LMFDB - Embedded newform 245.4.e.p.116.4

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			116.4
Root			$-0.522449 + 0.904909i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.p.226.4

$q$-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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.896821	−	0.442394i	$-0.145871\pi$
$2$	0.184657	+	0.319836i	0.0652863	+	0.113079i	−0.831535	+	0.555473i	$0.812537\pi$
$3$	−4.87035	+	8.43569i	−0.937299	+	1.62345i	−0.166817	+	0.985988i	$0.553349\pi$
$3$	−4.87035	+	8.43569i	−0.937299	+	1.62345i	−0.770482	+	0.637462i	$0.779984\pi$
$4$	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	−0.995926	−	0.0901746i	$-0.971258\pi$
$11$	−15.3180	+	26.5316i	−0.419870	+	0.727235i	0.576056	+	0.817410i	$0.304591\pi$
$12$	38.2985	+	66.3350i	0.921319	+	1.59577i
$13$	−36.4622			−0.777908			−0.388954	−	0.921257i	$-0.627164\pi$
$13$	−36.4622			−0.777908			−0.388954	+	0.921257i	$0.627164\pi$
$14$		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	0.427912	+	0.903820i	$0.359249\pi$
$17$	−39.8670	+	69.0517i	−0.568775	+	0.985148i	−0.996687	+	0.0813273i	$0.974084\pi$
$18$	12.5348	−	21.7108i	0.164137	−	0.284294i
$19$	−76.2092	−	131.998i	−0.920189	−	1.59381i	−0.799121	−	0.601170i	$-0.794701\pi$
$19$	−76.2092	−	131.998i	−0.920189	−	1.59381i	−0.121068	−	0.992644i	$-0.538632\pi$
$20$	39.3180			0.439589
$21$		0			0
$22$	−11.3144			−0.109647
$23$	−11.1104	−	19.2437i	−0.100725	−	0.174460i	0.811259	−	0.584687i	$-0.198783\pi$
$23$	−11.1104	−	19.2437i	−0.100725	−	0.174460i	−0.911983	+	0.410227i	$0.865449\pi$
$24$	−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	−0.235260	−	0.971933i	$-0.575594\pi$
$31$	124.978	−	216.469i	0.724089	−	1.25416i	0.959348	−	0.282226i	$-0.0910726\pi$
$32$	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	0.857508	−	0.514470i	$-0.172011\pi$
$37$	−3.77882	−	6.54511i	−0.0167901	−	0.0290814i	−0.874298	+	0.485389i	$0.838678\pi$
$38$	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	$-0.587348\pi$
$41$	−142.280			−0.541960			−0.270980	+	0.962585i	$0.587348\pi$
$42$		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	−0.999871	−	0.0160443i	$-0.994893\pi$
$47$	−165.564	−	286.766i	−0.513830	−	0.889980i	0.486041	−	0.873936i	$-0.338441\pi$
$48$	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	−0.355724	−	0.934591i	$-0.615766\pi$
$53$	243.668	−	422.046i	0.631517	−	1.09382i	0.987242	−	0.159229i	$-0.0509009\pi$
$54$	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	0.133612	+	0.991034i	$0.457342\pi$
$59$	−358.677	+	621.247i	−0.791454	+	1.37084i	−0.925066	+	0.379805i	$0.875991\pi$
$60$	−191.493	+	331.675i	−0.412026	+	0.713650i
$61$	177.296	+	307.086i	0.372138	+	0.644562i	0.989894	−	0.141808i	$-0.0452914\pi$
$61$	177.296	+	307.086i	0.372138	+	0.644562i	−0.617756	+	0.786370i	$0.711958\pi$
$62$	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	−0.891083	−	0.453841i	$-0.850054\pi$
$67$	−28.7942	+	49.8730i	−0.0525040	+	0.0909396i	0.838579	+	0.544780i	$0.183387\pi$
$68$	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	$-0.900438\pi$
$73$	−130.517	+	226.063i	−0.209259	+	0.362447i	0.742222	+	0.670154i	$0.233772\pi$
$74$	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	0.753096	−	0.657911i	$-0.228560\pi$
$79$	−135.672	−	234.991i	−0.193219	−	0.334665i	−0.946315	+	0.323245i	$0.895226\pi$
$80$	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	$-0.648786\pi$
$83$	−681.441			−0.901179			−0.450590	+	0.892731i	$0.648786\pi$
$84$		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	$-0.136165\pi$
$89$	80.3339	+	139.142i	0.0956784	+	0.165720i	−0.814213	+	0.580566i	$0.802831\pi$
$90$	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	$-0.472002\pi$
$97$	167.841			0.175687			0.0878436	+	0.996134i	$0.472002\pi$
$98$		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	$-0.898609\pi$
$101$	−206.697	+	358.010i	−0.203635	+	0.352706i	0.746062	+	0.665876i	$0.231942\pi$
$102$	143.417	−	248.406i	0.139220	−	0.241136i
$103$	−725.553	−	1256.69i	−0.694086	−	1.20219i	−0.970488	−	0.241150i	$-0.922475\pi$
$103$	−725.553	−	1256.69i	−0.694086	−	1.20219i	0.276402	−	0.961042i	$-0.410858\pi$
$104$	−213.620			−0.201415
$105$		0			0
$106$	179.981			0.164918
$107$	890.314	+	1542.07i	0.804391	+	1.39325i	0.916701	+	0.399574i	$0.130842\pi$
$107$	890.314	+	1542.07i	0.804391	+	1.39325i	−0.112310	+	0.993673i	$0.535825\pi$
$108$	1565.69	−	2711.85i	1.39499	−	2.41618i
$109$	−18.9460	+	32.8154i	−0.0166486	+	0.0288362i	−0.874230	−	0.485513i	$-0.838633\pi$
$109$	−18.9460	+	32.8154i	−0.0166486	+	0.0288362i	0.857581	+	0.514349i	$0.171966\pi$
$110$	−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	$-0.0617191\pi$
$131$	485.436	+	840.800i	0.323762	+	0.560772i	−0.657499	+	0.753455i	$0.728386\pi$
$132$	−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	−0.893234	−	0.449592i	$-0.851569\pi$
$137$	−91.8176	+	159.033i	−0.0572592	+	0.0991758i	0.835975	+	0.548768i	$0.184903\pi$
$138$	39.9682	+	69.2270i	0.0246545	+	0.0427029i
$139$	−1078.90			−0.658356			−0.329178	−	0.944268i	$-0.606772\pi$
$139$	−1078.90			−0.658356			−0.329178	+	0.944268i	$0.606772\pi$
$140$		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	0.650114	−	0.759837i	$-0.274721\pi$
$149$	−605.618	−	1048.96i	−0.332981	−	0.576740i	−0.983095	+	0.183097i	$0.941388\pi$
$150$	44.9673	−	77.8856i	0.0244771	−	0.0423956i
$151$	301.122	−	521.559i	0.162285	−	0.281085i	−0.773403	−	0.633915i	$-0.781447\pi$
$151$	301.122	−	521.559i	0.162285	−	0.281085i	0.935688	+	0.352829i	$0.114780\pi$
$152$	−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	$-0.966826\pi$
$157$	−801.035	+	1387.43i	−0.407195	+	0.705282i	0.587380	+	0.809312i	$0.300160\pi$
$158$	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	0.951214	+	0.308531i	$0.0998374\pi$
$163$	1545.81	+	2677.41i	0.742803	+	1.28657i	−0.208411	+	0.978041i	$0.566829\pi$
$164$	−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	$-0.771513\pi$
$167$	−3251.19			−1.50649			−0.753247	+	0.657738i	$0.771513\pi$
$168$		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	$-0.331647\pi$
$173$	−1127.27	−	1952.49i	−0.495405	−	0.858066i	−0.999986	+	0.00529826i	$0.998314\pi$
$174$	−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	−0.436765	−	0.899576i	$-0.643876\pi$
$179$	1342.73	−	2325.68i	0.560673	−	0.971113i	0.997438	−	0.0715379i	$-0.0227907\pi$
$180$	−1334.48	−	2311.38i	−0.552589	−	0.957113i
$181$	1293.25			0.531087			0.265543	−	0.964099i	$-0.414449\pi$
$181$	1293.25			0.531087			0.265543	+	0.964099i	$0.414449\pi$
$182$		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	0.878969	−	0.476879i	$-0.158232\pi$
$191$	69.9388	+	121.138i	0.0264953	+	0.0458911i	−0.852474	+	0.522770i	$0.824899\pi$
$192$	2242.15	−	3883.51i	0.842776	−	1.45973i
$193$	−1192.40	+	2065.30i	−0.444721	+	0.770279i	−0.998033	−	0.0626951i	$-0.980030\pi$
$193$	−1192.40	+	2065.30i	−0.444721	+	0.770279i	0.553312	+	0.832974i	$0.313364\pi$
$194$	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	$-0.890046\pi$
$199$	−497.518	+	861.726i	−0.177227	+	0.306966i	0.763703	+	0.645568i	$0.223379\pi$
$200$	−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	$-0.421348\pi$
$223$	1629.00			0.489173			0.244587	+	0.969627i	$0.421348\pi$
$224$		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	$-0.718678\pi$
$227$	1205.46	−	2087.91i	0.352463	−	0.610484i	0.986680	+	0.162671i	$0.0520110\pi$
$228$	5837.40	−	10110.7i	1.69558	−	2.93682i
$229$	−1833.29	−	3175.36i	−0.529028	−	0.916304i	−0.999427	−	0.0338499i	$-0.989223\pi$
$229$	−1833.29	−	3175.36i	−0.529028	−	0.916304i	0.470399	−	0.882454i	$-0.344110\pi$
$230$	41.0322			0.0117634
$231$		0			0
$232$	593.393			0.167923
$233$	1509.16	+	2613.95i	0.424329	+	0.734959i	0.996358	−	0.0852744i	$-0.0271767\pi$
$233$	1509.16	+	2613.95i	0.424329	+	0.734959i	−0.572029	+	0.820234i	$0.693843\pi$
$234$	−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	$-0.970954\pi$
$241$	−1567.64	+	2715.22i	−0.419005	+	0.725738i	0.576834	+	0.816861i	$0.304288\pi$
$242$	−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	$-0.536701\pi$
$251$	−914.967			−0.230088			−0.115044	+	0.993360i	$0.536701\pi$
$252$		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	0.938264	+	0.345919i	$0.112433\pi$
$257$	3167.09	+	5485.56i	0.768707	+	1.33144i	−0.169558	+	0.985520i	$0.554234\pi$
$258$	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	−0.999826	−	0.0186328i	$-0.994069\pi$
$263$	−2063.38	+	3573.87i	−0.483777	+	0.837926i	0.516050	+	0.856559i	$0.327402\pi$
$264$	−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	−0.311514	−	0.950242i	$-0.600836\pi$
$269$	2943.53	−	5098.35i	0.667176	−	1.15558i	0.978690	−	0.205342i	$-0.0658306\pi$
$270$	−367.663	+	636.811i	−0.0828714	+	0.143537i
$271$	−3618.86	−	6268.05i	−0.811181	−	1.40501i	−0.912038	−	0.410106i	$-0.865492\pi$
$271$	−3618.86	−	6268.05i	−0.811181	−	1.40501i	0.100857	−	0.994901i	$-0.467842\pi$
$272$	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	0.379248	+	0.925295i	$0.376183\pi$
$277$	−2820.08	+	4884.53i	−0.611705	+	1.05950i	−0.990953	+	0.134210i	$0.957150\pi$
$278$	−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	$-0.919053\pi$
$283$	−1266.63	+	2193.87i	−0.266054	+	0.460820i	0.701785	+	0.712389i	$0.252387\pi$
$284$	−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	$-0.518709\pi$
$293$	−589.215			−0.117482			−0.0587411	+	0.998273i	$0.518709\pi$
$294$		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	$-0.336920\pi$
$307$	5273.75			0.980420			0.490210	+	0.871604i	$0.336920\pi$
$308$		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	$-0.736214\pi$
$311$	1647.54	−	2853.63i	0.300397	−	0.520303i	0.976226	+	0.216755i	$0.0695474\pi$
$312$	1040.40	−	1802.03i	0.188786	−	0.326987i
$313$	909.686	+	1575.62i	0.164276	+	0.284535i	0.936398	−	0.350940i	$-0.114138\pi$
$313$	909.686	+	1575.62i	0.164276	+	0.284535i	−0.772122	+	0.635475i	$0.780804\pi$
$314$	−591.668			−0.106337
$315$		0			0
$316$	−2133.75			−0.379850
$317$	−943.953	−	1634.97i	−0.167248	−	0.289682i	0.770203	−	0.637799i	$-0.220155\pi$
$317$	−943.953	−	1634.97i	−0.167248	−	0.289682i	−0.937451	+	0.348116i	$0.886821\pi$
$318$	−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	0.884350	−	0.466824i	$-0.154602\pi$
$331$	228.193	+	395.242i	0.0378932	+	0.0656329i	−0.846457	+	0.532457i	$0.821269\pi$
$332$	−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	−0.376737	−	0.926320i	$-0.622954\pi$
$347$	3967.85	−	6872.52i	0.613849	−	1.06322i	0.990585	−	0.136897i	$-0.0437128\pi$
$348$	3879.05	+	6718.72i	0.597526	+	1.03495i
$349$	8649.40			1.32662			0.663312	−	0.748343i	$-0.269150\pi$
$349$	8649.40			1.32662			0.663312	+	0.748343i	$0.269150\pi$
$350$		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	$-0.712092\pi$
$353$	2465.53	−	4270.42i	0.371747	−	0.643885i	0.989834	+	0.142224i	$0.0454254\pi$
$354$	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	−0.991898	−	0.127035i	$-0.959454\pi$
$359$	−4121.82	−	7139.20i	−0.605965	−	1.04956i	0.385933	−	0.922527i	$-0.373879\pi$
$360$	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	−0.413611	−	0.910454i	$-0.635733\pi$
$367$	4089.55	−	7083.32i	0.581670	−	1.00748i	0.995282	−	0.0970290i	$-0.0309339\pi$
$368$	−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	0.842116	+	0.539296i	$0.181310\pi$
$373$	6397.73	+	11081.2i	0.888102	+	1.53824i	0.0459858	+	0.998942i	$0.485357\pi$
$374$	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	$-0.182340\pi$
$383$	−368.920	−	638.989i	−0.0492192	−	0.0852501i	−0.889585	+	0.456769i	$0.849007\pi$
$384$	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	−0.0323078	−	0.999478i	$-0.510286\pi$
$389$	6516.98	−	11287.7i	0.849419	−	1.47124i	0.881727	−	0.471760i	$-0.156381\pi$
$390$	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	−0.999559	−	0.0297035i	$-0.990544\pi$
$397$	−4156.82	−	7199.82i	−0.525503	−	0.910199i	0.474055	−	0.880495i	$-0.342790\pi$
$398$	−367.481			−0.0462819
$399$		0			0
$400$	1518.63			0.189829
$401$	7170.71	+	12420.0i	0.892988	+	1.54670i	0.836275	+	0.548311i	$0.184729\pi$
$401$	7170.71	+	12420.0i	0.892988	+	1.54670i	0.0567137	+	0.998390i	$0.481938\pi$
$402$	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	$-0.709340\pi$
$409$	3141.18	−	5440.68i	0.379758	−	0.657761i	0.991027	+	0.133663i	$0.0426738\pi$
$410$	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	$-0.152344\pi$
$419$	15226.1			1.77528			0.887640	+	0.460538i	$0.152344\pi$
$420$		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	0.497999	+	0.867178i	$0.334068\pi$
$431$	−4491.78	+	7779.99i	−0.501999	+	0.869487i	−0.999997	+	0.00230934i	$0.999265\pi$
$432$	−12094.7	−	20948.6i	−1.34701	−	2.33308i
$433$	−6836.59			−0.758766			−0.379383	−	0.925240i	$-0.623864\pi$
$433$	−6836.59			−0.758766			−0.379383	+	0.925240i	$0.623864\pi$
$434$		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	$-0.306098\pi$
$439$	−3901.48	−	6757.56i	−0.424163	−	0.734671i	−0.996342	+	0.0854573i	$0.972765\pi$
$440$	−897.433			−0.0972351
$441$		0			0
$442$	1073.70			0.115545
$443$	−2592.19	−	4489.80i	−0.278010	−	0.481528i	0.692880	−	0.721053i	$-0.256342\pi$
$443$	−2592.19	−	4489.80i	−0.278010	−	0.481528i	−0.970890	+	0.239525i	$0.923008\pi$
$444$	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	−0.994200	−	0.107548i	$-0.965700\pi$
$457$	−5766.37	−	9987.65i	−0.590239	−	1.02232i	0.403960	−	0.914776i	$-0.367633\pi$
$458$	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	$-0.323919\pi$
$461$	10400.7			1.05078			0.525391	+	0.850861i	$0.323919\pi$
$462$		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	0.956878	+	0.290491i	$0.0938186\pi$
$467$	7367.24	+	12760.4i	0.730011	+	1.26442i	−0.226866	+	0.973926i	$0.572848\pi$
$468$	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	$-0.810979\pi$
$479$	735.613	−	1274.12i	0.0701691	−	0.121536i	0.898975	+	0.437999i	$0.144313\pi$
$480$	−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	−0.966508	−	0.256638i	$-0.917385\pi$
$487$	−2805.00	+	4858.40i	−0.260999	+	0.452064i	0.705509	+	0.708701i	$0.250719\pi$
$488$	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	0.601289	−	0.799031i	$-0.294654\pi$
$499$	−4362.16	−	7555.48i	−0.391337	−	0.677815i	−0.992626	+	0.121216i	$0.961321\pi$
$500$	−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	$-0.724698\pi$
$503$	−14636.7			−1.29745			−0.648726	+	0.761022i	$0.724698\pi$
$504$		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	$-0.287797\pi$
$509$	−4265.28	−	7387.68i	−0.371425	−	0.643327i	−0.989785	+	0.142568i	$0.954464\pi$
$510$	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	0.417907	+	0.908490i	$0.362764\pi$
$521$	−6871.48	+	11901.8i	−0.577822	+	1.00082i	−0.995729	+	0.0923269i	$0.970570\pi$
$522$	1269.58	−	2198.98i	0.106452	−	0.184380i
$523$	1118.08	+	1936.58i	0.0934806	+	0.161913i	0.908973	−	0.416854i	$-0.136867\pi$
$523$	1118.08	+	1936.58i	0.0934806	+	0.161913i	−0.815493	+	0.578767i	$0.803534\pi$
$524$	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	0.935158	+	0.354231i	$0.115257\pi$
$541$	9743.93	+	16877.0i	0.774352	+	1.34122i	−0.160806	+	0.986986i	$0.551409\pi$
$542$	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	−0.719631	−	0.694356i	$-0.755689\pi$
$557$	3174.87	−	5499.04i	0.241514	−	0.418315i	0.961146	+	0.276041i	$0.0890226\pi$
$558$	−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	−0.443835	−	0.896108i	$-0.646382\pi$
$563$	7402.50	−	12821.5i	0.554135	−	0.959790i	0.997970	−	0.0636815i	$-0.0202842\pi$
$564$	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	−0.820322	−	0.571901i	$-0.806206\pi$
$569$	−12289.4	−	21285.8i	−0.905442	−	1.56827i	−0.0851200	−	0.996371i	$-0.527127\pi$
$570$	−1370.77	+	2374.24i	−0.100728	+	0.174467i
$571$	7804.97	−	13518.6i	0.572027	−	0.990780i	−0.424330	−	0.905508i	$-0.639490\pi$
$571$	7804.97	−	13518.6i	0.572027	−	0.990780i	0.996358	−	0.0852730i	$-0.0271762\pi$
$572$	−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	−0.453457	−	0.891278i	$-0.649809\pi$
$577$	7555.66	−	13086.8i	0.545141	−	0.944212i	0.998598	−	0.0529338i	$-0.0168572\pi$
$578$	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	$-0.676596\pi$
$587$	−14983.2			−1.05353			−0.526766	+	0.850010i	$0.676596\pi$
$588$		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	$-0.0895240\pi$
$593$	3465.51	+	6002.43i	0.239985	+	0.415667i	−0.720724	+	0.693222i	$0.756191\pi$
$594$	−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	−0.995921	−	0.0902332i	$-0.971239\pi$
$599$	−6154.59	+	10660.1i	−0.419816	+	0.727143i	0.576105	+	0.817376i	$0.304572\pi$
$600$	−713.343	−	1235.55i	−0.0485369	−	0.0840683i
$601$	−15293.6			−1.03800			−0.519001	−	0.854774i	$-0.673696\pi$
$601$	−15293.6			−1.03800			−0.519001	+	0.854774i	$0.673696\pi$
$602$		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	$-0.223790\pi$
$607$	−2669.40	−	4623.54i	−0.178497	−	0.309166i	−0.941366	+	0.337387i	$0.890457\pi$
$608$	−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	0.205827	−	0.978588i	$-0.434012\pi$
$613$	14424.3	−	24983.6i	0.950396	−	1.64613i	0.744569	−	0.667545i	$-0.232655\pi$
$614$	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	$-0.899781\pi$
$619$	−3191.58	+	5527.98i	−0.207238	+	0.358947i	0.743605	+	0.668619i	$0.233114\pi$
$620$	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	−0.422598	−	0.906317i	$-0.638882\pi$
$641$	9308.76	−	16123.2i	0.573594	−	0.993495i	0.996193	−	0.0871776i	$-0.0277847\pi$
$642$	−3202.80	−	5547.41i	−0.196892	−	0.341026i
$643$	−21168.8			−1.29832			−0.649158	−	0.760654i	$-0.724879\pi$
$643$	−21168.8			−1.29832			−0.649158	+	0.760654i	$0.724879\pi$
$644$		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	$-0.775450\pi$
$647$	2976.23	−	5154.99i	0.180847	−	0.313236i	0.942169	+	0.335138i	$0.108783\pi$
$648$	−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	0.907978	−	0.419017i	$-0.137625\pi$
$653$	1520.32	+	2633.26i	0.0911096	+	0.157806i	−0.816869	+	0.576824i	$0.804292\pi$
$654$	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	$-0.818832\pi$
$661$	773.951	−	1340.52i	0.0455419	−	0.0788809i	0.887898	+	0.460041i	$0.152165\pi$
$662$	−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	−0.871371	−	0.490625i	$-0.836769\pi$
$677$	−15159.1	−	26256.4i	−0.860579	−	1.49057i	0.0107919	−	0.999942i	$-0.496565\pi$
$678$	−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	0.100281	+	0.994959i	$0.468026\pi$
$683$	−14485.4	+	25089.4i	−0.811520	+	1.40559i	−0.911800	+	0.410634i	$0.865307\pi$
$684$	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	$-0.136525\pi$
$691$	1717.45	+	2974.72i	0.0945514	+	0.163768i	−0.814870	+	0.579644i	$0.803192\pi$
$692$	−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	0.570277	−	0.821452i	$-0.306836\pi$
$709$	−8047.18	−	13938.1i	−0.426260	−	0.738303i	−0.996537	+	0.0831487i	$0.973502\pi$
$710$	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	$-0.238703\pi$
$719$	−4325.96	−	7492.79i	−0.224383	−	0.388642i	−0.956134	+	0.292929i	$0.905370\pi$
$720$	−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	$-0.557137\pi$
$727$	−6999.43			−0.357076			−0.178538	+	0.983933i	$0.557137\pi$
$728$		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	$-0.208229\pi$
$733$	−2583.87	−	4475.39i	−0.130201	−	0.225515i	−0.923754	+	0.382986i	$0.874896\pi$
$734$	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	−0.671011	−	0.741448i	$-0.734140\pi$
$739$	6159.55	−	10668.6i	0.306607	−	0.531059i	0.977618	+	0.210389i	$0.0674729\pi$
$740$	−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	−0.919793	−	0.392403i	$-0.871644\pi$
$751$	−16458.9	−	28507.7i	−0.799728	−	1.38517i	0.120066	−	0.992766i	$-0.461689\pi$
$752$	−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	0.903505	+	0.428578i	$0.140985\pi$
$761$	17275.5	+	29922.0i	0.822912	+	1.42532i	−0.0805935	+	0.996747i	$0.525682\pi$
$762$	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	$-0.502597\pi$
$769$	−348.011			−0.0163194			−0.00815970	+	0.999967i	$0.502597\pi$
$770$		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	−0.268604	−	0.963251i	$-0.586562\pi$
$773$	15041.9	−	26053.4i	0.699897	−	1.21226i	0.968502	−	0.249007i	$-0.0801043\pi$
$774$	−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	0.235726	+	0.971820i	$0.424253\pi$
$787$	−15979.2	+	27676.8i	−0.723757	+	1.25358i	−0.959483	+	0.281765i	$0.909080\pi$
$788$	−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	$-0.502576\pi$
$797$	−364.165			−0.0161849			−0.00809247	+	0.999967i	$0.502576\pi$
$798$		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	0.311213	+	0.950340i	$0.399265\pi$
$809$	−15357.4	+	26599.8i	−0.667412	+	1.15599i	−0.978625	+	0.205652i	$0.934068\pi$
$810$	−1889.10	−	3272.02i	−0.0819461	−	0.141935i
$811$	18967.6			0.821260			0.410630	−	0.911802i	$-0.365309\pi$
$811$	18967.6			0.821260			0.410630	+	0.911802i	$0.365309\pi$
$812$		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	0.979423	−	0.201820i	$-0.0646855\pi$
$821$	7408.48	+	12831.9i	0.314930	+	0.545475i	−0.664492	+	0.747295i	$0.731352\pi$
$822$	330.303	−	572.102i	0.0140154	−	0.0242754i
$823$	13294.0	−	23025.9i	0.563063	−	0.975254i	−0.434164	−	0.900834i	$-0.642956\pi$
$823$	13294.0	−	23025.9i	0.563063	−	0.975254i	0.997227	−	0.0744198i	$-0.0237105\pi$
$824$	−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	$-0.931210\pi$
$829$	−7224.30	+	12512.9i	−0.302666	+	0.524233i	0.674073	+	0.738665i	$0.264543\pi$
$830$	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	$-0.191943\pi$
$839$	40032.0			1.64727			0.823635	+	0.567120i	$0.191943\pi$
$840$		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	$-0.430031\pi$
$853$	10864.4			0.436098			0.218049	+	0.975938i	$0.430031\pi$
$854$		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	0.0548144	+	0.998497i	$0.482543\pi$
$857$	−21006.8	+	36384.9i	−0.837316	+	1.45027i	−0.892131	+	0.451778i	$0.850790\pi$
$858$	−2009.25	+	3480.12i	−0.0799471	+	0.138472i
$859$	−8067.81	−	13973.9i	−0.320454	−	0.555043i	0.660128	−	0.751153i	$-0.270502\pi$
$859$	−8067.81	−	13973.9i	−0.320454	−	0.555043i	−0.980582	+	0.196111i	$0.937169\pi$
$860$	−9339.22			−0.370308
$861$		0			0
$862$	−3317.76			−0.131094
$863$	23123.4	+	40050.9i	0.912086	+	1.57978i	0.811112	+	0.584891i	$0.198863\pi$
$863$	23123.4	+	40050.9i	0.912086	+	1.57978i	0.100974	+	0.994889i	$0.467804\pi$
$864$	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	0.999812	−	0.0193992i	$-0.00617533\pi$
$877$	12547.0	+	21732.1i	0.483106	+	0.836764i	−0.516706	+	0.856163i	$0.672842\pi$
$878$	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	$-0.676576\pi$
$881$	−27546.6			−1.05342			−0.526712	+	0.850044i	$0.676576\pi$
$882$		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	$-0.204193\pi$
$887$	−3107.15	−	5381.73i	−0.117619	−	0.203721i	−0.918824	+	0.394669i	$0.870859\pi$
$888$	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	−0.998184	−	0.0602399i	$-0.980813\pi$
$907$	−12208.0	+	21144.8i	−0.446923	+	0.774093i	0.551261	+	0.834333i	$0.314147\pi$
$908$	−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	0.690635	−	0.723203i	$-0.257331\pi$
$919$	−7828.37	−	13559.1i	−0.280995	−	0.486697i	−0.971630	+	0.236506i	$0.923998\pi$
$920$	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	0.998977	+	0.0452250i	$0.0144005\pi$
$929$	15252.2	+	26417.7i	0.538654	+	0.932977i	−0.460322	+	0.887752i	$0.652266\pi$
$930$	−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	$-0.159744\pi$
$937$	50290.7			1.75339			0.876694	+	0.481049i	$0.159744\pi$
$938$		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	$-0.938225\pi$
$941$	−9340.83	+	16178.8i	−0.323595	+	0.560482i	0.657632	+	0.753339i	$0.271558\pi$
$942$	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	0.691219	−	0.722646i	$-0.257074\pi$
$947$	−8166.28	−	14144.4i	−0.280220	−	0.485355i	−0.971439	+	0.237290i	$0.923741\pi$
$948$	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	$-0.171013\pi$
$971$	−413.165	−	715.624i	−0.0136551	−	0.0236513i	−0.872772	+	0.488128i	$0.837680\pi$
$972$	−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	−0.928438	−	0.371486i	$-0.878848\pi$
$977$	−4351.76	+	7537.47i	−0.142503	+	0.246822i	0.785936	+	0.618308i	$0.212182\pi$
$978$	−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	0.314069	+	0.949400i	$0.398308\pi$
$983$	−20500.4	+	35507.8i	−0.665170	+	1.15211i	−0.979239	+	0.202708i	$0.935026\pi$
$984$	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	−0.680786	−	0.732483i	$-0.738361\pi$
$991$	9170.49	−	15883.8i	0.293956	−	0.509147i	0.974741	+	0.223336i	$0.0716948\pi$
$992$	−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	0.0974932	−	0.995236i	$-0.468918\pi$
$997$	28667.7	−	49653.9i	0.910646	−	1.57729i	0.813153	−	0.582050i	$-0.197749\pi$
$998$	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.p.116.4		12
7.2	even	3	inner	245.4.e.p.226.4		12
7.3	odd	6		245.4.a.o.1.3	✓	6
7.4	even	3		245.4.a.p.1.3	yes	6
7.5	odd	6		245.4.e.q.226.4		12
7.6	odd	2		245.4.e.q.116.4		12
21.11	odd	6		2205.4.a.ca.1.4		6
21.17	even	6		2205.4.a.bz.1.4		6
35.4	even	6		1225.4.a.bi.1.4		6
35.24	odd	6		1225.4.a.bj.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.3	✓	6	7.3	odd	6
245.4.a.p.1.3	yes	6	7.4	even	3
245.4.e.p.116.4		12	1.1	even	1	trivial
245.4.e.p.226.4		12	7.2	even	3	inner
245.4.e.q.116.4		12	7.6	odd	2
245.4.e.q.226.4		12	7.5	odd	6
1225.4.a.bi.1.4		6	35.4	even	6
1225.4.a.bj.1.4		6	35.24	odd	6
2205.4.a.bz.1.4		6	21.17	even	6
2205.4.a.ca.1.4		6	21.11	odd	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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