LMFDB - Embedded newform 245.4.e.n.116.1

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.5567659200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 17x^{4} - 28x^{3} + 289x^{2} - 238x + 196 $ x^6 + 17x^4 - 28x^3 + 289x^2 - 238x + 196
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$-2.24283 + 3.88469i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.n.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74283 - 3.01866i) q^{2} +(0.425119 - 0.736328i) q^{3} +(-2.07488 + 3.59380i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.96363 q^{6} -13.4206 q^{8} +(13.1385 + 22.7566i) q^{9} +O(q^{10})$	\(q+(-1.74283 - 3.01866i) q^{2} +(0.425119 - 0.736328i) q^{3} +(-2.07488 + 3.59380i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.96363 q^{6} -13.4206 q^{8} +(13.1385 + 22.7566i) q^{9} +(8.71413 - 15.0933i) q^{10} +(3.45382 - 5.98219i) q^{11} +(1.76414 + 3.05559i) q^{12} +22.1364 q^{13} +4.25119 q^{15} +(39.9888 + 69.2626i) q^{16} +(44.1515 - 76.4726i) q^{17} +(45.7964 - 79.3217i) q^{18} +(18.4780 + 32.0048i) q^{19} -20.7488 q^{20} -24.0776 q^{22} +(47.7641 + 82.7299i) q^{23} +(-5.70535 + 9.88195i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-38.5799 - 66.8223i) q^{26} +45.2982 q^{27} +269.029 q^{29} +(-7.40909 - 12.8329i) q^{30} +(98.5570 - 170.706i) q^{31} +(85.7046 - 148.445i) q^{32} +(-2.93657 - 5.08629i) q^{33} -307.793 q^{34} -109.044 q^{36} +(-1.07273 - 1.85803i) q^{37} +(64.4078 - 111.558i) q^{38} +(9.41061 - 16.2997i) q^{39} +(-33.5515 - 58.1128i) q^{40} -174.127 q^{41} -17.0345 q^{43} +(14.3325 + 24.8247i) q^{44} +(-65.6927 + 113.783i) q^{45} +(166.489 - 288.368i) q^{46} +(-264.014 - 457.286i) q^{47} +68.0000 q^{48} +87.1413 q^{50} +(-37.5393 - 65.0200i) q^{51} +(-45.9304 + 79.5538i) q^{52} +(320.557 - 555.221i) q^{53} +(-78.9469 - 136.740i) q^{54} +34.5382 q^{55} +31.4214 q^{57} +(-468.871 - 812.109i) q^{58} +(-321.487 + 556.832i) q^{59} +(-8.82072 + 15.2779i) q^{60} +(71.4836 + 123.813i) q^{61} -687.070 q^{62} +42.3480 q^{64} +(55.3410 + 95.8534i) q^{65} +(-10.2359 + 17.7290i) q^{66} +(-239.398 + 414.650i) q^{67} +(183.218 + 317.343i) q^{68} +81.2218 q^{69} +105.550 q^{71} +(-176.327 - 305.407i) q^{72} +(493.256 - 854.344i) q^{73} +(-3.73917 + 6.47643i) q^{74} +(10.6280 + 18.4082i) q^{75} -153.358 q^{76} -65.6042 q^{78} +(549.930 + 952.507i) q^{79} +(-199.944 + 346.313i) q^{80} +(-335.484 + 581.075i) q^{81} +(303.474 + 525.632i) q^{82} +1236.62 q^{83} +441.515 q^{85} +(29.6882 + 51.4214i) q^{86} +(114.370 - 198.094i) q^{87} +(-46.3523 + 80.2845i) q^{88} +(-355.849 - 616.348i) q^{89} +457.964 q^{90} -396.420 q^{92} +(-83.7969 - 145.141i) q^{93} +(-920.262 + 1593.94i) q^{94} +(-92.3899 + 160.024i) q^{95} +(-72.8693 - 126.213i) q^{96} +636.553 q^{97} +181.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9	\( 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20} + 368 q^{22} + 124 q^{23} + 420 q^{24} - 75 q^{25} - 446 q^{26} - 340 q^{27} + 664 q^{29} - 120 q^{30} + 320 q^{31} + 183 q^{32} - 106 q^{33} - 1164 q^{34} + 362 q^{36} + 54 q^{37} - 460 q^{38} + 982 q^{39} - 75 q^{40} - 724 q^{41} - 32 q^{43} + 264 q^{44} + 405 q^{45} + 336 q^{46} - 730 q^{47} + 408 q^{48} - 150 q^{50} + 1178 q^{51} + 1202 q^{52} - 110 q^{53} - 180 q^{54} + 740 q^{55} - 1912 q^{57} - 450 q^{58} - 180 q^{59} + 760 q^{60} + 1222 q^{61} - 928 q^{62} - 782 q^{64} - 220 q^{65} - 532 q^{66} - 204 q^{67} + 918 q^{68} + 1432 q^{69} - 272 q^{71} - 765 q^{72} + 310 q^{73} - 502 q^{74} + 50 q^{75} - 3592 q^{76} + 7576 q^{78} + 1034 q^{79} - 395 q^{80} - 2283 q^{81} - 6 q^{82} + 3320 q^{83} - 520 q^{85} - 764 q^{86} - 1574 q^{87} + 20 q^{88} + 242 q^{89} + 4110 q^{90} + 192 q^{92} - 1376 q^{93} - 1108 q^{94} - 840 q^{95} - 3156 q^{96} - 200 q^{97} - 6976 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * 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 $

$2$	−1.74283	−	3.01866i	−0.616182	−	1.06726i	−0.990176	−	0.139827i	$-0.955345\pi$
$2$	−1.74283	−	3.01866i	−0.616182	−	1.06726i	0.373994	−	0.927431i	$-0.377988\pi$
$3$	0.425119	−	0.736328i	0.0818142	−	0.141706i	−0.822215	−	0.569177i	$-0.807262\pi$
$3$	0.425119	−	0.736328i	0.0818142	−	0.141706i	0.904029	+	0.427471i	$0.140595\pi$
$4$	−2.07488	+	3.59380i	−0.259360	+	0.449225i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−2.96363			−0.201650
$7$		0			0
$7$		0			0
$8$	−13.4206			−0.593112
$9$	13.1385	+	22.7566i	0.486613	+	0.842838i
$10$	8.71413	−	15.0933i	0.275565	−	0.477292i
$11$	3.45382	−	5.98219i	0.0946696	−	0.163972i	−0.814801	−	0.579741i	$-0.803154\pi$
$11$	3.45382	−	5.98219i	0.0946696	−	0.163972i	0.909471	+	0.415768i	$0.136487\pi$
$12$	1.76414	+	3.05559i	0.0424387	+	0.0735060i
$13$	22.1364			0.472272			0.236136	−	0.971720i	$-0.424119\pi$
$13$	22.1364			0.472272			0.236136	+	0.971720i	$0.424119\pi$
$14$		0			0
$15$	4.25119			0.0731769
$16$	39.9888	+	69.2626i	0.624825	+	1.08223i
$17$	44.1515	−	76.4726i	0.629901	−	1.09102i	−0.357671	−	0.933848i	$-0.616429\pi$
$17$	44.1515	−	76.4726i	0.629901	−	1.09102i	0.987571	−	0.157172i	$-0.0502377\pi$
$18$	45.7964	−	79.3217i	0.599684	−	1.03868i
$19$	18.4780	+	32.0048i	0.223113	+	0.386442i	0.955752	−	0.294175i	$-0.0950449\pi$
$19$	18.4780	+	32.0048i	0.223113	+	0.386442i	−0.732639	+	0.680618i	$0.761712\pi$
$20$	−20.7488			−0.231979
$21$		0			0
$22$	−24.0776			−0.233335
$23$	47.7641	+	82.7299i	0.433022	+	0.750017i	0.997132	−	0.0756833i	$-0.0241138\pi$
$23$	47.7641	+	82.7299i	0.433022	+	0.750017i	−0.564110	+	0.825700i	$0.690780\pi$
$24$	−5.70535	+	9.88195i	−0.0485250	+	0.0840477i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−38.5799	−	66.8223i	−0.291005	−	0.504036i
$27$	45.2982			0.322876
$28$		0			0
$29$	269.029			1.72267			0.861336	−	0.508035i	$-0.169628\pi$
$29$	269.029			1.72267			0.861336	+	0.508035i	$0.169628\pi$
$30$	−7.40909	−	12.8329i	−0.0450903	−	0.0780986i
$31$	98.5570	−	170.706i	0.571012	−	0.989021i	−0.425451	−	0.904982i	$-0.639884\pi$
$31$	98.5570	−	170.706i	0.571012	−	0.989021i	0.996462	−	0.0840395i	$-0.0267822\pi$
$32$	85.7046	−	148.445i	0.473455	−	0.820049i
$33$	−2.93657	−	5.08629i	−0.0154906	−	0.0268306i
$34$	−307.793			−1.55253
$35$		0			0
$36$	−109.044			−0.504832
$37$	−1.07273	−	1.85803i	−0.00476638	−	0.00825561i	0.863632	−	0.504122i	$-0.168184\pi$
$37$	−1.07273	−	1.85803i	−0.00476638	−	0.00825561i	−0.868399	+	0.495867i	$0.834851\pi$
$38$	64.4078	−	111.558i	0.274956	−	0.476238i
$39$	9.41061	−	16.2997i	0.0386385	−	0.0669239i
$40$	−33.5515	−	58.1128i	−0.132624	−	0.229711i
$41$	−174.127			−0.663271			−0.331636	−	0.943408i	$-0.607600\pi$
$41$	−174.127			−0.663271			−0.331636	+	0.943408i	$0.607600\pi$
$42$		0			0
$43$	−17.0345			−0.0604125			−0.0302062	−	0.999544i	$-0.509616\pi$
$43$	−17.0345			−0.0604125			−0.0302062	+	0.999544i	$0.509616\pi$
$44$	14.3325	+	24.8247i	0.0491070	+	0.0850558i
$45$	−65.6927	+	113.783i	−0.217620	+	0.376929i
$46$	166.489	−	288.368i	0.533641	−	0.924293i
$47$	−264.014	−	457.286i	−0.819371	−	1.41919i	−0.906146	−	0.422964i	$-0.860990\pi$
$47$	−264.014	−	457.286i	−0.819371	−	1.41919i	0.0867752	−	0.996228i	$-0.472344\pi$
$48$	68.0000			0.204478
$49$		0			0
$50$	87.1413			0.246473
$51$	−37.5393	−	65.0200i	−0.103070	−	0.178522i
$52$	−45.9304	+	79.5538i	−0.122488	+	0.212156i
$53$	320.557	−	555.221i	0.830790	−	1.43897i	−0.0666227	−	0.997778i	$-0.521222\pi$
$53$	320.557	−	555.221i	0.830790	−	1.43897i	0.897413	−	0.441192i	$-0.145444\pi$
$54$	−78.9469	−	136.740i	−0.198950	−	0.344592i
$55$	34.5382			0.0846750
$56$		0			0
$57$	31.4214			0.0730151
$58$	−468.871	−	812.109i	−1.06148	−	1.83854i
$59$	−321.487	+	556.832i	−0.709391	+	1.22870i	0.255692	+	0.966758i	$0.417697\pi$
$59$	−321.487	+	556.832i	−0.709391	+	1.22870i	−0.965083	+	0.261944i	$0.915637\pi$
$60$	−8.82072	+	15.2779i	−0.0189792	+	0.0328729i
$61$	71.4836	+	123.813i	0.150042	+	0.259880i	0.931242	−	0.364400i	$-0.118726\pi$
$61$	71.4836	+	123.813i	0.150042	+	0.259880i	−0.781201	+	0.624280i	$0.785393\pi$
$62$	−687.070			−1.40739
$63$		0			0
$64$	42.3480			0.0827109
$65$	55.3410	+	95.8534i	0.105603	+	0.182910i
$66$	−10.2359	+	17.7290i	−0.0190901	+	0.0330650i
$67$	−239.398	+	414.650i	−0.436525	+	0.756083i	−0.997419	−	0.0718045i	$-0.977124\pi$
$67$	−239.398	+	414.650i	−0.436525	+	0.756083i	0.560894	+	0.827888i	$0.310458\pi$
$68$	183.218	+	317.343i	0.326742	+	0.565934i
$69$	81.2218			0.141710
$70$		0			0
$71$	105.550			0.176430			0.0882150	−	0.996101i	$-0.471884\pi$
$71$	105.550			0.176430			0.0882150	+	0.996101i	$0.471884\pi$
$72$	−176.327	−	305.407i	−0.288616	−	0.499897i
$73$	493.256	−	854.344i	0.790839	−	1.36977i	−0.134609	−	0.990899i	$-0.542978\pi$
$73$	493.256	−	854.344i	0.790839	−	1.36977i	0.925448	−	0.378875i	$-0.123689\pi$
$74$	−3.73917	+	6.47643i	−0.00587391	+	0.0101739i
$75$	10.6280	+	18.4082i	0.0163628	+	0.0283413i
$76$	−153.358			−0.231466
$77$		0			0
$78$	−65.6042			−0.0952335
$79$	549.930	+	952.507i	0.783190	+	1.35652i	0.930074	+	0.367371i	$0.119742\pi$
$79$	549.930	+	952.507i	0.783190	+	1.35652i	−0.146885	+	0.989154i	$0.546925\pi$
$80$	−199.944	+	346.313i	−0.279430	+	0.483987i
$81$	−335.484	+	581.075i	−0.460197	+	0.797085i
$82$	303.474	+	525.632i	0.408696	+	0.707882i
$83$	1236.62			1.63538			0.817691	−	0.575657i	$-0.195254\pi$
$83$	1236.62			1.63538			0.817691	+	0.575657i	$0.195254\pi$
$84$		0			0
$85$	441.515			0.563400
$86$	29.6882	+	51.4214i	0.0372251	+	0.0644757i
$87$	114.370	−	198.094i	0.140939	−	0.244114i
$88$	−46.3523	+	80.2845i	−0.0561496	+	0.0972540i
$89$	−355.849	−	616.348i	−0.423819	−	0.734076i	0.572490	−	0.819912i	$-0.305977\pi$
$89$	−355.849	−	616.348i	−0.423819	−	0.734076i	−0.996309	+	0.0858354i	$0.972644\pi$
$90$	457.964			0.536374
$91$		0			0
$92$	−396.420			−0.449235
$93$	−83.7969	−	145.141i	−0.0934337	−	0.161832i
$94$	−920.262	+	1593.94i	−1.00976	+	1.74896i
$95$	−92.3899	+	160.024i	−0.0997790	+	0.172822i
$96$	−72.8693	−	126.213i	−0.0774708	−	0.134183i
$97$	636.553			0.666311			0.333156	−	0.942872i	$-0.391887\pi$
$97$	636.553			0.666311			0.333156	+	0.942872i	$0.391887\pi$
$98$		0			0
$99$	181.513			0.184270
$100$	−51.8720	−	89.8450i	−0.0518720	−	0.0898450i
$101$	871.025	−	1508.66i	0.858121	−	1.48631i	−0.0155988	−	0.999878i	$-0.504965\pi$
$101$	871.025	−	1508.66i	0.858121	−	1.48631i	0.873719	−	0.486430i	$-0.161701\pi$
$102$	−130.849	+	226.637i	−0.127019	+	0.220004i
$103$	727.312	+	1259.74i	0.695769	+	1.20511i	0.969921	+	0.243420i	$0.0782694\pi$
$103$	727.312	+	1259.74i	0.695769	+	1.20511i	−0.274152	+	0.961686i	$0.588397\pi$
$104$	−297.083			−0.280110
$105$		0			0
$106$	−2234.70			−2.04767
$107$	590.833	+	1023.35i	0.533813	+	0.924591i	0.999220	+	0.0394943i	$0.0125747\pi$
$107$	590.833	+	1023.35i	0.533813	+	0.924591i	−0.465407	+	0.885097i	$0.654092\pi$
$108$	−93.9884	+	162.793i	−0.0837411	+	0.145044i
$109$	−1102.21	+	1909.09i	−0.968559	+	1.67759i	−0.268826	+	0.963189i	$0.586636\pi$
$109$	−1102.21	+	1909.09i	−0.968559	+	1.67759i	−0.699733	+	0.714405i	$0.746698\pi$
$110$	−60.1940	−	104.259i	−0.0521752	−	0.0903701i
$111$	−1.82416			−0.00155983
$112$		0			0
$113$	236.886			0.197207			0.0986034	−	0.995127i	$-0.468562\pi$
$113$	236.886			0.197207			0.0986034	+	0.995127i	$0.468562\pi$
$114$	−54.7620	−	94.8505i	−0.0449906	−	0.0779260i
$115$	−238.821	+	413.650i	−0.193653	+	0.335418i
$116$	−558.204	+	966.838i	−0.446793	+	0.773867i
$117$	290.840	+	503.750i	0.229813	+	0.398049i
$118$	2241.19			1.74846
$119$		0			0
$120$	−57.0535			−0.0434021
$121$	641.642	+	1111.36i	0.482075	+	0.834979i
$122$	249.167	−	431.570i	0.184906	−	0.320266i
$123$	−74.0249	+	128.215i	−0.0542650	+	0.0939898i
$124$	408.988	+	708.388i	0.296195	+	0.513025i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1667.21			−1.16489			−0.582446	−	0.812869i	$-0.697904\pi$
$127$	−1667.21			−1.16489			−0.582446	+	0.812869i	$0.697904\pi$
$128$	−759.442	−	1315.39i	−0.524420	−	0.908323i
$129$	−7.24169	+	12.5430i	−0.00494260	+	0.00856083i
$130$	192.899	−	334.112i	0.130142	−	0.225412i
$131$	445.861	+	772.254i	0.297367	+	0.515054i	0.975533	−	0.219855i	$-0.0705583\pi$
$131$	445.861	+	772.254i	0.297367	+	0.515054i	−0.678166	+	0.734909i	$0.737225\pi$
$132$	24.3721			0.0160706
$133$		0			0
$134$	1668.92			1.07591
$135$	113.246	+	196.147i	0.0721972	+	0.125049i
$136$	−592.539	+	1026.31i	−0.373601	+	0.647097i
$137$	200.213	−	346.779i	0.124856	−	0.216258i	−0.796820	−	0.604216i	$-0.793486\pi$
$137$	200.213	−	346.779i	0.124856	−	0.216258i	0.921677	+	0.387959i	$0.126820\pi$
$138$	−141.555	−	245.181i	−0.0873188	−	0.151241i
$139$	−515.050			−0.314287			−0.157144	−	0.987576i	$-0.550229\pi$
$139$	−515.050			−0.314287			−0.157144	+	0.987576i	$0.550229\pi$
$140$		0			0
$141$	−448.950			−0.268145
$142$	−183.956	−	318.621i	−0.108713	−	0.188296i
$143$	76.4551	−	132.424i	0.0447098	−	0.0774396i
$144$	−1050.79	+	1820.02i	−0.608096	+	1.05325i
$145$	672.573	+	1164.93i	0.385201	+	0.667188i
$146$	−3438.64			−1.94920
$147$		0			0
$148$	8.90316			0.00494483
$149$	−109.187	−	189.117i	−0.0600332	−	0.103981i	0.834447	−	0.551088i	$-0.185787\pi$
$149$	−109.187	−	189.117i	−0.0600332	−	0.103981i	−0.894480	+	0.447108i	$0.852454\pi$
$150$	37.0454	−	64.1646i	0.0201650	−	0.0349268i
$151$	87.5054	−	151.564i	0.0471595	−	0.0816827i	−0.841482	−	0.540285i	$-0.818316\pi$
$151$	87.5054	−	151.564i	0.0471595	−	0.0816827i	0.888642	+	0.458602i	$0.151650\pi$
$152$	−247.985	−	429.523i	−0.132331	−	0.229204i
$153$	2320.35			1.22607
$154$		0			0
$155$	985.570			0.510728
$156$	39.0518	+	67.6397i	0.0200426	+	0.0347148i
$157$	−459.821	+	796.433i	−0.233743	+	0.404855i	−0.958907	−	0.283722i	$-0.908431\pi$
$157$	−459.821	+	796.433i	−0.233743	+	0.404855i	0.725163	+	0.688577i	$0.241764\pi$
$158$	1916.87	−	3320.11i	0.965175	−	1.67173i
$159$	−272.550	−	472.070i	−0.135941	−	0.235457i
$160$	857.046			0.423471
$161$		0			0
$162$	2338.76			1.13426
$163$	−1184.25	−	2051.19i	−0.569067	−	0.985653i	−0.996659	−	0.0816808i	$-0.973971\pi$
$163$	−1184.25	−	2051.19i	−0.569067	−	0.985653i	0.427592	−	0.903972i	$-0.359362\pi$
$164$	361.293	−	625.779i	0.172026	−	0.297958i
$165$	14.6828	−	25.4314i	0.00692762	−	0.0119990i
$166$	−2155.21	−	3732.94i	−1.00769	−	1.74538i
$167$	−1079.37			−0.500144			−0.250072	−	0.968227i	$-0.580454\pi$
$167$	−1079.37			−0.500144			−0.250072	+	0.968227i	$0.580454\pi$
$168$		0			0
$169$	−1706.98			−0.776959
$170$	−769.484	−	1332.78i	−0.347157	−	0.601294i
$171$	−485.548	+	840.993i	−0.217139	+	0.376096i
$172$	35.3446	−	61.2186i	0.0156686	−	0.0271388i
$173$	−440.636	−	763.203i	−0.193647	−	0.335406i	0.752809	−	0.658239i	$-0.228698\pi$
$173$	−440.636	−	763.203i	−0.193647	−	0.335406i	−0.946456	+	0.322833i	$0.895365\pi$
$174$	−797.305			−0.347376
$175$		0			0
$176$	552.456			0.236608
$177$	273.341	+	473.440i	0.116077	+	0.201051i
$178$	−1240.36	+	2148.37i	−0.522299	+	0.904649i
$179$	1688.86	−	2925.19i	0.705203	−	1.22145i	−0.261416	−	0.965226i	$-0.584189\pi$
$179$	1688.86	−	2925.19i	0.705203	−	1.22145i	0.966618	−	0.256221i	$-0.0824773\pi$
$180$	−272.609	−	472.173i	−0.112884	−	0.195521i
$181$	−1435.58			−0.589533			−0.294767	−	0.955569i	$-0.595242\pi$
$181$	−1435.58			−0.589533			−0.294767	+	0.955569i	$0.595242\pi$
$182$		0			0
$183$	121.556			0.0491021
$184$	−641.023	−	1110.28i	−0.256831	−	0.444844i
$185$	5.36366	−	9.29013i	0.00213159	−	0.00369202i
$186$	−292.087	+	505.909i	−0.115144	+	0.199436i
$187$	−304.982	−	528.245i	−0.119265	−	0.206573i
$188$	2191.19			0.850049
$189$		0			0
$190$	644.078			0.245928
$191$	794.069	+	1375.37i	0.300821	+	0.521038i	0.976322	−	0.216321i	$-0.0694059\pi$
$191$	794.069	+	1375.37i	0.300821	+	0.521038i	−0.675501	+	0.737359i	$0.736073\pi$
$192$	18.0029	−	31.1820i	0.00676693	−	0.0117207i
$193$	488.852	−	846.716i	0.182323	−	0.315793i	−0.760348	−	0.649516i	$-0.774972\pi$
$193$	488.852	−	846.716i	0.182323	−	0.315793i	0.942671	+	0.333723i	$0.108305\pi$
$194$	−1109.40	−	1921.54i	−0.410569	−	0.711126i
$195$	94.1061			0.0345594
$196$		0			0
$197$	359.682			0.130083			0.0650413	−	0.997883i	$-0.479282\pi$
$197$	359.682			0.130083			0.0650413	+	0.997883i	$0.479282\pi$
$198$	−316.345	−	547.925i	−0.113544	−	0.196663i
$199$	1409.19	−	2440.78i	0.501983	−	0.869460i	−0.498014	−	0.867169i	$-0.665937\pi$
$199$	1409.19	−	2440.78i	0.501983	−	0.869460i	0.999997	−	0.00229158i	$-0.000729432\pi$
$200$	167.757	−	290.564i	0.0593112	−	0.102730i
$201$	203.546	+	352.551i	0.0714279	+	0.123717i
$202$	−6072.18			−2.11503
$203$		0			0
$204$	311.558			0.106929
$205$	−435.318	−	753.993i	−0.148312	−	0.256884i
$206$	2535.15	−	4391.02i	0.857440	−	1.48513i
$207$	−1255.10	+	2173.90i	−0.421428	+	0.729935i
$208$	885.208	+	1533.22i	0.295087	+	0.511106i
$209$	255.278			0.0844879
$210$		0			0
$211$	−1009.64			−0.329415			−0.164708	−	0.986342i	$-0.552668\pi$
$211$	−1009.64			−0.329415			−0.164708	+	0.986342i	$0.552668\pi$
$212$	1330.23	+	2304.03i	0.430948	+	0.746423i
$213$	44.8715	−	77.7197i	0.0144345	−	0.0250012i
$214$	2059.44	−	3567.05i	0.657852	−	1.13943i
$215$	−42.5862	−	73.7615i	−0.0135086	−	0.0233977i
$216$	−607.929			−0.191501
$217$		0			0
$218$	7683.86			2.38723
$219$	−419.385	−	726.396i	−0.129404	−	0.224134i
$220$	−71.6626	+	124.123i	−0.0219613	+	0.0380381i
$221$	977.355	−	1692.83i	0.297484	−	0.515258i
$222$	3.17918	+	5.50651i	0.000961139	+	0.00166474i
$223$	−1277.28			−0.383555			−0.191778	−	0.981438i	$-0.561425\pi$
$223$	−1277.28			−0.383555			−0.191778	+	0.981438i	$0.561425\pi$
$224$		0			0
$225$	−656.927			−0.194645
$226$	−412.851	−	715.079i	−0.121515	−	0.210471i
$227$	699.936	−	1212.33i	0.204654	−	0.354471i	−0.745369	−	0.666653i	$-0.767727\pi$
$227$	699.936	−	1212.33i	0.204654	−	0.354471i	0.950022	+	0.312182i	$0.101060\pi$
$228$	−65.1956	+	112.922i	−0.0189372	+	0.0328002i
$229$	1591.00	+	2755.70i	0.459111	+	0.795203i	0.998914	−	0.0465878i	$-0.0148347\pi$
$229$	1591.00	+	2755.70i	0.459111	+	0.795203i	−0.539803	+	0.841791i	$0.681501\pi$
$230$	1664.89			0.477303
$231$		0			0
$232$	−3610.53			−1.02174
$233$	1513.92	+	2622.19i	0.425666	+	0.737276i	0.996482	−	0.0838023i	$-0.0267064\pi$
$233$	1513.92	+	2622.19i	0.425666	+	0.737276i	−0.570816	+	0.821078i	$0.693373\pi$
$234$	1013.77	−	1755.90i	0.283214	−	0.490541i
$235$	1320.07	−	2286.43i	0.366434	−	0.634682i
$236$	−1334.10	−	2310.72i	−0.367976	−	0.637353i
$237$	935.144			0.256304
$238$		0			0
$239$	−4995.69			−1.35207			−0.676034	−	0.736870i	$-0.736303\pi$
$239$	−4995.69			−1.35207			−0.676034	+	0.736870i	$0.736303\pi$
$240$	170.000	+	294.449i	0.0457227	+	0.0791941i
$241$	−1878.26	+	3253.24i	−0.502030	+	0.869542i	0.497967	+	0.867196i	$0.334080\pi$
$241$	−1878.26	+	3253.24i	−0.502030	+	0.869542i	−0.999997	+	0.00234582i	$0.999253\pi$
$242$	2236.54	−	3873.80i	0.594092	−	1.02900i
$243$	896.767	+	1553.25i	0.236739	+	0.410044i
$244$	−593.280			−0.155659
$245$		0			0
$246$	516.050			0.133748
$247$	409.036	+	708.471i	0.105370	+	0.182506i
$248$	−1322.69	+	2290.97i	−0.338674	+	0.586600i
$249$	525.711	−	910.559i	0.133798	−	0.231744i
$250$	217.853	+	377.333i	0.0551130	+	0.0954585i
$251$	−6565.46			−1.65103			−0.825514	−	0.564381i	$-0.809115\pi$
$251$	−6565.46			−1.65103			−0.825514	+	0.564381i	$0.809115\pi$
$252$		0			0
$253$	659.875			0.163976
$254$	2905.66	+	5032.76i	0.717786	+	1.24324i
$255$	187.696	−	325.100i	0.0460942	−	0.0798374i
$256$	−2477.76	+	4291.60i	−0.604921	+	1.04775i
$257$	−3439.72	−	5957.77i	−0.834879	−	1.44605i	−0.894129	−	0.447810i	$-0.852204\pi$
$257$	−3439.72	−	5957.77i	−0.834879	−	1.44605i	0.0592494	−	0.998243i	$-0.481129\pi$
$258$	50.4840			0.0121822
$259$		0			0
$260$	−459.304			−0.109557
$261$	3534.66	+	6122.20i	0.838275	+	1.45193i
$262$	1554.12	−	2691.81i	0.366464	−	0.634734i
$263$	−1540.08	+	2667.49i	−0.361084	+	0.625416i	−0.988140	−	0.153558i	$-0.950927\pi$
$263$	−1540.08	+	2667.49i	−0.361084	+	0.625416i	0.627055	+	0.778975i	$0.284260\pi$
$264$	39.4105	+	68.2609i	0.00918768	+	0.0159135i
$265$	3205.57			0.743081
$266$		0			0
$267$	−605.113			−0.138698
$268$	−993.446	−	1720.70i	−0.226434	−	0.392196i
$269$	3355.17	−	5811.32i	0.760476	−	1.31718i	−0.182129	−	0.983275i	$-0.558299\pi$
$269$	3355.17	−	5811.32i	0.760476	−	1.31718i	0.942605	−	0.333909i	$-0.108368\pi$
$270$	394.735	−	683.700i	0.0889733	−	0.154106i
$271$	3921.48	+	6792.20i	0.879014	+	1.52250i	0.852425	+	0.522850i	$0.175131\pi$
$271$	3921.48	+	6792.20i	0.879014	+	1.52250i	0.0265891	+	0.999646i	$0.491535\pi$
$272$	7062.26			1.57431
$273$		0			0
$274$	−1395.74			−0.307737
$275$	86.3454	+	149.555i	0.0189339	+	0.0327945i
$276$	−168.526	+	291.895i	−0.0367538	+	0.0636594i
$277$	−2723.44	+	4717.13i	−0.590742	+	1.02319i	0.403391	+	0.915028i	$0.367831\pi$
$277$	−2723.44	+	4717.13i	−0.590742	+	1.02319i	−0.994133	+	0.108167i	$0.965502\pi$
$278$	897.642	+	1554.76i	0.193658	+	0.335426i
$279$	5179.58			1.11145
$280$		0			0
$281$	2126.76			0.451501			0.225751	−	0.974185i	$-0.427517\pi$
$281$	2126.76			0.451501			0.225751	+	0.974185i	$0.427517\pi$
$282$	782.442	+	1355.23i	0.165226	+	0.286180i
$283$	−1713.19	+	2967.33i	−0.359853	+	0.623284i	−0.987936	−	0.154862i	$-0.950507\pi$
$283$	−1713.19	+	2967.33i	−0.359853	+	0.623284i	0.628083	+	0.778147i	$0.283840\pi$
$284$	−219.004	+	379.327i	−0.0457589	+	0.0792567i
$285$	78.5535	+	136.059i	0.0163267	+	0.0282786i
$286$	−532.991			−0.110197
$287$		0			0
$288$	4504.14			0.921558
$289$	−1442.21	−	2497.98i	−0.293550	−	0.508443i
$290$	2344.36	−	4060.54i	0.474708	−	0.822218i
$291$	270.611	−	468.712i	0.0545138	−	0.0944206i
$292$	2046.89	+	3545.33i	0.410224	+	0.710529i
$293$	1749.82			0.348894			0.174447	−	0.984667i	$-0.444186\pi$
$293$	1749.82			0.348894			0.174447	+	0.984667i	$0.444186\pi$
$294$		0			0
$295$	−3214.87			−0.634499
$296$	14.3967	+	24.9358i	0.00282700	+	0.00489650i
$297$	156.452	−	270.983i	0.0305665	−	0.0529428i
$298$	−380.588	+	659.197i	−0.0739828	+	0.128142i
$299$	1057.33	+	1831.34i	0.204504	+	0.354212i
$300$	−88.2072			−0.0169755
$301$		0			0
$302$	−610.026			−0.116235
$303$	−740.579	−	1282.72i	−0.140413	−	0.243202i
$304$	−1477.82	+	2559.67i	−0.278813	+	0.482918i
$305$	−357.418	+	619.066i	−0.0671006	+	0.116222i
$306$	−4043.96	−	7004.34i	−0.755483	−	1.30853i
$307$	−7970.33			−1.48173			−0.740864	−	0.671655i	$-0.765584\pi$
$307$	−7970.33			−1.48173			−0.740864	+	0.671655i	$0.765584\pi$
$308$		0			0
$309$	1236.78			0.227695
$310$	−1717.68	−	2975.10i	−0.314701	−	0.545079i
$311$	−1280.36	+	2217.65i	−0.233449	+	0.404346i	−0.958821	−	0.284012i	$-0.908335\pi$
$311$	−1280.36	+	2217.65i	−0.233449	+	0.404346i	0.725372	+	0.688357i	$0.241668\pi$
$312$	−126.296	+	218.751i	−0.0229170	+	0.0396934i
$313$	−2430.56	−	4209.85i	−0.438924	−	0.760238i	0.558683	−	0.829381i	$-0.311307\pi$
$313$	−2430.56	−	4209.85i	−0.438924	−	0.760238i	−0.997607	+	0.0691430i	$0.977974\pi$
$314$	3205.55			0.576114
$315$		0			0
$316$	−4564.16			−0.812513
$317$	−4083.08	−	7072.10i	−0.723434	−	1.25302i	−0.959615	−	0.281315i	$-0.909229\pi$
$317$	−4083.08	−	7072.10i	−0.723434	−	1.25302i	0.236182	−	0.971709i	$-0.424104\pi$
$318$	−950.013	+	1645.47i	−0.167529	+	0.290168i
$319$	929.178	−	1609.38i	0.163085	−	0.282471i
$320$	105.870	+	183.372i	0.0184947	+	0.0320338i
$321$	1004.70			0.174694
$322$		0			0
$323$	3263.32			0.562155
$324$	−1392.18	−	2411.32i	−0.238713	−	0.413464i
$325$	−276.705	+	479.267i	−0.0472272	+	0.0817999i
$326$	−4127.89	+	7149.72i	−0.701297	+	1.21468i
$327$	937.144	+	1623.18i	0.158484	+	0.274502i
$328$	2336.89			0.393394
$329$		0			0
$330$	−102.359			−0.0170747
$331$	−1487.44	−	2576.33i	−0.247001	−	0.427818i	0.715691	−	0.698417i	$-0.246112\pi$
$331$	−1487.44	−	2576.33i	−0.247001	−	0.427818i	−0.962692	+	0.270599i	$0.912778\pi$
$332$	−2565.84	+	4444.17i	−0.424153	+	0.734655i
$333$	28.1883	−	48.8235i	0.00463876	−	0.00803457i
$334$	1881.15	+	3258.25i	0.308179	+	0.533782i
$335$	−2393.98			−0.390440
$336$		0			0
$337$	3496.34			0.565157			0.282578	−	0.959244i	$-0.408810\pi$
$337$	3496.34			0.565157			0.282578	+	0.959244i	$0.408810\pi$
$338$	2974.97	+	5152.80i	0.478748	+	0.829216i
$339$	100.705	−	174.426i	0.0161343	−	0.0279455i
$340$	−916.091	+	1586.72i	−0.146124	+	0.253093i
$341$	−680.796	−	1179.17i	−0.108115	−	0.187260i
$342$	3384.90			0.535188
$343$		0			0
$344$	228.613			0.0358314
$345$	203.055	+	351.701i	0.0316872	+	0.0548839i
$346$	−1535.90	+	2660.26i	−0.238643	+	0.413342i
$347$	−1979.54	+	3428.66i	−0.306246	+	0.530433i	−0.977538	−	0.210760i	$-0.932406\pi$
$347$	−1979.54	+	3428.66i	−0.306246	+	0.530433i	0.671292	+	0.741193i	$0.265740\pi$
$348$	474.606	+	822.042i	0.0731080	+	0.126627i
$349$	−5581.65			−0.856099			−0.428050	−	0.903755i	$-0.640799\pi$
$349$	−5581.65			−0.856099			−0.428050	+	0.903755i	$0.640799\pi$
$350$		0			0
$351$	1002.74			0.152485
$352$	−592.016	−	1025.40i	−0.0896436	−	0.155267i
$353$	−4948.22	+	8570.56i	−0.746082	+	1.29225i	0.203606	+	0.979053i	$0.434734\pi$
$353$	−4948.22	+	8570.56i	−0.746082	+	1.29225i	−0.949688	+	0.313199i	$0.898599\pi$
$354$	952.771	−	1650.25i	0.143049	−	0.247767i
$355$	263.876	+	457.046i	0.0394509	+	0.0683310i
$356$	2953.38			0.439687
$357$		0			0
$358$	−11773.5			−1.73813
$359$	−5958.79	−	10320.9i	−0.876025	−	1.51732i	−0.855666	−	0.517528i	$-0.826852\pi$
$359$	−5958.79	−	10320.9i	−0.876025	−	1.51732i	−0.0203589	−	0.999793i	$-0.506481\pi$
$360$	881.635	−	1527.04i	0.129073	−	0.223561i
$361$	2746.63	−	4757.30i	0.400442	−	0.693585i
$362$	2501.96	+	4333.52i	0.363260	+	0.629184i
$363$	1091.10			0.157762
$364$		0			0
$365$	4932.56			0.707348
$366$	−211.851	−	366.937i	−0.0302558	−	0.0524047i
$367$	−3550.79	+	6150.15i	−0.505040	+	0.874755i	0.494943	+	0.868926i	$0.335189\pi$
$367$	−3550.79	+	6150.15i	−0.505040	+	0.874755i	−0.999983	+	0.00582984i	$0.998144\pi$
$368$	−3820.06	+	6616.54i	−0.541126	+	0.937258i
$369$	−2287.78	−	3962.55i	−0.322756	−	0.559030i
$370$	−37.3917			−0.00525379
$371$		0			0
$372$	695.475			0.0969319
$373$	−147.158	−	254.885i	−0.0204277	−	0.0353819i	0.855631	−	0.517587i	$-0.173169\pi$
$373$	−147.158	−	254.885i	−0.0204277	−	0.0353819i	−0.876059	+	0.482205i	$0.839836\pi$
$374$	−1063.06	+	1841.28i	−0.146978	+	0.254573i
$375$	−53.1399	+	92.0410i	−0.00731769	+	0.0126746i
$376$	3543.23	+	6137.05i	0.485979	+	0.841740i
$377$	5955.34			0.813569
$378$		0			0
$379$	−9436.57			−1.27896			−0.639478	−	0.768810i	$-0.720849\pi$
$379$	−9436.57			−1.27896			−0.639478	+	0.768810i	$0.720849\pi$
$380$	−383.396	−	664.062i	−0.0517574	−	0.0896464i
$381$	−708.765	+	1227.62i	−0.0953048	+	0.165073i
$382$	2767.85	−	4794.05i	0.370721	−	0.642108i
$383$	−1580.41	−	2737.35i	−0.210849	−	0.365202i	0.741131	−	0.671360i	$-0.234290\pi$
$383$	−1580.41	−	2737.35i	−0.210849	−	0.365202i	−0.951981	+	0.306158i	$0.900956\pi$
$384$	−1291.41			−0.171620
$385$		0			0
$386$	−3407.93			−0.449376
$387$	−223.809	−	387.648i	−0.0293975	−	0.0509179i
$388$	−1320.77	+	2287.65i	−0.172815	+	0.299324i
$389$	−3911.38	+	6774.71i	−0.509807	+	0.883011i	0.490129	+	0.871650i	$0.336950\pi$
$389$	−3911.38	+	6774.71i	−0.509807	+	0.883011i	−0.999935	+	0.0113612i	$0.996384\pi$
$390$	−164.010	−	284.074i	−0.0212949	−	0.0368838i
$391$	8435.43			1.09104
$392$		0			0
$393$	758.176			0.0973153
$394$	−626.863	−	1085.76i	−0.0801545	−	0.138832i
$395$	−2749.65	+	4762.54i	−0.350253	+	0.606656i
$396$	−376.617	+	652.320i	−0.0477922	+	0.0827785i
$397$	−3967.59	−	6872.07i	−0.501581	−	0.868764i	−0.999998	−	0.00182682i	$-0.999419\pi$
$397$	−3967.59	−	6872.07i	−0.501581	−	0.868764i	0.498417	−	0.866937i	$-0.333915\pi$
$398$	−9823.87			−1.23725
$399$		0			0
$400$	−1999.44			−0.249930
$401$	244.190	+	422.950i	0.0304097	+	0.0526711i	0.880830	−	0.473433i	$-0.156985\pi$
$401$	244.190	+	422.950i	0.0304097	+	0.0526711i	−0.850420	+	0.526104i	$0.823652\pi$
$402$	709.489	−	1228.87i	0.0880251	−	0.152464i
$403$	2181.70	−	3778.81i	0.269673	−	0.467087i
$404$	3614.54	+	6260.57i	0.445125	+	0.770978i
$405$	−3354.84			−0.411613
$406$		0			0
$407$	−14.8201			−0.00180492
$408$	503.799	+	872.606i	0.0611318	+	0.105883i
$409$	5615.32	−	9726.02i	0.678874	−	1.17584i	−0.296446	−	0.955050i	$-0.595801\pi$
$409$	5615.32	−	9726.02i	0.678874	−	1.17584i	0.975320	−	0.220795i	$-0.0708653\pi$
$410$	−1517.37	+	2628.16i	−0.182774	+	0.316574i
$411$	−170.228	−	294.844i	−0.0204301	−	0.0353859i
$412$	−6036.34			−0.721818
$413$		0			0
$414$	8749.70			1.03871
$415$	3091.55	+	5354.73i	0.365683	+	0.633381i
$416$	1897.19	−	3286.03i	0.223600	−	0.387286i
$417$	−218.957	+	379.245i	−0.0257132	+	0.0445365i
$418$	−444.906	−	770.599i	−0.0520599	−	0.0901704i
$419$	7369.62			0.859259			0.429629	−	0.903005i	$-0.358644\pi$
$419$	7369.62			0.859259			0.429629	+	0.903005i	$0.358644\pi$
$420$		0			0
$421$	11972.5			1.38599			0.692997	−	0.720941i	$-0.256290\pi$
$421$	11972.5			1.38599			0.692997	+	0.720941i	$0.256290\pi$
$422$	1759.63	+	3047.77i	0.202980	+	0.351571i
$423$	6937.53	−	12016.2i	0.797433	−	1.38119i
$424$	−4302.06	+	7451.39i	−0.492751	+	0.853470i
$425$	1103.79	+	1911.82i	0.125980	+	0.218204i
$426$	−312.813			−0.0355770
$427$		0			0
$428$	−4903.63			−0.553799
$429$	−65.0050	−	112.592i	−0.00731579	−	0.0126713i
$430$	−148.441	+	257.107i	−0.0166476	+	0.0288344i
$431$	1784.30	−	3090.50i	0.199412	−	0.345392i	−0.748926	−	0.662654i	$-0.769430\pi$
$431$	1784.30	−	3090.50i	0.199412	−	0.345392i	0.948338	+	0.317262i	$0.102763\pi$
$432$	1811.42	+	3137.47i	0.201741	+	0.349425i
$433$	−2291.60			−0.254335			−0.127168	−	0.991881i	$-0.540589\pi$
$433$	−2291.60			−0.254335			−0.127168	+	0.991881i	$0.540589\pi$
$434$		0			0
$435$	1143.70			0.126060
$436$	−4573.92	−	7922.27i	−0.502411	−	0.870202i
$437$	−1765.17	+	3057.36i	−0.193225	+	0.334676i
$438$	−1461.83	+	2531.96i	−0.159473	+	0.276214i
$439$	−3664.83	−	6347.67i	−0.398435	−	0.690109i	0.595098	−	0.803653i	$-0.297113\pi$
$439$	−3664.83	−	6347.67i	−0.398435	−	0.690109i	−0.993533	+	0.113544i	$0.963780\pi$
$440$	−463.523			−0.0502218
$441$		0			0
$442$	−6813.44			−0.733218
$443$	−4148.69	−	7185.75i	−0.444944	−	0.770666i	0.553104	−	0.833112i	$-0.313443\pi$
$443$	−4148.69	−	7185.75i	−0.444944	−	0.770666i	−0.998048	+	0.0624461i	$0.980110\pi$
$444$	3.78491	−	6.55565i	0.000404558	−	0.000700715i
$445$	1779.24	−	3081.74i	0.189538	−	0.328289i
$446$	2226.07	+	3855.67i	0.236340	+	0.409352i
$447$	−185.670			−0.0196463
$448$		0			0
$449$	9758.62			1.02570			0.512848	−	0.858479i	$-0.328590\pi$
$449$	9758.62			1.02570			0.512848	+	0.858479i	$0.328590\pi$
$450$	1144.91	+	1983.04i	0.119937	+	0.207737i
$451$	−601.404	+	1041.66i	−0.0627916	+	0.108758i
$452$	−491.510	+	851.321i	−0.0511476	+	0.0885902i
$453$	−74.4004	−	128.865i	−0.00771664	−	0.0133656i
$454$	−4879.47			−0.504416
$455$		0			0
$456$	−421.693			−0.0433061
$457$	5872.50	+	10171.5i	0.601102	+	1.04114i	0.992654	+	0.120984i	$0.0386050\pi$
$457$	5872.50	+	10171.5i	0.601102	+	1.04114i	−0.391552	+	0.920156i	$0.628062\pi$
$458$	5545.68	−	9605.40i	0.565792	−	0.979980i
$459$	1999.98	−	3464.08i	0.203380	−	0.352264i
$460$	−991.049	−	1716.55i	−0.100452	−	0.173988i
$461$	10748.6			1.08593			0.542963	−	0.839756i	$-0.317302\pi$
$461$	10748.6			1.08593			0.542963	+	0.839756i	$0.317302\pi$
$462$		0			0
$463$	−9862.51			−0.989957			−0.494978	−	0.868905i	$-0.664824\pi$
$463$	−9862.51			−0.989957			−0.494978	+	0.868905i	$0.664824\pi$
$464$	10758.2	+	18633.7i	1.07637	+	1.86432i
$465$	418.985	−	725.703i	0.0417848	−	0.0723735i
$466$	5277.00	−	9140.03i	0.524576	−	0.908592i
$467$	−2330.39	−	4036.35i	−0.230916	−	0.399958i	0.727162	−	0.686466i	$-0.240839\pi$
$467$	−2330.39	−	4036.35i	−0.230916	−	0.399958i	−0.958078	+	0.286508i	$0.907505\pi$
$468$	−2413.83			−0.238418
$469$		0			0
$470$	−9202.62			−0.903160
$471$	390.957	+	677.158i	0.0382471	+	0.0662458i
$472$	4314.55	−	7473.02i	0.420748	−	0.728758i
$473$	−58.8341	+	101.904i	−0.00571922	+	0.00990598i
$474$	−1629.79	−	2822.88i	−0.157930	−	0.273543i
$475$	−923.899			−0.0892451
$476$		0			0
$477$	16846.6			1.61709
$478$	8706.62	+	15080.3i	0.833120	+	1.44301i
$479$	−8146.61	+	14110.3i	−0.777094	+	1.34597i	0.156516	+	0.987675i	$0.449974\pi$
$479$	−8146.61	+	14110.3i	−0.777094	+	1.34597i	−0.933610	+	0.358291i	$0.883360\pi$
$480$	364.347	−	631.067i	0.0346460	−	0.0600086i
$481$	−23.7464	−	41.1300i	−0.00225103	−	0.00389889i
$482$	13093.9			1.23737
$483$		0			0
$484$	−5325.33			−0.500124
$485$	1591.38	+	2756.36i	0.148992	+	0.258061i
$486$	3125.82	−	5414.07i	0.291749	−	0.505324i
$487$	1757.50	−	3044.08i	0.163531	−	0.283245i	−0.772601	−	0.634891i	$-0.781045\pi$
$487$	1757.50	−	3044.08i	0.163531	−	0.283245i	0.936133	+	0.351647i	$0.114378\pi$
$488$	−959.351	−	1661.65i	−0.0889914	−	0.154138i
$489$	−2013.80			−0.186231
$490$		0			0
$491$	−2516.79			−0.231326			−0.115663	−	0.993288i	$-0.536899\pi$
$491$	−2516.79			−0.231326			−0.115663	+	0.993288i	$0.536899\pi$
$492$	−307.186	−	532.061i	−0.0281484	−	0.0487544i
$493$	11878.1	−	20573.4i	1.08511	−	1.87947i
$494$	1425.76	−	2469.48i	0.129854	−	0.224914i
$495$	453.781	+	785.973i	0.0412040	+	0.0713674i
$496$	15764.7			1.42713
$497$		0			0
$498$	−3664.89			−0.329775
$499$	4373.74	+	7575.54i	0.392376	+	0.679615i	0.992762	−	0.120095i	$-0.0383200\pi$
$499$	4373.74	+	7575.54i	0.392376	+	0.679615i	−0.600387	+	0.799710i	$0.704987\pi$
$500$	259.360	−	449.225i	0.0231979	−	0.0401799i
$501$	−458.860	+	794.769i	−0.0409189	+	0.0708736i
$502$	11442.5	+	19818.9i	1.01733	+	1.76207i
$503$	−11426.1			−1.01285			−0.506426	−	0.862284i	$-0.669034\pi$
$503$	−11426.1			−1.01285			−0.506426	+	0.862284i	$0.669034\pi$
$504$		0			0
$505$	8710.25			0.767526
$506$	−1150.05	−	1991.94i	−0.101039	−	0.175005i
$507$	−725.670	+	1256.90i	−0.0635663	+	0.110100i
$508$	3459.27	−	5991.64i	0.302127	−	0.523299i
$509$	−4039.22	−	6996.13i	−0.351739	−	0.609230i	0.634815	−	0.772664i	$-0.281076\pi$
$509$	−4039.22	−	6996.13i	−0.351739	−	0.609230i	−0.986554	+	0.163434i	$0.947743\pi$
$510$	−1308.49			−0.113610
$511$		0			0
$512$	5122.12			0.442125
$513$	837.020	+	1449.76i	0.0720377	+	0.124773i
$514$	−11989.7	+	20766.7i	−1.02887	+	1.78206i
$515$	−3636.56	+	6298.70i	−0.311157	+	0.538940i
$516$	−30.0513	−	52.0504i	−0.00256383	−	0.00444068i
$517$	−3647.43			−0.310278
$518$		0			0
$519$	−749.290			−0.0633723
$520$	−742.709	−	1286.41i	−0.0626345	−	0.108486i
$521$	3613.07	−	6258.02i	0.303822	−	0.526236i	−0.673176	−	0.739482i	$-0.735070\pi$
$521$	3613.07	−	6258.02i	0.303822	−	0.526236i	0.976998	+	0.213246i	$0.0684037\pi$
$522$	12320.6	−	21339.9i	1.03306	−	1.78931i
$523$	4666.53	+	8082.66i	0.390159	+	0.675775i	0.992470	−	0.122486i	$-0.0390868\pi$
$523$	4666.53	+	8082.66i	0.390159	+	0.675775i	−0.602311	+	0.798261i	$0.705753\pi$
$524$	−3700.43			−0.308500
$525$		0			0
$526$	10736.3			0.889974
$527$	−8702.88	−	15073.8i	−0.719361	−	1.24597i
$528$	234.860	−	406.789i	0.0193579	−	0.0335288i
$529$	1520.67	−	2633.88i	0.124983	−	0.216478i
$530$	−5586.75	−	9676.53i	−0.457873	−	0.793059i
$531$	−16895.5			−1.38080
$532$		0			0
$533$	−3854.55			−0.313244
$534$	1054.61	+	1826.63i	0.0854630	+	0.148026i
$535$	−2954.17	+	5116.76i	−0.238728	+	0.413490i
$536$	3212.87	−	5564.85i	0.258908	−	0.448442i
$537$	−1435.93	−	2487.11i	−0.115391	−	0.199863i
$538$	−23389.9			−1.87437
$539$		0			0
$540$	−939.884			−0.0749003
$541$	−7631.57	−	13218.3i	−0.606482	−	1.05046i	−0.991815	−	0.127680i	$-0.959247\pi$
$541$	−7631.57	−	13218.3i	−0.606482	−	1.05046i	0.385333	−	0.922777i	$-0.374086\pi$
$542$	13668.9	−	23675.2i	1.08326	−	1.87627i
$543$	−610.291	+	1057.05i	−0.0482322	+	0.0835406i
$544$	−7567.97	−	13108.1i	−0.596460	−	1.03310i
$545$	−11022.1			−0.866305
$546$		0			0
$547$	−13226.0			−1.03382			−0.516912	−	0.856039i	$-0.672918\pi$
$547$	−13226.0			−1.03382			−0.516912	+	0.856039i	$0.672918\pi$
$548$	830.835	+	1439.05i	0.0647655	+	0.112177i
$549$	−1878.38	+	3253.45i	−0.146024	+	0.252921i
$550$	300.970	−	521.295i	0.0233335	−	0.0404147i
$551$	4971.12	+	8610.23i	0.384350	+	0.665714i
$552$	−1090.04			−0.0840496
$553$		0			0
$554$	18985.9			1.45602
$555$	−4.56039	−	7.89883i	−0.000348789	−	0.000604120i
$556$	1068.67	−	1850.98i	0.0815136	−	0.141186i
$557$	−3496.82	+	6056.66i	−0.266005	+	0.460734i	−0.967826	−	0.251619i	$-0.919037\pi$
$557$	−3496.82	+	6056.66i	−0.266005	+	0.460734i	0.701821	+	0.712353i	$0.252370\pi$
$558$	−9027.11	−	15635.4i	−0.684853	−	1.18620i
$559$	−377.082			−0.0285311
$560$		0			0
$561$	−518.616			−0.0390302
$562$	−3706.57	−	6419.97i	−0.278207	−	0.481868i
$563$	196.099	−	339.653i	0.0146795	−	0.0254257i	−0.858592	−	0.512659i	$-0.828661\pi$
$563$	196.099	−	339.653i	0.0146795	−	0.0254257i	0.873272	+	0.487233i	$0.161994\pi$
$564$	931.518	−	1613.44i	0.0695461	−	0.120457i
$565$	592.215	+	1025.75i	0.0440968	+	0.0763778i
$566$	11943.2			0.886940
$567$		0			0
$568$	−1416.55			−0.104643
$569$	−4405.86	−	7631.18i	−0.324610	−	0.562242i	0.656823	−	0.754045i	$-0.271900\pi$
$569$	−4405.86	−	7631.18i	−0.324610	−	0.562242i	−0.981433	+	0.191803i	$0.938567\pi$
$570$	273.810	−	474.253i	0.0201204	−	0.0348496i
$571$	12387.8	−	21456.3i	0.907905	−	1.57254i	0.0909362	−	0.995857i	$-0.471014\pi$
$571$	12387.8	−	21456.3i	0.907905	−	1.57254i	0.816969	−	0.576681i	$-0.195653\pi$
$572$	317.270	+	549.528i	0.0231919	+	0.0401695i
$573$	1350.30			0.0984458
$574$		0			0
$575$	−2388.21			−0.173209
$576$	556.391	+	963.697i	0.0402482	+	0.0697119i
$577$	−4425.31	+	7664.86i	−0.319286	+	0.553020i	−0.980339	−	0.197319i	$-0.936776\pi$
$577$	−4425.31	+	7664.86i	−0.319286	+	0.553020i	0.661053	+	0.750339i	$0.270110\pi$
$578$	−5027.04	+	8707.09i	−0.361760	+	0.626587i
$579$	−415.641	−	719.911i	−0.0298332	−	0.0516727i
$580$	−5582.04			−0.399623
$581$		0			0
$582$	−1886.51			−0.134362
$583$	−2214.29	−	3835.26i	−0.157301	−	0.272453i
$584$	−6619.79	+	11465.8i	−0.469056	+	0.812429i
$585$	−1454.20	+	2518.75i	−0.102776	+	0.178013i
$586$	−3049.64	−	5282.13i	−0.214982	−	0.372359i
$587$	46.0232			0.00323608			0.00161804	−	0.999999i	$-0.499485\pi$
$587$	46.0232			0.00323608			0.00161804	+	0.999999i	$0.499485\pi$
$588$		0			0
$589$	7284.54			0.509600
$590$	5602.96	+	9704.62i	0.390967	+	0.677174i
$591$	152.908	−	264.844i	0.0106426	−	0.0184335i
$592$	85.7945	−	148.600i	0.00595630	−	0.0103166i
$593$	−1364.97	−	2364.19i	−0.0945235	−	0.163719i	0.814886	−	0.579621i	$-0.196799\pi$
$593$	−1364.97	−	2364.19i	−0.0945235	−	0.163719i	−0.909410	+	0.415902i	$0.863466\pi$
$594$	−1090.67			−0.0753381
$595$		0			0
$596$	906.200			0.0622809
$597$	−1198.15	−	2075.25i	−0.0821387	−	0.142268i
$598$	3685.47	−	6383.42i	0.252024	−	0.436518i
$599$	2752.54	−	4767.53i	0.187756	−	0.325202i	−0.756746	−	0.653709i	$-0.773212\pi$
$599$	2752.54	−	4767.53i	0.187756	−	0.325202i	0.944502	+	0.328507i	$0.106545\pi$
$600$	−142.634	−	247.049i	−0.00970500	−	0.0168095i
$601$	7446.97			0.505438			0.252719	−	0.967540i	$-0.418675\pi$
$601$	7446.97			0.505438			0.252719	+	0.967540i	$0.418675\pi$
$602$		0			0
$603$	−12581.4			−0.849674
$604$	363.126	+	628.954i	0.0244626	+	0.0423705i
$605$	−3208.21	+	5556.79i	−0.215591	+	0.373414i
$606$	−2581.40	+	4471.11i	−0.173040	+	0.299714i
$607$	−12035.7	−	20846.4i	−0.804799	−	1.39395i	−0.916426	−	0.400203i	$-0.868939\pi$
$607$	−12035.7	−	20846.4i	−0.804799	−	1.39395i	0.111627	−	0.993750i	$-0.464394\pi$
$608$	6334.59			0.422536
$609$		0			0
$610$	2491.67			0.165385
$611$	−5844.33	−	10122.7i	−0.386966	−	0.670244i
$612$	−4814.44	+	8338.86i	−0.317994	+	0.550782i
$613$	2054.31	−	3558.16i	0.135355	−	0.234442i	−0.790378	−	0.612620i	$-0.790116\pi$
$613$	2054.31	−	3558.16i	0.135355	−	0.234442i	0.925733	+	0.378178i	$0.123449\pi$
$614$	13890.9	+	24059.7i	0.913014	+	1.58139i
$615$	−740.249			−0.0485361
$616$		0			0
$617$	3542.46			0.231141			0.115571	−	0.993299i	$-0.463130\pi$
$617$	3542.46			0.231141			0.115571	+	0.993299i	$0.463130\pi$
$618$	−2155.49	−	3733.41i	−0.140302	−	0.243009i
$619$	3242.40	−	5616.01i	0.210538	−	0.364663i	−0.741345	−	0.671124i	$-0.765812\pi$
$619$	3242.40	−	5616.01i	0.210538	−	0.364663i	0.951883	+	0.306461i	$0.0991450\pi$
$620$	−2044.94	+	3541.94i	−0.132463	+	0.229432i
$621$	2163.63	+	3747.52i	0.139812	+	0.242162i
$622$	8925.79			0.575388
$623$		0			0
$624$	1505.28			0.0965693
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−8472.07	+	14674.1i	−0.540914	+	0.936890i
$627$	108.524	−	187.969i	0.00691231	−	0.0119725i
$628$	−1908.15	−	3305.01i	−0.121247	−	0.210007i
$629$	−189.451			−0.0120094
$630$		0			0
$631$	3250.84			0.205094			0.102547	−	0.994728i	$-0.467301\pi$
$631$	3250.84			0.205094			0.102547	+	0.994728i	$0.467301\pi$
$632$	−7380.39	−	12783.2i	−0.464519	−	0.804571i
$633$	−429.218	+	743.428i	−0.0269509	+	0.0466802i
$634$	−14232.2	+	24650.9i	−0.891533	+	1.54418i
$635$	−4168.04	−	7219.25i	−0.260478	−	0.451161i
$636$	2262.03			0.141031
$637$		0			0
$638$	−6477.58			−0.401959
$639$	1386.78	+	2401.97i	0.0858531	+	0.148702i
$640$	3797.21	−	6576.96i	0.234528	−	0.406214i
$641$	−1400.31	+	2425.40i	−0.0862852	+	0.149450i	−0.905938	−	0.423410i	$-0.860833\pi$
$641$	−1400.31	+	2425.40i	−0.0862852	+	0.149450i	0.819653	+	0.572860i	$0.194166\pi$
$642$	−1751.01	−	3032.84i	−0.107643	−	0.186444i
$643$	−18910.6			−1.15982			−0.579908	−	0.814682i	$-0.696911\pi$
$643$	−18910.6			−1.15982			−0.579908	+	0.814682i	$0.696911\pi$
$644$		0			0
$645$	−72.4169			−0.00442080
$646$	−5687.40	−	9850.87i	−0.346390	−	0.599965i
$647$	−12261.3	+	21237.3i	−0.745043	+	1.29045i	0.205131	+	0.978734i	$0.434238\pi$
$647$	−12261.3	+	21237.3i	−0.745043	+	1.29045i	−0.950175	+	0.311718i	$0.899095\pi$
$648$	4502.39	−	7798.36i	0.272948	−	0.472760i
$649$	2220.72	+	3846.40i	0.134316	+	0.232641i
$650$	1928.99			0.116402
$651$		0			0
$652$	9828.74			0.590373
$653$	7649.80	+	13249.8i	0.458438	+	0.794037i	0.998879	−	0.0473446i	$-0.0150759\pi$
$653$	7649.80	+	13249.8i	0.458438	+	0.794037i	−0.540441	+	0.841382i	$0.681743\pi$
$654$	3266.56	−	5657.84i	0.195310	−	0.338286i
$655$	−2229.30	+	3861.27i	−0.132986	+	0.230339i
$656$	−6963.14	−	12060.5i	−0.414428	−	0.717811i
$657$	25922.7			1.53933
$658$		0			0
$659$	−2203.13			−0.130230			−0.0651151	−	0.997878i	$-0.520741\pi$
$659$	−2203.13			−0.130230			−0.0651151	+	0.997878i	$0.520741\pi$
$660$	60.9303	+	105.534i	0.00359350	+	0.00622412i
$661$	−1581.18	+	2738.69i	−0.0930421	+	0.161154i	−0.908790	−	0.417254i	$-0.862992\pi$
$661$	−1581.18	+	2738.69i	−0.0930421	+	0.161154i	0.815748	+	0.578408i	$0.196326\pi$
$662$	−5184.71	+	8980.18i	−0.304395	+	0.527228i
$663$	−830.985	−	1439.31i	−0.0486769	−	0.0843108i
$664$	−16596.2			−0.969965
$665$		0			0
$666$	−196.509			−0.0114333
$667$	12850.0	+	22256.8i	0.745956	+	1.29203i
$668$	2239.56	−	3879.03i	0.129717	−	0.224677i
$669$	−542.995	+	940.495i	−0.0313803	+	0.0543522i
$670$	4172.30	+	7226.63i	0.240582	+	0.416700i
$671$	987.565			0.0568175
$672$		0			0
$673$	−4443.07			−0.254484			−0.127242	−	0.991872i	$-0.540613\pi$
$673$	−4443.07			−0.254484			−0.127242	+	0.991872i	$0.540613\pi$
$674$	−6093.51	−	10554.3i	−0.348239	−	0.603168i
$675$	−566.228	+	980.735i	−0.0322876	+	0.0559237i
$676$	3541.78	−	6134.54i	0.201512	−	0.349030i
$677$	2228.16	+	3859.29i	0.126492	+	0.219091i	0.922315	−	0.386438i	$-0.126295\pi$
$677$	2228.16	+	3859.29i	0.126492	+	0.219091i	−0.795823	+	0.605529i	$0.792962\pi$
$678$	−702.044			−0.0397667
$679$		0			0
$680$	−5925.39			−0.334159
$681$	−595.113	−	1030.77i	−0.0334872	−	0.0580015i
$682$	−2373.02	+	4110.18i	−0.133237	+	0.230773i
$683$	5023.42	−	8700.82i	0.281429	−	0.487449i	−0.690308	−	0.723516i	$-0.742525\pi$
$683$	5023.42	−	8700.82i	0.281429	−	0.487449i	0.971737	+	0.236066i	$0.0758583\pi$
$684$	−2014.91	−	3489.92i	−0.112634	−	0.195088i
$685$	2002.13			0.111675
$686$		0			0
$687$	2705.46			0.150247
$688$	−681.189	−	1179.85i	−0.0377472	−	0.0653801i
$689$	7095.97	−	12290.6i	0.392359	−	0.679585i
$690$	707.777	−	1225.91i	0.0390502	−	0.0676369i
$691$	15905.6	+	27549.3i	0.875655	+	1.51668i	0.856064	+	0.516870i	$0.172903\pi$
$691$	15905.6	+	27549.3i	0.875655	+	1.51668i	0.0195910	+	0.999808i	$0.493764\pi$
$692$	3657.06			0.200897
$693$		0			0
$694$	13800.0			0.754812
$695$	−1287.62	−	2230.23i	−0.0702768	−	0.121723i
$696$	−1534.91	+	2658.54i	−0.0835926	+	0.144787i
$697$	−7687.98	+	13316.0i	−0.417795	+	0.723642i
$698$	9727.83	+	16849.1i	0.527513	+	0.913679i
$699$	2574.39			0.139302
$700$		0			0
$701$	−13907.2			−0.749312			−0.374656	−	0.927164i	$-0.622239\pi$
$701$	−13907.2			−0.749312			−0.374656	+	0.927164i	$0.622239\pi$
$702$	−1747.60	−	3026.93i	−0.0939586	−	0.162741i
$703$	39.6438	−	68.6651i	0.00212688	−	0.00368386i
$704$	146.262	−	253.333i	0.00783020	−	0.0135623i
$705$	−1122.38	−	1944.01i	−0.0599590	−	0.103852i
$706$	34495.5			1.83889
$707$		0			0
$708$	−2268.60			−0.120423
$709$	114.476	+	198.278i	0.00606381	+	0.0105028i	0.869041	−	0.494739i	$-0.164736\pi$
$709$	114.476	+	198.278i	0.00606381	+	0.0105028i	−0.862978	+	0.505242i	$0.831403\pi$
$710$	919.779	−	1593.10i	0.0486179	−	0.0842087i
$711$	−14450.6	+	25029.1i	−0.762221	+	1.32020i
$712$	4775.70	+	8271.75i	0.251372	+	0.435389i
$713$	18830.0			0.989043
$714$		0			0
$715$	764.551			0.0399896
$716$	7008.36	+	12138.8i	0.365803	+	0.633589i
$717$	−2123.76	+	3678.47i	−0.110618	+	0.191597i
$718$	−20770.3	+	35975.2i	−1.07958	+	1.86989i
$719$	18081.1	+	31317.4i	0.937846	+	1.62440i	0.769479	+	0.638672i	$0.220516\pi$
$719$	18081.1	+	31317.4i	0.937846	+	1.62440i	0.168367	+	0.985724i	$0.446151\pi$
$720$	−10507.9			−0.543897
$721$		0			0
$722$	−19147.6			−0.986979
$723$	1596.97	+	2766.03i	0.0821464	+	0.142282i
$724$	2978.65	−	5159.17i	0.152901	−	0.264833i
$725$	−3362.87	+	5824.66i	−0.172267	+	0.298376i
$726$	−1901.59	−	3293.66i	−0.0972104	−	0.168373i
$727$	−22268.3			−1.13602			−0.568010	−	0.823021i	$-0.692287\pi$
$727$	−22268.3			−1.13602			−0.568010	+	0.823021i	$0.692287\pi$
$728$		0			0
$729$	−16591.2			−0.842919
$730$	−8596.59	−	14889.7i	−0.435855	−	0.754923i
$731$	−752.099	+	1302.67i	−0.0380539	+	0.0659112i
$732$	−252.215	+	436.848i	−0.0127351	+	0.0220579i
$733$	−1166.60	−	2020.61i	−0.0587848	−	0.101818i	0.835135	−	0.550044i	$-0.185389\pi$
$733$	−1166.60	−	2020.61i	−0.0587848	−	0.101818i	−0.893920	+	0.448226i	$0.852056\pi$
$734$	24753.6			1.24479
$735$		0			0
$736$	16374.4			0.820067
$737$	1653.68	+	2864.25i	0.0826512	+	0.143156i
$738$	−7974.40	+	13812.1i	−0.397753	+	0.688929i
$739$	2414.58	−	4182.17i	0.120192	−	0.208178i	−0.799652	−	0.600464i	$-0.794982\pi$
$739$	2414.58	−	4182.17i	0.120192	−	0.208178i	0.919843	+	0.392286i	$0.128316\pi$
$740$	22.2579	+	38.5518i	0.00110570	+	0.00191513i
$741$	695.556			0.0344830
$742$		0			0
$743$	−25459.0			−1.25707			−0.628533	−	0.777783i	$-0.716344\pi$
$743$	−25459.0			−1.25707			−0.628533	+	0.777783i	$0.716344\pi$
$744$	1124.60	+	1947.87i	0.0554166	+	0.0959844i
$745$	545.935	−	945.587i	0.0268477	−	0.0465015i
$746$	−512.941	+	888.440i	−0.0251744	+	0.0436033i
$747$	16247.4	+	28141.3i	0.795798	+	1.37836i
$748$	2531.21			0.123730
$749$		0			0
$750$	370.454			0.0180361
$751$	2853.54	+	4942.48i	0.138651	+	0.240151i	0.926986	−	0.375095i	$-0.122390\pi$
$751$	2853.54	+	4942.48i	0.138651	+	0.240151i	−0.788335	+	0.615246i	$0.789057\pi$
$752$	21115.2	−	36572.6i	1.02393	−	1.77349i
$753$	−2791.10	+	4834.33i	−0.135078	+	0.233961i
$754$	−10379.1	−	17977.2i	−0.501307	−	0.868289i
$755$	875.054			0.0421808
$756$		0			0
$757$	−1900.91			−0.0912677			−0.0456339	−	0.998958i	$-0.514531\pi$
$757$	−1900.91			−0.0912677			−0.0456339	+	0.998958i	$0.514531\pi$
$758$	16446.3	+	28485.8i	0.788069	+	1.36498i
$759$	280.525	−	485.884i	0.0134156	−	0.0232365i
$760$	1239.93	−	2147.62i	0.0591801	−	0.102503i
$761$	−5791.91	−	10031.9i	−0.275896	−	0.477865i	0.694465	−	0.719526i	$-0.255641\pi$
$761$	−5791.91	−	10031.9i	−0.275896	−	0.477865i	−0.970361	+	0.241661i	$0.922308\pi$
$762$	4941.01			0.234900
$763$		0			0
$764$	−6590.40			−0.312084
$765$	5800.87	+	10047.4i	0.274158	+	0.474855i
$766$	−5508.76	+	9541.46i	−0.259843	+	0.450061i
$767$	−7116.57	+	12326.3i	−0.335025	+	0.580281i
$768$	2106.68	+	3648.88i	0.0989823	+	0.171442i
$769$	26059.7			1.22202			0.611012	−	0.791622i	$-0.290763\pi$
$769$	26059.7			1.22202			0.611012	+	0.791622i	$0.290763\pi$
$770$		0			0
$771$	−5849.17			−0.273220
$772$	2028.62	+	3513.67i	0.0945746	+	0.163808i
$773$	−8106.78	+	14041.4i	−0.377206	+	0.653341i	−0.990655	−	0.136394i	$-0.956449\pi$
$773$	−8106.78	+	14041.4i	−0.377206	+	0.653341i	0.613448	+	0.789735i	$0.289782\pi$
$774$	−780.119	+	1351.20i	−0.0362284	+	0.0627494i
$775$	2463.92	+	4267.64i	0.114202	+	0.197804i
$776$	−8542.92			−0.395197
$777$		0			0
$778$	27267.4			1.25653
$779$	−3217.52	−	5572.91i	−0.147984	−	0.256316i
$780$	−195.259	+	338.198i	−0.00896332	+	0.0155249i
$781$	364.552	−	631.422i	0.0167025	−	0.0289297i
$782$	−14701.5	−	25463.7i	−0.672282	−	1.16443i
$783$	12186.6			0.556209
$784$		0			0
$785$	−4598.21			−0.209066
$786$	−1321.37	−	2288.68i	−0.0599639	−	0.103861i
$787$	−685.670	+	1187.62i	−0.0310565	+	0.0537915i	−0.881136	−	0.472863i	$-0.843221\pi$
$787$	−685.670	+	1187.62i	−0.0310565	+	0.0537915i	0.850079	+	0.526655i	$0.176554\pi$
$788$	−746.297	+	1292.62i	−0.0337382	+	0.0584363i
$789$	1309.43	+	2268.00i	0.0590837	+	0.102336i
$790$	19168.7			0.863279
$791$		0			0
$792$	−2436.01			−0.109293
$793$	1582.39	+	2740.78i	0.0708604	+	0.122734i
$794$	−13829.6	+	23953.6i	−0.618130	+	1.07063i
$795$	1362.75	−	2360.35i	0.0607946	−	0.105299i
$796$	5847.79	+	10128.7i	0.260389	+	0.451007i
$797$	−7991.49			−0.355173			−0.177587	−	0.984105i	$-0.556829\pi$
$797$	−7991.49			−0.355173			−0.177587	+	0.984105i	$0.556829\pi$
$798$		0			0
$799$	−46626.5			−2.06449
$800$	2142.61	+	3711.12i	0.0946911	+	0.164010i
$801$	9350.67	−	16195.8i	0.412472	−	0.714422i
$802$	851.162	−	1474.26i	0.0374758	−	0.0649099i
$803$	−3407.23	−	5901.50i	−0.149737	−	0.259352i
$804$	−1689.33			−0.0741022
$805$		0			0
$806$	−15209.3			−0.664669
$807$	−2852.69	−	4941.01i	−0.124436	−	0.215529i
$808$	−11689.7	+	20247.1i	−0.508961	+	0.881547i
$809$	8830.69	−	15295.2i	0.383771	−	0.664711i	−0.607827	−	0.794070i	$-0.707959\pi$
$809$	8830.69	−	15295.2i	0.383771	−	0.664711i	0.991598	+	0.129359i	$0.0412919\pi$
$810$	5846.89	+	10127.1i	0.253628	+	0.439297i
$811$	24180.6			1.04697			0.523486	−	0.852034i	$-0.324631\pi$
$811$	24180.6			1.04697			0.523486	+	0.852034i	$0.324631\pi$
$812$		0			0
$813$	6668.38			0.287663
$814$	25.8288	+	44.7368i	0.00111216	+	0.00192632i
$815$	5921.27	−	10255.9i	0.254494	−	0.440797i
$816$	3002.30	−	5200.14i	0.128801	−	0.223090i
$817$	−314.763	−	545.186i	−0.0134788	−	0.0233459i
$818$	−39146.1			−1.67324
$819$		0			0
$820$	3612.93			0.153865
$821$	11670.5	+	20213.8i	0.496104	+	0.859278i	0.999990	−	0.00449269i	$-0.00143007\pi$
$821$	11670.5	+	20213.8i	0.496104	+	0.859278i	−0.503886	+	0.863770i	$0.668097\pi$
$822$	−593.357	+	1027.72i	−0.0251773	+	0.0436083i
$823$	−10315.2	+	17866.5i	−0.436896	+	0.756726i	−0.997448	−	0.0713930i	$-0.977256\pi$
$823$	−10315.2	+	17866.5i	−0.436896	+	0.756726i	0.560552	+	0.828119i	$0.310589\pi$
$824$	−9760.95	−	16906.5i	−0.412668	−	0.714763i
$825$	146.828			0.00619625
$826$		0			0
$827$	24113.7			1.01393			0.506963	−	0.861968i	$-0.330768\pi$
$827$	24113.7			1.01393			0.506963	+	0.861968i	$0.330768\pi$
$828$	−5208.38	−	9021.18i	−0.218603	−	0.378632i
$829$	20869.5	−	36147.0i	0.874338	−	1.51440i	0.0168723	−	0.999858i	$-0.494629\pi$
$829$	20869.5	−	36147.0i	0.874338	−	1.51440i	0.857466	−	0.514541i	$-0.172038\pi$
$830$	10776.1	−	18664.7i	0.450654	−	0.780556i
$831$	2315.57	+	4010.68i	0.0966621	+	0.167424i
$832$	937.432			0.0390620
$833$		0			0
$834$	1526.42			0.0633760
$835$	−2698.42	−	4673.80i	−0.111836	−	0.193705i
$836$	−529.672	+	917.419i	−0.0219128	+	0.0379541i
$837$	4464.46	−	7732.67i	0.184366	−	0.319331i
$838$	−12844.0	−	22246.4i	−0.529460	−	0.917051i
$839$	−30403.0			−1.25105			−0.625523	−	0.780205i	$-0.715114\pi$
$839$	−30403.0			−1.25105			−0.625523	+	0.780205i	$0.715114\pi$
$840$		0			0
$841$	47987.8			1.96760
$842$	−20865.9	−	36140.9i	−0.854024	−	1.47921i
$843$	904.126	−	1565.99i	0.0369392	−	0.0639806i
$844$	2094.89	−	3628.45i	0.0854372	−	0.147982i
$845$	−4267.45	−	7391.44i	−0.173733	−	0.300915i
$846$	−48363.6			−1.96545
$847$		0			0
$848$	51274.7			2.07639
$849$	1456.62	+	2522.94i	0.0588822	+	0.101987i
$850$	3847.42	−	6663.92i	0.155253	−	0.268907i
$851$	102.476	−	177.494i	0.00412790	−	0.00714973i
$852$	186.206	+	322.518i	0.00748745	+	0.0129687i
$853$	−5900.43			−0.236843			−0.118421	−	0.992963i	$-0.537783\pi$
$853$	−5900.43			−0.236843			−0.118421	+	0.992963i	$0.537783\pi$
$854$		0			0
$855$	−4855.48			−0.194215
$856$	−7929.33	−	13734.0i	−0.316611	−	0.548386i
$857$	−9113.08	+	15784.3i	−0.363240	+	0.629150i	−0.988492	−	0.151273i	$-0.951663\pi$
$857$	−9113.08	+	15784.3i	−0.363240	+	0.629150i	0.625252	+	0.780423i	$0.284996\pi$
$858$	−226.585	+	392.457i	−0.00901571	+	0.0156157i
$859$	−9972.10	−	17272.2i	−0.396093	−	0.686053i	0.597147	−	0.802132i	$-0.296301\pi$
$859$	−9972.10	−	17272.2i	−0.396093	−	0.686053i	−0.993240	+	0.116079i	$0.962967\pi$
$860$	353.446			0.0140144
$861$		0			0
$862$	−12438.9			−0.491497
$863$	−15415.1	−	26699.8i	−0.608038	−	1.05315i	−0.991563	−	0.129623i	$-0.958623\pi$
$863$	−15415.1	−	26699.8i	−0.608038	−	1.05315i	0.383525	−	0.923530i	$-0.374710\pi$
$864$	3882.27	−	6724.28i	0.152867	−	0.264774i
$865$	2203.18	−	3816.02i	0.0866015	−	0.149998i
$866$	3993.85	+	6917.55i	0.156717	+	0.271441i
$867$	−2452.44			−0.0960662
$868$		0			0
$869$	7597.44			0.296577
$870$	−1993.26	−	3452.43i	−0.0776757	−	0.134538i
$871$	−5299.42	+	9178.86i	−0.206158	+	0.357077i
$872$	14792.4	−	25621.1i	0.574464	−	0.995000i
$873$	8363.39	+	14485.8i	0.324236	+	0.561593i
$874$	12305.5			0.476248
$875$		0			0
$876$	3480.70			0.134249
$877$	22942.8	+	39738.1i	0.883379	+	1.53006i	0.847560	+	0.530699i	$0.178071\pi$
$877$	22942.8	+	39738.1i	0.883379	+	1.53006i	0.0358189	+	0.999358i	$0.488596\pi$
$878$	−12774.3	+	22125.8i	−0.491017	+	0.850466i
$879$	743.884	−	1288.44i	0.0285445	−	0.0494404i
$880$	1381.14	+	2392.20i	0.0529071	+	0.0916377i
$881$	−41132.6			−1.57298			−0.786489	−	0.617605i	$-0.788103\pi$
$881$	−41132.6			−1.57298			−0.786489	+	0.617605i	$0.788103\pi$
$882$		0			0
$883$	19850.0			0.756520			0.378260	−	0.925699i	$-0.376523\pi$
$883$	19850.0			0.756520			0.378260	+	0.925699i	$0.376523\pi$
$884$	4055.79	+	7024.84i	0.154311	+	0.267275i
$885$	−1366.70	+	2367.20i	−0.0519110	+	0.0899126i
$886$	−14460.9	+	25047.0i	−0.548333	+	0.949741i
$887$	14514.7	+	25140.1i	0.549441	+	0.951660i	0.998313	+	0.0580639i	$0.0184927\pi$
$887$	14514.7	+	25140.1i	0.549441	+	0.951660i	−0.448872	+	0.893596i	$0.648174\pi$
$888$	24.4812			0.000925154
$889$		0			0
$890$	−12403.6			−0.467159
$891$	2317.40	+	4013.85i	0.0871333	+	0.150919i
$892$	2650.20	−	4590.28i	0.0994789	−	0.172303i
$893$	9756.90	−	16899.5i	0.365624	−	0.633279i
$894$	323.590	+	560.475i	0.0121057	+	0.0209677i
$895$	16888.6			0.630752
$896$		0			0
$897$	1797.96			0.0669254
$898$	−17007.6	−	29458.0i	−0.632016	−	1.09468i
$899$	26514.7	−	45924.8i	0.983666	−	1.70376i
$900$	1363.05	−	2360.86i	0.0504832	−	0.0874394i
$901$	−28306.1	−	49027.7i	−1.04663	−	1.81282i
$902$	4192.57			0.154764
$903$		0			0
$904$	−3179.15			−0.116966
$905$	−3588.94	−	6216.22i	−0.131824	−	0.228325i
$906$	−259.334	+	449.180i	−0.00950971	+	0.0164713i
$907$	10514.5	−	18211.7i	0.384928	−	0.666715i	−0.606831	−	0.794831i	$-0.707560\pi$
$907$	10514.5	−	18211.7i	0.384928	−	0.666715i	0.991759	+	0.128116i	$0.0408930\pi$
$908$	2904.57	+	5030.86i	0.106158	+	0.183871i
$909$	45776.0			1.67029
$910$		0			0
$911$	−19225.5			−0.699198			−0.349599	−	0.936899i	$-0.613682\pi$
$911$	−19225.5			−0.699198			−0.349599	+	0.936899i	$0.613682\pi$
$912$	1256.50	+	2176.33i	0.0456217	+	0.0790191i
$913$	4271.06	−	7397.70i	0.154821	−	0.268158i
$914$	20469.5	−	35454.2i	0.740777	−	1.28306i
$915$	303.890	+	526.354i	0.0109796	+	0.0190172i
$916$	−13204.6			−0.476300
$917$		0			0
$918$	−13942.5			−0.501276
$919$	−10658.4	−	18460.9i	−0.382577	−	0.662642i	0.608853	−	0.793283i	$-0.291630\pi$
$919$	−10658.4	−	18460.9i	−0.382577	−	0.662642i	−0.991430	+	0.130641i	$0.958297\pi$
$920$	3205.11	−	5551.42i	0.114858	−	0.198940i
$921$	−3388.34	+	5868.78i	−0.121226	+	0.209970i
$922$	−18732.9	−	32446.4i	−0.669128	−	1.15896i
$923$	2336.50			0.0833229
$924$		0			0
$925$	53.6366			0.00190655
$926$	17188.6	+	29771.6i	0.609993	+	1.05654i
$927$	−19111.6	+	33102.3i	−0.677140	+	1.17284i
$928$	23057.1	−	39936.0i	0.815609	−	1.41268i
$929$	9994.78	+	17311.5i	0.352979	+	0.611378i	0.986770	−	0.162126i	$-0.0518352\pi$
$929$	9994.78	+	17311.5i	0.352979	+	0.611378i	−0.633791	+	0.773505i	$0.718502\pi$
$930$	−2920.87			−0.102988
$931$		0			0
$932$	−12564.8			−0.441603
$933$	1088.61	+	1885.53i	0.0381989	+	0.0661624i
$934$	−8122.93	+	14069.3i	−0.284572	+	0.492893i
$935$	1524.91	−	2641.23i	0.0533369	−	0.0923821i
$936$	−3903.24	−	6760.62i	−0.136305	−	0.236087i
$937$	−55676.4			−1.94116			−0.970580	−	0.240779i	$-0.922597\pi$
$937$	−55676.4			−1.94116			−0.970580	+	0.240779i	$0.922597\pi$
$938$		0			0
$939$	−4133.10			−0.143641
$940$	5477.98	+	9488.14i	0.190077	+	0.329222i
$941$	−54.4211	+	94.2600i	−0.00188531	+	0.00326545i	−0.866967	−	0.498366i	$-0.833933\pi$
$941$	−54.4211	+	94.2600i	−0.00188531	+	0.00326545i	0.865081	+	0.501632i	$0.167267\pi$
$942$	1362.74	−	2360.34i	0.0471343	−	0.0816390i
$943$	−8317.04	−	14405.5i	−0.287211	−	0.497464i
$944$	−51423.6			−1.77298
$945$		0			0
$946$	410.150			0.0140963
$947$	3892.97	+	6742.83i	0.133585	+	0.231375i	0.925056	−	0.379831i	$-0.124018\pi$
$947$	3892.97	+	6742.83i	0.133585	+	0.231375i	−0.791471	+	0.611206i	$0.790685\pi$
$948$	−1940.31	+	3360.72i	−0.0664751	+	0.115138i
$949$	10918.9	−	18912.1i	0.373491	−	0.646905i
$950$	1610.19	+	2788.94i	0.0549912	+	0.0952475i
$951$	−6943.18			−0.236749
$952$		0			0
$953$	41445.5			1.40876			0.704381	−	0.709822i	$-0.251224\pi$
$953$	41445.5			1.40876			0.704381	+	0.709822i	$0.251224\pi$
$954$	−29360.7	−	50854.2i	−0.996423	−	1.72586i
$955$	−3970.35	+	6876.84i	−0.134531	+	0.233015i
$956$	10365.5	−	17953.5i	0.350673	−	0.607383i
$957$	−790.023	−	1368.36i	−0.0266853	−	0.0462203i
$958$	56792.5			1.91532
$959$		0			0
$960$	180.029			0.00605252
$961$	−4531.46	−	7848.72i	−0.152108	−	0.263459i
$962$	−82.7717	+	143.365i	−0.00277408	+	0.00480485i
$963$	−15525.4	+	26890.7i	−0.519521	+	0.899836i
$964$	−7794.33	−	13500.2i	−0.260413	−	0.451049i
$965$	4888.52			0.163075
$966$		0			0
$967$	39155.0			1.30211			0.651055	−	0.759030i	$-0.274327\pi$
$967$	39155.0			1.30211			0.651055	+	0.759030i	$0.274327\pi$
$968$	−8611.22	−	14915.1i	−0.285925	−	0.495236i
$969$	1387.30	−	2402.88i	0.0459923	−	0.0796610i
$970$	5547.01	−	9607.70i	0.183612	−	0.318025i
$971$	−21720.4	−	37620.8i	−0.717859	−	1.24337i	−0.961847	−	0.273589i	$-0.911789\pi$
$971$	−21720.4	−	37620.8i	−0.717859	−	1.24337i	0.243988	−	0.969778i	$-0.421544\pi$
$972$	−7442.74			−0.245603
$973$		0			0
$974$	−12252.0			−0.403061
$975$	235.265	+	407.491i	0.00772771	+	0.0133848i
$976$	−5717.08	+	9902.28i	−0.187499	+	0.324758i
$977$	−5648.89	+	9784.16i	−0.184978	+	0.320392i	−0.943569	−	0.331175i	$-0.892555\pi$
$977$	−5648.89	+	9784.16i	−0.184978	+	0.320392i	0.758591	+	0.651567i	$0.225888\pi$
$978$	3509.69	+	6078.97i	0.114752	+	0.198757i
$979$	−4916.15			−0.160491
$980$		0			0
$981$	−57925.9			−1.88525
$982$	4386.33	+	7597.34i	0.142539	+	0.246885i
$983$	5432.97	−	9410.18i	0.176282	−	0.305329i	−0.764322	−	0.644834i	$-0.776926\pi$
$983$	5432.97	−	9410.18i	0.176282	−	0.305329i	0.940604	+	0.339506i	$0.110260\pi$
$984$	993.457	−	1720.72i	0.0321852	−	0.0557464i
$985$	899.205	+	1557.47i	0.0290874	+	0.0503808i
$986$	−82805.5			−2.67451
$987$		0			0
$988$	−3394.80			−0.109315
$989$	−813.638	−	1409.26i	−0.0261600	−	0.0453104i
$990$	1581.72	−	2739.63i	0.0507783	−	0.0879505i
$991$	−6942.04	+	12024.0i	−0.222524	+	0.385423i	−0.955574	−	0.294752i	$-0.904763\pi$
$991$	−6942.04	+	12024.0i	−0.222524	+	0.385423i	0.733050	+	0.680175i	$0.238096\pi$
$992$	−16893.6	−	29260.5i	−0.540697	−	0.936515i
$993$	−2529.36			−0.0808328
$994$		0			0
$995$	14091.9			0.448987
$996$	2181.58	+	3778.60i	0.0694035	+	0.120210i
$997$	15832.8	−	27423.3i	0.502940	−	0.871117i	−0.497054	−	0.867719i	$-0.665585\pi$
$997$	15832.8	−	27423.3i	0.502940	−	0.871117i	0.999994	−	0.00339788i	$-0.00108158\pi$
$998$	15245.3	−	26405.7i	0.483549	−	0.837532i
$999$	−48.5929	−	84.1653i	−0.00153895	−	0.00266554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.n.116.1		6
7.2	even	3	inner	245.4.e.n.226.1		6
7.3	odd	6		35.4.a.c.1.3	✓	3
7.4	even	3		245.4.a.l.1.3		3
7.5	odd	6		245.4.e.m.226.1		6
7.6	odd	2		245.4.e.m.116.1		6
21.11	odd	6		2205.4.a.bm.1.1		3
21.17	even	6		315.4.a.p.1.1		3
28.3	even	6		560.4.a.u.1.2		3
35.3	even	12		175.4.b.e.99.2		6
35.4	even	6		1225.4.a.y.1.1		3
35.17	even	12		175.4.b.e.99.5		6
35.24	odd	6		175.4.a.f.1.1		3
56.3	even	6		2240.4.a.bv.1.2		3
56.45	odd	6		2240.4.a.bt.1.2		3
105.59	even	6		1575.4.a.ba.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.3	✓	3	7.3	odd	6
175.4.a.f.1.1		3	35.24	odd	6
175.4.b.e.99.2		6	35.3	even	12
175.4.b.e.99.5		6	35.17	even	12
245.4.a.l.1.3		3	7.4	even	3
245.4.e.m.116.1		6	7.6	odd	2
245.4.e.m.226.1		6	7.5	odd	6
245.4.e.n.116.1		6	1.1	even	1	trivial
245.4.e.n.226.1		6	7.2	even	3	inner
315.4.a.p.1.1		3	21.17	even	6
560.4.a.u.1.2		3	28.3	even	6
1225.4.a.y.1.1		3	35.4	even	6
1575.4.a.ba.1.3		3	105.59	even	6
2205.4.a.bm.1.1		3	21.11	odd	6
2240.4.a.bt.1.2		3	56.45	odd	6
2240.4.a.bv.1.2		3	56.3	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)

\(f(q)\)	\(=\)	\(q+(-1.74283 - 3.01866i) q^{2} +(0.425119 - 0.736328i) q^{3} +(-2.07488 + 3.59380i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.96363 q^{6} -13.4206 q^{8} +(13.1385 + 22.7566i) q^{9} +O(q^{10})\)	\(q+(-1.74283 - 3.01866i) q^{2} +(0.425119 - 0.736328i) q^{3} +(-2.07488 + 3.59380i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.96363 q^{6} -13.4206 q^{8} +(13.1385 + 22.7566i) q^{9} +(8.71413 - 15.0933i) q^{10} +(3.45382 - 5.98219i) q^{11} +(1.76414 + 3.05559i) q^{12} +22.1364 q^{13} +4.25119 q^{15} +(39.9888 + 69.2626i) q^{16} +(44.1515 - 76.4726i) q^{17} +(45.7964 - 79.3217i) q^{18} +(18.4780 + 32.0048i) q^{19} -20.7488 q^{20} -24.0776 q^{22} +(47.7641 + 82.7299i) q^{23} +(-5.70535 + 9.88195i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-38.5799 - 66.8223i) q^{26} +45.2982 q^{27} +269.029 q^{29} +(-7.40909 - 12.8329i) q^{30} +(98.5570 - 170.706i) q^{31} +(85.7046 - 148.445i) q^{32} +(-2.93657 - 5.08629i) q^{33} -307.793 q^{34} -109.044 q^{36} +(-1.07273 - 1.85803i) q^{37} +(64.4078 - 111.558i) q^{38} +(9.41061 - 16.2997i) q^{39} +(-33.5515 - 58.1128i) q^{40} -174.127 q^{41} -17.0345 q^{43} +(14.3325 + 24.8247i) q^{44} +(-65.6927 + 113.783i) q^{45} +(166.489 - 288.368i) q^{46} +(-264.014 - 457.286i) q^{47} +68.0000 q^{48} +87.1413 q^{50} +(-37.5393 - 65.0200i) q^{51} +(-45.9304 + 79.5538i) q^{52} +(320.557 - 555.221i) q^{53} +(-78.9469 - 136.740i) q^{54} +34.5382 q^{55} +31.4214 q^{57} +(-468.871 - 812.109i) q^{58} +(-321.487 + 556.832i) q^{59} +(-8.82072 + 15.2779i) q^{60} +(71.4836 + 123.813i) q^{61} -687.070 q^{62} +42.3480 q^{64} +(55.3410 + 95.8534i) q^{65} +(-10.2359 + 17.7290i) q^{66} +(-239.398 + 414.650i) q^{67} +(183.218 + 317.343i) q^{68} +81.2218 q^{69} +105.550 q^{71} +(-176.327 - 305.407i) q^{72} +(493.256 - 854.344i) q^{73} +(-3.73917 + 6.47643i) q^{74} +(10.6280 + 18.4082i) q^{75} -153.358 q^{76} -65.6042 q^{78} +(549.930 + 952.507i) q^{79} +(-199.944 + 346.313i) q^{80} +(-335.484 + 581.075i) q^{81} +(303.474 + 525.632i) q^{82} +1236.62 q^{83} +441.515 q^{85} +(29.6882 + 51.4214i) q^{86} +(114.370 - 198.094i) q^{87} +(-46.3523 + 80.2845i) q^{88} +(-355.849 - 616.348i) q^{89} +457.964 q^{90} -396.420 q^{92} +(-83.7969 - 145.141i) q^{93} +(-920.262 + 1593.94i) q^{94} +(-92.3899 + 160.024i) q^{95} +(-72.8693 - 126.213i) q^{96} +636.553 q^{97} +181.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9	\( 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20} + 368 q^{22} + 124 q^{23} + 420 q^{24} - 75 q^{25} - 446 q^{26} - 340 q^{27} + 664 q^{29} - 120 q^{30} + 320 q^{31} + 183 q^{32} - 106 q^{33} - 1164 q^{34} + 362 q^{36} + 54 q^{37} - 460 q^{38} + 982 q^{39} - 75 q^{40} - 724 q^{41} - 32 q^{43} + 264 q^{44} + 405 q^{45} + 336 q^{46} - 730 q^{47} + 408 q^{48} - 150 q^{50} + 1178 q^{51} + 1202 q^{52} - 110 q^{53} - 180 q^{54} + 740 q^{55} - 1912 q^{57} - 450 q^{58} - 180 q^{59} + 760 q^{60} + 1222 q^{61} - 928 q^{62} - 782 q^{64} - 220 q^{65} - 532 q^{66} - 204 q^{67} + 918 q^{68} + 1432 q^{69} - 272 q^{71} - 765 q^{72} + 310 q^{73} - 502 q^{74} + 50 q^{75} - 3592 q^{76} + 7576 q^{78} + 1034 q^{79} - 395 q^{80} - 2283 q^{81} - 6 q^{82} + 3320 q^{83} - 520 q^{85} - 764 q^{86} - 1574 q^{87} + 20 q^{88} + 242 q^{89} + 4110 q^{90} + 192 q^{92} - 1376 q^{93} - 1108 q^{94} - 840 q^{95} - 3156 q^{96} - 200 q^{97} - 6976 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * q^99

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