LMFDB - Embedded newform 9.70.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,70,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 70, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 70);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	9.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:	$271.363457963$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 94\!\cdots\!36 $ x^5 - x^4 - 24985894640345560x^3 - 309075533549354721261224x^2 + 93046016582444120336711740360848*x - 941262570723617919770907675844106102736
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{43}\cdot 3^{24}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$5.13065e7$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83774e10 q^{2} -2.52566e20 q^{4} -1.12358e24 q^{5} -8.82897e28 q^{7} -1.54896e31 q^{8} +O(q^{10})$	\(q+1.83774e10 q^{2} -2.52566e20 q^{4} -1.12358e24 q^{5} -8.82897e28 q^{7} -1.54896e31 q^{8} -2.06484e34 q^{10} +6.35095e35 q^{11} +1.50107e38 q^{13} -1.62254e39 q^{14} -1.35571e41 q^{16} -5.11299e42 q^{17} -8.09143e43 q^{19} +2.83777e44 q^{20} +1.16714e46 q^{22} +3.60398e46 q^{23} -4.31642e47 q^{25} +2.75859e48 q^{26} +2.22990e49 q^{28} -5.01375e49 q^{29} -5.34810e51 q^{31} +6.65202e51 q^{32} -9.39635e52 q^{34} +9.92003e52 q^{35} -1.65367e54 q^{37} -1.48700e54 q^{38} +1.74038e55 q^{40} -6.67526e55 q^{41} -2.02257e56 q^{43} -1.60403e56 q^{44} +6.62318e56 q^{46} +7.63503e57 q^{47} -1.27054e58 q^{49} -7.93246e57 q^{50} -3.79120e58 q^{52} -2.97628e59 q^{53} -7.13578e59 q^{55} +1.36758e60 q^{56} -9.21399e59 q^{58} -1.35785e60 q^{59} -5.28661e61 q^{61} -9.82844e61 q^{62} +2.02274e62 q^{64} -1.68657e62 q^{65} -1.38691e63 q^{67} +1.29137e63 q^{68} +1.82305e63 q^{70} +2.36872e63 q^{71} +1.10475e64 q^{73} -3.03903e64 q^{74} +2.04362e64 q^{76} -5.60723e64 q^{77} -7.32931e64 q^{79} +1.52324e65 q^{80} -1.22674e66 q^{82} -3.62072e65 q^{83} +5.74483e66 q^{85} -3.71696e66 q^{86} -9.83738e66 q^{88} +6.55747e66 q^{89} -1.32529e67 q^{91} -9.10241e66 q^{92} +1.40312e68 q^{94} +9.09134e67 q^{95} +4.82901e68 q^{97} -2.33493e68 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 18005734368 q^{2} + 12\!\cdots\!60 q^{4}+ \cdots + 45\!\cdots\!00 q^{8}+O(q^{10}) $ 5 * q + 18005734368 * q^2 + 1258222332330311336960 * q^4 + 1863826173406730009099250 * q^5 + 76799665171164846436246213192 * q^7 + 45904305194055745607709713203200 * q^8	$ 5 q + 18005734368 q^{2} + 12\!\cdots\!60 q^{4}+ \cdots - 17\!\cdots\!24 q^{98}+O(q^{100}) $ 5 * q + 18005734368 * q^2 + 1258222332330311336960 * q^4 + 1863826173406730009099250 * q^5 + 76799665171164846436246213192 * q^7 + 45904305194055745607709713203200 * q^8 + 44330196388334747724288536990904000 * q^10 + 60667038452283127772973811588820340 * q^11 + 241757308976474000869098277194908009686 * q^13 - 354251192093531665156722201608564593920 * q^14 + 959158246463054504693505368032717942292480 * q^16 + 3406116484103989032025799295223462139713638 * q^17 + 50409644862695734347948203723209710229820500 * q^19 + 1423124021474831957749573329409407107348736000 * q^20 - 11532803895526133094453480299474752792963837056 * q^22 - 49597077165419749499080141147449313474867772376 * q^23 + 464109230075747674561453215791202707168413296875 * q^25 + 16366243363702391437841515238911258759405955787840 * q^26 - 145657936238300983941227399236934030905596038045696 * q^28 + 623609331535478016897341347681349171717970694417050 * q^29 - 7773979811443490840377264327630961134705736859811040 * q^31 + 59446525385187765185716890552455969166501734680363008 * q^32 - 257146382902997900108453969123952433606251002004626880 * q^34 + 746713702965644817139124842748848714607056852166946000 * q^35 + 1173349927804932358065167442366744839628119054724224302 * q^37 - 118225357325580676139934406348110667239400005459024000 * q^38 + 113448309945374158392264311043353386142011790732943360000 * q^40 - 126046983235211396249316718220813524712126370275682679410 * q^41 + 182990795236310295463906097926157021228111368794869386156 * q^43 + 207861964397629572369029141530074424104092312018072801280 * q^44 - 10254004636983168196931301388746633342901210187441053098240 * q^46 + 10227620449924872974485942387482033943920758356350760046928 * q^47 - 18333133463047872956569862100374253860638045246565546349315 * q^49 - 36528582075561740316450944849185458926809558787823115500000 * q^50 + 942523544779067327174672695236090488789159958525129397368832 * q^52 - 632699876044410239466855544904774161379655010323706866957246 * q^53 + 908306905388987301982805388456202130484984202488366374469000 * q^55 + 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 + 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 - 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 - 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 + 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 + 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 - 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 + 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 + 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 - 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 - 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 + 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 + 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 - 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 - 1783735577381778172290937711296356094085482547558896852990197505179424 * 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 $

$2$	1.83774e10	0.756397	0.378199	−	0.925724i	$-0.376544\pi$
$2$	1.83774e10	0.756397	0.378199	+	0.925724i	$0.376544\pi$
$3$	0	0
$3$	0	0
$4$	−2.52566e20	−0.427863
$5$	−1.12358e24	−0.863252	−0.431626	−	0.902053i	$-0.642060\pi$
$5$	−1.12358e24	−0.863252	−0.431626	+	0.902053i	$0.642060\pi$
$6$	0	0
$7$	−8.82897e28	−0.616634	−0.308317	−	0.951284i	$-0.599766\pi$
$7$	−8.82897e28	−0.616634	−0.308317	+	0.951284i	$0.599766\pi$
$8$	−1.54896e31	−1.08003
$9$	0	0
$10$	−2.06484e34	−0.652961
$11$	6.35095e35	0.749533	0.374767	−	0.927119i	$-0.377723\pi$
$11$	6.35095e35	0.749533	0.374767	+	0.927119i	$0.377723\pi$
$12$	0	0
$13$	1.50107e38	0.556360	0.278180	−	0.960529i	$-0.410269\pi$
$13$	1.50107e38	0.556360	0.278180	+	0.960529i	$0.410269\pi$
$14$	−1.62254e39	−0.466421
$15$	0	0
$16$	−1.35571e41	−0.389070
$17$	−5.11299e42	−1.81212	−0.906060	−	0.423150i	$-0.860924\pi$
$17$	−5.11299e42	−1.81212	−0.906060	+	0.423150i	$0.860924\pi$
$18$	0	0
$19$	−8.09143e43	−0.618054	−0.309027	−	0.951053i	$-0.600003\pi$
$19$	−8.09143e43	−0.618054	−0.309027	+	0.951053i	$0.600003\pi$
$20$	2.83777e44	0.369354
$21$	0	0
$22$	1.16714e46	0.566945
$23$	3.60398e46	0.377721	0.188861	−	0.982004i	$-0.439521\pi$
$23$	3.60398e46	0.377721	0.188861	+	0.982004i	$0.439521\pi$
$24$	0	0
$25$	−4.31642e47	−0.254796
$26$	2.75859e48	0.420829
$27$	0	0
$28$	2.22990e49	0.263835
$29$	−5.01375e49	−0.176780	−0.0883898	−	0.996086i	$-0.528172\pi$
$29$	−5.01375e49	−0.176780	−0.0883898	+	0.996086i	$0.528172\pi$
$30$	0	0
$31$	−5.34810e51	−1.88895	−0.944477	−	0.328578i	$-0.893431\pi$
$31$	−5.34810e51	−1.88895	−0.944477	+	0.328578i	$0.893431\pi$
$32$	6.65202e51	0.785741
$33$	0	0
$34$	−9.39635e52	−1.37068
$35$	9.92003e52	0.532311
$36$	0	0
$37$	−1.65367e54	−1.30464	−0.652319	−	0.757944i	$-0.726204\pi$
$37$	−1.65367e54	−1.30464	−0.652319	+	0.757944i	$0.726204\pi$
$38$	−1.48700e54	−0.467494
$39$	0	0
$40$	1.74038e55	0.932339
$41$	−6.67526e55	−1.52554	−0.762772	−	0.646667i	$-0.776162\pi$
$41$	−6.67526e55	−1.52554	−0.762772	+	0.646667i	$0.776162\pi$
$42$	0	0
$43$	−2.02257e56	−0.893802	−0.446901	−	0.894584i	$-0.647472\pi$
$43$	−2.02257e56	−0.893802	−0.446901	+	0.894584i	$0.647472\pi$
$44$	−1.60403e56	−0.320698
$45$	0	0
$46$	6.62318e56	0.285707
$47$	7.63503e57	1.56832	0.784160	−	0.620559i	$-0.213094\pi$
$47$	7.63503e57	1.56832	0.784160	+	0.620559i	$0.213094\pi$
$48$	0	0
$49$	−1.27054e58	−0.619762
$50$	−7.93246e57	−0.192727
$51$	0	0
$52$	−3.79120e58	−0.238046
$53$	−2.97628e59	−0.968627	−0.484313	−	0.874895i	$-0.660931\pi$
$53$	−2.97628e59	−0.968627	−0.484313	+	0.874895i	$0.660931\pi$
$54$	0	0
$55$	−7.13578e59	−0.647036
$56$	1.36758e60	0.665985
$57$	0	0
$58$	−9.21399e59	−0.133716
$59$	−1.35785e60	−0.109259	−0.0546294	−	0.998507i	$-0.517398\pi$
$59$	−1.35785e60	−0.109259	−0.0546294	+	0.998507i	$0.517398\pi$
$60$	0	0
$61$	−5.28661e61	−1.34678	−0.673392	−	0.739286i	$-0.735163\pi$
$61$	−5.28661e61	−1.34678	−0.673392	+	0.739286i	$0.735163\pi$
$62$	−9.82844e61	−1.42880
$63$	0	0
$64$	2.02274e62	0.983402
$65$	−1.68657e62	−0.480279
$66$	0	0
$67$	−1.38691e63	−1.38825	−0.694123	−	0.719856i	$-0.744208\pi$
$67$	−1.38691e63	−1.38825	−0.694123	+	0.719856i	$0.744208\pi$
$68$	1.29137e63	0.775340
$69$	0	0
$70$	1.82305e63	0.402638
$71$	2.36872e63	0.320701	0.160351	−	0.987060i	$-0.448738\pi$
$71$	2.36872e63	0.320701	0.160351	+	0.987060i	$0.448738\pi$
$72$	0	0
$73$	1.10475e64	0.573622	0.286811	−	0.957987i	$-0.407405\pi$
$73$	1.10475e64	0.573622	0.286811	+	0.957987i	$0.407405\pi$
$74$	−3.03903e64	−0.986825
$75$	0	0
$76$	2.04362e64	0.264443
$77$	−5.60723e64	−0.462188
$78$	0	0
$79$	−7.32931e64	−0.249418	−0.124709	−	0.992193i	$-0.539800\pi$
$79$	−7.32931e64	−0.249418	−0.124709	+	0.992193i	$0.539800\pi$
$80$	1.52324e65	0.335865
$81$	0	0
$82$	−1.22674e66	−1.15392
$83$	−3.62072e65	−0.224182	−0.112091	−	0.993698i	$-0.535755\pi$
$83$	−3.62072e65	−0.224182	−0.112091	+	0.993698i	$0.535755\pi$
$84$	0	0
$85$	5.74483e66	1.56432
$86$	−3.71696e66	−0.676069
$87$	0	0
$88$	−9.83738e66	−0.809520
$89$	6.55747e66	0.365411	0.182705	−	0.983168i	$-0.441515\pi$
$89$	6.55747e66	0.365411	0.182705	+	0.983168i	$0.441515\pi$
$90$	0	0
$91$	−1.32529e67	−0.343071
$92$	−9.10241e66	−0.161613
$93$	0	0
$94$	1.40312e68	1.18627
$95$	9.09134e67	0.533536
$96$	0	0
$97$	4.82901e68	1.38113	0.690564	−	0.723272i	$-0.257363\pi$
$97$	4.82901e68	1.38113	0.690564	+	0.723272i	$0.257363\pi$
$98$	−2.33493e68	−0.468786
$99$	0	0
$100$	1.09018e68	0.109018
$101$	−7.33834e68	−0.520608	−0.260304	−	0.965527i	$-0.583823\pi$
$101$	−7.33834e68	−0.520608	−0.260304	+	0.965527i	$0.583823\pi$
$102$	0	0
$103$	−3.22980e69	−1.16491	−0.582453	−	0.812864i	$-0.697907\pi$
$103$	−3.22980e69	−1.16491	−0.582453	+	0.812864i	$0.697907\pi$
$104$	−2.32511e69	−0.600887
$105$	0	0
$106$	−5.46964e69	−0.732667
$107$	−1.18986e69	−0.115281	−0.0576403	−	0.998337i	$-0.518358\pi$
$107$	−1.18986e69	−0.115281	−0.0576403	+	0.998337i	$0.518358\pi$
$108$	0	0
$109$	3.32583e70	1.70093	0.850465	−	0.526032i	$-0.176321\pi$
$109$	3.32583e70	1.70093	0.850465	+	0.526032i	$0.176321\pi$
$110$	−1.31137e70	−0.489416
$111$	0	0
$112$	1.19695e70	0.239914
$113$	4.20663e70	0.620481	0.310240	−	0.950658i	$-0.399590\pi$
$113$	4.20663e70	0.620481	0.310240	+	0.950658i	$0.399590\pi$
$114$	0	0
$115$	−4.04934e70	−0.326069
$116$	1.26630e70	0.0756375
$117$	0	0
$118$	−2.49537e70	−0.0826431
$119$	4.51424e71	1.11742
$120$	0	0
$121$	−3.14606e71	−0.438200
$122$	−9.71543e71	−1.01870
$123$	0	0
$124$	1.35075e72	0.808214
$125$	2.38840e72	1.08321
$126$	0	0
$127$	−2.36558e72	−0.620454	−0.310227	−	0.950663i	$-0.600405\pi$
$127$	−2.36558e72	−0.620454	−0.310227	+	0.950663i	$0.600405\pi$
$128$	−2.09383e71	−0.0418984
$129$	0	0
$130$	−3.09948e72	−0.363282
$131$	1.20684e72	0.108590	0.0542952	−	0.998525i	$-0.482709\pi$
$131$	1.20684e72	0.108590	0.0542952	+	0.998525i	$0.482709\pi$
$132$	0	0
$133$	7.14390e72	0.381113
$134$	−2.54878e73	−1.05007
$135$	0	0
$136$	7.91983e73	1.95715
$137$	6.91263e73	1.32673	0.663367	−	0.748294i	$-0.269127\pi$
$137$	6.91263e73	1.32673	0.663367	+	0.748294i	$0.269127\pi$
$138$	0	0
$139$	6.50475e72	0.0757216	0.0378608	−	0.999283i	$-0.487946\pi$
$139$	6.50475e72	0.0757216	0.0378608	+	0.999283i	$0.487946\pi$
$140$	−2.50546e73	−0.227756
$141$	0	0
$142$	4.35310e73	0.242577
$143$	9.53324e73	0.417011
$144$	0	0
$145$	5.63334e73	0.152605
$146$	2.03025e74	0.433886
$147$	0	0
$148$	4.17662e74	0.558207
$149$	−1.06021e75	−1.12322	−0.561612	−	0.827401i	$-0.689818\pi$
$149$	−1.06021e75	−1.12322	−0.561612	+	0.827401i	$0.689818\pi$
$150$	0	0
$151$	2.31654e75	1.54930	0.774649	−	0.632391i	$-0.217926\pi$
$151$	2.31654e75	1.54930	0.774649	+	0.632391i	$0.217926\pi$
$152$	1.25333e75	0.667518
$153$	0	0
$154$	−1.03047e75	−0.349598
$155$	6.00900e75	1.63064
$156$	0	0
$157$	2.67081e75	0.465698	0.232849	−	0.972513i	$-0.425195\pi$
$157$	2.67081e75	0.465698	0.232849	+	0.972513i	$0.425195\pi$
$158$	−1.34694e75	−0.188659
$159$	0	0
$160$	−7.47405e75	−0.678292
$161$	−3.18194e75	−0.232916
$162$	0	0
$163$	2.81849e76	1.34755	0.673773	−	0.738938i	$-0.264672\pi$
$163$	2.81849e76	1.34755	0.673773	+	0.738938i	$0.264672\pi$
$164$	1.68594e76	0.652725
$165$	0	0
$166$	−6.65395e75	−0.169571
$167$	−6.56343e76	−1.35960	−0.679802	−	0.733396i	$-0.737934\pi$
$167$	−6.56343e76	−1.35960	−0.679802	+	0.733396i	$0.737934\pi$
$168$	0	0
$169$	−5.02611e76	−0.690463
$170$	1.05575e77	1.18324
$171$	0	0
$172$	5.10831e76	0.382425
$173$	3.03200e76	0.185839	0.0929197	−	0.995674i	$-0.470380\pi$
$173$	3.03200e76	0.185839	0.0929197	+	0.995674i	$0.470380\pi$
$174$	0	0
$175$	3.81095e76	0.157116
$176$	−8.61004e76	−0.291621
$177$	0	0
$178$	1.20509e77	0.276396
$179$	−7.88055e77	−1.48980	−0.744898	−	0.667178i	$-0.767502\pi$
$179$	−7.88055e77	−1.48980	−0.744898	+	0.667178i	$0.767502\pi$
$180$	0	0
$181$	−6.89713e77	−0.888705	−0.444352	−	0.895852i	$-0.646566\pi$
$181$	−6.89713e77	−0.888705	−0.444352	+	0.895852i	$0.646566\pi$
$182$	−2.43555e77	−0.259498
$183$	0	0
$184$	−5.58243e77	−0.407951
$185$	1.85803e78	1.12623
$186$	0	0
$187$	−3.24723e78	−1.35824
$188$	−1.92835e78	−0.671027
$189$	0	0
$190$	1.67076e78	0.403565
$191$	−3.54584e78	−0.714607	−0.357304	−	0.933988i	$-0.616304\pi$
$191$	−3.54584e78	−0.714607	−0.357304	+	0.933988i	$0.616304\pi$
$192$	0	0
$193$	−4.62550e78	−0.650776	−0.325388	−	0.945581i	$-0.605495\pi$
$193$	−4.62550e78	−0.650776	−0.325388	+	0.945581i	$0.605495\pi$
$194$	8.87449e78	1.04468
$195$	0	0
$196$	3.20896e78	0.265173
$197$	1.64821e78	0.114269	0.0571346	−	0.998366i	$-0.481804\pi$
$197$	1.64821e78	0.114269	0.0571346	+	0.998366i	$0.481804\pi$
$198$	0	0
$199$	1.17255e79	0.573721	0.286860	−	0.957972i	$-0.407388\pi$
$199$	1.17255e79	0.573721	0.286860	+	0.957972i	$0.407388\pi$
$200$	6.68597e78	0.275188
$201$	0	0
$202$	−1.34860e79	−0.393786
$203$	4.42663e78	0.109008
$204$	0	0
$205$	7.50016e79	1.31693
$206$	−5.93554e79	−0.881132
$207$	0	0
$208$	−2.03502e79	−0.216463
$209$	−5.13883e79	−0.463252
$210$	0	0
$211$	9.43238e78	0.0612177	0.0306088	−	0.999531i	$-0.490255\pi$
$211$	9.43238e78	0.0612177	0.0306088	+	0.999531i	$0.490255\pi$
$212$	7.51707e79	0.414440
$213$	0	0
$214$	−2.18666e79	−0.0871980
$215$	2.27251e80	0.771576
$216$	0	0
$217$	4.72183e80	1.16479
$218$	6.11203e80	1.28658
$219$	0	0
$220$	1.80225e80	0.276843
$221$	−7.67497e80	−1.00819
$222$	0	0
$223$	−4.99323e80	−0.480689	−0.240344	−	0.970688i	$-0.577260\pi$
$223$	−4.99323e80	−0.480689	−0.240344	+	0.970688i	$0.577260\pi$
$224$	−5.87305e80	−0.484515
$225$	0	0
$226$	7.73071e80	0.469330
$227$	2.13100e81	1.11094	0.555472	−	0.831535i	$-0.312538\pi$
$227$	2.13100e81	1.11094	0.555472	+	0.831535i	$0.312538\pi$
$228$	0	0
$229$	−3.36412e81	−1.29583	−0.647915	−	0.761713i	$-0.724359\pi$
$229$	−3.36412e81	−1.29583	−0.647915	+	0.761713i	$0.724359\pi$
$230$	−7.44165e80	−0.246637
$231$	0	0
$232$	7.76612e80	0.190928
$233$	−7.16036e78	−0.00151759	−0.000758797	−	1.00000i	$-0.500242\pi$
$233$	−7.16036e78	−0.00151759	−0.000758797		1.00000i	$0.500242\pi$
$234$	0	0
$235$	−8.57854e81	−1.35386
$236$	3.42946e80	0.0467478
$237$	0	0
$238$	8.29602e81	0.845210
$239$	−1.50435e82	−1.32623	−0.663117	−	0.748516i	$-0.730767\pi$
$239$	−1.50435e82	−1.32623	−0.663117	+	0.748516i	$0.730767\pi$
$240$	0	0
$241$	−3.33974e81	−0.220864	−0.110432	−	0.993884i	$-0.535223\pi$
$241$	−3.33974e81	−0.220864	−0.110432	+	0.993884i	$0.535223\pi$
$242$	−5.78166e81	−0.331453
$243$	0	0
$244$	1.33522e82	0.576240
$245$	1.42755e82	0.535011
$246$	0	0
$247$	−1.21458e82	−0.343861
$248$	8.28401e82	2.04013
$249$	0	0
$250$	4.38926e82	0.819333
$251$	−1.19634e82	−0.194587	−0.0972933	−	0.995256i	$-0.531018\pi$
$251$	−1.19634e82	−0.194587	−0.0972933	+	0.995256i	$0.531018\pi$
$252$	0	0
$253$	2.28887e82	0.283115
$254$	−4.34733e82	−0.469310
$255$	0	0
$256$	−1.23249e83	−1.01509
$257$	2.11787e82	0.152477	0.0762387	−	0.997090i	$-0.475709\pi$
$257$	2.11787e82	0.152477	0.0762387	+	0.997090i	$0.475709\pi$
$258$	0	0
$259$	1.46002e83	0.804485
$260$	4.25970e82	0.205494
$261$	0	0
$262$	2.21787e82	0.0821374
$263$	5.20789e83	1.69118	0.845588	−	0.533837i	$-0.179250\pi$
$263$	5.20789e83	1.69118	0.845588	+	0.533837i	$0.179250\pi$
$264$	0	0
$265$	3.34408e83	0.836169
$266$	1.31287e83	0.288273
$267$	0	0
$268$	3.50285e83	0.593980
$269$	2.43999e83	0.363860	0.181930	−	0.983311i	$-0.441766\pi$
$269$	2.43999e83	0.363860	0.181930	+	0.983311i	$0.441766\pi$
$270$	0	0
$271$	1.78874e83	0.206589	0.103294	−	0.994651i	$-0.467062\pi$
$271$	1.78874e83	0.206589	0.103294	+	0.994651i	$0.467062\pi$
$272$	6.93173e83	0.705041
$273$	0	0
$274$	1.27036e84	1.00354
$275$	−2.74133e83	−0.190978
$276$	0	0
$277$	8.95601e83	0.485918	0.242959	−	0.970037i	$-0.421882\pi$
$277$	8.95601e83	0.485918	0.242959	+	0.970037i	$0.421882\pi$
$278$	1.19540e83	0.0572756
$279$	0	0
$280$	−1.53658e84	−0.574913
$281$	4.12597e84	1.36508	0.682540	−	0.730848i	$-0.260875\pi$
$281$	4.12597e84	1.36508	0.682540	+	0.730848i	$0.260875\pi$
$282$	0	0
$283$	−7.03383e84	−1.82205	−0.911023	−	0.412354i	$-0.864707\pi$
$283$	−7.03383e84	−1.82205	−0.911023	+	0.412354i	$0.864707\pi$
$284$	−5.98258e83	−0.137216
$285$	0	0
$286$	1.75196e84	0.315426
$287$	5.89357e84	0.940704
$288$	0	0
$289$	1.81815e85	2.28378
$290$	1.03526e84	0.115430
$291$	0	0
$292$	−2.79022e84	−0.245432
$293$	6.51453e84	0.509272	0.254636	−	0.967037i	$-0.418044\pi$
$293$	6.51453e84	0.509272	0.254636	+	0.967037i	$0.418044\pi$
$294$	0	0
$295$	1.52565e84	0.0943179
$296$	2.56148e85	1.40905
$297$	0	0
$298$	−1.94839e85	−0.849603
$299$	5.40983e84	0.210149
$300$	0	0
$301$	1.78572e85	0.551149
$302$	4.25720e85	1.17188
$303$	0	0
$304$	1.09696e85	0.240466
$305$	5.93991e85	1.16261
$306$	0	0
$307$	9.02219e85	1.40941	0.704706	−	0.709499i	$-0.251079\pi$
$307$	9.02219e85	1.40941	0.704706	+	0.709499i	$0.251079\pi$
$308$	1.41620e85	0.197753
$309$	0	0
$310$	1.10430e86	1.23341
$311$	4.22710e85	0.422483	0.211242	−	0.977434i	$-0.432249\pi$
$311$	4.22710e85	0.422483	0.211242	+	0.977434i	$0.432249\pi$
$312$	0	0
$313$	9.49223e85	0.760482	0.380241	−	0.924888i	$-0.375841\pi$
$313$	9.49223e85	0.760482	0.380241	+	0.924888i	$0.375841\pi$
$314$	4.90825e85	0.352253
$315$	0	0
$316$	1.85113e85	0.106717
$317$	2.99712e86	1.54939	0.774693	−	0.632338i	$-0.217904\pi$
$317$	2.99712e86	1.54939	0.774693	+	0.632338i	$0.217904\pi$
$318$	0	0
$319$	−3.18421e85	−0.132502
$320$	−2.27270e86	−0.848923
$321$	0	0
$322$	−5.84759e85	−0.176177
$323$	4.13714e86	1.11999
$324$	0	0
$325$	−6.47926e85	−0.141759
$326$	5.17966e86	1.01928
$327$	0	0
$328$	1.03397e87	1.64764
$329$	−6.74095e86	−0.967080
$330$	0	0
$331$	−6.30305e86	−0.733644	−0.366822	−	0.930291i	$-0.619554\pi$
$331$	−6.30305e86	−0.733644	−0.366822	+	0.930291i	$0.619554\pi$
$332$	9.14470e85	0.0959192
$333$	0	0
$334$	−1.20619e87	−1.02840
$335$	1.55830e87	1.19841
$336$	0	0
$337$	−1.24071e87	−0.777034	−0.388517	−	0.921442i	$-0.627013\pi$
$337$	−1.24071e87	−0.777034	−0.388517	+	0.921442i	$0.627013\pi$
$338$	−9.23669e86	−0.522264
$339$	0	0
$340$	−1.45095e87	−0.669313
$341$	−3.39655e87	−1.41583
$342$	0	0
$343$	2.93174e87	0.998801
$344$	3.13288e87	0.965334
$345$	0	0
$346$	5.57203e86	0.140568
$347$	−5.12646e87	−1.17071	−0.585357	−	0.810776i	$-0.699046\pi$
$347$	−5.12646e87	−1.17071	−0.585357	+	0.810776i	$0.699046\pi$
$348$	0	0
$349$	6.17210e85	0.0115599	0.00577997	−	0.999983i	$-0.498160\pi$
$349$	6.17210e85	0.0115599	0.00577997	+	0.999983i	$0.498160\pi$
$350$	7.00355e86	0.118842
$351$	0	0
$352$	4.22466e87	0.588939
$353$	−5.76707e87	−0.729001	−0.364500	−	0.931203i	$-0.618760\pi$
$353$	−5.76707e87	−0.729001	−0.364500	+	0.931203i	$0.618760\pi$
$354$	0	0
$355$	−2.66144e87	−0.276846
$356$	−1.65619e87	−0.156346
$357$	0	0
$358$	−1.44824e88	−1.12688
$359$	−5.64791e87	−0.399144	−0.199572	−	0.979883i	$-0.563955\pi$
$359$	−5.64791e87	−0.399144	−0.199572	+	0.979883i	$0.563955\pi$
$360$	0	0
$361$	−1.05924e88	−0.618010
$362$	−1.26752e88	−0.672214
$363$	0	0
$364$	3.34724e87	0.146787
$365$	−1.24127e88	−0.495180
$366$	0	0
$367$	1.92969e88	0.637540	0.318770	−	0.947832i	$-0.396730\pi$
$367$	1.92969e88	0.637540	0.318770	+	0.947832i	$0.396730\pi$
$368$	−4.88595e87	−0.146960
$369$	0	0
$370$	3.41458e88	0.851878
$371$	2.62775e88	0.597289
$372$	0	0
$373$	−2.69870e88	−0.509565	−0.254783	−	0.966998i	$-0.582004\pi$
$373$	−2.69870e88	−0.509565	−0.254783	+	0.966998i	$0.582004\pi$
$374$	−5.96758e88	−1.02737
$375$	0	0
$376$	−1.18264e89	−1.69384
$377$	−7.52601e87	−0.0983531
$378$	0	0
$379$	6.27131e87	0.0682819	0.0341410	−	0.999417i	$-0.489130\pi$
$379$	6.27131e87	0.0682819	0.0341410	+	0.999417i	$0.489130\pi$
$380$	−2.29616e88	−0.228280
$381$	0	0
$382$	−6.51634e88	−0.540527
$383$	−1.89265e89	−1.43454	−0.717269	−	0.696796i	$-0.754608\pi$
$383$	−1.89265e89	−1.43454	−0.717269	+	0.696796i	$0.754608\pi$
$384$	0	0
$385$	6.30016e88	0.398985
$386$	−8.50047e88	−0.492245
$387$	0	0
$388$	−1.21964e89	−0.590934
$389$	−3.32775e89	−1.47533	−0.737666	−	0.675166i	$-0.764072\pi$
$389$	−3.32775e89	−1.47533	−0.737666	+	0.675166i	$0.764072\pi$
$390$	0	0
$391$	−1.84271e89	−0.684476
$392$	1.96803e89	0.669363
$393$	0	0
$394$	3.02899e88	0.0864329
$395$	8.23504e88	0.215311
$396$	0	0
$397$	3.94681e89	0.866910	0.433455	−	0.901175i	$-0.357294\pi$
$397$	3.94681e89	0.866910	0.433455	+	0.901175i	$0.357294\pi$
$398$	2.15485e89	0.433961
$399$	0	0
$400$	5.85181e88	0.0991335
$401$	1.06622e90	1.65717	0.828585	−	0.559863i	$-0.189146\pi$
$401$	1.06622e90	1.65717	0.828585	+	0.559863i	$0.189146\pi$
$402$	0	0
$403$	−8.02789e89	−1.05094
$404$	1.85342e89	0.222749
$405$	0	0
$406$	8.13501e88	0.0824536
$407$	−1.05024e90	−0.977870
$408$	0	0
$409$	2.49992e90	1.96549	0.982747	−	0.184956i	$-0.0592143\pi$
$409$	2.49992e90	1.96549	0.982747	+	0.184956i	$0.0592143\pi$
$410$	1.37834e90	0.996122
$411$	0	0
$412$	8.15737e89	0.498421
$413$	1.19884e89	0.0673728
$414$	0	0
$415$	4.06815e89	0.193525
$416$	9.98517e89	0.437155
$417$	0	0
$418$	−9.44384e89	−0.350402
$419$	4.53380e90	1.54910	0.774548	−	0.632515i	$-0.217977\pi$
$419$	4.53380e90	1.54910	0.774548	+	0.632515i	$0.217977\pi$
$420$	0	0
$421$	−2.79687e90	−0.810850	−0.405425	−	0.914128i	$-0.632876\pi$
$421$	−2.79687e90	−0.810850	−0.405425	+	0.914128i	$0.632876\pi$
$422$	1.73343e89	0.0463049
$423$	0	0
$424$	4.61015e90	1.04615
$425$	2.20698e90	0.461721
$426$	0	0
$427$	4.66753e90	0.830474
$428$	3.00519e89	0.0493244
$429$	0	0
$430$	4.17629e90	0.583618
$431$	−1.36412e90	−0.175949	−0.0879747	−	0.996123i	$-0.528039\pi$
$431$	−1.36412e90	−0.175949	−0.0879747	+	0.996123i	$0.528039\pi$
$432$	0	0
$433$	5.03925e90	0.554030	0.277015	−	0.960866i	$-0.410655\pi$
$433$	5.03925e90	0.554030	0.277015	+	0.960866i	$0.410655\pi$
$434$	8.67750e90	0.881047
$435$	0	0
$436$	−8.39992e90	−0.727766
$437$	−2.91613e90	−0.233452
$438$	0	0
$439$	3.57299e89	0.0244347	0.0122173	−	0.999925i	$-0.496111\pi$
$439$	3.57299e89	0.0244347	0.0122173	+	0.999925i	$0.496111\pi$
$440$	1.10531e91	0.698819
$441$	0	0
$442$	−1.41046e91	−0.762593
$443$	−1.15300e90	−0.0576635	−0.0288317	−	0.999584i	$-0.509179\pi$
$443$	−1.15300e90	−0.0576635	−0.0288317	+	0.999584i	$0.509179\pi$
$444$	0	0
$445$	−7.36782e90	−0.315441
$446$	−9.17628e90	−0.363592
$447$	0	0
$448$	−1.78587e91	−0.606399
$449$	−1.27562e91	−0.401072	−0.200536	−	0.979686i	$-0.564268\pi$
$449$	−1.27562e91	−0.401072	−0.200536	+	0.979686i	$0.564268\pi$
$450$	0	0
$451$	−4.23942e91	−1.14345
$452$	−1.06245e91	−0.265481
$453$	0	0
$454$	3.91624e91	0.840315
$455$	1.48907e91	0.296157
$456$	0	0
$457$	6.82027e91	1.16598	0.582992	−	0.812478i	$-0.301882\pi$
$457$	6.82027e91	1.16598	0.582992	+	0.812478i	$0.301882\pi$
$458$	−6.18240e91	−0.980162
$459$	0	0
$460$	1.02273e91	0.139513
$461$	9.86987e90	0.124919	0.0624596	−	0.998047i	$-0.480106\pi$
$461$	9.86987e90	0.124919	0.0624596	+	0.998047i	$0.480106\pi$
$462$	0	0
$463$	−8.33764e91	−0.908864	−0.454432	−	0.890782i	$-0.650158\pi$
$463$	−8.33764e91	−0.908864	−0.454432	+	0.890782i	$0.650158\pi$
$464$	6.79719e90	0.0687796
$465$	0	0
$466$	−1.31589e89	−0.00114790
$467$	2.02146e91	0.163770	0.0818848	−	0.996642i	$-0.473906\pi$
$467$	2.02146e91	0.163770	0.0818848	+	0.996642i	$0.473906\pi$
$468$	0	0
$469$	1.22450e92	0.856040
$470$	−1.57652e92	−1.02405
$471$	0	0
$472$	2.10326e91	0.118003
$473$	−1.28452e92	−0.669934
$474$	0	0
$475$	3.49260e91	0.157478
$476$	−1.14014e92	−0.478101
$477$	0	0
$478$	−2.76460e92	−1.00316
$479$	−8.35529e91	−0.282089	−0.141045	−	0.990003i	$-0.545046\pi$
$479$	−8.35529e91	−0.282089	−0.141045	+	0.990003i	$0.545046\pi$
$480$	0	0
$481$	−2.48228e92	−0.725849
$482$	−6.13759e91	−0.167061
$483$	0	0
$484$	7.94589e91	0.187490
$485$	−5.42577e92	−1.19226
$486$	0	0
$487$	−8.46053e92	−1.61305	−0.806526	−	0.591199i	$-0.798655\pi$
$487$	−8.46053e92	−1.61305	−0.806526	+	0.591199i	$0.798655\pi$
$488$	8.18876e92	1.45457
$489$	0	0
$490$	2.62348e92	0.404681
$491$	−4.79826e92	−0.689878	−0.344939	−	0.938625i	$-0.612100\pi$
$491$	−4.79826e92	−0.689878	−0.344939	+	0.938625i	$0.612100\pi$
$492$	0	0
$493$	2.56353e92	0.320346
$494$	−2.23209e92	−0.260095
$495$	0	0
$496$	7.25048e92	0.734935
$497$	−2.09134e92	−0.197755
$498$	0	0
$499$	−1.37532e93	−1.13223	−0.566114	−	0.824327i	$-0.691554\pi$
$499$	−1.37532e93	−1.13223	−0.566114	+	0.824327i	$0.691554\pi$
$500$	−6.03227e92	−0.463464
$501$	0	0
$502$	−2.19857e92	−0.147185
$503$	1.11814e93	0.698879	0.349440	−	0.936959i	$-0.386372\pi$
$503$	1.11814e93	0.698879	0.349440	+	0.936959i	$0.386372\pi$
$504$	0	0
$505$	8.24519e92	0.449416
$506$	4.20635e92	0.214147
$507$	0	0
$508$	5.97465e92	0.265469
$509$	3.09546e93	1.28517	0.642587	−	0.766213i	$-0.277861\pi$
$509$	3.09546e93	1.28517	0.642587	+	0.766213i	$0.277861\pi$
$510$	0	0
$511$	−9.75381e92	−0.353715
$512$	−2.14141e93	−0.725915
$513$	0	0
$514$	3.89209e92	0.115334
$515$	3.62893e93	1.00561
$516$	0	0
$517$	4.84897e93	1.17551
$518$	2.68315e93	0.608510
$519$	0	0
$520$	2.61244e93	0.518717
$521$	−8.60888e93	−1.59973	−0.799863	−	0.600183i	$-0.795094\pi$
$521$	−8.60888e93	−1.59973	−0.799863	+	0.600183i	$0.795094\pi$
$522$	0	0
$523$	2.70276e93	0.440047	0.220023	−	0.975495i	$-0.429387\pi$
$523$	2.70276e93	0.440047	0.220023	+	0.975495i	$0.429387\pi$
$524$	−3.04808e92	−0.0464618
$525$	0	0
$526$	9.57077e93	1.27920
$527$	2.73448e94	3.42301
$528$	0	0
$529$	−7.80489e93	−0.857327
$530$	6.14556e93	0.632476
$531$	0	0
$532$	−1.80431e93	−0.163064
$533$	−1.00200e94	−0.848753
$534$	0	0
$535$	1.33690e93	0.0995162
$536$	2.14827e94	1.49935
$537$	0	0
$538$	4.48408e93	0.275223
$539$	−8.06916e93	−0.464532
$540$	0	0
$541$	1.15494e94	0.585130	0.292565	−	0.956246i	$-0.405491\pi$
$541$	1.15494e94	0.585130	0.292565	+	0.956246i	$0.405491\pi$
$542$	3.28724e93	0.156263
$543$	0	0
$544$	−3.40117e94	−1.42386
$545$	−3.73683e94	−1.46833
$546$	0	0
$547$	−5.12485e93	−0.177467	−0.0887336	−	0.996055i	$-0.528282\pi$
$547$	−5.12485e93	−0.177467	−0.0887336	+	0.996055i	$0.528282\pi$
$548$	−1.74590e94	−0.567661
$549$	0	0
$550$	−5.03787e93	−0.144455
$551$	4.05684e93	0.109259
$552$	0	0
$553$	6.47103e93	0.153800
$554$	1.64588e94	0.367547
$555$	0	0
$556$	−1.64288e93	−0.0323985
$557$	−9.14290e93	−0.169465	−0.0847325	−	0.996404i	$-0.527004\pi$
$557$	−9.14290e93	−0.169465	−0.0847325	+	0.996404i	$0.527004\pi$
$558$	0	0
$559$	−3.03602e94	−0.497276
$560$	−1.34487e94	−0.207106
$561$	0	0
$562$	7.58248e94	1.03254
$563$	−6.40420e93	−0.0820210	−0.0410105	−	0.999159i	$-0.513058\pi$
$563$	−6.40420e93	−0.0820210	−0.0410105	+	0.999159i	$0.513058\pi$
$564$	0	0
$565$	−4.72647e94	−0.535631
$566$	−1.29264e95	−1.37819
$567$	0	0
$568$	−3.66906e94	−0.346367
$569$	−1.41851e95	−1.26026	−0.630128	−	0.776491i	$-0.716998\pi$
$569$	−1.41851e95	−1.26026	−0.630128	+	0.776491i	$0.716998\pi$
$570$	0	0
$571$	−2.33130e95	−1.83507	−0.917535	−	0.397654i	$-0.869824\pi$
$571$	−2.33130e95	−1.83507	−0.917535	+	0.397654i	$0.869824\pi$
$572$	−2.40777e94	−0.178424
$573$	0	0
$574$	1.08309e95	0.711546
$575$	−1.55563e94	−0.0962420
$576$	0	0
$577$	9.49740e94	0.521242	0.260621	−	0.965441i	$-0.416073\pi$
$577$	9.49740e94	0.521242	0.260621	+	0.965441i	$0.416073\pi$
$578$	3.34129e95	1.72744
$579$	0	0
$580$	−1.42279e94	−0.0652942
$581$	3.19672e94	0.138238
$582$	0	0
$583$	−1.89022e95	−0.726018
$584$	−1.71122e95	−0.619529
$585$	0	0
$586$	1.19720e95	0.385212
$587$	−2.11763e95	−0.642444	−0.321222	−	0.947004i	$-0.604094\pi$
$587$	−2.11763e95	−0.642444	−0.321222	+	0.947004i	$0.604094\pi$
$588$	0	0
$589$	4.32738e95	1.16747
$590$	2.80374e94	0.0713418
$591$	0	0
$592$	2.24190e95	0.507595
$593$	−5.07974e95	−1.08506	−0.542531	−	0.840035i	$-0.682534\pi$
$593$	−5.07974e95	−1.08506	−0.542531	+	0.840035i	$0.682534\pi$
$594$	0	0
$595$	−5.07210e95	−0.964611
$596$	2.67773e95	0.480586
$597$	0	0
$598$	9.94188e94	0.158956
$599$	−3.02956e95	−0.457251	−0.228626	−	0.973514i	$-0.573423\pi$
$599$	−3.02956e95	−0.457251	−0.228626	+	0.973514i	$0.573423\pi$
$600$	0	0
$601$	−4.18382e95	−0.562865	−0.281432	−	0.959581i	$-0.590809\pi$
$601$	−4.18382e95	−0.562865	−0.281432	+	0.959581i	$0.590809\pi$
$602$	3.28169e95	0.416887
$603$	0	0
$604$	−5.85079e95	−0.662888
$605$	3.53484e95	0.378277
$606$	0	0
$607$	2.90050e95	0.276989	0.138494	−	0.990363i	$-0.455774\pi$
$607$	2.90050e95	0.276989	0.138494	+	0.990363i	$0.455774\pi$
$608$	−5.38244e95	−0.485630
$609$	0	0
$610$	1.09160e96	0.879398
$611$	1.14607e96	0.872551
$612$	0	0
$613$	−1.72442e96	−1.17289	−0.586445	−	0.809989i	$-0.699473\pi$
$613$	−1.72442e96	−1.17289	−0.586445	+	0.809989i	$0.699473\pi$
$614$	1.65805e96	1.06608
$615$	0	0
$616$	8.68540e95	0.499178
$617$	4.52024e95	0.245654	0.122827	−	0.992428i	$-0.460804\pi$
$617$	4.52024e95	0.245654	0.122827	+	0.992428i	$0.460804\pi$
$618$	0	0
$619$	1.70981e96	0.831039	0.415519	−	0.909584i	$-0.363600\pi$
$619$	1.70981e96	0.831039	0.415519	+	0.909584i	$0.363600\pi$
$620$	−1.51767e96	−0.697692
$621$	0	0
$622$	7.76833e95	0.319565
$623$	−5.78957e95	−0.225325
$624$	0	0
$625$	−1.95232e96	−0.680283
$626$	1.74443e96	0.575226
$627$	0	0
$628$	−6.74554e95	−0.199255
$629$	8.45521e96	2.36416
$630$	0	0
$631$	1.73259e96	0.434194	0.217097	−	0.976150i	$-0.430341\pi$
$631$	1.73259e96	0.434194	0.217097	+	0.976150i	$0.430341\pi$
$632$	1.13528e96	0.269380
$633$	0	0
$634$	5.50794e96	1.17195
$635$	2.65791e96	0.535608
$636$	0	0
$637$	−1.90718e96	−0.344811
$638$	−5.85176e95	−0.100224
$639$	0	0
$640$	2.35258e95	0.0361688
$641$	−1.24042e97	−1.80703	−0.903516	−	0.428555i	$-0.859023\pi$
$641$	−1.24042e97	−1.80703	−0.903516	+	0.428555i	$0.859023\pi$
$642$	0	0
$643$	4.85935e96	0.635770	0.317885	−	0.948129i	$-0.397027\pi$
$643$	4.85935e96	0.635770	0.317885	+	0.948129i	$0.397027\pi$
$644$	8.03650e95	0.0996562
$645$	0	0
$646$	7.60300e96	0.847155
$647$	1.58911e96	0.167863	0.0839317	−	0.996472i	$-0.473252\pi$
$647$	1.58911e96	0.167863	0.0839317	+	0.996472i	$0.473252\pi$
$648$	0	0
$649$	−8.62362e95	−0.0818931
$650$	−1.19072e96	−0.107226
$651$	0	0
$652$	−7.11854e96	−0.576566
$653$	3.72042e96	0.285816	0.142908	−	0.989736i	$-0.454355\pi$
$653$	3.72042e96	0.285816	0.142908	+	0.989736i	$0.454355\pi$
$654$	0	0
$655$	−1.35598e96	−0.0937408
$656$	9.04971e96	0.593543
$657$	0	0
$658$	−1.23881e97	−0.731497
$659$	−1.80448e97	−1.01112	−0.505562	−	0.862790i	$-0.668715\pi$
$659$	−1.80448e97	−1.01112	−0.505562	+	0.862790i	$0.668715\pi$
$660$	0	0
$661$	−1.61074e97	−0.812970	−0.406485	−	0.913657i	$-0.633246\pi$
$661$	−1.61074e97	−0.812970	−0.406485	+	0.913657i	$0.633246\pi$
$662$	−1.15834e97	−0.554926
$663$	0	0
$664$	5.60836e96	0.242124
$665$	−8.02672e96	−0.328997
$666$	0	0
$667$	−1.80694e96	−0.0667734
$668$	1.65770e97	0.581725
$669$	0	0
$670$	2.86375e97	0.906471
$671$	−3.35750e97	−1.00946
$672$	0	0
$673$	−6.18856e97	−1.67907	−0.839536	−	0.543303i	$-0.817173\pi$
$673$	−6.18856e97	−1.67907	−0.839536	+	0.543303i	$0.817173\pi$
$674$	−2.28011e97	−0.587746
$675$	0	0
$676$	1.26942e97	0.295424
$677$	−8.78367e96	−0.194253	−0.0971264	−	0.995272i	$-0.530965\pi$
$677$	−8.78367e96	−0.194253	−0.0971264	+	0.995272i	$0.530965\pi$
$678$	0	0
$679$	−4.26352e97	−0.851651
$680$	−8.89853e97	−1.68951
$681$	0	0
$682$	−6.24199e97	−1.07093
$683$	7.98957e96	0.130319	0.0651597	−	0.997875i	$-0.479244\pi$
$683$	7.98957e96	0.130319	0.0651597	+	0.997875i	$0.479244\pi$
$684$	0	0
$685$	−7.76687e97	−1.14531
$686$	5.38779e97	0.755490
$687$	0	0
$688$	2.74201e97	0.347751
$689$	−4.46762e97	−0.538906
$690$	0	0
$691$	1.70561e98	1.86161	0.930804	−	0.365518i	$-0.119108\pi$
$691$	1.70561e98	1.86161	0.930804	+	0.365518i	$0.119108\pi$
$692$	−7.65779e96	−0.0795139
$693$	0	0
$694$	−9.42112e97	−0.885525
$695$	−7.30858e96	−0.0653668
$696$	0	0
$697$	3.41305e98	2.76447
$698$	1.13427e96	0.00874391
$699$	0	0
$700$	−9.62517e96	−0.0672242
$701$	1.83692e98	1.22129	0.610643	−	0.791906i	$-0.290911\pi$
$701$	1.83692e98	1.22129	0.610643	+	0.791906i	$0.290911\pi$
$702$	0	0
$703$	1.33806e98	0.806337
$704$	1.28463e98	0.737092
$705$	0	0
$706$	−1.05984e98	−0.551414
$707$	6.47900e97	0.321025
$708$	0	0
$709$	−1.26968e98	−0.570690	−0.285345	−	0.958425i	$-0.592108\pi$
$709$	−1.26968e98	−0.570690	−0.285345	+	0.958425i	$0.592108\pi$
$710$	−4.89104e97	−0.209405
$711$	0	0
$712$	−1.01573e98	−0.394655
$713$	−1.92744e98	−0.713498
$714$	0	0
$715$	−1.07113e98	−0.359985
$716$	1.99036e98	0.637429
$717$	0	0
$718$	−1.03794e98	−0.301911
$719$	3.68969e98	1.02292	0.511462	−	0.859306i	$-0.329104\pi$
$719$	3.68969e98	1.02292	0.511462	+	0.859306i	$0.329104\pi$
$720$	0	0
$721$	2.85158e98	0.718322
$722$	−1.94661e98	−0.467461
$723$	0	0
$724$	1.74198e98	0.380244
$725$	2.16414e97	0.0450428
$726$	0	0
$727$	5.94826e98	1.12578	0.562889	−	0.826533i	$-0.309690\pi$
$727$	5.94826e98	1.12578	0.562889	+	0.826533i	$0.309690\pi$
$728$	2.05283e98	0.370528
$729$	0	0
$730$	−2.28114e98	−0.374553
$731$	1.03414e99	1.61968
$732$	0	0
$733$	−5.69595e98	−0.811857	−0.405928	−	0.913905i	$-0.633052\pi$
$733$	−5.69595e98	−0.811857	−0.405928	+	0.913905i	$0.633052\pi$
$734$	3.54627e98	0.482234
$735$	0	0
$736$	2.39737e98	0.296791
$737$	−8.80817e98	−1.04054
$738$	0	0
$739$	−1.30994e99	−1.40935	−0.704673	−	0.709532i	$-0.748906\pi$
$739$	−1.30994e99	−1.40935	−0.704673	+	0.709532i	$0.748906\pi$
$740$	−4.69275e98	−0.481873
$741$	0	0
$742$	4.82913e98	0.451787
$743$	1.09338e99	0.976466	0.488233	−	0.872713i	$-0.337642\pi$
$743$	1.09338e99	0.976466	0.488233	+	0.872713i	$0.337642\pi$
$744$	0	0
$745$	1.19123e99	0.969624
$746$	−4.95951e98	−0.385434
$747$	0	0
$748$	8.20140e98	0.581143
$749$	1.05053e98	0.0710860
$750$	0	0
$751$	−7.23723e97	−0.0446678	−0.0223339	−	0.999751i	$-0.507110\pi$
$751$	−7.23723e97	−0.0446678	−0.0223339	+	0.999751i	$0.507110\pi$
$752$	−1.03509e99	−0.610186
$753$	0	0
$754$	−1.38309e98	−0.0743940
$755$	−2.60281e99	−1.33743
$756$	0	0
$757$	7.29435e98	0.342120	0.171060	−	0.985261i	$-0.445281\pi$
$757$	7.29435e98	0.342120	0.171060	+	0.985261i	$0.445281\pi$
$758$	1.15251e98	0.0516483
$759$	0	0
$760$	−1.40822e99	−0.576236
$761$	2.12780e99	0.832072	0.416036	−	0.909348i	$-0.363419\pi$
$761$	2.12780e99	0.832072	0.416036	+	0.909348i	$0.363419\pi$
$762$	0	0
$763$	−2.93637e99	−1.04885
$764$	8.95557e98	0.305754
$765$	0	0
$766$	−3.47820e99	−1.08508
$767$	−2.03823e98	−0.0607873
$768$	0	0
$769$	5.23656e99	1.42754	0.713769	−	0.700382i	$-0.246987\pi$
$769$	5.23656e99	1.42754	0.713769	+	0.700382i	$0.246987\pi$
$770$	1.15781e99	0.301791
$771$	0	0
$772$	1.16824e99	0.278443
$773$	−4.81316e99	−1.09708	−0.548539	−	0.836125i	$-0.684816\pi$
$773$	−4.81316e99	−1.09708	−0.548539	+	0.836125i	$0.684816\pi$
$774$	0	0
$775$	2.30846e99	0.481298
$776$	−7.47996e99	−1.49166
$777$	0	0
$778$	−6.11555e99	−1.11594
$779$	5.40124e99	0.942869
$780$	0	0
$781$	1.50436e99	0.240376
$782$	−3.38642e99	−0.517736
$783$	0	0
$784$	1.72249e99	0.241131
$785$	−3.00085e99	−0.402015
$786$	0	0
$787$	−5.33226e98	−0.0654309	−0.0327154	−	0.999465i	$-0.510416\pi$
$787$	−5.33226e98	−0.0654309	−0.0327154	+	0.999465i	$0.510416\pi$
$788$	−4.16283e98	−0.0488916
$789$	0	0
$790$	1.51339e99	0.162861
$791$	−3.71402e99	−0.382610
$792$	0	0
$793$	−7.93559e99	−0.749297
$794$	7.25323e99	0.655728
$795$	0	0
$796$	−2.96146e99	−0.245474
$797$	−1.41086e100	−1.11988	−0.559941	−	0.828533i	$-0.689176\pi$
$797$	−1.41086e100	−1.11988	−0.559941	+	0.828533i	$0.689176\pi$
$798$	0	0
$799$	−3.90378e100	−2.84198
$800$	−2.87129e99	−0.200204
$801$	0	0
$802$	1.95944e100	1.25348
$803$	7.01621e99	0.429948
$804$	0	0
$805$	3.57515e99	0.201065
$806$	−1.47532e100	−0.794927
$807$	0	0
$808$	1.13668e100	0.562273
$809$	2.53533e100	1.20174	0.600871	−	0.799346i	$-0.294821\pi$
$809$	2.53533e100	1.20174	0.600871	+	0.799346i	$0.294821\pi$
$810$	0	0
$811$	4.13280e100	1.79897	0.899487	−	0.436948i	$-0.143941\pi$
$811$	4.13280e100	1.79897	0.899487	+	0.436948i	$0.143941\pi$
$812$	−1.11802e99	−0.0466407
$813$	0	0
$814$	−1.93007e100	−0.739658
$815$	−3.16679e100	−1.16327
$816$	0	0
$817$	1.63655e100	0.552417
$818$	4.59421e100	1.48669
$819$	0	0
$820$	−1.89429e100	−0.563466
$821$	5.53997e100	1.58004	0.790021	−	0.613080i	$-0.210070\pi$
$821$	5.53997e100	1.58004	0.790021	+	0.613080i	$0.210070\pi$
$822$	0	0
$823$	2.61490e100	0.685743	0.342872	−	0.939382i	$-0.388600\pi$
$823$	2.61490e100	0.685743	0.342872	+	0.939382i	$0.388600\pi$
$824$	5.00284e100	1.25814
$825$	0	0
$826$	2.20316e99	0.0509606
$827$	−2.23696e100	−0.496271	−0.248136	−	0.968725i	$-0.579818\pi$
$827$	−2.23696e100	−0.496271	−0.248136	+	0.968725i	$0.579818\pi$
$828$	0	0
$829$	−4.96571e100	−1.01356	−0.506781	−	0.862075i	$-0.669165\pi$
$829$	−4.96571e100	−1.01356	−0.506781	+	0.862075i	$0.669165\pi$
$830$	7.47622e99	0.146382
$831$	0	0
$832$	3.03628e100	0.547126
$833$	6.49627e100	1.12308
$834$	0	0
$835$	7.37451e100	1.17368
$836$	1.29789e100	0.198208
$837$	0	0
$838$	8.33196e100	1.17173
$839$	−5.71823e100	−0.771745	−0.385872	−	0.922552i	$-0.626099\pi$
$839$	−5.71823e100	−0.771745	−0.385872	+	0.922552i	$0.626099\pi$
$840$	0	0
$841$	−7.79243e100	−0.968749
$842$	−5.13993e100	−0.613324
$843$	0	0
$844$	−2.38230e99	−0.0261928
$845$	5.64722e100	0.596044
$846$	0	0
$847$	2.77765e100	0.270209
$848$	4.03497e100	0.376863
$849$	0	0
$850$	4.05586e100	0.349245
$851$	−5.95980e100	−0.492790
$852$	0	0
$853$	1.15331e100	0.0879433	0.0439717	−	0.999033i	$-0.485999\pi$
$853$	1.15331e100	0.0879433	0.0439717	+	0.999033i	$0.485999\pi$
$854$	8.57773e100	0.628168
$855$	0	0
$856$	1.84305e100	0.124507
$857$	−1.79317e101	−1.16355	−0.581773	−	0.813352i	$-0.697641\pi$
$857$	−1.79317e101	−1.16355	−0.581773	+	0.813352i	$0.697641\pi$
$858$	0	0
$859$	−2.06109e101	−1.23405	−0.617025	−	0.786943i	$-0.711662\pi$
$859$	−2.06109e101	−1.23405	−0.617025	+	0.786943i	$0.711662\pi$
$860$	−5.73958e100	−0.330129
$861$	0	0
$862$	−2.50691e100	−0.133088
$863$	2.70544e100	0.137996	0.0689979	−	0.997617i	$-0.478020\pi$
$863$	2.70544e100	0.137996	0.0689979	+	0.997617i	$0.478020\pi$
$864$	0	0
$865$	−3.40668e100	−0.160426
$866$	9.26084e100	0.419067
$867$	0	0
$868$	−1.19257e101	−0.498373
$869$	−4.65481e100	−0.186947
$870$	0	0
$871$	−2.08185e101	−0.772365
$872$	−5.15160e101	−1.83706
$873$	0	0
$874$	−5.35910e100	−0.176582
$875$	−2.10871e101	−0.667942
$876$	0	0
$877$	1.39865e101	0.409471	0.204735	−	0.978817i	$-0.434367\pi$
$877$	1.39865e101	0.409471	0.204735	+	0.978817i	$0.434367\pi$
$878$	6.56624e99	0.0184823
$879$	0	0
$880$	9.67404e100	0.251742
$881$	4.46892e101	1.11824	0.559118	−	0.829088i	$-0.311140\pi$
$881$	4.46892e101	1.11824	0.559118	+	0.829088i	$0.311140\pi$
$882$	0	0
$883$	−7.72337e101	−1.78716	−0.893578	−	0.448907i	$-0.851813\pi$
$883$	−7.72337e101	−1.78716	−0.893578	+	0.448907i	$0.851813\pi$
$884$	1.93844e101	0.431368
$885$	0	0
$886$	−2.11892e100	−0.0436165
$887$	−5.11089e101	−1.01189	−0.505943	−	0.862567i	$-0.668855\pi$
$887$	−5.11089e101	−1.01189	−0.505943	+	0.862567i	$0.668855\pi$
$888$	0	0
$889$	2.08857e101	0.382593
$890$	−1.35402e101	−0.238599
$891$	0	0
$892$	1.26112e101	0.205669
$893$	−6.17783e101	−0.969306
$894$	0	0
$895$	8.85440e101	1.28607
$896$	1.84863e100	0.0258360
$897$	0	0
$898$	−2.34426e101	−0.303370
$899$	2.68141e101	0.333928
$900$	0	0
$901$	1.52177e102	1.75527
$902$	−7.79097e101	−0.864900
$903$	0	0
$904$	−6.51592e101	−0.670139
$905$	7.74945e101	0.767176
$906$	0	0
$907$	−7.73852e101	−0.709915	−0.354958	−	0.934882i	$-0.615505\pi$
$907$	−7.73852e101	−0.709915	−0.354958	+	0.934882i	$0.615505\pi$
$908$	−5.38219e101	−0.475332
$909$	0	0
$910$	2.73653e101	0.224012
$911$	9.32355e101	0.734848	0.367424	−	0.930054i	$-0.380240\pi$
$911$	9.32355e101	0.734848	0.367424	+	0.930054i	$0.380240\pi$
$912$	0	0
$913$	−2.29950e101	−0.168032
$914$	1.25339e102	0.881948
$915$	0	0
$916$	8.49663e101	0.554438
$917$	−1.06552e101	−0.0669606
$918$	0	0
$919$	−1.85343e102	−1.08041	−0.540207	−	0.841532i	$-0.681654\pi$
$919$	−1.85343e102	−1.08041	−0.540207	+	0.841532i	$0.681654\pi$
$920$	6.27228e101	0.352164
$921$	0	0
$922$	1.81383e101	0.0944886
$923$	3.55562e101	0.178425
$924$	0	0
$925$	7.13794e101	0.332417
$926$	−1.53224e102	−0.687462
$927$	0	0
$928$	−3.33516e101	−0.138903
$929$	1.39993e102	0.561778	0.280889	−	0.959740i	$-0.409371\pi$
$929$	1.39993e102	0.561778	0.280889	+	0.959740i	$0.409371\pi$
$930$	0	0
$931$	1.02805e102	0.383046
$932$	1.80846e99	0.000649323 0
$933$	0	0
$934$	3.71493e101	0.123875
$935$	3.64851e102	1.17251
$936$	0	0
$937$	7.09610e101	0.211838	0.105919	−	0.994375i	$-0.466222\pi$
$937$	7.09610e101	0.211838	0.105919	+	0.994375i	$0.466222\pi$
$938$	2.25031e102	0.647507
$939$	0	0
$940$	2.16665e102	0.579265
$941$	−1.31529e102	−0.338985	−0.169492	−	0.985531i	$-0.554213\pi$
$941$	−1.31529e102	−0.338985	−0.169492	+	0.985531i	$0.554213\pi$
$942$	0	0
$943$	−2.40575e102	−0.576231
$944$	1.84085e101	0.0425093
$945$	0	0
$946$	−2.36062e102	−0.506736
$947$	4.24962e102	0.879580	0.439790	−	0.898101i	$-0.355053\pi$
$947$	4.24962e102	0.879580	0.439790	+	0.898101i	$0.355053\pi$
$948$	0	0
$949$	1.65831e102	0.319140
$950$	6.41850e101	0.119116
$951$	0	0
$952$	−6.99239e102	−1.20684
$953$	−7.22436e102	−1.20252	−0.601262	−	0.799052i	$-0.705335\pi$
$953$	−7.22436e102	−1.20252	−0.601262	+	0.799052i	$0.705335\pi$
$954$	0	0
$955$	3.98402e102	0.616886
$956$	3.79947e102	0.567447
$957$	0	0
$958$	−1.53549e102	−0.213371
$959$	−6.10314e102	−0.818110
$960$	0	0
$961$	2.05862e103	2.56815
$962$	−4.56180e102	−0.549030
$963$	0	0
$964$	8.43506e101	0.0944997
$965$	5.19710e102	0.561783
$966$	0	0
$967$	−4.25077e102	−0.427813	−0.213907	−	0.976854i	$-0.568619\pi$
$967$	−4.25077e102	−0.427813	−0.213907	+	0.976854i	$0.568619\pi$
$968$	4.87314e102	0.473270
$969$	0	0
$970$	−9.97116e102	−0.901822
$971$	3.95129e102	0.344886	0.172443	−	0.985020i	$-0.444834\pi$
$971$	3.95129e102	0.344886	0.172443	+	0.985020i	$0.444834\pi$
$972$	0	0
$973$	−5.74302e101	−0.0466925
$974$	−1.55483e103	−1.22011
$975$	0	0
$976$	7.16711e102	0.523993
$977$	2.08430e103	1.47095	0.735475	−	0.677552i	$-0.236959\pi$
$977$	2.08430e103	1.47095	0.735475	+	0.677552i	$0.236959\pi$
$978$	0	0
$979$	4.16462e102	0.273887
$980$	−3.60551e102	−0.228911
$981$	0	0
$982$	−8.81797e102	−0.521822
$983$	−1.66610e103	−0.951927	−0.475964	−	0.879465i	$-0.657901\pi$
$983$	−1.66610e103	−0.951927	−0.475964	+	0.879465i	$0.657901\pi$
$984$	0	0
$985$	−1.85190e102	−0.0986430
$986$	4.71110e102	0.242309
$987$	0	0
$988$	3.06762e102	0.147125
$989$	−7.28928e102	−0.337608
$990$	0	0
$991$	−1.55619e103	−0.672237	−0.336118	−	0.941820i	$-0.609114\pi$
$991$	−1.55619e103	−0.672237	−0.336118	+	0.941820i	$0.609114\pi$
$992$	−3.55757e103	−1.48423
$993$	0	0
$994$	−3.84334e102	−0.149582
$995$	−1.31745e103	−0.495266
$996$	0	0
$997$	−3.68617e103	−1.29298	−0.646491	−	0.762921i	$-0.723764\pi$
$997$	−3.68617e103	−1.29298	−0.646491	+	0.762921i	$0.723764\pi$
$998$	−2.52748e103	−0.856415
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.70.a.b.1.4		5
3.2	odd	2		1.70.a.a.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.70.a.a.1.2	✓	5	3.2	odd	2
9.70.a.b.1.4		5	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83774e10 q^{2} -2.52566e20 q^{4} -1.12358e24 q^{5} -8.82897e28 q^{7} -1.54896e31 q^{8} +O(q^{10})\)	\(q+1.83774e10 q^{2} -2.52566e20 q^{4} -1.12358e24 q^{5} -8.82897e28 q^{7} -1.54896e31 q^{8} -2.06484e34 q^{10} +6.35095e35 q^{11} +1.50107e38 q^{13} -1.62254e39 q^{14} -1.35571e41 q^{16} -5.11299e42 q^{17} -8.09143e43 q^{19} +2.83777e44 q^{20} +1.16714e46 q^{22} +3.60398e46 q^{23} -4.31642e47 q^{25} +2.75859e48 q^{26} +2.22990e49 q^{28} -5.01375e49 q^{29} -5.34810e51 q^{31} +6.65202e51 q^{32} -9.39635e52 q^{34} +9.92003e52 q^{35} -1.65367e54 q^{37} -1.48700e54 q^{38} +1.74038e55 q^{40} -6.67526e55 q^{41} -2.02257e56 q^{43} -1.60403e56 q^{44} +6.62318e56 q^{46} +7.63503e57 q^{47} -1.27054e58 q^{49} -7.93246e57 q^{50} -3.79120e58 q^{52} -2.97628e59 q^{53} -7.13578e59 q^{55} +1.36758e60 q^{56} -9.21399e59 q^{58} -1.35785e60 q^{59} -5.28661e61 q^{61} -9.82844e61 q^{62} +2.02274e62 q^{64} -1.68657e62 q^{65} -1.38691e63 q^{67} +1.29137e63 q^{68} +1.82305e63 q^{70} +2.36872e63 q^{71} +1.10475e64 q^{73} -3.03903e64 q^{74} +2.04362e64 q^{76} -5.60723e64 q^{77} -7.32931e64 q^{79} +1.52324e65 q^{80} -1.22674e66 q^{82} -3.62072e65 q^{83} +5.74483e66 q^{85} -3.71696e66 q^{86} -9.83738e66 q^{88} +6.55747e66 q^{89} -1.32529e67 q^{91} -9.10241e66 q^{92} +1.40312e68 q^{94} +9.09134e67 q^{95} +4.82901e68 q^{97} -2.33493e68 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 18005734368 q^{2} + 12\!\cdots\!60 q^{4}+ \cdots + 45\!\cdots\!00 q^{8}+O(q^{10}) \) 5 * q + 18005734368 * q^2 + 1258222332330311336960 * q^4 + 1863826173406730009099250 * q^5 + 76799665171164846436246213192 * q^7 + 45904305194055745607709713203200 * q^8	\( 5 q + 18005734368 q^{2} + 12\!\cdots\!60 q^{4}+ \cdots - 17\!\cdots\!24 q^{98}+O(q^{100}) \) 5 * q + 18005734368 * q^2 + 1258222332330311336960 * q^4 + 1863826173406730009099250 * q^5 + 76799665171164846436246213192 * q^7 + 45904305194055745607709713203200 * q^8 + 44330196388334747724288536990904000 * q^10 + 60667038452283127772973811588820340 * q^11 + 241757308976474000869098277194908009686 * q^13 - 354251192093531665156722201608564593920 * q^14 + 959158246463054504693505368032717942292480 * q^16 + 3406116484103989032025799295223462139713638 * q^17 + 50409644862695734347948203723209710229820500 * q^19 + 1423124021474831957749573329409407107348736000 * q^20 - 11532803895526133094453480299474752792963837056 * q^22 - 49597077165419749499080141147449313474867772376 * q^23 + 464109230075747674561453215791202707168413296875 * q^25 + 16366243363702391437841515238911258759405955787840 * q^26 - 145657936238300983941227399236934030905596038045696 * q^28 + 623609331535478016897341347681349171717970694417050 * q^29 - 7773979811443490840377264327630961134705736859811040 * q^31 + 59446525385187765185716890552455969166501734680363008 * q^32 - 257146382902997900108453969123952433606251002004626880 * q^34 + 746713702965644817139124842748848714607056852166946000 * q^35 + 1173349927804932358065167442366744839628119054724224302 * q^37 - 118225357325580676139934406348110667239400005459024000 * q^38 + 113448309945374158392264311043353386142011790732943360000 * q^40 - 126046983235211396249316718220813524712126370275682679410 * q^41 + 182990795236310295463906097926157021228111368794869386156 * q^43 + 207861964397629572369029141530074424104092312018072801280 * q^44 - 10254004636983168196931301388746633342901210187441053098240 * q^46 + 10227620449924872974485942387482033943920758356350760046928 * q^47 - 18333133463047872956569862100374253860638045246565546349315 * q^49 - 36528582075561740316450944849185458926809558787823115500000 * q^50 + 942523544779067327174672695236090488789159958525129397368832 * q^52 - 632699876044410239466855544904774161379655010323706866957246 * q^53 + 908306905388987301982805388456202130484984202488366374469000 * q^55 + 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 + 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 - 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 - 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 + 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 + 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 - 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 + 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 + 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 - 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 - 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 + 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 + 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 - 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 - 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98

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