LMFDB - Embedded newform 165.4.c.a.34.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, 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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 97x^{12} + 3674x^{10} + 68702x^{8} + 656605x^{6} + 2988841x^{4} + 5502384x^{2} + 3385600 $ x^14 + 97x^12 + 3674x^10 + 68702x^8 + 656605x^6 + 2988841x^4 + 5502384x^2 + 3385600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.7
Root			$-1.16334i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.a.34.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.16334i q^{2} +3.00000i q^{3} +6.64664 q^{4} +(9.37349 - 6.09407i) q^{5} +3.49002 q^{6} -19.4748i q^{7} -17.0390i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-1.16334i q^{2} +3.00000i q^{3} +6.64664 q^{4} +(9.37349 - 6.09407i) q^{5} +3.49002 q^{6} -19.4748i q^{7} -17.0390i q^{8} -9.00000 q^{9} +(-7.08947 - 10.9046i) q^{10} -11.0000 q^{11} +19.9399i q^{12} -8.26359i q^{13} -22.6558 q^{14} +(18.2822 + 28.1205i) q^{15} +33.3510 q^{16} -5.66364i q^{17} +10.4701i q^{18} +24.4710 q^{19} +(62.3022 - 40.5051i) q^{20} +58.4243 q^{21} +12.7967i q^{22} +15.3593i q^{23} +51.1171 q^{24} +(50.7246 - 114.245i) q^{25} -9.61336 q^{26} -27.0000i q^{27} -129.442i q^{28} -158.322 q^{29} +(32.7137 - 21.2684i) q^{30} +302.349 q^{31} -175.111i q^{32} -33.0000i q^{33} -6.58873 q^{34} +(-118.681 - 182.547i) q^{35} -59.8198 q^{36} +266.602i q^{37} -28.4681i q^{38} +24.7908 q^{39} +(-103.837 - 159.715i) q^{40} +81.4234 q^{41} -67.9673i q^{42} +22.6601i q^{43} -73.1131 q^{44} +(-84.3614 + 54.8466i) q^{45} +17.8681 q^{46} +15.1324i q^{47} +100.053i q^{48} -36.2671 q^{49} +(-132.906 - 59.0100i) q^{50} +16.9909 q^{51} -54.9251i q^{52} +453.069i q^{53} -31.4102 q^{54} +(-103.108 + 67.0348i) q^{55} -331.831 q^{56} +73.4131i q^{57} +184.182i q^{58} -292.859 q^{59} +(121.515 + 186.907i) q^{60} +255.185 q^{61} -351.735i q^{62} +175.273i q^{63} +63.0946 q^{64} +(-50.3589 - 77.4586i) q^{65} -38.3902 q^{66} +314.716i q^{67} -37.6442i q^{68} -46.0780 q^{69} +(-212.364 + 138.066i) q^{70} -238.686 q^{71} +153.351i q^{72} +744.418i q^{73} +310.148 q^{74} +(342.736 + 152.174i) q^{75} +162.650 q^{76} +214.223i q^{77} -28.8401i q^{78} +177.549 q^{79} +(312.615 - 203.243i) q^{80} +81.0000 q^{81} -94.7231i q^{82} +624.817i q^{83} +388.326 q^{84} +(-34.5146 - 53.0880i) q^{85} +26.3614 q^{86} -474.967i q^{87} +187.429i q^{88} -1521.53 q^{89} +(63.8052 + 98.1410i) q^{90} -160.932 q^{91} +102.088i q^{92} +907.047i q^{93} +17.6041 q^{94} +(229.379 - 149.128i) q^{95} +525.332 q^{96} -342.953i q^{97} +42.1909i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.16334i		−	0.411303i	−0.978625	−	0.205651i	$-0.934069\pi$
$2$		−	1.16334i		−	0.411303i	0.978625	−	0.205651i	$-0.0659313\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	6.64664			0.830830
$5$	9.37349	−	6.09407i	0.838390	−	0.545070i
$5$	9.37349	−	6.09407i	0.838390	−	0.545070i
$6$	3.49002			0.237466
$7$		−	19.4748i		−	1.05154i	−0.850627	−	0.525770i	$-0.823777\pi$
$7$		−	19.4748i		−	1.05154i	0.850627	−	0.525770i	$-0.176223\pi$
$8$		−	17.0390i		−	0.753025i
$9$	−9.00000			−0.333333
$10$	−7.08947	−	10.9046i	−0.224189	−	0.344832i
$11$	−11.0000			−0.301511
$11$	−11.0000			−0.301511
$12$			19.9399i			0.479680i
$13$		−	8.26359i		−	0.176300i	−0.996107	−	0.0881502i	$-0.971904\pi$
$13$		−	8.26359i		−	0.176300i	0.996107	−	0.0881502i	$-0.0280956\pi$
$14$	−22.6558			−0.432501
$15$	18.2822	+	28.1205i	0.314696	+	0.484045i
$16$	33.3510			0.521109
$17$		−	5.66364i		−	0.0808020i	−0.999184	−	0.0404010i	$-0.987136\pi$
$17$		−	5.66364i		−	0.0808020i	0.999184	−	0.0404010i	$-0.0128635\pi$
$18$			10.4701i			0.137101i
$19$	24.4710			0.295476			0.147738	−	0.989027i	$-0.452801\pi$
$19$	24.4710			0.295476			0.147738	+	0.989027i	$0.452801\pi$
$20$	62.3022	−	40.5051i	0.696560	−	0.452861i
$21$	58.4243			0.607106
$22$			12.7967i			0.124012i
$23$			15.3593i			0.139245i	0.997573	+	0.0696226i	$0.0221795\pi$
$23$			15.3593i			0.139245i	−0.997573	+	0.0696226i	$0.977820\pi$
$24$	51.1171			0.434759
$25$	50.7246	−	114.245i	0.405797	−	0.913963i
$26$	−9.61336			−0.0725129
$27$		−	27.0000i		−	0.192450i
$28$		−	129.442i		−	0.873651i
$29$	−158.322			−1.01378			−0.506891	−	0.862010i	$-0.669205\pi$
$29$	−158.322			−1.01378			−0.506891	+	0.862010i	$0.669205\pi$
$30$	32.7137	−	21.2684i	0.199089	−	0.129435i
$31$	302.349			1.75173			0.875863	−	0.482560i	$-0.160293\pi$
$31$	302.349			1.75173			0.875863	+	0.482560i	$0.160293\pi$
$32$		−	175.111i		−	0.967359i
$33$		−	33.0000i		−	0.174078i
$34$	−6.58873			−0.0332341
$35$	−118.681	−	182.547i	−0.573163	−	0.881601i
$36$	−59.8198			−0.276943
$37$			266.602i			1.18457i	0.805729	+	0.592285i	$0.201774\pi$
$37$			266.602i			1.18457i	−0.805729	+	0.592285i	$0.798226\pi$
$38$		−	28.4681i		−	0.121530i
$39$	24.7908			0.101787
$40$	−103.837	−	159.715i	−0.410452	−	0.631329i
$41$	81.4234			0.310151			0.155076	−	0.987903i	$-0.450438\pi$
$41$	81.4234			0.310151			0.155076	+	0.987903i	$0.450438\pi$
$42$		−	67.9673i		−	0.249705i
$43$			22.6601i			0.0803637i	0.999192	+	0.0401818i	$0.0127937\pi$
$43$			22.6601i			0.0803637i	−0.999192	+	0.0401818i	$0.987206\pi$
$44$	−73.1131			−0.250505
$45$	−84.3614	+	54.8466i	−0.279463	+	0.181690i
$46$	17.8681			0.0572720
$47$			15.1324i			0.0469634i	0.999724	+	0.0234817i	$0.00747515\pi$
$47$			15.1324i			0.0469634i	−0.999724	+	0.0234817i	$0.992525\pi$
$48$			100.053i			0.300862i
$49$	−36.2671			−0.105735
$50$	−132.906	−	59.0100i	−0.375915	−	0.166905i
$51$	16.9909			0.0466510
$52$		−	54.9251i		−	0.146476i
$53$			453.069i			1.17422i	0.809506	+	0.587111i	$0.199735\pi$
$53$			453.069i			1.17422i	−0.809506	+	0.587111i	$0.800265\pi$
$54$	−31.4102			−0.0791552
$55$	−103.108	+	67.0348i	−0.252784	+	0.164345i
$56$	−331.831			−0.791836
$57$			73.4131i			0.170593i
$58$			184.182i			0.416971i
$59$	−292.859			−0.646221			−0.323110	−	0.946361i	$-0.604728\pi$
$59$	−292.859			−0.646221			−0.323110	+	0.946361i	$0.604728\pi$
$60$	121.515	+	186.907i	0.261459	+	0.402159i
$61$	255.185			0.535625			0.267813	−	0.963471i	$-0.413699\pi$
$61$	255.185			0.535625			0.267813	+	0.963471i	$0.413699\pi$
$62$		−	351.735i		−	0.720490i
$63$			175.273i			0.350513i
$64$	63.0946			0.123232
$65$	−50.3589	−	77.4586i	−0.0960961	−	0.147809i
$66$	−38.3902			−0.0715986
$67$			314.716i			0.573860i	0.957951	+	0.286930i	$0.0926348\pi$
$67$			314.716i			0.573860i	−0.957951	+	0.286930i	$0.907365\pi$
$68$		−	37.6442i		−	0.0671327i
$69$	−46.0780			−0.0803933
$70$	−212.364	+	138.066i	−0.362605	+	0.235743i
$71$	−238.686			−0.398970			−0.199485	−	0.979901i	$-0.563927\pi$
$71$	−238.686			−0.398970			−0.199485	+	0.979901i	$0.563927\pi$
$72$			153.351i			0.251008i
$73$			744.418i			1.19353i	0.802417	+	0.596764i	$0.203547\pi$
$73$			744.418i			1.19353i	−0.802417	+	0.596764i	$0.796453\pi$
$74$	310.148			0.487217
$75$	342.736	+	152.174i	0.527677	+	0.234287i
$76$	162.650			0.245490
$77$			214.223i			0.317051i
$78$		−	28.8401i		−	0.0418653i
$79$	177.549			0.252858			0.126429	−	0.991976i	$-0.459648\pi$
$79$	177.549			0.252858			0.126429	+	0.991976i	$0.459648\pi$
$80$	312.615	−	203.243i	0.436893	−	0.284041i
$81$	81.0000			0.111111
$82$		−	94.7231i		−	0.127566i
$83$			624.817i			0.826296i	0.910664	+	0.413148i	$0.135571\pi$
$83$			624.817i			0.826296i	−0.910664	+	0.413148i	$0.864429\pi$
$84$	388.326			0.504402
$85$	−34.5146	−	53.0880i	−0.0440427	−	0.0677436i
$86$	26.3614			0.0330538
$87$		−	474.967i		−	0.585308i
$88$			187.429i			0.227046i
$89$	−1521.53			−1.81216			−0.906078	−	0.423111i	$-0.860938\pi$
$89$	−1521.53			−1.81216			−0.906078	+	0.423111i	$0.860938\pi$
$90$	63.8052	+	98.1410i	0.0747296	+	0.114944i
$91$	−160.932			−0.185387
$92$			102.088i			0.115689i
$93$			907.047i			1.01136i
$94$	17.6041			0.0193162
$95$	229.379	−	149.128i	0.247724	−	0.161055i
$96$	525.332			0.558505
$97$		−	342.953i		−	0.358985i	−0.983759	−	0.179493i	$-0.942554\pi$
$97$		−	342.953i		−	0.358985i	0.983759	−	0.179493i	$-0.0574456\pi$
$98$			42.1909i			0.0434890i
$99$	99.0000			0.100504
$100$	337.149	−	759.348i	0.337149	−	0.759348i
$101$	−1429.06			−1.40789			−0.703944	−	0.710255i	$-0.748580\pi$
$101$	−1429.06			−1.40789			−0.703944	+	0.710255i	$0.748580\pi$
$102$		−	19.7662i		−	0.0191877i
$103$			1688.33i			1.61511i	0.589791	+	0.807556i	$0.299210\pi$
$103$			1688.33i			1.61511i	−0.589791	+	0.807556i	$0.700790\pi$
$104$	−140.803			−0.132759
$105$	547.640	−	356.042i	0.508992	−	0.330916i
$106$	527.073			0.482961
$107$		−	1947.81i		−	1.75983i	−0.475129	−	0.879916i	$-0.657599\pi$
$107$		−	1947.81i		−	1.75983i	0.475129	−	0.879916i	$-0.342401\pi$
$108$		−	179.459i		−	0.159893i
$109$	−2172.13			−1.90874			−0.954368	−	0.298633i	$-0.903469\pi$
$109$	−2172.13			−1.90874			−0.954368	+	0.298633i	$0.903469\pi$
$110$	77.9842	+	119.950i	0.0675955	+	0.103971i
$111$	−799.806			−0.683912
$112$		−	649.503i		−	0.547966i
$113$			731.978i			0.609369i	0.952453	+	0.304685i	$0.0985510\pi$
$113$			731.978i			0.609369i	−0.952453	+	0.304685i	$0.901449\pi$
$114$	85.4044			0.0701654
$115$	93.6008	+	143.971i	0.0758984	+	0.116742i
$116$	−1052.31			−0.842281
$117$			74.3723i			0.0587668i
$118$			340.695i			0.265792i
$119$	−110.298			−0.0849665
$120$	479.145	−	311.511i	0.364498	−	0.236974i
$121$	121.000			0.0909091
$122$		−	296.867i		−	0.220304i
$123$			244.270i			0.179066i
$124$	2009.61			1.45539
$125$	−220.752	−	1380.00i	−0.157957	−	0.987446i
$126$	203.902			0.144167
$127$		−	1072.80i		−	0.749569i	−0.927112	−	0.374785i	$-0.877717\pi$
$127$		−	1072.80i		−	0.749569i	0.927112	−	0.374785i	$-0.122283\pi$
$128$		−	1474.29i		−	1.01804i
$129$	−67.9804			−0.0463980
$130$	−90.1107	+	58.5845i	−0.0607941	+	0.0395246i
$131$	1287.73			0.858853			0.429426	−	0.903102i	$-0.358716\pi$
$131$	1287.73			0.858853			0.429426	+	0.903102i	$0.358716\pi$
$132$		−	219.339i		−	0.144629i
$133$		−	476.568i		−	0.310705i
$134$	366.121			0.236030
$135$	−164.540	−	253.084i	−0.104899	−	0.161348i
$136$	−96.5028			−0.0608459
$137$			1759.23i			1.09709i	0.836122	+	0.548543i	$0.184817\pi$
$137$			1759.23i			1.09709i	−0.836122	+	0.548543i	$0.815183\pi$
$138$			53.6043i			0.0330660i
$139$	2634.80			1.60777			0.803887	−	0.594782i	$-0.202762\pi$
$139$	2634.80			1.60777			0.803887	+	0.594782i	$0.202762\pi$
$140$	−788.828	−	1213.32i	−0.476201	−	0.732460i
$141$	−45.3971			−0.0271143
$142$			277.673i			0.164097i
$143$			90.8994i			0.0531566i
$144$	−300.159			−0.173703
$145$	−1484.03	+	964.826i	−0.849946	+	0.552583i
$146$	866.010			0.490901
$147$		−	108.801i		−	0.0610461i
$148$			1772.01i			0.984176i
$149$	1557.85			0.856538			0.428269	−	0.903651i	$-0.359124\pi$
$149$	1557.85			0.856538			0.428269	+	0.903651i	$0.359124\pi$
$150$	177.030	−	398.719i	0.0963629	−	0.217035i
$151$	−216.999			−0.116948			−0.0584740	−	0.998289i	$-0.518623\pi$
$151$	−216.999			−0.116948			−0.0584740	+	0.998289i	$0.518623\pi$
$152$		−	416.963i		−	0.222501i
$153$			50.9727i			0.0269340i
$154$	249.214			0.130404
$155$	2834.07	−	1842.54i	1.46863	−	0.954814i
$156$	164.775			0.0845678
$157$		−	3003.68i		−	1.52688i	−0.645879	−	0.763439i	$-0.723509\pi$
$157$		−	3003.68i		−	1.52688i	0.645879	−	0.763439i	$-0.276491\pi$
$158$		−	206.549i		−	0.104001i
$159$	−1359.21			−0.677938
$160$	−1067.14	−	1641.40i	−0.527278	−	0.811024i
$161$	299.120			0.146422
$162$		−	94.2305i		−	0.0457003i
$163$			631.007i			0.303217i	0.988441	+	0.151608i	$0.0484452\pi$
$163$			631.007i			0.303217i	−0.988441	+	0.151608i	$0.951555\pi$
$164$	541.192			0.257683
$165$	−201.104	−	309.325i	−0.0948845	−	0.145945i
$166$	726.875			0.339858
$167$			2233.32i			1.03485i	0.855730	+	0.517423i	$0.173109\pi$
$167$			2233.32i			1.03485i	−0.855730	+	0.517423i	$0.826891\pi$
$168$		−	995.493i		−	0.457167i
$169$	2128.71			0.968918
$170$	−61.7594	+	40.1522i	−0.0278631	+	0.0181149i
$171$	−220.239			−0.0984920
$172$			150.614i			0.0667686i
$173$		−	620.035i		−	0.272488i	−0.990675	−	0.136244i	$-0.956497\pi$
$173$		−	620.035i		−	0.272488i	0.990675	−	0.136244i	$-0.0435030\pi$
$174$	−552.547			−0.240739
$175$	−2224.90	−	987.851i	−0.961068	−	0.426712i
$176$	−366.861			−0.157120
$177$		−	878.578i		−	0.373096i
$178$			1770.06i			0.745344i
$179$	1695.52			0.707983			0.353991	−	0.935249i	$-0.384824\pi$
$179$	1695.52			0.707983			0.353991	+	0.935249i	$0.384824\pi$
$180$	−560.720	+	364.546i	−0.232187	+	0.150954i
$181$	−3003.38			−1.23337			−0.616683	−	0.787211i	$-0.711524\pi$
$181$	−3003.38			−1.23337			−0.616683	+	0.787211i	$0.711524\pi$
$182$			187.218i			0.0762501i
$183$			765.556i			0.309243i
$184$	261.708			0.104855
$185$	1624.69	+	2498.99i	0.645673	+	0.993132i
$186$	1055.20			0.415975
$187$			62.3000i			0.0243627i
$188$			100.579i			0.0390186i
$189$	−525.819			−0.202369
$190$	−173.487	−	266.846i	−0.0662424	−	0.101890i
$191$	2399.00			0.908826			0.454413	−	0.890791i	$-0.349849\pi$
$191$	2399.00			0.908826			0.454413	+	0.890791i	$0.349849\pi$
$192$			189.284i			0.0711478i
$193$		−	2445.98i		−	0.912257i	−0.889914	−	0.456128i	$-0.849236\pi$
$193$		−	2445.98i		−	0.912257i	0.889914	−	0.456128i	$-0.150764\pi$
$194$	−398.971			−0.147652
$195$	232.376	−	151.077i	0.0853374	−	0.0554811i
$196$	−241.054			−0.0878477
$197$			4223.55i			1.52749i	0.645519	+	0.763745i	$0.276641\pi$
$197$			4223.55i			1.52749i	−0.645519	+	0.763745i	$0.723359\pi$
$198$		−	115.171i		−	0.0413375i
$199$	3058.60			1.08954			0.544771	−	0.838585i	$-0.316617\pi$
$199$	3058.60			1.08954			0.544771	+	0.838585i	$0.316617\pi$
$200$	−1946.63	−	864.298i	−0.688237	−	0.305576i
$201$	−944.147			−0.331318
$202$			1662.48i			0.579068i
$203$			3083.29i			1.06603i
$204$	112.932			0.0387591
$205$	763.222	−	496.200i	0.260028	−	0.169054i
$206$	1964.11			0.664300
$207$		−	138.234i		−	0.0464151i
$208$		−	275.599i		−	0.0918717i
$209$	−269.181			−0.0890893
$210$	−414.198	−	637.091i	−0.136106	−	0.209350i
$211$	−4391.13			−1.43269			−0.716346	−	0.697746i	$-0.754187\pi$
$211$	−4391.13			−1.43269			−0.716346	+	0.697746i	$0.754187\pi$
$212$			3011.39i			0.975580i
$213$		−	716.058i		−	0.230345i
$214$	−2265.97			−0.723824
$215$	138.092	+	212.405i	0.0438038	+	0.0673762i
$216$	−460.053			−0.144920
$217$		−	5888.18i		−	1.84201i
$218$			2526.92i			0.785068i
$219$	−2233.25			−0.689083
$220$	−685.324	+	445.556i	−0.210021	+	0.136543i
$221$	−46.8019			−0.0142454
$222$			930.445i			0.281295i
$223$		−	1965.61i		−	0.590256i	−0.955458	−	0.295128i	$-0.904638\pi$
$223$		−	1965.61i		−	0.590256i	0.955458	−	0.295128i	$-0.0953623\pi$
$224$	−3410.24			−1.01722
$225$	−456.522	+	1028.21i	−0.135266	+	0.304654i
$226$	851.539			0.250635
$227$		−	3139.70i		−	0.918015i	−0.888432	−	0.459008i	$-0.848205\pi$
$227$		−	3139.70i		−	0.918015i	0.888432	−	0.459008i	$-0.151795\pi$
$228$			487.951i			0.141734i
$229$	−4755.60			−1.37231			−0.686155	−	0.727455i	$-0.740703\pi$
$229$	−4755.60			−1.37231			−0.686155	+	0.727455i	$0.740703\pi$
$230$	167.487	−	108.890i	0.0480163	−	0.0312172i
$231$	−642.668			−0.183049
$232$			2697.65i			0.763404i
$233$			6585.59i			1.85166i	0.377944	+	0.925829i	$0.376631\pi$
$233$			6585.59i			1.85166i	−0.377944	+	0.925829i	$0.623369\pi$
$234$	86.5202			0.0241710
$235$	92.2176	+	141.843i	0.0255983	+	0.0393737i
$236$	−1946.53			−0.536900
$237$			532.646i			0.145988i
$238$			128.314i			0.0349469i
$239$	486.082			0.131557			0.0657784	−	0.997834i	$-0.479047\pi$
$239$	486.082			0.131557			0.0657784	+	0.997834i	$0.479047\pi$
$240$	609.729	+	937.845i	0.163991	+	0.252240i
$241$	−446.428			−0.119323			−0.0596617	−	0.998219i	$-0.519002\pi$
$241$	−446.428			−0.119323			−0.0596617	+	0.998219i	$0.519002\pi$
$242$		−	140.764i		−	0.0373912i
$243$			243.000i			0.0641500i
$244$	1696.13			0.445014
$245$	−339.949	+	221.014i	−0.0886471	+	0.0576329i
$246$	284.169			0.0736503
$247$		−	202.219i		−	0.0520925i
$248$		−	5151.73i		−	1.31909i
$249$	−1874.45			−0.477062
$250$	−1605.41	+	256.810i	−0.406139	+	0.0649683i
$251$	3060.39			0.769602			0.384801	−	0.922999i	$-0.374270\pi$
$251$	3060.39			0.769602			0.384801	+	0.922999i	$0.374270\pi$
$252$			1164.98i			0.291217i
$253$		−	168.953i		−	0.0419840i
$254$	−1248.03			−0.308300
$255$	159.264	−	103.544i	0.0391118	−	0.0254281i
$256$	−1210.34			−0.295493
$257$			2561.92i			0.621821i	0.950439	+	0.310911i	$0.100634\pi$
$257$			2561.92i			0.621821i	−0.950439	+	0.310911i	$0.899366\pi$
$258$			79.0843i			0.0190836i
$259$	5192.01			1.24562
$260$	−334.717	−	514.840i	−0.0798395	−	0.122804i
$261$	1424.90			0.337928
$262$		−	1498.07i		−	0.353248i
$263$		−	503.435i		−	0.118035i	−0.998257	−	0.0590174i	$-0.981203\pi$
$263$		−	503.435i		−	0.118035i	0.998257	−	0.0590174i	$-0.0187967\pi$
$264$	−562.288			−0.131085
$265$	2761.03	+	4246.84i	0.640034	+	0.984457i
$266$	−554.411			−0.127794
$267$		−	4564.59i		−	1.04625i
$268$			2091.80i			0.476781i
$269$	−2395.14			−0.542878			−0.271439	−	0.962456i	$-0.587500\pi$
$269$	−2395.14			−0.542878			−0.271439	+	0.962456i	$0.587500\pi$
$270$	−294.423	+	191.416i	−0.0663630	+	0.0431452i
$271$	−3339.95			−0.748662			−0.374331	−	0.927295i	$-0.622128\pi$
$271$	−3339.95			−0.748662			−0.374331	+	0.927295i	$0.622128\pi$
$272$		−	188.888i		−	0.0421066i
$273$		−	482.795i		−	0.107033i
$274$	2046.58			0.451235
$275$	−557.971	+	1256.70i	−0.122352	+	0.275570i
$276$	−306.264			−0.0667932
$277$			6951.60i			1.50787i	0.656946	+	0.753937i	$0.271848\pi$
$277$			6951.60i			1.50787i	−0.656946	+	0.753937i	$0.728152\pi$
$278$		−	3065.16i		−	0.661281i
$279$	−2721.14			−0.583909
$280$	−3110.42	+	2022.20i	−0.663868	+	0.431606i
$281$	9203.01			1.95376			0.976878	−	0.213797i	$-0.0685833\pi$
$281$	9203.01			1.95376			0.976878	+	0.213797i	$0.0685833\pi$
$282$			52.8122i			0.0111522i
$283$		−	6159.41i		−	1.29378i	−0.762585	−	0.646888i	$-0.776070\pi$
$283$		−	6159.41i		−	1.29378i	0.762585	−	0.646888i	$-0.223930\pi$
$284$	−1586.46			−0.331476
$285$	447.385	+	688.137i	0.0929852	+	0.143024i
$286$	105.747			0.0218634
$287$		−	1585.70i		−	0.326136i
$288$			1576.00i			0.322453i
$289$	4880.92			0.993471
$290$	1122.42	+	1726.43i	0.227279	+	0.349585i
$291$	1028.86			0.207260
$292$			4947.88i			0.991618i
$293$		−	657.854i		−	0.131168i	−0.997847	−	0.0655840i	$-0.979109\pi$
$293$		−	657.854i		−	0.131168i	0.997847	−	0.0655840i	$-0.0208910\pi$
$294$	−126.573			−0.0251084
$295$	−2745.11	+	1784.70i	−0.541785	+	0.352236i
$296$	4542.63			0.892011
$297$			297.000i			0.0580259i
$298$		−	1812.31i		−	0.352296i
$299$	126.923			0.0245490
$300$	2278.04	+	1011.45i	0.438410	+	0.194653i
$301$	441.301			0.0845056
$302$			252.444i			0.0481010i
$303$		−	4287.18i		−	0.812845i
$304$	816.133			0.153975
$305$	2391.98	−	1555.12i	0.449063	−	0.291953i
$306$	59.2986			0.0110780
$307$			277.936i			0.0516698i	0.999666	+	0.0258349i	$0.00822442\pi$
$307$			277.936i			0.0516698i	−0.999666	+	0.0258349i	$0.991776\pi$
$308$			1423.86i			0.263416i
$309$	−5065.00			−0.932485
$310$	−2143.50	−	3296.98i	−0.392717	−	0.604052i
$311$	−3187.55			−0.581188			−0.290594	−	0.956846i	$-0.593853\pi$
$311$	−3187.55			−0.581188			−0.290594	+	0.956846i	$0.593853\pi$
$312$		−	422.410i		−	0.0766483i
$313$			4947.44i			0.893437i	0.894674	+	0.446719i	$0.147408\pi$
$313$			4947.44i			0.893437i	−0.894674	+	0.446719i	$0.852592\pi$
$314$	−3494.30			−0.628009
$315$	1068.13	+	1642.92i	0.191054	+	0.293867i
$316$	1180.10			0.210082
$317$		−	8717.68i		−	1.54459i	−0.635266	−	0.772293i	$-0.719110\pi$
$317$		−	8717.68i		−	1.54459i	0.635266	−	0.772293i	$-0.280890\pi$
$318$			1581.22i			0.278838i
$319$	1741.54			0.305667
$320$	591.416	−	384.503i	0.103316	−	0.0671698i
$321$	5843.43			1.01604
$322$		−	347.978i		−	0.0602237i
$323$		−	138.595i		−	0.0238750i
$324$	538.378			0.0923145
$325$	−944.077	−	419.167i	−0.161132	−	0.0715422i
$326$	734.076			0.124714
$327$		−	6516.39i		−	1.10201i
$328$		−	1387.37i		−	0.233552i
$329$	294.699			0.0493839
$330$	−359.850	+	233.953i	−0.0600276	+	0.0390263i
$331$	−4666.23			−0.774862			−0.387431	−	0.921899i	$-0.626638\pi$
$331$	−4666.23			−0.774862			−0.387431	+	0.921899i	$0.626638\pi$
$332$			4152.94i			0.686512i
$333$		−	2399.42i		−	0.394857i
$334$	2598.11			0.425635
$335$	1917.90	+	2949.99i	0.312794	+	0.481119i
$336$	1948.51			0.316369
$337$		−	6034.32i		−	0.975401i	−0.873011	−	0.487701i	$-0.837836\pi$
$337$		−	6034.32i		−	0.975401i	0.873011	−	0.487701i	$-0.162164\pi$
$338$		−	2476.42i		−	0.398519i
$339$	−2195.93			−0.351819
$340$	−229.406	−	352.857i	−0.0365920	−	0.0562834i
$341$	−3325.84			−0.528165
$342$			256.213i			0.0405100i
$343$		−	5973.56i		−	0.940355i
$344$	386.107			0.0605159
$345$	−431.912	+	280.802i	−0.0674010	+	0.0438200i
$346$	−721.311			−0.112075
$347$		−	6089.63i		−	0.942099i	−0.882107	−	0.471050i	$-0.843875\pi$
$347$		−	6089.63i		−	0.942099i	0.882107	−	0.471050i	$-0.156125\pi$
$348$		−	3156.93i		−	0.486291i
$349$	8857.56			1.35855			0.679276	−	0.733883i	$-0.262294\pi$
$349$	8857.56			1.35855			0.679276	+	0.733883i	$0.262294\pi$
$350$	−1149.21	+	2588.32i	−0.175508	+	0.395290i
$351$	−223.117			−0.0339290
$352$			1926.22i			0.291670i
$353$		−	5357.93i		−	0.807858i	−0.914790	−	0.403929i	$-0.867644\pi$
$353$		−	5357.93i		−	0.807858i	0.914790	−	0.403929i	$-0.132356\pi$
$354$	−1022.08			−0.153455
$355$	−2237.32	+	1454.57i	−0.334492	+	0.217466i
$356$	−10113.1			−1.50559
$357$		−	330.894i		−	0.0490554i
$358$		−	1972.46i		−	0.291195i
$359$	6795.15			0.998981			0.499491	−	0.866319i	$-0.333521\pi$
$359$	6795.15			0.998981			0.499491	+	0.866319i	$0.333521\pi$
$360$	934.533	+	1437.44i	0.136817	+	0.210443i
$361$	−6260.17			−0.912694
$362$			3493.95i			0.507287i
$363$			363.000i			0.0524864i
$364$	−1069.65			−0.154025
$365$	4536.53	+	6977.79i	0.650556	+	1.00064i
$366$	890.602			0.127193
$367$		−	2865.06i		−	0.407507i	−0.979022	−	0.203753i	$-0.934686\pi$
$367$		−	2865.06i		−	0.407507i	0.979022	−	0.203753i	$-0.0653141\pi$
$368$			512.248i			0.0725619i
$369$	−732.811			−0.103384
$370$	2907.17	−	1890.07i	0.408478	−	0.265567i
$371$	8823.42			1.23474
$372$			6028.82i			0.840268i
$373$		−	12277.9i		−	1.70436i	−0.523248	−	0.852180i	$-0.675280\pi$
$373$		−	12277.9i		−	1.70436i	0.523248	−	0.852180i	$-0.324720\pi$
$374$	72.4761			0.0100204
$375$	4139.99	−	662.257i	0.570102	−	0.0911968i
$376$	257.840			0.0353646
$377$			1308.31i			0.178730i
$378$			611.706i			0.0832348i
$379$	5909.04			0.800863			0.400431	−	0.916327i	$-0.368860\pi$
$379$	5909.04			0.800863			0.400431	+	0.916327i	$0.368860\pi$
$380$	1524.60	−	991.202i	0.205817	−	0.133809i
$381$	3218.39			0.432764
$382$		−	2790.85i		−	0.373802i
$383$		−	12435.8i		−	1.65912i	−0.558420	−	0.829558i	$-0.688592\pi$
$383$		−	12435.8i		−	1.65912i	0.558420	−	0.829558i	$-0.311408\pi$
$384$	4422.86			0.587768
$385$	1305.49	+	2008.01i	0.172815	+	0.265813i
$386$	−2845.51			−0.375214
$387$		−	203.941i		−	0.0267879i
$388$		−	2279.48i		−	0.298256i
$389$	−9940.85			−1.29568			−0.647842	−	0.761775i	$-0.724328\pi$
$389$	−9940.85			−1.29568			−0.647842	+	0.761775i	$0.724328\pi$
$390$	−175.753	−	270.332i	−0.0228195	−	0.0350995i
$391$	86.9897			0.0112513
$392$			617.955i			0.0796210i
$393$			3863.20i			0.495859i
$394$	4913.42			0.628260
$395$	1664.25	−	1081.99i	0.211994	−	0.137825i
$396$	658.017			0.0835016
$397$			9437.35i			1.19307i	0.802589	+	0.596533i	$0.203455\pi$
$397$			9437.35i			1.19307i	−0.802589	+	0.596533i	$0.796545\pi$
$398$		−	3558.19i		−	0.448131i
$399$	1429.70			0.179385
$400$	1691.72	−	3810.19i	0.211464	−	0.476274i
$401$	923.119			0.114958			0.0574792	−	0.998347i	$-0.481694\pi$
$401$	923.119			0.114958			0.0574792	+	0.998347i	$0.481694\pi$
$402$			1098.36i			0.136272i
$403$		−	2498.49i		−	0.308830i
$404$	−9498.45			−1.16972
$405$	759.253	−	493.620i	0.0931545	−	0.0605633i
$406$	3586.91			0.438462
$407$		−	2932.62i		−	0.357161i
$408$		−	289.508i		−	0.0351294i
$409$	−12437.8			−1.50369			−0.751847	−	0.659337i	$-0.770837\pi$
$409$	−12437.8			−1.50369			−0.751847	+	0.659337i	$0.770837\pi$
$410$	−577.249	−	887.886i	−0.0695324	−	0.106950i
$411$	−5277.68			−0.633403
$412$			11221.8i			1.34188i
$413$			5703.37i			0.679526i
$414$	−160.813			−0.0190907
$415$	3807.68	+	5856.72i	0.450389	+	0.692759i
$416$	−1447.04			−0.170546
$417$			7904.39i			0.928248i
$418$			313.149i			0.0366427i
$419$	5835.23			0.680357			0.340178	−	0.940361i	$-0.389513\pi$
$419$	5835.23			0.680357			0.340178	+	0.940361i	$0.389513\pi$
$420$	3639.97	−	2366.48i	0.422886	−	0.274935i
$421$	3139.66			0.363463			0.181731	−	0.983348i	$-0.441830\pi$
$421$	3139.66			0.363463			0.181731	+	0.983348i	$0.441830\pi$
$422$			5108.38i			0.589270i
$423$		−	136.191i		−	0.0156545i
$424$	7719.85			0.884220
$425$	−647.044	−	287.286i	−0.0738500	−	0.0327892i
$426$	−833.019			−0.0947416
$427$		−	4969.68i		−	0.563231i
$428$		−	12946.4i		−	1.46212i
$429$	−272.698			−0.0306900
$430$	247.099	−	160.648i	0.0277120	−	0.0180166i
$431$	−3956.73			−0.442202			−0.221101	−	0.975251i	$-0.570965\pi$
$431$	−3956.73			−0.442202			−0.221101	+	0.975251i	$0.570965\pi$
$432$		−	900.476i		−	0.100287i
$433$			16363.6i			1.81613i	0.418825	+	0.908067i	$0.362442\pi$
$433$			16363.6i			1.81613i	−0.418825	+	0.908067i	$0.637558\pi$
$434$	−6849.96			−0.757623
$435$	−2894.48	−	4452.09i	−0.319034	−	0.490716i
$436$	−14437.4			−1.58584
$437$			375.859i			0.0411436i
$438$			2598.03i			0.283422i
$439$	3948.04			0.429224			0.214612	−	0.976699i	$-0.431151\pi$
$439$	3948.04			0.429224			0.214612	+	0.976699i	$0.431151\pi$
$440$	1142.21	+	1756.87i	0.123756	+	0.190353i
$441$	326.404			0.0352450
$442$			54.4466i			0.00585918i
$443$		−	14702.0i		−	1.57677i	−0.615179	−	0.788387i	$-0.710916\pi$
$443$		−	14702.0i		−	1.57677i	0.615179	−	0.788387i	$-0.289084\pi$
$444$	−5316.02			−0.568214
$445$	−14262.0	+	9272.31i	−1.51929	+	0.987752i
$446$	−2286.67			−0.242774
$447$			4673.55i			0.494523i
$448$		−	1228.75i		−	0.129583i
$449$	−3715.99			−0.390576			−0.195288	−	0.980746i	$-0.562564\pi$
$449$	−3715.99			−0.390576			−0.195288	+	0.980746i	$0.562564\pi$
$450$	1196.16	+	531.090i	0.125305	+	0.0556352i
$451$	−895.657			−0.0935141
$452$			4865.19i			0.506282i
$453$		−	650.998i		−	0.0675200i
$454$	−3652.54			−0.377582
$455$	−1508.49	+	980.728i	−0.155427	+	0.101049i
$456$	1250.89			0.128461
$457$			10215.4i			1.04563i	0.852445	+	0.522817i	$0.175119\pi$
$457$			10215.4i			1.04563i	−0.852445	+	0.522817i	$0.824881\pi$
$458$			5532.38i			0.564435i
$459$	−152.918			−0.0155503
$460$	622.131	+	956.920i	0.0630587	+	0.0969927i
$461$	−10460.8			−1.05685			−0.528423	−	0.848981i	$-0.677217\pi$
$461$	−10460.8			−1.05685			−0.528423	+	0.848981i	$0.677217\pi$
$462$			747.641i			0.0752887i
$463$			4244.77i			0.426072i	0.977044	+	0.213036i	$0.0683352\pi$
$463$			4244.77i			0.426072i	−0.977044	+	0.213036i	$0.931665\pi$
$464$	−5280.20			−0.528291
$465$	5527.61	+	8502.20i	0.551262	+	0.847914i
$466$	7661.27			0.761591
$467$			964.193i			0.0955408i	0.998858	+	0.0477704i	$0.0152116\pi$
$467$			964.193i			0.0955408i	−0.998858	+	0.0477704i	$0.984788\pi$
$468$			494.326i			0.0488252i
$469$	6129.02			0.603437
$470$	165.012	−	107.280i	0.0161945	−	0.0105287i
$471$	9011.05			0.881544
$472$			4990.03i			0.486620i
$473$		−	249.262i		−	0.0242306i
$474$	619.648			0.0600451
$475$	1241.29	−	2795.70i	0.119903	−	0.270054i
$476$	−733.112			−0.0705927
$477$		−	4077.62i		−	0.391408i
$478$		−	565.479i		−	0.0541096i
$479$	−20956.9			−1.99905			−0.999526	−	0.0307833i	$-0.990200\pi$
$479$	−20956.9			−1.99905			−0.999526	+	0.0307833i	$0.990200\pi$
$480$	4924.19	−	3201.41i	0.468245	−	0.304424i
$481$	2203.09			0.208840
$482$			519.347i			0.0490780i
$483$			897.359i			0.0845367i
$484$	804.244			0.0755300
$485$	−2089.98	−	3214.67i	−0.195672	−	0.300970i
$486$	282.692			0.0263851
$487$		−	1816.63i		−	0.169033i	−0.996422	−	0.0845167i	$-0.973065\pi$
$487$		−	1816.63i		−	0.169033i	0.996422	−	0.0845167i	$-0.0269346\pi$
$488$		−	4348.11i		−	0.403339i
$489$	−1893.02			−0.175062
$490$	257.114	+	395.476i	0.0237046	+	0.0364608i
$491$	770.176			0.0707893			0.0353947	−	0.999373i	$-0.488731\pi$
$491$	770.176			0.0707893			0.0353947	+	0.999373i	$0.488731\pi$
$492$			1623.58i			0.148773i
$493$			896.679i			0.0819156i
$494$	−235.249			−0.0214258
$495$	927.976	−	603.313i	0.0842614	−	0.0547816i
$496$	10083.6			0.912840
$497$			4648.36i			0.419532i
$498$			2180.62i			0.196217i
$499$	7346.80			0.659094			0.329547	−	0.944139i	$-0.393104\pi$
$499$	7346.80			0.659094			0.329547	+	0.944139i	$0.393104\pi$
$500$	−1467.26	−	9172.35i	−0.131236	−	0.820400i
$501$	−6699.96			−0.597469
$502$		−	3560.27i		−	0.316539i
$503$			14710.8i			1.30402i	0.758210	+	0.652010i	$0.226074\pi$
$503$			14710.8i			1.30402i	−0.758210	+	0.652010i	$0.773926\pi$
$504$	2986.48			0.263945
$505$	−13395.3	+	8708.79i	−1.18036	+	0.767398i
$506$	−196.549			−0.0172681
$507$			6386.14i			0.559405i
$508$		−	7130.49i		−	0.622765i
$509$	−10845.9			−0.944474			−0.472237	−	0.881472i	$-0.656553\pi$
$509$	−10845.9			−0.944474			−0.472237	+	0.881472i	$0.656553\pi$
$510$	−120.457	−	185.278i	−0.0104586	−	0.0160868i
$511$	14497.4			1.25504
$512$		−	10386.2i		−	0.896507i
$513$		−	660.718i		−	0.0568644i
$514$	2980.38			0.255757
$515$	10288.8	+	15825.6i	0.880349	+	1.35409i
$516$	−451.841			−0.0385489
$517$		−	166.456i		−	0.0141600i
$518$		−	6040.07i		−	0.512327i
$519$	1860.10			0.157321
$520$	−1319.82	+	858.065i	−0.111304	+	0.0723628i
$521$	−4527.40			−0.380708			−0.190354	−	0.981716i	$-0.560964\pi$
$521$	−4527.40			−0.380708			−0.190354	+	0.981716i	$0.560964\pi$
$522$		−	1657.64i		−	0.138990i
$523$			9145.34i			0.764623i	0.924034	+	0.382311i	$0.124872\pi$
$523$			9145.34i			0.764623i	−0.924034	+	0.382311i	$0.875128\pi$
$524$	8559.09			0.713561
$525$	2963.55	−	6674.71i	0.246362	−	0.554873i
$526$	−585.666			−0.0485480
$527$		−	1712.40i		−	0.141543i
$528$		−	1100.58i		−	0.0907134i
$529$	11931.1			0.980611
$530$	4940.52	−	3212.02i	0.404910	−	0.263248i
$531$	2635.73			0.215407
$532$		−	3167.58i		−	0.258143i
$533$		−	672.849i		−	0.0546798i
$534$	−5310.17			−0.430325
$535$	−11870.1	−	18257.8i	−0.959232	−	1.47543i
$536$	5362.45			0.432131
$537$			5086.55i			0.408754i
$538$			2786.36i			0.223287i
$539$	398.938			0.0318803
$540$	−1093.64	−	1682.16i	−0.0871531	−	0.134053i
$541$	−1476.23			−0.117316			−0.0586579	−	0.998278i	$-0.518682\pi$
$541$	−1476.23			−0.117316			−0.0586579	+	0.998278i	$0.518682\pi$
$542$			3885.50i			0.307927i
$543$		−	9010.14i		−	0.712085i
$544$	−991.763			−0.0781645
$545$	−20360.4	+	13237.1i	−1.60027	+	1.04039i
$546$	−561.654			−0.0440230
$547$		−	4789.25i		−	0.374358i	−0.982326	−	0.187179i	$-0.940066\pi$
$547$		−	4789.25i		−	0.374358i	0.982326	−	0.187179i	$-0.0599344\pi$
$548$			11692.9i			0.911492i
$549$	−2296.67			−0.178542
$550$	1461.97	+	649.110i	0.113343	+	0.0503239i
$551$	−3874.31			−0.299548
$552$			785.124i			0.0605382i
$553$		−	3457.72i		−	0.265890i
$554$	8087.08			0.620193
$555$	−7496.97	+	4874.07i	−0.573385	+	0.372780i
$556$	17512.5			1.33579
$557$		−	3655.56i		−	0.278081i	−0.990287	−	0.139040i	$-0.955598\pi$
$557$		−	3655.56i		−	0.278081i	0.990287	−	0.139040i	$-0.0444018\pi$
$558$			3165.61i			0.240163i
$559$	187.254			0.0141682
$560$	−3958.11	−	6088.11i	−0.298680	−	0.459410i
$561$	−186.900			−0.0140658
$562$		−	10706.2i		−	0.803585i
$563$			22937.0i			1.71701i	0.512802	+	0.858507i	$0.328607\pi$
$563$			22937.0i			1.71701i	−0.512802	+	0.858507i	$0.671393\pi$
$564$	−301.738			−0.0225274
$565$	4460.72	+	6861.19i	0.332149	+	0.510889i
$566$	−7165.48			−0.532134
$567$		−	1577.46i		−	0.116838i
$568$			4066.98i			0.300434i
$569$	1430.04			0.105361			0.0526805	−	0.998611i	$-0.483224\pi$
$569$	1430.04			0.105361			0.0526805	+	0.998611i	$0.483224\pi$
$570$	800.537	−	520.460i	0.0588260	−	0.0382451i
$571$	−20474.9			−1.50061			−0.750305	−	0.661092i	$-0.770093\pi$
$571$	−20474.9			−1.50061			−0.750305	+	0.661092i	$0.770093\pi$
$572$			604.176i			0.0441641i
$573$			7197.01i			0.524711i
$574$	−1844.71			−0.134141
$575$	1754.73	+	779.097i	0.127265	+	0.0565053i
$576$	−567.851			−0.0410772
$577$		−	17471.1i		−	1.26054i	−0.776376	−	0.630270i	$-0.782944\pi$
$577$		−	17471.1i		−	1.26054i	0.776376	−	0.630270i	$-0.217056\pi$
$578$		−	5678.17i		−	0.408617i
$579$	7337.94			0.526692
$580$	−9863.83	+	6412.85i	−0.706160	+	0.459102i
$581$	12168.2			0.868883
$582$		−	1196.91i		−	0.0852467i
$583$		−	4983.76i		−	0.354042i
$584$	12684.1			0.898756
$585$	453.230	+	697.128i	0.0320320	+	0.0492695i
$586$	−765.307			−0.0539498
$587$		−	6685.80i		−	0.470107i	−0.971982	−	0.235053i	$-0.924474\pi$
$587$		−	6685.80i		−	0.470107i	0.971982	−	0.235053i	$-0.0755265\pi$
$588$		−	723.163i		−	0.0507189i
$589$	7398.80			0.517593
$590$	2076.22	+	3193.50i	0.144875	+	0.222838i
$591$	−12670.6			−0.881896
$592$			8891.43i			0.617290i
$593$		−	4310.86i		−	0.298526i	−0.988798	−	0.149263i	$-0.952310\pi$
$593$		−	4310.86i		−	0.298526i	0.988798	−	0.149263i	$-0.0476901\pi$
$594$	345.512			0.0238662
$595$	−1033.88	+	672.164i	−0.0712351	+	0.0463127i
$596$	10354.5			0.711638
$597$			9175.81i			0.629047i
$598$		−	147.655i		−	0.0100971i
$599$	25652.9			1.74983			0.874916	−	0.484274i	$-0.160916\pi$
$599$	25652.9			1.74983			0.874916	+	0.484274i	$0.160916\pi$
$600$	2592.89	−	5839.89i	0.176424	−	0.397354i
$601$	−14398.6			−0.977257			−0.488628	−	0.872492i	$-0.662503\pi$
$601$	−14398.6			−0.977257			−0.488628	+	0.872492i	$0.662503\pi$
$602$		−	513.383i		−	0.0347574i
$603$		−	2832.44i		−	0.191287i
$604$	−1442.32			−0.0971639
$605$	1134.19	−	737.382i	0.0762173	−	0.0495518i
$606$	−4987.44			−0.334325
$607$		−	23370.0i		−	1.56270i	−0.624094	−	0.781349i	$-0.714532\pi$
$607$		−	23370.0i		−	1.56270i	0.624094	−	0.781349i	$-0.285468\pi$
$608$		−	4285.14i		−	0.285831i
$609$	−9249.87			−0.615474
$610$	−1809.13	−	2782.68i	−0.120081	−	0.184701i
$611$	125.047			0.00827967
$612$			338.797i			0.0223776i
$613$			16274.5i			1.07230i	0.844123	+	0.536149i	$0.180122\pi$
$613$			16274.5i			1.07230i	−0.844123	+	0.536149i	$0.819878\pi$
$614$	323.334			0.0212519
$615$	1488.60	+	2289.66i	0.0976035	+	0.150127i
$616$	3650.14			0.238747
$617$		−	16851.1i		−	1.09951i	−0.835324	−	0.549757i	$-0.814720\pi$
$617$		−	16851.1i		−	1.09951i	0.835324	−	0.549757i	$-0.185280\pi$
$618$			5892.32i			0.383534i
$619$	−7896.58			−0.512747			−0.256373	−	0.966578i	$-0.582528\pi$
$619$	−7896.58			−0.512747			−0.256373	+	0.966578i	$0.582528\pi$
$620$	18837.0	−	12246.7i	1.22018	−	0.793288i
$621$	414.702			0.0267978
$622$			3708.21i			0.239044i
$623$			29631.5i			1.90555i
$624$	826.796			0.0530422
$625$	−10479.0	−	11590.1i	−0.670657	−	0.741767i
$626$	5755.55			0.367473
$627$		−	807.544i		−	0.0514358i
$628$		−	19964.4i		−	1.26858i
$629$	1509.94			0.0957156
$630$	1911.27	−	1242.59i	0.120868	−	0.0785811i
$631$	8006.26			0.505110			0.252555	−	0.967583i	$-0.418729\pi$
$631$	8006.26			0.505110			0.252555	+	0.967583i	$0.418729\pi$
$632$		−	3025.26i		−	0.190409i
$633$		−	13173.4i		−	0.827165i
$634$	−10141.6			−0.635292
$635$	−6537.69	−	10055.8i	−0.408568	−	0.628432i
$636$	−9034.16			−0.563251
$637$			299.696i			0.0186411i
$638$		−	2026.01i		−	0.125722i
$639$	2148.18			0.132990
$640$	−8984.40	−	13819.2i	−0.554905	−	0.853519i
$641$	17163.6			1.05760			0.528799	−	0.848747i	$-0.322643\pi$
$641$	17163.6			1.05760			0.528799	+	0.848747i	$0.322643\pi$
$642$		−	6797.90i		−	0.417900i
$643$		−	11115.5i		−	0.681731i	−0.940112	−	0.340865i	$-0.889280\pi$
$643$		−	11115.5i		−	0.681731i	0.940112	−	0.340865i	$-0.110720\pi$
$644$	1988.14			0.121652
$645$	−637.214	+	414.277i	−0.0388996	+	0.0252902i
$646$	−161.233			−0.00981987
$647$		−	17769.6i		−	1.07974i	−0.841747	−	0.539872i	$-0.818473\pi$
$647$		−	17769.6i		−	1.07974i	0.841747	−	0.539872i	$-0.181527\pi$
$648$		−	1380.16i		−	0.0836695i
$649$	3221.45			0.194843
$650$	−487.634	+	1098.28i	−0.0294255	+	0.0662741i
$651$	17664.6			1.06348
$652$			4194.08i			0.251922i
$653$		−	9940.57i		−	0.595719i	−0.954610	−	0.297859i	$-0.903727\pi$
$653$		−	9940.57i		−	0.595719i	0.954610	−	0.297859i	$-0.0962727\pi$
$654$	−7580.77			−0.453259
$655$	12070.5	−	7847.53i	0.720054	−	0.468135i
$656$	2715.55			0.161623
$657$		−	6699.76i		−	0.397842i
$658$		−	342.835i		−	0.0203117i
$659$	12298.0			0.726955			0.363478	−	0.931603i	$-0.381589\pi$
$659$	12298.0			0.726955			0.363478	+	0.931603i	$0.381589\pi$
$660$	−1336.67	−	2055.97i	−0.0788329	−	0.121256i
$661$	−27922.0			−1.64303			−0.821513	−	0.570190i	$-0.806869\pi$
$661$	−27922.0			−1.64303			−0.821513	+	0.570190i	$0.806869\pi$
$662$			5428.41i			0.318703i
$663$		−	140.406i		−	0.00822460i
$664$	10646.3			0.622222
$665$	−2904.24	−	4467.11i	−0.169356	−	0.260492i
$666$	−2791.34			−0.162406
$667$		−	2431.72i		−	0.141164i
$668$			14844.1i			0.859782i
$669$	5896.84			0.340785
$670$	3431.83	−	2231.17i	0.197886	−	0.128653i
$671$	−2807.04			−0.161497
$672$		−	10230.7i		−	0.587290i
$673$			1088.77i			0.0623613i	0.999514	+	0.0311807i	$0.00992672\pi$
$673$			1088.77i			0.0623613i	−0.999514	+	0.0311807i	$0.990073\pi$
$674$	−7019.96			−0.401185
$675$	−3084.63	−	1369.57i	−0.175892	−	0.0780957i
$676$	14148.8			0.805006
$677$		−	15975.8i		−	0.906940i	−0.891271	−	0.453470i	$-0.850186\pi$
$677$		−	15975.8i		−	0.906940i	0.891271	−	0.453470i	$-0.149814\pi$
$678$			2554.62i			0.144704i
$679$	−6678.93			−0.377487
$680$	−904.568	+	588.095i	−0.0510127	+	0.0331653i
$681$	9419.11			0.530016
$682$			3869.08i			0.217236i
$683$			19460.4i			1.09024i	0.838359	+	0.545118i	$0.183515\pi$
$683$			19460.4i			1.09024i	−0.838359	+	0.545118i	$0.816485\pi$
$684$	−1463.85			−0.0818301
$685$	10720.8	+	16490.1i	0.597989	+	0.919787i
$686$	−6949.27			−0.386770
$687$		−	14266.8i		−	0.792304i
$688$			755.737i			0.0418782i
$689$	3743.97			0.207016
$690$	326.669	+	502.460i	0.0180233	+	0.0277222i
$691$	5766.25			0.317451			0.158725	−	0.987323i	$-0.449262\pi$
$691$	5766.25			0.317451			0.158725	+	0.987323i	$0.449262\pi$
$692$		−	4121.15i		−	0.226391i
$693$		−	1928.00i		−	0.105684i
$694$	−7084.31			−0.387488
$695$	24697.2	−	16056.6i	1.34794	−	0.876349i
$696$	−8092.96			−0.440751
$697$		−	461.153i		−	0.0250608i
$698$		−	10304.4i		−	0.558776i
$699$	−19756.8			−1.06905
$700$	−14788.1	−	6565.89i	−0.798484	−	0.354525i
$701$	−1217.15			−0.0655791			−0.0327896	−	0.999462i	$-0.510439\pi$
$701$	−1217.15			−0.0655791			−0.0327896	+	0.999462i	$0.510439\pi$
$702$			259.561i			0.0139551i
$703$			6524.03i			0.350012i
$704$	−694.040			−0.0371557
$705$	−425.529	+	276.653i	−0.0227324	+	0.0147792i
$706$	−6233.09			−0.332274
$707$			27830.6i			1.48045i
$708$		−	5839.59i		−	0.309979i
$709$	32859.5			1.74057			0.870286	−	0.492547i	$-0.163934\pi$
$709$	32859.5			1.74057			0.870286	+	0.492547i	$0.163934\pi$
$710$	1692.16	+	2602.77i	0.0894445	+	0.137578i
$711$	−1597.94			−0.0842860
$712$			25925.4i			1.36460i
$713$			4643.88i			0.243920i
$714$	−384.942			−0.0201766
$715$	553.947	+	852.045i	0.0289741	+	0.0445660i
$716$	11269.5			0.588213
$717$			1458.25i			0.0759543i
$718$		−	7905.07i		−	0.410884i
$719$	3283.68			0.170321			0.0851604	−	0.996367i	$-0.472860\pi$
$719$	3283.68			0.170321			0.0851604	+	0.996367i	$0.472860\pi$
$720$	−2813.53	+	1829.19i	−0.145631	+	0.0946803i
$721$	32879.9			1.69835
$722$			7282.70i			0.375393i
$723$		−	1339.28i		−	0.0688914i
$724$	−19962.4			−1.02472
$725$	−8030.84	+	18087.6i	−0.411390	+	0.926560i
$726$	422.292			0.0215878
$727$			28198.3i			1.43854i	0.694731	+	0.719269i	$0.255523\pi$
$727$			28198.3i			1.43854i	−0.694731	+	0.719269i	$0.744477\pi$
$728$			2742.11i			0.139601i
$729$	−729.000			−0.0370370
$730$	8117.54	−	5277.53i	0.411567	−	0.267575i
$731$	128.339			0.00649355
$732$			5088.38i			0.256929i
$733$			26259.2i			1.32320i	0.749857	+	0.661600i	$0.230122\pi$
$733$			26259.2i			1.32320i	−0.749857	+	0.661600i	$0.769878\pi$
$734$	−3333.04			−0.167609
$735$	−663.042	−	1019.85i	−0.0332744	−	0.0511804i
$736$	2689.58			0.134700
$737$		−	3461.87i		−	0.173025i
$738$			852.508i			0.0425220i
$739$	−37945.3			−1.88882			−0.944412	−	0.328764i	$-0.893368\pi$
$739$	−37945.3			−1.88882			−0.944412	+	0.328764i	$0.893368\pi$
$740$	10798.7	+	16609.9i	0.536445	+	0.825124i
$741$	606.656			0.0300756
$742$		−	10264.6i		−	0.507853i
$743$			37735.2i			1.86322i	0.363465	+	0.931608i	$0.381594\pi$
$743$			37735.2i			1.86322i	−0.363465	+	0.931608i	$0.618406\pi$
$744$	15455.2			0.761579
$745$	14602.5	−	9493.66i	0.718113	−	0.466873i
$746$	−14283.4			−0.701008
$747$		−	5623.35i		−	0.275432i
$748$			414.086i			0.0202413i
$749$	−37933.2			−1.85053
$750$	−770.430	−	4816.22i	−0.0375095	−	0.234485i
$751$	−23846.1			−1.15866			−0.579332	−	0.815092i	$-0.696687\pi$
$751$	−23846.1			−1.15866			−0.579332	+	0.815092i	$0.696687\pi$
$752$			504.678i			0.0244730i
$753$			9181.17i			0.444330i
$754$	1522.01			0.0735123
$755$	−2034.04	+	1322.41i	−0.0980481	+	0.0637449i
$756$	−3494.93			−0.168134
$757$		−	1757.41i		−	0.0843779i	−0.999110	−	0.0421890i	$-0.986567\pi$
$757$		−	1757.41i		−	0.0843779i	0.999110	−	0.0421890i	$-0.0134331\pi$
$758$		−	6874.22i		−	0.329397i
$759$	506.858			0.0242395
$760$	−2541.00	−	3908.39i	−0.121279	−	0.186543i
$761$	−3661.27			−0.174403			−0.0872017	−	0.996191i	$-0.527792\pi$
$761$	−3661.27			−0.174403			−0.0872017	+	0.996191i	$0.527792\pi$
$762$		−	3744.08i		−	0.177997i
$763$			42301.7i			2.00711i
$764$	15945.3			0.755080
$765$	310.631	+	477.792i	0.0146809	+	0.0225812i
$766$	−14467.1			−0.682399
$767$			2420.07i			0.113929i
$768$		−	3631.01i		−	0.170603i
$769$	−16269.5			−0.762929			−0.381464	−	0.924384i	$-0.624580\pi$
$769$	−16269.5			−0.762929			−0.381464	+	0.924384i	$0.624580\pi$
$770$	2336.00	−	1518.72i	0.109329	−	0.0710793i
$771$	−7685.75			−0.359009
$772$		−	16257.6i		−	0.757930i
$773$		−	9135.30i		−	0.425063i	−0.977154	−	0.212532i	$-0.931829\pi$
$773$		−	9135.30i		−	0.425063i	0.977154	−	0.212532i	$-0.0681709\pi$
$774$	−237.253			−0.0110179
$775$	15336.6	−	34542.0i	0.710846	−	1.60101i
$776$	−5843.58			−0.270325
$777$			15576.0i			0.719160i
$778$			11564.6i			0.532918i
$779$	1992.52			0.0916422
$780$	1544.52	−	1004.15i	0.0709008	−	0.0460954i
$781$	2625.55			0.120294
$782$		−	101.199i		−	0.00462769i
$783$			4274.70i			0.195103i
$784$	−1209.54			−0.0550994
$785$	−18304.6	−	28155.0i	−0.832256	−	1.28012i
$786$	4494.21			0.203948
$787$			26715.3i			1.21004i	0.796212	+	0.605018i	$0.206834\pi$
$787$			26715.3i			1.21004i	−0.796212	+	0.605018i	$0.793166\pi$
$788$			28072.4i			1.26908i
$789$	1510.31			0.0681474
$790$	−1258.73	−	1936.09i	−0.0566880	−	0.0871936i
$791$	14255.1			0.640775
$792$		−	1686.86i		−	0.0756819i
$793$		−	2108.75i		−	0.0944310i
$794$	10978.8			0.490711
$795$	−12740.5	+	8283.10i	−0.568377	+	0.369524i
$796$	20329.4			0.905224
$797$		−	5895.59i		−	0.262023i	−0.991381	−	0.131012i	$-0.958178\pi$
$797$		−	5895.59i		−	0.262023i	0.991381	−	0.131012i	$-0.0418225\pi$
$798$		−	1663.23i		−	0.0737817i
$799$	85.7041			0.00379474
$800$	−20005.6	−	8882.43i	−0.884130	−	0.392551i
$801$	13693.8			0.604052
$802$		−	1073.90i		−	0.0472827i
$803$		−	8188.59i		−	0.359862i
$804$	−6275.41			−0.275269
$805$	2803.79	−	1822.86i	0.122759	−	0.0798102i
$806$	−2906.59			−0.127023
$807$		−	7185.42i		−	0.313431i
$808$			24349.8i			1.06018i
$809$	19061.3			0.828379			0.414189	−	0.910191i	$-0.364065\pi$
$809$	19061.3			0.828379			0.414189	+	0.910191i	$0.364065\pi$
$810$	−574.247	−	883.269i	−0.0249099	−	0.0383147i
$811$	−39232.1			−1.69867			−0.849337	−	0.527850i	$-0.822998\pi$
$811$	−39232.1			−1.69867			−0.849337	+	0.527850i	$0.822998\pi$
$812$			20493.5i			0.885692i
$813$		−	10019.8i		−	0.432240i
$814$	−3411.63			−0.146901
$815$	3845.40	+	5914.74i	0.165274	+	0.254214i
$816$	566.663			0.0243103
$817$			554.517i			0.0237455i
$818$			14469.4i			0.618474i
$819$	1448.38			0.0617956
$820$	5072.86	−	3298.06i	0.216039	−	0.140455i
$821$	9139.16			0.388500			0.194250	−	0.980952i	$-0.437773\pi$
$821$	9139.16			0.388500			0.194250	+	0.980952i	$0.437773\pi$
$822$			6139.73i			0.260520i
$823$		−	37583.6i		−	1.59184i	−0.605405	−	0.795918i	$-0.706989\pi$
$823$		−	37583.6i		−	1.59184i	0.605405	−	0.795918i	$-0.293011\pi$
$824$	28767.6			1.21622
$825$	−3770.10	−	1673.91i	−0.159101	−	0.0706402i
$826$	6634.95			0.279491
$827$		−	33269.2i		−	1.39889i	−0.714686	−	0.699445i	$-0.753430\pi$
$827$		−	33269.2i		−	1.39889i	0.714686	−	0.699445i	$-0.246570\pi$
$828$		−	918.791i		−	0.0385631i
$829$	2894.26			0.121257			0.0606284	−	0.998160i	$-0.480690\pi$
$829$	2894.26			0.121257			0.0606284	+	0.998160i	$0.480690\pi$
$830$	6813.35	−	4429.62i	0.284934	−	0.185246i
$831$	−20854.8			−0.870572
$832$		−	521.387i		−	0.0217258i
$833$			205.403i			0.00854359i
$834$	9195.49			0.381791
$835$	13610.0	+	20934.0i	0.564064	+	0.867606i
$836$	−1789.15			−0.0740181
$837$		−	8163.43i		−	0.337120i
$838$		−	6788.35i		−	0.279833i
$839$	−11124.6			−0.457765			−0.228882	−	0.973454i	$-0.573507\pi$
$839$	−11124.6			−0.457765			−0.228882	+	0.973454i	$0.573507\pi$
$840$	−6066.61	−	9331.25i	−0.249188	−	0.383284i
$841$	676.918			0.0277551
$842$		−	3652.50i		−	0.149493i
$843$			27609.0i			1.12800i
$844$	−29186.3			−1.19032
$845$	19953.5	−	12972.5i	0.812332	−	0.528128i
$846$	−158.437			−0.00643873
$847$		−	2356.45i		−	0.0955945i
$848$			15110.3i			0.611898i
$849$	18478.2			0.746962
$850$	−334.211	+	752.732i	−0.0134863	+	0.0303747i
$851$	−4094.83			−0.164946
$852$		−	4759.38i		−	0.191378i
$853$			38057.5i			1.52763i	0.645437	+	0.763813i	$0.276675\pi$
$853$			38057.5i			1.52763i	−0.645437	+	0.763813i	$0.723325\pi$
$854$	−5781.42			−0.231658
$855$	−2064.41	+	1342.15i	−0.0825747	+	0.0536850i
$856$	−33188.8			−1.32520
$857$			29926.6i			1.19285i	0.802668	+	0.596426i	$0.203413\pi$
$857$			29926.6i			1.19285i	−0.802668	+	0.596426i	$0.796587\pi$
$858$			317.241i			0.0126229i
$859$	7416.41			0.294580			0.147290	−	0.989093i	$-0.452945\pi$
$859$	7416.41			0.294580			0.147290	+	0.989093i	$0.452945\pi$
$860$	917.851	+	1411.78i	0.0363936	+	0.0559781i
$861$	4757.11			0.188295
$862$			4603.02i			0.181879i
$863$		−	27998.3i		−	1.10437i	−0.833721	−	0.552185i	$-0.813794\pi$
$863$		−	27998.3i		−	1.10437i	0.833721	−	0.552185i	$-0.186206\pi$
$864$	−4727.99			−0.186168
$865$	−3778.53	−	5811.89i	−0.148525	−	0.228451i
$866$	19036.5			0.746981
$867$			14642.8i			0.573581i
$868$		−	39136.6i		−	1.53040i
$869$	−1953.04			−0.0762396
$870$	−5179.30	+	3367.26i	−0.201833	+	0.131219i
$871$	2600.68			0.101172
$872$			37010.9i			1.43733i
$873$			3086.58i			0.119662i
$874$	437.251			0.0169225
$875$	−26875.2	+	4299.10i	−1.03834	+	0.166098i
$876$	−14843.6			−0.572511
$877$		−	14417.3i		−	0.555118i	−0.960709	−	0.277559i	$-0.910475\pi$
$877$		−	14417.3i		−	0.555118i	0.960709	−	0.277559i	$-0.0895254\pi$
$878$		−	4592.91i		−	0.176541i
$879$	1973.56			0.0757299
$880$	−3438.76	+	2235.67i	−0.131728	+	0.0856415i
$881$	−23776.9			−0.909266			−0.454633	−	0.890679i	$-0.650229\pi$
$881$	−23776.9			−0.909266			−0.454633	+	0.890679i	$0.650229\pi$
$882$		−	379.718i		−	0.0144963i
$883$		−	17079.3i		−	0.650922i	−0.945556	−	0.325461i	$-0.894481\pi$
$883$		−	17079.3i		−	0.650922i	0.945556	−	0.325461i	$-0.105519\pi$
$884$	−311.076			−0.0118355
$885$	−5354.11	−	8235.34i	−0.203363	−	0.312800i
$886$	−17103.4			−0.648532
$887$		−	25030.3i		−	0.947504i	−0.880658	−	0.473752i	$-0.842899\pi$
$887$		−	25030.3i		−	0.947504i	0.880658	−	0.473752i	$-0.157101\pi$
$888$			13627.9i			0.515003i
$889$	−20892.5			−0.788201
$890$	10786.8	+	16591.6i	0.406265	+	0.624890i
$891$	−891.000			−0.0335013
$892$		−	13064.7i		−	0.490403i
$893$			370.304i			0.0138766i
$894$	5436.93			0.203398
$895$	15892.9	−	10332.6i	0.593566	−	0.385900i
$896$	−28711.4			−1.07051
$897$			380.769i			0.0141734i
$898$			4322.96i			0.160645i
$899$	−47868.6			−1.77587
$900$	−3034.34	+	6834.13i	−0.112383	+	0.253116i
$901$	2566.02			0.0948795
$902$			1041.95i			0.0384626i
$903$			1323.90i			0.0487893i
$904$	12472.2			0.458870
$905$	−28152.1	+	18302.8i	−1.03404	+	0.672271i
$906$	−757.331			−0.0277711
$907$			11688.5i			0.427907i	0.976844	+	0.213953i	$0.0686340\pi$
$907$			11688.5i			0.427907i	−0.976844	+	0.213953i	$0.931366\pi$
$908$		−	20868.5i		−	0.762715i
$909$	12861.5			0.469296
$910$	1140.92	+	1754.89i	0.0415617	+	0.0639274i
$911$	40671.2			1.47914			0.739570	−	0.673080i	$-0.235029\pi$
$911$	40671.2			1.47914			0.739570	+	0.673080i	$0.235029\pi$
$912$			2448.40i			0.0888976i
$913$		−	6872.99i		−	0.249138i
$914$	11884.0			0.430072
$915$	4665.35	+	7175.93i	0.168559	+	0.259267i
$916$	−31608.8			−1.14016
$917$		−	25078.3i		−	0.903117i
$918$			177.896i			0.00639590i
$919$	1094.61			0.0392905			0.0196452	−	0.999807i	$-0.493746\pi$
$919$	1094.61			0.0392905			0.0196452	+	0.999807i	$0.493746\pi$
$920$	2453.12	−	1594.87i	0.0879096	−	0.0571534i
$921$	−833.807			−0.0298316
$922$			12169.4i			0.434684i
$923$			1972.40i			0.0703385i
$924$	−4271.58			−0.152083
$925$	30458.0	+	13523.3i	1.08265	+	0.480695i
$926$	4938.11			0.175245
$927$		−	15195.0i		−	0.538371i
$928$			27723.9i			0.980691i
$929$	−4607.17			−0.162709			−0.0813544	−	0.996685i	$-0.525925\pi$
$929$	−4607.17			−0.162709			−0.0813544	+	0.996685i	$0.525925\pi$
$930$	9890.95	−	6430.49i	0.348749	−	0.226735i
$931$	−887.493			−0.0312421
$932$			43772.0i			1.53841i
$933$		−	9562.66i		−	0.335549i
$934$	1121.68			0.0392962
$935$	379.661	+	583.968i	0.0132794	+	0.0204255i
$936$	1267.23			0.0442529
$937$		−	40537.0i		−	1.41332i	−0.707551	−	0.706662i	$-0.750200\pi$
$937$		−	40537.0i		−	1.41332i	0.707551	−	0.706662i	$-0.249800\pi$
$938$		−	7130.13i		−	0.248195i
$939$	−14842.3			−0.515826
$940$	612.937	+	942.779i	0.0212679	+	0.0327128i
$941$	−23795.5			−0.824349			−0.412174	−	0.911105i	$-0.635231\pi$
$941$	−23795.5			−0.824349			−0.412174	+	0.911105i	$0.635231\pi$
$942$		−	10482.9i		−	0.362581i
$943$			1250.61i			0.0431871i
$944$	−9767.14			−0.336751
$945$	−4928.76	+	3204.38i	−0.169664	+	0.110305i
$946$	−289.976			−0.00996610
$947$			16391.8i			0.562473i	0.959639	+	0.281236i	$0.0907445\pi$
$947$			16391.8i			0.562473i	−0.959639	+	0.281236i	$0.909256\pi$
$948$			3540.31i			0.121291i
$949$	6151.56			0.210419
$950$	−3252.35	−	1444.04i	−0.111074	−	0.0493165i
$951$	26153.1			0.891767
$952$			1879.37i			0.0639819i
$953$		−	23390.8i		−	0.795072i	−0.917587	−	0.397536i	$-0.869865\pi$
$953$		−	23390.8i		−	0.795072i	0.917587	−	0.397536i	$-0.130135\pi$
$954$	−4743.66			−0.160987
$955$	22487.0	−	14619.7i	0.761951	−	0.495374i
$956$	3230.82			0.109301
$957$			5224.63i			0.176477i
$958$			24380.0i			0.822215i
$959$	34260.5			1.15363
$960$	1153.51	+	1774.25i	0.0387805	+	0.0596496i
$961$	61624.0			2.06854
$962$		−	2562.94i		−	0.0858965i
$963$			17530.3i			0.586611i
$964$	−2967.24			−0.0991374
$965$	−14906.0	−	22927.4i	−0.497244	−	0.764827i
$966$	1043.93			0.0347702
$967$		−	45545.1i		−	1.51462i	−0.653058	−	0.757308i	$-0.726514\pi$
$967$		−	45545.1i		−	1.51462i	0.653058	−	0.757308i	$-0.273486\pi$
$968$		−	2061.72i		−	0.0684568i
$969$	415.785			0.0137843
$970$	−3739.75	+	2431.35i	−0.123790	+	0.0804805i
$971$	30755.0			1.01645			0.508225	−	0.861224i	$-0.330302\pi$
$971$	30755.0			1.01645			0.508225	+	0.861224i	$0.330302\pi$
$972$			1615.13i			0.0532978i
$973$		−	51312.1i		−	1.69064i
$974$	−2113.35			−0.0695239
$975$	1257.50	−	2832.23i	0.0413049	−	0.0930297i
$976$	8510.68			0.279119
$977$			11653.3i			0.381597i	0.981629	+	0.190799i	$0.0611078\pi$
$977$			11653.3i			0.381597i	−0.981629	+	0.190799i	$0.938892\pi$
$978$			2202.23i			0.0720036i
$979$	16736.8			0.546386
$980$	−2259.52	+	1469.00i	−0.0736507	+	0.0478832i
$981$	19549.2			0.636245
$982$		−	895.976i		−	0.0291158i
$983$			11502.8i			0.373227i	0.982433	+	0.186614i	$0.0597512\pi$
$983$			11502.8i			0.373227i	−0.982433	+	0.186614i	$0.940249\pi$
$984$	4162.12			0.134841
$985$	25738.6	+	39589.4i	0.832589	+	1.28063i
$986$	1043.14			0.0336921
$987$			884.098i			0.0285118i
$988$		−	1344.07i		−	0.0432801i
$989$	−348.045			−0.0111903
$990$	−701.858	−	1079.55i	−0.0225318	−	0.0346569i
$991$	46171.2			1.48000			0.739998	−	0.672609i	$-0.234826\pi$
$991$	46171.2			1.48000			0.739998	+	0.672609i	$0.234826\pi$
$992$		−	52944.6i		−	1.69455i
$993$		−	13998.7i		−	0.447367i
$994$	5407.62			0.172555
$995$	28669.8	−	18639.3i	0.913461	−	0.593876i
$996$	−12458.8			−0.396358
$997$		−	25674.8i		−	0.815577i	−0.913076	−	0.407789i	$-0.866300\pi$
$997$		−	25674.8i		−	0.815577i	0.913076	−	0.407789i	$-0.133700\pi$
$998$		−	8546.83i		−	0.271087i
$999$	7198.25			0.227971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.a.34.7	✓	14
3.2	odd	2		495.4.c.c.199.8		14
5.2	odd	4		825.4.a.bc.1.4		7
5.3	odd	4		825.4.a.bb.1.4		7
5.4	even	2	inner	165.4.c.a.34.8	yes	14
15.2	even	4		2475.4.a.bq.1.4		7
15.8	even	4		2475.4.a.br.1.4		7
15.14	odd	2		495.4.c.c.199.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.7	✓	14	1.1	even	1	trivial
165.4.c.a.34.8	yes	14	5.4	even	2	inner
495.4.c.c.199.7		14	15.14	odd	2
495.4.c.c.199.8		14	3.2	odd	2
825.4.a.bb.1.4		7	5.3	odd	4
825.4.a.bc.1.4		7	5.2	odd	4
2475.4.a.bq.1.4		7	15.2	even	4
2475.4.a.br.1.4		7	15.8	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.16334i q^{2} +3.00000i q^{3} +6.64664 q^{4} +(9.37349 - 6.09407i) q^{5} +3.49002 q^{6} -19.4748i q^{7} -17.0390i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-1.16334i q^{2} +3.00000i q^{3} +6.64664 q^{4} +(9.37349 - 6.09407i) q^{5} +3.49002 q^{6} -19.4748i q^{7} -17.0390i q^{8} -9.00000 q^{9} +(-7.08947 - 10.9046i) q^{10} -11.0000 q^{11} +19.9399i q^{12} -8.26359i q^{13} -22.6558 q^{14} +(18.2822 + 28.1205i) q^{15} +33.3510 q^{16} -5.66364i q^{17} +10.4701i q^{18} +24.4710 q^{19} +(62.3022 - 40.5051i) q^{20} +58.4243 q^{21} +12.7967i q^{22} +15.3593i q^{23} +51.1171 q^{24} +(50.7246 - 114.245i) q^{25} -9.61336 q^{26} -27.0000i q^{27} -129.442i q^{28} -158.322 q^{29} +(32.7137 - 21.2684i) q^{30} +302.349 q^{31} -175.111i q^{32} -33.0000i q^{33} -6.58873 q^{34} +(-118.681 - 182.547i) q^{35} -59.8198 q^{36} +266.602i q^{37} -28.4681i q^{38} +24.7908 q^{39} +(-103.837 - 159.715i) q^{40} +81.4234 q^{41} -67.9673i q^{42} +22.6601i q^{43} -73.1131 q^{44} +(-84.3614 + 54.8466i) q^{45} +17.8681 q^{46} +15.1324i q^{47} +100.053i q^{48} -36.2671 q^{49} +(-132.906 - 59.0100i) q^{50} +16.9909 q^{51} -54.9251i q^{52} +453.069i q^{53} -31.4102 q^{54} +(-103.108 + 67.0348i) q^{55} -331.831 q^{56} +73.4131i q^{57} +184.182i q^{58} -292.859 q^{59} +(121.515 + 186.907i) q^{60} +255.185 q^{61} -351.735i q^{62} +175.273i q^{63} +63.0946 q^{64} +(-50.3589 - 77.4586i) q^{65} -38.3902 q^{66} +314.716i q^{67} -37.6442i q^{68} -46.0780 q^{69} +(-212.364 + 138.066i) q^{70} -238.686 q^{71} +153.351i q^{72} +744.418i q^{73} +310.148 q^{74} +(342.736 + 152.174i) q^{75} +162.650 q^{76} +214.223i q^{77} -28.8401i q^{78} +177.549 q^{79} +(312.615 - 203.243i) q^{80} +81.0000 q^{81} -94.7231i q^{82} +624.817i q^{83} +388.326 q^{84} +(-34.5146 - 53.0880i) q^{85} +26.3614 q^{86} -474.967i q^{87} +187.429i q^{88} -1521.53 q^{89} +(63.8052 + 98.1410i) q^{90} -160.932 q^{91} +102.088i q^{92} +907.047i q^{93} +17.6041 q^{94} +(229.379 - 149.128i) q^{95} +525.332 q^{96} -342.953i q^{97} +42.1909i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Introduction

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