LMFDB - Embedded newform 1075.6.a.l.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.07352 q^{2} +16.4032 q^{3} -22.5535 q^{4} +50.4156 q^{6} +104.896 q^{7} -167.671 q^{8} +26.0658 q^{9} +O(q^{10})$	\(q+3.07352 q^{2} +16.4032 q^{3} -22.5535 q^{4} +50.4156 q^{6} +104.896 q^{7} -167.671 q^{8} +26.0658 q^{9} -730.458 q^{11} -369.950 q^{12} +707.150 q^{13} +322.400 q^{14} +206.372 q^{16} -389.372 q^{17} +80.1137 q^{18} -973.008 q^{19} +1720.63 q^{21} -2245.07 q^{22} +1737.86 q^{23} -2750.35 q^{24} +2173.44 q^{26} -3558.42 q^{27} -2365.77 q^{28} +7772.69 q^{29} -4600.91 q^{31} +5999.76 q^{32} -11981.9 q^{33} -1196.74 q^{34} -587.875 q^{36} +9491.32 q^{37} -2990.56 q^{38} +11599.5 q^{39} -14128.5 q^{41} +5288.39 q^{42} -1849.00 q^{43} +16474.4 q^{44} +5341.33 q^{46} -6953.99 q^{47} +3385.16 q^{48} -5803.83 q^{49} -6386.95 q^{51} -15948.7 q^{52} +11585.9 q^{53} -10936.9 q^{54} -17588.0 q^{56} -15960.5 q^{57} +23889.5 q^{58} +23922.8 q^{59} +15807.1 q^{61} -14141.0 q^{62} +2734.20 q^{63} +11836.5 q^{64} -36826.4 q^{66} +37993.3 q^{67} +8781.69 q^{68} +28506.4 q^{69} +51039.1 q^{71} -4370.48 q^{72} +52241.9 q^{73} +29171.7 q^{74} +21944.7 q^{76} -76622.1 q^{77} +35651.4 q^{78} +105308. q^{79} -64703.6 q^{81} -43424.3 q^{82} -64430.7 q^{83} -38806.3 q^{84} -5682.93 q^{86} +127497. q^{87} +122477. q^{88} +93255.9 q^{89} +74177.2 q^{91} -39194.7 q^{92} -75469.7 q^{93} -21373.2 q^{94} +98415.5 q^{96} -146015. q^{97} -17838.2 q^{98} -19040.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) $ 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * 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 $

$2$	3.07352	0.543326	0.271663	−	0.962392i	$-0.412426\pi$
$2$	3.07352	0.543326	0.271663	+	0.962392i	$0.412426\pi$
$3$	16.4032	1.05227	0.526134	−	0.850402i	$-0.323641\pi$
$3$	16.4032	1.05227	0.526134	+	0.850402i	$0.323641\pi$
$4$	−22.5535	−0.704797
$5$	0	0
$5$	0	0
$6$	50.4156	0.571724
$7$	104.896	0.809122	0.404561	−	0.914511i	$-0.367424\pi$
$7$	104.896	0.809122	0.404561	+	0.914511i	$0.367424\pi$
$8$	−167.671	−0.926261
$9$	26.0658	0.107267
$10$	0	0
$11$	−730.458	−1.82018	−0.910088	−	0.414416i	$-0.863986\pi$
$11$	−730.458	−1.82018	−0.910088	+	0.414416i	$0.863986\pi$
$12$	−369.950	−0.741635
$13$	707.150	1.16052	0.580261	−	0.814431i	$-0.302951\pi$
$13$	707.150	1.16052	0.580261	+	0.814431i	$0.302951\pi$
$14$	322.400	0.439617
$15$	0	0
$16$	206.372	0.201535
$17$	−389.372	−0.326770	−0.163385	−	0.986562i	$-0.552241\pi$
$17$	−389.372	−0.326770	−0.163385	+	0.986562i	$0.552241\pi$
$18$	80.1137	0.0582808
$19$	−973.008	−0.618347	−0.309174	−	0.951006i	$-0.600052\pi$
$19$	−973.008	−0.618347	−0.309174	+	0.951006i	$0.600052\pi$
$20$	0	0
$21$	1720.63	0.851412
$22$	−2245.07	−0.988949
$23$	1737.86	0.685006	0.342503	−	0.939517i	$-0.388725\pi$
$23$	1737.86	0.685006	0.342503	+	0.939517i	$0.388725\pi$
$24$	−2750.35	−0.974674
$25$	0	0
$26$	2173.44	0.630542
$27$	−3558.42	−0.939394
$28$	−2365.77	−0.570266
$29$	7772.69	1.71623	0.858116	−	0.513456i	$-0.171635\pi$
$29$	7772.69	1.71623	0.858116	+	0.513456i	$0.171635\pi$
$30$	0	0
$31$	−4600.91	−0.859883	−0.429941	−	0.902857i	$-0.641466\pi$
$31$	−4600.91	−0.859883	−0.429941	+	0.902857i	$0.641466\pi$
$32$	5999.76	1.03576
$33$	−11981.9	−1.91531
$34$	−1196.74	−0.177543
$35$	0	0
$36$	−587.875	−0.0756012
$37$	9491.32	1.13978	0.569892	−	0.821720i	$-0.306985\pi$
$37$	9491.32	1.13978	0.569892	+	0.821720i	$0.306985\pi$
$38$	−2990.56	−0.335964
$39$	11599.5	1.22118
$40$	0	0
$41$	−14128.5	−1.31262	−0.656308	−	0.754493i	$-0.727883\pi$
$41$	−14128.5	−1.31262	−0.656308	+	0.754493i	$0.727883\pi$
$42$	5288.39	0.462595
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	16474.4	1.28285
$45$	0	0
$46$	5341.33	0.372182
$47$	−6953.99	−0.459187	−0.229594	−	0.973287i	$-0.573740\pi$
$47$	−6953.99	−0.459187	−0.229594	+	0.973287i	$0.573740\pi$
$48$	3385.16	0.212069
$49$	−5803.83	−0.345322
$50$	0	0
$51$	−6386.95	−0.343849
$52$	−15948.7	−0.817932
$53$	11585.9	0.566551	0.283275	−	0.959039i	$-0.408579\pi$
$53$	11585.9	0.566551	0.283275	+	0.959039i	$0.408579\pi$
$54$	−10936.9	−0.510397
$55$	0	0
$56$	−17588.0	−0.749457
$57$	−15960.5	−0.650667
$58$	23889.5	0.932474
$59$	23922.8	0.894708	0.447354	−	0.894357i	$-0.352366\pi$
$59$	23922.8	0.894708	0.447354	+	0.894357i	$0.352366\pi$
$60$	0	0
$61$	15807.1	0.543909	0.271955	−	0.962310i	$-0.412330\pi$
$61$	15807.1	0.543909	0.271955	+	0.962310i	$0.412330\pi$
$62$	−14141.0	−0.467197
$63$	2734.20	0.0867918
$64$	11836.5	0.361220
$65$	0	0
$66$	−36826.4	−1.04064
$67$	37993.3	1.03400	0.517000	−	0.855985i	$-0.327049\pi$
$67$	37993.3	1.03400	0.517000	+	0.855985i	$0.327049\pi$
$68$	8781.69	0.230306
$69$	28506.4	0.720809
$70$	0	0
$71$	51039.1	1.20159	0.600796	−	0.799403i	$-0.294851\pi$
$71$	51039.1	1.20159	0.600796	+	0.799403i	$0.294851\pi$
$72$	−4370.48	−0.0993569
$73$	52241.9	1.14739	0.573696	−	0.819068i	$-0.305509\pi$
$73$	52241.9	1.14739	0.573696	+	0.819068i	$0.305509\pi$
$74$	29171.7	0.619274
$75$	0	0
$76$	21944.7	0.435809
$77$	−76622.1	−1.47274
$78$	35651.4	0.663499
$79$	105308.	1.89843	0.949214	−	0.314632i	$-0.101881\pi$
$79$	105308.	1.89843	0.949214	+	0.314632i	$0.101881\pi$
$80$	0	0
$81$	−64703.6	−1.09576
$82$	−43424.3	−0.713178
$83$	−64430.7	−1.02659	−0.513296	−	0.858212i	$-0.671576\pi$
$83$	−64430.7	−1.02659	−0.513296	+	0.858212i	$0.671576\pi$
$84$	−38806.3	−0.600072
$85$	0	0
$86$	−5682.93	−0.0828565
$87$	127497.	1.80594
$88$	122477.	1.68596
$89$	93255.9	1.24796	0.623981	−	0.781440i	$-0.285514\pi$
$89$	93255.9	1.24796	0.623981	+	0.781440i	$0.285514\pi$
$90$	0	0
$91$	74177.2	0.939003
$92$	−39194.7	−0.482790
$93$	−75469.7	−0.904826
$94$	−21373.2	−0.249488
$95$	0	0
$96$	98415.5	1.08990
$97$	−146015.	−1.57569	−0.787843	−	0.615877i	$-0.788802\pi$
$97$	−146015.	−1.57569	−0.787843	+	0.615877i	$0.788802\pi$
$98$	−17838.2	−0.187623
$99$	−19040.0	−0.195244
$100$	0	0
$101$	26936.9	0.262751	0.131376	−	0.991333i	$-0.458061\pi$
$101$	26936.9	0.262751	0.131376	+	0.991333i	$0.458061\pi$
$102$	−19630.4	−0.186822
$103$	3331.08	0.0309380	0.0154690	−	0.999880i	$-0.495076\pi$
$103$	3331.08	0.0309380	0.0154690	+	0.999880i	$0.495076\pi$
$104$	−118569.	−1.07495
$105$	0	0
$106$	35609.4	0.307822
$107$	41468.1	0.350151	0.175075	−	0.984555i	$-0.443983\pi$
$107$	41468.1	0.350151	0.175075	+	0.984555i	$0.443983\pi$
$108$	80254.8	0.662082
$109$	106715.	0.860319	0.430160	−	0.902753i	$-0.358457\pi$
$109$	106715.	0.860319	0.430160	+	0.902753i	$0.358457\pi$
$110$	0	0
$111$	155688.	1.19936
$112$	21647.6	0.163066
$113$	45554.5	0.335610	0.167805	−	0.985820i	$-0.446332\pi$
$113$	45554.5	0.335610	0.167805	+	0.985820i	$0.446332\pi$
$114$	−49054.8	−0.353524
$115$	0	0
$116$	−175301.	−1.20959
$117$	18432.4	0.124485
$118$	73527.0	0.486118
$119$	−40843.5	−0.264397
$120$	0	0
$121$	372517.	2.31304
$122$	48583.2	0.295520
$123$	−231754.	−1.38122
$124$	103767.	0.606042
$125$	0	0
$126$	8403.60	0.0471562
$127$	−308181.	−1.69549	−0.847746	−	0.530402i	$-0.822041\pi$
$127$	−308181.	−1.69549	−0.847746	+	0.530402i	$0.822041\pi$
$128$	−155613.	−0.839499
$129$	−30329.6	−0.160469
$130$	0	0
$131$	240359.	1.22372	0.611860	−	0.790966i	$-0.290422\pi$
$131$	240359.	1.22372	0.611860	+	0.790966i	$0.290422\pi$
$132$	270233.	1.34991
$133$	−102065.	−0.500318
$134$	116773.	0.561799
$135$	0	0
$136$	65286.4	0.302674
$137$	−36457.0	−0.165951	−0.0829754	−	0.996552i	$-0.526442\pi$
$137$	−36457.0	−0.165951	−0.0829754	+	0.996552i	$0.526442\pi$
$138$	87615.0	0.391634
$139$	−304471.	−1.33662	−0.668312	−	0.743881i	$-0.732983\pi$
$139$	−304471.	−1.33662	−0.668312	+	0.743881i	$0.732983\pi$
$140$	0	0
$141$	−114068.	−0.483188
$142$	156869.	0.652856
$143$	−516543.	−2.11235
$144$	5379.25	0.0216180
$145$	0	0
$146$	160566.	0.623408
$147$	−95201.6	−0.363371
$148$	−214062.	−0.803316
$149$	204382.	0.754184	0.377092	−	0.926176i	$-0.376924\pi$
$149$	204382.	0.754184	0.377092	+	0.926176i	$0.376924\pi$
$150$	0	0
$151$	−167783.	−0.598831	−0.299416	−	0.954123i	$-0.596792\pi$
$151$	−167783.	−0.598831	−0.299416	+	0.954123i	$0.596792\pi$
$152$	163145.	0.572751
$153$	−10149.3	−0.0350515
$154$	−235499.	−0.800180
$155$	0	0
$156$	−261610.	−0.860683
$157$	410567.	1.32934	0.664669	−	0.747138i	$-0.268573\pi$
$157$	410567.	1.32934	0.664669	+	0.747138i	$0.268573\pi$
$158$	323666.	1.03147
$159$	190046.	0.596163
$160$	0	0
$161$	182294.	0.554253
$162$	−198867.	−0.595355
$163$	313804.	0.925102	0.462551	−	0.886593i	$-0.346934\pi$
$163$	313804.	0.925102	0.462551	+	0.886593i	$0.346934\pi$
$164$	318648.	0.925127
$165$	0	0
$166$	−198029.	−0.557774
$167$	−183762.	−0.509876	−0.254938	−	0.966957i	$-0.582055\pi$
$167$	−183762.	−0.509876	−0.254938	+	0.966957i	$0.582055\pi$
$168$	−288500.	−0.788630
$169$	128769.	0.346811
$170$	0	0
$171$	−25362.2	−0.0663280
$172$	41701.4	0.107480
$173$	569563.	1.44686	0.723429	−	0.690398i	$-0.242565\pi$
$173$	569563.	1.44686	0.723429	+	0.690398i	$0.242565\pi$
$174$	391865.	0.981212
$175$	0	0
$176$	−150746.	−0.366829
$177$	392410.	0.941472
$178$	286624.	0.678050
$179$	−142303.	−0.331957	−0.165978	−	0.986129i	$-0.553078\pi$
$179$	−142303.	−0.331957	−0.165978	+	0.986129i	$0.553078\pi$
$180$	0	0
$181$	304014.	0.689760	0.344880	−	0.938647i	$-0.387920\pi$
$181$	304014.	0.689760	0.344880	+	0.938647i	$0.387920\pi$
$182$	227985.	0.510185
$183$	259287.	0.572338
$184$	−291388.	−0.634494
$185$	0	0
$186$	−231957.	−0.491616
$187$	284419.	0.594779
$188$	156837.	0.323633
$189$	−373264.	−0.760084
$190$	0	0
$191$	517778.	1.02698	0.513488	−	0.858097i	$-0.328353\pi$
$191$	517778.	1.02698	0.513488	+	0.858097i	$0.328353\pi$
$192$	194156.	0.380100
$193$	671117.	1.29690	0.648448	−	0.761259i	$-0.275418\pi$
$193$	671117.	1.29690	0.648448	+	0.761259i	$0.275418\pi$
$194$	−448781.	−0.856111
$195$	0	0
$196$	130897.	0.243382
$197$	230995.	0.424070	0.212035	−	0.977262i	$-0.431991\pi$
$197$	230995.	0.424070	0.212035	+	0.977262i	$0.431991\pi$
$198$	−58519.6	−0.106081
$199$	−585466.	−1.04802	−0.524009	−	0.851712i	$-0.675564\pi$
$199$	−585466.	−1.04802	−0.524009	+	0.851712i	$0.675564\pi$
$200$	0	0
$201$	623213.	1.08804
$202$	82791.1	0.142760
$203$	815324.	1.38864
$204$	144048.	0.242344
$205$	0	0
$206$	10238.1	0.0168094
$207$	45298.6	0.0734783
$208$	145936.	0.233886
$209$	710741.	1.12550
$210$	0	0
$211$	419540.	0.648734	0.324367	−	0.945931i	$-0.394849\pi$
$211$	419540.	0.648734	0.324367	+	0.945931i	$0.394849\pi$
$212$	−261302.	−0.399303
$213$	837205.	1.26440
$214$	127453.	0.190246
$215$	0	0
$216$	596644.	0.870124
$217$	−482617.	−0.695750
$218$	327991.	0.467434
$219$	856936.	1.20736
$220$	0	0
$221$	−275344.	−0.379224
$222$	478511.	0.651642
$223$	−363722.	−0.489788	−0.244894	−	0.969550i	$-0.578753\pi$
$223$	−363722.	−0.489788	−0.244894	+	0.969550i	$0.578753\pi$
$224$	629351.	0.838056
$225$	0	0
$226$	140013.	0.182346
$227$	−952704.	−1.22714	−0.613569	−	0.789641i	$-0.710267\pi$
$227$	−952704.	−1.22714	−0.613569	+	0.789641i	$0.710267\pi$
$228$	359964.	0.458588
$229$	−795078.	−1.00189	−0.500946	−	0.865478i	$-0.667015\pi$
$229$	−795078.	−1.00189	−0.500946	+	0.865478i	$0.667015\pi$
$230$	0	0
$231$	−1.25685e6	−1.54972
$232$	−1.30325e6	−1.58968
$233$	1.42244e6	1.71651	0.858253	−	0.513227i	$-0.171550\pi$
$233$	1.42244e6	1.71651	0.858253	+	0.513227i	$0.171550\pi$
$234$	56652.4	0.0676361
$235$	0	0
$236$	−539542.	−0.630587
$237$	1.72739e6	1.99765
$238$	−125533.	−0.143654
$239$	1.16982e6	1.32472	0.662362	−	0.749184i	$-0.269554\pi$
$239$	1.16982e6	1.32472	0.662362	+	0.749184i	$0.269554\pi$
$240$	0	0
$241$	−987663.	−1.09538	−0.547692	−	0.836680i	$-0.684493\pi$
$241$	−987663.	−1.09538	−0.547692	+	0.836680i	$0.684493\pi$
$242$	1.14494e6	1.25673
$243$	−196651.	−0.213639
$244$	−356504.	−0.383345
$245$	0	0
$246$	−712299.	−0.750454
$247$	−688063.	−0.717606
$248$	771439.	0.796475
$249$	−1.05687e6	−1.08025
$250$	0	0
$251$	982108.	0.983954	0.491977	−	0.870608i	$-0.336274\pi$
$251$	982108.	0.983954	0.491977	+	0.870608i	$0.336274\pi$
$252$	−61665.7	−0.0611705
$253$	−1.26943e6	−1.24683
$254$	−947198.	−0.921205
$255$	0	0
$256$	−857046.	−0.817342
$257$	1.48362e6	1.40117	0.700585	−	0.713569i	$-0.252922\pi$
$257$	1.48362e6	1.40117	0.700585	+	0.713569i	$0.252922\pi$
$258$	−93218.4	−0.0871872
$259$	995601.	0.922223
$260$	0	0
$261$	202601.	0.184094
$262$	738747.	0.664879
$263$	321854.	0.286925	0.143463	−	0.989656i	$-0.454176\pi$
$263$	321854.	0.286925	0.143463	+	0.989656i	$0.454176\pi$
$264$	2.00901e6	1.77408
$265$	0	0
$266$	−313697.	−0.271836
$267$	1.52970e6	1.31319
$268$	−856883.	−0.728760
$269$	971971.	0.818979	0.409489	−	0.912315i	$-0.365707\pi$
$269$	971971.	0.818979	0.409489	+	0.912315i	$0.365707\pi$
$270$	0	0
$271$	999609.	0.826812	0.413406	−	0.910547i	$-0.364339\pi$
$271$	999609.	0.826812	0.413406	+	0.910547i	$0.364339\pi$
$272$	−80355.4	−0.0658556
$273$	1.21675e6	0.988083
$274$	−112051.	−0.0901655
$275$	0	0
$276$	−642920.	−0.508024
$277$	−791373.	−0.619700	−0.309850	−	0.950785i	$-0.600279\pi$
$277$	−791373.	−0.619700	−0.309850	+	0.950785i	$0.600279\pi$
$278$	−935798.	−0.726223
$279$	−119926.	−0.0922367
$280$	0	0
$281$	−863216.	−0.652159	−0.326079	−	0.945342i	$-0.605728\pi$
$281$	−863216.	−0.652159	−0.326079	+	0.945342i	$0.605728\pi$
$282$	−350590.	−0.262528
$283$	−1.03451e6	−0.767834	−0.383917	−	0.923368i	$-0.625425\pi$
$283$	−1.03451e6	−0.767834	−0.383917	+	0.923368i	$0.625425\pi$
$284$	−1.15111e6	−0.846878
$285$	0	0
$286$	−1.58760e6	−1.14770
$287$	−1.48203e6	−1.06207
$288$	156389.	0.111102
$289$	−1.26825e6	−0.893221
$290$	0	0
$291$	−2.39512e6	−1.65804
$292$	−1.17824e6	−0.808679
$293$	−651160.	−0.443117	−0.221559	−	0.975147i	$-0.571114\pi$
$293$	−651160.	−0.443117	−0.221559	+	0.975147i	$0.571114\pi$
$294$	−292604.	−0.197429
$295$	0	0
$296$	−1.59142e6	−1.05574
$297$	2.59928e6	1.70986
$298$	628172.	0.409768
$299$	1.22893e6	0.794964
$300$	0	0
$301$	−193953.	−0.123390
$302$	−515682.	−0.325361
$303$	441852.	0.276484
$304$	−200802.	−0.124619
$305$	0	0
$306$	−31194.0	−0.0190444
$307$	149876.	0.0907582	0.0453791	−	0.998970i	$-0.485550\pi$
$307$	149876.	0.0907582	0.0453791	+	0.998970i	$0.485550\pi$
$308$	1.72810e6	1.03798
$309$	54640.4	0.0325550
$310$	0	0
$311$	2.74945e6	1.61192	0.805961	−	0.591968i	$-0.201649\pi$
$311$	2.74945e6	1.61192	0.805961	+	0.591968i	$0.201649\pi$
$312$	−1.94491e6	−1.13113
$313$	2.56481e6	1.47977	0.739884	−	0.672735i	$-0.234880\pi$
$313$	2.56481e6	1.47977	0.739884	+	0.672735i	$0.234880\pi$
$314$	1.26189e6	0.722264
$315$	0	0
$316$	−2.37507e6	−1.33801
$317$	−2.75495e6	−1.53981	−0.769903	−	0.638160i	$-0.779696\pi$
$317$	−2.75495e6	−1.53981	−0.769903	+	0.638160i	$0.779696\pi$
$318$	584108.	0.323911
$319$	−5.67762e6	−3.12384
$320$	0	0
$321$	680211.	0.368452
$322$	560284.	0.301140
$323$	378862.	0.202057
$324$	1.45929e6	0.772288
$325$	0	0
$326$	964482.	0.502632
$327$	1.75047e6	0.905286
$328$	2.36895e6	1.21582
$329$	−729446.	−0.371538
$330$	0	0
$331$	−2.59225e6	−1.30049	−0.650244	−	0.759726i	$-0.725333\pi$
$331$	−2.59225e6	−1.30049	−0.650244	+	0.759726i	$0.725333\pi$
$332$	1.45314e6	0.723538
$333$	247399.	0.122261
$334$	−564796.	−0.277029
$335$	0	0
$336$	355090.	0.171589
$337$	1.25699e6	0.602915	0.301457	−	0.953480i	$-0.402527\pi$
$337$	1.25699e6	0.602915	0.301457	+	0.953480i	$0.402527\pi$
$338$	395773.	0.188432
$339$	747241.	0.353152
$340$	0	0
$341$	3.36077e6	1.56514
$342$	−77951.3	−0.0360378
$343$	−2.37179e6	−1.08853
$344$	310024.	0.141253
$345$	0	0
$346$	1.75056e6	0.786116
$347$	−639524.	−0.285123	−0.142562	−	0.989786i	$-0.545534\pi$
$347$	−639524.	−0.285123	−0.142562	+	0.989786i	$0.545534\pi$
$348$	−2.87551e6	−1.27282
$349$	76960.1	0.0338222	0.0169111	−	0.999857i	$-0.494617\pi$
$349$	76960.1	0.0338222	0.0169111	+	0.999857i	$0.494617\pi$
$350$	0	0
$351$	−2.51634e6	−1.09019
$352$	−4.38257e6	−1.88526
$353$	2.19166e6	0.936128	0.468064	−	0.883694i	$-0.344952\pi$
$353$	2.19166e6	0.936128	0.468064	+	0.883694i	$0.344952\pi$
$354$	1.20608e6	0.511526
$355$	0	0
$356$	−2.10325e6	−0.879559
$357$	−669965.	−0.278216
$358$	−437371.	−0.180361
$359$	−813547.	−0.333155	−0.166577	−	0.986028i	$-0.553272\pi$
$359$	−813547.	−0.333155	−0.166577	+	0.986028i	$0.553272\pi$
$360$	0	0
$361$	−1.52935e6	−0.617647
$362$	934394.	0.374764
$363$	6.11048e6	2.43394
$364$	−1.67296e6	−0.661806
$365$	0	0
$366$	796922.	0.310966
$367$	−1.54223e6	−0.597702	−0.298851	−	0.954300i	$-0.596603\pi$
$367$	−1.54223e6	−0.597702	−0.298851	+	0.954300i	$0.596603\pi$
$368$	358645.	0.138053
$369$	−368272.	−0.140800
$370$	0	0
$371$	1.21531e6	0.458409
$372$	1.70211e6	0.637719
$373$	306173.	0.113945	0.0569725	−	0.998376i	$-0.481855\pi$
$373$	306173.	0.113945	0.0569725	+	0.998376i	$0.481855\pi$
$374$	874168.	0.323159
$375$	0	0
$376$	1.16598e6	0.425327
$377$	5.49646e6	1.99173
$378$	−1.14723e6	−0.412974
$379$	1.12139e6	0.401013	0.200507	−	0.979692i	$-0.435741\pi$
$379$	1.12139e6	0.401013	0.200507	+	0.979692i	$0.435741\pi$
$380$	0	0
$381$	−5.05515e6	−1.78411
$382$	1.59140e6	0.557983
$383$	2.56925e6	0.894972	0.447486	−	0.894291i	$-0.352319\pi$
$383$	2.56925e6	0.894972	0.447486	+	0.894291i	$0.352319\pi$
$384$	−2.55255e6	−0.883378
$385$	0	0
$386$	2.06269e6	0.704638
$387$	−48195.7	−0.0163580
$388$	3.29316e6	1.11054
$389$	106746.	0.0357664	0.0178832	−	0.999840i	$-0.494307\pi$
$389$	106746.	0.0357664	0.0178832	+	0.999840i	$0.494307\pi$
$390$	0	0
$391$	−676672.	−0.223839
$392$	973135.	0.319858
$393$	3.94266e6	1.28768
$394$	709969.	0.230409
$395$	0	0
$396$	429418.	0.137607
$397$	4.82154e6	1.53536	0.767678	−	0.640835i	$-0.221412\pi$
$397$	4.82154e6	1.53536	0.767678	+	0.640835i	$0.221412\pi$
$398$	−1.79944e6	−0.569416
$399$	−1.67419e6	−0.526468
$400$	0	0
$401$	4.90778e6	1.52414	0.762068	−	0.647497i	$-0.224184\pi$
$401$	4.90778e6	1.52414	0.762068	+	0.647497i	$0.224184\pi$
$402$	1.91546e6	0.591163
$403$	−3.25353e6	−0.997913
$404$	−607522.	−0.185186
$405$	0	0
$406$	2.50591e6	0.754485
$407$	−6.93301e6	−2.07461
$408$	1.07091e6	0.318494
$409$	5.81418e6	1.71862	0.859311	−	0.511454i	$-0.170893\pi$
$409$	5.81418e6	1.71862	0.859311	+	0.511454i	$0.170893\pi$
$410$	0	0
$411$	−598012.	−0.174625
$412$	−75127.4	−0.0218050
$413$	2.50940e6	0.723927
$414$	139226.	0.0399227
$415$	0	0
$416$	4.24273e6	1.20202
$417$	−4.99431e6	−1.40649
$418$	2.18448e6	0.611514
$419$	−1.75973e6	−0.489678	−0.244839	−	0.969564i	$-0.578735\pi$
$419$	−1.75973e6	−0.489678	−0.244839	+	0.969564i	$0.578735\pi$
$420$	0	0
$421$	1.61239e6	0.443369	0.221684	−	0.975118i	$-0.428844\pi$
$421$	1.61239e6	0.443369	0.221684	+	0.975118i	$0.428844\pi$
$422$	1.28946e6	0.352474
$423$	−181261.	−0.0492555
$424$	−1.94262e6	−0.524774
$425$	0	0
$426$	2.57316e6	0.686979
$427$	1.65810e6	0.440089
$428$	−935251.	−0.246785
$429$	−8.47298e6	−2.22276
$430$	0	0
$431$	−1.53485e6	−0.397990	−0.198995	−	0.980000i	$-0.563768\pi$
$431$	−1.53485e6	−0.397990	−0.198995	+	0.980000i	$0.563768\pi$
$432$	−734358.	−0.189321
$433$	−6.18806e6	−1.58611	−0.793057	−	0.609147i	$-0.791512\pi$
$433$	−6.18806e6	−1.58611	−0.793057	+	0.609147i	$0.791512\pi$
$434$	−1.48333e6	−0.378019
$435$	0	0
$436$	−2.40680e6	−0.606350
$437$	−1.69095e6	−0.423571
$438$	2.63381e6	0.655992
$439$	−3.36983e6	−0.834539	−0.417270	−	0.908783i	$-0.637013\pi$
$439$	−3.36983e6	−0.834539	−0.417270	+	0.908783i	$0.637013\pi$
$440$	0	0
$441$	−151282.	−0.0370416
$442$	−846275.	−0.206042
$443$	−7.78352e6	−1.88437	−0.942186	−	0.335091i	$-0.891233\pi$
$443$	−7.78352e6	−1.88437	−0.942186	+	0.335091i	$0.891233\pi$
$444$	−3.51131e6	−0.845303
$445$	0	0
$446$	−1.11791e6	−0.266114
$447$	3.35253e6	0.793603
$448$	1.24160e6	0.292271
$449$	5.68127e6	1.32993	0.664966	−	0.746874i	$-0.268446\pi$
$449$	5.68127e6	1.32993	0.664966	+	0.746874i	$0.268446\pi$
$450$	0	0
$451$	1.03203e7	2.38919
$452$	−1.02741e6	−0.236537
$453$	−2.75217e6	−0.630131
$454$	−2.92815e6	−0.666736
$455$	0	0
$456$	2.67611e6	0.602687
$457$	3.94424e6	0.883431	0.441716	−	0.897155i	$-0.354370\pi$
$457$	3.94424e6	0.883431	0.441716	+	0.897155i	$0.354370\pi$
$458$	−2.44369e6	−0.544354
$459$	1.38555e6	0.306966
$460$	0	0
$461$	−8.35840e6	−1.83177	−0.915884	−	0.401442i	$-0.868509\pi$
$461$	−8.35840e6	−1.83177	−0.915884	+	0.401442i	$0.868509\pi$
$462$	−3.86295e6	−0.842003
$463$	1.99708e6	0.432954	0.216477	−	0.976288i	$-0.430543\pi$
$463$	1.99708e6	0.432954	0.216477	+	0.976288i	$0.430543\pi$
$464$	1.60406e6	0.345881
$465$	0	0
$466$	4.37190e6	0.932622
$467$	−2.46443e6	−0.522907	−0.261453	−	0.965216i	$-0.584202\pi$
$467$	−2.46443e6	−0.522907	−0.261453	+	0.965216i	$0.584202\pi$
$468$	−415716.	−0.0877368
$469$	3.98535e6	0.836632
$470$	0	0
$471$	6.73463e6	1.39882
$472$	−4.01116e6	−0.828733
$473$	1.35062e6	0.277574
$474$	5.30917e6	1.08538
$475$	0	0
$476$	921164.	0.186346
$477$	301995.	0.0607720
$478$	3.59547e6	0.719758
$479$	5.15610e6	1.02679	0.513396	−	0.858152i	$-0.328387\pi$
$479$	5.15610e6	1.02679	0.513396	+	0.858152i	$0.328387\pi$
$480$	0	0
$481$	6.71179e6	1.32274
$482$	−3.03560e6	−0.595150
$483$	2.99021e6	0.583222
$484$	−8.40156e6	−1.63022
$485$	0	0
$486$	−604410.	−0.116076
$487$	5.24784e6	1.00267	0.501335	−	0.865253i	$-0.332842\pi$
$487$	5.24784e6	1.00267	0.501335	+	0.865253i	$0.332842\pi$
$488$	−2.65039e6	−0.503802
$489$	5.14740e6	0.973454
$490$	0	0
$491$	−6.22256e6	−1.16484	−0.582419	−	0.812889i	$-0.697894\pi$
$491$	−6.22256e6	−1.16484	−0.582419	+	0.812889i	$0.697894\pi$
$492$	5.22685e6	0.973481
$493$	−3.02646e6	−0.560813
$494$	−2.11477e6	−0.389894
$495$	0	0
$496$	−949498.	−0.173296
$497$	5.35379e6	0.972234
$498$	−3.24831e6	−0.586927
$499$	−7.46960e6	−1.34291	−0.671454	−	0.741046i	$-0.734330\pi$
$499$	−7.46960e6	−1.34291	−0.671454	+	0.741046i	$0.734330\pi$
$500$	0	0
$501$	−3.01429e6	−0.536526
$502$	3.01852e6	0.534608
$503$	3.63182e6	0.640036	0.320018	−	0.947412i	$-0.396311\pi$
$503$	3.63182e6	0.640036	0.320018	+	0.947412i	$0.396311\pi$
$504$	−458446.	−0.0803918
$505$	0	0
$506$	−3.90161e6	−0.677436
$507$	2.11222e6	0.364938
$508$	6.95055e6	1.19498
$509$	−1.86644e6	−0.319315	−0.159658	−	0.987172i	$-0.551039\pi$
$509$	−1.86644e6	−0.319315	−0.159658	+	0.987172i	$0.551039\pi$
$510$	0	0
$511$	5.47997e6	0.928380
$512$	2.34547e6	0.395416
$513$	3.46237e6	0.580872
$514$	4.55994e6	0.761293
$515$	0	0
$516$	684038.	0.113098
$517$	5.07960e6	0.835801
$518$	3.06000e6	0.501068
$519$	9.34266e6	1.52248
$520$	0	0
$521$	4.23892e6	0.684166	0.342083	−	0.939670i	$-0.388868\pi$
$521$	4.23892e6	0.684166	0.342083	+	0.939670i	$0.388868\pi$
$522$	622698.	0.100023
$523$	9.67301e6	1.54635	0.773175	−	0.634193i	$-0.218668\pi$
$523$	9.67301e6	1.54635	0.773175	+	0.634193i	$0.218668\pi$
$524$	−5.42093e6	−0.862473
$525$	0	0
$526$	989222.	0.155894
$527$	1.79146e6	0.280984
$528$	−2.47272e6	−0.386002
$529$	−3.41620e6	−0.530767
$530$	0	0
$531$	623566.	0.0959723
$532$	2.30191e6	0.352623
$533$	−9.99100e6	−1.52332
$534$	4.70155e6	0.713490
$535$	0	0
$536$	−6.37039e6	−0.957754
$537$	−2.33423e6	−0.349307
$538$	2.98737e6	0.444972
$539$	4.23945e6	0.628547
$540$	0	0
$541$	−293228.	−0.0430737	−0.0215369	−	0.999768i	$-0.506856\pi$
$541$	−293228.	−0.0430737	−0.0215369	+	0.999768i	$0.506856\pi$
$542$	3.07231e6	0.449229
$543$	4.98682e6	0.725812
$544$	−2.33614e6	−0.338455
$545$	0	0
$546$	3.73969e6	0.536851
$547$	3.52245e6	0.503357	0.251679	−	0.967811i	$-0.419017\pi$
$547$	3.52245e6	0.503357	0.251679	+	0.967811i	$0.419017\pi$
$548$	822233.	0.116962
$549$	412023.	0.0583433
$550$	0	0
$551$	−7.56289e6	−1.06123
$552$	−4.77971e6	−0.667657
$553$	1.10464e7	1.53606
$554$	−2.43230e6	−0.336699
$555$	0	0
$556$	6.86689e6	0.942048
$557$	−1.02380e6	−0.139822	−0.0699112	−	0.997553i	$-0.522272\pi$
$557$	−1.02380e6	−0.139822	−0.0699112	+	0.997553i	$0.522272\pi$
$558$	−368595.	−0.0501146
$559$	−1.30752e6	−0.176978
$560$	0	0
$561$	4.66540e6	0.625866
$562$	−2.65311e6	−0.354335
$563$	3.95852e6	0.526335	0.263167	−	0.964750i	$-0.415233\pi$
$563$	3.95852e6	0.526335	0.263167	+	0.964750i	$0.415233\pi$
$564$	2.57263e6	0.340549
$565$	0	0
$566$	−3.17957e6	−0.417184
$567$	−6.78714e6	−0.886603
$568$	−8.55778e6	−1.11299
$569$	4.78234e6	0.619241	0.309621	−	0.950860i	$-0.399798\pi$
$569$	4.78234e6	0.619241	0.309621	+	0.950860i	$0.399798\pi$
$570$	0	0
$571$	−1.17147e7	−1.50363	−0.751813	−	0.659377i	$-0.770820\pi$
$571$	−1.17147e7	−1.50363	−0.751813	+	0.659377i	$0.770820\pi$
$572$	1.16499e7	1.48878
$573$	8.49323e6	1.08065
$574$	−4.55503e6	−0.577048
$575$	0	0
$576$	308527.	0.0387469
$577$	−4.56845e6	−0.571254	−0.285627	−	0.958341i	$-0.592202\pi$
$577$	−4.56845e6	−0.571254	−0.285627	+	0.958341i	$0.592202\pi$
$578$	−3.89798e6	−0.485311
$579$	1.10085e7	1.36468
$580$	0	0
$581$	−6.75852e6	−0.830637
$582$	−7.36145e6	−0.900858
$583$	−8.46298e6	−1.03122
$584$	−8.75946e6	−1.06278
$585$	0	0
$586$	−2.00135e6	−0.240757
$587$	−1.91888e6	−0.229854	−0.114927	−	0.993374i	$-0.536663\pi$
$587$	−1.91888e6	−0.229854	−0.114927	+	0.993374i	$0.536663\pi$
$588$	2.14713e6	0.256103
$589$	4.47672e6	0.531706
$590$	0	0
$591$	3.78907e6	0.446235
$592$	1.95874e6	0.229706
$593$	6.13688e6	0.716656	0.358328	−	0.933596i	$-0.383347\pi$
$593$	6.13688e6	0.716656	0.358328	+	0.933596i	$0.383347\pi$
$594$	7.98892e6	0.929013
$595$	0	0
$596$	−4.60953e6	−0.531546
$597$	−9.60353e6	−1.10280
$598$	3.77712e6	0.431925
$599$	−2.43235e6	−0.276986	−0.138493	−	0.990363i	$-0.544226\pi$
$599$	−2.43235e6	−0.276986	−0.138493	+	0.990363i	$0.544226\pi$
$600$	0	0
$601$	−1.53936e7	−1.73842	−0.869210	−	0.494443i	$-0.835372\pi$
$601$	−1.53936e7	−1.73842	−0.869210	+	0.494443i	$0.835372\pi$
$602$	−596117.	−0.0670410
$603$	990327.	0.110914
$604$	3.78408e6	0.422054
$605$	0	0
$606$	1.35804e6	0.150221
$607$	−1.26538e6	−0.139396	−0.0696978	−	0.997568i	$-0.522204\pi$
$607$	−1.26538e6	−0.139396	−0.0696978	+	0.997568i	$0.522204\pi$
$608$	−5.83782e6	−0.640459
$609$	1.33739e7	1.46122
$610$	0	0
$611$	−4.91752e6	−0.532897
$612$	228902.	0.0247042
$613$	−1.82568e7	−1.96234	−0.981168	−	0.193154i	$-0.938128\pi$
$613$	−1.82568e7	−1.96234	−0.981168	+	0.193154i	$0.938128\pi$
$614$	460646.	0.0493113
$615$	0	0
$616$	1.28473e7	1.36414
$617$	2.53502e6	0.268082	0.134041	−	0.990976i	$-0.457205\pi$
$617$	2.53502e6	0.268082	0.134041	+	0.990976i	$0.457205\pi$
$618$	167938.	0.0176880
$619$	1.08558e6	0.113877	0.0569383	−	0.998378i	$-0.481866\pi$
$619$	1.08558e6	0.113877	0.0569383	+	0.998378i	$0.481866\pi$
$620$	0	0
$621$	−6.18402e6	−0.643490
$622$	8.45047e6	0.875800
$623$	9.78217e6	1.00975
$624$	2.39382e6	0.246110
$625$	0	0
$626$	7.88297e6	0.803997
$627$	1.16584e7	1.18433
$628$	−9.25973e6	−0.936913
$629$	−3.69565e6	−0.372447
$630$	0	0
$631$	9.30353e6	0.930196	0.465098	−	0.885259i	$-0.346019\pi$
$631$	9.30353e6	0.930196	0.465098	+	0.885259i	$0.346019\pi$
$632$	−1.76571e7	−1.75844
$633$	6.88180e6	0.682642
$634$	−8.46740e6	−0.836617
$635$	0	0
$636$	−4.28619e6	−0.420174
$637$	−4.10418e6	−0.400754
$638$	−1.74503e7	−1.69727
$639$	1.33037e6	0.128891
$640$	0	0
$641$	1.76467e7	1.69636	0.848179	−	0.529710i	$-0.177699\pi$
$641$	1.76467e7	1.69636	0.848179	+	0.529710i	$0.177699\pi$
$642$	2.09064e6	0.200190
$643$	−1.09790e7	−1.04722	−0.523608	−	0.851959i	$-0.675414\pi$
$643$	−1.09790e7	−1.04722	−0.523608	+	0.851959i	$0.675414\pi$
$644$	−4.11137e6	−0.390636
$645$	0	0
$646$	1.16444e6	0.109783
$647$	400796.	0.0376411	0.0188206	−	0.999823i	$-0.494009\pi$
$647$	400796.	0.0376411	0.0188206	+	0.999823i	$0.494009\pi$
$648$	1.08489e7	1.01496
$649$	−1.74746e7	−1.62853
$650$	0	0
$651$	−7.91647e6	−0.732115
$652$	−7.07738e6	−0.652009
$653$	−7.28053e6	−0.668159	−0.334080	−	0.942545i	$-0.608425\pi$
$653$	−7.28053e6	−0.668159	−0.334080	+	0.942545i	$0.608425\pi$
$654$	5.38011e6	0.491866
$655$	0	0
$656$	−2.91573e6	−0.264538
$657$	1.36173e6	0.123077
$658$	−2.24196e6	−0.201866
$659$	−1.86505e6	−0.167292	−0.0836462	−	0.996496i	$-0.526657\pi$
$659$	−1.86505e6	−0.167292	−0.0836462	+	0.996496i	$0.526657\pi$
$660$	0	0
$661$	−1.52010e7	−1.35322	−0.676610	−	0.736341i	$-0.736552\pi$
$661$	−1.52010e7	−1.35322	−0.676610	+	0.736341i	$0.736552\pi$
$662$	−7.96731e6	−0.706589
$663$	−4.51653e6	−0.399045
$664$	1.08032e7	0.950891
$665$	0	0
$666$	760384.	0.0664275
$667$	1.35078e7	1.17563
$668$	4.14447e6	0.359359
$669$	−5.96622e6	−0.515387
$670$	0	0
$671$	−1.15464e7	−0.990010
$672$	1.03234e7	0.881859
$673$	7.66148e6	0.652041	0.326020	−	0.945363i	$-0.394292\pi$
$673$	7.66148e6	0.652041	0.326020	+	0.945363i	$0.394292\pi$
$674$	3.86337e6	0.327579
$675$	0	0
$676$	−2.90418e6	−0.244431
$677$	−9.88942e6	−0.829276	−0.414638	−	0.909986i	$-0.636092\pi$
$677$	−9.88942e6	−0.829276	−0.414638	+	0.909986i	$0.636092\pi$
$678$	2.29666e6	0.191877
$679$	−1.53164e7	−1.27492
$680$	0	0
$681$	−1.56274e7	−1.29128
$682$	1.03294e7	0.850380
$683$	−1.60532e7	−1.31677	−0.658383	−	0.752683i	$-0.728759\pi$
$683$	−1.60532e7	−1.31677	−0.658383	+	0.752683i	$0.728759\pi$
$684$	572007.	0.0467478
$685$	0	0
$686$	−7.28972e6	−0.591426
$687$	−1.30418e7	−1.05426
$688$	−381582.	−0.0307338
$689$	8.19295e6	0.657495
$690$	0	0
$691$	−3.88842e6	−0.309798	−0.154899	−	0.987930i	$-0.549505\pi$
$691$	−3.88842e6	−0.309798	−0.154899	+	0.987930i	$0.549505\pi$
$692$	−1.28456e7	−1.01974
$693$	−1.99721e6	−0.157976
$694$	−1.96559e6	−0.154915
$695$	0	0
$696$	−2.13776e7	−1.67277
$697$	5.50125e6	0.428923
$698$	236538.	0.0183765
$699$	2.33327e7	1.80622
$700$	0	0
$701$	−1.14322e7	−0.878691	−0.439346	−	0.898318i	$-0.644790\pi$
$701$	−1.14322e7	−0.878691	−0.439346	+	0.898318i	$0.644790\pi$
$702$	−7.73401e6	−0.592327
$703$	−9.23513e6	−0.704782
$704$	−8.64604e6	−0.657485
$705$	0	0
$706$	6.73609e6	0.508623
$707$	2.82557e6	0.212598
$708$	−8.85023e6	−0.663546
$709$	−5.94140e6	−0.443888	−0.221944	−	0.975059i	$-0.571240\pi$
$709$	−5.94140e6	−0.443888	−0.221944	+	0.975059i	$0.571240\pi$
$710$	0	0
$711$	2.74494e6	0.203638
$712$	−1.56363e7	−1.15594
$713$	−7.99571e6	−0.589024
$714$	−2.05915e6	−0.151162
$715$	0	0
$716$	3.20943e6	0.233962
$717$	1.91889e7	1.39396
$718$	−2.50045e6	−0.181012
$719$	−1.57087e6	−0.113323	−0.0566616	−	0.998393i	$-0.518046\pi$
$719$	−1.57087e6	−0.113323	−0.0566616	+	0.998393i	$0.518046\pi$
$720$	0	0
$721$	349417.	0.0250326
$722$	−4.70050e6	−0.335584
$723$	−1.62009e7	−1.15264
$724$	−6.85659e6	−0.486140
$725$	0	0
$726$	1.87807e7	1.32242
$727$	−1.59852e7	−1.12172	−0.560858	−	0.827912i	$-0.689529\pi$
$727$	−1.59852e7	−1.12172	−0.560858	+	0.827912i	$0.689529\pi$
$728$	−1.24374e7	−0.869762
$729$	1.24973e7	0.870955
$730$	0	0
$731$	719948.	0.0498319
$732$	−5.84782e6	−0.403382
$733$	1.33200e6	0.0915680	0.0457840	−	0.998951i	$-0.485421\pi$
$733$	1.33200e6	0.0915680	0.0457840	+	0.998951i	$0.485421\pi$
$734$	−4.74008e6	−0.324747
$735$	0	0
$736$	1.04267e7	0.709501
$737$	−2.77525e7	−1.88206
$738$	−1.13189e6	−0.0765003
$739$	−1.36691e7	−0.920725	−0.460362	−	0.887731i	$-0.652280\pi$
$739$	−1.36691e7	−0.920725	−0.460362	+	0.887731i	$0.652280\pi$
$740$	0	0
$741$	−1.12865e7	−0.755113
$742$	3.73528e6	0.249065
$743$	−8.37531e6	−0.556581	−0.278291	−	0.960497i	$-0.589768\pi$
$743$	−8.37531e6	−0.556581	−0.278291	+	0.960497i	$0.589768\pi$
$744$	1.26541e7	0.838105
$745$	0	0
$746$	941029.	0.0619093
$747$	−1.67944e6	−0.110119
$748$	−6.41465e6	−0.419198
$749$	4.34984e6	0.283315
$750$	0	0
$751$	1.16356e7	0.752815	0.376408	−	0.926454i	$-0.377159\pi$
$751$	1.16356e7	0.752815	0.376408	+	0.926454i	$0.377159\pi$
$752$	−1.43511e6	−0.0925423
$753$	1.61097e7	1.03538
$754$	1.68935e7	1.08216
$755$	0	0
$756$	8.41841e6	0.535705
$757$	−1.14963e7	−0.729155	−0.364577	−	0.931173i	$-0.618787\pi$
$757$	−1.14963e7	−0.729155	−0.364577	+	0.931173i	$0.618787\pi$
$758$	3.44661e6	0.217881
$759$	−2.08227e7	−1.31200
$760$	0	0
$761$	−1.50227e7	−0.940342	−0.470171	−	0.882575i	$-0.655808\pi$
$761$	−1.50227e7	−0.940342	−0.470171	+	0.882575i	$0.655808\pi$
$762$	−1.55371e7	−0.969354
$763$	1.11940e7	0.696103
$764$	−1.16777e7	−0.723809
$765$	0	0
$766$	7.89664e6	0.486262
$767$	1.69170e7	1.03833
$768$	−1.40583e7	−0.860063
$769$	2.44718e7	1.49228	0.746139	−	0.665790i	$-0.231905\pi$
$769$	2.44718e7	1.49228	0.746139	+	0.665790i	$0.231905\pi$
$770$	0	0
$771$	2.43362e7	1.47441
$772$	−1.51360e7	−0.914048
$773$	4.87919e6	0.293697	0.146848	−	0.989159i	$-0.453087\pi$
$773$	4.87919e6	0.293697	0.146848	+	0.989159i	$0.453087\pi$
$774$	−148130.	−0.00888773
$775$	0	0
$776$	2.44826e7	1.45950
$777$	1.63311e7	0.970425
$778$	328084.	0.0194328
$779$	1.37472e7	0.811652
$780$	0	0
$781$	−3.72819e7	−2.18711
$782$	−2.07976e6	−0.121618
$783$	−2.76585e7	−1.61222
$784$	−1.19775e6	−0.0695945
$785$	0	0
$786$	1.21178e7	0.699630
$787$	−2.35706e7	−1.35654	−0.678272	−	0.734811i	$-0.737271\pi$
$787$	−2.35706e7	−1.35654	−0.678272	+	0.734811i	$0.737271\pi$
$788$	−5.20976e6	−0.298883
$789$	5.27944e6	0.301922
$790$	0	0
$791$	4.77849e6	0.271550
$792$	3.19245e6	0.180847
$793$	1.11780e7	0.631218
$794$	1.48191e7	0.834199
$795$	0	0
$796$	1.32043e7	0.738640
$797$	8.76313e6	0.488667	0.244334	−	0.969691i	$-0.421431\pi$
$797$	8.76313e6	0.488667	0.244334	+	0.969691i	$0.421431\pi$
$798$	−5.14565e6	−0.286044
$799$	2.70769e6	0.150048
$800$	0	0
$801$	2.43079e6	0.133865
$802$	1.50841e7	0.828103
$803$	−3.81605e7	−2.08846
$804$	−1.40556e7	−0.766850
$805$	0	0
$806$	−9.99979e6	−0.542192
$807$	1.59435e7	0.861784
$808$	−4.51654e6	−0.243376
$809$	1.53842e7	0.826425	0.413213	−	0.910635i	$-0.364407\pi$
$809$	1.53842e7	0.826425	0.413213	+	0.910635i	$0.364407\pi$
$810$	0	0
$811$	3.00619e7	1.60496	0.802479	−	0.596680i	$-0.203514\pi$
$811$	3.00619e7	1.60496	0.802479	+	0.596680i	$0.203514\pi$
$812$	−1.83884e7	−0.978709
$813$	1.63968e7	0.870027
$814$	−2.13087e7	−1.12719
$815$	0	0
$816$	−1.31809e6	−0.0692977
$817$	1.79909e6	0.0942971
$818$	1.78700e7	0.933772
$819$	1.93349e6	0.100724
$820$	0	0
$821$	2.70586e7	1.40103	0.700514	−	0.713639i	$-0.252954\pi$
$821$	2.70586e7	1.40103	0.700514	+	0.713639i	$0.252954\pi$
$822$	−1.83800e6	−0.0948782
$823$	3.51747e6	0.181022	0.0905109	−	0.995895i	$-0.471150\pi$
$823$	3.51747e6	0.181022	0.0905109	+	0.995895i	$0.471150\pi$
$824$	−558525.	−0.0286566
$825$	0	0
$826$	7.71269e6	0.393329
$827$	2.98218e7	1.51625	0.758123	−	0.652111i	$-0.226117\pi$
$827$	2.98218e7	1.51625	0.758123	+	0.652111i	$0.226117\pi$
$828$	−1.02164e6	−0.0517872
$829$	2.95374e6	0.149275	0.0746374	−	0.997211i	$-0.476220\pi$
$829$	2.95374e6	0.149275	0.0746374	+	0.997211i	$0.476220\pi$
$830$	0	0
$831$	−1.29811e7	−0.652091
$832$	8.37016e6	0.419204
$833$	2.25985e6	0.112841
$834$	−1.53501e7	−0.764181
$835$	0	0
$836$	−1.60297e7	−0.793249
$837$	1.63720e7	0.807769
$838$	−5.40855e6	−0.266055
$839$	3.85923e7	1.89276	0.946381	−	0.323054i	$-0.104709\pi$
$839$	3.85923e7	1.89276	0.946381	+	0.323054i	$0.104709\pi$
$840$	0	0
$841$	3.99035e7	1.94545
$842$	4.95571e6	0.240894
$843$	−1.41595e7	−0.686246
$844$	−9.46208e6	−0.457226
$845$	0	0
$846$	−557110.	−0.0267618
$847$	3.90756e7	1.87153
$848$	2.39100e6	0.114180
$849$	−1.69692e7	−0.807967
$850$	0	0
$851$	1.64945e7	0.780758
$852$	−1.88819e7	−0.891142
$853$	−1.40252e7	−0.659987	−0.329994	−	0.943983i	$-0.607047\pi$
$853$	−1.40252e7	−0.659987	−0.329994	+	0.943983i	$0.607047\pi$
$854$	5.09619e6	0.239112
$855$	0	0
$856$	−6.95301e6	−0.324331
$857$	3.81717e6	0.177537	0.0887686	−	0.996052i	$-0.471707\pi$
$857$	3.81717e6	0.177537	0.0887686	+	0.996052i	$0.471707\pi$
$858$	−2.60418e7	−1.20768
$859$	2.18116e7	1.00857	0.504283	−	0.863539i	$-0.331757\pi$
$859$	2.18116e7	1.00857	0.504283	+	0.863539i	$0.331757\pi$
$860$	0	0
$861$	−2.43100e7	−1.11758
$862$	−4.71738e6	−0.216239
$863$	−1.05498e7	−0.482187	−0.241093	−	0.970502i	$-0.577506\pi$
$863$	−1.05498e7	−0.482187	−0.241093	+	0.970502i	$0.577506\pi$
$864$	−2.13497e7	−0.972987
$865$	0	0
$866$	−1.90191e7	−0.861778
$867$	−2.08033e7	−0.939908
$868$	1.08847e7	0.490362
$869$	−7.69231e7	−3.45547
$870$	0	0
$871$	2.68670e7	1.19998
$872$	−1.78930e7	−0.796880
$873$	−3.80601e6	−0.169018
$874$	−5.19716e6	−0.230137
$875$	0	0
$876$	−1.93269e7	−0.850946
$877$	−2.18090e6	−0.0957495	−0.0478747	−	0.998853i	$-0.515245\pi$
$877$	−2.18090e6	−0.0957495	−0.0478747	+	0.998853i	$0.515245\pi$
$878$	−1.03572e7	−0.453427
$879$	−1.06811e7	−0.466278
$880$	0	0
$881$	−2.79930e7	−1.21510	−0.607548	−	0.794283i	$-0.707847\pi$
$881$	−2.79930e7	−1.21510	−0.607548	+	0.794283i	$0.707847\pi$
$882$	−464966.	−0.0201257
$883$	−1.21178e7	−0.523023	−0.261511	−	0.965200i	$-0.584221\pi$
$883$	−1.21178e7	−0.523023	−0.261511	+	0.965200i	$0.584221\pi$
$884$	6.20998e6	0.267276
$885$	0	0
$886$	−2.39228e7	−1.02383
$887$	−1.67236e7	−0.713710	−0.356855	−	0.934160i	$-0.616151\pi$
$887$	−1.67236e7	−0.713710	−0.356855	+	0.934160i	$0.616151\pi$
$888$	−2.61044e7	−1.11092
$889$	−3.23269e7	−1.37186
$890$	0	0
$891$	4.72632e7	1.99448
$892$	8.20321e6	0.345201
$893$	6.76629e6	0.283937
$894$	1.03040e7	0.431185
$895$	0	0
$896$	−1.63232e7	−0.679257
$897$	2.01583e7	0.836515
$898$	1.74615e7	0.722587
$899$	−3.57614e7	−1.47576
$900$	0	0
$901$	−4.51121e6	−0.185132
$902$	3.17196e7	1.29811
$903$	−3.18145e6	−0.129839
$904$	−7.63818e6	−0.310863
$905$	0	0
$906$	−8.45886e6	−0.342366
$907$	2.47400e7	0.998576	0.499288	−	0.866436i	$-0.333595\pi$
$907$	2.47400e7	0.998576	0.499288	+	0.866436i	$0.333595\pi$
$908$	2.14868e7	0.864883
$909$	702132.	0.0281844
$910$	0	0
$911$	9.49375e6	0.379002	0.189501	−	0.981880i	$-0.439313\pi$
$911$	9.49375e6	0.379002	0.189501	+	0.981880i	$0.439313\pi$
$912$	−3.29379e6	−0.131132
$913$	4.70639e7	1.86858
$914$	1.21227e7	0.479991
$915$	0	0
$916$	1.79318e7	0.706131
$917$	2.52127e7	0.990138
$918$	4.25851e6	0.166783
$919$	−1.67640e7	−0.654772	−0.327386	−	0.944891i	$-0.606168\pi$
$919$	−1.67640e7	−0.654772	−0.327386	+	0.944891i	$0.606168\pi$
$920$	0	0
$921$	2.45845e6	0.0955019
$922$	−2.56897e7	−0.995248
$923$	3.60923e7	1.39447
$924$	2.83463e7	1.09224
$925$	0	0
$926$	6.13805e6	0.235235
$927$	86827.2	0.00331861
$928$	4.66343e7	1.77760
$929$	1.22216e7	0.464611	0.232305	−	0.972643i	$-0.425373\pi$
$929$	1.22216e7	0.464611	0.232305	+	0.972643i	$0.425373\pi$
$930$	0	0
$931$	5.64718e6	0.213529
$932$	−3.20811e7	−1.20979
$933$	4.50998e7	1.69617
$934$	−7.57447e6	−0.284109
$935$	0	0
$936$	−3.09059e6	−0.115306
$937$	−1.64302e7	−0.611357	−0.305678	−	0.952135i	$-0.598883\pi$
$937$	−1.64302e7	−0.611357	−0.305678	+	0.952135i	$0.598883\pi$
$938$	1.22490e7	0.454564
$939$	4.20711e7	1.55711
$940$	0	0
$941$	−1.05612e7	−0.388812	−0.194406	−	0.980921i	$-0.562278\pi$
$941$	−1.05612e7	−0.388812	−0.194406	+	0.980921i	$0.562278\pi$
$942$	2.06990e7	0.760015
$943$	−2.45534e7	−0.899149
$944$	4.93698e6	0.180315
$945$	0	0
$946$	4.15114e6	0.150813
$947$	−2.16559e7	−0.784697	−0.392348	−	0.919817i	$-0.628337\pi$
$947$	−2.16559e7	−0.784697	−0.392348	+	0.919817i	$0.628337\pi$
$948$	−3.89587e7	−1.40794
$949$	3.69429e7	1.33157
$950$	0	0
$951$	−4.51901e7	−1.62029
$952$	6.84828e6	0.244900
$953$	−5.16415e7	−1.84190	−0.920951	−	0.389679i	$-0.872586\pi$
$953$	−5.16415e7	−1.84190	−0.920951	+	0.389679i	$0.872586\pi$
$954$	928186.	0.0330190
$955$	0	0
$956$	−2.63836e7	−0.933662
$957$	−9.31312e7	−3.28712
$958$	1.58474e7	0.557883
$959$	−3.82419e6	−0.134274
$960$	0	0
$961$	−7.46081e6	−0.260602
$962$	2.06288e7	0.718681
$963$	1.08090e6	0.0375595
$964$	2.22752e7	0.772022
$965$	0	0
$966$	9.19047e6	0.316880
$967$	−5.31819e7	−1.82893	−0.914466	−	0.404662i	$-0.867389\pi$
$967$	−5.31819e7	−1.82893	−0.914466	+	0.404662i	$0.867389\pi$
$968$	−6.24604e7	−2.14248
$969$	6.21456e6	0.212618
$970$	0	0
$971$	2.11000e7	0.718180	0.359090	−	0.933303i	$-0.383087\pi$
$971$	2.11000e7	0.718180	0.359090	+	0.933303i	$0.383087\pi$
$972$	4.43516e6	0.150572
$973$	−3.19378e7	−1.08149
$974$	1.61293e7	0.544777
$975$	0	0
$976$	3.26213e6	0.109617
$977$	−1.99941e6	−0.0670141	−0.0335071	−	0.999438i	$-0.510668\pi$
$977$	−1.99941e6	−0.0670141	−0.0335071	+	0.999438i	$0.510668\pi$
$978$	1.58206e7	0.528903
$979$	−6.81195e7	−2.27151
$980$	0	0
$981$	2.78161e6	0.0922836
$982$	−1.91252e7	−0.632887
$983$	2.33430e7	0.770500	0.385250	−	0.922812i	$-0.374115\pi$
$983$	2.33430e7	0.770500	0.385250	+	0.922812i	$0.374115\pi$
$984$	3.88584e7	1.27937
$985$	0	0
$986$	−9.30189e6	−0.304704
$987$	−1.19653e7	−0.390957
$988$	1.55182e7	0.505766
$989$	−3.21330e6	−0.104462
$990$	0	0
$991$	−2.33765e7	−0.756127	−0.378063	−	0.925780i	$-0.623410\pi$
$991$	−2.33765e7	−0.756127	−0.378063	+	0.925780i	$0.623410\pi$
$992$	−2.76043e7	−0.890632
$993$	−4.25212e7	−1.36846
$994$	1.64550e7	0.528240
$995$	0	0
$996$	2.38361e7	0.761356
$997$	1.32278e7	0.421454	0.210727	−	0.977545i	$-0.432417\pi$
$997$	1.32278e7	0.421454	0.210727	+	0.977545i	$0.432417\pi$
$998$	−2.29580e7	−0.729637
$999$	−3.37741e7	−1.07071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.l.1.32		52
5.2	odd	4		215.6.b.a.44.67	yes	104
5.3	odd	4		215.6.b.a.44.38	✓	104
5.4	even	2		1075.6.a.k.1.21		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.b.a.44.38	✓	104	5.3	odd	4
215.6.b.a.44.67	yes	104	5.2	odd	4
1075.6.a.k.1.21		52	5.4	even	2
1075.6.a.l.1.32		52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+3.07352 q^{2} +16.4032 q^{3} -22.5535 q^{4} +50.4156 q^{6} +104.896 q^{7} -167.671 q^{8} +26.0658 q^{9} +O(q^{10})\)	\(q+3.07352 q^{2} +16.4032 q^{3} -22.5535 q^{4} +50.4156 q^{6} +104.896 q^{7} -167.671 q^{8} +26.0658 q^{9} -730.458 q^{11} -369.950 q^{12} +707.150 q^{13} +322.400 q^{14} +206.372 q^{16} -389.372 q^{17} +80.1137 q^{18} -973.008 q^{19} +1720.63 q^{21} -2245.07 q^{22} +1737.86 q^{23} -2750.35 q^{24} +2173.44 q^{26} -3558.42 q^{27} -2365.77 q^{28} +7772.69 q^{29} -4600.91 q^{31} +5999.76 q^{32} -11981.9 q^{33} -1196.74 q^{34} -587.875 q^{36} +9491.32 q^{37} -2990.56 q^{38} +11599.5 q^{39} -14128.5 q^{41} +5288.39 q^{42} -1849.00 q^{43} +16474.4 q^{44} +5341.33 q^{46} -6953.99 q^{47} +3385.16 q^{48} -5803.83 q^{49} -6386.95 q^{51} -15948.7 q^{52} +11585.9 q^{53} -10936.9 q^{54} -17588.0 q^{56} -15960.5 q^{57} +23889.5 q^{58} +23922.8 q^{59} +15807.1 q^{61} -14141.0 q^{62} +2734.20 q^{63} +11836.5 q^{64} -36826.4 q^{66} +37993.3 q^{67} +8781.69 q^{68} +28506.4 q^{69} +51039.1 q^{71} -4370.48 q^{72} +52241.9 q^{73} +29171.7 q^{74} +21944.7 q^{76} -76622.1 q^{77} +35651.4 q^{78} +105308. q^{79} -64703.6 q^{81} -43424.3 q^{82} -64430.7 q^{83} -38806.3 q^{84} -5682.93 q^{86} +127497. q^{87} +122477. q^{88} +93255.9 q^{89} +74177.2 q^{91} -39194.7 q^{92} -75469.7 q^{93} -21373.2 q^{94} +98415.5 q^{96} -146015. q^{97} -17838.2 q^{98} -19040.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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