07032e6	0.304119	0.152059	+	0.988371i	$0.451409\pi$
$542$	3.08404e6	0.450943
$543$	−1.76484e7	−2.56865
$544$	6.39227e6	0.926100
$545$	−1.59893e6	−0.230589
$546$	1.69368e7	2.43136
$547$	−173883.	−0.0248478	−0.0124239	−	0.999923i	$-0.503955\pi$
$547$	−173883.	−0.0248478	−0.0124239	+	0.999923i	$0.503955\pi$
$548$	−1.62258e7	−2.30809
$549$	2.56869e6	0.363731
$550$	6.09374e6	0.858969
$551$	0	0
$552$	9.56355e6	1.33589
$553$	7.52223e6	1.04600
$554$	−4.80010e6	−0.664471
$555$	−311280.	−0.0428962
$556$	−3.19507e6	−0.438322
$557$	3.92925e6	0.536626	0.268313	−	0.963332i	$-0.413534\pi$
$557$	3.92925e6	0.536626	0.268313	+	0.963332i	$0.413534\pi$
$558$	1.32501e7	1.80149
$559$	1.47567e7	1.99738
$560$	394265.	0.0531273
$561$	−6.51916e6	−0.874549
$562$	−1.85256e6	−0.247418
$563$	3.08751e6	0.410523	0.205261	−	0.978707i	$-0.434196\pi$
$563$	3.08751e6	0.410523	0.205261	+	0.978707i	$0.434196\pi$
$564$	9.34084e6	1.23648
$565$	449036.	0.0591779
$566$	−8.50834e6	−1.11636
$567$	3.31952e6	0.433628
$568$	2.41350e6	0.313890
$569$	2.66043e6	0.344485	0.172243	−	0.985055i	$-0.444899\pi$
$569$	2.66043e6	0.344485	0.172243	+	0.985055i	$0.444899\pi$
$570$	−1.67121e7	−2.15448
$571$	−8.70625e6	−1.11748	−0.558742	−	0.829342i	$-0.688716\pi$
$571$	−8.70625e6	−1.11748	−0.558742	+	0.829342i	$0.688716\pi$
$572$	−1.49227e7	−1.90703
$573$	1.32241e7	1.68259
$574$	−5.81063e6	−0.736111
$575$	6.25004e6	0.788339
$576$	−1.58539e7	−1.99105
$577$	6.32070e6	0.790361	0.395181	−	0.918603i	$-0.370682\pi$
$577$	6.32070e6	0.790361	0.395181	+	0.918603i	$0.370682\pi$
$578$	−4.29449e6	−0.534678
$579$	−1.87480e7	−2.32412
$580$	0	0
$581$	−2.86431e6	−0.352030
$582$	−2.28379e7	−2.79479
$583$	6.89564e6	0.840240
$584$	3.50555e6	0.425328
$585$	8.73192e6	1.05492
$586$	−1.03626e7	−1.24659
$587$	−5.13454e6	−0.615045	−0.307522	−	0.951541i	$-0.599500\pi$
$587$	−5.13454e6	−0.615045	−0.307522	+	0.951541i	$0.599500\pi$
$588$	1.24149e7	1.48081
$589$	1.41464e7	1.68019
$590$	−8.80579e6	−1.04145
$591$	−526562.	−0.0620128
$592$	−87556.7	−0.0102680
$593$	1.02117e7	1.19250	0.596252	−	0.802798i	$-0.296656\pi$
$593$	1.02117e7	1.19250	0.596252	+	0.802798i	$0.296656\pi$
$594$	3.24727e6	0.377618
$595$	2.09306e6	0.242375
$596$	4.52208e6	0.521462
$597$	−1.85451e7	−2.12958
$598$	−2.52760e7	−2.89039
$599$	6.14748e6	0.700052	0.350026	−	0.936740i	$-0.386173\pi$
$599$	6.14748e6	0.700052	0.350026	+	0.936740i	$0.386173\pi$
$600$	8.38832e6	0.951255
$601$	−6.08413e6	−0.687088	−0.343544	−	0.939137i	$-0.611627\pi$
$601$	−6.08413e6	−0.687088	−0.343544	+	0.939137i	$0.611627\pi$
$602$	−9.73396e6	−1.09471
$603$	−7.18667e6	−0.804886
$604$	−2.86225e6	−0.319238
$605$	−2.17090e6	−0.241130
$606$	8.76249e6	0.969273
$607$	2.82564e6	0.311275	0.155638	−	0.987814i	$-0.450257\pi$
$607$	2.82564e6	0.311275	0.155638	+	0.987814i	$0.450257\pi$
$608$	−1.87807e7	−2.06041
$609$	0	0
$610$	2.18278e6	0.237512
$611$	−8.60511e6	−0.932510
$612$	−1.41537e7	−1.52754
$613$	−61906.2	−0.00665400	−0.00332700	−	0.999994i	$-0.501059\pi$
$613$	−61906.2	−0.00665400	−0.00332700	+	0.999994i	$0.501059\pi$
$614$	1.08864e7	1.16537
$615$	−5.44919e6	−0.580957
$616$	3.43107e6	0.364315
$617$	−6.82587e6	−0.721847	−0.360923	−	0.932595i	$-0.617538\pi$
$617$	−6.82587e6	−0.721847	−0.360923	+	0.932595i	$0.617538\pi$
$618$	−3.18354e6	−0.335305
$619$	−8.07233e6	−0.846784	−0.423392	−	0.905947i	$-0.639161\pi$
$619$	−8.07233e6	−0.846784	−0.423392	+	0.905947i	$0.639161\pi$
$620$	6.81797e6	0.712321
$621$	3.33056e6	0.346568
$622$	8.58533e6	0.889777
$623$	3.53822e6	0.365229
$624$	4.46765e6	0.459322
$625$	3.03314e6	0.310593
$626$	4.83061e6	0.492681
$627$	1.91535e7	1.94572
$628$	−6.25386e6	−0.632774
$629$	−464818.	−0.0468442
$630$	−5.75983e6	−0.578174
$631$	386644.	0.0386578	0.0193289	−	0.999813i	$-0.493847\pi$
$631$	386644.	0.0386578	0.0193289	+	0.999813i	$0.493847\pi$
$632$	−1.50666e7	−1.50046
$633$	1.05283e7	1.04436
$634$	9.17243e6	0.906278
$635$	1.87760e6	0.184786
$636$	2.72324e7	2.66958
$637$	−1.14370e7	−1.11677
$638$	0	0
$639$	4.64353e6	0.449879
$640$	−7.57564e6	−0.731088
$641$	−1.43379e7	−1.37829	−0.689143	−	0.724625i	$-0.742013\pi$
$641$	−1.43379e7	−1.37829	−0.689143	+	0.724625i	$0.742013\pi$
$642$	4.55606e7	4.36266
$643$	1.39602e7	1.33157	0.665784	−	0.746145i	$-0.268097\pi$
$643$	1.39602e7	1.33157	0.665784	+	0.746145i	$0.268097\pi$
$644$	1.00959e7	0.959252
$645$	−9.12848e6	−0.863971
$646$	−2.49553e7	−2.35278
$647$	−1.53344e7	−1.44015	−0.720073	−	0.693899i	$-0.755892\pi$
$647$	−1.53344e7	−1.44015	−0.720073	+	0.693899i	$0.755892\pi$
$648$	−6.64883e6	−0.622025
$649$	1.00922e7	0.940536
$650$	−2.21700e7	−2.05817
$651$	8.86864e6	0.820171
$652$	−1.33263e7	−1.22769
$653$	−757046.	−0.0694768	−0.0347384	−	0.999396i	$-0.511060\pi$
$653$	−757046.	−0.0694768	−0.0347384	+	0.999396i	$0.511060\pi$
$654$	1.19515e7	1.09264
$655$	−8.72571e6	−0.794689
$656$	−1.53275e6	−0.139063
$657$	6.74460e6	0.609597
$658$	5.67619e6	0.511084
$659$	7.53160e6	0.675575	0.337787	−	0.941222i	$-0.390322\pi$
$659$	7.53160e6	0.675575	0.337787	+	0.941222i	$0.390322\pi$
$660$	9.23119e6	0.824893
$661$	−889957.	−0.0792256	−0.0396128	−	0.999215i	$-0.512612\pi$
$661$	−889957.	−0.0792256	−0.0396128	+	0.999215i	$0.512612\pi$
$662$	−2.30720e7	−2.04616
$663$	2.37177e7	2.09550
$664$	5.73708e6	0.504976
$665$	−6.14948e6	−0.539243
$666$	1.27912e6	0.111745
$667$	0	0
$668$	−1.80918e7	−1.56870
$669$	2.18341e7	1.88612
$670$	−6.10699e6	−0.525581
$671$	−2.50167e6	−0.214498
$672$	−1.17740e7	−1.00577
$673$	−1.01610e7	−0.864768	−0.432384	−	0.901690i	$-0.642328\pi$
$673$	−1.01610e7	−0.864768	−0.432384	+	0.901690i	$0.642328\pi$
$674$	3.07300e7	2.60563
$675$	2.92128e6	0.246782
$676$	3.60525e7	3.03437
$677$	558642.	0.0468448	0.0234224	−	0.999726i	$-0.492544\pi$
$677$	558642.	0.0468448	0.0234224	+	0.999726i	$0.492544\pi$
$678$	−3.35639e6	−0.280413
$679$	−8.40358e6	−0.699504
$680$	−4.19229e6	−0.347679
$681$	8.03333e6	0.663786
$682$	−1.29043e7	−1.06237
$683$	1.43138e6	0.117410	0.0587048	−	0.998275i	$-0.481303\pi$
$683$	1.43138e6	0.117410	0.0587048	+	0.998275i	$0.481303\pi$
$684$	4.15842e7	3.39851
$685$	−9.24665e6	−0.752936
$686$	1.91993e7	1.55767
$687$	2.62443e7	2.12150
$688$	−2.56766e6	−0.206807
$689$	−2.50874e7	−2.01330
$690$	1.56357e7	1.25025
$691$	7.07881e6	0.563982	0.281991	−	0.959417i	$-0.409005\pi$
$691$	7.07881e6	0.563982	0.281991	+	0.959417i	$0.409005\pi$
$692$	−1.46598e7	−1.16376
$693$	6.60129e6	0.522151
$694$	1.94767e7	1.53503
$695$	−1.82079e6	−0.142988
$696$	0	0
$697$	−8.13699e6	−0.634428
$698$	−1.06712e7	−0.829041
$699$	2.55171e6	0.197532
$700$	8.85530e6	0.683059
$701$	−1.86456e7	−1.43312	−0.716558	−	0.697527i	$-0.754284\pi$
$701$	−1.86456e7	−1.43312	−0.716558	+	0.697527i	$0.754284\pi$
$702$	−1.18141e7	−0.904809
$703$	1.36565e6	0.104220
$704$	1.54403e7	1.17415
$705$	5.32311e6	0.403360
$706$	4.12448e7	3.11428
$707$	3.22430e6	0.242598
$708$	3.98564e7	2.98823
$709$	5.87479e6	0.438911	0.219456	−	0.975623i	$-0.429572\pi$
$709$	5.87479e6	0.438911	0.219456	+	0.975623i	$0.429572\pi$
$710$	3.94591e6	0.293766
$711$	−2.89879e7	−2.15051
$712$	−7.08688e6	−0.523908
$713$	−1.32353e7	−0.975014
$714$	−1.56449e7	−1.14849
$715$	−8.50409e6	−0.622104
$716$	−1.70467e7	−1.24267
$717$	2.55565e7	1.85653
$718$	2.52654e6	0.182901
$719$	−2.75211e6	−0.198538	−0.0992689	−	0.995061i	$-0.531650\pi$
$719$	−2.75211e6	−0.198538	−0.0992689	+	0.995061i	$0.531650\pi$
$720$	−1.51935e6	−0.109226
$721$	−1.17144e6	−0.0839230
$722$	5.10178e7	3.64232
$723$	−2.15122e7	−1.53052
$724$	3.73167e7	2.64580
$725$	0	0
$726$	1.62268e7	1.14259
$727$	1.43880e7	1.00964	0.504818	−	0.863226i	$-0.331560\pi$
$727$	1.43880e7	1.00964	0.504818	+	0.863226i	$0.331560\pi$
$728$	−1.24827e7	−0.872934
$729$	−1.98357e7	−1.38238
$730$	5.73133e6	0.398060
$731$	−1.36311e7	−0.943490
$732$	−9.87961e6	−0.681494
$733$	−2.31183e6	−0.158926	−0.0794630	−	0.996838i	$-0.525321\pi$
$733$	−2.31183e6	−0.158926	−0.0794630	+	0.996838i	$0.525321\pi$
$734$	−4.79727e6	−0.328666
$735$	7.07492e6	0.483062
$736$	1.75712e7	1.19566
$737$	6.99916e6	0.474654
$738$	2.23920e7	1.51339
$739$	958886.	0.0645886	0.0322943	−	0.999478i	$-0.489719\pi$
$739$	958886.	0.0645886	0.0322943	+	0.999478i	$0.489719\pi$
$740$	658187.	0.0441845
$741$	−6.96835e7	−4.66213
$742$	1.65484e7	1.10343
$743$	1.04718e7	0.695901	0.347951	−	0.937513i	$-0.386878\pi$
$743$	1.04718e7	0.695901	0.347951	+	0.937513i	$0.386878\pi$
$744$	−1.77634e7	−1.17651
$745$	2.57702e6	0.170109
$746$	2.93328e7	1.92977
$747$	1.10380e7	0.723750
$748$	1.37845e7	0.900815
$749$	1.67648e7	1.09193
$750$	3.20187e7	2.07850
$751$	−8.70229e6	−0.563033	−0.281516	−	0.959556i	$-0.590837\pi$
$751$	−8.70229e6	−0.563033	−0.281516	+	0.959556i	$0.590837\pi$
$752$	1.49728e6	0.0965517
$753$	−1.00256e6	−0.0644352
$754$	0	0
$755$	−1.63112e6	−0.104141
$756$	4.71887e6	0.300285
$757$	−7.15506e6	−0.453810	−0.226905	−	0.973917i	$-0.572861\pi$
$757$	−7.15506e6	−0.453810	−0.226905	+	0.973917i	$0.572861\pi$
$758$	3.12807e6	0.197744
$759$	−1.79200e7	−1.12910
$760$	1.23171e7	0.773525
$761$	−1.78394e7	−1.11665	−0.558326	−	0.829622i	$-0.688556\pi$
$761$	−1.78394e7	−1.11665	−0.558326	+	0.829622i	$0.688556\pi$
$762$	−1.40344e7	−0.875603
$763$	4.39775e6	0.273476
$764$	−2.79617e7	−1.73312
$765$	−8.06586e6	−0.498307
$766$	−1.79348e7	−1.10440
$767$	−3.67171e7	−2.25362
$768$	1.69027e7	1.03407
$769$	−2.97524e7	−1.81429	−0.907144	−	0.420820i	$-0.861742\pi$
$769$	−2.97524e7	−1.81429	−0.907144	+	0.420820i	$0.861742\pi$
$770$	5.60955e6	0.340958
$771$	−4.23895e6	−0.256816
$772$	3.96419e7	2.39393
$773$	−2.01404e7	−1.21233	−0.606163	−	0.795340i	$-0.707292\pi$
$773$	−2.01404e7	−1.21233	−0.606163	+	0.795340i	$0.707292\pi$
$774$	3.75111e7	2.25065
$775$	−1.16089e7	−0.694283
$776$	1.68320e7	1.00341
$777$	856152.	0.0508743
$778$	2.30422e7	1.36482
$779$	2.39068e7	1.41149
$780$	−3.35845e7	−1.97652
$781$	−4.52237e6	−0.265301
$782$	2.33480e7	1.36532
$783$	0	0
$784$	1.99003e6	0.115630
$785$	−3.56392e6	−0.206421
$786$	6.52217e7	3.76562
$787$	1.62145e7	0.933181	0.466591	−	0.884473i	$-0.345482\pi$
$787$	1.62145e7	0.933181	0.466591	+	0.884473i	$0.345482\pi$
$788$	1.11339e6	0.0638752
$789$	4.26244e7	2.43762
$790$	−2.46329e7	−1.40426
$791$	−1.23504e6	−0.0701843
$792$	−1.32221e7	−0.749007
$793$	9.10145e6	0.513958
$794$	5.03946e7	2.83683
$795$	1.55190e7	0.870857
$796$	3.92128e7	2.19354
$797$	−3.87832e6	−0.216271	−0.108135	−	0.994136i	$-0.534488\pi$
$797$	−3.87832e6	−0.216271	−0.108135	+	0.994136i	$0.534488\pi$
$798$	4.59653e7	2.55519
$799$	7.94873e6	0.440485
$800$	1.54119e7	0.851397
$801$	−1.36350e7	−0.750885
$802$	−1.07344e7	−0.589309
$803$	−6.56863e6	−0.359489
$804$	2.76412e7	1.50805
$805$	5.75343e6	0.312923
$806$	4.69480e7	2.54554
$807$	−3.06259e7	−1.65541
$808$	−6.45812e6	−0.347999
$809$	−2.48931e7	−1.33724	−0.668618	−	0.743606i	$-0.733114\pi$
$809$	−2.48931e7	−1.33724	−0.668618	+	0.743606i	$0.733114\pi$
$810$	−1.08704e7	−0.582146
$811$	9.94138e6	0.530756	0.265378	−	0.964144i	$-0.414503\pi$
$811$	9.94138e6	0.530756	0.265378	+	0.964144i	$0.414503\pi$
$812$	0	0
$813$	−7.95480e6	−0.422088
$814$	−1.24575e6	−0.0658975
$815$	−7.59432e6	−0.400493
$816$	−4.12687e6	−0.216968
$817$	4.00487e7	2.09910
$818$	3.35897e7	1.75518
$819$	−2.40165e7	−1.25112
$820$	1.15221e7	0.598405
$821$	−3.54528e7	−1.83566	−0.917831	−	0.396971i	$-0.870061\pi$
$821$	−3.54528e7	−1.83566	−0.917831	+	0.396971i	$0.870061\pi$
$822$	6.91156e7	3.56777
$823$	3.38020e6	0.173957	0.0869787	−	0.996210i	$-0.472279\pi$
$823$	3.38020e6	0.173957	0.0869787	+	0.996210i	$0.472279\pi$
$824$	2.34633e6	0.120385
$825$	−1.57179e7	−0.804004
$826$	2.42197e7	1.23515
$827$	−46031.2	−0.00234039	−0.00117020	−	0.999999i	$-0.500372\pi$
$827$	−46031.2	−0.00234039	−0.00117020	+	0.999999i	$0.500372\pi$
$828$	−3.89060e7	−1.97216
$829$	−2.16589e7	−1.09458	−0.547292	−	0.836942i	$-0.684341\pi$
$829$	−2.16589e7	−1.09458	−0.547292	+	0.836942i	$0.684341\pi$
$830$	9.37972e6	0.472601
$831$	1.23811e7	0.621952
$832$	−5.61742e7	−2.81338
$833$	1.05646e7	0.527522
$834$	1.36098e7	0.677543
$835$	−1.03100e7	−0.511734
$836$	−4.04993e7	−2.00416
$837$	−6.18622e6	−0.305219
$838$	−5.08816e7	−2.50294
$839$	−1.83601e7	−0.900472	−0.450236	−	0.892910i	$-0.648660\pi$
$839$	−1.83601e7	−0.900472	−0.450236	+	0.892910i	$0.648660\pi$
$840$	7.72181e6	0.377591
$841$	0	0
$842$	−3.32606e7	−1.61678
$843$	4.77839e6	0.231586
$844$	−2.22616e7	−1.07572
$845$	2.05454e7	0.989859
$846$	−2.18739e7	−1.05075
$847$	5.97090e6	0.285977
$848$	4.36519e6	0.208456
$849$	2.19459e7	1.04492
$850$	2.04789e7	0.972208
$851$	−1.27770e6	−0.0604790
$852$	−1.78598e7	−0.842903
$853$	6.13295e6	0.288601	0.144300	−	0.989534i	$-0.453907\pi$
$853$	6.13295e6	0.288601	0.144300	+	0.989534i	$0.453907\pi$
$854$	−6.00359e6	−0.281686
$855$	2.36978e7	1.10865
$856$	−3.35790e7	−1.56633
$857$	−1.75647e7	−0.816937	−0.408468	−	0.912772i	$-0.633937\pi$
$857$	−1.75647e7	−0.816937	−0.408468	+	0.912772i	$0.633937\pi$
$858$	6.35653e7	2.94782
$859$	−2.99398e7	−1.38441	−0.692206	−	0.721700i	$-0.743361\pi$
$859$	−2.99398e7	−1.38441	−0.692206	+	0.721700i	$0.743361\pi$
$860$	1.93018e7	0.889920
$861$	1.49876e7	0.689008
$862$	−2.52731e7	−1.15848
$863$	−4.43920e6	−0.202898	−0.101449	−	0.994841i	$-0.532348\pi$
$863$	−4.43920e6	−0.202898	−0.101449	+	0.994841i	$0.532348\pi$
$864$	8.21281e6	0.374289
$865$	−8.35427e6	−0.379637
$866$	1.39647e7	0.632757
$867$	1.10770e7	0.500464
$868$	−1.87523e7	−0.844804
$869$	2.82315e7	1.26819
$870$	0	0
$871$	−2.54640e7	−1.13732
$872$	−8.80847e6	−0.392292
$873$	3.23843e7	1.43813
$874$	−6.85974e7	−3.03759
$875$	1.17818e7	0.520226
$876$	−2.59409e7	−1.14215
$877$	−3.02440e7	−1.32782	−0.663912	−	0.747811i	$-0.731105\pi$
$877$	−3.02440e7	−1.32782	−0.663912	+	0.747811i	$0.731105\pi$
$878$	−5.64971e7	−2.47337
$879$	2.67286e7	1.16682
$880$	1.47971e6	0.0644124
$881$	2.39578e7	1.03994	0.519969	−	0.854185i	$-0.325944\pi$
$881$	2.39578e7	1.03994	0.519969	+	0.854185i	$0.325944\pi$
$882$	−2.90725e7	−1.25838
$883$	−2.43343e7	−1.05031	−0.525154	−	0.851007i	$-0.675992\pi$
$883$	−2.43343e7	−1.05031	−0.525154	+	0.851007i	$0.675992\pi$
$884$	−5.01500e7	−2.15844
$885$	2.27132e7	0.974808
$886$	3.45006e7	1.47653
$887$	−924502.	−0.0394547	−0.0197274	−	0.999805i	$-0.506280\pi$
$887$	−924502.	−0.0394547	−0.0197274	+	0.999805i	$0.506280\pi$
$888$	−1.71483e6	−0.0729775
$889$	−5.16420e6	−0.219154
$890$	−1.15866e7	−0.490320
$891$	1.24584e7	0.525738
$892$	−4.61672e7	−1.94277
$893$	−2.33537e7	−0.980001
$894$	−1.92624e7	−0.806058
$895$	−9.71448e6	−0.405380
$896$	2.08363e7	0.867061
$897$	6.51956e7	2.70544
$898$	4.29411e7	1.77698
$899$	0	0
$900$	−3.41250e7	−1.40432
$901$	2.31738e7	0.951010
$902$	−2.18078e7	−0.892473
$903$	2.51072e7	1.02466
$904$	2.47372e6	0.100677
$905$	2.12659e7	0.863101
$906$	1.21921e7	0.493467
$907$	−1.41736e7	−0.572087	−0.286043	−	0.958217i	$-0.592340\pi$
$907$	−1.41736e7	−0.572087	−0.286043	+	0.958217i	$0.592340\pi$
$908$	−1.69861e7	−0.683722
$909$	−1.24253e7	−0.498765
$910$	−2.04084e7	−0.816970
$911$	4.20825e7	1.67998	0.839992	−	0.542599i	$-0.182560\pi$
$911$	4.20825e7	1.67998	0.839992	+	0.542599i	$0.182560\pi$
$912$	1.21249e7	0.482715
$913$	−1.07500e7	−0.426807
$914$	4.77709e7	1.89146
$915$	−5.63015e6	−0.222314
$916$	−5.54924e7	−2.18522
$917$	2.39994e7	0.942491
$918$	1.09129e7	0.427400
$919$	−3.07745e7	−1.20199	−0.600996	−	0.799252i	$-0.705229\pi$
$919$	−3.07745e7	−1.20199	−0.600996	+	0.799252i	$0.705229\pi$
$920$	−1.15238e7	−0.448877
$921$	−2.80798e7	−1.09080
$922$	3.63908e7	1.40982
$923$	1.64531e7	0.635686
$924$	−2.53897e7	−0.978313
$925$	−1.12069e6	−0.0430656
$926$	3.79247e7	1.45343
$927$	4.51429e6	0.172540
$928$	0	0
$929$	1.75146e7	0.665826	0.332913	−	0.942958i	$-0.391968\pi$
$929$	1.75146e7	0.665826	0.332913	+	0.942958i	$0.391968\pi$
$930$	−2.90420e7	−1.10108
$931$	−3.10392e7	−1.17364
$932$	−5.39547e6	−0.203465
$933$	−2.21445e7	−0.832841
$934$	2.29251e6	0.0859891
$935$	7.85542e6	0.293860
$936$	4.81039e7	1.79469
$937$	−9.11422e6	−0.339133	−0.169567	−	0.985519i	$-0.554237\pi$
$937$	−9.11422e6	−0.339133	−0.169567	+	0.985519i	$0.554237\pi$
$938$	1.67968e7	0.623333
$939$	−1.24598e7	−0.461155
$940$	−1.12555e7	−0.415474
$941$	1.40604e7	0.517636	0.258818	−	0.965926i	$-0.416667\pi$
$941$	1.40604e7	0.517636	0.258818	+	0.965926i	$0.416667\pi$
$942$	2.66391e7	0.978120
$943$	−2.23671e7	−0.819088
$944$	6.38875e6	0.233338
$945$	2.68917e6	0.0979576
$946$	−3.65324e7	−1.32724
$947$	2.07069e7	0.750311	0.375155	−	0.926962i	$-0.377589\pi$
$947$	2.07069e7	0.750311	0.375155	+	0.926962i	$0.377589\pi$
$948$	1.11492e8	4.02925
$949$	2.38977e7	0.861371
$950$	−6.01678e7	−2.16299
$951$	−2.36589e7	−0.848286
$952$	1.15306e7	0.412343
$953$	−2.40479e7	−0.857717	−0.428859	−	0.903372i	$-0.641084\pi$
$953$	−2.40479e7	−0.857717	−0.428859	+	0.903372i	$0.641084\pi$
$954$	−6.37714e7	−2.26858
$955$	−1.59346e7	−0.565372
$956$	−5.40380e7	−1.91229
$957$	0	0
$958$	2.93943e7	1.03478
$959$	2.54323e7	0.892973
$960$	3.47493e7	1.21694
$961$	−4.04572e6	−0.141315
$962$	4.53222e6	0.157897
$963$	−6.46052e7	−2.24492
$964$	4.54865e7	1.57649
$965$	2.25909e7	0.780936
$966$	−4.30050e7	−1.48278
$967$	−2.30205e7	−0.791679	−0.395840	−	0.918320i	$-0.629546\pi$
$967$	−2.30205e7	−0.791679	−0.395840	+	0.918320i	$0.629546\pi$
$968$	−1.19594e7	−0.410225
$969$	6.43682e7	2.20222
$970$	2.75191e7	0.939084
$971$	−2.28444e7	−0.777555	−0.388777	−	0.921332i	$-0.627102\pi$
$971$	−2.28444e7	−0.777555	−0.388777	+	0.921332i	$0.627102\pi$
$972$	6.40942e7	2.17597
$973$	5.00795e6	0.169581
$974$	−8.39048e7	−2.83393
$975$	5.71840e7	1.92647
$976$	−1.58365e6	−0.0532150
$977$	4.25936e7	1.42760	0.713802	−	0.700348i	$-0.246972\pi$
$977$	4.25936e7	1.42760	0.713802	+	0.700348i	$0.246972\pi$
$978$	5.67650e7	1.89773
$979$	1.32792e7	0.442809
$980$	−1.49596e7	−0.497570
$981$	−1.69473e7	−0.562248
$982$	−9.08273e6	−0.300565
$983$	4.68352e7	1.54592	0.772962	−	0.634452i	$-0.218774\pi$
$983$	4.68352e7	1.54592	0.772962	+	0.634452i	$0.218774\pi$
$984$	−3.00194e7	−0.988359
$985$	634494.	0.0208371
$986$	0	0
$987$	−1.46408e7	−0.478380
$988$	1.47343e8	4.80215
$989$	−3.74694e7	−1.21811
$990$	−2.16171e7	−0.700987
$991$	−1.93000e7	−0.624270	−0.312135	−	0.950038i	$-0.601044\pi$
$991$	−1.93000e7	−0.624270	−0.312135	+	0.950038i	$0.601044\pi$
$992$	−3.26369e7	−1.05300
$993$	5.95105e7	1.91523
$994$	−1.08529e7	−0.348403
$995$	2.23464e7	0.715566
$996$	−4.24541e7	−1.35604
$997$	−2.85427e7	−0.909404	−0.454702	−	0.890644i	$-0.650254\pi$
$997$	−2.85427e7	−0.909404	−0.454702	+	0.890644i	$0.650254\pi$
$998$	−1.60650e7	−0.510568
$999$	−597200.	−0.0189324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.6.a.h.1.30		33
29.4	even	14		29.6.d.a.16.10	✓	66
29.22	even	14		29.6.d.a.20.10	yes	66
29.28	even	2		841.6.a.i.1.4		33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.d.a.16.10	✓	66	29.4	even	14
29.6.d.a.20.10	yes	66	29.22	even	14
841.6.a.h.1.30		33	1.1	even	1	trivial
841.6.a.i.1.4		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)

\(f(q)\)	\(=\)	\(q+9.00678 q^{2} -23.2316 q^{3} +49.1221 q^{4} +27.9935 q^{5} -209.242 q^{6} -76.9940 q^{7} +154.215 q^{8} +296.706 q^{9} +O(q^{10})\)	\(q+9.00678 q^{2} -23.2316 q^{3} +49.1221 q^{4} +27.9935 q^{5} -209.242 q^{6} -76.9940 q^{7} +154.215 q^{8} +296.706 q^{9} +252.131 q^{10} -288.965 q^{11} -1141.18 q^{12} +1051.30 q^{13} -693.468 q^{14} -650.332 q^{15} -182.925 q^{16} -971.108 q^{17} +2672.37 q^{18} +2853.15 q^{19} +1375.10 q^{20} +1788.69 q^{21} -2602.64 q^{22} -2669.40 q^{23} -3582.66 q^{24} -2341.37 q^{25} +9468.82 q^{26} -1247.68 q^{27} -3782.11 q^{28} -5857.40 q^{30} +4958.17 q^{31} -6582.45 q^{32} +6713.11 q^{33} -8746.56 q^{34} -2155.33 q^{35} +14574.8 q^{36} +478.647 q^{37} +25697.7 q^{38} -24423.3 q^{39} +4317.02 q^{40} +8379.08 q^{41} +16110.4 q^{42} +14036.6 q^{43} -14194.6 q^{44} +8305.84 q^{45} -24042.7 q^{46} -8185.22 q^{47} +4249.65 q^{48} -10878.9 q^{49} -21088.2 q^{50} +22560.4 q^{51} +51642.0 q^{52} -23863.2 q^{53} -11237.6 q^{54} -8089.13 q^{55} -11873.6 q^{56} -66283.2 q^{57} -34925.4 q^{59} -31945.7 q^{60} +8657.33 q^{61} +44657.1 q^{62} -22844.6 q^{63} -53433.1 q^{64} +29429.5 q^{65} +60463.5 q^{66} -24221.5 q^{67} -47702.9 q^{68} +62014.3 q^{69} -19412.6 q^{70} +15650.2 q^{71} +45756.6 q^{72} +22731.6 q^{73} +4311.07 q^{74} +54393.6 q^{75} +140153. q^{76} +22248.6 q^{77} -219976. q^{78} -97698.9 q^{79} -5120.72 q^{80} -43114.0 q^{81} +75468.6 q^{82} +37201.8 q^{83} +87864.3 q^{84} -27184.7 q^{85} +126425. q^{86} -44562.8 q^{88} -45954.5 q^{89} +74808.9 q^{90} -80943.7 q^{91} -131126. q^{92} -115186. q^{93} -73722.5 q^{94} +79869.6 q^{95} +152921. q^{96} +109146. q^{97} -97984.1 q^{98} -85737.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 12 q^{2} - q^{3} + 422 q^{4} - 157 q^{5} - 166 q^{6} - 331 q^{7} - 453 q^{8} + 1622 q^{9}+O(q^{10}) \) 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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