LMFDB - Embedded newform 67.2.e.c.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (of order $11$, degree $10$, 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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.2
Root			$1.07319 + 2.34996i$ of defining polynomial
Character	$\chi$	$=$	67.9
Dual form			67.2.e.c.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.239446 - 0.153882i) q^{2} +(2.93826 + 0.862752i) q^{3} +(-0.797176 - 1.74557i) q^{4} +(-1.85253 + 2.13793i) q^{5} +(-0.570792 - 0.658729i) q^{6} +(-3.42222 - 2.19933i) q^{7} +(-0.158746 + 1.10411i) q^{8} +(5.36529 + 3.44806i) q^{9} +O(q^{10})$	\(q+(-0.239446 - 0.153882i) q^{2} +(2.93826 + 0.862752i) q^{3} +(-0.797176 - 1.74557i) q^{4} +(-1.85253 + 2.13793i) q^{5} +(-0.570792 - 0.658729i) q^{6} +(-3.42222 - 2.19933i) q^{7} +(-0.158746 + 1.10411i) q^{8} +(5.36529 + 3.44806i) q^{9} +(0.772569 - 0.226847i) q^{10} +(0.970471 - 1.11998i) q^{11} +(-0.836317 - 5.81671i) q^{12} +(-0.00143353 - 0.00997040i) q^{13} +(0.480999 + 1.05324i) q^{14} +(-7.28771 + 4.68353i) q^{15} +(-2.30542 + 2.66060i) q^{16} +(0.840698 - 1.84087i) q^{17} +(-0.754099 - 1.65125i) q^{18} +(-2.42907 + 1.56107i) q^{19} +(5.20870 + 1.52941i) q^{20} +(-8.15792 - 9.41474i) q^{21} +(-0.404721 + 0.118837i) q^{22} +(3.01862 + 0.886347i) q^{23} +(-1.41901 + 3.10719i) q^{24} +(-0.427315 - 2.97204i) q^{25} +(-0.00119102 + 0.00260796i) q^{26} +(6.77364 + 7.81720i) q^{27} +(-1.11097 + 7.72699i) q^{28} -0.275544 q^{29} +2.46572 q^{30} +(0.549710 - 3.82332i) q^{31} +(3.10199 - 0.910828i) q^{32} +(3.81776 - 2.45353i) q^{33} +(-0.484579 + 0.311420i) q^{34} +(11.0418 - 3.24216i) q^{35} +(1.74176 - 12.1142i) q^{36} +7.59724 q^{37} +0.821851 q^{38} +(0.00438990 - 0.0305324i) q^{39} +(-2.06642 - 2.38477i) q^{40} +(-4.52056 + 9.89865i) q^{41} +(0.504616 + 3.50968i) q^{42} +(2.67682 - 5.86142i) q^{43} +(-2.72864 - 0.801202i) q^{44} +(-17.3110 + 5.08298i) q^{45} +(-0.586403 - 0.676745i) q^{46} +(-4.68730 - 1.37632i) q^{47} +(-9.06938 + 5.82853i) q^{48} +(3.96666 + 8.68578i) q^{49} +(-0.355026 + 0.777398i) q^{50} +(4.05841 - 4.68365i) q^{51} +(-0.0162613 + 0.0104505i) q^{52} +(1.59861 + 3.50047i) q^{53} +(-0.418990 - 2.91414i) q^{54} +(0.596622 + 4.14960i) q^{55} +(2.97156 - 3.42936i) q^{56} +(-8.48405 + 2.49114i) q^{57} +(0.0659780 + 0.0424015i) q^{58} +(0.222104 - 1.54477i) q^{59} +(13.9850 + 8.98763i) q^{60} +(-7.88361 - 9.09818i) q^{61} +(-0.719967 + 0.830886i) q^{62} +(-10.7778 - 23.6001i) q^{63} +(5.87283 + 1.72442i) q^{64} +(0.0239717 + 0.0154057i) q^{65} -1.29170 q^{66} +(-0.437339 - 8.17366i) q^{67} -3.88356 q^{68} +(8.10480 + 5.20864i) q^{69} +(-3.14282 - 0.922814i) q^{70} +(6.68270 + 14.6331i) q^{71} +(-4.65874 + 5.37648i) q^{72} +(-1.71032 - 1.97381i) q^{73} +(-1.81913 - 1.16908i) q^{74} +(1.30857 - 9.10129i) q^{75} +(4.66135 + 2.99567i) q^{76} +(-5.78438 + 1.69845i) q^{77} +(-0.00574955 + 0.00663533i) q^{78} +(-0.402553 - 2.79982i) q^{79} +(-1.41732 - 9.85767i) q^{80} +(5.21023 + 11.4088i) q^{81} +(2.60566 - 1.67455i) q^{82} +(5.56611 - 6.42364i) q^{83} +(-9.93080 + 21.7454i) q^{84} +(2.37824 + 5.20762i) q^{85} +(-1.54292 + 0.991577i) q^{86} +(-0.809622 - 0.237726i) q^{87} +(1.08252 + 1.24930i) q^{88} +(-12.8991 + 3.78752i) q^{89} +(4.92724 + 1.44677i) q^{90} +(-0.0170224 + 0.0372738i) q^{91} +(-0.859189 - 5.97579i) q^{92} +(4.91376 - 10.7596i) q^{93} +(0.910563 + 1.05085i) q^{94} +(1.16246 - 8.08510i) q^{95} +9.90029 q^{96} -10.8656 q^{97} +(0.386788 - 2.69017i) q^{98} +(9.06862 - 2.66279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.239446	−	0.153882i	−0.169314	−	0.108811i	0.453240	−	0.891389i	$-0.350268\pi$
$2$	−0.239446	−	0.153882i	−0.169314	−	0.108811i	−0.622553	+	0.782577i	$0.713905\pi$
$3$	2.93826	+	0.862752i	1.69641	+	0.498110i	0.979903	−	0.199474i	$-0.0639232\pi$
$3$	2.93826	+	0.862752i	1.69641	+	0.498110i	0.716503	+	0.697584i	$0.245741\pi$
$4$	−0.797176	−	1.74557i	−0.398588	−	0.872786i
$5$	−1.85253	+	2.13793i	−0.828475	+	0.956111i	−0.999575	−	0.0291423i	$-0.990722\pi$
$5$	−1.85253	+	2.13793i	−0.828475	+	0.956111i	0.171100	+	0.985254i	$0.445268\pi$
$6$	−0.570792	−	0.658729i	−0.233025	−	0.268925i
$7$	−3.42222	−	2.19933i	−1.29348	−	0.831269i	−0.300993	−	0.953626i	$-0.597318\pi$
$7$	−3.42222	−	2.19933i	−1.29348	−	0.831269i	−0.992486	+	0.122358i	$0.960954\pi$
$8$	−0.158746	+	1.10411i	−0.0561254	+	0.390360i
$9$	5.36529	+	3.44806i	1.78843	+	1.14935i
$10$	0.772569	−	0.226847i	0.244308	−	0.0717353i
$11$	0.970471	−	1.11998i	0.292608	−	0.337687i	−0.590343	−	0.807152i	$-0.701008\pi$
$11$	0.970471	−	1.11998i	0.292608	−	0.337687i	0.882951	+	0.469465i	$0.155553\pi$
$12$	−0.836317	−	5.81671i	−0.241424	−	1.67914i
$13$	−0.00143353	−	0.00997040i	−0.000397589	−	0.00276529i	0.989622	−	0.143697i	$-0.0458992\pi$
$13$	−0.00143353	−	0.00997040i	−0.000397589	−	0.00276529i	−0.990019	+	0.140932i	$0.954990\pi$
$14$	0.480999	+	1.05324i	0.128552	+	0.281490i
$15$	−7.28771	+	4.68353i	−1.88168	+	1.20928i
$16$	−2.30542	+	2.66060i	−0.576356	+	0.665150i
$17$	0.840698	−	1.84087i	0.203899	−	0.446477i	−0.779864	−	0.625949i	$-0.784712\pi$
$17$	0.840698	−	1.84087i	0.203899	−	0.446477i	0.983763	+	0.179472i	$0.0574390\pi$
$18$	−0.754099	−	1.65125i	−0.177743	−	0.389202i
$19$	−2.42907	+	1.56107i	−0.557267	+	0.358133i	−0.788758	−	0.614703i	$-0.789276\pi$
$19$	−2.42907	+	1.56107i	−0.557267	+	0.358133i	0.231492	+	0.972837i	$0.425639\pi$
$20$	5.20870	+	1.52941i	1.16470	+	0.341987i
$21$	−8.15792	−	9.41474i	−1.78020	−	2.05446i
$22$	−0.404721	+	0.118837i	−0.0862867	+	0.0253361i
$23$	3.01862	+	0.886347i	0.629426	+	0.184816i	0.580860	−	0.814004i	$-0.302717\pi$
$23$	3.01862	+	0.886347i	0.629426	+	0.184816i	0.0485664	+	0.998820i	$0.484535\pi$
$24$	−1.41901	+	3.10719i	−0.289654	+	0.634253i
$25$	−0.427315	−	2.97204i	−0.0854629	−	0.594408i
$26$	−0.00119102	+	0.00260796i	−0.000233578	+	0.000511464i
$27$	6.77364	+	7.81720i	1.30359	+	1.50442i
$28$	−1.11097	+	7.72699i	−0.209954	+	1.46026i
$29$	−0.275544			−0.0511673			−0.0255837	−	0.999673i	$-0.508144\pi$
$29$	−0.275544			−0.0511673			−0.0255837	+	0.999673i	$0.508144\pi$
$30$	2.46572			0.450178
$31$	0.549710	−	3.82332i	0.0987308	−	0.686688i	−0.879000	−	0.476823i	$-0.841788\pi$
$31$	0.549710	−	3.82332i	0.0987308	−	0.686688i	0.977730	−	0.209865i	$-0.0673025\pi$
$32$	3.10199	−	0.910828i	0.548360	−	0.161013i
$33$	3.81776	−	2.45353i	0.664587	−	0.427104i
$34$	−0.484579	+	0.311420i	−0.0831047	+	0.0534081i
$35$	11.0418	−	3.24216i	1.86640	−	0.548025i
$36$	1.74176	−	12.1142i	0.290293	−	2.01903i
$37$	7.59724			1.24898			0.624490	−	0.781033i	$-0.285307\pi$
$37$	7.59724			1.24898			0.624490	+	0.781033i	$0.285307\pi$
$38$	0.821851			0.133322
$39$	0.00438990	−	0.0305324i	0.000702947	−	0.00488910i
$40$	−2.06642	−	2.38477i	−0.326730	−	0.377066i
$41$	−4.52056	+	9.89865i	−0.705993	+	1.54591i	0.126558	+	0.991959i	$0.459607\pi$
$41$	−4.52056	+	9.89865i	−0.705993	+	1.54591i	−0.832550	+	0.553949i	$0.813120\pi$
$42$	0.504616	+	3.50968i	0.0778639	+	0.541555i
$43$	2.67682	−	5.86142i	0.408212	−	0.893859i	−0.588160	−	0.808745i	$-0.700147\pi$
$43$	2.67682	−	5.86142i	0.408212	−	0.893859i	0.996371	−	0.0851139i	$-0.0271254\pi$
$44$	−2.72864	−	0.801202i	−0.411359	−	0.120786i
$45$	−17.3110	+	5.08298i	−2.58058	+	0.757726i
$46$	−0.586403	−	0.676745i	−0.0864603	−	0.0997806i
$47$	−4.68730	−	1.37632i	−0.683713	−	0.200756i	−0.0786124	−	0.996905i	$-0.525049\pi$
$47$	−4.68730	−	1.37632i	−0.683713	−	0.200756i	−0.605101	+	0.796149i	$0.706867\pi$
$48$	−9.06938	+	5.82853i	−1.30905	+	0.841277i
$49$	3.96666	+	8.68578i	0.566666	+	1.24083i
$50$	−0.355026	+	0.777398i	−0.0502082	+	0.109941i
$51$	4.05841	−	4.68365i	0.568291	−	0.655842i
$52$	−0.0162613	+	0.0104505i	−0.00225503	+	0.00144922i
$53$	1.59861	+	3.50047i	0.219586	+	0.480827i	0.987080	−	0.160230i	$-0.0512236\pi$
$53$	1.59861	+	3.50047i	0.219586	+	0.480827i	−0.767493	+	0.641057i	$0.778496\pi$
$54$	−0.418990	−	2.91414i	−0.0570173	−	0.396564i
$55$	0.596622	+	4.14960i	0.0804485	+	0.559531i
$56$	2.97156	−	3.42936i	0.397091	−	0.458268i
$57$	−8.48405	+	2.49114i	−1.12374	+	0.329960i
$58$	0.0659780	+	0.0424015i	0.00866333	+	0.00556758i
$59$	0.222104	−	1.54477i	0.0289155	−	0.201112i	−0.970243	−	0.242134i	$-0.922153\pi$
$59$	0.222104	−	1.54477i	0.0289155	−	0.201112i	0.999158	+	0.0410227i	$0.0130616\pi$
$60$	13.9850	+	8.98763i	1.80546	+	1.16030i
$61$	−7.88361	−	9.09818i	−1.00939	−	1.16490i	−0.986265	−	0.165170i	$-0.947183\pi$
$61$	−7.88361	−	9.09818i	−1.00939	−	1.16490i	−0.0231283	−	0.999733i	$-0.507363\pi$
$62$	−0.719967	+	0.830886i	−0.0914359	+	0.105523i
$63$	−10.7778	−	23.6001i	−1.35787	−	2.97333i
$64$	5.87283	+	1.72442i	0.734104	+	0.215552i
$65$	0.0239717	+	0.0154057i	0.00297332	+	0.00191084i
$66$	−1.29170			−0.158998
$67$	−0.437339	−	8.17366i	−0.0534294	−	0.998572i
$67$	−0.437339	−	8.17366i	−0.0534294	−	0.998572i
$68$	−3.88356			−0.470950
$69$	8.10480	+	5.20864i	0.975704	+	0.627047i
$70$	−3.14282	−	0.922814i	−0.375638	−	0.110297i
$71$	6.68270	+	14.6331i	0.793091	+	1.73663i	0.667585	+	0.744534i	$0.267328\pi$
$71$	6.68270	+	14.6331i	0.793091	+	1.73663i	0.125506	+	0.992093i	$0.459945\pi$
$72$	−4.65874	+	5.37648i	−0.549038	+	0.633624i
$73$	−1.71032	−	1.97381i	−0.200177	−	0.231017i	0.646782	−	0.762675i	$-0.276115\pi$
$73$	−1.71032	−	1.97381i	−0.200177	−	0.231017i	−0.846959	+	0.531658i	$0.821569\pi$
$74$	−1.81913	−	1.16908i	−0.211469	−	0.135903i
$75$	1.30857	−	9.10129i	0.151100	−	1.05093i
$76$	4.66135	+	2.99567i	0.534693	+	0.343627i
$77$	−5.78438	+	1.69845i	−0.659191	+	0.193556i
$78$	−0.00574955	+	0.00663533i	−0.000651008	+	0.000751304i
$79$	−0.402553	−	2.79982i	−0.0452907	−	0.315004i	−0.999855	−	0.0170004i	$-0.994588\pi$
$79$	−0.402553	−	2.79982i	−0.0452907	−	0.315004i	0.954565	−	0.298004i	$-0.0963207\pi$
$80$	−1.41732	−	9.85767i	−0.158461	−	1.10212i
$81$	5.21023	+	11.4088i	0.578914	+	1.26765i
$82$	2.60566	−	1.67455i	0.287747	−	0.184924i
$83$	5.56611	−	6.42364i	0.610960	−	0.705086i	−0.363004	−	0.931788i	$-0.618249\pi$
$83$	5.56611	−	6.42364i	0.610960	−	0.705086i	0.973964	+	0.226702i	$0.0727943\pi$
$84$	−9.93080	+	21.7454i	−1.08354	+	2.37262i
$85$	2.37824	+	5.20762i	0.257956	+	0.564845i
$86$	−1.54292	+	0.991577i	−0.166378	+	0.106924i
$87$	−0.809622	−	0.237726i	−0.0868006	−	0.0254870i
$88$	1.08252	+	1.24930i	0.115397	+	0.133175i
$89$	−12.8991	+	3.78752i	−1.36730	+	0.401476i	−0.881331	−	0.472500i	$-0.843352\pi$
$89$	−12.8991	+	3.78752i	−1.36730	+	0.401476i	−0.485970	+	0.873975i	$0.661534\pi$
$90$	4.92724	+	1.44677i	0.519376	+	0.152503i
$91$	−0.0170224	+	0.0372738i	−0.00178443	+	0.00390735i
$92$	−0.859189	−	5.97579i	−0.0895767	−	0.623019i
$93$	4.91376	−	10.7596i	0.509534	−	1.11572i
$94$	0.910563	+	1.05085i	0.0939174	+	0.108386i
$95$	1.16246	−	8.08510i	0.119266	−	0.829513i
$96$	9.90029			1.01044
$97$	−10.8656			−1.10324			−0.551619	−	0.834096i	$-0.685990\pi$
$97$	−10.8656			−1.10324			−0.551619	+	0.834096i	$0.685990\pi$
$98$	0.386788	−	2.69017i	0.0390715	−	0.271748i
$99$	9.06862	−	2.66279i	0.911431	−	0.267620i
$100$	−4.84726	+	3.11514i	−0.484726	+	0.311514i
$101$	−9.90709	+	6.36690i	−0.985793	+	0.633530i	−0.931020	−	0.364968i	$-0.881080\pi$
$101$	−9.90709	+	6.36690i	−0.985793	+	0.633530i	−0.0547727	+	0.998499i	$0.517443\pi$
$102$	−1.69250	+	0.496963i	−0.167582	+	0.0492066i
$103$	−0.641720	+	4.46326i	−0.0632306	+	0.439778i	0.933473	+	0.358648i	$0.116762\pi$
$103$	−0.641720	+	4.46326i	−0.0632306	+	0.439778i	−0.996703	+	0.0811305i	$0.974147\pi$
$104$	0.0112359			0.00110178
$105$	35.2408			3.43915
$106$	0.155880	−	1.08417i	0.0151404	−	0.105304i
$107$	−4.81435	−	5.55605i	−0.465421	−	0.537124i	0.473712	−	0.880680i	$-0.342914\pi$
$107$	−4.81435	−	5.55605i	−0.465421	−	0.537124i	−0.939132	+	0.343556i	$0.888368\pi$
$108$	8.24570	−	18.0556i	0.793443	−	1.73740i
$109$	0.530272	+	3.68813i	0.0507909	+	0.353258i	0.999330	+	0.0365985i	$0.0116523\pi$
$109$	0.530272	+	3.68813i	0.0507909	+	0.353258i	−0.948539	+	0.316660i	$0.897439\pi$
$110$	0.495691	−	1.08541i	0.0472623	−	0.103490i
$111$	22.3227	+	6.55454i	2.11878	+	0.622129i
$112$	13.7412	−	4.03478i	1.29842	−	0.381251i
$113$	−4.92204	−	5.68034i	−0.463027	−	0.534361i	0.475432	−	0.879752i	$-0.342292\pi$
$113$	−4.92204	−	5.68034i	−0.463027	−	0.534361i	−0.938459	+	0.345391i	$0.887746\pi$
$114$	2.41481	+	0.709053i	0.226168	+	0.0664089i
$115$	−7.48702	+	4.81162i	−0.698169	+	0.448686i
$116$	0.219657	+	0.480982i	0.0203947	+	0.0446581i
$117$	0.0266873	−	0.0584369i	0.00246724	−	0.00540250i
$118$	−0.290894	+	0.335710i	−0.0267790	+	0.0309046i
$119$	−6.92574	+	4.45090i	−0.634882	+	0.408014i
$120$	−4.01421	−	8.78990i	−0.366446	−	0.802404i
$121$	1.25292	+	8.71422i	0.113901	+	0.792201i
$122$	0.487648	+	3.39167i	0.0441496	+	0.307067i
$123$	−21.8227	+	25.1847i	−1.96768	+	2.27083i
$124$	−7.11208	+	2.08830i	−0.638684	+	0.187535i
$125$	−4.75343	−	3.05485i	−0.425160	−	0.273234i
$126$	−1.05094	+	7.30945i	−0.0936252	+	0.651177i
$127$	5.37328	+	3.45320i	0.476802	+	0.306422i	0.756878	−	0.653556i	$-0.226724\pi$
$127$	5.37328	+	3.45320i	0.476802	+	0.306422i	−0.280077	+	0.959978i	$0.590360\pi$
$128$	−5.37513	−	6.20323i	−0.475099	−	0.548294i
$129$	12.9222	−	14.9130i	1.13773	−	1.31301i
$130$	−0.00336925	−	0.00737764i	−0.000295503	−	0.000647062i
$131$	7.04590	+	2.06886i	0.615603	+	0.180757i	0.574644	−	0.818403i	$-0.305140\pi$
$131$	7.04590	+	2.06886i	0.615603	+	0.180757i	0.0409593	+	0.999161i	$0.486959\pi$
$132$	−7.32624	−	4.70829i	−0.637667	−	0.409804i
$133$	11.7461			1.01852
$134$	−1.15306	+	2.02445i	−0.0996095	+	0.174886i
$135$	−29.2610			−2.51838
$136$	1.89906	+	1.22045i	0.162843	+	0.104653i
$137$	−2.92420	−	0.858624i	−0.249832	−	0.0733572i	0.154419	−	0.988005i	$-0.450649\pi$
$137$	−2.92420	−	0.858624i	−0.249832	−	0.0733572i	−0.404251	+	0.914648i	$0.632468\pi$
$138$	−1.13914	−	2.49437i	−0.0969702	−	0.212335i
$139$	−3.74806	+	4.32550i	−0.317907	+	0.366884i	−0.892102	−	0.451835i	$-0.850770\pi$
$139$	−3.74806	+	4.32550i	−0.317907	+	0.366884i	0.574195	+	0.818719i	$0.305315\pi$
$140$	−14.4617	−	16.6896i	−1.22223	−	1.41053i
$141$	−12.5851	−	8.08795i	−1.05986	−	0.681128i
$142$	0.651629	−	4.53218i	0.0546835	−	0.380332i
$143$	−0.0125579	−	0.00807046i	−0.00105014	−	0.000674885i
$144$	−21.5432	+	6.32564i	−1.79526	+	0.527137i
$145$	0.510454	−	0.589095i	0.0423909	−	0.0489217i
$146$	0.105793	+	0.735808i	0.00875551	+	0.0608959i
$147$	4.16142	+	28.9433i	0.343228	+	2.38721i
$148$	−6.05634	−	13.2615i	−0.497828	−	1.09009i
$149$	7.86944	−	5.05738i	0.644690	−	0.414317i	−0.177033	−	0.984205i	$-0.556650\pi$
$149$	7.86944	−	5.05738i	0.644690	−	0.414317i	0.821722	+	0.569888i	$0.193013\pi$
$150$	−1.71386	+	1.97790i	−0.139936	+	0.161495i
$151$	5.38633	−	11.7944i	0.438333	−	0.959816i	−0.553568	−	0.832804i	$-0.686734\pi$
$151$	5.38633	−	11.7944i	0.438333	−	0.959816i	0.991901	−	0.127012i	$-0.0405387\pi$
$152$	−1.33798	−	2.92976i	−0.108524	−	0.237635i
$153$	10.8580	−	6.97803i	0.877819	−	0.564140i
$154$	1.64641	+	0.483428i	0.132671	+	0.0389558i
$155$	7.15563	+	8.25804i	0.574754	+	0.663301i
$156$	−0.0567961	+	0.0166768i	−0.00454732	+	0.00133521i
$157$	14.1102	+	4.14312i	1.12611	+	0.330657i	0.791179	−	0.611584i	$-0.209467\pi$
$157$	14.1102	+	4.14312i	1.12611	+	0.330657i	0.334935	+	0.942241i	$0.391286\pi$
$158$	−0.334453	+	0.732350i	−0.0266077	+	0.0582626i
$159$	1.67710	+	11.6645i	0.133003	+	0.925056i
$160$	−3.79924	+	8.31918i	−0.300356	+	0.657689i
$161$	−8.38103	−	9.67222i	−0.660518	−	0.762278i
$162$	0.508048	−	3.53355i	0.0399160	−	0.277622i
$163$	−11.3744			−0.890912			−0.445456	−	0.895304i	$-0.646958\pi$
$163$	−11.3744			−0.890912			−0.445456	+	0.895304i	$0.646958\pi$
$164$	20.8825			1.63065
$165$	−1.82704	+	12.7073i	−0.142235	+	0.989265i
$166$	−2.32127	+	0.681585i	−0.180165	+	0.0529013i
$167$	14.5504	−	9.35095i	1.12594	−	0.723598i	0.161232	−	0.986917i	$-0.448453\pi$
$167$	14.5504	−	9.35095i	1.12594	−	0.723598i	0.964709	+	0.263318i	$0.0848169\pi$
$168$	11.6899	−	7.51265i	0.901896	−	0.579613i
$169$	12.4733	−	3.66249i	0.959485	−	0.281730i
$170$	0.231902	−	1.61291i	0.0177860	−	0.123705i
$171$	−18.4153			−1.40825
$172$	−12.3654			−0.942855
$173$	−0.477135	+	3.31854i	−0.0362759	+	0.252304i	−0.999887	−	0.0150022i	$-0.995224\pi$
$173$	−0.477135	+	3.31854i	−0.0362759	+	0.252304i	0.963612	+	0.267306i	$0.0861336\pi$
$174$	0.157279	+	0.181509i	0.0119233	+	0.0137602i
$175$	−5.07413	+	11.1108i	−0.383568	+	0.839896i
$176$	0.742481	+	5.16407i	0.0559666	+	0.389256i
$177$	1.98535	−	4.34731i	0.149228	−	0.326764i
$178$	3.67146	+	1.07804i	0.275188	+	0.0808025i
$179$	8.20580	−	2.40944i	0.613330	−	0.180090i	0.0397098	−	0.999211i	$-0.487357\pi$
$179$	8.20580	−	2.40944i	0.613330	−	0.180090i	0.573620	+	0.819121i	$0.305538\pi$
$180$	22.6726	+	26.1656i	1.68992	+	1.95027i
$181$	−6.37349	−	1.87143i	−0.473738	−	0.139102i	0.0361437	−	0.999347i	$-0.488493\pi$
$181$	−6.37349	−	1.87143i	−0.473738	−	0.139102i	−0.509882	+	0.860245i	$0.670311\pi$
$182$	0.00981171	−	0.00630560i	0.000727292	−	0.000467402i
$183$	−15.3147	−	33.5344i	−1.13209	−	2.47894i
$184$	−1.45782	+	3.19217i	−0.107472	+	0.235330i
$185$	−14.0741	+	16.2424i	−1.03475	+	1.19416i
$186$	−2.83230	+	1.82021i	−0.207674	+	0.133464i
$187$	−1.24587	−	2.72808i	−0.0911072	−	0.199497i
$188$	1.33414	+	9.27918i	0.0973025	+	0.676754i
$189$	−5.98832	−	41.6497i	−0.435586	−	3.02957i
$190$	−1.52250	+	1.75706i	−0.110454	+	0.127471i
$191$	−6.34603	+	1.86336i	−0.459182	+	0.134828i	−0.503139	−	0.864205i	$-0.667822\pi$
$191$	−6.34603	+	1.86336i	−0.459182	+	0.134828i	0.0439569	+	0.999033i	$0.486004\pi$
$192$	15.7682	+	10.1336i	1.13797	+	0.731329i
$193$	−0.977858	+	6.80115i	−0.0703878	+	0.489558i	0.923884	+	0.382673i	$0.124997\pi$
$193$	−0.977858	+	6.80115i	−0.0703878	+	0.489558i	−0.994271	+	0.106884i	$0.965913\pi$
$194$	2.60173	+	1.67203i	0.186793	+	0.120045i
$195$	0.0571438	+	0.0659475i	0.00409215	+	0.00472260i
$196$	11.9995	−	13.8482i	0.857108	−	0.989156i
$197$	5.58808	+	12.2362i	0.398134	+	0.871793i	0.997456	+	0.0712845i	$0.0227098\pi$
$197$	5.58808	+	12.2362i	0.398134	+	0.871793i	−0.599322	+	0.800508i	$0.704563\pi$
$198$	−2.58120	−	0.757908i	−0.183438	−	0.0538622i
$199$	16.5656	+	10.6460i	1.17430	+	0.754678i	0.974330	−	0.225123i	$-0.0722785\pi$
$199$	16.5656	+	10.6460i	1.17430	+	0.754678i	0.199972	+	0.979802i	$0.435915\pi$
$200$	3.34928			0.236830
$201$	5.76682	−	24.3937i	0.406760	−	1.72060i
$202$	3.35197			0.235843
$203$	0.942975	+	0.606013i	0.0661839	+	0.0425338i
$204$	−11.4109	−	3.35054i	−0.798923	−	0.234585i
$205$	−12.7882	−	28.0021i	−0.893163	−	1.95575i
$206$	0.840475	−	0.969960i	0.0585587	−	0.0675803i
$207$	13.1396	+	15.1639i	0.913264	+	1.05396i
$208$	0.0298321	+	0.0191720i	0.00206849	+	0.00132934i
$209$	−0.608971	+	4.23548i	−0.0421234	+	0.292975i
$210$	−8.43826	−	5.42294i	−0.582295	−	0.374219i
$211$	9.62104	−	2.82499i	0.662340	−	0.194481i	0.0667507	−	0.997770i	$-0.478737\pi$
$211$	9.62104	−	2.82499i	0.662340	−	0.194481i	0.595589	+	0.803289i	$0.296919\pi$
$212$	4.83595	−	5.58098i	0.332134	−	0.383303i
$213$	7.01082	+	48.7613i	0.480374	+	3.34107i
$214$	0.297796	+	2.07122i	0.0203569	+	0.141585i
$215$	7.57243	+	16.5813i	0.516435	+	1.13084i
$216$	−9.70631	+	6.23787i	−0.660431	+	0.424433i
$217$	−10.2900	+	11.8753i	−0.698528	+	0.806145i
$218$	0.440566	−	0.964705i	0.0298389	−	0.0653381i
$219$	−3.32245	−	7.27515i	−0.224510	−	0.491609i
$220$	6.76780	−	4.34940i	0.456285	−	0.293237i
$221$	−0.0195594	−	0.00574316i	−0.00131571	−	0.000386327i
$222$	−4.33645	−	5.00453i	−0.291043	−	0.335882i
$223$	9.62712	−	2.82678i	0.644679	−	0.189295i	0.0569813	−	0.998375i	$-0.481852\pi$
$223$	9.62712	−	2.82678i	0.644679	−	0.189295i	0.587698	+	0.809080i	$0.300034\pi$
$224$	−12.6189	−	3.70525i	−0.843138	−	0.247568i
$225$	7.95510	−	17.4192i	0.530340	−	1.16128i
$226$	0.304457	+	2.11755i	0.0202522	+	0.140857i
$227$	5.08635	−	11.1376i	0.337593	−	0.739226i	−0.662357	−	0.749188i	$-0.730444\pi$
$227$	5.08635	−	11.1376i	0.337593	−	0.739226i	0.999950	+	0.00996246i	$0.00317120\pi$
$228$	11.1117	+	12.8236i	0.735894	+	0.849266i
$229$	0.113281	−	0.787886i	0.00748581	−	0.0520650i	−0.985736	−	0.168298i	$-0.946173\pi$
$229$	0.113281	−	0.787886i	0.00748581	−	0.0520650i	0.993222	+	0.116233i	$0.0370820\pi$
$230$	2.53316			0.167032
$231$	−18.4614			−1.21467
$232$	0.0437417	−	0.304230i	0.00287178	−	0.0199737i
$233$	17.1543	−	5.03695i	1.12381	−	0.329982i	0.333541	−	0.942736i	$-0.391757\pi$
$233$	17.1543	−	5.03695i	1.12381	−	0.329982i	0.790274	+	0.612754i	$0.209938\pi$
$234$	−0.0153826	+	0.00988578i	−0.00100559	+	0.000646253i
$235$	11.6258	−	7.47146i	0.758385	−	0.487384i
$236$	−2.87356	+	0.843753i	−0.187053	+	0.0549236i
$237$	1.23274	−	8.57390i	0.0800751	−	0.556935i
$238$	2.34325			0.151891
$239$	−22.3237			−1.44400			−0.722001	−	0.691892i	$-0.756778\pi$
$239$	−22.3237			−1.44400			−0.722001	+	0.691892i	$0.756778\pi$
$240$	4.34027	−	30.1872i	0.280163	−	1.94858i
$241$	3.11612	+	3.59620i	0.200727	+	0.231651i	0.847185	−	0.531299i	$-0.178296\pi$
$241$	3.11612	+	3.59620i	0.200727	+	0.231651i	−0.646458	+	0.762950i	$0.723750\pi$
$242$	1.04096	−	2.27938i	0.0669154	−	0.146524i
$243$	1.04989	+	7.30214i	0.0673504	+	0.468432i
$244$	−9.59689	+	21.0143i	−0.614378	+	1.34530i
$245$	−25.9179	−	7.61019i	−1.65584	−	0.486197i
$246$	9.10083	−	2.67224i	0.580247	−	0.170376i
$247$	0.0190466	+	0.0219810i	0.00121191	+	0.00139861i
$248$	4.13408	+	1.21388i	0.262514	+	0.0770812i
$249$	21.8967	−	14.0722i	1.38765	−	0.891787i
$250$	0.668102	+	1.46294i	0.0422545	+	0.0925244i
$251$	−8.68937	+	19.0271i	−0.548468	+	1.20098i	0.409025	+	0.912523i	$0.365869\pi$
$251$	−8.68937	+	19.0271i	−0.548468	+	1.20098i	−0.957494	+	0.288455i	$0.906859\pi$
$252$	−32.6038	+	37.6268i	−2.05385	+	2.37027i
$253$	3.92218	−	2.52063i	0.246585	−	0.158471i
$254$	−0.755223	−	1.65371i	−0.0473869	−	0.103763i
$255$	2.49501	+	17.3532i	0.156244	+	1.08670i
$256$	−1.40967	−	9.80445i	−0.0881042	−	0.612778i
$257$	19.7339	−	22.7741i	1.23097	−	1.42061i	0.357368	−	0.933964i	$-0.383674\pi$
$257$	19.7339	−	22.7741i	1.23097	−	1.42061i	0.873599	−	0.486647i	$-0.161780\pi$
$258$	−5.38900	+	1.58235i	−0.335505	+	0.0985130i
$259$	−25.9995	−	16.7088i	−1.61553	−	1.03824i
$260$	0.00778204	−	0.0541253i	0.000482622	−	0.00335671i
$261$	−1.47837	−	0.950094i	−0.0915091	−	0.0588093i
$262$	−1.36875	−	1.57962i	−0.0845616	−	0.0975893i
$263$	−16.5597	+	19.1110i	−1.02112	+	1.17843i	−0.0372918	+	0.999304i	$0.511873\pi$
$263$	−16.5597	+	19.1110i	−1.02112	+	1.17843i	−0.983826	+	0.179128i	$0.942672\pi$
$264$	2.10290	+	4.60471i	0.129424	+	0.283400i
$265$	−10.4452	−	3.06700i	−0.641646	−	0.188404i
$266$	−2.81256	−	1.80752i	−0.172449	−	0.110826i
$267$	−41.1686			−2.51948
$268$	−13.9191	+	7.27925i	−0.850243	+	0.444651i
$269$	−30.7313			−1.87372			−0.936859	−	0.349706i	$-0.886281\pi$
$269$	−30.7313			−1.87372			−0.936859	+	0.349706i	$0.886281\pi$
$270$	7.00642	+	4.50275i	0.426397	+	0.274029i
$271$	26.1989	+	7.69269i	1.59147	+	0.467298i	0.953156	−	0.302478i	$-0.0978139\pi$
$271$	26.1989	+	7.69269i	1.59147	+	0.467298i	0.638314	+	0.769776i	$0.279632\pi$
$272$	2.95966	+	6.48075i	0.179456	+	0.392953i
$273$	−0.0821741	+	0.0948340i	−0.00497341	+	0.00573962i
$274$	0.568061	+	0.655577i	0.0343178	+	0.0396049i
$275$	−3.74333	−	2.40569i	−0.225731	−	0.145069i
$276$	2.63110	−	18.2997i	0.158374	−	1.10151i
$277$	−7.66716	−	4.92738i	−0.460675	−	0.296058i	0.289643	−	0.957135i	$-0.406463\pi$
$277$	−7.66716	−	4.92738i	−0.460675	−	0.296058i	−0.750318	+	0.661077i	$0.770100\pi$
$278$	1.56308	−	0.458961i	0.0937471	−	0.0275266i
$279$	16.1324	−	18.6177i	0.965820	−	1.11462i
$280$	1.82684	+	12.7060i	0.109175	+	0.759327i
$281$	3.29999	+	22.9519i	0.196861	+	1.36920i	0.813323	+	0.581812i	$0.197656\pi$
$281$	3.29999	+	22.9519i	0.196861	+	1.36920i	−0.616462	+	0.787384i	$0.711435\pi$
$282$	1.76885	+	3.87325i	0.105334	+	0.230649i
$283$	−18.7567	+	12.0542i	−1.11497	+	0.716549i	−0.962371	−	0.271739i	$-0.912401\pi$
$283$	−18.7567	+	12.0542i	−1.11497	+	0.716549i	−0.152601	+	0.988288i	$0.548765\pi$
$284$	20.2158	−	23.3303i	1.19959	−	1.38440i
$285$	10.3910	−	22.7532i	0.615513	−	1.34778i
$286$	0.00176503	+	0.00386487i	0.000104368	+	0.000228535i
$287$	37.2408	−	23.9332i	2.19825	−	1.41273i
$288$	19.7837	+	5.80901i	1.16576	+	0.342299i
$289$	8.45060	+	9.75251i	0.497094	+	0.573677i
$290$	−0.212877	+	0.0625064i	−0.0125006	+	0.00367050i
$291$	−31.9261	−	9.37435i	−1.87154	−	0.549534i
$292$	−2.08200	+	4.55895i	−0.121840	+	0.266793i
$293$	1.28946	+	8.96840i	0.0753311	+	0.523939i	0.992191	+	0.124730i	$0.0398063\pi$
$293$	1.28946	+	8.96840i	0.0753311	+	0.523939i	−0.916860	+	0.399210i	$0.869285\pi$
$294$	3.45744	−	7.57073i	0.201642	−	0.441534i
$295$	2.89115	+	3.33657i	0.168329	+	0.194262i
$296$	−1.20604	+	8.38816i	−0.0700994	+	0.487552i
$297$	15.3288			0.889464
$298$	−2.66255			−0.154237
$299$	0.00450996	−	0.0313675i	0.000260818	−	0.00181403i
$300$	−16.9301	+	4.97113i	−0.977461	+	0.287008i
$301$	−22.0519	+	14.1719i	−1.27105	+	0.816854i
$302$	−3.10469	+	1.99526i	−0.178655	+	0.114814i
$303$	−34.6027	+	10.1603i	−1.98787	+	0.583692i
$304$	1.44665	−	10.0617i	0.0829713	−	0.577078i
$305$	34.0559			1.95003
$306$	−3.67370			−0.210012
$307$	3.97489	−	27.6460i	0.226859	−	1.57784i	−0.484359	−	0.874869i	$-0.660947\pi$
$307$	3.97489	−	27.6460i	0.226859	−	1.57784i	0.711219	−	0.702971i	$-0.248144\pi$
$308$	7.57593	+	8.74308i	0.431678	+	0.498183i
$309$	−5.73623	+	12.5606i	−0.326323	+	0.714547i
$310$	−0.442618	−	3.07848i	−0.0251390	−	0.174846i
$311$	4.18747	−	9.16929i	0.237450	−	0.519943i	−0.752966	−	0.658059i	$-0.771378\pi$
$311$	4.18747	−	9.16929i	0.237450	−	0.519943i	0.990416	+	0.138117i	$0.0441049\pi$
$312$	0.0330142	+	0.00969383i	0.00186906	+	0.000548805i
$313$	18.1268	−	5.32250i	1.02459	−	0.300845i	0.274078	−	0.961707i	$-0.411627\pi$
$313$	18.1268	−	5.32250i	1.02459	−	0.300845i	0.750507	+	0.660862i	$0.229809\pi$
$314$	−2.74107	−	3.16336i	−0.154687	−	0.178519i
$315$	70.4214	+	20.6776i	3.96780	+	1.16505i
$316$	−4.56637	+	2.93463i	−0.256879	+	0.165086i
$317$	−2.03553	−	4.45719i	−0.114327	−	0.250340i	0.843815	−	0.536633i	$-0.180304\pi$
$317$	−2.03553	−	4.45719i	−0.114327	−	0.250340i	−0.958142	+	0.286293i	$0.907577\pi$
$318$	1.39339	−	3.05109i	0.0781373	−	0.171097i
$319$	−0.267408	+	0.308605i	−0.0149720	+	0.0172786i
$320$	−14.5663	+	9.36117i	−0.814279	+	0.523305i
$321$	−9.35232	−	20.4787i	−0.521996	−	1.14301i
$322$	0.518416	+	3.60566i	0.0288902	+	0.200936i
$323$	0.831612	+	5.78399i	0.0462721	+	0.321830i
$324$	15.7614	−	18.1896i	0.875634	−	1.01054i
$325$	−0.0290198	+	0.00852100i	−0.00160973	+	0.000472660i
$326$	2.72355	+	1.75032i	0.150844	+	0.0969413i
$327$	−1.62386	+	11.2942i	−0.0897995	+	0.624569i
$328$	−10.2115	−	6.56255i	−0.563837	−	0.362356i
$329$	13.0140	+	15.0190i	0.717486	+	0.828023i
$330$	2.39291	−	2.76157i	0.131726	−	0.152019i
$331$	−2.27904	−	4.99041i	−0.125267	−	0.274298i	0.836600	−	0.547815i	$-0.184540\pi$
$331$	−2.27904	−	4.99041i	−0.125267	−	0.274298i	−0.961867	+	0.273517i	$0.911813\pi$
$332$	−15.6501	−	4.59528i	−0.858910	−	0.252199i
$333$	40.7614	+	26.1958i	2.23371	+	1.43552i
$334$	−4.92297			−0.269373
$335$	18.2849	+	14.2069i	0.999011	+	0.776207i
$336$	43.8563			2.39256
$337$	−20.3706	−	13.0914i	−1.10966	−	0.713135i	−0.148441	−	0.988921i	$-0.547425\pi$
$337$	−20.3706	−	13.0914i	−1.10966	−	0.713135i	−0.961219	+	0.275786i	$0.911062\pi$
$338$	−3.55027	−	1.04245i	−0.193109	−	0.0567021i
$339$	−9.56152	−	20.9368i	−0.519311	−	1.13713i
$340$	7.19439	−	8.30277i	0.390171	−	0.450281i
$341$	−3.74857	−	4.32608i	−0.202996	−	0.234270i
$342$	4.40946	+	2.83379i	0.238437	+	0.153234i
$343$	1.47552	−	10.2625i	0.0796707	−	0.554122i
$344$	6.04670	+	3.88598i	0.326016	+	0.209518i
$345$	−26.1501	+	7.67835i	−1.40787	+	0.413389i
$346$	0.624913	−	0.721189i	0.0335956	−	0.0387713i
$347$	−1.46217	−	10.1696i	−0.0784935	−	0.545934i	−0.990685	−	0.136171i	$-0.956520\pi$
$347$	−1.46217	−	10.1696i	−0.0784935	−	0.545934i	0.912192	−	0.409763i	$-0.134389\pi$
$348$	0.230442	+	1.60276i	0.0123530	+	0.0859171i
$349$	−1.58977	−	3.48112i	−0.0850985	−	0.186340i	0.862299	−	0.506400i	$-0.169024\pi$
$349$	−1.58977	−	3.48112i	−0.0850985	−	0.186340i	−0.947397	+	0.320060i	$0.896297\pi$
$350$	2.92473	−	1.87961i	0.156334	−	0.100469i
$351$	0.0682304	−	0.0787421i	0.00364187	−	0.00420294i
$352$	1.99028	−	4.35811i	0.106082	−	0.232288i
$353$	6.74741	+	14.7748i	0.359128	+	0.786381i	0.999827	+	0.0185892i	$0.00591745\pi$
$353$	6.74741	+	14.7748i	0.359128	+	0.786381i	−0.640699	+	0.767792i	$0.721355\pi$
$354$	−1.14436	+	0.735435i	−0.0608220	+	0.0390879i
$355$	−43.6644	−	12.8210i	−2.31746	−	0.680469i
$356$	16.8942	+	19.4970i	0.895392	+	1.03334i
$357$	−24.1897	+	7.10273i	−1.28025	+	0.375916i
$358$	−2.33561	−	0.685798i	−0.123441	−	0.0362456i
$359$	6.59064	−	14.4315i	0.347841	−	0.761665i	−0.652153	−	0.758087i	$-0.726134\pi$
$359$	6.59064	−	14.4315i	0.347841	−	0.761665i	0.999994	−	0.00357746i	$-0.00113874\pi$
$360$	−2.86408	−	19.9201i	−0.150950	−	1.04988i
$361$	−4.42944	+	9.69913i	−0.233129	+	0.510480i
$362$	1.23813	+	1.42887i	0.0650744	+	0.0750999i
$363$	−3.83681	+	26.6856i	−0.201380	+	1.40063i
$364$	0.0786338			0.00412153
$365$	7.38828			0.386720
$366$	−1.49333	+	10.3863i	−0.0780576	+	0.542902i
$367$	−19.9140	+	5.84728i	−1.03950	+	0.305226i	−0.756569	−	0.653914i	$-0.773126\pi$
$367$	−19.9140	+	5.84728i	−1.03950	+	0.305226i	−0.282934	+	0.959139i	$0.591308\pi$
$368$	−9.31741	+	5.98794i	−0.485704	+	0.312143i
$369$	−58.3852	+	37.5219i	−3.03941	+	1.95331i
$370$	5.86940	−	1.72341i	0.305136	−	0.0895959i
$371$	2.22788	−	15.4953i	0.115666	−	0.804475i
$372$	−22.6989			−1.17688
$373$	12.5278			0.648666			0.324333	−	0.945943i	$-0.394860\pi$
$373$	12.5278			0.648666			0.324333	+	0.945943i	$0.394860\pi$
$374$	−0.121485	+	0.844945i	−0.00628182	+	0.0436910i
$375$	−11.3313	−	13.0770i	−0.585144	−	0.675292i
$376$	2.26369	−	4.95679i	0.116741	−	0.255627i
$377$	0.000395001		0.00274729i	2.03436e−5		0.000141493i
$378$	−4.97528	+	10.8943i	−0.255901	+	0.560344i
$379$	21.5278	+	6.32112i	1.10581	+	0.324694i	0.783157	−	0.621824i	$-0.213608\pi$
$379$	21.5278	+	6.32112i	1.10581	+	0.324694i	0.322650	+	0.946518i	$0.395426\pi$
$380$	−15.0398	+	4.41608i	−0.771525	+	0.226540i
$381$	12.8089	+	14.7822i	0.656218	+	0.757316i
$382$	1.80627	+	0.530368i	0.0924167	+	0.0271360i
$383$	13.9776	−	8.98283i	0.714220	−	0.459001i	−0.132402	−	0.991196i	$-0.542269\pi$
$383$	13.9776	−	8.98283i	0.714220	−	0.459001i	0.846622	+	0.532195i	$0.178633\pi$
$384$	−10.4417	−	22.8641i	−0.532851	−	1.16678i
$385$	7.08456	−	15.5130i	0.361062	−	0.790617i
$386$	1.28072	−	1.47803i	0.0651870	−	0.0752298i
$387$	34.5725	−	22.2184i	1.75742	−	1.12942i
$388$	8.66182	+	18.9667i	0.439737	+	0.962890i
$389$	−3.60151	−	25.0490i	−0.182604	−	1.27004i	−0.850576	−	0.525851i	$-0.823747\pi$
$389$	−3.60151	−	25.0490i	−0.182604	−	1.27004i	0.667973	−	0.744186i	$-0.267162\pi$
$390$	−0.00353468	−	0.0245843i	−0.000178986	−	0.00124487i
$391$	4.16940	−	4.81174i	0.210856	−	0.243340i
$392$	−10.2197	+	3.00078i	−0.516173	+	0.151562i
$393$	18.9178	+	12.1577i	0.954277	+	0.613276i
$394$	0.544893	−	3.78981i	0.0274513	−	0.190928i
$395$	6.73155	+	4.32611i	0.338701	+	0.217670i
$396$	−11.8774	−	13.7072i	−0.596860	−	0.688813i
$397$	12.2650	−	14.1545i	0.615561	−	0.710395i	−0.359297	−	0.933223i	$-0.616983\pi$
$397$	12.2650	−	14.1545i	0.615561	−	0.710395i	0.974858	+	0.222828i	$0.0715289\pi$
$398$	−2.32832	−	5.09830i	−0.116708	−	0.255555i
$399$	34.5132	+	10.1340i	1.72782	+	0.507334i
$400$	8.89255	+	5.71489i	0.444627	+	0.285745i
$401$	6.67205			0.333186			0.166593	−	0.986026i	$-0.446723\pi$
$401$	6.67205			0.333186			0.166593	+	0.986026i	$0.446723\pi$
$402$	−5.13460	+	4.95355i	−0.256091	+	0.247061i
$403$	−0.0389080			−0.00193815
$404$	19.0116	+	12.2180i	0.945861	+	0.607868i
$405$	−34.0433	−	9.99602i	−1.69163	−	0.496706i
$406$	−0.132537	−	0.290215i	−0.00657768	−	0.0144031i
$407$	7.37290	−	8.50878i	0.365461	−	0.421765i
$408$	4.52699	+	5.22442i	0.224119	+	0.258648i
$409$	0.492764	+	0.316680i	0.0243656	+	0.0156588i	0.552767	−	0.833336i	$-0.313572\pi$
$409$	0.492764	+	0.316680i	0.0243656	+	0.0156588i	−0.528401	+	0.848995i	$0.677208\pi$
$410$	−1.24697	+	8.67287i	−0.0615834	+	0.428322i
$411$	−7.85130	−	5.04572i	−0.387276	−	0.248887i
$412$	8.30251	−	2.43784i	0.409035	−	0.120104i
$413$	−4.15754	+	4.79806i	−0.204579	+	0.236097i
$414$	−0.812761	−	5.65288i	−0.0399450	−	0.277824i
$415$	3.42191	+	23.7999i	0.167975	+	1.16829i
$416$	−0.0135281	−	0.0296224i	−0.000663270	−	0.00145236i
$417$	−14.7446	+	9.47580i	−0.722048	+	0.464032i
$418$	0.797582	−	0.920459i	0.0390110	−	0.0450211i
$419$	−11.0774	+	24.2562i	−0.541169	+	1.18499i	0.419617	+	0.907701i	$0.362165\pi$
$419$	−11.0774	+	24.2562i	−0.541169	+	1.18499i	−0.960785	+	0.277293i	$0.910563\pi$
$420$	−28.0931	−	61.5153i	−1.37080	−	3.00164i
$421$	11.5554	−	7.42623i	0.563178	−	0.361932i	−0.227865	−	0.973693i	$-0.573175\pi$
$421$	11.5554	−	7.42623i	0.563178	−	0.361932i	0.791043	+	0.611760i	$0.209538\pi$
$422$	−2.73843	−	0.804077i	−0.133305	−	0.0391419i
$423$	−20.4031	−	23.5464i	−0.992032	−	1.14487i
$424$	−4.11867	+	1.20935i	−0.200020	+	0.0587312i
$425$	−5.83038	−	1.71195i	−0.282815	−	0.0830420i
$426$	5.82480	−	12.7545i	0.282213	−	0.617959i
$427$	6.96961	+	48.4747i	0.337283	+	2.34585i
$428$	−5.86061	+	12.8329i	−0.283283	+	0.620303i
$429$	−0.0299355	−	0.0345474i	−0.00144530	−	0.00166797i
$430$	0.738386	−	5.13559i	0.0356081	−	0.247660i
$431$	−40.8613			−1.96822			−0.984109	−	0.177565i	$-0.943178\pi$
$431$	−40.8613			−1.96822			−0.984109	+	0.177565i	$0.943178\pi$
$432$	−36.4146			−1.75200
$433$	−1.32260	+	9.19885i	−0.0635599	+	0.442069i	0.933047	+	0.359755i	$0.117140\pi$
$433$	−1.32260	+	9.19885i	−0.0635599	+	0.442069i	−0.996607	+	0.0823132i	$0.973769\pi$
$434$	4.29128	−	1.26003i	0.205988	−	0.0604835i
$435$	2.00809	−	1.29052i	0.0962805	−	0.0618757i
$436$	6.01516	−	3.86571i	0.288074	−	0.185134i
$437$	−8.71608	+	2.55927i	−0.416947	+	0.122427i
$438$	−0.323971	+	2.25327i	−0.0154800	+	0.107665i
$439$	−13.8826			−0.662578			−0.331289	−	0.943529i	$-0.607484\pi$
$439$	−13.8826			−0.662578			−0.331289	+	0.943529i	$0.607484\pi$
$440$	−4.67631			−0.222934
$441$	−8.66681	+	60.2790i	−0.412705	+	2.87043i
$442$	0.00379964	+	0.00438502i	0.000180731	+	0.000208574i
$443$	−2.53064	+	5.54134i	−0.120234	+	0.263277i	−0.960174	−	0.279404i	$-0.909863\pi$
$443$	−2.53064	+	5.54134i	−0.120234	+	0.263277i	0.839939	+	0.542680i	$0.182591\pi$
$444$	−6.35370	−	44.1910i	−0.301533	−	2.09721i
$445$	15.7985	−	34.5938i	0.748919	−	1.63990i
$446$	−2.74016	−	0.804584i	−0.129750	−	0.0380982i
$447$	27.4858	−	8.07055i	1.30003	−	0.381724i
$448$	−16.3056	−	18.8176i	−0.770366	−	0.889050i
$449$	−14.2709	−	4.19030i	−0.673484	−	0.197753i	−0.0729300	−	0.997337i	$-0.523235\pi$
$449$	−14.2709	−	4.19030i	−0.673484	−	0.197753i	−0.600554	+	0.799584i	$0.705053\pi$
$450$	−4.58533	+	2.94681i	−0.216154	+	0.138914i
$451$	6.69924	+	14.6693i	0.315455	+	0.690750i
$452$	−5.99170	+	13.1200i	−0.281826	+	0.617113i
$453$	26.0021	−	30.0080i	1.22169	−	1.40990i
$454$	−2.93178	+	1.88414i	−0.137595	+	0.0884271i
$455$	−0.0481543	−	0.105443i	−0.00225751	−	0.00494325i
$456$	−1.40367	−	9.76275i	−0.0657330	−	0.457183i
$457$	5.64728	+	39.2777i	0.264169	+	1.83733i	0.500593	+	0.865683i	$0.333115\pi$
$457$	5.64728	+	39.2777i	0.264169	+	1.83733i	−0.236425	+	0.971650i	$0.575976\pi$
$458$	−0.148366	+	0.171224i	−0.00693271	+	0.00800077i
$459$	20.0851	−	5.89750i	0.937490	−	0.275272i
$460$	14.3675	+	9.23343i	0.669888	+	0.430511i
$461$	−0.847533	+	5.89472i	−0.0394736	+	0.274545i	−0.999993	−	0.00366731i	$-0.998833\pi$
$461$	−0.847533	+	5.89472i	−0.0394736	+	0.274545i	0.960520	+	0.278212i	$0.0897417\pi$
$462$	4.42049	+	2.84088i	0.205660	+	0.132170i
$463$	−19.5001	−	22.5043i	−0.906245	−	1.04586i	−0.998742	−	0.0501495i	$-0.984030\pi$
$463$	−19.5001	−	22.5043i	−0.906245	−	1.04586i	0.0924967	−	0.995713i	$-0.470515\pi$
$464$	0.635247	−	0.733114i	0.0294906	−	0.0340340i
$465$	13.9005	+	30.4378i	0.644619	+	1.41152i
$466$	−4.88262	−	1.43367i	−0.226183	−	0.0664133i
$467$	−17.0113	−	10.9325i	−0.787190	−	0.505896i	0.0842229	−	0.996447i	$-0.473159\pi$
$467$	−17.0113	−	10.9325i	−0.787190	−	0.505896i	−0.871413	+	0.490551i	$0.836796\pi$
$468$	−0.123280			−0.00569863
$469$	−16.4799	+	28.9340i	−0.760971	+	1.33605i
$470$	−3.93348			−0.181438
$471$	37.8849	+	24.3471i	1.74564	+	1.12186i
$472$	1.67033	+	0.490453i	0.0768831	+	0.0225749i
$473$	−3.96692	−	8.68634i	−0.182399	−	0.399398i
$474$	−1.61455	+	1.86329i	−0.0741586	+	0.0855836i
$475$	5.67753	+	6.55222i	0.260503	+	0.300636i
$476$	13.2904	+	8.54122i	0.609164	+	0.391486i
$477$	−3.49283	+	24.2931i	−0.159926	+	1.11231i
$478$	5.34532	+	3.43523i	0.244489	+	0.157124i
$479$	17.2506	−	5.06523i	0.788200	−	0.231436i	0.137229	−	0.990539i	$-0.456180\pi$
$479$	17.2506	−	5.06523i	0.788200	−	0.231436i	0.650971	+	0.759103i	$0.274362\pi$
$480$	−18.3406	+	21.1661i	−0.837128	+	0.966097i
$481$	−0.0108909	−	0.0757476i	−0.000496580	−	0.00345379i
$482$	−0.192751	−	1.34061i	−0.00877955	−	0.0610631i
$483$	−16.2809	−	35.6503i	−0.740808	−	1.62214i
$484$	14.2125	−	9.13381i	0.646022	−	0.415173i
$485$	20.1289	−	23.2300i	0.914006	−	1.05482i
$486$	0.872279	−	1.91003i	0.0395674	−	0.0866405i
$487$	1.65064	+	3.61440i	0.0747978	+	0.163784i	0.943337	−	0.331836i	$-0.107668\pi$
$487$	1.65064	+	3.61440i	0.0747978	+	0.163784i	−0.868539	+	0.495620i	$0.834941\pi$
$488$	11.2968	−	7.26004i	0.511384	−	0.328647i
$489$	−33.4210	−	9.81328i	−1.51135	−	0.443772i
$490$	5.03486	+	5.81054i	0.227452	+	0.262494i
$491$	14.3685	−	4.21899i	0.648443	−	0.190400i	0.0590611	−	0.998254i	$-0.481189\pi$
$491$	14.3685	−	4.21899i	0.648443	−	0.190400i	0.589382	+	0.807854i	$0.299371\pi$
$492$	61.3582	+	18.0164i	2.76624	+	0.812241i
$493$	−0.231650	+	0.507242i	−0.0104330	+	0.0228450i
$494$	−0.00117815	−	0.00819418i	−5.30073e−5	−	0.000368674i
$495$	−11.1070	+	24.3210i	−0.499223	+	1.09315i
$496$	8.90500	+	10.2769i	0.399846	+	0.461447i
$497$	9.31326	−	64.7751i	0.417757	−	2.90556i
$498$	−7.40853			−0.331984
$499$	16.1561			0.723247			0.361623	−	0.932324i	$-0.382223\pi$
$499$	16.1561			0.723247			0.361623	+	0.932324i	$0.382223\pi$
$500$	−1.54313	+	10.7327i	−0.0690109	+	0.479981i
$501$	50.8203	−	14.9222i	2.27049	−	0.666675i
$502$	5.00856	−	3.21881i	0.223543	−	0.143662i
$503$	5.74861	−	3.69441i	0.256318	−	0.164726i	−0.406171	−	0.913797i	$-0.633136\pi$
$503$	5.74861	−	3.69441i	0.256318	−	0.164726i	0.662489	+	0.749071i	$0.269500\pi$
$504$	27.7679	−	8.15339i	1.23688	−	0.363181i
$505$	4.74117	−	32.9755i	0.210979	−	1.46739i
$506$	−1.32703			−0.0589936
$507$	39.8097			1.76801
$508$	1.74435	−	12.1322i	0.0773932	−	0.538282i
$509$	2.15355	+	2.48533i	0.0954546	+	0.110161i	0.801467	−	0.598039i	$-0.204053\pi$
$509$	2.15355	+	2.48533i	0.0954546	+	0.110161i	−0.706012	+	0.708199i	$0.749508\pi$
$510$	2.07293	−	4.53908i	0.0917909	−	0.200994i
$511$	1.51203	+	10.5164i	0.0668881	+	0.465217i
$512$	−7.99069	+	17.4972i	−0.353142	+	0.773273i
$513$	−28.6568	−	8.41440i	−1.26523	−	0.371505i
$514$	−8.22973	+	2.41647i	−0.362998	+	0.106586i
$515$	−8.35334	−	9.64027i	−0.368092	−	0.424801i
$516$	−36.3329	−	10.6683i	−1.59947	−	0.469646i
$517$	−6.09034	+	3.91402i	−0.267853	+	0.172138i
$518$	3.65426	+	8.00172i	0.160559	+	0.351576i
$519$	−4.26503	+	9.33910i	−0.187214	+	0.409941i
$520$	−0.0208149	+	0.0240217i	−0.000912794	+	0.00105342i
$521$	−15.6407	+	10.0517i	−0.685233	+	0.440373i	−0.836388	−	0.548137i	$-0.815337\pi$
$521$	−15.6407	+	10.0517i	−0.685233	+	0.440373i	0.151155	+	0.988510i	$0.451701\pi$
$522$	0.207788	+	0.454992i	0.00909463	+	0.0199145i
$523$	−1.50374	−	10.4587i	−0.0657540	−	0.457329i	−0.995924	−	0.0901992i	$-0.971250\pi$
$523$	−1.50374	−	10.4587i	−0.0657540	−	0.457329i	0.930170	−	0.367130i	$-0.119659\pi$
$524$	−2.00547	−	13.9484i	−0.0876095	−	0.609338i
$525$	−24.4950	+	28.2687i	−1.06905	+	1.23375i
$526$	6.90600	−	2.02778i	0.301116	−	0.0884156i
$527$	−6.57609	−	4.22620i	−0.286459	−	0.184096i
$528$	−2.27371	+	15.8140i	−0.0989503	+	0.688215i
$529$	−11.0224	−	7.08365i	−0.479234	−	0.307985i
$530$	2.02911	+	2.34172i	0.0881389	+	0.101718i
$531$	6.51810	−	7.52229i	0.282862	−	0.326440i
$532$	−9.36372	−	20.5037i	−0.405969	−	0.888948i
$533$	0.105174	+	0.0308818i	0.00455558	+	0.00133764i
$534$	9.85765	+	6.33512i	0.426582	+	0.274148i
$535$	20.7972			0.899140
$536$	9.09401	+	0.814672i	0.392802	+	0.0351885i
$537$	26.1895			1.13016
$538$	7.35847	+	4.72900i	0.317246	+	0.203882i
$539$	13.5774	+	3.98670i	0.584822	+	0.171719i
$540$	23.3261	+	51.0771i	1.00380	+	2.19801i
$541$	−18.0418	+	20.8213i	−0.775677	+	0.895179i	−0.996789	−	0.0800694i	$-0.974486\pi$
$541$	−18.0418	+	20.8213i	−0.775677	+	0.895179i	0.221112	+	0.975248i	$0.429031\pi$
$542$	−5.08945	−	5.87353i	−0.218610	−	0.252290i
$543$	−17.1124	−	10.9975i	−0.734364	−	0.471947i
$544$	0.931123	−	6.47611i	0.0399216	−	0.277661i
$545$	−8.86730	−	5.69867i	−0.379833	−	0.244104i
$546$	0.0342695	−	0.0100624i	0.00146660	−	0.000430633i
$547$	−27.9553	+	32.2622i	−1.19528	+	1.37943i	−0.288692	+	0.957422i	$0.593220\pi$
$547$	−27.9553	+	32.2622i	−1.19528	+	1.37943i	−0.906592	+	0.422009i	$0.861325\pi$
$548$	0.832315	+	5.78888i	0.0355548	+	0.247289i
$549$	−10.9268	−	75.9975i	−0.466344	−	3.24349i
$550$	0.526130	+	1.15206i	0.0224343	+	0.0491242i
$551$	0.669316	−	0.430144i	0.0285138	−	0.0183247i
$552$	−7.03750	+	8.12171i	−0.299536	+	0.345683i
$553$	−4.78009	+	10.4669i	−0.203270	+	0.445100i
$554$	1.07763	+	2.35968i	0.0457841	+	0.100253i
$555$	−55.3665	+	35.5819i	−2.35018	+	1.51037i
$556$	10.5383	+	3.09433i	0.446925	+	0.131229i
$557$	−8.28692	−	9.56362i	−0.351128	−	0.405223i	0.552520	−	0.833500i	$-0.313666\pi$
$557$	−8.28692	−	9.56362i	−0.351128	−	0.405223i	−0.903648	+	0.428276i	$0.859121\pi$
$558$	−6.72777	+	1.97545i	−0.284809	+	0.0836276i
$559$	−0.0622781	−	0.0182865i	−0.00263408	−	0.000773436i
$560$	−16.8299	+	36.8523i	−0.711192	+	1.55729i
$561$	−1.30704	−	9.09069i	−0.0551834	−	0.383809i
$562$	2.74173	−	6.00355i	0.115653	−	0.253244i
$563$	−18.4953	−	21.3447i	−0.779482	−	0.899571i	0.217590	−	0.976040i	$-0.430181\pi$
$563$	−18.4953	−	21.3447i	−0.779482	−	0.899571i	−0.997072	+	0.0764698i	$0.975635\pi$
$564$	−4.08556	+	28.4157i	−0.172033	+	1.19652i
$565$	21.2624			0.894515
$566$	6.34615			0.266749
$567$	7.26117	−	50.5025i	0.304940	−	2.12091i
$568$	−17.2173	+	5.05546i	−0.722423	+	0.212122i
$569$	4.27215	−	2.74554i	0.179098	−	0.115099i	−0.448020	−	0.894023i	$-0.647871\pi$
$569$	4.27215	−	2.74554i	0.179098	−	0.115099i	0.627118	+	0.778924i	$0.284234\pi$
$570$	−5.98941	+	3.84916i	−0.250869	+	0.161224i
$571$	−10.9228	+	3.20723i	−0.457106	+	0.134218i	−0.502176	−	0.864766i	$-0.667467\pi$
$571$	−10.9228	+	3.20723i	−0.457106	+	0.134218i	0.0450703	+	0.998984i	$0.485649\pi$
$572$	−0.00407672	+	0.0283542i	−0.000170456	+	0.00118555i
$573$	−20.2539			−0.846119
$574$	−12.6000			−0.525915
$575$	1.34436	−	9.35020i	0.0560635	−	0.389930i
$576$	25.5635	+	29.5019i	1.06515	+	1.22924i
$577$	11.9869	−	26.2476i	0.499019	−	1.09270i	−0.477768	−	0.878486i	$-0.658554\pi$
$577$	11.9869	−	26.2476i	0.499019	−	1.09270i	0.976787	−	0.214214i	$-0.0687189\pi$
$578$	−0.522720	−	3.63559i	−0.0217423	−	0.151221i
$579$	−8.74091	+	19.1399i	−0.363260	+	0.795428i
$580$	−1.43523	−	0.421421i	−0.0595946	−	0.0174986i
$581$	−33.1762	+	9.74141i	−1.37638	+	0.404142i
$582$	6.20202	+	7.15751i	0.257082	+	0.296688i
$583$	5.47187	+	1.60669i	0.226622	+	0.0665422i
$584$	2.45080	−	1.57504i	0.101415	−	0.0651754i
$585$	0.0754952	+	0.165312i	0.00312134	+	0.00683479i
$586$	1.07132	−	2.34587i	0.0442559	−	0.0969070i
$587$	2.33510	−	2.69485i	0.0963799	−	0.111228i	−0.705511	−	0.708699i	$-0.749282\pi$
$587$	2.33510	−	2.69485i	0.0963799	−	0.111228i	0.801890	+	0.597471i	$0.203828\pi$
$588$	47.2053	−	30.3370i	1.94671	−	1.25108i
$589$	4.63317	+	10.1452i	0.190906	+	0.418027i
$590$	−0.178835	−	1.24382i	−0.00736252	−	0.0512074i
$591$	5.86246	+	40.7743i	0.241149	+	1.67723i
$592$	−17.5149	+	20.2132i	−0.719856	+	0.830759i
$593$	−33.5086	+	9.83901i	−1.37603	+	0.404040i	−0.884386	−	0.466756i	$-0.845423\pi$
$593$	−33.5086	+	9.83901i	−1.37603	+	0.404040i	−0.491646	+	0.870795i	$0.663605\pi$
$594$	−3.67040	−	2.35883i	−0.150599	−	0.0967838i
$595$	3.31440	−	23.0522i	0.135877	−	0.945047i
$596$	−15.1013	−	9.70505i	−0.618575	−	0.397534i
$597$	39.4891	+	45.5729i	1.61618	+	1.86517i
$598$	−0.00590679	+	0.00681680i	−0.000241547	+	0.000278760i
$599$	−17.4056	−	38.1130i	−0.711174	−	1.55725i	−0.825874	−	0.563854i	$-0.809318\pi$
$599$	−17.4056	−	38.1130i	−0.711174	−	1.55725i	0.114700	−	0.993400i	$-0.463409\pi$
$600$	9.84106	+	2.88960i	0.401760	+	0.117967i
$601$	−23.4890	−	15.0954i	−0.958135	−	0.615756i	−0.0346538	−	0.999399i	$-0.511033\pi$
$601$	−23.4890	−	15.0954i	−0.958135	−	0.615756i	−0.923481	+	0.383643i	$0.874669\pi$
$602$	7.46104			0.304089
$603$	25.8368	−	45.3620i	1.05216	−	1.84728i
$604$	−24.8819			−1.01243
$605$	−20.9514	−	13.4647i	−0.851797	−	0.547417i
$606$	9.84895	+	2.89191i	0.400086	+	0.117476i
$607$	−1.26977	−	2.78042i	−0.0515385	−	0.112854i	0.882111	−	0.471042i	$-0.156122\pi$
$607$	−1.26977	−	2.78042i	−0.0515385	−	0.112854i	−0.933649	+	0.358188i	$0.883395\pi$
$608$	−6.11309	+	7.05489i	−0.247919	+	0.286113i
$609$	2.24787	+	2.59418i	0.0910883	+	0.105121i
$610$	−8.15453	−	5.24060i	−0.330167	−	0.212186i
$611$	−0.00700305	+	0.0487073i	−0.000283313	+	0.00197048i
$612$	−20.8364	−	13.3907i	−0.842261	−	0.541288i
$613$	5.57157	−	1.63596i	0.225034	−	0.0660759i	−0.167272	−	0.985911i	$-0.553496\pi$
$613$	5.57157	−	1.63596i	0.225034	−	0.0660759i	0.392306	+	0.919835i	$0.371678\pi$
$614$	−5.20600	+	6.00805i	−0.210097	+	0.242465i
$615$	−13.4160	−	93.3107i	−0.540987	−	3.76265i
$616$	−0.957016	−	6.65619i	−0.0385593	−	0.268186i
$617$	11.6498	+	25.5095i	0.469003	+	1.02697i	0.985342	+	0.170589i	$0.0545671\pi$
$617$	11.6498	+	25.5095i	0.469003	+	1.02697i	−0.516339	+	0.856384i	$0.672706\pi$
$618$	3.30637	−	2.12488i	0.133002	−	0.0854750i
$619$	2.37014	−	2.73528i	0.0952639	−	0.109940i	−0.706116	−	0.708096i	$-0.749554\pi$
$619$	2.37014	−	2.73528i	0.0952639	−	0.109940i	0.801380	+	0.598156i	$0.204100\pi$
$620$	8.71070	−	19.0738i	0.349830	−	0.766021i
$621$	13.5183	+	29.6010i	0.542471	+	1.18785i
$622$	−2.41366	+	1.55117i	−0.0967791	+	0.0621962i
$623$	52.4736	+	15.4076i	2.10231	+	0.617294i
$624$	0.0711140	+	0.0820700i	0.00284684	+	0.00328543i
$625$	29.7418	−	8.73297i	1.18967	−	0.349319i
$626$	−5.15941	−	1.51494i	−0.206212	−	0.0605492i
$627$	−5.44349	+	11.9196i	−0.217392	+	0.476022i
$628$	−4.01617	−	27.9331i	−0.160263	−	1.11465i
$629$	6.38699	−	13.9856i	0.254666	−	0.557640i
$630$	−13.6802	−	15.7878i	−0.545032	−	0.629000i
$631$	−0.549487	+	3.82177i	−0.0218747	+	0.152142i	−0.997831	−	0.0658229i	$-0.979033\pi$
$631$	−0.549487	+	3.82177i	−0.0218747	+	0.152142i	0.975957	+	0.217965i	$0.0699419\pi$
$632$	3.15520			0.125507
$633$	30.7064			1.22047
$634$	−0.198484	+	1.38049i	−0.00788280	+	0.0548261i
$635$	−17.3368	+	5.09056i	−0.687992	+	0.202013i
$636$	19.0243	−	12.2262i	0.754362	−	0.484799i
$637$	0.0809144	−	0.0520005i	0.00320594	−	0.00206034i
$638$	0.111519	−	0.0327448i	0.00441506	−	0.00129638i
$639$	−14.6011	+	101.553i	−0.577611	+	4.01737i
$640$	23.2197			0.917838
$641$	1.92023			0.0758446			0.0379223	−	0.999281i	$-0.487926\pi$
$641$	1.92023			0.0758446			0.0379223	+	0.999281i	$0.487926\pi$
$642$	−0.911943	+	6.34270i	−0.0359915	+	0.250327i
$643$	10.5843	+	12.2149i	0.417403	+	0.481708i	0.925044	−	0.379860i	$-0.124028\pi$
$643$	10.5843	+	12.2149i	0.417403	+	0.481708i	−0.507641	+	0.861569i	$0.669482\pi$
$644$	−10.2024	+	22.3401i	−0.402031	+	0.880325i
$645$	7.94423	+	55.2534i	0.312804	+	2.17560i
$646$	0.690928	−	1.51292i	0.0271842	−	0.0595251i
$647$	−23.5861	−	6.92551i	−0.927266	−	0.272270i	−0.216974	−	0.976177i	$-0.569619\pi$
$647$	−23.5861	−	6.92551i	−0.927266	−	0.272270i	−0.710292	+	0.703908i	$0.751437\pi$
$648$	−13.4236	+	3.94154i	−0.527330	+	0.154838i
$649$	−1.51457	−	1.74790i	−0.0594520	−	0.0686112i
$650$	0.00825991	+	0.00242533i	0.000323980	+	9.51292e-5i
$651$	−40.4800	+	26.0149i	−1.58654	+	1.01961i
$652$	9.06739	+	19.8548i	0.355107	+	0.777575i
$653$	−8.25562	+	18.0773i	−0.323067	+	0.707419i	−0.999579	−	0.0290130i	$-0.990764\pi$
$653$	−8.25562	+	18.0773i	−0.323067	+	0.707419i	0.676512	+	0.736432i	$0.263491\pi$
$654$	2.12680	−	2.45446i	0.0831645	−	0.0959769i
$655$	−17.4758	+	11.2310i	−0.682836	+	0.438832i
$656$	−15.9145	−	34.8480i	−0.621358	−	1.36058i
$657$	−2.37052	−	16.4873i	−0.0924828	−	0.643232i
$658$	−0.804994	−	5.59886i	−0.0313820	−	0.218266i
$659$	5.13298	−	5.92377i	0.199952	−	0.230757i	−0.646914	−	0.762563i	$-0.723941\pi$
$659$	5.13298	−	5.92377i	0.199952	−	0.230757i	0.846867	+	0.531806i	$0.178486\pi$
$660$	23.6380	−	6.94075i	0.920109	−	0.270168i
$661$	−18.9258	−	12.1629i	−0.736128	−	0.473080i	0.118086	−	0.993003i	$-0.462324\pi$
$661$	−18.9258	−	12.1629i	−0.736128	−	0.473080i	−0.854213	+	0.519923i	$0.825961\pi$
$662$	−0.222229	+	1.54564i	−0.00863717	+	0.0600729i
$663$	−0.0525157	−	0.0337498i	−0.00203954	−	0.00131073i
$664$	6.20878	+	7.16531i	0.240947	+	0.278068i
$665$	−21.7600	+	25.1124i	−0.843817	+	0.973816i
$666$	−5.72907	−	12.5449i	−0.221997	−	0.486106i
$667$	−0.831764	−	0.244228i	−0.0322060	−	0.00945655i
$668$	−27.9219	−	17.9443i	−1.08033	−	0.694287i
$669$	30.7258			1.18793
$670$	−2.19204	−	6.21551i	−0.0846860	−	0.240126i
$671$	−17.8406			−0.688729
$672$	−33.8810	−	21.7740i	−1.30699	−	0.839951i
$673$	10.5428	+	3.09565i	0.406395	+	0.119328i	0.478540	−	0.878066i	$-0.341166\pi$
$673$	10.5428	+	3.09565i	0.406395	+	0.119328i	−0.0721446	+	0.997394i	$0.522984\pi$
$674$	2.86312	+	6.26937i	0.110283	+	0.241487i
$675$	20.3385	−	23.4719i	0.782831	−	0.903435i
$676$	−16.3366	−	18.8534i	−0.628329	−	0.725131i
$677$	15.4366	+	9.92048i	0.593275	+	0.381275i	0.802553	−	0.596581i	$-0.203475\pi$
$677$	15.4366	+	9.92048i	0.593275	+	0.381275i	−0.209277	+	0.977856i	$0.567111\pi$
$678$	−0.932342	+	6.48458i	−0.0358064	+	0.249039i
$679$	37.1846	+	23.8971i	1.42702	+	0.917087i
$680$	−6.12730	+	1.79914i	−0.234971	+	0.0689938i
$681$	24.5540	−	28.3368i	0.940911	−	1.08587i
$682$	0.231871	+	1.61270i	0.00887881	+	0.0617535i
$683$	−3.88859	−	27.0458i	−0.148793	−	1.03488i	−0.918200	−	0.396118i	$-0.870357\pi$
$683$	−3.88859	−	27.0458i	−0.148793	−	1.03488i	0.769407	−	0.638759i	$-0.220552\pi$
$684$	14.6802	+	32.1452i	0.561313	+	1.22910i
$685$	7.25284	−	4.66112i	0.277117	−	0.178092i
$686$	−1.93252	+	2.23025i	−0.0737841	+	0.0851513i
$687$	1.01260	−	2.21728i	0.0386331	−	0.0845946i
$688$	9.42370	+	20.6350i	0.359275	+	0.786703i
$689$	0.0326095	−	0.0209568i	0.00124232	−	0.000798392i
$690$	7.44309	+	2.18549i	0.283353	+	0.0832001i
$691$	1.46966	+	1.69608i	0.0559085	+	0.0645219i	0.783015	−	0.622003i	$-0.213681\pi$
$691$	1.46966	+	1.69608i	0.0559085	+	0.0645219i	−0.727106	+	0.686525i	$0.759135\pi$
$692$	6.17311	−	1.81259i	0.234667	−	0.0689043i
$693$	−36.8912	−	10.8322i	−1.40138	−	0.411482i
$694$	−1.21482	+	2.66008i	−0.0461138	+	0.100975i
$695$	−2.30422	−	16.0262i	−0.0874040	−	0.607908i
$696$	0.391000	−	0.856170i	0.0148208	−	0.0324531i
$697$	14.4217	+	16.6435i	0.546261	+	0.630419i
$698$	−0.155018	+	1.07818i	−0.00586753	+	0.0408096i
$699$	54.7494			2.07081
$700$	23.4396			0.885935
$701$	4.63910	−	32.2657i	0.175217	−	1.21866i	−0.692433	−	0.721482i	$-0.743461\pi$
$701$	4.63910	−	32.2657i	0.175217	−	1.21866i	0.867650	−	0.497176i	$-0.165630\pi$
$702$	−0.0284545	+	0.00835500i	−0.00107395	+	0.000315339i
$703$	−18.4542	+	11.8598i	−0.696014	+	0.447301i
$704$	7.63073	−	4.90397i	0.287594	−	0.184825i
$705$	40.6057	−	11.9229i	1.52930	−	0.449043i
$706$	0.657938	−	4.57606i	0.0247618	−	0.172222i
$707$	47.9072			1.80174
$708$	−9.17122			−0.344675
$709$	−0.225061	+	1.56533i	−0.00845233	+	0.0587872i	−0.993611	−	0.112858i	$-0.963999\pi$
$709$	−0.225061	+	1.56533i	−0.00845233	+	0.0587872i	0.985159	+	0.171646i	$0.0549084\pi$
$710$	8.48232	+	9.78912i	0.318336	+	0.367379i
$711$	7.49412	−	16.4098i	0.281052	−	0.615417i
$712$	−2.13413	−	14.8432i	−0.0799800	−	0.556273i
$713$	5.04815	−	11.0539i	0.189055	−	0.413972i
$714$	6.88510	+	2.02165i	0.257668	+	0.0756582i
$715$	0.0405179	−	0.0118971i	0.00151528	−	0.000444927i
$716$	−10.7473	−	12.4031i	−0.401646	−	0.463524i
$717$	−65.5930	−	19.2598i	−2.44962	−	0.719272i
$718$	−3.79885	+	2.44137i	−0.141772	+	0.0911113i
$719$	18.5731	+	40.6695i	0.692660	+	1.51671i	0.848649	+	0.528956i	$0.177416\pi$
$719$	18.5731	+	40.6695i	0.692660	+	1.51671i	−0.155989	+	0.987759i	$0.549856\pi$
$720$	26.3855	−	57.7762i	0.983330	−	2.15319i
$721$	12.0123	−	13.8629i	0.447362	−	0.516283i
$722$	2.55314	−	1.64080i	0.0950179	−	0.0610643i
$723$	6.05336	+	13.2550i	0.225127	+	0.492959i
$724$	1.81408	+	12.6172i	0.0674199	+	0.468916i
$725$	0.117744	+	0.818929i	0.00437291	+	0.0304142i
$726$	5.02515	−	5.79934i	0.186501	−	0.215234i
$727$	−5.42861	+	1.59398i	−0.201336	+	0.0591176i	−0.380846	−	0.924639i	$-0.624367\pi$
$727$	−5.42861	+	1.59398i	−0.201336	+	0.0591176i	0.179510	+	0.983756i	$0.442549\pi$
$728$	−0.0384519	−	0.0247116i	−0.00142512	−	0.000915871i
$729$	2.13975	−	14.8823i	0.0792500	−	0.551196i
$730$	−1.76909	−	1.13693i	−0.0654770	−	0.0420795i
$731$	−8.53973	−	9.85537i	−0.315853	−	0.364514i
$732$	−46.3283	+	53.4657i	−1.71234	+	1.97615i
$733$	17.5107	+	38.3430i	0.646771	+	1.41623i	0.894352	+	0.447364i	$0.147637\pi$
$733$	17.5107	+	38.3430i	0.646771	+	1.41623i	−0.247581	+	0.968867i	$0.579636\pi$
$734$	5.66812	+	1.66431i	0.209214	+	0.0614308i
$735$	−69.5880	−	44.7215i	−2.56679	−	1.64958i
$736$	10.1711			0.374910
$737$	−9.57878	−	7.44249i	−0.352839	−	0.274147i
$738$	19.7541			0.727157
$739$	−9.55981	−	6.14372i	−0.351663	−	0.226000i	0.352868	−	0.935673i	$-0.385206\pi$
$739$	−9.55981	−	6.14372i	−0.351663	−	0.226000i	−0.704531	+	0.709673i	$0.748843\pi$
$740$	39.5717	+	11.6193i	1.45469	+	0.427134i
$741$	0.0369998	+	0.0810183i	0.00135922	+	0.00297628i
$742$	−2.91791	+	3.36745i	−0.107120	+	0.123623i
$743$	25.8966	+	29.8862i	0.950053	+	1.09642i	0.995241	+	0.0974409i	$0.0310657\pi$
$743$	25.8966	+	29.8862i	0.950053	+	1.09642i	−0.0451885	+	0.998978i	$0.514389\pi$
$744$	11.0997	+	7.13337i	0.406936	+	0.261522i
$745$	−3.76602	+	26.1933i	−0.137976	+	0.959647i
$746$	−2.99973	−	1.92781i	−0.109828	−	0.0705822i
$747$	52.0129	−	15.2724i	1.90305	−	0.558786i
$748$	−3.76888	+	4.34952i	−0.137804	+	0.159034i
$749$	4.25618	+	29.6024i	0.155518	+	1.08165i
$750$	0.700906	+	4.87491i	0.0255935	+	0.178006i
$751$	−16.5173	−	36.1678i	−0.602725	−	1.31978i	−0.927440	−	0.373971i	$-0.877996\pi$
$751$	−16.5173	−	36.1678i	−0.602725	−	1.31978i	0.324716	−	0.945812i	$-0.394731\pi$
$752$	14.4680	−	9.29804i	0.527595	−	0.339065i
$753$	−41.9473	+	48.4097i	−1.52864	+	1.76415i
$754$	0.000328178	0	0.000718610i	1.19516e−5	0	2.61702e-5i
$755$	15.2373	+	33.3651i	0.554543	+	1.21428i
$756$	−67.9288	+	43.6552i	−2.47054	+	1.58772i
$757$	−0.148147	−	0.0434999i	−0.00538450	−	0.00158103i	0.279039	−	0.960280i	$-0.409984\pi$
$757$	−0.148147	−	0.0434999i	−0.00538450	−	0.00158103i	−0.284424	+	0.958699i	$0.591802\pi$
$758$	−4.18202	−	4.82631i	−0.151898	−	0.175300i
$759$	13.6991	−	4.02241i	0.497244	−	0.146004i
$760$	8.74227	+	2.56696i	0.317115	+	0.0931135i
$761$	−19.0824	+	41.7846i	−0.691735	+	1.51469i	0.157977	+	0.987443i	$0.449503\pi$
$761$	−19.0824	+	41.7846i	−0.691735	+	1.51469i	−0.849713	+	0.527246i	$0.823225\pi$
$762$	−0.792304	−	5.51060i	−0.0287021	−	0.199628i
$763$	6.29669	−	13.7878i	0.227956	−	0.499153i
$764$	8.31153	+	9.59202i	0.300701	+	0.347027i
$765$	−5.19624	+	36.1407i	−0.187871	+	1.30667i
$766$	−4.72916			−0.170872
$767$	−0.0157203			−0.000567629
$768$	4.31683	−	30.0242i	0.155770	−	1.08341i
$769$	25.8792	−	7.59881i	0.933227	−	0.274020i	0.220440	−	0.975401i	$-0.429251\pi$
$769$	25.8792	−	7.59881i	0.933227	−	0.274020i	0.712787	+	0.701381i	$0.247433\pi$
$770$	−4.08355	+	2.62434i	−0.147161	+	0.0945745i
$771$	77.6318	−	49.8909i	2.79584	−	1.79678i
$772$	12.6514	−	3.71479i	0.455335	−	0.133698i
$773$	2.84244	−	19.7696i	0.102235	−	0.711063i	−0.872648	−	0.488349i	$-0.837599\pi$
$773$	2.84244	−	19.7696i	0.102235	−	0.711063i	0.974884	−	0.222714i	$-0.0714916\pi$
$774$	−11.6972			−0.420449
$775$	−11.5979			−0.416610
$776$	1.72488	−	11.9968i	0.0619196	−	0.430661i
$777$	−61.9777	−	71.5261i	−2.22344	−	2.56598i
$778$	−2.99224	+	6.55210i	−0.107277	+	0.234904i
$779$	−4.47170	−	31.1014i	−0.160215	−	1.11432i
$780$	0.0695623	−	0.152320i	0.00249073	−	0.00545394i
$781$	22.8742	+	6.71646i	0.818502	+	0.240334i
$782$	−1.73879	+	0.510554i	−0.0621789	+	0.0182574i
$783$	−1.86644	−	2.15399i	−0.0667011	−	0.0769772i
$784$	−32.2542	−	9.47069i	−1.15194	−	0.338239i
$785$	−34.9972	+	22.4913i	−1.24910	+	0.802749i
$786$	−2.65893	−	5.82223i	−0.0948407	−	0.207672i
$787$	−7.65781	+	16.7683i	−0.272971	+	0.597724i	−0.995620	−	0.0934916i	$-0.970197\pi$
$787$	−7.65781	+	16.7683i	−0.272971	+	0.597724i	0.722649	+	0.691215i	$0.242924\pi$
$788$	16.9045	−	19.5088i	0.602197	−	0.694972i
$789$	−65.1449	+	41.8661i	−2.31922	+	1.49047i
$790$	−0.946130	−	2.07173i	−0.0336618	−	0.0737090i
$791$	4.35139	+	30.2646i	0.154718	+	1.07608i
$792$	1.50039	+	10.4354i	0.0533139	+	0.370807i
$793$	−0.0794111	+	0.0916453i	−0.00281997	+	0.00325442i
$794$	−5.11493	+	1.50188i	−0.181522	+	0.0532996i
$795$	−28.0448	−	18.0233i	−0.994646	−	0.639220i
$796$	5.37776	−	37.4032i	0.190610	−	1.32572i
$797$	24.7200	+	15.8866i	0.875628	+	0.562732i	0.899469	−	0.436984i	$-0.143953\pi$
$797$	24.7200	+	15.8866i	0.875628	+	0.562732i	−0.0238415	+	0.999716i	$0.507590\pi$
$798$	−6.70459	−	7.73751i	−0.237340	−	0.273905i
$799$	−6.47422	+	7.47165i	−0.229042	+	0.264328i
$800$	−4.03254	−	8.83004i	−0.142572	−	0.312189i
$801$	−82.2669	−	24.1557i	−2.90676	−	0.853501i
$802$	−1.59759	−	1.02671i	−0.0564130	−	0.0362544i
$803$	−3.87045			−0.136585
$804$	−47.1781	+	9.37964i	−1.66384	+	0.330794i
$805$	36.2046			1.27604
$806$	0.00931636	+	0.00598726i	0.000328155	+	0.000210892i
$807$	−90.2965	−	26.5135i	−3.17859	−	0.933318i
$808$	−5.45702	−	11.9492i	−0.191977	−	0.420372i
$809$	10.8504	−	12.5220i	0.381480	−	0.440251i	−0.532241	−	0.846593i	$-0.678650\pi$
$809$	10.8504	−	12.5220i	0.381480	−	0.440251i	0.913721	+	0.406341i	$0.133196\pi$
$810$	6.61332	+	7.63217i	0.232368	+	0.268167i
$811$	−22.2700	−	14.3121i	−0.782006	−	0.502565i	0.0876930	−	0.996148i	$-0.472051\pi$
$811$	−22.2700	−	14.3121i	−0.782006	−	0.502565i	−0.869699	+	0.493583i	$0.835687\pi$
$812$	0.306123	−	2.12913i	0.0107428	−	0.0747178i
$813$	70.3424	+	45.2063i	2.46702	+	1.58545i
$814$	−3.07476	+	0.902831i	−0.107770	+	0.0316442i
$815$	21.0714	−	24.3177i	0.738098	−	0.851811i
$816$	3.10498	+	21.5956i	0.108696	+	0.755997i
$817$	2.64789	+	18.4165i	0.0926381	+	0.644312i
$818$	−0.0692587	−	0.151655i	−0.00242157	−	0.00530251i
$819$	−0.219852	+	0.141290i	−0.00768225	+	0.00493708i
$820$	−38.6853	+	44.6453i	−1.35095	+	1.55908i
$821$	−4.16136	+	9.11211i	−0.145232	+	0.318015i	−0.968243	−	0.250012i	$-0.919566\pi$
$821$	−4.16136	+	9.11211i	−0.145232	+	0.318015i	0.823010	+	0.568026i	$0.192293\pi$
$822$	1.10351	+	2.41635i	0.0384894	+	0.0842800i
$823$	−0.417751	+	0.268472i	−0.0145619	+	0.00935835i	−0.547902	−	0.836543i	$-0.684573\pi$
$823$	−0.417751	+	0.268472i	−0.0145619	+	0.00935835i	0.533340	+	0.845901i	$0.320937\pi$
$824$	−4.82605	−	1.41705i	−0.168123	−	0.0493654i
$825$	−8.92336	−	10.2981i	−0.310672	−	0.358534i
$826$	1.73384	−	0.509102i	0.0603281	−	0.0177139i
$827$	28.5098	+	8.37123i	0.991382	+	0.291096i	0.736915	−	0.675985i	$-0.236282\pi$
$827$	28.5098	+	8.37123i	0.991382	+	0.291096i	0.254467	+	0.967081i	$0.418100\pi$
$828$	15.9951	−	35.0244i	0.555868	−	1.21718i
$829$	−5.46848	−	38.0341i	−0.189928	−	1.32098i	−0.832189	−	0.554492i	$-0.812913\pi$
$829$	−5.46848	−	38.0341i	−0.189928	−	1.32098i	0.642261	−	0.766486i	$-0.277997\pi$
$830$	2.84303	−	6.22536i	0.0986829	−	0.216085i
$831$	−18.2770	−	21.0928i	−0.634023	−	0.731701i
$832$	0.00877428	−	0.0610265i	0.000304194	−	0.00211571i
$833$	19.3242			0.669543
$834$	4.98870			0.172744
$835$	−6.96326	+	48.4305i	−0.240974	+	1.67601i
$836$	7.87880	−	2.31342i	0.272494	−	0.0800114i
$837$	33.6112	−	21.6006i	1.16177	−	0.746625i
$838$	6.38506	−	4.10343i	0.220568	−	0.141751i
$839$	−29.5182	+	8.66731i	−1.01908	+	0.299229i	−0.748263	−	0.663402i	$-0.769112\pi$
$839$	−29.5182	+	8.66731i	−1.01908	+	0.299229i	−0.270817	+	0.962631i	$0.587294\pi$
$840$	−5.59435	+	38.9096i	−0.193024	+	1.34251i
$841$	−28.9241			−0.997382
$842$	−3.90967			−0.134736
$843$	−10.1056	+	70.2858i	−0.348055	+	2.42077i
$844$	−12.6009	−	14.5422i	−0.433740	−	0.500563i
$845$	−15.2770	+	33.4519i	−0.525544	+	1.15078i
$846$	1.26205	+	8.77777i	0.0433902	+	0.301786i
$847$	14.8777	−	32.5776i	0.511203	−	1.11938i
$848$	−12.9988	−	3.81680i	−0.446382	−	0.131070i
$849$	−65.5120	+	19.2361i	−2.24837	+	0.660180i
$850$	1.13262	+	1.30711i	0.0388486	+	0.0448336i
$851$	22.9332	+	6.73379i	0.786140	+	0.230832i
$852$	79.5275	−	51.1092i	2.72457	−	1.75097i
$853$	10.6994	+	23.4285i	0.366341	+	0.802176i	0.999601	+	0.0282364i	$0.00898912\pi$
$853$	10.6994	+	23.4285i	0.366341	+	0.802176i	−0.633260	+	0.773939i	$0.718284\pi$
$854$	5.79056	−	12.6796i	0.198149	−	0.433885i
$855$	34.1148	−	39.3706i	1.16670	−	1.34645i
$856$	6.89873	−	4.43355i	0.235794	−	0.151536i
$857$	21.0500	+	46.0931i	0.719055	+	1.57451i	0.815224	+	0.579146i	$0.196614\pi$
$857$	21.0500	+	46.0931i	0.719055	+	1.57451i	−0.0961687	+	0.995365i	$0.530659\pi$
$858$	0.00185169	+	0.0128788i	6.32157e−5	+	0.000439675i
$859$	−6.17804	−	42.9692i	−0.210792	−	1.46609i	−0.770521	−	0.637414i	$-0.780004\pi$
$859$	−6.17804	−	42.9692i	−0.210792	−	1.46609i	0.559729	−	0.828675i	$-0.310905\pi$
$860$	22.9073	−	26.4364i	0.781132	−	0.901475i
$861$	130.072	−	38.1924i	4.43283	−	1.30159i
$862$	9.78406	+	6.28783i	0.333246	+	0.214164i
$863$	3.63412	−	25.2759i	0.123707	−	0.860401i	−0.829591	−	0.558371i	$-0.811427\pi$
$863$	3.63412	−	25.2759i	0.123707	−	0.860401i	0.953298	−	0.302030i	$-0.0976644\pi$
$864$	28.1319	+	18.0793i	0.957068	+	0.615070i
$865$	−6.21091	−	7.16777i	−0.211177	−	0.243712i
$866$	1.73223	−	1.99910i	0.0588636	−	0.0679322i
$867$	16.4161	+	35.9462i	0.557519	+	1.22080i
$868$	28.9320	+	8.49520i	0.982016	+	0.288346i
$869$	−3.52641	−	2.26629i	−0.119625	−	0.0768785i
$870$	−0.679417			−0.0230344
$871$	−0.0808678	+	0.0160776i	−0.00274010	+	0.000544769i
$872$	−4.15626			−0.140749
$873$	−58.2972	−	37.4654i	−1.97306	−	1.26801i
$874$	2.48086	+	0.728445i	0.0839162	+	0.0246400i
$875$	9.54870	+	20.9087i	0.322805	+	0.706844i
$876$	−10.0507	+	11.5991i	−0.339582	+	0.391899i
$877$	−1.65794	−	1.91337i	−0.0559847	−	0.0646098i	0.727066	−	0.686567i	$-0.240883\pi$
$877$	−1.65794	−	1.91337i	−0.0559847	−	0.0646098i	−0.783051	+	0.621957i	$0.786338\pi$
$878$	3.32412	+	2.13628i	0.112184	+	0.0720960i
$879$	−3.94872	+	27.4640i	−0.133187	+	0.926337i
$880$	−12.4159	−	7.97920i	−0.418539	−	0.268979i
$881$	−3.71354	+	1.09039i	−0.125112	+	0.0367363i	−0.343689	−	0.939083i	$-0.611677\pi$
$881$	−3.71354	+	1.09039i	−0.125112	+	0.0367363i	0.218577	+	0.975820i	$0.429859\pi$
$882$	11.3511	−	13.0999i	0.382212	−	0.441096i
$883$	−4.60683	−	32.0412i	−0.155032	−	1.07827i	−0.907623	−	0.419785i	$-0.862105\pi$
$883$	−4.60683	−	32.0412i	−0.155032	−	1.07827i	0.752591	−	0.658488i	$-0.228804\pi$
$884$	0.00556718	+	0.0387206i	0.000187245	+	0.00130232i
$885$	5.61633	+	12.2981i	0.188791	+	0.413395i
$886$	1.45867	−	0.937428i	0.0490048	−	0.0314935i
$887$	−16.8679	+	19.4666i	−0.566368	+	0.653623i	−0.964617	−	0.263654i	$-0.915072\pi$
$887$	−16.8679	+	19.4666i	−0.566368	+	0.653623i	0.398250	+	0.917277i	$0.369618\pi$
$888$	−10.7806	+	23.6061i	−0.361772	+	0.792169i
$889$	−10.7939	−	23.6352i	−0.362014	−	0.792700i
$890$	−9.10626	+	5.85224i	−0.305242	+	0.196167i
$891$	17.8340	+	5.23655i	0.597463	+	0.175431i
$892$	−12.6088	−	14.5514i	−0.422175	−	0.487216i
$893$	13.5343	−	3.97403i	0.452908	−	0.132986i
$894$	−7.82326	−	2.29712i	−0.261649	−	0.0768271i
$895$	−10.0503	+	22.0070i	−0.335943	+	0.735612i
$896$	4.75195	+	33.0506i	0.158752	+	1.10414i
$897$	0.0403138	−	0.0882749i	0.00134604	−	0.00294741i
$898$	2.77228	+	3.19939i	0.0925123	+	0.106765i
$899$	−0.151470	+	1.05349i	−0.00505179	+	0.0351360i
$900$	−36.7481			−1.22494
$901$	7.78787			0.259452
$902$	0.653242	−	4.54339i	0.0217506	−	0.151278i
$903$	−77.0211	+	22.6154i	−2.56310	+	0.752594i
$904$	7.05305	−	4.53272i	0.234581	−	0.150756i
$905$	15.8080	−	10.1592i	0.525477	−	0.337704i
$906$	−10.8438	+	3.18403i	−0.360261	+	0.105782i
$907$	−6.31827	+	43.9446i	−0.209795	+	1.45916i	0.564029	+	0.825755i	$0.309250\pi$
$907$	−6.31827	+	43.9446i	−0.209795	+	1.45916i	−0.773824	+	0.633400i	$0.781659\pi$
$908$	−23.4961			−0.779746
$909$	−75.1078			−2.49117
$910$	−0.00469552	+	0.0326580i	−0.000155655	+	0.00108260i
$911$	18.2200	+	21.0270i	0.603654	+	0.696654i	0.972518	−	0.232829i	$-0.0747983\pi$
$911$	18.2200	+	21.0270i	0.603654	+	0.696654i	−0.368863	+	0.929484i	$0.620253\pi$
$912$	12.9314	−	28.3158i	0.428201	−	0.937630i
$913$	−1.79261	−	12.4679i	−0.0593269	−	0.412627i
$914$	4.69193	−	10.2739i	0.155195	−	0.339830i
$915$	100.065	+	29.3818i	3.30805	+	0.971331i
$916$	−1.46562	+	0.430344i	−0.0484253	+	0.0142190i
$917$	−19.5625	−	22.5764i	−0.646012	−	0.745538i
$918$	−5.71680	−	1.67860i	−0.188683	−	0.0554022i
$919$	14.9149	−	9.58524i	0.491998	−	0.316188i	−0.271010	−	0.962576i	$-0.587358\pi$
$919$	14.9149	−	9.58524i	0.491998	−	0.316188i	0.763009	+	0.646388i	$0.223721\pi$
$920$	−4.12400	−	9.03029i	−0.135964	−	0.297720i
$921$	35.5309	−	77.8018i	1.17078	−	2.56366i
$922$	1.11003	−	1.28105i	0.0365570	−	0.0421890i
$923$	0.136318	−	0.0876061i	0.00448696	−	0.00288359i
$924$	14.7169	+	32.2256i	0.484152	+	1.06015i
$925$	−3.24641	−	22.5793i	−0.106741	−	0.742403i
$926$	1.20620	+	8.38927i	0.0396380	+	0.275689i
$927$	−18.8326	+	21.7340i	−0.618544	+	0.713838i
$928$	−0.854738	+	0.250974i	−0.0280581	+	0.00823861i
$929$	43.3880	+	27.8837i	1.42351	+	0.914836i	0.999960	+	0.00896445i	$0.00285351\pi$
$929$	43.3880	+	27.8837i	1.42351	+	0.914836i	0.423553	+	0.905871i	$0.360783\pi$
$930$	1.35543	−	9.42724i	0.0444464	−	0.309131i
$931$	−23.1944	−	14.9061i	−0.760165	−	0.488528i
$932$	−22.4673	−	25.9287i	−0.735942	−	0.849322i
$933$	20.2147	−	23.3290i	0.661800	−	0.763758i
$934$	2.39097	+	5.23548i	0.0782348	+	0.171310i
$935$	8.14045	+	2.39025i	0.266221	+	0.0781696i
$936$	0.0602841	+	0.0387422i	0.00197045	+	0.00126633i
$937$	−30.9105			−1.00980			−0.504901	−	0.863177i	$-0.668471\pi$
$937$	−30.9105			−1.00980			−0.504901	+	0.863177i	$0.668471\pi$
$938$	8.39847	−	4.39214i	0.274220	−	0.143409i
$939$	57.8532			1.88797
$940$	−22.3098	−	14.3376i	−0.727665	−	0.467642i
$941$	6.58079	+	1.93229i	0.214528	+	0.0629910i	0.387230	−	0.921983i	$-0.373432\pi$
$941$	6.58079	+	1.93229i	0.214528	+	0.0629910i	−0.172703	+	0.984974i	$0.555250\pi$
$942$	−5.32478	−	11.6596i	−0.173491	−	0.379892i
$943$	−22.4195	+	25.8735i	−0.730079	+	0.842556i
$944$	3.59797	+	4.15227i	0.117104	+	0.135145i
$945$	100.138	+	64.3546i	3.25748	+	2.09345i
$946$	−0.386813	+	2.69034i	−0.0125764	+	0.0874706i
$947$	−14.6439	−	9.41103i	−0.475861	−	0.305817i	0.280636	−	0.959814i	$-0.409455\pi$
$947$	−14.6439	−	9.41103i	−0.475861	−	0.305817i	−0.756497	+	0.653997i	$0.773091\pi$
$948$	−15.9491	+	4.68307i	−0.518001	+	0.152099i
$949$	−0.0172279	+	0.0198821i	−0.000559241	+	0.000645399i
$950$	−0.351189	−	2.44257i	−0.0113941	−	0.0792475i
$951$	−2.13547	−	14.8525i	−0.0692474	−	0.481627i
$952$	−3.81483	−	8.35332i	−0.123639	−	0.270733i
$953$	32.0915	−	20.6239i	1.03954	−	0.668074i	0.0946702	−	0.995509i	$-0.469820\pi$
$953$	32.0915	−	20.6239i	1.03954	−	0.668074i	0.944874	+	0.327434i	$0.106184\pi$
$954$	4.57463	−	5.27940i	0.148109	−	0.170927i
$955$	7.77245	−	17.0193i	0.251511	−	0.550731i
$956$	17.7959	+	38.9677i	0.575562	+	1.26030i
$957$	−1.05196	+	0.676056i	−0.0340052	+	0.0218538i
$958$	−4.91003	−	1.44172i	−0.158636	−	0.0465797i
$959$	8.11889	+	9.36969i	0.262173	+	0.302563i
$960$	−50.8759	+	14.9385i	−1.64201	+	0.482138i
$961$	15.4287	+	4.53028i	0.497701	+	0.146138i
$962$	−0.00904845	+	0.0198133i	−0.000291734	+	0.000638808i
$963$	−6.67275	−	46.4100i	−0.215026	−	1.49554i
$964$	3.79332	−	8.30621i	0.122175	−	0.267525i
$965$	−12.7289	−	14.6899i	−0.409757	−	0.472885i
$966$	−1.58755	+	11.0417i	−0.0510786	+	0.355259i
$967$	−39.9520			−1.28477			−0.642386	−	0.766382i	$-0.722055\pi$
$967$	−39.9520			−1.28477			−0.642386	+	0.766382i	$0.722055\pi$
$968$	−9.82031			−0.315637
$969$	−2.54665	+	17.7124i	−0.0818103	+	0.569003i
$970$	−8.39446	+	2.46484i	−0.269530	+	0.0791411i
$971$	−17.1296	+	11.0085i	−0.549714	+	0.353280i	−0.785827	−	0.618446i	$-0.787763\pi$
$971$	−17.1296	+	11.0085i	−0.549714	+	0.353280i	0.236114	+	0.971725i	$0.424126\pi$
$972$	11.9095	−	7.65374i	0.381996	−	0.245494i
$973$	22.3399	−	6.55959i	0.716185	−	0.210291i
$974$	0.160954	−	1.11946i	0.00515729	−	0.0358698i
$975$	−0.0926194			−0.00296620
$976$	42.3817			1.35660
$977$	4.76577	−	33.1467i	0.152471	−	1.06046i	−0.759591	−	0.650402i	$-0.774601\pi$
$977$	4.76577	−	33.1467i	0.152471	−	1.06046i	0.912061	−	0.410054i	$-0.134490\pi$
$978$	6.49242	+	7.49265i	0.207605	+	0.239588i
$979$	−8.27624	+	18.1224i	−0.264510	+	0.579195i
$980$	7.37701	+	51.3082i	0.235650	+	1.63898i
$981$	−9.87181	+	21.6163i	−0.315183	+	0.690154i
$982$	−4.08971	−	1.20085i	−0.130508	−	0.0383206i
$983$	19.7184	−	5.78984i	0.628919	−	0.184667i	0.0482872	−	0.998833i	$-0.484624\pi$
$983$	19.7184	−	5.78984i	0.628919	−	0.184667i	0.580632	+	0.814166i	$0.302806\pi$
$984$	−24.3423	−	28.0925i	−0.776004	−	0.895557i
$985$	−36.5122	−	10.7210i	−1.16338	−	0.341598i
$986$	0.133523	−	0.0858101i	0.00425224	−	0.00273275i
$987$	25.2810	+	55.3576i	0.804702	+	1.76205i
$988$	0.0231858	−	0.0507699i	0.000737640	−	0.00161521i
$989$	13.2756	−	15.3208i	0.422139	−	0.487174i
$990$	6.40209	−	4.11438i	0.203472	−	0.130763i
$991$	8.98326	+	19.6706i	0.285363	+	0.624857i	0.996976	−	0.0777147i	$-0.0247623\pi$
$991$	8.98326	+	19.6706i	0.285363	+	0.624857i	−0.711613	+	0.702572i	$0.752035\pi$
$992$	−1.77719	−	12.3606i	−0.0564257	−	0.392449i
$993$	−2.39094	−	16.6294i	−0.0758743	−	0.527717i
$994$	−12.1978	+	14.0770i	−0.386890	+	0.446495i
$995$	−53.4487	+	15.6939i	−1.69444	+	0.497532i
$996$	−42.0195	−	27.0043i	−1.33144	−	0.855663i
$997$	−6.62652	+	46.0884i	−0.209864	+	1.45964i	0.563733	+	0.825957i	$0.309365\pi$
$997$	−6.62652	+	46.0884i	−0.209864	+	1.45964i	−0.773597	+	0.633678i	$0.781544\pi$
$998$	−3.86851	−	2.48614i	−0.122456	−	0.0786974i
$999$	51.4610	+	59.3892i	1.62815	+	1.87899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.9.2	✓	20
3.2	odd	2		603.2.u.c.478.2		20
67.15	even	11	inner	67.2.e.c.15.2	yes	20
67.22	even	11		4489.2.a.l.1.5		10
67.45	odd	22		4489.2.a.m.1.6		10
201.149	odd	22		603.2.u.c.82.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.9.2	✓	20	1.1	even	1	trivial
67.2.e.c.15.2	yes	20	67.15	even	11	inner
603.2.u.c.82.2		20	201.149	odd	22
603.2.u.c.478.2		20	3.2	odd	2
4489.2.a.l.1.5		10	67.22	even	11
4489.2.a.m.1.6		10	67.45	odd	22

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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.239446 - 0.153882i) q^{2} +(2.93826 + 0.862752i) q^{3} +(-0.797176 - 1.74557i) q^{4} +(-1.85253 + 2.13793i) q^{5} +(-0.570792 - 0.658729i) q^{6} +(-3.42222 - 2.19933i) q^{7} +(-0.158746 + 1.10411i) q^{8} +(5.36529 + 3.44806i) q^{9} +O(q^{10})\)	\(q+(-0.239446 - 0.153882i) q^{2} +(2.93826 + 0.862752i) q^{3} +(-0.797176 - 1.74557i) q^{4} +(-1.85253 + 2.13793i) q^{5} +(-0.570792 - 0.658729i) q^{6} +(-3.42222 - 2.19933i) q^{7} +(-0.158746 + 1.10411i) q^{8} +(5.36529 + 3.44806i) q^{9} +(0.772569 - 0.226847i) q^{10} +(0.970471 - 1.11998i) q^{11} +(-0.836317 - 5.81671i) q^{12} +(-0.00143353 - 0.00997040i) q^{13} +(0.480999 + 1.05324i) q^{14} +(-7.28771 + 4.68353i) q^{15} +(-2.30542 + 2.66060i) q^{16} +(0.840698 - 1.84087i) q^{17} +(-0.754099 - 1.65125i) q^{18} +(-2.42907 + 1.56107i) q^{19} +(5.20870 + 1.52941i) q^{20} +(-8.15792 - 9.41474i) q^{21} +(-0.404721 + 0.118837i) q^{22} +(3.01862 + 0.886347i) q^{23} +(-1.41901 + 3.10719i) q^{24} +(-0.427315 - 2.97204i) q^{25} +(-0.00119102 + 0.00260796i) q^{26} +(6.77364 + 7.81720i) q^{27} +(-1.11097 + 7.72699i) q^{28} -0.275544 q^{29} +2.46572 q^{30} +(0.549710 - 3.82332i) q^{31} +(3.10199 - 0.910828i) q^{32} +(3.81776 - 2.45353i) q^{33} +(-0.484579 + 0.311420i) q^{34} +(11.0418 - 3.24216i) q^{35} +(1.74176 - 12.1142i) q^{36} +7.59724 q^{37} +0.821851 q^{38} +(0.00438990 - 0.0305324i) q^{39} +(-2.06642 - 2.38477i) q^{40} +(-4.52056 + 9.89865i) q^{41} +(0.504616 + 3.50968i) q^{42} +(2.67682 - 5.86142i) q^{43} +(-2.72864 - 0.801202i) q^{44} +(-17.3110 + 5.08298i) q^{45} +(-0.586403 - 0.676745i) q^{46} +(-4.68730 - 1.37632i) q^{47} +(-9.06938 + 5.82853i) q^{48} +(3.96666 + 8.68578i) q^{49} +(-0.355026 + 0.777398i) q^{50} +(4.05841 - 4.68365i) q^{51} +(-0.0162613 + 0.0104505i) q^{52} +(1.59861 + 3.50047i) q^{53} +(-0.418990 - 2.91414i) q^{54} +(0.596622 + 4.14960i) q^{55} +(2.97156 - 3.42936i) q^{56} +(-8.48405 + 2.49114i) q^{57} +(0.0659780 + 0.0424015i) q^{58} +(0.222104 - 1.54477i) q^{59} +(13.9850 + 8.98763i) q^{60} +(-7.88361 - 9.09818i) q^{61} +(-0.719967 + 0.830886i) q^{62} +(-10.7778 - 23.6001i) q^{63} +(5.87283 + 1.72442i) q^{64} +(0.0239717 + 0.0154057i) q^{65} -1.29170 q^{66} +(-0.437339 - 8.17366i) q^{67} -3.88356 q^{68} +(8.10480 + 5.20864i) q^{69} +(-3.14282 - 0.922814i) q^{70} +(6.68270 + 14.6331i) q^{71} +(-4.65874 + 5.37648i) q^{72} +(-1.71032 - 1.97381i) q^{73} +(-1.81913 - 1.16908i) q^{74} +(1.30857 - 9.10129i) q^{75} +(4.66135 + 2.99567i) q^{76} +(-5.78438 + 1.69845i) q^{77} +(-0.00574955 + 0.00663533i) q^{78} +(-0.402553 - 2.79982i) q^{79} +(-1.41732 - 9.85767i) q^{80} +(5.21023 + 11.4088i) q^{81} +(2.60566 - 1.67455i) q^{82} +(5.56611 - 6.42364i) q^{83} +(-9.93080 + 21.7454i) q^{84} +(2.37824 + 5.20762i) q^{85} +(-1.54292 + 0.991577i) q^{86} +(-0.809622 - 0.237726i) q^{87} +(1.08252 + 1.24930i) q^{88} +(-12.8991 + 3.78752i) q^{89} +(4.92724 + 1.44677i) q^{90} +(-0.0170224 + 0.0372738i) q^{91} +(-0.859189 - 5.97579i) q^{92} +(4.91376 - 10.7596i) q^{93} +(0.910563 + 1.05085i) q^{94} +(1.16246 - 8.08510i) q^{95} +9.90029 q^{96} -10.8656 q^{97} +(0.386788 - 2.69017i) q^{98} +(9.06862 - 2.66279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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