LMFDB - Embedded newform 13.10.b.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(12,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("13.12");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.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:	$6.69546587013$
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} + 3841x^{8} + 5134480x^{6} + 2823572208x^{4} + 614223235584x^{2} + 43308450164736 $ x^10 + 3841x^8 + 5134480x^6 + 2823572208x^4 + 614223235584x^2 + 43308450164736
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{4}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.2
Root			$-36.6220i$ of defining polynomial
Character	$\chi$	$=$	13.12
Dual form			13.10.b.a.12.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-36.6220i q^{2} +126.985 q^{3} -829.173 q^{4} -2095.65i q^{5} -4650.45i q^{6} +3353.27i q^{7} +11615.5i q^{8} -3557.77 q^{9} -76746.8 q^{10} +30203.0i q^{11} -105293. q^{12} +(102512. - 9782.63i) q^{13} +122803. q^{14} -266116. i q^{15} +847.191 q^{16} +16679.9 q^{17} +130293. i q^{18} -972084. i q^{19} +1.73765e6i q^{20} +425815. i q^{21} +1.10610e6 q^{22} +2.50891e6 q^{23} +1.47500e6i q^{24} -2.43861e6 q^{25} +(-358260. - 3.75421e6i) q^{26} -2.95123e6 q^{27} -2.78044e6i q^{28} +4.39277e6 q^{29} -9.74571e6 q^{30} -3.88604e6i q^{31} +5.91612e6i q^{32} +3.83534e6i q^{33} -610853. i q^{34} +7.02726e6 q^{35} +2.95000e6 q^{36} +8.44941e6i q^{37} -3.55997e7 q^{38} +(1.30176e7 - 1.24225e6i) q^{39} +2.43420e7 q^{40} +9.82468e6i q^{41} +1.55942e7 q^{42} +1.24058e7 q^{43} -2.50435e7i q^{44} +7.45582e6i q^{45} -9.18815e7i q^{46} +2.73739e7i q^{47} +107581. q^{48} +2.91092e7 q^{49} +8.93067e7i q^{50} +2.11810e6 q^{51} +(-8.50005e7 + 8.11149e6i) q^{52} -4.22423e7 q^{53} +1.08080e8i q^{54} +6.32948e7 q^{55} -3.89499e7 q^{56} -1.23440e8i q^{57} -1.60872e8i q^{58} -2.26630e7i q^{59} +2.20656e8i q^{60} -1.70888e8 q^{61} -1.42315e8 q^{62} -1.19301e7i q^{63} +2.17094e8 q^{64} +(-2.05009e7 - 2.14830e8i) q^{65} +1.40458e8 q^{66} +412548. i q^{67} -1.38306e7 q^{68} +3.18595e8 q^{69} -2.57353e8i q^{70} +2.40242e8i q^{71} -4.13253e7i q^{72} +3.37523e8i q^{73} +3.09434e8 q^{74} -3.09667e8 q^{75} +8.06026e8i q^{76} -1.01279e8 q^{77} +(-4.54937e7 - 4.76729e8i) q^{78} -1.13260e8 q^{79} -1.77541e6i q^{80} -3.04735e8 q^{81} +3.59800e8 q^{82} -5.09735e8i q^{83} -3.53074e8i q^{84} -3.49552e7i q^{85} -4.54325e8i q^{86} +5.57817e8 q^{87} -3.50824e8 q^{88} +4.18119e8i q^{89} +2.73047e8 q^{90} +(3.28038e7 + 3.43752e8i) q^{91} -2.08032e9 q^{92} -4.93470e8i q^{93} +1.00249e9 q^{94} -2.03714e9 q^{95} +7.51259e8i q^{96} +1.22103e9i q^{97} -1.06604e9i q^{98} -1.07455e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 2562 q^{4} + 67304 q^{9} + 45562 q^{10} + 46298 q^{12} - 111488 q^{13} + 169350 q^{14} - 209470 q^{16} - 1189686 q^{17} + 3516760 q^{22} + 2210916 q^{23} - 10109316 q^{25} + 7627230 q^{26}+ \cdots + 1047837276 q^{95}+O(q^{100}) $ 10 * q - 2 * q^3 - 2562 * q^4 + 67304 * q^9 + 45562 * q^10 + 46298 * q^12 - 111488 * q^13 + 169350 * q^14 - 209470 * q^16 - 1189686 * q^17 + 3516760 * q^22 + 2210916 * q^23 - 10109316 * q^25 + 7627230 * q^26 - 7880006 * q^27 + 7039224 * q^29 - 7573410 * q^30 + 39493506 * q^35 + 29007196 * q^36 - 50219652 * q^38 + 14502332 * q^39 - 23263606 * q^40 + 400842 * q^42 - 92334370 * q^43 + 102213790 * q^48 - 100714448 * q^49 + 77969322 * q^51 - 113165052 * q^52 + 29507556 * q^53 + 138590608 * q^55 + 437436342 * q^56 - 238375816 * q^61 - 565735320 * q^62 + 272247742 * q^64 - 351372138 * q^65 - 495101088 * q^66 + 550420050 * q^68 + 505082484 * q^69 + 1257672774 * q^74 - 1443387976 * q^75 + 530898576 * q^77 - 1745232606 * q^78 - 441679756 * q^79 + 1486784810 * q^81 + 518795296 * q^82 + 4793242032 * q^87 - 3927690208 * q^88 - 2656725444 * q^90 - 777339186 * q^91 - 4121025444 * q^92 + 6226353478 * q^94 + 1047837276 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	36.6220i		−	1.61848i	−0.587478	−	0.809240i	$-0.699879\pi$
$2$		−	36.6220i		−	1.61848i	0.587478	−	0.809240i	$-0.300121\pi$
$3$	126.985			0.905123			0.452561	−	0.891733i	$-0.350510\pi$
$3$	126.985			0.905123			0.452561	+	0.891733i	$0.350510\pi$
$4$	−829.173			−1.61948
$5$		−	2095.65i		−	1.49952i	−0.661709	−	0.749761i	$-0.730168\pi$
$5$		−	2095.65i		−	1.49952i	0.661709	−	0.749761i	$-0.269832\pi$
$6$		−	4650.45i		−	1.46492i
$7$			3353.27i			0.527870i	0.964540	+	0.263935i	$0.0850204\pi$
$7$			3353.27i			0.527870i	−0.964540	+	0.263935i	$0.914980\pi$
$8$			11615.5i			1.00261i
$9$	−3557.77			−0.180753
$10$	−76746.8			−2.42695
$11$			30203.0i			0.621990i	0.950412	+	0.310995i	$0.100662\pi$
$11$			30203.0i			0.621990i	−0.950412	+	0.310995i	$0.899338\pi$
$12$	−105293.			−1.46583
$13$	102512.	−	9782.63i	0.995478	−	0.0949971i
$13$	102512.	−	9782.63i	0.995478	−	0.0949971i
$14$	122803.			0.854347
$15$		−	266116.i		−	1.35725i
$16$	847.191			0.00323178
$17$	16679.9			0.0484367			0.0242183	−	0.999707i	$-0.492290\pi$
$17$	16679.9			0.0484367			0.0242183	+	0.999707i	$0.492290\pi$
$18$			130293.i			0.292546i
$19$		−	972084.i		−	1.71125i	−0.517599	−	0.855623i	$-0.673174\pi$
$19$		−	972084.i		−	1.71125i	0.517599	−	0.855623i	$-0.326826\pi$
$20$			1.73765e6i			2.42844i
$21$			425815.i			0.477787i
$22$	1.10610e6			1.00668
$23$	2.50891e6			1.86943			0.934717	−	0.355392i	$-0.115653\pi$
$23$	2.50891e6			1.86943			0.934717	+	0.355392i	$0.115653\pi$
$24$			1.47500e6i			0.907488i
$25$	−2.43861e6			−1.24857
$26$	−358260.	−	3.75421e6i	−0.153751	−	1.61116i
$27$	−2.95123e6			−1.06873
$28$		−	2.78044e6i		−	0.854874i
$29$	4.39277e6			1.15331			0.576657	−	0.816986i	$-0.304357\pi$
$29$	4.39277e6			1.15331			0.576657	+	0.816986i	$0.304357\pi$
$30$	−9.74571e6			−2.19668
$31$		−	3.88604e6i		−	0.755753i	−0.925856	−	0.377876i	$-0.876654\pi$
$31$		−	3.88604e6i		−	0.755753i	0.925856	−	0.377876i	$-0.123346\pi$
$32$			5.91612e6i			0.997383i
$33$			3.83534e6i			0.562977i
$34$		−	610853.i		−	0.0783938i
$35$	7.02726e6			0.791553
$36$	2.95000e6			0.292726
$37$			8.44941e6i			0.741171i	0.928798	+	0.370586i	$0.120843\pi$
$37$			8.44941e6i			0.741171i	−0.928798	+	0.370586i	$0.879157\pi$
$38$	−3.55997e7			−2.76962
$39$	1.30176e7	−	1.24225e6i	0.901029	−	0.0859841i
$40$	2.43420e7			1.50344
$41$			9.82468e6i			0.542989i	0.962440	+	0.271495i	$0.0875179\pi$
$41$			9.82468e6i			0.542989i	−0.962440	+	0.271495i	$0.912482\pi$
$42$	1.55942e7			0.773289
$43$	1.24058e7			0.553371			0.276685	−	0.960961i	$-0.410764\pi$
$43$	1.24058e7			0.553371			0.276685	+	0.960961i	$0.410764\pi$
$44$		−	2.50435e7i		−	1.00730i
$45$			7.45582e6i			0.271043i
$46$		−	9.18815e7i		−	3.02564i
$47$			2.73739e7i			0.818270i	0.912474	+	0.409135i	$0.134170\pi$
$47$			2.73739e7i			0.818270i	−0.912474	+	0.409135i	$0.865830\pi$
$48$	107581.			0.00292515
$49$	2.91092e7			0.721353
$50$			8.93067e7i			2.02078i
$51$	2.11810e6			0.0438411
$52$	−8.50005e7	+	8.11149e6i	−1.61215	+	0.153846i
$53$	−4.22423e7			−0.735371			−0.367686	−	0.929950i	$-0.619850\pi$
$53$	−4.22423e7			−0.735371			−0.367686	+	0.929950i	$0.619850\pi$
$54$			1.08080e8i			1.72971i
$55$	6.32948e7			0.932687
$56$	−3.89499e7			−0.529250
$57$		−	1.23440e8i		−	1.54889i
$58$		−	1.60872e8i		−	1.86662i
$59$		−	2.26630e7i		−	0.243491i	−0.992561	−	0.121745i	$-0.961151\pi$
$59$		−	2.26630e7i		−	0.243491i	0.992561	−	0.121745i	$-0.0388491\pi$
$60$			2.20656e8i			2.19804i
$61$	−1.70888e8			−1.58025			−0.790126	−	0.612944i	$-0.789985\pi$
$61$	−1.70888e8			−1.58025			−0.790126	+	0.612944i	$0.789985\pi$
$62$	−1.42315e8			−1.22317
$63$		−	1.19301e7i		−	0.0954142i
$64$	2.17094e8			1.61748
$65$	−2.05009e7	−	2.14830e8i	−0.142450	−	1.49274i
$66$	1.40458e8			0.911167
$67$			412548.i			0.00250114i	0.999999	+	0.00125057i	$0.000398069\pi$
$67$			412548.i			0.00250114i	−0.999999	+	0.00125057i	$0.999602\pi$
$68$	−1.38306e7			−0.0784421
$69$	3.18595e8			1.69207
$70$		−	2.57353e8i		−	1.28111i
$71$			2.40242e8i			1.12198i	0.827821	+	0.560992i	$0.189580\pi$
$71$			2.40242e8i			1.12198i	−0.827821	+	0.560992i	$0.810420\pi$
$72$		−	4.13253e7i		−	0.181226i
$73$			3.37523e8i			1.39108i	0.718489	+	0.695538i	$0.244834\pi$
$73$			3.37523e8i			1.39108i	−0.718489	+	0.695538i	$0.755166\pi$
$74$	3.09434e8			1.19957
$75$	−3.09667e8			−1.13011
$76$			8.06026e8i			2.77133i
$77$	−1.01279e8			−0.328330
$78$	−4.54937e7	−	4.76729e8i	−0.139164	−	1.45830i
$79$	−1.13260e8			−0.327156			−0.163578	−	0.986530i	$-0.552304\pi$
$79$	−1.13260e8			−0.327156			−0.163578	+	0.986530i	$0.552304\pi$
$80$		−	1.77541e6i		−	0.00484612i
$81$	−3.04735e8			−0.786575
$82$	3.59800e8			0.878817
$83$		−	5.09735e8i		−	1.17894i	−0.807789	−	0.589472i	$-0.799336\pi$
$83$		−	5.09735e8i		−	1.17894i	0.807789	−	0.589472i	$-0.200664\pi$
$84$		−	3.53074e8i		−	0.773766i
$85$		−	3.49552e7i		−	0.0726319i
$86$		−	4.54325e8i		−	0.895620i
$87$	5.57817e8			1.04389
$88$	−3.50824e8			−0.623615
$89$			4.18119e8i			0.706390i	0.935550	+	0.353195i	$0.114905\pi$
$89$			4.18119e8i			0.706390i	−0.935550	+	0.353195i	$0.885095\pi$
$90$	2.73047e8			0.438678
$91$	3.28038e7	+	3.43752e8i	0.0501461	+	0.525483i
$92$	−2.08032e9			−3.02751
$93$		−	4.93470e8i		−	0.684049i
$94$	1.00249e9			1.32435
$95$	−2.03714e9			−2.56605
$96$			7.51259e8i			0.902754i
$97$			1.22103e9i			1.40040i	0.713945	+	0.700202i	$0.246907\pi$
$97$			1.22103e9i			1.40040i	−0.713945	+	0.700202i	$0.753093\pi$
$98$		−	1.06604e9i		−	1.16750i
$99$		−	1.07455e8i		−	0.112427i
$100$	2.02203e9			2.02203
$101$	9.03571e8			0.864005			0.432002	−	0.901872i	$-0.357807\pi$
$101$	9.03571e8			0.864005			0.432002	+	0.901872i	$0.357807\pi$
$102$		−	7.75693e7i		−	0.0709560i
$103$	−5.09126e8			−0.445715			−0.222858	−	0.974851i	$-0.571538\pi$
$103$	−5.09126e8			−0.445715			−0.222858	+	0.974851i	$0.571538\pi$
$104$	1.13630e8	+	1.19073e9i	0.0952454	+	0.998079i
$105$	8.92358e8			0.716452
$106$			1.54700e9i			1.19018i
$107$	2.08796e8			0.153991			0.0769956	−	0.997031i	$-0.475467\pi$
$107$	2.08796e8			0.153991			0.0769956	+	0.997031i	$0.475467\pi$
$108$	2.44708e9			1.73078
$109$		−	1.40798e9i		−	0.955383i	−0.878528	−	0.477691i	$-0.841474\pi$
$109$		−	1.40798e9i		−	0.955383i	0.878528	−	0.477691i	$-0.158526\pi$
$110$		−	2.31798e9i		−	1.50954i
$111$			1.07295e9i			0.670851i
$112$			2.84086e6i			0.00170596i
$113$	2.87263e9			1.65740			0.828699	−	0.559694i	$-0.189081\pi$
$113$	2.87263e9			1.65740			0.828699	+	0.559694i	$0.189081\pi$
$114$	−4.52063e9			−2.50684
$115$		−	5.25779e9i		−	2.80326i
$116$	−3.64237e9			−1.86777
$117$	−3.64715e8	+	3.48043e7i	−0.179936	+	0.0171710i
$118$	−8.29964e8			−0.394085
$119$			5.59323e7i			0.0255683i
$120$	3.09107e9			1.36080
$121$	1.44573e9			0.613129
$122$			6.25825e9i			2.55761i
$123$			1.24759e9i			0.491472i
$124$			3.22220e9i			1.22393i
$125$			1.01740e9i			0.372732i
$126$	−4.36906e8			−0.154426
$127$	−8.57112e8			−0.292362			−0.146181	−	0.989258i	$-0.546698\pi$
$127$	−8.57112e8			−0.292362			−0.146181	+	0.989258i	$0.546698\pi$
$128$		−	4.92137e9i		−	1.62047i
$129$	1.57535e9			0.500868
$130$	−7.86750e9	+	7.50786e8i	−2.41597	+	0.230553i
$131$	−1.43810e9			−0.426647			−0.213323	−	0.976982i	$-0.568429\pi$
$131$	−1.43810e9			−0.426647			−0.213323	+	0.976982i	$0.568429\pi$
$132$		−	3.18016e9i		−	0.911729i
$133$	3.25966e9			0.903316
$134$	1.51083e7			0.00404804
$135$			6.18474e9i			1.60258i
$136$			1.93746e8i			0.0485632i
$137$			1.39944e8i			0.0339401i	0.999856	+	0.0169700i	$0.00540199\pi$
$137$			1.39944e8i			0.0339401i	−0.999856	+	0.0169700i	$0.994598\pi$
$138$		−	1.16676e10i		−	2.73858i
$139$	−4.54512e9			−1.03271			−0.516355	−	0.856374i	$-0.672712\pi$
$139$	−4.54512e9			−1.03271			−0.516355	+	0.856374i	$0.672712\pi$
$140$	−5.82681e9			−1.28190
$141$			3.47608e9i			0.740635i
$142$	8.79816e9			1.81591
$143$	2.95465e8	+	3.09618e9i	0.0590873	+	0.619177i
$144$	−3.01411e6			−0.000584154
$145$		−	9.20569e9i		−	1.72942i
$146$	1.23608e10			2.25143
$147$	3.69644e9			0.652913
$148$		−	7.00602e9i		−	1.20031i
$149$			9.59017e8i			0.159400i	0.996819	+	0.0796999i	$0.0253962\pi$
$149$			9.59017e8i			0.159400i	−0.996819	+	0.0796999i	$0.974604\pi$
$150$			1.13406e10i			1.82905i
$151$			2.85118e9i			0.446301i	0.974784	+	0.223151i	$0.0716342\pi$
$151$			2.85118e9i			0.446301i	−0.974784	+	0.223151i	$0.928366\pi$
$152$	1.12913e10			1.71572
$153$	−5.93433e7			−0.00875508
$154$			3.70903e9i			0.531395i
$155$	−8.14377e9			−1.13327
$156$	−1.07938e10	+	1.03004e9i	−1.45920	+	0.139249i
$157$	−2.29705e9			−0.301732			−0.150866	−	0.988554i	$-0.548206\pi$
$157$	−2.29705e9			−0.301732			−0.150866	+	0.988554i	$0.548206\pi$
$158$			4.14781e9i			0.529495i
$159$	−5.36415e9			−0.665601
$160$	1.23981e10			1.49560
$161$			8.41305e9i			0.986818i
$162$			1.11600e10i			1.27306i
$163$		−	1.39463e10i		−	1.54744i	−0.633525	−	0.773722i	$-0.718393\pi$
$163$		−	1.39463e10i		−	1.54744i	0.633525	−	0.773722i	$-0.281607\pi$
$164$		−	8.14636e9i		−	0.879359i
$165$	8.03750e9			0.844196
$166$	−1.86675e10			−1.90810
$167$		−	1.05022e9i		−	0.104485i	−0.998634	−	0.0522427i	$-0.983363\pi$
$167$		−	1.05022e9i		−	0.104485i	0.998634	−	0.0522427i	$-0.0166370\pi$
$168$	−4.94606e9			−0.479036
$169$	1.04131e10	−	2.00568e9i	0.981951	−	0.189135i
$170$	−1.28013e9			−0.117553
$171$			3.45845e9i			0.309313i
$172$	−1.02865e10			−0.896172
$173$	−1.08104e10			−0.917558			−0.458779	−	0.888550i	$-0.651713\pi$
$173$	−1.08104e10			−0.917558			−0.458779	+	0.888550i	$0.651713\pi$
$174$		−	2.04284e10i		−	1.68952i
$175$		−	8.17730e9i		−	0.659081i
$176$			2.55877e7i			0.00201013i
$177$		−	2.87786e9i		−	0.220389i
$178$	1.53124e10			1.14328
$179$	6.00306e8			0.0437053			0.0218527	−	0.999761i	$-0.493044\pi$
$179$	6.00306e8			0.0437053			0.0218527	+	0.999761i	$0.493044\pi$
$180$		−	6.18216e9i		−	0.438949i
$181$	−1.70336e10			−1.17965			−0.589824	−	0.807532i	$-0.700803\pi$
$181$	−1.70336e10			−1.17965			−0.589824	+	0.807532i	$0.700803\pi$
$182$	1.25889e10	−	1.20134e9i	0.850483	−	0.0811605i
$183$	−2.17002e10			−1.43032
$184$			2.91423e10i			1.87432i
$185$	1.77070e10			1.11140
$186$	−1.80719e10			−1.10712
$187$			5.03784e8i			0.0301271i
$188$		−	2.26977e10i		−	1.32517i
$189$		−	9.89627e9i		−	0.564149i
$190$			7.46044e10i			4.15311i
$191$	1.10778e10			0.602287			0.301143	−	0.953579i	$-0.402632\pi$
$191$	1.10778e10			0.602287			0.301143	+	0.953579i	$0.402632\pi$
$192$	2.75677e10			1.46401
$193$			2.09010e10i			1.08433i	0.840273	+	0.542163i	$0.182395\pi$
$193$			2.09010e10i			1.08433i	−0.840273	+	0.542163i	$0.817605\pi$
$194$	4.47166e10			2.26653
$195$	−2.60331e9	−	2.72802e10i	−0.128935	−	1.35111i
$196$	−2.41366e10			−1.16822
$197$			1.89470e9i			0.0896277i	0.998995	+	0.0448139i	$0.0142695\pi$
$197$			1.89470e9i			0.0896277i	−0.998995	+	0.0448139i	$0.985731\pi$
$198$	−3.93523e9			−0.181960
$199$	−1.03398e10			−0.467384			−0.233692	−	0.972311i	$-0.575081\pi$
$199$	−1.03398e10			−0.467384			−0.233692	+	0.972311i	$0.575081\pi$
$200$		−	2.83257e10i		−	1.25183i
$201$			5.23875e7i			0.00226384i
$202$		−	3.30906e10i		−	1.39837i
$203$			1.47301e10i			0.608800i
$204$	−1.75627e9			−0.0709997
$205$	2.05891e10			0.814224
$206$			1.86452e10i			0.721381i
$207$	−8.92612e9			−0.337906
$208$	8.68476e7	−	8.28776e6i	0.00321716	−	0.000307010i
$209$	2.93599e10			1.06438
$210$		−	3.26800e10i		−	1.15956i
$211$	−3.11662e10			−1.08246			−0.541231	−	0.840874i	$-0.682042\pi$
$211$	−3.11662e10			−1.08246			−0.541231	+	0.840874i	$0.682042\pi$
$212$	3.50262e10			1.19092
$213$			3.05072e10i			1.01553i
$214$		−	7.64655e9i		−	0.249232i
$215$		−	2.59981e10i		−	0.829792i
$216$		−	3.42801e10i		−	1.07152i
$217$	1.30309e10			0.398939
$218$	−5.15631e10			−1.54627
$219$			4.28605e10i			1.25909i
$220$	−5.24824e10			−1.51047
$221$	1.70990e9	−	1.63174e8i	0.0482176	−	0.00460134i
$222$	3.92936e10			1.08576
$223$			1.62856e10i			0.440994i	0.975388	+	0.220497i	$0.0707680\pi$
$223$			1.62856e10i			0.440994i	−0.975388	+	0.220497i	$0.929232\pi$
$224$	−1.98383e10			−0.526489
$225$	8.67599e9			0.225682
$226$		−	1.05202e11i		−	2.68247i
$227$			4.50169e10i			1.12528i	0.826703	+	0.562638i	$0.190213\pi$
$227$			4.50169e10i			1.12528i	−0.826703	+	0.562638i	$0.809787\pi$
$228$			1.02353e11i			2.50839i
$229$		−	2.06931e10i		−	0.497240i	−0.968601	−	0.248620i	$-0.920023\pi$
$229$		−	2.06931e10i		−	0.497240i	0.968601	−	0.248620i	$-0.0799771\pi$
$230$	−1.92551e11			−4.53702
$231$	−1.28609e10			−0.297179
$232$			5.10243e10i			1.15633i
$233$	6.61421e10			1.47020			0.735099	−	0.677959i	$-0.237135\pi$
$233$	6.61421e10			1.47020			0.735099	+	0.677959i	$0.237135\pi$
$234$	1.27460e9	+	1.33566e10i	0.0277910	+	0.291222i
$235$	5.73661e10			1.22701
$236$			1.87915e10i			0.394328i
$237$	−1.43823e10			−0.296116
$238$	2.04835e9			0.0413817
$239$			5.14346e10i			1.01968i	0.860269	+	0.509841i	$0.170296\pi$
$239$			5.14346e10i			1.01968i	−0.860269	+	0.509841i	$0.829704\pi$
$240$		−	2.25451e8i		−	0.00438633i
$241$		−	6.36131e10i		−	1.21470i	−0.794433	−	0.607351i	$-0.792232\pi$
$241$		−	6.36131e10i		−	1.21470i	0.794433	−	0.607351i	$-0.207768\pi$
$242$		−	5.29454e10i		−	0.992337i
$243$	1.93922e10			0.356780
$244$	1.41695e11			2.55919
$245$		−	6.10026e10i		−	1.08169i
$246$	4.56892e10			0.795437
$247$	−9.50954e9	−	9.96507e10i	−0.162564	−	1.70351i
$248$	4.51384e10			0.757728
$249$		−	6.47288e10i		−	1.06709i
$250$	3.72592e10			0.603259
$251$	−5.24270e10			−0.833726			−0.416863	−	0.908969i	$-0.636871\pi$
$251$	−5.24270e10			−0.833726			−0.416863	+	0.908969i	$0.636871\pi$
$252$			9.89215e9i			0.154521i
$253$			7.57767e10i			1.16277i
$254$			3.13892e10i			0.473182i
$255$		−	4.43880e9i		−	0.0657407i
$256$	−6.90784e10			−1.00522
$257$	−3.34058e10			−0.477664			−0.238832	−	0.971061i	$-0.576765\pi$
$257$	−3.34058e10			−0.477664			−0.238832	+	0.971061i	$0.576765\pi$
$258$		−	5.76925e10i		−	0.810646i
$259$	−2.83331e10			−0.391242
$260$	1.69988e10	+	1.78131e11i	0.230695	+	2.41746i
$261$	−1.56284e10			−0.208465
$262$			5.26662e10i			0.690519i
$263$	7.48096e10			0.964176			0.482088	−	0.876123i	$-0.339878\pi$
$263$	7.48096e10			0.964176			0.482088	+	0.876123i	$0.339878\pi$
$264$	−4.45494e10			−0.564448
$265$			8.85250e10i			1.10271i
$266$		−	1.19375e11i		−	1.46200i
$267$			5.30949e10i			0.639370i
$268$		−	3.42073e8i		−	0.00405054i
$269$	−8.42931e10			−0.981537			−0.490769	−	0.871290i	$-0.663284\pi$
$269$	−8.42931e10			−0.981537			−0.490769	+	0.871290i	$0.663284\pi$
$270$	2.26498e11			2.59374
$271$		−	1.47899e11i		−	1.66572i	−0.553482	−	0.832861i	$-0.686701\pi$
$271$		−	1.47899e11i		−	1.66572i	0.553482	−	0.832861i	$-0.313299\pi$
$272$	1.41311e7			0.000156536
$273$	4.16559e9	+	4.36514e10i	0.0453884	+	0.475626i
$274$	5.12505e9			0.0549314
$275$		−	7.36533e10i		−	0.776596i
$276$	−2.64170e11			−2.74027
$277$	9.28743e10			0.947844			0.473922	−	0.880567i	$-0.342838\pi$
$277$	9.28743e10			0.947844			0.473922	+	0.880567i	$0.342838\pi$
$278$			1.66451e11i			1.67142i
$279$			1.38256e10i			0.136605i
$280$			8.16253e10i			0.793622i
$281$			7.19876e10i			0.688778i	0.938827	+	0.344389i	$0.111914\pi$
$281$			7.19876e10i			0.688778i	−0.938827	+	0.344389i	$0.888086\pi$
$282$	1.27301e11			1.19870
$283$	1.23622e10			0.114566			0.0572832	−	0.998358i	$-0.481756\pi$
$283$	1.23622e10			0.114566			0.0572832	+	0.998358i	$0.481756\pi$
$284$		−	1.99202e11i		−	1.81703i
$285$	−2.58687e11			−2.32259
$286$	1.13389e11	−	1.08205e10i	1.00213	−	0.0956315i
$287$	−3.29448e10			−0.286628
$288$		−	2.10482e10i		−	0.180280i
$289$	−1.18310e11			−0.997654
$290$	−3.37131e11			−2.79903
$291$			1.55053e11i			1.26754i
$292$		−	2.79865e11i		−	2.25282i
$293$		−	1.30778e11i		−	1.03665i	−0.855184	−	0.518325i	$-0.826556\pi$
$293$		−	1.30778e11i		−	1.03665i	0.855184	−	0.518325i	$-0.173444\pi$
$294$		−	1.35371e11i		−	1.05673i
$295$	−4.74935e10			−0.365120
$296$	−9.81442e10			−0.743108
$297$		−	8.91361e10i		−	0.664737i
$298$	3.51211e10			0.257986
$299$	2.57195e11	−	2.45438e10i	1.86098	−	0.177591i
$300$	2.56767e11			1.83018
$301$			4.15999e10i			0.292108i
$302$	1.04416e11			0.722330
$303$	1.14740e11			0.782030
$304$		−	8.23541e8i		−	0.00553037i
$305$			3.58120e11i			2.36962i
$306$			2.17327e9i			0.0141699i
$307$			7.84382e10i			0.503970i	0.967731	+	0.251985i	$0.0810834\pi$
$307$			7.84382e10i			0.503970i	−0.967731	+	0.251985i	$0.918917\pi$
$308$	8.39776e10			0.531723
$309$	−6.46514e10			−0.403427
$310$			2.98241e11i			1.83417i
$311$	1.80862e11			1.09629			0.548145	−	0.836383i	$-0.315334\pi$
$311$	1.80862e11			1.09629			0.548145	+	0.836383i	$0.315334\pi$
$312$	1.44294e10	+	1.51206e11i	0.0862088	+	0.903384i
$313$	−1.76977e11			−1.04224			−0.521120	−	0.853483i	$-0.674486\pi$
$313$	−1.76977e11			−1.04224			−0.521120	+	0.853483i	$0.674486\pi$
$314$			8.41225e10i			0.488347i
$315$	−2.50013e10			−0.143076
$316$	9.39122e10			0.529822
$317$		−	2.45712e11i		−	1.36666i	−0.730111	−	0.683329i	$-0.760532\pi$
$317$		−	2.45712e11i		−	1.36666i	0.730111	−	0.683329i	$-0.239468\pi$
$318$			1.96446e11i			1.07726i
$319$			1.32675e11i			0.717349i
$320$		−	4.54952e11i		−	2.42544i
$321$	2.65140e10			0.139381
$322$	3.08103e11			1.59715
$323$		−	1.62143e10i		−	0.0828871i
$324$	2.52678e11			1.27384
$325$	−2.49988e11	+	2.38560e10i	−1.24292	+	0.118610i
$326$	−5.10742e11			−2.50451
$327$		−	1.78793e11i		−	0.864738i
$328$	−1.14119e11			−0.544408
$329$	−9.17921e10			−0.431940
$330$		−	2.94350e11i		−	1.36632i
$331$		−	1.57432e11i		−	0.720887i	−0.932781	−	0.360444i	$-0.882625\pi$
$331$		−	1.57432e11i		−	0.720887i	0.932781	−	0.360444i	$-0.117375\pi$
$332$			4.22659e11i			1.90928i
$333$		−	3.00610e10i		−	0.133969i
$334$	−3.84612e10			−0.169108
$335$	8.64554e8			0.00375051
$336$			3.60747e8i			0.00154410i
$337$	2.08704e11			0.881447			0.440724	−	0.897643i	$-0.354722\pi$
$337$	2.08704e11			0.881447			0.440724	+	0.897643i	$0.354722\pi$
$338$	−7.34522e10	−	3.81349e11i	−0.306111	−	1.58927i
$339$	3.64782e11			1.50015
$340$			2.89839e10i			0.117626i
$341$	1.17370e11			0.470071
$342$	1.26655e11			0.500618
$343$			2.32927e11i			0.908651i
$344$			1.44100e11i			0.554817i
$345$		−	6.67662e11i		−	2.53729i
$346$			3.95898e11i			1.48505i
$347$	−1.96465e11			−0.727450			−0.363725	−	0.931506i	$-0.618495\pi$
$347$	−1.96465e11			−0.727450			−0.363725	+	0.931506i	$0.618495\pi$
$348$	−4.62527e11			−1.69056
$349$			4.11506e11i			1.48478i	0.669968	+	0.742390i	$0.266308\pi$
$349$			4.11506e11i			1.48478i	−0.669968	+	0.742390i	$0.733692\pi$
$350$	−2.99469e11			−1.06671
$351$	−3.02538e11	+	2.88708e10i	−1.06389	+	0.101526i
$352$	−1.78685e11			−0.620362
$353$		−	3.57762e11i		−	1.22633i	−0.789955	−	0.613165i	$-0.789896\pi$
$353$		−	3.57762e11i		−	1.22633i	0.789955	−	0.613165i	$-0.210104\pi$
$354$	−1.05393e11			−0.356695
$355$	5.03463e11			1.68244
$356$		−	3.46693e11i		−	1.14398i
$357$			7.10257e9i			0.0231424i
$358$		−	2.19844e10i		−	0.0707362i
$359$			4.39389e11i			1.39612i	0.716037	+	0.698062i	$0.245954\pi$
$359$			4.39389e11i			1.39612i	−0.716037	+	0.698062i	$0.754046\pi$
$360$	−8.66032e10			−0.271752
$361$	−6.22260e11			−1.92837
$362$			6.23804e11i			1.90924i
$363$	1.83586e11			0.554957
$364$	−2.72000e10	−	2.85030e11i	−0.0812106	−	0.851008i
$365$	7.07329e11			2.08595
$366$			7.94705e11i			2.31495i
$367$	−1.49365e11			−0.429786			−0.214893	−	0.976638i	$-0.568940\pi$
$367$	−1.49365e11			−0.429786			−0.214893	+	0.976638i	$0.568940\pi$
$368$	2.12553e9			0.00604159
$369$		−	3.49539e10i		−	0.0981470i
$370$		−	6.48465e11i		−	1.79878i
$371$		−	1.41650e11i		−	0.388180i
$372$			4.09172e11i			1.10780i
$373$	1.29990e11			0.347711			0.173856	−	0.984771i	$-0.444377\pi$
$373$	1.29990e11			0.347711			0.173856	+	0.984771i	$0.444377\pi$
$374$	1.84496e10			0.0487601
$375$			1.29195e11i			0.337368i
$376$	−3.17962e11			−0.820409
$377$	4.50314e11	−	4.29729e10i	1.14810	−	0.109562i
$378$	−3.62422e11			−0.913063
$379$		−	1.30622e11i		−	0.325192i	−0.986693	−	0.162596i	$-0.948013\pi$
$379$		−	1.30622e11i		−	0.325192i	0.986693	−	0.162596i	$-0.0519867\pi$
$380$	1.68914e12			4.15567
$381$	−1.08840e11			−0.264623
$382$		−	4.05691e11i		−	0.974789i
$383$		−	3.82378e11i		−	0.908027i	−0.890995	−	0.454013i	$-0.849992\pi$
$383$		−	3.82378e11i		−	0.908027i	0.890995	−	0.454013i	$-0.150008\pi$
$384$		−	6.24941e11i		−	1.46672i
$385$			2.12244e11i			0.492338i
$386$	7.65439e11			1.75496
$387$	−4.41369e10			−0.100024
$388$		−	1.01244e12i		−	2.26792i
$389$	−2.34628e11			−0.519526			−0.259763	−	0.965672i	$-0.583644\pi$
$389$	−2.34628e11			−0.519526			−0.259763	+	0.965672i	$0.583644\pi$
$390$	−9.99056e11	+	9.53386e10i	−2.18675	+	0.208679i
$391$	4.18485e10			0.0905492
$392$			3.38118e11i			0.723238i
$393$	−1.82617e11			−0.386168
$394$	6.93878e10			0.145061
$395$			2.37353e11i			0.490578i
$396$			8.90990e10i			0.182073i
$397$			6.18037e11i			1.24870i	0.781145	+	0.624349i	$0.214636\pi$
$397$			6.18037e11i			1.24870i	−0.781145	+	0.624349i	$0.785364\pi$
$398$			3.78665e11i			0.756452i
$399$	4.13928e11			0.817612
$400$	−2.06597e9			−0.00403509
$401$			3.41938e11i			0.660386i	0.943913	+	0.330193i	$0.107114\pi$
$401$			3.41938e11i			0.660386i	−0.943913	+	0.330193i	$0.892886\pi$
$402$	1.91853e9			0.00366397
$403$	−3.80157e10	−	3.98368e11i	−0.0717944	−	0.752335i
$404$	−7.49217e11			−1.39924
$405$			6.38617e11i			1.17949i
$406$	5.39447e11			0.985331
$407$	−2.55198e11			−0.461001
$408$			2.46029e10i			0.0439557i
$409$			5.53029e11i			0.977221i	0.872502	+	0.488611i	$0.162496\pi$
$409$			5.53029e11i			0.977221i	−0.872502	+	0.488611i	$0.837504\pi$
$410$		−	7.54013e11i		−	1.31781i
$411$			1.77709e10i			0.0307199i
$412$	4.22153e11			0.721826
$413$	7.59950e10			0.128532
$414$			3.26893e11i			0.546895i
$415$	−1.06823e12			−1.76785
$416$	5.78752e10	+	6.06476e11i	0.0947485	+	0.992872i
$417$	−5.77163e11			−0.934730
$418$		−	1.07522e12i		−	1.72267i
$419$	−4.32597e11			−0.685678			−0.342839	−	0.939394i	$-0.611389\pi$
$419$	−4.32597e11			−0.685678			−0.342839	+	0.939394i	$0.611389\pi$
$420$	−7.39919e11			−1.16028
$421$		−	5.43312e11i		−	0.842908i	−0.906850	−	0.421454i	$-0.861520\pi$
$421$		−	5.43312e11i		−	0.842908i	0.906850	−	0.421454i	$-0.138480\pi$
$422$			1.14137e12i			1.75194i
$423$		−	9.73900e10i		−	0.147905i
$424$		−	4.90667e11i		−	0.737293i
$425$	−4.06758e10			−0.0604764
$426$	1.11724e12			1.64362
$427$		−	5.73032e11i		−	0.834168i
$428$	−1.73128e11			−0.249385
$429$	3.75197e10	+	3.93170e11i	0.0534812	+	0.560431i
$430$	−9.52104e11			−1.34300
$431$			8.14403e11i			1.13682i	0.822746	+	0.568410i	$0.192441\pi$
$431$			8.14403e11i			1.13682i	−0.822746	+	0.568410i	$0.807559\pi$
$432$	−2.50026e9			−0.00345388
$433$	4.87261e11			0.666140			0.333070	−	0.942902i	$-0.391915\pi$
$433$	4.87261e11			0.666140			0.333070	+	0.942902i	$0.391915\pi$
$434$		−	4.77219e11i		−	0.645675i
$435$		−	1.16899e12i		−	1.56534i
$436$			1.16746e12i			1.54722i
$437$		−	2.43887e12i		−	3.19906i
$438$	1.56964e12			2.03782
$439$	−1.08618e12			−1.39577			−0.697883	−	0.716212i	$-0.745874\pi$
$439$	−1.08618e12			−1.39577			−0.697883	+	0.716212i	$0.745874\pi$
$440$			7.35202e11i			0.935125i
$441$	−1.03564e11			−0.130387
$442$	−5.97575e9	−	6.26200e10i	−0.00744719	−	0.0780392i
$443$	6.98685e11			0.861915			0.430958	−	0.902372i	$-0.358176\pi$
$443$	6.98685e11			0.861915			0.430958	+	0.902372i	$0.358176\pi$
$444$		−	8.89661e11i		−	1.08643i
$445$	8.76229e11			1.05925
$446$	5.96413e11			0.713740
$447$			1.21781e11i			0.144276i
$448$			7.27974e11i			0.853817i
$449$			4.09612e11i			0.475624i	0.971311	+	0.237812i	$0.0764303\pi$
$449$			4.09612e11i			0.475624i	−0.971311	+	0.237812i	$0.923570\pi$
$450$		−	3.17732e11i		−	0.365263i
$451$	−2.96735e11			−0.337734
$452$	−2.38191e12			−2.68412
$453$			3.62058e11i			0.403957i
$454$	1.64861e12			1.82124
$455$	7.20382e11	−	6.87451e10i	0.787973	−	0.0751953i
$456$	1.43382e12			1.55294
$457$		−	9.16583e11i		−	0.982989i	−0.870881	−	0.491495i	$-0.836451\pi$
$457$		−	9.16583e11i		−	0.982989i	0.870881	−	0.491495i	$-0.163549\pi$
$458$	−7.57824e11			−0.804773
$459$	−4.92264e10			−0.0517655
$460$			4.35962e12i			4.53982i
$461$		−	1.25699e11i		−	0.129622i	−0.997898	−	0.0648111i	$-0.979356\pi$
$461$		−	1.25699e11i		−	0.129622i	0.997898	−	0.0648111i	$-0.0206445\pi$
$462$			4.70992e11i			0.480978i
$463$			9.10285e11i			0.920583i	0.887768	+	0.460292i	$0.152255\pi$
$463$			9.10285e11i			0.920583i	−0.887768	+	0.460292i	$0.847745\pi$
$464$	3.72152e9			0.00372725
$465$	−1.03414e12			−1.02575
$466$		−	2.42226e12i		−	2.37949i
$467$	−1.52449e11			−0.148320			−0.0741601	−	0.997246i	$-0.523628\pi$
$467$	−1.52449e11			−0.148320			−0.0741601	+	0.997246i	$0.523628\pi$
$468$	3.02412e11	−	2.88588e10i	0.291402	−	0.0278081i
$469$	−1.38338e9			−0.00132028
$470$		−	2.10086e12i		−	1.98590i
$471$	−2.91691e11			−0.273105
$472$	2.63242e11			0.244127
$473$			3.74692e11i			0.344191i
$474$			5.26711e11i			0.479258i
$475$			2.37053e12i			2.13661i
$476$		−	4.63775e10i		−	0.0414072i
$477$	1.50288e11			0.132921
$478$	1.88364e12			1.65034
$479$		−	6.05858e11i		−	0.525849i	−0.964816	−	0.262924i	$-0.915313\pi$
$479$		−	6.05858e11i		−	0.525849i	0.964816	−	0.262924i	$-0.0846870\pi$
$480$	1.57437e12			1.35370
$481$	8.26574e10	+	8.66169e11i	0.0704092	+	0.737819i
$482$	−2.32964e12			−1.96597
$483$			1.06833e12i			0.893192i
$484$	−1.19876e12			−0.992949
$485$	2.55885e12			2.09994
$486$		−	7.10183e11i		−	0.577441i
$487$		−	1.59806e12i		−	1.28740i	−0.765278	−	0.643700i	$-0.777398\pi$
$487$		−	1.59806e12i		−	1.28740i	0.765278	−	0.643700i	$-0.222602\pi$
$488$		−	1.98495e12i		−	1.58438i
$489$		−	1.77097e12i		−	1.40063i
$490$	−2.23404e12			−1.75069
$491$	1.47062e12			1.14192			0.570959	−	0.820979i	$-0.306572\pi$
$491$	1.47062e12			1.14192			0.570959	+	0.820979i	$0.306572\pi$
$492$		−	1.03447e12i		−	0.795928i
$493$	7.32711e10			0.0558627
$494$	−3.64941e12	+	3.48259e11i	−2.75709	+	0.263106i
$495$	−2.25188e11			−0.168586
$496$		−	3.29222e9i		−	0.00244242i
$497$	−8.05597e11			−0.592262
$498$	−2.37050e12			−1.72706
$499$		−	7.67603e11i		−	0.554223i	−0.960838	−	0.277111i	$-0.910623\pi$
$499$		−	7.67603e11i		−	0.554223i	0.960838	−	0.277111i	$-0.0893771\pi$
$500$		−	8.43600e11i		−	0.603631i
$501$		−	1.33362e11i		−	0.0945722i
$502$			1.91998e12i			1.34937i
$503$	−2.35067e12			−1.63733			−0.818664	−	0.574273i	$-0.805285\pi$
$503$	−2.35067e12			−1.63733			−0.818664	+	0.574273i	$0.805285\pi$
$504$	1.38575e11			0.0956636
$505$		−	1.89357e12i		−	1.29559i
$506$	2.77510e12			1.88192
$507$	1.32231e12	−	2.54692e11i	0.888786	−	0.171190i
$508$	7.10694e11			0.473474
$509$			2.89396e12i			1.91101i	0.294981	+	0.955503i	$0.404687\pi$
$509$			2.89396e12i			1.91101i	−0.294981	+	0.955503i	$0.595313\pi$
$510$	−1.62558e11			−0.106400
$511$	−1.13181e12			−0.734307
$512$			1.00504e10i			0.00646354i
$513$			2.86885e12i			1.82885i
$514$			1.22339e12i			0.773090i
$515$			1.06695e12i			0.668360i
$516$	−1.30624e12			−0.811145
$517$	−8.26775e11			−0.508956
$518$			1.03762e12i			0.633218i
$519$	−1.37276e12			−0.830503
$520$	2.49536e12	−	2.38129e11i	1.49664	−	0.142823i
$521$	2.02590e12			1.20461			0.602307	−	0.798265i	$-0.294248\pi$
$521$	2.02590e12			1.20461			0.602307	+	0.798265i	$0.294248\pi$
$522$			5.72346e11i			0.337397i
$523$	2.08491e11			0.121851			0.0609255	−	0.998142i	$-0.480595\pi$
$523$	2.08491e11			0.121851			0.0609255	+	0.998142i	$0.480595\pi$
$524$	1.19243e12			0.690945
$525$		−	1.03840e12i		−	0.596549i
$526$		−	2.73968e12i		−	1.56050i
$527$		−	6.48189e10i		−	0.0366061i
$528$			3.24926e9i			0.00181942i
$529$	4.49349e12			2.49478
$530$	3.24196e12			1.78471
$531$			8.06295e10i			0.0440118i
$532$	−2.70282e12			−1.46290
$533$	9.61112e10	+	1.00715e12i	0.0515824	+	0.540533i
$534$	1.94444e12			1.03481
$535$		−	4.37563e11i		−	0.230913i
$536$	−4.79196e9			−0.00250767
$537$	7.62300e10			0.0395587
$538$			3.08699e12i			1.58860i
$539$			8.79186e11i			0.448674i
$540$		−	5.12822e12i		−	2.59534i
$541$			1.72491e11i			0.0865721i	0.999063	+	0.0432860i	$0.0137827\pi$
$541$			1.72491e11i			0.0865721i	−0.999063	+	0.0432860i	$0.986217\pi$
$542$	−5.41635e12			−2.69594
$543$	−2.16301e12			−1.06773
$544$			9.86805e10i			0.0483099i
$545$	−2.95063e12			−1.43262
$546$	1.59860e12	−	1.52552e11i	0.769792	−	0.0734602i
$547$	2.20401e12			1.05262			0.526308	−	0.850294i	$-0.323576\pi$
$547$	2.20401e12			1.05262			0.526308	+	0.850294i	$0.323576\pi$
$548$		−	1.16038e11i		−	0.0549652i
$549$	6.07978e11			0.285636
$550$	−2.69733e12			−1.25690
$551$		−	4.27014e12i		−	1.97360i
$552$			3.70064e12i			1.69649i
$553$		−	3.79791e11i		−	0.172696i
$554$		−	3.40125e12i		−	1.53407i
$555$	2.24852e12			1.00596
$556$	3.76869e12			1.67245
$557$			3.95332e12i			1.74026i	0.492826	+	0.870128i	$0.335964\pi$
$557$			3.95332e12i			1.74026i	−0.492826	+	0.870128i	$0.664036\pi$
$558$	5.06322e11			0.221092
$559$	1.27175e12	−	1.21361e11i	0.550868	−	0.0525686i
$560$	5.95343e9			0.00255812
$561$			6.39731e10i			0.0272687i
$562$	2.63633e12			1.11477
$563$	−1.65646e12			−0.694854			−0.347427	−	0.937707i	$-0.612945\pi$
$563$	−1.65646e12			−0.694854			−0.347427	+	0.937707i	$0.612945\pi$
$564$		−	2.88227e12i		−	1.19944i
$565$		−	6.02002e12i		−	2.48531i
$566$		−	4.52730e11i		−	0.185424i
$567$		−	1.02186e12i		−	0.415209i
$568$	−2.79054e12			−1.12492
$569$	1.22732e12			0.490854			0.245427	−	0.969415i	$-0.421072\pi$
$569$	1.22732e12			0.490854			0.245427	+	0.969415i	$0.421072\pi$
$570$			9.47365e12i			3.75907i
$571$	−1.22316e12			−0.481526			−0.240763	−	0.970584i	$-0.577398\pi$
$571$	−1.22316e12			−0.481526			−0.240763	+	0.970584i	$0.577398\pi$
$572$	−2.44992e11	−	2.56727e12i	−0.0956905	−	1.00274i
$573$	1.40672e12			0.545143
$574$			1.20650e12i			0.463901i
$575$	−6.11825e12			−2.33411
$576$	−7.72370e11			−0.292364
$577$		−	3.19241e12i		−	1.19902i	−0.800366	−	0.599512i	$-0.795361\pi$
$577$		−	3.19241e12i		−	1.19902i	0.800366	−	0.599512i	$-0.204639\pi$
$578$			4.33274e12i			1.61468i
$579$			2.65412e12i			0.981449i
$580$			7.63311e12i			2.80076i
$581$	1.70928e12			0.622330
$582$	5.67834e12			2.05148
$583$		−	1.27585e12i		−	0.457393i
$584$	−3.92051e12			−1.39471
$585$	7.29375e10	+	7.64314e11i	0.0257484	+	0.269818i
$586$	−4.78937e12			−1.67780
$587$		−	3.17550e12i		−	1.10393i	−0.833868	−	0.551964i	$-0.813879\pi$
$587$		−	3.17550e12i		−	1.10393i	0.833868	−	0.551964i	$-0.186121\pi$
$588$	−3.06499e12			−1.05738
$589$	−3.77756e12			−1.29328
$590$			1.73931e12i			0.590939i
$591$			2.40599e11i			0.0811241i
$592$			7.15826e9i			0.00239530i
$593$			5.02255e12i			1.66793i	0.551817	+	0.833966i	$0.313935\pi$
$593$			5.02255e12i			1.66793i	−0.551817	+	0.833966i	$0.686065\pi$
$594$	−3.26435e12			−1.07586
$595$	1.17214e11			0.0383402
$596$		−	7.95191e11i		−	0.258145i
$597$	−1.31300e12			−0.423040
$598$	−8.98842e11	−	9.41899e12i	−0.287427	−	3.01196i
$599$	2.40170e12			0.762252			0.381126	−	0.924523i	$-0.375536\pi$
$599$	2.40170e12			0.762252			0.381126	+	0.924523i	$0.375536\pi$
$600$		−	3.59694e12i		−	1.13306i
$601$	1.55850e12			0.487273			0.243636	−	0.969867i	$-0.421660\pi$
$601$	1.55850e12			0.487273			0.243636	+	0.969867i	$0.421660\pi$
$602$	1.52347e12			0.472771
$603$		−	1.46775e9i		−	0.000452089i
$604$		−	2.36412e12i		−	0.722776i
$605$		−	3.02973e12i		−	0.919400i
$606$		−	4.20202e12i		−	1.26570i
$607$	−5.19956e12			−1.55459			−0.777297	−	0.629133i	$-0.783410\pi$
$607$	−5.19956e12			−1.55459			−0.777297	+	0.629133i	$0.783410\pi$
$608$	5.75096e12			1.70677
$609$			1.87051e12i			0.551039i
$610$	1.31151e13			3.83519
$611$	2.67789e11	+	2.80617e12i	0.0777333	+	0.814570i
$612$	4.92059e10			0.0141787
$613$			1.64456e12i			0.470411i	0.971946	+	0.235205i	$0.0755763\pi$
$613$			1.64456e12i			0.470411i	−0.971946	+	0.235205i	$0.924424\pi$
$614$	2.87257e12			0.815666
$615$	2.61450e12			0.736973
$616$		−	1.17641e12i		−	0.329188i
$617$		−	1.32890e12i		−	0.369156i	−0.982818	−	0.184578i	$-0.940908\pi$
$617$		−	1.32890e12i		−	0.369156i	0.982818	−	0.184578i	$-0.0590918\pi$
$618$			2.36767e12i			0.652938i
$619$			3.13560e12i			0.858446i	0.903198	+	0.429223i	$0.141213\pi$
$619$			3.13560e12i			0.858446i	−0.903198	+	0.429223i	$0.858787\pi$
$620$	6.75259e12			1.83530
$621$	−7.40438e12			−1.99791
$622$		−	6.62354e12i		−	1.77432i
$623$	−1.40206e12			−0.372882
$624$	1.10284e10	−	1.05242e9i	0.00291193	−	0.000277881i
$625$	−2.63080e12			−0.689648
$626$			6.48126e12i			1.68684i
$627$	3.72827e12			0.963392
$628$	1.90465e12			0.488649
$629$			1.40936e11i			0.0358999i
$630$			9.15600e11i			0.231565i
$631$			6.93718e12i			1.74201i	0.491273	+	0.871006i	$0.336532\pi$
$631$			6.93718e12i			1.74201i	−0.491273	+	0.871006i	$0.663468\pi$
$632$		−	1.31557e12i		−	0.328011i
$633$	−3.95764e12			−0.979761
$634$	−8.99847e12			−2.21191
$635$			1.79620e12i			0.438403i
$636$	4.44781e12			1.07793
$637$	2.98406e12	−	2.84765e11i	0.718091	−	0.0685265i
$638$	4.85882e12			1.16102
$639$		−	8.54726e11i		−	0.202802i
$640$	−1.03134e13			−2.42993
$641$	5.32648e12			1.24618			0.623088	−	0.782152i	$-0.285878\pi$
$641$	5.32648e12			1.24618			0.623088	+	0.782152i	$0.285878\pi$
$642$		−	9.70998e11i		−	0.225585i
$643$		−	2.08450e12i		−	0.480897i	−0.970662	−	0.240448i	$-0.922705\pi$
$643$		−	2.08450e12i		−	0.480897i	0.970662	−	0.240448i	$-0.0772945\pi$
$644$		−	6.97588e12i		−	1.59813i
$645$		−	3.30138e12i		−	0.751063i
$646$	−5.93801e11			−0.134151
$647$	1.70868e12			0.383347			0.191673	−	0.981459i	$-0.438609\pi$
$647$	1.70868e12			0.383347			0.191673	+	0.981459i	$0.438609\pi$
$648$		−	3.53966e12i		−	0.788631i
$649$	6.84490e11			0.151449
$650$	8.73655e11	+	9.15505e12i	0.191968	+	2.01164i
$651$	1.65474e12			0.361089
$652$			1.15639e13i			2.50605i
$653$	−1.51560e12			−0.326193			−0.163097	−	0.986610i	$-0.552148\pi$
$653$	−1.51560e12			−0.326193			−0.163097	+	0.986610i	$0.552148\pi$
$654$	−6.54775e12			−1.39956
$655$			3.01375e12i			0.639766i
$656$			8.32338e9i			0.00175482i
$657$		−	1.20083e12i		−	0.251442i
$658$			3.36161e12i			0.699087i
$659$	2.20118e12			0.454644			0.227322	−	0.973820i	$-0.427003\pi$
$659$	2.20118e12			0.454644			0.227322	+	0.973820i	$0.427003\pi$
$660$	−6.66448e12			−1.36716
$661$			4.09192e11i			0.0833721i	0.999131	+	0.0416861i	$0.0132729\pi$
$661$			4.09192e11i			0.0833721i	−0.999131	+	0.0416861i	$0.986727\pi$
$662$	−5.76548e12			−1.16674
$663$	2.17132e11	−	2.07206e10i	0.0436428	−	0.00416478i
$664$	5.92084e12			1.18203
$665$		−	6.83109e12i		−	1.35454i
$666$	−1.10090e12			−0.216826
$667$	1.10211e13			2.15604
$668$			8.70814e11i			0.169212i
$669$			2.06803e12i			0.399154i
$670$		−	3.16617e10i		−	0.00607013i
$671$		−	5.16132e12i		−	0.982901i
$672$	−2.51917e12			−0.476537
$673$	−4.56640e12			−0.858037			−0.429019	−	0.903296i	$-0.641141\pi$
$673$	−4.56640e12			−0.858037			−0.429019	+	0.903296i	$0.641141\pi$
$674$		−	7.64317e12i		−	1.42661i
$675$	7.19690e12			1.33438
$676$	−8.63426e12	+	1.66306e12i	−1.59025	+	0.306300i
$677$	−7.50044e12			−1.37226			−0.686132	−	0.727477i	$-0.740693\pi$
$677$	−7.50044e12			−1.37226			−0.686132	+	0.727477i	$0.740693\pi$
$678$		−	1.33590e13i		−	2.42796i
$679$	−4.09444e12			−0.739232
$680$	4.06023e11			0.0728217
$681$			5.71647e12i			1.01851i
$682$		−	4.29833e12i		−	0.760800i
$683$		−	9.92431e12i		−	1.74505i	−0.488573	−	0.872523i	$-0.662482\pi$
$683$		−	9.92431e12i		−	1.74505i	0.488573	−	0.872523i	$-0.337518\pi$
$684$		−	2.86765e12i		−	0.500926i
$685$	2.93274e11			0.0508939
$686$	8.53027e12			1.47063
$687$		−	2.62772e12i		−	0.450063i
$688$	1.05101e10			0.00178837
$689$	−4.33037e12	+	4.13241e11i	−0.732045	+	0.0698582i
$690$	−2.44511e13			−4.10656
$691$		−	7.56666e11i		−	0.126256i	−0.998005	−	0.0631281i	$-0.979892\pi$
$691$		−	7.56666e11i		−	0.126256i	0.998005	−	0.0631281i	$-0.0201077\pi$
$692$	8.96368e12			1.48597
$693$	3.60326e11			0.0593467
$694$			7.19496e12i			1.17736i
$695$			9.52496e12i			1.54857i
$696$			6.47933e12i			1.04662i
$697$			1.63875e11i			0.0263006i
$698$	1.50702e13			2.40309
$699$	8.39906e12			1.33071
$700$			6.78040e12i			1.06737i
$701$	−3.61849e12			−0.565974			−0.282987	−	0.959124i	$-0.591325\pi$
$701$	−3.61849e12			−0.565974			−0.282987	+	0.959124i	$0.591325\pi$
$702$	1.05731e12	+	1.10796e13i	0.164318	+	1.72189i
$703$	8.21354e12			1.26833
$704$			6.55689e12i			1.00605i
$705$	7.28464e12			1.11060
$706$	−1.31020e13			−1.98479
$707$			3.02992e12i			0.456082i
$708$			2.38624e12i			0.356915i
$709$			5.22097e12i			0.775967i	0.921666	+	0.387983i	$0.126828\pi$
$709$			5.22097e12i			0.775967i	−0.921666	+	0.387983i	$0.873172\pi$
$710$		−	1.84378e13i		−	2.72300i
$711$	4.02953e11			0.0591345
$712$	−4.85667e12			−0.708236
$713$		−	9.74974e12i		−	1.41283i
$714$	2.60111e11			0.0374555
$715$	6.48851e12	−	6.19190e11i	0.928469	−	0.0886026i
$716$	−4.97758e11			−0.0707798
$717$			6.53143e12i			0.922937i
$718$	1.60913e13			2.25960
$719$	−1.01261e13			−1.41306			−0.706530	−	0.707683i	$-0.749740\pi$
$719$	−1.01261e13			−1.41306			−0.706530	+	0.707683i	$0.749740\pi$
$720$			6.31650e9i			0.000875952i
$721$		−	1.70723e12i		−	0.235280i
$722$			2.27884e13i			3.12102i
$723$		−	8.07792e12i		−	1.09945i
$724$	1.41238e13			1.91041
$725$	−1.07122e13			−1.43999
$726$		−	6.72328e12i		−	0.898186i
$727$	−6.71570e12			−0.891634			−0.445817	−	0.895124i	$-0.647087\pi$
$727$	−6.71570e12			−0.891634			−0.445817	+	0.895124i	$0.647087\pi$
$728$	−3.99285e12	+	3.81033e11i	−0.526856	+	0.0502772i
$729$	8.46063e12			1.10950
$730$		−	2.59038e13i		−	3.37607i
$731$	2.06928e11			0.0268034
$732$	1.79932e13			2.31638
$733$			5.18892e12i			0.663910i	0.943295	+	0.331955i	$0.107708\pi$
$733$			5.18892e12i			0.663910i	−0.943295	+	0.331955i	$0.892292\pi$
$734$			5.47005e12i			0.695600i
$735$		−	7.74642e12i		−	0.979058i
$736$			1.48430e13i			1.86454i
$737$	−1.24602e10			−0.00155568
$738$	−1.28008e12			−0.158849
$739$			1.45229e12i			0.179124i	0.995981	+	0.0895618i	$0.0285467\pi$
$739$			1.45229e12i			0.179124i	−0.995981	+	0.0895618i	$0.971453\pi$
$740$	−1.46821e13			−1.79989
$741$	−1.20757e12	−	1.26542e13i	−0.147140	−	1.54188i
$742$	−5.18751e12			−0.628262
$743$			1.32192e12i			0.159131i	0.996830	+	0.0795656i	$0.0253533\pi$
$743$			1.32192e12i			0.159131i	−0.996830	+	0.0795656i	$0.974647\pi$
$744$	5.73190e12			0.685837
$745$	2.00976e12			0.239024
$746$		−	4.76048e12i		−	0.562764i
$747$			1.81352e12i			0.213098i
$748$		−	4.17724e11i		−	0.0487902i
$749$			7.00150e11i			0.0812874i
$750$	4.73137e12			0.546023
$751$	−3.80161e11			−0.0436102			−0.0218051	−	0.999762i	$-0.506941\pi$
$751$	−3.80161e11			−0.0436102			−0.0218051	+	0.999762i	$0.506941\pi$
$752$			2.31909e10i			0.00264447i
$753$	−6.65745e12			−0.754624
$754$	−1.57375e12	−	1.64914e13i	−0.177323	−	1.85817i
$755$	5.97506e12			0.669239
$756$			8.20572e12i			0.913626i
$757$	−2.98242e12			−0.330094			−0.165047	−	0.986286i	$-0.552778\pi$
$757$	−2.98242e12			−0.330094			−0.165047	+	0.986286i	$0.552778\pi$
$758$	−4.78364e12			−0.526316
$759$			9.62252e12i			1.05245i
$760$		−	2.36625e13i		−	2.57276i
$761$			1.29457e13i			1.39925i	0.714509	+	0.699626i	$0.246650\pi$
$761$			1.29457e13i			1.39925i	−0.714509	+	0.699626i	$0.753350\pi$
$762$			3.98596e12i			0.428288i
$763$	4.72133e12			0.504318
$764$	−9.18541e12			−0.975390
$765$			1.24363e11i			0.0131284i
$766$	−1.40035e13			−1.46962
$767$	−2.21703e11	−	2.32324e12i	−0.0231309	−	0.242390i
$768$	−8.77194e12			−0.909850
$769$			2.51079e12i			0.258906i	0.991586	+	0.129453i	$0.0413222\pi$
$769$			2.51079e12i			0.258906i	−0.991586	+	0.129453i	$0.958678\pi$
$770$	7.77282e12			0.796839
$771$	−4.24204e12			−0.432344
$772$		−	1.73306e13i		−	1.75604i
$773$			6.09264e12i			0.613759i	0.951748	+	0.306880i	$0.0992849\pi$
$773$			6.09264e12i			0.613759i	−0.951748	+	0.306880i	$0.900715\pi$
$774$			1.61638e12i			0.161886i
$775$			9.47653e12i			0.943608i
$776$	−1.41829e13			−1.40406
$777$	−3.59789e12			−0.354122
$778$			8.59256e12i			0.840842i
$779$	9.55042e12			0.929188
$780$	2.15860e12	+	2.26200e13i	0.208807	+	2.18810i
$781$	−7.25604e12			−0.697863
$782$		−	1.53258e12i		−	0.146552i
$783$	−1.29641e13			−1.23258
$784$	2.46611e10			0.00233125
$785$			4.81380e12i			0.452454i
$786$			6.68782e12i			0.625005i
$787$		−	1.14788e13i		−	1.06662i	−0.845920	−	0.533310i	$-0.820948\pi$
$787$		−	1.14788e13i		−	1.06662i	0.845920	−	0.533310i	$-0.179052\pi$
$788$		−	1.57103e12i		−	0.145150i
$789$	9.49971e12			0.872698
$790$	8.69235e12			0.793990
$791$			9.63270e12i			0.874891i
$792$	1.24815e12			0.112720
$793$	−1.75181e13	+	1.67173e12i	−1.57311	+	0.150120i
$794$	2.26338e13			2.02099
$795$			1.12414e13i			0.998083i
$796$	8.57350e12			0.756919
$797$	1.27357e13			1.11804			0.559022	−	0.829153i	$-0.311177\pi$
$797$	1.27357e13			1.11804			0.559022	+	0.829153i	$0.311177\pi$
$798$		−	1.51589e13i		−	1.32329i
$799$			4.56595e11i			0.0396343i
$800$		−	1.44271e13i		−	1.24530i
$801$		−	1.48757e12i		−	0.127682i
$802$	1.25225e13			1.06882
$803$	−1.01942e13			−0.865235
$804$		−	4.34383e10i		−	0.00366623i
$805$	1.76308e13			1.47976
$806$	−1.45890e13	+	1.39221e12i	−1.21764	+	0.116198i
$807$	−1.07040e13			−0.888412
$808$			1.04954e13i			0.866263i
$809$	7.93618e12			0.651393			0.325697	−	0.945474i	$-0.394401\pi$
$809$	7.93618e12			0.651393			0.325697	+	0.945474i	$0.394401\pi$
$810$	2.33875e13			1.90898
$811$		−	1.25687e13i		−	1.02023i	−0.860108	−	0.510113i	$-0.829604\pi$
$811$		−	1.25687e13i		−	1.02023i	0.860108	−	0.510113i	$-0.170396\pi$
$812$		−	1.22138e13i		−	0.985938i
$813$		−	1.87809e13i		−	1.50768i
$814$			9.34585e12i			0.746121i
$815$	−2.92265e13			−2.32043
$816$	1.79444e9			0.000141685
$817$		−	1.20595e13i		−	0.946954i
$818$	2.02530e13			1.58161
$819$	−1.16708e11	−	1.22299e12i	−0.00906408	−	0.0949827i
$820$	−1.70719e13			−1.31862
$821$		−	1.79790e13i		−	1.38109i	−0.723289	−	0.690545i	$-0.757371\pi$
$821$		−	1.79790e13i		−	1.38109i	0.723289	−	0.690545i	$-0.242629\pi$
$822$	6.50805e11			0.0497196
$823$	−8.39424e12			−0.637796			−0.318898	−	0.947789i	$-0.603313\pi$
$823$	−8.39424e12			−0.637796			−0.318898	+	0.947789i	$0.603313\pi$
$824$		−	5.91376e12i		−	0.446880i
$825$		−	9.35288e12i		−	0.702914i
$826$		−	2.78309e12i		−	0.208026i
$827$			4.47730e12i			0.332845i	0.986055	+	0.166422i	$0.0532215\pi$
$827$			4.47730e12i			0.332845i	−0.986055	+	0.166422i	$0.946778\pi$
$828$	7.40130e12			0.547232
$829$	1.12151e13			0.824719			0.412360	−	0.911021i	$-0.364705\pi$
$829$	1.12151e13			0.824719			0.412360	+	0.911021i	$0.364705\pi$
$830$			3.91206e13i			2.86124i
$831$	1.17937e13			0.857915
$832$	2.22548e13	−	2.12375e12i	1.61016	−	0.153656i
$833$	4.85540e11			0.0349399
$834$			2.11369e13i			1.51284i
$835$	−2.20089e12			−0.156678
$836$	−2.43444e13			−1.72374
$837$			1.14686e13i			0.807693i
$838$			1.58426e13i			1.10976i
$839$		−	2.74013e13i		−	1.90916i	−0.297953	−	0.954580i	$-0.596304\pi$
$839$		−	2.74013e13i		−	1.90916i	0.297953	−	0.954580i	$-0.403696\pi$
$840$			1.03652e13i			0.718325i
$841$	4.78929e12			0.330133
$842$	−1.98972e13			−1.36423
$843$			9.14135e12i			0.623428i
$844$	2.58422e13			1.75302
$845$	−4.20320e12	−	2.18222e13i	−0.283612	−	1.47246i
$846$	−3.56662e12			−0.239381
$847$			4.84790e12i			0.323652i
$848$	−3.57873e10			−0.00237656
$849$	1.56982e12			0.103697
$850$			1.48963e12i			0.0978799i
$851$			2.11988e13i			1.38557i
$852$		−	2.52957e13i		−	1.64463i
$853$			2.50168e13i			1.61794i	0.587852	+	0.808968i	$0.299974\pi$
$853$			2.50168e13i			1.61794i	−0.587852	+	0.808968i	$0.700026\pi$
$854$	−2.09856e13			−1.35008
$855$	7.24768e12			0.463822
$856$			2.42528e12i			0.154394i
$857$	−5.07930e12			−0.321655			−0.160827	−	0.986983i	$-0.551416\pi$
$857$	−5.07930e12			−0.321655			−0.160827	+	0.986983i	$0.551416\pi$
$858$	1.43987e13	−	1.37405e12i	0.907046	−	0.0865583i
$859$	1.75637e13			1.10064			0.550322	−	0.834952i	$-0.314505\pi$
$859$	1.75637e13			1.10064			0.550322	+	0.834952i	$0.314505\pi$
$860$			2.15569e13i			1.34383i
$861$	−4.18350e12			−0.259433
$862$	2.98251e13			1.83992
$863$		−	1.33449e13i		−	0.818967i	−0.912318	−	0.409484i	$-0.865709\pi$
$863$		−	1.33449e13i		−	0.818967i	0.912318	−	0.409484i	$-0.134291\pi$
$864$		−	1.74598e13i		−	1.06593i
$865$			2.26547e13i			1.37590i
$866$		−	1.78445e13i		−	1.07814i
$867$	−1.50236e13			−0.902999
$868$	−1.08049e13			−0.646074
$869$		−	3.42079e12i		−	0.203488i
$870$	−4.28107e13			−2.53347
$871$	4.03580e9	+	4.22913e10i	0.000237601	+	0.00248983i
$872$	1.63544e13			0.957880
$873$		−	4.34414e12i		−	0.253128i
$874$	−8.93165e13			−5.17762
$875$	−3.41161e12			−0.196754
$876$		−	3.55387e13i		−	2.03908i
$877$			2.15013e13i			1.22734i	0.789561	+	0.613672i	$0.210308\pi$
$877$			2.15013e13i			1.22734i	−0.789561	+	0.613672i	$0.789692\pi$
$878$			3.97782e13i			2.25902i
$879$		−	1.66069e13i		−	0.938295i
$880$	5.36228e10			0.00301424
$881$	1.63406e12			0.0913853			0.0456927	−	0.998956i	$-0.485451\pi$
$881$	1.63406e12			0.0913853			0.0456927	+	0.998956i	$0.485451\pi$
$882$			3.79271e12i			0.211029i
$883$	−1.70569e13			−0.944229			−0.472115	−	0.881537i	$-0.656509\pi$
$883$	−1.70569e13			−0.944229			−0.472115	+	0.881537i	$0.656509\pi$
$884$	−1.41780e12	+	1.35299e11i	−0.0780874	+	0.00745178i
$885$	−6.03098e12			−0.330478
$886$		−	2.55873e13i		−	1.39499i
$887$	2.37933e13			1.29062			0.645310	−	0.763921i	$-0.276728\pi$
$887$	2.37933e13			1.29062			0.645310	+	0.763921i	$0.276728\pi$
$888$	−1.24629e13			−0.672604
$889$		−	2.87412e12i		−	0.154329i
$890$		−	3.20893e13i		−	1.71437i
$891$		−	9.20392e12i		−	0.489242i
$892$		−	1.35036e13i		−	0.714181i
$893$	2.66098e13			1.40026
$894$	4.45986e12			0.233509
$895$		−	1.25803e12i		−	0.0655371i
$896$	1.65027e13			0.855398
$897$	3.26599e13	−	3.11669e12i	1.68441	−	0.160742i
$898$	1.50008e13			0.769789
$899$		−	1.70705e13i		−	0.871620i
$900$	−7.19390e12			−0.365488
$901$	−7.04599e11			−0.0356189
$902$			1.08670e13i			0.546615i
$903$			5.28257e12i			0.264393i
$904$			3.33671e13i			1.66173i
$905$			3.56963e13i			1.76891i
$906$	1.32593e13			0.653797
$907$	2.53316e13			1.24288			0.621441	−	0.783461i	$-0.286547\pi$
$907$	2.53316e13			1.24288			0.621441	+	0.783461i	$0.286547\pi$
$908$		−	3.73268e13i		−	1.82236i
$909$	−3.21469e12			−0.156172
$910$	−2.51759e12	−	2.63818e13i	−0.121702	−	1.27532i
$911$	−3.13091e13			−1.50604			−0.753022	−	0.657996i	$-0.771404\pi$
$911$	−3.13091e13			−1.50604			−0.753022	+	0.657996i	$0.771404\pi$
$912$		−	1.04577e11i		−	0.00500566i
$913$	1.53955e13			0.733292
$914$	−3.35671e13			−1.59095
$915$			4.54759e13i			2.14480i
$916$			1.71582e13i			0.805270i
$917$		−	4.82234e12i		−	0.225214i
$918$			1.80277e12i			0.0837815i
$919$	1.48314e13			0.685903			0.342952	−	0.939353i	$-0.388573\pi$
$919$	1.48314e13			0.685903			0.342952	+	0.939353i	$0.388573\pi$
$920$	6.10720e13			2.81058
$921$			9.96049e12i			0.456155i
$922$	−4.60337e12			−0.209791
$923$	2.35020e12	+	2.46278e13i	0.106585	+	1.11691i
$924$	1.06639e13			0.481274
$925$		−	2.06048e13i		−	0.925402i
$926$	3.33365e13			1.48995
$927$	1.81135e12			0.0805645
$928$			2.59882e13i			1.15030i
$929$		−	3.18888e13i		−	1.40465i	−0.711857	−	0.702324i	$-0.752146\pi$
$929$		−	3.18888e13i		−	1.40465i	0.711857	−	0.702324i	$-0.247854\pi$
$930$			3.78722e13i			1.66015i
$931$		−	2.82966e13i		−	1.23441i
$932$	−5.48432e13			−2.38096
$933$	2.29668e13			0.992277
$934$			5.58301e12i			0.240053i
$935$	1.05575e12			0.0451763
$936$	−4.04270e11	−	4.23636e12i	−0.0172159	−	0.180406i
$937$	−4.42511e13			−1.87541			−0.937704	−	0.347434i	$-0.887053\pi$
$937$	−4.42511e13			−1.87541			−0.937704	+	0.347434i	$0.887053\pi$
$938$			5.06623e10i			0.00213684i
$939$	−2.24735e13			−0.943355
$940$	−4.75664e13			−1.98712
$941$			4.26589e12i			0.177360i	0.996060	+	0.0886802i	$0.0282649\pi$
$941$			4.26589e12i			0.177360i	−0.996060	+	0.0886802i	$0.971735\pi$
$942$			1.06823e13i			0.442014i
$943$			2.46493e13i			1.01508i
$944$		−	1.91999e10i		−	0.000786908i
$945$	−2.07391e13			−0.845953
$946$	1.37220e13			0.557066
$947$			1.77369e13i			0.716643i	0.933598	+	0.358321i	$0.116651\pi$
$947$			1.77369e13i			0.716643i	−0.933598	+	0.358321i	$0.883349\pi$
$948$	1.19255e13			0.479554
$949$	3.30187e12	+	3.46003e13i	0.132148	+	1.38479i
$950$	8.68137e13			3.45805
$951$		−	3.12018e13i		−	1.23699i
$952$	−6.49682e11			−0.0256351
$953$	−2.25032e13			−0.883743			−0.441872	−	0.897078i	$-0.645685\pi$
$953$	−2.25032e13			−0.883743			−0.441872	+	0.897078i	$0.645685\pi$
$954$		−	5.50386e12i		−	0.215130i
$955$		−	2.32151e13i		−	0.903142i
$956$		−	4.26482e13i		−	1.65135i
$957$			1.68477e13i			0.649289i
$958$	−2.21877e13			−0.851076
$959$	−4.69271e11			−0.0179160
$960$		−	5.77722e13i		−	2.19532i
$961$	1.13383e13			0.428837
$962$	3.17209e13	−	3.02708e12i	1.19415	−	0.113956i
$963$	−7.42849e11			−0.0278344
$964$			5.27463e13i			1.96718i
$965$	4.38012e13			1.62597
$966$	3.91245e13			1.44561
$967$		−	2.61100e13i		−	0.960257i	−0.877198	−	0.480129i	$-0.840590\pi$
$967$		−	2.61100e13i		−	0.960257i	0.877198	−	0.480129i	$-0.159410\pi$
$968$			1.67928e13i			0.614731i
$969$		−	2.05898e12i		−	0.0750230i
$970$		−	9.37101e13i		−	3.39871i
$971$	1.63941e13			0.591834			0.295917	−	0.955214i	$-0.404375\pi$
$971$	1.63941e13			0.591834			0.295917	+	0.955214i	$0.404375\pi$
$972$	−1.60795e13			−0.577797
$973$		−	1.52410e13i		−	0.545137i
$974$	−5.85243e13			−2.08363
$975$	−3.17447e13	+	3.02936e12i	−1.12500	+	0.107357i
$976$	−1.44775e11			−0.00510702
$977$			5.80148e11i			0.0203710i	0.999948	+	0.0101855i	$0.00324221\pi$
$977$			5.80148e11i			0.0203710i	−0.999948	+	0.0101855i	$0.996758\pi$
$978$	−6.48566e13			−2.26689
$979$	−1.26284e13			−0.439367
$980$			5.05817e13i			1.75177i
$981$			5.00926e12i			0.172688i
$982$		−	5.38572e13i		−	1.84817i
$983$		−	2.90868e13i		−	0.993585i	−0.867869	−	0.496792i	$-0.834511\pi$
$983$		−	2.90868e13i		−	0.993585i	0.867869	−	0.496792i	$-0.165489\pi$
$984$	−1.44914e13			−0.492756
$985$	3.97062e12			0.134399
$986$		−	2.68334e12i		−	0.0904126i
$987$	−1.16562e13			−0.390959
$988$	7.88505e12	+	8.26277e13i	0.263268	+	2.75879i
$989$	3.11250e13			1.03449
$990$			8.24685e12i			0.272854i
$991$	−5.02879e13			−1.65627			−0.828136	−	0.560527i	$-0.810599\pi$
$991$	−5.02879e13			−1.65627			−0.828136	+	0.560527i	$0.810599\pi$
$992$	2.29903e13			0.753775
$993$		−	1.99916e13i		−	0.652492i
$994$			2.95026e13i			0.958564i
$995$			2.16686e13i			0.700853i
$996$			5.36714e13i			1.72813i
$997$	−3.97969e13			−1.27562			−0.637810	−	0.770194i	$-0.720159\pi$
$997$	−3.97969e13			−1.27562			−0.637810	+	0.770194i	$0.720159\pi$
$998$	−2.81112e13			−0.896998
$999$		−	2.49362e13i		−	0.792109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.b.a.12.2	✓	10
3.2	odd	2		117.10.b.c.64.9		10
4.3	odd	2		208.10.f.b.129.3		10
13.5	odd	4		169.10.a.e.1.2		10
13.8	odd	4		169.10.a.e.1.9		10
13.12	even	2	inner	13.10.b.a.12.9	yes	10
39.38	odd	2		117.10.b.c.64.2		10
52.51	odd	2		208.10.f.b.129.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.b.a.12.2	✓	10	1.1	even	1	trivial
13.10.b.a.12.9	yes	10	13.12	even	2	inner
117.10.b.c.64.2		10	39.38	odd	2
117.10.b.c.64.9		10	3.2	odd	2
169.10.a.e.1.2		10	13.5	odd	4
169.10.a.e.1.9		10	13.8	odd	4
208.10.f.b.129.3		10	4.3	odd	2
208.10.f.b.129.4		10	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-36.6220i q^{2} +126.985 q^{3} -829.173 q^{4} -2095.65i q^{5} -4650.45i q^{6} +3353.27i q^{7} +11615.5i q^{8} -3557.77 q^{9} -76746.8 q^{10} +30203.0i q^{11} -105293. q^{12} +(102512. - 9782.63i) q^{13} +122803. q^{14} -266116. i q^{15} +847.191 q^{16} +16679.9 q^{17} +130293. i q^{18} -972084. i q^{19} +1.73765e6i q^{20} +425815. i q^{21} +1.10610e6 q^{22} +2.50891e6 q^{23} +1.47500e6i q^{24} -2.43861e6 q^{25} +(-358260. - 3.75421e6i) q^{26} -2.95123e6 q^{27} -2.78044e6i q^{28} +4.39277e6 q^{29} -9.74571e6 q^{30} -3.88604e6i q^{31} +5.91612e6i q^{32} +3.83534e6i q^{33} -610853. i q^{34} +7.02726e6 q^{35} +2.95000e6 q^{36} +8.44941e6i q^{37} -3.55997e7 q^{38} +(1.30176e7 - 1.24225e6i) q^{39} +2.43420e7 q^{40} +9.82468e6i q^{41} +1.55942e7 q^{42} +1.24058e7 q^{43} -2.50435e7i q^{44} +7.45582e6i q^{45} -9.18815e7i q^{46} +2.73739e7i q^{47} +107581. q^{48} +2.91092e7 q^{49} +8.93067e7i q^{50} +2.11810e6 q^{51} +(-8.50005e7 + 8.11149e6i) q^{52} -4.22423e7 q^{53} +1.08080e8i q^{54} +6.32948e7 q^{55} -3.89499e7 q^{56} -1.23440e8i q^{57} -1.60872e8i q^{58} -2.26630e7i q^{59} +2.20656e8i q^{60} -1.70888e8 q^{61} -1.42315e8 q^{62} -1.19301e7i q^{63} +2.17094e8 q^{64} +(-2.05009e7 - 2.14830e8i) q^{65} +1.40458e8 q^{66} +412548. i q^{67} -1.38306e7 q^{68} +3.18595e8 q^{69} -2.57353e8i q^{70} +2.40242e8i q^{71} -4.13253e7i q^{72} +3.37523e8i q^{73} +3.09434e8 q^{74} -3.09667e8 q^{75} +8.06026e8i q^{76} -1.01279e8 q^{77} +(-4.54937e7 - 4.76729e8i) q^{78} -1.13260e8 q^{79} -1.77541e6i q^{80} -3.04735e8 q^{81} +3.59800e8 q^{82} -5.09735e8i q^{83} -3.53074e8i q^{84} -3.49552e7i q^{85} -4.54325e8i q^{86} +5.57817e8 q^{87} -3.50824e8 q^{88} +4.18119e8i q^{89} +2.73047e8 q^{90} +(3.28038e7 + 3.43752e8i) q^{91} -2.08032e9 q^{92} -4.93470e8i q^{93} +1.00249e9 q^{94} -2.03714e9 q^{95} +7.51259e8i q^{96} +1.22103e9i q^{97} -1.06604e9i q^{98} -1.07455e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 2562 q^{4} + 67304 q^{9} + 45562 q^{10} + 46298 q^{12} - 111488 q^{13} + 169350 q^{14} - 209470 q^{16} - 1189686 q^{17} + 3516760 q^{22} + 2210916 q^{23} - 10109316 q^{25} + 7627230 q^{26}+ \cdots + 1047837276 q^{95}+O(q^{100}) \) 10 * q - 2 * q^3 - 2562 * q^4 + 67304 * q^9 + 45562 * q^10 + 46298 * q^12 - 111488 * q^13 + 169350 * q^14 - 209470 * q^16 - 1189686 * q^17 + 3516760 * q^22 + 2210916 * q^23 - 10109316 * q^25 + 7627230 * q^26 - 7880006 * q^27 + 7039224 * q^29 - 7573410 * q^30 + 39493506 * q^35 + 29007196 * q^36 - 50219652 * q^38 + 14502332 * q^39 - 23263606 * q^40 + 400842 * q^42 - 92334370 * q^43 + 102213790 * q^48 - 100714448 * q^49 + 77969322 * q^51 - 113165052 * q^52 + 29507556 * q^53 + 138590608 * q^55 + 437436342 * q^56 - 238375816 * q^61 - 565735320 * q^62 + 272247742 * q^64 - 351372138 * q^65 - 495101088 * q^66 + 550420050 * q^68 + 505082484 * q^69 + 1257672774 * q^74 - 1443387976 * q^75 + 530898576 * q^77 - 1745232606 * q^78 - 441679756 * q^79 + 1486784810 * q^81 + 518795296 * q^82 + 4793242032 * q^87 - 3927690208 * q^88 - 2656725444 * q^90 - 777339186 * q^91 - 4121025444 * q^92 + 6226353478 * q^94 + 1047837276 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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