LMFDB - Embedded newform 1.30.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,30,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, 30, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 30 $
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:	$5.32780423830$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{51349}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 12837 $ x^2 - x - 12837
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-112.802$ 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)

$f(q)$	$=$	$q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} +O(q^{10})$	\(q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} -1.62061e14 q^{10} -7.97271e14 q^{11} -2.07203e15 q^{12} +1.10490e16 q^{13} -8.87385e14 q^{14} +9.00740e16 q^{15} -3.44548e17 q^{16} -7.47691e17 q^{17} +3.68651e18 q^{18} -2.49040e18 q^{19} -8.88669e17 q^{20} +4.93212e17 q^{21} -2.07880e19 q^{22} -1.63712e18 q^{23} +1.48837e20 q^{24} -1.47633e20 q^{25} +2.88091e20 q^{26} -1.05439e21 q^{27} -4.86602e18 q^{28} +1.87750e21 q^{29} +2.34858e21 q^{30} -4.79819e21 q^{31} -3.46987e21 q^{32} +1.15540e22 q^{33} -1.94952e22 q^{34} +2.11533e20 q^{35} +2.02152e22 q^{36} +7.91036e22 q^{37} -6.49345e22 q^{38} -1.60122e23 q^{39} +6.38347e22 q^{40} -6.06439e21 q^{41} +1.28600e22 q^{42} +6.72526e23 q^{43} -1.13992e23 q^{44} -8.78782e23 q^{45} -4.26862e22 q^{46} -1.90366e24 q^{47} +4.99319e24 q^{48} -3.21875e24 q^{49} -3.84936e24 q^{50} +1.08355e25 q^{51} +1.57976e24 q^{52} -1.65597e24 q^{53} -2.74920e25 q^{54} +4.95539e24 q^{55} +3.49535e23 q^{56} +3.60909e25 q^{57} +4.89537e25 q^{58} -8.93685e25 q^{59} +1.28786e25 q^{60} +4.59924e25 q^{61} -1.25108e26 q^{62} -4.81189e24 q^{63} +9.45048e25 q^{64} -6.86745e25 q^{65} +3.01259e26 q^{66} -1.04774e26 q^{67} -1.06903e26 q^{68} +2.37252e25 q^{69} +5.51549e24 q^{70} +1.75243e26 q^{71} -1.45209e27 q^{72} -4.56674e26 q^{73} +2.06254e27 q^{74} +2.13949e27 q^{75} -3.56072e26 q^{76} +2.71339e25 q^{77} -4.17501e27 q^{78} -3.28137e27 q^{79} +2.14152e27 q^{80} +5.57671e27 q^{81} -1.58122e26 q^{82} -4.40086e27 q^{83} +7.05183e25 q^{84} +4.64723e27 q^{85} +1.75354e28 q^{86} -2.72087e28 q^{87} +8.18824e27 q^{88} -6.06897e26 q^{89} -2.29133e28 q^{90} -3.76036e26 q^{91} -2.34072e26 q^{92} +6.95352e28 q^{93} -4.96357e28 q^{94} +1.54790e28 q^{95} +5.02853e28 q^{96} +1.44471e28 q^{97} -8.39253e28 q^{98} -1.12724e29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8640 q^{2} - 4967640 q^{3} - 89952256 q^{4} - 17477788500 q^{5} - 543908756736 q^{6} - 3020312682800 q^{7} + 3150297169920 q^{8} + 163469569523706 q^{9}+O(q^{10}) $ 2 * q + 8640 * q^2 - 4967640 * q^3 - 89952256 * q^4 - 17477788500 * q^5 - 543908756736 * q^6 - 3020312682800 * q^7 + 3150297169920 * q^8 + 163469569523706 * q^9	$ 2 q + 8640 q^{2} - 4967640 q^{3} - 89952256 q^{4} - 17477788500 q^{5} - 543908756736 q^{6} - 3020312682800 q^{7} + 3150297169920 q^{8} + 163469569523706 q^{9} + 34285866768000 q^{10} - 20\!\cdots\!16 q^{11}+ \cdots - 14\!\cdots\!48 q^{99}+O(q^{100}) $ 2 * q + 8640 * q^2 - 4967640 * q^3 - 89952256 * q^4 - 17477788500 * q^5 - 543908756736 * q^6 - 3020312682800 * q^7 + 3150297169920 * q^8 + 163469569523706 * q^9 + 34285866768000 * q^10 - 2055380519588616 * q^11 - 4290530276229120 * q^12 + 17139371179332220 * q^13 + 51175123348059648 * q^14 - 17192351392506000 * q^15 - 453469082063208448 * q^16 - 664795927907749980 * q^17 + 3301524864881760960 * q^18 + 1232169445452155080 * q^19 + 1734668101813248000 * q^20 - 27949113476248821696 * q^21 + 1145797484912974080 * q^22 - 18588430504374379920 * q^23 + 276660084668356362240 * q^24 - 207056854502617281250 * q^25 + 181912132597777755264 * q^26 - 1497723629507205824880 * q^27 + 690727602371844997120 * q^28 + 996096417765761595420 * q^29 + 4218653306492474688000 * q^30 - 1087258664181924030656 * q^31 - 8776107971762202869760 * q^32 - 428627571739162757280 * q^33 - 20940413403809031000192 * q^34 + 33844046536902649068000 * q^35 + 15071477561016892895232 * q^36 + 98878127759336138311660 * q^37 - 129833487351109249470720 * q^38 - 102115380027539490485328 * q^39 - 87313163228088238080000 * q^40 - 106699837259610025757676 * q^41 + 508720764303162503608320 * q^42 + 510640433114974031366200 * q^43 + 179059414424913371086848 * q^44 - 1127484267514124881450500 * q^45 + 252841215606439776920064 * q^46 - 4521107671109825795039520 * q^47 + 3955787455065109907374080 * q^48 + 2479210387392854586312114 * q^49 - 2813370491836752543000000 * q^50 + 11625042659032475755122384 * q^51 + 161134672249303679180800 * q^52 - 16141544629666790250663540 * q^53 - 19762893017614843677688320 * q^54 + 19124657798421120971058000 * q^55 - 39728224533177935352299520 * q^56 + 71545878452212360967003040 * q^57 + 64319996083339084169992320 * q^58 - 83497291515660150276062760 * q^59 + 37864111042200317349888000 * q^60 - 15876762943230179624113316 * q^61 - 189803556071494720042936320 * q^62 - 70756669640265175617870960 * q^63 + 245489542813624183222697984 * q^64 - 137266226551726798673511000 * q^65 + 510163218803227073870066688 * q^66 + 24468754434128844890782120 * q^67 - 126211850011481106095677440 * q^68 - 137724750477330905859409728 * q^69 - 580830557953085152481664000 * q^70 - 188428428253360067209577136 * q^71 - 1155729487872248549372067840 * q^72 + 995872721297568533052080980 * q^73 + 1717790650063115374837542528 * q^74 + 1573516410323456985690375000 * q^75 - 1223170019527541658110935040 * q^76 + 3784200478484579386131729600 * q^77 - 5186288053950004913991206400 * q^78 - 7218460852587735797823642080 * q^79 + 3368223393577622373924864000 * q^80 - 161317068789001769884865358 * q^81 + 1596346485209467674952913280 * q^82 + 2210846225248155523694669640 * q^83 + 6695585379451908015663218688 * q^84 + 3713635892367734904614943000 * q^85 + 20357697303796411232450244864 * q^86 - 35603430680717182696869516240 * q^87 - 8696387677835767416210063360 * q^88 + 5872964746600969363962031860 * q^89 - 18577446803723860542221616000 * q^90 - 18563550073842319069958420896 * q^91 + 3714393183413159199429918720 * q^92 + 104879397265778648689061310720 * q^93 - 4003342107705068447401638912 * q^94 - 26445947767121183571013410000 * q^95 - 253006717086360117933244416 * q^96 + 109649982219471997093227005380 * q^97 - 183262972410594366168864121920 * q^98 - 140506044809020243496724809448 * 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 $

$2$	26073.9	1.12531	0.562654	−	0.826693i	$-0.309780\pi$
$2$	26073.9	1.12531	0.562654	+	0.826693i	$0.309780\pi$
$3$	−1.44920e7	−1.74932	−0.874660	−	0.484736i	$-0.838916\pi$
$3$	−1.44920e7	−1.74932	−0.874660	+	0.484736i	$0.838916\pi$
$4$	1.42978e8	0.266317
$5$	−6.21544e9	−0.455415	−0.227707	−	0.973730i	$-0.573123\pi$
$5$	−6.21544e9	−0.455415	−0.227707	+	0.973730i	$0.573123\pi$
$6$	−3.77862e11	−1.96852
$7$	−3.40335e10	−0.0189664	−0.00948319	−	0.999955i	$-0.503019\pi$
$7$	−3.40335e10	−0.0189664	−0.00948319	+	0.999955i	$0.503019\pi$
$8$	−1.02703e13	−0.825619
$9$	1.41387e14	2.06012
$10$	−1.62061e14	−0.512481
$11$	−7.97271e14	−0.633012	−0.316506	−	0.948590i	$-0.602510\pi$
$11$	−7.97271e14	−0.633012	−0.316506	+	0.948590i	$0.602510\pi$
$12$	−2.07203e15	−0.465873
$13$	1.10490e16	0.778296	0.389148	−	0.921175i	$-0.372769\pi$
$13$	1.10490e16	0.778296	0.389148	+	0.921175i	$0.372769\pi$
$14$	−8.87385e14	−0.0213430
$15$	9.00740e16	0.796666
$16$	−3.44548e17	−1.19539
$17$	−7.47691e17	−1.07699	−0.538496	−	0.842628i	$-0.681007\pi$
$17$	−7.47691e17	−1.07699	−0.538496	+	0.842628i	$0.681007\pi$
$18$	3.68651e18	2.31827
$19$	−2.49040e18	−0.715060	−0.357530	−	0.933902i	$-0.616381\pi$
$19$	−2.49040e18	−0.715060	−0.357530	+	0.933902i	$0.616381\pi$
$20$	−8.88669e17	−0.121284
$21$	4.93212e17	0.0331783
$22$	−2.07880e19	−0.712333
$23$	−1.63712e18	−0.0294461	−0.0147231	−	0.999892i	$-0.504687\pi$
$23$	−1.63712e18	−0.0294461	−0.0147231	+	0.999892i	$0.504687\pi$
$24$	1.48837e20	1.44427
$25$	−1.47633e20	−0.792598
$26$	2.88091e20	0.875822
$27$	−1.05439e21	−1.85449
$28$	−4.86602e18	−0.00505106
$29$	1.87750e21	1.17168	0.585839	−	0.810427i	$-0.300765\pi$
$29$	1.87750e21	1.17168	0.585839	+	0.810427i	$0.300765\pi$
$30$	2.34858e21	0.896494
$31$	−4.79819e21	−1.13850	−0.569250	−	0.822165i	$-0.692766\pi$
$31$	−4.79819e21	−1.13850	−0.569250	+	0.822165i	$0.692766\pi$
$32$	−3.46987e21	−0.519564
$33$	1.15540e22	1.10734
$34$	−1.94952e22	−1.21195
$35$	2.11533e20	0.00863757
$36$	2.02152e22	0.548645
$37$	7.91036e22	1.44302	0.721508	−	0.692406i	$-0.243449\pi$
$37$	7.91036e22	1.44302	0.721508	+	0.692406i	$0.243449\pi$
$38$	−6.49345e22	−0.804662
$39$	−1.60122e23	−1.36149
$40$	6.38347e22	0.375999
$41$	−6.06439e21	−0.0249702	−0.0124851	−	0.999922i	$-0.503974\pi$
$41$	−6.06439e21	−0.0249702	−0.0124851	+	0.999922i	$0.503974\pi$
$42$	1.28600e22	0.0373358
$43$	6.72526e23	1.38809	0.694044	−	0.719933i	$-0.255827\pi$
$43$	6.72526e23	1.38809	0.694044	+	0.719933i	$0.255827\pi$
$44$	−1.13992e23	−0.168582
$45$	−8.78782e23	−0.938210
$46$	−4.26862e22	−0.0331359
$47$	−1.90366e24	−1.08186	−0.540928	−	0.841069i	$-0.681927\pi$
$47$	−1.90366e24	−1.08186	−0.540928	+	0.841069i	$0.681927\pi$
$48$	4.99319e24	2.09112
$49$	−3.21875e24	−0.999640
$50$	−3.84936e24	−0.891916
$51$	1.08355e25	1.88401
$52$	1.57976e24	0.207273
$53$	−1.65597e24	−0.164836	−0.0824181	−	0.996598i	$-0.526264\pi$
$53$	−1.65597e24	−0.164836	−0.0824181	+	0.996598i	$0.526264\pi$
$54$	−2.74920e25	−2.08688
$55$	4.95539e24	0.288283
$56$	3.49535e23	0.0156590
$57$	3.60909e25	1.25087
$58$	4.89537e25	1.31850
$59$	−8.93685e25	−1.87858	−0.939292	−	0.343120i	$-0.888516\pi$
$59$	−8.93685e25	−1.87858	−0.939292	+	0.343120i	$0.888516\pi$
$60$	1.28786e25	0.212165
$61$	4.59924e25	0.596216	0.298108	−	0.954532i	$-0.403644\pi$
$61$	4.59924e25	0.596216	0.298108	+	0.954532i	$0.403644\pi$
$62$	−1.25108e26	−1.28116
$63$	−4.81189e24	−0.0390731
$64$	9.45048e25	0.610723
$65$	−6.86745e25	−0.354447
$66$	3.01259e26	1.24610
$67$	−1.04774e26	−0.348472	−0.174236	−	0.984704i	$-0.555746\pi$
$67$	−1.04774e26	−0.348472	−0.174236	+	0.984704i	$0.555746\pi$
$68$	−1.06903e26	−0.286821
$69$	2.37252e25	0.0515107
$70$	5.51549e24	0.00971992
$71$	1.75243e26	0.251417	0.125709	−	0.992067i	$-0.459880\pi$
$71$	1.75243e26	0.251417	0.125709	+	0.992067i	$0.459880\pi$
$72$	−1.45209e27	−1.70088
$73$	−4.56674e26	−0.437950	−0.218975	−	0.975730i	$-0.570271\pi$
$73$	−4.56674e26	−0.437950	−0.218975	+	0.975730i	$0.570271\pi$
$74$	2.06254e27	1.62384
$75$	2.13949e27	1.38651
$76$	−3.56072e26	−0.190432
$77$	2.71339e25	0.0120059
$78$	−4.17501e27	−1.53209
$79$	−3.28137e27	−1.00107	−0.500533	−	0.865717i	$-0.666863\pi$
$79$	−3.28137e27	−1.00107	−0.500533	+	0.865717i	$0.666863\pi$
$80$	2.14152e27	0.544399
$81$	5.57671e27	1.18398
$82$	−1.58122e26	−0.0280991
$83$	−4.40086e27	−0.656002	−0.328001	−	0.944677i	$-0.606375\pi$
$83$	−4.40086e27	−0.656002	−0.328001	+	0.944677i	$0.606375\pi$
$84$	7.05183e25	0.00883593
$85$	4.64723e27	0.490478
$86$	1.75354e28	1.56202
$87$	−2.72087e28	−2.04964
$88$	8.18824e27	0.522627
$89$	−6.06897e26	−0.0328821	−0.0164411	−	0.999865i	$-0.505234\pi$
$89$	−6.06897e26	−0.0328821	−0.0164411	+	0.999865i	$0.505234\pi$
$90$	−2.29133e28	−1.05577
$91$	−3.76036e26	−0.0147615
$92$	−2.34072e26	−0.00784199
$93$	6.95352e28	1.99160
$94$	−4.96357e28	−1.21742
$95$	1.54790e28	0.325649
$96$	5.02853e28	0.908884
$97$	1.44471e28	0.224694	0.112347	−	0.993669i	$-0.464163\pi$
$97$	1.44471e28	0.224694	0.112347	+	0.993669i	$0.464163\pi$
$98$	−8.39253e28	−1.12490
$99$	−1.12724e29	−1.30408
$100$	−2.11082e28	−0.211082
$101$	−4.90236e28	−0.424371	−0.212185	−	0.977229i	$-0.568058\pi$
$101$	−4.90236e28	−0.424371	−0.212185	+	0.977229i	$0.568058\pi$
$102$	2.82524e29	2.12009
$103$	1.31966e29	0.859654	0.429827	−	0.902911i	$-0.358574\pi$
$103$	1.31966e29	0.859654	0.429827	+	0.902911i	$0.358574\pi$
$104$	−1.13477e29	−0.642576
$105$	−3.06553e27	−0.0151099
$106$	−4.31776e28	−0.185491
$107$	−2.31447e29	−0.867733	−0.433867	−	0.900977i	$-0.642851\pi$
$107$	−2.31447e29	−0.867733	−0.433867	+	0.900977i	$0.642851\pi$
$108$	−1.50754e29	−0.493882
$109$	6.73768e29	1.93119	0.965597	−	0.260043i	$-0.0837367\pi$
$109$	6.73768e29	1.93119	0.965597	+	0.260043i	$0.0837367\pi$
$110$	1.29206e29	0.324407
$111$	−1.14637e30	−2.52430
$112$	1.17262e28	0.0226723
$113$	5.10156e28	0.0867092	0.0433546	−	0.999060i	$-0.486195\pi$
$113$	5.10156e28	0.0867092	0.0433546	+	0.999060i	$0.486195\pi$
$114$	9.41029e29	1.40761
$115$	1.01755e28	0.0134102
$116$	2.68440e29	0.312037
$117$	1.56219e30	1.60339
$118$	−2.33019e30	−2.11398
$119$	2.54465e28	0.0204267
$120$	−9.25091e29	−0.657743
$121$	−9.50668e29	−0.599296
$122$	1.19920e30	0.670926
$123$	8.78850e28	0.0436808
$124$	−6.86034e29	−0.303201
$125$	2.07532e30	0.816375
$126$	−1.25465e29	−0.0439692
$127$	3.46836e30	1.08385	0.541926	−	0.840426i	$-0.317695\pi$
$127$	3.46836e30	1.08385	0.541926	+	0.840426i	$0.317695\pi$
$128$	4.32698e30	1.20681
$129$	−9.74624e30	−2.42821
$130$	−1.79061e30	−0.398862
$131$	−1.16207e30	−0.231631	−0.115816	−	0.993271i	$-0.536948\pi$
$131$	−1.16207e30	−0.231631	−0.115816	+	0.993271i	$0.536948\pi$
$132$	1.65197e30	0.294903
$133$	8.47570e28	0.0135621
$134$	−2.73186e30	−0.392138
$135$	6.55348e30	0.844564
$136$	7.67904e30	0.889186
$137$	−1.12214e31	−1.16842	−0.584210	−	0.811603i	$-0.698596\pi$
$137$	−1.12214e31	−1.16842	−0.584210	+	0.811603i	$0.698596\pi$
$138$	6.18608e29	0.0579654
$139$	−2.10245e30	−0.177423	−0.0887117	−	0.996057i	$-0.528275\pi$
$139$	−2.10245e30	−0.177423	−0.0887117	+	0.996057i	$0.528275\pi$
$140$	3.02445e28	0.00230033
$141$	2.75877e31	1.89251
$142$	4.56927e30	0.282922
$143$	−8.80906e30	−0.492671
$144$	−4.87146e31	−2.46265
$145$	−1.16695e31	−0.533600
$146$	−1.19073e31	−0.492828
$147$	4.66460e31	1.74869
$148$	1.13100e31	0.384299
$149$	−4.28030e30	−0.131909	−0.0659543	−	0.997823i	$-0.521009\pi$
$149$	−4.28030e30	−0.131909	−0.0659543	+	0.997823i	$0.521009\pi$
$150$	5.57849e31	1.56025
$151$	−9.32731e30	−0.236914	−0.118457	−	0.992959i	$-0.537795\pi$
$151$	−9.32731e30	−0.236914	−0.118457	+	0.992959i	$0.537795\pi$
$152$	2.55773e31	0.590367
$153$	−1.05714e32	−2.21874
$154$	7.07486e29	0.0135104
$155$	2.98229e31	0.518489
$156$	−2.28939e31	−0.362587
$157$	2.58823e31	0.373644	0.186822	−	0.982394i	$-0.440181\pi$
$157$	2.58823e31	0.373644	0.186822	+	0.982394i	$0.440181\pi$
$158$	−8.55583e31	−1.12651
$159$	2.39983e31	0.288351
$160$	2.15668e31	0.236617
$161$	5.57170e28	0.000558486 0
$162$	1.45407e32	1.33234
$163$	1.19680e31	0.100300	0.0501501	−	0.998742i	$-0.484030\pi$
$163$	1.19680e31	0.100300	0.0501501	+	0.998742i	$0.484030\pi$
$164$	−8.67072e29	−0.00664997
$165$	−7.18134e31	−0.504299
$166$	−1.14748e32	−0.738204
$167$	1.07804e32	0.635692	0.317846	−	0.948142i	$-0.397041\pi$
$167$	1.07804e32	0.635692	0.317846	+	0.948142i	$0.397041\pi$
$168$	−5.06545e30	−0.0273926
$169$	−7.94575e31	−0.394255
$170$	1.21171e32	0.551939
$171$	−3.52110e32	−1.47311
$172$	9.61562e31	0.369671
$173$	3.82198e32	1.35089	0.675446	−	0.737410i	$-0.263951\pi$
$173$	3.82198e32	1.35089	0.675446	+	0.737410i	$0.263951\pi$
$174$	−7.09436e32	−2.30648
$175$	5.02445e30	0.0150327
$176$	2.74698e32	0.756698
$177$	1.29513e33	3.28624
$178$	−1.58242e31	−0.0370025
$179$	−5.24041e32	−1.12979	−0.564893	−	0.825164i	$-0.691083\pi$
$179$	−5.24041e32	−1.12979	−0.564893	+	0.825164i	$0.691083\pi$
$180$	−1.25646e32	−0.249861
$181$	−7.54402e32	−1.38441	−0.692203	−	0.721703i	$-0.743360\pi$
$181$	−7.54402e32	−1.38441	−0.692203	+	0.721703i	$0.743360\pi$
$182$	−9.80473e30	−0.0166112
$183$	−6.66521e32	−1.04297
$184$	1.68138e31	0.0243113
$185$	−4.91664e32	−0.657170
$186$	1.81306e33	2.24116
$187$	5.96112e32	0.681750
$188$	−2.72180e32	−0.288116
$189$	3.58844e31	0.0351730
$190$	4.03597e32	0.366455
$191$	−1.08024e33	−0.908947	−0.454473	−	0.890760i	$-0.650173\pi$
$191$	−1.08024e33	−0.908947	−0.454473	+	0.890760i	$0.650173\pi$
$192$	−1.36956e33	−1.06835
$193$	1.91169e33	1.38305	0.691524	−	0.722354i	$-0.256940\pi$
$193$	1.91169e33	1.38305	0.691524	+	0.722354i	$0.256940\pi$
$194$	3.76693e32	0.252849
$195$	9.95229e32	0.620042
$196$	−4.60209e32	−0.266221
$197$	−2.82411e33	−1.51747	−0.758737	−	0.651397i	$-0.774183\pi$
$197$	−2.82411e33	−1.51747	−0.758737	+	0.651397i	$0.774183\pi$
$198$	−2.93915e33	−1.46749
$199$	2.05181e33	0.952288	0.476144	−	0.879367i	$-0.342034\pi$
$199$	2.05181e33	0.952288	0.476144	+	0.879367i	$0.342034\pi$
$200$	1.51624e33	0.654384
$201$	1.51838e33	0.609590
$202$	−1.27824e33	−0.477547
$203$	−6.38978e31	−0.0222225
$204$	1.54924e33	0.501742
$205$	3.76929e31	0.0113718
$206$	3.44088e33	0.967375
$207$	−2.31468e32	−0.0606626
$208$	−3.80692e33	−0.930369
$209$	1.98553e33	0.452641
$210$	−7.99303e31	−0.0170032
$211$	−4.24073e33	−0.842063	−0.421032	−	0.907046i	$-0.638332\pi$
$211$	−4.24073e33	−0.842063	−0.421032	+	0.907046i	$0.638332\pi$
$212$	−2.36767e32	−0.0438986
$213$	−2.53962e33	−0.439809
$214$	−6.03472e33	−0.976466
$215$	−4.18005e33	−0.632155
$216$	1.08289e34	1.53111
$217$	1.63299e32	0.0215932
$218$	1.75678e34	2.17319
$219$	6.61810e33	0.766115
$220$	7.08510e32	0.0767745
$221$	−8.26125e33	−0.838219
$222$	−2.98903e34	−2.84061
$223$	1.95826e34	1.74362	0.871808	−	0.489848i	$-0.162948\pi$
$223$	1.95826e34	1.74362	0.871808	+	0.489848i	$0.162948\pi$
$224$	1.18092e32	0.00985425
$225$	−2.08734e34	−1.63285
$226$	1.33017e33	0.0975745
$227$	1.22424e34	0.842345	0.421173	−	0.906980i	$-0.361619\pi$
$227$	1.22424e34	0.842345	0.421173	+	0.906980i	$0.361619\pi$
$228$	5.16018e33	0.333127
$229$	5.07275e33	0.307347	0.153673	−	0.988122i	$-0.450890\pi$
$229$	5.07275e33	0.307347	0.153673	+	0.988122i	$0.450890\pi$
$230$	2.65314e32	0.0150906
$231$	−3.93224e32	−0.0210023
$232$	−1.92825e34	−0.967361
$233$	−2.33456e34	−1.10038	−0.550192	−	0.835038i	$-0.685446\pi$
$233$	−2.33456e34	−1.10038	−0.550192	+	0.835038i	$0.685446\pi$
$234$	4.07323e34	1.80430
$235$	1.18321e34	0.492693
$236$	−1.27777e34	−0.500298
$237$	4.75536e34	1.75119
$238$	6.63490e32	0.0229863
$239$	−1.69274e34	−0.551849	−0.275925	−	0.961179i	$-0.588984\pi$
$239$	−1.69274e34	−0.551849	−0.275925	+	0.961179i	$0.588984\pi$
$240$	−3.10349e34	−0.952328
$241$	−2.26884e34	−0.655476	−0.327738	−	0.944769i	$-0.606286\pi$
$241$	−2.26884e34	−0.655476	−0.327738	+	0.944769i	$0.606286\pi$
$242$	−2.47876e34	−0.674392
$243$	−8.45454e33	−0.216670
$244$	6.57588e33	0.158782
$245$	2.00059e34	0.455251
$246$	2.29151e33	0.0491543
$247$	−2.75165e34	−0.556528
$248$	4.92790e34	0.939967
$249$	6.37771e34	1.14756
$250$	5.41117e34	0.918673
$251$	−9.82834e34	−1.57475	−0.787374	−	0.616475i	$-0.788560\pi$
$251$	−9.82834e34	−1.57475	−0.787374	+	0.616475i	$0.788560\pi$
$252$	−6.87992e32	−0.0104058
$253$	1.30523e33	0.0186398
$254$	9.04337e34	1.21967
$255$	−6.73475e34	−0.858004
$256$	6.20845e34	0.747315
$257$	−8.53561e34	−0.970966	−0.485483	−	0.874246i	$-0.661356\pi$
$257$	−8.53561e34	−0.970966	−0.485483	+	0.874246i	$0.661356\pi$
$258$	−2.54122e35	−2.73248
$259$	−2.69217e33	−0.0273688
$260$	−9.81891e33	−0.0943952
$261$	2.65454e35	2.41380
$262$	−3.02996e34	−0.260656
$263$	2.07906e35	1.69243	0.846213	−	0.532845i	$-0.178877\pi$
$263$	2.07906e35	1.69243	0.846213	+	0.532845i	$0.178877\pi$
$264$	−1.18664e35	−0.914242
$265$	1.02926e34	0.0750688
$266$	2.20995e33	0.0152615
$267$	8.79513e33	0.0575214
$268$	−1.49803e34	−0.0928039
$269$	−2.34883e35	−1.37862	−0.689309	−	0.724468i	$-0.742086\pi$
$269$	−2.34883e35	−1.37862	−0.689309	+	0.724468i	$0.742086\pi$
$270$	1.70875e35	0.950394
$271$	−8.82959e34	−0.465463	−0.232732	−	0.972541i	$-0.574766\pi$
$271$	−8.82959e34	−0.465463	−0.232732	+	0.972541i	$0.574766\pi$
$272$	2.57616e35	1.28743
$273$	5.44951e33	0.0258225
$274$	−2.92586e35	−1.31483
$275$	1.17703e35	0.501724
$276$	3.39217e33	0.0137182
$277$	−7.48695e34	−0.287308	−0.143654	−	0.989628i	$-0.545885\pi$
$277$	−7.48695e34	−0.287308	−0.143654	+	0.989628i	$0.545885\pi$
$278$	−5.48191e34	−0.199656
$279$	−6.78402e35	−2.34545
$280$	−2.17251e33	−0.00713134
$281$	3.79424e35	1.18272	0.591361	−	0.806407i	$-0.298591\pi$
$281$	3.79424e35	1.18272	0.591361	+	0.806407i	$0.298591\pi$
$282$	7.19320e35	2.12966
$283$	5.23811e35	1.47323	0.736616	−	0.676311i	$-0.236422\pi$
$283$	5.23811e35	1.47323	0.736616	+	0.676311i	$0.236422\pi$
$284$	2.50558e34	0.0669566
$285$	−2.24321e35	−0.569664
$286$	−2.29686e35	−0.554406
$287$	2.06392e32	0.000473593 0
$288$	−4.90595e35	−1.07037
$289$	7.70734e34	0.159914
$290$	−3.04269e35	−0.600464
$291$	−2.09367e35	−0.393061
$292$	−6.52941e34	−0.116633
$293$	−8.91980e35	−1.51626	−0.758131	−	0.652102i	$-0.773887\pi$
$293$	−8.91980e35	−1.51626	−0.758131	+	0.652102i	$0.773887\pi$
$294$	1.21624e36	1.96782
$295$	5.55465e35	0.855534
$296$	−8.12420e35	−1.19138
$297$	8.40632e35	1.17392
$298$	−1.11604e35	−0.148438
$299$	−1.80886e34	−0.0229178
$300$	3.05899e35	0.369250
$301$	−2.28884e34	−0.0263270
$302$	−2.43200e35	−0.266601
$303$	7.10449e35	0.742360
$304$	8.58064e35	0.854777
$305$	−2.85863e35	−0.271525
$306$	−2.75637e36	−2.49676
$307$	6.34791e35	0.548434	0.274217	−	0.961668i	$-0.411581\pi$
$307$	6.34791e35	0.548434	0.274217	+	0.961668i	$0.411581\pi$
$308$	3.87954e33	0.00319738
$309$	−1.91246e36	−1.50381
$310$	7.77599e35	0.583460
$311$	1.79660e36	1.28655	0.643273	−	0.765637i	$-0.277576\pi$
$311$	1.79660e36	1.28655	0.643273	+	0.765637i	$0.277576\pi$
$312$	1.64451e36	1.12407
$313$	−2.68729e36	−1.75357	−0.876783	−	0.480886i	$-0.840315\pi$
$313$	−2.68729e36	−1.75357	−0.876783	+	0.480886i	$0.840315\pi$
$314$	6.74853e35	0.420465
$315$	2.99080e34	0.0177944
$316$	−4.69163e35	−0.266601
$317$	1.03006e36	0.559119	0.279559	−	0.960128i	$-0.409812\pi$
$317$	1.03006e36	0.559119	0.279559	+	0.960128i	$0.409812\pi$
$318$	6.25729e35	0.324484
$319$	−1.49687e36	−0.741687
$320$	−5.87389e35	−0.278132
$321$	3.35412e36	1.51794
$322$	1.45276e33	0.000628469 0
$323$	1.86205e36	0.770114
$324$	7.97344e35	0.315314
$325$	−1.63120e36	−0.616876
$326$	3.12053e35	0.112869
$327$	−9.76422e36	−3.37828
$328$	6.22833e34	0.0206158
$329$	6.47880e34	0.0205189
$330$	−1.87246e36	−0.567492
$331$	1.57492e36	0.456827	0.228414	−	0.973564i	$-0.426646\pi$
$331$	1.57492e36	0.456827	0.228414	+	0.973564i	$0.426646\pi$
$332$	−6.29224e35	−0.174704
$333$	1.11842e37	2.97279
$334$	2.81087e36	0.715348
$335$	6.51216e35	0.158699
$336$	−1.69935e35	−0.0396611
$337$	−3.02595e36	−0.676438	−0.338219	−	0.941067i	$-0.609824\pi$
$337$	−3.02595e36	−0.676438	−0.338219	+	0.941067i	$0.609824\pi$
$338$	−2.07177e36	−0.443658
$339$	−7.39316e35	−0.151682
$340$	6.64450e35	0.130622
$341$	3.82546e36	0.720684
$342$	−9.18090e36	−1.65770
$343$	2.19130e35	0.0379259
$344$	−6.90707e36	−1.14603
$345$	−1.47462e35	−0.0234587
$346$	9.96541e36	1.52017
$347$	4.44778e36	0.650678	0.325339	−	0.945597i	$-0.394522\pi$
$347$	4.44778e36	0.650678	0.325339	+	0.945597i	$0.394522\pi$
$348$	−3.89023e36	−0.545854
$349$	−9.68519e35	−0.130359	−0.0651793	−	0.997874i	$-0.520762\pi$
$349$	−9.68519e35	−0.130359	−0.0651793	+	0.997874i	$0.520762\pi$
$350$	1.31007e35	0.0169164
$351$	−1.16499e37	−1.44335
$352$	2.76643e36	0.328890
$353$	−9.40660e36	−1.07325	−0.536623	−	0.843822i	$-0.680300\pi$
$353$	−9.40660e36	−1.07325	−0.536623	+	0.843822i	$0.680300\pi$
$354$	3.37690e37	3.69804
$355$	−1.08921e36	−0.114499
$356$	−8.67726e34	−0.00875705
$357$	−3.68770e35	−0.0357328
$358$	−1.36638e37	−1.27136
$359$	2.90920e36	0.259958	0.129979	−	0.991517i	$-0.458509\pi$
$359$	2.90920e36	0.259958	0.129979	+	0.991517i	$0.458509\pi$
$360$	9.02539e36	0.774604
$361$	−5.92772e36	−0.488690
$362$	−1.96702e37	−1.55788
$363$	1.37771e37	1.04836
$364$	−5.37647e34	−0.00393122
$365$	2.83843e36	0.199449
$366$	−1.73788e37	−1.17366
$367$	3.00435e36	0.195026	0.0975131	−	0.995234i	$-0.468911\pi$
$367$	3.00435e36	0.195026	0.0975131	+	0.995234i	$0.468911\pi$
$368$	5.64069e35	0.0351997
$369$	−8.57426e35	−0.0514416
$370$	−1.28196e37	−0.739519
$371$	5.63584e34	0.00312634
$372$	9.94198e36	0.530396
$373$	2.82375e37	1.44893	0.724466	−	0.689310i	$-0.242086\pi$
$373$	2.82375e37	1.44893	0.724466	+	0.689310i	$0.242086\pi$
$374$	1.55430e37	0.767178
$375$	−3.00755e37	−1.42810
$376$	1.95512e37	0.893201
$377$	2.07445e37	0.911913
$378$	9.35647e35	0.0395805
$379$	1.51814e37	0.618079	0.309039	−	0.951049i	$-0.399993\pi$
$379$	1.51814e37	0.618079	0.309039	+	0.951049i	$0.399993\pi$
$380$	2.21314e36	0.0867256
$381$	−5.02634e37	−1.89601
$382$	−2.81662e37	−1.02284
$383$	−2.59896e37	−0.908692	−0.454346	−	0.890825i	$-0.650127\pi$
$383$	−2.59896e37	−0.908692	−0.454346	+	0.890825i	$0.650127\pi$
$384$	−6.27065e37	−2.11111
$385$	−1.68649e35	−0.00546768
$386$	4.98453e37	1.55635
$387$	9.50865e37	2.85963
$388$	2.06561e36	0.0598397
$389$	−4.80732e37	−1.34163	−0.670816	−	0.741623i	$-0.734056\pi$
$389$	−4.80732e37	−1.34163	−0.670816	+	0.741623i	$0.734056\pi$
$390$	2.59495e37	0.697738
$391$	1.22406e36	0.0317133
$392$	3.30576e37	0.825322
$393$	1.68406e37	0.405197
$394$	−7.36356e37	−1.70762
$395$	2.03952e37	0.455900
$396$	−1.61170e37	−0.347299
$397$	−4.33277e37	−0.900126	−0.450063	−	0.892997i	$-0.648599\pi$
$397$	−4.33277e37	−0.900126	−0.450063	+	0.892997i	$0.648599\pi$
$398$	5.34988e37	1.07162
$399$	−1.22830e36	−0.0237245
$400$	5.08666e37	0.947465
$401$	−2.87417e37	−0.516320	−0.258160	−	0.966102i	$-0.583116\pi$
$401$	−2.87417e37	−0.516320	−0.258160	+	0.966102i	$0.583116\pi$
$402$	3.95901e37	0.685976
$403$	−5.30153e37	−0.886090
$404$	−7.00928e36	−0.113017
$405$	−3.46617e37	−0.539203
$406$	−1.66606e36	−0.0250072
$407$	−6.30670e37	−0.913446
$408$	−1.11284e38	−1.55547
$409$	8.54677e37	1.15296	0.576480	−	0.817112i	$-0.304426\pi$
$409$	8.54677e37	1.15296	0.576480	+	0.817112i	$0.304426\pi$
$410$	9.82800e35	0.0127967
$411$	1.62620e38	2.04394
$412$	1.88683e37	0.228940
$413$	3.04152e36	0.0356299
$414$	−6.03528e36	−0.0682641
$415$	2.73533e37	0.298753
$416$	−3.83387e37	−0.404375
$417$	3.04686e37	0.310370
$418$	5.17704e37	0.509361
$419$	−5.26548e37	−0.500420	−0.250210	−	0.968192i	$-0.580500\pi$
$419$	−5.26548e37	−0.500420	−0.250210	+	0.968192i	$0.580500\pi$
$420$	−4.38302e35	−0.00402401
$421$	9.94249e37	0.881870	0.440935	−	0.897539i	$-0.354647\pi$
$421$	9.94249e37	0.881870	0.440935	+	0.897539i	$0.354647\pi$
$422$	−1.10572e38	−0.947580
$423$	−2.69152e38	−2.22876
$424$	1.70074e37	0.136092
$425$	1.10384e38	0.853622
$426$	−6.62178e37	−0.494921
$427$	−1.56528e36	−0.0113081
$428$	−3.30917e37	−0.231092
$429$	1.27661e38	0.861839
$430$	−1.08990e38	−0.711369
$431$	−1.96737e38	−1.24155	−0.620777	−	0.783987i	$-0.713183\pi$
$431$	−1.96737e38	−1.24155	−0.620777	+	0.783987i	$0.713183\pi$
$432$	3.63287e38	2.21685
$433$	8.93739e37	0.527396	0.263698	−	0.964605i	$-0.415058\pi$
$433$	8.93739e37	0.527396	0.263698	+	0.964605i	$0.415058\pi$
$434$	4.25784e36	0.0242990
$435$	1.69114e38	0.933437
$436$	9.63337e37	0.514309
$437$	4.07710e36	0.0210557
$438$	1.72560e38	0.862115
$439$	−3.31662e38	−1.60310	−0.801548	−	0.597930i	$-0.795990\pi$
$439$	−3.31662e38	−1.60310	−0.801548	+	0.597930i	$0.795990\pi$
$440$	−5.08935e37	−0.238012
$441$	−4.55089e38	−2.05938
$442$	−2.15403e38	−0.943254
$443$	2.62823e38	1.11380	0.556902	−	0.830578i	$-0.311990\pi$
$443$	2.62823e38	1.11380	0.556902	+	0.830578i	$0.311990\pi$
$444$	−1.63905e38	−0.672262
$445$	3.77213e36	0.0149750
$446$	5.10596e38	1.96210
$447$	6.20299e37	0.230750
$448$	−3.21632e36	−0.0115832
$449$	1.08508e38	0.378348	0.189174	−	0.981944i	$-0.439419\pi$
$449$	1.08508e38	0.378348	0.189174	+	0.981944i	$0.439419\pi$
$450$	−5.44250e38	−1.83746
$451$	4.83496e36	0.0158064
$452$	7.29408e36	0.0230921
$453$	1.35171e38	0.414439
$454$	3.19206e38	0.947897
$455$	2.33723e36	0.00672258
$456$	−3.70665e38	−1.03274
$457$	−3.49142e38	−0.942360	−0.471180	−	0.882037i	$-0.656172\pi$
$457$	−3.49142e38	−0.942360	−0.471180	+	0.882037i	$0.656172\pi$
$458$	1.32266e38	0.345860
$459$	7.88356e38	1.99728
$460$	1.45486e36	0.00357136
$461$	5.84500e38	1.39034	0.695171	−	0.718845i	$-0.255329\pi$
$461$	5.84500e38	1.39034	0.695171	+	0.718845i	$0.255329\pi$
$462$	−1.02529e37	−0.0236340
$463$	2.77160e38	0.619164	0.309582	−	0.950873i	$-0.399811\pi$
$463$	2.77160e38	0.619164	0.309582	+	0.950873i	$0.399811\pi$
$464$	−6.46889e38	−1.40062
$465$	−4.32192e38	−0.907004
$466$	−6.08712e38	−1.23827
$467$	−9.01377e38	−1.77751	−0.888754	−	0.458384i	$-0.848429\pi$
$467$	−9.01377e38	−1.77751	−0.888754	+	0.458384i	$0.848429\pi$
$468$	2.23358e38	0.427008
$469$	3.56582e36	0.00660926
$470$	3.08508e38	0.554431
$471$	−3.75086e38	−0.653623
$472$	9.17845e38	1.55099
$473$	−5.36186e38	−0.878676
$474$	1.23991e39	1.97062
$475$	3.67665e38	0.566755
$476$	3.63828e36	0.00543996
$477$	−2.34133e38	−0.339583
$478$	−4.41363e38	−0.621000
$479$	5.62143e38	0.767330	0.383665	−	0.923472i	$-0.374662\pi$
$479$	5.62143e38	0.767330	0.383665	+	0.923472i	$0.374662\pi$
$480$	−3.12546e38	−0.413919
$481$	8.74016e38	1.12309
$482$	−5.91575e38	−0.737612
$483$	−8.07450e35	−0.000976972 0
$484$	−1.35924e38	−0.159602
$485$	−8.97952e37	−0.102329
$486$	−2.20443e38	−0.243820
$487$	−1.05085e39	−1.12816	−0.564081	−	0.825720i	$-0.690769\pi$
$487$	−1.05085e39	−1.12816	−0.564081	+	0.825720i	$0.690769\pi$
$488$	−4.72358e38	−0.492247
$489$	−1.73440e38	−0.175457
$490$	5.21633e38	0.512297
$491$	7.99399e38	0.762223	0.381112	−	0.924529i	$-0.375541\pi$
$491$	7.99399e38	0.762223	0.381112	+	0.924529i	$0.375541\pi$
$492$	1.25656e37	0.0116329
$493$	−1.40379e39	−1.26189
$494$	−7.17462e38	−0.626265
$495$	7.00628e38	0.593898
$496$	1.65321e39	1.36095
$497$	−5.96413e36	−0.00476848
$498$	1.66292e39	1.29136
$499$	1.14067e39	0.860401	0.430201	−	0.902733i	$-0.358443\pi$
$499$	1.14067e39	0.860401	0.430201	+	0.902733i	$0.358443\pi$
$500$	2.96724e38	0.217414
$501$	−1.56229e39	−1.11203
$502$	−2.56263e39	−1.77208
$503$	3.45164e38	0.231894	0.115947	−	0.993255i	$-0.463010\pi$
$503$	3.45164e38	0.231894	0.115947	+	0.993255i	$0.463010\pi$
$504$	4.94197e37	0.0322595
$505$	3.04703e38	0.193265
$506$	3.40325e37	0.0209755
$507$	1.15150e39	0.689679
$508$	4.95898e38	0.288648
$509$	−7.06121e37	−0.0399458	−0.0199729	−	0.999801i	$-0.506358\pi$
$509$	−7.06121e37	−0.0399458	−0.0199729	+	0.999801i	$0.506358\pi$
$510$	−1.75601e39	−0.965518
$511$	1.55422e37	0.00830633
$512$	−7.04246e38	−0.365856
$513$	2.62585e39	1.32607
$514$	−2.22557e39	−1.09264
$515$	−8.20230e38	−0.391499
$516$	−1.39349e39	−0.646672
$517$	1.51773e39	0.684828
$518$	−7.01953e37	−0.0307983
$519$	−5.53881e39	−2.36314
$520$	7.05310e38	0.292639
$521$	3.46255e39	1.39717	0.698585	−	0.715528i	$-0.253814\pi$
$521$	3.46255e39	1.39717	0.698585	+	0.715528i	$0.253814\pi$
$522$	6.92142e39	2.71627
$523$	−1.15392e39	−0.440453	−0.220227	−	0.975449i	$-0.570680\pi$
$523$	−1.15392e39	−0.440453	−0.220227	+	0.975449i	$0.570680\pi$
$524$	−1.66149e38	−0.0616872
$525$	−7.28143e37	−0.0262970
$526$	5.42093e39	1.90450
$527$	3.58756e39	1.22616
$528$	−3.98092e39	−1.32371
$529$	−3.08838e39	−0.999133
$530$	2.68368e38	0.0844754
$531$	−1.26355e40	−3.87011
$532$	1.21184e37	0.00361181
$533$	−6.70055e37	−0.0194342
$534$	2.29323e38	0.0647292
$535$	1.43854e39	0.395178
$536$	1.07606e39	0.287705
$537$	7.59439e39	1.97636
$538$	−6.12432e39	−1.55137
$539$	2.56621e39	0.632784
$540$	9.37001e38	0.224921
$541$	−2.74672e39	−0.641879	−0.320940	−	0.947100i	$-0.603999\pi$
$541$	−2.74672e39	−0.641879	−0.320940	+	0.947100i	$0.603999\pi$
$542$	−2.30222e39	−0.523789
$543$	1.09328e40	2.42177
$544$	2.59439e39	0.559567
$545$	−4.18776e39	−0.879494
$546$	1.42090e38	0.0290583
$547$	−5.50487e39	−1.09630	−0.548152	−	0.836379i	$-0.684669\pi$
$547$	−5.50487e39	−1.09630	−0.548152	+	0.836379i	$0.684669\pi$
$548$	−1.60441e39	−0.311170
$549$	6.50273e39	1.22828
$550$	3.06899e39	0.564593
$551$	−4.67573e39	−0.837820
$552$	−2.43666e38	−0.0425282
$553$	1.11677e38	0.0189866
$554$	−1.95214e39	−0.323310
$555$	7.12518e39	1.14960
$556$	−3.00603e38	−0.0472508
$557$	−4.48537e39	−0.686908	−0.343454	−	0.939170i	$-0.611597\pi$
$557$	−4.48537e39	−0.686908	−0.343454	+	0.939170i	$0.611597\pi$
$558$	−1.76886e40	−2.63935
$559$	7.43075e39	1.08034
$560$	−7.28833e37	−0.0103253
$561$	−8.63885e39	−1.19260
$562$	9.89305e39	1.33093
$563$	6.55822e38	0.0859834	0.0429917	−	0.999075i	$-0.486311\pi$
$563$	6.55822e38	0.0859834	0.0429917	+	0.999075i	$0.486311\pi$
$564$	3.94443e39	0.504008
$565$	−3.17084e38	−0.0394886
$566$	1.36578e40	1.65784
$567$	−1.89795e38	−0.0224559
$568$	−1.79981e39	−0.207575
$569$	−1.62256e40	−1.82420	−0.912099	−	0.409970i	$-0.865539\pi$
$569$	−1.62256e40	−1.82420	−0.912099	+	0.409970i	$0.865539\pi$
$570$	−5.84891e39	−0.641047
$571$	9.28706e39	0.992327	0.496163	−	0.868229i	$-0.334742\pi$
$571$	9.28706e39	0.992327	0.496163	+	0.868229i	$0.334742\pi$
$572$	−1.25950e39	−0.131206
$573$	1.56549e40	1.59004
$574$	5.38145e36	0.000532938 0
$575$	2.41693e38	0.0233389
$576$	1.33617e40	1.25816
$577$	−2.84801e39	−0.261513	−0.130756	−	0.991415i	$-0.541741\pi$
$577$	−2.84801e39	−0.261513	−0.130756	+	0.991415i	$0.541741\pi$
$578$	2.00960e39	0.179952
$579$	−2.77042e40	−2.41939
$580$	−1.66847e39	−0.142106
$581$	1.49776e38	0.0124420
$582$	−5.45902e39	−0.442315
$583$	1.32026e39	0.104343
$584$	4.69019e39	0.361580
$585$	−9.70968e39	−0.730205
$586$	−2.32574e40	−1.70626
$587$	−5.47078e39	−0.391559	−0.195779	−	0.980648i	$-0.562724\pi$
$587$	−5.47078e39	−0.391559	−0.195779	+	0.980648i	$0.562724\pi$
$588$	6.66934e39	0.465705
$589$	1.19494e40	0.814095
$590$	1.44831e40	0.962739
$591$	4.09269e40	2.65455
$592$	−2.72550e40	−1.72497
$593$	2.22596e40	1.37475	0.687376	−	0.726302i	$-0.258762\pi$
$593$	2.22596e40	1.37475	0.687376	+	0.726302i	$0.258762\pi$
$594$	2.19186e40	1.32102
$595$	−1.58161e38	−0.00930260
$596$	−6.11986e38	−0.0351294
$597$	−2.97348e40	−1.66586
$598$	−4.71641e38	−0.0257896
$599$	2.08204e39	0.111122	0.0555611	−	0.998455i	$-0.482305\pi$
$599$	2.08204e39	0.111122	0.0555611	+	0.998455i	$0.482305\pi$
$600$	−2.19733e40	−1.14473
$601$	−1.47384e40	−0.749498	−0.374749	−	0.927126i	$-0.622271\pi$
$601$	−1.47384e40	−0.749498	−0.374749	+	0.927126i	$0.622271\pi$
$602$	−5.96790e38	−0.0296260
$603$	−1.48137e40	−0.717895
$604$	−1.33360e39	−0.0630941
$605$	5.90882e39	0.272928
$606$	1.85242e40	0.835383
$607$	1.37809e40	0.606796	0.303398	−	0.952864i	$-0.401879\pi$
$607$	1.37809e40	0.606796	0.303398	+	0.952864i	$0.401879\pi$
$608$	8.64138e39	0.371519
$609$	9.26005e38	0.0388743
$610$	−7.45357e39	−0.305550
$611$	−2.10335e40	−0.842004
$612$	−1.51147e40	−0.590886
$613$	1.47390e40	0.562717	0.281358	−	0.959603i	$-0.409215\pi$
$613$	1.47390e40	0.562717	0.281358	+	0.959603i	$0.409215\pi$
$614$	1.65515e40	0.617157
$615$	−5.46244e38	−0.0198929
$616$	−2.78674e38	−0.00991234
$617$	4.06519e39	0.141236	0.0706181	−	0.997503i	$-0.477503\pi$
$617$	4.06519e39	0.141236	0.0706181	+	0.997503i	$0.477503\pi$
$618$	−4.98652e40	−1.69225
$619$	3.64687e40	1.20894	0.604472	−	0.796627i	$-0.293384\pi$
$619$	3.64687e40	1.20894	0.604472	+	0.796627i	$0.293384\pi$
$620$	4.26400e39	0.138082
$621$	1.72616e39	0.0546077
$622$	4.68444e40	1.44776
$623$	2.06548e37	0.000623655 0
$624$	5.51698e40	1.62751
$625$	1.45997e40	0.420809
$626$	−7.00682e40	−1.97330
$627$	−2.87742e40	−0.791815
$628$	3.70059e39	0.0995076
$629$	−5.91450e40	−1.55412
$630$	7.79818e38	0.0200242
$631$	−6.88296e40	−1.72723	−0.863613	−	0.504155i	$-0.831804\pi$
$631$	−6.88296e40	−1.72723	−0.863613	+	0.504155i	$0.831804\pi$
$632$	3.37008e40	0.826500
$633$	6.14565e40	1.47304
$634$	2.68577e40	0.629181
$635$	−2.15574e40	−0.493602
$636$	3.43122e39	0.0767927
$637$	−3.55640e40	−0.778016
$638$	−3.90294e40	−0.834626
$639$	2.47771e40	0.517950
$640$	−2.68941e40	−0.549601
$641$	5.79208e40	1.15716	0.578580	−	0.815626i	$-0.303607\pi$
$641$	5.79208e40	1.15716	0.578580	+	0.815626i	$0.303607\pi$
$642$	8.74550e40	1.70815
$643$	−6.13559e40	−1.17165	−0.585824	−	0.810439i	$-0.699229\pi$
$643$	−6.13559e40	−1.17165	−0.585824	+	0.810439i	$0.699229\pi$
$644$	7.96629e36	0.000148734 0
$645$	6.05772e40	1.10584
$646$	4.85510e40	0.866615
$647$	−1.10620e40	−0.193074	−0.0965369	−	0.995329i	$-0.530777\pi$
$647$	−1.10620e40	−0.193074	−0.0965369	+	0.995329i	$0.530777\pi$
$648$	−5.72747e40	−0.977518
$649$	7.12509e40	1.18917
$650$	−4.25317e40	−0.694175
$651$	−2.36652e39	−0.0377735
$652$	1.71116e39	0.0267116
$653$	9.61992e40	1.46869	0.734346	−	0.678776i	$-0.237489\pi$
$653$	9.61992e40	1.46869	0.734346	+	0.678776i	$0.237489\pi$
$654$	−2.54591e41	−3.80160
$655$	7.22276e39	0.105488
$656$	2.08948e39	0.0298491
$657$	−6.45677e40	−0.902231
$658$	1.68928e39	0.0230901
$659$	2.42717e40	0.324535	0.162268	−	0.986747i	$-0.448119\pi$
$659$	2.42717e40	0.324535	0.162268	+	0.986747i	$0.448119\pi$
$660$	−1.02677e40	−0.134303
$661$	−8.66824e40	−1.10920	−0.554600	−	0.832117i	$-0.687129\pi$
$661$	−8.66824e40	−1.10920	−0.554600	+	0.832117i	$0.687129\pi$
$662$	4.10643e40	0.514071
$663$	1.19722e41	1.46631
$664$	4.51983e40	0.541608
$665$	−5.26802e38	−0.00617638
$666$	2.91616e41	3.34530
$667$	−3.07370e39	−0.0345014
$668$	1.54136e40	0.169295
$669$	−2.83791e41	−3.05014
$670$	1.69797e40	0.178585
$671$	−3.66684e40	−0.377412
$672$	−1.71138e39	−0.0172382
$673$	−8.20694e40	−0.809027	−0.404513	−	0.914532i	$-0.632559\pi$
$673$	−8.20694e40	−0.809027	−0.404513	+	0.914532i	$0.632559\pi$
$674$	−7.88983e40	−0.761201
$675$	1.55662e41	1.46987
$676$	−1.13606e40	−0.104997
$677$	1.82761e41	1.65328	0.826640	−	0.562730i	$-0.190249\pi$
$677$	1.82761e41	1.65328	0.826640	+	0.562730i	$0.190249\pi$
$678$	−1.92769e40	−0.170689
$679$	−4.91685e38	−0.00426163
$680$	−4.77286e40	−0.404948
$681$	−1.77416e41	−1.47353
$682$	9.97446e40	0.810991
$683$	−3.66780e39	−0.0291948	−0.0145974	−	0.999893i	$-0.504647\pi$
$683$	−3.66780e39	−0.0291948	−0.0145974	+	0.999893i	$0.504647\pi$
$684$	−5.03439e40	−0.392314
$685$	6.97460e40	0.532115
$686$	5.71356e39	0.0426783
$687$	−7.35141e40	−0.537648
$688$	−2.31718e41	−1.65931
$689$	−1.82968e40	−0.128291
$690$	−3.84492e39	−0.0263983
$691$	5.62493e40	0.378169	0.189084	−	0.981961i	$-0.439448\pi$
$691$	5.62493e40	0.378169	0.189084	+	0.981961i	$0.439448\pi$
$692$	5.46458e40	0.359765
$693$	3.83638e39	0.0247337
$694$	1.15971e41	0.732213
$695$	1.30676e40	0.0808012
$696$	2.79442e41	1.69222
$697$	4.53429e39	0.0268927
$698$	−2.52531e40	−0.146693
$699$	3.38324e41	1.92493
$700$	7.18385e38	0.00400346
$701$	4.31831e40	0.235724	0.117862	−	0.993030i	$-0.462396\pi$
$701$	4.31831e40	0.235724	0.117862	+	0.993030i	$0.462396\pi$
$702$	−3.03759e41	−1.62421
$703$	−1.97000e41	−1.03184
$704$	−7.53459e40	−0.386595
$705$	−1.71470e41	−0.861878
$706$	−2.45267e41	−1.20773
$707$	1.66844e39	0.00804878
$708$	1.85174e41	0.875181
$709$	3.70730e41	1.71667	0.858336	−	0.513088i	$-0.171499\pi$
$709$	3.70730e41	1.71667	0.858336	+	0.513088i	$0.171499\pi$
$710$	−2.84001e40	−0.128847
$711$	−4.63944e41	−2.06232
$712$	6.23303e39	0.0271481
$713$	7.85524e39	0.0335244
$714$	−9.61528e39	−0.0402104
$715$	5.47522e40	0.224369
$716$	−7.49262e40	−0.300881
$717$	2.45311e41	0.965361
$718$	7.58541e40	0.292533
$719$	−3.14942e40	−0.119031	−0.0595157	−	0.998227i	$-0.518956\pi$
$719$	−3.14942e40	−0.119031	−0.0595157	+	0.998227i	$0.518956\pi$
$720$	3.02783e41	1.12153
$721$	−4.49128e39	−0.0163045
$722$	−1.54559e41	−0.549926
$723$	3.28800e41	1.14664
$724$	−1.07863e41	−0.368690
$725$	−2.77180e41	−0.928670
$726$	3.59222e41	1.17973
$727$	2.91745e41	0.939192	0.469596	−	0.882881i	$-0.344400\pi$
$727$	2.91745e41	0.939192	0.469596	+	0.882881i	$0.344400\pi$
$728$	3.86202e39	0.0121873
$729$	−2.60209e41	−0.804957
$730$	7.40089e40	0.224441
$731$	−5.02842e41	−1.49496
$732$	−9.52976e40	−0.277761
$733$	−3.81345e41	−1.08971	−0.544854	−	0.838531i	$-0.683415\pi$
$733$	−3.81345e41	−1.08971	−0.544854	+	0.838531i	$0.683415\pi$
$734$	7.83352e40	0.219464
$735$	−2.89926e41	−0.796379
$736$	5.68062e39	0.0152991
$737$	8.35331e40	0.220587
$738$	−2.23564e40	−0.0578876
$739$	5.69450e41	1.44581	0.722905	−	0.690947i	$-0.242806\pi$
$739$	5.69450e41	1.44581	0.722905	+	0.690947i	$0.242806\pi$
$740$	−7.02969e40	−0.175015
$741$	3.98768e41	0.973546
$742$	1.46948e39	0.00351810
$743$	2.24951e41	0.528140	0.264070	−	0.964503i	$-0.414935\pi$
$743$	2.24951e41	0.528140	0.264070	+	0.964503i	$0.414935\pi$
$744$	−7.14150e41	−1.64430
$745$	2.66039e40	0.0600731
$746$	7.36262e41	1.63049
$747$	−6.22224e41	−1.35144
$748$	8.52307e40	0.181561
$749$	7.87693e39	0.0164578
$750$	−7.84185e41	−1.60705
$751$	−6.45261e41	−1.29705	−0.648524	−	0.761194i	$-0.724614\pi$
$751$	−6.45261e41	−1.29705	−0.648524	+	0.761194i	$0.724614\pi$
$752$	6.55901e41	1.29324
$753$	1.42432e42	2.75474
$754$	5.40890e41	1.02618
$755$	5.79734e40	0.107894
$756$	5.13067e39	0.00936716
$757$	−8.68640e41	−1.55579	−0.777893	−	0.628397i	$-0.783711\pi$
$757$	−8.68640e41	−1.55579	−0.777893	+	0.628397i	$0.783711\pi$
$758$	3.95839e41	0.695528
$759$	−1.89154e40	−0.0326069
$760$	−1.58974e41	−0.268862
$761$	4.39407e41	0.729104	0.364552	−	0.931183i	$-0.381222\pi$
$761$	4.39407e41	0.729104	0.364552	+	0.931183i	$0.381222\pi$
$762$	−1.31056e42	−2.13359
$763$	−2.29306e40	−0.0366278
$764$	−1.54451e41	−0.242068
$765$	6.57058e41	1.01045
$766$	−6.77649e41	−1.02256
$767$	−9.87434e41	−1.46209
$768$	−8.99727e41	−1.30729
$769$	−3.86450e41	−0.551012	−0.275506	−	0.961299i	$-0.588845\pi$
$769$	−3.86450e41	−0.551012	−0.275506	+	0.961299i	$0.588845\pi$
$770$	−4.39734e39	−0.00615282
$771$	1.23698e42	1.69853
$772$	2.73329e41	0.368328
$773$	3.89700e41	0.515380	0.257690	−	0.966228i	$-0.417039\pi$
$773$	3.89700e41	0.515380	0.257690	+	0.966228i	$0.417039\pi$
$774$	2.47928e42	3.21796
$775$	7.08370e41	0.902372
$776$	−1.48377e41	−0.185511
$777$	3.90148e40	0.0478768
$778$	−1.25346e42	−1.50975
$779$	1.51028e40	0.0178552
$780$	1.42295e41	0.165127
$781$	−1.39716e41	−0.159150
$782$	3.19161e40	0.0356872
$783$	−1.97961e42	−2.17287
$784$	1.10901e42	1.19496
$785$	−1.60870e41	−0.170163
$786$	4.39101e41	0.455972
$787$	8.84928e41	0.902140	0.451070	−	0.892488i	$-0.351042\pi$
$787$	8.84928e41	0.902140	0.451070	+	0.892488i	$0.351042\pi$
$788$	−4.03784e41	−0.404128
$789$	−3.01297e42	−2.96059
$790$	5.31782e41	0.513028
$791$	−1.73624e39	−0.00164456
$792$	1.15771e42	1.07668
$793$	5.08171e41	0.464032
$794$	−1.12972e42	−1.01292
$795$	−1.49160e41	−0.131319
$796$	2.93363e41	0.253610
$797$	−6.26660e41	−0.531969	−0.265985	−	0.963977i	$-0.585697\pi$
$797$	−6.26660e41	−0.531969	−0.265985	+	0.963977i	$0.585697\pi$
$798$	−3.20265e40	−0.0266973
$799$	1.42335e42	1.16515
$800$	5.12267e41	0.411805
$801$	−8.58073e40	−0.0677412
$802$	−7.49409e41	−0.581019
$803$	3.64093e41	0.277228
$804$	2.17094e41	0.162344
$805$	−3.46306e38	−0.000254343 0
$806$	−1.38231e42	−0.997123
$807$	3.40392e42	2.41164
$808$	5.03489e41	0.350369
$809$	−8.71861e41	−0.595928	−0.297964	−	0.954577i	$-0.596308\pi$
$809$	−8.71861e41	−0.595928	−0.297964	+	0.954577i	$0.596308\pi$
$810$	−9.03766e41	−0.606769
$811$	9.09697e41	0.599922	0.299961	−	0.953952i	$-0.403026\pi$
$811$	9.09697e41	0.599922	0.299961	+	0.953952i	$0.403026\pi$
$812$	−9.13595e39	−0.00591822
$813$	1.27958e42	0.814245
$814$	−1.64440e42	−1.02791
$815$	−7.43865e40	−0.0456782
$816$	−3.73336e42	−2.25213
$817$	−1.67486e42	−0.992565
$818$	2.22848e42	1.29743
$819$	−5.31666e40	−0.0304104
$820$	5.38924e39	0.00302849
$821$	1.52548e42	0.842231	0.421115	−	0.907007i	$-0.361639\pi$
$821$	1.52548e42	0.842231	0.421115	+	0.907007i	$0.361639\pi$
$822$	4.24015e42	2.30006
$823$	−1.67746e42	−0.894037	−0.447019	−	0.894525i	$-0.647514\pi$
$823$	−1.67746e42	−0.894037	−0.447019	+	0.894525i	$0.647514\pi$
$824$	−1.35534e42	−0.709747
$825$	−1.70575e42	−0.877676
$826$	7.93043e40	0.0400946
$827$	−3.12102e42	−1.55048	−0.775242	−	0.631665i	$-0.782372\pi$
$827$	−3.12102e42	−1.55048	−0.775242	+	0.631665i	$0.782372\pi$
$828$	−3.30948e40	−0.0161555
$829$	−1.01143e42	−0.485174	−0.242587	−	0.970130i	$-0.577996\pi$
$829$	−1.01143e42	−0.485174	−0.242587	+	0.970130i	$0.577996\pi$
$830$	7.13207e41	0.336189
$831$	1.08501e42	0.502595
$832$	1.04418e42	0.475323
$833$	2.40663e42	1.07661
$834$	7.94436e41	0.349262
$835$	−6.70050e41	−0.289503
$836$	2.83886e41	0.120546
$837$	5.05915e42	2.11134
$838$	−1.37292e42	−0.563126
$839$	1.10356e42	0.444887	0.222443	−	0.974946i	$-0.428597\pi$
$839$	1.10356e42	0.444887	0.222443	+	0.974946i	$0.428597\pi$
$840$	3.14840e40	0.0124750
$841$	9.57314e41	0.372832
$842$	2.59240e42	0.992375
$843$	−5.49860e42	−2.06896
$844$	−6.06329e41	−0.224255
$845$	4.93863e41	0.179550
$846$	−7.01785e42	−2.50804
$847$	3.23545e40	0.0113665
$848$	5.70562e41	0.197044
$849$	−7.59106e42	−2.57716
$850$	2.87814e42	0.960587
$851$	−1.29502e41	−0.0424912
$852$	−3.63109e41	−0.117129
$853$	1.80886e42	0.573646	0.286823	−	0.957984i	$-0.407401\pi$
$853$	1.80886e42	0.573646	0.286823	+	0.957984i	$0.407401\pi$
$854$	−4.08130e40	−0.0127250
$855$	2.18852e42	0.670876
$856$	2.37704e42	0.716417
$857$	3.58273e42	1.06168	0.530838	−	0.847473i	$-0.321877\pi$
$857$	3.58273e42	1.06168	0.530838	+	0.847473i	$0.321877\pi$
$858$	3.32861e42	0.969834
$859$	3.55534e42	1.01855	0.509273	−	0.860605i	$-0.329914\pi$
$859$	3.55534e42	1.01855	0.509273	+	0.860605i	$0.329914\pi$
$860$	−5.97653e41	−0.168353
$861$	−2.99103e39	−0.000828467 0
$862$	−5.12970e42	−1.39713
$863$	−5.78959e42	−1.55057	−0.775285	−	0.631612i	$-0.782394\pi$
$863$	−5.78959e42	−1.55057	−0.775285	+	0.631612i	$0.782394\pi$
$864$	3.65859e42	0.963528
$865$	−2.37553e42	−0.615216
$866$	2.33033e42	0.593482
$867$	−1.11695e42	−0.279740
$868$	2.33481e40	0.00575063
$869$	2.61614e42	0.633687
$870$	4.40946e42	1.05040
$871$	−1.15765e42	−0.271215
$872$	−6.91982e42	−1.59443
$873$	2.04263e42	0.462897
$874$	1.06306e41	0.0236942
$875$	−7.06303e40	−0.0154837
$876$	9.46241e41	0.204029
$877$	−1.74620e42	−0.370340	−0.185170	−	0.982707i	$-0.559284\pi$
$877$	−1.74620e42	−0.370340	−0.185170	+	0.982707i	$0.559284\pi$
$878$	−8.64771e42	−1.80398
$879$	1.29265e43	2.65243
$880$	−1.70737e42	−0.344611
$881$	6.11305e42	1.21369	0.606844	−	0.794821i	$-0.292435\pi$
$881$	6.11305e42	1.21369	0.606844	+	0.794821i	$0.292435\pi$
$882$	−1.18659e43	−2.31744
$883$	−5.67511e42	−1.09029	−0.545147	−	0.838340i	$-0.683526\pi$
$883$	−5.67511e42	−1.09029	−0.545147	+	0.838340i	$0.683526\pi$
$884$	−1.18117e42	−0.223232
$885$	−8.04978e42	−1.49660
$886$	6.85281e42	1.25337
$887$	1.28948e42	0.232019	0.116009	−	0.993248i	$-0.462990\pi$
$887$	1.28948e42	0.232019	0.116009	+	0.993248i	$0.462990\pi$
$888$	1.17736e43	2.08411
$889$	−1.18040e41	−0.0205568
$890$	9.83542e40	0.0168515
$891$	−4.44615e42	−0.749475
$892$	2.79988e42	0.464354
$893$	4.74087e42	0.773592
$894$	1.61736e42	0.259665
$895$	3.25715e42	0.514521
$896$	−1.47262e41	−0.0228889
$897$	2.62140e41	0.0400906
$898$	2.82924e42	0.425758
$899$	−9.00859e42	−1.33396
$900$	−2.98442e42	−0.434854
$901$	1.23815e42	0.177527
$902$	1.26066e41	0.0177871
$903$	3.31698e41	0.0460543
$904$	−5.23947e41	−0.0715888
$905$	4.68894e42	0.630478
$906$	3.52444e42	0.466371
$907$	−6.85671e42	−0.892915	−0.446457	−	0.894805i	$-0.647315\pi$
$907$	−6.85671e42	−0.892915	−0.446457	+	0.894805i	$0.647315\pi$
$908$	1.75038e42	0.224331
$909$	−6.93130e42	−0.874255
$910$	6.09407e40	0.00756497
$911$	−6.18262e42	−0.755363	−0.377682	−	0.925936i	$-0.623279\pi$
$911$	−6.18262e42	−0.755363	−0.377682	+	0.925936i	$0.623279\pi$
$912$	−1.24350e43	−1.49528
$913$	3.50868e42	0.415257
$914$	−9.10348e42	−1.06044
$915$	4.14272e42	0.474985
$916$	7.25289e41	0.0818516
$917$	3.95491e40	0.00439321
$918$	2.05555e43	2.24755
$919$	7.15141e42	0.769691	0.384846	−	0.922981i	$-0.374255\pi$
$919$	7.15141e42	0.769691	0.384846	+	0.922981i	$0.374255\pi$
$920$	−1.04505e41	−0.0110717
$921$	−9.19938e42	−0.959387
$922$	1.52402e43	1.56456
$923$	1.93626e42	0.195677
$924$	−5.62222e40	−0.00559325
$925$	−1.16783e43	−1.14373
$926$	7.22663e42	0.696749
$927$	1.86583e43	1.77099
$928$	−6.51468e42	−0.608762
$929$	1.19347e43	1.09795	0.548975	−	0.835839i	$-0.315018\pi$
$929$	1.19347e43	1.09795	0.548975	+	0.835839i	$0.315018\pi$
$930$	−1.12689e43	−1.02066
$931$	8.01598e42	0.714803
$932$	−3.33790e42	−0.293051
$933$	−2.60363e43	−2.25058
$934$	−2.35024e43	−2.00024
$935$	−3.70510e42	−0.310479
$936$	−1.60442e43	−1.32379
$937$	−4.02931e42	−0.327345	−0.163673	−	0.986515i	$-0.552334\pi$
$937$	−4.02931e42	−0.327345	−0.163673	+	0.986515i	$0.552334\pi$
$938$	9.29747e40	0.00743744
$939$	3.89442e43	3.06755
$940$	1.69172e42	0.131212
$941$	9.40592e42	0.718376	0.359188	−	0.933265i	$-0.383054\pi$
$941$	9.40592e42	0.718376	0.359188	+	0.933265i	$0.383054\pi$
$942$	−9.77996e42	−0.735527
$943$	9.92816e39	0.000735274 0
$944$	3.07918e43	2.24564
$945$	−2.23038e41	−0.0160183
$946$	−1.39805e43	−0.988781
$947$	−1.85611e43	−1.29279	−0.646397	−	0.763001i	$-0.723725\pi$
$947$	−1.85611e43	−1.29279	−0.646397	+	0.763001i	$0.723725\pi$
$948$	6.79910e42	0.466370
$949$	−5.04579e42	−0.340855
$950$	9.58647e42	0.637773
$951$	−1.49276e43	−0.978078
$952$	−2.61344e41	−0.0168646
$953$	−3.20332e42	−0.203588	−0.101794	−	0.994805i	$-0.532458\pi$
$953$	−3.20332e42	−0.203588	−0.101794	+	0.994805i	$0.532458\pi$
$954$	−6.10475e42	−0.382135
$955$	6.71420e42	0.413948
$956$	−2.42024e42	−0.146967
$957$	2.16927e43	1.29745
$958$	1.46573e43	0.863482
$959$	3.81903e41	0.0221607
$960$	8.51243e42	0.486542
$961$	5.26074e42	0.296181
$962$	2.27890e43	1.26383
$963$	−3.27235e43	−1.78764
$964$	−3.24393e42	−0.174564
$965$	−1.18820e43	−0.629860
$966$	−2.10534e40	−0.00109939
$967$	5.23025e42	0.269053	0.134527	−	0.990910i	$-0.457049\pi$
$967$	5.23025e42	0.269053	0.134527	+	0.990910i	$0.457049\pi$
$968$	9.76368e42	0.494790
$969$	−2.69848e43	−1.34718
$970$	−2.34131e42	−0.115151
$971$	−2.58906e43	−1.25448	−0.627239	−	0.778827i	$-0.715815\pi$
$971$	−2.58906e43	−1.25448	−0.627239	+	0.778827i	$0.715815\pi$
$972$	−1.20881e42	−0.0577028
$973$	7.15536e40	0.00336508
$974$	−2.73998e43	−1.26953
$975$	2.36393e43	1.07911
$976$	−1.58466e43	−0.712712
$977$	6.80879e42	0.301716	0.150858	−	0.988555i	$-0.451796\pi$
$977$	6.80879e42	0.301716	0.150858	+	0.988555i	$0.451796\pi$
$978$	−4.52226e42	−0.197443
$979$	4.83861e41	0.0208148
$980$	2.86040e42	0.121241
$981$	9.52620e43	3.97850
$982$	2.08435e43	0.857735
$983$	−4.18545e43	−1.69713	−0.848566	−	0.529089i	$-0.822534\pi$
$983$	−4.18545e43	−1.69713	−0.848566	+	0.529089i	$0.822534\pi$
$984$	−9.02608e41	−0.0360637
$985$	1.75531e43	0.691080
$986$	−3.66023e43	−1.42001
$987$	−9.38906e41	−0.0358941
$988$	−3.93424e42	−0.148213
$989$	−1.10101e42	−0.0408738
$990$	1.82681e43	0.668318
$991$	2.63339e43	0.949397	0.474699	−	0.880148i	$-0.342557\pi$
$991$	2.63339e43	0.949397	0.474699	+	0.880148i	$0.342557\pi$
$992$	1.66491e43	0.591523
$993$	−2.28237e43	−0.799138
$994$	−1.55508e41	−0.00536600
$995$	−1.27529e43	−0.433686
$996$	9.11870e42	0.305614
$997$	−1.61216e43	−0.532511	−0.266255	−	0.963903i	$-0.585786\pi$
$997$	−1.61216e43	−0.532511	−0.266255	+	0.963903i	$0.585786\pi$
$998$	2.97416e43	0.968216
$999$	−8.34058e43	−2.67606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.30.a.a.1.2	✓	2
3.2	odd	2		9.30.a.a.1.1		2
4.3	odd	2		16.30.a.c.1.2		2
5.2	odd	4		25.30.b.a.24.4		4
5.3	odd	4		25.30.b.a.24.1		4
5.4	even	2		25.30.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.30.a.a.1.2	✓	2	1.1	even	1	trivial
9.30.a.a.1.1		2	3.2	odd	2
16.30.a.c.1.2		2	4.3	odd	2
25.30.a.a.1.1		2	5.4	even	2
25.30.b.a.24.1		4	5.3	odd	4
25.30.b.a.24.4		4	5.2	odd	4

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:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} +O(q^{10})\)	\(q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} -1.62061e14 q^{10} -7.97271e14 q^{11} -2.07203e15 q^{12} +1.10490e16 q^{13} -8.87385e14 q^{14} +9.00740e16 q^{15} -3.44548e17 q^{16} -7.47691e17 q^{17} +3.68651e18 q^{18} -2.49040e18 q^{19} -8.88669e17 q^{20} +4.93212e17 q^{21} -2.07880e19 q^{22} -1.63712e18 q^{23} +1.48837e20 q^{24} -1.47633e20 q^{25} +2.88091e20 q^{26} -1.05439e21 q^{27} -4.86602e18 q^{28} +1.87750e21 q^{29} +2.34858e21 q^{30} -4.79819e21 q^{31} -3.46987e21 q^{32} +1.15540e22 q^{33} -1.94952e22 q^{34} +2.11533e20 q^{35} +2.02152e22 q^{36} +7.91036e22 q^{37} -6.49345e22 q^{38} -1.60122e23 q^{39} +6.38347e22 q^{40} -6.06439e21 q^{41} +1.28600e22 q^{42} +6.72526e23 q^{43} -1.13992e23 q^{44} -8.78782e23 q^{45} -4.26862e22 q^{46} -1.90366e24 q^{47} +4.99319e24 q^{48} -3.21875e24 q^{49} -3.84936e24 q^{50} +1.08355e25 q^{51} +1.57976e24 q^{52} -1.65597e24 q^{53} -2.74920e25 q^{54} +4.95539e24 q^{55} +3.49535e23 q^{56} +3.60909e25 q^{57} +4.89537e25 q^{58} -8.93685e25 q^{59} +1.28786e25 q^{60} +4.59924e25 q^{61} -1.25108e26 q^{62} -4.81189e24 q^{63} +9.45048e25 q^{64} -6.86745e25 q^{65} +3.01259e26 q^{66} -1.04774e26 q^{67} -1.06903e26 q^{68} +2.37252e25 q^{69} +5.51549e24 q^{70} +1.75243e26 q^{71} -1.45209e27 q^{72} -4.56674e26 q^{73} +2.06254e27 q^{74} +2.13949e27 q^{75} -3.56072e26 q^{76} +2.71339e25 q^{77} -4.17501e27 q^{78} -3.28137e27 q^{79} +2.14152e27 q^{80} +5.57671e27 q^{81} -1.58122e26 q^{82} -4.40086e27 q^{83} +7.05183e25 q^{84} +4.64723e27 q^{85} +1.75354e28 q^{86} -2.72087e28 q^{87} +8.18824e27 q^{88} -6.06897e26 q^{89} -2.29133e28 q^{90} -3.76036e26 q^{91} -2.34072e26 q^{92} +6.95352e28 q^{93} -4.96357e28 q^{94} +1.54790e28 q^{95} +5.02853e28 q^{96} +1.44471e28 q^{97} -8.39253e28 q^{98} -1.12724e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8640 q^{2} - 4967640 q^{3} - 89952256 q^{4} - 17477788500 q^{5} - 543908756736 q^{6} - 3020312682800 q^{7} + 3150297169920 q^{8} + 163469569523706 q^{9}+O(q^{10}) \) 2 * q + 8640 * q^2 - 4967640 * q^3 - 89952256 * q^4 - 17477788500 * q^5 - 543908756736 * q^6 - 3020312682800 * q^7 + 3150297169920 * q^8 + 163469569523706 * q^9	\( 2 q + 8640 q^{2} - 4967640 q^{3} - 89952256 q^{4} - 17477788500 q^{5} - 543908756736 q^{6} - 3020312682800 q^{7} + 3150297169920 q^{8} + 163469569523706 q^{9} + 34285866768000 q^{10} - 20\!\cdots\!16 q^{11}+ \cdots - 14\!\cdots\!48 q^{99}+O(q^{100}) \) 2 * q + 8640 * q^2 - 4967640 * q^3 - 89952256 * q^4 - 17477788500 * q^5 - 543908756736 * q^6 - 3020312682800 * q^7 + 3150297169920 * q^8 + 163469569523706 * q^9 + 34285866768000 * q^10 - 2055380519588616 * q^11 - 4290530276229120 * q^12 + 17139371179332220 * q^13 + 51175123348059648 * q^14 - 17192351392506000 * q^15 - 453469082063208448 * q^16 - 664795927907749980 * q^17 + 3301524864881760960 * q^18 + 1232169445452155080 * q^19 + 1734668101813248000 * q^20 - 27949113476248821696 * q^21 + 1145797484912974080 * q^22 - 18588430504374379920 * q^23 + 276660084668356362240 * q^24 - 207056854502617281250 * q^25 + 181912132597777755264 * q^26 - 1497723629507205824880 * q^27 + 690727602371844997120 * q^28 + 996096417765761595420 * q^29 + 4218653306492474688000 * q^30 - 1087258664181924030656 * q^31 - 8776107971762202869760 * q^32 - 428627571739162757280 * q^33 - 20940413403809031000192 * q^34 + 33844046536902649068000 * q^35 + 15071477561016892895232 * q^36 + 98878127759336138311660 * q^37 - 129833487351109249470720 * q^38 - 102115380027539490485328 * q^39 - 87313163228088238080000 * q^40 - 106699837259610025757676 * q^41 + 508720764303162503608320 * q^42 + 510640433114974031366200 * q^43 + 179059414424913371086848 * q^44 - 1127484267514124881450500 * q^45 + 252841215606439776920064 * q^46 - 4521107671109825795039520 * q^47 + 3955787455065109907374080 * q^48 + 2479210387392854586312114 * q^49 - 2813370491836752543000000 * q^50 + 11625042659032475755122384 * q^51 + 161134672249303679180800 * q^52 - 16141544629666790250663540 * q^53 - 19762893017614843677688320 * q^54 + 19124657798421120971058000 * q^55 - 39728224533177935352299520 * q^56 + 71545878452212360967003040 * q^57 + 64319996083339084169992320 * q^58 - 83497291515660150276062760 * q^59 + 37864111042200317349888000 * q^60 - 15876762943230179624113316 * q^61 - 189803556071494720042936320 * q^62 - 70756669640265175617870960 * q^63 + 245489542813624183222697984 * q^64 - 137266226551726798673511000 * q^65 + 510163218803227073870066688 * q^66 + 24468754434128844890782120 * q^67 - 126211850011481106095677440 * q^68 - 137724750477330905859409728 * q^69 - 580830557953085152481664000 * q^70 - 188428428253360067209577136 * q^71 - 1155729487872248549372067840 * q^72 + 995872721297568533052080980 * q^73 + 1717790650063115374837542528 * q^74 + 1573516410323456985690375000 * q^75 - 1223170019527541658110935040 * q^76 + 3784200478484579386131729600 * q^77 - 5186288053950004913991206400 * q^78 - 7218460852587735797823642080 * q^79 + 3368223393577622373924864000 * q^80 - 161317068789001769884865358 * q^81 + 1596346485209467674952913280 * q^82 + 2210846225248155523694669640 * q^83 + 6695585379451908015663218688 * q^84 + 3713635892367734904614943000 * q^85 + 20357697303796411232450244864 * q^86 - 35603430680717182696869516240 * q^87 - 8696387677835767416210063360 * q^88 + 5872964746600969363962031860 * q^89 - 18577446803723860542221616000 * q^90 - 18563550073842319069958420896 * q^91 + 3714393183413159199429918720 * q^92 + 104879397265778648689061310720 * q^93 - 4003342107705068447401638912 * q^94 - 26445947767121183571013410000 * q^95 - 253006717086360117933244416 * q^96 + 109649982219471997093227005380 * q^97 - 183262972410594366168864121920 * q^98 - 140506044809020243496724809448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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