LMFDB - Embedded newform 2.52.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,52,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 52, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 52);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 52 $
Character orbit:	$[\chi]$	$=$	2.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:	$32.9462706828$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 313153613520 $ x^2 - x - 313153613520
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-559601.$ 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)

$f(q)$	$=$	$q+3.35544e7 q^{2} +6.18868e11 q^{3} +1.12590e15 q^{4} -1.09549e18 q^{5} +2.07658e19 q^{6} +5.28375e21 q^{7} +3.77789e22 q^{8} -1.77070e24 q^{9} +O(q^{10})$	\(q+3.35544e7 q^{2} +6.18868e11 q^{3} +1.12590e15 q^{4} -1.09549e18 q^{5} +2.07658e19 q^{6} +5.28375e21 q^{7} +3.77789e22 q^{8} -1.77070e24 q^{9} -3.67585e25 q^{10} +2.76058e26 q^{11} +6.96784e26 q^{12} -4.50422e28 q^{13} +1.77293e29 q^{14} -6.77962e29 q^{15} +1.26765e30 q^{16} -1.27389e31 q^{17} -5.94147e31 q^{18} -3.15165e32 q^{19} -1.23341e33 q^{20} +3.26995e33 q^{21} +9.26296e33 q^{22} -3.09548e34 q^{23} +2.33802e34 q^{24} +7.56003e35 q^{25} -1.51136e36 q^{26} -2.42868e36 q^{27} +5.94898e36 q^{28} -1.71576e37 q^{29} -2.27486e37 q^{30} -5.04231e37 q^{31} +4.25353e37 q^{32} +1.70843e38 q^{33} -4.27446e38 q^{34} -5.78829e39 q^{35} -1.99363e39 q^{36} -8.61273e39 q^{37} -1.05752e40 q^{38} -2.78752e40 q^{39} -4.13863e40 q^{40} +2.47563e40 q^{41} +1.09721e41 q^{42} -6.84643e41 q^{43} +3.10813e41 q^{44} +1.93978e42 q^{45} -1.03867e42 q^{46} +3.76615e42 q^{47} +7.84509e41 q^{48} +1.53288e43 q^{49} +2.53673e43 q^{50} -7.88369e42 q^{51} -5.07130e43 q^{52} -7.54414e42 q^{53} -8.14930e43 q^{54} -3.02418e44 q^{55} +1.99615e44 q^{56} -1.95046e44 q^{57} -5.75713e44 q^{58} +6.74504e43 q^{59} -7.63318e44 q^{60} +4.63115e45 q^{61} -1.69192e45 q^{62} -9.35592e45 q^{63} +1.42725e45 q^{64} +4.93431e46 q^{65} +5.73255e45 q^{66} +2.58670e45 q^{67} -1.43427e46 q^{68} -1.91569e46 q^{69} -1.94223e47 q^{70} +2.37862e47 q^{71} -6.68950e46 q^{72} -6.17989e47 q^{73} -2.88995e47 q^{74} +4.67867e47 q^{75} -3.54845e47 q^{76} +1.45862e48 q^{77} -9.35335e47 q^{78} +3.29722e48 q^{79} -1.38870e48 q^{80} +2.31050e48 q^{81} +8.30685e47 q^{82} -2.23304e48 q^{83} +3.68163e48 q^{84} +1.39553e49 q^{85} -2.29728e49 q^{86} -1.06183e49 q^{87} +1.04292e49 q^{88} -1.84441e49 q^{89} +6.50881e49 q^{90} -2.37992e50 q^{91} -3.48520e49 q^{92} -3.12052e49 q^{93} +1.26371e50 q^{94} +3.45260e50 q^{95} +2.63237e49 q^{96} +1.92793e50 q^{97} +5.14349e50 q^{98} -4.88814e50 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 67108864 q^{2} + 889619774904 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots - 38\!\cdots\!86 q^{9}+O(q^{10}) $ 2 * q + 67108864 * q^2 + 889619774904 * q^3 + 2251799813685248 * q^4 - 505483840206048900 * q^5 + 29850686242871574528 * q^6 - 643354673586906697808 * q^7 + 75557863725914323419136 * q^8 - 3851083609368509187112086 * q^9	$ 2 q + 67108864 q^{2} + 889619774904 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots + 67\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 67108864 * q^2 + 889619774904 * q^3 + 2251799813685248 * q^4 - 505483840206048900 * q^5 + 29850686242871574528 * q^6 - 643354673586906697808 * q^7 + 75557863725914323419136 * q^8 - 3851083609368509187112086 * q^9 - 16961223143292733803724800 * q^10 + 8633651576356340928868584 * q^11 + 1001622821689769732232708096 * q^12 - 30873827938122714686700161876 * q^13 - 21587400646754056881943085056 * q^14 - 518218042262091018782484754800 * q^15 + 2535301200456458802993406410752 * q^16 - 28786508886487364438075737136028 * q^17 - 129220923096870204460327766065152 * q^18 - 733631063673363153263332047098600 * q^19 - 569124208598442292511185148313600 * q^20 + 1665174179567796909159692020325184 * q^21 + 289697274730541649466537738764288 * q^22 + 37296287753107198187864526255185424 * q^23 + 33608884860037503575860611983081472 * q^24 + 660018354928185594047906228655428750 * q^25 - 1035953760129438837610281886057234432 * q^26 - 3575064390438116984306570668319898960 * q^27 - 724352967058265022369291275381768192 * q^28 - 23194678411449137027464383320498184180 * q^29 - 17388512060256459267547607495973273600 * q^30 - 129800975373654642467102773822295978816 * q^31 + 85070591730234615865843651857942052864 * q^32 + 98437929884585404216124665227928188768 * q^33 - 965914954949035988896630532580726276096 * q^34 - 9285300989933253704077715458627399490400 * q^35 - 4335934677031160688390164724145050353664 * q^36 - 25789302792252351651427869187425902532548 * q^37 - 24616573639115534137480053267790770995200 * q^38 - 24039068470338718288449686026859029730352 * q^39 - 19096639556970247209990671298498605875200 * q^40 - 203882450946716687707275069540502556740236 * q^41 + 55873973776463430778209063036944004415488 * q^42 - 33467992309941885786990047596406170114136 * q^43 + 9720627505531278100192776830800065724416 * q^44 + 712339103352393616929766121661281078294700 * q^45 + 1251455751264068270305223471441833956999168 * q^46 + 8806279885485657941703988618385547141157152 * q^47 + 1127727041631957931185971746264692402683904 * q^48 + 37870163930643294259238847312116747911144146 * q^49 + 22146541009189668398860074291795035422720000 * q^50 - 12228611477234719887303705066114004904215056 * q^51 - 34760839999407566674753246046539220856602624 * q^52 - 99098379674195138020688368913247711782836836 * q^53 - 119959254984577246557959892643334603900190720 * q^54 - 460199051579724120691106282378687695931470800 * q^55 - 24305252377154793731068862987990814838226944 * q^56 - 308346078222846036269177403532299006305628000 * q^57 - 778284259518838089846735782549590527191285760 * q^58 + 712226871819317398398708636329275000836581640 * q^59 - 583461645507055265053696002486325482828595200 * q^60 + 2408706483855080027751048376525714542502812364 * q^61 - 4355398001708969292146712261231610505054912512 * q^62 + 2974761151575637949390086313179192495631935344 * q^63 + 2854495385411919762116571938898990272765493248 * q^64 + 57702492314565594231165280615009498998199564200 * q^65 + 3303028824533088793962468382913280910899019776 * q^66 + 58707159210604447540899939401400632911497556792 * q^67 - 32410727673620491554984744234603764341876457472 * q^68 - 677847176080232479801768026593707081328511552 * q^69 - 311563000666248045952223826071861889537461452800 * q^70 + 46788357394330774716422574740179226361514926384 * q^71 - 145489825276884043199660971705123850228594638848 * q^72 - 377438296161584257430166537004916200775137018316 * q^73 - 865345406870041660327924139554377701567009652736 * q^74 + 441878421483850181351838555431634849641917845000 * q^75 - 825995146246694730359753098730463215586010726400 * q^76 + 3043673662184954736705603653654001505838711446464 * q^77 - 806617288331324539776941375209591486673074520064 * q^78 + 4524152078509109942054812726033351814263166080480 * q^79 - 640776893442868286030821700719823172934198886400 * q^80 + 6480637064382460651424982120769525803066610264722 * q^81 - 6841159836284940720938997226192064285966390525952 * q^82 + 6588319149229235680792772342053708577011195228824 * q^83 + 1874819453652125388534123087456851083967191842816 * q^84 + 4487139906243718217102092069955426963365972140600 * q^85 - 1122999472140467930591324036750374279475208650752 * q^86 - 12252833006238383868098806140839299965902039190960 * q^87 + 326170134631678894886007717060256310945447411712 * q^88 - 74128419248127559341182511518459490724337724847980 * q^89 + 23902134004378863656503886105187182974526187110400 * q^90 - 321968995571365152522594117998449878837368407235296 * q^91 + 41991886906799092819314240217298959465419506712576 * q^92 - 52696927043122570987761600597936076234198017215232 * q^93 + 295489719590496296380166450224391791330752058097664 * q^94 + 98363518423225283717613611630272738880850050562000 * q^95 + 37840240333000701428840368313959875226773674262528 * q^96 + 787178832911627057853470763263011645852667147707972 * q^97 + 1270711840439623133477620273892804193845628289155072 * q^98 + 67531435288273581330332755632379759261968934190088 * 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 $

$2$	3.35544e7	0.707107
$2$	3.35544e7	0.707107
$3$	6.18868e11	0.421703	0.210851	−	0.977518i	$-0.432376\pi$
$3$	6.18868e11	0.421703	0.210851	+	0.977518i	$0.432376\pi$
$4$	1.12590e15	0.500000
$5$	−1.09549e18	−1.64389	−0.821944	−	0.569568i	$-0.807110\pi$
$5$	−1.09549e18	−1.64389	−0.821944	+	0.569568i	$0.807110\pi$
$6$	2.07658e19	0.298189
$7$	5.28375e21	1.48916	0.744582	−	0.667531i	$-0.232649\pi$
$7$	5.28375e21	1.48916	0.744582	+	0.667531i	$0.232649\pi$
$8$	3.77789e22	0.353553
$9$	−1.77070e24	−0.822167
$10$	−3.67585e25	−1.16240
$11$	2.76058e26	0.768222	0.384111	−	0.923287i	$-0.374508\pi$
$11$	2.76058e26	0.768222	0.384111	+	0.923287i	$0.374508\pi$
$12$	6.96784e26	0.210851
$13$	−4.50422e28	−1.77037	−0.885184	−	0.465240i	$-0.845968\pi$
$13$	−4.50422e28	−1.77037	−0.885184	+	0.465240i	$0.845968\pi$
$14$	1.77293e29	1.05300
$15$	−6.77962e29	−0.693232
$16$	1.26765e30	0.250000
$17$	−1.27389e31	−0.535407	−0.267704	−	0.963501i	$-0.586265\pi$
$17$	−1.27389e31	−0.535407	−0.267704	+	0.963501i	$0.586265\pi$
$18$	−5.94147e31	−0.581360
$19$	−3.15165e32	−0.776822	−0.388411	−	0.921486i	$-0.626976\pi$
$19$	−3.15165e32	−0.776822	−0.388411	+	0.921486i	$0.626976\pi$
$20$	−1.23341e33	−0.821944
$21$	3.26995e33	0.627984
$22$	9.26296e33	0.543215
$23$	−3.09548e34	−0.584343	−0.292171	−	0.956366i	$-0.594378\pi$
$23$	−3.09548e34	−0.584343	−0.292171	+	0.956366i	$0.594378\pi$
$24$	2.33802e34	0.149094
$25$	7.56003e35	1.70237
$26$	−1.51136e36	−1.25184
$27$	−2.42868e36	−0.768412
$28$	5.94898e36	0.744582
$29$	−1.71576e37	−0.877621	−0.438810	−	0.898580i	$-0.644600\pi$
$29$	−1.71576e37	−0.877621	−0.438810	+	0.898580i	$0.644600\pi$
$30$	−2.27486e37	−0.490189
$31$	−5.04231e37	−0.470876	−0.235438	−	0.971889i	$-0.575652\pi$
$31$	−5.04231e37	−0.470876	−0.235438	+	0.971889i	$0.575652\pi$
$32$	4.25353e37	0.176777
$33$	1.70843e38	0.323961
$34$	−4.27446e38	−0.378590
$35$	−5.78829e39	−2.44802
$36$	−1.99363e39	−0.411083
$37$	−8.61273e39	−0.883073	−0.441537	−	0.897243i	$-0.645567\pi$
$37$	−8.61273e39	−0.883073	−0.441537	+	0.897243i	$0.645567\pi$
$38$	−1.05752e40	−0.549296
$39$	−2.78752e40	−0.746569
$40$	−4.13863e40	−0.581202
$41$	2.47563e40	0.185224	0.0926122	−	0.995702i	$-0.470478\pi$
$41$	2.47563e40	0.185224	0.0926122	+	0.995702i	$0.470478\pi$
$42$	1.09721e41	0.444052
$43$	−6.84643e41	−1.52061	−0.760306	−	0.649565i	$-0.774951\pi$
$43$	−6.84643e41	−1.52061	−0.760306	+	0.649565i	$0.774951\pi$
$44$	3.10813e41	0.384111
$45$	1.93978e42	1.35155
$46$	−1.03867e42	−0.413193
$47$	3.76615e42	0.865770	0.432885	−	0.901449i	$-0.357496\pi$
$47$	3.76615e42	0.865770	0.432885	+	0.901449i	$0.357496\pi$
$48$	7.84509e41	0.105426
$49$	1.53288e43	1.21761
$50$	2.53673e43	1.20376
$51$	−7.88369e42	−0.225783
$52$	−5.07130e43	−0.885184
$53$	−7.54414e42	−0.0810168	−0.0405084	−	0.999179i	$-0.512898\pi$
$53$	−7.54414e42	−0.0810168	−0.0405084	+	0.999179i	$0.512898\pi$
$54$	−8.14930e43	−0.543350
$55$	−3.02418e44	−1.26287
$56$	1.99615e44	0.526499
$57$	−1.95046e44	−0.327588
$58$	−5.75713e44	−0.620572
$59$	6.74504e43	0.0470174	0.0235087	−	0.999724i	$-0.492516\pi$
$59$	6.74504e43	0.0470174	0.0235087	+	0.999724i	$0.492516\pi$
$60$	−7.63318e44	−0.346616
$61$	4.63115e45	1.37968	0.689839	−	0.723963i	$-0.257681\pi$
$61$	4.63115e45	1.37968	0.689839	+	0.723963i	$0.257681\pi$
$62$	−1.69192e45	−0.332959
$63$	−9.35592e45	−1.22434
$64$	1.42725e45	0.125000
$65$	4.93431e46	2.91029
$66$	5.73255e45	0.229075
$67$	2.58670e45	0.0704432	0.0352216	−	0.999380i	$-0.488786\pi$
$67$	2.58670e45	0.0704432	0.0352216	+	0.999380i	$0.488786\pi$
$68$	−1.43427e46	−0.267704
$69$	−1.91569e46	−0.246419
$70$	−1.94223e47	−1.73101
$71$	2.37862e47	1.47651	0.738256	−	0.674521i	$-0.235650\pi$
$71$	2.37862e47	1.47651	0.738256	+	0.674521i	$0.235650\pi$
$72$	−6.68950e46	−0.290680
$73$	−6.17989e47	−1.88907	−0.944535	−	0.328411i	$-0.893487\pi$
$73$	−6.17989e47	−1.88907	−0.944535	+	0.328411i	$0.893487\pi$
$74$	−2.88995e47	−0.624427
$75$	4.67867e47	0.717893
$76$	−3.54845e47	−0.388411
$77$	1.45862e48	1.14401
$78$	−9.35335e47	−0.527904
$79$	3.29722e48	1.34480	0.672400	−	0.740188i	$-0.265264\pi$
$79$	3.29722e48	1.34480	0.672400	+	0.740188i	$0.265264\pi$
$80$	−1.38870e48	−0.410972
$81$	2.31050e48	0.498125
$82$	8.30685e47	0.130973
$83$	−2.23304e48	−0.258467	−0.129233	−	0.991614i	$-0.541252\pi$
$83$	−2.23304e48	−0.258467	−0.129233	+	0.991614i	$0.541252\pi$
$84$	3.68163e48	0.313992
$85$	1.39553e49	0.880149
$86$	−2.29728e49	−1.07524
$87$	−1.06183e49	−0.370095
$88$	1.04292e49	0.271607
$89$	−1.84441e49	−0.360092	−0.180046	−	0.983658i	$-0.557625\pi$
$89$	−1.84441e49	−0.360092	−0.180046	+	0.983658i	$0.557625\pi$
$90$	6.50881e49	0.955691
$91$	−2.37992e50	−2.63637
$92$	−3.48520e49	−0.292171
$93$	−3.12052e49	−0.198569
$94$	1.26371e50	0.612192
$95$	3.45260e50	1.27701
$96$	2.63237e49	0.0745472
$97$	1.92793e50	0.419192	0.209596	−	0.977788i	$-0.432785\pi$
$97$	1.92793e50	0.419192	0.209596	+	0.977788i	$0.432785\pi$
$98$	5.14349e50	0.860980
$99$	−4.88814e50	−0.631607
$100$	8.51184e50	0.851184
$101$	1.95515e50	0.151700	0.0758501	−	0.997119i	$-0.475833\pi$
$101$	1.95515e50	0.151700	0.0758501	+	0.997119i	$0.475833\pi$
$102$	−2.64533e50	−0.159652
$103$	−1.38603e51	−0.652265	−0.326133	−	0.945324i	$-0.605746\pi$
$103$	−1.38603e51	−0.652265	−0.326133	+	0.945324i	$0.605746\pi$
$104$	−1.70164e51	−0.625920
$105$	−3.58219e51	−1.03234
$106$	−2.53139e50	−0.0572876
$107$	4.96998e51	0.885255	0.442628	−	0.896706i	$-0.354046\pi$
$107$	4.96998e51	0.885255	0.442628	+	0.896706i	$0.354046\pi$
$108$	−2.73445e51	−0.384206
$109$	4.06802e51	0.451864	0.225932	−	0.974143i	$-0.427457\pi$
$109$	4.06802e51	0.451864	0.225932	+	0.974143i	$0.427457\pi$
$110$	−1.01475e52	−0.892984
$111$	−5.33014e51	−0.372394
$112$	6.69795e51	0.372291
$113$	1.50031e52	0.664783	0.332391	−	0.943142i	$-0.392145\pi$
$113$	1.50031e52	0.664783	0.332391	+	0.943142i	$0.392145\pi$
$114$	−6.54465e51	−0.231640
$115$	3.39106e52	0.960594
$116$	−1.93177e52	−0.438810
$117$	7.97560e52	1.45554
$118$	2.26326e51	0.0332463
$119$	−6.73092e52	−0.797309
$120$	−2.56127e52	−0.245094
$121$	−5.29220e52	−0.409835
$122$	1.55395e53	0.975580
$123$	1.53209e52	0.0781096
$124$	−5.67713e52	−0.235438
$125$	−3.41698e53	−1.15461
$126$	−3.13933e53	−0.865740
$127$	−4.28342e53	−0.965597	−0.482799	−	0.875731i	$-0.660380\pi$
$127$	−4.28342e53	−0.965597	−0.482799	+	0.875731i	$0.660380\pi$
$128$	4.78905e52	0.0883883
$129$	−4.23704e53	−0.641246
$130$	1.65568e54	2.05788
$131$	1.44016e54	1.47229	0.736145	−	0.676824i	$-0.236644\pi$
$131$	1.44016e54	1.47229	0.736145	+	0.676824i	$0.236644\pi$
$132$	1.92353e53	0.161981
$133$	−1.66526e54	−1.15682
$134$	8.67953e52	0.0498108
$135$	2.66059e54	1.26318
$136$	−4.81262e53	−0.189295
$137$	2.92845e54	0.955571	0.477786	−	0.878476i	$-0.341440\pi$
$137$	2.92845e54	0.955571	0.477786	+	0.878476i	$0.341440\pi$
$138$	−6.42800e53	−0.174244
$139$	−6.01206e54	−1.35564	−0.677822	−	0.735226i	$-0.737076\pi$
$139$	−6.01206e54	−1.35564	−0.677822	+	0.735226i	$0.737076\pi$
$140$	−6.51703e54	−1.22401
$141$	2.33075e54	0.365098
$142$	7.98132e54	1.04405
$143$	−1.24342e55	−1.36004
$144$	−2.24462e54	−0.205542
$145$	1.87959e55	1.44271
$146$	−2.07363e55	−1.33577
$147$	9.48651e54	0.513469
$148$	−9.69707e54	−0.441537
$149$	−1.61577e55	−0.619625	−0.309812	−	0.950798i	$-0.600266\pi$
$149$	−1.61577e55	−0.619625	−0.309812	+	0.950798i	$0.600266\pi$
$150$	1.56990e55	0.507627
$151$	2.36963e55	0.646797	0.323398	−	0.946263i	$-0.395175\pi$
$151$	2.36963e55	0.646797	0.323398	+	0.946263i	$0.395175\pi$
$152$	−1.19066e55	−0.274648
$153$	2.25567e55	0.440194
$154$	4.89432e55	0.808936
$155$	5.52378e55	0.774067
$156$	−3.13846e55	−0.373285
$157$	−6.96387e55	−0.703736	−0.351868	−	0.936050i	$-0.614453\pi$
$157$	−6.96387e55	−0.703736	−0.351868	+	0.936050i	$0.614453\pi$
$158$	1.10636e56	0.950917
$159$	−4.66883e54	−0.0341650
$160$	−4.65969e55	−0.290601
$161$	−1.63557e56	−0.870182
$162$	7.75277e55	0.352228
$163$	−2.95848e56	−1.14891	−0.574453	−	0.818538i	$-0.694785\pi$
$163$	−2.95848e56	−1.14891	−0.574453	+	0.818538i	$0.694785\pi$
$164$	2.78732e55	0.0926122
$165$	−1.87157e56	−0.532556
$166$	−7.49283e55	−0.182764
$167$	−6.45680e56	−1.35129	−0.675643	−	0.737229i	$-0.736134\pi$
$167$	−6.45680e56	−1.35129	−0.675643	+	0.737229i	$0.736134\pi$
$168$	1.23535e56	0.222026
$169$	1.38149e57	2.13421
$170$	4.68262e56	0.622360
$171$	5.58062e56	0.638678
$172$	−7.70840e56	−0.760306
$173$	−9.85210e56	−0.838211	−0.419105	−	0.907938i	$-0.637656\pi$
$173$	−9.85210e56	−0.838211	−0.419105	+	0.907938i	$0.637656\pi$
$174$	−3.56290e56	−0.261697
$175$	3.99454e57	2.53511
$176$	3.49945e56	0.192055
$177$	4.17429e55	0.0198274
$178$	−6.18882e56	−0.254623
$179$	−3.81297e57	−1.35991	−0.679956	−	0.733253i	$-0.738001\pi$
$179$	−3.81297e57	−1.35991	−0.679956	+	0.733253i	$0.738001\pi$
$180$	2.18399e57	0.675775
$181$	−2.86736e57	−0.770332	−0.385166	−	0.922847i	$-0.625856\pi$
$181$	−2.86736e57	−0.770332	−0.385166	+	0.922847i	$0.625856\pi$
$182$	−7.98568e57	−1.86420
$183$	2.86607e57	0.581814
$184$	−1.16944e57	−0.206596
$185$	9.43514e57	1.45167
$186$	−1.04707e57	−0.140410
$187$	−3.51667e57	−0.411311
$188$	4.24031e57	0.432885
$189$	−1.28326e58	−1.14429
$190$	1.15850e58	0.902982
$191$	−8.87857e57	−0.605330	−0.302665	−	0.953097i	$-0.597876\pi$
$191$	−8.87857e57	−0.605330	−0.302665	+	0.953097i	$0.597876\pi$
$192$	8.83278e56	0.0527128
$193$	−1.03831e58	−0.542772	−0.271386	−	0.962471i	$-0.587482\pi$
$193$	−1.03831e58	−0.542772	−0.271386	+	0.962471i	$0.587482\pi$
$194$	6.46907e57	0.296414
$195$	3.05369e58	1.22728
$196$	1.72587e58	0.608805
$197$	4.08835e58	1.26666	0.633328	−	0.773883i	$-0.281688\pi$
$197$	4.08835e58	1.26666	0.633328	+	0.773883i	$0.281688\pi$
$198$	−1.64019e58	−0.446613
$199$	−4.25578e58	−1.01912	−0.509560	−	0.860435i	$-0.670192\pi$
$199$	−4.25578e58	−1.01912	−0.509560	+	0.860435i	$0.670192\pi$
$200$	2.85610e58	0.601878
$201$	1.60083e57	0.0297061
$202$	6.56041e57	0.107268
$203$	−9.06564e58	−1.30692
$204$	−8.87625e57	−0.112891
$205$	−2.71203e58	−0.304488
$206$	−4.65075e58	−0.461221
$207$	5.48115e58	0.480427
$208$	−5.70977e58	−0.442592
$209$	−8.70039e58	−0.596772
$210$	−1.20198e59	−0.729972
$211$	6.35675e58	0.342005	0.171003	−	0.985271i	$-0.445299\pi$
$211$	6.35675e58	0.342005	0.171003	+	0.985271i	$0.445299\pi$
$212$	−8.49395e57	−0.0405084
$213$	1.47205e59	0.622649
$214$	1.66765e59	0.625970
$215$	7.50018e59	2.49972
$216$	−9.17530e58	−0.271675
$217$	−2.66423e59	−0.701211
$218$	1.36500e59	0.319516
$219$	−3.82454e59	−0.796625
$220$	−3.40492e59	−0.631435
$221$	5.73787e59	0.947868
$222$	−1.78850e59	−0.263323
$223$	6.82401e59	0.895912	0.447956	−	0.894056i	$-0.352152\pi$
$223$	6.82401e59	0.895912	0.447956	+	0.894056i	$0.352152\pi$
$224$	2.24746e59	0.263250
$225$	−1.33865e60	−1.39963
$226$	5.03419e59	0.470072
$227$	−2.35902e60	−1.96821	−0.984106	−	0.177584i	$-0.943172\pi$
$227$	−2.35902e60	−1.96821	−0.984106	+	0.177584i	$0.943172\pi$
$228$	−2.19602e59	−0.163794
$229$	−4.15752e59	−0.277351	−0.138675	−	0.990338i	$-0.544284\pi$
$229$	−4.15752e59	−0.277351	−0.138675	+	0.990338i	$0.544284\pi$
$230$	1.13785e60	0.679243
$231$	9.02695e59	0.482431
$232$	−6.48195e59	−0.310286
$233$	6.57173e59	0.281905	0.140953	−	0.990016i	$-0.454983\pi$
$233$	6.57173e59	0.281905	0.140953	+	0.990016i	$0.454983\pi$
$234$	2.67617e60	1.02922
$235$	−4.12577e60	−1.42323
$236$	7.59424e58	0.0235087
$237$	2.04055e60	0.567105
$238$	−2.25852e60	−0.563783
$239$	4.23262e60	0.949429	0.474714	−	0.880140i	$-0.342551\pi$
$239$	4.23262e60	0.949429	0.474714	+	0.880140i	$0.342551\pi$
$240$	−8.59419e59	−0.173308
$241$	4.16073e60	0.754631	0.377316	−	0.926085i	$-0.376847\pi$
$241$	4.16073e60	0.754631	0.377316	+	0.926085i	$0.376847\pi$
$242$	−1.77577e60	−0.289797
$243$	6.66053e60	0.978473
$244$	5.21421e60	0.689839
$245$	−1.67925e61	−2.00161
$246$	5.14085e59	0.0552318
$247$	1.41957e61	1.37526
$248$	−1.90493e60	−0.166480
$249$	−1.38196e60	−0.108996
$250$	−1.14655e61	−0.816436
$251$	−2.04621e60	−0.131604	−0.0658022	−	0.997833i	$-0.520961\pi$
$251$	−2.04621e60	−0.131604	−0.0658022	+	0.997833i	$0.520961\pi$
$252$	−1.05338e61	−0.612171
$253$	−8.54530e60	−0.448905
$254$	−1.43728e61	−0.682780
$255$	8.63649e60	0.371161
$256$	1.60694e60	0.0625000
$257$	−5.68633e60	−0.200234	−0.100117	−	0.994976i	$-0.531922\pi$
$257$	−5.68633e60	−0.200234	−0.100117	+	0.994976i	$0.531922\pi$
$258$	−1.42171e61	−0.453430
$259$	−4.55075e61	−1.31504
$260$	5.55554e61	1.45514
$261$	3.03808e61	0.721551
$262$	4.83238e61	1.04107
$263$	9.14538e61	1.78785	0.893924	−	0.448219i	$-0.147942\pi$
$263$	9.14538e61	1.78785	0.893924	+	0.448219i	$0.147942\pi$
$264$	6.45428e60	0.114538
$265$	8.26452e60	0.133183
$266$	−5.58767e61	−0.817992
$267$	−1.14145e61	−0.151852
$268$	2.91237e60	0.0352216
$269$	−1.42043e62	−1.56220	−0.781102	−	0.624404i	$-0.785342\pi$
$269$	−1.42043e62	−1.56220	−0.781102	+	0.624404i	$0.785342\pi$
$270$	8.92745e61	0.893206
$271$	−2.52674e61	−0.230061	−0.115031	−	0.993362i	$-0.536697\pi$
$271$	−2.52674e61	−0.230061	−0.115031	+	0.993362i	$0.536697\pi$
$272$	−1.61485e61	−0.133852
$273$	−1.47286e62	−1.11176
$274$	9.82624e61	0.675691
$275$	2.08701e62	1.30780
$276$	−2.15688e61	−0.123209
$277$	−2.83211e62	−1.47529	−0.737643	−	0.675191i	$-0.764061\pi$
$277$	−2.83211e62	−1.47529	−0.737643	+	0.675191i	$0.764061\pi$
$278$	−2.01731e62	−0.958585
$279$	8.92839e61	0.387138
$280$	−2.18675e62	−0.865506
$281$	−1.79084e61	−0.0647210	−0.0323605	−	0.999476i	$-0.510302\pi$
$281$	−1.79084e61	−0.0647210	−0.0323605	+	0.999476i	$0.510302\pi$
$282$	7.82071e61	0.258163
$283$	4.36016e62	1.31507	0.657534	−	0.753425i	$-0.271599\pi$
$283$	4.36016e62	1.31507	0.657534	+	0.753425i	$0.271599\pi$
$284$	2.67809e62	0.738256
$285$	2.13670e62	0.538518
$286$	−4.17224e62	−0.961691
$287$	1.30806e62	0.275830
$288$	−7.53171e61	−0.145340
$289$	−4.03823e62	−0.713339
$290$	6.30686e62	1.02015
$291$	1.19314e62	0.176774
$292$	−6.95794e62	−0.944535
$293$	1.30851e63	1.62800	0.814000	−	0.580865i	$-0.197286\pi$
$293$	1.30851e63	1.62800	0.814000	+	0.580865i	$0.197286\pi$
$294$	3.18314e62	0.363078
$295$	−7.38911e61	−0.0772913
$296$	−3.25380e62	−0.312214
$297$	−6.70456e62	−0.590311
$298$	−5.42161e62	−0.438141
$299$	1.39427e63	1.03450
$300$	5.26771e62	0.358947
$301$	−3.61749e63	−2.26444
$302$	7.95115e62	0.457355
$303$	1.20998e62	0.0639723
$304$	−3.99520e62	−0.194206
$305$	−5.07336e63	−2.26804
$306$	7.56877e62	0.311264
$307$	2.89087e63	1.09395	0.546977	−	0.837147i	$-0.315778\pi$
$307$	2.89087e63	1.09395	0.546977	+	0.837147i	$0.315778\pi$
$308$	1.64226e63	0.572004
$309$	−8.57771e62	−0.275062
$310$	1.85347e63	0.547348
$311$	6.03794e62	0.164248	0.0821238	−	0.996622i	$-0.473830\pi$
$311$	6.03794e62	0.164248	0.0821238	+	0.996622i	$0.473830\pi$
$312$	−1.05309e63	−0.263952
$313$	−3.38809e63	−0.782662	−0.391331	−	0.920250i	$-0.627985\pi$
$313$	−3.38809e63	−0.782662	−0.391331	+	0.920250i	$0.627985\pi$
$314$	−2.33669e63	−0.497616
$315$	1.02493e64	2.01268
$316$	3.71234e63	0.672400
$317$	9.04367e63	1.51124	0.755620	−	0.655010i	$-0.227335\pi$
$317$	9.04367e63	1.51124	0.755620	+	0.655010i	$0.227335\pi$
$318$	−1.56660e62	−0.0241583
$319$	−4.73648e63	−0.674207
$320$	−1.56353e63	−0.205486
$321$	3.07576e63	0.373314
$322$	−5.48807e63	−0.615312
$323$	4.01486e63	0.415916
$324$	2.60140e63	0.249063
$325$	−3.40520e64	−3.01382
$326$	−9.92700e63	−0.812399
$327$	2.51757e63	0.190552
$328$	9.35268e62	0.0654867
$329$	1.98994e64	1.28927
$330$	−6.27994e63	−0.376574
$331$	1.21362e63	0.0673702	0.0336851	−	0.999432i	$-0.489276\pi$
$331$	1.21362e63	0.0673702	0.0336851	+	0.999432i	$0.489276\pi$
$332$	−2.51418e63	−0.129233
$333$	1.52505e64	0.726034
$334$	−2.16654e64	−0.955504
$335$	−2.83370e63	−0.115801
$336$	4.14515e63	0.156996
$337$	−1.59005e64	−0.558275	−0.279137	−	0.960251i	$-0.590049\pi$
$337$	−1.59005e64	−0.558275	−0.279137	+	0.960251i	$0.590049\pi$
$338$	4.63551e64	1.50911
$339$	9.28492e63	0.280341
$340$	1.57123e64	0.440075
$341$	−1.39197e64	−0.361737
$342$	1.87255e64	0.451613
$343$	1.44751e64	0.324057
$344$	−2.58651e64	−0.537618
$345$	2.09862e64	0.405085
$346$	−3.30582e64	−0.592704
$347$	−4.90024e64	−0.816235	−0.408118	−	0.912929i	$-0.633815\pi$
$347$	−4.90024e64	−0.816235	−0.408118	+	0.912929i	$0.633815\pi$
$348$	−1.19551e64	−0.185047
$349$	−2.70042e63	−0.0388493	−0.0194246	−	0.999811i	$-0.506183\pi$
$349$	−2.70042e63	−0.0388493	−0.0194246	+	0.999811i	$0.506183\pi$
$350$	1.34034e65	1.79259
$351$	1.09393e65	1.36037
$352$	1.17422e64	0.135804
$353$	−8.99771e64	−0.968004	−0.484002	−	0.875067i	$-0.660817\pi$
$353$	−8.99771e64	−0.968004	−0.484002	+	0.875067i	$0.660817\pi$
$354$	1.40066e63	0.0140201
$355$	−2.60575e65	−2.42722
$356$	−2.07662e64	−0.180046
$357$	−4.16555e64	−0.336227
$358$	−1.27942e65	−0.961603
$359$	1.70743e65	1.19518	0.597591	−	0.801801i	$-0.296125\pi$
$359$	1.70743e65	1.19518	0.597591	+	0.801801i	$0.296125\pi$
$360$	7.32826e64	0.477845
$361$	−6.52722e64	−0.396547
$362$	−9.62125e64	−0.544707
$363$	−3.27518e64	−0.172829
$364$	−2.67955e65	−1.31818
$365$	6.76999e65	3.10542
$366$	9.61693e64	0.411404
$367$	−1.67860e65	−0.669826	−0.334913	−	0.942249i	$-0.608707\pi$
$367$	−1.67860e65	−0.669826	−0.334913	+	0.942249i	$0.608707\pi$
$368$	−3.92398e64	−0.146086
$369$	−4.38360e64	−0.152285
$370$	3.16591e65	1.02649
$371$	−3.98614e64	−0.120647
$372$	−3.51340e64	−0.0992847
$373$	4.31323e65	1.13822	0.569112	−	0.822260i	$-0.307287\pi$
$373$	4.31323e65	1.13822	0.569112	+	0.822260i	$0.307287\pi$
$374$	−1.18000e65	−0.290841
$375$	−2.11466e65	−0.486904
$376$	1.42281e65	0.306096
$377$	7.72814e65	1.55371
$378$	−4.30589e65	−0.809137
$379$	−4.39512e65	−0.772095	−0.386047	−	0.922479i	$-0.626160\pi$
$379$	−4.39512e65	−0.772095	−0.386047	+	0.922479i	$0.626160\pi$
$380$	3.88728e65	0.638505
$381$	−2.65087e65	−0.407195
$382$	−2.97915e65	−0.428033
$383$	−1.15975e66	−1.55882	−0.779411	−	0.626513i	$-0.784482\pi$
$383$	−1.15975e66	−1.55882	−0.779411	+	0.626513i	$0.784482\pi$
$384$	2.96379e64	0.0372736
$385$	−1.59790e66	−1.88062
$386$	−3.48400e65	−0.383797
$387$	1.21229e66	1.25020
$388$	2.17066e65	0.209596
$389$	−3.54132e65	−0.320221	−0.160111	−	0.987099i	$-0.551185\pi$
$389$	−3.54132e65	−0.320221	−0.160111	+	0.987099i	$0.551185\pi$
$390$	1.02465e66	0.867815
$391$	3.94329e65	0.312861
$392$	5.79106e65	0.430490
$393$	8.91271e65	0.620869
$394$	1.37182e66	0.895662
$395$	−3.61207e66	−2.21070
$396$	−5.50356e65	−0.315803
$397$	3.62429e66	1.95013	0.975067	−	0.221910i	$-0.0712290\pi$
$397$	3.62429e66	1.95013	0.975067	+	0.221910i	$0.0712290\pi$
$398$	−1.42800e66	−0.720627
$399$	−1.03057e66	−0.487832
$400$	9.58348e65	0.425592
$401$	3.36307e66	1.40137	0.700687	−	0.713469i	$-0.252877\pi$
$401$	3.36307e66	1.40137	0.700687	+	0.713469i	$0.252877\pi$
$402$	5.37149e64	0.0210054
$403$	2.27116e66	0.833623
$404$	2.20131e65	0.0758501
$405$	−2.53113e66	−0.818863
$406$	−3.04192e66	−0.924133
$407$	−2.37761e66	−0.678396
$408$	−2.97838e65	−0.0798262
$409$	5.03004e65	0.126656	0.0633282	−	0.997993i	$-0.479829\pi$
$409$	5.03004e65	0.126656	0.0633282	+	0.997993i	$0.479829\pi$
$410$	−9.10005e65	−0.215306
$411$	1.81232e66	0.402967
$412$	−1.56053e66	−0.326133
$413$	3.56392e65	0.0700166
$414$	1.83917e66	0.339713
$415$	2.44627e66	0.424891
$416$	−1.91588e66	−0.312960
$417$	−3.72067e66	−0.571679
$418$	−2.91937e66	−0.421981
$419$	6.52047e65	0.0886791	0.0443395	−	0.999017i	$-0.485882\pi$
$419$	6.52047e65	0.0886791	0.0443395	+	0.999017i	$0.485882\pi$
$420$	−4.03318e66	−0.516168
$421$	3.09924e65	0.0373304	0.0186652	−	0.999826i	$-0.494058\pi$
$421$	3.09924e65	0.0373304	0.0186652	+	0.999826i	$0.494058\pi$
$422$	2.13297e66	0.241834
$423$	−6.66871e66	−0.711808
$424$	−2.85010e65	−0.0286438
$425$	−9.63064e66	−0.911460
$426$	4.93938e66	0.440279
$427$	2.44698e67	2.05457
$428$	5.59570e66	0.442628
$429$	−7.69516e66	−0.573531
$430$	2.51664e67	1.76757
$431$	−1.26495e66	−0.0837344	−0.0418672	−	0.999123i	$-0.513331\pi$
$431$	−1.26495e66	−0.0837344	−0.0418672	+	0.999123i	$0.513331\pi$
$432$	−3.07872e66	−0.192103
$433$	3.36696e66	0.198060	0.0990301	−	0.995084i	$-0.468426\pi$
$433$	3.36696e66	0.198060	0.0990301	+	0.995084i	$0.468426\pi$
$434$	−8.93968e66	−0.495831
$435$	1.16322e67	0.608395
$436$	4.58019e66	0.225932
$437$	9.75587e66	0.453931
$438$	−1.28330e67	−0.563299
$439$	−1.80494e67	−0.747512	−0.373756	−	0.927527i	$-0.621930\pi$
$439$	−1.80494e67	−0.747512	−0.373756	+	0.927527i	$0.621930\pi$
$440$	−1.14250e67	−0.446492
$441$	−2.71426e67	−1.00108
$442$	1.92531e67	0.670244
$443$	−4.58387e67	−1.50639	−0.753195	−	0.657797i	$-0.771488\pi$
$443$	−4.58387e67	−1.50639	−0.753195	+	0.657797i	$0.771488\pi$
$444$	−6.00121e66	−0.186197
$445$	2.02053e67	0.591950
$446$	2.28976e67	0.633506
$447$	−9.99947e66	−0.261297
$448$	7.54123e66	0.186146
$449$	−4.95933e67	−1.15649	−0.578244	−	0.815864i	$-0.696262\pi$
$449$	−4.95933e67	−1.15649	−0.578244	+	0.815864i	$0.696262\pi$
$450$	−4.49177e67	−0.989689
$451$	6.83418e66	0.142293
$452$	1.68920e67	0.332391
$453$	1.46649e67	0.272756
$454$	−7.91555e67	−1.39174
$455$	2.60717e68	4.33390
$456$	−7.36862e66	−0.115820
$457$	−9.49057e66	−0.141068	−0.0705341	−	0.997509i	$-0.522470\pi$
$457$	−9.49057e66	−0.141068	−0.0705341	+	0.997509i	$0.522470\pi$
$458$	−1.39503e67	−0.196117
$459$	3.09387e67	0.411413
$460$	3.81799e67	0.480297
$461$	−1.49006e68	−1.77349	−0.886747	−	0.462255i	$-0.847040\pi$
$461$	−1.49006e68	−1.77349	−0.886747	+	0.462255i	$0.847040\pi$
$462$	3.02894e67	0.341130
$463$	2.99723e67	0.319452	0.159726	−	0.987161i	$-0.448939\pi$
$463$	2.99723e67	0.319452	0.159726	+	0.987161i	$0.448939\pi$
$464$	−2.17498e67	−0.219405
$465$	3.41849e67	0.326426
$466$	2.20511e67	0.199337
$467$	3.59713e67	0.307875	0.153938	−	0.988081i	$-0.450804\pi$
$467$	3.59713e67	0.307875	0.153938	+	0.988081i	$0.450804\pi$
$468$	8.97973e67	0.727769
$469$	1.36675e67	0.104901
$470$	−1.38438e68	−1.00638
$471$	−4.30972e67	−0.296767
$472$	2.54821e66	0.0166232
$473$	−1.89001e68	−1.16817
$474$	6.84694e67	0.401004
$475$	−2.38266e68	−1.32244
$476$	−7.57834e67	−0.398654
$477$	1.33584e67	0.0666094
$478$	1.42023e68	0.671347
$479$	−9.28575e67	−0.416161	−0.208081	−	0.978112i	$-0.566722\pi$
$479$	−9.28575e67	−0.416161	−0.208081	+	0.978112i	$0.566722\pi$
$480$	−2.88373e67	−0.122547
$481$	3.87936e68	1.56337
$482$	1.39611e68	0.533605
$483$	−1.01220e68	−0.366958
$484$	−5.95849e67	−0.204918
$485$	−2.11203e68	−0.689105
$486$	2.23490e68	0.691885
$487$	−1.76684e68	−0.519051	−0.259525	−	0.965736i	$-0.583566\pi$
$487$	−1.76684e68	−0.519051	−0.259525	+	0.965736i	$0.583566\pi$
$488$	1.74960e68	0.487790
$489$	−1.83091e68	−0.484496
$490$	−5.63463e68	−1.41536
$491$	2.43377e68	0.580366	0.290183	−	0.956971i	$-0.406284\pi$
$491$	2.43377e68	0.580366	0.290183	+	0.956971i	$0.406284\pi$
$492$	1.72498e67	0.0390548
$493$	2.18568e68	0.469884
$494$	4.76330e68	0.972457
$495$	5.35490e68	1.03829
$496$	−6.39188e67	−0.117719
$497$	1.25680e69	2.19877
$498$	−4.63708e67	−0.0770719
$499$	−6.41960e68	−1.01378	−0.506891	−	0.862010i	$-0.669205\pi$
$499$	−6.41960e68	−1.01378	−0.506891	+	0.862010i	$0.669205\pi$
$500$	−3.84718e68	−0.577307
$501$	−3.99591e68	−0.569841
$502$	−6.86594e67	−0.0930583
$503$	−1.36942e67	−0.0176423	−0.00882113	−	0.999961i	$-0.502808\pi$
$503$	−1.36942e67	−0.0176423	−0.00882113	+	0.999961i	$0.502808\pi$
$504$	−3.53457e68	−0.432870
$505$	−2.14185e68	−0.249378
$506$	−2.86733e68	−0.317424
$507$	8.54959e68	0.900000
$508$	−4.82271e68	−0.482799
$509$	−3.53376e68	−0.336460	−0.168230	−	0.985748i	$-0.553805\pi$
$509$	−3.53376e68	−0.336460	−0.168230	+	0.985748i	$0.553805\pi$
$510$	2.89792e68	0.262451
$511$	−3.26530e69	−2.81313
$512$	5.39199e67	0.0441942
$513$	7.65436e68	0.596920
$514$	−1.90802e68	−0.141587
$515$	1.51838e69	1.07225
$516$	−4.77048e68	−0.320623
$517$	1.03968e69	0.665103
$518$	−1.52698e69	−0.929875
$519$	−6.09715e68	−0.353476
$520$	1.86413e69	1.02894
$521$	1.00281e69	0.527057	0.263528	−	0.964652i	$-0.415114\pi$
$521$	1.00281e69	0.527057	0.263528	+	0.964652i	$0.415114\pi$
$522$	1.01941e69	0.510213
$523$	−1.97084e69	−0.939416	−0.469708	−	0.882822i	$-0.655641\pi$
$523$	−1.97084e69	−0.939416	−0.469708	+	0.882822i	$0.655641\pi$
$524$	1.62148e69	0.736145
$525$	2.47209e69	1.06906
$526$	3.06868e69	1.26420
$527$	6.42334e68	0.252110
$528$	2.16570e68	0.0809903
$529$	−1.84801e69	−0.658543
$530$	2.77311e68	0.0941743
$531$	−1.19434e68	−0.0386561
$532$	−1.87491e69	−0.578408
$533$	−1.11508e69	−0.327915
$534$	−3.83007e68	−0.107375
$535$	−5.44455e69	−1.45526
$536$	9.77228e67	0.0249054
$537$	−2.35972e69	−0.573478
$538$	−4.76618e69	−1.10464
$539$	4.23164e69	0.935394
$540$	2.99556e69	0.631592
$541$	8.99424e69	1.80898	0.904491	−	0.426492i	$-0.140251\pi$
$541$	8.99424e69	1.80898	0.904491	+	0.426492i	$0.140251\pi$
$542$	−8.47833e68	−0.162678
$543$	−1.77452e69	−0.324851
$544$	−5.41852e68	−0.0946475
$545$	−4.45647e69	−0.742814
$546$	−4.94208e69	−0.786136
$547$	−7.96428e69	−1.20912	−0.604560	−	0.796559i	$-0.706651\pi$
$547$	−7.96428e69	−1.20912	−0.604560	+	0.796559i	$0.706651\pi$
$548$	3.29714e69	0.477786
$549$	−8.20035e69	−1.13433
$550$	7.00283e69	0.924752
$551$	5.40747e69	0.681755
$552$	−7.23728e68	−0.0871222
$553$	1.74217e70	2.00263
$554$	−9.50298e69	−1.04318
$555$	5.83911e69	0.612175
$556$	−6.76898e69	−0.677822
$557$	−6.03154e69	−0.576927	−0.288463	−	0.957491i	$-0.593144\pi$
$557$	−6.03154e69	−0.576927	−0.288463	+	0.957491i	$0.593144\pi$
$558$	2.99587e69	0.273748
$559$	3.08378e70	2.69205
$560$	−7.33752e69	−0.612005
$561$	−2.17636e69	−0.173451
$562$	−6.00905e68	−0.0457646
$563$	−1.35576e70	−0.986776	−0.493388	−	0.869809i	$-0.664242\pi$
$563$	−1.35576e70	−0.986776	−0.493388	+	0.869809i	$0.664242\pi$
$564$	2.62419e69	0.182549
$565$	−1.64357e70	−1.09283
$566$	1.46303e70	0.929894
$567$	1.22081e70	0.741791
$568$	8.98616e69	0.522026
$569$	2.91962e69	0.162168	0.0810838	−	0.996707i	$-0.474162\pi$
$569$	2.91962e69	0.162168	0.0810838	+	0.996707i	$0.474162\pi$
$570$	7.16959e69	0.380790
$571$	−1.18115e70	−0.599909	−0.299955	−	0.953953i	$-0.596972\pi$
$571$	−1.18115e70	−0.599909	−0.299955	+	0.953953i	$0.596972\pi$
$572$	−1.39997e70	−0.680018
$573$	−5.49466e69	−0.255269
$574$	4.38914e69	0.195041
$575$	−2.34019e70	−0.994767
$576$	−2.52722e69	−0.102771
$577$	−1.23860e69	−0.0481891	−0.0240946	−	0.999710i	$-0.507670\pi$
$577$	−1.23860e69	−0.0481891	−0.0240946	+	0.999710i	$0.507670\pi$
$578$	−1.35501e70	−0.504407
$579$	−6.42579e69	−0.228888
$580$	2.11623e70	0.721355
$581$	−1.17988e70	−0.384900
$582$	4.00350e69	0.124998
$583$	−2.08262e69	−0.0622389
$584$	−2.33470e70	−0.667887
$585$	−8.73717e70	−2.39274
$586$	4.39065e70	1.15117
$587$	5.91302e70	1.48435	0.742177	−	0.670204i	$-0.233793\pi$
$587$	5.91302e70	1.48435	0.742177	+	0.670204i	$0.233793\pi$
$588$	1.06809e70	0.256735
$589$	1.58916e70	0.365787
$590$	−2.47937e69	−0.0546532
$591$	2.53015e70	0.534152
$592$	−1.09179e70	−0.220768
$593$	3.53403e70	0.684504	0.342252	−	0.939608i	$-0.388810\pi$
$593$	3.53403e70	0.684504	0.342252	+	0.939608i	$0.388810\pi$
$594$	−2.24968e70	−0.417413
$595$	7.37363e70	1.31069
$596$	−1.81919e70	−0.309812
$597$	−2.63377e70	−0.429766
$598$	4.67839e70	0.731504
$599$	1.21449e71	1.81975	0.909875	−	0.414883i	$-0.136177\pi$
$599$	1.21449e71	1.81975	0.909875	+	0.414883i	$0.136177\pi$
$600$	1.76755e70	0.253814
$601$	−5.10787e70	−0.702977	−0.351488	−	0.936192i	$-0.614324\pi$
$601$	−5.10787e70	−0.702977	−0.351488	+	0.936192i	$0.614324\pi$
$602$	−1.21383e71	−1.60120
$603$	−4.58026e69	−0.0579160
$604$	2.66796e70	0.323398
$605$	5.79754e70	0.673724
$606$	4.06003e69	0.0452353
$607$	−1.45211e71	−1.55127	−0.775636	−	0.631181i	$-0.782571\pi$
$607$	−1.45211e71	−1.55127	−0.775636	+	0.631181i	$0.782571\pi$
$608$	−1.34057e70	−0.137324
$609$	−5.61044e70	−0.551132
$610$	−1.70234e71	−1.60374
$611$	−1.69636e71	−1.53273
$612$	2.53966e70	0.220097
$613$	1.63589e71	1.35991	0.679956	−	0.733253i	$-0.261999\pi$
$613$	1.63589e71	1.35991	0.679956	+	0.733253i	$0.261999\pi$
$614$	9.70013e70	0.773543
$615$	−1.67839e70	−0.128403
$616$	5.51052e70	0.404468
$617$	2.52821e69	0.0178050	0.00890250	−	0.999960i	$-0.497166\pi$
$617$	2.52821e69	0.0178050	0.00890250	+	0.999960i	$0.497166\pi$
$618$	−2.87820e70	−0.194498
$619$	4.87090e70	0.315862	0.157931	−	0.987450i	$-0.449518\pi$
$619$	4.87090e70	0.315862	0.157931	+	0.987450i	$0.449518\pi$
$620$	6.21923e70	0.387033
$621$	7.51792e70	0.449016
$622$	2.02600e70	0.116141
$623$	−9.74543e70	−0.536236
$624$	−3.53360e70	−0.186642
$625$	3.85929e70	0.195690
$626$	−1.13685e71	−0.553426
$627$	−5.38439e70	−0.251660
$628$	−7.84063e70	−0.351868
$629$	1.09717e71	0.472804
$630$	3.43909e71	1.42318
$631$	−9.56203e70	−0.380016	−0.190008	−	0.981783i	$-0.560851\pi$
$631$	−9.56203e70	−0.380016	−0.190008	+	0.981783i	$0.560851\pi$
$632$	1.24566e71	0.475458
$633$	3.93399e70	0.144224
$634$	3.03455e71	1.06861
$635$	4.69244e71	1.58733
$636$	−5.25664e69	−0.0170825
$637$	−6.90442e71	−2.15562
$638$	−1.58930e71	−0.476737
$639$	−4.21181e71	−1.21394
$640$	−5.24634e70	−0.145301
$641$	6.50586e70	0.173151	0.0865755	−	0.996245i	$-0.472408\pi$
$641$	6.50586e70	0.173151	0.0865755	+	0.996245i	$0.472408\pi$
$642$	1.03205e71	0.263973
$643$	−7.60059e70	−0.186839	−0.0934195	−	0.995627i	$-0.529780\pi$
$643$	−7.60059e70	−0.186839	−0.0934195	+	0.995627i	$0.529780\pi$
$644$	−1.84149e71	−0.435091
$645$	4.64162e71	1.05414
$646$	1.34716e71	0.294097
$647$	5.06916e71	1.06384	0.531921	−	0.846794i	$-0.321470\pi$
$647$	5.06916e71	1.06384	0.531921	+	0.846794i	$0.321470\pi$
$648$	8.72884e70	0.176114
$649$	1.86202e70	0.0361198
$650$	−1.14260e72	−2.13109
$651$	−1.64881e71	−0.295702
$652$	−3.33095e71	−0.574453
$653$	9.82696e70	0.162979	0.0814897	−	0.996674i	$-0.474032\pi$
$653$	9.82696e70	0.162979	0.0814897	+	0.996674i	$0.474032\pi$
$654$	8.44756e70	0.134741
$655$	−1.57768e72	−2.42028
$656$	3.13824e70	0.0463061
$657$	1.09427e72	1.55313
$658$	6.67714e71	0.911654
$659$	−5.78815e71	−0.760259	−0.380130	−	0.924933i	$-0.624121\pi$
$659$	−5.78815e71	−0.760259	−0.380130	+	0.924933i	$0.624121\pi$
$660$	−2.10720e71	−0.266278
$661$	1.31771e71	0.160207	0.0801037	−	0.996787i	$-0.474475\pi$
$661$	1.31771e71	0.160207	0.0801037	+	0.996787i	$0.474475\pi$
$662$	4.07222e70	0.0476379
$663$	3.55099e71	0.399718
$664$	−8.43618e70	−0.0913818
$665$	1.82427e72	1.90168
$666$	5.11723e71	0.513383
$667$	5.31109e71	0.512831
$668$	−7.26971e71	−0.675643
$669$	4.22316e71	0.377809
$670$	−9.50832e70	−0.0818834
$671$	1.27846e72	1.05990
$672$	1.39088e71	0.111013
$673$	−1.58355e72	−1.21688	−0.608440	−	0.793600i	$-0.708204\pi$
$673$	−1.58355e72	−1.21688	−0.608440	+	0.793600i	$0.708204\pi$
$674$	−5.33532e71	−0.394760
$675$	−1.83609e72	−1.30812
$676$	1.55542e72	1.06710
$677$	4.37888e71	0.289302	0.144651	−	0.989483i	$-0.453794\pi$
$677$	4.37888e71	0.289302	0.144651	+	0.989483i	$0.453794\pi$
$678$	3.11550e71	0.198231
$679$	1.01867e72	0.624246
$680$	5.27216e71	0.311180
$681$	−1.45992e72	−0.830000
$682$	−4.67067e71	−0.255787
$683$	−1.62287e72	−0.856162	−0.428081	−	0.903740i	$-0.640810\pi$
$683$	−1.62287e72	−0.856162	−0.428081	+	0.903740i	$0.640810\pi$
$684$	6.28322e71	0.319339
$685$	−3.20808e72	−1.57085
$686$	4.85703e71	0.229143
$687$	−2.57296e71	−0.116960
$688$	−8.67888e71	−0.380153
$689$	3.39805e71	0.143430
$690$	7.04179e71	0.286438
$691$	−1.38145e72	−0.541558	−0.270779	−	0.962642i	$-0.587281\pi$
$691$	−1.38145e72	−0.541558	−0.270779	+	0.962642i	$0.587281\pi$
$692$	−1.10925e72	−0.419105
$693$	−2.58278e72	−0.940566
$694$	−1.64425e72	−0.577166
$695$	6.58613e72	2.22853
$696$	−4.01147e71	−0.130848
$697$	−3.15368e71	−0.0991704
$698$	−9.06111e70	−0.0274706
$699$	4.06703e71	0.118880
$700$	4.49745e72	1.26755
$701$	2.78807e72	0.757693	0.378847	−	0.925459i	$-0.376321\pi$
$701$	2.78807e72	0.757693	0.378847	+	0.925459i	$0.376321\pi$
$702$	3.67062e72	0.961929
$703$	2.71443e72	0.685991
$704$	3.94003e71	0.0960277
$705$	−2.55331e72	−0.600179
$706$	−3.01913e72	−0.684482
$707$	1.03306e72	0.225906
$708$	4.69984e70	0.00991368
$709$	4.32119e72	0.879275	0.439638	−	0.898175i	$-0.355107\pi$
$709$	4.32119e72	0.879275	0.439638	+	0.898175i	$0.355107\pi$
$710$	−8.74343e72	−1.71630
$711$	−5.83838e72	−1.10565
$712$	−6.96800e71	−0.127312
$713$	1.56083e72	0.275153
$714$	−1.39773e72	−0.237749
$715$	1.36216e73	2.23575
$716$	−4.29302e72	−0.679956
$717$	2.61943e72	0.400377
$718$	5.72918e72	0.845121
$719$	−1.05035e73	−1.49537	−0.747685	−	0.664053i	$-0.768835\pi$
$719$	−1.05035e73	−1.49537	−0.747685	+	0.664053i	$0.768835\pi$
$720$	2.45896e72	0.337888
$721$	−7.32345e72	−0.971330
$722$	−2.19017e72	−0.280401
$723$	2.57494e72	0.318230
$724$	−3.22835e72	−0.385166
$725$	−1.29712e73	−1.49403
$726$	−1.09897e72	−0.122208
$727$	1.08133e73	1.16099	0.580496	−	0.814263i	$-0.302859\pi$
$727$	1.08133e73	1.16099	0.580496	+	0.814263i	$0.302859\pi$
$728$	−8.99107e72	−0.932098
$729$	−8.54127e71	−0.0855008
$730$	2.27163e73	2.19586
$731$	8.72159e72	0.814147
$732$	3.22691e72	0.290907
$733$	−1.94900e73	−1.69692	−0.848460	−	0.529260i	$-0.822470\pi$
$733$	−1.94900e73	−1.69692	−0.848460	+	0.529260i	$0.822470\pi$
$734$	−5.63244e72	−0.473639
$735$	−1.03924e73	−0.844086
$736$	−1.31667e72	−0.103298
$737$	7.14079e71	0.0541160
$738$	−1.47089e72	−0.107682
$739$	−4.98000e72	−0.352206	−0.176103	−	0.984372i	$-0.556349\pi$
$739$	−4.98000e72	−0.352206	−0.176103	+	0.984372i	$0.556349\pi$
$740$	1.06230e73	0.725837
$741$	8.78529e72	0.579952
$742$	−1.33753e72	−0.0853106
$743$	3.59690e72	0.221674	0.110837	−	0.993839i	$-0.464647\pi$
$743$	3.59690e72	0.221674	0.110837	+	0.993839i	$0.464647\pi$
$744$	−1.17890e72	−0.0702049
$745$	1.77005e73	1.01859
$746$	1.44728e73	0.804845
$747$	3.95403e72	0.212503
$748$	−3.95942e72	−0.205656
$749$	2.62602e73	1.31829
$750$	−7.09562e72	−0.344293
$751$	−8.37096e72	−0.392606	−0.196303	−	0.980543i	$-0.562894\pi$
$751$	−8.37096e72	−0.392606	−0.196303	+	0.980543i	$0.562894\pi$
$752$	4.77417e72	0.216443
$753$	−1.26633e72	−0.0554979
$754$	2.59313e73	1.09864
$755$	−2.59590e73	−1.06326
$756$	−1.44482e73	−0.572146
$757$	−1.56620e73	−0.599658	−0.299829	−	0.953993i	$-0.596930\pi$
$757$	−1.56620e73	−0.599658	−0.299829	+	0.953993i	$0.596930\pi$
$758$	−1.47476e73	−0.545953
$759$	−5.28842e72	−0.189304
$760$	1.30435e73	0.451491
$761$	−2.05703e73	−0.688543	−0.344271	−	0.938870i	$-0.611874\pi$
$761$	−2.05703e73	−0.688543	−0.344271	+	0.938870i	$0.611874\pi$
$762$	−8.89486e72	−0.287930
$763$	2.14944e73	0.672899
$764$	−9.99638e72	−0.302665
$765$	−2.47106e73	−0.723630
$766$	−3.89148e73	−1.10225
$767$	−3.03811e72	−0.0832381
$768$	9.94483e71	0.0263564
$769$	5.43854e73	1.39431	0.697157	−	0.716919i	$-0.254448\pi$
$769$	5.43854e73	1.39431	0.697157	+	0.716919i	$0.254448\pi$
$770$	−5.36167e73	−1.32980
$771$	−3.51909e72	−0.0844391
$772$	−1.16904e73	−0.271386
$773$	5.54229e73	1.24484	0.622418	−	0.782685i	$-0.286151\pi$
$773$	5.54229e73	1.24484	0.622418	+	0.782685i	$0.286151\pi$
$774$	4.06779e73	0.884023
$775$	−3.81200e73	−0.801604
$776$	7.28353e72	0.148207
$777$	−2.81632e73	−0.554556
$778$	−1.18827e73	−0.226431
$779$	−7.80234e72	−0.143886
$780$	3.43815e73	0.613638
$781$	6.56636e73	1.13429
$782$	1.32315e73	0.221226
$783$	4.16703e73	0.674375
$784$	1.94316e73	0.304402
$785$	7.62884e73	1.15686
$786$	2.99061e73	0.439020
$787$	−9.42716e73	−1.33976	−0.669878	−	0.742472i	$-0.733653\pi$
$787$	−9.42716e73	−1.33976	−0.669878	+	0.742472i	$0.733653\pi$
$788$	4.60307e73	0.633328
$789$	5.65979e73	0.753940
$790$	−1.21201e74	−1.56320
$791$	7.92725e73	0.989971
$792$	−1.84669e73	−0.223307
$793$	−2.08597e74	−2.44254
$794$	1.21611e74	1.37895
$795$	5.11465e72	0.0561635
$796$	−4.79158e73	−0.509560
$797$	−8.19282e73	−0.843813	−0.421906	−	0.906639i	$-0.638639\pi$
$797$	−8.19282e73	−0.843813	−0.421906	+	0.906639i	$0.638639\pi$
$798$	−3.45803e73	−0.344950
$799$	−4.79766e73	−0.463539
$800$	3.21568e73	0.300939
$801$	3.26590e73	0.296055
$802$	1.12846e74	0.990921
$803$	−1.70601e74	−1.45122
$804$	1.80237e72	0.0148530
$805$	1.79175e74	1.43048
$806$	7.62076e73	0.589461
$807$	−8.79061e73	−0.658785
$808$	7.38636e72	0.0536341
$809$	−6.02363e73	−0.423810	−0.211905	−	0.977290i	$-0.567967\pi$
$809$	−6.02363e73	−0.423810	−0.211905	+	0.977290i	$0.567967\pi$
$810$	−8.49306e73	−0.579023
$811$	−2.75579e74	−1.82060	−0.910298	−	0.413953i	$-0.864148\pi$
$811$	−2.75579e74	−1.82060	−0.910298	+	0.413953i	$0.864148\pi$
$812$	−1.02070e74	−0.653461
$813$	−1.56372e73	−0.0970174
$814$	−7.97794e73	−0.479699
$815$	3.24097e74	1.88867
$816$	−9.99377e72	−0.0564456
$817$	2.15776e74	1.18125
$818$	1.68780e73	0.0895596
$819$	4.21411e74	2.16754
$820$	−3.05347e73	−0.152244
$821$	−9.42484e73	−0.455537	−0.227768	−	0.973715i	$-0.573143\pi$
$821$	−9.42484e73	−0.455537	−0.227768	+	0.973715i	$0.573143\pi$
$822$	6.08115e73	0.284941
$823$	−2.00596e74	−0.911228	−0.455614	−	0.890177i	$-0.650580\pi$
$823$	−2.00596e74	−0.911228	−0.455614	+	0.890177i	$0.650580\pi$
$824$	−5.23628e73	−0.230611
$825$	1.29158e74	0.551501
$826$	1.19585e73	0.0495092
$827$	−1.96111e74	−0.787248	−0.393624	−	0.919271i	$-0.628779\pi$
$827$	−1.96111e74	−0.787248	−0.393624	+	0.919271i	$0.628779\pi$
$828$	6.17122e73	0.240214
$829$	6.93185e73	0.261643	0.130821	−	0.991406i	$-0.458239\pi$
$829$	6.93185e73	0.261643	0.130821	+	0.991406i	$0.458239\pi$
$830$	8.20831e73	0.300443
$831$	−1.75270e74	−0.622132
$832$	−6.42863e73	−0.221296
$833$	−1.95272e74	−0.651917
$834$	−1.24845e74	−0.404238
$835$	7.07335e74	2.22136
$836$	−9.79577e73	−0.298386
$837$	1.22462e74	0.361827
$838$	2.18791e73	0.0627056
$839$	6.27596e74	1.74482	0.872409	−	0.488777i	$-0.162557\pi$
$839$	6.27596e74	1.74482	0.872409	+	0.488777i	$0.162557\pi$
$840$	−1.35331e74	−0.364986
$841$	−8.78240e73	−0.229782
$842$	1.03993e73	0.0263965
$843$	−1.10829e73	−0.0272930
$844$	7.15706e73	0.171003
$845$	−1.51340e75	−3.50840
$846$	−2.23765e74	−0.503324
$847$	−2.79627e74	−0.610312
$848$	−9.56334e72	−0.0202542
$849$	2.69837e74	0.554568
$850$	−3.23151e74	−0.644500
$851$	2.66605e74	0.516018
$852$	1.65738e74	0.311324
$853$	−6.83194e74	−1.24550	−0.622750	−	0.782421i	$-0.713985\pi$
$853$	−6.83194e74	−1.24550	−0.622750	+	0.782421i	$0.713985\pi$
$854$	8.21071e74	1.45280
$855$	−6.11350e74	−1.04991
$856$	1.87761e74	0.312985
$857$	−4.31139e74	−0.697599	−0.348800	−	0.937197i	$-0.613411\pi$
$857$	−4.31139e74	−0.697599	−0.348800	+	0.937197i	$0.613411\pi$
$858$	−2.58207e74	−0.405547
$859$	7.17278e74	1.09361	0.546804	−	0.837260i	$-0.315844\pi$
$859$	7.17278e74	1.09361	0.546804	+	0.837260i	$0.315844\pi$
$860$	8.44445e74	1.24986
$861$	8.09519e73	0.116318
$862$	−4.24448e73	−0.0592091
$863$	4.17063e74	0.564841	0.282420	−	0.959291i	$-0.408863\pi$
$863$	4.17063e74	0.564841	0.282420	+	0.959291i	$0.408863\pi$
$864$	−1.03305e74	−0.135837
$865$	1.07929e75	1.37792
$866$	1.12977e74	0.140050
$867$	−2.49913e74	−0.300817
$868$	−2.99966e74	−0.350605
$869$	9.10224e74	1.03310
$870$	3.90312e74	0.430200
$871$	−1.16511e74	−0.124710
$872$	1.53686e74	0.159758
$873$	−3.41379e74	−0.344646
$874$	3.27353e74	0.320977
$875$	−1.80545e75	−1.71941
$876$	−4.30605e74	−0.398313
$877$	1.75728e75	1.57889	0.789445	−	0.613821i	$-0.210368\pi$
$877$	1.75728e75	1.57889	0.789445	+	0.613821i	$0.210368\pi$
$878$	−6.05638e74	−0.528571
$879$	8.09798e74	0.686532
$880$	−3.83360e74	−0.315718
$881$	−1.19280e75	−0.954295	−0.477148	−	0.878823i	$-0.658329\pi$
$881$	−1.19280e75	−0.954295	−0.477148	+	0.878823i	$0.658329\pi$
$882$	−9.10756e74	−0.707869
$883$	6.84732e74	0.517039	0.258519	−	0.966006i	$-0.416765\pi$
$883$	6.84732e74	0.517039	0.258519	+	0.966006i	$0.416765\pi$
$884$	6.46027e74	0.473934
$885$	−4.57289e73	−0.0325940
$886$	−1.53809e75	−1.06518
$887$	−1.43044e75	−0.962539	−0.481270	−	0.876573i	$-0.659824\pi$
$887$	−1.43044e75	−0.962539	−0.481270	+	0.876573i	$0.659824\pi$
$888$	−2.01367e74	−0.131661
$889$	−2.26326e75	−1.43793
$890$	6.77978e74	0.418572
$891$	6.37833e74	0.382671
$892$	7.68315e74	0.447956
$893$	−1.18696e75	−0.672550
$894$	−3.35526e74	−0.184765
$895$	4.17706e75	2.23554
$896$	2.53042e74	0.131625
$897$	8.62869e74	0.436252
$898$	−1.66407e75	−0.817761
$899$	8.65138e74	0.413250
$900$	−1.50719e75	−0.699815
$901$	9.61040e73	0.0433770
$902$	2.29317e74	0.100617
$903$	−2.23875e75	−0.954921
$904$	5.66800e74	0.235036
$905$	3.14115e75	1.26634
$906$	4.92072e74	0.192868
$907$	3.89660e74	0.148491	0.0742455	−	0.997240i	$-0.476345\pi$
$907$	3.89660e74	0.148491	0.0742455	+	0.997240i	$0.476345\pi$
$908$	−2.65602e75	−0.984106
$909$	−3.46198e74	−0.124723
$910$	8.74821e75	3.06453
$911$	−3.78344e75	−1.28875	−0.644374	−	0.764710i	$-0.722882\pi$
$911$	−3.78344e75	−1.28875	−0.644374	+	0.764710i	$0.722882\pi$
$912$	−2.47250e74	−0.0818970
$913$	−6.16448e74	−0.198560
$914$	−3.18451e74	−0.0997503
$915$	−3.13974e75	−0.956437
$916$	−4.68095e74	−0.138675
$917$	7.60946e75	2.19248
$918$	1.03813e75	0.290913
$919$	2.42870e75	0.661954	0.330977	−	0.943639i	$-0.392622\pi$
$919$	2.42870e75	0.661954	0.330977	+	0.943639i	$0.392622\pi$
$920$	1.28110e75	0.339621
$921$	1.78906e75	0.461323
$922$	−4.99981e75	−1.25405
$923$	−1.07138e76	−2.61397
$924$	1.01634e75	0.241216
$925$	−6.51125e75	−1.50332
$926$	1.00570e75	0.225886
$927$	2.45424e75	0.536271
$928$	−7.29802e74	−0.155143
$929$	7.49514e75	1.55017	0.775084	−	0.631858i	$-0.217707\pi$
$929$	7.49514e75	1.55017	0.775084	+	0.631858i	$0.217707\pi$
$930$	1.14706e75	0.230818
$931$	−4.83111e75	−0.945867
$932$	7.39911e74	0.140953
$933$	3.73669e74	0.0692636
$934$	1.20699e75	0.217701
$935$	3.85247e75	0.676150
$936$	3.01310e75	0.514611
$937$	−9.49197e75	−1.57760	−0.788800	−	0.614650i	$-0.789297\pi$
$937$	−9.49197e75	−1.57760	−0.788800	+	0.614650i	$0.789297\pi$
$938$	4.58605e74	0.0741765
$939$	−2.09678e75	−0.330051
$940$	−4.64521e75	−0.711615
$941$	−1.31287e76	−1.95743	−0.978715	−	0.205225i	$-0.934207\pi$
$941$	−1.31287e76	−1.95743	−0.978715	+	0.205225i	$0.934207\pi$
$942$	−1.44610e75	−0.209846
$943$	−7.66327e74	−0.108235
$944$	8.55036e73	0.0117543
$945$	1.40579e76	1.88109
$946$	−6.34182e75	−0.826019
$947$	1.56080e75	0.197889	0.0989446	−	0.995093i	$-0.468453\pi$
$947$	1.56080e75	0.197889	0.0989446	+	0.995093i	$0.468453\pi$
$948$	2.29745e75	0.283553
$949$	2.78356e76	3.34435
$950$	−7.99488e75	−0.935105
$951$	5.59684e75	0.637294
$952$	−2.54287e75	−0.281891
$953$	−1.11418e76	−1.20250	−0.601252	−	0.799059i	$-0.705331\pi$
$953$	−1.11418e76	−1.20250	−0.601252	+	0.799059i	$0.705331\pi$
$954$	4.48233e74	0.0470999
$955$	9.72636e75	0.995094
$956$	4.76550e75	0.474714
$957$	−2.93126e75	−0.284315
$958$	−3.11578e75	−0.294270
$959$	1.54732e76	1.42300
$960$	−9.67620e74	−0.0866540
$961$	−8.92442e75	−0.778276
$962$	1.30170e76	1.10547
$963$	−8.80033e75	−0.727827
$964$	4.68456e75	0.377316
$965$	1.13746e76	0.892256
$966$	−3.39640e75	−0.259479
$967$	−2.28086e76	−1.69716	−0.848580	−	0.529067i	$-0.822542\pi$
$967$	−2.28086e76	−1.69716	−0.848580	+	0.529067i	$0.822542\pi$
$968$	−1.99934e75	−0.144899
$969$	2.48467e75	0.175393
$970$	−7.08679e75	−0.487271
$971$	1.38700e76	0.928935	0.464467	−	0.885590i	$-0.346246\pi$
$971$	1.38700e76	0.928935	0.464467	+	0.885590i	$0.346246\pi$
$972$	7.49909e75	0.489237
$973$	−3.17662e76	−2.01878
$974$	−5.92855e75	−0.367024
$975$	−2.10737e76	−1.27094
$976$	5.87068e75	0.344919
$977$	1.95838e76	1.12095	0.560475	−	0.828171i	$-0.310618\pi$
$977$	1.95838e76	1.12095	0.560475	+	0.828171i	$0.310618\pi$
$978$	−6.14350e75	−0.342591
$979$	−5.09165e75	−0.276630
$980$	−1.89067e76	−1.00081
$981$	−7.20323e75	−0.371508
$982$	8.16638e75	0.410381
$983$	4.66590e75	0.228465	0.114233	−	0.993454i	$-0.463559\pi$
$983$	4.66590e75	0.228465	0.114233	+	0.993454i	$0.463559\pi$
$984$	5.78808e74	0.0276159
$985$	−4.47873e76	−2.08224
$986$	7.33394e75	0.332258
$987$	1.23151e76	0.543690
$988$	1.59830e76	0.687631
$989$	2.11930e76	0.888559
$990$	1.79681e76	0.734182
$991$	7.98665e75	0.318044	0.159022	−	0.987275i	$-0.449166\pi$
$991$	7.98665e75	0.318044	0.159022	+	0.987275i	$0.449166\pi$
$992$	−2.14476e75	−0.0832398
$993$	7.51069e74	0.0284102
$994$	4.21713e76	1.55476
$995$	4.66215e76	1.67532
$996$	−1.55595e75	−0.0544981
$997$	−3.41550e75	−0.116608	−0.0583040	−	0.998299i	$-0.518569\pi$
$997$	−3.41550e75	−0.116608	−0.0583040	+	0.998299i	$0.518569\pi$
$998$	−2.15406e76	−0.716852
$999$	2.09176e76	0.678565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.52.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.52.a.b.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+3.35544e7 q^{2} +6.18868e11 q^{3} +1.12590e15 q^{4} -1.09549e18 q^{5} +2.07658e19 q^{6} +5.28375e21 q^{7} +3.77789e22 q^{8} -1.77070e24 q^{9} +O(q^{10})\)	\(q+3.35544e7 q^{2} +6.18868e11 q^{3} +1.12590e15 q^{4} -1.09549e18 q^{5} +2.07658e19 q^{6} +5.28375e21 q^{7} +3.77789e22 q^{8} -1.77070e24 q^{9} -3.67585e25 q^{10} +2.76058e26 q^{11} +6.96784e26 q^{12} -4.50422e28 q^{13} +1.77293e29 q^{14} -6.77962e29 q^{15} +1.26765e30 q^{16} -1.27389e31 q^{17} -5.94147e31 q^{18} -3.15165e32 q^{19} -1.23341e33 q^{20} +3.26995e33 q^{21} +9.26296e33 q^{22} -3.09548e34 q^{23} +2.33802e34 q^{24} +7.56003e35 q^{25} -1.51136e36 q^{26} -2.42868e36 q^{27} +5.94898e36 q^{28} -1.71576e37 q^{29} -2.27486e37 q^{30} -5.04231e37 q^{31} +4.25353e37 q^{32} +1.70843e38 q^{33} -4.27446e38 q^{34} -5.78829e39 q^{35} -1.99363e39 q^{36} -8.61273e39 q^{37} -1.05752e40 q^{38} -2.78752e40 q^{39} -4.13863e40 q^{40} +2.47563e40 q^{41} +1.09721e41 q^{42} -6.84643e41 q^{43} +3.10813e41 q^{44} +1.93978e42 q^{45} -1.03867e42 q^{46} +3.76615e42 q^{47} +7.84509e41 q^{48} +1.53288e43 q^{49} +2.53673e43 q^{50} -7.88369e42 q^{51} -5.07130e43 q^{52} -7.54414e42 q^{53} -8.14930e43 q^{54} -3.02418e44 q^{55} +1.99615e44 q^{56} -1.95046e44 q^{57} -5.75713e44 q^{58} +6.74504e43 q^{59} -7.63318e44 q^{60} +4.63115e45 q^{61} -1.69192e45 q^{62} -9.35592e45 q^{63} +1.42725e45 q^{64} +4.93431e46 q^{65} +5.73255e45 q^{66} +2.58670e45 q^{67} -1.43427e46 q^{68} -1.91569e46 q^{69} -1.94223e47 q^{70} +2.37862e47 q^{71} -6.68950e46 q^{72} -6.17989e47 q^{73} -2.88995e47 q^{74} +4.67867e47 q^{75} -3.54845e47 q^{76} +1.45862e48 q^{77} -9.35335e47 q^{78} +3.29722e48 q^{79} -1.38870e48 q^{80} +2.31050e48 q^{81} +8.30685e47 q^{82} -2.23304e48 q^{83} +3.68163e48 q^{84} +1.39553e49 q^{85} -2.29728e49 q^{86} -1.06183e49 q^{87} +1.04292e49 q^{88} -1.84441e49 q^{89} +6.50881e49 q^{90} -2.37992e50 q^{91} -3.48520e49 q^{92} -3.12052e49 q^{93} +1.26371e50 q^{94} +3.45260e50 q^{95} +2.63237e49 q^{96} +1.92793e50 q^{97} +5.14349e50 q^{98} -4.88814e50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 67108864 q^{2} + 889619774904 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots - 38\!\cdots\!86 q^{9}+O(q^{10}) \) 2 * q + 67108864 * q^2 + 889619774904 * q^3 + 2251799813685248 * q^4 - 505483840206048900 * q^5 + 29850686242871574528 * q^6 - 643354673586906697808 * q^7 + 75557863725914323419136 * q^8 - 3851083609368509187112086 * q^9	\( 2 q + 67108864 q^{2} + 889619774904 q^{3} + 22\!\cdots\!48 q^{4}+ \cdots + 67\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 67108864 * q^2 + 889619774904 * q^3 + 2251799813685248 * q^4 - 505483840206048900 * q^5 + 29850686242871574528 * q^6 - 643354673586906697808 * q^7 + 75557863725914323419136 * q^8 - 3851083609368509187112086 * q^9 - 16961223143292733803724800 * q^10 + 8633651576356340928868584 * q^11 + 1001622821689769732232708096 * q^12 - 30873827938122714686700161876 * q^13 - 21587400646754056881943085056 * q^14 - 518218042262091018782484754800 * q^15 + 2535301200456458802993406410752 * q^16 - 28786508886487364438075737136028 * q^17 - 129220923096870204460327766065152 * q^18 - 733631063673363153263332047098600 * q^19 - 569124208598442292511185148313600 * q^20 + 1665174179567796909159692020325184 * q^21 + 289697274730541649466537738764288 * q^22 + 37296287753107198187864526255185424 * q^23 + 33608884860037503575860611983081472 * q^24 + 660018354928185594047906228655428750 * q^25 - 1035953760129438837610281886057234432 * q^26 - 3575064390438116984306570668319898960 * q^27 - 724352967058265022369291275381768192 * q^28 - 23194678411449137027464383320498184180 * q^29 - 17388512060256459267547607495973273600 * q^30 - 129800975373654642467102773822295978816 * q^31 + 85070591730234615865843651857942052864 * q^32 + 98437929884585404216124665227928188768 * q^33 - 965914954949035988896630532580726276096 * q^34 - 9285300989933253704077715458627399490400 * q^35 - 4335934677031160688390164724145050353664 * q^36 - 25789302792252351651427869187425902532548 * q^37 - 24616573639115534137480053267790770995200 * q^38 - 24039068470338718288449686026859029730352 * q^39 - 19096639556970247209990671298498605875200 * q^40 - 203882450946716687707275069540502556740236 * q^41 + 55873973776463430778209063036944004415488 * q^42 - 33467992309941885786990047596406170114136 * q^43 + 9720627505531278100192776830800065724416 * q^44 + 712339103352393616929766121661281078294700 * q^45 + 1251455751264068270305223471441833956999168 * q^46 + 8806279885485657941703988618385547141157152 * q^47 + 1127727041631957931185971746264692402683904 * q^48 + 37870163930643294259238847312116747911144146 * q^49 + 22146541009189668398860074291795035422720000 * q^50 - 12228611477234719887303705066114004904215056 * q^51 - 34760839999407566674753246046539220856602624 * q^52 - 99098379674195138020688368913247711782836836 * q^53 - 119959254984577246557959892643334603900190720 * q^54 - 460199051579724120691106282378687695931470800 * q^55 - 24305252377154793731068862987990814838226944 * q^56 - 308346078222846036269177403532299006305628000 * q^57 - 778284259518838089846735782549590527191285760 * q^58 + 712226871819317398398708636329275000836581640 * q^59 - 583461645507055265053696002486325482828595200 * q^60 + 2408706483855080027751048376525714542502812364 * q^61 - 4355398001708969292146712261231610505054912512 * q^62 + 2974761151575637949390086313179192495631935344 * q^63 + 2854495385411919762116571938898990272765493248 * q^64 + 57702492314565594231165280615009498998199564200 * q^65 + 3303028824533088793962468382913280910899019776 * q^66 + 58707159210604447540899939401400632911497556792 * q^67 - 32410727673620491554984744234603764341876457472 * q^68 - 677847176080232479801768026593707081328511552 * q^69 - 311563000666248045952223826071861889537461452800 * q^70 + 46788357394330774716422574740179226361514926384 * q^71 - 145489825276884043199660971705123850228594638848 * q^72 - 377438296161584257430166537004916200775137018316 * q^73 - 865345406870041660327924139554377701567009652736 * q^74 + 441878421483850181351838555431634849641917845000 * q^75 - 825995146246694730359753098730463215586010726400 * q^76 + 3043673662184954736705603653654001505838711446464 * q^77 - 806617288331324539776941375209591486673074520064 * q^78 + 4524152078509109942054812726033351814263166080480 * q^79 - 640776893442868286030821700719823172934198886400 * q^80 + 6480637064382460651424982120769525803066610264722 * q^81 - 6841159836284940720938997226192064285966390525952 * q^82 + 6588319149229235680792772342053708577011195228824 * q^83 + 1874819453652125388534123087456851083967191842816 * q^84 + 4487139906243718217102092069955426963365972140600 * q^85 - 1122999472140467930591324036750374279475208650752 * q^86 - 12252833006238383868098806140839299965902039190960 * q^87 + 326170134631678894886007717060256310945447411712 * q^88 - 74128419248127559341182511518459490724337724847980 * q^89 + 23902134004378863656503886105187182974526187110400 * q^90 - 321968995571365152522594117998449878837368407235296 * q^91 + 41991886906799092819314240217298959465419506712576 * q^92 - 52696927043122570987761600597936076234198017215232 * q^93 + 295489719590496296380166450224391791330752058097664 * q^94 + 98363518423225283717613611630272738880850050562000 * q^95 + 37840240333000701428840368313959875226773674262528 * q^96 + 787178832911627057853470763263011645852667147707972 * q^97 + 1270711840439623133477620273892804193845628289155072 * q^98 + 67531435288273581330332755632379759261968934190088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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