LMFDB - Embedded newform 3.35.b.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,35,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 35, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 35 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$21.9676962128$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 $ x^10 + 789518143x^8 + 211496483076151936x^6 + 21382790524640936160081920x^4 + 613809329098098496707904510361600x^2 + 5042460246515433703013776627104481280000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.5
Root			$-3839.21i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.35.b.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-46070.5i q^{2} +(1.11570e8 - 6.50325e7i) q^{3} +1.50574e10 q^{4} -1.37507e12i q^{5} +(-2.99608e12 - 5.14011e12i) q^{6} -2.89657e14 q^{7} -1.48519e15i q^{8} +(8.21874e15 - 1.45114e16i) q^{9} +O(q^{10})$	\(q-46070.5i q^{2} +(1.11570e8 - 6.50325e7i) q^{3} +1.50574e10 q^{4} -1.37507e12i q^{5} +(-2.99608e12 - 5.14011e12i) q^{6} -2.89657e14 q^{7} -1.48519e15i q^{8} +(8.21874e15 - 1.45114e16i) q^{9} -6.33504e16 q^{10} +2.11971e17i q^{11} +(1.67996e18 - 9.79218e17i) q^{12} +1.85219e18 q^{13} +1.33446e19i q^{14} +(-8.94245e19 - 1.53418e20i) q^{15} +1.90260e20 q^{16} +1.25054e21i q^{17} +(-6.68548e20 - 3.78642e20i) q^{18} -1.89372e21 q^{19} -2.07050e22i q^{20} +(-3.23171e22 + 1.88371e22i) q^{21} +9.76562e21 q^{22} -9.09177e22i q^{23} +(-9.65854e22 - 1.65703e23i) q^{24} -1.30875e24 q^{25} -8.53312e22i q^{26} +(-2.67439e22 - 2.15353e24i) q^{27} -4.36147e24 q^{28} -1.52476e24i q^{29} +(-7.06803e24 + 4.11983e24i) q^{30} +1.41016e25 q^{31} -3.42807e25i q^{32} +(1.37850e25 + 2.36497e25i) q^{33} +5.76129e25 q^{34} +3.98300e26i q^{35} +(1.23753e26 - 2.18504e26i) q^{36} +5.80826e26 q^{37} +8.72447e25i q^{38} +(2.06649e26 - 1.20452e26i) q^{39} -2.04224e27 q^{40} -2.01941e27i q^{41} +(8.67835e26 + 1.48887e27i) q^{42} -1.60735e27 q^{43} +3.19173e27i q^{44} +(-1.99543e28 - 1.13014e28i) q^{45} -4.18863e27 q^{46} -1.09494e28i q^{47} +(2.12274e28 - 1.23731e28i) q^{48} +2.97842e28 q^{49} +6.02950e28i q^{50} +(8.13254e28 + 1.39523e29i) q^{51} +2.78890e28 q^{52} -2.12189e29i q^{53} +(-9.92142e28 + 1.23211e27i) q^{54} +2.91476e29 q^{55} +4.30195e29i q^{56} +(-2.11283e29 + 1.23153e29i) q^{57} -7.02465e28 q^{58} -6.32771e29i q^{59} +(-1.34650e30 - 2.31007e30i) q^{60} -1.22298e30 q^{61} -6.49669e29i q^{62} +(-2.38061e30 + 4.20333e30i) q^{63} +1.68932e30 q^{64} -2.54689e30i q^{65} +(1.08955e30 - 6.35082e29i) q^{66} +1.32113e31 q^{67} +1.88298e31i q^{68} +(-5.91261e30 - 1.01437e31i) q^{69} +1.83499e31 q^{70} +6.14008e30i q^{71} +(-2.15521e31 - 1.22064e31i) q^{72} +7.66818e31 q^{73} -2.67590e31i q^{74} +(-1.46018e32 + 8.51115e31i) q^{75} -2.85144e31 q^{76} -6.13989e31i q^{77} +(-5.54930e30 - 9.52043e30i) q^{78} +2.85419e31 q^{79} -2.61622e32i q^{80} +(-1.43033e32 - 2.38531e32i) q^{81} -9.30352e31 q^{82} +6.49866e32i q^{83} +(-4.86611e32 + 2.83637e32i) q^{84} +1.71958e33 q^{85} +7.40515e31i q^{86} +(-9.91589e31 - 1.70118e32i) q^{87} +3.14817e32 q^{88} +2.50617e31i q^{89} +(-5.20661e32 + 9.19303e32i) q^{90} -5.36498e32 q^{91} -1.36898e33i q^{92} +(1.57332e33 - 9.17063e32i) q^{93} -5.04445e32 q^{94} +2.60401e33i q^{95} +(-2.22936e33 - 3.82471e33i) q^{96} -4.22129e33 q^{97} -1.37217e33i q^{98} +(3.07600e33 + 1.74213e33i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	46070.5i		−	0.351490i	−0.984436	−	0.175745i	$-0.943767\pi$
$2$		−	46070.5i		−	0.351490i	0.984436	−	0.175745i	$-0.0562335\pi$
$3$	1.11570e8	−	6.50325e7i	0.863948	−	0.503580i
$3$	1.11570e8	−	6.50325e7i	0.863948	−	0.503580i
$4$	1.50574e10			0.876455
$5$		−	1.37507e12i		−	1.80234i	−0.433468	−	0.901169i	$-0.642710\pi$
$5$		−	1.37507e12i		−	1.80234i	0.433468	−	0.901169i	$-0.357290\pi$
$6$	−2.99608e12	−	5.14011e12i	−0.177004	−	0.303669i
$7$	−2.89657e14			−1.24514			−0.622569	−	0.782565i	$-0.713911\pi$
$7$	−2.89657e14			−1.24514			−0.622569	+	0.782565i	$0.713911\pi$
$8$		−	1.48519e15i		−	0.659556i
$9$	8.21874e15	−	1.45114e16i	0.492813	−	0.870135i
$10$	−6.33504e16			−0.633504
$11$			2.11971e17i			0.419373i	0.977769	+	0.209687i	$0.0672444\pi$
$11$			2.11971e17i			0.419373i	−0.977769	+	0.209687i	$0.932756\pi$
$12$	1.67996e18	−	9.79218e17i	0.757211	−	0.441365i
$13$	1.85219e18			0.214115			0.107058	−	0.994253i	$-0.465857\pi$
$13$	1.85219e18			0.214115			0.107058	+	0.994253i	$0.465857\pi$
$14$			1.33446e19i			0.437654i
$15$	−8.94245e19	−	1.53418e20i	−0.907622	−	1.55713i
$16$	1.90260e20			0.644627
$17$			1.25054e21i			1.51170i	0.654747	+	0.755848i	$0.272775\pi$
$17$			1.25054e21i			1.51170i	−0.654747	+	0.755848i	$0.727225\pi$
$18$	−6.68548e20	−	3.78642e20i	−0.305844	−	0.173219i
$19$	−1.89372e21			−0.345545			−0.172772	−	0.984962i	$-0.555273\pi$
$19$	−1.89372e21			−0.345545			−0.172772	+	0.984962i	$0.555273\pi$
$20$		−	2.07050e22i		−	1.57967i
$21$	−3.23171e22	+	1.88371e22i	−1.07573	+	0.627027i
$22$	9.76562e21			0.147406
$23$		−	9.09177e22i		−	0.644578i	−0.946641	−	0.322289i	$-0.895548\pi$
$23$		−	9.09177e22i		−	0.644578i	0.946641	−	0.322289i	$-0.104452\pi$
$24$	−9.65854e22	−	1.65703e23i	−0.332139	−	0.569822i
$25$	−1.30875e24			−2.24842
$26$		−	8.53312e22i		−	0.0752594i
$27$	−2.67439e22	−	2.15353e24i	−0.0124177	−	0.999923i
$28$	−4.36147e24			−1.09131
$29$		−	1.52476e24i		−	0.210105i	−0.994467	−	0.105052i	$-0.966499\pi$
$29$		−	1.52476e24i		−	0.210105i	0.994467	−	0.105052i	$-0.0335010\pi$
$30$	−7.06803e24	+	4.11983e24i	−0.547315	+	0.319020i
$31$	1.41016e25			0.625346			0.312673	−	0.949861i	$-0.398776\pi$
$31$	1.41016e25			0.625346			0.312673	+	0.949861i	$0.398776\pi$
$32$		−	3.42807e25i		−	0.886136i
$33$	1.37850e25	+	2.36497e25i	0.211188	+	0.362317i
$34$	5.76129e25			0.531347
$35$			3.98300e26i			2.24416i
$36$	1.23753e26	−	2.18504e26i	0.431929	−	0.762634i
$37$	5.80826e26			1.27238			0.636190	−	0.771533i	$-0.280510\pi$
$37$	5.80826e26			1.27238			0.636190	+	0.771533i	$0.280510\pi$
$38$			8.72447e25i			0.121456i
$39$	2.06649e26	−	1.20452e26i	0.184984	−	0.107824i
$40$	−2.04224e27			−1.18874
$41$		−	2.01941e27i		−	0.772500i	−0.922394	−	0.386250i	$-0.873770\pi$
$41$		−	2.01941e27i		−	0.772500i	0.922394	−	0.386250i	$-0.126230\pi$
$42$	8.67835e26	+	1.48887e27i	0.220394	+	0.378110i
$43$	−1.60735e27			−0.273619			−0.136810	−	0.990597i	$-0.543685\pi$
$43$	−1.60735e27			−0.273619			−0.136810	+	0.990597i	$0.543685\pi$
$44$			3.19173e27i			0.367562i
$45$	−1.99543e28	−	1.13014e28i	−1.56828	−	0.888216i
$46$	−4.18863e27			−0.226563
$47$		−	1.09494e28i		−	0.410891i	−0.978669	−	0.205446i	$-0.934136\pi$
$47$		−	1.09494e28i		−	0.410891i	0.978669	−	0.205446i	$-0.0658644\pi$
$48$	2.12274e28	−	1.23731e28i	0.556925	−	0.324622i
$49$	2.97842e28			0.550367
$50$			6.02950e28i			0.790298i
$51$	8.13254e28	+	1.39523e29i	0.761261	+	1.30603i
$52$	2.78890e28			0.187662
$53$		−	2.12189e29i		−	1.03284i	−0.856336	−	0.516419i	$-0.827265\pi$
$53$		−	2.12189e29i		−	1.03284i	0.856336	−	0.516419i	$-0.172735\pi$
$54$	−9.92142e28	+	1.23211e27i	−0.351463	+	0.00436470i
$55$	2.91476e29			0.755852
$56$			4.30195e29i			0.821237i
$57$	−2.11283e29	+	1.23153e29i	−0.298533	+	0.174010i
$58$	−7.02465e28			−0.0738498
$59$		−	6.32771e29i		−	0.497465i	−0.968572	−	0.248732i	$-0.919986\pi$
$59$		−	6.32771e29i		−	0.497465i	0.968572	−	0.248732i	$-0.0800140\pi$
$60$	−1.34650e30	−	2.31007e30i	−0.795490	−	1.36475i
$61$	−1.22298e30			−0.545520			−0.272760	−	0.962082i	$-0.587937\pi$
$61$	−1.22298e30			−0.545520			−0.272760	+	0.962082i	$0.587937\pi$
$62$		−	6.49669e29i		−	0.219803i
$63$	−2.38061e30	+	4.20333e30i	−0.613620	+	1.08344i
$64$	1.68932e30			0.333159
$65$		−	2.54689e30i		−	0.385908i
$66$	1.08955e30	−	6.35082e29i	0.127351	−	0.0742306i
$67$	1.32113e31			1.19584			0.597922	−	0.801555i	$-0.295993\pi$
$67$	1.32113e31			1.19584			0.597922	+	0.801555i	$0.295993\pi$
$68$			1.88298e31i			1.32493i
$69$	−5.91261e30	−	1.01437e31i	−0.324597	−	0.556882i
$70$	1.83499e31			0.788800
$71$			6.14008e30i			0.207387i	0.994609	+	0.103694i	$0.0330662\pi$
$71$			6.14008e30i			0.207387i	−0.994609	+	0.103694i	$0.966934\pi$
$72$	−2.15521e31	−	1.22064e31i	−0.573902	−	0.325038i
$73$	7.66818e31			1.61512			0.807558	−	0.589789i	$-0.200789\pi$
$73$	7.66818e31			1.61512			0.807558	+	0.589789i	$0.200789\pi$
$74$		−	2.67590e31i		−	0.447229i
$75$	−1.46018e32	+	8.51115e31i	−1.94252	+	1.13226i
$76$	−2.85144e31			−0.302854
$77$		−	6.13989e31i		−	0.522177i
$78$	−5.54930e30	−	9.52043e30i	−0.0378992	−	0.0650202i
$79$	2.85419e31			0.156972			0.0784860	−	0.996915i	$-0.474991\pi$
$79$	2.85419e31			0.156972			0.0784860	+	0.996915i	$0.474991\pi$
$80$		−	2.61622e32i		−	1.16184i
$81$	−1.43033e32	−	2.38531e32i	−0.514270	−	0.857628i
$82$	−9.30352e31			−0.271526
$83$			6.49866e32i			1.54346i	0.635948	+	0.771732i	$0.280609\pi$
$83$			6.49866e32i			1.54346i	−0.635948	+	0.771732i	$0.719391\pi$
$84$	−4.86611e32	+	2.83637e32i	−0.942832	+	0.549561i
$85$	1.71958e33			2.72459
$86$			7.40515e31i			0.0961746i
$87$	−9.91589e31	−	1.70118e32i	−0.105805	−	0.181520i
$88$	3.14817e32			0.276600
$89$			2.50617e31i			0.0181711i	0.999959	+	0.00908555i	$0.00289206\pi$
$89$			2.50617e31i			0.0181711i	−0.999959	+	0.00908555i	$0.997108\pi$
$90$	−5.20661e32	+	9.19303e32i	−0.312199	+	0.551234i
$91$	−5.36498e32			−0.266603
$92$		−	1.36898e33i		−	0.564943i
$93$	1.57332e33	−	9.17063e32i	0.540266	−	0.314912i
$94$	−5.04445e32			−0.144424
$95$			2.60401e33i			0.622789i
$96$	−2.22936e33	−	3.82471e33i	−0.446241	−	0.765576i
$97$	−4.22129e33			−0.708477			−0.354238	−	0.935155i	$-0.615260\pi$
$97$	−4.22129e33			−0.708477			−0.354238	+	0.935155i	$0.615260\pi$
$98$		−	1.37217e33i		−	0.193449i
$99$	3.07600e33	+	1.74213e33i	0.364911	+	0.206673i
$100$	−1.97064e34			−1.97064
$101$		−	5.19823e33i		−	0.438926i	−0.975621	−	0.219463i	$-0.929569\pi$
$101$		−	5.19823e33i		−	0.438926i	0.975621	−	0.219463i	$-0.0704306\pi$
$102$	6.42789e33	−	3.74671e33i	0.459056	−	0.267576i
$103$	2.48020e34			1.50056			0.750282	−	0.661118i	$-0.229918\pi$
$103$	2.48020e34			1.50056			0.750282	+	0.661118i	$0.229918\pi$
$104$		−	2.75084e33i		−	0.141221i
$105$	2.59024e34	+	4.44385e34i	1.13011	+	1.93884i
$106$	−9.77565e33			−0.363033
$107$			1.10751e34i			0.350610i	0.984514	+	0.175305i	$0.0560911\pi$
$107$			1.10751e34i			0.350610i	−0.984514	+	0.175305i	$0.943909\pi$
$108$	−4.02693e32	−	3.24265e34i	−0.0108835	−	0.876387i
$109$	−1.06092e34			−0.245150			−0.122575	−	0.992459i	$-0.539115\pi$
$109$	−1.06092e34			−0.245150			−0.122575	+	0.992459i	$0.539115\pi$
$110$		−	1.34285e34i		−	0.265675i
$111$	6.48030e34	−	3.77725e34i	1.09927	−	0.640745i
$112$	−5.51102e34			−0.802649
$113$			9.42920e34i			1.18070i	0.807146	+	0.590352i	$0.201011\pi$
$113$			9.42920e34i			1.18070i	−0.807146	+	0.590352i	$0.798989\pi$
$114$	5.67374e33	+	9.73392e33i	0.0611627	+	0.104931i
$115$	−1.25019e35			−1.16175
$116$		−	2.29589e34i		−	0.184147i
$117$	1.52226e34	−	2.68778e34i	0.105519	−	0.186309i
$118$	−2.91521e34			−0.174854
$119$		−	3.62226e35i		−	1.88227i
$120$	−2.27854e35	+	1.32812e35i	−1.02701	+	0.598627i
$121$	2.10545e35			0.824126
$122$			5.63432e34i			0.191745i
$123$	−1.31327e35	−	2.25306e35i	−0.389016	−	0.667400i
$124$	2.12333e35			0.548087
$125$			9.99235e35i			2.25008i
$126$	1.93650e35	+	1.09676e35i	0.380818	+	0.215682i
$127$	6.46878e35			1.11214			0.556069	−	0.831136i	$-0.312309\pi$
$127$	6.46878e35			1.11214			0.556069	+	0.831136i	$0.312309\pi$
$128$		−	6.66766e35i		−	1.00324i
$129$	−1.79333e35	+	1.04530e35i	−0.236393	+	0.137789i
$130$	−1.17337e35			−0.135643
$131$			3.35779e35i			0.340754i	0.985379	+	0.170377i	$0.0544986\pi$
$131$			3.35779e35i			0.340754i	−0.985379	+	0.170377i	$0.945501\pi$
$132$	2.07566e35	+	3.56102e35i	0.185097	+	0.317554i
$133$	5.48529e35			0.430251
$134$		−	6.08652e35i		−	0.420327i
$135$	−2.96126e36	+	3.67749e34i	−1.80220	+	0.0223809i
$136$	1.85728e36			0.997048
$137$		−	4.09884e36i		−	1.94273i	−0.237600	−	0.971363i	$-0.576361\pi$
$137$		−	4.09884e36i		−	1.94273i	0.237600	−	0.971363i	$-0.423639\pi$
$138$	−4.67327e35	+	2.72397e35i	−0.195739	+	0.114093i
$139$	−2.84153e36			−1.05269			−0.526345	−	0.850271i	$-0.676438\pi$
$139$	−2.84153e36			−1.05269			−0.526345	+	0.850271i	$0.676438\pi$
$140$			5.99735e36i			1.96690i
$141$	−7.12067e35	−	1.22163e36i	−0.206917	−	0.354989i
$142$	2.82877e35			0.0728946
$143$			3.92610e35i			0.0897942i
$144$	1.56370e36	−	2.76094e36i	0.317681	−	0.560913i
$145$	−2.09666e36			−0.378680
$146$		−	3.53277e36i		−	0.567697i
$147$	3.32303e36	−	1.93694e36i	0.475488	−	0.277154i
$148$	8.74571e36			1.11518
$149$			7.58984e36i			0.863110i	0.902087	+	0.431555i	$0.142035\pi$
$149$			7.58984e36i			0.863110i	−0.902087	+	0.431555i	$0.857965\pi$
$150$	3.92113e36	+	6.72714e36i	0.397979	+	0.682777i
$151$	−9.23227e36			−0.836952			−0.418476	−	0.908228i	$-0.637436\pi$
$151$	−9.23227e36			−0.836952			−0.418476	+	0.908228i	$0.637436\pi$
$152$			2.81253e36i			0.227906i
$153$	1.81470e37	+	1.02778e37i	1.31538	+	0.744984i
$154$	−2.82868e36			−0.183540
$155$		−	1.93908e37i		−	1.12708i
$156$	3.11159e36	−	1.81369e36i	0.162130	−	0.0945030i
$157$	−1.09003e37			−0.509498			−0.254749	−	0.967007i	$-0.581993\pi$
$157$	−1.09003e37			−0.509498			−0.254749	+	0.967007i	$0.581993\pi$
$158$		−	1.31494e36i		−	0.0551742i
$159$	−1.37992e37	−	2.36740e37i	−0.520117	−	0.892319i
$160$	−4.71385e37			−1.59712
$161$			2.63350e37i			0.802588i
$162$	−1.09892e37	+	6.58961e36i	−0.301448	+	0.180761i
$163$	1.44159e37			0.356167			0.178083	−	0.984015i	$-0.443010\pi$
$163$	1.44159e37			0.356167			0.178083	+	0.984015i	$0.443010\pi$
$164$		−	3.04070e37i		−	0.677061i
$165$	3.25201e37	−	1.89554e37i	0.653017	−	0.380633i
$166$	2.99397e37			0.542512
$167$			5.15715e36i			0.0843781i	0.999110	+	0.0421890i	$0.0134332\pi$
$167$			5.15715e36i			0.0843781i	−0.999110	+	0.0421890i	$0.986567\pi$
$168$	2.79766e37	+	4.79970e37i	0.413559	+	0.709507i
$169$	−7.13991e37			−0.954155
$170$		−	7.92220e37i		−	0.957666i
$171$	−1.55640e37	+	2.74805e37i	−0.170289	+	0.300671i
$172$	−2.42025e37			−0.239815
$173$			1.31796e38i			1.18336i	0.806171	+	0.591682i	$0.201536\pi$
$173$			1.31796e38i			1.18336i	−0.806171	+	0.591682i	$0.798464\pi$
$174$	−7.83744e36	+	4.56831e36i	−0.0638024	+	0.0371893i
$175$	3.79090e38			2.79959
$176$			4.03297e37i			0.270339i
$177$	−4.11507e37	−	7.05986e37i	−0.250514	−	0.429784i
$178$	1.15461e36			0.00638697
$179$			1.83650e38i			0.923614i	0.886980	+	0.461807i	$0.152799\pi$
$179$			1.83650e38i			0.923614i	−0.886980	+	0.461807i	$0.847201\pi$
$180$	−3.00459e38	−	1.70169e38i	−1.37452	−	0.778481i
$181$	9.72091e37			0.404735			0.202368	−	0.979310i	$-0.435136\pi$
$181$	9.72091e37			0.404735			0.202368	+	0.979310i	$0.435136\pi$
$182$			2.47168e37i			0.0937083i
$183$	−1.36448e38	+	7.95331e37i	−0.471301	+	0.274713i
$184$	−1.35030e38			−0.425135
$185$		−	7.98679e38i		−	2.29326i
$186$	−4.22496e37	−	7.24839e37i	−0.110688	−	0.189898i
$187$	−2.65077e38			−0.633965
$188$		−	1.64869e38i		−	0.360128i
$189$	7.74656e36	+	6.23784e38i	0.0154617	+	1.24504i
$190$	1.19968e38			0.218904
$191$			7.95406e38i			1.32746i	0.747972	+	0.663730i	$0.231028\pi$
$191$			7.95406e38i			1.32746i	−0.747972	+	0.663730i	$0.768972\pi$
$192$	1.88478e38	−	1.09860e38i	0.287832	−	0.167772i
$193$	−3.61070e37			−0.0504798			−0.0252399	−	0.999681i	$-0.508035\pi$
$193$	−3.61070e37			−0.0504798			−0.0252399	+	0.999681i	$0.508035\pi$
$194$			1.94477e38i			0.249023i
$195$	−1.65631e38	−	2.84158e38i	−0.194336	−	0.333404i
$196$	4.48471e38			0.482371
$197$		−	1.21476e39i		−	1.19830i	−0.800639	−	0.599148i	$-0.795506\pi$
$197$		−	1.21476e39i		−	1.19830i	0.800639	−	0.599148i	$-0.204494\pi$
$198$	8.02611e37	−	1.41713e38i	0.0726435	−	0.128263i
$199$	8.05000e38			0.668796			0.334398	−	0.942432i	$-0.391467\pi$
$199$	8.05000e38			0.668796			0.334398	+	0.942432i	$0.391467\pi$
$200$			1.94374e39i			1.48296i
$201$	1.47399e39	−	8.59164e38i	1.03315	−	0.602203i
$202$	−2.39485e38			−0.154278
$203$			4.41657e38i			0.261609i
$204$	1.22455e39	+	2.10085e39i	0.667210	+	1.14467i
$205$	−2.77684e39			−1.39231
$206$		−	1.14264e39i		−	0.527433i
$207$	−1.31934e39	−	7.47229e38i	−0.560870	−	0.317657i
$208$	3.52397e38			0.138024
$209$		−	4.01414e38i		−	0.144912i
$210$	2.04731e39	−	1.19334e39i	0.681482	−	0.397224i
$211$	−5.53346e39			−1.69901			−0.849503	−	0.527583i	$-0.823098\pi$
$211$	−5.53346e39			−1.69901			−0.849503	+	0.527583i	$0.823098\pi$
$212$		−	3.19500e39i		−	0.905236i
$213$	3.99305e38	+	6.85052e38i	0.104436	+	0.179172i
$214$	5.10237e38			0.123236
$215$			2.21023e39i			0.493155i
$216$	−3.19839e39	+	3.97197e37i	−0.659505	+	0.00819016i
$217$	−4.08463e39			−0.778641
$218$			4.88772e38i			0.0861680i
$219$	8.55542e39	−	4.98680e39i	1.39538	−	0.813340i
$220$	4.38886e39			0.662470
$221$			2.31622e39i			0.323677i
$222$	−1.74020e39	−	2.98551e39i	−0.225216	−	0.386383i
$223$	9.88371e39			1.18505			0.592526	−	0.805552i	$-0.298131\pi$
$223$	9.88371e39			1.18505			0.592526	+	0.805552i	$0.298131\pi$
$224$			9.92965e39i			1.10336i
$225$	−1.07563e40	+	1.89918e40i	−1.10805	+	1.95643i
$226$	4.34408e39			0.415006
$227$		−	1.96927e40i		−	1.74528i	−0.488364	−	0.872640i	$-0.662406\pi$
$227$		−	1.96927e40i		−	1.74528i	0.488364	−	0.872640i	$-0.337594\pi$
$228$	−3.18137e39	+	1.85436e39i	−0.261650	+	0.152512i
$229$	1.66216e40			1.26902			0.634511	−	0.772913i	$-0.281201\pi$
$229$	1.66216e40			1.26902			0.634511	+	0.772913i	$0.281201\pi$
$230$			5.75968e39i			0.408343i
$231$	−3.99292e39	−	6.85030e39i	−0.262958	−	0.451134i
$232$	−2.26455e39			−0.138576
$233$		−	4.22978e39i		−	0.240584i	−0.992739	−	0.120292i	$-0.961617\pi$
$233$		−	4.22978e39i		−	0.240584i	0.992739	−	0.120292i	$-0.0383831\pi$
$234$	−1.23827e39	−	7.01315e38i	−0.0654858	−	0.0370888i
$235$	−1.50562e40			−0.740565
$236$		−	9.52787e39i		−	0.436005i
$237$	3.18443e39	−	1.85615e39i	0.135616	−	0.0790481i
$238$	−1.66880e40			−0.661599
$239$			4.32007e40i			1.59487i	0.603402	+	0.797437i	$0.293811\pi$
$239$			4.32007e40i			1.59487i	−0.603402	+	0.797437i	$0.706189\pi$
$240$	−1.70139e40	−	2.91893e40i	−0.585078	−	1.00377i
$241$	3.68186e40			1.17972			0.589859	−	0.807506i	$-0.299183\pi$
$241$	3.68186e40			1.17972			0.589859	+	0.807506i	$0.299183\pi$
$242$		−	9.69992e39i		−	0.289672i
$243$	−3.14705e40	−	1.73112e40i	−0.876188	−	0.481970i
$244$	−1.84148e40			−0.478124
$245$		−	4.09555e40i		−	0.991947i
$246$	−1.03800e40	+	6.05031e39i	−0.234585	+	0.136735i
$247$	−3.50752e39			−0.0739864
$248$		−	2.09435e40i		−	0.412450i
$249$	4.22624e40	+	7.25058e40i	0.777258	+	1.33347i
$250$	4.60353e40			0.790881
$251$			1.00568e41i			1.61438i	0.590295	+	0.807188i	$0.299011\pi$
$251$			1.00568e41i			1.61438i	−0.590295	+	0.807188i	$0.700989\pi$
$252$	−3.58458e40	+	6.32911e40i	−0.537810	+	0.949584i
$253$	1.92719e40			0.270319
$254$		−	2.98020e40i		−	0.390906i
$255$	1.91854e41	−	1.11829e41i	2.35390	−	1.37205i
$256$	−1.69602e39			−0.0194694
$257$		−	3.25250e40i		−	0.349425i	−0.984619	−	0.174713i	$-0.944100\pi$
$257$		−	3.25250e40i		−	0.349425i	0.984619	−	0.174713i	$-0.0558996\pi$
$258$	4.81575e39	+	8.26196e39i	0.0484316	+	0.0830898i
$259$	−1.68240e41			−1.58429
$260$		−	3.83495e40i		−	0.338231i
$261$	−2.21264e40	−	1.25316e40i	−0.182819	−	0.103542i
$262$	1.54695e40			0.119772
$263$			1.55707e41i			1.12995i	0.825107	+	0.564977i	$0.191115\pi$
$263$			1.55707e41i			1.12995i	−0.825107	+	0.564977i	$0.808885\pi$
$264$	3.51242e40	−	2.04733e40i	0.238968	−	0.139290i
$265$	−2.91775e41			−1.86152
$266$		−	2.52710e40i		−	0.151229i
$267$	1.62983e39	+	2.79615e39i	0.00915061	+	0.0156989i
$268$	1.98928e41			1.04810
$269$		−	3.56146e41i		−	1.76133i	−0.473743	−	0.880663i	$-0.657097\pi$
$269$		−	3.56146e41i		−	1.76133i	0.473743	−	0.880663i	$-0.342903\pi$
$270$	1.69424e39	+	1.36427e41i	0.00786666	+	0.633455i
$271$	−4.37392e40			−0.190719			−0.0953593	−	0.995443i	$-0.530400\pi$
$271$	−4.37392e40			−0.190719			−0.0953593	+	0.995443i	$0.530400\pi$
$272$			2.37927e41i			0.974481i
$273$	−5.98573e40	+	3.48898e40i	−0.230331	+	0.134256i
$274$	−1.88836e41			−0.682849
$275$		−	2.77418e41i		−	0.942928i
$276$	−8.90283e40	−	1.52738e41i	−0.284494	−	0.488082i
$277$	−1.17525e41			−0.353161			−0.176581	−	0.984286i	$-0.556504\pi$
$277$	−1.17525e41			−0.353161			−0.176581	+	0.984286i	$0.556504\pi$
$278$			1.30911e41i			0.370010i
$279$	1.15898e41	−	2.04634e41i	0.308179	−	0.544135i
$280$	5.91550e41			1.48015
$281$			4.55949e41i			1.07376i	0.843657	+	0.536882i	$0.180398\pi$
$281$			4.55949e41i			1.07376i	−0.843657	+	0.536882i	$0.819602\pi$
$282$	−5.62811e40	+	3.28053e40i	−0.124775	+	0.0727293i
$283$	8.37173e41			1.74761			0.873807	−	0.486273i	$-0.161644\pi$
$283$	8.37173e41			1.74761			0.873807	+	0.486273i	$0.161644\pi$
$284$			9.24535e40i			0.181766i
$285$	1.69345e41	+	2.90530e41i	0.313624	+	0.538057i
$286$	1.80877e40			0.0315618
$287$			5.84936e41i			0.961869i
$288$	−4.97461e41	−	2.81744e41i	−0.771058	−	0.436700i
$289$	−8.79514e41			−1.28523
$290$			9.65942e40i			0.133102i
$291$	−4.70971e41	+	2.74521e41i	−0.612088	+	0.356775i
$292$	1.15463e42			1.41557
$293$		−	1.58031e42i		−	1.82807i	−0.405634	−	0.914036i	$-0.632949\pi$
$293$		−	1.58031e42i		−	1.82807i	0.405634	−	0.914036i	$-0.367051\pi$
$294$	−8.92358e40	−	1.53094e41i	−0.0974169	−	0.167130i
$295$	−8.70108e41			−0.896600
$296$		−	8.62635e41i		−	0.839205i
$297$	4.56485e41	−	5.66893e39i	0.419341	−	0.00520765i
$298$	3.49668e41			0.303375
$299$		−	1.68397e41i		−	0.138014i
$300$	−2.19865e42	+	1.28156e42i	−1.70253	+	0.992376i
$301$	4.65580e41			0.340694
$302$			4.25336e41i			0.294180i
$303$	−3.38053e41	−	5.79968e41i	−0.221035	−	0.379210i
$304$	−3.60300e41			−0.222748
$305$			1.68168e42i			0.983212i
$306$	4.73505e41	−	8.36043e41i	0.261855	−	0.462343i
$307$	2.55730e41			0.133792			0.0668959	−	0.997760i	$-0.478690\pi$
$307$	2.55730e41			0.133792			0.0668959	+	0.997760i	$0.478690\pi$
$308$		−	9.24506e41i		−	0.457665i
$309$	2.76717e42	−	1.61294e42i	1.29641	−	0.755654i
$310$	−8.93344e41			−0.396159
$311$			1.84247e42i			0.773523i	0.922180	+	0.386762i	$0.126406\pi$
$311$			1.84247e42i			0.773523i	−0.922180	+	0.386762i	$0.873594\pi$
$312$	−1.78894e41	−	3.06913e41i	−0.0711161	−	0.122008i
$313$	−1.93846e42			−0.729799			−0.364900	−	0.931047i	$-0.618897\pi$
$313$	−1.93846e42			−0.729799			−0.364900	+	0.931047i	$0.618897\pi$
$314$			5.02180e41i			0.179084i
$315$	5.77989e42	+	3.27352e42i	1.95272	+	1.10595i
$316$	4.29766e41			0.137579
$317$			5.77707e41i			0.175267i	0.996153	+	0.0876335i	$0.0279304\pi$
$317$			5.77707e41i			0.175267i	−0.996153	+	0.0876335i	$0.972070\pi$
$318$	−1.09067e42	+	6.35734e41i	−0.313642	+	0.182816i
$319$	3.23205e41			0.0881123
$320$		−	2.32294e42i		−	0.600465i
$321$	7.20242e41	+	1.23566e42i	0.176560	+	0.302909i
$322$	1.21327e42			0.282102
$323$		−	2.36816e42i		−	0.522359i
$324$	−2.15370e42	−	3.59165e42i	−0.450734	−	0.751672i
$325$	−2.42405e42			−0.481421
$326$		−	6.64150e41i		−	0.125189i
$327$	−1.18367e42	+	6.89943e41i	−0.211797	+	0.123453i
$328$	−2.99920e42			−0.509507
$329$			3.17157e42i			0.511616i
$330$	−8.73286e41	−	1.49822e42i	−0.133789	−	0.229529i
$331$	−6.86360e42			−0.998794			−0.499397	−	0.866373i	$-0.666445\pi$
$331$	−6.86360e42			−0.998794			−0.499397	+	0.866373i	$0.666445\pi$
$332$			9.78528e42i			1.35278i
$333$	4.77366e42	−	8.42859e42i	0.627046	−	1.10714i
$334$	2.37593e41			0.0296581
$335$		−	1.81665e43i		−	2.15531i
$336$	−6.14867e42	+	3.58395e42i	−0.693448	+	0.404199i
$337$	−1.24578e43			−1.33578			−0.667889	−	0.744261i	$-0.732802\pi$
$337$	−1.24578e43			−1.33578			−0.667889	+	0.744261i	$0.732802\pi$
$338$			3.28940e42i			0.335376i
$339$	6.13204e42	+	1.05202e43i	0.594580	+	1.02007i
$340$	2.58924e43			2.38798
$341$			2.98913e42i			0.262253i
$342$	1.26604e42	+	7.17041e41i	0.105683	+	0.0598550i
$343$	7.04816e42			0.559855
$344$			2.38722e42i			0.180467i
$345$	−1.39484e43	+	8.13027e42i	−1.00369	+	0.585033i
$346$	6.07191e42			0.415941
$347$		−	4.95559e42i		−	0.323217i	−0.986855	−	0.161609i	$-0.948332\pi$
$347$		−	4.95559e42i		−	0.323217i	0.986855	−	0.161609i	$-0.0516682\pi$
$348$	−1.49307e42	−	2.56153e42i	−0.0927329	−	0.159094i
$349$	7.20849e42			0.426395			0.213197	−	0.977009i	$-0.431612\pi$
$349$	7.20849e42			0.426395			0.213197	+	0.977009i	$0.431612\pi$
$350$		−	1.74649e43i		−	0.984030i
$351$	−4.95347e40	−	3.98873e42i	−0.00265882	−	0.214099i
$352$	7.26652e42			0.371622
$353$			3.47119e43i			1.69164i	0.533468	+	0.845820i	$0.320888\pi$
$353$			3.47119e43i			1.69164i	−0.533468	+	0.845820i	$0.679112\pi$
$354$	−3.25251e42	+	1.89583e42i	−0.151065	+	0.0880531i
$355$	8.44307e42			0.373782
$356$			3.77364e41i			0.0159261i
$357$	−2.35565e43	−	4.04138e43i	−0.947874	−	1.62618i
$358$	8.46087e42			0.324641
$359$			3.85182e43i			1.40948i	0.709463	+	0.704742i	$0.248937\pi$
$359$			3.85182e43i			1.40948i	−0.709463	+	0.704742i	$0.751063\pi$
$360$	−1.67847e43	+	2.96358e43i	−0.585828	+	1.03437i
$361$	−2.64485e43			−0.880599
$362$		−	4.47847e42i		−	0.142261i
$363$	2.34906e43	−	1.36923e43i	0.712002	−	0.415014i
$364$	−8.07826e42			−0.233665
$365$		−	1.05443e44i		−	2.91098i
$366$	3.66413e42	+	6.28623e42i	0.0965591	+	0.165658i
$367$	−5.67891e42			−0.142870			−0.0714351	−	0.997445i	$-0.522758\pi$
$367$	−5.67891e42			−0.142870			−0.0714351	+	0.997445i	$0.522758\pi$
$368$		−	1.72980e43i		−	0.415512i
$369$	−2.93044e43	−	1.65970e43i	−0.672179	−	0.380698i
$370$	−3.67956e43			−0.806058
$371$			6.14619e43i			1.28603i
$372$	2.36901e43	−	1.38086e43i	0.473519	−	0.276006i
$373$	−1.19236e43			−0.227696			−0.113848	−	0.993498i	$-0.536318\pi$
$373$	−1.19236e43			−0.227696			−0.113848	+	0.993498i	$0.536318\pi$
$374$			1.22123e43i			0.222833i
$375$	6.49827e43	+	1.11485e44i	1.13310	+	1.94395i
$376$	−1.62619e43			−0.271006
$377$		−	2.82414e42i		−	0.0449866i
$378$	2.87381e43	−	3.56888e41i	0.437620	−	0.00543465i
$379$	6.56483e43			0.955777			0.477889	−	0.878420i	$-0.341402\pi$
$379$	6.56483e43			0.955777			0.477889	+	0.878420i	$0.341402\pi$
$380$			3.92095e43i			0.545846i
$381$	7.21724e43	−	4.20680e43i	0.960830	−	0.560051i
$382$	3.66448e43			0.466590
$383$			9.44163e42i			0.114992i	0.998346	+	0.0574960i	$0.0183117\pi$
$383$			9.44163e42i			0.114992i	−0.998346	+	0.0574960i	$0.981688\pi$
$384$	−4.33614e43	−	7.43914e43i	−0.505211	−	0.866746i
$385$	−8.44280e43			−0.941140
$386$			1.66347e42i			0.0177432i
$387$	−1.32104e43	+	2.33249e43i	−0.134843	+	0.238086i
$388$	−6.35616e43			−0.620948
$389$		−	7.11826e42i		−	0.0665627i	−0.999446	−	0.0332813i	$-0.989404\pi$
$389$		−	7.11826e42i		−	0.0665627i	0.999446	−	0.0332813i	$-0.0105957\pi$
$390$	−1.30913e43	+	7.63070e42i	−0.117188	+	0.0683071i
$391$	1.13696e44			0.974406
$392$		−	4.42351e43i		−	0.362997i
$393$	2.18365e43	+	3.74630e43i	0.171597	+	0.294394i
$394$	−5.59646e43			−0.421189
$395$		−	3.92472e43i		−	0.282917i
$396$	4.63164e43	+	2.62320e43i	0.319828	+	0.181139i
$397$	−7.99956e43			−0.529209			−0.264605	−	0.964357i	$-0.585241\pi$
$397$	−7.99956e43			−0.529209			−0.264605	+	0.964357i	$0.585241\pi$
$398$		−	3.70868e43i		−	0.235075i
$399$	6.11996e43	−	3.56722e43i	0.371714	−	0.216666i
$400$	−2.49004e44			−1.44939
$401$		−	6.80463e42i		−	0.0379621i	−0.999820	−	0.0189811i	$-0.993958\pi$
$401$		−	6.80463e42i		−	0.0379621i	0.999820	−	0.0189811i	$-0.00604222\pi$
$402$	−3.95822e43	−	6.79076e43i	−0.211669	−	0.363141i
$403$	2.61188e43			0.133896
$404$		−	7.82716e43i		−	0.384699i
$405$	−3.27998e44	+	1.96681e44i	−1.54574	+	0.926888i
$406$	2.03474e43			0.0919531
$407$			1.23118e44i			0.533602i
$408$	2.07218e44	−	1.20783e44i	0.861398	−	0.502094i
$409$	1.69922e44			0.677568			0.338784	−	0.940864i	$-0.389984\pi$
$409$	1.69922e44			0.677568			0.338784	+	0.940864i	$0.389984\pi$
$410$			1.27930e44i			0.489382i
$411$	−2.66558e44	−	4.57310e44i	−0.978319	−	1.67842i
$412$	3.73453e44			1.31518
$413$			1.83287e44i			0.619412i
$414$	−3.44253e43	+	6.07829e43i	−0.111653	+	0.197140i
$415$	8.93614e44			2.78184
$416$		−	6.34942e43i		−	0.189735i
$417$	−3.17031e44	+	1.84792e44i	−0.909470	+	0.530114i
$418$	−1.84933e43			−0.0509353
$419$			2.16731e44i			0.573169i	0.958055	+	0.286584i	$0.0925199\pi$
$419$			2.16731e44i			0.573169i	−0.958055	+	0.286584i	$0.907480\pi$
$420$	3.90023e44	+	6.69127e44i	0.990494	+	1.69930i
$421$	−5.04802e44			−1.23119			−0.615596	−	0.788062i	$-0.711085\pi$
$421$	−5.04802e44			−1.23119			−0.615596	+	0.788062i	$0.711085\pi$
$422$			2.54929e44i			0.597184i
$423$	−1.58891e44	−	8.99903e43i	−0.357531	−	0.202493i
$424$	−3.15140e44			−0.681215
$425$		−	1.63664e45i		−	3.39893i
$426$	3.15607e43	−	1.83962e43i	0.0629772	−	0.0367083i
$427$	3.54243e44			0.679247
$428$			1.66762e44i			0.307294i
$429$	2.55324e43	+	4.38036e43i	0.0452186	+	0.0775775i
$430$	1.01826e44			0.173339
$431$			6.17185e44i			1.00995i	0.863133	+	0.504977i	$0.168499\pi$
$431$			6.17185e44i			1.00995i	−0.863133	+	0.504977i	$0.831501\pi$
$432$	−5.08831e42	−	4.09731e44i	−0.00800478	−	0.644577i
$433$	−9.20555e44			−1.39237			−0.696186	−	0.717861i	$-0.745121\pi$
$433$	−9.20555e44			−1.39237			−0.696186	+	0.717861i	$0.745121\pi$
$434$			1.88181e44i			0.273685i
$435$	−2.33925e44	+	1.36351e44i	−0.327160	+	0.190696i
$436$	−1.59747e44			−0.214863
$437$			1.72173e44i			0.222731i
$438$	−2.29745e44	−	3.94153e44i	−0.285881	−	0.490461i
$439$	−3.60164e44			−0.431125			−0.215563	−	0.976490i	$-0.569159\pi$
$439$	−3.60164e44			−0.431125			−0.215563	+	0.976490i	$0.569159\pi$
$440$		−	4.32896e44i		−	0.498527i
$441$	2.44788e44	−	4.32210e44i	0.271228	−	0.478893i
$442$	1.06710e44			0.113769
$443$			6.41952e44i			0.658627i	0.944221	+	0.329313i	$0.106817\pi$
$443$			6.41952e44i			0.658627i	−0.944221	+	0.329313i	$0.893183\pi$
$444$	9.75763e44	−	5.68755e44i	0.963460	−	0.561584i
$445$	3.44618e43			0.0327505
$446$		−	4.55348e44i		−	0.416534i
$447$	4.93586e44	+	8.46802e44i	0.434645	+	0.745683i
$448$	−4.89322e44			−0.414829
$449$		−	8.45159e44i		−	0.689844i	−0.938631	−	0.344922i	$-0.887905\pi$
$449$		−	8.45159e44i		−	0.689844i	0.938631	−	0.344922i	$-0.112095\pi$
$450$	8.74965e44	+	4.95549e44i	0.687666	+	0.389470i
$451$	4.28056e44			0.323966
$452$			1.41979e45i			1.03483i
$453$	−1.03005e45	+	6.00397e44i	−0.723083	+	0.421472i
$454$	−9.07252e44			−0.613449
$455$			7.37725e44i			0.480508i
$456$	1.82906e44	+	3.13795e44i	0.114769	+	0.196899i
$457$	2.16960e45			1.31161			0.655804	−	0.754931i	$-0.272330\pi$
$457$	2.16960e45			1.31161			0.655804	+	0.754931i	$0.272330\pi$
$458$		−	7.65766e44i		−	0.446049i
$459$	2.69306e45	−	3.34442e43i	1.51158	−	0.0187718i
$460$	−1.88245e45			−1.01822
$461$			3.98780e44i			0.207883i	0.994583	+	0.103941i	$0.0331454\pi$
$461$			3.98780e44i			0.207883i	−0.994583	+	0.103941i	$0.966855\pi$
$462$	−3.15597e44	+	1.83956e44i	−0.158569	+	0.0924273i
$463$	1.17118e45			0.567215			0.283608	−	0.958940i	$-0.408469\pi$
$463$	1.17118e45			0.567215			0.283608	+	0.958940i	$0.408469\pi$
$464$		−	2.90102e44i		−	0.135439i
$465$	−1.26103e45	−	2.16344e45i	−0.567578	−	0.973743i
$466$	−1.94868e44			−0.0845630
$467$		−	4.94974e44i		−	0.207107i	−0.994624	−	0.103554i	$-0.966979\pi$
$467$		−	4.94974e44i		−	0.207107i	0.994624	−	0.103554i	$-0.0330214\pi$
$468$	2.29213e44	−	4.04709e44i	0.0924825	−	0.163291i
$469$	−3.82675e45			−1.48899
$470$			6.93649e44i			0.260301i
$471$	−1.21615e45	+	7.08870e44i	−0.440180	+	0.256573i
$472$	−9.39784e44			−0.328106
$473$		−	3.40712e44i		−	0.114749i
$474$	−8.55138e43	−	1.46708e44i	−0.0277846	−	0.0476676i
$475$	2.47841e45			0.776931
$476$		−	5.45418e45i		−	1.64972i
$477$	−3.07916e45	−	1.74392e45i	−0.898709	−	0.508997i
$478$	1.99028e45			0.560583
$479$			2.32078e45i			0.630856i	0.948950	+	0.315428i	$0.102148\pi$
$479$			2.32078e45i			0.630856i	−0.948950	+	0.315428i	$0.897852\pi$
$480$	−5.25927e45	+	3.06554e45i	−1.37983	+	0.804276i
$481$	1.07580e45			0.272436
$482$		−	1.69625e45i		−	0.414659i
$483$	1.71263e45	+	2.93820e45i	0.404168	+	0.693395i
$484$	3.17025e45			0.722309
$485$			5.80459e45i			1.27691i
$486$	−7.97536e44	+	1.44986e45i	−0.169408	+	0.307971i
$487$	6.50178e45			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$487$	6.50178e45			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$488$			1.81635e45i			0.359801i
$489$	1.60839e45	−	9.37503e44i	0.307710	−	0.179359i
$490$	−1.88684e45			−0.348660
$491$		−	4.73253e45i		−	0.844710i	−0.906430	−	0.422355i	$-0.861204\pi$
$491$		−	4.73253e45i		−	0.844710i	0.906430	−	0.422355i	$-0.138796\pi$
$492$	−1.97744e45	−	3.39252e45i	−0.340955	−	0.584946i
$493$	1.90677e45			0.317614
$494$			1.61593e44i			0.0260055i
$495$	2.39556e45	−	4.22972e45i	0.372494	−	0.657694i
$496$	2.68298e45			0.403115
$497$		−	1.77852e45i		−	0.258226i
$498$	3.34038e45	−	1.94705e45i	0.468703	−	0.273199i
$499$	−8.44527e45			−1.14526			−0.572630	−	0.819814i	$-0.694077\pi$
$499$	−8.44527e45			−1.14526			−0.572630	+	0.819814i	$0.694077\pi$
$500$			1.50459e46i			1.97209i
$501$	3.35382e44	+	5.75385e44i	0.0424912	+	0.0728983i
$502$	4.63320e45			0.567437
$503$			4.59418e44i			0.0543941i	0.999630	+	0.0271971i	$0.00865816\pi$
$503$			4.59418e44i			0.0543941i	−0.999630	+	0.0271971i	$0.991342\pi$
$504$	6.24273e45	+	3.53566e45i	0.714587	+	0.404717i
$505$	−7.14795e45			−0.791094
$506$		−	8.87868e44i		−	0.0950144i
$507$	−7.96603e45	+	4.64326e45i	−0.824340	+	0.480494i
$508$	9.74028e45			0.974739
$509$		−	1.73226e45i		−	0.167652i	−0.996480	−	0.0838262i	$-0.973286\pi$
$509$		−	1.73226e45i		−	0.167652i	0.996480	−	0.0838262i	$-0.0267140\pi$
$510$	−5.15200e45	−	8.83883e45i	−0.482262	−	0.827374i
$511$	−2.22114e46			−2.01104
$512$		−	1.13768e46i		−	0.996395i
$513$	5.06455e43	+	4.07818e45i	0.00429087	+	0.345518i
$514$	−1.49844e45			−0.122820
$515$		−	3.41046e46i		−	2.70452i
$516$	−2.70028e45	+	1.57395e45i	−0.207188	+	0.120766i
$517$	2.32096e45			0.172317
$518$			7.75092e45i			0.556861i
$519$	8.57102e45	+	1.47045e46i	0.595919	+	1.02237i
$520$	−3.78261e45			−0.254528
$521$			1.68417e46i			1.09685i	0.836201	+	0.548423i	$0.184772\pi$
$521$			1.68417e46i			1.09685i	−0.836201	+	0.548423i	$0.815228\pi$
$522$	−5.77338e44	+	1.01938e45i	−0.0363941	+	0.0642593i
$523$	−2.29640e46			−1.40126			−0.700631	−	0.713524i	$-0.747098\pi$
$523$	−2.29640e46			−1.40126			−0.700631	+	0.713524i	$0.747098\pi$
$524$			5.05595e45i			0.298656i
$525$	4.22952e46	−	2.46531e46i	2.41870	−	1.40982i
$526$	7.17351e45			0.397168
$527$			1.76346e46i			0.945333i
$528$	2.62274e45	+	4.49960e45i	0.136138	+	0.233559i
$529$	1.16291e46			0.584519
$530$			1.34422e46i			0.654308i
$531$	−9.18240e45	−	5.20058e45i	−0.432862	−	0.245157i
$532$	8.25941e45			0.377095
$533$		−	3.74032e45i		−	0.165404i
$534$	1.28820e44	−	7.50870e43i	0.00551801	−	0.00321635i
$535$	1.52291e46			0.631917
$536$		−	1.96213e46i		−	0.788725i
$537$	1.19432e46	+	2.04900e46i	0.465114	+	0.797955i
$538$	−1.64079e46			−0.619089
$539$			6.31338e45i			0.230809i
$540$	−4.45888e46	+	5.53733e44i	−1.57955	+	0.0196158i
$541$	−3.02027e46			−1.03679			−0.518397	−	0.855140i	$-0.673471\pi$
$541$	−3.02027e46			−1.03679			−0.518397	+	0.855140i	$0.673471\pi$
$542$			2.01509e45i			0.0670357i
$543$	1.08457e46	−	6.32175e45i	0.349670	−	0.203817i
$544$	4.28693e46			1.33957
$545$			1.45885e46i			0.441844i
$546$	1.60739e45	+	2.75766e45i	0.0471897	+	0.0809591i
$547$	3.59015e46			1.02171			0.510855	−	0.859667i	$-0.329329\pi$
$547$	3.59015e46			1.02171			0.510855	+	0.859667i	$0.329329\pi$
$548$		−	6.17178e46i		−	1.70271i
$549$	−1.00513e46	+	1.77471e46i	−0.268840	+	0.474676i
$550$	−1.27808e46			−0.331430
$551$			2.88747e45i			0.0726006i
$552$	−1.50653e46	+	8.78133e45i	−0.367295	+	0.214090i
$553$	−8.26736e45			−0.195452
$554$			5.41443e45i			0.124133i
$555$	−5.19401e46	−	8.91089e46i	−1.15484	−	1.98126i
$556$	−4.27860e46			−0.922635
$557$			2.86942e46i			0.600145i	0.953916	+	0.300073i	$0.0970109\pi$
$557$			2.86942e46i			0.600145i	−0.953916	+	0.300073i	$0.902989\pi$
$558$	−9.42761e45	−	5.33946e45i	−0.191258	−	0.108322i
$559$	−2.97711e45			−0.0585861
$560$			7.57807e46i			1.44665i
$561$	−2.95748e46	+	1.72386e46i	−0.547713	+	0.319252i
$562$	2.10058e46			0.377418
$563$		−	7.09664e46i		−	1.23711i	−0.785740	−	0.618557i	$-0.787718\pi$
$563$		−	7.09664e46i		−	1.23711i	0.785740	−	0.618557i	$-0.212282\pi$
$564$	−1.07219e46	−	1.83945e46i	−0.181353	−	0.311132i
$565$	1.29659e47			2.12803
$566$		−	3.85690e46i		−	0.614269i
$567$	4.14305e46	+	6.90921e46i	0.640337	+	1.06787i
$568$	9.11917e45			0.136783
$569$		−	1.46145e45i		−	0.0212753i	−0.999943	−	0.0106376i	$-0.996614\pi$
$569$		−	1.46145e45i		−	0.0212753i	0.999943	−	0.0106376i	$-0.00338613\pi$
$570$	1.33849e46	−	7.80181e45i	0.189122	−	0.110236i
$571$	−9.93026e46			−1.36190			−0.680952	−	0.732328i	$-0.738434\pi$
$571$	−9.93026e46			−1.36190			−0.680952	+	0.732328i	$0.738434\pi$
$572$			5.91167e45i			0.0787005i
$573$	5.17272e46	+	8.87438e46i	0.668483	+	1.14686i
$574$	2.69483e46			0.338088
$575$			1.18989e47i			1.44928i
$576$	1.38841e46	−	2.45144e46i	0.164185	−	0.289893i
$577$	6.65273e46			0.763856			0.381928	−	0.924192i	$-0.375260\pi$
$577$	6.65273e46			0.763856			0.381928	+	0.924192i	$0.375260\pi$
$578$			4.05197e46i			0.451744i
$579$	−4.02848e45	+	2.34813e45i	−0.0436119	+	0.0254206i
$580$	−3.15702e46			−0.331895
$581$		−	1.88238e47i		−	1.92182i
$582$	1.26473e46	+	2.16979e46i	0.125403	+	0.215143i
$583$	4.49779e46			0.433145
$584$		−	1.13887e47i		−	1.06526i
$585$	−3.69590e46	−	2.09322e46i	−0.335792	−	0.190181i
$586$	−7.28058e46			−0.642549
$587$			8.11276e46i			0.695538i	0.937580	+	0.347769i	$0.113061\pi$
$587$			8.11276e46i			0.695538i	−0.937580	+	0.347769i	$0.886939\pi$
$588$	5.00362e46	−	2.91652e46i	0.416744	−	0.242913i
$589$	−2.67045e46			−0.216085
$590$			4.00863e46i			0.315146i
$591$	−7.89987e46	−	1.35531e47i	−0.603438	−	1.03527i
$592$	1.10508e47			0.820210
$593$			1.36306e47i			0.983068i	0.870858	+	0.491534i	$0.163564\pi$
$593$			1.36306e47i			0.983068i	−0.870858	+	0.491534i	$0.836436\pi$
$594$	−2.61171e44	−	2.10305e46i	−0.00183044	−	0.147394i
$595$	−4.98088e47			−3.39249
$596$			1.14283e47i			0.756477i
$597$	8.98142e46	−	5.23511e46i	0.577805	−	0.336792i
$598$	−7.75812e45			−0.0485106
$599$		−	7.94216e46i		−	0.482706i	−0.970437	−	0.241353i	$-0.922409\pi$
$599$		−	7.94216e46i		−	0.482706i	0.970437	−	0.241353i	$-0.0775911\pi$
$600$	1.26406e47	+	2.16864e47i	0.746789	+	1.28120i
$601$	−1.19385e46			−0.0685621			−0.0342811	−	0.999412i	$-0.510914\pi$
$601$	−1.19385e46			−0.0685621			−0.0342811	+	0.999412i	$0.510914\pi$
$602$		−	2.14495e46i		−	0.119751i
$603$	1.08580e47	−	1.91715e47i	0.589328	−	1.04055i
$604$	−1.39014e47			−0.733550
$605$		−	2.89515e47i		−	1.48535i
$606$	−2.67194e46	+	1.55743e46i	−0.133289	+	0.0776916i
$607$	1.55661e47			0.755046			0.377523	−	0.926000i	$-0.376776\pi$
$607$	1.55661e47			0.755046			0.377523	+	0.926000i	$0.376776\pi$
$608$			6.49181e46i			0.306200i
$609$	2.87221e46	+	4.92759e46i	0.131741	+	0.226017i
$610$	7.74761e46			0.345589
$611$		−	2.02803e46i		−	0.0879780i
$612$	2.73247e47	+	1.54757e47i	1.15287	+	0.652945i
$613$	4.35404e46			0.178675			0.0893376	−	0.996001i	$-0.471525\pi$
$613$	4.35404e46			0.178675			0.0893376	+	0.996001i	$0.471525\pi$
$614$		−	1.17816e46i		−	0.0470265i
$615$	−3.09813e47	+	1.80585e47i	−1.20288	+	0.701138i
$616$	−9.11888e46			−0.344405
$617$			3.98888e47i			1.46556i	0.680467	+	0.732779i	$0.261777\pi$
$617$			3.98888e47i			1.46556i	−0.680467	+	0.732779i	$0.738223\pi$
$618$	−7.43089e46	−	1.27485e47i	−0.265605	−	0.455675i
$619$	4.65103e47			1.61736			0.808682	−	0.588246i	$-0.200181\pi$
$619$	4.65103e47			1.61736			0.808682	+	0.588246i	$0.200181\pi$
$620$		−	2.91974e47i		−	0.987838i
$621$	−1.95794e47	+	2.43150e45i	−0.644528	+	0.00800417i
$622$	8.48835e46			0.271886
$623$		−	7.25931e45i		−	0.0226255i
$624$	3.93171e46	−	2.29173e46i	0.119246	−	0.0695064i
$625$	6.12228e47			1.80698
$626$			8.93059e46i			0.256517i
$627$	−2.61049e46	−	4.47859e46i	−0.0729750	−	0.125197i
$628$	−1.64129e47			−0.446552
$629$			7.26344e47i			1.92345i
$630$	1.50813e47	−	2.66283e47i	0.388731	−	0.686362i
$631$	−5.29430e47			−1.32834			−0.664170	−	0.747582i	$-0.731215\pi$
$631$	−5.29430e47			−1.32834			−0.664170	+	0.747582i	$0.731215\pi$
$632$		−	4.23901e46i		−	0.103532i
$633$	−6.17370e47	+	3.59855e47i	−1.46785	+	0.855586i
$634$	2.66153e46			0.0616046
$635$		−	8.89505e47i		−	2.00445i
$636$	−2.07779e47	−	3.56468e47i	−0.455859	−	0.782077i
$637$	5.51658e46			0.117842
$638$		−	1.48902e46i		−	0.0309706i
$639$	8.91012e46	+	5.04637e46i	0.180455	+	0.102203i
$640$	−9.16853e47			−1.80817
$641$		−	9.73157e47i		−	1.86895i	−0.356035	−	0.934473i	$-0.615872\pi$
$641$		−	9.73157e47i		−	1.86895i	0.356035	−	0.934473i	$-0.384128\pi$
$642$	5.69273e46	−	3.31819e46i	0.106469	−	0.0620592i
$643$	1.00525e48			1.83100			0.915499	−	0.402321i	$-0.131796\pi$
$643$	1.00525e48			1.83100			0.915499	+	0.402321i	$0.131796\pi$
$644$			3.96535e47i			0.703432i
$645$	1.43737e47	+	2.46596e47i	0.248343	+	0.426060i
$646$	−1.09103e47			−0.183604
$647$			6.56618e46i			0.107632i	0.998551	+	0.0538158i	$0.0171384\pi$
$647$			6.56618e46i			0.107632i	−0.998551	+	0.0538158i	$0.982862\pi$
$648$	−3.54263e47	+	2.12431e47i	−0.565654	+	0.339190i
$649$	1.34129e47			0.208624
$650$			1.11677e47i			0.169215i
$651$	−4.55724e47	+	2.65634e47i	−0.672706	+	0.392109i
$652$	2.17066e47			0.312164
$653$			1.14073e48i			1.59831i	0.601127	+	0.799153i	$0.294719\pi$
$653$			1.14073e48i			1.59831i	−0.601127	+	0.799153i	$0.705281\pi$
$654$	3.17861e46	+	5.45325e46i	0.0433925	+	0.0744447i
$655$	4.61721e47			0.614154
$656$		−	3.84213e47i		−	0.497975i
$657$	6.30227e47	−	1.11276e48i	0.795950	−	1.40537i
$658$	1.46116e47			0.179828
$659$			8.65814e47i			1.03842i	0.854647	+	0.519209i	$0.173774\pi$
$659$			8.65814e47i			1.03842i	−0.854647	+	0.519209i	$0.826226\pi$
$660$	4.89667e47	−	2.85419e47i	0.572340	−	0.333607i
$661$	−1.10241e48			−1.25579			−0.627895	−	0.778298i	$-0.716083\pi$
$661$	−1.10241e48			−1.25579			−0.627895	+	0.778298i	$0.716083\pi$
$662$			3.16210e47i			0.351066i
$663$	1.50630e47	+	2.58422e47i	0.162997	+	0.279640i
$664$	9.65173e47			1.01800
$665$		−	7.54268e47i		−	0.775457i
$666$	−3.88310e47	−	2.19925e47i	−0.389150	−	0.220400i
$667$	−1.38628e47			−0.135429
$668$			7.76531e46i			0.0739536i
$669$	1.10273e48	−	6.42762e47i	1.02382	−	0.596769i
$670$	−8.36942e47			−0.757572
$671$		−	2.59235e47i		−	0.228777i
$672$	6.45749e47	+	1.10785e48i	0.555631	+	0.953247i
$673$	−1.36930e46			−0.0114879			−0.00574397	−	0.999984i	$-0.501828\pi$
$673$	−1.36930e46			−0.0114879			−0.00574397	+	0.999984i	$0.501828\pi$
$674$			5.73939e47i			0.469513i
$675$	3.50012e46	+	2.81844e48i	0.0279202	+	2.24825i
$676$	−1.07508e48			−0.836273
$677$		−	7.44194e46i		−	0.0564519i	−0.999602	−	0.0282260i	$-0.991014\pi$
$677$		−	7.44194e46i		−	0.0564519i	0.999602	−	0.0282260i	$-0.00898580\pi$
$678$	4.84671e47	−	2.82506e47i	0.358544	−	0.208989i
$679$	1.22273e48			0.882151
$680$		−	2.55390e48i		−	1.79702i
$681$	−1.28066e48	−	2.19712e48i	−0.878889	−	1.50783i
$682$	1.37711e47			0.0921795
$683$		−	7.99538e47i		−	0.522020i	−0.965336	−	0.261010i	$-0.915944\pi$
$683$		−	7.99538e47i		−	0.522020i	0.965336	−	0.261010i	$-0.0840556\pi$
$684$	−2.34353e47	+	4.13784e47i	−0.149251	+	0.263524i
$685$	−5.63621e48			−3.50145
$686$		−	3.24712e47i		−	0.196784i
$687$	1.85448e48	−	1.08094e48i	1.09637	−	0.639055i
$688$	−3.05815e47			−0.176382
$689$		−	3.93013e47i		−	0.221146i
$690$	3.74566e47	+	6.42610e47i	0.205634	+	0.352787i
$691$	−1.79689e47			−0.0962484			−0.0481242	−	0.998841i	$-0.515324\pi$
$691$	−1.79689e47			−0.0962484			−0.0481242	+	0.998841i	$0.515324\pi$
$692$			1.98450e48i			1.03717i
$693$	−8.90984e47	−	5.04621e47i	−0.454365	−	0.257336i
$694$	−2.28307e47			−0.113608
$695$			3.90731e48i			1.89730i
$696$	−2.52657e47	+	1.47270e47i	−0.119722	+	0.0697840i
$697$	2.52534e48			1.16779
$698$		−	3.32099e47i		−	0.149874i
$699$	−2.75073e47	−	4.71918e47i	−0.121153	−	0.207852i
$700$	5.70809e48			2.45372
$701$		−	2.52645e48i		−	1.06000i	−0.847999	−	0.529998i	$-0.822193\pi$
$701$		−	2.52645e48i		−	1.06000i	0.847999	−	0.529998i	$-0.177807\pi$
$702$	−1.83763e47	+	2.28209e45i	−0.0752536	+	0.000934548i
$703$	−1.09992e48			−0.439664
$704$			3.58086e47i			0.139718i
$705$	−1.67983e48	+	9.79145e47i	−0.639810	+	0.372934i
$706$	1.59919e48			0.594595
$707$			1.50570e48i			0.546524i
$708$	−6.19621e47	−	1.06303e48i	−0.219564	−	0.376686i
$709$	1.93768e48			0.670340			0.335170	−	0.942158i	$-0.391206\pi$
$709$	1.93768e48			0.670340			0.335170	+	0.942158i	$0.391206\pi$
$710$		−	3.88977e47i		−	0.131381i
$711$	2.34578e47	−	4.14183e47i	0.0773579	−	0.136587i
$712$	3.72214e46			0.0119849
$713$		−	1.28209e48i		−	0.403084i
$714$	−1.86188e48	+	1.08526e48i	−0.571588	+	0.333169i
$715$	5.39867e47			0.161839
$716$			2.76529e48i			0.809506i
$717$	2.80945e48	+	4.81992e48i	0.803147	+	1.37789i
$718$	1.77455e48			0.495420
$719$		−	4.77661e48i		−	1.30235i	−0.758926	−	0.651177i	$-0.774276\pi$
$719$		−	4.77661e48i		−	1.30235i	0.758926	−	0.651177i	$-0.225724\pi$
$720$	−3.79650e48	−	2.15020e48i	−1.01095	−	0.572568i
$721$	−7.18408e48			−1.86841
$722$			1.21850e48i			0.309522i
$723$	4.10787e48	−	2.39441e48i	1.01921	−	0.594083i
$724$	1.46371e48			0.354732
$725$			1.99554e48i			0.472404i
$726$	−6.30810e47	−	1.08222e48i	−0.145873	−	0.250262i
$727$	5.41424e48			1.22307			0.611537	−	0.791216i	$-0.290552\pi$
$727$	5.41424e48			1.22307			0.611537	+	0.791216i	$0.290552\pi$
$728$			7.96800e47i			0.175839i
$729$	−4.63697e48	+	1.15188e47i	−0.999692	+	0.0248335i
$730$	−4.85782e48			−1.02318
$731$		−	2.01005e48i		−	0.413629i
$732$	−2.05455e48	+	1.19756e48i	−0.413074	+	0.240774i
$733$	9.14560e47			0.179657			0.0898286	−	0.995957i	$-0.471368\pi$
$733$	9.14560e47			0.179657			0.0898286	+	0.995957i	$0.471368\pi$
$734$			2.61630e47i			0.0502175i
$735$	−2.66343e48	−	4.56942e48i	−0.499525	−	0.856991i
$736$	−3.11673e48			−0.571184
$737$			2.80041e48i			0.501505i
$738$	−7.64632e47	+	1.35007e48i	−0.133812	+	0.236265i
$739$	−1.90775e48			−0.326262			−0.163131	−	0.986604i	$-0.552159\pi$
$739$	−1.90775e48			−0.326262			−0.163131	+	0.986604i	$0.552159\pi$
$740$		−	1.20260e49i		−	2.00994i
$741$	−3.91335e47	+	2.28103e47i	−0.0639204	+	0.0372581i
$742$	2.83158e48			0.452026
$743$			5.70257e48i			0.889736i	0.895596	+	0.444868i	$0.146749\pi$
$743$			5.70257e48i			0.889736i	−0.895596	+	0.444868i	$0.853251\pi$
$744$	−1.36201e48	−	2.33668e48i	−0.207702	−	0.356336i
$745$	1.04366e49			1.55562
$746$			5.49325e47i			0.0800331i
$747$	9.43047e48	+	5.34108e48i	1.34302	+	0.760639i
$748$	−3.99137e48			−0.555642
$749$		−	3.20798e48i		−	0.436557i
$750$	5.13618e48	−	2.99379e48i	0.683280	−	0.398272i
$751$	−6.57375e48			−0.854937			−0.427469	−	0.904030i	$-0.640595\pi$
$751$	−6.57375e48			−0.854937			−0.427469	+	0.904030i	$0.640595\pi$
$752$		−	2.08324e48i		−	0.264872i
$753$	6.54015e48	+	1.12204e49i	0.812968	+	1.39474i
$754$	−1.30110e47			−0.0158124
$755$			1.26951e49i			1.50847i
$756$	1.16643e47	+	9.39255e48i	0.0135515	+	1.09122i
$757$	−1.02690e49			−1.16654			−0.583269	−	0.812279i	$-0.698227\pi$
$757$	−1.02690e49			−1.16654			−0.583269	+	0.812279i	$0.698227\pi$
$758$		−	3.02445e48i		−	0.335946i
$759$	2.15018e48	−	1.25330e48i	0.233541	−	0.136127i
$760$	3.86744e48			0.410764
$761$		−	2.25359e48i		−	0.234064i	−0.993128	−	0.117032i	$-0.962662\pi$
$761$		−	2.25359e48i		−	0.234064i	0.993128	−	0.117032i	$-0.0373380\pi$
$762$	−1.93810e48	−	3.32502e48i	−0.196853	−	0.337722i
$763$	3.07303e48			0.305246
$764$			1.19767e49i			1.16346i
$765$	1.41328e49	−	2.49535e49i	1.34271	−	2.37076i
$766$	4.34981e47			0.0404186
$767$		−	1.17201e48i		−	0.106515i
$768$	−1.89226e47	+	1.10296e47i	−0.0168205	+	0.00980440i
$769$	−4.31209e48			−0.374921			−0.187460	−	0.982272i	$-0.560026\pi$
$769$	−4.31209e48			−0.374921			−0.187460	+	0.982272i	$0.560026\pi$
$770$			3.88964e48i			0.330802i
$771$	−2.11518e48	−	3.62883e48i	−0.175964	−	0.301885i
$772$	−5.43677e47			−0.0442432
$773$		−	1.97513e49i		−	1.57233i	−0.618015	−	0.786166i	$-0.712063\pi$
$773$		−	1.97513e49i		−	1.57233i	0.618015	−	0.786166i	$-0.287937\pi$
$774$	1.07459e48	+	6.08610e47i	0.0836849	+	0.0473961i
$775$	−1.84555e49			−1.40604
$776$			6.26941e48i			0.467280i
$777$	−1.87706e49	+	1.09411e49i	−1.36874	+	0.797816i
$778$	−3.27942e47			−0.0233961
$779$			3.82419e48i			0.266933i
$780$	−2.49396e48	−	4.27867e48i	−0.170326	−	0.292214i
$781$	−1.30152e48			−0.0869727
$782$		−	5.23803e48i		−	0.342494i
$783$	−3.28361e48	+	4.07781e46i	−0.210088	+	0.00260902i
$784$	5.66675e48			0.354781
$785$			1.49887e49i			0.918288i
$786$	1.72594e48	−	1.00602e48i	0.103477	−	0.0603147i
$787$	1.17946e49			0.692009			0.346005	−	0.938233i	$-0.387538\pi$
$787$	1.17946e49			0.692009			0.346005	+	0.938233i	$0.387538\pi$
$788$		−	1.82911e49i		−	1.05025i
$789$	1.01260e49	+	1.73723e49i	0.569022	+	0.976221i
$790$	−1.80814e48			−0.0994425
$791$		−	2.73123e49i		−	1.47014i
$792$	2.58740e48	−	4.56843e48i	0.136312	−	0.240679i
$793$	−2.26518e48			−0.116804
$794$			3.68544e48i			0.186012i
$795$	−3.25535e49	+	1.89749e49i	−1.60826	+	0.937427i
$796$	1.21212e49			0.586169
$797$		−	1.32082e49i		−	0.625248i	−0.949877	−	0.312624i	$-0.898792\pi$
$797$		−	1.32082e49i		−	0.625248i	0.949877	−	0.312624i	$-0.101208\pi$
$798$	−1.64344e48	−	2.81950e48i	−0.0761560	−	0.130654i
$799$	1.36926e49			0.621143
$800$			4.48650e49i			1.99241i
$801$	3.63681e47	+	2.05976e47i	0.0158113	+	0.00895496i
$802$	−3.13493e47			−0.0133433
$803$			1.62543e49i			0.677336i
$804$	2.21944e49	−	1.29368e49i	0.905506	−	0.527804i
$805$	3.62125e49			1.44653
$806$		−	1.20331e48i		−	0.0470631i
$807$	−2.31611e49	−	3.97354e49i	−0.886970	−	1.52170i
$808$	−7.72034e48			−0.289496
$809$			2.42411e48i			0.0890077i	0.999009	+	0.0445039i	$0.0141707\pi$
$809$			2.42411e48i			0.0890077i	−0.999009	+	0.0445039i	$0.985829\pi$
$810$	9.06121e48	+	1.51110e49i	0.325792	+	0.543311i
$811$	2.85977e49			1.00688			0.503439	−	0.864031i	$-0.332068\pi$
$811$	2.85977e49			1.00688			0.503439	+	0.864031i	$0.332068\pi$
$812$			6.65020e48i			0.229289i
$813$	−4.88000e48	+	2.84447e48i	−0.164771	+	0.0960422i
$814$	5.67212e48			0.187556
$815$		−	1.98230e49i		−	0.641933i
$816$	1.54730e49	+	2.65457e49i	0.490729	+	0.841901i
$817$	3.04387e48			0.0945478
$818$		−	7.82839e48i		−	0.238159i
$819$	−4.40934e48	+	7.78534e48i	−0.131385	+	0.231980i
$820$	−4.18119e49			−1.22029
$821$			5.12068e49i			1.46384i	0.681391	+	0.731920i	$0.261376\pi$
$821$			5.12068e49i			1.46384i	−0.681391	+	0.731920i	$0.738624\pi$
$822$	−2.10685e49	+	1.22805e49i	−0.589947	+	0.343870i
$823$	−2.01348e49			−0.552269			−0.276135	−	0.961119i	$-0.589054\pi$
$823$	−2.01348e49			−0.552269			−0.276135	+	0.961119i	$0.589054\pi$
$824$		−	3.68356e49i		−	0.989705i
$825$	−1.80412e49	−	3.09516e49i	−0.474840	−	0.814641i
$826$	8.44411e48			0.217717
$827$		−	5.62062e49i		−	1.41968i	−0.704363	−	0.709840i	$-0.748767\pi$
$827$		−	5.62062e49i		−	1.41968i	0.704363	−	0.709840i	$-0.251233\pi$
$828$	−1.98659e49	−	1.12513e49i	−0.491577	−	0.278412i
$829$	−4.27281e49			−1.03583			−0.517913	−	0.855433i	$-0.673291\pi$
$829$	−4.27281e49			−1.03583			−0.517913	+	0.855433i	$0.673291\pi$
$830$		−	4.11693e49i		−	0.977791i
$831$	−1.31123e49	+	7.64292e48i	−0.305113	+	0.177845i
$832$	3.12893e48			0.0713344
$833$			3.72462e49i			0.831987i
$834$	8.51345e48	+	1.46058e49i	0.186330	+	0.319670i
$835$	7.09146e48			0.152078
$836$		−	6.04424e48i		−	0.127009i
$837$	−3.77132e47	−	3.03682e49i	−0.00776535	−	0.625298i
$838$	9.98491e48			0.201463
$839$			4.10848e49i			0.812321i	0.913802	+	0.406161i	$0.133133\pi$
$839$			4.10848e49i			0.812321i	−0.913802	+	0.406161i	$0.866867\pi$
$840$	6.59995e49	−	3.84699e49i	1.27877	−	0.745373i
$841$	5.03413e49			0.955856
$842$			2.32565e49i			0.432752i
$843$	2.96515e49	+	5.08705e49i	0.540727	+	0.927677i
$844$	−8.33194e49			−1.48910
$845$			9.81791e49i			1.71971i
$846$	−4.14590e48	+	7.32020e48i	−0.0711742	+	0.125669i
$847$	−6.09858e49			−1.02615
$848$		−	4.03711e49i		−	0.665796i
$849$	9.34037e49	−	5.44434e49i	1.50985	−	0.880064i
$850$	−7.54011e49			−1.19469
$851$		−	5.28074e49i		−	0.820148i
$852$	6.01248e48	+	1.03151e49i	0.0915336	+	0.157036i
$853$	1.11189e50			1.65931			0.829654	−	0.558278i	$-0.188538\pi$
$853$	1.11189e50			1.65931			0.829654	+	0.558278i	$0.188538\pi$
$854$		−	1.63202e49i		−	0.238749i
$855$	3.77878e49	+	2.14016e49i	0.541910	+	0.306919i
$856$	1.64486e49			0.231247
$857$		−	6.36191e49i		−	0.876826i	−0.898774	−	0.438413i	$-0.855541\pi$
$857$		−	6.36191e49i		−	0.876826i	0.898774	−	0.438413i	$-0.144459\pi$
$858$	2.01806e48	−	1.17629e48i	0.0272678	−	0.0158939i
$859$	−9.69012e49			−1.28365			−0.641823	−	0.766853i	$-0.721822\pi$
$859$	−9.69012e49			−1.28365			−0.641823	+	0.766853i	$0.721822\pi$
$860$			3.32802e49i			0.432228i
$861$	3.80398e49	+	6.52615e49i	0.484378	+	0.831005i
$862$	2.84340e49			0.354989
$863$			6.57393e49i			0.804714i	0.915483	+	0.402357i	$0.131809\pi$
$863$			6.57393e49i			0.804714i	−0.915483	+	0.402357i	$0.868191\pi$
$864$	−7.38245e49	+	9.16800e47i	−0.886067	+	0.0110038i
$865$	1.81229e50			2.13282
$866$			4.24105e49i			0.489406i
$867$	−9.81277e49	+	5.71970e49i	−1.11037	+	0.647215i
$868$	−6.15038e49			−0.682444
$869$			6.05006e48i			0.0658299i
$870$	6.28176e48	+	1.07771e49i	0.0670277	+	0.114993i
$871$	2.44698e49			0.256048
$872$			1.57567e49i			0.161690i
$873$	−3.46937e49	+	6.12568e49i	−0.349147	+	0.616471i
$874$	7.93209e48			0.0782876
$875$		−	2.89435e50i		−	2.80166i
$876$	1.28822e50	−	7.50882e49i	1.22298	−	0.712856i
$877$	−1.50282e50			−1.39931			−0.699653	−	0.714483i	$-0.746662\pi$
$877$	−1.50282e50			−1.39931			−0.699653	+	0.714483i	$0.746662\pi$
$878$			1.65929e49i			0.151536i
$879$	−1.02772e50	−	1.76316e50i	−0.920581	−	1.57936i
$880$	5.54563e49			0.487243
$881$			7.88501e48i			0.0679535i	0.999423	+	0.0339768i	$0.0108172\pi$
$881$			7.88501e48i			0.0679535i	−0.999423	+	0.0339768i	$0.989183\pi$
$882$	−1.99121e49	−	1.12775e49i	−0.168326	−	0.0953341i
$883$	−8.22028e49			−0.681640			−0.340820	−	0.940129i	$-0.610705\pi$
$883$	−8.22028e49			−0.681640			−0.340820	+	0.940129i	$0.610705\pi$
$884$			3.48763e49i			0.283688i
$885$	−9.70783e49	+	5.65852e49i	−0.774616	+	0.451510i
$886$	2.95751e49			0.231501
$887$			1.37822e50i			1.05832i	0.848522	+	0.529159i	$0.177493\pi$
$887$			1.37822e50i			1.05832i	−0.848522	+	0.529159i	$0.822507\pi$
$888$	−5.60993e49	−	9.62445e49i	−0.422607	−	0.725030i
$889$	−1.87373e50			−1.38476
$890$		−	1.58767e48i		−	0.0115115i
$891$	5.05616e49	−	3.03189e49i	0.359666	−	0.215671i
$892$	1.48823e50			1.03864
$893$			2.07351e49i			0.141981i
$894$	3.90126e49	−	2.27398e49i	0.262100	−	0.152774i
$895$	2.52533e50			1.66466
$896$			1.93133e50i			1.24917i
$897$	−1.09512e49	−	1.87881e49i	−0.0695011	−	0.119237i
$898$	−3.89369e49			−0.242473
$899$		−	2.15016e49i		−	0.131388i
$900$	−1.61962e50	+	2.85967e50i	−0.971158	+	1.71472i
$901$	2.65350e50			1.56134
$902$		−	1.97208e49i		−	0.113871i
$903$	5.19450e49	−	3.02778e49i	0.294342	−	0.171567i
$904$	1.40041e50			0.778740
$905$		−	1.33670e50i		−	0.729470i
$906$	2.76606e49	+	4.74549e49i	0.148143	+	0.254157i
$907$	−1.82011e50			−0.956694			−0.478347	−	0.878171i	$-0.658764\pi$
$907$	−1.82011e50			−0.956694			−0.478347	+	0.878171i	$0.658764\pi$
$908$		−	2.96520e50i		−	1.52966i
$909$	−7.54335e49	−	4.27229e49i	−0.381925	−	0.216309i
$910$	3.39874e49			0.168894
$911$			3.27498e50i			1.59734i	0.601772	+	0.798668i	$0.294462\pi$
$911$			3.27498e50i			1.59734i	−0.601772	+	0.798668i	$0.705538\pi$
$912$	−4.01988e49	+	2.34312e49i	−0.192442	+	0.112171i
$913$	−1.37753e50			−0.647287
$914$		−	9.99546e49i		−	0.461018i
$915$	1.09364e50	+	1.87626e50i	0.495126	+	0.849444i
$916$	2.50278e50			1.11224
$917$		−	9.72607e49i		−	0.424286i
$918$	−1.54079e48	−	1.24071e50i	−0.00659810	−	0.531306i
$919$	2.90746e50			1.22222			0.611111	−	0.791545i	$-0.290723\pi$
$919$	2.90746e50			1.22222			0.611111	+	0.791545i	$0.290723\pi$
$920$			1.85676e50i			0.766237i
$921$	2.85319e49	−	1.66308e49i	0.115589	−	0.0673750i
$922$	1.83720e49			0.0730687
$923$			1.13726e49i			0.0444048i
$924$	−6.01229e49	−	1.03148e50i	−0.230471	−	0.395399i
$925$	−7.60158e50			−2.86085
$926$		−	5.39570e49i		−	0.199371i
$927$	2.03841e50	−	3.59912e50i	0.739498	−	1.30569i
$928$	−5.22699e49			−0.186181
$929$		−	5.81572e49i		−	0.203393i	−0.994815	−	0.101697i	$-0.967573\pi$
$929$		−	5.81572e49i		−	0.203393i	0.994815	−	0.101697i	$-0.0324271\pi$
$930$	−9.96707e49	+	5.80963e49i	−0.342261	+	0.199498i
$931$	−5.64029e49			−0.190176
$932$		−	6.36894e49i		−	0.210861i
$933$	1.19820e50	+	2.05565e50i	0.389531	+	0.668284i
$934$	−2.28037e49			−0.0727962
$935$			3.64501e50i			1.14262i
$936$	−3.99186e49	−	2.26084e49i	−0.122881	−	0.0695955i
$937$	−3.18119e50			−0.961648			−0.480824	−	0.876817i	$-0.659662\pi$
$937$	−3.18119e50			−0.961648			−0.480824	+	0.876817i	$0.659662\pi$
$938$			1.76300e50i			0.523365i
$939$	−2.16275e50	+	1.26063e50i	−0.630509	+	0.367513i
$940$	−2.26708e50			−0.649071
$941$		−	5.90386e50i		−	1.66002i	−0.557751	−	0.830008i	$-0.688336\pi$
$941$		−	5.90386e50i		−	1.66002i	0.557751	−	0.830008i	$-0.311664\pi$
$942$	3.26580e49	+	5.60285e49i	0.0901830	+	0.154719i
$943$	−1.83600e50			−0.497937
$944$		−	1.20391e50i		−	0.320679i
$945$	8.57750e50	−	1.06521e49i	2.24398	−	0.0278673i
$946$	−1.56968e49			−0.0403330
$947$		−	4.83635e50i		−	1.22059i	−0.792176	−	0.610293i	$-0.791052\pi$
$947$		−	4.83635e50i		−	1.22059i	0.792176	−	0.610293i	$-0.208948\pi$
$948$	4.79492e49	−	2.79487e49i	0.118861	−	0.0692820i
$949$	1.42029e50			0.345821
$950$		−	1.14182e50i		−	0.273084i
$951$	3.75697e49	+	6.44550e49i	0.0882610	+	0.151422i
$952$	−5.37974e50			−1.24146
$953$		−	1.06655e50i		−	0.241770i	−0.992667	−	0.120885i	$-0.961427\pi$
$953$		−	1.06655e50i		−	0.241770i	0.992667	−	0.120885i	$-0.0385732\pi$
$954$	−8.03435e49	+	1.41858e50i	−0.178907	+	0.315888i
$955$	1.09374e51			2.39253
$956$			6.50489e50i			1.39783i
$957$	3.60601e49	−	2.10188e49i	0.0761245	−	0.0443716i
$958$	1.06919e50			0.221740
$959$			1.18726e51i			2.41896i
$960$	−1.51066e50	−	2.59171e50i	−0.302383	−	0.518771i
$961$	−3.09652e50			−0.608943
$962$		−	4.95625e49i		−	0.0957585i
$963$	1.60715e50	+	9.10235e49i	0.305078	+	0.172785i
$964$	5.54392e50			1.03397
$965$			4.96499e49i			0.0909816i
$966$	1.35365e50	−	7.89016e49i	0.243721	−	0.142061i
$967$	−3.36710e50			−0.595670			−0.297835	−	0.954617i	$-0.596265\pi$
$967$	−3.36710e50			−0.595670			−0.297835	+	0.954617i	$0.596265\pi$
$968$		−	3.12699e50i		−	0.543557i
$969$	−1.54008e50	−	2.64217e50i	−0.263050	−	0.451291i
$970$	2.67421e50			0.448823
$971$			2.84226e50i			0.468745i	0.972147	+	0.234372i	$0.0753035\pi$
$971$			2.84226e50i			0.468745i	−0.972147	+	0.234372i	$0.924697\pi$
$972$	−4.73863e50	−	2.60661e50i	−0.767939	−	0.422425i
$973$	8.23068e50			1.31074
$974$		−	2.99541e50i		−	0.468763i
$975$	−2.70453e50	+	1.57642e50i	−0.415923	+	0.242434i
$976$	−2.32684e50			−0.351657
$977$			3.22972e50i			0.479686i	0.970812	+	0.239843i	$0.0770959\pi$
$977$			3.22972e50i			0.479686i	−0.970812	+	0.239843i	$0.922904\pi$
$978$	−4.31913e49	−	7.40995e49i	−0.0630428	−	0.108157i
$979$	−5.31236e48			−0.00762048
$980$		−	6.16682e50i		−	0.869396i
$981$	−8.71943e49	+	1.53955e50i	−0.120813	+	0.213314i
$982$	−2.18030e50			−0.296907
$983$		−	6.30288e50i		−	0.843586i	−0.906692	−	0.421793i	$-0.861401\pi$
$983$		−	6.30288e50i		−	0.843586i	0.906692	−	0.421793i	$-0.138599\pi$
$984$	−3.34622e50	+	1.95045e50i	−0.440188	+	0.256578i
$985$	−1.67038e51			−2.15973
$986$		−	8.78458e49i		−	0.111638i
$987$	2.06255e50	+	3.53853e50i	0.257640	+	0.442010i
$988$	−5.28140e49			−0.0648457
$989$			1.46137e50i			0.176369i
$990$	−1.94866e50	−	1.10365e50i	−0.231173	−	0.130928i
$991$	9.39428e50			1.09550			0.547749	−	0.836643i	$-0.315485\pi$
$991$	9.39428e50			1.09550			0.547749	+	0.836643i	$0.315485\pi$
$992$		−	4.83414e50i		−	0.554141i
$993$	−7.65774e50	+	4.46357e50i	−0.862906	+	0.502973i
$994$	−8.19373e49			−0.0907638
$995$		−	1.10693e51i		−	1.20540i
$996$	6.36361e50	+	1.09175e51i	0.681231	+	1.16873i
$997$	1.61786e49			0.0170264			0.00851318	−	0.999964i	$-0.497290\pi$
$997$	1.61786e49			0.0170264			0.00851318	+	0.999964i	$0.497290\pi$
$998$			3.89078e50i			0.402548i
$999$	−1.55336e49	−	1.25082e51i	−0.0158000	−	1.27228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.35.b.a.2.5	✓	10
3.2	odd	2	inner	3.35.b.a.2.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.35.b.a.2.5	✓	10	1.1	even	1	trivial
3.35.b.a.2.6	yes	10	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-46070.5i q^{2} +(1.11570e8 - 6.50325e7i) q^{3} +1.50574e10 q^{4} -1.37507e12i q^{5} +(-2.99608e12 - 5.14011e12i) q^{6} -2.89657e14 q^{7} -1.48519e15i q^{8} +(8.21874e15 - 1.45114e16i) q^{9} +O(q^{10})\)	\(q-46070.5i q^{2} +(1.11570e8 - 6.50325e7i) q^{3} +1.50574e10 q^{4} -1.37507e12i q^{5} +(-2.99608e12 - 5.14011e12i) q^{6} -2.89657e14 q^{7} -1.48519e15i q^{8} +(8.21874e15 - 1.45114e16i) q^{9} -6.33504e16 q^{10} +2.11971e17i q^{11} +(1.67996e18 - 9.79218e17i) q^{12} +1.85219e18 q^{13} +1.33446e19i q^{14} +(-8.94245e19 - 1.53418e20i) q^{15} +1.90260e20 q^{16} +1.25054e21i q^{17} +(-6.68548e20 - 3.78642e20i) q^{18} -1.89372e21 q^{19} -2.07050e22i q^{20} +(-3.23171e22 + 1.88371e22i) q^{21} +9.76562e21 q^{22} -9.09177e22i q^{23} +(-9.65854e22 - 1.65703e23i) q^{24} -1.30875e24 q^{25} -8.53312e22i q^{26} +(-2.67439e22 - 2.15353e24i) q^{27} -4.36147e24 q^{28} -1.52476e24i q^{29} +(-7.06803e24 + 4.11983e24i) q^{30} +1.41016e25 q^{31} -3.42807e25i q^{32} +(1.37850e25 + 2.36497e25i) q^{33} +5.76129e25 q^{34} +3.98300e26i q^{35} +(1.23753e26 - 2.18504e26i) q^{36} +5.80826e26 q^{37} +8.72447e25i q^{38} +(2.06649e26 - 1.20452e26i) q^{39} -2.04224e27 q^{40} -2.01941e27i q^{41} +(8.67835e26 + 1.48887e27i) q^{42} -1.60735e27 q^{43} +3.19173e27i q^{44} +(-1.99543e28 - 1.13014e28i) q^{45} -4.18863e27 q^{46} -1.09494e28i q^{47} +(2.12274e28 - 1.23731e28i) q^{48} +2.97842e28 q^{49} +6.02950e28i q^{50} +(8.13254e28 + 1.39523e29i) q^{51} +2.78890e28 q^{52} -2.12189e29i q^{53} +(-9.92142e28 + 1.23211e27i) q^{54} +2.91476e29 q^{55} +4.30195e29i q^{56} +(-2.11283e29 + 1.23153e29i) q^{57} -7.02465e28 q^{58} -6.32771e29i q^{59} +(-1.34650e30 - 2.31007e30i) q^{60} -1.22298e30 q^{61} -6.49669e29i q^{62} +(-2.38061e30 + 4.20333e30i) q^{63} +1.68932e30 q^{64} -2.54689e30i q^{65} +(1.08955e30 - 6.35082e29i) q^{66} +1.32113e31 q^{67} +1.88298e31i q^{68} +(-5.91261e30 - 1.01437e31i) q^{69} +1.83499e31 q^{70} +6.14008e30i q^{71} +(-2.15521e31 - 1.22064e31i) q^{72} +7.66818e31 q^{73} -2.67590e31i q^{74} +(-1.46018e32 + 8.51115e31i) q^{75} -2.85144e31 q^{76} -6.13989e31i q^{77} +(-5.54930e30 - 9.52043e30i) q^{78} +2.85419e31 q^{79} -2.61622e32i q^{80} +(-1.43033e32 - 2.38531e32i) q^{81} -9.30352e31 q^{82} +6.49866e32i q^{83} +(-4.86611e32 + 2.83637e32i) q^{84} +1.71958e33 q^{85} +7.40515e31i q^{86} +(-9.91589e31 - 1.70118e32i) q^{87} +3.14817e32 q^{88} +2.50617e31i q^{89} +(-5.20661e32 + 9.19303e32i) q^{90} -5.36498e32 q^{91} -1.36898e33i q^{92} +(1.57332e33 - 9.17063e32i) q^{93} -5.04445e32 q^{94} +2.60401e33i q^{95} +(-2.22936e33 - 3.82471e33i) q^{96} -4.22129e33 q^{97} -1.37217e33i q^{98} +(3.07600e33 + 1.74213e33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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