LMFDB - Embedded newform 70.6.a.h.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,6,Mod(1,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	70.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.2268673869$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1129}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 282 $ x^2 - x - 282
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$17.3003$ of defining polynomial
Character	$\chi$	$=$	70.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} -14.3003 q^{3} +16.0000 q^{4} +25.0000 q^{5} -57.2012 q^{6} +49.0000 q^{7} +64.0000 q^{8} -38.5015 q^{9} +100.000 q^{10} +425.904 q^{11} -228.805 q^{12} +399.303 q^{13} +196.000 q^{14} -357.507 q^{15} +256.000 q^{16} +1751.52 q^{17} -154.006 q^{18} +2874.23 q^{19} +400.000 q^{20} -700.715 q^{21} +1703.62 q^{22} -2313.43 q^{23} -915.219 q^{24} +625.000 q^{25} +1597.21 q^{26} +4025.56 q^{27} +784.000 q^{28} -2127.93 q^{29} -1430.03 q^{30} -10262.5 q^{31} +1024.00 q^{32} -6090.55 q^{33} +7006.08 q^{34} +1225.00 q^{35} -616.024 q^{36} -7266.05 q^{37} +11496.9 q^{38} -5710.16 q^{39} +1600.00 q^{40} -5893.44 q^{41} -2802.86 q^{42} +20157.7 q^{43} +6814.46 q^{44} -962.537 q^{45} -9253.72 q^{46} +20056.5 q^{47} -3660.88 q^{48} +2401.00 q^{49} +2500.00 q^{50} -25047.2 q^{51} +6388.85 q^{52} -33954.9 q^{53} +16102.2 q^{54} +10647.6 q^{55} +3136.00 q^{56} -41102.4 q^{57} -8511.71 q^{58} -4319.34 q^{59} -5720.12 q^{60} -12253.6 q^{61} -41050.1 q^{62} -1886.57 q^{63} +4096.00 q^{64} +9982.58 q^{65} -24362.2 q^{66} -17533.8 q^{67} +28024.3 q^{68} +33082.7 q^{69} +4900.00 q^{70} +1658.18 q^{71} -2464.10 q^{72} -8246.91 q^{73} -29064.2 q^{74} -8937.69 q^{75} +45987.7 q^{76} +20869.3 q^{77} -22840.6 q^{78} -9168.61 q^{79} +6400.00 q^{80} -48210.8 q^{81} -23573.7 q^{82} +95203.2 q^{83} -11211.4 q^{84} +43788.0 q^{85} +80631.0 q^{86} +30430.0 q^{87} +27257.8 q^{88} -14441.8 q^{89} -3850.15 q^{90} +19565.9 q^{91} -37014.9 q^{92} +146757. q^{93} +80226.1 q^{94} +71855.8 q^{95} -14643.5 q^{96} +62132.4 q^{97} +9604.00 q^{98} -16397.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 5 q^{3} + 32 q^{4} + 50 q^{5} + 20 q^{6} + 98 q^{7} + 128 q^{8} + 91 q^{9} + 200 q^{10} + 415 q^{11} + 80 q^{12} + 429 q^{13} + 392 q^{14} + 125 q^{15} + 512 q^{16} + 1319 q^{17} + 364 q^{18}+ \cdots - 17810 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 5 * q^3 + 32 * q^4 + 50 * q^5 + 20 * q^6 + 98 * q^7 + 128 * q^8 + 91 * q^9 + 200 * q^10 + 415 * q^11 + 80 * q^12 + 429 * q^13 + 392 * q^14 + 125 * q^15 + 512 * q^16 + 1319 * q^17 + 364 * q^18 + 1918 * q^19 + 800 * q^20 + 245 * q^21 + 1660 * q^22 - 1334 * q^23 + 320 * q^24 + 1250 * q^25 + 1716 * q^26 + 1835 * q^27 + 1568 * q^28 - 1131 * q^29 + 500 * q^30 - 5472 * q^31 + 2048 * q^32 - 6301 * q^33 + 5276 * q^34 + 2450 * q^35 + 1456 * q^36 - 9156 * q^37 + 7672 * q^38 - 5137 * q^39 + 3200 * q^40 - 7822 * q^41 + 980 * q^42 + 2078 * q^43 + 6640 * q^44 + 2275 * q^45 - 5336 * q^46 - 8507 * q^47 + 1280 * q^48 + 4802 * q^49 + 5000 * q^50 - 33395 * q^51 + 6864 * q^52 - 34242 * q^53 + 7340 * q^54 + 10375 * q^55 + 6272 * q^56 - 59558 * q^57 - 4524 * q^58 + 6952 * q^59 + 2000 * q^60 - 45138 * q^61 - 21888 * q^62 + 4459 * q^63 + 8192 * q^64 + 10725 * q^65 - 25204 * q^66 - 54556 * q^67 + 21104 * q^68 + 51986 * q^69 + 9800 * q^70 - 62272 * q^71 + 5824 * q^72 + 40896 * q^73 - 36624 * q^74 + 3125 * q^75 + 30688 * q^76 + 20335 * q^77 - 20548 * q^78 + 62069 * q^79 + 12800 * q^80 - 121958 * q^81 - 31288 * q^82 + 189600 * q^83 + 3920 * q^84 + 32975 * q^85 + 8312 * q^86 + 49671 * q^87 + 26560 * q^88 + 64190 * q^89 + 9100 * q^90 + 21021 * q^91 - 21344 * q^92 + 239216 * q^93 - 34028 * q^94 + 47950 * q^95 + 5120 * q^96 + 155547 * q^97 + 19208 * q^98 - 17810 * q^99

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−14.3003	−0.917365	−0.458682	−	0.888600i	$-0.651678\pi$
$3$	−14.3003	−0.917365	−0.458682	+	0.888600i	$0.651678\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−57.2012	−0.648675
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	64.0000	0.353553
$9$	−38.5015	−0.158442
$10$	100.000	0.316228
$11$	425.904	1.06128	0.530640	−	0.847597i	$-0.321952\pi$
$11$	425.904	1.06128	0.530640	+	0.847597i	$0.321952\pi$
$12$	−228.805	−0.458682
$13$	399.303	0.655307	0.327653	−	0.944798i	$-0.393742\pi$
$13$	399.303	0.655307	0.327653	+	0.944798i	$0.393742\pi$
$14$	196.000	0.267261
$15$	−357.507	−0.410258
$16$	256.000	0.250000
$17$	1751.52	1.46992	0.734958	−	0.678112i	$-0.237202\pi$
$17$	1751.52	1.46992	0.734958	+	0.678112i	$0.237202\pi$
$18$	−154.006	−0.112036
$19$	2874.23	1.82658	0.913289	−	0.407313i	$-0.133534\pi$
$19$	2874.23	1.82658	0.913289	+	0.407313i	$0.133534\pi$
$20$	400.000	0.223607
$21$	−700.715	−0.346731
$22$	1703.62	0.750438
$23$	−2313.43	−0.911878	−0.455939	−	0.890011i	$-0.650696\pi$
$23$	−2313.43	−0.911878	−0.455939	+	0.890011i	$0.650696\pi$
$24$	−915.219	−0.324337
$25$	625.000	0.200000
$26$	1597.21	0.463372
$27$	4025.56	1.06271
$28$	784.000	0.188982
$29$	−2127.93	−0.469853	−0.234926	−	0.972013i	$-0.575485\pi$
$29$	−2127.93	−0.469853	−0.234926	+	0.972013i	$0.575485\pi$
$30$	−1430.03	−0.290096
$31$	−10262.5	−1.91801	−0.959004	−	0.283393i	$-0.908540\pi$
$31$	−10262.5	−1.91801	−0.959004	+	0.283393i	$0.908540\pi$
$32$	1024.00	0.176777
$33$	−6090.55	−0.973580
$34$	7006.08	1.03939
$35$	1225.00	0.169031
$36$	−616.024	−0.0792212
$37$	−7266.05	−0.872557	−0.436279	−	0.899812i	$-0.643704\pi$
$37$	−7266.05	−0.872557	−0.436279	+	0.899812i	$0.643704\pi$
$38$	11496.9	1.29159
$39$	−5710.16	−0.601155
$40$	1600.00	0.158114
$41$	−5893.44	−0.547531	−0.273766	−	0.961796i	$-0.588269\pi$
$41$	−5893.44	−0.547531	−0.273766	+	0.961796i	$0.588269\pi$
$42$	−2802.86	−0.245176
$43$	20157.7	1.66253	0.831267	−	0.555873i	$-0.187616\pi$
$43$	20157.7	1.66253	0.831267	+	0.555873i	$0.187616\pi$
$44$	6814.46	0.530640
$45$	−962.537	−0.0708576
$46$	−9253.72	−0.644795
$47$	20056.5	1.32438	0.662188	−	0.749338i	$-0.269628\pi$
$47$	20056.5	1.32438	0.662188	+	0.749338i	$0.269628\pi$
$48$	−3660.88	−0.229341
$49$	2401.00	0.142857
$50$	2500.00	0.141421
$51$	−25047.2	−1.34845
$52$	6388.85	0.327653
$53$	−33954.9	−1.66040	−0.830200	−	0.557466i	$-0.811774\pi$
$53$	−33954.9	−1.66040	−0.830200	+	0.557466i	$0.811774\pi$
$54$	16102.2	0.751452
$55$	10647.6	0.474619
$56$	3136.00	0.133631
$57$	−41102.4	−1.67564
$58$	−8511.71	−0.332236
$59$	−4319.34	−0.161543	−0.0807713	−	0.996733i	$-0.525738\pi$
$59$	−4319.34	−0.161543	−0.0807713	+	0.996733i	$0.525738\pi$
$60$	−5720.12	−0.205129
$61$	−12253.6	−0.421638	−0.210819	−	0.977525i	$-0.567613\pi$
$61$	−12253.6	−0.421638	−0.210819	+	0.977525i	$0.567613\pi$
$62$	−41050.1	−1.35624
$63$	−1886.57	−0.0598856
$64$	4096.00	0.125000
$65$	9982.58	0.293062
$66$	−24362.2	−0.688425
$67$	−17533.8	−0.477188	−0.238594	−	0.971119i	$-0.576687\pi$
$67$	−17533.8	−0.477188	−0.238594	+	0.971119i	$0.576687\pi$
$68$	28024.3	0.734958
$69$	33082.7	0.836524
$70$	4900.00	0.119523
$71$	1658.18	0.0390379	0.0195189	−	0.999809i	$-0.493787\pi$
$71$	1658.18	0.0390379	0.0195189	+	0.999809i	$0.493787\pi$
$72$	−2464.10	−0.0560178
$73$	−8246.91	−0.181127	−0.0905637	−	0.995891i	$-0.528867\pi$
$73$	−8246.91	−0.181127	−0.0905637	+	0.995891i	$0.528867\pi$
$74$	−29064.2	−0.616991
$75$	−8937.69	−0.183473
$76$	45987.7	0.913289
$77$	20869.3	0.401126
$78$	−22840.6	−0.425081
$79$	−9168.61	−0.165286	−0.0826430	−	0.996579i	$-0.526336\pi$
$79$	−9168.61	−0.165286	−0.0826430	+	0.996579i	$0.526336\pi$
$80$	6400.00	0.111803
$81$	−48210.8	−0.816454
$82$	−23573.7	−0.387163
$83$	95203.2	1.51690	0.758449	−	0.651732i	$-0.225957\pi$
$83$	95203.2	1.51690	0.758449	+	0.651732i	$0.225957\pi$
$84$	−11211.4	−0.173366
$85$	43788.0	0.657367
$86$	80631.0	1.17559
$87$	30430.0	0.431026
$88$	27257.8	0.375219
$89$	−14441.8	−0.193262	−0.0966311	−	0.995320i	$-0.530807\pi$
$89$	−14441.8	−0.193262	−0.0966311	+	0.995320i	$0.530807\pi$
$90$	−3850.15	−0.0501039
$91$	19565.9	0.247683
$92$	−37014.9	−0.455939
$93$	146757.	1.75951
$94$	80226.1	0.936475
$95$	71855.8	0.816870
$96$	−14643.5	−0.162169
$97$	62132.4	0.670485	0.335242	−	0.942132i	$-0.391182\pi$
$97$	62132.4	0.670485	0.335242	+	0.942132i	$0.391182\pi$
$98$	9604.00	0.101015
$99$	−16397.9	−0.168152
$100$	10000.0	0.100000
$101$	−108138.	−1.05481	−0.527404	−	0.849615i	$-0.676835\pi$
$101$	−108138.	−1.05481	−0.527404	+	0.849615i	$0.676835\pi$
$102$	−100189.	−0.953498
$103$	138034.	1.28201	0.641005	−	0.767536i	$-0.278518\pi$
$103$	138034.	1.28201	0.641005	+	0.767536i	$0.278518\pi$
$104$	25555.4	0.231686
$105$	−17517.9	−0.155063
$106$	−135820.	−1.17408
$107$	6189.61	0.0522641	0.0261321	−	0.999658i	$-0.491681\pi$
$107$	6189.61	0.0522641	0.0261321	+	0.999658i	$0.491681\pi$
$108$	64408.9	0.531357
$109$	−68652.9	−0.553468	−0.276734	−	0.960947i	$-0.589252\pi$
$109$	−68652.9	−0.553468	−0.276734	+	0.960947i	$0.589252\pi$
$110$	42590.4	0.335606
$111$	103907.	0.800453
$112$	12544.0	0.0944911
$113$	−62835.9	−0.462926	−0.231463	−	0.972844i	$-0.574351\pi$
$113$	−62835.9	−0.462926	−0.231463	+	0.972844i	$0.574351\pi$
$114$	−164410.	−1.18485
$115$	−57835.7	−0.407804
$116$	−34046.8	−0.234926
$117$	−15373.8	−0.103828
$118$	−17277.4	−0.114228
$119$	85824.4	0.555576
$120$	−22880.5	−0.145048
$121$	20343.1	0.126315
$122$	−49014.5	−0.298143
$123$	84277.9	0.502286
$124$	−164201.	−0.959004
$125$	15625.0	0.0894427
$126$	−7546.29	−0.0423455
$127$	−198049.	−1.08959	−0.544794	−	0.838570i	$-0.683392\pi$
$127$	−198049.	−1.08959	−0.544794	+	0.838570i	$0.683392\pi$
$128$	16384.0	0.0883883
$129$	−288262.	−1.52515
$130$	39930.3	0.207226
$131$	−285132.	−1.45167	−0.725835	−	0.687868i	$-0.758547\pi$
$131$	−285132.	−1.45167	−0.725835	+	0.687868i	$0.758547\pi$
$132$	−97448.8	−0.486790
$133$	140837.	0.690381
$134$	−70135.3	−0.337423
$135$	100639.	0.475260
$136$	112097.	0.519694
$137$	406979.	1.85255	0.926277	−	0.376844i	$-0.122991\pi$
$137$	406979.	1.85255	0.926277	+	0.376844i	$0.122991\pi$
$138$	132331.	0.591512
$139$	13530.4	0.0593985	0.0296992	−	0.999559i	$-0.490545\pi$
$139$	13530.4	0.0593985	0.0296992	+	0.999559i	$0.490545\pi$
$140$	19600.0	0.0845154
$141$	−286814.	−1.21494
$142$	6632.72	0.0276039
$143$	170065.	0.695464
$144$	−9856.38	−0.0396106
$145$	−53198.2	−0.210125
$146$	−32987.6	−0.128076
$147$	−34335.0	−0.131052
$148$	−116257.	−0.436279
$149$	77129.8	0.284614	0.142307	−	0.989823i	$-0.454548\pi$
$149$	77129.8	0.284614	0.142307	+	0.989823i	$0.454548\pi$
$150$	−35750.7	−0.129735
$151$	−420464.	−1.50067	−0.750336	−	0.661056i	$-0.770108\pi$
$151$	−420464.	−1.50067	−0.750336	+	0.661056i	$0.770108\pi$
$152$	183951.	0.645793
$153$	−67436.1	−0.232897
$154$	83477.2	0.283639
$155$	−256563.	−0.857759
$156$	−91362.5	−0.300577
$157$	−481908.	−1.56032	−0.780162	−	0.625577i	$-0.784864\pi$
$157$	−481908.	−1.56032	−0.780162	+	0.625577i	$0.784864\pi$
$158$	−36674.4	−0.116875
$159$	485565.	1.52319
$160$	25600.0	0.0790569
$161$	−113358.	−0.344657
$162$	−192843.	−0.577320
$163$	282039.	0.831458	0.415729	−	0.909488i	$-0.363526\pi$
$163$	282039.	0.831458	0.415729	+	0.909488i	$0.363526\pi$
$164$	−94295.0	−0.273766
$165$	−152264.	−0.435398
$166$	380813.	1.07261
$167$	131971.	0.366173	0.183086	−	0.983097i	$-0.441391\pi$
$167$	131971.	0.366173	0.183086	+	0.983097i	$0.441391\pi$
$168$	−44845.7	−0.122588
$169$	−211850.	−0.570573
$170$	175152.	0.464828
$171$	−110662.	−0.289407
$172$	322524.	0.831267
$173$	55501.5	0.140990	0.0704952	−	0.997512i	$-0.477542\pi$
$173$	55501.5	0.140990	0.0704952	+	0.997512i	$0.477542\pi$
$174$	121720.	0.304782
$175$	30625.0	0.0755929
$176$	109031.	0.265320
$177$	61767.8	0.148193
$178$	−57767.3	−0.136657
$179$	20768.3	0.0484471	0.0242236	−	0.999707i	$-0.492289\pi$
$179$	20768.3	0.0484471	0.0242236	+	0.999707i	$0.492289\pi$
$180$	−15400.6	−0.0354288
$181$	−255866.	−0.580520	−0.290260	−	0.956948i	$-0.593742\pi$
$181$	−255866.	−0.580520	−0.290260	+	0.956948i	$0.593742\pi$
$182$	78263.4	0.175138
$183$	175230.	0.386796
$184$	−148059.	−0.322397
$185$	−181651.	−0.390219
$186$	587029.	1.24416
$187$	745979.	1.55999
$188$	320904.	0.662188
$189$	197252.	0.401668
$190$	287423.	0.577615
$191$	649260.	1.28776	0.643881	−	0.765126i	$-0.277323\pi$
$191$	649260.	1.28776	0.643881	+	0.765126i	$0.277323\pi$
$192$	−58574.0	−0.114671
$193$	−768642.	−1.48536	−0.742678	−	0.669649i	$-0.766445\pi$
$193$	−768642.	−1.48536	−0.742678	+	0.669649i	$0.766445\pi$
$194$	248530.	0.474104
$195$	−142754.	−0.268845
$196$	38416.0	0.0714286
$197$	−166160.	−0.305044	−0.152522	−	0.988300i	$-0.548739\pi$
$197$	−166160.	−0.305044	−0.152522	+	0.988300i	$0.548739\pi$
$198$	−65591.7	−0.118901
$199$	−74756.1	−0.133818	−0.0669089	−	0.997759i	$-0.521314\pi$
$199$	−74756.1	−0.133818	−0.0669089	+	0.997759i	$0.521314\pi$
$200$	40000.0	0.0707107
$201$	250739.	0.437756
$202$	−432551.	−0.745862
$203$	−104268.	−0.177588
$204$	−400756.	−0.674225
$205$	−147336.	−0.244863
$206$	552134.	0.906518
$207$	89070.5	0.144480
$208$	102222.	0.163827
$209$	1.22415e6	1.93851
$210$	−70071.5	−0.109646
$211$	−1.08646e6	−1.67999	−0.839997	−	0.542591i	$-0.817443\pi$
$211$	−1.08646e6	−1.67999	−0.839997	+	0.542591i	$0.817443\pi$
$212$	−543278.	−0.830200
$213$	−23712.5	−0.0358120
$214$	24758.4	0.0369563
$215$	503943.	0.743508
$216$	257636.	0.375726
$217$	−502864.	−0.724939
$218$	−274612.	−0.391361
$219$	117933.	0.166160
$220$	170362.	0.237309
$221$	699387.	0.963246
$222$	415627.	0.566006
$223$	−430809.	−0.580126	−0.290063	−	0.957008i	$-0.593676\pi$
$223$	−430809.	−0.580126	−0.290063	+	0.957008i	$0.593676\pi$
$224$	50176.0	0.0668153
$225$	−24063.4	−0.0316885
$226$	−251343.	−0.327338
$227$	−228724.	−0.294610	−0.147305	−	0.989091i	$-0.547060\pi$
$227$	−228724.	−0.294610	−0.147305	+	0.989091i	$0.547060\pi$
$228$	−657638.	−0.837819
$229$	−1.01797e6	−1.28276	−0.641378	−	0.767225i	$-0.721637\pi$
$229$	−1.01797e6	−1.28276	−0.641378	+	0.767225i	$0.721637\pi$
$230$	−231343.	−0.288361
$231$	−298437.	−0.367979
$232$	−136187.	−0.166118
$233$	−236710.	−0.285645	−0.142822	−	0.989748i	$-0.545618\pi$
$233$	−236710.	−0.285645	−0.142822	+	0.989748i	$0.545618\pi$
$234$	−61495.1	−0.0734177
$235$	501413.	0.592279
$236$	−69109.4	−0.0807713
$237$	131114.	0.151627
$238$	343298.	0.392852
$239$	1.73994e6	1.97034	0.985169	−	0.171587i	$-0.0548894\pi$
$239$	1.73994e6	1.97034	0.985169	+	0.171587i	$0.0548894\pi$
$240$	−91521.9	−0.102564
$241$	−332840.	−0.369142	−0.184571	−	0.982819i	$-0.559090\pi$
$241$	−332840.	−0.369142	−0.184571	+	0.982819i	$0.559090\pi$
$242$	81372.4	0.0893180
$243$	−288781.	−0.313728
$244$	−196058.	−0.210819
$245$	60025.0	0.0638877
$246$	337112.	0.355170
$247$	1.14769e6	1.19697
$248$	−656802.	−0.678118
$249$	−1.36143e6	−1.39155
$250$	62500.0	0.0632456
$251$	1.88585e6	1.88939	0.944696	−	0.327948i	$-0.106357\pi$
$251$	1.88585e6	1.88939	0.944696	+	0.327948i	$0.106357\pi$
$252$	−30185.2	−0.0299428
$253$	−985298.	−0.967757
$254$	−792194.	−0.770455
$255$	−626181.	−0.603045
$256$	65536.0	0.0625000
$257$	432608.	0.408566	0.204283	−	0.978912i	$-0.434514\pi$
$257$	432608.	0.408566	0.204283	+	0.978912i	$0.434514\pi$
$258$	−1.15305e6	−1.07844
$259$	−356036.	−0.329796
$260$	159721.	0.146531
$261$	81928.4	0.0744446
$262$	−1.14053e6	−1.02649
$263$	−1.20388e6	−1.07323	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	−1.20388e6	−1.07323	−0.536614	+	0.843828i	$0.680297\pi$
$264$	−389795.	−0.344213
$265$	−848872.	−0.742554
$266$	563350.	0.488173
$267$	206522.	0.177292
$268$	−280541.	−0.238594
$269$	548133.	0.461855	0.230927	−	0.972971i	$-0.425824\pi$
$269$	548133.	0.461855	0.230927	+	0.972971i	$0.425824\pi$
$270$	402556.	0.336060
$271$	−906590.	−0.749873	−0.374936	−	0.927051i	$-0.622335\pi$
$271$	−906590.	−0.749873	−0.374936	+	0.927051i	$0.622335\pi$
$272$	448389.	0.367479
$273$	−279798.	−0.227215
$274$	1.62792e6	1.30995
$275$	266190.	0.212256
$276$	529324.	0.418262
$277$	1.35338e6	1.05979	0.529895	−	0.848064i	$-0.322231\pi$
$277$	1.35338e6	1.05979	0.529895	+	0.848064i	$0.322231\pi$
$278$	54121.8	0.0420011
$279$	395123.	0.303894
$280$	78400.0	0.0597614
$281$	752309.	0.568369	0.284185	−	0.958770i	$-0.408277\pi$
$281$	752309.	0.568369	0.284185	+	0.958770i	$0.408277\pi$
$282$	−1.14726e6	−0.859089
$283$	−820710.	−0.609149	−0.304575	−	0.952489i	$-0.598514\pi$
$283$	−820710.	−0.609149	−0.304575	+	0.952489i	$0.598514\pi$
$284$	26530.9	0.0195189
$285$	−1.02756e6	−0.749368
$286$	680259.	0.491767
$287$	−288778.	−0.206947
$288$	−39425.5	−0.0280089
$289$	1.64796e6	1.16065
$290$	−212793.	−0.148581
$291$	−888512.	−0.615079
$292$	−131951.	−0.0905637
$293$	−1.92239e6	−1.30819	−0.654097	−	0.756411i	$-0.726951\pi$
$293$	−1.92239e6	−1.30819	−0.654097	+	0.756411i	$0.726951\pi$
$294$	−137340.	−0.0926678
$295$	−107983.	−0.0722441
$296$	−465027.	−0.308496
$297$	1.71450e6	1.12784
$298$	308519.	0.201253
$299$	−923760.	−0.597559
$300$	−143003.	−0.0917365
$301$	987729.	0.628379
$302$	−1.68185e6	−1.06114
$303$	1.54640e6	0.967643
$304$	735804.	0.456644
$305$	−306340.	−0.188562
$306$	−269744.	−0.164683
$307$	223229.	0.135177	0.0675887	−	0.997713i	$-0.478469\pi$
$307$	223229.	0.135177	0.0675887	+	0.997713i	$0.478469\pi$
$308$	333909.	0.200563
$309$	−1.97392e6	−1.17607
$310$	−1.02625e6	−0.606527
$311$	2.29818e6	1.34736	0.673678	−	0.739025i	$-0.264714\pi$
$311$	2.29818e6	1.34736	0.673678	+	0.739025i	$0.264714\pi$
$312$	−365450.	−0.212540
$313$	−1.62881e6	−0.939744	−0.469872	−	0.882735i	$-0.655700\pi$
$313$	−1.62881e6	−0.939744	−0.469872	+	0.882735i	$0.655700\pi$
$314$	−1.92763e6	−1.10332
$315$	−47164.3	−0.0267816
$316$	−146698.	−0.0826430
$317$	1.13620e6	0.635049	0.317524	−	0.948250i	$-0.397149\pi$
$317$	1.13620e6	0.635049	0.317524	+	0.948250i	$0.397149\pi$
$318$	1.94226e6	1.07706
$319$	−906293.	−0.498645
$320$	102400.	0.0559017
$321$	−88513.3	−0.0479453
$322$	−453432.	−0.243710
$323$	5.03428e6	2.68492
$324$	−771372.	−0.408227
$325$	249565.	0.131061
$326$	1.12816e6	0.587930
$327$	981757.	0.507732
$328$	−377180.	−0.193582
$329$	982770.	0.500567
$330$	−609055.	−0.307873
$331$	−3.77549e6	−1.89410	−0.947051	−	0.321084i	$-0.895953\pi$
$331$	−3.77549e6	−1.89410	−0.947051	+	0.321084i	$0.895953\pi$
$332$	1.52325e6	0.758449
$333$	279754.	0.138250
$334$	527882.	0.258923
$335$	−438346.	−0.213405
$336$	−179383.	−0.0866828
$337$	3.74913e6	1.79827	0.899136	−	0.437669i	$-0.144196\pi$
$337$	3.74913e6	1.79827	0.899136	+	0.437669i	$0.144196\pi$
$338$	−847400.	−0.403456
$339$	898571.	0.424672
$340$	700608.	0.328683
$341$	−4.37085e6	−2.03554
$342$	−442649.	−0.204642
$343$	117649.	0.0539949
$344$	1.29010e6	0.587795
$345$	827068.	0.374105
$346$	222006.	0.0996953
$347$	−1.14843e6	−0.512012	−0.256006	−	0.966675i	$-0.582407\pi$
$347$	−1.14843e6	−0.512012	−0.256006	+	0.966675i	$0.582407\pi$
$348$	486880.	0.215513
$349$	4.03275e6	1.77230	0.886151	−	0.463396i	$-0.153369\pi$
$349$	4.03275e6	1.77230	0.886151	+	0.463396i	$0.153369\pi$
$350$	122500.	0.0534522
$351$	1.60742e6	0.696403
$352$	436126.	0.187610
$353$	652660.	0.278773	0.139386	−	0.990238i	$-0.455487\pi$
$353$	652660.	0.278773	0.139386	+	0.990238i	$0.455487\pi$
$354$	247071.	0.104789
$355$	41454.5	0.0174583
$356$	−231069.	−0.0966311
$357$	−1.22732e6	−0.509666
$358$	83073.2	0.0342573
$359$	−2.84604e6	−1.16548	−0.582741	−	0.812658i	$-0.698020\pi$
$359$	−2.84604e6	−1.16548	−0.582741	+	0.812658i	$0.698020\pi$
$360$	−61602.4	−0.0250519
$361$	5.78512e6	2.33639
$362$	−1.02347e6	−0.410489
$363$	−290912.	−0.115877
$364$	313054.	0.123841
$365$	−206173.	−0.0810026
$366$	700921.	0.273506
$367$	−2.65232e6	−1.02792	−0.513962	−	0.857813i	$-0.671823\pi$
$367$	−2.65232e6	−1.02792	−0.513962	+	0.857813i	$0.671823\pi$
$368$	−592238.	−0.227969
$369$	226906.	0.0867521
$370$	−726605.	−0.275927
$371$	−1.66379e6	−0.627572
$372$	2.34812e6	0.879756
$373$	2.83283e6	1.05426	0.527132	−	0.849784i	$-0.323267\pi$
$373$	2.83283e6	1.05426	0.527132	+	0.849784i	$0.323267\pi$
$374$	2.98392e6	1.10308
$375$	−223442.	−0.0820516
$376$	1.28362e6	0.468237
$377$	−849688.	−0.307898
$378$	789009.	0.284022
$379$	−1.20678e6	−0.431551	−0.215775	−	0.976443i	$-0.569228\pi$
$379$	−1.20678e6	−0.431551	−0.215775	+	0.976443i	$0.569228\pi$
$380$	1.14969e6	0.408435
$381$	2.83215e6	0.999550
$382$	2.59704e6	0.910585
$383$	−2.22793e6	−0.776076	−0.388038	−	0.921643i	$-0.626847\pi$
$383$	−2.22793e6	−0.776076	−0.388038	+	0.921643i	$0.626847\pi$
$384$	−234296.	−0.0810843
$385$	521732.	0.179389
$386$	−3.07457e6	−1.05031
$387$	−776103.	−0.263416
$388$	994119.	0.335242
$389$	−3.74004e6	−1.25315	−0.626574	−	0.779362i	$-0.715543\pi$
$389$	−3.74004e6	−1.25315	−0.626574	+	0.779362i	$0.715543\pi$
$390$	−571016.	−0.190102
$391$	−4.05202e6	−1.34038
$392$	153664.	0.0505076
$393$	4.07748e6	1.33171
$394$	−664642.	−0.215699
$395$	−229215.	−0.0739181
$396$	−262367.	−0.0840758
$397$	−2.90335e6	−0.924533	−0.462267	−	0.886741i	$-0.652964\pi$
$397$	−2.90335e6	−0.924533	−0.462267	+	0.886741i	$0.652964\pi$
$398$	−299024.	−0.0946235
$399$	−2.01402e6	−0.633331
$400$	160000.	0.0500000
$401$	1.43777e6	0.446506	0.223253	−	0.974761i	$-0.428332\pi$
$401$	1.43777e6	0.446506	0.223253	+	0.974761i	$0.428332\pi$
$402$	1.00296e6	0.309540
$403$	−4.09786e6	−1.25688
$404$	−1.73020e6	−0.527404
$405$	−1.20527e6	−0.365129
$406$	−417074.	−0.125573
$407$	−3.09464e6	−0.926027
$408$	−1.60302e6	−0.476749
$409$	−4.78825e6	−1.41536	−0.707682	−	0.706531i	$-0.750259\pi$
$409$	−4.78825e6	−1.41536	−0.707682	+	0.706531i	$0.750259\pi$
$410$	−589344.	−0.173145
$411$	−5.81992e6	−1.69947
$412$	2.20854e6	0.641005
$413$	−211648.	−0.0610574
$414$	356282.	0.102163
$415$	2.38008e6	0.678377
$416$	408887.	0.115843
$417$	−193489.	−0.0544900
$418$	4.89659e6	1.37073
$419$	−2.08411e6	−0.579943	−0.289972	−	0.957035i	$-0.593646\pi$
$419$	−2.08411e6	−0.579943	−0.289972	+	0.957035i	$0.593646\pi$
$420$	−280286.	−0.0775315
$421$	−1.00260e6	−0.275690	−0.137845	−	0.990454i	$-0.544018\pi$
$421$	−1.00260e6	−0.275690	−0.137845	+	0.990454i	$0.544018\pi$
$422$	−4.34584e6	−1.18793
$423$	−772206.	−0.209837
$424$	−2.17311e6	−0.587040
$425$	1.09470e6	0.293983
$426$	−94849.9	−0.0253229
$427$	−600427.	−0.159364
$428$	99033.8	0.0261321
$429$	−2.43198e6	−0.637994
$430$	2.01577e6	0.525740
$431$	1.45620e6	0.377595	0.188798	−	0.982016i	$-0.439541\pi$
$431$	1.45620e6	0.377595	0.188798	+	0.982016i	$0.439541\pi$
$432$	1.03054e6	0.265678
$433$	−1.10726e6	−0.283812	−0.141906	−	0.989880i	$-0.545323\pi$
$433$	−1.10726e6	−0.283812	−0.141906	+	0.989880i	$0.545323\pi$
$434$	−2.01146e6	−0.512609
$435$	760750.	0.192761
$436$	−1.09845e6	−0.276734
$437$	−6.64934e6	−1.66562
$438$	471733.	0.117493
$439$	4.15410e6	1.02876	0.514382	−	0.857561i	$-0.328021\pi$
$439$	4.15410e6	1.02876	0.514382	+	0.857561i	$0.328021\pi$
$440$	681446.	0.167803
$441$	−92442.1	−0.0226346
$442$	2.79755e6	0.681118
$443$	−7.20799e6	−1.74504	−0.872519	−	0.488581i	$-0.837515\pi$
$443$	−7.20799e6	−1.74504	−0.872519	+	0.488581i	$0.837515\pi$
$444$	1.66251e6	0.400227
$445$	−361046.	−0.0864295
$446$	−1.72324e6	−0.410211
$447$	−1.10298e6	−0.261095
$448$	200704.	0.0472456
$449$	5.58367e6	1.30709	0.653543	−	0.756890i	$-0.273282\pi$
$449$	5.58367e6	1.30709	0.653543	+	0.756890i	$0.273282\pi$
$450$	−96253.7	−0.0224071
$451$	−2.51004e6	−0.581084
$452$	−1.00537e6	−0.231463
$453$	6.01275e6	1.37666
$454$	−914895.	−0.208320
$455$	489147.	0.110767
$456$	−2.63055e6	−0.592427
$457$	−3.54344e6	−0.793661	−0.396831	−	0.917892i	$-0.629890\pi$
$457$	−3.54344e6	−0.793661	−0.396831	+	0.917892i	$0.629890\pi$
$458$	−4.07186e6	−0.907046
$459$	7.05084e6	1.56210
$460$	−925372.	−0.203902
$461$	5.88069e6	1.28877	0.644386	−	0.764700i	$-0.277113\pi$
$461$	5.88069e6	1.28877	0.644386	+	0.764700i	$0.277113\pi$
$462$	−1.19375e6	−0.260200
$463$	6.65045e6	1.44178	0.720890	−	0.693050i	$-0.243733\pi$
$463$	6.65045e6	1.44178	0.720890	+	0.693050i	$0.243733\pi$
$464$	−544749.	−0.117463
$465$	3.66893e6	0.786878
$466$	−946839.	−0.201981
$467$	4.34743e6	0.922445	0.461222	−	0.887285i	$-0.347411\pi$
$467$	4.34743e6	0.922445	0.461222	+	0.887285i	$0.347411\pi$
$468$	−245980.	−0.0519141
$469$	−859158.	−0.180360
$470$	2.00565e6	0.418804
$471$	6.89143e6	1.43139
$472$	−276438.	−0.0571139
$473$	8.58526e6	1.76441
$474$	524456.	0.107217
$475$	1.79640e6	0.365316
$476$	1.37319e6	0.277788
$477$	1.30731e6	0.263078
$478$	6.95978e6	1.39324
$479$	−929680.	−0.185138	−0.0925688	−	0.995706i	$-0.529508\pi$
$479$	−929680.	−0.185138	−0.0925688	+	0.995706i	$0.529508\pi$
$480$	−366088.	−0.0725240
$481$	−2.90136e6	−0.571792
$482$	−1.33136e6	−0.261023
$483$	1.62105e6	0.316176
$484$	325490.	0.0631573
$485$	1.55331e6	0.299850
$486$	−1.15513e6	−0.221839
$487$	−5.44887e6	−1.04108	−0.520540	−	0.853837i	$-0.674269\pi$
$487$	−5.44887e6	−1.04108	−0.520540	+	0.853837i	$0.674269\pi$
$488$	−784232.	−0.149072
$489$	−4.03324e6	−0.762750
$490$	240100.	0.0451754
$491$	−670070.	−0.125434	−0.0627172	−	0.998031i	$-0.519977\pi$
$491$	−670070.	−0.125434	−0.0627172	+	0.998031i	$0.519977\pi$
$492$	1.34845e6	0.251143
$493$	−3.72711e6	−0.690644
$494$	4.59076e6	0.846384
$495$	−409948.	−0.0751997
$496$	−2.62721e6	−0.479502
$497$	81250.9	0.0147549
$498$	−5.44574e6	−0.983973
$499$	6.58017e6	1.18300	0.591501	−	0.806304i	$-0.298535\pi$
$499$	6.58017e6	1.18300	0.591501	+	0.806304i	$0.298535\pi$
$500$	250000.	0.0447214
$501$	−1.88722e6	−0.335914
$502$	7.54339e6	1.33600
$503$	−1.47714e6	−0.260317	−0.130159	−	0.991493i	$-0.541549\pi$
$503$	−1.47714e6	−0.260317	−0.130159	+	0.991493i	$0.541549\pi$
$504$	−120741.	−0.0211727
$505$	−2.70344e6	−0.471724
$506$	−3.94119e6	−0.684308
$507$	3.02952e6	0.523424
$508$	−3.16878e6	−0.544794
$509$	5.16474e6	0.883597	0.441799	−	0.897114i	$-0.354341\pi$
$509$	5.16474e6	0.883597	0.441799	+	0.897114i	$0.354341\pi$
$510$	−2.50472e6	−0.426417
$511$	−404099.	−0.0684597
$512$	262144.	0.0441942
$513$	1.15704e7	1.94113
$514$	1.73043e6	0.288899
$515$	3.45084e6	0.573333
$516$	−4.61219e6	−0.762575
$517$	8.54215e6	1.40553
$518$	−1.42415e6	−0.233201
$519$	−793688.	−0.129340
$520$	638885.	0.103613
$521$	294103.	0.0474684	0.0237342	−	0.999718i	$-0.492444\pi$
$521$	294103.	0.0474684	0.0237342	+	0.999718i	$0.492444\pi$
$522$	327714.	0.0526403
$523$	1.39098e6	0.222365	0.111182	−	0.993800i	$-0.464536\pi$
$523$	1.39098e6	0.222365	0.111182	+	0.993800i	$0.464536\pi$
$524$	−4.56212e6	−0.725835
$525$	−437947.	−0.0693462
$526$	−4.81550e6	−0.758887
$527$	−1.79750e7	−2.81931
$528$	−1.55918e6	−0.243395
$529$	−1.08439e6	−0.168479
$530$	−3.39549e6	−0.525065
$531$	166301.	0.0255952
$532$	2.25340e6	0.345191
$533$	−2.35327e6	−0.358801
$534$	826090.	0.125364
$535$	154740.	0.0233732
$536$	−1.12216e6	−0.168712
$537$	−296993.	−0.0444437
$538$	2.19253e6	0.326581
$539$	1.02260e6	0.151611
$540$	1.61022e6	0.237630
$541$	2.36315e6	0.347134	0.173567	−	0.984822i	$-0.444471\pi$
$541$	2.36315e6	0.347134	0.173567	+	0.984822i	$0.444471\pi$
$542$	−3.62636e6	−0.530240
$543$	3.65897e6	0.532548
$544$	1.79356e6	0.259847
$545$	−1.71632e6	−0.247519
$546$	−1.11919e6	−0.160665
$547$	4.52298e6	0.646333	0.323167	−	0.946342i	$-0.395253\pi$
$547$	4.52298e6	0.646333	0.323167	+	0.946342i	$0.395253\pi$
$548$	6.51167e6	0.926277
$549$	471782.	0.0668053
$550$	1.06476e6	0.150088
$551$	−6.11616e6	−0.858223
$552$	2.11729e6	0.295756
$553$	−449262.	−0.0624722
$554$	5.41351e6	0.749384
$555$	2.59767e6	0.357973
$556$	216487.	0.0296992
$557$	−8.40670e6	−1.14812	−0.574060	−	0.818813i	$-0.694633\pi$
$557$	−8.40670e6	−1.14812	−0.574060	+	0.818813i	$0.694633\pi$
$558$	1.58049e6	0.214885
$559$	8.04905e6	1.08947
$560$	313600.	0.0422577
$561$	−1.06677e7	−1.43108
$562$	3.00924e6	0.401898
$563$	−2.22527e6	−0.295877	−0.147938	−	0.988997i	$-0.547264\pi$
$563$	−2.22527e6	−0.295877	−0.147938	+	0.988997i	$0.547264\pi$
$564$	−4.58903e6	−0.607468
$565$	−1.57090e6	−0.207027
$566$	−3.28284e6	−0.430733
$567$	−2.36233e6	−0.308590
$568$	106124.	0.0138020
$569$	1.58379e6	0.205078	0.102539	−	0.994729i	$-0.467303\pi$
$569$	1.58379e6	0.205078	0.102539	+	0.994729i	$0.467303\pi$
$570$	−4.11024e6	−0.529883
$571$	1.25695e7	1.61335	0.806676	−	0.590994i	$-0.201264\pi$
$571$	1.25695e7	1.61335	0.806676	+	0.590994i	$0.201264\pi$
$572$	2.72104e6	0.347732
$573$	−9.28462e6	−1.18135
$574$	−1.15511e6	−0.146334
$575$	−1.44589e6	−0.182376
$576$	−157702.	−0.0198053
$577$	1.37636e7	1.72104	0.860521	−	0.509414i	$-0.170138\pi$
$577$	1.37636e7	1.72104	0.860521	+	0.509414i	$0.170138\pi$
$578$	6.59185e6	0.820706
$579$	1.09918e7	1.36261
$580$	−851171.	−0.105062
$581$	4.66496e6	0.573334
$582$	−3.55405e6	−0.434927
$583$	−1.44615e7	−1.76215
$584$	−527802.	−0.0640382
$585$	−384344.	−0.0464334
$586$	−7.68956e6	−0.925033
$587$	1.43475e6	0.171862	0.0859311	−	0.996301i	$-0.472614\pi$
$587$	1.43475e6	0.171862	0.0859311	+	0.996301i	$0.472614\pi$
$588$	−549360.	−0.0655260
$589$	−2.94969e7	−3.50339
$590$	−431934.	−0.0510843
$591$	2.37614e6	0.279836
$592$	−1.86011e6	−0.218139
$593$	2.58486e6	0.301856	0.150928	−	0.988545i	$-0.451774\pi$
$593$	2.58486e6	0.301856	0.150928	+	0.988545i	$0.451774\pi$
$594$	6.85800e6	0.797501
$595$	2.14561e6	0.248461
$596$	1.23408e6	0.142307
$597$	1.06903e6	0.122760
$598$	−3.69504e6	−0.422538
$599$	−5.51209e6	−0.627696	−0.313848	−	0.949473i	$-0.601618\pi$
$599$	−5.51209e6	−0.627696	−0.313848	+	0.949473i	$0.601618\pi$
$600$	−572012.	−0.0648675
$601$	6.92526e6	0.782077	0.391039	−	0.920374i	$-0.372116\pi$
$601$	6.92526e6	0.782077	0.391039	+	0.920374i	$0.372116\pi$
$602$	3.95092e6	0.444331
$603$	675078.	0.0756068
$604$	−6.72742e6	−0.750336
$605$	508578.	0.0564896
$606$	6.18560e6	0.684227
$607$	1.19865e7	1.32045	0.660225	−	0.751067i	$-0.270461\pi$
$607$	1.19865e7	1.32045	0.660225	+	0.751067i	$0.270461\pi$
$608$	2.94322e6	0.322896
$609$	1.49107e6	0.162913
$610$	−1.22536e6	−0.133334
$611$	8.00864e6	0.867872
$612$	−1.07898e6	−0.116448
$613$	−4.84046e6	−0.520278	−0.260139	−	0.965571i	$-0.583768\pi$
$613$	−4.84046e6	−0.520278	−0.260139	+	0.965571i	$0.583768\pi$
$614$	892915.	0.0955849
$615$	2.10695e6	0.224629
$616$	1.33563e6	0.141819
$617$	−9.94864e6	−1.05208	−0.526042	−	0.850458i	$-0.676325\pi$
$617$	−9.94864e6	−1.05208	−0.526042	+	0.850458i	$0.676325\pi$
$618$	−7.89568e6	−0.831608
$619$	−1.38913e7	−1.45719	−0.728597	−	0.684943i	$-0.759827\pi$
$619$	−1.38913e7	−1.45719	−0.728597	+	0.684943i	$0.759827\pi$
$620$	−4.10501e6	−0.428880
$621$	−9.31284e6	−0.969065
$622$	9.19270e6	0.952724
$623$	−707649.	−0.0730463
$624$	−1.46180e6	−0.150289
$625$	390625.	0.0400000
$626$	−6.51524e6	−0.664499
$627$	−1.75057e7	−1.77832
$628$	−7.71053e6	−0.780162
$629$	−1.27266e7	−1.28259
$630$	−188657.	−0.0189375
$631$	−7.29060e6	−0.728937	−0.364469	−	0.931216i	$-0.618749\pi$
$631$	−7.29060e6	−0.728937	−0.364469	+	0.931216i	$0.618749\pi$
$632$	−586791.	−0.0584374
$633$	1.55367e7	1.54117
$634$	4.54480e6	0.449047
$635$	−4.95121e6	−0.487279
$636$	7.76904e6	0.761596
$637$	958727.	0.0936152
$638$	−3.62517e6	−0.352595
$639$	−63842.4	−0.00618525
$640$	409600.	0.0395285
$641$	1.58175e7	1.52052	0.760259	−	0.649620i	$-0.225072\pi$
$641$	1.58175e7	1.52052	0.760259	+	0.649620i	$0.225072\pi$
$642$	−354053.	−0.0339024
$643$	−7.35926e6	−0.701951	−0.350975	−	0.936385i	$-0.614150\pi$
$643$	−7.35926e6	−0.701951	−0.350975	+	0.936385i	$0.614150\pi$
$644$	−1.81373e6	−0.172329
$645$	−7.20654e6	−0.682068
$646$	2.01371e7	1.89852
$647$	1.08644e7	1.02034	0.510172	−	0.860072i	$-0.329582\pi$
$647$	1.08644e7	1.02034	0.510172	+	0.860072i	$0.329582\pi$
$648$	−3.08549e6	−0.288660
$649$	−1.83962e6	−0.171442
$650$	998258.	0.0926743
$651$	7.19111e6	0.665033
$652$	4.51263e6	0.415729
$653$	−2.85006e6	−0.261560	−0.130780	−	0.991411i	$-0.541748\pi$
$653$	−2.85006e6	−0.261560	−0.130780	+	0.991411i	$0.541748\pi$
$654$	3.92703e6	0.359021
$655$	−7.12831e6	−0.649207
$656$	−1.50872e6	−0.136883
$657$	317518.	0.0286982
$658$	3.93108e6	0.353954
$659$	−214583.	−0.0192479	−0.00962393	−	0.999954i	$-0.503063\pi$
$659$	−214583.	−0.0192479	−0.00962393	+	0.999954i	$0.503063\pi$
$660$	−2.43622e6	−0.217699
$661$	2.26579e6	0.201704	0.100852	−	0.994901i	$-0.467843\pi$
$661$	2.26579e6	0.201704	0.100852	+	0.994901i	$0.467843\pi$
$662$	−1.51020e7	−1.33933
$663$	−1.00014e7	−0.883648
$664$	6.09301e6	0.536304
$665$	3.52094e6	0.308748
$666$	1.11901e6	0.0977575
$667$	4.92281e6	0.428448
$668$	2.11153e6	0.183086
$669$	6.16070e6	0.532187
$670$	−1.75338e6	−0.150900
$671$	−5.21886e6	−0.447476
$672$	−717532.	−0.0612940
$673$	−9.52991e6	−0.811057	−0.405528	−	0.914082i	$-0.632912\pi$
$673$	−9.52991e6	−0.811057	−0.405528	+	0.914082i	$0.632912\pi$
$674$	1.49965e7	1.27157
$675$	2.51597e6	0.212543
$676$	−3.38960e6	−0.285287
$677$	2.14827e7	1.80143	0.900714	−	0.434412i	$-0.143044\pi$
$677$	2.14827e7	1.80143	0.900714	+	0.434412i	$0.143044\pi$
$678$	3.59429e6	0.300288
$679$	3.04449e6	0.253419
$680$	2.80243e6	0.232414
$681$	3.27082e6	0.270264
$682$	−1.74834e7	−1.43935
$683$	−2.89672e6	−0.237605	−0.118802	−	0.992918i	$-0.537905\pi$
$683$	−2.89672e6	−0.237605	−0.118802	+	0.992918i	$0.537905\pi$
$684$	−1.77060e6	−0.144704
$685$	1.01745e7	0.828487
$686$	470596.	0.0381802
$687$	1.45572e7	1.17676
$688$	5.16038e6	0.415634
$689$	−1.35583e7	−1.08807
$690$	3.30827e6	0.264532
$691$	−2.09710e6	−0.167080	−0.0835399	−	0.996504i	$-0.526623\pi$
$691$	−2.09710e6	−0.167080	−0.0835399	+	0.996504i	$0.526623\pi$
$692$	888024.	0.0704952
$693$	−803499.	−0.0635553
$694$	−4.59371e6	−0.362047
$695$	338261.	0.0265638
$696$	1.94752e6	0.152391
$697$	−1.03225e7	−0.804825
$698$	1.61310e7	1.25321
$699$	3.38502e6	0.262041
$700$	490000.	0.0377964
$701$	6.59970e6	0.507258	0.253629	−	0.967302i	$-0.418376\pi$
$701$	6.59970e6	0.507258	0.253629	+	0.967302i	$0.418376\pi$
$702$	6.42967e6	0.492432
$703$	−2.08843e7	−1.59379
$704$	1.74450e6	0.132660
$705$	−7.17036e6	−0.543336
$706$	2.61064e6	0.197122
$707$	−5.29874e6	−0.398680
$708$	988285.	0.0740967
$709$	−2.22011e7	−1.65866	−0.829332	−	0.558756i	$-0.811279\pi$
$709$	−2.22011e7	−1.65866	−0.829332	+	0.558756i	$0.811279\pi$
$710$	165818.	0.0123449
$711$	353005.	0.0261883
$712$	−924277.	−0.0683285
$713$	2.37416e7	1.74899
$714$	−4.90926e6	−0.360388
$715$	4.25162e6	0.311021
$716$	332293.	0.0242236
$717$	−2.48817e7	−1.80752
$718$	−1.13842e7	−0.824120
$719$	1.87540e7	1.35292	0.676460	−	0.736479i	$-0.263513\pi$
$719$	1.87540e7	1.35292	0.676460	+	0.736479i	$0.263513\pi$
$720$	−246410.	−0.0177144
$721$	6.76365e6	0.484555
$722$	2.31405e7	1.65207
$723$	4.75972e6	0.338638
$724$	−4.09386e6	−0.290260
$725$	−1.32995e6	−0.0939706
$726$	−1.16365e6	−0.0819371
$727$	1.38593e7	0.972537	0.486269	−	0.873809i	$-0.338358\pi$
$727$	1.38593e7	0.972537	0.486269	+	0.873809i	$0.338358\pi$
$728$	1.25222e6	0.0875690
$729$	1.58449e7	1.10426
$730$	−824691.	−0.0572775
$731$	3.53067e7	2.44379
$732$	2.80369e6	0.193398
$733$	1.08280e7	0.744372	0.372186	−	0.928158i	$-0.378608\pi$
$733$	1.08280e7	0.744372	0.372186	+	0.928158i	$0.378608\pi$
$734$	−1.06093e7	−0.726851
$735$	−858375.	−0.0586083
$736$	−2.36895e6	−0.161199
$737$	−7.46772e6	−0.506430
$738$	907624.	0.0613430
$739$	−906866.	−0.0610846	−0.0305423	−	0.999533i	$-0.509723\pi$
$739$	−906866.	−0.0610846	−0.0305423	+	0.999533i	$0.509723\pi$
$740$	−2.90642e6	−0.195110
$741$	−1.64123e7	−1.09806
$742$	−6.65516e6	−0.443761
$743$	−1.76804e7	−1.17495	−0.587475	−	0.809242i	$-0.699878\pi$
$743$	−1.76804e7	−1.17495	−0.587475	+	0.809242i	$0.699878\pi$
$744$	9.39247e6	0.622082
$745$	1.92825e6	0.127283
$746$	1.13313e7	0.745477
$747$	−3.66547e6	−0.240341
$748$	1.19357e7	0.779996
$749$	303291.	0.0197540
$750$	−893769.	−0.0580192
$751$	1.96975e7	1.27441	0.637207	−	0.770692i	$-0.280089\pi$
$751$	1.96975e7	1.27441	0.637207	+	0.770692i	$0.280089\pi$
$752$	5.13447e6	0.331094
$753$	−2.69682e7	−1.73326
$754$	−3.39875e6	−0.217717
$755$	−1.05116e7	−0.671121
$756$	3.15604e6	0.200834
$757$	−1.88790e7	−1.19740	−0.598699	−	0.800974i	$-0.704315\pi$
$757$	−1.88790e7	−1.19740	−0.598699	+	0.800974i	$0.704315\pi$
$758$	−4.82714e6	−0.305152
$759$	1.40901e7	0.887786
$760$	4.59877e6	0.288807
$761$	9.74849e6	0.610205	0.305102	−	0.952320i	$-0.401309\pi$
$761$	9.74849e6	0.610205	0.305102	+	0.952320i	$0.401309\pi$
$762$	1.13286e7	0.706788
$763$	−3.36399e6	−0.209191
$764$	1.03882e7	0.643881
$765$	−1.68590e6	−0.104155
$766$	−8.91171e6	−0.548768
$767$	−1.72473e6	−0.105860
$768$	−937184.	−0.0573353
$769$	6.11920e6	0.373146	0.186573	−	0.982441i	$-0.440262\pi$
$769$	6.11920e6	0.373146	0.186573	+	0.982441i	$0.440262\pi$
$770$	2.08693e6	0.126847
$771$	−6.18642e6	−0.374804
$772$	−1.22983e7	−0.742678
$773$	1.47893e6	0.0890223	0.0445111	−	0.999009i	$-0.485827\pi$
$773$	1.47893e6	0.0890223	0.0445111	+	0.999009i	$0.485827\pi$
$774$	−3.10441e6	−0.186263
$775$	−6.41408e6	−0.383602
$776$	3.97648e6	0.237052
$777$	5.09143e6	0.302543
$778$	−1.49602e7	−0.886109
$779$	−1.69391e7	−1.00011
$780$	−2.28406e6	−0.134422
$781$	706226.	0.0414301
$782$	−1.62081e7	−0.947795
$783$	−8.56609e6	−0.499319
$784$	614656.	0.0357143
$785$	−1.20477e7	−0.697799
$786$	1.63099e7	0.941662
$787$	2.39360e7	1.37758	0.688788	−	0.724963i	$-0.258143\pi$
$787$	2.39360e7	1.37758	0.688788	+	0.724963i	$0.258143\pi$
$788$	−2.65857e6	−0.152522
$789$	1.72158e7	0.984542
$790$	−916861.	−0.0522680
$791$	−3.07896e6	−0.174970
$792$	−1.04947e6	−0.0594506
$793$	−4.89291e6	−0.276302
$794$	−1.16134e7	−0.653744
$795$	1.21391e7	0.681192
$796$	−1.19610e6	−0.0669089
$797$	6.21796e6	0.346738	0.173369	−	0.984857i	$-0.444535\pi$
$797$	6.21796e6	0.346738	0.173369	+	0.984857i	$0.444535\pi$
$798$	−8.05607e6	−0.447833
$799$	3.51294e7	1.94672
$800$	640000.	0.0353553
$801$	556032.	0.0306209
$802$	5.75106e6	0.315727
$803$	−3.51239e6	−0.192227
$804$	4.01182e6	0.218878
$805$	−2.83395e6	−0.154135
$806$	−1.63915e7	−0.888750
$807$	−7.83847e6	−0.423689
$808$	−6.92081e6	−0.372931
$809$	−4.98100e6	−0.267575	−0.133787	−	0.991010i	$-0.542714\pi$
$809$	−4.98100e6	−0.267575	−0.133787	+	0.991010i	$0.542714\pi$
$810$	−4.82108e6	−0.258185
$811$	−3.09722e7	−1.65356	−0.826780	−	0.562525i	$-0.809830\pi$
$811$	−3.09722e7	−1.65356	−0.826780	+	0.562525i	$0.809830\pi$
$812$	−1.66830e6	−0.0887938
$813$	1.29645e7	0.687907
$814$	−1.23786e7	−0.654800
$815$	7.05098e6	0.371839
$816$	−6.41210e6	−0.337112
$817$	5.79381e7	3.03675
$818$	−1.91530e7	−1.00081
$819$	−753315.	−0.0392434
$820$	−2.35737e6	−0.122432
$821$	−2.87667e7	−1.48947	−0.744734	−	0.667361i	$-0.767424\pi$
$821$	−2.87667e7	−1.48947	−0.744734	+	0.667361i	$0.767424\pi$
$822$	−2.32797e7	−1.20170
$823$	3.55713e7	1.83063	0.915313	−	0.402743i	$-0.131943\pi$
$823$	3.55713e7	1.83063	0.915313	+	0.402743i	$0.131943\pi$
$824$	8.83415e6	0.453259
$825$	−3.80660e6	−0.194716
$826$	−846590.	−0.0431741
$827$	3.01542e7	1.53315	0.766575	−	0.642155i	$-0.221960\pi$
$827$	3.01542e7	1.53315	0.766575	+	0.642155i	$0.221960\pi$
$828$	1.42513e6	0.0722400
$829$	−3.11697e7	−1.57524	−0.787618	−	0.616164i	$-0.788686\pi$
$829$	−3.11697e7	−1.57524	−0.787618	+	0.616164i	$0.788686\pi$
$830$	9.52032e6	0.479685
$831$	−1.93537e7	−0.972213
$832$	1.63555e6	0.0819133
$833$	4.20540e6	0.209988
$834$	−773958.	−0.0385303
$835$	3.29926e6	0.163757
$836$	1.95864e7	0.969255
$837$	−4.13124e7	−2.03829
$838$	−8.33644e6	−0.410082
$839$	3.63050e7	1.78058	0.890291	−	0.455393i	$-0.150501\pi$
$839$	3.63050e7	1.78058	0.890291	+	0.455393i	$0.150501\pi$
$840$	−1.12114e6	−0.0548230
$841$	−1.59831e7	−0.779238
$842$	−4.01039e6	−0.194942
$843$	−1.07582e7	−0.521402
$844$	−1.73834e7	−0.839997
$845$	−5.29625e6	−0.255168
$846$	−3.08883e6	−0.148377
$847$	996812.	0.0477425
$848$	−8.69245e6	−0.415100
$849$	1.17364e7	0.558812
$850$	4.37880e6	0.207878
$851$	1.68095e7	0.795666
$852$	−379400.	−0.0179060
$853$	1.00191e7	0.471472	0.235736	−	0.971817i	$-0.424250\pi$
$853$	1.00191e7	0.471472	0.235736	+	0.971817i	$0.424250\pi$
$854$	−2.40171e6	−0.112687
$855$	−2.76656e6	−0.129427
$856$	396135.	0.0184782
$857$	−1.17397e7	−0.546014	−0.273007	−	0.962012i	$-0.588018\pi$
$857$	−1.17397e7	−0.546014	−0.273007	+	0.962012i	$0.588018\pi$
$858$	−9.72791e6	−0.451130
$859$	−1.69498e7	−0.783756	−0.391878	−	0.920017i	$-0.628175\pi$
$859$	−1.69498e7	−0.783756	−0.391878	+	0.920017i	$0.628175\pi$
$860$	8.06310e6	0.371754
$861$	4.12962e6	0.189846
$862$	5.82478e6	0.267000
$863$	−2.11590e7	−0.967091	−0.483546	−	0.875319i	$-0.660651\pi$
$863$	−2.11590e7	−0.967091	−0.483546	+	0.875319i	$0.660651\pi$
$864$	4.12217e6	0.187863
$865$	1.38754e6	0.0630528
$866$	−4.42905e6	−0.200686
$867$	−2.35664e7	−1.06474
$868$	−8.04583e6	−0.362469
$869$	−3.90495e6	−0.175415
$870$	3.04300e6	0.136302
$871$	−7.00131e6	−0.312705
$872$	−4.39379e6	−0.195681
$873$	−2.39219e6	−0.106233
$874$	−2.65973e7	−1.17777
$875$	765625.	0.0338062
$876$	1.88693e6	0.0830799
$877$	1.01611e7	0.446109	0.223055	−	0.974806i	$-0.428397\pi$
$877$	1.01611e7	0.446109	0.223055	+	0.974806i	$0.428397\pi$
$878$	1.66164e7	0.727446
$879$	2.74907e7	1.20009
$880$	2.72578e6	0.118655
$881$	−3.50223e7	−1.52021	−0.760106	−	0.649799i	$-0.774853\pi$
$881$	−3.50223e7	−1.52021	−0.760106	+	0.649799i	$0.774853\pi$
$882$	−369768.	−0.0160051
$883$	−2.15600e7	−0.930566	−0.465283	−	0.885162i	$-0.654047\pi$
$883$	−2.15600e7	−0.930566	−0.465283	+	0.885162i	$0.654047\pi$
$884$	1.11902e7	0.481623
$885$	1.54420e6	0.0662741
$886$	−2.88319e7	−1.23393
$887$	−1.29121e7	−0.551048	−0.275524	−	0.961294i	$-0.588851\pi$
$887$	−1.29121e7	−0.551048	−0.275524	+	0.961294i	$0.588851\pi$
$888$	6.65003e6	0.283003
$889$	−9.70438e6	−0.411826
$890$	−1.44418e6	−0.0611149
$891$	−2.05332e7	−0.866486
$892$	−6.89294e6	−0.290063
$893$	5.76472e7	2.41907
$894$	−4.41192e6	−0.184622
$895$	519207.	0.0216662
$896$	802816.	0.0334077
$897$	1.32100e7	0.548180
$898$	2.23347e7	0.924249
$899$	2.18379e7	0.901181
$900$	−385015.	−0.0158442
$901$	−5.94727e7	−2.44065
$902$	−1.00401e7	−0.410888
$903$	−1.41248e7	−0.576453
$904$	−4.02149e6	−0.163669
$905$	−6.39666e6	−0.259616
$906$	2.40510e7	0.973448
$907$	2.63522e7	1.06365	0.531825	−	0.846854i	$-0.321506\pi$
$907$	2.63522e7	1.06365	0.531825	+	0.846854i	$0.321506\pi$
$908$	−3.65958e6	−0.147305
$909$	4.16346e6	0.167126
$910$	1.95659e6	0.0783241
$911$	−4.82227e6	−0.192511	−0.0962555	−	0.995357i	$-0.530687\pi$
$911$	−4.82227e6	−0.192511	−0.0962555	+	0.995357i	$0.530687\pi$
$912$	−1.05222e7	−0.418909
$913$	4.05474e7	1.60985
$914$	−1.41738e7	−0.561203
$915$	4.38076e6	0.172980
$916$	−1.62874e7	−0.641378
$917$	−1.39715e7	−0.548680
$918$	2.82034e7	1.10457
$919$	−121562.	−0.00474798	−0.00237399	−	0.999997i	$-0.500756\pi$
$919$	−121562.	−0.00474798	−0.00237399	+	0.999997i	$0.500756\pi$
$920$	−3.70149e6	−0.144181
$921$	−3.19224e6	−0.124007
$922$	2.35228e7	0.911299
$923$	662117.	0.0255818
$924$	−4.77499e6	−0.183989
$925$	−4.54128e6	−0.174511
$926$	2.66018e7	1.01949
$927$	−5.31450e6	−0.203125
$928$	−2.17900e6	−0.0830590
$929$	1.74856e7	0.664725	0.332362	−	0.943152i	$-0.392154\pi$
$929$	1.74856e7	0.664725	0.332362	+	0.943152i	$0.392154\pi$
$930$	1.46757e7	0.556407
$931$	6.90104e6	0.260940
$932$	−3.78736e6	−0.142822
$933$	−3.28646e7	−1.23602
$934$	1.73897e7	0.652267
$935$	1.86495e7	0.697650
$936$	−983921.	−0.0367088
$937$	−1.97882e7	−0.736304	−0.368152	−	0.929766i	$-0.620009\pi$
$937$	−1.97882e7	−0.736304	−0.368152	+	0.929766i	$0.620009\pi$
$938$	−3.43663e6	−0.127534
$939$	2.32925e7	0.862088
$940$	8.02261e6	0.296139
$941$	2.05948e7	0.758199	0.379100	−	0.925356i	$-0.376234\pi$
$941$	2.05948e7	0.758199	0.379100	+	0.925356i	$0.376234\pi$
$942$	2.75657e7	1.01214
$943$	1.36340e7	0.499282
$944$	−1.10575e6	−0.0403857
$945$	4.93130e6	0.179631
$946$	3.43410e7	1.24763
$947$	6.90803e6	0.250311	0.125155	−	0.992137i	$-0.460057\pi$
$947$	6.90803e6	0.250311	0.125155	+	0.992137i	$0.460057\pi$
$948$	2.09782e6	0.0758137
$949$	−3.29302e6	−0.118694
$950$	7.18558e6	0.258317
$951$	−1.62480e7	−0.582571
$952$	5.49276e6	0.196426
$953$	3.72040e7	1.32696	0.663480	−	0.748194i	$-0.269079\pi$
$953$	3.72040e7	1.32696	0.663480	+	0.748194i	$0.269079\pi$
$954$	5.22926e6	0.186024
$955$	1.62315e7	0.575905
$956$	2.78391e7	0.985169
$957$	1.29603e7	0.457440
$958$	−3.71872e6	−0.130912
$959$	1.99420e7	0.700199
$960$	−1.46435e6	−0.0512822
$961$	7.66904e7	2.67875
$962$	−1.16054e7	−0.404318
$963$	−238309.	−0.00828085
$964$	−5.32545e6	−0.184571
$965$	−1.92160e7	−0.664272
$966$	6.48421e6	0.223571
$967$	1.88878e7	0.649555	0.324778	−	0.945790i	$-0.394711\pi$
$967$	1.88878e7	0.649555	0.324778	+	0.945790i	$0.394711\pi$
$968$	1.30196e6	0.0446590
$969$	−7.19916e7	−2.46305
$970$	6.21324e6	0.212026
$971$	−4.20566e7	−1.43148	−0.715741	−	0.698366i	$-0.753911\pi$
$971$	−4.20566e7	−1.43148	−0.715741	+	0.698366i	$0.753911\pi$
$972$	−4.62050e6	−0.156864
$973$	662992.	0.0224505
$974$	−2.17955e7	−0.736155
$975$	−3.56885e6	−0.120231
$976$	−3.13693e6	−0.105409
$977$	4.61174e7	1.54571	0.772855	−	0.634583i	$-0.218828\pi$
$977$	4.61174e7	1.54571	0.772855	+	0.634583i	$0.218828\pi$
$978$	−1.61330e7	−0.539346
$979$	−6.15083e6	−0.205105
$980$	960400.	0.0319438
$981$	2.64324e6	0.0876928
$982$	−2.68028e6	−0.0886954
$983$	3.25827e7	1.07548	0.537741	−	0.843110i	$-0.319278\pi$
$983$	3.25827e7	1.07548	0.537741	+	0.843110i	$0.319278\pi$
$984$	5.39378e6	0.177585
$985$	−4.15401e6	−0.136420
$986$	−1.49084e7	−0.488359
$987$	−1.40539e7	−0.459202
$988$	1.83631e7	0.598484
$989$	−4.66335e7	−1.51603
$990$	−1.63979e6	−0.0531742
$991$	1.68209e7	0.544084	0.272042	−	0.962285i	$-0.412301\pi$
$991$	1.68209e7	0.544084	0.272042	+	0.962285i	$0.412301\pi$
$992$	−1.05088e7	−0.339059
$993$	5.39906e7	1.73758
$994$	325003.	0.0104333
$995$	−1.86890e6	−0.0598451
$996$	−2.17829e7	−0.695774
$997$	7.67044e6	0.244389	0.122195	−	0.992506i	$-0.461007\pi$
$997$	7.67044e6	0.244389	0.122195	+	0.992506i	$0.461007\pi$
$998$	2.63207e7	0.836509
$999$	−2.92499e7	−0.927279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.6.a.h.1.1	✓	2
3.2	odd	2		630.6.a.s.1.1		2
4.3	odd	2		560.6.a.k.1.2		2
5.2	odd	4		350.6.c.k.99.4		4
5.3	odd	4		350.6.c.k.99.1		4
5.4	even	2		350.6.a.p.1.2		2
7.6	odd	2		490.6.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.h.1.1	✓	2	1.1	even	1	trivial
350.6.a.p.1.2		2	5.4	even	2
350.6.c.k.99.1		4	5.3	odd	4
350.6.c.k.99.4		4	5.2	odd	4
490.6.a.u.1.2		2	7.6	odd	2
560.6.a.k.1.2		2	4.3	odd	2
630.6.a.s.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	70.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -14.3003 q^{3} +16.0000 q^{4} +25.0000 q^{5} -57.2012 q^{6} +49.0000 q^{7} +64.0000 q^{8} -38.5015 q^{9} +100.000 q^{10} +425.904 q^{11} -228.805 q^{12} +399.303 q^{13} +196.000 q^{14} -357.507 q^{15} +256.000 q^{16} +1751.52 q^{17} -154.006 q^{18} +2874.23 q^{19} +400.000 q^{20} -700.715 q^{21} +1703.62 q^{22} -2313.43 q^{23} -915.219 q^{24} +625.000 q^{25} +1597.21 q^{26} +4025.56 q^{27} +784.000 q^{28} -2127.93 q^{29} -1430.03 q^{30} -10262.5 q^{31} +1024.00 q^{32} -6090.55 q^{33} +7006.08 q^{34} +1225.00 q^{35} -616.024 q^{36} -7266.05 q^{37} +11496.9 q^{38} -5710.16 q^{39} +1600.00 q^{40} -5893.44 q^{41} -2802.86 q^{42} +20157.7 q^{43} +6814.46 q^{44} -962.537 q^{45} -9253.72 q^{46} +20056.5 q^{47} -3660.88 q^{48} +2401.00 q^{49} +2500.00 q^{50} -25047.2 q^{51} +6388.85 q^{52} -33954.9 q^{53} +16102.2 q^{54} +10647.6 q^{55} +3136.00 q^{56} -41102.4 q^{57} -8511.71 q^{58} -4319.34 q^{59} -5720.12 q^{60} -12253.6 q^{61} -41050.1 q^{62} -1886.57 q^{63} +4096.00 q^{64} +9982.58 q^{65} -24362.2 q^{66} -17533.8 q^{67} +28024.3 q^{68} +33082.7 q^{69} +4900.00 q^{70} +1658.18 q^{71} -2464.10 q^{72} -8246.91 q^{73} -29064.2 q^{74} -8937.69 q^{75} +45987.7 q^{76} +20869.3 q^{77} -22840.6 q^{78} -9168.61 q^{79} +6400.00 q^{80} -48210.8 q^{81} -23573.7 q^{82} +95203.2 q^{83} -11211.4 q^{84} +43788.0 q^{85} +80631.0 q^{86} +30430.0 q^{87} +27257.8 q^{88} -14441.8 q^{89} -3850.15 q^{90} +19565.9 q^{91} -37014.9 q^{92} +146757. q^{93} +80226.1 q^{94} +71855.8 q^{95} -14643.5 q^{96} +62132.4 q^{97} +9604.00 q^{98} -16397.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 5 q^{3} + 32 q^{4} + 50 q^{5} + 20 q^{6} + 98 q^{7} + 128 q^{8} + 91 q^{9} + 200 q^{10} + 415 q^{11} + 80 q^{12} + 429 q^{13} + 392 q^{14} + 125 q^{15} + 512 q^{16} + 1319 q^{17} + 364 q^{18}+ \cdots - 17810 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 5 * q^3 + 32 * q^4 + 50 * q^5 + 20 * q^6 + 98 * q^7 + 128 * q^8 + 91 * q^9 + 200 * q^10 + 415 * q^11 + 80 * q^12 + 429 * q^13 + 392 * q^14 + 125 * q^15 + 512 * q^16 + 1319 * q^17 + 364 * q^18 + 1918 * q^19 + 800 * q^20 + 245 * q^21 + 1660 * q^22 - 1334 * q^23 + 320 * q^24 + 1250 * q^25 + 1716 * q^26 + 1835 * q^27 + 1568 * q^28 - 1131 * q^29 + 500 * q^30 - 5472 * q^31 + 2048 * q^32 - 6301 * q^33 + 5276 * q^34 + 2450 * q^35 + 1456 * q^36 - 9156 * q^37 + 7672 * q^38 - 5137 * q^39 + 3200 * q^40 - 7822 * q^41 + 980 * q^42 + 2078 * q^43 + 6640 * q^44 + 2275 * q^45 - 5336 * q^46 - 8507 * q^47 + 1280 * q^48 + 4802 * q^49 + 5000 * q^50 - 33395 * q^51 + 6864 * q^52 - 34242 * q^53 + 7340 * q^54 + 10375 * q^55 + 6272 * q^56 - 59558 * q^57 - 4524 * q^58 + 6952 * q^59 + 2000 * q^60 - 45138 * q^61 - 21888 * q^62 + 4459 * q^63 + 8192 * q^64 + 10725 * q^65 - 25204 * q^66 - 54556 * q^67 + 21104 * q^68 + 51986 * q^69 + 9800 * q^70 - 62272 * q^71 + 5824 * q^72 + 40896 * q^73 - 36624 * q^74 + 3125 * q^75 + 30688 * q^76 + 20335 * q^77 - 20548 * q^78 + 62069 * q^79 + 12800 * q^80 - 121958 * q^81 - 31288 * q^82 + 189600 * q^83 + 3920 * q^84 + 32975 * q^85 + 8312 * q^86 + 49671 * q^87 + 26560 * q^88 + 64190 * q^89 + 9100 * q^90 + 21021 * q^91 - 21344 * q^92 + 239216 * q^93 - 34028 * q^94 + 47950 * q^95 + 5120 * q^96 + 155547 * q^97 + 19208 * q^98 - 17810 * q^99

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