LMFDB - Embedded newform 35.10.e.b.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(11,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("35.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.e (of order $3$, degree $2$, 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:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	35.11
Dual form			35.10.e.b.16.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.6621 + 18.4672i) q^{2} +(-95.0320 + 164.600i) q^{3} +(28.6405 - 49.6068i) q^{4} +(-312.500 - 541.266i) q^{5} -4052.95 q^{6} +(-374.098 - 6341.42i) q^{7} +12139.4 q^{8} +(-8220.66 - 14238.6i) q^{9} +(6663.79 - 11542.0i) q^{10} +(39944.3 - 69185.6i) q^{11} +(5443.53 + 9428.46i) q^{12} -148270. q^{13} +(113120. - 74521.3i) q^{14} +118790. q^{15} +(114768. + 198783. i) q^{16} +(98403.5 - 170440. i) q^{17} +(175299. - 303626. i) q^{18} +(371548. + 643540. i) q^{19} -35800.6 q^{20} +(1.07935e6 + 541061. i) q^{21} +1.70356e6 q^{22} +(-629107. - 1.08964e6i) q^{23} +(-1.15363e6 + 1.99815e6i) q^{24} +(-195312. + 338291. i) q^{25} +(-1.58087e6 - 2.73814e6i) q^{26} -616127. q^{27} +(-325292. - 163064. i) q^{28} +4.19204e6 q^{29} +(1.26655e6 + 2.19372e6i) q^{30} +(3.39385e6 - 5.87831e6i) q^{31} +(660375. - 1.14380e6i) q^{32} +(7.59198e6 + 1.31497e7i) q^{33} +4.19674e6 q^{34} +(-3.31549e6 + 2.18418e6i) q^{35} -941775. q^{36} +(-4.55871e6 - 7.89591e6i) q^{37} +(-7.92294e6 + 1.37229e7i) q^{38} +(1.40904e7 - 2.44053e7i) q^{39} +(-3.79357e6 - 6.57066e6i) q^{40} +1.68499e7 q^{41} +(1.51620e6 + 2.57015e7i) q^{42} +1.19411e7 q^{43} +(-2.28805e6 - 3.96302e6i) q^{44} +(-5.13791e6 + 8.89913e6i) q^{45} +(1.34152e7 - 2.32357e7i) q^{46} +(-2.74105e7 - 4.74763e7i) q^{47} -4.36263e7 q^{48} +(-4.00737e7 + 4.74463e6i) q^{49} -8.32974e6 q^{50} +(1.87030e7 + 3.23945e7i) q^{51} +(-4.24653e6 + 7.35520e6i) q^{52} +(-1.64212e7 + 2.84424e7i) q^{53} +(-6.56918e6 - 1.13782e7i) q^{54} -4.99304e7 q^{55} +(-4.54134e6 - 7.69813e7i) q^{56} -1.41236e8 q^{57} +(4.46959e7 + 7.74155e7i) q^{58} +(-3.63706e7 + 6.29957e7i) q^{59} +(3.40220e6 - 5.89279e6i) q^{60} +(-6.34963e7 - 1.09979e8i) q^{61} +1.44742e8 q^{62} +(-8.72177e7 + 5.74573e7i) q^{63} +1.45686e8 q^{64} +(4.63344e7 + 8.02535e7i) q^{65} +(-1.61892e8 + 2.80406e8i) q^{66} +(-4.48429e7 + 7.76702e7i) q^{67} +(-5.63665e6 - 9.76296e6i) q^{68} +2.39141e8 q^{69} +(-7.56858e7 - 3.79401e7i) q^{70} +1.94271e8 q^{71} +(-9.97941e7 - 1.72848e8i) q^{72} +(1.11122e8 - 1.92468e8i) q^{73} +(9.72105e7 - 1.68374e8i) q^{74} +(-3.71219e7 - 6.42970e7i) q^{75} +4.25653e7 q^{76} +(-4.53678e8 - 2.27422e8i) q^{77} +6.00931e8 q^{78} +(-1.13984e8 - 1.97427e8i) q^{79} +(7.17297e7 - 1.24239e8i) q^{80} +(2.20359e8 - 3.81673e8i) q^{81} +(1.79654e8 + 3.11170e8i) q^{82} -1.48052e7 q^{83} +(5.77535e7 - 3.80469e7i) q^{84} -1.23004e8 q^{85} +(1.27317e8 + 2.20520e8i) q^{86} +(-3.98378e8 + 6.90012e8i) q^{87} +(4.84901e8 - 8.39874e8i) q^{88} +(2.23785e8 + 3.87607e8i) q^{89} -2.19123e8 q^{90} +(5.54676e7 + 9.40243e8i) q^{91} -7.20717e7 q^{92} +(6.45048e8 + 1.11726e9i) q^{93} +(5.84505e8 - 1.01239e9i) q^{94} +(2.32217e8 - 4.02212e8i) q^{95} +(1.25513e8 + 2.17396e8i) q^{96} +6.78338e8 q^{97} +(-5.14889e8 - 6.89464e8i) q^{98} -1.31347e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} - 268 q^{3} - 3563 q^{4} - 8125 q^{5} + 6080 q^{6} - 8462 q^{7} - 9390 q^{8} - 82107 q^{9} + 625 q^{10} - 129087 q^{11} - 356068 q^{12} + 71778 q^{13} + 828653 q^{14} + 335000 q^{15} - 1379187 q^{16}+ \cdots + 10532284198 q^{99}+O(q^{100}) $ 26 * q + q^2 - 268 * q^3 - 3563 * q^4 - 8125 * q^5 + 6080 * q^6 - 8462 * q^7 - 9390 * q^8 - 82107 * q^9 + 625 * q^10 - 129087 * q^11 - 356068 * q^12 + 71778 * q^13 + 828653 * q^14 + 335000 * q^15 - 1379187 * q^16 - 251650 * q^17 - 391089 * q^18 + 22537 * q^19 + 4453750 * q^20 + 1067860 * q^21 - 1735386 * q^22 - 1640451 * q^23 - 3300104 * q^24 - 5078125 * q^25 + 215949 * q^26 + 9666692 * q^27 - 1349311 * q^28 + 350384 * q^29 - 1900000 * q^30 - 3363236 * q^31 - 11618029 * q^32 - 1855346 * q^33 + 60169436 * q^34 + 4080625 * q^35 + 5720266 * q^36 - 57134155 * q^37 - 28383363 * q^38 + 10216786 * q^39 + 2934375 * q^40 + 92086974 * q^41 - 67569966 * q^42 - 46945552 * q^43 - 171806579 * q^44 - 51316875 * q^45 + 53075341 * q^46 + 1336787 * q^47 + 609090752 * q^48 - 122434224 * q^49 - 781250 * q^50 - 234254040 * q^51 - 80069087 * q^52 - 122467755 * q^53 + 99983754 * q^54 + 161358750 * q^55 - 344492982 * q^56 + 65304060 * q^57 - 37365152 * q^58 + 136056496 * q^59 - 222542500 * q^60 + 50448822 * q^61 - 218462072 * q^62 - 294191035 * q^63 + 2218017678 * q^64 - 22430625 * q^65 + 500348610 * q^66 - 585418818 * q^67 - 480342846 * q^68 - 1042832072 * q^69 - 93881875 * q^70 + 994388160 * q^71 + 870751121 * q^72 + 346232592 * q^73 + 613439215 * q^74 - 104687500 * q^75 - 2872390426 * q^76 - 1532634653 * q^77 - 655224276 * q^78 - 136453862 * q^79 - 861991875 * q^80 + 344488883 * q^81 + 224863259 * q^82 - 1046084628 * q^83 + 557627890 * q^84 + 314562500 * q^85 + 2285275668 * q^86 - 2310323838 * q^87 + 1816859183 * q^88 + 843350780 * q^89 + 488861250 * q^90 + 164707640 * q^91 - 344655826 * q^92 - 198172924 * q^93 - 2777934057 * q^94 + 14085625 * q^95 + 1583073484 * q^96 + 1389946316 * q^97 + 4300632129 * q^98 + 10532284198 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	10.6621	+	18.4672i	0.471201	+	0.816145i	0.999457	−	0.0329404i	$-0.0104872\pi$
$2$	10.6621	+	18.4672i	0.471201	+	0.816145i	−0.528256	+	0.849085i	$0.677154\pi$
$3$	−95.0320	+	164.600i	−0.677367	+	1.17323i	0.298404	+	0.954440i	$0.403546\pi$
$3$	−95.0320	+	164.600i	−0.677367	+	1.17323i	−0.975771	+	0.218795i	$0.929787\pi$
$4$	28.6405	−	49.6068i	0.0559385	−	0.0968882i
$5$	−312.500	−	541.266i	−0.223607	−	0.387298i
$5$	−312.500	−	541.266i	−0.223607	−	0.387298i
$6$	−4052.95			−1.27671
$7$	−374.098	−	6341.42i	−0.0588904	−	0.998264i
$7$	−374.098	−	6341.42i	−0.0588904	−	0.998264i
$8$	12139.4			1.04784
$9$	−8220.66	−	14238.6i	−0.417653	−	0.723396i
$10$	6663.79	−	11542.0i	0.210728	−	0.364991i
$11$	39944.3	−	69185.6i	0.822599	−	1.42478i	−0.0811421	−	0.996703i	$-0.525857\pi$
$11$	39944.3	−	69185.6i	0.822599	−	1.42478i	0.903741	−	0.428080i	$-0.140810\pi$
$12$	5443.53	+	9428.46i	0.0757818	+	0.131258i
$13$	−148270.			−1.43982			−0.719910	−	0.694067i	$-0.755817\pi$
$13$	−148270.			−1.43982			−0.719910	+	0.694067i	$0.755817\pi$
$14$	113120.	−	74521.3i	0.786979	−	0.518447i
$15$	118790.			0.605856
$16$	114768.	+	198783.i	0.437803	+	0.758298i
$17$	98403.5	−	170440.i	0.285753	−	0.494938i	−0.687039	−	0.726621i	$-0.741090\pi$
$17$	98403.5	−	170440.i	0.285753	−	0.494938i	0.972791	+	0.231683i	$0.0744230\pi$
$18$	175299.	−	303626.i	0.393597	−	0.681730i
$19$	371548.	+	643540.i	0.654069	+	1.13288i	0.982126	+	0.188223i	$0.0602728\pi$
$19$	371548.	+	643540.i	0.654069	+	1.13288i	−0.328057	+	0.944658i	$0.606394\pi$
$20$	−35800.6			−0.0500329
$21$	1.07935e6	+	541061.i	1.21109	+	0.607099i
$22$	1.70356e6			1.55044
$23$	−629107.	−	1.08964e6i	−0.468758	−	0.811913i	0.530604	−	0.847620i	$-0.321965\pi$
$23$	−629107.	−	1.08964e6i	−0.468758	−	0.811913i	−0.999362	+	0.0357067i	$0.988632\pi$
$24$	−1.15363e6	+	1.99815e6i	−0.709770	+	1.22936i
$25$	−195312.	+	338291.i	−0.100000	+	0.173205i
$26$	−1.58087e6	−	2.73814e6i	−0.678445	−	1.17510i
$27$	−616127.			−0.223117
$28$	−325292.	−	163064.i	−0.100014	−	0.0501356i
$29$	4.19204e6			1.10061			0.550307	−	0.834963i	$-0.314511\pi$
$29$	4.19204e6			1.10061			0.550307	+	0.834963i	$0.314511\pi$
$30$	1.26655e6	+	2.19372e6i	0.285480	+	0.494466i
$31$	3.39385e6	−	5.87831e6i	0.660031	−	1.14321i	−0.320576	−	0.947223i	$-0.603876\pi$
$31$	3.39385e6	−	5.87831e6i	0.660031	−	1.14321i	0.980607	−	0.195985i	$-0.0627903\pi$
$32$	660375.	−	1.14380e6i	0.111331	−	0.192831i
$33$	7.59198e6	+	1.31497e7i	1.11440	+	1.93020i
$34$	4.19674e6			0.538588
$35$	−3.31549e6	+	2.18418e6i	−0.373458	+	0.246027i
$36$	−941775.			−0.0934514
$37$	−4.55871e6	−	7.89591e6i	−0.399884	−	0.692619i	0.593827	−	0.804593i	$-0.297616\pi$
$37$	−4.55871e6	−	7.89591e6i	−0.399884	−	0.692619i	−0.993711	+	0.111973i	$0.964283\pi$
$38$	−7.92294e6	+	1.37229e7i	−0.616397	+	1.06763i
$39$	1.40904e7	−	2.44053e7i	0.975287	−	1.68925i
$40$	−3.79357e6	−	6.57066e6i	−0.234303	−	0.405825i
$41$	1.68499e7			0.931255			0.465628	−	0.884981i	$-0.345829\pi$
$41$	1.68499e7			0.931255			0.465628	+	0.884981i	$0.345829\pi$
$42$	1.51620e6	+	2.57015e7i	0.0751857	+	1.27449i
$43$	1.19411e7			0.532644			0.266322	−	0.963884i	$-0.414192\pi$
$43$	1.19411e7			0.532644			0.266322	+	0.963884i	$0.414192\pi$
$44$	−2.28805e6	−	3.96302e6i	−0.0920298	−	0.159400i
$45$	−5.13791e6	+	8.89913e6i	−0.186780	+	0.323512i
$46$	1.34152e7	−	2.32357e7i	0.441759	−	0.765149i
$47$	−2.74105e7	−	4.74763e7i	−0.819362	−	1.41918i	−0.906153	−	0.422951i	$-0.860994\pi$
$47$	−2.74105e7	−	4.74763e7i	−0.819362	−	1.41918i	0.0867904	−	0.996227i	$-0.472339\pi$
$48$	−4.36263e7			−1.18621
$49$	−4.00737e7	+	4.74463e6i	−0.993064	+	0.117576i
$50$	−8.32974e6			−0.188481
$51$	1.87030e7	+	3.23945e7i	0.387119	+	0.670510i
$52$	−4.24653e6	+	7.35520e6i	−0.0805413	+	0.139502i
$53$	−1.64212e7	+	2.84424e7i	−0.285867	+	0.495136i	−0.972819	−	0.231567i	$-0.925615\pi$
$53$	−1.64212e7	+	2.84424e7i	−0.285867	+	0.495136i	0.686952	+	0.726703i	$0.258948\pi$
$54$	−6.56918e6	−	1.13782e7i	−0.105133	−	0.182096i
$55$	−4.99304e7			−0.735755
$56$	−4.54134e6	−	7.69813e7i	−0.0617075	−	1.04602i
$57$	−1.41236e8			−1.77218
$58$	4.46959e7	+	7.74155e7i	0.518611	+	0.898260i
$59$	−3.63706e7	+	6.29957e7i	−0.390766	+	0.676826i	−0.992551	−	0.121832i	$-0.961123\pi$
$59$	−3.63706e7	+	6.29957e7i	−0.390766	+	0.676826i	0.601785	+	0.798658i	$0.294456\pi$
$60$	3.40220e6	−	5.89279e6i	0.0338906	−	0.0587003i
$61$	−6.34963e7	−	1.09979e8i	−0.587170	−	1.01701i	−0.994601	−	0.103773i	$-0.966908\pi$
$61$	−6.34963e7	−	1.09979e8i	−0.587170	−	1.01701i	0.407431	−	0.913236i	$-0.366425\pi$
$62$	1.44742e8			1.24403
$63$	−8.72177e7	+	5.74573e7i	−0.697545	+	0.459529i
$64$	1.45686e8			1.08544
$65$	4.63344e7	+	8.02535e7i	0.321954	+	0.557640i
$66$	−1.61892e8	+	2.80406e8i	−1.05022	+	1.81903i
$67$	−4.48429e7	+	7.76702e7i	−0.271867	+	0.470888i	−0.969340	−	0.245723i	$-0.920975\pi$
$67$	−4.48429e7	+	7.76702e7i	−0.271867	+	0.470888i	0.697473	+	0.716611i	$0.254308\pi$
$68$	−5.63665e6	−	9.76296e6i	−0.0319691	−	0.0553722i
$69$	2.39141e8			1.27009
$70$	−7.56858e7	−	3.79401e7i	−0.376767	−	0.188867i
$71$	1.94271e8			0.907289			0.453645	−	0.891183i	$-0.350124\pi$
$71$	1.94271e8			0.907289			0.453645	+	0.891183i	$0.350124\pi$
$72$	−9.97941e7	−	1.72848e8i	−0.437632	−	0.758000i
$73$	1.11122e8	−	1.92468e8i	0.457979	−	0.793243i	−0.540875	−	0.841103i	$-0.681907\pi$
$73$	1.11122e8	−	1.92468e8i	0.457979	−	0.793243i	0.998854	+	0.0478599i	$0.0152401\pi$
$74$	9.72105e7	−	1.68374e8i	0.376852	−	0.652726i
$75$	−3.71219e7	−	6.42970e7i	−0.135473	−	0.234647i
$76$	4.25653e7			0.146350
$77$	−4.53678e8	−	2.27422e8i	−1.47075	−	0.737265i
$78$	6.00931e8			1.83823
$79$	−1.13984e8	−	1.97427e8i	−0.329249	−	0.570275i	0.653114	−	0.757259i	$-0.273462\pi$
$79$	−1.13984e8	−	1.97427e8i	−0.329249	−	0.570275i	−0.982363	+	0.186984i	$0.940129\pi$
$80$	7.17297e7	−	1.24239e8i	0.195792	−	0.339121i
$81$	2.20359e8	−	3.81673e8i	0.568785	−	0.985165i
$82$	1.79654e8	+	3.11170e8i	0.438809	+	0.760039i
$83$	−1.48052e7			−0.0342423			−0.0171212	−	0.999853i	$-0.505450\pi$
$83$	−1.48052e7			−0.0342423			−0.0171212	+	0.999853i	$0.505450\pi$
$84$	5.77535e7	−	3.80469e7i	0.126567	−	0.0833801i
$85$	−1.23004e8			−0.255585
$86$	1.27317e8	+	2.20520e8i	0.250983	+	0.434715i
$87$	−3.98378e8	+	6.90012e8i	−0.745520	+	1.29128i
$88$	4.84901e8	−	8.39874e8i	0.861948	−	1.49294i
$89$	2.23785e8	+	3.87607e8i	0.378074	+	0.654843i	0.990782	−	0.135466i	$-0.0432533\pi$
$89$	2.23785e8	+	3.87607e8i	0.378074	+	0.654843i	−0.612708	+	0.790309i	$0.709920\pi$
$90$	−2.19123e8			−0.352044
$91$	5.54676e7	+	9.40243e8i	0.0847916	+	1.43732i
$92$	−7.20717e7			−0.104886
$93$	6.45048e8	+	1.11726e9i	0.894167	+	1.54874i
$94$	5.84505e8	−	1.01239e9i	0.772169	−	1.33744i
$95$	2.32217e8	−	4.02212e8i	0.292509	−	0.506640i
$96$	1.25513e8	+	2.17396e8i	0.150824	+	0.261234i
$97$	6.78338e8			0.777989			0.388994	−	0.921240i	$-0.372823\pi$
$97$	6.78338e8			0.777989			0.388994	+	0.921240i	$0.372823\pi$
$98$	−5.14889e8	−	6.89464e8i	−0.563892	−	0.755082i
$99$	−1.31347e9			−1.37424
$100$	1.11877e7	+	1.93776e7i	0.0111877	+	0.0193776i
$101$	−9.36500e8	+	1.62207e9i	−0.895492	+	1.55104i	−0.0622964	+	0.998058i	$0.519842\pi$
$101$	−9.36500e8	+	1.62207e9i	−0.895492	+	1.55104i	−0.833195	+	0.552979i	$0.813491\pi$
$102$	−3.98825e8	+	6.90785e8i	−0.364822	+	0.631891i
$103$	9.35746e8	+	1.62076e9i	0.819201	+	1.41890i	0.906272	+	0.422695i	$0.138916\pi$
$103$	9.35746e8	+	1.62076e9i	0.819201	+	1.41890i	−0.0870709	+	0.996202i	$0.527751\pi$
$104$	−1.79991e9			−1.50870
$105$	−4.44391e7	−	7.53298e8i	−0.0356791	−	0.604804i
$106$	−7.00337e8			−0.538804
$107$	−5.42118e8	−	9.38976e8i	−0.399822	−	0.692512i	0.593882	−	0.804553i	$-0.297595\pi$
$107$	−5.42118e8	−	9.38976e8i	−0.399822	−	0.692512i	−0.993704	+	0.112040i	$0.964261\pi$
$108$	−1.76462e7	+	3.05641e7i	−0.0124808	+	0.0216174i
$109$	5.67818e8	−	9.83490e8i	0.385292	−	0.667346i	−0.606517	−	0.795070i	$-0.707434\pi$
$109$	5.67818e8	−	9.83490e8i	0.385292	−	0.667346i	0.991810	+	0.127724i	$0.0407673\pi$
$110$	−5.32362e8	−	9.22077e8i	−0.346689	−	0.600482i
$111$	1.73289e9			1.08347
$112$	1.21763e9	−	8.02154e8i	0.731199	−	0.481700i
$113$	−1.05120e9			−0.606502			−0.303251	−	0.952911i	$-0.598072\pi$
$113$	−1.05120e9			−0.606502			−0.303251	+	0.952911i	$0.598072\pi$
$114$	−1.50587e9	−	2.60824e9i	−0.835054	−	1.44636i
$115$	−3.93192e8	+	6.81028e8i	−0.209635	+	0.363099i
$116$	1.20062e8	−	2.07954e8i	0.0615666	−	0.106637i
$117$	1.21888e9	+	2.11116e9i	0.601345	+	1.04156i
$118$	−1.55114e9			−0.736517
$119$	−1.11764e9	−	5.60257e8i	−0.510907	−	0.256110i
$120$	1.44204e9			0.634837
$121$	−2.01212e9	−	3.48510e9i	−0.853337	−	1.47802i
$122$	1.35400e9	−	2.34520e9i	0.553351	−	0.958432i
$123$	−1.60127e9	+	2.77349e9i	−0.630802	+	1.09258i
$124$	−1.94403e8	−	3.36715e8i	−0.0738422	−	0.127899i
$125$	2.44141e8			0.0894427
$126$	−1.99100e9	−	9.98056e8i	−0.703726	−	0.352767i
$127$	−1.82342e9			−0.621969			−0.310985	−	0.950415i	$-0.600659\pi$
$127$	−1.82342e9			−0.621969			−0.310985	+	0.950415i	$0.600659\pi$
$128$	1.21520e9	+	2.10479e9i	0.400132	+	0.693048i
$129$	−1.13479e9	+	1.96551e9i	−0.360796	+	0.624916i
$130$	−9.88041e8	+	1.71134e9i	−0.303410	+	0.525521i
$131$	1.32303e9	+	2.29156e9i	0.392509	+	0.679845i	0.992780	−	0.119951i	$-0.0382739\pi$
$131$	1.32303e9	+	2.29156e9i	0.392509	+	0.679845i	−0.600271	+	0.799797i	$0.704941\pi$
$132$	8.69752e8			0.249352
$133$	3.94196e9	−	2.59689e9i	1.09240	−	0.719650i
$134$	−1.91247e9			−0.512417
$135$	1.92540e8	+	3.33488e8i	0.0498905	+	0.0864129i
$136$	1.19456e9	−	2.06904e9i	0.299422	−	0.518614i
$137$	3.18838e8	−	5.52244e8i	0.0773265	−	0.133933i	−0.824769	−	0.565470i	$-0.808695\pi$
$137$	3.18838e8	−	5.52244e8i	0.0773265	−	0.133933i	0.902096	+	0.431536i	$0.142028\pi$
$138$	2.54974e9	+	4.41628e9i	0.598466	+	1.03657i
$139$	−2.75678e9			−0.626376			−0.313188	−	0.949691i	$-0.601397\pi$
$139$	−2.75678e9			−0.626376			−0.313188	+	0.949691i	$0.601397\pi$
$140$	1.33929e7	+	2.27027e8i	0.00294646	+	0.0499460i
$141$	1.04195e10			2.22004
$142$	2.07133e9	+	3.58765e9i	0.427516	+	0.740479i
$143$	−5.92255e9	+	1.02581e10i	−1.18439	+	2.05143i
$144$	1.88693e9	−	3.26826e9i	0.365700	−	0.633410i
$145$	−1.31001e9	−	2.26901e9i	−0.246105	−	0.426266i
$146$	4.73915e9			0.863202
$147$	3.02732e9	−	7.04703e9i	0.534724	−	1.24474i
$148$	−5.22254e8			−0.0894756
$149$	−3.93257e9	−	6.81141e9i	−0.653639	−	1.13214i	−0.982233	−	0.187665i	$-0.939908\pi$
$149$	−3.93257e9	−	6.81141e9i	−0.653639	−	1.13214i	0.328594	−	0.944471i	$-0.393425\pi$
$150$	7.91592e8	−	1.37108e9i	0.127671	−	0.221132i
$151$	−5.78394e9	+	1.00181e10i	−0.905373	+	1.56815i	−0.0849576	+	0.996385i	$0.527075\pi$
$151$	−5.78394e9	+	1.00181e10i	−0.905373	+	1.56815i	−0.820416	+	0.571768i	$0.806258\pi$
$152$	4.51038e9	+	7.81221e9i	0.685357	+	1.18707i
$153$	−3.23577e9			−0.477382
$154$	−6.37298e8	−	1.08030e10i	−0.0913060	−	1.54775i
$155$	−4.24231e9			−0.590350
$156$	−8.07112e8	−	1.39796e9i	−0.109112	−	0.188988i
$157$	7.78524e7	−	1.34844e8i	0.0102264	−	0.0177127i	−0.860867	−	0.508830i	$-0.830078\pi$
$157$	7.78524e7	−	1.34844e8i	0.0102264	−	0.0177127i	0.871093	+	0.491118i	$0.163411\pi$
$158$	2.43062e9	−	4.20996e9i	0.310285	−	0.537429i
$159$	−3.12108e9	−	5.40587e9i	−0.387274	−	0.670778i
$160$	−8.25469e8			−0.0995774
$161$	−6.67455e9	+	4.39707e9i	−0.782899	+	0.515759i
$162$	9.39793e9			1.07205
$163$	5.58079e9	+	9.66621e9i	0.619229	+	1.07254i	0.989627	+	0.143663i	$0.0458882\pi$
$163$	5.58079e9	+	9.66621e9i	0.619229	+	1.07254i	−0.370397	+	0.928873i	$0.620778\pi$
$164$	4.82588e8	−	8.35867e8i	0.0520930	−	0.0902277i
$165$	4.74499e9	−	8.21856e9i	0.498376	−	0.863213i
$166$	−1.57854e8	−	2.73411e8i	−0.0161350	−	0.0279467i
$167$	5.25167e9			0.522485			0.261242	−	0.965273i	$-0.415868\pi$
$167$	5.25167e9			0.522485			0.261242	+	0.965273i	$0.415868\pi$
$168$	1.31027e10	+	6.56818e9i	1.26902	+	0.636141i
$169$	1.13795e10			1.07308
$170$	−1.31148e9	−	2.27155e9i	−0.120432	−	0.208594i
$171$	6.10874e9	−	1.05806e10i	0.546348	−	0.946302i
$172$	3.42000e8	−	5.92361e8i	0.0297953	−	0.0516070i
$173$	−3.79654e9	−	6.57579e9i	−0.322240	−	0.558137i	0.658709	−	0.752397i	$-0.271103\pi$
$173$	−3.79654e9	−	6.57579e9i	−0.322240	−	0.558137i	−0.980950	+	0.194260i	$0.937769\pi$
$174$	−1.69902e10			−1.40516
$175$	2.21831e9	+	1.11201e9i	0.178794	+	0.0896263i
$176$	1.83372e10			1.44055
$177$	−6.91274e9	−	1.19732e10i	−0.529384	−	0.916919i
$178$	−4.77203e9	+	8.26539e9i	−0.356298	+	0.617126i
$179$	−6.35315e9	+	1.10040e10i	−0.462541	+	0.801145i	−0.999087	−	0.0427265i	$-0.986396\pi$
$179$	−6.35315e9	+	1.10040e10i	−0.462541	+	0.801145i	0.536546	+	0.843871i	$0.319729\pi$
$180$	2.94305e8	+	5.09751e8i	0.0208964	+	0.0361936i
$181$	−1.36557e10			−0.945718			−0.472859	−	0.881138i	$-0.656778\pi$
$181$	−1.36557e10			−0.945718			−0.472859	+	0.881138i	$0.656778\pi$
$182$	−1.67723e10	+	1.10493e10i	−1.13311	+	0.746470i
$183$	2.41367e10			1.59092
$184$	−7.63699e9	−	1.32277e10i	−0.491182	−	0.850752i
$185$	−2.84919e9	+	4.93495e9i	−0.178834	+	0.309749i
$186$	−1.37551e10	+	2.38245e10i	−0.842665	+	1.45954i
$187$	−7.86132e9	−	1.36162e10i	−0.470120	−	0.814271i
$188$	−3.14020e9			−0.183335
$189$	2.30492e8	+	3.90712e9i	0.0131395	+	0.222730i
$190$	9.90367e9			0.551322
$191$	−2.77900e9	−	4.81336e9i	−0.151091	−	0.261697i	0.780538	−	0.625108i	$-0.214945\pi$
$191$	−2.77900e9	−	4.81336e9i	−0.151091	−	0.261697i	−0.931629	+	0.363412i	$0.881612\pi$
$192$	−1.38448e10	+	2.39799e10i	−0.735244	+	1.27348i
$193$	6.15671e9	−	1.06637e10i	0.319404	−	0.553224i	−0.660960	−	0.750421i	$-0.729851\pi$
$193$	6.15671e9	−	1.06637e10i	0.319404	−	0.553224i	0.980364	+	0.197197i	$0.0631839\pi$
$194$	7.23249e9	+	1.25270e10i	0.366589	+	0.634951i
$195$	−1.76130e10			−0.872323
$196$	−9.12365e8	+	2.12382e9i	−0.0441587	+	0.102793i
$197$	6.37549e9			0.301589			0.150795	−	0.988565i	$-0.451817\pi$
$197$	6.37549e9			0.301589			0.150795	+	0.988565i	$0.451817\pi$
$198$	−1.40044e10	−	2.42563e10i	−0.647545	−	1.12158i
$199$	−2.14340e9	+	3.71248e9i	−0.0968869	+	0.167813i	−0.910395	−	0.413741i	$-0.864222\pi$
$199$	−2.14340e9	+	3.71248e9i	−0.0968869	+	0.167813i	0.813508	+	0.581554i	$0.197555\pi$
$200$	−2.37098e9	+	4.10666e9i	−0.104784	+	0.181491i
$201$	−8.52302e9	−	1.47623e10i	−0.368308	−	0.637929i
$202$	−3.99401e10			−1.68783
$203$	−1.56824e9	−	2.65835e10i	−0.0648156	−	1.09870i
$204$	2.14265e9			0.0866194
$205$	−5.26558e9	−	9.12025e9i	−0.208235	−	0.360674i
$206$	−1.99540e10	+	3.45613e10i	−0.772017	+	1.33717i
$207$	−1.03433e10	+	1.79152e10i	−0.391556	+	0.678196i
$208$	−1.70166e10	−	2.94736e10i	−0.630358	−	1.09181i
$209$	5.93649e10			2.15215
$210$	1.34375e10	−	8.85238e9i	0.476796	−	0.314104i
$211$	2.59322e10			0.900676			0.450338	−	0.892858i	$-0.351303\pi$
$211$	2.59322e10			0.900676			0.450338	+	0.892858i	$0.351303\pi$
$212$	9.40623e8	+	1.62921e9i	0.0319819	+	0.0553943i
$213$	−1.84620e10	+	3.19771e10i	−0.614568	+	1.06446i
$214$	1.15602e10	−	2.00229e10i	0.376794	−	0.652626i
$215$	−3.73160e9	−	6.46332e9i	−0.119103	−	0.206292i
$216$	−7.47942e9			−0.233790
$217$	−3.85465e10	−	1.93227e10i	−1.18009	−	0.591562i
$218$	2.42165e10			0.726201
$219$	2.11202e10	+	3.65813e10i	0.620440	+	1.07463i
$220$	−1.43003e9	+	2.47689e9i	−0.0411570	+	0.0712860i
$221$	−1.45903e10	+	2.52711e10i	−0.411433	+	0.712622i
$222$	1.84762e10	+	3.20018e10i	0.510534	+	0.884271i
$223$	1.98676e10			0.537990			0.268995	−	0.963142i	$-0.413308\pi$
$223$	1.98676e10			0.537990			0.268995	+	0.963142i	$0.413308\pi$
$224$	−7.50038e9	−	3.75982e9i	−0.199052	−	0.0997818i
$225$	6.42239e9			0.167061
$226$	−1.12080e10	−	1.94128e10i	−0.285784	−	0.494993i
$227$	5.66647e9	−	9.81461e9i	0.141643	−	0.245333i	−0.786472	−	0.617626i	$-0.788095\pi$
$227$	5.66647e9	−	9.81461e9i	0.141643	−	0.245333i	0.928116	+	0.372292i	$0.121428\pi$
$228$	−4.04506e9	+	7.00625e9i	−0.0991330	+	0.171703i
$229$	−1.38220e10	−	2.39404e10i	−0.332132	−	0.575270i	0.650797	−	0.759252i	$-0.274435\pi$
$229$	−1.38220e10	−	2.39404e10i	−0.332132	−	0.575270i	−0.982930	+	0.183981i	$0.941101\pi$
$230$	−1.67689e10			−0.395121
$231$	8.05476e10	−	5.30632e10i	1.86122	−	1.22614i
$232$	5.08890e10			1.15326
$233$	1.78507e10	+	3.09182e10i	0.396783	+	0.687247i	0.993327	−	0.115333i	$-0.0367934\pi$
$233$	1.78507e10	+	3.09182e10i	0.396783	+	0.687247i	−0.596544	+	0.802580i	$0.703460\pi$
$234$	−2.59915e10	+	4.50186e10i	−0.566709	+	0.981569i
$235$	−1.71315e10	+	2.96727e10i	−0.366430	+	0.634675i
$236$	2.08334e9	+	3.60846e9i	0.0437177	+	0.0757212i
$237$	4.33287e10			0.892089
$238$	−1.56999e9	−	2.66133e10i	−0.0317177	−	0.537654i
$239$	6.44509e10			1.27773			0.638864	−	0.769319i	$-0.279405\pi$
$239$	6.44509e10			1.27773			0.638864	+	0.769319i	$0.279405\pi$
$240$	1.36332e10	+	2.36135e10i	0.265246	+	0.459419i
$241$	2.89890e10	−	5.02105e10i	0.553550	−	0.958777i	−0.444464	−	0.895796i	$-0.646606\pi$
$241$	2.89890e10	−	5.02105e10i	0.553550	−	0.958777i	0.998015	−	0.0629807i	$-0.0200607\pi$
$242$	4.29068e10	−	7.43168e10i	0.804187	−	1.39289i
$243$	3.58187e10	+	6.20398e10i	0.658994	+	1.14141i
$244$	−7.27426e9			−0.131382
$245$	1.50911e10	+	2.02078e10i	0.267593	+	0.358321i
$246$	−6.82916e10			−1.18894
$247$	−5.50894e10	−	9.54176e10i	−0.941742	−	1.63114i
$248$	4.11993e10	−	7.13594e10i	0.691604	−	1.19789i
$249$	1.40697e9	−	2.43694e9i	0.0231946	−	0.0401743i
$250$	2.60304e9	+	4.50861e9i	0.0421455	+	0.0729982i
$251$	1.40076e10			0.222757			0.111378	−	0.993778i	$-0.464473\pi$
$251$	1.40076e10			0.222757			0.111378	+	0.993778i	$0.464473\pi$
$252$	3.52316e8	+	5.97219e9i	0.00550339	+	0.0932892i
$253$	−1.00517e11			−1.54240
$254$	−1.94414e10	−	3.36735e10i	−0.293073	−	0.507617i
$255$	1.16894e10	−	2.02466e10i	0.173125	−	0.299861i
$256$	1.13825e10	−	1.97150e10i	0.165637	−	0.286891i
$257$	3.47263e10	+	6.01477e10i	0.496545	+	0.860042i	0.999992	−	0.00398442i	$-0.00126828\pi$
$257$	3.47263e10	+	6.01477e10i	0.496545	+	0.860042i	−0.503447	+	0.864026i	$0.667935\pi$
$258$	−4.83968e10			−0.680030
$259$	−4.83659e10	+	3.18625e10i	−0.667868	+	0.439979i
$260$	5.30816e9			0.0720383
$261$	−3.44614e10	−	5.96889e10i	−0.459674	−	0.796179i
$262$	−2.82125e10	+	4.88655e10i	−0.369901	+	0.640688i
$263$	−5.61545e10	+	9.72624e10i	−0.723742	+	1.25356i	0.235748	+	0.971814i	$0.424246\pi$
$263$	−5.61545e10	+	9.72624e10i	−0.723742	+	1.25356i	−0.959490	+	0.281743i	$0.909087\pi$
$264$	9.21623e10	+	1.59630e11i	1.16771	+	2.02254i
$265$	2.05265e10			0.255687
$266$	8.99869e10	+	4.51090e10i	1.10208	+	0.552454i
$267$	−8.50670e10			−1.02438
$268$	2.56865e9	+	4.44903e9i	0.0304157	+	0.0526815i
$269$	−2.35857e9	+	4.08516e9i	−0.0274640	+	0.0475690i	−0.879431	−	0.476027i	$-0.842076\pi$
$269$	−2.35857e9	+	4.08516e9i	−0.0274640	+	0.0475690i	0.851967	+	0.523596i	$0.175410\pi$
$270$	−4.10574e9	+	7.11135e9i	−0.0470170	+	0.0814358i
$271$	−3.06570e10	−	5.30994e10i	−0.345277	−	0.598037i	0.640127	−	0.768269i	$-0.278882\pi$
$271$	−3.06570e10	−	5.30994e10i	−0.345277	−	0.598037i	−0.985404	+	0.170232i	$0.945548\pi$
$272$	4.51741e10			0.500414
$273$	−1.60035e11	−	8.02232e10i	−1.74375	−	0.874114i
$274$	1.35979e10			0.145745
$275$	1.56033e10	+	2.70256e10i	0.164520	+	0.284957i
$276$	6.84912e9	−	1.18630e10i	0.0710467	−	0.123056i
$277$	5.34610e10	−	9.25972e10i	0.545605	−	0.945015i	−0.452964	−	0.891529i	$-0.649633\pi$
$277$	5.34610e10	−	9.25972e10i	0.545605	−	0.945015i	0.998569	−	0.0534865i	$-0.0170334\pi$
$278$	−2.93929e10	−	5.09101e10i	−0.295149	−	0.511213i
$279$	−1.11599e11			−1.10266
$280$	−4.02482e10	+	2.65147e10i	−0.391323	+	0.257796i
$281$	9.68968e10			0.927110			0.463555	−	0.886068i	$-0.346574\pi$
$281$	9.68968e10			0.927110			0.463555	+	0.886068i	$0.346574\pi$
$282$	1.11093e11	+	1.92419e11i	1.04608	+	1.81187i
$283$	−1.47162e9	+	2.54892e9i	−0.0136382	+	0.0236220i	−0.872764	−	0.488142i	$-0.837675\pi$
$283$	−1.47162e9	+	2.54892e9i	−0.0136382	+	0.0236220i	0.859126	+	0.511765i	$0.171008\pi$
$284$	5.56402e9	−	9.63717e9i	0.0507524	−	0.0879057i
$285$	4.41362e10	+	7.64461e10i	0.396271	+	0.686362i
$286$	−2.52586e11			−2.23235
$287$	−6.30350e9	−	1.06852e11i	−0.0548420	−	0.929639i
$288$	−2.17149e10			−0.185991
$289$	3.99274e10	+	6.91563e10i	0.336691	+	0.583165i
$290$	2.79349e10	−	4.83847e10i	0.231930	−	0.401714i
$291$	−6.44638e10	+	1.11655e11i	−0.526984	+	0.912763i
$292$	−6.36515e9	−	1.10248e10i	−0.0512373	−	0.0887456i
$293$	5.41297e10			0.429073			0.214536	−	0.976716i	$-0.431176\pi$
$293$	5.41297e10			0.429073			0.214536	+	0.976716i	$0.431176\pi$
$294$	1.62417e11	−	1.92298e10i	1.26785	−	0.150110i
$295$	4.54632e10			0.349511
$296$	−5.53401e10	−	9.58519e10i	−0.419013	−	0.725751i
$297$	−2.46108e10	+	4.26271e10i	−0.183536	+	0.317893i
$298$	8.38586e10	−	1.45247e11i	0.615991	−	1.06693i
$299$	9.32776e10	+	1.61562e11i	0.674928	+	1.16901i
$300$	−4.25275e9			−0.0303127
$301$	−4.46715e9	−	7.57237e10i	−0.0313676	−	0.531720i
$302$	−2.46675e11			−1.70645
$303$	−1.77995e11	−	3.08296e11i	−1.21315	−	2.10124i
$304$	−8.52833e10	+	1.47715e11i	−0.572707	+	0.991958i
$305$	−3.96852e10	+	6.87368e10i	−0.262591	+	0.454820i
$306$	−3.45000e10	−	5.97557e10i	−0.224943	−	0.389613i
$307$	1.11130e11			0.714014			0.357007	−	0.934102i	$-0.383797\pi$
$307$	1.11130e11			0.714014			0.357007	+	0.934102i	$0.383797\pi$
$308$	−2.42752e10	+	1.59921e10i	−0.153704	+	0.101257i
$309$	−3.55703e11			−2.21960
$310$	−4.52318e10	−	7.83437e10i	−0.278174	−	0.481811i
$311$	−1.94090e10	+	3.36174e10i	−0.117647	+	0.203771i	−0.918835	−	0.394642i	$-0.870869\pi$
$311$	−1.94090e10	+	3.36174e10i	−0.117647	+	0.203771i	0.801188	+	0.598413i	$0.204202\pi$
$312$	1.71049e11	−	2.96266e11i	1.02194	−	1.77005i
$313$	−5.20934e10	−	9.02284e10i	−0.306784	−	0.531366i	0.670873	−	0.741572i	$-0.265920\pi$
$313$	−5.20934e10	−	9.02284e10i	−0.306784	−	0.531366i	−0.977657	+	0.210207i	$0.932586\pi$
$314$	3.32027e9			0.0192748
$315$	5.83552e10	+	2.92525e10i	0.333951	+	0.167404i
$316$	−1.30583e10			−0.0736706
$317$	1.40486e11	+	2.43329e11i	0.781388	+	1.35340i	0.931133	+	0.364680i	$0.118821\pi$
$317$	1.40486e11	+	2.43329e11i	0.781388	+	1.35340i	−0.149745	+	0.988725i	$0.547845\pi$
$318$	6.65544e10	−	1.15276e11i	0.364968	−	0.632143i
$319$	1.67448e11	−	2.90029e11i	0.905363	−	1.56814i
$320$	−4.55268e10	−	7.88547e10i	−0.242713	−	0.420391i
$321$	2.06074e11			1.08331
$322$	−1.52366e11	−	7.63787e10i	−0.789837	−	0.395932i
$323$	1.46246e11			0.747608
$324$	−1.26224e10	−	2.18626e10i	−0.0636339	−	0.110217i
$325$	2.89590e10	−	5.01584e10i	0.143982	−	0.249384i
$326$	−1.19006e11	+	2.06124e11i	−0.583563	+	1.01076i
$327$	1.07922e11	+	1.86926e11i	0.521969	+	0.904076i
$328$	2.04548e11			0.975803
$329$	−2.90813e11	+	1.91582e11i	−1.36846	+	0.901516i
$330$	2.02366e11			0.939342
$331$	1.95213e11	+	3.38119e11i	0.893888	+	1.54826i	0.835175	+	0.549985i	$0.185367\pi$
$331$	1.95213e11	+	3.38119e11i	0.893888	+	1.54826i	0.0587137	+	0.998275i	$0.481300\pi$
$332$	−4.24028e8	+	7.34439e8i	−0.00191546	+	0.00331768i
$333$	−7.49512e10	+	1.29819e11i	−0.334025	+	0.578549i
$334$	5.59937e10	+	9.69840e10i	0.246196	+	0.426423i
$335$	5.60536e10			0.243166
$336$	1.63205e10	+	2.76653e11i	0.0698567	+	1.18416i
$337$	−1.89901e11			−0.802034			−0.401017	−	0.916071i	$-0.631343\pi$
$337$	−1.89901e11			−0.802034			−0.401017	+	0.916071i	$0.631343\pi$
$338$	1.21329e11	+	2.10148e11i	0.505638	+	0.875790i
$339$	9.98975e10	−	1.73028e11i	0.410824	−	0.711569i
$340$	−3.52291e9	+	6.10185e9i	−0.0142970	+	0.0247632i
$341$	−2.71130e11	−	4.69610e11i	−1.08588	−	1.88080i
$342$	2.60527e11			1.02976
$343$	4.50792e10	+	2.52349e11i	0.175854	+	0.984416i
$344$	1.44958e11			0.558124
$345$	−7.47316e10	−	1.29439e11i	−0.284000	−	0.491902i
$346$	8.09579e10	−	1.40223e11i	0.303680	−	0.525990i
$347$	−1.90977e11	+	3.30782e11i	−0.707129	+	1.22478i	0.258789	+	0.965934i	$0.416677\pi$
$347$	−1.90977e11	+	3.30782e11i	−0.707129	+	1.22478i	−0.965918	+	0.258849i	$0.916657\pi$
$348$	2.28195e10	+	3.95245e10i	0.0834064	+	0.144464i
$349$	2.33327e10			0.0841881			0.0420940	−	0.999114i	$-0.486597\pi$
$349$	2.33327e10			0.0841881			0.0420940	+	0.999114i	$0.486597\pi$
$350$	3.11614e9	+	5.28224e10i	0.0110997	+	0.188153i
$351$	9.13531e10			0.321249
$352$	−5.27565e10	−	9.13769e10i	−0.183161	−	0.317245i
$353$	−9.21584e10	+	1.59623e11i	−0.315899	+	0.547154i	−0.979628	−	0.200820i	$-0.935639\pi$
$353$	−9.21584e10	+	1.59623e11i	−0.315899	+	0.547154i	0.663729	+	0.747973i	$0.268973\pi$
$354$	1.47408e11	−	2.55319e11i	0.498893	−	0.864107i
$355$	−6.07097e10	−	1.05152e11i	−0.202876	−	0.351392i
$356$	2.56373e10			0.0845954
$357$	1.98430e11	−	1.30722e11i	0.646549	−	0.425934i
$358$	−2.70951e11			−0.871800
$359$	5.66481e10	+	9.81175e10i	0.179995	+	0.311761i	0.941879	−	0.335953i	$-0.109058\pi$
$359$	5.66481e10	+	9.81175e10i	0.179995	+	0.311761i	−0.761884	+	0.647714i	$0.775725\pi$
$360$	−6.23713e10	+	1.08030e11i	−0.195715	+	0.338988i
$361$	−1.14752e11	+	1.98756e11i	−0.355613	+	0.615939i
$362$	−1.45598e11	−	2.52184e11i	−0.445623	−	0.771842i
$363$	7.64865e11			2.31209
$364$	4.82310e10	+	2.41775e10i	0.144003	+	0.0721862i
$365$	−1.38902e11			−0.409629
$366$	2.57347e11	+	4.45739e11i	0.749644	+	1.29842i
$367$	−1.12129e10	+	1.94213e10i	−0.0322642	+	0.0558832i	−0.881707	−	0.471798i	$-0.843605\pi$
$367$	−1.12129e10	+	1.94213e10i	−0.0322642	+	0.0558832i	0.849442	+	0.527681i	$0.176938\pi$
$368$	1.44402e11	−	2.50112e11i	0.410448	−	0.710917i
$369$	−1.38517e11	−	2.39918e11i	−0.388941	−	0.673666i
$370$	−1.21513e11			−0.337066
$371$	1.86508e11	+	9.34937e10i	0.511112	+	0.256212i
$372$	7.38979e10			0.200073
$373$	5.19902e10	+	9.00497e10i	0.139069	+	0.240875i	0.927145	−	0.374704i	$-0.122256\pi$
$373$	5.19902e10	+	9.00497e10i	0.139069	+	0.240875i	−0.788075	+	0.615579i	$0.788922\pi$
$374$	1.67636e11	−	2.90354e11i	0.443042	−	0.767372i
$375$	−2.32012e10	+	4.01856e10i	−0.0605856	+	0.104937i
$376$	−3.32747e11	−	5.76335e11i	−0.858557	−	1.48706i
$377$	−6.21554e11			−1.58469
$378$	−6.96962e10	+	4.59145e10i	−0.175589	+	0.115674i
$379$	2.82403e11			0.703060			0.351530	−	0.936177i	$-0.385662\pi$
$379$	2.82403e11			0.703060			0.351530	+	0.936177i	$0.385662\pi$
$380$	−1.33016e10	−	2.30391e10i	−0.0327250	−	0.0566813i
$381$	1.73283e11	−	3.00135e11i	0.421302	−	0.729716i
$382$	5.92597e10	−	1.02641e11i	0.142388	−	0.246624i
$383$	−2.97665e11	−	5.15571e11i	−0.706860	−	1.22432i	−0.966016	−	0.258482i	$-0.916778\pi$
$383$	−2.97665e11	−	5.15571e11i	−0.706860	−	1.22432i	0.259156	−	0.965835i	$-0.416556\pi$
$384$	−4.61932e11			−1.08414
$385$	1.86789e10	+	3.16630e11i	0.0433289	+	0.734478i
$386$	2.62573e11			0.602015
$387$	−9.81639e10	−	1.70025e11i	−0.222460	−	0.385313i
$388$	1.94279e10	−	3.36502e10i	0.0435195	−	0.0753780i
$389$	2.67430e11	−	4.63203e11i	0.592157	−	1.02565i	−0.401784	−	0.915734i	$-0.631610\pi$
$389$	2.67430e11	−	4.63203e11i	0.592157	−	1.02565i	0.993941	−	0.109912i	$-0.0350569\pi$
$390$	−1.87791e11	−	3.25264e11i	−0.411040	−	0.711942i
$391$	−2.47625e11			−0.535796
$392$	−4.86472e11	+	5.75971e10i	−1.04057	+	0.123201i
$393$	−5.02921e11			−1.06349
$394$	6.79760e10	+	1.17738e11i	0.142109	+	0.246141i
$395$	−7.12403e10	+	1.23392e11i	−0.147244	+	0.255035i
$396$	−3.76186e10	+	6.51573e10i	−0.0768730	+	0.133148i
$397$	3.71004e11	+	6.42598e11i	0.749586	+	1.29832i	0.948021	+	0.318207i	$0.103081\pi$
$397$	3.71004e11	+	6.42598e11i	0.749586	+	1.29832i	−0.198435	+	0.980114i	$0.563586\pi$
$398$	−9.14125e10			−0.182613
$399$	5.28361e10	+	8.95636e11i	0.104364	+	1.76910i
$400$	−8.96621e10			−0.175121
$401$	−1.10299e11	−	1.91043e11i	−0.213021	−	0.368963i	0.739638	−	0.673005i	$-0.234997\pi$
$401$	−1.10299e11	−	1.91043e11i	−0.213021	−	0.368963i	−0.952658	+	0.304043i	$0.901664\pi$
$402$	1.81746e11	−	3.14794e11i	0.347095	−	0.601186i
$403$	−5.03205e11	+	8.71577e11i	−0.950326	+	1.64601i
$404$	5.36436e10	+	9.29135e10i	0.100185	+	0.173525i
$405$	−2.75449e11			−0.508737
$406$	4.74204e11	−	3.12397e11i	0.866160	−	0.570610i
$407$	−7.28378e11			−1.31578
$408$	2.27043e11	+	3.93251e11i	0.405637	+	0.702585i
$409$	3.55205e11	−	6.15233e11i	0.627660	−	1.08714i	−0.360360	−	0.932813i	$-0.617346\pi$
$409$	3.55205e11	−	6.15233e11i	0.627660	−	1.08714i	0.988020	−	0.154325i	$-0.0493204\pi$
$410$	1.12284e11	−	1.94481e11i	0.196241	−	0.339900i
$411$	6.05997e10	+	1.04962e11i	0.104757	+	0.181444i
$412$	1.07201e11			0.183299
$413$	4.13089e11	+	2.07075e11i	0.698664	+	0.350229i
$414$	−4.41126e11			−0.738008
$415$	4.62663e9	+	8.01355e9i	0.00765681	+	0.0132620i
$416$	−9.79138e10	+	1.69592e11i	−0.160296	+	0.277642i
$417$	2.61982e11	−	4.53766e11i	0.424286	−	0.734886i
$418$	6.32953e11	+	1.09631e12i	1.01409	+	1.75646i
$419$	−5.27046e11			−0.835382			−0.417691	−	0.908589i	$-0.637161\pi$
$419$	−5.27046e11			−0.835382			−0.417691	+	0.908589i	$0.637161\pi$
$420$	−3.86414e10	−	1.93703e10i	−0.0605943	−	0.0303749i
$421$	7.36474e11			1.14258			0.571292	−	0.820747i	$-0.306442\pi$
$421$	7.36474e11			1.14258			0.571292	+	0.820747i	$0.306442\pi$
$422$	2.76491e11	+	4.78897e11i	0.424400	+	0.735082i
$423$	−4.50664e11	+	7.80573e11i	−0.684418	+	1.18545i
$424$	−1.99344e11	+	3.45274e11i	−0.299542	+	0.518821i
$425$	3.84389e10	+	6.65781e10i	0.0571506	+	0.0989877i
$426$	−7.87372e11			−1.15834
$427$	−6.73669e11	+	4.43800e11i	−0.980665	+	0.646044i
$428$	−6.21061e10			−0.0894617
$429$	−1.12566e12	−	1.94970e12i	−1.60454	−	2.77914i
$430$	7.95732e10	−	1.37825e11i	0.112243	−	0.194410i
$431$	−3.50130e11	+	6.06443e11i	−0.488744	+	0.846530i	−0.999916	−	0.0129488i	$-0.995878\pi$
$431$	−3.50130e11	+	6.06443e11i	−0.488744	+	0.846530i	0.511172	+	0.859478i	$0.329212\pi$
$432$	−7.07113e10	−	1.22476e11i	−0.0976814	−	0.169189i
$433$	7.26185e11			0.992777			0.496388	−	0.868101i	$-0.334659\pi$
$433$	7.26185e11			0.992777			0.496388	+	0.868101i	$0.334659\pi$
$434$	−5.41476e10	−	9.17868e11i	−0.0732615	−	1.24187i
$435$	4.97973e11			0.666813
$436$	−3.25252e10	−	5.63353e10i	−0.0431053	−	0.0746606i
$437$	4.67486e11	−	8.09710e11i	0.613201	−	1.06209i
$438$	−4.50370e11	+	7.80065e11i	−0.584704	+	1.01274i
$439$	−1.64244e11	−	2.84478e11i	−0.211056	−	0.365560i	0.740989	−	0.671517i	$-0.234357\pi$
$439$	−1.64244e11	−	2.84478e11i	−0.211056	−	0.365560i	−0.952045	+	0.305957i	$0.901024\pi$
$440$	−6.06127e11			−0.770950
$441$	3.96989e11	+	5.31590e11i	0.499810	+	0.669272i
$442$	−6.22251e11			−0.775470
$443$	7.42652e11	+	1.28631e12i	0.916154	+	1.58682i	0.805203	+	0.592999i	$0.202056\pi$
$443$	7.42652e11	+	1.28631e12i	0.916154	+	1.58682i	0.110950	+	0.993826i	$0.464611\pi$
$444$	4.96309e10	−	8.59632e10i	0.0606078	−	0.104976i
$445$	1.39866e11	−	2.42255e11i	0.169080	−	0.292855i
$446$	2.11830e11	+	3.66901e11i	0.253502	+	0.439078i
$447$	1.49488e12			1.77102
$448$	−5.45008e10	−	9.23855e11i	−0.0639222	−	1.08356i
$449$	−6.21938e11			−0.722168			−0.361084	−	0.932533i	$-0.617593\pi$
$449$	−6.21938e11			−0.722168			−0.361084	+	0.932533i	$0.617593\pi$
$450$	6.84760e10	+	1.18604e11i	0.0787194	+	0.136346i
$451$	6.73056e11	−	1.16577e12i	0.766049	−	1.32684i
$452$	−3.01069e10	+	5.21466e10i	−0.0339268	+	0.0587629i
$453$	−1.09932e12	−	1.90408e12i	−1.22654	−	2.12443i
$454$	2.41665e11			0.266970
$455$	4.91588e11	−	3.23849e11i	0.537712	−	0.354234i
$456$	−1.71452e12			−1.85695
$457$	−4.79623e11	−	8.30731e11i	−0.514371	−	0.890917i	−0.999861	−	0.0166749i	$-0.994692\pi$
$457$	−4.79623e11	−	8.30731e11i	−0.514371	−	0.890917i	0.485490	−	0.874242i	$-0.338641\pi$
$458$	2.94742e11	−	5.10509e11i	0.313003	−	0.542136i
$459$	−6.06290e10	+	1.05013e11i	−0.0637564	+	0.110429i
$460$	2.25224e10	+	3.90099e10i	0.0234533	+	0.0406223i
$461$	1.83403e12			1.89127			0.945633	−	0.325236i	$-0.105444\pi$
$461$	1.83403e12			1.89127			0.945633	+	0.325236i	$0.105444\pi$
$462$	1.83874e12	+	9.21729e11i	1.87772	+	0.941270i
$463$	1.43862e12			1.45489			0.727446	−	0.686165i	$-0.240707\pi$
$463$	1.43862e12			1.45489			0.727446	+	0.686165i	$0.240707\pi$
$464$	4.81111e11	+	8.33308e11i	0.481852	+	0.834593i
$465$	4.03155e11	−	6.98285e11i	0.399884	−	0.692619i
$466$	−3.80650e11	+	6.59305e11i	−0.373929	+	0.647664i
$467$	2.17072e11	+	3.75980e11i	0.211192	+	0.365796i	0.952088	−	0.305824i	$-0.0989320\pi$
$467$	2.17072e11	+	3.75980e11i	0.211192	+	0.365796i	−0.740896	+	0.671620i	$0.765599\pi$
$468$	1.39637e11			0.134553
$469$	5.09315e11	+	2.55312e11i	0.486081	+	0.243665i
$470$	−7.30631e11			−0.690649
$471$	1.47969e10	+	2.56290e10i	0.0138541	+	0.0239960i
$472$	−4.41518e11	+	7.64732e11i	−0.409458	+	0.709203i
$473$	4.76980e11	−	8.26154e11i	0.438152	−	0.758902i
$474$	4.61974e11	+	8.00162e11i	0.420353	+	0.728074i
$475$	−2.90272e11			−0.261628
$476$	−5.98024e10	+	3.93967e10i	−0.0533934	+	0.0351745i
$477$	5.39973e11			0.477573
$478$	6.87180e11	+	1.19023e12i	0.602068	+	1.04281i
$479$	7.29674e10	−	1.26383e11i	0.0633314	−	0.109693i	−0.832621	−	0.553843i	$-0.813161\pi$
$479$	7.29674e10	−	1.26383e11i	0.0633314	−	0.109693i	0.895953	+	0.444150i	$0.146494\pi$
$480$	7.84459e10	−	1.35872e11i	0.0674505	−	0.116828i
$481$	6.75920e11	+	1.17073e12i	0.575761	+	0.997247i
$482$	1.23633e12			1.04333
$483$	−8.94622e10	−	1.51649e12i	−0.0747959	−	1.26788i
$484$	−2.30513e11			−0.190937
$485$	−2.11981e11	−	3.67161e11i	−0.173964	−	0.301314i
$486$	−7.63803e11	+	1.32295e12i	−0.621038	+	1.07567i
$487$	−4.20780e11	+	7.28812e11i	−0.338980	+	0.587131i	−0.984241	−	0.176831i	$-0.943415\pi$
$487$	−4.20780e11	+	7.28812e11i	−0.338980	+	0.587131i	0.645261	+	0.763962i	$0.276749\pi$
$488$	−7.70809e11	−	1.33508e12i	−0.615258	−	1.06566i
$489$	−2.12141e12			−1.67778
$490$	−2.12280e11	+	4.94149e11i	−0.166352	+	0.387236i
$491$	−9.35646e11			−0.726515			−0.363258	−	0.931689i	$-0.618336\pi$
$491$	−9.35646e11			−0.726515			−0.363258	+	0.931689i	$0.618336\pi$
$492$	9.17226e10	+	1.58868e11i	0.0705722	+	0.122235i
$493$	4.12512e11	−	7.14492e11i	0.314503	−	0.544736i
$494$	1.17473e12	−	2.03470e12i	0.887500	−	1.53720i
$495$	4.10461e11	+	7.10939e11i	0.307290	+	0.532242i
$496$	1.55801e12			1.15586
$497$	−7.26765e10	−	1.23196e12i	−0.0534306	−	0.905715i
$498$	6.00048e10			0.0437173
$499$	1.45278e11	+	2.51628e11i	0.104893	+	0.181680i	0.913694	−	0.406402i	$-0.133217\pi$
$499$	1.45278e11	+	2.51628e11i	0.104893	+	0.181680i	−0.808801	+	0.588082i	$0.799883\pi$
$500$	6.99231e9	−	1.21110e10i	0.00500329	−	0.00866595i
$501$	−4.99077e11	+	8.64427e11i	−0.353914	+	0.612997i
$502$	1.49350e11	+	2.58681e11i	0.104963	+	0.181802i
$503$	−1.11722e12			−0.778185			−0.389092	−	0.921199i	$-0.627211\pi$
$503$	−1.11722e12			−0.778185			−0.389092	+	0.921199i	$0.627211\pi$
$504$	−1.05877e12	+	6.97499e11i	−0.730912	+	0.481511i
$505$	1.17062e12			0.800952
$506$	−1.07172e12	−	1.85627e12i	−0.726781	−	1.25882i
$507$	−1.08142e12	+	1.87307e12i	−0.726870	+	1.25898i
$508$	−5.22235e10	+	9.04538e10i	−0.0347920	+	0.0602615i
$509$	7.38141e11	+	1.27850e12i	0.487427	+	0.844248i	0.999895	−	0.0144578i	$-0.00460223\pi$
$509$	7.38141e11	+	1.27850e12i	0.487427	+	0.844248i	−0.512469	+	0.858706i	$0.671269\pi$
$510$	4.98531e11			0.326307
$511$	−1.26209e12	−	6.32667e11i	−0.818837	−	0.410470i
$512$	1.72981e12			1.11246
$513$	−2.28921e11	−	3.96502e11i	−0.145934	−	0.252765i
$514$	−7.40508e11	+	1.28260e12i	−0.467946	+	0.810506i
$515$	5.84841e11	−	1.01297e12i	0.366358	−	0.634550i
$516$	6.50018e10	+	1.12586e11i	0.0403647	+	0.0699137i
$517$	−4.37957e12			−2.69603
$518$	−1.10409e12	−	5.53465e11i	−0.673787	−	0.337758i
$519$	1.44317e12			0.873101
$520$	5.62473e11	+	9.74231e11i	0.337354	+	0.584315i
$521$	2.74228e11	−	4.74977e11i	0.163058	−	0.282425i	−0.772906	−	0.634521i	$-0.781198\pi$
$521$	2.74228e11	−	4.74977e11i	0.163058	−	0.282425i	0.935964	+	0.352096i	$0.114531\pi$
$522$	7.34859e11	−	1.27281e12i	0.433198	−	0.750322i
$523$	7.45465e11	+	1.29118e12i	0.435682	+	0.754623i	0.997351	−	0.0727386i	$-0.0231739\pi$
$523$	7.45465e11	+	1.29118e12i	0.435682	+	0.754623i	−0.561669	+	0.827362i	$0.689841\pi$
$524$	1.51569e11			0.0878254
$525$	−3.93847e11	+	2.59459e11i	−0.226262	+	0.149057i
$526$	−2.39489e12			−1.36411
$527$	−6.67933e11	−	1.15689e12i	−0.377211	−	0.653349i
$528$	−1.74262e12	+	3.01831e12i	−0.975779	+	1.69010i
$529$	1.09026e11	−	1.88839e11i	0.0605314	−	0.104843i
$530$	2.18855e11	+	3.79068e11i	0.120480	+	0.208678i
$531$	1.19596e12			0.652817
$532$	−1.59236e10	−	2.69924e11i	−0.00861864	−	0.146096i
$533$	−2.49833e12			−1.34084
$534$	−9.06991e11	−	1.57095e12i	−0.482689	−	0.836041i
$535$	−3.38824e11	+	5.86860e11i	−0.178806	+	0.309701i
$536$	−5.44367e11	+	9.42872e11i	−0.284873	+	0.493414i
$537$	−1.20750e12	−	2.09146e12i	−0.626620	−	1.08534i
$538$	−1.00589e11			−0.0517642
$539$	−1.27246e12	+	2.96204e12i	−0.649372	+	1.51162i
$540$	2.20577e10			0.0111632
$541$	−1.04739e12	−	1.81413e12i	−0.525679	−	0.910503i	−0.999553	−	0.0299101i	$-0.990478\pi$
$541$	−1.04739e12	−	1.81413e12i	−0.525679	−	0.910503i	0.473873	−	0.880593i	$-0.342855\pi$
$542$	6.53733e11	−	1.13230e12i	0.325390	−	0.563592i
$543$	1.29773e12	−	2.24774e12i	0.640598	−	1.10955i
$544$	−1.29966e11	−	2.25108e11i	−0.0636262	−	0.110204i
$545$	−7.09773e11			−0.344616
$546$	−2.24807e11	−	3.81076e12i	−0.108254	−	1.83504i
$547$	3.14192e12			1.50056			0.750279	−	0.661121i	$-0.229919\pi$
$547$	3.14192e12			1.50056			0.750279	+	0.661121i	$0.229919\pi$
$548$	−1.82634e10	−	3.16331e10i	−0.00865105	−	0.0149841i
$549$	−1.04396e12	+	1.80820e12i	−0.490467	+	0.849513i
$550$	−3.32726e11	+	5.76298e11i	−0.155044	+	0.268544i
$551$	1.55755e12	+	2.69775e12i	0.719877	+	1.24686i
$552$	2.90303e12			1.33084
$553$	−1.20933e12	+	7.96681e11i	−0.549896	+	0.362261i
$554$	2.28002e12			1.02836
$555$	−5.41529e11	−	9.37956e11i	−0.242272	−	0.419627i
$556$	−7.89554e10	+	1.36755e11i	−0.0350385	+	0.0606884i
$557$	−1.40463e12	+	2.43290e12i	−0.618322	+	1.07097i	0.371469	+	0.928445i	$0.378854\pi$
$557$	−1.40463e12	+	2.43290e12i	−0.618322	+	1.07097i	−0.989792	+	0.142521i	$0.954479\pi$
$558$	−1.18987e12	−	2.06092e12i	−0.519573	−	0.899926i
$559$	−1.77051e12			−0.766912
$560$	−8.14689e11	−	4.08391e11i	−0.350063	−	0.175481i
$561$	2.98831e12			1.27377
$562$	1.03312e12	+	1.78942e12i	0.436855	+	0.756656i
$563$	6.99701e11	−	1.21192e12i	0.293511	−	0.508376i	−0.681126	−	0.732166i	$-0.738510\pi$
$563$	6.99701e11	−	1.21192e12i	0.293511	−	0.508376i	0.974637	+	0.223790i	$0.0718429\pi$
$564$	2.98419e11	−	5.16877e11i	0.124185	−	0.215095i
$565$	3.28500e11	+	5.68978e11i	0.135618	+	0.234897i
$566$	−6.27620e10			−0.0257053
$567$	−2.50279e12	−	1.25461e12i	−1.01695	−	0.509781i
$568$	2.35834e12			0.950690
$569$	1.24247e12	+	2.15202e12i	0.496914	+	0.860680i	0.999994	−	0.00355978i	$-0.00113312\pi$
$569$	1.24247e12	+	2.15202e12i	0.496914	+	0.860680i	−0.503080	+	0.864240i	$0.667800\pi$
$570$	−9.41166e11	+	1.63015e12i	−0.373447	+	0.646830i
$571$	1.62196e12	−	2.80931e12i	0.638523	−	1.10595i	−0.347234	−	0.937779i	$-0.612879\pi$
$571$	1.62196e12	−	2.80931e12i	0.638523	−	1.10595i	0.985757	−	0.168176i	$-0.0537877\pi$
$572$	3.39249e11	+	5.87597e11i	0.132506	+	0.229508i
$573$	1.05637e12			0.409376
$574$	1.90605e12	−	1.25567e12i	0.732878	−	0.482806i
$575$	4.91489e11			0.187503
$576$	−1.19763e12	−	2.07436e12i	−0.453339	−	0.785206i
$577$	−3.65715e11	+	6.33437e11i	−0.137357	+	0.237910i	−0.926495	−	0.376306i	$-0.877194\pi$
$577$	−3.65715e11	+	6.33437e11i	−0.137357	+	0.237910i	0.789138	+	0.614216i	$0.210528\pi$
$578$	−8.51418e11	+	1.47470e12i	−0.317298	+	0.549577i
$579$	1.17017e12	+	2.02679e12i	0.432708	+	0.749472i
$580$	−1.50078e11			−0.0550669
$581$	5.53860e9	+	9.38861e10i	0.00201654	+	0.0341829i
$582$	−2.74927e12			−0.993263
$583$	1.31187e12	+	2.27222e12i	0.470308	+	0.814597i
$584$	1.34895e12	−	2.33645e12i	0.479887	−	0.831189i
$585$	7.61798e11	−	1.31947e12i	0.268930	−	0.465800i
$586$	5.77134e11	+	9.99626e11i	0.202180	+	0.350186i
$587$	−1.33193e12			−0.463032			−0.231516	−	0.972831i	$-0.574369\pi$
$587$	−1.33193e12			−0.463032			−0.231516	+	0.972831i	$0.574369\pi$
$588$	−2.62877e11	−	3.52006e11i	−0.0906890	−	0.121437i
$589$	5.04390e12			1.72682
$590$	4.84732e11	+	8.39581e11i	0.164690	+	0.285252i
$591$	−6.05876e11	+	1.04941e12i	−0.204287	+	0.353835i
$592$	1.04638e12	−	1.81239e12i	0.350141	−	0.606462i
$593$	−2.70666e12	−	4.68807e12i	−0.898850	−	1.55685i	−0.828967	−	0.559298i	$-0.811071\pi$
$593$	−2.70666e12	−	4.68807e12i	−0.898850	−	1.55685i	−0.0698832	−	0.997555i	$-0.522263\pi$
$594$	−1.04961e12			−0.345929
$595$	4.60157e10	+	7.80023e11i	0.0150515	+	0.255141i
$596$	−4.50523e11			−0.146254
$597$	−4.07384e11	−	7.05609e11i	−0.131256	−	0.227342i
$598$	−1.98907e12	+	3.44516e12i	−0.636054	+	1.10168i
$599$	1.63721e11	−	2.83574e11i	0.0519619	−	0.0900006i	−0.838875	−	0.544325i	$-0.816786\pi$
$599$	1.63721e11	−	2.83574e11i	0.0519619	−	0.0900006i	0.890836	+	0.454324i	$0.150119\pi$
$600$	−4.50638e11	−	7.80528e11i	−0.141954	−	0.245871i
$601$	−7.56209e11			−0.236432			−0.118216	−	0.992988i	$-0.537718\pi$
$601$	−7.56209e11			−0.236432			−0.118216	+	0.992988i	$0.537718\pi$
$602$	1.35078e12	−	8.89868e11i	0.419180	−	0.276148i
$603$	1.47455e12			0.454185
$604$	3.31310e11	+	5.73845e11i	0.101290	+	0.175440i
$605$	−1.25758e12	+	2.17819e12i	−0.381624	+	0.660992i
$606$	3.79559e12	−	6.57415e12i	1.14328	−	1.98022i
$607$	−2.39876e12	−	4.15477e12i	−0.717195	−	1.24222i	−0.962107	−	0.272673i	$-0.912092\pi$
$607$	−2.39876e12	−	4.15477e12i	−0.717195	−	1.24222i	0.244912	−	0.969545i	$-0.421241\pi$
$608$	9.81444e11			0.291272
$609$	4.52469e12	+	2.26815e12i	1.33294	+	0.668182i
$610$	−1.69251e12			−0.494932
$611$	4.06415e12	+	7.03931e12i	1.17973	+	2.04336i
$612$	−9.26740e10	+	1.60516e11i	−0.0267040	+	0.0462527i
$613$	−2.22393e12	+	3.85196e12i	−0.636134	+	1.10182i	0.350140	+	0.936697i	$0.386134\pi$
$613$	−2.22393e12	+	3.85196e12i	−0.636134	+	1.10182i	−0.986274	+	0.165119i	$0.947199\pi$
$614$	1.18487e12	+	2.05226e12i	0.336444	+	0.582739i
$615$	2.00159e12			0.564206
$616$	−5.50740e12	−	2.76077e12i	−1.54111	−	0.772533i
$617$	−1.63327e12			−0.453707			−0.226854	−	0.973929i	$-0.572844\pi$
$617$	−1.63327e12			−0.453707			−0.226854	+	0.973929i	$0.572844\pi$
$618$	−3.79253e12	−	6.56886e12i	−1.04588	−	1.81151i
$619$	8.87723e11	−	1.53758e12i	0.243035	−	0.420949i	−0.718542	−	0.695483i	$-0.755190\pi$
$619$	8.87723e11	−	1.53758e12i	0.243035	−	0.420949i	0.961577	+	0.274534i	$0.0885236\pi$
$620$	−1.21502e11	+	2.10447e11i	−0.0330233	+	0.0571980i
$621$	3.87609e11	+	6.71359e11i	0.104588	+	0.181152i
$622$	−8.27761e11			−0.221742
$623$	2.37427e12	−	1.56412e12i	0.631441	−	0.415981i
$624$	6.46848e12			1.70794
$625$	−7.62939e10	−	1.32145e11i	−0.0200000	−	0.0346410i
$626$	1.11085e12	−	1.92404e12i	0.289114	−	0.500761i
$627$	−5.64157e12	+	9.77148e12i	−1.45779	+	2.52497i
$628$	−4.45946e9	−	7.72401e9i	−0.00114410	−	0.00198164i
$629$	−1.79437e12			−0.457072
$630$	8.19736e10	+	1.38955e12i	0.0207320	+	0.351433i
$631$	−5.81058e12			−1.45911			−0.729554	−	0.683923i	$-0.760272\pi$
$631$	−5.81058e12			−1.45911			−0.729554	+	0.683923i	$0.760272\pi$
$632$	−1.38371e12	−	2.39665e12i	−0.344998	−	0.597555i
$633$	−2.46439e12	+	4.26845e12i	−0.610088	+	1.05670i
$634$	−2.99575e12	+	5.18879e12i	−0.736383	+	1.27545i
$635$	5.69817e11	+	9.86953e11i	0.139077	+	0.240888i
$636$	−3.57557e11			−0.0866540
$637$	5.94173e12	−	7.03487e11i	1.42983	−	0.169289i
$638$	7.14139e12			1.70643
$639$	−1.59704e12	−	2.76615e12i	−0.378932	−	0.656329i
$640$	7.59500e11	−	1.31549e12i	0.178944	−	0.309941i
$641$	−9.07793e11	+	1.57234e12i	−0.212386	+	0.367863i	−0.952461	−	0.304661i	$-0.901457\pi$
$641$	−9.07793e11	+	1.57234e12i	−0.212386	+	0.367863i	0.740075	+	0.672525i	$0.234790\pi$
$642$	2.19718e12	+	3.80562e12i	0.510455	+	0.884134i
$643$	8.51767e12			1.96504			0.982521	−	0.186154i	$-0.0596023\pi$
$643$	8.51767e12			1.96504			0.982521	+	0.186154i	$0.0596023\pi$
$644$	2.69619e10	+	4.57037e11i	0.00617681	+	0.104704i
$645$	1.41849e12			0.322705
$646$	1.55929e12	+	2.70077e12i	0.352274	+	0.610157i
$647$	2.14450e12	−	3.71437e12i	0.481123	−	0.833329i	−0.518643	−	0.854991i	$-0.673562\pi$
$647$	2.14450e12	−	3.71437e12i	0.481123	−	0.833329i	0.999765	+	0.0216622i	$0.00689582\pi$
$648$	2.67503e12	−	4.63329e12i	0.595993	−	1.03229i
$649$	2.90560e12	+	5.03264e12i	0.642887	+	1.11351i
$650$	1.23505e12			0.271378
$651$	6.84368e12	−	4.50848e12i	1.49340	−	0.983821i
$652$	6.39346e11			0.138555
$653$	−3.98371e12	−	6.89999e12i	−0.857390	−	1.48504i	−0.874410	−	0.485188i	$-0.838751\pi$
$653$	−3.98371e12	−	6.89999e12i	−0.857390	−	1.48504i	0.0170197	−	0.999855i	$-0.494582\pi$
$654$	−2.30134e12	+	3.98604e12i	−0.491905	+	0.852004i
$655$	8.26895e11	−	1.43222e12i	0.175535	−	0.304036i
$656$	1.93382e12	+	3.34947e12i	0.407707	+	0.706169i
$657$	−3.65397e12			−0.765105
$658$	−6.63867e12	−	3.32786e12i	−1.38059	−	0.692067i
$659$	−5.80696e12			−1.19940			−0.599701	−	0.800224i	$-0.704714\pi$
$659$	−5.80696e12			−1.19940			−0.599701	+	0.800224i	$0.704714\pi$
$660$	−2.71797e11	−	4.70767e11i	−0.0557568	−	0.0965736i
$661$	−2.29121e11	+	3.96850e11i	−0.0466830	+	0.0808573i	−0.888423	−	0.459026i	$-0.848198\pi$
$661$	−2.29121e11	+	3.96850e11i	−0.0466830	+	0.0808573i	0.841740	+	0.539884i	$0.181532\pi$
$662$	−4.16275e12	+	7.21010e12i	−0.842403	+	1.45908i
$663$	−2.77309e12	−	4.80313e12i	−0.557382	−	0.965414i
$664$	−1.79727e11			−0.0358803
$665$	−2.63747e12	−	1.32212e12i	−0.522986	−	0.262165i
$666$	−3.19654e12			−0.629573
$667$	−2.63724e12	−	4.56784e12i	−0.515922	−	0.893603i
$668$	1.50411e11	−	2.60519e11i	0.0292270	−	0.0506226i
$669$	−1.88806e12	+	3.27022e12i	−0.364417	+	0.631188i
$670$	5.97648e11	+	1.03516e12i	0.114580	+	0.198458i
$671$	−1.01453e13			−1.93202
$672$	1.33164e12	−	8.77262e11i	0.251899	−	0.165946i
$673$	−1.20278e12			−0.226005			−0.113002	−	0.993595i	$-0.536047\pi$
$673$	−1.20278e12			−0.226005			−0.113002	+	0.993595i	$0.536047\pi$
$674$	−2.02474e12	−	3.50695e12i	−0.377920	−	0.654576i
$675$	1.20337e11	−	2.08430e11i	0.0223117	−	0.0386450i
$676$	3.25914e11	−	5.64500e11i	0.0600265	−	0.103969i
$677$	−4.53875e11	−	7.86134e11i	−0.0830400	−	0.143829i	0.821514	−	0.570188i	$-0.193130\pi$
$677$	−4.53875e11	−	7.86134e11i	−0.0830400	−	0.143829i	−0.904554	+	0.426358i	$0.859796\pi$
$678$	4.26046e12			0.774324
$679$	−2.53765e11	−	4.30163e12i	−0.0458161	−	0.776639i
$680$	−1.49320e12			−0.267811
$681$	1.07699e12	+	1.86540e12i	0.191889	+	0.332362i
$682$	5.78161e12	−	1.00140e13i	1.02334	−	1.77247i
$683$	−2.35063e12	+	4.07142e12i	−0.413325	+	0.715900i	−0.995251	−	0.0973416i	$-0.968966\pi$
$683$	−2.35063e12	+	4.07142e12i	−0.413325	+	0.715900i	0.581926	+	0.813242i	$0.302299\pi$
$684$	−3.49914e11	−	6.06070e11i	−0.0611237	−	0.105869i
$685$	−3.98548e11			−0.0691629
$686$	−4.17956e12	+	3.52306e12i	−0.720563	+	0.607381i
$687$	5.25413e12			0.899903
$688$	1.37045e12	+	2.37369e12i	0.233193	+	0.403903i
$689$	2.43477e12	−	4.21715e12i	0.411597	−	0.712907i
$690$	1.59359e12	−	2.76017e12i	0.267642	−	0.463570i
$691$	−1.44409e12	−	2.50123e12i	−0.240959	−	0.417352i	0.720029	−	0.693944i	$-0.244128\pi$
$691$	−1.44409e12	−	2.50123e12i	−0.240959	−	0.417352i	−0.960988	+	0.276591i	$0.910795\pi$
$692$	−4.34939e11			−0.0721025
$693$	4.91369e11	+	8.32930e12i	0.0809297	+	1.37186i
$694$	−8.14484e12			−1.33280
$695$	8.61493e11	+	1.49215e12i	0.140062	+	0.242594i
$696$	−4.83609e12	+	8.37635e12i	−0.781182	+	1.35305i
$697$	1.65808e12	−	2.87189e12i	0.266109	−	0.460914i
$698$	2.48775e11	+	4.30891e11i	0.0396695	+	0.0687096i
$699$	−6.78553e12			−1.07507
$700$	1.18697e11	−	7.81950e10i	0.0186852	−	0.0123094i
$701$	4.88547e11			0.0764145			0.0382072	−	0.999270i	$-0.487835\pi$
$701$	4.88547e11			0.0764145			0.0382072	+	0.999270i	$0.487835\pi$
$702$	9.74013e11	+	1.68704e12i	0.151373	+	0.262185i
$703$	3.38756e12	−	5.86742e12i	0.523103	−	0.906042i
$704$	5.81932e12	−	1.00794e13i	0.892885	−	1.54652i
$705$	−3.25609e12	−	5.63971e12i	−0.496415	−	0.859817i
$706$	−3.93040e12			−0.595409
$707$	1.06365e13	+	5.33193e12i	1.60108	+	0.802596i
$708$	−7.91937e11			−0.118452
$709$	−6.14501e12	−	1.06435e13i	−0.913302	−	1.58189i	−0.809368	−	0.587302i	$-0.800190\pi$
$709$	−6.14501e12	−	1.06435e13i	−0.913302	−	1.58189i	−0.103934	−	0.994584i	$-0.533143\pi$
$710$	1.29458e12	−	2.24228e12i	0.191191	−	0.331152i
$711$	−1.87406e12	+	3.24596e12i	−0.275023	+	0.476354i
$712$	2.71662e12	+	4.70533e12i	0.396159	+	0.686168i
$713$	−8.54036e12			−1.23758
$714$	4.52976e12	+	2.27070e12i	0.652278	+	0.326977i
$715$	7.40318e12			1.05935
$716$	3.63915e11	+	6.30319e11i	0.0517477	+	0.0896296i
$717$	−6.12490e12	+	1.06086e13i	−0.865492	+	1.49908i
$718$	−1.20797e12	+	2.09227e12i	−0.169628	+	0.293804i
$719$	−5.39121e12	−	9.33785e12i	−0.752326	−	1.30307i	−0.946693	−	0.322138i	$-0.895599\pi$
$719$	−5.39121e12	−	9.33785e12i	−0.752326	−	1.30307i	0.194367	−	0.980929i	$-0.437735\pi$
$720$	−2.35866e12			−0.327092
$721$	9.92786e12	−	6.54028e12i	1.36819	−	0.901339i
$722$	−4.89397e12			−0.670261
$723$	5.50977e12	+	9.54320e12i	0.749914	+	1.29889i
$724$	−3.91107e11	+	6.77417e11i	−0.0529020	+	0.0916289i
$725$	−8.18759e11	+	1.41813e12i	−0.110061	+	0.190632i
$726$	8.15504e12	+	1.41249e13i	1.08946	+	1.88700i
$727$	−1.23298e13			−1.63701			−0.818503	−	0.574502i	$-0.805196\pi$
$727$	−1.23298e13			−1.63701			−0.818503	+	0.574502i	$0.805196\pi$
$728$	6.73344e11	+	1.14140e13i	0.0888477	+	1.50608i
$729$	−4.94104e12			−0.647954
$730$	−1.48098e12	−	2.56514e12i	−0.193018	−	0.334317i
$731$	1.17505e12	−	2.03524e12i	0.152205	−	0.263626i
$732$	6.91288e11	−	1.19735e12i	0.0889936	−	0.154141i
$733$	−3.12663e10	−	5.41547e10i	−0.00400044	−	0.00692897i	0.864018	−	0.503460i	$-0.167940\pi$
$733$	−3.12663e10	−	5.41547e10i	−0.00400044	−	0.00692897i	−0.868019	+	0.496532i	$0.834607\pi$
$734$	−4.78211e11			−0.0608117
$735$	−4.76036e12	+	5.63615e11i	−0.601653	+	0.0712343i
$736$	−1.66178e12			−0.208749
$737$	3.58244e12	+	6.20497e12i	0.447276	+	0.774704i
$738$	2.95375e12	−	5.11605e12i	0.366539	−	0.634865i
$739$	−6.87645e12	+	1.19104e13i	−0.848133	+	1.46901i	0.0347387	+	0.999396i	$0.488940\pi$
$739$	−6.87645e12	+	1.19104e13i	−0.848133	+	1.46901i	−0.882872	+	0.469614i	$0.844393\pi$
$740$	1.63205e11	+	2.82679e11i	0.0200073	+	0.0346537i
$741$	2.09410e13			2.55162
$742$	2.61995e11	+	4.44113e12i	0.0317304	+	0.537869i
$743$	5.86908e12			0.706514			0.353257	−	0.935526i	$-0.385074\pi$
$743$	5.86908e12			0.706514			0.353257	+	0.935526i	$0.385074\pi$
$744$	7.83051e12	+	1.35628e13i	0.936940	+	1.62283i
$745$	−2.45786e12	+	4.25713e12i	−0.292316	+	0.506307i
$746$	−1.10865e12	+	1.92023e12i	−0.131059	+	0.227002i
$747$	1.21709e11	+	2.10805e11i	0.0143014	+	0.0247707i
$748$	−9.00609e11			−0.105191
$749$	−5.75164e12	+	3.78907e12i	−0.667765	+	0.439911i
$750$	−9.89490e11			−0.114192
$751$	−4.50641e12	−	7.80533e12i	−0.516953	−	0.895389i	−0.999806	−	0.0196877i	$-0.993733\pi$
$751$	−4.50641e12	−	7.80533e12i	−0.516953	−	0.895389i	0.482853	−	0.875701i	$-0.339601\pi$
$752$	6.29166e12	−	1.08975e13i	0.717439	−	1.24264i
$753$	−1.33117e12	+	2.30565e12i	−0.150888	+	0.261346i
$754$	−6.62706e12	−	1.14784e13i	−0.746706	−	1.29333i
$755$	7.22993e12			0.809790
$756$	2.00421e11	+	1.00468e11i	0.0223149	+	0.0111861i
$757$	1.10513e13			1.22316			0.611580	−	0.791183i	$-0.290534\pi$
$757$	1.10513e13			1.22316			0.611580	+	0.791183i	$0.290534\pi$
$758$	3.01100e12	+	5.21520e12i	0.331283	+	0.573798i
$759$	9.55233e12	−	1.65451e13i	1.04477	−	1.80960i
$760$	2.81899e12	−	4.88263e12i	0.306501	−	0.530875i
$761$	−1.29137e12	−	2.23673e12i	−0.139579	−	0.241759i	0.787758	−	0.615985i	$-0.211242\pi$
$761$	−1.29137e12	−	2.23673e12i	−0.139579	−	0.241759i	−0.927337	+	0.374226i	$0.877908\pi$
$762$	7.39022e12			0.794072
$763$	−6.44915e12	−	3.23286e12i	−0.688877	−	0.345323i
$764$	−3.18367e11			−0.0338071
$765$	1.01118e12	+	1.75141e12i	0.106746	+	0.184889i
$766$	6.34745e12	−	1.09941e13i	0.666147	−	1.15380i
$767$	5.39267e12	−	9.34037e12i	0.562632	−	0.974507i
$768$	2.16340e12	+	3.74711e12i	0.224394	+	0.388661i
$769$	1.38646e13			1.42968			0.714838	−	0.699290i	$-0.246500\pi$
$769$	1.38646e13			1.42968			0.714838	+	0.699290i	$0.246500\pi$
$770$	−5.64813e12	+	3.72088e12i	−0.579024	+	0.381450i
$771$	−1.32004e13			−1.34537
$772$	−3.52662e11	−	6.10829e11i	−0.0357339	−	0.0618930i
$773$	−1.80722e12	+	3.13020e12i	−0.182056	+	0.315330i	−0.942580	−	0.333979i	$-0.891608\pi$
$773$	−1.80722e12	+	3.13020e12i	−0.182056	+	0.315330i	0.760525	+	0.649309i	$0.224942\pi$
$774$	2.09326e12	−	3.62563e12i	0.209647	−	0.363120i
$775$	1.32572e12	+	2.29622e12i	0.132006	+	0.228641i
$776$	8.23464e12			0.815205
$777$	−6.48272e11	−	1.09890e13i	−0.0638062	−	1.08159i
$778$	1.14054e13			1.11610
$779$	6.26053e12	+	1.08435e13i	0.609105	+	1.05500i
$780$	−5.04445e11	+	8.73724e11i	−0.0487964	+	0.0845179i
$781$	7.76003e12	−	1.34408e13i	0.746335	−	1.29269i
$782$	−2.64020e12	−	4.57296e12i	−0.252468	−	0.437287i
$783$	−2.58283e12			−0.245566
$784$	−5.54231e12	−	7.42145e12i	−0.523925	−	0.701563i
$785$	−9.73155e10			−0.00914679
$786$	−5.36218e12	−	9.28757e12i	−0.501118	−	0.867962i
$787$	−2.11082e12	+	3.65605e12i	−0.196140	+	0.339724i	−0.947274	−	0.320426i	$-0.896174\pi$
$787$	−2.11082e12	+	3.65605e12i	−0.196140	+	0.339724i	0.751134	+	0.660150i	$0.229507\pi$
$788$	1.82597e11	−	3.16268e11i	0.0168704	−	0.0292205i
$789$	−1.06729e13	−	1.84861e13i	−0.980478	−	1.69824i
$790$	−3.03828e12			−0.277527
$791$	3.93252e11	+	6.66610e12i	0.0357171	+	0.605449i
$792$	−1.59448e13			−1.43998
$793$	9.41460e12	+	1.63066e13i	0.845420	+	1.46431i
$794$	−7.91135e12	+	1.37029e13i	−0.706412	+	1.22354i
$795$	−1.95068e12	+	3.37867e12i	−0.173194	+	0.299981i
$796$	1.22776e11	+	2.12655e11i	0.0108394	+	0.0187744i
$797$	2.23662e13			1.96349			0.981747	−	0.190193i	$-0.0609113\pi$
$797$	2.23662e13			1.96349			0.981747	+	0.190193i	$0.0609113\pi$
$798$	−1.59766e13	+	1.05251e13i	−1.39467	+	0.918781i
$799$	−1.07891e13			−0.936540
$800$	2.57959e11	+	4.46798e11i	0.0222662	+	0.0385661i
$801$	3.67932e12	−	6.37278e12i	0.315807	−	0.546994i
$802$	2.35203e12	−	4.07384e12i	0.200751	−	0.347711i
$803$	−8.87736e12	−	1.53760e13i	−0.753466	−	1.30504i
$804$	−9.76414e11			−0.0824104
$805$	4.46578e12	+	2.23862e12i	0.374814	+	0.187888i
$806$	−2.14608e13			−1.79118
$807$	−4.48279e11	−	7.76442e11i	−0.0372064	−	0.0644433i
$808$	−1.13686e13	+	1.96909e13i	−0.938328	+	1.62523i
$809$	2.54865e12	−	4.41440e12i	0.209191	−	0.362329i	−0.742269	−	0.670102i	$-0.766250\pi$
$809$	2.54865e12	−	4.41440e12i	0.209191	−	0.362329i	0.951460	+	0.307773i	$0.0995837\pi$
$810$	−2.93685e12	−	5.08678e12i	−0.239718	−	0.415203i
$811$	7.10602e12			0.576809			0.288405	−	0.957509i	$-0.406875\pi$
$811$	7.10602e12			0.576809			0.288405	+	0.957509i	$0.406875\pi$
$812$	−1.36364e12	−	6.83570e11i	−0.110077	−	0.0551799i
$813$	1.16536e13			0.935517
$814$	−7.76602e12	−	1.34511e13i	−0.619996	−	1.07386i
$815$	3.48799e12	−	6.04138e12i	0.276928	−	0.479653i
$816$	−4.29299e12	+	7.43567e12i	−0.338964	+	0.587103i
$817$	4.43670e12	+	7.68459e12i	0.348386	+	0.603422i
$818$	1.51489e13			1.18302
$819$	1.29318e13	−	8.51920e12i	1.00434	−	0.661639i
$820$	−6.03235e11			−0.0465934
$821$	7.19321e12	+	1.24590e13i	0.552559	+	0.957060i	0.998089	+	0.0617929i	$0.0196818\pi$
$821$	7.19321e12	+	1.24590e13i	0.552559	+	0.957060i	−0.445530	+	0.895267i	$0.646985\pi$
$822$	−1.29224e12	+	2.23822e12i	−0.0987231	+	0.170993i
$823$	5.52731e12	−	9.57358e12i	0.419966	−	0.727403i	−0.575969	−	0.817471i	$-0.695375\pi$
$823$	5.52731e12	−	9.57358e12i	0.419966	−	0.727403i	0.995936	+	0.0900685i	$0.0287086\pi$
$824$	1.13594e13	+	1.96751e13i	0.858388	+	1.48677i
$825$	−5.93123e12			−0.445761
$826$	5.80280e11	+	9.83646e12i	0.0433738	+	0.735239i
$827$	−6.53464e12			−0.485788			−0.242894	−	0.970053i	$-0.578097\pi$
$827$	−6.53464e12			−0.485788			−0.242894	+	0.970053i	$0.578097\pi$
$828$	5.92477e11	+	1.02620e12i	0.0438061	+	0.0758744i
$829$	−3.29351e12	+	5.70452e12i	−0.242194	+	0.419492i	−0.961339	−	0.275368i	$-0.911200\pi$
$829$	−3.29351e12	+	5.70452e12i	−0.242194	+	0.419492i	0.719145	+	0.694860i	$0.244534\pi$
$830$	−9.86588e10	+	1.70882e11i	−0.00721580	+	0.0124981i
$831$	1.01610e13	+	1.75994e13i	0.739150	+	1.28025i
$832$	−2.16008e13			−1.56284
$833$	−3.13472e12	+	7.29705e12i	−0.225578	+	0.525103i
$834$	1.11731e13			0.799697
$835$	−1.64115e12	−	2.84255e12i	−0.116831	−	0.202357i
$836$	1.70024e12	−	2.94490e12i	0.120388	−	0.208518i
$837$	−2.09104e12	+	3.62178e12i	−0.147264	+	0.255069i
$838$	−5.61940e12	−	9.73308e12i	−0.393633	−	0.681793i
$839$	4.76554e12			0.332035			0.166017	−	0.986123i	$-0.446909\pi$
$839$	4.76554e12			0.332035			0.166017	+	0.986123i	$0.446909\pi$
$840$	−5.39466e11	−	9.14460e12i	−0.0373858	−	0.633736i
$841$	3.06609e12			0.211350
$842$	7.85234e12	+	1.36007e13i	0.538387	+	0.932514i
$843$	−9.20830e12	+	1.59492e13i	−0.627994	+	1.08772i
$844$	7.42711e11	−	1.28641e12i	0.0503824	−	0.0872649i
$845$	−3.55609e12	−	6.15933e12i	−0.239948	−	0.415603i
$846$	−1.92201e13			−1.28999
$847$	−2.13478e13	+	1.40635e13i	−1.42520	+	0.938898i
$848$	−7.53849e12			−0.500614
$849$	−2.79702e11	−	4.84457e11i	−0.0184761	−	0.0320016i
$850$	−8.19676e11	+	1.41972e12i	−0.0538588	+	0.0932863i
$851$	−5.73583e12	+	9.93474e12i	−0.374898	+	0.649342i
$852$	1.05752e12	+	1.83168e12i	0.0687560	+	0.119089i
$853$	−1.95984e13			−1.26751			−0.633754	−	0.773535i	$-0.718487\pi$
$853$	−1.95984e13			−1.26751			−0.633754	+	0.773535i	$0.718487\pi$
$854$	−1.53785e13	−	7.70898e12i	−0.989356	−	0.495948i
$855$	−7.63592e12			−0.488668
$856$	−6.58100e12	−	1.13986e13i	−0.418948	−	0.725639i
$857$	1.31674e12	−	2.28066e12i	0.0833847	−	0.144427i	−0.821317	−	0.570472i	$-0.806760\pi$
$857$	1.31674e12	−	2.28066e12i	0.0833847	−	0.144427i	0.904702	+	0.426045i	$0.140094\pi$
$858$	2.40038e13	−	4.15758e13i	1.51212	−	2.61907i
$859$	−9.94322e12	−	1.72222e13i	−0.623100	−	1.07924i	−0.988905	−	0.148549i	$-0.952540\pi$
$859$	−9.94322e12	−	1.72222e13i	−0.623100	−	1.07924i	0.365805	−	0.930691i	$-0.380794\pi$
$860$	−4.27500e11			−0.0266497
$861$	1.81869e13	+	9.11681e12i	1.12783	+	0.565364i
$862$	−1.49324e13			−0.921188
$863$	1.08273e13	+	1.87535e13i	0.664467	+	1.15089i	0.979430	+	0.201786i	$0.0646746\pi$
$863$	1.08273e13	+	1.87535e13i	0.664467	+	1.15089i	−0.314963	+	0.949104i	$0.601992\pi$
$864$	−4.06875e11	+	7.04727e11i	−0.0248398	+	0.0430238i
$865$	−2.37284e12	+	4.10987e12i	−0.144110	+	0.249606i
$866$	7.74263e12	+	1.34106e13i	0.467798	+	0.810250i
$867$	−1.51775e13			−0.912253
$868$	−2.06253e12	+	1.35876e12i	−0.123328	+	0.0812461i
$869$	−1.82121e13			−1.08336
$870$	5.30942e12	+	9.19619e12i	0.314203	+	0.544216i
$871$	6.64886e12	−	1.15162e13i	0.391440	−	0.677994i
$872$	6.89299e12	−	1.19390e13i	0.403723	−	0.699269i
$873$	−5.57639e12	−	9.65858e12i	−0.324929	−	0.562794i
$874$	1.99375e13			1.15576
$875$	−9.13326e10	−	1.54820e12i	−0.00526732	−	0.0892875i
$876$	2.41957e12			0.138826
$877$	−1.41619e12	−	2.45292e12i	−0.0808395	−	0.140018i	0.822771	−	0.568373i	$-0.192427\pi$
$877$	−1.41619e12	−	2.45292e12i	−0.0808395	−	0.140018i	−0.903611	+	0.428354i	$0.859093\pi$
$878$	3.50236e12	−	6.06626e12i	0.198900	−	0.344505i
$879$	−5.14405e12	+	8.90976e12i	−0.290640	+	0.503403i
$880$	−5.73039e12	−	9.92532e12i	−0.322116	−	0.557921i
$881$	−2.62782e13			−1.46962			−0.734809	−	0.678274i	$-0.762728\pi$
$881$	−2.62782e13			−1.46962			−0.734809	+	0.678274i	$0.762728\pi$
$882$	−5.58427e12	+	1.29991e13i	−0.310712	+	0.723279i
$883$	1.46614e13			0.811620			0.405810	−	0.913957i	$-0.366989\pi$
$883$	1.46614e13			0.811620			0.405810	+	0.913957i	$0.366989\pi$
$884$	8.35746e11	+	1.44755e12i	0.0460298	+	0.0797260i
$885$	−4.32046e12	+	7.48326e12i	−0.236748	+	0.410059i
$886$	−1.58364e13	+	2.74295e13i	−0.863386	+	1.49543i
$887$	−1.04541e13	−	1.81070e13i	−0.567059	−	0.982176i	−0.996855	−	0.0792494i	$-0.974748\pi$
$887$	−1.04541e13	−	1.81070e13i	−0.567059	−	0.982176i	0.429795	−	0.902926i	$-0.358586\pi$
$888$	2.10363e13			1.13530
$889$	6.82137e11	+	1.15631e13i	0.0366280	+	0.620890i
$890$	5.96503e12			0.318682
$891$	−1.76042e13	−	3.04913e13i	−0.935764	−	1.62079i
$892$	5.69019e11	−	9.85569e11i	0.0300943	−	0.0521249i
$893$	2.03686e13	−	3.52794e13i	1.07184	−	1.85648i
$894$	1.59385e13	+	2.76063e13i	0.834505	+	1.44540i
$895$	7.94144e12			0.413709
$896$	1.28928e13	−	8.49350e12i	0.668282	−	0.440251i
$897$	−3.54574e13			−1.82870
$898$	−6.63114e12	−	1.14855e13i	−0.340287	−	0.589394i
$899$	1.42271e13	−	2.46421e13i	0.726439	−	1.25823i
$900$	1.83940e11	−	3.18594e11i	0.00934514	−	0.0161863i
$901$	3.23181e12	+	5.59766e12i	0.163375	+	0.282973i
$902$	2.87047e13			1.44385
$903$	1.28887e13	+	6.46088e12i	0.645079	+	0.323368i
$904$	−1.27610e13			−0.635514
$905$	4.26742e12	+	7.39138e12i	0.211469	+	0.366275i
$906$	2.34420e13	−	4.06028e13i	1.15590	−	2.00207i
$907$	−9.45744e12	+	1.63808e13i	−0.464025	+	0.803714i	−0.999157	−	0.0410542i	$-0.986928\pi$
$907$	−9.45744e12	+	1.63808e13i	−0.464025	+	0.803714i	0.535132	+	0.844768i	$0.320262\pi$
$908$	−3.24581e11	−	5.62191e11i	−0.0158466	−	0.0274472i
$909$	3.07946e13			1.49602
$910$	1.12219e13	+	5.62538e12i	0.542477	+	0.271935i
$911$	−7.67112e12			−0.369000			−0.184500	−	0.982833i	$-0.559067\pi$
$911$	−7.67112e12			−0.369000			−0.184500	+	0.982833i	$0.559067\pi$
$912$	−1.62093e13	−	2.80753e13i	−0.775866	−	1.34384i
$913$	−5.91384e11	+	1.02431e12i	−0.0281677	+	0.0487878i
$914$	1.02275e13	−	1.77146e13i	0.484745	−	0.839603i
$915$	−7.54273e12	−	1.30644e13i	−0.355741	−	0.616161i
$916$	−1.58348e12			−0.0743159
$917$	1.40368e13	−	9.24717e12i	0.655550	−	0.431864i
$918$	−2.58572e12			−0.120168
$919$	1.76242e13	+	3.05260e13i	0.815060	+	1.41172i	0.909285	+	0.416174i	$0.136629\pi$
$919$	1.76242e13	+	3.05260e13i	0.815060	+	1.41172i	−0.0942255	+	0.995551i	$0.530037\pi$
$920$	−4.77312e12	+	8.26729e12i	−0.219663	+	0.380468i
$921$	−1.05609e13	+	1.82919e13i	−0.483650	+	0.837706i
$922$	1.95546e13	+	3.38695e13i	0.891167	+	1.54355i
$923$	−2.88046e13			−1.30633
$924$	−3.25373e11	−	5.51547e12i	−0.0146844	−	0.248919i
$925$	3.56149e12			0.159954
$926$	1.53386e13	+	2.65673e13i	0.685547	+	1.18740i
$927$	1.53849e13	−	2.66474e13i	0.684283	−	1.18521i
$928$	2.76832e12	−	4.79487e12i	0.122532	−	0.212232i
$929$	1.74239e13	+	3.01790e13i	0.767492	+	1.32933i	0.938919	+	0.344138i	$0.111829\pi$
$929$	1.74239e13	+	3.01790e13i	0.767492	+	1.32933i	−0.171427	+	0.985197i	$0.554838\pi$
$930$	1.71939e13			0.753703
$931$	−1.79427e13	−	2.40262e13i	−0.782732	−	1.04812i
$932$	2.04501e12			0.0887816
$933$	−3.68895e12	−	6.38945e12i	−0.159381	−	0.276055i
$934$	−4.62888e12	+	8.01745e12i	−0.199028	+	0.344727i
$935$	−4.91333e12	+	8.51013e12i	−0.210244	+	0.364153i
$936$	1.47965e13	+	2.56282e13i	0.630111	+	1.09138i
$937$	2.95277e13			1.25142			0.625709	−	0.780057i	$-0.284810\pi$
$937$	2.95277e13			1.25142			0.625709	+	0.780057i	$0.284810\pi$
$938$	7.15453e11	+	1.21278e13i	0.0301765	+	0.511528i
$939$	1.98021e13			0.831222
$940$	9.81311e11	+	1.69968e12i	0.0409951	+	0.0710055i
$941$	1.31023e12	−	2.26939e12i	0.0544748	−	0.0943531i	−0.837502	−	0.546434i	$-0.815985\pi$
$941$	1.31023e12	−	2.26939e12i	0.0544748	−	0.0943531i	0.891977	+	0.452081i	$0.149318\pi$
$942$	−3.15532e11	+	5.46517e11i	−0.0130561	+	0.0226139i
$943$	−1.06004e13	−	1.83603e13i	−0.436534	−	0.756098i
$944$	−1.66967e13			−0.684314
$945$	2.04276e12	−	1.34573e12i	0.0833249	−	0.0548928i
$946$	2.03424e13			0.825832
$947$	6.91366e11	+	1.19748e12i	0.0279340	+	0.0483831i	0.879654	−	0.475613i	$-0.157774\pi$
$947$	6.91366e11	+	1.19748e12i	0.0279340	+	0.0483831i	−0.851720	+	0.523996i	$0.824441\pi$
$948$	1.24096e12	−	2.14940e12i	0.0499021	−	0.0864329i
$949$	−1.64760e13	+	2.85373e13i	−0.659407	+	1.14213i
$950$	−3.09490e12	−	5.36052e12i	−0.123279	−	0.213526i
$951$	−5.34027e13			−2.11715
$952$	−1.35676e13	−	6.80120e12i	−0.535347	−	0.268361i
$953$	1.17712e12			0.0462278			0.0231139	−	0.999733i	$-0.492642\pi$
$953$	1.17712e12			0.0462278			0.0231139	+	0.999733i	$0.492642\pi$
$954$	5.75723e12	+	9.97182e12i	0.225033	+	0.389768i
$955$	−1.73687e12	+	3.00835e12i	−0.0675698	+	0.117034i
$956$	1.84591e12	−	3.19720e12i	0.0714742	−	0.123797i
$957$	3.18259e13	+	5.51241e13i	1.22653	+	2.12441i
$958$	3.11193e12			0.119367
$959$	−3.62129e12	−	1.81530e12i	−0.138255	−	0.0693049i
$960$	1.73060e13			0.657622
$961$	−9.81656e12	−	1.70028e13i	−0.371282	−	0.643079i
$962$	−1.44134e13	+	2.49648e13i	−0.542599	+	0.939809i
$963$	−8.91314e12	+	1.54380e13i	−0.333974	+	0.578459i
$964$	−1.66052e12	−	2.87611e12i	−0.0619295	−	0.107265i
$965$	−7.69588e12			−0.285684
$966$	2.70516e13	−	1.78211e13i	0.999531	−	0.658472i
$967$	4.43188e13			1.62993			0.814965	−	0.579510i	$-0.196756\pi$
$967$	4.43188e13			1.62993			0.814965	+	0.579510i	$0.196756\pi$
$968$	−2.44260e13	−	4.23071e13i	−0.894157	−	1.54873i
$969$	−1.38981e13	+	2.40722e13i	−0.506405	+	0.877120i
$970$	4.52030e12	−	7.82940e12i	0.163944	−	0.283959i
$971$	−6.31337e12	−	1.09351e13i	−0.227916	−	0.394762i	0.729274	−	0.684221i	$-0.239858\pi$
$971$	−6.31337e12	−	1.09351e13i	−0.227916	−	0.394762i	−0.957190	+	0.289459i	$0.906524\pi$
$972$	4.10346e12			0.147452
$973$	1.03131e12	+	1.74819e13i	0.0368875	+	0.625289i
$974$	−1.79455e13			−0.638912
$975$	5.50406e12	+	9.53331e12i	0.195057	+	0.337849i
$976$	1.45746e13	−	2.52440e13i	0.514130	−	0.890500i
$977$	9.12910e12	−	1.58121e13i	0.320555	−	0.555218i	−0.660048	−	0.751224i	$-0.729464\pi$
$977$	9.12910e12	−	1.58121e13i	0.320555	−	0.555218i	0.980603	+	0.196006i	$0.0627972\pi$
$978$	−2.26187e13	−	3.91767e13i	−0.790574	−	1.36931i
$979$	3.57558e13			1.24401
$980$	1.43466e12	−	1.69861e11i	0.0496858	−	0.00588269i
$981$	−1.86714e13			−0.643674
$982$	−9.97592e12	−	1.72788e13i	−0.342335	−	0.592942i
$983$	−1.06639e13	+	1.84704e13i	−0.364271	+	0.630936i	−0.988659	−	0.150179i	$-0.952015\pi$
$983$	−1.06639e13	+	1.84704e13i	−0.364271	+	0.630936i	0.624388	+	0.781114i	$0.285348\pi$
$984$	−1.94386e13	+	3.36686e13i	−0.660977	+	1.14485i
$985$	−1.99234e12	−	3.45084e12i	−0.0674374	−	0.116805i
$986$	1.75929e13			0.592778
$987$	−3.89791e12	−	6.60744e13i	−0.130739	−	2.21618i
$988$	−6.31115e12			−0.210718
$989$	−7.51224e12	−	1.30116e13i	−0.249681	−	0.432461i
$990$	−8.75273e12	+	1.51602e13i	−0.289591	+	0.501586i
$991$	−1.69551e13	+	2.93671e13i	−0.558431	+	0.967231i	0.439197	+	0.898391i	$0.355263\pi$
$991$	−1.69551e13	+	2.93671e13i	−0.558431	+	0.967231i	−0.997628	+	0.0688400i	$0.978070\pi$
$992$	−4.48242e12	−	7.76378e12i	−0.146964	−	0.254549i
$993$	−7.42060e13			−2.42196
$994$	2.19760e13	−	1.44773e13i	0.714018	−	0.470381i
$995$	2.67925e12			0.0866583
$996$	−8.05925e10	−	1.39590e11i	−0.00259494	−	0.00449457i
$997$	1.07106e13	−	1.85512e13i	0.343308	−	0.594627i	−0.641737	−	0.766925i	$-0.721786\pi$
$997$	1.07106e13	−	1.85512e13i	0.343308	−	0.594627i	0.985045	+	0.172298i	$0.0551192\pi$
$998$	−3.09792e12	+	5.36576e12i	−0.0988514	+	0.171216i
$999$	2.80874e12	+	4.86488e12i	0.0892210	+	0.154535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.e.b.11.10	✓	26
7.2	even	3	inner	35.10.e.b.16.10	yes	26
7.3	odd	6		245.10.a.l.1.4		13
7.4	even	3		245.10.a.m.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.e.b.11.10	✓	26	1.1	even	1	trivial
35.10.e.b.16.10	yes	26	7.2	even	3	inner
245.10.a.l.1.4		13	7.3	odd	6
245.10.a.m.1.4		13	7.4	even	3

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(10.6621 + 18.4672i) q^{2} +(-95.0320 + 164.600i) q^{3} +(28.6405 - 49.6068i) q^{4} +(-312.500 - 541.266i) q^{5} -4052.95 q^{6} +(-374.098 - 6341.42i) q^{7} +12139.4 q^{8} +(-8220.66 - 14238.6i) q^{9} +(6663.79 - 11542.0i) q^{10} +(39944.3 - 69185.6i) q^{11} +(5443.53 + 9428.46i) q^{12} -148270. q^{13} +(113120. - 74521.3i) q^{14} +118790. q^{15} +(114768. + 198783. i) q^{16} +(98403.5 - 170440. i) q^{17} +(175299. - 303626. i) q^{18} +(371548. + 643540. i) q^{19} -35800.6 q^{20} +(1.07935e6 + 541061. i) q^{21} +1.70356e6 q^{22} +(-629107. - 1.08964e6i) q^{23} +(-1.15363e6 + 1.99815e6i) q^{24} +(-195312. + 338291. i) q^{25} +(-1.58087e6 - 2.73814e6i) q^{26} -616127. q^{27} +(-325292. - 163064. i) q^{28} +4.19204e6 q^{29} +(1.26655e6 + 2.19372e6i) q^{30} +(3.39385e6 - 5.87831e6i) q^{31} +(660375. - 1.14380e6i) q^{32} +(7.59198e6 + 1.31497e7i) q^{33} +4.19674e6 q^{34} +(-3.31549e6 + 2.18418e6i) q^{35} -941775. q^{36} +(-4.55871e6 - 7.89591e6i) q^{37} +(-7.92294e6 + 1.37229e7i) q^{38} +(1.40904e7 - 2.44053e7i) q^{39} +(-3.79357e6 - 6.57066e6i) q^{40} +1.68499e7 q^{41} +(1.51620e6 + 2.57015e7i) q^{42} +1.19411e7 q^{43} +(-2.28805e6 - 3.96302e6i) q^{44} +(-5.13791e6 + 8.89913e6i) q^{45} +(1.34152e7 - 2.32357e7i) q^{46} +(-2.74105e7 - 4.74763e7i) q^{47} -4.36263e7 q^{48} +(-4.00737e7 + 4.74463e6i) q^{49} -8.32974e6 q^{50} +(1.87030e7 + 3.23945e7i) q^{51} +(-4.24653e6 + 7.35520e6i) q^{52} +(-1.64212e7 + 2.84424e7i) q^{53} +(-6.56918e6 - 1.13782e7i) q^{54} -4.99304e7 q^{55} +(-4.54134e6 - 7.69813e7i) q^{56} -1.41236e8 q^{57} +(4.46959e7 + 7.74155e7i) q^{58} +(-3.63706e7 + 6.29957e7i) q^{59} +(3.40220e6 - 5.89279e6i) q^{60} +(-6.34963e7 - 1.09979e8i) q^{61} +1.44742e8 q^{62} +(-8.72177e7 + 5.74573e7i) q^{63} +1.45686e8 q^{64} +(4.63344e7 + 8.02535e7i) q^{65} +(-1.61892e8 + 2.80406e8i) q^{66} +(-4.48429e7 + 7.76702e7i) q^{67} +(-5.63665e6 - 9.76296e6i) q^{68} +2.39141e8 q^{69} +(-7.56858e7 - 3.79401e7i) q^{70} +1.94271e8 q^{71} +(-9.97941e7 - 1.72848e8i) q^{72} +(1.11122e8 - 1.92468e8i) q^{73} +(9.72105e7 - 1.68374e8i) q^{74} +(-3.71219e7 - 6.42970e7i) q^{75} +4.25653e7 q^{76} +(-4.53678e8 - 2.27422e8i) q^{77} +6.00931e8 q^{78} +(-1.13984e8 - 1.97427e8i) q^{79} +(7.17297e7 - 1.24239e8i) q^{80} +(2.20359e8 - 3.81673e8i) q^{81} +(1.79654e8 + 3.11170e8i) q^{82} -1.48052e7 q^{83} +(5.77535e7 - 3.80469e7i) q^{84} -1.23004e8 q^{85} +(1.27317e8 + 2.20520e8i) q^{86} +(-3.98378e8 + 6.90012e8i) q^{87} +(4.84901e8 - 8.39874e8i) q^{88} +(2.23785e8 + 3.87607e8i) q^{89} -2.19123e8 q^{90} +(5.54676e7 + 9.40243e8i) q^{91} -7.20717e7 q^{92} +(6.45048e8 + 1.11726e9i) q^{93} +(5.84505e8 - 1.01239e9i) q^{94} +(2.32217e8 - 4.02212e8i) q^{95} +(1.25513e8 + 2.17396e8i) q^{96} +6.78338e8 q^{97} +(-5.14889e8 - 6.89464e8i) q^{98} -1.31347e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} - 268 q^{3} - 3563 q^{4} - 8125 q^{5} + 6080 q^{6} - 8462 q^{7} - 9390 q^{8} - 82107 q^{9} + 625 q^{10} - 129087 q^{11} - 356068 q^{12} + 71778 q^{13} + 828653 q^{14} + 335000 q^{15} - 1379187 q^{16}+ \cdots + 10532284198 q^{99}+O(q^{100}) \) 26 * q + q^2 - 268 * q^3 - 3563 * q^4 - 8125 * q^5 + 6080 * q^6 - 8462 * q^7 - 9390 * q^8 - 82107 * q^9 + 625 * q^10 - 129087 * q^11 - 356068 * q^12 + 71778 * q^13 + 828653 * q^14 + 335000 * q^15 - 1379187 * q^16 - 251650 * q^17 - 391089 * q^18 + 22537 * q^19 + 4453750 * q^20 + 1067860 * q^21 - 1735386 * q^22 - 1640451 * q^23 - 3300104 * q^24 - 5078125 * q^25 + 215949 * q^26 + 9666692 * q^27 - 1349311 * q^28 + 350384 * q^29 - 1900000 * q^30 - 3363236 * q^31 - 11618029 * q^32 - 1855346 * q^33 + 60169436 * q^34 + 4080625 * q^35 + 5720266 * q^36 - 57134155 * q^37 - 28383363 * q^38 + 10216786 * q^39 + 2934375 * q^40 + 92086974 * q^41 - 67569966 * q^42 - 46945552 * q^43 - 171806579 * q^44 - 51316875 * q^45 + 53075341 * q^46 + 1336787 * q^47 + 609090752 * q^48 - 122434224 * q^49 - 781250 * q^50 - 234254040 * q^51 - 80069087 * q^52 - 122467755 * q^53 + 99983754 * q^54 + 161358750 * q^55 - 344492982 * q^56 + 65304060 * q^57 - 37365152 * q^58 + 136056496 * q^59 - 222542500 * q^60 + 50448822 * q^61 - 218462072 * q^62 - 294191035 * q^63 + 2218017678 * q^64 - 22430625 * q^65 + 500348610 * q^66 - 585418818 * q^67 - 480342846 * q^68 - 1042832072 * q^69 - 93881875 * q^70 + 994388160 * q^71 + 870751121 * q^72 + 346232592 * q^73 + 613439215 * q^74 - 104687500 * q^75 - 2872390426 * q^76 - 1532634653 * q^77 - 655224276 * q^78 - 136453862 * q^79 - 861991875 * q^80 + 344488883 * q^81 + 224863259 * q^82 - 1046084628 * q^83 + 557627890 * q^84 + 314562500 * q^85 + 2285275668 * q^86 - 2310323838 * q^87 + 1816859183 * q^88 + 843350780 * q^89 + 488861250 * q^90 + 164707640 * q^91 - 344655826 * q^92 - 198172924 * q^93 - 2777934057 * q^94 + 14085625 * q^95 + 1583073484 * q^96 + 1389946316 * q^97 + 4300632129 * q^98 + 10532284198 * q^99

Introduction

L-functions

Modular forms

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