LMFDB - Embedded newform 2.70.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,70,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 70, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 70); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [3,51539607552] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$60.3029906584$
Analytic rank:	$0$
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} - 90823593763357992496952650x - 190864638684342453433100893828514036648 $ x^3 - x^2 - 90823593763357992496952650*x - 190864638684342453433100893828514036648
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{5}\cdot 5^{4}\cdot 7\cdot 23 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.04450e13$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.71799e10 q^{2} +3.22422e16 q^{3} +2.95148e20 q^{4} +6.21700e23 q^{5} +5.53917e26 q^{6} +1.85055e28 q^{7} +5.07060e30 q^{8} +2.05176e32 q^{9} +1.06807e34 q^{10} +5.55655e35 q^{11} +9.51623e36 q^{12} +1.02810e37 q^{13} +3.17923e38 q^{14} +2.00450e40 q^{15} +8.71123e40 q^{16} +5.26112e41 q^{17} +3.52490e42 q^{18} +1.07488e44 q^{19} +1.83493e44 q^{20} +5.96660e44 q^{21} +9.54608e45 q^{22} +1.83588e47 q^{23} +1.63488e47 q^{24} -1.30756e48 q^{25} +1.76626e47 q^{26} -2.02871e49 q^{27} +5.46187e48 q^{28} +6.22079e49 q^{29} +3.44370e50 q^{30} +4.33641e51 q^{31} +1.49658e51 q^{32} +1.79156e52 q^{33} +9.03854e51 q^{34} +1.15049e52 q^{35} +6.05573e52 q^{36} -3.89377e53 q^{37} +1.84664e54 q^{38} +3.31481e53 q^{39} +3.15239e54 q^{40} -5.46062e55 q^{41} +1.02505e55 q^{42} -2.76635e56 q^{43} +1.64000e56 q^{44} +1.27558e56 q^{45} +3.15401e57 q^{46} +3.45102e57 q^{47} +2.80869e57 q^{48} -2.01581e58 q^{49} -2.24636e58 q^{50} +1.69630e58 q^{51} +3.03441e57 q^{52} +2.16209e59 q^{53} -3.48530e59 q^{54} +3.45451e59 q^{55} +9.38342e58 q^{56} +3.46567e60 q^{57} +1.06872e60 q^{58} +7.71756e60 q^{59} +5.91624e60 q^{60} +4.12788e61 q^{61} +7.44990e61 q^{62} +3.79690e60 q^{63} +2.57110e61 q^{64} +6.39168e60 q^{65} +3.07787e62 q^{66} +1.64023e63 q^{67} +1.55281e62 q^{68} +5.91927e63 q^{69} +1.97652e62 q^{70} +1.10556e64 q^{71} +1.04037e63 q^{72} -1.41363e64 q^{73} -6.68944e63 q^{74} -4.21585e64 q^{75} +3.17250e64 q^{76} +1.02827e64 q^{77} +5.69481e63 q^{78} -1.23625e65 q^{79} +5.41577e64 q^{80} -8.25297e65 q^{81} -9.38127e65 q^{82} -1.32003e66 q^{83} +1.76103e65 q^{84} +3.27084e65 q^{85} -4.75256e66 q^{86} +2.00572e66 q^{87} +2.81751e66 q^{88} -5.61568e66 q^{89} +2.19143e66 q^{90} +1.90255e65 q^{91} +5.41855e67 q^{92} +1.39816e68 q^{93} +5.92880e67 q^{94} +6.68255e67 q^{95} +4.82530e67 q^{96} -7.29513e67 q^{97} -3.46313e68 q^{98} +1.14007e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 51539607552 q^{2} - 23\!\cdots\!52 q^{3} + 88\!\cdots\!68 q^{4} - 58\!\cdots\!50 q^{5} - 40\!\cdots\!68 q^{6} + 92\!\cdots\!16 q^{7} + 15\!\cdots\!12 q^{8} + 36\!\cdots\!19 q^{9} - 10\!\cdots\!00 q^{10}+ \cdots - 38\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 51539607552 * q^2 - 23599132956604452 * q^3 + 885443715538058477568 * q^4 - 587490642683186853894750 * q^5 - 405430017050287634192007168 * q^6 + 92822810951720092367950893816 * q^7 + 15211807202738752817960438464512 * q^8 + 360980955501866421731693210831319 * q^9 - 10093012388121236906140325904384000 * q^10 - 509274110792982797907767113259693484 * q^11 - 6965234656190831104991528684630310912 * q^12 + 7834895590094608745617272520593597978 * q^13 + 1594683749441713726665793149894754566144 * q^14 + 18875987947658567039619857828092558929000 * q^15 + 261336857795280739939871698507597986398208 * q^16 + 4967316390875888119306952352764938090375926 * q^17 + 6201605593437390193192664108902992310173696 * q^18 - 184984635808419508942952000685700142802011700 * q^19 - 173396632500414285579763685384443612102656000 * q^20 - 6033798863281848119455186189501782268814730144 * q^21 - 8749262602221366973217747903338845875057197056 * q^22 + 35974040337240872869646777015551826362695662568 * q^23 - 119661820229221694123992632230132332869407735808 * q^24 + 631927580098712863031014956677090471784593578125 * q^25 + 134602481308123864433367075234675959289926909952 * q^26 + 7133064620900697654535058788167357626641855543320 * q^27 + 27396458205259274856895458802795186814140595306496 * q^28 + 776562456047673498739227646952671871923395881922570 * q^29 + 324287003659534820837563302575308522644031143936000 * q^30 + 535024307859328290623064740469352760185031230857696 * q^31 + 4489733029880533764721719806104421436383024772022272 * q^32 + 55162120855953533331751137789189801686228499139159056 * q^33 + 85337845790786769069513226162222657094517178062864384 * q^34 + 566033708111654538399806624048816674995593399035218000 * q^35 + 106542772826017052413414456699405337634942049597784064 * q^36 - 224280698679915935005818627014916916595704989659002494 * q^37 - 3178011844238529249433433490571406752788680218037452800 * q^38 - 9360473508215785058537246514019142180875141120785930552 * q^39 - 2978931463303240252065157712538474004548069258952704000 * q^40 - 40466511646066995115304735045305566994309424274413096994 * q^41 - 103659875153750051613996504086004053513087786606181482496 * q^42 - 130655866429367441132707038005276122980890393770376026572 * q^43 - 150311186962626512409538940526451648959020653939789922304 * q^44 + 1983921746212333503311562158101265740647122671144784348250 * q^45 + 618029307013737439398506313414398310483394020522445504512 * q^46 + 7339686181426242035045937632049134482673351071844837562576 * q^47 - 2055774417857353599185054897493495661705168256739072540672 * q^48 + 19781422708172737640545674992957467313292125369821364086731 * q^49 + 10856433159857568793650946690459841634992160698793984000000 * q^50 - 69497068540871228286732941680178420808175296628401561006984 * q^51 + 2312453020715373187433796637184419081230653841896707719168 * q^52 - 369115890096858790809204423808052339323629841619045623370382 * q^53 + 122545117068092537959247934322464771124651791453262845050880 * q^54 + 653706957610031437756402615506622860725713353691650243000 * q^55 + 470667568071277762844164302595682563011777148749485665419264 * q^56 + 12481281692967217206857231257350457421549587786484913331071600 * q^57 + 13341241408104780375883519903843038998920343720474063017082880 * q^58 + 38578917583431570694877146973225322119219615217374421327266340 * q^59 + 5571208300942137496282214851562810727464756851242354868224000 * q^60 + 42160813990176668950743005591046609837464403749066286816298986 * q^61 + 9191647619283403107014586094426391181128160181089721399640064 * q^62 + 263970019424261365547519517899258340018377492900879483964793368 * q^63 + 77133026124431533226014180432375804921065743701574056094466048 * q^64 + 1292235810014064170178090670488124705597047938689799821445701500 * q^65 + 947678020217279810222068220861439762316308229543409193848930304 * q^66 + 2993347235244117409237593760959435267788424710342123090992039836 * q^67 + 1466093027130081725052254628024791611564694642760844645452742656 * q^68 + 8632576534983629121115497409302771615986187297165281123150131488 * q^69 + 9724385059092664635508582492055338906422138371878957048922112000 * q^70 + 26646575855686316197580656331060326374382559599868244979540086456 * q^71 + 1830390899651602952215731852870216111159656359510770035799883776 * q^72 - 5710803445695397409111916726207379330620701493216226637172343362 * q^73 - 3853113063817077251517010290946761043742850338597735614849744896 * q^74 - 54072646335858632291364391220794357295239004871249262032114937500 * q^75 - 54597827749220516597824093483981265423763753341892036316574515200 * q^76 - 158223680416273048529171640921537494742344414386511280173757390048 * q^77 - 160811710371444736549531677502408884739331391092641430151068909568 * q^78 - 142432313881134689670165256806051731841701152927734113846799658320 * q^79 - 51177652847651364053802595345739659965120450908579275563073536000 * q^80 - 1507828852199947063074312141010808769071090216675887820898139650357 * q^81 - 695209376412243484180902344374129954269183981452771124733223632896 * q^82 - 3693839858054266827490757641969940192981240698342129309480559474292 * q^83 - 1780863094771197773761708003630871124648583805802305195044465803264 * q^84 - 7298167608699350794635920443621695725374460108742430656285081769500 * q^85 - 2244650693378709814528727696726760094610393096817308670996667957248 * q^86 - 18423700805232461573101824374922338279567771244103990158383145308280 * q^87 - 2582326528909689780246031631998395420817064611439725077624243879936 * q^88 + 17367740242183938631288441850820944138495579389220797635234884292270 * q^89 + 34083516071220737074273068670864471249138438996268046626825699328000 * q^90 + 167600534303234335258348276576983776372645923384732916198248855289616 * q^91 + 10617662646374182899789466109457467356175325076903425103285041758208 * q^92 + 255004111116610178339751215151729450803024282160488117255709371492736 * q^93 + 126094848448515328706811151949226856272751686017200494870785094057984 * q^94 + 131857598419242140445720532480583107388104295729280077734565490165000 * q^95 - 35317935570603088406430812146796784958966309027486592670231479451648 * q^96 - 100964021638279059474796282561587605930271300796565380448075947866714 * q^97 + 339842254399814640339727510755989409718314658230858656458474210197504 * q^98 - 388490136121756142284718847173053098694146354616452114117724862417532 * q^99

Coefficient data

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

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

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

$2$	1.71799e10	0.707107
$2$	1.71799e10	0.707107
$3$	3.22422e16	1.11620	0.558100	−	0.829774i	$-0.311531\pi$
$3$	3.22422e16	1.11620	0.558100	+	0.829774i	$0.311531\pi$
$4$	2.95148e20	0.500000
$5$	6.21700e23	0.477656	0.238828	−	0.971062i	$-0.423237\pi$
$5$	6.21700e23	0.477656	0.238828	+	0.971062i	$0.423237\pi$
$6$	5.53917e26	0.789272
$7$	1.85055e28	0.129247	0.0646233	−	0.997910i	$-0.479415\pi$
$7$	1.85055e28	0.129247	0.0646233	+	0.997910i	$0.479415\pi$
$8$	5.07060e30	0.353553
$9$	2.05176e32	0.245901
$10$	1.06807e34	0.337754
$11$	5.55655e35	0.655779	0.327890	−	0.944716i	$-0.393663\pi$
$11$	5.55655e35	0.655779	0.327890	+	0.944716i	$0.393663\pi$
$12$	9.51623e36	0.558100
$13$	1.02810e37	0.0381056	0.0190528	−	0.999818i	$-0.493935\pi$
$13$	1.02810e37	0.0381056	0.0190528	+	0.999818i	$0.493935\pi$
$14$	3.17923e38	0.0913912
$15$	2.00450e40	0.533160
$16$	8.71123e40	0.250000
$17$	5.26112e41	0.186462	0.0932310	−	0.995645i	$-0.470280\pi$
$17$	5.26112e41	0.186462	0.0932310	+	0.995645i	$0.470280\pi$
$18$	3.52490e42	0.173878
$19$	1.07488e44	0.821037	0.410518	−	0.911852i	$-0.365348\pi$
$19$	1.07488e44	0.821037	0.410518	+	0.911852i	$0.365348\pi$
$20$	1.83493e44	0.238828
$21$	5.96660e44	0.144265
$22$	9.54608e45	0.463706
$23$	1.83588e47	1.92412	0.962061	−	0.272833i	$-0.0879605\pi$
$23$	1.83588e47	1.92412	0.962061	+	0.272833i	$0.0879605\pi$
$24$	1.63488e47	0.394636
$25$	−1.30756e48	−0.771844
$26$	1.76626e47	0.0269447
$27$	−2.02871e49	−0.841725
$28$	5.46187e48	0.0646233
$29$	6.22079e49	0.219338	0.109669	−	0.993968i	$-0.465021\pi$
$29$	6.22079e49	0.219338	0.109669	+	0.993968i	$0.465021\pi$
$30$	3.44370e50	0.377001
$31$	4.33641e51	1.53162	0.765812	−	0.643065i	$-0.222337\pi$
$31$	4.33641e51	1.53162	0.765812	+	0.643065i	$0.222337\pi$
$32$	1.49658e51	0.176777
$33$	1.79156e52	0.731980
$34$	9.03854e51	0.131849
$35$	1.15049e52	0.0617355
$36$	6.05573e52	0.122951
$37$	−3.89377e53	−0.307192	−0.153596	−	0.988134i	$-0.549086\pi$
$37$	−3.89377e53	−0.307192	−0.153596	+	0.988134i	$0.549086\pi$
$38$	1.84664e54	0.580561
$39$	3.31481e53	0.0425334
$40$	3.15239e54	0.168877
$41$	−5.46062e55	−1.24795	−0.623977	−	0.781442i	$-0.714484\pi$
$41$	−5.46062e55	−1.24795	−0.623977	+	0.781442i	$0.714484\pi$
$42$	1.02505e55	0.102011
$43$	−2.76635e56	−1.22249	−0.611245	−	0.791441i	$-0.709331\pi$
$43$	−2.76635e56	−1.22249	−0.611245	+	0.791441i	$0.709331\pi$
$44$	1.64000e56	0.327890
$45$	1.27558e56	0.117456
$46$	3.15401e57	1.36056
$47$	3.45102e57	0.708877	0.354439	−	0.935079i	$-0.384672\pi$
$47$	3.45102e57	0.708877	0.354439	+	0.935079i	$0.384672\pi$
$48$	2.80869e57	0.279050
$49$	−2.01581e58	−0.983295
$50$	−2.24636e58	−0.545776
$51$	1.69630e58	0.208129
$52$	3.03441e57	0.0190528
$53$	2.16209e59	0.703649	0.351824	−	0.936066i	$-0.385561\pi$
$53$	2.16209e59	0.703649	0.351824	+	0.936066i	$0.385561\pi$
$54$	−3.48530e59	−0.595189
$55$	3.45451e59	0.313237
$56$	9.38342e58	0.0456956
$57$	3.46567e60	0.916441
$58$	1.06872e60	0.155096
$59$	7.71756e60	0.620992	0.310496	−	0.950575i	$-0.399505\pi$
$59$	7.71756e60	0.620992	0.310496	+	0.950575i	$0.399505\pi$
$60$	5.91624e60	0.266580
$61$	4.12788e61	1.05159	0.525797	−	0.850610i	$-0.323767\pi$
$61$	4.12788e61	1.05159	0.525797	+	0.850610i	$0.323767\pi$
$62$	7.44990e61	1.08302
$63$	3.79690e60	0.0317819
$64$	2.57110e61	0.125000
$65$	6.39168e60	0.0182014
$66$	3.07787e62	0.517588
$67$	1.64023e63	1.64182	0.820910	−	0.571058i	$-0.193467\pi$
$67$	1.64023e63	1.64182	0.820910	+	0.571058i	$0.193467\pi$
$68$	1.55281e62	0.0932310
$69$	5.91927e63	2.14770
$70$	1.97652e62	0.0436536
$71$	1.10556e64	1.49683	0.748413	−	0.663234i	$-0.230816\pi$
$71$	1.10556e64	1.49683	0.748413	+	0.663234i	$0.230816\pi$
$72$	1.04037e63	0.0869392
$73$	−1.41363e64	−0.733999	−0.367000	−	0.930221i	$-0.619615\pi$
$73$	−1.41363e64	−0.733999	−0.367000	+	0.930221i	$0.619615\pi$
$74$	−6.68944e63	−0.217218
$75$	−4.21585e64	−0.861532
$76$	3.17250e64	0.410518
$77$	1.02827e64	0.0847573
$78$	5.69481e63	0.0300757
$79$	−1.23625e65	−0.420700	−0.210350	−	0.977626i	$-0.567460\pi$
$79$	−1.23625e65	−0.420700	−0.210350	+	0.977626i	$0.567460\pi$
$80$	5.41577e64	0.119414
$81$	−8.25297e65	−1.18543
$82$	−9.38127e65	−0.882437
$83$	−1.32003e66	−0.817316	−0.408658	−	0.912688i	$-0.634003\pi$
$83$	−1.32003e66	−0.817316	−0.408658	+	0.912688i	$0.634003\pi$
$84$	1.76103e65	0.0721325
$85$	3.27084e65	0.0890648
$86$	−4.75256e66	−0.864432
$87$	2.00572e66	0.244825
$88$	2.81751e66	0.231853
$89$	−5.61568e66	−0.312930	−0.156465	−	0.987683i	$-0.550010\pi$
$89$	−5.61568e66	−0.312930	−0.156465	+	0.987683i	$0.550010\pi$
$90$	2.19143e66	0.0830541
$91$	1.90255e65	0.00492502
$92$	5.41855e67	0.962061
$93$	1.39816e68	1.70960
$94$	5.92880e67	0.501252
$95$	6.68255e67	0.392173
$96$	4.82530e67	0.197318
$97$	−7.29513e67	−0.208645	−0.104323	−	0.994544i	$-0.533267\pi$
$97$	−7.29513e67	−0.208645	−0.104323	+	0.994544i	$0.533267\pi$
$98$	−3.46313e68	−0.695295
$99$	1.14007e68	0.161257
$100$	−3.85922e68	−0.385922
$101$	4.31349e67	0.0306014	0.0153007	−	0.999883i	$-0.495129\pi$
$101$	4.31349e67	0.0306014	0.0153007	+	0.999883i	$0.495129\pi$
$102$	2.91423e68	0.147169
$103$	−2.56474e69	−0.925036	−0.462518	−	0.886610i	$-0.653054\pi$
$103$	−2.56474e69	−0.925036	−0.462518	+	0.886610i	$0.653054\pi$
$104$	5.21307e67	0.0134724
$105$	3.70943e68	0.0689091
$106$	3.71444e69	0.497555
$107$	−1.17988e70	−1.14314	−0.571568	−	0.820555i	$-0.693665\pi$
$107$	−1.17988e70	−1.14314	−0.571568	+	0.820555i	$0.693665\pi$
$108$	−5.98769e69	−0.420862
$109$	−2.64776e70	−1.35414	−0.677072	−	0.735917i	$-0.736751\pi$
$109$	−2.64776e70	−1.35414	−0.677072	+	0.735917i	$0.736751\pi$
$110$	5.93480e69	0.221492
$111$	−1.25544e70	−0.342888
$112$	1.61206e69	0.0323117
$113$	1.07543e71	1.58627	0.793135	−	0.609045i	$-0.208447\pi$
$113$	1.07543e71	1.58627	0.793135	+	0.609045i	$0.208447\pi$
$114$	5.95397e70	0.648021
$115$	1.14136e71	0.919070
$116$	1.83605e70	0.109669
$117$	2.10941e69	0.00937020
$118$	1.32587e71	0.439107
$119$	9.73599e69	0.0240996
$120$	1.01640e71	0.188500
$121$	−4.09199e71	−0.569954
$122$	7.09165e71	0.743589
$123$	−1.76063e72	−1.39297
$124$	1.27988e72	0.765812
$125$	−1.86611e72	−0.846333
$126$	6.52302e70	0.0224732
$127$	−2.92448e72	−0.767043	−0.383521	−	0.923532i	$-0.625289\pi$
$127$	−2.92448e72	−0.767043	−0.383521	+	0.923532i	$0.625289\pi$
$128$	4.41712e71	0.0883883
$129$	−8.91933e72	−1.36454
$130$	1.09808e71	0.0128703
$131$	3.86451e72	0.347724	0.173862	−	0.984770i	$-0.444375\pi$
$131$	3.86451e72	0.347724	0.173862	+	0.984770i	$0.444375\pi$
$132$	5.28774e72	0.365990
$133$	1.98913e72	0.106116
$134$	2.81790e73	1.16094
$135$	−1.26125e73	−0.402055
$136$	2.66771e72	0.0659243
$137$	−7.64047e73	−1.46643	−0.733214	−	0.679998i	$-0.761981\pi$
$137$	−7.64047e73	−1.46643	−0.733214	+	0.679998i	$0.761981\pi$
$138$	1.01692e74	1.51866
$139$	9.18748e72	0.106951	0.0534756	−	0.998569i	$-0.482970\pi$
$139$	9.18748e72	0.106951	0.0534756	+	0.998569i	$0.482970\pi$
$140$	3.39564e72	0.0308677
$141$	1.11269e74	0.791248
$142$	1.89935e74	1.05842
$143$	5.71267e72	0.0249888
$144$	1.78734e73	0.0614753
$145$	3.86747e73	0.104768
$146$	−2.42859e74	−0.519016
$147$	−6.49941e74	−1.09755
$148$	−1.14924e74	−0.153596
$149$	−1.50052e75	−1.58970	−0.794848	−	0.606809i	$-0.792449\pi$
$149$	−1.50052e75	−1.58970	−0.794848	+	0.606809i	$0.792449\pi$
$150$	−7.24277e74	−0.609195
$151$	6.96162e73	0.0465592	0.0232796	−	0.999729i	$-0.492589\pi$
$151$	6.96162e73	0.0465592	0.0232796	+	0.999729i	$0.492589\pi$
$152$	5.45031e74	0.290280
$153$	1.07946e74	0.0458512
$154$	1.76655e74	0.0599324
$155$	2.69595e75	0.731590
$156$	9.78360e73	0.0212667
$157$	3.17365e75	0.553377	0.276688	−	0.960960i	$-0.410763\pi$
$157$	3.17365e75	0.553377	0.276688	+	0.960960i	$0.410763\pi$
$158$	−2.12386e75	−0.297480
$159$	6.97106e75	0.785413
$160$	9.30422e74	0.0844385
$161$	3.39739e75	0.248686
$162$	−1.41785e76	−0.838228
$163$	2.84744e76	1.36139	0.680693	−	0.732568i	$-0.261679\pi$
$163$	2.84744e76	1.36139	0.680693	+	0.732568i	$0.261679\pi$
$164$	−1.61169e76	−0.623977
$165$	1.11381e76	0.349635
$166$	−2.26780e76	−0.577929
$167$	5.54430e76	1.14849	0.574247	−	0.818682i	$-0.305295\pi$
$167$	5.54430e76	1.14849	0.574247	+	0.818682i	$0.305295\pi$
$168$	3.02542e75	0.0510054
$169$	−7.26876e76	−0.998548
$170$	5.61926e75	0.0629783
$171$	2.20541e76	0.201894
$172$	−8.16483e76	−0.611245
$173$	−3.12593e77	−1.91597	−0.957984	−	0.286823i	$-0.907401\pi$
$173$	−3.12593e77	−1.91597	−0.957984	+	0.286823i	$0.907401\pi$
$174$	3.44580e76	0.173118
$175$	−2.41970e76	−0.0997583
$176$	4.84044e76	0.163945
$177$	2.48831e77	0.693150
$178$	−9.64767e76	−0.221275
$179$	3.10675e77	0.587322	0.293661	−	0.955910i	$-0.405126\pi$
$179$	3.10675e77	0.587322	0.293661	+	0.955910i	$0.405126\pi$
$180$	3.76485e76	0.0587281
$181$	−8.20229e77	−1.05688	−0.528438	−	0.848972i	$-0.677222\pi$
$181$	−8.20229e77	−1.05688	−0.528438	+	0.848972i	$0.677222\pi$
$182$	3.26855e75	0.00348251
$183$	1.33092e78	1.17379
$184$	9.30899e77	0.680280
$185$	−2.42075e77	−0.146732
$186$	2.40201e78	1.20887
$187$	2.92337e77	0.122278
$188$	1.01856e78	0.354439
$189$	−3.75424e77	−0.108790
$190$	1.14805e78	0.277308
$191$	−5.26000e78	−1.06007	−0.530035	−	0.847976i	$-0.677821\pi$
$191$	−5.26000e78	−1.06007	−0.530035	+	0.847976i	$0.677821\pi$
$192$	8.28980e77	0.139525
$193$	−1.29881e79	−1.82733	−0.913665	−	0.406468i	$-0.866760\pi$
$193$	−1.29881e79	−1.82733	−0.913665	+	0.406468i	$0.866760\pi$
$194$	−1.25329e78	−0.147534
$195$	2.06082e77	0.0203164
$196$	−5.94961e78	−0.491648
$197$	−1.02044e79	−0.707459	−0.353730	−	0.935348i	$-0.615087\pi$
$197$	−1.02044e79	−0.707459	−0.353730	+	0.935348i	$0.615087\pi$
$198$	1.95863e78	0.114026
$199$	8.60112e78	0.420847	0.210423	−	0.977610i	$-0.432516\pi$
$199$	8.60112e78	0.420847	0.210423	+	0.977610i	$0.432516\pi$
$200$	−6.63009e78	−0.272888
$201$	5.28848e79	1.83260
$202$	7.41053e77	0.0216385
$203$	1.15119e78	0.0283488
$204$	5.00660e78	0.104064
$205$	−3.39487e79	−0.596094
$206$	−4.40619e79	−0.654099
$207$	3.76678e79	0.473144
$208$	8.95599e77	0.00952639
$209$	5.97265e79	0.538419
$210$	6.37276e78	0.0487261
$211$	6.89007e79	0.447177	0.223588	−	0.974684i	$-0.428223\pi$
$211$	6.89007e79	0.447177	0.223588	+	0.974684i	$0.428223\pi$
$212$	6.38136e79	0.351824
$213$	3.56459e80	1.67076
$214$	−2.02702e80	−0.808319
$215$	−1.71984e80	−0.583931
$216$	−1.02868e80	−0.297595
$217$	8.02476e79	0.197957
$218$	−4.54882e80	−0.957524
$219$	−4.55784e80	−0.819290
$220$	1.01959e80	0.156619
$221$	5.40894e78	0.00710524
$222$	−2.15683e80	−0.242458
$223$	−1.31339e81	−1.26437	−0.632186	−	0.774817i	$-0.717842\pi$
$223$	−1.31339e81	−1.26437	−0.632186	+	0.774817i	$0.717842\pi$
$224$	2.76950e79	0.0228478
$225$	−2.68279e80	−0.189797
$226$	1.84758e81	1.12166
$227$	−3.17818e80	−0.165686	−0.0828430	−	0.996563i	$-0.526400\pi$
$227$	−3.17818e80	−0.165686	−0.0828430	+	0.996563i	$0.526400\pi$
$228$	1.02288e81	0.458220
$229$	4.86259e80	0.187302	0.0936512	−	0.995605i	$-0.470146\pi$
$229$	4.86259e80	0.187302	0.0936512	+	0.995605i	$0.470146\pi$
$230$	1.96085e81	0.649880
$231$	3.31537e80	0.0946060
$232$	3.15432e80	0.0775478
$233$	3.07932e81	0.652643	0.326322	−	0.945259i	$-0.394191\pi$
$233$	3.07932e81	0.652643	0.326322	+	0.945259i	$0.394191\pi$
$234$	3.62394e79	0.00662573
$235$	2.14550e81	0.338600
$236$	2.27782e81	0.310496
$237$	−3.98595e81	−0.469585
$238$	1.67263e80	0.0170410
$239$	3.52234e81	0.310530	0.155265	−	0.987873i	$-0.450377\pi$
$239$	3.52234e81	0.310530	0.155265	+	0.987873i	$0.450377\pi$
$240$	1.74616e81	0.133290
$241$	−1.81960e82	−1.20334	−0.601670	−	0.798745i	$-0.705498\pi$
$241$	−1.81960e82	−1.20334	−0.601670	+	0.798745i	$0.705498\pi$
$242$	−7.02999e81	−0.403018
$243$	−9.68217e81	−0.481456
$244$	1.21834e82	0.525797
$245$	−1.25323e82	−0.469677
$246$	−3.02473e82	−0.984976
$247$	1.10509e81	0.0312861
$248$	2.19882e82	0.541511
$249$	−4.25607e82	−0.912287
$250$	−3.20595e82	−0.598448
$251$	1.08392e83	1.76301	0.881507	−	0.472171i	$-0.156530\pi$
$251$	1.08392e83	1.76301	0.881507	+	0.472171i	$0.156530\pi$
$252$	1.12065e81	0.0158909
$253$	1.02011e83	1.26180
$254$	−5.02421e82	−0.542381
$255$	1.05459e82	0.0994141
$256$	7.58855e81	0.0625000
$257$	5.84133e82	0.420552	0.210276	−	0.977642i	$-0.432564\pi$
$257$	5.84133e82	0.420552	0.210276	+	0.977642i	$0.432564\pi$
$258$	−1.53233e83	−0.964878
$259$	−7.20563e81	−0.0397036
$260$	1.88649e81	0.00910068
$261$	1.27636e82	0.0539356
$262$	6.63918e82	0.245878
$263$	3.63091e83	1.17908	0.589539	−	0.807740i	$-0.299310\pi$
$263$	3.63091e83	1.17908	0.589539	+	0.807740i	$0.299310\pi$
$264$	9.08427e82	0.258794
$265$	1.34417e83	0.336102
$266$	3.41730e82	0.0750355
$267$	−1.81062e83	−0.349292
$268$	4.84112e83	0.820910
$269$	−1.02126e84	−1.52294	−0.761470	−	0.648200i	$-0.775522\pi$
$269$	−1.02126e84	−1.52294	−0.761470	+	0.648200i	$0.775522\pi$
$270$	−2.16681e83	−0.284296
$271$	−1.54612e84	−1.78568	−0.892838	−	0.450377i	$-0.851289\pi$
$271$	−1.54612e84	−1.78568	−0.892838	+	0.450377i	$0.851289\pi$
$272$	4.58308e82	0.0466155
$273$	6.13424e81	0.00549730
$274$	−1.31262e84	−1.03692
$275$	−7.26550e83	−0.506159
$276$	1.74706e84	1.07385
$277$	1.96597e83	0.106666	0.0533328	−	0.998577i	$-0.483016\pi$
$277$	1.96597e83	0.106666	0.0533328	+	0.998577i	$0.483016\pi$
$278$	1.57840e83	0.0756260
$279$	8.89729e83	0.376628
$280$	5.83367e82	0.0218268
$281$	3.77859e84	1.25015	0.625075	−	0.780565i	$-0.285068\pi$
$281$	3.77859e84	1.25015	0.625075	+	0.780565i	$0.285068\pi$
$282$	1.91158e84	0.559497
$283$	−1.42513e84	−0.369166	−0.184583	−	0.982817i	$-0.559093\pi$
$283$	−1.42513e84	−0.369166	−0.184583	+	0.982817i	$0.559093\pi$
$284$	3.26305e84	0.748413
$285$	2.15460e84	0.437744
$286$	9.81430e82	0.0176698
$287$	−1.01052e84	−0.161294
$288$	3.07062e83	0.0434696
$289$	−7.68435e84	−0.965232
$290$	6.64425e83	0.0740824
$291$	−2.35211e84	−0.232890
$292$	−4.17229e84	−0.367000
$293$	1.71289e85	1.33905	0.669526	−	0.742788i	$-0.266497\pi$
$293$	1.71289e85	1.33905	0.669526	+	0.742788i	$0.266497\pi$
$294$	−1.11659e85	−0.776088
$295$	4.79801e84	0.296621
$296$	−1.97437e84	−0.108609
$297$	−1.12726e85	−0.551986
$298$	−2.57787e85	−1.12408
$299$	1.88746e84	0.0733198
$300$	−1.24430e85	−0.430766
$301$	−5.11928e84	−0.158003
$302$	1.19600e84	0.0329223
$303$	1.39077e84	0.0341573
$304$	9.36356e84	0.205259
$305$	2.56630e85	0.502301
$306$	1.85449e84	0.0324217
$307$	5.38546e85	0.841296	0.420648	−	0.907224i	$-0.361803\pi$
$307$	5.38546e85	0.841296	0.420648	+	0.907224i	$0.361803\pi$
$308$	3.03492e84	0.0423786
$309$	−8.26929e85	−1.03252
$310$	4.63160e85	0.517312
$311$	8.56444e85	0.855984	0.427992	−	0.903782i	$-0.359221\pi$
$311$	8.56444e85	0.855984	0.427992	+	0.903782i	$0.359221\pi$
$312$	1.68081e84	0.0150378
$313$	−2.43129e85	−0.194786	−0.0973928	−	0.995246i	$-0.531050\pi$
$313$	−2.43129e85	−0.194786	−0.0973928	+	0.995246i	$0.531050\pi$
$314$	5.45229e85	0.391297
$315$	2.36053e84	0.0151808
$316$	−3.64877e85	−0.210350
$317$	5.50838e85	0.284760	0.142380	−	0.989812i	$-0.454524\pi$
$317$	5.50838e85	0.284760	0.142380	+	0.989812i	$0.454524\pi$
$318$	1.19762e86	0.555371
$319$	3.45661e85	0.143838
$320$	1.59845e85	0.0597070
$321$	−3.80420e86	−1.27597
$322$	5.83666e85	0.175848
$323$	5.65510e85	0.153092
$324$	−2.43585e86	−0.592717
$325$	−1.34429e85	−0.0294116
$326$	4.89186e86	0.962646
$327$	−8.53697e86	−1.51149
$328$	−2.76886e86	−0.441219
$329$	6.38629e85	0.0916200
$330$	1.91351e86	0.247229
$331$	−1.46082e87	−1.70032	−0.850160	−	0.526525i	$-0.823495\pi$
$331$	−1.46082e87	−1.70032	−0.850160	+	0.526525i	$0.823495\pi$
$332$	−3.89604e86	−0.408658
$333$	−7.98909e85	−0.0755390
$334$	9.52504e86	0.812108
$335$	1.01973e87	0.784225
$336$	5.19764e85	0.0360663
$337$	2.00726e87	1.25711	0.628553	−	0.777767i	$-0.283647\pi$
$337$	2.00726e87	1.25711	0.628553	+	0.777767i	$0.283647\pi$
$338$	−1.24876e87	−0.706080
$339$	3.46744e87	1.77059
$340$	9.65381e85	0.0445324
$341$	2.40955e87	1.00441
$342$	3.78886e86	0.142761
$343$	−7.52409e86	−0.256334
$344$	−1.40271e87	−0.432216
$345$	3.68001e87	1.02586
$346$	−5.37030e87	−1.35479
$347$	−5.21635e87	−1.19124	−0.595620	−	0.803266i	$-0.703094\pi$
$347$	−5.21635e87	−1.19124	−0.595620	+	0.803266i	$0.703094\pi$
$348$	5.91985e86	0.122413
$349$	−3.23555e87	−0.605998	−0.302999	−	0.952991i	$-0.597988\pi$
$349$	−3.23555e87	−0.605998	−0.302999	+	0.952991i	$0.597988\pi$
$350$	−4.15701e86	−0.0705398
$351$	−2.08571e86	−0.0320744
$352$	8.31581e86	0.115926
$353$	−7.98746e87	−1.00967	−0.504837	−	0.863215i	$-0.668447\pi$
$353$	−7.98746e87	−1.00967	−0.504837	+	0.863215i	$0.668447\pi$
$354$	4.27489e87	0.490131
$355$	6.87329e87	0.714968
$356$	−1.65746e87	−0.156465
$357$	3.13910e86	0.0269000
$358$	5.33735e87	0.415299
$359$	−4.12498e87	−0.291517	−0.145758	−	0.989320i	$-0.546562\pi$
$359$	−4.12498e87	−0.291517	−0.145758	+	0.989320i	$0.546562\pi$
$360$	6.46796e86	0.0415271
$361$	−5.58575e87	−0.325899
$362$	−1.40914e88	−0.747324
$363$	−1.31935e88	−0.636182
$364$	5.61533e85	0.00246251
$365$	−8.78851e87	−0.350599
$366$	2.28651e88	0.829994
$367$	5.04350e88	1.66630	0.833150	−	0.553047i	$-0.186535\pi$
$367$	5.04350e88	1.66630	0.833150	+	0.553047i	$0.186535\pi$
$368$	1.59927e88	0.481031
$369$	−1.12039e88	−0.306874
$370$	−4.15883e87	−0.103756
$371$	4.00106e87	0.0909443
$372$	4.12663e88	0.854799
$373$	1.87047e88	0.353180	0.176590	−	0.984284i	$-0.443493\pi$
$373$	1.87047e88	0.353180	0.176590	+	0.984284i	$0.443493\pi$
$374$	5.02231e87	0.0864636
$375$	−6.01675e88	−0.944676
$376$	1.74987e88	0.250626
$377$	6.39558e86	0.00835802
$378$	−6.44973e87	−0.0769262
$379$	−6.44808e87	−0.0702065	−0.0351033	−	0.999384i	$-0.511176\pi$
$379$	−6.44808e87	−0.0702065	−0.0351033	+	0.999384i	$0.511176\pi$
$380$	1.97234e88	0.196087
$381$	−9.42916e88	−0.856173
$382$	−9.03661e88	−0.749583
$383$	5.69135e88	0.431378	0.215689	−	0.976462i	$-0.430800\pi$
$383$	5.69135e88	0.431378	0.215689	+	0.976462i	$0.430800\pi$
$384$	1.42418e88	0.0986590
$385$	6.39275e87	0.0404848
$386$	−2.23133e89	−1.29212
$387$	−5.67590e88	−0.300612
$388$	−2.15314e88	−0.104323
$389$	6.70814e88	0.297400	0.148700	−	0.988882i	$-0.452491\pi$
$389$	6.70814e88	0.297400	0.148700	+	0.988882i	$0.452491\pi$
$390$	3.54046e87	0.0143658
$391$	9.65876e88	0.358776
$392$	−1.02214e89	−0.347647
$393$	1.24600e89	0.388129
$394$	−1.75310e89	−0.500249
$395$	−7.68577e88	−0.200950
$396$	3.36490e88	0.0806284
$397$	5.87445e89	1.29031	0.645155	−	0.764051i	$-0.276793\pi$
$397$	5.87445e89	1.29031	0.645155	+	0.764051i	$0.276793\pi$
$398$	1.47766e89	0.297584
$399$	6.41340e88	0.118447
$400$	−1.13904e89	−0.192961
$401$	6.46147e89	1.00427	0.502135	−	0.864789i	$-0.332548\pi$
$401$	6.46147e89	1.00427	0.502135	+	0.864789i	$0.332548\pi$
$402$	9.08555e89	1.29584
$403$	4.45825e88	0.0583634
$404$	1.27312e88	0.0153007
$405$	−5.13087e89	−0.566230
$406$	1.97773e88	0.0200456
$407$	−2.16359e89	−0.201450
$408$	8.60128e88	0.0735847
$409$	−7.32374e89	−0.575810	−0.287905	−	0.957659i	$-0.592959\pi$
$409$	−7.32374e89	−0.575810	−0.287905	+	0.957659i	$0.592959\pi$
$410$	−5.83234e89	−0.421502
$411$	−2.46346e90	−1.63683
$412$	−7.56977e89	−0.462518
$413$	1.42818e89	0.0802611
$414$	6.47128e89	0.334563
$415$	−8.20663e89	−0.390396
$416$	1.53863e88	0.00673618
$417$	2.96225e89	0.119379
$418$	1.02609e90	0.380720
$419$	1.33621e90	0.456553	0.228276	−	0.973596i	$-0.426691\pi$
$419$	1.33621e90	0.456553	0.228276	+	0.973596i	$0.426691\pi$
$420$	1.09483e89	0.0344546
$421$	−3.13405e90	−0.908603	−0.454301	−	0.890848i	$-0.650111\pi$
$421$	−3.13405e90	−0.908603	−0.454301	+	0.890848i	$0.650111\pi$
$422$	1.18371e90	0.316202
$423$	7.08067e89	0.174314
$424$	1.09631e90	0.248777
$425$	−6.87921e89	−0.143920
$426$	6.12391e90	1.18140
$427$	7.63887e89	0.135915
$428$	−3.48239e90	−0.571568
$429$	1.84189e89	0.0278925
$430$	−2.95466e90	−0.412901
$431$	5.52645e90	0.712820	0.356410	−	0.934330i	$-0.384001\pi$
$431$	5.52645e90	0.712820	0.356410	+	0.934330i	$0.384001\pi$
$432$	−1.76726e90	−0.210431
$433$	−2.59298e90	−0.285080	−0.142540	−	0.989789i	$-0.545527\pi$
$433$	−2.59298e90	−0.285080	−0.142540	+	0.989789i	$0.545527\pi$
$434$	1.37864e90	0.139977
$435$	1.24696e90	0.116942
$436$	−7.81481e90	−0.677072
$437$	1.97335e91	1.57978
$438$	−7.83032e90	−0.579325
$439$	2.51327e91	1.71875	0.859377	−	0.511342i	$-0.170852\pi$
$439$	2.51327e91	1.71875	0.859377	+	0.511342i	$0.170852\pi$
$440$	1.75164e90	0.110746
$441$	−4.13596e90	−0.241793
$442$	9.29249e88	0.00502417
$443$	−1.41275e91	−0.706542	−0.353271	−	0.935521i	$-0.614931\pi$
$443$	−1.41275e91	−0.706542	−0.353271	+	0.935521i	$0.614931\pi$
$444$	−3.70540e90	−0.171444
$445$	−3.49127e90	−0.149473
$446$	−2.25638e91	−0.894046
$447$	−4.83800e91	−1.77442
$448$	4.75796e89	0.0161558
$449$	−2.64831e90	−0.0832663	−0.0416332	−	0.999133i	$-0.513256\pi$
$449$	−2.64831e90	−0.0832663	−0.0416332	+	0.999133i	$0.513256\pi$
$450$	−4.60900e90	−0.134207
$451$	−3.03422e91	−0.818383
$452$	3.17412e91	0.793135
$453$	2.24458e90	0.0519694
$454$	−5.46007e90	−0.117158
$455$	1.18281e89	0.00235247
$456$	1.75730e91	0.324011
$457$	9.09464e91	1.55481	0.777404	−	0.629002i	$-0.216536\pi$
$457$	9.09464e91	1.55481	0.777404	+	0.629002i	$0.216536\pi$
$458$	8.35386e90	0.132443
$459$	−1.06733e91	−0.156950
$460$	3.36871e91	0.459535
$461$	1.96557e91	0.248775	0.124387	−	0.992234i	$-0.460303\pi$
$461$	1.96557e91	0.248775	0.124387	+	0.992234i	$0.460303\pi$
$462$	5.69576e90	0.0668965
$463$	−2.64121e91	−0.287911	−0.143955	−	0.989584i	$-0.545982\pi$
$463$	−2.64121e91	−0.287911	−0.143955	+	0.989584i	$0.545982\pi$
$464$	5.41907e90	0.0548346
$465$	8.69233e91	0.816600
$466$	5.29023e91	0.461488
$467$	−1.34827e92	−1.09231	−0.546153	−	0.837685i	$-0.683908\pi$
$467$	−1.34827e92	−1.09231	−0.546153	+	0.837685i	$0.683908\pi$
$468$	6.22588e89	0.00468510
$469$	3.03534e91	0.212200
$470$	3.68594e91	0.239426
$471$	1.02326e92	0.617679
$472$	3.91327e91	0.219554
$473$	−1.53714e92	−0.801684
$474$	−6.84781e91	−0.332047
$475$	−1.40547e92	−0.633712
$476$	2.87356e90	0.0120498
$477$	4.43609e91	0.173028
$478$	6.05134e91	0.219578
$479$	−5.36884e92	−1.81261	−0.906306	−	0.422622i	$-0.861110\pi$
$479$	−5.36884e92	−1.81261	−0.906306	+	0.422622i	$0.861110\pi$
$480$	2.99989e91	0.0942502
$481$	−4.00317e90	−0.0117057
$482$	−3.12605e92	−0.850890
$483$	1.09539e92	0.277584
$484$	−1.20774e92	−0.284977
$485$	−4.53538e91	−0.0996607
$486$	−1.66338e92	−0.340441
$487$	4.31506e92	0.822692	0.411346	−	0.911479i	$-0.365059\pi$
$487$	4.31506e92	0.822692	0.411346	+	0.911479i	$0.365059\pi$
$488$	2.09309e92	0.371795
$489$	9.18077e92	1.51958
$490$	−2.15303e92	−0.332112
$491$	8.02436e92	1.15372	0.576858	−	0.816844i	$-0.304279\pi$
$491$	8.02436e92	1.15372	0.576858	+	0.816844i	$0.304279\pi$
$492$	−5.19645e92	−0.696483
$493$	3.27283e91	0.0408983
$494$	1.89852e91	0.0221226
$495$	7.08783e91	0.0770254
$496$	3.77755e92	0.382906
$497$	2.04591e92	0.193460
$498$	−7.31188e92	−0.645085
$499$	−7.25600e92	−0.597350	−0.298675	−	0.954355i	$-0.596545\pi$
$499$	−7.25600e92	−0.597350	−0.298675	+	0.954355i	$0.596545\pi$
$500$	−5.50778e92	−0.423166
$501$	1.78761e93	1.28195
$502$	1.86217e93	1.24664
$503$	−2.42944e93	−1.51849	−0.759244	−	0.650806i	$-0.774431\pi$
$503$	−2.42944e93	−1.51849	−0.759244	+	0.650806i	$0.774431\pi$
$504$	1.92526e91	0.0112366
$505$	2.68170e91	0.0146170
$506$	1.75254e93	0.892227
$507$	−2.34361e93	−1.11458
$508$	−8.63153e92	−0.383521
$509$	1.97970e93	0.821933	0.410966	−	0.911651i	$-0.365191\pi$
$509$	1.97970e93	0.821933	0.410966	+	0.911651i	$0.365191\pi$
$510$	1.81177e92	0.0702964
$511$	−2.61599e92	−0.0948670
$512$	1.30370e92	0.0441942
$513$	−2.18063e93	−0.691087
$514$	1.00353e93	0.297375
$515$	−1.59450e93	−0.441849
$516$	−2.63252e93	−0.682272
$517$	1.91758e93	0.464867
$518$	−1.23792e92	−0.0280747
$519$	−1.00787e94	−2.13860
$520$	3.24097e91	0.00643516
$521$	4.40568e93	0.818676	0.409338	−	0.912383i	$-0.365760\pi$
$521$	4.40568e93	0.818676	0.409338	+	0.912383i	$0.365760\pi$
$522$	2.19277e92	0.0381382
$523$	−4.74724e93	−0.772917	−0.386458	−	0.922307i	$-0.626302\pi$
$523$	−4.74724e93	−0.772917	−0.386458	+	0.922307i	$0.626302\pi$
$524$	1.14060e93	0.173862
$525$	−7.80166e92	−0.111350
$526$	6.23786e93	0.833733
$527$	2.28144e93	0.285590
$528$	1.56067e93	0.182995
$529$	2.46006e94	2.70225
$530$	2.30927e93	0.237660
$531$	1.58346e93	0.152703
$532$	5.87088e92	0.0530581
$533$	−5.61405e92	−0.0475540
$534$	−3.11062e93	−0.246987
$535$	−7.33531e93	−0.546026
$536$	8.31698e93	0.580471
$537$	1.00168e94	0.655569
$538$	−1.75451e94	−1.07688
$539$	−1.12009e94	−0.644825
$540$	−3.72255e93	−0.201028
$541$	2.81517e94	1.42626	0.713130	−	0.701032i	$-0.247277\pi$
$541$	2.81517e94	1.42626	0.713130	+	0.701032i	$0.247277\pi$
$542$	−2.65621e94	−1.26266
$543$	−2.64460e94	−1.17968
$544$	7.87368e92	0.0329621
$545$	−1.64611e94	−0.646815
$546$	1.05385e92	0.00388718
$547$	4.85247e93	0.168035	0.0840175	−	0.996464i	$-0.473225\pi$
$547$	4.85247e93	0.168035	0.0840175	+	0.996464i	$0.473225\pi$
$548$	−2.25507e94	−0.733214
$549$	8.46944e93	0.258588
$550$	−1.24820e94	−0.357909
$551$	6.68663e93	0.180085
$552$	3.00143e94	0.759328
$553$	−2.28775e93	−0.0543740
$554$	3.37751e93	0.0754240
$555$	−7.80505e93	−0.163783
$556$	2.71167e93	0.0534756
$557$	1.39008e94	0.257652	0.128826	−	0.991667i	$-0.458879\pi$
$557$	1.39008e94	0.257652	0.128826	+	0.991667i	$0.458879\pi$
$558$	1.52854e94	0.266316
$559$	−2.84408e93	−0.0465837
$560$	1.00222e93	0.0154339
$561$	9.42559e93	0.136487
$562$	6.49157e94	0.883989
$563$	−1.23722e95	−1.58456	−0.792279	−	0.610159i	$-0.791105\pi$
$563$	−1.23722e95	−1.58456	−0.792279	+	0.610159i	$0.791105\pi$
$564$	3.28407e94	0.395624
$565$	6.68597e94	0.757692
$566$	−2.44835e94	−0.261039
$567$	−1.52726e94	−0.153213
$568$	5.60588e94	0.529208
$569$	6.90461e94	0.613431	0.306716	−	0.951801i	$-0.400770\pi$
$569$	6.90461e94	0.613431	0.306716	+	0.951801i	$0.400770\pi$
$570$	3.70158e94	0.309532
$571$	2.21707e95	1.74515	0.872575	−	0.488480i	$-0.162448\pi$
$571$	2.21707e95	1.74515	0.872575	+	0.488480i	$0.162448\pi$
$572$	1.68608e93	0.0124944
$573$	−1.69594e95	−1.18325
$574$	−1.73605e94	−0.114052
$575$	−2.40051e95	−1.48512
$576$	5.27529e93	0.0307376
$577$	2.66164e95	1.46077	0.730387	−	0.683034i	$-0.239340\pi$
$577$	2.66164e95	1.46077	0.730387	+	0.683034i	$0.239340\pi$
$578$	−1.32016e95	−0.682522
$579$	−4.18764e95	−2.03966
$580$	1.14147e94	0.0523842
$581$	−2.44279e94	−0.105635
$582$	−4.04090e94	−0.164678
$583$	1.20138e95	0.461438
$584$	−7.16793e94	−0.259508
$585$	1.31142e93	0.00447574
$586$	2.94273e95	0.946853
$587$	−1.80219e95	−0.546746	−0.273373	−	0.961908i	$-0.588139\pi$
$587$	−1.80219e95	−0.546746	−0.273373	+	0.961908i	$0.588139\pi$
$588$	−1.91829e95	−0.548777
$589$	4.66114e95	1.25752
$590$	8.24291e94	0.209742
$591$	−3.29012e95	−0.789666
$592$	−3.39195e94	−0.0767981
$593$	−1.78168e95	−0.380578	−0.190289	−	0.981728i	$-0.560943\pi$
$593$	−1.78168e95	−0.380578	−0.190289	+	0.981728i	$0.560943\pi$
$594$	−1.93662e95	−0.390313
$595$	6.05286e93	0.0115113
$596$	−4.42874e95	−0.794848
$597$	2.77319e95	0.469749
$598$	3.24263e94	0.0518449
$599$	5.22978e95	0.789329	0.394664	−	0.918825i	$-0.370861\pi$
$599$	5.22978e95	0.789329	0.394664	+	0.918825i	$0.370861\pi$
$600$	−2.13769e95	−0.304598
$601$	1.26651e96	1.70388	0.851940	−	0.523639i	$-0.175426\pi$
$601$	1.26651e96	1.70388	0.851940	+	0.523639i	$0.175426\pi$
$602$	−8.79486e94	−0.111725
$603$	3.36537e95	0.403725
$604$	2.05471e94	0.0232796
$605$	−2.54399e95	−0.272242
$606$	2.38932e94	0.0241529
$607$	1.53810e96	1.46884	0.734420	−	0.678695i	$-0.237454\pi$
$607$	1.53810e96	1.46884	0.734420	+	0.678695i	$0.237454\pi$
$608$	1.60865e95	0.145140
$609$	3.71170e94	0.0316429
$610$	4.40888e95	0.355180
$611$	3.54798e94	0.0270122
$612$	3.18600e94	0.0229256
$613$	−2.40310e96	−1.63450	−0.817249	−	0.576284i	$-0.804502\pi$
$613$	−2.40310e96	−1.63450	−0.817249	+	0.576284i	$0.804502\pi$
$614$	9.25215e95	0.594886
$615$	−1.09458e96	−0.665359
$616$	5.21395e94	0.0299662
$617$	−3.11063e96	−1.69048	−0.845241	−	0.534385i	$-0.820543\pi$
$617$	−3.11063e96	−1.69048	−0.845241	+	0.534385i	$0.820543\pi$
$618$	−1.42065e96	−0.730105
$619$	−3.72010e95	−0.180812	−0.0904061	−	0.995905i	$-0.528816\pi$
$619$	−3.72010e95	−0.180812	−0.0904061	+	0.995905i	$0.528816\pi$
$620$	7.95703e95	0.365795
$621$	−3.72446e96	−1.61958
$622$	1.47136e96	0.605272
$623$	−1.03921e95	−0.0404452
$624$	2.88761e94	0.0106334
$625$	1.05493e96	0.367588
$626$	−4.17692e95	−0.137734
$627$	1.92572e96	0.600983
$628$	9.36696e95	0.276688
$629$	−2.04856e95	−0.0572797
$630$	4.05536e94	0.0107345
$631$	5.34080e96	1.33842	0.669211	−	0.743072i	$-0.266632\pi$
$631$	5.34080e96	1.33842	0.669211	+	0.743072i	$0.266632\pi$
$632$	−6.26854e95	−0.148740
$633$	2.22151e96	0.499138
$634$	9.46333e95	0.201356
$635$	−1.81815e96	−0.366383
$636$	2.05749e96	0.392706
$637$	−2.07244e95	−0.0374690
$638$	5.93842e95	0.101709
$639$	2.26836e96	0.368071
$640$	2.74612e95	0.0422193
$641$	−2.94492e96	−0.429014	−0.214507	−	0.976722i	$-0.568814\pi$
$641$	−2.94492e96	−0.429014	−0.214507	+	0.976722i	$0.568814\pi$
$642$	−6.53556e96	−0.902245
$643$	1.02451e97	1.34041	0.670207	−	0.742175i	$-0.266206\pi$
$643$	1.02451e97	1.34041	0.670207	+	0.742175i	$0.266206\pi$
$644$	1.00273e96	0.124343
$645$	−5.54515e96	−0.651783
$646$	9.71538e95	0.108253
$647$	−4.89118e96	−0.516674	−0.258337	−	0.966055i	$-0.583174\pi$
$647$	−4.89118e96	−0.516674	−0.258337	+	0.966055i	$0.583174\pi$
$648$	−4.18475e96	−0.419114
$649$	4.28830e96	0.407233
$650$	−2.30948e95	−0.0207971
$651$	2.58736e96	0.220960
$652$	8.40415e96	0.680693
$653$	1.03477e96	0.0794947	0.0397474	−	0.999210i	$-0.487345\pi$
$653$	1.03477e96	0.0794947	0.0397474	+	0.999210i	$0.487345\pi$
$654$	−1.46664e97	−1.06879
$655$	2.40257e96	0.166093
$656$	−4.75687e96	−0.311989
$657$	−2.90042e96	−0.180491
$658$	1.09716e96	0.0647851
$659$	4.68643e96	0.262601	0.131300	−	0.991343i	$-0.458085\pi$
$659$	4.68643e96	0.262601	0.131300	+	0.991343i	$0.458085\pi$
$660$	3.28739e96	0.174818
$661$	−1.62969e97	−0.822534	−0.411267	−	0.911515i	$-0.634914\pi$
$661$	−1.62969e97	−0.822534	−0.411267	+	0.911515i	$0.634914\pi$
$662$	−2.50967e97	−1.20231
$663$	1.74396e95	0.00793087
$664$	−6.69335e96	−0.288965
$665$	1.23664e96	0.0506871
$666$	−1.37251e96	−0.0534141
$667$	1.14206e97	0.422034
$668$	1.63639e97	0.574247
$669$	−4.23465e97	−1.41129
$670$	1.75189e97	0.554531
$671$	2.29368e97	0.689614
$672$	8.92948e95	0.0255027
$673$	5.17767e97	1.40480	0.702400	−	0.711783i	$-0.252112\pi$
$673$	5.17767e97	1.40480	0.702400	+	0.711783i	$0.252112\pi$
$674$	3.44845e97	0.888909
$675$	2.65265e97	0.649680
$676$	−2.14536e97	−0.499274
$677$	−8.38372e97	−1.85408	−0.927038	−	0.374966i	$-0.877654\pi$
$677$	−8.38372e97	−1.85408	−0.927038	+	0.374966i	$0.877654\pi$
$678$	5.95701e97	1.25200
$679$	−1.35000e96	−0.0269667
$680$	1.65851e96	0.0314892
$681$	−1.02471e97	−0.184939
$682$	4.13957e97	0.710223
$683$	3.70902e97	0.604985	0.302493	−	0.953152i	$-0.402181\pi$
$683$	3.70902e97	0.604985	0.302493	+	0.953152i	$0.402181\pi$
$684$	6.50921e96	0.100947
$685$	−4.75008e97	−0.700449
$686$	−1.29263e97	−0.181256
$687$	1.56781e97	0.209067
$688$	−2.40983e97	−0.305623
$689$	2.22284e96	0.0268129
$690$	6.32221e97	0.725396
$691$	−5.73502e97	−0.625954	−0.312977	−	0.949761i	$-0.601326\pi$
$691$	−5.73502e97	−0.625954	−0.312977	+	0.949761i	$0.601326\pi$
$692$	−9.22610e97	−0.957984
$693$	2.10976e96	0.0208419
$694$	−8.96161e97	−0.842334
$695$	5.71186e96	0.0510859
$696$	1.01702e97	0.0865589
$697$	−2.87290e97	−0.232696
$698$	−5.55863e97	−0.428505
$699$	9.92842e97	0.728480
$700$	−7.14170e96	−0.0498791
$701$	−1.75231e98	−1.16503	−0.582517	−	0.812818i	$-0.697932\pi$
$701$	−1.75231e98	−1.16503	−0.582517	+	0.812818i	$0.697932\pi$
$702$	−3.58322e96	−0.0226800
$703$	−4.18535e97	−0.252216
$704$	1.42865e97	0.0819724
$705$	6.91756e97	0.377945
$706$	−1.37224e98	−0.713948
$707$	7.98235e95	0.00395513
$708$	7.34421e97	0.346575
$709$	−5.43642e96	−0.0244353	−0.0122177	−	0.999925i	$-0.503889\pi$
$709$	−5.43642e96	−0.0244353	−0.0122177	+	0.999925i	$0.503889\pi$
$710$	1.18082e98	0.505559
$711$	−2.53649e97	−0.103451
$712$	−2.84749e97	−0.110637
$713$	7.96111e98	2.94703
$714$	5.39293e96	0.0190211
$715$	3.55157e96	0.0119361
$716$	9.16950e97	0.293661
$717$	1.13568e98	0.346614
$718$	−7.08667e97	−0.206134
$719$	4.76605e98	1.32133	0.660666	−	0.750680i	$-0.270274\pi$
$719$	4.76605e98	1.32133	0.660666	+	0.750680i	$0.270274\pi$
$720$	1.11119e97	0.0293641
$721$	−4.74618e97	−0.119558
$722$	−9.59624e97	−0.230445
$723$	−5.86680e98	−1.34317
$724$	−2.42089e98	−0.528438
$725$	−8.13403e97	−0.169295
$726$	−2.26663e98	−0.449849
$727$	−9.13259e98	−1.72845	−0.864225	−	0.503106i	$-0.832191\pi$
$727$	−9.13259e98	−1.72845	−0.864225	+	0.503106i	$0.832191\pi$
$728$	9.64707e95	0.00174126
$729$	3.76441e98	0.648033
$730$	−1.50985e98	−0.247911
$731$	−1.45541e98	−0.227948
$732$	3.92819e98	0.586894
$733$	−4.74182e98	−0.675862	−0.337931	−	0.941171i	$-0.609727\pi$
$733$	−4.74182e98	−0.675862	−0.337931	+	0.941171i	$0.609727\pi$
$734$	8.66467e98	1.17825
$735$	−4.04068e98	−0.524254
$736$	2.74753e98	0.340140
$737$	9.11405e98	1.07667
$738$	−1.92481e98	−0.216992
$739$	−8.28685e98	−0.891572	−0.445786	−	0.895140i	$-0.647076\pi$
$739$	−8.28685e98	−0.891572	−0.445786	+	0.895140i	$0.647076\pi$
$740$	−7.14481e97	−0.0733662
$741$	3.56304e97	0.0349215
$742$	6.87377e97	0.0643073
$743$	−7.21940e98	−0.644744	−0.322372	−	0.946613i	$-0.604480\pi$
$743$	−7.21940e98	−0.644744	−0.322372	+	0.946613i	$0.604480\pi$
$744$	7.08949e98	0.604434
$745$	−9.32870e98	−0.759328
$746$	3.21345e98	0.249736
$747$	−2.70839e98	−0.200979
$748$	8.62826e97	0.0611390
$749$	−2.18343e98	−0.147746
$750$	−1.03367e99	−0.667987
$751$	−1.90103e98	−0.117331	−0.0586653	−	0.998278i	$-0.518684\pi$
$751$	−1.90103e98	−0.117331	−0.0586653	+	0.998278i	$0.518684\pi$
$752$	3.00626e98	0.177219
$753$	3.49481e99	1.96787
$754$	1.09875e97	0.00591001
$755$	4.32804e97	0.0222393
$756$	−1.10805e98	−0.0543950
$757$	−9.69436e98	−0.454686	−0.227343	−	0.973815i	$-0.573004\pi$
$757$	−9.69436e98	−0.454686	−0.227343	+	0.973815i	$0.573004\pi$
$758$	−1.10777e98	−0.0496435
$759$	3.28907e99	1.40842
$760$	3.38846e98	0.138654
$761$	3.44446e99	1.34695	0.673474	−	0.739211i	$-0.264801\pi$
$761$	3.44446e99	1.34695	0.673474	+	0.739211i	$0.264801\pi$
$762$	−1.61992e99	−0.605406
$763$	−4.89982e98	−0.175018
$764$	−1.55248e99	−0.530035
$765$	6.71098e97	0.0219011
$766$	9.77767e98	0.305030
$767$	7.93440e97	0.0236632
$768$	2.44672e98	0.0697625
$769$	2.57365e98	0.0701601	0.0350800	−	0.999385i	$-0.488831\pi$
$769$	2.57365e98	0.0701601	0.0350800	+	0.999385i	$0.488831\pi$
$770$	1.09827e98	0.0286271
$771$	1.88338e99	0.469420
$772$	−3.83340e99	−0.913665
$773$	−6.37046e99	−1.45204	−0.726020	−	0.687674i	$-0.758632\pi$
$773$	−6.37046e99	−1.45204	−0.726020	+	0.687674i	$0.758632\pi$
$774$	−9.75112e98	−0.212565
$775$	−5.67010e99	−1.18218
$776$	−3.69907e98	−0.0737672
$777$	−2.32325e98	−0.0443171
$778$	1.15245e99	0.210294
$779$	−5.86954e99	−1.02462
$780$	6.08246e97	0.0101582
$781$	6.14312e99	0.981587
$782$	1.65936e99	0.253693
$783$	−1.26202e99	−0.184623
$784$	−1.75601e99	−0.245824
$785$	1.97306e99	0.264324
$786$	2.14062e99	0.274449
$787$	−3.80820e99	−0.467295	−0.233648	−	0.972321i	$-0.575066\pi$
$787$	−3.80820e99	−0.467295	−0.233648	+	0.972321i	$0.575066\pi$
$788$	−3.01180e99	−0.353730
$789$	1.17069e100	1.31609
$790$	−1.32041e99	−0.142093
$791$	1.99015e99	0.205020
$792$	5.78085e98	0.0570129
$793$	4.24387e98	0.0400716
$794$	1.00922e100	0.912388
$795$	4.33390e99	0.375157
$796$	2.53860e99	0.210423
$797$	−1.46568e99	−0.116339	−0.0581697	−	0.998307i	$-0.518526\pi$
$797$	−1.46568e99	−0.116339	−0.0581697	+	0.998307i	$0.518526\pi$
$798$	1.10181e99	0.0837546
$799$	1.81562e99	0.132179
$800$	−1.95686e99	−0.136444
$801$	−1.15220e99	−0.0769499
$802$	1.11007e100	0.710126
$803$	−7.85488e99	−0.481342
$804$	1.56088e100	0.916299
$805$	2.11215e99	0.118787
$806$	7.65922e98	0.0412691
$807$	−3.29277e100	−1.69990
$808$	2.18720e98	0.0108192
$809$	4.97434e99	0.235782	0.117891	−	0.993027i	$-0.462387\pi$
$809$	4.97434e99	0.235782	0.117891	+	0.993027i	$0.462387\pi$
$810$	−8.81477e99	−0.400385
$811$	2.72384e100	1.18567	0.592834	−	0.805325i	$-0.298009\pi$
$811$	2.72384e100	1.18567	0.592834	+	0.805325i	$0.298009\pi$
$812$	3.39772e98	0.0141744
$813$	−4.98504e100	−1.99317
$814$	−3.71702e99	−0.142447
$815$	1.77025e100	0.650275
$816$	1.47769e99	0.0520322
$817$	−2.97351e100	−1.00371
$818$	−1.25821e100	−0.407159
$819$	3.90358e97	0.00121107
$820$	−1.00199e100	−0.298047
$821$	−9.60494e99	−0.273940	−0.136970	−	0.990575i	$-0.543736\pi$
$821$	−9.60494e99	−0.273940	−0.136970	+	0.990575i	$0.543736\pi$
$822$	−4.23219e100	−1.15741
$823$	5.21342e100	1.36719	0.683594	−	0.729862i	$-0.260416\pi$
$823$	5.21342e100	1.36719	0.683594	+	0.729862i	$0.260416\pi$
$824$	−1.30048e100	−0.327050
$825$	−2.34256e100	−0.564975
$826$	2.45359e99	0.0567532
$827$	4.30086e100	0.954147	0.477074	−	0.878863i	$-0.341697\pi$
$827$	4.30086e100	0.954147	0.477074	+	0.878863i	$0.341697\pi$
$828$	1.11176e100	0.236572
$829$	9.09591e100	1.85659	0.928293	−	0.371850i	$-0.121276\pi$
$829$	9.09591e100	1.85659	0.928293	+	0.371850i	$0.121276\pi$
$830$	−1.40989e100	−0.276052
$831$	6.33872e99	0.119060
$832$	2.64334e98	0.00476320
$833$	−1.06054e100	−0.183347
$834$	5.08911e99	0.0844137
$835$	3.44689e100	0.548585
$836$	1.76281e100	0.269209
$837$	−8.79732e100	−1.28921
$838$	2.29559e100	0.322832
$839$	5.00901e100	0.676028	0.338014	−	0.941141i	$-0.390245\pi$
$839$	5.00901e100	0.676028	0.338014	+	0.941141i	$0.390245\pi$
$840$	1.88091e99	0.0243630
$841$	−7.65683e100	−0.951891
$842$	−5.38426e100	−0.642479
$843$	1.21830e101	1.39542
$844$	2.03359e100	0.223588
$845$	−4.51899e100	−0.476963
$846$	1.21645e100	0.123258
$847$	−7.57245e99	−0.0736646
$848$	1.88344e100	0.175912
$849$	−4.59492e100	−0.412062
$850$	−1.18184e100	−0.101767
$851$	−7.14847e100	−0.591076
$852$	1.05208e101	0.835378
$853$	2.37146e101	1.80831	0.904157	−	0.427201i	$-0.140500\pi$
$853$	2.37146e101	1.80831	0.904157	+	0.427201i	$0.140500\pi$
$854$	1.31235e100	0.0961064
$855$	1.37110e100	0.0964359
$856$	−5.98270e100	−0.404159
$857$	−2.22421e101	−1.44324	−0.721619	−	0.692291i	$-0.756602\pi$
$857$	−2.22421e101	−1.44324	−0.721619	+	0.692291i	$0.756602\pi$
$858$	3.16435e99	0.0197230
$859$	−6.02462e100	−0.360716	−0.180358	−	0.983601i	$-0.557726\pi$
$859$	−6.02462e100	−0.360716	−0.180358	+	0.983601i	$0.557726\pi$
$860$	−5.07607e100	−0.291965
$861$	−3.25813e100	−0.180036
$862$	9.49436e100	0.504040
$863$	−8.62662e100	−0.440016	−0.220008	−	0.975498i	$-0.570608\pi$
$863$	−8.62662e100	−0.440016	−0.220008	+	0.975498i	$0.570608\pi$
$864$	−3.03612e100	−0.148797
$865$	−1.94339e101	−0.915174
$866$	−4.45471e100	−0.201582
$867$	−2.47761e101	−1.07739
$868$	2.36849e100	0.0989786
$869$	−6.86929e100	−0.275886
$870$	2.14226e100	0.0826908
$871$	1.68632e100	0.0625625
$872$	−1.34257e101	−0.478762
$873$	−1.49679e100	−0.0513061
$874$	3.39020e101	1.11707
$875$	−3.45333e100	−0.109386
$876$	−1.34524e101	−0.409645
$877$	4.31920e101	1.26450	0.632248	−	0.774766i	$-0.282132\pi$
$877$	4.31920e101	1.26450	0.632248	+	0.774766i	$0.282132\pi$
$878$	4.31777e101	1.21534
$879$	5.52275e101	1.49465
$880$	3.00930e100	0.0783093
$881$	1.44190e100	0.0360799	0.0180400	−	0.999837i	$-0.494257\pi$
$881$	1.44190e100	0.0360799	0.0180400	+	0.999837i	$0.494257\pi$
$882$	−7.10552e100	−0.170974
$883$	6.46049e101	1.49493	0.747466	−	0.664300i	$-0.231270\pi$
$883$	6.46049e101	1.49493	0.747466	+	0.664300i	$0.231270\pi$
$884$	1.59644e99	0.00355262
$885$	1.54698e101	0.331088
$886$	−2.42709e101	−0.499601
$887$	−3.88485e101	−0.769147	−0.384574	−	0.923094i	$-0.625652\pi$
$887$	−3.88485e101	−0.769147	−0.384574	+	0.923094i	$0.625652\pi$
$888$	−6.36583e100	−0.121229
$889$	−5.41190e100	−0.0991377
$890$	−5.99795e100	−0.105693
$891$	−4.58581e101	−0.777383
$892$	−3.87643e101	−0.632186
$893$	3.70944e101	0.582014
$894$	−8.31161e101	−1.25470
$895$	1.93146e101	0.280538
$896$	8.17411e99	0.0114239
$897$	6.08559e100	0.0818395
$898$	−4.54975e100	−0.0588782
$899$	2.69759e101	0.335944
$900$	−7.91821e100	−0.0948987
$901$	1.13750e101	0.131204
$902$	−5.21275e101	−0.578684
$903$	−1.65057e101	−0.176363
$904$	5.45310e101	0.560831
$905$	−5.09936e101	−0.504824
$906$	3.85616e100	0.0367479
$907$	−1.61004e102	−1.47702	−0.738509	−	0.674244i	$-0.764470\pi$
$907$	−1.61004e102	−1.47702	−0.738509	+	0.674244i	$0.764470\pi$
$908$	−9.38032e100	−0.0828430
$909$	8.85027e99	0.00752493
$910$	2.03206e99	0.00166344
$911$	5.23191e100	0.0412360	0.0206180	−	0.999787i	$-0.493437\pi$
$911$	5.23191e100	0.0412360	0.0206180	+	0.999787i	$0.493437\pi$
$912$	3.01902e101	0.229110
$913$	−7.33482e101	−0.535979
$914$	1.56245e102	1.09941
$915$	8.27434e101	0.560668
$916$	1.43518e101	0.0936512
$917$	7.15148e100	0.0449422
$918$	−1.83366e101	−0.110980
$919$	−8.39784e101	−0.489534	−0.244767	−	0.969582i	$-0.578711\pi$
$919$	−8.39784e101	−0.489534	−0.244767	+	0.969582i	$0.578711\pi$
$920$	5.78740e101	0.324940
$921$	1.73639e102	0.939054
$922$	3.37682e101	0.175910
$923$	1.13663e101	0.0570374
$924$	9.78525e100	0.0473030
$925$	5.09132e101	0.237105
$926$	−4.53756e101	−0.203584
$927$	−5.26223e101	−0.227467
$928$	9.30990e100	0.0387739
$929$	1.68209e102	0.675005	0.337502	−	0.941325i	$-0.390418\pi$
$929$	1.68209e102	0.675005	0.337502	+	0.941325i	$0.390418\pi$
$930$	1.49333e102	0.577424
$931$	−2.16676e102	−0.807321
$932$	9.08855e101	0.326322
$933$	2.76137e102	0.955449
$934$	−2.31631e102	−0.772377
$935$	1.81746e101	0.0584068
$936$	1.06960e100	0.00331287
$937$	−2.64553e102	−0.789762	−0.394881	−	0.918732i	$-0.629214\pi$
$937$	−2.64553e102	−0.789762	−0.394881	+	0.918732i	$0.629214\pi$
$938$	5.21468e101	0.150048
$939$	−7.83901e101	−0.217419
$940$	6.33239e101	0.169300
$941$	3.41300e102	0.879617	0.439809	−	0.898091i	$-0.355046\pi$
$941$	3.41300e102	0.879617	0.439809	+	0.898091i	$0.355046\pi$
$942$	1.75794e102	0.436765
$943$	−1.00250e103	−2.40122
$944$	6.72294e101	0.155248
$945$	−2.33401e101	−0.0519643
$946$	−2.64078e102	−0.566876
$947$	3.95402e101	0.0818398	0.0409199	−	0.999162i	$-0.486971\pi$
$947$	3.95402e101	0.0818398	0.0409199	+	0.999162i	$0.486971\pi$
$948$	−1.17644e102	−0.234792
$949$	−1.45334e101	−0.0279695
$950$	−2.41458e102	−0.448102
$951$	1.77603e102	0.317849
$952$	4.93673e100	0.00852049
$953$	5.57782e102	0.928452	0.464226	−	0.885717i	$-0.346333\pi$
$953$	5.57782e102	0.928452	0.464226	+	0.885717i	$0.346333\pi$
$954$	7.62115e101	0.122349
$955$	−3.27014e102	−0.506349
$956$	1.03961e102	0.155265
$957$	1.11449e102	0.160551
$958$	−9.22359e102	−1.28171
$959$	−1.41391e102	−0.189531
$960$	5.15377e101	0.0666450
$961$	1.07885e103	1.34587
$962$	−6.87740e100	−0.00827721
$963$	−2.42083e102	−0.281098
$964$	−5.37052e102	−0.601670
$965$	−8.07467e102	−0.872836
$966$	1.88187e102	0.196281
$967$	1.21649e103	1.22433	0.612163	−	0.790732i	$-0.290300\pi$
$967$	1.21649e103	1.22433	0.612163	+	0.790732i	$0.290300\pi$
$968$	−2.07489e102	−0.201509
$969$	1.82333e102	0.170881
$970$	−7.79172e101	−0.0704707
$971$	1.44003e103	1.25692	0.628460	−	0.777842i	$-0.283685\pi$
$971$	1.44003e103	1.25692	0.628460	+	0.777842i	$0.283685\pi$
$972$	−2.85767e102	−0.240728
$973$	1.70019e101	0.0138231
$974$	7.41321e102	0.581731
$975$	−4.33430e101	−0.0328292
$976$	3.59589e102	0.262899
$977$	1.02741e103	0.725075	0.362537	−	0.931969i	$-0.381911\pi$
$977$	1.02741e103	0.725075	0.362537	+	0.931969i	$0.381911\pi$
$978$	1.57724e103	1.07450
$979$	−3.12038e102	−0.205213
$980$	−3.69887e102	−0.234839
$981$	−5.43258e102	−0.332985
$982$	1.37857e103	0.815800
$983$	−3.79071e102	−0.216583	−0.108291	−	0.994119i	$-0.534538\pi$
$983$	−3.79071e102	−0.216583	−0.108291	+	0.994119i	$0.534538\pi$
$984$	−8.92743e102	−0.492488
$985$	−6.34406e102	−0.337922
$986$	5.62269e101	0.0289195
$987$	2.05908e102	0.102266
$988$	3.26164e101	0.0156430
$989$	−5.07868e103	−2.35222
$990$	1.21768e102	0.0544652
$991$	−3.01753e102	−0.130350	−0.0651748	−	0.997874i	$-0.520761\pi$
$991$	−3.01753e102	−0.130350	−0.0651748	+	0.997874i	$0.520761\pi$
$992$	6.48978e102	0.270755
$993$	−4.71001e103	−1.89790
$994$	3.51484e102	0.136797
$995$	5.34732e102	0.201020
$996$	−1.25617e103	−0.456144
$997$	−1.49967e103	−0.526031	−0.263016	−	0.964792i	$-0.584717\pi$
$997$	−1.49967e103	−0.526031	−0.263016	+	0.964792i	$0.584717\pi$
$998$	−1.24657e103	−0.422390
$999$	7.89933e102	0.258571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.70.a.b.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.70.a.b.1.3	✓	3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.71799e10 q^{2} +3.22422e16 q^{3} +2.95148e20 q^{4} +6.21700e23 q^{5} +5.53917e26 q^{6} +1.85055e28 q^{7} +5.07060e30 q^{8} +2.05176e32 q^{9} +1.06807e34 q^{10} +5.55655e35 q^{11} +9.51623e36 q^{12} +1.02810e37 q^{13} +3.17923e38 q^{14} +2.00450e40 q^{15} +8.71123e40 q^{16} +5.26112e41 q^{17} +3.52490e42 q^{18} +1.07488e44 q^{19} +1.83493e44 q^{20} +5.96660e44 q^{21} +9.54608e45 q^{22} +1.83588e47 q^{23} +1.63488e47 q^{24} -1.30756e48 q^{25} +1.76626e47 q^{26} -2.02871e49 q^{27} +5.46187e48 q^{28} +6.22079e49 q^{29} +3.44370e50 q^{30} +4.33641e51 q^{31} +1.49658e51 q^{32} +1.79156e52 q^{33} +9.03854e51 q^{34} +1.15049e52 q^{35} +6.05573e52 q^{36} -3.89377e53 q^{37} +1.84664e54 q^{38} +3.31481e53 q^{39} +3.15239e54 q^{40} -5.46062e55 q^{41} +1.02505e55 q^{42} -2.76635e56 q^{43} +1.64000e56 q^{44} +1.27558e56 q^{45} +3.15401e57 q^{46} +3.45102e57 q^{47} +2.80869e57 q^{48} -2.01581e58 q^{49} -2.24636e58 q^{50} +1.69630e58 q^{51} +3.03441e57 q^{52} +2.16209e59 q^{53} -3.48530e59 q^{54} +3.45451e59 q^{55} +9.38342e58 q^{56} +3.46567e60 q^{57} +1.06872e60 q^{58} +7.71756e60 q^{59} +5.91624e60 q^{60} +4.12788e61 q^{61} +7.44990e61 q^{62} +3.79690e60 q^{63} +2.57110e61 q^{64} +6.39168e60 q^{65} +3.07787e62 q^{66} +1.64023e63 q^{67} +1.55281e62 q^{68} +5.91927e63 q^{69} +1.97652e62 q^{70} +1.10556e64 q^{71} +1.04037e63 q^{72} -1.41363e64 q^{73} -6.68944e63 q^{74} -4.21585e64 q^{75} +3.17250e64 q^{76} +1.02827e64 q^{77} +5.69481e63 q^{78} -1.23625e65 q^{79} +5.41577e64 q^{80} -8.25297e65 q^{81} -9.38127e65 q^{82} -1.32003e66 q^{83} +1.76103e65 q^{84} +3.27084e65 q^{85} -4.75256e66 q^{86} +2.00572e66 q^{87} +2.81751e66 q^{88} -5.61568e66 q^{89} +2.19143e66 q^{90} +1.90255e65 q^{91} +5.41855e67 q^{92} +1.39816e68 q^{93} +5.92880e67 q^{94} +6.68255e67 q^{95} +4.82530e67 q^{96} -7.29513e67 q^{97} -3.46313e68 q^{98} +1.14007e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 51539607552 q^{2} - 23\!\cdots\!52 q^{3} + 88\!\cdots\!68 q^{4} - 58\!\cdots\!50 q^{5} - 40\!\cdots\!68 q^{6} + 92\!\cdots\!16 q^{7} + 15\!\cdots\!12 q^{8} + 36\!\cdots\!19 q^{9} - 10\!\cdots\!00 q^{10}+ \cdots - 38\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 51539607552 * q^2 - 23599132956604452 * q^3 + 885443715538058477568 * q^4 - 587490642683186853894750 * q^5 - 405430017050287634192007168 * q^6 + 92822810951720092367950893816 * q^7 + 15211807202738752817960438464512 * q^8 + 360980955501866421731693210831319 * q^9 - 10093012388121236906140325904384000 * q^10 - 509274110792982797907767113259693484 * q^11 - 6965234656190831104991528684630310912 * q^12 + 7834895590094608745617272520593597978 * q^13 + 1594683749441713726665793149894754566144 * q^14 + 18875987947658567039619857828092558929000 * q^15 + 261336857795280739939871698507597986398208 * q^16 + 4967316390875888119306952352764938090375926 * q^17 + 6201605593437390193192664108902992310173696 * q^18 - 184984635808419508942952000685700142802011700 * q^19 - 173396632500414285579763685384443612102656000 * q^20 - 6033798863281848119455186189501782268814730144 * q^21 - 8749262602221366973217747903338845875057197056 * q^22 + 35974040337240872869646777015551826362695662568 * q^23 - 119661820229221694123992632230132332869407735808 * q^24 + 631927580098712863031014956677090471784593578125 * q^25 + 134602481308123864433367075234675959289926909952 * q^26 + 7133064620900697654535058788167357626641855543320 * q^27 + 27396458205259274856895458802795186814140595306496 * q^28 + 776562456047673498739227646952671871923395881922570 * q^29 + 324287003659534820837563302575308522644031143936000 * q^30 + 535024307859328290623064740469352760185031230857696 * q^31 + 4489733029880533764721719806104421436383024772022272 * q^32 + 55162120855953533331751137789189801686228499139159056 * q^33 + 85337845790786769069513226162222657094517178062864384 * q^34 + 566033708111654538399806624048816674995593399035218000 * q^35 + 106542772826017052413414456699405337634942049597784064 * q^36 - 224280698679915935005818627014916916595704989659002494 * q^37 - 3178011844238529249433433490571406752788680218037452800 * q^38 - 9360473508215785058537246514019142180875141120785930552 * q^39 - 2978931463303240252065157712538474004548069258952704000 * q^40 - 40466511646066995115304735045305566994309424274413096994 * q^41 - 103659875153750051613996504086004053513087786606181482496 * q^42 - 130655866429367441132707038005276122980890393770376026572 * q^43 - 150311186962626512409538940526451648959020653939789922304 * q^44 + 1983921746212333503311562158101265740647122671144784348250 * q^45 + 618029307013737439398506313414398310483394020522445504512 * q^46 + 7339686181426242035045937632049134482673351071844837562576 * q^47 - 2055774417857353599185054897493495661705168256739072540672 * q^48 + 19781422708172737640545674992957467313292125369821364086731 * q^49 + 10856433159857568793650946690459841634992160698793984000000 * q^50 - 69497068540871228286732941680178420808175296628401561006984 * q^51 + 2312453020715373187433796637184419081230653841896707719168 * q^52 - 369115890096858790809204423808052339323629841619045623370382 * q^53 + 122545117068092537959247934322464771124651791453262845050880 * q^54 + 653706957610031437756402615506622860725713353691650243000 * q^55 + 470667568071277762844164302595682563011777148749485665419264 * q^56 + 12481281692967217206857231257350457421549587786484913331071600 * q^57 + 13341241408104780375883519903843038998920343720474063017082880 * q^58 + 38578917583431570694877146973225322119219615217374421327266340 * q^59 + 5571208300942137496282214851562810727464756851242354868224000 * q^60 + 42160813990176668950743005591046609837464403749066286816298986 * q^61 + 9191647619283403107014586094426391181128160181089721399640064 * q^62 + 263970019424261365547519517899258340018377492900879483964793368 * q^63 + 77133026124431533226014180432375804921065743701574056094466048 * q^64 + 1292235810014064170178090670488124705597047938689799821445701500 * q^65 + 947678020217279810222068220861439762316308229543409193848930304 * q^66 + 2993347235244117409237593760959435267788424710342123090992039836 * q^67 + 1466093027130081725052254628024791611564694642760844645452742656 * q^68 + 8632576534983629121115497409302771615986187297165281123150131488 * q^69 + 9724385059092664635508582492055338906422138371878957048922112000 * q^70 + 26646575855686316197580656331060326374382559599868244979540086456 * q^71 + 1830390899651602952215731852870216111159656359510770035799883776 * q^72 - 5710803445695397409111916726207379330620701493216226637172343362 * q^73 - 3853113063817077251517010290946761043742850338597735614849744896 * q^74 - 54072646335858632291364391220794357295239004871249262032114937500 * q^75 - 54597827749220516597824093483981265423763753341892036316574515200 * q^76 - 158223680416273048529171640921537494742344414386511280173757390048 * q^77 - 160811710371444736549531677502408884739331391092641430151068909568 * q^78 - 142432313881134689670165256806051731841701152927734113846799658320 * q^79 - 51177652847651364053802595345739659965120450908579275563073536000 * q^80 - 1507828852199947063074312141010808769071090216675887820898139650357 * q^81 - 695209376412243484180902344374129954269183981452771124733223632896 * q^82 - 3693839858054266827490757641969940192981240698342129309480559474292 * q^83 - 1780863094771197773761708003630871124648583805802305195044465803264 * q^84 - 7298167608699350794635920443621695725374460108742430656285081769500 * q^85 - 2244650693378709814528727696726760094610393096817308670996667957248 * q^86 - 18423700805232461573101824374922338279567771244103990158383145308280 * q^87 - 2582326528909689780246031631998395420817064611439725077624243879936 * q^88 + 17367740242183938631288441850820944138495579389220797635234884292270 * q^89 + 34083516071220737074273068670864471249138438996268046626825699328000 * q^90 + 167600534303234335258348276576983776372645923384732916198248855289616 * q^91 + 10617662646374182899789466109457467356175325076903425103285041758208 * q^92 + 255004111116610178339751215151729450803024282160488117255709371492736 * q^93 + 126094848448515328706811151949226856272751686017200494870785094057984 * q^94 + 131857598419242140445720532480583107388104295729280077734565490165000 * q^95 - 35317935570603088406430812146796784958966309027486592670231479451648 * q^96 - 100964021638279059474796282561587605930271300796565380448075947866714 * q^97 + 339842254399814640339727510755989409718314658230858656458474210197504 * q^98 - 388490136121756142284718847173053098694146354616452114117724862417532 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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