LMFDB - Embedded newform 1.70.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 70);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	1.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:	$30.1514953292$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots - 94\!\cdots\!36 $ x^5 - x^4 - 24985894640345560x^3 - 309075533549354721261224x^2 + 93046016582444120336711740360848*x - 941262570723617919770907675844106102736
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.13065e7$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83774e10 q^{2} +2.28315e16 q^{3} -2.52566e20 q^{4} +1.12358e24 q^{5} -4.19583e26 q^{6} -8.82897e28 q^{7} +1.54896e31 q^{8} -3.13110e32 q^{9} +O(q^{10})$	\(q-1.83774e10 q^{2} +2.28315e16 q^{3} -2.52566e20 q^{4} +1.12358e24 q^{5} -4.19583e26 q^{6} -8.82897e28 q^{7} +1.54896e31 q^{8} -3.13110e32 q^{9} -2.06484e34 q^{10} -6.35095e35 q^{11} -5.76645e36 q^{12} +1.50107e38 q^{13} +1.62254e39 q^{14} +2.56529e40 q^{15} -1.35571e41 q^{16} +5.11299e42 q^{17} +5.75416e42 q^{18} -8.09143e43 q^{19} -2.83777e44 q^{20} -2.01578e45 q^{21} +1.16714e46 q^{22} -3.60398e46 q^{23} +3.53651e47 q^{24} -4.31642e47 q^{25} -2.75859e48 q^{26} -2.61990e49 q^{27} +2.22990e49 q^{28} +5.01375e49 q^{29} -4.71434e50 q^{30} -5.34810e51 q^{31} -6.65202e51 q^{32} -1.45001e52 q^{33} -9.39635e52 q^{34} -9.92003e52 q^{35} +7.90809e52 q^{36} -1.65367e54 q^{37} +1.48700e54 q^{38} +3.42717e54 q^{39} +1.74038e55 q^{40} +6.67526e55 q^{41} +3.70449e55 q^{42} -2.02257e56 q^{43} +1.60403e56 q^{44} -3.51803e56 q^{45} +6.62318e56 q^{46} -7.63503e57 q^{47} -3.09528e57 q^{48} -1.27054e58 q^{49} +7.93246e57 q^{50} +1.16737e59 q^{51} -3.79120e58 q^{52} +2.97628e59 q^{53} +4.81470e59 q^{54} -7.13578e59 q^{55} -1.36758e60 q^{56} -1.84739e60 q^{57} -9.21399e59 q^{58} +1.35785e60 q^{59} -6.47904e60 q^{60} -5.28661e61 q^{61} +9.82844e61 q^{62} +2.76444e61 q^{63} +2.02274e62 q^{64} +1.68657e62 q^{65} +2.66475e62 q^{66} -1.38691e63 q^{67} -1.29137e63 q^{68} -8.22840e62 q^{69} +1.82305e63 q^{70} -2.36872e63 q^{71} -4.84996e63 q^{72} +1.10475e64 q^{73} +3.03903e64 q^{74} -9.85500e63 q^{75} +2.04362e64 q^{76} +5.60723e64 q^{77} -6.29825e64 q^{78} -7.32931e64 q^{79} -1.52324e65 q^{80} -3.36906e65 q^{81} -1.22674e66 q^{82} +3.62072e65 q^{83} +5.09118e65 q^{84} +5.74483e66 q^{85} +3.71696e66 q^{86} +1.14471e66 q^{87} -9.83738e66 q^{88} -6.55747e66 q^{89} +6.46524e66 q^{90} -1.32529e67 q^{91} +9.10241e66 q^{92} -1.22105e68 q^{93} +1.40312e68 q^{94} -9.09134e67 q^{95} -1.51875e68 q^{96} +4.82901e68 q^{97} +2.33493e68 q^{98} +1.98855e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots - 31\!\cdots\!35 q^{9}+O(q^{10}) $ 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9	$ 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) $ 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * 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 $

$2$	−1.83774e10	−0.756397	−0.378199	−	0.925724i	$-0.623456\pi$
$2$	−1.83774e10	−0.756397	−0.378199	+	0.925724i	$0.623456\pi$
$3$	2.28315e16	0.790406	0.395203	−	0.918594i	$-0.370674\pi$
$3$	2.28315e16	0.790406	0.395203	+	0.918594i	$0.370674\pi$
$4$	−2.52566e20	−0.427863
$5$	1.12358e24	0.863252	0.431626	−	0.902053i	$-0.357940\pi$
$5$	1.12358e24	0.863252	0.431626	+	0.902053i	$0.357940\pi$
$6$	−4.19583e26	−0.597861
$7$	−8.82897e28	−0.616634	−0.308317	−	0.951284i	$-0.599766\pi$
$7$	−8.82897e28	−0.616634	−0.308317	+	0.951284i	$0.599766\pi$
$8$	1.54896e31	1.08003
$9$	−3.13110e32	−0.375258
$10$	−2.06484e34	−0.652961
$11$	−6.35095e35	−0.749533	−0.374767	−	0.927119i	$-0.622277\pi$
$11$	−6.35095e35	−0.749533	−0.374767	+	0.927119i	$0.622277\pi$
$12$	−5.76645e36	−0.338186
$13$	1.50107e38	0.556360	0.278180	−	0.960529i	$-0.410269\pi$
$13$	1.50107e38	0.556360	0.278180	+	0.960529i	$0.410269\pi$
$14$	1.62254e39	0.466421
$15$	2.56529e40	0.682319
$16$	−1.35571e41	−0.389070
$17$	5.11299e42	1.81212	0.906060	−	0.423150i	$-0.139076\pi$
$17$	5.11299e42	1.81212	0.906060	+	0.423150i	$0.139076\pi$
$18$	5.75416e42	0.283844
$19$	−8.09143e43	−0.618054	−0.309027	−	0.951053i	$-0.600003\pi$
$19$	−8.09143e43	−0.618054	−0.309027	+	0.951053i	$0.600003\pi$
$20$	−2.83777e44	−0.369354
$21$	−2.01578e45	−0.487392
$22$	1.16714e46	0.566945
$23$	−3.60398e46	−0.377721	−0.188861	−	0.982004i	$-0.560479\pi$
$23$	−3.60398e46	−0.377721	−0.188861	+	0.982004i	$0.560479\pi$
$24$	3.53651e47	0.853664
$25$	−4.31642e47	−0.254796
$26$	−2.75859e48	−0.420829
$27$	−2.61990e49	−1.08701
$28$	2.22990e49	0.263835
$29$	5.01375e49	0.176780	0.0883898	−	0.996086i	$-0.471828\pi$
$29$	5.01375e49	0.176780	0.0883898	+	0.996086i	$0.471828\pi$
$30$	−4.71434e50	−0.516104
$31$	−5.34810e51	−1.88895	−0.944477	−	0.328578i	$-0.893431\pi$
$31$	−5.34810e51	−1.88895	−0.944477	+	0.328578i	$0.893431\pi$
$32$	−6.65202e51	−0.785741
$33$	−1.45001e52	−0.592436
$34$	−9.39635e52	−1.37068
$35$	−9.92003e52	−0.532311
$36$	7.90809e52	0.160559
$37$	−1.65367e54	−1.30464	−0.652319	−	0.757944i	$-0.726204\pi$
$37$	−1.65367e54	−1.30464	−0.652319	+	0.757944i	$0.726204\pi$
$38$	1.48700e54	0.467494
$39$	3.42717e54	0.439751
$40$	1.74038e55	0.932339
$41$	6.67526e55	1.52554	0.762772	−	0.646667i	$-0.223838\pi$
$41$	6.67526e55	1.52554	0.762772	+	0.646667i	$0.223838\pi$
$42$	3.70449e55	0.368662
$43$	−2.02257e56	−0.893802	−0.446901	−	0.894584i	$-0.647472\pi$
$43$	−2.02257e56	−0.893802	−0.446901	+	0.894584i	$0.647472\pi$
$44$	1.60403e56	0.320698
$45$	−3.51803e56	−0.323943
$46$	6.62318e56	0.285707
$47$	−7.63503e57	−1.56832	−0.784160	−	0.620559i	$-0.786906\pi$
$47$	−7.63503e57	−1.56832	−0.784160	+	0.620559i	$0.786906\pi$
$48$	−3.09528e57	−0.307523
$49$	−1.27054e58	−0.619762
$50$	7.93246e57	0.192727
$51$	1.16737e59	1.43231
$52$	−3.79120e58	−0.238046
$53$	2.97628e59	0.968627	0.484313	−	0.874895i	$-0.339069\pi$
$53$	2.97628e59	0.968627	0.484313	+	0.874895i	$0.339069\pi$
$54$	4.81470e59	0.822213
$55$	−7.13578e59	−0.647036
$56$	−1.36758e60	−0.665985
$57$	−1.84739e60	−0.488513
$58$	−9.21399e59	−0.133716
$59$	1.35785e60	0.109259	0.0546294	−	0.998507i	$-0.482602\pi$
$59$	1.35785e60	0.109259	0.0546294	+	0.998507i	$0.482602\pi$
$60$	−6.47904e60	−0.291939
$61$	−5.28661e61	−1.34678	−0.673392	−	0.739286i	$-0.735163\pi$
$61$	−5.28661e61	−1.34678	−0.673392	+	0.739286i	$0.735163\pi$
$62$	9.82844e61	1.42880
$63$	2.76444e61	0.231397
$64$	2.02274e62	0.983402
$65$	1.68657e62	0.480279
$66$	2.66475e62	0.448117
$67$	−1.38691e63	−1.38825	−0.694123	−	0.719856i	$-0.744208\pi$
$67$	−1.38691e63	−1.38825	−0.694123	+	0.719856i	$0.744208\pi$
$68$	−1.29137e63	−0.775340
$69$	−8.22840e62	−0.298553
$70$	1.82305e63	0.402638
$71$	−2.36872e63	−0.320701	−0.160351	−	0.987060i	$-0.551262\pi$
$71$	−2.36872e63	−0.320701	−0.160351	+	0.987060i	$0.551262\pi$
$72$	−4.84996e63	−0.405291
$73$	1.10475e64	0.573622	0.286811	−	0.957987i	$-0.407405\pi$
$73$	1.10475e64	0.573622	0.286811	+	0.957987i	$0.407405\pi$
$74$	3.03903e64	0.986825
$75$	−9.85500e63	−0.201392
$76$	2.04362e64	0.264443
$77$	5.60723e64	0.462188
$78$	−6.29825e64	−0.332626
$79$	−7.32931e64	−0.249418	−0.124709	−	0.992193i	$-0.539800\pi$
$79$	−7.32931e64	−0.249418	−0.124709	+	0.992193i	$0.539800\pi$
$80$	−1.52324e65	−0.335865
$81$	−3.36906e65	−0.483923
$82$	−1.22674e66	−1.15392
$83$	3.62072e65	0.224182	0.112091	−	0.993698i	$-0.464245\pi$
$83$	3.62072e65	0.224182	0.112091	+	0.993698i	$0.464245\pi$
$84$	5.09118e65	0.208537
$85$	5.74483e66	1.56432
$86$	3.71696e66	0.676069
$87$	1.14471e66	0.139728
$88$	−9.83738e66	−0.809520
$89$	−6.55747e66	−0.365411	−0.182705	−	0.983168i	$-0.558485\pi$
$89$	−6.55747e66	−0.365411	−0.182705	+	0.983168i	$0.558485\pi$
$90$	6.46524e66	0.245029
$91$	−1.32529e67	−0.343071
$92$	9.10241e66	0.161613
$93$	−1.22105e68	−1.49304
$94$	1.40312e68	1.18627
$95$	−9.09134e67	−0.533536
$96$	−1.51875e68	−0.621054
$97$	4.82901e68	1.38113	0.690564	−	0.723272i	$-0.257363\pi$
$97$	4.82901e68	1.38113	0.690564	+	0.723272i	$0.257363\pi$
$98$	2.33493e68	0.468786
$99$	1.98855e68	0.281269
$100$	1.09018e68	0.109018
$101$	7.33834e68	0.520608	0.260304	−	0.965527i	$-0.416177\pi$
$101$	7.33834e68	0.520608	0.260304	+	0.965527i	$0.416177\pi$
$102$	−2.14532e69	−1.08340
$103$	−3.22980e69	−1.16491	−0.582453	−	0.812864i	$-0.697907\pi$
$103$	−3.22980e69	−1.16491	−0.582453	+	0.812864i	$0.697907\pi$
$104$	2.32511e69	0.600887
$105$	−2.26489e69	−0.420742
$106$	−5.46964e69	−0.732667
$107$	1.18986e69	0.115281	0.0576403	−	0.998337i	$-0.481642\pi$
$107$	1.18986e69	0.115281	0.0576403	+	0.998337i	$0.481642\pi$
$108$	6.61697e69	0.465093
$109$	3.32583e70	1.70093	0.850465	−	0.526032i	$-0.176321\pi$
$109$	3.32583e70	1.70093	0.850465	+	0.526032i	$0.176321\pi$
$110$	1.31137e70	0.489416
$111$	−3.77558e70	−1.03119
$112$	1.19695e70	0.239914
$113$	−4.20663e70	−0.620481	−0.310240	−	0.950658i	$-0.600410\pi$
$113$	−4.20663e70	−0.620481	−0.310240	+	0.950658i	$0.600410\pi$
$114$	3.39503e70	0.369510
$115$	−4.04934e70	−0.326069
$116$	−1.26630e70	−0.0756375
$117$	−4.70001e70	−0.208779
$118$	−2.49537e70	−0.0826431
$119$	−4.51424e71	−1.11742
$120$	3.97354e71	0.736927
$121$	−3.14606e71	−0.438200
$122$	9.71543e71	1.01870
$123$	1.52406e72	1.20580
$124$	1.35075e72	0.808214
$125$	−2.38840e72	−1.08321
$126$	−5.08033e71	−0.175028
$127$	−2.36558e72	−0.620454	−0.310227	−	0.950663i	$-0.600405\pi$
$127$	−2.36558e72	−0.620454	−0.310227	+	0.950663i	$0.600405\pi$
$128$	2.09383e71	0.0418984
$129$	−4.61781e72	−0.706466
$130$	−3.09948e72	−0.363282
$131$	−1.20684e72	−0.108590	−0.0542952	−	0.998525i	$-0.517291\pi$
$131$	−1.20684e72	−0.108590	−0.0542952	+	0.998525i	$0.517291\pi$
$132$	3.66224e72	0.253481
$133$	7.14390e72	0.381113
$134$	2.54878e73	1.05007
$135$	−2.94366e73	−0.938366
$136$	7.91983e73	1.95715
$137$	−6.91263e73	−1.32673	−0.663367	−	0.748294i	$-0.730873\pi$
$137$	−6.91263e73	−1.32673	−0.663367	+	0.748294i	$0.730873\pi$
$138$	1.51217e73	0.225825
$139$	6.50475e72	0.0757216	0.0378608	−	0.999283i	$-0.487946\pi$
$139$	6.50475e72	0.0757216	0.0378608	+	0.999283i	$0.487946\pi$
$140$	2.50546e73	0.227756
$141$	−1.74319e74	−1.23961
$142$	4.35310e73	0.242577
$143$	−9.53324e73	−0.417011
$144$	4.24486e73	0.146002
$145$	5.63334e73	0.152605
$146$	−2.03025e74	−0.433886
$147$	−2.90084e74	−0.489864
$148$	4.17662e74	0.558207
$149$	1.06021e75	1.12322	0.561612	−	0.827401i	$-0.310182\pi$
$149$	1.06021e75	1.12322	0.561612	+	0.827401i	$0.310182\pi$
$150$	1.81110e74	0.152333
$151$	2.31654e75	1.54930	0.774649	−	0.632391i	$-0.217926\pi$
$151$	2.31654e75	1.54930	0.774649	+	0.632391i	$0.217926\pi$
$152$	−1.25333e75	−0.667518
$153$	−1.60093e75	−0.680013
$154$	−1.03047e75	−0.349598
$155$	−6.00900e75	−1.63064
$156$	−8.65586e74	−0.188153
$157$	2.67081e75	0.465698	0.232849	−	0.972513i	$-0.425195\pi$
$157$	2.67081e75	0.465698	0.232849	+	0.972513i	$0.425195\pi$
$158$	1.34694e75	0.188659
$159$	6.79528e75	0.765608
$160$	−7.47405e75	−0.678292
$161$	3.18194e75	0.232916
$162$	6.19147e75	0.366038
$163$	2.81849e76	1.34755	0.673773	−	0.738938i	$-0.264672\pi$
$163$	2.81849e76	1.34755	0.673773	+	0.738938i	$0.264672\pi$
$164$	−1.68594e76	−0.652725
$165$	−1.62920e76	−0.511421
$166$	−6.65395e75	−0.169571
$167$	6.56343e76	1.35960	0.679802	−	0.733396i	$-0.262066\pi$
$167$	6.56343e76	1.35960	0.679802	+	0.733396i	$0.262066\pi$
$168$	−3.12237e76	−0.526398
$169$	−5.02611e76	−0.690463
$170$	−1.05575e77	−1.18324
$171$	2.53351e76	0.231930
$172$	5.10831e76	0.382425
$173$	−3.03200e76	−0.185839	−0.0929197	−	0.995674i	$-0.529620\pi$
$173$	−3.03200e76	−0.185839	−0.0929197	+	0.995674i	$0.529620\pi$
$174$	−2.10369e76	−0.105690
$175$	3.81095e76	0.157116
$176$	8.61004e76	0.291621
$177$	3.10016e76	0.0863588
$178$	1.20509e77	0.276396
$179$	7.88055e77	1.48980	0.744898	−	0.667178i	$-0.232498\pi$
$179$	7.88055e77	1.48980	0.744898	+	0.667178i	$0.232498\pi$
$180$	8.88535e76	0.138603
$181$	−6.89713e77	−0.888705	−0.444352	−	0.895852i	$-0.646566\pi$
$181$	−6.89713e77	−0.888705	−0.444352	+	0.895852i	$0.646566\pi$
$182$	2.43555e77	0.259498
$183$	−1.20701e78	−1.06451
$184$	−5.58243e77	−0.407951
$185$	−1.85803e78	−1.12623
$186$	2.24397e78	1.12933
$187$	−3.24723e78	−1.35824
$188$	1.92835e78	0.671027
$189$	2.31310e78	0.670289
$190$	1.67076e78	0.403565
$191$	3.54584e78	0.714607	0.357304	−	0.933988i	$-0.383696\pi$
$191$	3.54584e78	0.714607	0.357304	+	0.933988i	$0.383696\pi$
$192$	4.61821e78	0.777287
$193$	−4.62550e78	−0.650776	−0.325388	−	0.945581i	$-0.605495\pi$
$193$	−4.62550e78	−0.650776	−0.325388	+	0.945581i	$0.605495\pi$
$194$	−8.87449e78	−1.04468
$195$	3.85069e78	0.379615
$196$	3.20896e78	0.265173
$197$	−1.64821e78	−0.114269	−0.0571346	−	0.998366i	$-0.518196\pi$
$197$	−1.64821e78	−0.114269	−0.0571346	+	0.998366i	$0.518196\pi$
$198$	−3.65444e78	−0.212751
$199$	1.17255e79	0.573721	0.286860	−	0.957972i	$-0.407388\pi$
$199$	1.17255e79	0.573721	0.286860	+	0.957972i	$0.407388\pi$
$200$	−6.68597e78	−0.275188
$201$	−3.16651e79	−1.09728
$202$	−1.34860e79	−0.393786
$203$	−4.42663e78	−0.109008
$204$	−2.94838e79	−0.612833
$205$	7.50016e79	1.31693
$206$	5.93554e79	0.881132
$207$	1.12844e79	0.141743
$208$	−2.03502e79	−0.216463
$209$	5.13883e79	0.463252
$210$	4.16228e79	0.318248
$211$	9.43238e78	0.0612177	0.0306088	−	0.999531i	$-0.490255\pi$
$211$	9.43238e78	0.0612177	0.0306088	+	0.999531i	$0.490255\pi$
$212$	−7.51707e79	−0.414440
$213$	−5.40813e79	−0.253484
$214$	−2.18666e79	−0.0871980
$215$	−2.27251e80	−0.771576
$216$	−4.05813e80	−1.17401
$217$	4.72183e80	1.16479
$218$	−6.11203e80	−1.28658
$219$	2.52231e80	0.453394
$220$	1.80225e80	0.276843
$221$	7.67497e80	1.00819
$222$	6.93854e80	0.779992
$223$	−4.99323e80	−0.480689	−0.240344	−	0.970688i	$-0.577260\pi$
$223$	−4.99323e80	−0.480689	−0.240344	+	0.970688i	$0.577260\pi$
$224$	5.87305e80	0.484515
$225$	1.35151e80	0.0956144
$226$	7.73071e80	0.469330
$227$	−2.13100e81	−1.11094	−0.555472	−	0.831535i	$-0.687462\pi$
$227$	−2.13100e81	−1.11094	−0.555472	+	0.831535i	$0.687462\pi$
$228$	4.66588e80	0.209017
$229$	−3.36412e81	−1.29583	−0.647915	−	0.761713i	$-0.724359\pi$
$229$	−3.36412e81	−1.29583	−0.647915	+	0.761713i	$0.724359\pi$
$230$	7.44165e80	0.246637
$231$	1.28021e81	0.365316
$232$	7.76612e80	0.190928
$233$	7.16036e78	0.00151759	0.000758797	−	1.00000i	$-0.499758\pi$
$233$	7.16036e78	0.00151759	0.000758797		1.00000i	$0.499758\pi$
$234$	8.63741e80	0.157920
$235$	−8.57854e81	−1.35386
$236$	−3.42946e80	−0.0467478
$237$	−1.67339e81	−0.197142
$238$	8.29602e81	0.845210
$239$	1.50435e82	1.32623	0.663117	−	0.748516i	$-0.269233\pi$
$239$	1.50435e82	1.32623	0.663117	+	0.748516i	$0.269233\pi$
$240$	−3.47779e81	−0.265470
$241$	−3.33974e81	−0.220864	−0.110432	−	0.993884i	$-0.535223\pi$
$241$	−3.33974e81	−0.220864	−0.110432	+	0.993884i	$0.535223\pi$
$242$	5.78166e81	0.331453
$243$	1.41680e82	0.704517
$244$	1.33522e82	0.576240
$245$	−1.42755e82	−0.535011
$246$	−2.80083e82	−0.912063
$247$	−1.21458e82	−0.343861
$248$	−8.28401e82	−2.04013
$249$	8.26663e81	0.177195
$250$	4.38926e82	0.819333
$251$	1.19634e82	0.194587	0.0972933	−	0.995256i	$-0.468982\pi$
$251$	1.19634e82	0.194587	0.0972933	+	0.995256i	$0.468982\pi$
$252$	−6.98203e81	−0.0990064
$253$	2.28887e82	0.283115
$254$	4.34733e82	0.469310
$255$	1.31163e83	1.23644
$256$	−1.23249e83	−1.01509
$257$	−2.11787e82	−0.152477	−0.0762387	−	0.997090i	$-0.524291\pi$
$257$	−2.11787e82	−0.152477	−0.0762387	+	0.997090i	$0.524291\pi$
$258$	8.48635e82	0.534369
$259$	1.46002e83	0.804485
$260$	−4.25970e82	−0.205494
$261$	−1.56986e82	−0.0663380
$262$	2.21787e82	0.0821374
$263$	−5.20789e83	−1.69118	−0.845588	−	0.533837i	$-0.820750\pi$
$263$	−5.20789e83	−1.69118	−0.845588	+	0.533837i	$0.820750\pi$
$264$	−2.24602e83	−0.639849
$265$	3.34408e83	0.836169
$266$	−1.31287e83	−0.288273
$267$	−1.49717e83	−0.288823
$268$	3.50285e83	0.593980
$269$	−2.43999e83	−0.363860	−0.181930	−	0.983311i	$-0.558234\pi$
$269$	−2.43999e83	−0.363860	−0.181930	+	0.983311i	$0.558234\pi$
$270$	5.40968e83	0.709777
$271$	1.78874e83	0.206589	0.103294	−	0.994651i	$-0.467062\pi$
$271$	1.78874e83	0.206589	0.103294	+	0.994651i	$0.467062\pi$
$272$	−6.93173e83	−0.705041
$273$	−3.02584e83	−0.271165
$274$	1.27036e84	1.00354
$275$	2.74133e83	0.190978
$276$	2.07821e83	0.127740
$277$	8.95601e83	0.485918	0.242959	−	0.970037i	$-0.421882\pi$
$277$	8.95601e83	0.485918	0.242959	+	0.970037i	$0.421882\pi$
$278$	−1.19540e83	−0.0572756
$279$	1.67454e84	0.708846
$280$	−1.53658e84	−0.574913
$281$	−4.12597e84	−1.36508	−0.682540	−	0.730848i	$-0.739125\pi$
$281$	−4.12597e84	−1.36508	−0.682540	+	0.730848i	$0.739125\pi$
$282$	3.20353e84	0.937637
$283$	−7.03383e84	−1.82205	−0.911023	−	0.412354i	$-0.864707\pi$
$283$	−7.03383e84	−1.82205	−0.911023	+	0.412354i	$0.864707\pi$
$284$	5.98258e83	0.137216
$285$	−2.07569e84	−0.421710
$286$	1.75196e84	0.315426
$287$	−5.89357e84	−0.940704
$288$	2.08281e84	0.294856
$289$	1.81815e85	2.28378
$290$	−1.03526e84	−0.115430
$291$	1.10253e85	1.09165
$292$	−2.79022e84	−0.245432
$293$	−6.51453e84	−0.509272	−0.254636	−	0.967037i	$-0.581956\pi$
$293$	−6.51453e84	−0.509272	−0.254636	+	0.967037i	$0.581956\pi$
$294$	5.33099e84	0.370531
$295$	1.52565e84	0.0943179
$296$	−2.56148e85	−1.40905
$297$	1.66388e85	0.814752
$298$	−1.94839e85	−0.849603
$299$	−5.40983e84	−0.210149
$300$	2.48904e84	0.0861684
$301$	1.78572e85	0.551149
$302$	−4.25720e85	−1.17188
$303$	1.67545e85	0.411491
$304$	1.09696e85	0.240466
$305$	−5.93991e85	−1.16261
$306$	2.94209e85	0.514360
$307$	9.02219e85	1.40941	0.704706	−	0.709499i	$-0.251079\pi$
$307$	9.02219e85	1.40941	0.704706	+	0.709499i	$0.251079\pi$
$308$	−1.41620e85	−0.197753
$309$	−7.37410e85	−0.920749
$310$	1.10430e86	1.23341
$311$	−4.22710e85	−0.422483	−0.211242	−	0.977434i	$-0.567751\pi$
$311$	−4.22710e85	−0.422483	−0.211242	+	0.977434i	$0.567751\pi$
$312$	5.30856e85	0.474945
$313$	9.49223e85	0.760482	0.380241	−	0.924888i	$-0.375841\pi$
$313$	9.49223e85	0.760482	0.380241	+	0.924888i	$0.375841\pi$
$314$	−4.90825e85	−0.352253
$315$	3.10606e85	0.199754
$316$	1.85113e85	0.106717
$317$	−2.99712e86	−1.54939	−0.774693	−	0.632338i	$-0.782096\pi$
$317$	−2.99712e86	−1.54939	−0.774693	+	0.632338i	$0.782096\pi$
$318$	−1.24880e86	−0.579104
$319$	−3.18421e85	−0.132502
$320$	2.27270e86	0.848923
$321$	2.71663e85	0.0911185
$322$	−5.84759e85	−0.176177
$323$	−4.13714e86	−1.11999
$324$	8.50911e85	0.207053
$325$	−6.47926e85	−0.141759
$326$	−5.17966e86	−1.01928
$327$	7.59336e86	1.34443
$328$	1.03397e87	1.64764
$329$	6.74095e86	0.967080
$330$	2.99405e86	0.386837
$331$	−6.30305e86	−0.733644	−0.366822	−	0.930291i	$-0.619554\pi$
$331$	−6.30305e86	−0.733644	−0.366822	+	0.930291i	$0.619554\pi$
$332$	−9.14470e85	−0.0959192
$333$	5.17782e86	0.489577
$334$	−1.20619e87	−1.02840
$335$	−1.55830e87	−1.19841
$336$	2.73282e86	0.189629
$337$	−1.24071e87	−0.777034	−0.388517	−	0.921442i	$-0.627013\pi$
$337$	−1.24071e87	−0.777034	−0.388517	+	0.921442i	$0.627013\pi$
$338$	9.23669e86	0.522264
$339$	−9.60435e86	−0.490432
$340$	−1.45095e87	−0.669313
$341$	3.39655e87	1.41583
$342$	−4.65594e86	−0.175431
$343$	2.93174e87	0.998801
$344$	−3.13288e87	−0.965334
$345$	−9.24524e86	−0.257727
$346$	5.57203e86	0.140568
$347$	5.12646e87	1.17071	0.585357	−	0.810776i	$-0.300954\pi$
$347$	5.12646e87	1.17071	0.585357	+	0.810776i	$0.300954\pi$
$348$	−2.89115e86	−0.0597843
$349$	6.17210e85	0.0115599	0.00577997	−	0.999983i	$-0.498160\pi$
$349$	6.17210e85	0.0115599	0.00577997	+	0.999983i	$0.498160\pi$
$350$	−7.00355e86	−0.118842
$351$	−3.93266e87	−0.604771
$352$	4.22466e87	0.588939
$353$	5.76707e87	0.729001	0.364500	−	0.931203i	$-0.381240\pi$
$353$	5.76707e87	0.729001	0.364500	+	0.931203i	$0.381240\pi$
$354$	−5.69730e86	−0.0653216
$355$	−2.66144e87	−0.276846
$356$	1.65619e87	0.156346
$357$	−1.03067e88	−0.883212
$358$	−1.44824e88	−1.12688
$359$	5.64791e87	0.399144	0.199572	−	0.979883i	$-0.436045\pi$
$359$	5.64791e87	0.399144	0.199572	+	0.979883i	$0.436045\pi$
$360$	−5.44930e87	−0.349868
$361$	−1.05924e88	−0.618010
$362$	1.26752e88	0.672214
$363$	−7.18292e87	−0.346356
$364$	3.34724e87	0.146787
$365$	1.24127e88	0.495180
$366$	2.21817e88	0.805190
$367$	1.92969e88	0.637540	0.318770	−	0.947832i	$-0.396730\pi$
$367$	1.92969e88	0.637540	0.318770	+	0.947832i	$0.396730\pi$
$368$	4.88595e87	0.146960
$369$	−2.09009e88	−0.572474
$370$	3.41458e88	0.851878
$371$	−2.62775e88	−0.597289
$372$	3.08395e88	0.638817
$373$	−2.69870e88	−0.509565	−0.254783	−	0.966998i	$-0.582004\pi$
$373$	−2.69870e88	−0.509565	−0.254783	+	0.966998i	$0.582004\pi$
$374$	5.96758e88	1.02737
$375$	−5.45305e88	−0.856172
$376$	−1.18264e89	−1.69384
$377$	7.52601e87	0.0983531
$378$	−4.25088e88	−0.507005
$379$	6.27131e87	0.0682819	0.0341410	−	0.999417i	$-0.489130\pi$
$379$	6.27131e87	0.0682819	0.0341410	+	0.999417i	$0.489130\pi$
$380$	2.29616e88	0.228280
$381$	−5.40097e88	−0.490411
$382$	−6.51634e88	−0.540527
$383$	1.89265e89	1.43454	0.717269	−	0.696796i	$-0.245392\pi$
$383$	1.89265e89	1.43454	0.717269	+	0.696796i	$0.245392\pi$
$384$	4.78051e87	0.0331167
$385$	6.30016e88	0.398985
$386$	8.50047e88	0.492245
$387$	6.33286e88	0.335407
$388$	−1.21964e89	−0.590934
$389$	3.32775e89	1.47533	0.737666	−	0.675166i	$-0.235928\pi$
$389$	3.32775e89	1.47533	0.737666	+	0.675166i	$0.235928\pi$
$390$	−7.07657e88	−0.287140
$391$	−1.84271e89	−0.684476
$392$	−1.96803e89	−0.669363
$393$	−2.75540e88	−0.0858305
$394$	3.02899e88	0.0864329
$395$	−8.23504e88	−0.215311
$396$	−5.02239e88	−0.120345
$397$	3.94681e89	0.866910	0.433455	−	0.901175i	$-0.357294\pi$
$397$	3.94681e89	0.866910	0.433455	+	0.901175i	$0.357294\pi$
$398$	−2.15485e89	−0.433961
$399$	1.63106e89	0.301234
$400$	5.85181e88	0.0991335
$401$	−1.06622e90	−1.65717	−0.828585	−	0.559863i	$-0.810854\pi$
$401$	−1.06622e90	−1.65717	−0.828585	+	0.559863i	$0.810854\pi$
$402$	5.81923e89	0.829978
$403$	−8.02789e89	−1.05094
$404$	−1.85342e89	−0.222749
$405$	−3.78540e89	−0.417747
$406$	8.13501e88	0.0824536
$407$	1.05024e90	0.977870
$408$	1.80821e90	1.54694
$409$	2.49992e90	1.96549	0.982747	−	0.184956i	$-0.0592143\pi$
$409$	2.49992e90	1.96549	0.982747	+	0.184956i	$0.0592143\pi$
$410$	−1.37834e90	−0.996122
$411$	−1.57825e90	−1.04866
$412$	8.15737e89	0.498421
$413$	−1.19884e89	−0.0673728
$414$	−2.07378e89	−0.107214
$415$	4.06815e89	0.193525
$416$	−9.98517e89	−0.437155
$417$	1.48513e89	0.0598508
$418$	−9.44384e89	−0.350402
$419$	−4.53380e90	−1.54910	−0.774548	−	0.632515i	$-0.782023\pi$
$419$	−4.53380e90	−1.54910	−0.774548	+	0.632515i	$0.782023\pi$
$420$	5.72033e89	0.180020
$421$	−2.79687e90	−0.810850	−0.405425	−	0.914128i	$-0.632876\pi$
$421$	−2.79687e90	−0.810850	−0.405425	+	0.914128i	$0.632876\pi$
$422$	−1.73343e89	−0.0463049
$423$	2.39060e90	0.588525
$424$	4.61015e90	1.04615
$425$	−2.20698e90	−0.461721
$426$	9.93875e89	0.191735
$427$	4.66753e90	0.830474
$428$	−3.00519e89	−0.0493244
$429$	−2.17658e90	−0.329608
$430$	4.17629e90	0.583618
$431$	1.36412e90	0.175949	0.0879747	−	0.996123i	$-0.471961\pi$
$431$	1.36412e90	0.175949	0.0879747	+	0.996123i	$0.471961\pi$
$432$	3.55182e90	0.422924
$433$	5.03925e90	0.554030	0.277015	−	0.960866i	$-0.410655\pi$
$433$	5.03925e90	0.554030	0.277015	+	0.960866i	$0.410655\pi$
$434$	−8.67750e90	−0.881047
$435$	1.28617e90	0.120620
$436$	−8.39992e90	−0.727766
$437$	2.91613e90	0.233452
$438$	−4.63535e90	−0.342946
$439$	3.57299e89	0.0244347	0.0122173	−	0.999925i	$-0.496111\pi$
$439$	3.57299e89	0.0244347	0.0122173	+	0.999925i	$0.496111\pi$
$440$	−1.10531e91	−0.698819
$441$	3.97820e90	0.232571
$442$	−1.41046e91	−0.762593
$443$	1.15300e90	0.0576635	0.0288317	−	0.999584i	$-0.490821\pi$
$443$	1.15300e90	0.0576635	0.0288317	+	0.999584i	$0.490821\pi$
$444$	9.53582e90	0.441210
$445$	−7.36782e90	−0.315441
$446$	9.17628e90	0.363592
$447$	2.42062e91	0.887802
$448$	−1.78587e91	−0.606399
$449$	1.27562e91	0.401072	0.200536	−	0.979686i	$-0.435732\pi$
$449$	1.27562e91	0.401072	0.200536	+	0.979686i	$0.435732\pi$
$450$	−2.48373e90	−0.0723225
$451$	−4.23942e91	−1.14345
$452$	1.06245e91	0.265481
$453$	5.28900e91	1.22457
$454$	3.91624e91	0.840315
$455$	−1.48907e91	−0.296157
$456$	−2.86154e91	−0.527610
$457$	6.82027e91	1.16598	0.582992	−	0.812478i	$-0.301882\pi$
$457$	6.82027e91	1.16598	0.582992	+	0.812478i	$0.301882\pi$
$458$	6.18240e91	0.980162
$459$	−1.33955e92	−1.96980
$460$	1.02273e91	0.139513
$461$	−9.86987e90	−0.124919	−0.0624596	−	0.998047i	$-0.519894\pi$
$461$	−9.86987e90	−0.124919	−0.0624596	+	0.998047i	$0.519894\pi$
$462$	−2.35270e91	−0.276324
$463$	−8.33764e91	−0.908864	−0.454432	−	0.890782i	$-0.650158\pi$
$463$	−8.33764e91	−0.908864	−0.454432	+	0.890782i	$0.650158\pi$
$464$	−6.79719e90	−0.0687796
$465$	−1.37194e92	−1.28887
$466$	−1.31589e89	−0.00114790
$467$	−2.02146e91	−0.163770	−0.0818848	−	0.996642i	$-0.526094\pi$
$467$	−2.02146e91	−0.163770	−0.0818848	+	0.996642i	$0.526094\pi$
$468$	1.18706e91	0.0893288
$469$	1.22450e92	0.856040
$470$	1.57652e92	1.02405
$471$	6.09784e91	0.368090
$472$	2.10326e91	0.118003
$473$	1.28452e92	0.669934
$474$	3.07526e91	0.149117
$475$	3.49260e91	0.157478
$476$	1.14014e92	0.478101
$477$	−9.31904e91	−0.363485
$478$	−2.76460e92	−1.00316
$479$	8.35529e91	0.282089	0.141045	−	0.990003i	$-0.454954\pi$
$479$	8.35529e91	0.282089	0.141045	+	0.990003i	$0.454954\pi$
$480$	−1.70643e92	−0.536126
$481$	−2.48228e92	−0.725849
$482$	6.13759e91	0.167061
$483$	7.26483e91	0.184098
$484$	7.94589e91	0.187490
$485$	5.42577e92	1.19226
$486$	−2.60371e92	−0.532895
$487$	−8.46053e92	−1.61305	−0.806526	−	0.591199i	$-0.798655\pi$
$487$	−8.46053e92	−1.61305	−0.806526	+	0.591199i	$0.798655\pi$
$488$	−8.18876e92	−1.45457
$489$	6.43502e92	1.06511
$490$	2.62348e92	0.404681
$491$	4.79826e92	0.689878	0.344939	−	0.938625i	$-0.387900\pi$
$491$	4.79826e92	0.689878	0.344939	+	0.938625i	$0.387900\pi$
$492$	−3.84925e92	−0.515917
$493$	2.56353e92	0.320346
$494$	2.23209e92	0.260095
$495$	2.23428e92	0.242806
$496$	7.25048e92	0.734935
$497$	2.09134e92	0.197755
$498$	−1.51919e92	−0.134030
$499$	−1.37532e93	−1.13223	−0.566114	−	0.824327i	$-0.691554\pi$
$499$	−1.37532e93	−1.13223	−0.566114	+	0.824327i	$0.691554\pi$
$500$	6.03227e92	0.463464
$501$	1.49853e93	1.07464
$502$	−2.19857e92	−0.147185
$503$	−1.11814e93	−0.698879	−0.349440	−	0.936959i	$-0.613628\pi$
$503$	−1.11814e93	−0.698879	−0.349440	+	0.936959i	$0.613628\pi$
$504$	4.28202e92	0.249916
$505$	8.24519e92	0.449416
$506$	−4.20635e92	−0.214147
$507$	−1.14753e93	−0.545746
$508$	5.97465e92	0.265469
$509$	−3.09546e93	−1.28517	−0.642587	−	0.766213i	$-0.722139\pi$
$509$	−3.09546e93	−1.28517	−0.642587	+	0.766213i	$0.722139\pi$
$510$	−2.41044e93	−0.935243
$511$	−9.75381e92	−0.353715
$512$	2.14141e93	0.725915
$513$	2.11987e93	0.671832
$514$	3.89209e92	0.115334
$515$	−3.62893e93	−1.00561
$516$	1.16630e93	0.302271
$517$	4.84897e93	1.17551
$518$	−2.68315e93	−0.608510
$519$	−6.92249e92	−0.146889
$520$	2.61244e93	0.518717
$521$	8.60888e93	1.59973	0.799863	−	0.600183i	$-0.204906\pi$
$521$	8.60888e93	1.59973	0.799863	+	0.600183i	$0.204906\pi$
$522$	2.88499e92	0.0501779
$523$	2.70276e93	0.440047	0.220023	−	0.975495i	$-0.429387\pi$
$523$	2.70276e93	0.440047	0.220023	+	0.975495i	$0.429387\pi$
$524$	3.04808e92	0.0464618
$525$	8.70096e92	0.124186
$526$	9.57077e93	1.27920
$527$	−2.73448e94	−3.42301
$528$	1.96580e93	0.230499
$529$	−7.80489e93	−0.857327
$530$	−6.14556e93	−0.632476
$531$	−4.25156e92	−0.0410003
$532$	−1.80431e93	−0.163064
$533$	1.00200e94	0.848753
$534$	2.75141e93	0.218465
$535$	1.33690e93	0.0995162
$536$	−2.14827e94	−1.49935
$537$	1.79924e94	1.17754
$538$	4.48408e93	0.275223
$539$	8.06916e93	0.464532
$540$	7.43467e93	0.401492
$541$	1.15494e94	0.585130	0.292565	−	0.956246i	$-0.405491\pi$
$541$	1.15494e94	0.585130	0.292565	+	0.956246i	$0.405491\pi$
$542$	−3.28724e93	−0.156263
$543$	−1.57471e94	−0.702438
$544$	−3.40117e94	−1.42386
$545$	3.73683e94	1.46833
$546$	5.56071e93	0.205109
$547$	−5.12485e93	−0.177467	−0.0887336	−	0.996055i	$-0.528282\pi$
$547$	−5.12485e93	−0.177467	−0.0887336	+	0.996055i	$0.528282\pi$
$548$	1.74590e94	0.567661
$549$	1.65529e94	0.505392
$550$	−5.03787e93	−0.144455
$551$	−4.05684e93	−0.109259
$552$	−1.27455e94	−0.322447
$553$	6.47103e93	0.153800
$554$	−1.64588e94	−0.367547
$555$	−4.24215e94	−0.890180
$556$	−1.64288e93	−0.0323985
$557$	9.14290e93	0.169465	0.0847325	−	0.996404i	$-0.472996\pi$
$557$	9.14290e93	0.169465	0.0847325	+	0.996404i	$0.472996\pi$
$558$	−3.07738e94	−0.536169
$559$	−3.03602e94	−0.497276
$560$	1.34487e94	0.207106
$561$	−7.41390e94	−1.07356
$562$	7.58248e94	1.03254
$563$	6.40420e93	0.0820210	0.0410105	−	0.999159i	$-0.486942\pi$
$563$	6.40420e93	0.0820210	0.0410105	+	0.999159i	$0.486942\pi$
$564$	4.40270e94	0.530383
$565$	−4.72647e94	−0.535631
$566$	1.29264e95	1.37819
$567$	2.97454e94	0.298403
$568$	−3.66906e94	−0.346367
$569$	1.41851e95	1.26026	0.630128	−	0.776491i	$-0.283002\pi$
$569$	1.41851e95	1.26026	0.630128	+	0.776491i	$0.283002\pi$
$570$	3.81458e94	0.318980
$571$	−2.33130e95	−1.83507	−0.917535	−	0.397654i	$-0.869824\pi$
$571$	−2.33130e95	−1.83507	−0.917535	+	0.397654i	$0.869824\pi$
$572$	2.40777e94	0.178424
$573$	8.09566e94	0.564830
$574$	1.08309e95	0.711546
$575$	1.55563e94	0.0962420
$576$	−6.33340e94	−0.369030
$577$	9.49740e94	0.521242	0.260621	−	0.965441i	$-0.416073\pi$
$577$	9.49740e94	0.521242	0.260621	+	0.965441i	$0.416073\pi$
$578$	−3.34129e95	−1.72744
$579$	−1.05607e95	−0.514377
$580$	−1.42279e94	−0.0652942
$581$	−3.19672e94	−0.138238
$582$	−2.02617e95	−0.825722
$583$	−1.89022e95	−0.726018
$584$	1.71122e95	0.619529
$585$	−5.28082e94	−0.180229
$586$	1.19720e95	0.385212
$587$	2.11763e95	0.642444	0.321222	−	0.947004i	$-0.395906\pi$
$587$	2.11763e95	0.642444	0.321222	+	0.947004i	$0.395906\pi$
$588$	7.32652e94	0.209595
$589$	4.32738e95	1.16747
$590$	−2.80374e94	−0.0713418
$591$	−3.76311e94	−0.0903190
$592$	2.24190e95	0.507595
$593$	5.07974e95	1.08506	0.542531	−	0.840035i	$-0.317466\pi$
$593$	5.07974e95	1.08506	0.542531	+	0.840035i	$0.317466\pi$
$594$	−3.05779e95	−0.616276
$595$	−5.07210e95	−0.964611
$596$	−2.67773e95	−0.480586
$597$	2.67710e95	0.453472
$598$	9.94188e94	0.158956
$599$	3.02956e95	0.457251	0.228626	−	0.973514i	$-0.426577\pi$
$599$	3.02956e95	0.457251	0.228626	+	0.973514i	$0.426577\pi$
$600$	−1.52650e95	−0.217510
$601$	−4.18382e95	−0.562865	−0.281432	−	0.959581i	$-0.590809\pi$
$601$	−4.18382e95	−0.562865	−0.281432	+	0.959581i	$0.590809\pi$
$602$	−3.28169e95	−0.416887
$603$	4.34254e95	0.520951
$604$	−5.85079e95	−0.662888
$605$	−3.53484e95	−0.378277
$606$	−3.07905e95	−0.311251
$607$	2.90050e95	0.276989	0.138494	−	0.990363i	$-0.455774\pi$
$607$	2.90050e95	0.276989	0.138494	+	0.990363i	$0.455774\pi$
$608$	5.38244e95	0.485630
$609$	−1.01066e95	−0.0861609
$610$	1.09160e96	0.879398
$611$	−1.14607e96	−0.872551
$612$	4.04340e95	0.290953
$613$	−1.72442e96	−1.17289	−0.586445	−	0.809989i	$-0.699473\pi$
$613$	−1.72442e96	−1.17289	−0.586445	+	0.809989i	$0.699473\pi$
$614$	−1.65805e96	−1.06608
$615$	1.71240e96	1.04091
$616$	8.68540e95	0.499178
$617$	−4.52024e95	−0.245654	−0.122827	−	0.992428i	$-0.539196\pi$
$617$	−4.52024e95	−0.245654	−0.122827	+	0.992428i	$0.539196\pi$
$618$	1.35517e96	0.696452
$619$	1.70981e96	0.831039	0.415519	−	0.909584i	$-0.363600\pi$
$619$	1.70981e96	0.831039	0.415519	+	0.909584i	$0.363600\pi$
$620$	1.51767e96	0.697692
$621$	9.44205e95	0.410588
$622$	7.76833e95	0.319565
$623$	5.78957e95	0.225325
$624$	−4.64625e95	−0.171094
$625$	−1.95232e96	−0.680283
$626$	−1.74443e96	−0.575226
$627$	1.17327e96	0.366157
$628$	−6.74554e95	−0.199255
$629$	−8.45521e96	−2.36416
$630$	−5.70814e95	−0.151093
$631$	1.73259e96	0.434194	0.217097	−	0.976150i	$-0.430341\pi$
$631$	1.73259e96	0.434194	0.217097	+	0.976150i	$0.430341\pi$
$632$	−1.13528e96	−0.269380
$633$	2.15355e95	0.0483868
$634$	5.50794e96	1.17195
$635$	−2.65791e96	−0.535608
$636$	−1.71626e96	−0.327576
$637$	−1.90718e96	−0.344811
$638$	5.85176e95	0.100224
$639$	7.41670e95	0.120346
$640$	2.35258e95	0.0361688
$641$	1.24042e97	1.80703	0.903516	−	0.428555i	$-0.140977\pi$
$641$	1.24042e97	1.80703	0.903516	+	0.428555i	$0.140977\pi$
$642$	−4.99246e95	−0.0689218
$643$	4.85935e96	0.635770	0.317885	−	0.948129i	$-0.397027\pi$
$643$	4.85935e96	0.635770	0.317885	+	0.948129i	$0.397027\pi$
$644$	−8.03650e95	−0.0996562
$645$	−5.18847e96	−0.609858
$646$	7.60300e96	0.847155
$647$	−1.58911e96	−0.167863	−0.0839317	−	0.996472i	$-0.526748\pi$
$647$	−1.58911e96	−0.167863	−0.0839317	+	0.996472i	$0.526748\pi$
$648$	−5.21855e96	−0.522652
$649$	−8.62362e95	−0.0818931
$650$	1.19072e96	0.107226
$651$	1.07806e97	0.920660
$652$	−7.11854e96	−0.576566
$653$	−3.72042e96	−0.285816	−0.142908	−	0.989736i	$-0.545645\pi$
$653$	−3.72042e96	−0.285816	−0.142908	+	0.989736i	$0.545645\pi$
$654$	−1.39546e97	−1.01692
$655$	−1.35598e96	−0.0937408
$656$	−9.04971e96	−0.593543
$657$	−3.45908e96	−0.215256
$658$	−1.23881e97	−0.731497
$659$	1.80448e97	1.01112	0.505562	−	0.862790i	$-0.331285\pi$
$659$	1.80448e97	1.01112	0.505562	+	0.862790i	$0.331285\pi$
$660$	4.11481e96	0.218818
$661$	−1.61074e97	−0.812970	−0.406485	−	0.913657i	$-0.633246\pi$
$661$	−1.61074e97	−0.812970	−0.406485	+	0.913657i	$0.633246\pi$
$662$	1.15834e97	0.554926
$663$	1.75231e97	0.796881
$664$	5.60836e96	0.242124
$665$	8.02672e96	0.328997
$666$	−9.51550e96	−0.370314
$667$	−1.80694e96	−0.0667734
$668$	−1.65770e97	−0.581725
$669$	−1.14003e97	−0.379939
$670$	2.86375e97	0.906471
$671$	3.35750e97	1.00946
$672$	1.34090e97	0.382963
$673$	−6.18856e97	−1.67907	−0.839536	−	0.543303i	$-0.817173\pi$
$673$	−6.18856e97	−1.67907	−0.839536	+	0.543303i	$0.817173\pi$
$674$	2.28011e97	0.587746
$675$	1.13086e97	0.276967
$676$	1.26942e97	0.295424
$677$	8.78367e96	0.194253	0.0971264	−	0.995272i	$-0.469035\pi$
$677$	8.78367e96	0.194253	0.0971264	+	0.995272i	$0.469035\pi$
$678$	1.76503e97	0.370961
$679$	−4.26352e97	−0.851651
$680$	8.89853e97	1.68951
$681$	−4.86539e97	−0.878097
$682$	−6.24199e97	−1.07093
$683$	−7.98957e96	−0.130319	−0.0651597	−	0.997875i	$-0.520756\pi$
$683$	−7.98957e96	−0.130319	−0.0651597	+	0.997875i	$0.520756\pi$
$684$	−6.39878e96	−0.0992343
$685$	−7.76687e97	−1.14531
$686$	−5.38779e97	−0.755490
$687$	−7.68078e97	−1.02423
$688$	2.74201e97	0.347751
$689$	4.46762e97	0.538906
$690$	1.69904e97	0.194944
$691$	1.70561e98	1.86161	0.930804	−	0.365518i	$-0.119108\pi$
$691$	1.70561e98	1.86161	0.930804	+	0.365518i	$0.119108\pi$
$692$	7.65779e96	0.0795139
$693$	−1.75568e97	−0.173440
$694$	−9.42112e97	−0.885525
$695$	7.30858e96	0.0653668
$696$	1.77312e97	0.150910
$697$	3.41305e98	2.76447
$698$	−1.13427e96	−0.00874391
$699$	1.63481e95	0.00119952
$700$	−9.62517e96	−0.0672242
$701$	−1.83692e98	−1.22129	−0.610643	−	0.791906i	$-0.709089\pi$
$701$	−1.83692e98	−1.22129	−0.610643	+	0.791906i	$0.709089\pi$
$702$	7.22722e97	0.457447
$703$	1.33806e98	0.806337
$704$	−1.28463e98	−0.737092
$705$	−1.95861e98	−1.07010
$706$	−1.05984e98	−0.551414
$707$	−6.47900e97	−0.321025
$708$	−7.82995e96	−0.0369498
$709$	−1.26968e98	−0.570690	−0.285345	−	0.958425i	$-0.592108\pi$
$709$	−1.26968e98	−0.570690	−0.285345	+	0.958425i	$0.592108\pi$
$710$	4.89104e97	0.209405
$711$	2.29488e97	0.0935963
$712$	−1.01573e98	−0.394655
$713$	1.92744e98	0.713498
$714$	1.89410e98	0.668059
$715$	−1.07113e98	−0.359985
$716$	−1.99036e98	−0.637429
$717$	3.43464e98	1.04826
$718$	−1.03794e98	−0.301911
$719$	−3.68969e98	−1.02292	−0.511462	−	0.859306i	$-0.670896\pi$
$719$	−3.68969e98	−1.02292	−0.511462	+	0.859306i	$0.670896\pi$
$720$	4.76943e97	0.126036
$721$	2.85158e98	0.718322
$722$	1.94661e98	0.467461
$723$	−7.62512e97	−0.174572
$724$	1.74198e98	0.380244
$725$	−2.16414e97	−0.0450428
$726$	1.32004e98	0.261983
$727$	5.94826e98	1.12578	0.562889	−	0.826533i	$-0.309690\pi$
$727$	5.94826e98	1.12578	0.562889	+	0.826533i	$0.309690\pi$
$728$	−2.05283e98	−0.370528
$729$	6.04585e98	1.04078
$730$	−2.28114e98	−0.374553
$731$	−1.03414e99	−1.61968
$732$	3.04850e98	0.455463
$733$	−5.69595e98	−0.811857	−0.405928	−	0.913905i	$-0.633052\pi$
$733$	−5.69595e98	−0.811857	−0.405928	+	0.913905i	$0.633052\pi$
$734$	−3.54627e98	−0.482234
$735$	−3.25931e98	−0.422876
$736$	2.39737e98	0.296791
$737$	8.80817e98	1.04054
$738$	3.84105e98	0.433017
$739$	−1.30994e99	−1.40935	−0.704673	−	0.709532i	$-0.748906\pi$
$739$	−1.30994e99	−1.40935	−0.704673	+	0.709532i	$0.748906\pi$
$740$	4.69275e98	0.481873
$741$	−2.77307e98	−0.271789
$742$	4.82913e98	0.451787
$743$	−1.09338e99	−0.976466	−0.488233	−	0.872713i	$-0.662358\pi$
$743$	−1.09338e99	−0.976466	−0.488233	+	0.872713i	$0.662358\pi$
$744$	−1.89136e99	−1.61253
$745$	1.19123e99	0.969624
$746$	4.95951e98	0.385434
$747$	−1.13368e98	−0.0841262
$748$	8.20140e98	0.581143
$749$	−1.05053e98	−0.0710860
$750$	1.00213e99	0.647606
$751$	−7.23723e97	−0.0446678	−0.0223339	−	0.999751i	$-0.507110\pi$
$751$	−7.23723e97	−0.0446678	−0.0223339	+	0.999751i	$0.507110\pi$
$752$	1.03509e99	0.610186
$753$	2.73143e98	0.153802
$754$	−1.38309e98	−0.0743940
$755$	2.60281e99	1.33743
$756$	−5.84210e98	−0.286792
$757$	7.29435e98	0.342120	0.171060	−	0.985261i	$-0.445281\pi$
$757$	7.29435e98	0.342120	0.171060	+	0.985261i	$0.445281\pi$
$758$	−1.15251e98	−0.0516483
$759$	5.22581e98	0.223776
$760$	−1.40822e99	−0.576236
$761$	−2.12780e99	−0.832072	−0.416036	−	0.909348i	$-0.636581\pi$
$761$	−2.12780e99	−0.832072	−0.416036	+	0.909348i	$0.636581\pi$
$762$	9.92559e98	0.370945
$763$	−2.93637e99	−1.04885
$764$	−8.95557e98	−0.305754
$765$	−1.79876e99	−0.587023
$766$	−3.47820e99	−1.08508
$767$	2.03823e98	0.0607873
$768$	−2.81396e99	−0.802336
$769$	5.23656e99	1.42754	0.713769	−	0.700382i	$-0.246987\pi$
$769$	5.23656e99	1.42754	0.713769	+	0.700382i	$0.246987\pi$
$770$	−1.15781e99	−0.301791
$771$	−4.83540e98	−0.120519
$772$	1.16824e99	0.278443
$773$	4.81316e99	1.09708	0.548539	−	0.836125i	$-0.315184\pi$
$773$	4.81316e99	1.09708	0.548539	+	0.836125i	$0.315184\pi$
$774$	−1.16382e99	−0.253701
$775$	2.30846e99	0.481298
$776$	7.47996e99	1.49166
$777$	3.33345e99	0.635870
$778$	−6.11555e99	−1.11594
$779$	−5.40124e99	−0.942869
$780$	−9.72552e98	−0.162424
$781$	1.50436e99	0.240376
$782$	3.38642e99	0.517736
$783$	−1.31355e99	−0.192162
$784$	1.72249e99	0.241131
$785$	3.00085e99	0.402015
$786$	5.06371e98	0.0649219
$787$	−5.33226e98	−0.0654309	−0.0327154	−	0.999465i	$-0.510416\pi$
$787$	−5.33226e98	−0.0654309	−0.0327154	+	0.999465i	$0.510416\pi$
$788$	4.16283e98	0.0488916
$789$	−1.18904e100	−1.33671
$790$	1.51339e99	0.162861
$791$	3.71402e99	0.382610
$792$	3.08018e99	0.303779
$793$	−7.93559e99	−0.749297
$794$	−7.25323e99	−0.655728
$795$	7.63502e99	0.660913
$796$	−2.96146e99	−0.245474
$797$	1.41086e100	1.11988	0.559941	−	0.828533i	$-0.310824\pi$
$797$	1.41086e100	1.11988	0.559941	+	0.828533i	$0.310824\pi$
$798$	−2.99746e99	−0.227853
$799$	−3.90378e100	−2.84198
$800$	2.87129e99	0.200204
$801$	2.05321e99	0.137123
$802$	1.95944e100	1.25348
$803$	−7.01621e99	−0.429948
$804$	7.99752e99	0.469485
$805$	3.57515e99	0.201065
$806$	1.47532e100	0.794927
$807$	−5.57085e99	−0.287597
$808$	1.13668e100	0.562273
$809$	−2.53533e100	−1.20174	−0.600871	−	0.799346i	$-0.705179\pi$
$809$	−2.53533e100	−1.20174	−0.600871	+	0.799346i	$0.705179\pi$
$810$	6.95659e99	0.315983
$811$	4.13280e100	1.79897	0.899487	−	0.436948i	$-0.143941\pi$
$811$	4.13280e100	1.79897	0.899487	+	0.436948i	$0.143941\pi$
$812$	1.11802e99	0.0466407
$813$	4.08395e99	0.163289
$814$	−1.93007e100	−0.739658
$815$	3.16679e100	1.16327
$816$	−1.58261e100	−0.557268
$817$	1.63655e100	0.552417
$818$	−4.59421e100	−1.48669
$819$	4.14963e99	0.128740
$820$	−1.89429e100	−0.563466
$821$	−5.53997e100	−1.58004	−0.790021	−	0.613080i	$-0.789930\pi$
$821$	−5.53997e100	−1.58004	−0.790021	+	0.613080i	$0.789930\pi$
$822$	2.90043e100	0.793202
$823$	2.61490e100	0.685743	0.342872	−	0.939382i	$-0.388600\pi$
$823$	2.61490e100	0.685743	0.342872	+	0.939382i	$0.388600\pi$
$824$	−5.00284e100	−1.25814
$825$	6.25886e99	0.150950
$826$	2.20316e99	0.0509606
$827$	2.23696e100	0.496271	0.248136	−	0.968725i	$-0.420182\pi$
$827$	2.23696e100	0.496271	0.248136	+	0.968725i	$0.420182\pi$
$828$	−2.85006e99	−0.0606467
$829$	−4.96571e100	−1.01356	−0.506781	−	0.862075i	$-0.669165\pi$
$829$	−4.96571e100	−1.01356	−0.506781	+	0.862075i	$0.669165\pi$
$830$	−7.47622e99	−0.146382
$831$	2.04479e100	0.384072
$832$	3.03628e100	0.547126
$833$	−6.49627e100	−1.12308
$834$	−2.72928e99	−0.0452710
$835$	7.37451e100	1.17368
$836$	−1.29789e100	−0.198208
$837$	1.40115e101	2.05332
$838$	8.33196e100	1.17173
$839$	5.71823e100	0.771745	0.385872	−	0.922552i	$-0.373901\pi$
$839$	5.71823e100	0.771745	0.385872	+	0.922552i	$0.373901\pi$
$840$	−3.50823e100	−0.454414
$841$	−7.79243e100	−0.968749
$842$	5.13993e100	0.613324
$843$	−9.42020e100	−1.07897
$844$	−2.38230e99	−0.0261928
$845$	−5.64722e100	−0.596044
$846$	−4.39332e100	−0.445159
$847$	2.77765e100	0.270209
$848$	−4.03497e100	−0.376863
$849$	−1.60592e101	−1.44016
$850$	4.05586e100	0.349245
$851$	5.95980e100	0.492790
$852$	1.36591e100	0.108457
$853$	1.15331e100	0.0879433	0.0439717	−	0.999033i	$-0.485999\pi$
$853$	1.15331e100	0.0879433	0.0439717	+	0.999033i	$0.485999\pi$
$854$	−8.57773e100	−0.628168
$855$	2.84659e100	0.200214
$856$	1.84305e100	0.124507
$857$	1.79317e101	1.16355	0.581773	−	0.813352i	$-0.302359\pi$
$857$	1.79317e101	1.16355	0.581773	+	0.813352i	$0.302359\pi$
$858$	3.99999e100	0.249314
$859$	−2.06109e101	−1.23405	−0.617025	−	0.786943i	$-0.711662\pi$
$859$	−2.06109e101	−1.23405	−0.617025	+	0.786943i	$0.711662\pi$
$860$	5.73958e100	0.330129
$861$	−1.34559e101	−0.743538
$862$	−2.50691e100	−0.133088
$863$	−2.70544e100	−0.137996	−0.0689979	−	0.997617i	$-0.521980\pi$
$863$	−2.70544e100	−0.137996	−0.0689979	+	0.997617i	$0.521980\pi$
$864$	1.74276e101	0.854110
$865$	−3.40668e100	−0.160426
$866$	−9.26084e100	−0.419067
$867$	4.15110e101	1.80511
$868$	−1.19257e101	−0.498373
$869$	4.65481e100	0.186947
$870$	−2.36365e100	−0.0912367
$871$	−2.08185e101	−0.772365
$872$	5.15160e101	1.83706
$873$	−1.51201e101	−0.518280
$874$	−5.35910e100	−0.176582
$875$	2.10871e101	0.667942
$876$	−6.37048e100	−0.193991
$877$	1.39865e101	0.409471	0.204735	−	0.978817i	$-0.434367\pi$
$877$	1.39865e101	0.409471	0.204735	+	0.978817i	$0.434367\pi$
$878$	−6.56624e99	−0.0184823
$879$	−1.48736e101	−0.402532
$880$	9.67404e100	0.251742
$881$	−4.46892e101	−1.11824	−0.559118	−	0.829088i	$-0.688860\pi$
$881$	−4.46892e101	−1.11824	−0.559118	+	0.829088i	$0.688860\pi$
$882$	−7.31091e100	−0.175916
$883$	−7.72337e101	−1.78716	−0.893578	−	0.448907i	$-0.851813\pi$
$883$	−7.72337e101	−1.78716	−0.893578	+	0.448907i	$0.851813\pi$
$884$	−1.93844e101	−0.431368
$885$	3.48327e100	0.0745494
$886$	−2.11892e100	−0.0436165
$887$	5.11089e101	1.01189	0.505943	−	0.862567i	$-0.331145\pi$
$887$	5.11089e101	1.01189	0.505943	+	0.862567i	$0.331145\pi$
$888$	−5.84823e101	−1.11372
$889$	2.08857e101	0.382593
$890$	1.35402e101	0.238599
$891$	2.13967e101	0.362716
$892$	1.26112e101	0.205669
$893$	6.17783e101	0.969306
$894$	−4.44847e101	−0.671531
$895$	8.85440e101	1.28607
$896$	−1.84863e100	−0.0258360
$897$	−1.23514e101	−0.166103
$898$	−2.34426e101	−0.303370
$899$	−2.68141e101	−0.333928
$900$	−3.41346e100	−0.0409099
$901$	1.52177e102	1.75527
$902$	7.79097e101	0.864900
$903$	4.07705e101	0.435631
$904$	−6.51592e101	−0.670139
$905$	−7.74945e101	−0.767176
$906$	−9.71982e101	−0.926265
$907$	−7.73852e101	−0.709915	−0.354958	−	0.934882i	$-0.615505\pi$
$907$	−7.73852e101	−0.709915	−0.354958	+	0.934882i	$0.615505\pi$
$908$	5.38219e101	0.475332
$909$	−2.29771e101	−0.195362
$910$	2.73653e101	0.224012
$911$	−9.32355e101	−0.734848	−0.367424	−	0.930054i	$-0.619760\pi$
$911$	−9.32355e101	−0.734848	−0.367424	+	0.930054i	$0.619760\pi$
$912$	2.50453e101	0.190066
$913$	−2.29950e101	−0.168032
$914$	−1.25339e102	−0.881948
$915$	−1.35617e102	−0.918937
$916$	8.49663e101	0.554438
$917$	1.06552e101	0.0669606
$918$	2.46175e102	1.48995
$919$	−1.85343e102	−1.08041	−0.540207	−	0.841532i	$-0.681654\pi$
$919$	−1.85343e102	−1.08041	−0.540207	+	0.841532i	$0.681654\pi$
$920$	−6.27228e101	−0.352164
$921$	2.05990e102	1.11401
$922$	1.81383e101	0.0944886
$923$	−3.55562e101	−0.178425
$924$	−3.23338e101	−0.156305
$925$	7.13794e101	0.332417
$926$	1.53224e102	0.687462
$927$	1.01128e102	0.437141
$928$	−3.33516e101	−0.138903
$929$	−1.39993e102	−0.561778	−0.280889	−	0.959740i	$-0.590629\pi$
$929$	−1.39993e102	−0.561778	−0.280889	+	0.959740i	$0.590629\pi$
$930$	2.52128e102	0.974897
$931$	1.02805e102	0.383046
$932$	−1.80846e99	−0.000649323 0
$933$	−9.65109e101	−0.333933
$934$	3.71493e101	0.123875
$935$	−3.64851e102	−1.17251
$936$	−7.28014e101	−0.225488
$937$	7.09610e101	0.211838	0.105919	−	0.994375i	$-0.466222\pi$
$937$	7.09610e101	0.211838	0.105919	+	0.994375i	$0.466222\pi$
$938$	−2.25031e102	−0.647507
$939$	2.16721e102	0.601089
$940$	2.16665e102	0.579265
$941$	1.31529e102	0.338985	0.169492	−	0.985531i	$-0.445787\pi$
$941$	1.31529e102	0.338985	0.169492	+	0.985531i	$0.445787\pi$
$942$	−1.12063e102	−0.278423
$943$	−2.40575e102	−0.576231
$944$	−1.84085e101	−0.0425093
$945$	2.59895e102	0.578629
$946$	−2.36062e102	−0.506736
$947$	−4.24962e102	−0.879580	−0.439790	−	0.898101i	$-0.644947\pi$
$947$	−4.24962e102	−0.879580	−0.439790	+	0.898101i	$0.644947\pi$
$948$	4.22641e101	0.0843497
$949$	1.65831e102	0.319140
$950$	−6.41850e101	−0.119116
$951$	−6.84286e102	−1.22464
$952$	−6.99239e102	−1.20684
$953$	7.22436e102	1.20252	0.601262	−	0.799052i	$-0.294665\pi$
$953$	7.22436e102	1.20252	0.601262	+	0.799052i	$0.294665\pi$
$954$	1.71260e102	0.274939
$955$	3.98402e102	0.616886
$956$	−3.79947e102	−0.567447
$957$	−7.27001e101	−0.104730
$958$	−1.53549e102	−0.213371
$959$	6.10314e102	0.818110
$960$	5.18891e102	0.670994
$961$	2.05862e103	2.56815
$962$	4.56180e102	0.549030
$963$	−3.72558e101	−0.0432600
$964$	8.43506e101	0.0944997
$965$	−5.19710e102	−0.561783
$966$	−1.33509e102	−0.139251
$967$	−4.25077e102	−0.427813	−0.213907	−	0.976854i	$-0.568619\pi$
$967$	−4.25077e102	−0.427813	−0.213907	+	0.976854i	$0.568619\pi$
$968$	−4.87314e102	−0.473270
$969$	−9.44569e102	−0.885245
$970$	−9.97116e102	−0.901822
$971$	−3.95129e102	−0.344886	−0.172443	−	0.985020i	$-0.555166\pi$
$971$	−3.95129e102	−0.344886	−0.172443	+	0.985020i	$0.555166\pi$
$972$	−3.57835e102	−0.301437
$973$	−5.74302e101	−0.0466925
$974$	1.55483e103	1.22011
$975$	−1.47931e102	−0.112047
$976$	7.16711e102	0.523993
$977$	−2.08430e103	−1.47095	−0.735475	−	0.677552i	$-0.763041\pi$
$977$	−2.08430e103	−1.47095	−0.735475	+	0.677552i	$0.763041\pi$
$978$	−1.18259e103	−0.805645
$979$	4.16462e102	0.273887
$980$	3.60551e102	0.228911
$981$	−1.04135e103	−0.638288
$982$	−8.81797e102	−0.521822
$983$	1.66610e103	0.951927	0.475964	−	0.879465i	$-0.342099\pi$
$983$	1.66610e103	0.951927	0.475964	+	0.879465i	$0.342099\pi$
$984$	2.36071e103	1.30230
$985$	−1.85190e102	−0.0986430
$986$	−4.71110e102	−0.242309
$987$	1.53906e103	0.764386
$988$	3.06762e102	0.147125
$989$	7.28928e102	0.337608
$990$	−4.10604e102	−0.183658
$991$	−1.55619e103	−0.672237	−0.336118	−	0.941820i	$-0.609114\pi$
$991$	−1.55619e103	−0.672237	−0.336118	+	0.941820i	$0.609114\pi$
$992$	3.55757e103	1.48423
$993$	−1.43908e103	−0.579876
$994$	−3.84334e102	−0.149582
$995$	1.31745e103	0.495266
$996$	−2.08787e102	−0.0758151
$997$	−3.68617e103	−1.29298	−0.646491	−	0.762921i	$-0.723764\pi$
$997$	−3.68617e103	−1.29298	−0.646491	+	0.762921i	$0.723764\pi$
$998$	2.52748e103	0.856415
$999$	4.33246e103	1.41816

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83774e10 q^{2} +2.28315e16 q^{3} -2.52566e20 q^{4} +1.12358e24 q^{5} -4.19583e26 q^{6} -8.82897e28 q^{7} +1.54896e31 q^{8} -3.13110e32 q^{9} +O(q^{10})\)	\(q-1.83774e10 q^{2} +2.28315e16 q^{3} -2.52566e20 q^{4} +1.12358e24 q^{5} -4.19583e26 q^{6} -8.82897e28 q^{7} +1.54896e31 q^{8} -3.13110e32 q^{9} -2.06484e34 q^{10} -6.35095e35 q^{11} -5.76645e36 q^{12} +1.50107e38 q^{13} +1.62254e39 q^{14} +2.56529e40 q^{15} -1.35571e41 q^{16} +5.11299e42 q^{17} +5.75416e42 q^{18} -8.09143e43 q^{19} -2.83777e44 q^{20} -2.01578e45 q^{21} +1.16714e46 q^{22} -3.60398e46 q^{23} +3.53651e47 q^{24} -4.31642e47 q^{25} -2.75859e48 q^{26} -2.61990e49 q^{27} +2.22990e49 q^{28} +5.01375e49 q^{29} -4.71434e50 q^{30} -5.34810e51 q^{31} -6.65202e51 q^{32} -1.45001e52 q^{33} -9.39635e52 q^{34} -9.92003e52 q^{35} +7.90809e52 q^{36} -1.65367e54 q^{37} +1.48700e54 q^{38} +3.42717e54 q^{39} +1.74038e55 q^{40} +6.67526e55 q^{41} +3.70449e55 q^{42} -2.02257e56 q^{43} +1.60403e56 q^{44} -3.51803e56 q^{45} +6.62318e56 q^{46} -7.63503e57 q^{47} -3.09528e57 q^{48} -1.27054e58 q^{49} +7.93246e57 q^{50} +1.16737e59 q^{51} -3.79120e58 q^{52} +2.97628e59 q^{53} +4.81470e59 q^{54} -7.13578e59 q^{55} -1.36758e60 q^{56} -1.84739e60 q^{57} -9.21399e59 q^{58} +1.35785e60 q^{59} -6.47904e60 q^{60} -5.28661e61 q^{61} +9.82844e61 q^{62} +2.76444e61 q^{63} +2.02274e62 q^{64} +1.68657e62 q^{65} +2.66475e62 q^{66} -1.38691e63 q^{67} -1.29137e63 q^{68} -8.22840e62 q^{69} +1.82305e63 q^{70} -2.36872e63 q^{71} -4.84996e63 q^{72} +1.10475e64 q^{73} +3.03903e64 q^{74} -9.85500e63 q^{75} +2.04362e64 q^{76} +5.60723e64 q^{77} -6.29825e64 q^{78} -7.32931e64 q^{79} -1.52324e65 q^{80} -3.36906e65 q^{81} -1.22674e66 q^{82} +3.62072e65 q^{83} +5.09118e65 q^{84} +5.74483e66 q^{85} +3.71696e66 q^{86} +1.14471e66 q^{87} -9.83738e66 q^{88} -6.55747e66 q^{89} +6.46524e66 q^{90} -1.32529e67 q^{91} +9.10241e66 q^{92} -1.22105e68 q^{93} +1.40312e68 q^{94} -9.09134e67 q^{95} -1.51875e68 q^{96} +4.82901e68 q^{97} +2.33493e68 q^{98} +1.98855e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots - 31\!\cdots\!35 q^{9}+O(q^{10}) \) 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9	\( 5 q - 18005734368 q^{2} - 48\!\cdots\!04 q^{3}+ \cdots + 58\!\cdots\!80 q^{99}+O(q^{100}) \) 5 * q - 18005734368 * q^2 - 4858082326815804 * q^3 + 1258222332330311336960 * q^4 - 1863826173406730009099250 * q^5 + 656206758200548766362988160 * q^6 + 76799665171164846436246213192 * q^7 - 45904305194055745607709713203200 * q^8 - 317098314648431447640165640938735 * q^9 + 44330196388334747724288536990904000 * q^10 - 60667038452283127772973811588820340 * q^11 - 11483075252723727688688753994339790848 * q^12 + 241757308976474000869098277194908009686 * q^13 + 354251192093531665156722201608564593920 * q^14 - 22070061029664005246083216762166031993000 * q^15 + 959158246463054504693505368032717942292480 * q^16 - 3406116484103989032025799295223462139713638 * q^17 + 24028760578245796491398335690330074428977056 * q^18 + 50409644862695734347948203723209710229820500 * q^19 - 1423124021474831957749573329409407107348736000 * q^20 + 3013464004165585730133470747616333350946636960 * q^21 - 11532803895526133094453480299474752792963837056 * q^22 + 49597077165419749499080141147449313474867772376 * q^23 - 3758573903021835292505270073849755869023436800 * q^24 + 464109230075747674561453215791202707168413296875 * q^25 - 16366243363702391437841515238911258759405955787840 * q^26 - 4656668144254073384201536267744600116223141335000 * q^27 - 145657936238300983941227399236934030905596038045696 * q^28 - 623609331535478016897341347681349171717970694417050 * q^29 - 3363430262026080628144709187077082169492181498016000 * q^30 - 7773979811443490840377264327630961134705736859811040 * q^31 - 59446525385187765185716890552455969166501734680363008 * q^32 - 114056291760419605293140369499335251414708842916007568 * q^33 - 257146382902997900108453969123952433606251002004626880 * q^34 - 746713702965644817139124842748848714607056852166946000 * q^35 - 2051949564713522439077005513759167028086223411246648320 * q^36 + 1173349927804932358065167442366744839628119054724224302 * q^37 + 118225357325580676139934406348110667239400005459024000 * q^38 + 14057637047001351842470294363781888979755467326981836280 * q^39 + 113448309945374158392264311043353386142011790732943360000 * q^40 + 126046983235211396249316718220813524712126370275682679410 * q^41 + 293618058653079520265272756273690037096976372387400909824 * q^42 + 182990795236310295463906097926157021228111368794869386156 * q^43 - 207861964397629572369029141530074424104092312018072801280 * q^44 - 1643209216033810606361059101690783215624601629799145190250 * q^45 - 10254004636983168196931301388746633342901210187441053098240 * q^46 - 10227620449924872974485942387482033943920758356350760046928 * q^47 - 32395077603800850016659260748043884333789001078303069569024 * q^48 - 18333133463047872956569862100374253860638045246565546349315 * q^49 + 36528582075561740316450944849185458926809558787823115500000 * q^50 + 118668467511484226348705374365583184000267089107653013314760 * q^51 + 942523544779067327174672695236090488789159958525129397368832 * q^52 + 632699876044410239466855544904774161379655010323706866957246 * q^53 + 180558070990413352422035814551902697653880540863671629472000 * q^54 + 908306905388987301982805388456202130484984202488366374469000 * q^55 - 3333324356971334653614007426143869616663160772285360681779200 * q^56 - 10204523476105540193819201045109650965597050176490899356681200 * q^57 - 21357003692165570079369319070573084097392679296022668457345600 * q^58 - 33658105593968338077893783802509858432791301363490818469557700 * q^59 + 4120988224178099264267892216282931461935581678787045796864000 * q^60 + 26493274349159915694337742892910871952893265772033046389592710 * q^61 + 44671386079622887685677726725261963790680651281391262992405504 * q^62 + 328016742630707922691415372382087941549150107260006661759940136 * q^63 + 1145396334142953198321101499067029773326674384142624569121832960 * q^64 + 32395374544526764253115310833548550857549161202925434554654500 * q^65 - 338570852359916448113902185281844117937336911423509879777978880 * q^66 - 1263671747756647516553966063420040358632142902313472768464353788 * q^67 - 4242259843001640357556603344412218995999623052710587648746797056 * q^68 - 6814317814451425604632002110369996993863432815743912687188684320 * q^69 - 12017797477418109745097884516334700669100677302053986880978752000 * q^70 - 11362995327515584413483941817933086342825689164345402588802686840 * q^71 + 33340305480431860824635017027459448788044465030309454443456921600 * q^72 + 33966190478000707541728805214544524983949148170634721693934875026 * q^73 + 33287841323757960873231466351855256670579388646335713232882057920 * q^74 + 133279503236831559979066107911998455423803652698542098545072437500 * q^75 + 183360103953987098564098859807800968353232769985153900286854041600 * q^76 - 68777883874935499089374017393044391085266332314302726754935189536 * q^77 - 57072566318401512231072936702879380800620122459787990692269387008 * q^78 - 368980120609165108452324012570275063461532695000205866878292977200 * q^79 - 2297307515344457444954054326919281387940022207684288488149352448000 * q^80 - 1101671322957552996191157562976784281568686466036132881049220065795 * q^81 - 931502706981052883685780503022082242955330053475976826093455630016 * q^82 + 1154866061089842220595327582106550433201200060522873707675675258516 * q^83 + 2982792317318014581404535874546389828859810656181796104246410117120 * q^84 + 7495188972487466607434575375594377348887576076812903274045952741500 * q^85 + 18898926811527982953627013747012343020261345543532646428747294271360 * q^86 + 12567354207673775260644045622671132292173268168085315900596903577400 * q^87 + 15163923620712287826914767806325902037685216056349718267565463961600 * q^88 - 18794883963687081977506023684762454245562992435196209807107213565150 * q^89 - 85191607767474905371023384802405560846731062106202026396755774248000 * q^90 - 80964793679514484977485771721533938042559852862777758867826841866640 * q^91 - 21013231692212615201045059193164259260053682303043508524037104345088 * q^92 - 112906043990099714252090302813260364787306717550744493130306572821888 * q^93 - 320329342040387206482715898781454186419182431678416100998048980820480 * q^94 + 150021391313508674306348088796351704171326160875536630528081545795000 * q^95 + 782790419970794266899143250915194035456012168622622133055202797813760 * q^96 + 368226872658277176269129285066418598650754906087385239386955040860522 * q^97 + 1783735577381778172290937711296356094085482547558896852990197505179424 * q^98 + 586262466890180722819447934223042169763434625676688596008715148885980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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