LMFDB - Embedded newform 95.11.j.a.31.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,11,Mod(31,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.31"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.18
Character	$\chi$	$=$	95.31
Dual form			95.11.j.a.46.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-32.4277 + 18.7221i) q^{2} +(7.34597 - 4.24120i) q^{3} +(189.037 - 327.422i) q^{4} +(698.771 + 1210.31i) q^{5} +(-158.809 + 275.065i) q^{6} +3275.68 q^{7} -24186.2i q^{8} +(-29488.5 + 51075.6i) q^{9} +(-45319.1 - 26165.0i) q^{10} +182211. q^{11} -3206.98i q^{12} +(-198093. - 114369. i) q^{13} +(-106223. + 61327.7i) q^{14} +(10266.3 + 5927.26i) q^{15} +(646392. + 1.11958e6i) q^{16} +(-905022. - 1.56754e6i) q^{17} -2.20835e6i q^{18} +(209253. + 2.46724e6i) q^{19} +528375. q^{20} +(24063.1 - 13892.8i) q^{21} +(-5.90869e6 + 3.41138e6i) q^{22} +(2.67155e6 - 4.62727e6i) q^{23} +(-102579. - 177671. i) q^{24} +(-976562. + 1.69146e6i) q^{25} +8.56491e6 q^{26} +1.00114e6i q^{27} +(619226. - 1.07253e6i) q^{28} +(-1.74608e6 - 1.00810e6i) q^{29} -443884. q^{30} +4.87781e7i q^{31} +(-2.04734e7 - 1.18203e7i) q^{32} +(1.33852e6 - 772794. i) q^{33} +(5.86956e7 + 3.38879e7i) q^{34} +(2.28895e6 + 3.96458e6i) q^{35} +(1.11489e7 + 1.93104e7i) q^{36} +8.37391e6i q^{37} +(-5.29776e7 - 7.60893e7i) q^{38} -1.94024e6 q^{39} +(2.92728e7 - 1.69006e7i) q^{40} +(-7.81864e7 + 4.51409e7i) q^{41} +(-520206. + 901024. i) q^{42} +(7.54695e7 + 1.30717e8i) q^{43} +(3.44447e7 - 5.96600e7i) q^{44} -8.24229e7 q^{45} +2.00069e8i q^{46} +(-1.96280e8 + 3.39967e8i) q^{47} +(9.49675e6 + 5.48295e6i) q^{48} -2.71745e8 q^{49} -7.31334e7i q^{50} +(-1.32965e7 - 7.67676e6i) q^{51} +(-7.48937e7 + 4.32399e7i) q^{52} +(3.61021e8 + 2.08436e8i) q^{53} +(-1.87436e7 - 3.24648e7i) q^{54} +(1.27324e8 + 2.20531e8i) q^{55} -7.92263e7i q^{56} +(1.20012e7 + 1.72368e7i) q^{57} +7.54952e7 q^{58} +(3.04328e8 - 1.75704e8i) q^{59} +(3.88143e6 - 2.24094e6i) q^{60} +(3.53904e8 - 6.12980e8i) q^{61} +(-9.13231e8 - 1.58176e9i) q^{62} +(-9.65950e7 + 1.67307e8i) q^{63} -4.38602e8 q^{64} -3.19670e8i q^{65} +(-2.89367e7 + 5.01198e7i) q^{66} +(-1.13863e9 - 6.57388e8i) q^{67} -6.84332e8 q^{68} -4.53224e7i q^{69} +(-1.48451e8 - 8.57081e7i) q^{70} +(1.39153e9 - 8.03402e8i) q^{71} +(1.23533e9 + 7.13216e8i) q^{72} +(-1.53483e9 - 2.65841e9i) q^{73} +(-1.56777e8 - 2.71547e8i) q^{74} +1.65672e7i q^{75} +(8.47386e8 + 3.97886e8i) q^{76} +5.96865e8 q^{77} +(6.29176e7 - 3.63255e7i) q^{78} +(1.51513e9 - 8.74761e8i) q^{79} +(-9.03360e8 + 1.56467e9i) q^{80} +(-1.73702e9 - 3.00861e9i) q^{81} +(1.69027e9 - 2.92763e9i) q^{82} -6.13289e9 q^{83} -1.05050e7i q^{84} +(1.26481e9 - 2.19071e9i) q^{85} +(-4.89460e9 - 2.82590e9i) q^{86} -1.71022e7 q^{87} -4.40700e9i q^{88} +(-9.29342e9 - 5.36556e9i) q^{89} +(2.67279e9 - 1.54313e9i) q^{90} +(-6.48888e8 - 3.74636e8i) q^{91} +(-1.01005e9 - 1.74945e9i) q^{92} +(2.06878e8 + 3.58323e8i) q^{93} -1.46992e10i q^{94} +(-2.83990e9 + 1.97730e9i) q^{95} -2.00530e8 q^{96} +(8.38457e9 - 4.84083e9i) q^{97} +(8.81207e9 - 5.08765e9i) q^{98} +(-5.37314e9 + 9.30655e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) $ 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−32.4277	+	18.7221i	−1.01337	+	0.585067i	−0.912175	−	0.409800i	$-0.865598\pi$
$2$	−32.4277	+	18.7221i	−1.01337	+	0.585067i	−0.101190	+	0.994867i	$0.532265\pi$
$3$	7.34597	−	4.24120i	0.0302303	−	0.0174535i	−0.484809	−	0.874620i	$-0.661111\pi$
$3$	7.34597	−	4.24120i	0.0302303	−	0.0174535i	0.515039	+	0.857167i	$0.327777\pi$
$4$	189.037	−	327.422i	0.184607	−	0.319748i
$5$	698.771	+	1210.31i	0.223607	+	0.387298i
$5$	698.771	+	1210.31i	0.223607	+	0.387298i
$6$	−158.809	+	275.065i	−0.0204229	+	0.0353735i
$7$	3275.68			0.194900			0.0974499	−	0.995240i	$-0.468931\pi$
$7$	3275.68			0.194900			0.0974499	+	0.995240i	$0.468931\pi$
$8$		−	24186.2i		−	0.738105i
$9$	−29488.5	+	51075.6i	−0.499391	+	0.864970i
$10$	−45319.1	−	26165.0i	−0.453191	−	0.261650i
$11$	182211.			1.13139			0.565694	−	0.824615i	$-0.308608\pi$
$11$	182211.			1.13139			0.565694	+	0.824615i	$0.308608\pi$
$12$		−	3206.98i		−	0.0128881i
$13$	−198093.	−	114369.i	−0.533521	−	0.308028i	0.208928	−	0.977931i	$-0.433003\pi$
$13$	−198093.	−	114369.i	−0.533521	−	0.308028i	−0.742449	+	0.669903i	$0.766336\pi$
$14$	−106223.	+	61327.7i	−0.197505	+	0.114029i
$15$	10266.3	+	5927.26i	0.0135194	+	0.00780544i
$16$	646392.	+	1.11958e6i	0.616447	+	1.06772i
$17$	−905022.	−	1.56754e6i	−0.637404	−	1.10402i	−0.986000	−	0.166743i	$-0.946675\pi$
$17$	−905022.	−	1.56754e6i	−0.637404	−	1.10402i	0.348596	−	0.937273i	$-0.386658\pi$
$18$		−	2.20835e6i		−	1.16871i
$19$	209253.	+	2.46724e6i	0.0845092	+	0.996423i
$19$	209253.	+	2.46724e6i	0.0845092	+	0.996423i
$20$	528375.			0.165117
$21$	24063.1	−	13892.8i	0.00589188	−	0.00340168i
$22$	−5.90869e6	+	3.41138e6i	−1.14651	+	0.661938i
$23$	2.67155e6	−	4.62727e6i	0.415073	−	0.718928i	−0.580363	−	0.814358i	$-0.697089\pi$
$23$	2.67155e6	−	4.62727e6i	0.415073	−	0.718928i	0.995436	+	0.0954301i	$0.0304226\pi$
$24$	−102579.	−	177671.i	−0.0128825	−	0.0223132i
$25$	−976562.	+	1.69146e6i	−0.100000	+	0.173205i
$26$	8.56491e6			0.720869
$27$			1.00114e6i			0.0697714i
$28$	619226.	−	1.07253e6i	0.0359798	−	0.0623188i
$29$	−1.74608e6	−	1.00810e6i	−0.0851284	−	0.0491489i	0.456832	−	0.889553i	$-0.348984\pi$
$29$	−1.74608e6	−	1.00810e6i	−0.0851284	−	0.0491489i	−0.541960	+	0.840404i	$0.682318\pi$
$30$	−443884.			−0.0182668
$31$			4.87781e7i			1.70379i	0.523711	+	0.851896i	$0.324547\pi$
$31$			4.87781e7i			1.70379i	−0.523711	+	0.851896i	$0.675453\pi$
$32$	−2.04734e7	−	1.18203e7i	−0.610156	−	0.352274i
$33$	1.33852e6	−	772794.i	0.0342022	−	0.0197467i
$34$	5.86956e7	+	3.38879e7i	1.29185	+	0.745848i
$35$	2.28895e6	+	3.96458e6i	0.0435809	+	0.0754843i
$36$	1.11489e7	+	1.93104e7i	0.184382	+	0.319359i
$37$			8.37391e6i			0.120759i	0.998175	+	0.0603795i	$0.0192311\pi$
$37$			8.37391e6i			0.120759i	−0.998175	+	0.0603795i	$0.980769\pi$
$38$	−5.29776e7	−	7.60893e7i	−0.668613	−	0.960297i
$39$	−1.94024e6			−0.0215047
$40$	2.92728e7	−	1.69006e7i	0.285867	−	0.165045i
$41$	−7.81864e7	+	4.51409e7i	−0.674857	+	0.389629i	−0.797915	−	0.602771i	$-0.794063\pi$
$41$	−7.81864e7	+	4.51409e7i	−0.674857	+	0.389629i	0.123057	+	0.992400i	$0.460730\pi$
$42$	−520206.	+	901024.i	−0.00398042	+	0.00689429i
$43$	7.54695e7	+	1.30717e8i	0.513368	+	0.889180i	0.999880	+	0.0155056i	$0.00493579\pi$
$43$	7.54695e7	+	1.30717e8i	0.513368	+	0.889180i	−0.486512	+	0.873674i	$0.661731\pi$
$44$	3.44447e7	−	5.96600e7i	0.208862	−	0.361759i
$45$	−8.24229e7			−0.446669
$46$			2.00069e8i			0.971382i
$47$	−1.96280e8	+	3.39967e8i	−0.855830	+	1.48234i	0.0200433	+	0.999799i	$0.493620\pi$
$47$	−1.96280e8	+	3.39967e8i	−0.855830	+	1.48234i	−0.875873	+	0.482542i	$0.839714\pi$
$48$	9.49675e6	+	5.48295e6i	0.0372708	+	0.0215183i
$49$	−2.71745e8			−0.962014
$50$		−	7.31334e7i		−	0.234027i
$51$	−1.32965e7	−	7.67676e6i	−0.0385379	−	0.0222498i
$52$	−7.48937e7	+	4.32399e7i	−0.196983	+	0.113728i
$53$	3.61021e8	+	2.08436e8i	0.863283	+	0.498417i	0.865110	−	0.501582i	$-0.167248\pi$
$53$	3.61021e8	+	2.08436e8i	0.863283	+	0.498417i	−0.00182728	+	0.999998i	$0.500582\pi$
$54$	−1.87436e7	−	3.24648e7i	−0.0408210	−	0.0707040i
$55$	1.27324e8	+	2.20531e8i	0.252986	+	0.438185i
$56$		−	7.92263e7i		−	0.143856i
$57$	1.20012e7	+	1.72368e7i	0.0199458	+	0.0286472i
$58$	7.54952e7			0.115022
$59$	3.04328e8	−	1.75704e8i	0.425678	−	0.245765i	−0.271826	−	0.962347i	$-0.587627\pi$
$59$	3.04328e8	−	1.75704e8i	0.425678	−	0.245765i	0.697504	+	0.716581i	$0.254294\pi$
$60$	3.88143e6	−	2.24094e6i	0.00499155	−	0.00288187i
$61$	3.53904e8	−	6.12980e8i	0.419022	−	0.725767i	−0.576819	−	0.816872i	$-0.695706\pi$
$61$	3.53904e8	−	6.12980e8i	0.419022	−	0.725767i	0.995841	+	0.0911044i	$0.0290397\pi$
$62$	−9.13231e8	−	1.58176e9i	−0.996832	−	1.72656i
$63$	−9.65950e7	+	1.67307e8i	−0.0973311	+	0.168582i
$64$	−4.38602e8			−0.408480
$65$		−	3.19670e8i		−	0.275509i
$66$	−2.89367e7	+	5.01198e7i	−0.0231062	+	0.0400212i
$67$	−1.13863e9	−	6.57388e8i	−0.843350	−	0.486909i	0.0150512	−	0.999887i	$-0.495209\pi$
$67$	−1.13863e9	−	6.57388e8i	−0.843350	−	0.486909i	−0.858402	+	0.512978i	$0.828542\pi$
$68$	−6.84332e8			−0.470676
$69$		−	4.53224e7i		−	0.0289779i
$70$	−1.48451e8	−	8.57081e7i	−0.0883268	−	0.0509955i
$71$	1.39153e9	−	8.03402e8i	0.771262	−	0.445288i	−0.0620628	−	0.998072i	$-0.519768\pi$
$71$	1.39153e9	−	8.03402e8i	0.771262	−	0.445288i	0.833325	+	0.552784i	$0.186435\pi$
$72$	1.23533e9	+	7.13216e8i	0.638439	+	0.368603i
$73$	−1.53483e9	−	2.65841e9i	−0.740366	−	1.28235i	−0.952329	−	0.305074i	$-0.901319\pi$
$73$	−1.53483e9	−	2.65841e9i	−0.740366	−	1.28235i	0.211963	−	0.977278i	$-0.432014\pi$
$74$	−1.56777e8	−	2.71547e8i	−0.0706521	−	0.122373i
$75$			1.65672e7i			0.00698140i
$76$	8.47386e8	+	3.97886e8i	0.334205	+	0.156925i
$77$	5.96865e8			0.220507
$78$	6.29176e7	−	3.63255e7i	0.0217921	−	0.0125817i
$79$	1.51513e9	−	8.74761e8i	0.492396	−	0.284285i	−0.233172	−	0.972436i	$-0.574910\pi$
$79$	1.51513e9	−	8.74761e8i	0.492396	−	0.284285i	0.725568	+	0.688150i	$0.241577\pi$
$80$	−9.03360e8	+	1.56467e9i	−0.275684	+	0.477498i
$81$	−1.73702e9	−	3.00861e9i	−0.498173	−	0.862861i
$82$	1.69027e9	−	2.92763e9i	0.455918	−	0.789673i
$83$	−6.13289e9			−1.55695			−0.778475	−	0.627676i	$-0.784006\pi$
$83$	−6.13289e9			−1.55695			−0.778475	+	0.627676i	$0.784006\pi$
$84$		−	1.05050e7i		−	0.00251189i
$85$	1.26481e9	−	2.19071e9i	0.285056	−	0.493731i
$86$	−4.89460e9	−	2.82590e9i	−1.04046	−	0.600709i
$87$	−1.71022e7			−0.00343128
$88$		−	4.40700e9i		−	0.835083i
$89$	−9.29342e9	−	5.36556e9i	−1.66428	−	0.960870i	−0.970637	−	0.240547i	$-0.922673\pi$
$89$	−9.29342e9	−	5.36556e9i	−1.66428	−	0.960870i	−0.693639	−	0.720323i	$-0.743994\pi$
$90$	2.67279e9	−	1.54313e9i	0.452639	−	0.261331i
$91$	−6.48888e8	−	3.74636e8i	−0.103983	−	0.0600347i
$92$	−1.01005e9	−	1.74945e9i	−0.153251	−	0.265438i
$93$	2.06878e8	+	3.58323e8i	0.0297371	+	0.0515062i
$94$		−	1.46992e10i		−	2.00287i
$95$	−2.83990e9	+	1.97730e9i	−0.367016	+	0.255537i
$96$	−2.00530e8			−0.0245936
$97$	8.38457e9	−	4.84083e9i	0.976387	−	0.563717i	0.0752097	−	0.997168i	$-0.476037\pi$
$97$	8.38457e9	−	4.84083e9i	0.976387	−	0.563717i	0.901177	+	0.433450i	$0.142704\pi$
$98$	8.81207e9	−	5.08765e9i	0.974872	−	0.562843i
$99$	−5.37314e9	+	9.30655e9i	−0.565005	+	0.978617i
$100$	3.69213e8	+	6.39496e8i	0.0369213	+	0.0639496i
$101$	4.05179e9	−	7.01790e9i	0.385514	−	0.667729i	−0.606327	−	0.795216i	$-0.707358\pi$
$101$	4.05179e9	−	7.01790e9i	0.385514	−	0.667729i	0.991840	+	0.127486i	$0.0406909\pi$
$102$	5.74902e8			0.0520706
$103$			3.75179e9i			0.323633i	0.986821	+	0.161817i	$0.0517353\pi$
$103$			3.75179e9i			0.323633i	−0.986821	+	0.161817i	$0.948265\pi$
$104$	−2.76615e9	+	4.79111e9i	−0.227357	+	0.393794i
$105$	3.36291e7	+	1.94158e7i	0.00263493	+	0.00152128i
$106$	−1.56094e10			−1.16643
$107$		−	2.00353e9i		−	0.142849i	−0.997446	−	0.0714245i	$-0.977245\pi$
$107$		−	2.00353e9i		−	0.142849i	0.997446	−	0.0714245i	$-0.0227545\pi$
$108$	3.27797e8	+	1.89253e8i	0.0223093	+	0.0128803i
$109$	−1.46221e10	+	8.44209e9i	−0.950338	+	0.548678i	−0.893186	−	0.449688i	$-0.851535\pi$
$109$	−1.46221e10	+	8.44209e9i	−0.950338	+	0.548678i	−0.0571521	+	0.998365i	$0.518202\pi$
$110$	−8.25764e9	−	4.76755e9i	−0.512735	−	0.296027i
$111$	3.55154e7	+	6.15145e7i	0.00210767	+	0.00365058i
$112$	2.11737e9	+	3.66740e9i	0.120145	+	0.208098i
$113$		−	1.40413e10i		−	0.762105i	−0.924553	−	0.381052i	$-0.875562\pi$
$113$		−	1.40413e10i		−	0.762105i	0.924553	−	0.381052i	$-0.124438\pi$
$114$	−7.11882e8	−	3.34261e8i	−0.0369729	−	0.0173605i
$115$	7.46722e9			0.371253
$116$	−6.60148e8	+	3.81137e8i	−0.0314305	+	0.0181464i
$117$	1.16829e10	−	6.74513e9i	0.532871	−	0.307653i
$118$	−6.57910e9	+	1.13953e10i	−0.287578	+	0.498100i
$119$	−2.96456e9	−	5.13477e9i	−0.124230	−	0.215172i
$120$	1.43358e8	−	2.48303e8i	0.00576123	−	0.00997875i
$121$	7.26347e9			0.280038
$122$			2.65034e10i			0.980624i
$123$	−3.82903e8	+	6.63208e8i	−0.0136008	+	0.0235572i
$124$	1.59710e10	+	9.22088e9i	0.544784	+	0.314531i
$125$	−2.72958e9			−0.0894427
$126$		−	7.23386e9i		−	0.227781i
$127$	−2.54058e10	−	1.46680e10i	−0.768978	−	0.443970i	0.0635320	−	0.997980i	$-0.479764\pi$
$127$	−2.54058e10	−	1.46680e10i	−0.768978	−	0.443970i	−0.832510	+	0.554010i	$0.813097\pi$
$128$	3.51877e10	−	2.03156e10i	1.02410	−	0.591262i
$129$	1.10879e9	+	6.40162e8i	0.0310386	+	0.0179201i
$130$	5.98492e9	+	1.03662e10i	0.161191	+	0.279191i
$131$	1.36056e10	+	2.35655e10i	0.352663	+	0.610830i	0.986715	−	0.162460i	$-0.0519429\pi$
$131$	1.36056e10	+	2.35655e10i	0.352663	+	0.610830i	−0.634052	+	0.773290i	$0.718610\pi$
$132$		−	5.84347e8i		−	0.0145815i
$133$	6.85446e8	+	8.08189e9i	0.0164708	+	0.194203i
$134$	4.92308e10			1.13950
$135$	−1.21169e9	+	6.99571e8i	−0.0270224	+	0.0156014i
$136$	−3.79130e10	+	2.18891e10i	−0.814880	+	0.470471i
$137$	−6.90042e9	+	1.19519e10i	−0.142979	+	0.247647i	−0.928617	−	0.371039i	$-0.879002\pi$
$137$	−6.90042e9	+	1.19519e10i	−0.142979	+	0.247647i	0.785638	+	0.618686i	$0.212335\pi$
$138$	8.48532e8	+	1.46970e9i	0.0169540	+	0.0293652i
$139$	−4.71520e10	+	8.16696e10i	−0.908711	+	1.57393i	−0.0928546	+	0.995680i	$0.529599\pi$
$139$	−4.71520e10	+	8.16696e10i	−0.908711	+	1.57393i	−0.815857	+	0.578254i	$0.803734\pi$
$140$	1.73079e9			0.0321813
$141$			3.32985e9i			0.0597489i
$142$	−3.00828e10	+	5.21050e10i	−0.521047	+	0.902479i
$143$	−3.60947e10	−	2.08393e10i	−0.603619	−	0.348500i
$144$	−7.62446e10			−1.23139
$145$		−	2.81773e9i		−	0.0439601i
$146$	9.95421e10	+	5.74707e10i	1.50052	+	0.866327i
$147$	−1.99623e9	+	1.15253e9i	−0.0290820	+	0.0167905i
$148$	2.74180e9	+	1.58298e9i	0.0386125	+	0.0222929i
$149$	1.20343e10	+	2.08441e10i	0.163867	+	0.283825i	0.936252	−	0.351329i	$-0.114270\pi$
$149$	1.20343e10	+	2.08441e10i	0.163867	+	0.283825i	−0.772386	+	0.635154i	$0.780937\pi$
$150$	−3.10173e8	−	5.37236e8i	−0.00408458	−	0.00707471i
$151$		−	7.07032e10i		−	0.900646i	−0.892866	−	0.450323i	$-0.851309\pi$
$151$		−	7.07032e10i		−	0.900646i	0.892866	−	0.450323i	$-0.148691\pi$
$152$	5.96732e10	−	5.06104e9i	0.735464	−	0.0623767i
$153$	1.06751e11			1.27325
$154$	−1.93550e10	+	1.11746e10i	−0.223454	+	0.129011i
$155$	−5.90365e10	+	3.40847e10i	−0.659876	+	0.380979i
$156$	−3.66778e8	+	6.35278e8i	−0.00396991	+	0.00687608i
$157$	−3.16696e10	−	5.48534e10i	−0.332005	−	0.575049i	0.650900	−	0.759163i	$-0.274392\pi$
$157$	−3.16696e10	−	5.48534e10i	−0.332005	−	0.575049i	−0.982905	+	0.184114i	$0.941058\pi$
$158$	−3.27548e10	+	5.67330e10i	−0.332652	+	0.576170i
$159$	3.53607e9			0.0347964
$160$		−	3.30389e10i		−	0.315083i
$161$	8.75115e9	−	1.51574e10i	0.0808976	−	0.140119i
$162$	1.12655e11	+	6.50415e10i	1.00966	+	0.582929i
$163$	−2.54979e10			−0.221598			−0.110799	−	0.993843i	$-0.535341\pi$
$163$	−2.54979e10			−0.221598			−0.110799	+	0.993843i	$0.535341\pi$
$164$			3.41333e10i			0.287713i
$165$	1.87064e9	+	1.08001e9i	0.0152957	+	0.00883098i
$166$	1.98876e11	−	1.14821e11i	1.57776	−	0.910920i
$167$	−6.53231e10	−	3.77143e10i	−0.502903	−	0.290351i	0.227009	−	0.973893i	$-0.427105\pi$
$167$	−6.53231e10	−	3.77143e10i	−0.502903	−	0.290351i	−0.729912	+	0.683542i	$0.760439\pi$
$168$	−3.36015e8	−	5.81994e8i	−0.00251080	−	0.00434883i
$169$	−4.27688e10	−	7.40777e10i	−0.310237	−	0.537346i
$170$			9.47196e10i			0.667107i
$171$	−1.32186e11	−	6.20676e10i	−0.904079	−	0.424506i
$172$	5.70661e10			0.379085
$173$	7.72882e10	−	4.46223e10i	0.498750	−	0.287953i	−0.229447	−	0.973321i	$-0.573692\pi$
$173$	7.72882e10	−	4.46223e10i	0.498750	−	0.287953i	0.728197	+	0.685368i	$0.240359\pi$
$174$	5.54585e8	−	3.20190e8i	0.00347714	−	0.00200753i
$175$	−3.19891e9	+	5.54067e9i	−0.0194900	+	0.0337576i
$176$	1.17780e11	+	2.04001e11i	0.697441	+	1.20800i
$177$	1.49039e9	−	2.58143e9i	0.00857893	−	0.0148591i
$178$	4.01819e11			2.24869
$179$		−	8.86223e10i		−	0.482256i	−0.970493	−	0.241128i	$-0.922483\pi$
$179$		−	8.86223e10i		−	0.482256i	0.970493	−	0.241128i	$-0.0775174\pi$
$180$	−1.55810e10	+	2.69871e10i	−0.0824580	+	0.142821i
$181$	1.56059e11	+	9.01008e10i	0.803335	+	0.463806i	0.844636	−	0.535341i	$-0.179817\pi$
$181$	1.56059e11	+	9.01008e10i	0.803335	+	0.463806i	−0.0413011	+	0.999147i	$0.513150\pi$
$182$	2.80559e10			0.140497
$183$		−	6.00392e9i		−	0.0292536i
$184$	−1.11916e11	−	6.46148e10i	−0.530644	−	0.306367i
$185$	−1.01350e10	+	5.85144e9i	−0.0467698	+	0.0270025i
$186$	−1.34171e10	−	7.74639e9i	−0.0602692	−	0.0347964i
$187$	−1.64905e11	−	2.85624e11i	−0.721151	−	1.24907i
$188$	7.42086e10	+	1.28533e11i	0.315984	+	0.547300i
$189$			3.27943e9i			0.0135984i
$190$	5.50722e10	−	1.17288e11i	0.222415	−	0.473682i
$191$	−3.63005e11			−1.42806			−0.714028	−	0.700117i	$-0.753131\pi$
$191$	−3.63005e11			−1.42806			−0.714028	+	0.700117i	$0.753131\pi$
$192$	−3.22196e9	+	1.86020e9i	−0.0123485	+	0.00712941i
$193$	−1.16760e11	+	6.74113e10i	−0.436021	+	0.251737i	−0.701908	−	0.712267i	$-0.747668\pi$
$193$	−1.16760e11	+	6.74113e10i	−0.436021	+	0.251737i	0.265888	+	0.964004i	$0.414335\pi$
$194$	−1.81262e11	+	3.13954e11i	−0.659625	+	1.14250i
$195$	−1.35579e9	−	2.34829e9i	−0.00480859	−	0.00832873i
$196$	−5.13700e10	+	8.89754e10i	−0.177594	+	0.307602i
$197$	5.86987e10			0.197832			0.0989162	−	0.995096i	$-0.468462\pi$
$197$	5.86987e10			0.197832			0.0989162	+	0.995096i	$0.468462\pi$
$198$		−	4.02387e11i		−	1.32226i
$199$	−1.84479e11	+	3.19527e11i	−0.591127	+	1.02386i	0.402954	+	0.915220i	$0.367984\pi$
$199$	−1.84479e11	+	3.19527e11i	−0.591127	+	1.02386i	−0.994081	+	0.108642i	$0.965350\pi$
$200$	4.09099e10	+	2.36194e10i	0.127844	+	0.0738105i
$201$	−1.11524e10			−0.0339930
$202$			3.03433e11i			0.902205i
$203$	−5.71960e9	−	3.30221e9i	−0.0165915	−	0.00957910i
$204$	−5.02708e9	+	2.90239e9i	−0.0142287	+	0.00821494i
$205$	−1.09269e11	−	6.30864e10i	−0.301805	−	0.174247i
$206$	−7.02416e10	−	1.21662e11i	−0.189347	−	0.327959i
$207$	1.57560e11	+	2.72902e11i	0.414567	+	0.718052i
$208$		−	2.95708e11i		−	0.759533i
$209$	3.81283e10	+	4.49559e11i	0.0956127	+	1.12734i
$210$	−1.45402e9			−0.00356020
$211$	4.80824e11	−	2.77604e11i	1.14967	−	0.663763i	0.200864	−	0.979619i	$-0.435625\pi$
$211$	4.80824e11	−	2.77604e11i	1.14967	−	0.663763i	0.948807	+	0.315856i	$0.102292\pi$
$212$	1.36493e11	−	7.88042e10i	0.318736	−	0.184022i
$213$	6.81477e9	−	1.18035e10i	0.0155437	−	0.0269224i
$214$	3.75104e10	+	6.49699e10i	0.0835762	+	0.144758i
$215$	−1.05472e11	+	1.82682e11i	−0.229585	+	0.397653i
$216$	2.42139e10			0.0514986
$217$			1.59782e11i			0.332069i
$218$	3.16108e11	−	5.47515e11i	0.642027	−	1.11202i
$219$	−2.25497e10	−	1.30191e10i	−0.0447630	−	0.0258439i
$220$	9.62758e10			0.186812
$221$			4.14025e11i			0.785354i
$222$	−2.30337e9	−	1.32985e9i	−0.00427167	−	0.00246625i
$223$	5.30304e11	−	3.06171e11i	0.961614	−	0.555188i	0.0649446	−	0.997889i	$-0.479313\pi$
$223$	5.30304e11	−	3.06171e11i	0.961614	−	0.555188i	0.896669	+	0.442701i	$0.145980\pi$
$224$	−6.70644e10	−	3.87197e10i	−0.118919	−	0.0686580i
$225$	−5.75948e10	−	9.97571e10i	−0.0998782	−	0.172994i
$226$	2.62883e11	+	4.55327e11i	0.445882	+	0.772291i
$227$			4.85828e11i			0.806034i	0.915192	+	0.403017i	$0.132038\pi$
$227$			4.85828e11i			0.806034i	−0.915192	+	0.403017i	$0.867962\pi$
$228$	7.91239e9	−	6.71070e8i	0.0128420	−	0.00108917i
$229$	−9.91196e11			−1.57392			−0.786959	−	0.617005i	$-0.788346\pi$
$229$	−9.91196e11			−1.57392			−0.786959	+	0.617005i	$0.788346\pi$
$230$	−2.42145e11	+	1.39802e11i	−0.376215	+	0.217208i
$231$	4.38456e9	−	2.53142e9i	0.00666601	−	0.00384862i
$232$	−2.43821e10	+	4.22311e10i	−0.0362770	+	0.0628337i
$233$	1.88493e10	+	3.26480e10i	0.0274484	+	0.0475419i	0.879423	−	0.476041i	$-0.157928\pi$
$233$	1.88493e10	+	3.26480e10i	0.0274484	+	0.0475419i	−0.851975	+	0.523583i	$0.824595\pi$
$234$	−2.52567e11	+	4.37458e11i	−0.359995	+	0.623530i
$235$	−5.48620e11			−0.765477
$236$		−	1.32858e11i		−	0.181480i
$237$	7.42007e9	−	1.28519e10i	0.00992354	−	0.0171881i
$238$	1.92268e11	+	1.11006e11i	0.251781	+	0.145366i
$239$	−4.50202e11			−0.577322			−0.288661	−	0.957431i	$-0.593210\pi$
$239$	−4.50202e11			−0.577322			−0.288661	+	0.957431i	$0.593210\pi$
$240$			1.53253e10i			0.0192466i
$241$	−1.28422e12	−	7.41446e11i	−1.57963	−	0.911999i	−0.994911	−	0.100761i	$-0.967872\pi$
$241$	−1.28422e12	−	7.41446e11i	−1.57963	−	0.911999i	−0.584717	−	0.811237i	$-0.698795\pi$
$242$	−2.35538e11	+	1.35988e11i	−0.283781	+	0.163841i
$243$	−7.67167e10	−	4.42924e10i	−0.0905437	−	0.0522754i
$244$	−1.33802e11	−	2.31752e11i	−0.154709	−	0.267963i
$245$	−1.89888e11	−	3.28895e11i	−0.215113	−	0.372586i
$246$		−	2.86751e10i		−	0.0318295i
$247$	2.40724e11	−	5.12674e11i	0.261839	−	0.557643i
$248$	1.17976e12			1.25758
$249$	−4.50520e10	+	2.60108e10i	−0.0470671	+	0.0271742i
$250$	8.85139e10	−	5.11035e10i	0.0906382	−	0.0523300i
$251$	7.89006e11	−	1.36660e12i	0.791975	−	1.37174i	−0.132767	−	0.991147i	$-0.542386\pi$
$251$	7.89006e11	−	1.36660e12i	0.791975	−	1.37174i	0.924742	−	0.380594i	$-0.124281\pi$
$252$	3.65201e10	+	6.32547e10i	0.0359360	+	0.0622429i
$253$	4.86787e11	−	8.43139e11i	0.469609	−	0.813386i
$254$	1.09847e12			1.03901
$255$		−	2.14572e10i		−	0.0199009i
$256$	−5.36139e11	+	9.28620e11i	−0.487615	+	0.844575i
$257$	−1.50496e12	−	8.68892e11i	−1.34233	−	0.774997i	−0.355185	−	0.934796i	$-0.615582\pi$
$257$	−1.50496e12	−	8.68892e11i	−1.34233	−	0.774997i	−0.987150	+	0.159799i	$0.948915\pi$
$258$	−4.79408e10			−0.0419379
$259$			2.74302e10i			0.0235359i
$260$	−1.04667e11	−	6.04296e10i	−0.0880935	−	0.0508608i
$261$	1.02979e11	−	5.94548e10i	0.0850246	−	0.0490890i
$262$	−8.82393e11	−	5.09450e11i	−0.714753	−	0.412663i
$263$	5.66569e11	+	9.81327e11i	0.450271	+	0.779893i	0.998403	−	0.0564994i	$-0.0179939\pi$
$263$	5.66569e11	+	9.81327e11i	0.450271	+	0.779893i	−0.548131	+	0.836392i	$0.684661\pi$
$264$	−1.86910e10	−	3.23737e10i	−0.0145751	−	0.0252448i
$265$			5.82595e11i			0.445797i
$266$	−1.73538e11	−	2.49244e11i	−0.130312	−	0.187162i
$267$	−9.10256e10			−0.0670822
$268$	−4.30486e11	+	2.48541e11i	−0.311376	+	0.179773i
$269$	−4.64938e11	+	2.68432e11i	−0.330091	+	0.190578i	−0.655881	−	0.754864i	$-0.727703\pi$
$269$	−4.64938e11	+	2.68432e11i	−0.330091	+	0.190578i	0.325791	+	0.945442i	$0.394370\pi$
$270$	2.61949e10	−	4.53709e10i	0.0182557	−	0.0316198i
$271$	−2.81017e11	−	4.86735e11i	−0.192259	−	0.333002i	0.753740	−	0.657173i	$-0.228248\pi$
$271$	−2.81017e11	−	4.86735e11i	−0.192259	−	0.333002i	−0.945998	+	0.324171i	$0.894915\pi$
$272$	1.17000e12	−	2.02650e12i	0.785852	−	1.36114i
$273$	−6.35561e9			−0.00419126
$274$		−	5.16762e11i		−	0.334609i
$275$	−1.77941e11	+	3.08202e11i	−0.113139	+	0.195962i
$276$	−1.48395e10	−	8.56761e9i	−0.00926563	−	0.00534951i
$277$	−1.22740e12			−0.752643			−0.376321	−	0.926489i	$-0.622811\pi$
$277$	−1.22740e12			−0.752643			−0.376321	+	0.926489i	$0.622811\pi$
$278$		−	3.53114e12i		−	2.12663i
$279$	−2.49137e12	−	1.43839e12i	−1.47373	−	0.850858i
$280$	9.58882e10	−	5.53611e10i	0.0557154	−	0.0321673i
$281$	2.26379e12	+	1.30700e12i	1.29212	+	0.746008i	0.979030	−	0.203714i	$-0.0653013\pi$
$281$	2.26379e12	+	1.30700e12i	1.29212	+	0.746008i	0.313094	+	0.949722i	$0.398635\pi$
$282$	−6.23420e10	−	1.07980e11i	−0.0349571	−	0.0605475i
$283$	−7.80942e11	−	1.35263e12i	−0.430216	−	0.745156i	0.566675	−	0.823941i	$-0.308229\pi$
$283$	−7.80942e11	−	1.35263e12i	−0.430216	−	0.745156i	−0.996892	+	0.0787848i	$0.974896\pi$
$284$		−	6.07492e11i		−	0.328813i
$285$	−1.24757e10	+	2.65698e10i	−0.00663500	+	0.0141307i
$286$	1.56062e12			0.815582
$287$	−2.56114e11	+	1.47867e11i	−0.131530	+	0.0759386i
$288$	1.20746e12	−	6.97129e11i	0.609412	−	0.351844i
$289$	−6.30134e11	+	1.09142e12i	−0.312567	+	0.541383i
$290$	5.27539e10	+	9.13724e10i	0.0257196	+	0.0445477i
$291$	4.10619e10	−	7.11212e10i	0.0196777	−	0.0340827i
$292$	−1.16056e12			−0.546706
$293$		−	7.94249e11i		−	0.367806i	−0.982944	−	0.183903i	$-0.941127\pi$
$293$		−	7.94249e11i		−	0.367806i	0.982944	−	0.183903i	$-0.0588732\pi$
$294$	4.31555e10	−	7.47475e10i	0.0196471	−	0.0340298i
$295$	4.25311e11	+	2.45553e11i	0.190369	+	0.109910i
$296$	2.02533e11			0.0891328
$297$			1.82420e11i			0.0789385i
$298$	−7.80491e11	−	4.50617e11i	−0.332114	−	0.191746i
$299$	−1.05843e12	+	6.11085e11i	−0.442900	+	0.255709i
$300$	5.42446e9	+	3.13181e9i	0.00223229	+	0.00128881i
$301$	2.47214e11	+	4.28187e11i	0.100055	+	0.173301i
$302$	1.32372e12	+	2.29274e12i	0.526938	+	0.912684i
$303$		−	6.87377e10i		−	0.0269142i
$304$	−2.62702e12	+	1.82908e12i	−1.01180	+	0.704474i
$305$	9.89193e11			0.374785
$306$	−3.46169e12	+	1.99861e12i	−1.29027	+	0.744939i
$307$	2.10490e12	−	1.21527e12i	0.771863	−	0.445635i	−0.0616757	−	0.998096i	$-0.519644\pi$
$307$	2.10490e12	−	1.21527e12i	0.771863	−	0.445635i	0.833539	+	0.552461i	$0.186311\pi$
$308$	1.12830e11	−	1.95427e11i	0.0407071	−	0.0705068i
$309$	1.59121e10	+	2.75606e10i	0.00564853	+	0.00978354i
$310$	1.27628e12	−	2.21058e12i	0.445797	−	0.772143i
$311$	−3.30918e12			−1.13741			−0.568707	−	0.822540i	$-0.692556\pi$
$311$	−3.30918e12			−1.13741			−0.568707	+	0.822540i	$0.692556\pi$
$312$			4.69271e10i			0.0158727i
$313$	1.53422e12	−	2.65735e12i	0.510701	−	0.884560i	−0.489222	−	0.872159i	$-0.662719\pi$
$313$	1.53422e12	−	2.65735e12i	0.510701	−	0.884560i	0.999923	−	0.0124005i	$-0.00394730\pi$
$314$	2.05394e12	+	1.18585e12i	0.672885	+	0.388490i
$315$	−2.69991e11			−0.0870556
$316$		−	6.61450e11i		−	0.209924i
$317$	5.24752e12	+	3.02966e12i	1.63930	+	0.946449i	0.981075	+	0.193626i	$0.0620250\pi$
$317$	5.24752e12	+	3.02966e12i	1.63930	+	0.946449i	0.658223	+	0.752823i	$0.271308\pi$
$318$	−1.14667e11	+	6.62028e10i	−0.0352615	+	0.0203583i
$319$	−3.18155e11	−	1.83687e11i	−0.0963132	−	0.0556064i
$320$	−3.06483e11	−	5.30844e11i	−0.0913390	−	0.158204i
$321$	−8.49737e9	−	1.47179e10i	−0.00249321	−	0.00431837i
$322$			6.55361e11i			0.189322i
$323$	3.67813e12	−	2.56092e12i	1.04620	−	0.728423i
$324$	−1.31345e12			−0.367864
$325$	3.86900e11	−	2.23377e11i	0.106704	−	0.0616057i
$326$	8.26839e11	−	4.77376e11i	0.224560	−	0.129650i
$327$	−7.16092e10	+	1.24031e11i	−0.0191527	+	0.0331734i
$328$	1.09179e12	+	1.89103e12i	0.287587	+	0.498115i
$329$	−6.42951e11	+	1.11362e12i	−0.166801	+	0.288908i
$330$	−8.08805e10			−0.0206669
$331$			3.34675e12i			0.842332i	0.906984	+	0.421166i	$0.138379\pi$
$331$			3.34675e12i			0.842332i	−0.906984	+	0.421166i	$0.861621\pi$
$332$	−1.15934e12	+	2.00804e12i	−0.287423	+	0.497832i
$333$	−4.27702e11	−	2.46934e11i	−0.104453	−	0.0603059i
$334$	2.82437e12			0.679500
$335$		−	1.83745e12i		−	0.435504i
$336$	3.11083e10	+	1.79604e10i	0.00726407	+	0.00419392i
$337$	−2.61081e12	+	1.50735e12i	−0.600657	+	0.346789i	−0.769300	−	0.638888i	$-0.779395\pi$
$337$	−2.61081e12	+	1.50735e12i	−0.600657	+	0.346789i	0.168643	+	0.985677i	$0.446061\pi$
$338$	2.77379e12	+	1.60145e12i	0.628767	+	0.363019i
$339$	−5.95519e10	−	1.03147e11i	−0.0133014	−	0.0230387i
$340$	−4.78191e11	−	8.28252e11i	−0.105246	−	0.182292i
$341$			8.88792e12i			1.92765i
$342$	5.44854e12	−	4.62105e11i	1.16453	−	0.0987666i
$343$	−1.81545e12			−0.382396
$344$	3.16155e12	−	1.82532e12i	0.656308	−	0.378920i
$345$	5.48540e10	−	3.16700e10i	0.0112231	−	0.00647966i
$346$	−1.67085e12	+	2.89400e12i	−0.336944	+	0.583604i
$347$	4.11435e12	+	7.12626e12i	0.817813	+	1.41649i	0.907291	+	0.420504i	$0.138147\pi$
$347$	4.11435e12	+	7.12626e12i	0.817813	+	1.41649i	−0.0894780	+	0.995989i	$0.528520\pi$
$348$	−3.23295e9	+	5.59964e9i	−0.000633437	+	0.00109714i
$349$	−1.02016e12			−0.197033			−0.0985166	−	0.995135i	$-0.531410\pi$
$349$	−1.02016e12			−0.197033			−0.0985166	+	0.995135i	$0.531410\pi$
$350$		−	2.39562e11i		−	0.0456118i
$351$	1.14500e11	−	1.98319e11i	0.0214916	−	0.0372245i
$352$	−3.73049e12	−	2.15380e12i	−0.690323	−	0.398558i
$353$	−6.56088e12			−1.19698			−0.598492	−	0.801129i	$-0.704233\pi$
$353$	−6.56088e12			−1.19698			−0.598492	+	0.801129i	$0.704233\pi$
$354$			1.11613e11i			0.0200770i
$355$	1.94473e12	+	1.12279e12i	0.344919	+	0.199139i
$356$	−3.51360e12	+	2.02858e12i	−0.614473	+	0.354766i
$357$	−4.35552e10	−	2.51466e10i	−0.00751102	−	0.00433649i
$358$	1.65920e12	+	2.87382e12i	0.282152	+	0.488702i
$359$	3.16339e12	+	5.47914e12i	0.530493	+	0.918841i	0.999367	+	0.0355760i	$0.0113266\pi$
$359$	3.16339e12	+	5.47914e12i	0.530493	+	0.918841i	−0.468874	+	0.883265i	$0.655340\pi$
$360$			1.99350e12i			0.329688i
$361$	−6.04349e12	+	1.03256e12i	−0.985716	+	0.168414i
$362$	−6.74752e12			−1.08543
$363$	5.33573e10	−	3.08058e10i	0.00846565	−	0.00488765i
$364$	−2.45328e11	+	1.41640e11i	−0.0383919	+	0.0221656i
$365$	2.14499e12	−	3.71524e12i	0.331102	−	0.573485i
$366$	1.12406e11	+	1.94693e11i	0.0171153	+	0.0296446i
$367$	−5.72351e12	+	9.91341e12i	−0.859670	+	1.48899i	0.0125730	+	0.999921i	$0.495998\pi$
$367$	−5.72351e12	+	9.91341e12i	−0.859670	+	1.48899i	−0.872243	+	0.489072i	$0.837336\pi$
$368$	6.90748e12			1.02348
$369$		−	5.32456e12i		−	0.778309i
$370$	2.19103e11	−	3.79498e11i	0.0315966	−	0.0547269i
$371$	1.18259e12	+	6.82768e11i	0.168254	+	0.0971413i
$372$	1.56430e11			0.0219587
$373$			1.06410e13i			1.47379i	0.676005	+	0.736897i	$0.263710\pi$
$373$			1.06410e13i			1.47379i	−0.676005	+	0.736897i	$0.736290\pi$
$374$	1.06950e13	+	6.17476e12i	1.46158	+	0.843843i
$375$	−2.00514e10	+	1.15767e10i	−0.00270388	+	0.00156109i
$376$	8.22253e12	+	4.74728e12i	1.09412	+	0.631692i
$377$	2.30590e11	+	3.99394e11i	0.0302785	+	0.0524439i
$378$	−6.13979e10	−	1.06344e11i	−0.00795599	−	0.0137802i
$379$			3.23284e12i			0.413417i	0.978403	+	0.206708i	$0.0662751\pi$
$379$			3.23284e12i			0.413417i	−0.978403	+	0.206708i	$0.933725\pi$
$380$	1.10564e11	+	1.30363e12i	0.0139539	+	0.164527i
$381$	−2.48840e11			−0.0309953
$382$	1.17714e13	−	6.79622e12i	1.44714	−	0.835509i
$383$	−6.95250e11	+	4.01403e11i	−0.0843621	+	0.0487065i	−0.541588	−	0.840644i	$-0.682177\pi$
$383$	−6.95250e11	+	4.01403e11i	−0.0843621	+	0.0487065i	0.457226	+	0.889351i	$0.348843\pi$
$384$	1.72325e11	−	2.98476e11i	0.0206392	−	0.0357481i
$385$	4.17072e11	+	7.22390e11i	0.0493069	+	0.0854021i
$386$	2.52417e12	−	4.37199e12i	0.294566	−	0.510202i
$387$	−8.90193e12			−1.02549
$388$		−	3.66039e12i		−	0.416264i
$389$	5.78072e12	−	1.00125e13i	0.648983	−	1.12407i	−0.334383	−	0.942437i	$-0.608528\pi$
$389$	5.78072e12	−	1.00125e13i	0.648983	−	1.12407i	0.983366	−	0.181635i	$-0.0581389\pi$
$390$	8.79300e10	+	5.07664e10i	0.00974573	+	0.00562670i
$391$	−9.67126e12			−1.05828
$392$			6.57249e12i			0.710067i
$393$	1.99892e11	+	1.15408e11i	0.0213222	+	0.0123104i
$394$	−1.90346e12	+	1.09897e12i	−0.200477	+	0.115745i
$395$	2.11746e12	+	1.22252e12i	0.220206	+	0.127136i
$396$	2.03145e12	+	3.51857e12i	0.208607	+	0.361318i
$397$	−8.78696e12	−	1.52195e13i	−0.891017	−	1.54329i	−0.838658	−	0.544659i	$-0.816659\pi$
$397$	−8.78696e12	−	1.52195e13i	−0.891017	−	1.54329i	−0.0523597	−	0.998628i	$-0.516674\pi$
$398$		−	1.38153e13i		−	1.38340i
$399$	3.93122e10	+	5.64622e10i	0.00388743	+	0.00558333i
$400$	−2.52497e12			−0.246579
$401$	−4.43840e12	+	2.56251e12i	−0.428060	+	0.247141i	−0.698520	−	0.715591i	$-0.746158\pi$
$401$	−4.43840e12	+	2.56251e12i	−0.428060	+	0.247141i	0.270460	+	0.962731i	$0.412824\pi$
$402$	3.61648e11	−	2.08798e11i	0.0344474	−	0.0198882i
$403$	5.57869e12	−	9.66258e12i	0.524816	−	0.909009i
$404$	−1.53188e12	−	2.65329e12i	−0.142337	−	0.246535i
$405$	2.42756e12	−	4.20466e12i	0.222790	−	0.385883i
$406$	2.47298e11			0.0224177
$407$			1.52582e12i			0.136625i
$408$	−1.85672e11	+	3.21593e11i	−0.0164227	+	0.0284450i
$409$	1.41590e13	+	8.17468e12i	1.23713	+	0.714256i	0.968506	−	0.248990i	$-0.0800985\pi$
$409$	1.41590e13	+	8.17468e12i	1.23713	+	0.714256i	0.268622	+	0.963246i	$0.413432\pi$
$410$	4.72445e12			0.407786
$411$			1.17064e11i			0.00998194i
$412$	1.22842e12	+	7.09229e11i	0.103481	+	0.0597448i
$413$	9.96880e11	−	5.75549e11i	0.0829645	−	0.0478996i
$414$	−1.02186e13	−	5.89973e12i	−0.840217	−	0.485099i
$415$	−4.28549e12	−	7.42268e12i	−0.348145	−	0.603004i
$416$	2.70376e12	+	4.68304e12i	0.217021	+	0.375891i
$417$			7.99924e11i			0.0634407i
$418$	−9.65312e12	−	1.38643e13i	−0.756460	−	1.08647i
$419$	4.21587e12			0.326450			0.163225	−	0.986589i	$-0.447810\pi$
$419$	4.21587e12			0.326450			0.163225	+	0.986589i	$0.447810\pi$
$420$	1.27143e10	−	7.34062e9i	0.000972852	−	0.000561676i
$421$	−2.22780e13	+	1.28622e13i	−1.68448	+	0.972536i	−0.725865	+	0.687837i	$0.758561\pi$
$421$	−2.22780e13	+	1.28622e13i	−1.68448	+	0.972536i	−0.958617	+	0.284700i	$0.908106\pi$
$422$	−1.03947e13	+	1.80041e13i	−0.776691	+	1.34527i
$423$	−1.15760e13	−	2.00503e13i	−0.854787	−	1.48053i
$424$	5.04127e12	−	8.73173e12i	0.367884	−	0.637193i
$425$	3.53524e12			0.254962
$426$			5.10349e11i			0.0363763i
$427$	1.15928e12	−	2.00793e12i	0.0816673	−	0.141452i
$428$	−6.56000e11	−	3.78742e11i	−0.0456757	−	0.0263709i
$429$	−3.53534e11			−0.0243301
$430$		−	7.89863e12i		−	0.537291i
$431$	−3.97859e12	−	2.29704e12i	−0.267512	−	0.154448i	0.360245	−	0.932858i	$-0.382693\pi$
$431$	−3.97859e12	−	2.29704e12i	−0.267512	−	0.154448i	−0.627756	+	0.778410i	$0.716027\pi$
$432$	−1.12086e12	+	6.47131e11i	−0.0744962	+	0.0430104i
$433$	−3.67064e12	−	2.11925e12i	−0.241159	−	0.139233i	0.374551	−	0.927206i	$-0.377797\pi$
$433$	−3.67064e12	−	2.11925e12i	−0.241159	−	0.139233i	−0.615709	+	0.787974i	$0.711130\pi$
$434$	−2.99145e12	−	5.18135e12i	−0.194282	−	0.336507i
$435$	−1.19505e10	−	2.06989e10i	−0.000767257	−	0.00132893i
$436$			6.38348e12i			0.405158i
$437$	1.19756e13	+	5.62310e12i	0.751433	+	0.352832i
$438$	9.74978e11			0.0604817
$439$	2.55813e13	−	1.47694e13i	1.56892	−	0.905815i	0.572623	−	0.819819i	$-0.305926\pi$
$439$	2.55813e13	−	1.47694e13i	1.56892	−	0.905815i	0.996295	−	0.0859961i	$-0.0274073\pi$
$440$	5.33382e12	−	3.07948e12i	0.323426	−	0.186730i
$441$	8.01336e12	−	1.38796e13i	0.480421	−	0.832113i
$442$	−7.75144e12	−	1.34259e13i	−0.459485	−	0.795851i
$443$	1.77421e12	−	3.07302e12i	0.103989	−	0.180114i	−0.809336	−	0.587346i	$-0.800173\pi$
$443$	1.77421e12	−	3.07302e12i	0.103989	−	0.180114i	0.913325	+	0.407232i	$0.133506\pi$
$444$	2.68549e10			0.00155636
$445$		−	1.49972e13i		−	0.859428i
$446$	−1.14644e13	+	1.98569e13i	−0.649644	+	1.12522i
$447$	1.76808e11	+	1.02080e11i	0.00990749	+	0.00572009i
$448$	−1.43672e12			−0.0796127
$449$		−	1.52364e13i		−	0.834931i	−0.908693	−	0.417466i	$-0.862918\pi$
$449$		−	1.52364e13i		−	0.834931i	0.908693	−	0.417466i	$-0.137082\pi$
$450$	3.73533e12	+	2.15660e12i	0.202426	+	0.116871i
$451$	−1.42464e13	+	8.22518e12i	−0.763525	+	0.440822i
$452$	−4.59743e12	−	2.65433e12i	−0.243682	−	0.140690i
$453$	−2.99866e11	−	5.19384e11i	−0.0157194	−	0.0272268i
$454$	−9.09575e12	−	1.57543e13i	−0.471584	−	0.816807i
$455$		−	1.04714e12i		−	0.0536966i
$456$	4.16893e11	−	2.90264e11i	0.0211446	−	0.0147221i
$457$	−2.07703e13			−1.04198			−0.520992	−	0.853561i	$-0.674438\pi$
$457$	−2.07703e13			−1.04198			−0.520992	+	0.853561i	$0.674438\pi$
$458$	3.21422e13	−	1.85573e13i	1.59495	−	0.920848i
$459$	1.56934e12	−	9.06058e11i	0.0770288	−	0.0444726i
$460$	1.41158e12	−	2.44493e12i	0.0685357	−	0.118707i
$461$	−4.28719e12	−	7.42564e12i	−0.205906	−	0.356639i	0.744515	−	0.667606i	$-0.232681\pi$
$461$	−4.28719e12	−	7.42564e12i	−0.205906	−	0.356639i	−0.950421	+	0.310966i	$0.899347\pi$
$462$	−9.47874e10	+	1.64177e11i	−0.00450340	+	0.00780012i
$463$	−2.48168e13			−1.16638			−0.583190	−	0.812336i	$-0.698196\pi$
$463$	−2.48168e13			−1.16638			−0.583190	+	0.812336i	$0.698196\pi$
$464$		−	2.60651e12i		−	0.121191i
$465$	−2.89120e11	+	5.00771e11i	−0.0132988	+	0.0230343i
$466$	−1.22248e12	−	7.05800e11i	−0.0556304	−	0.0321182i
$467$	−3.61942e13			−1.62950			−0.814750	−	0.579813i	$-0.803126\pi$
$467$	−3.61942e13			−1.62950			−0.814750	+	0.579813i	$0.803126\pi$
$468$		−	5.10033e12i		−	0.227179i
$469$	−3.72978e12	−	2.15339e12i	−0.164369	−	0.0948984i
$470$	1.77905e13	−	1.02713e13i	0.775709	−	0.447856i
$471$	−4.65288e11	−	2.68634e11i	−0.0200732	−	0.0115893i
$472$	−4.24961e12	−	7.36053e12i	−0.181401	−	0.314195i
$473$	1.37514e13	+	2.38181e13i	0.580818	+	1.00601i
$474$			5.55679e11i			0.0232237i
$475$	−4.37758e12	−	2.05547e12i	−0.181036	−	0.0850048i
$476$	−2.24165e12			−0.0917346
$477$	−2.12920e13	+	1.22929e13i	−0.862231	+	0.497809i
$478$	1.45990e13	−	8.42874e12i	0.585038	−	0.337772i
$479$	−2.12477e13	+	3.68021e13i	−0.842626	+	1.45947i	0.0450411	+	0.998985i	$0.485658\pi$
$479$	−2.12477e13	+	3.68021e13i	−0.842626	+	1.45947i	−0.887667	+	0.460486i	$0.847675\pi$
$480$	−1.40124e11	−	2.42703e11i	−0.00549930	−	0.00952507i
$481$	9.57713e11	−	1.65881e12i	0.0371972	−	0.0644274i
$482$	5.55258e13			2.13432
$483$		−	1.48462e11i		−	0.00564779i
$484$	1.37307e12	−	2.37822e12i	0.0516969	−	0.0895417i
$485$	1.17178e13	+	6.76527e12i	0.436654	+	0.252102i
$486$	3.31699e12			0.122339
$487$		−	2.20594e13i		−	0.805282i	−0.915358	−	0.402641i	$-0.868092\pi$
$487$		−	2.20594e13i		−	0.805282i	0.915358	−	0.402641i	$-0.131908\pi$
$488$	−1.48257e13	−	8.55961e12i	−0.535692	−	0.309282i
$489$	−1.87307e11	+	1.08142e11i	−0.00669900	+	0.00386767i
$490$	1.23152e13	+	7.11021e12i	0.435976	+	0.251711i
$491$	2.47813e13	+	4.29225e13i	0.868394	+	1.50410i	0.863638	+	0.504113i	$0.168181\pi$
$491$	2.47813e13	+	4.29225e13i	0.868394	+	1.50410i	0.00475589	+	0.999989i	$0.498486\pi$
$492$	1.44766e11	+	2.50742e11i	0.00502159	+	0.00869765i
$493$			3.64941e12i			0.125311i
$494$	1.79224e12	+	2.11317e13i	0.0609201	+	0.718290i
$495$	−1.50184e13			−0.505355
$496$	−5.46112e13	+	3.15298e13i	−1.81917	+	1.05030i
$497$	4.55822e12	−	2.63169e12i	0.150319	−	0.0867865i
$498$	9.73956e11	−	1.68694e12i	0.0317975	−	0.0550748i
$499$	−1.82704e12	−	3.16453e12i	−0.0590535	−	0.102284i	0.834987	−	0.550269i	$-0.185475\pi$
$499$	−1.82704e12	−	3.16453e12i	−0.0590535	−	0.102284i	−0.894041	+	0.447986i	$0.852142\pi$
$500$	−5.15991e11	+	8.93723e11i	−0.0165117	+	0.0285991i
$501$	−6.39815e11			−0.0202706
$502$			5.90875e13i			1.85343i
$503$	2.35056e13	−	4.07128e13i	0.730013	−	1.26442i	−0.226864	−	0.973926i	$-0.572847\pi$
$503$	2.35056e13	−	4.07128e13i	0.730013	−	1.26442i	0.956877	−	0.290493i	$-0.0938193\pi$
$504$	4.04653e12	+	2.33627e12i	0.124432	+	0.0718406i
$505$	1.13251e13			0.344814
$506$			3.64548e13i			1.09901i
$507$	−6.28357e11	−	3.62782e11i	−0.0187571	−	0.0108294i
$508$	−9.60528e12	+	5.54561e12i	−0.283917	+	0.163920i
$509$	−3.34132e13	−	1.92911e13i	−0.977978	−	0.564636i	−0.0763189	−	0.997083i	$-0.524317\pi$
$509$	−3.34132e13	−	1.92911e13i	−0.977978	−	0.564636i	−0.901659	+	0.432448i	$0.857650\pi$
$510$	4.01725e11	+	6.95808e11i	0.0116433	+	0.0201669i
$511$	−5.02762e12	−	8.70809e12i	−0.144297	−	0.249930i
$512$			1.45568e12i			0.0413730i
$513$	−2.47006e12	+	2.09493e11i	−0.0695218	+	0.00589633i
$514$	6.50701e13			1.81370
$515$	−4.54082e12	+	2.62165e12i	−0.125343	+	0.0723666i
$516$	4.19206e11	−	2.42029e11i	0.0114599	−	0.00661635i
$517$	−3.57645e13	+	6.19459e13i	−0.968275	+	1.67710i
$518$	−5.13553e11	−	8.89500e11i	−0.0137701	−	0.0238505i
$519$	3.78504e11	−	6.55589e11i	0.0100516	−	0.0174098i
$520$	−7.73162e12			−0.203354
$521$		−	3.57548e13i		−	0.931420i	−0.884938	−	0.465710i	$-0.845799\pi$
$521$		−	3.57548e13i		−	0.931420i	0.884938	−	0.465710i	$-0.154201\pi$
$522$	−2.22624e12	+	3.85596e12i	−0.0574407	+	0.0994902i
$523$	−4.75918e13	−	2.74771e13i	−1.21625	−	0.702204i	−0.252138	−	0.967691i	$-0.581134\pi$
$523$	−4.75918e13	−	2.74771e13i	−1.21625	−	0.702204i	−0.964114	+	0.265488i	$0.914467\pi$
$524$	1.02878e13			0.260416
$525$			5.42688e10i			0.00136067i
$526$	−3.67451e13	−	2.12148e13i	−0.912579	−	0.526878i
$527$	7.64619e13	−	4.41453e13i	1.88101	−	1.08600i
$528$	1.73041e12	+	9.99055e11i	0.0421678	+	0.0243456i
$529$	6.43886e12	+	1.11524e13i	0.155429	+	0.269210i
$530$	−1.09074e13	−	1.88922e13i	−0.260821	−	0.451756i
$531$			2.07250e13i			0.490932i
$532$	2.77577e12	+	1.30335e12i	0.0651365	+	0.0305846i
$533$	2.06509e13			0.480067
$534$	2.95175e12	−	1.70419e12i	0.0679788	−	0.0392476i
$535$	2.42489e12	−	1.40001e12i	0.0553252	−	0.0319420i
$536$	−1.58997e13	+	2.75391e13i	−0.359390	+	0.622481i
$537$	−3.75865e11	−	6.51017e11i	−0.00841706	−	0.0145788i
$538$	1.00512e13	−	1.74093e13i	0.223002	−	0.386250i
$539$	−4.95150e13			−1.08841
$540$			5.28980e11i			0.0115205i
$541$	2.69723e12	−	4.67175e12i	0.0582013	−	0.100808i	−0.835457	−	0.549556i	$-0.814797\pi$
$541$	2.69723e12	−	4.67175e12i	0.0582013	−	0.100808i	0.893658	+	0.448749i	$0.148130\pi$
$542$	1.82255e13	+	1.05225e13i	0.389656	+	0.224968i
$543$	1.52854e12			0.0323801
$544$			4.27907e13i			0.898162i
$545$	−2.04350e13	−	1.17982e13i	−0.425004	−	0.245376i
$546$	2.06098e11	−	1.18991e11i	0.00424728	−	0.00245217i
$547$	2.89156e13	+	1.66944e13i	0.590466	+	0.340906i	0.765282	−	0.643695i	$-0.222600\pi$
$547$	2.89156e13	+	1.66944e13i	0.590466	+	0.340906i	−0.174816	+	0.984601i	$0.555933\pi$
$548$	2.60887e12	+	4.51870e12i	0.0527898	+	0.0914346i
$549$	2.08722e13	+	3.61518e13i	0.418511	+	0.724883i
$550$		−	1.33257e13i		−	0.264775i
$551$	2.12185e12	−	4.51895e12i	0.0417789	−	0.0889774i
$552$	−1.09618e12			−0.0213887
$553$	4.96309e12	−	2.86544e12i	0.0959679	−	0.0554071i
$554$	3.98019e13	−	2.29796e13i	0.762702	−	0.440346i
$555$	−4.96343e10	+	8.59691e10i	−0.000942577	+	0.00163259i
$556$	1.78270e13	+	3.08772e13i	0.335508	+	0.581117i
$557$	1.90298e13	−	3.29606e13i	0.354943	−	0.614779i	−0.632165	−	0.774833i	$-0.717834\pi$
$557$	1.90298e13	−	3.29606e13i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511670\pi$
$558$	1.07719e14			1.99124
$559$		−	3.45254e13i		−	0.632528i
$560$	−2.95912e12	+	5.12534e12i	−0.0537307	+	0.0930643i
$561$	−2.42278e12	−	1.39879e12i	−0.0436013	−	0.0251732i
$562$	−9.78793e13			−1.74586
$563$			8.49667e13i			1.50213i	0.660230	+	0.751064i	$0.270459\pi$
$563$			8.49667e13i			1.50213i	−0.660230	+	0.751064i	$0.729541\pi$
$564$	1.09027e12	+	6.29467e11i	0.0191046	+	0.0110300i
$565$	1.69943e13	−	9.81165e12i	0.295162	−	0.170412i
$566$	5.06483e13	+	2.92418e13i	0.871933	+	0.503411i
$567$	−5.68993e12	−	9.85524e12i	−0.0970938	−	0.168171i
$568$	−1.94313e13	−	3.36559e13i	−0.328669	−	0.569272i
$569$			1.63925e13i			0.274843i	0.990513	+	0.137421i	$0.0438815\pi$
$569$			1.63925e13i			0.274843i	−0.990513	+	0.137421i	$0.956119\pi$
$570$	−9.28841e10	−	1.09517e12i	−0.00154371	−	0.0182015i
$571$	−7.34384e11			−0.0120988			−0.00604940	−	0.999982i	$-0.501926\pi$
$571$	−7.34384e11			−0.0120988			−0.00604940	+	0.999982i	$0.501926\pi$
$572$	−1.36465e13	+	7.87879e12i	−0.222864	+	0.128671i
$573$	−2.66662e12	+	1.53957e12i	−0.0431706	+	0.0249246i
$574$	5.53678e12	−	9.58999e12i	0.0888583	−	0.153907i
$575$	5.21788e12	+	9.03763e12i	0.0830146	+	0.143786i
$576$	1.29337e13	−	2.24019e13i	0.203991	−	0.353323i
$577$	−5.95229e12			−0.0930690			−0.0465345	−	0.998917i	$-0.514818\pi$
$577$	−5.95229e12			−0.0930690			−0.0465345	+	0.998917i	$0.514818\pi$
$578$		−	4.71898e13i		−	0.731492i
$579$	−5.71810e11	+	9.90403e11i	−0.00878737	+	0.0152202i
$580$	−9.22586e11	−	5.32655e11i	−0.0140562	−	0.00811533i
$581$	−2.00894e13			−0.303449
$582$			3.07506e12i			0.0460510i
$583$	6.57821e13	+	3.79793e13i	0.976708	+	0.563903i
$584$	−6.42968e13	+	3.71218e13i	−0.946510	+	0.546468i
$585$	1.63274e13	+	9.42661e12i	0.238307	+	0.137587i
$586$	1.48700e13	+	2.57557e13i	0.215191	+	0.372722i
$587$	3.06004e13	+	5.30015e13i	0.439073	+	0.760497i	0.997618	−	0.0689772i	$-0.0219736\pi$
$587$	3.06004e13	+	5.30015e13i	0.439073	+	0.760497i	−0.558545	+	0.829474i	$0.688640\pi$
$588$			8.71481e11i			0.0123986i
$589$	−1.20347e14	+	1.02070e13i	−1.69770	+	0.143986i
$590$	−1.83891e13			−0.257218
$591$	4.31199e11	−	2.48953e11i	0.00598054	−	0.00345287i
$592$	−9.37529e12	+	5.41283e12i	−0.128937	+	0.0744416i
$593$	6.44987e13	−	1.11715e14i	0.879584	−	1.52348i	0.0277856	−	0.999614i	$-0.491154\pi$
$593$	6.44987e13	−	1.11715e14i	0.879584	−	1.52348i	0.851798	−	0.523870i	$-0.175512\pi$
$594$	−3.41528e12	−	5.91545e12i	−0.0461843	−	0.0799936i
$595$	4.14310e12	−	7.17607e12i	0.0555573	−	0.0962280i
$596$	9.09975e12			0.121004
$597$			3.12964e12i			0.0412689i
$598$	2.28816e13	−	3.96321e13i	0.299213	−	0.518253i
$599$	6.27040e13	+	3.62022e13i	0.813132	+	0.469462i	0.848042	−	0.529928i	$-0.177781\pi$
$599$	6.27040e13	+	3.62022e13i	0.813132	+	0.469462i	−0.0349102	+	0.999390i	$0.511115\pi$
$600$	4.00697e11			0.00515300
$601$			8.18950e12i			0.104444i	0.998635	+	0.0522222i	$0.0166304\pi$
$601$			8.18950e12i			0.104444i	−0.998635	+	0.0522222i	$0.983370\pi$
$602$	−1.60331e13	−	9.25674e12i	−0.202785	−	0.117078i
$603$	6.71530e13	−	3.87708e13i	0.842323	−	0.486315i
$604$	−2.31498e13	−	1.33655e13i	−0.287980	−	0.166265i
$605$	5.07551e12	+	8.79103e12i	0.0626185	+	0.108458i
$606$	1.28692e12	+	2.22901e12i	0.0157466	+	0.0272740i
$607$			3.36214e12i			0.0408011i	0.999792	+	0.0204006i	$0.00649415\pi$
$607$			3.36214e12i			0.0408011i	−0.999792	+	0.0204006i	$0.993506\pi$
$608$	2.48795e13	−	5.29863e13i	0.299450	−	0.637743i
$609$	−5.60214e10			−0.000668755
$610$	−3.20773e13	+	1.85198e13i	−0.379794	+	0.219274i
$611$	7.77633e13	−	4.48967e13i	0.913206	−	0.527240i
$612$	2.01799e13	−	3.49527e13i	0.235051	−	0.407121i
$613$	−1.77416e13	−	3.07293e13i	−0.204970	−	0.355018i	0.745153	−	0.666893i	$-0.232376\pi$
$613$	−1.77416e13	−	3.07293e13i	−0.204970	−	0.355018i	−0.950123	+	0.311875i	$0.899043\pi$
$614$	−4.55048e13	+	7.88166e13i	−0.521453	+	0.903183i
$615$	−1.07025e12			−0.0121649
$616$		−	1.44359e13i		−	0.162757i
$617$	−5.53258e13	+	9.58271e13i	−0.618731	+	1.07167i	0.370987	+	0.928638i	$0.379020\pi$
$617$	−5.53258e13	+	9.58271e13i	−0.618731	+	1.07167i	−0.989718	+	0.143035i	$0.954314\pi$
$618$	−1.03199e12	−	5.95817e11i	−0.0114480	−	0.00660953i
$619$	−7.37694e13			−0.811752			−0.405876	−	0.913928i	$-0.633033\pi$
$619$	−7.37694e13			−0.811752			−0.405876	+	0.913928i	$0.633033\pi$
$620$			2.57731e13i			0.281325i
$621$	4.63256e12	+	2.67461e12i	0.0501606	+	0.0289602i
$622$	1.07309e14	−	6.19549e13i	1.15262	−	0.665463i
$623$	−3.04423e13	−	1.75758e13i	−0.324367	−	0.187273i
$624$	−1.25416e12	−	2.17226e12i	−0.0132565	−	0.0229609i
$625$	−1.90735e12	−	3.30362e12i	−0.0200000	−	0.0346410i
$626$			1.14896e14i			1.19518i
$627$	2.18676e12	+	3.14074e12i	0.0225664	+	0.0324111i
$628$	−2.39469e13			−0.245161
$629$	1.31265e13	−	7.57857e12i	0.133320	−	0.0769722i
$630$	8.75519e12	−	5.05481e12i	0.0882192	−	0.0509334i
$631$	3.27684e13	−	5.67566e13i	0.327574	−	0.567374i	−0.654456	−	0.756100i	$-0.727102\pi$
$631$	3.27684e13	−	5.67566e13i	0.327574	−	0.567374i	0.982030	+	0.188726i	$0.0604357\pi$
$632$	−2.11572e13	−	3.66453e13i	−0.209832	−	0.363440i
$633$	2.35474e12	−	4.07854e12i	0.0231700	−	0.0401316i
$634$	−2.26887e14			−2.21495
$635$		−	4.09984e13i		−	0.397098i
$636$	6.68448e11	−	1.15779e12i	0.00642366	−	0.0111261i
$637$	5.38307e13	+	3.10792e13i	0.513255	+	0.296328i
$638$	1.37561e13			0.130134
$639$			9.47645e13i			0.889491i
$640$	4.91762e13	+	2.83919e13i	0.457990	+	0.264420i
$641$	2.16904e13	−	1.25230e13i	0.200437	−	0.115722i	−0.396422	−	0.918068i	$-0.629748\pi$
$641$	2.16904e13	−	1.25230e13i	0.200437	−	0.115722i	0.596859	+	0.802346i	$0.296415\pi$
$642$	5.51101e11	+	3.18178e11i	0.00505308	+	0.00291739i
$643$	6.44157e13	+	1.11571e14i	0.586053	+	1.01507i	0.994743	+	0.102400i	$0.0326523\pi$
$643$	6.44157e13	+	1.11571e14i	0.586053	+	1.01507i	−0.408690	+	0.912673i	$0.634014\pi$
$644$	−3.30859e12	−	5.73064e12i	−0.0298685	−	0.0517337i
$645$			1.78931e12i			0.0160283i
$646$	−7.13274e13	+	1.51907e14i	−0.634007	+	1.35026i
$647$	−3.24584e13			−0.286290			−0.143145	−	0.989702i	$-0.545721\pi$
$647$	−3.24584e13			−0.286290			−0.143145	+	0.989702i	$0.545721\pi$
$648$	−7.27669e13	+	4.20120e13i	−0.636882	+	0.367704i
$649$	5.54519e13	−	3.20152e13i	0.481607	−	0.278056i
$650$	−8.36417e12	+	1.44872e13i	−0.0720869	+	0.124858i
$651$	6.77665e11	+	1.17375e12i	0.00579576	+	0.0100385i
$652$	−4.82006e12	+	8.34858e12i	−0.0409086	+	0.0708557i
$653$	4.21194e13			0.354745			0.177373	−	0.984144i	$-0.443240\pi$
$653$	4.21194e13			0.354745			0.177373	+	0.984144i	$0.443240\pi$
$654$		−	5.36271e12i		−	0.0448224i
$655$	−1.90143e13	+	3.29338e13i	−0.157716	+	0.273171i
$656$	−1.01078e14	−	5.83575e13i	−0.832028	−	0.480372i
$657$	1.81040e14			1.47893
$658$		−	4.81497e13i		−	0.390359i
$659$	6.89936e13	+	3.98334e13i	0.555113	+	0.320495i	0.751182	−	0.660096i	$-0.229484\pi$
$659$	6.89936e13	+	3.98334e13i	0.555113	+	0.320495i	−0.196069	+	0.980590i	$0.562818\pi$
$660$	7.07240e11	−	4.08325e11i	0.00564738	−	0.00326052i
$661$	−8.32314e13	−	4.80537e13i	−0.659599	−	0.380820i	0.132525	−	0.991180i	$-0.457691\pi$
$661$	−8.32314e13	−	4.80537e13i	−0.659599	−	0.380820i	−0.792124	+	0.610360i	$0.791025\pi$
$662$	−6.26583e13	−	1.08527e14i	−0.492821	−	0.853590i
$663$	1.75596e12	+	3.04142e12i	0.0137072	+	0.0237415i
$664$			1.48331e14i			1.14919i
$665$	−9.30260e12	+	6.47700e12i	−0.0715313	+	0.0498041i
$666$	1.84925e13			0.141132
$667$	−9.32949e12	+	5.38639e12i	−0.0706690	+	0.0408008i
$668$	−2.46970e13	+	1.42588e13i	−0.185679	+	0.107202i
$669$	2.59707e12	−	4.49825e12i	0.0193799	−	0.0335670i
$670$	3.44011e13	+	5.95844e13i	0.254799	+	0.441325i
$671$	6.44853e13	−	1.11692e14i	0.474076	−	0.821124i
$672$	−6.56871e11			−0.00479329
$673$		−	2.52538e14i		−	1.82916i	−0.404405	−	0.914580i	$-0.632521\pi$
$673$		−	2.52538e14i		−	1.82916i	0.404405	−	0.914580i	$-0.367479\pi$
$674$	5.64418e13	−	9.77600e13i	0.405790	−	0.702849i
$675$	−1.69339e12	−	9.77680e11i	−0.0120848	−	0.00697714i
$676$	−3.23396e13			−0.229087
$677$			2.03623e14i			1.43180i	0.698201	+	0.715902i	$0.253984\pi$
$677$			2.03623e14i			1.43180i	−0.698201	+	0.715902i	$0.746016\pi$
$678$	3.86226e12	+	2.22988e12i	0.0269583	+	0.0155644i
$679$	2.74652e13	−	1.58570e13i	0.190298	−	0.109868i
$680$	−5.29850e13	−	3.05909e13i	−0.364425	−	0.210401i
$681$	2.06049e12	+	3.56888e12i	0.0140681	+	0.0243667i
$682$	−1.66401e14	−	2.88215e14i	−1.12780	−	1.95341i
$683$			1.19718e14i			0.805480i	0.915314	+	0.402740i	$0.131942\pi$
$683$			1.19718e14i			0.805480i	−0.915314	+	0.402740i	$0.868058\pi$
$684$	−4.53105e13	+	3.15477e13i	−0.302634	+	0.210711i
$685$	−1.92873e13			−0.127884
$686$	5.88708e13	−	3.39891e13i	0.387507	−	0.223727i
$687$	−7.28130e12	+	4.20386e12i	−0.0475801	+	0.0274704i
$688$	−9.75657e13	+	1.68989e14i	−0.632929	+	1.09627i
$689$	−4.76771e13	−	8.25791e13i	−0.307053	−	0.531831i
$690$	−1.18586e12	+	2.05397e12i	−0.00758207	+	0.0131325i
$691$	2.03087e14			1.28912			0.644559	−	0.764555i	$-0.277041\pi$
$691$	2.03087e14			1.28912			0.644559	+	0.764555i	$0.277041\pi$
$692$		−	3.37411e13i		−	0.212632i
$693$	−1.76007e13	+	3.04853e13i	−0.110119	+	0.190732i
$694$	−2.66838e14	−	1.54059e14i	−1.65749	−	0.956950i
$695$	−1.31794e14			−0.812776
$696$			4.13638e11i			0.00253264i
$697$	1.41521e14	+	8.17071e13i	0.860313	+	0.496702i
$698$	3.30813e13	−	1.90995e13i	0.199667	−	0.115278i
$699$	2.76933e11	+	1.59887e11i	0.00165955	+	0.000958139i
$700$	1.20942e12	+	2.09479e12i	0.00719596	+	0.0124638i
$701$	−5.10523e13	−	8.84252e13i	−0.301596	−	0.522379i	0.674902	−	0.737908i	$-0.264186\pi$
$701$	−5.10523e13	−	8.84252e13i	−0.301596	−	0.522379i	−0.976498	+	0.215528i	$0.930853\pi$
$702$			8.57471e12i			0.0502961i
$703$	−2.06604e13	+	1.75227e12i	−0.120327	+	0.0102052i
$704$	−7.99182e13			−0.462150
$705$	−4.03015e12	+	2.32681e12i	−0.0231406	+	0.0133603i
$706$	2.12754e14	−	1.22834e14i	1.21298	−	0.700316i
$707$	1.32724e13	−	2.29884e13i	0.0751365	−	0.130140i
$708$	−5.63478e11	−	9.75972e11i	−0.00316745	−	0.00548619i
$709$	−5.26622e13	+	9.12136e13i	−0.293946	+	0.509130i	−0.974739	−	0.223346i	$-0.928302\pi$
$709$	−5.26622e13	+	9.12136e13i	−0.293946	+	0.509130i	0.680793	+	0.732476i	$0.261635\pi$
$710$	−8.40840e13			−0.466038
$711$			1.03182e14i			0.567877i
$712$	−1.29773e14	+	2.24773e14i	−0.709223	+	1.22841i
$713$	2.25709e14	+	1.30313e14i	1.22490	+	0.707198i
$714$	1.88319e12			0.0101485
$715$		−	5.82475e13i		−	0.311707i
$716$	−2.90169e13	−	1.67529e13i	−0.154201	−	0.0890277i
$717$	−3.30717e12	+	1.90940e12i	−0.0174526	+	0.0100763i
$718$	−2.05163e14	−	1.18451e14i	−1.07517	−	0.620748i
$719$	1.56648e14	+	2.71323e14i	0.815233	+	1.41202i	0.909161	+	0.416446i	$0.136724\pi$
$719$	1.56648e14	+	2.71323e14i	0.815233	+	1.41202i	−0.0939275	+	0.995579i	$0.529942\pi$
$720$	−5.32775e13	−	9.22794e13i	−0.275348	−	0.476916i
$721$			1.22897e13i			0.0630760i
$722$	1.76645e14	−	1.46631e14i	0.900358	−	0.747375i
$723$	−1.25785e13			−0.0636702
$724$	5.90020e13	−	3.40648e13i	0.296602	−	0.171243i
$725$	3.41031e12	−	1.96895e12i	0.0170257	−	0.00982978i
$726$	−1.15350e12	+	1.99792e12i	−0.00571920	+	0.00990595i
$727$	−1.16165e14	−	2.01204e14i	−0.572010	−	0.990750i	−0.996359	−	0.0852517i	$-0.972831\pi$
$727$	−1.16165e14	−	2.01204e14i	−0.572010	−	0.990750i	0.424350	−	0.905498i	$-0.360503\pi$
$728$	−9.06102e12	+	1.56941e13i	−0.0443119	+	0.0767504i
$729$	2.04387e14			0.992696
$730$			1.60635e14i			0.774867i
$731$	1.36603e14	−	2.36603e14i	0.654446	−	1.13353i
$732$	−1.96581e12	−	1.13496e12i	−0.00935378	−	0.00540041i
$733$	3.25560e13			0.153855			0.0769275	−	0.997037i	$-0.475489\pi$
$733$	3.25560e13			0.153855			0.0769275	+	0.997037i	$0.475489\pi$
$734$		−	4.28625e14i		−	2.01186i
$735$	−2.78982e12	−	1.61070e12i	−0.0130059	−	0.00750894i
$736$	−1.09392e14	+	6.31573e13i	−0.506519	+	0.292439i
$737$	−2.07471e14	−	1.19783e14i	−0.954156	−	0.550882i
$738$	9.96872e13	+	1.72663e14i	0.455363	+	0.788711i
$739$	−2.01556e13	−	3.49104e13i	−0.0914476	−	0.158392i	0.816673	−	0.577101i	$-0.195816\pi$
$739$	−2.01556e13	−	3.49104e13i	−0.0914476	−	0.158392i	−0.908120	+	0.418709i	$0.862483\pi$
$740$			4.42456e12i			0.0199394i
$741$	−4.06002e11	−	4.78705e12i	−0.00181734	−	0.0214278i
$742$	−5.11315e13			−0.227337
$743$	2.93809e13	−	1.69631e13i	0.129754	−	0.0749136i	−0.433718	−	0.901049i	$-0.642799\pi$
$743$	2.93809e13	−	1.69631e13i	0.129754	−	0.0749136i	0.563472	+	0.826135i	$0.309465\pi$
$744$	8.66647e12	−	5.00359e12i	0.0380170	−	0.0219491i
$745$	−1.68185e13	+	2.91305e13i	−0.0732834	+	0.126931i
$746$	−1.99222e14	−	3.45062e14i	−0.862268	−	1.49349i
$747$	1.80850e14	−	3.13241e14i	0.777526	−	1.34672i
$748$	−1.24693e14			−0.532517
$749$		−	6.56293e12i		−	0.0278412i
$750$	4.33480e11	−	7.50810e11i	0.00182668	−	0.00316391i
$751$	−2.85015e14	−	1.64553e14i	−1.19307	−	0.688822i	−0.234071	−	0.972219i	$-0.575205\pi$
$751$	−2.85015e14	−	1.64553e14i	−1.19307	−	0.688822i	−0.959002	+	0.283398i	$0.908538\pi$
$752$	−5.07496e14			−2.11030
$753$		−	1.33853e13i		−	0.0552910i
$754$	−1.49550e13	−	8.63429e12i	−0.0613664	−	0.0354299i
$755$	8.55726e13	−	4.94054e13i	0.348819	−	0.201391i
$756$	1.07376e12	+	6.19934e11i	0.00434807	+	0.00251036i
$757$	1.40205e14	+	2.42843e14i	0.564008	+	0.976891i	0.997141	+	0.0755608i	$0.0240747\pi$
$757$	1.40205e14	+	2.42843e14i	0.564008	+	0.976891i	−0.433133	+	0.901330i	$0.642592\pi$
$758$	−6.05257e13	−	1.04834e14i	−0.241877	−	0.418942i
$759$		−	8.25824e12i		−	0.0327852i
$760$	4.78234e13	+	6.86864e13i	0.188613	+	0.270896i
$761$	−4.39248e13			−0.172102			−0.0860510	−	0.996291i	$-0.527425\pi$
$761$	−4.39248e13			−0.172102			−0.0860510	+	0.996291i	$0.527425\pi$
$762$	8.06931e12	−	4.65882e12i	0.0314096	−	0.0181343i
$763$	−4.78974e13	+	2.76536e13i	−0.185221	+	0.106937i
$764$	−6.86214e13	+	1.18856e14i	−0.263629	+	0.456618i
$765$	7.45946e13	+	1.29202e14i	0.284708	+	0.493129i
$766$	1.50302e13	−	2.60332e13i	0.0569931	−	0.0987150i
$767$	−8.03800e13			−0.302811
$768$			9.09549e12i			0.0340424i
$769$	−6.85104e13	+	1.18663e14i	−0.254756	+	0.441250i	−0.964829	−	0.262877i	$-0.915329\pi$
$769$	−6.85104e13	+	1.18663e14i	−0.254756	+	0.441250i	0.710073	+	0.704128i	$0.248662\pi$
$770$	−2.70494e13	−	1.56170e13i	−0.0999319	−	0.0576957i
$771$	−1.47406e13			−0.0541056
$772$			5.09730e13i			0.185889i
$773$	1.04971e14	+	6.06052e13i	0.380341	+	0.219590i	0.677967	−	0.735093i	$-0.262861\pi$
$773$	1.04971e14	+	6.06052e13i	0.380341	+	0.219590i	−0.297626	+	0.954683i	$0.596195\pi$
$774$	2.88669e14	−	1.66663e14i	1.03919	−	0.599978i
$775$	−8.25060e13	−	4.76349e13i	−0.295105	−	0.170379i
$776$	−1.17081e14	−	2.02791e14i	−0.416083	−	0.720676i
$777$	1.16337e11	+	2.01502e11i	0.000410784	+	0.000711498i
$778$			4.32909e14i			1.51879i
$779$	−1.27734e14	−	1.83459e14i	−0.445267	−	0.639516i
$780$	−1.02518e12			−0.00355079
$781$	2.53553e14	−	1.46389e14i	0.872596	−	0.503794i
$782$	3.13617e14	−	1.81067e14i	1.07242	−	0.619163i
$783$	1.00925e12	−	1.74808e12i	0.00342919	−	0.00593953i
$784$	−1.75654e14	−	3.04241e14i	−0.593031	−	1.02716i
$785$	4.42596e13	−	7.66599e13i	0.148477	−	0.257170i
$786$	−8.64272e12			−0.0288096
$787$		−	3.08386e13i		−	0.102146i	−0.998695	−	0.0510729i	$-0.983736\pi$
$787$		−	3.08386e13i		−	0.102146i	0.998695	−	0.0510729i	$-0.0162641\pi$
$788$	1.10962e13	−	1.92193e13i	0.0365212	−	0.0632566i
$789$	8.32400e12	+	4.80587e12i	0.0272237	+	0.0157176i
$790$	−9.15525e13			−0.297533
$791$		−	4.59948e13i		−	0.148534i
$792$	2.25090e14	+	1.29956e14i	0.722322	+	0.417033i
$793$	−1.40212e14	+	8.09512e13i	−0.447114	+	0.258141i
$794$	5.69882e14	+	3.29021e14i	1.80585	+	1.04261i
$795$	2.47090e12	+	4.27973e12i	0.00778072	+	0.0134766i
$796$	6.97467e13	+	1.20805e14i	0.218252	+	0.378024i
$797$			1.86476e14i			0.579871i	0.957046	+	0.289935i	$0.0936338\pi$
$797$			1.86476e14i			0.579871i	−0.957046	+	0.289935i	$0.906366\pi$
$798$	−2.33190e12	−	1.09493e12i	−0.00720601	−	0.00338355i
$799$	7.10552e14			2.18204
$800$	3.99872e13	−	2.30866e13i	0.122031	−	0.0704547i
$801$	5.48098e14	−	3.16445e14i	1.66225	−	0.959699i
$802$	9.59514e13	−	1.66193e14i	0.289188	−	0.500888i
$803$	−2.79663e14	−	4.84391e14i	−0.837641	−	1.45084i
$804$	−2.10823e12	+	3.65156e12i	−0.00627534	+	0.0108692i
$805$	2.44602e13			0.0723571
$806$			4.17780e14i			1.22821i
$807$	−2.27695e12	+	3.94378e12i	−0.00665250	+	0.0115225i
$808$	−1.69736e14	−	9.79974e13i	−0.492854	−	0.284549i
$809$	−3.54388e14			−1.02267			−0.511335	−	0.859381i	$-0.670849\pi$
$809$	−3.54388e14			−1.02267			−0.511335	+	0.859381i	$0.670849\pi$
$810$			1.81797e14i			0.521388i
$811$	8.55454e13	+	4.93896e13i	0.243833	+	0.140777i	0.616937	−	0.787012i	$-0.288373\pi$
$811$	8.55454e13	+	4.93896e13i	0.243833	+	0.140777i	−0.373104	+	0.927789i	$0.621707\pi$
$812$	−2.16244e12	+	1.24848e12i	−0.00612580	+	0.00353673i
$813$	−4.12868e12	−	2.38370e12i	−0.0116241	−	0.00671117i
$814$	−2.85666e13	−	4.94788e13i	−0.0799349	−	0.138451i
$815$	−1.78172e13	−	3.08603e13i	−0.0495509	−	0.0858247i
$816$		−	1.98488e13i		−	0.0548634i
$817$	−3.06718e14	+	2.13554e14i	−0.842615	+	0.586676i
$818$	−6.12190e14			−1.67155
$819$	3.82695e13	−	2.20949e13i	0.103856	−	0.0599615i
$820$	−4.13118e13	+	2.38514e13i	−0.111431	+	0.0643345i
$821$	−2.75456e14	+	4.77104e14i	−0.738477	+	1.27908i	0.214704	+	0.976679i	$0.431121\pi$
$821$	−2.75456e14	+	4.77104e14i	−0.738477	+	1.27908i	−0.953181	+	0.302400i	$0.902212\pi$
$822$	−2.19169e12	−	3.79612e12i	−0.00584010	−	0.0101154i
$823$	−3.65704e14	+	6.33418e14i	−0.968569	+	1.67761i	−0.268866	+	0.963178i	$0.586649\pi$
$823$	−3.65704e14	+	6.33418e14i	−0.968569	+	1.67761i	−0.699703	+	0.714434i	$0.746684\pi$
$824$	9.07417e13			0.238875
$825$			3.01873e12i			0.00789867i
$826$	−2.15510e13	+	3.73275e13i	−0.0560489	+	0.0970796i
$827$	3.07766e14	+	1.77689e14i	0.795597	+	0.459338i	0.841929	−	0.539588i	$-0.181420\pi$
$827$	3.07766e14	+	1.77689e14i	0.795597	+	0.459338i	−0.0463322	+	0.998926i	$0.514753\pi$
$828$	1.19139e14			0.306128
$829$			2.70660e14i			0.691275i	0.938368	+	0.345638i	$0.112337\pi$
$829$			2.70660e14i			0.691275i	−0.938368	+	0.345638i	$0.887663\pi$
$830$	2.77937e14	+	1.60467e14i	0.705596	+	0.407376i
$831$	−9.01648e12	+	5.20567e12i	−0.0227526	+	0.0131362i
$832$	8.68838e13	+	5.01624e13i	0.217933	+	0.125824i
$833$	2.45935e14	+	4.25973e14i	0.613192	+	1.06208i
$834$	−1.49763e13	−	2.59397e13i	−0.0371171	−	0.0642887i
$835$		−	1.05415e14i		−	0.259698i
$836$	1.54403e14	+	7.24993e13i	0.378116	+	0.177543i
$837$	−4.88339e13			−0.118876
$838$	−1.36711e14	+	7.89301e13i	−0.330813	+	0.190995i
$839$	−1.22590e14	+	7.07771e13i	−0.294879	+	0.170248i	−0.640140	−	0.768258i	$-0.721124\pi$
$839$	−1.22590e14	+	7.07771e13i	−0.294879	+	0.170248i	0.345261	+	0.938507i	$0.387790\pi$
$840$	4.69595e11	−	8.13362e11i	0.00112286	−	0.00194486i
$841$	−2.08321e14	−	3.60823e14i	−0.495169	−	0.857657i
$842$	4.81617e14	−	8.34185e14i	1.13800	−	1.97107i
$843$	2.21730e13			0.0520818
$844$		−	2.09910e14i		−	0.490140i
$845$	5.97712e13	−	1.03527e14i	0.138742	−	0.240309i
$846$	7.50768e14	+	4.33456e14i	1.73242	+	1.00022i
$847$	2.37928e13			0.0545794
$848$			5.38924e14i			1.22899i
$849$	−1.14736e13	−	6.62426e12i	−0.0260112	−	0.0150175i
$850$	−1.14640e14	+	6.61873e13i	−0.258369	+	0.149170i
$851$	3.87483e13	+	2.23713e13i	0.0868170	+	0.0501238i
$852$	−2.57649e12	−	4.46262e12i	−0.00573893	−	0.00994012i
$853$	2.87079e14	+	4.97235e14i	0.635705	+	1.10107i	0.986365	+	0.164571i	$0.0526240\pi$
$853$	2.87079e14	+	4.97235e14i	0.635705	+	1.10107i	−0.350660	+	0.936503i	$0.614043\pi$
$854$			8.68166e13i			0.191123i
$855$	−1.72473e13	−	2.03357e14i	−0.0377476	−	0.445071i
$856$	−4.84578e13			−0.105438
$857$	−5.38833e14	+	3.11095e14i	−1.16560	+	0.672960i	−0.952640	−	0.304101i	$-0.901644\pi$
$857$	−5.38833e14	+	3.11095e14i	−1.16560	+	0.672960i	−0.212961	+	0.977061i	$0.568311\pi$
$858$	1.14643e13	−	6.61891e12i	0.0246553	−	0.0142348i
$859$	−1.09482e13	+	1.89628e13i	−0.0234087	+	0.0405450i	−0.877492	−	0.479590i	$-0.840785\pi$
$859$	−1.09482e13	+	1.89628e13i	−0.0234087	+	0.0405450i	0.854084	+	0.520136i	$0.174119\pi$
$860$	3.98762e13	+	6.90676e13i	0.0847659	+	0.146819i
$861$	−1.25427e12	+	2.17246e12i	−0.00265079	+	0.00459130i
$862$	1.72022e14			0.361450
$863$		−	2.70509e13i		−	0.0565103i	−0.999601	−	0.0282552i	$-0.991005\pi$
$863$		−	2.70509e13i		−	0.0565103i	0.999601	−	0.0282552i	$-0.00899509\pi$
$864$	1.18339e13	−	2.04968e13i	0.0245786	−	0.0425714i
$865$	1.08013e14	+	6.23616e13i	0.223048	+	0.128777i
$866$	1.58707e14			0.325842
$867$			1.06901e13i			0.0218216i
$868$	5.23160e13	+	3.02047e13i	0.106178	+	0.0613021i
$869$	2.76074e14	−	1.59391e14i	0.557091	−	0.321637i
$870$	7.75057e11	+	4.47479e11i	0.00155502	+	0.000897794i
$871$	1.50369e14	+	2.60447e14i	0.299963	+	0.519552i
$872$	2.04182e14	+	3.53654e14i	0.404982	+	0.701449i
$873$			5.70996e14i			1.12606i
$874$	−4.93618e14	+	4.18650e13i	−0.967907	+	0.0820908i
$875$	−8.94121e12			−0.0174324
$876$	−8.52545e12	+	4.92217e12i	−0.0165271	+	0.00954193i
$877$	5.36197e14	−	3.09574e14i	1.03354	−	0.596714i	0.115542	−	0.993303i	$-0.463139\pi$
$877$	5.36197e14	−	3.09574e14i	1.03354	−	0.596714i	0.917996	+	0.396589i	$0.129806\pi$
$878$	−5.53029e14	+	9.57874e14i	−1.05993	+	1.83584i
$879$	−3.36857e12	−	5.83453e12i	−0.00641950	−	0.0111189i
$880$	−1.64602e14	+	2.85100e14i	−0.311905	+	0.540236i
$881$	−2.01693e14			−0.380024			−0.190012	−	0.981782i	$-0.560853\pi$
$881$	−2.01693e14			−0.380024			−0.190012	+	0.981782i	$0.560853\pi$
$882$			6.00109e14i			1.12431i
$883$	−3.21953e14	+	5.57639e14i	−0.599776	+	1.03884i	0.393078	+	0.919505i	$0.371410\pi$
$883$	−3.21953e14	+	5.57639e14i	−0.599776	+	1.03884i	−0.992854	+	0.119337i	$0.961923\pi$
$884$	1.35561e14	+	7.82662e13i	0.251115	+	0.144982i
$885$	4.16576e12			0.00767323
$886$			1.32868e14i			0.243361i
$887$	−2.16569e14	−	1.25036e14i	−0.394438	−	0.227729i	0.289643	−	0.957135i	$-0.406463\pi$
$887$	−2.16569e14	−	1.25036e14i	−0.394438	−	0.227729i	−0.684081	+	0.729406i	$0.739797\pi$
$888$	1.48780e12	−	8.58983e11i	0.00269451	−	0.00155568i
$889$	−8.32212e13	−	4.80478e13i	−0.149874	−	0.0865296i
$890$	2.80779e14	+	4.86324e14i	0.502823	+	0.870915i
$891$	−3.16505e14	−	5.48202e14i	−0.563627	−	0.976230i
$892$		−	2.31511e14i		−	0.409966i
$893$	−8.79854e14	−	4.13132e14i	−1.54936	−	0.727497i
$894$	−7.64462e12			−0.0133865
$895$	1.07260e14	−	6.19267e13i	0.186777	−	0.107836i
$896$	1.15264e14	−	6.65474e13i	0.199596	−	0.115237i
$897$	−5.18346e12	+	8.97802e12i	−0.00892602	+	0.0154603i
$898$	2.85258e14	+	4.94082e14i	0.488491	+	0.846091i
$899$	4.91732e13	−	8.51705e13i	0.0837395	−	0.145041i
$900$	−4.35502e13			−0.0737527
$901$		−	7.54556e14i		−	1.27077i
$902$	3.07986e14	−	5.33448e14i	0.515820	−	0.893427i
$903$	3.63205e12	+	2.09697e12i	0.00604941	+	0.00349263i
$904$	−3.39606e14			−0.562513
$905$			2.51839e14i			0.414840i
$906$	1.94479e13	+	1.12283e13i	0.0318590	+	0.0183938i
$907$	−1.77377e14	+	1.02409e14i	−0.288976	+	0.166840i	−0.637480	−	0.770467i	$-0.720023\pi$
$907$	−1.77377e14	+	1.02409e14i	−0.288976	+	0.166840i	0.348504	+	0.937307i	$0.386690\pi$
$908$	1.59071e14	+	9.18396e13i	0.257728	+	0.148799i
$909$	2.38962e14	+	4.13895e14i	0.385044	+	0.666916i
$910$	1.96047e13	+	3.39563e13i	0.0314161	+	0.0544143i
$911$		−	1.87292e14i		−	0.298489i	−0.988800	−	0.149245i	$-0.952316\pi$
$911$		−	1.87292e14i		−	0.298489i	0.988800	−	0.149245i	$-0.0476842\pi$
$912$	−1.15405e13	+	2.45781e13i	−0.0182916	+	0.0389560i
$913$	−1.11748e15			−1.76151
$914$	6.73532e14	−	3.88864e14i	1.05591	−	0.609631i
$915$	7.26658e12	−	4.19536e12i	0.0113299	−	0.00654130i
$916$	−1.87373e14	+	3.24540e14i	−0.290556	+	0.503257i
$917$	4.45674e13	+	7.71930e13i	0.0687339	+	0.119051i
$918$	−3.39267e13	+	5.87627e13i	−0.0520389	+	0.0901340i
$919$	1.06891e15			1.63066			0.815331	−	0.578994i	$-0.196555\pi$
$919$	1.06891e15			1.63066			0.815331	+	0.578994i	$0.196555\pi$
$920$		−	1.80604e14i		−	0.274023i
$921$	1.03084e13	−	1.78546e13i	0.0155558	−	0.0269434i
$922$	2.78048e14	+	1.60531e14i	0.417316	+	0.240937i
$923$	−3.67536e14			−0.548646
$924$		−	1.91413e12i		−	0.00284192i
$925$	−1.41641e13	−	8.17764e12i	−0.0209161	−	0.0120759i
$926$	8.04751e14	−	4.64623e14i	1.18197	−	0.682411i
$927$	−1.91625e14	−	1.10635e14i	−0.279933	−	0.161619i
$928$	2.38322e13	+	4.12785e13i	0.0346277	+	0.0599770i
$929$	−5.82918e14	−	1.00964e15i	−0.842420	−	1.45911i	−0.887843	−	0.460146i	$-0.847797\pi$
$929$	−5.82918e14	−	1.00964e15i	−0.842420	−	1.45911i	0.0454234	−	0.998968i	$-0.485536\pi$
$930$		−	2.16518e13i		−	0.0311229i
$931$	−5.68635e13	−	6.70461e14i	−0.0812991	−	0.958573i
$932$	1.42529e13			0.0202686
$933$	−2.43091e13	+	1.40349e13i	−0.0343844	+	0.0198518i
$934$	1.17369e15	−	6.77632e14i	1.65128	−	0.953366i
$935$	2.30462e14	−	3.99172e14i	0.322509	−	0.558601i
$936$	−1.63139e14	−	2.82566e14i	−0.227080	−	0.393314i
$937$	8.40925e13	−	1.45653e14i	0.116429	−	0.201660i	−0.801921	−	0.597430i	$-0.796189\pi$
$937$	8.40925e13	−	1.45653e14i	0.116429	−	0.201660i	0.918350	+	0.395769i	$0.129522\pi$
$938$	1.61264e14			0.222088
$939$		−	2.60278e13i		−	0.0356540i
$940$	−1.03710e14	+	1.79630e14i	−0.141312	+	0.244760i
$941$	1.48770e14	+	8.58924e13i	0.201636	+	0.116414i	0.597418	−	0.801930i	$-0.296193\pi$
$941$	1.48770e14	+	8.58924e13i	0.201636	+	0.116414i	−0.395783	+	0.918344i	$0.629527\pi$
$942$	2.01176e13			0.0271220
$943$			4.82386e14i			0.646898i
$944$	3.93430e14	+	2.27147e14i	0.524816	+	0.303003i
$945$	−3.96911e12	+	2.29157e12i	−0.00526665	+	0.00304070i
$946$	−8.91851e14	−	5.14910e14i	−1.17716	−	0.679635i
$947$	4.14010e14	+	7.17087e14i	0.543577	+	0.941503i	0.998695	+	0.0510721i	$0.0162638\pi$
$947$	4.14010e14	+	7.17087e14i	0.543577	+	0.941503i	−0.455118	+	0.890431i	$0.650403\pi$
$948$	−2.80534e12	−	4.85899e12i	−0.00366390	−	0.00634607i
$949$			7.02147e14i			0.912215i
$950$	1.80438e14	−	1.53034e13i	0.233190	−	0.0197774i
$951$	5.13975e13			0.0660754
$952$	−1.24191e14	+	7.17016e13i	−0.158820	+	0.0916947i
$953$	−1.27048e14	+	7.33509e13i	−0.161622	+	0.0933128i	−0.578630	−	0.815590i	$-0.696412\pi$
$953$	−1.27048e14	+	7.33509e13i	−0.161622	+	0.0933128i	0.417007	+	0.908903i	$0.363079\pi$
$954$	4.60300e14	−	7.97262e14i	0.582504	−	1.00893i
$955$	−2.53657e14	−	4.39347e14i	−0.319323	−	0.553084i
$956$	−8.51049e13	+	1.47406e14i	−0.106577	+	0.184598i
$957$	−3.11621e12			−0.00388211
$958$		−	1.59121e15i		−	1.97197i
$959$	−2.26036e13	+	3.91505e13i	−0.0278666	+	0.0482663i
$960$	−4.50283e12	−	2.59971e12i	−0.00552241	−	0.00318837i
$961$	−1.55968e15			−1.90291
$962$			7.17218e13i			0.0870514i
$963$	1.02332e14	+	5.90812e13i	0.123560	+	0.0713375i
$964$	−4.85531e14	+	2.80322e14i	−0.583220	+	0.336722i
$965$	−1.63177e14	−	9.42102e13i	−0.194994	−	0.112580i
$966$	2.77952e12	+	4.81427e12i	0.00330433	+	0.00572327i
$967$	−7.59527e14	−	1.31554e15i	−0.898278	−	1.55586i	−0.829694	−	0.558218i	$-0.811485\pi$
$967$	−7.59527e14	−	1.31554e15i	−0.898278	−	1.55586i	−0.0685843	−	0.997645i	$-0.521848\pi$
$968$		−	1.75676e14i		−	0.206698i
$969$	1.61581e13	−	3.44122e13i	0.0189134	−	0.0402803i
$970$	−5.06641e14			−0.589986
$971$	3.64635e13	−	2.10522e13i	0.0422438	−	0.0243894i	−0.478729	−	0.877963i	$-0.658902\pi$
$971$	3.64635e13	−	2.10522e13i	0.0422438	−	0.0243894i	0.520973	+	0.853573i	$0.325569\pi$
$972$	−2.90046e13	+	1.67458e13i	−0.0334299	+	0.0193008i
$973$	−1.54455e14	+	2.67524e14i	−0.177108	+	0.306759i
$974$	4.12998e14	+	7.15334e14i	0.471144	+	0.816045i
$975$	1.89477e12	−	3.28184e12i	0.00215047	−	0.00372472i
$976$	9.15044e14			1.03322
$977$		−	1.45308e14i		−	0.163237i	−0.996664	−	0.0816184i	$-0.973991\pi$
$977$		−	1.45308e14i		−	0.163237i	0.996664	−	0.0816184i	$-0.0260089\pi$
$978$	4.04929e12	−	7.01358e12i	0.00452569	−	0.00783872i
$979$	−1.69336e15	−	9.77664e14i	−1.88294	−	1.08712i
$980$	−1.43583e14			−0.158845
$981$		−	9.95779e14i		−	1.09602i
$982$	−1.60720e15	−	9.27918e14i	−1.76000	−	1.01614i
$983$	1.03635e15	−	5.98336e14i	1.12911	−	0.651895i	0.185403	−	0.982663i	$-0.440641\pi$
$983$	1.03635e15	−	5.98336e14i	1.12911	−	0.651895i	0.943712	+	0.330768i	$0.107308\pi$
$984$	1.60405e13	+	9.26099e12i	0.0173877	+	0.0100388i
$985$	4.10170e13	+	7.10435e13i	0.0442367	+	0.0766202i
$986$	−6.83248e13	−	1.18342e14i	−0.0733152	−	0.126986i
$987$			1.09075e13i			0.0116450i
$988$	−1.22355e14	−	1.75733e14i	−0.129968	−	0.186667i
$989$	8.06483e14			0.852341
$990$	4.87011e14	−	2.81176e14i	0.512110	−	0.295667i
$991$	3.94323e14	−	2.27662e14i	0.412557	−	0.238190i	−0.279331	−	0.960195i	$-0.590113\pi$
$991$	3.94323e14	−	2.27662e14i	0.412557	−	0.238190i	0.691888	+	0.722005i	$0.256779\pi$
$992$	5.76574e14	−	9.98656e14i	0.600201	−	1.03958i
$993$	1.41942e13	+	2.45851e13i	0.0147016	+	0.0254640i
$994$	−9.85417e13	+	1.70679e14i	−0.101552	+	0.175893i
$995$	−5.15634e14			−0.528720
$996$			1.96680e13i			0.0200662i
$997$	5.77598e13	−	1.00043e14i	0.0586340	−	0.101557i	−0.835218	−	0.549918i	$-0.814659\pi$
$997$	5.77598e13	−	1.00043e14i	0.0586340	−	0.101557i	0.893852	+	0.448361i	$0.147992\pi$
$998$	1.18494e14	+	6.84123e13i	0.119686	+	0.0691005i
$999$	−8.38348e12			−0.00842553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.j.a.31.18	✓	136
19.8	odd	6	inner	95.11.j.a.46.18	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.j.a.31.18	✓	136	1.1	even	1	trivial
95.11.j.a.46.18	yes	136	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.4277 + 18.7221i) q^{2} +(7.34597 - 4.24120i) q^{3} +(189.037 - 327.422i) q^{4} +(698.771 + 1210.31i) q^{5} +(-158.809 + 275.065i) q^{6} +3275.68 q^{7} -24186.2i q^{8} +(-29488.5 + 51075.6i) q^{9} +(-45319.1 - 26165.0i) q^{10} +182211. q^{11} -3206.98i q^{12} +(-198093. - 114369. i) q^{13} +(-106223. + 61327.7i) q^{14} +(10266.3 + 5927.26i) q^{15} +(646392. + 1.11958e6i) q^{16} +(-905022. - 1.56754e6i) q^{17} -2.20835e6i q^{18} +(209253. + 2.46724e6i) q^{19} +528375. q^{20} +(24063.1 - 13892.8i) q^{21} +(-5.90869e6 + 3.41138e6i) q^{22} +(2.67155e6 - 4.62727e6i) q^{23} +(-102579. - 177671. i) q^{24} +(-976562. + 1.69146e6i) q^{25} +8.56491e6 q^{26} +1.00114e6i q^{27} +(619226. - 1.07253e6i) q^{28} +(-1.74608e6 - 1.00810e6i) q^{29} -443884. q^{30} +4.87781e7i q^{31} +(-2.04734e7 - 1.18203e7i) q^{32} +(1.33852e6 - 772794. i) q^{33} +(5.86956e7 + 3.38879e7i) q^{34} +(2.28895e6 + 3.96458e6i) q^{35} +(1.11489e7 + 1.93104e7i) q^{36} +8.37391e6i q^{37} +(-5.29776e7 - 7.60893e7i) q^{38} -1.94024e6 q^{39} +(2.92728e7 - 1.69006e7i) q^{40} +(-7.81864e7 + 4.51409e7i) q^{41} +(-520206. + 901024. i) q^{42} +(7.54695e7 + 1.30717e8i) q^{43} +(3.44447e7 - 5.96600e7i) q^{44} -8.24229e7 q^{45} +2.00069e8i q^{46} +(-1.96280e8 + 3.39967e8i) q^{47} +(9.49675e6 + 5.48295e6i) q^{48} -2.71745e8 q^{49} -7.31334e7i q^{50} +(-1.32965e7 - 7.67676e6i) q^{51} +(-7.48937e7 + 4.32399e7i) q^{52} +(3.61021e8 + 2.08436e8i) q^{53} +(-1.87436e7 - 3.24648e7i) q^{54} +(1.27324e8 + 2.20531e8i) q^{55} -7.92263e7i q^{56} +(1.20012e7 + 1.72368e7i) q^{57} +7.54952e7 q^{58} +(3.04328e8 - 1.75704e8i) q^{59} +(3.88143e6 - 2.24094e6i) q^{60} +(3.53904e8 - 6.12980e8i) q^{61} +(-9.13231e8 - 1.58176e9i) q^{62} +(-9.65950e7 + 1.67307e8i) q^{63} -4.38602e8 q^{64} -3.19670e8i q^{65} +(-2.89367e7 + 5.01198e7i) q^{66} +(-1.13863e9 - 6.57388e8i) q^{67} -6.84332e8 q^{68} -4.53224e7i q^{69} +(-1.48451e8 - 8.57081e7i) q^{70} +(1.39153e9 - 8.03402e8i) q^{71} +(1.23533e9 + 7.13216e8i) q^{72} +(-1.53483e9 - 2.65841e9i) q^{73} +(-1.56777e8 - 2.71547e8i) q^{74} +1.65672e7i q^{75} +(8.47386e8 + 3.97886e8i) q^{76} +5.96865e8 q^{77} +(6.29176e7 - 3.63255e7i) q^{78} +(1.51513e9 - 8.74761e8i) q^{79} +(-9.03360e8 + 1.56467e9i) q^{80} +(-1.73702e9 - 3.00861e9i) q^{81} +(1.69027e9 - 2.92763e9i) q^{82} -6.13289e9 q^{83} -1.05050e7i q^{84} +(1.26481e9 - 2.19071e9i) q^{85} +(-4.89460e9 - 2.82590e9i) q^{86} -1.71022e7 q^{87} -4.40700e9i q^{88} +(-9.29342e9 - 5.36556e9i) q^{89} +(2.67279e9 - 1.54313e9i) q^{90} +(-6.48888e8 - 3.74636e8i) q^{91} +(-1.01005e9 - 1.74945e9i) q^{92} +(2.06878e8 + 3.58323e8i) q^{93} -1.46992e10i q^{94} +(-2.83990e9 + 1.97730e9i) q^{95} -2.00530e8 q^{96} +(8.38457e9 - 4.84083e9i) q^{97} +(8.81207e9 - 5.08765e9i) q^{98} +(-5.37314e9 + 9.30655e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) \) 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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