LMFDB - Embedded newform 245.4.e.q.226.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + \cdots + 784 $ x^12 - 2x^11 + 27x^10 + 22x^9 + 399x^8 + 492x^7 + 4046x^6 + 8784x^5 + 22536x^4 + 22736x^3 + 18792x^2 + 4256*x + 784
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.4
Root			$-0.522449 - 0.904909i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.q.116.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.184657 - 0.319836i) q^{2} +(4.87035 + 8.43569i) q^{3} +(3.93180 + 6.81008i) q^{4} +(-2.50000 + 4.33013i) q^{5} +3.59738 q^{6} +5.85867 q^{8} +(-33.9406 + 58.7868i) q^{9} +O(q^{10})$	\(q+(0.184657 - 0.319836i) q^{2} +(4.87035 + 8.43569i) q^{3} +(3.93180 + 6.81008i) q^{4} +(-2.50000 + 4.33013i) q^{5} +3.59738 q^{6} +5.85867 q^{8} +(-33.9406 + 58.7868i) q^{9} +(0.923287 + 1.59918i) q^{10} +(-15.3180 - 26.5316i) q^{11} +(-38.2985 + 66.3350i) q^{12} +36.4622 q^{13} -48.7035 q^{15} +(-30.3726 + 52.6069i) q^{16} +(39.8670 + 69.0517i) q^{17} +(12.5348 + 21.7108i) q^{18} +(76.2092 - 131.998i) q^{19} -39.3180 q^{20} -11.3144 q^{22} +(-11.1104 + 19.2437i) q^{23} +(28.5337 + 49.4219i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(6.73302 - 11.6619i) q^{26} -398.211 q^{27} +101.285 q^{29} +(-8.99346 + 15.5771i) q^{30} +(-124.978 - 216.469i) q^{31} +(34.6517 + 60.0185i) q^{32} +(149.208 - 258.437i) q^{33} +29.4470 q^{34} -533.791 q^{36} +(-3.77882 + 6.54511i) q^{37} +(-28.1452 - 48.7489i) q^{38} +(177.584 + 307.584i) q^{39} +(-14.6467 + 25.3688i) q^{40} +142.280 q^{41} -237.530 q^{43} +(120.455 - 208.634i) q^{44} +(-169.703 - 293.934i) q^{45} +(4.10322 + 7.10699i) q^{46} +(165.564 - 286.766i) q^{47} -591.700 q^{48} -9.23287 q^{50} +(-388.333 + 672.612i) q^{51} +(143.362 + 248.311i) q^{52} +(243.668 + 422.046i) q^{53} +(-73.5326 + 127.362i) q^{54} +153.180 q^{55} +1484.66 q^{57} +(18.7030 - 32.3945i) q^{58} +(358.677 + 621.247i) q^{59} +(-191.493 - 331.675i) q^{60} +(-177.296 + 307.086i) q^{61} -92.3126 q^{62} -460.367 q^{64} +(-91.1556 + 157.886i) q^{65} +(-55.1049 - 95.4445i) q^{66} +(-28.7942 - 49.8730i) q^{67} +(-313.499 + 542.996i) q^{68} -216.445 q^{69} -696.174 q^{71} +(-198.847 + 344.412i) q^{72} +(130.517 + 226.063i) q^{73} +(1.39558 + 2.41721i) q^{74} +(121.759 - 210.892i) q^{75} +1198.56 q^{76} +131.169 q^{78} +(-135.672 + 234.991i) q^{79} +(-151.863 - 263.034i) q^{80} +(-1023.03 - 1771.94i) q^{81} +(26.2730 - 45.5062i) q^{82} +681.441 q^{83} -398.670 q^{85} +(-43.8617 + 75.9707i) q^{86} +(493.292 + 854.407i) q^{87} +(-89.7433 - 155.440i) q^{88} +(-80.3339 + 139.142i) q^{89} -125.348 q^{90} -174.735 q^{92} +(1217.37 - 2108.55i) q^{93} +(-61.1453 - 105.907i) q^{94} +(381.046 + 659.991i) q^{95} +(-337.532 + 584.622i) q^{96} -167.841 q^{97} +2079.61 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9 + 10 * q^10 + 16 * q^11 + 160 * q^12 - 336 * q^13 - 160 * q^15 - 298 * q^16 - 4 * q^17 - 354 * q^18 + 308 * q^19 + 140 * q^20 - 472 * q^22 + 336 * q^23 - 92 * q^24 - 150 * q^25 + 56 * q^26 - 1928 * q^27 + 352 * q^29 + 120 * q^30 + 392 * q^31 + 770 * q^32 + 188 * q^33 - 1624 * q^34 + 460 * q^36 + 140 * q^37 + 20 * q^38 - 140 * q^39 + 330 * q^40 - 1312 * q^41 - 776 * q^43 + 160 * q^44 - 350 * q^45 + 388 * q^46 + 628 * q^47 - 2792 * q^48 - 100 * q^50 - 744 * q^51 + 1520 * q^52 + 676 * q^53 + 2284 * q^54 - 160 * q^55 + 2936 * q^57 + 2012 * q^58 + 996 * q^59 + 800 * q^60 + 740 * q^61 + 728 * q^62 + 2852 * q^64 + 840 * q^65 - 3620 * q^66 - 1768 * q^67 - 2940 * q^68 + 2096 * q^69 - 448 * q^71 - 2858 * q^72 + 2640 * q^73 - 928 * q^74 + 400 * q^75 + 2680 * q^76 + 16 * q^78 - 1636 * q^79 - 1490 * q^80 - 4442 * q^81 - 1756 * q^82 - 280 * q^83 + 40 * q^85 - 1180 * q^86 + 1940 * q^87 + 5652 * q^88 - 1904 * q^89 + 3540 * q^90 - 3904 * q^92 + 1592 * q^93 - 3332 * q^94 + 1540 * q^95 - 6460 * q^96 - 1032 * q^97 - 5608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.184657	−	0.319836i	0.0652863	−	0.113079i	−0.831535	−	0.555473i	$-0.812537\pi$
$2$	0.184657	−	0.319836i	0.0652863	−	0.113079i	0.896821	+	0.442394i	$0.145871\pi$
$3$	4.87035	+	8.43569i	0.937299	+	1.62345i	0.770482	+	0.637462i	$0.220016\pi$
$3$	4.87035	+	8.43569i	0.937299	+	1.62345i	0.166817	+	0.985988i	$0.446651\pi$
$4$	3.93180	+	6.81008i	0.491475	+	0.851260i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	3.59738			0.244771
$7$		0			0
$7$		0			0
$8$	5.85867			0.258919
$9$	−33.9406	+	58.7868i	−1.25706	+	2.17729i
$10$	0.923287	+	1.59918i	0.0291969	+	0.0505705i
$11$	−15.3180	−	26.5316i	−0.419870	−	0.727235i	0.576056	−	0.817410i	$-0.304591\pi$
$11$	−15.3180	−	26.5316i	−0.419870	−	0.727235i	−0.995926	+	0.0901746i	$0.971258\pi$
$12$	−38.2985	+	66.3350i	−0.921319	+	1.59577i
$13$	36.4622			0.777908			0.388954	−	0.921257i	$-0.372836\pi$
$13$	36.4622			0.777908			0.388954	+	0.921257i	$0.372836\pi$
$14$		0			0
$15$	−48.7035			−0.838346
$16$	−30.3726	+	52.6069i	−0.474572	+	0.821982i
$17$	39.8670	+	69.0517i	0.568775	+	0.985148i	0.996687	+	0.0813273i	$0.0259159\pi$
$17$	39.8670	+	69.0517i	0.568775	+	0.985148i	−0.427912	+	0.903820i	$0.640751\pi$
$18$	12.5348	+	21.7108i	0.164137	+	0.284294i
$19$	76.2092	−	131.998i	0.920189	−	1.59381i	0.121068	−	0.992644i	$-0.461368\pi$
$19$	76.2092	−	131.998i	0.920189	−	1.59381i	0.799121	−	0.601170i	$-0.205299\pi$
$20$	−39.3180			−0.439589
$21$		0			0
$22$	−11.3144			−0.109647
$23$	−11.1104	+	19.2437i	−0.100725	+	0.174460i	−0.911983	−	0.410227i	$-0.865449\pi$
$23$	−11.1104	+	19.2437i	−0.100725	+	0.174460i	0.811259	+	0.584687i	$0.198783\pi$
$24$	28.5337	+	49.4219i	0.242684	+	0.420342i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	6.73302	−	11.6619i	0.0507867	−	0.0879652i
$27$	−398.211			−2.83836
$28$		0			0
$29$	101.285			0.648555			0.324278	−	0.945962i	$-0.394879\pi$
$29$	101.285			0.648555			0.324278	+	0.945962i	$0.394879\pi$
$30$	−8.99346	+	15.5771i	−0.0547325	+	0.0947994i
$31$	−124.978	−	216.469i	−0.724089	−	1.25416i	−0.959348	−	0.282226i	$-0.908927\pi$
$31$	−124.978	−	216.469i	−0.724089	−	1.25416i	0.235260	−	0.971933i	$-0.424406\pi$
$32$	34.6517	+	60.0185i	0.191425	+	0.331559i
$33$	149.208	−	258.437i	0.787087	−	1.36327i
$34$	29.4470			0.148533
$35$		0			0
$36$	−533.791			−2.47125
$37$	−3.77882	+	6.54511i	−0.0167901	+	0.0290814i	−0.874298	−	0.485389i	$-0.838678\pi$
$37$	−3.77882	+	6.54511i	−0.0167901	+	0.0290814i	0.857508	+	0.514470i	$0.172011\pi$
$38$	−28.1452	−	48.7489i	−0.120151	−	0.208108i
$39$	177.584	+	307.584i	0.729132	+	1.26289i
$40$	−14.6467	+	25.3688i	−0.0578960	+	0.100279i
$41$	142.280			0.541960			0.270980	−	0.962585i	$-0.412652\pi$
$41$	142.280			0.541960			0.270980	+	0.962585i	$0.412652\pi$
$42$		0			0
$43$	−237.530			−0.842396			−0.421198	−	0.906969i	$-0.638390\pi$
$43$	−237.530			−0.842396			−0.421198	+	0.906969i	$0.638390\pi$
$44$	120.455	−	208.634i	0.412711	−	0.714837i
$45$	−169.703	−	293.934i	−0.562174	−	0.973714i
$46$	4.10322	+	7.10699i	0.0131519	+	0.0227797i
$47$	165.564	−	286.766i	0.513830	−	0.889980i	−0.486041	−	0.873936i	$-0.661559\pi$
$47$	165.564	−	286.766i	0.513830	−	0.889980i	0.999871	−	0.0160443i	$-0.00510727\pi$
$48$	−591.700			−1.77926
$49$		0			0
$50$	−9.23287			−0.0261145
$51$	−388.333	+	672.612i	−1.06622	+	1.84676i
$52$	143.362	+	248.311i	0.382323	+	0.662202i
$53$	243.668	+	422.046i	0.631517	+	1.09382i	0.987242	+	0.159229i	$0.0509009\pi$
$53$	243.668	+	422.046i	0.631517	+	1.09382i	−0.355724	+	0.934591i	$0.615766\pi$
$54$	−73.5326	+	127.362i	−0.185306	+	0.320959i
$55$	153.180			0.375543
$56$		0			0
$57$	1484.66			3.44997
$58$	18.7030	−	32.3945i	0.0423417	−	0.0733380i
$59$	358.677	+	621.247i	0.791454	+	1.37084i	0.925066	+	0.379805i	$0.124009\pi$
$59$	358.677	+	621.247i	0.791454	+	1.37084i	−0.133612	+	0.991034i	$0.542658\pi$
$60$	−191.493	−	331.675i	−0.412026	−	0.713650i
$61$	−177.296	+	307.086i	−0.372138	+	0.644562i	−0.989894	−	0.141808i	$-0.954709\pi$
$61$	−177.296	+	307.086i	−0.372138	+	0.644562i	0.617756	+	0.786370i	$0.288042\pi$
$62$	−92.3126			−0.189092
$63$		0			0
$64$	−460.367			−0.899153
$65$	−91.1556	+	157.886i	−0.173946	+	0.301282i
$66$	−55.1049	−	95.4445i	−0.102772	−	0.178006i
$67$	−28.7942	−	49.8730i	−0.0525040	−	0.0909396i	0.838579	−	0.544780i	$-0.183387\pi$
$67$	−28.7942	−	49.8730i	−0.0525040	−	0.0909396i	−0.891083	+	0.453841i	$0.850054\pi$
$68$	−313.499	+	542.996i	−0.559078	+	0.968352i
$69$	−216.445			−0.377637
$70$		0			0
$71$	−696.174			−1.16367			−0.581836	−	0.813306i	$-0.697665\pi$
$71$	−696.174			−1.16367			−0.581836	+	0.813306i	$0.697665\pi$
$72$	−198.847	+	344.412i	−0.325476	+	0.563741i
$73$	130.517	+	226.063i	0.209259	+	0.362447i	0.951481	−	0.307707i	$-0.0995615\pi$
$73$	130.517	+	226.063i	0.209259	+	0.362447i	−0.742222	+	0.670154i	$0.766228\pi$
$74$	1.39558	+	2.41721i	0.00219233	+	0.00379723i
$75$	121.759	−	210.892i	0.187460	−	0.324690i
$76$	1198.56			1.80900
$77$		0			0
$78$	131.169			0.190409
$79$	−135.672	+	234.991i	−0.193219	+	0.334665i	−0.946315	−	0.323245i	$-0.895226\pi$
$79$	−135.672	+	234.991i	−0.193219	+	0.334665i	0.753096	+	0.657911i	$0.228560\pi$
$80$	−151.863	−	263.034i	−0.212235	−	0.367602i
$81$	−1023.03	−	1771.94i	−1.40333	−	2.43065i
$82$	26.2730	−	45.5062i	0.0353825	−	0.0612844i
$83$	681.441			0.901179			0.450590	−	0.892731i	$-0.351214\pi$
$83$	681.441			0.901179			0.450590	+	0.892731i	$0.351214\pi$
$84$		0			0
$85$	−398.670			−0.508728
$86$	−43.8617	+	75.9707i	−0.0549969	+	0.0952574i
$87$	493.292	+	854.407i	0.607890	+	1.05290i
$88$	−89.7433	−	155.440i	−0.108712	−	0.188295i
$89$	−80.3339	+	139.142i	−0.0956784	+	0.165720i	−0.909892	−	0.414846i	$-0.863835\pi$
$89$	−80.3339	+	139.142i	−0.0956784	+	0.165720i	0.814213	+	0.580566i	$0.197169\pi$
$90$	−125.348			−0.146809
$91$		0			0
$92$	−174.735			−0.198015
$93$	1217.37	−	2108.55i	1.35737	−	2.35104i
$94$	−61.1453	−	105.907i	−0.0670921	−	0.116207i
$95$	381.046	+	659.991i	0.411521	+	0.712775i
$96$	−337.532	+	584.622i	−0.358846	+	0.621539i
$97$	−167.841			−0.175687			−0.0878436	−	0.996134i	$-0.527998\pi$
$97$	−167.841			−0.175687			−0.0878436	+	0.996134i	$0.527998\pi$
$98$		0			0
$99$	2079.61			2.11120
$100$	98.2951	−	170.252i	0.0982951	−	0.170252i
$101$	206.697	+	358.010i	0.203635	+	0.352706i	0.949697	−	0.313171i	$-0.101391\pi$
$101$	206.697	+	358.010i	0.203635	+	0.352706i	−0.746062	+	0.665876i	$0.768058\pi$
$102$	143.417	+	248.406i	0.139220	+	0.241136i
$103$	725.553	−	1256.69i	0.694086	−	1.20219i	−0.276402	−	0.961042i	$-0.589142\pi$
$103$	725.553	−	1256.69i	0.694086	−	1.20219i	0.970488	−	0.241150i	$-0.0775245\pi$
$104$	213.620			0.201415
$105$		0			0
$106$	179.981			0.164918
$107$	890.314	−	1542.07i	0.804391	−	1.39325i	−0.112310	−	0.993673i	$-0.535825\pi$
$107$	890.314	−	1542.07i	0.804391	−	1.39325i	0.916701	−	0.399574i	$-0.130842\pi$
$108$	−1565.69	−	2711.85i	−1.39499	−	2.41618i
$109$	−18.9460	−	32.8154i	−0.0166486	−	0.0288362i	0.857581	−	0.514349i	$-0.171966\pi$
$109$	−18.9460	−	32.8154i	−0.0166486	−	0.0288362i	−0.874230	+	0.485513i	$0.838633\pi$
$110$	28.2859	−	48.9926i	0.0245178	−	0.0424660i
$111$	−73.6168			−0.0629495
$112$		0			0
$113$	457.320			0.380717			0.190359	−	0.981715i	$-0.439035\pi$
$113$	457.320			0.380717			0.190359	+	0.981715i	$0.439035\pi$
$114$	274.154	−	474.848i	0.225236	−	0.390119i
$115$	−55.5518	−	96.2185i	−0.0450455	−	0.0780211i
$116$	398.232	+	689.757i	0.318749	+	0.552089i
$117$	−1237.55	+	2143.50i	−0.977876	+	1.69373i
$118$	264.930			0.206684
$119$		0			0
$120$	−285.337			−0.217064
$121$	196.215	−	339.854i	0.147419	−	0.255337i
$122$	65.4780	+	113.411i	0.0485910	+	0.0841621i
$123$	692.952	+	1200.23i	0.507979	+	0.879845i
$124$	982.779	−	1702.22i	0.711743	−	1.23278i
$125$	125.000			0.0894427
$126$		0			0
$127$	−2545.41			−1.77849			−0.889246	−	0.457429i	$-0.848771\pi$
$127$	−2545.41			−1.77849			−0.889246	+	0.457429i	$0.848771\pi$
$128$	−362.224	+	627.390i	−0.250128	+	0.433234i
$129$	−1156.85	−	2003.73i	−0.789577	−	1.36759i
$130$	33.6651	+	58.3097i	0.0227125	+	0.0393392i
$131$	−485.436	+	840.800i	−0.323762	+	0.560772i	−0.981261	−	0.192684i	$-0.938281\pi$
$131$	−485.436	+	840.800i	−0.323762	+	0.560772i	0.657499	+	0.753455i	$0.271614\pi$
$132$	2346.63			1.54733
$133$		0			0
$134$	−21.2682			−0.0137112
$135$	995.528	−	1724.30i	0.634677	−	1.09929i
$136$	233.568	+	404.551i	0.147267	+	0.255073i
$137$	−91.8176	−	159.033i	−0.0572592	−	0.0991758i	0.835975	−	0.548768i	$-0.184903\pi$
$137$	−91.8176	−	159.033i	−0.0572592	−	0.0991758i	−0.893234	+	0.449592i	$0.851569\pi$
$138$	−39.9682	+	69.2270i	−0.0246545	+	0.0427029i
$139$	1078.90			0.658356			0.329178	−	0.944268i	$-0.393228\pi$
$139$	1078.90			0.658356			0.329178	+	0.944268i	$0.393228\pi$
$140$		0			0
$141$	3225.42			1.92645
$142$	−128.554	+	222.662i	−0.0759718	+	0.131587i
$143$	−558.530	−	967.403i	−0.326620	−	0.565722i
$144$	−2061.73	−	3571.01i	−1.19313	−	2.06656i
$145$	−253.212	+	438.576i	−0.145021	+	0.251184i
$146$	96.4040			0.0546469
$147$		0			0
$148$	−59.4304			−0.0330077
$149$	−605.618	+	1048.96i	−0.332981	+	0.576740i	−0.983095	−	0.183097i	$-0.941388\pi$
$149$	−605.618	+	1048.96i	−0.332981	+	0.576740i	0.650114	+	0.759837i	$0.274721\pi$
$150$	−44.9673	−	77.8856i	−0.0244771	−	0.0423956i
$151$	301.122	+	521.559i	0.162285	+	0.281085i	0.935688	−	0.352829i	$-0.114780\pi$
$151$	301.122	+	521.559i	0.162285	+	0.281085i	−0.773403	+	0.633915i	$0.781447\pi$
$152$	446.484	−	773.333i	0.238254	−	0.412669i
$153$	−5412.44			−2.85994
$154$		0			0
$155$	1249.78			0.647644
$156$	−1396.45	+	2418.72i	−0.716701	+	1.24136i
$157$	801.035	+	1387.43i	0.407195	+	0.705282i	0.994574	−	0.104030i	$-0.0331737\pi$
$157$	801.035	+	1387.43i	0.407195	+	0.705282i	−0.587380	+	0.809312i	$0.699840\pi$
$158$	50.1058	+	86.7857i	0.0252291	+	0.0436981i
$159$	−2373.50	+	4111.02i	−1.18384	+	2.05047i
$160$	−346.517			−0.171216
$161$		0			0
$162$	−755.641			−0.366474
$163$	1545.81	−	2677.41i	0.742803	−	1.28657i	−0.208411	−	0.978041i	$-0.566829\pi$
$163$	1545.81	−	2677.41i	0.742803	−	1.28657i	0.951214	−	0.308531i	$-0.0998374\pi$
$164$	559.416	+	968.937i	0.266360	+	0.461349i
$165$	746.042	+	1292.18i	0.351996	+	0.609675i
$166$	125.833	−	217.949i	0.0588346	−	0.101905i
$167$	3251.19			1.50649			0.753247	−	0.657738i	$-0.228487\pi$
$167$	3251.19			1.50649			0.753247	+	0.657738i	$0.228487\pi$
$168$		0			0
$169$	−867.505			−0.394859
$170$	−73.6175	+	127.509i	−0.0332129	+	0.0575265i
$171$	5173.17	+	8960.20i	2.31346	+	4.00704i
$172$	−933.922	−	1617.60i	−0.414017	−	0.717098i
$173$	1127.27	−	1952.49i	0.495405	−	0.858066i	−0.504581	−	0.863364i	$-0.668353\pi$
$173$	1127.27	−	1952.49i	0.495405	−	0.858066i	0.999986	+	0.00529826i	$0.00168650\pi$
$174$	364.360			0.158747
$175$		0			0
$176$	1860.99			0.797033
$177$	−3493.77	+	6051.38i	−1.48366	+	2.56977i
$178$	29.6685	+	51.3873i	0.0124930	+	0.0216385i
$179$	1342.73	+	2325.68i	0.560673	+	0.971113i	0.997438	+	0.0715379i	$0.0227907\pi$
$179$	1342.73	+	2325.68i	0.560673	+	0.971113i	−0.436765	+	0.899576i	$0.643876\pi$
$180$	1334.48	−	2311.38i	0.552589	−	0.957113i
$181$	−1293.25			−0.531087			−0.265543	−	0.964099i	$-0.585551\pi$
$181$	−1293.25			−0.531087			−0.265543	+	0.964099i	$0.585551\pi$
$182$		0			0
$183$	−3453.97			−1.39522
$184$	−65.0919	+	112.742i	−0.0260795	+	0.0451711i
$185$	−18.8941	−	32.7256i	−0.00750877	−	0.0130056i
$186$	−449.594	−	778.720i	−0.177236	−	0.306981i
$187$	1221.37	−	2115.48i	0.477623	−	0.827267i
$188$	2603.86			1.01014
$189$		0			0
$190$	281.452			0.107467
$191$	69.9388	−	121.138i	0.0264953	−	0.0458911i	−0.852474	−	0.522770i	$-0.824899\pi$
$191$	69.9388	−	121.138i	0.0264953	−	0.0458911i	0.878969	+	0.476879i	$0.158232\pi$
$192$	−2242.15	−	3883.51i	−0.842776	−	1.45973i
$193$	−1192.40	−	2065.30i	−0.444721	−	0.770279i	0.553312	−	0.832974i	$-0.313364\pi$
$193$	−1192.40	−	2065.30i	−0.444721	−	0.770279i	−0.998033	+	0.0626951i	$0.980030\pi$
$194$	−30.9931	+	53.6815i	−0.0114700	+	0.0198665i
$195$	−1775.84			−0.652156
$196$		0			0
$197$	−1008.67			−0.364797			−0.182399	−	0.983225i	$-0.558386\pi$
$197$	−1008.67			−0.364797			−0.182399	+	0.983225i	$0.558386\pi$
$198$	384.016	−	665.135i	0.137833	−	0.238733i
$199$	497.518	+	861.726i	0.177227	+	0.306966i	0.940930	−	0.338602i	$-0.109954\pi$
$199$	497.518	+	861.726i	0.177227	+	0.306966i	−0.763703	+	0.645568i	$0.776621\pi$
$200$	−73.2333	−	126.844i	−0.0258919	−	0.0448461i
$201$	280.475	−	485.797i	0.0984239	−	0.170475i
$202$	152.672			0.0531782
$203$		0			0
$204$	−6107.39			−2.09609
$205$	−355.699	+	616.089i	−0.121186	+	0.209900i
$206$	−267.957	−	464.116i	−0.0906285	−	0.156973i
$207$	−754.184	−	1306.29i	−0.253234	−	0.438614i
$208$	−1107.45	+	1918.16i	−0.369173	+	0.639426i
$209$	−4669.51			−1.54544
$210$		0			0
$211$	2307.30			0.752802			0.376401	−	0.926457i	$-0.377161\pi$
$211$	2307.30			0.752802			0.376401	+	0.926457i	$0.377161\pi$
$212$	−1916.11	+	3318.80i	−0.620751	+	1.07517i
$213$	−3390.61	−	5872.71i	−1.09071	−	1.88916i
$214$	−328.806	−	569.509i	−0.105031	−	0.181920i
$215$	593.826	−	1028.54i	0.188365	−	0.326258i
$216$	−2332.99			−0.734905
$217$		0			0
$218$	−13.9941			−0.00434770
$219$	−1271.33	+	2202.01i	−0.392276	+	0.679442i
$220$	602.275	+	1043.17i	0.184570	+	0.319685i
$221$	1453.64	+	2517.78i	0.442455	+	0.766354i
$222$	−13.5939	+	23.5453i	−0.00410974	+	0.00711827i
$223$	−1629.00			−0.489173			−0.244587	−	0.969627i	$-0.578652\pi$
$223$	−1629.00			−0.489173			−0.244587	+	0.969627i	$0.578652\pi$
$224$		0			0
$225$	1697.03			0.502824
$226$	84.4475	−	146.267i	0.0248556	−	0.0430511i
$227$	−1205.46	−	2087.91i	−0.352463	−	0.610484i	0.634218	−	0.773155i	$-0.281322\pi$
$227$	−1205.46	−	2087.91i	−0.352463	−	0.610484i	−0.986680	+	0.162671i	$0.947989\pi$
$228$	5837.40	+	10110.7i	1.69558	+	2.93682i
$229$	1833.29	−	3175.36i	0.529028	−	0.916304i	−0.470399	−	0.882454i	$-0.655890\pi$
$229$	1833.29	−	3175.36i	0.529028	−	0.916304i	0.999427	−	0.0338499i	$-0.0107768\pi$
$230$	−41.0322			−0.0117634
$231$		0			0
$232$	593.393			0.167923
$233$	1509.16	−	2613.95i	0.424329	−	0.734959i	−0.572029	−	0.820234i	$-0.693843\pi$
$233$	1509.16	−	2613.95i	0.424329	−	0.734959i	0.996358	+	0.0852744i	$0.0271767\pi$
$234$	457.045	+	791.626i	0.127684	+	0.221155i
$235$	827.821	+	1433.83i	0.229792	+	0.398011i
$236$	−2820.50	+	4885.24i	−0.777961	+	1.34747i
$237$	−2643.08			−0.724417
$238$		0			0
$239$	−546.873			−0.148010			−0.0740048	−	0.997258i	$-0.523578\pi$
$239$	−546.873			−0.148010			−0.0740048	+	0.997258i	$0.523578\pi$
$240$	1479.25	−	2562.14i	0.397855	−	0.689105i
$241$	1567.64	+	2715.22i	0.419005	+	0.725738i	0.995840	−	0.0911228i	$-0.0290456\pi$
$241$	1567.64	+	2715.22i	0.419005	+	0.725738i	−0.576834	+	0.816861i	$0.695712\pi$
$242$	−72.4651	−	125.513i	−0.0192489	−	0.0333401i
$243$	4589.19	−	7948.70i	1.21151	−	2.09839i
$244$	−2788.37			−0.731587
$245$		0			0
$246$	511.835			0.132656
$247$	2778.76	−	4812.95i	0.715823	−	1.23984i
$248$	−732.205	−	1268.22i	−0.187480	−	0.324725i
$249$	3318.86	+	5748.43i	0.844674	+	1.46302i
$250$	23.0822	−	39.9795i	0.00583938	−	0.0101141i
$251$	914.967			0.230088			0.115044	−	0.993360i	$-0.463299\pi$
$251$	914.967			0.230088			0.115044	+	0.993360i	$0.463299\pi$
$252$		0			0
$253$	680.756			0.169165
$254$	−470.029	+	814.114i	−0.116111	+	0.201110i
$255$	−1941.66	−	3363.06i	−0.476830	−	0.825894i
$256$	−1707.69	−	2957.81i	−0.416917	−	0.722121i
$257$	−3167.09	+	5485.56i	−0.768707	+	1.33144i	0.169558	+	0.985520i	$0.445766\pi$
$257$	−3167.09	+	5485.56i	−0.768707	+	1.33144i	−0.938264	+	0.345919i	$0.887567\pi$
$258$	−854.487			−0.206194
$259$		0			0
$260$	−1433.62			−0.341960
$261$	−3437.66	+	5954.21i	−0.815272	+	1.41209i
$262$	179.279	+	310.520i	0.0422744	+	0.0732213i
$263$	−2063.38	−	3573.87i	−0.483777	−	0.837926i	0.516050	−	0.856559i	$-0.327402\pi$
$263$	−2063.38	−	3573.87i	−0.483777	−	0.837926i	−0.999826	+	0.0186328i	$0.994069\pi$
$264$	874.162	−	1514.09i	0.203792	−	0.352977i
$265$	−2436.68			−0.564846
$266$		0			0
$267$	−1565.02			−0.358717
$268$	226.426	−	392.181i	0.0516088	−	0.0893891i
$269$	−2943.53	−	5098.35i	−0.667176	−	1.15558i	−0.978690	−	0.205342i	$-0.934169\pi$
$269$	−2943.53	−	5098.35i	−0.667176	−	1.15558i	0.311514	−	0.950242i	$-0.399164\pi$
$270$	−367.663	−	636.811i	−0.0828714	−	0.143537i
$271$	3618.86	−	6268.05i	0.811181	−	1.40501i	−0.100857	−	0.994901i	$-0.532158\pi$
$271$	3618.86	−	6268.05i	0.811181	−	1.40501i	0.912038	−	0.410106i	$-0.134508\pi$
$272$	−4843.46			−1.07970
$273$		0			0
$274$	−67.8192			−0.0149530
$275$	−382.951	+	663.291i	−0.0839739	+	0.145447i
$276$	−851.020	−	1474.01i	−0.185599	−	0.321467i
$277$	−2820.08	−	4884.53i	−0.611705	−	1.05950i	−0.990953	−	0.134210i	$-0.957150\pi$
$277$	−2820.08	−	4884.53i	−0.611705	−	1.05950i	0.379248	−	0.925295i	$-0.376183\pi$
$278$	199.228	−	345.073i	0.0429816	−	0.0744463i
$279$	16967.3			3.64089
$280$		0			0
$281$	−2593.05			−0.550492			−0.275246	−	0.961374i	$-0.588759\pi$
$281$	−2593.05			−0.550492			−0.275246	+	0.961374i	$0.588759\pi$
$282$	595.598	−	1031.61i	0.125771	−	0.217841i
$283$	1266.63	+	2193.87i	0.266054	+	0.460820i	0.967839	−	0.251569i	$-0.0809466\pi$
$283$	1266.63	+	2193.87i	0.266054	+	0.460820i	−0.701785	+	0.712389i	$0.747613\pi$
$284$	−2737.22	−	4741.01i	−0.571916	−	0.990588i
$285$	−3711.65	+	6428.77i	−0.771437	+	1.33617i
$286$	−412.547			−0.0852952
$287$		0			0
$288$	−4704.40			−0.962532
$289$	−722.262	+	1251.00i	−0.147010	+	0.254630i
$290$	93.5149	+	161.973i	0.0189358	+	0.0327978i
$291$	−817.443	−	1415.85i	−0.164671	−	0.285219i
$292$	−1026.34	+	1777.67i	−0.205691	+	0.356268i
$293$	589.215			0.117482			0.0587411	−	0.998273i	$-0.481291\pi$
$293$	589.215			0.117482			0.0587411	+	0.998273i	$0.481291\pi$
$294$		0			0
$295$	−3586.77			−0.707898
$296$	−22.1389	+	38.3456i	−0.00434728	+	0.00752971i
$297$	6099.82	+	10565.2i	1.19174	+	2.06416i
$298$	223.664	+	387.397i	0.0434781	+	0.0753063i
$299$	−405.109	+	701.669i	−0.0783546	+	0.135714i
$300$	1914.93			0.368528
$301$		0			0
$302$	222.418			0.0423798
$303$	−2013.37	+	3487.26i	−0.381733	+	0.661182i
$304$	4629.34	+	8018.25i	0.873391	+	1.51276i
$305$	−886.480	−	1535.43i	−0.166425	−	0.288257i
$306$	−999.448	+	1731.09i	−0.186714	+	0.323399i
$307$	−5273.75			−0.980420			−0.490210	−	0.871604i	$-0.663080\pi$
$307$	−5273.75			−0.980420			−0.490210	+	0.871604i	$0.663080\pi$
$308$		0			0
$309$	14134.8			2.60226
$310$	230.781	−	399.725i	0.0422823	−	0.0732351i
$311$	−1647.54	−	2853.63i	−0.300397	−	0.520303i	0.675829	−	0.737059i	$-0.263786\pi$
$311$	−1647.54	−	2853.63i	−0.300397	−	0.520303i	−0.976226	+	0.216755i	$0.930453\pi$
$312$	1040.40	+	1802.03i	0.188786	+	0.326987i
$313$	−909.686	+	1575.62i	−0.164276	+	0.284535i	−0.936398	−	0.350940i	$-0.885862\pi$
$313$	−909.686	+	1575.62i	−0.164276	+	0.284535i	0.772122	+	0.635475i	$0.219196\pi$
$314$	591.668			0.106337
$315$		0			0
$316$	−2133.75			−0.379850
$317$	−943.953	+	1634.97i	−0.167248	+	0.289682i	−0.937451	−	0.348116i	$-0.886821\pi$
$317$	−943.953	+	1634.97i	−0.167248	+	0.289682i	0.770203	+	0.637799i	$0.220155\pi$
$318$	876.569	+	1518.26i	0.154577	+	0.267735i
$319$	−1551.48	−	2687.25i	−0.272309	−	0.471652i
$320$	1150.92	−	1993.45i	0.201057	−	0.348241i
$321$	17344.6			3.01582
$322$		0			0
$323$	12152.9			2.09352
$324$	8044.71	−	13933.9i	1.37941	−	2.38921i
$325$	−455.778	−	789.431i	−0.0777908	−	0.134738i
$326$	−570.889	−	988.809i	−0.0969896	−	0.167991i
$327$	184.547	−	319.645i	0.0312094	−	0.0540563i
$328$	833.569			0.140324
$329$		0			0
$330$	551.049			0.0919220
$331$	228.193	−	395.242i	0.0378932	−	0.0656329i	−0.846457	−	0.532457i	$-0.821269\pi$
$331$	228.193	−	395.242i	0.0378932	−	0.0656329i	0.884350	+	0.466824i	$0.154602\pi$
$332$	2679.29	+	4640.67i	0.442907	+	0.767138i
$333$	−256.511	−	444.290i	−0.0422124	−	0.0731140i
$334$	600.356	−	1039.85i	0.0983533	−	0.170353i
$335$	287.942			0.0469610
$336$		0			0
$337$	8174.42			1.32133			0.660666	−	0.750680i	$-0.270274\pi$
$337$	8174.42			1.32133			0.660666	+	0.750680i	$0.270274\pi$
$338$	−160.191	+	277.459i	−0.0257789	+	0.0446503i
$339$	2227.31	+	3857.81i	0.356846	+	0.618075i
$340$	−1567.49	−	2714.98i	−0.250027	−	0.433060i
$341$	−3828.84	+	6631.75i	−0.608045	+	1.05317i
$342$	3821.06			0.604150
$343$		0			0
$344$	−1391.61			−0.218112
$345$	541.113	−	937.236i	0.0844422	−	0.146258i
$346$	−416.319	−	721.085i	−0.0646862	−	0.112040i
$347$	3967.85	+	6872.52i	0.613849	+	1.06322i	0.990585	+	0.136897i	$0.0437128\pi$
$347$	3967.85	+	6872.52i	0.613849	+	1.06322i	−0.376737	+	0.926320i	$0.622954\pi$
$348$	−3879.05	+	6718.72i	−0.597526	+	1.03495i
$349$	−8649.40			−1.32662			−0.663312	−	0.748343i	$-0.730850\pi$
$349$	−8649.40			−1.32662			−0.663312	+	0.748343i	$0.730850\pi$
$350$		0			0
$351$	−14519.7			−2.20798
$352$	1061.59	−	1838.73i	0.160747	−	0.278423i
$353$	−2465.53	−	4270.42i	−0.371747	−	0.643885i	0.618087	−	0.786110i	$-0.287908\pi$
$353$	−2465.53	−	4270.42i	−0.371747	−	0.643885i	−0.989834	+	0.142224i	$0.954575\pi$
$354$	1290.30	+	2234.86i	0.193725	+	0.335542i
$355$	1740.44	−	3014.52i	0.260205	−	0.450688i
$356$	−1263.43			−0.188094
$357$		0			0
$358$	991.781			0.146417
$359$	−4121.82	+	7139.20i	−0.605965	+	1.04956i	0.385933	+	0.922527i	$0.373879\pi$
$359$	−4121.82	+	7139.20i	−0.605965	+	1.04956i	−0.991898	+	0.127035i	$0.959454\pi$
$360$	−994.233	−	1722.06i	−0.145557	−	0.252113i
$361$	−8186.19	−	14178.9i	−1.19350	−	2.06720i
$362$	−238.809	+	413.629i	−0.0346727	+	0.0600548i
$363$	3822.54			0.552703
$364$		0			0
$365$	−1305.17			−0.187167
$366$	−637.802	+	1104.71i	−0.0910886	+	0.157770i
$367$	−4089.55	−	7083.32i	−0.581670	−	1.00748i	−0.995282	−	0.0970290i	$-0.969066\pi$
$367$	−4089.55	−	7083.32i	−0.581670	−	1.00748i	0.413611	−	0.910454i	$-0.364267\pi$
$368$	−674.901	−	1168.96i	−0.0956022	−	0.165588i
$369$	−4829.06	+	8364.18i	−0.681276	+	1.18000i
$370$	−13.9558			−0.00196088
$371$		0			0
$372$	19145.9			2.66847
$373$	6397.73	−	11081.2i	0.888102	−	1.53824i	0.0459858	−	0.998942i	$-0.485357\pi$
$373$	6397.73	−	11081.2i	0.888102	−	1.53824i	0.842116	−	0.539296i	$-0.181310\pi$
$374$	−451.070	−	781.277i	−0.0623644	−	0.108018i
$375$	608.794	+	1054.46i	0.0838346	+	0.145206i
$376$	969.986	−	1680.06i	0.133040	−	0.230433i
$377$	3693.07			0.504516
$378$		0			0
$379$	−5735.40			−0.777329			−0.388664	−	0.921379i	$-0.627063\pi$
$379$	−5735.40			−0.777329			−0.388664	+	0.921379i	$0.627063\pi$
$380$	−2996.40	+	5189.91i	−0.404505	+	0.700623i
$381$	−12397.0	−	21472.3i	−1.66698	−	2.88729i
$382$	−25.8294	−	44.7379i	−0.00345955	−	0.00599212i
$383$	368.920	−	638.989i	0.0492192	−	0.0852501i	−0.840366	−	0.542019i	$-0.817660\pi$
$383$	368.920	−	638.989i	0.0492192	−	0.0852501i	0.889585	+	0.456769i	$0.150993\pi$
$384$	−7056.62			−0.937778
$385$		0			0
$386$	−880.745			−0.116137
$387$	8061.91	−	13963.6i	1.05894	−	1.83414i
$388$	−659.917	−	1143.01i	−0.0863459	−	0.149556i
$389$	6516.98	+	11287.7i	0.849419	+	1.47124i	0.881727	+	0.471760i	$0.156381\pi$
$389$	6516.98	+	11287.7i	0.849419	+	1.47124i	−0.0323078	+	0.999478i	$0.510286\pi$
$390$	−327.922	+	567.977i	−0.0425768	+	0.0737452i
$391$	−1771.75			−0.229159
$392$		0			0
$393$	−9456.98			−1.21385
$394$	−186.259	+	322.610i	−0.0238162	+	0.0412509i
$395$	−678.361	−	1174.96i	−0.0864103	−	0.149667i
$396$	8176.63	+	14162.3i	1.03760	+	1.79718i
$397$	4156.82	−	7199.82i	0.525503	−	0.910199i	−0.474055	−	0.880495i	$-0.657210\pi$
$397$	4156.82	−	7199.82i	0.525503	−	0.910199i	0.999559	−	0.0297035i	$-0.00945631\pi$
$398$	367.481			0.0462819
$399$		0			0
$400$	1518.63			0.189829
$401$	7170.71	−	12420.0i	0.892988	−	1.54670i	0.0567137	−	0.998390i	$-0.481938\pi$
$401$	7170.71	−	12420.0i	0.892988	−	1.54670i	0.836275	−	0.548311i	$-0.184729\pi$
$402$	−103.584	−	179.412i	−0.0128515	−	0.0222594i
$403$	−4556.98	−	7892.93i	−0.563274	−	0.975620i
$404$	−1625.38	+	2815.25i	−0.200163	+	0.346692i
$405$	10230.3			1.25518
$406$		0			0
$407$	231.537			0.0281987
$408$	−2275.11	+	3940.61i	−0.276066	+	0.478160i
$409$	−3141.18	−	5440.68i	−0.379758	−	0.657761i	0.611269	−	0.791423i	$-0.290660\pi$
$409$	−3141.18	−	5440.68i	−0.379758	−	0.657761i	−0.991027	+	0.133663i	$0.957326\pi$
$410$	131.365	+	227.531i	0.0158236	+	0.0274072i
$411$	894.368	−	1549.09i	0.107338	−	0.185915i
$412$	11410.9			1.36450
$413$		0			0
$414$	−557.063			−0.0661308
$415$	−1703.60	+	2950.73i	−0.201510	+	0.349025i
$416$	1263.48	+	2188.41i	0.148911	+	0.257922i
$417$	5254.64	+	9101.31i	0.617077	+	1.06881i
$418$	−862.259	+	1493.48i	−0.100896	+	0.174757i
$419$	−15226.1			−1.77528			−0.887640	−	0.460538i	$-0.847656\pi$
$419$	−15226.1			−1.77528			−0.887640	+	0.460538i	$0.847656\pi$
$420$		0			0
$421$	−2026.55			−0.234603			−0.117302	−	0.993096i	$-0.537424\pi$
$421$	−2026.55			−0.234603			−0.117302	+	0.993096i	$0.537424\pi$
$422$	426.060	−	737.958i	0.0491476	−	0.0851262i
$423$	11238.7	+	19466.0i	1.29183	+	2.23752i
$424$	1427.57	+	2472.63i	0.163512	+	0.283211i
$425$	996.676	−	1726.29i	0.113755	−	0.197030i
$426$	−2504.41			−0.284833
$427$		0			0
$428$	14002.2			1.58135
$429$	5440.47	−	9423.18i	0.612281	−	1.06050i
$430$	−219.309	−	379.854i	−0.0245953	−	0.0426004i
$431$	−4491.78	−	7779.99i	−0.501999	−	0.869487i	−0.999997	−	0.00230934i	$-0.999265\pi$
$431$	−4491.78	−	7779.99i	−0.501999	−	0.869487i	0.497999	−	0.867178i	$-0.334068\pi$
$432$	12094.7	−	20948.6i	1.34701	−	2.33308i
$433$	6836.59			0.758766			0.379383	−	0.925240i	$-0.376136\pi$
$433$	6836.59			0.758766			0.379383	+	0.925240i	$0.376136\pi$
$434$		0			0
$435$	−4932.92			−0.543713
$436$	148.984	−	258.047i	0.0163647	−	0.0283446i
$437$	1693.42	+	2933.10i	0.185372	+	0.321073i
$438$	469.521	+	813.234i	0.0512205	+	0.0887165i
$439$	3901.48	−	6757.56i	0.424163	−	0.734671i	−0.572179	−	0.820129i	$-0.693902\pi$
$439$	3901.48	−	6757.56i	0.424163	−	0.734671i	0.996342	+	0.0854573i	$0.0272351\pi$
$440$	897.433			0.0972351
$441$		0			0
$442$	1073.70			0.115545
$443$	−2592.19	+	4489.80i	−0.278010	+	0.481528i	−0.970890	−	0.239525i	$-0.923008\pi$
$443$	−2592.19	+	4489.80i	−0.278010	+	0.481528i	0.692880	+	0.721053i	$0.256342\pi$
$444$	−289.447	−	501.336i	−0.0309381	−	0.0535864i
$445$	−401.669	−	695.712i	−0.0427887	−	0.0741121i
$446$	−300.806	+	521.011i	−0.0319363	+	0.0553153i
$447$	−11798.3			−1.24841
$448$		0			0
$449$	−772.951			−0.0812424			−0.0406212	−	0.999175i	$-0.512934\pi$
$449$	−772.951			−0.0812424			−0.0406212	+	0.999175i	$0.512934\pi$
$450$	313.369	−	542.771i	0.0328275	−	0.0568588i
$451$	−2179.45	−	3774.91i	−0.227553	−	0.394133i
$452$	1798.09	+	3114.39i	0.187113	+	0.324089i
$453$	−2933.14	+	5080.35i	−0.304218	+	0.526922i
$454$	−890.387			−0.0920439
$455$		0			0
$456$	8698.14			0.893262
$457$	−5766.37	+	9987.65i	−0.590239	+	1.02232i	0.403960	+	0.914776i	$0.367633\pi$
$457$	−5766.37	+	9987.65i	−0.590239	+	1.02232i	−0.994200	+	0.107548i	$0.965700\pi$
$458$	−677.063	−	1172.71i	−0.0690766	−	0.119644i
$459$	−15875.5	−	27497.2i	−1.61439	−	2.79621i
$460$	436.837	−	756.625i	0.0442775	−	0.0766909i
$461$	−10400.7			−1.05078			−0.525391	−	0.850861i	$-0.676081\pi$
$461$	−10400.7			−1.05078			−0.525391	+	0.850861i	$0.676081\pi$
$462$		0			0
$463$	−13855.4			−1.39075			−0.695374	−	0.718648i	$-0.744761\pi$
$463$	−13855.4			−1.39075			−0.695374	+	0.718648i	$0.744761\pi$
$464$	−3076.28	+	5328.27i	−0.307786	+	0.533101i
$465$	6086.87	+	10542.8i	0.607036	+	1.05142i
$466$	−557.357	−	965.370i	−0.0554057	−	0.0959655i
$467$	−7367.24	+	12760.4i	−0.730011	+	1.26442i	0.226866	+	0.973926i	$0.427152\pi$
$467$	−7367.24	+	12760.4i	−0.730011	+	1.26442i	−0.956878	+	0.290491i	$0.906181\pi$
$468$	−19463.2			−1.92241
$469$		0			0
$470$	611.453			0.0600090
$471$	−7802.64	+	13514.6i	−0.763326	+	1.32212i
$472$	2101.37	+	3639.68i	0.204922	+	0.354936i
$473$	3638.50	+	6302.06i	0.353696	+	0.612620i
$474$	−488.065	+	845.353i	−0.0472944	+	0.0819164i
$475$	−3810.46			−0.368076
$476$		0			0
$477$	−33081.0			−3.17542
$478$	−100.984	+	174.910i	−0.00966299	+	0.0167368i
$479$	−735.613	−	1274.12i	−0.0701691	−	0.121536i	0.828806	−	0.559536i	$-0.189021\pi$
$479$	−735.613	−	1274.12i	−0.0701691	−	0.121536i	−0.898975	+	0.437999i	$0.855687\pi$
$480$	−1687.66	−	2923.11i	−0.160481	−	0.277961i
$481$	−137.784	+	238.650i	−0.0130612	+	0.0226226i
$482$	1157.90			0.109421
$483$		0			0
$484$	3085.91			0.289812
$485$	419.602	−	726.772i	0.0392848	−	0.0680433i
$486$	−1694.85	−	2935.57i	−0.158190	−	0.273992i
$487$	−2805.00	−	4858.40i	−0.260999	−	0.452064i	0.705509	−	0.708701i	$-0.250719\pi$
$487$	−2805.00	−	4858.40i	−0.260999	−	0.452064i	−0.966508	+	0.256638i	$0.917385\pi$
$488$	−1038.72	+	1799.11i	−0.0963536	+	0.166889i
$489$	30114.5			2.78491
$490$		0			0
$491$	−3193.98			−0.293569			−0.146784	−	0.989169i	$-0.546892\pi$
$491$	−3193.98			−0.293569			−0.146784	+	0.989169i	$0.546892\pi$
$492$	−5449.10	+	9438.12i	−0.499318	+	0.864844i
$493$	4037.92	+	6993.89i	0.368882	+	0.638923i
$494$	−1026.24	−	1777.49i	−0.0934667	−	0.161889i
$495$	−5199.03	+	9004.99i	−0.472079	+	0.817665i
$496$	15183.6			1.37453
$497$		0			0
$498$	2451.41			0.220583
$499$	−4362.16	+	7555.48i	−0.391337	+	0.677815i	−0.992626	−	0.121216i	$-0.961321\pi$
$499$	−4362.16	+	7555.48i	−0.391337	+	0.677815i	0.601289	+	0.799031i	$0.294654\pi$
$500$	491.475	+	851.260i	0.0439589	+	0.0761390i
$501$	15834.4	+	27426.0i	1.41203	+	2.44572i
$502$	168.955	−	292.639i	0.0150216	−	0.0260182i
$503$	14636.7			1.29745			0.648726	−	0.761022i	$-0.275302\pi$
$503$	14636.7			1.29745			0.648726	+	0.761022i	$0.275302\pi$
$504$		0			0
$505$	−2066.97			−0.182136
$506$	125.707	−	217.730i	0.0110442	−	0.0191290i
$507$	−4225.05	−	7318.01i	−0.370101	−	0.641034i
$508$	−10008.1	−	17334.5i	−0.874085	−	1.51396i
$509$	4265.28	−	7387.68i	0.371425	−	0.643327i	−0.618360	−	0.785895i	$-0.712203\pi$
$509$	4265.28	−	7387.68i	0.371425	−	0.643327i	0.989785	+	0.142568i	$0.0455360\pi$
$510$	−1434.17			−0.124522
$511$		0			0
$512$	−7056.93			−0.609131
$513$	−30347.4	+	52563.2i	−2.61183	+	4.52382i
$514$	1169.65	+	2025.90i	0.100372	+	0.173849i
$515$	3627.76	+	6283.47i	0.310405	+	0.537637i
$516$	9097.05	−	15756.6i	0.776115	−	1.34427i
$517$	−10144.5			−0.862967
$518$		0			0
$519$	21960.9			1.85737
$520$	−534.050	+	925.002i	−0.0450378	+	0.0780077i
$521$	6871.48	+	11901.8i	0.577822	+	1.00082i	0.995729	+	0.0923269i	$0.0294305\pi$
$521$	6871.48	+	11901.8i	0.577822	+	1.00082i	−0.417907	+	0.908490i	$0.637236\pi$
$522$	1269.58	+	2198.98i	0.106452	+	0.184380i
$523$	−1118.08	+	1936.58i	−0.0934806	+	0.161913i	−0.908973	−	0.416854i	$-0.863133\pi$
$523$	−1118.08	+	1936.58i	−0.0934806	+	0.161913i	0.815493	+	0.578767i	$0.196466\pi$
$524$	−7634.56			−0.636483
$525$		0			0
$526$	−1524.07			−0.126336
$527$	9965.02	−	17259.9i	0.823687	−	1.42667i
$528$	9063.69	+	15698.8i	0.747058	+	1.29394i
$529$	5836.62	+	10109.3i	0.479709	+	0.830880i
$530$	−449.952	+	779.339i	−0.0368767	+	0.0638723i
$531$	−48694.9			−3.97962
$532$		0			0
$533$	5187.84			0.421595
$534$	−288.992	+	500.549i	−0.0234193	+	0.0405634i
$535$	4451.57	+	7710.34i	0.359735	+	0.623079i
$536$	−168.695	−	292.189i	−0.0135943	−	0.0235460i
$537$	−13079.1	+	22653.7i	−1.05104	+	1.82045i
$538$	−2174.18			−0.174230
$539$		0			0
$540$	15656.9			1.24771
$541$	9743.93	−	16877.0i	0.774352	−	1.34122i	−0.160806	−	0.986986i	$-0.551409\pi$
$541$	9743.93	−	16877.0i	0.774352	−	1.34122i	0.935158	−	0.354231i	$-0.115257\pi$
$542$	−1336.50	−	2314.88i	−0.105918	−	0.183455i
$543$	−6298.59	−	10909.5i	−0.497787	−	0.862193i
$544$	−2762.92	+	4785.52i	−0.217756	+	0.377165i
$545$	189.460			0.0148910
$546$		0			0
$547$	−15949.3			−1.24670			−0.623349	−	0.781944i	$-0.714228\pi$
$547$	−15949.3			−1.24670			−0.623349	+	0.781944i	$0.714228\pi$
$548$	722.018	−	1250.57i	0.0562830	−	0.0974850i
$549$	−12035.1	−	20845.3i	−0.935599	−	1.62051i
$550$	141.430	+	244.963i	0.0109647	+	0.0189914i
$551$	7718.83	−	13369.4i	0.596793	−	1.03368i
$552$	−1268.08			−0.0977773
$553$		0			0
$554$	−2083.00			−0.159744
$555$	184.042	−	318.770i	0.0140759	−	0.0243802i
$556$	4242.04	+	7347.43i	0.323566	+	0.560433i
$557$	3174.87	+	5499.04i	0.241514	+	0.418315i	0.961146	−	0.276041i	$-0.0890226\pi$
$557$	3174.87	+	5499.04i	0.241514	+	0.418315i	−0.719631	+	0.694356i	$0.755689\pi$
$558$	3133.14	−	5426.76i	0.237700	−	0.411708i
$559$	−8660.88			−0.655306
$560$		0			0
$561$	23794.0			1.79070
$562$	−478.825	+	829.350i	−0.0359396	+	0.0622491i
$563$	−7402.50	−	12821.5i	−0.554135	−	0.959790i	−0.997970	−	0.0636815i	$-0.979716\pi$
$563$	−7402.50	−	12821.5i	−0.554135	−	0.959790i	0.443835	−	0.896108i	$-0.353618\pi$
$564$	12681.7	+	21965.4i	0.946803	+	1.63991i
$565$	−1143.30	+	1980.25i	−0.0851309	+	0.147451i
$566$	935.571			0.0694788
$567$		0			0
$568$	−4078.65			−0.301297
$569$	−12289.4	+	21285.8i	−0.905442	+	1.56827i	−0.0851200	+	0.996371i	$0.527127\pi$
$569$	−12289.4	+	21285.8i	−0.905442	+	1.56827i	−0.820322	+	0.571901i	$0.806206\pi$
$570$	1370.77	+	2374.24i	0.100728	+	0.174467i
$571$	7804.97	+	13518.6i	0.572027	+	0.990780i	0.996358	+	0.0852730i	$0.0271762\pi$
$571$	7804.97	+	13518.6i	0.572027	+	0.990780i	−0.424330	+	0.905508i	$0.639490\pi$
$572$	4392.06	−	7607.27i	0.321051	−	0.556077i
$573$	1362.51			0.0993359
$574$		0			0
$575$	555.518			0.0402899
$576$	15625.1	−	27063.5i	1.13029	−	1.95772i
$577$	−7555.66	−	13086.8i	−0.545141	−	0.944212i	−0.998598	−	0.0529338i	$-0.983143\pi$
$577$	−7555.66	−	13086.8i	−0.545141	−	0.944212i	0.453457	−	0.891278i	$-0.350191\pi$
$578$	266.742	+	462.011i	0.0191955	+	0.0332476i
$579$	11614.8	−	20117.5i	0.833673	−	1.44396i
$580$	−3982.32			−0.285098
$581$		0			0
$582$	−603.788			−0.0430031
$583$	7465.05	−	12929.8i	0.530310	−	0.918524i
$584$	764.657	+	1324.43i	0.0541811	+	0.0938444i
$585$	−6187.75	−	10717.5i	−0.437320	−	0.757460i
$586$	108.803	−	188.452i	0.00766997	−	0.0132848i
$587$	14983.2			1.05353			0.526766	−	0.850010i	$-0.323404\pi$
$587$	14983.2			1.05353			0.526766	+	0.850010i	$0.323404\pi$
$588$		0			0
$589$	−38098.0			−2.66519
$590$	−662.324	+	1147.18i	−0.0462160	+	0.0800485i
$591$	−4912.59	−	8508.86i	−0.341924	−	0.592230i
$592$	−229.545	−	397.584i	−0.0159362	−	0.0276024i
$593$	−3465.51	+	6002.43i	−0.239985	+	0.415667i	−0.960710	−	0.277555i	$-0.910476\pi$
$593$	−3465.51	+	6002.43i	−0.239985	+	0.415667i	0.720724	+	0.693222i	$0.243809\pi$
$594$	4505.51			0.311217
$595$		0			0
$596$	−9524.68			−0.654608
$597$	−4846.17	+	8393.81i	−0.332229	+	0.575437i
$598$	149.613	+	259.137i	0.0102310	+	0.0177205i
$599$	−6154.59	−	10660.1i	−0.419816	−	0.727143i	0.576105	−	0.817376i	$-0.304572\pi$
$599$	−6154.59	−	10660.1i	−0.419816	−	0.727143i	−0.995921	+	0.0902332i	$0.971239\pi$
$600$	713.343	−	1235.55i	0.0485369	−	0.0840683i
$601$	15293.6			1.03800			0.519001	−	0.854774i	$-0.326304\pi$
$601$	15293.6			1.03800			0.519001	+	0.854774i	$0.326304\pi$
$602$		0			0
$603$	3909.16			0.264002
$604$	−2367.91	+	4101.33i	−0.159518	+	0.276293i
$605$	981.075	+	1699.27i	0.0659279	+	0.114190i
$606$	743.568	+	1287.90i	0.0498439	+	0.0863321i
$607$	2669.40	−	4623.54i	0.178497	−	0.309166i	−0.762869	−	0.646553i	$-0.776210\pi$
$607$	2669.40	−	4623.54i	0.178497	−	0.309166i	0.941366	+	0.337387i	$0.109543\pi$
$608$	10563.1			0.704590
$609$		0			0
$610$	−654.780			−0.0434611
$611$	6036.84	−	10456.1i	0.399713	−	0.692323i
$612$	−21280.7	−	36859.2i	−1.40559	−	2.43455i
$613$	14424.3	+	24983.6i	0.950396	+	1.64613i	0.744569	+	0.667545i	$0.232655\pi$
$613$	14424.3	+	24983.6i	0.950396	+	1.64613i	0.205827	+	0.978588i	$0.434012\pi$
$614$	−973.838	+	1686.74i	−0.0640080	+	0.110865i
$615$	−6929.52			−0.454350
$616$		0			0
$617$	−12346.6			−0.805602			−0.402801	−	0.915287i	$-0.631963\pi$
$617$	−12346.6			−0.805602			−0.402801	+	0.915287i	$0.631963\pi$
$618$	2610.09	−	4520.81i	0.169892	−	0.294262i
$619$	3191.58	+	5527.98i	0.207238	+	0.358947i	0.950844	−	0.309672i	$-0.100219\pi$
$619$	3191.58	+	5527.98i	0.207238	+	0.358947i	−0.743605	+	0.668619i	$0.766886\pi$
$620$	4913.90	+	8511.12i	0.318301	+	0.551314i
$621$	4424.27	−	7663.06i	0.285893	−	0.495182i
$622$	−1216.92			−0.0784473
$623$		0			0
$624$	−21574.7			−1.38410
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	335.961	+	581.901i	0.0214500	+	0.0371525i
$627$	−22742.1	−	39390.5i	−1.44854	−	2.50894i
$628$	−6299.03	+	10910.2i	−0.400252	+	0.693257i
$629$	−602.602			−0.0381992
$630$		0			0
$631$	25708.6			1.62194			0.810969	−	0.585090i	$-0.198941\pi$
$631$	25708.6			1.62194			0.810969	+	0.585090i	$0.198941\pi$
$632$	−794.858	+	1376.73i	−0.0500281	+	0.0866512i
$633$	11237.4	+	19463.7i	0.705601	+	1.22214i
$634$	348.616	+	603.820i	0.0218380	+	0.0378246i
$635$	6363.52	−	11021.9i	0.397683	−	0.688807i
$636$	−37328.5			−2.32732
$637$		0			0
$638$	−1145.97			−0.0711120
$639$	23628.6	−	40925.9i	1.46280	−	2.53365i
$640$	−1811.12	−	3136.95i	−0.111861	−	0.193748i
$641$	9308.76	+	16123.2i	0.573594	+	0.993495i	0.996193	+	0.0871776i	$0.0277847\pi$
$641$	9308.76	+	16123.2i	0.573594	+	0.993495i	−0.422598	+	0.906317i	$0.638882\pi$
$642$	3202.80	−	5547.41i	0.196892	−	0.341026i
$643$	21168.8			1.29832			0.649158	−	0.760654i	$-0.275121\pi$
$643$	21168.8			1.29832			0.649158	+	0.760654i	$0.275121\pi$
$644$		0			0
$645$	11568.5			0.706219
$646$	2244.13	−	3886.95i	0.136678	−	0.236734i
$647$	−2976.23	−	5154.99i	−0.180847	−	0.313236i	0.761322	−	0.648373i	$-0.224550\pi$
$647$	−2976.23	−	5154.99i	−0.180847	−	0.313236i	−0.942169	+	0.335138i	$0.891217\pi$
$648$	−5993.60	−	10381.2i	−0.363350	−	0.629340i
$649$	10988.5	−	19032.6i	0.664615	−	1.15115i
$650$	−336.651			−0.0203147
$651$		0			0
$652$	24311.2			1.46028
$653$	1520.32	−	2633.26i	0.0911096	−	0.157806i	−0.816869	−	0.576824i	$-0.804292\pi$
$653$	1520.32	−	2633.26i	0.0911096	−	0.157806i	0.907978	+	0.419017i	$0.137625\pi$
$654$	−68.1560	−	118.050i	−0.00407509	−	0.00705827i
$655$	−2427.18	−	4204.00i	−0.144791	−	0.250785i
$656$	−4321.40	+	7484.89i	−0.257199	+	0.445482i
$657$	−17719.3			−1.05220
$658$		0			0
$659$	−3335.95			−0.197193			−0.0985966	−	0.995127i	$-0.531435\pi$
$659$	−3335.95			−0.197193			−0.0985966	+	0.995127i	$0.531435\pi$
$660$	−5866.58	+	10161.2i	−0.345995	+	0.599280i
$661$	−773.951	−	1340.52i	−0.0455419	−	0.0788809i	0.842356	−	0.538922i	$-0.181168\pi$
$661$	−773.951	−	1340.52i	−0.0455419	−	0.0788809i	−0.887898	+	0.460041i	$0.847835\pi$
$662$	−84.2752	−	145.969i	−0.00494781	−	0.00856985i
$663$	−14159.5	+	24524.9i	−0.829425	+	1.43661i
$664$	3992.34			0.233332
$665$		0			0
$666$	−189.467			−0.0110235
$667$	−1125.31	+	1949.09i	−0.0653256	+	0.113147i
$668$	12783.0	+	22140.8i	0.740404	+	1.28242i
$669$	−7933.77	−	13741.7i	−0.458501	−	0.794148i
$670$	53.1706	−	92.0941i	0.00306591	−	0.00531031i
$671$	10863.3			0.624998
$672$		0			0
$673$	19632.4			1.12448			0.562239	−	0.826975i	$-0.309940\pi$
$673$	19632.4			1.12448			0.562239	+	0.826975i	$0.309940\pi$
$674$	1509.47	−	2614.47i	0.0862649	−	0.149415i
$675$	4977.64	+	8621.52i	0.283836	+	0.491619i
$676$	−3410.86	−	5907.78i	−0.194064	−	0.336128i
$677$	15159.1	−	26256.4i	0.860579	−	1.49057i	−0.0107919	−	0.999942i	$-0.503435\pi$
$677$	15159.1	−	26256.4i	0.860579	−	1.49057i	0.871371	−	0.490625i	$-0.163231\pi$
$678$	1645.15			0.0931885
$679$		0			0
$680$	−2335.68			−0.131719
$681$	11742.0	−	20337.7i	0.660726	−	1.14441i
$682$	1414.05	+	2449.20i	0.0793940	+	0.137514i
$683$	−14485.4	−	25089.4i	−0.811520	−	1.40559i	−0.911800	−	0.410634i	$-0.865307\pi$
$683$	−14485.4	−	25089.4i	−0.811520	−	1.40559i	0.100281	−	0.994959i	$-0.468026\pi$
$684$	−40679.8	+	70459.5i	−2.27402	+	3.93872i
$685$	918.176			0.0512142
$686$		0			0
$687$	35715.1			1.98343
$688$	7214.41	−	12495.7i	0.399777	−	0.692434i
$689$	8884.69	+	15388.7i	0.491263	+	0.850892i
$690$	−199.841	−	346.135i	−0.0110258	−	0.0190973i
$691$	−1717.45	+	2974.72i	−0.0945514	+	0.163768i	−0.909421	−	0.415876i	$-0.863475\pi$
$691$	−1717.45	+	2974.72i	−0.0945514	+	0.163768i	0.814870	+	0.579644i	$0.196808\pi$
$692$	17728.9			0.973917
$693$		0			0
$694$	2930.77			0.160304
$695$	−2697.26	+	4671.79i	−0.147213	+	0.254980i
$696$	2890.03	+	5005.68i	0.157394	+	0.272615i
$697$	5672.27	+	9824.67i	0.308253	+	0.533911i
$698$	−1597.18	+	2766.39i	−0.0866103	+	0.150013i
$699$	29400.6			1.59089
$700$		0			0
$701$	16304.4			0.878471			0.439235	−	0.898372i	$-0.355249\pi$
$701$	16304.4			0.878471			0.439235	+	0.898372i	$0.355249\pi$
$702$	−2681.16	+	4643.91i	−0.144151	+	0.249677i
$703$	575.962	+	997.596i	0.0309002	+	0.0535207i
$704$	7051.92	+	12214.3i	0.377527	+	0.653896i
$705$	−8063.56	+	13966.5i	−0.430768	+	0.746111i
$706$	−1821.11			−0.0970800
$707$		0			0
$708$	−54947.2			−2.91673
$709$	−8047.18	+	13938.1i	−0.426260	+	0.738303i	−0.996537	−	0.0831487i	$-0.973502\pi$
$709$	−8047.18	+	13938.1i	−0.426260	+	0.738303i	0.570277	+	0.821452i	$0.306836\pi$
$710$	−642.769	−	1113.31i	−0.0339756	−	0.0588475i
$711$	−9209.59	−	15951.5i	−0.485776	−	0.841388i
$712$	−470.649	+	815.189i	−0.0247729	+	0.0429080i
$713$	5554.21			0.291735
$714$		0			0
$715$	5585.30			0.292138
$716$	−10558.7	+	18288.2i	−0.551114	+	0.954557i
$717$	−2663.46	−	4613.25i	−0.138729	−	0.240286i
$718$	1522.25	+	2636.61i	0.0791223	+	0.137044i
$719$	4325.96	−	7492.79i	0.224383	−	0.388642i	−0.731751	−	0.681572i	$-0.761297\pi$
$719$	4325.96	−	7492.79i	0.224383	−	0.388642i	0.956134	+	0.292929i	$0.0946301\pi$
$720$	20617.3			1.06717
$721$		0			0
$722$	−6046.56			−0.311676
$723$	−15269.9	+	26448.2i	−0.785466	+	1.36047i
$724$	−5084.81	−	8807.16i	−0.261016	−	0.452093i
$725$	−1266.06	−	2192.88i	−0.0648555	−	0.112333i
$726$	705.860	−	1222.59i	0.0360839	−	0.0624992i
$727$	6999.43			0.357076			0.178538	−	0.983933i	$-0.442863\pi$
$727$	6999.43			0.357076			0.178538	+	0.983933i	$0.442863\pi$
$728$		0			0
$729$	34160.1			1.73551
$730$	−241.010	+	417.441i	−0.0122194	+	0.0211647i
$731$	−9469.63	−	16401.9i	−0.479134	−	0.829884i
$732$	−13580.3	−	23521.8i	−0.685716	−	1.18769i
$733$	2583.87	−	4475.39i	0.130201	−	0.225515i	−0.793553	−	0.608501i	$-0.791771\pi$
$733$	2583.87	−	4475.39i	0.130201	−	0.225515i	0.923754	+	0.382986i	$0.125104\pi$
$734$	−3020.67			−0.151900
$735$		0			0
$736$	−1539.97			−0.0771251
$737$	−882.141	+	1527.91i	−0.0440896	+	0.0763655i
$738$	1783.44	+	3089.01i	0.0889559	+	0.154076i
$739$	6159.55	+	10668.6i	0.306607	+	0.531059i	0.977618	−	0.210389i	$-0.0674729\pi$
$739$	6159.55	+	10668.6i	0.306607	+	0.531059i	−0.671011	+	0.741448i	$0.734140\pi$
$740$	148.576	−	257.341i	0.00738076	−	0.0127838i
$741$	54134.1			2.68376
$742$		0			0
$743$	16942.4			0.836548			0.418274	−	0.908321i	$-0.362635\pi$
$743$	16942.4			0.836548			0.418274	+	0.908321i	$0.362635\pi$
$744$	7132.19	−	12353.3i	0.351450	−	0.608729i
$745$	−3028.09	−	5244.80i	−0.148914	−	0.257926i
$746$	−2362.78	−	4092.45i	−0.115962	−	0.200852i
$747$	−23128.5	+	40059.8i	−1.13284	+	1.96213i
$748$	19208.8			0.938959
$749$		0			0
$750$	449.673			0.0218930
$751$	−16458.9	+	28507.7i	−0.799728	+	1.38517i	0.120066	+	0.992766i	$0.461689\pi$
$751$	−16458.9	+	28507.7i	−0.799728	+	1.38517i	−0.919793	+	0.392403i	$0.871644\pi$
$752$	10057.2	+	17419.6i	0.487699	+	0.844719i
$753$	4456.21	+	7718.38i	0.215662	+	0.373537i
$754$	681.952	−	1181.18i	0.0329380	−	0.0570503i
$755$	−3011.22			−0.145152
$756$		0			0
$757$	−9433.45			−0.452926			−0.226463	−	0.974020i	$-0.572716\pi$
$757$	−9433.45			−0.452926			−0.226463	+	0.974020i	$0.572716\pi$
$758$	−1059.08	+	1834.39i	−0.0507489	+	0.0878996i
$759$	3315.52	+	5742.65i	0.158558	+	0.274631i
$760$	2232.42	+	3866.67i	0.106551	+	0.184551i
$761$	−17275.5	+	29922.0i	−0.822912	+	1.42532i	0.0805935	+	0.996747i	$0.474318\pi$
$761$	−17275.5	+	29922.0i	−0.822912	+	1.42532i	−0.903505	+	0.428578i	$0.859015\pi$
$762$	−9156.82			−0.435323
$763$		0			0
$764$	1099.94			0.0520871
$765$	13531.1	−	23436.6i	0.639501	−	1.10765i
$766$	−136.248	−	235.988i	−0.00642667	−	0.0111313i
$767$	13078.2	+	22652.1i	0.615679	+	1.06639i
$768$	16634.1	−	28811.1i	0.781552	−	1.35369i
$769$	348.011			0.0163194			0.00815970	−	0.999967i	$-0.497403\pi$
$769$	348.011			0.0163194			0.00815970	+	0.999967i	$0.497403\pi$
$770$		0			0
$771$	−61699.3			−2.88203
$772$	9376.60	−	16240.7i	0.437139	−	0.757146i
$773$	−15041.9	−	26053.4i	−0.699897	−	1.21226i	−0.968502	−	0.249007i	$-0.919896\pi$
$773$	−15041.9	−	26053.4i	−0.699897	−	1.21226i	0.268604	−	0.963251i	$-0.413438\pi$
$774$	−2977.38	−	5156.98i	−0.138269	−	0.239488i
$775$	−3124.45	+	5411.71i	−0.144818	+	0.250832i
$776$	−983.323			−0.0454887
$777$		0			0
$778$	4813.64			0.221822
$779$	10843.0	−	18780.7i	0.498706	−	0.863784i
$780$	−6982.25	−	12093.6i	−0.320519	−	0.555154i
$781$	10664.0	+	18470.6i	0.488590	+	0.846263i
$782$	−327.167	+	566.669i	−0.0149609	+	0.0259131i
$783$	−40332.7			−1.84083
$784$		0			0
$785$	−8010.35			−0.364206
$786$	−1746.30	+	3024.68i	−0.0792474	+	0.137261i
$787$	15979.2	+	27676.8i	0.723757	+	1.25358i	0.959483	+	0.281765i	$0.0909198\pi$
$787$	15979.2	+	27676.8i	0.723757	+	1.25358i	−0.235726	+	0.971820i	$0.575747\pi$
$788$	−3965.91	−	6869.15i	−0.179289	−	0.310537i
$789$	20098.7	−	34812.0i	0.906887	−	1.57077i
$790$	−501.058			−0.0225656
$791$		0			0
$792$	12183.8			0.546630
$793$	−6464.61	+	11197.0i	−0.289489	+	0.501410i
$794$	−1535.18	−	2659.00i	−0.0686163	−	0.118847i
$795$	−11867.5	−	20555.1i	−0.529430	−	0.917000i
$796$	−3912.28	+	6776.27i	−0.174205	+	0.301732i
$797$	364.165			0.0161849			0.00809247	−	0.999967i	$-0.497424\pi$
$797$	364.165			0.0161849			0.00809247	+	0.999967i	$0.497424\pi$
$798$		0			0
$799$	26402.2			1.16902
$800$	866.293	−	1500.46i	0.0382851	−	0.0663117i
$801$	−5453.16	−	9445.15i	−0.240547	−	0.416639i
$802$	−2648.25	−	4586.90i	−0.116600	−	0.201957i
$803$	3998.54	−	6925.68i	0.175723	−	0.304361i
$804$	4411.09			0.193492
$805$		0			0
$806$	−3365.92			−0.147096
$807$	28672.1	−	49661.5i	1.25069	−	2.16625i
$808$	1210.97	+	2097.46i	0.0527249	+	0.0913222i
$809$	−15357.4	−	26599.8i	−0.667412	−	1.15599i	−0.978625	−	0.205652i	$-0.934068\pi$
$809$	−15357.4	−	26599.8i	−0.667412	−	1.15599i	0.311213	−	0.950340i	$-0.399265\pi$
$810$	1889.10	−	3272.02i	0.0819461	−	0.141935i
$811$	−18967.6			−0.821260			−0.410630	−	0.911802i	$-0.634691\pi$
$811$	−18967.6			−0.821260			−0.410630	+	0.911802i	$0.634691\pi$
$812$		0			0
$813$	70500.4			3.04128
$814$	42.7550	−	74.0538i	0.00184098	−	0.00318868i
$815$	7729.03	+	13387.1i	0.332192	+	0.575373i
$816$	−23589.3	−	40857.9i	−1.01200	−	1.75284i
$817$	−18102.0	+	31353.6i	−0.775163	+	1.34262i
$818$	−2320.17			−0.0991720
$819$		0			0
$820$	−5594.16			−0.238240
$821$	7408.48	−	12831.9i	0.314930	−	0.545475i	−0.664492	−	0.747295i	$-0.731352\pi$
$821$	7408.48	−	12831.9i	0.314930	−	0.545475i	0.979423	+	0.201820i	$0.0646855\pi$
$822$	−330.303	−	572.102i	−0.0140154	−	0.0242754i
$823$	13294.0	+	23025.9i	0.563063	+	0.975254i	0.997227	+	0.0744198i	$0.0237105\pi$
$823$	13294.0	+	23025.9i	0.563063	+	0.975254i	−0.434164	+	0.900834i	$0.642956\pi$
$824$	4250.77	−	7362.55i	0.179712	−	0.311270i
$825$	−7460.42			−0.314835
$826$		0			0
$827$	−11287.0			−0.474592			−0.237296	−	0.971437i	$-0.576261\pi$
$827$	−11287.0			−0.474592			−0.237296	+	0.971437i	$0.576261\pi$
$828$	5930.61	−	10272.1i	0.248917	−	0.431136i
$829$	7224.30	+	12512.9i	0.302666	+	0.524233i	0.976739	−	0.214432i	$-0.0687899\pi$
$829$	7224.30	+	12512.9i	0.302666	+	0.524233i	−0.674073	+	0.738665i	$0.735457\pi$
$830$	629.166	+	1089.75i	0.0263116	+	0.0455731i
$831$	27469.6	−	47578.7i	1.14670	−	1.98615i
$832$	−16786.0			−0.699459
$833$		0			0
$834$	3881.23			0.161146
$835$	−8127.97	+	14078.0i	−0.336862	+	0.583462i
$836$	−18359.6	−	31799.7i	−0.759545	−	1.31557i
$837$	49767.7	+	86200.2i	2.05523	+	3.55975i
$838$	−2811.61	+	4869.85i	−0.115901	+	0.200747i
$839$	−40032.0			−1.64727			−0.823635	−	0.567120i	$-0.808057\pi$
$839$	−40032.0			−1.64727			−0.823635	+	0.567120i	$0.808057\pi$
$840$		0			0
$841$	−14130.4			−0.579376
$842$	−374.217	+	648.163i	−0.0153164	+	0.0265287i
$843$	−12629.0	−	21874.1i	−0.515975	−	0.893696i
$844$	9071.86	+	15712.9i	0.369984	+	0.640831i
$845$	2168.76	−	3756.41i	0.0882932	−	0.152928i
$846$	8301.23			0.337355
$847$		0			0
$848$	−29603.3			−1.19880
$849$	−12337.9	+	21369.8i	−0.498745	+	0.863852i
$850$	−368.087	−	637.546i	−0.0148533	−	0.0257266i
$851$	−83.9682	−	145.437i	−0.00338236	−	0.00585843i
$852$	26662.4	−	46180.7i	1.07211	−	1.85695i
$853$	−10864.4			−0.436098			−0.218049	−	0.975938i	$-0.569969\pi$
$853$	−10864.4			−0.436098			−0.218049	+	0.975938i	$0.569969\pi$
$854$		0			0
$855$	−51731.7			−2.06922
$856$	5216.05	−	9034.46i	0.208272	−	0.360738i
$857$	21006.8	+	36384.9i	0.837316	+	1.45027i	0.892131	+	0.451778i	$0.149210\pi$
$857$	21006.8	+	36384.9i	0.837316	+	1.45027i	−0.0548144	+	0.998497i	$0.517457\pi$
$858$	−2009.25	−	3480.12i	−0.0799471	−	0.138472i
$859$	8067.81	−	13973.9i	0.320454	−	0.555043i	−0.660128	−	0.751153i	$-0.729498\pi$
$859$	8067.81	−	13973.9i	0.320454	−	0.555043i	0.980582	+	0.196111i	$0.0628312\pi$
$860$	9339.22			0.370308
$861$		0			0
$862$	−3317.76			−0.131094
$863$	23123.4	−	40050.9i	0.912086	−	1.57978i	0.100974	−	0.994889i	$-0.467804\pi$
$863$	23123.4	−	40050.9i	0.912086	−	1.57978i	0.811112	−	0.584891i	$-0.198863\pi$
$864$	−13798.7	−	23900.0i	−0.543335	−	0.941083i
$865$	5636.37	+	9762.47i	0.221552	+	0.383739i
$866$	1262.43	−	2186.59i	0.0495370	−	0.0858006i
$867$	−14070.7			−0.551171
$868$		0			0
$869$	8312.93			0.324507
$870$	−910.900	+	1577.73i	−0.0354970	+	0.0614826i
$871$	−1049.90	−	1818.48i	−0.0408433	−	0.0707426i
$872$	−110.998	−	192.255i	−0.00431063	−	0.00746624i
$873$	5696.62	−	9866.83i	0.220849	−	0.382522i
$874$	1250.81			0.0484089
$875$		0			0
$876$	−19994.5			−0.771177
$877$	12547.0	−	21732.1i	0.483106	−	0.836764i	−0.516706	−	0.856163i	$-0.672842\pi$
$877$	12547.0	−	21732.1i	0.483106	−	0.836764i	0.999812	+	0.0193992i	$0.00617533\pi$
$878$	−1440.87	−	2495.67i	−0.0553840	−	0.0959279i
$879$	2869.68	+	4970.43i	0.110116	+	0.190726i
$880$	−4652.49	+	8058.34i	−0.178222	+	0.308689i
$881$	27546.6			1.05342			0.526712	−	0.850044i	$-0.323424\pi$
$881$	27546.6			1.05342			0.526712	+	0.850044i	$0.323424\pi$
$882$		0			0
$883$	5825.31			0.222013			0.111006	−	0.993820i	$-0.464593\pi$
$883$	5825.31			0.222013			0.111006	+	0.993820i	$0.464593\pi$
$884$	−11430.9	+	19798.8i	−0.434911	+	0.753289i
$885$	−17468.8	−	30256.9i	−0.663512	−	1.14924i
$886$	957.333	+	1658.15i	0.0363005	+	0.0628743i
$887$	3107.15	−	5381.73i	0.117619	−	0.203721i	−0.801205	−	0.598390i	$-0.795807\pi$
$887$	3107.15	−	5381.73i	0.117619	−	0.203721i	0.918824	+	0.394669i	$0.129141\pi$
$888$	−431.296			−0.0162988
$889$		0			0
$890$	−296.685			−0.0111740
$891$	−31341.7	+	54285.4i	−1.17844	+	2.04111i
$892$	−6404.89	−	11093.6i	−0.240417	−	0.416414i
$893$	−25235.0	−	43708.4i	−0.945642	−	1.63790i
$894$	−2178.64	+	3773.51i	−0.0815040	+	0.141169i
$895$	−13427.3			−0.501481
$896$		0			0
$897$	−7892.08			−0.293767
$898$	−142.731	+	247.218i	−0.00530401	+	0.00918681i
$899$	−12658.4	−	21925.0i	−0.469611	−	0.813391i
$900$	6672.39	+	11556.9i	0.247125	+	0.428034i
$901$	−19428.7	+	33651.5i	−0.718383	+	1.24428i
$902$	−1609.80			−0.0594242
$903$		0			0
$904$	2679.28			0.0985748
$905$	3233.13	−	5599.95i	0.118755	−	0.205689i
$906$	1083.25	+	1876.25i	0.0397226	+	0.0688015i
$907$	−12208.0	−	21144.8i	−0.446923	−	0.774093i	0.551261	−	0.834333i	$-0.314147\pi$
$907$	−12208.0	−	21144.8i	−0.446923	−	0.774093i	−0.998184	+	0.0602399i	$0.980813\pi$
$908$	9479.25	−	16418.5i	0.346454	−	0.600075i
$909$	−28061.7			−1.02392
$910$		0			0
$911$	−3493.35			−0.127047			−0.0635236	−	0.997980i	$-0.520234\pi$
$911$	−3493.35			−0.127047			−0.0635236	+	0.997980i	$0.520234\pi$
$912$	−45093.0	+	78103.4i	−1.63726	+	2.83581i
$913$	−10438.3	−	18079.7i	−0.378378	−	0.655369i
$914$	2129.61	+	3688.59i	0.0770690	+	0.133488i
$915$	8634.93	−	14956.1i	0.311980	−	0.540366i
$916$	28832.6			1.04002
$917$		0			0
$918$	−11726.1			−0.421590
$919$	−7828.37	+	13559.1i	−0.280995	+	0.486697i	−0.971630	−	0.236506i	$-0.923998\pi$
$919$	−7828.37	+	13559.1i	−0.280995	+	0.486697i	0.690635	+	0.723203i	$0.257331\pi$
$920$	−325.459	−	563.712i	−0.0116631	−	0.0202011i
$921$	−25685.0	−	44487.8i	−0.918947	−	1.59166i
$922$	−1920.57	+	3326.53i	−0.0686016	+	0.118821i
$923$	−25384.1			−0.905230
$924$		0			0
$925$	188.941			0.00671605
$926$	−2558.51	+	4431.47i	−0.0907968	+	0.157265i
$927$	49251.4	+	85305.9i	1.74501	+	3.02245i
$928$	3509.69	+	6078.96i	0.124150	+	0.215034i
$929$	−15252.2	+	26417.7i	−0.538654	+	0.932977i	0.460322	+	0.887752i	$0.347734\pi$
$929$	−15252.2	+	26417.7i	−0.538654	+	0.932977i	−0.998977	+	0.0452250i	$0.985600\pi$
$930$	4495.94			0.158525
$931$		0			0
$932$	23735.0			0.834189
$933$	16048.2	−	27796.3i	0.563124	−	0.975360i
$934$	2720.83	+	4712.62i	0.0953194	+	0.165098i
$935$	6106.85	+	10577.4i	0.213599	+	0.369965i
$936$	−7250.39	+	12558.0i	−0.253191	+	0.438539i
$937$	−50290.7			−1.75339			−0.876694	−	0.481049i	$-0.840256\pi$
$937$	−50290.7			−1.75339			−0.876694	+	0.481049i	$0.840256\pi$
$938$		0			0
$939$	−17722.0			−0.615904
$940$	−6509.66	+	11275.1i	−0.225874	+	0.391226i
$941$	9340.83	+	16178.8i	0.323595	+	0.560482i	0.981227	−	0.192857i	$-0.0617753\pi$
$941$	9340.83	+	16178.8i	0.323595	+	0.560482i	−0.657632	+	0.753339i	$0.728442\pi$
$942$	2881.63	+	4991.13i	0.0996694	+	0.172633i
$943$	−1580.78	+	2737.99i	−0.0545888	+	0.0945506i
$944$	−43575.8			−1.50241
$945$		0			0
$946$	2687.50			0.0923660
$947$	−8166.28	+	14144.4i	−0.280220	+	0.485355i	−0.971439	−	0.237290i	$-0.923741\pi$
$947$	−8166.28	+	14144.4i	−0.280220	+	0.485355i	0.691219	+	0.722646i	$0.257074\pi$
$948$	−10392.1	−	17999.6i	−0.356033	−	0.616667i
$949$	4758.95	+	8242.75i	0.162784	+	0.281950i
$950$	−703.630	+	1218.72i	−0.0240303	+	0.0416217i
$951$	−18389.5			−0.627046
$952$		0			0
$953$	−34233.6			−1.16362			−0.581812	−	0.813323i	$-0.697656\pi$
$953$	−34233.6			−1.16362			−0.581812	+	0.813323i	$0.697656\pi$
$954$	−6108.65	+	10580.5i	−0.207311	+	0.359073i
$955$	349.694	+	605.688i	0.0118490	+	0.0205231i
$956$	−2150.20	−	3724.25i	−0.0727431	−	0.125995i
$957$	15112.5	−	26175.7i	0.510469	−	0.884158i
$958$	−543.345			−0.0183243
$959$		0			0
$960$	22421.5			0.753801
$961$	−16343.6	+	28307.9i	−0.548608	+	0.950218i
$962$	50.8858	+	88.1368i	0.00170543	+	0.00295389i
$963$	60435.6	+	104677.i	2.02233	+	3.50279i
$964$	−12327.3	+	21351.5i	−0.411862	+	0.713365i
$965$	11924.0			0.397770
$966$		0			0
$967$	53792.0			1.78887			0.894434	−	0.447200i	$-0.147579\pi$
$967$	53792.0			1.78887			0.894434	+	0.447200i	$0.147579\pi$
$968$	1149.56	−	1991.09i	0.0381696	−	0.0661117i
$969$	59189.1	+	102518.i	1.96226	+	3.39873i
$970$	−154.965	−	268.408i	−0.00512952	−	0.00888459i
$971$	413.165	−	715.624i	0.0136551	−	0.0236513i	−0.859117	−	0.511779i	$-0.828987\pi$
$971$	413.165	−	715.624i	0.0136551	−	0.0236513i	0.872772	+	0.488128i	$0.162320\pi$
$972$	72175.1			2.38171
$973$		0			0
$974$	−2071.85			−0.0681586
$975$	4439.59	−	7689.60i	0.145826	−	0.252579i
$976$	−10769.9	−	18654.0i	−0.353212	−	0.611782i
$977$	−4351.76	−	7537.47i	−0.142503	−	0.246822i	0.785936	−	0.618308i	$-0.212182\pi$
$977$	−4351.76	−	7537.47i	−0.142503	−	0.246822i	−0.928438	+	0.371486i	$0.878848\pi$
$978$	5560.86	−	9631.69i	0.181817	−	0.314916i
$979$	4922.23			0.160690
$980$		0			0
$981$	2572.15			0.0837130
$982$	−589.792	+	1021.55i	−0.0191660	+	0.0331965i
$983$	20500.4	+	35507.8i	0.665170	+	1.15211i	0.979239	+	0.202708i	$0.0649743\pi$
$983$	20500.4	+	35507.8i	0.665170	+	1.15211i	−0.314069	+	0.949400i	$0.601692\pi$
$984$	4059.77	+	7031.73i	0.131525	+	0.227808i
$985$	2521.68	−	4367.68i	0.0815711	−	0.141285i
$986$	2982.53			0.0963317
$987$		0			0
$988$	43702.1			1.40724
$989$	2639.05	−	4570.96i	0.0848501	−	0.146965i
$990$	1920.08	+	3325.68i	0.0616406	+	0.106765i
$991$	9170.49	+	15883.8i	0.293956	+	0.509147i	0.974741	−	0.223336i	$-0.0716948\pi$
$991$	9170.49	+	15883.8i	0.293956	+	0.509147i	−0.680786	+	0.732483i	$0.738361\pi$
$992$	8661.41	−	15002.0i	0.277218	−	0.480155i
$993$	4445.52			0.142069
$994$		0			0
$995$	−4975.18			−0.158516
$996$	−26098.2	+	45203.4i	−0.830273	+	1.43808i
$997$	−28667.7	−	49653.9i	−0.910646	−	1.57729i	−0.813153	−	0.582050i	$-0.802251\pi$
$997$	−28667.7	−	49653.9i	−0.910646	−	1.57729i	−0.0974932	−	0.995236i	$-0.531082\pi$
$998$	1611.01	+	2790.35i	0.0510978	+	0.0885040i
$999$	1504.77	−	2606.34i	0.0476565	−	0.0825434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.q.226.4		12
7.2	even	3		245.4.a.o.1.3	✓	6
7.3	odd	6		245.4.e.p.116.4		12
7.4	even	3	inner	245.4.e.q.116.4		12
7.5	odd	6		245.4.a.p.1.3	yes	6
7.6	odd	2		245.4.e.p.226.4		12
21.2	odd	6		2205.4.a.bz.1.4		6
21.5	even	6		2205.4.a.ca.1.4		6
35.9	even	6		1225.4.a.bj.1.4		6
35.19	odd	6		1225.4.a.bi.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.3	✓	6	7.2	even	3
245.4.a.p.1.3	yes	6	7.5	odd	6
245.4.e.p.116.4		12	7.3	odd	6
245.4.e.p.226.4		12	7.6	odd	2
245.4.e.q.116.4		12	7.4	even	3	inner
245.4.e.q.226.4		12	1.1	even	1	trivial
1225.4.a.bi.1.4		6	35.19	odd	6
1225.4.a.bj.1.4		6	35.9	even	6
2205.4.a.bz.1.4		6	21.2	odd	6
2205.4.a.ca.1.4		6	21.5	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.184657 - 0.319836i) q^{2} +(4.87035 + 8.43569i) q^{3} +(3.93180 + 6.81008i) q^{4} +(-2.50000 + 4.33013i) q^{5} +3.59738 q^{6} +5.85867 q^{8} +(-33.9406 + 58.7868i) q^{9} +O(q^{10})\)	\(q+(0.184657 - 0.319836i) q^{2} +(4.87035 + 8.43569i) q^{3} +(3.93180 + 6.81008i) q^{4} +(-2.50000 + 4.33013i) q^{5} +3.59738 q^{6} +5.85867 q^{8} +(-33.9406 + 58.7868i) q^{9} +(0.923287 + 1.59918i) q^{10} +(-15.3180 - 26.5316i) q^{11} +(-38.2985 + 66.3350i) q^{12} +36.4622 q^{13} -48.7035 q^{15} +(-30.3726 + 52.6069i) q^{16} +(39.8670 + 69.0517i) q^{17} +(12.5348 + 21.7108i) q^{18} +(76.2092 - 131.998i) q^{19} -39.3180 q^{20} -11.3144 q^{22} +(-11.1104 + 19.2437i) q^{23} +(28.5337 + 49.4219i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(6.73302 - 11.6619i) q^{26} -398.211 q^{27} +101.285 q^{29} +(-8.99346 + 15.5771i) q^{30} +(-124.978 - 216.469i) q^{31} +(34.6517 + 60.0185i) q^{32} +(149.208 - 258.437i) q^{33} +29.4470 q^{34} -533.791 q^{36} +(-3.77882 + 6.54511i) q^{37} +(-28.1452 - 48.7489i) q^{38} +(177.584 + 307.584i) q^{39} +(-14.6467 + 25.3688i) q^{40} +142.280 q^{41} -237.530 q^{43} +(120.455 - 208.634i) q^{44} +(-169.703 - 293.934i) q^{45} +(4.10322 + 7.10699i) q^{46} +(165.564 - 286.766i) q^{47} -591.700 q^{48} -9.23287 q^{50} +(-388.333 + 672.612i) q^{51} +(143.362 + 248.311i) q^{52} +(243.668 + 422.046i) q^{53} +(-73.5326 + 127.362i) q^{54} +153.180 q^{55} +1484.66 q^{57} +(18.7030 - 32.3945i) q^{58} +(358.677 + 621.247i) q^{59} +(-191.493 - 331.675i) q^{60} +(-177.296 + 307.086i) q^{61} -92.3126 q^{62} -460.367 q^{64} +(-91.1556 + 157.886i) q^{65} +(-55.1049 - 95.4445i) q^{66} +(-28.7942 - 49.8730i) q^{67} +(-313.499 + 542.996i) q^{68} -216.445 q^{69} -696.174 q^{71} +(-198.847 + 344.412i) q^{72} +(130.517 + 226.063i) q^{73} +(1.39558 + 2.41721i) q^{74} +(121.759 - 210.892i) q^{75} +1198.56 q^{76} +131.169 q^{78} +(-135.672 + 234.991i) q^{79} +(-151.863 - 263.034i) q^{80} +(-1023.03 - 1771.94i) q^{81} +(26.2730 - 45.5062i) q^{82} +681.441 q^{83} -398.670 q^{85} +(-43.8617 + 75.9707i) q^{86} +(493.292 + 854.407i) q^{87} +(-89.7433 - 155.440i) q^{88} +(-80.3339 + 139.142i) q^{89} -125.348 q^{90} -174.735 q^{92} +(1217.37 - 2108.55i) q^{93} +(-61.1453 - 105.907i) q^{94} +(381.046 + 659.991i) q^{95} +(-337.532 + 584.622i) q^{96} -167.841 q^{97} +2079.61 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^3 - 14 * q^4 - 30 * q^5 - 48 * q^6 - 132 * q^8 - 70 * q^9 + 10 * q^10 + 16 * q^11 + 160 * q^12 - 336 * q^13 - 160 * q^15 - 298 * q^16 - 4 * q^17 - 354 * q^18 + 308 * q^19 + 140 * q^20 - 472 * q^22 + 336 * q^23 - 92 * q^24 - 150 * q^25 + 56 * q^26 - 1928 * q^27 + 352 * q^29 + 120 * q^30 + 392 * q^31 + 770 * q^32 + 188 * q^33 - 1624 * q^34 + 460 * q^36 + 140 * q^37 + 20 * q^38 - 140 * q^39 + 330 * q^40 - 1312 * q^41 - 776 * q^43 + 160 * q^44 - 350 * q^45 + 388 * q^46 + 628 * q^47 - 2792 * q^48 - 100 * q^50 - 744 * q^51 + 1520 * q^52 + 676 * q^53 + 2284 * q^54 - 160 * q^55 + 2936 * q^57 + 2012 * q^58 + 996 * q^59 + 800 * q^60 + 740 * q^61 + 728 * q^62 + 2852 * q^64 + 840 * q^65 - 3620 * q^66 - 1768 * q^67 - 2940 * q^68 + 2096 * q^69 - 448 * q^71 - 2858 * q^72 + 2640 * q^73 - 928 * q^74 + 400 * q^75 + 2680 * q^76 + 16 * q^78 - 1636 * q^79 - 1490 * q^80 - 4442 * q^81 - 1756 * q^82 - 280 * q^83 + 40 * q^85 - 1180 * q^86 + 1940 * q^87 + 5652 * q^88 - 1904 * q^89 + 3540 * q^90 - 3904 * q^92 + 1592 * q^93 - 3332 * q^94 + 1540 * q^95 - 6460 * q^96 - 1032 * q^97 - 5608 * q^99

Introduction

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