LMFDB - Embedded newform 387.10.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,10,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("387.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	387.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:	$199.318868595$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 $ x^15 - 2x^14 - 5425x^13 + 14888x^12 + 11288030x^11 - 37600244x^10 - 11474166224x^9 + 47465836576x^8 + 5986976782464x^7 - 32493903147264x^6 - 1516975415483904x^5 + 10892588268404224x^4 + 139803541742443008x^3 - 1349125586394823680x^2 + 2103623681144094720x + 529838441422848000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-35.4490$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-33.4490 q^{2} +606.833 q^{4} +752.925 q^{5} -7164.62 q^{7} -3172.07 q^{8} +O(q^{10})$	\(q-33.4490 q^{2} +606.833 q^{4} +752.925 q^{5} -7164.62 q^{7} -3172.07 q^{8} -25184.6 q^{10} +30954.5 q^{11} +41893.4 q^{13} +239649. q^{14} -204596. q^{16} -187328. q^{17} +668619. q^{19} +456900. q^{20} -1.03540e6 q^{22} +2.17863e6 q^{23} -1.38623e6 q^{25} -1.40129e6 q^{26} -4.34773e6 q^{28} -2.40487e6 q^{29} +8.05328e6 q^{31} +8.46763e6 q^{32} +6.26594e6 q^{34} -5.39442e6 q^{35} -1.64001e7 q^{37} -2.23646e7 q^{38} -2.38833e6 q^{40} -1.13061e7 q^{41} -3.41880e6 q^{43} +1.87842e7 q^{44} -7.28730e7 q^{46} +4.31570e7 q^{47} +1.09782e7 q^{49} +4.63679e7 q^{50} +2.54223e7 q^{52} +3.13129e7 q^{53} +2.33064e7 q^{55} +2.27267e7 q^{56} +8.04403e7 q^{58} -4.51423e7 q^{59} +7.25780e7 q^{61} -2.69374e8 q^{62} -1.78480e8 q^{64} +3.15426e7 q^{65} +2.83598e8 q^{67} -1.13677e8 q^{68} +1.80438e8 q^{70} +1.90718e8 q^{71} +2.75834e7 q^{73} +5.48567e8 q^{74} +4.05740e8 q^{76} -2.21777e8 q^{77} +2.64422e8 q^{79} -1.54046e8 q^{80} +3.78177e8 q^{82} +5.42519e8 q^{83} -1.41044e8 q^{85} +1.14355e8 q^{86} -9.81898e7 q^{88} +2.40619e7 q^{89} -3.00150e8 q^{91} +1.32207e9 q^{92} -1.44356e9 q^{94} +5.03420e8 q^{95} -1.30561e9 q^{97} -3.67209e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) $ 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8} - 36237 q^{10} + 104484 q^{11} - 116174 q^{13} - 416064 q^{14} + 996762 q^{16} + 884265 q^{17} - 689535 q^{19} + 3077879 q^{20} - 7276218 q^{22} + 2504077 q^{23} + 1315350 q^{25} + 13343414 q^{26} - 28059568 q^{28} + 18406221 q^{29} - 12033699 q^{31} + 18952630 q^{32} - 30383125 q^{34} + 27855546 q^{35} - 8722847 q^{37} + 63941843 q^{38} - 39665611 q^{40} + 18689389 q^{41} - 51282015 q^{43} + 68723220 q^{44} - 2067521 q^{46} + 104960741 q^{47} + 92663095 q^{49} + 42446347 q^{50} + 149226080 q^{52} + 215907800 q^{53} + 384379852 q^{55} - 430441344 q^{56} + 295963139 q^{58} - 185924544 q^{59} + 247538102 q^{61} - 139798853 q^{62} + 848556290 q^{64} - 94294394 q^{65} + 467904656 q^{67} + 88234341 q^{68} + 647526126 q^{70} + 8252944 q^{71} - 715627902 q^{73} - 725122989 q^{74} + 346300359 q^{76} + 1236779964 q^{77} + 560681783 q^{79} + 1157214179 q^{80} + 941346367 q^{82} + 1442854698 q^{83} + 699302088 q^{85} - 109401632 q^{86} - 1464507256 q^{88} + 396710008 q^{89} - 3278076852 q^{91} - 155864647 q^{92} + 4666638949 q^{94} + 3854114395 q^{95} - 3063837815 q^{97} + 6161086984 q^{98}+O(q^{100}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8 - 36237 * q^10 + 104484 * q^11 - 116174 * q^13 - 416064 * q^14 + 996762 * q^16 + 884265 * q^17 - 689535 * q^19 + 3077879 * q^20 - 7276218 * q^22 + 2504077 * q^23 + 1315350 * q^25 + 13343414 * q^26 - 28059568 * q^28 + 18406221 * q^29 - 12033699 * q^31 + 18952630 * q^32 - 30383125 * q^34 + 27855546 * q^35 - 8722847 * q^37 + 63941843 * q^38 - 39665611 * q^40 + 18689389 * q^41 - 51282015 * q^43 + 68723220 * q^44 - 2067521 * q^46 + 104960741 * q^47 + 92663095 * q^49 + 42446347 * q^50 + 149226080 * q^52 + 215907800 * q^53 + 384379852 * q^55 - 430441344 * q^56 + 295963139 * q^58 - 185924544 * q^59 + 247538102 * q^61 - 139798853 * q^62 + 848556290 * q^64 - 94294394 * q^65 + 467904656 * q^67 + 88234341 * q^68 + 647526126 * q^70 + 8252944 * q^71 - 715627902 * q^73 - 725122989 * q^74 + 346300359 * q^76 + 1236779964 * q^77 + 560681783 * q^79 + 1157214179 * q^80 + 941346367 * q^82 + 1442854698 * q^83 + 699302088 * q^85 - 109401632 * q^86 - 1464507256 * q^88 + 396710008 * q^89 - 3278076852 * q^91 - 155864647 * q^92 + 4666638949 * q^94 + 3854114395 * q^95 - 3063837815 * q^97 + 6161086984 * q^98

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 $

$2$	−33.4490	−1.47825	−0.739125	−	0.673569i	$-0.764761\pi$
$2$	−33.4490	−1.47825	−0.739125	+	0.673569i	$0.764761\pi$
$3$	0	0
$3$	0	0
$4$	606.833	1.18522
$5$	752.925	0.538749	0.269375	−	0.963035i	$-0.413183\pi$
$5$	752.925	0.538749	0.269375	+	0.963035i	$0.413183\pi$
$6$	0	0
$7$	−7164.62	−1.12785	−0.563926	−	0.825825i	$-0.690710\pi$
$7$	−7164.62	−1.12785	−0.563926	+	0.825825i	$0.690710\pi$
$8$	−3172.07	−0.273803
$9$	0	0
$10$	−25184.6	−0.796406
$11$	30954.5	0.637466	0.318733	−	0.947845i	$-0.396743\pi$
$11$	30954.5	0.637466	0.318733	+	0.947845i	$0.396743\pi$
$12$	0	0
$13$	41893.4	0.406818	0.203409	−	0.979094i	$-0.434798\pi$
$13$	41893.4	0.406818	0.203409	+	0.979094i	$0.434798\pi$
$14$	239649.	1.66725
$15$	0	0
$16$	−204596.	−0.780472
$17$	−187328.	−0.543980	−0.271990	−	0.962300i	$-0.587682\pi$
$17$	−187328.	−0.543980	−0.271990	+	0.962300i	$0.587682\pi$
$18$	0	0
$19$	668619.	1.17703	0.588515	−	0.808486i	$-0.299713\pi$
$19$	668619.	1.17703	0.588515	+	0.808486i	$0.299713\pi$
$20$	456900.	0.638537
$21$	0	0
$22$	−1.03540e6	−0.942334
$23$	2.17863e6	1.62334	0.811669	−	0.584118i	$-0.198560\pi$
$23$	2.17863e6	1.62334	0.811669	+	0.584118i	$0.198560\pi$
$24$	0	0
$25$	−1.38623e6	−0.709749
$26$	−1.40129e6	−0.601379
$27$	0	0
$28$	−4.34773e6	−1.33675
$29$	−2.40487e6	−0.631393	−0.315697	−	0.948860i	$-0.602238\pi$
$29$	−2.40487e6	−0.631393	−0.315697	+	0.948860i	$0.602238\pi$
$30$	0	0
$31$	8.05328e6	1.56619	0.783096	−	0.621901i	$-0.213639\pi$
$31$	8.05328e6	1.56619	0.783096	+	0.621901i	$0.213639\pi$
$32$	8.46763e6	1.42754
$33$	0	0
$34$	6.26594e6	0.804138
$35$	−5.39442e6	−0.607629
$36$	0	0
$37$	−1.64001e7	−1.43860	−0.719299	−	0.694701i	$-0.755537\pi$
$37$	−1.64001e7	−1.43860	−0.719299	+	0.694701i	$0.755537\pi$
$38$	−2.23646e7	−1.73994
$39$	0	0
$40$	−2.38833e6	−0.147511
$41$	−1.13061e7	−0.624863	−0.312431	−	0.949940i	$-0.601143\pi$
$41$	−1.13061e7	−0.624863	−0.312431	+	0.949940i	$0.601143\pi$
$42$	0	0
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	1.87842e7	0.755538
$45$	0	0
$46$	−7.28730e7	−2.39970
$47$	4.31570e7	1.29006	0.645031	−	0.764156i	$-0.276844\pi$
$47$	4.31570e7	1.29006	0.645031	+	0.764156i	$0.276844\pi$
$48$	0	0
$49$	1.09782e7	0.272049
$50$	4.63679e7	1.04919
$51$	0	0
$52$	2.54223e7	0.482169
$53$	3.13129e7	0.545108	0.272554	−	0.962141i	$-0.412132\pi$
$53$	3.13129e7	0.545108	0.272554	+	0.962141i	$0.412132\pi$
$54$	0	0
$55$	2.33064e7	0.343434
$56$	2.27267e7	0.308809
$57$	0	0
$58$	8.04403e7	0.933357
$59$	−4.51423e7	−0.485009	−0.242504	−	0.970150i	$-0.577969\pi$
$59$	−4.51423e7	−0.485009	−0.242504	+	0.970150i	$0.577969\pi$
$60$	0	0
$61$	7.25780e7	0.671152	0.335576	−	0.942013i	$-0.391069\pi$
$61$	7.25780e7	0.671152	0.335576	+	0.942013i	$0.391069\pi$
$62$	−2.69374e8	−2.31522
$63$	0	0
$64$	−1.78480e8	−1.32978
$65$	3.15426e7	0.219173
$66$	0	0
$67$	2.83598e8	1.71936	0.859678	−	0.510836i	$-0.170664\pi$
$67$	2.83598e8	1.71936	0.859678	+	0.510836i	$0.170664\pi$
$68$	−1.13677e8	−0.644737
$69$	0	0
$70$	1.80438e8	0.898228
$71$	1.90718e8	0.890695	0.445347	−	0.895358i	$-0.353080\pi$
$71$	1.90718e8	0.890695	0.445347	+	0.895358i	$0.353080\pi$
$72$	0	0
$73$	2.75834e7	0.113683	0.0568415	−	0.998383i	$-0.481897\pi$
$73$	2.75834e7	0.113683	0.0568415	+	0.998383i	$0.481897\pi$
$74$	5.48567e8	2.12661
$75$	0	0
$76$	4.05740e8	1.39504
$77$	−2.21777e8	−0.718967
$78$	0	0
$79$	2.64422e8	0.763794	0.381897	−	0.924205i	$-0.375271\pi$
$79$	2.64422e8	0.763794	0.381897	+	0.924205i	$0.375271\pi$
$80$	−1.54046e8	−0.420479
$81$	0	0
$82$	3.78177e8	0.923703
$83$	5.42519e8	1.25477	0.627384	−	0.778710i	$-0.284126\pi$
$83$	5.42519e8	1.25477	0.627384	+	0.778710i	$0.284126\pi$
$84$	0	0
$85$	−1.41044e8	−0.293069
$86$	1.14355e8	0.225431
$87$	0	0
$88$	−9.81898e7	−0.174540
$89$	2.40619e7	0.0406513	0.0203257	−	0.999793i	$-0.493530\pi$
$89$	2.40619e7	0.0406513	0.0203257	+	0.999793i	$0.493530\pi$
$90$	0	0
$91$	−3.00150e8	−0.458830
$92$	1.32207e9	1.92401
$93$	0	0
$94$	−1.44356e9	−1.90703
$95$	5.03420e8	0.634124
$96$	0	0
$97$	−1.30561e9	−1.49741	−0.748704	−	0.662905i	$-0.769323\pi$
$97$	−1.30561e9	−1.49741	−0.748704	+	0.662905i	$0.769323\pi$
$98$	−3.67209e8	−0.402157
$99$	0	0
$100$	−8.41209e8	−0.841209
$101$	−8.39059e8	−0.802318	−0.401159	−	0.916008i	$-0.631393\pi$
$101$	−8.39059e8	−0.802318	−0.401159	+	0.916008i	$0.631393\pi$
$102$	0	0
$103$	−1.97091e9	−1.72544	−0.862720	−	0.505681i	$-0.831241\pi$
$103$	−1.97091e9	−1.72544	−0.862720	+	0.505681i	$0.831241\pi$
$104$	−1.32889e8	−0.111388
$105$	0	0
$106$	−1.04739e9	−0.805805
$107$	−1.26639e9	−0.933983	−0.466991	−	0.884262i	$-0.654662\pi$
$107$	−1.26639e9	−0.933983	−0.466991	+	0.884262i	$0.654662\pi$
$108$	0	0
$109$	−9.70279e8	−0.658381	−0.329191	−	0.944264i	$-0.606776\pi$
$109$	−9.70279e8	−0.658381	−0.329191	+	0.944264i	$0.606776\pi$
$110$	−7.79576e8	−0.507682
$111$	0	0
$112$	1.46585e9	0.880257
$113$	1.93357e9	1.11559	0.557797	−	0.829977i	$-0.311647\pi$
$113$	1.93357e9	1.11559	0.557797	+	0.829977i	$0.311647\pi$
$114$	0	0
$115$	1.64035e9	0.874572
$116$	−1.45935e9	−0.748341
$117$	0	0
$118$	1.50996e9	0.716964
$119$	1.34214e9	0.613529
$120$	0	0
$121$	−1.39977e9	−0.593637
$122$	−2.42766e9	−0.992130
$123$	0	0
$124$	4.88700e9	1.85628
$125$	−2.51428e9	−0.921126
$126$	0	0
$127$	−2.17278e9	−0.741137	−0.370569	−	0.928805i	$-0.620837\pi$
$127$	−2.17278e9	−0.741137	−0.370569	+	0.928805i	$0.620837\pi$
$128$	1.63455e9	0.538212
$129$	0	0
$130$	−1.05507e9	−0.323992
$131$	2.34464e9	0.695594	0.347797	−	0.937570i	$-0.386930\pi$
$131$	2.34464e9	0.695594	0.347797	+	0.937570i	$0.386930\pi$
$132$	0	0
$133$	−4.79040e9	−1.32752
$134$	−9.48605e9	−2.54164
$135$	0	0
$136$	5.94218e8	0.148943
$137$	−2.32762e9	−0.564508	−0.282254	−	0.959340i	$-0.591082\pi$
$137$	−2.32762e9	−0.564508	−0.282254	+	0.959340i	$0.591082\pi$
$138$	0	0
$139$	−3.92528e9	−0.891875	−0.445937	−	0.895064i	$-0.647130\pi$
$139$	−3.92528e9	−0.891875	−0.445937	+	0.895064i	$0.647130\pi$
$140$	−3.27351e9	−0.720175
$141$	0	0
$142$	−6.37932e9	−1.31667
$143$	1.29679e9	0.259333
$144$	0	0
$145$	−1.81068e9	−0.340163
$146$	−9.22637e8	−0.168052
$147$	0	0
$148$	−9.95214e9	−1.70506
$149$	3.42450e9	0.569192	0.284596	−	0.958648i	$-0.408141\pi$
$149$	3.42450e9	0.569192	0.284596	+	0.958648i	$0.408141\pi$
$150$	0	0
$151$	−2.21822e9	−0.347223	−0.173611	−	0.984814i	$-0.555544\pi$
$151$	−2.21822e9	−0.347223	−0.173611	+	0.984814i	$0.555544\pi$
$152$	−2.12090e9	−0.322274
$153$	0	0
$154$	7.41822e9	1.06281
$155$	6.06352e9	0.843785
$156$	0	0
$157$	−1.02245e9	−0.134306	−0.0671530	−	0.997743i	$-0.521392\pi$
$157$	−1.02245e9	−0.134306	−0.0671530	+	0.997743i	$0.521392\pi$
$158$	−8.84465e9	−1.12908
$159$	0	0
$160$	6.37549e9	0.769084
$161$	−1.56091e10	−1.83088
$162$	0	0
$163$	1.02522e10	1.13756	0.568778	−	0.822491i	$-0.307416\pi$
$163$	1.02522e10	1.13756	0.568778	+	0.822491i	$0.307416\pi$
$164$	−6.86090e9	−0.740601
$165$	0	0
$166$	−1.81467e10	−1.85486
$167$	1.77286e10	1.76380	0.881901	−	0.471436i	$-0.156264\pi$
$167$	1.77286e10	1.76380	0.881901	+	0.471436i	$0.156264\pi$
$168$	0	0
$169$	−8.84944e9	−0.834499
$170$	4.71778e9	0.433229
$171$	0	0
$172$	−2.07464e9	−0.180744
$173$	−1.17358e10	−0.996104	−0.498052	−	0.867147i	$-0.665951\pi$
$173$	−1.17358e10	−0.996104	−0.498052	+	0.867147i	$0.665951\pi$
$174$	0	0
$175$	9.93180e9	0.800492
$176$	−6.33318e9	−0.497525
$177$	0	0
$178$	−8.04846e8	−0.0600928
$179$	−7.44591e9	−0.542100	−0.271050	−	0.962565i	$-0.587371\pi$
$179$	−7.44591e9	−0.542100	−0.271050	+	0.962565i	$0.587371\pi$
$180$	0	0
$181$	8.28250e8	0.0573599	0.0286799	−	0.999589i	$-0.490870\pi$
$181$	8.28250e8	0.0573599	0.0286799	+	0.999589i	$0.490870\pi$
$182$	1.00397e10	0.678266
$183$	0	0
$184$	−6.91077e9	−0.444474
$185$	−1.23481e10	−0.775043
$186$	0	0
$187$	−5.79866e9	−0.346769
$188$	2.61891e10	1.52901
$189$	0	0
$190$	−1.68389e10	−0.937394
$191$	−1.78976e9	−0.0973071	−0.0486536	−	0.998816i	$-0.515493\pi$
$191$	−1.78976e9	−0.0973071	−0.0486536	+	0.998816i	$0.515493\pi$
$192$	0	0
$193$	−1.53821e10	−0.798007	−0.399004	−	0.916949i	$-0.630644\pi$
$193$	−1.53821e10	−0.798007	−0.399004	+	0.916949i	$0.630644\pi$
$194$	4.36712e10	2.21354
$195$	0	0
$196$	6.66192e9	0.322439
$197$	−6.72162e9	−0.317962	−0.158981	−	0.987282i	$-0.550821\pi$
$197$	−6.72162e9	−0.317962	−0.158981	+	0.987282i	$0.550821\pi$
$198$	0	0
$199$	2.38746e10	1.07919	0.539593	−	0.841926i	$-0.318578\pi$
$199$	2.38746e10	1.07919	0.539593	+	0.841926i	$0.318578\pi$
$200$	4.39721e9	0.194331
$201$	0	0
$202$	2.80657e10	1.18603
$203$	1.72300e10	0.712118
$204$	0	0
$205$	−8.51263e9	−0.336645
$206$	6.59250e10	2.55063
$207$	0	0
$208$	−8.57122e9	−0.317510
$209$	2.06968e10	0.750317
$210$	0	0
$211$	−9.62380e9	−0.334253	−0.167127	−	0.985935i	$-0.553449\pi$
$211$	−9.62380e9	−0.334253	−0.167127	+	0.985935i	$0.553449\pi$
$212$	1.90017e10	0.646073
$213$	0	0
$214$	4.23593e10	1.38066
$215$	−2.57410e9	−0.0821585
$216$	0	0
$217$	−5.76987e10	−1.76643
$218$	3.24548e10	0.973251
$219$	0	0
$220$	1.41431e10	0.407046
$221$	−7.84781e9	−0.221301
$222$	0	0
$223$	3.02591e10	0.819378	0.409689	−	0.912225i	$-0.365637\pi$
$223$	3.02591e10	0.819378	0.409689	+	0.912225i	$0.365637\pi$
$224$	−6.06673e10	−1.61005
$225$	0	0
$226$	−6.46758e10	−1.64913
$227$	1.66730e10	0.416771	0.208385	−	0.978047i	$-0.433179\pi$
$227$	1.66730e10	0.416771	0.208385	+	0.978047i	$0.433179\pi$
$228$	0	0
$229$	4.62782e10	1.11203	0.556015	−	0.831172i	$-0.312330\pi$
$229$	4.62782e10	1.11203	0.556015	+	0.831172i	$0.312330\pi$
$230$	−5.48679e10	−1.29284
$231$	0	0
$232$	7.62840e9	0.172877
$233$	−2.27489e10	−0.505661	−0.252830	−	0.967511i	$-0.581361\pi$
$233$	−2.27489e10	−0.505661	−0.252830	+	0.967511i	$0.581361\pi$
$234$	0	0
$235$	3.24940e10	0.695021
$236$	−2.73938e10	−0.574843
$237$	0	0
$238$	−4.48930e10	−0.906949
$239$	−4.02770e10	−0.798485	−0.399242	−	0.916845i	$-0.630727\pi$
$239$	−4.02770e10	−0.798485	−0.399242	+	0.916845i	$0.630727\pi$
$240$	0	0
$241$	−1.88067e10	−0.359118	−0.179559	−	0.983747i	$-0.557467\pi$
$241$	−1.88067e10	−0.359118	−0.179559	+	0.983747i	$0.557467\pi$
$242$	4.68207e10	0.877544
$243$	0	0
$244$	4.40427e10	0.795463
$245$	8.26574e9	0.146566
$246$	0	0
$247$	2.80107e10	0.478837
$248$	−2.55455e10	−0.428827
$249$	0	0
$250$	8.41002e10	1.36165
$251$	−6.83951e10	−1.08766	−0.543830	−	0.839195i	$-0.683027\pi$
$251$	−6.83951e10	−1.08766	−0.543830	+	0.839195i	$0.683027\pi$
$252$	0	0
$253$	6.74385e10	1.03482
$254$	7.26772e10	1.09559
$255$	0	0
$256$	3.67078e10	0.534169
$257$	8.21993e10	1.17536	0.587678	−	0.809095i	$-0.300042\pi$
$257$	8.21993e10	1.17536	0.587678	+	0.809095i	$0.300042\pi$
$258$	0	0
$259$	1.17501e11	1.62252
$260$	1.91411e10	0.259768
$261$	0	0
$262$	−7.84259e10	−1.02826
$263$	1.78524e10	0.230089	0.115044	−	0.993360i	$-0.463299\pi$
$263$	1.78524e10	0.230089	0.115044	+	0.993360i	$0.463299\pi$
$264$	0	0
$265$	2.35763e10	0.293677
$266$	1.60234e11	1.96240
$267$	0	0
$268$	1.72096e11	2.03782
$269$	−1.12924e11	−1.31492	−0.657462	−	0.753488i	$-0.728370\pi$
$269$	−1.12924e11	−1.31492	−0.657462	+	0.753488i	$0.728370\pi$
$270$	0	0
$271$	−1.05452e11	−1.18766	−0.593831	−	0.804590i	$-0.702385\pi$
$271$	−1.05452e11	−1.18766	−0.593831	+	0.804590i	$0.702385\pi$
$272$	3.83266e10	0.424562
$273$	0	0
$274$	7.78565e10	0.834483
$275$	−4.29101e10	−0.452441
$276$	0	0
$277$	−7.65554e10	−0.781298	−0.390649	−	0.920540i	$-0.627749\pi$
$277$	−7.65554e10	−0.781298	−0.390649	+	0.920540i	$0.627749\pi$
$278$	1.31296e11	1.31841
$279$	0	0
$280$	1.71115e10	0.166370
$281$	1.62567e11	1.55544	0.777721	−	0.628610i	$-0.216376\pi$
$281$	1.62567e11	1.55544	0.777721	+	0.628610i	$0.216376\pi$
$282$	0	0
$283$	8.09281e10	0.749998	0.374999	−	0.927025i	$-0.377643\pi$
$283$	8.09281e10	0.749998	0.374999	+	0.927025i	$0.377643\pi$
$284$	1.15734e11	1.05567
$285$	0	0
$286$	−4.33763e10	−0.383358
$287$	8.10038e10	0.704753
$288$	0	0
$289$	−8.34960e10	−0.704085
$290$	6.05655e10	0.502845
$291$	0	0
$292$	1.67385e10	0.134739
$293$	1.52458e11	1.20849	0.604247	−	0.796797i	$-0.293474\pi$
$293$	1.52458e11	1.20849	0.604247	+	0.796797i	$0.293474\pi$
$294$	0	0
$295$	−3.39888e10	−0.261298
$296$	5.20223e10	0.393892
$297$	0	0
$298$	−1.14546e11	−0.841408
$299$	9.12703e10	0.660403
$300$	0	0
$301$	2.44944e10	0.171996
$302$	7.41972e10	0.513282
$303$	0	0
$304$	−1.36797e11	−0.918640
$305$	5.46458e10	0.361583
$306$	0	0
$307$	2.31912e11	1.49005	0.745025	−	0.667037i	$-0.232438\pi$
$307$	2.31912e11	1.49005	0.745025	+	0.667037i	$0.232438\pi$
$308$	−1.34582e11	−0.852135
$309$	0	0
$310$	−2.02818e11	−1.24732
$311$	−4.82364e10	−0.292384	−0.146192	−	0.989256i	$-0.546702\pi$
$311$	−4.82364e10	−0.292384	−0.146192	+	0.989256i	$0.546702\pi$
$312$	0	0
$313$	2.96278e11	1.74482	0.872408	−	0.488778i	$-0.162557\pi$
$313$	2.96278e11	1.74482	0.872408	+	0.488778i	$0.162557\pi$
$314$	3.42000e10	0.198538
$315$	0	0
$316$	1.60460e11	0.905264
$317$	4.42421e10	0.246076	0.123038	−	0.992402i	$-0.460736\pi$
$317$	4.42421e10	0.246076	0.123038	+	0.992402i	$0.460736\pi$
$318$	0	0
$319$	−7.44415e10	−0.402492
$320$	−1.34382e11	−0.716418
$321$	0	0
$322$	5.22107e11	2.70650
$323$	−1.25251e11	−0.640281
$324$	0	0
$325$	−5.80738e10	−0.288739
$326$	−3.42925e11	−1.68159
$327$	0	0
$328$	3.58637e10	0.171089
$329$	−3.09204e11	−1.45500
$330$	0	0
$331$	1.85279e11	0.848399	0.424199	−	0.905569i	$-0.360556\pi$
$331$	1.85279e11	0.848399	0.424199	+	0.905569i	$0.360556\pi$
$332$	3.29218e11	1.48718
$333$	0	0
$334$	−5.93002e11	−2.60734
$335$	2.13528e11	0.926302
$336$	0	0
$337$	3.97119e11	1.67720	0.838602	−	0.544744i	$-0.183373\pi$
$337$	3.97119e11	1.67720	0.838602	+	0.544744i	$0.183373\pi$
$338$	2.96005e11	1.23360
$339$	0	0
$340$	−8.55902e10	−0.347351
$341$	2.49285e11	0.998394
$342$	0	0
$343$	2.10464e11	0.821020
$344$	1.08447e10	0.0417545
$345$	0	0
$346$	3.92550e11	1.47249
$347$	3.90891e11	1.44735	0.723675	−	0.690141i	$-0.242452\pi$
$347$	3.90891e11	1.44735	0.723675	+	0.690141i	$0.242452\pi$
$348$	0	0
$349$	5.12370e10	0.184871	0.0924355	−	0.995719i	$-0.470535\pi$
$349$	5.12370e10	0.184871	0.0924355	+	0.995719i	$0.470535\pi$
$350$	−3.32208e11	−1.18333
$351$	0	0
$352$	2.62111e11	0.910005
$353$	−4.84133e9	−0.0165950	−0.00829752	−	0.999966i	$-0.502641\pi$
$353$	−4.84133e9	−0.0165950	−0.00829752	+	0.999966i	$0.502641\pi$
$354$	0	0
$355$	1.43596e11	0.479861
$356$	1.46016e10	0.0481808
$357$	0	0
$358$	2.49058e11	0.801359
$359$	3.55635e11	1.13000	0.565001	−	0.825090i	$-0.308876\pi$
$359$	3.55635e11	1.13000	0.565001	+	0.825090i	$0.308876\pi$
$360$	0	0
$361$	1.24364e11	0.385400
$362$	−2.77041e10	−0.0847922
$363$	0	0
$364$	−1.82141e11	−0.543815
$365$	2.07683e10	0.0612466
$366$	0	0
$367$	−3.97521e11	−1.14383	−0.571917	−	0.820312i	$-0.693800\pi$
$367$	−3.97521e11	−1.14383	−0.571917	+	0.820312i	$0.693800\pi$
$368$	−4.45740e11	−1.26697
$369$	0	0
$370$	4.13030e11	1.14571
$371$	−2.24345e11	−0.614801
$372$	0	0
$373$	−5.47884e11	−1.46554	−0.732772	−	0.680474i	$-0.761774\pi$
$373$	−5.47884e11	−1.46554	−0.732772	+	0.680474i	$0.761774\pi$
$374$	1.93959e11	0.512611
$375$	0	0
$376$	−1.36897e11	−0.353222
$377$	−1.00748e11	−0.256862
$378$	0	0
$379$	6.83539e11	1.70171	0.850857	−	0.525397i	$-0.176083\pi$
$379$	6.83539e11	1.70171	0.850857	+	0.525397i	$0.176083\pi$
$380$	3.05492e11	0.751577
$381$	0	0
$382$	5.98656e10	0.143844
$383$	−5.16638e11	−1.22685	−0.613426	−	0.789753i	$-0.710209\pi$
$383$	−5.16638e11	−1.22685	−0.613426	+	0.789753i	$0.710209\pi$
$384$	0	0
$385$	−1.66982e11	−0.387343
$386$	5.14514e11	1.17965
$387$	0	0
$388$	−7.92286e11	−1.77476
$389$	4.39607e11	0.973399	0.486700	−	0.873569i	$-0.338201\pi$
$389$	4.39607e11	0.973399	0.486700	+	0.873569i	$0.338201\pi$
$390$	0	0
$391$	−4.08119e11	−0.883063
$392$	−3.48235e10	−0.0744878
$393$	0	0
$394$	2.24831e11	0.470028
$395$	1.99090e11	0.411493
$396$	0	0
$397$	4.04283e11	0.816823	0.408411	−	0.912798i	$-0.366083\pi$
$397$	4.04283e11	0.816823	0.408411	+	0.912798i	$0.366083\pi$
$398$	−7.98579e11	−1.59531
$399$	0	0
$400$	2.83617e11	0.553940
$401$	8.05560e11	1.55578	0.777890	−	0.628400i	$-0.216290\pi$
$401$	8.05560e11	1.55578	0.777890	+	0.628400i	$0.216290\pi$
$402$	0	0
$403$	3.37379e11	0.637155
$404$	−5.09169e11	−0.950924
$405$	0	0
$406$	−5.76324e11	−1.05269
$407$	−5.07658e11	−0.917057
$408$	0	0
$409$	−4.85519e11	−0.857929	−0.428965	−	0.903321i	$-0.641122\pi$
$409$	−4.85519e11	−0.857929	−0.428965	+	0.903321i	$0.641122\pi$
$410$	2.84739e11	0.497644
$411$	0	0
$412$	−1.19602e12	−2.04503
$413$	3.23428e11	0.547018
$414$	0	0
$415$	4.08476e11	0.676005
$416$	3.54737e11	0.580747
$417$	0	0
$418$	−6.92286e11	−1.10915
$419$	−6.38311e11	−1.01174	−0.505871	−	0.862609i	$-0.668829\pi$
$419$	−6.38311e11	−1.01174	−0.505871	+	0.862609i	$0.668829\pi$
$420$	0	0
$421$	−3.95759e11	−0.613991	−0.306995	−	0.951711i	$-0.599324\pi$
$421$	−3.95759e11	−0.613991	−0.306995	+	0.951711i	$0.599324\pi$
$422$	3.21906e11	0.494110
$423$	0	0
$424$	−9.93268e10	−0.149252
$425$	2.59680e11	0.386090
$426$	0	0
$427$	−5.19994e11	−0.756960
$428$	−7.68485e11	−1.10698
$429$	0	0
$430$	8.61010e10	0.121451
$431$	−5.11706e11	−0.714287	−0.357144	−	0.934049i	$-0.616249\pi$
$431$	−5.11706e11	−0.714287	−0.357144	+	0.934049i	$0.616249\pi$
$432$	0	0
$433$	5.74450e11	0.785337	0.392669	−	0.919680i	$-0.371552\pi$
$433$	5.74450e11	0.785337	0.392669	+	0.919680i	$0.371552\pi$
$434$	1.92996e12	2.61123
$435$	0	0
$436$	−5.88797e11	−0.780327
$437$	1.45668e12	1.91072
$438$	0	0
$439$	7.80007e11	1.00232	0.501162	−	0.865353i	$-0.332906\pi$
$439$	7.80007e11	1.00232	0.501162	+	0.865353i	$0.332906\pi$
$440$	−7.39296e10	−0.0940332
$441$	0	0
$442$	2.62501e11	0.327138
$443$	−1.03032e12	−1.27103	−0.635517	−	0.772087i	$-0.719213\pi$
$443$	−1.03032e12	−1.27103	−0.635517	+	0.772087i	$0.719213\pi$
$444$	0	0
$445$	1.81168e10	0.0219009
$446$	−1.01214e12	−1.21124
$447$	0	0
$448$	1.27874e12	1.49980
$449$	5.64317e11	0.655262	0.327631	−	0.944806i	$-0.393750\pi$
$449$	5.64317e11	0.655262	0.327631	+	0.944806i	$0.393750\pi$
$450$	0	0
$451$	−3.49974e11	−0.398329
$452$	1.17335e12	1.32223
$453$	0	0
$454$	−5.57694e11	−0.616091
$455$	−2.25991e11	−0.247195
$456$	0	0
$457$	−2.62462e11	−0.281478	−0.140739	−	0.990047i	$-0.544948\pi$
$457$	−2.62462e11	−0.281478	−0.140739	+	0.990047i	$0.544948\pi$
$458$	−1.54796e12	−1.64386
$459$	0	0
$460$	9.95417e11	1.03656
$461$	7.04852e11	0.726848	0.363424	−	0.931624i	$-0.381608\pi$
$461$	7.04852e11	0.726848	0.363424	+	0.931624i	$0.381608\pi$
$462$	0	0
$463$	−1.58919e12	−1.60717	−0.803584	−	0.595191i	$-0.797076\pi$
$463$	−1.58919e12	−1.60717	−0.803584	+	0.595191i	$0.797076\pi$
$464$	4.92027e11	0.492785
$465$	0	0
$466$	7.60928e11	0.747492
$467$	1.90216e12	1.85063	0.925317	−	0.379195i	$-0.123799\pi$
$467$	1.90216e12	1.85063	0.925317	+	0.379195i	$0.123799\pi$
$468$	0	0
$469$	−2.03187e12	−1.93918
$470$	−1.08689e12	−1.02741
$471$	0	0
$472$	1.43194e11	0.132797
$473$	−1.05827e11	−0.0972127
$474$	0	0
$475$	−9.26859e11	−0.835396
$476$	8.14452e11	0.727167
$477$	0	0
$478$	1.34722e12	1.18036
$479$	4.06033e11	0.352412	0.176206	−	0.984353i	$-0.443617\pi$
$479$	4.06033e11	0.352412	0.176206	+	0.984353i	$0.443617\pi$
$480$	0	0
$481$	−6.87056e11	−0.585247
$482$	6.29066e11	0.530866
$483$	0	0
$484$	−8.49424e11	−0.703591
$485$	−9.83025e11	−0.806727
$486$	0	0
$487$	−2.54024e11	−0.204642	−0.102321	−	0.994751i	$-0.532627\pi$
$487$	−2.54024e11	−0.204642	−0.102321	+	0.994751i	$0.532627\pi$
$488$	−2.30222e11	−0.183763
$489$	0	0
$490$	−2.76481e11	−0.216662
$491$	−5.49800e11	−0.426911	−0.213456	−	0.976953i	$-0.568472\pi$
$491$	−5.49800e11	−0.426911	−0.213456	+	0.976953i	$0.568472\pi$
$492$	0	0
$493$	4.50499e11	0.343466
$494$	−9.36929e11	−0.707841
$495$	0	0
$496$	−1.64767e12	−1.22237
$497$	−1.36642e12	−1.00457
$498$	0	0
$499$	2.09406e12	1.51195	0.755974	−	0.654601i	$-0.227164\pi$
$499$	2.09406e12	1.51195	0.755974	+	0.654601i	$0.227164\pi$
$500$	−1.52575e12	−1.09174
$501$	0	0
$502$	2.28775e12	1.60783
$503$	−2.16997e12	−1.51146	−0.755730	−	0.654883i	$-0.772718\pi$
$503$	−2.16997e12	−1.51146	−0.755730	+	0.654883i	$0.772718\pi$
$504$	0	0
$505$	−6.31749e11	−0.432248
$506$	−2.25575e12	−1.52973
$507$	0	0
$508$	−1.31851e12	−0.878412
$509$	1.57264e12	1.03848	0.519242	−	0.854627i	$-0.326214\pi$
$509$	1.57264e12	1.03848	0.519242	+	0.854627i	$0.326214\pi$
$510$	0	0
$511$	−1.97625e11	−0.128217
$512$	−2.06473e12	−1.32785
$513$	0	0
$514$	−2.74948e12	−1.73747
$515$	−1.48395e12	−0.929580
$516$	0	0
$517$	1.33590e12	0.822371
$518$	−3.93027e12	−2.39850
$519$	0	0
$520$	−1.00055e11	−0.0600101
$521$	−6.40632e11	−0.380925	−0.190462	−	0.981695i	$-0.560999\pi$
$521$	−6.40632e11	−0.380925	−0.190462	+	0.981695i	$0.560999\pi$
$522$	0	0
$523$	1.66251e12	0.971642	0.485821	−	0.874058i	$-0.338521\pi$
$523$	1.66251e12	0.971642	0.485821	+	0.874058i	$0.338521\pi$
$524$	1.42281e12	0.824433
$525$	0	0
$526$	−5.97144e11	−0.340129
$527$	−1.50861e12	−0.851978
$528$	0	0
$529$	2.94529e12	1.63522
$530$	−7.88603e11	−0.434127
$531$	0	0
$532$	−2.90697e12	−1.57340
$533$	−4.73650e11	−0.254206
$534$	0	0
$535$	−9.53493e11	−0.503183
$536$	−8.99591e11	−0.470764
$537$	0	0
$538$	3.77719e12	1.94379
$539$	3.39824e11	0.173422
$540$	0	0
$541$	−3.01359e12	−1.51250	−0.756251	−	0.654282i	$-0.772971\pi$
$541$	−3.01359e12	−1.51250	−0.756251	+	0.654282i	$0.772971\pi$
$542$	3.52726e12	1.75566
$543$	0	0
$544$	−1.58623e12	−0.776551
$545$	−7.30547e11	−0.354702
$546$	0	0
$547$	5.31804e11	0.253985	0.126993	−	0.991904i	$-0.459468\pi$
$547$	5.31804e11	0.253985	0.126993	+	0.991904i	$0.459468\pi$
$548$	−1.41248e12	−0.669066
$549$	0	0
$550$	1.43530e12	0.668820
$551$	−1.60794e12	−0.743169
$552$	0	0
$553$	−1.89448e12	−0.861446
$554$	2.56070e12	1.15495
$555$	0	0
$556$	−2.38199e12	−1.05707
$557$	4.53326e12	1.99555	0.997775	−	0.0666751i	$-0.0212391\pi$
$557$	4.53326e12	1.99555	0.997775	+	0.0666751i	$0.0212391\pi$
$558$	0	0
$559$	−1.43225e11	−0.0620392
$560$	1.10368e12	0.474238
$561$	0	0
$562$	−5.43770e12	−2.29933
$563$	−1.58678e12	−0.665623	−0.332811	−	0.942993i	$-0.607997\pi$
$563$	−1.58678e12	−0.665623	−0.332811	+	0.942993i	$0.607997\pi$
$564$	0	0
$565$	1.45583e12	0.601025
$566$	−2.70696e12	−1.10868
$567$	0	0
$568$	−6.04970e11	−0.243874
$569$	1.94543e12	0.778054	0.389027	−	0.921226i	$-0.372811\pi$
$569$	1.94543e12	0.778054	0.389027	+	0.921226i	$0.372811\pi$
$570$	0	0
$571$	5.49369e11	0.216273	0.108136	−	0.994136i	$-0.465512\pi$
$571$	5.49369e11	0.216273	0.108136	+	0.994136i	$0.465512\pi$
$572$	7.86935e11	0.307367
$573$	0	0
$574$	−2.70949e12	−1.04180
$575$	−3.02008e12	−1.15216
$576$	0	0
$577$	1.70113e12	0.638922	0.319461	−	0.947599i	$-0.396498\pi$
$577$	1.70113e12	0.638922	0.319461	+	0.947599i	$0.396498\pi$
$578$	2.79285e12	1.04081
$579$	0	0
$580$	−1.09878e12	−0.403168
$581$	−3.88694e12	−1.41519
$582$	0	0
$583$	9.69277e11	0.347488
$584$	−8.74965e10	−0.0311267
$585$	0	0
$586$	−5.09955e12	−1.78646
$587$	3.76857e12	1.31010	0.655051	−	0.755585i	$-0.272647\pi$
$587$	3.76857e12	1.31010	0.655051	+	0.755585i	$0.272647\pi$
$588$	0	0
$589$	5.38458e12	1.84346
$590$	1.13689e12	0.386264
$591$	0	0
$592$	3.35540e12	1.12279
$593$	−2.20370e12	−0.731823	−0.365912	−	0.930650i	$-0.619243\pi$
$593$	−2.20370e12	−0.731823	−0.365912	+	0.930650i	$0.619243\pi$
$594$	0	0
$595$	1.01053e12	0.330538
$596$	2.07810e12	0.674619
$597$	0	0
$598$	−3.05290e12	−0.976240
$599$	−2.10006e12	−0.666515	−0.333258	−	0.942836i	$-0.608148\pi$
$599$	−2.10006e12	−0.666515	−0.333258	+	0.942836i	$0.608148\pi$
$600$	0	0
$601$	−1.35259e12	−0.422892	−0.211446	−	0.977390i	$-0.567817\pi$
$601$	−1.35259e12	−0.422892	−0.211446	+	0.977390i	$0.567817\pi$
$602$	−8.19313e11	−0.254253
$603$	0	0
$604$	−1.34609e12	−0.411536
$605$	−1.05392e12	−0.319822
$606$	0	0
$607$	4.40577e12	1.31726	0.658631	−	0.752466i	$-0.271136\pi$
$607$	4.40577e12	1.31726	0.658631	+	0.752466i	$0.271136\pi$
$608$	5.66162e12	1.68025
$609$	0	0
$610$	−1.82785e12	−0.534509
$611$	1.80799e12	0.524821
$612$	0	0
$613$	2.69654e12	0.771320	0.385660	−	0.922641i	$-0.373974\pi$
$613$	2.69654e12	0.771320	0.385660	+	0.922641i	$0.373974\pi$
$614$	−7.75722e12	−2.20267
$615$	0	0
$616$	7.03493e11	0.196855
$617$	2.92929e12	0.813727	0.406863	−	0.913489i	$-0.366623\pi$
$617$	2.92929e12	0.813727	0.406863	+	0.913489i	$0.366623\pi$
$618$	0	0
$619$	5.71068e12	1.56343	0.781717	−	0.623633i	$-0.214344\pi$
$619$	5.71068e12	1.56343	0.781717	+	0.623633i	$0.214344\pi$
$620$	3.67954e12	1.00007
$621$	0	0
$622$	1.61346e12	0.432216
$623$	−1.72394e11	−0.0458487
$624$	0	0
$625$	8.14411e11	0.213493
$626$	−9.91019e12	−2.57927
$627$	0	0
$628$	−6.20459e11	−0.159182
$629$	3.07221e12	0.782569
$630$	0	0
$631$	6.26095e12	1.57220	0.786101	−	0.618099i	$-0.212097\pi$
$631$	6.26095e12	1.57220	0.786101	+	0.618099i	$0.212097\pi$
$632$	−8.38765e11	−0.209129
$633$	0	0
$634$	−1.47985e12	−0.363762
$635$	−1.63594e12	−0.399287
$636$	0	0
$637$	4.59913e11	0.110675
$638$	2.48999e12	0.594983
$639$	0	0
$640$	1.23069e12	0.289961
$641$	7.96482e12	1.86344	0.931718	−	0.363181i	$-0.118309\pi$
$641$	7.96482e12	1.86344	0.931718	+	0.363181i	$0.118309\pi$
$642$	0	0
$643$	5.28675e12	1.21966	0.609831	−	0.792532i	$-0.291237\pi$
$643$	5.28675e12	1.21966	0.609831	+	0.792532i	$0.291237\pi$
$644$	−9.47210e12	−2.17000
$645$	0	0
$646$	4.18952e12	0.946495
$647$	−2.49240e12	−0.559176	−0.279588	−	0.960120i	$-0.590198\pi$
$647$	−2.49240e12	−0.559176	−0.279588	+	0.960120i	$0.590198\pi$
$648$	0	0
$649$	−1.39736e12	−0.309177
$650$	1.94251e12	0.426828
$651$	0	0
$652$	6.22137e12	1.34825
$653$	4.23455e12	0.911376	0.455688	−	0.890140i	$-0.349393\pi$
$653$	4.23455e12	0.911376	0.455688	+	0.890140i	$0.349393\pi$
$654$	0	0
$655$	1.76534e12	0.374751
$656$	2.31318e12	0.487688
$657$	0	0
$658$	1.03425e13	2.15085
$659$	−9.53023e11	−0.196843	−0.0984213	−	0.995145i	$-0.531379\pi$
$659$	−9.53023e11	−0.196843	−0.0984213	+	0.995145i	$0.531379\pi$
$660$	0	0
$661$	−6.93404e12	−1.41280	−0.706399	−	0.707814i	$-0.749681\pi$
$661$	−6.93404e12	−1.41280	−0.706399	+	0.707814i	$0.749681\pi$
$662$	−6.19739e12	−1.25414
$663$	0	0
$664$	−1.72091e12	−0.343559
$665$	−3.60681e12	−0.715198
$666$	0	0
$667$	−5.23932e12	−1.02496
$668$	1.07583e13	2.09049
$669$	0	0
$670$	−7.14228e12	−1.36931
$671$	2.24662e12	0.427837
$672$	0	0
$673$	−9.52595e11	−0.178995	−0.0894974	−	0.995987i	$-0.528526\pi$
$673$	−9.52595e11	−0.178995	−0.0894974	+	0.995987i	$0.528526\pi$
$674$	−1.32832e13	−2.47933
$675$	0	0
$676$	−5.37014e12	−0.989066
$677$	9.34347e12	1.70946	0.854731	−	0.519072i	$-0.173722\pi$
$677$	9.34347e12	1.70946	0.854731	+	0.519072i	$0.173722\pi$
$678$	0	0
$679$	9.35418e12	1.68885
$680$	4.47401e11	0.0802430
$681$	0	0
$682$	−8.33834e12	−1.47588
$683$	6.37568e12	1.12107	0.560535	−	0.828130i	$-0.310595\pi$
$683$	6.37568e12	1.12107	0.560535	+	0.828130i	$0.310595\pi$
$684$	0	0
$685$	−1.75252e12	−0.304128
$686$	−7.03980e12	−1.21367
$687$	0	0
$688$	6.99474e11	0.119021
$689$	1.31180e12	0.221760
$690$	0	0
$691$	6.11546e12	1.02042	0.510208	−	0.860051i	$-0.329568\pi$
$691$	6.11546e12	1.02042	0.510208	+	0.860051i	$0.329568\pi$
$692$	−7.12166e12	−1.18060
$693$	0	0
$694$	−1.30749e13	−2.13954
$695$	−2.95544e12	−0.480497
$696$	0	0
$697$	2.11795e12	0.339913
$698$	−1.71382e12	−0.273286
$699$	0	0
$700$	6.02695e12	0.948760
$701$	−3.82093e12	−0.597638	−0.298819	−	0.954310i	$-0.596593\pi$
$701$	−3.82093e12	−0.597638	−0.298819	+	0.954310i	$0.596593\pi$
$702$	0	0
$703$	−1.09654e13	−1.69327
$704$	−5.52477e12	−0.847690
$705$	0	0
$706$	1.61937e11	0.0245316
$707$	6.01154e12	0.904896
$708$	0	0
$709$	−6.49775e11	−0.0965728	−0.0482864	−	0.998834i	$-0.515376\pi$
$709$	−6.49775e11	−0.0965728	−0.0482864	+	0.998834i	$0.515376\pi$
$710$	−4.80315e12	−0.709354
$711$	0	0
$712$	−7.63260e10	−0.0111304
$713$	1.75451e13	2.54246
$714$	0	0
$715$	9.76385e11	0.139715
$716$	−4.51843e12	−0.642508
$717$	0	0
$718$	−1.18956e13	−1.67042
$719$	−3.00170e12	−0.418878	−0.209439	−	0.977822i	$-0.567164\pi$
$719$	−3.00170e12	−0.418878	−0.209439	+	0.977822i	$0.567164\pi$
$720$	0	0
$721$	1.41208e13	1.94604
$722$	−4.15984e12	−0.569717
$723$	0	0
$724$	5.02610e11	0.0679841
$725$	3.33370e12	0.448131
$726$	0	0
$727$	−1.31825e13	−1.75022	−0.875109	−	0.483925i	$-0.839211\pi$
$727$	−1.31825e13	−1.75022	−0.875109	+	0.483925i	$0.839211\pi$
$728$	9.52096e11	0.125629
$729$	0	0
$730$	−6.94676e11	−0.0905377
$731$	6.40438e11	0.0829562
$732$	0	0
$733$	1.12951e13	1.44519	0.722593	−	0.691274i	$-0.242950\pi$
$733$	1.12951e13	1.44519	0.722593	+	0.691274i	$0.242950\pi$
$734$	1.32967e13	1.69087
$735$	0	0
$736$	1.84479e13	2.31737
$737$	8.77863e12	1.09603
$738$	0	0
$739$	−1.22652e13	−1.51278	−0.756388	−	0.654124i	$-0.773038\pi$
$739$	−1.22652e13	−1.51278	−0.756388	+	0.654124i	$0.773038\pi$
$740$	−7.49321e12	−0.918598
$741$	0	0
$742$	7.50412e12	0.908829
$743$	1.25794e13	1.51430	0.757149	−	0.653242i	$-0.226592\pi$
$743$	1.25794e13	1.51430	0.757149	+	0.653242i	$0.226592\pi$
$744$	0	0
$745$	2.57839e12	0.306652
$746$	1.83262e13	2.16644
$747$	0	0
$748$	−3.51882e12	−0.410998
$749$	9.07317e12	1.05339
$750$	0	0
$751$	1.42829e13	1.63846	0.819231	−	0.573463i	$-0.194400\pi$
$751$	1.42829e13	1.63846	0.819231	+	0.573463i	$0.194400\pi$
$752$	−8.82976e12	−1.00686
$753$	0	0
$754$	3.36992e12	0.379706
$755$	−1.67015e12	−0.187066
$756$	0	0
$757$	−1.33564e12	−0.147828	−0.0739142	−	0.997265i	$-0.523549\pi$
$757$	−1.33564e12	−0.147828	−0.0739142	+	0.997265i	$0.523549\pi$
$758$	−2.28637e13	−2.51556
$759$	0	0
$760$	−1.59688e12	−0.173625
$761$	−1.24325e13	−1.34378	−0.671888	−	0.740653i	$-0.734516\pi$
$761$	−1.24325e13	−1.34378	−0.671888	+	0.740653i	$0.734516\pi$
$762$	0	0
$763$	6.95168e12	0.742556
$764$	−1.08609e12	−0.115330
$765$	0	0
$766$	1.72810e13	1.81359
$767$	−1.89116e12	−0.197310
$768$	0	0
$769$	−1.49843e13	−1.54514	−0.772569	−	0.634931i	$-0.781028\pi$
$769$	−1.49843e13	−1.54514	−0.772569	+	0.634931i	$0.781028\pi$
$770$	5.58537e12	0.572590
$771$	0	0
$772$	−9.33435e12	−0.945815
$773$	−8.29355e12	−0.835473	−0.417737	−	0.908568i	$-0.637177\pi$
$773$	−8.29355e12	−0.835473	−0.417737	+	0.908568i	$0.637177\pi$
$774$	0	0
$775$	−1.11637e13	−1.11160
$776$	4.14148e12	0.409994
$777$	0	0
$778$	−1.47044e13	−1.43893
$779$	−7.55946e12	−0.735482
$780$	0	0
$781$	5.90358e12	0.567788
$782$	1.36512e13	1.30539
$783$	0	0
$784$	−2.24609e12	−0.212327
$785$	−7.69832e11	−0.0723573
$786$	0	0
$787$	−1.33986e12	−0.124501	−0.0622505	−	0.998061i	$-0.519828\pi$
$787$	−1.33986e12	−0.124501	−0.0622505	+	0.998061i	$0.519828\pi$
$788$	−4.07890e12	−0.376856
$789$	0	0
$790$	−6.65936e12	−0.608290
$791$	−1.38533e13	−1.25822
$792$	0	0
$793$	3.04054e12	0.273037
$794$	−1.35228e13	−1.20747
$795$	0	0
$796$	1.44879e13	1.27907
$797$	3.09254e12	0.271489	0.135745	−	0.990744i	$-0.456657\pi$
$797$	3.09254e12	0.271489	0.135745	+	0.990744i	$0.456657\pi$
$798$	0	0
$799$	−8.08453e12	−0.701769
$800$	−1.17381e13	−1.01319
$801$	0	0
$802$	−2.69452e13	−2.29983
$803$	8.53832e11	0.0724690
$804$	0	0
$805$	−1.17525e13	−0.986387
$806$	−1.12850e13	−0.941874
$807$	0	0
$808$	2.66155e12	0.219677
$809$	1.40195e13	1.15071	0.575353	−	0.817905i	$-0.304865\pi$
$809$	1.40195e13	1.15071	0.575353	+	0.817905i	$0.304865\pi$
$810$	0	0
$811$	−2.03904e13	−1.65513	−0.827565	−	0.561370i	$-0.810274\pi$
$811$	−2.03904e13	−1.65513	−0.827565	+	0.561370i	$0.810274\pi$
$812$	1.04557e13	0.844017
$813$	0	0
$814$	1.69806e13	1.35564
$815$	7.71914e12	0.612857
$816$	0	0
$817$	−2.28588e12	−0.179495
$818$	1.62401e13	1.26823
$819$	0	0
$820$	−5.16575e12	−0.398998
$821$	−2.45678e13	−1.88721	−0.943607	−	0.331067i	$-0.892592\pi$
$821$	−2.45678e13	−1.88721	−0.943607	+	0.331067i	$0.892592\pi$
$822$	0	0
$823$	−1.21005e13	−0.919399	−0.459699	−	0.888075i	$-0.652043\pi$
$823$	−1.21005e13	−0.919399	−0.459699	+	0.888075i	$0.652043\pi$
$824$	6.25187e12	0.472430
$825$	0	0
$826$	−1.08183e13	−0.808629
$827$	4.05700e12	0.301599	0.150800	−	0.988564i	$-0.451815\pi$
$827$	4.05700e12	0.301599	0.150800	+	0.988564i	$0.451815\pi$
$828$	0	0
$829$	1.18554e13	0.871809	0.435904	−	0.899993i	$-0.356429\pi$
$829$	1.18554e13	0.871809	0.435904	+	0.899993i	$0.356429\pi$
$830$	−1.36631e13	−0.999305
$831$	0	0
$832$	−7.47713e12	−0.540979
$833$	−2.05652e12	−0.147990
$834$	0	0
$835$	1.33483e13	0.950247
$836$	1.25595e13	0.889291
$837$	0	0
$838$	2.13508e13	1.49561
$839$	1.24519e13	0.867575	0.433787	−	0.901015i	$-0.357177\pi$
$839$	1.24519e13	0.867575	0.433787	+	0.901015i	$0.357177\pi$
$840$	0	0
$841$	−8.72376e12	−0.601342
$842$	1.32377e13	0.907632
$843$	0	0
$844$	−5.84004e12	−0.396164
$845$	−6.66297e12	−0.449586
$846$	0	0
$847$	1.00288e13	0.669535
$848$	−6.40651e12	−0.425442
$849$	0	0
$850$	−8.68602e12	−0.570737
$851$	−3.57298e13	−2.33533
$852$	0	0
$853$	7.48447e12	0.484050	0.242025	−	0.970270i	$-0.422188\pi$
$853$	7.48447e12	0.484050	0.242025	+	0.970270i	$0.422188\pi$
$854$	1.73933e13	1.11898
$855$	0	0
$856$	4.01706e12	0.255727
$857$	−1.28244e13	−0.812129	−0.406064	−	0.913844i	$-0.633099\pi$
$857$	−1.28244e13	−0.812129	−0.406064	+	0.913844i	$0.633099\pi$
$858$	0	0
$859$	1.30938e13	0.820536	0.410268	−	0.911965i	$-0.365435\pi$
$859$	1.30938e13	0.820536	0.410268	+	0.911965i	$0.365435\pi$
$860$	−1.56205e12	−0.0973760
$861$	0	0
$862$	1.71160e13	1.05589
$863$	2.48587e13	1.52556	0.762780	−	0.646658i	$-0.223834\pi$
$863$	2.48587e13	1.52556	0.762780	+	0.646658i	$0.223834\pi$
$864$	0	0
$865$	−8.83617e12	−0.536650
$866$	−1.92147e13	−1.16092
$867$	0	0
$868$	−3.50135e13	−2.09361
$869$	8.18506e12	0.486893
$870$	0	0
$871$	1.18809e13	0.699465
$872$	3.07779e12	0.180266
$873$	0	0
$874$	−4.87243e13	−2.82452
$875$	1.80139e13	1.03889
$876$	0	0
$877$	2.55056e13	1.45592	0.727959	−	0.685621i	$-0.240469\pi$
$877$	2.55056e13	1.45592	0.727959	+	0.685621i	$0.240469\pi$
$878$	−2.60904e13	−1.48168
$879$	0	0
$880$	−4.76841e12	−0.268041
$881$	4.40986e12	0.246623	0.123311	−	0.992368i	$-0.460649\pi$
$881$	4.40986e12	0.246623	0.123311	+	0.992368i	$0.460649\pi$
$882$	0	0
$883$	7.48100e12	0.414130	0.207065	−	0.978327i	$-0.433609\pi$
$883$	7.48100e12	0.414130	0.207065	+	0.978327i	$0.433609\pi$
$884$	−4.76231e12	−0.262291
$885$	0	0
$886$	3.44633e13	1.87890
$887$	−1.64901e13	−0.894473	−0.447237	−	0.894416i	$-0.647592\pi$
$887$	−1.64901e13	−0.894473	−0.447237	+	0.894416i	$0.647592\pi$
$888$	0	0
$889$	1.55671e13	0.835893
$890$	−6.05989e11	−0.0323750
$891$	0	0
$892$	1.83622e13	0.971144
$893$	2.88556e13	1.51844
$894$	0	0
$895$	−5.60621e12	−0.292056
$896$	−1.17109e13	−0.607023
$897$	0	0
$898$	−1.88758e13	−0.968641
$899$	−1.93671e13	−0.988884
$900$	0	0
$901$	−5.86580e12	−0.296528
$902$	1.17063e13	0.588829
$903$	0	0
$904$	−6.13340e12	−0.305452
$905$	6.23610e11	0.0309026
$906$	0	0
$907$	−2.16035e13	−1.05997	−0.529983	−	0.848008i	$-0.677802\pi$
$907$	−2.16035e13	−1.05997	−0.529983	+	0.848008i	$0.677802\pi$
$908$	1.01177e13	0.493965
$909$	0	0
$910$	7.55915e12	0.365415
$911$	6.95722e12	0.334659	0.167330	−	0.985901i	$-0.446486\pi$
$911$	6.95722e12	0.334659	0.167330	+	0.985901i	$0.446486\pi$
$912$	0	0
$913$	1.67934e13	0.799872
$914$	8.77910e12	0.416095
$915$	0	0
$916$	2.80831e13	1.31800
$917$	−1.67985e13	−0.784527
$918$	0	0
$919$	8.46725e12	0.391582	0.195791	−	0.980646i	$-0.437273\pi$
$919$	8.46725e12	0.391582	0.195791	+	0.980646i	$0.437273\pi$
$920$	−5.20329e12	−0.239460
$921$	0	0
$922$	−2.35766e13	−1.07446
$923$	7.98982e12	0.362351
$924$	0	0
$925$	2.27343e13	1.02104
$926$	5.31568e13	2.37580
$927$	0	0
$928$	−2.03635e13	−0.901336
$929$	3.72600e13	1.64124	0.820619	−	0.571475i	$-0.193629\pi$
$929$	3.72600e13	1.64124	0.820619	+	0.571475i	$0.193629\pi$
$930$	0	0
$931$	7.34022e12	0.320210
$932$	−1.38048e13	−0.599319
$933$	0	0
$934$	−6.36252e13	−2.73570
$935$	−4.36595e12	−0.186822
$936$	0	0
$937$	−1.23351e13	−0.522774	−0.261387	−	0.965234i	$-0.584180\pi$
$937$	−1.23351e13	−0.522774	−0.261387	+	0.965234i	$0.584180\pi$
$938$	6.79639e13	2.86659
$939$	0	0
$940$	1.97184e13	0.823753
$941$	1.46321e13	0.608348	0.304174	−	0.952617i	$-0.401620\pi$
$941$	1.46321e13	0.608348	0.304174	+	0.952617i	$0.401620\pi$
$942$	0	0
$943$	−2.46318e13	−1.01436
$944$	9.23594e12	0.378536
$945$	0	0
$946$	3.53982e12	0.143705
$947$	1.11462e13	0.450353	0.225176	−	0.974318i	$-0.427704\pi$
$947$	1.11462e13	0.450353	0.225176	+	0.974318i	$0.427704\pi$
$948$	0	0
$949$	1.15556e12	0.0462483
$950$	3.10025e13	1.23492
$951$	0	0
$952$	−4.25734e12	−0.167986
$953$	−3.70196e13	−1.45383	−0.726915	−	0.686728i	$-0.759046\pi$
$953$	−3.70196e13	−1.45383	−0.726915	+	0.686728i	$0.759046\pi$
$954$	0	0
$955$	−1.34756e12	−0.0524242
$956$	−2.44414e13	−0.946381
$957$	0	0
$958$	−1.35814e13	−0.520953
$959$	1.66765e13	0.636681
$960$	0	0
$961$	3.84157e13	1.45296
$962$	2.29813e13	0.865142
$963$	0	0
$964$	−1.14126e13	−0.425634
$965$	−1.15815e13	−0.429926
$966$	0	0
$967$	−2.16109e13	−0.794792	−0.397396	−	0.917647i	$-0.630086\pi$
$967$	−2.16109e13	−0.794792	−0.397396	+	0.917647i	$0.630086\pi$
$968$	4.44015e12	0.162539
$969$	0	0
$970$	3.28812e13	1.19254
$971$	−1.75506e13	−0.633586	−0.316793	−	0.948495i	$-0.602606\pi$
$971$	−1.75506e13	−0.633586	−0.316793	+	0.948495i	$0.602606\pi$
$972$	0	0
$973$	2.81231e13	1.00590
$974$	8.49684e12	0.302512
$975$	0	0
$976$	−1.48492e13	−0.523816
$977$	2.50109e13	0.878219	0.439110	−	0.898433i	$-0.355294\pi$
$977$	2.50109e13	0.878219	0.439110	+	0.898433i	$0.355294\pi$
$978$	0	0
$979$	7.44825e11	0.0259139
$980$	5.01593e12	0.173714
$981$	0	0
$982$	1.83902e13	0.631081
$983$	2.10182e13	0.717966	0.358983	−	0.933344i	$-0.383124\pi$
$983$	2.10182e13	0.717966	0.358983	+	0.933344i	$0.383124\pi$
$984$	0	0
$985$	−5.06088e12	−0.171302
$986$	−1.50687e13	−0.507728
$987$	0	0
$988$	1.69978e13	0.567528
$989$	−7.44831e12	−0.247557
$990$	0	0
$991$	−5.45177e13	−1.79559	−0.897793	−	0.440417i	$-0.854830\pi$
$991$	−5.45177e13	−1.79559	−0.897793	+	0.440417i	$0.854830\pi$
$992$	6.81922e13	2.23580
$993$	0	0
$994$	4.57054e13	1.48501
$995$	1.79757e13	0.581411
$996$	0	0
$997$	−6.06106e13	−1.94276	−0.971382	−	0.237522i	$-0.923665\pi$
$997$	−6.06106e13	−1.94276	−0.971382	+	0.237522i	$0.923665\pi$
$998$	−7.00442e13	−2.23504
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.c.1.2		15
3.2	odd	2		43.10.a.a.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.14	✓	15	3.2	odd	2
387.10.a.c.1.2		15	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-33.4490 q^{2} +606.833 q^{4} +752.925 q^{5} -7164.62 q^{7} -3172.07 q^{8} +O(q^{10})\)	\(q-33.4490 q^{2} +606.833 q^{4} +752.925 q^{5} -7164.62 q^{7} -3172.07 q^{8} -25184.6 q^{10} +30954.5 q^{11} +41893.4 q^{13} +239649. q^{14} -204596. q^{16} -187328. q^{17} +668619. q^{19} +456900. q^{20} -1.03540e6 q^{22} +2.17863e6 q^{23} -1.38623e6 q^{25} -1.40129e6 q^{26} -4.34773e6 q^{28} -2.40487e6 q^{29} +8.05328e6 q^{31} +8.46763e6 q^{32} +6.26594e6 q^{34} -5.39442e6 q^{35} -1.64001e7 q^{37} -2.23646e7 q^{38} -2.38833e6 q^{40} -1.13061e7 q^{41} -3.41880e6 q^{43} +1.87842e7 q^{44} -7.28730e7 q^{46} +4.31570e7 q^{47} +1.09782e7 q^{49} +4.63679e7 q^{50} +2.54223e7 q^{52} +3.13129e7 q^{53} +2.33064e7 q^{55} +2.27267e7 q^{56} +8.04403e7 q^{58} -4.51423e7 q^{59} +7.25780e7 q^{61} -2.69374e8 q^{62} -1.78480e8 q^{64} +3.15426e7 q^{65} +2.83598e8 q^{67} -1.13677e8 q^{68} +1.80438e8 q^{70} +1.90718e8 q^{71} +2.75834e7 q^{73} +5.48567e8 q^{74} +4.05740e8 q^{76} -2.21777e8 q^{77} +2.64422e8 q^{79} -1.54046e8 q^{80} +3.78177e8 q^{82} +5.42519e8 q^{83} -1.41044e8 q^{85} +1.14355e8 q^{86} -9.81898e7 q^{88} +2.40619e7 q^{89} -3.00150e8 q^{91} +1.32207e9 q^{92} -1.44356e9 q^{94} +5.03420e8 q^{95} -1.30561e9 q^{97} -3.67209e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8}+O(q^{10}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8	\( 15 q + 32 q^{2} + 3242 q^{4} + 4717 q^{5} - 9680 q^{7} + 20394 q^{8} - 36237 q^{10} + 104484 q^{11} - 116174 q^{13} - 416064 q^{14} + 996762 q^{16} + 884265 q^{17} - 689535 q^{19} + 3077879 q^{20} - 7276218 q^{22} + 2504077 q^{23} + 1315350 q^{25} + 13343414 q^{26} - 28059568 q^{28} + 18406221 q^{29} - 12033699 q^{31} + 18952630 q^{32} - 30383125 q^{34} + 27855546 q^{35} - 8722847 q^{37} + 63941843 q^{38} - 39665611 q^{40} + 18689389 q^{41} - 51282015 q^{43} + 68723220 q^{44} - 2067521 q^{46} + 104960741 q^{47} + 92663095 q^{49} + 42446347 q^{50} + 149226080 q^{52} + 215907800 q^{53} + 384379852 q^{55} - 430441344 q^{56} + 295963139 q^{58} - 185924544 q^{59} + 247538102 q^{61} - 139798853 q^{62} + 848556290 q^{64} - 94294394 q^{65} + 467904656 q^{67} + 88234341 q^{68} + 647526126 q^{70} + 8252944 q^{71} - 715627902 q^{73} - 725122989 q^{74} + 346300359 q^{76} + 1236779964 q^{77} + 560681783 q^{79} + 1157214179 q^{80} + 941346367 q^{82} + 1442854698 q^{83} + 699302088 q^{85} - 109401632 q^{86} - 1464507256 q^{88} + 396710008 q^{89} - 3278076852 q^{91} - 155864647 q^{92} + 4666638949 q^{94} + 3854114395 q^{95} - 3063837815 q^{97} + 6161086984 q^{98}+O(q^{100}) \) 15 * q + 32 * q^2 + 3242 * q^4 + 4717 * q^5 - 9680 * q^7 + 20394 * q^8 - 36237 * q^10 + 104484 * q^11 - 116174 * q^13 - 416064 * q^14 + 996762 * q^16 + 884265 * q^17 - 689535 * q^19 + 3077879 * q^20 - 7276218 * q^22 + 2504077 * q^23 + 1315350 * q^25 + 13343414 * q^26 - 28059568 * q^28 + 18406221 * q^29 - 12033699 * q^31 + 18952630 * q^32 - 30383125 * q^34 + 27855546 * q^35 - 8722847 * q^37 + 63941843 * q^38 - 39665611 * q^40 + 18689389 * q^41 - 51282015 * q^43 + 68723220 * q^44 - 2067521 * q^46 + 104960741 * q^47 + 92663095 * q^49 + 42446347 * q^50 + 149226080 * q^52 + 215907800 * q^53 + 384379852 * q^55 - 430441344 * q^56 + 295963139 * q^58 - 185924544 * q^59 + 247538102 * q^61 - 139798853 * q^62 + 848556290 * q^64 - 94294394 * q^65 + 467904656 * q^67 + 88234341 * q^68 + 647526126 * q^70 + 8252944 * q^71 - 715627902 * q^73 - 725122989 * q^74 + 346300359 * q^76 + 1236779964 * q^77 + 560681783 * q^79 + 1157214179 * q^80 + 941346367 * q^82 + 1442854698 * q^83 + 699302088 * q^85 - 109401632 * q^86 - 1464507256 * q^88 + 396710008 * q^89 - 3278076852 * q^91 - 155864647 * q^92 + 4666638949 * q^94 + 3854114395 * q^95 - 3063837815 * q^97 + 6161086984 * q^98

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