LMFDB - Embedded newform 38.4.e.b.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 165 x^{16} - 56 x^{15} + 18435 x^{14} - 11748 x^{13} + 1092662 x^{12} - 1833567 x^{11} + \cdots + 3892796082289 $ x^18 + 165x^16 - 56x^15 + 18435x^14 - 11748x^13 + 1092662x^12 - 1833567x^11 + 46842546x^10 - 93643115x^9 + 1273086000x^8 - 3159018183x^7 + 24752942108x^6 - 51265274250x^5 + 247917053361x^4 - 421854393530x^3 + 1634375353605x^2 - 2066139456366x + 3892796082289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.2
Root			$1.11938 + 1.93882i$ of defining polynomial
Character	$\chi$	$=$	38.23
Dual form			38.4.e.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 + 0.684040i) q^{2} +(0.541460 + 3.07077i) q^{3} +(3.06418 + 2.57115i) q^{4} +(8.27240 - 6.94137i) q^{5} +(-1.08292 + 6.14154i) q^{6} +(-13.7717 + 23.8533i) q^{7} +(4.00000 + 6.92820i) q^{8} +(16.2353 - 5.90915i) q^{9} +O(q^{10})$	\(q+(1.87939 + 0.684040i) q^{2} +(0.541460 + 3.07077i) q^{3} +(3.06418 + 2.57115i) q^{4} +(8.27240 - 6.94137i) q^{5} +(-1.08292 + 6.14154i) q^{6} +(-13.7717 + 23.8533i) q^{7} +(4.00000 + 6.92820i) q^{8} +(16.2353 - 5.90915i) q^{9} +(20.2952 - 7.38685i) q^{10} +(-35.7617 - 61.9411i) q^{11} +(-6.23628 + 10.8016i) q^{12} +(4.04443 - 22.9371i) q^{13} +(-42.1989 + 35.4091i) q^{14} +(25.7945 + 21.6442i) q^{15} +(2.77837 + 15.7569i) q^{16} +(-19.6933 - 7.16777i) q^{17} +34.5544 q^{18} +(-73.6649 - 37.8482i) q^{19} +43.1954 q^{20} +(-80.7047 - 29.3741i) q^{21} +(-24.8398 - 140.874i) q^{22} +(76.3526 + 64.0674i) q^{23} +(-19.1091 + 16.0344i) q^{24} +(-1.45601 + 8.25742i) q^{25} +(23.2909 - 40.3411i) q^{26} +(69.0313 + 119.566i) q^{27} +(-103.529 + 37.6816i) q^{28} +(-15.1843 + 5.52662i) q^{29} +(33.6723 + 58.3222i) q^{30} +(3.55074 - 6.15006i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(170.843 - 143.354i) q^{33} +(-32.1082 - 26.9420i) q^{34} +(51.6494 + 292.918i) q^{35} +(64.9410 + 23.6366i) q^{36} +214.770 q^{37} +(-112.555 - 121.521i) q^{38} +72.6244 q^{39} +(81.1808 + 29.5474i) q^{40} +(49.0074 + 277.935i) q^{41} +(-131.582 - 110.411i) q^{42} +(-293.698 + 246.441i) q^{43} +(49.6796 - 281.747i) q^{44} +(93.2869 - 161.578i) q^{45} +(99.6712 + 172.636i) q^{46} +(83.8608 - 30.5228i) q^{47} +(-46.8815 + 17.0635i) q^{48} +(-207.819 - 359.954i) q^{49} +(-8.38480 + 14.5229i) q^{50} +(11.3474 - 64.3546i) q^{51} +(71.3675 - 59.8845i) q^{52} +(-394.308 - 330.864i) q^{53} +(47.9486 + 271.930i) q^{54} +(-725.791 - 264.166i) q^{55} -220.347 q^{56} +(76.3366 - 246.701i) q^{57} -32.3175 q^{58} +(760.688 + 276.868i) q^{59} +(23.3886 + 132.643i) q^{60} +(-485.384 - 407.286i) q^{61} +(10.8801 - 9.12948i) q^{62} +(-82.6344 + 468.643i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-125.758 - 217.819i) q^{65} +(419.140 - 152.555i) q^{66} +(37.4928 - 13.6463i) q^{67} +(-41.9143 - 72.5977i) q^{68} +(-155.394 + 269.151i) q^{69} +(-103.299 + 585.837i) q^{70} +(132.616 - 111.278i) q^{71} +(105.881 + 88.8445i) q^{72} +(94.1080 + 533.713i) q^{73} +(403.636 + 146.911i) q^{74} -26.1450 q^{75} +(-128.409 - 305.377i) q^{76} +1970.00 q^{77} +(136.489 + 49.6780i) q^{78} +(-164.688 - 933.994i) q^{79} +(132.358 + 111.062i) q^{80} +(27.5667 - 23.1312i) q^{81} +(-98.0149 + 555.870i) q^{82} +(-166.966 + 289.194i) q^{83} +(-171.768 - 297.512i) q^{84} +(-212.665 + 77.4036i) q^{85} +(-720.547 + 262.258i) q^{86} +(-25.1926 - 43.6349i) q^{87} +(286.093 - 495.528i) q^{88} +(-166.638 + 945.049i) q^{89} +(285.848 - 239.855i) q^{90} +(491.426 + 412.355i) q^{91} +(69.2309 + 392.628i) q^{92} +(20.8080 + 7.57349i) q^{93} +178.486 q^{94} +(-872.104 + 198.239i) q^{95} -99.7805 q^{96} +(-850.583 - 309.587i) q^{97} +(-144.350 - 818.648i) q^{98} +(-946.619 - 794.308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) $ 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$3$	0.541460	+	3.07077i	0.104204	+	0.590970i	0.991535	+	0.129838i	$0.0414456\pi$
$3$	0.541460	+	3.07077i	0.104204	+	0.590970i	−0.887331	+	0.461132i	$0.847443\pi$
$4$	3.06418	+	2.57115i	0.383022	+	0.321394i
$5$	8.27240	−	6.94137i	0.739906	−	0.620855i	−0.192906	−	0.981217i	$-0.561791\pi$
$5$	8.27240	−	6.94137i	0.739906	−	0.620855i	0.932812	+	0.360362i	$0.117347\pi$
$6$	−1.08292	+	6.14154i	−0.0736833	+	0.417879i
$7$	−13.7717	+	23.8533i	−0.743602	+	1.28796i	0.207243	+	0.978289i	$0.433551\pi$
$7$	−13.7717	+	23.8533i	−0.743602	+	1.28796i	−0.950845	+	0.309667i	$0.899783\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	16.2353	−	5.90915i	0.601306	−	0.218857i
$10$	20.2952	−	7.38685i	0.641791	−	0.233593i
$11$	−35.7617	−	61.9411i	−0.980232	−	1.69781i	−0.661460	−	0.749981i	$-0.730063\pi$
$11$	−35.7617	−	61.9411i	−0.980232	−	1.69781i	−0.318772	−	0.947831i	$-0.603271\pi$
$12$	−6.23628	+	10.8016i	−0.150022	+	0.259845i
$13$	4.04443	−	22.9371i	0.0862863	−	0.489354i	−0.910785	−	0.412880i	$-0.864523\pi$
$13$	4.04443	−	22.9371i	0.0862863	−	0.489354i	0.997072	−	0.0764736i	$-0.0243661\pi$
$14$	−42.1989	+	35.4091i	−0.805581	+	0.675963i
$15$	25.7945	+	21.6442i	0.444008	+	0.372567i
$16$	2.77837	+	15.7569i	0.0434120	+	0.246202i
$17$	−19.6933	−	7.16777i	−0.280960	−	0.102261i	0.197697	−	0.980263i	$-0.436654\pi$
$17$	−19.6933	−	7.16777i	−0.280960	−	0.102261i	−0.478657	+	0.878002i	$0.658876\pi$
$18$	34.5544			0.452475
$19$	−73.6649	−	37.8482i	−0.889467	−	0.456999i
$19$	−73.6649	−	37.8482i	−0.889467	−	0.456999i
$20$	43.1954			0.482939
$21$	−80.7047	−	29.3741i	−0.838630	−	0.305236i
$22$	−24.8398	−	140.874i	−0.240721	−	1.36520i
$23$	76.3526	+	64.0674i	0.692201	+	0.580825i	0.919543	−	0.392990i	$-0.128559\pi$
$23$	76.3526	+	64.0674i	0.692201	+	0.580825i	−0.227342	+	0.973815i	$0.573004\pi$
$24$	−19.1091	+	16.0344i	−0.162526	+	0.136376i
$25$	−1.45601	+	8.25742i	−0.0116480	+	0.0660593i
$26$	23.2909	−	40.3411i	0.175682	−	0.304290i
$27$	69.0313	+	119.566i	0.492040	+	0.852238i
$28$	−103.529	+	37.6816i	−0.698757	+	0.254327i
$29$	−15.1843	+	5.52662i	−0.0972292	+	0.0353885i	−0.390177	−	0.920740i	$-0.627586\pi$
$29$	−15.1843	+	5.52662i	−0.0972292	+	0.0353885i	0.292948	+	0.956129i	$0.405364\pi$
$30$	33.6723	+	58.3222i	0.204923	+	0.354938i
$31$	3.55074	−	6.15006i	0.0205720	−	0.0356317i	−0.855556	−	0.517710i	$-0.826785\pi$
$31$	3.55074	−	6.15006i	0.0205720	−	0.0356317i	0.876128	+	0.482078i	$0.160118\pi$
$32$	−5.55674	+	31.5138i	−0.0306970	+	0.174091i
$33$	170.843	−	143.354i	0.901212	−	0.756206i
$34$	−32.1082	−	26.9420i	−0.161956	−	0.135897i
$35$	51.6494	+	292.918i	0.249438	+	1.41464i
$36$	64.9410	+	23.6366i	0.300653	+	0.109429i
$37$	214.770			0.954270			0.477135	−	0.878830i	$-0.341675\pi$
$37$	214.770			0.954270			0.477135	+	0.878830i	$0.341675\pi$
$38$	−112.555	−	121.521i	−0.480495	−	0.518772i
$39$	72.6244			0.298185
$40$	81.1808	+	29.5474i	0.320895	+	0.116796i
$41$	49.0074	+	277.935i	0.186675	+	1.05869i	0.923784	+	0.382913i	$0.125079\pi$
$41$	49.0074	+	277.935i	0.186675	+	1.05869i	−0.737109	+	0.675773i	$0.763810\pi$
$42$	−131.582	−	110.411i	−0.483419	−	0.405636i
$43$	−293.698	+	246.441i	−1.04159	+	0.873999i	−0.992185	−	0.124779i	$-0.960178\pi$
$43$	−293.698	+	246.441i	−1.04159	+	0.873999i	−0.0494074	+	0.998779i	$0.515733\pi$
$44$	49.6796	−	281.747i	0.170216	−	0.965340i
$45$	93.2869	−	161.578i	0.309031	−	0.535257i
$46$	99.6712	+	172.636i	0.319472	+	0.553342i
$47$	83.8608	−	30.5228i	0.260263	−	0.0947279i	−0.208593	−	0.978002i	$-0.566888\pi$
$47$	83.8608	−	30.5228i	0.260263	−	0.0947279i	0.468856	+	0.883275i	$0.344666\pi$
$48$	−46.8815	+	17.0635i	−0.140974	+	0.0513104i
$49$	−207.819	−	359.954i	−0.605887	−	1.04943i
$50$	−8.38480	+	14.5229i	−0.0237158	+	0.0410770i
$51$	11.3474	−	64.3546i	0.0311561	−	0.176695i
$52$	71.3675	−	59.8845i	0.190325	−	0.159702i
$53$	−394.308	−	330.864i	−1.02193	−	0.857503i	−0.0320627	−	0.999486i	$-0.510208\pi$
$53$	−394.308	−	330.864i	−1.02193	−	0.857503i	−0.989869	+	0.141983i	$0.954652\pi$
$54$	47.9486	+	271.930i	0.120833	+	0.685278i
$55$	−725.791	−	264.166i	−1.77937	−	0.647639i
$56$	−220.347			−0.525806
$57$	76.3366	−	246.701i	0.177387	−	0.573269i
$58$	−32.3175			−0.0731637
$59$	760.688	+	276.868i	1.67853	+	0.610934i	0.993107	−	0.117212i	$-0.0373958\pi$
$59$	760.688	+	276.868i	1.67853	+	0.610934i	0.685421	+	0.728147i	$0.259618\pi$
$60$	23.3886	+	132.643i	0.0503242	+	0.285403i
$61$	−485.384	−	407.286i	−1.01880	−	0.854878i	−0.0293274	−	0.999570i	$-0.509337\pi$
$61$	−485.384	−	407.286i	−1.01880	−	0.854878i	−0.989477	+	0.144692i	$0.953781\pi$
$62$	10.8801	−	9.12948i	0.0222867	−	0.0187007i
$63$	−82.6344	+	468.643i	−0.165253	+	0.937198i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−125.758	−	217.819i	−0.239974	−	0.415647i
$66$	419.140	−	152.555i	0.781706	−	0.284518i
$67$	37.4928	−	13.6463i	0.0683652	−	0.0248829i	−0.307611	−	0.951512i	$-0.599530\pi$
$67$	37.4928	−	13.6463i	0.0683652	−	0.0248829i	0.375976	+	0.926629i	$0.377307\pi$
$68$	−41.9143	−	72.5977i	−0.0747479	−	0.129467i
$69$	−155.394	+	269.151i	−0.271120	+	0.469594i
$70$	−103.299	+	585.837i	−0.176380	+	1.00030i
$71$	132.616	−	111.278i	0.221670	−	0.186003i	−0.525189	−	0.850986i	$-0.676005\pi$
$71$	132.616	−	111.278i	0.221670	−	0.186003i	0.746859	+	0.664982i	$0.231561\pi$
$72$	105.881	+	88.8445i	0.173308	+	0.145423i
$73$	94.1080	+	533.713i	0.150884	+	0.855704i	0.962453	+	0.271448i	$0.0875024\pi$
$73$	94.1080	+	533.713i	0.150884	+	0.855704i	−0.811570	+	0.584256i	$0.801386\pi$
$74$	403.636	+	146.911i	0.634077	+	0.230785i
$75$	−26.1450			−0.0402528
$76$	−128.409	−	305.377i	−0.193809	−	0.460910i
$77$	1970.00			2.91561
$78$	136.489	+	49.6780i	0.198133	+	0.0721144i
$79$	−164.688	−	933.994i	−0.234543	−	1.33016i	−0.843574	−	0.537013i	$-0.819553\pi$
$79$	−164.688	−	933.994i	−0.234543	−	1.33016i	0.609031	−	0.793146i	$-0.291558\pi$
$80$	132.358	+	111.062i	0.184976	+	0.155214i
$81$	27.5667	−	23.1312i	0.0378144	−	0.0317300i
$82$	−98.0149	+	555.870i	−0.131999	+	0.748604i
$83$	−166.966	+	289.194i	−0.220806	+	0.382448i	−0.955053	−	0.296435i	$-0.904202\pi$
$83$	−166.966	+	289.194i	−0.220806	+	0.382448i	0.734247	+	0.678883i	$0.237536\pi$
$84$	−171.768	−	297.512i	−0.223113	−	0.386443i
$85$	−212.665	+	77.4036i	−0.271373	+	0.0987718i
$86$	−720.547	+	262.258i	−0.903471	+	0.328837i
$87$	−25.1926	−	43.6349i	−0.0310452	−	0.0537719i
$88$	286.093	−	495.528i	0.346564	−	0.600267i
$89$	−166.638	+	945.049i	−0.198467	+	1.12556i	0.708927	+	0.705282i	$0.249179\pi$
$89$	−166.638	+	945.049i	−0.198467	+	1.12556i	−0.907394	+	0.420280i	$0.861932\pi$
$90$	285.848	−	239.855i	0.334789	−	0.280921i
$91$	491.426	+	412.355i	0.566104	+	0.475017i
$92$	69.2309	+	392.628i	0.0784546	+	0.444938i
$93$	20.8080	+	7.57349i	0.0232009	+	0.00844445i
$94$	178.486			0.195844
$95$	−872.104	+	198.239i	−0.941852	+	0.214094i
$96$	−99.7805			−0.106081
$97$	−850.583	−	309.587i	−0.890347	−	0.324060i	−0.143969	−	0.989582i	$-0.545987\pi$
$97$	−850.583	−	309.587i	−0.890347	−	0.324060i	−0.746378	+	0.665522i	$0.768209\pi$
$98$	−144.350	−	818.648i	−0.148791	−	0.843837i
$99$	−946.619	−	794.308i	−0.960998	−	0.806373i
$100$	−25.6925	+	21.5586i	−0.0256925	+	0.0215586i
$101$	−37.3519	+	211.833i	−0.0367986	+	0.208695i	−0.997663	−	0.0683231i	$-0.978235\pi$
$101$	−37.3519	+	211.833i	−0.0367986	+	0.208695i	0.960865	+	0.277018i	$0.0893462\pi$
$102$	65.3473	−	113.185i	0.0634348	−	0.109872i
$103$	484.230	+	838.712i	0.463230	+	0.802337i	0.999120	−	0.0419506i	$-0.0133572\pi$
$103$	484.230	+	838.712i	0.463230	+	0.802337i	−0.535890	+	0.844288i	$0.680024\pi$
$104$	175.090	−	63.7277i	0.165087	−	0.0600867i
$105$	−871.519	+	317.207i	−0.810014	+	0.294821i
$106$	−514.733	−	891.543i	−0.471653	−	0.816928i
$107$	805.621	−	1395.38i	0.727872	−	1.26071i	−0.229909	−	0.973212i	$-0.573843\pi$
$107$	805.621	−	1395.38i	0.727872	−	1.26071i	0.957781	−	0.287499i	$-0.0928237\pi$
$108$	−95.8972	+	543.860i	−0.0854418	+	0.484565i
$109$	1191.35	−	999.663i	1.04689	−	0.878444i	0.0541255	−	0.998534i	$-0.482763\pi$
$109$	1191.35	−	999.663i	1.04689	−	0.878444i	0.992763	+	0.120090i	$0.0383184\pi$
$110$	−1183.34	−	992.940i	−1.02570	−	0.860665i
$111$	116.289	+	659.510i	0.0994387	+	0.563945i
$112$	−414.117	−	150.726i	−0.349379	−	0.127163i
$113$	469.062			0.390492			0.195246	−	0.980754i	$-0.437449\pi$
$113$	469.062			0.390492			0.195246	+	0.980754i	$0.437449\pi$
$114$	312.219	−	411.429i	0.256509	−	0.338016i
$115$	1076.33			0.872772
$116$	−60.7371	−	22.1065i	−0.0486146	−	0.0176943i
$117$	−69.8763	−	396.288i	−0.0552143	−	0.313136i
$118$	1240.24	+	1040.68i	0.967569	+	0.811887i
$119$	442.185	−	371.037i	0.340630	−	0.285823i
$120$	−46.7771	+	265.286i	−0.0355846	+	0.201810i
$121$	−1892.30	+	3277.55i	−1.42171	+	2.46247i
$122$	−633.624	−	1097.47i	−0.470210	−	0.814427i
$123$	−826.939	+	300.981i	−0.606200	+	0.220639i
$124$	26.6928	−	9.71539i	0.0193313	−	0.00703603i
$125$	720.201	+	1247.43i	0.515334	+	0.892585i
$126$	−475.873	+	824.236i	−0.336461	+	0.582768i
$127$	341.817	−	1938.54i	0.238830	−	1.35447i	−0.595567	−	0.803306i	$-0.703073\pi$
$127$	341.817	−	1938.54i	0.238830	−	1.35447i	0.834397	−	0.551164i	$-0.185816\pi$
$128$	−98.0537	+	82.2768i	−0.0677094	+	0.0568149i
$129$	−915.790	−	768.439i	−0.625045	−	0.524475i
$130$	−87.3503	−	495.388i	−0.0589318	−	0.334219i
$131$	−1676.60	−	610.232i	−1.11821	−	0.406994i	−0.284209	−	0.958762i	$-0.591731\pi$
$131$	−1676.60	−	610.232i	−1.11821	−	0.406994i	−0.833997	+	0.551768i	$0.813953\pi$
$132$	892.080			0.588224
$133$	1917.29	−	1235.91i	1.25000	−	0.805770i
$134$	79.7979			0.0514440
$135$	1401.00	+	509.924i	0.893179	+	0.325091i
$136$	−29.1134	−	165.110i	−0.0183562	−	0.104103i
$137$	−317.710	−	266.590i	−0.198130	−	0.166251i	0.538325	−	0.842737i	$-0.319057\pi$
$137$	−317.710	−	266.590i	−0.198130	−	0.166251i	−0.736455	+	0.676486i	$0.763502\pi$
$138$	−476.156	+	399.543i	−0.293718	+	0.246459i
$139$	−107.944	+	612.180i	−0.0658682	+	0.373557i	0.933999	+	0.357275i	$0.116294\pi$
$139$	−107.944	+	612.180i	−0.0658682	+	0.373557i	−0.999867	+	0.0162820i	$0.994817\pi$
$140$	−594.874	+	1030.35i	−0.359115	+	0.622005i
$141$	139.136	+	240.990i	0.0831018	+	0.143936i
$142$	325.355	−	118.419i	0.192276	−	0.0699826i
$143$	−1565.38	+	569.753i	−0.915412	+	0.333183i
$144$	138.218	+	239.400i	0.0799870	+	0.138542i
$145$	−87.2480	+	151.118i	−0.0499693	+	0.0865494i
$146$	−188.216	+	1067.43i	−0.106691	+	0.605074i
$147$	992.809	−	833.066i	0.557044	−	0.467416i
$148$	658.094	+	552.206i	0.365507	+	0.306696i
$149$	290.068	+	1645.06i	0.159485	+	0.904484i	0.954570	+	0.297987i	$0.0963151\pi$
$149$	290.068	+	1645.06i	0.159485	+	0.904484i	−0.795085	+	0.606498i	$0.792574\pi$
$150$	−49.1365	−	17.8842i	−0.0267465	−	0.00973494i
$151$	2042.23			1.10063			0.550313	−	0.834959i	$-0.314509\pi$
$151$	2042.23			1.10063			0.550313	+	0.834959i	$0.314509\pi$
$152$	−32.4393	−	661.758i	−0.0173103	−	0.353129i
$153$	−362.081			−0.191323
$154$	3702.38	+	1347.56i	1.93731	+	0.705125i
$155$	−13.3167	−	75.5227i	−0.00690079	−	0.0391363i
$156$	222.534	+	186.728i	0.114211	+	0.0958347i
$157$	−118.835	+	99.7148i	−0.0604083	+	0.0506886i	−0.672492	−	0.740104i	$-0.734776\pi$
$157$	−118.835	+	99.7148i	−0.0604083	+	0.0506886i	0.612084	+	0.790793i	$0.290332\pi$
$158$	329.377	−	1867.99i	0.165847	−	0.940565i
$159$	802.505	−	1389.98i	0.400269	−	0.693286i
$160$	172.782	+	299.267i	0.0853724	+	0.147869i
$161$	−2579.72	+	938.942i	−1.26280	+	0.459621i
$162$	67.6311	−	24.6157i	0.0328000	−	0.0119382i
$163$	−108.321	−	187.617i	−0.0520512	−	0.0901553i	0.838826	−	0.544400i	$-0.183243\pi$
$163$	−108.321	−	187.617i	−0.0520512	−	0.0901553i	−0.890877	+	0.454245i	$0.849909\pi$
$164$	−564.445	+	977.647i	−0.268755	+	0.465497i
$165$	418.207	−	2371.77i	0.197318	−	1.11904i
$166$	−511.614	+	429.295i	−0.239211	+	0.200722i
$167$	−138.294	−	116.043i	−0.0640810	−	0.0537703i	0.610185	−	0.792259i	$-0.291095\pi$
$167$	−138.294	−	116.043i	−0.0640810	−	0.0537703i	−0.674266	+	0.738489i	$0.735540\pi$
$168$	−119.309	−	676.635i	−0.0547910	−	0.310735i
$169$	1554.75	+	565.884i	0.707671	+	0.257571i
$170$	−452.626			−0.204205
$171$	−1419.62	−	179.179i	−0.634859	−	0.0801295i
$172$	−1533.58			−0.679851
$173$	−1203.91	−	438.188i	−0.529085	−	0.192571i	0.0636447	−	0.997973i	$-0.479728\pi$
$173$	−1203.91	−	438.188i	−0.529085	−	0.192571i	−0.592730	+	0.805401i	$0.701950\pi$
$174$	−17.4986	−	99.2396i	−0.00762395	−	0.0432376i
$175$	−176.915	−	148.449i	−0.0764200	−	0.0641240i
$176$	876.641	−	735.589i	0.375451	−	0.315041i
$177$	−438.316	+	2485.81i	−0.186135	+	1.05562i
$178$	−959.628	+	1662.12i	−0.404085	+	0.699896i
$179$	−1236.73	−	2142.09i	−0.516413	−	0.894453i	−0.999818	−	0.0190566i	$-0.993934\pi$
$179$	−1236.73	−	2142.09i	−0.516413	−	0.894453i	0.483406	−	0.875396i	$-0.339400\pi$
$180$	701.288	−	255.248i	0.290394	−	0.105695i
$181$	−892.256	+	324.755i	−0.366414	+	0.133364i	−0.518664	−	0.854978i	$-0.673570\pi$
$181$	−892.256	+	324.755i	−0.366414	+	0.133364i	0.152250	+	0.988342i	$0.451348\pi$
$182$	641.511	+	1111.13i	0.261275	+	0.452541i
$183$	987.864	−	1711.03i	0.399044	−	0.691164i
$184$	−138.462	+	785.256i	−0.0554758	+	0.314619i
$185$	1776.66	−	1490.80i	0.706070	−	0.592463i
$186$	33.9257	+	28.4670i	0.0133739	+	0.0112221i
$187$	260.286	+	1476.15i	0.101786	+	0.577257i
$188$	335.443	+	122.091i	0.130131	+	0.0473640i
$189$	−3802.71			−1.46353
$190$	−1774.62	−	223.986i	−0.677603	−	0.0855245i
$191$	−730.516			−0.276745			−0.138372	−	0.990380i	$-0.544187\pi$
$191$	−730.516			−0.276745			−0.138372	+	0.990380i	$0.544187\pi$
$192$	−187.526	−	68.2539i	−0.0704871	−	0.0256552i
$193$	−351.706	−	1994.62i	−0.131173	−	0.743918i	−0.977449	−	0.211173i	$-0.932272\pi$
$193$	−351.706	−	1994.62i	−0.131173	−	0.743918i	0.846276	−	0.532745i	$-0.178839\pi$
$194$	−1386.80	−	1163.67i	−0.513230	−	0.430651i
$195$	600.778	−	504.113i	0.220629	−	0.185129i
$196$	288.700	−	1637.30i	0.105211	−	0.596683i
$197$	2371.67	−	4107.86i	0.857739	−	1.48565i	−0.0163407	−	0.999866i	$-0.505202\pi$
$197$	2371.67	−	4107.86i	0.857739	−	1.48565i	0.874080	−	0.485782i	$-0.161465\pi$
$198$	−1235.72	−	2140.34i	−0.443530	−	0.768217i
$199$	−1395.19	+	507.807i	−0.496997	+	0.180892i	−0.578343	−	0.815794i	$-0.696300\pi$
$199$	−1395.19	+	507.807i	−0.496997	+	0.180892i	0.0813461	+	0.996686i	$0.474078\pi$
$200$	−63.0331	+	22.9422i	−0.0222856	+	0.00811128i
$201$	62.2053	+	107.743i	0.0218290	+	0.0378089i
$202$	−215.101	+	372.566i	−0.0749231	+	0.129771i
$203$	77.2851	−	438.305i	0.0267209	−	0.151542i
$204$	200.236	−	168.018i	0.0687221	−	0.0576647i
$205$	2334.66	+	1959.01i	0.795413	+	0.667430i
$206$	336.343	+	1907.50i	0.113758	+	0.645153i
$207$	1618.19	+	588.972i	0.543342	+	0.197760i
$208$	372.655			0.124226
$209$	290.021	+	5916.40i	0.0959864	+	1.95811i
$210$	−1854.90			−0.609526
$211$	−2594.14	−	944.188i	−0.846387	−	0.308060i	−0.117821	−	0.993035i	$-0.537591\pi$
$211$	−2594.14	−	944.188i	−0.846387	−	0.308060i	−0.728566	+	0.684975i	$0.759813\pi$
$212$	−357.530	−	2027.65i	−0.115827	−	0.656885i
$213$	413.515	+	346.980i	0.133021	+	0.111618i
$214$	2468.56	−	2071.37i	0.788540	−	0.661664i
$215$	−718.942	+	4077.33i	−0.228053	+	1.29335i
$216$	−552.250	+	956.525i	−0.173962	+	0.301312i
$217$	97.7994	+	169.393i	0.0305947	+	0.0529916i
$218$	2922.82	−	1063.82i	0.908066	−	0.330509i
$219$	−1587.95	+	577.968i	−0.489972	+	0.178335i
$220$	−1544.74	−	2675.57i	−0.473393	−	0.819940i
$221$	−244.056	+	422.717i	−0.0742849	+	0.128665i
$222$	−232.579	+	1319.02i	−0.0703138	+	0.398769i
$223$	−1565.58	+	1313.68i	−0.470130	+	0.394486i	−0.846842	−	0.531844i	$-0.821499\pi$
$223$	−1565.58	+	1313.68i	−0.470130	+	0.394486i	0.376712	+	0.926330i	$0.377055\pi$
$224$	−675.183	−	566.546i	−0.201395	−	0.168991i
$225$	25.1557	+	142.665i	0.00745354	+	0.0422711i
$226$	881.548	+	320.857i	0.259468	+	0.0944385i
$227$	6785.36			1.98397			0.991983	−	0.126368i	$-0.0403320\pi$
$227$	6785.36			1.98397			0.991983	+	0.126368i	$0.0403320\pi$
$228$	868.215	−	559.663i	0.252188	−	0.162564i
$229$	4473.40			1.29087			0.645437	−	0.763813i	$-0.276675\pi$
$229$	4473.40			1.29087			0.645437	+	0.763813i	$0.276675\pi$
$230$	2022.85	+	736.256i	0.579924	+	0.211075i
$231$	1066.67	+	6049.41i	0.303818	+	1.72304i
$232$	−99.0266	−	83.0932i	−0.0280233	−	0.0235144i
$233$	−236.787	+	198.688i	−0.0665769	+	0.0558647i	−0.675469	−	0.737388i	$-0.736059\pi$
$233$	−236.787	+	198.688i	−0.0665769	+	0.0558647i	0.608892	+	0.793253i	$0.291614\pi$
$234$	139.753	−	792.577i	0.0390424	−	0.221420i
$235$	481.860	−	834.606i	0.133758	−	0.231675i
$236$	1619.01	+	2804.22i	0.446563	+	0.773470i
$237$	2778.91	−	1011.44i	0.761644	−	0.277216i
$238$	1084.84	−	394.849i	0.295461	−	0.107539i
$239$	−148.745	−	257.634i	−0.0402573	−	0.0697277i	0.845195	−	0.534459i	$-0.179484\pi$
$239$	−148.745	−	257.634i	−0.0402573	−	0.0697277i	−0.885452	+	0.464731i	$0.846151\pi$
$240$	−269.379	+	466.578i	−0.0724514	+	0.125489i
$241$	459.572	−	2606.36i	0.122837	−	0.696641i	−0.859733	−	0.510744i	$-0.829370\pi$
$241$	459.572	−	2606.36i	0.122837	−	0.696641i	0.982569	−	0.185897i	$-0.0595190\pi$
$242$	−5798.33	+	4865.38i	−1.54021	+	1.29239i
$243$	2941.53	+	2468.24i	0.776541	+	0.651595i
$244$	−440.111	−	2495.99i	−0.115472	−	0.654875i
$245$	−4217.74	−	1535.13i	−1.09984	−	0.400310i
$246$	−1760.02			−0.456157
$247$	−1166.06	+	1536.58i	−0.300383	+	0.395832i
$248$	56.8118			0.0145466
$249$	−978.453	−	356.128i	−0.249024	−	0.0906373i
$250$	500.247	+	2837.04i	0.126553	+	0.717721i
$251$	−544.394	−	456.801i	−0.136900	−	0.114873i	0.571766	−	0.820416i	$-0.306258\pi$
$251$	−544.394	−	456.801i	−0.136900	−	0.114873i	−0.708666	+	0.705544i	$0.750703\pi$
$252$	−1458.16	+	1223.54i	−0.364505	+	0.305856i
$253$	1237.91	−	7020.52i	0.307615	−	1.74457i
$254$	1968.45	−	3409.45i	0.486265	−	0.842236i
$255$	−352.838	−	611.134i	−0.0866493	−	0.150081i
$256$	−240.561	+	87.5572i	−0.0587308	+	0.0213763i
$257$	4525.49	−	1647.14i	1.09841	−	0.399789i	0.271682	−	0.962387i	$-0.412420\pi$
$257$	4525.49	−	1647.14i	1.09841	−	0.399789i	0.826731	+	0.562598i	$0.190198\pi$
$258$	−1195.48	−	2070.63i	−0.288478	−	0.499658i
$259$	−2957.75	+	5122.97i	−0.709597	+	1.22906i
$260$	174.701	−	990.776i	0.0416710	−	0.236328i
$261$	−213.863	+	179.452i	−0.0507194	+	0.0425587i
$262$	−2733.55	−	2293.72i	−0.644578	−	0.540865i
$263$	−1168.56	−	6627.24i	−0.273979	−	1.55381i	−0.742185	−	0.670195i	$-0.766210\pi$
$263$	−1168.56	−	6627.24i	−0.273979	−	1.55381i	0.468205	−	0.883620i	$-0.344901\pi$
$264$	1676.56	+	610.219i	0.390853	+	0.142259i
$265$	−5558.52			−1.28852
$266$	4448.75	−	1011.25i	1.02545	−	0.233097i
$267$	−2992.26			−0.685854
$268$	149.971	+	54.5850i	0.0341826	+	0.0124415i
$269$	−401.999	−	2279.85i	−0.0911163	−	0.516746i	−0.995868	−	0.0908077i	$-0.971055\pi$
$269$	−401.999	−	2279.85i	−0.0911163	−	0.516746i	0.904752	−	0.425938i	$-0.140056\pi$
$270$	2284.22	+	1916.69i	0.514863	+	0.432021i
$271$	−4358.13	+	3656.91i	−0.976892	+	0.819709i	−0.983618	−	0.180268i	$-0.942303\pi$
$271$	−4358.13	+	3656.91i	−0.976892	+	0.819709i	0.00672598	+	0.999977i	$0.497859\pi$
$272$	58.2267	−	330.220i	0.0129798	−	0.0736123i
$273$	−1000.16	+	1732.33i	−0.221731	+	0.384049i
$274$	−414.741	−	718.353i	−0.0914432	−	0.158384i
$275$	563.542	−	205.113i	0.123574	−	0.0449773i
$276$	−1168.18	+	425.184i	−0.254770	+	0.0927286i
$277$	1438.56	+	2491.66i	0.312038	+	0.540466i	0.978803	−	0.204802i	$-0.0656550\pi$
$277$	1438.56	+	2491.66i	0.312038	+	0.540466i	−0.666765	+	0.745268i	$0.732322\pi$
$278$	−621.624	+	1076.68i	−0.134110	+	0.232285i
$279$	21.3055	−	120.830i	0.00457178	−	0.0259279i
$280$	−1822.80	+	1529.51i	−0.389047	+	0.326449i
$281$	−497.740	−	417.653i	−0.105668	−	0.0886658i	0.588423	−	0.808553i	$-0.299749\pi$
$281$	−497.740	−	417.653i	−0.105668	−	0.0886658i	−0.694091	+	0.719887i	$0.744193\pi$
$282$	96.6427	+	548.088i	0.0204078	+	0.115738i
$283$	290.883	+	105.873i	0.0610997	+	0.0222385i	0.372389	−	0.928077i	$-0.378539\pi$
$283$	290.883	+	105.873i	0.0610997	+	0.0222385i	−0.311289	+	0.950315i	$0.600761\pi$
$284$	692.470			0.144685
$285$	−1080.96	−	2570.69i	−0.224668	−	0.534297i
$286$	−3331.69			−0.688836
$287$	−7304.58	−	2658.65i	−1.50235	−	0.546812i
$288$	96.0049	+	544.471i	0.0196429	+	0.111400i
$289$	−3427.13	−	2875.70i	−0.697563	−	0.585325i
$290$	−267.343	+	224.328i	−0.0541343	+	0.0454241i
$291$	490.114	−	2779.57i	0.0987319	−	0.559936i
$292$	−1083.89	+	1877.36i	−0.217226	+	0.376247i
$293$	4703.26	+	8146.28i	0.937772	+	1.62427i	0.769615	+	0.638508i	$0.220448\pi$
$293$	4703.26	+	8146.28i	0.937772	+	1.62427i	0.168157	+	0.985760i	$0.446218\pi$
$294$	2435.72	−	886.530i	0.483177	−	0.175862i
$295$	8214.56	−	2989.85i	1.62125	−	0.590088i
$296$	859.081	+	1487.97i	0.168693	+	0.292184i
$297$	4937.35	−	8551.74i	0.964627	−	1.67078i
$298$	−580.135	+	3290.11i	−0.112773	+	0.639567i
$299$	1778.32	−	1492.19i	0.343957	−	0.288614i
$300$	−80.1129	−	67.2227i	−0.0154177	−	0.0129370i
$301$	−1833.72	−	10399.6i	−0.351143	−	1.99143i
$302$	3838.14	+	1396.97i	0.731325	+	0.266180i
$303$	−670.716			−0.127167
$304$	391.703	−	1265.89i	0.0739004	−	0.238828i
$305$	−6842.41			−1.28457
$306$	−680.489	−	247.678i	−0.127127	−	0.0462706i
$307$	1134.50	+	6434.08i	0.210910	+	1.19613i	0.887864	+	0.460106i	$0.152189\pi$
$307$	1134.50	+	6434.08i	0.210910	+	1.19613i	−0.676954	+	0.736026i	$0.736700\pi$
$308$	6036.42	+	5065.16i	1.11674	+	0.937059i
$309$	−2313.30	+	1941.09i	−0.425887	+	0.357361i
$310$	26.6334	−	151.045i	0.00487960	−	0.0276736i
$311$	2235.93	−	3872.75i	0.407679	−	0.706120i	−0.586950	−	0.809623i	$-0.699672\pi$
$311$	2235.93	−	3872.75i	0.407679	−	0.706120i	0.994629	+	0.103503i	$0.0330050\pi$
$312$	290.497	+	503.156i	0.0527121	+	0.0913001i
$313$	−7618.40	+	2772.87i	−1.37577	+	0.500741i	−0.920895	−	0.389811i	$-0.872540\pi$
$313$	−7618.40	+	2772.87i	−1.37577	+	0.500741i	−0.454880	+	0.890553i	$0.650318\pi$
$314$	−291.546	+	106.114i	−0.0523978	+	0.0190712i
$315$	2569.44	+	4450.40i	0.459592	+	0.796037i
$316$	1896.81	−	3285.36i	0.337670	−	0.584861i
$317$	−703.229	+	3988.21i	−0.124597	+	0.706625i	0.856949	+	0.515401i	$0.172357\pi$
$317$	−703.229	+	3988.21i	−0.124597	+	0.706625i	−0.981546	+	0.191225i	$0.938754\pi$
$318$	2459.02	−	2063.36i	0.433631	−	0.363860i
$319$	885.340	+	742.888i	0.155390	+	0.130388i
$320$	120.013	+	680.627i	0.0209654	+	0.118901i
$321$	4721.09	+	1718.34i	0.820889	+	0.298779i
$322$	−5490.57			−0.950240
$323$	1179.42	+	1273.37i	0.203172	+	0.219356i
$324$	143.943			0.0246816
$325$	183.512	+	66.7930i	0.0313213	+	0.0114000i
$326$	−75.2388	−	426.701i	−0.0127825	−	0.0724931i
$327$	3714.80	+	3117.09i	0.628224	+	0.527142i
$328$	−1729.56	+	1451.27i	−0.291155	+	0.244308i
$329$	−426.836	+	2420.71i	−0.0715265	+	0.405647i
$330$	2408.36	−	4171.40i	0.401745	−	0.695843i
$331$	1118.41	+	1937.14i	0.185720	+	0.321676i	0.943819	−	0.330463i	$-0.107205\pi$
$331$	1118.41	+	1937.14i	0.185720	+	0.321676i	−0.758099	+	0.652139i	$0.773872\pi$
$332$	−1255.18	+	456.846i	−0.207490	+	0.0755202i
$333$	3486.85	−	1269.11i	0.573808	−	0.208849i
$334$	−180.530	−	312.687i	−0.0295754	−	0.0512260i
$335$	215.432	−	373.138i	0.0351352	−	0.0608559i
$336$	238.618	−	1353.27i	0.0387431	−	0.219723i
$337$	−3581.21	+	3005.00i	−0.578876	+	0.485734i	−0.884578	−	0.466393i	$-0.845553\pi$
$337$	−3581.21	+	3005.00i	−0.578876	+	0.485734i	0.305702	+	0.952127i	$0.401109\pi$
$338$	2534.89	+	2127.03i	0.407929	+	0.342293i
$339$	253.978	+	1440.38i	0.0406908	+	0.230769i
$340$	−850.659	−	309.615i	−0.135687	−	0.0493859i
$341$	−507.921			−0.0806612
$342$	−2545.44	−	1307.82i	−0.402462	−	0.206781i
$343$	2000.72			0.314952
$344$	−2882.19	−	1049.03i	−0.451736	−	0.164418i
$345$	582.792	+	3305.18i	0.0909462	+	0.515782i
$346$	−1962.88	−	1647.05i	−0.304985	−	0.255913i
$347$	−2120.40	+	1779.23i	−0.328038	+	0.275257i	−0.791900	−	0.610651i	$-0.790908\pi$
$347$	−2120.40	+	1779.23i	−0.328038	+	0.275257i	0.463862	+	0.885908i	$0.346463\pi$
$348$	34.9973	−	198.479i	0.00539095	−	0.0305736i
$349$	5052.66	−	8751.46i	0.774965	−	1.34228i	−0.159850	−	0.987141i	$-0.551101\pi$
$349$	5052.66	−	8751.46i	0.774965	−	1.34228i	0.934814	−	0.355137i	$-0.115566\pi$
$350$	−230.946	−	400.010i	−0.0352702	−	0.0610898i
$351$	3021.68	−	1099.80i	0.459502	−	0.167245i
$352$	2150.72	−	782.798i	0.325664	−	0.118532i
$353$	−963.767	−	1669.29i	−0.145315	−	0.251693i	0.784176	−	0.620539i	$-0.213086\pi$
$353$	−963.767	−	1669.29i	−0.145315	−	0.251693i	−0.929490	+	0.368846i	$0.879753\pi$
$354$	−2524.16	+	4371.97i	−0.378976	+	0.656406i
$355$	324.630	−	1841.07i	0.0485340	−	0.275250i
$356$	−2940.47	+	2467.35i	−0.437766	+	0.367329i
$357$	1378.79	+	1156.95i	0.204408	+	0.171518i
$358$	−859.027	−	4871.78i	−0.126818	−	0.719223i
$359$	−3800.41	−	1383.24i	−0.558713	−	0.203355i	0.0472002	−	0.998885i	$-0.484970\pi$
$359$	−3800.41	−	1383.24i	−0.558713	−	0.203355i	−0.605914	+	0.795530i	$0.707192\pi$
$360$	1492.59			0.218518
$361$	3994.02	+	5576.17i	0.582304	+	0.812971i
$362$	−1899.04			−0.275722
$363$	−11089.2	−	4036.14i	−1.60340	−	0.583588i
$364$	445.589	+	2527.06i	0.0641626	+	0.363884i
$365$	4483.20	+	3761.85i	0.642907	+	0.539463i
$366$	3026.99	−	2539.95i	0.432304	−	0.362746i
$367$	−339.329	+	1924.43i	−0.0482639	+	0.273718i	−0.999384	−	0.0351041i	$-0.988824\pi$
$367$	−339.329	+	1924.43i	−0.0482639	+	0.273718i	0.951120	+	0.308822i	$0.0999348\pi$
$368$	−797.370	+	1381.09i	−0.112950	+	0.195636i
$369$	2438.01	+	4222.75i	0.343950	+	0.595739i
$370$	4358.80	−	1586.47i	0.612442	−	0.222911i
$371$	13322.5	−	4848.99i	1.86434	−	0.678563i
$372$	44.2868	+	76.7070i	0.00617248	+	0.0106911i
$373$	−5497.22	+	9521.46i	−0.763097	+	1.32172i	0.178150	+	0.984003i	$0.442989\pi$
$373$	−5497.22	+	9521.46i	−0.763097	+	1.32172i	−0.941247	+	0.337720i	$0.890344\pi$
$374$	−520.571	+	2952.31i	−0.0719735	+	0.408182i
$375$	−3440.60	+	2887.00i	−0.473791	+	0.397558i
$376$	546.911	+	458.913i	0.0750128	+	0.0629432i
$377$	65.3529	+	370.635i	0.00892797	+	0.0506330i
$378$	−7146.76	−	2601.21i	−0.972459	−	0.353946i
$379$	−13272.1			−1.79879			−0.899393	−	0.437141i	$-0.855991\pi$
$379$	−13272.1			−1.79879			−0.899393	+	0.437141i	$0.855991\pi$
$380$	−3181.98	−	1634.87i	−0.429559	−	0.220703i
$381$	6137.89			0.825338
$382$	−1372.92	−	499.702i	−0.183887	−	0.0669293i
$383$	−382.300	−	2168.13i	−0.0510042	−	0.289259i	0.948628	−	0.316395i	$-0.102472\pi$
$383$	−382.300	−	2168.13i	−0.0510042	−	0.289259i	−0.999632	+	0.0271359i	$0.991361\pi$
$384$	−305.745	−	256.551i	−0.0406315	−	0.0340939i
$385$	16296.6	−	13674.5i	2.15728	−	1.81017i
$386$	703.412	−	3989.25i	0.0927532	−	0.526029i
$387$	−3311.99	+	5736.54i	−0.435034	+	0.753501i
$388$	−1810.34	−	3135.61i	−0.236872	−	0.410274i
$389$	−3146.11	+	1145.09i	−0.410062	+	0.149250i	−0.538811	−	0.842427i	$-0.681126\pi$
$389$	−3146.11	+	1145.09i	−0.410062	+	0.149250i	0.128749	+	0.991677i	$0.458904\pi$
$390$	1473.93	−	536.465i	0.191372	−	0.0696538i
$391$	−1044.41	−	1808.97i	−0.135085	−	0.233974i
$392$	1662.55	−	2879.63i	0.214214	−	0.371029i
$393$	966.071	−	5478.86i	0.124000	−	0.703237i
$394$	7267.23	−	6097.93i	0.929232	−	0.779719i
$395$	−7845.57	−	6583.21i	−0.999376	−	0.838576i
$396$	−858.324	−	4867.80i	−0.108920	−	0.617717i
$397$	−2558.04	−	931.049i	−0.323386	−	0.117703i	0.175226	−	0.984528i	$-0.443934\pi$
$397$	−2558.04	−	931.049i	−0.323386	−	0.117703i	−0.498612	+	0.866825i	$0.666157\pi$
$398$	−2969.46			−0.373984
$399$	4833.35	+	5218.37i	0.606441	+	0.654750i
$400$	−134.157			−0.0167696
$401$	5389.09	+	1961.47i	0.671118	+	0.244267i	0.655029	−	0.755604i	$-0.272656\pi$
$401$	5389.09	+	1961.47i	0.671118	+	0.244267i	0.0160889	+	0.999871i	$0.494879\pi$
$402$	43.2074	+	245.041i	0.00536066	+	0.0304018i
$403$	−126.704	−	106.317i	−0.0156614	−	0.0131415i
$404$	−659.108	+	553.057i	−0.0811680	+	0.0681080i
$405$	67.4805	−	382.701i	0.00827934	−	0.0469545i
$406$	445.067	−	770.879i	0.0544047	−	0.0942317i
$407$	−7680.54	−	13303.1i	−0.935406	−	1.62017i
$408$	491.251	−	178.801i	0.0596092	−	0.0216960i
$409$	−12106.0	+	4406.24i	−1.46358	+	0.532700i	−0.946350	−	0.323144i	$-0.895260\pi$
$409$	−12106.0	+	4406.24i	−1.46358	+	0.532700i	−0.517233	+	0.855845i	$0.673038\pi$
$410$	3047.68	+	5278.74i	0.367108	+	0.635849i
$411$	646.611	−	1119.96i	0.0776033	−	0.134413i
$412$	−672.686	+	3814.99i	−0.0804390	+	0.456192i
$413$	−17080.2	+	14332.0i	−2.03501	+	1.70758i
$414$	2638.32	+	2213.81i	0.313203	+	0.262809i
$415$	626.190	+	3551.30i	0.0740686	+	0.420064i
$416$	700.362	+	254.911i	0.0825434	+	0.0300433i
$417$	−1938.31			−0.227625
$418$	−3501.99	+	11317.6i	−0.409780	+	1.32431i
$419$	−2280.86			−0.265937			−0.132968	−	0.991120i	$-0.542451\pi$
$419$	−2280.86			−0.265937			−0.132968	+	0.991120i	$0.542451\pi$
$420$	−3486.07	−	1268.83i	−0.405007	−	0.147411i
$421$	1042.67	+	5913.29i	0.120705	+	0.684551i	0.983767	+	0.179453i	$0.0574326\pi$
$421$	1042.67	+	5913.29i	0.120705	+	0.684551i	−0.863062	+	0.505098i	$0.831456\pi$
$422$	−4229.52	−	3548.99i	−0.487890	−	0.409389i
$423$	1181.14	−	991.092i	0.135766	−	0.113921i
$424$	715.059	−	4055.30i	0.0819017	−	0.464488i
$425$	87.8607	−	152.179i	0.0100279	−	0.0173689i
$426$	539.805	+	934.970i	0.0613935	+	0.106337i
$427$	16399.7	−	5968.99i	1.85863	−	0.676486i
$428$	6056.29	−	2204.31i	0.683976	−	0.248947i
$429$	−2597.17	−	4498.43i	−0.292290	−	0.506262i
$430$	−4140.22	+	7171.08i	−0.464324	+	0.804233i
$431$	950.585	−	5391.04i	0.106237	−	0.602499i	−0.884482	−	0.466574i	$-0.845488\pi$
$431$	950.585	−	5391.04i	0.106237	−	0.602499i	0.990719	−	0.135925i	$-0.0434007\pi$
$432$	−1692.19	+	1419.92i	−0.188462	+	0.158139i
$433$	3574.32	+	2999.21i	0.396700	+	0.332870i	0.819216	−	0.573485i	$-0.194409\pi$
$433$	3574.32	+	2999.21i	0.396700	+	0.332870i	−0.422517	+	0.906355i	$0.638853\pi$
$434$	67.9307	+	385.254i	0.00751332	+	0.0426101i
$435$	−511.290	−	186.094i	−0.0563551	−	0.0205116i
$436$	6220.80			0.683308
$437$	−3199.66	−	7609.33i	−0.350253	−	0.832960i
$438$	−3379.73			−0.368698
$439$	10352.4	+	3767.96i	1.12549	+	0.409646i	0.836655	−	0.547731i	$-0.184508\pi$
$439$	10352.4	+	3767.96i	1.12549	+	0.409646i	0.288840	+	0.957377i	$0.406730\pi$
$440$	−1072.97	−	6085.09i	−0.116254	−	0.659307i
$441$	−5501.02	−	4615.90i	−0.593998	−	0.498424i
$442$	−747.830	+	627.504i	−0.0804765	+	0.0675278i
$443$	145.710	−	826.364i	0.0156273	−	0.0886269i	−0.975997	−	0.217786i	$-0.930117\pi$
$443$	145.710	−	826.364i	0.0156273	−	0.0886269i	0.991624	+	0.129159i	$0.0412277\pi$
$444$	−1339.37	+	2319.85i	−0.143161	+	0.247962i
$445$	5181.44	+	8974.52i	0.551964	+	0.956029i
$446$	−3840.94	+	1397.99i	−0.407788	+	0.148423i
$447$	−4894.53	+	1781.46i	−0.517904	+	0.188502i
$448$	−881.389	−	1526.61i	−0.0929502	−	0.160995i
$449$	701.670	−	1215.33i	0.0737503	−	0.127739i	−0.826792	−	0.562508i	$-0.809837\pi$
$449$	701.670	−	1215.33i	0.0737503	−	0.127739i	0.900542	+	0.434769i	$0.143170\pi$
$450$	−50.3114	+	285.330i	−0.00527045	+	0.0298902i
$451$	15463.0	−	12975.0i	1.61447	−	1.35470i
$452$	1437.29	+	1206.03i	0.149567	+	0.125502i
$453$	1105.79	+	6271.22i	0.114689	+	0.650436i
$454$	12752.3	+	4641.46i	1.31827	+	0.479812i
$455$	6927.58			0.713780
$456$	2014.54	−	457.929i	0.206885	−	0.0470274i
$457$	−8806.65			−0.901439			−0.450719	−	0.892666i	$-0.648833\pi$
$457$	−8806.65			−0.901439			−0.450719	+	0.892666i	$0.648833\pi$
$458$	8407.23	+	3059.98i	0.857739	+	0.312191i
$459$	−502.433	−	2849.44i	−0.0510927	−	0.289761i
$460$	3298.08	+	2767.42i	0.334291	+	0.280503i
$461$	−6833.77	+	5734.22i	−0.690413	+	0.579325i	−0.919028	−	0.394191i	$-0.871025\pi$
$461$	−6833.77	+	5734.22i	−0.690413	+	0.579325i	0.228615	+	0.973517i	$0.426580\pi$
$462$	−2133.35	+	12098.8i	−0.214832	+	1.21837i
$463$	2192.05	−	3796.75i	0.220029	−	0.381101i	−0.734788	−	0.678297i	$-0.762718\pi$
$463$	2192.05	−	3796.75i	0.220029	−	0.381101i	0.954816	+	0.297196i	$0.0960515\pi$
$464$	−129.270	−	223.902i	−0.0129336	−	0.0224017i
$465$	224.702	−	81.7850i	0.0224093	−	0.00815632i
$466$	−580.924	+	211.439i	−0.0577485	+	0.0210187i
$467$	2777.82	+	4811.32i	0.275251	+	0.476748i	0.970198	−	0.242312i	$-0.0779058\pi$
$467$	2777.82	+	4811.32i	0.275251	+	0.476748i	−0.694948	+	0.719060i	$0.744572\pi$
$468$	804.804	−	1393.96i	0.0794916	−	0.137683i
$469$	−190.831	+	1082.26i	−0.0187884	+	0.106554i
$470$	1476.50	−	1238.93i	0.144906	−	0.121591i
$471$	−370.546	−	310.925i	−0.0362502	−	0.0304175i
$472$	1124.56	+	6377.67i	0.109665	+	0.621941i
$473$	25768.0	+	9378.77i	2.50489	+	0.911705i
$474$	5914.51			0.573127
$475$	419.785	−	553.174i	0.0405496	−	0.0534345i
$476$	2308.92			0.222331
$477$	−8356.82	−	3041.63i	−0.802164	−	0.291964i
$478$	−103.317	−	585.940i	−0.00988622	−	0.0560675i
$479$	4026.31	+	3378.47i	0.384064	+	0.322268i	0.814295	−	0.580451i	$-0.197124\pi$
$479$	4026.31	+	3378.47i	0.384064	+	0.322268i	−0.430231	+	0.902719i	$0.641568\pi$
$480$	−825.424	+	692.613i	−0.0784902	+	0.0658611i
$481$	868.622	−	4926.20i	0.0823404	−	0.466976i
$482$	2646.57	−	4583.99i	0.250099	−	0.433185i
$483$	−4280.09	−	7413.34i	−0.403211	−	0.698382i
$484$	−14225.4	+	5177.63i	−1.33597	+	0.486254i
$485$	−9185.32	+	3343.18i	−0.859967	+	0.313002i
$486$	3839.90	+	6650.90i	0.358398	+	0.620763i
$487$	−532.889	+	922.992i	−0.0495842	+	0.0858824i	−0.889752	−	0.456444i	$-0.849123\pi$
$487$	−532.889	+	922.992i	−0.0495842	+	0.0858824i	0.840168	+	0.542326i	$0.182456\pi$
$488$	880.221	−	4991.98i	0.0816511	−	0.463066i
$489$	517.478	−	434.215i	0.0478551	−	0.0401552i
$490$	−6876.66	−	5770.20i	−0.633991	−	0.531982i
$491$	−1651.68	−	9367.14i	−0.151811	−	0.860964i	−0.961643	−	0.274303i	$-0.911553\pi$
$491$	−1651.68	−	9367.14i	−0.151811	−	0.860964i	0.809832	−	0.586661i	$-0.199558\pi$
$492$	−3307.75	−	1203.92i	−0.303100	−	0.110319i
$493$	338.641			0.0309364
$494$	−3242.56	+	2090.20i	−0.295323	+	0.190369i
$495$	−13344.4			−1.21169
$496$	106.771	+	38.8616i	0.00966567	+	0.00351801i
$497$	827.997	+	4695.80i	0.0747299	+	0.423814i
$498$	−1595.29	−	1338.60i	−0.143547	−	0.120450i
$499$	−6238.28	+	5234.54i	−0.559647	+	0.469600i	−0.878192	−	0.478308i	$-0.841250\pi$
$499$	−6238.28	+	5234.54i	−0.559647	+	0.469600i	0.318545	+	0.947908i	$0.396806\pi$
$500$	−1000.49	+	5674.08i	−0.0894868	+	0.507505i
$501$	281.459	−	487.502i	0.0250991	−	0.0434730i
$502$	−710.657	−	1230.89i	−0.0631836	−	0.109437i
$503$	−4582.77	+	1667.99i	−0.406234	+	0.147857i	−0.537051	−	0.843549i	$-0.680462\pi$
$503$	−4582.77	+	1667.99i	−0.406234	+	0.147857i	0.130818	+	0.991406i	$0.458240\pi$
$504$	−3577.39	+	1302.06i	−0.316170	+	0.115076i
$505$	1161.42	+	2011.64i	0.102342	+	0.177261i
$506$	7128.82	−	12347.5i	0.626314	−	1.08481i
$507$	−895.863	+	5080.69i	−0.0784747	+	0.445052i
$508$	6031.67	−	5061.17i	0.526795	−	0.442034i
$509$	804.179	+	674.787i	0.0700287	+	0.0587611i	0.677130	−	0.735863i	$-0.263223\pi$
$509$	804.179	+	674.787i	0.0700287	+	0.0587611i	−0.607101	+	0.794624i	$0.707668\pi$
$510$	−245.079	−	1389.91i	−0.0212790	−	0.120679i
$511$	−14026.8	−	5105.35i	−1.21431	−	0.441971i
$512$	−512.000			−0.0441942
$513$	−559.831	−	11420.5i	−0.0481816	−	0.982899i
$514$	9631.84			0.826541
$515$	9827.56	+	3576.94i	0.840881	+	0.306056i
$516$	−830.371	−	4709.27i	−0.0708431	−	0.401771i
$517$	−4889.62	−	4102.88i	−0.415948	−	0.349022i
$518$	−9063.07	+	7604.82i	−0.768742	+	0.645051i
$519$	693.705	−	3934.20i	0.0586710	−	0.332740i
$520$	1006.06	−	1742.55i	0.0848436	−	0.146953i
$521$	−5232.15	−	9062.35i	−0.439970	−	0.762051i	0.557716	−	0.830032i	$-0.311678\pi$
$521$	−5232.15	−	9062.35i	−0.439970	−	0.762051i	−0.997687	+	0.0679807i	$0.978344\pi$
$522$	−524.683	+	190.969i	−0.0439938	+	0.0160124i
$523$	−15445.4	+	5621.65i	−1.29135	+	0.470014i	−0.894171	−	0.447725i	$-0.852234\pi$
$523$	−15445.4	+	5621.65i	−1.29135	+	0.470014i	−0.397183	+	0.917740i	$0.630012\pi$
$524$	−3568.40	−	6180.65i	−0.297493	−	0.515272i
$525$	360.061	−	623.644i	0.0299321	−	0.0518439i
$526$	2337.12	−	13254.5i	0.193733	−	1.09871i
$527$	−114.008	+	95.6639i	−0.00942364	+	0.00790737i
$528$	2733.49	+	2293.67i	0.225303	+	0.189052i
$529$	−387.695	−	2198.73i	−0.0318645	−	0.180712i
$530$	−10446.6	−	3802.25i	−0.856173	−	0.311621i
$531$	13986.0			1.14302
$532$	9052.65	+	1142.59i	0.737749	+	0.0931158i
$533$	6573.22			0.534180
$534$	−5623.60	−	2046.82i	−0.455725	−	0.165870i
$535$	−3021.40	−	17135.2i	−0.244162	−	1.38471i
$536$	244.515	+	205.173i	0.0197042	+	0.0165338i
$537$	5908.21	−	4957.58i	0.474783	−	0.398390i
$538$	803.997	−	4559.69i	0.0644289	−	0.365395i
$539$	−14863.9	+	25745.1i	−1.18782	+	2.05737i
$540$	2981.83	+	5164.69i	0.237625	+	0.411579i
$541$	−9581.59	+	3487.41i	−0.761450	+	0.277145i	−0.693416	−	0.720538i	$-0.743895\pi$
$541$	−9581.59	+	3487.41i	−0.761450	+	0.277145i	−0.0680345	+	0.997683i	$0.521673\pi$
$542$	−10692.1	+	3891.60i	−0.847351	+	0.308410i
$543$	−1480.37	−	2564.07i	−0.116996	−	0.202642i
$544$	335.314	−	580.781i	0.0264274	−	0.0457735i
$545$	2916.31	−	16539.2i	0.229213	−	1.29993i
$546$	−3064.67	+	2571.56i	−0.240212	+	0.201562i
$547$	12727.0	+	10679.2i	0.994819	+	0.834752i	0.986258	−	0.165211i	$-0.0528305\pi$
$547$	12727.0	+	10679.2i	0.994819	+	0.834752i	0.00856093	+	0.999963i	$0.497275\pi$
$548$	−288.076	−	1633.76i	−0.0224562	−	0.127356i
$549$	−10287.0	−	3744.18i	−0.799709	−	0.291070i
$550$	1199.42			0.0929879
$551$	1327.72	+	167.580i	0.102655	+	0.0129567i
$552$	−2486.31			−0.191711
$553$	24546.9	+	8934.33i	1.88759	+	0.687028i
$554$	999.212	+	5666.81i	0.0766290	+	0.434584i
$555$	5539.89	+	4648.52i	0.423703	+	0.355529i
$556$	−1904.77	+	1598.29i	−0.145288	+	0.121911i
$557$	−864.886	+	4905.01i	−0.0657925	+	0.373128i	0.934079	+	0.357068i	$0.116223\pi$
$557$	−864.886	+	4905.01i	−0.0657925	+	0.373128i	−0.999871	+	0.0160601i	$0.994888\pi$
$558$	122.694	−	212.511i	0.00930830	−	0.0161225i
$559$	4464.81	+	7733.28i	0.337820	+	0.585121i
$560$	−4471.99	+	1627.67i	−0.337457	+	0.122824i
$561$	−4391.99	+	1598.55i	−0.330535	+	0.120305i
$562$	−649.753	−	1125.41i	−0.0487690	−	0.0844704i
$563$	867.704	−	1502.91i	0.0649544	−	0.112504i	−0.831719	−	0.555196i	$-0.812643\pi$
$563$	867.704	−	1502.91i	0.0649544	−	0.112504i	0.896674	+	0.442692i	$0.145976\pi$
$564$	−193.285	+	1096.18i	−0.0144305	+	0.0818393i
$565$	3880.27	−	3255.93i	0.288928	−	0.242439i
$566$	474.261	+	397.952i	0.0352202	+	0.0295533i
$567$	172.115	+	976.112i	0.0127480	+	0.0722978i
$568$	1301.42	+	473.677i	0.0961378	+	0.0349913i
$569$	23207.0			1.70982			0.854912	−	0.518773i	$-0.173611\pi$
$569$	23207.0			1.70982			0.854912	+	0.518773i	$0.173611\pi$
$570$	−273.077	−	5570.74i	−0.0200665	−	0.409355i
$571$	5378.99			0.394227			0.197114	−	0.980381i	$-0.436843\pi$
$571$	5378.99			0.394227			0.197114	+	0.980381i	$0.436843\pi$
$572$	−6261.53	−	2279.01i	−0.457706	−	0.166591i
$573$	−395.545	−	2243.25i	−0.0288379	−	0.163548i
$574$	−11909.5	−	9993.25i	−0.866015	−	0.726673i
$575$	−640.201	+	537.193i	−0.0464317	+	0.0389608i
$576$	−192.010	+	1088.94i	−0.0138896	+	0.0787718i
$577$	−7535.61	+	13052.1i	−0.543694	+	0.941706i	0.454994	+	0.890495i	$0.349641\pi$
$577$	−7535.61	+	13052.1i	−0.543694	+	0.941706i	−0.998688	+	0.0512112i	$0.983692\pi$
$578$	−4473.80	−	7748.85i	−0.321947	−	0.557629i
$579$	5934.59	−	2160.02i	0.425964	−	0.155038i
$580$	−655.890	+	238.725i	−0.0469558	+	0.0170905i
$581$	−4598.82	−	7965.38i	−0.328384	−	0.568778i
$582$	2822.45	−	4888.63i	0.201021	−	0.348179i
$583$	−6392.93	+	36256.1i	−0.454148	+	2.57560i
$584$	−3321.24	+	2786.85i	−0.235332	+	0.197467i
$585$	−3328.83	−	2793.22i	−0.235265	−	0.197411i
$586$	3266.85	+	18527.2i	0.230294	+	1.30606i
$587$	−7909.24	−	2878.73i	−0.556132	−	0.202415i	0.0486371	−	0.998817i	$-0.484512\pi$
$587$	−7909.24	−	2878.73i	−0.556132	−	0.202415i	−0.604769	+	0.796401i	$0.706734\pi$
$588$	5184.08			0.363585
$589$	−494.333	+	318.654i	−0.0345817	+	0.0222919i
$590$	17483.5			1.21997
$591$	13898.4	+	5058.62i	0.967353	+	0.352088i
$592$	596.711	+	3384.12i	0.0414268	+	0.234943i
$593$	−7287.55	−	6114.98i	−0.504661	−	0.423461i	0.354585	−	0.935024i	$-0.384622\pi$
$593$	−7287.55	−	6114.98i	−0.504661	−	0.423461i	−0.859246	+	0.511563i	$0.829067\pi$
$594$	15128.9	−	12694.7i	1.04503	−	0.876883i
$595$	1082.42	−	6138.73i	0.0745799	−	0.422964i
$596$	−3340.87	+	5786.55i	−0.229609	+	0.397695i
$597$	−2314.80	−	4009.35i	−0.158691	−	0.274860i
$598$	4362.87	−	1587.95i	0.298346	−	0.108589i
$599$	19387.5	−	7056.47i	1.32246	−	0.481335i	0.418212	−	0.908349i	$-0.362657\pi$
$599$	19387.5	−	7056.47i	1.32246	−	0.481335i	0.904245	+	0.427014i	$0.140435\pi$
$600$	−104.580	−	181.138i	−0.00711576	−	0.0123249i
$601$	−1771.67	+	3068.62i	−0.120246	+	0.208272i	−0.919865	−	0.392236i	$-0.871702\pi$
$601$	−1771.67	+	3068.62i	−0.120246	+	0.208272i	0.799619	+	0.600508i	$0.205035\pi$
$602$	3667.45	−	20799.1i	0.248296	−	1.40816i
$603$	528.067	−	443.101i	0.0356626	−	0.0299245i
$604$	6257.76	+	5250.88i	0.421564	+	0.353734i
$605$	7096.87	+	40248.4i	0.476907	+	2.70468i
$606$	−1260.53	−	458.797i	−0.0844978	−	0.0307547i
$607$	5479.87			0.366427			0.183214	−	0.983073i	$-0.441350\pi$
$607$	5479.87			0.366427			0.183214	+	0.983073i	$0.441350\pi$
$608$	1602.08	−	2111.15i	0.106863	−	0.140820i
$609$	1387.78			0.0923411
$610$	−12859.5	−	4680.48i	−0.853552	−	0.310668i
$611$	−360.936	−	2046.97i	−0.0238984	−	0.135534i
$612$	−1109.48	−	930.964i	−0.0732811	−	0.0614902i
$613$	7243.83	−	6078.30i	0.477285	−	0.400490i	−0.372159	−	0.928169i	$-0.621382\pi$
$613$	7243.83	−	6078.30i	0.477285	−	0.400490i	0.849443	+	0.527680i	$0.176938\pi$
$614$	−2269.00	+	12868.2i	−0.149136	+	0.845793i
$615$	−4751.55	+	8229.92i	−0.311546	+	0.539614i
$616$	7879.99	+	13648.5i	0.515412	+	0.892720i
$617$	7295.07	−	2655.19i	0.475994	−	0.173248i	−0.0928716	−	0.995678i	$-0.529605\pi$
$617$	7295.07	−	2655.19i	0.475994	−	0.173248i	0.568866	+	0.822430i	$0.307382\pi$
$618$	−5675.36	+	2065.66i	−0.369412	+	0.134455i
$619$	−11727.0	−	20311.8i	−0.761467	−	1.31890i	−0.942094	−	0.335348i	$-0.891146\pi$
$619$	−11727.0	−	20311.8i	−0.761467	−	1.31890i	0.180628	−	0.983552i	$-0.442187\pi$
$620$	153.376	−	265.654i	0.00993502	−	0.0172080i
$621$	−2389.55	+	13551.8i	−0.154411	+	0.875709i
$622$	6851.29	−	5748.92i	0.441659	−	0.370596i
$623$	−20247.6	−	16989.8i	−1.30209	−	1.09259i
$624$	201.777	+	1144.34i	0.0129448	+	0.0734137i
$625$	13631.7	+	4961.55i	0.872431	+	0.317539i
$626$	−16214.7			−1.03525
$627$	−18010.9	+	4094.08i	−1.14718	+	0.260768i
$628$	−620.514			−0.0394287
$629$	−4229.53	−	1539.42i	−0.268112	−	0.0975847i
$630$	1784.71	+	10121.6i	0.112865	+	0.640087i
$631$	17591.6	+	14761.1i	1.10984	+	0.931270i	0.998047	−	0.0624609i	$-0.0198949\pi$
$631$	17591.6	+	14761.1i	1.10984	+	0.931270i	0.111797	+	0.993731i	$0.464339\pi$
$632$	5812.15	−	4876.97i	0.365815	−	0.306955i
$633$	1494.76	−	8477.23i	0.0938571	−	0.532290i
$634$	−4049.74	+	7014.35i	−0.253684	+	0.439393i
$635$	−10628.5	−	18409.1i	−0.664218	−	1.15046i
$636$	6032.86	−	2195.78i	0.376130	−	0.136900i
$637$	−9096.80	+	3310.96i	−0.565821	+	0.205942i
$638$	1155.73	+	2001.78i	0.0717175	+	0.124218i
$639$	1495.49	−	2590.27i	0.0925834	−	0.160359i
$640$	−240.026	+	1361.25i	−0.0148248	+	0.0840754i
$641$	−3401.05	+	2853.82i	−0.209569	+	0.175849i	−0.741530	−	0.670920i	$-0.765900\pi$
$641$	−3401.05	+	2853.82i	−0.209569	+	0.175849i	0.531961	+	0.846769i	$0.321455\pi$
$642$	7697.33	+	6458.83i	0.473192	+	0.397056i
$643$	−3000.61	−	17017.3i	−0.184032	−	1.04370i	−0.927193	−	0.374584i	$-0.877786\pi$
$643$	−3000.61	−	17017.3i	−0.184032	−	1.04370i	0.743161	−	0.669112i	$-0.233325\pi$
$644$	−10318.9	−	3755.77i	−0.631400	−	0.229811i
$645$	−12909.8			−0.788098
$646$	1345.54	+	3199.92i	0.0819498	+	0.194890i
$647$	20791.9			1.26339			0.631696	−	0.775216i	$-0.282359\pi$
$647$	20791.9			1.26339			0.631696	+	0.775216i	$0.282359\pi$
$648$	270.524	+	98.4628i	0.0164000	+	0.00596911i
$649$	−10054.0	−	57019.1i	−0.608096	−	3.44868i
$650$	299.201	+	251.060i	0.0180548	+	0.0151498i
$651$	−467.214	+	392.039i	−0.0281284	+	0.0236025i
$652$	150.478	−	853.401i	0.00903859	−	0.0512604i
$653$	6988.19	−	12103.9i	0.418788	−	0.725363i	−0.577029	−	0.816723i	$-0.695788\pi$
$653$	6988.19	−	12103.9i	0.418788	−	0.725363i	0.995818	+	0.0913605i	$0.0291216\pi$
$654$	4849.33	+	8399.29i	0.289945	+	0.502199i
$655$	−18105.3	+	6589.80i	−1.08005	+	0.393107i
$656$	−4243.24	+	1544.41i	−0.252547	+	0.0919195i
$657$	4681.66	+	8108.87i	0.278004	+	0.481517i
$658$	−2458.05	+	4257.47i	−0.145630	+	0.252239i
$659$	−5743.83	+	32574.9i	−0.339526	+	1.92555i	0.0373865	+	0.999301i	$0.488097\pi$
$659$	−5743.83	+	32574.9i	−0.339526	+	1.92555i	−0.376913	+	0.926249i	$0.623014\pi$
$660$	7379.64	−	6192.26i	0.435231	−	0.365202i
$661$	−18645.9	−	15645.7i	−1.09719	−	0.920648i	−0.0999527	−	0.994992i	$-0.531869\pi$
$661$	−18645.9	−	15645.7i	−1.09719	−	0.920648i	−0.997233	+	0.0743444i	$0.976314\pi$
$662$	776.838	+	4405.67i	0.0456083	+	0.258657i
$663$	−1430.21	−	520.554i	−0.0837780	−	0.0304927i
$664$	−2671.46			−0.156134
$665$	7281.69	−	23532.6i	0.424619	−	1.37226i
$666$	7421.25			0.431783
$667$	−1513.43	−	550.845i	−0.0878567	−	0.0319772i
$668$	−125.395	−	711.150i	−0.00726299	−	0.0411904i
$669$	−4881.70	−	4096.23i	−0.282119	−	0.236726i
$670$	660.121	−	553.907i	0.0380637	−	0.0319392i
$671$	−7869.55	+	44630.4i	−0.452758	+	2.56772i
$672$	1374.15	−	2380.09i	0.0788823	−	0.136628i
$673$	−5348.59	−	9264.03i	−0.306349	−	0.530612i	0.671212	−	0.741266i	$-0.265774\pi$
$673$	−5348.59	−	9264.03i	−0.306349	−	0.530612i	−0.977561	+	0.210654i	$0.932441\pi$
$674$	−8786.02	+	3197.85i	−0.502114	+	0.182755i
$675$	−1087.81	+	395.932i	−0.0620296	+	0.0225769i
$676$	3309.07	+	5731.47i	0.188272	+	0.326096i
$677$	2736.50	−	4739.75i	0.155350	−	0.269075i	−0.777836	−	0.628467i	$-0.783683\pi$
$677$	2736.50	−	4739.75i	0.155350	−	0.269075i	0.933187	+	0.359392i	$0.117016\pi$
$678$	−507.956	+	2880.76i	−0.0287728	+	0.163179i
$679$	19098.6	−	16025.7i	1.07944	−	0.905756i
$680$	−1386.93	−	1163.77i	−0.0782150	−	0.0656302i
$681$	3674.00	+	20836.3i	0.206737	+	1.17246i
$682$	−954.580	−	347.439i	−0.0535964	−	0.0195075i
$683$	−13835.1			−0.775087			−0.387543	−	0.921851i	$-0.626676\pi$
$683$	−13835.1			−0.775087			−0.387543	+	0.921851i	$0.626676\pi$
$684$	−3889.27	−	4199.09i	−0.217412	−	0.234731i
$685$	−4478.73			−0.249815
$686$	3760.12	+	1368.57i	0.209274	+	0.0761695i
$687$	2422.16	+	13736.8i	0.134514	+	0.762868i
$688$	−4699.16	−	3943.06i	−0.260398	−	0.218500i
$689$	−9183.80	+	7706.12i	−0.507801	+	0.426096i
$690$	−1165.58	+	6610.35i	−0.0643087	+	0.364713i
$691$	8170.26	−	14151.3i	0.449799	−	0.779075i	−0.548573	−	0.836102i	$-0.684829\pi$
$691$	8170.26	−	14151.3i	0.449799	−	0.779075i	0.998373	+	0.0570272i	$0.0181622\pi$
$692$	−2562.35	−	4438.12i	−0.140760	−	0.243804i
$693$	31983.4	−	11641.0i	1.75317	−	0.638103i
$694$	−5202.12	+	1893.42i	−0.284539	+	0.103564i
$695$	3356.41	+	5813.47i	0.183188	+	0.317292i
$696$	201.541	−	349.079i	0.0109761	−	0.0190112i
$697$	1027.06	−	5824.72i	0.0558142	−	0.316538i
$698$	15482.2	−	12991.1i	0.839558	−	0.704473i
$699$	−738.335	−	619.536i	−0.0399519	−	0.0335236i
$700$	−160.413	−	909.749i	−0.00866150	−	0.0491218i
$701$	12270.6	+	4466.12i	0.661131	+	0.240632i	0.650724	−	0.759314i	$-0.274465\pi$
$701$	12270.6	+	4466.12i	0.661131	+	0.240632i	0.0104062	+	0.999946i	$0.496688\pi$
$702$	6431.21			0.345770
$703$	−15821.0	−	8128.67i	−0.848792	−	0.436100i
$704$	4577.50			0.245058
$705$	2823.79	+	1027.78i	0.150851	+	0.0549053i
$706$	−669.425	−	3796.50i	−0.0356858	−	0.202384i
$707$	−4538.52	−	3808.27i	−0.241427	−	0.202581i
$708$	−7734.47	+	6489.99i	−0.410564	+	0.344504i
$709$	4535.34	−	25721.2i	0.240238	−	1.36245i	−0.591060	−	0.806627i	$-0.701290\pi$
$709$	4535.34	−	25721.2i	0.240238	−	1.36245i	0.831298	−	0.555827i	$-0.187598\pi$
$710$	1869.47	−	3238.02i	0.0988169	−	0.171156i
$711$	−8192.87	−	14190.5i	−0.432147	−	0.748501i
$712$	−7214.04	+	2625.70i	−0.379716	+	0.138205i
$713$	665.126	−	242.086i	0.0349357	−	0.0127156i
$714$	1799.89	+	3117.50i	0.0943405	+	0.163403i
$715$	−8994.61	+	15579.1i	−0.470460	+	0.814861i
$716$	1718.05	−	9743.57i	0.0896741	−	0.508567i
$717$	710.594	−	596.259i	0.0370120	−	0.0310568i
$718$	−6196.25	−	5199.27i	−0.322064	−	0.270244i
$719$	−1577.77	−	8947.95i	−0.0818369	−	0.464120i	−0.997994	−	0.0633017i	$-0.979837\pi$
$719$	−1577.77	−	8947.95i	−0.0818369	−	0.464120i	0.916158	−	0.400818i	$-0.131274\pi$
$720$	2805.15	+	1020.99i	0.145197	+	0.0528474i
$721$	−26674.7			−1.37783
$722$	3691.99	+	13211.8i	0.190307	+	0.681016i
$723$	8252.38			0.424494
$724$	−3569.02	−	1299.02i	−0.183207	−	0.0666818i
$725$	−23.5272	−	133.430i	−0.00120521	−	0.00683510i
$726$	−18080.0	−	15170.9i	−0.924260	−	0.775546i
$727$	−10099.9	+	8474.81i	−0.515246	+	0.432343i	−0.862971	−	0.505254i	$-0.831399\pi$
$727$	−10099.9	+	8474.81i	−0.515246	+	0.432343i	0.347725	+	0.937597i	$0.386954\pi$
$728$	−891.178	+	5054.12i	−0.0453698	+	0.257305i
$729$	−5500.86	+	9527.78i	−0.279473	+	0.484061i
$730$	5852.40	+	10136.6i	0.296722	+	0.513937i
$731$	7550.30	−	2748.08i	0.382022	−	0.139045i
$732$	7426.31	−	2702.96i	0.374979	−	0.136481i
$733$	525.939	+	910.953i	0.0265020	+	0.0459029i	0.878972	−	0.476873i	$-0.158230\pi$
$733$	525.939	+	910.953i	0.0265020	+	0.0459029i	−0.852470	+	0.522776i	$0.824896\pi$
$734$	−1954.12	+	3384.63i	−0.0982669	+	0.170203i
$735$	2430.30	−	13782.9i	0.121963	−	0.691687i
$736$	−2443.28	+	2050.16i	−0.122365	+	0.102676i
$737$	−2186.07	−	1834.33i	−0.109260	−	0.0916803i
$738$	1693.42	+	9603.87i	0.0844657	+	0.479029i
$739$	−9522.36	−	3465.86i	−0.473999	−	0.172522i	0.0939638	−	0.995576i	$-0.470046\pi$
$739$	−9522.36	−	3465.86i	−0.473999	−	0.172522i	−0.567963	+	0.823054i	$0.692268\pi$
$740$	9277.08			0.460855
$741$	−5349.86	−	2748.70i	−0.265226	−	0.136270i
$742$	28355.0			1.40289
$743$	27808.5	+	10121.5i	1.37308	+	0.499759i	0.920072	−	0.391749i	$-0.128130\pi$
$743$	27808.5	+	10121.5i	1.37308	+	0.499759i	0.453005	+	0.891508i	$0.350352\pi$
$744$	30.7613	+	174.456i	0.00151581	+	0.00859659i
$745$	13818.5	+	11595.1i	0.679557	+	0.570216i
$746$	−16844.5	+	14134.2i	−0.826702	+	0.693685i
$747$	−1001.85	+	5681.76i	−0.0490706	+	0.278293i
$748$	−2997.85	+	5192.43i	−0.146541	+	0.253816i
$749$	22189.5	+	38433.4i	1.08249	+	1.87493i
$750$	−8441.03	+	3072.28i	−0.410964	+	0.149579i
$751$	−24546.3	+	8934.11i	−1.19268	+	0.434101i	−0.860665	−	0.509171i	$-0.829952\pi$
$751$	−24546.3	+	8934.11i	−1.19268	+	0.434101i	−0.332019	+	0.943273i	$0.607730\pi$
$752$	713.942	+	1236.58i	0.0346207	+	0.0599649i
$753$	1107.96	−	1919.05i	0.0536208	−	0.0928739i
$754$	−130.706	+	741.269i	−0.00631303	+	0.0358030i
$755$	16894.2	−	14175.9i	0.814359	−	0.683328i
$756$	−11652.2	−	9777.34i	−0.560563	−	0.470368i
$757$	3141.74	+	17817.7i	0.150843	+	0.855474i	0.962488	+	0.271323i	$0.0874613\pi$
$757$	3141.74	+	17817.7i	0.150843	+	0.855474i	−0.811645	+	0.584151i	$0.801428\pi$
$758$	−24943.3	−	9078.62i	−1.19523	−	0.435027i
$759$	22228.7			1.06304
$760$	−4861.86	−	5249.15i	−0.232050	−	0.250535i
$761$	−3589.77			−0.170997			−0.0854986	−	0.996338i	$-0.527248\pi$
$761$	−3589.77			−0.170997			−0.0854986	+	0.996338i	$0.527248\pi$
$762$	11535.5	+	4198.57i	0.548407	+	0.199604i
$763$	7438.30	+	42184.7i	0.352929	+	2.00156i
$764$	−2238.43	−	1878.27i	−0.105999	−	0.0889441i
$765$	−2995.28	+	2513.34i	−0.141561	+	0.118784i
$766$	764.599	−	4336.26i	0.0360654	−	0.204537i
$767$	9427.09	−	16328.2i	0.443797	−	0.768679i
$768$	−399.122	−	691.300i	−0.0187527	−	0.0324806i
$769$	2160.94	−	786.519i	0.101334	−	0.0368825i	−0.290856	−	0.956767i	$-0.593940\pi$
$769$	2160.94	−	786.519i	0.101334	−	0.0368825i	0.392189	+	0.919884i	$0.371718\pi$
$770$	39981.5	−	14552.1i	1.87121	−	0.681065i
$771$	7508.36	+	13004.9i	0.350722	+	0.607469i
$772$	4050.79	−	7016.17i	0.188848	−	0.327095i
$773$	−2410.58	+	13671.1i	−0.112164	+	0.636111i	0.875952	+	0.482398i	$0.160234\pi$
$773$	−2410.58	+	13671.1i	−0.112164	+	0.636111i	−0.988116	+	0.153713i	$0.950877\pi$
$774$	−10148.5	+	8515.63i	−0.471294	+	0.395463i
$775$	45.6137	+	38.2744i	0.00211418	+	0.00177401i
$776$	−1257.45	−	7131.36i	−0.0581699	−	0.329898i
$777$	−17333.0	−	6308.69i	−0.800279	−	0.291278i
$778$	−6696.04			−0.308567
$779$	6909.22	−	22328.9i	0.317777	−	1.02698i
$780$	3137.04			0.144005
$781$	−11635.2	−	4234.88i	−0.533087	−	0.194028i
$782$	−725.441	−	4114.18i	−0.0331736	−	0.188137i
$783$	−1708.98	−	1434.01i	−0.0780001	−	0.0654499i
$784$	5094.36	−	4274.68i	0.232068	−	0.194728i
$785$	−290.897	+	1649.76i	−0.0132262	+	0.0750095i
$786$	5563.38	−	9636.06i	0.252467	−	0.437286i
$787$	17769.7	+	30778.1i	0.804858	+	1.39405i	0.916387	+	0.400293i	$0.131092\pi$
$787$	17769.7	+	30778.1i	0.804858	+	1.39405i	−0.111530	+	0.993761i	$0.535575\pi$
$788$	17829.1	−	6489.28i	0.806011	−	0.293364i
$789$	19718.0	−	7176.77i	0.889708	−	0.323827i
$790$	−10241.7	−	17739.1i	−0.461243	−	0.798896i
$791$	−6459.78	+	11188.7i	−0.290371	+	0.502937i
$792$	1716.65	−	9735.60i	0.0770183	−	0.436792i
$793$	−11305.0	+	9486.06i	−0.506247	+	0.424792i
$794$	−4170.66	−	3499.60i	−0.186412	−	0.156418i
$795$	−3009.71	−	17068.9i	−0.134269	−	0.761475i
$796$	−5580.75	−	2031.23i	−0.248498	−	0.0904460i
$797$	−7713.76			−0.342830			−0.171415	−	0.985199i	$-0.554834\pi$
$797$	−7713.76			−0.342830			−0.171415	+	0.985199i	$0.554834\pi$
$798$	5514.14	+	13113.5i	0.244610	+	0.581722i
$799$	−1870.27			−0.0828104
$800$	−252.132	−	91.7686i	−0.0111428	−	0.00405564i
$801$	2879.03	+	16327.8i	0.126998	+	0.720243i
$802$	8786.46	+	7372.71i	0.386858	+	0.324613i
$803$	29693.3	−	24915.6i	1.30492	−	1.09496i
$804$	−86.4147	+	490.082i	−0.00379056	+	0.0214973i
$805$	−14823.0	+	25674.1i	−0.648995	+	1.12409i
$806$	−165.400	−	286.481i	−0.00722824	−	0.0125197i
$807$	6783.22	−	2468.89i	0.295887	−	0.107694i
$808$	−1617.03	+	588.551i	−0.0704047	+	0.0256252i
$809$	10365.2	+	17953.1i	0.450461	+	0.780221i	0.998415	−	0.0562878i	$-0.0179264\pi$
$809$	10365.2	+	17953.1i	0.450461	+	0.780221i	−0.547954	+	0.836509i	$0.684593\pi$
$810$	388.605	−	673.083i	0.0168570	−	0.0291972i
$811$	−2259.83	+	12816.1i	−0.0978464	+	0.554914i	0.895992	+	0.444071i	$0.146466\pi$
$811$	−2259.83	+	12816.1i	−0.0978464	+	0.554914i	−0.993838	+	0.110843i	$0.964645\pi$
$812$	1363.76	−	1144.33i	0.0589394	−	0.0494560i
$813$	−13589.3	−	11402.7i	−0.586219	−	0.491897i
$814$	−5334.85	−	30255.4i	−0.229713	−	1.30277i
$815$	−2198.39	−	800.149i	−0.0944863	−	0.0343902i
$816$	1045.56			0.0448552
$817$	30962.6	−	7038.15i	1.32588	−	0.301388i
$818$	−25766.0			−1.10133
$819$	10415.1	+	3790.78i	0.444362	+	0.161735i
$820$	2116.90	+	12005.5i	0.0901527	+	0.511281i
$821$	−27141.6	−	22774.5i	−1.15377	−	0.968130i	−0.153971	−	0.988075i	$-0.549206\pi$
$821$	−27141.6	−	22774.5i	−1.15377	−	0.968130i	−0.999801	+	0.0199456i	$0.993651\pi$
$822$	1981.33	−	1662.53i	0.0840716	−	0.0705444i
$823$	4267.92	−	24204.6i	0.180766	−	1.02517i	−0.750510	−	0.660859i	$-0.770192\pi$
$823$	4267.92	−	24204.6i	0.180766	−	1.02517i	0.931276	−	0.364315i	$-0.118697\pi$
$824$	−3873.84	+	6709.69i	−0.163776	+	0.283669i
$825$	934.989	+	1619.45i	0.0394571	+	0.0683418i
$826$	−41903.9	+	15251.8i	−1.76516	+	0.642466i
$827$	−19515.1	+	7102.92i	−0.820564	+	0.298661i	−0.717980	−	0.696063i	$-0.754933\pi$
$827$	−19515.1	+	7102.92i	−0.820564	+	0.298661i	−0.102584	+	0.994724i	$0.532711\pi$
$828$	3444.08	+	5965.32i	0.144553	+	0.250373i
$829$	13168.4	−	22808.4i	0.551699	−	0.955571i	−0.446453	−	0.894807i	$-0.647313\pi$
$829$	13168.4	−	22808.4i	0.551699	−	0.955571i	0.998152	−	0.0607638i	$-0.0193536\pi$
$830$	−1252.38	+	7102.60i	−0.0523744	+	0.297030i
$831$	−6872.38	+	5766.61i	−0.286884	+	0.240724i
$832$	1141.88	+	958.151i	0.0475812	+	0.0399254i
$833$	1512.58	+	8578.27i	0.0629145	+	0.356806i
$834$	−3642.83	−	1325.88i	−0.151248	−	0.0550498i
$835$	−1949.52			−0.0807974
$836$	−14323.3	+	18874.6i	−0.592561	+	0.780850i
$837$	980.448			0.0404889
$838$	−4286.62	−	1560.20i	−0.176705	−	0.0643154i
$839$	−3325.98	−	18862.6i	−0.136860	−	0.776172i	−0.973546	−	0.228490i	$-0.926621\pi$
$839$	−3325.98	−	18862.6i	−0.136860	−	0.776172i	0.836686	−	0.547683i	$-0.184490\pi$
$840$	−5683.75	−	4769.23i	−0.233462	−	0.195898i
$841$	−18483.0	+	15509.1i	−0.757843	+	0.635906i
$842$	−2085.34	+	11826.6i	−0.0853512	+	0.484051i
$843$	1013.01	−	1754.59i	0.0413878	−	0.0716858i
$844$	−5521.24	−	9563.07i	−0.225177	−	0.390017i
$845$	16789.5	−	6110.89i	0.683524	−	0.248782i
$846$	2897.76	−	1054.70i	0.117762	−	0.0428620i
$847$	−52120.3	−	90275.0i	−2.11437	−	3.66220i
$848$	4117.86	−	7132.35i	0.166755	−	0.288828i
$849$	−167.610	+	950.562i	−0.00677544	+	0.0384254i
$850$	269.221	−	225.903i	0.0108638	−	0.00911578i
$851$	16398.3	+	13759.8i	0.660546	+	0.554264i
$852$	374.945	+	2126.42i	0.0150767	+	0.0855045i
$853$	40415.2	+	14709.9i	1.62226	+	0.590456i	0.983812	−	0.179205i	$-0.0573526\pi$
$853$	40415.2	+	14709.9i	1.62226	+	0.590456i	0.638453	+	0.769661i	$0.279575\pi$
$854$	34904.3			1.39860
$855$	−12987.4	+	8371.86i	−0.519485	+	0.334867i
$856$	12889.9			0.514683
$857$	−40184.6	−	14626.0i	−1.60172	−	0.582980i	−0.621945	−	0.783061i	$-0.713657\pi$
$857$	−40184.6	−	14626.0i	−1.60172	−	0.582980i	−0.979780	+	0.200080i	$0.935880\pi$
$858$	−1803.98	−	10230.9i	−0.0717794	−	0.407081i
$859$	26902.9	+	22574.2i	1.06859	+	0.896649i	0.994924	−	0.100634i	$-0.0320871\pi$
$859$	26902.9	+	22574.2i	1.06859	+	0.896649i	0.0736616	+	0.997283i	$0.476532\pi$
$860$	−12686.4	+	10645.1i	−0.503026	+	0.422089i
$861$	4208.96	−	23870.2i	0.166598	−	0.944826i
$862$	5474.20	−	9481.60i	0.216302	−	0.374646i
$863$	−13039.6	−	22585.2i	−0.514336	−	0.890856i	−0.999862	−	0.0166337i	$-0.994705\pi$
$863$	−13039.6	−	22585.2i	−0.514336	−	0.890856i	0.485526	−	0.874222i	$-0.338628\pi$
$864$	−4151.56	+	1511.05i	−0.163471	+	0.0594986i
$865$	−13000.9	+	4731.93i	−0.511032	+	0.186000i
$866$	4665.94	+	8081.65i	0.183089	+	0.317120i
$867$	6974.97	−	12081.0i	0.273221	−	0.473232i
$868$	−135.861	+	770.509i	−0.00531272	+	0.0301299i
$869$	−51963.1	+	43602.2i	−2.02845	+	1.70207i
$870$	−833.615	−	699.486i	−0.0324853	−	0.0272584i
$871$	−161.368	−	915.166i	−0.00627757	−	0.0356018i
$872$	11691.3	+	4255.28i	0.454033	+	0.165254i
$873$	−15638.8			−0.606293
$874$	−808.315	−	16489.6i	−0.0312834	−	0.638178i
$875$	−39673.6			−1.53281
$876$	−6351.81	−	2311.87i	−0.244986	−	0.0891677i
$877$	−3098.67	−	17573.4i	−0.119310	−	0.676639i	−0.984526	−	0.175240i	$-0.943930\pi$
$877$	−3098.67	−	17573.4i	−0.119310	−	0.676639i	0.865216	−	0.501399i	$-0.167181\pi$
$878$	16878.7	+	14162.9i	0.648779	+	0.544390i
$879$	−22468.7	+	18853.5i	−0.862174	+	0.723450i
$880$	2145.93	−	12170.2i	0.0822038	−	0.466201i
$881$	15149.0	−	26238.9i	0.579324	−	1.00342i	−0.416233	−	0.909258i	$-0.636650\pi$
$881$	15149.0	−	26238.9i	0.579324	−	1.00342i	0.995557	−	0.0941604i	$-0.0300167\pi$
$882$	−7181.07	−	12438.0i	−0.274149	−	0.474840i
$883$	−16884.2	+	6145.34i	−0.643485	+	0.234210i	−0.643090	−	0.765790i	$-0.722348\pi$
$883$	−16884.2	+	6145.34i	−0.643485	+	0.234210i	−0.000395147		1.00000i	$0.500126\pi$
$884$	−1834.70	+	667.775i	−0.0698049	+	0.0254069i
$885$	13629.0	+	23606.1i	0.517666	+	0.896623i
$886$	839.112	−	1453.38i	0.0318177	−	0.0551099i
$887$	1332.76	−	7558.46i	0.0504507	−	0.286120i	−0.949136	−	0.314866i	$-0.898040\pi$
$887$	1332.76	−	7558.46i	0.0504507	−	0.286120i	0.999587	+	0.0287462i	$0.00915148\pi$
$888$	−4104.06	+	3443.71i	−0.155094	+	0.130139i
$889$	41533.2	+	34850.5i	1.56690	+	1.31479i
$890$	3598.99	+	20410.9i	0.135549	+	0.768736i
$891$	−2418.60	−	880.299i	−0.0909385	−	0.0330989i
$892$	−8174.88			−0.306856
$893$	−7332.83	−	925.522i	−0.274786	−	0.0346824i
$894$	−10417.3			−0.389716
$895$	−25099.8	−	9135.57i	−0.937422	−	0.341194i
$896$	−612.206	−	3471.99i	−0.0228263	−	0.129454i
$897$	5545.06	+	4652.86i	0.206404	+	0.173193i
$898$	2150.04	−	1804.10i	0.0798974	−	0.0670419i
$899$	−19.9263	+	113.008i	−0.000739243	+	0.00419245i
$900$	−289.732	+	501.830i	−0.0107308	+	0.0185863i
$901$	5393.66	+	9342.10i	0.199433	+	0.345428i
$902$	37936.3	−	13807.7i	1.40038	−	0.509696i
$903$	30941.8	−	11261.9i	1.14029	−	0.415030i
$904$	1876.25	+	3249.76i	0.0690300	+	0.119563i
$905$	−5126.86	+	8879.98i	−0.188312	+	0.326166i
$906$	−2211.57	+	12542.4i	−0.0810977	+	0.459928i
$907$	23378.2	−	19616.6i	0.855855	−	0.718147i	−0.105216	−	0.994449i	$-0.533553\pi$
$907$	23378.2	−	19616.6i	0.855855	−	0.718147i	0.961071	+	0.276302i	$0.0891090\pi$
$908$	20791.6	+	17446.2i	0.759903	+	0.637635i
$909$	645.336	+	3659.88i	0.0235473	+	0.133543i
$910$	13019.6	+	4738.75i	0.474281	+	0.172624i
$911$	23698.8			0.861885			0.430942	−	0.902379i	$-0.358181\pi$
$911$	23698.8			0.861885			0.430942	+	0.902379i	$0.358181\pi$
$912$	4099.34	+	517.403i	0.148841	+	0.0187861i
$913$	23884.0			0.865766
$914$	−16551.1	−	6024.10i	−0.598973	−	0.218008i
$915$	−3704.89	−	21011.5i	−0.133858	−	0.759145i
$916$	13707.3	+	11501.8i	0.494434	+	0.414879i
$917$	37645.6	−	31588.4i	1.35569	−	1.13756i
$918$	1004.87	−	5698.88i	0.0361280	−	0.204892i
$919$	10095.0	−	17485.1i	0.362356	−	0.627619i	−0.625992	−	0.779829i	$-0.715306\pi$
$919$	10095.0	−	17485.1i	0.362356	−	0.627619i	0.988348	+	0.152211i	$0.0486392\pi$
$920$	4305.34	+	7457.07i	0.154286	+	0.267231i
$921$	−19143.3	+	6967.59i	−0.684900	+	0.249283i
$922$	−16765.7	+	6102.22i	−0.598861	+	0.217968i
$923$	−2016.03	−	3491.87i	−0.0718944	−	0.124525i
$924$	−12285.5	+	21279.0i	−0.437405	+	0.757607i
$925$	−312.706	+	1773.45i	−0.0111154	+	0.0630384i
$926$	6716.84	−	5636.10i	0.238368	−	0.200015i
$927$	12817.7	+	10755.3i	0.454140	+	0.381069i
$928$	−89.7900	−	509.225i	−0.00317619	−	0.0180131i
$929$	−4170.95	−	1518.10i	−0.147303	−	0.0536139i	0.267317	−	0.963609i	$-0.413863\pi$
$929$	−4170.95	−	1518.10i	−0.147303	−	0.0536139i	−0.414619	+	0.909995i	$0.636085\pi$
$930$	478.247			0.0168627
$931$	1685.38	+	34381.5i	0.0593297	+	1.21032i
$932$	−1236.41			−0.0434550
$933$	13103.0	+	4769.10i	0.459778	+	0.167345i
$934$	1929.45	+	10942.5i	0.0675949	+	0.383350i
$935$	12399.7	+	10404.6i	0.433705	+	0.363922i
$936$	2466.06	−	2069.27i	0.0861172	−	0.0722609i
$937$	−2634.82	+	14942.8i	−0.0918632	+	0.520982i	0.903800	+	0.427954i	$0.140766\pi$
$937$	−2634.82	+	14942.8i	−0.0918632	+	0.520982i	−0.995664	+	0.0930276i	$0.970346\pi$
$938$	−1098.95	+	1903.44i	−0.0382538	+	0.0662576i
$939$	−12639.9	−	21893.0i	−0.439284	−	0.760862i
$940$	3622.40	−	1318.45i	0.125691	−	0.0457478i
$941$	8391.57	−	3054.28i	0.290709	−	0.105809i	−0.192549	−	0.981287i	$-0.561675\pi$
$941$	8391.57	−	3054.28i	0.290709	−	0.105809i	0.483258	+	0.875478i	$0.339453\pi$
$942$	−483.713	−	837.815i	−0.0167306	−	0.0289782i
$943$	−14064.7	+	24360.8i	−0.485695	+	0.841249i
$944$	−2249.11	+	12755.3i	−0.0775449	+	0.439779i
$945$	−31457.6	+	26396.0i	−1.08287	+	0.908638i
$946$	42012.5	+	35252.7i	1.44391	+	1.21159i
$947$	−4370.30	−	24785.2i	−0.149964	−	0.850487i	−0.963247	−	0.268619i	$-0.913433\pi$
$947$	−4370.30	−	24785.2i	−0.149964	−	0.850487i	0.813283	−	0.581869i	$-0.197678\pi$
$948$	11115.6	+	4045.76i	0.380822	+	0.138608i
$949$	12622.4			0.431761
$950$	1167.33	−	752.478i	0.0398665	−	0.0256985i
$951$	−12627.6			−0.430578
$952$	4339.36	+	1579.40i	0.147730	+	0.0537695i
$953$	3887.31	+	22046.0i	0.132132	+	0.749360i	0.976814	+	0.214091i	$0.0686788\pi$
$953$	3887.31	+	22046.0i	0.132132	+	0.749360i	−0.844681	+	0.535269i	$0.820210\pi$
$954$	−13625.1	−	11432.8i	−0.462398	−	0.387998i
$955$	−6043.12	+	5070.78i	−0.204765	+	0.171818i
$956$	206.634	−	1171.88i	0.00699061	−	0.0396457i
$957$	−1801.86	+	3120.92i	−0.0608631	+	0.105418i
$958$	5255.97	+	9103.61i	0.177258	+	0.307019i
$959$	10734.5	−	3907.03i	0.361454	−	0.131558i
$960$	−2025.07	+	737.064i	−0.0680820	+	0.0247798i
$961$	14870.3	+	25756.1i	0.499154	+	0.864559i
$962$	5002.19	−	8664.05i	0.167648	−	0.290375i
$963$	4833.97	−	27414.8i	0.161758	−	0.917373i
$964$	8109.56	−	6804.73i	0.270945	−	0.227350i
$965$	−16754.9	−	14059.0i	−0.558920	−	0.468990i
$966$	−2972.92	−	16860.3i	−0.0990188	−	0.561563i
$967$	32389.0	+	11788.6i	1.07711	+	0.392034i	0.818830	−	0.574037i	$-0.194623\pi$
$967$	32389.0	+	11788.6i	1.07711	+	0.392034i	0.258276	+	0.966071i	$0.416846\pi$
$968$	−30276.7			−1.00530
$969$	−3271.61	+	4311.19i	−0.108462	+	0.142926i
$970$	−19549.6			−0.647114
$971$	−14779.1	−	5379.14i	−0.488448	−	0.177781i	0.0860430	−	0.996291i	$-0.472578\pi$
$971$	−14779.1	−	5379.14i	−0.488448	−	0.177781i	−0.574491	+	0.818511i	$0.694800\pi$
$972$	2667.16	+	15126.2i	0.0880137	+	0.499151i
$973$	−13115.9	−	11005.6i	−0.432145	−	0.362613i
$974$	−1632.87	+	1370.14i	−0.0537171	+	0.0450740i
$975$	−105.741	+	599.690i	−0.00347327	+	0.0196979i
$976$	5068.99	−	8779.75i	0.166244	−	0.287944i
$977$	−2140.29	−	3707.08i	−0.0700858	−	0.121392i	0.828853	−	0.559467i	$-0.188994\pi$
$977$	−2140.29	−	3707.08i	−0.0700858	−	0.121392i	−0.898939	+	0.438074i	$0.855661\pi$
$978$	1269.56	−	462.082i	0.0415093	−	0.0151081i
$979$	64496.6	−	23474.8i	2.10554	−	0.766353i
$980$	−8976.84	−	15548.3i	−0.292607	−	0.506810i
$981$	13434.7	−	23269.7i	0.437246	−	0.757332i
$982$	3303.36	−	18734.3i	0.107347	−	0.608793i
$983$	−30638.8	+	25709.0i	−0.994126	+	0.834171i	−0.986160	−	0.165797i	$-0.946980\pi$
$983$	−30638.8	+	25709.0i	−0.994126	+	0.834171i	−0.00796655	+	0.999968i	$0.502536\pi$
$984$	−5393.01	−	4525.27i	−0.174718	−	0.146606i
$985$	−8894.72	−	50444.5i	−0.287725	−	1.63177i
$986$	636.438	+	231.644i	0.0205561	+	0.00748180i
$987$	−7664.54			−0.247178
$988$	−7523.80	+	1710.25i	−0.242271	+	0.0550710i
$989$	−38213.4			−1.22863
$990$	−25079.3	−	9128.10i	−0.805122	−	0.293041i
$991$	4768.76	+	27045.0i	0.152860	+	0.866915i	0.960716	+	0.277534i	$0.0895171\pi$
$991$	4768.76	+	27045.0i	0.152860	+	0.866915i	−0.807855	+	0.589381i	$0.799372\pi$
$992$	174.081	+	146.072i	0.00557166	+	0.00467518i
$993$	−5342.94	+	4483.26i	−0.170748	+	0.143275i
$994$	−1655.99	+	9391.61i	−0.0528420	+	0.299682i
$995$	−8016.68	+	13885.3i	−0.255423	+	0.442406i
$996$	−2082.50	−	3606.99i	−0.0662514	−	0.114751i
$997$	−46756.3	+	17017.9i	−1.48524	+	0.540585i	−0.952193	−	0.305498i	$-0.901177\pi$
$997$	−46756.3	+	17017.9i	−1.48524	+	0.540585i	−0.533051	+	0.846083i	$0.678955\pi$
$998$	−15304.8	+	5570.48i	−0.485435	+	0.176684i
$999$	14825.9	+	25679.1i	0.469539	+	0.813265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.b.23.2	yes	18
19.5	even	9	inner	38.4.e.b.5.2	✓	18
19.9	even	9		722.4.a.t.1.6		9
19.10	odd	18		722.4.a.u.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.b.5.2	✓	18	19.5	even	9	inner
38.4.e.b.23.2	yes	18	1.1	even	1	trivial
722.4.a.t.1.6		9	19.9	even	9
722.4.a.u.1.4		9	19.10	odd	18

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.541460 + 3.07077i) q^{3} +(3.06418 + 2.57115i) q^{4} +(8.27240 - 6.94137i) q^{5} +(-1.08292 + 6.14154i) q^{6} +(-13.7717 + 23.8533i) q^{7} +(4.00000 + 6.92820i) q^{8} +(16.2353 - 5.90915i) q^{9} +O(q^{10})\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.541460 + 3.07077i) q^{3} +(3.06418 + 2.57115i) q^{4} +(8.27240 - 6.94137i) q^{5} +(-1.08292 + 6.14154i) q^{6} +(-13.7717 + 23.8533i) q^{7} +(4.00000 + 6.92820i) q^{8} +(16.2353 - 5.90915i) q^{9} +(20.2952 - 7.38685i) q^{10} +(-35.7617 - 61.9411i) q^{11} +(-6.23628 + 10.8016i) q^{12} +(4.04443 - 22.9371i) q^{13} +(-42.1989 + 35.4091i) q^{14} +(25.7945 + 21.6442i) q^{15} +(2.77837 + 15.7569i) q^{16} +(-19.6933 - 7.16777i) q^{17} +34.5544 q^{18} +(-73.6649 - 37.8482i) q^{19} +43.1954 q^{20} +(-80.7047 - 29.3741i) q^{21} +(-24.8398 - 140.874i) q^{22} +(76.3526 + 64.0674i) q^{23} +(-19.1091 + 16.0344i) q^{24} +(-1.45601 + 8.25742i) q^{25} +(23.2909 - 40.3411i) q^{26} +(69.0313 + 119.566i) q^{27} +(-103.529 + 37.6816i) q^{28} +(-15.1843 + 5.52662i) q^{29} +(33.6723 + 58.3222i) q^{30} +(3.55074 - 6.15006i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(170.843 - 143.354i) q^{33} +(-32.1082 - 26.9420i) q^{34} +(51.6494 + 292.918i) q^{35} +(64.9410 + 23.6366i) q^{36} +214.770 q^{37} +(-112.555 - 121.521i) q^{38} +72.6244 q^{39} +(81.1808 + 29.5474i) q^{40} +(49.0074 + 277.935i) q^{41} +(-131.582 - 110.411i) q^{42} +(-293.698 + 246.441i) q^{43} +(49.6796 - 281.747i) q^{44} +(93.2869 - 161.578i) q^{45} +(99.6712 + 172.636i) q^{46} +(83.8608 - 30.5228i) q^{47} +(-46.8815 + 17.0635i) q^{48} +(-207.819 - 359.954i) q^{49} +(-8.38480 + 14.5229i) q^{50} +(11.3474 - 64.3546i) q^{51} +(71.3675 - 59.8845i) q^{52} +(-394.308 - 330.864i) q^{53} +(47.9486 + 271.930i) q^{54} +(-725.791 - 264.166i) q^{55} -220.347 q^{56} +(76.3366 - 246.701i) q^{57} -32.3175 q^{58} +(760.688 + 276.868i) q^{59} +(23.3886 + 132.643i) q^{60} +(-485.384 - 407.286i) q^{61} +(10.8801 - 9.12948i) q^{62} +(-82.6344 + 468.643i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-125.758 - 217.819i) q^{65} +(419.140 - 152.555i) q^{66} +(37.4928 - 13.6463i) q^{67} +(-41.9143 - 72.5977i) q^{68} +(-155.394 + 269.151i) q^{69} +(-103.299 + 585.837i) q^{70} +(132.616 - 111.278i) q^{71} +(105.881 + 88.8445i) q^{72} +(94.1080 + 533.713i) q^{73} +(403.636 + 146.911i) q^{74} -26.1450 q^{75} +(-128.409 - 305.377i) q^{76} +1970.00 q^{77} +(136.489 + 49.6780i) q^{78} +(-164.688 - 933.994i) q^{79} +(132.358 + 111.062i) q^{80} +(27.5667 - 23.1312i) q^{81} +(-98.0149 + 555.870i) q^{82} +(-166.966 + 289.194i) q^{83} +(-171.768 - 297.512i) q^{84} +(-212.665 + 77.4036i) q^{85} +(-720.547 + 262.258i) q^{86} +(-25.1926 - 43.6349i) q^{87} +(286.093 - 495.528i) q^{88} +(-166.638 + 945.049i) q^{89} +(285.848 - 239.855i) q^{90} +(491.426 + 412.355i) q^{91} +(69.2309 + 392.628i) q^{92} +(20.8080 + 7.57349i) q^{93} +178.486 q^{94} +(-872.104 + 198.239i) q^{95} -99.7805 q^{96} +(-850.583 - 309.587i) q^{97} +(-144.350 - 818.648i) q^{98} +(-946.619 - 794.308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

Introduction

L-functions

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