LMFDB - Embedded newform 3.42.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,42,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 42, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	3.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:	$31.9415011369$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 14982256920x + 433388802120300 $ x^3 - x^2 - 14982256920*x + 433388802120300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$30895.0$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-467196. q^{2} -3.48678e9 q^{3} -1.98075e12 q^{4} -2.77079e14 q^{5} +1.62901e15 q^{6} +3.80292e17 q^{7} +1.95278e18 q^{8} +1.21577e19 q^{9} +O(q^{10})$	\(q-467196. q^{2} -3.48678e9 q^{3} -1.98075e12 q^{4} -2.77079e14 q^{5} +1.62901e15 q^{6} +3.80292e17 q^{7} +1.95278e18 q^{8} +1.21577e19 q^{9} +1.29450e20 q^{10} +1.78075e20 q^{11} +6.90645e21 q^{12} +2.06379e22 q^{13} -1.77671e23 q^{14} +9.66116e23 q^{15} +3.44339e24 q^{16} -2.32357e25 q^{17} -5.68002e24 q^{18} +2.05644e26 q^{19} +5.48825e26 q^{20} -1.32600e27 q^{21} -8.31962e25 q^{22} -4.66038e27 q^{23} -6.80891e27 q^{24} +3.12982e28 q^{25} -9.64193e27 q^{26} -4.23912e28 q^{27} -7.53263e29 q^{28} +1.57858e30 q^{29} -4.51366e29 q^{30} -4.51602e30 q^{31} -5.90294e30 q^{32} -6.20911e29 q^{33} +1.08556e31 q^{34} -1.05371e32 q^{35} -2.40813e31 q^{36} -1.32006e32 q^{37} -9.60760e31 q^{38} -7.19598e31 q^{39} -5.41074e32 q^{40} -3.66611e32 q^{41} +6.19500e32 q^{42} -6.46266e32 q^{43} -3.52723e32 q^{44} -3.36864e33 q^{45} +2.17731e33 q^{46} +2.68528e34 q^{47} -1.20064e34 q^{48} +1.00054e35 q^{49} -1.46224e34 q^{50} +8.10180e34 q^{51} -4.08785e34 q^{52} -1.90002e35 q^{53} +1.98050e34 q^{54} -4.93410e34 q^{55} +7.42624e35 q^{56} -7.17036e35 q^{57} -7.37507e35 q^{58} -3.62437e36 q^{59} -1.91363e36 q^{60} +2.16433e36 q^{61} +2.10987e36 q^{62} +4.62346e36 q^{63} -4.81426e36 q^{64} -5.71832e36 q^{65} +2.90087e35 q^{66} +3.15856e36 q^{67} +4.60242e37 q^{68} +1.62497e37 q^{69} +4.92289e37 q^{70} -4.01004e37 q^{71} +2.37412e37 q^{72} +7.75186e37 q^{73} +6.16729e37 q^{74} -1.09130e38 q^{75} -4.07329e38 q^{76} +6.77206e37 q^{77} +3.36193e37 q^{78} -8.36639e38 q^{79} -9.54091e38 q^{80} +1.47809e38 q^{81} +1.71279e38 q^{82} -1.97827e39 q^{83} +2.62647e39 q^{84} +6.43814e39 q^{85} +3.01933e38 q^{86} -5.50417e39 q^{87} +3.47741e38 q^{88} +3.68899e39 q^{89} +1.57381e39 q^{90} +7.84841e39 q^{91} +9.23105e39 q^{92} +1.57464e40 q^{93} -1.25455e40 q^{94} -5.69796e40 q^{95} +2.05823e40 q^{96} +4.15034e40 q^{97} -4.67449e40 q^{98} +2.16498e39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 36\!\cdots\!03 q^{9}+O(q^{10}) $ 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9	$ 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 26\!\cdots\!04 q^{99}+O(q^{100}) $ 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9 + 303684786396357841224 * q^10 + 2162403578017276790604 * q^11 + 7860140147941716898800 * q^12 + 44715417115247213223642 * q^13 + 320671470159767900457984 * q^14 - 134766121552486207386426 * q^15 - 5459234621059712438935296 * q^16 - 10989933423479049968718714 * q^17 - 3518185230541894056433380 * q^18 + 196397070114735534584831028 * q^19 + 531636782784591447776761824 * q^20 + 155518294615858001587027968 * q^21 - 4513503674461058254096349328 * q^22 - 4665149638066794122614978584 * q^23 - 7908141906446322929993781696 * q^24 - 4609009761244207114343812899 * q^25 + 122894273592250273312332501576 * q^26 - 127173474825648610542883299603 * q^27 - 599824891534617466777136050176 * q^28 - 941555486655490244273102003214 * q^29 - 1058883376027837523993877946824 * q^30 - 6480085319036017864686465368808 * q^31 - 9194142460916956643740243289088 * q^32 - 7539835064497227221977370568204 * q^33 - 50410977973081452147630100226760 * q^34 - 153374925211463555312750388019200 * q^35 - 27406614057517010739893935618800 * q^36 - 442820255707228186224391784737998 * q^37 - 832008681100278182323288015176048 * q^38 - 155913018881652402326915850008442 * q^39 - 830400317719830554628641188275072 * q^40 - 438132779830146983268076758934098 * q^41 - 1118112279998815693097419367107584 * q^42 - 1310999240696843410630649721463476 * q^43 - 1443247128257998435455229084014528 * q^44 + 469900410412478810682641155940826 * q^45 + 7997471516728167525889026089716512 * q^46 + 64523854533555761088559286850643968 * q^47 + 19035174118110151421625255141117696 * q^48 + 171140726678012788361144930683431723 * q^49 + 28333303327284754376413888152266724 * q^50 + 38319528429015278581227949931980314 * q^51 - 20984793566307791589805690265685024 * q^52 + 34693992770270063328682081068689946 * q^53 + 12267153381682064972966523079705380 * q^54 + 100035221507232528994896069839569896 * q^55 - 568132015233041377672136741101977600 * q^56 - 684794240478163142230784839651194228 * q^57 - 2740694640626009342372591817401518296 * q^58 - 4582685445865314260503003260089664948 * q^59 - 1853702841211138803266019258215507424 * q^60 - 8693740159306202291599355552752714662 * q^61 + 265004064722629998116825545352842464 * q^62 - 542258763736695967164682362773127168 * q^63 + 16981741764860889983034117450588819456 * q^64 + 2721360738989032295650621165564283148 * q^65 + 15737614205967000002335445187917232528 * q^66 + 32867814173503669322418795877934200116 * q^67 + 33261671085355608094778443956314848800 * q^68 + 16266370986342093542812388655640268184 * q^69 + 98543364272473044599951459881688524800 * q^70 + 149748844745311390685366673232301225496 * q^71 + 27573985840291440136110933044612124096 * q^72 + 6619123649433674932122580558210670046 * q^73 + 14490759310413784046620539770501448744 * q^74 + 16070623339563035717907230167095788499 * q^75 - 536779250932404614788199202699778310208 * q^76 - 954944421253262491346753072408971247616 * q^77 - 428505836133684487473427567420504715976 * q^78 - 1112771209183156752666617542198723627800 * q^79 - 2423764999311265237507278994973679346176 * q^80 + 443426488243037769948249630619149892803 * q^81 - 107939940778839787676218322470600048296 * q^82 - 1187635824307222104653182519688468749260 * q^83 + 2091460075134421134660653723208430104576 * q^84 + 6153092316082135211652182465439269196852 * q^85 + 2889811785377479896729751911427106623344 * q^86 + 3283000983546327044739131648688427064814 * q^87 + 11348012623814378178834124633898985613056 * q^88 - 2907470395792485617492963651915834875602 * q^89 + 3692098038012081220424316844483830692424 * q^90 + 19747616149564653802226421926044582182912 * q^91 + 10266693573432860781998326486887076136832 * q^92 + 22594660407563895447746096203786446364008 * q^93 + 34628213999509804914437049475497096849408 * q^94 - 84590150972982168777889232049326900017896 * q^95 + 32057992513296996581786794596336971916288 * q^96 - 52479807025249236413871256717456940920314 * q^97 - 268218382984038433881798894561914095373892 * q^98 + 26289779289001760785343260072210213785804 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−467196.	−0.315054	−0.157527	−	0.987515i	$-0.550352\pi$
$2$	−467196.	−0.315054	−0.157527	+	0.987515i	$0.550352\pi$
$3$	−3.48678e9	−0.577350
$3$	−3.48678e9	−0.577350
$4$	−1.98075e12	−0.900741
$5$	−2.77079e14	−1.29933	−0.649664	−	0.760221i	$-0.725091\pi$
$5$	−2.77079e14	−1.29933	−0.649664	+	0.760221i	$0.725091\pi$
$6$	1.62901e15	0.181896
$7$	3.80292e17	1.80139	0.900693	−	0.434455i	$-0.143059\pi$
$7$	3.80292e17	1.80139	0.900693	+	0.434455i	$0.143059\pi$
$8$	1.95278e18	0.598835
$9$	1.21577e19	0.333333
$10$	1.29450e20	0.409358
$11$	1.78075e20	0.0798094	0.0399047	−	0.999203i	$-0.487295\pi$
$11$	1.78075e20	0.0798094	0.0399047	+	0.999203i	$0.487295\pi$
$12$	6.90645e21	0.520043
$13$	2.06379e22	0.301180	0.150590	−	0.988596i	$-0.451883\pi$
$13$	2.06379e22	0.301180	0.150590	+	0.988596i	$0.451883\pi$
$14$	−1.77671e23	−0.567534
$15$	9.66116e23	0.750168
$16$	3.44339e24	0.712076
$17$	−2.32357e25	−1.38661	−0.693303	−	0.720646i	$-0.743845\pi$
$17$	−2.32357e25	−1.38661	−0.693303	+	0.720646i	$0.743845\pi$
$18$	−5.68002e24	−0.105018
$19$	2.05644e26	1.25507	0.627533	−	0.778590i	$-0.284065\pi$
$19$	2.05644e26	1.25507	0.627533	+	0.778590i	$0.284065\pi$
$20$	5.48825e26	1.17036
$21$	−1.32600e27	−1.04003
$22$	−8.31962e25	−0.0251442
$23$	−4.66038e27	−0.566240	−0.283120	−	0.959085i	$-0.591369\pi$
$23$	−4.66038e27	−0.566240	−0.283120	+	0.959085i	$0.591369\pi$
$24$	−6.80891e27	−0.345738
$25$	3.12982e28	0.688255
$26$	−9.64193e27	−0.0948878
$27$	−4.23912e28	−0.192450
$28$	−7.53263e29	−1.62258
$29$	1.57858e30	1.65618	0.828090	−	0.560595i	$-0.189427\pi$
$29$	1.57858e30	1.65618	0.828090	+	0.560595i	$0.189427\pi$
$30$	−4.51366e29	−0.236343
$31$	−4.51602e30	−1.20737	−0.603685	−	0.797223i	$-0.706302\pi$
$31$	−4.51602e30	−1.20737	−0.603685	+	0.797223i	$0.706302\pi$
$32$	−5.90294e30	−0.823178
$33$	−6.20911e29	−0.0460780
$34$	1.08556e31	0.436856
$35$	−1.05371e32	−2.34059
$36$	−2.40813e31	−0.300247
$37$	−1.32006e32	−0.938555	−0.469277	−	0.883051i	$-0.655486\pi$
$37$	−1.32006e32	−0.938555	−0.469277	+	0.883051i	$0.655486\pi$
$38$	−9.60760e31	−0.395413
$39$	−7.19598e31	−0.173886
$40$	−5.41074e32	−0.778084
$41$	−3.66611e32	−0.317787	−0.158893	−	0.987296i	$-0.550793\pi$
$41$	−3.66611e32	−0.317787	−0.158893	+	0.987296i	$0.550793\pi$
$42$	6.19500e32	0.327666
$43$	−6.46266e32	−0.211012	−0.105506	−	0.994419i	$-0.533646\pi$
$43$	−6.46266e32	−0.211012	−0.105506	+	0.994419i	$0.533646\pi$
$44$	−3.52723e32	−0.0718876
$45$	−3.36864e33	−0.433109
$46$	2.17731e33	0.178396
$47$	2.68528e34	1.41574	0.707871	−	0.706342i	$-0.249656\pi$
$47$	2.68528e34	1.41574	0.707871	+	0.706342i	$0.249656\pi$
$48$	−1.20064e34	−0.411117
$49$	1.00054e35	2.24499
$50$	−1.46224e34	−0.216837
$51$	8.10180e34	0.800558
$52$	−4.08785e34	−0.271285
$53$	−1.90002e35	−0.853300	−0.426650	−	0.904417i	$-0.640306\pi$
$53$	−1.90002e35	−0.853300	−0.426650	+	0.904417i	$0.640306\pi$
$54$	1.98050e34	0.0606321
$55$	−4.93410e34	−0.103699
$56$	7.42624e35	1.07873
$57$	−7.17036e35	−0.724613
$58$	−7.37507e35	−0.521786
$59$	−3.62437e36	−1.80620	−0.903100	−	0.429430i	$-0.858714\pi$
$59$	−3.62437e36	−1.80620	−0.903100	+	0.429430i	$0.858714\pi$
$60$	−1.91363e36	−0.675707
$61$	2.16433e36	0.544580	0.272290	−	0.962215i	$-0.412219\pi$
$61$	2.16433e36	0.544580	0.272290	+	0.962215i	$0.412219\pi$
$62$	2.10987e36	0.380387
$63$	4.62346e36	0.600462
$64$	−4.81426e36	−0.452731
$65$	−5.71832e36	−0.391332
$66$	2.90087e35	0.0145170
$67$	3.15856e36	0.116133	0.0580664	−	0.998313i	$-0.481506\pi$
$67$	3.15856e36	0.116133	0.0580664	+	0.998313i	$0.481506\pi$
$68$	4.60242e37	1.24897
$69$	1.62497e37	0.326919
$70$	4.92289e37	0.737412
$71$	−4.01004e37	−0.449110	−0.224555	−	0.974461i	$-0.572093\pi$
$71$	−4.01004e37	−0.449110	−0.224555	+	0.974461i	$0.572093\pi$
$72$	2.37412e37	0.199612
$73$	7.75186e37	0.491232	0.245616	−	0.969367i	$-0.421010\pi$
$73$	7.75186e37	0.491232	0.245616	+	0.969367i	$0.421010\pi$
$74$	6.16729e37	0.295695
$75$	−1.09130e38	−0.397364
$76$	−4.07329e38	−1.13049
$77$	6.77206e37	0.143768
$78$	3.36193e37	0.0547835
$79$	−8.36639e38	−1.04998	−0.524992	−	0.851107i	$-0.675932\pi$
$79$	−8.36639e38	−1.04998	−0.524992	+	0.851107i	$0.675932\pi$
$80$	−9.54091e38	−0.925221
$81$	1.47809e38	0.111111
$82$	1.71279e38	0.100120
$83$	−1.97827e39	−0.901954	−0.450977	−	0.892536i	$-0.648924\pi$
$83$	−1.97827e39	−0.901954	−0.450977	+	0.892536i	$0.648924\pi$
$84$	2.62647e39	0.936799
$85$	6.43814e39	1.80166
$86$	3.01933e38	0.0664802
$87$	−5.50417e39	−0.956196
$88$	3.47741e38	0.0477927
$89$	3.68899e39	0.402172	0.201086	−	0.979574i	$-0.435553\pi$
$89$	3.68899e39	0.402172	0.201086	+	0.979574i	$0.435553\pi$
$90$	1.57381e39	0.136453
$91$	7.84841e39	0.542541
$92$	9.23105e39	0.510036
$93$	1.57464e40	0.697076
$94$	−1.25455e40	−0.446035
$95$	−5.69796e40	−1.63074
$96$	2.05823e40	0.475262
$97$	4.15034e40	0.774932	0.387466	−	0.921884i	$-0.373350\pi$
$97$	4.15034e40	0.774932	0.387466	+	0.921884i	$0.373350\pi$
$98$	−4.67449e40	−0.707294
$99$	2.16498e39	0.0266031
$100$	−6.19939e40	−0.619939
$101$	−2.21812e41	−1.80883	−0.904413	−	0.426658i	$-0.859691\pi$
$101$	−2.21812e41	−1.80883	−0.904413	+	0.426658i	$0.859691\pi$
$102$	−3.78513e40	−0.252219
$103$	1.19436e41	0.651584	0.325792	−	0.945441i	$-0.394369\pi$
$103$	1.19436e41	0.651584	0.325792	+	0.945441i	$0.394369\pi$
$104$	4.03011e40	0.180357
$105$	3.67406e41	1.35134
$106$	8.87680e40	0.268835
$107$	−3.26711e41	−0.816199	−0.408100	−	0.912937i	$-0.633808\pi$
$107$	−3.26711e41	−0.816199	−0.408100	+	0.912937i	$0.633808\pi$
$108$	8.39663e40	0.173348
$109$	−1.38640e40	−0.0236943	−0.0118472	−	0.999930i	$-0.503771\pi$
$109$	−1.38640e40	−0.0236943	−0.0118472	+	0.999930i	$0.503771\pi$
$110$	2.30519e40	0.0326706
$111$	4.60278e41	0.541875
$112$	1.30949e42	1.28272
$113$	−1.13961e40	−0.00930355	−0.00465177	−	0.999989i	$-0.501481\pi$
$113$	−1.13961e40	−0.00930355	−0.00465177	+	0.999989i	$0.501481\pi$
$114$	3.34996e41	0.228292
$115$	1.29129e42	0.735732
$116$	−3.12677e42	−1.49179
$117$	2.50908e41	0.100393
$118$	1.69329e42	0.569050
$119$	−8.83635e42	−2.49782
$120$	1.88661e42	0.449227
$121$	−4.94681e42	−0.993630
$122$	−1.01117e42	−0.171572
$123$	1.27829e42	0.183474
$124$	8.94510e42	1.08753
$125$	3.92803e42	0.405060
$126$	−2.16006e42	−0.189178
$127$	−1.88436e43	−1.40342	−0.701710	−	0.712463i	$-0.747580\pi$
$127$	−1.88436e43	−1.40342	−0.701710	+	0.712463i	$0.747580\pi$
$128$	1.52299e43	0.965812
$129$	2.25339e42	0.121828
$130$	2.67158e42	0.123290
$131$	−9.29935e42	−0.366767	−0.183384	−	0.983041i	$-0.558705\pi$
$131$	−9.29935e42	−0.366767	−0.183384	+	0.983041i	$0.558705\pi$
$132$	1.22987e42	0.0415043
$133$	7.82046e43	2.26086
$134$	−1.47567e42	−0.0365881
$135$	1.17457e43	0.250056
$136$	−4.53741e43	−0.830349
$137$	−1.16680e43	−0.183749	−0.0918746	−	0.995771i	$-0.529286\pi$
$137$	−1.16680e43	−0.183749	−0.0918746	+	0.995771i	$0.529286\pi$
$138$	−7.59181e42	−0.102997
$139$	−1.12714e44	−1.31878	−0.659391	−	0.751800i	$-0.729186\pi$
$139$	−1.12714e44	−1.31878	−0.659391	+	0.751800i	$0.729186\pi$
$140$	2.08714e44	2.10827
$141$	−9.36301e43	−0.817379
$142$	1.87348e43	0.141494
$143$	3.67510e42	0.0240370
$144$	4.18636e43	0.237359
$145$	−4.37392e44	−2.15192
$146$	−3.62164e43	−0.154765
$147$	−3.48867e44	−1.29615
$148$	2.61472e44	0.845395
$149$	−8.33811e42	−0.0234827	−0.0117414	−	0.999931i	$-0.503737\pi$
$149$	−8.33811e42	−0.0234827	−0.0117414	+	0.999931i	$0.503737\pi$
$150$	5.09852e43	0.125191
$151$	4.48224e44	0.960434	0.480217	−	0.877150i	$-0.340558\pi$
$151$	4.48224e44	0.960434	0.480217	+	0.877150i	$0.340558\pi$
$152$	4.01576e44	0.751578
$153$	−2.82492e44	−0.462202
$154$	−3.16388e43	−0.0452945
$155$	1.25129e45	1.56877
$156$	1.42534e44	0.156627
$157$	−1.18993e45	−1.14704	−0.573521	−	0.819191i	$-0.694423\pi$
$157$	−1.18993e45	−1.14704	−0.573521	+	0.819191i	$0.694423\pi$
$158$	3.90874e44	0.330801
$159$	6.62494e44	0.492653
$160$	1.63558e45	1.06958
$161$	−1.77230e45	−1.02002
$162$	−6.90557e43	−0.0350060
$163$	−1.65419e45	−0.739161	−0.369580	−	0.929199i	$-0.620499\pi$
$163$	−1.65419e45	−0.739161	−0.369580	+	0.929199i	$0.620499\pi$
$164$	7.26164e44	0.286244
$165$	1.72042e44	0.0598704
$166$	9.24240e44	0.284164
$167$	−1.65893e45	−0.450962	−0.225481	−	0.974248i	$-0.572395\pi$
$167$	−1.65893e45	−0.450962	−0.225481	+	0.974248i	$0.572395\pi$
$168$	−2.58937e45	−0.622808
$169$	−4.26953e45	−0.909291
$170$	−3.00787e45	−0.567619
$171$	2.50015e45	0.418356
$172$	1.28009e45	0.190067
$173$	−7.93101e45	−1.04564	−0.522821	−	0.852442i	$-0.675120\pi$
$173$	−7.93101e45	−1.04564	−0.522821	+	0.852442i	$0.675120\pi$
$174$	2.57153e45	0.301253
$175$	1.19024e46	1.23981
$176$	6.13183e44	0.0568304
$177$	1.26374e46	1.04281
$178$	−1.72348e45	−0.126706
$179$	−1.74304e46	−1.14241	−0.571204	−	0.820808i	$-0.693524\pi$
$179$	−1.74304e46	−1.14241	−0.571204	+	0.820808i	$0.693524\pi$
$180$	6.67243e45	0.390120
$181$	2.91732e46	1.52255	0.761277	−	0.648427i	$-0.224573\pi$
$181$	2.91732e46	1.52255	0.761277	+	0.648427i	$0.224573\pi$
$182$	−3.66675e45	−0.170930
$183$	−7.54655e45	−0.314413
$184$	−9.10067e45	−0.339084
$185$	3.65762e46	1.21949
$186$	−7.35665e45	−0.219616
$187$	−4.13771e45	−0.110664
$188$	−5.31888e46	−1.27522
$189$	−1.61210e46	−0.346677
$190$	2.66207e46	0.513772
$191$	3.24072e46	0.561639	0.280820	−	0.959761i	$-0.409394\pi$
$191$	3.24072e46	0.561639	0.280820	+	0.959761i	$0.409394\pi$
$192$	1.67863e46	0.261384
$193$	5.78799e45	0.0810219	0.0405110	−	0.999179i	$-0.487101\pi$
$193$	5.78799e45	0.0810219	0.0405110	+	0.999179i	$0.487101\pi$
$194$	−1.93903e46	−0.244145
$195$	1.99386e46	0.225935
$196$	−1.98182e47	−2.02216
$197$	−1.23332e47	−1.13375	−0.566875	−	0.823804i	$-0.691848\pi$
$197$	−1.23332e47	−1.13375	−0.566875	+	0.823804i	$0.691848\pi$
$198$	−1.01147e45	−0.00838142
$199$	−8.02314e46	−0.599592	−0.299796	−	0.954003i	$-0.596919\pi$
$199$	−8.02314e46	−0.599592	−0.299796	+	0.954003i	$0.596919\pi$
$200$	6.11183e46	0.412151
$201$	−1.10132e46	−0.0670494
$202$	1.03630e47	0.569877
$203$	6.00321e47	2.98342
$204$	−1.60476e47	−0.721095
$205$	1.01580e47	0.412910
$206$	−5.57998e46	−0.205284
$207$	−5.66593e46	−0.188747
$208$	7.10641e46	0.214463
$209$	3.66201e46	0.100166
$210$	−1.71651e47	−0.425745
$211$	4.89315e46	0.110103	0.0550514	−	0.998484i	$-0.482468\pi$
$211$	4.89315e46	0.110103	0.0550514	+	0.998484i	$0.482468\pi$
$212$	3.76346e47	0.768602
$213$	1.39821e47	0.259294
$214$	1.52638e47	0.257147
$215$	1.79067e47	0.274174
$216$	−8.27804e46	−0.115246
$217$	−1.71740e48	−2.17494
$218$	6.47720e45	0.00746499
$219$	−2.70291e47	−0.283613
$220$	9.77323e46	0.0934056
$221$	−4.79536e47	−0.417618
$222$	−2.15040e47	−0.170720
$223$	1.26157e48	0.913402	0.456701	−	0.889620i	$-0.349031\pi$
$223$	1.26157e48	0.913402	0.456701	+	0.889620i	$0.349031\pi$
$224$	−2.24484e48	−1.48286
$225$	3.80513e47	0.229418
$226$	5.32422e45	0.00293112
$227$	−7.98999e46	−0.0401806	−0.0200903	−	0.999798i	$-0.506395\pi$
$227$	−7.98999e46	−0.0401806	−0.0200903	+	0.999798i	$0.506395\pi$
$228$	1.42027e48	0.652689
$229$	1.47316e48	0.618903	0.309452	−	0.950915i	$-0.399855\pi$
$229$	1.47316e48	0.618903	0.309452	+	0.950915i	$0.399855\pi$
$230$	−6.03288e47	−0.231795
$231$	−2.36127e47	−0.0830043
$232$	3.08261e48	0.991780
$233$	−1.22067e48	−0.359585	−0.179792	−	0.983705i	$-0.557543\pi$
$233$	−1.22067e48	−0.359585	−0.179792	+	0.983705i	$0.557543\pi$
$234$	−1.17223e47	−0.0316293
$235$	−7.44036e48	−1.83951
$236$	7.17897e48	1.62692
$237$	2.91718e48	0.606208
$238$	4.12831e48	0.786946
$239$	−3.67173e48	−0.642265	−0.321132	−	0.947034i	$-0.604063\pi$
$239$	−3.67173e48	−0.642265	−0.321132	+	0.947034i	$0.604063\pi$
$240$	3.32671e48	0.534176
$241$	7.53187e48	1.11059	0.555295	−	0.831654i	$-0.312605\pi$
$241$	7.53187e48	1.11059	0.555295	+	0.831654i	$0.312605\pi$
$242$	2.31113e48	0.313047
$243$	−5.15378e47	−0.0641500
$244$	−4.28700e48	−0.490526
$245$	−2.77229e49	−2.91699
$246$	−5.97213e47	−0.0578043
$247$	4.24405e48	0.378001
$248$	−8.81876e48	−0.723016
$249$	6.89780e48	0.520743
$250$	−1.83516e48	−0.127616
$251$	1.42036e49	0.910093	0.455047	−	0.890468i	$-0.349623\pi$
$251$	1.42036e49	0.910093	0.455047	+	0.890468i	$0.349623\pi$
$252$	−9.15792e48	−0.540861
$253$	−8.29899e47	−0.0451913
$254$	8.80366e48	0.442153
$255$	−2.24484e49	−1.04019
$256$	3.47132e48	0.148448
$257$	1.04474e49	0.412458	0.206229	−	0.978504i	$-0.433881\pi$
$257$	1.04474e49	0.412458	0.206229	+	0.978504i	$0.433881\pi$
$258$	−1.05278e48	−0.0383824
$259$	−5.02009e49	−1.69070
$260$	1.13266e49	0.352488
$261$	1.91919e49	0.552060
$262$	4.34462e48	0.115551
$263$	7.26469e49	1.78700	0.893499	−	0.449066i	$-0.148243\pi$
$263$	7.26469e49	1.78700	0.893499	+	0.449066i	$0.148243\pi$
$264$	−1.21250e48	−0.0275931
$265$	5.26455e49	1.10872
$266$	−3.65369e49	−0.712292
$267$	−1.28627e49	−0.232194
$268$	−6.25631e48	−0.104606
$269$	1.15272e50	1.78567	0.892835	−	0.450384i	$-0.148713\pi$
$269$	1.15272e50	1.78567	0.892835	+	0.450384i	$0.148713\pi$
$270$	−5.48755e48	−0.0787810
$271$	−3.19469e48	−0.0425166	−0.0212583	−	0.999774i	$-0.506767\pi$
$271$	−3.19469e48	−0.0425166	−0.0212583	+	0.999774i	$0.506767\pi$
$272$	−8.00096e49	−0.987369
$273$	−2.73657e49	−0.313236
$274$	5.45126e48	0.0578909
$275$	5.57344e48	0.0549292
$276$	−3.21867e49	−0.294469
$277$	−1.21524e50	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$277$	−1.21524e50	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$278$	5.26594e49	0.415487
$279$	−5.49042e49	−0.402457
$280$	−2.05766e50	−1.40163
$281$	−1.33789e50	−0.847110	−0.423555	−	0.905871i	$-0.639218\pi$
$281$	−1.33789e50	−0.847110	−0.423555	+	0.905871i	$0.639218\pi$
$282$	4.37436e49	0.257518
$283$	1.22161e50	0.668822	0.334411	−	0.942427i	$-0.391463\pi$
$283$	1.22161e50	0.668822	0.334411	+	0.942427i	$0.391463\pi$
$284$	7.94289e49	0.404532
$285$	1.98676e50	0.941510
$286$	−1.71699e48	−0.00757294
$287$	−1.39419e50	−0.572457
$288$	−7.17659e49	−0.274393
$289$	2.59093e50	0.922678
$290$	2.04348e50	0.677971
$291$	−1.44714e50	−0.447407
$292$	−1.53545e50	−0.442473
$293$	−3.57046e50	−0.959263	−0.479631	−	0.877470i	$-0.659230\pi$
$293$	−3.57046e50	−0.959263	−0.479631	+	0.877470i	$0.659230\pi$
$294$	1.62989e50	0.408356
$295$	1.00424e51	2.34685
$296$	−2.57779e50	−0.562040
$297$	−7.54883e48	−0.0153593
$298$	3.89553e48	0.00739832
$299$	−9.61802e49	−0.170540
$300$	2.16159e50	0.357922
$301$	−2.45770e50	−0.380115
$302$	−2.09409e50	−0.302588
$303$	7.73410e50	1.04433
$304$	7.08111e50	0.893703
$305$	−5.99691e50	−0.707588
$306$	1.31979e50	0.145619
$307$	−1.10483e51	−1.14014	−0.570069	−	0.821597i	$-0.693083\pi$
$307$	−1.10483e51	−1.14014	−0.570069	+	0.821597i	$0.693083\pi$
$308$	−1.34138e50	−0.129497
$309$	−4.16446e50	−0.376192
$310$	−5.84600e50	−0.494247
$311$	1.79220e50	0.141840	0.0709199	−	0.997482i	$-0.477407\pi$
$311$	1.79220e50	0.141840	0.0709199	+	0.997482i	$0.477407\pi$
$312$	−1.40521e50	−0.104129
$313$	−2.12064e51	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$313$	−2.12064e51	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$314$	5.55932e50	0.361380
$315$	−1.28106e51	−0.780198
$316$	1.65717e51	0.945764
$317$	9.10910e50	0.487260	0.243630	−	0.969868i	$-0.421662\pi$
$317$	9.10910e50	0.487260	0.243630	+	0.969868i	$0.421662\pi$
$318$	−3.09515e50	−0.155212
$319$	2.81106e50	0.132179
$320$	1.33393e51	0.588246
$321$	1.13917e51	0.471233
$322$	8.28013e50	0.321360
$323$	−4.77828e51	−1.74028
$324$	−2.92772e50	−0.100082
$325$	6.45928e50	0.207288
$326$	7.72831e50	0.232875
$327$	4.83407e49	0.0136799
$328$	−7.15908e50	−0.190302
$329$	1.02119e52	2.55030
$330$	−8.03772e49	−0.0188624
$331$	1.92970e51	0.425614	0.212807	−	0.977094i	$-0.431739\pi$
$331$	1.92970e51	0.425614	0.212807	+	0.977094i	$0.431739\pi$
$332$	3.91846e51	0.812427
$333$	−1.60489e51	−0.312852
$334$	7.75045e50	0.142077
$335$	−8.75171e50	−0.150895
$336$	−4.56592e51	−0.740581
$337$	−9.78943e51	−1.49398	−0.746990	−	0.664836i	$-0.768502\pi$
$337$	−9.78943e51	−1.49398	−0.746990	+	0.664836i	$0.768502\pi$
$338$	1.99471e51	0.286475
$339$	3.97358e49	0.00537141
$340$	−1.27523e52	−1.62283
$341$	−8.04192e50	−0.0963595
$342$	−1.16806e51	−0.131804
$343$	2.11010e52	2.24272
$344$	−1.26201e51	−0.126362
$345$	−4.50246e51	−0.424775
$346$	3.70534e51	0.329433
$347$	−1.94813e52	−1.63254	−0.816268	−	0.577673i	$-0.803961\pi$
$347$	−1.94813e52	−1.63254	−0.816268	+	0.577673i	$0.803961\pi$
$348$	1.09024e52	0.861286
$349$	−1.88816e52	−1.40643	−0.703214	−	0.710978i	$-0.748252\pi$
$349$	−1.88816e52	−1.40643	−0.703214	+	0.710978i	$0.748252\pi$
$350$	−5.56078e51	−0.390608
$351$	−8.74863e50	−0.0579621
$352$	−1.05117e51	−0.0656973
$353$	5.89357e51	0.347534	0.173767	−	0.984787i	$-0.444406\pi$
$353$	5.89357e51	0.347534	0.173767	+	0.984787i	$0.444406\pi$
$354$	−5.90414e51	−0.328541
$355$	1.11110e52	0.583541
$356$	−7.30697e51	−0.362253
$357$	3.08105e52	1.44211
$358$	8.14344e51	0.359920
$359$	3.41142e52	1.42396	0.711981	−	0.702198i	$-0.247798\pi$
$359$	3.41142e52	1.42396	0.711981	+	0.702198i	$0.247798\pi$
$360$	−6.57819e51	−0.259361
$361$	1.54423e52	0.575193
$362$	−1.36296e52	−0.479686
$363$	1.72485e52	0.573673
$364$	−1.55457e52	−0.488689
$365$	−2.14788e52	−0.638272
$366$	3.52572e51	0.0990571
$367$	5.39142e52	1.43235	0.716174	−	0.697922i	$-0.245892\pi$
$367$	5.39142e52	1.43235	0.716174	+	0.697922i	$0.245892\pi$
$368$	−1.60475e52	−0.403206
$369$	−4.45713e51	−0.105929
$370$	−1.70883e52	−0.384205
$371$	−7.22560e52	−1.53712
$372$	−3.11896e52	−0.627885
$373$	1.69349e52	0.322665	0.161333	−	0.986900i	$-0.448421\pi$
$373$	1.69349e52	0.322665	0.161333	+	0.986900i	$0.448421\pi$
$374$	1.93312e51	0.0348652
$375$	−1.36962e52	−0.233861
$376$	5.24376e52	0.847796
$377$	3.25785e52	0.498808
$378$	7.53167e51	0.109222
$379$	−1.30321e53	−1.79024	−0.895119	−	0.445828i	$-0.852909\pi$
$379$	−1.30321e53	−1.79024	−0.895119	+	0.445828i	$0.852909\pi$
$380$	1.12862e53	1.46888
$381$	6.57036e52	0.810265
$382$	−1.51405e52	−0.176947
$383$	−1.57363e53	−1.74312	−0.871561	−	0.490286i	$-0.836892\pi$
$383$	−1.57363e53	−1.74312	−0.871561	+	0.490286i	$0.836892\pi$
$384$	−5.31034e52	−0.557612
$385$	−1.87640e52	−0.186801
$386$	−2.70413e51	−0.0255263
$387$	−7.85708e51	−0.0703374
$388$	−8.22080e52	−0.698013
$389$	−3.61986e52	−0.291558	−0.145779	−	0.989317i	$-0.546569\pi$
$389$	−3.61986e52	−0.291558	−0.145779	+	0.989317i	$0.546569\pi$
$390$	−9.31522e51	−0.0711818
$391$	1.08287e53	0.785152
$392$	1.95383e53	1.34438
$393$	3.24248e52	0.211753
$394$	5.76201e52	0.357192
$395$	2.31815e53	1.36427
$396$	−4.28829e51	−0.0239625
$397$	−5.10834e52	−0.271065	−0.135533	−	0.990773i	$-0.543275\pi$
$397$	−5.10834e52	−0.271065	−0.135533	+	0.990773i	$0.543275\pi$
$398$	3.74838e52	0.188904
$399$	−2.72683e53	−1.30531
$400$	1.07772e53	0.490089
$401$	1.32940e53	0.574375	0.287188	−	0.957874i	$-0.407280\pi$
$401$	1.32940e53	0.574375	0.287188	+	0.957874i	$0.407280\pi$
$402$	5.14533e51	0.0211241
$403$	−9.32009e52	−0.363636
$404$	4.39354e53	1.62928
$405$	−4.09548e52	−0.144370
$406$	−2.80468e53	−0.939938
$407$	−2.35071e52	−0.0749055
$408$	1.58210e53	0.479402
$409$	−1.41227e53	−0.406995	−0.203498	−	0.979075i	$-0.565231\pi$
$409$	−1.41227e53	−0.406995	−0.203498	+	0.979075i	$0.565231\pi$
$410$	−4.74579e52	−0.130089
$411$	4.06839e52	0.106088
$412$	−2.36572e53	−0.586909
$413$	−1.37832e54	−3.25367
$414$	2.64710e52	0.0594653
$415$	5.48137e53	1.17193
$416$	−1.21824e53	−0.247924
$417$	3.93008e53	0.761399
$418$	−1.71088e52	−0.0315577
$419$	5.25506e53	0.922976	0.461488	−	0.887147i	$-0.347316\pi$
$419$	5.25506e53	0.922976	0.461488	+	0.887147i	$0.347316\pi$
$420$	−7.27739e53	−1.21721
$421$	1.41717e53	0.225755	0.112878	−	0.993609i	$-0.463993\pi$
$421$	1.41717e53	0.225755	0.112878	+	0.993609i	$0.463993\pi$
$422$	−2.28606e52	−0.0346883
$423$	3.26468e53	0.471914
$424$	−3.71030e53	−0.510986
$425$	−7.27236e53	−0.954338
$426$	−6.53241e52	−0.0816914
$427$	8.23076e53	0.980999
$428$	6.47133e53	0.735184
$429$	−1.28143e52	−0.0138778
$430$	−8.36594e52	−0.0863796
$431$	−5.32701e53	−0.524444	−0.262222	−	0.965008i	$-0.584455\pi$
$431$	−5.32701e53	−0.524444	−0.262222	+	0.965008i	$0.584455\pi$
$432$	−1.45969e53	−0.137039
$433$	1.65417e54	1.48108	0.740539	−	0.672014i	$-0.234570\pi$
$433$	1.65417e54	1.48108	0.740539	+	0.672014i	$0.234570\pi$
$434$	8.02364e53	0.685223
$435$	1.52509e54	1.24241
$436$	2.74611e52	0.0213425
$437$	−9.58378e53	−0.710669
$438$	1.26279e53	0.0893534
$439$	−7.22284e53	−0.487736	−0.243868	−	0.969808i	$-0.578416\pi$
$439$	−7.22284e53	−0.487736	−0.243868	+	0.969808i	$0.578416\pi$
$440$	−9.63519e52	−0.0620984
$441$	1.21642e54	0.748332
$442$	2.24037e53	0.131572
$443$	−1.23574e54	−0.692866	−0.346433	−	0.938075i	$-0.612607\pi$
$443$	−1.23574e54	−0.692866	−0.346433	+	0.938075i	$0.612607\pi$
$444$	−9.11696e53	−0.488089
$445$	−1.02214e54	−0.522554
$446$	−5.89401e53	−0.287771
$447$	2.90732e52	0.0135578
$448$	−1.83082e54	−0.815543
$449$	1.61171e54	0.685862	0.342931	−	0.939361i	$-0.388580\pi$
$449$	1.61171e54	0.685862	0.342931	+	0.939361i	$0.388580\pi$
$450$	−1.77774e53	−0.0722790
$451$	−6.52844e52	−0.0253624
$452$	2.25729e52	0.00838009
$453$	−1.56286e54	−0.554507
$454$	3.73290e52	0.0126590
$455$	−2.17463e54	−0.704940
$456$	−1.40021e54	−0.433924
$457$	3.90797e54	1.15789	0.578947	−	0.815365i	$-0.303464\pi$
$457$	3.90797e54	1.15789	0.578947	+	0.815365i	$0.303464\pi$
$458$	−6.88255e53	−0.194988
$459$	9.84989e53	0.266853
$460$	−2.55773e54	−0.662704
$461$	1.14081e54	0.282711	0.141356	−	0.989959i	$-0.454854\pi$
$461$	1.14081e54	0.282711	0.141356	+	0.989959i	$0.454854\pi$
$462$	1.10318e53	0.0261508
$463$	−3.28172e54	−0.744203	−0.372101	−	0.928192i	$-0.621363\pi$
$463$	−3.28172e54	−0.744203	−0.372101	+	0.928192i	$0.621363\pi$
$464$	5.43566e54	1.17933
$465$	−4.36299e54	−0.905730
$466$	5.70292e53	0.113289
$467$	5.71824e54	1.08709	0.543546	−	0.839379i	$-0.317081\pi$
$467$	5.71824e54	1.08709	0.543546	+	0.839379i	$0.317081\pi$
$468$	−4.96987e53	−0.0904284
$469$	1.20117e54	0.209200
$470$	3.47611e54	0.579546
$471$	4.14904e54	0.662245
$472$	−7.07757e54	−1.08162
$473$	−1.15084e53	−0.0168408
$474$	−1.36290e54	−0.190988
$475$	6.43628e54	0.863805
$476$	1.75026e55	2.24989
$477$	−2.30997e54	−0.284433
$478$	1.71542e54	0.202348
$479$	−1.67327e55	−1.89099	−0.945494	−	0.325638i	$-0.894421\pi$
$479$	−1.67327e55	−1.89099	−0.945494	+	0.325638i	$0.894421\pi$
$480$	−5.70292e54	−0.617521
$481$	−2.72433e54	−0.282674
$482$	−3.51886e54	−0.349895
$483$	6.17964e54	0.588907
$484$	9.79839e54	0.895004
$485$	−1.14997e55	−1.00689
$486$	2.40782e53	0.0202107
$487$	4.35887e53	0.0350777	0.0175388	−	0.999846i	$-0.494417\pi$
$487$	4.35887e53	0.0350777	0.0175388	+	0.999846i	$0.494417\pi$
$488$	4.22645e54	0.326114
$489$	5.76780e54	0.426755
$490$	1.29520e55	0.919007
$491$	−3.19181e54	−0.217203	−0.108602	−	0.994085i	$-0.534637\pi$
$491$	−3.19181e54	−0.217203	−0.108602	+	0.994085i	$0.534637\pi$
$492$	−2.53198e54	−0.165263
$493$	−3.66795e55	−2.29647
$494$	−1.98280e54	−0.119091
$495$	−5.99872e53	−0.0345662
$496$	−1.55504e55	−0.859740
$497$	−1.52498e55	−0.809021
$498$	−3.22263e54	−0.164062
$499$	−1.24829e55	−0.609895	−0.304948	−	0.952369i	$-0.598639\pi$
$499$	−1.24829e55	−0.609895	−0.304948	+	0.952369i	$0.598639\pi$
$500$	−7.78044e54	−0.364854
$501$	5.78433e54	0.260363
$502$	−6.63585e54	−0.286728
$503$	3.88562e55	1.61182	0.805910	−	0.592038i	$-0.201676\pi$
$503$	3.88562e55	1.61182	0.805910	+	0.592038i	$0.201676\pi$
$504$	9.02858e54	0.359578
$505$	6.14595e55	2.35026
$506$	3.87726e53	0.0142377
$507$	1.48869e55	0.524979
$508$	3.73245e55	1.26412
$509$	−3.56393e55	−1.15935	−0.579675	−	0.814848i	$-0.696821\pi$
$509$	−3.56393e55	−1.15935	−0.579675	+	0.814848i	$0.696821\pi$
$510$	1.04878e55	0.327715
$511$	2.94797e55	0.884900
$512$	−3.51127e55	−1.01258
$513$	−8.71748e54	−0.241538
$514$	−4.88099e54	−0.129946
$515$	−3.30931e55	−0.846622
$516$	−4.46340e54	−0.109736
$517$	4.78183e54	0.112990
$518$	2.34537e55	0.532661
$519$	2.76537e55	0.603702
$520$	−1.11666e55	−0.234343
$521$	−1.50481e55	−0.303605	−0.151802	−	0.988411i	$-0.548508\pi$
$521$	−1.50481e55	−0.303605	−0.151802	+	0.988411i	$0.548508\pi$
$522$	−8.96636e54	−0.173929
$523$	1.25388e55	0.233869	0.116934	−	0.993140i	$-0.462693\pi$
$523$	1.25388e55	0.233869	0.116934	+	0.993140i	$0.462693\pi$
$524$	1.84197e55	0.330363
$525$	−4.15012e55	−0.715806
$526$	−3.39403e55	−0.563000
$527$	1.04933e56	1.67415
$528$	−2.13804e54	−0.0328110
$529$	−4.60203e55	−0.679372
$530$	−2.45958e55	−0.349305
$531$	−4.40638e55	−0.602067
$532$	−1.54904e56	−2.03645
$533$	−7.56606e54	−0.0957110
$534$	6.00941e54	0.0731537
$535$	9.05248e55	1.06051
$536$	6.16795e54	0.0695445
$537$	6.07762e55	0.659570
$538$	−5.38545e55	−0.562582
$539$	1.78172e55	0.179172
$540$	−2.32653e55	−0.225236
$541$	−9.58874e55	−0.893753	−0.446876	−	0.894596i	$-0.647464\pi$
$541$	−9.58874e55	−0.893753	−0.446876	+	0.894596i	$0.647464\pi$
$542$	1.49255e54	0.0133950
$543$	−1.01721e56	−0.879047
$544$	1.37159e56	1.14142
$545$	3.84142e54	0.0307867
$546$	1.27852e55	0.0986863
$547$	1.58424e56	1.17783	0.588913	−	0.808196i	$-0.299556\pi$
$547$	1.58424e56	1.17783	0.588913	+	0.808196i	$0.299556\pi$
$548$	2.31114e55	0.165511
$549$	2.63132e55	0.181527
$550$	−2.60389e54	−0.0173056
$551$	3.24625e56	2.07862
$552$	3.17321e55	0.195771
$553$	−3.18167e56	−1.89143
$554$	5.67754e55	0.325245
$555$	−1.27533e56	−0.704074
$556$	2.23258e56	1.18788
$557$	4.01202e55	0.205746	0.102873	−	0.994694i	$-0.467196\pi$
$557$	4.01202e55	0.205746	0.102873	+	0.994694i	$0.467196\pi$
$558$	2.56510e55	0.126796
$559$	−1.33375e55	−0.0635527
$560$	−3.62833e56	−1.66668
$561$	1.44273e55	0.0638920
$562$	6.25055e55	0.266885
$563$	1.77020e56	0.728785	0.364393	−	0.931245i	$-0.381277\pi$
$563$	1.77020e56	0.728785	0.364393	+	0.931245i	$0.381277\pi$
$564$	1.85458e56	0.736247
$565$	3.15763e54	0.0120884
$566$	−5.70732e55	−0.210715
$567$	5.62105e55	0.200154
$568$	−7.83071e55	−0.268943
$569$	−2.37062e56	−0.785346	−0.392673	−	0.919678i	$-0.628450\pi$
$569$	−2.37062e56	−0.785346	−0.392673	+	0.919678i	$0.628450\pi$
$570$	−9.28206e55	−0.296626
$571$	−2.39316e56	−0.737788	−0.368894	−	0.929471i	$-0.620263\pi$
$571$	−2.39316e56	−0.737788	−0.368894	+	0.929471i	$0.620263\pi$
$572$	−7.27945e54	−0.0216511
$573$	−1.12997e56	−0.324263
$574$	6.51360e55	0.180355
$575$	−1.45861e56	−0.389717
$576$	−5.85302e55	−0.150910
$577$	−6.12915e55	−0.152509	−0.0762546	−	0.997088i	$-0.524296\pi$
$577$	−6.12915e55	−0.152509	−0.0762546	+	0.997088i	$0.524296\pi$
$578$	−1.21047e56	−0.290693
$579$	−2.01815e55	−0.0467780
$580$	8.66364e56	1.93833
$581$	−7.52319e56	−1.62477
$582$	6.76096e55	0.140957
$583$	−3.38346e55	−0.0681014
$584$	1.51376e56	0.294167
$585$	−6.95215e55	−0.130444
$586$	1.66810e56	0.302219
$587$	−3.83130e56	−0.670294	−0.335147	−	0.942166i	$-0.608786\pi$
$587$	−3.83130e56	−0.670294	−0.335147	+	0.942166i	$0.608786\pi$
$588$	6.91019e56	1.16749
$589$	−9.28691e56	−1.51533
$590$	−4.69176e56	−0.739383
$591$	4.30031e56	0.654571
$592$	−4.54549e56	−0.668322
$593$	8.56740e56	1.21682	0.608412	−	0.793621i	$-0.291807\pi$
$593$	8.56740e56	1.21682	0.608412	+	0.793621i	$0.291807\pi$
$594$	3.52678e54	0.00483901
$595$	2.44837e57	3.24548
$596$	1.65157e55	0.0211519
$597$	2.79749e56	0.346175
$598$	4.49350e55	0.0537293
$599$	8.04501e56	0.929558	0.464779	−	0.885427i	$-0.346134\pi$
$599$	8.04501e56	0.929558	0.464779	+	0.885427i	$0.346134\pi$
$600$	−2.13106e56	−0.237956
$601$	−1.48001e57	−1.59713	−0.798563	−	0.601911i	$-0.794406\pi$
$601$	−1.48001e57	−1.59713	−0.798563	+	0.601911i	$0.794406\pi$
$602$	1.14823e56	0.119757
$603$	3.84007e55	0.0387110
$604$	−8.87820e56	−0.865103
$605$	1.37066e57	1.29105
$606$	−3.61334e56	−0.329019
$607$	2.38634e56	0.210070	0.105035	−	0.994469i	$-0.466504\pi$
$607$	2.38634e56	0.210070	0.105035	+	0.994469i	$0.466504\pi$
$608$	−1.21390e57	−1.03314
$609$	−2.09319e57	−1.72248
$610$	2.80173e56	0.222928
$611$	5.54185e56	0.426393
$612$	5.59547e56	0.416325
$613$	3.94981e56	0.284208	0.142104	−	0.989852i	$-0.454613\pi$
$613$	3.94981e56	0.284208	0.142104	+	0.989852i	$0.454613\pi$
$614$	5.16171e56	0.359204
$615$	−3.54188e56	−0.238393
$616$	1.32243e56	0.0860932
$617$	−1.22003e57	−0.768286	−0.384143	−	0.923274i	$-0.625503\pi$
$617$	−1.22003e57	−0.768286	−0.384143	+	0.923274i	$0.625503\pi$
$618$	1.94562e56	0.118521
$619$	−1.86279e57	−1.09775	−0.548876	−	0.835903i	$-0.684944\pi$
$619$	−1.86279e57	−1.09775	−0.548876	+	0.835903i	$0.684944\pi$
$620$	−2.47850e57	−1.41306
$621$	1.97559e56	0.108973
$622$	−8.37309e55	−0.0446872
$623$	1.40289e57	0.724468
$624$	−2.47785e56	−0.123820
$625$	−2.51165e57	−1.21456
$626$	9.90757e56	0.463653
$627$	−1.27686e56	−0.0578309
$628$	2.35696e57	1.03319
$629$	3.06726e57	1.30141
$630$	5.98509e56	0.245804
$631$	6.46073e56	0.256850	0.128425	−	0.991719i	$-0.459008\pi$
$631$	6.46073e56	0.256850	0.128425	+	0.991719i	$0.459008\pi$
$632$	−1.63377e57	−0.628767
$633$	−1.70614e56	−0.0635679
$634$	−4.25574e56	−0.153513
$635$	5.22117e57	1.82350
$636$	−1.31224e57	−0.443753
$637$	2.06490e57	0.676147
$638$	−1.31332e56	−0.0416434
$639$	−4.87527e56	−0.149703
$640$	−4.21989e57	−1.25491
$641$	−4.46188e56	−0.128507	−0.0642537	−	0.997934i	$-0.520467\pi$
$641$	−4.46188e56	−0.128507	−0.0642537	+	0.997934i	$0.520467\pi$
$642$	−5.32216e56	−0.148464
$643$	2.22872e57	0.602186	0.301093	−	0.953595i	$-0.402649\pi$
$643$	2.22872e57	0.602186	0.301093	+	0.953595i	$0.402649\pi$
$644$	3.51049e57	0.918771
$645$	−6.24368e56	−0.158295
$646$	2.23240e57	0.548283
$647$	−5.44697e57	−1.29604	−0.648018	−	0.761625i	$-0.724402\pi$
$647$	−5.44697e57	−1.29604	−0.648018	+	0.761625i	$0.724402\pi$
$648$	2.88637e56	0.0665373
$649$	−6.45411e56	−0.144152
$650$	−3.01775e56	−0.0653070
$651$	5.98821e57	1.25570
$652$	3.27653e57	0.665793
$653$	−7.53963e57	−1.48467	−0.742335	−	0.670029i	$-0.766281\pi$
$653$	−7.53963e57	−1.48467	−0.742335	+	0.670029i	$0.766281\pi$
$654$	−2.25846e55	−0.00430991
$655$	2.57666e57	0.476551
$656$	−1.26238e57	−0.226288
$657$	9.42445e56	0.163744
$658$	−4.77097e57	−0.803481
$659$	5.72637e57	0.934821	0.467410	−	0.884040i	$-0.345187\pi$
$659$	5.72637e57	0.934821	0.467410	+	0.884040i	$0.345187\pi$
$660$	−3.40771e56	−0.0539278
$661$	−1.76604e56	−0.0270939	−0.0135469	−	0.999908i	$-0.504312\pi$
$661$	−1.76604e56	−0.0270939	−0.0135469	+	0.999908i	$0.504312\pi$
$662$	−9.01549e56	−0.134091
$663$	1.67204e57	0.241112
$664$	−3.86311e57	−0.540122
$665$	−2.16689e58	−2.93760
$666$	7.49799e56	0.0985651
$667$	−7.35678e57	−0.937796
$668$	3.28592e57	0.406200
$669$	−4.39882e57	−0.527353
$670$	4.08876e56	0.0475399
$671$	3.85414e56	0.0434626
$672$	7.82726e57	0.856130
$673$	6.90741e57	0.732836	0.366418	−	0.930450i	$-0.380584\pi$
$673$	6.90741e57	0.732836	0.366418	+	0.930450i	$0.380584\pi$
$674$	4.57359e57	0.470684
$675$	−1.32677e57	−0.132455
$676$	8.45688e57	0.819036
$677$	−9.79667e57	−0.920473	−0.460236	−	0.887796i	$-0.652235\pi$
$677$	−9.79667e57	−0.920473	−0.460236	+	0.887796i	$0.652235\pi$
$678$	−1.85644e55	−0.00169228
$679$	1.57834e58	1.39595
$680$	1.25722e58	1.07890
$681$	2.78594e56	0.0231983
$682$	3.75715e56	0.0303584
$683$	5.61812e57	0.440521	0.220261	−	0.975441i	$-0.429309\pi$
$683$	5.61812e57	0.440521	0.220261	+	0.975441i	$0.429309\pi$
$684$	−4.95217e57	−0.376830
$685$	3.23297e57	0.238751
$686$	−9.85833e57	−0.706576
$687$	−5.13659e57	−0.357324
$688$	−2.22534e57	−0.150257
$689$	−3.92122e57	−0.256997
$690$	2.10353e57	0.133827
$691$	−2.14965e58	−1.32760	−0.663800	−	0.747910i	$-0.731057\pi$
$691$	−2.14965e58	−1.32760	−0.663800	+	0.747910i	$0.731057\pi$
$692$	1.57093e58	0.941853
$693$	8.23325e56	0.0479225
$694$	9.10157e57	0.514336
$695$	3.12306e58	1.71353
$696$	−1.07484e58	−0.572604
$697$	8.51846e57	0.440645
$698$	8.82141e57	0.443100
$699$	4.25621e57	0.207606
$700$	−2.35758e58	−1.11675
$701$	2.04727e58	0.941793	0.470897	−	0.882188i	$-0.343930\pi$
$701$	2.04727e58	0.941793	0.470897	+	0.882188i	$0.343930\pi$
$702$	4.08733e56	0.0182612
$703$	−2.71463e58	−1.17795
$704$	−8.57302e56	−0.0361322
$705$	2.59429e58	1.06204
$706$	−2.75346e57	−0.109492
$707$	−8.43532e58	−3.25839
$708$	−2.50315e58	−0.939302
$709$	−8.36202e57	−0.304834	−0.152417	−	0.988316i	$-0.548706\pi$
$709$	−8.36202e57	−0.304834	−0.152417	+	0.988316i	$0.548706\pi$
$710$	−5.19101e57	−0.183847
$711$	−1.01716e58	−0.349995
$712$	7.20377e57	0.240835
$713$	2.10463e58	0.683661
$714$	−1.43945e58	−0.454343
$715$	−1.01829e57	−0.0312319
$716$	3.45254e58	1.02901
$717$	1.28025e58	0.370812
$718$	−1.59380e58	−0.448625
$719$	1.73291e58	0.474061	0.237030	−	0.971502i	$-0.423826\pi$
$719$	1.73291e58	0.474061	0.237030	+	0.971502i	$0.423826\pi$
$720$	−1.15995e58	−0.308407
$721$	4.54203e58	1.17375
$722$	−7.21457e57	−0.181217
$723$	−2.62620e58	−0.641199
$724$	−5.77848e58	−1.37143
$725$	4.94067e58	1.13987
$726$	−8.05841e57	−0.180738
$727$	4.93894e58	1.07691	0.538454	−	0.842655i	$-0.319009\pi$
$727$	4.93894e58	1.07691	0.538454	+	0.842655i	$0.319009\pi$
$728$	1.53262e58	0.324893
$729$	1.79701e57	0.0370370
$730$	1.00348e58	0.201090
$731$	1.50165e58	0.292591
$732$	1.49478e58	0.283205
$733$	−2.27310e57	−0.0418781	−0.0209391	−	0.999781i	$-0.506666\pi$
$733$	−2.27310e57	−0.0418781	−0.0209391	+	0.999781i	$0.506666\pi$
$734$	−2.51885e58	−0.451266
$735$	9.66639e58	1.68412
$736$	2.75099e58	0.466116
$737$	5.62461e56	0.00926850
$738$	2.08235e57	0.0333733
$739$	−3.92889e56	−0.00612433	−0.00306217	−	0.999995i	$-0.500975\pi$
$739$	−3.92889e56	−0.00612433	−0.00306217	+	0.999995i	$0.500975\pi$
$740$	−7.24484e58	−1.09845
$741$	−1.47981e58	−0.218239
$742$	3.37577e58	0.484276
$743$	−1.05436e59	−1.47135	−0.735675	−	0.677334i	$-0.763135\pi$
$743$	−1.05436e59	−1.47135	−0.735675	+	0.677334i	$0.763135\pi$
$744$	3.07491e58	0.417434
$745$	2.31032e57	0.0305118
$746$	−7.91193e57	−0.101657
$747$	−2.40511e58	−0.300651
$748$	8.19578e57	0.0996799
$749$	−1.24245e59	−1.47029
$750$	6.39881e57	0.0736789
$751$	1.36881e59	1.53364	0.766822	−	0.641860i	$-0.221837\pi$
$751$	1.36881e59	1.53364	0.766822	+	0.641860i	$0.221837\pi$
$752$	9.24647e58	1.00812
$753$	−4.95247e58	−0.525443
$754$	−1.52206e58	−0.157151
$755$	−1.24194e59	−1.24792
$756$	3.19317e58	0.312266
$757$	−1.35209e59	−1.28688	−0.643442	−	0.765495i	$-0.722494\pi$
$757$	−1.35209e59	−1.28688	−0.643442	+	0.765495i	$0.722494\pi$
$758$	6.08855e58	0.564021
$759$	2.89368e57	0.0260912
$760$	−1.11268e59	−0.976547
$761$	1.00172e59	0.855776	0.427888	−	0.903832i	$-0.359258\pi$
$761$	1.00172e59	0.855776	0.427888	+	0.903832i	$0.359258\pi$
$762$	−3.06965e58	−0.255277
$763$	−5.27235e57	−0.0426827
$764$	−6.41906e58	−0.505892
$765$	7.82727e58	0.600553
$766$	7.35195e58	0.549177
$767$	−7.47992e58	−0.543991
$768$	−1.21037e58	−0.0857066
$769$	6.49599e57	0.0447874	0.0223937	−	0.999749i	$-0.492871\pi$
$769$	6.49599e57	0.0447874	0.0223937	+	0.999749i	$0.492871\pi$
$770$	8.76646e57	0.0588525
$771$	−3.64278e58	−0.238133
$772$	−1.14646e58	−0.0729798
$773$	1.39210e59	0.862959	0.431480	−	0.902123i	$-0.357992\pi$
$773$	1.39210e59	0.862959	0.431480	+	0.902123i	$0.357992\pi$
$774$	3.67080e57	0.0221601
$775$	−1.41343e59	−0.830978
$776$	8.10469e58	0.464057
$777$	1.75040e59	0.976126
$778$	1.69118e58	0.0918563
$779$	−7.53912e58	−0.398844
$780$	−3.94933e58	−0.203509
$781$	−7.14090e57	−0.0358432
$782$	−5.05914e58	−0.247365
$783$	−6.69179e58	−0.318732
$784$	3.44525e59	1.59861
$785$	3.29706e59	1.49038
$786$	−1.51488e58	−0.0667137
$787$	1.95672e58	0.0839550	0.0419775	−	0.999119i	$-0.486634\pi$
$787$	1.95672e58	0.0839550	0.0419775	+	0.999119i	$0.486634\pi$
$788$	2.44290e59	1.02122
$789$	−2.53304e59	−1.03172
$790$	−1.08303e59	−0.429819
$791$	−4.33385e57	−0.0167593
$792$	4.22772e57	0.0159309
$793$	4.46671e58	0.164017
$794$	2.38660e58	0.0854002
$795$	−1.83563e59	−0.640118
$796$	1.58918e59	0.540078
$797$	−7.27616e58	−0.240994	−0.120497	−	0.992714i	$-0.538449\pi$
$797$	−7.27616e58	−0.240994	−0.120497	+	0.992714i	$0.538449\pi$
$798$	1.27396e59	0.411242
$799$	−6.23945e59	−1.96308
$800$	−1.84751e59	−0.566556
$801$	4.48495e58	0.134057
$802$	−6.21091e58	−0.180959
$803$	1.38042e58	0.0392050
$804$	2.18144e58	0.0603941
$805$	4.91068e59	1.32534
$806$	4.35431e58	0.114565
$807$	−4.01928e59	−1.03096
$808$	−4.33149e59	−1.08319
$809$	5.83880e59	1.42357	0.711785	−	0.702397i	$-0.247887\pi$
$809$	5.83880e59	1.42357	0.711785	+	0.702397i	$0.247887\pi$
$810$	1.91339e58	0.0454842
$811$	−5.49280e59	−1.27311	−0.636556	−	0.771231i	$-0.719641\pi$
$811$	−5.49280e59	−1.27311	−0.636556	+	0.771231i	$0.719641\pi$
$812$	−1.18909e60	−2.68729
$813$	1.11392e58	0.0245470
$814$	1.09824e58	0.0235993
$815$	4.58341e59	0.960413
$816$	2.78976e59	0.570058
$817$	−1.32901e59	−0.264835
$818$	6.59806e58	0.128225
$819$	9.54183e58	0.180847
$820$	−2.01205e59	−0.371925
$821$	6.58660e59	1.18748	0.593741	−	0.804657i	$-0.297651\pi$
$821$	6.58660e59	1.18748	0.593741	+	0.804657i	$0.297651\pi$
$822$	−1.90074e58	−0.0334233
$823$	7.46037e59	1.27957	0.639785	−	0.768554i	$-0.279023\pi$
$823$	7.46037e59	1.27957	0.639785	+	0.768554i	$0.279023\pi$
$824$	2.33231e59	0.390192
$825$	−1.94334e58	−0.0317134
$826$	6.43944e59	1.02508
$827$	−6.94575e58	−0.107859	−0.0539295	−	0.998545i	$-0.517175\pi$
$827$	−6.94575e58	−0.107859	−0.0539295	+	0.998545i	$0.517175\pi$
$828$	1.12228e59	0.170012
$829$	4.42746e59	0.654315	0.327157	−	0.944970i	$-0.393909\pi$
$829$	4.42746e59	0.654315	0.327157	+	0.944970i	$0.393909\pi$
$830$	−2.56088e59	−0.369222
$831$	4.23727e59	0.596026
$832$	−9.93560e58	−0.136353
$833$	−2.32483e60	−3.11293
$834$	−1.83612e59	−0.239882
$835$	4.59655e59	0.585948
$836$	−7.25353e58	−0.0902238
$837$	1.91439e59	0.232359
$838$	−2.45515e59	−0.290787
$839$	3.15752e59	0.364943	0.182472	−	0.983211i	$-0.441590\pi$
$839$	3.15752e59	0.364943	0.182472	+	0.983211i	$0.441590\pi$
$840$	7.17461e59	0.809232
$841$	1.58343e60	1.74294
$842$	−6.62094e58	−0.0711250
$843$	4.66492e59	0.489079
$844$	−9.69211e58	−0.0991741
$845$	1.18300e60	1.18147
$846$	−1.52525e59	−0.148678
$847$	−1.88123e60	−1.78991
$848$	−6.54249e59	−0.607614
$849$	−4.25949e59	−0.386145
$850$	3.39762e59	0.300668
$851$	6.15200e59	0.531447
$852$	−2.76951e59	−0.233557
$853$	−1.17009e60	−0.963307	−0.481654	−	0.876362i	$-0.659964\pi$
$853$	−1.17009e60	−0.963307	−0.481654	+	0.876362i	$0.659964\pi$
$854$	−3.84538e59	−0.309067
$855$	−6.92739e59	−0.543581
$856$	−6.37993e59	−0.488769
$857$	−9.58112e59	−0.716654	−0.358327	−	0.933596i	$-0.616653\pi$
$857$	−9.58112e59	−0.716654	−0.358327	+	0.933596i	$0.616653\pi$
$858$	5.98678e57	0.00437224
$859$	−1.69896e60	−1.21150	−0.605750	−	0.795655i	$-0.707127\pi$
$859$	−1.69896e60	−1.21150	−0.605750	+	0.795655i	$0.707127\pi$
$860$	−3.54687e59	−0.246960
$861$	4.86124e59	0.330508
$862$	2.48876e59	0.165228
$863$	−2.10049e59	−0.136175	−0.0680877	−	0.997679i	$-0.521690\pi$
$863$	−2.10049e59	−0.136175	−0.0680877	+	0.997679i	$0.521690\pi$
$864$	2.50232e59	0.158421
$865$	2.19752e60	1.35863
$866$	−7.72821e59	−0.466619
$867$	−9.03402e59	−0.532709
$868$	3.40175e60	1.95906
$869$	−1.48985e59	−0.0837986
$870$	−7.12517e59	−0.391427
$871$	6.51858e58	0.0349769
$872$	−2.70732e58	−0.0141890
$873$	5.04585e59	0.258311
$874$	4.47751e59	0.223899
$875$	1.49380e60	0.729669
$876$	5.35378e59	0.255462
$877$	−2.03764e60	−0.949810	−0.474905	−	0.880037i	$-0.657518\pi$
$877$	−2.03764e60	−0.949810	−0.474905	+	0.880037i	$0.657518\pi$
$878$	3.37448e59	0.153663
$879$	1.24494e60	0.553831
$880$	−1.69900e59	−0.0738413
$881$	1.81214e60	0.769457	0.384729	−	0.923030i	$-0.374295\pi$
$881$	1.81214e60	0.769457	0.384729	+	0.923030i	$0.374295\pi$
$882$	−5.68309e59	−0.235765
$883$	−2.81878e59	−0.114253	−0.0571263	−	0.998367i	$-0.518194\pi$
$883$	−2.81878e59	−0.114253	−0.0571263	+	0.998367i	$0.518194\pi$
$884$	9.49840e59	0.376166
$885$	−3.50156e60	−1.35495
$886$	5.77331e59	0.218290
$887$	3.17942e60	1.17466	0.587332	−	0.809346i	$-0.300178\pi$
$887$	3.17942e60	1.17466	0.587332	+	0.809346i	$0.300178\pi$
$888$	8.98819e59	0.324494
$889$	−7.16606e60	−2.52810
$890$	4.77541e59	0.164633
$891$	2.63211e58	0.00886771
$892$	−2.49886e60	−0.822739
$893$	5.52212e60	1.77685
$894$	−1.35829e58	−0.00427142
$895$	4.82961e60	1.48436
$896$	5.79180e60	1.73980
$897$	3.35360e59	0.0984613
$898$	−7.52984e59	−0.216083
$899$	−7.12889e60	−1.99962
$900$	−7.53701e59	−0.206646
$901$	4.41482e60	1.18319
$902$	3.05006e58	0.00799051
$903$	8.56945e59	0.219459
$904$	−2.22540e58	−0.00557129
$905$	−8.08328e60	−1.97830
$906$	7.30163e59	0.174699
$907$	−6.08024e60	−1.42223	−0.711117	−	0.703073i	$-0.751811\pi$
$907$	−6.08024e60	−1.42223	−0.711117	+	0.703073i	$0.751811\pi$
$908$	1.58262e59	0.0361923
$909$	−2.69672e60	−0.602942
$910$	1.01598e60	0.222094
$911$	−1.17767e60	−0.251707	−0.125854	−	0.992049i	$-0.540167\pi$
$911$	−1.17767e60	−0.251707	−0.125854	+	0.992049i	$0.540167\pi$
$912$	−2.46903e60	−0.515980
$913$	−3.52281e59	−0.0719844
$914$	−1.82579e60	−0.364799
$915$	2.09099e60	0.408526
$916$	−2.91796e60	−0.557471
$917$	−3.53646e60	−0.660690
$918$	−4.60183e59	−0.0840729
$919$	1.05431e61	1.88365	0.941824	−	0.336106i	$-0.109110\pi$
$919$	1.05431e61	1.88365	0.941824	+	0.336106i	$0.109110\pi$
$920$	2.52161e60	0.440582
$921$	3.85229e60	0.658258
$922$	−5.32981e59	−0.0890692
$923$	−8.27586e59	−0.135263
$924$	4.67709e59	0.0747654
$925$	−4.13156e60	−0.645965
$926$	1.53321e60	0.234464
$927$	1.45206e60	0.217195
$928$	−9.31826e60	−1.36333
$929$	−8.77778e60	−1.25621	−0.628105	−	0.778128i	$-0.716169\pi$
$929$	−8.77778e60	−1.25621	−0.628105	+	0.778128i	$0.716169\pi$
$930$	2.03837e60	0.285354
$931$	2.05755e61	2.81762
$932$	2.41784e60	0.323893
$933$	−6.24901e59	−0.0818913
$934$	−2.67154e60	−0.342492
$935$	1.14647e60	0.143789
$936$	4.89967e59	0.0601191
$937$	−2.70984e60	−0.325299	−0.162649	−	0.986684i	$-0.552004\pi$
$937$	−2.70984e60	−0.325299	−0.162649	+	0.986684i	$0.552004\pi$
$938$	−5.61184e59	−0.0659093
$939$	7.39422e60	0.849665
$940$	1.47375e61	1.65693
$941$	1.22601e61	1.34867	0.674336	−	0.738425i	$-0.264430\pi$
$941$	1.22601e61	1.34867	0.674336	+	0.738425i	$0.264430\pi$
$942$	−1.93842e60	−0.208643
$943$	1.70854e60	0.179944
$944$	−1.24801e61	−1.28615
$945$	4.46680e60	0.450447
$946$	5.37669e58	0.00530575
$947$	9.52407e59	0.0919704	0.0459852	−	0.998942i	$-0.485357\pi$
$947$	9.52407e59	0.0919704	0.0459852	+	0.998942i	$0.485357\pi$
$948$	−5.77820e60	−0.546037
$949$	1.59982e60	0.147949
$950$	−3.00701e60	−0.272145
$951$	−3.17615e60	−0.281320
$952$	−1.72554e61	−1.49578
$953$	−7.74450e60	−0.657036	−0.328518	−	0.944498i	$-0.606549\pi$
$953$	−7.74450e60	−0.657036	−0.328518	+	0.944498i	$0.606549\pi$
$954$	1.07921e60	0.0896118
$955$	−8.97937e60	−0.729754
$956$	7.27279e60	0.578514
$957$	−9.80158e59	−0.0763135
$958$	7.81747e60	0.595763
$959$	−4.43725e60	−0.331004
$960$	−4.65113e60	−0.339624
$961$	6.40401e60	0.457744
$962$	1.27280e60	0.0890574
$963$	−3.97204e60	−0.272066
$964$	−1.49188e61	−1.00035
$965$	−1.60373e60	−0.105274
$966$	−2.88710e60	−0.185537
$967$	4.02534e60	0.253256	0.126628	−	0.991950i	$-0.459585\pi$
$967$	4.02534e60	0.253256	0.126628	+	0.991950i	$0.459585\pi$
$968$	−9.66000e60	−0.595021
$969$	1.66608e61	1.00475
$970$	5.37264e60	0.317225
$971$	1.95124e61	1.12802	0.564010	−	0.825768i	$-0.309258\pi$
$971$	1.95124e61	1.12802	0.564010	+	0.825768i	$0.309258\pi$
$972$	1.02083e60	0.0577826
$973$	−4.28640e61	−2.37564
$974$	−2.03645e59	−0.0110513
$975$	−2.25221e60	−0.119678
$976$	7.45263e60	0.387782
$977$	−3.24028e61	−1.65099	−0.825493	−	0.564412i	$-0.809103\pi$
$977$	−3.24028e61	−1.65099	−0.825493	+	0.564412i	$0.809103\pi$
$978$	−2.69469e60	−0.134451
$979$	6.56918e59	0.0320971
$980$	5.49122e61	2.62745
$981$	−1.68554e59	−0.00789811
$982$	1.49120e60	0.0684307
$983$	3.28427e60	0.147602	0.0738008	−	0.997273i	$-0.476487\pi$
$983$	3.28427e60	0.147602	0.0738008	+	0.997273i	$0.476487\pi$
$984$	2.49622e60	0.109871
$985$	3.41727e61	1.47311
$986$	1.71365e61	0.723512
$987$	−3.56067e61	−1.47242
$988$	−8.40640e60	−0.340481
$989$	3.01184e60	0.119484
$990$	2.80258e59	0.0108902
$991$	3.77304e60	0.143609	0.0718046	−	0.997419i	$-0.477124\pi$
$991$	3.77304e60	0.143609	0.0718046	+	0.997419i	$0.477124\pi$
$992$	2.66577e61	0.993881
$993$	−6.72845e60	−0.245729
$994$	7.12467e60	0.254885
$995$	2.22304e61	0.779067
$996$	−1.36628e61	−0.469055
$997$	−4.67033e61	−1.57071	−0.785356	−	0.619044i	$-0.787520\pi$
$997$	−4.67033e61	−1.57071	−0.785356	+	0.619044i	$0.787520\pi$
$998$	5.83198e60	0.192150
$999$	5.59591e60	0.180625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.42.a.a.1.2	✓	3
3.2	odd	2		9.42.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.a.1.2	✓	3	1.1	even	1	trivial
9.42.a.a.1.2		3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-467196. q^{2} -3.48678e9 q^{3} -1.98075e12 q^{4} -2.77079e14 q^{5} +1.62901e15 q^{6} +3.80292e17 q^{7} +1.95278e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\)	\(q-467196. q^{2} -3.48678e9 q^{3} -1.98075e12 q^{4} -2.77079e14 q^{5} +1.62901e15 q^{6} +3.80292e17 q^{7} +1.95278e18 q^{8} +1.21577e19 q^{9} +1.29450e20 q^{10} +1.78075e20 q^{11} +6.90645e21 q^{12} +2.06379e22 q^{13} -1.77671e23 q^{14} +9.66116e23 q^{15} +3.44339e24 q^{16} -2.32357e25 q^{17} -5.68002e24 q^{18} +2.05644e26 q^{19} +5.48825e26 q^{20} -1.32600e27 q^{21} -8.31962e25 q^{22} -4.66038e27 q^{23} -6.80891e27 q^{24} +3.12982e28 q^{25} -9.64193e27 q^{26} -4.23912e28 q^{27} -7.53263e29 q^{28} +1.57858e30 q^{29} -4.51366e29 q^{30} -4.51602e30 q^{31} -5.90294e30 q^{32} -6.20911e29 q^{33} +1.08556e31 q^{34} -1.05371e32 q^{35} -2.40813e31 q^{36} -1.32006e32 q^{37} -9.60760e31 q^{38} -7.19598e31 q^{39} -5.41074e32 q^{40} -3.66611e32 q^{41} +6.19500e32 q^{42} -6.46266e32 q^{43} -3.52723e32 q^{44} -3.36864e33 q^{45} +2.17731e33 q^{46} +2.68528e34 q^{47} -1.20064e34 q^{48} +1.00054e35 q^{49} -1.46224e34 q^{50} +8.10180e34 q^{51} -4.08785e34 q^{52} -1.90002e35 q^{53} +1.98050e34 q^{54} -4.93410e34 q^{55} +7.42624e35 q^{56} -7.17036e35 q^{57} -7.37507e35 q^{58} -3.62437e36 q^{59} -1.91363e36 q^{60} +2.16433e36 q^{61} +2.10987e36 q^{62} +4.62346e36 q^{63} -4.81426e36 q^{64} -5.71832e36 q^{65} +2.90087e35 q^{66} +3.15856e36 q^{67} +4.60242e37 q^{68} +1.62497e37 q^{69} +4.92289e37 q^{70} -4.01004e37 q^{71} +2.37412e37 q^{72} +7.75186e37 q^{73} +6.16729e37 q^{74} -1.09130e38 q^{75} -4.07329e38 q^{76} +6.77206e37 q^{77} +3.36193e37 q^{78} -8.36639e38 q^{79} -9.54091e38 q^{80} +1.47809e38 q^{81} +1.71279e38 q^{82} -1.97827e39 q^{83} +2.62647e39 q^{84} +6.43814e39 q^{85} +3.01933e38 q^{86} -5.50417e39 q^{87} +3.47741e38 q^{88} +3.68899e39 q^{89} +1.57381e39 q^{90} +7.84841e39 q^{91} +9.23105e39 q^{92} +1.57464e40 q^{93} -1.25455e40 q^{94} -5.69796e40 q^{95} +2.05823e40 q^{96} +4.15034e40 q^{97} -4.67449e40 q^{98} +2.16498e39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 36\!\cdots\!03 q^{9}+O(q^{10}) \) 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9	\( 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 26\!\cdots\!04 q^{99}+O(q^{100}) \) 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9 + 303684786396357841224 * q^10 + 2162403578017276790604 * q^11 + 7860140147941716898800 * q^12 + 44715417115247213223642 * q^13 + 320671470159767900457984 * q^14 - 134766121552486207386426 * q^15 - 5459234621059712438935296 * q^16 - 10989933423479049968718714 * q^17 - 3518185230541894056433380 * q^18 + 196397070114735534584831028 * q^19 + 531636782784591447776761824 * q^20 + 155518294615858001587027968 * q^21 - 4513503674461058254096349328 * q^22 - 4665149638066794122614978584 * q^23 - 7908141906446322929993781696 * q^24 - 4609009761244207114343812899 * q^25 + 122894273592250273312332501576 * q^26 - 127173474825648610542883299603 * q^27 - 599824891534617466777136050176 * q^28 - 941555486655490244273102003214 * q^29 - 1058883376027837523993877946824 * q^30 - 6480085319036017864686465368808 * q^31 - 9194142460916956643740243289088 * q^32 - 7539835064497227221977370568204 * q^33 - 50410977973081452147630100226760 * q^34 - 153374925211463555312750388019200 * q^35 - 27406614057517010739893935618800 * q^36 - 442820255707228186224391784737998 * q^37 - 832008681100278182323288015176048 * q^38 - 155913018881652402326915850008442 * q^39 - 830400317719830554628641188275072 * q^40 - 438132779830146983268076758934098 * q^41 - 1118112279998815693097419367107584 * q^42 - 1310999240696843410630649721463476 * q^43 - 1443247128257998435455229084014528 * q^44 + 469900410412478810682641155940826 * q^45 + 7997471516728167525889026089716512 * q^46 + 64523854533555761088559286850643968 * q^47 + 19035174118110151421625255141117696 * q^48 + 171140726678012788361144930683431723 * q^49 + 28333303327284754376413888152266724 * q^50 + 38319528429015278581227949931980314 * q^51 - 20984793566307791589805690265685024 * q^52 + 34693992770270063328682081068689946 * q^53 + 12267153381682064972966523079705380 * q^54 + 100035221507232528994896069839569896 * q^55 - 568132015233041377672136741101977600 * q^56 - 684794240478163142230784839651194228 * q^57 - 2740694640626009342372591817401518296 * q^58 - 4582685445865314260503003260089664948 * q^59 - 1853702841211138803266019258215507424 * q^60 - 8693740159306202291599355552752714662 * q^61 + 265004064722629998116825545352842464 * q^62 - 542258763736695967164682362773127168 * q^63 + 16981741764860889983034117450588819456 * q^64 + 2721360738989032295650621165564283148 * q^65 + 15737614205967000002335445187917232528 * q^66 + 32867814173503669322418795877934200116 * q^67 + 33261671085355608094778443956314848800 * q^68 + 16266370986342093542812388655640268184 * q^69 + 98543364272473044599951459881688524800 * q^70 + 149748844745311390685366673232301225496 * q^71 + 27573985840291440136110933044612124096 * q^72 + 6619123649433674932122580558210670046 * q^73 + 14490759310413784046620539770501448744 * q^74 + 16070623339563035717907230167095788499 * q^75 - 536779250932404614788199202699778310208 * q^76 - 954944421253262491346753072408971247616 * q^77 - 428505836133684487473427567420504715976 * q^78 - 1112771209183156752666617542198723627800 * q^79 - 2423764999311265237507278994973679346176 * q^80 + 443426488243037769948249630619149892803 * q^81 - 107939940778839787676218322470600048296 * q^82 - 1187635824307222104653182519688468749260 * q^83 + 2091460075134421134660653723208430104576 * q^84 + 6153092316082135211652182465439269196852 * q^85 + 2889811785377479896729751911427106623344 * q^86 + 3283000983546327044739131648688427064814 * q^87 + 11348012623814378178834124633898985613056 * q^88 - 2907470395792485617492963651915834875602 * q^89 + 3692098038012081220424316844483830692424 * q^90 + 19747616149564653802226421926044582182912 * q^91 + 10266693573432860781998326486887076136832 * q^92 + 22594660407563895447746096203786446364008 * q^93 + 34628213999509804914437049475497096849408 * q^94 - 84590150972982168777889232049326900017896 * q^95 + 32057992513296996581786794596336971916288 * q^96 - 52479807025249236413871256717456940920314 * q^97 - 268218382984038433881798894561914095373892 * q^98 + 26289779289001760785343260072210213785804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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