LMFDB - Embedded newform 775.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.a (trivial)

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:	yes
Analytic conductor:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.144209.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 6x^{3} - x^{2} + 6x - 1 $ x^5 - 6x^3 - x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.32352$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.14876 q^{2} +2.39873 q^{3} -0.680351 q^{4} -2.75556 q^{6} -1.07521 q^{7} +3.07908 q^{8} +2.75390 q^{9} +O(q^{10})$	\(q-1.14876 q^{2} +2.39873 q^{3} -0.680351 q^{4} -2.75556 q^{6} -1.07521 q^{7} +3.07908 q^{8} +2.75390 q^{9} -5.14144 q^{11} -1.63198 q^{12} -5.42473 q^{13} +1.23516 q^{14} -2.17642 q^{16} -6.47228 q^{17} -3.16357 q^{18} +1.08474 q^{19} -2.57914 q^{21} +5.90628 q^{22} +0.461088 q^{23} +7.38588 q^{24} +6.23171 q^{26} -0.590331 q^{27} +0.731521 q^{28} +4.22759 q^{29} -1.00000 q^{31} -3.65797 q^{32} -12.3329 q^{33} +7.43509 q^{34} -1.87362 q^{36} -1.68963 q^{37} -1.24610 q^{38} -13.0124 q^{39} +10.7521 q^{41} +2.96281 q^{42} +2.31233 q^{43} +3.49798 q^{44} -0.529679 q^{46} -10.5885 q^{47} -5.22064 q^{48} -5.84392 q^{49} -15.5252 q^{51} +3.69072 q^{52} -1.97929 q^{53} +0.678148 q^{54} -3.31066 q^{56} +2.60199 q^{57} -4.85649 q^{58} -3.00025 q^{59} +0.212783 q^{61} +1.14876 q^{62} -2.96103 q^{63} +8.55498 q^{64} +14.1676 q^{66} +6.84637 q^{67} +4.40342 q^{68} +1.10602 q^{69} +14.1523 q^{71} +8.47947 q^{72} +0.548064 q^{73} +1.94098 q^{74} -0.738001 q^{76} +5.52814 q^{77} +14.9482 q^{78} -2.43509 q^{79} -9.67774 q^{81} -12.3516 q^{82} -16.3360 q^{83} +1.75472 q^{84} -2.65631 q^{86} +10.1408 q^{87} -15.8309 q^{88} -8.75556 q^{89} +5.83273 q^{91} -0.313701 q^{92} -2.39873 q^{93} +12.1637 q^{94} -8.77449 q^{96} +6.34274 q^{97} +6.71326 q^{98} -14.1590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.14876	−0.812296	−0.406148	−	0.913807i	$-0.633128\pi$
$2$	−1.14876	−0.812296	−0.406148	+	0.913807i	$0.633128\pi$
$3$	2.39873	1.38491	0.692453	−	0.721463i	$-0.256530\pi$
$3$	2.39873	1.38491	0.692453	+	0.721463i	$0.256530\pi$
$4$	−0.680351	−0.340175
$5$	0	0
$5$	0	0
$6$	−2.75556	−1.12495
$7$	−1.07521	−0.406392	−0.203196	−	0.979138i	$-0.565133\pi$
$7$	−1.07521	−0.406392	−0.203196	+	0.979138i	$0.565133\pi$
$8$	3.07908	1.08862
$9$	2.75390	0.917966
$10$	0	0
$11$	−5.14144	−1.55020	−0.775101	−	0.631837i	$-0.782301\pi$
$11$	−5.14144	−1.55020	−0.775101	+	0.631837i	$0.782301\pi$
$12$	−1.63198	−0.471111
$13$	−5.42473	−1.50455	−0.752274	−	0.658850i	$-0.771043\pi$
$13$	−5.42473	−1.50455	−0.752274	+	0.658850i	$0.771043\pi$
$14$	1.23516	0.330111
$15$	0	0
$16$	−2.17642	−0.544105
$17$	−6.47228	−1.56976	−0.784879	−	0.619649i	$-0.787275\pi$
$17$	−6.47228	−1.56976	−0.784879	+	0.619649i	$0.787275\pi$
$18$	−3.16357	−0.745660
$19$	1.08474	0.248856	0.124428	−	0.992229i	$-0.460290\pi$
$19$	1.08474	0.248856	0.124428	+	0.992229i	$0.460290\pi$
$20$	0	0
$21$	−2.57914	−0.562815
$22$	5.90628	1.25922
$23$	0.461088	0.0961434	0.0480717	−	0.998844i	$-0.484692\pi$
$23$	0.461088	0.0961434	0.0480717	+	0.998844i	$0.484692\pi$
$24$	7.38588	1.50764
$25$	0	0
$26$	6.23171	1.22214
$27$	−0.590331	−0.113609
$28$	0.731521	0.138245
$29$	4.22759	0.785044	0.392522	−	0.919743i	$-0.371603\pi$
$29$	4.22759	0.785044	0.392522	+	0.919743i	$0.371603\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−3.65797	−0.646645
$33$	−12.3329	−2.14688
$34$	7.43509	1.27511
$35$	0	0
$36$	−1.87362	−0.312270
$37$	−1.68963	−0.277773	−0.138887	−	0.990308i	$-0.544352\pi$
$37$	−1.68963	−0.277773	−0.138887	+	0.990308i	$0.544352\pi$
$38$	−1.24610	−0.202144
$39$	−13.0124	−2.08366
$40$	0	0
$41$	10.7521	1.67920	0.839599	−	0.543207i	$-0.182790\pi$
$41$	10.7521	1.67920	0.839599	+	0.543207i	$0.182790\pi$
$42$	2.96281	0.457172
$43$	2.31233	0.352627	0.176313	−	0.984334i	$-0.443583\pi$
$43$	2.31233	0.352627	0.176313	+	0.984334i	$0.443583\pi$
$44$	3.49798	0.527341
$45$	0	0
$46$	−0.529679	−0.0780969
$47$	−10.5885	−1.54450	−0.772249	−	0.635320i	$-0.780868\pi$
$47$	−10.5885	−1.54450	−0.772249	+	0.635320i	$0.780868\pi$
$48$	−5.22064	−0.753535
$49$	−5.84392	−0.834846
$50$	0	0
$51$	−15.5252	−2.17397
$52$	3.69072	0.511810
$53$	−1.97929	−0.271876	−0.135938	−	0.990717i	$-0.543405\pi$
$53$	−1.97929	−0.271876	−0.135938	+	0.990717i	$0.543405\pi$
$54$	0.678148	0.0922843
$55$	0	0
$56$	−3.31066	−0.442406
$57$	2.60199	0.344642
$58$	−4.85649	−0.637688
$59$	−3.00025	−0.390599	−0.195299	−	0.980744i	$-0.562568\pi$
$59$	−3.00025	−0.390599	−0.195299	+	0.980744i	$0.562568\pi$
$60$	0	0
$61$	0.212783	0.0272441	0.0136221	−	0.999907i	$-0.495664\pi$
$61$	0.212783	0.0272441	0.0136221	+	0.999907i	$0.495664\pi$
$62$	1.14876	0.145893
$63$	−2.96103	−0.373054
$64$	8.55498	1.06937
$65$	0	0
$66$	14.1676	1.74391
$67$	6.84637	0.836417	0.418209	−	0.908351i	$-0.362658\pi$
$67$	6.84637	0.836417	0.418209	+	0.908351i	$0.362658\pi$
$68$	4.40342	0.533993
$69$	1.10602	0.133150
$70$	0	0
$71$	14.1523	1.67956	0.839782	−	0.542924i	$-0.182683\pi$
$71$	14.1523	1.67956	0.839782	+	0.542924i	$0.182683\pi$
$72$	8.47947	0.999315
$73$	0.548064	0.0641460	0.0320730	−	0.999486i	$-0.489789\pi$
$73$	0.548064	0.0641460	0.0320730	+	0.999486i	$0.489789\pi$
$74$	1.94098	0.225634
$75$	0	0
$76$	−0.738001	−0.0846545
$77$	5.52814	0.629990
$78$	14.9482	1.69255
$79$	−2.43509	−0.273969	−0.136985	−	0.990573i	$-0.543741\pi$
$79$	−2.43509	−0.273969	−0.136985	+	0.990573i	$0.543741\pi$
$80$	0	0
$81$	−9.67774	−1.07530
$82$	−12.3516	−1.36401
$83$	−16.3360	−1.79310	−0.896552	−	0.442938i	$-0.853936\pi$
$83$	−16.3360	−1.79310	−0.896552	+	0.442938i	$0.853936\pi$
$84$	1.75472	0.191456
$85$	0	0
$86$	−2.65631	−0.286437
$87$	10.1408	1.08721
$88$	−15.8309	−1.68758
$89$	−8.75556	−0.928088	−0.464044	−	0.885812i	$-0.653602\pi$
$89$	−8.75556	−0.928088	−0.464044	+	0.885812i	$0.653602\pi$
$90$	0	0
$91$	5.83273	0.611436
$92$	−0.313701	−0.0327056
$93$	−2.39873	−0.248737
$94$	12.1637	1.25459
$95$	0	0
$96$	−8.77449	−0.895542
$97$	6.34274	0.644008	0.322004	−	0.946738i	$-0.395644\pi$
$97$	6.34274	0.644008	0.322004	+	0.946738i	$0.395644\pi$
$98$	6.71326	0.678142
$99$	−14.1590	−1.42303
$100$	0	0
$101$	−2.12914	−0.211857	−0.105928	−	0.994374i	$-0.533781\pi$
$101$	−2.12914	−0.211857	−0.105928	+	0.994374i	$0.533781\pi$
$102$	17.8348	1.76590
$103$	18.3340	1.80650	0.903252	−	0.429111i	$-0.141173\pi$
$103$	18.3340	1.80650	0.903252	+	0.429111i	$0.141173\pi$
$104$	−16.7032	−1.63788
$105$	0	0
$106$	2.27373	0.220844
$107$	−2.66696	−0.257825	−0.128912	−	0.991656i	$-0.541149\pi$
$107$	−2.66696	−0.257825	−0.128912	+	0.991656i	$0.541149\pi$
$108$	0.401632	0.0386470
$109$	−10.9820	−1.05188	−0.525942	−	0.850521i	$-0.676287\pi$
$109$	−10.9820	−1.05188	−0.525942	+	0.850521i	$0.676287\pi$
$110$	0	0
$111$	−4.05296	−0.384690
$112$	2.34011	0.221120
$113$	−9.28329	−0.873298	−0.436649	−	0.899632i	$-0.643835\pi$
$113$	−9.28329	−0.873298	−0.436649	+	0.899632i	$0.643835\pi$
$114$	−2.98906	−0.279951
$115$	0	0
$116$	−2.87625	−0.267053
$117$	−14.9391	−1.38112
$118$	3.44656	0.317282
$119$	6.95907	0.637937
$120$	0	0
$121$	15.4344	1.40313
$122$	−0.244437	−0.0221303
$123$	25.7914	2.32553
$124$	0.680351	0.0610973
$125$	0	0
$126$	3.40151	0.303030
$127$	−18.3675	−1.62985	−0.814926	−	0.579566i	$-0.803222\pi$
$127$	−18.3675	−1.62985	−0.814926	+	0.579566i	$0.803222\pi$
$128$	−2.51166	−0.222002
$129$	5.54665	0.488355
$130$	0	0
$131$	−13.2364	−1.15647	−0.578235	−	0.815870i	$-0.696259\pi$
$131$	−13.2364	−1.15647	−0.578235	+	0.815870i	$0.696259\pi$
$132$	8.39071	0.730318
$133$	−1.16632	−0.101133
$134$	−7.86483	−0.679418
$135$	0	0
$136$	−19.9287	−1.70887
$137$	−10.3404	−0.883437	−0.441718	−	0.897154i	$-0.645631\pi$
$137$	−10.3404	−0.883437	−0.441718	+	0.897154i	$0.645631\pi$
$138$	−1.27056	−0.108157
$139$	7.08349	0.600813	0.300407	−	0.953811i	$-0.402878\pi$
$139$	7.08349	0.600813	0.300407	+	0.953811i	$0.402878\pi$
$140$	0	0
$141$	−25.3990	−2.13898
$142$	−16.2575	−1.36430
$143$	27.8909	2.33235
$144$	−5.99364	−0.499470
$145$	0	0
$146$	−0.629594	−0.0521055
$147$	−14.0180	−1.15618
$148$	1.14954	0.0944916
$149$	6.01411	0.492695	0.246347	−	0.969182i	$-0.420770\pi$
$149$	6.01411	0.492695	0.246347	+	0.969182i	$0.420770\pi$
$150$	0	0
$151$	6.46561	0.526164	0.263082	−	0.964773i	$-0.415261\pi$
$151$	6.46561	0.526164	0.263082	+	0.964773i	$0.415261\pi$
$152$	3.33999	0.270909
$153$	−17.8240	−1.44098
$154$	−6.35050	−0.511738
$155$	0	0
$156$	8.85303	0.708809
$157$	15.7225	1.25479	0.627396	−	0.778701i	$-0.284121\pi$
$157$	15.7225	1.25479	0.627396	+	0.778701i	$0.284121\pi$
$158$	2.79733	0.222544
$159$	−4.74777	−0.376523
$160$	0	0
$161$	−0.495767	−0.0390719
$162$	11.1174	0.873465
$163$	20.9904	1.64409	0.822046	−	0.569422i	$-0.192833\pi$
$163$	20.9904	1.64409	0.822046	+	0.569422i	$0.192833\pi$
$164$	−7.31521	−0.571222
$165$	0	0
$166$	18.7661	1.45653
$167$	−12.4819	−0.965882	−0.482941	−	0.875653i	$-0.660431\pi$
$167$	−12.4819	−0.965882	−0.482941	+	0.875653i	$0.660431\pi$
$168$	−7.94138	−0.612691
$169$	16.4276	1.26366
$170$	0	0
$171$	2.98725	0.228441
$172$	−1.57319	−0.119955
$173$	16.5085	1.25512	0.627560	−	0.778569i	$-0.284054\pi$
$173$	16.5085	1.25512	0.627560	+	0.778569i	$0.284054\pi$
$174$	−11.6494	−0.883138
$175$	0	0
$176$	11.1899	0.843473
$177$	−7.19678	−0.540943
$178$	10.0580	0.753882
$179$	−11.2312	−0.839459	−0.419729	−	0.907649i	$-0.637875\pi$
$179$	−11.2312	−0.839459	−0.419729	+	0.907649i	$0.637875\pi$
$180$	0	0
$181$	22.1626	1.64733	0.823666	−	0.567076i	$-0.191925\pi$
$181$	22.1626	1.64733	0.823666	+	0.567076i	$0.191925\pi$
$182$	−6.70041	−0.496667
$183$	0.510410	0.0377306
$184$	1.41973	0.104664
$185$	0	0
$186$	2.75556	0.202048
$187$	33.2768	2.43344
$188$	7.20392	0.525400
$189$	0.634731	0.0461699
$190$	0	0
$191$	0.562131	0.0406744	0.0203372	−	0.999793i	$-0.493526\pi$
$191$	0.562131	0.0406744	0.0203372	+	0.999793i	$0.493526\pi$
$192$	20.5211	1.48098
$193$	−17.5437	−1.26283	−0.631413	−	0.775447i	$-0.717525\pi$
$193$	−17.5437	−1.26283	−0.631413	+	0.775447i	$0.717525\pi$
$194$	−7.28629	−0.523125
$195$	0	0
$196$	3.97592	0.283994
$197$	−0.893835	−0.0636831	−0.0318415	−	0.999493i	$-0.510137\pi$
$197$	−0.893835	−0.0636831	−0.0318415	+	0.999493i	$0.510137\pi$
$198$	16.2653	1.15592
$199$	23.8425	1.69015	0.845076	−	0.534647i	$-0.179555\pi$
$199$	23.8425	1.69015	0.845076	+	0.534647i	$0.179555\pi$
$200$	0	0
$201$	16.4226	1.15836
$202$	2.44587	0.172091
$203$	−4.54556	−0.319036
$204$	10.5626	0.739530
$205$	0	0
$206$	−21.0614	−1.46742
$207$	1.26979	0.0882564
$208$	11.8065	0.818633
$209$	−5.57710	−0.385776
$210$	0	0
$211$	14.5947	1.00474	0.502369	−	0.864653i	$-0.332462\pi$
$211$	14.5947	1.00474	0.502369	+	0.864653i	$0.332462\pi$
$212$	1.34661	0.0924855
$213$	33.9474	2.32604
$214$	3.06370	0.209430
$215$	0	0
$216$	−1.81767	−0.123677
$217$	1.07521	0.0729902
$218$	12.6157	0.854441
$219$	1.31466	0.0888362
$220$	0	0
$221$	35.1103	2.36178
$222$	4.65587	0.312482
$223$	−11.9288	−0.798811	−0.399406	−	0.916774i	$-0.630783\pi$
$223$	−11.9288	−0.798811	−0.399406	+	0.916774i	$0.630783\pi$
$224$	3.93310	0.262791
$225$	0	0
$226$	10.6643	0.709376
$227$	−20.8616	−1.38463	−0.692315	−	0.721595i	$-0.743409\pi$
$227$	−20.8616	−1.38463	−0.692315	+	0.721595i	$0.743409\pi$
$228$	−1.77026	−0.117239
$229$	2.00158	0.132268	0.0661342	−	0.997811i	$-0.478933\pi$
$229$	2.00158	0.132268	0.0661342	+	0.997811i	$0.478933\pi$
$230$	0	0
$231$	13.2605	0.872477
$232$	13.0171	0.854614
$233$	−9.88672	−0.647701	−0.323850	−	0.946108i	$-0.604977\pi$
$233$	−9.88672	−0.647701	−0.323850	+	0.946108i	$0.604977\pi$
$234$	17.1615	1.12188
$235$	0	0
$236$	2.04122	0.132872
$237$	−5.84112	−0.379422
$238$	−7.99430	−0.518193
$239$	−4.23948	−0.274229	−0.137115	−	0.990555i	$-0.543783\pi$
$239$	−4.23948	−0.274229	−0.137115	+	0.990555i	$0.543783\pi$
$240$	0	0
$241$	6.65199	0.428492	0.214246	−	0.976780i	$-0.431271\pi$
$241$	6.65199	0.428492	0.214246	+	0.976780i	$0.431271\pi$
$242$	−17.7304	−1.13975
$243$	−21.4433	−1.37559
$244$	−0.144767	−0.00926778
$245$	0	0
$246$	−29.6281	−1.88902
$247$	−5.88440	−0.374415
$248$	−3.07908	−0.195522
$249$	−39.1855	−2.48328
$250$	0	0
$251$	11.7345	0.740676	0.370338	−	0.928897i	$-0.379242\pi$
$251$	11.7345	0.740676	0.370338	+	0.928897i	$0.379242\pi$
$252$	2.01454	0.126904
$253$	−2.37065	−0.149042
$254$	21.0998	1.32392
$255$	0	0
$256$	−14.2247	−0.889041
$257$	14.1060	0.879911	0.439956	−	0.898020i	$-0.354994\pi$
$257$	14.1060	0.879911	0.439956	+	0.898020i	$0.354994\pi$
$258$	−6.37177	−0.396689
$259$	1.81671	0.112885
$260$	0	0
$261$	11.6424	0.720644
$262$	15.2055	0.939397
$263$	−24.5143	−1.51162	−0.755809	−	0.654792i	$-0.772756\pi$
$263$	−24.5143	−1.51162	−0.755809	+	0.654792i	$0.772756\pi$
$264$	−37.9740	−2.33714
$265$	0	0
$266$	1.33982	0.0821498
$267$	−21.0022	−1.28531
$268$	−4.65793	−0.284529
$269$	23.0144	1.40321	0.701606	−	0.712565i	$-0.252467\pi$
$269$	23.0144	1.40321	0.701606	+	0.712565i	$0.252467\pi$
$270$	0	0
$271$	−22.1893	−1.34790	−0.673951	−	0.738776i	$-0.735404\pi$
$271$	−22.1893	−1.34790	−0.673951	+	0.738776i	$0.735404\pi$
$272$	14.0864	0.854113
$273$	13.9911	0.846782
$274$	11.8786	0.717612
$275$	0	0
$276$	−0.752485	−0.0452942
$277$	−8.26245	−0.496442	−0.248221	−	0.968703i	$-0.579846\pi$
$277$	−8.26245	−0.496442	−0.248221	+	0.968703i	$0.579846\pi$
$278$	−8.13722	−0.488038
$279$	−2.75390	−0.164872
$280$	0	0
$281$	−22.3820	−1.33520	−0.667601	−	0.744520i	$-0.732679\pi$
$281$	−22.3820	−1.33520	−0.667601	+	0.744520i	$0.732679\pi$
$282$	29.1774	1.73749
$283$	−1.36193	−0.0809584	−0.0404792	−	0.999180i	$-0.512888\pi$
$283$	−1.36193	−0.0809584	−0.0404792	+	0.999180i	$0.512888\pi$
$284$	−9.62850	−0.571346
$285$	0	0
$286$	−32.0399	−1.89456
$287$	−11.5608	−0.682412
$288$	−10.0737	−0.593598
$289$	24.8904	1.46414
$290$	0	0
$291$	15.2145	0.891891
$292$	−0.372876	−0.0218209
$293$	−12.0907	−0.706346	−0.353173	−	0.935558i	$-0.614897\pi$
$293$	−12.0907	−0.706346	−0.353173	+	0.935558i	$0.614897\pi$
$294$	16.1033	0.939163
$295$	0	0
$296$	−5.20250	−0.302389
$297$	3.03515	0.176117
$298$	−6.90877	−0.400214
$299$	−2.50127	−0.144652
$300$	0	0
$301$	−2.48624	−0.143305
$302$	−7.42744	−0.427401
$303$	−5.10722	−0.293402
$304$	−2.36084	−0.135404
$305$	0	0
$306$	20.4755	1.17051
$307$	31.2714	1.78475	0.892376	−	0.451293i	$-0.149037\pi$
$307$	31.2714	1.78475	0.892376	+	0.451293i	$0.149037\pi$
$308$	−3.76107	−0.214307
$309$	43.9783	2.50184
$310$	0	0
$311$	12.3726	0.701586	0.350793	−	0.936453i	$-0.385912\pi$
$311$	12.3726	0.701586	0.350793	+	0.936453i	$0.385912\pi$
$312$	−40.0663	−2.26831
$313$	−22.4114	−1.26677	−0.633383	−	0.773839i	$-0.718334\pi$
$313$	−22.4114	−1.26677	−0.633383	+	0.773839i	$0.718334\pi$
$314$	−18.0614	−1.01926
$315$	0	0
$316$	1.65672	0.0931976
$317$	−25.1857	−1.41457	−0.707286	−	0.706928i	$-0.750081\pi$
$317$	−25.1857	−1.41457	−0.707286	+	0.706928i	$0.750081\pi$
$318$	5.45405	0.305848
$319$	−21.7359	−1.21698
$320$	0	0
$321$	−6.39731	−0.357063
$322$	0.569517	0.0317380
$323$	−7.02071	−0.390643
$324$	6.58426	0.365792
$325$	0	0
$326$	−24.1129	−1.33549
$327$	−26.3428	−1.45676
$328$	33.1066	1.82801
$329$	11.3849	0.627671
$330$	0	0
$331$	−12.5652	−0.690643	−0.345322	−	0.938484i	$-0.612230\pi$
$331$	−12.5652	−0.690643	−0.345322	+	0.938484i	$0.612230\pi$
$332$	11.1142	0.609970
$333$	−4.65306	−0.254986
$334$	14.3388	0.784582
$335$	0	0
$336$	5.61330	0.306231
$337$	30.5561	1.66450	0.832249	−	0.554402i	$-0.187053\pi$
$337$	30.5561	1.66450	0.832249	+	0.554402i	$0.187053\pi$
$338$	−18.8714	−1.02647
$339$	−22.2681	−1.20944
$340$	0	0
$341$	5.14144	0.278425
$342$	−3.43164	−0.185562
$343$	13.8099	0.745667
$344$	7.11984	0.383876
$345$	0	0
$346$	−18.9643	−1.01953
$347$	20.0600	1.07688	0.538438	−	0.842665i	$-0.319014\pi$
$347$	20.0600	1.07688	0.538438	+	0.842665i	$0.319014\pi$
$348$	−6.89933	−0.369843
$349$	−32.2476	−1.72617	−0.863087	−	0.505056i	$-0.831472\pi$
$349$	−32.2476	−1.72617	−0.863087	+	0.505056i	$0.831472\pi$
$350$	0	0
$351$	3.20238	0.170930
$352$	18.8072	1.00243
$353$	20.5755	1.09512	0.547561	−	0.836766i	$-0.315556\pi$
$353$	20.5755	1.09512	0.547561	+	0.836766i	$0.315556\pi$
$354$	8.26737	0.439406
$355$	0	0
$356$	5.95685	0.315713
$357$	16.6929	0.883483
$358$	12.9019	0.681889
$359$	8.20937	0.433274	0.216637	−	0.976252i	$-0.430491\pi$
$359$	8.20937	0.433274	0.216637	+	0.976252i	$0.430491\pi$
$360$	0	0
$361$	−17.8233	−0.938071
$362$	−25.4595	−1.33812
$363$	37.0229	1.94320
$364$	−3.96830	−0.207996
$365$	0	0
$366$	−0.586338	−0.0306484
$367$	−4.59241	−0.239722	−0.119861	−	0.992791i	$-0.538245\pi$
$367$	−4.59241	−0.239722	−0.119861	+	0.992791i	$0.538245\pi$
$368$	−1.00352	−0.0523121
$369$	29.6102	1.54145
$370$	0	0
$371$	2.12815	0.110488
$372$	1.63198	0.0846141
$373$	−5.88799	−0.304869	−0.152434	−	0.988314i	$-0.548711\pi$
$373$	−5.88799	−0.304869	−0.152434	+	0.988314i	$0.548711\pi$
$374$	−38.2271	−1.97667
$375$	0	0
$376$	−32.6030	−1.68137
$377$	−22.9335	−1.18114
$378$	−0.729153	−0.0375036
$379$	−34.6399	−1.77933	−0.889667	−	0.456611i	$-0.849063\pi$
$379$	−34.6399	−1.77933	−0.889667	+	0.456611i	$0.849063\pi$
$380$	0	0
$381$	−44.0586	−2.25719
$382$	−0.645753	−0.0330396
$383$	6.13428	0.313447	0.156724	−	0.987643i	$-0.449907\pi$
$383$	6.13428	0.313447	0.156724	+	0.987643i	$0.449907\pi$
$384$	−6.02480	−0.307452
$385$	0	0
$386$	20.1535	1.02579
$387$	6.36792	0.323699
$388$	−4.31529	−0.219076
$389$	−33.3188	−1.68933	−0.844665	−	0.535295i	$-0.820200\pi$
$389$	−33.3188	−1.68933	−0.844665	+	0.535295i	$0.820200\pi$
$390$	0	0
$391$	−2.98429	−0.150922
$392$	−17.9939	−0.908829
$393$	−31.7506	−1.60160
$394$	1.02680	0.0517295
$395$	0	0
$396$	9.63309	0.484081
$397$	10.1322	0.508523	0.254261	−	0.967136i	$-0.418168\pi$
$397$	10.1322	0.508523	0.254261	+	0.967136i	$0.418168\pi$
$398$	−27.3893	−1.37290
$399$	−2.79769	−0.140060
$400$	0	0
$401$	−12.0648	−0.602490	−0.301245	−	0.953547i	$-0.597402\pi$
$401$	−12.0648	−0.602490	−0.301245	+	0.953547i	$0.597402\pi$
$402$	−18.8656	−0.940931
$403$	5.42473	0.270225
$404$	1.44856	0.0720685
$405$	0	0
$406$	5.22175	0.259151
$407$	8.68712	0.430604
$408$	−47.8034	−2.36662
$409$	−10.6557	−0.526891	−0.263445	−	0.964674i	$-0.584859\pi$
$409$	−10.6557	−0.526891	−0.263445	+	0.964674i	$0.584859\pi$
$410$	0	0
$411$	−24.8037	−1.22348
$412$	−12.4736	−0.614528
$413$	3.22590	0.158736
$414$	−1.45868	−0.0716903
$415$	0	0
$416$	19.8435	0.972908
$417$	16.9914	0.832070
$418$	6.40675	0.313365
$419$	−3.54779	−0.173321	−0.0866605	−	0.996238i	$-0.527620\pi$
$419$	−3.54779	−0.173321	−0.0866605	+	0.996238i	$0.527620\pi$
$420$	0	0
$421$	25.9541	1.26492	0.632462	−	0.774591i	$-0.282044\pi$
$421$	25.9541	1.26492	0.632462	+	0.774591i	$0.282044\pi$
$422$	−16.7658	−0.816145
$423$	−29.1598	−1.41780
$424$	−6.09438	−0.295969
$425$	0	0
$426$	−38.9974	−1.88943
$427$	−0.228787	−0.0110718
$428$	1.81447	0.0877056
$429$	66.9027	3.23009
$430$	0	0
$431$	24.4460	1.17752	0.588762	−	0.808306i	$-0.299616\pi$
$431$	24.4460	1.17752	0.588762	+	0.808306i	$0.299616\pi$
$432$	1.28481	0.0618153
$433$	−37.6380	−1.80877	−0.904384	−	0.426720i	$-0.859669\pi$
$433$	−37.6380	−1.80877	−0.904384	+	0.426720i	$0.859669\pi$
$434$	−1.23516	−0.0592896
$435$	0	0
$436$	7.47160	0.357825
$437$	0.500159	0.0239258
$438$	−1.51022	−0.0721613
$439$	33.5872	1.60303	0.801514	−	0.597976i	$-0.204028\pi$
$439$	33.5872	1.60303	0.801514	+	0.597976i	$0.204028\pi$
$440$	0	0
$441$	−16.0936	−0.766360
$442$	−40.3333	−1.91846
$443$	−7.03358	−0.334176	−0.167088	−	0.985942i	$-0.553436\pi$
$443$	−7.03358	−0.334176	−0.167088	+	0.985942i	$0.553436\pi$
$444$	2.75743	0.130862
$445$	0	0
$446$	13.7033	0.648871
$447$	14.4262	0.682336
$448$	−9.19841	−0.434584
$449$	−12.6447	−0.596740	−0.298370	−	0.954450i	$-0.596443\pi$
$449$	−12.6447	−0.596740	−0.298370	+	0.954450i	$0.596443\pi$
$450$	0	0
$451$	−55.2813	−2.60310
$452$	6.31589	0.297075
$453$	15.5092	0.728688
$454$	23.9649	1.12473
$455$	0	0
$456$	8.01173	0.375183
$457$	−19.8545	−0.928752	−0.464376	−	0.885638i	$-0.653721\pi$
$457$	−19.8545	−0.928752	−0.464376	+	0.885638i	$0.653721\pi$
$458$	−2.29934	−0.107441
$459$	3.82078	0.178339
$460$	0	0
$461$	−21.2965	−0.991878	−0.495939	−	0.868357i	$-0.665176\pi$
$461$	−21.2965	−0.991878	−0.495939	+	0.868357i	$0.665176\pi$
$462$	−15.2331	−0.708709
$463$	15.6214	0.725990	0.362995	−	0.931791i	$-0.381754\pi$
$463$	15.6214	0.725990	0.362995	+	0.931791i	$0.381754\pi$
$464$	−9.20102	−0.427147
$465$	0	0
$466$	11.3575	0.526125
$467$	20.8505	0.964845	0.482422	−	0.875939i	$-0.339757\pi$
$467$	20.8505	0.964845	0.482422	+	0.875939i	$0.339757\pi$
$468$	10.1639	0.469825
$469$	−7.36130	−0.339913
$470$	0	0
$471$	37.7140	1.73777
$472$	−9.23800	−0.425213
$473$	−11.8887	−0.546643
$474$	6.71005	0.308203
$475$	0	0
$476$	−4.73461	−0.217010
$477$	−5.45076	−0.249573
$478$	4.87015	0.222755
$479$	−39.8990	−1.82303	−0.911515	−	0.411267i	$-0.865086\pi$
$479$	−39.8990	−1.82303	−0.911515	+	0.411267i	$0.865086\pi$
$480$	0	0
$481$	9.16576	0.417923
$482$	−7.64154	−0.348063
$483$	−1.18921	−0.0541110
$484$	−10.5008	−0.477309
$485$	0	0
$486$	24.6332	1.11738
$487$	−0.148760	−0.00674095	−0.00337048	−	0.999994i	$-0.501073\pi$
$487$	−0.148760	−0.00674095	−0.00337048	+	0.999994i	$0.501073\pi$
$488$	0.655177	0.0296585
$489$	50.3502	2.27691
$490$	0	0
$491$	−29.3127	−1.32286	−0.661432	−	0.750005i	$-0.730051\pi$
$491$	−29.3127	−1.32286	−0.661432	+	0.750005i	$0.730051\pi$
$492$	−17.5472	−0.791089
$493$	−27.3621	−1.23233
$494$	6.75976	0.304136
$495$	0	0
$496$	2.17642	0.0977242
$497$	−15.2167	−0.682561
$498$	45.0148	2.01716
$499$	−34.0629	−1.52486	−0.762432	−	0.647068i	$-0.775995\pi$
$499$	−34.0629	−1.52486	−0.762432	+	0.647068i	$0.775995\pi$
$500$	0	0
$501$	−29.9408	−1.33766
$502$	−13.4801	−0.601648
$503$	12.7364	0.567888	0.283944	−	0.958841i	$-0.408357\pi$
$503$	12.7364	0.567888	0.283944	+	0.958841i	$0.408357\pi$
$504$	−9.11723	−0.406114
$505$	0	0
$506$	2.72331	0.121066
$507$	39.4055	1.75006
$508$	12.4963	0.554435
$509$	45.0306	1.99595	0.997974	−	0.0636266i	$-0.0202667\pi$
$509$	45.0306	1.99595	0.997974	+	0.0636266i	$0.0202667\pi$
$510$	0	0
$511$	−0.589285	−0.0260684
$512$	21.3640	0.944166
$513$	−0.640353	−0.0282723
$514$	−16.2045	−0.714748
$515$	0	0
$516$	−3.77367	−0.166126
$517$	54.4403	2.39428
$518$	−2.08696	−0.0916958
$519$	39.5994	1.73822
$520$	0	0
$521$	−32.5888	−1.42774	−0.713870	−	0.700279i	$-0.753059\pi$
$521$	−32.5888	−1.42774	−0.713870	+	0.700279i	$0.753059\pi$
$522$	−13.3743	−0.585376
$523$	−8.72008	−0.381303	−0.190651	−	0.981658i	$-0.561060\pi$
$523$	−8.72008	−0.381303	−0.190651	+	0.981658i	$0.561060\pi$
$524$	9.00541	0.393403
$525$	0	0
$526$	28.1611	1.22788
$527$	6.47228	0.281937
$528$	26.8416	1.16813
$529$	−22.7874	−0.990756
$530$	0	0
$531$	−8.26238	−0.358557
$532$	0.793508	0.0344029
$533$	−58.3272	−2.52643
$534$	24.1265	1.04406
$535$	0	0
$536$	21.0805	0.910540
$537$	−26.9406	−1.16257
$538$	−26.4380	−1.13982
$539$	30.0461	1.29418
$540$	0	0
$541$	18.6684	0.802619	0.401310	−	0.915942i	$-0.368555\pi$
$541$	18.6684	0.802619	0.401310	+	0.915942i	$0.368555\pi$
$542$	25.4902	1.09490
$543$	53.1620	2.28140
$544$	23.6754	1.01508
$545$	0	0
$546$	−16.0725	−0.687838
$547$	7.08710	0.303023	0.151511	−	0.988456i	$-0.451586\pi$
$547$	7.08710	0.303023	0.151511	+	0.988456i	$0.451586\pi$
$548$	7.03507	0.300523
$549$	0.585984	0.0250092
$550$	0	0
$551$	4.58582	0.195363
$552$	3.40554	0.144949
$553$	2.61824	0.111339
$554$	9.49157	0.403258
$555$	0	0
$556$	−4.81926	−0.204382
$557$	−22.5799	−0.956742	−0.478371	−	0.878158i	$-0.658773\pi$
$557$	−22.5799	−0.956742	−0.478371	+	0.878158i	$0.658773\pi$
$558$	3.16357	0.133925
$559$	−12.5437	−0.530544
$560$	0	0
$561$	79.8220	3.37009
$562$	25.7116	1.08458
$563$	−27.4367	−1.15632	−0.578160	−	0.815923i	$-0.696229\pi$
$563$	−27.4367	−1.15632	−0.578160	+	0.815923i	$0.696229\pi$
$564$	17.2803	0.727630
$565$	0	0
$566$	1.56453	0.0657622
$567$	10.4056	0.436995
$568$	43.5759	1.82840
$569$	−24.3611	−1.02127	−0.510635	−	0.859798i	$-0.670590\pi$
$569$	−24.3611	−1.02127	−0.510635	+	0.859798i	$0.670590\pi$
$570$	0	0
$571$	−12.8908	−0.539463	−0.269731	−	0.962936i	$-0.586935\pi$
$571$	−12.8908	−0.539463	−0.269731	+	0.962936i	$0.586935\pi$
$572$	−18.9756	−0.793409
$573$	1.34840	0.0563302
$574$	13.2806	0.554321
$575$	0	0
$576$	23.5595	0.981647
$577$	−28.5849	−1.19000	−0.595002	−	0.803724i	$-0.702849\pi$
$577$	−28.5849	−1.19000	−0.595002	+	0.803724i	$0.702849\pi$
$578$	−28.5930	−1.18931
$579$	−42.0827	−1.74890
$580$	0	0
$581$	17.5646	0.728703
$582$	−17.4778	−0.724479
$583$	10.1764	0.421463
$584$	1.68753	0.0698306
$585$	0	0
$586$	13.8893	0.573762
$587$	21.5226	0.888334	0.444167	−	0.895944i	$-0.353500\pi$
$587$	21.5226	0.888334	0.444167	+	0.895944i	$0.353500\pi$
$588$	9.53714	0.393305
$589$	−1.08474	−0.0446958
$590$	0	0
$591$	−2.14407	−0.0881951
$592$	3.67734	0.151138
$593$	−20.5018	−0.841910	−0.420955	−	0.907082i	$-0.638305\pi$
$593$	−20.5018	−0.841910	−0.420955	+	0.907082i	$0.638305\pi$
$594$	−3.48666	−0.143059
$595$	0	0
$596$	−4.09170	−0.167603
$597$	57.1917	2.34070
$598$	2.87336	0.117501
$599$	19.7989	0.808963	0.404481	−	0.914546i	$-0.367452\pi$
$599$	19.7989	0.808963	0.404481	+	0.914546i	$0.367452\pi$
$600$	0	0
$601$	−19.3663	−0.789969	−0.394984	−	0.918688i	$-0.629250\pi$
$601$	−19.3663	−0.789969	−0.394984	+	0.918688i	$0.629250\pi$
$602$	2.85610	0.116406
$603$	18.8542	0.767803
$604$	−4.39888	−0.178988
$605$	0	0
$606$	5.86697	0.238329
$607$	−13.9735	−0.567166	−0.283583	−	0.958948i	$-0.591523\pi$
$607$	−13.9735	−0.567166	−0.283583	+	0.958948i	$0.591523\pi$
$608$	−3.96794	−0.160921
$609$	−10.9036	−0.441835
$610$	0	0
$611$	57.4399	2.32377
$612$	12.1266	0.490187
$613$	−20.4549	−0.826166	−0.413083	−	0.910693i	$-0.635548\pi$
$613$	−20.4549	−0.826166	−0.413083	+	0.910693i	$0.635548\pi$
$614$	−35.9233	−1.44975
$615$	0	0
$616$	17.0216	0.685819
$617$	−19.1597	−0.771339	−0.385670	−	0.922637i	$-0.626030\pi$
$617$	−19.1597	−0.771339	−0.385670	+	0.922637i	$0.626030\pi$
$618$	−50.5205	−2.03223
$619$	7.32609	0.294461	0.147230	−	0.989102i	$-0.452964\pi$
$619$	7.32609	0.294461	0.147230	+	0.989102i	$0.452964\pi$
$620$	0	0
$621$	−0.272194	−0.0109228
$622$	−14.2132	−0.569896
$623$	9.41409	0.377167
$624$	28.3206	1.13373
$625$	0	0
$626$	25.7453	1.02899
$627$	−13.3780	−0.534264
$628$	−10.6968	−0.426849
$629$	10.9357	0.436036
$630$	0	0
$631$	28.6658	1.14117	0.570583	−	0.821240i	$-0.306717\pi$
$631$	28.6658	1.14117	0.570583	+	0.821240i	$0.306717\pi$
$632$	−7.49784	−0.298248
$633$	35.0086	1.39147
$634$	28.9324	1.14905
$635$	0	0
$636$	3.23015	0.128084
$637$	31.7017	1.25607
$638$	24.9693	0.988545
$639$	38.9739	1.54178
$640$	0	0
$641$	18.8022	0.742644	0.371322	−	0.928504i	$-0.378905\pi$
$641$	18.8022	0.742644	0.371322	+	0.928504i	$0.378905\pi$
$642$	7.34897	0.290041
$643$	11.4688	0.452285	0.226142	−	0.974094i	$-0.427389\pi$
$643$	11.4688	0.452285	0.226142	+	0.974094i	$0.427389\pi$
$644$	0.337296	0.0132913
$645$	0	0
$646$	8.06511	0.317318
$647$	28.7688	1.13102	0.565509	−	0.824742i	$-0.308680\pi$
$647$	28.7688	1.13102	0.565509	+	0.824742i	$0.308680\pi$
$648$	−29.7985	−1.17060
$649$	15.4256	0.605507
$650$	0	0
$651$	2.57914	0.101085
$652$	−14.2808	−0.559279
$653$	11.2620	0.440715	0.220358	−	0.975419i	$-0.429278\pi$
$653$	11.2620	0.440715	0.220358	+	0.975419i	$0.429278\pi$
$654$	30.2616	1.18332
$655$	0	0
$656$	−23.4011	−0.913660
$657$	1.50931	0.0588839
$658$	−13.0785	−0.509855
$659$	−19.0993	−0.744003	−0.372002	−	0.928232i	$-0.621328\pi$
$659$	−19.0993	−0.744003	−0.372002	+	0.928232i	$0.621328\pi$
$660$	0	0
$661$	−41.5940	−1.61782	−0.808910	−	0.587933i	$-0.799942\pi$
$661$	−41.5940	−1.61782	−0.808910	+	0.587933i	$0.799942\pi$
$662$	14.4343	0.561007
$663$	84.2201	3.27084
$664$	−50.2997	−1.95201
$665$	0	0
$666$	5.34525	0.207124
$667$	1.94929	0.0754768
$668$	8.49210	0.328569
$669$	−28.6139	−1.10628
$670$	0	0
$671$	−1.09401	−0.0422339
$672$	9.43443	0.363941
$673$	34.3810	1.32529	0.662644	−	0.748934i	$-0.269434\pi$
$673$	34.3810	1.32529	0.662644	+	0.748934i	$0.269434\pi$
$674$	−35.1017	−1.35207
$675$	0	0
$676$	−11.1766	−0.429868
$677$	13.7267	0.527559	0.263780	−	0.964583i	$-0.415031\pi$
$677$	13.7267	0.527559	0.263780	+	0.964583i	$0.415031\pi$
$678$	25.5807	0.982420
$679$	−6.81979	−0.261720
$680$	0	0
$681$	−50.0412	−1.91758
$682$	−5.90628	−0.226163
$683$	19.9784	0.764454	0.382227	−	0.924069i	$-0.375157\pi$
$683$	19.9784	0.764454	0.382227	+	0.924069i	$0.375157\pi$
$684$	−2.03238	−0.0777100
$685$	0	0
$686$	−15.8643	−0.605702
$687$	4.80126	0.183179
$688$	−5.03260	−0.191866
$689$	10.7371	0.409051
$690$	0	0
$691$	46.4451	1.76685	0.883427	−	0.468568i	$-0.155230\pi$
$691$	46.4451	1.76685	0.883427	+	0.468568i	$0.155230\pi$
$692$	−11.2316	−0.426961
$693$	15.2239	0.578309
$694$	−23.0441	−0.874743
$695$	0	0
$696$	31.2245	1.18356
$697$	−69.5906	−2.63593
$698$	37.0447	1.40216
$699$	−23.7156	−0.897005
$700$	0	0
$701$	−3.85063	−0.145436	−0.0727182	−	0.997353i	$-0.523167\pi$
$701$	−3.85063	−0.145436	−0.0727182	+	0.997353i	$0.523167\pi$
$702$	−3.67877	−0.138846
$703$	−1.83280	−0.0691254
$704$	−43.9849	−1.65774
$705$	0	0
$706$	−23.6363	−0.889563
$707$	2.28927	0.0860970
$708$	4.89634	0.184016
$709$	−22.1782	−0.832920	−0.416460	−	0.909154i	$-0.636729\pi$
$709$	−22.1782	−0.832920	−0.416460	+	0.909154i	$0.636729\pi$
$710$	0	0
$711$	−6.70599	−0.251494
$712$	−26.9591	−1.01033
$713$	−0.461088	−0.0172679
$714$	−19.1762	−0.717650
$715$	0	0
$716$	7.64115	0.285563
$717$	−10.1694	−0.379782
$718$	−9.43060	−0.351947
$719$	2.68962	0.100306	0.0501530	−	0.998742i	$-0.484029\pi$
$719$	2.68962	0.100306	0.0501530	+	0.998742i	$0.484029\pi$
$720$	0	0
$721$	−19.7129	−0.734148
$722$	20.4747	0.761991
$723$	15.9563	0.593422
$724$	−15.0783	−0.560382
$725$	0	0
$726$	−42.5304	−1.57845
$727$	15.7575	0.584414	0.292207	−	0.956355i	$-0.405610\pi$
$727$	15.7575	0.584414	0.292207	+	0.956355i	$0.405610\pi$
$728$	17.9594	0.665621
$729$	−22.4034	−0.829755
$730$	0	0
$731$	−14.9660	−0.553538
$732$	−0.347258	−0.0128350
$733$	8.88736	0.328262	0.164131	−	0.986439i	$-0.447518\pi$
$733$	8.88736	0.328262	0.164131	+	0.986439i	$0.447518\pi$
$734$	5.27557	0.194725
$735$	0	0
$736$	−1.68665	−0.0621706
$737$	−35.2002	−1.29662
$738$	−34.0150	−1.25211
$739$	−22.7733	−0.837728	−0.418864	−	0.908049i	$-0.637572\pi$
$739$	−22.7733	−0.837728	−0.418864	+	0.908049i	$0.637572\pi$
$740$	0	0
$741$	−14.1151	−0.518530
$742$	−2.44474	−0.0897491
$743$	−5.63705	−0.206803	−0.103402	−	0.994640i	$-0.532973\pi$
$743$	−5.63705	−0.206803	−0.103402	+	0.994640i	$0.532973\pi$
$744$	−7.38588	−0.270779
$745$	0	0
$746$	6.76389	0.247644
$747$	−44.9876	−1.64601
$748$	−22.6399	−0.827797
$749$	2.86755	0.104778
$750$	0	0
$751$	26.7532	0.976236	0.488118	−	0.872778i	$-0.337683\pi$
$751$	26.7532	0.976236	0.488118	+	0.872778i	$0.337683\pi$
$752$	23.0451	0.840369
$753$	28.1479	1.02577
$754$	26.3451	0.959432
$755$	0	0
$756$	−0.431839	−0.0157058
$757$	4.27347	0.155322	0.0776610	−	0.996980i	$-0.475255\pi$
$757$	4.27347	0.155322	0.0776610	+	0.996980i	$0.475255\pi$
$758$	39.7929	1.44534
$759$	−5.68656	−0.206409
$760$	0	0
$761$	−40.9053	−1.48281	−0.741407	−	0.671055i	$-0.765841\pi$
$761$	−40.9053	−1.48281	−0.741407	+	0.671055i	$0.765841\pi$
$762$	50.6128	1.83351
$763$	11.8080	0.427477
$764$	−0.382446	−0.0138364
$765$	0	0
$766$	−7.04681	−0.254612
$767$	16.2755	0.587675
$768$	−34.1211	−1.23124
$769$	−18.7967	−0.677827	−0.338913	−	0.940818i	$-0.610059\pi$
$769$	−18.7967	−0.677827	−0.338913	+	0.940818i	$0.610059\pi$
$770$	0	0
$771$	33.8366	1.21859
$772$	11.9359	0.429582
$773$	−21.9504	−0.789501	−0.394751	−	0.918788i	$-0.629169\pi$
$773$	−21.9504	−0.789501	−0.394751	+	0.918788i	$0.629169\pi$
$774$	−7.31521	−0.262940
$775$	0	0
$776$	19.5298	0.701079
$777$	4.35779	0.156335
$778$	38.2753	1.37224
$779$	11.6632	0.417878
$780$	0	0
$781$	−72.7629	−2.60366
$782$	3.42823	0.122593
$783$	−2.49568	−0.0891882
$784$	12.7188	0.454244
$785$	0	0
$786$	36.4738	1.30098
$787$	6.32800	0.225569	0.112784	−	0.993619i	$-0.464023\pi$
$787$	6.32800	0.225569	0.112784	+	0.993619i	$0.464023\pi$
$788$	0.608121	0.0216634
$789$	−58.8032	−2.09345
$790$	0	0
$791$	9.98150	0.354901
$792$	−43.5967	−1.54914
$793$	−1.15429	−0.0409901
$794$	−11.6395	−0.413071
$795$	0	0
$796$	−16.2213	−0.574948
$797$	19.0162	0.673589	0.336795	−	0.941578i	$-0.390657\pi$
$797$	19.0162	0.673589	0.336795	+	0.941578i	$0.390657\pi$
$798$	3.21387	0.113770
$799$	68.5320	2.42449
$800$	0	0
$801$	−24.1119	−0.851953
$802$	13.8596	0.489400
$803$	−2.81784	−0.0994393
$804$	−11.1731	−0.394045
$805$	0	0
$806$	−6.23171	−0.219502
$807$	55.2053	1.94332
$808$	−6.55578	−0.230632
$809$	19.0862	0.671037	0.335518	−	0.942034i	$-0.391089\pi$
$809$	19.0862	0.671037	0.335518	+	0.942034i	$0.391089\pi$
$810$	0	0
$811$	12.5700	0.441392	0.220696	−	0.975343i	$-0.429167\pi$
$811$	12.5700	0.441392	0.220696	+	0.975343i	$0.429167\pi$
$812$	3.09257	0.108528
$813$	−53.2261	−1.86672
$814$	−9.97941	−0.349778
$815$	0	0
$816$	33.7894	1.18287
$817$	2.50827	0.0877531
$818$	12.2408	0.427991
$819$	16.0627	0.561278
$820$	0	0
$821$	−12.5078	−0.436525	−0.218262	−	0.975890i	$-0.570039\pi$
$821$	−12.5078	−0.436525	−0.218262	+	0.975890i	$0.570039\pi$
$822$	28.4935	0.993826
$823$	2.64856	0.0923229	0.0461614	−	0.998934i	$-0.485301\pi$
$823$	2.64856	0.0923229	0.0461614	+	0.998934i	$0.485301\pi$
$824$	56.4519	1.96659
$825$	0	0
$826$	−3.70579	−0.128941
$827$	−17.3532	−0.603431	−0.301716	−	0.953398i	$-0.597559\pi$
$827$	−17.3532	−0.603431	−0.301716	+	0.953398i	$0.597559\pi$
$828$	−0.863902	−0.0300227
$829$	−20.0627	−0.696808	−0.348404	−	0.937344i	$-0.613276\pi$
$829$	−20.0627	−0.696808	−0.348404	+	0.937344i	$0.613276\pi$
$830$	0	0
$831$	−19.8194	−0.687526
$832$	−46.4084	−1.60892
$833$	37.8235	1.31051
$834$	−19.5190	−0.675887
$835$	0	0
$836$	3.79439	0.131232
$837$	0.590331	0.0204048
$838$	4.07556	0.140788
$839$	−3.96564	−0.136909	−0.0684545	−	0.997654i	$-0.521807\pi$
$839$	−3.96564	−0.136909	−0.0684545	+	0.997654i	$0.521807\pi$
$840$	0	0
$841$	−11.1275	−0.383706
$842$	−29.8150	−1.02749
$843$	−53.6885	−1.84913
$844$	−9.92949	−0.341787
$845$	0	0
$846$	33.4976	1.15167
$847$	−16.5952	−0.570219
$848$	4.30776	0.147929
$849$	−3.26690	−0.112120
$850$	0	0
$851$	−0.779066	−0.0267061
$852$	−23.0962	−0.791261
$853$	18.9123	0.647543	0.323772	−	0.946135i	$-0.395049\pi$
$853$	18.9123	0.647543	0.323772	+	0.946135i	$0.395049\pi$
$854$	0.262822	0.00899357
$855$	0	0
$856$	−8.21178	−0.280673
$857$	11.8017	0.403140	0.201570	−	0.979474i	$-0.435396\pi$
$857$	11.8017	0.403140	0.201570	+	0.979474i	$0.435396\pi$
$858$	−76.8551	−2.62379
$859$	0.421369	0.0143769	0.00718846	−	0.999974i	$-0.497712\pi$
$859$	0.421369	0.0143769	0.00718846	+	0.999974i	$0.497712\pi$
$860$	0	0
$861$	−27.7312	−0.945077
$862$	−28.0826	−0.956498
$863$	35.5067	1.20866	0.604331	−	0.796734i	$-0.293441\pi$
$863$	35.5067	1.20866	0.604331	+	0.796734i	$0.293441\pi$
$864$	2.15941	0.0734647
$865$	0	0
$866$	43.2370	1.46925
$867$	59.7052	2.02770
$868$	−0.731521	−0.0248295
$869$	12.5199	0.424708
$870$	0	0
$871$	−37.1397	−1.25843
$872$	−33.8144	−1.14510
$873$	17.4673	0.591178
$874$	−0.574562	−0.0194349
$875$	0	0
$876$	−0.894427	−0.0302199
$877$	−7.75153	−0.261751	−0.130875	−	0.991399i	$-0.541779\pi$
$877$	−7.75153	−0.261751	−0.130875	+	0.991399i	$0.541779\pi$
$878$	−38.5836	−1.30213
$879$	−29.0023	−0.978223
$880$	0	0
$881$	37.8395	1.27485	0.637423	−	0.770514i	$-0.280000\pi$
$881$	37.8395	1.27485	0.637423	+	0.770514i	$0.280000\pi$
$882$	18.4876	0.622511
$883$	−12.1037	−0.407322	−0.203661	−	0.979041i	$-0.565284\pi$
$883$	−12.1037	−0.407322	−0.203661	+	0.979041i	$0.565284\pi$
$884$	−23.8873	−0.803418
$885$	0	0
$886$	8.07990	0.271449
$887$	−8.24017	−0.276678	−0.138339	−	0.990385i	$-0.544176\pi$
$887$	−8.24017	−0.276678	−0.138339	+	0.990385i	$0.544176\pi$
$888$	−12.4794	−0.418780
$889$	19.7489	0.662358
$890$	0	0
$891$	49.7575	1.66694
$892$	8.11577	0.271736
$893$	−11.4858	−0.384357
$894$	−16.5723	−0.554259
$895$	0	0
$896$	2.70057	0.0902198
$897$	−5.99988	−0.200330
$898$	14.5257	0.484729
$899$	−4.22759	−0.140998
$900$	0	0
$901$	12.8105	0.426779
$902$	63.5049	2.11448
$903$	−5.96382	−0.198464
$904$	−28.5840	−0.950689
$905$	0	0
$906$	−17.8164	−0.591910
$907$	−43.4987	−1.44435	−0.722176	−	0.691710i	$-0.756858\pi$
$907$	−43.4987	−1.44435	−0.722176	+	0.691710i	$0.756858\pi$
$908$	14.1932	0.471017
$909$	−5.86343	−0.194478
$910$	0	0
$911$	7.41325	0.245612	0.122806	−	0.992431i	$-0.460811\pi$
$911$	7.41325	0.245612	0.122806	+	0.992431i	$0.460811\pi$
$912$	−5.66302	−0.187521
$913$	83.9903	2.77967
$914$	22.8080	0.754421
$915$	0	0
$916$	−1.36178	−0.0449945
$917$	14.2320	0.469981
$918$	−4.38916	−0.144864
$919$	41.0186	1.35308	0.676539	−	0.736407i	$-0.263479\pi$
$919$	41.0186	1.35308	0.676539	+	0.736407i	$0.263479\pi$
$920$	0	0
$921$	75.0115	2.47171
$922$	24.4646	0.805698
$923$	−76.7721	−2.52698
$924$	−9.02179	−0.296795
$925$	0	0
$926$	−17.9453	−0.589719
$927$	50.4900	1.65831
$928$	−15.4644	−0.507644
$929$	−37.3567	−1.22563	−0.612817	−	0.790225i	$-0.709964\pi$
$929$	−37.3567	−1.22563	−0.612817	+	0.790225i	$0.709964\pi$
$930$	0	0
$931$	−6.33911	−0.207756
$932$	6.72644	0.220332
$933$	29.6785	0.971631
$934$	−23.9522	−0.783739
$935$	0	0
$936$	−45.9988	−1.50352
$937$	28.6925	0.937342	0.468671	−	0.883373i	$-0.344733\pi$
$937$	28.6925	0.937342	0.468671	+	0.883373i	$0.344733\pi$
$938$	8.45636	0.276110
$939$	−53.7588	−1.75435
$940$	0	0
$941$	−12.9444	−0.421977	−0.210988	−	0.977489i	$-0.567668\pi$
$941$	−12.9444	−0.421977	−0.210988	+	0.977489i	$0.567668\pi$
$942$	−43.3243	−1.41158
$943$	4.95767	0.161444
$944$	6.52980	0.212527
$945$	0	0
$946$	13.6573	0.444036
$947$	30.3427	0.986005	0.493003	−	0.870028i	$-0.335899\pi$
$947$	30.3427	0.986005	0.493003	+	0.870028i	$0.335899\pi$
$948$	3.97401	0.129070
$949$	−2.97309	−0.0965107
$950$	0	0
$951$	−60.4137	−1.95905
$952$	21.4275	0.694470
$953$	−47.6001	−1.54192	−0.770959	−	0.636885i	$-0.780223\pi$
$953$	−47.6001	−1.54192	−0.770959	+	0.636885i	$0.780223\pi$
$954$	6.26161	0.202727
$955$	0	0
$956$	2.88433	0.0932860
$957$	−52.1385	−1.68540
$958$	45.8343	1.48084
$959$	11.1181	0.359022
$960$	0	0
$961$	1.00000	0.0322581
$962$	−10.5293	−0.339477
$963$	−7.34454	−0.236674
$964$	−4.52569	−0.145763
$965$	0	0
$966$	1.36612	0.0439541
$967$	32.4833	1.04459	0.522297	−	0.852764i	$-0.325075\pi$
$967$	32.4833	1.04459	0.522297	+	0.852764i	$0.325075\pi$
$968$	47.5237	1.52747
$969$	−16.8408	−0.541004
$970$	0	0
$971$	5.72115	0.183600	0.0918002	−	0.995777i	$-0.470738\pi$
$971$	5.72115	0.183600	0.0918002	+	0.995777i	$0.470738\pi$
$972$	14.5890	0.467941
$973$	−7.61625	−0.244166
$974$	0.170889	0.00547565
$975$	0	0
$976$	−0.463106	−0.0148237
$977$	−50.4461	−1.61391	−0.806957	−	0.590610i	$-0.798887\pi$
$977$	−50.4461	−1.61391	−0.806957	+	0.590610i	$0.798887\pi$
$978$	−57.8402	−1.84953
$979$	45.0162	1.43872
$980$	0	0
$981$	−30.2433	−0.965593
$982$	33.6733	1.07456
$983$	−4.69142	−0.149633	−0.0748165	−	0.997197i	$-0.523837\pi$
$983$	−4.69142	−0.149633	−0.0748165	+	0.997197i	$0.523837\pi$
$984$	79.4137	2.53162
$985$	0	0
$986$	31.4325	1.00102
$987$	27.3094	0.869266
$988$	4.00345	0.127367
$989$	1.06619	0.0339027
$990$	0	0
$991$	36.6180	1.16321	0.581604	−	0.813472i	$-0.302425\pi$
$991$	36.6180	1.16321	0.581604	+	0.813472i	$0.302425\pi$
$992$	3.65797	0.116141
$993$	−30.1404	−0.956477
$994$	17.4803	0.554442
$995$	0	0
$996$	26.6599	0.844752
$997$	−30.1706	−0.955514	−0.477757	−	0.878492i	$-0.658550\pi$
$997$	−30.1706	−0.955514	−0.477757	+	0.878492i	$0.658550\pi$
$998$	39.1301	1.23864
$999$	0.997439	0.0315576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.h.1.3	✓	5
3.2	odd	2		6975.2.a.by.1.3		5
5.2	odd	4		775.2.b.g.249.4		10
5.3	odd	4		775.2.b.g.249.7		10
5.4	even	2		775.2.a.k.1.3	yes	5
15.14	odd	2		6975.2.a.bp.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.h.1.3	✓	5	1.1	even	1	trivial
775.2.a.k.1.3	yes	5	5.4	even	2
775.2.b.g.249.4		10	5.2	odd	4
775.2.b.g.249.7		10	5.3	odd	4
6975.2.a.bp.1.3		5	15.14	odd	2
6975.2.a.by.1.3		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q-1.14876 q^{2} +2.39873 q^{3} -0.680351 q^{4} -2.75556 q^{6} -1.07521 q^{7} +3.07908 q^{8} +2.75390 q^{9} +O(q^{10})\)	\(q-1.14876 q^{2} +2.39873 q^{3} -0.680351 q^{4} -2.75556 q^{6} -1.07521 q^{7} +3.07908 q^{8} +2.75390 q^{9} -5.14144 q^{11} -1.63198 q^{12} -5.42473 q^{13} +1.23516 q^{14} -2.17642 q^{16} -6.47228 q^{17} -3.16357 q^{18} +1.08474 q^{19} -2.57914 q^{21} +5.90628 q^{22} +0.461088 q^{23} +7.38588 q^{24} +6.23171 q^{26} -0.590331 q^{27} +0.731521 q^{28} +4.22759 q^{29} -1.00000 q^{31} -3.65797 q^{32} -12.3329 q^{33} +7.43509 q^{34} -1.87362 q^{36} -1.68963 q^{37} -1.24610 q^{38} -13.0124 q^{39} +10.7521 q^{41} +2.96281 q^{42} +2.31233 q^{43} +3.49798 q^{44} -0.529679 q^{46} -10.5885 q^{47} -5.22064 q^{48} -5.84392 q^{49} -15.5252 q^{51} +3.69072 q^{52} -1.97929 q^{53} +0.678148 q^{54} -3.31066 q^{56} +2.60199 q^{57} -4.85649 q^{58} -3.00025 q^{59} +0.212783 q^{61} +1.14876 q^{62} -2.96103 q^{63} +8.55498 q^{64} +14.1676 q^{66} +6.84637 q^{67} +4.40342 q^{68} +1.10602 q^{69} +14.1523 q^{71} +8.47947 q^{72} +0.548064 q^{73} +1.94098 q^{74} -0.738001 q^{76} +5.52814 q^{77} +14.9482 q^{78} -2.43509 q^{79} -9.67774 q^{81} -12.3516 q^{82} -16.3360 q^{83} +1.75472 q^{84} -2.65631 q^{86} +10.1408 q^{87} -15.8309 q^{88} -8.75556 q^{89} +5.83273 q^{91} -0.313701 q^{92} -2.39873 q^{93} +12.1637 q^{94} -8.77449 q^{96} +6.34274 q^{97} +6.71326 q^{98} -14.1590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

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